bdbdeebcdeaabbbccdcedecadaedbceadeeaabedaaeabbebdaadcececdcedaaeaddbaebcaceeabbceddcbdbbcdabadbdacbebddedbacaaeceadcaeaeeeaabbaebdacdcdcacebaadcdbddaccccdadebebccabbabaebbdabeecccbdbceadbacdcdbdddeaeedabbeeeacaadbeccedbbcccdecbdaacecabcbcddbddcbdadccedccacaedecddabddaddebdbdeccaeecabceedaddececeaebbdcbbecbebbaadbdbebaeebcbeceadcbdceddabcbeebddeacecbedbbdececaddadeecaaeeaadbececadcaadbbccbabbbcdbdbebdecebccbeeaddeaaceecbbdcbdabacbebbcadacbadaaeabbdcedbbceddaceaabaaeecbebaaeeecebcbeccbeacddeaeaaecbceeababdddacbbcabdaeeaecbbbdecaeaecceabdadaeedeaaddbcdaabeadcaacdbdeadabddaebeabdddebaaaecbaabbaaeeebaaceaaaaaebccbadddbbccaedcacdadcbaacdaadbbddcdbcaebeaeaaeacbaabbbcadebaddbacadaababaeabccccadcbbdddeccdbdcbcbadabebcceabcbaaebddabadbbaaedacdbeededdadaebddbddeddadcebbedbccabedbebccdaedcabcbaedcacadadbcaddcaaaaccdbeccbcdbadbbceaedeaeceaddebecabceaabcebeacbdddcdbceeecbbcdccdcaaaccaaeddacaccdeebdcdbebabecbbbaaecbcbbcbedbadcabeabcecedbcebbbeceddbabaabdeaadeeddbbbeaaecbbaeeedbecbaeeeedadcaaecddddeccdddeeddbeacbbcaebacebeababcaeddeaaceadedcecabeadbecbbddabdcecaeeeddddaacbdbedbeceeeecedcecabadeceadbadbebbaaebbeadeebddbdceceeededceeecddcdcabbcbaaadbaebbcceaddedbdcbaadbacdbdabeddcddecacbbbaaecbdbebeedcbccaaaadaeacabdbdcbccacabcddcddcacbcdaacdcacbbccdcabaaeaaebedaccddedebbecdedbbdceecdabbbbacbbccbdbcbaccbeaaeaccdbddddbdbdbedbcbbcaedbdbcdecdecaadddbababcebabcaceceaeabebdececaadbcdcceecdcaecaacebaebabeacebcdbedeaadabedcceddaddcdbebaeceadeedccaeddecdabeaeaecebbaddcdadcdedcdaeaeceecebcdddbeecbaabcedeaadabcbeacedcbeaeaccabccabceaedabaacceebbceeddbbebbeeaedaadeeacbbbdbebecddaadbebebdacaebccbdcabaeeebdeaecabacbaceeecaeccddaeaacadcedadccbceabdedaebbbbbdcaaeeaedecddaacdcaadbacdbabebdcabccdcbdcceaccbdbedabbebedaceebaadddeebaacbdabedaabcaedccbeeadadacbeeaeebaeeddbadaacbedbcaabbddaddbdeddedecbdcacecdccadcccaeccceebcecdadbdebeabbebaeacabaecaaaedcbccdcbdceecadacbccbeaebaaabddcabaacaeadcedcbdcbcbeeaccdabceadcceaaedcabcbcdbbacabdabdbbdbbabaccedebeebdeabbdbdaedcbddcacabcbdadaecaebeabeadceccaadaeecbdacaaaceacbadebeaeedaacdbddcdeecadccaeecebaaeaacbacedbdbedacbceecddaeaaddaddeedabaaadbdbedcbbaccceadeebbdcbbcccabbbddbabdecdcccdbdecccabbcdcaeaddbdecbcbdeaadacccdacadedbbcedeaecaedaaabcaeeadaddbcdbbaedbdcbbadedeeccccdeaaebeabbcceacccabeabbbeebceaabcbddcdcbeebebabddebebadeebccadecbbcddbccbedccbdaeabdcaceadcbecaeccddcbeadaecbaacedabaecccdcdcdbdeeaceecbdaeeecccddcabaecebcaedccdbccadcdabcbdabdeceebbabebaedbabcbeedcdaaeaccbeaedaccccabdddbaeaebcbddadeeaceebdaebdcaeccacbcdcababeddbbcdaebccacdbeebebbcaadeadcbdaebaabeacbebeccdeeaabecdbdabadeccaabaabccdbbdabacceedbbabcecbecbccebdabbbcceaedaecebbdeceebceeabcbcaccecdadbdedacabaedabccdaaeccdcccbaeadcbbdabbabdceabddbcaabebabdceebbbbbbdeebdabcbdcddecbabdbdbabdbacdbccbabbbaeebbadaeacebcbacebeaeeaceaaeddbdceedcebaaecccaeedcbdacddeecceebebbccbdddccbabecbeebaabbcccdcaeedebeabebeacccaededcdbbbbadcacdeecdaebbeecaedadecabbbdcdcbaadabccebabbacbbebcacebeeccebbbdbacabaccccdbbbcbbbdceaadabbabcdbbdcddabcebddddcebeabaadbbbacebabeeeaeebdddbecbebcabbaeaadaabbaebbbedeaaeebaddcececaabcceeeeaedaddebbabccdbbccacabebedaaeccaddececddedeeebabbabcbdabdecdaabaadddececdabbdbbeedceabadcececbdedacaecbaaceebaedbdbbdbbcbdaeebeaebbddeabbcacaadeabbccbeeeabbbcadebacbacddcecebebbecaddacdceeddcddecabaaacceacaecddadaceedebddcaccadaebbecebdbcdbcceecbaccaacccccebbddabbacbcedeaabeaccbbcaabeddebacbcbadeeaebaabcecdbabccdeacedcdcebaeedbacebaaabaaebacaddadddceaadbaccedccbdceebecaaacbaaaddedcceeeccbcdacbdbeaddeacdbdebecacdacbeddcbabcbeedcddbcadadaddadabbbdeaebbbbbadcceacdbdeeaacaaaeaceceaccbbeabdeceabbcbceccacedabecddedceeaacbbadacabeebcdaaedbdadcbbaaadabbadbadbadcbbccccbebaebeecedcdceceddbdcacdbacacccecaaacbbcddeaacddbcadaddebedeeebacadabbbebacbddbbaeddaceeeeadcbedcdacedcacadcedbccdacaeccbacbbeecacacecdeecabddbecdbdddcddeedacdccdceebbbddadedbbeeacadcebbddceabacdbcdbabbdadebaededbdbcedebdbbbecaaaddbccaeeccceebddbcecceeacebdabbddadbecdbdededccbcbbbeccbccecedbceccabcceedabcdbcdbadeeaacabcbbcdeabbeaacdcaaeaeecbbdaaabdeebcdaedabbabebaacdbbdbbdedcdaaacddeeceddddacedbcedbccddbddaabcabdceecdbdeaabaeccdadedeabedaeddeecdbbddeadacdbecccbaedccdadcdaedcacbcbabccdaaadadddecaadcbdbcabdebbbbbbabaaeccdaeacdbdcdaabbcdedeccacccebceedcbbacbcdebaebddbcdbcbbdbdbaddbeaccbdabdbeabbaedbccddbcccabdbdcadabbbcebcadedeaaccbdaabaabaabcbaddcddbddeedcccbdadadbecdcaceeeeccdcbaadaacdbaaeccacddbddbdaacdacdbbebaadaeceabdcaaaadeeecaadacdadeccdcebbdddbcdaeeaebbabecbdaeccedbcaeebeeaeacddecbcbdbbabbcddabbbcabeabdabdabdeddcceaadadeedbeacdbdceaaccceccbcabbdbbdebdeecaebeabeccdddedbcedcbedacbdbcabddaeddeddaadcddacbdcbadeecabeddadbbaaeababcabeedbcdaadedcbedcedacabdaadcbcadeacdbecadcdcdcacbdebceabdaabbbbcbacdeeedaaeccdbeaaaacdbdaadedccbdedddacebbbcceebcecebbecebbedabcedeebceaadbaaadeccdbeecacabccccbeaacbadbacecadbdeadcaebbeeddbaeecbceeaabaeeccededbcbadeeaddacebdacbaebdcdadccbdadeeecdcaddeabebabdcddcebeadaabdabacbcbeaebdaaceadbbececcbdadcbbadbdedbbeeeaacceeabddcdceeeaaecbddcebdaadcedbbabedbabbcdbecdcbedabaceadbdbeddbdddabaeedbaebaaceecabaaaacaeaceedceeeeeddabbcbadddcdecdaeecbbaeeededaaceeeaedbabbedbcabcbbbadedddbdeecccadeeddecddacbcdcbeacdbcedcbcdcdcaaabbeaeeaededcdcdaeadedccaeecdddaddaccbbededcacaaadecabaccdbcccbccdeaeaaaacbbacadddbaececedadedaebedbaadbbceeabbcbecbcabeebedacaeebddaecbcbddbdbeccacebebdbdeadcdaeaaabbebbadcddabcabbcbccadbceacdbaadddabecabcbdaadecbebdeddddcdddabbddaabbeccccacdcccbdcbcaadabbdecbeaadecbdcbdaaceaacebeaebcdeeaecbaedaebbddeaceedbceecbdcedbddebadaabccaaedcaeecdedddaacebdeaacbdeeaebdeedceeccaaeadeaecbcbcbdcdedbdbbbcdeedbededdbcadcdcecdadecbbdeccdbacccdccababdaecdbdaeacddeeaaedbeeddcbadeebadedeabddebbeedebacdccabbcddedddccecaeedcbddeaecacdeaeacbabbeddabcbbebeacccdccdddabeaabebbeabbcceadbbcbcaebdcbabeabbaadaeddaebadbaeadceaaeaabaedbcdccdcdaeaabacadacecbdeedddebcccccdaedecaceedecaebcaaddeececdbadcecdeaddddeedcbbecaddebacdbccaddebbcaedbdadbeddbabaddbbecbbdbacbbaaedcbdcacbebbcbbcbbdeedabeaeadeeebbbcaebbeaeadcabcedcbacebddccdbbbbcecbcdbddeaedeeebcdababddacadeeccdabadeaacacddeaebdddcedbdbabbcbbeeaaedcaababccecddebacbbecccdadcdabeabcabbccbcceeedbdebcddbeddbecbebaecabadbdcdaedeeedcecbadbcccacadbddacdecdcbcdaadddacbaacadebeeeacaeabbdbcbbeaedaabbbbddbcadbcbacbacacacdacbecbbacddadabaaebcdcadabdaeccaeddacdcddabdeabeedbedcedbeceaeebbbecaaebddddbbdeddcbdecaadccedaeccbcccbddceeadadbdbdaecedbadcdbbeedaaeacdbeecbcddaeededbcdedcbdedbacbcbceddeeaedddbdbeaaedabecbabbaeebbdcabdaccebbbcebdeccacaeabdcaddddaababadcccbbaecbcedbadabcdddddccadbdedaadbbcddebbaaadbccdeeaabadebbdaacecabcaadecbbeaabedaaabccdbeaebbeddaecbbcedbccedbdceaadbccaebaaebebdbdebaeeeaeddaaececdeebcedbaccbeeabcbaddbadcbaadababbddbbdbdcddddabadeddedbebdcddcaaabaaabeecdddeaebdaadbccecdaeceaaacbcadcededaaaadceaeedeadadeaedeaeccaacbebacbdccaeaedddeeacddaebcdceecbdaedeaabbccddeedadecdbdcabcdbdbaddebbebcadedbdccbebdccbbeadcbbaacbceddacdcbabaaacebabbbecbccdeccbaddabebabbdeecdedddcdebbdbbbdcebeaeaaebbbedeeadccbbbdabcecccebaaebecdcddeddeaacecbaddebedcebdcbadececeedcbdbdedcacadaceecedcabcddcecbdbbcabcaacdebdaebbababcedbeecddcedecdaecbebebaabebaedeebcbbebbbdaabccaedecedeedcaccbaabbcdccdaedceaedadcbcdcabadabaecddbabaacbebaaeaeacbaddacccbdeabddaaeaedbbedbddeddadcbdaeeabaeadbdddaecaedbebecbcadbbddbbbddeedcbdbbddaaaeedaebbacaadcceaacaeebdeababedebbbdebdeaaebebeceaaedebdaabdcdcacaebddeecbcbdbebdabaedcccecdaeccaccbaccebbbddabbbacacdceedaebdeedeeadceaecddaecbcbacaceedaeeeaecabdeccacaecbaeabdbcebcbdecacdcdeebdedcebbabcbeabebcdacdcdbedbadeccddeadaebebdebbcabbdcbededeedcaabcdcdebeaccbebbbedebabecbeaeeaeeeeadeaadcdbaecaaacceccbebcdecdcbabaebeaaabadaeccbcbebbaecacaedaabeceadbedbddbcebbdcddaececacaddceeeeddacbacceabceadaddcacaddeaaeadadcdbabcacecdeacedabdecedcabeadaabcedbceaeddedaacaaaccdbcebacccdaddeccebcbacbbdacabacaabccbceeccacddcadaeeeeeeacedbaadcdebaaaccebceecbdcabbbaaabbadcaccbccdcaeacaddecdcacaaceaebabdededceeddecbdceedecaeadbbcaddcdeaadbccaacadedcdddeceecbcbdbbdbaabaddceccaabcebedebaaacabebeebbaacdebaccaeeaeeaadbecaabdeedeceddaadabcaabdbedadbcbaeacacedbcacbceeedaeecacbdacedcecaadaaaebbbbebdbdbecccebdadddbaccdbbcdecdbdccddabeeecdaddacdacdbeeadddbaacbbbaedaacecadabeddaccdadedebaabaeeeabaaaabbeddecceaaedbdebbccbdcdcabcebecdadeeddbebaaadceabedcdddcdccbcaabeddabeabdcccdcdcecdcbdcebddcccdbdacadaaecbccaecbcdacdbbcdabaaaeadacbbccbbcaccceeeeabebccabedbadbeacbadccababbbbddbdbdcaeaadbdcddbbaabcdddaaedabaecdacaccbdcaabdaddeebeaceedcbccaeebdbeeeebdcbbabbbcbcdebccbdadecedbbcadcbddaaddbecaecaeccdcdbbecebbcaadbededcbabababebccebaaacdecdabacadcbaaaaecaeeaaabeeaecadcbcbdebabbaaaebabaadeaeadbcbcbcbeaceeeabebcdeeaddaabbcacbbbacdecabcccabbcaddddcbdcadeadcbececaaebeeeeeddeeaaaecdeacbeebcdacccbbbaadaadbaddecaaceeaebbdaedeaeccbcbeadadcbaecdedbdceedacaaadbdedaaddbcbaeddeccdabcebbaaebdcbcceabaccbdbdbbcadabcbcdacdbadbdaeadbccbeaaebaeaeecdcdabdcbbeedaebebebdebcdebcbcebddddacadedadddbdacbecddacbbedbbdebbaaeebabcaceeeecdceedaebeadbeeaccaeceeadbccdecabdaadcbedecebeecbecdedebbacbdeaeebceeebbebbdedaaebdbacbcaedbaceaabedaaceecbdcbdebbcdeebccbecbbbccccaadbbdcdbaeccdedcaeadcaacedbcaaddbdcecaadeadccecddcbadecbabccacddedbadacacddbccccbdeededdadaceaacaaceaaccceecdacdecadcabebdcdadcecdaeddbaaceddeabccebeccddecadecbaddacbdcbaecebeaeeebdcacdeebdcdedeabdcecabcbaebdcdbeabacecdaaebcabdcdabdeddbbaacbaaccccbeabdcbbecdebdabcaadedacaeecbeadbeacadceccdbdecbedecccaeabbebdabdbebccbddbdceabcddcecebdeadaacbedeebdbedddeedbadcecaeadaecceeabedeeeecbddadbbccdebdcecdaacdaebeebcaccbaacbbeacdebdbaabeeeeeddeeaadabbddbddeabbdbacededcaebeecbeebeeccbbbbeedcbdccddcbbdbeedaeaeedeaabddbecaeebbadcbededcdbcabcadcaadeeacebbebaadccdecbadddacddddbacdcedaccbdcadcecaebadcdeaceeccdcaaebcdaecaeddcddedabbbbdbddeacdaccbaeabeecaebdcceddbdeddeaecdbeeaadcebaeeabcdebadbdbbcdaaceceecdbcdcecebeaaebbbcaaeededcbacbdccdbbaecdbaaacdbcdddaabababdbbeccbbccecccdbcdeeceebcbbebbcadeadeedbbdbbeedecdcbcacddebaebaeaccbcdceedacbacbaeddbbdaeaabaecdbeebeecddabbbebaaaacedbaeaccaeadbaccaecbaeaaddeedbcdcdddcedcaeebbabcddcdeacdbbeadbeddcceeacdccbcbaecbdddedebddcdabcabdeededeebcdccedaceedbaccedcadadacacbdbadadbeaaeeeeddabbabdbbbedddeccbecbeaeadccbecbcddcbadaaaccbdbacebbacbbbdaaaddaeeeaccebdddcdcbacaaaabaadeebeecbbbdecbecaadabeddaacebbccbdbabaddbbdbdaaadccadaccaccbadeedcaaeadacadcedaeacadddceadcaaadeeeebaccbdbcdabdbcacbacdcbaaacaecedabdeacedbbedcabebdeadbcdaebaaeecdecdccdeeaeeadeaeeabbebaabbaeaddcbbaebbcadcdceaaccadbceaeaaebbbacaadeaabebdaacaaeaadeeacdbbbdadebbecbbaedbbdadbcbcaecbbccbacaecdeacdcaeeaddcbdebcebedddecbcacddbeecabdcdbedddcecaaeeaeecaeaaebbabaaeaecebecaecabccdeeecbbedaeaddddecbdccebaadbaaaeaaecebcedbedebbadaaddaaebdcdcebdcecaeeacddcdaedaacbcaebaabbaaebccdeadadabdbaeaddeeeeaeaebaadccdecbcecceacbdcaeedaecdebdddbadbdabcbcccdececaacacacbeadcedddcdedcdbdecebedcbecccaeccacddcaadcabeceeadddbcbcdebcecbccecaddacedcebddbdceadedcdeaebbeaababcdeaadddacebecdadeaecbbbeebcececcdccddbcceaedecbaaadbdcdedaaeebeeaeddcaedabcbabbdebccaaadcbaceddecabcacdbcacccaacbecbcceeceececbacbbcbcecdabeeeaaabbccebdacebdbbaedbabadebecceceddececbbaaceeabebabadaaccaeaadacbdeebbaabcbadcaabbaddceaeddeedbeadacaebabacbceedacaebaeabeeabebdeeddeceabdcbcddbaacaadeddbabccdadacdcbabbdaeddbcceadaecabdacdebccaebdbedebcbbceadbaceaeeddeccecbdabcdbcbdecaabacbdcabeebabcddcacdbaadbecbcdcdddddaecbcedcaceeedcaeaabdeebcdecacdaceaeabcdcbbbeabccaedaacecdbbddceacddbbcaeceaabebbebebdbedcaabbbbcaeabdbaaaabbaecdbececcecaadbdcdddcceabdccdbcbdabeccedbeabacbabebebbdbabecebdedcebebbacbceaaeeaeacdbdaacadeaebececabcadaeadbdabddbadbcecdaccaecbcbeeeadbbabbcabeeecbaabdddbbacdcbceeeedaacabeaaeeabbeacebacccdbcecaaccecbccabcdddeedabddbbeaacadbcdbecebeccdcaaedcababbaebebbbedcbadaddddbdbaedceddbbdededacceebdebccbeadabaaaeaaddcdedbdbcddebcedbadceadbbdddaabadedaccdccabcaddceeaceeceebceceedceddcceeedaeccdcdaedebddeebaecabacdeaebbbcbaecbeaeddeeecabdddeedaccaaabebdceaadaabceeaceedbdedcdeeeaceecbacaedcddaabeddeebcdaceaabedabdddcceedeebceaaaccddacddecbeaeccbacdacdadcacaaaaaeebdaacebedacccacbeacedbbdbeadccecbbdeeeaedbbacdddbedadecbedabcadbbeedcbacadceeedeedeedeedbeeeebbaddedabdeabcbacaccaddaacecdbdbddedeaabecaeaaedcaedebccddeaeddcaaaaaccbbbbadaeadeebabbdddceaadadabebeeeeeabbaebcbeaedbdadcdecabdcacdeeaeddbcdadbbeceeebceecbcdcecbeaccdaccaabdbbcddcbdbbbdeceabbebceaebbbaabcccebaecebddeecccadcabeeeedebceaababeabadaeaadaadaaaabacbeebaaeaadceabbaeabbecdaaeaacaebccaedcabcdacbebaeedabcebbaedcccdadccbcccdbedabdebddcacaeedbdaedadbdeacdbebdaddddcbabbcbddcabcbeaeeedacbabcecbdbceecdccbcabdcaeeabbddbbcdebacecbdbccddedacbbaacacebeeddacdcbacaeecbdbcdeaeaacacbcbcccacedbdbcddacacabddabeedaabbbabeebbcbbeacceceeaecbbacaecaccedbdaebcaabcbdeabebdbbcbcaceaeacdaaacebbdadddaadeeebebcaadcbaccdcdeeddbdcaccdadcddcdcdaabeddeeabaddbeccdcacadebeeaddddbbacdbeabcdeceeecaaceacccaacdacccaccbdeadecbeacddadcbebaeabeedeebacdcadacdbaacabebacbeeccddbcebcdccbababdeebebbcecbbdaddcacebecbeadbedebadadedbcabeccacddcddaabbccbbbcebdbebcbbccbbdadcdadeceebababadeeccddebdbcbeaacbececcbedddcdaacabbddcbedbceeecaaebdbeaaebcdedbcebadcdbabaedaeebcabecbdbdabddbcaccdcadbbceeccaeadabedcedccecbbdbbbbddbbaacdacdabbaeabceacbdbcdabdbcececceaabdbbdedcaccadbcebbbdbcaaeabeeaecbedabbaaecbacdeccdecedaadbbcddecddaebeeaaadbaaeeadbeeeecbedacdedabeaedabddaccbcddecebbadceaacbcecdbbedbdcdbcdeecadcdcaedeccbdbaceeaddaabeedacdccececddbacaeeabdbddeeebbdeeecabedbbdcdecaeeeeddbbbcaabcdaabceeeceaecaddbabbbaaedadcbaaabaeadbbcdabadebccaccdabeebacecacdcebacdbdeeaccebdcebbedcdcddbdebbcaceeedbaddbceecbaebcbaeeaccddcdcdeedbacceeadabbdeadbbdcaceeeccacaecdccedbbbcdabbcdedecaaebcbccbbaedabaaddacbabaabcaadaadbadcaeabcbdccaedaaeebcbccaceabdaeddceececaaadedbeebcabcdedebedaeceeeaacdacbdeacecebeaaaccdcababcdcaddadebcdadaaedcaaadeeebbeddaaeddeaadedaccbccededbaaacacebdcbdeeadbbacbbbcbacecccaccdebcadadcececebcbedadebbbdbeadaceabeaaaebbabccccdaeabadabcccdeabdcedbbacbbaadbeaeacbaeeababdaaaaadcddabbedaaabbcdaaebcbeabacbeadccceaecdaeccabceaebaeeaacebedeaebdcdeccdcddcecebebaabccdbccbeccbcddcdabbbdceacdedbbdbceecdbbcdedcdbaedaebbbeddeeebceaecceabaecebcaebbedacaaccdeabdadedaddccecddbdacbebccddccdcbdadacdbeceebbcbbbeaeddaecbdaebebbaecddeacbddceacdcbdaaaddebacbbccbbaaebeaabeadcddbacddacbceabcceeaecbababdbabcaacdbabbababbaaebeaedbadbaeebcddeeeceddaaeeecacbcaedadadcadcaaddddaceaabdaadaaeddaebaacaccbbcecabbeaceebdeddddbbaacacdbceaaccadbbacabcdaebcdbcbbaadcccdcdbcebbcbabdadbccabbbcddbdccaedabadeebdddabebadcaedcccacbbbcbcedeccabebeadaeddbaebcbdedcdccdabdeadadceddaeeeeeaebcbdaaabbcecaeacbbddeabadbdbacadddaacaabaaeccbdacddadaededebeaaeebedbaaeabadbedcdecbababebdeceeaaceddeceacbcbbaececebcecbdeadccbebcaeabeadeabdadebedbaccadcbebbbbecadcecdeeaaddcbeeaeeeaabdcbaecbeeeacdaddbcbddcaeddcbaaabebaaaaeaeecacacecedabeeeaceebedabcdabcaeadabcddccadaccbcdaceadabcbcaedaebcdbaaadcaddccadeceaedebbddeceecbeedcbbbcdbcdeabeebdeacddeadbaedbcabddedabbcaabbcadbccbeebcacecddecbcdecbedddeedeccebccabbbbdadcddcedbbdaeceecbdbddccbdcdbbeeaddeeecceddbccecbbbbeddebcbaedcbacdaecbabedeaaeeedaaebabceaddabdeeaeeeededebecddaecadaabaedbeccdebddeaacdceebeeabaaabecbdedaadddcadacebaceaaabedabdbbacbbdcebbcbadecccdddabcccdedeccaccebecdaaaecdccdaaadaedadabeaeaccabaddceababadeddededecdbbdecbaadbdbedceadacbaddeeaebedeaeaebabacdbedccdcbedeeacccdddebbdddabbbdeeeccacccbaeadcbaeabebbebabeeeaabaedcacbcbcbcbccadbedbbeceecdccedbbeccdaaccaaccaaddccabbccabddadbeebebadaceeeabdddabbeeadbeeeebedcaacdecdcecedddbbdabaaaaaaabeecabaaccadccbeaaeaadcadbaabdebcbaacaaebcdecbaebbdcacadcebbbedcbcaccdbcddccccdcdeaecbcdeddbcdebecbdacddbbaabcdbaebdcacceeccaccedacdcdcbdebcdeccceeebcbbaedabdadcacdbadbeecaccccaeaebdacadebceaeabcdcabcebabaeedbabcceeadbaebdcdbdbcaedcdaaaecdaccaeedcacedcbbdccabdabceccbecaeeebadcedccadccedddabecbcbccbbadcaeecadaebbdcbeecaeceaeebcbcbededecbeacaaaeebebbceacaeeabdaebacaebadcacbabbbbacbbcdedbcdddaaeedeaebaabaaebdcabbccbeabbceddbbcccbaabebcdbbecdedcddaabbecdeceeadaddacddaaabcaaeebddcbcbdeebadbcdacbdbcacbaccaeaedbbdcedacbaabdaccbaaddddbdaeaebecadcaacecdaecdececebdceabcabecebddcbcabcabeabdaccbcccbcebddeabdcdeacbaeaadceaebdcaedacbbaecacbbebcaeecbdbdacebeebdeccccadacebdbdccaecdbdeaaceaabdabdcadceadcecbbecaedbbbaeeaadedaecbeedcbcadacceaeacbdceccbacaebbecaddbdabbaaecceceebbebdedddbbceaadcbcdcabdadcccbbacacaebccbeceedcceabbbdeeeccdbccaebabddbccceccbaecccdcbbbeccdeadbebeaeadbbbcbccadedcdbccbeeecccabcaecacdcedebedecceaeeddaaececacdcbaceadcbebddaaecceceebbbcccebdcedeadeceeebdbdeedbdebceadcaaaddbdcddcceadcbcedaaadadeeedbbccaccadbdecebbaeeadadadadcabdeabcaaadcebabebcbdcbabbcebeacdbdcbbbedddeadceadcbadeeaecbbeeaecaeacacbccbccdedcdbddbaaecbbbabaeabeeacbdebbcadcecdcbedbcbebcbeaaaaaddbbbeceeebbbedaebbcaeacceccedddbceacaaebdaeabeccaeddedaadeccbadaabcbcdeddddeeedcbceebacedacededbeceebdbecaedcdcdbacecdaabacbdeacdbcbbcebadccddeacddcbdaeabebaecadbbdeaaddcabcebbbeabcaaceabbdbccaecadaaaaadcebaaaadbebbbecdcdedebaabdaedcbeeecabbbbbaedeeeabbbdcaadcdcdeeeedcbcebdeabbdaacbbdebeaceeabceeedebccecbacbeaebbaaeabceedebbbdeaedecdbdaacaedcebcdceacdadbbeecdabccbbdaaedcedcbeadbbebcdadabbeedabaebbcdaaaceeaaedcdaabbeeececebaaacdbdbeccdcdacabcbbdadcccadceccaacbabdecbbcbedeaadebbceecaeebccccdcbbdecddaeaddeceabbcadbcecadecbcadbecbedbcecacceeaabddecaabeecdacccdcdcbbbebdcbbbbbdbcdcdbbbdebacadddeeabdcbdcbcdceaeacaabddcdbacdcaedbeedbdbedeccaabaecbbceabbdcdacadcdacdeebdbcdeacbdbbbebedecccbaadbeecedaceabbdbbebceeaeacbbaceaabdceeebecdeeabbceeaaccbaebebbdaaedbeceaeebecedebcbddabdaaabcdcdecaacadbcbdbadedcddedadbbbbdcbcdbcbcdeccceedaeeacdcdaacbecbdabceadceebcadeeeeedecadedeeeaececacccceaadcedcdebecdddadadaeedbceccbececeaedeecdacdeecbecdeeaabbebedabceaeeeccecaaabacceaeacebdcbcbabbbddbadeddadbebbdddccdbdeeededcecbedcedaaeaaecbcdddbebecceedaccdbaccdacbeceaabdccbaaaababedebdcddaaebbedaaacebbdeaebcbaacbdcaeeddbcddeadabdcdeaadcbecebcdbcdeadedaecdddaaeeebbdeddceceeeabbdcbceedabccbedcdcacbbbcacaebacdcdecadcedacdacccaddaabcbddbdcbaccadecddaeaaedaccdeeccaccabeecbeebaebeabaaebdcceecadacebaeadabaaacbbcdbddbcaedcbdaaabedbeedcecddbedeeadabcaeeadcbaaabedcaaebdaddbcbedaaadeadcebdbcecadaeddaacddaaddbaceddeeaeeebdeebcebddadcacbeadcbdaabcbbeaccacbeaeeaabebbddabcabcebcbccaceaacbcdbebeeabbadeebacdeecbbcccbacaaaeaeaaabdbbaceabeeceeadbbbdbaeeeecdbdacbaaacbedcaedccaeeaecabbdbecddecebcaaecbacdddbacdeecaaaacebceadbddbccaceadcbdaebccddabdbcbdedcddecddeecccccccebedaeccdaeacaaecbaccdababdedecedabcecadcccdbebddecacbcceecbadecdacecaccdbacacdcbdeaccdbbbddbeedcdadbacababdecbaaebceccaeaeebbadcaaaccbecaabcdcccecdbbabbcbbbceaebaecedccacdddabeaeeedabbdcdecbadbcbacadcccadeaecbcdacabdcdcebdbbcdbebcceacbdeccddcdeabdcdedcbdbbcdeeccabbeecdbaadddeaceaababcbdedeacbcecaccdbdabdbdbacdccaccaccbecaecedeadedbbecaccbacacbbdccbacbcbbeebadaebcddccbacccadeecaebccbecbebbddacaeecbbdacccceebeadeeedcdeeaabbbbcbdeccbceeeacecbbbccccdaacebceaedabddbdaccbdeedabbcbcabeabdbecacabecedbcadcedbddcbaeccebaaaacdcbaadacaabbadeebebcccaeebdeeaacccbccbddaaadeececabdacabdaeacbeebcdedacceabcbacdaaadaeedeaecbbcdbdeadcbedbaddcceacbcbbacebebbabdbaebaeeadaebbbbdbcdcbbadbabcbeeeabdcaddaccdeccdecdcacacedbccdccbdeedbbddbdebccbcdabbbeccbcdcaaedacbdbdcbedbabeadabdaacbecdeaeaceccdbccbaedaadabceadaadccaedacdabbceeadcdbebdceeedebaacebcabbdcbeccdecbbbbacacebabbeaadcbdbdcdeeabcccbceeecaddecdcbdacebaaebacaeecbcbceabbadeddddcecaabbdeadddbccbbebdedbeddeddadbdcccaacdaeebbccddbbbcadbcdacacacccaaeceaedcdccddaacbeaddaedbaaebcdbabaeacdeebecbacbaecdecedaedcbbaddddecccadcbccebddccecbebabcadddaddaadaaeaadeadeecaadeaeacaacbcecadebdeeecceeebbbcacbbcbeacebcdbecceaedbdbcaaaadbcaaadedeeeeacacdbdeadaaecbadabeaaedeeebacbeebeebbbaeceddebbdecddcbabedcabcbacbeaeaddadaabcbbaacecdbbbebbbaadbeeebbceaaecdaeaceeddbaeacbedddbcbdaeaacecdbacbbeeeeeccccadcbabadaedecbeadaadadcaceadcabbadcddcbaccebaeaecceadacababccdbbdceeccbdcddbcbaebedacdcddbcedbdccdcadddbeebeceddeebcabbccdccadccdbedbcdddeaceccaecbabcbceeeabadeabdccebcdcaecebddaebceeaeeacbaadaddcacdbaeccdbeabdebebecbccadbeeeaecbdaeaedadcedebaecdeddebbaceedcedcdbdcccaecbcebaabbebeceabadbcdedbcaeadcbccccccedaaaebcdcbaedeebbeaaeeaadadbaebcbbbdcabeeaccccabeaddcdedacdadadadbdacaedcdaebccdcecbdacdbaacacdcbcaacecabcaabbdbecadadeabcdadabdcccedabebadccccbabadbeecedbdebcbecadaaecedcdedcdacebabeaddcdddbcaedeaadcceaeadbccaecdeacdabbddbcabdbdecaaeacbcbcadbbadaccdddddbcedccaeaaaababbeacbcacbeabdecbcabcaedbaccdbcbdccbddbbeaebbcaeaabcedaadbbadeabdbcdeaecbdbecbebacbdbdeeedaedbcceeedbeadbadacdecdeacadbdbcaaceeddecddacabccedadcdaaddcdcbccebebaeeadbeeccabcecdbabdccbcacabdcbbccdcaddcbdbcdbebabcdaecbdaabadedaeabdbbceaddacebbcaeeecacbddeebdbdcdbbbeeaacacacadeaaeabcddbbcbebebacdbccdcdbbbcacdbecebcbdccaebcbddebecbbedcbedbeccabbdcacbdacdeedcebdaccbcbeeeaaaacabccdddcaccedaccddeedbdbbbdbbeedacbddccbcaaaaecceeaeaddcdaeccaebdbdcdcaeadcebecbdccceabbecaeacececcaabcbeaabedeaebbdeaeaedbbbbbdaadbaebacaedcebcbaeccceabdddbdeecbdeadaeeebbbecbcdbceedabdccdaceaaaddaaeaddedcabceecbccbbcbcdcecdaaccdbdabcaddebcdedbaebeeceabbedecadeaacaaacebeccbbddcbabbaaadebeeaddcacdbcbaacbdadeadeabbdbcabbcaeccccadcacbbbbeeabeccadeacbbbbdabbadbdcdccccaaecedabbeaedbeaccacccaecbebaaaaaeedebbeccbecdecbdcbdcbddabbdceaeaaabdedccbbdecaadceedbeddadbebbaedceababbccabbeaeacacbdaebebacbdaaceedadedebacacceacedcccedaacdbdbbbcdeaecaaedbacdceacbdaebccbaaddaacdddedadcaadeeceedabcacecddcecaecddaacadbdceabadcccdaddadeaededdccadbebaedbebcdbadcaddbebecedeeaddbddeebbeecddeeaaabddeadcbeacbeeecdecbbaecdaeecbccaddaabbcdcadbecdeaddbdacacbbddbebdbdcececcdcebebeaedddbcbdbdcebadccaaaeaaccbdabaeebeadbcceacacdeceecbeddeedcdedaedbbdebbeeccccdaabbaaadcecbbadcadbcabbdcceebecbdeddbaaadbaabbdeebddadaceeedbcdcbaeaeecaaeeebbaccdbeacbdeabcaaaeccdeeadecaaeeebbdabacbbdccadbeeeabdbcaeedaabdbbcaebbeadbcdccbdddcacedeaaeeeeedcedceeadcaceedcacaabdccebcdbcdaeecddedddeccdcceccdbaccdbcbdcdcaaeddecaaecdbbecdebeaabedddccdeccedaeacddeeeeeabecaceecdeccbdaabdccabceaebeabcdccdbacabbdcaeecadabaacbcbbadacaabcabcdbadecaeedeeededcedbadbedeccededbeecbdaedbdbcdcbebaaedadccadcdddaeedddcdecdcaebeebabcacbaacdccecbcacccdbbcedaadbebbcacdbccaeceebbeedbebceabadaeddcccaadeebccbadcedabbcdcbceeaaeacabdbabacbaeeeedabecdcebddecbbabaecaebbbedbababcedeeeceabbdcdebabacdebeeaeaecceabdbaabedcbadbcdcabeccdedebdecaeedaeceaadbbbacbaaaecceddcacceebeeabdeedbdbedcdeddacedcdeccddcbdaaadaeabdbeaedbbabbdcbecacdedacdddeaecdbcaaaabaabbbdeeabbeaccebbabdbbecceabbadabaddcecccdcddbaabbdacbdbbddeecbdaeceaacbdeeaedbbabeacadeabbbcacebccbbaaacdccaabaaeceddecbdceabecdcceeabbabeacecebebccbaeeecdbddeacaabeebbcdebbeecceaccbacadecadedeadeedadecdebbcbadbdeaceeebededeebaecdceedbbaeecbdaededaeeacbccaeecabbeccaccaadddbebcdceabaeadbacbabcadeecedaaaccbaaddaaaecddadbecadbbdebaedabcebcebcbcdeebcdbdeaceddbeebbbaaeecceaeceedcbdbaadccdababeecebabaddcbdcccadddddbbcdaebceddebccbceaaedebcdaeacdababcabbdcceccacddccdbebbeedcebdececaadaadedcddbacdebcbcecccdecdabaaabbbccbdeddcaaababbdcabbacaaecbceadacbecbabcbeedeccceaebdabeaccacbbbecaaadeaaaabcabddccddbcbabbdddbbdceabcdaccabbeecaaadebddbeacabcbcdaaaaeccccadacbdbaaaeccbbbbbaeabcbdbeadcddaabcadcdaacccdebbeeeccecbbaeeedeadbecabbddeddeebaebbbdcccdceaaeeebcaceedebaceddbaaaebebdcccaeeebebeecbeebecbbdaaecdbbbceaeeacdceebdecaccaccbebacbebbeeaebccedcbdacebededdecadadddaebaaeeaddcbacdbebccebceaebacddacccecabdbaeccedcbaeedddadedcebdbbacddeceaeecaccdadcaacbcdbbebcbdecddcdccceecadcddcadacacdeacddbabedeceedadbabeabbabcaddddbbcddabacecbcebbedbbadbbdaaaeebdccbebaeceadddadcbdeebbebadccbabbaaebaccdebeceaacabcabacdaececcdbcceabdedcbddcbcaebcdbaccdceceeabdaaebceeaaaabaeddaccaecaacdebdbaeaebbbeaceadcbeaabeeedbbccbdcacebeadcabdcbddbeebaedaacdbeebeebcbacedbedbbdbadabcbedadddeecdcbdcedecdbbcdaabdacacbbaacddadccbbecbdacdceeadaababdeeebacebaecaceeeababaadecebebbddbcdbbebbbddbddeeaacebdeaeecddbbbadccbddedadabbeecaabceceadcaeacdcaedbbdeaccddacdaadeaccabbeaeceaeaaceebdecbccdccddbcaeebbaacdadcacecdeaceaaecdddecbcadbebeabdebddcabedbaebbbbadcbdcabedaaeccecdceccdbceeedcdbdcccdacacedabbacbcebbccceeabbdeeeabcdeecbcacbebcceebbadcebaddabadddebdecbeeeabcbadebbcaddeaababcdeddebbceccdbecedbbeacebcacadedebecdbbbcbdbcbdaeabecddbcbbcddbedbabcebdaabecdaaaedcbeaaeadacaeddbaaccecacccedcbeecbcbcdbacbacdaceecbbaabacdbcdaedcdbecdedeedbbceaabaacbcedebbedaebcbcbcbdeceecddbebaceacddddeeaadccbacdceeaceecdccedacaddaaccaedacceeccecedacbcebaedeeacecddadbdabdbbcdbcdcebbecdacabccdbaccbbeeabdecbaeaebddecdeeeaeddbbbeacecbcdeaedaaededbaaeabadccadbbabeddacccbbecaeabdecccaddabeeabeedabbdddceeedaecdaaadabbaebbdbaadabdbeabeedbebdeaeccebcadbdeaeabcadedaeeeecdcadbdbbeecbbabbdebdbacdbdaaccbdbeddabddacedaadeaabdcebbbbdaaaeceecadabaaeacdeeccedbcaaeeedddbcddebdeccdebebceabdaeccdbadebecbdcbcdbdeccacbabdcbdcddbdddacdbdbccdbcdcdceeadeacbbdadddaeccaaabbeaaecbcadebebcdcebeccaabdeacceedecdcbbecbbdcedcdabebbceaeacabdbaeabeaebadeabaccaaabdbbdebcdecedabeaddeddbedbcaadeeecdcdbacbdbabcddddddedebadddeebceedccababbdccdeaeabbbaebeabaebddbbcebdebebeacedadaedbacecdaedecdcdcaaceccaeabeccacbdeccddabbbcadceecdbccbabaeedecacddbdebccebaeeaadaeecbcabbaeaedbdaabccbadebededbabebadbacbbaeecbbbbdcbaedccbdcddadbadcddacdcbaabacdddadaeecdaeeecaacdaeeccadbbbbcaebcddacabcddddeddeccdadaeebbaddeaeaadaaecbbbaeccdeeaaabcdcaaebaadedbbaddaadccabecabeaeeecebcbbbdeeddecebadacebedeeedbaddcdbddbeaeabbccabdcaabdeeeebceabdbecddaccceddbebdbeaeadecbeeadaaacebadbeaeebedadeccbdbdeaddaabacedcbbedcdcdbaeaebdcbeebbbdacdeedaeacecebaacbaedaebbacacbdbcbddcaedaacababbeceedabeeecccadbdaccbbdabccacaccbeadcaebdbdedbaedadeddbeedecbadddecabcaaeecebababcbbbbbccacaaadbdeddccabeeebbedaeeedbbddbacbabcbdbcddcabadccbcaaeddbaeccebedeedeedaaaecacaebbbcbbcbaeeececadadbcdbddebdbadadbbdcadeabedccedcbeeaddddbabccddbbdbcccbebeedaebdaecaaedddbaacbcdaccacdcdebeddcdbeeaacadbabdeccbcaeeebcadddbbbcdbeccabeddcdbdbcacbbbaceedccbbebdabeabcbeecbecccedaeebcacbdbdaeddcbbaeecedbcbcadaebccebcbadcaeccaceeddacbaceeceadccbddcdcbedbdbadadcebdacbeeeeedbdbcdacbbceecdbcebccebacedebddbecddacbdaaddeddbbeaadacddbedeeadccbaeacdebeccaeeebcacdacecaedabbeeabdaaeabeaeedcaecacabcbadbaedabaceaebbebacbbeabcccdbceabebaaceecbaabccdbecedccbacaababccaaaeedbdcbecaaadacabeddbccbcbccecaacceaacadbabbadeceabbacbedaaeaaecbcebdedeebbeecbabadccdaabbcbedcadbdaacbbaeedcecbcbecdbdacebbaadabaaedaaaeeeedcbdaebadbdeddddbcccdeccceacdbaaacbcdaecadaddbcbedcaeeaebebdaecdbddbdddbccbddcadbddbdceeacedadabcabeaececbcdbdbbadaadbdcadeccccaabbcebddbebcbaabcaadbcdaecacadebbccacaaeecccbcccbcbaccaabbeeeecbccdcdcdccdabaccbdceedaeabddeaaedcdbbaccccbddabbacdddbceaeddacccccabecabaebaeeaddadddedaaacdcaacbbcdcabbeaddacbbdccdceddbbaceedceecdbadeaebcabbbaddcbaedaaabedeeabbdaeededebecbebbdeeedecabddbdedbecaeedabdbbdeddacdedeabcecaaabdbabbadaaeeeadccacabeccaaabdebbdaaccaaacbccaacaeeeecbbabdcbbbaecabbedeacbbeeccbebcbdceedaecaceecebaececcdbaaabdccdbecdccabecdbdebaeebbbebaeeabdcecceddddbcacdddccbdbbebdaaaaacccacbacbbbaedcdeaaedaaeeaccdeaabeecbdecceaddeacbaabeddbbaceeeddaaddbacbbdaddeceaeedeecddbbcedddaabdecccbaebabddbdceadcceeabbbbdbcbcebdebdccbedacbdbcbcaeaebccbddccccecddadeeeddcecacabeecdecceeadaabdadadddbdddbecedcabbbaebdbbbcadcccaacbaebdbccdeeecabcaacebddbbdacbdeeceedaeddaecabbaccecaeeadbcdeedeedadcccedbebaabebeaeceabaeacdceacdddecbbecbdcdcaeadebabbdaadecaeceeadadbdbabcddceccccccdabaeeedbaeaaddaadaacaecacbdddcecbbdbceddcbeceeceecbbeeadbaaebdecbccbdddebcedbdeddecbccbdebcbdaacbabedeaddadcbdaabaedeaadbabebadaaabbbedddbcdeaccceacdaecbeebdccdbbecddadeadeedeeedcaabadacecccbbccececcbcbdebeccbcabbaaceaabdbcdabedaeddecbbccddeecedeccceacddbcdaaaedabcacbcaeecbaecbacbeeadaccbbcaccecbdaaeabdbdcebeaadbeebdeadccdbbcddeacceecbedabaeebdcbbaaeeecdcccdcbecebaeaddbeddccdbcbdcaecbeaeebccbaadbdeebbdabcecaedaccaabcbdceadedaccbddababcaaceaeececeeeeadedcaadccadbacddcecccceeecbbdcbeeeccacdccaedaabbdcdeebddeaebddbdeebcbceacebbeccbaceeadbbebdddcbcaaaeadbbaededcbbeddbcbccacececaecddcdedeedabcbbdddbbeedcbaeebdcaccbddccebbebbacbeacebecbccbeacbcabcbdcaeeecccaaeceadabccedbccbdacdabeeaccecaadbceaacacdcbadeaaacddadbdcbcdcedddaedeecaeddadaceabbecddadcecebcacccdaccededdbcbdccedeeddabbdbbcaacbeecadbeaeacceabebbeccebecadbaebaecbeadbeabccdbebccbebaeedddedbaacbacecbacdbbcbbbbdabeadbedaeeebbbcdecdcbaabeadceeccdbddacedadecbdcdaacacccbcbbcbadacacadabaddecdbeeecebbdedadbdaddbbbbdddaabbadbbbaaddbbaaaadeddabbadbcdcedaedaecccdeadcaeddcbbdaeabadbabdcebabbeaeaddaebeabccaedeabebabdccdbaebceebebedabcceabbabcbbceabcaceceadacadddccdeecebeedcdbeacdadeecccbadeaecbcbddddeeeadcabbeeeaeebbdcedbcbcbaecbaaadcbbabdadeeaacbbaceeaeddebeaacdeccbceaadeeaeddaebaadeeacecbcbdcbbcacceebdadedbcaeaaeeeaacbceebeeeeeebedebbdcebeabaabdddddceecdccdbdeebcdaaddcdacaebdecedccdcebcbbabdcdeddeccececaaedaebccbebebbbdbedcaceaeacccbacbbebecaeeeaaaecddaeeababaddbdeaeeecdbbacbebcedbadacabbcebbaaceaaecbecbdbdcbebaadceabbacecbaadaabbedaeccbbdbeebbddcabdadddaccdeecccbcaaedbaccaacccaaaebdaeaeaebcecaeecbcebebdadedccdcbdeebdedbdbcacaaeaaaadeeaacdcbdebccddaaaabeeedcbadabecaebbdecacadbbdabeedeabebcbbacaedcbaebebebbddaacddbebaebcddcaeadecacbaaeeabdbccdbedceacdabeabbdaebcacdaeababbeeaacabcccbadabbedebbcbeccbecbeccecedaebdcceaaacbbdddcbabececabdbbeccbbacadbaddaccbebadeeeaebebededcaabcbdeebeaddbbedebdddcabcaeedbbaebccbaeabcbcbcbdcdeeaecebbdaeaabbdacdcddaeaaabaaedebcecaeddbddbbbbabecdddeeacabdadcbadbcadcaeaeebcedccdececacecbccdcceaeebeedbcddeabbddcbdcabbaacbeacbeeabbbbdadbbcccccabbbbaeebaedbcbecbededaaedccacdbaaaeabacaabdbaecddbbcbaceddacdaedeedbabecdedbcaebbcdecbebbaedddceebeeadaadadaaaaabdbecebcaadbdeaabdacdebadedbaacecddbcddbaeaabddaebceadeaadadacccedadecebceadbddbeaadedbcaecaecdcabcaddcaddecbbeaecdcdabddebdadddddadebecdedcacebeedcdbadbdadbbdecedaaecbdcdaeacccaebcbeabadceacdbdecaebbddccbddddabeadcabdaabadecdadeacccbeacbcaedbcdeeeccaedbbadbcadeacecbcdbdbabecebbcbeedddbbcebecddabccbbecaaadbbacbeceacbdebbeaedcddcbdcdcddcccceecedcbbebccaaebaecbecbcedcbcacabeeadddeaecabccabcbeeadbdadeabeddcedbadcacbebeaebececeadceaeeeedebccbbcabbdacacceddcadbdedebbbdedbaaaeabadaebbaccceaaecaddeaedbedceaecccacaedabaabaccccbebbbbaadecacbbebaddbbbcedccebeadaddcebbdaebdaaaeabeeaaabcbbcbedcbbedceecbeadeaacdbadbedbcebbdbcabdcecedebeeacecacedbadabecbebcaedaadcebdcbaeedcaddeceedcdadeadbaedededdeeaeaaecdecacadbdeadbddbcbebecbdabcccbaceedcceddabbadabbbcbceadddaadcdececedbaddbccaabaecceebbebadbaedbaaaedcbccbaccdaebbccbeeddbccadcdcecbebabbaddbceaaccaccbadcbbbccadecdcdabececbecaabbabbaeacdaaacebdebebeecaeedbecaccbcddaccebbecacaacbdecdbcecccbeceeabcbedcdeadeadcdabcebbdcddaebcadbbcdaedbbebdadeeebcdeeeadbabecabacbdaaabeabededcceabcbddbbeabedadddedebddbcdacecccacadebabaeaaacececdbdaababebcbdabccdaaceaeeaacebccaebddeeecadbebaacbabeeabcbdbbaedadbdbecdebcecdbcebbdaabdcbcebabdbbecdaadbdddaaedaeecdacaaeaaddcbbeabbcabeaabadebadcaddcdbdecbdaabeedcebecdddbbbcccdedacaeecaeacddcdddedbabaecdeacddababccbaaeeceeebdcaccbacdcebcabeadcbabdedbaaaebddeebaeeacaadddecdcbdbceeeebbccccdcbeeccabacadaabdbaeacecbebaedbbaaacbcbdaebccacebdeebaacedaeaeeaeeabdaacddbddadaeabaccccbabdbebeaececdcddaecaaecccaedbcdaeaabdddcabbedbdaceaadcddebcacccddbadeaeecbdcadcdbbacbadcdeeadeaeddcecadbeeaedecbbdcddabcabadbaedabbbdacecdcccaaaebcacdccbceebdbaaecadaeeaededeaadbaceacbdaaeeedccbcdeeedccbaaeccacdcededecabaddadaddddccabdeceacbabdaecbbbbbcaeeadebbcdbcbabcddcddcbdbdcaeebcacccdeeaeeacdecdcdcedadcabdabeecadbbcdedacdddcdbccadabeabcadaacddbaecacedeeceabebaeeeadcabeedeeaaebcbedebdcaabdadddbbaabeeddbeececbecadeceebaccdbaccdedcbaeabebeaeaeddcaddeceeabacdcbdbddbdbeaeabadaeaebbadecedbadecedebeeecaceebddceebaeabcdcecedbdcaaaebbdddeabebdcbccccabadaddbaccdaccdbecdcbdecdcabdcadaceceaedabddbbbecabdebeeeceaacbcadbbbbeaceebdbbcadaaecdcaacdcbbcecccccaeceaeaedbcbbeaabedaccedddcdbbdccbdbbecbcabdaddbbdabdaadaadedecbddaeceaeacdeecccdaddeecbcaadadcddbcbdecebbdddaadddcbecdbcbdaeccdcacbccaadaeccaaaeebbcaebcdddeceaebdcacdacecaacddbabedaecdcbceaccabeadebabdeecbddebedcdaecebebcbccbaebcdcdcddcedeabecdcbdcdbaebaccdeacdaebaaddeedeacededbaabeddddbaacbaebbabeccdaeeeaaaaccdbaaadcadebebadbeacaacbbcbeddedeecadcbceadbcdabdedadcecccecbeebddacadddbaadeaacddeaabadbbebbceaccccabbacacbddbaedccbcbdcbdebebadccadbddccbbabaadaeeeaadcaddcebceeadebaabcacbcdcdbedcceeebbdeccdcacdeecaddececeeaddedaddcdcccacedbbedcbdbecdebaebdaeeccbcdecaedecedaaabbaccabadaacdcbabdccbadaacccecabaabdadeaacbeddcbeaddcdcdebceeabccaeccaaeaecbedddddacaedbaeeaabcceacdbcbaebbabaebbaecabbddbaeaedabeaddbbbaabaedcdbecbbabbaadbaddaedecdaddeebeecadbecdbbbbdadcaebaadbadebabccdeacabebbcceebebbbbddabebcdcaecadaaeaabbbeccaecbbcdacbbaadaddaebcccbbaceaeeeeedbadbddbeaabeacaceecedceaadddcbebbbdbddacacaabdcdeddbdbeccbedeedbacddcdcbbbccdcacebbcedbbbdcdeddcaceaaaacdbdbbddaeeaeebcebabceddbcbebcbeddabebcdbedebcdbdbcdbdcdddebcccddcbebeddebeabbdcbdeebecceadddbdedecbccbebdabdaceebddddcccdddebaeabeeebbcbeecdcceaedbcadcebbbcaacdaecdecceeaccbaadabcddadeedaeabaaccbbacbeeaaaccbbebacccddbcdbbbdbbbceadbeedbbdccbadcbccdcccbdaeadcaaecbaabebddbaaacadbcadbabcbebcbbbaedbdbbdbcaddeeecdbdcabaeecaebecbcaedabaaaabecaabeecabacdbcdaadaecccdcdbbbcbddbaebeedccbdaeaccaabaccbaabeabbcaccebbbdeeaadcbbbddeceedcadedeaeedceaedceeeeaddaccdcbbbadccbccaeaedcaddbeabaebeadeaddecddbbedbaaacebccdabcdaedccabbbdeddcedbecabdedadeedecbadabedbbccbeedebdcaabebcaacdecacecadcdbadaeecbdcbaeecddeeeaeeeedcddbedebdbcbaebdebccbbebcdcbcbdbaeeaeadbeadbdeccdececabcbadeedaeaaaeaaceadedccbcbacaacbbdaeeabddbebcaddabacbdddbaccdccadadadedcddacbedacdeacedbdeacadbededbbaaaaeabadadadaadddccdbaeeebbedcadaaccebeaeddddeebabcacebeeaaeaccdabcedcebdeabbeadbcadedddcedadbbdedbbdedcbedbeaaecacddcaadceaecddbececcbdbcbdadddebbdbececaeaaacbedebeaabdedeaacbacdecdbcbcdaecbaddaecdeadaebacabbecacaaadbaceaebbccdcebeecbdacdcaaebececeddabeaebeaaeaaccaccddccdcdeadddbabdaedbaacbacaeaedeeaddceecabeacadbedaeecbebbebddcccdddabadabebaddaabbadaedabbdebaecdbcdddabcacdceeadbbbaacddaeaabccbebdccdecddeabeedececaccecebecaaecadbacdeedceadedbcaecddabcdbecdeddaeaabacbaaaabbacbcecadabcabebdbbdbacdeddaaabcdaabdbabbebbeceacbcccbaeabdedadadebcaeeacbccddadadecbdadacbdabcbbcedcabeacddbdaacbaaecaeecbcbcdbeebaecccddcacbaeadeadcebbdeaedbdbabdbbcececeebbeadbbabbaacabacaddddcecabdabceaedeaacdbcadcacaebadcaccecdaebeebbdcdccecbcceedeecaaceeeeacedeedeeabacaebadbbeddbbbebcbdbcbdcdedccbceaddbcbbcbcabdbceaadcdeabccdcbcebedddbdbcebeaedddaadeceeaaceaeabdeabadbbdaabadeedadaceaebcbeedbdadcdaccacabbbbbbeababdeabccbeeabceddbbbcbeaddeabedcacadbbbdaadaaecbbddbbdebbabcaaabedcdbedcbbaabadacddedaceaebaeecdbcbcebcaadedaacacbeaccdebaaedeedaaebcacadabdbbeadedbecddeacdcbccdddbcadeabbacdeaabdacebdcdedeeadeaaddcdbeadeaabccebacbbaaedeaeeadaaeedbabccceedacebdeebcddebedcadcacdadadcdeabcbaadbadcbddcaecdcbdaacedbaedcebcdedbeaedaabbbaebaaaecccdcebeaaddeebbdceabebadbcbadeedddbadbcccadbceecdbcedbeebcdcaceeadedceadababdeaedbbbddaccaacabedadbbcaaecddebbebbecdedcecdecbaeaadcbbbaceddbcbccaececbededabccaaabbcbcccdeaaaddededeecdebaccdaebdadddceabacdeacadccbeeeeddcdccaacaebcbcadbeeddeebaadbbdabbeadedddecbcecdbdacedbcbacbcedaeecaaedecdedddaeecbaccacadcacdbddcdeababdeecdeaedbdbcceceebebbebaeadcbcdaadedaabccebdaebcdaaecdbbdadbddbacecbabcbbdaabcdebbeababdbeceeeceedcadceadacbdebbdacdacbdbebceacebcbecdcabecdacadcadbdadacededbebabdcadbeddadeacdcdaeeadabbcacbddadcaeaacceecabaeecbcabaddabccbbcdeedcebddcdeebeabcbbabdbaaaddbbcdabcadeabccccedcaccaddcaceeceacbdbaeabcedebbdacabecabccbcdebecddddcbedcacaaaeedaeadacdedbacdcbbccdbbeedcedbabdbebbbbaceccaebbcddcadedceebddadecbcdbcccdcbcebccdebcedaeeceadadcbaeacbeeabeddccaddcddabdedccaddceadaddbcaabaeeacddadbdbccbaaacedbeaddcaccacceeeedecdaedddeadadcbbeabbdecebcbbddadedbbcbdedcecbbdbadcecededcaabedaeecadcddedeeadcacabebcaadbeccbeadccbbcaabdcbeeeeeecbaeadcdaeecbbaddaeaacebcaddaeaaedeaddccbecbcdbaddbaeacebcccacaaaaeecbdbebadbeadaaeddcbabceceeeeddedbeecbdcdcebedacbecedaccabeedbcbdecaabcbbdceaaacdcbebaebdceeccdbeaadabeaccddcdadcbdeedddabdcdbbddedaeadbdabbbecedbeaedadaeddddbddbdcdebcdcacaccdcdcebddababbbaacdacebacbaaebccdaececbbcdedeaecbbbadeaacadbdbbabedaeebcedcdbbaaaddecccbcceecaecadcdeeaeecbddecdddcaaaedcecbcacdacaadadbdeedcaeaaecdcdcaccabccbdceaaedbbddddacabcddaebddccbbecceadedcababadaaacacebcdbdbdebadbbadedadacbbbcacdddaebedaaddedaaceacaedbaebabeeceecbdcccddeeeeeabaabcedecdeaeaddaeddaebeecebcabbabddcbdccccdaabcdddeacacebbcdaceeebdbcdbdaebcddaabbeeadbacdacbabddeaadeccddbbccaccbaacedebdecddadcdeddecdccdcaebdcceddaccaedccebcbdcbebdecebceceeacedaedabeccbdddcacabdebcdedccbbbbcebeeeeeadcaebaaaedadbaedaedbebacdcebcdaaedadbcebcedadceecccebeaadbecdaabcbdeeebabaadecceeabadedabdbdcebadcbbbadecbdeecebabccdaddcdeaeccabddeacacedbcbacbcdbddbdebbeddabbcccebbeccddddebddbeebdcecababcaeaddcdeebecdcaddedeeadbecbeacbecacaedcbbabeebbbdebccbebaebcabcdcacccbcaeecbdceeeadbbdecddadedcbbeeedaebbdcdedbebebbcdcdbccabaedacacedcddecbdeaddebbdeacdaccabaebeaceaebdbebdebdbadacbecaebbcddddcbdeeeeeaaddcacaaceacdbbeabadcecbecaeabeabddecdaddbedccebdddaebebccbacdddacddddeeccacaeddcecacdceccbedbeaaeddaecccabaedabccccbccddabdadbcddaacabccaabdabaebbebbacbdcbccbcdbeedddbbdbeadadcacabaebeebdbebbcbeeddabbbddcadbcebceccdecbdbbabcbcdddaecaeadcaecceedeadacddbadedeebdaedbdcdaacecbcdcedbcaecdcdeccbbccbebacbbdaeaaededbccebcaabbccacadebbacbaaececbecedcceeeccaedbddecccedbadddceeedeaaadcbcadcdeaedaeebdcecceebedcdcacbaaabdcdaaeaececeecdedcedeadbdedaddcdeacdabdabdaeaedacbacecdeeeccbceeaaceadbedcbeeeaebbbeebbceeedadbdaadcacbcceacbabbaaebdabeeddaeebaeebdadceaeeedbacceecebaeabdabedbccccbdeddbddbbedebadadcdedeadbcadcdbaccacbdaeaebbbacebaeccdbeccabdcabdbbadadbceebeaeebadeadddbbacdaceadeeaaecdecdacbdeddcecadadeaecdebeacbdddeeebdbdaccddaecadecbecaeddccbedbdcebcdbdcabacaadbecebcacaaeabdaeedebcbbbceddeaddababaeaeaedcadddabecbdebebdabdbaaeddeedaeeabeeeeeccddacbcabececcebdcbcaccccdceeeecbceaccdceedbbeaadbdbdaedcaddbcbbcabeaebdbeddcdcbedaadeeabdaaabbbddaebddaecccacabbebceabcadbeeeaebabbbdeaaeddbeddacdaddecaabbccdbccbaebcebeedabedcccddbddedbecdceaeeeeaecdedcaebebabbaabccdddabaddbdbddddbbaaecbbdabdbdabceecaaccdcecccedcabbacdcbeebdadacbabedebaeeecaedcebadecbcccadeabacdbeeabbcacdbcbdcaeceddbdeeaacdecbaebbeeadddcdecedcdddcdcbbacdbdecaceabceeacbebddeaaababacbaccbaeeeccbebceccabccacadeeaccbbdedebdeabeeaebbadddbbabbbdceedccdceaabbeaedadceaccecaadccccbdbddabeededdbeebdabbdbbcdabcbceeaccacbabedeeceaedeaedbdacedbebdecccedbebcbdddcebabecaeeacadeecabeabdbcbaadcecbbccddbeaccbeaaddbddcccbedbaecadedcacccdcaacceadacebcaabbecabddedddcecbdaeecabdcaadcaaceceddcbdeacbbacacdabeaaedadcadadedbdacebdaadebcebbbccebbedeadabcdabccbeeabbdeebdccaaddbaeccbddececdbcceecceecdbccdedbdcdeabeaccdbbabadeeacdcacadaaceebaedbcedaeceaadacbaaddbaeceeaeebbbcdebabcebbbebcecbadcacbaaeeaaecaaabdcbeaaadabeedeaaceedebdadecceeddbebeebedabebdadcedccabedebbececeddecbecdacabcdceecececddadebdbebecbaecaebaeabbbeeaceabeaccadcaaaebbdbaeabeaeaedabcdcbbdabccacbccdbcaebaaeecabdebbedccccdbceaabdaabeaceacbcddbcaaceadbadddccdcdeedbbdcdedbedcdbbadcccdadbcdcecbeddcaeeecacacdbcddacbeebaeaeacdbacebedebbaabeacabedaeadcbbdeeeeddeedcedbeeabcceddabeccbecabcdaeddbabbbdeebcbceddeeeadcbdcbbabdbbcbaacdccebdccaeddccdedbedddbdebbbeddccebdabbeceeaadecbcbdcbbbebaaabbcbceccdebcadacaaaaddaeaeedecbedccbddceeccaecbcdbedeececdaadddbbbcedbeecaaabedbddbccacdbaaadcaebcebaedaeaedeedebdddeabaebaaecbdcbbebbcbbdeecdadbbbeabeabdbaaadaececddeecbdeebdeccebacaeeebaeebddeedbaeabcebaeebcadbacbbadcebceeeeadcdedeaabebbcebbcabbadebaadabbeaaeeacedcbacbaebcaebcbbacbaceeeaedbebdccbdedcbdccedddbacbabecabcecaabbbcdbbcbaeddddccdabcaccecccdacebececedceccdcbdacebcdbaedeeeedebbebbecedcadbcbcecacabbbdebbaedeebdbdaadacaaaccbbbdabccddaadabeebaecedcabceebeebedbbcbdbecdbeebcddbdeddaeaeeaddcaebbcbeacbbbbdebbcccdbeacacceaaecabcdeceeecbdbaaebdddecbcacbabbdebdecaccbdbcebadbaaaebbabcaebbccadcaceaaedbecdabedcdaadabbedccdcacedddeaabdcadcacdbcdbcccebaadbbebaaedeccabbaaabecbccabcedcccdaedcbdacaaaeebdbadbeedbdbaccbdeaeacccbcabaaedeeaeccbaeeaeddaecaabcccdcaeaaaaeebcacabbbbcacedbcadebcbedcecbddbaddadaeeeedcedaaedadedeaaebbbdcbadaceabcccecbbabddcbecdadaaacdabaddaebccbdcbcdddeceeaaebccaeedcbcaeeececeacedeccddededeabeebecdaebdbecabadaaddaeceaecdbccccbabaebabbdcbeddbccbdccbcdaeaeaaeaddbdcaebcebcdbebceccbeabbdbbceebedcbeaddccbedbabedaddbdcdeecaddcaecaaeaedcccbaaabdaacbeecdceccebdcecaaaadddaeeececadacbbdbecaedcaeeaedaecaebeabbeebabebdadaaceabbbbbacdeedcbcbcbbdaaccacdbaedadaadbceebebaaaeeceddcdbcaaeacdbcdcbabaadabebaacadcccaaabecbcadecacaabdbddaaabdebbdaadbeaeececbeaaabdddabccdbaaeebebeeeadebdeeadcedcadbdcebedbedabccabecbeedbcdcabbcdbcccaddacaaedadbbbbdcebbaecddabeaedaebcccacbeddaaedcbebcdedecbeeccdaaadaaaccaaedecbdeabcbbecdebddadabaaddbecbaaadaedcbebcececddbcdcbecdddbedadeebcccdbabbcaebdaccaccaecbcebcaceaedecdddedbdddbcdeeabbbbaaccebcaebbebaddcdcbbeaaaeeddacdebbbcbababbeddeaaeaaabdbaeeddeeeaebedbbeddcacbabddccdaeedbcbdecceadcdeecddbadadeccadaabdbddcbaecbbaaaceedaaeebcdedbebeaadddeacebdcceebedadaeadcabddcaeebceccbcdccbcacddaccdaededebabbbcbadceaacebeeaeaaabedeebadcbebcececcdaceacbdbaeaebcdcddebcddedbceeddceedeeabaaacbaaaeaeddcdedbccbbeedbabeeecbcdcadccaababdcdcbbecaddbccababbcbbaddeebecddbedeecccddadaccccecacecccbcdcdbcdcadcddcccbbbabdbdcadbedecbeceeeededbdbebdcedccebaaabbacdadcaeadbdacaedacadcbacdbdcabecddbeacdcaededabbecdbcbbebdacadacaecceacebbabcccbbceeecbcdcadbdceddbccdeabccaaaaaabdcecabebaadbdedeecadabcddabedebedaaebdacaceacceacdddceacdeccccdcdaeceebdaebecbbcdecedbaebbbeeebbcbdcaebbcedcabbdadbabddabebbacdbbecdcaaddeaedeeaecadbacdedaacccedbeecddbdaaeddabacaeebbdcbddebaabbacbbcceaacacbbcecdbadeaababbaecbacbceecbdebeadcaacaeecadcaaedeebcdebecbaaecbbccecadacabebacaabecaabcceeacabeccbaedecabacaaebbaeebacbdcacbdccddacaececcdbdbecdcbcddaaecabbbeaddcddddaeedaaeadacbcebebcabddebdcbaddadeddebbadaedccadabdcebaeaedaaabeaadaadaecabeadaecacacbcebaabcbbddeddbcddebcbabdccdbddccbdbbecedaacaadbebbdcdeaabebecaedaedabadbabdeedbddedddddddaabebeabebadcceaaeccedeaaecbcdceccbbabceaaecdcdbaccdedaedddbeedeabcdedecdceaebcacacbaceacbabbacebeeaeebcacdceeddeaaebbbcaadebbdceeeddadbacedadccbbeeaedeeeabdcddeaeaaebeebbccecdaceeeebacaedaadabdcdeecbaceeebbaeddabcbccaaaebbdcaedebececbdccdbcbccecdcddacbacddaaadbbacabeeddabebdccadbccdceceaabaabadbecdbbdaaacbbcdadecadbdeaacecbadcebaeddbedaaccabcdbeeaebdacbddeceaaceccddbbdeddccdccbddbcaadcaecacaeecaebcecebeadccaaabceeabaddcbecceacbaacccecabeaadeaadecbbecbebbbbebedcebcbcdbeebcbaabcaceedecbeabbedaedaadcbcbddebdddbcabbcaceedeccdbdbddcadbdcaeddbadabadecbcdbbcdeebbebbdedacbbaeddeccdbbbbeabcdcdccadabbeaaceeebadaabccdcecdeddccceaccadcccacecabebcbccdeebaccdbcebcaddeddcabcdbeebeedadaaceabdbcbaedecdaebceabdecceebadeabcdeedbaddbdbcbdeaeacaddadebcacccaebaacebecabdceeecbceeadbaaebccbadabbebedaeeddbeeeabaddaacbbdbdabaccdcebbdbdeeaeabdddebddedbdcdebdebcceddcbcbbdbbbbbdabeadeddbcdbeebbeabacbdceccdadecadceccacaceadbdebecebbbaedeeeccbeddececaceabdaedeabebeceeddbaaaeccddbdeacaccecbeadaccceedcddddcdeceecccdcbdbecdaaadeedddabbccbaedaabdcbeccabadebebcdddcabdceaadedbaecbeddcbadbaeceeecdbbcbcacceedbcdeadddcedadbbdbccebbabedaaedbceeaeaaddedbaacaaddbaeadadbabdcbdcbdaeeacbcadcaacbdabcaacaddbdbabbaddbcaeeabccccecabaedbdabebaceccccdceaeecddcececdeeeeabcdbeabddccbaaaceeaebecabdabaacdeddcdeccddecddccaebaeacaadaabdedcabdcebdbdbeeaeeedbeebeebddadcaacbbbeecdadbacbaedaaaadebebdcadacdbedbccedcdaaeeeccabdceceaadbbbaabdddcececcbbbaedcadddbbaecbbacaeebceedcacaccbbeedecdedbbcbdacadbedeaecbccdbecbcccebbeaabedbcbdebeceeceacebccaabebcdaceaccebeccdeebcecbbaadcecceedbbcbbaebedbbbacebbbedaadccaecebabbaadcceddebdcbbcadeadbeeeccecdbccdaccdeceaaeddbaededabddbdbbbcebcadeaaccabadcddedcebbbdaccacaeeabeeaebeebeababeccbacadebdaaabdeaccaeaddabaeabdcdcbbddedaeebbabcedeeacbbeecdadbccbbbccbecdebabaaabcceaeddaddddbabbdcbcdcedbccdcbdabedbddbdeadcabaacccdcceadadbbbebdadeebaebacecddaccaadacdedcebadbcbdbcebabcaccccadbabdabbaeadcdbcacbbcbceeacbcddaacebbedebedabebacccededdcbcdadbaaddedaeaaeaebadacddaaeceabcdcecbcdcdcbdcdeabbabcceddeecebeaddcadacbededcebdbecbddbacacdedddbcdccbdbcdcebcdcccbdbaaedcbabebbedcecbedaebbaabbcccacbbceddccbecbcadeeceedeeedecbebbecaeedcdbcecaaaeeedaaaabaecaecbbcbecdbcbababdabbdbeaebeaaaedeaecbbbdbabbcdbdcaedbabbbbeadbcacbbdcdeddbbdbcdeddbabcaaceeeecbadddebebbcadeeceddbbdcddcedebbaabebeedaadeebdccceccdeebceaeccaaccebbadbbbdaedcebeebbadecebbbadeeecbcbaebecdedcdbeaabeebcaedadacabddeaeacbdbdabbabcebeeeaaecabeebbeabedaedaebbdababbeccaeeaadccdaddaccbebdaccbaaeacbaedeababdcccbbacdeededddddaacbbbbbedeaebeaeacbbcedcccddbcacceadcaedabdbdabaeaddeadbccaadebcacadeaedbdadbcbbdeacbbcdeddedcdbcebeecedabcdeabbdccadbcabcdeeaacadaabacbaceebddbeecdbaaedaaacceeaeaddddcbaceddaacededdabcdbaceccbadadddeabbebcceebccbeadeacbdbdecadbdeadbeecbeeaaaebadeecbadbbdabebeceeadeedacacdceebccedaaaaaabbcaaecebebaebabadcddcbccbbbbaedbcaedcdccbaaaecbebcbdddbadbeaeacaadbaedabaccbbcddcbabcdeaecceebaecbbedbbccdaccadbcaeceddbbabbcabcdcabdbdcabeaceebaccababaecbccecdeeebcdbeeabebdeabbdbecdabccedeeabedbccbeccdcceeaedabcbbbebbecedeacbdeddbacaadbededcdaaabbaaaecbdaeeecccabedcbaceecbaeaabacebaddcbceeaacadbaaadcceeeeadebdaabdaedabdcccddedadbcbaebedbeccbcebdedcdbacdcbadbaddeddccecbdeeaeeeacdbbdadeaedbbdcaabacceaedaceecedbeccabedeedbaeeaeccabaeddeabeeececeacecabddaadecadcebcbbcceabeeaaecaccaddebdeebcacccbeaecacaabbccccccdbecebddecddbdaaecbcbbbabdaebacecebcdeccbadaeceddcaddddcadcccbaecddeaeacdaceebcdedbdcaaadbdbbeecccdcbdaeddbebddebaabbbadaadaacbadadcaebacedceabebbdbadaedbbacbaeaeadbebeebbeceeacbcecabecbdbcacbeaadeabbedebecbebddbeabadddbbeddcbcbbdeabadccdbedbccccbddcbadcbbececbececeedbdaceeeadaacedbdebccbbccbceaedbbcdceddcdbaddaceeaaaabcadebaebcceeabcbedebddddbebdbabedcecbdebeebaddaceadeaeedbdecabdccdcecccdbccdbdeaddddbcacebaacedadedcebceddcaeaabdbbdbdbaebdeeecedbbcdadbaeabbddcccaaaeabcdedabebcdbdebdebbaecddcaadebceecadaacbcabcbbdbebaaddedeeadabdbcadaebebdbdaaecbcabaedceeeccbabeebdbadcdaaacecdbdeedcaeadeecbedbcccccaccacaeacadebaeacdaaeebdbddabbccbdadacecdaadebdcedbabebbecdeeaceaeacaadeeaccadadacbedecaadcbecddbedebbbeddbcbbaacadaaacceaaadabddbaaabbcbdcdcdeeddcecdbcaddaacadbedbececcadcebccaadccaeecbddbdabdcbaebaeedbeebdbbaacbddbaadeeddbaddddddccdaeacaacedcebabeaeeeeacbadbeaacacddaaadbccccaaccbbbaccdabbecebcdaaebddabacdbaacccdacdaecdcecdebbebbcacaecddedbbacceeadaebcadeddbdbdeacebcdacadeaededcdedaadaabedbdadbaeecdbdacbcacdeceedcceaedbdaecaeeddadcacdccdaabaabecaedbaeaedcedaabacecbacbdcbcdbbceabebdedabdbeabaeacaabebbecdbdaebadbeeadebcccdbbcdcebaacbadccecebaeecdeaeaeabcbdeedbdddbdccdddecbeddceeeeceeeccaccddabacecbbadccdacdeeecbdbcbacceeedebcbaaeadeeaceaebaacadccbaababcdeddceaddeaadaebcbdecbbbaabdbbbeaaeeaabeaabeebceaaaabdabedbeeedccacebeeaadbcaacedbddbbbdacdbaadacbaedbaecadaeebbaccdaadbcacedbdeaabbaedabdabdadebcdcbdcedcecddebcedbbeadbdbcdadbedeaceeecbceeddcecbcabbbccbdeccdccaddadcbadccaabaacecedbecaacababdbeedabcbccaadcccaeacaadebbbaaeeaeeebecbadbccabbbbdecbaebdadbbbbabeacdabccdbabddbbeacacabecadaaddeebdebedabccbaadbadeccaadebcadeeedcbccbdcccedbaddacceaacaabdbdedbeddaedaccbbebbeeeccedaccaabaccbbabebecdbaecbaecdcecdacaaebdededddecbdddccbbaabcdbbcdebeeaacabdceeabedbeacddcaebdedabbaacdaaabdbaadeceadeadaccedaddaaadaeeddeeacbbeccbabeceacebbdeeeeebabddacecdddcbddbbcdbbaabccadccbddaeaaccdbaaabaeaddacedbbdeeddbadcabedbdcdcdbccacbbddbdcdceeebdddeaacecbcdabbbdcbbcecaceedbacddccdabbdebcedeccabbdeeadcdcacecadebdabacbacddbceecaadbbbbdaacdbcedaabcbccedcabbaabdcaaeeadeacccbbadacbebcbedddddbeababbbdceddccccddbdaeabbaddccdbeedcdbcbeeaadaccebdccebbdcddbcdbbebddecbebadbcccedacceaceeadecebabbccbdebeacaddecedacbbbaedcacaacceeadccdacdeaabbcabadaaedaaabcccababbcbbebbaecaabeeaebceddaadebccccdecbcbacaeceeaecdddccdaebebccecdccaeeaaabaeadcbecbacaabcebaccbdaaaedbdaeeacacbbcabbaacbbbabecdaabeabeedaaabdbacbbcacbaeeabeabadcdabccebecdbacbabdebddcacecabdbcaacbbbacedeedcedaddedcbbeadbbedebcbcebeeecceaccbeccebaccdbeeadbdddecabbaaebeedabbaeebcdbecacdeeeaaebaabadcbceeeeccdaedceedabaaeabdeadceeabcaabedcededaeaeddcddecacadbabddbabbbdabdeacecedcecbbabcdccacbdbddddaebeacbeedcaababbbcaddcbbdabbdddaacbcddbdcdbcdcbcdddcbebbcdabaadcbadaaeaaceabbcadedbcdbcbacaaadcccdcbccdaceaebbcbecabebcbebdcdecebcebdbdbebbbeeedaeeeadcceecccbbdbdabbbdbbbdbcdccbaaaddebbbcbcebcbbaedbbadadecbbeabdccaceeaecdddbadebaceaabadeddbedaceeecbdabccbeeadeaadaecddeaaacdaacdbbcdddaeabadbecccbbbdcbbbbdbdabbdebdeeeedcbeddcaaaaececdaeedccceaaddacecabbcebdbbbedcbaabaedcedaeccdbbaeedbebabbdccaeebeddbeacbdadbcdaeaedaccbddbabbaceccacdbebadbbeaacadddecbdeebaebbdaaceebdcecddabdaabddaeacedbbdbdebcaceeeaacdeadbdaadeebadbdaabddbbdddceaacdbedbedecbedeabceaaacddececaadcaebacadebbdcecaebbbacbbdedbaeadecbbbbdaedcdaecbcabaedabeedcbabcdeabbeddbededaddceccaebebcaccaccebccaaeccbdcbeabcbcbcbbeacbebeaeaccbaddeadeecbbcccadedaebdceaaaadbdecbdbabcbebcbbcbcecdccabcbcdaebaedaddcaadaceabdaeecaabcddebddabcdbbccddcabcbaddbbedabcacdaedbddacbcbecdbcecdabdeedadedabedbdeeacbeaeacecdeccaccbeeebabcdcebcaabacceeaeebacaaaaaabcadcddbcaacadbdeaaeeedccadbbdeeadbebdaccbadacdedbeebddeecdebdedbbcdeaeadccccccaddeeddaecaaaeccdaccddadbbadebdbaaecbacececdddedeabaaeaadadbdcbeebcaecbddccabbaecadbcacbabceebcdddaceababcdcbadcacdebdcaacdcedacbbcdeaadbceaeadabceebcdbcccebdadbcbbbcdeceedddbacbdecddbeeaababbaadccadcecdebbaedbdaddccbdaccaebedeeddcaabadbabbadeacaaaecbdaebaaedbbceadddbeadacbcdccbdeedbeeaceaebebbadeceecdbaeeeeebcaacaaecdddbabdcdacacecbbbaeddeceaacddcaceeaacddbeceacececdbbbcdecceeaeaadcebdccdacdbccddbdbcdabaabebcdbdeaebbadaddaaabeaaeaeaecbaaedbbaebbbeaceeddcbdeeedeeaeeeccbcebadeebdeeeabacdedeabbbebeeacecdbedabeaedadaebebcbbcdadaabeebbaaadbdaccbedeeadaadbbbbebeadbcadadbeddaaddadbcdecbbacaeeeceebdbdbbddaeccedadadedcdbebbdbebbebeabcaadedbbbbccabedbccabbcdcebcabacdddeccbaceeccebaaeaceebbecedabbecedccebecadbbbedcdaadabbbcccaaaeebaddbeecaaaaecabebdbbeaedaaccbcbdcebaeacdeedebaaebecbeaadbbdbdccaeabdbeeeccaccbccbbbebaebedbadddbacedbadcededcbdebadcbcadccbddabcbccbbecacdcbbaaabeeabceabcdeebcaebbecdbdaedeebaeaadcebcaadadccedbdceadbedaeecadcbecadaeadbaaccbdaaaeddbccdbbcebeabddbaaabcbabaaddccbdadccebeeecdabbeeeeceecaaaaeddeacaacdaeaceebebddebbcbceaabeebaceeadbdcdbbcecdeccbeddbcdaccececbbdeedbceabacdbdeacdecebcebaaeedbbacedbddceaedbcdbcadecddbdceabcbadacccceadddccacdebccebeaedeeebbaacdbcebbbdebedccacddeedddcccadeadbbceeebbbedbcdbeebeadbebcdebecdebbcdacdccbaedecedeecccceadaacddaaaadbdedbdeecbeedcaebbeebecbbeddcaaadbbbabeaaccdeeddccebbedceeecdabededbddaabdcbebcbdedcccdaaedddcebcccdcbdaacaacabeabcceedeeecabccbdceacedadadcbecaebbcdbbdcbccebdeddbeebeeddeccdddbadcbaaedcbdcbdacbcbbdceecdcdadecbecbbabeddbebdeccbaacacbebbbdabbaddedbeadccddbeedaecaebdadabeceeaaaddbccbababdeaeaecbecbddaacaeeedabbbceeeebacacbaacaeddedcaddcabbcdbcebacdcbdebabdaddaecdcaadcceabcacdbcdbcdecdecabacaddbeaacebcdcbabebacdbcadeeecddcecdaabbbebddbbdebaebdeecedcedbdcdcbededacebececddedeccaddeaadeadbeabdabdbeaaedbebbeceaecddbdebedecaaccccddeceedbaceeacaaaadcceaccccbdcebaeacebbaedeabbaadbbcedabceeecdeebbceddddcecdaeeaaecbcdbdaeeacceddaaeeaeeaadedddadcacdcccdbaccdecbdccaceebdccdaacedabcebdbaeaaceaacbebabeebabeecaaccabedcbdbbdbabccacaaeeedaeacacabacdaebbacedcaadcaaacebedcbeadbeabeadabadeaaddbecbbabaacdaeddcbeaebcabeceddccdbedcabbdccdabbacacbddeddcdacaeaeaecdbaeedbcadccabdadcebddabcbabdeacdccaadaacbbeaddbbdcdbcdbcababdbeabcaadaabbceeacceeaeececbbdbedbeddddccddaeeadaeeeabebedbdcbaddecdccabdaebbcbaeedcecbbedcbebedceeebbecccadaaabdeccdbbdabcebeeceddbacadbeacaccccacaedaddcbebbceeaabacbdebeacacddaabbbbddbadcbacbdcbaccdaedaeceeccebaaaddbbbacadbdeedcaddbcebcdbdbaabcccbdebabcdeececcaaeaeeddbadcdecbbdaaacbadceccbeaebabeacebdbaaaacacaacbaddbebeaaedbbeaceeeaecdabccdecdaaedbeeebeadbaededabeaaacdcabaabbabdbceeebdedeaddcedabbcaaccbceeceacddecebbbedaddaadadaaaeedebdcbabcdabceabdadebdbbaddebeceaaddaedacdcdcbabdacdabdbceaccaabdcaecabadadaddecbabaaccbbceaeceaecadaeedbddabeddbdddebacabadcadedddbccddabcdaecacbeddcbaedcbeceacadbaececebaddbebdbacdbbdccdcabebcabcdbabdcdcdabdebcabadeaaeeecdeadbacacdbebacadecebdeeabdacabdcacabbaeaabaaabdbcbbddedddeebbddaacbecedeadaabcdeaddcadbdbccdaddaebddaabbebbeacabaccaddaeacbeebaeccebdedcaadacbedbecccedaaeebbcaebabecbacdecedaacccdcbaebdbabbbbcedecdbeabcceccceddeacabacccbdacecdbeeabcdceaccdebbcdbdeacdcdadbbbddcabbbeaeddebbabebdbecbebdbbeacdeeaabbaedbdaaeeebdaabdabddecbddbbbeccabcacbcbaccebccbaabbdcdbeacababbcecadecccceeecbdddbaabeccadbcdbabeadeabbbbbceabcacdaccaedddabddadcbbabeadebbaedebddeeeabeeadcceeabecceeccbbcdcbcbaecbeccbceaadccaaacbcccbbcecaaadbacbcdcedaacbbadceaedbbebdbbdedebcaceeabccdeacebddadebceebadbcebdcaceebdababcacceaaeaadabeaddbaedabbabeaacdddccadaddadbcdadcceceeceabbcaadbadebcadeeabeeaacaabacceccbdabeacaeeaecaddebeeeaeaaecbdabbebedacecaeccbdabecdebbcddedcbeaaababcbcbebcbabaeabdadbbcbacccaaaacbbccbceacddebbdcbcddedcdabeddcebdaabeeebedbebceaadbbbacdcabeadbdabdaeacbeeceecedabadeddbccaccdccdabddbbadebabbacbccaddaebebbedaaacdadcaccddecaababaaeaaeaedeebdbeacbdeadecbdbccdcedcaacbaeaedaadbecdbeaecdacadcbebcedeaebaaebcadbeddcabbbceedecdaaeccbceecaeeecbaaaceaaabbababcdbedebabeebdbeadcceaaaebbdaeadededabcccbdbaaabcebcacbecadccecdabaacdeedbcebbeaedddecaedbbbdeeecbbaacbbaaabcaeeeadadaaaadaacecceacacabbaedceeeadcedaabbacadccdeceabaeacabcbddbcecdcbdcddebbddcdbabbeecaeecaaacedcebaccdcdcdaeabdeeaabeaaaacddeaacdaebcaeedebeedddebdbaaebdabadbaedbbaaedebeadbebaebbdceabdeccacabcebeeedceacacbbcbbadcaebaeeacaeadbbaecacecabdabbaeaeddeaacaaceaacbeccecaadbbeacdecceddcededaddaaadbdeaddcbcaedcaacccdcdabecaeedbaeeaaddaeccdcdddcaeddbbcdaeeecbdbeabaceddccddbdaaedcaeeeeacbecabcaeeddbbbdcdaabbaabeeadecacaaacedacabcdbeabbaeaeeedddabdadeaaecbddaeeadcadcabddbbebdebeecaadacdcccdccbeebdceddaededdbeedccebbbabddbcbdcabccccbcbebbabccbccbaeacbbbebabedcdcbbdbadbedebaabbbcecceabaddbeaeeeaedebaaccbcbeeaacdebebdcceddabebdceeccccddccbebcebbacddbecdcddbbcdbededecccecabcdadbdbeeebdcacbaddddbecadabcdbbcbcadacdbedbcaceaabebbbadbcbcaddccdbdccdbcacbbaacbcccadeeccdeaeeaaebcecebcbeadadbcabcdddeeeacbacacdadbedbebbdbcabbcdebdcdadecddbbacbabdcbbecaebdbddcdebccababeabcbaecddaddebcaebdeeeeeecdaeaeaecaddedebedbeaebbeebaaaebcacdcbadabbdabbbeeeadccdccdaabadbedddeddadeacdaedbcbaaaeeaecccbdaaeeebbaccebabdcedaecaabebdabbcaecaaaddddcddccbbabeeccddbbacdeebdabeebeeeeaceeaeceabbdbeaadabaedccdeccedecadccdeebaaaacaecbacadbabdbeddebabcacccbdbbdbbecdedbecddcebbbececaebdadaeabebeebdceaeaddadebcbbdbdddadaedcddcbceebddaceddccbaaaacbcbcbeacbebdedaaceecdabdeaadbdaedbacdcdebeeecbdbdadcbbccaaaaaabebbcbaddbcbddbadcbdceabddceabdebdeebdececadbeabadeadbbcacdcbcaebdedaddeddaedcceadabedbeebdeebeadcdebdedcaaadccdcbbaacbcdeabceabcbbbebdaaebaedcebddbdbeeebabeabdadeecdacacecdaeaaacaeeaabeaaacaecebbedbbdccdcbbeccdeeaeaaecadebbbcdccecbabeccbcbcddeeddebdebaeaabddbbeddccdebddaddcdabaaecddeacaeacadeeadeeaedbceddedeedbbcacdbdeddddebbddadecdbbecbacccedebeecdcdcbebcbdddcdcdbebdcddcecdddaaeaedebadbbbabeddbadeeececedbabebcdeecbeaaeddcdbbaaebebaebcdacdbaeebccacbdddcddcdbaedbccdeaccacaaeaeecebbbcdbecacbbccbeedcdeeaebccccaabccbeecdaeceedbacbeddedadaccceaeadceacbabdebcbaaebabeedcaceecbbcbaceaaddbceecbbccddccaedadacceabacbbabecabbcdbdaaaceabaadabbddcdbacdcbacaedcadcebaccabbcbacadceecddedbeedcacdecbecebeacbaddebeecbdadaadecdbecadddaeeebadedebbbecacedbbebaacabdbcbaeacbaceeebebcabbcbeebccbeaaebcedddcbedabeaaabdbeadabdbacdedbccebdddeeeeacdaadceaaedecdebbcdbacadccadbeecbecaebacecebdbccbedbddcddbceedadebceeddbddcedddcbdecdcecebdaddabeabecaaccecdaadaaddecdcdaadeeddccdeabbceeacccabbbdccbeadccaddbdceacabebcdcbbcbaeabdecedabaeeddaadbaebaeabbdddcbdaaaabacaeecaebcdaeaddcceaebcebaebaaedecedcbeddabbaeaeaaecdebeeaacececdeebaddabaeedecdbcadacbccbabaaeadbeabeabaedbdbdeaedabecdccdadeaaecbceaecedcbeccadbdccadddbadbdebbccecedabbcaaaaadbeacbcaccaedebcdcecbcacbcdaacbebbbeaaddceeaebccbcebaaeaadccbdabcbadeddbdecebaadbeaadddaecacabcddecddebbbbaadbaddebcdaeedccbbdccbaadbbeccddaacdaeaccceeeecdcaeedaaeadaaaecccbeacceaedbaacdabeedcdcaedebadacdebadbdcbeecabdedcabbdebbbecbaadbdaadbebccabdecaeeecbedabbeebcbbbdceaacebdadcaeadcbbaccbcbccdbacaeddacecdacbdacddbcaceebbdadedbbdebcbedcdcbccdaaabacddcdaeebbddedecbdebcbeecdabbcdbcadbcdbdeaaddbecbccdacceadedbdacbbcddbccaaeeacaedddbabbeebddebdbdcdcdeadcdcaaaadaabdcecdabeacbaacbedaaeebcabbeabdaadcacaadbcbeccabbadbbaceccbbbaeeddedddcabebeebbbbecaacddbcaacddcebbccabbdbeceedbbceddbeabaecddbadcebbdedadbcdceacddaddedbdaaecbccccabeadeeddcaeadddddbbabcdabcbadcaadbecebabbbaddabebeadabeaccbccbecccbcaadcbbdbcdaddaabaabacacaabcbabddceaedbdecebdbccabdbbbddbeeccaddcaeaedaaeaaebeadeccccaaaeeedabeeeaadedcbebcaecccdddaebdccadacdaecacccaccaadbbcdcecccdeaeddbebddceddeeeabdeebcecaaebadbebbbbadcaedbdceebbbcdcebecdbceabcebcabaebeebcbccdebdadbdbdcbadbaaecedeaceeccacdccbbbbdeabaacecebbddeabaaccaeadbaabeeaaccdddbcdaedbdcabbebecdeeebeeecccdabebccbceececadbaabbdecbdeaeecdebbdcaaaccbebeadddeadeaaddbcecdcdbeeacabaebdcdaadacbbbeecedecdbbcccdedccdebabaecbadbdeacdcebbcbcdadbdaecebbeaeacbcdccaddedbbbbbacbacbbeaaadbcaeeecdceeaaeddcedebdaababbdacbacdeaebcceaceddbebabcebbabbbdcdbaeccecadbadbcdccdbbcbedbadddbedeedcdecdbdececaabdaccbcdaccdeabbaacaecbbadeeaeadbcececebaadcecdddaaedddbebdedcbaebaabbdeaaacbdddcebcabcaddcddddddaabdabbbcebabdecaedebacccdbbebcdecccaaabcbcbbecbceaecabaeedacaecaebbbaaaadcbaeceeebabacdaebccbddeebeecceccddddcabddcbadaedcddccededaaacaedabaaeeeabbceeeebcdebcaeddedeabdedcdecbddaccdabbcbcebdbcedeaadbbedeaacdcdbceebeaddbcddbbccaccdaacaedbdedddaaaccaadadbbbedebebecabacdeadcdcccbdbeedcddcceacedadcdccebaddebeeeadaccaaadecbbbededacccecddedaecdabcebeaebedaccedcbdbeadebcebdddaeedebaeaabaeaccbdadecdabaecebdaabbdeaceadcaadcabaddabbbaacaccdaadaadcddbcedccdbebabcecceeaaabdaadaadeecdbaceabbaacbeaabcaecaaaaabbbbcdeeccdececdcbcddabebddedbcdddcceceeabcccdbeccabebbdeeebdcbccdecbedadaaedceaeabaaabdacedabdaeabdecedddbaebaadceccdedaaadcbbcaaacbccaacdcdedccceeecacccddaeecdbdbbaecbdbdabeebdcebadcdcaebbacecdacaadcdddaacdcaaecddddadbacaadecedcbbbbbaaaadcddeccabdcabeccddebdbbeabbddcccedaebcacddebaedaaeadeaaedecabcbeacbebcdedcdbcdecbeeaedcabdddbedbccecaddededeccbbaccacaaddbeecdbadbbcebeccdcdeebbcabaccddeddadedcccbeeecebbccbbbcabdabeeedcbebdbccbcadbbbeadeaaebdcbbbabeacdebeeacccbdabbecaceedaeabdeecdbccdeeeaadccbebdbceedeeaacdccaccedcbbbbbacecaadaddaddacecdcdeeeeddcdaadaeaacaddacbaedecacbbdedbdedccdcceaadcaedcbcaabbceabacacacebceeebbdbbbbaacbaacaeccccdbedeeddeccbdabbeccccbcaeccdadccaddaaebcbadeecbbaacbccbbbbaceadbaaeeeeacbedbaaceecaceadbedddedcddddaaecabeebaedeaebeaaceaacddcccaaadddabcecddadddacdacbaeecbeaedeadbbecaacbdbacaecddecbaeeaecceecedeeaadcbeebcaddaabceaeaedaaddeddabacaebaaedbdbdeeaeccbebadcbbaabdcbbaaaabbcebeacbebcddbaadedebaabcccebcadbacdddeadbcdcdcdeaaabccaaeacdddbaaaabdaccaacaccddedeadbcecdceaeeedecddcaebeeeaadaadacbccecbaededdbcacbdacababcbaababcdabecdceedaddadcedccdceceeccdbaecbaecddbdaacebcbebbddbedecdacdeccbddaaeedeaacaadadabeaeaedcaeaacbecadaeaeeceeeaecadceaabdecddbebdcacccacebecbadcacbeeeacaaacaeacaacabbdddbcbabbbcadbdaddaceaeeddbaeaaabdecbecdebdcdabecbecdadceedcedcbacbcdeaeabdbaeddccbbcaeabdaecccbbbddbdcebedcbdecaabcaaadcaceaceeceadaecabdeeeeacedadccaccadaedcecbdceadbbaabeeedbacabbeecbedebdeebebeceedbaedcbceabbedcecddadabbdeeedaeedaadbdeceebdbbdbbadbacaddbcbabbccaacdddccbbadcbbdcddbbbaadebebabbaebceaeaaaeeccbbcddedceaceccaabadacdeacecabbddeaaeeedccdcecddecaceadcbadccdbdbbeecadeaceeedbcebbecaeaaaecbeebeccdeecedaaacbbbeceeabeaaacabbbdeeacbbeaecceacbcedbceedbeeadcabedabaaaabdbbaaaeecaaeeeabcbbeadcddccdececebcacebdeeecddadecadeeddeddbabbdbadebaceccceececbeebeaeabaeedecbbebeeeaababdebccbbdbabccdddadcacaadcacebbdacabadcbececedcbccbbbdbbceedcadecbaddecbbdcdaaecccebaeccddbebbebbedccadeebccdbdccdacecceeeaacdedacacbeeaeadbdabccdabaecbbaacacdadddbeeebeddbcbbabdaecadabdeabaccbcadabddadcbadcdaadacbcbdbeedbbaeabcbcbaceaabeceacabeabbcccdabcaaadadbbbceacdaecccaedeacbecceababdbbadcacbbeedeccadccbcbaadcdadceedcaaeeeddcebdbdaddabcaaeebbebaadacbceabdcddedeadabaaeeabdacebabbeadcaecaceebaaeacaddbceabeabceecacddabdddcdbaceeaddaeeeaeedbdcdeebcccbeecdccbeaeaeedacebeadeccabacacddcaceaceceaaeadadaaccdabedaaabccedcdbcbecdceaacebeddcbbbddaaabcbedabcbcedeeecedeeebbcedbbcbbeededbcddeabedeaeecbeaacdecccbcadaebbcdbecebaaeacebeeebdddcccceeaabdbdcabeddcaaaebeaccdabeacbaaaccadceabdebceebdacbedbedbaebacbaaabbbeabeccaabbebbeaddceadbdbcaeebabaeceecebedaacbcdbddcdacdbcbcbdabbeabbeedcdcdddaaaddddababeeaebeeeabedeeceecbdeabdbecbbccaeedadecbdcdeabbbaaeabdbebddebdeeddebaeebdebebbdaebeabbeabbddbbabcacbeabbdbacddabdbebccadcbbadadedbbcaccccebcddccecdbccbdaccbcecbdbeebdbedbbaeeacbeadecaaccceacdbbadeddbbbbaeaebabaaebaadbcdcddcbdabbdbeaaeadbdeddbcecaabbecbadaacbeccaabbeadbadaedabdadacabbdbaeccaedcdcccabdaaaecaceabebcdbbeccaeadcdcdbacdcdcaccdbadaabaaadebbabaaadbcaaceccbacadcdbebecaaabdaaadaaaaccbdeaecbbacadcbbcdebdbadadbbaecededbeaaedccaacdceacedceabedabeceaceceeeabcdaacbdebadcbeebcdebcebcbbaabccebccdeaabcbdceadadaaddeebacedcdaecacabebccacdcbdbcdbcdaabdaccbcdecdcdaabcbedcdbebbdddbdcdcaabbdabedabbbdebcabdccecdbccbdcedaedabbbdbbadceeebdbecaaeddbaabbbdaacabecaedabcecddbdbaeabecabcbdebaaaecabbbcddcaeeebbedbbeaacebddaeddeccaaacadbabbebedcacceeaacabdabbedcacbaebeacaeaacedececcbabacacdeebaebcccaecdbaaaddacacdaaaecdaaaacceabadbddeccdbcbcdebabdddeadabeddbadaedbbacdcbdbeeabbadadadbbaecbccdcdcaeadbccdcdacceedaadadaaadcbadadbcbbadcaceedcaeabadceacbedebbddaeaeeaaaaebbaeedcdbaaeaeabdbabedabcbecdaacacadbecacecbbdcbabcaebadaddcabdaeeaedcbbbecacdabecccdedcbbcdeabbebceddddecaaeaaedadbccaacbcaceaebadbcdaeccaebbdaedbddcadedbceabdbeeebaedcceeaeeeadaedeaceabecdabeccdcaceceaadbadddbdbbdabecabdcdabddcecedaabaccddedebebcadccecaebbbbbddacaadeadbdeaaebccdeccacebebeeedecaaeddddcaedacaedcbbabbeeeebedadebdbeacaaaaeebddeddedbcadbaadddaabdeebacbcbdcedbabccdaeeccbbbeedbcbcaebbccabadaeccdaebaecdbdceabeeaaedbeccedbeddeebdedddbcaacbaeaaedcebaabcadcebcaaceccdaecceaabacbabeddcbeeecddbccbbdcbbdaaabbabbadacebcdccdeeeceecdaaeebaacadedcdabebcacdeaeccbedababeabdcbdadcbbcdcaacbadebedbcdbbeaeaabaaccabbbacccbdcabacedceecceabebadadedeacedcdbedebbdebaebddaaddcbadccbeeadeccabaddaeaacebeecbbcbcacaeaeabaabeebedccddaecbddbedabababdabacadeeccbbeaabeecacddedadbbcceeecdcceaebcdaacdecdebebbbaeebaabbcecbdbcbaedaacaddecaecedbbbecbdedeeeecebaecbbacaddbbceeaaaeeecacdbdebedbaeeaecdcbeebbaeaaeddaedccedecaaaeddaceccdcdadedcebcbcacdbeadbaabecdbdebbbcacceabceabceadbcaadbccbcdbaecbdadabacacdecddaabbccdebebccacdeceecdeaedeedacccdbeccacaaacedeceeaadaaddbabedaeaadacdccbbcadbaeaedcdecceaeabbdcbbddeedddccedbecacebaedcddcdceecedbbadcdabaecccbcdcdeeeebdedadddacebeacaecbbbccebeebbbebddcecacedcdedeaeaeccdbedacebceaaecebbeecadecebecbaabebeeedbcadbdcaaedbabeceebcebccebaeacebeeddaaaabcbbedaccccbcedecbdedbedbaeabbbcccdcdddccdddaaecacbdcabbccccbbbdcdedbccbbadbeddeabecbddbdddedecaaeeeaedcbebddebacaecbeacaeceebececccdabbdbdcbedbdddedceedcedaaecdabdbedeeddeedaeeedbbcbcbcccbbddcbceebebadddaeabbaebaedbbcbcadebadeecacaaceecaadbaceabbaecccabbdcedecceabddeccdcbcdccdcabcccedcbabaaaabcadbcececcddbbbcbbaeaabbcccbeeabeacecdbdcadeadbcecabaddccabdcbbcadccecbbedbcaeedededcbbbeebebbeedececacdcdacabdebaadbeaabceebccedaadceeacadabeadadcebcddbbecbcdaabaecbadcaeddcbedcbbbeacbceabcdebbcabdcbeeebdeacbecaaaccaebeedcedaccbeaededcbeedaabcdcbdddeebbcbbcacddadaacbeebcbbcbeceabaeaaadcbdaabecaedbecbabbcedcedbcdbcbaaeeaeeabcabdcabdadceccbebaeaddbdedcdbacbcddecedaaeeadceadbebbbaecdeacdbeaacadddaccdcddbcabedebcaadcaadabdedebecbcdbdaccbcceaaeaeccbdceebaeebdabeceeaadababbbcecaaabceaddecdadcddcebdbeebdceeaaacbcdbaccdaccebdebebecbeaeddcbccadbaebedeadaacabbeecaacdccbebdaaabceacdbcbdcbcebcecabddeccaeedcbdbccedbebdadbeabbeabdedeacbeebceaaeebbdebadbdaabacdcedcadecdcdeedccebbabedbacbbdbceaeaeeaaeecbcdceaebadccaebdccecaadaecdceedeaedeaabcbcceceadcadccdcdbeeaebaacebeccdcddccdecacdaadaddebadeecabeecdbbedaadccddcbcedcdcccbadeeedeebeeeadcedbadbbcbdeaeecaaebebeeddceacdceeeedeeaeeacceaababeccaadcecbbcbbaeebcbbbcaecaabdaeedaaaedcbacecbcdacdcedceacedddedbdccdceaeadecccbcdaddabbacedebeebbdeadaddbadcecdaadbbeccbceabbbebebadaeebbbdeddeebdcdddaaebeeeccccdcdaceebabdbacbdcbbeedeabacabbbcebcbcbcaedbcbbccebcdbeaebabcedcacbabacceeadcdabcbabcdccbdcceedcabeebeccebbabcadacbbdeebbdcdeaadcacbcdaeccceeeaeeabaebacebebaecedcbaceabbddcecbaacdbdddeebbeabadbbbccddeabeebbbbdcaababcabdddddadaaacadddcbacaeeceadeeebaabedbaddebdacdccaaebbceeddbddbbebbadddaaebadecadeceacbabbebbeaaeceeecceadcbcceaaeacdaaeadacdcdccbedabeadcddeeaaccbaebdbbacdbbaaabcbcaeabcecbbedbedbdbbcaddeceaaeedaeeccbbbcccdabdaddeeaaedcbceeaeebbbdcedcbadecaedbdcbdabdbebabcdeadecaccbcaeeaebbedcedbeeedabacaddcbeccaecaecdbdbbbdaeacbabddebaeeabeccacebcccbbdebbeaddbddebdeebcdceecbbaededbabbedbbaadcabbdbedaaceedcbacdecddeadbebaadddcecdbdecedbaeecacecababbabdabedbdabcdecccbdbdedbacadbdbadaeabeddaaddacecdccadddecabdadacecdeeaebecbcbcdabbdcbdbaeaccaedadddebaabddecdbceeeeebccdeabbaccbcedbbdcccdaaeeebecddeaabeceaaedbebacedcdceeadddacbbdadabcbbeecbaacbaabebbdecccecbbbbebccdedddebecccdeddecdcbcecbcedecccddaaecbdccbadacadaabcabbbeebabcdecaaacdcdbbebcceaeacccbadbcaaadcebaececcdbacecbaabbbcbabaeceebabddaeaecaccebccadeaddacbbecbaadccababbbdecbcbabcececbdbcbdcbacecaaaccaceaabeebbcecacbdbbbdccdcebbdbbdbbdeaaaeaabceecdaabaacbdacdcdbadbaebbadcbcecebadaecddaccedbccaeddaacdaccccaaeaecdaedbadbadbbaadaaabdeecaaedddddbaabbdacbceebcdcdcaebccecdeabadccceaddcaaecebeaaecedecdaedaebcbbdbdebcebeccbabbbbaceceaabdabdccadaaaacbcddeecacdcbaeacaccbeaddbbccbbdebdccaacedcdaeecebaeecccccdaeedbaeebeccadbbcbcedddcebcadcadaaeeeccbaedaeaecbbadbeceeceeccaccceadaecceaaceedbbbdacbcdcedccdaccbdddadcebeeacdbcbccbeaeadbbeadacccceccebaeacbbddbbdbdaacebbdebdcbbedbcebbdbbceecabeacaeaabbcebbcdcbcaaadbdeacbababccdbeeabdadcbceaaaeaeabeaaaecaaceebccdabebddbabdeaeceddcceacdcbacdbddbadaceacbddcaddbddedbeecdceeeccecdbebacdddacbccdeeebcebedadabbcdaacaadcceacaecdeacedbecaaccbbeebceceaddaadddadaaeadebacabdcdadcadedddedeeaaebebacdecbbceccdcbcdaebeabdcaaeeeabbadbeeeecbcdaabbcedecacbbebcacbeeacdcaeddaecdeaaaebdebddebabbaedeabbcecadcececebaeceaeacadacdeadcdbabbcebcdacebcddaeceecaaabccbbbabdccbabdcdbdbdbbddbaeebdcceacadbbdaeaeabcbdaddaaebbedbeceeacddcaeaaeebebebeeceaeebabadacaeeeaddbeaaedcedbcbcacbaaecbcddaedddbcaabacbebcdddbaeccadcdddbedcdabaaeadeddadaeeadcbdaaccccaadabaebcbddbdbdbbcdeddbecebdaeaabeabcdccbdcdbdbeeebebdebbdeebcacacebdcddabeeeecebedaecaeaaaebbeacbcadadedacaaecddabaadecdeaedbcedaabbeeaaabcedeaaedadceedccdbbccdcbdaeadeedccbddbdbeeabdaebbcaacdbaadbeddbeaaeebeeedbcededcddcceaaadaeaebdeaeeacadbdaeadeedacbcaaddcbdbabbeddeaaedabaaddcdcadaedaddbeedccecbdddcaebeeacedbbcbebebcdcabbebddcabedbbaebadeeaddabbadddeceebbdcaccdcadceacbebdcdcabdaadabdccbdebbcdbecccddababbaadacaabbecdbabecceaaabaeeabdacbdbcdceaeaaebbedbcddceaeabbbdbeedbcdccdbdbbaabdbbedaeaeacbdcaabaeeeacaeadcaadbaabbcbaeadbededabadcebcecdccbeadcbeccaddebeadbdaeededacbdabcedacbbdaebcddeedaeebeadaeecedbceaeacbeccedcaacaacdedacdeebddcdeedbbdeaeebcbeadacaaaedaaeadacdbddcddeeeccbcedaceaecbaecadbaccabcccdadaadaeacddecdebdceedccbabceccbcccdacbbceabadddebdadbdaadadcaddbbeeedbcaacdddcdcdeccaceabddceababebdccdaacacacabaacacbbcacebacdabbcbaecbcdaddbadacebedceaeddcddbbebebaddcebeebcbbeabbbdaceeacacbacedacecbadaeaaeeebbbdeabddeebddbddddcceccdcabbdcdceceecbdcaaaedcbdadedddcadeaaeadabbdcceaaaddebbadbbdeaddbbebadeaedabcddbddcbcecbceebbcccdcbbaaebdbeaaebaaeeaacbaeddeabcdadebedbedceecdaabaebecaeeacebbaadcccdecdbcadcdcdeeaaebaeaaeddbdddbddddaebbdbdadbdaeccdedbaabeeeeededeceeaaacaeedaaceaabededddaddcddeebdaebbedbcabadaebbddaeaccddbcececaeebeceebcaadaabcdcbbcadebeadeeaccdccaacceedeccceecadcacbeedaabbbbdcbedbceccbcababadedcdbdbddeaadbbbddebbdabbacceababedcebcdbcbbebaabdcbaaeacaadaeaacdbebaebccbbcdeedeabeaddddbbedabbabbdcdbbeabedeadabecdcadbdbebccbeaaaceddaabadabcbcccdadcaaabacacdacdadebdbaaebccbbccbddebdebcaecdedadeeadddbebceeebbbdbaeccacbdceaceebdcedeedcbaadcecedccdacadbebddbcceddcecddeaeeddbaeacdbbbaccccecbbccdbacbbdecdebaeeebbaaaeededaedbecadbadadcbeddbdadddbacccaeedcbacdcdececbdcceceeaccaddbeecabbedacdbecdbbcbddbceecddbedddddaeddeebbacabdedbececeddaadddeebebedaadbdabbdccedcdbbebddeedbaaaaacaceedcaadadcadabdaebbdcbceccbdeecadbbdecddadaadbabbadcbbcedbadeedbcacebbdccdaaedaccebcdebbeebeaddcabcecacecadddbabeceecdabcedaccdcddeedbcaaddebbedcecacbaabeccdebedbdbbcdddbebcddadcddbaaacedadbdaeebbddaaccdbcaceaddbeaacadccaadecdbadadaceeeeaadbdedabbaeeccbdabeaaaeecdaebbadeeaebeccdaaedadbadcecabcdebecdabedbeabebebceecadbcabccdcdcaadcbaaecabaccdddcbecbcceedceddccddbabaaebaeeecdbadeecbbbcbdaeebadaacedcdaaadbeabeeaedececebbbdaaceadedacadeecbacdbbaecccecbcdaaabdebdeabbcddeaaacaeeabedeaeeadceacbcedbdcbaebdcccacbeeabccccbdbbddcdbdceeacdaacaccdaccbcedbbeddddacddbaeedabddaebdaeedeebadcaecdebabbaecedaababbcaeaadcaedceadbbcceeabecbbcddeecdbdeeccdecddbeaabddaacccddbedaedeaabbcacdcedaebecebecbaeacabbcddbbaeeebdabedcaddccaecbbedcadbecdaeddcebceacccdeeadebadeadccbccdedecaabdebcaecabecdeebbcaaaecdeeddbbabdcbbbdbabcebaeddaddeeacbeedccbcbdabcedcddeebacedabbccceeaeeedacdcebebdacbbaadadeddacabbeceeeaeabccbaabebdbbedbcbceeebeabdaceaebaacaccecbebeabddbaccddaeabaeedbacaddabdacebcdeeaedbbaadcbdabdadbebbddbeadacbadddeddbcbdceddabeeacaecdcbccaeabaadcdbaaddccbecaabdaecdacabcdbcadddcbedaccadedaaebeabdedeebcdaaceadbbedbcdbecdbbeddebbebcacbbacaacdcadeccacddbccccbddebbcaaeeacebeddccbadbddebdddecdeaaeeeeadcaabbcebcdcacdadebeabdeedececeabeebbbbedcddbdcdadeeaeccbaacbaecdadbaaedeadabaaeddcecacdcdbebbecedbbaedbbdccdcdccbeebdcdcbdabaccaacbbababdaeecbcdeedabdbacbeeceacdacbbdcaecbdaeaddcebedbdcdbbaaccecdbdaccdedcdabddbceddacebbdeeeababaddbbaadddbdabceabbadcadaedeacbadadbbddbbecbaeddabeeedcbecbaeadddddecbcbcdbabbcbdccacecccddebebacedebdadcebacbaebdcceebdaeceddbeccdbcbeedbdbebbbacccacbcbdacdebddcdeddbabdacbebdaecdeacacbeebcccbbdeeebcdeaadbdedcaddeacbcbaddeacdeaebaadcadadabceebbccdcbceaaedbacbecdeababecaeacebbadcbdaadacaedcccabdeaebaccdccedabccdddbbbcdabebcccadccebcbdcdaaaedbdaddbdedaedebebdaaceacaaebaedbbaaebdabedcbcbeaeddacaaaebbebdccecedacdabdacccaeaacedcabdaadebbcaacedadbeabdebcabdcaccdadaaeeebdccbeecdadaedbadbdbbdaaaddbeacbdaeeaddbbaecbacaddeadcacceccdcbbeecabcbcaaebddaaebebddeccdbccabebdeeaccaaeaedbaeececcadadbaeebaebcddeececadddcabdebdcdaaeacaaccbaccebebaacadcdebbecacbcbbcbbbcaaaaebebebbdbadceeebbdddbbebccddbcbaebcdcecbbceebdccaccbbcabaaaeeaededaebbcaecadaeecbecbbceccbdaddaaeeaddeeebeaeccbcbeabeedcdcacecaeaababebaebdeacaeacaacbdeebbdbcbdecedaccbeeaeddadeacdaddbdeecdabdcedebdbeadddeadccbaeaddebeeedbdcdbcdbabededbbebbaaabcbecaaedabccbaaccebedbcbacebbdceececccecdabaeabadabbeaadbaedccadbdeedbcebdccbdcdbbceaeaccdacddebebbbcbbeecbccdccbcdabecdbabdeaedbbdeabcdcaaccaeababceeeabbdcabbdadaccaadbbeaacdacaaedcaccbdcebbeedcbaedccbaedccdecabcccaabaaaddcabceeedeaaebcebbeaabddebebeddaeedcaacaacceaeadbbadcbaedabdceecaebdcbaebbdddcbcadceaaadabbbbcededbabddeadbbcebddaaeaaeabceedebdbdbaeecdbdeedddcddbdeaceeecacbeeebbbdcbeccdcdcaaecdededcbeaeaeededaeeecebeecbdbeacbbecdabbedecedcadabedddceebaacaedbbbcaaebebedeebbebeedadabcddceadeaebcabdaddeeccccbebacbdcdcecabeeebbeaecccebaadddeebdddcaabacdcaaeadcbbdbaabeaadecdbacbeaecaeaaadcbbcbbcaeaadaddeddebaddbeceeebeedecddaecdeeddaaeaaacaeaecbbceacaeddbedcebdcaebbabbdeccccdedceaacbcbeaebbecbdccdebcceacabaeaecebdceedabacadeddddbacadbcebcdbcddbedcaeadbdaecbebdddbebebddccabbadeebeaaadaeceecebdaeaabeccebaeedcababdbddebdaddacbbbbdeadeddceceeadbeaecccddecceebcaaebbadacaddcceababccaccecccacbaebceaccdaecaddbcaaccbdaeeeddbbaeddabbcbdeadceeeadaeebcedaacbecaadaeccbccbaacebbaacdeaaeeadbccacadabcddadabbceadabaeecbdcadbddcacadaedaecaaadbcbdeccbaedcddcecbbaadbcabccceabedccecbdeeaceedeceebcaacdadeaaabeaeabbeddaceddbedabddacbdcbdcedcebbedbdacecccbaecdbeddcabdbbdccceadbbeecabbccbedcbadaeecbcbbebbdaeccbedeccaabcaecbacedaadbcaacaabcbaeedceaaacacedcdddaaabdcdcccdebbebdcbbaacceeeebdcbbcdccbecdacbbaadabbaeeadeabaecccbaccccccddcaceaaacaeaccddbdadbcdbaaabeeddaddebabbcecacecacedaeaaebecdbdbeaeecbcdaadcedbedceaeaacbeaaeecaeaacddcecddcedeceeadecaecebdddddcaebabdbbecdbacaebdbdeccabbccedacbdebcbdbbcdbbcaecdbdbabceabbecbcecceacbeaecaccaaecacddaadceacbcdbcbaaedeecceaaecaaceacdcdddbadebbaebbadddcdddcdcbccebbddeeabcecedbbeceeeecebbddbcaebebabbbbaaaedabddecbccacabcdaecddaebebdedbcddeedecadccddeedddccaeababbeaacbeedcdeaabcceedbecdececeebdbaeaaedaebcbadbacbabbeceabcaaaacceedbcbeaabceeaadaaeebadcbeeaabcdaccecaeaeebbadbcbaaeabbdcbdabeabeaaeaceaeddbdcbccaececaeeaecccbbaedcbcbaecbbaddababbabeddaeeeeacceccabadaabbcebcbcbeaccdddedebebaadadecbddaecbdeabdbbecaebcaacdbddaddaaeabbcccdcaddacddabaaaacbededddbeddedbcacddcbbabeebdcaedadebebaaacbabdceedcbcaaccacbcbbdccbedbdcdeebedadbcadbdcbdecedceaeeaeaeabedaaeeeacadaccbcdacdcceddbaebdbacaabadbababbccdcdebbacacaeabedccaddedcaccdbaddcbaeacdecddbbeaddbdaaeacadbddebadbbaddbeabaddecbdaeebecadabdbedaaabaadedcdbcbcdaecaaacedbddcaababccaedbcaadaeebdbccddbebbadecdbaaacbcddcdacecbeeacadddcabcbdadddceddeecddcebbbacebaeeeeecedbdadeababcecededcbdcbebcdebcbedecbebaddddaddeabedecabbaaecbacdcaadbeacaccbebcdabbeaacceccebcabaedbaaddecadcadeebaebdcecbcbdbccdbacccdecccababbcabeebbbececeabeeacdcecaddddbacabbecaedcdeaebcdcbaeaadddeeecbcbddecbccdbbaeebdebaccbcceabcaaabeeeebcbadaaddbceedcbaeeeceeaedbdaadaeaaeaedaedabcaebaecacdcadadeecccddccedeedcdcabbecbedbbacdeccdcbccbbaaaebbdddebdbcedcbdcbcbbbaebdbcaadcbacbbcecaccadcecbeccddeccaadabbcdeedbdeacaeebbddcbaeaeeeeeadedbbeaabbecbbaaeedaeeaaeccbbedbebcaccdcaaccabedabcbcccbbaceabdebeddabccdcbddacbbdbdaadedccaddecbdacbacdddbbdbcaeadcceceeecaaebdbcccbacbbeabbdcdecadaabecdbdecbcbacbbacabadcbdaaecbacceeeeedceaccbacadbbbcdecbbcbabbcdbdcadebaaebbccacbcacededadecdbbeeddeabeeeaacbdbdadcacccdaddecdcdbcddbbdeeababbedaadacbaaccbcaeaceebcabcdccdeeeebbaeaebceddaedcacdadeaabddeddcbddecbaebdeaceecaceaaecaaedcabecaaecbbdcdcaeceeaddddedaecdbeeaeabdaeecabacaecccabbaacddcebeecbabecbeccdccbdabdaacbacdbdddeaeebeecdbadbbeebedabdaeeedbccdddedbdddbecddbaececccaccdaedcdddbeaaaecbeecbecdacdabcacebeaddcaddaaeeabbedccdbadaeddbeadbdedeadecbdcbbbbebccbacdaecebedcedeccbaabbeddcebdbccdbedaedeecedcbaddadddcdbcdcbcbaeecbccdcaecddddadebcacabdbeacbadacdeaebccbdaebddbbcddaeadcbbaebecaceeadacabdadcbbacaacaabcebeebcbdacedbaabbbeabdaabaaebbebbbeabbbcddeaacdebccdcceaeebdebabbebaebdadaaeabaeebbecabbbbedbdaededcdcaeaadcdedbaadccbdaebdcedcbbdbaebdbecdeabacbecadeecbbabedeebeddbedccbcebecbcdddbaebbdeddeedabdabcbaceaabacbdbaeedabceccaabadedeaabaecdbbeecbaebcddbebebdaabcaccedaedacadbcedbecbdecbcadeaddbccbdbaccdacaabceeecbbdeebbcccbaebeceecdabacabcaaaddeddcadaaaadacabdeadeebdbdbeedddaacebbeccdedecdcccabcabccdcdcdbddedeedddceedbcadaceabdecaebeedabadaccbeeabbadeedbdcdddcbbaacbcbceccaddcedbeacdeaaceccaabdabdbecbeadedaeaeeccedbdeceddaadbbaaebdcabccceccacbcaceebdcddeedbbdaecdcbaeeeebbedabdcddcedacedadcbcceabaacbebcedeceaeeaaaceceedbdabecdddcdeadbeadeaadcddbdadadbbadebaaaceacddaaabecccbceccebdcccedaecbeeeddeeaedacdaaadabbccecbaacecedbceebedcbedacbadabdcbbcaccececceeeacbbeceadeddedaccadcedbbecaddbcedaaccdaceabdbabeaeebecabeccebcaacabcaabbebbebcaebebebdedbadcaceaabaeadbddceeecadaeacdeeedacedcbedadadbcbbdcbaeaabacacbcbaeddaaadaceebcecadcbcadbbccaadaadaedeeeddbbcbdcbaccebedacaaecdbacadbcebbddbaeedebabbebabeeebbbaacabcecbebabeeecacdacecaeaccbeedeacedbdbbaccbededdebcbdbdaacbebedaecbedceebdddbbddcaabcbcaedbaebdaadedacabeaacccbaeeddabccceedaceacadebbabdaaaddbaceeabbbdabedcdddccdecdcbeeedbabbbbbadbcdbaacddebddaecacccdcbcaaeedbcdcccecadbbecebeccbeaeceebadceacadeccecabddeaebebecccccbcdadacacbecdbbcbbdaacddacbddededaeebeeabacdebaaaccdaadbdaedadabbeabbddbcebdaacadbbebccdeecaadeecbebcceebdcbadedeceebdddbdaecabaaceabbdcceadecceaccdaccabadbeadcadecbacdabaabeecdcbcebaaaceeceabcecaadebeeececddcdcaadebebeecdacdcdedcebbddbabcaeeacdbccbbdedbbeeedcadaedebaacbedbeaeeebbabaceacebeadeeedabbaecbddccbccbebbacdadadbeaebdcaebedeaaaeeddbedeecdbececacbdbdccbcecaaccdeacbedddeccecccaeeadabedeeeaaaaccaddaaeeeadeddeceabddddeaeaceddecdeabdecddceacbddabbcdadbebbcdccdaaeeadeacdebcdaeababbbbbbebdedccbccadecdebcaeedcbcdcaaaebaadedcacbedebbdbcecbcabcebcbcdeebebaeeccedcebbddaecacabbcdabaecceacaadbcabebacccededbbececbdcebaebdddcebcaeedacddebbbcececbabdcebdcddedabbdaceababdeccaebbcbaaacaeededacbcaccbadccdebedbbbcbebcdbccccbccdbdbeaccbadbeabbdccabaddbaeaaadbadaecacccccdaeccabdbcceceadbbbdebacbedebdccdedbadeeabbeabdecceaedcbacadadccbebeebdbbdaabddebcdbcddddadbadccaedeabaaebceeaecabbabddabaddcaabddeedababbbdbedccdbdcdbbcdaaedabadabeebecbdaaccdacabbbcdbceebbdbccccbbbdedeeecaccdcbbcaceeadecbaeaaaecebbacbbedadbecddeeadadbdcddeaccbdbeeccebdccacebedaeaacdbdebcaeaabcdcadbcebbacdbcacadcdebcadabadbcadaeebdacedbbdcebeacbdeeadddaddabcbdabceceababeeadaccddaabdcbacecaeebcbcceaaebaebcedbdbadabddedbaddecbbabccbbaebcbadbdcedacdaedbddaaddcdeaaacbadceedaabeabdadeddcecaebaccddacbadaaebdbbcdcaaecbdaadcccbcbadbceaaddecddcdeaaccbcadcedeccdadccbbbcbabaacdddecbcecbaaacddbbaebcbbbdcabbddabadcbdecacceaaedccdbcccedcdeceadbaacbdcaadabbbedcdddaaedbacdccbdbccebcaaadbcecddeeeaadcaeccadcbdaddedcdbeacdceadbcacdeecbaddceddcbcdbeabbaedcbbedbdbdcecadeabeeabacabddbadaeeccbbecaccaeebeedebcbbeabeeaeddaacdbdbcbcebeeeaedbeaeaebbaebdbdaaabacadebbecbdeedeadeaeadaacadbaabccaaddbdacabceacdedbbcbdddaeecbeebddaecdeedcdcedeadecaddecedebaebaedbdbbbbbeccdcddcdacbacbcecdacdacdacaaaeabbeedeebebbbccaacadbedebbdadabcdbccbdddceeaccbeeedcdbdcbcbcedeabebaecdddcdbddeebdbdbbbcabcadedecbeaeeedeecaaabaababdecabdcabecabcddeacbbbbddadcdbccbbabacceaaddaedcdedabcaeadbccbbacebddcdabecbeaecdcccdbdaedaaaddbecedacadeeadabeaaeeccdcbccaedaabacedccebdaadcbbdedaaacccbcebaaaedddacdeadcdeeeeebdbccecdadeeaedcaabecaaddecdcaacdcccbdbcaacdccbaabceeaecadebbdbdbaeeeeeebdcbdcbbaddabababdeaceaedbcebcdaeedbbeacbeeabdedbcdbaebcebabaacebcecdbcceceadbdbcccaecdaedcbddddbcbebddbabcebcdccbaaedbcaddeaabaeccddceabceeddddaecabadadeedcabcbaacedbdeaacccbbbebdbccaededcdbedaaceeeedebeaccadcededacaaeeaebdcaecebbcbdadbababaacddebaddaedabaabadbbedadcdaadcecdbdbeebedaaceacbbbbcceaeeeaeaacccdedbdbabdadbbeedccadcdddbbaddacdbeddbdaddcadacbabccdeaecbebeadbdcddaacacbacbabaabaccbebeccaaeebedcdeccaeabbeeebbaeaeddecbcdaedccbaaaeeecabccdcbaabcadecdcebdabbbdbcaebebdadecebaacdeaccaabecbabdaaaeaeeadbdccedaabbadcdccebeedbbcbabaabbaddedaaeadacaabcceebeadcaeadaecacbaaeababcecddbebddbeedbdbcadcacebebebaeacdeebebacaeedbdecaeeccbdeedeadecbacdcceecbedbacbaadabccabacdbaeddbaeacedaaeeecdccccdddbbaebacdbbbeccbcddbeeadacdbccaeeebbebdaebdcabbcbdbcddddcbebbddaeaebdbebbdaadbdaecdaeadbaaddaabaaedbedbedcabbeecbeddbdbddacccdebdeebecdebececbabeebeddeaeaaddaaeceecdaedbeecaddcdbdddbceaeddecbcddccabdedddbccddbdebbccbaabdacbbebceacbebbcceddedeacddbabaeaeeaececabdecdbbdaeeccdcbeedebeadebccccebbdabbcccadbceecebcadaabeeddccaceaceeaacdadeddbeebaeeddabeacabacadeeeacddaaaedaacaddadedaeaeeaeaabdbaddabadabcbcbecaeebdbdcdddbbcaaaeeecbbeacaaebdddeebedcdcbecaadaaddbcbbbdcbccbadaedeabdcdaccbcedeceeebecadaedcdaacbbdedcdbedbecedcabedbbcabbcaecaacdeaaceebcccbbaebcacdcbbbdbaddbadcbccabebdbcdcaceaaccedeaabebceebccacaebeecbdaebedadeddeddceedbcbaceacddedcdceecdabbadadeadabdadaeedbddaadadebaddabdddadcbcbcbedabbccaaacdbdbddaedeecadcdceeeabddacccebbedeacaebbaddcaacabdecbebaabacaeceaaacbbabbbaddbacdeadeceecaaaadbededbbcdaaadcbdcceaecebbaebcccaddacadeeabceceeaaddeebbaceeccbaebeaecabedbadaebbabcaadcdeeeddbdcaeaedcaacadbecceeccebcbdacdaeedbdedacdeddececcbdcceccebbcddbceccadcaeacdbbceaddecabcaabddaababdbbcddaedacddedaccacdeaeeabeabdcbcbcabcddccbcbabdaadbdabdbcbadaeeabbabdabddcbdbbadaaddbbedccabdddadbbeadaacadceecceadbebcdecdcaceedcecbccaaaddecbdbebacabdeccdebceddbcadaeeededaaedddcbbebbdbaececccdcadaddddccaeacbceaebbecababbadbddacaccbaaceebdddebeeebcaeccdddcbbeebbcababaabebbbbbbaccabdcddadcbabccadbdbedaaebcdbbdebbedcbcbbccedaebcdaabedaaabbebddccabcdbdebabeebaaedccaedaceebdadeeedebaceebebceebdccbdebbddaebbeacbceabbbedcacebcaeeaebaecadeeebeabcaebbbcacebcaeedeecbddddcdbddacacebedddebcdcbecebecddcaacccadbedcdaabcdcacbadbacadcdcbbbeaaaededbbbccaaadebedbbbceacdddeddabedbbdccdeeabbebeccdedbabbcbddbdaebdaaaebdaadcdeacbcdeceacbaccebacaaebedbbbddecbacbdcdedaecabbdaceedecbbeeeedaedbecceeaacebeabacdabaaaabdbcaabeaaccadcebecbcdecaecbbdcabaeabddddcdeccbdeceaccaddcdaeaabaaabcbeedcbcbbdbdedeccdbbcededbeabddeccabeabaaeddabdabbdbabcbbcdeddcdcdeccdeebaacddebdecdbbedccbaabcdbccdaadcaecedaeacdabbabebcecaddbaadbecdcdddabbdcdcccabbabbbeaaebceeddabedbaccdddcaaeacbebaaacdbabbeddeabcbdbcbddaacaabcbbebaccdddbaecdcebeeccaaceebeaeccabbabeadeedccdccabacccddbbbaebbdbbcdcadcbbadacbcacdbccedbaebbeebeaaadedbdaaeecbaedcecbceaecededabdbaddcbdecdbaccbbadaebeabecabbbaccbdaadecabdcaacdcecbaeabebcbccbcbddaddcabadbcebddbaceabeeaddbaabcdcbdcbdedbbbbdbaccacccbdebceedaeddedebeedbbeaebdaadabdbdecaacecdcccbcaeaaeccbdcccbecebbaddacbeacacccbbbdeceeaddadcabdacecbcbcadecdceadaddadbdaaadeddbaabddbdbbbdccdccbdbdbaadcbcbcaecedebcedeacbccbededbbedecbaaedbbaaccddbecdbaabbcadeaaebceeabbbdeadabaddbcabeceabbbcdaecbbedeeeddcbccbceccddbebcebcbeecbacaaaaccaededeedbdbdadbbeadacbeaccbcbabdaeebcbaeaecbbeabeebacadeddccbabdadbbaaeaadaddccaadbecdaabaebebcaaedcbcdcdcbbaedcbabdeaebadecbeabbcaccadcbecccddbdabdcccbbbdcdceedebacdbedceaaecaceacdddeaeeaabccdaaedcddecddcdaceaedaabbbdeadeaebcdacddecdcaaaccbadeadceebadccabebebcbdecdcbceecaeeecadacaacbdadeebbacbaabeddacdbbdccbdaaaacbbadcecacccdbdadbecdcaccddebeaacdebcedaccaaabaabccecbadbcdbbcdeecedcdbcecaeacddcecaaacacdddbdcbabaceababaeaeccdabbebedebeebceeaeccbaecbbbaeecacdcebdcbabceebadedabcdcbabdaebdbdadbadbbaceacdcdedeaeddcacccbdcacebbccaecabcbcaadbcdeecdcecdbedecebebabdabcedcdcddbbaddbdaeeeccabbceebddacaaeadcbeabedbaccbecbadcadccbbaeebadeedecbbbcaddcadacaeeeecccddbbbdcbcbbedccdabceedceebbdecadbebcadabeeaaaeeadbaeeabedbbeadcbaedaebdeddeecbacadaabcbbaeabcaaebcdbcccabdaccddabcccbeedaabbecdaeecadedbbcadbabbedbddaacadedabbcccebeadbdaabeaeacbbecbbdeecbacaaeccebcaadaeaeadedcccbadabdbedbcbdaadbeaaedebecedadbcedecbacadedcabeeaaecaaecaeaabccaaeacbeddbbecbcebebddbbeeaeaadcedcdebbccecaddbdcbacbbdecaeedecdcebddadbcdaeebbcaedcaccbecbaacccebbdbdedbdaabdeeabebadcdbdecbcedbcbccdccabbceeeeaeeeeeaebbddecdddaeadceeceeeadcccdbbeabbcabaeabdccdbaeeadabbacbcbbccacaeabbaaabaeeebabddebadceaeeccacadcbaceecdbebbebaebbcbecabebbceceaadbbaadabbbcbddaacdeeebcebbecababceacaaaddddacbbbcbbdacccdccadedcbbdacadecbeacbacdadbcedcacbbecaaedeecbcbacdbaedbbbeabdeccdcccdabdccbacedeadcbccbcbedcadacacdaeccdcecceaeedebacecbebaddebbbbaaddbaecacbebeacabebaedeadaabaceeaeeddcacadbbccadcabdbbacebceeecdddadeacabdebcbbceeabcadeaeaacaeedcbddeaadaddcbaadeedbaccaeabedbdcacabebabbaeaacceecdabbeeaccbbebeabdbebaedcecceceaacdacbdacdccecedceebddeacdcbaebeacbbebbedcbeecbeddcbbaabdcaeeedddcbbadaececcaeeebdecebcdcecdaccabbccbedeccdcddbbcbddedbcccbdcddeebdbeeebcbcbdaedabdeddbecddedcdedabbbaadacdaaebbadcbcccbdadcddedacaceddeabdedabbcaadacbaeccdeeeaaddbeaceedaabcbaaccdeceadeaccaaedcecdccdbbceaaabaacdaccacddbccbcadcdabbbbcaaecadeccebeddbeeeeeccaedeacaebceadeabdcddcdceeaddecdccecaaaceacbdbdedeedcdcadbcddbbdddabdabdbcbcccbcaeddcaccbeeaecceabcdacabacaddacbbceedeabedcaddabebcabeebcabdabaedeccedcccdbbeaeabeddeaceadcaedadddbedbaaacaabaacadecdadedcdeacdbadbdbacbeeceadbcdbdbedccacdcacdcccdabcabcddcadcbcdcceaeeadebeacdbeeccccbbeaadddecabbcecccacbecaabdcddbaadcaadebaaadcacbaddacaedddbbbcbacebaddedcdddadcedcbaceaadbdedcddbeadcbeceadaebcacdbedabeaebdbcbaaebdbbeceaaccddedcdecbdcbbcdecccbcaebddebbbddadebcedecbdccdebacbdbdbdccabaaceaabddceeccdbaaeaeddecdadcbebcbedcbabcdcacaabdaedcccacbabdabbcebaeeacdeabcbcdcedacdccdebaadbceaababbbeacdbbabbaeddedebaedbddebdabaeaedcccaeadeeebceaedacdbaeedbeaebbcedadacbbaaebedbeeeedeeacbebabeecbbaecabebdedeceeaadcabdbbddedbdabbeacaeeadacaeaaeabdebeaedcccdedebeaecbccadbdcdabaabbeadcaadedacdaecdecccacabcabbeaedbebdbcaacaeeadcdceeccbeddadddbbbabdacaeaebbeedeacccbcdeeabaceeadcdaccdeddbbbeabaeeeacbdeeeadeeeecabbbedbeeaacbadbaadecedbdcbcaaabbccaaedddbaebedaaaedacbadebceeebbdaacabbbabcedaaacbebeabecbededebbbeaecbbdbdedcacdddbbabbbdbaadaebcacceabbcbecaccaebaedebedeedbbcbdcbdaadedaacabbbbdeeebcbbccdeaddaddcdcbaaddecadcddeacbccbddaedbedeaeddcedabbabecabbdcdaccaabceabaeceabcbcecbcccecdddadddabbccaeeabdabcdccdebaeadccbadeaabdbcbbddebdeacecedeeeedaedecddebccaaccdeeedaaedcadcdbdcebcdedbdaccabbebcedaeaadadcccabebbcdaaccccdbbbeacabeadabbcdaadcdaaecbbbcbaabdbadcedabebebcaeecdcebabceeddcaaacbcbaebcadbaaddccddacedccdbbdbbeaecbabeacddecebedcceedabaeadbddbceaabcadadeaeedcdeceeecdaedecdebbcbaebaeceadaeecbceecddcddcaacacbdbbeeedddedeacadbdcccbcbdaeaddeceebebebebbcaabccdabedadcabbebebaaaebbcebdbbeecabddeaaeedbeaebbcdeadddbcedaabbdebcdecddadbeaaaddcbdcaeedebecaeaaccdaceedaadebaabdbcebeceebaadcccbeebcbebcbcdabebbddedadeebbcdbededdcdeecdaddaacacddbbadeecacecaaeebcdeeaeaccdcbecdcbbddbaebabacebabbaadacbbccdacaeaaeaacbabcbdacaecbcceebdbdaddaecccaedeceeecaebceabeeaeecbdadbecadbddbeddeddaddbacdcebcdebaddbeeeceaceeeacbacadcceeeaeceededccdccbeeebcabeedeaacebcdccddadaeedeeabcdcbcaccebceadbdabbbddabebdadecccbaeedebddaaabdeeededdcdeddceaabebbddaaabceebbbabaadeaccbedbaceeaaaabaaeabacabcddacbeeaabbbecdcbbddabaedbddbdbedaceceaaaebebcdcbadbdeddedabdedbebccbccbedabcadadcaabbdecbcbeebcdbcdabdbddcbbdbedbcaaaddecdadcaddcceeeccbebbbddddcccbeabadcecbbbcdcbcbdacdaaedceaaaacbcdcbeceadccaacaacaacaeddcadcebaebadaedeacddccbddeedadeebacddcddbeabcddbddcbceeedbedecbcaeddeaaeadebebbaeccabdcbbcdbbcbbcdbcadddcbcbabbaadcedceebedaedaaeabcbdeacacadbaddaeacbeceaecbacdaedcdebaeebbcaddaacbbadeebcdadbbcadecacbbcacecdaeaacebcacebaceeacababcdeabaecdcacaabdbdcddcdbcaeecbaeeddbddcbcbbdbcdddedbeedebbbcaeecbaeabcbdecdecadabaebdcebadaacabacaceaeacdbbddcaeaaabaacedbcdbdaacebbeaabcddadcdbcdcabcedacedbedbbeeeccdadcbcccedadecbddbaaaaceddccbbcdacebcadbbbdeaaebdbecdaaacdcecbceebcbecabebcbecaeddcbadacedddeebbcacdbddcaebbbeeccebbeadbbdbaccaddebcdbedbacabaebbddedbdceadcadeccdbdcbecddcecdcebcacdadaadbbcecccadadeeddadbddbdecebcdbccadecdabacdddaabdacabedbaebcaaabeebcbecbcbedabebddcaaebeabbacecdcadaedabedadbcbeecbbaabeabdebdeabcccadecbdcebdeccbcdabdcebbaabcdedaceabebccbbaaadebebcabcbdcabdbaeecacaeceaecedcdcddeedaacadceeddbbaaacbabbaedbdbccbadebdedcdecddeedeaeadeecdcaabbcadbbcadbeecddabeaeeacdbeddaeadcdaeddeebbedddeddaedacdbeecbdeecbadbaadececbbeeceabbacbaeeecdbcceebecddcbadbccdedabdcaeeceabcaacaaeeaecbdbcbbccedbdccdbaecbdceedeecabceaeeecbcadbdaabbeedebbcbacdabcaccdbbaeabaeaacacebdececaabbaaeececbbcdacebdbbdadbdadcbbabeebaabcecadeaacbedeededeabbeaaddeddeadbdcdbdeedbbdbcecaccdbdccadeeaecbcbcdcbeecebdecbebebddaccdcaaaceeddaeadcccbdbddaabeacccebdbaceceabeeaadebbeaaceeaaebaaaecdeeecbeabdceedabeeeebcadbbcbcccbdcaeabbebbabaccbaacbbaacadeceedeaaadedcadddbbcecccceecbabccececddddbaedcdcbcbdbabedcadecbdbeddcddcbdaadeeaabaebdadcebcdedeabcdbdebedcabdcabcecbacbacaeeabebaeabebdbeaebadcddcbebcbeedcecdecaebbdcadceddeeecabdabbdadeeadabcaebeceeeeadebcbdadaeaaceecbadaccbbddcaebdaaddeaaadcabeaabadeacddcaaeccdbcdbebaeaccebaecdbbaadbddebebeceebabdbedccdceaaebaceaabceccecebeceabadaeeebaadccaddbecacccbbdcebeccbcecaeddbaddbccecdceaebebddcebcaeaedacaebccccddddeecbbaabdecbdbedcdbabbecaabdbebddbaeacdbabeedcaddabbdbccdbdcdeadadbeadcdbbcccbeeccedaaadaeedceabbcaaaebebabbdacbcbadcacbabeddddadcacaaeadbeababddebcabbededbddcabdcbdeaeededbdabaaabbdddadcbbcacecebcabbadceebaabceedecbabdcabbcacbbeebdebbbadcdeebaeacbbcebcecdaddcebddedcdaccdeacaaaeaabedaeebcaecdeedcbaddbbddbcccabddaeeaadabebccacdabdadbaaceaabaeeaecddabbdcbeeeaaebeeddbdbacbdeeaacecbaeadccbccdbebcccedcebbaddacaddbbedaedcabbcaaddbedaacdbadeedbebbddebabdeceebacaaebbbaeeaadaddcedebdedbceaadebcdeadeeadadbdeecacbbbeedddbdcddbaecbcaeeadeededbadeeaabcccecddadbcdbccbadcccaacaaedaebccccbdacceebabbbeddcedadeaceecaabdcdadcbcdabccebbcedcbadeedeabcccbdcadebebadebecededecdbededaadabcdbadbbeddcabbdbdcbdbbdbbeabaddbabebeeedaebadbedbedaacdcecacbeebdedaaaaabeedbedeededceabbdcdeecdaddaaecdebebdbadbccedeeacdcadcddcedeacbcdeddbdacbacaaabebcbbacacedbcbddeaeadeeccebaaebcbadcecaaddddeddcaaacccccdeaedbcecddaabecccbddddccacbdcdbdacedeaccaccbddabececdeaebbabceaebcdabebbadbdadcdcbbbeecaeaedeedbdcadadadcaaddceebdbeedcdaabddadeaeeeebddaadccbbbdeaadbeceabddceabaacdaecebbbbebcabbcbceedbcbdbbddcddcedaebdceccbdecbedebceeaeadedeeeacbccaebabddbaaeaeedcceddcbccdbeacdacadcceeddeeaaaaaaedaaebaaabbbdbbdcbcdadddcdcbcecbabaadacaebeeaecabbdadadcabdadeacbacbdaeaeadddbcaceadcccdcbbbcdcaedccadddabcbdabebbcedebdbaccaedbdaedbadddacbeebedcedddcecdabceaadebbbbdededaabcacdaecebbaaedcdaeecdcddbaaadcdcecaecebcaddadccacedcbcaaaadbbababbadadecaddbebcdbebebdbacecebaabdccaaeedbaabdcabadcbeeeecebaeaaccbbbcedcbabcbcdacbdceeabddcedaacdcbdaeacaeaaaaebeebeecaebcacbbadabaacaeadebcbebbaeddaabdedcabacaaceccddbadaaaeaccbaaddeeedbcdcedbaeceeebcacbabdbdcbbdecddeecbdcbdacebbaebdeccedbbdcccbbdebdccccdadcabceaeedddabbdadaaaeedbdceeeedcbaceadbdaeaadebebbbcececbcdaaaddccdedbcebbacaccbbadbcebabbccbeebcacdecedabcddadadadaabedbeedabbaadccebaaaaeaccaeeaaeececadcedabbaeaccbaebeceaabebddcddebccdadeeceacebbcceeddecccdeaddcadcecdeaccebbabbbbdacadededddbcebeeecbadedadacdacbecbeaeecaeacdaacecaecadcbebdcbdaccacaaccbaaeddaceccdbcddbabcaaaeaaddeddeaeeacbeadeaddcdadbdaeccbccaeaddeabaaededcbeccdbbcbecdadecaedecadeadceaaebdedddbaaabdaeaeadebcceadadacccbbaeebaeaebdcdbbbaccceceaaedaabdbeceedcaeacdaeeccebeddecbbebbabaeecedbcdedbeecbaabeedddabbcdeebdceaaedbbaeddbbadeaaddcbddaadcdaddaecbdccdaeacaecdedcddcbdaadddbacaecdcbbdbaeacebadbccdacdbbcaaaaacacecdcabebaaacbabcabedadbcaaececaedaddedeeeeedecacabcaceaadaecaeeacdecabadcaddcebedbdaebaabbaabdbaeaaadadaccccddbcbbedddeeaaabdbbddcddadcedabdddeddbdebbbdbacdabbeaacabceceebeaecceadcdebdccdadecbcdddabeaaaaabdbaeaedebeebcebcdcbaedcedcddddbccbadeadcaacbecadeaecbabbeedaaceaadbbaddbceddbaaeaebbdeaacdcbecbdbebacbbcbbdadbedeedcbebeadcacedbbcedaedccddedecaceccccddcbbacbababcdebeabeebcbccaadecbaddecababbeedacadeabcdcbeccdacacbabdcdebbebaabeccaadedaecccdbdaeaeadacadaabaaebdbdedbdbbddaabbebdbecbeaceeddaaeacebddecabadcebaaceecacbabcceacbcddadcedadddceecdbcaceccacbebdcbcbdbecdddcbcadbbecacebebdcbccdaabbccbbeeaeecdacbbeeddcaaaaeaadcdbdbedadbcaadeecdeaaebeedaecdaaceceedcdcaceaecababebcceeabbcacbcadbaecdbbeaebdcaeaeedddaebedceeeceeaeedbcdaeedcdeddbcdccdaebddacedebdebabacedcadbeaeaaeaccdadbacaadbaeaacdddbaccbcdddcbddbbeebebdccceddecedeaaeecdcabdbbedaddcebbaebbaaeccdacbaeddaacdebdeeeabdbaededdcbebebaabadaeaaedbeedadcecbdbcbcbeddededbeabbdabebceebaabaaceabddcbdbcabdbdddebaccdeecbebbacdaeaeaaedbbccacbeaddbbcaaeebaabecacaddaeaabbadaebacccaceceadabedabebdacceacbddeeaebacacdeeedcedeabbedbddbcecbeddeebddbaecbccacabbedbaeedbebeeddabacbcaebaababaddeadbedbcacbdbccdacceeceaeebbadbdbcbcbaeededadcdbbecaddbeaaadcedbbbbdccbadabdbeadcbcddceeabbbbbdcbeeadaecdedcbabbbbeeececbbaceceebbeaceabddeedeeadcccebbcabacccddabbdecbeeacdaceabdedeeaaabacaabeabbeecbdeebeacaccaccaaededaddbbacbaaceccdbbdcdccdbdabbeacabcceeecedcdbedcaeebdaccadbdcccaadbdaaccdecabecdbecdacedebbcebcaabebbaaddecebaaaedbbcbdededcedebceccdadbcebdabcaaebdeeddecbddbeccabcaaeaebbbecdacddaaabdebbeacbaecadedcbcabeabcaabcdacbcebbcceaccaccaccdaaacbdbeeaceaeddebadbbedecaaeaaecbccbbeaaeebecbbabbecebceeabcadebcddeadacdcdebeececcdecccaacebbeecbbcebecbddeaedbcbacebdacbdcdeeeeeebccbbaeebbbeecdaebaeabadcecbebbcaacadababdbcdcbceecbebadbadadcdcbebecebdbcaecdcebadecebacedccaaabdceabecabddccdcedbdbeaedbbedaeceacdeadddbaecccaeaecbddbcedaeddabbdbaeebcdbeabceebcbaaeadddecceebabddbbcbbddcbbabbcdedaadccacacbbaaedddeacdbddebdacdceeabaaadecdcabbdaaebdcecededbadaeaecdbcbccdbbcadaebdcbcaaccecaebcbbcbdeeddccbebccdcccbacbceccaeaebeadeeacebdaedbdccccbeedceedbceddebecdeeeaedbbdcaabcdbedaadabcccaebabecbdbeabdacdcbabdaaadcccceddeccdbabcdbadebbccbbccdeceebdaecdaedbddabdddceecdedddeeceaccbccedcddccdaaadddeeeacdabeacdcddadbdadcaeebbcbeeaccabacdbbcaaaeddbebaccdcdecdcdeadbecbddaddecbaeadabecadbaddbadbbdebddbddcacbcbabedecdccdeebacdadceccaccbceabbabecdcaededbceeddbbebebdccbadbeaecddceaaaeabdbebabbcdcbebccdeadbaababcbcdcddddccebebdaaedcdbababbcecaeacdebacdcebedeebabcebccaebcdbbbdcdcedacaddbbaeadadbdddceccbabadeabdcbcbaececbcbacdbbeebbbcabeedeeeebecedcbbdeeddcaccbbeacebdbdbcccddbedccbecaedcbacdecbecebbaabedeaddbcaadbacbdedadaaedaeaababbbaecabdbedecedbdedcebcaeecbbaeeabbbecaecbebdeeddaaceecbacadbceddddddebbeddabbbdaccbdbbeeadaacbdeabdebeabbecdcdebecdcdbbabaccdbdbadceacecbdcabbebaadcceaeaecbabbeacaadeeddacbaddccaaabaaccbdbdaecaadaaacccbcebabeabedcaddeebbdaebddbabcbadeebbecdabdbdccdebabecabccabdacacddbdaaebcbbacbddcbcdabcdbdcdeabeddeecbaacccbeaabaecbabebbcdedcbdbeeaadbbecccbadcaddedcddddabcccaebabeddcacaeeeeedbdbccddbadaabcbdcbbaedcebdaccabddcbeeabbbaaeddaaebecbbcdccbcebbdeabdacccdbdbabcdecbdbdabcecebadaccdbedcedcdbcdabecaebdebabcabeacaeddccbdabbeddeccabaeccdeacbcaeeacbeccdaeeacdacdbaccaccadbddacaebdaebbcbecabdbaaeedeecdbaaadaebebccaabccbebedacdeaacecdadaddaacbbedbabbaddececdceaaaeabbaacbedebdbacddceaadedebeddaeeacebabaecbaeaecddddebabcddacbbceccaedcdabecaedecbacebdcdebecacedbbbacaebdedcadebeacdbaadacaabeaeadbdbeeeaecadabebcbbdeeabcedccaadabdcbaebeecccdaeabcebdcebaeeecabbbddcadabbbeacdbcacdeeecabcadcbaadbbdedcabadddcaebabbacdeccabedbcabbebcadcbbabcccabbaccbcbcaedadeacaaaeaacdbadaecdccecebcdecdbcecaaeadcecaccddebdbdaebbbcdbbddebedaaadcaedbcddddbecbacbccbceceeaeaeaaeaccacabcaacacacdbdeaacebbdcaddedeccdabaebabccbbcabccedecaedbddacddedaceaccdabbaeacbbcbcdaecbaaaeddeeebddaaaabdbcbeebbbacdbbeaacebdecedaedccdcdecebcaabebdcddecaabdbdbeaecddddaedddabacccbbcecbdbcddeaaaacabeadecedddaaeccbeeccbccabcacaacecbadebcbcddbddcdcdaaecdcbbacbedededbedbbcbdeeadebcdabeeaccaceddddaeccdaebeaceeacaecbbcacabeedeabcaabeebebbddecebeaabbeeeaeccbdceaaaaecbddcdcbaecccbbaecadaeeacbbaaabccdbdaecedbbaceeaccdeedbbacacbdbcacacaecbddacaedcabacdbdaaacddbedaeadacccdbcebedaddbdbcbbcdccebaddaaaadadbdcceabaedbdceebdaebccbbdddddadeabdbaebbadcaebbcaecbcadcbedeedababbccaaecbedcecbbdedcebbabaeebbccbdeaaeeacddbbcccebeebacdbaeacbbdcdcbcaacecccdbbceadaccbbddccbecbdcbedebbacccedddadcaeebcaadebbcebdcadcbacbccadcbedeaccccbceedcdecedeeaddaeeeaccadcbbabadabcbeaecdacdaeeeecdbcebadcbadcbbdcbbbacdcadabaacaaececaccbadbceadedbaccaabcbadbccccbbcbeceaacdaceacaadadcaabebacddebbddaaaaebdceebeadbbcbdbdcacebccbbbcbabdbbbeeddeeaddeadcdebebeedddedcbeccbbdabbabbdccaaabbabebabacbabaebcdbcdbabbacbbebacbacdabaacbdbadacadacedaedddaeeeaddcadaddddbceaadcdbdedacaaadcacbedcbcccadeedebedaebcbaedababecabaeccdcdcdeadcddcaaabdcbdabeadbaaebebdccdbccdceacddceabaaddcadbebcccebaedadbaabbceeeaedaeebbdaacbebeaeecabdecaaeecddebaccbbbeaebdbbedbacddabacadcdabaadbecadedcdaedbecbbabcbdbdadeebbbabaeeedadcdbbdbaceeeedeaacacbbacdcedcccadbeccccceaedeaacbcbadebcdedbbbcbbbcddaeddddbadbbdadabbaeccbadbeaeaeabdbcddeacecbcdcadcbabbeceabaadcedcacdaadcadbebaabcebbacdadabacdbbbbbbcdedeecccbeeeaacddeedecedcdddcbceecccaaecaeddbeabcdbbddabeddccbbddbcbebdcdcbcbddcadeadbebcededbbcccaadcbcecaeccadbbcccddaacdcadcbaeadcaaabbbceaebceeabebbbedbeedebaddcedcddadacadbebdcaaddecedcbdecbedeeaecaecdaabeaedabdabdccbaedbdbbcbcdacccdbeeaccbceaaeeccbaccceddccbdbadcecdcdcbdaeccdbbeaebbeabccbdccedaedccadcececcbbbabbdaebdbcbbbcacbeebbcdaceaabedaccaeaecadbaeadeadedbebbacedbacbddbeabbcaaedaeddadbdedbeceaaedabceeadacbdbaaedccabeaacdcaeccebaaabedeabdadacebbadebdbceeabcbaecddaccedabecdaedcacbdcdcdccdcebaaeaaddebeaaddbdbeabcceacaeabbabdbadaeaaedddaedbdbeacbcdaadabcbcecddebeadaeaceeacdcadeaaaddabdccedcaebeaeeceaedddecddabdcacedabbadabaceabacdadceaccccaeebecabaedcbabdeeedbaeccaabbceaedccbcdacacdebcebeeaddbaecccbaaaadadbcabdcadbacabccdceaddaaebdedcdbcccaccababaadeebcaaedaaeebbabdacccdbcadadcaebecdedeeabdacbbdabcbebcabebcccbaceceeeedeabdacadcaedabacadbdbdebedbaedaadeacaaaddccbacbaaadebeabaacbbabdbbedeecdedeabecccabacecbaccaeeacdbabdbdbdbdeeecebaaeecdaedeaeecccecdcdcdbcabbdceacebaeaeeadcdbbbccdececeaaaaebcccdedeedcbebcecddacaabadeedcbbcadebadecaabdaebbccddadaddeccbededbadbdedccbbacceacddcadbaacbacaaccababbccabadcbcbdebabcaebacbcdddbbddebecbcabbaebadbbdbeeaaedbedebbdabcedcbadbbeebaddcebcbecebdecedbbceddbeabcbaedaccaacaddddaadceabeebeddaadaaeabaeadaeeaacebedcdbedcecbbccadbdbeebcbbcdbcebebedbddcbabbcadaadeddcbbdebeedbadbeeeacdeaddccddaacbcdddbdccdcaceabddcddbbdaccdbeabbebedabcbdaebeadbeadeedcedbebebcbecbbdacadabdacbecdabbdcddcbbddccddbdecbedeaddeeaaebdcaabacdbedddceeaaeddbcadeabceebdcdbdecceebbeebcadacdbaeedcdabbdabddaeebbeeaddaeaeeaaeadeaeabebaeebeebaaddbcbabbeadbbcacbaabbdcbeccacdceaccbababbcdccaadbecaadeeddadaacccecccceacaebabceebbadbdababbeaabaadeaacecadaaadcaeceacabaaeaadcbcdedacadedcbadaeedcedbdacaeebaceaeecddeacaeadadcaaabeacdecccaceacdacceeddccbaedbeebdbadaacedceedaeedaebdccaacedccddadcbdaeeeaecbccbdbeedeadbbadeaccaabdebceeaadaadacbeaecbbcdadcaceceaecceaeebbdeabbdadcaeedeebacebabeacbdcdddceaaadcadebaceecaddccbaacdceedbccdaaebdbbeaceebadaeeddbabdbdcebdddcdcbdecbceacccbdadcdadbdedccdabcacacacdaabcdddedaeddccebbcaceaaabaedaaedbdccbcdebecebbdbeaacbaebaaedaedbaecdceccbadeaddbdcebcdddedceaaaabbceaeebbaededdcdeeebcbbcdabaaabedaabaaacddebacbeeebbeebaaeeabaaaacdcdceeceaaceaceadbdcaaeadcadcecaaedcadebbebbadcedbececdceecaabbabeddcbcebbaaededbcdcbdeaeaacdddadebdceeebabeeabbaddddcaebdeabaaedccdadabbabdeedbdbdbdddccdbaacbaabbeceabacaabbbdeedcdcdebcaaaddddaabcbbceaecdadaebeceadadcdddcccacdebdccdbdbbbdadbddcbccdabecceedbacdbdedddddceceeddbddddabbbdcdddedcacceeaeaeeeddabcbcaeeeaaaccceabedbcabccdacdbdeecaacdbbebacdbdaccacbadbeebdcaadeeaeabccedcdeceeccbabdaacaaadcaebbcdceadbebbbccccabeababadcdbbbcceddeecbdbedebeaecbedbcbebbcdedadeccdeadecdaddaaeccadabccedbdcdeedbbbacdeaaebeceaebecacdbcbdbebdaedcaaccddaabcbbecebcdccadccdaabcaeeceaecebeadebdddcececbcdeecdcbbaccacececbcbabecabeccaeadacbedebdaddbcbbeddeaaededadeeacaadccdcbebdcdbacdbcdbddddabdebbcdcdcedbebcddeacabcdbaaddebbeabbbadebcceaaaeecdbacdedbadabcbeeebadecbcccddebddcecdacceabdecdaeeadddeedacdaadebbaeeeeedaecabadddcccdccebaeadcbeeccbbaabbeddbcbcbddbbdadcdcadbddababeddbcdbcbaceaeabeaeaedadcecdecdbdabbccbcbeaaabdcdbaeaacbacbeaabecdbbcceecdeddaadeabeeaeeccbaacecacebabbdccbdbacccebcbcaedaaadadbdcdceaedabeceaeecdccbecceeaadaeeabddedeabdbdebbacaaecdbbaedccdcbeddaccacaccceaddcddaabadcccbcabeeeaadbecdbceaaedceddebadbabccdaebeeedaaceebbcaaabdeceaccdbdbcebaccebcabccbedcabddebabddeebddecdedeaadacbebcaddcbcceaaeceedacddedeaecadbeeddcbbeeeaebdddedabacdbdecbedcbebacecddeaacaabadcedebeaebeaecbaeaaaadccccdebbcaaedbececaaaabdcbcdcbcdebebccbcdcdbecdbececebbcdbccaaadcdadbbbcdcdababedabceabebbcbccdaebacacabceabdddbaedadeaddececdacadbeeaddbcbacbbbceacbacaeaacacedcdceebadeabcbaeaaaeccdcbeddcdddabdccdcaacedaccecbdddaebcededbbdcaaeeabcaecaebaabecccbcaebeedeccebedbddedcacdcbaacdebcabddaeeececedaeeaadbccbdbccacedeebbcdadbdacbcdbabedcbedadcbceaaccaddcbedadccaadbedcceebdedcaececaabaabaeaacadeaebeddcadadabeaaacbdaebddbdcacadbbccceebababecbeadaebcedcaacecdadebabbadacebeeabdbbdcbcedacebbedddaacbddbecdaeadaaccdeaddacebcbdcdbddeeaadaabecbcbbeaeddccdcdbdddbacbcaaeeecadcadceacaecbcebcedddbedeaeeaeaadadbececacbeddddcaccadbbeeabbcbbacbdaccecddceebaccaecaabecdeeacbdcbeadbdcecbaeccddcdaedaacceacebbcacbdbdcaebeadeabbcecceeacdcaedaacbeebdebabdddebddeebbbcadacecacbaabaebebcbcdccddcddaedbabecdecbabaddeedbeeddebaeedcdaedcdcaecccedacdeccacccddbeceeececbecadacaccabeeaebedcabceecbdbcbabbebbbdeabeccaedbbeabbadcebabdcbcbcdaceeaedbeecbaebcdddacbdcccabaaeaeaeaaddbcdeccebecadcabecabbcccecedbcdeeaacdeaedaabbedbbaeedeadedeeabbadeddecadaeccceeccbdedddaeceaedababdeaedbcacdbddcaadaadeebbdeabeabcdcbbabbabddcabeeaebccaedcaccedcdabcdedeccedeececacbbddbdddedaddacecadbebbaedcebacaabbeeaabbcddaceeadecdbacbebadbeddbbbdcedaaeadbbebbdabbeaeeacedabddbdcebaecaedeebabdeacbddcaaaccdbccdababbdeeebdbbdaadceabcdbbaaeaacadeacddbbeabddebdeabdebeadbcdbbaebcaebdbebecaccbbedbeaaaeddacacccddcacbdbecebbaabbddabedcccbbedabbbabcccadbbcacccadbedcedebeecdccdcecdacddeabcbccaacabcebaacecddcebcceecdaabeacbeabceaacbecaabcbaadaccabedbabedecdbaeddcabdedcddcaacbccbebeabadbccbebbbbabbdabeaeedeccdeeebbcdbaaeaabdbbedacbdbcecbbddccbaddbdabbabdaebdebdecdbeaccccbaccdccbdedddebacadbcceeaeabaeedaadcecabbdbbcaacdaebbcbbdadaccaebaddaaeebdaeebeccaccccaaebabaaadeeeeadeeabbcdcbecdaeecddbadabcaabbcbedebdddedddecdccdcbcdabeceadaebacaabbdaccabaddcbbaceaddcccccaaacbdcdcededdddabdcddccdcdbddbcdabcbaeebdedcaeddeadccddcdacceddeecaddbacabcbddedacdeebeebbacdbaccbabdbedbdecbdceeecaadedbaabbddbcdecdcbaebbaccddbbbededddcdbeabaebdbacedaabdebaadaebaecaddeccbeacbdbacaedaebecbbcedaddebbdcebeeedcbbdadeecbdabaacceeeebabddbbccaabdaabebaddaacabcaedeaedebccadecccceccdaeacaacbdcecdedecababddddecaaadceacddbcddedddbdadacdacdaadeedebeaddadbbeddaeaeeccdcdbedacebcaabecabedcdabdeaaaccbbbeaeaadbdbddacbacbadcaaaebdccecbeecbddcabceecacaebeaeccacedadbedeadabeceebbcdebcedbceacdbccdbcaabadecbccbdeaedbaecdbabcaedccbbdbaaadedcedebabecebcbbbebaeaadddcdeedcdbabeeaecaddebccecedbeebceccdecdadcdbbbcebecdaeeabccedceaeddbcdcbceebeceecdbabceabeeaeccbaebecadadebccdabbadacaabeeadcaaadbcbacdeebeddbaeaddacccadbdaaeabadbadbbabaeeaecbdbccdbadbacbbbedcbecedccceacbbebedcdeedbcbccdbeabbdceabcdabaabccbbdbdbcaeeaddcddabcdcaedacdeebacbdddabadeadcdbbebaeacdcdcdceabeeaadbcaecddbeaeedbeeceebbbeddcccbecbddbaaebacdeeeaeccdcacabcebebbebacedbbacebaeceadaeedeeceeaeecaccbceedadaebccdbccaccddcbbcbebdeaaebcccedddbccacedcbacbadedabebabbaececbbbcbbaaebdeabdbebcbcaeeebcdacceebdbeeeedcbcacbebaedbddebcddbdedbeeabeaecdbdcdeceddaeadaebdcdcddebedadbddddedaacebcebeaceaacddbecbbecbbececdadeeaccbbdcacbaeeeadbedadcbcecdedadbbdabdaedbbcebaacecbbbabeedcdbecaeeeccbcbeeeabecdcccdabbdcacbcdedaadebdbaacaccdadcbcabbdcacdeddbbbcdaebaababadaeaeeedbebbbcccacdeccbabaeddaeacdadccacecdcaedcdbababbdaaeddeeebdabeeedddbbdebbdecddeebdebdcdebbbcbaebabccbdbaceeedbdedbcecabcabdaedbcaabdebebbbacbeabdeaacbcabccdccedebedeccacacdeadabdcbedeceeccaaedadabcadacbeeeecbeaabceedcdbabddadebbaeecdeadcbeacdeaeeebabdecdbceaecccacbbbedccbaadabdbbeddeaaabbacdaecceeaaaaddeedecdabcbeaeecacabdadbeecabcacbeecdabbbeebcdcdcacadbebceaaddbacaecccdedbcacdcccceaceddeeaaacddebcaacbccabebbddbebbbbbddcbdbbdddebbacaaecddcbeeecaeeedcacaccdebdeeeedbbebcccdeeaeeaedbacaeacbdceabdbbeeaaaedcabebbabceadcdbbbabacdbdedbccadabaadebbadaabcbabeaebdbdaabdadedabbdacecdabdcaabcdbecbbcdbceacecdbeadbccecebdacceaacccddadacedaaadceeeadbeebeeeaabbddabccebbaccdddbcbacbeaedcbeebadceccedadaaceadaedeaebbcbcadedbdaeebabbbccbcbbebbcbbbecacbdbacaebcbdcccbcadabaaabbddcdbbedddcdebeeabdeccabeddbbdcadeaedadabcdebadeaabbabcdeabecdcadbbadbbadcccbceccdbaebccbddabeabceaaedaceacbaecbdedecaaeebbabdeacdcacbeacabceaeaccdccacbeceabeabbbbbedbbdeaeecabeeddececcaabddcccdcceddcbbddecbbcccecaeedcaaedecddcadcdbbccebaedbbaaedabeabcdcabbedeaebdbaacbbecedadebabbbbbceaedaadabdecadeecbcaaaaccedadbccadbcaedcbaaeeccebadcbcabaabeebaecdaadcacadcbdccedabbbdabcedcdcdcbbddeceadbacdddbceeabecbeaedebdcbdbecbcaddeeabddcedaebaebbdbbecaccedeaaacbcdbeaadadceedcbdecaeadeedeebeebccdadceebdcacebabaaddeacedbbbbbaccaaecdcbbbbbcaddaaaaababbbacbbbcadbdedcbcbddadbbcbdbdbbcacecddbbdcdcaddedeacdcacccaadbbbbdaeeebadabdecbbedeadcdebacddbdacebdbccccccccbabcbdececdbaccebebcdacebaadcaebacacabcdadcebdedbceecbbbbbbdcabcadddbdbebbedacdeacebabdbddeeddedcbeeeecbccdecadeadaddedbddaebebebeceeebcedaaececabcecbabdecdeeaeabeccdecbacbbeebbdcdbccbcdabbbbbccecaaecceabbeccadabeaddaadccddabedbabccdaaddadbcdeeaecedacdbbaacddecbcdeabeeeecaecececcdaedbbeebdaecabdaaeadedcaeedacaaeaebceacccbceadbcadeeebeaaebccaedbeadaabbbccbbccdbdebeaaaaaeeabcccdbaddaeceaebaddccebedcadabeebabadcdebaebddebbeaddeeeccabdcdcdaeaeadaadbdcddcabcbeaecaecdebbcddbedbccadacaddecdaaaedceebcdddeadabcdcaabeedeeecadbdcddcaceedeabdbbaaebadcbdcbbbeacbabadbcbeeadaedccebccdadbbaabdcaabedadaaabcbccaaadbdcaebddbdecabcbceecbcaddedaccedaaacdbadabcdcabacecaeacceacccaacdbacbeaddbbcaadeddeebbbdedcaebddcaaceadbaacededdbbccedeaadbbcededabbeaadbeeaabeceeeeaaadcbbccdcdbecedecedbeaeadccaeeaceedccadacbdcbccdccceddcbcdeabaceaaacaacdeeadbeedeebaaebececaaccadaacaabeabbebeeebaccddeceabdddbdabcccbadcdddcdeddabbdcacecaddcaeecdbbbeeabdcaedcdbbbadbddccecaeadabbcacbbaceadacbadbadbedeedabaebbeadedbcadddaedddbdcbcdeceeebaaddbeccebcdbcebdcccecdbaceaeebceadbeeddabcecaabebcaddaaedccadceabbddbeadacabbedcbbdbcebdabadbddeebbeacaedebdbcdecbdadaccacdbaacbeaecadeddadcabaeebdeeaddebeeecbebbcbcacebebcbbdadebebbebcadecebbaaeeaaeacbbaceaeaeacadccdebcbebadeecaccccdaccbaabbdcaadeedcdaecbcaacddcceecbeaeddbbddacecdacacabdbacaabbdabcdebcaaeaeccecabcdebaddedbaedbbededdedcbaacdeeebdbdcdaceadbedaabbbccccacdccededaddaceccabdabebdbccbaeadcdcbbcaebccbdbededdcaccdeacccadbaeccaabbcadcdadeadeadaaacadaccedbebedbbeededdcabbbcceedebcdbaeadabcbdeebecbeacebacbdebcebeabaccdbdeddcabedeadccdaedcbeddcedbbbcdedcceabeeeeecaeadbaaebcceeeceddaadabccaaceeedcedaeeebdecedabceedcabbdabdaadecacdcaebaaaccbedecaabdaaeacaabbbadeedbcaebcedebbebccdcdaebcacebdaadcedbeecbdaeccecccebbadedaacebecdcdbaaeacdbaddddbbbbecbecabaebbaedeabeeccdadbccabbeaedaecadcccbeccceaaaacdabeeeebdbedabacbdcaacbcddabeddcedacaccdcaebcbdadeeeaebacedbacaabcdaabaaeedccbedaeebbadbeebcceeaedcdebedccecaaebccaeadacaaeedbcbaeecaadccacbcaacaaebaccdaaabcacedcddacadadebcebabdebecceabcbeaebaccddeacbdeeeaadabdbcbdcecebeeebecaaeedcdbaeeebcadeecbecddcccedccedbeeacaadddeadeaaaaaadbdeccecdeabedecaeacbbebeacecabacedcbaeeadcdcdbeceabbccbdeacbabebadddaabbcedaabdaedacaddcaeadbdcaacdebbcaaedeeddbacdcdedbeaeaebacadedacabcadeeccdaabeebbcdabeedcbcbbeddadaeaeeeaaabaadddadacbadebdcbaadecceeebedbcebddddabadeeebabeebcabeadcbdadebccaaaeebdedcedbbcbedcaaaaeeabcaabcddabeecdccaaadccadddbbdcebebaacdcbbeaadacbbcababebdcdbadaeeacbaadceddbdecacbebdeacaedeccbacaeeeaaaeaaacccdedeaebcbcbedbeabddcbcbbbbebdddbbebddbddedccadbdbecaececacacdeaecddebdebeeaadaabbdeccdcccbceddddcacdeadeceeeabcddceebddadebedbeedccebdabaaccecbbeedccceedbcebabebbceddaacbeababccbcdcceddccbaaaeeedddbaebdbbebdcbbbcbddeddcebccedbdbcaaebacabbaadacbecedcdeddccdbbcddcbeecbdddddeeacdedebcedeeeacdccbaabedaeebeccbdbcbecabdcbebecbcdeecabeabdaaadddcaeaaccbceccdcbcbbabcdccdbeeccaeecbcdbaddcaeecccabcabcceaadadbdbdadadbeebcbaadcbcaaecbcddaddeacdbaabeabbbcdccdadecbabdcddabceecbeaeebbcdeabeeadbcdebbceabcecaddabeeeebcebdbeedcbaedcebdadeedbacbddccdaceeceaceeeabedadceadabacdeaeeeeacdadadedbddebebeeebeedbdcaabaaddedcadaeddbdedacdbaabdbabceeaccccebedabaaeabadbdcceecebebaabbeaaebeeeababeccbddbdcbdeeebdbcacecedbabdcbcaecdebdbadaedbcddbbecdaebaebcceaabbeccaaadedcceebcaeacddddbccbbdbbecddaaabcbecbaebeebdbdbadabaaabccebcdddeeedcdebbcecebeaaccdebdeccbdccdbeadeecaebbbdabbceaeaacabadbadaabcdeddbbeedbceacdaaecdcdccbdbcbddebdbcebdbdaecbbccbcaebbccbabbadcaebcaababbcaebdaebdbdebceccceeccdecdbaeabadcbeceaaacaeaaeeeeebbdcdcdcdaedcecdbeeaeadcdbebbacbbdbecbcedaeacbadcecccbaaeebaddbdbbeaeecdcdbbbbadbbdbabeebeedeeaabaecbdbbbaaaebeeebbdcbacbcedadbaecabacbaaeeeabdccbaaadebeaacbabbaecebdaeeccacaceccbacdadbebeccdeaeaddcedaceaeaaedecdabdaebbaceedcbcbbcbdccaedcceddabbccecdbaeecedadaaaabaeededdcecbcbbcbadbbbedacacbbbeadbcaddcaddbcbebdaedbaacbcaccbebbbeeaabaceeebdebdddcbcebcbdcbedebbccceedaebadcacbcbbdbeeaaddbcabddcedbbecaaebcbabedaecadabbaecdaebdccdeedacceaddebacbbbddabdaceddcacdeeedadeccdccbdbcbaebbcebabdcceebeacbdbedcdceaaccbcaadddaddabbedeadaebbacddacbdabadedbedbccbabdaecbcbdaeaeddaccceeaeaebcabcbcdededadeadccbbcccadddbddeedeeebeeaababbaceccbbbaecbaabdcbcaccbecaecbcbaecaddedaaedbdbdedaaedcaacaeecebeeadbbceecceaddbebedabdabbeedbdbaedaedaecdaebedadddbdcaedecdbabbdbedbecbaaebeaadebbeedeadeebdeddccaceeabdedbaeeddecacdedccddaddceecddeacbdbceebcaecedaecdadcaeacbeabbabdecbddeeeabeddacdccaeedeaacaabbdaddeedcaabdadbbcccaddedbeeacdabcbbbedecededcbdcddabbbeecdedeeedadbaaeecdedbbdceaacbdbcdabaacebaccabdccaabadbcebcdacccbeabbaaccecccbccbabeebebddadecceadabbeaaedbbaaadbecddbbbbcadbeebceeabddbbadabadcdecdeaaedccdcedebdbcbeccbaaabaddbdcadcbdbedcbeaccceaaabaeabeaaaaebedcbebcebaddadccedcecaeecdddcbcbcddaedceabaaaaaecbdbbdbdbbdceccbadaddbdbaabdcaeaaecbedcbacedbabbdbcbecbbedbbedaecbbcaddcceecacaadaaedabcecaaadbbeabeccbcccddbdeaaebcdbddabbbbbdebabbeadddeebcbaabcddaacbbacdceeabaddeacdddaaaecedeeadaecddbacceecaaaacdaddccedaddeacacbbeaccadacdeceedeabdbebbdbbeaddbabbaeeebccbadaddddaacdeeabdbaaaddaeebabecdbaabdbdbeaeedcecdbdbaedecaeebeedbedbdceaedbcacbdaceaedcebbbdbcdcbbbcdddcddcaaaedaedaaeacdbdbacecdbbacbbddcceadbadabaddadebedaddeeaceaedccebceeceddcbaeddbceeabbbebaadeadabdebbbcbacaddaeececeadeecbaededccedcbbcaebcabebbbaecbeecaebcccededdcaecccbceeccedaaadbcddccdbbcbeebcdadddecaecceebbcddedeeaccceaecdaaababacaacbbdbacedbaeadbcbbabeddccbcbdadacbceccbeedabcabcdecceedceaebdacbbaccbedaeeecceacadaccaeeabeeacedacaaaaacacbcbbdadebbecaaddebdbcbeadebddaddbdbcdccdaeecaaeeaaecbeaaccaacbaeceebbabcccceceebbccdcbbdbceeeadbebcdebbbeeaacabebdbaebbadddeabcbebbaabbceeddaedcdcddccabdcebbbbcaccbaeaebaeeacdbbabeabbdbadcabeabeeaddecabcedbecbaedebbdaacceaaccdcdbbcacadadcaebbbdacdedecbbbebeacbecbaacedcabdeacacbdceccdbcecacbddccabadeaeadceeeaeaeadaddccacbebcbdbeecbdccaebbbbabdadedccbdbceddbbdbbaaaecadbecaedcdbdbacdaddeeecaababecabceaadacdacbbbdedbcdcabadcbcaeddaeedaaeddbadaeececdacdbdbcedecdbecbedbbadcdcbddbceacccdbbdabceacdddeededebcedcaabdececdaecdcbddecaebdbbbdaedcadedeecdceceddeaeaacbcadddcccedcbdacbedbabccaadedcabaccbadabeaeacebecdaebcbaeebbecaaeceddcddebcccdaaccbeeecbbebadadbddaccabcbbbbaadecadccbdecaaedbecddaddacdeaccbbebbeaaeedecdaabebeecbaacdcebaaadecddcbdebcbbdbbddecadbbcbabaaecdddddbbdcdbccdcabceaddcdbcacbdcecadaeabcbdbbeadebdbdeceeadabddcddaaedcccaeabbabecacdbbbecdbccaaedeaebbbcddcdcdcdeaeedacdbccaedeaeceedcadbaeabcbdecedccceadbedeedbbededdbeaaaedaaadeecaaeceeeedaaaaaedaebeccaebaebdababbcaabdcccbacbecadbaeacbbccbdaeddbacddededeaeddbaddceeeecceadaceedcccbccbcabdacdebebdceddceeacadbdccaabeeadeedccdbbabebaaecacebbdddcdbedcecccbcdbddaacaebebacbeecdbdabbeeeecbdcebcdcbbdcbcccbeecaabcebdcaabeacabeabebbdbadcbdeacdeaedbcacaeeaeabdeaaadedcddadabcdccdbeedcdcdebeeabcbaacbbceedcedabeccebeceaddcbbdbebabedbeeaabdbbdbbededccabccbacbdeabbdbbbdbbdabaabeeaedcdaddacbddedebbecdbeeeebcebbacdbdcdaaeabdbbedaaaecedbeabeceaaaddeedbecbcdaeadaccebbbccabeddcadbdabcbdbeedeebeceaddaedbdcaddebcbdddebccbdabbcbeceedcceeaedcbddbdcaaceebbcececcccacdccddaeacabcedcccccedcbbdcedebebbdeebbceeedcddecebdeddeeeccbbaabdccdebeacddddbaeeebeecdabdecbaeabadcdbccecacdcabdabcecdeecdcdddcbeddccccbcdaeecadcaabedaeadcebcecbcadaacdbcadeeadccdbbdecadeabaacabaecbddeddbbdcbbbbdbeacdabaccbdeaaccccdcdeabcacbcadaccbdcbbbaecdcdaecdaacbeabdcabcbcdcebcbbdeebdccddcebdaeadceedccdecaaeecaecdaceacabdccacddcbbcbadbccceeecbecaaaecabeecdbaaaeeadabacbcdcbcedbadcbebdecccdacdcdbcceedbdabeccaebaaeedeaebcddaaabeceddbdcdbceeeddcaccedabdcdbbacddbddeaabcaddcebdddceebbedaddcaecdcebddaabcadeaecbbcadbdeedeeececddebcecbbeaacadcdbcbabdedcbacbcbbabeececcacedaabbecebeedbdccbabecbccecbabebacebdcccaaabbacbaceaeaeaeccbdcddadbaddddcdbaeaccbcdbcabeadbddaccbaddbeaedbaeaceddaccabbaadbddadbdcaabecdbaeeabeccbccdebebeecbcebabaccbeabdeccbcabbaecccbdcaeecccbeaecacadbcabddaeebeebaeeaccddaceebddaacbeeeacceaaaccdbdacaacaaeabeecdebecbedeaadeabecacdddacbcaadeacbcceaaaeaedecddddadacabbbabcdeedceecabbbdeadccbeeaaabddcebcacdebecdaacabbeaeedbcdbdecabbcadaaedbecaecaacaaaeabcaebbbdabeedbbaeabcccaeaeddccdcaccdcabebbebdacadaedcdcdbaaddaebbdbbabdcbebcedbaaddbbbecdcdababaeabedddbeacdbecebdacbeaaeebeeccbedcaeeabeddeeeacdbdbdabbbceabbbceceecacbaeeacbcecdecadaaabeccaedacbacdecbabdeedeccbecbebebbeadebecebddcdcedbcdabaabeabcdbecdbaaeeddeaaaebeddbdbcccaaacdbdeeebdbbbbecbcdcdecbbaceecadcaadbedcabeaedbcdabbadaeeccbcdeaceacdeaecdeecbbdaeacdcadcceeaeacbbddecadbdbdeeaacaccadbaaaacdedbebbecaaeacaceaacadcdedcbebebebdbaecdebbddccebccaecacdeabedcbacbdbcdcdeacdedbededbecbeeabccccdecccabadeddacbbdccdeccccbbdceedcbcaceacadebaeaaaceaedddbaeebabdcdbbdeeeddecaddcdbcdddbcbedacdccecddeebaacdadaadccbdaaeadcceabceaabccbdcaccbdaeaedecdaeddbcbceeeeddcbabccadcccdacebbbcdddebaacbebaabebecabeaebcacaadedbdaeadacceaccbbeeddaaaedebcbacaccccabddeabdcebebececdeecbccbbcadaadbdaddacecebbebabebdcbcaadabcecdeccdbcdbeeecbcbccadbbeccaedbdccbdddddedbbaaabaadbdebecabedaadbeeceeccdeecdcadddeeaeaadbaadabeccdceaceccdcbaedaadbddcacbbcdbacaedabccbbeebbdaebcaaadaebaedccdddbbabbdaedbbddbcbbecdaedbcadcbdbcaeeeaeacdcebbdddeecbeababdeeccaeeabcebccceaacebbabbdbbcbbecabeacddeabaeecaaedaaccbcedcbacdabebaeadcbdeeacdbaedadecaaedadeeecbbadbeeeeaebecbdeaaedccebadbcbdaeabacacebabcdcdbddccddcabadbdbcebabbbddddeaabecebebebacebcacdbabeaeccedebcaaaadedaadeebeedccdedadbabeabaaabeecdcebeeabcababdcacecbcedbcabcadecbdaecdabbcdcabecbabeaceebbbbeadcecaccbababaeabbbddbbeccebecbebdaaededeaedbdadcbaadbadbeeeeecaccbecbecdbedccdadeeaedbebdbadedecdeecccbedebaeaabbebbebdebaeceadadbccbbbcacdaadecbadbbcdacdadabaddaadbdbabbceeddbbeaedeeaceeebabeaeebbeaebbaddcaabddedeacabbabaabbebdbdddaabbbbdceccdecaaedeabcddbdecdaaadaeeabdaddeedbecdbaabbadbbebababaecccdbbbcedaedaeaccbdecbecceabaddedbebababddeecdeedaeeebbaaadbebdaebbebdabecbedcbaadcbaeeaabdbceedeadcbdbcdbddbdaebebcaeeabdaeecccbbeceedbcddadcbadeaaeadcceaddbaadaacbcadeddeaeadcbdcaaeaeaedddeddbbdebbdeaaddccdbddbbbeebaaacabacbebcdbcebecdebaeaebdeeddaecaeabbeddedcbdccbeacacacadadeedadadddeaadbddcebeeebdeaddccacaccedddddddedbebbcecdceeabdbcccdbdceedcbcddbbedebcdaecabcadedcecabeeeddddbbeecbbaedbceedbbbeedcebbeadcdeaebbeaedbbeedcceeeddecdcaceadbcaceecebdccbbbabbbbeaedcadcedeecaadcdeeeedebecbaaeaceedeebabbcedcaedcaedcacdaadcecdbbbeccdbacdbacedbaeabecbbdadabaabdaceddbdaedabeddcdbbbcddaaddcccdbbccacaccccadaaebccceedbccecedbbdaccdecbeceaebbebebabaeedeaedaacadbaadeeeeaedbbaccbaadaeeaacaaceecccedabbdeadbacabeeecebbcedbdeecbbdbbdaceadaaddeddadbdbccdeaadcaabeceeeeabccecdceeabdcbabdcbcedbeabebaccddbbcdeebebccaeecaebcdcacadcadbecbbadcaabeaabcaeaecbcadeadcbabdbceabeadccecedbeccdbddbbeacaaddeecebddbbcdabadbdbdaaaceeccaecddccebccebdebcccbdbebedbdeeebaadaddaceadeacedeaccecedaedeeacedabbdbeeebcedaabaabaacacbebdadeebcacacceceadeebeaeebeacdacaeceebebbbceeaeadcaacccaedeadccacebcedeecbabadcdcebdcbbcdcebcdbbcaadabcbeabdecbbacdeeaaddeddecdcceaececebecbedcbeddcdbdcbccbeedabecceceeacdbedecbdeaabebacaadbbadbbadacbcedbbeabbbbcedbbedecbdcadcaaebdadccdbaebcbebcedbbdacccaccababdbdcbadcbeeaeccacaebcaeaeaecdeedcaadbdcadccaabaeeeecebaadcbeccbaadcdaaacbeccdcbeaadbadaddbddaabcacdddacddeedbaabaeebccacbeeacbcbedaedcbecacaededdbaeeccddebabebdbaaabecaadeaabceedbeabbebbeaaadcdabecbbdeeebaaceabbaebbbedceaddbcbbaadabcdedbceccdedccdacaababdaedbacedcaaaebdccdcadbddeadebdceaaccbbdaebebaddcbcaeabcbacbbcecadcaadddceedbcdcceacbdbccbcbedeeabdbbeaebabeadceaaacebdecddbbeaaddeddccaeccebeacabcdddaaeceedaccceeedabdbabdadbeddeeecacabdbccaeabeccbebecebeaebdacaddcbdddecbbcdcbbcccabedbcccabbdbeeacdadccbccdaddedddebcdceddceeeebbecbcaaccabbaadccacbeeeeddabbceadedbbbeadeeddedacaaebababdabcddadecdbdededceeeecddecbeeaccbacdaebdbbedccbcbeddbaababecaaabdaccecacaceaceabbbccbdeacaaeeabddaccebeeaceeaddcbddddaadaebcbbebaecbdceeededadadbcceecdbabbaedbaedadeedebaaeaadbeeedbdaddbbcacbadacacbebeeebceabdcdbbacaeeaaacbdeadbbcddaccbdeedcbccccbebdaaeccadacebaccaaccbcdaddddcdccdccbedddaecedcaebadabaaccbbddebebebecdaddccbeddeadcdcaaeeecdecbabbdeaecbacbeaaacdcabceebbbcadeacdebcebaeddceaaaeaeccdabbaedbddedbbbcbedaddeedbbeadcdbedaddbcbddeddaecdcdcdacccbecbdaccdabedcceebeceabdddeadeeacaededdbbaadbdabebcdbbccccdabadcbccaeabebcebbbacdbcaacbacbeccddbcaacccaaabeaccbbeaadeaacbcbdcdbbeceebddceceaacdbcbeddcaaaeaaceddccbcadcbabecbdccacbadeedacbadbbabbaadeebaedbbeaabbaeeaacedeaeeaeaebdbdddcacbababadbddadaccceaedecbcebcedadcccdcabdeddbcabceecbddaacdecebbacbccdbeddcbcdbabebaccedcbaaedaaddedccabdeabbaeaaeaeeeaeebddddcbdecababcceaeaebcbcbcadcccdcbcebdabbdcbcccadedeabecbcdbabecedcbbeeebcaeadaeceeaaacceceddadddcbdebbeeddeecadaacdcccbaeabdcddeaeaaabbceeebcddddedaadbedebbeecccbbedeaeaabebecceaeeccbdcdaacbbceababdbdcacbacacccdbbbeceecadbceebeadbcedaaddebbabacedddbdddcadeedadeeebedccccaaebcdcdbecabccdbeeedaaaaecbdadcebdbdebdacecdcdabaceadeedabdbcbebebbddedcbbababccabdbecabbbaddabcdddebbceeaaacdeceaaedaabcbcceebebdacddaaeceaaedadceacebedbacacceeadeacabbcbcbeccacdcdbedeedbbddcaeaeeeccabccddabbbecedadcdddcedacecaadceceaacdcbcaddbdcbeeadcacbebdeacbdcabeaecbecddebebbbadcbcadcdedbcbabaceababeedecbcebccecacdaaadbdbcceebceaaccbedbeebdcdddbcbbebbbeecbcbdcddbccaaaacbaadcbdeacbbbbcedbdadbdeaddcadcaedaccedccbcdaaacaadadaeeadaeceeecbdbacaeadecdebddcaacbddaccdadbcaddddccecbddbcdbacbeacacacadcbccecaddebbecbbdbccdebeecdcebbaedaeeeabbbccdaaeadeeeeaabccdabcebbaabdbddaaebcbddcdcbadbbbadbaaeddcdacadbbeabeeceebaedbcbdbdaaaeaaadbedbbaecddcdaedbbdcbdcecdaaeaabbdcbebacaacbadbbdbaeaebdacbdcabbeadaabdaeaecddbbcccceeaebecbdcceebcdedbcbeadbaeecdddacabbabbbadbbaebeedadedcdbaecdedabedaecbbecbedddebcaebbccbbdaadddabccadadcebedcdebacecebaecaedaceaeedbdbceadacbdbbebedabadbdcebcacacaeabbbacadccaaecdacacbcdcaacedeadbcadbcedeceeabdaaabaeadececaabcaaeabcbcebaebedcbebcdbdbbaebccbeedacbedcdbbeeedcbcbbdaaaadacebcbcbeeccddcddedeaeabdebcedebecaadcacaceacebecddbecbeeaddddccbbbbbdddcecbceeabaacbdcecccbaddadeabbdccceacbabedcebedccedecdaadabaeddbdabaeaeddcacadbadcedccaaecededaadbdbdaccaadbdbcabdeabaabcbcacdbdcdcaaecdbacaebcccabccdbecdbdadbddadcbbebceaedbebdecaccedecbabcdcababeaeeecabdbdcdbaacebdbaaaaedbacbebbcdabccccbbebbbcbdcebcbaddabbeccdcdcbdddecaabcebaacbeadbceccbecbcccdacdabacaeecabcaccacbccbddbcaaedcbddbcdcdadbbaeaabaaecbbdadebeedbcddbddcbaebabccaabceaaacbbdaacececdeebedbbbdbeecacbceaaacbdebaddcdecbbcdebbcadcbeededacbecedbcbeddeaceeebbdcadeabecbdeddaeabbbbabaabedccebddeddeacacedccadccbdacdbeacddddebaceedceedcaaaeabceeeecccbaccbaaecdbdcbadeccebedbdbcebdddaaccaedbadddbbdebacaccadbabdceaceeaaaabcdbdeddaaeaaebaecabaccbcdecaddeecabdabdabbcbddabdeaaeadaadabededbcdcdbdeeadcecebecabcbabcccbdcacdadabceebbdeabcdecccaaaebeebeabaebbeabaccccdbaacaaeeabbabedeceecdabececadabdedbceaecbcccdaeaccbaeabbbeecebbbdbdaeddbadececcedabeebdabcbdeebccddedcdcadababdeadbededbbcdcaeaabbcddedacddbebdcaedbcaeecaedaccadeeeccdabbdcbccdbeeeadbbdedcbebeaceebbcebebcacbacdcedebacccdaedaeaceeccacdeecbcbcbdbadcecbadcdbdbeebaccbcecbaaabbcecbbbdccacadcdceecbadacaeccbbeaadacabdebceebdddedaaeabbccbabeededdedcabbacebcaaebdbceabcbadbbbbcdaddabababbaadaabccdddcdccddadbcdddbebaeabceceeeccebdaaeeaaddcdcbbcadececacdddbeaeceacbcaacbbcdaecabdbcdbcbeddedcceecbdeabccacbbdadacaebbddbdccecdedaeadcacaccbcccccbbadabcbccddbdeedadeacdcaddbdaeeceadbcbeaedcbaddceecadcaeadebcebcddabdedbcdddbdeabddceebbcdcdaabaadcbecabbaabacddbbbdbdceeaacdbdbcdbecdddbbedeeeebbeebaaddecacebabedbecaeebaceddeacabddceeacdeaddbbdadbecabbdcdaababcbcbccddadcededccdaeadedbdeeedbdcbebcdaeaebbddeeadaaeedebbaabededacabaacbedacacddceebdaabdcacdebdadbaabecdeeebbdebbbcdbacadacaabceeeedcaacbcedbdeddcbdeceedbedbbbbcbacaeeebebdeaeaacedeebedbaadcedcaabbebccdedebbcaeacdcdeacdbcdeccdcccccecabaeeeabeeeaedceeccebdaaccbccebeabadaabddedbdedaaaeabbcaacedceaaececebaabeeeadcaeebdaedabbebdbdeebcbedacbadbdcccbcdabbecbddeeabbbbbaeaaadeaccadeddccbbcdcaaceaeddcdebcdeddccbcddabaabaebcbcaabceeceedebdbdccadacaecddeaaadddacbbdcadeadbbadecccaebdabbbdeecedbbbccbcbcbbcadabeecdbacceebcccabcadbaebacebddeaaeacaddadcdedaebaedccabaabdaeecebdebaaaccdaacdcecddddddeabcdecedbddaeecdeeabeacccdecbdaecbcaebcbcabaaccbcedcaabcdcaeedcdecebbccdbaecbeddbabdeebdbadcabdbbbeadcaebcabdbdabbcbcdecacdeececbabadadabbbbedebaadebabedbcdbeaeeaaddebaedabacdceadaddcacdadabaaeecbdabdecccedacaebdecbbaecbbdecacdabbcbadbaeaadeebdbcbeecdcbcadcceeeebceddebceaeabccccacaecdebecbabbebaadaecbecdabdacdbdaddabddeeedcdbbaeccddceeceadabceccadddbbaaedbeaeeddaedbbdcebadcecdeabcbbaedebaebacddeaedaccabceadabaeabdcddbedbddeaacbeccddadeaceadcaccbdabcebcaecbccdaecadebbadcbdbeaebeacebdbccadccbbacadeedcceddbeeedadadeecdacaceaccbaedacbeeebccabbbeaeadbddccecaaeedcbcaaadcadbbaeebeddcecebdddddedbdaddeaeebdcccabaabaabdbebabbcccdaedbcedecddadebaeeebdacdbdbbdeaabeeaedbaceedddbdbadadddaedeedaacbeebbbadadccbccedbabebcacecccdabbaccabcbbceedacaeeeeadaacedededccbcbdebcedccebcaeeaedcebcdeaeebcaeeaececddcebebaaaaaecdedbdeebbaddbbdaedccabdbaccdeaaeedeeddadccddcbacdaeacdcebccabbbcaebecabedeeaedeecdcadededceedbceaeecbacbebaeaddadbdcdadcacddaabaddbaeaeceaccccbddaebbaddbbcdebacbbbdbbabeccbdbdbdccecbcceebededacbbbabcbbcbccaceabeacedaccdebcddbbeacaebcdacbbdcbccdebcabecbaebdadaeedbcbadecbbecdccecacbbacddccdbadcbdcdcdaeaccabacbacecaedcadadcbaaeaaaeeeabbdcbaeaddbbdabcdeacbcdaccabdacaeebbadeceadbebcaadaeacccccadbbdebedbabadeabeccabcbdceaaceccababeeaaccbaeebebcaedecdbecdacdaaceedcddaabbdaebceabacbdacceaecbbeeaaebebddecbcacadccceabbcdbcccbbeabdaecbcbebecbabccaebbebdeddcddcbbcddbcabdacabcbccadcacadabecedcbeeeedcdddbdcaabbeedcbddedcbdcdeabbeaebacabecdcdeacdbcbecdeecbbddaeccdbabbebcbcbddeecabccceeccdbcddebacddadedaeddbbbabadabecaaddecbedaaccaacddcbcdebaecadeaaecccdaaabdebcaddacdabeabbdddadbecadacebddbabdbaabaaaceaeeabeacbabdbcbbeddadbacabdbdbcbebaebbdddeeeaaaacbedcaaddcebbececacebccdcebeeacdbcdebaccdebbecddbecbceaaedacccbdccaccbaadaccbceaeedbcdeacdbddbdaccbcbdcbecccceebbaddbcadceceaabeadceeedeebbcacbcbebcdcdaacbdebaaadeddeeeedbcdcaeddaaecbcdacdaadbebbabeececcacebeddaaeedbeadbdaeebaaedebdebacbceeccbcedadeedabcadaddeecbebbacbcabaeabdedbddcddaeabceceaeaaddaadcbbddcccabccedbaadeebeaedddedddedecddbeaacbddcbecebdeabebebbbbbdeecacdcbcaebbcbbaedbebccbadcdceacddeaabbbaddbeaabbbdabdaeebedaedebcbaabbabbddbdcccdccaaeeedbceeececbeebcbceaccdadaeaaadbadadaabdeaaaeadbeeebaeebaaaedbbbdbadadcddacdacaadcbedcaccdeccacbeaadedebcbaeeccccacddddccedddccdbcabaacdcbcceebeabbdbaebebccdadaecaacbdbdbcebeddadacebabbbbeeaacdabdbdccedeeaeedecdddeabcbbddbcedbcdceeaedddbbbadcacbabcdbdaeabbdaeecacadebcbceedabebbaceaeeabcaaeabbbbcdedaaeeeeabadedbedcedbdcebbacadcbaeaaaededdeeccedbbcedcaeaccaccbbbdedcecbdccdcbacdbacdcdaccaacdcbeebadbdebcbdadccbdadabbebbeaacaaeeedeebbdcaccebdeeccaeeaebecdcedbebeaddbccaccbeebcddcceaeeacceeccbaacebbacceaadadcedacedbadbcddcaaeeaeaeadaaeebedbdcdcaeccedadeceacbeddeeaaecabbeeedaecabbcccebcccbaccbeebcdecaebabdcceadeddeedcbbddaccababcdddbadbebceabedaedeecbdccbaebdecaecdaeeacebebcbbccabcbdaebdaabcbadbacddbcbddedcdeebcccbeccdeceaddeceeaaecacbccbbadecabcaacddbdcadbddebcdbbeeabbcccebdebbdbcabacabdaacbebcabbcaebdadcbebcaccdccccaebebbeabeceabcedebdabaceeeccaeccababbecacadaaceccccaccddadddeaaaebecddeeaabadacdaccadedbadedaabddbedebccdbebcceeeaaecdececcccdbcacebddbedcbdeacbbeaedeebdbadcadaecdabeeccaeeceacbbcdbcacbcbeeccceddaabcbecddacccdabccaebdaaaedbbbeccdcedcbeadaaeebdcaadaaabaaebeebebdabcadaecbdacbdabdacbbccabaeddaebceecdcabdbaeadababebdebaaddadccacaabcadbdacddbceadeadacaadadececbbbdcccdbebbcadacacaadaebceadcacceacaccaaaadaaedabecebacddccdddcddceccdadeaacdcaadbdabbeccedeecdaebabaedaaadddcabceacbabcbcdabcbcbddcadbedbccaeccededddedcddbdbbcceaadcdbdaceaecbaacdbcaecdcabdcbebdaabdeabaaedeacaeabdaecececdbedccedcdeedeacedcbdbcbebcbdebecbbaabacbeadbcabedebacabadadcbadeeebdbdabccdebeaaeeadebbcedaaebededdcbddbadcbacacabceacecccdcdaccaabaeddcdadaeedbdeebcabecbbbebeddeeaceaebebaadbabcddddcccbbbbdcdeddbacbaadbdaedcedddccdaadabcedbcbadbbaeebdaacdcabbedbaaaeceabddeededeedebaeeebaeddadccaeedabeeeadabbbdbeecabeadeeececbeadcdbdbacbadaecceeeeabcdeedbccacbebdbdcedebdebcccbccebdcdbedebdebccedbebaaddebccccedeadeacbaceacecaecdedcabddaabeecadbcdeeccccddcaecbeadbbeadeeeaaeecabadedacaadcabeddadeecddceebdcdeecaadcbbaaadbcaacaeebbcadeaaadaeadeadadbccbedcbeadcbeceacdbdaceeacbcacbaaaeebadcaebcbcebcdabceececadaeaabaebabbedbdadbecbaeacadebabedaacbadaceabeabcdeaabbabaecdbebdcdcacccadcaedbdedbbcbebbcabbdaebeccbcccceeaccebddcaeccdeaecdcddeceabbdbebadcecdaeeadbbeccecdcdcececbdeacbacccdaededaccacacccaadcaacececabbdbcadaedbbcbccbececebedeeccebcacdecbabbeaabcdbabadecbdadeebbacdcdebbcebabedebdcdddbaedbbaeebdbcebcdebccaeddcdabdbaacaecadebceabdebaacbbcdddbdceaddecdcdcebddacbebaabbbdcebaeaebcdaeeeedbcdcbecabeaeeecbccdbbbbbeeddddedbeeccbcabbdadcbdcbdcebbccaaccbcddcadbbdeebbcaaddeeddbbebcbdaddddaecbbedecbbadaabbbeeeaaadebaacbaccaaecbebdaeeddbcaccdcbdbdaaaecceadccbebdbecbbdabaecddadedaeadadbdadceddcaecaeebedbdbeebbddbcbddaceceddbddddcebdcbbaaedbddbededdbdcdabbecabebcecdcecceebeaadecbbdbaaeedaeebacdaaadaabddcceebaedecacbcbddebabceadbddbcbebbcacaacddbbdbacadeedbceeddbaddcaacaeebdeabcbcabddbecbdccdebdbaabccceddacbdcbcbaddcdabcbbccaacbebeaeeceddcccbaaedbabceddbaebceccbcbdbaecccaccccecebddbeecbcecdadcaebdaddcbeebaacbbdbddecdceacbeecacaeadebaebcadceebbccaeebacdcabccbdceabadedadbbdaecededebbaccbaacdabcddadbdccddcabccbeaaabaeebeabdcbdeadbbcaccadcdbddadaabebabcddbebcaeebccdbacbbedadabcaeaeabeccdecccccacdbccbbdeceeceabcbeacedbecaadbcdaebbadccabdebbcccdabcedcdbedcbcdabeeaaeaebbdcaceddcacbedcdbddaddacccdbaaeabceccbcbccbcabcbcaaedadbdabbdaeebeeceedccaeacbeccbdcbbeadabdaeadbaabeeecadccbeddaabedccecbeccbaacbcbedbdbbabedaacaaaeeabaeebbccaecbcbbcdeeceaeeedaedbeedaabbabddcacbacebcebbccedcacacaaaddcbeedecbaababbabedbcbddcccaadabddadedadeebaedcecadddabbaeecaaaaacdbddaeaaacebdeeebcdcbdcabeaaaaeadedbecbbbcebcdbabbebccbcacedcedbdcdaccbacedadaeeaaddbbaeabcaeadbecddcadddaaabaeeeeabedbaeeceabcdeebdceccacecdedeadadeccebedcbdabadbeccbdbcebddcececebbbcbebccacaaccaeeedbdbbbcebcceccabbeeaacbaedbeddabeedeacaabaccdeaedecbeebdabddeaccadabdaaebbccebddaceadecedecedddabebcdcbecbaadbaebdaedbaccbdaaeeedcbcdadcbbdbcdcbcabdecdadadabdcdeeaaeebebcecedcceaeeacbeebadaecabedeebedebeaeacbceeedebddeedbbadceabecbaaabeedeaedacdaceccebaadeaaaccecdededeabcaaeccceaaeeceaaaedadbddeddcaeebadcabeecccecebcadbaadccaaebcddedbbbbeacaeecaabceacdeacbebeaccebeceecaeceeaecedeeccecceeeeeeabbbbdebaadbacbabecdddebeceabccedceedbeddedcbececbcbeacdecdabedbdbceacdbccbddbdaedcbecdbeddcdababeabdedebbebebdaedabebaaacbcbedeeaaedecaeeaaaedeedecdcaacceddbdcbceaaeeeeedabdecdccadeaabceceabbabacddbccdaabdbaeadedbdbeabbbebdbebbdebcaeedecadbbecdccabceaebdcdababddabeedcdcbbecbcabbbccadbddceabaeaacdaeeacecdeabdaedbabcdabeaaaeedbaadedbdedaecdcbcdeebbeeeedccccdbabcedadbbacddeeedbaaeedeedacecccbcabeedcadbabcbdebaaaeaeadbaabdcabccaebdbadeacceaaeadaddbdaedebaacebdeaceddebbddddbbdaadeaceaabbbbcdbcaeedcaeecabcddacceecdcbecdddaedcbacdaadeedbcecaeaccbceaeeabeccdeddddacaeadbadbdebbdaeaaecaddacadbabbbcecbccbaaacddcccbddcdeccdbccdabbebacdcbccacbaecbcaedabeedddccbeebbaadbecdadaaeccbadedbdadbceebddeeceaeebddbbabecedebbbacdaeaccaeaabccedddccaacebbedebabdcbcdbbeccaeebedcdccaedcabdeacbeaadaacccecceaaaabeaedcccdaddddbcbcadacaacbecbdccbaedabacadcaccccccaebaeccacbbdbebcdecccceedebebadacacbddecdebeadceadcdcbbdaceadadececabebcceaecadabcebcdebeabcbaabdaeabeecccbcadabbdedbedbddcebaecadbddcbdcbbbaebbdebdcbbcdcccdeccacdeeccccedaddcadbeecdddeadbcbdbcabcdbdeaedbbaecceebdcbbdadbeaedaabaecdbcaaebbccaebaebbebdeeeededcbcabecdbccdcaedbcddadceeacdadbdccabceabbeadabaacaeadcaeebaeebbceccededbebcaaccaceddcddcbaebccdcecdcbcebbdccedcecbeecebbdbacaeddebbedbbbdeeaaaacacdcedadecdcbeedaaacadeaccbacecdbadadbaaacaaccdecebcbdeededddcecbcbcbaeddeedbaceebabbddacddebebbdaebdbbbdbaedebacccdecebeeddccaecccebdbccbceabcbcbeaeecdcbdaadeaeededcdcaceaaaaedecbdcebeedadabccdadecccacceeeaeecbbddebaeddbddecdcacabbdbaebdbdabcbedecadecceeaabbbddbcecdaedbaddeacdaedabebbcdbeaaadbdeaecbdbadddbecbacaaabacebaecabbeedcdedcdeedddbbaadadcccbdebacdaadadaceabdaaabcadbcbceeaeebeadbebedebebbbeaadabaacdedadebccbadbdcebedbbbdbdbcbccbdaecdedadaccabceeecbdeaeecaeadbababdbccbcccdbbbcdabbdececcaddeeebbcdabdacceadabeaaeaabbceeecbadcdaddbecbcddaadbdaacebbeccaeeeedaeedcdaaadababadbbeeecdcdbeabdbaaebcbccdaeabdcaabbcaddbecdccdabcdbccdebcbdddedaddcbacecddeaedbcaddadeeddbbceebdcdeabaaeebddbadbaaedaebaeaedccacbbcbbbabbbcbabecbbdeeaaacbaeeabcaeccebbeedcdccbcecbbdacdabdcabccdabcdbeccbbcdadebcceeadbebbaebaadbcadbcdadedeecaacadeaabbcceeaeacabdeedaeedabecaeabdcadaebbbbedebdcdcdeccbbacdbbcabedbeedaebbcbabdcbceacaaeeadabeaddaeddabcbeabcccddcaeaeadaeaecadcabbeaadaddebceaaeecbccdaadebcecacdadbaceedabebecdceebaebbcacbbebbccbceececdbcbbdbdccceaaddbbeeeaaedecdcdecdbeddacabdecdbbebddeabaacaedaabbdbdcacbdadcbbbdacbedeeadaabaceddbaaeaeadbedeadeddccadceadedadbddedabcdcaabadcaecceeaabedcdaacedcbbbeadbabdaeacacededeadabbcbcddcbdbeabeedebacdccdbcddbcbbddccdcdecddedbbbeeaecebbbbcabdebeddcaccabcaeadbcbaeedcebebdaebaedaaabdedaadeeecdebeaecdddbeeabbabaaceaadbeaecbeeacdeacecddedacbdaacbbacbbcaddebdbcdadabcbdabdeaeccacbebbebcebecabbdaaadadcaedbdedbceebddcbcbbecccceedbaadaacdcdeaaecdbcbdaaabebccebddeddeeecadeebccecdededaaecccdbbdddaeeadccebabbaaedeebdaeceddccedebbaacaacdcaacbcacadddbdcdcdabeedcccbccacbbebaccdeacbadaebbcaaaacbaebbbaaaebdaecbacdbaecbbeecdbddaeeddcbcabeceeedbcebbbdaeedccacabaadabdadeacdbadabdebcbaaabdcaddacceedbcbbbeadbdaebbbababdcdbdcaaaecadeeabdccccceedaacbbdcabdeedaabeaeaeaecceccaaccaedbcecddcadbebeadbebbdbddddadaeadeeccdbeebeecbbebabaedcceacbeddcdcaaeceeaeacdaabdaceeeceedbbeecaeeaebcdbeedaaddcceeccdeacaebedeaebdbddcdeccaeadcbeaabdbbeddccebebaebcabaeecbedbaaadabcbaedecaebaeaccdcaedbbbbcbebcddadddceeeebeccbabdedbeddacacbebadadbbbeedddccdadcbbadddebbbeeaaadcbaacabbdcebeddacbdebcebaabbcaacbebccacbcdceaadbaecedbcabbcebaeaccedacbdabbecaebdbbaaccbeaaabdcaaccabbceaebadeedccbcbbacadadbddddbaadaadcbdceeeeceeeebaddadbaacbaabbeddaceabcebeddccccdcaabdcdddecbbbcecadeaacacdacbedccdceebbcccbcbaabebaacebccdcaeeeadbcdebcbedbcaeeccbcedbaeeeacdcceebacbdbddeddcbceaebcaaebeaeadceeccaebbaccbbddbadbacadbbddaaebdeaaadbecacaceabeddacedeeaaeeaeeebccbeeebdbdcbcaacbbcedecaecebcbeeadbcedbdbdbacbdaadaceaaeecdcbbacddabaebbccdcabbdbdcbaadabecacbbdecdccdbbdddaabcbedddcbbbaeeeebccacbcbedeecabecedeebdeecdeecbaebceabdcabcedcaabdceaaaceeebdceeccddbeaadcdedbcbdbceebbaccbbceedddebcbbabbdbbdcaadaddbdabaeacadcdcaedadeadabceeeeddebcadbeeeeddcabdedabdcbcccdcaebeacdceacdadaeababcabadceacbebbbebaedaeedbcbbacbecccdaaecccdbcabbcddbedcbeacdddeccdeadedabecbdccacabebabbbdebcabbecbbdedbaaddcccbcacaceecedcdaccbaedeaddeececaddabcbbdeaeabadcaacccbecebbecbbcbddeeeabbeeaebabcbedaabdcbcbaeeecacdcddabdeaccdeaceaebedbaeccceaecadcabacaebebecaccecaeadccdbabcbbdadeaaaacebcdaccbdaedaabcbdecdedccaccabaebddcadcdadebebeaddccbadbdcdceddabddaeeaddcaadcabcabccdeaaceeccdddebcdddcaccbeeabdbdeaaadbaccdbbcabccccbabbdedabdeaedacaadecebddeddeededbddcbcbaccbeaccddbedbdddebbddabbdaddecdebcaeeaeddacbaeeebecebcdabeedeacbaeacadbbeddbbedcdedecbbdbecdbdbcbbcbeeadbccaccbeebbbeeccacbccceaabaaeaebcdacbaaaacdeadcadebacceeeceaaaedcccabeedbcaabcdceccaadceebedaddcbdeaaabbddaccadcabeedbaadadcacbccdbceecabebecbeebdadbaaaebacdacadbbeeacabedbaaaeecdaecaadebcbeeadcedabcccbacbdabccdbdcbcaaaadbdcdbaadbdedcceaeeabdaabcaebbdeabbbbadcabeadededdbcbacaacaeebeeaaedbcaebadceaeccacacbebeceebaaabcedcdbbebabeecdcaecedbbedbddedcbdbeecaeadcadaaebeaccecebbbbededdcbdbdedbabcadabececacaceacccaddaddacbbceebdadacceababcdbddaedcbddcbbbaeccdbdadcbbbcbbbabbdceeebeacbebabdaddaeaeadbbbdaebaabcadccaaceadadbdbeedcbdcbdccbbcbebbbeadbcdcddaccddaccedceaecccdbdeaacedcbdccaeadbbecdedcdbbabbbbbdaddccadbaaddbdcbedbeecebddecacceeedbabbeaddcdaedaedaedeeaddabecebceaeccdaaadcdecacdcdeeecbacdedaacabbeeedebcbdaddacececbcbceadeeedebadcbdebeeaadaeceebbeedaeeacaccacdedcbabbbecdaaebaabbebccdaecdaceecaacecebbbeadaddcdecbaddbccaabdeedcdbbcaebeddbeeeaabbccceeeadacbedaabcebbebceedebbeaccdabaecbcdecaccabdcdcaaecaaaecdcedebaaeaebadcdcbdbbdeddddacaebebdacbcddbbdeacbabcaddeeecbbccdeecaaaeedaaedebeccbcdabaedabebdaacadbbbabbabaaeedcdaaabceadeeaacadcdecdeecaedebaaeecaccceeecbdbdeebeceaeeceebeddcdaaedeeaddaecaecacdcdccdbaabacdccdeaacccabadbcdececbbdcbcaeddaddedebedbdbcacbeeaeabaeeebbdabdabedeeebbcdadebbdebcbbddedcebdccbdaeddaebedecddaeeeddbdbecedebaecaabeddaedecbcceeebceeeddecabadcebceedbdcdbdeedccdeeccdebcceaadacaecadaeeccbedbbdcbadbdceaeeddcaaebeccbeabaeedebcbbebcbcbeeeaeeaedeedbbeacacedbeaaacbbdbecdaecdebdebddcdaaccceedacdedaaaacceebbebadbbcabccabbcbbeecddedeecdaaccecbedbbcccebaebecdaccbbadebecebbcbbabacadeddabaacbcaceaabbecebebedcdecdedbadedadcddedddeddadbcbbedebdedadbbbdecacdaeebbceceeaebbdccbbdceccceacbaeaacbaabcdaabecbadbdecabdaebaccbdebddeaecccbaebaeedbddbbbbcbabedcbbbdeeceebbeaadadacabbebcccabeabaacedeaaacdeeecdbbdceeddbabbdeacecbbcbdbeccecebbbacebeddddbeceedbabacaabbcbeccdbeeeabeaecdeedbbdbbcddcabddaeaeedcceeddcebcbcdacadcbdbdecbbeacdeddccbeaaadcedeecddbadccadecdddedaeacaadabdddecaddaaebccedeeaedcaedeeccaaabbceabaeecbccaedddeeddbaaecebdebaddadecedadbcdcdcdcaeaebcbbacbbeadeabbeeeccededbdecdaecccaeebdaddddadbbbceadcbceaeeedcaccdabbaaccdbcaecbababdbdcdeaeebaeeeaceceebdbddeccaacdedccebacbdddebdebbdaaadccddeeedbadaabaacbacddbbeeeecbaeeabecdcdccaebeebdbedeedeeeebdeadbcbdecbdebeedcccdecbdbceeeddaebaadbeaccdbcbbcccebccdecbedbeaadeaeeaadecabceebeedcccbacdcabaddeeadbcddeababceecbeaecaabbadccedeccdeeeeaaedaeecdeeeacddacebbbeeaacebadeaceabeaabcabedccebdaedbdbaadbbdaeecbabdbbbdbdbbbddbedaaeabebceeacbcedbaeeaacaedbddaadcaecdcadaeeebbddcacedeabbcccdcbbcdbbdacdcbbcadcabaededddbcdacccbaeceeccaeabdddeadbeceeabdccbdaebcaedaaccacdbeaeaaeaabdecabcadbddccbccadacbeeaabbebddacbdcccbcebdcbcdbcbebaeecdbcaebcbeedddedbbacabcecccadcecddecceacdbaeabbccebbbeebcebddaeadaeeebeeeedbaeeedcabeebaaccabdccbacaebadbbdeceeedaababbdbdebacadaaabedceccbbbbcbaadedccbcdadeaacebbbaaedeceddbacdbbbadccdcedacdedbccbbaebdcddcadecacbacadabaebcecaadedcbbbeebbaddbbdcdbeecbaddbaccdabccabcceacaaeadedbbbdbedeacbbadaeabdaaacbebcebaaadceccadecdbccdbeddabeedecbbbadeebaaababbeacebcaadbdeecccebededbdeabcbdbcecabbbecacaecabaedacbceacbabebcaceacabbadecdeeccecebdcdacbebdcabbcccdeeacabaeacaacabdcdcaedeecacdceaeccaecddaeeebddeddbedeacacabbddecbeceeedacbedbaeebeacbadeadcaaecbababecbecaceebeeaaddcdbbbcdabcdeebbcaedebeecdbccadddadccdeceabbaadbcacacbbeddadcdaedbeddbbcdbdebebcdaecabdcaeecaabdccddbeeebbedadceccddbdcbaabdbeadccbabddecccecdbcdacbbaacdccdedabccbeaabbbebbdbedbacbddbcadeeaddcecbbccbceaaaaeeadecbdacdaceeebbbddacbbebbedccdacdceccbccbeadcbbdbcecdbeeaceceddeceaccaaaceecddbaddaceccecadcacdbcbdbecbcedcdcabbbadcdcabcaabebcbececcabeabdbbbbcaedacbbeccbeaddedbcbaccbecbbedadcbabddbdaebcabeedddacacbbbbedccaabcdebcbdbcedcaddeaecebebeadeaacdecdcacecbaaebdcbeecacddbeadbebadaedcebaaacdbaaaddeedcecaebcaeeaddcbcabcbbdaaebddcdadaedeceadaeaebbccbbdbbaaaeaabdbdcbceadcedcbaacbddceeeaeccceaebcaeeedcbccdcceabeadaddcaebdcadbbcdaaeacbaedaedbbbdabddcabbcddaccdcaaaadecbcaaaeddbdecdaacaceaaaccacaccdbdaebeabbaedaeadaddbeddeacdaacbaeadeabcaadcacaaeddaeacdeabaedcccccaaccadcdbbaecacbdaaeaeedeaaddacddaaebcddddecdeddddedddebbadadebecaeadcbadabdbabedbdaaeeebadcabcabbdcdcceeabbcbbcbebdbaaaaebcbdbbbbdbeebcabdabbaebdddccdccdcdeaecebdbcbbcdcdebeeddbbcddaaceadcbdccaaaeaebecbddbdadcbeebcaeceedbcabcabecccdacaabaddaecddebdcabeabcecabccadbcdcdcbecbddddbddedebcabeaccadebedabddeecdddddccdbbeaadedebeaaadeebcdaeadcaeabdaeacebcabbccccebdcdadadaabceacdbdeaaaadcadecdbdceeccbdbececcacbaccbdaabcedeaddecededebeddaabdebbacaccdabcedeadabcebbcaddeeeabceeebbdabeaedcbdabdcbdaabdddecabdaecdeeccdececdbbddedbdcebdcdcbddbbddbdeaaacbcabdedcaecabeadeebccaccababbeaecbaedbabaedbaaccacadabddaadcaebcdeeaccaebecbeaaacddaedcdcbadeadabbacecdbcdaddaddddcdedebeaebeceacaccacddadcecaaacadadedccdeeacacbaebddaaaaeaeabaebcaebbeaaeccbceeeaedaedaacdcaeeadbecbabaebdcbcddebedcdbaebecbeceacbdeaaacdabdaecdccdaedabbabadbcbaeebbdcdccaaebcbdcecbccbeebdcebbcdcebedddbeeceddeeacdbdbaccccdecaadddaddcbabddaacceacbeadebaeeecabaeeeecabdccdacdbdbbcebbeceeeaedeaaaabacbeebaabeabaadeedeebdccacecacdadaccbcbedeecabadabaeedaeaeaebbeebbccbecacebddaceaeccbbceeacbbdbcbeceaedbbbbeeecaddcadbadabedcebceeceeeebaabeeaeedbaeaadddebbcbcbcbcdcbaddacdabdbdddecdddecdcbeaacbcccbbbacbbacabeeeedbccdbcccdeadeacbbedadbabcebdbccbebeecaddddacdcbaaccbabcdaaaeeeddcbecccedeeaabbcababbadccedbaeddbebbdaabbdcdcbaebbbdbaedaeaedbddaccbebdcacbabbdbdadabaddbedebcdeacebdcbbccaababccbaddcadcebdccdddebedbbadcadebccaaaeceeeecabeaccdecddcebedbbbaecdeeaaacbabbabcebccacbbdabababbedcceaeecbdbdbaabbdbecedacbecdbcdaceeeedaacceeaeeeebeaddcbeccaeceaabdedccceecceabccddabeecceeacdebbbbadaabdbedbdaddbcbddedbadbebacdeaebebdebeccdbaaacabcccebcbabaaebbbadadacdbdcaeabcceadcddcbececcddbbaaedceeedabaaebedbcecbbeaecdbcbbaaececbdabdbecddbbcabbbdaebbeabebbbcbedacceecaeedadbcacbeddeadcdcccbdecbcbbdebaccdcaebedabecbcceedcdeeaeedadeebdacedbddceaaaaebcdceebbebbcdaeabebdaeaabeebdebeadecaddacbaaecdbabccacdcabbeaaceabcbdbceaecaacbebcdaddacdedcdeeaedbccecbeaddbeddacaaebdccdacacbaeabedaeddaabcbcaddbacbeaceedcbcaedcbaaaceaaadcaccdaaceebcaaeabaaabbaeeeccbbaabecaabbabeaeaabdeceabdacdbaeebbeddcacceeadddecebcaaecedceaacdbccdaeecbccdbcdbebaedabcbcbcaddeedbdadbeabdebbbeeddacdbbababbbebdebcbadadbbadbdaabadbdadcabacebeecbadaabacddcaadacbaccdbbaecbdedecadbedbbbbbaebbdebbaaaecdbadddcdaedcdcaceccacacacebdbbdddedcceddebcddaabedcececcbbbededbbdebeccdccceccbaecedaddaaceaaadbddceacbacbbabcaceaabcabbcaddadbddbccebecccdcdebacadcdaacbbeccaccecccaedbbdddcbdbecddcaddccccbbcbacbcabeebdccacbedcecacdebeedecbcbeaeddccbedcaadeeadadbcbededdeddadceddadcaabddcecabdcabaeaebcaccabeaceaacbdcaaeacdbaceadceaedeadedddbadaadccbddbebababdecdcbdeccedcedcbcedbacbcadcaecdeaedaaccceadaceedcebdbdddadaacceeaaccebbddcedabaeebaeacbddebaecbddccdcbecedebdecccbbbbbdebabacbbeeadcecadedceebbecabeeeddadababbbbbeeedaadeaebeebebcadeacbcceedcaaaaeceedcaaedbdebdbaaeeceaccdbccdacaebbeabdeabdaeaaedbadaebaadbdaaeddabbbdbaecdadaccaccecabceddaceeebeceadaeebccecdbccddeaddebaeeaaaecbcdddbcaeeddbaabdcbedebaccdbdedacbdaedaacdbdbdabdcabbbaadaccdaddacceaeaebadeeddededdcaebaebdcaceebcedeaaeadbbbdaaaedbacccaeadbdebbeeaddcedbeeedcedcbcababeacbcbaaddbcdaeaccbadacdbedeaedaccccedacbaabaedaddbadcacecaddaeceecaacabaebeddcacecbdabbcbccebeebeacabeacecbdbadcddeaedaadecaeabeaccdbdceecbedeedcbbeeaaadccbaabbeccceabbbaedaabcdbeecbbacacbcddaeddbeaabcccdcebeaceaecebebaacbbbbdbebbdbadaadbcadbadaeacccdebdbaabddaddeaeabedecbabdcedeebbeacddadebbdbacebeadbcbacbddebcadccdcbeeeceaaeeebeaacbecdcbeaedcebabbdeacbabdccdbbcdceaacbdbbbbdbbebddecbacccbcbcdbbbabccdcbcbdaadaeacedacdeeddaaabaecaedeceeeaeeeacebbdeabedaddaaaebabcebdaebadecddeecadaaeaeeaaecccaacdbccadebecbceeaceedeededdcbedeebecdbaadaadbbbbaecacdaabdbdcecbbacddaaeaceacdbeadcdbeebbbbeedddadbecdbccdbadbaadecbacbadeedbbbeedecbcaebecdbebcdcbbabbaddddcbacebdecdaceaaeceecaebedeabcbddbdaecbdddbcccbeaaacaccdcdbbceaccbbdcdabbaebdecadddceebedbcaeaebcdbeceeadedceacebbdbacabbbedbbdbbddebccecdaeccbdbaabdccaedcbabbeddedbbbdcdeaecbbabededeeeecdbcbacacccddbeadecedbadbadeecaebadddceebbabacaecbcecddccabbeeabbdaeabcbcaeceaeadcdddecdabbdbadaedcededbceabbebbddbdeeddeedbaebedebaeacacbcabeedbedbbcabacaeaeadabeccbbaecdeacbeaddadabbbcaeeccecbebaeaabcdcbdadededceceedbcececbbbccaeeeabaaeccdccbcbdaedebdcadcdbcaecbbcbebbacecedceadbebdaaaedeaceadddeeabaaeeadcaeabeebdecaedcccdabbbbaedbbacacadedbccedacaeadbbdecdcccabeeceacdcaeebaaacdbbaaeadababccaeabbaebabbedaadbadecdcedebaaecababbeaeeaababceedaeadcebbeabeeecbadedadbeedaedcaebabebaebccabdebaabdabbddcddaeeaebddccebeccdbeaaeabcbcaedaabddbbbcdadaeddbbbaaaabcaeacedcbcabdeaccbbccbdcedddccadbeabcaadbabaacdadedeabeaacaddeaaceccdddaabcbdbceacdabaddcacaaddceadddebeeabddedceeeaeacbacedbcadccbbacaedddceeebcaeabccdbbdecbbbbaeaeececbcaeadaedbebacceeccbcdbcaecdeabaceebdacceeccabacaeeeecbbeddabebecadbbdecbbaaacddabcabadecaabbddddaaaebbcecbcebcbbdcaaaeadddceabdceecdadbbeabbdeceeadddcbdedadbeaadbedccadbdadbecdecabdcecabeceabdecdaeaadcbacdacaaeddabbeaadcedcbccacdaeecaecdceaeedaeccabbeaabedbcbebedcebaedacdecbeaccadccacaacdddbabdceabdebbbcdaacceaaceebecabdecbcbddaabcecdbdceabeaeaadcedaedeeededdccabddccaccedcdddeacbabbcaababcceacdcdcdaddbddcbabebbeecdaeacecbabbdadaddcbaeaedaabadceabeaaeedbbabeaaaadaaeecaedddacaaedbbcacbebaedbccbeeeddbcaccbeccdabddacbdbbcccdadeedbbccaacddbcccbaaaeeedddabcaeeedbceaeddbddbaadbebacaedabebbaeeaecabbdddbdabdedabebbecddcacaeccaeebadabcdadbbcdeecdeabebeaaabacceddcaddbaedebbebbeeccbcaaabdedaebdddbdababcaaeccdadbabbeedcbecacdbbceeabeeaecbdebedccedbdebdccebdbdbccecdcdddbdbbcebbdeadeadaebdabaadeeccbebeabdbacacbddecadaacaebeebbbacbbcbdabaebededdbbddceaaaebedaadcdabecedbedddecddadddebaeeaacaeadecdddaabbdceebeeeaedddceaadbaebdbeaaeeccbbaaccbccddbacccaaedcebbebebaeaabbdabdaebddbccaddcddbdbeebbcbeccbddcceecbcababadbbbaebbcbccdecbcedbdeeaeebcdeeaeedeaedcaeaadadccbcaabcccabedabaebdaeaeedaeacdeebdaabbbdeeecedbbaddcdaddbeeadbdbddbddedaebecaeeabdbcbbcacceddebcbdbcaacaacddbcabbbebadeaddacbccadcacaddeccbeeeecabdbcededadccccabadbccceadadaedaadcdadbbaceadaecdeeabacbeabbcdcaabdbaaeeeeebeacaccedabcacebaaeeeaedebaaccebeceeeebdbeeeaebcddaecabbccacaeaccabdbacabaddddecbddabacbebbccdcebaadbdabccacabeeaeebdeddaabbcabcdceaadcdddbbcebdceadbabeddbeacabbbcdeeaeadccadecbceaceecabcabaaceacbbeaaaccabcebbdebabecaaedcdabdebbadbceeeadaaccccdecacbcbecbcbdbedeeadcbcbbeaecdeeaaeebbeacedbabeacdbbccaaadaacebeeadbecdaacecdbedcecacbdaaceadacaaacdabeecddbcdadddaedcbbabbacbcccebecbccdbabdbadcdecebeadabbaeddcdcdcecebbaeaadccdbbdaeeaeadbaebedaaaeeebabddddeadabaaeebcdcaddbcdbecdacecbabedcbdceddacdbabedecdcddcedebbdaabeeaeeabbbeeedeadeeadbbcdcbaddeddcddceecaeecaaababaeadbaebaedbcacdadbedaaeddebddbacbeabedaaccaeeecedadcabecccaedcedceddedbdabdeaccacabbdeeeadacebabdbcedeeeeddcacbceebabccdeadebcaacccbdccabacecedabdeeadacdeaedbbebbeeaeccbaddacddeebdbcdbcabdebcaaeadcecabdbecbbdeadacceeaceadbebdbadbacccecddbeeaecddeacebdeabadccecabdaebcbccdbbdeebddaecabdabbeaacecaccaadaaeaecbcedddaedbbaacbabcbacecdccdbaaeecadaeccdbbeaccbededabdcaedbbabaeaebeebbaaebebecbdeeeebcaeaabecccabebdebeaeaaccedccaacdcdabdbdaedebdddeeaddecdaccacdaabdeeabbbbeaeaebecdbdcacecadbabddebacdacaaaabdcdabdadceabebecebdbaabcaeddbecdcadaecdddceeedbaebeeabcdecbcdbecdeadcaddedacdbeeccbbabbadedbceebccceeedacacceadeeecdebbebaddeabddceeddacecddbcadeedadedbcecdddcaadebcdeccaebebbdaedbbabdbeeebcdaddceabedcaaecbebacbedbeeedbbeaadbebdcaeedbbcacdadbdedcdadadabaceeaaadaceedceddddabdddbdccbcdabdbedebdddeaccdbcecedecdcecddbdbcdccdecaddcadbcdeeeababbbadbcbbeadceacdecbedeaceddababaaebeebbcdeeddddcebaaaaeacdabacbdecabcbeddcbbdaccbdaebdaccccbbebdbbbdeeedabedadeedaecbbdaabcaecbeabdacbeeaaabaddcbaebcbacecbddaebbbcdbcccdcadeaaccabdaabbdabecbdcedeeceeebdbcaaebddecbadbbcdadccdcbaceaabcebeeabbdebbaeaddbbacaeadedaadeebadbaaaccbdadacceacdebabecacddccdaaaabbdbdbecbcddbdaceeebeaaddabeabbadcdcdabeebcebcdebcdecdcbdcbacabdeacedbaaeaedccaeeacecbbebecaaaaceadccdeeacddadaaaaddaabaccdcdecacabdddeebbdbaabaaadeaeacdebbacbbdddbbdaebbeedcebcbeebeceebcaeaaadadebadcadadebadebbeceabbeebdcdacdabbceaebbaaeddceacbedbdeadcabeceedbbebbacddedeacaeadabbddbeecaaececbdddeddccbedbcbaaebdceecabcaeabdbdeaadabeadbecaecbccabaaebaebabdaabcdbcedbcdcaadceaebeaceedbeecdaccedeccedbbdcdadcdbaebcadcacabbcbcebdcadaeacabaebeaeecbacddeebaedddcdbdecddbbeccbceddbdcbbbbabacaddaeeadeeacdcabcdedbcceadcbbcccaaeddedecdcbeaebdeabcdbeeaaadabcaecbcdbcdbedcecedaddabdaebddcdadbbecccaacdbbdcdbbaececdbddbebadbaaaddedccbcdceecadcaceabeddabbcbdaaaaeabdaeeebcbdccceecbebaacecdddbbddedababcbeebcbcaeabdecabdadaedaeedaeebacaddccbbadedceaedcacaddeddeadcdbceebbdbddeadaaeeaaddacbcdaaedeebdbdeecbbaedbaabeaaebdecccaaeabbaedaacdebbdeeacadedaacabebeabdcbabacdaeceeaabdeebceccdcccedbaccceaeabdaadcdddbdcebbcecddceeeeaacbeeaaecabdeeabededeeaaaccbcddbdddaacbcebcedecdaacebcecabbabbcaaddadcbacdcedaddeeaaaadebadeebbeecdeeccdbeedcdccdceecaabddebdedaedabbbecdbbcdaebadedabadbaecbdccbecacabcaaabcdbecacdcebdccaccdbbdaaeacbcbdeabaadbacdcbbbababbadbbbadabaeeaccdbaedcccbaeedbdbeeedcaaeeceedcedcdbbcdbeddedeadceeeeeacdbbdecdabedacdadbabbcdcbeccaaeaccccaacddbcdabdcaddebdeabdaebceeedbdacdacabceaaabcecaebeebbeccddeddedaeeaddaabebcebcddbebdccacaabeeebaceebbaeceaddaeabececdbddaeddaceeaaaaeedecbadbebbddddbedaceedcebbbbceabaaeabadddbadcadcbeeaaecddaaecdddaddceceddaaeccbdacaeeacdbbdeaadedddcadbacdbacadeddbccbaadbeccdeaeaeedacbebedadaadebaddecabbdcdabbbadaddedbdbbbedecbcbabcbecccceabaedbadddbcecedaadcdbdbccaabdccaeddaecaebaacdbcdbaccedbaaceeabcdceedabeceaabcdcbcbcccbdedeeabccdbeddabacbdacabadcecbdebaeddbabeaadccdacbeaadcddaeadbbaeedeadeededaccecdccaedabbacadedddacdccecbaeaacdeadcebbccbadbeecaccbbbdeebeaecceedeedabdaccbcadadadbeeaecabeccdaceeeaadaceadcdaebdcabeaaccbebdecdcdbdeacdbeabdeaecccbedbbdadddddbbeebebbabdbdccedcbbcacebaaadaeceeebacbdbcaecceccebcdbeeebbaecddabeaebbcddbbbcadddeccabcabcadcbcbeadaeedeaeedbabccbabddbedbeebaceaecdcccabebcbcedebcaebedccadebbdecdeadbeaeedebddcdabcdecaddadbdedcbbdcbcaecabbcadeeacbceaeedeedeedaeeeabcbdbaadccaeedbbcdcedbcbdcbeecccbaeddaaabcdbcdebebbcecccccbebadeeaedeacaaabcecccbebaeabadeabeabdbbbcdeacdcebcabcebcaebcccaadaceddaedcdceccdbdecacdaeccccdaccbedceacbecadcbeedaeeccdbeddadbaaadcddeeaaeedbdacbdecaaebabdcacbdbaecdbeebbebeccabeeecddcccabecccdddcbecccaeacebabddcbeeaecedbaacaaceabeaaaaaadbeaeacbccecbcecbbbcdcecaeaccbaccaeacadcabdcedcacabccababedcbccaeebedbdbeabcdcdceecccebebadcbdccdbccccdbdeacccceeaccccbedecebeeedeadedeedeeeedbbbbdbcceccaceeadaeacdccbceaceedcdbdddbeeebbdaecbcdccebaccbcdececccbbbccebdadddddeacbadbcdedaacedbeaecebbeecabedcaaeacedbacdaccaeeebbadebbbdeaaeecaaeacdbaebecdbdbeeddaceeabebeaededcaccecbdcbdeaccbbdedbdcbacddeedeacecaacadeecddabccdcbddaebaeeacbdbadeeccdcecdddbebaaadcaeebdebbedacceeaaeadaaabaaeabdaeccdaaecbabdbdddaadedbccacabeeeaccbdabdebcdaecdcccececcdcdeeeaddbddebdebcaadbcecdccebcdbeadeaecdcacaadaddbdcaedcbaedcdaaaeedadeecdaccbccbabbcebcbdcbbbdbbcdddaaebaecadceeeacdacebadbddaaddcabadcecbcccdacbcbbbbeceedbabecdeabcaebcbaeedaddbcdeabbcaadbccbbcdeaebdddbabacdddbbcacaeceabcabcebcbaaeabbeeabdbdebeaabedbbcadbaddcabecedeeadcbdbabdbbacbadaebaceadcedabeadddedeadbdacbbedeaecbceebcebaabacadedeaabcacaedbbeeaeaebdbdebbbdedacccbadabaabdeaadceebaddeacdedbcecdbecdaceeabbcbcbaacbdcadedceacceeaecdaeceebbddddecacaccdaebcebbbeadaecebbeddebebdedabbbbcdecbadeabeaddeabdcacbbeccbbaabaccaedcbdbbdcacadcbdcbadbdadbadeebbaeeacbaacdaddddececbdcaadadcaeaaeedbadaadbbecbbdabbbdddcebccedaecddbeeeecbbaebaccabeebabbdbedcaccabbaaddccebacdaaabededbeabedcbdadacdcacbcebcccceebdeeacbecccebcccabaaaedbbbbedaeaceceacbedacebcccaaabdbdccebbeecbcabebaedaadedcedadcdacdecdeddebcebadbcebbdddaddbeccebabacceedcbcebedabdbbecedaebdbaecceebceabbbebaddbedbdeaecdcbbeecdcacccdddaaaaccbcccccecabdbcbbcdbcdcdbeeddebaeaccbbabdedacccebcddabbebedbdbdccbceaddcbcaebedbebcaaacacdddaeeeadaeeaebeedacacecbddcdcbabcabbcddadddcadcbbceabbacecaaecabeeebcaadaeeaddcecdadebbbcbbbabadbccbdbcdacbccdaacaeaceddccdceacceaceddacdebebaedabebabceedaeddbdaebddcaabaedbebbbdcddebeaadecedbbaddcdceddaaeaebecabbbedaabaccbbccddbeaccbcebeabdcdbcebabbdccedbdcbdebbebcaedaaadeccbacecddaadbadbeedeeedddacaeccdbddcbdcaeabbeccdbbebebacbaabcdededcaceaabdbadeeecbadbabacbbceeaddececadadccacebdbebcdccbdcdcaadecacccaadecbccbbbdcdcaacaedebeeddbebdbedabdbaacebeceddbbcaaeddbcaccdaeebbadaeebeadcbedaadbacedaeaacaceedcbdaeeeaeccdaaaddbebbececbacbcbcbebeacbadcabbcccdaddbbbaccdeaacdbdbbaccdaeccddbcecdeedaecdaecccababaeaaadebcabbabadcabbbdccedbebcadeceeccbcccdadeddacaddbdbaedebdebabcdaaeadebabbcbddbebbbdbeedaeaceebbddeebaebcdadeddceaeadeaeccbacdceebeedcdabbbcecbbcbecdcddaaaabacdadbdeadadbcaaaaaebacceabeccaecbbaaddaecdcbcdabbbcdaceeecccedcccdacedccdcddecaaeceecabeedccdeadabceaabcddcadcdedcbacaeadccedaacdbbccddbecbcdeeecbbadceabbebbdebdadedbccbbbdaeddbedbdeaedadebedcdeeedddcabaedcbaadabdaadedeedcebdbedbabbbdbbdabbbdcbebdccbaaaaddcdeceaebdbaddccbdcddaedacdedebcacbdacbeabebbddbaeeaaceeacceacaaaacddeeadcbcceaceaccbbccaceaaaecdbdeaccaebddcaaacdbdbeebcaaebbbbdccbeccccbcbbcaeacacbadaccdccaecadbbdceeedaebdaddadeddcdcdbdddeceaeeedcdedeaaadeccdebedaecbadcdebbcdeebdbbeabdebdbeebdadeddcacccbbcaccacdbecaaeaabebecbaaeadbddceebcaeaeedcabccdbcbeebacaededebacaecaabbcebcaaabbcecbcebdbcaacbcdecdacdcebdadbbbeaaccaaeacabbebdcacbecaeadcacdbeadecebddcaeaadceacacccedbadadbedbeecaedbdadbabddaaadedabacbceddbaebebeeeebbeddbeaceeeaddcdddbbceecdbaebbeceddcabacdcadaabecbeeedeaadcdaddbeacecbadebeccceaaccecdbeebcbcbeddeeacebadacdedcbdcdaeebebbaeddbdbaaabedcadceddebcecabdcaaaeadcebbdaeedadebdbccddeaddaaedbdbcbddbeacccabddeeaeadcebabaeedebddaeaadcbadebaaadabababcbcdbdeeaacdcdcdecdcedaedaeedbaadccccecbcceacdaeddecceeacaadacebdcbabbaededdccbdaeaebacbedcbdebcbabeabaacedebaceeeacdeeaebedcbbeebbdaaeebecdcaacebcddebcddadcbeaaddceebbaadecbacbbdddababddeacdbeccceeecccaedbadbdddccbccabbaacaeaccddebceccebacededecbdebbeddecaacaeacdedbadebeacedbbacbbcedaabeaeeebabecacaedabccaeedcdcaddadecdecddcbbaccddcbcadbdcceecadeeadbdbdbecdabdeeacabcbbceecbedeeacacadaddeadbabdecbccbaaaabbceeabeceeddcecbbbebccdebdeabbbceecdbdcbedaaaeecaecadabacbdaebdbaeeacabbbaddedbcabcdcacdbdbdaeaebdccaeabaeecaccdaaadeeedecbaccdadccbbcabccadcbbaccdbbcdaaaeabdddedbccbceeddeadeebbecdcebeebaebeeacceedcbaaabbbabcbdaebbdeccdaebadaacecedeadcdadcadbbaceacaebbecbaccdcbdbacdebbdbbabacdbbbdddaacdccccbaeeebdeccbbebcacbdaeddebbccecbeddaaacbeceddaeaabcabbecedaaacadcceddccccbacddbdadeacaaccbbbcacdeddbbcaeedaebcdaeaeaeaaaaebbaeeddbbccaeadeaceccbaccdcabadccdbebadeeeeaaddbabadbdaccbdcaebcadadaadbceddccdbbdaacdeeacbddbcbbedbeeeabbbcacedcaeeeacbceaebbdecdeaadaebbdeabbeaaaddadabadebcbaebbccabeabbdbcdeeacccdebccbccdeaeccabeabecdecbdeabedccdbaeadbbaddeabdabacdcacaeeeaabdecbaddaaaaadabccaceabeaacacaaccecbcaeabcacbeebdcdcbeedbbddcadbebcadebbcbedbbecceceeaadbebdeabadebbbbccaeccecdaaacdeeadedcaacdbdaaedeeebbbbdcaeaecaccecadadbabddcbddbcabbabedcdcedbacaecccceaaececaeeabeddadbcecdaeabecdeceabeabbeccabebaeedbbbeaebdbddabcaadbbaeddbabaacecbbcaecccbeeeeeeccedbacbbcbeacccebcccadeccbdbcacaabebacbbbeccdbdddcebdcbcdcdabeaebddbcbbbaadeadecbddedbbedaebdadbaeeeaacdabedaecaabdeebcacedceddbcbacadcbbeaeeeaedbdeeaebccddcecbcdeedbbadceebecddccceabbcccddeeadebadecdebabaebaebbdccdeeeaaeedacbddbcecbdddabbebcdcbbaaeaabbbddadceeaaebcbabbcbebcedaadbebdeeaaccdabcdacbcbcbeeebbbdddebcaddccdeaeaddadebbacdabaaabbddeecdcbedbacadeabadabedeebabbcdbbaecdabebeccbeeebbedddabdbbaeddbdcdabaedaecceadaeceedbdbaacbdebeeddaebbcecbdeccddecddaddeecdbbcececdbedbeddcbbebccbbdbbdcdddeacbcabbeabbcbbcbdebabdbaceadcdcebebceeabebaacccabdbecebacdddbdaeeebaebedaebcbcbcedcbdabcbedaecabdaeccdcaddeaaeeaeebbdaedebbdccdececcdaeaccbcdabdabbaaeebebbbcdeeacdebbacaeaeaecbdbacceaeebeaaaecdbabccdcaadbdaecacedeacdebbaeeaaabcbbdaeaaaacdeacaeebbeaddceabeddceeaeedbbcddcdeeeaddecbbdabbbbdecebbcababebbcaecabdacaddaacbacdeebdddcdebeabdcaebdcabddbdeaabceecabecbaccceebdcdedabbaeccdcebbbccebcadbcbdddddababadddcccccbcbbeaaaaebbccdceebbaeabbedbbdecbbacbbeadaebcadcdcbaddbbbcacddddcdecbdaeaebabadbcbeecddeebaedeabeacecadebdedadcdadcadecdcbdcecbbaabacbdeccbeceadcbbecccddccabbecacaedacacecbbbaebddeceeaacaeddaaaeccccdeecabebcaacbcedcacdbccccdccedadaddaaabebdeacebaddaddcccecabeadbeeabeeeeaababeabbedeacecbecedddebcabcdeaddaabbcdcdccbcacebacaabbeaddecebabeecbbcbcaeadccccddcbbddbbccebceeaecdbebbdeaccccceeadccceababedcabaccdcbbeeabcbccbeedbabbcbcbaadadeccabdebdcdccebebbeeeeecaaeaeacbedaabaccdaeadeaadcbcdebebcbadebcdcedbebcbddadbdcdecebbeceaaabdcebbacecadecdcbacececceacbdacaeaecebcaeaebeecbaeeaedadeaeccbbcddccaaeedaabaeeeaaccbceaceacdcbabaedcebcadcbbacadbadacabcecaccbaabcaddabcbebdaebbcedbacaeedbcebaaaeddecbdcbeaacbbadddabebaabadcdabcdadceedadedbbdbbcbeaccacdcaddabcdeeabeeaccceceeddeeecbaaadaebabcaeceaebdebcbbcedaeaddbedcadbabababbdcdebdeababdeaebcabaeddbebdbbcadebddcabeccceabeabbbdacebbbbaaeecebdcaabcbeaeeeebadedddeabbaecbddbeebbbbaddccdabbdceedabdcbdcecbdaebeebbbebccacadebeaeeeeddaebdcaeeeedbdaebbbdeaeebeaaaacbebbebcaacaaceecabddcbdaebcaceeaacbbeaccaeeecabdbcdccbcbcaacbacbcbabbdacbeaebbaedbaeddadadeedddabdbcdcbeacdcbbabdbeebeeebdcebcccdceecbdddcbeedcbddbdcabedabeecdcbeacdcbdcbbbacedacebadbbccdacaebcdeeecaedbebeaeebcaadceedabdcaaecbaaaccddaddbdcabeadbbcbeabbceacbdcedbcbdaebdcbbbbbbdedeabbecdbccbbbbdedbbeccabbaadebecabdeecdbbaebaccbdebccbbeecbdeacebbdaadaaecbbbbbeddcbaabadceecaeabbbcaccbebcbdcedeaaeebedcbabadebeabcdadbcdeecbbdbcbdbbbbceeccaaeedccbbebabbdebeaaaceceeaaaacdabaddadeeaccaadbaeccddaceccaaeaddabbacaceabacaedcebeeaccacbcaebeccecbaabdcaddbecdabbcedbcdaeacdeaadebcbbaedeacedeebbecddddeceadcbacaadbeecbcaedbecbbeeabdebeeacdbbeedcccdcbcedeccecdbbabbcebbeabdaecaeeecaddbeebccddadeedddbebddacdcaceacbedabdaadacdecdaeaaeecaddcdeebcddccdceaddbabedcdeaceddaabaccbbccabbedcaddeaeaaaecbdabdedaadceedbbceadedbaeccceceabdececbbceaaeeeddddacbbbbbedccbcbaaaadadabdddadcebbcbadbeeedbbabedcedeadcebebecdeaeecacdcbeeedaecdaeeebeedcccdacbceedeacbacacbeabcceecbcbddddadbebbadecdcaaddaebedaaaadcdcdbeaabedadbecaecbddbaecceebadcceaccadaaaccdabaabadadeebedddceebcbcdbabcdcebceadabcccadddcadbbdeeaeadecadaecdebedeecccdbebaeddbaaceaceeacddaeedccedaececeeeadadaccecbebaedceedeedcaabbabcdbdceeddcdcbdbcdbeeccddecedaeaabeceeecccbccadbcaaaabadbbcbddaaaaeadbbddedbebbaeedebbdccadeddacbebaacddcecdadbcbbbbceaeeebaeececcdadadbbaaedacddecaabdcbdcaeceacabdbdddecdedbeedaabcaaedeaccacecbdedccbcaecbcbbbbdabccbcbcecbeaeacbdcedbeccbccedbbdeccbbbccbbbbcaceadecaecaacbddededbeacbccacceaeebacaddbcbcccaabbccacacbbbdbaaceaccbbadeeacccddaaeadcaebbbeaceccebbcbaebbcbecabcdecceedbeaaceaeabbdbcabacbaaccebaebbbaedecabbebdaeceaddadaabccbdbbedbaebecdeecabbeceaaddbecdbdedecddbcddadbcbdeaabbaaabdacdbacaacedaceccdeddaaecedceebaeaeabacebaeedbbccdadbedcddadddcebcecbccdadcacbeaedaddcbaabddeccabbaabcdddadecbbaedbddcaadbdcedbebdabcaecdbaeecccaaeebaaadcecbeddacbacadbacabdbbdccadedbadebbbcdeadedceddddcaebeddceecbccdadceaccedaccbecdccabddadeaeadebaedbcaeeabcdcedbbddcddaeeceababcebabdbcaacdcbddbddbdeebcbeebddaceeaecaadaadeaaecdcebeeccdaebeaaaacaacebaaecccbdbceacacdbeaeaddcedeacbdbdaddddecbdecdcbeeceeadddcaebdaedbadadcdeeedecdcbcecdccedbaabaacdceaebbacdcbbacbccbdbcecccddceedabbbbeabeaeeccaedbebbcacbcbdabadbeadaaeeddaadadeacdcdbcaeedeadbcebcdacabaddebbcbcdceeabbbdaaeaadedebcddacddeddaddccddbddbbcdacdccebeeacacebdaabbadaeebdbdccbeeebeedcaccbabcbbdeededcbabbecdeeceddbdccaecdbcdebeabcaeedabbcbabcababaecbacabeceabddaeaebabcbedaecdabddacaaedaacebdbaaccaddadebeaabaadccedcceaeceeccbbebbdcecbdecdcddcaadebacdcdbbebcddacceedbaecbdabbebacdcebcacdeaaeebaeaceaeeabecbeadcacdbbadedcaeabcedcbbcbababbdbbabeadddbaebadabbadeeddeaaadbbcdabaceebcccbccbcdabebdeebdebceadebdcdeadecacdcaeacacacabadebcecbbeaebbdcdabeeabedcbbdecbdcbbedadeadaeecbdbdcccdbbaacecaaecbdadaaacaddadedbceceeaebcecdddeddabdacceddaebedabdbbcaccebedaceeddddadaaaacacbbaaabddaabeacbecbbeabdebcbebccebbccbdaadccecadccdcddbeacacabaedadcbeadbbacbbabbbeeecceedadcbcbccdecdeddcdecaacadcbbcadbeebabcababaacbdadedcbbebddadeeabcaaacbddebeadccebdcdddbeeddeaeecdddabaedbdccbdcaabbebcdcceecbebeccaeaceaedcebadcdeacadabceeadacddbccccceebdeeeccceedababbeebdddcbcdbcacddabebaaccebdaedebedababaacdbeecabebadbdeddddbaeadabbcbecbddcadedcccdaecdbacabccbcdcbabadadbaabaeeebdebacaacaddbedeaaeebcdbdbdcebbccdaddccacbcbdaccaaacaeadacbbddcdaedadcbbdbbadbbeabeaabeecaaddadeceaadacadebeacbadddbccddddacdaeeccbdeaddcecbbeddeceaddbacadbbeaddebbbebcdedcdaccaebccacaeabbbdbeedcedaccdebeeaecbadccebcbeaabbaadaaebbedabecdbdccdcabdaebebbccacecabbaebdaaeeaebeeddebcecbbbdeccdeeabeabcabededcddcacdbdeaccaacaeeeaedbccebcababcbacabcedbeccceddceebdceeecaaadacdcbacadcdadeebdedbddeabebecddddbceaebcededadedddbbccedcdddcdbaebedbdbcadacbabeebbbcedbacbeaaabeccbeabbcaababedcededddebadbcaeceedbedccedebbabbceacddeceaeedebeaaeedccdaadaacbececebedbeaacabdadaaabbeacabbaecbebdbaeeecacaceadbcbeaaaacbcbcdcbeecabdbbebeccaaabccdabecddeeebcececcdabdedcaeceebceaecabcbaecceeabdecececcbebaeddceddddebaaadacdbebcdbaacdcdacdbeebaeddbcddebdabbdacddedddabbcdcaaebbbcaeacbecbbbbdbcbeededbdddaaaaeeaeebbbeadbdbbebeaccaeadabebbdabacccaedddcaaedeabbaeccedbacdcbcdaeaabbabecbcadddacccdcacadaddcedbabdccaaceabeadabecdacdededbeececebecebdbaccaedeadbcaedaeaabaaacbedbbaacdadaeabeddebbcbcbaaeeebaebcadceaecbdadddbbcbceecaddddceebcbbbeeddbebceeadeeacbeecceddddbccceabacbbbbedcdaceeeacadbdbceecbdbcbcedddeddaedecaeeebacecaeabeedabcbeaedabbdeedbdcbadabeccaaecedeeddadddeacbeccbabaeaebdbbadbcdbcadcacebbaadacaceaadcbebdeddbaddbbbeabbdcebdcacdeecdacbbbeccbceccbebdedbddeedcbaeceabbadddddddbedbdadbaaacadcebbadddaecacdcadebecdbcceccdaebaddeccdbcbcdceeaddbdaeaabacbceeadadaccdabcbbbcbadeebaaeeedeeabbbdcabccbbedeedbcaabaaeaabeeedddceedbdbaacacccaccdcbaadccebccaecdedecacbaccdcdcabdecabedadadceedadbbebbeacbddcbeddeccdadccebbcccbddaadabcbeacaaedabcebccadcccdeaadbdabbeeaeaccdadccaabeeeccdacbacebdbcceadedadcdbbbbccaebbebeeacccdaddaaaceabbcbaebbdebdcaadccedbdcabdcbaeaabacdbbaecbbedaacbadbeaeddeaaaddbadbccaebebbbdebbccedaabeceadaaeeebdceeaadcaeeccecbcebccceecebbeacddeddecedccecbebdcccbbecbedadbeaeaadeeaabbdbbcaebabbcbebeebbaabcdaeaeeddcecadccbebaedbebaeadaeacbdbcdaebeaaaccdbbbbacadbdcbacddbbbaeecebadcacaadadbdabbceaceeebdbeaceccccaeadaeaadaacaccdcaccabededbeddeceddeccbcadeedacaeacaabbabeabdddcdebaeabebddabeedddabccedaaeddbbecbcadcebeccbadaaedbabbdccdadbcceaeacbbcadacabbaacdeedadeecbaeeebabcabccecaadbedabbcddcaccaceeeceddbabcabdaecdbebadbddaddabbbdbcaaacbbbceececdebecaeceeabcbcbbabeddabdabcacaedbacabbbdcedebdabaeeaececbaabeaebaaabbeeadaaeecbecabbbbcbcbbeddcceabbbabadcccbedceabbeddebacdbadcbacceadcabdccceddbeacbcddbeaaaebbbbdabbdacbbaceadeddddcedccbddedbcedeaaaeededebdacbebaeebcddcdaeedeaebcecceabecbadabdccbdeccadbaeddacaccacddacddacdcdcbbeeebcccaacbecdaeaddeccceadedcadccdbacbebadcdcbdccbedbeeecdbaebaedeccedcdcccedececddaccaebadbeaaadaaeebbcccabdcecedaecbbecdbcdecbcdaeacdadbcbadccabecabddbebaacbccbacecbbccaedbeadcceadddaadbbcdddbcaebbbadcdedceddcccadaaebbbaeabccbbddadecacdbdbdccbeebcadebbdadbcedebabbcaacbedcaadcbbbcdabeacbadbadaaceadbaaaccaddceedebebbbbabaeaabdeecaaccdbbebdbaaeadcacacaaecdcbdedbcdbbccdeccbcabbbebbaecbaddbaabdedbcedebeebeccacacdbccadebeedaaeeaabebcebecdeabeeadeccdeabbbedeabebdaaeeedebaebadbaaaacdcdbbeaebaeaddcbcdbadbbadebdadabedadadbeaaaacbdabbebbaebbabeddbdceacbdbeaadeccaecdddadeeaecbcaaccdaabeebaecceddbbdbebdcbeedeeebdbdeaaadcdbbcbadecdcbdedecdebaacabdbbececedddbbbccbcabaebcdebabdacaeacddabbdaceaeeeebcdbedbdadcceaceacaccbeaaacdeeaacaacdbaecdddaccebccaaeddedbeadcccbccceadbecedbebaaeeaadccdeabaaadccceaecebceabbeedcecabeadbcadaeadbcbddeeeeacdbccbadadeaebbddcbcedbcabdddbdaabaceabdaaccddebdaacdcaaabbbbaecceeededbbedaadeebabecbacbebbaaabcdbbadbecbacbeaeacabbbdedeaccbecaedebdabdebdbecaebecaecaeaacaaadbbeabddccdcbadddcdcbbacceddabeacaabbbbeeebaebbbdbadbcdbbceaaeecdeadebabbcdccabaecbcbbecdbadedaaadbbcacaeaecdbaeceeaeecabcdddbdddcabdbbbeadbadedcadbeabcecadbcebccddedeebacdebcacaeadddbbaaccdbdbbdaecbcecbeaaebccacebbbeabbeaaeeaadebeebbaedeecbbbdeeeceabcdadedcabbdccbddbbceaacacaebedcadadbeaeabddbeaecddcebdcaacdadacbdbbdaddceedecdebbbcdebbeacbcbdbecdaaaebecebabdeebcabcdedabcbcecbebdedddbbbebeeebeaccbceebccadaccbbcddbebeacaccdaeebddbaaeedcbdecbedceecbcbbbaeeeceeedabacedaecdbccceebaecaebbeecbdbbbeeedeaccedadcdadcdeeecdcdcbddbbcdeadbcbaebaadcbacddebaeaabedabaadbebeadcedccbdcdbacbdcdceacdccacdbdbdadeeedeeebaacaeddaaeaeeebccbbdebeccdbecbedddddbbcceecabdeabccecabbddedeadcadecacdecdbbdeedcbebdcdbabcceadaabddcbeabeaecdcdeabccaeabdeddcbaddbcbeeaacccbcabccebdbdecadecdbbdcaaecddedcbddaceeccdcbcabccedbcddbcccbbeaabaaacbbbbbeaccaebceebebacdccdceaccccdcabadceeeeecebedeccbacdaabbaecbaeabbccbbdcacaadbdbcdeaeeccbbbbceeccedbbdeaaeaabaeaadacdacccdcacebcbbddcaddceccdebeeadaccbaccdcbacebbabbeeeccaacbecadcabbcaddacccdedaeebaadbaeabbdabbcbbebceaadeeabedddaadbccaddaaccdbbadccadebbedbcaeeaeeedaaceebdbdacabcaeadabbdeadaceedaabbeaabcdadbaebccdbdbdbabcccbcabebbeedabdcbdbececdeeacdedceebdcdcabceababccaaeaddbaddcdcddddaabeccbbbbdddedacadadedeeacbabcbbeebeeeccadecbaaeeccbedccadebbaecbeddeecbaaddedcbacedbaebebdcaaccebdddebaccbeaeaaeeeecddbcbecdbebcbadbdaadcdcdbcdaadababadbeacaccdbccdcaadbccbbaceaabacbceddbbbcceeaedbcbdbcbaeaeadbeadaacbeaaaebeaedceedababccbbbbccaeadedaecdbcaedaccbdacacaaedebdcbbdebadcbddebdbdabeccabeeaacadeeaebbbbebaeebaceededeeadedbdcaeecedddeadeeddcdadbdababeedeacdaddaacbaacebdcbcebcacadeeaebcbddcdbbccbbccecbeeccdbacaddbaccecaccbddaecdaddadbdaaceeeaecdabbeaeadaecabaacaaedbdbabeeebcbebecebddaadcadddbadbbaedbabcaddaaaebeadbeeccaeedcbaebadecceaecbdcddbacdbcbaddeedadcbdceaacaccececcdcccedeeaeaaaceeabcbcaaeecacceaecedcdcddccacbacedacccedccdbeddabddaeccbdeebbadcabbadabccbbbbeeaeacbeccbdcedbeebecaccaaeabdbaeaadcdbdcdcccdaecbcaceaadcaaaacbdadbcbeaeeeeebeaabcabbbdeecaeeedaebddcdbaccbcbaaacadeeaeadeeadcccdccababddeecbedadcaeecbdeebebebddaedbbdedebceebdddcaddccbccebddcdbcbabdaadeadabccdeccaabbecebedcddadbdbdbbbaabdaaebbaaaaebaceeebdbddddbbabdccbdceeeeebaccbaacebacedecbceededccaebeeeeddadabbdecabdceedcedeaecededcacdcaaaccdadbabbbcbcbecdbbbbabcbdbbdbcbececbeeadaacebdcaccacebdbacadcedbddabecbcaddcdbadcdebaccbededddaeebeabecceddadabdccccabbbaccebcebcaeeeabdbcdeddaedacdbdebccdcaddcdbecebcdaabddcbbbaddcbdadcbcdbbcaebecadbeecbabddecbbabbedaadcdcdbacaccecccdccdaedaadecaeaaecbcbdabbbebbdbccdbabbdadebeaedceeeeedacdadeececaebacbbebedabaadbdaebeeaecdedcacbdecdadcaababbeaaacaaeecdabecebdbabcaaecddabbaaecebdcaeeaaeeddbbbcaccdecdbcbaecdeeaeeaeceeacdcbcdebbbdabebcbbdadbdbdccccccbedbbadaedbeaeccbaebaebbdbbeeeebadbdceacaccbeaabaccabdcdaacbbdaebccedeababaedaddbdbebbddaaabdcdcbbcabddbeaebacbdbdcebacbadccabecddeddeabcddceeeeecbbebadabbeeecdbbbdcdaabdbcccaeaadaaecbddabecbdbdbbcceeccbcebcebaeabbacebeadeacdbedadbebcdadbbeaababbaabddbdbaacdcaecbddacddacdcdcaaaebbbbbaabbcadcdbdcdaabdacacccaeaebadaebabcadeadcbcaebaedcddcceedbdadedaaceaaabeebbecaeacbccaaeabcdccbbabdbdbebaedbebeccecaeaacacadccbadadaccadcbabcddcaacdacddddaaeeeaaccbcaaccedebddabedcadbacaabbaddbedaaebcbdebcdeeedcbcedcdababcabeeadaccecdacdbdabbcceacdceddbceecddceacdbccaccdabcadbddaaaeaccdcacebccdcbcdaaacabadceceedaaaadabecbcacccdaabcceddddbeaeddebdabdbbdbedbbaeeededdceceadacacbbdaccdbedaacabcdbbdbcedeeeddabebeebadedbbbedcaaabaddacdeeebdbcabbadebbdcebddacaddebeaaeabdaacddbdeaccccbddeadbdcdbbcbbdacbebaecbdddacbeacaaeceadcdeceeeceadeddedcaccbccedeeddbcbacaabbbdebcaedccbdcbbaadccbdceabadecbaccaacaeaeebeeabdcadaaaacbdcdaecdcabebcbddbdbdcbbecbdaadbaaabbdeceeadcddeabdeedbbcbaadeaadaacdbbbedabbceddddccaaabdadadebcbcccbaccaaeaebbceeeedbeadeccddacbecaccededcaedcdadbbaadbeccbdecebddacdadebbccaacdddabbccdbabdeceeaaebdbcdaebecaaeadabceecccbcbdebabdaaddadaecdcebcadcdcbcaedbcbebcacddcbdbecabaecbceeacaebdabbeecceeedebecadaaaeccaeacdeaabececdacbdeacbdbaebabcbeceabddbcbcdeecedeebddbdcddadecacbbeadbacbdecdbbccbedeeedecbcdcdcdbecaeccdbcedcaaacbbceadabddbdeabdcdbbbcbeadbeeaadbbcebdeacebbdaddeddbcdbbeeccedddbdbaebcdacbdbedadcecabebedaebbbecacaadcacaacaaebccdeaaceeebbbaeecbeeadabdebbabddabebdbbbbadecacbdcdaecbbdceeeedcdbcdeeabdaedbadacabdcabddadcabcaabbceabddeeccabdccdceeddeacbbecedeccddbbeadbdbebeddeaebeaeabaaaebdaccdbbdaedbeedcbecdbabddbdbbebdbebeacceadccdedbbecbaddddddadeeecabbdedaabdaceecaebebadedcbcabebdcaedebdbdcdecaceeaedabbebcededbecbbeccaaedcdeaddebbeaacaaceccdbdcdcddbeeccaddebccdadcedddaaddcdbeaeeeeeecbcdadebbbdaaaabbbeeeacbdeaaaddeeeddeedccdabddbcadacdccddebeddbbebbaacbddbebdaaaeeddbdcbededadcaadcebcbbcadacceaeebebcedcdabedbecbcbabebaadecbddaecbebcbeeccecbccaabaeaaceecceeaeecbbbaadacebaaeebcedbeeeaccabdaaabcaabdebbcdebaedbeacdbabebbaceacededbdbeaceccbeccadeeabedaddbdeaacdaabebebbeccdeabedacccdcbbeeacbdeaeddcdeccabeceebeaddceeaaedaadabbcbddcdaedcbeecaaebabcacecebecebdcbddccacbaabaedbaeeaaaeddabddecadeaebeaceacdbabccbceddacacccdeadccabdadacdabacbeceecdbaaacedaaebddcccccccaeaccddeaddccaacccddbbaaddcbcddbdddccddbedadccdbbacebaacdeecbebaaccdaaeceeebcadaeaaecaaacbdbaebbbbccbacabdabcdceaaedbaebeceadcebaacbdeecddcecdebabdcaeedbeaeacedeaccceecedccecbbcbbabdbaacbacbceccebbedeccacdcdbbabebccdbbcbcaaadedcddbcccabccabeabcbbeadbcaebbdadddaddcceeaeeaaadacdebaedacdacbedcebbbeeaaebebbbcdbacaccdccdcadceeacecadccdceeaabedeeeaacddcdcebebdeabebccbececeacdbabadabaabeabdcedededceaadcdeebcbadbddedacebdcaeaaddbebdbdebebacbceadecddedbaeadddabeebcabaeadbddbbcdedbaeeeeabceccedaebcdabebbeddaaaabcbbcadcbeccdeeaaaceeacbbdbbceaddcaadcccddcecaddaeadbdcccbccabcbdbaeadeebcadcadaacbbdaacaadeeeabecbcabbcbdaddbbcdbbcbceaabeeccebeeadbcebcdeeacbbeddaeaeebcdbacddeebaadcdddbbbaababdcaececceccbcecacdbbbababecbcceacaedddbaeaacadcaedbbecddccebcebdecedcebadcbdbdbacabdccccadeedaeeaeaecbceeeabdabecdcceaacccbacadebedbceaeeabadbadaebdeeaecebadcbaabdbdeeecccbaaeccdbebbcabacebeeaaaddadbedccdbeeaedccdeeabcebdbaadccceaaedcceedebcbecaddbedbcbaaeecbbdebbeadaeecbebddceedbcbdcebdeebbbbeedccddcdaadedccbabbbcdeeaabaaebadbbdacbaaaaedcbbbbebbeabedebdcbccebcaeeaadbcdeececdaaeaedbacdabbeeebdccadadedabecbececabcabadbdbdbeedeaeaddeaddceeeeddecedccedbddcebaddabdcedebbbacaecbdeaabddbbeedabdaedbdeccadebbbdcbddeddeabdadabecadeabcbbceebdaaceaaedadcbeacbaedaacedcececcdbdeadbbddaeeebdaaeeaddaeacedcbcbaaadbbbbbcbbddedecbecbbcdaddccdabacaadeddebddcccaeeeddaeaaaaacadaacbdadecbaeccdadbcdbbdeaaabaeaeddeeebbdeccacaebdececeaccdbbadcddbeacaacddcabeaddecaeeccacceabdcbdbeaddcdccbdcebacaddecbccbabdcdbcbaadaaebedcdbcbaebcdaeadacbbbaecdcabcaebbceacbdeeccaebdeaddeabdddeddeadcbbeeccceaccaecbcdababcdbacadbdbbbdebbececbccbdeeeeceedabeeddecdeadaaddeaebeaedcbacdbedcedaadbbedccbaadaeedaceeebedcdcecddabcedeadebcbecdcbcbddbbacdbbdcceaadeededeadadbddabeabeaccbeeaeebdaebbcceeeeaaaccebadceaeaccdcbbcbcbacadabaddcacbacbaeeaeaebcebadcbadbbcedbcaeaedadeabdbbbcecbaccbbececcccaeeeacbadddeedbecadeabaeccdcbdccddddbecbdcaaecbaebebdcaadebeebcebbeadacecaaeeabcebcddbbdcecdaccedbaadcddcaabccabcdcaaddeebddbadcbdceaabdaaeaaeccbaabacceabaccadacabeccceacecbecacebbdededabddccecadcccebaeeaabbbbbeebbdcbaaedddaeadaadcaadcbcddededccdcecdbeeeccbadbccaaeacddeccbaeabaabcdeeebbbedeeddbbbddceebbabebacceccacdebdededbadcdccbeabeeadebeedeeebbaeabdbdbccbbaacdddebaeaaedebedbcdacabcaadaabbbedabbadceeaeeecaaaedbacdabbbbbdceeaceceaeaeebabaaaaabecaacaaedacbaaeedcaceacabdbcabaedbaaacacaebcbecbdedcbcececcdbecbdbcdcacbbbbaabcacdbaccaeeeaaaacaceaedebbaabcdbbaccbdcecbddbcddbebdbbebccaeeeecbcaabcdbdcdcdaeadeebacecdeacaceeecdcaeddedbdbbcdcbdcaadbebeaaccabbbeeedbacaaaceaaddbbcdcdbabdbcebcbaeddceaaaadcbdebbbbabdcbbbbeaeaebadaddeacaedccbddddbbaadabddddededdeedabdabeaebadeadccadbccbaaeebbcaaeabdbedbdeaaacecaeaabaddabbcebadbbacdcaedeecdbceaadeebebededddbdcdbcdddaabdceccbcacedbebeebcbdaeccddeabecdecbcccdebeaacadbcbeeabdeeecabdebdcebbeaacddaedeebcbccecbbbccbbbdeddeaddcbaadbacadaabcacbbccaaeceebeabbdebaeeeadadccceeeeedaaebecddbcacbeecabcadbbeecdbccdaaabbacabbabaddbbcdedeaedcdbbddbeabdadedbabbdceddaeddaaccedcdddeaabbbeddcdbcaebbdabedbbadddceebcdadbcbebdadbddeacbcabbecaacdccaeacaedcebededdabdbbbcdacecaecabdbceeedebbceaacddabccebaaeeadbdedccbabadbdaabacbacbdcdedebddeacadcbbbadceeaddebceeeaccbabaebeccdadcddeddccddcbbcbececdddaebeaeccedeadddcdeacdedbbeaabdadbcbdabaedcedbcbddaadbeddceadbdabecdcedacbbbdedaeccaececadadabebeeeebebeabcedadbabacbaadebcdbebcbcecaebaeddadeadeaedededdededcceadcaadccacbcebccdbdeedacbbddcbdcbeadecdcbaacbccaeeeaaedddbceaeebddaebecdbcbbdbdbeaaebbedeaeaddbbacbebcacdaeeddecbcaeaddaaccdcdceaacaddbccdceebcecdaadbcaaacbabedeceabccbecbcddbbaacaadbadeccddccceaeeccceecaebabbbddcbbeecdcaadeededacbceccbbbecbbcdabbbeabecadcecacdaeabbcdbccaacaeaeecbccbccbcaaaabddeedecebbbcdccaceedbcadcbadbadedcbacedcdddacbdceabadbabdccedcaeeedcdcdbecdcdaabeeeadbbbebdcdddcececbeebedabddaadbcddeeebeaeeebaededdaccebeeaeacbabebbdddcdddccdecbbabbcaaeaceabbccbecbbeaceddbbceaaacdeaabcddebbdcdebeeccbbeabdeaecbcccdeeedeaddeeababaaeadcebdeeddceaecbcaeeeceeacebbecddbcbabddacbebebeaebbcdeebddcbecceeeaddbdbebadbddcbeccdeccdcdbabcabadbcbcbcaccebdaadeacaaaecceacdadbabccdbbbdceceaacebaebbaaaecccdaccdcabadacbeaadaaecaadaabcabacdbacdcbbcdeebceaeeedcbdbbcedebeedadbdddbeedbeecaedbeaacdedeedadadbadebdcbcbeaedabdbadeccbabcaebcddebacaeeaadbbaebdeecaedbdddedeaecccddedecdcdcccaadbadeededbecabeacabdeebeebbccddbebcddcbabbdbcdcbaaadecedabcebddcccdabecebadadadcccbddbeaebeceddaceabdcedddeabeedacbcaddeaddcaddceabcbedeeaacebdaeeacdbeebcbabbceeabeadccdaaddaceaacebbdebdeddcaedbadcdcccbcadacaddccecddacbddeceececebdccebabbabcecccdaeabaecddbeaebbabccccbccadadceebaebbcaeeadcebaeaebcabbedeeecccebeacebcabcdeeccabccecdddcbdeadbaabacabcddbbdccdceedabdecebddadbcedcacebbdaaddcdabbdcaddacbdbebdeebddabccddbaadeeaadbcacbcbaedeeaaddabbaaeaecbbedeccebcabbeebcceaeacaaeabcedabaaabebceedbceedacecccaaddbdeebdbaeacdedbdbabcacaddaccdbabebbeabbcadbcddedabceceaccabdbdeebdcadebbbdddbaebbaceabbdcdeccbdbbcbadddbdeecccbcaabbccecaaacdcebdccaedaabeaddceadeddaaacdaaadddbdeebedeadeaeecedeadaaaedbedbdccbceeececeedaaeacadbcdadabbbdecbcdacaeeeeeaccdcdeaaecdcaedcedccccabeddecacaebcabdbaaedaeebbadaceaaabbdccaccedeeabcdbdabdcadadddbcbedaedaedacdbddbbdaaaebdbbddbdeabbcbbbedcecbebcaebadaabccddebcddbcabedcbabedeeaedaedaecdbeccebabbebdeaebeacbbaccbdbbbdebacbbdebdedaaeeebeecdaebaadecadeedddbacbaebbeeddacbadcdadaababbacecdccbddebabaebededebdedcccbebbeedddbeaecaacaaadecbbbaadcaeabedbaedcceaddcabebbdcbbdceacceddbbaebeebccaeedcdcacbcbddecccbabaecadbcecacdaddcbdecccbbabcdabcabeaeacbbdbaaaebaddedeceadcedbbebeaaedcddedbbbeadcbabebbdebdbdbdcabbcdeabecadcddbbbaacccaddabecebeabaeaddebcbddccadcbacedaaedeaccebabcbeaeedaedcdcadaaccaabacaeceadecbcaeaabdceddedddacbaeeacbbabdeecddaacaddbacabacdcddadaaaddeebaaaebbaceebadcdadbbadaacaacddeeeaddcaabdcadaabbedcbaedaeecacaeabdeccddaaaddbdccbeebcdecacdbebdacdedecccedbbecebbccdbeaeebcdddbddcbadaaccccbdbbabddbeecabbbbeeeaacbcdaaeeadddebbeeebecacebdccbddbecaeedaebbacddddbdadeaeaedaaadabbebdebbaaeddececbbbbbbadbbdbbcdededdcbbcaeddebedadeaececbdbdaaaeeaecbbebaacabaaacabeddacbeccbdbdcccebdebbeacdecdcacebcacbecdddeaeeebebbedceecebedaeccbdedbcbdaadcaaeaebeaeaeeaeeadccdacbcaddccdabcceacdcaacdcddbdaceeaedabcbbacbbdcbcbdeadacaeeeccbddcbebabbcdccebeabadbbcdbaecaeebeaeaacbecadebebadbdebbbdebbbcaacdaddadabcadcbbcaecbceeeacebaaaaadeadcacaaaececbaeeacdeaacecbecdacecdababcbdbdbabcadaeadaaeacaedededdddacbdbdddeebebebdeedadcebdbaddbedcddabdacccaacedbebccbeabdedcccabcbcaddbdcebabaeecdddbedcedaabebeaaedbaebeddabdaaddcabddeabbbebddedddeacbababaccebaeebdbabbaedabaebabcacdaeebeccacdbaabbaebadeadabbdddbecadacbdcbccadccddcddddbedddbdebbbeccbaeabcabcdaadaccaccedddebaadbbcbececcabbbbabbaecbddcbebdceeebdeeedccdecabbbbceeecacedaabcdaeabbcdecadbaeddbdebaadbcadbbaabbbeebcdededcbcceddddedddecbcaacadccdddaeaadccecbdeedcddacebcbcccebabebbedbdcaadbcdcaaccecaccecddddeecacddaadcdcebbdcacabaeeeaabdaedcbcdecbcecadbeceeeeeedadddcbcedaaebecbbebbceaaeedecedbcaaecacadaecebaecdbdeaebbcbaddbecdaddbeaedcdcceeebebccadcdadadeaebcaededbacedbaceccecdeebcadadbddaecdbbcabddcdbbaabdecbacdcdcbbbdbeeccddbedceaccbbebeabaeabbeadecbdaebecbaaacabeebeaacdebdcaecccdcddebdbdeaebcdbaeecdeabdaebeaabbbacadebabcdabbcecbecbccebcddbababedeabccdbeeecccaaaeaededbadbaeaddcbccdecbacbcedadcacadacaaaaceaebeaadccddcebdcdbaebbecebdbebaddbbbabdbecdebbebbececcabadebcbbaaeadcaeebccbbabddccdcbbeeeeeddabcbaaccecdabdddcddaeadbcbbeacdbcbecdbdbcccdbadcceabeccaebdbcbeecbcbcecaeaeadddeddadbaedeaeabedabdecdcedabeeadacaedecabdcddddccdabbbdddeacccddbbeaedacadbebcedcabecbaddbaecbaebbdceaedaabaedaccbeceaedbdbbacdebdaeedcacadcbeacbecedadcdccabaecaeedbeddebccdcadbaaeccaaceeadecbdebdcecaceccebeaeaceeccbcaebdaeedceebcbceedbccadbccecdecceeaeeadddaccbbbccadccadbcedebdbeeedebbbacecaebcbbdcdebebeaeeaeaacaeddadacadbcceadbbdadcdedeabcaedddaaaccbeabcddcbdbcedcabedeabddaeeddbaadbabadeedcccaedecabedaceabbbdeabaaaddabeccddbbedeabbababdbeaeddedaeccaeaeeeeaaaccadcbdbdcadddbdceeaedabcbddbaaecdeebbbddaceccadcaeabbeeddcbcbeceeebccdedaddeaebdadbedeccedeecdadadacaeeaebbeebdcbcacaababddebdadbdeeeaeaebdcbeccbcdcedeecabedeaaedbccddcededacecddececeaceaddeecebdbdacebeeeeccdbdabecbcbdabdadacabaabbcbeabedecdaecebbecdaedaecbcaaddccbabecacadeeddbbceedaeeceeadaccbdebaddeecccedadacadccbaaedebabbeaaedbedcaddccbeabbeaaeaabdaacbecdccddbeeadbabebcebabbbaadbcbbabbceaaaceaceacbecbbdbdecabcbdaccdbaeceacccbeecabdacaaeeacedcaadeddaddcbbbaadbebcedcecaacbdebacbcaebbdeccaddabdbbebaabeacbdccaebeecbbdecebaecbbbcdaceaacdcbdbedcabbcbdcaedcdcadcaaccddedeacdabadaeeaadaaaaceaeeeedcaabeacaaedeeadeedcddebaecbcabbaeaececcbbeadaccdeadcdaaaedcebecedcaecaeeebddccbdaabdceaadbdbbaecbaabbbbcdadceccabccdcbbceccdaddbbeeedaeccdcaecbbbbabdceaecaeccedcddeeeeaebbaeebcbdcbabedcbabdcccedbebabeeedeeababacabbcdeccbabcbeedaddddeeeccdaeeabdeebccbbdaeaedceaddcceabcacdababcdaacdddbdaaeeeececcdeccdcbbdacababeececebcacadeddaaaeeeeabdeddeebabdbdaeddbaadabcbadacbbcccddbaeeeeecbbbcaeebbdebdacaccceccddcbadaabcaecedaeeaaaebaeaeaaedbcbcedbeaaadccdbaaacbbbabeccdaaaecebbaabadbcabccdedcbecabbcbadbeddebeaedabecadddeeaceedbbecdbdebdcadaaacccbadaebaaeabeacdeaccaacaddeababdababaedeeceddebedeadaaaebbaccbedbbbecbcddaaeebcabcdcababdaaceadcebeddedaddabcaacdadcaababbcbcceeaabdaceeaaeacbdababceadaabbeacddadacadcceabebaaebbbbbdecdbbbbdbcbebaabaedceebaedcddcdddaaaaddebdaeeabeaaaeebbbaeeaddcdbebdacdedcebddbacacbeaebdaceddcadbcbadebdececadbeccedddedccebacbcddcaeacdcaebeecabcceeeadddaecdabbddaccbaaddcbabbddbdaecbceadceaeacdcadcaebceceeaabaccdeaaccbbcebadecabedcedeceddceeddcedabdeccccdbbdddcaabbabdcbaaeddecccdbbdbabeedcbdeeabaeddbdcaacddcababcebceabeecebdebcadedccabeadceceadbacacbbbebeeaededccdcadeebddccbaddcbebddbcbcdcbbdacdcabdeaecadcacebecdbdbdbbdbedcebbdadcbdcaacbdabebcabacdbabdcddeaaeaceeedaceebaaeceedccbabdbeaadbeceaaaabaabecccabbddeccdedbdcaacccbceecdcddbededdccadbcdeeebbeadbdaddcdeceebbeccbddddeeaaabaadbdcadddceebbcaebdcebbaccddbbcdedeceacbccdeeeeecaeddedccbaeebbaccecdabaebddaedcbdcdcddbdadcdcdcbcbbedbdcdadbdbabcdcbadebaaeeacdabdddaeeecccadcbeaaecdcaabcababcbbaccdbaabdceacaebbcabadedbeebddacbebaccabbdddeeaebddaccdebebdeceeccaecaeeccddeecccbccbabcebccaaeaaebceeccbcaaacacccedaeaebecddceacedecccbcacaeccaaadacaaddeaebccbceabddeeccadcbdcabbbaabddecdacbaebdcbbdadeaeaacecbecdbeeeebcbecddaedadeadbbacddedbaeddeabeceacecbbebbddcccdeeeaddebdcdaacbddcebbeeaabccaadacdcabadcdaacaadaceeedbababeabeccebbdeacedaaecbdabaadaaaebbcbccbcbdcccbaabeebbdcdbcccacdbecedbdeedebeedceeacadbacdcbadabbdaaccecbebccdcecbbbdeacabbeedeecacbbededaecbecdcbeaadeaebceeddbbcabcdbebabdbdcaebdcbaeededbeebabbcbaacbcacddeebccaccdaaaeddcdbddbdcaeeeaeddbaabedbddbdbcedaddbbdceaaabdedabecbedbedecbbddcbedbedecacbdeabcabeecbcbcceeecdbbeecbecdaaaedbccceabdabeacadedddddedbdaedcaeabddbcbcbceceedbcedbebdbaeceaadddacaaddeabbbaceeaaecedeabbbbacdaeecebdbbaebacbeebedddbeadcaceeeaebeedadcababeeaecaeecbdcbebddebbbdacecdbeedbeaceaedcacbeeabaddcbebeeddbdbceeedccbccbadedcababeedaaedccabccaebeaabeabeadaeecaceebbeaaaabeebbbeadbeddbdeebedbdbddbaeaccdecbdeeedcaeebabdbadccddeeadbaebbdebeecadadbdcbdbeebdbebeedabccbdbebbeaceebaaaeddcecccbbdbbcaecbdbbadbeebedbeaabbdbeededeaabadacabaaedddaadebcbbeabacecbabaabcdbbbbccaabebbdaaeacbbabaaedbdbbcbabcaaedbddccacdabbbebaaacedadaacdcdcdeaddbbbcadabeaddbbcdcdcbacadaeccccabeddccebbcbcbddcaebeaceadccdcdcacdebdeaadccbbddeedcabbdbdabcebbabaaedacdabcebccccbaeabcaadaaebabdbcddeceedbacdcdcecbabebcdbbadeabaddbabccbceeeccedeeddebbdedaeecaebedcceecabedaebbcdaadddeebddabeddddbcecbbcbcdadacecebdadeabbdaacecbebacbbeaacabdbcaeebaebcccbedddbdeeadeeeaeadebeccabbeedeaceddaadbdbcddedaeeccbeeccadcebebccaabdcaebbbcccbcaaccceaddaeaeedbcbeedebeadaddceceeaebedebdbdeedbdbabdccbbcdaecdbddbdbeeaedbedacabadabecbcdeeeddcdecdeabaecbdcddbdaacdabadaeeddaebacbcacdbbddeeeecadcaeddbbcaeecebeaaabebaadcedaebeccceeabeecbeecaeaaecdbebdbacbecaebdebedbbcdcadcecbdddbbcacbaaaeabbdbbbbbeeeabbaadcadccadbacadbeaedadcdabdceceaddbcdcdbcccbaecebcbeeeeeaeabcddbabdcaeeeaecbadaeebcedacdddcdbcecabcdebcaadaadeebeabeadbccbbabcecddcdbcbabbebcddbdedbabbbecbbadeedbeaaacbadcaeebeedeededddcabcbedcdbbaebddeadedbdeaadecaeaacdbbdccaacbcebaecaedeecbdaebbadeaacbaeadedbdaadecddcdcbcbebbcdcdedcdccbbdbeacccccbaeaadbabbaeabcebceececebbccdaadbdcddedbdbcbdeaadeadccddabbaddeabceebacdeaddbabeadbbbbcdcecdabacedeeeacecbebcabeadaeeddcbcdadeceaadeebdcbebeeaebcdeebebeaeebabbaeaeabbddaceaacadaaeadbcdcbedebdeddeeccccedbadacbcbcaebbaecddbedcddbbbeddbcadcbabdbbbceddaaaabedcacdaceaaddbadcbeebadededceddbbadabeadbcaaaeeebbecaddbdaaebadeeecbddddabcaabbbeeeecdbaccacbadcbaecddcbcebeebddbabecaabcbaaabaabdddaaeccecdbabeaacbebbababaebccdbddcddcccdeacebdbdddbacedbcbbecdbbaaaebebbbdadcaadcbbcdedcbbbadcdbcccabdeaedddddecadceddbacdcdcebbaccbdeebababababeccecaaedddbdcaddbedeedaeedbaeedcaedceabbeebdcdcdbeebabbcbcbaaccaaaabddccbbecdaceaeedbbeddabbacacaebdabcccacecedbacbbaaeeaceadddcbdaccebebabdbaaebbcbeecccedebeedebbeacdbcbaddbbaddcadabeecababbbecabaadddcdabbabcaadadedeedcbcdadeceeebccaeacebaebdadddeabcabcbddedbeaecadeedcccccdbabaeeebbacbdbbcaaacbdbcdcadebaedbccddbacebacaaaeaeacbbcaceabccbaebbdebcdbdedaeceaadabeebbedaaecabeeabacdcdeedeadaaaacebbbcbbcacdabaaaacdededededaeeaacadcacebedadbaedcdbbeeeddccccedabeaacedcbbdbbcecadcdaedcaedceabbbbbaebcabceceedcdcdaadbebaddcbadaebcabcaacbabcecdeebcdaebcdacbddbcbbbddeaccaadecbdadddbabececbeedcbaebcdaecccedadbccdbabdaaeddcceacbbdacabcceebaedbecedecebadbeaaeceddedcabcacdacbebeecbadcacddbdedeedaccabcbeeddcdddccadcdacabacbddccdeccddeedadeebbecdecaceecdaadceabeccaebdcadcddaacacbacabbbeedbedbeebcabcdeedceaaebcddcebebcebbcadeeebdaddcedbaccceaaaeeebecebdcddccccecaacbbbdaeaceaaaaaeeedaebacbcbcaacabebabbcadebdadcdaacebcccaebbbabeabdebddcdabdaebadbabdadeabcdcadbbbdeadedcebaceceadcaeadcbaedceacdacdcbaeddcccddaeebacdbddabdaaaeeddeeeecedbdbbcaabdbaacecdeebaaaadbedaeedddaabcdadbccebdcbcceadbecdaecdaabcebeaccbecacaedcadaebdedbadeabcddcedacadababaeaeebcedcecddcbccbaddaecbeeeedcecbbcbccaecbdaacededdedeedabaacedebaeccddaceeeceaccebbcdcbabeccddaeaaabbadcccbdbdbecaacccbbcbcbdabcccaebbbbecbceacedcdaeceddbdbedbeaabeceeaddacaebbdedbabcceadaececebeceecddbeebedaceddaababdcddddbaebbbcbdabecabcbdabdbcebcbaeaddddddbdabbceaddcaaaccadeaaadedaeaaeeeeebadbbdeaceaabdadabedcebdcddcecdbccbabadebbbccedeabbbebccbbdcaebeecbbabbdeebbecdecbcdbadbcaecdeeaddeadcccbadacacbaeaebaaabebcbebcaaeabecbaaaeabaaabadeaededcdbebcbbcddbcdeedeaeadaaabdaecccdbecabaccabadbcacbbcdbecdacaeccddbedceeadcddeeccaccecaeabadeddadddcaadccbddebacecedaabeddcddddecddccdaabaabacdbdcbbceabcddbaabddbbbaebedbeeeedeababccabcdddcadbadddbdebecdcbbbcddbadbbcddcccacbabeebceebdbbcaadbaacbdccebacbcabeebbedcbeddcabaebcdecbcecddaadcbacebebadbdccbeeaadedbbaeeeabbeecdedececdeeeeacdbcdeebeddabdeddbedeeecbccaccdcddacedddcbebbdedacdeebaecccaeecbcbeacdedddcedccdbbebddeeeadabdcadabddeeeececbbddaaccdbbaceeebcbddddaaaecebededcdeeddbcdaeaabbaadabbbddbbbdedbacddadabdbebbebbcbcdededcdbdebcabddccbcbcdabcbeabcaeaaaeaddacdbcdeeeeeeadeebcecccbedcbbaaddbabcbcbcddededccdbdaadadcedabdcadebbabdecbeccbaaaadabaababbaeeacedaeeaeadecdcbabdbaaccaadcbcaabcaeaececbabaaddddebaabdacdadbeadabeaccecabbabdceebbacaebcebcedaebacabcbeebdcedeeaecacbdabaebdadcbecdaaaccdeedebecdededbacbdedcbccebdceeeccbdedbbeacdebaacabcedacaebbaaedcbaeaabcedebddbeeaacabdcbaeceddbeccebbdeacceeccbadceacadcdadcdceeadaebaeccedddbddacaedecdbcceacbeaddbeaeccddbadaceddebdeedaeeceeadbedddbedabdbaeaaacdbcbdcaecedbdaccebebebdaccaaeabdeaabdacdbdebcdceaabbdedeeeaceabcebdddeaccdecdaeecbdbbadbbbdbeecaddeedabbddedbedeaccbbceacebdccceabcabadddddbbebdaedcccdeecdbabcaacaaaaaebeecbabcabebbcedeedeeaacdacbdeeabdcbdedccbceddcbadeadeccddcbcebbccbaacdeedbededbbedeebaaaddbcdaebddbbceddebeedbdeedeedaaebabeddebbceedacbdaadcdcdcdbacacbecddeaebceeeddeeccaddabdddbaaecdacbaabacdcbdccedecbcbebdbbabddeebedeeecdcacacccecaeaacbbadcbbcabeebbccceaacddecbbcedbeaddacbadaecedceddacebcaaaabebaeddbaecbeabedbacabaacacebeecdadeecddaebbbabcbeaaacdcbbedceceeeebaedeecbbddeedddcdbeeaecebdcdcdaccadcbdbdebeecabeeddacdcdeacabaeccedbbcacaacebebdbaaebacdcccbaedaceadbdabdaccbcbcaddaeedcdccabecbabbdcccebacdcedddbaadcedacdbeedbdacaacdacbdebdadccdedcbbdbabcadccedabeeccddebeeadeaccaaaddcbacaadccccdbeaacccecabaedcebeaeaeaadabbdcdeeeeebaadeeceeaaabeceadeeabbddbaceeaedbcdbdedbedcddabbaecaddbdbeedeceaecaaecbdaadacdeebecbaaddcccebcedbeddaddddbddaeeabcebbecaaeabacbceabedcabaaeaeaccbbddcbdeddadaecdccaacdbbebabddbccbadcedebadcbaebdaddbeacbebdccdcbdaadaacaeabebdccbbbccbcdbddbdbbaacdcecdceddedcdcdeaddcadadceeeeabcbdcccbeacbcccbbcccabdddebabbcebeccbbabdcebacebeebbcabeadbddaeebbbcdebabbadbbaaabbbcdbdbbddaabaeacecdaeeabddddacdeeeeebeacdbacbabccaeadedddcabbbacabbacedbeacdbabadcbedcdccbcadeaaeceadddacdcadbcaeceeadbdaeecddcdecdaaecbbbdcbbceeeeaadabbabeebbdcbbbcacbbcdddbeaecdeececacdbeeacabaceacccdbbdbbabaaebcaaaeddbccabaedccdebaaaecedaebedbbecacaacdddecaddeccbadeaddeeeeabbeaaccadabbbccbecacadebbdcebdbaebabeeeeebddeeaeddbcbccceabcacaacccdacdbbdaadcdbccdacaaeeabcacaaadbedaeaeabbddaaccddeacbdebbacdceadcddabbdeddeaadcacdaccbcedccbedbcddeabdaceadaccbbaaaabaedceddcdbbddadeaeeeddebdcdcbddceaadbdcacbbdddececbadbceeedceeedcbedebacaeecddaebccaeaabcededeebdacadedacaaccecddbccbdadabdedeceaeddadaeebbacacdcadeacabaaaeecaebacbbeaddbbeeececddcbebecbbbaacabeabdddaebcbdebcebeaacbcdeeebcbbcacecbecbedaaaaeadbeeddcbbbdaeecaeadabbbeebebadbccdcbbeaabdebddccbeceaddecbbcdadcebeedeaaddaeacbedbeaaaceaeeedeaadaeadacaabeeecceeeccdacacdeacaaedbaacdcabddedcccddecedbccceccedacceabebabdeeebadbeabedcbbacceadacdbdcadcdeaaddabbadcecdcbeccaebdceeadcaabdbbcbdebdcbbaacbddaaacebaacbbcccecbedbceeacecbbbacabdcdeadccdebacdbcbacabcdaaaacbdbadacbdcbcbcaccccbeacddceccdbccccecceacabcebaaaacbbbdddeccddaebabbaaaabbeeaceeacdbcabbbaddeedceccdbaeedbecdcaaceaeecdeaedccebdeabaccaadabadccbebcedacbbcbeacbcebbaaaeaddebbcaedcbabaededcabedabdededdabbbabbbeececcadbccebcdbbbaeebedcebbccabdacebbbeaaceedabadcdccccdaceebceedadebcccbdaebdebcdceeadcccecdaabbcadaeddaceecceebcadccbcbcdbcecadecacabacbecbaeddeaeacbdaebbaedcdcddeaeeabcdbdaaccbdbeecbcbadedeaedcedccaceababcacbacdeedccdcbdaeaeaddbdebcdbceabddaebadccceeabddcbbdbcadcddeccddadeabcdbcceedbcebaacbbcdacddbceaaddbcdddceadebbdcadaeacaabeeeeebaaccabbcbbeebcedcadaeaeddadaceebadacaeeaecaedaaccedcdcebccedcdccddcadedcdebedecaacbcdbbdabdacdeaeeecbddcbdadebaeceadddeaeadadcdaeddeebddbdceedaadeddccedbabbeebdebacecbcadeccdcaceeaaabbeeedbeedccaccdaccdadeeedcdbddcdcabddaececedbceadadceceabebdebaccdeeacddcbbdadbbcedecacddadbcebedadaceccdbcbadaebaebbcdddaddbeeaeccbacbddacdabeeecadeaabbdaecdcbecadaaecdeacbaceaebdaacecdeebdbcbcedbaeebaabbbdebebaebbbcceebdadaaddabbadcdcbeaeddbdbaeddecdaaeeaedbebaadccddebeabbddbebcebebdaaebcbeecaeecebdabaddccbddaaedbdcaacacbbccdbadceabeebccadcddcbbabecbdaeccdacacabebdcccccbeeadcdabcaebabbdbccaeedcdcbadbbaaaecdcecaeeddddbebeeeccdcbadbabacdccecedecaaaeceaebacaebdeecdaeddbdadaeecddbbecbcccabcbbebeeededbbcabcbadbdedababddbaccaeabbabedddcdbbebdbcdbdacecebdcaeeeaaedacbdccecddbccabacdbeaadbaeaebadcecbadddaedccbadbdbdeacabcddacdbbedaceceacecccdaeeddbdcaaebeecdeacabaacdacbcdaccbdaaacadacbbbdbecdbdeeadabeebdaedecbcdecdaeaadeecadaabcbaebbbadcdbdbceabdabecbecadabceacbaedeadeacaddaeabbdcdeecabdaddbcedccdedaabaedcaeebdbbceacabcedacecaebebcdcbeddeecddadaeccedcdceadccbcaccbaccdbcaceeeaeedcdbdaacebcedceadaccbbadeaaceddaacbebdeebcaabbaaddbaceadeadddbebbcbaedebddcedeecaacaeabcdbceabecaaddbbebbacbaadbaaceeecceaeceaadcdadaeadcedabedcdcaceddddeabaadeacbbaccabceecdbbdccbbadaedaecbeedabbdbbbccbbdcacebbecabdadbccbeaccacdebcbacadededadabacaebdcacbccdebdeeecbacdedadbbeeadeacdbeebbdbccddacadeadcdbcbdabdceccaedbdbddedbeaaebedecbecaecdbdcaeaeaaedbbcbacbabaaeeabbdaaeabddcbddedcdeaaebdbeecbbadbaedccbccecdcbeadaeddbbebbbaeadbaeeeeeacbceeadeeaecdacdaeaebbeaaeaaeeebcbaedddbedbebedbbddbbadaecabceabdcecbebcebdaccccdbcccaaebddcadaebadbaecdabdddcacbcbbadaaedecbbadcbecadbccdeacdbecddbeeedababcdccbcaadbdbabadaabecbbcecebaabecaeadaaacecadcaabeebaedaaeceaccadcbbcbcdbecaebaeadaaaddacedbbbecaceaacbbcbdcddbdbbbdceaeacbcdcbebdecbddcccaaeeceeeaceebbeeddbebcebecdebecaebbecebceaacabbeecabbdbbdcdcceeeceaaaccbadbcaedeabaacedcbedcbeeabceabcebeecacecedddeebbcadeeaeecddeaaedbcaaecccdeaceadcbaedecdcdbdecedaecebecedaadaabeddbceacabdecbaebbadeaaeeebbbccbcbaaaacaecceedcdddbccaadddeeaceeebdaecedbcccdabacdadedaabaaacebcbeeccccdbbbdabcceaccabbbacebcaddaccbcbaddbbeeaeccbcacebccaeecbceaebcccbbbbeeeeeeddbebeadaaccadbcddccedcbcccabbedaedebbbddbeebaabccaccccdcdaebdaeeeeeecdaaacecabadcabddcdaacdadadddcbcbccebabdabcbacaaeeedbaacbeaedeedaddebbdccbbebcdcbeabdbadbceaeecdebbddeedbbebbcdcddddccbbdecdaaaeabaccaaacededacabdebeebdbababbdaecabeabdadabbcbeaeccdedcadaccceedcbdaaecbeacccceccaeccbdabbedcbecaedabaaaaddeebbecbaedeccbacebcabceaeccacbecacadedbebbcbdeeaebbddbeedbcaabbecbddcdcdababeacbbdddeacdbcabebbdadbdacdbaaaecdbbdcedeecdaacbacdeeceaddadeddbeabbcbebaeddeeabdbdaadbbaccabdebedeacddccdeebdaacdaadbdccbeddbbbdededadacbbbbaeaedcbeeabbadbceeaaedbadcdadccbbabacadebcecebacecddadbeddaeaeceedaeeeeeddeacddbdacbdaaacbcdabceecbcbbecaddaeeecdebabbcdbddeaecdcedbcceaecaacdbdddaddbbadbcbdcdeeecbbdbaceeadcbaaaadcdcbdbeadbcedddceecbddaaaceabbeddeaabeabeccdcceccebebaaaeeccceecebbbecabadcbebbeeaccbdbddcbeeeebbedddacccadadbedcddbeccbebedcebaabaacddceebccbcebcacdbadacaebadbbaebadeececedcbcbedebcbeceaddaeceeedbdbeceacccecceccbadebbecbcaecaedaadcbecbeaeaeeabcbcccdbbacededcecbbadbacaeaeeceeeaaeaccbdccaeccdbeebccebababcddcecddadcadebdeedcedabddacecccddaaeadecabddcdaecadeebcaeaeadecbecbdecebacbabcbadcdaedbdecbeeaaabbbbcaedbebcecbdebdedaebebbbedceaaabdedcbaabcdceecccdaedabbdeacbbeabaceedebdbedbaebaceeadddaacaccbbbcbededbdbacbbdaadbbabcccbcdcdaddadedbdbbebcbceecbcadeedbbababbadbebaaccdaeccadadeeeabbdacbacebacabadeecbbcbacccedbaebcbbaedbeadcdebeddacaaacddabdaebbdebebcbdceaebbaeebccceeedcaadaeddedeacdcecddbbbcbccbecceeedbebeacabdeeeccbbcbeeeadbadbdddaabbdbddacadacbcecbaccabecadbddeedbeaceaddcacbbbdeeccbcdaaeebececabbeedebebddabdccbdeadeeaabdadbbbcdedccccdddebacaaebddbabccacbbbeadddbcdeeedabaebcaebbcdecacbeddbcbedabdeaadddacccdedcdabdbebecdbbebabedaacdeccedcbdcaaccddbdadbaaeabdadaaecbaeccaaddabbdecdaaabbeedcabebdadbeaccccebcbbcaedabccdceabaeacbddaeeccbeccabbbcbeddccbbcaaacdbddbbecadacebbbcdbeacadaadecddadedcbacebabbecaacedaadeedcbaeeeeabdcecaeddaaccacdececbadedaaceecebbedcdeddebbeccbbdecddeccaccdcebbeececcbaaebbcbdeaecaebaceddbadaecbadcbeeebbdeebdcaaeeacaebedadcebaedaabbdbbbedcbaeacbccddcaccbebceecdcbceaabadcaabceadbdccebbbcecdeeecbbdabbbbddbaabadeccacadcbcaadccbbebedabacccdbaedeceabceaeeebcdceaaeecedeaadcdcdeabebccddeeeecbaecaeeecdecebcecbabddebcbaceacacacacaaccaeecaddabeacaccecaabbabebcbeccdbbcaceabadccaeaebaaeacbecbdbaabcdbecdaaeaedadddaaaebdeebadcaedcadbceebaaaabdaaaabaadbbdbdeaacddcaeddedeaadcdedbaceeeeaeeeceebaaadeebeddcacbeaabebadbcaebcdcddcabbcbebbdadaaadedebdebdeebacccaaaecdbadeddcdcbebddcbacabddeaacbbddccdacebeadecadeaeacebcaeeaeaeaaaeadedaabbcaaddaaecbacaceacddcdaecabcdabcddcddccedbabbcccebcddbbdbbadebcacddbeebcebcdabebbdbdbabdbbabbddedccdaaebcbededbebcdbecbbceddeaeacaceabbddddabedebbebcacdeaeeecdcbabcbcececcbaaebabdedceccacbbaebbebbcbbbaeeecbaeabddcbedcaaacaadcceecbbcbecececdbbacbdaabcdbaecbccceabedddbbcbeabbccaaaceceedaadbedcdccecbebecaeaceeecaaeaebceaededbbbcbadbcaeaaaeeebebddaaddddaecaeaababaadabbceabbccdceddcbeaabdcbeabaecedceacbaecdcdbeeecdaaebadbedeceebabbabdcecaedadbedceaceedccecabeaaeabdedeaabcbbcbaadaaeddaadabbdebbeececbbbadeaeebceeeeabcaabcbdbabebccbbbdbabacdccbbbaeecdceaaeacbbbeeeaabedccdaacdadacbdadacccaadcdcbbaaadbeeeedbaccadedeeccddccbaddedbbbebcadbdbbebddcbbbdbcbababecabaacaabccedbbbadbedaabedbababbbacecdcbeeceddcdcbbbbadcbcedacbeeadbbddabdecbbcdceceadcabdebaabbaaaccaaadddeddeadceabcebdadecddadebeaabdcacceaebbcbcdbccabcdaeaccacccecacaebbaeedbbdbbaddbccaebdaceeedeaecdbecedebeacdebebebbbebcccedebebaaeccbcdcdcdeeecdbcdcbebcdcdddcdddbdabbacadcabaccedacecbaedbccbeacbcdcdbcbccdbcbebbedcdebecccabbdacbadcbededccbdcebeeaccceeaeddbdabbeddabbddcecadaeddbbbcbdbbdaccaadecbacdccdddeccceacbdbbdadabccdcdacabeaeaccbdabebdccadaeebeaebbbdbeeccdeabdebdbbdcbdeaccedddcdbdacdcbbcececbbeecbebcebdaaebebeeeceabeaeecbedebddceddbdbbeeaaacdbacbaabbacaabedbbacbcaabdeabdababeacdcccedeccbaabceeabcaeddeaadbaaaeaabbcaceabecadbcbadedccbcacadbcbcbbedbccadedcabdadceeaccbcedeccedabebadcbbbbbccccaabcaacbecaebeadbdbdebeeaddeaaebaadbeecdbebbbbceebeaeacaccdbeaddcdbccbdbabaccbdcaabaabeaceaccceabbddbecaadcdabdebbedddcdedabaeebccdddcaccacdcddecbbecdedecbeacbcacbccdaccedceaeaddabaecebdccbcecebcccdabeaceadceaaaadddeacbebbdccdbcbdddecbbbebaecacbecbbacebceacbbacbdadadaaebaeedbcbbddbccacaddbdeddaecedbbebedeeaeecaaedcbaaaddecdbeeebacacaccbcccecdadeadcacebdbcaebadabbbceabccbceceeebcbbabcaeadeabebaadcebcbbecbacaccbecaeeebdcdadebadecdbaeedbbaebdacebecddedeabdcceaacbcbeebadabedcbdcdacacceaddacdbeebedbddcbedecbaabaddabeebddbbeeabedbbcbacdbeddbaeddbaedbdeeaacaccdadabdebdbacbbeecaedcbeadbaabdceaeddcbeadbeceddbeeacbadbdcbbdabdaaadeaabaeeccdeaaeaddedebbddebdcbaecbadcaeeaccbccdaeeceeacbbadcacbbaceacbadabedbeddabecacdedeecdeeeceecaecaabedaaacacbabddeaecaeadbaddbcbeaeeaeaddeedcaabaaecbddcabadbeadbedbadeedbddbebcaebeaeccbecdbddbacbaceebcdeccdabdacecdcadcaaedccadeecdebcceaeddadbddebcebededeaebcabdbccdcbacbbdebedeedaecbcdbbabecddcaeaeaceedebccdeebaeedaddedbbcacadbbebbdbadcdedcdaababcdacbbcdccbcdebaacbbceaeccdbbbdcebcaaeabdeccbeaddcedbeebeddcddadeaeeeedbcecceebedecbddddeecdadaabbcccdeacbbaebddbaaaaeebababcdcbeebceaedebcbeddebdedaabdceceebddbbdbddaaccbecddbabcdeeaeacbdadbbeaebbddaaccbeadedeabdbeadacccddaadedabeadcdbcdddcababebabaeccacecdcbcbcdbcbedacecdbebaacddaaeaadbbdaaccaedeeeacadcbebadabeabbcbedecbccaaeeebadcacdaebcebeaaecbdabcdcedcecdeddceceedbebacdabdcaeddbaeeecbbdcaecaccacacabebbdadaadeabadaadaebeaeacbaebdaebebcdcceedbabcbdeecdabcaecbccbbacedeabbcddceeeadacdceecaebbcacadccadaccbdbeaeeaeeadaeebabcbbeeadadeedbcaaceadedbdcdedcbeddbdaabbbebaeeddccbdbeebabbdaddddbdbeabdebadcdbcaccbcbdccbbebbdebbdeaeceeeddedeabcdeabeaacaadccaaaddabdeadcdcbebaacdbcbdcbadaadbdbeaaabcbbacbbbbcbeebdecaeaddebecaadbaadbcbbaeecbabbdbbecccdcebebadddeabedbbbedecbcbaacbcebbdeaebebbeaeadcaaabdceaccbebaaacaadddbdacbedcbedaceabaeebdeadacaccabaeebbccbbaeacbaaeacdcedecceccecdcceceebbbceedebdedebeeaeddaccccacbbdebedadebdedeebbaaecddcaebddecbbddcaacaacaddedebadeacadacddceabaaddccbccbabdacadcbecbaacddbbabaddeacabdccbdbaeaadebddaeacdbcbdaacebbadeeecdcedecbaddcccbaeaaaedcaccdaddedbecbaadeabddccdeddbaddeaecbbbeccedbccaceebcebbeacededddccadbdcdbbccebdcdebacedeceacbccdaaadddaacdbaaadeebcedadeecbcbbcbbedeeecebdcddbdaeaaeeedbeddcbbbeddacbbeeabeaecaeeddbdecbaaccbcaabaabeaededcacdcaddbdaaaeebdddeebeeeceebeabadbbaaadecdcaaedeceddcddaaacddbdddaaacaedbbaccadccdeadccdbaaabbbbabeaabdbebddbaadcdbbcadeebcabdeacedccacdaababdeaebebbadcebcbbacdaadbcdabebedaabeddbaadccebaedaeaaeaacebeececadccaedebacdbdbdedadcdaeecceceababeceeabaecaaebcaabcbaebbaaeadaddcbaddeceedccdbbbababeabeddecaedcbacdeadcdbdbcacebceaaaddbeecdcdcadadeeadccebbbcabebdeeeccabababdeecbadbdaedecadacceeeaedceebacedcbdaaeeebacadecaedaecebecdcacbbcebcbeeecbaceddeaebdeeceeccdcdeddaeacccaeacdaeccdcaeedbeadacdebdadbdabddedcbdebdccebbaddadcdaeabeeaedbaebbbbdadbeadecdbbbdbabeabcabcebaeeddcadcdeaecdaedacaddccdbeddbacdeeceeeeccedbcbdcecddbcdebedebddcbacbbbebcdaccecebadabcdcbbeecdcbedeabbccaaeaacdeedcbabecccbebeddecccabadbebaacbeeebaccbccaeeecedaebebbdcadccdcaccbbdebacecedbedcacbcddecdcbcdddcbadecebeabddedbceccdbdcedbbeaddedbbaaabaebabccececeebaedeeeaddbddccadabdbeceadedaaaabdcdcdbebeaebdcbcaccdeebdbedbadadcbdcddddbbecaebabeaeecbdacaadbedcccbbabaecdceabbcdadabadabebdbebacecddcedbdcdeeacdcdecbbbeddacaecbbcdadceddcbabdbcbdeedabebceaddbceaeeaedddcccceabbecadedaaadbcdedacacaeaeceaddccedeccaeceebcdabddbadcddadeaaaaaceecbadeabbeacbecbbcaadecadbeedabaceebbeeedcccddceadeeebacdccdebabebeeddecbdbecadaaeedabaeaeeabeacecdebdaecceebaecbdddebecdbbbebdaaecbaebeedcaecbbeeebdadcdcdedcbbdeedbcebcebdebbdacacaadaebedabeaddaaddcdeeeaabdcdeababcbddaaeeacdabaaccdbebbadbdabddadeaacdabebbcdbdebdaddcadadedccaacedecdadbeeecddbcdcaaecdeecabcecbdecccccbacebecabaadacecdceddaaebacedcedeeabbecdeddaacaeeabeaebbadeabceadcbaadacbacdaacabdceddcebcadedacbcbdcdabbabdcedecbabbedaaabeaedcbabeabebdbaeaabbeaaeccaaceddacbccdcccbbddabeddebcbbdacbdaeaabdeeeebbcbddaaccbaebeececaccddaedaaeccddaadeaacaeacaddcacaaccaeccdbbdadeededddceaedcdbbddaacceccbeedbcdeebeaeedbdabaadeebbedaebcddecdbdccbeeabddaeccdaecedccecbacecaaaeecdbdaccaddecaeeabdabdbaacbeeededcecddeabdddaeabcdceedeeabbbcaecceedcadbbeaddccccbacdebcbbebaddacacaceddcbbeaaecacecceabddbacceaaeedcdaceaabbeaedbacedccedadbbedecaaccabbcceadaecbddececeaabdddeaecbddeccedeabdaaeadbcceaaebecdcaabeccbbbaebdbbdeeebeecbdcdaaeabdeadadbbabdcbecdcecceeddbeaedddcccceddabaddadccbddbaeeeaaaaccdbcdddeecacaeabaddecbcadbadeddeecdabaceacebccbcbeecddbcceadbedcaaadaeadcebabdccdaadcdaebaabdecbeeecdacdddaeceaebdbdaccaceeadbbabdbbcabecbaeadeadadabccbcbbdedabaecdbcbedaebeaeddebadeaddeecbcbcbcdececddeabdaacbbbceeebaadbbeedcabbbbaadcdcddddadbceaaabeadbeedccccecedbbeeadebddaaceaebbdadaeccbbebeaddbcdcccdaabbdeeaadebbbeabaebacbaebcdcdeeeadabbbadcbcdddadaccedbbacbdedececbaaecaabddeaecbdeedbeaccbcadbceebdecaaadacecedeccacdeadbebbbacecaeaabcdeeaaecdaadadbbdcbaccbecbabecddddaaaebdeddacdecdbeebecdaeebbdcebacbbecccbcbcdbcbdaccadcdceedeebddbcddccaecbcbeebcbecbaeadeedbcedcbebbdcecabaddeaecdcacaaceaabcebcbddbadeeeabbbceaabaacaeecbbdadeadededdabadbbeccdeebccaaeabacdecdbadeddaeebdeadcbedbdebadbeecddebbbccedbbecdecccceedbaaebdbdadcdaaebcbebcbdabaddbeaaadeacebdbecdecbedebebebabaddceaebbddacccbededccabeecdccaabcaabbcbebdcaeaedbedaaacecbadacdeebdacaaaeeceeddacbbcabcedecccaddeadccccaccdecbdccdddbbadbabcdccadcdeedaeaebbabcdcddddddcbdaeceeaacdedcdadbdcaeaaabbbdadecdabbaebcbaedcacddebbabbadeceacebabaeecccabbccabbaadbaccdbaadbadcaedaccbceeeecbeddcdedaeedeceacebaceebabeeeadbcaedcbdbdecaedbaddebaeddccdcebcdbcecdcdaccdccecdaceeaeadbcedebdedceabdaededbbcdccbaacbcbadcdbeaeeecdbeaaddcecaecbeceddaecebdeeedcbababacbaaddaaceacceadcbaabcdebdcaebbdbdadcdceccebddcdacbedccceaabbabbdacdeeadbadababcbbbbcdccdabdededccddbbecaeceaacecadcbcdcaebabdaeebbeedebddbdabdccbbacacabbdeaeccbceeecbdcbeadcedddecacaceeaddbceacdacdbdcbaecacbdbcdccddecacbbeaaedaebadcdbdeecbaeebcbbaeeddccdabcdddedecaabeddcbcaaddedaaecdbedddacacabaabaabdabddaaeddaccbcdbaaebccdccdcdeaccdacbeccbcdcedcdbeabbaedaececdabeebebecbdeeeedcbbaaaeacbccebeaddaddccccaeaababdecbddbdabebaadccddbabeccbeddacdbeddedeaeecadceaccbaddadbcddcaaacaddbceebebacecebaaaeabebeabceededebebdcbcaedcecdbdccaceecbeedaeadaeaedbebadcccbbadeccbadadbaeddcabdbabaecbdebbeeaecdcacdabaeaaedbeeeceebcbabcacabcccbbeeeceabeecccaaaecbbdcddcdeedebbeedcbcccebdbeedacbbbceabbbeebccdacdeaedadecbeadaadcbbaabadabaaeedbcbcaebecceedcdbababeabccecbdcbbabeeecdbdcebcdbcddceaebaceadebbcdaabccbbaeadbcebcdedbdabcecdaaeacdcebeaeddeeddcaeeabebbacecebdbbabbdbabaaeeabdcacccebaeebcedaaddcbbbcdcccebcebccdacbacdbdbcdbedbdcdddceeecedcecbeedecaadeedcedcceaebccadbbbadcdbaabdaebbaedcaceeaadbbceeaecbadaeddccbeaaaedcddacaaacbeeccdbbebbaadbcedaacebbbcaadcaeaabadbdbedabcbbdcaabceaeaedeeeceeaadaeaccdaaebbcaddbacbcbbbaaaaadcaabedcaaeeaceebdeabbdceecbbdbbadaceacadcadddccacebbaedaedebccdeceecdddbeccabcbbddaecbaceddcabcbccbaeebdaddbaacecbdbdcedbdcebeaaaeadeeaeedbeeeebdedaeadcbdabdcbdbeabdedbadbbdcebaabeadecaabeeadcaaaadaedbaaacbeaebaddcebdccdcedacdbcabbaaeeedacaddcbeadbeacbdedcedebaaddaceaadcbdbbdbeabccdebcdcebabadbddcbadaeccaacedecbdcbaedadceabeedeeecdadaaebbeaabcacddcababebeadbbdeecedaacccaeeeaadccdeaadecebcddcdcdeeaebbdbabdeaddecedaedcaccaaaeecebeeeddddddbbcbbdeaaebaacaeeeaeaababbdcaeccbebbddccdbbacddbceababbacdbbbbccdccbbdbbcababaacaacacabdccdeabbccdcecadddcbbcddeedabbdcbdccaabcdbdaeabbdcabddbaadadbacdbcdeddcbebdbddbedceecbbbdeecadbdeadecddaceeadaaeddaeaaaaaaceebbdbebccadeddbceeabbedbcecdabaedaeddadaeeadadcdedcdaeaacbddbacaeedcccddcdcacaebdbcaaccaadebeedcbaaeeebbceccbaccaaddbcbbebcbceaebbadbeabeddcbacabdbccadbcdebdedceecdddebbdbdcceebdbcbbbbdbedaacaeeecaaadddcedabeaedbbabeddcedbaedbcddaadebbbeeebaadbbebcbabdeddbbbadececeedeeaecceddbcdecaddeebbbccaabdcccdeccddebbbccccccabceabaeddceedceeeedbbccaaceababaeedcdcaebcdaadcbcbcadedbecaceedccebcbddccdbcaceeadaacceecedbebbedadecabccdadbbceadecbaeebeccadbeddcecdebddbcbeedbbeeecadbcaadedeadaaedcbcebbddeacadcbdedccaaceaaaeecabecacabdbbaececececdedeedebecaeddbdedecaeeceacaaeadeabbcebbeddeedaedbaaabacabedbcaeabeecabbedecceecacaebedcbabebeacccdaacdbeedacdddeecceddbadabeccaabaadaaedddebcabaebdcacdccbeeceabceaedeebbccdaedeedbaebdbecaaccadacddacbcbcebdaecbaddeaeadbeebbceaabccacaaedeaedeccaeeedeeaeddeccddabcccbbabdeeaddbcadacedeccaeaadddbebaecadebdcaababaadebaeddddacaacadbdceacbcbaaacbcaeebaedcdcdcebcaedbaebbeeabcbeadaeacedbacdabcdcdebbbabdaeabedcdeaecadacdeeeeedcdcaaeaccbbdaaaeedaedddeeecdcccaabcbacdccdeeaadadaacaceddedbcbcdadebecddeacedccdedcecdcaebacccdecacaecdbcabeeeecdcecdabdbaeccecedabcacbdabaaeaadbdbeadccdaaaebccdbcacbdadcbaeecceeeeadcadbceaabcaacdbadccdaebceaaddcceecbeddadcaaaebabceddcdcacdcdacbecbcbdacaebcbbabccbbdaaaaacbedddbaadebcaaceadddaadadabaabbeebadccabdeaccceeeccbcabbdcdbebadbabaeabcccdccedabccddbddcedadaeedbabccbdbaedabeecaeaaacaecdbeceebddcabaaeccedadbacabaeecaddbeeacddecccaaeacddccabecdcdeaebadedeaeebdbebababddeacddeeaeeacadadeadccdbdedeeedaccababaaccedeaaedcbcaeadbcddbcaceddbeadddbcbdabdbcdcbaecbaebeaeaeaadcbabcebeaeeabcbeaceadedabbeaecceaadbddcaecaaedaacdeabbeebabaecaadcdceecebddbaacdbadbdaaeeebebeacbaabceedaadcadcaccecbceacddbcdceaeeedadeddcceceedaddacebbacdacadbbeeeccdaceeecaecdbbbbbdebbcaecbcccadbddcbbbbbdcdbbddaabcedaebccadebabecebacebabdaeddbebabacbcedaaadeddecedcdbaebcddbcbedaaeeebecceaaaadaabbbdeeceeceadecdbababebcdccabbdbceacbbcbacdcbdedcedadebceeacaabcdbddccbeddbedabbdeeddbedcacecaaedccdddebddddaaeddbcddacdbbebeaddbdacaacbaddeedcacadbeccebbcedeadebaaeaedebccebbeabeadbbbaeecddccdcddbdcbdecdbceeedcdeeabddecdbacdedceeeeabeddcacdeccddeddcacbbacedbaacdeaabbbcaaacebecadadaeabcaaebadbccddaabcbdbbbbabacddedecdbcdbeacaeacaccaadabddbebdbaddebadcdbacdadeceabdadbcbedecaeaeeccceeacbeaedbedbdbacecdcbabdabebbcabeabbdcbbcbbdcecaddeacabbcdeabbacbabbddcdcdddedeaccccccdabdacbdbdbdbacaebaeaecebcdbeaedceacbbabccdaecacabcbebebaaddeabdcabbebeedbbabebbeeadddecaadeebcceabedbedddebbdcecedaeceabaedabeccceaadabaeaecbcbdeeddeeecbabcadcaecbadcabddacaaeeeadabcddabeddbeaddaaacdbbaeadedaeddcebddcedcaabcccbbcaebabeacdddeaabaeaaadcbeedabaddecbcccdbadaeaeeeaecdddcbaddbdabacbbeaeedccdaedbcdabbdddebadedbceedebbdaddebbebcddcaaacaeeadeaaccdeacedcdaacaeaaecebdedacdeabcacbdeacbdabaedacadeedebeaccbbabecacceadababacaddebaeacbbdcacacdaeaccecacbcbcbdaaeddacedaacbbccabeddddbadeedeeceeadccdeeecdccdcdcecaacbcbeaeabcdcadacecaddcbbeebeeeaebeaabaeaebebadbaebcadcaebbcaeadadbebbacceaecabacdadecccdbadcddccaaaeaaddccbaaddaaeddcaaadcadadcdceaaaeeeebbdccaddcedaacccbcecebacaacccceeeaaeaadeadccaeaaeeccabdeddecddcbbcaebddacaeaaaaecbcedcabdcadaabaccecdddadbddbdedeeaabdbecbaedbcacdacabbdbdbdcbdacaaaaecacadcbdbbacdceebaddbadedbcbedbbebcdbacbcceeadebaacdbbbebddcbaccbccccdbdeaaaaedecacdcdbaeddeedcebedbeebedbacbaeccdaebcddbbdcdbaecdaddcdeacbeddcdccdedcdccaddaebacceddbdbdadbdabeecacabdacbacdbbccdbacccbdacecaaabbbceebbeaddbdccbcccaaddbdaaaeadcebacbcbcdbbebbbadbddcacacaeeecbabddaaacbccdbedaddecadbcacdadadabecdeaeeadbcdebdedceacebdacabebccbddabaeddccabedeacacecdbadadcbbcbcabebeacbabbeaeddabeeaddcdebabceceaddbedaaaacaebabdaaeacdcaaaaccabbccbbdcbeadabaaeebdeaeecbebcdaccbcaccaacbcbdabadcddadabcbdedeedddbeceaaaeedebacceecbcadcbbadbebeaeeccddebeeebaeabbeeeabcdabcbbaeccbeeecdadcacbbebbcdebcaeddbdccdedeaebbbadeaeddabbeadebeabdcaaddbbccbddddbcaeeedecbcdaaadebebecebccedcbcbbceddcbeccebdeccbcdcdaccedaaddcbbcdbcaebeedcacbbbbbdcadbcdaadeebdcbabaaedcbcbaadaeadbaabcdeacbaaaceabbeceeeceecaccbeeebeecceecdededbccecadaceccdeeeceddedceaccbbcacaabbaccacbdaeaceeaaaaebcadbbbacbacbbedcabddaedaddddcabbecdcebadcbdcdebcdecdbdeebabaddedbaaacabbbebbeebadeedebcdaddcbacaecedbbcccbcedaabdebcbeadbeeaecbbedbecbbaebbdaeabaaabedeceecbaaecbdecebadeccdcddbdaebdbbbabeeaeaabbcbaaedcdbebccdbddabdcaaadecddbbacaebcdebeedecdacadbeabaedaddbdcbccccaadcdeaedccedaccacccbbaeaeebacbaebbbcaaddacbceebcecceeeabcbabbabdbeeddebbbabedeecdcceddbccedeacdeacedeeaaecbdeedadbeedddebadaabdaceebccdecbadcbbebcaaabcdeddbedeeaadeaadddadeeebacbcdcedeacdacaeeeaaeecbebdeceaeadbbdaaeeabeabdacecdbbdceceaeebceaaacabeddacdacbbbbaabeacbcaecceddbdaceadbaaeebbabbaaacddcbddebdedcddaddabebdeadaddabbbbaaaedccddeeeeecdecedbdceaeeaeedecdccabceaeadaaccbcbeadabdaabdccbddceacabedcbcdaeaedcddacdaecbbcbeddcaaaacadbebdeccbebaaabdcccddabcedebccaabbccaaedcdadbaeeaeddcbddbbddadcacbddacccebddaecaeabdebabeddedeccdaebbabddbecdebcceecdeebdaedbbcacbbcbceeeeedaecebcebdabeeaeecaaacaeaaaacbcccddacdbeaaabcacebdedeaddbcbbbcbecdedeadebbeacdaabdccebeaeaedacbbcdabaceededbadbaaecbecedccedcbecdbbeebddbeccceebdeaaecbbdaaccabbceeaabababcbededabbdddcbbecaeceabccacaeabdaedcebcbecedbedcdebddabadcbaaacbaedacabdebdaabddcccccebdbadeeceeaaccededaaaccceaebbedbebcbeaabbaaddbecdabbbdbcaaebddcadceadecddbaebcaaeaaeecdeeaaebdecdaaeaeadbabacabedcbdcacadebedddeaadbadaceadaaebaacaaabcaceeeabcbbadbcedaecdebedbacdcdbadedeeeeecababeddcbbedcbeaaeeecdaaeabccdcadeeaeedcbedbaddaababaddaddbcbabceaecedaaccadcddbbcacaeaaacebbeacccadbceceaaecdbeabdacdaedeebabcbdbbaaadecbcdebacdcdcbeecadcbaadbbdbaebbbadeddacbcacbaedbbeaccdcdadadeaacabbeabaccacbeceabcdccbccdbbecbbcedcecbbdbcaccceceaaeccdadbaeaebdbbaabdbbabaeebdacceaadcecbcbeccccedaceceedeaebaddebacbcbaabaccbcabcdbbacecdbedbacedbbaaaacaedbebaadbaaaeccdebbbcedeeaebbccdbdbbcadcdcceccbcdbcddedebacbdcbceaeddcebbaaeadebcbcdccdcddbcccaadbcdbbbaeeaebdccdadddacababdcbcbedeeaaddbcbcdacadeadcceeaddeabadebadaddaeacdbaceadadeeccebbcddacababcacbaebdcdebceaebcbbaaaacaddeacdaadcacaacdadecaddebdebabeeabebbecaecaacaeeeabcceaecbacebebdbceedbbbdbaddabccaabeceabbabdeecddbbcadddedcddaedccadcbebdbdaaeebebccdaeadddaddcdcccdbbaceeeebecedacbcbaaaacbddbbecbdaccaaaecabedbebddcdcedeaeededbbbabcdcbbdacbdaacccabbdbdbaeadddaedeaccceebbaaccbdcebdeabcdcbebdcdaadbbedaddaebedeccbdbadeaddeeabecccabbedaeedcbeedadadcdbbbeeaaaceaeccaebddcdeadbbacdadabaaedbbbdcbddaddbaadebdaddeccedeebeaeebeeeaddabbdedcbbadaebcabbdadbceccbbbeabdeddbeeaabecdeadecaeebcbecaaaeaacdcaaaacdaadbebecbcceecdcbbceccacaacbcabbdebdbadaadedbaeceeeddabedeeaaeabeacedeabecbeaeaedbbbbeeeebbbbeceddabceeaebcdbaebbaacdeaebcccecebeaeaeebbceddbbecbdddebaeaeacdcecadebbeadeebaeaabbebddddbeeeeaecebaeabecbddedabebbdaddbbeeceeaddeacdcdcabbcdbddcebdabebbadccbedceaaeedceecdcbbcbedbadeeccdeceadaaebcbadcececaaacaaaaddcbdeeeccaadabdccebdedbbbcaaeeedeaadebabbecdcacdcadaeadbbdcbabccbcbadbddaceddebabadadebccdecbbddedeeeddcaaeaaccbbbadbaeabeeacdbbabeaacaddbccddcbdeadcbcaeaabeacaedbebbbceeadaddeaddccaecacaecedcabacbcdaacbbceeeeaaabadddeeebdcadedecacdebebcdebaccbecdcadbecddabbededbbccaccabcbaadacaaeeaabdbcdacedbabacadcebaaadeeceebdbeacbdadddcddaacbcccacccadaecebbdeacbeebadddecaebeedccbaaaababceabeccaddeaeeeeaadadbcdbedbebbeeacdcbedacaadbcedcdadeedeaddebbaaeeebeaaabaddaaeeecdecabcbdcbbbceddebdccddeeeecebeebedabbbbaaebcacaddadbcbcebdcdeeadaadbdddcbcbdbccbcaddedaeeddbaaaaebacedbabaaaebaebdabcbacdccceedcdbdeecdcacbbeadccadbbbbedcbebcdbeecdbceecaaeccccbdacbebaaacaaeeacebcbecedbecdbabdeceaaeecebbdabbbacdcdbdeedacdbecddadebcdbcbecdeabdcabddaebceeecbbdbeabecbaecacbaecbeabbcbcbecddbeedeceebedaeedaceddecbedacaccdaacbedbaccdddbdedcceabaccbabebecededadcadeedbaeacbaadbcbadaeabbedecaabedbdbaccdddebbbbdcdadbaeddcadbcebaaacbcccdcdbcbdaedccaaceacabceacebecdbacaaecbacabbeadcabaedcecccbedebbccddaacccebcaacbbadaceeebadaddedeedeaacddbaebedcbdcebedcbbbbcbcaabdbbcaceecaeacbacaeebadecabedbcabccbabdeecdeceebcbbcdedebbbedcccdeaaeddddaaedddcdbbadbdabbeceadeeaeaacbdcbbccbbecddecabdacbbcaadaebcbdeaecebbaebadeacccddbecedbccddbcaedeabdeeeadaaecebdcbcbebcbbabebbebbaaccaebabeeadaeccedbaccbddedcbeceacacecbbbbdbbbaeeabadacabceaddbaebddcecedbaaceacdbeeccdddbeecccdcdedcdbbaacbeebaeddaccbeedaedcecbadcaaadeebcbebdaaaeacdeadcbaaecaccdabacaadcebaeecdedbbdaeddcbcdecaadaeeebdddecbcedabaeaecbedaedcedaacaaaababceecaccacdcedcdddbcebdaeaddcebeadaaaaddcaddacdcedcceecdcacdcebcbcccaabacccbbbedddebdcbcecbeaadbbcddcecbaeeddbaecdacdbabaddbcaecbdccaacaaabeaccbecbeacdaaaecedaedbdaeabebacaadbcdbdecabbacabadbccebddaaaedacbdceabcbdbababaebeceedecdddeeeaedeedacecbacadaabedeadcececaecbbddebecbecaeeabaccdbacdbccbdacaedecdaaebebaecdbdddedebceabbdecbaaecccccaccccdceddedebdecabccbcdcddabdcdbcbdbeceedcbabeacbbdaebdbebdabeccddcbdbeacbaebabbbbcddcdddadbacbcdbaabcbdacbdcabecbeddbddcdadacaaeacdbbdccadadcddeddbbdcaacaadadedaabdcaaccacdceadedebaeedbeedcebeddcaadbdacaeaacaebbceaecbdadbdaaedbdcacdddcedcadcaecdcabceababecacbcabdbdbebddebbeeeadcdceccaaadcebecaaaadbcdeebcebaababaaddcdabdecebadbdadeedebaeebaabdcdbdccdadbbbbddcaadcbebbddbeceabedbccbecbebbaeabceabadcbdccdaadddabbaeaebebacdbcaedbebbeceddadccbeadbabcccabebcbbaaeaabaeeaedddbceaadadcbbcdcaabbeddcbdeaeaecceecaaeaccbbbddaeceabccbeebbbbeadaccaeabeecbbebacaddacebabdabebabebbbdeccccccebaebbaabecaeccedeebbadececbaabeaececaddccccedccdcbdedecaedbbbdeacbdddeeacdebbeaeaccbaecccbbceececabccdeadecdeebeeebdadbacdebcdbcdabdbcacecaebebdeadbbdbcbcddbbbdeabdcabbcbeeadbaceeecbdcbebcedcdbcebdabcaeabeeeabceccadeeebcabebbaedbcdbdbbaddabcdaceeecdaeaeeecbeebacbcadbaeeaeaeddceeeedccbedabeddceeccdddeeabceceaadadcabccedecacadedeecccdbbacdbdecedabddaceebbccbbbaeadacaacbadedcccdcedbdadeaaacbdaecacabacbecbbabbaadcaaddacaacbbeebccebccccbddacbccaedeeeddbadceeecebbeeeaddbcaeeddcdeaebabacdcaaebeecddcbbeeadaaaeccacbcccccbddcbeeabacacadbaaceddacaabadedcecaeaeceaebcebbeacbbcbebcddedaccbecdcdebdcecadeeeeacbeaccebbdeeebeabbbbeaadabcdbceecbedcadceddcbcedddcdacebebdbebcbeaebeccacccbebcddcabbaddcedceacabaeeddeacbcceeebaeedadbeeddcdebddbbabacaeccecbacddcaebaaeddccdcabbdddabbdeddbebbabacbadaecbecdbceedccbeebacebebdcebbbeedcdcadeeeeecbaeaaadacbebdbebaedbbdaaebabceaecaadebcadaacbbddecbaedaabbeebcbceeceeebddccaebbbbbaeacdaedccddcaeeebebbabbddeeceeceabbbdcbeabebacbadaaccaccacacbeecdacbacebeedbaedeadcdcabbdcdeaddebdeeaabbebdcbddecbeebaacadbacddacbecebbcaecbbbccacccbddbeddbaececdceeceaccedacbbccedaadceccbceaaedeccbedecbacdccabaabecebdecdbbdacccebbbdceebacddcbacdedadacbacdbbecabdaecebcebadbeadacaabcbbebebbcacbecccebddcacccaeeabaaecbdaccbcdaaabeeabaedddcadedcdebeaaaeedaeeccdebdbccdabeccedadaedeebebbccedcacaceaebabeedcabbcdcaccadccebaaeebcbababccbbcecacecaeabbbebedeceecaaeebcdbcbdbcbeabaaceebdbabbdbcabadaecedcbcccaccaceaebcddabedbabbdbeaabadbbacbcdbacbdecbabbebddbabbadadeeeedbabeacdeecebddaedcddeaaccecddbaeadbcbcbdbadcecbceacdbdcabcdacadbedbedeaadcbbaabbdbebdbdcddecbeabdeccaeacbadbdabcbcabdebdbeebadaaacdedacddbeeaaacccebacadbabdeddddaccaeabeaabaceaedccbcaceeaeebeabbcdaabcdbbddaecbeddeaecbdedbaababbdcdadbbcbedbcaaecccceacccdcaaadcaaedebceaaeaacddbedbecadddeedddbbbdbbcedcacbddbaeaaeeceacdadbeceabeddccaeaddddbbccecdebdebeabbeeeaedaaebcacccbdbbeedaccbbecabbeddeabbddcceeeaceedcabcbceeecdbaacdabadccbadaecccaeceacbccdedcdbebbeecadcbeacedcdaccccdbcedcebbcadaeacabeebdecccabcbdbeebeccdadebdeccacbaadaebceaaacdcbbbbdeedcedcbecaecebdadbbaebbebdaebeedacabecdceedebdbeaddaeabeddaceedecdebaabeadacadecddecbecbaeccacdebaaedabccbadabebbeeabdeddddbbaebdbbadbedbadaecdaceeebbacbdbeedbacaddaeebdcbcaebacbacebcbacdedabbddcaddddbaaebdacdcddcdbcbdabcabdccddeabeeedeaadabebececdbecaaccebabbbbabdccbaccbeaeebbcbabdecaacaaaabdecdbcacbbeeeccbbaecccbbbcbdddaaedbbabebccbbddacaeaeddcbeadaaadeaddcecdccabdabeddbbaeeeebdcbcadcebccbacecbddbecceebdbcbceaebddcbbeeeaccdeadccdccebeeaeabeacbbbacbceaeaeedceaebababaacddaeccebccccbacccecbdeeddeaecdaabdacbbabedcdcccbbcbdddcacbadececceeddeeaaceaceadaeabbcabbedeeaccacedbcebabcdadbcedbbabaeaeecaceebdacabeccadeedddcecaececcabddeecdcbcccedceeeeeddbebbdeaaecddeebbddebcdddedabebecbeddeaebccabadcbcaadcdaaddeeadbdbbcbaddddbebcabbebcaabbdadddddbedcacecddedccbddadadabbcaecedadcaeeaaccceeebbdccabaceaabbeddbdbdccccaccaeedabaaccabcacbacbbbbbdeccdaddbaaaccddbcbbbbaabacacdcbabeeedcabdbaaacabedaedddbdcdaeaeeddceaeeebcbdcddaeeecbacbdcbddaedceeaceddedbcdeeaeeadbaebdeededbdecaedaabeebcadcdaedaecacdcaeabdddebacbbebbabaeaebecacaaabddbdaceebbdadebdccaceeacbcccbeaeacaaebeadbabadbadaadbaedcadccdedcebbdcacecababebecabdecdcacbcbcaebebbaeecddbcdebbddcaacbeadadeccdcadcbcdaaacbdeecdadbcbaaacacbebabaebaccdeeddbacceebddadebbbadedcbddebaabdeaccbbbccecddbadebabccedddeecedcaddcbbcaccacbeabaceceaecccddbbebaceeaecaeceaaeecbccaeacdcabeeabaeecbdeeccdaadecbbaeeceaccceeadebddecbdddedaeaedddcdbbcabebeddeaceeaabbcebbadcecddaebbcdddcadaeabcbededeebbeeceeecbddcdaaaabddaeacaecacecbcaabdcdeadeaeeddacccaceeeccdbbccccacbddeeacbbcbdaaaabdcadcedddedbdceeeeaccabbcebccecedadacaceecbdbccaadceedcecacaccbdccdabbacdbaeebecadaeebdbacbdabecbcdeeddabceaceebdccebaacebacdacbaaebdaeaccdcbbbaeddcdeddbcbedcddcecdbdecbebbebaaedbdeecaacdecddcdeaeecdddbaedcbaabeeeaaaceecddcdabddeeedebbeadadebcaceaceccccbbacdedbaeabcdaccbacbaebecbccececdbedaeeceecacaeadbddeddeaaaebdccbaacbaeeadddaebabdabeabbbdddcccccbaacecacbdccabccccaecebebacaccadbaeabdbaebcdeeaecceaadcbadbeecabddedbceecdcedbcbddeecabeaedbedeeebabddbbcddcadebccbcabaaaaccdceaecbdebddbabedbaddcddabccebddadeeabdedeeacbdeedabeaadebbcccaedeeecadebddcebcbccccddaeccdaeaddacacdcccaceececedaeceababdceaacddadccedaeddebdaeedcecccdbbaddeaceeeccacbccedaadedcbcaeaddcbcaccdaeacdbaedbbebeebebcddccdadeabbbcdbdaaccaaddeaacadbeecbdeabbbabeddbbcbeebdededcebebdeaacaaadbcedeccdddbaeebdedebcaeeabebaceeaccdccecedeaccedcadaababccabbbcceedcecdeeedadbeabbbbaabecbdddcbcbeadeeebeabdaceacabdcddcceecddaccaaddbeadbedeeccabbedcbebeabbecddedeacacccbebdedbaecadddcadeeeaaaeaaadbcedaaeddcdabaeddcbaebeadadddebbacdbcabcddbaabbadcbeddeaecaabbdbdeceacbceeacebcbbbebdabeedeaaecdeaeedbccdabecdbaccdbeeacebbacdbebaeeecaecbdcbdaceebeccbcdecddaceacedaecebaebbaddbbbaeceaedbaaddaedccacbbbbbdebeecdcccccbdccaecdaacacedeebceeecedbadbebcbeedcccbacacbadadcedceeccbdbcbadcbdeabdceeeddcecbddbcbbcacabeddeababceadbcedbebdaaaedacbcddebbcccdacababeaaacabbdbdeaceeeadcaeccebdaecdbcbbebedeeaacddecbcbbeeadaabccaecdbabacaddabeeebebbaeecdacaccaadeeeeddabbeeaebeeacaacbddaeabaccbbbdaeedddbaaabaecaaceacacdeadadebcaceadecbceaaccbceaeabaaaceceadcbeabcacabdadbccadeaceeecdbdedabcbbebdaacaeaecceadbceaaadebaaaeadeabdbebbcacbbbdaabdebdeebbebaaeccabbdeaccaeacbeddabadcbddcaecdbbbeccdabceeeebdbaceeacceeedadcabcabcddebddcbedadbbcbaedccdaecbeacaeaecbeadbdaacdbccdbbabddccaddcbbdcdbebbdecadcbdbabbbdddcddbadbbaacdeeeddcebddaccddecbabebbaaabdacecbbeabbaaeebdbccabcadcebdcabababbaeadbbeedcadbecbceebcadbcddeedbedadcebbddccbebeebdabacdbbacbdceaaeabeedddadadddbadcabecaebeabaaabbcedcdcdbbebddeeaedcacccbdabaebddbcacadadceeccbcdbdcaecbebdbbcbaaaacacdccdbdaddbddacbdcbcdababdddbacbaaeeecdeaaebceedabeabeeddadeacbecacecbecacaebcddddcedebebdddcbddecbabdcddadaadcceaeeeabdeedcbccbababdebebacbdeeeddccaedabcddabacbbdabecaeeddbaaedccdbedabeacddadbebcabaabbbcbbdbcaccadcbbeebdaecadbdabbbcbedcdecaecabeedaeecbcadcbaacbdbbadcedaebeceeecdedbbdebadcbecbbccbcdbaacaacbddcabddbccddececeaacaecbeedeedbadebcadcdedcdbececbdcddcbbdbebaeceaddeeebaeeaebaeeebcdbaadaaeecaabdecbacddcbedcdddcddacdadacebbacadbceccbcaadbdeddeeeebdbbeaaabcdeeeabcebaebadeccbebdacdbecebbbceaceabdebdcbacdabeceeebecacbaebdadabaadcaedcadddbdbabcdbdcaebabebecbdcddbccadbabddedccccdbcaabaadcdadbddbecabcebbddcbdbdbababdeddaeadcddabdcdbabbdaeebadcadadbcccbdddbcbeddadcbcdcaeaeeedbdcbaddedbdacddeccbdbaecededeeaeccccebadddbededddcebecbbecdebecbaeececcdecccadcdeadccdeceddeaabdbadbccddcacbabaedaedbcacecaecebabbbbcddebbdbacbebcccbaadadaaebceaaeadcedaeacddbddbbcdddccaaedebacddddecdaaeaaabadbaeeeabcdbdddabededdacabcadebdabeedcebccdbcededeaaaeecabdceecdbcdcabbcdcdabceecbceecebaccdbcaeddadaadaeaeaeeeabbbdcdccadcdccceeeacbbccbcccddcaceaadeaccdcdbdecdbebbebebddccacbcaecceebededccabeccdbdbaadcecdeaaeedbcdbcbbceebaccbdbbeaaddcddcdadabaadbccceaadedbedbcbeebbedcceaaddaaeecdcbcbadbebeaabceddaaececbdecdacabaccbaddcdcbcbaabdbdcecaaedbdadcebbdbbbbbdcabededccedaceceebaaedcaeeabdebdbddbeaecacebdbdcdcebddcaccbeedddacbdddacdddcbeaadbcdbcbceaeaeebbeceebacdeaaaedcdeccbeeaebbaacdeeabcceddcccdbddebaebcbdeadbecdebeabaeaddbedbeadaceedcbcbccabadceeabbcaedaabeeecdceeebccedbbedcaacbcdbaedaabdaeaabbaecdadbedddbceccbdaeedddececdceeebdadeecdaeabdeccebecebbecbbcabcbacadcebbdacdbbeddaedceadceeedeeaeeadbeeccbbdcbdebcbbabddaedaeebdacbccacacdbcaacadababaccebedecbbadccececaacadebbbadeeecdececdabcdcdcebcedbdaccadcedeaddacdddceabacbbbbbaebcbebceaeeddedbcbabcceabcbabdbbaddeeabaebdcdccaecdacccdccdeabbacdcadbcbccdbaebacbdadbaaacbddaceaaddbbaeebcaebaeecdcadaaceeaecbacaadcdecceedcbdebcaccdddbcaacdccecedbabbbeddedddadcdcdaabeaecacbdcebcdabbeebdcececaccebeabbbcecaedeaeedcacadbdcdebaadddaeddbceddeeacbcbcbbbaaabbbddcdebdbbdaebaabbadabeaedabacddcdcaceadacbbbadadcbcacebabaaeeedebbececdbaecacacdbaeddaedcaeceededabebeeecccbecebcccbeeaeabecadedbaecdabecedbeaeabeccdbcccedecabcadddaeabdacbacbccbcacdecabcececacdddcbddbdbceedcabebcdabbbaeabaccdeebecececccbddebceeeebbacaaaabcadceaebbcebabbeeeebebeeaabddebcecdccdebdaedebeebdedaacceaadededecebbdcacdbaaacbcececccbacbddededbbeebbdeedbeacdddcbbababdaddeedadacaacdebaeedaeabbebbbaeaaeaaadaedbcdeddcbbceddabaadbceabccbeebabccebaebedbaaceabccaacebeedaabaabaccbcacedeaadcecaddddbcaeaeeddbbeacbddaedaddeedecbdabeadcccdedcdceaccedeedecaeabdacecbaebedecedcccecbadbcdabbdcabdbaeeeeacdcbbbeceabddadabeadbeaaaeeebbcbdeaecdeeaeebbbdaeadccaabcdbacdeceeccbacabbebedadacddcddddcbaedeadadbbbcbbccdbbcecaeaabeecaaaddcedaacdddbbbcecebcaabbbbcedcbccccbaeaadbbddaecacbbeeccaebbdbbbdbbbbeedeccdcedeeedbbecadcdabedcdcecaecdbaacdaaeebedceeabaddcadbebdacdcecdacbdeaecaaaabacddccadacccbedcecdcbebedaaaccdbecbcddddeadceeaccdadcbcacdeebacdcdebadadeaedcaadaeabaadbcbcbebdbebcbbdabadceadeabebdceddecbcaacccddcbdaecdecedcedeeadecbbebacebaabcdaabaaeebadebbdcecbebbbdbedcadeaedccabeeeecdeebcadceeedabbebecbbcebdbceecceecdcbaccddcceadacdeeccabbdeabbcaaaccdddeddcbdeaabdadedbbbacaabeccddbbdaaaeecdedeaecbcdcbecdceaddbaaacbedebccebbedcabacebdaecbccdecaeabddeebebcabcdacbccacacaacbaecdceedbdcebdbcebdaedabecbdcadadedabbcdadaabacbccdabdceccbedbadcdcbacccdeebeeacbdabccbdeccccaecebaabedbaccebeaeaccbcbcbdbdabeacadacaeddcebbdddacecadddcaaebdebbcaaeaeabcebabcbadaaccbccdbbbcccdaddbadaeeebcecabbeddacaabeececdaaebdeabeebdbeebbaceecebaebbaebeddedeacbddecbdcabadcdaeeabebabcebedcedbacebebcbdcdaececaccdaaabbcdbdddeaedbccbabaacaccbebbbadcedeccbedaaedccadaeddbaacecadedeebddeacdddecbbccadbbecbebbcababeadccadbcdccadaaccbbecddabbeebeaedabcddcaddcadaaccbbbacdeacedbdabadbcbbbabceadbbcdbdeaadbbaddbaaeeabebceebedebabaecdcaccbabeebbabdbecaadceeeeddebcbbcddbdceddcadecccdbbcdeacbcbbdbaadceaedaabbebcdcbcaacdcebdacbaaddbeeeecbcacbbeeedbbcccbbbdadbabbcdcceababbaeddebcedbbdbcddaaebbecbacadaddbcaecdacaeccdbcdabacaaeaeebaaeedddacaeadcdaaecbbdcecbececceecebeddbdedbbdcbabaceaaacdaecbcaaabbebdeaecbeaadaddaabdacacccecbbaebecddabcdeadbbdacaadbabdecacdcdccdedcedbbddedceaecedddacecacbddedbeaabeacadcedbaeaedceedddaaddbaeacacdcaedeedeeabbcdcadedebbdbbdecdcecbeabbeaedbbddddcebbcdeddadddcaadbdaeadddececdbdddceedbcceadbcadcdeaaccdcadcbacbecbcadbbdadcadeaabccaedaadcedbceebdcaadcccbcdbaebbaadcebedeedeeaaaeebbeacddeeceaccecbaaebabceeeeeaecaadadebbddbacaeabaaeeccbdcbbdabbbdacdbcdabcbbdebcccdbcbacabaddecacdedaceeaebccacecedeebcbcccaebbadbdadbbaeeeedbaeccadabbdaabbaedceabcbaedeceaebddbbdcdbcadbdbbacbcadaeebccdbccdeebabdbccaabcecbbaacddbdeeecbeeeecedbbeabbbeeedaecebbaaddbabccceecaebcdabbecacdabaeaadcaedceaadecdcecadabecebbeccecbbbbbddbaeddeedebcecadadcbacaaadedabccdceecbbbedbabeecbdddcebbddcdedacaedecbacccabedeebeecdabeecbbdabeedbadaddaedcdbeaaccbebacebeedabeececbdbdadccdcbcaebdeaeeecdabeabeedcaedecbabccbccccabbccccbebbacdcaddaacdcbaddcccbccebbaceadbabaaaceececdbbdbeaadeabccebedaedcacebbceaaeecdeaebeadccdbccaeebbaaeeadabcccaeecdbcbbabeaececdedaeaccbecddeeeaaaebbaaebdbeebcaecdeddebebacceecbcaccbeacbcaedaaeaaaaceeaebdbaaabeedddcdadadabaeaedaaabbcebbbddcdaebcacccaddbcdbbcdebbddabdcbadcbaeaaeeebddeeabceaeddeebeeacbeebdbcbcdddeebebbbaacdbdeaeaaadbdaaeebedebeeccbdbccaaddabbdbbaecdddbdeaebebcdeececdcadddaabdaeddecbcbdbbdeccbadeebbadbbdbecdeeaeecdcebdbeeceabeebbbaebbaddbcecdccdedcccceddbbeedeacdaadbbceabeecaabecaeddbaeeceaedbacaeebddecdcbddeaacbcadaeaebbacdedabeebacbcddbeddcbdabbaebecaacddaabaadeaeebeaadbaeccdccccddbcbbdeedabeceaacecccabcecaddaebccebdebbcbdbeddddaceecacdeacddcdbeedeaceabeaadcabcbcedcdbeaaccceacebcdccdcdcdaeaccdeacacdaeddccddbcbaabbdcedacddcbdbdeededcecddbaabceaeabdaccccbdacdabceceebbdedbdeccdbedaaecddcaedebedeeddbaabcbdbbcbccdbeecdabcedcdccbabaeaeebcdacebcccedbcabcddebdadcaaaedecbceccbdbcdeacadcddabaeecdcbcdceabdcdadacabbcdccbbeaabecabbeaaecddbcdecabcdceeeceadaebdbbebdedbabbcbdccbdcedcecadcadbdeddcbcedecbcbbdbbbaaeacbbbebdcdcdaeaddddceceadceeaaecabbedbddbcdaabdaeaceaaebcdceaedabaaabdeeeaeaeeadbbacedeedcdeaddbdacaeeaeaecabbcebbebedebaaceabcccceeeddbddbdbaaccdaaaeeeabddcdcadcaadbddbaeeadcaeaaccdaeababdeabdcbcbdcbcdecddedcecedeeeabaedadcabeeadebeedeebecccbaedcccaddaadcbdeeecddecbeeacabedbdadceedebdbbdeecbaeaccddadddcacbedccbbdcccbbacdeebacaebeceddababbabbeaebaebbbcdabdbcabeedccebcecebdbeededbdedcdcacbebacbdcbdadbedeeeedddbebeeebdcccbeacdcbccecaaaeceacbceeaecceebbabbebbdbaedebabbeceebdbdcbdabacdabdedbceeceaabdaabeabcddddbecdaaedeabaaeadedbacebebbddcdcbeacdbebabdadcceecaacecbabcbcbaeacadcdcbeecbddeaeabdadaedecccdadaaeaebddaedbdeeecdabbeadacdceccbecebebeaeeacdaccbcaaecbadbabbbdbbcaccdebebddaedbeaeedaecbabaaaebaadabccbcdacdccbeecbcdbabbcdadcdacbcabbdcddadbaabdccbcbaabdebaadadeacddadabdbecbbcabebaebdbbbcebbdccadbcaddadcdadebcdbaddedbdabaccddaccebbaccccbdceadcedbeecdbabbcccabeabdbcaebddeaddcebaaaecccaedcbeebcbababcbbcbbcebdbdccbcaeabababbadedbbbdaaddedcdaadbcadaeaedcecedbaccdddabecdadbaeabbddeeeabbecacdadabbaacdabeacbcaeddeedceddcaecddddacaedbdadcaccceeceedbaeaebdeebbbeecedcaceebccadbbcabbaebcecbdbceecedbbbcdcdeaaaceeabdbcdaddabbedaaaedbcadcacebcaeeadaebdcdedbddaaedbcbeaadebbaccddbaceaabcceabecdcdbddcbbecdacdceddddacdcdcaeabbebeebdebbbcecbaaeadeddabaeeaeeeedbbbcceabaebaadeabdaeaadccdeeecccecbddadbcccedddddacbdeaeecbeeeabcadaaeebaeacddedcbacecbdbeecededcedeeabccebebbbaeeccbbadcddbceacbbbdcebddeabaddeeabbccdbccabeeceedaaeaecdebcbbaddccbddeceeeaabbbddbeeecedbacecbaeccaddbeadadeaacbcdecbcabacdeaabbeccbbcabaeaedacaaacedcdeadadebcdabecddeccbbbecbdbcdabdedebecaceebadbbbbbcedbaaabdcaebceccaecbadccebadeeabbaccdbeabadedbbaaecbdcdadebacbaebbdbcbcdcdbedabebbaaabaeeebceccdedadaebaeceabdecaacbacabeedbcdebbecdeebccccbcdbbeddcdbbdcaceaacbacabdacddcccdbceaddcdddebaadcdcdbebcacdbebcceeadedeebecdcccbeaaaeabeaedbdcbdebdacedaaaadabdcaabdebbdebddcedbcdddabdeadecbedccddecddbacbabbbbdabdcaaeadadadedbedededdbdaecbeaccceeaccaccaadbdbbcdeccbbeacdcbccaaebddceabeaaabadedaadcdedccedbcebbcddbabbdaacedebccbecbecbcbccbbadaabdebaeeaebebaceeaecbcecddbaabbabeabbabacaeecabaaaadbabaecaabeeeedcbdedecaedacdeececdddcaadedeedceaccdeecdbeeeceeedaecdcdbebbebeaadbabeecaddbacebebaadaaebbabeaeceeadceebdbbdeeeaedcadbdcdcecdbccceaacbaabadaaaeeeacacbcdceaccdabadbdbddbdbacacccadaaeceabaeaeabdbbedbaacdabdddaccaacccaabbeeeaeccbbabdccaebeacecbbebebaadeeeeaddbcbccdcabeebaeceabedeebbeaeaededaeccceabccbacadaabcdebaedeeebdbaebabccccbcdebddbaadbbbbedcbbebbadbbcdcdccbeeacadddccebbdcdcbedbdceedadedbedcdccbebbdebdbcbbbecaddddcaeaacbeaaadbdaabdacddcdeaadcbccadaacbbbeaadaddeacbbdaacbeadddcbddacabcdbeaebeedbcbbbaaacceedadeadeedabcabcdbdeddddcccaeacdbbecbddedadeccbadcacbccedacbecedaeddddeecddabeeeaaaaadbdddeaebecdccecadcebcdddababebdccedaadedbdedbdbccaeddcddeceacdbedcbaddbbdccbeabaacaeaebdebcddaacbbbbeccbdebabbadeceaecbedeaedaebeaddeacdcadcacdbbbedbaceceebceededaceaaaaadbccedcaeddbcadcaacaadbdebaecbacdddccdeecabbcdaedabbacecccaedeedeadbeeecccbdacbbdcbaebeddddadceeabcabceedceabddbeeeebddebeececeaabaccaabdddcabaebbebcbbccbececacbcecdcdecdccbedacabececbaccadececeaebbaaacebbceaeecacbbdecbdabdebeaaadbcceeecaedeeceadedbaccaebbacdcedccaccbedcbbcdcbbedaabccdcddadeccbaaedbbececdbdecdebacbcdadccaeaeceeecbbeedbecbeecaeeaebdceebadbebdeaabadcacadedacaedabcadbbecddadcccccaddbeecddbddaddaacddeabacdccacededcebcdabbcbbeedbeabceccecababeaabedcabadbeaeeeebcccccbabadadbeaccedbdaecbeacbdbebadddeaebcaceeddbcebcccaddcddbbdbabbededadceddedceeadeeabdaaaddebbddadebcdedbceeaedecadecbacdadcdccabbbecdbcbeaadbebeadcbcdcbeeaeceaaabcbebaaccadeedeceacbdbaecddbecdcddbcadaddacbedacedddcbbdbebdcdddcdbecccbdaceecdddcdcedeabedcedcadeebaacaaeedddeccccabbdaceaaeccabcdccdeaebbecceedeccadebcbcccddebebbbaaecbbbbdaecacebcdebbdddbaddeddcbdddbaeededeeddbcaaecdcbcabdaecbdacdeaadaddccbabcebdaaabcdecacddebceededadceceabaededeaabecdcaeadabdcebabbcdbadbcbedbcabcdadbeadaabccadedbccaccbdeaeaeeecddedecceaecddebedadddddddeecadbeeeabcdecedbedcbbacdccabedbdaedabeaabebdbbcdcaaaebaeedcbaddbacbdbeedbbccaaaeeadebcdeadceedeedcadaddbcbabadbdadbabcbecdbdbcdcddcdcaeaccadedcdecddcaabdceeeeebbeadbcccbbacaecbecebcccbddaebcaeaeabdeeacacbeeeaabadbaecbebacddcdabdeeaaeceaabdeeeeeebbaaaaebadcecccddcddeabdbbacabbcebcddcedcbaccceeeacdebaceabcdcdcdbbbeebdabbeeddddccbaebecdcbecccecdaacabebbccbceddeecdddedaadcdadccadcccdabebcdddacabeadaccbdeceaecdbdcabdbdecebccedaacecaadeaebdbccbcccbeeebacaaccbbebaaaedccdcdedacdedcabbcddadaadaddebbacaadceebaeaacddbdebccaceaaeceedaabaadacdceabcbcaaaacccbdeeadbbbaacaceeaeddbaaccadbdddececccbddccacadbddacdacbadccecdddeecedabddaabaadddecacebbbadbdeacbecaacbdbdedbaecedecbdbeaeaedceddaadcdaeabbeabbcaeddbebdeadbaadbacedebcaaeedecdbdaedccaacbceadcdeacebdbdcceecbbbcdeaceeceaecaceeaeeebdaceeebbbeeadaecddeeecceaaadccabeddbaaebddecbbcebeeaeabbabcedadeacebaccacebedcebbbeaebeedeebeaaeedadacebeecdbbdacebbdaeeececbaaceaadddbaaceeabbcabedceabbbdceabeaadbadaeabcacabbdbabdadbcedaaccddcddaecbbaabaeceadeadccaecddaddaadbceccaeacabeadecbbacecbbbacbcacbabcaecaadedbaadcabdeebbdaadbaddaeaaebeddeeeacdaabeedcadecdebcacbacecadeccbddbecadddeeaeebeaecddcbbabbbaaeabdcabdddcdacbeabeddcccbcdbdaebeacecdeebccdeabdeaabdceaacccbaabcbdebadcdadbcdbcdcedbcaaeaedbacaddcabcbbaacaaeadbdaccedaaeebeddddacadbcdbdccdaaaebdeeaedeecabebaadbccbdbabdabbeeacdeacaceccdbdbeaebaeedeacecaabcaebeebbcddbcadecccecdebccdbcbceeedcaaabbeaaaaaaaeddbceecceaceccccbaeadddbeeadabceeedcaceabcceadabdcbceeaedebebedebcecacebaedecdaceeeeceececbabaabbbcacaeeaaaaebeadeabaedcaecedeceedcececdbebadceabadecdcaedceacbbdebdbddeddacaaebbadedcdeedaabbbbedecdbedcadbaeabedbeecdcddcaeecbbebbcacddaebdccaccdaccbcbbbeeaaccabedcbcbdbabdceeaebecabadaaadbeaadbdadbaadecccbeacacdaddedecedacddeecaeadaecaedaededcaeaaaaadaabbdbeaddabaaecabdccaacacabcbbdcdbcdceecabbaadbdadebcdedabedddbaedebcaddbcbcdebedcaeaaacabcdccaaeccdbbbcaeeeaceeebebacbdcabebabebaaacaccbecbbeaddcbbbaccbbacecaeebacbeeccaddecbdbcaecaabaabaeceeacbaecdcecbddecaaaedcdbeebbcdaecadbbacdcbdeeabbbdabceebbaebdecddceaceeceeecdbabbcedddacdbeddceaecaddcaeebeaeebecdaceabeaedeedcabcdabcedaacdcebcddadeaedbbdabceeabeedeaeeaceddadadbccbbdebabaccebaceecddbededacbdbeddecacedddcdebbabbaabedeeebdeaebaeaceceeeaabeebbabbeecbdebacaedacddaeebbabcdadbadccdbebccaceddcabeddccedbdebadcecccceacccbeaeceaaaaecbadbcaeaebeddecdcecbedaddbdbebacbccbbcdbccdacacebceadccaaabbbdadecabaacdecdadeaacbdccdddbddcbdeedabebbcaedcebbdcadaddacecdcaeeddecedcbcadeeceebeeedacbbcbeedbbeddbcaebccdabcbbaeaeaeadedbaeaacababbadbaaabebaaccbcbeeeedaabdcbbedecbdbdedaccedadebeeedebabecddeaabadabebddbbccaddcdaaecdcaecceeccaadeeaccbdccabcaaabddaacbaeccacbccbcdccbdabbbcddcbebaceeebccdbdacddedecadaadaacecbcabadbcdeebbdeadadbebbbdcbabebecbecbecbdbdadbdabaeebcebbaeebebaaeedbdbaecbdaaccacddaeeaceaabcbaaeeacecbdaadcbdcebabdedebebaaabaeabcedceceacedaebcaeeaabadcbeecebabbbeaeaeaacacceddaedeabdccddedaddbbaacbdbdacabccbecdbeebdebcbeaacecdedcaeceaeebcbecedcadabacbcabbdbcaeebdebacbababdbaeeeabaccbcbeaadcbcaecbeeaadbbabeabceacddbedaabbccdddddacdecbdababdbabcbddbcdccdeeecccdabdcaacccdeadcdabedccadaedeadaaabbadbaaccbadbdbebbbaeadaacdecbcdbdddcbebcdcaebbbeccbbeecbceebeaeceaadebbbebebbdbdadebcadbecedbbceaccabebcddadddabbceabdebabbcdecdcddedceabeceebedecdaadaddcccbccbaeacbddeccaadbaeeddcdabcdbdbcaeeedecbbebcddcecddbbaeddeecebeaddccacabecdeceeadeecbdbeacbcdabcaeeccccedeabdcdbcdeaaeccdcbaedbecdadebbcbbbcabeeedbcdcebdcaaaabbadbbbaddeceaabeaadcddbceceaaacdccbbcabbcbeaabaadceadeadcdabdaebcbcdebbddeedbcdeaadbebddccebeeedabccddcbbadbcaadaacaccacadcbacdbebdadcaaadaababbaacdbcbdbbddebdadbebbbcacaebabccdeabeddcbedecebaaaddaeadeaedbacecbeeaabaaedbdceeceeaabbbcbbebeaddccceceeaaebecadddaeadacddceebbaebdaeadbaebdeadbcebeeaeeabccbecadedecdeaeebdcdccbacabedddaceacdecbadaedceebbbbbdcdcaedeadbeccbdacdbccbedaddcdabdabaaadecebebecaacdcaebbbdaecdaebcaacdbcdbecccdccdbbaeaccacbdcbcbccdbccdbaaeaaaaacabeeedaececeaeaeaacadddabcbececddbcbdbccbbcccdadbbccbbdcdccbeaeadbcddcdbedbbeaaeecdcababbeceedadccdedbbdecabbcbbcceacdabdcbbbdcbbcbaddccaaaeccdacbcebaadaaccddebbbdcadcdaeccbadeecaaabbbeedbbabedcbeadcdaeadcbceadebcddbddadbddbaeabdababaaaabcabbcaabccdbcdaeddacbbbabdbababbacadcbcedbeccddcbdceeecdccbbebbbcdbbcbaaeccabaadbedaaeebcbecaaebddbeabcdbedcccdabccaebeddacdccedbabaabbdaedbabadabcdaaeadabbaacddbdeebaecdcabaabbbddcbebaabebcebbcbaaeacdadceebcdeaeceaaacadeebdddbebeeacdbaddcadeaabaeeaabeaceecdcbbbeccdcbceaeeeeacbecabcbacbeaabdecbcbeeccededbaccadbddbdeabecbbbbeeaebebebdeedadabcbccadeccaadeabcdaddbdbacedaecebacbceceadacccccbabdcbaaadaadaebbcccedbcbcbcddbcdebcceacecddaeacbccdebcebbcdebedbdcdddccbcaebdcbddbcecbdcebdcdedadbbbebcedecbcdaaaaccebccdbaaacdbeaadccedbcaddbdddaaaaaebcbcdacdacdebcccecaaceecebebbcddcecadeaeebbebbdeacddacaedacddebededebdbaaaabaccdcddbaadcbdaecaadcbcdcbbbbeeeebbdcddbabdecaebddbcadceaeaecbbcbdceedebeccebbeeecdbcdddaddaaedbaddaaddebcededdaddbaebdddcacdebadadececcbcbbeecdbeaadeabaaedcecebabeadccddddcabadbeccbddbdabbeedebcdeebecbcbeccbcdacbaebddcddddcbeacdaadeeeeeaacadbdabadbeddceedaaeaeeececcdbccdadbecebccebcecdddeedbeacdcddbbbbacbaebeacacabcccaecabcecceebbddbedcdabdcbeabadbbcceeaeaaecbbcaacaaaaabdbccbdeaceaeccaabedcbeaaebcdeadaeebbbbbcbeddaaaaeeaeabcebbbabcdcebccadbceeaabeedaeddbcadadddcbcedadaeebcababbbbcaeabedddeabceeaaebdddeaabebddabebedbaadbeddeddaecdebabaaddbebdaedaeaecebdedaccedeaeadcdeeabbeeeebacccccedccedbeacbacbbdedbdbbaabcbbdccaabbbbadbbadcbeeeedbeebedeccdbceeeeabdacccdeebadaaaebabbadbcecbbeeadeababdaeabdeeecebddcdebaebeabbebdcecaeabbdaebdbeadbeebedbedeaebbddaecdcddbadaaceaedadaceabeabcdcdeccacababcddcaeedcebdebedbedbbceadcddccdaadacbbcbadbbbcbcedeeaddeaccddbbeeedcddcaadeaeadacebbbcbbbcdabbbaeecadacccaacbecececcabbcdedcaebaccdcbbddadcddbbdbdaabceadbcdbeeccceeaceeaceacdbeceecbebabbecebcedebddabcdaaddbcaadeeacecccbbbebcabcddedecddbcbedceaebacdaababaebedceeaccadaceaeeeaacadbeacaececdbeccdabaacceccbdabeadebcebaeeccbdebeebdcaabaeedaaeecaeceeacbedceeadabeccbeaaaceabcdadddcdccccbcaccbbdeeaecbcdbebceeddebaaeeccabebcdaedbebcbaaecaacbbedbbabdccddaccddedbbbcddbcabcbabbebdadaadceeceddddceebeadddeeaadceceedddacdaebaebdecdcaacabcadaacabceeababceaaacbedbdeecbedcabbcdaebdbacbbbabdcbcabcdedcbdcbccaeaeaceecdeaaabaacbadedeeeedecddeeacdcdcbcecebeeeecaebdecccabecbcbbabdebdaeacdddecaedeeebaeebedeedbabaabaddcdebdeeababdedaacabbabedbccecbcddaecdcdacbdcebcceabecabbaeebbebaecdcedadbddbdcecaadcdebcdbbadcbdeeeeecdbebcbdddcecaaabdcdedeaacaecceaeeceacaddeedcdeccaddbddeedacaadccacdddebadcddbbdcaaaaadbedabcabacbebecbdbaeabaaddddbaeddbdddcebbcbaecbadcabbbbeabcaedccabecbdecdbdbeeddedceadedbaaeeccadcdcbeaedcaddeeaaaaedcbaaedadaddedccbdacdbacaadaebdeeaaecadaacacccbaaeebabdcceccbdbdcabbdbccbebccadbcdbbededeebabcdeaeaedaceeacbeadccaacebcecacedcebcdcebeaeaecdcbbaabcabaceebcdebbbeeedabcaaedccbabacdcebdadccaabbbeaaadceeedbbbbdeebcdacbdceebdcbdcdeabccdaccddbbccdceadadddbbdabddaeebceabddddddcdacacbbaddadeebedacaacbcaaadcdacadbeadcaaadddacdbbcdaceabcabadabcabcdaecebeeccbaecccecdbbddabaacaeadbebeadcacecbdbeadcdaacccceeadacdcbdbdecdadaccedbecbbaceddcdaeadabbdbeddbabbbecccddaddaeedbaecbadaceddcadeecdebddbaebcebaedbeacccaeecabbbddbbeebdaabbabeeecbbbcddbddddcbcdbcbaebdbecdceadaebdbcbacdccedebecaecaaedaeededaedecaecccdcecbbdbbedddadeddadeeecabaaecebbbdeeddcebbbbbdedecabcdbaebceeedeadecacedbabbaaedaeddaadebabddbabaaaaacebddccbebeebaacedacbcabaaeacddccebbedbeeaedeabdeadbcacdbccdaebadcdabcacbaddabcdbddaaddaadebeeddcdbcaeebceeaccdeddddbccaecdebaecacabdecdeaadedeccccbcccbcedacccbabbaaeedeeebcddcebacbeecedbbbaabbabeadcadecabbcdaeadacacdeaadcaccaadabddceabdcaeaecdeaeaabbcaecdacbbccabacccabccdedcbdebdbedcdabdeacaeacaadabadeeeeecaaababeabaeeebbcbcaaabacddedeeeaeabdeedbbddeaaebaacabaccaedbbaaadbbeaeccceaaedaeaeaaacceebecacdabbcaeabdbbaedeeaabebbeacbdcecebedececdecabbcdbaabaeaabceeacaeedeccbebcaebadddddecaebbcbacaaddbdccadeeeecacbabaebddaabccedecdebbbaacbbadbacddceaaccdecbbbbbbbbdcbacbdcbadedbccbceeeebdbeedecbeabccbcbbccbadadeececdcacdbbdacbedbebbccdecbeacadbeaaceaeccbbeeececacddeaadeebeacabdacdadabeecdcaabbdcbeeabbbeddccbebbbaedcbbebccacacbdaeaacecabbcbcdaaaeaebbddededeeabadcadcbcbcddabcdbceeaeaabebcdceacaaedaccbdaededeaadeecccdecdcbdecaacaddeedbebcbbedeceedaccbbedbbcabedeebdcadeececaedadececeeedaabebaceeceebebbcdddbaeaacdaadcdddcbceeaedebcccbbddedbaaecbadceeddbeedbebdceabacdcbcdabacbaaecabbdcdeeaddccacebbaaabaaddaebcdceecdeedbbaebeaeddcaeedddaecbcccdbaedbeedcedabdbebaabdaadbadeceacaacababdecdadcdadabaeeacacbebddbddcdabcbeabdcaadccebdcdadaeaaceaebeabeeeeceaaadeeababdcbcceeaeaddcadbeabbdebceeaebaedddcddbcdcbbdcedbcbbecadcccbedaedcbebcbeaebdcdaebbbedabcddeceaccdacdedaaecececcacababbaddcdcbacbddbdacbbcadecbaebaabbccdedadbacdeedcdecacbbcdaaadebbeacebceacebbadadeecaaaaccbceecdaacaadbebdcecaaadedeaaccabeddcbdcdcabadccdaaeacdacdceaaaedeeccaabbecbabacaceeaeccecdaeaddcddcbdecddbcedcddecccbdbadceaeaeceabdcbdddcbebdbbacecdccacbabaacaebdadbebdcdcdeccbcceadbcacbabbcadaaeadcedbedeeddebddddbeaabebaebbcdecceccebbaeccaccdccbeebcbbadabdbaebedcdadbcbabceeeecdeebdedeababdeebcaceadabbcaccbddadbadcdbaaaedacbcbaedaddebcbebdaadbabbbdaebdbeaedecbbaabcbceadbbbcdacedabebbcadeddacecbacaecccadadbbccbbddababcebebbaabdeeeddceacbbcbbcebcddbadeebcbdeeeeebceaceeaabecababddaaabebabbaeaacecedbcadbbccebbcaddcdacadcbecacbbadeabdaeddedcceedccdcdacdbaecaabbacedbeeddaacaecedaeaceddaedecebeedcaddcaacbceecaecbadaeaacaeecbbcbddabbabecbecdccedadeabdeadcecedddaedcbccbbdecceddcbbdcbccdbaaedbccbacbabecaecdcebcbbaeccbbdbdaadddbdbbadeaccabeecaddadbebbddadacacbdbacaaddabeecdbebaeaaebadcedbdecdbdbebbcedabeeeaedcabcccecdacebebbebdaeabdddeaaaabeebebbeacbedccebbeaddcbeebddcbacbeaadeaebdbdaebbbdeedcadaebbedababccccdabaacedabcebcebdbcaebeeaadbcbeebbbaeccccbdeaaecebcdaaebaebbcecdeceebcacdbeececbceedabaceedcbbcbbcceecdbebebbdeeaaebbcbdadcaceabebdcccbbeaadababeceeddbccbdddbdbbbaddabcdbcabdedeeadcdabcedbeeddbebdaeedbeeccedebcecdaebaabbeeaadcbdecaadcbcacadbedcbaeaeecaacbcbbeecdcbdedacaccbeadaebeebdedecaaceeeaacaaadcaaeddbcceedaeeecbeddddaeddcdbddbaebccebebbeebbdadbdceeceaeabadcbbebcacddedaceedddeebcabceeacaabaabceddbdebadaaaedddcdabcdbbbdadceceeedececaaeeabadeabaeacacdbaddeedbcaeeedabeaabbbcdecbcdaeddaedadeeecabdabdeacbddddcadcbaaabecedebddcbbbacceedabadcdaaadadbeacdcbbaddbdeabaeeeadaaabcecabeaedcebaebaaeecdbddbabbaaebceebdaebcdeaaabcebadeebacecacdbbdbcaeddbbdaeaeecdceadbadaeecaeaaadccceabbebcedcbcceccccaaedbcabbcbebcddeeccaccbeaaccebeeedbdaacccbcabdbacdeadddcabbedaaaaccedbaedceeadaeeacdaabcdccddadabecaedcceeeabacdcbbbceaaaceaceecbacebacecccdedaedbadadebaccaabebaccdedceadeabdcedebeceebcdabbcaaedaadeadbabcccdbaccbdbddadcbbddcbbbbaadecceeeceeeabbbdecdacaeecebdaadcdabaceeaeeebeabedbadbeceeaddbceacceaaeaceeddddbdaadabdcaaddebcbcdedbedcbacaacadbdbcdaedeecadaeacabeadcdcceaaecdaecdbcdbbaabacdbbcddabbaedddddcecbcbdcecaeaedecbbaabedadabbaecaacbbcdbbebbdaccbbaaccbececacbbebbaeacdcbaedabccbadbebeaebbaabbdeaadeadedeeaddcccaeeabeacaacdeaacacedcbebbabdaeccbbeeeaebcaeeadeadeecedcbcebdccdacedeccceadcdeadbadecbcdbebdababcceeaeceadbcbbaccaaccabaaeededaddcbdedcdecabddadcbbcbabbbbbedebbaaababbabbadecaddbebededaaabcbddbeabeeccbdadbcbbaeccabdbecdeddcbeddbeebcbacacecaedeebdedcbacbabaebdbaabcccbadebbabbeaaeaaccbaceddabbedaeceeecababdbeacadccebabbdbbeccbedacedbeabaeebbbeeeebecccdeaceacbecbbeabcdbeabdcdbdaeccecbaddcdaecccbdabcdcabaeccccbeaddbdbbadbcbbdcaaaaabddbbcdcadacdaeeabecaddcbbdcdddddddeeecdaeeacededbebaddeddddcababdacbeecababaccdaebeeaaaccedbdaecccacbeccbacadebccbddceeddebadbccccbabededdaadbcaccaaeccadecceaacedbebaecbcdebaabbdcbddbbbcdededadbbbbdddccbbadbbcdeedacbaaedbbadcaddaeddcaadaacaccadbbbbbcadebbdeeddbebeebabdeedcdcccbebbceecbeebbabdededabbdcaaedccccbdeddebcccdecaaeeebaabbcecdaeeedbaadebbcbebbdddecdbbbcdbeacabdeaadbeabaeeeeeaeeecebeeadcaeeabbcedbdadbacadbbabcbaeebaeeabcdebeeeaaeeeacebbbdabaededaddccdecddcdbdcdbebbadeaadeadcbbacaaebcddbeeebddbdbdbddcbcdeebaababbbbacbadacecbdccececdaddbeacebdecdbedbedbcdadeaaebdbbccaacbdbcbdeecedbbaebddaabcedcedbcdebddebcebaedddbcdadddabcaaacdccdeeccdbdabeeaacbceecabedeebceebadcacbcbadcbbedccababedbddcdbaaeededbcdbbebbcdeaacadccbceaedbcedacacaadaaaeddaaececeebbbedaaceadbcedeaabeaeccdeacbceeaadabcdceabacbdbbdccabcbcabdacaababacaaacdcdbbbcbbabdbcdaddaccacbecdacdecaddeebdecbacebecabdedcdeebbcaccbccebadeddeecddedcccadbcabdccdecaeadcdcabbedaddccbecdabcccbebbadcdcaeeddeeccdcaabebeddaedbdabbbbcdbbcebbabdbdbdaccddbcacbdbdbedceecceddaedbadbccdcaaedcbbcceabdaceacdabbabadbedbceebbcccbdbeaeecdaebbcbcebeaeccaaddebeccacdeceaedbabdcedcbeeaeacccacaecacdbacaddbdcdcabeebbaadedebbaeadcbbedebcaaebdeedcecdbbaeeddeceadbacdaddceeacbaabbdcbcbbbacaccdaabeabdeddebeebbadbecedcddbccbaccebbdedbabebabcbdebcddeacbcccdabeabebedbdeeeeebcedcbadcdabdedbedadbdabcacaaeddaedcaacebccdeaaedadbbeadceaedaeeeabdcaadcacdbbbcecdeddbceacdbbbaebbdeadaeeaecdbbcadaceedbabdbddcdcdebabdbdaceccedbbecaececdbccccbcbacdeedcbccbbabcddbadabadecbcaaebabaaacccacdcddeaaabcaecabdacebddceaabcdebbadbddbaaeebddaabcabccadcdcbececdddccabbccdbdaacdeacaeaadabadeabbdddeebaecceaaeddbaacceddddebcaebaaebcaecbbaeddcababaeecaaecbadbaddbddededeeceeaecddaacdbeceaabdccbddcccbdadaddabdcdaaaaabaddddaecabbcaabeebaaddadcbeccbcdacbaeeacaacadbacbcbbbababaddaededeaaeadbceecdededbcdedbdeddbeadcbbaebbaaeddbbdaaecbcbdeaccebadcebbabbcecbdeaedceeabedbeecaeeeabcadcccabacbbbabdaaaedcdcadaceebbbbaadaebdadbbdcbddeedbedebcdcabecbdcceddceacbdbcccbbbddcdbbdaeaebcbbbababeadeebcecbbbcbbdceeedcdccddacabdabbedabdbabacccebbcbdcdaacdaadcabcccdbaebeacbdcbdabcdccdbbacbaaadbadeabdccebdddceedcbebcbecdddeaebedcddacddbdeccbaeaabbabebccbeeaaebddedabdbdcdcebacbacebbddbbabdbadcaccedbeaacbbcdededbbcceaacabecceaeceecabedecbdedbabcdddecedbdededbacadbeccaaedbccaedabebbebebeaaeebacbbadacdaaaddbcaeaadcbbabcbaacdaddeadcddccbaecbcceedeceeabbdbcaaaedceadeacedbccdeddbbeedcabdceeddceeaebabaebabedbcbaddaecbdeddedadbcabbbaadddcdaacaceabbeedeceabcddaecbaceabcddcaedaeadebebbdcdedaddbcebabecaebcebebeabbecdcbeebcaadabcdaeacaadbdceeaaaabcebbbcccdabcaacdeeadaacddedbabcdcebecceadbdebacbcbebccaabadccdaebedaeadbeecccbdbcbddcaeecaaadccebabbdbbcaedeeedcacabdaceccddaedebaabdbddabbaebaebccaebbebddeededcaecdeacececdcdcbdbcdddbdbdccbeabadcbbdbadaebaeabbeedebadbdcbdeccdaeecedbdaadcecddedacdddcbecccddcdbaeaceeddbabdecadeecbdeeeccecdaebcbbbdbbeeddbddbbebddecbddaeadbbddcbeaaaedcaadcaebedccebbdcbdeeeeceabadecbcebebdaceceeeadeccaeaddccaaddbbdebebbbccdebcdecdeccaccaececceecceeeedbccebddebeceacbdcaaeedbeeebedebccaaceecdbeacebdecbdbccbaebdaeaadeceaddbbbcedcedccbdecccaaaedbebaeeaccbdecbdbaaceeebaaaeaddacaebcdcaeecccaacecbdcbdaaabeaacabdbbededdeedadebbaecaacbceebcaeeabaeaeabeaddbdbecbcdeaecaedaccdcceeecebdeddcaadcaaaddccacdcdbdededacdcbbbadcdcdbbaadeabdbaecdddcdaecdbdcdaedcaaecdcbcacecccaeaecddacdcaebeddcccedcaeccadabacbedeecdaebccdeaebbbeaddaeaeeedcbaeaabcebbabbecedcabebaecaeecbecbcddabbcaedbeaabacaadebedcebdccaaacdbdaaceecbceecdedcdeecaadbdbbcdaaddedaecdebddddaeedecbaaeecabcbbcabedadbbcccaacbacdcdcbdaecebbcbbecdcadbbedadbbeeebeabbdddeccacaacdcdacbccddecdcdbaaecccbadddeababcccccedceccbaeedbebaaccbdeeddecebabbbaecebdceddabadacddbadbaababdedceeadcedcbbddeeabddcedeebabcaabbabcddcbdadaaedaaccbcdebabeaeeeddaaebddbbdecaacaabaacadeccbdccbbbeaacbbbecdecbacbeccaccbdbbcaeeecaaaaddddcdaebcdcdbbddedeccaacbdbcddcdcdcabadcacaddaededebddeaddabaceaeaecceebecaadebdacccbadcdddddedbeecccdeebdacabbaacadabacebcaeadcdaabddeeeceedbcaeecbcadcccebaeaeeebceacdcebbccdaacacbbbeecdcecbbaacdaacaeddbcaebddeaadeebccdbdddcdadcceccbeedeabaeacbbccbcbaeeecdcebaeaceeebdcbedbbaabbddadbddecdcecdebbaebdcabbeebdbecccdaddeadcacddbebdecaedeaadaadedabeeacacddadabdedaeecaecebbbacabdbaabbdbccdbaedbdecdbedeacbbabeebeabbcadccddccbbcbeadebcbeeddcbcbbebabaebceccbcebdcedbebeeceabdcbbebaaedddcdeeabadebaacceccccdccbebbedbacbdcacccadcbdaabcdddbaedbaebaedecacdbbaabecdbaabeeadcdccaabdadbcbddceeabbcabecbdadadcbdeeecdeaecedbceaeceddaeaaeaaeccbaebecececedcdeabdaccbeeeedbaecaaccecdaccacdbbbacaadeeaadeedeaeabcbcdecebedadbccadaeeddcacebecadbbebebabbccecceeebabcdcbeedeeabccaceeaecabadaabcbdbbddbeeabebcbcdcadadaaabaedabbeebaeaedcdaddeceaacdcabbaacbaeeecbabdccaaeeabeaaecccbadbcdeaccabeccddaeaecaddcbcbdebbeebecacccbbbcedeabbbdbddeccacaacadcdbcadeeeedebbddeedbabcedecceceabbaeacbcdccdadceebdeecccdcbbeecceadddcbaeaddedbdadbaebbdcbeedbcdebbdabeceedbeeedcdbbbaebdececbedcccaedcbdbaddadbdaeebbbceddabdaaceacceaacdcccaeaabdeaacdddaabddeddeabddacebddabadacbebadcedcdbbdeadbccaabdcbbbaabddbedddedaedbebbaabcebcabdaadcacbdeeadabecdebdbbecaeeabbaabcbadaabeececcebcbccabccadcbabacaebbcacbbddeeedecabadecedcaaacdecddcabdbaeaaddccdeeccaecbbbcebcaedeacbaaedcbeaaadedeceedbbbdebdcdcbeadadcdacedceaceadadddeaeaeddcecbbedbdcaeeccededeaeeabaedaccbccbbedddcdcdacabdbdbdbbaeaabdbceaacccdbbbccdeeecddeeebaeabcebcdaceeaeebbbbbcacabcbeecedceedebbbeeeddaeeabaccdcdcacdeeceaeaabaadeccbcecddbcdcbdcdbabdcbaaeebaaebabbdacebbdbeededcbddbbdbadccbcbaccecdcbaadedbaacdabbdabbaaeeadeebebeeeabcdceccdabbdaaabaeeacdddabaabbababecaeddaadedcceacbadbbddeeaebdddbdbbcccebdeabbbebbbdaadedaddcbceabddabbccdccdddababddbebbecbaacecacdeaeddeeacbcdabcbdbdbbccbeabccbeadadebccbceabbeacacbbbbabcbedabeddaaedaededdacecccedecddeeebdacdbbdacdbdaeeaedebbecdaceadbbbbaecedebbaebbaacedebaedaccedcbdbdddaebcbdabcbbebbcdacccbdebeabbaedebabcdbeaedccacdebdcaacceaedbcadddcbeacabebaddbebaedbcbacbccdcabbcccaecaabbeaccddaadbdbdebbcdadccaaaeaddadecceeddceeedbbbedadabaceceddbabebabdbcdddadcabddabbdbebbecacadebababeedababbadeebbedaeebdeccabcedddcaecbbdccceaeeeabbeeeccdbbcbedadeacccbcdebbaddedccdccbdaccdebaebbbebedcebaeadcdabbeeadeeddabacbbeacccdaccebecdeddcedadadaedcbadebdadbbcecabadabcddeebbaaebceceddbcceecbeaabdaabeaabacdebabeccedddcaaddcaaebbacadbccebcbedaebdacaccedaacdbbcdeeaebeaccbeacebbecdccddbdeeeeddbaaeaccadceacececcdadbccccbedbcddaabeabedaebedaddaaeeeabeabbcddbbcdaedbeceabdeaceddbbebbdcaeeddbaaebccabaccdecaaeeebdabccbacaaaaccddecadabccecbcadddaaacdaaaedcddaceecdacdddbdbaceaebdedaebbadddededbddaedecbebcbbbdbbaadbdbdbcdcecebeaedeeacbcddacccedeacdaaeebdbeecbeacebebbaedebebcabbaaeaeddceecbddadcceebbdeadcaaecbcadbcbaceaededeecbeecbddbdbcceadededbccbeebcccbcdcbaaceeecedbedebdbbaccaedddadceeabeababecbcdcaaeeecdaaedececabbccceddbaaeadbdabaeddeebbbecabeaddcbbbabaeaccedadacbacddcddbcbacddcbbacdbaddcbdebcacaebbcbbdeeaeacaaeeacedbeadbebbeeebdddeeedebcaabdcaaaeeeaceebabacdeecabdeeaeeeabaaccbacbddeadbccbcaedcdabbcbabdacdedaeddebaaddeccceacaacabaaeeaacecebeebbeccbaabcbcabedcebbdbadedeabdbacbedcbdceddeccdecedcbbebaadacbbdadaecdbbdeacbaeceaaacbbbdbacabaedcabbadbbcbceceecdababeeedeaaaadabdbbdbbcbceabeebcecebcacdcecbcbbbabaacceaeecebbcddaaeabaeddcecaedececbdaeeebddeecddeeceabdceacbbcaececacebedaebbabddbdeeacadebdcecbccbdcebebcbcccdaeccdccdaaccdaabadddddedcbdbcadddcacbcbcebaaeebddaababebcbccbdadbcdeceebcdcedbeedcdadcbbdabcdbcacdacdedebedceebabdceeecbeacdaceebccdcacdccbacbadcbbdedaadebedebebdabbadcaceadbcabeaabbbcbeeedddeaccdadecddadecaeedbaeeabceadbebdccaaccadeabaaadccddbadacacedaedaacdbaddcbddbcbcaabbbbeaaeeecdcecdceaccebdbdaaaecddcbaceccbadcbeedaeaeaadddbcbebcccdaaaceccaecaadabeeadbbceaaddbaeaadddadbdadeeadebdabbdedccceaabededdcacaebdeebdacbebeeeebcabaebdbeabdccdabdccbcbbdbaaadccedbbbaabeacacaabebadebdacaaecbeadbeeebbdbabbdbaaaeccceeabcccededbaadcdeeaecdbdbdddadcabaeeeaeeaeacccaebadebddbcddbbecbbdadcabbaeabbaedcbdecaccedbbeddddaccaebceaddaddeeeebaeabdedcbbacdabbebbdeaecaccddeedcdeccecadccddcadaddaabbbeedcabbedecdecbbaedbadecabceadcccbadabcaeaacbcdeabddcacdedbaaaedecabeedacaeabbcedebcbbbecceedcceeacdcaaadecebcbabbceadcccdbebabcdbebaedabdbbdddddeeadceaadecebbdedaceceedaabccacecdbddadeeadbbaceabebdcdeedebeccdacbecaecebebcabebebbdbaceaaeecebdcacccecadccaeaddceecbdbcaaeaadbcecaccaaecddbcedaaebbcabdedcdcabbdcdecababbecaeedbccedccebeecbdbdedbccabebbeedbebcabacbdbaabdeeacebaabdbdccaaebbdceedacebacdeadcaceaadecbdcbebedecddabbcacdbbbbcaabcadebdcdeadceccabcdaedabdbbeeddbbbeaddccbbadacaddbbeaeacedaacededbabeeaeeaebddbacdeacbcedddadeeecdaaaeedeaebcbebeebbbcdceccaebeabacbbedaeaeaaaddddaaccbeedaecbdcccededbbdbeadeaaeadcaceeccbeadaeacadbaadabcbcbbddabccadebebcecddeadcaddbedaeacdeeebcaadeaeeeabdbbaaedededdbaeaaadbddceebecdbabacbcdcdaeeccbccddeaddcdcdeccaabedcbabeeeeaacdbeaddbebebcdbbbbdebabadbbcccbcacbdedcdeeecccabbeddacaceeedadadacbdcbdabdddbbaebbeaadadbbadbeadaeebbeaebbbcbdcbcbbacaadeaeccedcbebdaedebcbbbacbdebcceedcaeeeedeeaeaaacaeecabcbbacbaddabdcbdacbecdccdbbebeabbceedacbacedeeaccaedbdabcdebdbbceceeadebaeccccbcbcaeeeccababdbedeececdbccaddccceeabbaacbcdebdadbcbdbddeeabbacdaddcaaacdecadcceeababceddaababedbdbeaebeccdaeadbabddaecedaddcdbdbbabbeddecebccebdebacdedeaadacbabceeacbcbcaaeeedecaebcebcebeeaaeddbbbbdccaeaaacbecaabecbeaabdadcedbdeddeecbdcdacbcdcddabceaeadaabaceecbdaecebcacdeaeeaecdaaaadddcdcbacccdbbcedeccaaeaeecdbbdeddababcdeeebccbbacdbcadbadacbbcacdaeaebadcdeccbbdbaadcebcdcadeadabcedcbccbaeaadecaabeeccaadaeebcbbdcebabdecaedbdaceccedcbacbcbdadebdaeabbbddbaaaeadaacbdddeddedaeddeaebaacddceabbcaeedeedacbcbacecceeabdcadbabdaadaebdecbcdaedbaddddabcccebedbecdddeeaaababdedebdaaeabddcacabccceacbcbaeecccaecdeedeccbcdeadecacbeaaeecbccdacebbddebbbeaacecedeadcabbbaccaadbdcbbbedcdacdaecdeaceeeeaadccaceaeedadedbbddddedaddedaedeeaadacaaadbaecccababebcbbccdddbaeccabbdbbdaadeabeabbabaaccbcbdbdeaaabecbcecbcbdeabbabecedccebeaedbbeaccdcdeaedeeabbeeadbeaddccebeeddbccebbceeaebebecdbcdbaaaceeaeaaecbcdcedbadebeaceebdeceebacbbbeeadbddbdecdcecccdbccccabaaebdaabaaeeacdbdbcddbaaedaccbeaabedaabbadddeddbcacccceeeaaaabaaaaedbcaaabdeceabebcdeebacaadcacaddcbabdadbcbebbadcebebcbacadbebadedbddcaeddebacdeaaeaecbabceedcdedeedeeacaaaabbaedbbcdedeaddccecadebadebedecaccebabddaccaeabaccabbcdebbbecaabcabdadbebacadccaaecdbecabdbcdebcdceaecaacecabdadecbacacdcaedddcceededeeeeabcdbbbabcacdaeeccbaabdadddaaeebccabcceacaeeeecdadcbceabaddabcdaebcbabcacadabecdbbdbdacadcdeadbcbbbedbeadcccdbeebcadacdbdcaccaeabbbdddbaecacbebbbbdcacabaeaebdbcdbaeeedbcbedbaaaadcaeceddddeaabbaaacbdadaabaaebbcddddcbdabcbecbbadaeedbabbaeebdaebecbedbbdeebceadceebaebdacdcdceebdbcdcebeaedaedeceaaccccdebddbdbdccacaddcabdaccbadddacdbaabccedcaddadeebebaecabbbceeeccaceaadacaeeeadbcbaaedabaeddebdceccabdedcecebdcaceebdebbeabbcacdeadadcdaacbcbaaddccbcdecdebabbaecbeebebadeaadcdccebcceedebeeeadebdbcdbdeaccacbdeecdcadcceabebebeaedceccbacbbaabdbdceaecbbabdaeeebcdddaceaebebdbabcbcaeeaaebaadebedcdbeebeedcedbbebecdddbbbebdeeabdebebadcbebbacddcaccedbcaecdbbaeceddeddaebacadcbeeacbbdebacdcecbaaeccedebaebbdbacadaeadaadaabbeadccbebdcbdcdaeeaadaadbdacdabbdecbecaadebecedddceedcdbadaebbdedbdaddbdabbecceebcccbbdbedcabcccaeaacecdacbacbdecceebdbdecbbdceeeeeedaadbbcbecbebeebbccddceddabadaabdacdbccadecaabbcebaddcbacbcadcdcdcbadddcaaecedadcbbedadecacbaeeaecbeedabddbcbadaeacbecdeceadbdbabdeadaebddbbadbdabadecdddebbacaaacedcbadbcaadbaabaabddadaaaeacaeabbbdabdceeabcaeaabcebbcbdbadbdbedebdaceaecadadccaecdbdaaaabcbedbeaedebdccabcbebbedeababdeeedecaccaabeebeceadaececbceadceadadabcbadddeebeaacedaeddaebbbecbcebecceeaaebaeadbddebaebaddccacdabeeccdaacbaacbeedccebcdaddbdedeadddadcccdeceadccededeadaabccabbadabebbabcbbbaebeacecddbaaddadaebcdedccebeeddcecdccacdaceadadbaccdabbeeececcacabcbadabbeaddaacaadbaabddadedeccdecbeebedaaaecddebabbbaccdbaacacacbbbecdcdadaaaedbecebdadcbcdddbedbeaabbaebaeebdccedccadacdbbdcadadabadeaeebbdcddedeacabdebebdddcddaeedcecaeceeddbadbbcdbcdcabbdcceacdaaadccdcecddbbccadbceabddebdbeecadebcbcebdbcaecdaddebaabcecddebedbaccadaddacacdecdeaacbeabbcacbcbacabacddeaaacbeeddeacdbcecbbccebbceabcbebbadbdabeaeabbccededdabddcbebdedadcacdbccaabebabbbecadebbbbacdbbadbaaebcdbaaeaaeeedacbceeaaecebebcaeeebcdececacddeeeeebeceeacdcbbbddbdcedbcbccaecebbdceacaceacdcbabdecdedddcdedecebdecdabaeccecdadbebeaadaacbbbbecaaaabadddddbdbebbdaadbedebddaabbceebeeaabaadededabccacbeddbecdaeaacdecadcebcbccbcdbdcdbebbdadeaaadbdecbdcbeccbbacacaaededadcadacaaaeaaecbcaedbcdbcddabdcdebababdbacbdbcaccdcaabccadbbdddccebedceceecdaedbcbdcadcedaecacdcdccdebdaadedeadaaccaabeabbebdbbcbadbbabbdedcbaeeaacdddcabcdcadceedbedaabedcbeebbcbceccaabbddabcdbcddaecaecdbebeaeeedadadddabaccdbeecbadebbdcdaaacecebbbabadbdcaaeaebaabebbcdeaebcecdadebdbbadceebddcdeceaaabadbbeecddcabbdadeeaaebdaaeedbacddbbceaceadecaebcceadddadcaaaeeccbdbddbabdbbdabdebeceddbacbcabdacaeacddebbebdceacdbdbdacceedbbcbdebbcaddbaeccabccbccecaeaadbccebebaaadcdddedceedebeaddceddcddecaaeaedbadedababaedceebcecedcdeedbdedbedbeaebcbaaadeecebcecdecbdcceeedcdcebaeeabeceaaaaaceeaebecddadddcdedaebbeabbabdabcadadcbcacbaabcabdddcacbedcbadbbedcecaceaabcacaccbcdcadbddcdecaaeeebbabaeeddacabddedecedbcceaadcbacbaadebdcceecebdacebdcbddbaebacadeacacceedecacdcccadddebdddecbbaccceedcabedceeccddcbdabeacbdabdcbebdddeebbebaadbabcbeccbaaeebbeadbabbeddbccdadaaaaaaadbbceebdcedeaaaadbedbecdabbdcadbbdecaeeeecbdaaadbdbbabedbedaeadaddaaedddbbecabeacbdeccededcdcdaceedacceadbddbcdbbeeccbdaaceebeadbadebceecccdbaceacaeadddbaddcbbbbdbcacedcddddcaaacaedbcededdadcedabccbeacdebeecddcebabdbdcddcabddeddceedcccddbadadebbbccebcbecdcdaabdcececeebcbadcecdeedbdccaacbbbdeaedaaceaebbbbbbbadddaecacecaededbacceedbeaddebdabeebcccddddcadddebbecbbeadddaaccbdcbecbcacbcabcddddadebddacbdcdaecdcdbbaadceceadacdeecdeaacadecaedebdbddceaeaeccbbeeebddeabcdbededdaadbbabcbecacdbaacddbbdbbddadcceabbadcaaeceddcbeaaacecbdeddcbbdccaebabcbdaacccbcaebbbccddddbaedcbcdbbdedacecdcebbdcdebdcdabcbbdabbbedcddacbedbabbcaabcaddaabbdaddbbccbcadeeaecaddbadacdeadeddececaeeeaabaeaececaddeeeaaeaccbcbdbbddbabbeebdecddbcbdabbbebdaaebdeeceeccdeeaeecbcdbbedeaecccdbabbabcbdbdbdcddebaeecacacdcbadacedbccbebacaabbbcdabeaedacaccacbaaaedadeadeecbcdeeaeddedaebaecbbbbecbcccccbacaaeabccacaeccddcaebdabcdcdeeadeabcaaacddedddcbcbbeaecbcddabcaeddbebececaaeeeaaaeaedadadaaeadceaeeaaaaddedddbeecededabcacacbbccbaadceeebbddcdccaebcebcbbaaeceabeeddbaabdabceadaabaabbcceecdeebddbcccacddbaeabbceddecaebceecdabeedecdddabaddebcbbdedeeaeccbbbdaebcbecbcdcceecabadceeaeeedbcbbcebdaedbadcaacbbaccaabccecdbededdebcdddcecaeacbedadcedcebbadcecedebaccaabeddbcbbebccceaecebeeadcebaccdbcededebbcdbbbabcaeaebbcaecceadecdbcabaaaaebdeddeaadacccbdadbaabeeebdaeaaccdcedeaacbebdcdbaddddceacdedcaeedeaceddbcdddaceeabcbaeadccdcbdebadecbbbcaaabeacaeedbdebdadceacaebadcbeaceadedddacbddaedddaaceadbecccebeadcddecddcdeadbcebceaebbcecbbedabaeabbaedabecdabcabcaeccdeadbeaeccecaeadedeedbceeacbcdbddaaecceeadceabbdddcbaacdebacccdaacdbcdacaadaedbbcbaddbebcbadbacbbdeabcdbaabeeedbeadaceeacdddeddecebcdecedeedccdbdacebdeebeadbecdadeddbeaddabcdbdedaaecaebcadbcccceceadebabceccadcdebcabdcecbbeecadbcebebadbeccaeeeceabbdcaedaaaceeedebdbeebdedadabcddebaabdeaaacbeeecabddabecacdabadddaceabedbceeeeacedeaccedabbbdcceacdaadbbadabeadeadcbddccdddbeeaedbcedeaeaddeddcdcbcbccedcacddeecbdbceeaabcabacbcdccaadaeecdaadaaeeaeecddbbdceaecbbbaceddbbbaaacbbaddadbcbacdcccdecbacbceaedcdeaccadecedbaacacbebdadccabbbcebeebbcebceaadeebeaedbedbedeeddacbabbbebdaadbdecaedaacecbaedcebeeaaaeadddbdaccacbaccdecaccccebaceeaacdaebaeedddceeaadaecbddccdeedabcdcebaacddaaededddadeceacededabeeddaaaedbbdbbeedbecbaabccbcbeeebdccedebbebccbcbeedaadcaecccadccdacdcebbbcdecccbadabeccbaabebeecbebbaadbcacdadedbccbaededbaacaeeacaeeaebacbdccdebeebbeddbbbdaeeedacebebcdebecbabededeacccecbcabdecbededabeaddaebbcaeabbbcdedbdbdbebedcbedecdbdeeceaddaeedecbbbccaaaccaabccaedaaaeeacbeeacceaebdadbdcdcedebbaecbadcceaadedddcbabbadeaabbabbceacdbbbbcceccdcceaaaeacddedeacdbdcbbedccabbddedbadbebddebadcadbdeabecccedabdacdecadbecbdbddcaeadabdaecedbcbdbccdbdcdcdeddaecdeceadcbcdecbabcecbecedecdebaeeaccbaacebcdbdddbccddcbdeccbbdebddcadcbddeecbbeccdecdebcecbdceaeebccbeddedebeaadaacadebcaaaabeeaebeebccdbebddcceccdecddbdeeecabeabcdeadcdbdabedbabbecbcacdcdaededeebeebbaaebceeacaeecceadbecedebcbeebaabddddcabcddcaeecdcddeaddddcdbaccaadddbebdbdaaeacdcbadecddeaaccababcacaedbbbdaeacbeddaadaaccddcbacababecdccbcebbddceceeccaaadbdcaaadaaedadbbdcbdcececaeeeabacbacaecabddbddbbcaeadcccbeaecdeeacdbedcbaacbaacbcebacaacaacaeedcacbebadccbcaecccacebccddccbcbdbbceecbbdacbaeadebceaececaadbcccaaaadadacddbcbdccecebdccccebbaabcecbbedddccadececeaedcbbeedbbdcdedbbaacbeccaeebdaaebaaedeabdeccdaeeaaeeaebddbcbbcdcbeedbbccaaecbabbcdedebabedbdbedcbeadcaadabbccbebcebbaabbdcebbcbabeaacbbababdededdcdabbeeeacacbbadbdddbadebbacbadaccacabdcdaeecababbdaecedbccadeddaaecedadabcacabdacdaecaedddacabcabeabbdaaacbcccdebbddaebaacddccdecabadcccbbcebacabcdeaebdcdbbbabbeecaadccbcedebddbcecdbcbeedeacdecbedbbeaecceaaeaacabddddadedbbecbedeacdceccdedbcbdbcdecdbcdcbcbeaadbaadceaaecaaccabeabdcecbcbdcdaaddcecbcadebdeebdeedbacaabbeadbaeecebbbcaccbcdcaddaddacceaecdbacaccecabaaddcddbaddbeddaecabaeeadcaccddedeadeddeececcdedabdcedeecedcecaaebaccecdaacdddecbdeaabacdbadeeedbeebceddaabbdedbaddaeaadbaeccaadabeceaceccbecedbeeddeabcbaccaebbebdbebeedcadcceddababaccedeccabdeeaeacccddbcaebcedbaededbcbbcabaedacbeeebccacaaedbdedaaadbbcedaabbceecbaccacbeeababdaedbcadddeaebecbbbecdeeccadbbbbaeeaeacdebdcdcbccddadbaeeebeabecccaabcaacdaccdaaedcbadeebbdbecdbdebcadeebccebbbaebdeddeaaeeebbadbbaecdacecbdabddecdbbddbabcdbebbeabedcddbaaadacebdadececeaadbaddabebccccdeebdcedadbbecbecccdeeeedbcceabcecbcdccbccceedeebbbcdeabddddcbedcebabedcceebbbccacbbdaabeeccdebabaccedbeebbabedadeaebeeabbabdecbeeccceeaabedbdebdecdabbcaeeaccbcdaadabcbcddcbbdbbcaeccadcdddbcddbeccccdacedddcaaddadddbbbcadcdbadcdaddbbbbaebbdbacacbccdcccebabdabbbeeecbecbbcabcdcbcdeccedaeeabbecddbdcbadceedbeadbabddbcbbdedcbaaecdadacdddbbbddccbecbcecdbeebedbaccabccaadeaebdccdcbaedebdcdacbcbebeaadccadadaebecedeaacecdcaeedcaacdbcdbaecdabcdaccecebdacdabeeecbcadcdcedbdabecbceeeeccadabcaeaceaedacabdbbecdaeeecdcbedaceabcebccabaecdbbceaadadebbaceacaeccacdeeebecedcacbbccabcbcaeaaeddeadebebeaaebbaaebcdcaecedcecdacdbdceeeebcedadebeebeddebddbbbbbecdbaaddedbebddaacedccacdbdbdcabdaebdbcbcecbcabccbebebdbdddccbabecbdaaadeabddeabebdcabeaeaaacdeeadcebeaacebdebbacecaadcacabcedadcecabbceeedabbdadceddeaeeeeebdabcedbddbdbcbbcecbbbbcbebcdcdccbcdcdabddebcabbceebedcccbebdeaceeaabdbcceecabbcacedcceceacebacdbdddaaeccabadddaaceddccdaebeecacbcabeeabdcddcceebbebaeecaeccceccbbeebaccddacbbeceadcacbacdbddeaabadcbdadaaccccaaadccdbbaadeabbdaebdaaaaacaeabdbdbbcdcecdaaedaaacadbcbaecaaddccdbddcdabcedbadcebeebaaddaaeeccaebaabbdaecebdacecaadccceacaeebaadaadaccecddbbaedadbacbdebbaccdaccceebeaabaaeacbabbaebcbceccebedbbdaceebbdecbdbdbcbdbcceabdabaadeeaddccbecabddedbbbbabecbbecabadcacabaebdeebadaeeacdddacdeaadbdbadddedeaaecbdecaebdbbcaccdeaeccdeceadcedeceeeccecbdbacbadccaaecaabebacdacbdedbcacecdceaccccdbadbcdbbecddabaeaeebcadbbcaeceecebabdcbdbbbbebdbeabcecdbcdcbadcdabaadecbbbaeddcbdebededdcedecaeedceaadeabcccdbdcadeaadcadcacdaeadeeabbcebdbabebaedaaddeccbaecddcaecdedabeedadcddcadbdedeecdbbebdacecddbedceaeebaedabbaacaacaebcccbecaaacdbdbdebcecdbdccaeeabaebccacbeeeebadcbebeedbcdccdecdeabccddceaacbcdbaeaedbcabccdacebcebbebcedacdcebebabaeabdbdadacadcbddebcacabbacacdaadbeaadecaddbcedecebddaceeadabedaabdaeedcececccecddbddacdededcabdddacdbcaaaccdeabeeababaeeceadeceebbbdcebceddecbcedbbcedcccbdddaeaeaeaaaebbcdbabbacccebeeebeedceacbacdddcbdccdecddaddebeaeebdddebcaaeabbdceabbbaddaedabcccebcdacbaaeabdaabeacabcceeccddadeeebddcebbeaddeaaedceabbaaccecbddeaeaadcdabacacddbdcbbecdaeddbcacdccacabedaededdebdcaeaeadabcbadacbdbaaadebecedaecadeceabebbddaecabebccbaabedaedadebceadcdbdaddcebedeeecdebebbacabeccecbcbaaabececbadbdebeddcbdbddbebbdeeddccadacddbdebdecbbbabeddbaeddeeaabcddebddebdddeebaceeecdbacecbeeaceaaddaaaaddadeeeceededbddcedbbbbabccdabdbbbcdeeaecebdeadcdbcacccbdebbcbbbbbbdaacddddbeedaaddbbadaddacaaecdebaaadadcadacaaccdadabaececacbaaabcedeeaaddecddbcddeadeeebaeaecabaecbdbaceddebbaededcddcbbeabebdddeeecdcbebeecdbeaacadccededdaadbcdebcacbbbccbeebaccebeaedaaebabadbbabedadebaadcacdcbbbeddddadcaebccceeaeceabcacaddeedacbdeccedcecebbcadbacdeabbbdebaccddededababcdebeadcaddbdaadaecdeebabbacceedcacaaacabcdaaaaeceebadbcadcecddbdeadbbaebddceeeedbbddcbccadaaaabeddaddedeccdbbbedabaddadaeecdcecbacbbdcdbbecbceddaaaabbdedcccaabeccbcabadacebcacabbedbdbbacaeeecbedcacedababaebeabebbdabaabbcaceeeeadabddebdadcdedcccebcebacadaacebacecbcedabddeccaceabdacacccabaeddbdeaecbdccaeeeacbaaeebaceebcccaeecacbacbdaebdeceaadddbebbdcbceeabdeaadaaeeaaeddececedecdededacedcebcaacecadadddddbdedeeecbaaeceeaeabbcaaacedccabdebaabcbeddcbebcbddeabadabdcdbcdeadcdbdbbaedcaeaadaddeaeaeebecadadaeadedcedcabbedcbccabbbaabdebbdaecccbbbdcdbaebaeeeddababdddbaddedceeeaceccebebacadcbedcbeceaabdceeaeebabeceeecdaabcceceebbaedabcbeabeedddecabdeddaaecbabaddadcdcbceaeebcbcaecbbedadddaebbacdbcbedaebeeacebbabcbcceaedabdeadaecadcbbbcccaddccdbdaddbeabebcecaeeaaadbacdededeadaadaebedacddbeccbbeaaccdcecbbaaacaaeeacaebdbebbdcabcbacbcadddecbdacdbabdddeaeedbdcdbdedbbdbeabaabebbadaebbacaebaedbebcbbaeedbadbcebddabaabcbaeadaccccadebbcaabbeedbdaadaebeedbddbccdacdeddcdaaccdabbdabbdeaececadaecebbeeeacabcdabdadcbdbbbbeabbebdcccddeebbebccdbbbeaccbbdbeddcabbdabceeadbebbedccbbccabacaaabecbbabbcdeebebaddeaecaecbbacdaebacacbaddcdacdbcbdeabbbcdddaacadaabdecbbbdbbacaeaacccaeccecbaecaeaccccbcdaeecddbcdeaedbaadcbcbbabeebdcbabaabecdeedbbdebceeceedbbebbebcabddabeeeddeababbceeebbdacbdcacebeddeededaaedaabcebedbebabbaecedacadbbdecacccbbdaadacadebabbaabccceeaadecdebdebaedbacbdedcceeddecbacbeabaeeaacccadaaddeadabaaacbcdcdbacdccadbaedbeeabaacbbdcbbdbbbedbcabeabbaddbdbedeedcdeaadbaeaccbacedbaeebeddcebaebeeedadabaccacbbcdaeaceebdceabcbaccacbdcdbcdaadadabbdeeacdaddceaadcbeeaadacbbbeabbeaeaeedadabcdecbccbeccecaccbbacceddeebeabaeeadbdaeeeaeabeedaecbbaccceabdaadbecbbdaccdadbaceeccacacddcedebcbbbdacabeaceeedbaacabdadeacebadbaeeabaccbbecaecbbebeebdccbaaeddcbecccbaddddeedbbdbebaaacbabcdabacbceaaccccdcdcdddbeacbabdecebaabddccacdceeaaaebcaaeeeecbebaddcecadbebceeaeecceebcdeeecadeacadeaabcbcecacbeedbbeaececdbbcacacabcaeaadedebaaebabeeeabddcdedcedccaaebedcaddabedddaddbaebcbabeecddbedacbedabdaccaccdddedceabeaabaaacdcbbdeaeccabbbbacbbbdccccccecabeccdeaebecdaabebeadcbbdaeadcecebcdcdaeabccaaacacedbcddbebdceeadccabeeabebadbadbeddccecdcabaddbdecaaccbccdadbeabcccdebddebdccebebceeebadddcabadbeaecadaebeabacbddabbaaeaedcbcdcbecbdababbbcbdadccebcdbecbbcceaadaeeabecbdeaedacbaabddbaedccecedbeabeedeabaeceaabeccedaadabddeaabaeceaacaeaadbaecbaaebdbdeabacedbbdcaccdeacbabeeabedacabebbbdbdbceeeadeedebbbbacebbbbbeecddeadaceebbddeeadeedeeecdebeddccaadbdeacdebdcadccaabaadeabeedcaaaedeeccaabbdbebbecaddceceeedbaebbeaccadbacbbadedddcadebebdddddbaebeebaaceedcaedcbbeeaaccacbcbbdbaacacdcdcaebedbdbbecbbbbddcceacccaabbaaebcdacdbeeabddbedeacdbbcbcaccbbaaecbdcabedeaecbaaabedaabcbdbecdbeedaaacdcdbaaaccdbbbcaddddedaeebcdbaaaebadabbaeedebddebccecdcbdabaedddbaedeeacbbebddcaadabeddedeceedaceeaebececccecdabcbccecebdaeecddccbcdaddecdeaedbcdedeccaaceeeaacbcacabbbeaadbcbadebccdedecedcecbdadccacddacdeccbbdcbcacecadbcdbddebebeeeddbdedeeccdeadcccdbbceddbaadccacbaedcaabcabceadeabbbbbccebeeabbcbbcdddcbdaaecacbcbdeceadccceedadedccebbeaddeedaeccbdbcdbabadcedddbcdeacaacedbeddacbedcaebaabecdccdaaedbaaeaaadcbaaaeeeddecbdcbacccacaedabcabbcadbcabbdbadbbbcaacebccaeeccbbccbcbcedbbedcadaedabbcbaeccdddecddbbacdebacccaeaeaddaceeebcadaaedccdadbdcccbcbbbdcdaccaaadcbcaeecaeedadaacdcecbabdbcdbeccddbaaeddbaaddcbcceabcddbabeedaeacebbadbaaabaecedcbedadadacabbbcabacddeaddaadcaebedaaebedbababebebbeeccdbcadeaaceaaebabccecabecaeebdbeccaecddbcdbeddabbaccabebbceeabbaebbdabcbeecdeeeebdbcdeeeceebedadbbbbacebbcebbddbbdcceedeeebcbeadaabeabdbdcedceaeadaccadebebceecedededabcaedeeebaeecdbeaadeeaeeaadbebddceaeedddadadeeebeddedaaacbabdacdbabacecacbeadcbedccedcebaacabeebbbedaceabbbdeaebdecedeaabacecaeabedbbddbbcdacdcdadbcbcecedcecacaeadcbdccbdecaeaddccbadbcbaeabbdccbcaebddbbaaebcedacaeadaccbebdedbdbbcbedaabccbcdaecaebccccecebcbecbecbaedeedaaaddcccacbbbccedccbbbecebbabcbaabbccebbccabcdacccedbcdacddbcdbdadecdecbdccebdbdccbbbdaaabebbeedcceaeebaaedabcdebdaccdeedddeddabdedbabdcdcbcabaeebeebbaeccebaecabceabbbaeaadecababbbebbdbedcabeecaaddbceeccceeabedeeaadbdebcedaabcebcdeebeaeadabebeccaddeaaabedadaecacbdecebdbbaaeeddcabebbacddbeaebbcccaceabdadbeeacebdeedadadcabebeddcbdebdbdbdeeadceecacbbdaacadbaabbdebecdaebadcdddbdeeadceeebadccdddceaeabacbeeeecadabbcdaaeeeecebedeabdcaecaadcaeddedcdcccdabcdaecddbecddddcabbcbcadcbbdeaddaeaddcdbadcdabdcbdcebaabbdeaabbeacacaacaaaadbcdeceadceabaabcceabdaacbabddbccaceebcbddedbceaaacabaaebdeeaddaddeedeebaedebddededbcaeecbecdbccdeeecabbcdebdabceaccddacdabbacccbceabebdaaedddbdbbeccaebecbadadbcebcaedbbbcbeedbbdeccaaaaabcccaabcdccdcdeaedbeedeecebeceaedacceecdddecbcadcbacabebadacbcdceebeeebcdabaddbeebceeddedbdeebadadbadbacbcecbbddaaabcccabeedcabccdaecbecabdeeadbaebbebaeeccebedbabceadcaaeccebbccbdbabedcdeddadcebabaaebdccedbaeacadbbbceedbbaabcaedddeeabedacdeaeeecadaabcecdcdacbccddcecdcacdedcaccbedddddddebbebbcdadbbcebaccdeeeaeeccdddaacaedccbecbadecaedecbebaaedbbdaaaccddaabdabbeccccdaaadaaebdbcbbcdadeeccddbeaaacebcaadededdcbbaeaadceaaabaeacbbbbbddeebabdbadcbaccaeececbddcceccebececcbdbdeddbedddcdabceacdbcdecdebecdecbadbbcdaabeabcececbddbbacbcbeaaacacddeecddbedaebbeacdebdccbbabbddcddeaaceececcbdeeeaadcbdbaeccedebecbedcecdbebeecbaebdaebedcdcbdacdeacadadbecbaeadabaadedadaaeceaacddabbcebbcaeecedadbeceadeadbbadedeaebeebcddaedbecdbdecbddabcaecebbedabaecdcecaaaaaeecccebbabbaaaceddebddbdebeecdeadabebadedeedacbbbdddcbeacaceadccdebadbcaaedacdacdebbaaecddcccaebdcacbcacecbdeabcbdceebbdbadbbeccebedcdedeacadbdadeddabddbeeacbcbaaeacbbeeadcecbeeaeddedcdcddcaeeebadbbadecacedebabbbbdeacdbeadabbbddaddbbacbbaaadcaaabeadddacdeeeddcdedbaaebddcdabeaddecbbcacadbdebabeecbebddbdadcebeeabdecaeaadeddaebaebeddbeccabdbebcaeddbbbbeeabaeceeababebcbdebcaabeeaaadbcbbbdbeebeceaabedeaaeedddebecdbabaecddddecedabebcccbebaaabedcabdccbeacbebcadbedadddecbedbdabaedecdbbcedcddcecbdcaeaaceedaabbabedbcdbabdaccdcdceaccaecdecaebeddcebbbddcbbedbaccedeeddeabebeddbbeaecaedeaeabebcdceeeaaeaccecabdabdaacaedbdbddeadebddaeaacdedcaeacaeaaabbaaeaaeabcdaacbccdedaacbdceebebcbddbbdebcebdeeaaeccdeeddedceaedbabddcbaddadebeddbdbabdccadcadcccbcadeccbdedebaadbdeababcddcdeaebcbbdadeabbeeadaabeeaaeaaeeddaaaceedbdcbedbebaadbadaedbebcddcceaeceabcabebcbbbbeeaeacabdacceebecbcdadababaeecebdbbdcdcbebcbaeddbabdebbcceabbdaecadbcbdaacbebdcaeceabcbdacbcdddbacdccdcddaacbbeebdabbecebdeaabcaecceeccdbbdcdbdddbcacbbcbcbaadeeeaeedbeedbbdaedeeccdebdbaaaacbbcbaaacabbcdaddadaadeddebaeacabaaaaebcabbaaccdcededbabdaaecdbbedbabbbbacacceacebcebddcaadaadccacacbcbebdbebcebebcddadbeedebdddbecaecaeceeecebecbccbdcdbccebeebebddcbbadacacaabbadbccddcdebcdbabdcacccddeeedacbaebcdbcabbdeaebebbecdaeedcddbadacbcbebbabbdcdeedaececddbbabadbaceeeabcdcdeddaebcddccbbcbdcdeddbbceeecdcebcddbbecedaecbaabedbdaceaccdbebdbbacbccecdbcaedbbdbccbddedeaceecdadbcbbbbadbabecbbcaddabecaecbaedeacaabcdabccebadeedbcadedbacdebcbabaeeeecdbdcdeabaacbdcaebceecabdecebbdbadacbbdacaadceccabbaabcdacbadeadeaceedabcbcedbbccbbbbacbcecdbaadcaeaacabedaeebedcbbeebaccbdccbdcdedbebadedeeacadabcbbdbaebbabebeedceaebdacedeccbbadbebeacabedcccecbcecbeedebcdbbcecdabdccaadbeeaaedccbdadbadbbbededbebcdbbedabceeaddedccedaeebbaeadbadcddeedbeaccdcdadecbcabbbddaebdbaacadeadddeacadaaaebbadcdcaddeabaedceededdbacdeecdccaedbcdacadbacbacaddeecdabdbcabdadccedeabcaebddcddccabcddecbaaaeceeabebabcbaeeeeeeaaaadcabbedaaaddcccddccecdcbacceceebabdccaebecbdaeaaebcddeeedaadabacebcbaaceabaeeddbbaabedbbacbbcbbbcdedcaceacbdbbeaceabbeccdadcbaeaecccecebabccccbbebbaabdacabcdabdeedbeaeabdbcdeacbddaecbbddeaddeebaedccecedbeceddddcadcdedaabcddbceadbaacabecaaaebccaeadddebeaaccaecebdbedbbecbadbceaedcdbedeceabbadaabaebdbeddccecdcccebbbccdccdbbbccaeceaaeadeabcbcdbbeedebadbbcecaaddcebccebcbddeddedabdeecdcceddbcdaecbaaaecededaddbdcdaeaebdcbabccecbdcbcdaeddddaddddadebdabadcebcbbecbdaadccceccaeacdbcbcdabbdcdbcedbedcbdedebaccaeeebbeabbaececaedeebaecebbedcedeacdcabdccbcdcceeabdebdabcccebebacdeecbcccadbdbbcecbddeedbaecdbdbeceebbccdecaccebbaddebcecdbeedecaadbacbdabcdcdeebebdcaeadbaeeedcdeacacedebdbcabadaedbdeabaedddddeddecdcabacddccecaeacbccdbddeeeacccdeabbadadbcecdbbdcccceedabaacecdddcbdacccdcaebaadeaabcbbbceccabdbdaecdecedeaceebbbcbcaddedbbabddccadeabcddcebbdadadcbecbbbaaaecbacdcebdceeaabceabaadbbadccedaceddbdedbdbaeeeddbeccceddededddbeabbadccdedeaecebabcbeddaadeecbeebbebebeaebeccbcdeaacaceeedeaddccdccecaacbbcaebaaccdabacbcaeecdddacdedebaedaedddcdbedadacbcdaadcccbdadedaeedaddabcececbaabdbbabdebaceeebbbeeeeeeacdecbeadbdcbdbbacabbadebeadcbccedddedebcedcaabccedcaebececbaeaeecdeeddabcaddecbebbccacedcccedddcabceedcdedaceecaeacaaaacebcbccaebabbbdabeabaaeeacdebecaaacdcaccdeebeeaaeccdedbceeccaaabddbebddcbaecccabbdbcebbabadaacadaedccedabdbbaacbdbcdbedebddedccacdebabaacdadbcbbabbeedceadbeadacebdbdbaddcdcdeceabcaabaaddccdeaeeddcaedddaedadcdacaedecdcdaaeaecdcdaeabccbbbbcbacadeaeeccccdaaebacadcaecdbacddeebaadeaabbadbdaebeaebbcbceacdabbdadeebdcbbebddabbdcceccabcedaecdadaaecaecbdcbabbacaedaddadbebccaabeebedbdbceecaeddeccbeeabddeedccadabceeccbccbedddeeddaceecedbaebdcaceeacabbdadeabaaabaeaeccaadbcdabbabddccbbddeecaaeeccbedddeedeaecdddbeecdaedecbabebdccdbecaeebeaededdaacbcdaabcabbbbeacbbabcdcddbdbdeecbadbeecedeebbcebcacbccebaecedecbcbaacadaaeabbccededddebdbdbaadbadadcdbadadeaaacdcbdaeaadccadddaaddcbeabecdaaeedadaaccdadddedbcbeceddaceaedaebebebdbeadbcdedcdcaedbcccaeabbbcbccdbedebcbecacbaeeadeaabacebcbddaddaabdbcacabdebedcddbceacdadccaeceecbeaaaceeccbbddeccbbacdeaebaeeeeebceccebaeacbbcdbdddacbdceabddcaeeadeeccceaacbaccdeaedaeacebddabccbcebceaedebdeeeededbedbcdbdaedeaeaaadcebdccbeaaaadadaaacdeaadabbceaaeaeaecdcedcdedeaaadceaeaecddcdbabddabbebddaaecddeceabeeeacdabaaadbbedcadceadeecbbdaddcdeeeeddedaaaaeacebeccbcbabdddabcdcaeacecdababceaceeccdbbddcbeccddaccacdcaeecaabaeecdeebbbdebcdcededbcbbbadabbdacecceddeaadeddbbdbccddabdbcebcedbdceceacedaddbcbbcabcdccdaccabaceeeddeebdaccbdaaedcbcbabcbbdadbecdddbddcbdabdbbacdebecbbecaabedabbcbcbdcadaaabccdbbcebaecadacadddcbbeeabbbabadedbbcabeeecaabaccbccbcbbcacdacddaeaeeeaddceedddbeacecdeeaacedebaecaedbdadccbebadcacabdbbebdabbbaddaeedcbcecccdaaecdcdbdbbedcbcdbedecacbedcccededccebdadacadbdbdbebeeadbbaeeeabaaaebbbdabacabedccceddbbbaaccedebcabeacbcccadacbbcddedacdadebadceccedbddceacacebededdacacdadaeedbadcdbabeaccdcacdcdeeecdbaaeebbaeceaabedeabaeeabaacbdacbacbeadceaaaddccaabbcabdbadddcbdbcddcaecabcabccbeaabdbcecbbbeeabbdaceebbbbcceacaedddecceeccaaeacaeccbbeaaecdbdbdcccbabebeebdeeadaaecbbceadbabbeeebebdbdadeadcdacdbcbcecadddcaaacabcdaeaadabbdbbeaeebdabddeeedcbccbbccdcdcbdadbdbeecbabdcadcedabdbccaeecdaadebdacacededdeeedebeaaedddeaaebbbedeebcaacadbcaadbabdadaeccdedcddecbcaccdaebdddcaeddabbecceaaebaecaeddbbcaeeddcecbcdeadbddebcbbbbecbcadcddbdedebdbdcbeaceabbdccadacadbacdaeddbbbdedbcbaaccacebbdabcbecbaabdbecdccacaccbddabbaecbddaeebcdcabcaebcdcebcbbbcaddeeeaccbbaeadcdeaceceebdcdddbdceedeeeacbbcdabddebecdcbcbdadabbabaacbecbebebaadbbcbbeacaeaadddeeecdceabdddbdadedbebebadeeaccdacbedceedabebdabeeedeaeeecbbcaabbebdecdacbaadeebdbaeedddcddcdeddebdeadbcdcddeaeedceebeeacdedabdaabdebbaadeabeeceebbcddcbcabcbbbcccebcddacdebcbacaeaabedadaebbccccebcdeeceeabaceaccabeaeaebcdedcebecdcedddcbaadbdeecbaecdbabdbdbccadcacbecbdacccebebbdceddeecddcadadedebeadebedccbadedebabceedcacdaadbdceddeddbbaabbcebabcdcaddedebcabececceeecbebbecbcbbbddebcbdeacedececeaecbcaacbdedabcdeecdcbedaaebdbcaddaeeeecebcbdeebeaceddbacccdaddadaebacdebebabbbaeceeacaeeedeccacaabeccabdbdbcaddbdabbdbddebcbbabdddbabeddadbeccbdbdebaeeaacababebaeeaebbaedbacecccbcceadaebcabccbcccaaabaadcccbeaebbaacababcbdbbecaabbeadbdcdeacdcbeedeaebaedcbbedbaeeceaccdbeacaaaabceccedbabcddabaaaebbaaddacedcaeecbeadbddaaabeaacdccebbeedccddceddaabaeeaeedaddceeceddbbbddeadeaeaaacccbdcedddeceaedceecdcacecbdaabdbaddccddabaddebdedebaadecbaaddbdbdedbeddbcaebaaeaaeaabcceaeceeabbabecbcacecddbcddebeceeeeedadeaddeeacebdaadadacbedddedcdaedbaedbdebeacbeabcacbedcbbcbcdaceeaebdbbebaecdacecccebeaaacdacacebbcabebdabaeaaadcebdeedabadbccaecbcabababccbdbbebccdbbedcccdcebbdaaaaaaabedaeacadcaddacadabaebbccebbddaccdaecdcdcdbaabdbcccabecebeaeeadcaabaaccabababacdecdbaccabbbeceadeddbbcccecbcdabcaeecdcdcabdadadbbaaeecccdaacbeabeecdecddeebadbcbadbcebeedeaccddaeeaacbedecbaaedeaaeaccdabbcbaeaaebdebccddeebdadeacceceeeebecaaedddeeaeebeebacdedcdddbdabcbbcaebbbadabceceacecdbdeeeecbbadbccedbceeccecabebecbebaeadcbbabcbcbebbadbabbdeebbbaaccaebecaaccbddabbeccbaedbddebbecbbbddaedceaddbdbdcabdbcecbddaececdacabacbceeacaecceeacecdbdaacbedeeedcbbebabeebebedbcebbcabbacccdedbebbdcaabcddcecccdeacecbaeccdcdaddbbcbadedbaebecaebdaadbbeeeeaddabedbbaedeaabaabcaabaeadaacebdcbaaeccecddddabaadacbadaceacdeaeaaadbaeddeaebadbdbabdccaaedebeeadabebccdabcaabecbabddeceaebabbeecdcecbbeeaabdecdbbdecbdeadbebacbadecaaebbebbbbcdacdedaeacaccbbedceededcbaceabcbcaeacbdaaaeeeedcbbcbabdcecaddbdecdedcacecccbacccccaaceccbeaeddbccbcadcecccdecbbacccdbbaceebaebaeddebeebcdbbeccaddcabbbaabeeadcdcbedeceadaeaeeabecccdbcadadaadbacbdacbbcbeeaeedcadaecbdeabbcabdaeccbaddacbddadddaceeccbdbcceceddcdedeebdcbcbceaaddcccceebcddcbbcebdaaedaaeeaebecacdeedaddcecdcbebcadbdeeaeddcebbeacadcbeacdbccbabedeaabeaeeadddceccbeddeedcdbbebebabcedbbbdacddeddaebbecbdddcdebdcccdadddbccbbecacdcaeaeecabbccbccecdeabebecdaaeceedcccacaaeecdaaebaabcbbdeaddbdaeeceabaeebddccdbdcedceeceedbeceaaeecbcbbcaeeedacecaccbbeeaacdccbacacdeeacebbbcbdaaaedccecebddecccbabdbddbbdcdbcdccbdcbbaeceeaaceaabecdaacecaceececccadececeeecbaaeaeacbedadedadaeadeeaaaaaebdceabbddbdeddbbbabedecaeccdccaadccabebaedeeddeacaeedeedadcbdcebabeaeadbbcededbbdaaeedaecabbcacdebabcedaecebdcaadcecdcbbdcceeabcddbecbedbdcaaccaddceedbeecdeacbbaaaccbeceebdaeeaacaebaebaebdabdbaeebedcbeccbdbabdcaacabaceceaabdebbacaacabdcdbaddedecadeecadcebdeabeddeddaebbabaeccaccbcaeedbaabcdcceadbddcdddeacaddaedeeadbdabbdebdebddabecabbaeedebeecaeceebcebeddaababaeeeeaddadeadcaeecbcdaceaedeaccbbbddcaeeddabeebaaeddeecdadeddbcbacbbadeebaeedcadaddedcdaaeeabcadabecbbccabbeeabdabddcbacbcadeaeeabebdabaaadcbdbbcecdeacbaaaaeacccaaebbbccaadabdbbadadacebcdabbeaeaebeebcdbbaeeceeabeaccaccbeaccdadadabcaaecdeaccdbedeaadacdebcaeaecbdddcccdbebbceecbddbbebcbdcdcdaabdcceeabbabaabcdccbaadbceddccaddddedbbcbcbeaaabbcbcacebdeeedeedcbdedaeadececadeeaeaccbcababecbbaebddedcddebeabcceacedebeccecedbecaeedeecdaeaeabdabeacbdbcddbdaecddcceebdabcbcdbccceedecaecedbddbdbecdcacccacbceacabedbdaecebacaddeeecaceaeebcabcabaacbbddacbcdbeddaaaaaceececdcabbaddaacbedbdedabaaddcbabcccaabcacecbbdaccceabdcabbdbadcbceeccbdbcacdbdbbabcabebadcdaedcecaaaadebdaaceacbeddebbdeabdaeedcbadbecddcaabedadddbddecbabbebedbdcecaeebdbbbabbebbcdcdabdedcbacbdeabbcacdddaeaccccdccbcceeebebcebbcededcadebbbaaaedddeeccbaaeaadabaeccbbaaacedccbcceedbbcdcbaeecdcecbcdcbeacbeddecacabdebbaeeddcddeeeaceccaceecbdcbaedbcbbcbeeedcabdbbbeaaeddaeabebbeaacaadbeeccadbabbcaecddccabdbecadcbdcedccadcddedaadbbabeabccbcabdbebecaccdbbdcbecbadbaeddacaabeceacdddecababececcbceacdaadabcbeacecedeaaeeabacaeaeebdddedebeeddcdcbbcbdcaaeaaaadbbadabdcebedeabacbcaabaeaebeaccdabbadbadababdeecbebddceedadedabedcbdceedbcadebacedbaccaccedacabdadcbaddbeebccabdcdeeaedbeaeeecaaecddccbdbcceadabceeadacbedcdebebaebedbdccedaceabccadebecaceebececcbbdbadbccabdaebaaeeadbcebcbcdcadabdcbbcdbecedeebbddbabcbbdaeddbedbeacccbbcacebabeaddbbabbdebbcdeeccdadecaebadddceeecebddeeaacbdceeadbadbcbbebdbcabddcaacebebeebbccebddddbbacbdbeadbcbdcbbadcaeeecbeeacceebceebadeabdbccddeabdebbadeeaabbabbdedbebecaaeaddaceceaeaacbbedabbebcabddebdbadabdabaaacadedacdbdaaceaeeccbabcdcbebceaecaceaddcddddddacaacbdcacbdcaaacdccccbcaabaabcacdbcedbbaebeabcdbaaebceeaedbbedcbeecdbeebddedeaceabbddeaceeaeeeddddceebddaedbaacddaeaecaccdddadaebcdcbeedcbabebabaaaaabbaaeadadcbaccdcaedaaccaccbdebaaadbcddbecaaddccebbccebdbeaebdbadebbaadcecacebdddccacdbaddceacbddcdebcdadbbdbbabebdbdaacddcbbbbdbcccecbeecedaabbdddadcbbaedeecacceadddaedeaacabcbbdaccaadbbacbddeeeedaaeccaccccbcbeaebdacabaeadecaedddbcebeaceabecbcabcbbdbcaaababcabdebebbceeccbaaddaaeecaadaccaeedaeeabdbbdeecbdcedbcebbedcadabcedbbbceaadddabeabebcccbbdecdecaaabebbebdacddadbeebaeeebcacacedcbeeadabbeddeebacaeadedaabbeecdebcaaeebbbdabdebebdaaaeceeeebedacbcabbdbdadadbdabcbaeebcecbaadcbaabcbeeacdaebddcabbcdeaaedbccbeaeabdeadebebaadebaacdddcdecbebbacacbacbebcdeaeeedddcbabaadceaaeccdabbdcecdbbaceedbabacccceaecedcddacebabeacbdcebaaedceeedbadbaacedaabadebeddeededbddcbbbeabaadbbecaddaabcaadbbadecccbddacbabacbaeadbdbedcebecabbbccdcdbabbdddaeeeccddeabbcaeddadbaeecceadcbbbddceebaececcdedaaecbdcbdbbeeeccaceeaeadbbddebacadbaceecdadebdaaabacbecdeadbdeaaacaebbcbdbdbebdcdadeeaaaaccebecebdaaabdacbececdbcececcdebceeaccebdabceebbedddcbbaccbbedecbbabceacacbaeaeaebcbbbcebedacceddccaaabbbddbaaeadaabbabcdbdaabeaaecbcbacbbbeabadcdaccbbaacdeebcbadaeeeaaddbcdbbbccaeedeaceaaabcecbceecdcdbacccacebcadbbeddddbacdbaeceebcaccdedcebaabeeddaaccdbddabeaaadeceaecccacdbecddeeaaededaddcbbabebddddbbbbeeccdedebaadebbcaeaaecbcdceaecdedddceceddebdcedaaecddcdadbecacedbceecceabadaadaacadbeebeeebeeccaaaaeceabbceabeeadaaeddbbacabedddbedceabddeeeaceedaadbabbccdbdbcceaccabaecbbdeddcbcacaeacdadbacedabbaabecdcbacaebbeaedccadcadbcddeccbcabbaadcaebdabaecdeceaeaaebaddedecaeecbcbedacdabeebbbacadccabecbddedbbebbbcccbabccbdeccadcecaadacabdbceedcdadbbdaccababeaecccebbaddededcdaabceacebeacddeaeaeeeeabcebecadaedbccbeacbceaeeedeabbaacaedcebabdccdaeddbcecacbcccddedcddedcdabcaccdceeeccbcdbbaadeeadabbcdbbeaedabcadeaeabedacbadddeddbcbeccdacbeeccbbecadbececbbabcaaaadacbdddeeeaebbcbecdcdeceababdeeabcccbecbbbdadbecdebbadccbdaddbaacabccbbeceacacacaeaddebbcadadbcbcaedbddbebddccdbcebcbcbeecaeeeeddcbcdeeaebdbabbbceebaebddcabbcaadbaedadaeabcdeccdecaaebabbdbdbbcaeaadededadaddeabdcdbedeaccdbbbdbaceecbdaebceecabbcdebaccbbddaababecbccadadabdadeaeadccacadbadabebcbedbdaccdcddbaadadcbdedeecdcebabddacabcdbcaccedbdcddbbcdcdcbcbaedaaacaecbeacdcabcaeccdeaaaabebccdacdedeaedeeecaabedabedccdedbcedeeeeddbbcbbebdaecbcadddccdabaeeecccbaebaebcddaaeacccdabaadbcccdaeabeabdbbbdaddaedabcaddadbeceeecededdeccedceabeadddabdbbceaaaceddacdcdccdcebbdcdceecbceccbeeeeaeeaddcbcceccceddddebddcddcccebdcadcadedbccdcccedaecebeeddbcccbbbedadeacdabbebeabdddaaeebaeccaadbabcbcbdcaeecaaeaababcdaabbbcbcdccdcdbadadadcdcddabebdddcddceedebabbeebaadacacdbeddbdbabcecdccbebbccdbaebccbbccacddeacbbdaecebebdebdabbdddeddcedbebecebabdabaddcaaaebbedeecaebcdcbdbdbdbbccabbdbabadacdebabaaecaadaaadbadbddddaedcbdbecaeddeececbebbeabdbbdbaadabeebbabadbaadaedaabdbbbccededeeaeaabbbddbedcebcecaebccaddcbacabbbaeaaedebeadcdddbbbadaccebaaaabcdcccabcaaeaaaeaadeaccdaababecaaeceacbeecdceadbadbbdadaddcbbadeddaaeaedbdcbbdccecaecdeabbdbddebabeceedbdcbcbabcdddacecdaeaaeeeeacacbdcebbebcdaeeacceaadbacbbbbcaaeacccbdbaabadccceccddedacbedaedcccdaecbbedcaadaaedcdabbadaeecdcdcdaedaacaeeacaabecebbdcedcaecdcaddacebedbebcaaccaedbbaccedcacbbbdbcedcabdaddadbbcbcacbeedcecdeccdcdbdccbddbdccdebddbbbddbcecdabbaeabbaebbacdbeaeddabbdeddabedbbeeaceceeeeadcacadccbdedeedecbdeacdeacbeacedcacaaecbadddecaebcdbdbeadeccaeccdeddeaaadbadedadaddaaccabbabeaecbeadeedbdebdaeddcaecddcddbaaeeceadcdeadbdbdeecddbaeabcbcebdeacdccbbeadcdbbddcecaaebeeabbebdbbcacccabaaaddceddacedcadbaceaaacaabbcceaacecadeabcbbaddecaccdeacbaaaaaddadceeddeaaebaadeaadeceadaeeddecddbadadcbededecaebdcebcadecaceeeaadecacdebcbedabeaeeebbdcdebbddcbcceacbacaccbcdeeedbdcdeaebaecaceddaebcdeeedbaaebbaebadcbdaaacdddbceabeeeabaccecdeaaedccbcdcdadaaaaaaebceabbdcbcebbacdaebebddcabbdcdbaedecbaaceabccddbedeedbcdcdeadceddaebdccdaaccaabcadbcebdcabdceeaaaaeabcdcccdcbebececedcaeddeacaaecedabeaddaabbcabeaeaebebadbabbceaddbedabdbbcbacbeadbbbeddceedccccebeccaddbcaecdbdbddcdcdcaeeaadbabbbdbecbcedabcbebdeebeeeeacbaabcceabcbbdabacceaaaacaaebceeccdcebcdeccaccabeaeeebcbdaccbbecbbdcebebedcedcdbdbeeedaaeccbedbadcbccaacddaaebccdcbabeeadeeccaadbecadaeecdadbaeeaabaedceabebbdbadbeddbcccdedecaebbdbdabccdcadcedaeadbbaeddbcedbbabaccaeccedebbabaeebccaecddbbcabacedcacabaaeeacaeeeccabebecdacaebcdcabdacadacccbccdadbadbbecbcbdcdcebacccceaabbdbedebbaeadbbadccbdbdcbdacaeceecaacccecabbaacbceceddebacddedbcbbaaeadedadbeaecabcedccedbcbaaaceaeebadbaaabeaceaadeecbaddabbddabceaeceeadbcebdbdceeeceecbcdbbcdeedbccdacddabbedeaddeaadabaaaaaeaaecbaceaedddcedbeeecadeddeadabbadacbedaecadebcedbaeabcdeabacccabcbcbdeeadadecebecdbceaecdaedadaeeabdeeaddedededaaadacecdcccccedddcceecddcbdddbcbadababebcecaeecddbadecbdcbdceddacdacdbaedecbaacaabcdabeceabccaecbeebcbeaaaecddacccedbdedecedecbebbbbccdacbbacabbaeceaaccdaabbeceaedaadcbbccccdbcbeeceecedeebeeecbeadaabaeebdcaadcaedbcdddeecbadbabbeedaeaecececaacbabdcabaceaadbdadbbecbeaaecddabbcbedeceecbbedaebbebeeabbbaeecbaddaadccbdccdadedccdeccbcbceeddbbeddacccadbceeedeaaeabaccededacbceaacbddbdacbbddababcdbbebdbababcaaddeaebcdedddcedcbdcbdeaeeccedeadbadcddcdadeacedcccdbeadccdbabadbcceecabadaeeacbbbceaebbebdcdeceeabbbdbccdaeacdddbbdcadcecaeacdcecdadceebcadddddcdcbbaddeaadbaacaedbcdeabbecdeccccdaebacddcbbabacecbdaeaacabdbacadbcdeeceacdabdbacbabcedcdadacdddacebdaadbdcdaaedbeedcaaacabbabbaebdeeccdbcacacdbabbcdbcdaabcdaceeedcdadebbaccbedcddecebdacedcdaaababedcbabacaedddcbabbccceaccaeabddbdebbbaeeadcdbddcadcebbaabdaeebedbcbbcdaeeadbedcbdeeccaacebedadaeecedbacaaeddbbcbbcebeeadbcdbabeeaebbbdebcdccccbeddbebbaecdeabeedcbeaabeeeadcebcccccaedddbeccaacedeabedaaecaeaddddccaabdcddbdbaeacaedccbbaebedcaecdbcbbbabaeacaccdeddeeacdbddcdedcbceaaaedddaadedbedcdbedcddbdeaabddecbbebdecaaabbddeacbeaaacdeceaadacbeeaeeeaeecddcbecbadaaddcdacdeecceceddbbbcadeccdbbadbeccaeebeacbcdbaeabecabbbbaaabcccdbccdcaaadacddecbdcbaeacddddccebccbbabeececcabeeeceacdbbecddebddcebdbebebdaaabcedaedeaaadcdbbddddcdeaddbbceadcbcccbbbeaccdeebaaaddecbadcededabcbeaadbeeeacbbcdbdadedaedeaeccbaaaccedebeebdcddeabebcdedcceedabbaebdeaeedececdabebabeaedccbbccabaadcdbabbaabddceacbbceededbedbdcbadbdcdedaaebceeedbbdddaadceaccdbeadccdacacddeebeaedccdbbceabdbcabbeddbcddceddddbebebabdaececdadaeabedaacdedebdbdadbecacbeccdbcaabdccbecdcdddecddaccaccdacdebdedcaaeeaadcabcbdbcedaedabddeedddadaeeebaabaaeecbadbddcddbbddcaeadcbbbcdddbdeaddcebedeebebeabaecddceecebceaabcdcacaddbcaaaeeeeabeecdcabeaecacabeeadddabdddcadaaaaddbcecedcbebdadcbbbaebebaadaecdbdcbdaceaaebddaebdadbdbbdaeeeceeddddabcdcbccacbbdabbeceacddcbbdbddebbabebdceeecaccdeabedcdddeadbbbbbecaeedbcbaaebdbbbedcdbdcadddeeeecbbaaebddcbeaaccbaacaadcbcbbdeeecebcbbedadcdbddcbebbcebaccbdccebebaeeecbcabeaacedbebbeedcadeeecdabccedebcedbebbccceddbeaaeeaddcbbdbceadabdaadcaedeeadadbdcbbdcdaacacaeeeeccddbbcbbdaebeccabbaeadcabbebdaaccddebdadecacbbddabdddbddabedebeddaddeaabecabebbbbdcadeeaabebaaabeccaadccadecacaacccebbcacbddbdacaadcaadadaddeebaccbdcbaaeaecabccecbeadcbcdddbbeebaddeabdccaacbeabcdaeecdddeeaaedcacebeaeaedbacceeedcbbaebacacceebcbedcebadcddbbdedecbadcecabdaddecaceebbbbcdcbcccadbdddaededceebbcdabacdaacddbcabedbcabacdedcedeeeaebeaddaceecdcabcadbabcdedabedcabaeaebbbededabbdcdbbddacceceacebebebbbbbcabcdaaecbbcebcecbbabaaeebabddcbebcbecdeeccbcceebcecedbcdecebcdecbacbaaaedcaddcddedeadeaacaeadacbdbcbdcbbaabecbbedbaecebcbabbadceeebbecdbeeaacbabbabdebbadabdcdbeedcdcbbbbbaeccddedeadddaabbecccceccaaacdcacbccbabcbadeabbbcaedaacededacdeeceadbeaaddbedbabebadebaddadecbcddccebadcaecddcdaebaccbbdebaeacbecabcabecbcdecdccbcacbeeaadcaadadeebdcecbeecbbcdccaeabaceadbaacceadeeeeeecbdedbdebcdecdcbeadadaacaeccaacaeaeecabecbdadeddceeedadeeddedbdedbddbaddbadbbaaeebbdccaebbadcbbacdbdedeceaadbdeebcacadaababcddddadabdbaedceacaedbebcbaaddbebddacdceadcabccaecceecbcacbbbbaabaeeedccabeebbdcaaebabeccaadebdeabcedebdcccdaacdeeaceccdebeebdaeaeaeabdddaaaaeabcaddaceabdebddaaddeededbccdcceaeecabcabedaeceaabeabebaceebeeebadaebdbebbcbddbcedcbdecacaabaebdddaececedaececbdbdcdcbebbaccceedeacedbaaaeaeacbdeeeeebcabeeabbdbdbeedaddedacacaabcbccedaaccbdcddccedbaaedebbdebacbacaceebecedcbeebbaeedcbdaacdaacecabacecdacebdadeebcbdcadadaacaaadcbccaddcaccbdcdcbecbaebbdaccedaaaeeddbebcccdeeaedabbdbdededdbbdecdabbdeeaaadcdaeaebacacaabebaabbadaddbdbbebaeaadcaeebcdbccdbacdaabaceacecdbdcacbbccecdddeeacdaeeacaccbeebebaacabacbccaacababadceecbbddccebadbbebbbccaacabadddacaccebeddbcbbcabcdadbdaaaaaceeeaaabadccbabeabcabaeeccedcccbbcadbceaecddddeabdebcababeaabaabdcdbbcdedbddecedbeaeabcacacbaeabccbcdeacdcecebbaeedbabbedbdacbceabdcacacbecdbbddcabebcedbaeebcdeedadcceedbdecabcaccbbedbbdababbbbeacbcbdcbebaccdaaacddaecddbdebbcbeddbdadcbbcecedbeacaadcaeebedceedbeecdddbaecddbabdddaebadeebbebeccaebaebbddbdcdaebabedaebbeaccecdbbddebccceadabcdacbcdbcbbaccbccdedbdededebcedabeddcaccabbcecebdeebeeccbeaceecbeeadaebeeecdbbbebaedcbdcbbcdbedbcabccddccbaadaebcdbacbbddbaaacccdeddeecebdeadbdbcebaacaeecabcaebdbeadeabcceaeeecabcaedeabcdbeecdcceceacbcbeacbecbadbebabadebdcaddcccdaacbbcedabaddbdbbcbdacdcdecbecdeabbaedcdeaadbbeeacedcdccceebebebbedcdddabcadbaaacbaecaacadebbdbeceeadcbaacbdeeeaacdbacbedceddbebadadebcdcbcbaebcdaecceedbeccaecbadadbbcdcbabdeaabbeeacaeaedbcebdcdedaccbdaebaeebcebbbcecedccceaecbdeaebebceecaeaddedababccecbceaeddebeaebdbeedadcebcedbddeaddcebbedcabbdadadcdcebbdebecacecdbeebcacabdabadacaaaebcadddceacebbcecaabbeaaceeadacdadbbeccbedcedaedaeedaeadcaaddaeecbcaeadddadaebcebaeacbabaacdeeaadaeaebdabeddecdaadccebaabbbeeeadeadcbbadbedeebbdbbcaabebaaceecbcedeaebadebbbdbcdbecaddcabacecdcababaceedaaddeebaeaecbcebecaeccabcdcdcdbddeaebcbaccbcbdbbeccebaeabadececdadbadddebaaecbeecadeaeeaeebbacceebdbbcdaeedbcddbabeecaabcaceacdaaedeaadadbcceceeadacdeacbbcbccccebaceadccbaececaabbebdbedcdebdccbeacdcedeeebdedadbbcaaccbbbeddeccaeddbddddababbdaaaecddaeaedecaaaedbaedcaececdacddecddccdddedbbdeecaeccbdcaebbbcdeeaaecbcbebcdddedebecbdbecdeaddcadbdcacebddcacbadbdbbcaacccabdedbeaaadeacabdebeacebecdbaddacdcddccbebddeecaeaeecdabbceddbbedadecddcbccdcdceaceddacdeecdecebbccbdbcddaacddddeebcdbbadceedbacabedeebaadaacdaaaaabacbaaaedbdddcbbdaeabeeeeeaecedcddebbceeccecccccdedceaabbaaddcbaadebcbdcabcaabddbddccabdacdacbecebdbdbabedbcaccbcddbcedcabdbdbebeccaecececccdbecebbcdbebacccdacceeacecabaacbbcaeeebdcbedbbeabcaccbcbdeeeddcaadcbdaaaedbbbccddaeecbcdaedaeaddceecdaabdadbcaeedaeaecbdcdeebeaeadecbaedecedddddbdbccdaeebdcbcaeaadceaaeccedacbcccbaebbddddbaebadedaaaabadcbaeecebcebccdbbddddcdecbdecdcbedbeccdcdcdbadcebbcecccabeebeeaaabbedcedaebebceedbadbdbaacbbabebcaeecebebaedbadbdaaacccdadcbdeccdeaddbaaeebadacaeeabacabbbeeabedcdcbbcbaecbdedbebaadbcaabadabebabccdedcbbdedebcdabdbacbccbcdedaebedadeaaadeabeaaeecabdbacbedbdabebedcabeebaeeacbbbceeaeaabadcdbdbdaaeacaceacbbababebaaaedadadecbaccccccbadcdcddeccdcedabaaedcaccbdaaaabedcedaaecaeaaceaeedbdacadbaaeecdeedadbcdbcddedcdedebbcadeeaaecedaaebecdebaedbcacebadedadabeeaebdadeeededcbbeedecbeeebcdcbbccccedeaecacbcaaedaaedcadaeedabcacaebeadaadcaeabceacdddeccaeeabebbdcedbdccccedceacdaaeddcbbcebbddbcaddcbcaabedceedadeeeacbcabdaeccccadccedcadaeeddceeccaddcdbcdabaddaabecdbecbedcdbbdedebadbbdecdeccadaecabeadadedcebdbddeacddcbdbedbbcebbacceccbdbadaabbccbeccaedccdbdeabcdecddacebaedaaedbacbcbeaedaeacbbdbcdaeedacdcaedeeccbcbdaeedbcdecadebedeecccaaededbdcaadadebddcbbcecaddbbcedbabddedebdcedabbeeaaddedaeabdeccaccdcabbdecedcedbeebeddedabeebbeaacdcbeeaacbadeaecdebcceedcacadceeaabebaeedababdbbceedadccdbbbcdebbcddbabbbdaebeededbcccdeadaacadbadecaaaddaccbccddcbadadbacbedcebddcccdcccadcddcebddbecabeccbebbaddadaaecaabdedaddcbadccdabdddacaaadeecaadbabaacededdacaeacecdcbbbeceaaeeaedcdebcdcdeecabaeddcaccebeacdcaadbedbaeabcbeaaccdcebcabecdabddeecbceaaccddcedaddaabdedacccacebeeeaeacadabbeadcbebbaacbbcdecdbcebabdaeccccaabcbbceaacdebadccddeaebbeaceecbbbaaccebbdababebbeecaacdbbbaeeabaddbacbeaadeaaaccbccacaacbcdedeaaedeabbbdceaaaaeceddabceadcddeebadaedeceaaecbcadadccbcabcaceccdebdddcdbebaeeecaebeecdcabaedacadbedbecbdabedbeaadcccccaeaeaeeebcddebebcebeebbaaedadabcbebedcdedeaadecadcacbadcdbacbecdccecadcbaecbbccabbdeaaecbcadeacdddbcecbaddbddbcdcdddebeeadcaacbcdcebdedbebdbceeddbbbeeabeeddacbbbedeabebedeaecbbbeaccabcaacedbddeababdeccaccdaaaaacdabeebacddecdaceaddaaddabeacbccdeccabdbecacebabdddaababbdcecdaaabacbcdcdaccabcdceccebceebeabddbddabeaabbebdcbcccdeadebedbdcdecededbdbacbdbabeddaabeccdbebcdbdddaddcbcaeceddcbdccbedccadcbddbbbcdabcdceedcdedccbcecdaceddeddbbdcaadabdabeaaeaaecbdadaedcbeadebcccccabaaccadeeccdbadeeadaebcbdaeeddbcaabcbaacbdbbbccbaaebeabadeecccdcbdddcddcdeacabadccabdeeeacebccbadecccaaaedadbddadeacdbabadbdeccbdcddcbcaabeaeccbeccccbbecedccbceeedddabcdcbbebbadddabeaccececbabdaeaadadaacabaabeaabddeaaadbadeaeaaeedccdebaddbeceebadacbecddcbceacbeabcdebeeeaeeeaccabeeddacebedacdabeabeaccaceeabbeaccdbbdbdccadaddceabbcbcdadaecbeaccebddeabdcbbdbedddabdeddabdbccccbdabcdadecbabbabeadacdeccdcceaacdadcaceadaebcbddeaaeaceacaeebedaeeceabdadacdcaddbacdbeccecbedbcbddecabeabdaeddddcaeededbbbddadebecebdecaaedcaebdbcabbeaedebecbaabadbbacaecbaecdccbdbdaeeedccdecadbeecbeecddebcbaeabeabdaeaabeabdcdcbecaeedadbedbeecaeddadbbeadcbcddbeceeccdecadeacaebecaecdaaaeecdceccbeaaeddbeacdbceeeadbccabdecdadaaececdecbebedcaadcbaaaeddecdbacecdcadeeeceddceccbaddeecaaccaebecbddaaabbcdbeebbcaaceddeadccdbcbadbedccedabeceeaaeecedaecddaebbaeaaccdceceaedbdcbadbaaadbbebdbbccbdccceecaaaedaccadbcaadaacdaaaddeddbadacbeaecaaaaecdadcecddceabdecacbcdaceacaaabecccdbecaabccbacddcbcdcbabbadceddcacedbabecdedadebdedbecabeeaebbdaaeaccbaecadcadaedddcaceabcbbbdecdaeadcccbcbdeddeabbaadeeacecadebcddbebcadccaacdecbbdcdcaecbaecdcdcaceeacbbbaebccacadedcacdeeaeebdeabebbcdeeeaaddbceecedccaaaabcabbcabbcddecdcbbccbcdeabcaedececeebbdedbaddecbdabcbcadaebedcdbcadbbcedaadebdccdccbcabdcecbedaedbabddbccbdceeadcceeebdbacecbdbdcbeeaaeddadbcdedadadadceddbaadcbdeccbeabdeaedecedcdcccbaccadddaabddbaaedabeeddcacacdbeddeebeadadcbdacabcbededbaebddeebdbbdbabdaddacbeaeeaeddaeeccdddcdcdabaecdbdabbbdeceeeedcaddeacedeecdbcabadbcedaeddeeceabacdcaddaccecabbbcdeceddbdaedbcaabbdadeabacadebcbecdceabbadddeddabacccdbccebbdbdebaceedbbbaadccebddedeccaeaeddaddacaaeaceeedebdedaebccbbbcbbccaadaaababcaadbdbedebaeeddeabddbabadbeedccbcdabaeabcdabbcaecbdbbcdadabdbeccdeecebbdabecadadcacebeabedbbdaecddcebbccebedaabebedbceadbccbceaadadddddabbccedccbdaaeacdcddacaaeabddaeaceabbebceadabaaaebcaebbdeeebabcbcecacadecaebaebccdbceacaeedddaccedabdaeddacdacbdabeabbcddabbddcebacbdaeddcdebbabccedcaceedcaeedbedcdbcabeaabaabcabceeeedcbdbbdcdcbdbeebdbacececbebabcdaeadbdedbdaceaadedcccecadccedcedcccbdeebeeebbbaebebababbddadeadbaecbacadacbbebdaaccecbdcadddcbbaddbddbecececaabecadaaecbaccdecacccecbdedaebccaaddeeacabcaceabbeeabbeeecdbeeeeccbeeeeeacedbceabdebeccdbeaebccccacccaceeeecceebedcbcdacbcaebceccbccbdebdbdedcddabbcdadcabdddbcdaddeaeeaecbcdadbcaddadddcebdcbeebaacebabedcbcbaabcabbaecbceaaaaabdacabbddceddcebaceabaaabbeaaddadcadebeacbecbeeddcdbbeecddcaebcebcccdccebeddddebcdaacabbeecccacdeededacdbcaddcbbbcdbeeacacdadeaaebedceaabccedbdddddcbbaddaebdccccabbcdedbcbaaabdbdbbacaecacabbaeccbdacaaabdabcdeebdbadecdaeeabcedeacaacbceaeaeeeeadebbbdcdeacedbbcbeaaaceecddecdbbdceeecddbdcdddbebcbaccdcbdedcdabbadddcaabdaeececaabedaadddcdbcdeaeaddebeadaeeebadecaacbeecbaebebbcdbaedcaacacaacbaacbcaaadcbcbaaceeeddddceabdbccdaeebcdcbdaacadcdebbbeddaddddbaecadccbdeebceceaadbedececcadaebcabcbdadcbbaedaedcdbaabaaaecadbbcdecdecadaedeeebdbabaecdaeecbaabaeabedebcaebcebbccabdbcbcecdbaeeecdadbcadebecadeebcbededaedaacbeeecbeeececbccaccbbecbedadbdbcaeebdcbecaadcccddacdcddecaecabeadedeedebebbaaebdccdaeaebccbbdaaaccbcaebdcebceecbcdedbaccaeeeddeebebbbececaedcceecbbedcaaebccaeceebeebbcedabbeacabdbbeccdbcacacebbadcabbdbecbdcaacdedeeaddddcabddeeedddcecadaacdbdbabacecbacdbdcadbbeaacedaeabcdaddbdcdcaceadeaececaebebebdeeedccacdbcaacdbeebebbecdbcceeadcdecedeadeedacdeedaacbadccbbbebaaebedecceeeeeddcecaedbeaabecaecbaadacdaaaddecedceedebebadabddeecadcabecaeccddcdabadbccaababbcacecaedebcbdaccbccacccbbbbbbbbeaeeaaebecdcbceeecdebdbebbdeeecededcecabddabbdebaacccabaecbbeeedbeaabbadcbdbdeadcacdcccbbbeacdcebaaadcddebabeebcbabdedbaedeaeccadbeddecababcecbcadebcbbddcdbaeacbebbcedeabeceaddacaddcdabaadcedcabecadceeccebabecceddceabbbadebaedabaadadcccdebbeddbccaaabccccdecaebcaadeadddedaccdeabaeedabaedeeacaedcdbedbbcbcbcaceadaeaeddcdddedcecccccdeaadecebbdedbeabbadcdebcedbeaeaabaaceecaeacaaccdeeaeeeedcadcecbaadabbbddbadccbbbbeecccabdacbdcebbeadcadadaaaebdedaebadccabcbbebddaaeddeddacccdcebbeddeccdcedcddbecebdebacddceecbddecabdddabbadebabbdacadadacbbcceabadceecdabcacbbbceadcabacccabcceebdadbcbdbaadccaeedcdacadbebdcbdaeeababceddbaeddaaaceaaaacdbcdddedecbadeeccecddbdabccebdababcccdecdaddbdacbdccdbdaaaebcdeecbacedebcbaaccbabebedbdcaebebccedccbbbcbeddeddbbaacadeacaeedbedcbebeadedeabacbebcbbdbdecdcacdadbdaabebbcccdbacacceeabdadedacaaeeacecbecbbddcadbebbcbbebcceadbacebdcedcaebeebabaddbcaeaadedadadaedabddecdeebceddaecbcbbaddeaaeeeecebaeabbaedeaecaddcaabdbaeebecdebbeccedeceaaceaaaebdcddaebeceaaebbbabdceddddceddaaebeccddcdcbeddbaddbabdedccbacadcabcdbdbbeeddbddebedacadeddbcbecadeebeecbdcaeacdbeeadddaeddccecdceeeabecdcdcededcbdcbebdbcabecbdacaaaaaeaceabdabdddecdeddeecbcbdadadcebceaecacadabaacdadbeccaabaedbbbbbbbaddaccdcbddaddbbbedabcceccebcdbebeeedaaabebedadbcaaeecdebabdbbcceacdbbddababcdceacbedbaeecadeadcbaecbdaaeeadabeeddaeccbbcccccbcbabddacbcbadeabeccbadcaebedaaeacbbbaabaceaeabceecbccdacccbadbdeaddeedeeabcbbccbddacebecacdcdaedabcceadaacbeddbdccabaadbedbbbaadcebbcecebecdaaecdcadeccacecebbabbaebbbeecadebbeaedadcdebedacabcbaeaadedbadddcdddacabeaaeccddeecdcecaaedeceedaebeeaacadbbaabbacacaecdbdcdbacdeddbbebebebeaaabcbeddececbdbabaeeeecbbbdbcaccbaedbbecbbebeacabeeeadeebbbcbacdaabbecabbcaaeebeaddeecabdceaceccbaaadbeabebabbabaacccadbcaccabebaeeacbacaaeadadaeddaadaacedbedecadeebdcdcbedecebebaabdaaecabdaacddabbbaeabbeddebbcddeeeccbccbedabbdebadaebcbabaaaecbceecabeadeaaaaccdedaceaaacaaeccaaabbdcaeebbcacdbbeadbedbacbddceddccccddbeaeedceedbdaaaaacdbbddebedbdaaeeaeaedabdbaecbdabdebbbbcbdceaeaaaeabbcbdaebceaaeacdadabbdccddccadbbcdabeeecddcaecdaabddadbecccbdbcecaebeababddbacdaadebdedbedebabebccdebbebadaeebeeaebcddbadcbcbeaaacbcbdcdbeeececddbcdcbdccbccbbbedaebacebdadedaaebbacbeaedececcaaeaccdedebeadebcddebeeeeebebebdaecacaecabddeeabbcdbbaccdadbabdddccbeddccdecdacacecebbaadcdeaaaabcbabcbcccdbaaaedaccddebeaedebaaacccdddbccbcaacbdacceceaebeaecacceccdcbbabdbaddaaeadedccdbaeedbedcaeeedacddbdcccaaacadeecaaaabdeaecceedaaedeaadeecbcadcdadecdecbbebebbaedaceedeaecaecabaddcedddacebbbdabcdcaacacedeeecacaecbebcbaddcacccebbbacaadccdecaeddbdeabceaecdcdbeaeacabaeebeaaaacaacacbdabbcdedddbccadcaebadcbbaceebddbadccbcecccdeedcddbeedbaedddeadddeadbddbbddcdbcceebeccdecebcaceabacdadbbcddeddddcdbebdbcbcdbecaaceabeecebddcdbbccedaabbceebedcaacbcaceabacbbdbbeecbaedbeecbccadebaaeaebbebbddbaabecccecbbcaedbedbedbdbebabaaeacedecadceecacceaedabdcadebadaedaedcaeccebcebeeecbbdbaeddeaaaaecacbcadcadecbbebebbdcaadbbdcaccaaedcadaabadcdbadadbaacdcaeadbebdbddcbbcaedeadbadccabbbbdbabdcbaaaaeddbedcecdaeceddeeedcaaedaacbbebedacbdacadcbbacdabbeddabcddcdeaedbbbcecddadeecedcbadcaccbaccacedbbbdbdacecbacebdaacbcaaadeadededddebdeebecdadedacbccbbaaaaadaebddacbbabbedecbebceaeaedcbeaaeccbccdcbdeaeccbbcddabedbcedceaaedbccbddeabeeecaebbdecbcacbadcbbebebabbaccadaceccadebedbdacdcaedacdacadaadbecdbdcadeeabbebeeacecbbeecdebdabdaddbadeaceedaadceaaecbbbdebacbdbbbeeeccbaededddbacbaaecdcececeaedcdbdbabbcbbedcddaeccbdeaaaeaeebdbdadabaceebbbabbeeddabdadeecaccdddcddcacceaeaadbdaedebdbbbcbcbabdceccbcdecccceebbededeacebdabbdcebccdaabdebebbbccebeaeadbccdceacdebadbcabdccaaadacaadcbcddbaceeaecdeaadbccaebacdaaabdbacebcdadcbacebcbbceaccdbdeceeeadcbaaaccdacbbccbbabbaabdbeaaeeceaabedeacbcbdcdeaeabddaaecccdccdbdcccbdcdbaabaecbabcbabdddeeeaaddabdecddbedeebaaecdaedeceaeeaaadbccdddaaabebadddeeaebadeeecddcdaeebbdabddbbeecbedcadbaeddcadbcdebbbaacdcedbecdeebbaedcaceebbcedeaacbbabaccdbbdbacbbeadcdeebbebeaecebbbbccbdcbddebbbcbdebadeebbcaecebdceeaebbbdbebbbecabbbbacadcedcceebeabacacbeacabeaeeadaabbedaebaaedbacaebacecdedcaeeacaaaebeaaaacdeabddaebecdbdddbbccaceaeaaccbddebbbeaeeddcaaaeebedbdcadcdececaeceeadeebbbdadeeaddabbeaeddeababddbeebaeeccbabddcdebaedbdbcdbbaedbeddaaebaecbddbcbcceabbaeeacaebbcdedabebeacdbdebbcbacaaebdebaeaecbbcdbdbeebeacaedaedbcceeadbbbecbdadcadeabbceeaaacebbbabdabbbcbdbeaaedabcbbedeacaadebebecaeeecbdebaaecdceeccbabecdaaacdaccaddeceddeaebeaeeaebdeebdebdaddedcddebacaddcadacebcdcbcebeadaaebaccaeddaadbebdebcbaeeceaddddeeeebedbdbedbbdedbebacbdbceebbbdaddcdcbabbebedacbccceeebabdeadeabdecaedaeaeaeaadacddaaacbdbeddeeddadbbdcceabbeebebdbcdddebcdcacebdadcbabeaaecbdbabbddbbdbeebaaadbcadaeeccbcddaeabdcdebbddcabadeeeabeddbcbdcdadbcbbbdacbececbaccacbceecaadcbeadaeacaebcbdbbcacceaccadebbabaedbeccededdabadcebeecdbedaabedecaebddbccaaacbdbdebdcdecebedcdcbbabbdbaeccdaedcccaaebbcdcdedccebaabcddedadbccecddbabcbbdcdbeddecedbdecbddbdaceaabbcdadcdccebecbbacebbebbbdcaabceebddbccbeddcdddbacdacccaceddbcbceccdababbccbceaebbccdbeaecbacdddcdcbcdadaceeadbbddeaabbcdeccbcbbaadbadacabaeebdaecdbccaecdabcaddddbadeaedadbedddadeaedeaadaadbdebeccedbdccaaedddbbdbbcbccddadadecaccbeccdebccadbccdcacbbaeceabaaeceabbdabaadbedccedbaabcbbeaeddadecbeacdcdbaaceacdabcdbeaadcdceccaecaedacddaaabaeeeeababcdaaedebacdcbadbadeacdedcadcebccaeababbbbbbabceaebdcebdeeaabbaecddbecedbbcdcebedcdeededdcedddecdeedacbeabaddcaadeceebadeabbaaecacdcdaadbbbceeacedbcdacceedebabccdeeddaedadcadacadacbbdeaabebddddeecededcedaeeccdddddeebcdebecdaeccbddbcebcbaacdacdadeccaceddecbabdbdecdeaadecbcbecebbcecceeaaebcdeddbedcacbdcaebdabdeccbbbaceedbebcdecaadcbdebcbddccddcabadabaaccddcabbdbdeccabbcccbabebbcbbdcbecaeaceadadcdbbcbacdceacebaccababedceacdcbcbaabacacdaaedadcbededaccacceaecdadcbedbcbcbacbecaaebbeaddbeeebadcdceaaaeaeaedddadeedcbaaabeabccbdececaecadccaabdaabccecaaceccbcdaceeceecaabccdedcedcccebccdaacbcecbecdaedcdeccabbcdaeeacecccdaaddeaddddbddbaaccdbebeecdaadaabdeadcdbcabbbaecabcdcccaecdcdedcdeecacecddbccacdcccebbcccadbeebcacebcabdcacabbabcedbbaadeccdabcbbcbbbabeecdceeacbbbaadcdebeceabbdbceaaabccadaacdacdabaeaadbdacbddebbedecabebbdbadcdababdaccccaeaecdddeceabedddbebeaceacadbdceddabdebbcdcbedeaddbdcedaeeebbdaadcaaeabadecdeaaedabbdcebaeeccdedcebccacdeeabbbedcabeccaaaacbcdedbbcaeeacadebdbadbdcaedbcbaeddcccbbcaeaebdbdcbbeebaceababccccbccdedcdadcebacbcaebbbcbacdecadedbbccaeecdcdceacdabbeddbbebbaaedddccbabbabcceeadbddccccbecbbcbbccddecbbabcadbcbdaaeeacaaeaeaabcccecdccdeebbdebaeecadaccdcbddeebebabcebcdbeeebaaddaadecdebcbeceeadddcbeaebebadbabebedbacdbdccbbcabbedceadceadcebdcdabaaaeccdaeecadbbebccdbadaeaabcaecebedeecebebddaaecbbecbeacbdaaddaaeddcdecbebbcdebceddddcbcedaaaaebeceedecdedcadacdcdbecdbbbaacdebeeeecaecadbbdebabacbeccdadedaceebcbdcaeeebecaaccbdddacccedbebaaeddeabeaabebdddcddbeaaaccacdebccbecccccdabdaeaadecdbcebebcbdcccabeaadeeaadcecacbabaeaaedbeacdccaeaabdeaaddeaccecacdcaabbecceeecbecbbeaddddaebecbcabdbeeddabcbecdebbdbddcecaebceebebabdeedeeccbeeccbbccabaddabaeacedebbaecbccebeacdedadbbbbedbcbeeeddecbcaeddaceeaeaaabcaddbabdbabbbbdecdaeaebbceebbcbcaebdeeadaadbaccbbddddcedacdbccacdaaedecbaeecbdadbeeeaecadcecdbebbaadddcedbadbcdadbcbeebeaaeaadaedabcabcacdaabdbeebaacdbceddcbabebedcbeecceeeccebaaebacebcecaddbaaeddbdaabcdbabeaabcbdabbbccacadabaeeddcbccbdacacbceceeedeceaecbeabbbbeaeaaacaacbecceadbdbddebeacbbaadcceccadeabdeaabbdbbdccaacecdaebbaabccababadcebbacdccbbbaeceeeabacebbecbeadbadeddbceccabaccdaeabcdcabcdaceaadeeeebeaaccbdcdeadedbeccdeacebdccbbeecaecbdedbdaddecaabbddabcaeaadaadcdbaabccedcbbdebbcaebddaecbaecbacbabccdaecbddcedabccdebcbcedcaadaecaddaabeceededddedbecdabeacccdaaaddbccbdcaaeacdceebbbbaaaecbeaadaabaaaeabbadeccaabedadedcbcdecedcdbaeabeddeabcbeceecbdcaaadaeaabdcbbdbadeadbdebadddedcdaaaebaacecbdedccbebccbecabbcabceaebbacdebbbbbdbeaacaaecccbbaeadacbbbabaabcbdbbaaaacdbdeecdaacdacccdcaecbacdbceeadeaaddabbeadbdaeedbcbdcdaddcdebbbacbccedcbbeaaccbecbeaeadeadabaabdccecbcbbccddaceaadacbdbadcbccbdbbadcccbbadecbcbbcbcccbadccadeeacabeebeecbcaaebbaececadeadaaeecdacdadddeaaeccbcaeaadbcdcbbcceaecdddaadbcbbdecbbdceceeebcdcddbaebadecacecadbcbadddcbdecdbcdebcbebbdacecccbbdddbbbaddbbecdadececeebbeedebdbaedcbeecdbeedacbeaeabbbedbeddcbcccecedccdceeaaeeaeeadbbdeaadadeaacdabcdeaaeeebebbecbccddeadbebadcbdcdcdeadabadbdaeaccbdbbcbcbabddcbbdcbaaacbcacbabddeaeadbdccddacbbebcdeeadabeccebaaabdbecebdabbdbaaebcbbeabbbebddddadcabbbaebdbceeddacdbedcececabcaddaabcededbbcacebdacebcbbaecdddbadeccddaaabcdcdacdbccdbdecbbdedebaeeaeaaeaabecdbadbacdcaccbeabaeeaddacddddbcebebeececdecdbdadbdcaaadbedbdeeacacbabaadddadddaebacbbaeadadceadadeebacbebbcebeebbcedceeebcebcadebebeededcadcebdccebebaacdeddbcbaaedeaeaecdaceeaacbaeedcebabcddacbdacdecebbceabbeaaceddeeaaabdbcbaebaeabbeacdeaecccabaccbbbacaccdaeebdeedbedcbeccbdccdcabbcbebbbeaeeacaebadaccddecaeaabaeabceececaabceaadecabbeddbbcdaccdebbadadacadeddcecccecebabaabaeeebcbecdeecccbabdccbabcccbcadeeaaebdcddbbeeeeedccccdaceabbcdecadeecdebbdadbbecebdcedbdbacdacecacedbaebdeddcbcadebddaedabbaddabeedbbabdeacebebdbeaebcadacbccbdeeadabbaedeeecebeeebccacdbedbcedabbebcabaddeecdcbeecaddbcccbddccceebadcbedeebeaaaacaadbebaeccdeabeacbbdbddecccdebbaeecdaacbdaedbccccddcdaabbccdbcebdaadeebcbbadadbbbcdacddcabbaadaaaeadaebaeecdbeecadeabeecbacbabbeccdcebecaabdeccdecabdceebddbcdceadaccdbbbbdabccececdbcdecbbdcaaaebacecabbdbedbdabcceddedbbcdcdcddebcacbabecbbcebbbedebceaaaebababdbacccbbcbebacbccedacaacaddbbeccadbbdeccbdacadaeebacbeddadabedaceddcbeeacabddccdbbebaeeeebcdedeceabededcbecdcadedcbababcebdddcaaacaeceedcbbebebbacbdbabeacbcddecedcbabedeedceedeeedcacbceeedcadbdceacdadccdeaaaabaaedbbdcabdaccdababeeddbcaecdecddeccbeabeedcacdabdbeeaadabcbaabaccbaaeaecbbdacceededddbedccedceececacdaeeeeaddbdcdcadcebeccadebdaebadebecddcaaedddebaaaaeedbebbacdcecdbacadddbdcecabeedbcedacbaeadecacddeebacecacebceddcebcabaacdcbeebcdbdabcdbaedaeaecebbbddbcbaebcdbcbbcaceacacceeeebaaadedadeebdcdbadadcedddeeececdaecdebbabecadebddaabeaedeedaceaeceabceacebbbbcaccddcdbdeacaebbcbaedccabceadeeebdaceccadcdcabbeaccbccebdbbedaeaaedadbeccabeaecccdcbbbadabcacbbcaaaaccccaccdeceecbcbaeceedacaceccabbcabebadbecacaabcbdaccabebedcdcbcdaeacdaebdeaecdcdeebabedaacaebcdedcaccabaaadaeecaacbdedbebedccbbdcbdbadecebbdeaddbcedeedecbbdbacadccdcedcdacdadbeacccdbcabebbcaaedcdecaeaebeedbadeadccceceaeebccbbabcdbeeeddaccceabeabceddeeaaccaeedbbcadebcbdceaabcdcbcccaddebdccbeaedabdcabedeabccebdeaeccaeebccbedebddbecadeeaaaceaeacedeeedabeaabdddbeadcbeeabdbecaabecccedccbeacbdabedbecaaeedbddebadebacdccddccdcdebdccbadaaecbcabddbcecaabbbdaabdebbbabcddeadebabeaabacbebedcababaeebdceeadaddadbcacdbebaecabbaebcdcabdbcedcdcbddcbcecaeeeebcdeaecabceedcdbcecacdddbccbcbeadcbaddeaccbccabdeabbddcdcdbbcceaeadbaebedececadddeedcabdbdeadeabeaadbccabcbcccedddbceaacbcdcdccaaabeeadadcddbabaecadeedbdbbabebacceeeaebcaeccdeecbdbbecdaecdbaeabaaaaacadbdbbebaccddbacddcacacaabecbbbccbdcdbceaddccceadccacbbdaecadaeaaadadbaabcebcdcebebbdadeabcaacabacbaeceaeeeabbaebcebdbcdbcbccbcadbecebbdaddbbdababeadbbbcbcdadeedbcbdcdbbdbcdadcacecbdbcdcaebbceeeeaabdeaabcbcecebcadaabaacbabbabeedadebdebeaaaeebdceedcaaaadbcdaaacadacaebbddcbdecbaeedcacdecdeebcdceeccbbaaecacadabccdadceebaeaadcbcbdceabaaeadaeacdbcdbecaccacbdabddedeedeccadbdacecddeaddebeadecedbcccebeecabcaeeedcdbbebceddebbabacbdaabedeeeecedceacccbbadebbabbeabedddedaedecdaddbeecebbbbdedbbddccdacbbbebdbaeddcbbeadeecceacaebabbacebdadbeecdcdbccadccccdebcadbaadecdacebcabadabbddccbbdbebaceaababedeeebadedbceeaabebedabcdedabadaecdeaddccaaaaacccbaeadcdaeaccbceedebebaecaaceebdbdbeddacadbbacdacdbbccaaebdabeeadacdecbecbbedcecceaacbacdeeeedeaabbcedbaaaeadbbadbddcabadedbabaaabadbcbddaeaebcdeacedacacaaadaaccabccedcedebedbddedddbacdeaeaaaadeabbdbaccaecbcceceeadaccaaecdccdecebddadedccbbdcbadebaaeaebdbabccacddcdaebebeecacbdecaaeaaeecdbbcaceabbedbbeabdaeeaecdcddcabdcdaddaacaabdedddddadcdacddcbeecedbaeacbdadbaeabbcbcdacdeeaecbcdbcaebaadbdaedcbeeacaececdacaccabeeebcaceaeaddcebaaabccadbbbcecbecededdeebbbdabdddbccceadadedaddabedaabbedcbbbdeababeaeaeebdbaeeabbcbeeccacddabbbaecbbedbdbaccaccdeaecbddaaaeaaeaadeaeaddcceccacaeabacbbdebbcbbcddcbeedeeebccaabaeecdaeedccadbbcaadaedebeaaddcaecbbadcedaaacebbbbbddebdadacbddddccdbecbbceeedbdccbccdaebecededbbabcaeeeeaedecaecaabeaedcaaedcdacbcdaeeeaadedddbccbcceaeebbeebddebbeecdbeccbebabceeddeebdeddcbbcedcdabdcdddeddbabcadbeccecbbddabdaeccebcabaadddbedadeaebcdccebbabaccaaabbecbeaaddbabacddcaaabddddcaddcbbbbbeceaeecdbcebbcacbbeabccabadaadccaecbaaccbbdbcbaedeeceaaaedabbbcacdbacadbdbcadceddeeddaceddceabcebccadccbecebaaeeebaeacdcdbdccedeaebcaaeebcbeedddebadbeaabebabbdbedaebdededebcabeaacabbecdcceeacddbbebeaccbadbebcbcabeaacbcbeaedbdeaedaacbeeabcbbcddeaaddcdbccdddabaebbeccbcbcceddababbabbadcaccebcdeaabbbdaceecdbbaabecacbecaeadbedccbadabcdaddcaabbcdbbcdeeaaaaaabdbaebeeaabcedbdedccdeadbdaebccacbadeedecaddadeaeeceacbabcbdbbddacaeeddbbbdedddeebdbdbcedaabdedaeeedddcebdcbadeccacabcedecbcbddbebaccaadeebdacedaaecdebbeaedcaeceabeeaaaeedccecbbacabdbeccdcabeaaabcbbdebeedbddcbcebdaceeeaaabdceaabaedcdababebdeeebacbebacdbbbabcebbebeacecceacecadeaadaabdbcddacecbbceeacedcdbeddebaebacdacbcacbcdcadbcddcbddbabdbbbebbcdbcacaecbabebdadadbaaccbbbbdddddbecbceadcaacdccdebebaaebaddabeecdcbbaaedeaabcdeacaeabdebeccecdcadaaaddcebdcbeacabdcbddecadadcebbeddcdeeabbbadacbaaeebeddbcadcdadaaadcbaadeacabccdddbedcedccadebbdaddbaebbcdaaadabaddeddbcbcbcdeccdbcbbccbbedbacddcdacdcccddedaceebdcccebaabdeadddadcdbeacbcbcddaebedbeaaddabeeaaebddadeccdaceeedebaacbbdbcdbccbeadcecabcdcaddceaceeeebcdcdabbdaecedebdbccebbbbbdbdebecebebebdbceeaebdddddebdaabeeecbaeaceeeebeeeabccebebbbaededbacaccdddaceecacaebbdccbbcbdddcdaddcacababdadcadddaeeabaeacbbeaaabbceebdbdaaabdbdecaebacbcecabacdbddbcdcaaddaededcbdcbdccccccecebdaceebcbadaaadedbaebbeadcdcadabacbbeeeeeddbaccceeedccecccebaceaebedceecedbdeaeeccacaadbcedcaacaaceebcbaabedceacbabddbdcebaecacadcaeacdcbededecabbbaeededbbeedaddbaadebaddabacaaaacbddbaceaccebcebbeecbbadbbabadbdebaeeccdbeadcddeacbaaeccbeedbbcbddcddbaacecaacebbbecadaebedcdcbeccebadcdeabedcabbebeeaabcbacaaeedbbedbbbabedbeaaebecbdabaacbeedcdcddbebcecaadbbcebabdabbedcadadceccabeedadeddedccaecbcabbaacdcdedabbddddebaaeedccaaedcbcebdcebcdaaeacaacababdedbcdebbabbacebadaaedededbecaddcaebccccddcdecdcbabaccbeaeaaebaaddeeeaeeaeeebbcabdaacdedebceecebddcdeaeecbbabdedbadbcbccebabaacadeaabddcbbbacdacbeccdacadccbcbbdcccdcbaedabebaebdeeaedaadbdabaecdbaacdacbccbdbdaccebdbbeadcaeececedaebcbcbdaaaecbcaaddeebaeabecebacdcabeacbadeaedecabebdceeedacdecbbeedaeaebbaeaadbbbeaacaeceecbdcdbacbaacebcbceacbbcdbbecceaedbaceaddbabdcecbbdcdaecdbcdbbaddeeedeeeeddaddceaeaadcdbccaaccaddcdbbcdeddebbeadcecbadbabddeabeeccbceeccbeeddcbdebedbcbecccacdbaddebaeecaacaecbdaeddbcbebdedaebecdcaadbebdbeddbedeabeabeadaaececcdbaeabbcdeeeaadaabdadddedeaadbedceeadbcebbeadeaeeaddecebbdeccebedcaecaecbdabbcadbadabdbcbebcbebbaabeceaedbcabbcaedbabdbaedcaebedadcaacbcdeaedebaaebddbdaeeeddbeacbbaccebaacddcbbabedbabedeeabceaddeceaecdedcbbeceecebecbaececdbaecaaedcacbddbdcdcceabbeceeadccdabebaececeabbdcddcddeddcabbbcaeaedbebbebcdbadacbeceedebabbaedecdebbdccdabcdeecccacaeccabeddbdeededcdcbcacadeecababbeedcdeddebbebdbdacebecabdbbcbbbbcccbdaceabebdbcbbcbbaeabdeaeecbbbcacacbcaebcddedecbebdaadaddeadadcadeccbeabacdaeacdceabebacbedebbbbbbabbeebaccacdeacadecadeabbbebedddaeebcaedebebbacacbdacdeacdccccedbbeabcbadaadbeadbdcaeecacdbbbccbdbdccdddcbccaeedaebcadaadbeddcbddbcaddbdcdddacceabcebaabbdddcececdaaddaccabcbcedceebbeebbabeaabbabaaabcbbbadeeeaaaecdcddcbeebacdcbedadbdcbddaeadeaebbbccdecddcecbeabacdbeaabceeecbaeeddccbdecbabebeebdabbeeadcbeaabbbadbedeecbcaeedaeeecbebcbbbeaccdcaddabcdcdaddcabcadcadbabdaebdeeecedbaaadbaabacebbdcddabaeccabdadbddccecdcecceacebbcaeddedbdbdedcceeccbabdceddcdbbbdbeecbbacbbaaaecadccdacbcdaeecdedcdaeabbdbcacaabdcccbebacebccbcaecabcddeabcccbaeeeeaabceabcdaedabadaeadaeacdabccebaedbbcddecbbdebcdeeebabebcaadcccbbecadbdabbaebbeededdacbdcdcddabdcaeaebdecebaccddaadbdedcacbcddcccbceadaedcdccaedbdbdbabadccbdbeabecddabbeacccbbcdececbedaeadcbddbdebabeecaeaecbbaaebedccecaaedcbceeebdcddcbdaaebaddddbacaddacbcccbecbeacbdcaebcccceaaaececebecbacbeeddcdddbcdececcbacdedbcebcceebccdecbaacaeebcccaeedadecaacdccebceacaadeedacbebddbbaccadededcedeaadddaeebececccadbaaecaeaadeacacbcaadeeebdbaacbeecbecedeadbadcdddcbabcaececdcdaddadbbdacdaaacbddecbebdbbecaebaedcdcedcacdddacedeeaabeeadbeedadbcbebebeaaeebdaceeebbdbaecedaadebebeaeaebcececadebaecebbcbacaebdcecccacdddccaabedaeeccbeceaaaccebddcbbdbecdaccbaadbbdebedddeddecbbbadbdcebaeccabecbbcedebeacbeddebeababdddcedeebacacdcebedceadbbcbaabbaeeccedccccebcdadecadeaddceecdaadeebcecebcecdbbdbebcdebcdaeceabbecebccadabdbcdaedacdaebadecbeedcceeabbaceaccebdaccbccbcbbaaeccecaececbdeeeebdadebccbdbbbdbecdeeccecdaebeeabbeaebaeebddaadcaadcbaddabdcabcecccbdadccacacddbabeadbaecaddbaacabdabeabdbeceabcbdbaacdbdeadacadaddaeaeececcdcbbadcaedeadcbeebbbaebbaeadcddcddcedaacdeceaeabbbbaebbcccdcdcdbabeeecacaeebaccdaeccebdcabecaedaeecdebeeddceaedcacadcdadacaaabccbacbaedadaaccaededdceecdbadabbaeebceaceccddcecaeaebbeebceaddaccccaedcadeebaedacdeaabdacbdbdadbbdbacdadcabdcccbbeebbedabcdecabadabbeddbcddeececdaedebdecaccdcaadbdcebcbbabaeeecbbcebeddecebdeebdacaabceaadaeedacdaabecaacadadbadabccebbddebccabedeebdcbcdeabbadeeedeacdebeeeabaeaadcbadddabbbaabbaeaaebdcceadbbedcdcaeaaceebaeceabccbbcbeecbbebdaabbcecededceccaaeebdeccbdbcceeeeddbebdbabbadabaaabadadabebcdeddbdeaeabaeeaccaeddbeeecabaecedaaacdbbbdcdacbbddbdbadeeaabadcbcbdecdbcaaeebeedcacbeebaedddbddabbaecdeececedbdeebabcbcdabadccdeadacbcaaaadceadeccbcdcdacabebcbdeecaedadbeeeebdabddebeeecbbaacbabcdaaabcbebeddcababbdedeadbdaaaeecbebbddabebaccbeacedbecceecaeaedbccdebcdbeddabaddabcdacdaeadadadbabaddddeabcbccdcbddceebeddbdcabdeddeacaebcccccababebbabacacabcebbebdacbeadddddabbaeadaebbcbbbaddadaaaadcccbedeaceebabbdbaddbedededcdaeccdccadbdeeddacabbbecabcbaaeceebabbbaaddbaabacdddedabeeadccadbceaabbbbbebdcdddbbbbbbddadbdcceeaabaadbbacaccbccbcdaabaaadeebdabeabcacccbadcdcebacacecdeebdcdabaadcebaabaeccdaeabababedbcaaaeedbdcdaaedbdcabaacdcabbebecddadbacabcbbecdbadbaeeddebedaabdaadeccabecdedeadcbbeededbbebdbbbadbeeecedeeabccbecbdedaaaebccabbccabcbaecadaeddeaedbedbeecedddceeadccdbbaecdbbcadeedccecedbdbeadeeacbadbcdbaaecbbbdedecadcceebebccaadecebcebcdabebbbceeaadaeccaeebeecbedaedbcbcbaaaaedbacacaebbadabddeebacdcadecbcceddecadacdbbaeedbdeaabececeaecbaddcbcbcdaaaaccabcecbcbcecbaadedbeedcdbceebaddbcbdbcaaecedadcaacecdbbecbdcbebabaaddcccebdbaadbdecdaceebaabadacbeeedbcaedbcbedaeaabeeceeedcadecedcedaeeabaabddcabaceecedccdebbacaccedcddeabbceaaaceecbabebdcbecdacabaedcacdcdeecceeaecdaacbdabbcbeeaeccbdeceeccacbcceecabbccaceedbbeabdedbadddeebbcdaabdaeecdbcbecdebbacdadcdeeadabcdddabeacacacedaeeedbbcedebccbbcabdabebebacacaacaceedaadaceebdbcaadbaaaacaedebdacbecdadabcaecabecaddccdbdcbeaabcdceaacdbecacabccdbbbdddcdbeabadeeaaedecabdcbdbbdbaeeebdbcdedebcceacabdeddedadcdeedbdaceccbcacbbcabedeccdccbdbdcedcdbceedccacebabeeeecbedabdebdceaabeadcbbedaebcdddacdddecbdaecbcdcedaadaededeaacaaaeddecabaeeaaadacaadcadddcbeeadaabbdecaedddcdbcadeecdabbbadeedbdddecdaeeebbebaabdeeaaedeeabbccbabddbcecccdcdaeaeeccaadbdaeacbcaeeaadbccabaadbceeaaeddadbdbdcbecbdbbeceaababcaeeecebaceddeedaebedddecaeebbbecabcbdebaecbecdbcaeeceeddbdcdcaeccaebacbceddababcbcacbadbebcecabaddaadccccecdbdbacbabaadccabdecaadaaeceeeccbbabbbbdecaeabeecbebaeaceccebedcdcaeaacbbcadaeeadbccdbdebeeadedeedbeabbcbdbbadadcdcbbeaaebaddeabebddacedceaaedcaedecadcedcdeaeddccbbeeaeceebcaecadccccbabaeaaceadeeeccedaadbdabdbcdaadbbadcadbbdaceeecdcdeebbaecdaeddaddbbcdaaaddedaaaaebaacecbdccebbccebbcadeeecdcacdbeecbaedbbcccaddddbedabadababdbaeaeeebaebcddbbcbdaccdadbacdbedcbbeccdabecebcdbddebbacdcbeebdbbeddecdcbeddeedbcaeaeabbaaaeccaddeddcccbcdacabbcbbaedbcedcabddddbeaeabbbbedcbaaebaceaaedbbdeacdcddcccaaeceeedbbbbcbcdbdbabeedabaaaedaddceaecdccaeaceacdebeedbebbeabdddeaaadbdebbdabedadccabbceeaceaedbaeecbdcbcbededeeaacbadceeddbdeabeaaceccccdecacbebeadbeddebeabecaaadecbabadbbbebaebceecdacceaedecaeaecdcbeaeccadaeedbccbaebaedcdabecdbdbadbadeccdcebabccbecedbdddcbecabeecbbeeaabedbedebedadabebebcabaeedcebcdbccaaebabedaeabedcaccbeabeebeceaaecabeebdbdacccbdeaadceaabdbbeebebceeebeabbbadeadbebbbabceeaabaaedababebbcababadebceeeedccdcbbbbdcdcddeeccceeacbcceccebabbdeabdcccdcdcccebeaacdceadbccbddeaeccaabddadcadeadbcbeccebeeaecddbabdecbbeeadeaddebaedaeabbddbbeeaccaaeabccaabedbeaedcddcaecaaededbbddedceeebdabaacbaaebabbbbdcbdddaddcbbeacbdecacaacadaaadeeadecabdccccdabdaceebaddbbcbcdeaadbbababcdbecbedacedcbdabceaabcbdbbcadaddccbbeaeadecdcecaeaaccbcbdddadcebddbaccaadbddbcaddcccbccbabbabcaedeeedeeabdbebaccaabbadebaaedadcebdcaabbccebedddcbedabcaadaeceaebadadcaabbccadbdadecaeaecaeccdccdbaccdbabcdaaecedeedaaeaceaebeadcaaedbaaaeabddabdaeccbcabeabdacddddeeaaaadbbdbedbbabccbcdbedcedcddbdacdbeababdaeccbdbaaebbaeaccbebbcedbeebebccecaddccecaecbdeadcaacaebdcebdcdcddedccaedaeadeddecbcebadbddaebccebdaadbccbcbcaddaccabdebdcebcadeaeaaaebaabbcdecaaeccdcbcbedbddecebdbbcdbdaaaecdccecdcbccbddededbbeaeecbccbbdddadadcaedacacedabbbadedbbabacaadbeceedbeabcbbeecebbbcddbccabbeaedecbbeaeeabbadddeacccaebeeecddbadebccdedcbaeabdbdddacebdccbaddaadcabebdbcabeaabbacbbccbdbeaceabedebeabccbdccedabaabceaecaebecaacedcbcdadadeaccbaadbbebdeaecacaeeaacbaceabeeeebbbacbedbbcbcecdccdabcaccdadaebbeabdbbbebeeedbccaeabeccbbbaccdaceeabcaedbdaabebccccaecbacedddaebaacebbdeecadcbbaedabdccdceaeedcaadaadbeecccadbcddbecadebdceddcbcdbbdaabcedadbcdaceaeccaeecbdbddeeeddaeebeabebcbabddeabaddcaedbacbedaadeacabbdaeeabcadaccbbbbbcaccaecccdbbabccbdedaddbbacbebcaccceebcdaddeadebbaeaebbeacccbcebddbbbdcabacbcabeccbcadbbebbcbbbaccdacedeabcaacdceccbebbbcacdbbacccdaceacddbbdbdcdebeaabacdcadaabedaaabdcaddeddddeebadbccbbeeeeddeccbeabaccdcbeddbceeabdcedeecddbbdbeddadbbcaddacbdecdacbbdbeeeeebacddbabcebaeadbeadabaecaeeceeccdecabebccdaaceaabcebdbdddcadeebbdbeccadbcabcaccdbbcebebdbaacabedbbecaacdecaeebccaaabcceaccddcecebecacceaaceedebedbaeabeceebcedaebdbdeceedccebbaacecabaacdbdadbebaacbebccbcabecaccedaaeadbdceebeceaebbbdaabecedcadeeddcdcdeacdbdbbbcdcbabceebccadbceaecadbdbbebddeaaccebebdccdadbebeeeddbabdeabbbbacbddcdebddbddeaddbadeeebeaedbeabbaeecacdebeccacbddaedaeaaddeaeeebbdedbdbabdabbaceabbdbcdddbbeededceaadbaecdececdbdbceebebbabeaecabacbcaedccbdecaddddcecdbbecbcadcaabbccddcbaabdcabdcbceacdedbaaeeebcabdecdbcadcadacecbeacccabaadcccbccebecbbaebccdcbebbabbdbabeadbebddaaccbdadccdabadecdbdaedacbebcecaaabeeadccbbdeaaccabeaeacedaeaabeadabcbeaaebcadaacacaacaadbbcddacbdadedacdecadbbaebedbebacdcbbcbebabcebbedcccacbbccccabccaebcadbeadbeddbddeacdadbbccdcadcdacaeaedeccdeaeaedbdbbeabbcbabbebecaccadeabdaceeceedbabbeadcdcccadceebbbcdaccaceaeddbcaeceeaeaceacbdabbedcebdccbcdeacddbdaaaabdcbadacddaebcbedbceedebeedbeedcabcbacdaadcbeaaabddceaccabddeabcdceeaccebeadbdaddedaccadbccbecdcabbbceceecbaecbadceedacdbadbbbababbbecdcccceaceacbacdeceacbbedbbceeccacacabcdbeebeadeccecceadbedcedeebaebdcdeccadecdedbaedcdadbadbbaacdcdcedcaeececacdadacbaeebeaedcbccacbabbcbadeeaebaaaccdbcbdaeaabbeaebceddaccdcdbdeceeabababaccebedaacaddaeccdacaebbaaaaaecdacecbedbecbbbcbaeebceadbedcaddaeedaceddedacabdbcdededadccccadacddedcececbaddbbcdbccccadcccbabbdacabacdcaeeeabdbceeeadeabdadabbcbadbbbcdbdeeacdccceddaeccbababeabdbdaadcebcaabedbdbcebdecdeacdeebbcaeaecdbbecaebbbadaaaedaadcdedaacdeacbbcdabdbeedcdaeccdaaabccbaccbbbbccececeacebbacbeaddcdbacbcdcdacbccdbddebbddcaceebbdbbdbdecdaddaebebabbacebdebcedadcdeabdebebeddbaddddadcbcecddbaccdadbabcdddeebaacbaeadeaaccbeebcaacaeccddbeabcedaddabababebeeabbadbaacebabcceadbecadaceabbeddaacdcdeedbdbbcadaeeacabdaabddebbadddadddbeaecdcddedacebbabeaceedeedaeebecaebdaecbcdbcdcddcbcaaceeebcdecedecacaeaebeaeacadcedcacccaeebaeeaaebaedaccccaaedddddddaeeeacadebdebbadcccdaaabebedcbbbdddbcdbcecbedccaabeacedeaeeacacdcbacceccdecededeceeacdcbdaabccecbdeebdaecbcbecebccbdaaaaddacaedebbacaececbcabaacadbbcddbddcdeabaaaacaabdccdeabecbcdccdceebaadadabdcbeceeebacdbcacbacdeacdbeaadcaedacdbbceeadbebcaccaadbbbeaaebdbcaeeeebceaedbbabcabddcaaddbbeeecdabbdaedadcedcbadccecdeaebcdaadecddcdccacddabdaeedaccaaccdabacbbbcedcccbdbabeabbcacbeaaacedbaeedddebebceddcedeeadcbcbcaaadcbaedcdccbebababdbecbdadeacdbccaeebbedacdadecaceaeceabdbbcbbebacdbedbbaaebeeeadbccbbaddeedcabadcdbeabaabbcbaedebbdcdaceeccebdeebcbcaaddababecaebdbdceebbdccdaceadbeececbbbdbdcdecbbabcbbcabebabaadeccebaeddedecadbbcabbedecceadbaddbbbaeaaaabaedacccacbdacdccbdeddaccdbadceecceddcaacdbadeaaebdebbdacbbbcbcaadededdbdceadddeaacdddcacacaeedccbdddcadeeacdbaadbcdaaaececbaabcdbcaeabcdcccbcebaacbcbbedcaceeebdbdbadcbebdebbabdcacaeedabdeeccaddcebbdaaedecddacdeebccdeaaccacacdeeaecacbeddcdbdadecbdebedaccccaeeddddadcaddaaecaeebaedbccacccabaacaeeaaadbbddabaddeacdcdeccddddabaeddeeddcebdecaccccdcdbbecbdbdceadababcaaaccddaecbeacedaabdbdddeaecdccabdacedeeceacbbdceceeeeceedbccadaacebbebbaaebadddcccdcbcabcdaaabeabbaddbeabcaebaebcbecbcdaeeddebbeadebbecdbddcdeacccbbccaaababcbaabacaacbacceeddbaaedacdeeaceabbadeeaaebedabdacdcaeaacdcbaabaeebbcccbdaeacddadcdaedaaeaebdaebbecbbebbddbabacbbcbcceeacadcaaccdbddebbbebeceedbddbecaacbcaebcaccbebdcbabbeaeebccbcabdcbadbadecdbeaaddadcaebdcbeddeebbbcdeaccccdbdadecbadebbacadbcbadcbcddadecbbeabdbaeedbbcccddcaadddebbcdbeccccdcdaecdedadcbdbcbddaabecccabdaabbbbdbeddbaceaceeebcaeaaeeadceeecbaaedaeceecdcbeacbccdaadecbebcccaecdeceebbacbacebecebcaeeabbdddcaebeacecbbebeceedcdcecedeccdbdbbaadabacccdebdaccbadaacbabbececccabecccbadbcbbcbcaabadeacaedbbccabadccbceaecaadababcabcdbedeeeaacaabcdaeceaebdeebebbcaaebacabbeeccbaabecccaabcaccbeacbdeedbbecceaccaeeedceedeabedebaadaeaadddeedebceccdcbaadabbaeccbbacedabdbecddacbcbaaacbdcceacecedadddaaaceccecbaabbaadcabbadddeaddadecacdabaabdecdedccedbbabdeccebeccdaccacebcaddccdbcadbeeaddcacabeddeeececbcdccbdacbaaebdaaeaecdaabccbdebdecbcbcebcbeecdeaacdecaaedeccdccbbeeedadaecdbbccacdebbdcdebbddddaaacccbabccaaebabdcaecceabdadcedbeedaddbdaedbabdadbceeaabebbdbaddcbdcadbaebeaccbaddddddaeebaccdedabecaaceeadddaecdadadabebadabcbbcacbaadbbaaadcabbddcdabbbababdbdbbaedeecaeebbaaadeeccdcdadaeaedadaeebbdaebdbcddbebbbcebcbccbaebceccabddbcadaacbedbbcadcadadbdbdadceccbdcadeaacebcdceabedebcbbdadbaaaebabcbecbbbcbdcccbbcadaabceedcdadbbaabaadacacadeebeebdcddecbbcaaddadeabcebcadcaddbabdeeadaccebbeadbdcecabbabdbdededbebdeeceadcebbaddbacdabebebbbddabedadebeeeeadebaabbcebacabdedbccceddebdaeeaccbcdbeedceeaecddbbeeddeedebaccdaacddeddceecbedeaeeabebbbdccdcbaadbacdddedcdcbadccabbcecadcbbdecaccebdceebeecdcbaacdadceaabbaddbbdaabbcddcceaadedcdccdbbedbceaedbddacecddcbbcedbacbecabdaeaceacbabdbcecebceddbedeaabbcbaaeeadbbabcbccdcbaccaaedbceceebeaeacdcdebadedddddcebaeeaebbaedaceeededbcebdecadecdeeadededebeecdeedbaedaabacbaadbdebaceeeeeaeacebaccccbcdedbcbcdeebbcddbcecdcebcdebbbdddaadecbacbebebdbadadbabcaaaecaddcaccccadaaecdbccedbaaddecedbcaadbabccacebbceabcbcdabcbaedcbdceccccbeeeabbbcbecccddbbbccdcdaacdbcbbcddcedaabebeeedaccadeeeeebdeeddbabacdcccceaeadaacbbaacdedceabbcbeeebdaeadbbbcdadeebbdacedecadeeebbeccddbccbacabaeceeacadbdcaaaeadacdddacdedddcecdacddbddeebccaeeebbcebbadaeacbabbceecccdcadcbaeaadbbeadabeeebabbebedcedcbacdacaacaededdbdadcdabcdaadbeddbecdddcedacebeebccaddeaacdcebcbcdbdabddedaedacdbcdaecbbdbdadcbddcaebaadcaececcbddcdecbabdcdeeabacecbeeedadeccebbabeedddcdcaaaaaadcdabbbecbcaedcaaedcabedaaedabbeedbabaabddcccaeabddedabeedcbdeeebeacddccdbddddebbbabbbbabaeaaaddbedbedcdcbadbedadecdcabddebadccdaeeeeacaebccecbcedeadaeacceededeacbedcacdaeabdeeaebbbacacbcbdeaedcaabecdaacabaceaeddddacbbcccecbbdacbabadbebecbbcbecbcdbdccaccbedcccddddccaeaecadaccbebecdbaddabeaeecceaadddbeabcadcedbcddaceebcdceebdaadabeecbbcdabeadcbcedebabecdcdaeebeebaabdebdabcecdeebbceddddecdeacedcddecdeabcaaadadccdeeaebeedebdeceeeebadbbdbaccabcecdcbddeecdebcdaadeadbaabdddbcbccbbebadcaeaadbddeccceccceddccbebaeecdccbecccdaaadabbdaadbecebbaaadbbcbaecbbdaccbcabdcedbebbeabaedddeaeaedabecddcecdaeaddaccdbddcdecabebeececceeadedeadecdaebedaacacceedebeabeeadcecacddedececdcdeddebcbdaaddadddaddcdeedaeeeeecabcbeecebbcaedecebccbbccdbbcdaccaeeddcadcbddeddbcedeaaecadbbbeccadbcbdbdebcdaabcbedebbeababdeceaebceeeccabaabcadbceeadceecaaaaadacdbdeabdeadaccdebcbebcbbdabcaeeaccedaacaadccabebdebcdadabddccadabcbddcaeaddddeeccccceabebbadbbdecaeeebbacacecaadebdadcbbbedaaedcaddeacbbecbbadaaeacdcacbddddcaaadccebdcaeddecbdccacdbdaeceaceddceacabceabacccaecbbdeeacadebcdcceddbeacabcaccadddcedbceddbaaebcbaabcbeacaaddbbdabbeeeceaaddeedeeacddaccedcaddcecdebacceedbaaabedcdcaabdabdaabcdeceeabaadebcbcceecddceedecadbcbedbdeadbcdbdccecddaecdddabecceaedecdabecbedceaddabedceaeaedcbabdedeebedebaaaebeddadbceebbbbacecbcdcededccbabcebabecedcbbcedaedacddeaabedccccbcaaaaacdacabdbccbbdbdecdeaeedebceeedeabcbadedecbbccddaeedddbeececebdebddbbcdedecadbbedaaecbeabcecbadbccbaaecbdbdedbecadcdcebebedbddeaecbcbebddedecbbaecbbedecbbcaeedddebaaacdadedeadaadadecaecdbaabcbdabebccaccaeaeeaaebdaaaacabaaaeecbdabdaddceacacacacaebdcbbaacccebeaeaddcddedaccccbcdcdbeedbadcaeebceaebaacbdcdededbabaacbdeddcccccbededbcacaebeaccdcbecaeeadbeecaedeebdacccddabcdeedcdbbcadcceccddadadcdedabebebdbbbdbcacbeebcbcedceadaaddbdceaaebcbbbcbabbcaebcdaccdcbabacdeabbaeebeeedaabceaecbadebbeeedecbedccabdeeabeedbdababddeccabcbddbdcddcdaebdaadbdddaaabbecdbbaebaaaadccbcaacebacbbdabedaabaceecbbccebdbabddcbeadccecabcebdbcceebcaacbcbccbdaaedeebeeadddacdeabbcededddcdcedaaebdcbcbaceaadccbbadcbbbddcdbcdbdecbaedababaadedaaccbecbadeaededeacdacbdcaeebdeaabecccadcddecbbdacaecbeaeeedddbedebbadecdceddcdccdbcdbadabccaceacbeeaeabeaacaccddbcddabbdbcabcbebdaeaecacacbcccaaabbdcccaebecbeeaaeadcccccccdedcaccceaaedcddeceddddaddecbbcbabdecbdddcedceaebdddbdaeaeeeebdacbcacdddcdbbcaeecccaaabbccecbdadddcdaddbebaaebcdbcebbaacdedebeeadcaacccbdadedaeabeaeebcedececbeecadabdbbbbabadecaecaacdcbacaebaaaacdaceeacbceedeadcbeebaeccccceeacecaeeaadaceecedbbcddccbebedbebdbabcbabeecddbeadcdeebadaccceedecaedbceeadbbaceecbbccceccacccbbebedaaababdeaabbbccededbcecebedccbbbcaacaadabaddaacbdbbebcccbabecedbaeabbcacdbabbceeebbcbabdadadbdaecbadccdaddeecdaeaedbbeccdaaaaaecbdaabdeadeadeaabdceaacbdaddadebbbaaaecacdabcdabcdcdbbdeccecdbbcddcbddddeebbdccbaeaeeebcdbabaeaccedbddbdbbbceaddeeaeeddcedaaeddacadedaeccdedbaadcecbecbaabbdadcdaaacaddbddebaaeeacbadadecbcecdbbadcbbecebbaedbbeabeaaaedacbbbbaeecbbeadcaeabcdcbbacadacdccbdbebddcedaabaeedbbdcdebdbedebbacdeceedadedcccdcaeecacdcabdbbaedacaaaebecccecddaaedeedaabdaaceabacccaabbecdcebaeebceedceccdaddbddaaaccceccddcabebcbecbecaaaabbacdedaccbacaeebbaceaabadedbdadccbdbdaaebabecbadbeaaccaaccbcbdcbcaaaceaeedaccdcdcaaaabdbabccbbdabcbabcdeeccaadaaaceebbebbebbdcbbeecbcdccddbddbebeececbeadeeebdedbbbceaecacbcbeeaeaeeacadcacdbdabcadcddebacbdeebeeadedeacccbbdaabadecdedaadddeecbdacacaaabcbdaeaaaaaabadcbecbadcabaacaabebbbecbbbeeacaabdbcaddbdaeecceabebeedabcacaeaaaadceadcddbaeaeabaaacaeaabcddaeabecedeaeadbdddeddbeebceadcdcbbaeabbacdbcaaadcceddbbecaeceedbcadbebeecdcceebbdcaabccbcacccdbebcedcdbaabdbcaedbecdecddaebcbbeaecabedaeeccebeccdebaeaaaddbeccbbbdbdccedeaaabaebcecccedeaeceeccedcdbdaceacdcacbeccecdeecdbeeddbdcdbccbbdeeacdbedddadabeaadbaabbebabdedcadebbedcaddaacbeabdaaeecabcaabbdacedebadcecaacbaacdecaaccdaaeebaaaaedcbaabacaecbcadccbdbbedbcbadddacdedcdaecbdbbebededebbcdbdccbbeeedeeccaccdbecedbaeecacabedaeccadaedaccaceccaaaadcececadbdbdbbccbeadcbebebdcdceeebbdecbadeeaadaecacaccebbadaeccaaabddbbbedccbdbecadcbbbbadecddecaecdbcadbbddddaebcccaabadbcdddadadeaccdacbdbbbcaceaacececaecbaddecdbecababbddcccdbccccbceecdebbaaacbbdbebbdebabbbdceaaedacbadebdebbbaceabcabdadbecddbaecdeeaeadeacaeeebcbeedcdddadccecccecedabeecdababeeecabeaecdadcdebdcbedcbbebcadadaaddbaebeddbeabebecbdbbbaaaaeacadedeaeaddaebbacdbbeaadcacdeeebdeddbcecebeebabdecabbccbcebabaccdbbeaaceedabeeabdeeceacacbbccdcebaeaabccdabaabdeacaddadacdcddcacacccebddbdddeeedeccbcccadecbbecbedbceadcdbbdebaceaebbabcecaaaebedaddabdaccbccaaeccdabdeecedadcbaebaeeedeaabeeaacabceadceeddebccdadbbaeeeeadbeccdebbadaeabcdacaceebbcbbddebebacbbddeabbaaeacbedeeadaebdcabcadbcdcbdbedccebceebbeeadbdedaceecbbebaedaccdaabddeeaecbbdaddeebedebcbcadbddaccbadbdabececadcbdecbbdbbbceccceccaecbbcebcdbbcddecdcdbeeabbebcbaaecdaaedaeaaadecbdecbdedeadbacbcaebaaaeecacddeebccebcbaebdeaaedbabadebccacceecbedcbedeccacccebbababeaaccdbdceaabbbbeeeeecbcabbbacdddabecccaebccddbddcdcbccdaedaceddbededcaeeabebbddaaebdbeebbcbbbdbbcbebbabaeedeabcdcbecbdaeceeeaeccbaebeaddbaaebdcddbbceeadaecececaababceacdedbecaccbeedaebdcdabcadcbbbedeeaeccaecabcaeedeabdcbbdddeddedccaeaebbaabaddbdeeacddbcecddcabcadbbbdbbcebcabbebeeecaedcaabbbcdcbbcaebadddbbaaaedabeddedaeedbabedaaacceddcabededacecbbcaeddeebaeacadbcdbcaeedbddaeaeaaecacaacedccdecbadacbcceedacaedbddbdeebdadceaebcadecccaeeccaccdbbadaccdcddecaabbedbaadbacdeaaebebbebabcaeadcadddbeaabeaebeadedadabccbebebeacebaeceeeedeccbdccddebeaceaaaaedcadccbcadcdaabbbabcdeebdabebddecddbbaedabdddebeeaccebdedbdceaaabdcaeecabebbcccbdaeddcacecdcdabceeceadbabbedbabdbaedbdabaaeebbbebaadcaaaecccaaedadbcbeecdeedaddccbbebadbdaebdcdcaebbebcdbdecdabacbacbbeecddedcdbbbbebcecabbbbebaeabdedbebcaccacbaaccddaddeebaddaceeadcbdeaceadddbbbabadddbaebeedddbdbecaeecdeddcdcadbbbcececbbbbcbaccaabeeeacdbcdccdaecceeabcdbcaeeeddddbdccedcdcececbcbeecdceaaabdaacaaebaaebcceacbbabbaaeebebaedadcebbcddccabdedabebcdcbbdabdeacccbddabbcbdddaacdacccdcdbacddaecaabbbdabbcdddacebebccebdbcecdacdabccecaebdecacadccbdddeeedbaadbedcedddbeaabebbabbabcaeddeeeaedcebcbacdcaaeaccdbedeebbbddaecaeeceddcecedebacddaeebbcbcaecbcacbadbdaadbeaebaedcbbdcabdeaadbaeccabecaebacbeebaabedccdcaeabecddaabaaaeacddbeddeddcadabccccccdccebcacaeabacdcbdcacedbccbabdabeccaaebaeadcecdaebbaacaabcedceaacaadeeebbeeeabaaacbbcebcbaacecbbcdcababceeebcdccddadebabbdeddbadbebbbecdadbaccdcbeeceaedbdecdcabadeabeacdedeadcaeededdceeebcaeddedabdbacebbbbceeabeadbdddeccdebeccceabbbcdcecaddbaccaddebbcdadecbececcecebacdbeededcabdaddbaebdadcbbdcddcdbabbaecacceceaaecaaeecceedcccaedcacdddbdacbceebecedaccaabbeabcbceddbacecdcbaaaabcaddccbccbcadaebeebdebecddaddedccbaeeadddebceebaddeadbccbbccabddaabbbcddebebbeabcccaaabeebdcacbadbdbeccbebececbacabadacdcdababedebeddbbbdebcbaaaecbedebadccdadaacbcceebdbabeddadcccbecdeacdeeacedeecececcbeceeccbadcbcebeeddeddbcadeaebcebacebebcebdeabadedccedadcbcaeddddedecdbddacccdcbbdebacebaebbaedcbedadbccdbdaeeedbccdccdeebebcedbcaebeadbaeedcddabddcdeebbcdbaebbddcaeddccbdccbcbdabeaebecbaeaaeebbadddacebbdadadeadbedcdcdbdabbcdaedcbecaeabaaacbededbddececedaedcebccabdbaaaadbadbbcbecaeecccdbebebeacecabccadaecbeabceaaaedbadabbdbbdabceaaeeaaabbbedeccbbbcdaddecbcbbdebaedaecdecadbebdedddbdbabdeaadecdceabcebdcaeeacbdcdcbbccbbeebddcbcbaacacbddecbebbdbbadaeccabaeeebabaadddedacebddecacbacebecaeddacadeaeaabbecaeadcacdaccadccebaacdeaaedddbeacabddbdeaaaeedacacccdbeeeddccbdabbacbadbdeadbcdccbbacaebddacadcdaebcbddababaaeabeaaddbbeaabdcadaceccadecddeabcbbeacdddaaeecddbddcaeaccdcdcbbcecbcbaccbeadeadbdcdaddbeacdbcccbebaceaccdccacbeeedaebacabeabeeecbdcacebbbaaeeeabccdbddcadbeaaadbecdcbbbcdeddbcedecebadddddcaebababcbcdeedddbeeddcddeebeddedbbddcadcbaadbcadaeaeecddaccbcddcdcadccbddcdeceadbdebcbddbaeacaabbbbbdbaaddbddcbcccbeeacbddacbcbcbdabacababbbaadacbaddeabccebceddabedcabbcbadebadbaaddacbacaddbeaccabacaccdcdeabaebddeeaeabcdcdebabcacaedeeaeacacdadbcebacbbcdabaedbcebbbaeebebadddaaedeadaedaeaebcbacbccdecdcbeedaebbbacaddcebaacedaecdccdcbaedaedbbccaadacadbcaceaeaddeededddcdeabbdeebddbcecdcdebbacebcacddeecedaeabaacaacbebeddeaddbbaeaebbcaabcdbbedcbadbeeabcbbbccdbebdbececccbbdbcccccdecabaecdceddacaedaaecbaeddcbabccceddaaeaebacbddccaeddaabbdcebadebbabcccacdbbadbcaddebecbbcebceebaedccecdbebbdcdcbeebeaaeaeaaccbddaeebddbbabdcdcebeccaeaabddacccbbbdbdadddbbadadcdabcbcbedebaebadaababdcbeddadbbbbbdeacbcabacdeddbddddcbeddacbedebddeadadebccbebbabaadebadeacaacaadebdcdedbeeecadcddcceacdedbcbdeebbdeabdaaaddabaeacbdabcaaddaacbbbdccaebbdeacdbcebcedaaccedbbacccedcaaeccaaabaddcbcadddacecebaaccecebdabdeaeecbdedcdabbabaaedddbecaddeaebaccbbedcabddcaaeadccbeaeecccaeccceaceedcddebdbeebadaeaeeadeeebeaeeecccabcdbbbcceecdcdcbdabaecbdccccaddcbedddaacbddcecbdccbbbaaecabebacdaadbddcedddebcedaceacececddcbebaabdeeeccdaebddcaaaaaaecbbdabcbaaadaebcbebdaebbcebbdaedbbedcdccadaedeececdbebdbbabdcacecaddeddacaabaaedaabeeaaceccdaaccecdeddcaebdeeeebdcceeadbccacedecbedbcaedaadeceaaaebadebdbddbedebbaccababaaadbcecdbdbaddedebdcaecdecadbbaecbcbbeeaacaccabdacccbcdbecdbdddedbabaddddaaacbddaeabaeadcccdebddccedddedbbdaaddabeeeacedbcaccccdeddceebeeadddeacdaeeaebbccdbacddcbbbdebadacbadadbdbbeabdcbcdddccebeaceadcdaabbdeacbeedbccddbcabeadaceddbeeeaeccabdeeceaebbdbdceacbcaccbbeabcdccedcbebdeabbdacedeabecebbaeecdddeaddbceecaadabebaacebddecbbdddcbadccbddbcbeeddeeedddeadbbbebacccabbabcbbcdbccccdccaedbbdbdeaedaeeaeabaaebabcccaeceaeaaebdaeeccdededecaabebeacdcceedaebeddaeabcecabccbaaeeeedddacaedaccaacbeaadecdcdabbebcbdeebccbecadddbbaaddcddccdaabdcccbedccebccebdbbeaeaccdedccedbdcaecaeebeecaabedeaadddabddaeaabdbbbedabbcbaabcecebeadebbccaaabbddabeeecaaababbdaeaeeeaedbecceabebeaaecbdbabaabaebcddebbcaecdaabacebbcecbebaedbdedaadeaabbcbdacdabceedeeebbadaecbbcdcbdcacbbcaeddedaedaeecabbabbbaacccdcdbdeebecceaebbbaeedbedecddbadebeccdeaeabedaeeceeeacbcdadeccabbbceeadbceaeabbbdcdddddaebbbcabcbaacddaceacdcdcdccdbdacccdabadbababcbcdcabaeecacaddedabbbdbbabbddadccedaaedeaeacdbecaacbdceeedbcacccebbaecbedbbedeabcbdcbccbbaeaabcbcceeaddcdecdabddcbdcebecdbdceeaddbabbacdbcceedddcacecbbbbebebebecadcdbadddaacbaaacccadacebbbeacbaabebcecbcbdbadeccadababeabedcddcacdaadddceabcaccbecbdaaaacdbbceabedcaacccbeacecaeecebbcedcaaadceddeceaadbbacbcbeddcdcbeedcabddabeddeccccaadbbbbcaeaddbeebedcedbdbcabcdabbeecaebedecaedbececaeaeadcbbbdbdcedebedbebaddccceeaeaaddcecdababccedaaecdbdbacebcdeedaaceeeaeecbbcbcdcedcecddacccaeeebcecdaeacccddcdddadceacbccedeabedaeecaeabddadbdaebaacbaeebaadebdbeaedaedbcccbccddaacaceceabacaabddaedbaebdbaaacdcceebccbaadbdbaeeccdecbcdddcbeeeecaabccaeacdcabceeaaaebccddbacdddcaecebbbcabedbaabeaebdcebcacbcdbeceeeebedbbbeedaeeeadbbabdbcdbacbdbbaaeebadeaeaebdacbbedcacceacccebcebdeddbaccacbebacabeeacdddcdceeaaaebdaebeceaddebcdddeecbcdcdaaebaeddecbbdddecccbddccacbebaadebddabdaeadedadbaeebbbcbbeaebbbbbdcedaaaebdbbeddbebaeebbdeecbecadbbbbedebbebaccdcabdbcdebebdacebdeeccbbcaabcbbcddcaadeccacbbddbebbebcbaaeedaeebbbabddedccacacdddaeedaaedadeebaaeeaebdbaaabbeadabccabcbbadebeabecedcaaadedeadcbccbedacccdabbeecbeaeabcecaabeacdcbacbeaedaaeabcabcbaaececccaebaeacdbdedcbbeadeddbcaabbbddacaccccdaedabeacacebaccddedcbbdaaddcdddbbbeeedbaebaeddceaaeeaceabaaadbeacbabeaeedbcaccbbacbecbeeaeccceccaccbeebedeaeccdeddccbceacabddaddeecacedbbeddbdecdcdbeabeedeaabcaedbcdeadcadadcbcbeaddbdbadabaeeadececaaccdeecebabcdbedeecabedcaeeababdebecceedbeaabbaeabcededcdbddddadabeeabbbcabcdbacbcbeecbabbbecbddcbdeedecbbeecdbdeebedbacdbddceacccdbbadaaccedaaeaddadcadaddeeeecdecacbbeceaaeaceddecbbccacbcddddabdbcedadacdbaedaeaddbeecaebdacaadeaabbeedbecdbdeccebccccdadcdbaebacedddddcebbebdbaadaaacdcacaedaedabacddaccbcaceaeecebdebedbcebdbcebbbacecddcaaeadebeccaaeddecdcebabcbaebcbcadeabecdabcababaebacecbcabccbaecbbbecbbdbcddaeacabbddcebbceccebbcadcaeecbdbceceebdcecbcabddebacdbaadbeddaeaebbadaecddeebcbcdabdcadbaeecdadcadecabdbdeebcdaebcaddceecbcbdcaadddbebedddaebbbabcccaeadbcdacbeabaaebcddeaecbedcadacbacbdcbdeeeecceeabbeddcebdbadceeacccdcdedeacdddcdcebababdecaaabcbbdbdbaaecaeebabccebbdddeccecaeaddeeaeeacebaeeeeadbdedabdadeaddcbbeaaccaaeedbebeabbbbaebeddddceadacdaabccaebdbdebaeaaddbaeedbbbcadccccaedddbeaecccedebdcedbececcaedaceedceeaeeedadbcadeddeeccccccbadcbbadbcacecacecdbeecccddedccaacacdeacdebdacdaadcebdcbbabaacdeadcbbaaceaeadcbcadedbbdecbebccedbdddbddccdaeaccccaaebbccebeacbaaeedeeccebabecebaecebceeedbadcedcbeeddddbdabceeddcbdadbedacdbedddccddadecadecebbbadcdbbbdcadedadedcebceacebabeddccdebcaaaeccbabcccccdcecdddadbcbbecbbcacdcecadadaaaabbcbeddbaadedccbbddbadcaddadecdcbeddadebcdcbbbbcdcadddeaceecbeaddebccdaccbddcbebbeadadcdcdbbeaceaeeaacaedaabbdddbbabdacaacaedbdcebddbeceecceabbeecdcaeadceebadeaebdeaeeeededbeddbccbcaebbcabaaeccadedeceebacaadcdeddababbdbeedceebdbedbeeaaeedebacbbdcbccedebbeacdaadeddcccceedddeddeccdaaaeaadceadbdcdcabccdbbeaecdebcccbabebccbcebacaddcbdadbeecadaaebbecbdceaadadcdaabdedcebccbbecbadbdedadabadeecbdadbcaeebadbbbcccaedcbdaabcaceacbaaadaaccbeeeacddaabcaadbbebaeecbececedbacdacdbbbedbeabeedbbdaaabcdeabcbcceabaeadbbeabdceaaacbbdeaabeaccdeaaeadacbbadacbbbaedcccebcaccbcdcccceccdcabeabaabccdeeaeeccdaedccbdcaeaccbebabeabaabadddcbeaedbaccbededdcebbddabcbeeacbebeaccbacddeadeadabddedebbeaeebccbedcccabdebecadabcddadeebbdaaceddacbeeeebacbbdceeedeeabddddebbcaebdedbcadbddecdeecdaccebbeaaacaeebcdaeaabbcbaadbcdbacbdbbdabaedadadecaeecccdedbbddcbbebdaddbbbabacdbccaaaacbceddcdbcdbbeccddcecdeeeabecdddbbebaaeaeaedcabdcababceabcddbcbbaabcdbccaaccdecbbabdddabedaeddbaabadbcacceaabbdacdadaecbbacdeadebbaddddddeacebeedbdbbadeedeecebbdbbaedaecececeeccddaaaacdaaddbcbeaeeecdbcbcacedbacecbacabaceeeadaccdcdbaedebecbdaaceedabddadcecdbaedcddaacadcdacdbadadadddedeaabeeeedebdaebacbbbebdbeadeeadccbccdebbbddbbbdbcccaebebaaddbcaadbddeeeececdaadbcdebedcabaedbbbbecabbbcbeedebaccadedbbbaddbbdcdbdedcaeececeddccdddbdcacaaaebebecdbdcebdebebecdadaecedaeceaceebbdecddabcbdaacebcdccbbdbbbbdadecbbdcdedccccdaceedceccecaeddcceababddedcaaabadddcaebbaabaadbceadccdddeaecacecacecdbdecadebcbcecddbacedcebcaadadaeecbeabbebbeacbaddaecedcadbdbaccacbedcaaadcdacabbdcebcbbaddccabdadbdbaddaddcbeadaebebbaedcedcdaaaacbadbdbebbdababbbcddceaeeecaecccccadaeccbccddcbabcabddadccceedbdbdaeebaaacaddbcadacbbebcaddebcadcacbcbabebcddecdcaedcbacdceceddccbeeddccbcbacbbcaaebcdedcdeadddbceaebddbbeaaeeccccedddbbbbdbcabbccabaabcddcdceeecacdbcbbbdeacacadadbadbbbbbabecddcbdbbdedeabbcceceeeeabbcebceaaccbcddccabeecdedbabedededbceadcebabadddacbdabbedcbbcdccebeaeaadbccebbebbcbeeccdababcbacbadabceddebeeddedacedddbbcaaaebadebdcacbedbccabceacebdeaadbcedbdccbceaadeacbabedcbababaaccbaaeeacdaabeedaeaaceaadebcdaeeaceebdaacdcacebceebbecabbbeececcadcccceaebccbbcbcbeeecbeadeaabaeaddabebabaedaaeabadecbaacdbddaaeddececbbeaedaaaaeebdaeeddbbadcddbeadceebbcdecbdecaadcaeedebeccbcdabcccbeedcbdceddcedabaceeebeccdcebdcbebdcbbccabdabaaababeddeaccaadcddbedaeaaacaeddbbceecaaeeabccdcccabeaeccaccbcceacecdbcddabadadacaeebebcaabbbabaadecdcabecaddedacbbdcaeceecbcdeeaeadedaacbbcdedeadcdbdecddbcdeeddbbbcdacadabedbbecbbcacaedaaadedaeedcbdeccabaaaebaaacbbeeeabbedddabeddebebaceaecbbcaddaccdcbaeddbcbdcbddccbecaddddebaceaccdcabbaedadbacaacbdceaadbbdddaedbbbcbccdabbecddaeabedadbcbbabecdbbbdbacbeeedadbaccbbcbbeacdcbcaaadaeedaecabaaabdbbddeadddbbeaeaaeaabaaeccacbacbbceedcbebdebbcdaceebbedbaddbabeeaedebdeeedbeabdcdeccebaeaeadabeadcdacbbacacaaeadedcbaeadcbeecaaddbbccdbddcadedaceaacbddbcbedeaacbdeecdcaeaddeedebecaebdabbcbecdbbadebaabebaeecbdbaaecceaaadbcdadcdcacdaaddbacdaaebcabbcedcadcbbcdeecebcaaacbecedbdecebebdbebbbeeecebdbeedbccbbaacbedaabeacdcaadaaddcdaccceacdeedcdbeaeaddabedadabadbaadbaececbaaaeedbcecbccaadacdeedddeedacacdeccddeabaddecbedbcdeebbcdbddbdaabbacddcccbdcbeaaabeccedeadacddbabdbabbcaacbbcbcaadedcaddadaceaaedeacddaaabbbcebabcabbdaecbddeadacebdacacdeceaaeecaacbaaabadacdcadceaccbdbaaaabbeebebaeecbedbaeeeccadbccdebedaecedadceccabcebcccbbaecbddadcecdceeeeedaadaaebbbbaeddadcedecdabdbdddcdeedbddbddeadeecbcdebbabccaaeeaaebbedebddaeadecacbcdadcbcabcdeaebbeeacbeabbbebdbeaddcaeabdbdecbeedecbdceaaacebedbcddceedddacebdacdccdabecaadacaeddbdcecedbedcbdbddeecacecbeabadeebdecdeeebbebedbbacbaebbbebbcaaddeeceddebcddcccaecaeceaeaaeaacacdcdabdbbdaadeeccdccbdbbdadceeeebceaaceebbccaeebbadaccbcdcaecaacbaeeaeeacedcbabaceedcbaaddaccbbdbdaabdcdddbebdbbbceaccdeccbcbeeaaaccedaecdbddbcacdcccbeadecdcebbbcebccaedbddabdcdddaddeadbddabedcbcedadcadccdbddcbbdebbedabcdaeddcaaeeeddcbabaeaceedeeceadacecabddbadcecdebbabaedcbbcacccacacbaddabeeebdeedacaddbccabcadabcddedcbcdaacceeaaebdaddcaaaabcaeceacceceacdecccbeaebbbaccadcaeacccaddbbeadcaaddbdeedaeaebeceeccecccebaedeedbcaccabeabdcddaaedeaacdceebcecbbaedbedbdadadddcdcaabceddcacbdaecceaccccdbedeceddeeddecdadecaacedbceceadcbdacaddbceaedddbbddcdccdceddbcdacaacdadabccacabbcabcbabdaeccadbcaaabecdcdeeeadecdbbbebbedaeabedecabeaacaabeaabcceacbeccaecabeaaeddbeebbeebaceaceecdbcdaeadaebaceeabacdbebaeeddacacbcdeccbadaccacbbabcccccbcebaeddaccdaddbdabadeeccdbdbdbcdcdbdadeebcdceacddaeedeabcebddecbebddbcbddebaceadababebbcabddeaecdeddceebbbadcabaecbdbaaddbadacbaeeadcdddecbebabdcbdeceddecbcddabbeeacbbcbddaecbecdabccacaabeddecceeebdebebeeeecdecbddcbcbadeedecadeeabaccdacdebeccbdebbdcbdedadcaaddebecabccecdbdcaeddcaadbddeaedbeeeecbbeaddabceecccbecddeabeabedcebacaadbcecbdcddacccccbbbdbddabebdaecddcbedbebcabddbbcdbcbcabadbaadbedccbbaecbeaeeaeceebdaacdaebeddcceecadebdbcddaeeacbbaadededaadabcbcccdcabcdabacdddbacbebbecdbccdaddadaadbbaadeaceccdeaeabeaeceebbdaeacdbbbdabcbbaadedeaebbacedecabbacbdbcaebeceedddeeccbacaaedbaebdcbbcabdeedabeeeeddadeeedabdcdebadceacbaebbaeedddbabebabeebaddddeabdadcaaddbdaeaaadacddeeadcacecceceabcbacaecbebbdbdaacddbdaeebabcabbdaddcccdbcbceeedabaaaaccbaedaedcaecdadbaabedecddceeccceceaadceeddeebedbeecdecedcdcbebbbccaadcbbbbddcbcdceeaecdbcceaaddeaaeeadbcadecceaceeceecaaddbdaececdeaabcadaceddeceacbccedebdbadcebeedabbdaeabdaeddbbcecaeaeceecdaabdcceaeccedeecacecdabbccddadcebbccbcedecebbbbcdcddceddddaadecbcbbcaabcaacedbccdbabeaeebabaebbecebecdbceddccacacaeaadbaacccbcaabccecdacbcccebdcbccbebbbbbdbdbbedaeaebbdceeeebbbceadcdeeedacedacbabcedcbcdcdbdccbeaecdeaeebdebdeaaedbdddadeacaaaadbabebeeebadcbdaebbdcbedbabddbbbbabadbcdaabaacacbbdcdaeecdbdeddadaeecbaebdbcbbbdbcdbcccbbcccddccddcbaabdaccaeedceadcabedcdabacdcbedaaadaaccbeaaabcbeaedbbdcdbddcceecaaacabbdcbdbbaeeddccdabbcedecdaedaedddedacecadbdcbaecaababeceeeedaacedecdeadaecbccbedbcadccdaeacdccaaedddebbcbcaacdcabccddeaddbcececcacbdeeadaaddebceaacbdbaadabceedaeedaadebedbcbdbbdadcbcbedbdbedbaedecbedebbbadbbbdcbdabbceaaccccdcccbbabcaddaababeaaaeecdaaeababecccacadbcedbdaddabeabdccaddaeedacbebaeeabdcadecadcadacdcaabdbcceabeeaadadecbebdbdccdabededadccbeacdeaabbbeacaaddcdabedcddbadbceeaabceaeabaedbebadbdbdedeeaddbedcaabeabaacceeccddebdccebedbaaaeecaeaadbddcceeeebdecbcccdeecececcaabdcceddeeaadddddcbcdedecdabebabddabcaacbedebaeceeeaebedbaacaddebccadebebdbebabdbbdcacbbcecadbececbeaccabebcaadbcdbcbecdbdacaabaabacbceeceebcddbaeeeedcecbaceaebeedbbecadaebaacecaabcdcabdcacbacdecdcddbdbaebecdecbccdbabcdbecabacecceceadcbadecbebedebcdbdebababcaadebedbcaacbdcebecdbecceedbabbedeeeabcbbdcdaeebccdeeeecbddeeedbabbdbdbaddecbdbadaacccadeeeccaadbbccbbceccaecbccebdbcaddddaacebacdcbadddcebdcbcbdaeddceabdcedbeaecceaddcccdbeaacedeeadcbddbbdeceebddaecacececcadadaeddedeeddedcdeaebbcbcbbaaaaceadeeacabbbdceacccabdacccdbbcacebdeabdeabbbebcceeeaaeeecdabaaedbaedbdedcdcddababacaaeccbdedbccbcbedcebbceadaaaeddccaabeadaccadecbdbbdbdacedcdebaaaaedbaceeaceabcdcdedbaeccadacbecdddbbcdccbeacacaecedaddebcccbbdbdbaccdaaaedbacebdadbbeddbeaedcacededcaaebeaedeaacdedbcbacdabdcdacddeeadaaebdcadeebaabdeccdbacdddabdbaecdceeaaeaddbecacdaaaeacdddaebcdeadcbaedcedcadbedbcdeeaaebecaabaeabcbdceacedeccadccbdbbaedcdeeebcccecadbdbbecaddaabaabcaeccdaedcadcbabacbcbcbdccbdaedabedcbcadcaadeeecdccceacedbecccebaccabbcedabddcbabacacececdcdadadbabedccdaddeaacedaaccdeeddabbaedbdadeeabceeabbeaedeaccaeeabdabdbbbbecddacbaeddcccabdbaacbdbbcdbbcdccabcbcaebaaceecadadbcbdbdedeabebadbcbddbecbbcebdecdbdecbbdbebdeaebedccdcbddadeecdbbddeeccdaedcadccbebebeaedccabbbeabdceabdedbbbbaeeadbdadaadcbddddbdddadcececddcebbadbcddedcaedcaabeacedabedecaaaebdceadcecbccadcacdbbeaccdccabaaabdceddacaceaedbbeebcdcebeeabacadadedeaceabcbccdacddacdebcbbccdddbedbdecaadcdbccbcdaecbcccdcedbededaeaecaeedcdabdecaaeddcbcdaccbaeedebcdbcdcedabebcdabccbcedbedacedbdeecbabccaaedcebcbabcceabacdebadedbeeadedceaaddebcbbbccbacdedbbdbbbadececabcbbbeedabcbaaecbbeabbaaadeceebcdddcaaabeaccedadaeaaeccdecbcdddbdccbbaebdcedcedcaeabcdcecedddaccbccabaaadcccdbbabaabccadcadeabcdbdcbddadeaacccdbcebdeedcccccccdbdebdaeecebaaedbecdaeeedccccbdeadaadedccbadcddeaeebdadeabeeadbdbcebccaeecaaecdcabebcccbbcbccecbebcecccebaaaecbbeeecebcaeacaceabadedbcebcbaeeedeaabddabdeccbcdbcbbcccaebdeebbacebcaaabbdcddacbdceaeacdbabecdedadeeeededeadcccbeaeadbeaeebbebdbcbbadbaeedecdeddacccabcbadbcaabebbcddeccceaaecbcaaebcadbaebddcdbccaeccbacddedbabbaeaceddaaeddecadaedddddeedcbcdaabceddaccbeadbdaabdedbcdddbcaaccacdcdecaccceacacacadabbeebbeaaaedcaaaadaebdcbdaabdbedadaebabebddbaceedbbddaedeebacadddbbccdbdbaaeecdcadaecaadceceeeccdbaeaadcadeadeebceaacadadcceccaebceccadadcdbbceeeeaddcaeabbcdcbbceecdbaaaeecabccdcdcecddaeaaecccbcadeebdbccdccaeceadddbaeddacbebcdaeaaeddbbadbdececadedcebdadbadcdaccebccbecceaddeeeadeeaebbbaeeeeebbeaebecdcbcdeeeeeebbaeadceedacecddccabccdedcdccdbabbbebbcdeebaccadaabecbbcbacbaeaeeaddaddacebcdacadbcaaacedebcadbbaaecedaecacbebaabdeaedcdbcaedaebeededbbcaaedaedbadeeddabdeabecccebebebbcbecacaeaadebeaaaeadbccaadebaebacbcdbaadbccebdebacdeabbacecaedeeedbcebebdedddcbbecedbebdabbeeadadaeedcacddadbddddedbadabaaabeacbbacdeddcdcebdbadcbcbbecacaeebaabbceabadccaddeaaeacaedbecccaaebeeebcdeaeeabcaaadaebaaccdcdeeaaeecdbbcceedcdadadcaccaccabcebacaeadbaebdcbebecadcceddabbabadaebbbaeedbebcdbacabadbdebebcbebdadedeaeccaaddbeccbedccadcedbacbeabaaedcbaaaacccbdcbbabcbdbbddaeedddbcdcacdbeaedcadcbbddcbabbdccbeaeeceddbaeadeaddccaddbdcabceeecbccbdacacadaabbcabdaebcedebcababcbbededcdeadceddcdcacecbdbdcdecdccdbdedeedadcdebcaccaaaecabbdabadacaccbacbdbcbddccbbeadddaccdbebbcecacaeecdeebabbcadaaeaecbaebeadabecddadcdeaaecbcaeebcbdbddadccaaecbcebadccceedacbdbaaeeeeacddbadbeecacdbebbdbeebebeebedeadbeeebbadebebddcecaadcddebedbdadaaebcccacadadeccacddacbadbbddababaeeebbaabaacebbddaaddbeacdcbcedccbedadeadddbeccbecacecbddcdceceabccbeaaaeccaababcbadcbaedcdaaacedcbeacadbdacaecadebdadedebeeacbcedcaabdddddbcceccedcaaeedbdbdecbdaaedbabdbcbcacbccddcbdbabcbbeccdabbeeebadeaecdcccddebecbdbdaeeeeeeaabeccdccccbcaebebbdbdbacccddecbcbaaaeddccaedadabdaaedcbaacbcabbbbadaecbceeecaaecaaeddcbcdaebbdddcabaedbdbdedddaaccceacadabbbecadadaacebeebabdeedbabcdcbecdcbbababebbeaeaecbaecdbbadbeeceadbdeccbeadbcacdedbdbdddabecabcbceeaddabbccebabaadcbeabdcebdacdaaaabeecbebebcdedeebbbdecbaebbcabcabaeeccaaadcaecaacdeeccedeeecbbacaaeeebeadebdebcbddcdadaedcbadecacdacaeaaecaaabcabceccaaceddaaacddbabcdcbbdebbbeedecbacaaeecddcddcabdacabbecdbeedcedaeddbdbacbdeabcaececcceecebdaeecbebecaacbaebecadaeaedbdbcdcccaebbabcbceeaecaebcebcbecdeccbecddceeebddeaeaaebdceeeaaecacedcacdaaeabccacebacbaaaeedcbceddbadcebeccccbbadaedddccebdcbcbecebdcaccdcceeacebcbecdddbccceaaabdcdbacbdebabbacdebeebccccbcddaaabaedacadecbddcbecbeedaccaacbbaccadbecacceaababbceabdeecdbbbcdceaeeaabeabdebdbdbcddcddeedcdcaeacbabcbbaebedeadaddcbbbcbedbebdedebecbadbbbcaacabdadcababeaacaceaaceceaeabebccadcddcbccabdcaaeabdebdbbdedaddbdbbacbcaebeceaecbabcaaaadabbddcbdcecadeaaacaccbaceaaaacbeecccdbecddbdedaaebbcedcedbaaccecadcbcdbbddedecadbbeadeedaccbdcaeababbaecbbeedabdcdaadbdbbeadddbdaccdaecabeadcacadebebbecdaccbecaecbbbcbaebeadaaedabecebbeccccadcedbcdabdcbbcdccbbdddbebcbcdcabedbbabaebcbbaecbcaeeaeecabeedeadccbdeecabdbdaddbbdcedbaaeaaaadbdbacaaeeceadcbeeccaadcebddaeadadbdeeaacaeeedcbbaedadcddbbecbdbaedeaebdeeaebdcaceeeddcabeaacebdeadebcaebdbebceabceccbbdeebcadaecedeacbdceddeaaebebcaecebdcbdebebbbcdcbbeaacbabacebadabdaacbadaceabebbceccacaeaccddcdcedbeaedacddeadbddbddacdcdebbbacedbeacbaedadadbacdbbdeeebcbabaeeababceaddedcbddedbaeddddeeceedbcedaddaeebaabcccdaddbdbaeedebbcadeeceedcdbbadbdaecdddcdcbaebbeeacebedbdbcabcaddbddeaeecedbedcddedbdddbaecbbeaebcdacedbacdbdeccecdeeaddaabaccbbcceeadddcbddbabdabcceadcdbcbaedbcaabbdbdaacbbbdbaaadcdddcebcadecaecadcebcddeadcccaecddbbdccbaeaadebdcadedcdebecdacacbbeaebcdcdeacedabbaecdadeecebcacabeaecddaeacaacbbdbcbcbeaeceaececbddbdacbcdadbdadcdaeeaeecbcceadadceabccbcebebbdcceeaaaabcecdbadaaebcaceacaccdedacdcabedaaccebcdbecdacaeceedececedbbbccecbeaaadbbbdbcadabcbacdeecbcacebeecaddbeacbeedcabbecddbbbcceadbcccbccbedeadaebdabbdedacebadeeeaecceeeadcaeceebcccabdaacbabbdaeedeeddcccdabcaebaaceecbaccbdaaabededbebbbeeadadebbdccddacdaeadcccbeddcbeedbecbccdeaeeecdacdacddbaabdabedcdeedcdbbdebdeddddabaadaebdacdcdcabbdbecdccdbabebccdebdddbdcadacbeddbbbbeaabdecdeaebddccebbadeaabeacdedaabbcecceacdbcccbcbbdeceeccedbdaeccccbcceebadcddceadddcaecedeaacecdecbaadebeeedbdcabddcbbcbbbebceecdcaecbebdadcceaacccdbcdeaeddaedecacbedeaccadcdaecdbcabecadddecaabcddaabebdebececadecdbcbeedceadcababcedcdedebaebbadcbbdccdbbaabaeecccabcedecdbbbccdecaadedbbdaebbdbbcccacbdeadebeedaaabdcaadeceeedcdacedaebbbdacaaababadeeeeeacaeaeebeaecebdecededacbbeaceabdeecedbebbbccbbaceddcadedacebeaadabaaedccdbbbdeaaeccecbeddbabbdeceedcaebebdaaabbaabdedabaebbacbbebddbccebbceddcbdbbeaeeadaaabdddecabcddcadaccdacddcacddcbbccaeadadbcdcdbcdecdbcbddbaaddcaadecaaceebacceacebdbeceaaaacbeabbeabeeedeaaabccaabdaaacdcbbdccdcbcddcedaedcbcdeebbbebcaacbbcaaecdbebdbddcbeeedcbeaccaacaeabbdbbdeaeccbdbecccbeccdccacebecebcdacbadaebbdaebbeeeedaeaebcbaccdbdcccdedabaaddbedcbecdcdedddbccbabaebcaceeabbdccbadbebadddeedbdbdecedebdabdcaaddbebdbdcdbdceabaebbbbbeaecccadcadbccebadccadabdcccacaebecdedbecdbaacbdaedeebecedadcbcbadbcdadeaabeebbbdeeeedaeaececdaabadcbcdadddaebdeacdecbaabeabdaadccdbaadddaccedddeadeadccbebaccaadbecbbbebdeaeceeedcaeabcebddcbecdcbbabdbadadbeacdadadebacabceccecadccebdecccbdaeaddeebcbcaabdaaeabedebdeecbebecaabacdbdecccbcdedddbbacecedaeeaacbddaecadccdeaacbadbcdbbbedbaaddbedddcbcbdcdcaabbedaecdbaadedddecdcdeebedccbaeeaeabacceeedaccdebaeaacaaebdcbbaaccaacecdcebacdbbdcaabedbeabcdcedddbeaabaadadbecbaeeccaaeeddbdbdbdeecebecbecaadcccbebbccabbddacdcceabbecdccccbddbcbddaccaebdbbededcbedcdeaadeeedbcbabebddbeaedccbceceedcaccecebadbbaebbaeccedcbceecebbdbcacbedaebccdedabdcccddeecdbdaabbebaeadabdabcbcbaecadaeaadbbdddaeecdadaadeadadeacdacbdcbcedcdeaedbcedbeeeddacbddbaccadbdaacabdbcdbbdaddaebdecaedacbccbaabbeedbbaccbcdaacbaaeecdedddbcaeaddcebbddeebcdedceeeaeaaebbeeabdeebeadeedddeebadccceeadccdbbcbbcdbecebecdbeecddeeaebcdccaacbedbebcdcadddcaacdcedebeeddeeccaaabccdecdedabbaecadbdaedbbecaedebbaadcbdaabccabcdaaecbeacaeadeeececdcacbecdeeaddebaacdddadeadebcceadcedcaabaacaacebddebeddbcbaacceecccdeeabebacaacedcebccbbceadecceeedeebcebedeacddbbbceeddbcabbaeddadbadddbdeabaccbdbceeabddcecccccecaeeaabacbaaababaadcbdbbbdcdcbcbccaedebcbdaacabcadeabaaaacdccaacadcaeabeebabbaaeabeeccdabbaebedceeccaecbecbbaeaaacdbdbdeacddcbeabcdcceaaebdaddccbaabbebbbaddaaabaaddbabcdababbcbaceeaedaadeaceebeacdadecddebabeceeeeddbaeadcadcdbdccdcdeaeaacbeaadacbceccacddeedeedccbddbcdaabbdaabdbcddeeacaaeaebeeeceacdbebcccddadddabebaabbdaaabedebadacacaedaeccacedccedecabeddedbebacadbadddaaedeccdbbedabcbbbecdcbcadadaecaecedbcddaaedcebdcddecbaeebbddbcbdcdecaacddebedacebddeccdceabcecabeadceccdabcbaadeacdbebcbebeacecbceeabbdceebcdecdebededdaaeacbdeeeecedaeaaddeedbcecaacedccaeaedabadbbdceebdcabbabdccbcbbdabdcdeacddadececacecabedcabdbcdbaeadaebbcdcbeeebbccccebeeeacdccddacbdebecceadecdbeeaababdaddadecdacbacceddbddabcccdccdaeadbcacabbadbabcbbebebecaacebdbebcdababbabadecbebeccebdcdaeddaacdaeadaecbeccdedabacddeeadeadedeadbbdaaaebbacdeeeaeaccdbedaddedbadcdeecdeddedbbdbaaedaecbbdddeadcacbbeccbaeeeddeaceeedaabadbabcdcdbacedbeaccedaadcaaaaabdeabadcbcbcdaacedebdaecadcbdadedabadcbbadecbcccdbaeecdccacbacdcabeaacdeccbacedeebcbcabddaecdbebcdcddaceadadeaccaedeecaccedbbdbdebceacbcbaeacdacbdaabbdebebbdabbaebaeaceeeabcdbecddecdbccebdadecabbbddaaeccaaabcccaacbdceaeebcdbacddaedaaeaeedbaedbdcadcacebdbdcdbcbdcaceaddaaacecabeeaeeadebbbeececeabcacacbadaaacbbbecabcecacaccaabdedddcebedacbaecbbeeeeccacedbebbeceeedcdbadebbcdceabeaadecdabcbaaedabceecedddbecdbdadaccaeaaebbcaebccacabeebcdabbbbbaeeacdbdbedaacbbaeadddaccaccbbdcebcaedbacdeadaedebaedeaaeecabaeaecbedbeacdaedbebbcdacadacdbcdcdcbaaebdcadbcdaeeeabcdcebbedadcdccaabebceacaadcbddacbadedcacdadabdcbaceaacaeacabbbcebebdacbbcdcceebccbcccadeecaadcddcedaceaececceecabeababbeebeaeddcbcbbdedccbbccbbbbadbabeceebaededdaaaacdbbeceacddceceadbaceccbaceceeaaeabceacdaaecadcbedabccdeaaecaeebdaeedbaabecaccaaccacdacebeabbebcddeaccbbeabbcdedddacabadedbaceeddedbbdeaaecedcdcaddadcbbaeebacecbbecceeecbaecbdeebedadbdbeddeecdbaaeccdececaebeadedaeacbeaadedcbebcbbeddddbbbacecbebbdaadbcdbcabceceeebeaacdeeaacbbaceeaaeddcbaaabbcecaadeacaccaddcadbecdbbeeecdacbdacdbceebcadeeadebdcabcbcaccaeebbbcabeeedcecbadceabdccdbeaccedacddbcddaceedbdceddbcedbcdaaeccdcabcebbcdcbbbbdeeddbddadaecbabdacacdeacdccddebcdebeebdbaebbddbbcbbbececedeccceeddaeabceaeeeecebeddceeaacedaacbadbdaedbcbbeebbcbddecccdbaebcecdeaccaaabbaeebeddbbdedaadecccaedaebcadbdabeeaaaacdebcebecbccdacdcbcaaaceeeebaadedcecbdacbbdeaeadbadcaeeaecbbcbeeedeedccacdacabebecbeeeeedabcbdbeeeddebcdceacdcdcceebbbcadddaccabadbabecbdbccababbbeebccadbeadeccabeeacbdaebeabecebdecdcbdaecbeaadecdbbdcccabbcddcdebbccedcdcabeaeccdeabeabbdacacabbcbdcdceecaaedbdedebcddaaaedebbeecdbeacedadcbaebbdeebdbabbcbadaaeabccdcacedbbdcacddbabccdcdadceebcdabcdebcaccdaccbacacbecebccabcddeeaebbdddbaeedccbdaddbbaabadeaadeddcbaecbcebdbdcdbccbeabeaaebbadeccceedaeabdadccabeeadebbdceccdaabdadacceaddebddecaeddebbddbccbcdcdbbdcedcebdbedabdecceadcbccbcceeaddcbbcccebbadabeacdbbaabececcedbaecaaaeacecdcdcdcdaadcdcecaeedceecbebbcabdebadeaecaceeacadceddecdadbbaaeadcbacbcdaaebeaacbabebcccddbcabaecabccbbdcdceebbbbcbcabdbbadbdebbabadcbaeedbdddaadddecaddbdeaacbdabccdccaaaacaeacddabeceebddabcbddacbacbaecbdeddaddabdcccbedeedabbaeecccbdcebeecaecdabebdbaaaacaaabedebbeaccedbcdcbcddebbacaacedadcbcaedacddedbebcedbbebedbbeabadeeedcbbaaacbedeaadcadbeaccbadaacdceeeacadceedbdeedeaadababdecbbbebbdbabeecebbceaaecbedccbaecbddeadcdaacbddabddddcebbcbabcedcbaeabababadeaaaccabacaaeaaeebaedbbaadecbaeeaeebcedcabcceaebcbcebaddabcceaddcccbeaaabcdebedbcaceaddbeaaddabeddbabeecacaaedbcdeaeccabececaacdeebbebdacaebcdabdebeadbeeecbbbaaecdeedcceaeabeeabbaeeddcabaebdadbaccbadaedaaaeebbadadeddcebbbecdcdcebddadeaecdceaaadacaadcbbdcadbbdaaedbcddbecdeedcadacbdaababaeddabbbcadcaeedbdcdabdaaaedadeacdccbbccbdaabaaabceecdcaccacbabcadcddadaabcccccecedbbbddbccdaaddcecbcceddedaaddeeecdeceedeaccdaeadcbeceebbaeeaabaaedccaacbdeddaeeedaadaaebdcaaeedbbccaaddbbbcbeecdaabcebcadacccdbacaeeeddeeecebdddbaadabcebdbacadbaecdaaadceedeaadaaecbebebadabcbeebebbccadcbdbbeacdeeadaaedededbdaedcaaceaaedddbaeaeccceccbdbcedbdcabdbbebdeedebaedbbbbcadaeccceaccedbeedcdeaaaabbedacbccbbcaebaaabeabededebcbdaceddcecedebacabeeceecdbbcedeaddceaeabcbbebdaeaacebeabadbadecacbbacecdcecaedecaedcddaedbeebccbecababaedcbbdcddceedeedbbaaddbbceeeecacbdccbaecaaeaaddacaaeabdceaceeedccbbbbbbbaddecabcbebcdaabacdbeddcdcbeebadbcbcceaebacecbaebbdaccdacadabddaaccdedbddeeeeddcabeeaecaddbabddccbdbaddbdeabbdeeaaadbdddecedacbbcecaeeccccaeecababdeecaccecbdebaeeaabdcdaaeeaccbaeedcbbdcbcdacaddeebbddeecdbcbccacadcccccddcbdeebabbacbaabaddcbeecddbeadeceacebacbcdcaaaebabeeeabccdccecacebcdaeadbaeccdeebcccaabceaedbeccaabaeadcbbcaabeeebdcecbcacbbaaeabdbccccabbecbcbdcedbbebaecbebdccbaddacbcececdacaaeabeaeacedadccabdaedebeaadedebdebbdcdeddbbbabaedaeecbdceeeedaeadacdacbacbddcadbedadebddeeecbadadddccbcacceaabcddbacecdeaeeadaababacbdacbdcedbabaddbaecbeaaddbdbedebaceaeddbebacdcdcacbbecabdaacdbbbbaeebcacaebbadbeceebbaeadceacacabbcdcededcecdacbdababaebeddcdddaededbacbaaaedccdaacddbaeeaedbccdbaedbcdbeebbdcccdabaaeabccebcdebaaaedacddbccaaadaecbcbdbdeabcceabcecedbcccbbaeccaeccacaecabbdedccacaddebdbdaccebcbbeacdabcdbcbceccaccdcddcbdaaabaeaedaaebdaabcdcabeeeeacaedeedbaeadeaedacaaadeceeeaaebeceeceecdebcadecccabbdadbeedbadeaacabcbebaaecaabaddceeeecceddeeadaacacdbcaccbaacaacdedeaccbbdbbacdbdbcebbceedeeadccdaadaabecababbaaccdddbaedddecebbbbddbcebedddbcebcbacaddcccdbeecebcaaadbbcdacabeebededaacccaaacedadaeeadacbdebbccaecaeddaabdecbacccbdeebcdeccabeaceceddbdadbadeeaacdbdeccbccdbebebaedaceaddcbacdbcbadceceedababacedcdaecedadbdcccdbaeabddcaeaceeccdaebdcbebabbaaeaeccbcebaabddedaadcdcaaeccedbdabceaceedeeebcaebaddcbbbdeceddcadabebceababcdadbaeeaadcbdacabccccabbdcebeccbedaeeabdcdddccaaabcaddabbbedeebdbdadcdedaddabaeddacdbabacaedaaedeebccacceeaecbbccdadadabcbebbeebabcceccaebbcdbcacbdaaeccddbabeadeebcccbacaecaaadaaddbacaebbdadadecedaeeddecabebebbabdcdebcacceabacedcededbaeceeaceccbcdbccdecddaabebdcaaacbbdaeacaaeebcbeebedaebbcedccdeedbdaddceecdaecbacddbebbdbeddbcbeacbaeadecbdadaaadbedcbbaaeaebcbbeebcebbbbccddedcbdedaeaacecebcaddabdbabeedbdcedcabcdacadadecbbbbabeccbbdddaeeccaeadaecaeeacdeabcddddedeecbdcaebadcdbbcacbeeabadcaeaceecadbaaadabceececebbbaeadddcedecebaeedbcbdebdceddabdacecabbdedcccbaeebbeacebeddcdddedcceaedbebbeebdeddbbaceaaadebbcaaccddecccebacebbdcacedbbecbaeddadcabbcdaeccaeddcabdbcadaabcebdbbcdceaeadbbcacbdddddccecaabbbdadbeaeaccbbbbddcababdccbcbeabdadbbdacabeedaddeadacbeeebbcedacbbedbbadacabeaeabddcbeabbedccbcbdbececabeacdbedcabacdcaaaecddaeaccbecaedeaecacbdaadbceecdacadcbbacceeabdedcdeddaedcbbeecedcbebeececaeeddeecebddeadbadebebadaeeadabdbcdbacbadecadbbdbdcbcdccbcbceecebaaecddcebcccabcbabacecbcebeadbdaaecaccabbceeadcdddcdacbedbdbbedbecdedbeeadcadccdbcdccaecedadecdccedaeebbdbadaebcdcaeaadddbadccdbadebbbccddeabeabceadcabdcaeeadbccdcdedbccccdbebbccabbbbacaabcdcdaebdacdbabbcbccadcaceacbdaddbeccbdabeccaeccadbbccdaabbdbecbebdabedbcacaacaccdbdaccdbaeabaaaedbedabbbcddedcddeabbeabcbbcaaebadeadaacadbbaebeddcbbccaabacdbceccbaecbccdadecceacabdabbaceccadbebeaacbdacabeeebdaeaeeaacbbeebeeaeacbbdcbcceeeebacbaaeeeedacaeabcbecabdebacbaabbddcabcaaabedededacadadcaaedbabbedddbdadcdeaddebddcacdeddbabdbdedcabcbedbbadcaceddcdbdddceebbeebddeaaaaceababccdacdeedeebebbaeabbdcdacaecbacbaadcdcabcabeccccccacaabdaceaababdccbdcedbcdcdebbbeacecebdececdedabbecdedabbedceceeecbbcadaccbbeaabaecababedcbeebbaadcceacadcebedadbbdedbddbdcccdddbaaeaeadbcdcabebcdcbebacebeeaacdeaaedcedeedbbddecdcabeecbbecbbaadbaaecebcbadecabadecbbcadbdadedaceebdaaebeecaeaeccebacaaaaeaabdecbedcaeadcbabdbebccdebeeaadadadbeacedbcedcadacdbbabddaeaadceeedbeecededcaaeebeddcbadceebadbbbabddbbdcacdbbcaecebcbbbbddbdeddebaeaaacbabacbcbeebcccedbcbbaaaeadcedaddecbeaabcaecbbaeedbebaecaedbbccbecdebabddaddbacdeccacdedbbadaeeddabdcbbcdcccdeaecbcaaddadbaecaeabccaedaceaccacbbeacbadbbaaceedacdeddcabcacdaececabbcbceaeccbddbbbdcadeeecbabcaebcbdccbaeaedeebceebecadddbcedadcecdbacadeccacbbecabbeecdabdbcbecdaccbbbcebbcdaaccbddaabeccdbcdceebcaceeecdbadbdeabcbbeeeebbedebbeecaadbdebccabaeacdeeadaddecbddcdcbdbdcecacbeebbbededceabaceebcabcbdeeecabcbaecdbeeabcebbdedadeecedcddccaedadcaddcdeeacddcdceaecaabcddbeeabedddecdcecbeadebaacccbaaccbbdcbcdcdebbabeabcbbaabecbddbbccedabcabccbacaaedbabdcbdbdacedcbababebbceceedebdcbaddbdeccdececebcbcdeaadeededcecbabccceeeebedaeebbcccabbebeabdedcaabbbeadbbeaeeccbcbbabadaaeaeaeedabdaceebeaecccebbebcdbcccecebdeeebcdcdebaaaaaadadebebdcbbbbeebdddabeaabbbeccaadcbecddabcaedeadedbcccacaccdeacadadcaeecdbaacdacbbdbcedebbdbeededcededeeacdeacdedcbbbdddabdcadddcbaedceebceadbcdecadcbacdbdbedaebbbabddaeceddedecababbeabeecadebcdbbcaddaabbdcdbaccaaddadcbededcaedaabaaceedadaaabbaceacdaababecbdacbcbddcacebebeeeadcbcabaebaaddbddabddecdaaedddacdbecdccddddceacedaededeebcedddcbdebbbddbccedcceeacbddbcabdbdcdadeabcabdcaaededdabcddcbbbeacbcccedecdeaacedcdecebceadadceabaddbdaeabaeeebddabccaccdeeabcedddbbadcceceddedbdcdbcdbdeddcdebecccabceccacbcbacdbadeceaabaacbdacbedbceaaebbecceadceadbdaabaeeeebaabbbdebbeacbdaadbddebddeadbedebbecedbcddceabdcceacddbddcabedaeccdddcecbbbbddbeacbbcdebeabcdecdadbaaeaceaaaaaabdeadbcbabaddeeecbbacdedcaeddcaecaaaccecbddaedeaaeebddbabeabaccaedaedabebddabdbedbadacbaceeadbdcaddadaabdbcadccedabdaaaeedecdaacbdaacbbabacdeeedcbbccdddbdebacceedadeacaadebdbbbdbebeecaddcecdbebcbbddcbdbeceaaadcddaebaeaeddbedcbdeebacbecaedaedbdccbaadeadaaedbcecceabaeaaddceacbddedabdaeabcccdbcecbedceccecaebeabcdbaaacaaebdcadcabacdecddabddbaaaccbeeeacaeacaacdedddcbdddaebcebabebdaabaccabedabbacddaebaccaadbedeaeabeebaeabeaacdabaeeddcbaaebaaacdbeeedeebcceceddaebdbeabddccebeeecdaccaabdbbbaebaddbbadaeaeaeaedbbecadddbdaeaacecebacaecdabbbceeccebbcacddaaadeaedadbdcdadbdeacadcbdebbeaccacadabdedaebdcaabaceceeebebdacbcddaadacbcacacaddccdbecdbcabddaabdaebdeacaeaaccacbdaeabbbdcecbacbcdbedbcaaabcebcadeedadbbacceadeecccbdabcbbcddbcbcebecdacbcacaaacbcbcdecabdebdbaaccdcaaebcccedcabbeccdecbdbbcabddcabebaceebeaeccebadcaeeabecaadbbcdbceadedcaddcacaadcaeddabcaddceaaaeaeecccdeabecebdcbebabbcbdddceaabcabcbdbbcadaabdebecccebebdaababeecedcaceecceebbdcccccccdaecabedaabdbabcccbadaeaaeddaeebccadaebdcdbddeabacaaececdbaeeeeaabebbaceeceedccdaaabccecbcbeaeaadeedaaaeaeadcdbcaaacccacecdbabdbdadcbbcdeebaaccdeabeedbaaaceedbecabddeedaaedceedecbdcebedcbaaeecdadccceeaedcaacecdacbaceebbdebbabbacaccdacedaeddcdaeaeababeacbbdcdcceadeabbcccbeadebbbaeadbbbcdaceaddbdebcdabcccbabeebcebededbbeaedddbcbaecebecebbddcaabbdbadbdbebdcebabccbecbedceeebececddbbacccaedeedbdbcbbbccedeccabacbbaadbcbabeebbdcbddbbbadbeecdeabdadabbdaadbdaccdbdbbeccedacaabcebbdcdbaccbbcbddcecceeaccacacbdbbdbeedcdbbbcebedeecdaaabaeaeebceaddddcdddaecababdedddadbbaaebaabcbebeaaaceebeceeecbccceebeedceccabeeeadedacbdbbdeacccedddddbbdaebecabeabacedbdaebeccaddabcaddacdbabbedecdccccdededbdacdedacdaaddededacabbedddadadabbceadebbcbecedceedeccedddcdadcdaceecaceaacedacdaedbbddeddadaaaaccaadebdcddbaeaebeecabadcddaedbbedbceabdddeeabceeabdccdbabeeebeaaaebaadecbdcdaccaddbebebaeeebdcddedcecddeececcbecdcdcbdccbbbcbcbbabbbcbceebeeecdbdbeeebaadceebbaacbdddadbddaeaabddadcdaaaddedcddcaebbceeccbecacbbbbebdcceeeabbabbbbbdaabbadbbadecbecdcaeedabdcddcbddbdddcbedcddccbdeaadeddddbdccdbabcbaaedeeedbdbcacaddaedccaeaaeaeaadeeabccbcbdcbcccbbdadecdeaeeeecdecbbcedbdaedbccadbbeabadabbcaaebecaeeeaaccccceaaecececccccaaddbdcaaaacdecbbaadebdddedcaeecabddceeacdaeddbaedceeeccabbdbecbbcdeabdcbcceadebeebbcdaebdbcbaaecdcbddaebbebcbacaaecdeaacdbaccebeaebadbedbadcdacabbebdeddcdedbbcdbbddccaaacccabaecebaebedddedddedbeabddbcbcbebbdddedadddebaacbeeeedbcbbacdcdacedeacdaacccbbadbdbcdabeeabbeedcdacdcdcccbecbaabaddcdeddceeddccbdadcebcaccecbcadeabeabbaedcaeddcedcacdebacbeaceedcdcadbeaabbdcbabeedcabaaceaccacbdbbcddeebceebaceaceeebdbdceadadecbbdaabdaaebbccaaaeedeabccedeacbedbcaadbeceadddacaedeabbbebcadcaeedcedecbaecdebedcacecbcaebdcbaacebaeaddabadbedadbeadaacdcbcbeaeaabbdedbbcebbeebccbcadcccdccadcdbccdeeeadcccddcbeccbdcbeeadddcebdedbacbecbabaeaacacccadeacddebdccdeebabbdeedbadbbadcaccdbbaeaeedbcaecbcdcdacdadaebddccdaaccaccbbedbaabaedbcaacadbeddbdcaaeadbceaeaeaeceddcacbcccaadcecedcdabbcaececdcabbdcaceddaebbcbbcedddcebbceedddabebbeabacdacbbbdcddeddddaacbbaedbdeceaddaebeeedbdccadbccbeeacdbaecdcaeedbdebddeeacdbeacbdaadbedbdaeeababcabdeedbcdacddbeccbccaeddaaedcbdcdcdcbeeebceedbaabdbcdceabdeadcccabcecbcdbdaceaadaeecaacbcccdbdebdabdabeaecabadcdbabbeedbeeaaacdebccbebaebebbeacccaacaeeecbdeccccbcdbcbaabcaabddaaacadddcdedccbbdeedbcccadadcdbeabdeabbdebaeacaeecadaeabcacacedaddcccadabbedaeababecbeedecaaccddcbedbeeeeabccceacbeadeabcedcebedcacaacdaabdcdcaccdaaceacbadbcdbbdbcbbddabbdbbacbcaecaeaecbbaddedbcaddaaeeddeaaeabacebecddcbacbadddadbcaccdeceedceeacaebceccaadebcbbddeabbdbebdbcabcabcaddbcaebecececaebabbcdebebdabbdaceeecdabcbccecbadbebeaccddaccebcecbbaceecedacaaeceebedaacadcbadebbbeecebdacbadacacbaeeeadacdcadadcbabeccddabdcadbdacadddcbdbddbacdbdccebcacccedadaacabecdbceeeeaeeeaaadbadbdeabeaeaaeeaacebcdeadaccccbacaabeaececbbcaadbeceabdaadeeabebeebbcccaeaacbbbeaedceabbbbbcddeceeeddddddebadbaabbeecdecdeaccccbcbbceeeedceadaceddbddaadeceebbdcdeaedeeaadadddaaacebdcebbdeacadadeacdacbcdeaaceebaadbbaadcdbdeeaaeecebabedeedecbabdbeceecdacaaaccabeabeaecbbbdcabbedeaadacbbcdddcecedeedabcdcacbceddabcddabeecaedbeabaacbbdcbcdceddddbcebebbdcabebddadcecaacecedeacedeadcbddeacbacbcdbbeabcadbcbaeecdcbbeebebddacacbbbcbbcbecabbadbbcbaaeacdbcdaacaddbdccedaddabbbcccecbbbddbeedaeddacdeaebebbbbcaaacabababbacedaceccebcccddedabebeeebddceeaeadeccdcebebebcdeebcccebecaabcdadedabebbbdddbedadaeaebdabebedeadecddbddbbaaccdabaaccebabbcedceabebeaddcedeabcbccceeadbaceadeebccdacaeabccbccccbacbddaddbeaeabaeddecbabadaeccaadbeebdadcdbbbeebcdeadadceaddabceaabbdbbeddaccabebbbbbbdcaaededebebbbceddaaaddebaebacbecedaeceaacadabdabccdaecbeceecdbebdbbbcebcbbacadbaddbadeccaeadcdebedebeaeaacbddeeeaccdcbbbbacdbbbbdecbddddbeeedebbecabaacbaeeddecaebebddecbdadadcdcbbcaabedabbbacaabacdaaaeeeadaeccdebccceeadedaaccbdeeacdbbeeeeedebcbaccedbeedbabeccbccddacbaddcacbcabcbddbbcbcddeebbaaabeadeeedecbddbbbbadebdceacccedadebaacbaacedeccebbdcdbeaabaededadebcabbdbbbadacebcdeeebdaeaeceaaaaaacbbdaeaaeadcadabacbcddcedaadbecdbbaecbebadbdbcdcaaabeccaeaddebbedcecbcbeeddbcccedcbdacabeeababebbbacecaebdaaeaeaaaecdddbbdceeebdabcbedcaedacddcbadaccbceebdaebbcbeadbbbcbbceebdbdecacdcddaaacadcbbeddecbbddbaacbebabacbaebceedeacacedecaabedcaedbacaebadddccbaeadebbeccbedbcdcebdeedadeedcacedebbdaeadaeabacacadeaedcccbaddcedeeabeabdeaeeadcccbcbcdbaeceddebcdeceececdecbceaadcacedbeeabeaedadcdadddaededaecbcaceaeaabccbeebdedaddcedebcecadedadceaecdccaaaebebabadcdcaaabcebaddbdeebabaebeeeabccccdcbcccbadcceadabebeeaedeaaddaaacedeebcbcdeadaaddbbdcceadbbbbcabcceebceaaacdddeeadbccddbddadbbbabcdcaccebdedebebbaccdacebadacdebacabeeaceecccddeaecadaeaeebccbbdcaddbdebbaadcebbedbbacdddbedaebceddbcbeeedcdecadabaaaccadbbbabddeedabdaabacaeabddaaeeabdaadbdcbaccedecddbdbbcdcccbbedcceeecddebeedadbcdddbedbceeccacbbcacdceabddaeedaaacbbccbaedbeebeebbedcdbceaaabcbeeabbbcadcdcdeccaedbcccadeaeeddebcbeddccbbebcadcaaadaebeaccacbdbccceeddbceeebacaeadeceabeccbcaedbddbedbccbacdcaecbaeddebebeacdbabcdceebacacdbacecbceddbabadaabbdbbbbabdeedebcccdeebbbadbbceaebaaedaeccdadbbeaabedacabcaecdbaebbcbaeeacbebedbbbebeedabbebbeccebcabadeaccdccaaddddcbdcbdeeababbbebcccdaccabbdadacdadcbdaedeabbbacedbdeddeaccdbdeccccdcaaeeadedcbeabedaecbbedaccababddecaccaacbbebdcceaaaaebcbccbbbeeaaecbacaaccebedcbcebebedeacedeececdededbcdccacdcedbcebbdaebdbbbaeabddbecbecebdeeeeabccccaaaeeedccbdacbbdbacebaebdbcbdcddababbdccebbedcbedbcebbeededdbdecbccbdabadeeeccabbdbdebddebdeacdeeccccedebcdbbaacdadbdebcbeacbdeacabbebcaacccecdbebdbceededbaeadbccacbdbbeacecbbeabbaacaadedcdddaeedecbbecaaabadebdabcacdccaebdaddbabecaaeceeecadcebedebbeeedecdbdcccaccbbccceeabdbdecbeaceeabcbbbecaeecdcaebeccaccdbabbdcbdedecdcbceaebaabbbaeddaacdcaabedcddcdecabdcbdbedbbbcccbeaaeddedcbaeebdaddedddaeaebacaecabbbcaebbecdeccbaaacddebdbcbebebdebcceaedacacedcebcaeccbadbebccbacdbbabacbedabcccdaceabddccbbcddacbcbeecdbcbbebecdbedeadbbacecbdddbcbdecaeedacbbeddcdcbdabadeccaeabaaedcedebdaaecdabbbaaedbededadedcbcaabdcaebeeaeeecaaaabbadeaeeacccddadbeeebbadbbebcecaacddedabddadbabcdbcebbeaaaaaeebabaadedeebaebbcbcacebdbcbdabdeaadbbccaacdbcebaeebbcaccadcadeddadbeaecaaeabbaecdcabcbeddcedcabceedaecdbabbbccbabaaeedaaedacacbaadeccdebbdaeedbeaecbdeadccdddddeaeeebbbaadedcebbbecaddceadedcaecccbbccedaeeaacebababacabebacbdcdddbbacaebedceeeeeedebdcedbdeaedabcadbaeedcbbdeaaeebbdcdbeebbcaedbbdbbdbbadbeceeabeacecbcaedebdbdadebdeececcacaeeacdbabddebedaeecadccecedeacbcabdaaaeaddcbddccedadaadceeabbeadcdadeceeebebbddcecdedbdaddcdbaecdeceeabbecbdadabdeddabdceeeaecdcdabccebdeeaaadbbeadadbaabebccdaebceeebabbdacbdbaddbacabcebaceabcedaeaaaececdbbaedbdabaccadddacadceeddceebdcbceeaededaadddbbaebdacbeeaddabcddeeecdebcdacedccbddbcbbbcadecceacacadcacabcebdddedbcebabaedebdcecdeadcbcdeaebedbcdaaecccaecbcecabbcebddabadcebcdbeeebbaabaeabbaddebebabbccecceabecbdbebaaedeccebadedaecadacdaebdabccabadcbcaccaeeddacdabaaddddeebbdcaddbadebbecebbaeabacabcbadadbbbaddddccabeebecebaceaeadcbbabbabecbdeaadccadaabbbcacdeeeeeddbeaceecacdbbeeebabecaddbadbadbaddcddbcbdbedebeababdeabaebecdeaceecbadabcccdadaaacdedecaeacabdcdbbeebbabedeabeabdaeadaabbcdcddddcdeebababaacbacadddecaadaebdcedddadababdeeacadaaedcbdbeeebedababcaeacbdedbaebcbceabcdeeaddeecbbbdcdccddededdebdeaeacdbccecadcccccebbacbacbaaadaceddbababdbdbedaaddcecdcaeeaebccccebbebeecbabbbcdeeadcadaedeaaaaeaecddaecdcedbacbababadadcecaaabccdbaebbbaeaebabdccbaceecceebecccababadcdeebedcdabaeeabbddadbebddaadcdddaaddeaaddcaaaedddeadaaaebbdaececbcddaececdabbbadeabebdbbeddcaadbcaadbdbbddcadebcbdabcdcdceaddcbdeebaecbddadeccebbeeabddceebecbebcaadcbcdddbdcbcddbabebbaebcbcbebeedceeebccabccbebcbbbbaeddeeedeceeeaacacbcdddecebaddbdbdcdbaacbbeaccdcaadecededdddeccaaacdbeedadbdeecbbbdaeebbbacadbbeadbddebdcebaeeeddcdedcbadaceedecbecbeebebddebdceadbecdccdcdbabdbcdaeccedcbdcdbaddeabddadabcabeeaaecdaebdcbcccbacebbedebccbaabbcbdeebbccaddeaabcccbddabecabcddacddedbdaadeadcccecaddaedcbaeadddbdceaedaacacdacceebabbededbcedabaebabebeaaedeaeccaaddaeebeabadcdcbccbeaebecaaadaecbbadeeaceeeeedbebedbcdaeadbadcdcecbcdedacccceaeaddeecadbdbeacedbaeddeccdbaebcabacbcdceedbbadecddaaaaceeebacabdececbceeedbbceadedeadbcddeaebccebceecddadeacccebdbbcaaccbeaeccddadedcbadcabdaceebeacabbddbeadeadaeecaecaaeabcaddaeeebdbcbcaaeaacccbbdddbdbbadccbcccdddebccedbdaebaaaeddacbceccccbddaeecededcdeceebbeaadebcddaeaecbeaebdddecbcdcdbeceecbdbdbdacecadabededacacceccbebcbbdddebaaccdcddcbcddcabbdcccbcabdecccbdeccdcadeacbbddbcbeccbaacdcddcacaeaeddeaabbbcbcdbadbdabaeaabadabdaeccabeccdbbcdbeadccbbacebabeaaddabeadedcbddaccebeebdaeabdebbdcbceabdeebaaeceecaaccbdaccaccaeaddeaaeabbcdbeaceceecdbaaadaabaaedcbceeddbbcdcccebcbecdeceeabecbecbecaebbbdcdbcaaddcadcbbcceebceacacbeecbaadabacabcadcbadcedacedeaedbedeecddcedcccadacaebaaddecbdccdceabaadabceabcedbeceabecddceeaaabdacadadebdaccdcbbcceccaadadcabcabadedbaceaeaccdeccbcbabceeaabdabaeaaebedaaceeddeaadadcdbbcabbbbadddcbcbeedbceedabdecededecccdcceccaebdecebcaeaacebddbaeaaacbccadecacabaecbabadceaacddbeaaccbcabedbddcabaddeeaeaceddcbacbeaddbbaaabaeceddacdeedcbeeddabdaeceadeaebaadeeeacdcdaaeaeddcebdcabadecdbdedbcdabeccceaddaeecaddbaaedcdcdabdadcecaeeadceccbbeeaecbabaacccedcbebedccaecdaeeeebcedeabbaeeabebcddbdbaeeaeedddcdbaacdecdebabdbbbcadcababececaaeacdbcbecebadccdacedabbbbacccaecdcdcaddaecddacaebcdedaeaddabedbeaeedeeccccdcdceabcaecbaccabddeccedebadbbceeeabeccebdadbabeabbbcbacdeacaddbeceaadcbeedcbebcdacacdcbbaadebeacebcbaebadecdcccdceedcdaadeaabadaadbaabccbadbcbdbeeadbcbbdedadcadcebcdabbaedaebdebbbebcdbecaebaeaddaccacbeadbdaeceeebbdeeabaababeabbddecbaecbabcdaddbadbbbbeceaedbcbecccebaceeedabaabeebbdabbbaadbdabadadccbcbccebceccbcdadebabdedeebcddaccaacdeacbeebcabceeedcdbcbaedcdbcbdcccbecceedcbeeeabebeedccceeebbacebdcdcbbcdbbbeedcbceedaebbdceddaeabcdabdbceadeecaccadbbeaaeecdcedaadaddcaedccccbcbdcebbebaaeabeaaabbecdcccaddbebeaadccbccaeaadbabbaaadadbecdedcbbeaeabddedddbeecddcbcadebedacceeacecaecdeeceeecbeedbacbacdbcadbcdcddeeabeacadbdcaaebaabceecbdedabaaaaedeacddbadccbbaaeadacbabaccebdbdcdddcbdcadbadabaebebacdddacbbccbadeadbbabebdeadebdaccceccbdecbbedcacaeaebeedadcdeccdcebeccaacabdcddeeeabdabbaebbecaedeebdeedbeabdcedabeccebebbbabdddaaedcedbabbcbddbaacddbaceadebdcacbeecaacddaedabbbdedeebedadaecbdeadbeedbebddeeceacbaddcebdbaacceabecdaadbabdcddaebcceeadeecabebacdceeecaebcdddedabacdabeeebccbeeceeeddaccdbbdaadaceeadbdeaaccbbddbcdbeeeddbaebccbaaacdbdcabbaeeaccaaeacececccabebddebeaeebcedddbbaecadaeedeaacccaceeaabbabbbeabdacbdadbaaceaedcdcbdbdbaecddaeaaaacccdadcdcbabeeaadabbbdcbeddbeadceaacabeebdbbdcdeabddbccbbbeceeedceddcddbeadaeeeeeedeccbadddacdeebdeaccaaeadbecbebaebdbcbcceaeabdcdcbdaecbbebeeccacdaceccdaecdedbbaddbabeeccedaebaeddbcceeedaaacedddebcadbecceabaaacbaeeabeaecabeeecdebcbebbeaaedbbaedabaebdecbbcabbadbaaabededbcabdddeeaeccdaaeceeddcaecbbedbeaaeccbdbadcbeceabdaadadcceadbadedadcedbdbebeedeebadbeaededeeeaccbcdbcbdeaaaebeeacaeacbeabadeeaacaedeeaadecababacdccddceaeacbbbaaedabbeadcdeddecaacccaaaddababbdcccedddaaedecebabacaaaabbbebdaddeeeacbbadaacecdcabebcaabceaaebdbbcabdbadbddcdedbdeaacabccbabceccabedeeebcecbeccebedccedceeeedebbedcacecaaacececcdccbecbaaaedebdbababaabadbecbcaebbeeeeaceaaceeebaaceeabdeaeebcedcdadacccbdcacadeaceddabedbdbceabcbbdbddbbaecdecadbabdaeabcbdeceeedbcccdeacadaeacdceddeecdebbceeaebcebabbbaaaaeeabdbacddabcdddbaaeacadedcbdabdeaddddcdebbcacbcebaadeacdebecaceaaadbcddbddbbceeeeaabecadeccacebbabbbbeaccbdbbcbeeadddabdcddbdecabcdecdceadadabbeeceaaddcaecbaadcdedcacebdbdabbeeaeaebcaebcababeddbbdbedbbeddaaeedeeeabbaebcdbabdaccecaeadeeaecacaabdbbbaaebcdaecbcecccdbeedecdbcaecabeaccacedddaaedbadeaaaaadddaddddbdccebececcebadaacbabcacaccedbbcdddcadcceacdebacbddcbbddbccbcbbedbaeaaeeccdbacebcdeacdbedddedecedcaaedacaebeceacdeaadaddceaebeceabdadebcbdddecddccaaeeaaecdcdabbabececeddbbbcbdcdabbdbcdceebbcccddaacbdedbacbeeabddcbabecdcdddacdedbccadddeeedbdcaaeccbabdaeabacacacaddacbcaedbaecdbbdacedaccbcaaccccceddababbcedebcdbdacbddcebcdecababdceedddaaaadccbccdceecbeeabebebedbdbbdcbdbebaecbaabedebdeecedecbddcdedddeebcaadcaebbceebeaaceadcaeeeacaddbecadebbdddabdaceabdbbedeeeedeebcddcdcabeccadddebbbedcacdcacecaecbdbbebecccbaddeccdaceedebddcdeddbbebebccebbaeedebcbebdccedebaebcabdaeacbcacbcbbeabedbbebceccdeadadceacecbbcbecdaaddcdbeedabbcadccdeceecdeddcbceddbecbdeadccececbcdeeacaddcaaeaadebdcbebeecbbbbbcbeacbebeecdcaddeecaebcacebbdacebacddaceaaabcbbaddabbbebcaeeccbdbcdceabebccacbdeababcdceebcaeeabbabadbdaaeeecaabaceebaaaecdebaeaceeedaccdebebeccbbbbeadddccbeedceeedceabdccbdebddaebbceedddacdedbdcaddbaababdebaeebeebabdeeececadbacbcbbeddabdaaadbddceccbbebcaadeedeeccabadcbcbcaebeeceadabaeadddeebceaecbebdabdcebccbbeeeacdbabedbcbbbdccaeeaaddacbbcdaadcbcebdaadaaddbaecdddccecccedbcbddecdccdddbeccbbadceebacecbbcedbbbaecdccbcdbbabdcadabeacccbaacaeccabebdddeaebeaceddebeadbaaeedaddcabccbdabddddebbddadeeedeaeaebdddbbcecdeebeadccaedbbeecdcbbaeddedeeaceaaebdceeedbcdcecdeaedcebcbdaeeadeecababecbadbbcaebeadbcbcbcabbcdaecebbbadaebadbcacaeaabdecbceccddcdaaabdeebdbebeeedabbabddcabcadceacacaceacedbeadccabadbaccccebadbebbbaccacaabcbbeddacaebddbcbdbdcbdddedbbeebeaccaceacbaeaacacabbaceceedbabccdcbebddeaebccbedaeaabcceeadecebebdaebbbeabacdbcabeecaeceeebcadacaaddadbbadeaeadbcadebcadaabdedaeeacbbccadbbeaaecebceceedcebedbdccdbdcedaebddbdbbddaddcccbecaddacccabcccabdcbdaaacdddbcedbadedcabeacdcddebebeaaedcadbdbabcedababddbadddaddaddbbaaeecdacacddbebedcaadedeebecabbbbcebbaacbcebbcaeedecbcebbaeadeecbdebcccbadedaaddacecbacaabaaebbeeaaddcdcbbdddcceaaeeaaedddaebdeeceddcabbcebaddbdccaadeabdeabcccdcaaceabeaeabdeacdebbbcccceaceacadbbcabdadcecddbeaddbccaadeacdbbbbaeaedcbcccbcbcbaeebbabbdaeeeeecedeabcacabadbebbbddbbcbaacaaeeebaddbdcaddaacecacaeedababdedcdccebbabeadacacdbaaadccbccbdbebbdcecbdbaedeabdebcacccccebeecbdbedeeabeacaabaeccbedbdcaabcaeddebbdacdccdeeedaadceebceababeebacddacaeaaccadaedbeebbbacaddbbeabdeacadbdaaabbedadabcbddaebaebddcceeddacbecceaecabecdaecedebaaeecccdaaeaeecabcedadddadcdddbecabcccbeebcabaeeecebeeeebaaeabdddbeaeaebbbcbbbabeabdeeeceeeebbeabbddeeabcecbbcaebdbabbbeeacdcdcbabbaacdedcabbeceeaebaeadecdeeeecbebcdaebcebdcebccebdebbaabcbbeacbaadddbcbacdbbbeedbaddecbdeeaabdeeecedaeebeebbbdbccdaddababdbcbccdbdcbabceaccbacabdcaeeeaebccabaeacddaeabeaaacbdceeacedcaaceadeaebcdbdbaccaaeccbcdcaeacedccdcdacabeeadabaaadadbebdeecaeeacadedcaacbecadbaecccccadaccabbdeccdccaadbcccaddcaddeceecceaeddceeabaddaddceabbadcddccbbcdcaddacedaaebdbcbbbdddebdaebbdedccbeeddedddceedbcdebebcccbaacaeaeebdaaceacebceeacdeecdcbebcbbeeadeaedccaeccedbeeacabacdabbeecedccdedccbceebcceedddadedbecddcabbcbeccadbdabebdecaabadaeabaabdeeccabcbdbecbcabbddcbaeccdcaeecebbecddddcbbcbeadbbccdceaaedcbbeccaaaabacabecadedabadbbdcaaccaeedcdbdbedaecbaccaebeddbceecddecadcaccdbddaadbddaecebbcabbecbceecddbacbccacebdebadddccbdcdaecdbaebdebeadedacbeaceddaabaaeeeaaeedacacddcdbdeddbbadcbcebbddcbceccaabbabbaddbcbcaabecbdcaaedaaacccbabcdbecaaebadedcacebebbabbbcdaadbebeddadccbaeaeebddceedcedbddcecebedeebabcecacdbeabbaceadeabbeebabeceeebddaccedcedbaeacaeeeaeddbabaeeaeeeddeebeeabebeebbcedceaacdaedbbdcbeadcedcedccbdbebbcebdcdbbedadeedeadcebbebebebcabbccbaeebbedddcccdccbdaacadbecabbdcdddbeeccdbcdeccbaccbbaeacbccaaacbdadbaaabbdcbeeaabacebaeaabcebeeeeecdbccaeedaeadaadebacaabdeedbcdaaacecbebdaaecddeceaeaaebaedecceeebbeadabbbeebbdedabebcaaaabaeebbbaeaadbaeacaacdbcbbcbccbddadddccbdabbcaebabaebceccdcbaeedaebccdedadaeaacbabceecebccbdbacbbbaaeaaedbecddebdbceecaedbaaeccdabeabbbbdceaadeebacaccdcacabaaabcecdadddecdceaeaeaacdbbdbddbaabdebadbbdecdbcacbdedbcbbeeaedadedecbdaccaebebbcadbaadabcbbabdcdabbeedbdddeedeacadecdabaaecbadabddaaddcacdbcaccecaabccadcadbddaeeccdcaadaeaeebabbeeccadbaaebcdddcbeecbbbbeceaacbadcccbabeaabdbcaaedcddbcecbeccecedaedcdedbccaeedcbdbcbeebbeabcdeeaaceecedbebadadecdcbcececcbdbadbabacadeeedcacdccaacacaaaebccdacacecceccbcecdbecdabcebcbdeabedacbbaaebebadbbabeeddacbcaddedbedaadbeacdbcabedbcdbdabbeeaebeaebdeccbabaeacaeeeddbdbdbccbaccabdcabdddeccecdbbddbbebddcadcaeadebdcddacaddbdabdcbaddeaadecbcdadbdadadddaccbdceacdebdbaaebdeedcbdccdcddbddebdbeebbcbbbdacadeedbacbdabebabbdcaeaebabeecbccbdeaacaccbacabdadcebbdeacbdaeabbcbbecedeacadceaecdabedbcddebdacacdbbdcecedbeccceccbecddcdcbbbabccccbcbdcebbdcabbcbdaecbebcaddacacbcadbdcdbcddcecbbbabdcbcbedbacaeaebaceeeaaeedbeecbedbcdabedabbabdbabaeabbdaeeeeccebbaaadbebcdecdcbcbdaceaacebacdbcbbccaedbecbbcbdabccbeabaededadbeeacbdbebdcebdacddeeeebaebeabcbecceabbbeacdbacdbddedceccbbdaabeadcebacdcbcedaebeadbaeaddadacabebacdeaccaecadbdceebbabdcdcaaaacabdceaeeebcabecebbebabebaabeddbacbaaecbddecdbbaacbcbebaaeaddbdbecbeeccecedeadebbdcbaebbdddedcbdcecdeedadcaadbebbbaebbabdabeeaaacebcecdceacbaaacedddecbcabdbdbbcedbdecaadcdccdddacbeeededbedbbaacdcceceacbabbbdacbecdaeecadedccdaeeeececabeebacbecebccacdeadedeedaaccaaedeecbacbddbbaededdaaaacdcdcbedcecaeaacabdadcbdbcddcddccbbcdebdbddbaabbaabeceeacddbcaaacadcedabcbdddcacdabeebaccebebbeeecedabbbbbcccbbbabdbebaceeaeabdcaedaddacabbecbddbabeccbbddbceacbeaaedcbcdbabadeebcbddcbcaedabcebaaccdaadabebbaaccdedbdebedbaeccdcadcaeabaeedbcebeabbaeeaaddceacddedceccddaaebbcaedbecdbaaadcebbbedaecdddecdbbabdbbbabdabcbabcaaecbaccabbbeddaadcaacaadbabecebeaecdbcddbdbdcaaaadcebbadbbadcccdbcababaddbebacadecdeecdddbbddcbbadceebebbedabbeccbcbdbcdaaaabbadedadababbadecbaccabeadbbecebabdacaceadedbbcbbebbabbeccbabdbcbedeccdddcabbeabccacbbdcebdbccaaceddebdddccdebdccecdadbacecdccbaeeadbabbaedbdbacedaadcbaebcdeeadebbccbbeaaebecdbacaecdccceccaadadeaccccaaeceebbcaabdcdbeccedbabdaaadaeeedddaecabedbbedaabacdccbcbbdbcdcdeeaceddeecbeedddbddcdeacccabeeaeadbaecdeddcdbbcedaabeaaebddaceddaedbdaadadddedeadadabdbbeedebeeaddddebdadedddbbbebabeaacccebcceeaaccaecedccabeaaabeabebbdaebaabeeebeeceecdcdacedebeecbdcabbcbdedcccecebcadcbeeddbabcbdbecabacbebbeeceeecedeacabaeccceecebbdcadbeecabeecbbcbadabebaaadcbcdddddaececbcabdceddaadabeadabaecbdccadbaebaebdddceadaadbcecebbcaababaabcbcdcdaebbebaceddcbedaaeadcabaababbeaeaacbaccdcaadedeeaeecccaeedeaceeeaaabccaeadccdcdacedaccbabdeaddaabdabceaccbbcdddcacbcaabdeddacbeedabebcbecbdecebebcceddacedccddbdbdadadeeacdaeceaabdbbcddccccaedaabeccaddacacaeeacaabdcdaccdcceededebbedeebdceaccccdcdecdbcebedbecbceccbbbacbaddaebdbdecddedcdbbbadbcaeaacaacbadacddebeaeaeaceaeaabeeeabbadbcedddedbbbbacdbddebbdeeebaaaeedcbdeaeabcdaadcadaeaecedcecbdabebacccbbedbeccadeeceaeaadeadbbeaadbbcabcabcebdcdddeaeebdbdebadcdebccebeadacadbeebadbdeccbaaabeabcdbbacaedebecbebaceedebdadaaeaebedcbcbceeeebdadceaddaaacddbecdeaaedaceedbabcadaeadcebcaabcdaceaeecacababcddeadceaeedbcbdbdecadedeabdcebaeebeacacadcaeecbddabedeccadbebcbaeabcbcadcbebdeebaadbabbcdeaacadbaeadecedadebddbeccccdebeccacabcdddbcdddabcdebaaedbebdeccebbeecbcaedceaabcaabedbcedadddbbaaddcdbaadceddcbdbeedbabbacaabeabaddaacdbbdceccaceadeeecbacdacbeebbaceadbbdbbcbaadbcaeeaaaababdeedbcdceceeeaecaebbeeabbbcacdbaaeccdbaaecaccedcabaaaeecbbeebeeaebcdbcabbcedeacaadecccceeeaebcdedccccbddeddabbacadaecabeaedcebabcedaaaacdccedeebabacedaccbbaccbbcebbadcddcaaeaaddabddbcdecbdcbeecaeceaeededbeadbdcbeeeaeacdbaddabecbaceaceaeddbccbebedcbbdaeaebbadabaedccdabcbbaecbbdadebbcdcbecedbaaeceddbcdcaeeeacbbaecdbaabbaaecddacdbabacddcbecbccdcbedceeebddcbdedebddeccaaebdbbbdaabdcdedeabdcccaabdbadbabaddbdecdaaceeacdbaedadcbaececaeccccabcdbaaadaaccbdbbdcbaccbdecaeeccaeceddeadcdbbdbdcedaaecaaaebdcbecaebacdaddcacdddbaeadcacecacdedceaeaadcecdcbbcaccaaedeadadbcaacddddeceecbdceabdbdbcebddaecdcccaadbadaceeabdecceeeeeebedbaaaaeebcebcdabaacabaeaedeeaaddedbcbbcadcbbcaddaeeadadbdecddedbacbeccdebaebeecbadecacecceccbebadaaeebdadebebaaeccdaaabddbecbcdbbecedbcaeebddbdcccbbcbaceecacaabebdccdadcdcededcacdcdceecdddceeaabdcceaaaddeaaaeaabaadabeeddaeebbbabecccbeceebebeddceeeaadacedbeebcedeebdadeaedbebacbbbcceedccecaeeaabcddcdccaebccbbebacdccbcaeddacaceecaeaeddeaabcbbddcbdcebdbcbccaaabbeacbbcccedcbaaccadcbeadbedabeeeddbcddecaaadbcdeeaeccbddbacebbdbecbebbdcabbeddadedecdcceabbbbceeeddaaecbdadcdeeceacadbebeeaaaaeacccedeebecdaeaebbdbcceddbaabecdeedadbdcadbcbbdcabaaebcaebbadcebcadadcddbeeabcadddeecdbbedbcbbbdedaccbdcbabaccbddebcdbcdaabdacaaedbacebdcdbabdcdaacbdbbedcccbbeebcbdbeebdbcabacaadcaccdceedcccbdabbbbdeedeaecadbeddcbdbdabdccbecaedcdeeaccbaadedaeadababeaaebddcabcbddabcbdbdddcacaeebabceaebaeadbdbcdaaeddbecdaaeebaccaaadbacbcaedbacaccdcbdeeecdaadebaaacbcebdbaecbadbcededccebddecedbbcccbadedcbdccdbdceabbbeaceacabbacdddeebbbdadbccacdbeceacdecaddebddadcadecaadedcddbdaebaccabbadeaeddddbbbeaebdbadecccdecdcceaecdeebeeabeeadccebcbeeabdacbedcceecadacbebbdebcdbabedecaceddaabbbdeeacecaeeacbdabaeecbeaddbecaedebccdceebcbaeedbdacbeaaebeeeedcecdbdcaebbddccdeadbcbccbaabedcedbeedbdbeedbdcbddacbdadebddbebceccebdaaccaaadaebcdbbceabcdadabedadcaabcaccbabebceccbebdbadbcadadcadedeecaeddacbccebbabeadacbbdaccaabcdbbdabadddacaaccddecdbccbacddddacdcdbcdeddccaccddbbdaadcadbabbabdecdecadceeeaeeecabecdedbbbddbccbecbbacedbebcbabbbcdddacabedbeabbcaebdeeedccadbdbbcaacbcabbbaddbbeaadddbacaacbdecdabcbbbabcabbeddbacbccbccecaebdebcdbabaabdabedccedbebdbabbbebeedcbbaccebddeeacbeabcbcdbcccaedccddeaaaeccecccebdcdddecdaccdbaceeaddcaacbecdabdbdedebbacdbdeebabeceaaaccbceeacbbeecddebaacaedaecbbceeccabbeaeeccbccabdaeeeeebacecadbbbedbabdeecccaecabcbdcedcadbebbbebdcddceddedbdcbbbbaedcdbbeaccdbebceadaeecdcbdeaebcdcbbdcaadebbaddeabbcecbeadddedceddeabcebabebccdedbeeabaddccebbcebcddeabcbebeedcbabdeedbabacabcabdceabdbaabceeebecbcbbedcbeacddddceceadcdcecdbaccbddcceacbceacdcbddeccaedcadaaddcbeccacabbaabdcccbceaaaabedebdcebebbadbabaaeacdddadebabbbacbdbeecbdaaecedaceebbaacdbeeacadadceddedbabadebdabbbdbcceeeddebdaeeeeadeecadedababecbecdadabaacacaaccebeddecdedcddcebcbbaacdebdddbcdcacaeaaccdddccadaeabeadadddabcccddaeaedbaadeaeecdcaaacaaddecceedecddeccdacbdabeecebddbacdbccaedbdeaedaeeebacacbddcceacdbebebbdeabecebeddbacbceecbddbabdbeaebceeabecceadcaccaeeaecedaddbebcddaaabeddbaacbdbbdbccddaddacdacbbeeccaebdceeddecbdcababdaaeacedcacebbcbaeeccddbaaeabacadebbaabbaaacaedccbdcbeabaeadddeceacbbdccbdadedbdeceedcccaeadbabdbdaeeceeaaacbebabbdbaadbeeababadbedccecaceceaeaecddebaecdcddaaadedcbbbeceabebcedecaeceeaddecedbcaaacdadadcebddadbcbbbbbcecceacdeacbedaeddebdebbbaadcbcbdadcecbecacbcecceabcecdaaababccdebddccedccdeaedabcccbcbdcbacccbbaaadececeddabddbcbaaebbdadeecbccdabbaeeaebdbbebaccacbcbdabecbddebccbaeabecbbcecaaabadeabbebdccaeaddacabeebdaecbbbabbadbcacedbeaebbcddceaacdeebaacabaeedbdddccbbcceaecdacbaddcebdacdbdacebaaaddcdddedaedabaeddabbadaeaecbbbdebbaccdebaaebacdebbddadcedbcbceeedbdddbdedabaddeedcebbcccaeeaadabcaaebbeddcbbadeaebebccdbaceeeeacebedabbdbcabdeebcdcbdcbdeeecdaaddddcebdcceccaecdbdcdbacceeeebbdcecbaaeecebdececceababdebcbaaedaeeceadcddbbacebdedebddaadcbabccabdacedebacdcabaadcbbeaccaadceededebceccdaddcccacbacceebdbbbcdeacedbecdddcbacbdedcccaeccbeedbdeeeabdacacdaebadaadcdbbeececadcdcecbcdeddcaacbdabdadcbeccacdedaddaeeedcedbbbbdabbebcedaecbdaccbebcdaaadaddabdaeccdececadddbdbadbcbdadeaebcbcddeaaddeddbdabacacebbacabeaaccbbdedcdcacabecaacdadebecaabbecbeeaeaedbadbecbbeceeeedebbbaceccccdeecddbaabbcbdeecddbecbeecbdcdadaaaaeecbabeaebcbebdbdadcdaedaeadaebbecedbecaeeadebcabbbabdceadadecdeeacbdebbbadcbeceecbeadcdeadbacbdaddcaddacbadabdbdeeeecdbacadbbbdaedeeaeebcebbcaaecbebcbcdeddcaeedaebbcbaaededaeceacbdbebccacaadaabecddbcedccdbceaeccddbecbaaebbeebceeabeddedacaaedaceaaccbeeadbdbabeecbbbdcbdadacadadccaabbdbbdaedeebeeacbdeaacbebecbbcbbbbebedcceebdadeeeddbedcabeeadabdedbdccdbeadabaeaaeccddccbbbdcdbdbaedeccadbcebabbdedddcaececcbadcdaaedbdaabddbbadbbbbeabaaeadcbaeadebcaceadecddaddacbebceabaacdaaebccdccbbdcedbcabcaddeeceaaacaaeecaedeecacbeecedddbeeebadedceabacdcaacacddbecccedccadaedaecdedcebdbcadbeabcaeeadbdcaaedeaaadbbebdbabeabcbdbbeccbdddcaeababcebbcebcdcaacbcbaecebbcadeecceebbebdbdcbaaedbecdcceadceacdecbaceeadeadccaddbcdbbcddbbeabcdeaadddecaaccbbaeaaecaabecbabadedddbecadebcdcdbaceeaacddadcbaacbcbbdbaaaceacecdabaddbdcdebeabbcabadadbdaeceeddcbeadcccadbdbbbebdcecbcddcccdbcbeddedebeabadbdcebeccbdeecaececbbdeabebaccccbbeaeedebaaeedeaadcaecdabdaaeeddbdcbcaaddcebcdeeaacaeabbeedbdabcaccaeaccaebbadcebceaaeadabaddbbbcbcbbebabbcbecbdcaacbdbddaebaeeceeebaadccedecadeadbaebeaededdbdbebdcbbedddddbaccdacbceeecadbbccdddccaecabedacbacdecceadbcabcebebceddadabcaeecdbebebabccddecaeabcdaaebdbdadcbbaabaabaecdeadacdacebccbedccdaecbdebadbbacabcebcacbdcdaecabbcaeeadcdaeaddbdadcaeabaedcecdcbccdbadbcaddbacbcacddaedaaeaacdbbbabdbeddadaabcebbdbebaedcdedabdcbabacabdaecaaeaeccccbbeaeedacdcbdbcaabaeebadebecedebbcaeeaaedeedadaaedbcdecdecbaabcebebbabebbadcadcedcbdcddadbbecdcddcacdeabeebbaabbdecdcccecdbbeacdadecbceedbcaedacadcaebaebeeeebaaeebeaaebedeecbceaccebdacddeeabbdedebdbecbdbacddacabeacdbadaeccdeacdbcdeabbdacdaccaecccecbbddecebcdcadbedeedadceacaddcbcdecabeebadecadbcbbccebbddbbbaeceddbbbebdcdabaacceecddcacadbaadcbdacdccdaadebedccecdabdbbedbbcbadceebcaccdeceecdbacdabeececbcaedccbeeccccdcbecceecdbdeebadcbdadccbcdbabdceadcaddaceeddaececdaddaebadbabbecbceabeeaaddecdbbaeceecaebebcdbedeeedccdddaaabcdababceceacbdbeeeaebebadadaacebcddbceeebdbeadbcecdcaddccbabdabeeecaedeababcccdadbccedbddaadacadbaebbbeabebceccdcadceecbdbbeaaedebbeeabedcbadcddeacaaccaeabdcaddabacecdbdddabbbcbaedbebcadadbcdeaaddceadbabbeeeeddcedacdeeaebeedcceeccadabdbdadbdbacbcddbbbccaeeeeeaedeccbccdccbccaadadbaceedaedcdaddacdddabdcbbebdabbeceeddaabbaecdceeccaaaddcebbbbaceeabdbdabdadbcdbdcaebcbbadddbeedeababaeadddaedeeadebcbdaeccdadcaacceeccecaaddcaedbaabdbabbbbcddbacdebacbbccaebacaaabbceeeebdcbecedeeeebbdcbbabddcaacbcdcbbcccccaddeaebaeaeaacdcdacceadbdeddccdecdeeaebcbedbabbbadcabbbdadcaabbdaedaeabcccceebcbcadbeacdeebdddcbdbddcdcdbabcdbcbceeaaadbccbddabebbeabbbcbdbddccadecadbabadcdcdedbacbebedabcecbadceaecacdeabbccaabececdccbedaebceeaedcaddcabeeabbadecdaecccdbbbeaaabaebabdabdeadcebdaddaebddeaebdbccbcddeccadabdbcdaeaacaebaadceedbcccdccedeadeaabaacbcceabbcceedaeabeecabecbddbbeedcccedbbcdaaaacdccbbddcadebbcdcedacdeaceadbdcecbdbaceebcaeaaaadbaadbaacadedbcacdcbeccbcdaddcddbeeebcccbcbeadcbdbddceddaacbeabaeccddedaeebabadcceeeacbcbebbecedcadcaecbaaaadbcecaeccbcdeeedadadceccebaaaccabcdcdaeecabebeddcdbccdcbdadecceeabaeceeebaadecedeecbeaacadececeaeaaccacbbdebdcdbaccbbacddcbdeaedabbcabdccdabeacceedbcbdaeebdbaeaaacedbccdebaccdaeacabeeddbecadaaeeeaebbadbababccccbedbabbbcceeecbcdecbeeaabcacddbcebddbeaecdecbdaebbcceacbccdaeedbdaaddcabeddadbaceededabbeedeeaecbcedbeeccbeaebadecdedcdcebedeaaccaeacccdcbeeaaaaacccedaaecedebccdeaaaaacdaabbddbbadbeebecdeebcacaddbedceddaeedadccaddddebbcaacdecdcaedbcbcccdbcdcbacdeadacecbacdbabcdcbdeaacddccbbaacdccbebeaeaddbaadbbedcddddbadcdccaebcebbeadacddbddcbaeebddadcccabaccdcebbaabaebdbabeeebbaaaabbdbecbbdcbedbeaeebeedaecdadccbebbbbcbcaedccebedeaacddaaaceeeadcababacaedbbedbdebcecdabaaaadabeacdbdaceeadbdbbedaaadcdbadcecbcebaeedebadebdacacebdbeadddbedecabbcbebddaeebddcaedbbdadcddedacbedbdeaaaeaabdeecdddbbeebecedbebdccbcbeeccddbaebacddacbeaabbcdaededaecedcbdcdedecebcaebecdbadeccdeddaedebbbeabcbeeebedeeececdacccbadceccadcbadeaededcdeeaadabceecbaeddbaacaaacccdaadccddeeabbadebebaababebecbcdaccdebcddbeacdacbcbbcaceabcecdebbeedcaebbaaddddcbedccbbaddeddcdecdedeaedcbbbecaadabebdcdccbbbcebdceeaebdccdbbbeddaacaabaebabbedcecaccacabdeadbeaeecbbbabbeeececeeeeecccadbadeabeebbecdacacccbacdeabdcdebeccdcadbedaccccdeeaccbacabacebdcddabcaedadcdacceceebebeceddcdacbeaedbbecccaceebaecccabadecaebaebdeaceddbecdddcbcbcbcedeeabbeccdbceeacdacbeadaecbddaeaaecdccddcdeabaeeebdbdcdccecaaaebddccacadcceddeecdddedceceecbbcdaeadbecabeebeaebdbaaaabbcdceaeecabddbccdeccaadddeaaeebeaeecdecbdbcdddbaeecbdcaecdddddacdaaedababeaddcadeaeedebedbeaeeabccabeabecdadcabdbebccbddccdcaaadcbeecceacedaebeecedbedecbabeddaeeebeeaadbadcaccceddeebcabeddedeaaaccdaaeaebbeedcebecbabcadaaedbedacbdbedbadacedbddceabbdbaeedebcaadceedcebacbccbbaaaaddccacaadaaaabaabeadbccccaddeeabddadceadacabbeacdbcacaeccdabeedaeacaccecacdbadcdaeeaabaccedeededdbacabcceeacceccbbbccbbaebecbabcaedeedcbcdacbbbdbaaddbaccaeaadaaaedebddaebeeeeebbbcebbaabedecbaccabebadaedccdddaaeedaaabcdeaedcbbacedaebdddabceaebedbacccbebadaedeebcdcdedeeeebecabbbdaaddbabbadbbbaadedacbbcbdeabcebcebcaadabdeadddccaebbabeeacdedbbbeabeabebbbcaaecccddbbadebeeccbdcaccaeaaceedbcecbabbaadbacebaedadbabeeaeeadbecacebdebbbcdeccaacccdbcdacbacdbdabeddeedaddbcebbeeeaccbaeeadbeccbcdcbbdbcabedddeaaedebcdaeddecbbdbeedbaaaaaeedaedeebadbdcebacaceecebddceeedbbeeecebceaaceabeeedcdcdbaececdaeccbcdebaadedddcacdcecbdcbcbeddeeacbdedbacddaeebdecddbbcaedccacbdbdacabaaeaedadeeaedacabadbbebbbbdddaceddbdececebcbacddcbeebadddedebdcdccaebcceebbeaaeaddddbebdeecdededdebdeaddceedeaeebadebdebddadabdbdbecaadeeceddacccdbeaccaddababdadcdedbcaadcedabbbeabeddeadebedeabcaaecccbebaeeadaccadececaeeadbcaabebcbccbebdeaaaaccacacabaabadcccbcaedededdaadecbaeedbebccbbbedceabcbdadcdbabedbdadaeedccddabedecadbecbdaaabbcebebbccbeceaabeebdcbadceaaddecebedabbcbcecebdcceacaabeecdaedadcdadbbcededeeaccacacbacbceedddcaeaaeacbcbaeaaccdbceeeeddadcadcebcabcbeccababdadcceaecaccdbbadeabbdddbeceeddaabbbddbacabedebccdceaaaeaabcdaebdadbcadcceadbaceeaaccceeeaadabbecebadedabdaaeaaaddcbcabecaceadadadccaaebabdedcdeecddbecebaedbbbbeebcedcdccdeabcaedbceeccdcaaadecaeceaebaabaeadabbbdccbaadbccbabbaaaadeccbedcbaddbbaadbdccbacdebcabccebcdcaddcbeedddaeedaeceecbdaccabaaabebedadabbeabaeebdaaceeaebeebadaedbaebaedcdcccecebdebeedcabcbeecddcddbeedeeadeaeeebeccbecaebcdbaecddeabdcedacdddbdeacdabbcaabcaddecddbddeeebdbbdbeeeaebeacebbabddcddbbaccdcdebbaeaaabedaddcedbcacbdeaeebeabcecbedcbceaedadabcacadbdcbdeadabdadcedaedccdebcceeaddbcdbddbeacddbacaedcabadcededabceeeeabdebbeaedcbdaaedddedebdbcbabeecdcabdaebacabcedecbabaceeceacaddbedddeecedcddbbacbeedbbabdabaebbbacbdebabdddaecdedbbccaaaebbdaecedabbcebbbbbaadcbacebcbddbceabecddcbaddbabdebeaecbeedaaadecdcadacaebcecdbedacbddebcedacbeebbbaecbedccebedbdeaacdaaecdbbbaacabdeaccaceeecdbebabeeeaeebaeceacabdebbdccbacbceadcbbbecdeabadacbaaeaebbcaceadebbccaeadebeacdccddaaebdbaacbcaddacbcabbcaecacbabacecccbaadceddedddbecebdbecaadcbdeddeeabcddcacacdcdeaaadaebdcaabaecdcadceedddebaebbdedbedbebdaaacacaecceaeaedeadccedccacbaeeeaebbebeebccbececcedbcecaccbcbbdcdbcedbecaceeebaebecdcbcaedeebcbbbaaedaaecebbabbeebebadcdaeedcdeebedadedbceedeecebbdebdebbebacaabedaecaaedcaeaccbbdaddbbacdbaaddbaacbcacbcbbdeaeebcddcbaccaecdeedeeeaeecaececbdbbdaabdaedaaaabbdbcadbedbbcebdadacdacaddcdcaceaeabeeadccadaebabdbedeceebadbceeabcdcccdcddadacdecacddbaaaabaebbdcdbdcdecdbbedebeceadbbdacedbbcbcddaacdcaddaabcdadbcdcebbcebaedacbcdebdeeaeabedaceebbcbeeaaeadbadcceaaebcdbccacadeebadbebddeeecaccceadddbacabccabbbabcaeccdeccadecebcdceecddaaaecdeabacccbbcdeccacbabcbbbbcabdceacebbcdbeaeaadbbcaeddaedbccbdbeaabcaadadcdeadeccccbeccebdbcbcdacbacbeaededabcddcacdbcebddcecbcbecbdbdcbaeeaebcbbedbaaeeacdcaddbdbaadbcadeccbdcbaedaabaebdaccdbecbadadddeeddbdbdbcbacbddccaebcabddeeeaecabdcebabebccbedeedabaddedbecbabeeeadcecdababddcbdeeceebddbbaebaaeacdddaaceecacdbdabebabcbaaecbacbabeaacaabbaecdbedecabbbbdccbabbdaddeebabdbdcbbbdecbcedeadcadceebbcedeeeddadebcadbaeceeccdeeeeebdcdbcdcedaaaecedeaeedceddcebccbdaedeadabcdebebccacceccddadacdbbbcebececccaebbdaadbcbbbaeebbaaeedbbbabbceccacdbadccedceaacceeebbabbacdcdbacaadcddaebaeceabaebcceadbcaedcceaedecebcacdabcecdebaebdcbebbaadccccaabdbabbebaddecbdabdeebbcecbabaeeccdeadbedaeaaecdabedacebbaabbbdcbadecbacbabbcdabbbeacbaabeccceadcaacaeaaabadedbeeeaadddaadceeabbbecdaaeaebecaecdddaaacaeacdabbdbbaeaededaecbabbbeaaeddeacebbdceabadeeeecdbbdbeadeeaececedabcbeedddcccabeeabcdaabecdadbbcebacaadaecededcceacaebecabceacbdecbaaedaeeeabcaedbaecdcccaeeeecdcdabdbbcabcbababdeabdaaaeeadacedccecaadadabebacacbaeeadceaeceebddaeddadaabdaebbbecebabbbaeeedbbceccaacacdbaacecadecdedaacbcbcddacdbcdbeccccececdcddeebadddcccbdcdbbddceddeddeddddadebaeebdedeacaaebabaabdaaaaeebbaacdaedbccbadeeeebbaaacaecbcdcaeedadcabbcecacccddeceadccaadcaeebeeaebcebdceccccbbcaeeddabadbcdcccbaaccaddacdbbebacdccdbabcbabbeaedbcdbdacccbeebebadceebabbbedccbeddcedaeecbecccbeccecdbeecdbdbcbcbdbcacddbcdebdaaebbcbbeecaceccbdabaccabdbaabebedcacebbcceceabceeebdcebcbcbbdaddaebeaccbdcddacaccbeccbaabdeadeaacaeacaeecedcedaeeededbdbbcbbccebccdcbbdecbddccacaccbdcdbdbdbcddbaaddadebeabbcddabeecdeabceeeeebdbdbccbbeddbbecbbeddaceecbdadbbbebaacbcceaeabdabeaabccbdceebbaeacbeaabcabbccaebcbbbaadeabacdeedbadeaaebbbeebaabbdbdcceeddadbcceebdabdbeddbeebedcbbbbabcddabebaaeccabebaddceecdeadaaaebabcdadeecdadbaebaabaebaadaddccabadaebabbbdebddbeccdebdbcdaeaeacebbcceeebbacaaaecababbeceaddedeeebdcdcdbbebbccbaacbeeabdadbacbecbecbadbcabadcaebbbdacceeeeaccbbeeaaecdedccbbbabaeeeddaeaebdaedbbacdabcbdeabadccbaededadaccdabdbcccbabaedeeaadcbddaecbaadeaacceceddaaabcceccedeebdcbdcedeececcdabbdcadcbeabceeedbddcbedbbdceeeeddcbebdcddebbeccaccccebbcbaebdeaaabaeabcaaedeaadaedededbcbcedaedbbdbaaabbbeaecbebaeecdacbdeaadccdececebcdbedededbdecbadaecedbbcdbdbeaeabdbaeeabedabeaebeadcccdbeedceaecbbbaabeebcbedabdddedcddabccaddbaccaecbdecaecaecebcbdbeabaabdaeaaadbaaabaabaaaaeadecdbeacdcbdebbdbcaeeedebbecaabaeebbaadbabbeabdaecaecacadbbabdbedbbecadcceccbbddcabadbdbaabdacedddcbcaaecbaabbecaccbcbeecccbcbdadbceeacbeabcecadceadbeeedebccbddaaaedeccdcdddeebadccddecebeacbeddebaccbcecaecebdddbacbdbcaebdedcdcdbabbecbacadabadaddcebcbdddaabeacbeaeaaabecdbddaddabdaeccacddbaabbbadeecdbdcedeadbbcdabecaccebedbeadceebaecacedacdabacedddcaeeadcbedaadeaddeeacbcaecddbcbeebccbeedaaabeecdaddbbccceaabbaabcddbbbbcbdabbdcbdcedecbebadceedabeaaccdbeaeebbddcbadecacbccddedabeedbedbedeeadeacaccedcacecabdadbddbbeeebbceceedbbeecbebdbbccdecadacbaddebbcdacdabbceecbebcbaacabedeeaaacedababcbdddddbabbeceacbbbdbcdcaceaeebdabaaaeccacccacdcaedbcbdeeadacceaddeddacdbdccadeabceceaacaddccdceabacabbaaadcdcdceaeddeceebccbdaecebbcdaedadcacadcccccebaacdaeddeabdbdcebedcdadaebdbcaaacaaacdacedbedbeaacdbabdeaccaccdcebcebcaedbbaddcdcedccdeabadbccbbcebabaacbadacaeccaabddcbeecbcaeebcaecebacdcadacbecbdcddcccccbdcdeedbaddcecdbebbeaacbbbdedddbcebedccaecaadeadabbddcdaaaecacccabadebeebaeaabeaddbedaaeebadedbaccbacacabdcdabbaddeccbddeacdeaadacebaaaedbcbabeeeaebdcdceedadbeabdcdcdeacaeacccebbaaddcceaddeabdeaebcbbbeaacdddbddbeedacbbbadaacadabdbdbcdeacacacdbdebbccdebacadabeaddcbceaaccebeeebacdcccedeebdeabcebaedddacecdcddeccbbdbacebebacdcbdaeaeaabbbdbacabbcdbadaeeebacaeaacbaaaacdbbcddeadceeddaebadecaaabcdcabcbcaacadddddabcbccaceadacdccaecdcdbcbecebecdcdddaccaaacccecabaeccacdbabddcdbdbebecededccadbccbacceecbdbedcdcdedeaccacaacadeaacbbeebacedbbeabdaabbecdbbbabdcbaaeceaceebccdbedacdadcbaecdccbcbbeabcdddabebeceaadcbbcbecdabcaaacdbbebcaabbcbebcccaaaddbeacbabbeadeebddddabadceeeedbdedecadddbcadeababbacaabaeeebdbdeeeabeedaddbeceeeaaaccbcacabcdceaddceecbeacaccadbdeeeabdbdbbeabebaebededdbceeebcaceaedbeabbcbcedadcaebdeecedcaeeaceaebdacdecbbddebdeeccddcaabedbecacdbdcaeaeeddadedcedaeaeecbcebbcbeaabbadadccedaadebebeaeedceebdcecdcabbecbeeabaeaddcbacdaaeacedacedaaabeebbadebcbbbebadaeabdbdadcbbccdccbbbbcbadddeadaaabcccdabddbeecddeaacaabccabcdbaacaecedaecebcaaceabbbebcedcaccecadacdcabecadbebeebbecebeeebabddecddebbdddaaaaadcbccdbeaaccbbeebdabbaebdaaadcadbbcbaeceebeadecadeddbaadbeadbcccadbabdbddcbbebdbacccaadacdbccedbedceccdbbddcbccbbcdacaeceeaaedcceababdaaadbaedababdcccebcbeaedaababaaeebddaabaccabcccddecbcebccecdbeadadbecebbeccdeaedadccdcbbaebbebddeedaeccbadccbeebeeddedeceadceacbddcddceadaddcaeeceedebaaacbdbbbcebccddbcdbcadabbabddbbbceedaaebadbdbcacdbceacdbbcedcceedddeeddeeededddecdcbebcebcbebaeeadebeccdedcaaeaceedeebdccccaaacdaedcebbdeacacccceaebebbaedcbcabbcbeaebdeabbeedbaabeddceabdbeadddcbaccccaebbedccaeddeaacacbcbaacceedadcdbadabbddadbdaceecedacdcecaaabbedadbbdaaabedebddaedebdeeadccbeebcdcbabdcacebcceeeaeedabcbebbeaecbbcdaaebbcbcceadddccecbddeeccecdcaecacaecededdeccecdccbbbeecdbcadaaadbaabccbbbedcacbeeeaeccbceccaadbbabbadbdbeccecbdabdbedbeeeadaabaaaebedebbacbbbcbacbadbdeabadbacbedecaeacecabcbdadadbccacaceeabbadbbabddadcbeabebbaacecaeabedddacebaccaeecdaddedbeccedaceccbdedebaabdebeeebbebdcacdadacbdabdaccaadabeebcedadabbbcdbaaaebdaaaebdbabbcdcedeeccebcbcdcdeceaecdbcddaabdcebcdbdecdabddddceeaecddbbddacaabaaeadeeebccbbcdcdbcebcbaabaebbecaaccdeeddebdecdbdacaccbadcdbdabbaeceaeccecbdaceccbbcddaebdeebbddbaaccaaccccaadacbbeedbcbabdbadbcaeceaaddecbcecaddddecdddbcddcddcdeabbeebbecbdcbeeeadccceeaaaeaebcdabcadebddcccedbbedccdbabacbccbcccceabdbcedbeabacdadcabbcdddeeabdabceddcccccbbeeeceedcbdaeacaddeeabeebdacbddbdcceadbbeccbdbdbcbeadeabddaeebebbecdabcaaddcaaddbeaadedcbdcdeaeabeebebecaebdabeadeeaecbcdecbcddcaecdeadcccabcdedbecbecaebcedacecdaaabbbcbaeaebbbddecbcaeeaecabcaecceeedecdcbedddedcedeaeabecbddaeaaceaeeeabaaeceedbbbdaecccacbdedaabaddabddcadcabedcaebaeacdedbcabacdbadedadabcbaceecdeeaebdeaabeebcedcdaecceaebdaabbcacbbdddaddaecacccdedadccebcedebeeaadccbaddacbdaececdbacdabededebdccaceadcbcabbcdcabadccbeecaabdcdebcacadbaadcbdadccbaeccbaeabdebddadcdabbebddacdcbcccacebeacccadceaacaedeaadcdcedeacebadccedaadaaececedccabbeeabcaebbdddbabbbcbaecbacbedcecddcbcebabcdceebbbbdbaaebdbbcddbaadbddabcebeeaecdedbcccdbdcadbcaaeaaceedbabceadceddedabcaddaeceadebcaceaacbaddeddcbeabddddaebaeedbbdccdedbdaabdaccccecbaeeedccaeccaceadaacdadaacadadaedaaecdaddbcdceddeacdbbcdedaeaeebadeddbeadabebeadddeceeceabdadeeeebebbdedbeabeeddddbdccaddbccecbdbdcbddaedbddcceecdedbeaccbbacedbeedeabceeecbcacdbbccacaaecebbaedecacddbabadabeeaaebddbdaaeebdbbeeaccaaecdacdacbbbdcccaeeeeeeabaddcbbdbbbcdaddebcadcedccaddeecbcdcbacedbdbacabbcaeaaeccacedceadcaebaebeddbbcecdeabecbeebddaeccdcebabeaadaadbbebbbbcbacbebadddccaeebdcdadbcacdbedcbacdeeaedaadecaaceeaedabebadbbcdabddaedbdeedcabedbdeccebeedebdeadbaaaebaacedcdedaaedeccbcedaccbddbcaecdabdabecbadaadedeaeaaddbbddddeabecebadeecdbacbeeedacdbbaccedbabdeedeeccbacaeaeaecbdbbbbbacaecbdebddccdcdcbebbdececadcebbdbebccdcbbecbaaacacceebebaaadaeddbaccbcebbdabcaecdedebabbecebdcacccaaabbbbeddabbbecdccbecdcadeedaaaeacbacadbcacbaccebbcceaaabbdeeccdbbceaccaaaeeceeacecedaaadebabeaeacddaeaddcdbdabcbbbcdcebeeeddabdedaabbdcbedebbbdeeaddaaabdaaebcbdedadadacadbbbdacbccadcedcecdcebcaaebbbadebedbaddceadceddddacecbcdeceecebbeaceecaededdadadbdccdcbadadbabbbaaabdeccecddebbadbebaaecaedcaeedbcaeaadacedbbaccbdbcddddcaababbcbceeebbaceeaecbccedabeeceddcaccbcaaeaaaeeeabbbeddbdbdcddcdcedadcadcebdeaacddbadcabeeaaedcedebeedbdbebceabcddceeaedeceddeddbaeeabcceadecbbdaedcdbecbaeeaeddcaadedbdbddbaecadecacaaaeccbcbcadccbebaaaacabbbebadabacdcedddbedbcdceeddccdcbdcebeccdbeccaadbeedcdcdaaaacbdeeeaebeddddbcecdaaadecbcabaeeccaebdbbedabdecaaebbeddbcbebeabeddabebdabccecdcceeeecbcbcdcceededddadacecebadddbaebecacaddacddacbbabceacdbaceecccabaeceedebccbedbbcddaccaebcddccdcccceddedbbddcdcceaaebedceaddaaabaecdedddbceceededebceadcccabadedccccbadcebbeeccceccaebddedbcaacbdbaacbedeeeebaebdbbbcebbcadcdebcbabceaebdbdaacdbaaabeeddaedcccadaadabaecdeeabeabaaabcddbdbbddbacaeebbbbbbbbeeccecbecaaabbbcceaddcddcaedabeecdbeaacbcebdbccdbedcdccabecaccacebbdccedebcbdcaddeccbbdcababcbceeabdbcadcddadbcaddeebecacceabbcdbbdbdbecaeacabdbcbeedddcbdcadccbdaebdbadacccdbceedbcebecbceeecabdcdadbccdbdeceaddaecccdecdedcbeaaddadebdbddcedceebeabcedcaccaaaaaabdacddebbaabacebcecbcacceebadddcaaeabcbeaccdccdabdceaabddccadcdaaebdaacadadbcedeaeedaabdcdedceededeecdebdeadbdacadadadcecaeabadcbbabbdceadacdadacecddbdebeaedcbeeaabdebaabcdecbeeabcacdcbaadcdbcccdbbaaadaaddbceeddcbaaecbcecdabbcdeaeadbbabdeadedabdbccaacebeddbecbabdedeebaebbbecbebacdabcbacedaeededcdedcacebeeaccdabcdacddeeabeacaceeecedacbdbacadcecedbaaedceeebedcebddadaaabaebedecaddaecdaecdbcbbaadeccdceceebaabedccbdecbcecbadcebccadcbcacdebeaeadcdabababadcbddeecebabcedeceacbdbceddadeddceebeccdeaaebbbebcecbdccdeeccbcbceacdcddeebadecabddccecbbecaecbacaadebaabcecbbdeceecadbbaabbebaeccddbdaacbdeddedacebbdcccdacacbcdecdeaeaeedddaebadcceebcecceaceeecdcbedebbaadaeacebcbabeaddbaaebcdaebcadbcdaabeeeeacaeeccbaaebeccdaebcdcdaeddecadccdcbcbaddccaacdbdacecabbbabdbdeccecaececdeaaebcbdadebaecaecbacccbacacdbacedcdeaaecabaebadabeadbbcbadbdccebabcabacddeebccbbaadccbabeaeddaebbbbabcdbeacdbdcceaeeeabaebeecaaaebdedacaabedbbcedcdeadbaccbebadacabbdcbababedbecaedbcaeeebacddacaeaaaeaacddedacebbacbacbedeccbeaddbddadeaadbdacadbedcccccdcbcdddccddcdabaebcdceaedaacdaadaceaccebedccbdcaeaaabcebaebcdbddccbaeeacdcaeebcdddbcaebceeaeccbdabdaceaeaccebacddbddadebcdeeedaccbbdeeaabcedbdbddbbdcccdcaeeaddabbeedcabedebaeedeeebabecaabbeaceaaecccdaeacdbbabcebbaccbccecabeebbeaecdbebacacabeacccbeddecaeccaadeeddbaeabddbdeebebdccebbcdebbeceddeeabaabddbcebddeaccdaacacbedcecaceebdaaadccacdadeebbeecaddaeedebdadedcabedbcadbddccaeeaccbbecebebecbaebccdcbcaadaadcebbeeeecaadbcbdaaaaaeacdadbaddbebbecbccdabceacdcdcdcccdaeceeecdabeceeaaeebadeaadedbbbadbbddccbaeebecebdbccbaceedeccdddadcdacccaabcecaedbccbdaaebbadccdbcbbeaadddbedaaaedaebbacdecccdbacdecccdaaddcccbadcabababbbaabaccdaaccecbbacdeecabddcaebdbdbbaabbbcadbdacacdacedcacacaaaecadecaabeacebeaeaebbeeddcbcdaecbabaecebedcaaaecccbacceaabbccdbaccabcabccadbeedaeceddbbaacbedebedacdedeadbdaedeaeacdcadceddacaaddaaabdbbccbbabeaebeaadaebbbaedaeeeaabcacdabbebaebeaadbcededdeeddbeacdeebceccccdedbbaccbeeabbeaecbcdaceeaedeccdecdeeedbabacacaeceaadedccdbdecbdbbeabdbdacdacdabdcaaabeeedbdecaadacbadddcacceebadcbddddebaabcddcddbacaaabbaeddddeaececbdcacaddacdecbadcebbcdebebabcbeeaeebcdecbbebbcdadecacdedcecdbcabeadcececccdcceadbeeeaacecbecaaccabaedbaabaeeccaccbbecadaeadddcbcdecaaaededdeaeaacdccbcaeeddecbddaeddbbbdaeceecddcbbaebecddabceeacbadeebccabadcbbeedabdecbbbbdeacdbaeedcdccddaddcacaeedbabedebcbabebbdeebebedccbccbdddbbaeaccdbaedbedadeaedeeeaebaedebaecbdaaadadcbeccbaedcdaebbcdacceceacbeaebdbbdaaecbebdbcbcdeeebebbdddcbbbcbabebabcaceaebedaecabaedbbeeecbbcbbbcabdbdcddeadcaabadcacdbcabbcebcbdccccaddbcaededaeadbcbdacdbbcbebddbecabbedcdaedbecddeccceeececccccdbeaeaaedcccdaebededbebcbdcccebabcccbddaeccbceeabbdecceecaccbdadcbcceebbaddcebdaadbcceccebaddecdbdcbcbebdbbaebdacadacecddeccddbbcbebcbcddbedabeabdabeaedabbedecdddadcabdddbebcaeceddcccaacdaddccddadcdecdcaecebebbddabdbbadbeaadcacdbeedeccbdedccbdbecceddcacceeaedbebedbebcecdbcdbbabcdccbdaeaebacecbdabeddaaabcbdabedaaadabbceabdbedbecacebccbbcbdbdeebeaedeccecededbbbeeedeebebeaedaedbdedadedacdbcadeeacbccccceaaadaeaeabcdbbecbdabdaaadcdcdbecbcceebeccbeaedbbbbbcecbcddcecdbecaddedbcdeaeaeaaaedeadadcddaadddcbebecdcbabaeaeeeacbbcdccaccbccccebcaeddeecdcccddeebdcbbddcbddbdeaabebecaddbbddddbacbcbcabcbccddecabdbedebbdbeededdcecbaccdaacaadcdbacacbeadedadceadeabededebbcebdeaaddceaacbcedebceeeaaabbbdeabadcceccdadeaabdceeeccdbcdceaadbcdcbdbabbeddbdeaaadeeebabccdadbbbccdbcbebeaeecdcbbabedcddbbcadeeacbcbdedabcadebaeaaebaeeaceadbdbebccaacaadabebebdaaedebdecebadacbdccabdbbbadedcccbacdebddeebddbceeadceedeacaaadcabebbadcedbeaedbcccdeacedcbcabcaddadbccaaecddeaccdecaeabbeaeebdbeabcbeddeabcdecabeadaadebeedadeeeababadebcdadebdedbebabceaadaeacdddabcababccbabaddaddedeaadcbadaeebebdddbbbbbadeeedadebeaeeacaaaecacdbdbccaaaaccaaaabccadbabaacdbccceebdcbcddadabbeddedbbcbdbbdcceabdcdebdabebdbbbeeeeabeebbeeeeacddaaabbdbedbaeeaeaabbdbdabccbebaeceeaccdcabebcebdacceedcdbbadcbcccdabeddaeebeceeeebdcaeaabbebabaedeaabeddbedbeeecdbecdcbbbabcbdccbeddbeeaacebecebcccbdccadabdbdaadbadbaeddbbababebeeebecadaaeaddecbdcdebcbeeeccbdebcaadececabadddcaddbcbdacaaaadacdbddeabaaeddedccbcecaceeacdaddcbeeedacebddeebedbaccecbeeeeccddeeddadaeaacbcaedcbeebcdcdcddbacebecaabceedacbeaaecbbcaeeabcdaeadcacacaeabadbebedeccaaecbebaacebdabedbbbecbebadbdeacedeaceedcabcaccbedeacebcbcaedadadbbccadbbeabceccaadbbdccbdbccebddcebabceababeebdddceeadbedaacabbdddaeadcadcdbdbccbdedebddbbdeecedacbeddabdeeedaccaaeeddaeceeaceebdeaabaddcaabccabbaedecadceceaebaecbcedcbbadeecaadcdeababcabbbeaeccecdcbebccadeedbddcebbddcccebaacaacbaadaebabbcababadecbcbaccadedaaacacedaebaddabddebdcdbbeabaedbbccededdeccedbcdcebedaeccbeadeebedeabdbeedbdbabadeaaebdbdbddeebdeaaadabbcadabeadbbceecebebdedaaaacbbcabdcacbcdacbeebacbbaeeaccbabbcedddecebccecaeedcedbeedcddaacedebdbbdbbdadccaddabbcedcecbaeddeaaaacdcaecebbccbdbccabacbecabcdcdacbbaabcdecbdedcecbbedbcaecaddaceaddbcbcebbecdebbddadcacbaacbccaeeabdcbdbdaeeceaabbccbaddcebbbbacbbacbdeebddcebaacbeacbadbdaaeabebeceeaebcbdaadacbdebbeecaddacbabeddbdcccebebacecdcabeecaaaebbeccaccadcaaecbbccddaeedacddecaaaebeacaaeeeccbebbdbdaacabeddbecbceacadacbedacadbbbdbdaacebcaecbbcaecbadadbeedbeccaecbbaadceaddcbcbacceedcdbbabadeeeacabadeedabcaaeebbcbabedebdbeeedebdcebcacddcaaaaccdbdebeabceaebabdddabbdeddcbadacaaadbbadaaebeeaecbeacbacbceedbecadbbadcaabdcbbdeaddcebdacacbebebbcacaaaaadbabdacabdedabbbbebccdceebcdcdddedaceecbcadddacecccedabecbaedabbebcdcdbbcadbbebdcbaeedaceabaadcaaeedbecbbacebbcebaacbcaabceedbbbedadabaceebbbbddcdacabaddcaecaaaeeddaceabbeececcdbcecaeaaaccdebdbebcccacaaacecedaacaeaebacdcdcaededdebabeecddaacebaabcdcdabaceedaceebeedebdeadbdcbaceaeaeeabbbacedddedacbbecadeaabacabbebdcdeecceebdbeeeceeadacbdcdbabbbdcbecdebcbdbebbebbbadddceaeeceedddbddedbabddddbedeacaeacbbbdacacabdbeebceddaececedcccbebdbdccadccedbabadaeaadcdbbccacddacaceebbeecbddceaccacdbaccacdecdedbdbceddaabcedaebeadecbdceabcdddecabcaecdacaabaeddcdddcddacbbbdbbabbaeebbdcdacdbaddecdbcecedaebcbbebdaccdeaceeaecbdcdcbaadbceaebdcceddabadcbbedccabeceaadebcebdeadbdcedbcedabececeeadeccccdbaaddaaaeccecdbdccdbbbdcadcdaedbedccacbeadbdeacbddcdcccddedcbbdaacbddaaddbbddabdecabdbcecdbabadbbccaedbcaadcaedcbccadedbdacbbcbbecedadeaacdbacadceacacddabeabcdececcbcadaeabaedbdeedadddcecadccddbedaadadbbbcededcecbaeeeaebadaebecebebceadcdcecbbccceaaeaebddbaaabadcaccddeacacadebebeaaaeeebbbbbecaddbdecaabeacbdbeddabbeadbadeeebaaddbeabdbabcbbeddccabbaeeaeecbdeabdddadcbcecedaaddeeedbaeeaeddbdaccccdedecaadbbbcdcdeadedbddcddedaccbbbddceaaacabdedaadecebecbdabbbedbcecedcbabaeedeaeaebeaaedbaddcbdaaeebeebbdbeacdbddedaabdbaeeebabbedbbaebcbaeadbdaedaeecdeecdecdbdccbcadeccdddbeeadadbabbdaedaddccddcaaccdddbacdadeaecaaddbdedabcdcccbcbdebdcaaedecabeadebebddbaccbdebbceccbbbbccecacbbcebeebccedaacecdbaaeaadebddeddcaedaccdddaeeaacbbecebaaedeeadbccacececcdababebdaecebeeaccbecbcdbcbebabcdbeeadababdabcebbcccbaaabacdbcecccecbbeaeadcacdededdedeacaccccebeaadadaacadbdcbcceaaeecedbebecddcecacdacebbcdecdadacedccbaaebeedadbecdddcdbddeeababeadeaeaadceeccaacdedeabaaeebddeecbedbcbadbcdbcdebadddcecaddebebebacdcabbbaaadddccacadbaeebaeacbbaaebddbedcbdcdaebabcdbbddebcddcccddcaedbaababdeceaabcecbaaeaabcaaebedabeacdeaddbeacececeacabdadbeceeadcbcaadebbdcbcedcbeecbddececbcceaecbbaebecaaddcbecaaccacbeedabddcdcebababdcccebdcbecaecdeadcedddbaacecbccbaccbccbdbecbaedbdcadccbaedcdaeaecbbabdedddabdcbbbebdaacdabbeeeabeadaaaaaddceedacdbbbaeabbeaedabdbcdedccbaeaacbdeacecceabbbbedbdddaaddcacbcebbabeabacadeaacbbeacaccabbbbbccdbbcecaeddbcbbadbdeccdecddadbcdeebeadaceeaeaedeeaaeebbadaaebacdadeedcadaadbbdacadaaacecebecedbeaebcadbcadeeeccdadbcadcabecbaacabecdaeaccbcbbebbaadcbdccdeabdcaecadeadadcadabdcdaecaddaddeebbdceaeebbaccaeeddaeaabeceacadddadccacabbecbbccacadedececcddceabebdccedeccdacbadcdcbecedbcbcedbbcbccacedbaaceaaeaccadaabaeeadbcbadaaedbbccabccbaaabdabddaaaabceedeebddeeaddeaececbeeabdcccbeceebeceaaedddabcadbdbaeacbaddccceabeeabbacebcacbebbdbdcedbdebeeebddbdaadcbbeeeeaaeccdccbcdddcbebdacedabcddeecdaeabdadcdcbbabeddecdcdabccebaceebeebdbcebbdebdadccaaaccbcebcceaaeaaaebebceeeebcdecbdcdbdccdaecabecaeeeacaabedbaceaadcdeaeebbccaeaabebdbdcdadddcdedcdeaceadcbebecedcbadbccdddcadedecbdcbcbaaacddbedcaacbbebacbeedebaedddbdccbaccebcdadcdabeabcdadedbcbcbccadaeddabcebdbecacaacddcecaeadbeeadddccabdacdaddddeeeabcaabedcabbecbdbeedcbcdbbcbcdceabdbadabcdbdcdadebacbadecabbcaacbeabcdeadbddcdbbdbcacbacebbacecaaadabcaabcedbbaebeeecdeaedebecbcbabccbbdcbedededcabdaddcceeaebbeceabcaabbebabdaadeaeeaeeaedaacebcdddeecdcaabaebcabcccecedbebceedaacbcbeaaceccedbceaedaceceeaceebecdcdbaaebdabececbcbbcaaecbaeccccdcbdbbdddaccdbdaddadabcebbbbbbeaceedabdebebeaceeaedcabccbecaeedebabcbebccedadaeedbbcadeccdbceceaebeadacaaebcaecaeedcacdbdbcecbbdeadaeacdbeedeacacbbadebaedddededabbdadadebbeeacbacbdddbbbbedcdaccaeadecdbbececdddaddedceaecbcdaacaeecbaccebecdeabbcabeacdaabeeeecedcbdcaebccbbbcbadcdbeddcbcebbbaedecabacbddaabbccddebdaeddbaceeaddeaabcaedaedaaeaceaacbddeedcceceeedcaebdbdccecedcdeccbabcbbaddbbddedabebcbdebebbaebbbedabeceaccacbabbaececddcdacdbbbceeccbeddbdacabcaaccdbabbbdebbacbabeeeedcbdedbceaadddbcadecaaccbbbcdbebeeabbbdedccaddbedaaceecddacacbaabdceddaeecbbaddccbebcabadbdedcbccccaceedababbcececdecedccaacbacedeacaaadceaedabeebaedddccabadababcbabdbdadaceaeeacecedccedaadebaaebeebdcddadcecbebdddcbbaaeebaeabdddcadeedbedddddbbabcddccbebdebdadedccabbecccbcabdaddcaecaabeeebabbcdbcbadcddcecbeadedecabccacabecdccccadaaecbdabceedcdedeabbeaececbbeadaaeaabdeebbbbdaddaeaceeecdcaeeedceecaccbedacddadbacacbceaaebdeebeaeebaaddccbabcdebcbcabbbdaddbdbaeeeacedabdddbabbddccdacaabcdabaaecbcebdaadaecedaaeeebedddccbeeebcbbacdbcaadcebdceacacdcaacecedbcccdececedeeccebeadbcbadbacacababedcabcabadaadaadeebdaceaadeeedbbbbacadadbcedaddaddceaeccacdbdbebebbeaabeecbaeedcccaeaebcaabdeaaebcabdaaeebedeceaddeebaadeadaaeedbaebaededebdabedbcaecbabbdeaadcccedebecaeeaedeeaaadcdaaceacbadbeabceecbbbedbadaaebabebdeadeeedcbdbddccccdabcdecbdcbabcdccdedcebddbbabaecdbdbaebebececddacdaaeebeaebcbbcbbcbbdedceddeedccdceeacaabdccdcdaebdedeeaaebeaabbaaeabcdeaadaaeaebcccaadcadecebedadebecbcedeccbbaaceebdcdccdedbdeaaacacddeeacedbaadccbdcdcebdcccbebceacbadcdeddbcbbeccaadaaabeaaeacceedbdaddeebbbabcacceaedaceedadacbeadceeecdbaadcadbbccbedcdaeaeaeeddbaacceddaeedeebabeddcbdeedaebbcdaebaadeccbadcabcddaeccdedebbbbcccdcbbbbcceabbdabaececbaabecbcdaabbbeaecbedcedceabbbdeaedeecbaaecddaeacabcecdcaaccadbaeaeeadacbbdbabbbbacbadabdccadcecacaaaededbdbcbaaeddceedadccdeeabebbabccaecebadcecbbeeeddaacdbcceecbbcccdddcccebbecacdeecdeddddddcdeeabbadaacecaebdebeacebaebbebbcdadbccabbadccaabdcceebabdcbebbeedcacccbaebdcbeaebaeabbbdedcdccabdbdbcaeddcdccbeebacccceeceaeaddadabacdacbdedecedcccbedbbbebbddccaaeaccdeaecddcbcbbdebeabbcdececadceebeccddbeaedddadaeaebedadcbacbbadaececebeedeaaaabdddaebeeccdbbaedbcaabedeabdbbededeaadadbbdccaaeaeadadccabaabaadcaabbeebdabddbbcaaeadbbdaaadbcdbededcaedbdcdecabcdcbadbeeebbaddeeddbabdbdeaedbbeeeeeeebedecacacaadcdbbcecdcecbdbddacabdcceccbbdaaebceceddecbbcceccdabededcdabaceedadbdceecebcedeaebdabeaeaedabbddecabdddceacdceaeaebcebecbdddaebbdbbeccabeaebacceebbcbdbedcadcbeeeedbabecaebdeeaebebcacbacbcedbbbcbbecbcdaaedaecedcbbabdedccbecbcadcdcabbeecbeaebeeaecacebdebbaeeebbdbbddddbecddacdcdaccaddecdbeddabcbdddcadeeebaecccaecebaeadcddcddaeadaebcdcdaadeaadcdccbddaacbcedbbaccaebabccccbacedbddaeddeabdecedaeabbaeaaebbebbeaedabceddacedaaeccecadcbedeadadddddacdcdedceeeebdadcbccbbdacaeccdebadeeebddbbdeeaebddaaacaacbbddaacbececcdedcdaacceaccbeeedabdcaaaabeaccdccecccebeeeececbaaaacedebcbaeabaaeddcdedbceadcbcaeaeedebcdbeebaadadcacaccdcbddcaabcaeeccdddaecaacdcceabaabbbcbbbabbededcbabcbadeacbaaabdbbddacbdbcecaedcdcacaadacecaadcbebbebdeacbdcebbeeccebbabcaeaadeaeebebaccecbbaddbedeaeecbcecdbbceaadcdcdedcabaaecbdccaaaddacaececbacacaecbcaaacededeedbdaddbcecabeecadbbcedaadbcdcdbbebbaceeadbaeadcabdcdbaeaeaeeceecbaedeeebddcdcdcdaebeabebcaeacbeadcacacbddcadacdebbebdedbcbbaddeeacccdebabebedbebeeeacdbaaadddedeabeeebddcceeabeedaedadddbbacebdebdeeddcddbcedbcdaeaebebedbaaedaabcdbbabccecbaebcdcaadebcecdccdebeeabebabeaddcaacbacdabadededcbcaaccddbcedcbdceddebbdabbcabebaccadeddaabaabbabbedacbbcdddbbcaccbdecddcdcdaacddbaaacdebcebbcbadccbbeedaadbaaadecdbacdacebbaeeecbcbdcceecedccdeaecbeabedbbabadaeabaecbeebdbdbcdecbecacebedceaeaeeeeeedbdcdedacaeeeedeedacddcdbedededcdaedbdaedcdbdebaaedcebeddedbcabcebebbadacacaacdaebeecbedbeabddacdcbadbeddeebbceaadedebdcdeaedeabebbeddeaabeceebeacaeabaaedabbeaadbebaaeabcdcacccdbbceacdeaeabcddbdaabeeebeceacbadbbceecdeeddecedcceeecddbeeeabdabcbeeebedcccbeebaabeadbccbdedbedaabedcedceddceddcddaaaabeebededacbacddabeaccdedeecacacceeddddbbcaebdceadceebaaedcaddcbdecedeaddcebaadbceabeecaaceebbadbbecccccdacbbbaceacbdcbaaceceebedbeabcacbecaeaadcbcaedcdacbcbcddceedabbcdbeeebccbaadedebbcdbcddaaaaadebcedbcccdeebcdababedbcdabacddbdcaeadeeabeedccbacacdddbeaabcedddbcccebdecbdbebaaccbdeeaeaebecbdceebeeceaececbbccbcadceccebaedaeabebcdcecbeeccaebbbbdacedaeaabbaabbcceeceaabdddecebcccaecebedbbccceaadeccbbcecbaecdbadabebecaadbabaeddedcbedddbbbccbebaeaacbceabbeecaaeedcbccedccbcbdabadcaacccbabddebeeddecbcabcdaebecdbbbddebaaededeadeddaeedadadceeedacdcddbecbaddebabebdacbceeaebdadeeedbbdecbadddecaeacadadaeddebcdedbccecacdcdebeeebcedcdcccebadaebbeddddbadbacedcababcdcbceadddabcdcdccacaeddddbabdcbbdbcdaecebacaccedcdedadcbeedacaeabccdadacaebaceaacddbaeeaacbbdeaaebdbadaeabdbcddcecbedbdccbbaeedebdbdecbabedacaaacdaceabeecddaacbdcccdaebebeceadcdbceabbaabdcecdadeeeceabcadccabcbeddcebebdaddbaaacecbeacacceebbceeeccabadeeeddbddecaacbdcdeececdbcacccdbaddcebdcdeabbdcebbcebaebbcbebcebaabbebbebeabeecbbdeacbeeacaeddcaabacabebaececeacaebabbcdadbbbbcaeedbccddeebabccccdbaceaeceecaccebcaccbdebeabaccbaaaeedcaeebbbbecbcbbaeedcdcabaedbdeadcabbbebdbaabbcabeecaacadcebdabeaadadaebecacccbbbbeeddccaeeedcbacaadcbcbadeadaabecbdedbdcceededbccacbceaadeccbccebebbbabebbceabadeddbaaccaececdbbbcbadccebbceedeecedaadcaaccecaaecaceddbdabecaaccbcbcbcadadbabaabcecddcebceeddbccbdebdcccaeaadbddddcbacacddcacadaecbeabccaaebdcbbccededeebbccedbeaebacbbaacadbdaddaddacebbecbddabbdeabecceaccaeadbcdccbdeccbdceaaaccbaceadddbedbbabddcdebebaecdebbaedabdcabcdcadbaccebcebeadeebcddeacdeedbbdedcacecaacaadbebcabadadcbdadadaaacacdaeeabaedaceadcdcddedccecbeebcbabdaebbcdeaaeebedddbaecaaccdcbabedeebccaeddaceecdabbdbabcccedaabededddddccdcadcaadeedcddaddeecaabadaeceeeaaeaecbaebbedbbeccaeebdeebdeaeedecbdeeeaeedcbaaceaedaaabcaaebebdacadececeeedaadcaeaebbaabccbebeeabcbcccaddbdbcbbeabaecacabadcdbccdbccbacbdeacbceeaaebadcbbadeeddcbadcacaaceaedbcaddcaabbeecaadccabdabcbdaecadaddddabebdebddcaccddebdceebdeaedbbacaacabdcdcdacababecabbdcaeebecdddadcdcdebbeeaddcbedeebaabaddceedcceecccceabbebbaddcaeadbceedacdcdceddceaaaacadbaccbbabceebeebcbabcbbbedacdcaaccbbdccebecbacaebaeebedddabcebdbdadedccdecedbdeeecdbecaccaadbebacdecdedcaedaddeccccecacbacadbddbebaaccbdaacaaedcacbdeeebdaeacaceedaedbddbeddbeddaadeeddbbaadcdacdbaeaaccadcbccccaaaedadcaccdcecbeaeacacbcdeececdbbcedcdebeebdbabeacecbcbbcbabeeceddbabcabeddececaedccaaaabeabcccbbabccdbdeedccddecbdeabbbbbeedaedcbabdeeabbbdeadabbdcdecceeaadacebdacbcadbaceddeaaceeaeceaedeeccbaabccbdddebdcbceedeeedeadcdeedbaeebcaccacdeebbcdbceaeaddeecccaebcaeecaddedcbdbedaaecbececbbbcbabdbcbdeeaddeabaaecdcbbcbdcddcdaaebddaccaaaeeccadcbccccebcbcadacebdecacedeeadeccccdedcedeedeaedaeebdeebcbcdaaebdbdbddacabccadceeaaeaceadeccadadccabcbbaedaacceecebcdecceabeecdbaeccaddbdcaacbdbeccdcaaeaaebbbdacdcbebeddeaaebdaeabdeccbcbedccceebdaeeccacbacdeeeccadbebcabcbcabdddbcbceeeccccceccaedbadeeececacdaeeeadadacaeddbcbabebaaebdaeabcdccceeebbbdeeeabcccebbdcdeaabdbbdaeaeececbcacceccbbecaaacbcddbacedbecdaaadaddacccaedcccbccbcecbbedadcaecdaecdbaaebabaebbcbabcaabcabadbbdbcaaddbeddccbdeeebdabcadbdebeceeccacebcedaddcedbdeebaddadebbebebdeaacdcdcdaaeeedbdabeadacbcbdcaedceceaedeceaeccdbeaeecdbaadeeadbacdbccbaacbccaeadcecdbeabedacaaccebaccabbbcccaeacccaeccdbaeaaccdaedbaebdeaaaeacdcbdbdbeacdcdccbebaedabcdceabdbbabcaecbebcdccbadadcccbcdddbddbbdeecddbecbeaeeaceebaadecccedbccacdccaeadbabddbddaebadeeeaaaadeaebdeabbedeeaaceabecdaeecbaacccbbdddcbaeeadbaadaaaadbadcaebdbbeebebaadaabbdedebcacdccbedcabadbeddceeecdccadbeddaeeeeabcdbddcaeecdadaadbeecdeeaeedadccdeeddeeecedaddbbdabaabadcbedbabedbdaedbdabdaaeccdcacdceeacbababbcbbcaecaeecbabebccbbaadcecccdaeadbbdacebccbbabbadcaacdacdbacbdeaeebbeaeaceceeebcbbedeccbaebccddcbdebdedcbdaeacbcdccadeaadeedbaabbebcdaeecbcedbaeeeeedabecedaaeacbbdaeebddebbbbbdddbebeeccaabceadbddbcbdddcbacdabadbcdbcebbcddccceabbebadeaebcedcccbadcacbdbcedbaeeeecaabdaedcbeedabdedaccbeddbeadbbebdaddcbeadcdaebdeadddedceacdedbbccecadcbaaaadeceeaeecbebebcadaeebcaadebedabbaaedeccaedddaedaddeedccedccecebacbaddaaddabcaedeadcadcadecbecddceddbadccddcdbcdeabcbcccdddcacbaaacaebdaabcabccdbbbbdcbecceddccabceebabcabdaadbbddccaeacdebaaceebdcbdabacdcdddebcdaedbbcbcaebcdbaacbaadebbcecdacdeccdcdbcdadaadebedddbdebadeecbceceaaaeeeabdeebecaebadeceebbaeabebccdcdcaccebecbbcaacedccaeedbabdcbadbcaadadcabaddbdcadebdcabbaebceacdbbaadcbbbbdecbdddabdeebbcdeeeabebdccbdecccdbbbdadcebcddaededceeeeceaecbbecaeebbabaeabbdddcedeaabeaacadaccbdbcceaceceebdcaeebdebbababaeecdaeecaadbdbebebdbeaabcbdbaebbcceaecedacbedbebaedeacccadeccceeecbcedbcecaadaeebeeedeecacbadebabdaaecbceceeebeccddbaeabaadabcaacebaaeeccbdeecdbdbcbdedddbadbbaadcadaebbddbddaddebadbaccadecdcbdbccebecddbeedbcbeaedbadadcbcedbddbecaedeeaaabcdbcbcecbadbaabbaedbadecbbdebcddbaaabebaaaddbeccacccaadaccdcaacdbdceeaabeddbaabaabceedcdcbbbadbecebbaebbebedcaadadceeacbebebdeccabbbabcbcabeeebeabddbaaccbabcdbdadaadaebaebdacdcaddeaabedecdbedabaceaeeddcdbbbedbeccdcdaeacebbccdaeaecbcbabdacbecdaaeadeebebaabdddaddcaacbaabeeeaacecacaacaabbbedcdccdbeeaecadbdbebdbcadcbcbedbdeaeaebaedcdddccbdeebbdceeebedcbaedecbcbbbeccdbbedeacadacbdcaabcecbcbbeeacebeeeebeabcaeacbdacdadcadadaebcddaaebbcddaebebcceaadddbbacbdebbeeddbacebcbedbabdbbbbadaeebbccdebcbdeedcbacccdcbdcdbcebeabbcbdeaebabecbabbedebabbaebedaaedeedccacccbdeecabcddceaacabeeedbeedcaceacbbbbaaddbaabeceedcabaccbbccdacecabeedbeceadbeaeebdabbcaadaccbbcededadeabcbdeecebeddacabcceebcebecaadcceedeaaddaddbadddbbacbbbecabbcbaeaeedcbdaacbcdbabccbcadbcaacbedcbabbcdddadbddddbedecaaebacaabcbdbbdecababeddeaaecdcdbaacaddeadbdeacddedacdededecaaadaaaeebbebdccaddcbededdedbcaeecdaadebabbeeecdaceebedacecebdadecadcebccdbaeaeddacdbaaebeceeadebababeddeedabadcddeabacdebbaeeedecadbaccddaaccabbedeeeacebbabbbadcaeacdacdeaeabcbcceceadeedcdeabeacaddadbecaaaedbdedbeaacddbecaaeadcaaebbeceddbbddeedbbbabdceccdaacdeadddceabdebbacedecbeccecebbaabbcbbaedbcbaeaacdbcaebdcabecbadccabddcaeabcbedabcabdeccecabadcecacabccaeeceaebbabdddebbdebdbcdbcbaeaaaccccbeaabaebaaecabdaeccecdebcdacddbaedabbedeaaceedccccaebdbacbcdddedceacddaaedcdebdedaeecdeaeadacdebaebceccdbecdeaabcecacdcbddbbeddbeaeaccebadcebabeceabcbdbbebdcdadddcaedcbabbadcdccebaccbddcecdcbeaeadddbcaedeedbdecededabcbdaccaaddecdaedddacaaeaeebdbbdecbadadbbbbbbcadccdaaeaebcbbbecadbadcbdbaaaeecdaebababbabeddbebbbeeabcaccebbcabaccaeedeaebeabbececaceaaecdeedcbbbcaabdbbeedccdcbeedceddcecedeaccaacecddbeaceaabdbbeebbcaabacaebbbbacbbddeaacbebecdcdbcececabeabeeeedcdaaccaddeeddedbbbeaedcecadbadcaeababbabcadccbabbbdacaadeccabdeaebaebbebaabadaadebebeebceebaeaccceadddbdccebeebdddebddbbacdcdebbbbeddbeedddbbdadabccccecebcadbcedddadbccaeaaecbdbcbdaeebececaedeeddcebcecaccabdcccdaccdcccceedadcacbbceedecbacebaddebdbceaaeeaceebedcbaabdaabbbcadcaecdddaeeeaaaadbeabeadeaaedbccdcabacaabbcddeeabbbabbdececdbceccaceeacedebaabdadbdecadeebcbdabbaedaaaecdccbdbdabaabcadababcdbdabceebcbcddecdddeccdabceacbbeebbcdbbeaaaebeacdbaecbebabeaabcdbaabbedbddebdaebaecdaaceaebdbecabeabcaacebbcdbbdbdeababbbcdeceeebecebdbdddeadccddabbaceccacacadbaaadbaddebedadcabeecbaabceaceaeddbceebccdeedbebddeddbeadebdabccaeceddaacdabededabbcececdcacdcaedbecbabaeaddcccbecaadbaedbeceaddeebbaddaecdbbcddcbabacaebbeeceeccbedaaeddeacabbaaebaacdbceceeaecebdecbccecaeddecacaadcaaeaabdddeeddeacaaaeaadcddededdddbcabbceeadedabeccdebdbabbceebceeabbbebeadabdeacaecbaecdabccadccccaaeecbbccabeeccebabcedbbccdaebebdcdeedababdaaaccddeacddeadbbccdaaeeaeaceddbacddbcccdcecbbceadedaeecdcddebbdacebcbceeecceabaeacbabdecedecdbdedbbbeedccaeeeacbeeabbddbbcecebaeaaebbcbecdbedbdcaebabeecbcceebeedebccdadcdeceebcabebbbbcdcaddccddbdeeabebeeebbedceaeabbddcccdcdceeecacbcdbccbbdecccaddccaebcceaaceeaebbccdaceebeeeebccaaebebaeaecaccddcbdcccceeaaccdbdbccdabacbdabaaceacdacaddbbecccedaedadcdeecacecedcbdbbcbdceaeeebebaceeceeaacdeaeaccaaddeaeeeaacbeccecbaeeaccbbaeabddecddeeaceccbadccdaaeccdccaaeaceedeeddaacdebaedbdaebdbceecbcacaeccedbbedddecdddcbcaecaedecaddcdbddaaaaacadcdbeedcbeebeedcedeedaeabcdbedeecacadcbbabebeededbdcbceacdacbcecbecbadaececeebbbaceeabebaccdaaadadbbddddcadbcdbbebacceedeeabdeaaccdcbcbaaabdedcddeccbeadecdbcaeadbbbaeedeccdccddbecbceecbbeedddcecdbebddbddaaedbaeddcbdbbadbcebcdadceececbceadbcacdaeebaddeaddebbaacbbbdccddaeadbbceeaebbecadbaebbcbdedceccebddbeeaeaddabeccbcdedacbcebababeacababedadccadeddbedbadaacbeccaedccceedecddcdbeaaeaabeecebcceeebeddcbeeabadcbbacadceadeeaddadaecbeebcbeecbaabddeadabeacacbaceacebedbeaadbacecbcddbdeedcddcbbeeadcbacbabcbaeaeccaebeaebcaebcbcadbcacedbbeecccedceaacbbecdeebcaeaaeaedcdbeaeddccecccbecbabcddcddabddecbcadcedcbeebaadcaddccecbaccbeddadaaeecdebaedcbdaeabadddbadcddaeebdbabbcbdddebdaddbccdededabcaceadeeabcebcddddcdeedaedbeebddbccccbbbaaccdceceedbaaabacbcddedaadbddbdbccdacaeeeeddcecbbadcbdacdadceedbeaeddbdeacbcabbadadaeaacabdcdaeceabadbabdeacabeecbebcbccabceecbedaabedeabdedccadebdadbddbeabdddccccbeaaecacbdddbdacececdebcccdaacdbcbacaeddabbaecbdebdaceeaedadacaacbcacdaedbbcaedcdcccbddbddaaccbaddabacacbbbdcbedbdceeaccaecadcbcedcedbddddbaacadbdebaccaabaaaaeaaeacaaeabdeaeeadacbebededeebbccaccdedebaceddaedadedaabccbaaceacbeceeaceedcecbeebecccebacbdbbcdadbeecedeaecdceeecacaadaaedebdeedcaacbccceedcbcccadddadaeececdacabdbdeeeedaceaecaeaebeedeadabdaeebbdabdbbbddbdaeacbdcadebaeaababbdedbacaceaaabbdedcebadccaaececcaebdbbaabdedbacdcceaaecbebddcacbbccecabdcbdecacabecbbebdcaaaddabbbdbbcedcacbeaeebbebdaeeacedaddeceddedcbeaedcbbdaacededccdaaadbbaddbcbceecebbeaeccaecdbbabdccdaeeaebcbcaaebeadadbbeeecebaedbbccebbebdbbdcdccdcbcdcacebbadabcaebbedbaaaeaaabbcabddcacbdccbdaebacbccbabbcbaebceecceecccaeceebbadaddceeabbdecabdcbddeaccaeaaaedbdaabecaaabaedacdbccbddcedbcaadacddacddbbbbebcadeaeaaeaeeaabeeccbdcedaebeaaacaeebdabbdaceaabaadebeebcbebcdbbcdaadacecbdbcaaacdeaeddacbcbdacebcebebcdbeeeaaeabccdbddccecebcbebeeddcddcdbcbcdcccccecabbcbbccdbcdbaedaeeeabdecdaebddbbdededeabadbabdddbacabaaebbcbaaadeabccdbebecacbddbccebdedcbaedcdeedbceddabecdbddbccadbbcabddcbbadccdacedbedbcbeebecabcdadbdbedbcbcaabdccbecbcbccadedecacbaceccaacaeeddbcdacdbcedaeebedcbcebcaabeccccdcbceeaaaccacabbddbeacabeeaecceacdbeeccdcdbaccbdeaabaabcccaadededcaaaddcbdaadaadaeceaccebbabadaebaeadbadbbadeaaccbccaeabbabbdaaadcecdeedbdebaadabdebedcdbdabbabeecebcadbecaebaebbdddeaeadbaabebacdcaebabaacedbbbbdaebbdabdbbdaaacbaebdbadceebeaaaaaecdbbedebaeabdaedaabbedacedcbbeccececabccdebdbdddddcbadddccccaeaadcadaaccaadcebdbaeabeebbeeeaececececebaedcedbccebeeedeedddbeedbecedaedaebbdecabaebadbbacceddecdbadcacbabdebeccdaacbdadaeaadbadceabededaaaeaaddbaddeccecacedaaccbbeebaabaceeceeedecddcbddcaedebddbececcbaeccceccbbcbbddbecdcabeaacaeeddbcbabbdebbeddcadabbaacbcbcbdcaaebedddbbaaadedaeaadcdbcddbcdeeaeebdaadceadbcbeeeecedeeecbebcadbceadaadbaeabecaaadeeecebcabcbddbcbeaeeabbbccbadaacdbadbbcbecaddabebadeaedaabdcbeceaeddbaeebbbceadbdceabacdedbecdcaeeabbeebadeddeebaabebbedadbeadadaebededaeeeceeaabbadbcbdacbcbcabedaceddeebdecbcbbdcbaababcbeabeacaedabaaaaeaeecbabeabecbabdcdbdccacdcbacbcbbdceedcbbeccbeaaabcdccddbeecdacaacaeeaabcdaecbdaddaaccabaacddddacbbebabdabacdaddbbccbdebbdaacadcedebdedceabdadcaccaaeceeccccdacbdbdcbdeceeeededaaeaabcdcadcebaaeccbbcccbbaaadeacdcabbbcceacacbdcbedbcddebccaecaebabeadcbecbcbbdecbcaaacabacbcabcedabdecadcdbdeacdaeeaaedaabccbbadaebcbedbcadeabedeaeeeacbeecbeaddddddcebbbecbebddabaeccacbdbbeeaeaddebeeeccdbdaacdeeaeccacbadbbcaabdaebddaaaccededcdacbeeebccddedacadebdeadccedbddbeeabdbacdadebdbebbeebadaeeeacbaeeddadedececcbebcedcacbaaeedababedeaedadbacaaebcbacbcccacbacdabcbcaaeedaaaaaecccbeacedadeaceeaaebdeabdcbdcebcddedcadbacecbadeeaebbbcdeacddabbbdcbcbaeedcaabacaeabddedbecadaddecacdbabadadbbdbbdbadaadddbeedacdbabceaacccebaeceacbdaacaeedaeddbbebdcedecacdaaeeceddaceeccbeecccbeddebeaadabcdaebebbdeeeebcceccbbdcdaaeececadbdeaadbbacdbdbedadccdaeabbcbdacdabadedbaddceaeebdcaaceedcdaecaaeaebbeacbdaeebbdbeabdaebbccabebbedcccedabbeecdbcbdaeadaadbdbdcdbabdbbabbebebeaaccdedeccedecbeedddabdbdcedcddbdeeececbaccdbeecddceabdccbebcebdabacdbebaceaaddabdbceeeeadaabeebcbecbbccaaaadbabcedaeceecdcceccadcebddedcbabbbacddccedbadcbdacdecdedbddeaadeaecabacaabcaeceadbaededccddddbacbecdeddcddcbcadedbebeddaddabccbaaaaadedececdcaaecdbacacbacbeeadebcabbbaacbaaaadcbcdbdadbcbadaebcebbbccbecbdbbabecebdbbacaebedacceeccacbeadececbcacacbccaccbcaeccecdadaddabeaabcacbeaeedadabdeccaccbcbcbeddaadcadeeadeecedebacaabebeaedabcedccedddcabcebeacaabbbeedbccbecadcaeadaeadcbaeceeeabcecbceccedaedbeacebdeadbacdaccbbcacbcbcbddccdecdeebddeebadcaeeaececbcdedaeacaadabdcddabaaacebcbebadbcbcaaadeecdbddebdabddeddbdcedebcadabbecacbaecdaadeeeccccacdedeaeedecdcdccebaddcaabaaaededddeeaadeacccbeebebbdaeabbdccdbddcacaeacbdbebccedbcbcedebabdbdebcbbeaaebcaaddebedccbdceeaeddeabdcdbdbacbdeeddebaccdcacedbaaceeaebddaaedcdaceebccdcaabbedeedbeebbbbbcebeecbbdabbcdcaeaacaabdeeeabaedccdbcbadbdeedaacaadecbaabbbabbccecdecbbcecdadedceeccecabccbbecddcceddbabaadabebaeabdecccbbbbcddcdaedbccdacceeecebcedacaaccdadeddddeebddbaaeecadbdabbebbdcaaecbaccceceaedbeccdcdbaccebecbdedeaedcaaddccebedadececaceaeeabcaaaeddaccdaedbaeacabacbbbacedabbaccbcdacbabbedadbacacecbbacbdebababbedadedeeeecbbbeebaacbdabedbecddaecdbdededdacccaadbeabbaadadbbbecddddebbebccedbaedcdeeeddaacdbdacabbbbaaebdbcbdecebeddccbabaabbbcdddcbcaebddebaabcecbcecdbccadabccbcecedbacbecedbedcbbebbbbdcaaabdbdebbaababcdedbecdeaceabaedddebdccbebeedeeecdebbceabaedceeebbccbeabacbcbebcecabccadcbaadeecceadcebbedbacbaeeeaadabcbecccccadddccbeeedaaceaaaaaaecabedabbaaccbbabcdebbbabbbdbececbbcceadcdbecbaecbdbbceeadddeeabacacebccadebacadccaecadbcbeddbeeddaceaedbeeaaabdbadcacecdbbbcaecdedacadedbdadcecccaeceadedcceeebabbbccebdeecabdaebebdbbebdabedceecdeaebcedeccaceebbbbdedceebebccaabeaaaddcaebeddadaccebeeacbacaedcaeaeecaecadaeecccbaccaeecdebdbedbeceaabbcccaadbdeacebebbaecdbbadcecdaeededcdcababaeccedcebccbbdbcceaeaebdecabeedeebcdeabeeeeabbcbcbabbaedcedccccdedadadaadaedcdcacdaddecbacdeaccdccebbcbcacaddcccecdceadbeebacabccccceaeeeebcbeabdeebaacccabbccadceddaececcaaeabdebdddbbdaaccdcdcaaaecdebaeadcbcddeadecebabcabeadcaeabcebdaeeedabcabaedeadaeabbbaeddebebbaebabbddcbadadebcadaaccddbaedeedadbbbbaceaccecaedbeacbcbbebbbcceebeeaeaeecedadccbeebddceaadbbbaadabcceabcbddeedeecaacacaadbdeeccaadcdebeabaedadeceecaeddcdabdcccebbeadaddeabbdbcbadedcccddedeccbdcaaeaeadebccaccbbcdedccacdbceadabedadabbecbcccbdbcabedbddeaddbcdbbebecdcabcdedddbaccdabddddcdbdbdcacebddaaadccdecdbebddeacccceddbdabdddceacacccccdaaceedbdeceacbaacaddeacaedcadccbcacaddabdbdadededccccacbaedbacbccebdcdcbbeeecaccaaddbbaaabccbbeceaeaeecbcabddaebedbadcbdeddbeeceebdadcedbbcbddadccddecaacacbddccacaadcdedbedbdbeadeecddddebbdeedcbcedecdcdaededbdecbaaeddaebcddddbcbcdcaaaebedcbebcecaadacdacbecccacbceeacaebcdcbaddaebacacedebdddacddcdcbbdababeaaedbdaddeecbcbeacececdebcebecaecbadbbcebaaebccbcecedaececccdcebacbeeaccdbdbbdbbadedabcdceebeedbedabaadeeaaacdacdceabbddccabbbdbbbddbceaacdcbeeeeecdabddcbbcdacceebccdbdeabeedbbaedabaaaaddcdbbcbcecddddcaeabdebdddaebeeccebeccebccdcacdaeaddceecabeecbeadebeecaaeaeaabdeeeabbeebdbebcebeabddaebeccbaedacbddeeaaecdadbcadbbecddedabbbbabeaadcbcdbaeeccdaeadcdedddcdecbedccebdaeaadcadddeeeeaacebcbcedbadeacaaebdbaaaababbacaebacabdcabaadccccccddccedabaeadaacaadadbbbdbeaebacbbbbecbdbcaaecbcceedaaadbebebcabbbdccdeddeaacacdabcabddacacbebcdaaebccbaaebcaeedceecbaebaebabdccadbebbddbbeccacbbdcdbddedcddaaaaedadbedacdbebbdbcdbaeedbabacabbcccddeaacaaabacdcddbbedbecabbedeeeedeaecbedbacabdbdddcdcbbcacdeaebabdeebaeaeccedaaebaadcaacadcdccddcdecbebddbbcecaabacdedebdaeadceddeeaacbceabeaacbdedadcbbdaeddcaabcddcddcdccdebecbaaabcaccdcccdeddeebaaeeaeccebbdaaecabbdeaeabbeedcbdbbdedaeacbcdddbcbbbaeececdbccdaceeadbcabdbdcdebbadadaddadaebbcaecaaebcbcdceabdbbcedbbcacecabceabeadaccdaabdaadcdadbadcadbddcabaebdabdacebbbbcbbebdedcecadccdbddbdebedcaebbecbbbededacdcaebcdbbcbbebcaedcedecdbadeedadaeabcaeecdddecbdcdecacedeaacbdaaabadddacbadaabdbeabdbabbcdabaabccbdceddecbceecaabbabadbdceedaceccaabbbcbcdacdaccbbacabaecedaaddcddbeacdacbdaaacceebcaebededcbeeaceeaaaacdbcaccdbebbdbaeaabddabebdacaeeabccdbeddbdbcbdabdabaaddbbadeaaeccbcdabddcddebcaeadbeaddaebcaecabddddaecccbaebbbcecdacdcebccbeeacdcddabdeebdbbacdcaacecabdbddebacddbedaecdcbbaeabedcebcaecebacbbdbbaeeceacaaebdacabcbcbeadcccccddbacaabdcedcaddadbdebcecbbbacaabaacadccccccaadedccadbeadeacabebdabbaceaeacacaedcbcbacacbdbebdadebddccacccbceeddbbbaedadeaedbdcbbacacedebecdacedccdccbaacebaddedacaaceaaddebdecedbccadcceaaebbbadccadcaaccbaaaabadbeeeabaaadddddaddeedeabaeadabacdaedaeeaabedccebdcccebeaabedededdacdeeedaebaecbbccddeedaacdceacaebecabccccccbeeccbaaeadbcaedceaeecedcedacdbeeeecceddbcebabeaddbbaacbaedeccbedbdbddceedcdcadcabbbccbbeebcaadadbeececcaeeaacdcaabbbbbdbdaacaadeacbcacbceadacbeaadacdcbaeeacccbbcabcadbbdcdcddcddaebacbceaebadccbbdedbbeddeeeddebadeadabaccdcaceabddddebdeadcdadecebecceccdbaabddbcaccadacccbaabdddbceebdabaeebbacecaeaeddbebcbdedcdccdadaacecdeadcaccbeadecabeeddddecbcdcacebedeacdcbddcaedbbabcedeecaebcacbbdeddbdedcaadbddaeeadccdbeadeaccadcbbbbabaceedeadebadcbceedeaabedacebdcbedaaaaccbbaddbbbcccbbaeaceebeebaadebabbeddbddecbdcecdbebacceeaabbdbcebabcddeaaccbaabacdcbececbecddcadbcddedcedadebddccedaeeedcebacbdccdcddbbadadaeecdeadabadcbadebedcceddbddcabeaadbaecdddadabdbadeabaededcedccbcdbadddecbbabdaebaeaebceeaaacedaddbcccbcdecdaebdbecceecadbddedcacbbbaebabddbedbdcceceddeaadaadedbccdbaaeeadaabdbdcebdbdaacdeabdaccbbcdceceaaeababcbebcedaeeaccdabebaadbdadacaebddedacbaaabeaeeadbaeccccdeacabcaacecccaedbbdcaabdbaeaaedaccbbaeebacadebdbcbbeaebbcaedbbcbaadaaecbbbccdddcebaabcedcdececcedbedaabbecabdbacbcedcbeaaadbadebdaaeebdbebededdebdaeedacdcbebcadbdbecdbbdeeccccabdbbedbadeaabdacdabbacecdaadcadbbddeaecebbdaacccedcbedbdadadaabdadbcedaebceeeaedcebbeaebadabeacecaaeeebedcadebbbcddcbabcddadeadeccabbdedbecabbeccbaecacbacbdbcbaeebccddeecbbeeaaeabdaadccbbeabadacebeaadccadecbecedabdadeaeecdacaaeddaaacdcbcaacbdeaddcabdebacedeebdccbdcdbbddaadbecbbcdbbaaabeaaeeeacdcaacddedaeaeacaeeeaecdadaaeceaaaebceaadaaedcdabecdcbeedebbacbebaabacadaadcbadabddddcadabcceebadaebaaecdccccaebdaaedacccaedaeeeeecedacbcdbecbdcdcabdaadddaeebdababdbcaeedeeaeaddcbacbdabbaeeaaedbcddcadceecbdeaabecaeaddcecbcecddddbaeebdbdbcadceacbdbdcdbbbeeeecdbbbadceadbbbbabbbccecbddbbabaadbcebbddcbdaaaaaeceeddbdbceddadaceebbaecbadaeebcdcaadaaddcaacbbeeabeaeddecaccbedabaebeebbccdaaeaaccbcccdadbbccaaebcacecaeaaacebcedbaebcaeccaddedaddcdddabbddcaeecbaddecececcbeededcebddcbaacdeaabbebddceabdcbadbeecbbbacabcaebeecddcdaaccdaceaececdadccdecbedeebedebadedcbaeeaeeeaedebcedadacbddceeeaecdbaeaabadceccdbeacedabdacbacdeadaaababdedacaaaabbceacbdcdedccbbbbeceeccbcaaedbaaeaeabcedaadeccdeacedecacabecceedbbebcdaaabadebcbebdeabddcdcecaeecdccbdabcddedaaadcbcebeaebbedadaacccedeadbabdbcdacaedeebaedcddcdaededabcbbadaeeeedabeabadbedbccaacebaeebabbbcbcdabadabbeecbbcddcdccbabaaaddbcdbbeadadceedebbeeedabaebdcdecdeeeaddaabcbcedbedcbbbdbacabaacddabaccdacdaaccdaeadabeeacbdccdcaedacbcebeadcacbdbabdbdbeaecbabeedacddcaacddcdddaacdaddbacabdacedadbebacaceebcddcecbcceabadcebadcccbeddedbdacedcbeceeecadaebadcbacdceaadaaabaeadcbcbadbddedaceadadecacccdecdbaebeaccebaaecaeebabbadaccdccaebcbacabbaedcceeecaaabbbabccbbdaaceaaabcbbdddcedbddceadeaccdaddecceeceaebecebaabaaeadbdbeeeddddbaaeecbadabeceeedcadecaadecdeeedbeedabcbebebeabbeccacbdccebdbbdbddedacaaabbdcebddbabaeaaeabbaeebebaecdbbbcbbbddadcaaaedbdbeaaeedbccbcaddacbbceabdadccbbbaeeeceadaaddeedaaebaaadcecbdaecabcdeeaabedaeeeabecdbbbebcaeecbecccceabadbadeccaabeecddeababbaecdeeeebeeaedbbbbcebbbbaebdecddabedbddebacccabbcbcbccdabccebaebbeabebeaaedaacacbdcdaeaadebedcdbcabaddaccaccebcccdcababccebdccccccbbceebabbeaebdbcdeebadadddbdcbdbaaedecddbddabcbbbabeacdcaedeabbeacdbaadcebbecdcdedbaabeeaeaeaeddabebdaaeaceccadbeedadddeecaedaedcbdceebbaeaaaebbeecacaddadcacbbbddcdeaddaccccbaecbddadcbdceaedcccbdcddcaadadaacababeaebcabdbbbedeeabadbddddcbcecbddbbeeeadaabeaabdaaebcccddeedadbacddeedbbadadcdcaabcaccebbecbaecaedaedbdebbedeededbdaeacbadaaecbdeddaebddceedadabbdbbbeceaccabcebaeacedebbcebdedddcddbacabdacaebcccdcaaedebaccdeaceeeaecbccccccdedddbceeddaeddcecddaceeabedeaecdbaecbdbbdbeddbabbcaeeecaeaceabbbdbdadabacbaadeccdeebbbaeabeebdabaebdabdcecabdbbbcdbbbdbdeaebaecbdebbbaeadbadeaaabcbdbaedacebabaeacbdccacccacdcddabebabeaedeabaaabcdbedceccaceaadbcccbecdabceebbcdcdeeebecdbeebcacebaddeedddcceddbeccdadaeacbbbebbcdebeacdecbbbdcadbcdbdbaadbecdcddebaeebddcdadeacccaedbbdceacdbacebbacaeabdacbaaabbcbbeeadabacaedaeabebaabebbedccaddcabddeecabcacbbdeeceaacabdcebeebdeaaeeaebceadedcaacbcdcdbbeeaeadbbbdebdaecdeacdacbbeeeeaebcbcdbebbdcbcbbacabdaaddbadedeaecebcdeaeaeccdcbdbecebadaabeedcdeebcadacabbdbbaaecaaeebecbaeeaebbacbcbaabdaeeccadeaeecdbbdedccebcdbecddadcacebcdeeabcdabecbaeeaebacdcbaebeaecbcadacbedcabdecceaddadcbceebcabacedbdbaaaaeebeaadcddbbccdbbbccbabccbecaddecabebedddececbaeccacaeebbbaadcdccbebddbbbdcededadccecaeaebaeddaacabeecbbcadedddaadeaedbabeaabbecabecadcdaaeaacbdbdccbbabbaabcaaeeddebeedbcacabecaedaeaaacbabdcdaeecddedecdcaebacacaaeebddeebddcbeaadbbbedebbbdccacdabaedeabddcdabceeaaccbdbedebcbaecbadcbdaadcbbaebacabbbadadcdbceacbadbdaacdcbddcabceadbbcabaebdcebaebebddeacccaaaacbdcaacddbdebbaaeabaadbabcbedbbecbddcdeacbecdbdaeacdadcdaecabebdbcbdabbadabdbebbeeceedadbcaceebcdbebbeeacacaabaaaeedaadbcdaeddbaaadceccaaacbabedaccdebbcadebdbbbbccbabbaacebdedcabbceaccaaaaaaabecedccbcbeececcadcebdacadddacbdbdddcdebaaebbdadedcbdcabadeeacebebdbeeebaeaedbbbeadaebabbcebdbddeadadabebaebabdabbebcdebbeebdabeeeaddccaeabdacdcdedbedcebddcbbdcdbacceadceeddaaaabdeddcbeddabdbedebdebacaaeaebdcdecbaaadbcdedeaceaccadacbaeeeecaaebeddeabcbecebcaebbdabdaeaaaebedcedaadeaaaecdbbcacccbbdbdeacbcbdaadccccedaaadaaadebecddbeacbbdddbdedaadcaddcadacdbbbabebcbbbcedbebbdcadaededbecedddeddaaaecbcededeaebbcecdcbecebceaddaccdddbddcdcbbeeededdcbccacbacaecaeebabeaccdbceaecaccbbeaacaaeeedcacdbdaceabdadaeeaaaeedadbccbcdeadbbacaeacbbceaaddecaabdccccecacdaedbabbdecabdcceeabdeccabdbadbddcabbabbecaaeedbbcacbcaadcdeeecbaedaaececacabaabccdcddbabbdebcbbabdebbdacabcceaeaadaeacdbaddecbdcdbaaacbccadebbdaecbddeadddeaebbaabeeddbbcadcaaaacaedddcceebbcecdcbbbecadacbbabdbdbabaccbeaaccabaabadaecdacacaaeddccddaecabddbbeaceebddcccadbcdbddcaccadeaebdcddcdecbacbedbabdcccbcccbcadecdccebabeaedcaeecebedcaebbcadabbcebaeacadacbeebdaedbdaddedbbbdceaedeeacddbcdbcaeeebcedbbecbceeacbdcacaebdebdaaccaaeebdbcadacbeabcceeaebaadbbdebceacabedcacedeecaeaccacdeaeadacbbdeabdcccebbdcecceaebbaddddbdeeeabacedacacbeccabdccbbacdbdbabdedddbabeabeceabcaebdabbabddadaddaababdaccaeacacdedbaaaccddeebbabbeabeaccbcedaebacaadccedebaeaacecdeeabbcabcbabbeecbeeadcaceecaaacedccaeabebbaadcbabbcdaaabdbdebebbddccecadbdbcbabdaaecbddbeaebccdaacacbcaacbecbdcebdbcddbabdbeceddadaeedccdacacdeaeeebacccbebaabddceeacebbaddddedcdbcbaaebdbacaabaeabbcedebdeaacacdaaeccbbbcaaecbeededaaeabebcceaaddbcedabbdaaaaeecdecaeaecbbbecaccbbeaacdeadecddaababaadbcbaaceeeacaeaaedabcdbaabececeddbaceadbbdcdcbaeebabbcbcaeeceaedaddbabdbbdedaaaccdaccbcbbcbdddbccccedcaedebdcddacddacccbdaedebcaabdcbbcbbabecccdccccecacdbaacbcbceabdcdbceeabddeceaddeeeabeecbeaaedcbebeecdbcdcebecebaabebdeacbcbcbccbcdaddbcdccadaeebacbcacaacebdcbdbccacdccaaabbdadbadaededdabdeacbdeccacceaacdbcddacbedbaeecabdeccdacddcdbbebddccaabdddadcebbccbcadcedcebbbbcedcdbebadecdeccadaddbcdeabeddcbcaaadaddaebbdcbabdccbcadebabadcccaccdebeaccedddcacedaadadbbccceeabbcdeddbdbdbbebddabbadaaecbcbccbbceaeaeddedbcabeaeadaeccebbdbdaecadcaeaeaecddbbbcdacaaccbcecbdcaceeedcceecdbdedaaddadaaedceebcbaedebbeddabebecaacaaabbeaeaaeabccdeaeeeaeaecedbeedebbdcecaabeebcaddacebbaebbadcbacdbaacababedbdaaedeaacebacecacebabedbdcccddbbbcededbdcbcaaacdabddbeaadcbcdcebadedaaebccbcdceedaabaecbcbedcbadebcebbccccbadebcabecbbcacbcbbaedcdbedadadcdabbbcdecbbcdddeebacebdcedcebaaecdbaabcbbbbeadcdcccaceccbaaeaeceebdbbbacadabdabdbaeaaddbabbdddbbceacbcdceccccdcabaedbbecbbbcaddbecbabeacbacececcdaabcbdddacebdbdaeeaaecbcbeebeaeeaabedaacebebdabdccdbecdbcdecbacdeaaceeecedceebcdaeebddcacceccdcaddbcdcabceeaddbbdbbededecdaaeccbbcbdacdacedcaaeccddcdedaeabaaaaaaaeeeddddbeacceebdbecccbccebecbdbeecaeabdeceaabbbbcdbcdbadcbddbbedbeedcbbdcddbabebcedebbddbedbecbddeadcdbdbeadecadacdcecbeededceebecdbeaebbcecacbcbbbababbbebebbceecaddccddbbdedcdeebbaebedacaabcbacaaabacaacdeaebecdccadebbaacaeccbeceadadaccacadbddbceecbaddeeddcdecdbceeceeceeedacacdbddbadcbeceeadcccbebbdeddbceacedbcdebdcaebdebaddbabeaccebbabcdedcaaeecebccbecaecccdbaeedadababccbcccdddbccaadaedebaeddcabebcecaeddbbaadbcaeabcedbeabaddbcacaecbeeddbcadbedaaaaebadbbddceedcccabcabbdaadcabaacecdcbaccdcbcebccdeaedcbececabcdcdcebabcabaacebbcbbabdbdaccebcbbdedeeaddedcedaedcabaaeabecccddcecbadbecdcebdacdeedbcccbdccaecabdcedbbacbcbbedbcdbbaebaccaceaccdeedeaeceaceecddbbcccdeacdcdacdaeabcbacecbdbeabbccdedcebbbdabaacabbddebbaebdeaeebacebdcdbaceeabbecdeaceacbcdcbbeaadbadaaeccbdabdebbdeacbacedabacdcbddbeebdaddceaadaccedbadbdaacaeeacbbccdacdebdecadacababacbbeabbadaddbcddbecedceeaeaeeeeedadaddccabbbdeecceeceabaaedceeedbbbadaeeebebcabcaecdcbcabacbdbbbbdcccddeaaabaedbacbadceaccbeabacaadebbbdbbcbcbbeabddcebdaaabcebeacddeecceacedbadedecbaeceaabadcdeedbdacccaceccdcecaeecbbbdaedddbcbdbdbdeeeedaccabeabdaceaeaceceabcbeabacaabacbdacdaeaadcebdbaeecaebebbeaabcbcaadacccabbebaeaddecbdaedddcdadaeacbaddacaaeeecacdcdadcaccaedbdbccecdcecebbcebbddeacdbadaedacbdeaadcbaeccdbdbecbbdddbcbcceeecccbdeddacadaecddacbcacceabadcbedcabcbdeadedcdadcaeaeadabbbbdebccaeccacdbabadeeeccaddbcadacbcceebcceeeeccceaeebbcddcaaeaeacccaeeeacadaaadedbdaebbbcceaaccabacececcecedbaceacdceeadcababedaeceebdaedeeaadcaabcabbabdcdadcacbababebdaababdbcabedbbcdcaaeaebdaeedaeaaccaceaabbbabdeabeeadceaaedcaedcebccbdbdcbceaaeebaecceebabeacaeabedeeacaabdcbabcbaaeccdadcdbdedeaddccebaccaeaebaacaadecdcedbbcaddecebdcdabecaeadbedecacdaaaaacbcaaeeaccadacebddecbbdeceeceacaeaeeccdadebdbbcbcdabebcdebcadbdaccebcdeebdeacdbbaaaacbeccbdcceebdcdaaeddddaacedadbdcdddbdaccaacdadbecdebdbbdcaaabdeccabdebdddabbabaecdbaaddabacebdbeeadabdaeddacaeacecbacdcdaddbceaebbcbcbaecabdddeaecacbacceddaebdebabbddeddecbbcddeeeaeaadcabaeaadeceedcdbdeeabdecaaaeabdaeedecccaadecbcacabeccdeaaddbceacbdedbceebeebbbdcadbbaecdedcddeeacceceeeeababddbedaaeccbabeebeeeccadedddbbabbdcecbcbbbacaccaaaacacebccccdabdddcecbceaadbdecacdeeaaeceaeeeeceadaceebaedcedbbecbeaabdbeacbbbbaaadebcedcbddddaabeaddeacbebcbdbdbcacbceacdadbdbabceecadabceeeccbecacbcdbeeeecaddbeddabaaaeccdbddaadaabcdcdeaadbdacbecdbcbbcacaaaabbcbabbeabceaaacbccebdcdddbdebbccecbdaeacbccebdcaadcdbdeddaaceaeddbdaacdcbeddabdacaecabdccaacbbdbcacceedaeccdeaebdeacbdabdabcccecbdccadacbdbbebedaadbdaaebbdbeacbddeaeabedcdbaceeeccbedebeccaedeabeacaadcccedeabbbdcbadaabdccbcceaedbddbcadeaeebadbddcdaceeaaccbdcabdaeeabdcecabceedebecdbbceecdecaaeaccdedddcaeddcdcebabcdacebdbdbbadaaaedcaaeddddbbaabeeacbbcbeabaebdaecbbacceeebacebdbeaebddaccaaacaeecbdaeeccbeeccabaebbabedaeaaeaddadbeddbddcaddabeeaeadadecaeedcbabdbbdbaeddcbbcdaadcbdbebacaaddcdbabcaceacdecbaaabccccbbacedcbbeaabbddbbaabbbebbdeaddeccbacbacaedacdaceddcbdceaadccecdddabeaccdeaddeabeabeaacddcedaeeebeadedaaadebadbacdddababddeadaabbcaeeeadbadbeabedaeeaeedbeaebeecaeacdddceebdbbddecbdbcebccacebbbcccecdbaaeabadccbcedbbadeabeccadacaccdeacacbdececbeaabacbdbcadcccebbbebdcbcececbbacacaabbeeedbcbbbdbabaacaaaacbcbcdddbddedaacddcdaaaebbedbeabbcaaeebedcecdcedaebecaadcacaebeaadeabdddcacedadcecebddcdedaebebdeadddddeaecacdebdbadeacddcbcbbbccddcbdbdabddbaadeccadabdcacedabdadeccebeebbeccaaadedbeccddadbabeacaacdaccdcccbbddabdccccedbbebddcaddacebbbcbbebeaedbdecccbecaeeeabacbcbaeacdadbaceacddcbdbebabccaceecdeeebbbbaeacceeedaedbebdbdaeaeadeceadecaeaedddabadbecebbeedcbecbbbcdbacedbbdcadacccacedbabedaceaacabdbcdbadbbcaedccbecebecccebcdcabbcadbcdaaadaecceaddbdccdadddbcddcebcddddcaecdeeccdddabbbeacdabcaeabedebeeebdcedaccabecababdeabeaabdbecbbaaeaddadbedcdeeddaddeecaaadaeecceedecbabbdabbcacebccaebeddcacdcbccceceedadcceecaeeaeacadebdcaadeaabbebdcccaedcacccecdedbabbeeaedcddeccbbaedcbeaebdbddbacadbbadadabdadadacebcbddcbaeaccdccbdbadbacccadeadcbcdcdeeccaaeddbabbaeaeccccbccdecacaebddbbbaccceecaebdeebeddddccacaadcaebeadbeabcbeeabaaabcacadcaceacddcbbaadcecbcebaaeaeaaadbeaaaceaeddadabddbcbdddebebeccbddcdebcaabcbddebacecdddbaacdabbdaecacdaecdbbdadcebbcbeedbaecbccbbaeeabbaeabcaeeedbcdbebadccacaadceaaceccacaccaeadbcedeceeaadcbceabacabaadbceeaadddeccaebedabdedcdcddbaebceccdaebcabaedeaddeacbeddbcbecbaebaddbadbecccbdbcdcddcccabaccecaacdcdbbcacbeaceaeabeeabeccdebcdadcdbeedcdceaebaccaeabadabccdbaecaebbbbddabdeeecabbdacdbdadceaabcdacdcedeabadbcecbddbdbcdddaaeabaccdccbebbdacdbeadcbcedebacbcabddaeecbdcbdbadecbcceaadadebbecdcebcedacddeeebccddecaabecdbbcbacdbccacceeadbdebaecdbdaccbcaabaacebeecdebcabadceeeeabccceaeadabcbdaaccdbcebeecbeeebdeebdebecbeccbbacbceddaecdcaabcaeccbadedcdabddeadeceacabcebeeeeacbdeedeebdeaabcdcbceabedabedcadddbdeabbaabccceaccaebebaeddbcabcaeadeeabbcaebedaeedbdeaedadceabdeaecbcdeeeeebabababeaeddadeaaebaedbcabbecbcddebeadcbebedabdaaeacacdbedaaebcedbaaddeadacdacadeebdacecedbeabbbcaebdeeabcceebbaddecdbcbacdceaadcdcdadacdacdcccbeaaaebdaecaccccbbeebabecbeacceceacebcbcaaeaaacaedbeabeacbebdcbedbadecddbababcbebccebcaceeeccdabdbccacacecbdabececebacbcedbabbdddddacedcebbcedaccecbbccbcdaebdcbbeaeeebcdeccdedaabbacabadddeedbcdccaaaebecdcdaceccabecbcbcababcbcceaaeadcaaebccdaebecaccebecbebcebeedebccacecaacbcbeadacaaceebaaebceebbdddcdaacbbeccbbbebdbcecaedeeccbbdcbceaccdecabccabeeedaaeedddcceeaadbbeaabdbcedddddbeadccbceadccbdecdaaadedbdcaaaecacdaccdeaeaaeddabedaaceccbecbdbdbccbbdeccdaddeacadddcdbaabeddaeaebabcdcdbeabaabbadccbacbcdbbddabeabaddbacacacbedaacbebecdedbdedebdecaacdacecdacebbddbbabecedbaabeaeeebdebccacbedbbdabeeabbceaaedeedccadbadededeaacadbbbbcddaeabdbeabadbecbabedecdddeeacbeebdbbdabeccaecaadacdbbaabaaeabacdaebecadedbaebbadeeecbedcdbdbcacaccbbbeacddacababeeadbabecebaeeacacedbaabbcaaeccabdbabaacbeacdccebbadbabbaaedacbbdcccadbacdbacecadbbbebabbbdedcebdaaabacdcceedbdbeebddcebaeddaeaaadabcdeaacceabbacbaccbebacabbbaeddadcaaabaecdeacbbabbedddeedbabeedbadbbedeebccdbdebedeaeebdeedbcceecacaaeddddddbbabbaeadacbbedcedacbeadabceaaedacaabdbdbbaddaedabeeccadeebaecdbccdbcdeeddbdcebeceddacaeceedcdcababbdedbcbdbbccdbdbeabbeaadebabcbeeddddacacbcabebbcdcaddbaaeaabbcdedcaeaddcaeebbbbbedbebaebeddabdaaecddbbeaecabaeceedcccdecabcabdbecebdabddaeecebdedbebbdcdecdebebebbdbbdaeebbcdecdcbeedabddbbeaeebecebbcabccbdaebdabcbeeeebeeeaddacdbedbacecbcebddcccdbaeceeeebedceceadebeabcdbcecdcdeebedcceadebaebcdbaedbdaeabadceadadebedcacbdeeccebbaeceadccebceddadeddaddaebdcdeaaabdecebdebbeeebaeedabcaebcbdcadababceeedccaabdacddaddabdeddcdbbbaeaaccabacaebeeeaaceeadeeadaeabcdbbceabcbdadabddecccaaccbdbccddbbacbdebeccabbadadabecddcddceceaeacacdccaaedccddbceaeeccbbebdadbeeecaddedebbaeaddbbabcdeeeedeabaccbcbeeddcabdeccacebaaabbbdcbcacbbceeddeeceeeddbceddecbdbdaeacccedbaaddecddbaedaabcadbdabbcbaeacdacdddcdcaccadeabbedebdaeeaeaeaabbecebddcaccdddadeeaaecdadcdabbdddeaabdbdbdaddcbaeaeecaccbbcaaeaabccaacbdedcabdcabcbedceddceacdddddadeecdacddeddcccdbcdaceaebebcbdbcdcddaddebedecbccadcdcaaaeeeaeecbaebabbbbeccbabbbdeaaececcddabedaaacadcbbdbccacbaecddcdaaaeaddeedbeabdaaadcceaabbcceaaeabdbbcdbebbbbbdebdecaebaadebbbaeedddbaaacbbbdecaecdaabdecccbadedbccccdadbbdcdccdddacdbbcceadbbcaecdeeedcbeaacacdcacbadecabedeccacbdadadaaabedaecdebdadceacccbbceadabedccacabaddadeaeaedabddbcddabeedbaccceddcbbadededddddaeacddcaadcdcaeeeaeedabdbdddbcaddbcabbcaeedcacecddabcacdeaddcbcdedaedddcddebaacecddaaaccbbbacdcbbccabdadbcdaedaceabdeccdeadbbbceabcaedddcecbdcbeeceadecdabadcadeecaeeeaadeecbaeaedbbebbbdecbadadacccecedbeadcbbedaeaebbcdedaaaaccecbbeccddedccbbedbacbbdadabbddedcceceeeceadaadcdbecdbcccccccdbbeccbeedccceebedebdbccabebeedbbeaeecbedcacebdadcabcddbcadccdbadeabbcbababdaecadceebcbdbbcedceddbdbadecdcacedaeadceeecbadddbecdcbbecbaccccccbbeeaeebcbecbbdbaddddcbcbeabbcbbdcaeaababebccbabedbedaeaddccbaccbeaecdcaededbabeabbabdaacabbceecdbbbedbceaabccceabebcbceadcaaadedabccaaccacaadceceacbadcaaabbddeacddddacdbeeaaabcdbdbcaddecbacbdbbbddeaecbbcbcdcabacceebbecddabeadebecedcbaaccedaddadbcbeacbbaecebdcacbaceadadcccdecadbceabddcaebecdeabedcebcebaedcbbaeeeaaeabbaeacdbcabcaaebbadcceaeedcbeadbeebbbaeaddacbaecdbceacdabebaedaeaaaccdccebaeceadacddbebdaabeebeceaddecacdbddadddeddcdcabaacdbadbcdddbabbbebdcdedccdcbaaaaaebcdeaeddbbdcbabdaebddbaeaccbccddcebaaebdeddedaaedddedabdeaadecabaccbbceadbeaadcbdebaddbeddcdeeeeaebdedcacabdceeaedadaacbdbedbabcdbeedcdaeecbecdabedcdddaebbcacdedaebccdddeccdbaecbbedcdadcebcaddbbadcaccdbbeebedaaccdbccdedeceababedcbeecaacadebdbceaecddbcdaddbcabeaeccceccbabcbbdcbeaadcbadceddcdaeeccdaabbcdcdbeabccaedceddedaedbaadbeedbedeabdacebadbcdeaddbaabbdadcaadaccdddaaabbdddedeaddecaeaedeeeaeddeaaecceedceebababbbaaaaacdadebeacdbcdcabebcebcebecaceebccacadbbebeebdeebdbbaabeeadcabcbdbddbcabcdeacaaabcdabddbbbebebedaecebeeeedacdcacdaeccbdebceeeebeabedbeeeadecbeebcabbeacebcabbeedabcaedcbdedbabbbecdcbbedbebcaeecabaedeaebeaeadcdeeacabacaeaebdaabacdeabbaccdcaecdcadaddaceeebcbcdddeeeaebeadbadabdbadaaacbbeaecbceadebcddcbdabbcbbeeadaeabbaacaecaecbdbeaeaaddddebabaaedaeaacdabdaeabeeebbeebdedbeababaceecbccbcabdeccaadaeebcbddeceeeccaaaeabaabbbacbaedacdddcdbdbaedaceecdacdacaccdbdddecadbdebddcecceeaccbbebaadaeaddbceaebedeaecdbeaeedaadaedbcddeceeaebbbebbbcbceaabbaedceecabaabcbdacbaedcedebedeaccdedeedebcbacaacdcbdccdbccecdcaeaaabdcaaeddaebbdecdeddcbaaebabbbbedaadeabecebedabdeacaaaaaaabeadcdaadebbacbeadeecdbcaddacbccbcdaddaebecccdeaacbacabbacbdcbdeddaabaaadcbcacbdbdabbcdbbebecaccbceacbecbbddeedccebbababedecdaebdbcaaddabdceaaaabaecaceccacceeacbceeeedbabccecdbdbacebeeabcdeeaedadeaaceceaacecceecacadcacbadcaedceaaddbeeaedadbededddcdabecadeebebdaeeadaadebaedadaceeecbdadabbaddbbdbebccbceeecbbaaceebcabebaeabbaacdcdbaedaeddcbcdeddcbcebeadebdbededbdbdbabbdbacdccddbecbeeedebeaadadbbdaacaaeebbddccccdadbdacdeeeecbedebddbaeaaacddabebddeedacedadcbaedebdbdbcbcaebbdedaddebaaeaeabbebaeeabdeaeaabdddadccbeecbabdabcdcceaeeeeecebdecbdbebccccdddbbdbbbebaaeeabebceaabdaccbbddbdeebbeaecbebbabeecbcceddddbedaaccbaedaedaceeebbddccebadcbceaccdadecdaebaaeacdaeeddedeeedbaccdaedddacaebceebcdbbcbcbaecabacbcbddcbacddbccadaedadacddceceacaeeceabbdadebebdcaeacdeaaaabcbeabdeeeabbbccedbbeacddbbebebcecacaeeeebdcccceacaeddbbebceddebdbdbddcdbcabcdebcecdebcbbdabbdbedbceecdbdccbccabacbeadbabedadccdbdcddcaddeaccebadababeaaaddcedeabdeedaaddceebecddecdecbdebcbdaabedddcdddedabadcdddbecdbdaceadcadeccbedbcbbedbcaaebdeebcddadabaabaccadedbadabecbddaebcdceedaceacdabdceeddeadbcbdeebdaceedabccadacbcdbdbcbceedbbebbdabbadbdaeaebcbebcadbbbacbdeadbdcbbcddbdaacddccbaacaaedacaecdacabedeacebadaecdabceedcdcadeebacdaeeaaaeddeeeacbadccdebeceacecacadbacbcbbaeebccedbbecccdadacbeaedbeeecdaadabbbccdaaabebedbecbaebacaddaaaaecccbeccabddcebdbdcccebadcccdaadaebdcddadbcaebbcbcbaaaadbdbbabddbacdeacadecdbbbadeedacebbbaaeabbccebbdecebabcabdcbccedbbcabaaadcabcadeaedccadedebecaabeceaccdacadecabeceecbeabbcddbcbddbecebbbadeaecebddbdcceadacddcabaedeadccebbcbeebaceceeaceeecebddecdcebebdccedcdbadededbbbdddaabcdadcabbeaaeccadcaaaaeaecabebaacdbbdeaebcbccdbdedbcddeccdaaaebabacbbeedbbbdcaceddaadbebddadaadbccaeeccbdaecccccbdcceaeaebddaeacccddbddaccbabeddddccbabdedabeadbdcabaabeedddeecacebecceeeeceebeadbaaebcdcbacbbdbdebcbbcccbbcadcceaedaddecceacddbadaecedaeddceabccbedebbebceabeaaabcbaeaddeeeeaecbaacecddcdcacaaddeadedeeebcadedeedbcedddbedcdedcdaacedaabdbbedbadbaceccadcbeddddabebebceeeeaaebbdaedccbaadbabdadaaaeaaccaeebccdacceacbdbcabbacedcbaaacdbbbccecbbadbacdcaeecdcbbbeaacaebeccccbddbadcabaabaeceacdcceaacbabeacbbbaceddbaeaaeeddabcaecbcaeaeadeedeedacabdceedebebdceedadcaaedaddccdeeaabdbeaaeebaeeaecbdbaabbebdabaaaeaeeacacacceedcdeabdabebcacecaeebabddddcaaecaceddabcabacbbaceaabceeddacebbbbaccbedcddaadcdbdacaddbabbcaadbdabeceeedecbbacdceaacbabeabbbccdcabadbdbbeccaedaeeebddbebcdabddececdbaddbaacaaecbbebeddbaeebdaeceeaaddcdcbeaadaaebaaddddcdebbaedbaaceedeeabdbdbbaaadacbccddbebaaaceebcaeaabcecedadeceddaddaddacebdceeaccebdbddcdedaaeedcdeddadabcaebeebaeadaecbaaeecdedecbcdbccbedaadeeaaadebbecadcccecdbbbeecdbccebddcacceccdeddecccaadcabdebcdaaeedaadbeeacbcdcbebadceaaabbbcaacabddeadceabcecbcebadcccdbaaadebadeababaebaaadaebdabcaebbddebbcecbdbdeabddadddcbcabbdadebbcdddeeedbcbebbcadecaabeacdebeabeceecabeaddbedcdaceabcbbcbedebabccbbbbebddbdbceebebeedeacadebcdbebddacbcaeabeadeceeaecdaaaabdbcdbcbecbbdcecadccbbedaeadddaacbabeeedcaadddedcadacaacdcccaccceedecbaaaebdeddeccdbacdedbddbdddaeabbddadbdeeeecaeddadaeccdaacdebccecadecaaaccbeaeececddabcaedcadbeccdaeaecbbdeaaccbdcbceabbbdbccdbecdcbcccccccdcdabcdcdebcbcabcecebbbdaededadeeaacdaedbadcbaacacabbbbddadeeaeaaaabcaddccaaabdedeaaecacdeceedaedbdeabececbdbdaeccdacbcdceaeadbebbacebebeceeadbbbceebaacabdcbeddeeccaedeacdacdeaaacdcbaddbcdaaddeeacdcccaeeccbeecddbababeacaedcdacbcebabedcabbeadeebbabaccebeccddddaabddcbcebcebcabeecbadaadadaadccbdeddcdcdadaeeaadbdaedacbcbbcddadceacdacacbdcebeccbecaceebabcaccaeedaadbdedecccedccabeedcbedaaaeccaebccdddddbecbaccecdbeabbbccadabcaebabeddcdedebdeebbdaaebededbcbbabbccbdabdddcdacddebeaeaedacbeeaebabcaedecdbbcdceceedaedbeabaecabbbbceeeaeaabeaedeaeadbddaacbdcdeebecbcbdeecedccacbdaeccceabadeccbbbecabaeedbccaedcacadacbaeecbdceecaebaacdcedeaddbcbccacdaaedddbbeceeaaddeeaaedcacbadebebadbebbbededcdcacbccbcdeceeaaabcbdcdebbcaaacacceebadaaadedbedadeacddadbdedbadeabedddedebddbbeddcdebcaadcbbbddaadabecbbdadddbdadbaccdbedcbeaadecbadbbddddcaadbeacceacdbdbdadebaaabdccdaaebadeaabbddcbcadacbdbcdeeccceceebcdddcadeacbeecdececbcccecedacdddddcedbdbebedbaecaeeddbeeedeaedcdebbccaaadddbaaeaccabeedeceddbbdcdcbaebbabedddbaecddecccdebecacdddbbddcbcacacdaaceeeeceeadaaeadbbbbcabecececdeccecdccdeddbeccddbbcabcbecacadbbeebecbbbeccbdadcaaaadedaaaebcddabcdbbbebbeaebdabadcaacccddcebdaedcbaaaadedeaccaecaddcceebccaecebbbebeececdeccedcaaedaeacaadceabcbbbcebddceabbceedcddadcedbccbdcedabacbcbaacddaaeadaacabbaaaeaddcdeacdcabaceeacabcebaceabcbdcdedaaacaeecbabdcdbcddccaabccedcbcebdbecedecabcaeeebeddcaabcebcbdbdddecddeaceedebcaacacdccdaecccededecaecbaeedddbdcceedcaabebdbcadbabebbecabdadabcacabdbdadcaeccbededbacedecbbebeeaaddedabebdedcabddeadddddcaeeadaaedbcdbcdbbeeeebadebecdceadcedcdceccacbeadcdaaaceeaddddbbeeebdcaceccabecbccabbdeeaccaaababcdeaeaeabeddecdedabbcbdaabebcaeaaecaddbcedeedbeabedcbceecdecdadeadceeadcdaebaebdeedddddacedbdccddacbcedcebebbdacdeabccccedebeecaacdcdebcaaaceccdebedcdadcdaaebedacedacdaebccacebeddabbcdbcdeabeadcacacecdbcecebcbdbbcecbbccbadaecedddbabdcdedbddbabbedaceeeaadbebeaabaaddbaaecdcecbbedbbddccaddbbdcaadaddcbaedacdbabadabdccbccdaacbbdabbbdaeecccccdabcddececdeeaeabedcadcebedcbebebaddbecaaebaaadadcaedeacbaaabbeeaebbacabcbebcdedcedcbdedcccbbbbeacceabdbcdcbbaedcedecabedceacdbcabaeddacbcadbddaacceccabaeeeaceadeeeeeeeacedecddeacbacabcdabbccdcddbadcebbbdacabceaceecdebacedacabbdbaaacabdaedbdcecccbbbddbedddaaddcaadbbaebdbbcbbbeacaebbeaebbcacddbadeeadecbeeadceebeacbcbcdeaeceeeabadaaeacceacbbccaebeeacdbeebabddcdaebaaaaeabbdedcdebabbebedeadccadaccdddaebccbccdccaeaaeabccdcebaebeeaabbacbbedaaccaaadbdaabbcbbcaabdbdaaeddecadcbacdaadcecdcacaadaabdcbcabecaadecccbcdadabbdbaceeedabedeeeedbbcdcecbdebbdbbbdeeabcebebebdbaacddadedabcddeceabdbdeccdabaecedbcdbcccabababbbedaebeadbcecaedaaccecdebadebccbcaeccabbaacdeddaedcebecbbcaceadcccdebccecbdabbbdecdcecdbceddababecccdabcccccbbecceeeddabbdcaaaddeeaedddadabcdacebbddddcdadbddbcadddcbeccbaabedcccdaeeeeadcbebbcdaacdcbeeedacbbedbdbbeebbdacaaabccaacadaeaceabcecedcddabadeadbedaddcbbaababaccbecedbedecaecebaadabebcacdaeaccbeadeaacdadeecdbdbdbdddecccaacabdccddbcdcacedbdacceaabddecacbbcbaabbbededdeccbceccabbdebaabaadccaadddaaabbccdcbbdddddcddbceebadedcadbdebdddeebdbeaeaaabadaaeedcdbcadaabdbdedbedaeeacabdcadcdbabbddeadacecaacdbedacadaedecdbcbbdaccceebbbcddbbbeedebbcdebbabacddccdebacaeeeaebdbddbdeddaebbbdbabcddabcdaedbaedbdaeeeccbdaeaddbadcceeaedabdbaeecadceadaedadcdeadecdbbcceeecabbddabbaabcceacbaabdaadedaaebccaaedbdeeeebdbdedeeededceadceeaeccebccddbbccdbdccbbedbeeebecdadbaeeccebeaabcdbdbaeadabdbbaadabcbdcdadbbbacdddcebdabddbeedbdbddabaeaaeeddcddeaabeadaecbcceaeddaaabacdbcadedbdcdcdabdabebaaedcdabeeeceebaedcacaddaabaeddeeaaceabaccccaecabeececedbacdadababccbadbeccebdaeecbbbcbcaecbccbccdabaccbaeeebadcbedbccaaddadcecdbebaedaacdbcedaabdceadebedddacbcdbebdbabcaecaeadbaddcbcbbdaccdacabaedadeadbddabebaadaebbdadaeeaccaacaddcacabddebbbbbcacedeadabcdbaadebdbccdbecdebbedceecacedeaecddaebdabdbceceacebdcbccebecacabbbbcbacbaacedaedddcbaedbbbedcdeabbedbedacbedacacbbabaeaecbbbcccbceeebcdabeebaadabcbeaecdeebbdbccddbecadddaceeecbbadaebaacbbdeabecddacbaebbbedadbcacbedccbdcbddeddecceeaacddcacedcbbcbbdadaadaecabdcdecdcdebcceaddcadabedbddeaedeadcaeadbabbeedadbcaadaebbdcbbeacadbcdebdcdeddcebaaebedecdaeecaaaededccebcbebddeacbadaacebadedcaecdbcdcbdcaaccbbbabcabebddbcdeeeccaadeeaecabdacdaaacaeddddbcabecaeedbaebbbecddebbebbebedaadbddeacaccdcacedaedddaedceecdaebedbacabbdcccceedbaabedcaddeabecbebcccbbddbbbcbbdbdaabcbbbceaacbccccddccaddddaddcdcabdadaebeacbbaeedabaeacdedaeaeebabaeabacceaedcbcceddabeaaacbbccbabcbcbbddeabcbcecbeabcddebdbcbeccacdcecccadadedbabaeaaeacdbaccdbbccdedbdbeeededccbbeeddbbbdbbbeadebaedcaabdacbceeebeeabdaeddeedaeeabddbdededeceaaddeeabacedbbabaacababaeceeedadebbcdddddccbbdbecdcbceacaebbddbeabccbeebbbabdbebdedbeecadaccdeedceebebadebccccaadbdbacceeeacbacacebbdadabcdbdddeaddcdbaadaccabbceddebbbcaaeabbbceaaddddacabbcdbdcebbdddaecbeebbaadacbabbdbcdbeacccddbeebebdecbabdbadcaeabbdebeadcedeecebeeaadacacadcddddeabedccebebcbadaebddadbdcebdaddacaeceddebdbeceedbabcdaaceccabbdccbdbdbdedaeeabdbbaceebcaedadeaececeacdbccdbcdaeceeeaebebccbccccbadeeedadbbccaeabbbeadecccddaddcacaaedaebadbabeebddcccbdbeccdaccbebeecaccadbaaaaceacbadddbecdacdeabedadcabedeaadcbcbcbaaeaadecdcaebedaaddbbedeececdaddedccecdccdceeedbcbcacdadddcbcecaddccdedbbddcbaccbaebddbabdaedddebbdacbeadbeeceebaddadcbbaebbbbddcdcadbcacbabdcabecedbedeeadeacbeebdacedbbbedaeceaaaacaaabebeabedbacbaaacddcaeadeceeeeadeeaeaabdbcaccecaabdbeedbddecdbedaeabdcdddceccbabdcaeedceadaddbdbedebbcdeccbeaaddcbedeacadaecdeaedcbdbaecdccbaeedaccbaaeeedcdbdbdbaaadcbdbaebccbbaebbadaeebecddecbadbadccdbaccaaabeaebbadeeceeddebebeaadaaecbcdcdcdcbabddedddcaecacabbdcbdcdabdbdaaccbeddcacbbccdabdbaabcebbadcaddbadbadcebecddabbbeaaccdbedeccaadadebaedbecebabbbcbacdeeedbaaeeabeedccceeaeebaacebdbdbdcdacebdeecdbbbbcaaaceaacdbabbdedcbeddceccdbbbcdbbebadddeeceabaaacdbdcdaeebbcdeddabbadceedaceedcdbedacdaebaacadceabbdbdeebadebaddccabcbebcabebaddaeeadaebecaaedbbdebecceeacccaddbbdbdeccdcecaedaddeebedaeaaaabadbabcedcddadcdabcedeadecaaadbcecadbeabebbdaedbdeaeccedbbccdeebbceabaacccdeddebdbabcbbacebbbcabbceacaecccdedcbccdeadaebabbebdbabdccededaebceccbdcedcdaacebeaceabbedacebdacbbecaaabbacbbdacadecddcaaabdccbabededdededadacaaaaaecbadbbdabdabeeabadbdeddeacbbecbababdecbabcdeaceedcdedcbdcbebddebdebceaaebbcccbcccbaaebecddbbbaceccadbcadcedaedaebcbcdaaabbabaacbeeeceaecaebceceaccbaccaabeabaadbdabdbeaaedadacbacebaebedabbbaebeebaabdecdcbcbdedebdeeddaabcbdcdbbbccddbaadecdadbedaaadbbaaadbcdacbabecccdeaaecdbebbbdbbbedcbcaaadeacdabddaadeceecdaededbbbeedbabdeeabcbdeeeabcabbaabbeabdccbdcecdbdebcdccacbadcebbaeacdaaabadbecbdbbddaeeedcbaadbaeedaccceabdcceaebcdddbedeaaaebadadedbbbdacedcedecedacecccbcddcbdebbddccebbbaaaeacbeeeacdebedcbdacbdbddbeaecccaecbbeadacababdcdcaeedacebdbdbdacecbeddaecbccaeeebcbdbaaccaecdbaeadeebddbbdbceabeebabdbeaeeeddcbdceeaacdcaceaaccabecadbcddeaebaebbdceddeecbeaddddeaaaeacebaccddbbdcedaeacbcdeedcaebacbabebaebaaddbabdcbcaeddcbceddbabbdcadbabbbbebadaebcbccebadcbdcacadddbcbbcdebdbbbcdbacadaceabccdeabbacedaabdabebccaccdecacaecdceeddedebeacedbceedcdbcbebecadecbdecaaacaeddacbdaabacadcacccecbcdcacbddeaebadcdaedcebbebbdecaacaccadcbeabdaeecdedcecaddebbeaeddeacaddaeadcacdcecdcbddaddedccdacaccacebecdacabedaecdadceaeeecacedcaaeebceeedaacadabccaeaddeaeaedaeadcabedecbbaabeddebcabecaabeedcecbdaeeaacdebdcaaeadcbedacabbbadcedcedcdbadceededbabdebeacabceeaebaaaeddeeccbedddcdcedecdceccaaeebaecacaecaaccbabacbcdadcaabaceabbcbacecdcbcdcebcbadbacebaeeeeaceeeececdecaabdbabaeacbeeeaccbcbabbabeddeadaeeabeeebaeeeaccbeacabbceebcaaeedceebeacddaaabbeacbaededbadbbaadedbdebbdabeeddbbaedddbcdabadabdedcbccaccdadddbeaddabecbdebcddedcbaccbeeceaeeeeebebcebddcbeaebbaadbccbdeabadccbabcacdecaebeeadbeeececeadebcceebdaabddcabbbeaccbabdeabaacdeadacceeedddccbeddbacbcdadedbaecddbaceaaedebdabbdeaeebbeacebbbaeecbceebbaeabaedbeeddedcaddcacedebeedaebddbbbbaeddabdbbdaebabbebdcaddcacbdccbcabcadacbbdcaadbeedadeaaaeeceeadcbecabcabddedebaaddaebebecaabcbebecaeebebacadbbbeccacabddbbdeecdeaeeedebbbedbcdacccdecbceaacedbedbdcbdecaeeaaadcecbcbacbadadeaceceaadaeaaddcccaabadcdbaeaacaaccdcaddddbdeaaaabbdaebaccedebededcceabbddbbcbabcdebcbdbbadaeabcaacbebabdbddcacdabbacdccabacacbeccceaaeecccccbbbbddcdbdebabbdacaecccaecdcdddcdeedcbdabedbddaebeadadabaccddcdcbaaedceebaaaebccedaccbddbeddbbadeceaacbacbdeaaebceaddbedaecdcadddbaaabbbabcbdebcddcceceebbeedeaabbddbeaaeabeccedcddeceeadedccbbebdbacabecedcedcabbdcedeabddedccbcdccaabddaaddbaacaeadacbcabbdbeacedeacabadaccbecceeaacebeceedaddaeeecaddbdcceddacbadabaacdebadcaeecacdeaeebacdbbbadaebcebbabdadceeedddceadbadabbdccdadabdeadeaeeeecceaaccebadbceddbeacaaaebedcebdeebcbdeeadaedababcdceaadcebddabaadcbdaebbaecbdcdabaddcededceacdcceeeeabcaaabbaccdddadddecaeedcdebdcdcabecbcdeabbaaacbebabceebaeeadddbbcadcddecebebcabebdceccadebaccceaadaaebbceacaadcdcccbdaaddccdacdbeebabdbaedbceedeecdecdbcbeedbabdddbcdedccbdbeadbbaaebacbceecddddeccabdabcbbbcdaecceeaacbbdabcdacbedbdedbabecbcacdddeaacacbeaacddecdbebccdbceadeddbcdcababaeecaabddeedbbaaccdedbbdaebbecbdabeaedeaeabbdbdbddeadcebdccbcaedacecaaadbedeeabdbbbeabdaddaccddcacacbeaacddcdaacaaccddcaaececbdcebdbccaccabcaabeaededbeacbcacdcceeabdceedcdcdadcedcccebddbcbecccdddeebebababaaaaedbdebdeccaeecbbcbccdecceadcbaacbececcbaeaedebdccaadcdaddbabbebbedcedabddebbaeebbccdddbaeedcbbadbbaaecabeaddaadeebdeeeaeaaeadccadebbacaeecbeabddbdcdbeadebedacddaaadedcccdddbabcbabeeecdaaccbcedddcdccdbdabedbdecedaeddbebdbdcccdbdeaebccecdbabbbadcdcebceaaeaddeebcebeccbabbaebdaadcccceeaeaeeaccdadeadadadedbacbdadeaebdbecdadbeebcbbacaeedbbbebaadcacbedddeacdbaadaccaceebddeebacaeaecdebceddcabacccacddceaaeceecaebcdebdbadeabecdeedccddddaaccbddbbdcbadeeeeabbdcecbddbcdbbedaceaccebcacebbadccbdeabececaeccdbdadabddbadeedaeabdebacdddeabdedadbeacddeaaadcdbddbdeaadacdddcbddadceddbcbdabbbcdeabadbecdddaceecceddedccabceebbccbdeabeeecbbbbcdaeeeaeacdbcbbcdbaadadccecbcdedabcaceaadbaeeeaabcabaaeceaceabeeaccccbcbadaeecbacaaabceabeeacbeaadcdeadabcbbadebacedecaadedaddcddeccdbadeadccaebeddcbcecbcdebeecdaeabececabdedcabaebdeddbcdaeedcddeeadababaeadeedcabdcaccbdbdaeebeaedcdcbbacdbbeeababbaceccaebcbeeedbccabcccbaaacedbdacadedacbbbbebdcbdaacddcbdcddbbeebebbacdbdcabccdccbdeedabbcdebcbbbdecdaadcdadddaaaaadbdcedccbbeacebcdccaaaeebeaceeaebcdeeccacddbecaeeceaedeacabddbadddeeeeebededbcaaeececaaceacaeadadcaebebbccdcdbdbbabaaabecabbecebddacccacabcabbebaaddbdebdebbceaccecaaeaceaceebccbdacdbabbccdcabdbbeeadbbadcddccecbddaaddceaddbbedbacdccbaddabdbcabbdbeeeabcdaacaedcbeededccabbcaaaeccaceaeeabbabddacedabcccebeaccceddaedddecdbbdbeedbaaeaaacbaeaabbeacddacadbccbcbbecbddedacebccbbadebbcdbcbbaabebdabeabecdbdedcbcbaeadacbbadccaedaebacbdadbccbebbabddaadeaabccbbcbebbbdaaecabebdbcbcecbddaeeadceebddaebddaacedeaaeacdcadeaedbebccaecedcdeedeabdadadeeecdaedceddacdcdabcebcaebccaadaaeceadbaeeebdaaaebabeeaeabcdddbdabceeebebcbeabeddeeadabbcbcdaaabdbdeeccddeabbbedebedccbbededcbaccebdddaceeadedbebdabbbccadcaaabdcebbaaeeadabbbccecedceadeeedcecedddaabdeedcccdebcaebacdaabcbbaadccecddcaaccbabaedceebdaedbbddcabccbcdbcaddeccedaceabcbacceaaadaedbebcabcacababedbceaecadeaccbbccbdccebaecdaaeebadaaebccaacbaabbaacdacbcdebabaebcdeeabaddcababecbdaacadaebaecabebabbdabcdbdbcbabbceccedbcebdbeceadebebdeccaaeceaeaddecbebabceaccebabcecbbebcebadecaedbececebccbdcdcdebaeaedeebadacddecccdaecccbbdbeeeeaebbaeccecdecadabbcaedbbcadbeadbddcaababeacddacaadcdceaeaedcbecdebdcadedaadaecbadbcedddbcacacccdddacbccbbeeeabbbdcdaddceabdcaadcbdedbdcaebbaacbcdcbabbeeecaeecccaeabadbedbccaedceaacbeeededaaabdddaeaaadaaecdcebdeaebdeebaddcdbcddaeaebdaebcedbdaededbebdadcbaaacbbddcbbbaadaeebaddedcecccbddccdacededdcaeeabcceabceeebabaebedeecddcceecdbbaeaedcddabeccaedcbdddedeabbaecacacddaadcabeaccdacaacabdceedacdcccaecbbadaabddacacaaedaebadcacbdacdadadedbeaaedbccdeadddbcdecadaacecaeaacedbabeebcdaacacadbccbcaadccbaabbadcdacceddeadadddbbbbdbadcebeecaabdbaccaebcccbccbceacabdbdedcebcdceadbaedeaeddeedaaabccdecddceabcebdbbccaeedccaedbeedaeeddbccddbbbbebaacebacaeeeaaededeaddbdbcccaddaeecbcccabdbbcedcbdcacdbeeccddcceddbecaeabddebadacaaeabbbcddbbcceabeadceeacccbeacebddacaaeeabbeeeaeacdcceccaeccdebaceaddbbbcabbeeedaddbaaecbdbebaaabdbdbaadecdceebedaaaaabedcecdceabdceaaebdabecddcbccacbceeecdbaecaddbccdbabaddbbbdceebdacebddbebaecaddbddedbdbacdcecbcbacccadcceeaededaaccebeababcacacbabadcccebecadbcebcaeabccadcacddbaebebbacbcebadbacbdcaebaabbcdceedabeeaeecdedcccbbbbedabdbdedcabacebbbccbdabecceaeaccedaacbdcadeeaaaaaaeccbededeabdcdcbdbeaecebcedcdeaaecceaaeedeaeadedbddeaacdcaaeceeccbacdbadbecbabeedadacebcabdacbaadbdcdecadedbbcbaedaaddbebcdcdeaeddaaececeedceadabdacebaecbdbccababdecccaaedabadadbdecadeedbbddaedbcbcddaeaeeeecbbbedbcabaaadcbcbeeaebdeeababaaeeabcbbeebcceaacebabdcaebadccadbdccbcccdbacbbcabaeeddeceaaeccbecaaebaaadadabecbecebaedbbccdbbceadaeaaabdceaeddcceaeaadbdbbacdceeceabccccbdedacacaebdbedbcedacaacebaaaaedeabecadaeeedaaacecadcedcedcceaeccdaecebeebaacebbbdbdbebbbcecccadcdbbabaceeeaedbdabaebdaaadeebbacdabbaacaeadbbbbedeeddeeacbcdbbceceecbbacebeeaedeaaaaadcbcadadeddcddbabcbbaccecacacbacedbddcadcccaccbacdcbabbacedceadbeaabcecaeebdcceccbddbbddbeebaeadecedbbbebdaaebbddecbadaeebccedcbbddaecbbadddecbbedacaecdedeebceeebaccbdbcadebdadadcdabbdcdccdedbacbabbcbcaaaaececcbaaddccccddabdaedbeecedbdbbccaecbebbbedcaabbccceebeacbacddaadbebeeaababdbbcaabdaeaebbbdbcabaedccddddeccdadbaeecbbaadcdedcbdddaeddcddcedeaddecebedabcdaaccbbcbebcaddbaabbaeabbcdbdcddecaeadbdacaebbdebbbadecccdaaecbbccdabcdcecdcdcbaacbadcadeeecdbaccdeededbeabdaedaaccbdeddecbcdabeaecaddbbabbddbdddcdbdcdcadcbaacdcddcceddcccdeaccecdabddcbacecaceebcbadaaadcbddcbdbbaceeeedbcdaeccddeeebadeeebaebcdaeaaacdedbcbcaeeddabedaaebbdacabbccaeeaaacceebeeabdbeeebcbceeadadcccdebdaebbbbbaceeeaaededaaeaaeddbcdeeeeaeaaddcbbbdabcbbabaebcaddcbbdaeecbcbbcbadbcdeeebaadbdcedcccecceccdedecaedebdcabdbcaeaacbdbcadbcbeeaaeecbeebaaabdebcddbacbabdedceedadceaecdcdcddecdceeebcdeadddedcbdcccbdacbceeaeedaababbaacacbdeacedeaecdaceabdadcedbcbddbbdcccdddaaddccccceeeddddacbabcbbacbcbdcbcdedacaaacbabcacedaddbdebbcecccebedbebbeecaeaccbdabebaebbbbacdcdacbaaadbccddcabdabaacdcbbcbcaedcaabdbccceadbddcacccdabbcceeeaabdadabedecbaabacaececbcedeabcbbecacdbbdcbdbecabbabcebbadbaccebecbbeacabceedeeacacececbcdcbaedadaaebcebbacdedbaacaadbecddcebadeabdeedcdaacaaeceaccbcdbaebdbecbeaedacdeadababdbaeebeccbbeaecabcabdcdedceebbdbddeacccdbcbccabaaadedccbccbcbecbeeadbddeceeaccaccbeeddedaadcbddddbadbeeaebebeacacbaedaacccdecabdcabdecbeecaebaaeadbecbdabcadabaaaabdbdbeeceebcedbbceebcedeedddbeaadcdedcacdbaddbaadbbacbeeabbeaacbbcbbbbdacbaaecaeddacbdbdbaddbdadeacecbeacccbceadbdcbaddebaddcdcdacaebeaccebdbbccadbedcedcedadddbcdedaadddaeebbbcccbeedbeaabeebaedebbdbadedebcaadedcbeebdadeccecccadaecbbacacecebbbeddcedcddedaeddadebdcaebeddeaadedaabecdbebaecadccecbedbbbbbaedbcbdaeeddcccabbdccedadeccccdacbebcbeaeeeebbdadecaaeebaddbcedcaebbbbacebebceeeeaacaaeddeedecaecceabebbceabdbaedbbdbacdbaabdabdabcecbaedcedcedaebeccceedbdbdbaedecbadadabdbcbdbccadeedeceacdbbedcbdeecedecbcdceedbeadcbaddddeddabecbbdebbcaaabdedcadcbbcaebeeedddadacbedeadbcbecaedabbccebddadebdcddcbedbbcacbeabbaebcbeeddcbebdbbbadeceeededdeeecedabaadadeebadaccbdddaaddceacbabdaecdcaedaadaeebbbbdebbbdddebdcbbebcecdabbbdcebccbdccabbacaadceabadaaddcdeaadadbabcabcecdeccbccbbccdcbcbccbeabeaebdabedddaacdddbeadcdcebcbcbccaddeebcaaaeddeaddcbabeddebdcbeadbccedaebbbedededbcdbdacaadabeccbbbbdebccedcddeaaddcacaebcedacdebceaeedcadcdccbccbadeeaacdeaadaeddaddbbabaaaddbcebcdbdcddacbedbdaebabaaaddddaedaabccebcecbdbaebeccddbaaabacdeceeadbecbbddcedecaaccccaccbbccdbecddadbabacccdddcdaebbdebeadbeacebaedabeddbbedbdecdbebadeebbaabbeabaaceeedbcdbdaeedaabaaccebebacaabedeeaeebdbccecdadbaaaccbedccbeeaaeaadcdabeeaaebacecbdcebcecadcdcadbcaebadcaddacdbeeaccaeeabcbbedbcaceccbabdccedaeaebcbddacdccaebaddcceaacabaecdedabddbbddcbcbaaabacaccdeeeeeccabaddebdbdecaeadbcdddcdbbadadbccccdaabcaddbddbacabcdaecbbaaaadabebdbccadddacddcddedecbdeaceabecbaccaebcaaebecebbeeacddbedeeeacbceababedeaacbabbbdcedbbddedaecbdabbadcdbebdcdcbeecadbbecabbcebddceaaadeeceacbbaabeeeeaecbbebeadacdbdaabbaeaddbdbeeadbcaaedceeeaeaeeebcdcadeecdceecabcadeeaccccaadcadcedecedbdcdcccabdabcdaddaeeaebcaebbcccccdddaccbaebceaaebddecebcbcdbedaebcceccadeccbccecabbcdadbaeebbeccbbacbabbccdedcedeecabcaadaccbbcbdeaccadcacbaccacdecceeacbeecaceddcdacbcacbbbcacddeeccbeedeeeabaaccdaedbccadbdeeebabbdbecbebdcdecdadaeadacbcedadacbcebcbcbecacdcdcdbcdebeddbdcdaaddcaecdcbdadcdbcaaebeebaedbadcabdbaaedecaddaaaaabbdedbaccbbdacbddebbedddebcacedbaeacbeaeebacbeadbbbdcaddeadabcdccbedccecaaaaadbecadbeeaadeacbcceadbbaeadeacccaccdbcdabdccbecbeebecdcecbcaebaebaeacbabbeeaadcecbedbaabcdecaecbcbeadbacecceeeacbdaaacadaebbabbdebdabadaecbadabbdceeabddaecbaececbceaceddbaacdbbeadeaabecdcdabcaddcaeacadaccdecaeabddbaaddcdaebaaaeaadbeaaacedddcdaaacebcddeceacadbcecedbcaaeaaaccbacbbddcbbacbcdcaeebcabedbdaaceebeabbaddabdddedbbcaecdcadcdeadbbadeeeddebbbacadecedeeceeccbbbdbabedeaaeaebcceeccbbbbdecaceeabaedbeadccaadeddcbdbbedaeccecddddedebbdcdabecbadacebbcedaceaadbbabcadbbcbabdadcabbeecbeedebcaebacbaacebadbddadcbddcceeededeeccdaeacbbeaaaaccabeeebcdcbbeacaeabeedcdbddbeacdeecbdbeeeccdaaeaddbadaeeeedcdebabcceaabdaaddacdeceebbeecabaccbeeeceeebdccededcccbcaccadbaebcacaebeadaedddcbeaeedcebeabbaeadbbedecaaabceddebdabbbbacdaccaaeccbceedbbdecdadaedcdecdaeaabccbcceebceadadaccdedddcdadebddcdcadbacaaccedccdbdacbccedddeacedaccdabcacacbcbecceacebacadecedebceddcdddbbaddbbcadbabeaecdeeceecaeeadeecbdddedadeabbcdbbccdaedbbddddcacdcbecdceeeabbeaeeeedccdcecabbcddaeaeaaadededdbbdaabaeacacddeceaccebeeabcebdccbbdccaecbdaaadaadeacbacebddacedbecdbaeadcddccadbbedeadaadabacebadeeecbbaedbaeaaaabbadadeecdeccbdacceacedbcdcceaebcdaddebccabcaebaacdbcecdceecaadabbcccdddcabcaaadaaaeabcaecbacddecbddcccceecadadcacbbdbcacdbcdcdceebeedcdbedcacebcdabdeeaeaccbcecacedebbddeddcecaadcebdadedcbcabaacdeaeeeccaaeaebcadcaedceacacdebedbcdaeedeeebabccbbccdbbcaaecedebacadbddeaebabedbbcccaedccbeaddaaccdebbbddacaeccdebaccabdadedacebdecdcbababbdbaaadcabcabcabcbaabbcabadebdbedddddbbcbaecbeeabaceaceddbecbaadbacbababebdcbbdaebddbcbcbaceadaacddedbbabeaeeecbcaaedaddabaebdabdccdaddaececeacecbddceaccaabacdbbdbcbbdaccdcbccebbcdbaebadececcdccbebcbbbaccdeebdaacbdbeadbeeabbacecbbedbebcaeecadcbdeecadbeebbcccbbdecebbecdbcdeaeaaeeeeccbddcdcbcaaadbdbbbacdebebceebdeeedcebcabadcaaaecceedacceebeedccbcdeacedbbabeedeabdccebbcdccababcedbadaeddbaadaaedadbcceecbeecddedaabaebabbbcbaaabeedcebcaeaebaabedaaecbaecdedecccedccdccbbecbeabdcadaecaaaeaaebaaaebbaeedcdabbeacacbebddbaaeccddedbbcbeebbebeacbdceacebbacbeedbdcddecaceddcdbebdeddeceecaccadcbedeecaabcacedeaebdeeccadeacccaebacdaecbccbaebdeaebcddaeadbecaaacdecacceccaeccdddcabceebeedbebdadbbabdbcabccbbbbcecaadaeeedadaccceeacbbaabaacbdbcabdccdbbaabbcbbaabcbeabdedaadeecbdabddbbbbacdebbebccbebdbaddbbbbabbaaadcecbdeccbaadbdbedadecacbedecdacabddcccbcbcabcaebadbbbdeedceeccaaedddecdddcbbdccaccebbaecabdecaedcddcddddacdeedcdeadcaccebcaaecddcdcaaeeacdacbdaeebcaebbbddbbecaeccedbbcbbcbbceeaecdccaeaeacacccaaabbacdbbdacbccdaebdacdcaccecccdddcceaacaacececeeacaabceebcbadacbacadecacbaccdadbebcaebdbeabcdedbaddcccdeceeccdabaeeabdebdaadebddbacdbacabbdeeecdbebcbdadeceeeaedabeaeaccabbacceebeabcceaaceeeeacabdecabeecaeededabadbecacaaabdebcbdecadeeecebdcebdecaacbaddacdbbaeccaebebdeeadbcacebeeeadeabddaeaaddacbeeabaabbaecdcddacacdbdceebadddeeaddcddecdbcbeebbceacccdabebccadabbdbeeddcbceaacddedbcedaaacaeebabccbddedbaddccdbddbccbaceecbdbaabacacdcaaeadbcbadcccaaedabcbdbedadeeabdcbebaeacacaacebddcceaabaaabbaeebaeceadbdbabaecbcbaadeeceddcddeadedcaceedbceedaebbbccdeeababebdebaaaacbcaebbabbdacccbdddcdabadbaabcaccdaececaacddadcaecdeeedbeacdcaadeccbecbdcdbbdbaadeeadaebeabcdcbcadbcbeeeebaebdeccdddddbdcbdacdceaeaedeccdbbbbdbddcbedcecebacacaceabacdabceecbbdccaaeddceddcadeaadddcaeccecbcbdbbcacbacecdccdddcccaeadcebdbedbdedcdcddcadbdbbaeeebcacbdceeeeaaabcdabedbddeabddadaacdccbcbdecdeebbbecdababbcddeaeacadbbbcceecaaeedaaeaedaaeedebdedaaaabcbabdbcccccebbbbebabbabeeebaaddecbbebbbdeaecabbbeeceeebaeaeeccdcaeeacaccddbdddcaaccaeddbbcaeddeaeeccbabbbddabccdadaeadacbcedccadbeebecceedcacedeaedbeddbcebdceebabdabdeaabcccdbdaccdabbbcddaedbceabbedcebdeeedabcbdbcceabebadeacdbbeeececbdaccabbcdccddbdcbdbaecdeaaccacedcaeabaacbdbedbaaceccbdcedaceedcbaaeebdadcbabaacacebcbbdcbbabeaaadcdcdecadaaabbcbdabebbdbbabeddcabcdbecdeacebcdeaeccadeedbcdcbceedbdcabbeeddbdadaceecebadcabaaecdaeddbedaccbbdbeddceebeddabaaabceeedcdecdeceecebcdebbacbdebebeeecabeaddbeacdabeebdddaecbbddcdbbaebabbbabcbebaceccedcbcdceecacabeebbecaebdebaebbeeceaaceedcccabdddcceceaeddbccebcbeedecaccccedbceaceaaddaeedeadaeeebbbdcbcedaedbabaeccebcaeacbdeeececeebdddcedbdccabbacedaeaeebccecbcebeddbeeaacacbcbdeadaabcacaaddebbaaaceceaecaaaaaceccbacecbebeecdaeaacccedbaccacadabbdadadcaaabcabdccbebcacadbcbaeadddeababeeaaebadbbabeacebacaabdecdbdbcccddcbececcdacbabbadccdbedcbdeadecaaaddcddbbddbcabeaaadeacadabddacadbbcadbeacdeeedaceebceeaebbddddbebdbaceaedceebaedcedbedbbaaeadeaaebbdcbeadbaabacbbdeadbbeabaeaeacdcdaeecbbdeacebcdeebdbcbeeececeddbdeacbdabddbaebaaddbdedddabdeaaabdccecdcbdcdabdbecccaebdbdbbeacacdddbcebadccdbcedaaabeaccabaedebaaacdbedeaaaabdbeedebdaaebbceeebebadaaacdecbebeaaccdcadcedcbdadbabaeebaceacaddcbbaabecbaaaceaeadcebbbaaedaaddadabecbaccbdecedadadecabcebcddacedeacccabddaecbddaadddcededbbcacdabccabbbadacedceeecbaaeacdadacadacbebddebcaeaacbebcddaddaeaecbccdedcdcadecceabbeeeabbebaebbaaccecdabeeddbcddbdddbcdaadabecedadedbcdebbdeceaaebadabeccbabbabbeaebdabbdbbddebebccecadedccaeedcedbadebebcebbacaaacbaeeaeaceaddaadacbeeadceecabaedcaadbdcbcabcaceeaddebcedaddebcaeeeacccbbbbcdbabbdceaddacbbbaeddeeaedbdeadabbdabccbdeadddbebbeaaeacddbcdcbebbaaacdbcddddaaadaedcbbbbaabcebacdceeaedcecbaaedbeadbaecadeacedabceacaecdcacedbceaedceeeedadcacaadddbcceeaaedcaebdcedeabdebdadcecbeedbeeacebbebcbbddbdcacaeecccaedebeddbdddbeebacdbdcaceacaecbbeaebebcdcabdeaabcebdbaaacacdbaddcaeeecdccbcaabcaaeecdcbaacacecacabeacbcaeeabbbbddeedcdeeacbddeeebbaceaccbeeebddcebcccddcccecabceeacadbcbcaadbadadaeaabeddeeaaaccedcaaaebdbedeaeeaebbceebbebdbdbbbeaaeabacbacdbabcbbbecbcdbabbdbedccddbbaeeceaeecaacbcaaaedabbedeadccaaabebebbdddccceecabccabcaebbacbceabdcecaccceaeaacebeaddeadedaedbbdadcddeddbddcaceddbddcbaebcbbcdbbedacceacedaebceebeccdeaccdaecbcdbceaacadaeacccecacacdbebcadaabeddcabeceeacecccbdbbdeaedcedbcaaecdbceecbceedbdbebabdbbebdceecaabadcbcacdcddccddcaabcadcecbbcaaeedcbbcbbbaeeeadaececbdaeebcaeebbbcdcbccceeaddabdaebcccbbbbacbddbbcbddeceeececbdeabeeadaaadbeeaddbcdceadedaddcdebddeaedaebdabebddeeceeadabecdececeddeeabbdbacddedddcaaeecbcccecedaceeaacbddcddbcbacadbadddceecedbecaacaedeecdacadbdbccbaddddeadbdcaaeddcadeddccbdbdbbcbcadacdeecdaeaecdeebcaebdadebbcdbedcbccebdebabcdcecdbabeeccebadcaabccacbdcbaacabeceebbabcdcbedaaaabaecedbabaaaebbddaebabedccadeccdaedcbbcdabbadcecccacbddebaccaaabccabeddaeccbacbbddbddbedbeebaccaeaceccbeacaccdcddccdddbeebbceecbcccbedebcacdbbceabecdbbbdcaacdeebdadbcecaeddaeacbdbadeddedccabebccaaecaecdceeddcacccadabbcebbbeddecccaddbaebeeaeaabcecadcbacbbecebdbaadcbebebcadaaaeaaecbbaedcddbbacabdbcedeedeecadaeacecedbcddeeaabcdebdaabedaadebeaacbdbaeeabdedbbdaaedbccabcdecebbdedbaccdcdaadaaeaabbddadaedecedaadbadecdbdcaeadceccbcaeaddceeaacccbcddaececbebeeeadebacabdaeabbedcaabebeebdcdbebdbedbbaaacedbbadebcceddbddbcacebeaaadbdaababdeaacaddaacebcbdebbcbbcbebabeadcaccbedccbbeceecbceaaedadddbecbcadbaecdbbdabeecebbebecdeedcabadaecaeaadeeabbeeaddbadedadeeaabdeeeccccdeacccabbbdaebaaaacecaaebdbbebdadadcbbcddeeaadbbadddedbceecadcbcbcdddccabcbdbebedacabcdadcdccaaabcebdedbbdbddbadcedeebabbcbdaadaaddccaeebabbbcbccacabcebddcdaddaacbedddebbaaabacadeceebddcbcacebbbabbbdcbcccabdebbcceedddeeaebbbbbeabcabdddecdeadabedcaabeacbbedacbecaeaedbbcbaddeeeecbceaebbdadeabddcdbecbbabcecedbcdebbbcacaaaccdbedecbeecaabcadecdacbdeccdcaacdcbbaeddcbcdbaadeaedaeeaacbedcdccbbeaecdceeabcbbaeceadebcdaedbdedbbeccacbcbdccdddbdcaeebbacaaeeeaadbbdaecdeedbaedaaebdaeacdadcdcacadeebbbabdcddcaadabbabdbccbbcedcbccdbcdbcbbecccdcbcdaeddcaaecbcdcecadcacceebcceaadcacdaadaeeabebaedddccceaddadadbddccbebbcebdbcceeaaaecacddbebebdaadccadccabeeddcbcceedccaaccaeabcbeaeacbcbdaabbdbdeacdcadaedbcbdbbecededdbdbbbbebbaaebcbeaacddcbbedcecdaecaeaaadaddabcbcedeebcedcddeebabdddadbcebdbeebbdcdaeeaedebadcaeaaadbbceaddaaccbbbebadcaaedebbedadadddbedaaeeabccbbebeddadbedaeceedaadeaadeaaeaccbbadbabbbcaeeeccaedbcdebeeceddebcabacaeacabcaecabbcddcaadabecdecadaceadccecbeaecddedceaebddacdacdcaadaebdcaabadbcdcbccedecbbdbedcdccbbcddcabebbdeaadabeabacddddaddceaabdabcdddcdddddbacdeddbbebebcabbeabacaacedabeedcbaabdecbbdaadeddeeedeaabebcaddcbdadcbacbcbeaadadcaaeaddaaacdbcbeabddbdbddaabaebbeccedeaadaaddcdeacabbcaabcebeacdeeeebcedabbaacabeacceeaebcedebbbccbbbdcaecacbcdaecaedbceadcabcbccbbbdebeecdbbdeacdeaacaecadbcaeaaeecbcbdbaddeaadaacacecaaddbbbadcedebbaeddecacebdcdbeaaadbdadebadbddabcdbabbcadbbeccdbcedecbdbaccbcdddcbbabdbadebcabdbddcaedabeaccdbdbaecbebaabbbcbcbbceabeceebcebecddebcccbeabeddbdccdbdbcbaeaceadabceeeeceacbcbbeccddecdeecabcaeecaebdcecccadcabaaaaebeaccbcedcccdeeabaccdbdecbaccedabdaaddebbddddeccdebedacbbcabcbeaedaaabadaecebaaadebbcecacbcddddbccaeeacceedddceeeebacedcbebbbaeecebaacaaeceebdebdacbdeaedccdddbebcebcceccbeabecaacacdcccecebbddabaaceebeddacdabbadceaadcbacadcdcddddabbcdbbdcabbdeaedaadbdeadddebbcaebebcdabadaecdceaebebcedabadbcdadbdbcdbddbdbeddbddccebacebeabbaeccceeaecbedddbcccebaabdbbdbceabaeadbbecddaecabdbcdceebadeeddbeedeceacababcbeeacdbcdcedaeebbaecacdaeadabdddaebeaecbbdccadebdaabcddabecaaedeacbdcbcdecbccddedbccbbbdabeeaabadbebeddbddbebdcdaddaccbbdbdbdaaebaabcaebdaaddbcdbaeceeaabacdccbaedbebccbeabbbcbbebccdbbddcaeedcccdadceacbedcedaddeedbbaedaeecabcccdacbeaebccdabcecdcabcedbadbbeeeebdaacbaadccaebcececceedddadadbbbadcbcccabacbdcbdedcdebcccadabbcaaaaaaedbeeecceaabcaebeebebcceddbcddebaedcbbddedcebddedabaedbaebbeecabbaccaaeaceececdebbaeeadedcacabaaddcbbeecaabeeaeeebececaecbdadadebbceadecdbeabcecbcababaaadaadbeadeddcdcecccdcceedddcdaabbeddeeacaaababcdddebccdcaabcedebacbaecdceedabceaddbeacceacadecaccbecddbabbdccacebddcacccaaabcecaecbebeacabddceedecaedaecadbceddeecdcaceededcdaadedbdcbdbbaccacccabebaedebdbbbbaddacabacacdccaeeedddecebebdbecadaeeceaadedadacceaaddcbabdabbbadedcdbedbbeaddbadddcdddbdbcdecdaaeceadcedabdebeceaabcaaebbcbbadecdccdadaacceeacaaaaaadeacdeabdbacbdbcebbbabbedaccbecaacbbbdcbdccacababbbddbddebdcbabecedcccdeeaeedbbbdbbeedeadaaedccaeddebabddbbecbeeeacbecbeeadabdacedebbcbacabbaeceabbccbdeadcddeadceceeddebececdcdadccbeabebbdebcaebebececbaccaeedeedeadcccedeaaedadbaccebcbbeabbedcddcaedabbbaeecacddceadcaabcabeeeabdbdcacebbcebecbcdebceccacaabdaeebeeabbdaceddbaadbbcbdbdbdedaeaeccabbadecdcadabacaecededeadbaeaccadccecebcaadadbbeeacaadbeadcbdeaecbcedbceacaacababedabceeddacacbcabcccadbbbaaaecadaeeddabbeaccccdbaaccaacaecbbcebeeabeecebabeeaabacbdbdeaebeabdbeaecedaddececdacbbbdbedcebaeeebceaacdeeeecccdcaecbbbdeaacaeccabddaecedcbedadbacebeecaecdacaedceaabeeccdcecebdbcdaebaededeacddedadbbbcbdaadbadedbccbaccbbadbdcaaeedaebaaddcddceaebbabcedecebabbaaeabddeedeeaabcdcaaedabedbbadddddadcabbceacdbdbceebbabcadabdcdcbbbadabebeddcdedcaaccbdebadedbabdcecebdbccaaaadccdeddaedcaeecbbbedecbcccbdaeaeaecdadcbcdbeaeeeaacedaadeeecebdaceaddadceadbcabeacedceddaeebabdecbedcaeabbceaedcccdbddbbcdaeebcbedccdbaacbcaeacdebbcdbacceebdbcbbcdceddebebcbbaebcdcedbbaeabdbddbaceabdaeacdeebaeebeadaedabcebbbeeccbcaaebaeabaeedbcddeabcddcceccacacaabdacdccadeabaaddcaecedbdebecdbcdadebcedaebadbececaabdabecbccbbdabcbbbaebcecdaebdcadbdcbeebbaebccdedbabcccaddbaceeadcaeaaeeaeeaddddcccceeabcadbeabdcdccadecacedeabcecaddceedceeccdecdbcaaecdbaddbaceebbbbbaadabbabccdebeeaacdcdaeaceecaabbaacaeceaeadeeabcbdacdaedbabcccdeadeecbebddedddddbbbbddcbbbaeebbcbbeeacacbaabebbcdacabdaaaaecdabdcbebccbaaaeddaecabaeaebebbcbcecbceebabdeabdddccaadcdbcedaacdaeacecaceaabdedbcebaccadcebdaaccaacdddbedddaeadaeaaecbaedcdaecbebccdbddebccedeabdcadeeceadeeedbebdacdadebacacaebddcbbbcadeeababcbdeccbacdacedaacabbcaeacbbccadacecadebaaeaabdceddebbcecececbbdeddbeeaddedeadbedceeeaabbbdbdbcecabcddedddecddbacbcebbcadcebaadaddebbdebaacebccbdcdecaaadedaddabdcdedcabeeacacbeeadccbebdbdcaadaaaeaecbbebabdedccbadcaeaceabaaeebeaacaecddcabcbedbbbcaececcbddaeceaaeadedcaaaabebdcbdbebacabddddbcdaebadaabdceabebcabcedaccdcdeaabccecbdabaceeaeecccddbedaaddaacccbeabbabcdbecbcbcdecbeeebebbbbddaabebeccaeaeadacbccebcceacaadedeabcedbdcbbcaddabbbceabebadeeecacbbbabbbadebddeabddbaaacdedeebdadabeabeaeecdebcdcbadaabeedcabaeebbebcbaecbddaaaeccdabcaccbebacabcccaabddbdcdddddcdcebcdceaedcadbacaaeeeeacaabacbbcbecddeabeecdadcceeceabcbedeaaeebbdacdcdbedbcbbcbbeddcdbbaeaaaaeadeaecacaebedccaeacddcaceeeeedddaeedddbcaaedeaaeeeecaedcaeeabbcdaabadbdeaddcadbbabbeacedceaebabbadaaaebceadeccecbddcdaddddeabdeeaabcadaacedcadaeaaabdcedeaedcbbabbaedcadcbacbacbbebebddbbacdeeeecbcaaeeeaeeceddceddebdbcbeabddeecabcbeddcdeeedbbecbbececbeabcddaddbdcdbebeaeadeeddcebcbdcadbebdcbdbebbbeacbdedaedcabdcbaaaaaebbedbaadcbdccadecbcabcbcceaabcbebecdbedadceeddebebeaebebdabebdbeaaabbeecdadebebbeceebdccedaebaaedbcceebcdecdbbddeeebabaaeebbadcbacbbbeabbaeddeeebececaeddaeaacbddccddbadbaebebcadaebabbeeabacbedcbceaaabbaceadaedcaebcdbabddecdbbbaadecbcedaebcbbbbdeeeebcdbdbdbeedebadeeabbcceecaabbbabaecdcbeadeccadccddccecccdccdeadbebeabdedbebbccdcddbcadbbdcaaaebaedcdecacabaaaeaeadeddeaecdcdadbddddbadeeeecaccdcbbbabdacdadaabeabeaabdbdecbdcbceaebcbaeaacdbadccaeddaeacbaeddeaeddacbceddbbeebbbedeebeccbdceabaccdebdecaecacaadbabcaccaceeacdbdeabdacdeeaecdacbbaecbeccdedddbdbcdeccceadbcaceeebbdcbdaebdccaceedebaabcabdbaebbdabedaceebbcbecedccbaeaddbbcaeeabdbcdbccdbccbdcebaeeacebeeeeaabeeacecccabcadbacbddabbdededdcacccdabededccddedbbdbdabdeaeceeceeacadabccbaedddaddddbdcbdddadedecbeaccadcbceadbdccdcaacadcbcbdacabdedbceaeeedbabcccbebaacaadbcbeaabddabbdcbebbeaccdceeedabadeedceceeeeabebdcbacbcabeeebeeaacedeacdeedccbdbcddcdadbbcdbadcaabddebdbedabbaeedabdacccdadbcecbcdbabbdbeaaccbeddccbeecbdadbeeeaeddbbddeccdbbedbdacabdebacddeaabdceebcebaadeeeedaddeedddeeccbdcbecdcebbcdbaecbdccbbdacbcbebdaebcdbbdbdeaceacaeadaacdbadbebbaaebdcbceddbadcdbceabeebddcecdecaedceceabdbdaaedbedbaacedceeecdbdbeabdecacbbabebccbdebcbdedeeabbeceabdbdbdaaadbdadaccacbaebedeeeeacbaaaadabcbbccacadeccccaccbbdebbaecdaceecbbbdcabadbcdcdabbeedaadcdbeceaaeedcaedcbaabccddbcabeaadaeaadacceddeacdeacaeacbadbddbcaddccbbddcaeaadebaaacbcaceedbaeaacdedadcacbebbddaaacdaeaeeebedceeaccedabbedececaeaabcabaeaadaebabbaaeabcdccdaeabccacebbdedbabcbcaeeedecdbddaebdddaabadcaeeeedacdadabceddbddeacadddaccbaaeedbceebbaaddbceeeddaabeaadaecdebabadcbddaedadabebddcdaeccdccddbbabeeebaddbedaaadbbcaadcadacaccbdaadceeaeebedcaaddebaeeababdcdddaabccaeccbceaccdebbbeaaeccdaebeaebadadbeeebdbdccdebdeeebddaadadeeceeaddbbcbbcebcbdbbedceeeabadbdedbeeddaadccededcbedcaaebbdcacdcadeddadeacaaeecdedbebdadddeebdccaebbadecbcedcddacabdccacedeccebedaadaacabeccccbeadcaebcbcacdcebbebabadedcaedaacbeccadebcadcacdeaeddbaedebdecabcbeabdecabcbabceedacbdbeebacbdedcdcbaeeebcbdbbecddbdbcaebbcedaedaebaccdcaadcaeecdcaabebaedadeddccaaaddbcbeaabeabedebececebeabbeacdacbacaecdcbdeebccaabddcbadcdcceadabacaeecbdccbccbbeededeecaecbceebaebbcdbdabccabbdaebeacabcdbaaabddeecaebecedcacacadaecccdddadbbeceedddddeaceeeabcbacaeccabaeeaacdbbccdeaacdecaaccdbcbcbdeeeeeacabcbeccbeaecddddadedededaaaacbeedccebeaeaacddeccecacadddcbbbcbbedaaeabdecedbeaaadaddcceebbdbebeeeddbdaeabdceeebdcdcdbcdcbbbbcebedddeaeeddbcccccbcdbeaccccbbedeadaeeadedcbbaaabdeabcebbebcbbaeecadacccdacddbdcaddecbecdcccbbbaaeaadedbeddeaeeaeabcdeeabaadeaadadaabbaceabbcdbadceaabbceabdaadeeddebbeadbcdddaabccdedbdaeaadccbaaaeedaedddccbabedcbabbeceeedacbddcecedabcebebdbcbebbaadbeedeaaadaccddeeaaddeacceaaaeeabbadccaabeddaacdbacadccedaebbddcbecabcebbaddccdeabdabdaeabcdabceebaabbbceddaaeadbdcedcebdaabcaabaeacedaaacebeebcabeeecdbcaccdedcbebaaedebcedbbcbabdddceebeacabeadcbbccceeaecacbdaecdebdcddbbdcdabcacaaaeeebedeeacdadbceacdadbedebecebacbbdcabadbbdaebdbbcdbdeeebcaeeaedbaabadbbcdddeeadbedbbeebdaccaecebaccabbeaeebecedcdccdabecedabbbbbdcbbdaacbccadeeeadeaedcdcaddbdddabbecabaabadebeeedabaaadddebdbdbcabcbaeedbedbbebcbdadecdecbabaacabaccccebcdbaeeedebbedcdaecbdebbdebbbeeecedebebcebeaedcbbdbbbdceecccbdebdebeadbddbadecbeeabacebedacbecbeebddbebeecccceaecaeaeccadeabaeccedbddceddccdcaeebedcecabadbecdebebacacabadcbcbceebebaedbdeeeeaaddebaccbaeceadecbdeacbeaaceabdbedbadacbbebbbcacdecedbeedadcdcbececaeeeccccecbecdecaeaeaedeeeeaedbeecabdedccecabccdacaabbdbeedcbbdaedabddbeceadcbccadaebeeaaeceeaeadecdaadcdbdeecdbecadcbbedabcaacbddbeaeacddcdceebbbcbaececaececeabeaebeecaeccaccecbcbcceddbcaebaaaecddcddaccbcaeeeceecbaadcbaabacdcbddeadabaceaaaedcecdddbebaaeebbebddbcbaababbecaaabceeeadaacedbeabdbecebdcebbcdcebddcadddacbbbdabebabdbcaebddbcbcbeaeeddccccebdeacbeadabcebdadedcabcebecacaaeebebddbdccaadcaecdeceebadbbdccbdbccbededbacccabdabdeaceebbadaaaebdecdddadabaeaaedeceabbbccbacadcccabdaaeebdaeeeddbdcdbbacedbcaeeaebaedbaeeadebbdadeeadddebaddcbaccacdabedecdcebcceeccdecdddcbdbadadcddcaeedcacacbceeeadaccdcdaadcebbeddcdebaddcbecddeaeecaeebcbeaebebedacececdceebcbebcadcaadabbdadeedbeeeeddeeeadeedbcbaededbceabeabacbeeaaecddcdbbaaaaeedddbbeecaedcabdbbeedbbbdeacabdceddadcaabddbeccaadeecbdbddcbaeabdcaaabbdbdcddeaccebaadcebdbbbeabdecbdeeecceeaacabacacbedbebbbebecadadeebddbaebbcadbceacabbabacebcbbceaedacccbbccaaacdbbeddbbeaccaedabeabacadeddbabdcacbdaeabebbbddebbcaaecedeadacbcbcbbdbeaeecabbbaccdebcbeadebeacabbeceebbcadebddcbdbeedebecaaacecdcedbeeaebedeeadcaaddcaabddaebeaaadddacebabaeedcacddbbdabbbaddabadaeacdebaeaabbeeaacaadecaacaacbbdeecaaaecdbdbdbcebaddaaeadeabbabeaadecbbccbaeebabeaabbcecadbcddbedbeacdebdcaadbabeacddbbeaedacceeeedbadabbeacbdacceecaecbabcacbaedbdeeddedacabcecabecbadabcaaddedbadbcedadabaddccceceaccbeecbecceadecdcdcbcebcccbddcbadeedecdaadebcadcebaeebabdcacacedddcedaedcaacacbebbacccdbcbccddbaaedeeddbdbdaeceeaedaaadcacbaeacaebdcbaedeceeaebedabebddceeaeeebebaabdceacddcacdbbdcbadaaeaedecabdceaaecdceadcbaaeacdbaccdbcdababdccbeeeaabeceaeaceadacbaececbeebbecaedcdbcbbdeceaadcbdebbcccdabdeadaabeddbcdbebceaaebeebbeeebceddecabcbdeeeaddeddbbdbbdecddadcbaeaadbeaabcebcbceaadbaadbdabdbdaddcabdeebadddcaeabbbeccdeaebbbdbabbdbebbebcaadeceeadabbeaededcbbeedbcbaeecacceccdabaacbbeaccbddddacddeceebacbaeddbaebeeacecceebdbdcaeeebcadaceaedcdbdddbbbeabbccccebbbeceadaaeaadccdbecceedbeddeaaceccceceeaecbadcececaeadaddadbebbcbdbaebdacaeccbcaacbacdbcccbbbcbecdbaecdebbeacbeaecdcedbedcaebbddacdbbdaeeddedadeaeccededdbbccccccccdcaecadecebdccadccbadacededbebeceaaedcaadbeabceaddabdbeccabedadaebbcceaedeecadddbbcedaadaedceebbdeabbdeebaddacbadaadecaeacedaceceabccbcdaddaecdbedbdcaaabdecbebeeabeacaeacbbededaaceaeeabecacedccbececbbbbaaaeaadddbdecdcaeecdaccbcddcbecabcccecacdcbedaccbbdccddebaaebdcadadecddedbedccbcdacdddbbeaaceabbacedccedacceddeddaebbcdaeeadeaeeaeeecdccdebabcdebdbcaeebaaeccbcddaeadceaabeeeedbdddeaaedcdceeeceecadbcdadbcedacccdeaddccabacedcdcedcddbaacabddacecabcebdabdebabedeebeadaaabddeaadeaeebaadbbabcbccaaeaedebaccbcbbebadaadaabdbbebcabaccaadcbeedbdabdeaaaebebcecdbbddabaabbdcbdbabaceaabbacdeabaaaeaaceaebeeceecddeacadbceaeacbabebecaebbaabeedbcebbacededbeebbceddabacccbddcbebddedacdeeaecaecbeeaeeaddadacdddeddddddadebecabbcdecbadebdacdedcececbcbdccdddabedbeacbcadcebbbbbadbdacbcbeeaceaccebebcceebeaeddacadececcddbeebddbecabdaebecacdcbbdaecceedadbdeaebdadeaccabcddbcedebbbbcceedececccadabeabbacdcdbaeebdceaeeedabbdceeadcdedebecadcddbccbccabbebebebcadbaddcbcdbdcdedbdbdddbcbadebdcadaccedddaadaccaeedaeabadbacabddecaabadcbaaadbebbcecbcbbdcdcacdcadeaabbaacdebabeedcccbcdabbecbddbaebacabbbcbceecaaeadbbdacbbeeeaaeaeaebadeeacacdcbaaedccccdeeaccddaadaaeebeaddabebedeecdececcecdeeaadaaacebcdabeeedebaaebabbdacaaaaebececbbcaeccddedaeececcccccccbacbedbacacabdcdedededcdadbccecaacbabdbdceadbebbbaadcacbdccddabebaedcaeeabdcadeadaeaacccbcdbdadccdadbccbcbebbbabdccbaaebdaddcabeebabddccbaeecaecadabbccadbbaedbbbececeabcebcdecbdcbdbacbaaabceaebdebedaceeecaccbcbedbcbdcdaabbcccccecdbebaaeccdbbabadaeccaedebdeddceebebabbecdbeadedaeedeeebdebdcccbeecdddeedaebddacddcabdabbeaeeeeebacdacabceceddbadcdebbdeaabbcbadacedcabcaebaadadcdaacdbdaadddadcdecabccebcccaedbbecaadcbbdaccbaeeebdcbbbcabaccedbeeceecedaceebcacebcaaadaaabcabbdcdbeeadeceedebeadaceccadcdbdbcedcbcbecbeaabeadcaeeebaaaecbdbcdaadacacbabadaaaecddadcbbebcdecabacbbbeaebaeecbcbeeabbcaeabcadbebbdddcceccbbaeeeddeecabceaaedeaccbdeabeccdaaeaededdaccbbdecacbacdcdbaeedeeebaaaadebbaaeacadbccdcccdbbedeccbeebcaeabcedabdccedaabddbddccccbacddacebdceeeebccdedaceadbbedeaaadaddaabaecdaeacaaeabeceedceaacbccabccdbecedeeeaabdeeebabecbdebabbdebbddeaecedaebdedbeebbdecccaedaeaabbdcadeadedbbbbccaccabdaaeaaeeddbeaeadbdbccdceebbeddcececbedcccedaecceccaaccdeeeecdbaceedbcdaecbcddabdbadddcbcccdbbeccceeacabdcadacaeccbdbcddedbaeebbdbaabcbbaaccaedebcceebdbdacdcbeabcaabcaddaaaabbdaaeadceaabadbbddebaaceacdbebcbbbccadcdeabddbbebedccbabbdbeccacaccbeabdabacedceacbeebecdaadacbcbeeccacdacadebcedacdabcadaacccbdbdeaebbbecbbdbecedcacdeabcebdeaecddcdcdcecedbdeedacabbacdcecbdaecdbddedddecaebecbaeccaadbecaddeabacdceadebeeebcbbbdedacdbaebcdceaacecabcadcaebaceabbcdbcdcaaacdedeeccbceadaaabaeccedcdcbbeadeecbddbeaaccaadeabbeddeddcdccadaecacadadccbeeeeeaddeeeabedeaeaedbeadcecadbadcaeacacabbdbbcaccadddbbcebacdaaecaaceeaadddbadcddbeeaaebecacbedccbbdcbbecdaeaedccdcccdacbacdbeeadcebadeeddcaabdabacceccdaceacdeadcbcaabeaddbbeaabbbedeaccbceccacabaabadababedadedbddccecaddacccbceaadedaebbbdbedcecdabebeceedbddcabbaeeedddbeabcbceaeceeedaaaeabdaadebdeaacaabcbbeeeeaccdbacceaaeacedbedcdbeeeaecabddcbbcdaebdebccbdbbaddaaccacbaaacdcddaccbebddacbaddeebceacccceeeededbcbeecabaddbcbeabdeeabaccdaeebbdcdeacacdebaaaacbdcdcacdebcecdcbedaadddcccdeeebeccdaebcbcbaedbaccddccdbdbbadbdaecbbdcebeeacccaadbeedadbbceceaedcceaabeebeabddcadbcbbadddacadaecbaebccaaaacdadccceaadcecdaddedccabeddcceddddeeadeddedebababdebeaccaaaacdeaaceaadedccadacccadbdcaacbedbabaddbdddcddbebbcceadcadedeadeacdecddbccecdbddeddbdaacacbecdacdcbccebcccaebabcadeacbdbdaabaaacaeabcbddcbbcbdadccddebccbebacccbcbecaabebeeadddddbdbcdebbbdeaceccaeadabccbecbabeeccbaccabceadbebeaababeedbcbedbeabbadcdddbeeacdeaaebbceeddbdbcdbecbdbdbeeeabcddddaebbcaacabdaedddbebadcccbaacaecaeddcbceaeaacceadadedaeebadecaabccdeccdceddcdcbbabecbbaecddbccabdedcabccedcbadedabdadebcddcbceaeaecbeaeaabdedacaededbadbcdabcdaadbacadbbeacaebecbebbacddeccdedbbebbbeadecaabcecacacbeeaccddbcebecaddeadebccdadcbccbabbdacabcbabebdcebbcbdaccaedaaaacbdbceddedabecaacdebccbbbceeedebedbeaeaebcdcdaabbdabdeabdaebaabadadaecadeeeedeecbcbcaaccadcbbecbddacaaaddabcaabbdeaabaaaaacadeecdebbaebebbdcadbaeeadaeabdabceaeaeceddaccbcedddebbbdeecaacbdbbececebeddebddcacdbcbaccccdeaadbbdddbebedccaadabcececabdebedcdeeadebccecbecdaaaabccddadcccbeeaabbeedcbcdcbabaebedddccbddbdbdaaaadbddacaaacaacdacecaeebabcbaddbccbabdeacdedbedccaeacdeebebcbcddbaadeebbbcccaebcbcbcbdabdadccebeaddbbcedbaacadceacaacbccedbdeceedbdedaeecedddebbbacbddaabaeebeddbeedadbdddaccebdcbaaebccbadacebcbbcdaeddeddceaabdccceadbccebabaadcaacacaaabedeeecdadbbbebdebcedcbdedebdcebdcacedabccbcbebacaccbcaccbddecbdeddbbbbebbbcadccbaedbececcdeecadccdbadeabadcdceccdbababbadcdcaccbbacccaecbabacdacdaddccdecdacabebbdddadeceabceeeeeaddedecccedbeeeedddeecebbebdbbeedcadcaacddcabbcebddaebcabddcadeccdbdebbdabdacecdbdbdeabbadeddbaaaeeabeedadbdebaedcabdeabeecbbdacbeadabdbbebbaabcebeedbbbbedcbccbeddbccddccdcbadbdecdaeebebcabedaeaeecdccbdcebbdabacacacdbeacbabbaeabeeccdbbcacadbccaecaabcdecccebdeedeabcbedbedacbebeaccbdceadcedcddabecacaddecedededcaeebbbcdcdcdccbebcaabccceabcbcaabeabeaccaccaecceddcbabcaaaeeeadabcbdaeedbbcbbedcadeeddccabcddcbeadccdabcddbeadcddcdddbbacbdcacdbadeddbddcbaaebdeabdccbabedacbbdcedcaaeeabdbabadcacbbcedaaaebbbdedeedecaccbacacabdcdbeaadbeabcddbdeaaddcddeeccebdcbdccecceaedaebdbbaccacbdcbadccdeecbdcadcdeceeacebcdeccbcdedbdaebebaeeccadacdddbaddaabcbdeeaeccaaabdabccbdeeceaddebddeecbcddadedceedeebbcbcabeaecbaeabcecdbacbdcddabeccdaecbbbcebabeedbdbacacedaacabcaebecddabcecdeeecdbbccbcebdbaaebcaaaeeabdaadacaabebddeecacabccedcedbaaddcabaddbcddbeceebeadacaabbdabebbdcaececabdedadeceacccddaabadbbaaaeedeeaddceacceadeeeddedbabdaeeddaddadbbbddaeebaaedccddceadcceeccdeacaedccadccaccadacbedcecdaedcddbbdbadcacdbbaeadaadadcadcbebebeceeebeedbcbdbdedbeeaaeeeebadaacdbbebaccccdeadaecbecaaeacdddadbeecbceadbcddbeccadcdaadbdbdeabcdbedcabdccbdebbbcaeadcdeeceacaabaebbaeebebeedeedddbaabccdeccccbeedaaaeccebabdccbceebebeabeedeaeaabebbedeaacceceeabdeaecdecbceaaaeeacbeacabbcdddaeaebcabaeccbbbcddedaeddbcddcaebcbbaeedaaedddeeabbdccdebdbbddaeedbcbaacaddbdebaadedcebdbeacccbdecdcbcaeaedcabdabaeeadebcddcdaccdcdbcddbddceceabbbddbdddaebbdcadaeabeedaddbbbbeebacaeeaacbcbabdbecceaedeccbeebabcacaebebaebcecbabbbdcdddaedddeeadeaddcdeeeeeddccdbddccccebaeadaddcbbaddedcebaacadbdbcadabaadbcebcadcbcababdcaeebcdaaececacdabcceecedaeccabdeeaeeeeebaacdbdeaeaaadabedbaaadebdddabacdcaeedcacbbbaaebbbdbabbeebababccdeceeddebcacdaeebebbadebbccccdcbcceaabcdaeaaaeacceeeadcbbdaeccecbddedeebbddcebeeaccdeceeccbcbeaeaaacbdadacaddaeabeacddabdcbdddabecdbcabbeacedaedeabcdbebadebaccaddebaedadbccdaddcbececebadeecccbcedaeaedcbceeadccabebababbbdadcdebeebdcecacedcaadbcaebcdcdaccaadcbbbcbeebddaedaceabddbbbbacccccdabcbdeaeaeabbbdaddaebabeabbedcacdbcbccbaacacdcbcbeabdcbdaeeadbaabadebaaabbccebacabadddedcaadceeadcabbebabaaadaabdbdccbaeaaaccbdcdbbaacaaacabcdbadacedcbdecdccbebabcacdabaebddaebedabeabeaccccecebbdbcebeeebdabddbecdeaedbbbcbdbaccbadddacadebaaebbebbeeedceddaadcbedbcdcaeccebcbaaacdceaaddbecedbbeaddbabcaebabccddaadaeceacbaddcceaaacaaedebbecabaaddcabaebacddeabdcccdccbdbaddecedababdaebccbcbaabecbdadbbcacaddceadccbeeacecaeccdbeacdcbcddebeeedbddeacdcebeabccdebacadbebccadadceadbcebcbadedbecdcdcededbeeebcdecddcedaacbabbeeeaabadacdaebebcccaacdedcbbdddbbcbabbcdbebabcbaacddeecadecedeccbdabbcebcccbebadbdeceacacccecddcacdcbabdcedddedcbaecedadaecbdeeabdeebcbdabcacccadadcaeceaeabbeadbccceeaccdddceaecadaadcbcaaceeeabbdabcdeacdacedcbabeeabbbbccaeeacdcccababbeabadebbcaddcdcddccceacabcbdeeebbecadbedaeeacdccebaedcdbbacecbdaeaadcbeccecaabccbadacaccecddcdcaebbcbebcdceacadcaddcccbbaddebeddbacdcdbebddbdacdadaaecdacaebecbdadcbdaedecabdacececabcabcbedeabeddabbdbddceaeecebccebbaccbbabedbcceadbaabdbadabbdbebedcceecaadbceaecceebdbeaeacddaaecdaebbbccaeeacdaabbbaccacbbceaeaccdecbaceaecccadaeecadcddebebacbdddbcdabaadcebebeacddbaacbaaccaadacdcadecdbcbacdbcbbbeadaebadbcbaabbaebabcdbcbadcccbbdbabddedadeaecedbceccbecedcabeaaecdbadbacccecbceddbdaecbdedeadaaceccdabbddcdbeecadeccbcbbaacdadbcccbeddeddacbdaaeedaadeaddcbebcbaadbdcceaacacdbbdaceedddcdbcabcdeacbdcebddbabddbebdceededcabaaddebbeeaacdbcdecddddecaeaeaebbeecbbeddccecbeebebbabddecddeddabeebbcccaeadbbbdeebedbadbdeddbcbddabcaecadaeecbaaaabbbedddeabcdebbadeaabdedbbcadcdbbbceecdabaecacebebcbddbdadedcdadeacbbeeecaaedcbbbbeecacdedeeddbadebddcbdacceccbaadadbbdaeabbadccecbcccecdbeaeedabcdbcabacaaeedbeaaecbdcabecbedabbcbccddbdabbdabaceedbcbbeacceddadceedcdaeecaebecdccabdaabbeecacbddaeddbcebcabedddbedcbacecbcdddecebeecedcabaeeceedcebebcccedbabaebcccadcedbececacdacbbdbdaaeceabaecebeddacbdddcbddddedebedacecddcadeabcaccbaacaecdbbcececbaedebecedeccbaeaeabdeaccededebbeeadecebdbdbcdbeaadeebabaaebeeebcabaceccdeecdabdadbbcbedbaedebbdcddeecdbbdecbbdeaabcaceaedaaacacceebecaaeeeceebbcaecbeebbabedbeaebccbecedbaceacdabaedbcaacdbdbededdaedabccbcbbdcabadaabadcdcbccabcedbbaeddbbdbecddabdecdeeeaacdeceecebaaaadebecaabecabebdbeecdeadccedabadcddbbcedcadacdbeebbeadacceecdedbadcedbedeeadbbaddccbbcededebbdaeccdbccddbceeeeacbbadacbedbaddadcadbdbacaeabccdcbdbcbcbdaeddbceaeddecbdbaeceebcaedccaddadeaedabdbcbdebacacdcedbebedaacdeabcadaeeacceaacedbcbececebeedcadddbbeecaadbcbdecccebecbaeedebaaddabcaaabaaabbedcabbebecbceacaceeabdcaebebbcaeaccccbaddbeecdaeddaecbadcaeaccaeaedbbdecccccdbccecadaaaeeacdadeedcabeabcebdececbebbeaccdeabeccdbaccdcdcabadeccecbcccbbdceddbdbbcbbbbccadededaadeabdbbedabccaaaecbebbcebbaebaedaddcceebccacaebbcbabdadcdcededbecaeaaddaebecedcccacaeaceaabebbbebcacdacaedebedbeeaeebcadcbeeeeaeacacceccecddcbaedcdcebbebbbbabdeecbcdccbbddbeddeebbbcabeaeceddaccbadbceedebbeebbabbbccebcccecddadbebaaececeebecdbecdedaaccceadecababbacaeecddacebbccbcbcabeebccdcdecccacaebceceedcaddeeeedbdaabeaeeeeadccccaadebcacebbdedeaadaaeccababeccacddeedbedaaebcdbbbaebaecbaaeadbaeabadebccadeeadeeccedbbdaddcaeaccaeabbedbbaedbccdaddedbcebecdececaebdecacbeaadacebdcbaabbcaadeecbdeeaddcdbedcacdebebddcbabbebceddeaedacbedcabeeeecdbeaebabbdabeaacbcdabebecebbdbbbedcdaaccbabdbcbeeacdacbdecaaacddaecbadaaebbdeebbaccccecceecadaebacbadbaddbeecdeadddecebaacdcbdceeeaecacabadddaaacceaaadbeaaaeeddeccacccdbdeaeebccebeeceabddbabadedbaccaaeabcebbcebdbeacbedbdabcdebbdadcaecacecdddceaddbeadccaeadcccdabbacabeabccbadbceddecbbebbceeecacabdedceabbaaeacbcaebabcccdeaaaeedccbaebeabdedaccbccabbccbaeccdcceabeaecdabbdedcaededccdddebdacacaeccaceeacedaebdcbeccedbceeeaceebdceabddcccacdeabbdecbddbeeccdcedadccccbecacbbadcdebadabcddacadabacabeeabbdedaebabcbabaaccacdbcbbacaaeeaddcadbcdaabbcbcbebdccccbccecbdababdbedceecedabceaedadbdeacbebeabbbeacaaadbbdeabeedcbdeecdaabadeccdddbdddabddceabbbeecacbadbbaaadeacdcdbdbaaaeaabaccedebdeaeddcecdeecedcbcadcbbcbeaebbcebddbddcdedbaacbccdbcbcaedceacdbacabdeaeedbaeeeaabeaacedcbbdcdabadebccbbddadebceeadaadcdddcdaaabbaaedcbcdadaabaaeddadbcaabbbbcbbeecbebaeeddacecbcdebcbbdcceeeacccaddbdccdeeeacadeeaadbbabcdcaedccdeccacebabdcaddabcdeebaaaebeabdccbbddbcbdedadcdaecbedbdbcdeaddedcdbaacccbebcaeadcebceddccaadccedcddbddccaacbdcdeeceebbadcbeddcaaacabeccadeeeeebeeacddeccdcaeddeabbedbbeccacababadadecaddcceabcdabbbbacccccebaebdcdaaeeccbbacbbcebadbbbccbcddddacddeaebbceceeaecceaaaeabdccebeeeaecbbbbabcbdcbdeeaeccaacdedcebadeecbbacaabdaeddddabddbbbaaadebedcbabbdcdcedacbbddaebecdbddaaaeaacebdddbaaedbeeddddacbccdaddcedacdddbdecbeaedbcadaabdcabacaabbcccaedbbecaddcdccbaaacbdecdebbeaaadccdebcccdeadcbeeaecbbbcdccddadacaadccdeddcbecbeacdbbeeaadeabddbccceeeedaaecddbcabebcadcceaaeddcacbdbcddaeabbeedccebadaeaececedcdeebebbccabbeaedacedeaaaeeecbaedcddbadeeddcbcaedcdceecceeabcceedaeebbaaadecabedabdadbbdceaecccbeedecbdeddacaecdedaeccdbdeddbedadaadbacbcbcbbaecdeaedcdeeecabbadbaecbcaccdeceeacbdcdecedbaacbecaebdbdddeadaabeadceccbcbededcddebdeaeaeabbdebcbcecacdaeacabdacbebddbeeacbadbbcdebabebbdeadecbaaaaaccabeceabbeabdaddcecbaebcddbdecddebdddccdeabbcbedadecbccdbdebabeebdecbccabdebdcadeddbcccbedcccbdebbeadedadeccaedaecddbaecbbadeceeaceceacebacabcaadebcdedacddcdbcadbbaeaeaedbcebbecdadbbdccedcdddcadbcecbebcccbddbaeaecacaadbeacdcbcecadebbbbccaccadeecdedaebdcabbeacbcecedbebccdbbeecedddeeccaacabeddadbceeabbccadcacdcadbcdadecaaebdeaddbcdcabdbeabadecadbbebacbbabbddbcbedddebaaeaecadbcbcddcdbbabebcdcebccddebedebdedadbcadbccacdddbccccaeaadeacaddbecadddeedceaedebdcdccccabaeedddaabddcecdeccdacbccabbedabdceebdcdadaddeecbeedccdabdaababbaceacacceacbebdddabcbeceaeaceaeedabbadcaaadeaadacaccdeecdadccaecacaabbedbaecbaeeebeaabcaececeeedaeebebeeceedaaacdeaacedcccbeaeadcaedabccbcebbaaebcabcebbbcaedaaceabbdbaceeeabeaadeecdecdacdcacadacbededaadbeeaacbaaecbbceceacaabbadecdcacedbedababdeebabaddbedbceaadadccbbaccbaceecbabcbcddeaebcaceeaaacbabddbbadcbeebcbbbcbcdabdcbcedebbcbbdcccdcadbaabddabeabaceceddddbbdabedebbabcdcaccbeabaeebbedbdedbcbbccabccadebbeccecbdeaebaeecadddaedccdeadcdcecdeaeadcedeebccccaeddcddebdcabaecebabbdacbbdbcbccacbcbbaeaeeaedbdbbecacebcdaedbebdcaebbdcabadacccadcebcacbdcadcedabaebcbcdcbacbdcaddcaccaeeeadeaddccdaabdaeacbdbaebedbdedeededaaddbccdcdeccebcaccebeeabcccecdebceccbedddcccdbdbadababebcbbcdcbcbeeebcbdddbccdbdaedbceaedebbacaccacbacabaacadebeeebcaaebbbdbabeaebabcdaeabcbccdbedecebddbebbbcbeddabddddeaeaabddcbeababadcbaeceebcccaedcabaccedbdbdabddcbdededbadbcdaeabbdddbdebaacbebcdaadabcdaadcacbceadecadceeeddcadbdbbaccedceabacbaceedabdeccaaccbaadecdbedceaebeedbdabbacdcbdadbbddabeadebaecdccececbabdedeebdeacbcaecccccceceeecdcbdcceccccaaaeddaceeedbaabcbdbaabedacdcaeeaeeeaabaecceeaabbbbdaabebaeeeeecbbebeedcdeeacaaddcbceeeaaadbdecaceecadaebceeeddabbbacebbaecbdaeadeecbedcecaadabbddeabebaabebaabdcbeaaacaddbabaccddbbebbccaccbcebadcdadceacbcacacaecabeaddaacbacebddddaebdedaeaaaccceccebcdbbcccacdebccddeaacebbcceedcaacecacebecbcacaeaacbaebeeabbbdadecbdedabadbdeccbccaacbeaebeabedadeccdcdccebcebdcaccceecceeebcebadaaaaaeecdcdbccbaaddbdeaaadebbbeaedadceabadceeaacdbcaecbadbcabeeaeacbcadcbbceeceebbaababdaecbbccdeacabdcbceabccebaeeecebcecdddbbbdaceeadabaedbacbdccdbdbcbcecdbdabdcadeddeeededcccacbbbbdacbadcceedbecddbaababdcebbeebebececbacbdabbabdadcbcaceedaedddbacbcccecaadccdcbaaabcababccabccbbacabcacacdbddacdbbbedccaeaeaddcecdeadeacecceccaeeebdddaabedddeadbebdcccecdaedbaadaadadccbbdacdbdcaccbabebecaabdcebdbbdbbaddbdcedcedddbbdeecacdcdaececaeadbaababaadecceeaeecbbccbabaaeabcbeeedcaeebeeebdaaeabccbdabadbccdbdadecdcebeccccddedbabbdbdccbccbccdcabbbabdabdeacbaaebbccdcebcceacecaaaeaccdeddacddcbcecdbeddcecaecbddaecacbdeaabbcacaecabdabdeebcbaabecabbcbaebbbdeeccbecddbdedbceeaeeabbeabbbdeabcadcbcabcbceeaebdcbeaeacaecdebdabececbbecdcdabcacdcdcddecaeeeadcbdacdacbabbdcdebecbbcabceddbdaeccdcbccbaadbdbedbeaddcabaaccbaadaedbcaadacadbcadedbdddaacaeedbdcbcacdabecaedddddcedbbcaacaedbaebccaccbebdcdbccacbbeaccadebacecacaabdcbeaebaaaeddbdbdcecbbcdadcedbdbebeebcddeababadbdcdabddceebeeedeeebbaebeedaeceedbdbaddeaedbbedbaddeddbecebacedcdaaaeedbceeedebbbbeaabccddbecbdddbabcdaeadcbaeacbcbbdeaceedaecbcedcbadeacdcdeeeebadecebebacdedcbdbbcecabebcecddbcbedccaeaeeebeeeadbaadcaeadabecebebccdeaacbcddebbecbddbbccaaebaadecddcddceebdcaaecaaacaceaeaeddbbedbabdecdcbbdaaccdcbdceabcbebcadabbcceccdebdddecaeebccbcdccddcdabcedcecaadeacaeadacbedebbbecbbbcadadbcddbdbccdecbdcababcdbceeeabccedadddaadcccdaeaeaaeebaaaeaebbabcabedbcbbaaeebaddcdabdebacceebbbaeeddbeebeebebadeaedddadacdaaccbdbeccebdedbcdbbcaabbebbdabedbbcceaedaaecabdbeebacccdeedacccdcadeccceadddadabaaedebeebbbeaebeabaacbeaeacbddeadcaeeddcdccbeedccaceeacbddaebddcceddedacddedadcddaaebeadbbeaaeabbbadcebdbcaabacaabeeaaaecddbcbcdeaedcdeecbcdbcdabbdbaebadcebcecdbdeedacbcaabeeaaaacebdecdaadbeebbbbebbcceabeccebdcdacceececeadcabeadaacdeadbaeeaeedaaaccbecbaebcbdbbbcdbdaababbaadcadccebcbeecbdaacaacebadbaddeaadcbcdbaeeeadddbdeaacacbbcccdaabebedcdeedcaeeacdeddeabeaebbccaeceaeccabcbdabdbbeeaebdddabaeabacccaedecaeccaabdadddeeaeddeadbeccabbeebaaebbaedebcecbeabebcabcecbadabcaccdababdbccdecdbbcbdbebbcdadecddababdcdccebbdabedacddedaabbeedadceabdaedeedecaaebddbcbdebccbdadaaeeedacdcdecbcacabbbbeeeeaaccaeddcabddacaecdecdeedeaabacccdcbbdbbeedbbecacbbcdecdeceeededacbabbcbabbddeacdddbedadbcebeaeebabcaccdecaecabadbdeebebdccdbaecdccddeeddbdaacdecbeedbadebacebecbaacbcaadcdeaebaeacddacbdedaaebdeaebdbcdcbcbeeaddceaabedcedecdeecbdcbcdcaabbbcaeebcddedebaebededcdaabbbccdacdcabecabcedbbaacedecbbcdeacabbdadbdeadeeecdbcbedbdacdeaccdedccaaecbdcbdebcbabdaecebaedaddaccecbdcdcbdaeabccdddbccbcaecebbbaaacaeadaeceaaecccabcebdedacaaaebcdaabadbecbdeaaeccecdddcbceebadeccdadcdaaeabcacbcacdeabceeadecbbecbbaebbcbcbeeacdbdacddeaececeecbccadecbccdeeedccbbacbabedbdaadeaacbcbeacaedeaeeebbaacbcbaaeccaaccdcabcecaeaaccaadabebadcdddaaacbccdbbbedecdcdccbbdaabeabdebbaaeabddeeeaeeaaaddbedcbeccceaceccacdcdcbbaeedeeccceccebdbccbcddeeadaebdbdcccaadcaedceabddacdccbeaeaeeeacccdbeaedcdcacaebcdbbeeddadeadcebdcedcbbdbdeeeceacacaaadbbabedccebbebeabedcbeeceacceaddaaccacbaadedbeebbbcdeecbdaceceadbacebaeceddcdbedddbdadcdebabbebeecabceededeaeadbdeaccdaceacbaedebccaabceddecdbcbaaccdddcdcbebbcabecaeeecedadcccaeaaaadbcebbeadacaedadedeccecedeadeeecdeeabcdbbadacacdbdcacaeacccecebeecbcbeaccabbeeaddbdebccbaeacaccdceaecbbeaadabdcdcebebceacebbeccbddcecdbaceeccdaeeeebbcaaceccbebbdbeaaabdceaadeecbccabcadcceabbabccbebeadecbaabceabbaadbbeebbbdabcaededeccbdccaeebaebecbbccdeaabcacededaecbaddcabeeadeabeabdbbdcdcebccaaeeeebabcbdedcdcdcecbdedcabcaecddcdadabccecaaabbcdeebbdddbcbeeadaeaaeebeacedbebdcbadaadeeddcbceadaabcddabbbeecdaadacdadceeebeecaaaabadabbecdebbeddeeaddcabbdeacecceeddbbcabacdddddebddabedaebebbedadccebeeaddbbceaaeebadeceecedbbeaeeddbdbaeaccbcedaabedadbdeccbbeeeeaeabcdcaddcdabbedbdbcccdeeddcbcabeaaccccddeecceddacbceeabcceceeeebcbcbbeedcabadaebbecdeeeebecadcedecbccdebeeebdabaaaebaecbaccacabacdcceaadedbceccccceeaeadddacedbceaceedcddebcddeeecdcdcecbbbdcaebeaeeaebbabdcbcdeccaccdccbbccebccadaedeeeebcdbcdcdbcbdacdaaecacbbbbbcdadabdcaebebeaccbadeecadeccceeeaebcdebebababbbecaecdddbccbbaceaddcbdbebbceaecebbccebdceddcbcdbbabdbccecadaaedcecacdcaaeeacdcceeadebdbbcaacbebeeeaeccedaebedacaedeabdabacdddcebbbeadbdedecedeeddbbbdadbaaedbbeeaebaddebdcbeedbacacbccabbaaddbcdcbcaeabaecacbeaaeedcadddaeaaebddecdbeaadecaaecdbcdabcbeeeacbbeeadcebbccceeeddacdcaaabdceaadeeddaadabcbaecbbdabedddcededebbeaedcecbcebaadaddbcdbaeeccaadcaecbbddecbebcdabadcceacdedcbccedcbdacdabedcebbadccedeccbeaeaabeddeedcdaebaedbeddceaccbdbbcccccdccbdcbebccdaaeeaecdcdabbaadbbcdccabcedaebeaeccceebbdbcebdceecbaaceccaeaddecbcdcccbbbcdeaddabedccbeeceacccbabecbdeebaceddbdacbdcedbcdbdaedbcaededebbccacecdcbdabbdbbaedbecdbaadaebbbcbabbebebaaeddebcadebaedcbaccecbaebabacbdeaabacddacadcbceaacbdbabeeeeedaebbecabeddcbcaecadbbbdeebcebacdaeeeceaabceceaccaaceadddacedbbcacdeeebcddcdadaeaecbaaaedcbbcaceccabaaeadcccecdeadbabdcecbbacdabadcbedeeceddeeeeecbebbecacabeecebcdebdceebebbecdaeddbaaaabbbbdadeababacbaacbeadbdabbdadcebcdabaacdebcbcccacecbcbebbcececcdadcaadccabaacaabeddccaecdcbcaabddadbacacbbdaacceeddaebceacdddddbaeccecaacdeebdbadbbebccbbaebdecdcabacbacebaadbecbcaacbadedcacdabdacdaddcdedaeabecabdceccbeadbabdcdbeacbcdcbeaeebdddcccedbcecaebedcaddcbddecaddddbacbeabcaccdbeeebecceedbaedeccbadeacedbdcecddbcbceaeddadaebbbdbaecbbebddadacaeebeeaecaceaededdddedbebaacaaceccccbbbddcbabbaceedccbcbccedbacbaccecdcebdebbeaabdeaecaddebedccdbedceeedbdabebdcbbeddebdaaeadcbacabceebbbcecbaceeaccbaabadccaebeebdddaebabbdcabeeaceddaabecadcdcbcaecaeccbdebaebcadebeacedbabdbdcccabadaaebabadeadabceddaedababaccaeadaedbbebebbebeccaecebcbadbdcbeaccaddaadaedbcbebbaaabbedddcacebceebbacdcddccdadcacaeacceeaeebeeeacacaaeeecdccbeeacacaadddcecdaceceadaedaeebcabbadbdeecacbcabeadcaacadeeaacebbabcdecbbbbaacabeaaaebebeddddebdaebbdabeaeacacbcccdcedcecebcacabceadbceedecdebddebbbbaaddacbcccdbcaaaedcaeeecbadbeaecbeaacdcaddecdaeaecdaccbbebcadbadbdedeadbbcbddcebbacceaaccebaccbebdbbadcccceededecbdbadacdccebdaedceceadbbadcdaedcadaebeadaaeeddabaeaddbedccbbaedcbcbadeaeceaaabbaeeddaacababbecbcadebcaaadbeadbcdbaecdbaaeaeabbcdaaaeeaaadeccabeeebdecdacaedabacddddeeccddebcaccbeeabcccdbabedabedebdecebaeccbdadbbbedeabebdedccdcdcedacddbecbeacaaebbdbeddeaddabdbeaebeadabaacbbdebdeeccacacbdebbeebbaababbbedeaedcbedadecbbeabebeadddcbdaecaaebaeeebcbbcceadddeadaabbebacadceeeecadddabeedacdaccdebaddcbadeecddcdebdeddaecbbdaebacecdecddeecdacaaadbacedcdaaccdcbedaedadbcceceeeecedaabcdbcbaeebeeddeedcdacbeadeedcebdaacddecdbdabeaeaabbdecebecbebbaacdcdbaceadceebcadbcbecaeaceaebceaedbaeaebdcacecdadedacccddaedbbcaecacaeebdddeaaeebebcdaaabadcbabaceecccaaceaebdbddbbacaabaecdabeabdbbadeaaeaeeebddddaaacbddabbecdbbbbccbcbacedabcbdeddbbdbaebcedbdeccacddacccbeadcdaaebdacaebcadcecabbbccebbbdcaddcddcbabcdccbedbdccccddcabdbbabecaeddcdbbacdacceacebdadabecddeecdcceadbcbdcedebaaedcabeddbeceeccecaeeddadbadedeceddeebcabdbacddaedbeecdcebdaacacaaddbdadcbbaacbbdbbdacbccdcddabccbcbecececbbebdcbeaacaacdbadceababeddedaeddccddaccbeaebeabccadbabdaaacbeaacedebbaedddbdeaecbbcaababdcbaaadbacebaaaecaedeadccaedcecabcdcaeecbbaabbcbebbebdeebdbddbdccddcdbcdccdddabcbeaeeaeebeaccbceadabcacceeddddbebbaebcececeebbdeaebeeadaadcaadabbacdcecbdbedecccbddeddcebbababecaeadcaececcaadaeaabdbbdbcdbbeedeeaddbdeacedaadbeeebcaaaecbabcdcdbbaebbebdacbedbbdeaaceadbeaccecddaeadacadebdeadeddadbacccdeeabcebceaaebbabceeebbdaacaddbdddbecdeedbebbbccedcbeedbcbddebccbdddeaaacbeeeebbeaeadbebedeadaecddbebddaadcabbbadcdeebecbbdbddacbdddbabceacebedebcdeddcdcdbbabcacceccdbdabbcaeedbcaacbbcedbdbccdeeabbdedbcbbaabcbccaebecbabaebbbeaaaaeaeaeabcaebaeeaebaabecdabeecbdebaecbbbdaddadadaaddbeadaabbeeeaeeeebcbbacdddedcedebcdbaaadebaccdeedbdacbcbbbbddbdeedbbcdbceddebccceedcaebadbacdaaddbaccaceebadeeaeddcbcaedcaddecbaeaddbcdecadadadbaebbabaabbcbdcbedeaeeccdbbdeaebbdaeddeaebbcdedcdccdcbbdabdcddddcbdbbebbebbcdbaaeeeedddeeecddcbceddcdcdaebecaeccccedeeadadeeaaabcbdeceaddeadebaeaecbeabbededbbeabebedbdccaaacccdbebcbcbddecdabdbddddaebddccadebecaebdedeaadbbaabbaebeddbccaacaddcecedaaaedccaeebacaadeedebdebeaadebcdcbdcabacbdcddeddceaaeedeceedbacaaabceeeaecabebbdcabdcaabbdebeacbecaadcceeceebebccdacaddeabeddcceaebcdedaeeaacdaaacabccdcacdebdcceeccecbdecddbacdcaeccaacacceeebaaddebdeaadcebebcedecdcbeaaacacadbcaccdbcccccdacaccceedbcdaeebdacaedacbeeacaababaaadeeedbbceaedaaeeddaecceaaddebbadcdeabdbdddebacbaaedaadeacecdbcaddecacccdbddcebeabeeecebbabecaebeddecbedabacbecdbddccdecabcabbceabeccebbaebaacbeeacdaaecdaacaeecbbdbadcecedecbbbbbeeabbabbccebaadebeabbedeedbccaeadddeabeddcacbbadcbeeaeacbbebdbdbecebcdcbcebccdbaeeeddddadcbbeeaccebdcbdcededcdcbdcbeeccbcebdcaccdabecebcdedabeadeaeebddbdecdbadacaebbbdceecabcecacdbedebbabecbabddceccdeeabcbaccaabdcaedacccadaebedecccadcbaddaebddebecccbaddeabddbbdacadccbaecdbeedbeeabaadccbebedceabcbcdeceeceeedccbabaaeebbbabbddedbabeeacbbedbaebbceabbacccecaecbaacabccddddadbcdaedbdddcceaabaaebdabbeeeeedaaaaaacddbeedccccaaccbcaeebbdcbccddebcdcbccaccdcddecdcbececbadadadebdcaabedebcceedbcbcebbccddaccaaaadeecbdcadeedabcccceddcbacdbaddcbdedbeeebcbdccadadacacdeaedbbcbeebebebdaecdbedeeeabeecbaeecebcbdedddaaedcabadaaaabedddddcbeaabcbbecbaeaccedebebeacebaeebbcaaaabaeeabcbaccebcedbdbdcdaeaebcedeeddbeceaaaacdccbeedceeccbecdacdcebdedbeacebdabdaceccaaddbcdedeadeaacdecacabcdceecddbdadabecaedcceabdbaeedaaebdebecaaabbecadccbbaeacabdbdbdaaeaacbdceecdebbadddccacdddddbbbbcbdebebcbedcaabcccbbbdacdaabadabaebbdcaeeaacaabcdededdbbcbaaeaaeeaedaddbdbddadbbbabcebcbaaeabbbbdbacaaacddbaeccbeacdcccdcbdebcaddceaaaacddcdbaadecaedbbacdcddaaccbbadcaadadedbbcddabbababdcdbebcdcccccbbcedcbdddeabadcacdeabccacdbebccbcedcecbcaddacbacaaedbbeadccedbabbceeaaedbdbddebeeaadaeddccbbcabbedbcdcebbebcedecbdccdabeceddcdbeacbbbeceedcceadddccddabebcbbeddabadadbdacedacdbdcaaeeaabddbcdccbdadbcaeeccabeccaaabdadddbabaadedadeebcbbaceedbaaeaadcedccbcaaacbcbcdcccbebbacaebabcedebdecabbeecaaceeaacccdcbbcaedeabecaabaaeeceabddcaeedacceaaedcbcabdaeeeddabbeacebbeadaeedabcebaceceaeaedcbadedbeccdccbebedbcecbaacbaaabbcdabecbabbdcdceaadabbccedcbceacdedeaaaaedbceebaddbaaecdbcbdcdcacbccbdeedddccdcaddeedbaeddcdadbcdcabedeeeacdbdabeabaadabeadcaaadacadeebcceeddbbbebaecceacdbcbcdceededbccdddadccbbcceabcaddbadcbeddabaebaddeccddadbbacdceaaaedaeecdebedabeaeaeabbbdccabedbadbaaaeeeeedbedbcdbeecccdceaadddebbedaebabaabebedaccedbbcaebdcebebacebedbedeaeacbecadabacaabcbabcdceccadeeaaecbeeaadcbcdcbdeedeaabbbaccccabddaebccaaeeeadbadabeaaeebcdeacddcbdceaeababdeccaabbcbbccbeadecdccbabbccacdacecdecadeeeadeedeecaaacdbcadabbbeabdadabbceddcdeebaebcebaeaceabeaacaaeccaadcdddddceaacaaeebdbbaedcadaccdcbbecaecebcaaeccbdaedadeabddeaabdbdeedcececdabdbcbadedeaeacccbecaacacaecacdcbdcabeaacebcddaccaeecccabbddbbeadbdedebdabbabcdaccdbccddeeaadbeeedeabaacdcbeecddcbcbadedddecaeeabaecacaacaadacbedaabadeccbdbaaacdceccbdbeebaecceecdcaaadbbdbcabeeeabbcebacedabbbaaaaaedbdddddbcccceeededbccdaaecedebaedbdcacbbdcdccccdacddbecebeaeebbdcdeabedaedcebdadacecacdaacddbdbddadbbcedbebcbeeccddecededaeaaadebeabceccbbcdbaedabacbccdbddabebdddcaecebeddeccacdaeeeaacbbeeadbddbdcebddcacddaedcdcbcaecdaecdadddbdddebcdaecbbebaeaebedaeadbdaceacbcdcebcbcdaebaacabceedbcbeebbaccaebeaebddcdaebcbebbadededbbaaedcaddcdaeabceababebaabbccceaeeecedddaaacaceaedaaceccdbceadcbabccdededccacbddbaaeacbbccaacaabcbcaadccaccadebcdeddbcadbedddeecbdccaaaebdbebeabbdcaadaacccebebbacceaedeedaeaabbdbbceaebcccaeeceebbddbbeadcdebcdcddaecdcdededacadeccbcddabdcbebbbebcceceaeaaaeabeddbedebadaceabdcdbeaabbbebdceebdcadddadbadcedaeeacdaeebbcabccabeedbdebdeeaedeabaedceeacabdbcceeddddeddddcbedaaedecabababcecdcbaacebaaebbbddbdedaaecedecbeaebdbdceddeabbddbeabbbcdeaddacdbdceededdecaaeabbdddecbdbcdcccbeccdcdcdcaceddaaebcabeeaadeabaddcdbdcdedaecadcedcadbaeebdeeeedcdcdddcecaccabcacccbbebbedecebaddcecbabebbabdbabecbeacaaadcaaeabbddaabddcdeeaadcebedadaebccbcbbedbbeabcaedabdcddadecccceebbdcdadbeaabccbbbcbdbeeaacabdacdccdeaddceaecdadcdebbabebbbeabcedbaaeeadabbcdebeeadcdbabdbaedbccddcdeddeebaeaacebcdabaeaadcbbdbaaccdbbaabddaecaebdcbccdbeaabccacddeebbbecdaedeecdcacaacabaeabcabaecacbecdbbebdcceededdeadeecacdbdcaaebbbcacddecadeaaebaeedbbadbaabeeaaadccababbdaeddccdccaaacbbdececaceadbdacebcbacdbadcceacbadbbdacbdceaebdeccdecdabddadadadaeecbccaeecbacccabdecdbceaaeadccbcdceaaeadbddeadceeecebcaeaebcdaacebacbeeabaeceddeebbcdbddcbadcebedccdbabaaecbeedeabeadbcbbacaedaebcccadabaadaddbbaebcdaebddbeceecddaaeeccceccebaeddaaecaceaaeaedebddaceceeeacdddeadccbecdbbddacaaeacdeabdbdebebbdddedaacdceecdeaeccaadabbcdaaaeaaeaecedebdbededceedadcdcaceeeeaacececceeacdaaabebebdaaeccacbbcecdddbccacaddcbdcebddbdeebdbacdcdcdcaacbcbcbbcceaecabaddaebeebbbaccccbeabcaceadabaeaeacebacbadebbcdedecedabadaedaeebcbbbacbecbdacadbdeeedadcbcdadcaabdabccaaaccadcbabeabaacddadeebbcaaeebbbeadaaedadcabeaaeddbbcbabddebacaadceddbadbeecabddcebbeebdceeaddaddababbedeebbeacdecbdbcbbeeaecabcccbcaabdaadebaecdbeeaedcdadeedbaaccbacdcaebeedbdeaebbabdaadbecdcdebecabdbbeabcbbdebedbbdbccbbaabcaeecaebadebcadbaeecbecbcbcedbabbeeaeacbacbabbcdbeedebcbbadbcddaeabeccdaedbbbcbcceeaaceabccaedeedaaedabeaadbbcecaaaccdeedcbbebdcaccceaabaabdabbbbdddabdabadcebadcededbecabdbbdacadaccdaebeedbcaeebaeddbcccecabdbeeadeeadeaaeacddedaaacbdabaabacadaceaeecbbceedbbdedeecbdbadebcecdcecdaadaadbccbccaacddacbaabdeadcaacaadbddaaaeebcbdededaccbeacbcaaaccdeebcebcceebabecabddebcbaaaaeecadbadacedeadbedccdbacdeccdcbaadbabeadbcebadcdadadabbcbbaadbaabacdcbdedebebabbdeaebabbaccaaabbeaaacdddacbedddadecddbebdddbddadbaddbbbbcaacdaaabbdebadcdecdeabdadedcdddcaeeeeebddcbeaebdabcdceabaeccaaaabdcaabaebdaeacecabccabdbeccabcbacaebaeaedcecdbaadcbddcaeaaeeedabacaeccadcacdeebcdbdedceacbbcbbbbeaaacdddceaccbaeacecdbbdadbaacdccbecdecdebebeaaecccebaaaaaceeabeaadcabeedaeecbaaaabddccbbcbbddcbdeadceddedabebaccccbdcdddbbdeaacbddccbceacdbecdacbeaceeabacdedacdbadeeabaebeeccdceaababcacebdcdadbdacbabeccbcdcceddbcbbacdacccaeaaedabdbacbbcbadaaabedadbecabcaaaccedcbadecdcaaeaecbeddcdccaabdaabcaeecebecbeebbabbabebcadbbedacadedeeeabaeaabcceeebadddeeadcccabdaaddcbdeeededeaeacebaadaadacdaebcabdccbaeabeaacbbebabceeeacbecadcecaddcdebcccbcdbedaaadcacadcabbacaecdeaeeddbabbbbabbcdebbeeebebdcbddaceeeacaedcacdbcecbcdceddeaaabbcdebaaedeeadacbcacbadddabbbbaddaebbbebbedcdbebebbcedeeeecdecaabdcbcdabcadebedcccaccabcdbbdccbdddeccbcbacebeaadcddadedbcdbabbcaacdbbcbbddeaddebadbaeccaeebcadaaebdbddbadacbeebecbbcaddaeaebebcadeeeeacaccaaedbaacdbabeaabbdabcbeddaaedbabecccbaaeaeaacabaacbeaecccadbabdeacdadcddedcdadedadceeacadaccccceaabddececadcebddedacdcdeeebbdabdbedeadbeacbdccbbebbdbcdeaaecaddaecaedcaceedcbacdccdbeebbaecbebaebbedbcbaceccbebeadbbccadaadadadadcbdeebcecacaccdaecdcacbeddecaaadacecdddbadaeebacbbceadbdcccebcbbbbccbbebbbcdaecdecdeeadcabaaaadebedeadcdaccdabdcbbddaecccbdaccccbbbecdcdbccbdeebdbdeaebacaacaddeeabbbdbbebecbbcbdabccbadecdaedbadcbddbeedaaccbbbcbebdecbaeaebceeabbaebcdadbebbeedcdaccbbacdbaccbeeacbebdbcacacbbccbddbebaabbcaaececbcdcaeeecaedaddcbabaaaeacbceebbbcdaecddceddbbbbcdabbdeeabaedaebdacddeedaeeaaadebabdccbbdedbdcbdeddceecbeaccebceeaeebbaeeaedccbaabbdedccaeededddedbabcdccecdadbaaecabebebddaaacaccabeeeeecadecedabacdcabddbccebeedbabbcddadbbebcaccbeeddabaecbeebdcdececddadcdcdccdeddaecccdaddccbedccbdaddaecebdbeeddeececcbbebaabcebadedddacbbadaddcaeeddcbbbdedacacdaaadaedeebeeaadebeaaaebdbabccdcecadbeacedecadbbebccaedadaedcacaaaedadaabcebdacaaaacaeaeacdcccdedebadeaaeedceacdccdccacbdebaddbcebddeedbecdaebadbcadcadabbcebabcabdebaaebababcbbbbeabaccbacbcabcaccebbadaaacccabdbbccbabadcdcccdcebcebbeadcbebeaddcedbecaeadbcdecbadcabadbceedabebaaabcaceeabeaeacacecaebcbddddcdacdbadeedebeaedecddabadbeddbedbccecedcceccddcedcaedecadeaacadacbbaabddbabeebeccdebdaddbedcbeccabcaecebdbcecdaababddeeeddbaccaeacdccdebbcbeadecbbcebedcacdbadacddcabecccebddccbcdebbbbdcecceaddcebcececdbcececeacddbacabedcebcdbdeabbbcddcaadbcecbadbceddcbaaacdeeecabacbeabaaebcdadedaceeeaccabdadcaabbbaebccabeacbedaabeaddcdabeaecacbdeddebedbbbebededebdeaceeecedcacadadeecebaadbdabbaaeecebbaabeebaeedecddddaabbbcdcabdabbbdeaadeaaedeebaeecbeaebaadddeaeddcdceccabcdbbacbebbdedbdeccaccbeeedebedcccadeccadcdbbeabddddaccaddabcabbcbaadabaaeaacabeddeecaedabdcaddaaadabeeabbbdbebbebecaeeaddeabaacdeedaddcedcbadcedcceddcebacccdceeeceecebebaeebdcabcaeaadacdccedebeeaaceecdbadbbdaaedbbbeacabaeccdabcebdeddecdcbbdecbecccdcceecbebdbbbedeaabcadbbbdacebecabcebdaeabedddaebddaeaebccdcdebcbeaeecebcaecdabdecaaaddcebeddddacacecddccbbaeccbedbdaabddebdaedaeaabadadceeeedceaeddbddaeddceeaeaacbbbaeabeaceabeacbcbcbaacdcaadaeebcddcbceadeedcbebbbbbabbaaedcaebcadccbcedbecadcacecbbaccebcaeeeaaddbdceaabaededceebbbadeacddddadcaebcbaabbadeeaebcdeadcdcbdbcedcddccbbacabcdeccdebbbabddaceabeaabadeeeaadeeedbbaabecbcaaccbdbadadabaaabecaebbbdbadcbbcceddebbeccbcbdecdaddbaabccbdbeaaeccecbeeeadeacecbcbbabdaeadbadeadbbebabaadaccbeaebbacbacccccbdececadddebaebacedaacebadecddebdbeddcadcacbcaaddcbdaccbcdcbaabeaddcddacceeededbdddccaecddecadcecbebdbcdddcbddccbddbceadacacdbcacebebbcbabccbecedeadbeaabdebddeebacabcadaaecabaebccbaddbdebbbdbbaeccbdadcedeedbadcaacebebbcdcdedebabddbdaecdcdabddbeabecdddcecbaeccddbebccedacbdbdbabedbedaabddbeaadacaacbcaeaeddbdbcbcaacbceeceecbecceccdaedeedacceccddceecadacbeacbddcbcadaaabbcababeadacbbcabbbcbbaababeabebbeeeecbaddabdeebbadaeedbbddbbdebbaeaabbcbbecaaedecebdabcaddcedaebdbcbedabddbbeccddeacbbccaaadecaeeececedbdcdbdbeedacbbdcbbecbaebacaeeecedcdbcabeacebbbededacbecbdbbcccacedbbdbbdacdcbacbcdccdeddaadcbdabbecbdcebdcadcdaabedadbcadebcccbaabebadcbdbaaaccdccdeedbdddcbdbebeedbbcabeacaaababddaccbaaecdaaececbcdaceeebdccebdcceedaddebdabcadccdaabbbcebecabdeadbeeaceccebecdccdaacdbecadcbebbbebddaeadbbdaaebbbcadeebedaddaeeecceedbdeaddeaedaaadcbaccddeaceebbcacbedaecdbdbbeceabddbcccdaaecbaedcdeeaccbeeebddedaaaeeeedecedaceeccccbdcaadedabacdbbdcaeceebeaccadeadeabadeaceabaadbaaacaeeceaddbeabeacccbebecadeacdceebcecdebbbbaddcbdebaadceebbbeebcdaabeababeddebeadbcbcccdbacdcecedcedbbaebcccdbcacbaacebcadbbaaebcabbcbdbcdbdbeaddacdeeecaddacbeececcbebecedcccaadaceaaacabcdcdaddaaadebbdceecebdcbddeaaddacedbdeeaaaeccbebdcdaeebbadebbddedededcebcacdedaeadceeabecdcbbeaaacaeccdbdebdcccdeccdeadbaabbadddecacaedacbdabeebcbbedddcdcaecccbedaddebccdaeadeebdedecdcdacabcbeaeaacdccbcdbbabddbcdedcbcdcddadcaabbecccceaccacdcedcededbaaabcbadeaedbdceccecaeabdccebacdeaaedcaeacbaedcaacbaebabcdedddcdbcbadceaccaedcdcaaeeeeaacecdbceecaddbdddebbbacadeeabccecccecccebaaebbaaeecdedaeaadeeeaecbecadeecadaaddbaaabeabbcbbbececdcbacbeeaadcaebccddcccdaabaddcdcdcbcdcddaeddeadecbdaacbdadebbddabebceccdadcecadeebdbcabbccaaaeebacaccceedececdbabecbaecbdbacbdbbbdeecddacdaebaceaecaccaaeaaecccaaedecceeaadbadeabbabdeaddebcbaadadcbbacdbadaacabaacdabadcbcbcdecccaaaebbaedbbbaebbddbcbbbbeebbccececcbaabbacbdbbddcddbcbeedecaadeebdaeedaabdcaddebdeebabaeabcaeeedbbaacdaebacdeebcccddcebecdacdaeccaebcaadbecbbceaebccdcceaebadcabbacaebdbaeaccbaededdadcccdcaeaeaeedeebcbbdbcdcdaedcecbcbdbaaadcbeceaddacdadaabaabedabeacdceecebcbeedccbeacccdcdaaceeaddbbebdcdbddccbebeeaeadedeaccceedcecaddbbdcecedebabeedcbedcbdaaaeeaadcabdaacbcddeebcceaadabcdbaaeddebedbabeccabbaeededecceedcdcbaddecdecdbedbccdecebeadaaebcacedebbaaeaeeabedcacecbbaccccebadaedebbeacdcceceaddeacaaadbaedcbeddeecdaaccaddccbebceedbbebccbecaebdbbbdeceedaaedaebedacaeedecaabdbccbbbbaabbdbcedebbcbaddaeacabecccdbabcccaaeaadcebaebcbbbaabdbebdcbceeacaccaacbdaaeedceeadaacebcbeeeeccaaaaeacdaeddbaeddaadaebcaeacdacceaeccdeadaddbecbdecadbdeaacadcbcccebecabdaadddcedeacbbddebcedcdddcacbdbbdabaedbacdcbebacdcebddaddeddacacbeddceedbaccaadcaaceeaeaedcebaceccaebcaecbadebadbbdcbdcaedaeeaecdeddbbdaaeeaabbebdaaeedbaceeeecacbadceedccdbbdbebbccdcbadcdcbacaaeddddebbadbbdebeaecacecccacbbdededabdbeddaecacabdddedadcedbbcddacabbaeceaedecebdbecdbbcdcccabacdbaacccdbdbeaaeaeacbdcbdeedaabaacddcdceecbcbeeceadebddecccdbdebcabcbeedeedcccdecbecadadccddcceadcccecbcccbcddeadceccebbccdaabdcaeebbdaaebcaebcccebeeceeeedbcdcebdddbcdadeceaadbdeedadeabbaadacbcbcecabaddbdaabedacedadccebddeadeccbbddbbdebcedcacebaaacabeabaadaaddadbcbceaeeebeadcdaacccdaadbacdcbddcdbeecceeeeccddacbaceebebbbbdaeccaabaaabccbacacbaaddcaabebebcccdccadabcdcbddccbddbdececadbddeeebeebbebdbbdadbecaaccdeeaebbbdcaaeaabcccbbdbadadcaccbeccddbadbbdaeebabeaeacbeecdbcdbadcaccadcedaeaceadaeedccabeadededcdeaaaeeaeccdeeaaabadadeabccadcbebeeabbddaeccadaaeeebbdcdcdceedcbdccabdabaedcbeebdaeaaeeeccadbdaedeacaebaeabadabdbaddbbbcbebbeacdbabacbdaadbbebcabdaecadabaaeecbbaeceedabebacadbdaeabecbeeaacabbcbbcbacabdacbbcedbcbdeeacbcbeaaddebacaabeddcceeebecbacabeabdddeaeaddcaccbbbceeceeedbcbceddedaaeeebecbdadeacbdcdbddcecdbecacababbcccebcbcaccbcbdebdeccaddededdbbbcecdabbacebcabaaceaecbaaeeeabbaecdcddcbbbbbaceeaacbdeeabdcdbacdadeedcdbccdddecdeabeabedbcbbaeaeceddebeaeaeedecbbceeccabbacddecbbcebaadaceeaabbeeecdabcdebbbddaebbaeaecbabcbeaaaeccdaaecbacdcbeaddadeebdacccacbabdcbaabacdedccaceacaaeecbbeaceeeccedebddcbdaeacbddebddbdabbdadacdaadbbccdcaddacbebdceaeabaaccbeaeceeabbdecbcdabebbedaeabeaedebbbdbdacbabcacbeebbcabdebaaeaadeccddadccdcbeeebcadedcdcdcebbaecdbcaeeeccdbbaecacceabadedbabbbecbcbaeeacaebccdbdaabcecedbabcdaaaeceebddddcabcabdaadaaecedbbbdcbeecaecceedeebcbeebbacddadedcdaedcccdbaebdccebcbdecdbaaadddabbdcbaabececebcbbebdacdeabbcaebabcecaeaccbdeccaecbdeceabebecceacedeccecbaabcdeceedbddedeebedcceeaaaeabbebaacbccdcbdcbeaaadadcaebeedbbacebebdcbbdeaaddbdccbeaecaacedbbaaebbbebceeaeaddbcdcacdbdcadddcbacaaeaceebeeedadeccdabdbaccdeddbcdeecedbedbdcbaaececeddbebdbeddedebaaeabdcdcdddaebbaaeedceabdedacdbddeceeacbcccedbacdbabceeabeadeddecaadbeabbaaeddcaedeeaeadeeedeaecdbeacdeeedcddadeabebccabcdbaedecebcededdabbbaaabaedbaeebcbbaaeedbeeabcdeeaedbdaaeebadaedddbaacaeedadddbcddeadbdacaaeadaabcbdceacedcebccbdeeecbcabacdbbacccdddebbdcdedbaaaebededbddbbdabaecdcbecabbdbebcdaddddbdcbbbecaaeccededcddbcdeabbdbdeddcbbeaddbacdbcabccbadabbcebbcaeeccaebaaebacecddbbebbaabcacddcdbeeeebcaaaeaebaeadebbedcddbebaaeeccddabaebacbabddbdcbcbbeeaeabecedacdeabeeecaccadebdbdcacbababaedeceacbcdceedaebbbccdecabaceeaacccecdbebceedadaeecedbaecebbcaaeaaebdedccdcaedbacdabddadcaddededceaeabedcaeebecedbccbdebbadcbceaeacebbcdbacaadcbceddcdaebdbbbedeaecedacceddcdcbceaeaeaebcaccecdccbcabaaccaaababdbedbecebceeebcddbdddcaccddccdcededceaecbaacbecbbcaeeecbebeaabeacaacbbbcbdaaaecdaaeadddccccdeeabbccbeebeddabbcbebabdbccaedbbcebbcadaeaccdeedebebdceaecbbbedbccbaedcbabdbebeacacdeadbcdcbdbbecaeceaecebebcdaeaeaadedbeddbcebaeeeaecebdbddadbbaeeebacedbedbddcbabbbebadacadbaceacaaadacaddebeebeeeadcccababaebcdecddbbdaaeaabeceeadeccaebdcbcdbcacccbedcbdbcbdecaeddeaaacdbebbbabdaaadbcbdacdbcaadaeadecdddddbecabadcbbeecabbacaabacacebbbbdcabdabbddbddcbdaecaddeeabcdddeccdaddeabeaebbcdceeabbadebceaaccebaabbcacbaabaddaabdababbeebbadcbbcbbaaebcbbcbbaaecdadacecaccbdcaaedcbdaecdeacbcedebdcddcbacbcdbecbbbcdddcceebcabaedaccbcabaaaebebddabacdacababcdcdcdcadacecddbddceedcbbdddcaaeeacaebeccedddbcabbdadceebbdacadebdbbcabcabbadcecababdeaedbceaeaececccaaabbedeeeeaeadbbecbceaeeacdacececdbbdacaeaecaebabcbccccabeacaecccdcebcacabebaeededccbbceaabbedeabeccacbedacbdadbdadebabeceecebceecbbbcaacbdcceeaeebeadddbdabeaacddceebcebaecdecdeaedcbbeeddececaecbbdabdcdbccccdadbebaddecddbdcbbbecdcedaddbdccdbacdabbcdebecdadebaeebcbabecbccdddbcbdecdbcadaeccbdeddabacdceeeebdbdaccddeecceddeebabcadacebeabdceeebaebbdeeababaecdaadccdadcbdacbcbaeebaeaccdaddeaddbbdceceeadacabdaceaeeadbabcaeddeaadbdbeedcdbdbabceaaabcbdbbadaedebeabdeeaeddcccecbddeebeadccdeccddeddcbecbdbcaeccdebbcadbdbeabdaedbeedceaddeecbeabbadeccdddccaedbcabaebcacededccdcbbdeeceddebcdbdbeadcbdaeeaeeaacbbbeceebcababccaccdbaddbcecedaeaadbcebcababcbebaddebcedaddcaedadbdaeabedcbbbebdbaeacbbcddeeeaeccaacdbaeadbbacbeddadeeeecdeaccdcdcccebadddedaaccabebdeaeeacabadeacdaccdceacacdecbbdddcdaedddbbeeacccaecbddedbabeebedabcabadcacdeabbdcbcadbeadcecbcabebddaeabdeacdebdebabbdedabdaacdcbbabdacbcddddcacdcecaaedccedaaecebdedeebddaaebeededbadeadcecbcedccadaabcdcacbbaadabbdbeecbdbbbbaebeeaadeccacbaacaededebcbcdbdebbeecccbdacaccabcdbcdebdcccedddebecbadbbcdcccccbecccceadcbedddeadedbdcedeebcbdaeabacdadcebedabbedacdbaddacecaaaadecaadcebcdcbaeebbaaacdebecacabbbececceeabcccbccddbbecddebeeeeddcbeeaaabceeacaebccabbcacdddbebcbebbdbcdcecbeabbdbbcdaccdeaaddacdceeaebdcdedeadaaccecebebaaeacbcbeebbdbabdebcaccbdcaedbcbcdddeddbccadbbeccdbeddddedaebaeddacdeecbbbeadbccdbdaedecbbeacbedcabdebbdaedadddececdccbddcdbcdeaaaadcbbddbeebcbabadecdbbccdeaeebbddceeaabecbacbcbaadccabecedccedaebddddecdbcbcbacdbeaeeddcbaececcddebcccaaaccbeeccdbdceacadaaacaecdeadebcacbecdedbdadbacdedbaeedeaacedbabeaabbbaeadabdadaabbabeedccbaceadeaecececebacbecedecacbddaecaabaecaedaaadbdccdccdadbcdbcdbdebdeeabddcdbeecddacadeedabbbaebcabaedeeccbeeccbdecaedcebbbbeadaeedbaaedcdecdecbdbbecaeebeeebccdecdcacaebabdecdadcebabbacbabcedbcbcdeaadeebabaddddaaebcdacdeabecbeccccebbdeabbbedbdbddcdaadbebdacedcbbbbcceabcdcebaeabbbadadbacaecdbddaadaabaecaabbebdabcecaaeacacdedbbdccdeddccccbcbadceddadcbebcababdecabaedaaeacdccacaacaaccddbecbcbadbcaddbddcaddacdbaceaaebcddbcbebecebbdbdabeadaebcdabbacbebaaaacbedbbcecadbdaeaabdaccccdeabaaceaabeabebeabcdeaaaebdeebeedebcbadcaaceaabcedeeeacbccdcdbeaecdbeebabbbbcbdaaaedbceadacbedeaeebaeadcbeacebcddadaabbcbbecbcdebadbbccecaaedbcccbbdbbbcebbcaabdcabddcebdbadcadeedaaeebaacdeebeceeeecdeabbeedcdaaedddbeebedacaabdcdacacebdeeeebaaaccdcceecbbaceddcaebddbbcdaccaadabecbceacbacaaadcaeccacacaaedddcdaaaaadbabebaedabdadbccdcddebbabadddbdbcbcebdeeddeeedadcaccdadedaeaccadeededebcbecdbdddedcbdcbdddcadbbdcdadecaaeabeeacebcdcaaededdedaeeeaaaebdcadcaaabebadaecdebbddcbcaadecbaaeaeddebceddacdcbebcdcccebebaacbbaeaeceacdcbdceccecceecccccdddbcbeaeaceeaaddbdeacbdabdeadabaabbdbdcddaedeaddebaadcbeeacdaadcdecdddeeaeecabbcacaeecccbdeedccdddaeaadedbbdecacbdeaabbcdcebedbcdeddadabdcbeaaeccdbbbdecbbadcabbeedceddbabcadbcedbcbeaecbdcaceeeddbabaccbeaaaddaacccaebbadbccbaddcddbccedccdcaccecdbcbcdabedabeedbccddcddceacbdaaebedacdaceededdddbdbcdceadacadeeccdebcabecddeccdcccbacebabecedbeaeeaeceecdedeedbbddeeceddedebccaaecdcaecddebecdbcddadebebacbaedaaeaabbbbdbcdecbddeccbbcbeebcebdaeeddcbcacdeedeedddddcccbaddcbaebcebedbbdcebdbbebabddcdaebcbebbcccdcbeacbbceadeeebadecbadcddbdccdaccaccddacebadbeecbdcecbccdeecbdddaceaeddaeeedaedebddbbaeabaebbbdddbbeecbeacceddbddacdedcaabedaccedebcdadeeadedccdcdbacecdcbacbadbcabadaebbbbaaccecedbcdbbcceebbdbebbdbbbdebabcebbcdbbcbcccbedceebadaccabcdbdadaabbadeceeaddcddabbaeecbaabdcebeccebddeacadecbdacabeebdbecdbcbabdcdaeaaedcbebaeecbabeabdddcdedbcbdabbecaaaabcaaadeadadbbdecdccdbcabeddbadcadcddbebdedbeeacaddacbecadbeeecdddabcdeababaccceebdbacdbbdedeeedeaebadbbbdceecadbeecdeebedaecebcdabccbaddcecdaaadbcddedeeedbaccbdbceeacadabdcbdebdadebebaadcaccddaadbcaecdbdaaadaeaaeeaabdcddbeeeacebcaececdcdaecbebcaedeedbabdabeedbcdbdcbbbccbcdbdecbdbbedbabeaeceaeceaaccddbceaebcabaedebadacdcbdbcdeeeaecddecadbeeacbdcddbaaddccbecdcedececabecbaecddbaebecddbbbaabadaebecdeeaeacbbbecbcdedcceeeeddbeaccddbbeecaedaeeeabdccbaecdbebecabbcedbdaadcccbdaaccabacbeadcbbaadcabeedbceeeddbeabeccdcaadaddcddcadccbebcdecdaddaaaaaaddbbccbccdbedceebddecaebdbbeeeedccbdbbebeedaccbdacddedeaaecacbcdeababcbececaebbebaabcaaccadaecadddaeeeabbeceaddadbebaceeccaebbacbebdbdcbbcccbbecbedaebbbccddcceeecccabaccbeeacdadcecbdccceddbaceeeddbeeedecddcdbbbdbbbaaedcdbbddabaebbaccadecedcbeddcdcceedcddcebabddbcbabdedcdeddaeaecccaddebcccbecaeabeddddbccadeaaccdbcbdabcdecedabeebbdcabbacbaaecaceebaddabedbbccdcbdaeacdddabdbacebbebcdccadecbdaebbbcebdcbcbbeaedcebbccaacaeeddacabbceedcaabcddbddeebebcebbbbebbcbacbcebedbebabbedbbeabdbcedddcadccecadcdcdaeddeeedbcbebaabcdbddaabcaacdecdbaecdaeacddbdedeeebdaacddeebeccaeabeedaaeadeceebddccccdbbedebaecbbbbeaabacbbdeaddcbdacbbdeeaeedccaccddedddbebecebedebdccbaadaedededcabbaebbbdeeaadebededecedaeddadeadcedbbbceaedadeabbddeaeaceceadeeeebacdabdaaadebeadeaaaeededaeedbbcaecaacaacacdccddeacedcccacaaddccaaebbaabddeadadebcecbaaecedacaebdcdbcdbedbbdabdbcbdbdccddabeeecbacaccbebceaebaeeaacecaebcedcedbadadaedcadcdaebcbeccccedbbcddcbbadaaedcdeeeacacbdcddeaeacadadadddbdbcaeaaecdceeeadabedbaaceedcbcaedacdbdacdbeccaebbcebdceebcbcdabcadecdbeceddabecdbcdbaebcbcdeaeceddabaabccbccdbaeaadbaeddbdccdadaaeadeeababbccbdddeacbcbddcacadadbeecddddabbbcebbbdabcaedbdaeddedabababcbbeedebdaecbdbdebadeeebdbbebbdaaaaeddddcbeabccbabadddbddcaebdddedabeccecaeecceccdeadcdcaeebbbabeaadeeabbddbecdadedbaabcaceabcceacdaeabeacceaabcacbaabbdbbacbdcacdccedbbabeacdabbeeadebeceacacbabcadbbcecadbbaeecdceceddcccadeebbbeeceacdbbaceeabdcbbdeeecacaadcabcdcddaaeceacccdedbacccdacabaebabadbacabdedcceccdeaabaebbeeeaabcdbadeecacdbbbeddcaacaebcbedddecdbcacaebcedbecaacbbcceeceebbdcccdeaeadedceebaeceedbddeeaeebaaeaccaaaaedbedbbccdaacbddaccdccbbdacbaaeabadceeabecebbbdedddcacdeaadcebdcbabaeaaadadeeeaedbdcbbbdbaabebcbbeaabcddeaedaebabcdbcaeadccededadeebbabadbbddeebcacbaeebdeedcecbedadebacbedaddabaadcebdddcbcabcaeebbccedbaebbeedbbceddcaebbcdbedddceacdeadecbbaadbdccaaccdceccbccddbbcdbebecbaaaabdacbbccacadccdaebdbceeaceeeebcceabeddcbbecbcedcebabeddabeddedebcddcdabcebbabdacedddbeaadccbedcdcbccadaabebdadbebbbbaacddedaeeadcedddddeaeeebccaecdeabddbcccddecbeebadaacabebedbbbcaabebbbeaadddecdaceeadddebccddcacdbacdacdcdcacaccbadedacececcdbbcbaccaeeaeebdbdaedccdeddaeccabceccabbdcdedcacaacdedbdccebacecdbdbabecbaebaecbebacadcdeddcbbbecabaeadecdeecaceebcdbeecdddbaeeecdecadbdadecdacceedadbeaddabadbbaccadbbbadbaaaddcedcccceebdeccdebeabbdeacebeacbaacedbecededbbebbaaebaedacedbbbcbdbdabdebbacdedbceccccaebaeedebbbdcaeeeeadcbddccedbccbccbbdaabecdbaabddadddbeeccceeedacbdabdeecaeeedeedebdbdadaaadbdaacceedcdbaaabddddcbcccdcbacaeedddeaebdedabbbcebcdeeacdaeeddbccadadbdebbceebecccbcabddbacdceaedbcebdabecdacacbdaeeadbbeeabbddecabddcabecadcbbabdebdcadaeaecaeceabbadeadbbdbebdcdaeeeceaedebdedabceadabaeceedbdeaeeacedaeebbaeedeebdbbbdcaeeedeccbadbebbecedebdbbddddebdedddaabdbbadcedebbbdbdbeabdebcaeeadeddcbbecabaeaecbedaebedcceeedddecccecacaecbcdbaedbedebddddcebeeecbaaeabcabbceceeabeaabcbdbcacdaadedecbccaeabaeceeddecdbbabbcbeaaceddbeedeadbaebacbaceeababaabbbcaabaabeaedebacabeceddcaabdcabdececebaadbbbdccacaabdcaaebcbabaebbcededddcaddeeeabaceecccbeceabadacaceebddadceedbcbaddcbdbccabbeabaebeabcaeeacaaadbecdedbceaaacdbadbcecaecabeeaccecbedeabdeaadcbeedcebacebddbecbeeddccddceadedeadaeadddbcccccbbadbadeeeaacbaeecadaabbacebbcaecebcbcdcbeeacadabaeecdadccdeabcecdcaacbdcedcbaeadeeeabbebebcaccdcbadbdecbebbeebaedcbbbadbcabedaaeddbcbabedbbaaecddddeaedbeabdadddebebaabadbdccdcaadecddeebcdecccecbeabdcdcdaebcdeabebaabbbbbcdccaaadbddebaebcecdebadbbbebccbaebdcddacebcebdedabceecaadceceacaccdadebaddecaeaeeecebacedbacedaabbacddbcbbbbdbaeaaccbadcdbedcbebdceededdeebbeabcabbcebbeadbceacbadeddcbbbbebccbbcbbecbcebdabcaaeccaccbadcbaabcceebebadbabcbadaaeedbaaecbeabacecdeedadeeeecaabbcdbebdabbdeceaceedacceeeabcdeecdecedcbcdbaebccccadeecacdaaeabaeeadedddceeeedcbadccbcdeadeccdbcedbabaccdaebbabbecbcbcaccdcebbabeacbbcdaeaeabedaeaeacbbddeccbdbdabdabeeceaeedbeecaeabdebcbacccecbccdcadddebcacaedaacadebbaebdeacceeadddadceaedaecdabacbadbddcbbceaecdcacacbbeddaebaccecaacacebeaabcdcbbdaaedacedacbacbcebecdeaeccdbaddeecbdbdcbbabceaddecaecadcbddcdacaeaeadecaacdcebdcedbdaccadabdcacdcebbeceddcdeadeaaabbcdcbadadacccdbcbbbbacddcedeabaaeabdecbedacadcddceadbdcbdaedddbcedddaccadebaacebccedbedbcabdacadcebeedbbaadbdbbcacdacaabceaeeecccbbbbcecebcbaeadabcaecddcddccaeedcdcbebbeccbeeebabcaecacbdadacaceeeebbaacbddedddccccaabdccdcadcccceeadbebddadbebeaaeeebeddecaaeecbbdcdadbbbacadbaccaaccdcdbdaeadaacccddcdcbbbdcccbadebeedccddebdbeeeaedcaeeadadbeacacddeabecebcddbceadecadebeebdaadbeaddbacdcebcecedaecbaedbcaceadbddcbddcdbacccecdddacdadcccbecdebdaeaeebbaaedbdebbcbbaddcdeabbbbeacedceeceeabacaacadeadbebcdeacabacecaadacaecdabdcaebcbeedaabaedacdaacddcdacebdcaaebbabcbdbadebdaaccdaaabdebbadcdebdbdbbdeccceaabcbeadacdecddaecceeeaeacdaacebbcabecebededdacaabddbabeaaebaabbacbedeecbaaadaacdcdbbbadeabbebbabddbdeedbaaebebbdaebeddcaadebaaadedcadbdeadeaaacededabacbbdddabbabcaccbabcedbeeadecaaadadacdadbcdbcdaeeaedadeedadcaecedecbdedbaabcadedbeebdabedacaacaecbacdbdcaeccbbbebbacdbbddaecdeebeddacdccbbcbdbcddececdbaaadbbceeaceebccbacabaecbeaedbeceaccabbccacdbbbbeadddbaaabedabecebebacbbaedbabeadabdcccbdeccacedbbebaadedabeddabbacbdedeedcedbddadecbbdeecceadbcdaeebababdeebceccddccecabdeacdccecdaaaeeaaaeeceadaceacdabbacdeccadbebaabbabeaedadaaeeccccdabcadbbccbcbabadcaacebdcebbeeedbbcdecbddbaedcaceeaecebedaeebaabcbcebaccbccbabeecbaecedadebdedabbabadbebaeceaaceedeecabbadebadaedaddabebacbdccedddeeacceccdbbeaddcbeeedcebcbbebabbdebabdecbbcbabdcbaeccdaaeccdcadbeecaccbcabeccabadeeaddacdeeccbacccbbadebbbcccddcacdeceadedeacbdaddcbacaacaadeeeeadccaccbbecdbadedcddeeecceadceaaeeaddcaccedbbecebdcabedaebdedeceabbeeeaedaadecdbdbcdabeaebeeeceddadedededbdedcaeeacaebcadccbaedcceadbadeecbbcaaecccdaeedbaeadabebdebeeacadeeedcacbceecadbbbdeceddedcadcabddacceeaabecedcaeaecdeaeecdbaceccddbaedbbdedaeecdcdedaeceeacdacabbcadeddcdcbbdceedebaadeccecbcbbdbcbcecdccbbadacdcadeebecdcceaaebdcaeeabceebaccdedabddebdcceedcbcdcacebbcdedeebaccbcebcbaebdaedcebbbcaecbdacecbdddeeccbdbbceaadbabcaeabdaaadaedeacbedcdbbebabacdddeecbdbdaedbbdacbdaadacdedbddaddbddaddadbaddbeeddcebaedabaecbacabebaeaaaaacdabcabbbbecacadeacedbdaeeecbbdbbbdadddbeeaeabcbabceedaebcbedabbaedcdbdddeebecbecbecaeeadeaddcddcdbcdaddbddeedbadebeccdbbabbbddccddceecaddebbcccddedeaeebbceecbbeceebbeecedeacedbeeebccbbebddeacaaeedbedeaabdccdcadcacaeeeedeadecaccdeddbcddaaacbddaaeccbcdddecbceabbceceeddaecbcceeabdbeebceeddadddebbabeecebdbebbbbabcdacbbbdebaaedcabebccdcdbcacdcdbcceccbdabeddbdedeabdbdacebeecaeababeebaacdacbaeadedaebbccacebeeaececaaceaddaabeccacdddbdbbcbdadecdbccaccddecadbedddbaecbeaccbdaecbacbcdceaecaecdbccaddaeabbdddbcccbeecbcaacdbeadbbeebebdacbbbddecaedeaeaeeeabeddaacdeccccccedceacdddccaadacdbebcbbcdacccbadedabaccbedbaebceadaccbbdeabddcdceebdbababeddababdeebbebaadddbeebacdebbcbeceeebccceddebaadcaadbcdbaabddcabedadabbbddcabeccabbbdbabecebdabaecdaddcbaaceeceeeebdbdaeeaaecbbadbacedccebceeecdebbddddbdabeedebcaedcdabbcbbabddccaeeeceddbddcccddebdaaacedadebdcaebbcabeadaccdcecceceeeadaadeecadeddacbbaaadcabecbcaccbeabbeedbcebcdebdeacbedebabeddeeacaaccdeecbddcddcabcebcdbbcdaceeacceebacabceabecccabaecbbbcbdbbdadeeccaeaeadbdaebdbcadacaedbeceddeedeceeedadaecbdedcbaebceaabbcebdaecdadcdcbebbeaacccbeabdeebaaccdbbcacddcecedbeccadddedebedceaabadddcdaabbcacbeedbdabcddbcbbebccdddebcccaaaeebccdbdebcebeacccdadaadcdccaddbeddcdabbeaedeeaacaaadeddbccccdbaaedebcdedebcedededadaeebbeeaaeccbcecbadbceeaddbebbbbaeebdcabdecdaaeaababeabdcdcbaaeecbeecacbebdbdbebbbacabcedeedbeeedbdecaecabccdcaaecccbcdbbdcbbccedeccbadababedebaeaeabeabecbcecabaddaaeacdccaaeeeadbebcacddebadacdbbcbadaceaebaebcaddaecccdaabbcaecebddebdeddadaeccbcbacdbaadaabaedbbaadbabbbeccbaababbadadaabaddaecddbeddbedaecbbccadbeacdabdaeececdddabcdbcdcbbbddceeedbadbbeecadecadedcdccedececbaeeadbceebcaebbaedeadebaeeecdbbacebcadeaceabebecadbdeeeccadcddecdbaeeadeddceaeddbacebeaeebebcccdcddddabccdaaecaacdaaedecdebdaeeadcbebecbbddeeaddddddaaadedcbbeaeadbbedcdcedbdeeeaabcceaccececbdebeecdeabdcbdcddcaadceddbbbeccdabbabdaceaecbcdaabeebdaccabaeadddeaadecdedbbdceababaaebdceeaadddedadcbdcdddcbeaaaaddbabdcdbdabaabebeccacbcdcceeeeecaedbcbdeeaceddcaaabcddddeceecedcebeedcbaabbacebdeaedcbedebebdbeccbccdaadcdddcacdaaecaecbabbbcdaacdbaceecbacdbdbbcadeedbadedcbabaecdeabbeecebeabaedbebdeeedaabbddecaaaedbabaaddabbcaeeaacddcaeccaaadbbcaadbadccababbcbbddabcebbaaccadeaebbbebbaabbbebdbbedecaeacdbabcdbdeaaaedbcacecddaddeedbeadeccbbaceedbccbcaeebecdacbeeccebdddacbebcacadcbebadbecbeecacbedaccedcadbedcabcdddacbaedaeeccccbbaaaedddaadcceadaebbdcaeaeecaaadbcceebddebdbecbaedbdcdceeacbdbeeeddbbcbccdcbcdebeaddecabdccecbdccaeddaebaceaddeaeddbedbeeaeebacdcbaddcaadcdbecaaaebdeceebbaebdbedccbaadeccedeeebeccbacadabaedbccddabedcaccbdbeecabebecacaddeaaebecebcbebaebcaaabdadddebcdcdceeacddacacccdeaecabadeccdcecaecbcadecddbdcadeacaebbcadadccaeddaebcdecaeadbecdeddbdeabcbedbbbddabdebaecdabcebcdbdbeeeacceceeeeeddededbebbbddadbcadcbaccbacddecacdacddbdcdbbdabcdebcbccdcdcebbcdbbcaeedbdbceceaadcbdbdecaaecbaeeadedeaaccbadcecbacbabbcddedcaeccaceddebbbedcaecadbdbbaacbcadcadbceaedebbedcdbeadcdccaddabdddebbcabadbdbbdedecceebebdbbbdbdecabadcbbbbcbaecdaebdbeeedebecdedbeddadbbcbadeebeabbdadcebaddadecebbaeecebbdaaddbdccebecbbdddcadbdccdecdacdcbaeaecedebbbdabbadaccdbbecbdebbadbbddadbadcaeacbcbdeabdeaaebdccabadbdbeedbadaecdbcdceabcdcaeacabadccccccbdebcbabdbbedccdecaabdbcbdddcbbcbbabeddbaccbeecceacdeccbbbcaaecdbbdbcbeebebbdbdddadaadddbececdebbbcdecdabcddcdaedecabccacdccdccacbdbadbaaeddcecdacdcbbaacbcaceedaedecdadeacaaacbbbadcdcbacacbbdbadbeedbeecdecbdedabadebceccddbbbdebcacadbdcadcbabaeeedcdbddbabaebbcaaaacedebacdcbecbdbcccacdebabacacdaadaabcdbdaeaeccdebedbdaedcccbadceeedcaddddadaccdaaeddbeccbdccdcddacaacecaacdbbdbdcaecceaeedcdebebcbcbeddabcdaaceebaebaaaacadceddddecadbcbcbecdbccebacedadcccbdbbbbabdccbbabcaaeadeaeadeeddacdddcdabeddeeeccceddabdcebbeeeeeeebbebabdaebbcbcbaabaabceaeaeadcabdadbcdbaebdddbedbaaabeebdaeaddcadaadeaebbedacaeacbdbdabcadebbabcabeecbbcebccadbdcebeedaeaccbcdddaddbebaeeccebbcadacdcbbccdbdeaebcddecabacedeaeccbecadebbdeaabbbddaecbaeccccbdbaeeaedadebdcaabbabbddddadbeddadbcebddcddeaeacccdccdaceddbcacbbeaadaaccdedeecbcbbdabebbbbcccedebeedbbeedddaedcdaeeddeabeaadbbcedaeeeccdbaedceccbdcdeceaaccaadcabddbaaeddaaacecbbcdaabbbcaaeadcbcaecaaebabdbabbbcddcdccecbcecababadbbaceccaeeaaecbaacababdbaacddcaaddbdaceaadccbbeabddbcaceebcdaddebaedeebedadacedecdecddcedbdbdbcbcacdcdceecebceeeacbecceedecadeeeccdcdadbedbeabeaacebaedcdcaacbbedabccbeaecadcecddaadeabcdceccdabababaaadcedecdacebcdcbccbbbedecdcdbeeeaedebeccceacedbdbccdbaadaecbaadbccaadedcacacbacdaddaedbaaddbaccebdbdbaabeaeecdbcddbdbdbedecaeabaebcdacebdbdbdbdedddeecebeecaeaecccaaccdbbebdcaddcceeeccdacdacdadcaccdedeacdbcadbcececdabdeaebddceabaeeddecacadedbaccbededdedddbccbddedeecacbbacddbacccbbecdecbeebacbabdccacccdeacbacaddaacdaadcbccebabdecaceabcbeaecdabaedaaeeecbadaedabaeddcabeaebacbdabedbceccdbaecaccdabecbbeaeeccbedaecedaebecaacbceedaccaaaeaaebbcbbdaecebdbdecdeeaadebbbedabadbedddadbdabbeabeaaccbdceeacdebaeebadadacdeacebdabddeeebeccdbdbabdecbaecedcabbcebbabaebccaabdcaedceccceedccecdbbedaabceecedadaacdaccdcaceabbbcbddeebdbebdaaccaedceadaddedebcdccaeeedccabadaeebbacdbbcbedaebdbaccdcccacdeeeeabededcdcbbdaedddcaedcbeadddbaecacdacaadccdeacecdcbaaebaaebcccecaeabdceabacdeacbbcebdeeceabaaadebdbdbacaebdcebcbadacebedbdbcecaebdeadeaaadcbcaacbbdddaedcaaaadaabdacbbbcdccdddecabbdecabaeaddeaaadabcababddcbaecddddccbacaaddcedcacdedcaebdcbbeecbdbeccbcaebbedaaceebdbeddeadccbcaeeadcbbdbcdecdaadaabddecceccbbeebcaebacebddcbaaddaacebabbdadaecbddbdddaaedeeebbccaeaeadcdcecdcaddbcdddbcedcaceddcdccecbaabceedbacddaabbaadadaaacadcbcddadacdeacaeddcaabecabbdbbdbabaacadabcbccbdadbdcccbeedaadcaeeeeebcbcdccedceeaebecebeaaeaadbebcaadceedcecaececdaebcabaadeddeaceecdddbdabbacadababbbabdcbcaeadcacccdcbecbddcdacdcdeecccebaedabbaedceabbcaacdeccadecdaeccadcbdeaddaecaddaebbccbecdbbeeecaabbeaeaaabeeaedeababebdaaddedeecddbdbdeacccecebaccaebdacecbbaebbededacbbcababccbdcbceadcdcacbebdecacbdabcaedebcbeeebcbedddceecdaadbdbdcdedacaccebbdcddadbabbaabadcabcdbdeecbdcbadadbabacbaaeccabdcdececacbdeecedbcccaaecccdbeebaaaacceacccdcdbbdeecbeeeabeecaedbbaeccbbeeacdaeeceecbdeaebebbeeebadeadeebcbaabaceddaccdbababaccedbcbdbbdcdbcbecdabdabcecbbbaadceceeacdcdddebbdbdcdcabebccbbebbbeedccddccdbccdbaeddcadccbddcaecabdadeceacddabbeebcebecbecdcccdeddbbaaeebbcbcacaaeabcaabeadeccccbccdacecdbbccceaceacaaadadabaabadacaceaddccaddeddcdbaaeadddeddeebeeceaccacceebdccdadebdcacaddbccecccdebbeecaabeebbadaaedbbdbeebccebceaddbedecaedaebccacadbbedcbdbbcddedecbdbbbbbcedcdacaaecaeaaeeddcdedcbbcbeaddeeeccaedbebddaabdaddaadccbabeededeaceabcaadcaabeebadabcdddecebcceeadbedeaacbeabcabedadbbcdcabbedadebbeabeeaedcdaeeeecaacdaeebbeabdaaacadcaadccddbaceedeaacedebccdbcababccabbbeeecadbcaceedcdacddebdbccbaaaeccecabcadddbcebecadacdaacebbaddcabadddbaaaeaeeddbbccaecdbaddeacbceedeebcecccdcdcdacaaacadadaedebbdaeeacbbadbdcceeeeceabcbbaebdecaebecbacaaadedabdebdbbcdacedccdceebedebabdddbccabcabeebaebbdcdebeebaaabaededddbcdaceecebdedcabcdccbeaeceaaadabbecbebaebceeaceecbdeddcabaaaacbbbccedbaaaeedabbccddceeccdcdacaccdccaadededeaaedbbdedecdbaebbbebbcebaacaceecdbeecaecaccacdeabcdeccadecddaccdabdeccdbeaabcceceddabddcbcbbcdecbcddcceceebbdadaeedadbeccccdabcceabbeccbcdeabbbccbaaabeccbbedaceecdbebbbdadebdbeebaebbcbdddbbcaccbaeddedaaaeeeabeeecbbdbaedbcaedbedcacaeccaceacbcccadbabececaceceeddddcceeceeabebccdecbdecbccccaceebbbbccdbcbddaaaabebcbbeaabaebacbddebdedbeeaeaedcaceecadebdccdceebeadbdeedadaeebacbaaaedbcdadbebcdeaebbcdeeebbadaacedcedcdcecccdabbacbeadddbbeaeabbcddebcadddebbbdeeaccbcdcabdcadaecebddedeeebcdcdeebdaceacedbddebdabcabdaccabeddcbbdccbcabaecabeeeacdacccbaaecabbdeceaabeaedcccaaeadaaddaeaaddeeeccabbdedbaaecbddcabddacaacdbddcaaddeedebaaccbccdbcaccdedcdcbadcbbcaecebccedaaaaeaaeeebadbceccdbbbaedbdccdabcdadacbacdddcceceecabbdcbccbcacbcebbedebececaacacdeaaabedcdedaecdedebcdecaeccdebbcadcebadbcdbbadeaadbdeaaabcdadbdeceeccddbcdeeeebcdacdecbaeccaeddcabbcdcbdbeabedcbbacaecaaaedbebbeddeddcacbcbcdacaadbbcaaeeebadcbecbddadbcacacddedcedaeeadeccbacddcadeeaedaaaeddaaeeabbcdacddaacddbedaabdcdaeaebdbaabdbaeaadddcbecbedbaaeceeedbcbbbebaabeabbecaeadeaccaddacecceadbeeebdaddcaebadccdbcccabecaaaacceadccdcdbbaecaaeecaebeeceabdceaaddbbaaaccaeebdccbbacbebdacecddeabdddebdabaddcebdaebadaccecdeabbbcbeecbedeebbaadedaaecdcedaecabeeebcdbdddccbbabadcbbcbeccecebdbccadbbabdbcabcedaebbcdabbaabcabaabecebcbdeabdbcedaddeaeeaaaccccdbcbcbbdaabcdadcaeebedecdceecbceaceccbaeadabcdeeddcbadccecdccbeccacbdaeaebbdabaeddeaeeeeaaacdcaccacedeeaaceeebabeaedcbaeaadbadcaacedcbddaabcacadccceeebcbeecdcaededdacebdbdedcbbdeabbdaaadaadebbbacedaededcbcbeebdbeadacbaccbdaebdaeedeebcdaecaeceedbdccdaeedbedabbdcbdaadabaaacedededacabeddcedadaedaddacdacaacddccbdaebdcaebeccbdacdcaabecabbdebedbaabedbbbbecdeeaebbeabbccddbdedaadcaabaacaaaeaceeaabbacaacaccddeeccbaaaaebddcdbdadbbecbdedeaeadebdbcaedbadcceabdbdcbebebbcadddcdeeedddcaecbcaaedadddccbcaaedaaedcaecdcedeebcbbcceddaaeeaecccebceeccccdbcaeeeacdbaedebbbceaedecaaeeecccaadaabebabbaddaeadceababcdaaaebcccecaaadcaadddeeedcbebaeecddbceaebddbdddcbbcdbbccbebbeeedabeaecebacbabcbecdbebddaebdeccbebcebcbbdecdecdbccddcdddecaccbdadbabaecbebabebdbbbebeacdecdbccdbbceaebdaebcbbdebccdcabececcdbabbddcdebdbaddabaeaecdeaacdcdecedcdaecedeeaecdcbbadadaadeaaaaebdcadaadceaaeddbcbebceeabbebbbeabeebadcbdcdebeccbabdeccbeaadbabcaeaaacedbcacbceadeaedcdaeaeddcbacdcaaeadbecacececcdcecbeabbdeeecdaacbedcbbabadeedeeaebeaadbdbcaebdaaebeebeeedadebacaddecaaaaabbadaeebeabeacdddbccccaedbbeedebbcedcaaaaaebdaaecdabcbcdebecaebccecdbdcceaedccbbdaaeaddebcceadbacdeaddbbddaebccbebbbedbcedbdddacbcecadebdaaabcadaddbddeceeecbbdaabeccebabecdecdacbcebddbcadadaececdbddedbddacadecbdacccabebaaccceadaebeadabcaabaedeeddbaacdbdaebdcebdebacdeebcbdabbabadaaeddcbcdbeabebbacdaabedbbbccdddbddeeedebaedbcdccebbdbadcbedeaebecabcbeccabeccabbccdeccadccbcbebebcaeabcbbedaecacecccdabacbadbccccbacceebebebbdbdbadaccbebdcddddeecdebbcbecdecabaacbdedbcbdbcbbeaabaeceaeecedcbbecebcadedaeeebaddbedcaaebeedaaecdedcbcbebebccdadcdceebbedcabbbdedbecbcbaaeecebbaaeaaebeceebdaebecbccceaadcabecabdaaaeeddbbccbcebbcaaeaecbeebbbbdabbaddaebdbeddaddbeeebdeebcdeabdbeababbcaebaadcceebceeacbbdabcabaaeecebaeaebdacaabcbadaabdccddadeecbbbbbabdcdacedaeedbedcdeecceedaaceacebbccadacbbabeaeaabeadbbeccddeadcecbcbaedecbbacceeecaaabaabaececbeabccecacddaebcebddcaeecceebadedebedecbeceeaadeebdebbdbcbbccbddeccedcbbbcbcccccccdcdbceebadeabedbacbccacbcaebcccdaeaedbeebcbeabdcbadadecdcddcceeebedabecbbbddcceeeccbdaccdaeeebceaeacaecddbdeedebdceadedcbadbedbedbecdedbcdbbbdaddaeebccaccccbaadaacbbaeabededcdaeadadbebdebeddebdbebdbbeebacbaeadddbcbaedbedebcbaacdaededeeceedeaedabcbbcedbdbdbedbddeabeacaecddaeceadbcaeaccabcdeadaaadddeeaedaebedccbbebbeebbecbadceeceabaadeabbeaabdcbddeeaececadaeadcadeccaeaadaededabcdbacceabecbddeacedeebececedadbeaccdeaaeaacecbbcbbaaacdbaeddbeaabbabaaceebbbbbcbeaccddbacbeddddddbbcccaaaddeccaebbbbddddedbbdebbdbceddbeccabaaaeacaeebaddbddadccaabaaaacdccaabdacabcdbededceeaebedcdeaecaebaebecdebadcccaebccbcaaaaadbecdaaaaeeebbccceeabacebaedcbcebbbbbbbcdddbeabccdcbcbeccbdbdaccecbbeaadddaddaacadbbebdbacddadbdbaeaeddceaceeaddcadaaaadcbabbcbbbaebcddabbbdbcaabaeececcbeacececeeabecbabdbbadbaedacbdcbacaecdcdbadbedbddadeccaeebabcbbbdccbcdceadbbccbeaebdeeabdccdbaacebabeaacbdabaaebccbeceaecaeceeaddaaebdbbddedcadecaeceeaecacbaaeaacbdcbbdcdecbadedccddcdccdeebbedeadaaaeddbcdecaddbedeeccdeadaccdcaeebcceebeabdcbbbdaadbceeabcbcebbcdecacbadcaebeccbedadcebbdadaddcbeccadbecdeabdebdaebaccdedbaadbbbdbdacecddeceedabbabbbdbacdaccedaabbbaddabccedcecbdebaeaeedaebdbcdebddaabeeaabeeaceddbbeebaeaccabbcdccacedceacececccecdcbebeadbdaceeccddaedbceebadeabeadeceacddbecebceeeededadaededabcccbdaebedceddbceaeaadcabdbccdebaddcbabadbaccdddedebcbbeccdaccbeccbccebeacbaccbdccddeaebebcbeadebebcbeabbedbcecaebcbaeecccbdcabbbecbbdbeacbbdeadaeebcccbedbadcaaaccbaadeeabccbaedccedcaceaeedeedcaaeedbbacdbeebbaacaaebdccdddecabdbbacebaeeaebcebdbaaabaeccbcaeaaabedaadbbdabbdddddaccbdebeeebecccbbeaadbdcaccdbdbbacddaedebbdebeacbddebcbbcbdedddbaccbbbccbceaeaeeeadebacdadecaeaebecbbccbeedbdddcadabecddceeaccdddccbddbeddbacdacadbeaeaaedcabadaddccdddcadadebdbcadeaeebeceacdedabdbebebbbccbcbadebaaadeaabebddeecbedbaecdebdabbdebabedcacebecdcbadadbcacdddaeedecdbabbdabadaeadcbedceeabeebeabbacbcaadbbccdcdaabbdadacaacccbbbaeacedecbbecdbaecdabcbcbbaababbabcacbbcadacedadaaaecbbcdadeaaaceaeabcccbadabeadabbdaabaebcaedbdcbcdaedccadeabdeaaedcecdbbeeeacaaceeeebedbeeecdadbccaecbadbabbeadcecadaaaaeebcaadaaedacdabbabbbabedcbadacdbabbebdaeddbccbdcaecbaabedbabdbadccedeabeeaebcbeedbdcecceecaebceeddbabccdebddcbeecadbaeceeacdaaeabeaedeeabbcbdedadbacbbeaebdcecdbeaeeadbbbdaedaddabeccdabcdecbbeecbedaebcdcceabdceebdcbcbeddbdbbaddbbebccecdccdbecacecddbbeeeadadcbdaabbaacaadddaabeececeedaddbabcdbcceadeaeadbeadbaecabeacecadbebbaadbaebaaaedcdabbacecebbeccbebabceeeeedaeaeeeeeccdaadbcdecdeddcacceeaeccbddebdcbbdcccdecbddaadeedabdaedaaababcbcdecedbacecadcddbabbeaabadddceaccbcedbbbcbbbbadcecdcbbedcebceecbdaadaebbbddabcbeedecbebecbcebcbcdcbacdbcacdebedaeeedcbbbaeaabdeadbeeadaeadecbaebdecacbdaccddbbcaeabccbecbcdabeccbbcadbbedaecdadaacadcaabddbacacabcadeaaaeabcacaaccaeadaabdebcbdacacaeeeeacabadabbeaceeaeacecdaecbceaccccaecceacadaaeccbdabaccdbddebbbbeeacabeedaadcdcdbbbeededbdbecbcebdcebbbdeaeedacdabcbcedbeaedcacebcaeebdbbaedddecbadbabbcbcbbaeddeeeccbbcaadaecceadcbcbddebbaadcaccceebbdbecbbddcdebcebaeaebdadceccbadaeedaadbadbdeeabeeacdaccacdddabdabbebdbdccaebccdbcbbabbddacdecbaebeaceadcaaeeabcecedbeaeacbeccdbdcaadccdcebadccdecabcdcabadbbeabddedabbdeeaccedebdabeadeabcebbcabbaccebeeeeeedcceeabbdbcbaabdcaaeaecbeaececddbdbbedeecbbecededdcdaecaebaebaccabcbeebbeebcacbbcdcebcceebecaaabbebeaeceabcbbbddddbdcccadbebbaedbcaacbdccecaaeccaaceabcbdabadedbdcecdcbeedbabceaeeaeeeeedecbceacdeeceeacccccdcaebdcedbdacdaddaabcdbdddecabbadaceabebeadccdeaaedbbdcbaecbbcedacececbcedcbedcacbdbdbbdbcdbcabcecadbeedbaedddcbceceecabbddccbbddedddddebcedcbddeddcecebdcaebbccedabadceadcdaebcebabaabdedaedacddcddabaadebeaedddeecebebcbcbaedacdbdcdeeeeecebbbcabdbddeaeabbcebcccebbaeedbbcaaddcadebaceebccceabeaaeccddebddbcaeeddbaaceababdedbcaaedbdcdcbbcdcebcbcbcbcbcddcdeeacabddcabacaacddbedbcbdaccdbadcbdccccbbdceadeebaeccdeedebcbcaadedaabcbebbabbebeaddecbcaddacbaecbeaeaeeecccbaadcbccccbaabbdeadddddeaaebbaabbbddccaeaedcbcccabbdcedeaecbcdadcdbdecbeceaaebbabccabebababcabdeadccabdaaedebbacaeaebcbedabbaecbeedcaeaedabebaaebdbcdbbbbaceaeebdededeebdeecdebdacdddcaacebdeeaecdeeadececbcbbaaeccaeadbdbccdbbccecbabadddaaecaebbcdcdbedceedbeaadddebaddcccbcdaabcebbaeeccabbacdabbcadbbdebcdabbadcedddadebdbbeeadacedcacdaeacecdeabaeacecdeeeebbebebcdacdaedcbaedacbebedeaabdadabecaaaecaaeaebbbabbedcbbbeddadbeddadaebdcccacccedcaabbbabbaaebebdebebaddabdcdcedbaaadbaabdbeaedeaccbaeeeeecaecaebbdedadddccddcdbddbeacceceeaacbebacdbdcdeabdabaeebbdbacebebadaeeedbdeceedcdcbdceebacbcbaaeaecebbecaeaeaceadedcdbdadcaabaaecbcabeceeacecaeeccddaeaceeecddcaebdccaddebaeadccaccaecbcdcbaedecceeccabbaccecbbdbbddedebddcbcaaebdcddbcbcccbddcbccebdbceccedebdcdeeecaabbbdadcacacedcbbaeadbdcdeecdadbbebeadcaadbceabcbccabacaecedacaebdcacaaeeacaabdddcdacabbcddbddaaccadcebdabbdadedadabaedbbcbcdbcbdadbbddbbeeaeabedaccccddaeaacbddebbdebacbeadcecabaeceeacddbaadababadaeaaaddaeedcdcdaebbbbeccaecececddccddacedebadcccecadedaaacbdbaaabeeeeccdedadaecbcedaedcaaacaeedacaaeaadeecaaeeaabddbccabcbceaabdceadacaabddcebebdacdbddeeadeeebbbcacabdbbaeaddddacecdbebaaecccaeebbbaceeaeccadaadcedcbeadcbdebdeeabdbcbebabdceadaecacdbbdcdbabbacebbeadeaebcdebebecaeccbdabbddbeabceecddcdaacebebadacacddacddeeedaaacaaecdedaeeebeccbcdaacaeedddceccababbddcaaacbadcbcabecddeeddeedbbeedbeaebcdcdeeaedadacbcaceababccecdadccceacebaacabdaaecdecddcdbedacacabeeabbccdaaabcdaabaeabdbedebabcbdecdeeaaaadcdbdebbecceeadecccebbdbbeacbbdabbaadcbebceedecebccbdbabbdeebbcaddaacdaeaddecdadcaeeacbacaabdaeacbdcdedaadbbbdcbaedaaadcaaeaadebbbbaedcbbbdbbbbddccebbdeaeeeccedcebcdcaaebdacadcaeabaabadadeeddecacbdadaedbbaaedcaeecbadcaaabccbdcbbdcaababaadcbecabebdcccaaaaaeeacbeedbccededcabeeccebcacedeadedcbebbeadababbeddbcbcdbebdabcbdecabdddabcccacccdcbddaeecebeabeaadaecccccdccdcadaaaddeeadddbdcccacdbcdadedbacbaaeacdcbbaadcaebeadcdbabbaaabaadecaadeadcbcaecdacaccededccdaabbaeadbadcbebccbecabceebeaddaaaaeddddceeaebddbabbcacccddcebccccdecbeebebeaccdecaebaeddddcaddadcecbbbcedeaebbdcabedcabcadeecbacbbbcecdbbedaebbeaccabeeddceecceaebcadccedeabcddcecdcacddddbddbedeedeaedcdeacaecbeaacdddcdceecbbababeeadddcdeaececdcbeccdecdaeadebeaaadabcceabbceedacbaedbbcbacdedacceeeceecbcaacabcaadcecadbaadceedcdadedbcecabbeabaadecdcdcaddaebadcdcccbebabeabedcecccdeeedcebeacdacccedeccabeabadacdadcaaebdbbddeaadcbadcedadbdbdbdaaddaabcbdceceadbaecaddaaedaebceedddeedeecdaddbbeecaabaeaecdcbaaedbbeddbeaeabcacbecdbcabecaeebacbcecacddcbbeebaadeebcbddedcddedbeabbaccecaeaaaedabbaceadccdcdcdddabcdecbbeedaacaebebbbacaaeaaaedcddbeceaebbeecadcbccdeabecdbcecbecebeddaeaaeeeaaeeabaadabbdcacddabbddeecebcbabadaabadbcbdaaaaeeeeeeddbbabaedbabdaecaebdddceedebdacadecddaedbebdbdbabadbceacaabeeecedecadadcdeacdcbcdbeecdbbaebebeececdcccaaaddecddeccbdedbcddaecdcdecdacdbabdddeeebdceddeddaeecaebdcdaeceaccaaacbbdbcceabeecabbcbbaacbdacebcbcbacdaecaedeccbdecbedabeadeedcedecadddaaccbbddabbeabaaacdceddadceeeedcadeccadbbadceabcdaaeecedbaabadeebeaaeccdacabddabecbeccdaaabdbbbaedcbbecbedcebbeceaddadaddbbbaebbccadcebeddddbccdccebadbceabcabdccdecdddacbbaebccccdaacebedcaabbcdddeaeadaeebeedcdcdddacdcdacccaebcdaceabbbddbeeabcedabcbcdeebddbbdacabcadcbaeddbbdceebdaeadcbcdaaaeceeeceeabbbdcbcceecbceadbaceccababdbdcebebeecaceaabaeaadaaadbbbeabbdaacaeceababbeebdedebddaabcedbdcbedadbdcdbebbacacabaebaddbaabedadacdcaebdecabeeadecadaddabcdcdacbebdcaebeeadceecaadeebbbddeabecccabceecbaaeceaeacadacaddbadcdcabdcaaabeadceadbdaaabdabbbcadcaceebdeaccabaedbabcecdccccbdbadadcbedcdbedebedceaadecdcaaaaedccacbecaaeaddbbebebcbeaeadcbaaeceedeaebbbdedcbcbdbecbceecdeccaaadbdbaecadccbdabeccebaddcbcecdccebcebaedcadbdbcbabcebadccbdeeaeaabdceedeeebdeadddaccaacaedcccdbecaaaaceaedcaabbcaeacaedcabedceaeeeecaceeccbbccbdacbadeabbeaededababcdedabceeacbaedeabcbcdeacabdbdabcbbbecccbceaaeebceeaeedbacdaaceabcabdaabbbdcaaadbaedaabeebdbecbbabbbecaadabceabbbcaaeabbbecbaedbcccebeaccbdeceecebaeabbabcdcbcedbcdaedeaebeaeccbacbaeeadddccaeaecbbdcdaebbcdeeedeaceeceeeeabcaeaeabdadaeedbdecbaeedaddbccbaadebdeecedbcbcdebceadcbcaecaaaeadccdcbdacddbaedcacaadbaeacedcbdabebbedcdcdcaceddaeaebdbbacbeeaddcacbccdbcbccbeedbedebcaabbbcbaabbdddebbbebaebacabcecddadcdcbbaaaeddcedeaceaeeaadadaacaddaaaecaacdcbaadcdaeabbacebdcdedeaacedbdbdaddebeadebedaeaecddcadebaacebaaababddadbccbdbdbadbeacadbcceaebeddbcbdceaebbdeacbeaccdeeeecccedeaddacacdaabdeeebbebbaebcaeeceaacaaccbacbdedcdbbcbcedabedcacdcdbbadbdedacccbaedcddeceedaddabcdedcdbbbbdcdacceeebddcceecaacadbcecbcbaaccbccddcbbcdbcdcbadadceccdadacbbecdceaacccbdbacbbcebedbebddcedceeacaeeaaccdaaadaaaecebceceaddbdbebbdadcedeecbeaeaedaeecbbeaaeabcbbbeaeabecebedabcedaaeccbadbeeeebbbcddaedebaecdbbecedccdbcacbccdedbceaecabbacbddadddeadcccddedcaabcdbabaceccacbcdcecddbabdaebaebeaaeaceacdedeebebbaddcdbecdddcdebeecdccddeacaeaaddeebcacbbeecaaaaeaaddaabcddcacaabdbbdecedaeddeedddceddccaacbdccecbecaccbadacecdaadecdbecedadebaaacecbcdccaceaeeddbbccdedebdbcebebcadacdabbadaecdabebabcdbbbceabcaeaacbaeccbaaebeeceabaeacadecacdcdecdedbbbdcecbbbedcbcdeeeaeecbdadebacbccddaaabceaeabebddaadedbdeecaacadebcbedceeaceaadeeadccabcacbeccecdcddbdbccdecccadbbceaecbeddadbdebdaebbabaadcddcdccdaeeababcdedbdbabbeaacddcdbbadecbebbeabdccccceaaaccddecedbabacceaccbadddecbcaddbbbdbedecedcadddeecbeeedcdebceebddcaabedabbdaadddedcdeeaeebddbbdcbcadddededaebaebcaecacddddbcbedcbbaabdecbcadaaacdbddbedbabaabdbdebcbbbcacddbeaeebddbbeddbcaabbdacabdcaeadedceeebecbddbcbdcdacbcebdecdebccdceebbbbeedaaddbccebaccaeddedebbbacaceebadcbbcdedeedebeabbabbcbabeaeccdcabbdddecaecaecddbadcdadabaabacacedceddaacebbabdcebeeddeddecdccccddcaaaddabebebaddcacebdbeacbceceeeeeececcbcbdbddadceabacadebacbccdcbadbdedcaecedbecdcaedcceaabdcaaacbccccaaeabaddbcaadcdcdebdbbdbebbdebbaeadececcdabbddabbcecccbbdecadedbdbadecccaabadacddaebbeecceddcddbccbddeaaecbbaaddceeccdeedcbaeeaacbbcaeccecdaecaeeddceaaceebeabecbddaaaacebdcedaedcbcaaceeeebbdedcdcaeaaabeedecdeebeeeeaecaabaedcaddadecdccabccdadcdacecacbecdccedaebcbdbdcaeeabebdedddeedaeabbcaecbeeeacadbacecebaccebbccaeccdcbebecaedabcbadbddaccaccdabdcddddcaebeaaddddeabebbccabdbedddabdcacdcaeeeeedabeeabbacaebbaccabebbcaeccbaaaecbbcbcbbdcedbcbedecabdcdbeaebbabaacabcbccdabddecabbeceaeceacbaaecaceeacdcadbaddbbddcbccbaddcbbbebeebebdbeadccedecebbbdabedeecaeabcabcbaeabcbcbcbbdeadcddcebeabcdecdecbaacaeebdbedeaaaeeccbedeccbebbaebbcabdabacdcdbcacbdbdadeeceececdeceabcdcbcbdeeaacddebddacccaaedbcdbbcdeaddebeeccdbdaaacdbbdbdcbdccddaccedadeaedadadcbddcadcadacbbdeabcedccbccadeaacdcbcbccebdcddadbdeaeeadddedaeceeeeacccecaddadaeaabeebbceebbecacadbeecedbcbcbdbdcadacdabeaacdcbbecddadaccceecebbcaabcbccaaedcabedbddedccdadbcacbcadbdadadaebcbeeeedcdeeaeabccacccbdabdddacddebabcbbcdcbeeeadaabeadccbacbaeedcddaacaacbccaeaccddabdabeccdabcaebdecaceddbeaddacddbcaacbcdccbcdcddbadeaaacdcabadbcabdcbaeceebeddbecdbbecbecabeddaeeebeacbedcedeaceadcaddedaedbaabcdbcddedaddbeebeacdaabcdbdeaadbddcddcdaaeedcaeabbebacebaecdceabdccdadaccebabcabdebccaaeebdebbcbdbdedbcdecacbbcedecacbecbeddebddbeaceebbbaabdbcaeaebedadedaadcacbadabccddbbadceccaceebacaaebeeababbddcaebbdcbceacedcacaccaadccacbbbcabcacbeeeddbaeccaebcaedbbdbcecbceacadcdbceeecaedcbeaeaccadcbdebcbaecddecdacbbbebaecaddaedceceadadabeddabeccaeacaddcdcedbebceeeeeccaaeddaabbadcedbdededbdeaebeaeeacecaecdbabddacceadecebddbdcbaecaabebdebccaddaeeccdbddcdaddbcacaaedacecbeedceabeabadbceebedcbbaadbccaaabdbbbecdbeabcddecddcbccbddddddaedeacedaaebdcdcdaebaaddeedcbdaedaadaceeddeceedeebaecdbddcceadedececdeacccedcbadcbeadcddccaeaeebeecbdaceeccababbcbeccacedabdddbadcaacdceddaacbedadbadbddcbaebdeeaadaaddbbaaaaceceebaaceaacdaacdbddeecdceebedddacbddbabcaaddeacabddaeadcdabbaceddaceeeeacebbbadecdeedcdeebcadabcbdbbaadcaabadddbbdccbebcccacdaeebdcaabcdecedabadbdbaeedcacdeccddbadcbdcecbabaaeceadcdccaccadeadaaabbdaedceeddccaeaacceebcecbcabeabcaeceaedddbdebadebdeabdadbecdbabeaecdaebebcaabcccacccecbcabddbacabddbdcbedeeeccacbecdbeddaedaaabddeebaceebdbeebaabbdedadcabeeecdabacdbcbeaabcaaecdedacbabbebeeaeeedecdbbcbabeeacbacdddabaacecebbbeaabaacebabacaeeacaebeeeaddadccdacdcacebabaddcadbddacaaaddcdbadaedebaeaaeededdecceebecdbdbcaadcdddeadbbbaecdaabedecadcaeeaccacedbedcaaebcebbcbddebbbcaababaaadbbacdcadecaedaecddebbadbddbbcbacecaceeaadeedebdeceedbaedaacdeecaaebdadecbeeaeeeecceeddeadabeacbbbadbcbbbbdbbbceecaccdacaceadeaababbceaaaccdddcddbdbeabcbbbcceacccdccccadcdaacdbcedceabbddabceebabccadbdccbacdbceaedbededdebabbdbdbeadeacccecddabcddaccadaacdbbacbeebcbacbbcabeebabacdcacacbeacacedcdacecbecabeacbcbccaeedcdcbeeaedabadcbcbbdcddcbacdaeceddcabbcdacbbbcccdeabaaedbeececebbcaabbebaeaeccebcccbaaeeebcbeedaacccdbcddaedeebecdcdccbbbaeaaaabecbadacedaaccbeaddacecdecebeebbcdbadbcacadeacabeadecceddbaeeabbaeecacceaadcdeedabbcaaaaaeadcddcdacbcededbcaebeaaaddedbcdaddcacceaeebcaebcaeeaeecbbaaabeaaccbcadcbcddeacaaeeeccbddceeebecebcbdbeceedbcdbcaceecaacccccbbdedccbdedbacbabeadadcebbcaeddabecaccdabaceaebbbecbaadbeeecabdadbeaddbecbdbdedbeaeaaebecbdadedaecdddecdecddcdeadbabdacedbdaecdeaeebabbceaddebdadedeeeedebbdabbbcaadeaaacacdbadddcecbdaaeacacbcaacebbceddcacbdaeeccaadebdbbdbecaeedcaeecececccceebdbbaccddddcdbcceeedebaededceaedecdabbbabbedcdcabddccbbcaeccdbbcaaacdeabcbaccdaceabedaeeeeadddacdcecabeeecacabeebaccacaecacbbaccadbebcbbacdacecdddaeecdeaabbcceedaacccaeaeebeaeedeabddebabbdeabacbebabeeebdbadcdbbebaebbadecdecaedbdaccdbcbdaccdebdaaaecebbdeceabccaabccdccceabcdcaebcdebaadabcadaebeedacebdeaaaeaaeaaeaccdbbbabbeaecdbadeeaabcbbdcbcbbeabaebaadbcbccebeccdaccddcbeadbaaeddcccabbaecdaaebbaaacbbddbcdcdececedaabeccbaebdeaeaecadebdeadaaadcbdbeaddcbadcebccdddbccacddcdececeacaddccdbaaabcbaaabaceedacacdedbbcdccaeaedecebdcdbbbacaaecbcaeedececeeeabdddbcebdbacebceaccabadaeababebddaebbbbaccddeebabcdcdebdcaddcbabcbcedcbcaeaccccbccbaeceecccadbedbeeecabdacbabcdcbbcadcbbecceceecdbdbecccaeadbcacaadaadaaebceceaacceecebdabeecbdeedbaabebbadaeedbeecaaccdcdeebceddcecddbaceeadddbcaecadbabbddbcdbabcacebaabdcbeabbbaecebdaccabbbabdcecbbedbcbcbcaceacdaaeddddecbcbdadebcabdbecebebcbeaccacccabadebabeaccaceaebddaeccbebeedcdaabbcaadcbbededcdeeaceedececdddeedcdbcdabbbeabecebaaacdbabeecedcaeccbccdbacdaaabebccdabeddaedbacceeabebabcbbbaddadebdcdaabababcaebeddadbcccbeddccdbbdecbdecbbcdddebcedebeeaaeeadaeeaaaeeaecdddbdbbaaecdecdbebecdcdedbacbbcacaedcaaccecdbacadddaaceebdbabedacdcaebaccdbaaedacdaababaaebbaeaacaccadcaeebedabbbbdddebdbcecbbedbadacebacedbadbccabddadcaebbaabaadabebbeaaeaebaceebeaebdadcecbdcceeabdaccaacebececcccdcbebbcccccaaccecbcecbceadadeabacebdcbdccedebbcaaedadbbdcceaaebadadacacbbddebebbcacdccadbddbdbcaeeaeeeabaacaeedcdcaadabdcbeecddceaedabbbdaaeccdcbaaabebcccdccedeaccbcaecbcddcecbeedbcacbbebabaeeacdedcaadbceecadcdbceaebabebbdbbdcedecbbaabcedacbbdbbcbbbdabedbeadacdebbabadcbcceaaaaacededbebdccdbadebabceacadaacaecbacbcbeeaccdcebadddadecacaacdcdabbeaedecaaaedaaadbbabbdeceecbabdadebcdbadbdedbcadbadeebbdcadceacbcacecbeaadecbdbaaedcbddedeecaeaeacccceccedddedbdcebccbecddadaebeeaaddbdccebacbdbdbdbebadaebdeaababdcdcccbacdeeaebabcdbacdebceaccbcddebdaeabccbdeeaeddecadcbcaddadddbaaccedaaaeddacbcdcaadcdeebcceecececccecbaacdaaaabdaeeebadbdcedcbcdddcdaebdeebebacddbaebcebcdbecaaebbdeacdabedcddebeaaebededbeeadabcceacbadeddaaaeaaceecdbadcadbeeaaabbceecdcaaedabdbeacbcecdecaeeebaeebeeecdcbdcbdcadabaddbaadceceedacacbcdbebadceccbeabebcaadeabccbceabceeccdcaebeaaaabdbecabccbaedeecaeddeaebeccccbebeaeecdcbbbcdbceeeadeccdecaddadaabdebaabadebdaadeedcecccdbbbeeabacdeaaeaadbebaceceedddccbeacaaacdeeaceedaabeeebbedaabaeaebdabebbcccabdebcdbaddadceebabededdaeebdddedbedecebcdcecadabbedacdddaaedaadbacecdcedcbbbcdcceaaedacbbbacccbdeccccacdbaaacaeaaeddaacbdceecddccbcbbeaeadbaaccedcdeeadeaeeacadccaadcbcbeddcaaeddcbbcbcbdeebbaeeeaecbdcbacbeeaeecbdeaccebbeaddbbbeeeacdcaadcbdabeeddeeacbedbaeaccacebeacbcaccaededebabdcbcdacbdbaaedabecbcedecdeeaebadacebebbaebbddebadaecedbeddacbdbcbaddbabebeceeaaadcabeaddedcdddedeaeadaddeeabbcdddcbdeedccdbeaedbcdbbdbdcdebbadadbeabecdceabdcccbcebeeadecebbedceebbcbcccdaabcadcaecbacabcdcedaeeceaeecbccdebabbacacdedebeedacadedaacddbadebdcbdebccbaabbceeccedccdebeadeccabbecbecadeebaacccebdbcadcaacabbdbbabceddcbbaccbdedebedabeceeacbbcdcdebdbdacbceeadbbdeecccddbecdddacdaddebddcebbcedaddceddeebddeaaccaabdacbbbcbddcadbabdbadedadababbdebacaacebdccebceaeabedcebdabbccbbbcdedadcabbeccbbbbbcbeeaeecaebaceaebbbccadeeddeceeeeeddbbdccbabdcabebaacaedaaacabeddbdadbcaeddabeadbacddaecbcddaaabaaadabceedbbdbceedbdaedddededbabdcccddccaeddaadebddbbbbdbcecdabedcdcadeabbdcaeaccacdebcaabcaeeddeabeebdbcdaaddbbedddebeadcccdbcaccebeebcddaadaaebcbeddcdccaecabbecdabcaccbaebbeabeaadbbeadabcdeadaecdaeaabcabadeceebecbbeecddecaeddceadaeaeebdaabbbeebbddcdbeccdbceeddeaccbdeeddeeeacbdbdaaecedaeacbdeeaeddbdabcabeebceacbecaccebddbbccaecacbeaacdcadeeadcdbdecbabcedbaecaadacbcdddbadcbdedcbbabdbabecbeebdbddaabeccdacdeeccedcccdadaccbdbddddecbcbaeccbcbccacbabadaddbadcacddbbdaaddaccbededbccbcecdbbcbadeccacacdcaedbbebedeabadbbdeedaadaebbebbcabedcaaeeeacdaaceeadebdadbcdceabeecbdecabaacdadbdacaaceeaebeaaebeceaeebeeedebbbdbceadeecdadabdaaceceeaaaaccccdceddacdecacabccaddcdabcdcbabccaccecbeadabbacceaeddddccccabbbbbbcddccccecdcbebceacebbcceebdccaacaeadbcdbdeddecceebeabdebdceadedcaedbdbbbadebccbeceabdcebeabdaadaccbabaddbaccaaaddbdbbebbcedacdbceedbebdabbdbbddecbecdecdadeaaadcbedeccbccdacadadddaadcecdaaccedcaccaadeaebdcdccdeabbbcbcbdcbbdbcadeccbbedbebbbedbbdcabaadcaabbacdbbaeaddedcdbecadaeaabebebbebbaaecebdbbbeaabebbbceebbdccbbaacebdcadbedbdccbebbcdcdbbbbbdbcaedeedeccabccbaadcbedbeddcbdcbbacbeebddcbbddddbbcececdadcbceadbbdaceebaeeaaddcdaeddbdddbbebebaccabaaccddbacebceddddaaadecdaadaaaccdaecdeddaacebacbcaaccaceeaeddddcdabaeccadcbececabccacbbdcbabcbccdcdabaacdbaacdcadebbeecdbcabadadabdbdaadacdacdddbebcdddbaeabbcbdcdcccadccdeeeaadecbceeeddbabbdbdeabaabbbeabdcaedebacabdebddcbbcbecbeaeaaadabedebcbaecdbccedadbcbdcaebcddccdaeaedebaacdbaabaebdaedbedcabbedcbedadbdcaacacceddbdadbabebcbcebabeddceaabedaaebbbbcbaddbababdaccedccdaeaedadcddaacdbdcebebbdddeaebadeeacbddedaadcdaadaadbcdeebbadbbeaadccbacdddecdcdbdccbebbaebcdceeddeccccecbcdbcccccebaeeddcbcbdedccbbbbcccbebbbededdcebeeccbbcacabeeaddababaeaaacceccbebababdebdacaccacbcaaedabecadaaddcbcacbeeaebaadecbdacaebcddbedbaddbbbddaebbcadbcdadabbcaceaabedcdcdcbcccebdbabecbaabceadddbcadbeecadcdccadbddeceaacaadeaeeddaecdcadbbedccdcdadcddbaddddbccacdaccaebedcebcdeedadceecabdaeddbaaeededabcddadeaebddddeadbeedbddeaaacedcaebcdcbdeccacebebabcbebbbaadcaeaddacbdbacddeaecdbeecbebbedbcbeeaeccedcebeecaebaededeaabbbdcbdbacdbaddbbacbcadbdebeddabbccdcdddadbdddaeedceccabbacedeecaccedcbddacbeebedccdedcbaaebabecbccbcbdacecaadbdadbeecadaadbdeeccdececadeaadaaacdbbdbdbdddaaeccbccbdecebaccdcebabcbdcdeebdeaaeebeedcdadaeddecaedceecebedddaeceebecaebeedcddccabdddbbeceaebbbbabaebebaeabdbdaccbbecbddcababcbbcdababdddacadabcabaabdebbeeddaeceecbdcbdadbcdadcecccbdbaceebececbebedddedcdbbbbbedabdeabeabccaaedbddacaeccbdbcdaadedecaaaaacdaceccebaddeeeeacaabadeacebcdadeccdbdaeebbeebdeeadeaaaadabdaacaccbebbaebdaedeabcddabeadeeaadbedecbedacabededebbbbeebcacaebbbcccbebbbaddbececcbbacadedaeebababadaebdeccecbdacabbbaadabddaebbabbcbdeadbedceaabbbcebdcbeabbeddabbadedacedaaabebdbedebeabaacccdbaedddcbedbcebbbeadebbbddaacddcceaeaddeebdbceeaceabddebadbeaccdaaeebebaedbeedceadbcdbbbedcaebbaebecedbedacbcbcaeabbedecdabbedbccaeebbcdaacbbcdedcbeabbcaedaddbcaabebdabdcecbbbabbdcdddaedddaceeebacceebbdebacaccbeeaaeadbccaadcccbbdeeaccaccbcabbbaeedcadbceebbdeedceabdcacdbcaacebcdceeeaeaeddaaebeaeabaacabebbaaaeebdbeeaeaabbcababcadebcbeecacdeaeceabeaccabaedcacaeecdaeaeddecadcbecadcaaceeddeeaeeaccedbabbbadbbbcababacbadaebcaebbecccecadcebadebcdbaccdeccabbdddaacbacbbbeaccebdcaaceacdecddedeedbbebbaeaeaabaceeebdaaccbbecbbbeacacdbebaaaedddbaaddebbdecdcdececbadbaeeadceccdcbebdaadceaacceeeebadeaebcadeeabdbedaaeaaaeedbebacaedeceeeeaabdaebacaedabaadaddacbcadcdbbceaaddecccacaeeeeecbdebdadbaaceeddbacebcceabaabbcabacbeebaecbcebcacedbcbbaabdddadcbebaccdedaecebbdbeecdbcbecadabadaecdecbeceaadecabbcaccbeaddbaacdcdebbcddceadccadcadcdaaddedeccbbeaaeaebceecdaeaeeabcbccaeaedeecdeeddcdecdcadbeadceebcbecdeeadeaeaaaacddceacaedceecdadabcdeccebebaebdbdecceabeaccebadeaedcdebeeecceccdbddaecbaadbcaddbcdbcaeeaeeededecadcebbcbadcedaadeabdeeeeabedcececeeeeabdacbbaeecaccedeecabdadbdccceaecbceadccaadebabcbdcbacacabdecabbeeaebbcadeeeadecaadaadcdaabcccadedcdbbdcebaccaddaeaaceddbaedeeecccbdaeeebbbcbeeeedaeedceacedcdbdedaecabceabecaadcdebbbecaaacdaeacbbcbedbddcdbbcbedcececeddcbbccdcdededbaedeebedbaccaaccdbdabebeedabadecdaaceeebdecabbacbaececebbecaebdbddddcdbecbaeeecebbaabbdadcadbaecabedeabeeeddddcaccdacedcaeeaabebeadbaccbecddbdcabddaeeaaeababcbdcceabdbbedbbdcecbbccaddabeeeaeedddecdadbcaeabacbccacbaeabdbacaecacadbccccedbbacecaebbcedcebabccecddabbacddcbcddadecbbeccbbdbbbecbdbcbdcdcbdaeecbaecaecebbcccdebdabecbbcacdcaddccdeaeacccadacebbecbeeaaccbbdaacdacabbddaddcbdbddedabaabdbbcbdcaeedcbceaddcdcccbebacaeedbbaedbaeeecdabcdebacebaecdbdabbcdadabecbdabcdbdcbeeedaedcbdbcbddddebcacceeddadcbeedeeeebbbddbadcdcbceeacbedadedeeebeecbcbeadececbbddbecbabbabcdabebcedeccbdedeebccaacddbecbcebbdddbbabaecbaccbacecbddebcbdebdbcbabaeadeecededadcedcccaeebcabbddcbdaadbededdbcbcabbbeebadebcadcdeacbababcbbadeaedabededaeabedcedeabebeccebeebbcdecdeedaecaceeddcbeddcebceaaeaadabaedddaadcceebbadcebdbbcdccbacaeedaeedbbeaaebadcabacbceabbcccbddddaeddaccbddebedcbbdbaadeacaeeeacbcbeebcabeaebccabdeccddedeaabebdededeeeebaddcbdcdbbdeceadcbaddbcaaecadecededeacbeaadcaadeaececdabaceaabdeaaaecdbbcbdcaaeeaddbdaccdbbaeebeadebebbebacbbecaedadbaeeaeaadadbabdaabddbabbbdaadeeeadaeddcdcdbbcccdecdddaceceeecccddbcaaaaaacaccbcedcccdceabbecbecedeceaecaeadecabddbcabdadeadeebbabbdbebadbcebdbdeebaddbeabaedeceeabbcbaeeabbeaeaaeeddbeccbdeebdabdbbbedeedaccacbeacbbbaceeaeeeaaacdddeedabbcebbcbccddaecedddedabcdbebabecadaedaceeacbabaecebebcceebbeecaddedabecbbaddebbccbadbcdebdbcbedebabaeecdbbdccdbbbdaddadeabceddebcddbbdbebcebbaabdaebeaaeecabececaeddedbdaeaabdcdaaabadadebdabddccceccedebebbccbaeeceadebddbeceaddccccebedbdeedbeecdacdacdcadeccdbbcaabbedadbcdebbedecbceeddedeaabdaccaddbcabceaaeecdbebebacbaaeccecbacadbecbbdcddabcaaeccdbdcccececeaeeaebcbbaeccbedbdbbddaaeeedeaeceebbaeaeebcadecbabbbbaddbeaabccdadeacdcddeaadbabaccbebdeaceaabceadbaadacdaabeddabaacacbddaceebbecdbbabdbbcbecdebdaeaebcdaddaeeadbebdeedabcabacaeddcdcdcbcdcacccdbebebeacddbaecccdddedbdcbceddecbbbeecbabeeeaaacceeaaebedeeeadedededdccbbbaedbbebecdedebaddebaadcccadbaaebeacebbceadaadbaebdeebcbccbabcbebbdcbbbadadcddbbeeddccdcbeebaabaadebcadaaeaacbacabadbedeeceddacdaaadbcacdabedcdcbdedabdededbdccdbebdacbabcbeceedceedbaebdeebcaebacaeeabaadeebcaecebedcdbbcaeecbdbceebaecadeacdccbacccedaaccadbecacadecddaabcdddcabacdcbdccbbcbcbcdbcceacecaeeecacbedbbcdbaaebedbecdcaebcebeaccaecdbdeeaebcdcadaedbedbcddccbddacbbadcbdcadbeeeeeeeccccbceebebeacadedaaebdaeabecaaececcccbdaeebcabaccaeadbaeaeeacbbaeaacebedbeecabdbacdceaabaeecaaaabedcdadccacdbeedeeeaacccbbeeeababdecebacdeedddecebdcdddeaacbcadeedbacaccaadbecccaaadbedddabebaabdccabaddbcdbbececdeaedabbedabadbbbadbdbbcecbceeecccacddabccbbdcdecdabeacceacabecedeceaeebedeaedaedbedeedaeaeaaeebcecbeacbccaaabcdaecbeadddbcdcbbcebacedbecaeacadececaadaddcaedbabbccbbeabaceceeddebaaedadcbcbcadaaababedbcaaebeddeddbbaeddbcddcbbbddeceacbdcccdbddaadbbeaedeedeadeebdcbcdbdbcdeaaaddddcdbcdbbebbccdeeeecccdadccbbdceadbdbadedaacbccaeccbbbbadabcaedccbbccecebcaeabccdbdbedcecaebaeadbbadbaadddcecdeaebbdcecebdbaaaedbcbcdbaabeaedbabbdadaeaeeabebaaddcabbdbabdbdedbbdaabdccadcdabdebbbbaeeaabbaeddaddbdcdadbbabaaedecdcccedbeacecbcddbbebeedcbdddeabcbabbcbcaeaaddedbadeaacabcbadeebdcabddbddddecbabaedaeadddbcbedaedeecdcbccbecbbeaebcbebabaeebdbacabbbcbedddccbcedbeeebcabacddbaecbecdcabceecaadaececdecbeeceaceaccebeedbcdcbbdcceacbadbaadecbeeaabcdbbbccdebbaccacddeeccbedebaeecccaddccedddcdacadcdaaaadbcbceaadbbecbabdcbbbbdbaccdedbeccaabccbceddcceebdeebcadadcedddbcbdaeeeebdcadaedabcebddcababebacccceeacaaebbbcbdbbddebdcbebaaecedccbaabbacdecbcabadbcdcceddaadcedcecceaebeacdabdecbcebecdecddbaeabbcaeabcaeaeeaaebabbdebcdaeebdcabebcacdaeddbcbbaecdcdcacdbaeecedebecdaeabbaeeceabbeaacebbddcdadebdabbebadceadddeeaccbdbbabdadacdccceeeabcadeddeebbbebdeddadbcabbedaccbadbdbecdaccbdbeacaabebbeadaeaceedaadebddabeacddadddecaadceededdbabbeabeeecbbaeeaecbabeabbabbdaedbdeacbdddbdbaacdaeabdccdbaeacecabcbdeaacdeaccacedbdcaecacdebdbacbdabcecedbceebbaddcbdeebcbdedceeccdcbccdeedaaaddaaedceeeaccddcaceedcdcecadaaadadbeadbcbbcbbcddddeaeabeacecdcabcdeccedcadaacbaadecddbcceeedebdaacdbebbaccbcddbeccecdcdcadbbcdbabedbbacdcdbbcceccdbaeeeadcaeeadeceeeebcbdbeadcebaebdceeceadbdeeeecbcdbebcbeacbdbadcbaccbeabbcbbcebbcbddbddebdeeeaebaedbecbadaddedbababdcaebeaeeebcbcbbddebebedadbbeacecaaedaaaabcaaeacccdacabddddccdbbcbabccdbcedabcaaddeadcbddaddaeeaccdeabcaceecaedcbacbbbbcadabcacbacabaebcacdcedcdeabecbbcaaccddaadabababacdabbcabdbcdabdbecebadadacceddbdacbedecddeacdcdeecaaedebecdcdaaabbdebedaadbebabdaeaabdabaddedbeedeabcaceddcedcabacbddaecaeaadecababbacbecceccaebabbdeadbeeeeaebcbedaaceeedccdbecdcedaabadebebacbdeaeaadeadcaecaabaeaeccaccbbacecacdeddddeaacaeddddaaccebdaccdcceabcedabecaabcbeadbddcbdeecadaaecaebdcaacdeddbcecaeccbdeacecadcecebbedbedeadabceabdabbcbadcdbdbcabddcbebceebcbeeebdedbbbacdbedeadcccdeecdcedddeacdeeaabaaaebdcdbebadabbaaadbcbbeeecbebcbdbbaebceddacbabaabaaceeddceeebcecadbcddcadcdabbecebbebdaacededeaeeecbaadbbcaaedbdcdbddcaedcecdeceebdebebacceecabebabacbdbaedaeeecdebebecccaabbeaeddcaeadacceaaabcbbcceceadaededdeedbeabececebddeaeccecdebbbbdaaceeadaeaaeacedeccedbcbdecaaeeeabaeeabcbbedacddbebadddcbdccabdaddaeeaaeaeadedbdcbdbaaedceeeaeadcdddaededacbcdbcccedcceadccaaaacdcdbcecbbeecaebddebccdeeaceeccebecbbabaaebbedeaaeaceddaeeebadcdcceccccadebdaaacbeadeaccccebcbbabdacecdaeecbbaabcbdaeedbceaaddaecdaaabecbcdbaebebddccaadabddadacabbbcdecbedaeeeeabdaabcebccedeceeceaaebabdadbcbbdcabbdcaaccdedaeddbecdeabbcecaccbbdbdebedbbcbbacbddaacccecccaeeaaeaaddaaedaaeceecaaceddccdebcabaabbabeeabcccdaccecbedbbdabbebdcdbebbdcbddeccddbbbadeaaadbebccaaecccacccdcbbaeecaeeabaacdcebeaacceeaebaabeedeeadebcacdebcbacaebdbaebdeaadddecebdccdebdbeceecacaebdabbeadbdaddbbadbdccdacdeeaeebeddeceeabbdbbdcddcceddcbababaacececbcedcdbbdbecbedaecaacdbbadcabdbbaebbeeebcccceabdccdebbdeaaccdedbcecebaacbcadabdebdbdeebccbbacebaeeedaadebcdaaeacdbbbaabecacadeadaceacecaaabaeddecbcbbbbbbdadceabbaeecbaeedadabacececbeedaabaaedcbddbbadbdcdddbddecebeeebdecbeacccbebeeccddbcaadceeaecadbacebcdedccceacaecccdeeebbdacaacacaeebccdceeddbddabeacbccbaabeccabaeeacdeedeacacaaebbaaedeaddeabaaccccbdbabaebdcdebccbabbddcccdcbcbdacbdeddebdcedcbdeabcbdbaceaeaadcceeeceebceadcacdcebdbdedaedbebacdceeabcdbacbeaaebbbacebbedaeddecbaabbdbdbdadbdbebeabdebadbacbeddaadbdcaaebaceacaeceecbcdcaeceadbbcebcacdaeaaeeeedbdcbaecdbeecebebebecaaaccddabcceaabbaadbedcedbbbddaaaebdaedbedeccccceccaceeabbbdcebecdddeeacdeceadbddaeaecabecccacdcaeadbeaebeaccabeabbaeabadeacdedbdbbddabebbcdcceeabcabdedbadabbdedaadbacdbabbdeecdcdecdecedbeedabceddcdcecaacedabeeabcacbeeaeeddaadabebecdedcdcaedadbecccdcbdbbcdeeabadeabadddbaabaeeaaddabacbbaabebaabddcbeebedaccbacdeeeabebdacbbdedcdceccdddccbdeadddadbaccadedcbccadabcadabaacceabbdcaddadeebcddcedaddbbcbdecbbbcaeddcebedadecceaeccbecadbbabbadedbaeaddbcacdebaeebcaecdecccccedcadbccddbcdbdebeabeceeeeceeabdcecaedcbcddacbcadaabeebebdadabaddebbacaacacccbdeadbdecdccadcbeedbdbaedaaccacacacddcddcedaeadaededbebbedaceebedaabbebadaadaeddebaeacacadbceecddbdbcaddebcedbeddadeddadceeaabeddcedcecceceecdcbdcaeabddbbdabcbecdadecdddababbcdaabeadceaeadcbabceaedaacddccebdbbababbacdecbcdddbcaebedbddebcebbabcbedebcdadcbabdeaabbccabddeecadddddbcdcacacbdadcebdbacbdcbdbcacaecddbbeaccdabacbeebdddadbbdebdbaceeecbdaeacdbdddcbccbddedacdccbeddabbcebeedceacebbeabdacdbbcdaacdcdddacedbcebeccabceacdeccccecabadaebdcbceedceaaeebbdabcdcbbaedabdceeccdcddeabebbacdccedbbcaccbbadbacedcbedeadaaddaedddeecaedbebaecdadddbdbbbadedadeccaacdebeabdcbbdcbcabcbedabdbebbcebacaacaaabbeacbdddecdeacedbbaeedccbabdbceabeaddaaaabdcacadacabaaebdeaeeabaaddeaaceacaddadcaadaeeaaeeaebaaaaddbaacecaddaccdeccbaaebceebbebcbeceedeecebbcecabdeccbeeacaeedcddcdedeedddaeebaacccaadaeccbdccdbbeacbbddbbbdaeacdbbbbcbcedaaecebddccceaabbebedcdabdbdbdbeaccbacdeacadeaacbdbeddcdacbaaaecbbaedbdadeaaebdeaaeaacededbdedeebdeddcdeecaccdedccccceccaeaedaadddebddbbdceacaaaadaeccbdecadbddbbbcdadcaaaabcdcadeaedaacabcceedebddcbbabeebdbaaaecbdebecabacadebdcbddeceebacbcbeeccabceeeaedbccabdaddeeecaeeccaaceacbdbcbebcccecdeebdaaebeddeeaaaaaabecadecbbbbacaabceedecbbbaecdaeacdcaddbcbdccecddebaaddaccbbeddaadcaccccadcbcebecbacbabeeabaeddeaadcabdecdeccababaecaebeabbedcbaabadcebccebdaacebacdbcecddedbbaeeaebdaeebbbebcdeecbcedbdcbabeaceaabaeecabcaeddbbcdccdecebaaaeaaaebaeccdadadeedaaaebdaececabddcacddaecbcabcacecaddcecdbbacaaedebaceccceecebcdaeaaedbcebbcbacaccabdadeeddbeedbacabadadaaabcaebabddddbbdbbbbbaccbaebdebbecabeeeedacbabaaabadaaebcdcadcebcddbadeecebbcdcccbdecdbcdbdeeeeaabddbdeabcdedabdeedbaeeaedeecdadbbaecaceebaedddbebecbbcacbcaaeabdaaddbbadececddbacaabbdeaabdceeaccbbcccdddbcaabcdeeacebeaebbdbcdbbaaaaccdababbcabebbecdcccaabceacbbbcdaeaeaeeeebaebbbabbccacebdababcbabbcdcbbcaabcecbdcbcccaaebadbbeaadddbdebdcbecdcceaeadaeedddbecdaddbbeeebadbeabcaecebaeebcbbcbcdcbdaeddcbedcbebcedbabdccdeeeeddcbbdddbceeedcdaccedeabeceaabdbcaebecebabecaceedbcbbebaebacbaadeecceddcceebbacaacbbcddaedbdaebabedaedeabcdcecbbeaececebdbecbdaccbdcbceaedadaebdccbcdaeecdadacacdeeccaeceedecedabbcacacbbadebdddbcdbdceddaccdcebabaedeadebabadebeecbebbeededababdceadcabbbcbebbdebdbecaddbcccebcabdbacdbaaccbebaaccacaacedbbecebabaaaeedecabdcdcbbabcddacceebaeecdceeabaccdcaecbcceaccaceaadecaebbdabbacdddbbdcadbbcbcacdeddddbaabccecbedbcbebdbebaababdcbebeddbaadedeabcaacacadedecdbcccaaadeecceeadeceaaddedcaadacebbdcdaddbecdaacabaccecaaacbcadbaaaedbebadaacedcddacedecdacbebcdcedddbbccbdaedbebbdcdbebdebaecdaccdbeadccdeeadddcddddedbddededaaaccdbedbdbcdbeeabcdeeeebeeabceaaaaeeceadbdabbcbdcbbcebdbabcadadbdedcdebdaddaddbebdaaebacecaececcedacaadbacdaeeaaacbbcddedbcabaedcacebabeccdddacacdacbdccbcbecaabecbdcdacdeacdaceebababdbdbecbacdccebdaeddebbaecaeedacbdbbaaedbabddeeceabecbaeecbbdeaddcbaeacdcdedabcbdabbbecabccccdaeacabbdedaddcabaeaacbbcabbbdbacadbdaabebcbccecceabeededbdacbecdededbcacebbcdeeebcccbcaebbaebccabcbacdebbadcddeecbaebecdabeabadcdceebbeecaebacaecbbebabacabbaadacacdecbccacebadbcdbcccaadaddbceabbecdedaecdbacbabdeddcecdabadabbbaeacedccbeacddccdeccecdadcdbdedabcceabebecbbaeddceabcceeaedcdcdbedeaccebdaddbadedbababbbbececaacdceadcababbeebbcecdaedcdebaabddeabbadbadbbadaaceccbdcbceeeededbeabedcacadacacbcacceddedccdcedbdadcadacccdadbcddcabeceabccbeeddcbaadaecbbabbcbcbbbbcccbdbabaaedbdaceebbddbadcceaacccaebeebebececdbaeadbceeeacbaedaabdeaabadebdebcddeaccccebacbbccacaeabceacdbceeedbcecaadcecdcaacbeddbadcbdbcdddcabaaaabaaeeeebaedbecdccdddadbaaecacebeadeaebbaabcbbddadabdcddaaedbecebaccaedaacaaabbdeeceeeedddcaceeaadecbebcddccacceacccbdbddaccceabbdcbebaacbeccdceecccdaaecebaacbeeadadeabbccdacddadcceadedeebdcbceccddacdbcaebdcaaedaacbcdbbaaaeccceaddcbcadaaccdacdedddbaeaaacbabebaedbeaccecdecdaccdeaccddaabddedeaabeaadecaebaaedadedbcdccbdceabbcbcdccbcdbdccedaecddabadaeacceadccebcdebbbeeabeabbbceebdecdeccebcadbedeeadecdcebdcdccbabecddcecccbcabaeaaabaeaaccedbceebadbbbadadcaaacbbbcbbddecbecabceddddbdcdccdcaacdaaceecceeeecbbceddcbccbadbaaceabeedbeeaabdbdadeaaebceecbbdeecabeedcacceabaacddaadeadcaebeccaceeeeaebccbbeddebdacdececadcdedbbdceaabbceaeedaedcadabadcdeebcaaccceddccdaedbbbabbbabecaddadcaccdadcacebdeceebbbdebcccceedbaaecdedacbacbbedbcbebbebbdedaeceaeaedebbebbedaaaaceaadadedccdaadacdccaaabeeeaadeaabbcddccbbcbebdecaabbdbdacaacacddedeedbcceddcddcedacbbbbeceaabcebcbbecceaacbccbdcdedcbdbbdeeddbaecaabbdadaaeeeadebeccdecceeceeacebaaaebddecceaccbadaacecdadaeacdbaadadceceedaaebececaabaabaebeccacbcedaddbcededcceaedbccbaecaaeacebedbabddbaddbacebeedccadbebbebbdcedddceedaeaeebcdaaebcacbdbcedeaaeeeadbbaecdcdbcbedacbdabaaadcceeadaaaebaeedbacaaaabbbebccdeabbbcebeeaebcdbcadeacbdcedeaedeeaebabdcaedccacbecacaabddbbebdbabdaaddaedccaeeaadededaebdbaacaddcbbaaaeaaeceadbacbbdcdcbaedaeeddeddcbcebecdceeadeaacadeebaebedeaaddddcaaabccceddeedbbdddcddabacdedbcbadbabcbdabcbeedaaeadddeeabbcaadcacdacbccadcdcdcdbcbccadcbaaabaacbbecdddcbdcbebcacaadabecdbbacabcdaadeebebbeeeceedacabaadbbaaeceeeaabedebacbebeeecbceeedacabecadaadcbaaccadabdcbcaaeebaaeeacddcabebccabcedccebacacadeacaebeecbabadbebadebeabdcdebcbebccdceaaadccbbbdbdebdbeabebecbabddccccebddcdcdcacecedccaccdcaaabbcdcadbddbcecdabbcabebdeebddccccccbeccdeabbbcabddbcdaaaddcbccabcacaddbeeabdecdbbddaceaaeeaaeabbdabbeaeabebddacbcdaeeabacabeacbdbbcddebeccbdacdeecdbcecbdbdcaaadabaaeeccccadededacaececadebaebdbcbdcabedcbabcceccedebddadbaecaebcccebbaabbbaaddaccedaddbdbaceaebbacdceaabecdadedcceeaebcddcdbdcdcbdcbcebbbcecbeaeccedacebbeaadacbdaaeadbcbcaeeacbeaaaebeccbeccebabddacdbdbcecedccdadacdcaadbeaadaaabaacdedbdaacabdeaecbedceebacecedeccecabaebbdeadbadaaabddecabebeebebecbaaaebdeeebcacdebdedbaebcededeeddebddbbdaabebcedddabdccadcdbaebcbbebacaeebdceaccadbaebcdbbccedbabcdccdbebbeaedeacbdcceecaceadaabbbeedceaaabcbceccecedbedaebcdebeadabacebccdacbcbaabddadaabaaaaadacaecdccbcabbccedcddacaadadbacdecaeebeceacbeaccebccbecdbaddebcabdbacdbcdadedaccccebdbaddaaddadcadccebcbbeadabaacdaecbedcbacabbedcacaababbedcecbdedeeacadceabebecdccdabeecbceeababdaeceecccdedcbccdbcaeeaebebdecacebccecabddcbabcaaacacaaebdcaceaccaaaedebddaeddcccaececccbbeeebdbcbceaadacccebbbdbaabebdaedaaabcecbdeacdeedebebbdbdbaebeaeebbdccdeaccacaecdccebdeccabeceecdeccacecabbcaedcadbcebacbdedbcbebbabbbbdbcbdedadbccedcacebdecddcaaacceebbeaeeaaedabcbaddbddbaaadbbdcbcbcdadeacbbeaccdddcceddbdeabbceeacbcbdebcccbcbdedbedeecbddcbebdeaeadebaccdedbeaaeacddeaceaeecdabcaebdbdaaabdcbdbddeecdbcdeecbdcdbceaaedecbdabcbceaabbeabbaacabdeddbebccabbdbcccecaeeeaeabbccccaaecaeceddbdadabcacdecccbaaaecdbddceaaadadebaacbcbcdaeaabccceadaacdcbadeeadcbabbaadadbdbcbecdccbecbcbecbddbcecbbbdeddacdbcdaebbaaadbaccdddcabdebcedbacaddbbdedbdabdaeeebbbbcaedbbbebcabacbdeaddbbdbdbaeccceebadbbaddaedaeeddbecceabbcbbcbeabbecdadeccaeabedeecabadbbcedadbbceeeaaeacddaabaecdabbdacbbeccdccbbbaababdcebbeedeededbbabdcbdbebdcecbedeedbcccedadeedccaaadeeeecaebddcbdccbeabcbabeacabadbedbdaebeeaaeebebcadedcebcdabcebeecbdaeeedaecbaceedaebaaaceadeeebbcdbdebcabdadacdeceaacbcedcbabecdbddddcacbcecaacdedbeeeaedcdadbcacdadbabdabdeaebecdacadadaaaaaacbabdacbdbabedaceaacaeebcdaecaaadbbadbcbdbebedabcbdbdcdddaadaddcbceebdddbdbaacceebbbbacdbeeabdccabcbcdebeaddbbbddeabbddecddebcabbbcdddbadbababbcbbaeaecdddecaeadceddbbbadecbecccdbacecbceeddcccebcbdcededdaeebcdcbbeabebedebeeeccdadadcdddceceebccbbbabdbaeabeeabdedecbcaaabaceceacbdccbdbcbdecccccdeeeadcabcaddcaebaaecdadacbbbacadababcaeadebadccaccccacadbdeeaedcbcbebacaacaacebeababdceccceecbddeadccdeedccebdeebabbbeaacdcaddcadbdbeaedbbacecaaecdddedcaddbeeedeeeecabacaecdbaecbebeecacbccdaedadaeebebdacdebdedbbbaadeadcdbabbeacdbaedcaecabedeedbadceecebecabadeeccdccbdeeacdaaeeddeadabebedceceabedbceacdcdababddcaaaeabdeaedcdcdedebaeaddacecededaabbdecbadcabadeebbbaeddcbacbbcdeeccbeacececacecbcbccabadbeabcdeeadbcaeaeceecdcadcecaeedbdbdcbbeeccbeadadbeeeceadcddeacecabdcaceababdceaecedcebdeecdadcededdddbbddcacdcceabcbacdecccabcddaebddcebceededcecdbeccdecccdaadddbbacebcceacaebedbecabbeebebeceaabccdbacebbbeddddcbedeabbccddeeedcdcbeaaedecdeabacacabaeacedaeceabddbeecdccabdcbedebcabecbdbaabcbeadeaaeddaadccecacbaaedaebebceabdeeecdaceccaeeeadcabebacdebbcacedccbddaeaadcdaeaacbbacacaacdbdaaceabbdedeceaddcabbedbdeedcdcecbbdaacbabebacbddbddeddaeedccecaebbceddcadabbdceaacaacaeeceeacecdbaebdebdcbddecaebdaeebbddeedbeedeaebaadbdbaddbbadaeacdddcacaeeedabbbbbacdbdbceddacbebebbdcddbadbeaebbdddeadbcebecacdeadebadaaebcbddadebaccabaebbccaebbbabdaebeebcdadadcacedaaecedbaededbbcebcbadcecdbacdcdebcaddcecbdeeacdbbdacedbedddadcceacbadcaadaaadddbbacebdeacedcdedededdededabdabdebcddeacdacbcdcededacebcaaedbecdbddbebcceaacbebbeaebeeeebadaabaadbcacddcdcacbdbadddccaccecbdeeccbbbddaaeeddccdcabcdeeeccdbebeccadcecaaaeeaecdbeecddedcaaaeaadaacebdaacbbdbebdabcddcaeddebaabedaebdccabbdaecdeeeecbcdddccbedabbedcaeeaceaabaeedbbabeaddbdacdeccccbcbaacdebacaecccbabcbeccadaacecedbcadaaededcadceacbecdcbadaecdbedcdabaabeacadaeeadaabacdccbceeedcdcbdceecdebdedaddbeedeebbbbcbbeaaebdcebcadeeabedbeedaecaacadcaaddcacaabcebeddbbbdeaddcaabaacaeeaebcabebdbbcadccedeeccdabaccedceceedabdcaeaadbdcddbabdcbdabbebacbcbceccdbeeedaecbcedbcbcbdbdecbdebbeadaeaceabdeddaecdbdbeabecaaadececadabaadbabbceacedddaeebebdabedadcdddbdcdbcbddcbbedeebcbcbbbaeddbedbecdeedadedbebbdaebcddeeaebdcacddbebcdceaccddbdbeadbbcdaeedcbedddebbcbcbeeeaecacebadaabcedbcdaaabbadcddbcadbedbdddabeecadceedabdacebeacbaabbeebaabdcabdadebabbedbdcaddacbdcabbceeedaedbbaaedcdbdaabaddbcbaeddbbeedddcdcdedadaeaedcbbbdabcadcedaeacadcceaedeaacaaaccdaebcdbacadaaebcbedebbcacceddbcbbbaadacccacbadadabbeccbbaddadbeadacdabebddadcaccebaedcbcdaecdadcadcacaebaeacbdabeebbbabebaeaeeedebacccccbdcbdaabddceaeaddedebeeadddcdeacacdeedccededebdbcaadbbedeaeebaceebcadcceadbcbbebeaddaaedecededaebeceebabcdbbddddebbdcbecdacadbdbcebeedbacacabaebbdacbdacddacbecdceecbedbabcdbeecccbbecdecdabcbedcbdccecbedbcaebabcededddaebbadcbbccaddecebebdcdadcaccbaaecacddbeebeaccacedbaabdccbddedddceaaceaccadbcaaedaeebccbacdcccacedcbeaeaceaadeeecbebcdadedaceeeeeddcbeccbdddddcbaecabbbdbdadbcecbbadaecebbabaceeabceaaeccdbdcceedcccedbeddadcbacdbdcbbebbeddeecbcbceaeabebacaecaeddccbababbeeadaaebbacdbbbdccbdbdacdbddcbcbbeebdbcdddddbdadcbeeeaadcbdebeaeadccededcbcabaeeaaaeddbedccdaacbecbbdaedddbbecaaedaeebeaaebcdbdaeaebcaadeabaabdcddcaeeaeedccdabbeaeedaaaaceecaedbeebacccbedabaeabaccddbabccddcddecdacaadecaeacacaecddedabcbddedeebeeccadadccdccbdaeebcabddbadecbdccbbcbbabacdebdddbddbccebcbaaeddcdebbbcbeaddaecdbbbaeeccbbdecaaadcaebcaccbbdebaccbeaaabbedccbbecddcacadaebbdebbdcecdcaaacbcaddcdaedeacacecaaacdeecaacebcbbedeedbaacaeedddcbbbcbacbcdaddbbdedddabadabaabbadbceccbbbaaadcaadbcdcbabbbeddecbcabcdaccbdadcbeaeeeccbceabbdedcaadcdeabcadcdaddddeeabadabdcddcebdaacadecabebadeeddddaebaebceddebccccbcceacdaedccadddabacbdeacaeaacaabbceeceeacdcdbaeaedecdbdddeeaeedabeeaacbedeeccbaebcccdcacaeedecaddeebcaebaaaaeebdcedddabbddbedecdebdddcdecbacdddeceeadabbddaaccadadcbcbeeaabdbddbcbdebebcbaedcdcecbebbbcbaaebeddeecadaaeebddabbbbbbbdeeacaacbecebdabaedbebdcedbcebbacbebdddebddcabaabcbbadcebaeaeedbdacebbaccbedcaaadbcaaedceaedeecebadccdddebadaacebacdeecedcddaedecbeadedebdeecbcebecdaaebaeceebdcdbcbadecadddcaeceeccebebbccadaaaeddadacadaedbddddacddbcabbeedacbbcbcbdeaaaeecbadaedcdaddaecabdcbdebdaaababddbcecaaabcdacadedadccbbcdddadaacbbcbbeecdadeeececbaadccceeebaddaabcbedeccaeccbaecdddddcbedcaacdbdcedacddbaabeaeaedbdcacbcababaedaabeaeebedbcadbeabccedaabdaeacbbdecaccbaccaedbeaeeebcaedbdcbbdebdebddcccbdabecaecbbbdcabacddbaecdadcacabbacacababaebaebbeaeeaeccbcccbcbeceabecbeebccbaaabdbaeacdcddabeadbabdcededccacdacbaccccedadabcaeedcbcedcdeedbdceebdaedbbbebeadebabaaacadbdbdbddcdaaedeceadccdddcebadbcaebbeeacbcaededaedccebeaebccccaecdadadeadadbcebcbedabbcddddeeddebeceeccdbbeecbaabebacacbbdaddccabddbeebdeebdeccbeaabcdcdbdcceeaaeaeabbbacebacacaeccabddebbaececdcbaaeebeacbbcdddbdcadadcaecdccbeadbcedbccecadaeebbbdbdebbcddbbdbbadbdaececbebcccdaebddccccaaccaccaddcebdddacebacbcecdcccabaacaddbabedeabcbeabbebbadedbccadabadeeaadadeacdaaddebdbbececcabdbebdbceeaedcddbbaabbacaeddeaddeebcbbcaaddbddaceeaaaecbdbaabdebaceecbdaaebdddeccabdedccbdabdacaeabcdeaeccdcbeebaddeddddccdabdaecdcdeacecabaaedaceabdcaccecacecdecaeecebdedaaeeeecddcedeadbaaadeeaeebabadbedaebdbaedcabaebaddcbeaddbdeebcbbdcebebaababcbccbdbaabcaacaabbeaaabdddbdbaacbecacedeaeaedbebdbabdabaeaeaccdeaadbbceeabeddbadbedbebedeebddccbcdccbedadbedbcbbccbcdbebdeaadddeeeccccaecadeebddbbadbcdceadddddedcbceaaeebcabdddccbceaabeedeedaadbbeaeebcbacaaacabccdccbcdedbaacdaadadcdbbebddcbbdebdeaacdaecadcebbdaeddddadbebceacebbccbeeeababbbeaecdceabdaeedcdadcaebbeecbcdbbcedeacbadecdaeddbaccabdbbbeaeccbccacdcdbeeedabdbbceaddbdecdaaebdadabaaddccbebaedddbdbeeedaadaabadcadebdebdcddabdbdbaeeaadcecedcdbdccadedebadbbcbbdedbcaddbccccdaceaecdcadadcbddcdbcadddedbecdeccedbabadeedbdcbdddcacccacacdadedccaadaebddaabaacaebccdbbaebdcdbaaabdbbdcebbbeccaeabedacabdbcdbdbdeaedacdddbbeeedbdbecddcbdddaaeeeaeadaecacdecbacddcbdaccdaeaebabbeccebadcabedadccbeeaaecaaaadacebccebbabdddaddbecdeacbededcaadadbdabcddcdbabbbcbccccdddcbbbaecaeacbbabdeabeeaecaeeebbccaadddddbdaeeeccaecececeebeeddeedcddddbeecccddabaabebbdabccabacadbababcdadeaedcdebcadeacbccdbecbbdbecebbebdbcacabccdaadabdedecdbdadddabbabccaeccecbceaaacddadaaecbabcadcbdebbdeaaeaceabaedeacbdcedecddaacbaaecddbbbccabcbabcbbcebbccccddaaeeabbaccdcdecadbbdadbaaeebacccbcacbbedabaeeebeaabdecabbbcddeaabbebebedceeacebcaeeacadceadeccbbacaadabccccabecccdcedbbabbaceecaeebaabdceeaeeaaadedaddaadeddcdaedbdbcedadcdcebccdcceeeeabccbaecaadaeeeabddcebeaecdeaebeacebbeeecdedbdeacbebadedceeaacecebceabdeacacdbeadbdcaaadedaabdecdebbcabdaaacaebceaeabdedacaaecceebcbacbbbaaabbbbacecedcacecbbabccabebcebaecccdddcceedbabcedddaacecadbddcedccceeeebecbadeeabcacbcdacbcedeeccbbeccdcaedbccadbadeacaddeeabdbdaebeaecaebaebcdbecabeaddbebbbebadcbecccccabecbadcedaadeecdbedaecceedccbaeceabaddabadeecdaaaecdbeadbcacaaddceeaaccacedadcdaedcdbaccaebabcbdaedcbebaceddeaebabeeaaceeadbeecadbbcdaedcecebabbdcbeaddaabaddabdaddeeeebcbcddbdccedeedcdddcbbeeaedbdbbceabeeccdadaadbdbecabbdecbadecaecaebcdcadadeacccbaedeccabddaabbdbeaedeecdcecddaedaaadceecdccaaaedcbcdadeeaeaaaacadacacbbbebeaebcedbbcecbcccabeedabbdadddbacbedbdadacecdecabeacdacdcbbadabadbccecabedbaabeabcbeacaeaeccaaaeddccadacedabdaeabdaaedbdcbabccedabaedcbabaccecabaeaaaeddceecebbbddbbcaeeebdcadabebbaabebcdacdacadcbbabbddbdaeecedbbeedaeccbbdaebbecbaadcabcdabddbbeddadcacaedeedeeabebdbcbedbededbeaaceeaacadbdeececdaaedeacebeddeecdacdaccccacdcabbbabcbeceadddebddeabeaadeddeadcbbceeceeceeeecaebaedebccedceedadebacabdbbbabaccabdedcbedddaacacecccdaaebaaecdceabcedceeedcbabbaecbddebdcaddededdccaaaaecaaaabadebadaeedcbbecbbacbecbdcedbbeebadaeedcaeaebaccbbdaadacdcaeddebaeaddbaebbaebcbecacaabebdddaabcbcddaeededacaccacabceaeaaeeceaeabcedcaeeaceabebbcdcabccabcdbddcabcdcdddadecccedbaacedaedaacbcabdacbcbeeeabdcdccebecadbaabdbebaebaccccdedaedbcaabccaddedbdceaddbceeaabbebdabcacedabebcedcaaadcdcccecccedabdceeabddcebdeaedeebbcbdcccaedbccbebadeebdadbbbccbcdaeedabecceceedadcdcbdececddabeeeaedaaabacbcabaaacadbeacdeadacbdebcbacedecaacdceaddbaaeadbdacddadbcdacdbebebaedddddeadecdceddbdeeadbbdbcddcabdeaaedeaddbedbbbcdcdacebcaaccdaeebeddebabbddddebeebebcdbbbeeadadabddcacbeacebceedadeecbcaeecadbdcabbebebbeaaaacdccbbddebdecdddadbcdcbbceccabdabaccaeedbbbdcbccaeadaabeacbcdadcdbcbdbccbadaaeaedcbdcdaddeaacabdbbbddddbccecceecedaababbbbcdcbebddaebeaabacabeddcacdbabbcaaaadbabeccabebaccebbcbbeccacacdbeabcaadeacbcdaddcbbceebdaddbbccbdbeadbccbaaaeebbceeddabdaedbabcbdcdeebecdedaddacedaebdeaebbbbebabecacccadaacecdcacaddecebcebcaabdbedaecccbccdceebebeccabbbdacdabddaecbebeacbbdbcbadaedeadcbceadebbcdcebcdcbebbabaebecedcdabbebdebcebebaeecdbaeaddcddaeacebeadbdceeebacbbebbbddaedecdebddcceccaeeddddcecacdcebbededcdaedaddedbadecbcbceeceedebebaadebddcabdbadededcdaecdadbecacdacbecdcbccebedaabdeabbbeaecdcbadeedbebbeadbcbeddddbecacbaadabbbabebdebeceedbadeacdcbeddaaecbaecccadceacbaebcebeedcabbccaeedbccbadecdeeabcecedddcedddbbceaeaccebbbcccdeecacddcdbbaaeecaccbdbacbabdceaaedebadbcddeccccabccbebeecebcddacaacbaacbcbeaaacbadccaaebcdacecbbbdbdabddeeabcbccbbaaccbdbebbbeaeeeaccdbaceabdccaeddebaedceecaabbabcbabeacacbeaadddbcebeecadbbcecacaaccbccaaaadcdcddebcbbebcedebbbdbdadcdacdbcecaaaacaeaedacadccabedbdadbedbdcbedcabcbeaabdecbcadadabeaacedbaaccbeeaaaddaebbaaedbbebdcccedaddceecbebbccaacbcbbdccaaacabaecedacabdeeabacbdecddbeabdbeccacaadcddddcabdeaedeeaeceaaddbcdcddadccddcadebaebccaaaeadbdeecbeedddebdbeadebeabeecdbeecbededabddebecdedaaabbcccbeadcacacdcdeabeeeddeccdccbabecccbacbaaeebcbcaedccccacaababaabcaedaaeedacbbcddcacdaaacbcbdaaacacbcbeaccdbddbdebbbedaddacbbaeaaaadeacbbdddadbaedbeabcaceeeeecedadbbebdcaecabdbddaccdadeabedbeacbbeacacbddcbdbceeeddbeddeeceeaceacbddaebeadddbdcaedecccbddedbbeadcecdebcadeeeadbeabccbcaeaaededdbbeedacdbdbdcaeccedaadbdedcaeecbaaabbceeaabcddcadbbbcbbcbdcdbbbcaadacecdcdbcdeadaebdabcccabdbedbaaadbacedcaaabdcebeebbbdaddaadaabdbabbeadbaddaeadddaacbccbdaccccdbccadebbdaecddadabecdedbddcbdbeeebacaecaedaaebabcaedbadcbcbebdedcdbdcdcbcbedecaecbcaabbdbeaabeeabababebacadedbedcacdbbcbeedbbbebdeacedcacdeaecbaccabcddbbddebebeebcabbaeaeeeadcadcadeabaaacecbebdbeddcedbcdbceebbbbdbbaccdccebebddaccaacaebbadbbaacdcbdeaeacdcaaecbabacacccbbbccbaecdbbddedeadbaccddbacdcadcedaabeadaccdcaccabceaadaceedbaaedcbacebaacdcbeabadacbcbcabeabcecdebaaabcaeeceeacdcabbbbacaecaedeacdeccaaedbeaaabaeaabbeeccebeddbdaebacaeaedcbebbbabdccacebcedaaadebebaaebacabbcbeeaeeabdabedbeebaeaecdcdbccbbbbeeebdebbcbdaeabddeaadbeeceacbbccbedbcaeeacbbecdbeceaadceaccbbaeeddbcabcdcdaaabcdaaeaceecccacadccbdcddcbeedeceaebedcacbcaeacddadbaceddddbdbabedbbbcabbccddeecaabcceaecdabebbaabbacecdedbbcdbeaeeadebabaecbebccdedabdeecbdadbbeaddaeececbbccdeebbebdbcdbeeeebdacbacbbbbcbbcdadebedeedadcabeebcdbbccceecdccdabdbbbedbebdcaadddaaebebccebeaddccedddaeeaaaccaabeaabaccacabbcbeaebbbcbeabdddbdbabcadeaeacbebcaddabbadcabbbededbadecbeddbecaaddcbeecbaccdccdbccecbeadeaaedbebeecdebbcaeecbcadbbbabeadbcdbcdededcdcdaebdabcebacbacaebeaaaadadceeacbedceabccaadddeccecabbeaeadebedaeccdededeeabecbbabebaaccbadccadebabeeeaadabbebeaeecbadcbdeecdeaeecabeaacbabcbcccaadadbeaceeaabadadbbbddececcbbaeadecaaaebddaebddadbccaacdcaeccaeebecabaddacdbbeaaebaababcbbabdaceeedaacedceddeacddabbbccccecadaaacedadbcdaadaacdebadaddbaabbeccbdbabcacbcbcbcecbeacabcaceeebbeddcbbadbcdadeccbbbecbdadbedcabedeeecadeeedeccbeadcceeddbecbebcdeccdabddabebcbeeabddebaaabedebbcbadeebccdadccddaeaadecbdebebdeecedbdaaddcadddbbbeaabacdaedacceaebadbadbecbaacddceacabeeadcbedbbbacebabcedebdbebbbbbcadebaacdacabceebaeaeadcdbacebeaabbcceeaccceedccdeabbceababaaecbcaaaddcceccbbccdebcdccebcdceabebccbbcbccbabdbcebdaeeeababbaaeecdddbeacbeabeabadedebadbaaddaabdcacbccddcdababeedaadebddeccddcecbaeeaebedeecbcaaceacbbabdeacedbebccbbdccadebacceebdabacbeccedccedaabddabbbaedddecbcceaedbdedddaabbdeddccdbcebdcbeeedbbabbdcccddeadacaccadadaddaeddbaaecabeceeabadbecdbcbacbbcbaceadeecceddaabbbeaeaccbedaccbaabbbeacbbebccbcccbaecaeaacddaebbbdeabacedbababacbeccedacdcbdedecbeeedbaebaebadedebdceadeccdabcbeabcbbdbeecaebdacdbdcedaacecabeaabcbcbbcbbaaaebcbbacccccecedddbdedbbdbbdbdcddecaeebaeacdeabcebebdcddeaaaedecabdecbaeadbbeeadaaddadeeeeeabedcddeacbaaeaebbabdcabcbdacbbbacdccecebaadebcedbdcebbadedebceaeccecceadadaecbebcddbebcdbbdbcdacbabedcceaabdbaebceecddcbddccdacaecdaeaaecbacbdeccaeabdaeebbaabcadaebcceccecbbeabcbaaeeecbadcbebcdbcbcbbccaacceadebddeeaedeeecbbdeaccaaabcdddceeeabaeaebddaaaabedebbcbeadebecacdbcabceedbbaacdcadbcdbccbeedeeebcacddadcbdbebeaeecbdbeabdbbbabecbcacabecbbadbdddcdcccbdccedccbcadadbaacaaccdadabddacccabbceedccdccccbcbaaadcedebbcebbabcdaecddbeabaecdecaddcdaadbabcbdaeccdecddbbbdcccadcdaebebabadbdbdbbabeaacadddedbbdacaebaddedaccaedbdccdcbddaabececcdeaddcbaacabcedeeadedcceadedadadbbbeddabdbebbedadccbdaecddbabbcbbdeeaceaddbabacabaedcabdeaabdececcceaddabaaecadbecbdbbbbcdebdebcdbdeeadbcdccddedbbdadccdaecaacceeaddadbbbbecdaaeadbbdceadccacbeaacbbcbccedaddbeecebeaebabbbbbaeeedebeadbbeecbdcaeeecabdabeadbdcdeeedbaabbeaedddbdaebacabdcedeaeddaacddcdcbdcddeabbcebdbeaacebbeadbaaeaddbdedcdcbbecdaecbdccedaaebcaedcdebdcedacaadeeccbabbbdccdddcdddaedadddcdeacaeedbeeddaccabbbaeaddebeaabcecacbcaceabcceccdbadabbeebdecddaddcdbebabccebdcaabaaadbeabeeaaaacbedebceaadcaedcbbcdadcbeacabddddcaeeeeebcecdcecbaedaacdbcadcdaeebacdebdecebecedaaedbbbcacceddddcaaedcdddaeeadceaccbecdcdcaeaedecdbbacbebdbeeaeceaacbbcaecededeaeeccdbcacdaabdaebbddbbdbaeaebecbedadbeebadabdcbdcaeaaaeeaabccdaaceecaceaddadeabbacdaadaebddeaeceaebcacebebadbcedecbaaeadaddcbeabdaadccddebeceadaebacbeabdcbaeeeadcecceccccddeaacddadcbdcbebdceecdcbbcbdcccecdbabeaeebaecdcddcbcceeeebceeabddaaaccbeccdebebcaecdecdcabbeaadccbeaebcadaecbaaeedebaeccadbbacdcbdcddbbabdededdebddbdacbebebccdedddbabdbeebdecbcbacaaaebdecbeceedcaceaebceaaacceddbeceaeaceaccdcdbcaadbeccebecdeedbcbdccdedbcbacecdeacbdabdcbedeedacbabedbbaecadeabeadbebadecbcccecdbdbeaababeedceccecebcdbcebeacbebddeaeaccdcabbcbeacbedbcbecbdccddeddbcdeaccceceedebbddeacaddcdccadeddbebedbcbecedeeababbcbbebccbbbbebacdecacbbeebbeeecdccdecaaacecdedaebbaeeaecebcedeeccaabbabccebebcaedbdccddbdeaaebaacbaadebbdbccabdcaeacbbeecddcccdaaadcbbcdaadadbdbbcedeadabedeeecbeaaccccbabcaecebdeaccccebccdddebcdedbdeadeabdbcbeadeaabceecaebdcdcacaacebbddbddacdedddddecbbdceeabbddcbdbeaddeaacacecbdbecaeaaabbbbeaebaaceeccdddabaeeabaaaebceaeabdddcaccaaabeeedccbcbecabaeaecedbcbaedbcecabbceaacddddcebebbaeebaacdadccedeeecebadaeacbbcdaeaabdbbbcdcdecedabedcacacedaaebeddbccabebbeabacdcbdbebeeebcbeacecbbcdbcacdcdcaeddabcaccbbeecbccdcbbbbaddebedabdccdbddedbdecbbacbeddcabcaeeadddeddbadcacaecaabdecaabadcdbeaecedabeedaaccdbaccccceadcadbabdbbbbbdebcbcebacbbaebbdcdbbaddeeeccaecdeebbeeddadddbccedaedbaaadcbddaebecbceeecedcacdaadcacccaaabeadadcebdecadaaaaaaebecebeabbeceadeacdbaadccbcceceeacebdbabdcdeabecaaccdccacbceaabcecdecbddcbadebaaaadeaecbedaaddbdcaccdaccededdadaddedaacbcddcdcecccaecceabaceabdebcbccaaeaebaeebabcabceaadbacbdabedcabecceaeacbdaeababbedcbcddeedccaabeddccacabecedaaacbbeebcbeabcbccccdccabcedaaeeadaeddebaccbaacbebecccceebbdcdbaeeedccdadaccabbcacdacabcedbbaaceddbedcdceadaedbadbdededcadddaeecdbaccdaddabccacbedcbaededbaedacdecdadbaebecddceabbbddebdcbdddeecbaccbbbebedccbabdaddaeedaadeaabedacbeadbcbcbbddeecdeeedbedbdedcadbdeeaecaabdcedbebbbbbbbebbaccdadbeedbbdecceecaadbcbcadabbebcdcbbaeaaebcdecadbbbabaadedbccedaadedbaacabccabeadcdbcdcceaddaabbbcdaeddaeddedaaecabcdababdebcdebacedecedbaaeedcbdddecdeaebabdecceaadeceacabbacaaccdbbacdeebeaabbdcdcacedaeeabdededdbbbebaaeaddbaecbdcabbcbdbbdbcccccaeccaaccbcacabadeceaebbbeebeacedeeeeadedcdcbcbeedbdebbdcbcdceeaaadbeabacebaeabdeddabbdcebbeccddbacdebddcdcabdddabbaedeccabbddebcaeceaeabebdaccbdbebabecaedbcacdeabebbadeeeebdcccdaedebaadabcaadabdedecceaaeabeabcacceddadceccbdcadcecbbdbaacadaddbeabaedcddcddccbceeeacdeabacbcaceceeecaaeabbbdacdcbecbebbbabaeedbeddaddacbebaadedbbaeaedaebbceadcdbbdabacdedbbdaccbaeadabcbbdadebdebaccacaebeecdaccdbbdaabcebcabbdcccbdcdccdbeabbccbecaabdcddddcdbcaebebacbcbedebeceaedebcabceccbbdaecabdacdccbacbaeebaebbdbeecadeceabbacbecddbdbedddbadedcbcaeacabacdcdddcdadadeabcdbceddecaaabcabbeeaebaeebcaedbdddddcaabdbdcddeedcbabdecbacccdcebeedcdbadacbbdbcbbacabbdbebdabbeccbdbabcadbadbeaaeadaaaebeceadeccbadbecbcacbabbacebbdcabdcacdcbabaabbbdadebcbaabbaebddeabcecabaabbcaaaeebccdbbebdeeaaddadbcbebbbbcceeebacbababecbddaccaddceacedeecbcccbaaddacababbeedaacdeeebaeabeaaaecdcacbbebcecdbbbdbeaadacdcdacccbeceedbaeecdbaaabddadebdaadacbbaeeeadebeedadeadaadbbcaeecebdddeecadadddccccabbeceaadaddaddeebebdbabdcbcdeabedebcabeeeddaeeeedddbcacdebecdaccecdceccaeacebeaeeaaeaceaebceddebbccbbabaedcacbecabcdeeddaaaeedbbdbcacedaabbaccbeabeecebdbdbedcabdcdabadbcbaaeceeebeabeeaadaadabaaaddcededeceaceceebdcdcaabbcbeabeddbebedaacddcbdcbbcbebcdbcbbceeedceacaedeccddaeaecdcdcddacdedceaeacddbecaaddaecbecadbabcacedeecddcabcbbaccaeeaddeedbcaabdcdcaadaeacdadccacbaaaccbbabbaabececccecadedadcdcacbdccbeaaaabaeeacceedbedddacdddddaecccaeedddcdadeebcbcbdcadcbeabbcedacecbdbdccbaeededadbecccddaadcaacbddacccaacdaaeaebbadeabdeaddadcebaeadbddaecbddcbaabececddbcddbdedadbcceddbdbecabbeeaacecbabdeecdbceccbcbdcbcdbecaedbeecdcadacdddebccdaecdabdbdbbccceabebcadaaaaddeadcbaddcacebdccaeeabaadbaeadbecbbaecbdcccddbcabdeedadaeecadbcdcdabbbecbdbecbbceadaeacaeebedbdecdabceddbbdeccddaecaabcbeddceaacdeedebccecbceccaaddccedadebcbcaececbccaadeeadbdbaaeccddeeadbcdcbdacbabebbdeebedbbabccecaaababeaccceceebccddcceeaedbbccedbaadedbadeadddddebdcaecaaecdaddcaebbbaedeeebebaeadbbdacaaacbedccdcaebedeebaddcbebebaeeeccbccbacabeecbebeddbaceabebdaaeadadccacabaaedcdedceaaabaacbceeddbbddecedbceeaaaebacdedbccedabbeeeabdbdcbbdeedcaacbeeaacacbdadbdeeebbcdcdabedbedbdbdcbddeabbbbbaeeddbccbadeceebebbcecdacbccdbcddbeecaedcbabdbcdebaabaaabeaeaaaebeacdcbdcecbbdbeabbdacacadaedbcbcaebdbcbcbededdeeecdaedadbddeddeeabaeaedbeeeebccbbbbcaccceedddcdeddddbbaaaccbcacbceebbebeebecaedcaceddeaceddeebeceecdcabacbaaddcbaeeedeebeeceeddceecebbaaeddaaeacabadedcdbacbedeeaccdcdcadccbabcacadeaeebcabddeaaabdeccecacebebbdaabedcacbacabcdaebecddbcbceeedcceebceacadbdacddcbdbdbcaaebacccbdacbeaadbccdbddebeedcdbecbeaedebeaabcbeabcbabcaecccbdeeaacabedeaebeecacdeadccdcceeeaacbddceaeaadbdecacdeabaeaacdeaeeebeeededcdbceabecabdcacacabdeeaedaaaebacbaeaccbedaecbdbdecebcbebaabcbceceacbddeeabdaaeababaaadddecabaddbbdcdedddadaaddcdccbbcecdbbcabaecdaddaceadedecbeeceeeccdaabeaecaaaeecbbbaccedaaaedbbeccecaedceeecececdecdeebeabdebdcbeddcbdacaacbbebbbbbeaceeaaeecbeceaddeacbeccccdaccbddeacdedbaddedabaebeebbcdeceeadbaeeccdcddabadaeceedbbbabbaaaabcabccaeecabdeeeddeaddcbbdcaabadaeccbadbdbaecabdadceecbdedeacdaaacedaeebaebdbbaebaeddebeaddbcbecedcdecdcbbbeccbdddcbeaaddcaddaecaecaebacdbddbcdaedceaebeadddecdaeeaededacaebeeaadecdaceebddebeddbcabcebedabaaeeceeacebddabcbeddbbceacbceadeeebccacededbdeadabadeccbddeaddabbcdaccceccaceeddeadeeaedcceecbdeeaebebcacbadadecccdadadcddbddaaceacbeddbccbabddccbbdedabaeeecdddbadeadbedbccedcbbbebdedbcacdebbabcceeddeaadedeabebccecddbaebeddebaedcebbaeeccbaaceedecadddbddeacddbebaadddcadbddcbadccbbdeaaedeeccdbcadeaeacdbaaecedecceddadcbdeeebedabcedeaeebcceaacecbddacaabbedcdecaeedbaedcabaabcbdbbabadeacaadeebcbaacdbdecbdabdbbbaadcceebbabecaaaabebadcdecdddcbbbbbecdaceabecccbcedcccbcbbbdaddbcdcbecdcacdbceeeabbeeaedbcccbdabcddebaddadcbeeebabeaaecedecbadcbaabacebedcbcaceaaeedcceeddcdceecadbcaadebcdaabedeaadbdadcbeaaabadeeaceccbaccdcbeedccbaabddbdeeeaaecabddbdcebeedabdacdaabcbbcdeaeacadeaacdbdbcaeaeedbdddcedaedcbccdbbbddbcbceaaeaedddbcebcddabbceabbbcedbcaabcdedbdbdebbcabaeededceaaaceeeeaaadbdcaedaeceaccabaccddabaaedeedbbcbbadbdbbcaebbecdeebedceacccdbdeececdcedeaaeeaacdaeebbdbadceedcbeeaebdeeaebacacaeaedddbbdbedceedddedaeabebddcabdacebeebccdadabaeedbebdeccdaedaacbabcadeadbaadacbedddbdeedebecadaceedadebcabeebacabaaceaabdcacedbdbdbebcebbdedddcbcaaceaaabcdeebbedccddebaaeaecbbeeaadbcdbdbcbbdaebcdcebeadceabadedaeddacceceaeadbdbaddadabcaacbeebbbaadadadeadccaadbeedcecbebbacecbecbaebaaccbbaabcaccbbadeeeaebbeddbeccdcbccdecceeccedcadbaceebdcddcedcdbcaaedbdaecdabcdaaabceccacddbccdbabdbacaadbcacdcddbbedaddcbcebbccbbebbdbeabeebeceeebcbadcaeeccecdcadaaceebeeeecabedcedeeddaeccddbadbccbeabbccedbecdeaeeabebdabbccdacecebdacddaceaaeceecbcbedbcecbedecaceceddbeaaaaaaecacaecbaecadeaebcbdbeaedacbadecddbadbcdabbdebeabcbcacdbadddbabecaceeeecaacaebaaccbbcaeaceebdbeeadcacbedcbcebacaececebeaacdecddbbdaedacabeadcddcbdaedcbabcbcbdeacbebaadbcdcabddaaeccaaebdaebdabadcadbbddcdbdccdedacbddeecabbdbcababbdceebeabcdbdecdddaabaecbadeddbcaddaedddcccbdbbeaebaeedbbcaddebadaedbdcdbaddbccdcceccdbaeaeaebebbeeeeceeacdccceecedcbebcdeaabaeeacaaddeccdcbcbdcaabdacecdaecdcdacdbdcadecbbbcadbceeeeaeabaecbabecdabbacebdccbacaaddccedecabdddaccecbcedbdaedeacdbbcdbcaacbeaaebcedbdddddeaccedcaddcebbcbcaeaeaeaabacbcdbeddabcbbcebebdeabceeedeabcdacbcbcadcdcbcecebdebaecccbdcdeeeaadcdbcdccadaaceadaaaaccaabdebeaceeecdceeeecaeedadbaeacebcabbdcbdabbaddbdaebecbbbbabebbbcacdaccebcddedccbdcddcabcccbaecceccebeaecaadbdebacaebeaeaacbcbcbdceacdebbbcaabbebeecdadaccdddddcbddbaaaeaadccdceabdcccbcbaabeccbacbdadcdabaabcaddcbaedccdbccbccbbedaabceaabeacedabbbdebbeebeddadbddcddacbebccccdebecbbdceaadddcdaeabbbdaaaedebbcbbcecdddbcebcdcaccbdacbcbedcadbcdbbbedebbdabaddbccbaebadbedcaecedeebeedbceecadeaddcaeaaacaeaaedccaaccacbadaeaecaabbddbccdabacebbedcdbddcaaaaebebcbeedcaeaebaceaecaeeccbcddedacadabdedcadcceadaadadbcacbcebbedadecbeeccaaddceccbeceacdadcddaededbdecdeebdcdcdeaeadcebaeabaccadddadbbdcbaddcbeaceddeacbcaaddcdabbababababebacdebeeddeebbeccbdcbbddebddcdabbadcbebcbaadbaedcbacddebbccaaebabbcbeedddbbbbcdccabcdddcebacbbdacadaaccbdcdcbedbbdbdbdedaaecedbeacabdebbabcbaabaaaeabeaddecaeeabadbecaedadacbdbdaeecdbbaceaeedddbcbaecbaccdcddcccdabcddadceaceccaecdaddeaedecbdbcceeabdaaabbbdcecdccaacdceaeadcacdbdddecadcaeebeaeebccceabeceeccbcecadedbaaaccddaadbaedcadcdccddccdacbcaadaddabebccbbbeaaacaaaceccddcbbadacaddebbaacceeadcedeeedbedbabdbaaecedcacaccdccadddaeaeaebceaadaadaddbebdddcacaebadcceadedbcebdebcbcebaadadcaeaeeddecaebcbeedceacbabceacaeabaaedbdcbaedcbdcabdabcdbcaddeaaecaecebdbbaebcbdaceebebecadbaddccaaceadaaabdabebdbaadbdaaecddcadbcddedeebeeceaebeaebeadeaaaadcbbccdcaaebdcbccacedaeddcabdbeedeedbdbbcebcddbcddcdecadeedccdcebcceaddddedabdccecdbcbaebbeacaedabdecabbddcecceaccddeeeecdeccbdceccaeecaabeccdaabccbbcdccccdddabcedecbcdbcbeadbedcbcbeeadabdddebbaacecbecbddecebebedcbcbbbaeadacaadadbeccaddaaaceedebdacacbedddcdeccabdadbeeececedaecbceabbadaadadddaecedbdbcedcbaacbcedcbbecaaeaabdbeeccdcdbbaecdcaecedddddcaeeeddcaeeebbdedeaabbaeaaacebceecdebdeccdddbdccadccbcdabdbcbbeaaeeecedeeacdedaedceacadcbcbdeaddadeaadeccecebddcbebddbddcdecebaeabcccbcbeaacabeeedecababeeebabcbbceecadaacacbccbccaaaeddbbcababbaaaecbddaeadbbbcebdddadbdeaecacceaabacdcbddacbcdadeebcbdbababedadedeaedccddadedadcacdabedbbeaacbebbeaccbebcdcbebbdaddabceeaaedecccdcaabeedaabacbacabccedccababcbcebacadccbcaaaabadbbbcccaeccacdaeebaeedbabddbccddceebbdebebaabebcccadaabdaacdbeeddecdadbccdeabbebabdceebdeaecaaebbddbabeaaaabeaaecceeebbbbadbebabeeacbeeacdbdedaadaacccabaebbdcaaadeaaeaebacecaaaecacdaebabaebabccedbebdbebedddbaaadaacbeaaaadbcaeedebdececcabcbdebbcbaecccbaacddaddbaeadceabbeacccbcdcdcaeecedaceecbbedbdaeacebcabedaaaedeaaaaaeeccdbdeaeaaebeadeabeddaabdbdeabbdaddaceaedbcaaacddcaeeedabccceabddebdecacabcaeccdbbdeacdaeeacbdbbcbeaadadababedeeddbebabacddaacbcccbcbdeadcddaeaaceaaadbabdaccbaeecbcaccaaecbeebcdcacbdbdcededaacebdbbceddacbbacbabeadebdecedeedcddcadccdadedbbceabceecabdcebbdedeecdacedbddaaeabdadeadaddacebedcedddceedccbbdaabeadeceaaecddcecbbaaebeaabbbcbbebcacddbeadddaacbbedaebabbcaedcabddeaebcaebdeddbbbbdbcacedaeadcbcbecadddeeeeceadeecbdcdcbacacbaadebabbeaddbedbbabceceeeddadccecadcedaadadcacaeadbbeebedcaaaadadeebdecaaeaddcecbdabdebddddeacbdddbbcededdebdeaddebecccccaedabbbdddeddcecadacdcedbaebdcaacdbceaeeeebdbaaeaddcbadcbddaebdabcbbbeaddbdacadddedbbbedecbdbabbaabdbabbbcceedaaccdadbaeaabaaeacacbcdaeccaadddedccddcdebecdcedcecaddccebceddebdaddaaddbabcbeaebaaaecbadeedccdddeabaabbbecabacbddbaeedebddadacaebceeabaccabaeeedacdbbeeeacdaadecabbecadddcedbeacbbcbacbdeebcaccacededaaaaadeccbaddecacebaaeaddccbadabceecacadabccabcacbbecddbbeddaabecbdddaeabbaeaebaceddddebeeaacddccebeecadceedbbbcaaacdbdcdaacbddceeabbdceeaecaedceabdcccbcdaabeeebecbeaecacdeddebdadcaccdacdeecebaccacebedccdbdeabaabadcdabccacabedceaabedcdcbbabdddcbeceecbcacededeaadcbcceaabdebcabcbcdaadbedbebdbebebdddebeeeeaacdbabbaababebbccaaacadeeaebadeadbeeeaccacdcdeebedbbcaacbccacebdbbcaeedbaebeeacdccdeaebeaadebacdceacddcebceceeccedebdaabbecbdcebdbabadebbcaadebceebbcacbcadedecbbeebcbbebaeeacacaebcabaeeeaceecbdbaedbbabeeabddbddcddacceebebbbddaaaadbbdadabebceeeaaedddbbaceabaeedceacddebebdececcaabcabdacdeaebdbddbadbbedcbbdbcaabceadecdbacbabdbecacddabdeadcedbdadcbdebacbaadecaddbbddbaacbcecedceadaebeeddaeeabeceaeededeaccedbbdcaeaadeebdebedbccddaaeeeaeaaccbebcdbacadccaeabcaacdebccbddcceaabedbeacebdeddeadeadcabbdeebbaaddaacdccccdaeddcdbebbcccdbcedbdadaebeccdbeddbadaaebdeedbbabaebcbbcbdbddbaaaebbdacbcacdcabbbdaeeebaeeddceeadcdccbcdadbbaedaacbdbddcdcaabccdaabceebaccabeecbcecaebdceccedbccbdaeabededebaedbdeebcdabcdbcdebbbadbbbadaaaebcedbabccccbddacacceadeadaeeadcbdcabeabdabbcceaecabecddacebccbbedcacdbeaedaddaaeeacdddcdadddddcebbeccedeecededaabaabeecadcabcabdcdaaaadecdacededceaeeaadcabdddccccaceabacaaedddcbbcedbdbabccdeebdacebceaebceccbbbbadddeeddcdaaedccddeadbdbaccbeedebaaaabebaedeacbeaddedcebbdaadccbbbdbdbabcdbdcedaebaacaabdbcbcbbecbecdabdcdcacdceabeeabbabcadebdeddbdbcaaebebbbccbdddaacccdcedeeaadbdacaabbedcadaaddcbabbeaebdcdbddedecadacdebbceeeaccccedacceccaddebdbecadaeebcdceadbcceeaaaddabbaeecbdbddaabbaccdcccaaecbceeeaceeacabeeecccdbacadaedacddeeebcbccdbdebabbbecdcebacdbdbcdaabcaedeadacbccdccbabeeeceaddccacdcaddbcbeeeddacabececacacbacacdebeeadbaccedecdadaaeaadaadcddcbccbcebbaaaabbadaccbabdbcbaeeebbbadaccceddbddedecaaabdcadaaadcacdbdcadaaaadbabecaeeeeadeaadeadeecbbcabbecddbbededcebbedbeaecabaccabddadccabdcdbccacdaaacbdbdaadcbecdbacdbdbadbcdbdeeadeddbdceacabcacddeebbbcbbbebbaddeabdcecbedadbbbbadbdabbcbaeccbaedddccededcddcdddbeedebdbceabdbeeceddabcbabdecbdddbbacbdbacdadacedebbceaadeeaacdaaeecaebaaaddcdaecebaebcdbbccdedcbbadbcbbabcaabcabddbbeaabbbadaeabbbeeaccbbaeeddaecdccbcadedeaeabdbeeeadedbabcbdebcaecdebcbbcdeeeaaaddaddedeeabccaeaedbacbadebabedaaaadeaebdacbecdebadcdaedaadccecdabecdcdcaedbadbeecacaeaeaedbcaaaeecceecdcccdbaddbaabaaecdeabdedbdedacabeeacbbacddeddccecebadaccbbacbeeeaabaacdaceaebeaacbdeddeebdbabebcbeedeadbcbaaacaaacebeeaddcadbcbcbceccccdddcbceeccaceaadcddbeeeeadcbbcaddddccbaddceeaeaedeeabceeaecbeeddacddddaacdbdceeedccceeeecacdeacbbceedeaababcddcbbeaaeabdababcdbdbebdaebdabaaccabdacebedccbaaaeaccaaebbdbaaacdedeadceeeaecdedcdedecaaaedcebbcdbbdeebbdcabbcdadaddbdaeacecebccebccaddecdbeeeeedeecdbcdbbaecebacbccebebcbebdecebddbbbdeaabbebddeebbbdddceacdaceeedeaebbdcadcebaaadadeeebebedeaecbeadebaedeacdcdebadcdeeecadcbcdcaeabddadabebaeaeedacccaccaecccbcacebcadceedaaebdbbdecbeacaededdadeebabeebeebecceaebcddbbaeddbdacbeecedcccabdbabdcceadbaedbdcbedcecaebaaebedcaacacabcbadacddbebdeeeaadcceedaccaddcaddaabecbbdebbaecbdedacdaeacedbaebedeedaddcabdddadadbaaeabcecbdccaccedcaebccabebeeeacdccbedaeaadcbdeadddcaeccaeebacbeebedadccecededebabaaaddcbeeebaccbcbeaeeeadcceeddbbcecbdcccbcbabbeddaaaebdaeebdbbabbdcedaedccdcbdeceecbdccddabbeacbbeabaabedcbbaacacdceaedaddcedbcdaecbedcccdbcddebcbbeabdddacddbbedeecbcebabaaecbecedcaedbebaeebacbddccdebdbeaaaaabbdcacbeececcbddebdbbebabdbadcbcbacacdecbdbcceaacdedddbdbcedeceaedacdcaebecaeebaebdcabdbcbeddaaabcaadaaddaccbedbbdecdbecdbddadacadaacddececbdccdbadeadbdbcceaacbabcaaaabdbaeadadebddcdeddbabcaebdeaaabeccdbbecaeeacacadcbddcaadaabcdaabdecdbcbaeeeacaebdbaabcbdceeabbdeaabcdaeacadedcadcdddbcebbdcdcceddadebebdacbdebeacbddddbabcdaaacabebabbcaebaaebdeaaeaedadbdbcccbcbebdcdaaedcabcaccdeecbccbcbabaaeaaaaeeaeccbcdddecabbbaabcbddcceacbbecccdebbaacceeedbcbeecdcecaebddbbacbedbbcacbdaeacdbcdeccebdcbbbebcedbdcadcadbdcaebeadbadcdbebdbdaabcbbcceebabadadaaecaedeaaeeecebcdaddbaabddacabdbdcaceacecddceeddacadcaabcdaacaadddddacaeadbbdbddbeaabadaccecdbecddcbcbbdaacdbbccddeedaebcacabcbadddedaccbebaedecdbbbabaddaadbdbdbcddcbcddccdbdebcebbeadedacdedbaebabcbeaeebbddaccececaabbeeabcecbdbdcbecacbbaeabaaecbbcbcdcbcaaebcceebeeeceeabbaeaacdeacceceadecbbddabcdabbacbaabddcacdcdccceaeeeabeccaedbadbbdeaedbddbbceecbddecdeadbccbaccaebbbaaddaadaaeceaaceeaaebbeeebdbbccdbabedeadcccaebdccaccdcedbdacbcbbbcdabbbebeadbbccbcbedebbbabbccdccdceebaabeeabcbedbccdedbaedbbcdbdeedbcaccdeebcbabbaacadeebdabcadeeebecabdbcedddecdbdacabebccbdbadedcaabdebbedcdeccceacbaacacddedbabaecddeeaaeecadddceabcbededbdadbbccbdadaeeceeebebdccbeebbcadcdbbcaddbcebdceccedeaacbaeaeceabebcdbbcbcebebaccaaebddbbacecadbbcdbaeecadcddcbccabbdbdddbabcdccbdaccabeadecbbecccabeabaabbdccedaeecabdedcabecadcaaaaeaaecebedeaccbeaeabdedcbecccccbbeddcabbaacbeacddeadbdbeeedbeedcabeccdccadadecabdeceabcccdaddeacdbbbcabbcccbbbacdbbaabcadcbcebaaaecbdcdacbabbcdcdeaebcdcdaceaaeccbdbbecbdccaacdbcbdadcabacdecdaddedbbadaaecbbbcdbbbeebdceeeaabaaeeadacbdaadcabbaccaebaecabbdbdebdabdbeeabdecbeaeccdbabaedaadeecdaaeacaecddcbdeccccddbeeddedcabbaaeacadceacdecbbaddbaabbcdccacbeddaeabdeceddedddccedbbabacdabddadeedcbdbabebdddbbddadaabdabcbeaededddbdcebaeedbdeeaadebdebecabeaadacabcddabeaacaddabcbbdbccddccbcdeeceaebadcbbebdabeedccabbebebacbbeebadcedbddbdbccaaadcbabdaabcabacebdccbaadddabaedbebcabcecbaedddcdbecaddbdbdcddeedbeeaaecedbecdbacebebeacbeedaaaeacbebdbaceecccdcbcbaddeadedbcadbbceccbacaceebeadacecbbebeeaeccaddaeeeccaadbbcddeecddeabddecbbeadeddeeddadcbceedabcadedddadcbabaaacbbccdcdaeaccdaebedbdbdbacaceeaeedabbcbaedccdacdcabbcdacbdddbacccebadcdbaadbccadccbcaabdaebedecbaaeacddecaeeeebeceeeaeadcbedeedeaaddeaaebeadeedbbccacaaaaecdaabdebdbbccdcbbdecdaccebeceaadedceeddbddbeaacdbacaddedebeabdabebbebeceeaacaedabddddcadadbcaeeebebcdabecceedabadebcbccdadbbdabcdddbcbeaeebababddaedeabebdcdaedadeeaebdeccbcadcdebcadddbedbecbcecdddcabadbeccedaadaedbccaaadacebcaeeecbacaaceceadeeddbeeeaacbebaaebbcedbdaeadddddbdadabbdbccbdddbdcddbeadcaaddbeeceddabeeddabbaadbddcceeddeadaddabeebbdbabacbebddbaccbeedeacebdcbaeddeeaabdccedeabdadcdbecbceacdbeabeaacdbbdadcddaabaceebdcbddacebaedbcabceaebadcbbdeedebecacdcecaedaebaabbdecddaeedbbdabcccdeedcbbbbeceabdddcbaacaebbaeecedbbdedeceeccddabeabccbaacdbaebbddddecaceccdacadcbbdbaaeabebeecaeaaabcbaedcaeedcceeeddbbdcbdbbacedadbdcdcbccbdcdeecccbcdaccdcebeacecaaedaeecccbadecdeaeeaceccceaeccdedbbedcbcabcdbbbaddcacedcceddbeddbbeeedbbeeecbebbebbcdeddebadaabeddeececdedbbeaaaceecdacbbadbeececcebddedbcdbbbcebaeecdaeebddbaacacdcacacddbbcccedaaeddebdbbaedbcaeeacaddcddddaadcedacaaceabaceededdaebccdcedbeedcbbdcbedbeabeabeacbacdedcdaebacdcedeecedaacbbbeddbabbabebcbeecddedeedacdbeadedccabdbbbdedceeeabdcacecbcccaaaceeceebdcedbdaccaeeddbddcbcdedbedddebbdeccabdcaedaaccdecbdeeddaaacdcbdccaccdadcebbebcaddcbaceeedaceccaeaeebabeaceeccdebbbbeedaabdecabadeaacaaeeaaebcaaeeedccacdebcaaeebebaadcebabbddaacabbebabcdbeaebebadbebcdecbcbaccdddbdbadebccbcceacbdcdecaacceddadbacccbdadbcbccceddbadcaadddeaceaacdeceebccadbeaeedeacecaabaeeeeccebdcaebaceaadaecadcdddbdcbebeecbeacbbedeebdebddedbadbcecdbddabccbedbcabccbbaedccebaddaeeddceaeccdbcdadcceeddecdcbceecceaaaeeadaaadacccecbbaddbeecacbadebeaeecbcdcabaedaebeeabcadcbadaebccccbcedabdbccbdaeddbdebabdaaeedccabaeaedadbacceaaecadaeabdaecaaddbbcbbdddaadbaecabedebbddcaecbdddaaeeecbceeaaecacababeccbdeabbebededaaebcecbecceabdeaaccaddddcddeaceacdbeeaacabebddcceabcbbcdeebbabbecadeeabdabbededcadabbbdeddedbedccdbbcbbdcccaaccbaabaacdbedcddacaabbadcbdcdabcddecbeeceebeaeebeecdbedbbaeebcbaedacdeceedebbbcbddbcebedadcbaedeaadccdcbbbecbabadadbceedacbbddbdbaedbceaabdcecadbaedddbbadcbbcecbeccecccaaabaedbccaabcdadaeaeaeaeddcbebcceabbdbedbcdddeccbbdbeacbacaaaeadadecaacebbeceaedeecacceacdccecbceedcceadeedebcabccbbccbcdeedeecccabbecdeeaebacebaedaaaceeabdcdcabedbacbbcabcadbbddbcbdeadbbedecdbccdadeeedebbecbddacadbacaceebcdadbabaaadcbeadecbcbaacbdaaaeccdeecdabceaddedcdbbbbdddcadbdbdddaedbabbdacaddbceeddceccedebecdcdcdaeeaedcebceccbabbbecddabaaacbeeebdcbcdcacceeabcedabebcbddbdddabdcdcceebbcbdbbedcbbdddecbacceebdcaaabccccbcacdcebeeacbadaadeebdaedbdacdccdbbbbdbaebdbedeaecbcacdcaadeeeecdacbdddbbbbcbeebedecededdbdcebcadbbbaedcbdbeaabdaacedeaaeaaedadaaaadcadaedaababededccbdbaabcccdeebcddebdbdeaabbcbbddbaebbecaaadedecbcacccacceccebdbeacdeacdbbbeedabbaabdccbdcdbadebbabcbecaeabdabeaeeccecdacacdeeddbaccadcacbabbeeeeeeeedcaeadebccecebccbadeedecbbaddbadaedbbeabacadaceeacaabcaacdebcbcaebecdbacdecabaabedcacecdecabbadaabadbeeaedcaadeadddebbccbeeebdeaddcaaeeaddaccaeaaccbdacdbdccaecedbddbacecbecbaaddebeccadaeebaecddbbcecdeddbcdbecccadcaceddebbddabaeeecedadbcdbdeaceedebbaeebdeacaeedaaabbaeaaacabcdadecdcadebabaebbecabdaacaabceeecdacaeeededdbddceebaaaebdbeaebddcdeeeecbebdeacccacacdcbdecbdbadddeeaaecaedeecbcaeaccedadcbdbedcabaeaebbaebebaeedcacadddcaebdddebbeaeeceadbeaabeacdcebaaddddeceacdbbecacedbabacbeacebcdbbaceacaedbccbeaebdbbeececbcdbcaddccdbbbeccabeeeeccaaecabaebbcccbbbabdaecdcbdaadaeacaaebcecaedaeaeaeaeeedbdebdcbacdedbdcedaaadacceebbebbddecebddccbebecaaebdeebdedbdbeecbeaccebdecacadadbdccbbbbddcdbaaacecadbadbecaeedbadbadadaacddabdcebeceaceeaeebcdddddcadcbcacdbdcdedcbeeddecacbbababcacbaeaadedceddabebbbdcecccccbdeabddcaacddabebabbacecbbcbbbdbbbaadacdaeaaabdabaecdebddeaabadeabedccbaabcaedbabaaccdbeacaddcbbdbbadcaaaeccbcbcdcbaadeaedacebedbcbcedaacddcdecbedcdbaeaccbcaececbbaeecbaeededadccbeabdbbcceedadabeabedbecebcecbcccdcdadbdccbaeebedbeadbbddaacbabcacebaeabaebadcdacdecadbacbadceadbebadcebeabcceaabcdbeadcbbeccbdaaceccadeeaaccdccbcbbbadbdcedcecadbcaddaebcdeacdcabbcbecdaacedcdbaebbbaeadedecbeaaceaedcbbccdccaedebbacdddadeecccbdedcccddadbdbedebcbadcdaebadbbbecbebcdbedbcbceccecddebdddbebadcaddeedcebddecaadaacccabbaabbcbbbcadebbeaecdaaceeabececdcbbcaacacecedededeccedaccbacebcaaadacbacddbdedeecedbcdcddaeeddabaeaecadddabaeaacceccbbeacedaddecbaaecbeaabbbaddbdcdeecdacddcebcdbaadbbedddeeedcbbeacabceabccdeccaabbebbdbadaadeeddebbadddacbaabddacdbaecaaeeeeaebebaedccabcecdabceadceaedcccbadbeadaaccadcebeebacdcaabeadeeedbcedaaeacbdeabbdacccedbdbdabadcaddaddcdaaecaedabccacbacdccdcecdeecddcdcdbacbdcbcbdcbeecbddbddbaeeddebbdeaacbbbcbcbdaebcbecdbeeaddaebbbbdccaacbdaceaceabccaabeaabbcdaddcddebbebeddaadbcdbeeabadbbaeacbdbaeadaaaaeddbacecacaaaaceddcecccecdceceaedddddabbedacedcddcaadcccadabeccdcecbbccceabbdebdcbaeeabbbceaaadacebbbaaabcbddceacecbdbdebceebccaabbddeecdcddcadcbbccececabceddceebcaeacbcdacbcebbbdbbabadccdceeddccddeaabbddcececdebbbabcbddacdadebebaccebbddeceadadbdeedaceadebeaacdaadeabcaaceacdbabcdaecadaeddbaaacdebedeadbabecabacadacccecdecbbbabdbddbbebeddebcccdbeddbbcecdabaaeebbcbdabbddbbdcaeaeaddadceeeadeebadebceebddbdeaebaddedcdececccccabeecaecacdbedecbbecccaebdabeaddcbbdbbbdbcaeccddddeeabbdcbdeaedbdedadadbecdccadcbddadcbeaeeaeedbbcbdbbbbcddaecacbaabbbecdcbddcbeaaccbbcbabcbebebdccabbeddabcddbeadccadededaabbcadcdedddcababcedadedbbacacabadcbcdccadbdcbcceadabeacbbdecbbecbbabbaabeceebdcdacebebaebdbbedcaabcadacebacdeeacbbcbecaacdedebeeeaeaaecbacaccdcecaccbdebeeddcaacbecdeeeebddabaddbededcbbaabcddebdcbedecbadaadabdaeacbdcdcbbbbbdceeaedadeaadeccbadccbdbaabbdbebeabbcddaecadcbcacdaaacbadaabbbddceddebaeabebcceecdcadeddabeedbdbadccdedddeacdabccccabcbbbebdbddddcbecedbdbecccaaccabaedabecaddbddedaabaedbaacbedbedccaaeabbbbdddadbceccbbeccdceedaceeecbcdceeadccecbeebcddbbedccbcebbeecceaabececccddadccbebbabdaadbacaeccdbecbedcaddbebebccddeaadcbdeeacaeeaddabaddcbeebdeddeeecbbeccbceacbeadaebaadcdeddeabccbbbeebbedbebeeadbacadcceedadcdabbabbaddabddbdbbebcacbeccadedbcbecdedbadbcddcdccabbbecdebacbbddcbcbdeabcdcedadecdecedacdecadcacacbdcabaabaebceedecdeddceddbeacebdcccdcbeceaaebbcecdaeeecdeabccebdeccacbcdbbbcceaecebdddeeecabeeaecebccadcdaaccbdbbceadaadeceacbcedccaaceebcaceedbcadddeedcecdacdadedcdaedcbdebbbaadbaecececdcaaaedcacdaeccdceceaacedacdbbeeabaabbccaeeadadbaaebaaedeaaadaaccbadddaaceeacabddedbacbbcccccaeaadbdadbcecdcedceabdacdabaeabbedebdaccedaedadceacadddcadabacddcdcdbaaddccdbdcceabaabdeeadcbddbdaccbdcebbbaaaedaadaadecccbeaaceebecadeccdaebbbaecebbedacdbcbdccabadbcbdeeaceaabbecbdbccabdddacadaeccbcdcbbccddbecedbcbcaaaebcebdcccaeacdcdaddacdddacdaacbabcecdbdddbddcdcaedecdbdbeddbcbcccdecbbcedbacbedcebeeeabcabaceaacdcdacddaaaaddcdcdacabecbcdaaeddbdeccecbcabdabeadddbadbebdbcedbdecebdcdeddaaecbcdbdbaeccbbbbabedcdcecaeccddbddcbcedcbecbeddacedddeabcbcedaaababdcbbccaaebecccddacdcdceceaebbbdbaaceeeababedcebceeaabcbdeedecbabbedabbaecbabdbeabedaabcbccdeaabecdcbceabcdccdebddcddcabeaccdaedbeaabbdcedabeeebececbcbadecadcbcbbbdaedbdaaedbabdeeeadccdabecdbcbdabeadbcbabceaceaeeceeccecdddaaddabddadbddcaceabcedcaddecadebaddeaaaaaeccbaeebbdbeaecbcebccbaedccdaaeecbaeaccabebebaddedeaedebdebceeaaeddeddcedacecaacedeacdebedcdadceedabaaebabbaebebddbacdebcbdeccbdcaacdeaedbdeabeceeceecebebdabcccecadbbeadbaabaccacdacaaebadebcedacbbcaadccceecbddbcacccaecbecdecaebcbbaaadccddcabcbacdbebccadebdbddbbbeaeeddcaabacbcdaaadbecddabebeecdbabbaacbdcecdceaedbbeacccecbdaadccbeeadeeadaeedcaabcedcaccbcdacababebeaacaebeccaaceadadebaaedcdebebbeabbeeecbbadaebdeacaabdbdccdadcdaadbcaaeabbaaecdecabaebebeacbadcdeeadabbaddceabbabdeebcadecaacdeeaadcacabbcdaedaedcebdabdebbcebbaeadaedaecbaedebdbaebbababcbcdaeedddaeacecbddadcabccababbbbebdbceaeeaebcbaabdcacaccdaabaaeeacdadebdebabbbabcebeaceceabbdabacceaaabebacacabcccdbbddaecabbebcebeeaecdedaaeeceadeeedbedbbbeddcdbbadddddbdeecaaaaeebeaeaeaebbebeabeeabacbabaeebdcacbbbebbcdecdadccbaedddbadaeebeeccbdeacbaabeeceeabdaaeabddddabbeaedadbacaaeecaabcbeaacdaacbabdeeaceecacdbbadabecaaaeaecdbbecaebbbbddbcebacbbddbdcaebedcaedaedcedacbbdcaabeadceaddaceadbaeaddadebadbcabeccbabebadcaebabcbcddeaeacdbbbdaeabdabceadcadcbebacdebbcaecaccbbbdadaaaabbcadabededeeebbadbbecbbcacedabbadcebcacdbadedaceaebdabdbbddacaaddaebbadadabcbdeaecacdcbcdeceaeaaceecddccbdbbdbadbbaeebacddddcabdebebcababeabaadedbeadadbedacabccaabadccaebcddaebddecbcdabadebdbccdccdcbeaddbeebdeecaaebcccadddbbbbcdaeeceecdcabdaedaedebdcdcebddcbcbebaaeccebaedeabedaababddaabcdeacdaedceaeaaccbccceeebcebbaeaadebcbababbdbaadcaceaabeaecbedcbddaabadeeaecdbebecbabceebeeaaeedbaeaaaaddcdbddaedadeaaddcaeaabdeabddccbeeaecdeacdadddabddaebaccddadedceedacebadaaecdbaacebaaaccacdeddacacecdaeebebdabcadbacaccebbddbbdebddbeeddeecbcabdabddbeaccacdbdeedcaecbdabcdddaecddedcbcdedeadcacbaababebdbecbdccccbecdbaadcaeabadadebbddbcedddcaebeeeeceedeabeecbabebcbdaddaecaebecaaeebbacaedcccededdabdadcbdebccdcaaeceeabeadabaecacbeabeacbdcecbedbbebacbebadedaccacaaaeeacecccadebacaacdcadcabacdeecabacddbaeeaaccecedadbaccdcadeccadadecbaaebacceceaacaaeadbbeaeebdcdbbcdabebcbacecdccbdededbcbdbdaeccdbeaddacdbcaedacaeabcdddcadcbcdddbccadbdeabbdbadbeaecccbaadcbdadcebcebabbeabdecddbecbebeebdeddebabedaacbdddaccdeccedeedbbdeadddcaeacbcddddeceeaebbadbebdceedacacceccbddaabacedbcbbbbebbcbdedcccadcaeaaaaacbcdaeecbedccdcdbbabbeccccbdecbaebbabebadacdceeceebbcbbebecbcdbceaadaeccaeabecebacdbecccabebeaeccbebabcdeecddbecadddbeedaeacbbdabbaecddbaeaaccccdebcdaebaaaeabebaadeccbbaeebccccbcdbdabcdccedadccdabbebccaeccebeeaceddacaabbbbdebedbdaddcaacabadececebdadbabcbbadeedbdeecbbbeaabbcaeebaabcbcbcbcdbeeaccccbbedbacbbdaddebbbccecbceeccceecceacaabbcdbaeadcaaedbbbdbabeebadbaeabdbbcdceeedcacaabcedadbdbcbeabeddcbeeecbbeddbbeaaaeddccdbdcedabeddcbabcebbccaebdccbeadadaddeadadddcdedccdcceedcdcbaadcceddccceecaecdccedaddbaadbdaacbadbecacdbdbccaacacbcdbdbedbcadbacedceddeeedeceedcdedaabccbbeeebcdababcecbddcaededdbbeeecabbcccdbcbbdcaedecbcbeecaabadbbeceabddabbacaccecbaccdcceeabebbabbdaecdbebcccdacbdabbaebebeaeebddadaccbadbecbedbbebeccdbedcdbbabaebbadedabddbebeaaeddbcdebdbcdbdcccaaddcaeccdbeaeccdcddcccadbcbaadebbeccbccacdeaaecdbdebcaecdebececcccbcdebbabedabcabecdbcbcaaadeccedaabacbbeecbbeaaadacdeeaebbbaebcbcbbaeccedcaadecbbeeccdecacacbbecbecbadaccbdbdaaaadcddacabdadbdeeaaaaabdeadedaabbceeebabaabdabaccebbbdbeebbcdceaaebcdddaaaeccaeecbedaaadaaddaedaceccebccebbbaeccdccacbdcacbcdcaedebceebecbeabdaadaeaddabccabbaeaebaaebbcaababaaeeddbaadacccaddecadbdcdaaacddbeeacdbaeaaaecebaecdaaeececcbcbabcaeabcadabebaeeceddcdbaccdbaeaabaaeddcecbcaccacdcdcadabbdedaedaecdeaeecbeadeceacecebdcbeacbaebcedddcacbedadcbacabaeeeebbbddaadedeeeedadecadaacebdadebcdecbceddacceceeeeedcebebbedaebabadadabddebceecedebcaedbcebaacaaceebadecaecdacacbbcaedddecdaccddbbcaeabcdbbaddcbcebbcbaaeabdeabbcaadabcddeeccbabeadbdcccccdbecebebcbcedecbbceaedddcdccaabceaedcedeadbdceaebcabbeecacbdcecdbadadccdaedcbdaecdeebcedeaacaacdebebacacbcceabcbebeedbdbbedacdeadebabcacdeaceedacacebaaabbcabaeecdccdddcadceebeabebabddccadacbaebeadcaaddeedcdaccddabdcdeaddaedeaddeccdceedebdedbeccedeccadacdceebbabeecbbcbeeeacbaeebebeeddedccacaaacdccdbcdddbeaaebebbdacbeabadbcceeabdeddbedbecddebbdebbdcabcdcabacceccbaabeaabdaadadbabccbdadecdaccbdbaddcdcdcebdcdaadabbabdcccbacccddecbddceabcadddceedaabdbebccdeebcabecbbaeccddddceddeebeaebcccaaecacacdebbbbabdbababcbcdcdcebebaccdbabbaaaaadcddddbdbccdbddcadededcabcdabaabcbcedeacabeccccdcaabeebaddadddaedccebbedacacaaabcbdaeeedeedcaecaecdcaebadbbaaeddccabddbdadedaebbdaedcdeeebebdcdabeaebccbceaabaeceaabadecacbccbceddeaeaebccdeabdebbcdbeaacdbcabcdebbcaceceeeeeedaabaaccedddbdcacbcabdcdeebcbaceacaecadbaceeeebaabdaacaacecbeaeccbabcccdaddabddbedccebbbcbbeaaeaaaedcaedbadcabdddecbecabebadceddecabdbadcacbdbbbeaaccdaaeeddcddecbdbdabcbbadccacdadbbacbcdccbdccdeccbddabcceeceabedbeecbdeaacbddcaaabecaeaadabcbbcdaccabaababcdcacacaceccdbdcabdeabbceaadebcedceecbeddabacabcdaaceccccdeaccaebcadabbcdcccbbdcacdaebcdbaeebbaddacdbacbabbdcdaebabceaeadcbccbdbcbcebdeaeadeadacbecdedaebdcddadeacbabcdedcbbbcaedbeacdeaeeaaeddcbcaccabcceabcebbdcceececaeddacdbbcbeeaaccecbedcdaabeddeacadcaeebabbccebcedcabecebdeebeedcebbacbddbdcabaeeaaecaaebcbdecccbcbeaaeeacdaeaceedecdaceeceacbeabacadabbcdbaeedaeacebccaabcabaacadcbaeeaaabedbcececedcabbaecbbdebddcdaadedaceeadcaeddcabcbdbdabcccebddadcadacaeadeaadaeabdedebdbedabbecddaeecedacbcbccdcdbdaadecebecaaedbaacabaebccadddabecadabcccbedbaecbcddceabcebabdbddbacecbdbbcdbcbbbdeecaecbbbadeceedbdeeaedbdabbcbbabcdccceeaaecdadeecbbcbebacdccbedcdeecaaecabbbebaceacdabcdbdbbebdeebdabcaeaeeaabcbaedeeddaddcbdeedacecedbbbabcecddebbbbacbecdacdddebbcbeeddadddacaaebbbeacbdeedbdaccceedaeaceabeaecaebcecbeaeeabadacdeddeaabbbdeceaceddbbaaceacddbcaccbacabcbccbacbbdcedaebaacbcdbadabaaecacbdcbceaadbdaadbeecabcbadbcbcbaeccdcaadaeeacbcbadaedcdadaebadcbeaebedadbabbdcceaecdbeaaaacedcbeddaaddcdabeeeceebcacbeeebebbaedbaedcccacedcdddccabededcbdddbeabbcbaaedcadbdcbbbccadaddbdbabcdbdbccbebcdcbdcdacecdaadabbbadcdbdbcaabaadeedaaedeaeeeaeaabebccaadbdcabdabcbbddbdcdeaddabecebabcdbddecabcebbcabbbaacadabcedcdbdeedccdcaeeadcbbcbdeaeadabdbaaaabebdadcbcebbabeceeebbadadacebacbddadaaeaadbadaeaacabaebdedddccbbeeeadbcacaaadcaeedecbbaccceebeabccabbcdbddadcbaeeebedecdbdabedddeebabeebdccababeaedaecddaacebdbeceabaddebbbdccbdcadaeddabceecabdceccdccbecbecbddbbcadaddeaeeaebcecbacbcacbebcbdddbbdcdeceaecbedcabadabcdddebcdcddbbbebbdeedbcadcbeabceceaebecdadbebeecbcbcbbacbababdcdeebbaacabcecccbbbbeeeeeebcedebecacecbdaabbabdeebccbbaebbadbbeaedbebceaccaecaedecbbedbadacadcecccbbbadabeadbadbcbceecaabaccdcadbbdbbbbdadbdddbccadeadacaeaeeabdbdddcededacbdadaadabbaeaceeeadbddeaebbaacbdaacccaeddeeaabcebdaddccbdbedcdcddaebeadeedebcbdbadcadcbcbcedbbaaebaaddadbedadacdcdbebcdaabceaeebeabddedcecbacccdcedaaadeaddebdcebdabdabbeaaaeaaaddbceacdbaaceecaecbbaedacdbdebedbadbbdebabbbaeeeebcddcdbedbebcbdecaadaababbcbcddaacdcdaebcaabbaddaadedcaaadcdcdbebaaeadacbdabebeededddabaddcadabdbeabdcbadecbbeacdecacbecaccaddaecdbaddabadacddddccebcaacbbaaadbeacceccebcaedccdaeebdcddaaacbaeebdbdecdaaabacaacabbbaaaebacbddeadbbccaedeebeaccbbddabeececbccceeeceacacadcaacebdcccedaadedebbebeaccaeacbcbdeaaebcdababeacbdbddaedbbaaeddccdedacdceacbdbaabbcbbedcdbbeeddbecceabddabaaaddeaaacdeddcdccaeaebcaacbbbbcedbccbecdaaeabcedccaceedbcbddceaabceacecbbbebbbbbedcbcbeeddedaadbbccbbbacdebcddeaceebebdbdccdeaecdbddeeedcbcdbbebcaceccbebdceddbdacccaebeddaaaaaddaccbbcecacccabdeccccaddcbcddecebbcebcddeaddcebabceaddcaebcceeecdbbabdddedecbaaeaebdcaedeeeebbadeaaddceccdcaaddcccdeddababbeeaeedadccdcbeebbecabbdeeaeacecbaedbbdeebeadbbaebccdaedadedcbdadcedcbcceacbceddbbbabbdbeebdebbdddabaaeaeddbaadaaecdebedcaccebccabbedabadcdeaebdbdabeaabccbbcdbeecbdcaacadbbeedacdedbadadadcdbaadbaceaaaabaabdeacbbbebbbdccacacddedbbdcdccacacacecccdbcdbcbeebddeddcbbdbeeabacaddbbccadbadeeebcbcddcbadedecbacacdbeeabaedbccadccebddcdabaccbaabaceceaacedeeabebabedbdebabbaaedddbebdebeccbabdaebbddbcedcbdceddebbabdccdaaeadcabcbeacedcccbeeaeebdecbadcabeddadddeaadadabaaecdabaccbacddcadbabdacbdbbdebbadeebcccdbcbeeddaeacbecaabaceccaecaddbcddbdebaebcbadcddacdcbddccabdcdbdeccddcdaeaeceeceddbaeccacbbcccaeaddcadcecaeccbeeadecdcdaebedacbbcdacdedabcadbedeeadddadeeaeeeaaacdccebaaceccabaedbbbcbebaacadaadbccddadcaeaccaeeceaeabcadbdcdccedeeeeadbaabbedadaaccbebbccbdaddccbeacbaecccddaaebbcbdabceeeceacaebccdbebabdedddbacdecbadcdbddbadcdccdbaceebaaeaeaebbabdeaecbaaaeeacdedbbbcccecaddeecadcaecacceaabbeebdedebaadeeeabaedcbceccacbadbcecdcbaeedebdccebebcacceaecceeedbacaceedccaeaaccecddcdccdecebbebcdabbbdeaacbdbebbaeabbcadadcaccdbdcbeabdaeaeeeddaeeaddddaacdabbebeeabebbdbdacbcdbebacbcadadbaecdebcbccedaedcebedcbceccecccddeeacedddcecedbdaccbcdccebeaabdaabbccacbaaededaabbcbceabecacadedccbbbaddbbbdbdacbabddbedadecaedaddacdcaedcbacbaaabacacccedebcedebacebacdcbaeabcddedcdaeebabddbaacbddbaedacdeeacebcdedaedbededdeebceaadacdbcebaeadadccaceedbdeabdbdecbcdcbbdbadeabbcbbdaeeddebbcdcbdcbddcadeeddabaeecbaeadcdebeeededbddaebdecaddeccccebbcbdcbaeeeccdcdaeaecbcabcdbaaaadcabbcbbabdaeccdaebacebebebacebcadbceeecbbaacececcceebacbbdebdadbaaeacdaacadedaececcbbadaeeeabddccadceaeeebbbdeacebeaebcdbedadecedaabdeacccddbcdddadaaeebbecacddcbedeeeceabbcdcdebcbbbdddaeddeacbecbcdceebbaddbbbadbdadcecdcaecbeaeeabaaacdbdaeeeaaceabbcbaadcbdddbdabaddeecdddedcccbcaabdccbaaebeccaacecdbceeabeacbdbbaedeaccabeaacaeacaeebbeaadacabedcaecaeeadacaaccceeeebacaaccadcbeccdcecedcacaabecdebccdddcbcebbaeeeeaabaeadcbddeeacacdbdeeebaaebcacbeecabaccaeabdcdcaaeeebbcbcbeaebbdbabdccccaaacbdceacbdccabacdceadcbbadccadcaaccddcdadebccbdbbdebcecebeabaccccdbeadcabbdaeacdebdbdbbececbccbddbecedbcbeaaebccccddeebceabeeeaebedeaceabdaaceaddcdaaaadbeeccdacedeeeaabaebccdededbebeaecdeaaeabeecbeeebecbceaecbdbbcbccdeddcdaebaeacdbbececaaaebccddbacdbdbacedededcdbcbdcaabdaeebeeebcbaddbbacebcebddccabbcdeedaecddeedadcebdccbbdabeddbedbcabccbcebeeacddbaddeddcebdcebacacddbdacbbdedacceeaaccdceccccaaddbceccbebbbdaeaddeeaedbaeaeeaedceeeccbeebdaecabdeabcaebdedcdbacabdbadeebadbcbacceaebbcbcbdeacbbbccccadaddbeddbeedbbddadddebddeccccbcbabdcbccaedaadcbacdccdddaadeedadcddbeecaadceaeedeacecabeeadbbbcdedccdedabacdddaccebaceaedbbaedccaaebaebedaceeaddccdbaceddcdaddcbdebbcdedcdacdadbedadbcbeabaecaaeacdecbbcdebabeabcbabeccacaabaddabebacbccccddaabdeeededbbccdccdecbddddbdcbcdcceedbbabbcddaddacdadddccddaceaaeeebdcabdcccbabceadeebeeceebcdaccecacadedccaadacebdddadadbcaeddcabccacbcaaeebcebaccdacdbacbbddacdaaccdcacbbabbeddbedeceddbaccaadcabccbddddaedecadcdbcbacdccbaebbbaedaedadbcdbabebccccedbdccdeccbbdaecbaeccacdaaacbdabccdaccbeecacbdbdaeeccababdebbaecaddaecbbcdbdbeedcdaceddcaddebdabeeacdbdeaccccbcbbaeddacceccbbceceebbedbeddabbcbbaceddacbcdcccbaaabadedbaadabcbaddabcdadbbebadeabacbedcdcbcdbcdcebacaaabdedbccaebebcebcbeabebccecaccceeaacdcdcebdcdbcbabadbaccbeeabcbebacedecaccceecbaebebccbdccbcbedbebdaebddceddeaeacdddebcedcdebbcecbddebbacacdaeebbdcddeabddaeecbaaaeaccbedecedbeccceadbaecaddcebeccedbccdeedddacdbccbadbdebadbeaadceecaaaeecbbbeaedccaeddcecdacadcabdbbcbdbcdccdbbedddcbaebcacddbddebeaabedcbeeeecbbcadaebecaaebcaebcdeecaadbeacdeeeadeddddacbbbddebadcebddbaabddaeaacaeabdebbcdaebccbdaabbbaeceebccedbdccbabccebbadbeccdcdbbabdedbbeeaedccebedbdeedcabeeedbbcabebaaecbeabadbcbbedccbecdaacbddebccededddbccbdccabadaaccabdadcedabbecedcbbdeedacbaaedbdcddbbdbdeebadaccceceabdcbcdabdededbabdeceddcccccaecbeadaeaaabdcdcebadddaeeccbceeeeecbadbacaadcddabbaabccacdebbacbcbabcdbecdedebedcaeeedadeececbcedaabcbaceabccbabceadeddddccbecbcbbbecdcebeedabccdccbeabdeccdecdbeaedcbdedaeeadeaeaaceababcbbcddbcbdbbbaeeebeedabbeebaecaacecdceeaedcceaaddacbecaedbeacbdcccadadbacdebacddedbcbedddeaacaededcacadeabeaabeaebabdedbcadacdeadbeebdbccbcadbadcecbaebedeadceaaebcbbbcbabbeadaabcbabeceedcacdabdcedaeeaaedcceaceeaeddaaeedabbddcdbcceebbebcaabaccdcadddaeedcbaaadcbaaccdbcddeaaebbabcdeaccacdceaecaaedcacbcaebcebdcaebebadedeadabaabaebaabebddacdeaaabbacdbcacedaaeebeacddcabeedddcbaceecbebbeeaccedeeacdeaebbaaabbecaebaedcedebedebacdeeedceeccacccbebececcbaeeeeaabdacabceeeadebbdcbbdcededaadadecbeaccaaaacaacdabadeaabcedbdddaaecdecdebdaebaabdbcbbecbcbbbecaccddeddedebddeaacbceeeddbcbbabdeacdcaaebdeddecadcedbbbbdcdcddedcdebeeabcddeaabbedbaddccaecaaebccbbdabcdeecceadaacebdecadacacddeddacacceadbeeaaabaccdeeebaeeacbdaabceacdceeacccdbbcedeeebceeebaebcbedbaedccbbdeccaccccdacdcacbbcbdedcaebcddcbbadbdaedacbcaaaaceadbbbabeaabdbbcabaacaddaedbaebbceaebeeeadaacaaaabebdddaacdebecddceceacdebdbaebeedebacedecedcdcaaabbbeeecdbcaadabcdbcbabebcbebbacabcccaabbcbecebcddbddcdbaecaebbbaecdabddacbbadceecebeccddebddbbbdbdadceeaddabbbcccaceadcebeabddcbacbbbbbadacbdebdceeeeddaedebcacaeccbaebacaeacbcabccbecaddddeeebaecbddddbbecccbabbadabcdbdceddaccdccbdccebddeaeddebdabadceedcdeaccecebebbedbbaddeebaaabacedcbbcedaeccdaaccabaeedeaabebadbceccdccbbbdeadbbbbcdcceabddedaeabaacbdecddcaeecaccaadccebcbbbaddceebcabddbcddccdbcdedbabecaebedacaedcbdecdecdedaebbddabaadcadbbdacbeeacdccececdecadeaccabcaeeaeebbdbaacdddbabcdebcbaaeaeecedecbceebbbbacabdcaaedddcdadeacddbcdddbbcbdbbccadbbbceacaedeacbabeaaeecbecaeacdcecedbdcdddcdcdeaecbbaeadbebcebeaaccdeecbccbadacedbcedabeeecedcbecadebaaebbceeecccdabdddbddebadcebcdcddceabaddebbebeebdacadcaedcaeabbedaaebaacaceeecebbcdebdbebdcabebabaadbccbdaaedaeeaceacbecbdeaedcceadaeccbcabdeecbdcaebddebceacdebecebdbbbbadbccdaabadbcedbecaaebeedcbaaaabcbbdadbadccccabbeebdcbebaeaadddccaccbecccdedacbbccdccbaaebaecceceeeadbeecaeeddbcdcccdbbaeaabcacebebbcbecedeebdbecaedcbbbeaabecbddbacadebdaebdcbbbdabbabbaaabbbdeccbbcebdececbcbaedcbcdbbcceadebcdacdbbcdbeabeebbddadbbebadbbcadaacbdcccabcdeaeabceedbbcabceeaecdcdcddaeccdaeecebbdadcaadddaeabaabcbccaecccdadeabdceceaccaeddbcaaebcbbbbeddeecdcdaadedcbcdacaeebeabbdcaebaebaeabcdcdabedbbabaebcacdbcadedadaaaccdeacdecaceabbbdabcaaabedeacddecadeabebdebcdebeedccaaabddcbcdedeaacaedecedbdacadeddbbbdbbbaeaadbddcdccaabeabecebdeeacbaeacceddcadcbdbbaebaacdddeadeaebeaeedcaebaebcaebeecdbedaeddcecbabdcdbeebdbdeacdbaedbdbadaadaccbcddaebdabecbccdabddeeebbbbeaddbdedbbebdbcadddebbeeeedaeabbaaddcaeaebabdcbdceabcacaccedbbddddcddecadbabecadadccccededcdbcccddebbdecdcabcdcdaacbecaacccdeddaeaeebdbeeacabbeebcceeadaceedcbaaacbbcaccebaabddaacabeddecbdbbbbabecceabaebaccaeaccbcdbedcbcaaabdcdebaabcdcedbceeaecababeabaeccbdebecdcddceeecaddaacabceecbaeccdbcebebceadadaeecbaedbcbeabbcaadedbdeeaabadccbcaecddcbaccdcbecdeccdabcdebccdbcdbccdbdbdbabdcdbeeddceebeabebdbdeebdcabcadddbdccecccbaeeddbdcceeedeadaebddbdbaccbdbaaeaebbbcbeeddbedcabcadcdaeeeeddcabaeeeedeeabdceebcecdaabcdeedddeecccbaceaedcadecebeaadbbdbcbeeadbdacbeabaecccaedecbedbcedbcdceadbbcceaaccacbdececcedebdbadeaeebbcadaebabddcabdeeeeadddcdbdecadaaeddbdabcbeeacabdcadebabacbaaadbdbbbbcbadeaaceceaacebdeeacdbccadacabddabebcdcdcbcbcdedcdacebdeedbbcbdedaeebbdcddaecacbbcababcbdeccccdeaccccdbbdbeebeddcececebbbbaaaadeebdcaabcecededdbbccadeeaddacdccdccbabeeceecaabaabaaaadecdbbcceeabcadaccceeaedbaabadbaacbbdebceaacdeceabeaaecdedbcecbadedbecdebbeddbbcbcaecbadbccedebbedeadccccbacbbbaabcebeabddcdedaedbcaaeaceceacbdebcbdbcbacccddabbbacbbcdacabdeedaeddcbcecaeedaedbcbdcbaabadddaabacceddaaddbeeaddeeeccacbaceeaeddebdeaadcbedabeeaabaabeabddabadcebbdaebadcbbbeaddaeeecbdbaaedbaaebecdeddeaaaaebaceeaecadbbcecceadeaaddcbecdcedceabaecaacbadcbdecdebdecdddeeaceebadbccbabeadcbadacbababedecaaccddeaccdbedeaebeaacbeeeaeaeecbbcaeeececbcdeeeabcdcddaacbcccaedbaecbedbdcebcccebaaeebabeecabbbbbbbbaeabeeebadcaecaceedbcdbebaaeeabdeadeaaecbabaacebcaddcaacababdbaaeaaebdcbbbbcddbaccdceaaacaadbaaeadabbadcdbaccbeaceebacaedbbecaebaeebdcddccdbdeadaeeccabebcebbddbccadceabecdaebcdeeeccacdddddbeaabccbdadcabbecddcaabadacaeceecaaeeadabbbadbdbbeadeeebaceaaecdeeceeebacdeaaeccdceeaccaddbbcbcbcbcacddbbcbedecebdeeadbbeeedbbbaaaaccbeeddaaebebaedadbddbeebdadaabceeebacebceaebecbcacedcacecaacbabdbbbbbaddecbacbccbbdcebceadeeadacdcaadbebeedceadccddbcbccdaebadecddaabaeeebbceeacbccdacdcdaeadceecccaecadecdaceabccaaeaeeaeceaaebdedcacdadcadbedcbdaccdcdcebbacacbdeceedcabdcddabcceedcbdccecddbedeceaabeebbbbddadbdacebaabbdbbcdddddaceddddbdbddbabbdeecacbdeaddbebcdedbcdccecdaeaaabbabcbdeecbaccdcaeeedebadabecddeebcbddedbadcbdceadaceddabcecadceddddaceebabcaecbddceaacaebabeadcbaaebabddacdcabababaceccbdabbbdcddcdcedadacbdedccddeccaecbedcadbdebbcddbedbccbeeaeaaddbbeccaedeeaeaacedabbadaeebeaaceebbbbdbcdebeaaaaddbabdcbacadceaebabaeabebecdaceaccdaeadcdbebaecbcbebaddcaabaccaceaacbdaabdaeecccabceaeaebddcdaaceeeeedebdecddeedecdbdeecdcedaeecdebacbaddcdceeeaeeeadaeddcacaaebddeeacdabeccbebecbadeecccdbcdcbcccaddcabbebedbcbcbbcecddadeaccbeacbeddecebcdbddaddecbbebcdadcedebaaaddaccecccebdbcbadcddaebbacdbaddbbdebebacaaadbceebaacdededdacbcddeaccadabecaabaeacbebaceaedaeccceaeaededeccdecdbdccbdbdcaeecaabceddbecabbececdadcbdcedeccdcdbeeebbeaacbcecaaaacdccbcccdedbcbbebcbadbbaaecaebcdbcabacbaaebeccbabbecccbaeabdbedbbceabcbddbadaeccbbeddcccccaecdeccedcecdeedcddaabcaeabccbbcceddabeaabcbcdaecdbdeaadbdbddebceadabaacbadecabccbbbbeabbaaeeaeeadbcecaeedabdbceeeabcecacdaabccecaaadabdcddbecbabdeaabdddeadbccacbabbdbaabadaeddddcbecbcdebbecabbadbaaadacdbeeccbacebaadcceeedeebaddccdcebcbedabcbddcdebbccecebebdcbebcbaecbcaaedbcbccabdcbecadacdbdadbceaccaccbcaadcbeeacaaddddacabecbebdccdbdccbddaeceaaabaacaacdddcedbadaabdbbecbbbadabbbaacbcadcebbedabdbbddeadcbccaeaaccaddcaeaccedeccaaabdcaccbdeecbdbbdeceabaaacadddbdaddaceeabdeedadcdcadedaedbdaeeaabbcbabaeceeeadbcbaeebcddbbdbaaadadaececdaaddaeeebecdbedaceabdbddeccbbaceccecaccdacbadbaeddeceabccdbadcedadebecccabaeddcccadcaeabbceadececbddebbcaeeddaaadccacedbedeadeedbbbebdeeacaaabdcbeecdbbbccdbccbcccecdceceaecbbebcbcbeecaaeadecdeeaaaddebdbebcabdabbaeabeeccaeeaeeecdacbbbeededdedbeaaaeccdeeaabadabbdbcbeaeadaddbeccbecbccdbcdcadeecbedbbecedabdddcebceddaaecaedabaaaccdcedacbaecbdecbcdbceccdacebccdccdeacddeeedbebeabbedabceccaedcebdbcdebecebdbaeaceacbdbbdceeebebbacabcedaacceaddcaadedacddceddadcdedeabacbdeebadeebcabeeebcccaabcbdbdeabeceecdbecdddedbebabedebcaacdabaeaaaabeaecdaaceeabccdeeebcabecaecbebaaaeedcdcddedeacdcbdbedcdbdcdebdddbdcddcccdecdeecaccdabadeacdebadaacaaadcecbcdecccbaadbeeeabdcddeccdcaaeaedabecbeacdebbbceedcdaedaeeabdbcbaadeebdaeccccddadabdddbdcebdaccbeccebdacdbbcbdaacddcebbabccaebcaabbccdcbcbecccbabeeadbdcdaacdaedcdbccadeaceddbdbeeebaaababbaaaeeebdbaccaecbedaceccacacaacaeadadceaddabccdacbbaaabcdcbddecbaedbacddbebaacbcceeabbebedbececcecdcaeabeceaecbabddeeabaececdcbedeededeeedadbdaebebeebacabebabdceecadaecdbdbacbaeeedabdbecdededdcdadcbbaebcedcbadabeaeccdbabbabccddcbddcabbabbbebbdbeaabadbebebdbabbdaebcbacceebabbdbccdbedddacdedddacecbbddaeeebdedeaccbddebdbecddebddaebaaeadaabdccccbcdccddedeadeebabdddbbedddcacebcaccbaeccbaabeacdeadbddbeacdabdaedddabdcaaecddddbdcadbaadbebeebcaedcbdebbbdceeeeccabadcdddeecdebedbeabeeaadacebddbbddddccaebcbccaecbbdbaeebcbcdedabacdbacaaeddbbbaaeecececaeecccdceeacdbbdbdedcabcaaeaacaeabdadcadccaabceaddebbdbedddadaaeebbcdcdabcdbbdcaeecdaaadebacaadbeebebbaaecdddcccececbbbedbdcccbbeccceaecadeadaabeeedacbcedbbeadebabdedbabddcbcecaeeeabacacccaabdbdccabcdcabbdedccbaeeacdcbdbadcdacbceeaceedbcdaeeeadeacebeaabbcaecacbcebbbcbdcdbeabeebcbaabecddccdbeeabccedacdeaecdebdcadadbaaadecaedcdbacbcbbdaeccacdaacccdcabcdcececedbdccdcacdbdcebcadccdaabeecacddcadceeebcecbedcabebebceebacaeccbdeaaebedbddbedbdbdbaeebcbbddacddabbeceecaaeccaacdccebaceedddedcadbeacbcbdddabeaeccdabeaabcbbeedccbbacbcdbbaaecaecbadceceddbdecccdacdcbbcdabcaabdeadcabbdedacaeedcaacdbedbdcedbceaaabcbbeabbbdbeccadecebdebcedceeadecaadecbdabdcbddaaebaabecbcbabcdaaacccebcaccebdbcaeceebbbeaadccbcdddcebccdebdcabcedacedbececdecaecadcecaecedceeeeaaccbbeadbecbabbbcaebbdbaedabcdcccecdeeddececdcccbbebeceeccebdececacdecbabeabdccebabedbeadcbdeeabbbccbebeebbaccebeebdcbedadaacdcbcdaabdeccbcadecabebbebeeceeeddcccdddacaeebbddecadadbecaecddcdeeccbddebbdeddeabeabeacebdbebdaeababccbabbbacbddcbcaebaccddaabaccdaaacdaeadebeaebebcccadceabbeaaabdbcdcdebbcdceedebdecedbadeccdeabceaeeaddcbdbeccbacbdaeaabdbcdcdbdbcdbeeeebaddaaaceabbbbaeeebeecdebdcaeaeeaacaabaabcbdbeadddaaecacbaecaadadaaabbdaecccecadabebebaedcaedcacbbeacbacdccbccbaeedcebaebdbdacbaebbeceaaacdbdcbecadcbaedcaadcecbdecaddecceeeedcddbeedbdcbecabbeecaadedacbdaaacaddedbaeeebdeeccdedeeeacdeabdeaaaeacdecddcaccdecaecccddceedaddcbbcbdbadcbedeabcadebaeaaccecdecbcacddabaacdbcbbcbdddbdddadadebeddacdddcbdbcccdaedaeaecdcadbacaeccdbbbbcbaabcbccdaeecbbdaadceebbeedbdeeddaabcaddbbceadabaecbdeaceecbecadecedaceeaececbbeededcebddaddaceeeedaeabccbacccdaddadbbadedddbeeeeeeeeadaacdcbacaeceaedcecdeaabcececbdeebaeaddabbbabceadddbccccbcaeeecededeebeedcaaebcdeabeeacecdceeecccceacdebdacebbcedbebccebbcadeaccbbbbbeadcdadceceaceeeeecabdacbcdabcebccdcdcbcadeabdaceaeacdabacaacbbbabdcecacaaedcccecdcbedacadacdecebecadabceeaadedcdabaedecadbddcadeddeacbebcbeabedcdcacbacdabaccdeeaeaddbebbcddbddaaadbcbaedabdcbbeadadeeeabdddcdcdceebcbaaabeaabdbbdbdeccdeadabeecbdccacbdecdcdeeccacaddbabddbbeccccbbebbbbbaedeaddadedbcbddbbccacaebeadeccabbbdbcbccebbedcaaddeeebdceceeeebdccedaadacbebbccbacdbabbdcacaaeddcddcadababaceeaebcbbabbabccaebaaeadbcbadaaceceedcaaebacbbcebaebdaacccadadddebdacdbdbccddcbbbcdaddaabeeceeaeddeebaeabaaabbbaadabbdabcaddcadadaacbacacccddbaeececebcbdcabebdabddbadedaedbccadadadebecbebedbdecaabeeacceaccaddbeacdcaaceadeabaabdadceccdeeacbecbbaeccdddedaadabbddcdaacedbcacccebabbdbbdebbacaebbcaabdbdeeaaaccdbdcaecacddddeeceddbcebbceebacedaedaccbaebeedacbcadddbcadbdcebcabbdbbeececbacedccabebabaadbbdcbcebeccaaaeeebeabcecdbadebaecebababbeebaacadecdadcacdedcebeebdbeddbccaaadbabeeedddccaeaeecbbcbacbebbcbdeedbdedbdaebadecaeadabecacecebdebbeedeabbdaccdaccaeecceccaeddedecbbcaeebdedebabdddcbacbdccbeceaeedaeeebebceaeaeedeccdaaaadedddbddbadaeceaadaadeddcebbacecacbdadbcabdccadacabdadcaeaaceedacbecebcccddcbaadcdccdebcedccdebeeeecadceaedbcabbbdeeaccbdeebdbbddbccebcbcaeeeddccdabaaaecdccdacdaaececcdcacccebcdbbeaebdceeebdcbbaaeacadcbcbdeebabdedecbdccceaddcadeeeeecaaaeeaaddaedcaceacbbceadbaecccbaeaaddeaecbabacbdebdbcdaebadaadeaeadaeaeaebbbcacdeecbcaeceecaaecbbeddddeebecadaacabcbbecdabbcaadbedddaddeecceccbbeaeaedacbcecbedbbeaccabbccbabbeaaaaabecaeeeeeeabaaeaacbcdbecdbdbbdadaccbdcbcabbbccedaaccdbcddddbbccbcebdeadcbaccbacbaccdaadddbebbadedbaddcccbbeeeddeececdaeadaadecbdcceadbeeedeadedacceabbbeeaccabcacbabbccacabaacbaeebabdccebbbcdeaadeacabbdcdececaeccdeadcdcadbcddebcacbabedcbcdecdeeccebcadbacaddacbeecddbbdcaddbcaceedbebabecaabbabaddddebaaaabaacddcbecbeccacbbbabbcabbabdcdeededcbdaceaacaaddbecdadabbaabcceedbedededeadadaddcadadaecadaedddecaedbebdaebcecaebdabbadebbbbeaeaebcaaaeadceabbdcdececeeccbecaceacecedecdaaeacbeeecceeddaaeadaaadeeaaaddeaebecabcaaaeabaeeeaeddcbcddaabcaaecabdcdebcdeceaabaccbececdaeadbdcdabcbcdbcedccadebdbceaaabcccebecdabaacccdcdbeebbcaecbcbceedddddcdcabcbacadbaeaceecadaaadcedddbcbbbabedcbaeeeaecbcbdebbeaaebbbdecbcebeabbdeadabeadedeaaadebcbedeeecbdeeeabaadeebacdacaaedbeeaddcdacdccbaccdbdbcbceeededecbeedbaeaccebbabebebebeedcadcaebdabeeacebeccbcedbdeaeaadddadceccaddbabeddaedbddedeeacecbeeecbeaaabcabceddeedbadabeadbeaccbacaeeddebeeccbecacabaabcdcaeaabaacedaddabaabecddbdabccaddabedbaeedeadddedbededebecbbadadebcdaababdeedbaacdeedbddceaedccdaaabdccbcaacabeaacedecbeabbbebacdcedcaabcdedcddacebcebacacbcdbeeeaaceeebbccaeaaedadeaabedceecdddbeedaeebadccbacebcccdbcdceaccecaaaecaecdbadceaaeabbebaeecddedccbbeaadaedaededaddcbbaedacadcedaeeaeddacdddcdedcdccccdceabbeaabadecbbbbbecedaccdceacdaedcceaebaadecccbecbdbedacebaecdaabcbaedcedaeaebaaacbbbdedaabeabdabecdeadedbbcdeeaaddeebcdbaddcabddedbeebcdecdcedbbadbcdeedecdcbeeeaeeaacadadbaaedcaecbeeceeeaaddacdbaaeeeaccdeebcebdbeddcbdbdbcabcbeceabdaebebdadecbcbccddcbedadacbdeaabeabbbbcddcdbacdcececbaddbedbedbeabddbbeeebadadcaecebbbabcdddeccbceddeecdaddbdccadadcdcbaebeacccceecabdaaebeeadeddaedebeababccceacacdbaecbddedeedadedcceabdcebbceeabddcbaeedcccecaeaebbcbbcbdcebeedeadbdddbdceeaeedacebbbaeeeaeebdedcebcbacabbecdeabbddbbadeabebcbebcbaacabdabcddabcecccebecebadaaaadecdeedcbdecebcdebdedddbdaaaaebddcbbeaaacddebadecbaebecbbeaeecbceddaeeededdabbbebddddecdcbabecdddecdddbbcbdebdedebcaccbddcdaabeadbcdadaeccbccbeedcdedcacbceddbbabcbaccbacbcecccaeadcccbccebcaccedaacabdbcaacbdecbbecdcdcddbbeabebbbddbcabdeddecddeeaabbcbbcabbaaaaabdebadecbaebaaeeecbbdceadabbcecdbcdedaddcbacdaeaaeececebadacdbdccecdcadccaaaaceadacabbacacccbdebeceddddedecedbbbacaabbcbaddaccbbdebacaabcdddaeadabadbedddeccbcceadebdeebdeadaedadedbbddcdaacbdabacadadeccddadedebcecbeeabeceaebccecacdebbedadadeedbecbcaaabadcdddebdbccdecdabdebbaeebcdaeebdcaddbecbaceadaebccebcdaacbeaaaebbebeeccdeabadaedbeddecbbdbedddbadacadaacbcccabecebadaaabaaddaadadbdabbacadcadceaabcedbcaeccedaceaeceddeacbdacacaabedabddddbdaeddacadddcacadeececdcdabecddccacdbbeaeabbededbdaccebceaaeccccdbcbeecceeadcdcbdbbbccbccbedbadbbabebaccbaeaccbbaacecaabddbadbebccbdbacacdaadecbbecdcaececbdddcaecccabebcbedabeeeedcedcbadbdebbcbaecbcbbeddaedaaeaebeacccdcadadecccadcebacbdaebcbadccebacacaceeababcbabadcdbaecdbbdabdbaeeabeaddabcaebbacdccaeccaddeeeaaeedacecbcdcbabdccaedbeadccceeddadbbaeeeaacebcbdbeccdedeecdbebcbbcbddaabbbccbecbbedddeccdcaeeaabcceadcecedaebdcccbdcdacabcceecedcedeaddebadaaddedbcebabbdcddbaaededbbaaadbaeebeeecbebdcceaaecedcdebeaeacabccccabbdcddeccdaeebdcbdedcbedabebebaadecddedbdedeadecbdaadcbccedeedbeabdbadeababcbcdaeedadbddbcedcdeacdaeedaadbeecbbabecdbcdaadceeecdbcdddeaeebeaebcbdbababcdcdcbdcaeccabbcebcadddeebaabbdaaecbbeedcebbccecededccadedbecededcaaeeceaebacedaadbecccbbaeeacdaddabacdaadbeaddbbbadaadeebaeccbcacdebaeaacbaddaaeceddbadcddcaabbebbbeeaecadddbceeedbbceceddbcbbecdbbbcacaddaeaedaacbaeabbdabcdbbcbdbabeaebdecaebcebedacaeaaddbedacebabbcdaeddedaddeeccecccdcbbbdebcecaabadbdbabaeeeeeebaacdacdedccadbbedcadccbebddbeecbccdcdabbbbdbeebcceaddbdbdceedddddbeeedcaeaedaceaddabacdebcdcbedbdadaeeecbbeddeabeabeecaabaedabdbddbcaaaaebbaabbeadcddbaceddbdbabaedaceeddbcbaaccbcccabdbacdcebacdddaeeeecabcbecbebecaeceaeadbdebdacedebbbbddbddbbedeeccdbecdbacecccaaaaadeecbcbcebccedcdbabadebacedccddbbcdbdedadebbeabeccbadacbebbceedadadcbddcbadedcedeeeacdacccbaeccdadaadaebbddbaadcacddcccccbcecbeadcbdbdaeaaabadabcbdaaebdbbbbcaecabdecdddedcaaaaaebeedecbbabdeeadbdccebabcbbaeeabeccdddbbaabaeaeeaeebccdabacbdbdcccdeeeceacbbaeaeacdcbaceaebbdeaedeacaeedbabcedebbcdcbaceaecdbdcaebbdcbdedbbeccacabeceeaabadcbebaccddcadbcceeeeacedeeadeeedadcbceaccdaeeddcedeedaeaadaceeadeecceadeadddcaedaeababbcdddeccdccddeddaeacbbcdbdebdcbcabdcbcdaecdeadbdbdbdacbacccadaaecedaaaaadbdeceaaaacbcacbbadececadbdcceadeabdbdebbcadbdccddcceaaebebecceebbbbbccddbabaebcdcadecdddebebcbbbdeabccebcbadedebcbedddbeaaeaadacdbaadeacdceabaaddabbeaaeaeadacbebabbedacbbbaadeacedeadcdedbdebbaedeacbcecacaccecaaeadbbebcbbbadcadbdccccaaaadbaedbadebbdcecadceddaebacebacaacecdadbbdcceacecebeddbeaaebcedbebdeaadebadaceaabeeccedaaaceeadbceccbdceacebcdbbdedaecedcceaaceaedceebcbcbdcdbccaebdaadaabececdadecaceccbbddedeaacbaebebbaddedaadbecdbaeadaeadcbaaeeddbdeacdbcbaddebcdacedbacadbbaeaaabbadabbdbbebdeaddcdccaedbdacddddadceacacbeeedbacbbeebacbdebbebaccdcacbbddebbcadaedaeabbaaaddcadeebdbeebabbebeadccaeeceeabeeaecbddbeecdedcedabbaebddaaabcdbcdbaadbcdebcdeebbbddbcceeacccdaaabaebcccccabeacdeedddcbddabedbdbeecdbadbebacbbaaccecccdccbabccaddbddeebeebaeaacdbcbbcbaaebccbdbcdcadaaebeabcadbcadceaebaddbebeeebebdebebedddbbedecedbbdbdbdcbecbccecbbabaccaaedbdaeebdcebcedadbeacaabdeabcccdcbebcececaacbeeabbcdeedaabacbbbadbebddcbdeacabacadacbcecdddbeabeadcdcecdcadacdecaedbdcbbadebaddeaaabdcbcdeaaeeabaeddcddeedabcedcadbadabeccbeebbaabccedbdececdcebbaadbbbceceddbddcbaaaddcbdbadbcdabaaaddabeadcadbdcecbdbcecccabdacccadadbddbccaaaeeeaccedaebdabcaccadbcbbeedacbceaaacbaabdbcbedcddacedbeadbbaadbbeaececcdbccecedacecaaebbcacdadbeeecaeecedcdaebddcecedceadcceeeaadebddcbeaaebacbdccebaddaccacaebaeabedeebdedbedcdbadadaddbddbabcdbcdebbeacbeededbacbdbcccbbbebdebecdebdbbacebaaeeceecabbbeddabecdabdaabadeacbdaaeeaaecaddcaabadebceabdaaedababbdcdaacbeddaddadddccdbedadedeaeddbbddcadbcdcccedbedaceaaeaaeddcbddcbbedeeadbbbdaabcaabbcaecbdacebdacedadabbbceeadeddbbedcbdcebcbbebeabcbeedddeeeeeccbecebaaeecedcbadabbddbaadedbcedbeeeaaecaedabaddadbedeceabbcbdebbaeacebdebddcbbaecdbccddbdabcabaeaceadabcdcecacbcdabbbcdedbcaadcaaeeacedaeedcbabebcabdbeadbdacdabaebbeabadceeeadededecdaededdaeceaaaeaabedbcabbedceaebabaaedbcbcdaccabccbddbdcdabedbadabbdadcaacdddbdbddadbdaaaeeccdeecdbbebeebbddedeaccadbdceecaeebeecbbbacbbcdabcacedbbbbeaecaeadabbeabadcaccaeaebbeabceecaaaaddacebcadccdeecbbbcaecdcbebbacedebabedbedbceedabeaacdaabadeebeecdedbabebedcbeebeadcbbabcbdccbdbdddcbaddcadbdebdeaaeebebbebbbbbcccbbaceecccbabebcaebeadddeedabdcbeeecdcbcbcabcbeeeddadeaacedaaabbdcbdadaebeadaecaceeeccccaccccbadcaaedcccabcbacdedecadedaeaeebcecdeecaeaaeaabdcdbeabebcebcdacdddcccccebbeeceeaaebceecddddbcccdaecbdccdbdbbbeeaeedaeaceebeaeceacaebbdcbebbcbaaadacebaeebaaaccedcbebdababecddaaddcdbbedcbcbcccadaeaebebdbeaedbddcebcbeddeacaeaccbccbbeebeeabbaacabdbaaaccebecdbadeadacdaadcbeaddbedbaeeeedeacbabceaccddccdbcedddaeddecdacabedabcdcaeddceaddbdceeeceeaaededbddeaaeadcbacadcebdbbacdcebdabdcdadabbbcaebeaddeedabbdcdbbcaaaebdcccbcddbbbbcdacaedacbcdcaedecaacaeecaddebddcdecccdbbcebadeeecbdbdaddccebaaebbdebbabcdbdbaaabeececbbddecbbcaebaaeabaaedcdabbabcaaedcddbcecbeedcaecebbebcceeaceeaaaccabbbddbedebadddcbdadedbecedebcbcabebddcdeeabcaebcedacaebdbebdcadaebedeacbdccebdebadedeabeaabcebebcbaebeebdebbedaabedcccbcbededcdceadccedeedecccbeeabdebbcedadbddabeabaabadbcebdcaedabbbebbdadbaaaebedadceeddcaddcccaedbddbaaabcbbadcaadebabcabeeceaebaeedadaeeddabdbcaacbceaedbcebaccaaddeedabaddccdaecdadebcbedcacbaedddacedbcdadbdaaeddaaedacdcedacabcdcedbcbacddeedcbddaabbbaacacbbdeedebaabdedabceddbecdccaabbcdeaceaaabbecccebbdbbcacbebdedeebaebadddebcbaedbabadcababebbadccaddcbabbadbebaddbbabaacabbddaeddeeaddcacbeceeddddaaeebddccdbaccbdccadeaeaebedcecbcebadbeaeaedcdaadbedcabaeddbacbedeabbaaaeeecedbbdadbdaeabcebeecaaeddabdbbccebdceecabbdebabcdbebcbdedeededeecdebeabeedeedacbeeccaeecdaeddabadebcceabedeaddaebeebbcadccacbccccbacbedeabeabeabdbbadbacbebcadcbcedaeedbadedacdebbaebabbcdaaeaabcadbeedccbcacbbbcdeeadeabeabddbbbeadacacaacddbdbeeceeaaadbdbdbeeaaacaaacbbdccbaddbdccceacdacbcdbaedebabcddeeacbaecbcbeeedccddebaaeceddcbaedbcbebeebeaeceebdebcbabcdcddeeaebbdaeeededcebbbedaceddaadbcedddecaaebcacbaecceeeccabaddccbbdaeaceadbabcbbdaeaabaceabacacdaaadabaebdeeeabaedebeeaeaedbabddeeaabbecdbedeabaaeabdaaebdcccceececcdecebceddbedabbeedbcddedecbbabbdcaabebcbbcceceedaacccbbabdaaecdbeeaaadbccddddcbddcbaaabbeebeeaeaceeececcdbaceeccabdebceebdeaebbebcbddceeabddeaadedbcecccacdecdadddecedcaabdadecdceeacdceccadcedcebceabaaaeecbaaaccdcddaebbeeeaecbaceebaccbbeebecceeaccdbaaadcaedacaddeecdaddeaaebbaacbebbceaaadeecdcbabbbccbaacdeceabddbcdeaadcadcabbaecdbbceeceebeeaaecdcbcbeabdeaeedeecadadcebbadebecbdecdcbadedaeaadeaccdebdedebbdaaaeebdebcdcbdbeecaecddacbcbdcbcdebdcbbbdbaabeaeeebeccaaececcbaebcddeebbbeaedadcdaadeeaedcbbbabdcbbeecbdacdbcceadbdcaabadbadcecddaddcecbadabaeeabcddeecababbbaadbbbdbaeedeccbdcddcbbeebeddecbaaccbdacaeaadbbecaabaeebeabadcacaacccceebaccbedbcbeedcaabdeacddbaaebcdcdccdacecdeddabbecceebbeaeecddceedccbceadebecabdccecbdbcddebdcdaaecdacaadeabeeccebabcceebaacbdaaedeeecdbacbaadedcbecbdbaddebcccabdbeccaaeeabeaceebadddcccaadeadeacbbecdaaadbecdabdcbdcdaeddacbecaeecddbaebabddababcdcbbcddedadbcdacedaababbdadbdceebbdecceeaaeeeecaacdaabaebebcbaeddacebdededcccbdedeecdebeaebeabeedcccececcaededbcceabcedbdddbaaccdadabbcbbacebedeeacacaeaaaecbdcacddbbcccedaebddbceededcbdeaccadbdcabdbaddcdbeebedaecbedcbebdbaeecbaadbedaeeacdcaedeaccdbacdadbcaebbcaaccabdcdeeaccdbdeebeeabccabddadcadeeaceeedaaaeebcaddeedcaeddedcbcacbcdddebebacedabdbcedbebaeddebecebebbbdbaabaadbbaddbecbeaddbedabecbcdebdacddabdaeececbaacaaeadbaacabadeecdecbdadcadcdaddebcaeedacecdbecbdecbcaeabcdbeddecdeadddacabcebabcacebaaecceaabcbacaebdceedcddedcbeebebeeaceaccdeccacbaebaebeeacbecdbedbecacbcaeaacdcdeaacecdecddbaedabdeacbadbceaeaedbbbaeaddbbaaddeadeaadabbadccceececddabeeadeaccbededcccddeedbcdcccaaeabddebceaebaeeadbabeeaebabaebdeabcccdacedaddebcedbbaceceabceadbddddacddabeeddbcbdeebbaadeeddeeabbdeaeacebedbdaeacdaecaabbebddbbabbceebcecababcdbedcbbaceddabdaddcbecbecaaeecedcebbdcbdadaaebbccbbeabebcaedbbdacacaaceaaedbabcdadcdaacdbaceabdbeedddbbdaabbbacbebabbbebcdcaaaeecceebbcbeeaadabceeddcadecedcbbeeebadcbccedbccdcbeeaecbeeabddaacdcadaabaaaeeeaeedcadbaedddedacdecdbcddaaddeacdaaeeacbccddcbeebedabbdcedebacdedaccadbdaacbacebddaebebedeeaceebdbcceeaacbbedaddbcaeadcdeeddaeddbbbeadbdedebaecdbdeebecdecbebaedbcabadcbcdbccadcccdbcdbeeaecdabdeabbbdceabcccbbacbdeddacbdecededbebebbdabacdbbdbabdadbbdedeecaacaccaaebdbddedccbddddededadabdbdcbebddeecdcaeddebdeecdabedbeedaabaeeecebecbbebcacdacaeaeacbbccebaddeadaaeeddeceaeaeceacecdeaeaaecaceedbaabebaeadabceaedadcbadbbeceaeeeeadbcababaeecaaabadbedbcbedcecaceabdacbabebcbceeabcbcaacccebbedcacabddaacadbcadcdadbcddebedecceebeeedebdaacededcdaabadadeceaccbeddcabdccadeecebabbacccbddbddccbccddaaacdedbcddeadbdeeabaeeaccbcadceacadeeaceadedeaededecdedcabbdacadbddcdbbbddcbaacacdbbdbdbcdacadbbaeeacdecaabaadcbeecddcccdacaaedabbdddacabebbdbcebcceaaeddecedbbcdedabbacaaaaaaecdbecedcbccbbdecdbaabaaedbeebeebbaaecbedbaabbddcbdeecebddcccccddbcbecabccbcdadacccbbdbcacbcbeceedadbebaccdeaddedbeacdedbeddcbcdbddceabecdceabbebdebaabbbcbabbedcbedbbdbacecedbacdadbdeacdaacaeeddbbaacbaabdbecddeadddcdecccddedbcebadbcddaaaeddecdacbaaadecabbaebcbcbdbcbebebcbbbdcdcbbdebedcbdddddcbbbaacebdebacdeebcececaeccaeaeedccbebbdaedeccbbbceddaeeebdaedaebcecbcaeccebaddeaeecccdddeeaebbabbdbceeecadaecdcbddabddbecaceaeecaddadaebbaeccadbeecdddebebdeacadcdcabedecacadcbebbedceacaebbdbaecdbdceaabbdcdbabbdbbebbaeecbabaeebecbeeaeeadadbaaacbbbabcddcdeeeeaebaddcbcdbdaadeccccabdcbbbebabaaeeaadebbaecbdabdcdbbeabdeaeeaccbceccacbcbbaecacdbcebcaedbeabbbdbdadcdeacdebdeeabbceabcadbdecadeaaaadcdbaacaacceedbdcccdbcaaeebebcacbdaeabeebdaddcddcebeaabbacdbeebaedbbacebaadddabbbcedcbebcdcacdcabbeaceeaeddbebbbbdeccbccbddbcbdbeebdcbaeacbedbdbedbbcbddccdbadcbbbeaacceecdbdeedcbaceeddccccdeeaecdbbcabcabceadecebaddccbdabbccdbcbaeabeedacdddbcdcccccdcceddcaddadcdadccbbdaadbebaeaccedbddcbdcebccaebcbaaeecbaaadacddaacedcbbcbecaabecbaaabcbbcadbbeabddacceadececeaadabadeaeadcedededbcdbdbaebececbbacbaeadbdbacccdeecdbeddbaebbacdacaaaeaaeddacbbbaeeedeeabddaeeaeaedceeccdeeabccdbcebeabaeddeaccceccabecccaacbebbdacbacddddaeeddbabeddeadadacdceeadaabacccabbcdcdaadeeeabdeeaaceaadebecaedcadbcdecdabbaeeedeedaabdbbcaebcdbabcaedcabeaccbababdcdaaadeabdddeaddaadbacaaedeeadceddbaebbdaaceebdccdcdaadcedeedacddcacdbcebcecbdaabaabeceeccedcbedbdeedaccabeecbbabcebededbaeaedbbaabcbbaeddacbbcdeddceadcabbaecccacceddeeecadbbdacdcedbbeeabeeecdbbaaedaebbedaebbebabcbeabcdeccdacdbccceecdcccbcccebaaaadcbdbccaaadbdeeaacebcecddaeadbaabddcdcbbaaacbadebecceeddeaedbdacadccacddabcbcbcabbecaeeaaecdcbadebdaeacacdedccbdebebbaeecabccddaaddacaccdcddaeecbbddbaccacecaeddaceeeabcdcbdededdbcabdaadbdddaadabcccdaabdeedeeaaddcdbbbacbbcebcedbdadecedccbedcbbcbbadeebeadbbeecbcbadeeeaaabdbcaaeabbabceebbadbecbeecbceadaccebdddedbccbaaddcaeabdacdcdccbbaaecabeaadeaaadbceeceadbabaeedacccbceddbcbdeeeccceebbddccebaaceebbabcacaecaabeedbabaedbaeeedbeabacdeedbcdcbcdbabeedeaaeccbcaeebbcebcdacbaeebdcecccbdcaadcaaebadabcccbcaecdbbeaeadeedebcbeacdaebabadeedbadbeadbddcebecadabacaeecbeaaadabaebaaecddedbcddbdcdaeeadbdbaebdaebebcdeedccbeceebbecbeababdbcdccdbcbacbbcdbcddebadbaeecdcabbdabadaedeaebcceddccccdddbdadddcacebdeababbeacabdaacdebdceadbbdcbdbedabaeedadbbcedddbccdcceddedadbddaceaaaddeeebcddcbecccbbbedcadeebceabcdaacbaeabdcaededbbecbcbdabadacebdebebcbbcbcbadceddbeaaceaecddcbcdaebcacdbcddacdcebbceedeaecddbbbcbebacbaaabdaeabadaacaabddbeedebaaeedcaacccceaacceccbdbaceeddeadeeaaceaaceebddceebdcccbecddebdaeadeecebcaaadaeabbaeabddbdbdabdbaeccbdccebecddaeedbccbdebaaeecbedddbbabceabcebedecedccddeecabadbbabdcbdaeaeaabadddcddcabedebabcaccceabcabceeabbebecebabeaabbcbbdababcbbcdbbabccdbaedadecbeddccebdcbecdeaceddcbedcaddecbddacadecbbaadaceabddbbbcaccbcdbcbbbdecacadebeeddaddceebbdbdddebeeabebaeebceaeeddceeddbbabcabbeeadcbbdcebeadbeebaceaabddeababbdbcbbdbbeddceccccabdaaceedbcaadcadcbdaeccdccdaaeeaaeceadaeeddcdabaeeadeadbaabcbcbabdbdbbbbaeabceacceebdaebddcbcedaedcebaaeaaecddbcecbedababebaaeaececcecdcddbdcaadacdbcacccdccdedeacbdbccbecbddeabacbcccdbbdadbbdadddddcbbcdccbcbeecaedaccbedcbdabcdbaedbaddaebbbbccdcdcdcabdbeabdddcbcebadabbcedabeedcdaaeabecdcdbcbddeeaeacbccacbccaedddaabbceeadecaaeaaacadbcaaeacdacbadadaabbeabccbdadebcbeaeeddbbcebadabcaccdabcbabaadebabdaabaeeacecbedabcdaaceababdcaedbcbeceecaadaabeedddeadccbedaeddecccbdeadcabcdaeeeabaccbdbdbeaecbabdcdcccbcaacdcaecbcddccbacbdaaeceadacdecedaeacacaeaaebbcdebcbdaaabeaceccdaeebadabaabbbdcaaeaceeceaeadaecbabadabbbebedbceacadbbdeebbecebdecceebcaaceecbeabdcdcebddedcbaacbdcdbacaadccbaeddebcbceaadeedacbbddccceccddcaccbbababacacabbcbcdbdcaaebcebaaeecceceeeeaecbbdaebdedebeadeaceacdaeceeacebaaedbaaebaecebecddbbbcbeaddccaabcabaeaebbabeadacbbeedbbabdcdacbbdccdbcdddbdcbbedebacdcaebecacbebdbdbdcabbddaeebdbedcdeecbcccbcaabdecbeebdcaeeccaeaaddeeacabbdbdbdccdeeccccaeedcdbdbbcddeacbeccdcbaeaeabddabeecbccaaeddaeecdbeecaadcbdeeacebcecabadaceaaeabcdcadacaeecddceacdcdeebaddaedbdcccaacccabeccdebdabbbedacdacedcaccaadcacecdcdddabdbadaacdcbbedbdabacaccbddadadeddceeaeecabbbcedccceccdcaacaacceeccdcbbbaeeecddbeddeaacecbeadebecadebebbcbceaabbabdcedbbdaccdcaeebdedecdbcaebbcecddbaaccdadebcdcebdcaeecddcdcdcbdaababaadeabdbabdcdddddaedbddadcaccedadeceabdadadcddbeedcbbbcdeecbbcdeeddaebaddbeabddcebbbcecbacdadecbabbbdcaeadceaabbdabccaddecacaedabddcebdcbaeacbdceabcbbdeceadabcdddbaeddeedadbbadcceacaaeccdbdbcaebcbacacacdbcadcadcdeddeaddebeaceeaeaecdddaaacddabaaadcdccebacacdbbdbdccacaaaeadccceccaeebeccdaaccddebcabeacaccdbaebecaaeaaebddadadacacebcaaacddaabaadeceaebdeaeabaaccbeebaebbaddadaacccdcdbbbdddacaadbedecababadbaeaeceabcccacdbbedbbcdbaebaeccbbccbbcbabeadbedeceddedabcbcebeedebbeccaeaabcaeeddedcdbcccbebcdacadbedebddbdedeaaeeedebeededaeedeaeadedbdbecadeabcebbbceacabccebadeaacbedbbbeeadaaaceceabbccedbedadaecbcbdaddbacbaabdccaebdacbaedddadddadebdaedeccdaedbecdbbaececcaabacadededacecdbbdbdbabbddbebdabadcacaddadccdaccbbdeabcdadedcbbdaedddeeebcaccccaaadeddddcdbaaccadbebeadcebbbaaedbabcbdceabcbbccabddeabbcabbcccdbebccdaddbbbaecdbcbeaabdeebecbdeebcabeeddecadadaddbdbcaadaeecbaaabacdebcddbaaaaaaaeeaeebeaeaeeccebcdbeccaccebaadabceadaedadaeeebbcdcabbcbdaccebbbcebbddbacaddccbdccceaedabdcdccecbdaacdaebebdeaeebceebebeaadbacdadcaadcebdaaecbdbcdaeeabddcbbbceaaebaebebdeeaebabdeaccbcabeadcbceedcacacaeceaabedeaccebaabbeebaebcdeebbdccabcedabcbdceddcdacbbeaccddaebcadedbdbaaeeeaceabcbbbdaacbabadececdbbacacdadbaabadeacebddaeacabcacacecaedebdabbabdabcdbabbeedbbddadcdceaeecedddebeedeadbbbbcaabdaccceaeeabeebdcceabebdaaddcecedabececcebdeedbbcabbeeaeeacaebacdecbabedddaedbaecbaaabacebebebbaaabceacbcdedeedabadbdeadbadbbddcaeaeaadedecddeedeadebbdcccdbabdbbedccdadcadceabeccaaeeadaeddcaedeeaacccbdcddeaceeacdaeccddcedaacccbbddcbaecabecdededeeadcaaeacbdcedbabaedcabacdedaacaabbadeeeeedddadbbdeadeaecbbccacbdeadeedeecabbcddeccddeedbacbdcdbbbadaebbacedeeeddcededabaadcebcaaebcbbbdadabcccccebbcbdbceeabedcddecedaadcbdadcebcadceabdccadeeeddebdaadabdeeeacaebdbdacaebdbbbcccdeeaaedacaeabadaacddabdeaaccbbaaccceddacdbbedddedabbcbcdceeebdbbedaccecdabcbeccdebbebbddbceecaebbcaddaecbacbbecbeddcebecabcbdcdbaedadbdbccccdddaecdddaeeaaeeacecabedcddaddddaebcdbdaacbedaabaadcabcadeabcccebdacaaabbaeccbaceadaabdeeecacbaedbeaababdcccebabbbbcaeecccdaeadcedeedceeeadccdbbaaeeebdbdebadabcdcedbeadeadceedbdeeddbbdeaaccabaceabdebceebeaebbbaeacabaaaaeadceaceaabeeaabeeeaeecaaaabdbeccdedcccbceebadeabaddeaaedaeebbcecaeddbdbbbacccacebbdddddbaeadbbbdccdaddddbdbeebdcecebccaaddaebedbdadbcdedbabeaeeddebbabacebaecdbecbbcacacaebcbddcbbdacabeeeeebacceeacbbbccbbebdeecbcdabbcaccdecbeededbddeacadeacadabeaeacbcdddbaddcdadadbbaccabecaecbdcdeebebdaaedebecedbbbceaacdbbdeaeadadeabaeaaeaacbdbebcbaeeccedbadaeabacdecbdbcbdbeedaddcababecdaddbceeabbabbebcedcbbddddebbabcbacdcabeaddbcdacabbeadbaecbccececeecacaeacedcddeccbadabcabdaaddceddebadcbcbbdddeddcebddccaccedbdbbeaadeeedecebedecbacdbeeeeabaecedcdabbbaedbceeecdebdabaaeeccbbebebdbcdacbcadabbcbebabeadbdcccbabcedbaadbcebeaaaaccacccbcecebeaabbcdbbdacbbdecdeabceaebbdceceebbbedaaecdcdacdcecceccedeebecedacdeaaedcdcaaaeaedbbeaeceabbbbecccbaecbadeabcaaeeecbcbccaaecdeeeeeacbceeddadadadcaccaddcbcaaabacdadbccdbabdbceaaccbacaacdacbcedddcabcdbcaadaedcbcdaceeccbaccebaeeddceeebdeecccccaacbeabbebdddadcaddebbbecdaeebaadeadadaecaddeecbdeccabcaacabcbdeeabdacddeeddcaddacecedaccbeeaaebbadececebeaacbaabebbeadaaebdcdacbdcdcccdeebbeaaecaccceccbceeaabdcbbadbecbcaebcaccaacbacabcbabccdcdcadacaddedaaacebadedededbcaecdaeabaaadadaabebecaeabdcdeaeeeedddecdaaddabbbbbadbddbecccbeceddbaaededbceeceaccedaeedececdbdaadaccddbaedbdcbdcedbcbecccddebddaddebcacbedebdcbdaeebaedaacebcdcaccaeccebbeebadebdcaaabbdecbabcceaedecaccddecdeedbaeebceddcddebcddbabdbbeeaaeebcedcaaccdabeaadadcbcdacdaeccaabdcaecddaacdbcacaeeeeecceaababaedccceeedabeceaeacdbaadbadaeccaccddbabbddbaccceabbeddcbdedeebaeebaacabcabbaaeeaeedaaabadeadecdbdebbbabcdcbaecceadbecedadcdacdadaadacdbadeeaadcbaaedccbbacaacaacddababaeadecebaacabdabebabecaddebdadebbaddbbddaddeccbbeadeeccccbcdabeabedbdabeeccebeaccddcdaceaebdcbbcdcbbdaecbcdedbbaadcadaecabeceebdeabbacceceaacbeadbbccaacbacdbebbadabacbaacadddbcadcbcabdbdbabaadcccdeacbdaedcbbecebbabbacccdcaeccabadaaeacbbecedadcdeacabeaddbeadaeedcaaeadcaecebdddeceacadcceddcaaceddbeeecaccadbcebebbaeeabeedbaeceacbaacbbaceadcdccdbddacbdbdbcddbbeedebecaccbbcdcacdeaeabcddcdebccdabecdbaaeabeeaddcdbeddcbebacdeaadcaabebcbbbbbacdddacedccdeaaddadcdccacbbbdceeaecddbbebeaaabbdceeeceaebabacecbaeceaddeeeccbeadeeedadbedceaebddecadbbbeabceedecaaaddceacbdaacdabdcdceedcceddbcacddbdceddecacadbaadceaeaccbbaaabaaaceeababdaaebdbecabcaaeabaecccdeadccceadcccbebdaadecadabedbeaeeddddeabacabcddeebeacabbcddebaacdaddbadeeaacbedccbbabddeeaacbeebcadcbcbcdcbaaebaadadbbcbbaeadccdadbbbecedbedaebdebbacdaabdbcbbbacacbecaececbcbcecabdeecdbeeeddaddcacebeadaebdebcabdbdaecaeccdadceddebaccabeeccbaeeaeebcadeebdbdaccccacecdccebeecabdcedaeccdbbcaeabdabaecbaeeeedbacddeaebeedbacccecdcdbdbdbcdddcddbdadedabcccddaaadcddececeabdabeceedccbbdebceadebabecabccdaebcdabebebcabdbdedbdabacecebbbaedbccbbeabddebecddadcbaaeedccedbbcecbdecdbbabaabbbdaacadebecccdbacceceecebcaabeadabdddbcbceadcaacdaabbbdcaddeecaaabdcabbecdbecebbaccbeecdeccdbbccbdececaceaaabeedeaedeeababcedddaadadecbbabbededeaacbbcdbccbeaadbbceddbeaaddbbbeddaaaeeccedebacbebaddceacddeeebcccbbbbacceddecadaeeedbccbbddeceeceaaadaaadeeadbdaeeeeeaacdedccdaddbeaecdabbceadbceecbcccaadbcbcdaebeadbaaacbaacebabbbbbcdbacecebdbdcbabeeaecbadbdeecbbbaaedacbcddccdedcbbeebddbcecabdedebcaceebcbdebbacbeecbbdedeababcdadccbccdadeebbeecbbdaaeeabdebadbedbcadccaaadbccddecedcebbecbeaacdacabbbbeddcacdceedbcbbbdaddcbcbcbdedebceaadaaddccaadeadcdccbeaabddedcbbaedcadcaebdeddacbcdaccebaadbdaeabcbebccebdcbebacdbdbdbbbdcbaebdeabbddabadebeedeebabdabbdeeccdeacddbddeeddbaeddedbddccddadbaedebcbabdecadceadecadeeadaaedbcbbebcbaadbecceecddeaabcadccebcbbabeaedadbbbcccabeeaacbbdaeaaeebeedabeeeacecdcaabbcdeaadecbdbeebdbdcbcddddeeccdedacabaceabdbcecbabedcccccecdcccadaadeeecbbadcdcaabcbeadbecaacdddcbecddeacceedacdeeeddcdbeaabbddedbdcdbeeedecaddcdaccbacacbcbdebacacaccdbcdddaedbcebcaebacbaabbabbeddbacdcecbccdddcddccacdecbbdacbceadebbeeeadbdebbdeeeddebeebcddbacbbadeceaaedbdbcaabcaceacdccabbdadcdedaaecdbaadebbbeedbecdbccdccbebdcbdddddeeddedddccbdbaeebdcdddabeacdbadeacbcccbeddcdbeddceceedebdedeaeabddaaebeedcbdaddadcbbcccecebceebbddeceedebceadadeeabeaccbebeaecbcedeacadaaabedeeceaaeeaabcbaedeeddacdbccebdcedbaedcabbccaddcebabbabdadccccebdddcdabebcedadecaabebeecaaccbbaadaacabaebecacbeeaddbbbcecbeccddaecdadedbccdacccecdabdeacedceaebbeeebbedddeeddcbbccbaeabdeddbccbbacdaeececbcbdcdbeacbeacecccdcdeeacdaddbdddabcbcdaabdcaeecedbbcaececbeaedacabbdaccdcabbbccbbadbddeaaaeedeaaaacdddccbddbeaeaaaacbbaacebccbbadedabeddecaeedbebccccebaebaececeacacbaeeddaecabcebabebccdddeaccccedbdabbddabdabaedabdeedcdacecebacecbbddbabddeccaeccaedaceadaddbcabddbbeecdcebbceaeebdeacdecdacbcceaebeecaabbcbeebcdbcccbaedaacbeebeedaabbbeccbdbcdeecaadbbdececdeaaaebdbdbbbddebeaadeeaeadbcabbadbabcceaebdbbaedadaebccdeedeaeebddccabdaaacbabddaceaddeabcceacebbcaaedcdecaccabdcaacadbbeaedbebceedadbbacbaededeadbccccbabbeeccadacdaedebeaddaddddaaacbaebcbecacddeceeadbcaddbcaaacbedbbceaaecabddddeaeedcaebccedaececcedecbcaeeedaebccabeebdebceebdabeeeaaeeeccdcdcddbddedceeacaaedbebbbbccbadeacdadbbdaabbebdceceaeabadaeecabcceeeebddacededbedabcaaaabdbcbcaacbeeedbadabeaeebadcdceebddccddebaaeccabeaeeabbcaededecbcceeccdaedeaccbbedceeeeddceeabcaeaeedcdedebdeceeaeaeddcaccedaceebbcdbbbddeecdadadbcdcadedbecbdacbcdbcbaebdeecebdbddbecebdcddccdebdddebcbdecaaacdbcdccacdbadaabcbbcceaccdaddabbecadaeedcdecedcddbedcdcedcbbdaedbdbecdcaebbebaceadcdacaccaddbdcbeceeaceecbcdceceebccedbeebabcccdbddddddeaaddcbdabdecceabecdcacbddccddbdeceebdceeddcceeacccbadaadbdecacebebadedacdbacdeebeaebcabccebababbdbbaeeececcbbadedeecdbecceeeccddcadaddbbabcbecdbbbeaabdbdeebdccbeedebababbecabcedeeccdbebaddbdaaedadceecdbcaecdcdddcbbdbbeeecacbadedcaecccdaaecbeaeabadddababebeeceeecdeeaedceaacbbabdddaccadccbaaeeadbeedcddcbdceccecaeecdecddabcecabdbeabdabbceeceaeaebbbaeaaecbbbcdceebbdebcaebcacbadbddedaeddecbeecccbaddabeaacdabeecdbcecdebcebacaeabbccdcadadbbbaabbdeecdeceeacbdeacecadcccdcdeaadebbcadabeeaadedaceeecedbeabcbadaaabacccacccbcaddabbcbeabeaabbbabbadddedbbecbbdadeabadddaeeecdecaaddcbdaeebeccbcabeecccccedbdcccdaddbbacedadccaebbaeabdcdaddbeaaedbdedcaebecbbbbbeccaeeadeeddbbaebdeabceadcbbdbececcaabebaeacdcbacacededecbcebcdaeabbadcdedbaeeeebdedccdbbccebadebdaaadbabcacebaebbbbadeccddbdbaeeccabdecdeaedcededebaabaecabbedbecadaebaecbceedadcadaccbbbacccdedaddbdeeebdcdcbceceaecadcddbbeeeeaaacbbaadaabbebbeebaabdecaecdadaddecaccdebbacebeabaeebdbeaddcaecabeacadbdaaeeeecabcbaeadbbddccaabccaebddecbebbbdddebeaeacdedcbbdbcbccaddccbcecbeedabbaedbbeaeddccacdaaeedcdbadaaacacbbccaeabaaeeaaeccddcbdeedcdcaccaeacaceaabababeadacbddedadcdeebaddbaabbdbbabcddeaaebcbcaacbbaadaaaedadabdadeebbcdbaebebcdadebaaabbccdbdebeeeeabeebbdbcebebcdaeaaabcbeecceeeebebdbebdbdccbbbddbedaedeeebbbcbdbcedddeaeddcbbdbebcdcedebbacdaddaabccbbbabdcddeedccdcdebbbbdccaadcabebdbdbadcbecadbdbbbcaccdbbbeacceaaebaebaacbdeebdeaecbabdbaceeaeebeddbbbacbecedcadecddeccbdbdadddeccaebbdedbbeebbbedadaeacbababbacbdcececdabebdaccacacebbecddcdacabcebbebbadacbdccebaebeccdddabeacbeecabdbdbdbbaeaabcadabcaacabdbadadcbddddeaddceadcebdbecdaeceeecdedaecaacbbabbeeecdeeaeaceccecdaecebdcbbddcabdbbadadeeabbbdbeddcdadaaccbbcddbeeadedebcebebbbddcdbaadaacdacaaaadacdedabdbbbedecceeccccddeeaeceadcebcbacaebeaaabbbaedeceeaaaccedecacddececccbdddcbecceedecaaaadaceeebdeeeabedebddbeecabeebceddddedadbdabeedbaceabadadebdeebeaadeaedceebcbbaccaedadddeddaddbbceccacdbbbdabeaaaeceaaccaabedccdeddebdeacebabcdeebcabedcdeeaaebaaabdcbaccabdeeaaaeadbdeddedccdbacdebdcdcdcbadabccceebaadcbcdacbddabccabcbaacaaadbdbeeeeecbadcdccaccbebeeceecbccbdbeabedcacbdacccbbaeaddccbbbabeaeecbdcbcdbaadeecbeeabbeebbdadcbcdcbcacdeeeacdabecaddbdcdcacdebebbebbdabbeedaedebbeabccddaaabebdbddeabdacedadbbbdaeababaabaedcbbadddcabccbecebeaaedadcabaeacdcebaaedbddecaeeaaeeddedceecdcaaabaddceabedadcbdbeecddbaadcacbeeabeedaeedbeabddcededeaaacaebadbaceccadeadcdbbadbdabaecaebcdadbdaeacaeccabdaebddbcdbedeebebacbddbcbcadcacaebdcacedeadaccbbdcaadaabbabbcecaadaceeedddbebddedeaedbccccbacdacaeedcdcaaacdacabdbeecdceadabbedcbdccacaeccbcaebdebbdedacdeedeeddaaeebdaabbecabcebbdcddacbcdabcbbcdbacdddaabbbdddcdecbcbadcdaaebbcdebcaeabebddbaddbbcdeaededbebbadcaeabbcdeddcbdbaddceadaccedacbaaddbebcdecbacaedcbbadbebabdeeededaacabbbbbbaccdedcdddbabecbbdcbdbcbaadecacaebddddeeeadcbbbcbacdcbceaeccedbbcbddcabbebdbdddbcaaceebebbebadcbeececcedaeccbabecaeaeaeeadaacbddabecabdcdcbdbeecbdebdeeecaeeddbbbabebbaaeecacecaeacbaccbaaddacabbeeabdabbcbcccbeeeecebddedcdbdabdcdaedccaeeaadcabcbeecaababcbbcbcbdaadbaaaddacbedacdbcabceacedbcddcdcceecacbeeeebacdcdeecddadceacddeaccadeaaaaebeeadbaebecbbcadaaaddcbaeeadaadcccadadcebeabcaadaeaaaececbcecaacabdcceaadcaeabdbdcceaaaaaaeebbeaedacdbdecdeaccdadcbccbaadbededcbecbbceaacabadcdcebebdcbbaddedecdeeddcbbebceecadaeddbedbbdcaaadbbbbaeadaaabebbeeeebdedbedeacebbaacecdebadecbebebaacaabdaebaeecabaacddaaeeaeaedbadbbebdcaaaedadbcedbddbacdebcdaabdcbaaeeaaecdaebabdedeeccceebbeaaaeabddecababcbeeceabcbbbecdeceecaedaeeeeacdaddbbbcabcddeddbbcacddaaecbdbddddecbdbbecddddacbaeadeaaeedccbacecebaeddadaaeccdcacdbecccbdcbbcaebbacdbeccbcebdcecbddaeeecdbcaadcaeaebbcadaebdcbdbdcbaeebbaeaaeedebeaddbccaaacabcbbbbecdbbdcdbdebadedebaecbcdbaccbaddcceaaebeedaabbbedccdcdacccaaccebbabaacbeadbedbcdcbddccdebceccabccdbbeaaeeabceaecdbcedadedebcdcbdcedbdadddbdbacecbdaaaaccebabadcaecddecedcedcddbbacbeeacdceeaaeaaacdeaaddbbdeddecdeeaebcccbaaaecdaaacaaceaaaccbebeaeeeeaeeadbabadddcbbeeadaacedbecbdcbcdecdcbdbdedadaccddeedbceadaecdcbbaebdcdbbdccbcdecbdbacaadeacacabaceadeaddbcaaaeebcbdcebccdedadbabccbaacbedaeaadcaaeeeebdecaceaaddececeabaeebeadaaccebbeedaeddedaebcbdabacbdecacaecaaccebcabbbecdeacebaaeecbbcaecceaaededaeebcccbdeddacceddbacebddeaaebadebedbdbbeeebeaeaacadecaeadcacddbeaccdaeddbedccbaaabeedaecdcdacbbaeddecaddcedaadedcabeeddadedbddcdbeddbcbdbcaaeeebcccaeaaacbcbcbbebebcdaabbdbdaecebcbacdcbdbeeeecaeacccdedddddedddddaacdcbdaedccdbbcbeebcaedcacccbdadbddceaabcecdbebaadaaaaaababeeeaaedccaddedaebccdcbedbbdbbacbedbbbcebcddbccebbbbedecbbbcbaaecaaddccecbacecbedcbdebcddbddacdacaacbecbceaedccedcbacaccdaecdacdccaddaaeaceaedbbbdaabbdedaccadceedcceaeeaaaeaadacdeabdbdeccadaeacaeaeeaeaabbeedbdaabbebbadddbbddeadbebdebaadcecaaedeadddcaeebdcabadbbddcbaaebdeaccabbbddaebebbbbbccdeddaaaeebbadeedbaabaadeaabaabdebabaccdedbbcaebacaccbdeaddddebacbddaddeeebdeeedebcaeecebadbdaebebcebcebcdaddebedcdeeaeebcdbdebcaedeccadcacbddceeceeebbebbacbadaaedebaaaecadcccdeeeceadababdebabecbbeeecaacbdebadcaddaadedadebbcacbacbeabaadddaaaeddbeaeaadcceebaacdaebddacbaecdadebabcbadddabddcaeacadbededbcbabddceaecebcccaabeddcdccebabecdaeaecdabbabedeaadcedbdababccacbedbabaacddbaeacabacbedccdcedcdbceebaccededabbedbddccebedaedbbeedcedbdbcabeaacdaaeabadeddeeeadceddeebabcaadceceadbcbcaedcbcbeecdebccdabceeedaeedadddaceeeeaaadcedcaabcbacaeeeeacbdadbeaebdcdeaeacbebeabdbbedcbedbaecdeccadeececcdbbeeacdddbdedaecebaeabdedbabeaacaabdacbadabcaabebcdecedebbbbbdcadaadcaeebaaeaeeaacbaeaddedadeaeddeccebdeaedeccaebcedcdaacbcceceadbacbccbeededbedddbcecbacbbcebeadcebaeecaaacbabcdcbddeadeebedebcdbcebadeececbbedcadaddeeadaaccbbabdbaeedeadabeaebddacbbadcdbceeaaaaaaaacbcdeaeaeeeeeabbaededebbabcaccacaaecbdadebebeebbacdcebcacaceadccaedceebcadacbeabccedadeddeadccccecdeedcceadbacbaeddeadadabbacabbdddbbdacbdcbceedecbebcdbedaabbddadaedcdabbbdbceaccceeecdcdadbcbbbdedbddbececebbbcdbaaebcecdbbbbccaccdcabdbbbbebcbbbaebaacbadadceeddbebdbadaabaceeddaddbeaabcedcbbbcccdaebcabcdbeecaaadeeaebcdedccecdcddedadabbabeabaeadcdbbccaddbadbaebcbbcdeadaabdeeadeaaccabbddddbaacbceceebceabccdeaeedbcadcdacaaeabcbabaccdbccbadbabdddaaddcbcbbeaadbaaadbbceeabadebcdcbcccddeeaebebecebaccdbbddbdccdbcdeddcccdbecbbbddaddbbeecddeedccbadeadacdcedeeeebedadccbdacaabcadaddcccbbeceadececbbacddddabcdcbaeeaeecddaadabdceddadcddbcdecdacdeceaabbcabcbdedbedbaceedcadceedebeeaddecaccdcbbdeceedadbdacdccdeedeedacdbbebeaedcacbebdedceedbbaadbaaebcbcdceabcaecdaadeeaeaceebaaaecadcbecddbcaeadedcccdbcdddddbbdbcebacdbbccaaebeeeddacaeabececebabddcccecdcaddaabcccaaaaaaeeeadabaabeecaaeedbbbdecacbebebaebbabcceebddbdbdccddcbbeadbaadedbacdaadaebdecdbeddbeeecebeeecdbaacaecaeddadaaceccdeacacaedcddccacbbecceeeebcceedbadaaddaaadbcbceaadaebbbbeaeaaddaacddbeaccebebebaaaedeecdeaacacaedccabddbeadbbabeedbddebebbeadbbbceaedccddcecdebcaebcaceccbacabecddaaaededaaeeaceebaceadbaccaeacebbabecaabcbdcbbabeeeebdadedbdbdccadbaeeeeebdbabdddbbeeeaeeccbdcdaaeeadacaacbdeceebaabeacabcbdadcdddaabbeccbcdceccdebcadbbbdbccacacdaeacdabeecccbaeccdcbccacecaebbdadecaedaeaacecbadabbaabcbddaaedcbcaddddbbddecadaebabaacaacaaecbcdebbeaaecaccadaeaededddcedceebbeabaccdacaeeacaececbbacdaababedadbcbdaadcedcbebbaccdbacdaccddaaeeaddadcbcdbbdddebedacbecdcbbcdbaecebcbccdbeedccaeebdaddcbedaebcecdddbedadcadbbdbcccdbdabaedecabebdaaacccbbebcbddbcbdddddcabdceeebacbeeeecaddeebebcbcbddbdcbddbcdeedceebdbccecbcbedebaceeddebeacebacdccecccbdcddabeccbeedabbdbedebbccdcceabbedeaebbddcccceabcbcbdecbccddacdaaeabbcecbeacbdabeceacdbeabeccbbbbaceccdcadacdadcceddebdceaedcdebcbbaaddddeecadebdccddbdceebcbeaebcbabeabebeadacbaeaacdcedbddacdebbacaeaecccbbbcbeadacddaaceaaaddceedaaeeabeecacaccccbbcdcedcddcdabacddcccbebbbabeaecbcdabdacacbceaeadbdadddbdeedbdbecaaadbedbecaedcdaededdeeedccaccbeaeebdbebdbbaedcadaceecceaaabcebeaedeaddebabbdbdcaecdbcecadcbbbbdabccabebbbbebddcbbdcdbecaebbcaddaaadbaaddbdcbabedbceeeaeeecdbbcaeacdedbdacaecbabececbbceabcdabdeaadeadeedbbdaecddeeebaedcdcdabcbabcdbeceedcaeddaabeeccaededcbccdbdaaededeadaadeacbceeecccccedacbaaeaebcccababadaeebdcbddacbeacdacbbdcbccacecbceedeeeedadaccdebbcedbeaabddbadbceacadedaeabbcdddacdbcddebaebeccaddbaabdeaccaceabacceebdacbcdaceedcdebbebeababadeceadecabdcbccebabaabaaaeacdebacaaaccaecdedddbdbeaaeeabdbcdcecbccbabaaeadedabedeaddecbddcbeaedbdcdeaabecaecbabbaeddbedaddeabdebbeabbecbbbadbbadaaacdcbbeeadbaadaadddceacceeeadaeeddcebaabaeadcebbbdddacecebbcdacecaaacedaebcbeaaaebbadbeaacbecaeacbdccabbeaccbbeeabbddcbaedababecaabbacaedbdbcbdcedcdbbcaeecccadcddbacccaeecbeeedbbeddbeaeadedcedcdeccaeecaacdddebadacceeaebebaeccbceabddbdacdedacadaaebabcaebadbccbdaeaddabbeccdcabbaeebdcbbdcbabccaecebcbddbcbdbdecccbeaceeededddaecdbecdcbaccebcdebabbdeeecbcdaccceddbdebcddabbedabdabcadacccecadeadcdecdedddaababdcdaeadabdaceedeeddbdccecdeedebbbbacaecddbecacaededebcdacdadddadbbbdaacececdeebeeaeaaeccdbacaedcbcbaccbdaadbaacaeaadbcaabadabeddeecaabdebddecedbcbbaedbcacdeadeaddabadbaedebcebbaedaabacceeaecabdadbecaeaabcaeecbabeddbbcaadaeddeaceccaabaebbccbdbbaecdccadebeddabcdaeecddcbedabebaecbedecbadcbbaeadeaacbecdbcdbbbecddeadedbceedbcddbcadbdcaedcbeacedcbedddcbbdcedeaaeeadaeaeededccccdebacabeebdaecaeaeabeceaaabbbcdeedaabdebacbecebcadeacabccebacebcceeebeedabaeeaabcdaaeebdaecdbbaeebbebbdaddbeccccbecebcecacbddbcaebceabeebdcaecdcbeeccbccebabceaabdeaeeacbaeeadeedbbecbbddbeacecddcbbecbddebccbcccbccbedbbbbdebeccbcadceceebcecdabdcacaecdaaeeccbcbbecbccbcdaeaebdadddcaddbdcaeeadaebcacaabcdabbcdcaddcaaadbcbbcabeeebdcbecbacddcdcadbbcbbeecaabceebeaaaedcbbecabbcacadbdeaaaccdedcaeecebceadeccadacebeeedacaacdaeeaebbadecceecbbeddbebbceebcdbacbedeebebebacdbadecbeebdcecddcbbdeedacccaebbddbaeecaccceddeeadbadbebcbbedcbeaacadddeedddbabaaadaaaacebeaecdaaceadbdcdbcaaacceaebaaeaccccdbebcbdbabdebdebcaadcddbabdbdcacedadadbaecbccdcdbbaededaedabddcadbecdbbeebceecccbbaebddabbaadbcbeadaccbebaaaeeeaaabdedbabccabdaabdbacdaadadedadddaaaecdbbdcbbabdcadbdedccbbcebeceabcbbdbbaeeedbdaeedcabccdbbcecbdcabaedbacaccdcdbdddcbbbbeeaabacbbecadeadcbebeedcbeaeeeedcebdcbaaeecebbaacdecacceeeadbcdbdabbcbcbadcaaedddddedacbdcceccaeabcadbacccdabbadbdacabdeaadecdabdbccebebabdeddbdedbcacedeaeddbdaadbccabaaebabdcebecdbaceddecbbdacccdcedadbbddbdbaaebceacaeedcebdeaadadbebdabadabeeebacdccedbaabbeeaeababbbdbccdeeaaaeacbbbacacbeeadaaabbabbaecadadededadecceaaddecebbadaabbcebeecdbbcaecabccaeedcaddaadbceaecccabbdeddcadeecdaecceabecdabceededbcbbeeacdcdaeeeeedbbaedeeacdadcbadadadecaadeeacdddbdadcdbebddebebdeaccceccceedbbabceedddedeecbdbaabcbddddbceabcbecdedabecbbbdbdeeecadecdbdaacceedaadcceccadcddcdabcadadecadcaabaeedcaeceadcaeaaaaacadaedaeaebedbcabbaaceacacacedbeadcaeeacebdedcbbebddcaddbedccadebadbcebaeaebdeebbeecedddadabbedbaaecdabbbdaaebeebbebeacdcecbbbedcdcccaabbbacabccbecabdddcabeddadeaeecdabadbeeeeadbccbaadeedaaecbacdbbdadeaabaaacbaaecacecdeeddadaecebcdbecbcdecedbbdcceccadecbeeadccbdeabdcaecdaaecdadcccdcbcaadcdaceddbcecedadabbdcacddddedbebaaddbebabdebdaadcebaebacbcbbdbaabccbbadeecbbacbdbeadbbcaeaeccbdbbdcabaeebaabebbcacdcebbeebdecedbabedabdcdccdcbbeecccecebacedabbbcdbbcedeadcebcdbecabbaeaaecabcbabcecdbacaecebbceeadaacbcccddedebdeeddbedddcdaacecaebacdbabdbabeabdaedeadceedddcbbdaabbeadccbaabaceebbedddcaebdaccddedadabadbeebebbacccaddaceacdecebeecabaacaadccadbedeeccedceedcdaddadcacbeedccaecceeacdebbdebaeabedbbddbabdecbbcdedbcdeccdcedddcbaabcabdbbacecadeaabcccedecdeabebcbceccdddbdbcacdeccaddaaacbdeabbbdcaeaecedeaacceaaaacacbcedecaeecbacaeddadbddbaadbccdebadeaabaadadabcbbedabcbaadbdecaceccbeddccdeabcebacdeeabcdabecaccdbaadbacccdcdaeeceeadbddaececbbdedaecbeeacedcabcecaebdaedecbadceecadcedeeabcddbaebdbdcbbadbbebbcdceceaeddabddeeddbeaadbeddebacbaeaabddbaebcbbdebccedaddeccbbbadaecdbcbeeaaebcadddecdddbebbeddaebcddcbdbcbeecbcbbbaeedbcaddadcaeeadabdaddeaabaebdaddbdbdcaceebeddecdcbebcdbcccaddeaeecdceabdccabdeeecabdeaebdbdaeaeeedcbecccccbabdbdddedaacbbaeeeabcedeeeaaeaaeadbdeeeeeaacebeeeabadeabadddbabdabadaabbdbebadaccaedbaedbcbeabcdcdaaaccecabdeebccbaaeabedeccdabaabbeaecdbeeaabedbbbdeabaacbdaecbabceaeeacbbddeadbceabedcebaabdeaaceceebdbedaceacbbeedabeacaddeacaceddedcedbaecaebdaedcdaeccaebcecdcbddbaddabbeddadbddebdedeaaecaeeaeecaddbdcaaceeccbeceeaeeaebbceccdcabeebecdedbdddedaabcbaaccbaedbeabaddecccaebaaecbdaceadcddaddaebbcbcaddaaddebadeaeedaecaddaebbecdbdeedabbeaaeedecceccacdbabdeeacdadeecdceacdcbeaeddbdccaaeeaababceddaadadcdadccadbbeedeaadddbbdecaddbdddeceddbbaeaecaabcbdcbdddeccbcdbaaacaaecdedbcaeaacaeedddeeecbcadbbdaadcacdbcadaebeccbeadccbcecbbaeaeccedebadedddacbeeadbabbccacdaadbceabdaecebcdaebaeddbacacdabacaaddaccdcbddcebceaabddddaabdeaaadebdcddbeaecbccaaddbcedabaccacacdbbcdeceeaaceacecabcaadacbecdeaadbdecabbabebbadcdedcddacbdbcabcdddaddcebeaabccbcebadeeceeecbeaeadbcdcadbedeaeecbadeeeecbededbceacbdcbddccdccdebcbebbddccecaaaceddadddaeceaaaacbaedebecedbddcbcebbdcbdcdceeadecaaddebeaaadeeccbacbabecebccdceebceeecdedbcbdceeccacdecbbdddaeccadbabadaedbbbcccaaaabaeebeededbedbbdbeaddaedddcaaeadbccadaeeebcdebcbbcdccacbaeaabccdbeeddcabbbccbcbadbaeedaaaacbccaccaecdbcbcdacddecaaaeeabebedaecdcadbbcbbbaacbaecbcaacbcdcbdcedbecacbaadccadbcdcbdcbaabcebaedbadbddbacaabeecaabcdaecebdcadacbbadbccbcccbbeaeeedbcabbbcccdebbeecbaaacadbacdbecbbbaeadedeeaddbdacaaeebecaddaabcdebdebbaaadabdaecdaccbbebbebcececcbbcecabccaceaaedcaacbccacadcadeaeeabaceeacaccdaadcaeabecbbaabebdcbceddeeaaebeddebcceadebabedcceaeacbdebceadbbcbbcdadacecbbeedddacdbdadbbcaacdbcecadacedeacedbabcadbcabeaaaeaecabbdddbbabaeecaebbadddeacadebbacceeaabbdcaaeacccaceaeeacbccedecbddccaadbdcdddeadaecacacccadabbaccbcabbedadebcaeaaeecdecdddcbbbeebebedcdecccaacceacdcecaecbbceeabdbbeaaeacadbebcecaddcdaecceebdaedcbabdbedaeccadbeeeebbdbdecaacbcdcdbabdbbbcbccbddbaceaccadcccabaeebccecbccddebdaadadbeabbcaadbedeaedddedeacddcadaadeebedaabdabeaaeddccbdcadcebecdceaaeedcedaeebaccdcbcbdaccecdccceedeebcbddccecebdbaecbebdeccedeeebddbdeebdcbabaaebaeeacbaabdaabaccdcdacbebcdbbaebadacecabaccdabccceeecbcdcacccecaceddbbbcabecbdbddecbdcccebcbabcabdaabecaaaeaaebccacecacacbceeaddcbdcdadebebbdddcbecddddeadcaceecdacddcecaaaedbeaaacebaadeecedcbdabeeaeadeaaeeaebbceeeaeababadbdebecdeeecbdbeceacebebcbecedbededbeddcbdceadcabbdaaacddbebdbcaaaccdccddbbbcdbacabddedbaadcccbadecaecabbaddacdbdeeeababaabdbabedbeddbeecacacecedeaabaecdeddbbceaeeddeedbdbaabaedbbddadedcabcbedacdcbebebceecabcaeceebddaeaebececdbbacaaebaaabadaedacaaadeaacaecdecbbbdaaccaccddbdaadeccdeadaacdaaeceabbbddcdadaddccbebeeadacacceecebaacbebabccdececdebdbcbbdcbbdaeccdeaedebacccdedddeebabdabbbeccaddaeecbbebcdbedddbeedddaaaceeceebdaebceddeabaccbeebabbebbeacaaaebacdaaceadaebbabddbbbaabedbeacddedadedbbcdddaeedecaccccececcdbecccadeaaceceaadbebcdacabbbdbaebbacadaeaedcedbaaebdeeadaccbbebceaebaadbedecaddaecbbaaaccedeccbaeeaedbacdbdaadeaecddeeeacddcdeebbcedbaebcdecbbebecaeaaeabdecdddbbddbddbccdbcbdccceddccdaaacebcdddbbbcdddbdaecaaedaaadeaebcbedbabdacdcebeccadbdbcacaeadbbcaebdbabcbdaaddabbdceaeaacccbedcdbccddcaaccdcbddeaddaeebbdcedbdbadedcaeabdeeeedebecbeecabeddbdddbcaebacbebbdbcceccecedecbbebbeeaecbdeddcbacaeaeddbaeabbecbbbbcddaedaabaaacdbaebcdeeabbbdbdbeeeadcabaeedbcddeecbbecbddcbaabdeaadadedebddcedbbbeedeacaaebedcbaabcddbbdbcaacddeebcceecdeaddacbdeddbebbeadedabeaadcbbcbcdedbaaebecebbcbdeeeaebdcacabadcecdedbccbaeaaacaacecaabbbbcccdbeedcaaabeceaacaecebedbcacbcbccdaedaebbaaaecdedddccddebeddbbbabadadeaeadecdcbbaecdacebababedcaeabdaeadaecdecccdeecaadcbeeaadbcdeeabecdecdeeeedecbebaeaedadbbacbdeabddecdbababbcceeadbddeaacebabebeccbccdbabceceabddaeadebecdbadeeebaedeebeebedbddbbcdddabeddcdccdcaacdaacadeebcabbaedbaaadcccbecdcedccbdcdedcaabaebbeddaaacbdcacaaaadebbadbcdbacedebaddeedcbabeabbedebdbeaddcabbaccddcbddccadececcbbcabcdacaecceddcbbcbceababbaebeacdaeabdbcacaadbcbcdeccdcbbcecbbeeabeeeeeabeadeabdbebaacecdcaabecaaddedcbaebeecbaedededbebaaabddeedcccdabcdcdacbeadcddeecddaeacdacbebedbbedaedeccdcaaabbdebeacbcebadbaecdaddbbbddccbcacbeccceaaecccceeebcacedbabaccccddedbbaababccadbccceeedbeaadbdbebcbbbabeabbcddacbdebdeddcedbcddcabaeddaaaeaecaeceeaaddedeeebddebecadbaddcdacabcdeeddceebbebbcdcaccaaaedaacccbbdabacedadcadcdeeadceeaaadbeeedabebcabbcbdaecdcceeecddbbaededaababbeeacbacbdbecabacdaeccabbcaeeacdceebbbeeecaeedceccdbccdddcceddaddaddcbecdceabbabecebeedcadbeeccbccbebedbbcedeacdeddcaaecceeeacebcacedeabbedeabdceecceddbcadaabbceecababaecceebdaacbceeabbceabdaaddeaeecceabacbebbbdcccecdbcbddcbccaaabcbdecdcdbacecaecdbbaadcaadaeaebeadbeacbdaeceaecaeabcbabdeacadceacacebaceacdbcbacabaeaeaceebbecdbececbeddedabaeaaeacabadbceeabbadecaeebbecdcecccddcbaeddcccbabccaddecbbcecceabcabbdceaddaccabcecacdeabcccacebbccbabaadaabdbdbaeecbbcbbdebcebbdeacaccdabdbcccdcbbdddddbdaebaddedeaccdedeccadbeaceebbcebdcbeaacadaedbdbceccddeadabbdbdedbcddaaaadadabcbbaeeaeeebdccdaacbcbabaabbedbdacdeddacedabcaabebaaebdebeadccbcdadadeadaeaabaacadbccdebdedbaabcbcdbbbbbbadbebdcaaacccbeabccadbaeaadedeecbeeaddceeadaacceaccbadcbacdddeccbaaeaedbeaceddaedaadeeeebcbdcadccdaceccceddbdecabdecccbddbdabcdbcadaceaecbbdebddaaeddadbedeadddaeaccbcabecdaeaccbacddbdbeadeedadbddaeceabeeaedaaebccecbdeaabddbdcadcdacbbcdcbdbabebbcdbabbdcbcbecaaebeedadadcaeabcddcaebccdbbaaadbbdaccccbbeabacbbadbdaeccbeacacceeabecbaadedcecdbbedebbdccddddcbbdeadacaebeeeebebeedadbdeadbacbebcbabcaacadddadcdcedeeecccadecaedcbbeaeeeeadeeacbadbdacbdacdccadaeadcdbedddecdbcaeecbedaabeddcdcbdecebebdaeccacdddbcccbeccbecedeccccdbcabccdecacccdadbdbaeacddbbebedccdcaababebdddadcbaabedcdbdeabdbcbbcbebdebcbcdecacdbbeeedbcaeddaeabdabecdedebcbcdaecebcdcebaabcdbbdbeaaecdbcaeeeeeeeabcceeeaaeadbdebbecccbeebccaaddcceeeaabdeebdcaaadbeeabddbcaeeaacebcbdcaeadddeccebcbeaeeceeaacbdcdacbbbeecebdcdacbbcecbbdaaadaabebdacbcdddaadceaacaaeeaeadacebbbbceedecddddaadaadbaddaceaaaaaeadcbbceecbdbecbbdbdabceedeccddbdcbbbabebbdbcaaacadcbeddcabaaedecceaeebbddbeabacedabbdcbbdbbeabebbddbccbdeceabebcbecbaacebeccbaeeabdceacddccedecdaeabddaabbbddaccdeccaaecbccbbeddbcbbedabddddcaeedebbeeebcdddeeeeaecbddacaeabceceedbcabbebbedddbaeecabecdcbebbbdddabceeaccabddbdebddcdacddacebebadedaadeeacaeedcbaedcbdaedbebddddebbaecdaebecadaaebcdcdabcacdacadbacbeddedabbeaebbbaaddeaaadbbcdbdbdedbbdbadcaacabceabedddacdcaebdeeecabaddaedabcbbadddbeeedacebceacdcbdabcdaedbdcdebaaeebacdeadaeaaedecbdcabbdbeebeeecdbedddeeeccadecbbebabcabaddbebbdbeeeaceacddaaceeadcbabdbaeaaeacddecdecbbdaaacceeabdbcbcadbabcbacacadeddbcbdeedbadecedbbbcabbbbdbeaeecddadbaeeceaeadaaaeceabeedcddcacecebadacdcddacaaacaeebdbbbccbabbbaaebcdbbaacabbdbceccbcaaeccdbddcedcbcbbaeaecddaccccccdcaaacecccceddbcacdbedceeddaeaddbcdccdadbebbbceabaaedddcbeddeccbaacebeeaabacdbebdabeeebaeeaaabdeceedcbadcdccbbeedacaeebddaaceeccbeacceeaebddaecaaacedeedceecbebcdcdaaabaabdaeceaddddcabeedbceebdbcaceaccbccacdcbcdcedededebecacebcdabdcaacddaaeabeebcebacbdadcdbcebecebcbccdecccccbceecdededeceaceabebbeaebdacccdebbebecdaebeddaecacbdeacedabbbdcbecbdaaadcdacaceaebcdedcdaaeeebebecabcccebbaceaccaddcaecdadcdabcadbccaaaceeacbbdbaaaaabadacabdaedbaebdbecbeaeccebedaeecdcbcdbabbcbcdbacaaedeeaeeeceadcdbedbcecceedcbdcabcadadcddbedbedeadaddebabdccaccabbcacadacbabbcdedbdccabcaebacedbbcdedacaeeedcaeadadcccaabbbebaeadbcbdebeecbccddcadbebeabadedceaacebaddeeaceacecdeabaabeadcdbcbbdeecebcaaabeedddaceaacbdebebadeacdebaaeabeaabdbbcacbaccbeabdbdedcdaabcddbbcaadcdedbdaeaaddeaeeaacbeaaedabcdeebddcceaeadedcbccadadacbdaaecdcddcdbabcbbeaaccdbccbaddabbeeceacedadaaecceeeaabeadbeeebddabdebbcaadcdeadcddcbdabeeeadceccedebdacbeacbceebecaaeeababbeddcaabbbdedeebbbcabcebbabcbbecabaceaeaecebddddeedeedcaacaadcedbabdcbadabeeddedebbaaddbeeeabedeabbaadbedeaabecddeabeecbabbeadacccbcebaacecbcbcebeeecdccdeceeaeadcddddcadeceebeeceabacabaadcbacaaadaebbbbeeebbdccdbbebcccadaebaeeebdaeedddeeecebdedeebdbddddddaceaaccccabadacececbcdccbddbdbdeecbccceacbbeabedbabedaedbbbdaaaeecaebccdbbbbcbceccdbdebbdeadabcccdedcabcdadaabadbbacbbdcdeadacadccadcbbabbdccccdedddebdedebeaccdbedcdbcecbdeecdbedaadaaecdceececebbcecdbaecbacaddaccaccdccccebcdcbcccceaceaadabcccbebcaabadababecdbdecdddccdbcedcedccaddaecdadbbabaddcbceacaaeaddeeebacddaadabcddccbdecccedcebdadcaacecbcebbaacdaaeecbecccccebaadaebabcdbcaebcaadadadeabcbecddbbcecbdabbbbbaeedabeaecebbabcebacaedabeaebaccaaddcdabcbebbbcaedbcaebecdebdcbdddddcbbbeebcddbeababaabcebbabaacddacbeecbedbecadedcaacdecebdcbcedbcebccebccacdceebadbcbeeadceddccaacacddeabcaabedaaaabaedccccacaaebddcabccbbddbdacacdedebcabceedbaedbacdebbdeeaedeebccbeddcbabcccbebdcaadaebcdcdabcabeccabbcccedebcdcebecebaabddbabcbccaacdcecbadddcbdcbedccacaecdcdbedcbbedcccaccdaaceddeacaabbedadadccccddbabdaecebecabcdaecdeecdcccedaabaabcbcdeaebeadccaebdaaedddcbccebecddabeeddaccedabcbebbdeedecadcceccbababebbdcddbadcdccacbdecbbdbaccddbcedadcabaadadadcaabdbbbaebbabecbbbaaceaaaceedaaeaedcaaabaccaebccccaadcbbacebabcdbdbbbbccbeabecbcdadbbaabaacdaacdbbcadceeecaceddeaeccecaacddbaeedeccbabeeaabcbaccbbeeabbeecbbdbadeacbaabbdcdbadceabbaebebadbeaadbddbeeaababdacceaaddededaaebdadebebddcceedebdacbacabadabdaaedbcadadacebcbababdecbbabbacaebaddebecbaacdaaecabbaeeecdbceecbebbebdbebedbbaaeeebdccebcddbaddabaadaddbdcddaaecebeccdacebeccabacebbbccbcedcbebacaadabadacaeceabeaebbccaacdddbdcecbcbdbbdbebaeeacdddcdeebdbabbbdecacedeecacecbdccabbacaadadcdcbdeadeedcecccbbcaeabdebaaddabbbabcdbebceedcddbbcbedacaeabcedcacaaaabcaebdbdbedeaedbbdecbebedeebaabddcaacadecbcbceadeedbbabbaddabcacabbbbcaebedaabadacdbdcedaceebcebdcdaceaedaadeecbaeedeaddbcabccacbdbbceeaedbcaeadbdbaabcbcbcecdcdabdbceaeabeceeceadddbcbcecebaadeeceeedbbaddbededaceadedbaadedabddcecabdeeebbacadedcaebbbdcadbacdcbcebdeeedcacebbdacaaadaebbdbbdaaebebaeadbcaddeccbbacbdddcdabdebcbaeeabcededabaacebabcedaeeccecacdedcecebbabdddcaceeabcabecddbabbbcceceadacbdbebacaeeaadbeecaeedacadabbdeecdbebaedbaceeaebdaebdbbbceebadbbcddedaadddaadcccdbdbbdabcdccbaddaadeadcacbdddcacbedcceaccaacdbcbeddeccbdacccceabdcaeeacebaddeceebebbbaebabaeaaceecbbceecebbdaccbaeaeadbdeedcebddaacedcbebdeabbcedceacaabaeeeceabbebdccbbedecaceeddeaebeabdeeaebdccddbaebcccdcdcbeaecbdeabadeddeabcacbcddbbaddcadaaadeebbbbdbdaeaebdaebedbeacbacaeecebbaddcaabeabccaacecaecdccdcbccaeccebbcbbabbdeeadeabcbccbebccebeddaaebbadcedeceddecedcbeceadddaadcaceaebeeddecaabdbbaeecbddcbbaecdeaccdabeaabcaeababdbedcebdcdcaabcbbbcbcacdbaedacedaceddedcdccdbbddbebbbaadaebddccaebdbaaeeebebcecbccccdcbabcccaddcbaecddcdaacaadbcbdbbbbaccbabdeceddcccceebccbdaaeeadeacdbbcabdccaeeeceababcdcebbabbdadacdbaaadbabbbdbaaeaebdecdaeadebbbaadacceecbeaeeebbebacecccbabacecceaccaadeeeecbbcbecbbcdceeebacbbeeabcbcddbbdcbbeedabceedcabecdaacaaabeeabeeebeeddebbcccdabbabaebddacdecbaadddeaaaabccdabecdeeeacbecdeacbaacaddcaaeedcbdedbbbdebdbbbccabeceaacdcadecbdeeadccdadabadaedadacbaadecaaaadecaaaeadcebedaeeddedccabeedcccdacecccebbcdcaadecbdeddcedcedcacbecedadeccbecbadaadbeedbeeeacdedbeaeacaeacdeacedeecbbbbbaceadedecaeebabaebbdaddacdbcdbeecabebdaebededaeddaacbaecdbbabcbceadbeebbcdabaaceeacecdbacaecdaedceedbcaccbbadeccacbaebbdbdeccadebecceceeeedaceccdeacccccbdcbabcbbdedecacccccbccaeaedbbcbeeaadbbbdbbebdccabdbdadeecbbbdaddaceedaccaebaadcdebcbaccaabacabbecaceeddceecacaaeacbdeccecbacaebcdddbaeaddeeccecaebadbdbcecdbbbaaebebcabbebdecabedcaccabbaeebbcddddbaccacddddbacbebedeceebddcaddeebecbddddcdeceeddecbdcaaeecbebebaddacecccbeaaccaddbdedaeadbcdbaedabddeabaabeabceaccecbaedccccbddaaeacccddddabcebddaebacadddbdabdccebeaccabacaceaabecbceadbbbbbbcdecaaeeadeeabaaacabbcecdddbedbbaeaebabbbeedeccdcabecbdecdccceedbdbcdeccacabaadcaacacabccadcadeeaedadbedecabbaddebecdbabbcaabdeadacddccbbeaddaeddedcdecaebadadcbebcaaaadbecbcdccbbcdabdaaacaaacadadeedbabdbadacbabebdcdabcacbabdbedabeeddcabbdcebbeaaeeaabecabbbabdccbcebaacbdabaccbcaadbcbcadcebbecebdccddbeccbdadddbbedbdbabdcccabebdeedaeeaceaebdccdecbdcdeedbedcdddcaddcaacabeabceaedddcaadcccacdcdaaaddaadccebeddcccebbacccbcadbbcbddddeabbdbbeeeebabdeaacceddeadacdbceceaeedabaecaadbddbbbcdcedeadedeeabceabbcdcabaceebaedcbddaeecdaabccecacddabeadeccaacddebddbbbbdcacdacedaddbaadeccabedaacecbdcdccabbddccacaaddacdcbacacbbcbbcecebbcbacededadaacdbeaeccbadcedeaeccdbdbaacecddeddaddabadaadadeddedbbdbaebecbaeeeadedeedaccacacddaccbbbdbbbcaaceaceceaceddecdbeddadabacacdbdedccceaababadbccbabaeddaacdacedecedaaadccbbbbceceeebccdbeacdbceabebbbdececcbcbabaeaabcedaeabdccdbbeaccacebbbbaeeeaeeaaceaaabceecebbbbddacdeedddccdabadaabeeecaebebbbadcaedebcdecdbcedadbaddaecbbaddbeccddbdbebadccccaeeeebeadbcdbbcedebedadaecddbdedcebbeacabdbcbdddbeeeeceddeadbcddcccbeabecaedbbaebceadeddbbaabedccaeeccdceecadeceecbdcabdebdaedebbdbacbbccadbbcdbcabbaccccaeebeeadeabdabebcceceddcdaccceacbaebadaecbdbdbcdbabdaacdaeebabddcdadaeddbedabdbeccaeacaeddaadddbddabebecaeedecedcaceccdddaeadaebaebdbcdaccddbccecedbadaccacadbeeccacecababbacabbaeccaedeecbeaabcedbceaacdedcdacddcceeeccecbdbdcddebdcbeaddcbbcadcebeaecdeaacaaabdccaecadeacbeebebbeabebecdbdebaddceccbceeeacabebbcaddcbeeabdcbddbecadbdbbdcbabeecaeebdcddadbcbedaabebddcaeabdaadaabdceccbbeedbadeeebdeebabcdcecbbdcdeddeedcbbeddcaeadacaaeeebbeadddbbddcdeeaabccbeccaeaecccbdebcdabbebaceacadbadecbcadacadaeacddacdbaecbddadcacbbebaaccbadeeebaaabebeddecbbbeddadcdacaacacbbeaaaeecabdaeeaaadbbdcadaeddbcedeeedbeaecdecacdacbeccdcdeacbdcaaaeecdcaaeaddabbaaaadabbeaeecdeabdeacbcdeaccacaebbbdebbcaddcabbbbaacdbcbacddeaedbceeedaeeedcadebdddabeaacccaeeeebabeedaacaacbcaeadacabddbadacebaeccdbaebacdbccedbadbcceecaaeceecccecadeaeabbbaebbdbeadeedbcecbcedabebcebabdddceccbbbbcdabbbaecbcbcadbdcdbecbceaaaedacdbcbccbaebbadabdceaeaddbeccbeebdebeeeababcabdcddaccedbacdbdacbedeeecadbadebabbcacccaacaacacdbbddaceadaaebaeceebabaabeaadcdcacbebbccedeabccadaadeebeabcccbcccabcaceecedcacdbabecbcdbbbdcbaacdddbdcdddbaedebebeebbedeeaeebdcadbebbebddeebadbcbceaaeaaabaaeebdeeadbabbbeeabceadcddaeaaedeaeaddeceddcbaceeebccadacedaebceebecbbceeacddaedbcaeeebedcdccaeebebbeaccbddcedeedddcecbdeddcdadddecdedddcacdbaaabebddebeddddecbdbbeeeebebccbcbaedeeeebecaaaddadebbbadcdbbbaddddaedcbeeaceadaddeebcadaeeeccedeabaedbadaaeedaeedaedccdeccabecdccabedcaacbceaddbcedcdabecaaaebbbbaeccceebecebbadaeaccaaaabedcdcaaedddbcbddaebaadabecdebcbaeadaccccdbdcabbdacbcecaaacaeedcdcacdeabbddbceeaecdecaccddbccbedcdaddbbebecdabaeeeebcbcdeadebaeadeecbeeacbeadaddbbddbcebabbdcdeaeddcdecabedeeecacabbedeeabeecdeabebdebdbdedeacadadddeadebddddbecebbbdbaedceebbddbcabaeaebaaeecaacecdadebdbecceebecbeedcdbccbdecbacadbbebcedecdaacadeddbbdbddaddddcedbeaacabbabdeacaeeeabddddbedcbbadeadacabdabaeacceeaecbedbebcedcdbdbcaabbdceaecadaadcbcecbaecadceecabcceaeeaceaddbeacaecabdbdcdacbaeededdcaaaccaecdedadcbbaaaecddbdbbcbdacdeecbcdabceeeacadabeacdedceabddcbdaacedeabeadeaccbedccaacabdcdbcdbedebacdcbccabebaabbeebbbecdccbcdebabdaaadbcdcdebdadebbcdcabccdaacdcbedacdddbbcbcdecbccaddecccabdaadbbbdcabbbabdcbabeecccddecceacccecbcebcbebecdbdaebcdaecdbcecaecdaadaebadddabdbdcbdaeededddcbaaaacbeeadabecbedcacbdacceabebeddcdeadbedbcbacbeeebabaccbcecacceebecaddaeddcbcadebaddebbadcbcedaebacbceddbdddecaebbabeabcdabacbaacaddbceeebaadbcebcdacabadcaaacceabedbeebbaacbecbaedeeeaddeeadbaabbbcaebaabceecdcbcbdddecbbbebabbccdeeacacdbaaeaaabbbceceeaebebdbecebbbbaaceacaeacecdbacedeecbcbcaabebdbeeedecddbedeedbaeadcbcbecceebbeebcddccbadeabdecbdacbdebddccdbcbbeaeeebdcdaeeecddcbbbdaeecdbacbdaecdccebdbbaeabbeebbedddbcebbeabcaeecddecddbeebdcbabceaddbddcabbaaacacaebdadcaebdbacacbacbcecccaacbeeadeabbeaaccbccabdabbeddebabacdcddcedaddaebcdbeadeaecbcccbdcdbacecddaecbaedecdcddebacadbddaeddbcebabdcbceaecaeeccdadcaabddbebebcebbeeedeccbcdaedaebcaadceeecbdbdeececeeceeecaecdcdbbbcedcaaabcddbedadaeebaacbdcacbdeaabbaadbbccbdababcacbeeadecceeeeddaddebeceaceccaacdcbcdabedbbaccbbeacaeeedabccbaadccecdbedebdbbeaecbeedaecdbdddebcacebdaecdcbcdcadeeedadcecdbdbbbdbdceacebaccbddeaabaccdbbebeaedcdcbaaccceeaebbbcbacdaebaccabacceecacdeedceeddbadbdedaaccaecdadcedecbedeaaebcbaccabeaebdbedccebecddaeebdbacbeadaeedcaedaebadeccacddccabccebdadcabcbabcbeeabeaccdbeeebebbacccccddeddabdddbeaeaebdaccbcbecbdabddbdaacdbabcdbecddaebcddbccdeecabdeeaddcdedeaaaeebbabadbcbacdaedcbdcdbaadbabbabdccdbbcaecedadbdecbcbbccaeeebdbdbbbebebbdeddacacbbdedecaedeedabdaabebcbcdecacbeeadbaabaeaaadeadaccceadecbbabcaadacccaebbabbeebccddedcbbdceabbbcadecaeadeebeecdcdabccdbbabcabaabebbcbabaaedebecedcbcadcdeadcecddebeaeaeedbcbabcddebdbadeeecbcadeecbbcddcbabdbdcaaabdacbabaaaebdbccadacbeaaddedbbbaddaaedaeacceeddbceeabaccbaddbcdcccddbeadbccbdcaeeecbbdbaeeeddadbcacbacedcbeeeebeecacadbcdceaaedabebbddbbcdebedcaabcccaddebdbeacacacacdbddeacdadceaedcadcdcaeaedacdecdecdecccbdceeebddedcbbdcabdebabcedaccbccbdbedcedabdeccbdcababdcbceaaebaebedddbaaacbbbaaeeeedcaededabbbeaeacadbaddaabdebadddbcbaacecabeeebdbecaeadddbbddcddaccdcdebddbeebbdccebeecabaeaabcaeccdacccbdbeaaeedcabeabdbcaebdcbddeecdddcebecaaedccbecededebebcaaeaaaeceaabaebcbddebebadeeebbcecaceaecaeeaceeecbaeedacacecdbbacabbebaeddebedcbbbbceccddeabeaecdddddaddcbebaabdbcecbbdcdddeaceaacacbadedcabdeeadccdcceeabdabbcbaadeaccdbadceedaadcacdeedeebaabacebabdaebcccecbdebdbcceebcaeeaaaaaceeccaabcebeeacddcbdecbcbddeaabcaadbddddbdccecdccceecceadacecabcdecbbaccbadccbedcabdbdcbedcdecedceeeadebbcedcdbbcccaaaeaeaedbecccccaaecdbdbbacbbdabdeaaccdeacedcccdbccbcbeceeadbecdbadaaebcadccbbbbddbeadacdcceabeccaedbcaedbdeaeccbbddcabadecabeccbeedbcccadbcbeabddbddcaabecaceedeabedaeeccddbcedabadacbeedccacaebbecaaadecbbedbacdcadabeeebbaabbecdeaabddccbdabaccededcbdebaaaeaeabcddbddbceaabbeecaeeccebddbedaaceecdecdaaedbcaddcbddaedccbcddcbdabbbcbdceaeabdaabaeaecdaaeeeebceccbcaadcabcbdaddaaedaadecaeecbeeedbaeeebcedaacbbadbcaabdcdceaaaeccbddabedddaeaeeecbabdacceadceccbdcabbddbceabbedceadddaaccbdbabaabacebdbaabbcdbbddbbdacedcdbdddbceeeedcadebceaebceaaaadceeecbdbaccedbeccbbccbaebddbabaaaadebaccabbddaeaeecdddccdcebcddcdeacdcabdebaedebdbeecaaadebdbdcddedecdebccacecebecbccdcbbdcacbcdccaaebdaedacbceaaecacdbedacccaaedeeaecdadacdadbbaadeeeebcebdcbcedccccebdbdeadbeeeabdcbbeacedecdbbcbeeaecbaeebaadeaacbecbabeedccddaeeacbaadeeecbaedaeeeeccececcacbbacaecceaceaeceabddacdbcaeaedbcdcccedabcbdbebdeeaaeebadbdcceddeeccbdbcacacdbadacbaabeeeedebadcbaaeaaabdadaebaddddeabdbecddcacabcebadebbcbcccbaacceeceedebabbedcaddcbcabcadebbeecccdcdbaceeddcdcddadcbccbadbdecbaaceeecabebaccebdbcdcdadadecdcdcdbcabcdebdaadadbadeaaadeebecdacaabdeedabbcabbebdbddddcaededadecaeecedadbbbedcaecdcbdebeedecdbabcdaccebdaaababbcddbacbbacaaccadaacbdcadbeaaecbcebebccbbbeddddedeadbddcaeeddcaaebacdcedcdacececbcbdbdbeceecdbabedeedcedcbbdabbeebdcdbccaeecdbbebabcbacbceccdacbbdddadbdeadccaccceadeabcedacabccbbcbdeddbdccdbccdaabbcbeedededdddadcadbaddbeaebdcaaadcddbcdeccceadeebbbaceccdcadedbbcbcebebacbaabcdbddebaeddedacccabcaeebdeeedebbdbecabaedaddcaacececeaebddaeebebeccacabbadcacbedebdbacbdeaaecedbababaccdbcaacaedacbdeabaeaacaeaabbaddedebebebcbcaecbaeaebbdcbdccbaaedededaccaddcceaecbbedeaacbecccededabededdbdcdeaacbeaabcbeecedabeecaedcdddebcebbedabaccaebceddbdbdcaeeaddeceaaabeeebeebbddbbdeebceedddbbdcdeadceeedbabbeacedebedddecededabbedbaacecabaaeddeddcbceacaaebaceccebecabeadaaedcaabdecbcebecabaccdcddcbbeabcdabcadedbacdbecbabdaebbccdcaacbeacdbedacaaaadbbbbabddeebdbadbceaedccbaabaaadadabbadbbebaabbdcdedccdbdcbeaadecddbebcdcaccbcbebeceaeecdecaecbcedcbecaebecaaeaeebcccebdcceaaadbcdbebaebdbbdcaeecccbbbccbcbbebdacedacebbdcbeddccdccccbcaadbdedbaacccbbeaeeeadeaaaaaacdceaadebdeeaccacadecdbabaedabecbbdcadacbedcaecaccbcbeacaeadcbeceeaebddbbcccdebceccbeacebadcccdceabeadbcccceddeeecddabcdaeabdedeaaabbaebabebcecdbddddbbcccecdeaccebddabbcabcdcbdacaabcddecabccbcabdaaabddacbeaccadbddbeaecbbaacbbccccbabeccbaeeecbdbacecbdaecedcabdaecdbdebbbabeccacedbdadadbdcbadaccdbbeabcecceaaedeaeaecbbabbccbdeadabdeadbabbadabbdaccecbcabbbeccdcaedebdcaaeaaeeedabedecedcaddbadadcdbeecaaaacbcebebadaabcabcccedbeedcdaeceaecaebccbcaaddbaacaaababaeaaecebededcaecdacedaccdedceaeeeccbababadacccceabcbeadcadeaabcbbebcddaeeeabcddbeaeecadbdeedaceadebcccecaddeaddbabcceecaaccdbebebcbbbaaeacdadceacaddaceedadbbadddddedbbcbeccedcbbceeaadebddadbaeececeaeceebcbcadbaeebaeeedbdeddacdcdedeeaadcceaadccbcbeadabbbeddaacedadabcadaabbaadbbcdecceeaacbaaeecdcacdaceadaabeeaceceebacecdeccacabccacdebdbbeedbeeddeececacdacbbdbbabaedcbabbbaeaceeacbccaaeacbecacdccabddadecbeeccbcaccbddeddbbdbddcdbcbbddaabcadadbceccbeeeccaadddbcedccdeacdeaabbebecedcabceaddcaedcacbedddbbdadabbeabbeabacebedecebcabeededecbcdacccbebbdbebebaaeeadcddbaccdeacdabccbcceaaecdcdadcddabdcaccdadbecbaeaaaebbddaddabbaebceeebbdbacddececdaadbeeedeeddaccaeadacaadebacebadaadbabdbedccbedadaeaedbecddccbddbbdaadcdcebddedbcddaeadcdabcbddedbddbceecdadeddccedaebcaacccdaccebcddebaceebbaaeaaeeacecacaedeeeedabecebaadbbaddeaacebcdbdedaadbbbddaeddddbbbaeecbdeabeabbccabcaeadccbedbaecadbedebaedddadedacabaeceaedcaecdbdcadbeeedcbcacdebbccbbeebddecedeccceecbacbceacdaeccdaacaecaacdcccabecdceedebaccbbbddecbbacebadaeadbdbccebbbeddcaaacdebceecebbaadddedbedeedaeaebdaddaedaedaddddeeccabceddaecaacbacaadbacbdadedcdcbbbdeecbbdbbbeceeeadbdeacbcaabeceabbaebdbeebecccbbbbdaeadcebededbceebdcdbbaaedabedcabeedddcedeebdaeadedbeadacabcadebdcabdcbdcacebdabecddbbcbcdbeeeebedbddeaaacadceeaeabededbdabcbdbbdabacdeccbcceeeecdebaadaccdebdcbdaebcaeddeacdeaddbebdcccceacbccdbbdadbbdedadbabbcbdcbcbeadbacbdaeaaedbdbcbaeabddcccbacedccdecaebadbdeecbcddcbccddcceabcadedceebcbebdcedbdacbaabccdeacbebecbecbceecdebcdaeeabadcedcbaeaaeaededadedbedcabbadcacbbcdcbadcbaeebbcdbcaaeacebcaebaeddcdbeeaadbdbcaaaaacbbcbaceabdbeceadbabdccabeeedabcdcabeadbeadedaedcdabdddbbeabbbacbbcbdedbecebecddacebbbabaaebdcdbcbcbadbaecaaddebadbdadeacaddcdebdabaaeccbedabddbdeedadbdeaccacdeedaabdcedbdababcaedbdebceadabeaabdbcadbaeaebdbeaddecddcaebeaecebcedaddeaaeacabadccbdedeccbcadebcacdceeebaaaadcccadcbbddbcedecaecbcaeceebceaaaaccdbbebdaccbceddeadccbcaeacbdcabcdeebacebbddbcedeeebebbecbcabcadaaededecbaedccbaecbdcccccdbaeaabeacbaccccdacbddeabdcbdcbeceecbbcaeccacccbdcbeaedbdcdeccdaddddcbebeeacbcecacccbebdcdcacddacddaebbbcaabebdccdbbbdcedbeaecdaabedbeccacedecbbdeabeadbeebbcdabaddeacaededbbccdcaebbecddeebaedabdcebdebeeaaaaaebbedecedadcbdcbebdadceccaebeceecaabacdcdeabcbdecbcaadeddcbeabddbcaecbacbedbebbecebedabacbeebeabcecbeadbadceabdbacedaebbccaaeddbeacebedcdacbedcaececdddeeadbcbdbeeaedcdcdebedecadbeeaedacaadccadeeaebaddbbdaeacaeddadeddecaddaeebabddccbdcadabedcbbcbceedacadcccabacedbebeaaaeedbeebabaebcebcdecbcebeaadebdcdbdbeedabedcdaadebbdeadadcdcceedcaaaeeddaeeeedadaaeedabcddceddeeaebaaebeaecbceadceebbcdbcabaaacedabbeddddedbaacedceebeceddcadbadebdcebccbdceeddaabaeebeeeacbbecbdbaacccebaeeeebeadbabbeabdcaaddaceccbbebededdddeeacddacceceddbbeccaddcbacbaebdeeeabdcaeecbccddecddaeadbdbcbbedddecabbdcdcababddbcceeaabaacdbbdbaaadbbddaeacbccdebbccabbbbdaeabedaecedcababcadeeccbbbdebbcedaedddecbbcebebaedaecebdcebdcddecdbdeabbdcecccdabbaecbdabbeeadcbcacbebadcbeeabdcbdebbcebeeeccaeeecbbedcbadcbcdbcacceaeadcdbeebdceaabcaccbcbbcbbdadeacccbecdedbdbebeddccceeaabebbaeeaabeebaeeaccceecaceeaccbddceecccecdadaeaaabeaddacdbeaaedcdcecdeebcbcabacddebdccbeabcdedbcbccecedeccceeaceeeaccbbbbdccadbdabdbbcebdeeaeadebadacbdbabbeaebaebbbacdbabcdcbcceaccbdbbeceaedebabededdeaeeecccbbcaaaacebadbdcecdbdbacacbaeebbdeceabccadbbaaaddcbdeacacdceceabbaadabaeeeddddbeaadebcdcedaccbebdddbaabdbeecaacbdebceddaebebdebbcadeaacdbbbacdbabbbabbebbbbecabaedeaebddababeccdcecdceacbeaeaeccdbdbddeeccccccbbaecdecaacadbeeeaecbcbcaaaacbbabbbabebcbabdbbcceacedccdceebdbcaabccccdbcdacabdcbecaacbbbadbcdccecabbdebbddeecbddcaaaddeabbcddbceaabebcbbaddbcdbadaeddddacbeaaeadcabeecdccbaeaabbacdceebccbdcceedebdedecdccacbabaebdcdaadebaaeebecedcbdbebbbabdaeabdbadbecdbddeabbbaaedbacdacccbccedeeebabedcbcbccadddbaccdecaebbccceaabdbbaeddecececcbbaadabedceabcaaaabddbcacdcbbaddccadebacddcdcbeddaeeeebbcacbdadebcdaededbdccccbebacbddaedeabdcdbceebecadddadaeccbcbaacbeadaedaabccedbcaecdcecbdeedccaaaedecaaabecdaadbeaadaebabdbcdacbabdedddcebeddacaecadaddececceecdddcbeeabbaadbacabdeabbccbdabedbbedcbccbbcceeabdcaebccbcaeeebceeddcaeedceeebdccecccbbebcaedcecaddbcdcacbdebceaeebdbeebeabacacbcaedaebccddceacddebadabbbdceddcbeccdbedeeaeabdeabddbbadeacccdacebdcebbecdbbbbebdbdabcaddabbeccabddbdedecbbebedadeccacacdadddeacdabbcccdbaebbaabddcdeaedbddbbacabadbeaabdaaeeadbaeedabdddcadecdbdbaddccdbadeadaddcebaadccbcadacbbeebdecaadddbccbcbbbcdabcebdacebecdbbeecaccddcebcccdcbdbdedabdccebeedadcdacedbaddbabbabaedcaeedcbdcdceabdccdcdbbcdcdeeddebaadabdaebaeadeddeacbeaaeddbcaabbadebbaaaccbaddbdaadaddaccaebecbbebdabbabbeeeaebdcdeeccdbbcdedeeedabcdebbcccddaaecdaeeceadaadddcdaebecaadacbddeaadaacceabbdbbeccedbbeabeceebabdabeeebddaadbabdbbcabbadadebaadaebababceeaebcebbcadccaedadeeedcbddcebccadadacdcbeadaecbbeccdedcdddbcbcbdcdabbdecabcedeedcaddadeedbbebdddeddbbcebebcdaacdbbabbceadedcbdeaccbddcecceacceceeadaabdcbcdcbbdeedbcdbbaadbbbbadeaedbcbdeeeeacacdacdebdcebadeebdadaadbabbabadaabeedddbdaabebcedbeabbeddbccdacaadbcdcbdddacccdeacabcbdeaddaccbebeeeedabdeabbcebadcdbcebcedbbadacabaceecebbcaadadeabccedbebabcdbbaabbcbeaeacaaccacdddecbecabcdbbdceebdedcdaaeeedaabdacbbaaabcebcaedabbcbdcebeedbccedadeaebacdecbeeccccddbecdecbecbabbaeacdecddbdaabdddbdccbcdddccdbcbbecdbabcbdeceedcccadeeeabaceddedcdeaedcabdbaeeaacdaeddeacbdeabddeaeedcceccdaabeacceacaacddccacbcbabcaacbdbbebcaabedecbddadedecaabebeaccdacdadeceeaeddbbecbacdcabdcebdcedbbececbebeecbebddceacccbddbdcaceebbccbaecdadbbcbdaacaaebbecadbeeebdccdbdabaddbccedabcbadaaacbaeddabeceeaadedacbabcddcbbdabbdcdccbdcbeeadbddbceebeaaebebdddeecdaadbcaadbeeadeacbddeaaecbbbedbdbbdacdabcdebbadedddebeaddedaddeeebddbbbecaacaadadeeeeaddebadabbcacccbddccdacbeeeadedebeaaeaedbaddcabadcbbabcaadbdaaaabcceaaeeeaecadcdababaeddcdbcaeecddacddbbcbcbedbddaabbddcceeaacdecbdddeeaedcbdaddadbcdcdacbbabbcbdceabcdeaedcaceeeaacbabddcadbcceccccccedaebacebdcdaabcdcdaeebdabedebdebcbddaebabcbcadaadecbbaabeacdcabaceaaeeeadacbccccbdcedaaeeaadcbadceedeadaeaaaaacaabdaeececbdeabdbbbceebaccdbabaaeebbcccbbdaaadcdcedeecacbbedecbbccdaadeceeebaaecbbbeaaebeecabcaadabcceadecddbaebddbecdbbedebdabbeadbbecbbcacddaabaaeacaeeceecabbeaacebeeccdddeeeebaceebccbaaecbeabdcabedcadedbbeacdcabbbabadbcdecdceedcddadddeadbcabcaceeabeceabebedebabccacadcabdbdaeeeedcbcdcdaddcabceeaddbcdbabebcaadaedecaebbedbcbdcaadbabbedbbaadebbceacddbabcccbceabddadccebbccdedecebbbbecbbaeecbdedcdbceacdeebcccceacdbddedbeecacdedadaaaababaaabeccdcbbedeecbdcedbabcceebcebdacdcacdcdaaedeccabbababbddbbbcbabeacebdbaaaadeabdecdbbccbedacddecdaabbaeddaeddbceacccddeeecedcaeaacdaceaaebecaedcecdeabbaeadceecddabbdbdabcbcbbdaedbacbcedcacbcaeadddebecaebdaacbaebbdbeacddceeecebeacbddadacbbddddbdbdaeaaceaecadebdbecbccaeebbbadaaebaddbbbdeadaecaeabedaceddbdbcacaabaecceebcddceadbedacdacedadcaaeceeecaabccadeeeedbabdadbbdbcbbaccdecbadcacbdedbdaddaaebbdeebaecdceacaddebdaabccbabcbdcabeacdbdaaabcdbbadebbbabccecdddceaececbdbacaddddebadecaebaebabacdceacddeebadcbcabcedbdecbaeeabcadaeaaedcaaaebacbeddceebdaeaecccbcbeacccbbbcdbdbeddcddbdecbeeddcdbcbdcabebbbecbebeccddeebeebdacdaabbddebdceebaeeaccbbeebcbeaeeaeabdbeabbecbcabeaadabbccbdcbaccccabcbadddcaeaecdcbcabadedccbdcabadeecdccbacabdccdbcccddbadaabcdcaaccacddedebacdbcbbdeaeadeddceebabbabdbdacabeebddbaadddcccbbaabcbabbacbddeecddebbaddeadaedbedabddddadcbccceabbdbdcdadeccaeceeaaabbbbcaceaccecdcedeeaaabdaaabadbebeebaaddcaceabcecedbdedccdbddebabdbdbddbbdedccaeadeddbceaadccabadababadbbbbdaadbedaacaacbebddeedbecacebbdeeabbedcdaabdcabaaaeadebdbaecededeacecbadbcbeadbbccbcbcdcbaacbcbdbeaeeacaaaccdccebddabccecacbdbbdacbcccddebeaeeedaddcdaaccbceeddcdebbbbbadcbcaabcecbddeaaaabcbccacebbaeebddacbcaabcbeedebedadbcdadaddecbbaccdcaaadecbcdbaacebcacbccabdcbdcbeaabcadabbbeceebaeecddaddebacbeebedacdbcdbbccceccccdabbcacecbbdbecbdccccaabaeedbdecebdeedbadcdedadcdababbbcaedbbdaaabdbbedbecadbaebcadbdecdeddaceaccdbadecacbbcabcaecdaaadcbeabdabbcdbeceeacbcceccdaedbdcaeceedceedbebbddaddabebeacbdadccdeaeeccbbeeeeabbadcdccbbdcbecebecbbbbcabdcceaaadaeadecbeaeddcededbbcdcbaabaaacebeeeacceaabddbedeedddebacccbaccdbcbbdaddbdabcabdecbaabdeeeccaaeaeceebadbbcccecadddedecccecdcadbbebbbdaeedceaccdeececeaddebabcebcbaabddeddbbceedcaacadaddcabbccdbedbcaedadebececacaabeaadcaabddacdaceeeeceaaaecbdeddaccedadcdbadaeabeaddbaccbabcbeabbeeddcecedbdccddbbcaacabaaebddbebdddecdadabcbdbaebeceedcbcbebaaabeeccebaeedbbacaacedcbedcabcbdccbaababdceddddeaedaddcbebabecbcedcadebbcdbabebbdaecadbbbbabcbebdbabeeaedccababadbeaceeaedbecedcdabcbdaddceaeaccdecbbbdababbabebdbeabaeddeadbbeaaebaceedcebbbaedcdaddabcbdcdceedebedaacaceddadedcbbbaaecccbbcbecabddbaaaaaeaaacabaeadbbaabbaaadcedeebdadedecdbdbacdcaedbababdecddecdbdcdecaeeabcadebcbeaccccbcbcdeecdbeeebcdceeeadedccaaaccebcddcaeeeeebbedbcbccaccacbebeacedcdcddcaccbceacdaeabeadacbabdebaabebcbbaebeabeeedbbdaecebbcaecbedaeaeacddacbecbdbccabbdcbdccabcdcbeecdddebaecccdecdcabaaaddcdbcbbdbceadebddddadbcdbaacaeadacebccdacaaeeddaaceeaeabbdedadebededebbbceabecceccaadcdaecacadbdddbaeecccdeceedadaecbecaeadeadccecebecbaaaebbdceebdcbeacccbadbccdcbecedbccbcaccccaadbcceaacabdecacbdbedaaddabccdeeebbeaacdaddecadddbcebaddbddddcdeacbcceedbadbecadbddccdeecaeaddcdceeaedddbbddcdadcdbdcceeacaeccaabddbcabeadadbeebdbddeecccdecbdcbcbacebbacdcaaddebdaeaeabdddcddccccbabaaeabdccedeccccdedeeeaccbbbdaddddbaebccbdbbcdaecacaccebbacadbecabacacabcbdeddcceeebcceabedededcbccddccbaeceadcddeccbadeceabcdbabeddeccbbdecbeabcdbecccdecebbbabaacbaebaceccaeabddbdddececdaaccaaabcdbeaccbdcadcabdceecaecacdaadddddcabedeabbdbbdacdcdaadabbcbccacbddacacceecbbebeebdcbdebdadcaacaccdbeaceeaeccecbabbeccdaecbbeeddebeedcdcbadaabaaaaeecaaeabcabddabbdeedbebdcbaebdcdaeadecbbdccbbbaacaabedecaaeddadacdcbcedccddecbaaeaadccbaaaccaaccccbcbabebaaacacdecbadcaabbbeccdacceaccdebddcbbeebbdbacddddacceecddaccbeabcadbccbacdbdaacdbeaaaebcddeabaaebaeebbecceabaedacbeadcdaeedabbbdccdbceceddeaaadccdaedcdbdceacaccecdccdcacccddeeabadcdebdbedbecdacaebccddeacdbedadceadbbeacdeceaebcabdbacdaacdaabedacadecddecdccbacddbcedbeeaddddeeebdadcceaabdecddeadacadcecbbcdbabeeedbbebebbdccddebdbdaadbecbbaabbacdeaeaccebeecbceacdcaeebcaddbdebccdaddcdebbbedaceabbaeeadacbadbbdbeeeddaddacbcecbdccbbbeeecdaaeeceecebbbecbbdceecedcedecbecedbdcdeaaeeabedcdedbddaedacbebdddaebecbbbbdcadaebaccbcdbeddebacbecceecdddacaabaabccaaccacedbcabcddbeeaaacacededabdedeabcdabedabdddedaacbcdcccccacddcdedaaececcebdecbeadeacacebebdeaaeedbeeedbeceedbadbdccebbddcdbdceacaadaecddeaccecbdccbebdebcdccacbcccedcadceabaabddcceaaadadeaeaeebcaeabcbccdbebadabceaeecbbccbadecbdecebdadbedbdabacaecedeaeddeaeccdeecceacdbdadccaeebacbbcacbabdaddbecddbbeedaddbedceeaaebcdaaacbbeeeccbbdccbbcabedccdbebdcdcbaaddaddebeebaeaadadedadacddbccbaccedaddeaedaadceadddcbcddadcdbdcdaacacccbdabdcceecbaeebccdeaadedbeacaadeabbbbdeadbadaeaccdaeebdccbeecbaeeeaecdaaccbebecadedadbdbaaeeebeceddaacbbebceabebdbcadacecbacccecdcabbbeacbadaddabdedacddccdacbdcaaeebbebaecacbddabecabaeeebbbacdcdecddabceeeaaaecceebddeecdeecadabdcdeaceaabbdddbbbdcaeeddabadcbcdbbeebedcddecdaeddbccccebbdbebbbbebcbdaedbeceaaedbbccebcebcdcebcdbdccbdcebabecbadbabebededbddddbdcbccbbadccccbebcbdbbaddadcaccdaeabddecdbcdeeecbbcaaebbebedceadbbdadaeeabbedbaeaecbebdbdeedbecabdabdcddddbacbdddccbabbacebeeccdbbdeeedbdecebaeadbdeeebedcdbcdbceeebcbacceccbdaceccdbdbbcdeadbaecbaabbaaabecdbdeeaecbdceceeacabdbdbdeceedabcededeaacedaabdcbadbcaeabcabdcdeacaccdcadceaeeecaecddcbbcbeaaddddeeaadcaeddbecacadaeabaeacacdabeddccdddeaadacbcbaaebccabdebdaeabacdeddeaecbbdaedccaceaedecceddeebadccbbbdabcebcbdcecedbabbdabbccdcbbedbaeebcbcdacaedccdddecdbcdaaadcedeacbaadcbdbedceedbbcddabecebeeacedbcdbbbeccdbedcdcbeadecdabbbedbbaeaccdebbdebdbddaaebcbaacadebbcaaeadabcbceabbddddcdadcebceedbdadbdcedadaaaaccbecebaacebabaeccacedaaeebadbeeaddcbcececdbdbdcdcacacaaebadedebcecaabdceeadeeecdbabdcadeeecddcdacaddaebabcbedccdaacbbccbbbaeeecbdcbbccccaccecdecdeaaabebdedcacadcdeaebdcccecdecaeacedeabdcededddbdcacdebebadacecbdabbebcbabaebdecbaebebdbbeabdacbdeaebbaddaeccadabbcccdcbebedabecccbdbeedaeeebabcbaddaebdeecaabebddadeaccdaacaccccbeddbdeeaaaeaedcdbabecacaeebebddcbbaaadedeaaddeceaabdbbccbabcbadeaccdddacdbeebdaadbddaedebabddbbadcdcdeccecbcadddaebdbbdaebceadaeddaaecbaeaccadaeedecaabecccbdeedadbddebdabaaeecdcaebeeabbbdabcbdceddccbdbaaeeabcdaebdcdabdacbcacecaccacceddcebddbadeccadabbabcacddcbccaeeebadccdbcecbadceeecabeaaddebaceeebaebaaeabddeaccdbabbecaabecacecdadbebdbddbceebacbdadcabbbbcedddeaaeabcedebadbdebcadccdbeeacebdbcebdabbeaceedabcdeedaddadbcbaacdabecebbcaebacddbdabaeeceddaadbdcbcddbadcddeaebaeecdabeaaddadaebadddeedaddcaeeaecaadcabbadcacbbbcabebdaeaecedecdaeccbceedbcdaababbccedddacabbcdbeebacbeeadabaadecceddbdbbedcceabbecbcaedcaaceaaecaedbdcdccaacccaeacdaedabccdddbbaadcaeabdddededdcacadbcacddacabeadebccbbbdedccdaadccecbcbaecdacabdbbbcccddbbcbbceacaeaceddedcddcbaaedeabddacbcbacebcbabddbaebdabdccbacabaabeceaaecebdbbbdaaadbccdcecabeccaadabdbeeacdeeceabdcacecaedbccbddcbedeccbcccebbddcbdeaecbaeddabaeceaeadccecabbadcdbbebebbcddeeeecdbdbaaceeacbbedecaedacadbbbeeecdacaacbacdbbbdeeceeeedeadceaeeceaecbbaedcdaeeabedaabeedcacdbdeddcdbebbbabccccaaeabbadddbaeaecdcccdccdebacecddccaeaaeebcaeecdbddeccaeaacabaaddcbaccedeacdedebbebacccddadcddaaebaabdcbabdedbedbdecceebddacbbcaeeeaaddbbdcabeacabbbeacbeacbbbceccebcaddbaabecbeadcebbdaddbcdabaeccbdcddbbddbeeaddceaacbbadaccdecbeedebddebdbbdddcbccccedcedccbcbbdecaddaadddaebabbaeccddccabccdabdaddbceddadeddabebbdbeebdaebbdbdedebaebebcceaeadcbecbbcddadeacdceacdacaceeeadddaebdccadcbaeceacaadbbddaddcedcbccebebbacdbdcdeaecdcebcebbceeeceaeeecbedeccedaddeeebbeacaebdacdadabdceeedaddebdceeeedababeebcbeedebcbdebaddcdbcbdbcbaaebbcaceddbcdaddaaaeaecdcecddaaabdeceeecbebdbbdadedcbdbbbaebedeeaadbcbbedbcdcaecdadaaebdeaabbbccdceacbcdbeccdccaeeecbccaacaacbbbbeccdaebaaaabcbbdeeecaecbdbbadabbeebaccaabeeebeccaadaedabbdeaccaabdaabdbecabaccddbeedcacdededdacbdeaeacbeacedaacbdbbdcdadabdbdadbeaeeecebecaceecebeecbdccdcebadbdedbeddaabbabaacccacababaacabeadccbeceabdbadeabbebbdcddbbaebceeaadabbcabdecccaacbbedaecdadddacdadddbaeadaceadaeaedcabaaeddaabdcdedbdacaeacdedadbcebaebaabdbedbadebebdaaaeddccceeddbaaabbbcaeccdcabaaddbbeddddacadeeaadbbcdcbcdcacbedeaebdeeecdcedabeccaebdbeeecebbdddedbcdbbaaacbaebddadeababdaaeacaeeaedadbcbbbedbcccddcbebbddabecbcacecdcabdaccdccbdcccabcaecebdbedeadcddceeedcbbbdabaeeaeccbcbabbbecdbebadebaabbadacadcabaaaebdcecebeedcaaabbdebebdcdaebebeccbaaaedaebcccecdaaaecddecdacdedcebcdabcebaabecdeaaddabdcbadbdeabbbedcacdcdaaaadaecaaecbeedcabdabedbecdacdcdeaabddccadbadbadecaaeaeabbbdaadbaddbbaebbaebdabcbbbbbacaaebddcecdacddcecbdeeaebddebbadecbdaaebabbdcdadedbbecdacbcdabeabeebdecbacdacadeddccbabacaaebbdabadbaedaadccddadadbaacaeaeadadabcaaaaaaaacbbdbbcceeacbcbeedbeddeccdccaaaaeaccbaedabedcededdaeaaabdcdebbdecbdebadaadcbbaccbeeaccbaeaddddbaebbaaddaacabceeabadcccdccdecbbacbebabcdaaadcbabeedbadeebccaaacadacdabcadebaaedecadddeccacadcabadaaeccceceaaceecbedbcbededabecadbdadbdddbadaccddcccbdeecbdcdcaaddddaedddadaeeddbdebacbcabacceececbebdeacbadccabbbeaedeebeabaadabcabdeaabbbcdecabbcececdaecddbdbabcbbcebaceedadcaaaedcebcdeccaddcacdbbbbcbedaaedcdabcdaacdedbdeecadbabecaeccbebdeedebdcadbaebcaeceebaadeebcaadadeecaadddebaaeacbebdeacdbaeeaaabbcaaeeedddddcbbdbbedecaaecbbecdbbcceabcbbebacadddadecebeceeeacaeaeecdceccaaecdbbbabbbbdbadbcdbedceaccbedbddccacbedcdcbaebddeeaebccaebdccadaebaaccacccccdcbbaceaabccbbaeebaaabacbeddbccbaacdebdebababbccebeedbdaaddbcaeeecbbcbcbceabccacaedaeccdddaceadcdeebbacdcccccaeceaccacedbaadadbdadeaeabbdaabeabdbdabdeeddbcbaeedbbcebbbbecbbcccebacaddcdecaabdbcaaeacbbaababdadabdebceaebcddaacbbabadaacacbaeccdcbdeebdecdebaabeddbdabaeedddcedcecdccccececedebaeeeeaeaeeeeecebaeaabcbdebbcaebcededaedbcaccedacdebbdebeedbdccacdcbbeabbeaddcceabeeaabbccabecadaedacedabdbaabcaabaadcebedaaacabcebececceedadddcbcccedbccebccdbeadadcbeacbaecdadecdbbdeeacebcccbebbebcdbadccaaeeadbcdacdebdddbaaacdeeaececdceaddbdbcaadbadacaadeadccceaddaeebabccaecbaeadeedadebdbacbdebbccacdcedcacbeadcaceddeaeaaedcaaeeacecbaaacaddeebbacbbebebdbedeedacdeaeaaaeababdbaaedaedcacedbdccddccebcddbabbaedcacdbaaaebceecacecabdacbbedacadedadbeabcdddcaacbaccabeaddbbdbdbecdacddaadabaacabacbadadaebedbabcaaadbdeceebdaedcecccbcbddaebbabedbbcdeabecbaabcdccaddaaaeabcacaacccaebbbbbdbbcabaaeeccbcedceabdcbdbbcdbbdbbaabcbebaeacbdecbdeeaebbaeeeaaedcedcbcbdabdaaacaedadabcdddeddbdebabdccccabdadeabbbabbdbcdabcdceecebbcadbcddbaeadcabaeaeabaaacacaecaedecebccdbcaeabcabdbadedeadebdcceeebdadcaaaeadeabaebdacdcdebaadbaeccbbdeaebcecbbebebaeddbadcbceeebcebebceedebcceabceaeeecbddabcadeebcdcbbdabeebdaeabcacdaeedccdccaecdbdeaaaeacdbbababeadcacedadbacccecaecddadbccebcebacabcaeadbcbbcccbcbdeabbddddaaaedeabdbbaeeacbcbececdedacecabdcaceddddddacbbbccbbaadaedbdabddabdccddbaaaecbaeebbabebbccdaddabdabcbbaadcbbdebdaaabaedbacebeaddbaedbeaccecedcdaaacccaecaabbdbbaacabedbdbbdeaaaedcdcddebbccbcccbedabdcbeedadebcdabedbcbcdcebabdccceedaccecccadeddbbebbedbbbeeceaedaedbdcdcacdbdbaceddbcaeacadaacaeaeabddcbecabdbdaeceaabeaeaacaeecacebbedacaaeaabbecebaebccacbbcceacaeedacaeecadaeedccaeddadccdabbdbedadcbbecbdeaaaadbdbadebdeabbebdcadbaededbbddeddbdacbcabedbbeddbcbebedbbbbbcbebecbdeedbceeccaedaedcecabccadaeaccecedaeabdbadaceeabdacbadedbbdddceacbbabaedbbbbcaddedeeddbcbcddabbaddabbebcabbacbbeebbbccbcecbeeecbdacbcecaccdcbbdcaadbbaeacbcadddeeddeceeebeabedacbccebaaabecadcdacabbbbeebdaaedddaadaeadaedbecceaaebecceedacaaabbbeabcdeacebeedacaeceacacbcbdedddbbdeeacdcecdadbadbeeddaccbeadaeadadbbedbcaedbeadddabdbebbedddeeaebebdebaadebaadcccecebbadbaebbcdeeddcdeceaccaddddeedecbedccbaeabaaaacaedcaaeecbbabeaddaebadecbbdaddadbbaddcbaecccccedeaccdedaadbaccccbbadbcdeddabeaebdeaacbebaadabbceccdaccbbabddecbbaabaabbaceabbeebdadecccdbdeeadebaeaedabcbaedcbeaeccebedacaeabbeadcddcabcaeaacdeadcabdbcceacdaacbedebdeeeeedbebceceeaddddbadcecabaeacaacedacbbbbbecbbbebaeaccebbeebaecbdadaceeaadcdcedcdbcedebabbbdeddebeaacabbeabbcdabbcbdccdaecdbbeabeddcbabaaabadceaaaccdaabaceaaaacecacaecbeceeadddebdeacbbcbaaaacbdabeadcaddadbabbccccdeeeaaadabeabcacadbaecbacdbdddddabecaccdbbcbeedeececedcaaacaaeebdeabadabdccaeadcadedecbdadedbeadceaddacbaccbbbceaaecebdceddcaecedcbdeababbaedbbbdacbbdbdedcaccaceebececceccedbbeaddebebbeeeecbacaaeaadecdceabbbecbebecdccdacbdabdaedccccecbaedeccbeedaaeaebbecaaccadaadeabedacabdbbbeecccdeeaeebbabbbbdaebbeeddaddaabaeeeacadadaecaecdcbdcaedaaebedabaacaaacdeaacebcbedccceadceddeeabbacedcabbeceaccaadeddabcddebbddcdbdccedcabadcbbccadebababaabecbadaacccdcaacecabdecbbaccaecabcebcdcbbbaacabaaedadccebacbcccbacaceeeaedecabaaaecdbddabaabeeeeaabedecabadebbdeebecddacabeeeceaddceabdecbaccedacabebaabcaceeebeabbaddeecdbecaaddceedcadddeceddaacacaecaabdebdddecbabaabbbacaeeecaedbabbedeedcaedbaedbabbecbacddaeccccbcedecaacbcbcecebabbebbdecacacceaddbbaeaddecbbdeebcbeecdbbbbdcbdeedebbccddadbaabdcddadadcadbcaacdcebbcbcaedadedebeeaddadbcdceecdbacccbaabebecbceddcbabeceebeabcbeecacecacacacbebbdcaedbdebabceaedbabcbebcddaaccbabecdcdaedbedceebddadbbaabacdbaccacbcadceeddbdaededcebbebcabababbbdbbcdccdabcadbbedabbcddedcdadbebdebadcbacbaddebebaaddedebccacbdacaaaaeeadaadbdaceeecceacaebeccabdeeccdcaebebaddeeaedbbdebcebabdbedcbedcabeeabaceaecceacebaccbdeabadceeebcebbacaecdbbeaabcebcdddedcdaaaeddbceabdacccbbdcededbbaadeabddeeaccdcedccbbcaadebcbedbdcaeeadbcceacbdcdddbcdcdabadddbcadaaddcdaadeeabcadcccdcaecbeebbbeebecdcbdcdedcbabceedbaabdcdbbdaceeeeddbbabeaebcdeeacdecbebbbccccdedbcddebcaabcbcacbdeccadcbccacecdcdededadceabcdbcbbdadbecdebbcadebbcbaeaaeaeadebabdacacbdacadcbcabcbdceeaadbbaaddeecedebeeecbeecddcdebdbabdccdebbdcbdbddecebbcaedceaaaadbcecacdbaacdbeacebeadebdbdbbdaeeccacbbbdbaaccbaaacbeeebccacddabaecbdebadcbadedbbcdcaccbaeecddaebeeddbadbbcadcdabcdddbccdbddbedbccbbdaaebadcbdeedeeaaaaeadeeddaceaadbaeecdebedcebeebccacbdcbbebcebeeaadbcbbabadceeecacccaeabbbeaaacabaeeddddbcbaaebabedeabddeccaceedddadbacebecbbbbcabeebbbedadabababcbdaeebdadccabedacebdaabbecbbadcadebeceedcecdebbdadeebdcdebdeccbabeaedbbabaaabdebceddcaedbebdcedcdebacbdebbebccaaecbcdccbdcdaebdbbebabbbebeabcdaaeeceecdceeceeedaabdbacbbadabebbaeecabcaeeadbcacbbedbaededbebacdbbdbbadecebdcacbcebceaeeeacadacdcbadcbbadbaabaaedadceddeeeebeedddcbebaecbcacdbaedacacbeeeadddbcaabeeecdeabdcbebdaaaaccbccedebedcecbaaaccbadaaabbbbbdbdebddabaacaeecaaecdaebbdeeaededbaecbabedaabdeabedcdbbdcbdccaaabeeadecbeaccceeedeccacddcbebadaecadbcbbbcccaacbeadaecbddbbceedcbddceedeebdcceaecaeceaedcbedcaeeebbcadbcddabdaddccddbeadeabceaeccedebdebababdcdbcebcdeaabccbcebadddbcbedabbcbbebeeaddcebccaccbbbbedbcacdabdceaeaaabebaeebdaeadbaabbdecedbddbbbbcbccdbcdceabbdecdaaeaddedecdaedbbdeebbcdccdaebaacddacdcddbcebdcdcabcdaaceacdcdaeadedbabbcdbcbabcededbecaabccbcdddedbcaadedccbceacdbccaadcececebcdadaceabeaacabbaeebbaaddbabdeaaeeddbdbbcededcecbebdecccaaeebacbdcadbeddcacadccdadddbcdadababcdcdbcaccdbbdbaedacddaebbdebdacaeacbabccadcdbcaeecbbdbcaebceaedbaedaeabecccadacebdedecbcdedaacaaaceedecaebebedaeceeabeabcecaebcadaceeadcdcbebbcaebadaabebacbadbdddcaddcbecbedabeebcabbcbcbeaeeaacbddbbadcaabeaccddeabaebdebeaaeedaedeceaaecbacabdcceaccdbaedbbbbbaebbbdeedaadcedecceecbacabebeacdbbdadcaaabdbcadaadeebbcdbdaccaceceacaeebdebbbadabaccdebeeaaabeaecdceaaaccebecdddeeaebbacabeaaabdebebabbceaacbbaeacadacaabbbbedadaebdbebedaccedbbebeadadebadaebeaedddbbebbebdadddcaaacbdcccceaeeacddbedcadecccbdddadccaacaacedcccbecadebaebbcceacdacbacdaecabcbbbdddbdaaebcabeccdeaabbdacbeecadcabdebacddcbccaacedbccbbdadaedccdbcacccbbecbeaeedaebeaedaadccbeaaadbabdddeccdbcabdcadbeddbddcdbabacddcdecdcbcbdcddbdbbcddacccccbccbbdcdeceeedcedadacdadaecbdedcccbbaeccbaecbeaabedadcacedcecaaebadbccdeebbedaddbdbaedcdabedcacddebbacbedbedaecbeccaeeacbbeeaebaceceabcbedcbcedbdebabbcaebbabccccbbededebbecbbeddcecabdeddedbdcbebabcecebcbddecaaeccbcecacbddcbcabbebedabaabaadbddcedeedaaeaaaaacebaacedeaadadeeaeecaaeecbccbebddaadcdcedbabbbaeecadedebabedaedaabaadeaaaddebebbdbeeadddcbbdadbbdebaaeebdabeeebbadbeedcaccbbbccaadaeebaceabcadebabcaaeabecbdccdeebacbaeddbbaddbdeabdaadbbeabeacedbddecbdaaeaddadbebabddcdcdbbbeddecceaaeaecdcadbbdedcbdaeaaeedebbcdaaabeacceeeebccaacbeadbaaadabdbdbbbbeccaabdabeaeecacebcbeecbeaecdcdbcdcebdcaebeaedceccdebeceddccdcabcbdcbaaeeaaddcccddbedbbcdcaccdcabdccbaabdaddbeaeadbbdcdcabdcbeedddabccadddcbecdbbbedbbabaddcbbebdaeabcdbcaeddcaabebdacbdabdeaeddbdbaeeaabadebdeadbecdaeececbaecbdbccecdbadeececcadbcadecddccebebbdabecccaedababeaddbaebbdbaceecaeeedddddceddbaaaecbecabdaeeabdeebaeaadeedaaadeaeaccbaedaadecbcebedaeeebcaabdacaaaeccaadcbcadcebedcbacccdaaeaedccbebdeedccdbaacadddacdbbdededeedcdbdabcaccdcdadbbcdccdeaeedecdbaddbaadcbeecbceeeaceeaacecbbaabaaedbadcbcadbecbbaedbededdedcbaaeaacdddbbddeddeaabdbbcabdaceeedecdabaeedcbcabaaecaacbbeaeeadeaeddcabbabcdaadecbbbbedecdeabbadcdcaccecbdceebbededcbcdebaaabeaaeaaceadeaaaccadccedbeadcaadbdaccdeeeeeceacedabcadcbedbbdbbaceadecdacddcabdedbbdebbcddabcbcbdbacdecbddddbbeabdbaaebecdebbaaeadcdbcecaaceaacbcaabedebbbddadecadeabecdcbbbeeacabcddcedbddacabacceaaecbcadabbcadcbaacacbabdcedebbbbbdcddccdcededadcccdcbadadcddbbcbdcbdeabceaacdeebdcccaccdbbcbcebacadbadabeedbbecbdbecbbedaeedbbbbaaadaaceebdcbaadebbeebdabbedacabedeeadbbadaebceabeddeebcdbcedaaeaebbdddddadeaaabcdeebecabbadbcdbddcddabdababaabbceecbbabbdcbbcccebddeccecabeaceadabcabbbeaaabcaebcccdadebcaddacceceacceaabdcaabccbbeaddaecdeeaedbaddaebbaeedadddbccaabdcedebecdbcadadacdbebeecdcecdcadaacbdddddbadedcbeeeeaaeecaaaeceebdacecbdaaeccecededadddcaddcbdabcebedecceccaceaebbcacdebebacaeadacedbdaeccdebaccdeababeabeaeeaabadedddddbecbcbeabdacacbebedbcaedadeaabcbbcaaedddcccdcdceeeeacbcddcbaadaccaeacaeeacddecaabcedcbbbdbcdbecbeddbdaaecbbbeeaeebaecabddbecccaddcdbbbcebaeecdeeedcddcdddcecacccbeacecebebddbbdceadbaceeaacbecdbdaaebaaacbdeaceaebcbbbeaccbcdeddaaebcbbdacabdcaedabeddbedabbaaecedcedaeaaabccdeeebdeedcaeedabcbebdbeecdbcaddeccdbddddeccddcddeedcacebdeecbceabaedcddceddaacbeccdabacebecdeedeebeaedcdaceabaedadacbaaeeaabcedbccbcbbaaddebecabcddbbecbcdbeadbadccdedeecebcdbabedbaebeedaccbcdcbdeaaecdeeccceddaececbbadadeeddebbdbcbaaaaaeeaebdebcceedcdbdcdbacbbedacdbdecabcdaceaebaaebabcebcaebadedaaaeacbbedeecbcbeaaacbcbeabcceccaeabebccdeacdedbbbcaaabdbdeddbeecddcedaeedacacacbbedbababaccdbadcbacbebaeeaaaeaebccdecdecacbbebdcabddbcbdeccdadeebbbdacbebacaebaeebbcbceadaecbacadabaddeabbcceaddebabbecceaccaccecdadadabdedabedeeccaadccdaadadacaccceeebebdadcceecabbdabaaeddcababeaaaadeceaeaabcacaebbaedaebdaaebcbcadaeeaebbdaecbacebbeeeabeabecdaaceabcadebbeccbdaebbcbdebdbcaaadbddbcbedbdbebabacedbcbbcdedaceaedbbabdabccedacbbbcebbeadedbbacabadcccabbabddabaeccaccdbecdcddebebdbedebdddabacaaabcbdbdaabeeaebbaeaebbadcacbeadcabbdcabcbddddbbbeaaeadccbaecadacedbbbbdaccadaeeadeebcdcabcdccbeacaabeaaacbaddabeceddcedcecadcbddcaaeadddcdcccddabcbebbcacbeaebdabdaeebaaeacdecebcabeaabaaeeddbbcbbabedbaaaabccaedaedbacdebbabadaccbebebacbadedbeecabedabcdeaeabdceeecdebecedeaebbbdcdceccdaddbabbbdecdaceececbbaecaadcaaeabcbccbaedacebdebecaeeaeeaccadabdedadcdcacdababcdedcacdaeeeebddbdeadccdaeacbcaaacddbabdeaaaeccaeeadcabcbecccabbbdbebeebddbbebeacacdacddccbeaddedabaadbcacdaaeaeebdadceccdbddeccededeabcabccdcabdccceaaabeebedcaabcaadaabcacddabeeddcacddecdbdebccbdbcebaebebeaadbaceeceacecdaaccbeeabaccedebccaccdbdddddcdaaebaedebcdcdcaaeeccaeaceecaaadadeaaebbecbdedeccbeebaaeeccadaeabbcdcaaeacbbccaaebeeceadcbbadcccaeaedaeedbdebaadbbaabdabadbadcccbcdedacabecbeaecaeeebceeaddcbaeddabccaeccccacaaababceedbecceacebbbecddedcbdcaeccabebcaacdbddbaacbcacaaeebbebeccedebeecceaacbdceabedcedcbadaeaeadeeeeeedaedddedcdcbdecbeeecebbbbcaacabcbbceeeabcdaeaaddbcdbaaeedaeadeaddbdddcbebbcaccceaccbecdbeaaddadeabdabecedddacbaeaebeadadbedcdecdedabaccdbcccceddeeababbcccdecceccbebeadccabbabeadedbdacedbdbbbeedaebdbdccbaaadbaecadccabdecccaaabadceaabaaeacededdcaebaececebccdeeeeddeadbdcaeaacaecbdbcadceeaaeadbdeebabebeaaadacacbdbaacbedbaebcaabecbbedbcacdaedddedbdbbdeddcaaaeacdbdbeeaccebeebabbbcbdaabcbcaacbacadbcabaabecbcdeebddbedbdbbcededcadebdbdeeabcaecbdbbbcbdededbbbdeebdbedaebceeeeebabecacdbdbcdcacebddceadebeababbccaceddeceecacbaccecdeabbadbddcabeeeccaecbebddedacbecbceaeabaeeedabbdcaabcdbedeaaacbcdaaecaaddabeddaacbabcebbdbdbcabcabbcdabaacdabbbbcceabeabdeeddedbddcebcedaeaabebddcaccedaeddaacedcccdaeacedbbecdededeaebbbaeabdacaceddedbdbbdaecadbabdbbdcedeabcecaacaadeaacbbabedddeaabdceeabdaeeccdbcbcddedccaaddececbaebbadccbadeeaaeecbcccdbbcdbbceedbdebacadcddcebceabebdeeacbcdcdcbceaadbdcebecaccabdeaccadeaabcacdadaaabccadbbceabdaceceebacbcbabaacbabbaccbecbbaaaeddcbdadecbbcdadadacdcdadbcdcaddddcabaccdcbcebbdeecaabceecbbabbbbbaeeaaeebddbadeddcaeeaddbececaebabdcbbbccbeceabcaedbdccccdcaaaaaeaaebececcbaadbccaabaabdabcccaadddeadbcaaaedbeedebdcedadbcabacaacbceedbedcbedbeabecebdcdbbecdcdabdcceddaecbaecdaecdadbdeeebdbaeccacddedcaaccdbddabadbabebcbcbdececbbcdbcdaeabeeaadacabdabcaeececdaecaeabebbdebedecbaedcaaedbeccabcdeebbddccdabeddebdebcebeaabebccbeebaedeadaaeacaedccdadbbdaaacbccadddebecdcbaeeeaeeededecacedbcbbeaedebbbdeddbaecaecceaceedecacdbeddbababddbedacabcaeeddbdeabbeeddcccbbbdabdeadaeebdccbcabeeecdddeacdcdaacddebabcbccdecbceaaaabdbbeebceaccaebcebbbcbaeeeabddcdcdadcaacaaacbebdbaddbccababdeeacadcabdbacabeebadcecaacaddeeadddaabdcdbddbddcdbbdebcccebeccceabaaeaabaabcebacbcdedaeabbcebedcaadbcebabcddddbcaddabdcbbcaacbaadaeecedcccdeecaeddbbdbbaacddcadeaabadbcaabdcbeeaacceeedcdceabccbdebbdcdedadbeebdadbeaccacbddabddcebeaadbedccaeadcceceeaeeaccdacdcccabadaeebabccdbceedebbebeeebbadbaccaabecdeccbeeccbbdeaaaedabcaadaddcbbbbaaedacceaeecebecdeedceecdeaaacdeeebbeadbeabcbccbdaaceaabaebedadeaebdcbcdcaceebdabcbbdeedbbaddaabdeadeabceaacaacedbecabdbcaedeecdddbddaabcbbaccaaeabeedcceaacddbeeeeebebbeaeedadecabddeacdebbbbabaeebbddcbbdebaeaeceeebdbdaadbdeeccdddeecadbccadbeeddebcdacabbbdcaecceaaacaacdaeeebeeaaadabeeeeeabbacebadeddabaddcacccbbcaaceeceadcccbebaedcabecbdcbcdaadaaecbebebedcdbeccdbbeeecdbeedeedccaeaeeddaecbabeebeeabcdbcabacbaaddeaccdbcdeeebbabebbeddadabaeccbbaedeeeeeabcebcaabecdacccdbcaecbbcbecaaebbcbededabacacddbacdeedeeaceaaadebcaeeaeaeddacbcabbadebebaacabbedcbbdecceccaedeaeacdbcbcdbecbcceeaeddaacceacaebdcccddceadbcdbdbadbceebeccabbaebdaebabcdbbadbbdbcdecebadbebbbceebeaadccbeaeebbbdedcebbcbbddccaacebabddcdedeeceebdaeaeaddbdbecbacddccdaebbebdcaedccbdadbacecddccbdbccedbdccbcbdacdeaababebcaaeccaecdeeabecebdbcbacdacabababeeaeabbcacbdbdcdcedcbcdcdadbcceebebbeaecbdcadddcdaecadaacaddecbcedabeabedecceccaedcbacceeadaaaebbadcdbadccddbccbcbdccddbebbebccedebbcedbedcecdaabaeebcdcccceddaeacaeaecdecddccdacabbbdccaaaadedeaaabaceaebcecacecabdcababcdbddbabceebebbbbeeaaaeabadcbaadeaeecdababdcecdaaecceeabdedeeedcbccecaecdbacecbbdadacccbbacceccdaceaeabedddcccadabbeaaaabbeebdccccadbaecddcccbbaaeaabbddaebedeedbadeaadaceeebbbbababccadbadbebbedaedaaeaeeabddedbcdbbcedaaadadcaedcdebacbecdeceadaadeaeabbcecddeadaadabbacceaaadccadccdaedbdebdeaceaaeadaabacebcbcceebbcabbecaceeceaeecaaabcbedbeaeabebbeeedcbdcbebaddadddacbcaecccceedeececabccbabebaaebbdeddbdaddeddadadeeaaedadacedcbdeedcaebbcedbaacecdaedaebaecaaeedcdcaebaabdbacddbbaaaecbadcdbbdebdaadceadaddeeadaabeebdacedcdbedbeacedbdabddebdbbdaeedeebaabdbcdcbeacadedeadcddceddddebedcaaadeeababdacabdcaededcbbeeddeabceeccaedccdabdadaaddcaebaacabaaabddbdeadcaceaeeddaaaaececceaeceebcebcaaaabaaebdddebcdbbcdebebbcaeebebebacbbcabcccaddeeabebeaadbcebbaeccbaccaabddbddbbbecccccceaebeddcbcdaabeddaadeabbadcbecdeaabeaebdaccebebabbdddacbdecbededbcbdadcadeceacbedbbedcabbadccdecbbadaadcbbcbaeeccbccccaabcaeeccaabbbdadeeeadecabbdebdcdbccaabecaebdacaebecebebbaececbadabbccabdcccabbcabdbecbbeccdbadebaabdbecbebbbcbbbdccadedbdacaecddcbddbeebdeeedcebadacdcdebcbbbaebcacacadbccccebcddddbbebaebecccbdcdadaccbccdbbaaeacebcceeabcedbeeadaecadebbeddeadebcaebdbcbaececdbcadbbcbcadcbedcbcdecbccebaacedcddceacaaaadbeddcaebccaadebbacbacadeedeacdbaadcaaaaebbeccdaacbdbaaecceaabdbabcaeecadaaecdeecdbddcedaabadbaceccaedaeededbbecceaccdabdacddabbbbedaaecdbaabcdbbaacebadebbbbbecdaccaededbcbcecdeabbcecdcdabeabedadadadbdbeeedcbabdddcdcdaeabdeeabbdddeecdddecccdaeadbaebcbcdddcccebeccecbdbdecbaeaadacbaeddeadbdedeeaecbaeebbcbecaeccdecbdecdeccabdeaaabeddaedbadaebcacecccbdceeaddcecdadeceabaabddaabdbdbdeeebbabbcdeccbdebbadaabcbaaabbcbbdbddcbaeacdcbaacacebcebdabdbbbccdbaaeeeeeaeacebdbdccadbaaaeedcaaceacabeaccccedeebadcacaedddbbabbdcbbdbebcbebedebaabddbaddaadbadabbdcaaecadcebecbccbccaddbacbcdbebeaebbebebbaadcdcbbbdebeeeaddabaadeabdbbaadabebdcbcbdebccccaadeeebddeedebdebbcdecbaeceaacaebaaddbecceadebbdabddcabedbeceaddecbccebbebbbcbbabcbecdcbabeeaedcbcddbbecccccddebbeabbdabeabbaeccbcccaddcaebebabaeececcddecabcaecdbbbaacecccdbbdadcbbbdceecccbddacabdbdaaadbeebdbabdadcbbacbedeaacdaccbadaaabcbdaedccbeabaadbaaebecacdaceddebbcddecedbacceecababbbcdcededcbcdbeedbbbecdaeeebbdcecbabcceabbbeddaeeeabeeaedccbecddbcdbcedecdcabbaececeaeabeccaebaaebbceacbcbdbdabcccaadeaaceeddabdcabdadbceebaeeecccaceebebbddaabbaaebdacdbcedacecbbecdcaebadaeadaeceabeedaadabdeccadedbccdeaabccecdbaacbbecdccebcdbcbeddcaebdaebaaccdaedeeeaadcdbeabcddadbbbaddbcbaaabcceacaacdaecededebaadebeccbcbddcdabbebecdcbbdcdabacbdbccdededaadbadcdbdbabbcadcbbadcedcacaeaddadeacddabbdedbdaaceadcbebdaeceecceedddedeededabeaaedcdbddecdebcbdcbacdcccadbcaaacaceaaaebaecceebdceccddadebbacbcdbdeaeecbcdbddaacbccdcbdcabbbbbbcebaebcbdbbceacebaaedeabeedcadecdbbcaaecaccabbedeadaecabcbeebacdcadaddedcccaecebcddbeadabdbadabebbddaeedaebbebaaecbbadeeaadecedbeeaaacdebeddddabbbaebeecbdccdaebdbeddaadcddedabaebdbebbbdaeabcadddcdcaddccadeaacbedccdabedaedbeeebabebbaabaeeddedbdaadeebcbcbebdecebdaadebbbbaaadecdbbdccbebaccaaabaaaaaadbececeddadccaeadbaccadaeececdabbcadcbabbeadacdbeedebbcdabedccaeccaebacdcaaeabdedceacabeceabdabdcdcbdcebebbecdacbeedcceaadaacdaddbdadadadbdaddebbeeeccabaecaedcabaccebbcabbdabbbadedeccbabebbdaceecdaebceaaeaaeaabeadbeceadddeebaaaaeaebcbcbbddadebccccbabcbaddebedcdcedaceaecabccaaacadecaecadcacaadcddceeccbbeddbedbbecebaeceaaeaadacceeaaacbaecdceeebceacedaeadeccdceccebadbbbdeeecdcebcdeecebedccecdacaaedaeceddebccddaebeacaededddeacdaebaedbeddcedaadbdceeadaeeebcbaebecebccaabdbacccdededbcebdcdaaaeedaaabacdecaadedabddddbaeaaebedbbeaeeeebdeaeacabbebcccaacaeaeedcadeecaaaebabbddcedbddddbdeadcdabadbbcdbdebedcdddcbdaebbadeaddbcdabaadcdebecbcaebecaabbabacbecebcedcbcdaabeadecbceadcaedaeaaadddbaeccdcbbbcbbcaeeddbaababcbecaabbdebceeebaedaecbabbbbcbbebbccecbedbcedeaebbbdcecedcaddeeeeccbbaaeccebcbeaabceaebbcaebdddebcbecddcabcbceaedabdabccbbaccdaedecdbbadeaecdccacecccabbcededaeceebdcebceeabedadeeecadaabbbdecadeebdcaeaaadccaabaeebddbbbacccebdbbbeeaaeeadedeebbebddbecbabadadeaadbbebaabbddbccabbeebcbbadabaaeddadebaaccbeeaedccbccbbccaadcedeecceaddaaeddecdebcccbeadbedbbeabbddaacbedbcbcaeecbaccbbecbbaaedcbaccacabaedecbcdbababcacecaaaaecaacdaeecaeeddbecabebeaeadbdccadbcbebcaabbbbabdbacdcedbddaeeadcececacaeeaddaccbcdcbccabebaddedbbcbceacaaebaccdeeaccccddacaabcbecddedcadebcaacecebeaebdadbcdaebdeececcdeeddeeeddadbdaceedbaeecdbdceabaaaeccdeeddedcdadecbbccecebaaebabdaebceacbebdcbaccaaecbcbcbdbabeaedbacbabaaebadacdaacbcdbbbcdabbddaddaccdeceeccacaecacddabacbaabcbbcbeaabedbbbdddcbbadaccdddedeebaabceadbacebebdadaacbabbcbeaebdeccbabbaacabddeabdaddbdaddddcbebeabdbeeaeebcdabeedebcccdecedcdcaaeeabcbcaaeaeeabddabaabccccbabecddecbcdeebecdcebeeceebdecaecbddeaadecdedebadbcadbbbebbdbdadbeccaecdcddeeacceccedabdcdacebabcdebbeeaddabcbcbbeacbadeceddaebabbacadddcecdccebbebebeececceeeeecddbabdaebaeddddddddacdccdbbcaeedceddbdbdbcbebabceebbeaedcecebecbcddddbaaeeecebcdbdbbaabeedbbeeccdcdbedeebdbbeadeaaecdeedaaeaeaebbbeaebcebadbddedbaeeddecdaddaccadaabeddbdbacadaaadbcdeaecdeeadbcdbeccdbaeeaccdecaacbdabcddabaaebdebaeccceddebcdbecdeceeaabeaeccedbbaeaaebaeeedbddcaabcebaadbbeadbacabdcabbbebccebabdceadcdaebaacbbeecebabedbbaacedaeeeedbeccedaadebbbedeacaedbeaedbbbdeacaaaadbeaeacdebadacecdbaccacaabdbbdeccddbaebaebcaceebbedabecbceedccdcccecadcddcbbccdacacdbddccaeccbcbcebecedabdeabcaaeeaccbddbeeabebadbaebaaddcdceecbaacbcceeabccccbcccddadedeabaaaddddedcabcedeacaeceaabbdddbabcdbbddddedadabbdeaabbeecdebcbbbeeebcdaeadcaaddbeaccaaaeddecacaeaedaeddbcbeaccceeeacbdadcaacabddaabbacecdcedbeeebeacedaabbcebbccbceedcecccbbcaaecbdbbcabeacceaddbbbcbcdbabeaaaeacccbbabceeedadedcaececaaeeadecccaaacdeacdbdaeeeaebdeacebcbecedbcecaeabaecaabbcaeabcbdeedacdabcddebdaacbbbcabbacecaddcbedabbeecbedbdccdcecacbeecbeadaaadaeddbaecbecebbbadabaaddaeabbddedcedbbecdcdcdcacdabedeabbbaeaeabbdbdaaaccbcedbceecdccadaebebeadcbadeadbcddddebddaeeabedaedadccceccebcbdbbbbbbbadeccbeeaedecdbcecdddbbdcccbeadecbdaeadbdcdeaacbdaeeaeeaacadcddbbcadacbedbbdbbccdebeabeacdceebbbcabbccdcebeeebadeaadbcaecdabcbdbadcdbaaddcbeeddadeedeaeeaddecccbabcdccececcaaaadaeebbeeecbccccbbaaceebdddeceeedeaaddaaeecceabbabcdbdeccadcabeccadaedcadccbecbaadbccbcdcbeedebdaddecaacecdaacaddbbcdeadcbaeddcceadacbebdbabebbdbcccdadababaadebcdcebcabddccdacabdbcddbddaaedcdcbedadccbcceaeabdcaedeccedaeceeadbdbbaaaaddaeebeebaabcbdcbcdceeaaeacacbbbeeddaddeaceaeaebbaaceebbebabbbecaaaaaeecccdbbececbceacddbbbaaddedeccdccdddcbdabebdcceceaacbbbebbeaccbadcccdeabccdecdbcbceceebecaeabbdacacdbbbebaeeadbebecbadacebcbebceeccbdcdeaeebeaaadbcbeababbabbcdcacaebcedcbeadbaebeebbcbccadebbceeeaceccaceaeeacaaddbecadbdedaebbabaaedaeadecacaaddebaccacbeedbaecadaaebeeeabdccccceddabbaaabdbedddbbdbcccbeebcadaddaaabdbdabcdabcbbdcabacbdeeebbbacdbcaedcbedbbeeadebeebdeeeedbabeecdbbadcebbdbacdeabdceecdedadeccadbadcbbdecdadaabaaaaeaceaeeddbdbadcaceccbdebcabbecccbceceedbbeddcabbdddebedadbbacceebeaedaddcccaceccbeaaacadcddaadcaaccccababeebadcabecbaedbeadcddcababacadbdaaccdebbbcadcbcacebabbceeaececbacdcccacbdebddeaebbdcabaadcecccababeecbcdbeeeeaaecbbabcebbcbbabdadaabdbbadaeccecdabeeecdeaacdabdceedebbcadeaebacdddacebeecaabbeabdcbdbabeeadbacadadcbaccdcccddcdbedbedddbcbceeabbaebbceacbceabacacbbdadbdbddbeddececacddebcecbeabcaceddebdbbccddeaaddcdabceaeabdacbdbcacdceebadeabebcddeedbaeedceecceaaeddebbaadbaaccddaaaaadbcbececabbaeebbadcacbcdeeccbabcedbcddaacecdbeebaaeebdbdeacebabdceabcbdabadbeebbeedbdbabbababedcaddbabeaccbbedccdbaeddaecdbbcbabdcadbdeeabdabdaeeeceaebbecabedddeabeabaaeabaedbcbcecebbabeebbeaaabcdabccbaadaecbcedbadeecccdbcabaeeecccdccabccedcbbaaaeecabcddaaceeaddbbebedcaecdededccbabaedaacabadbabdabecedbeaebaeeadabaedacbededcacddcdacccdbdbbaeabadddcbadcabdbcaebadcabdbeddeaabcbcdcccaebdebacdebcdeecdabacdbbacccdbcabaeeacecececcdbbbdbadcecaacecedddcdddeeddebceaeeaddcedaeeececccbdaaccecccaabdedbdbcbaabeebeabcccedebaeadadaadeeaeabdbdadeecbdacbedbeecaaebcedbaaadccababdccaaaeadedbbccdacdbebdbaedbbebeeaacabcbcdeecbebbbcabedcdeebacbadaadcdcabccbebedaaaebacccdccbcbdacdcebdbbbacbdeacccdceebdbdcbacbceddbeabccbaeaacbadbabcedcdacacbdcdbeedadeacbdedeaeaccabcecedabadbaebbeecbadddddbbeadbdbcccaaaedbaeddadaebdebcdccedbdacebcdbdedaeebeebcbdbbdcabdbadcaabaaeeabbecbdddaebbbcddccecbbcdbbabacdedbcccddceeccdbdcaeacebaddabdeeebebdbeebabdbebadacbbcadaaceddccbeabdcabceedaecabaebacdddadeceaeeaacdbaeecccdeeeaccbbeaaedaeebabbdcdacdbdacaecaabdecccccaccbdbceaebadccabebecceaecbcbaebdaaaccbaaddbdeddbcbcbcdcdbdeaecaaecadbdeededbacdbadcecdeddaeeabddeeacddaceacabaecddaacbdcbbcabaadbdcceecbbbbeaaebabecbbdadcbbebcbdccebccbbebeabacaeeaebaeacdcdaccccadddccebbabccccbbcabebaeddbbddaeeeaadbebdceaaaccddaeebbdeadcbabaadeedecbddedddaeaecceaeabbbbdddceebcdacddeecceaddbcccacbdeabcdcaaebbbaedaecbdebedceeccaacdcbcbedabeedcbceccdbadbeccbddbcecccbdbcccaabbdaabbeebddbaeabeddcaddacccaebbecbccaecdcbbcddcdaeadcdecabbaacbeeddbdbdebbdbdcbdcbbdeaeabdaabbcabdadcaabbdacabedeeaaebdeeeebadccbccbaaacbbbbbdababbaeebedbcdaeeaabbcbaaaceceabbbcdbabdebddbbacadebdcaccadcadbecdabdedcededcbccaaeddbabdbdaabddaaabeabecdabccaccdbdbbbcdcedecbabeeddcaccebccabbeaaacadcdebeeadedbeabaccececcacbddebabeaeeebeecaeecedebadbaccaeaacaadbceaddebbeeabcddaeceabaddedcaeadaebbcaadaecddaeecbcceccecaebbdbdeaadaebbcdcceecbdceaaceeadcdaaacaaedcaeedbdbcacaaabdbbeadcbdabcacceedabdccbaddcadbecaebdcedbbeeaedecddcabeebeeecbcaaccbdcedaacbbbeabedbcabbaeadabbddedcecbdaeedcabccdbedeeeaecdbcdbaeeecccdacdddedbdedddaabaaeedbbdcaeaadceeceabcecaeaebebaabcbbadaccadeeccaebeadbaebbebbacddcacceadaeadebebbabdbaebcdacccddcdcdcacababaadccabdacebdbcdeebceeaeedabcdcacaeeeadbedbbdddaecedeccddaecbeceeebedcaceaeadbcdbaebecbeceeeddcececedbedcedcaeadeaacbcebadcdbbdaacdaeadcdbccbdcdecaeebdbcdcabbddcabeacadcceccddbebceecbbaccabaeddccbbeaabdbedcebcddadccbabdcdcbebbdadeedccabbaeeeedacabcbccdeedabdeeaaadceacbbacbdedaadebaddbeddaacbbbbeccbcdaeeedaeaccedcdecebdcabdcbbeaacebaccccadddcdacdcaebbedbccdbbeacaabebceadccedacbeccbebacdddcadbaabbceccccebeaeedaacaddecdebebadeabcdedbdcbbdbbbcbddccdabcbcbbcdecbaacdbbcbbbbeabaadddbeabaecccbaebeccdbecddedebaabbccbcacdaebcabdadadaceececccbebadeadedecdceaaeaaaceebecaeecdbcbbcddbbaeaeaaeecaccbcadacdaeddbbdbebdecbceaedaccadaedcddeeeedcbbedbebedebadbddedcbaddabedaceccceadedeebeebecdedacdecbdeeddcaaddcbbacbacdbacbbecebbaddbebccbdbddecacdcaadeccedccbdabdaebabeebceeaaaaacdcacbddaebccbbdddaeeebededeaabeeeeaceeaddbabdabbbceddbdedeceeadddcacacacbceeaaaaeedbbcbabaacabbbacdaabdddadbdbdadaeaabdaddacaaeedeabbadaddcebceddbcacaaccaddcecadcbadebceaeeeabeabbdadddadbddaeabacaacdbeaacdaccbacdcdedabcdccaadeadccacacddccddaabbddeeebacadbcdcaaacbaccbcdadddbddaeedcadacbdbdeaeabebbdacbacadecaeedcdcbebecbbebbbadddabdceaacdddebbbeedcacacbabeccdaabcabaaaebaccecbcaaaeebcbaaeeedbcbaacbeddcbeedaeceaddbabebecbecdbccdaacdecccaeeaaeddecbbdababdebeeccdcbccbdccbadcaaddacccbaabadecabeaedbcdcaccecebecacbbccdeacaaeabdbcacebbaaccaaededccaecbcdcbdddbbbebbadadadbedecaddaaaabebeeddcbdbcbdeaceecddcdbedbdeabeddacacdcebadbdbcdeaaaeaccababcbdbecacceaabeabbbedeaecdeceaededddedeaabbccbdababddaccdebeabeabeeaceceeedcbdcebceeeddaeeaccbdbedebaccbeabedcdedaeaadadbcaccdabbcbaaccaadaecbdedecbbbaacaeaabacedadeaabcccdcddebaeaeadbbbdacedcedcdedcedecbcdbceacbbcaeeaaecbbeecdcaccdcaddeceeeedbbecbccbbbaaabebaeaebaccbbeedabdeaaecccbecbacdcedeacbcaaabecdbeabbaccccaabbdadbceadeaacceacaccdbcecbacdbabddbdaebbbadedcccaabeeaeaedaedccdacdabadbcdaeecbdbccdeecdbbaacedcccedbccadddcabbacbebdeeccdeadabacaaedacdbdbceeeeadecbdddeeebebecbcdabbbcaceeaeddeddecdaddaacaedabadcbddbbdaccebdeddcddbbedbebbbdddcbcbeccccccedbcbbaceccedaccdebebdaabadeeebddbeeabebcebbeeabbccaadeaccdbeedcaceebecabdbceebbaaeadceacededebacaccaddacaddacbebaecdbddeededbdebbedcbbcddcabdeeeacbccdedcacbbbbbbaabacdbbdbacebbdcebecacdcdacecdacbaebdaceecddbbdabdbbbadbcaebccaabccaeeacaddacaddeeeedacbccedcaeadbdcdeacccabacbacddadabacebadbbbeeadabdbbaedbbbbdedddecdccbdeaeccbeacceeacbbccaabceacdedceaddaedbdaaabdcdddedbdabbabcbcbabcbedaceaebbebbbbecadbacabdbbeddbaedeabdaeeddaceecbbaadecddadeddcdbcbadcbbadbacbbdcccdcabccabedcbbbcaeedbcdccddadbacdcbcceecaadccaaeabdbedcccbcacecbdbdaecdebccaabbeeeabcdaacaceaebcdecbeecbecdbecbabeedabcdcebdcebdaedbbbbdadeaedbaececbddbcbbceddadcbcaebcdadcadabacbadbbcbbacdcbcdededdaadcbdedaadaccdaeccecebdcddaebdeaecccecabaecbebaddccdadcecacebdbbeccbdaddaccaccbbedcddaeddcebeedaadabeebcabccbddebeddaadacbdcacbddedbbdbaadbebdaeacbdcdedecebcadcdbeececaaadbccbedacaabbaddbeedecbbecdbedeebcbbddacaeeacadcbebacddbabcbabadcdedaeddcebecbddbeebeaebaebbabeddadccaabadcdabedeeecbadeebadcaeadddbbaabeabccceecbbcedbbabacbbcabbccdcecedbbcebecceeacccecddaacdacddbceaeabacdaddcdbcbdecdeabeeddaeaaacdddaebbabddcdcedbbdeeccaaaacadbddeabdcdcccdbceedccecedbdacedcbdceabeeccdcddcebbccdecbeebccadbceacccabbcdebcadcadebaaabdbebeebbaadcddecebbaccadeedcbeeedacaabadccbacbabbcecaaedecbdacbcebededdedeabaddeeaaddbcaeebadadebcbcdacbbdabcdbbdcbddebbcbecbeebbeccaeccbdbeababeeadadadaaacdcceabecaeedcceabbeecbbdcbaaeceeaeadedddaedcbaddedcacedbbedabbbacdbcbbabeacbdccaccbbaecdacdcdadbaacbeabebdcbbceacddccbcacedacbeccddcdedccacbdcbcdabbaedbbceaecdedcabbbbeaabadeacbaeccdeddcdecbdcecddaaadeabaeadcbeddcbbbdddabbeaaddcbdaaeaabaebecbdebdebeccebcdccdcbbdcccbaceabaadaabdbdaddbdeaaecedbcbbbdacadebccbbbdbbadccbabecaaeabcccabecccadaaedaaabbedaecaacbcebbedebacbcebcacbcedebaecabaeecbdebcadadcbacdeadabadaacacecbedbeceacaecedbecdddedaddbeadbaeebabccedabbeeeeeaebdcaaaddcbcbcddebdccaaaccaeddabadeebeccbeabbedebabaacddcdcabecaacadbcceadbebbbcaadcdcceaaaeaeaabcedceedeeedaaccdcdabbaceebeabbecabddadabeeeeadebbaecdaedadbbcbeebeeccbeabccecdeaebdaabeeabddacebdaeecccdbcdcebabedccdbdbbaaceadccebbbbbeeadbbebceadeecaecacebdecbdddcdaddcccdaeeeebdabdebaddbcbdbddbdeebeeddcdeaeecebaacbbcccabedebabdeedeeacdaadbbaeabbbcecccdedeadcedbbbeeeadeecbcbedaaebeddcaedbbecbedeabcdbcedbadbbcccbaedcaeeebadcccdaececbaeecaeabdebaadbbabcddddbbbeaeacbacbbaeeecbdcbdaaddabcedbadebcbebaeaebeceedbbebbabecdcddbadcdbcdaababaddaaeceeedbecbeccdbadecbbcebaaccedddaadaedeabababbbeeebbeaecbbebacaccbdbcdcebbacebbeebddbdcccaedeacedabcaddecdaebecceaeeccdaacdaaeaeacdabbbcdedeaaeecaceaddaacecbebaebccaaacaddaddbeeadadcadabbacbbcebbdedbabebbaadadbacbecbdaebeaabcabbacedcddbddedbdaaabeaeaececcbdbaaceecaddddeaeeedcebcaddaccbcdcdaadddedabcacacadaecddebdcebdbeacedeecaaccdaaecbdbeeeebebddeacdbcaacccadcbeeadaaedcbddeabcdcbaeaeedabaaacceaccecedeeaaedcbebbbcbdedcbdebedbcdedddeaebabccedabbcbacbcbbedccbdeeacebcbaebdadddabeeddadaabddbeceaccccccbeaddcedacceeadbdaccdbceaeaaaaeeadcccececaadcecceabaceadaaaeedcceccccabeaeaddaadccabccebceccbbdbdedbeadbdbeddcdcdddedddbeebadbedcdcabdebcabdbabecdedcaaeecdedadaebaeedbedaaeceebaeccaebeedadaedbdabeeeeeccecceedbddbddadaeabceaacdbeceebcacbddcbbbbdbddbddaceccaecbceeccdcacacccecbbbceceaaadebccaadebbbaeebbbacaaaabaadbbecccacddcbaebadbdcbccceeebdddeddcadcdebceebcdacaddddbbacccaebbedcebcbebcbeccaabcddbdbededbbedccbaeeeedeeeddcaaccbbdbbccaabeceedabbaacdaeedaacaabeadcacbdeaedacccdaecedecaabbacbdeacbeaababdebcaebabebeaadcaccdcadaccaedeabebceecbeadbeaccdccbaeecdeaecacddcbeeaacebcccadebaacaaebbbbedacabecacaaeaccdbbcebaebbdecadbedaddbcbdbdcabddaabaddabebdabbeeaccebceeaccccadcebadbbcbcadbbabedcdcceeabecbceddeedbebabaacaeebdcbdccecaddecaaccaabdcdbbbaccceadedbebbcdddacebceaebbbbeadcddececceaeddbcddeaacbecdbaeacbaaabaeacedcecbcbadecbaacbaeebcaaaeeeedcdbcaeadbcebceedeaeacaabcbbbacccabdeddedacdadddeceddbcbecccbdcdcecdbccbbaceaaeabcbdbaddbcddcaebebbbaeceacbbcdbcecaebebaaeaededbaacddeaaddeddabadbddecbedadcadcaeddaabcabdeaddbeebeeddccbaadabddcdbeababceaddcbeeedacdceeedadcebaabecedecdccaeeeecaaeeabbbcdcbaeccabcebaeaaeeeadaecaaaeacdebadabeaeeebbedcadedaceacbcdaddcedbceccdaeceebcabaaecaaabceaadacbabdeebbabdbdabcdccaadebebebbacddbadbeeabdbaeabcbdeeadbaedddcaeeacebbebbedbdcdebdcedebbecadcecdecbcdacebbdbecbcdbebdcddebedcccbbddeedbeceaababedebcbabcbbebaadeecceebeccbbbdbabcbcbaccbebbbadbadcbcecdddabdadebccecbeedcbadeabaeabbaacacbdcbbdaccbcededdbcdcdbbebbccaaadeddbcddabadaaedaaccbabebeceaddaadeacadebcacbccacdaabeebddeddbbcddaadeecbcbecdbdbaaedcddddebcbeedaadcbccebbbadceabbbdcddadebbddbeadacdeabebbbeddecdddebceceeccabbeccbcceeebaacadcacbccbbeebdeebdaeedaacedbdacdbdbcbceaceccacccdeedbbbdcbacbdceebcdbabccbddcbaebacaaeccbeedebdabcebddbbdacccabbaaadcbbedcabaebceeadeedbdececccdeeaadbbeaccdcbaebdbaabbecbdbeabdeeeddabedabceaebddddcdaaebebeabecaedbbbaedbdbadcbeceeeceeaaccabeadbaaadbcbbdeceebaddecedacddcadbbccdeebbebacaaeebcadabdaddaedcadeacbbbaccbdcabbcaddaadbaaacccaaadbeedadbcbaeeaddaeeccbbdceecbcadccaccaedabcddbbbebacbbadbbdbcedcadaacddbeeddecdcccddebaebdcbccabcbdceeaeebeacabbebaccdebeeedeacdbcbaebdcebceabdadaaebbabeedbeebbeababccbcbeddaadcbcdbcddbccccabbabbaebedbdabadbddacaaaadadecaecbccababdbeecdedbbbeecaaecedbbdaaaadacdeeeacabeadedabcababdbdceaecbaeaeaacabaeaaadaeeccdcdbeceaccabdecbbaedadaadebacddbeebcbdebeabdacadccbdbebdddceebadeeaedeabacadbeebdededcdcacbeaedadebcadacdebbaeacbcdbdddebddedddaccbaeedcbbdcdcbcabbcdadbaabbcddcaecdecabdeeecbbecdaacbccadcdecdbadedceaacceaadcbbdaacdacecbebcbadbebabababeaddddccedaddacebedcebddcadbaaeaacbebcddedaceaaeaeaceedececcdcbeabeeacecddbacaadbcbbdaccedadbedddacdcaaeeaabdccaceddeaccedadaceddcecbdccebbcaadbaacecbdcecaebbdcddbedaceeaeeaaadbdabaccecabecdcabedacdabcaebaeeedccccbacdadedeaadaebdbcaeececaaaabadabcddbebdbdadbdccaeeeeccaeaccccbebaebadbccebbadbcacaaeadeeabcecacdcdecaaeadeebaeeaabeadcedcbcacdededcbbbacdbcccccababcddddbdceccadbddcaeedeaaeadcbbadabbacacaaaeaaacbabddcabbedeeeebabbdcdcbbadaddeceaeaaeeecabebdabbacedccccdcaebcaeccebeacdcccbccdebdccabcbcdadecddbccbedbecdaceecedceeadaacabbedbecebeccbebbacbdcedcdddbeddecedcacabeddbbbdecadabdcdcceacecdbbadccaabbdaeddbcbebcaaabccbaabbebeaaabcaeaedbaceaeaeadadabbbacabeeecdebecaedacaeaecdeaaadbbaeecccccbdebeacaebaeddecaaeabcebcabaceeebeeacebcdcacedcdaaacaaebdeeccccdaeaabbddeebbdbedbbbbedbccadadbcaaaecedaebddeeaeabccdbdcccbaaccdceedecaeddabbaebeccedbbddddcecebbaedacbcbddaabeaebdbececbbdadcaabbcaeccbaadecdbdecabbbadbcecadbcebbbcbbdcaaeceeacaedebcccdbdbbbaabaddddbddbdeabebcbaaeadeaccbebbddbabcbebabeecdbbaadeebcaeeeccdbeccabaeeeeaccceacdebebebbdeeabcacddcaaaaeaaaceabacdaecaddaaaeeeabdecaabebcbeaebdaecdccceebdecdbedacebacdceedbeaaddccbcdbdcdbdbbcedcaacbcedcddcdeadbeeacadbcbddabaaddbbdeaebedabdcabaddeecdbaacdcdacebebbdcaabbabbbbbdcbecaadccbbacdaccdeccbeccbeeadccacbdeaebcbabbebcaedecabdccccbcaacebcbbaeeeeddbbbdeeabbddaccdaeedeebdeceaaaeebaceebcbccaacccbaccdcabaecacbaceaaacbaaacbdcbadaaadedcdeecccceabaaaeadbbabedabbdbbcdedcaaedceceaaecedbabceeaaeeeaddcabddbbeabdbababebbdababbaaccbdeddbbddebdcedeaeababecbecdddcdbdcddebabecdaabecdbdbcbcebcbdecbecaebbceaecaedddaabeecbeccdbaeccbbdeceadebedebedcddbcedaedbcacacbcdceedadcecbdabebdddbbcacdadceadddaecbcedcbcabebeeaabccdbebebabbcccdeabacbdcededadecbbaaeeddbcdeeedddcdbccebeaaedbdbbbeccdedacababedccedcadabdcaecbccebdbcabaabadcbcaeaabcbbcdeadccbdbcbdbccdedaedbcdbecebddcebcbdaacaadeacbbdaeccaacdadaedbadbededdbceeeebbdbddedcaadbddccbecdebbcacdebabbccebebacccadbaeeaabaaeceecaabbeecdebdbbacaaaeedeeeddaacbdbcbcaaacccbecbacdedaceaddabdbdcccacebddcbbcbdbaeabacecaeddddbbadabeacdcabceaadecbbeeaddbaadacaebeecebdacbaeebaaaabebdeacaeccaeabeacdcccdcaeeacedddbccaedbbadbdabeeaeacdadedbccdbaebddaedbbdeacbedeaaebdebedecdcebdeacdadcaccddddaccacbcecceabddaeebbeeecbbedcaeeeedaccdbbbabcbbabbeabeebdcbbbcddeaccbeaebebcebdaeecdaebedcacdbcddbcecdcdcabbeeededbccbaaccecadbccaedbddbecaabeedcbdababdbaecdeecdaecceccbebccceabddeacbdadbdebdbebddaaaaebedbacccdeaeeeaaedcbbdbdacddcbcceeacbbeddcdbdebbcedacebbacbaadbdbeabcabaebaddbededccacaaeeddeaaabbeccedbcbbcaeecaccccddadbdabebcaedaebabaeeaecebceddbcacebdacbdedabbbeebecddbcdcccbeebcedbccbbedecacceaeecadbbbeeabebbabbcdeeacacbdabaacbaebceccbdcbdbdbeadcaadeecdcacddcdbaeccaadabbebbcaeeeeaaccbacdabecddcdacacbacabcdaccbbeddebdeebeadabdddbeebddeaadcaeacddddcecbacaccbbcacdaabaecbbdebedbeeccddbacacaceeedebeaacbeecbbaceececccdcabcedbeaccddbeddaeaceeeabcdadcadbeeaaeddcbeaaddeebceadedbcdbdccbdaaccdbdbcbdcbdbddbaaaaaacabbcabadaabaecdadeeadececbdceddbcbbcaabeeacdaedadeebebbecebceabebbacecbabbbaaccdaeaabdbbeeccceecaddcceaadedebdbcaddabddddceeeaaabcbacbadbcecddcacacabbbecbdcdbcacacaaeededbcaeedacbbbbcadcecdcebdebbddaddecbdeadedadeeeaebdecddecddeaaccadaabadadedcacdcbadccaeebecadbcdeedaeebacddddcaeccccbedadeeccceacaaedeeabbeabbaccbceeecbbceacecabadbdbbebbdaacbaeadebecbcbaddebdcdcbabbcbdddaabaedeaeabacabcbecbacddcdadeccecdbcdeaaaccedcaedebcebaabecccadaacbaeaacedbcdbcdeddcecbccddeceeeabadeadbaeddbaeaabeeccceedbeabcccceaebcdbcacdaeabbccadadbebbdbdbccbecbceadbacddbceddebcbbcabebcdebdddcdabaccbbeaacccbbbabeccaccaedebbcbbaabedaaceebdbbbdaeaddaeabebddbbecdeddacdaadbabadabadaebdebcddcddceadedbacbceaddbcddbadbaedbbbaeaabebbeebeeaeacdcbcdabdadaaceceaabebeccaceaacadeedcaadcbbabceddcabacedddebdeedcedcacedcacdadddeaaddebceebeadabdeaecbbcbaceddeaaedddaaecdaaddeaabbeaabddebcaeacaddeebbaecaeebaddecdddebabacceadcbaacabbbeadebcbbedcedbbbddbcccdceccbecbbcdcdccdaddeaccadbadcbaeecdeaaecaebcddaaebacabcdcdeddecdcaaccbcdcbecdebdbebaccdedcbdbbdaadacaddccddeaeaccdbdacaabedabcacbcdabdadeedcccbaccbacddcabdcacceccaaadebdbebdbecccbbacdbbeaebbcabadbaadacacadadeecaebcbccaaeacadcaabdeaacbacccbbdeddabccecccdeccbcdcceacabbdcabebaeedddbdedcebccaacdedadaabadddcbaadcbdbcdbbbddbbbdbaacadcaedcdbcbbbceebdbcebcbddcdaeaaeeeaececbacbdddbeebddadacbececbccadeeeeaeddaeebeadcbaebeabbcdcdeecdeedcbbabedbbadadedbbbcccecccbdbebddccbddebdbabceaedcaceadedcaecdacebaebacabceddcebeaecdacdabcebaceededbeeaddeceddaeabecbadcdedabcadddcbbaccdcadcecbdbdabbdabceaeedcaabbaabaecdadcaaebaebeaabaadbbcddedeaecedbbbddcceabbecbcdedebbdacadbdedeedcddcbbcccadaddaacdaddbcbdccbdceaaadcaccaddedadccedaddbdbbbdaababeaeaaebcebdeadeebadbcdcbeadcaacbddededebdddcbdadedcbadcededeeeceecabcaceecbbbbedcabeaaeedcbeccedebbdbbcdcedebcbceebeaabccadbacceaacccdeddedbaaaaecebaaaaadbdeaadecdbeadcbdedaddccadbdbbddcbedcecdbbdbaebebdbeaecbebdeabdeddeecddbdbebdbbedeacddebaeebeebabeeebabbacbebbbdaaedbcabaedbeecaecedcbeeeacdcecbaeebabbdedaebbccdcbadbebacdbbcbcecebedceabbeaadcaeaabcaeabeeceadeebccacbdbeecbbebbddaebebdcadaabbabbeecdaabcceaecdbdecacbecccbeaacbddcabcddcdaeeaceedaaaabadeecebcdbedbaeacbeeeaecbdcecdbbadeeedcbcdbabdaaacccabebdccabaaecaadcacedebbbdacbcedcbbaeddddaeabebbaeadbccaeaaaaadeaabbaecdbdedaabcdbecddeccbbcacaddbcabcecdccdbedcaecbeaddaebddacbdeeeecbeacdddcddaebcbbdebbdcaecbdddecdceacedecbebecbcceabcbcacbeaaeedaabbacecebabcccedbdabceeddacbbeeddabadaecbececdbabaadbebbeacbebdcdedbcdaebaaabaaaaabdeabddebaeceabbaadaeddbbcdbbcdcaeaabdebdacbdaedcacdbadecededcdaccaecdbbbeabcbcacbeeaabcedadecdeeeaaeedeeadbaabebdceeeecbaccaacdcddebdceaabbbbbeadbeeabdeaeadcececbdababdeaddaebcadbbcaeeaaedddebaadeebbccccbababcbcecedaeeeaccedeacaacbccaabcdaeaaedadcbbdcadbaaddbadabdddbaacecddbaadddbcdeecacdbbabeabdaeaadaebdeabcdbcbcdcdebeaedeabcbeeeaedceaddadaeeddedceaaeabbbceaaeeecdbdddeadcddbceabadabeaecbbbedacaddabcadabddbbdcacabeabcdbeedcebeacaabdaaaeababdbabeecddaacdcaebbeecdabcbceebcdeebadddedaeedbcedcbaddabadeaddcbccacbbdbcbebedeecebbcdaabceadacaaaeaedcebacdaaaeecaaeedbebddddbecabddaeccabdaecdaabaddaedadacaeebabeceddbddecccccbcbabeeacaadacccbbbdbbaabedbebeddcbaccacdaaeeaeaeadabeeebcabcbdbeacadaceeeabeadcdcbbaacbbededccaabcbebacadaaeccacdbbaedecaccebdceacbccceeeddebeebcceccdcdcbcdbecbdeeaeeacaacbbbbadcabaeadbdaadcceddecdbaaabebedbecadbdbcbddebddcaabbededddedecbadbeabededdcaecaeaacaeedcbeabbdddbcacebeaeebeeaccabdcabaecbbddaabcdabbaddecebddaeceebacabeaebaddeabddcacdebccacbdedcaaacbacdaddececbeacabcadceacaeebdecddacbeccebdbeaaccdaaaacacacabbddcabddadaabeeeaecabaebeeddadacedababdbccdaabdeaebeadcaaaedcdaabeeceebedcaddadbabbdbeadeacebdcbcbaeebeeeccbabdbedeaaacaaadcccebabbdccdadcacabdadabcbebcbecbdaceebaccbbbbaeeddecebabcaadcbdbdcddeecbbdbaaedbbcebeebaaeeabadcebcabeaaaadceeeecaecadadacdaeccbecaadbeaecdbceacbbabbbcddabbddacaaaceacdeeaaddaaaaeeeeecabecacdbadbaebcbcbbaebacdedbaceceeacccdaebcbbcddbbdceccaecebeadaebccabbcbdccaebababbececbebdbbaaedddadcdbabcaaabecdebaecbedabcdddcaeaeeaddaabdaebeceaaeaeaadbecbdcbecabadcdcaabebbbebdeabbceddcaddcecaedcdbeabedaebbebdddacaedcdeedeebaebcbccbbdaaedacdabaddceebcacaedaaebcdacbaacecbecaeadcebdabdcbbacccdbbededadbaccacedadcbebccdeabdaaddbbeedacaceecdaebdbebccbdbdcbaccdabaadccccacccdadcabdbbcdbdcbadabbdcbcecdccdebaeddaeabceeedecdaeccadccdabacbccaedebcacdeebccabaeeddcbbbbaecccececbdcbbebbbdbeabcbebddebabccaeaabddcaeddcbcbadeacbbdedccccccdaddcaebaaddddaccbdebcaccccadadbceebdececabcabacdbedbaaaebacdcabddcbceabbddbeadedeeccccbbccadebddedaaabbaaeceebadbaccadadccbdecbdcdcdbdacaddeacabcdbdaddccdaebbbdeccbdeaccedeabdedacbbdcabcbeebcebdaddadbacdaaeddbcdebcababdecdbabaeddcceebdcdaaddcaadbbbaceeaebeedaacbbebddecccaacdacdccebacdedadddacacadaaecdcaabebecbbeadccbdbedabdcacaabaaeabaaedbecbbaeaceebcdeaabeaeabcdcebbaeabbdbccbedbcedecbeceacbcbacceabbedaacaebebaabdabbcaeccebcedcdbcbdcdddebebbbcbcdbeecdcaabeaedabadceaccbcdaebadcdddddaabbddddecaaececaadedeaeeabaacbcbeeaaebebebeeedacabedbcabddcbdbbedaceebeaeceaeabcacadcdededebdeaecaeeaedcceddbaccacadedeadcebcabeaeaeddeebaaadaacbbaddedbbeeaeebdedebdaeeacbddecceebbdcabdaebcacecbcdacaddadcbbdddcdcedcdbcbdacddcaecaadbacdeadbeeeebccbacadcdacbdabeadccacbecbbecdbababbdcdcecedcceddeedeacecbedadaaabaaeebdbdeeccbbcaeabaccaadaaaaccedebcbcceeacbdaebcededeeddcceabbacbeedccecbebaacebebedbcbddcdbceeeeeaeebadecbaaebedaaeedbedbcdbaeaedbdbdbcdcaadbbacbdecdaabdbaabcdbadbeaddccaccabdeeeceeecebbbeacebdebdaebbeaacbabeaebdbbaedbdecbedbbbaddcebdcddedbbcecaeaaabcdbeccdaaceeaeabececccdcdeebdcadebeebcaacadbbabccbcdcbbebcabbaacedaedbcbbbbdcdacdaabceccadbbbddeeaadbbeaecaabedeceaeaaeebaccbdbdbaedebdcacbeeabdadceeacaceccaeacccceabcaabbcaacccdedacbdcdddeeddbddddbebbeabbccbadbabadbbeaebcaaebbacedcdabdcdcacdbcbcddbccaccaabaeacedeedcedabadeecabbaaaadcdaeeeabddcbeedbbdcddddedbecbabbbcaadadbeacadddabeeaebaedaececebdedaeaebecacdccbeabbbeaabdbeecbbbbbddedabbdaebdbedeaceeddbebcdaaecbcddaacbbcdceabaaaacaccebbcaecdddeaeaacdacbccedbebadbcecbcedeedaadcdacbdaceaadedeaddeaabddaeacdacdcbcebaacacedcccceeccdaedeebeaddcdccdbccebccaabdddadaaeeaeddbcdbcaccaecdeacabeddbaecbadbaacaaedceaabbceadebbaaedcbddccdadcdacdeedbcacdecbbbbedacaccdebccebcbaaeebeedddedeebbabcabaebdccdaeedeabdacdaabaedaddccedacddabbccaecbedebedeecadccecdccbccbaeebacedadeebbcccdabadceeddabedcccbcedaacbadaaabbebbdebcadebbaccaadadeeacdcbdecbadcbbceedecbedeccbeeacedeecdceeedebbbaedeaacbaaedacbdedccabaaecbaaebdabbeececedcccebabcabadadaddeeadedaecbbdaabcdacedecdacbbcceddcacebddeeccaaecceabcccdaadacccbbbbeaeccbbdbbdebaadccacacbeaaaacedeeaaccbcabeaccdcedaecddbbceacecccceadcdaeabedbedcdecdbeaceadbeadbcaceeebcabcebdbaceacedacdddacddecceaadacbceadeeebadecbbeadbbcecdbdacdcaeeebedeecccbeeccdcedeccabbcbbcaeddaaaecebbdcacecadeecabebddbbabadbabddddbeadadceaccbcdbdceabeabccebbecabcbebdccaaacbddeabeebbaaeabaaaedeecbcaaccecdeabdaecdbaccaacabaadadadbebaedebaaaddeabdedacddaecbccdeaeddababadceaacaaddeedcbbacbbedbaedebaaeaccdbaceccdbeaabbbeeadecbcaadaeacebaacbbdddeeaceabdbcbdeaeddbbbeeeecabcbcaccaaeadbecaeeebdbbcedbabbdeccceeaebdaebcbceddabadbcdaaeebbcebaaedcebadebcceebbdedbbcecbcdedbedceacaacaedaacbcbacedabddeebcbbecedbacebdddeadcaebedbdceeecadbcaacdcdecedcceecedddddaebbeccadbaecddcdbbdcbcbbdbddcabcdccdcbbbbbbeadaeecdeaaadcbadcbadbbcaccacaeadddcbadbdcceececbceebdaccbbbeceeaddeacedebbbcaacadaecaebcbbceabbcbbddeceaadddaeaededdcaabedccbdaccecdbcccdccabccaaeadcabbaddeaeaaaabedcdbadeacbdcdeeeacaceeeabbcaacacddaacbbabecaabdeabeadcdbedeeeedcaaaecbedbdbacceccbcbdbececadbcabecddbbaebacddeaeecdeeebeeeeabbcdeeaccebcdedecdeeabadbbbdcdeebacddabbbccabcccdbebdaabebcbebdebecaceebbaabbadeaaabaedbdcadabbaaeeaddbaccebbbdeebbedeebecdccceebdebdecbbeedeebcaaecaebababdeededebeecabadababdcacadaeccccbaaeddcbcaacccdeeededabaebeadcedaacaaecebdaeacabdbaecdcbbbecbabbadadcbdebddbdcedcaecdccaaaaaaaacadeedaebcdbbdecebcccedbddadabacccadadacebacaeadecbceedbdabbaaecccbbeaeccacaeddceabcbadbdbcacddceabcacaebdbcaacedcddadccddbabddaccbdbbebaadedabebacbbcbebebccddbebabaededeeacbcedbbbbababddbbceeabdcdbddcecdeaeecabaebcdeacdaddabbadebbbeacebcdaeaccecccacaedaadcbacbbbdbaaecbdbaccdaaaceeceeaccbeccbeaadbccceabacadeeeddeccebcdacdacdeeaadcaebbdbccbedbaaacabeedadebabbddcdaebceaacceabaccdaddddccbbeebdacaebaddcebcedaaeeceabcaceccdcdaadabddceecddabbabbcceeebdaaabbdbdabebdcdabacbedcaececbdaeccedbcaeecbbaadbccdeadcccbeaebddcaabadeaaababadcbcedecbcdabbabbaabecdbedabbbcbcaeacdbdbbedecdbdeabdaeeacccdddebeadbbbabbbbcaabdabadebaebadcaeceabdebebccbbaadbdcbccacedccadccbddabdceedcbddbdadedbbbebbedebcdcbbbaecbddbeecccabbaacadcdbbcbdcdeeaebcdaeaeebabebebdadbbaeebdaebdecaabededbbbebedaabdcbaabbdcbcbbbeedcdccbbbabbaadadedeadbdaccabbccaacbeaabdcaaddadcbdddbcedbcacdceeaddacddeaddaeaceacebbdbaaeddeaadaaaabebedadbcdcaabdadabaacadcbcbacaddaaeaedcaaedbbabdabebcaeaaaabedbabbebedaedeccdaeccaaecdeccecdbeeecdbcecabbdcdbeeaaadaacecbdedebaedeecacecbaecaeadbcceacbadddbecacbebddbacbbbdebcbbcdbecdbbabdcbddeceaddadeaaddabeceecaeedadceaecdcbecaabbbaebccbdcbaadecceaeeacacdaeeeeabbbcdbabddebabbdaeadadbbeacaaebcedbeebceccbadbbeaeecdacbeccaacabbdbaeadcbdbeeaaddaeebaedeacaeceaeaebeeabddbbbebcaddbbeeedbcbaeecaadecabddbeeeaedceeaeeddccbbbeccceeaedebdaccdebcaaeedbcebbdbabcacadaeecebbbacbbdbdabedcaeceeaaddaaadbcdbbbedaaeecdbebdddddbdbbbbeccacbdbedbbaaabeeabacbdbadcebcdbeaebcabedabadbdcacaecccabbbdedaccdedccdcabdaddccaabddadeddedabcaaccaddbeacddcdadbdbaddeedbebaeadccaecbeedaaeebececabedadbdbbbcadebaeeaaeeedebedabbdbaaeacedaccdbbaceeeabdaacbdcaeabacedcdeaebabbceacadcacccadbabeccbcecdbeccbbcecbcadeedbecadbcbacbbdeddbebeacdeddbebbbdeceaaaaabcbadeabedccdeabcedceadcbaceebddabeeeaaaacabedaaceeadedcddeaecacbcddbbcbdecdbdebcbeeceedaceebbccdceaebaedbdbedbabeeabcebedeadedcddddebacebbaddacbeacaecaeceecadeadbabadedcecbecbaaecbeabddedcadbcbdcbebbdbddecedbaecabaadebacaadccddeabededcdbcbbeebbedcbeeeadaceedbcacaaeadccecabbaaabadeaddbeccddcccceedbccaacaaeeeaadaedeceddeededcadeeedaecbddbeadcdecdbcdedbcccaedebdbbddccdabbadbcccdebcecaadcceceddddcceebaceaabbbbbaeaddeccdacdbaccdccaabddebdebdbeecbabbcadacaddabaecebcbbcbebebcbaabcacaedecabcbcedabbeaadceaabccdedbaddaebbbbcaeacbbaeedabcbabbaedbccccaeebeececbeedbbedecccccadecdcdbaccdbecdedbbcecaeebaeeeecebaabdcddeedeadbcdcdcbbeaeccedbcaecbbcddcedcabeddbaaccdedcceeeaacadaecabddbdbabbdaacdeaaeabdccdabcccdabcddccbeedaabaaaadebbadaaccbacddaebdacabeacacdacbccacdccbadacccaacacaeaeeeeedbdcbacaabaeccbceeeebadaccbddcbabbaecddbaadeabedeaecdebceebbcdbabcbdbedabecbbadabdbdeaaadbcaeaeacdaabcdaacbbaccabcbccccaebcdeacdceebedddbbbebadbdababdcdcbbeddbdecceebdccbabdaaaedebeeccbabdbdccedcddeababbadaabcacdabeedebabbbbbcccacddaececdbbccaedaadeabbcbbceaaacbaceedebaedadaaddcaacbecebdcdccdaaebbaceeabcedaadaaaebaedcdaeeccbabcaeceaeeccbdabcbceebadcbbeeadcbcaeaccadaeddcccdbdaccbbeedadaaaccebeaacdabeecbcccaecebdddbcbbddcecbecaeacdecbdcaeacadabbcbcceededdcdcdbaadeaeaddebbcbccddddceaaddddddaeeabcbadaeabebdecbccbdecdccedecdedaaedcbaecbbeeebacebdcaaebdcddebabedaadeadaacbebeddabeaeeebdcbadaccceacaedbbacbbddbcaddecaacddaeddeeceacdedecaeaeebcddaaceddcbbbbcaddcddadcdadbaabadbdddebeadcbccaeecdddebcbaebcdaacdbebecabccccabbedcaaddbcebcebaebabcedbccdaaeeabbceaecbbebdbbacadbbbaaaadbdccadaedccabbcedcedcbccbdacedaccadcdcbdedbebaaabbbcbdecdaecceeabbacbddadbbccccecacacdeebbaccbadcedeabcabcbbecedecdbabadaebbadceeecdcdaededbbbdcbbbdcadbaabbcdbbedecebbcabdadccebdecdbbcecaeadbbadeeeeedccacbaecabcdbdaceececbcdacaabbacedcacaaaacdcaaedbabedcacdddceddeddcaeaadbdebcbdacecbbaebdabaadcacbddcbdcedebdebaabadbecdeabecddacaebedbddadcceedadebcddecabaebcdacdbcbadbddbbebdeceeadccaccbbaaebbbaaccbbdbaccbeedaeeccccaecaedbdddedeaabeaddbeebddaedccaaaacabbceeeaaebcbaeacdaebdbbabbbdbddceebdececeebadcceeaeddeebdeacddbdaecbdecbcdaeeeaeeeaabebedaceaeabbddbdaeddedadbeedbddccadddcebcdccabedbddaccaadabebdebebbccddeedaeebebabbcdacaaaeaaeeceedabebbdedadeccabbeebadeabcaebcbeaccaeaeebdcceebccabbadbccddbcaadaaaceebddcdaecaccebaacbabdbccedebdaebceededecbddcaacdbadeadcbeaadbbcaebcdbbcecdaacecdacdcabedddddabeebcaecceebaeddbacdcedeadacceabccabdeaeacedddeadebeaeceaeaaacdcaadbaeadaceeacdbbbdadccaeadbeceaeabaeaddeeebdbeeeeaacedbebaecdaebabeedbcceecbbddaacedabdabcbaceaaeccaceaacdcbbccaeeedeccecaececcebdacdaccccbbbbbceccabeaeeaababbebdebceaddecededebdabeeebccdcecdaddaeedbedadebdeabaecbbbcaecebeaecdedcecedbeedcdccbecebdebaeacccdcddddecebcbacabbdaadabcbccbeedcebedaeeeeedaeeccedbdbadedecdadaabdccabcdddbcdceebeadcbbeeeaedabeaedccabeabcacadeaecebeddbbbdbaaeeedcaabdeebecdbccdaccdebddbcabbdcaaddcceeeebabddabbbbabcecdeebdcbceddeccdedbdadbddbdbbbdeedbccbcdebebbccdebceeacecacbeeeeacdcdabceacbaaaacdabddcaebeededcabcaccbbabdcbcdedbacdeeacdeebbcdeaddbddebdedcbabcadaebbdbcbbcccaedbeebaeedbcaaeebdebaaddbdcaaeadeaaeeaddeeaeddccdcceacedebcbdadeeddeadeccbccbdcdaadcbbbaaeacdeddbbcdeeaedadddcadebdbeeddbdcaabaabdaeceebeababbedaadbaddcecbebcdaabddebceecddbaacaecaacbcecadaeaccaadaabaeabadbccabacbbebacbbececbbadccacecddbdbbccbbabdcccaacaeeaaecccbeccabdeabdddecaddcbebacbdaceccbecbadeabcddbcceccdbcaabcbdcbeecededcacccadcaccdbbbaabeebccdddcbdcdaadbccacaaddceecbcaabcddeadcaecdebbabeadeedbaaadebdbddbdaeaaacaacceaaedcedcdbadacbcebecdeacadddadaadbceebaeccdbbaaaabbcddcaecabcadaecaadaaccccdbecdcbebbccbaeaacaadbaaaaedbeceeababedaabeabcbededcdcaecaedbddddbbdbaabedabddbeeddeacbacdedaaacccacecdacdecccbeeeaccdbeadbedddaecaecedbeaaacbdacdecbcecbdedebedadbaebcbaddbddacaacdccebbabbaddeadebebdedaedddbebbebcceaaeecabacbdabedceeeccdbbbbacbbececaedcabecabaebbccaccccbddeabeadcdbddeecceacebabcdebdeddebccceddcbdcddaccdbababbbccebebdcbdcdbbaabddeccdeceeddaacadebdecdeaecccdabcbbeaabcbadeaeeedbeaebbccbacdccebeedabdcdeabdbcccedddbaacedceaedaeedcaddeabaaeecbbaadbcaadbccaebccbecdbdaeabaceecbcabeadedcdcedcaecaeceeabadebcdbaebcbedbeeaddaacaddcbdccedacebaceeddeedcdcbadeecbabeeddbdebbebdaeacdaecbaedaccbedabcadebaedbddeacdebbdccebdcadddbeaaabbdbaebebcaeeeeedccdcdcecbddbecebacacdacddeedcebddacdadaabceacbdecbcacdbadbbcbcbbdecaaddaeedddceddeeececebaebeebcceadaaddccbdbaedacbcbbbcdacaaabcddebbecddbcaadcaadbeacabcdebcdebaccdbacbcedaebbcdaccbacaeeebedabaedaeaccbdbbbdadcbbacdbcbadadaeccaacbbbcdcbaeabeabcdbdccdabcccdddabcdcadaaeebddebebdadbcaeabdeceababecddedebcecdedeaaaedecbaaccdaeadcbdadaedaaabcdabbbbcdbbbeacaacaeaeadcbeecbceccddedabecacbcbebedadddcbdcedcdeaecaceebbdaeadedcbbbecbbbdedcdcadbeecccaceacbcdaabdddbecaceebbcdebdeebdebaddddcdecaabebeadacaaabeecdbdaaaddeeddaadcaacbbbdeeacddaaecebedcdebcebabcaebadbdcbceeaccbbbeeaadcaeeecddbaddabbccabacbccceeebeebaecccaaacccebdcaeabbdaeecadcabaabbbdadebeaaeabdeaebbbeaedeacaaecbeebdaeeceaaecceeeeeaadddadcdaceaacaaaddedbbaddccddebcdedcbadceebecebbccdbdbbbbbbabebedccdcaceabcdeebebabaedbededadcaddceceedbdcdabcddbdddbaeccebeebacadbbcebaebdcbbdbdeadcabcbdbeacaeccdebecedaddaadeccbeeaeaaabedddcadcbbcdaadcebeaddcebaedeaaecccbdcecebadadbbcebdecebcbbbadddcceadeadebbbabaedabbadeaecbebbebeebaacbdaecdcdcbcbdadcddbbeddebaccacacacdeccbccdaadabeaadbeecaaeaddbdaebcdbeabaebccdbbebbaedacbdbbdaccbedaaabbcadcbebdcbabeaaedcaeeaadeacdacbceabadadbbebebecbcabcecbdceeaadeddcecccaabdbdcaedbeceaebedcddcbbecdcaeeacabdbcebabaaaabbdedacceebedbdcecadcebaabbdeecceccaccabdbcedababbcedeccaaeacaeadaabaeaaaedeaabdeaddcecdcbaaabaaedbebbeabeeceaecaceabbdbadacaeabdcceadbccebcecdbabbddedbcbeadceaabdcadbebdbeabbbccdcbbcbbadcbbdebdccccbcdcdaecaecbcabaabbaebeeeacbdaaeaedaaedecedbaedcacdceadcabbcaebdacdaceadaabceabeadddedebcbebdeccdbcdeccadbeeecbccdaeebdceecbbacddbcedabdceecedcadecbbccbabcdbbeebeaabdecbbbdedeadcdadbdaceadecbcbbbdbccacbcdbcccccddaccdedbeddbeccacdccdddcebbdacbecacbabccbacaebbeabeaeccebebeabadbbbdbdcbedcebceaceeceaadcacbacceecbacebaeebbbedebccbbdcabeababbcbecddddcaebedbbabcdaacebcdcdddcaaceccaacabededdadcdaeaadbeadaaacebaacaddccaebacaecabaeedccbabadecabeeceeceeeadeccbbecccbbbbbcbbeeaacabecbccacbdedceecaccbdacaaddcbababaaeaaecbdcbadebcebaedbeadaacdebcacabceccbccbbbdecebdbbbbcbacaaebaadeebddcabeecdedbdbdacdceadaadbbacddddadadecccdaacecebebdedbdaeabeaceebabaaedeeacadaebeeeeccddacdbcababbabbededededdaebababbbcadbaeeeceeaacdaabbabbaebbabdecaccaaebebcdeebcdebbbbdacebebbcacecdaeacabaaadaacaacccdbaddeedcceecbbacaccecabbbdddacaeeeaeadbdcadcacbdcbeaedcacdccbbcadaecdeccbbdaadeaadababdbcabecebaabcecdbebaececddcdbedeaabaddbeacdcaaaacdbedeaebecdecccaadaecbcdeecbdcaeeeecbcbcddcebbeeddccbecebcadcdbebeaaeeceadacedeabcebcabeadccacabacaaabaccecebedacdceabeecedabcaeebaaeecedacabebcacbbcdcdddedbbdbbbcddbcdaaaaacaadabcbebceaacaddbaaceaedbedcabdacabcededccdadbcbddccaeeedabdeecdbcdaaebaadaadaaedcadbadaccecaacecaebceedaccedbeeadbdcacdabdcdcdebdbdadceaddeacadcebbddedddbcdedceaaaedcbcebaaeedbcddcdabadddcacbbaddbdaeadecbabcabcaaeedeabddaaedbdaacacbcebacdbbbaabacedbccaaccdbcbbaaaddbaebbbcacaecbeccaeddeccceedcdbbbadecccedacecdccadeeabedcdbccaccaeaccdadccbddbddbbeeeaeaeecbcedabdbaababccacababbebcbacbecceecebcaabcbdcbedcbcaecdbccceacaabdbbdbacabcebedcecbeceddecdcbbadebbbedbabececadecedbeaabdbeecacaecbeebcedacdabeaabbaadedeecbecdcbacdcebebecbadbecdcbeebbcadddbbabdbcbedacaaaadcbcbaebbaebaecccaaedbdbeeebedecbcbadbdddeadaacabeddcdceeadbeadeadbaeceeeabceaeccacadccccdcbaabadcadbebceeddceecdceeedbaacceeacabeeadbaeddeccddbddcacdbcbbebceabeabaaacdbaededdaeaabbdadbbbadcdddbbaaccbdaaeaaeadebbdbdadcedddaecbadcbcbccccedcebbbaababeaedededdacbdadccaeeeeacdcdebabbcabbeaceeddeacbdadcbdaaaeaebaebdddeaeeacbdceabdbdbaeccecdbbbbdecebbcbbbbdececedcbaddbecdeaceccdadbbddacbcaebceabdcadbaaeacaccebcbbadeccbbcaadecbaeaadcaaccdabecdedceccbcabcbeceebcebaabeeaeebedbccabdccbebdbbdcbeaaabbceecedcbddbbbceddccbecbceebeecaeddacaeaaadebaddabdbcddbdabbaeabcbbdeabebddbcabbdcdaeeeddbbbbaaeaaeedebabbceaabadecdeceaaecbbcacebaabbedcbbeeabdebeeabcdbddaaadcdddbccddcebaaebaaaceadaddebabcceaaeabdecdbbbceccbaaeadeaacedbdedcacdebebbaedbadadeaeeaeaacebdccbbdcecccabceecdddeeeeceaadcadccbbceccbcdebadecbccdbddbdaeccaeaeabcebaeecbbbadabbdebbccceabeceaeebeacbdaeccbaddbceabdceeabeebebceaedccebcebccbeebbcbaebeaaeecbdacdeccddcecccecabeebcecaeacecebddebcdcaccadbdccdcceaeaecaaaebdedeaedacededceabeeeacdbaabeddeeeeebdbeebcedaaaeccbcccbcbacdddcadebaaedeeddacccaeeaeacabdecbbdbcbaabbeccbddbdebbaadccaebcbcabebbbdeacbaeaaddbdaecccadbdbcbacddbeeaccceedaddcabcadbbccabadaececabadbbbdbeecbcadbcdacddcedbbaaddbabedcaadbbcbcceecaeaebeacbcedeabcdcebceaabdcedeabbeccaadabacbddabdbdaecacddaeccdbabdbacaadabaabbecabbceddedabebdbcdeecadccbbcebdbdbaaeebbbaceebabaaebbdbcddaeaecdceceeadacabbdebcadecdaaccacceabbcddbeaadcaddbdcbdbbcdcbdedabbcabaecbeeadaccaadeeacbaacbcdcededdebaaadcbbbabdadcbaabacdacccdadebcacddbdcbeadabcacacbdbaabdecebaddcebcdaaeabbabadacababecebeeacbebbbeaecdceddebbeeabadbcdabdaecdeaaedbbebeabdccebbeaacdabdacebaadcadaebbcdacebdabdebcdeebddcdbdaeedeeaeecbcdbbabdbcadcabeecabeaeecdbdedaccaedeacaabaabdedaabcdddbcdaecdadaabcbccabacaacdcaeebedeacecaeccddbddbcdbdddabadbcccadbebaaeabecaadadbbbdabbccaacdcaacceccaaddeaabeabdcabbedeabeeedbaecebcbbedcebebccdaebdbebdcaecaadeabbaedcebaaeeadaaebcabacdabdadacddbcdbaeeeebaacdbadeedbdcbbceecbdeeacbedcaaeadeaabaabaedeccddbaecbacbcbceaeacebcebcccabbccaeddadaccadaaeadddeacecabdaeabbdcabaaddeceeadadddeecddbbdecebedbbecaecbccbceedbcceccddbadbaceeabcaceebecaacdebceedaabebaaeccddadadaeacabdbaeaeacdeadbbcddecbcecabdbcbcdabacbaaebaabebabebcaebedbcdeeaedbdeeabaadbaccdacdbdcdccabbbdebbceaccbcaabaaaaddbecbccaaecbccbabaddadeacdaceddddcaaadeacdcbbccebdabbeadbbddcbdaebbaabbbdcaebdcbebdecbeebbadbadabeaaceaebdcaaeadbacddaddedbdacaeceedaaaceadbdbbcebbdeaeaacadbabdadddcdcccdcdeddecdeddceeaaeeeaebcbcdebabebbdcbcadbbeddaaedbdddcacedbccdacedcdbccacacadebddadccaadededcbeddcaaeeaabbadcadbebbcceacbbbeebedaaddcabbcbdaecdcabccbdcaccbdeaaaacaaabdebaacdabedeececbeacdbdeaededbedcdbbacbabcebcabdbccabebcaebdbdadbbdaaeeacaceaceabeaeadeaaaccadcacccdaddddebceecaddbadcdcacbeaaacbbcddedebbbbacbdcccadbabcabbeccdaeaedcbaaaeacababbedbedbaddcdcaddacdccebeacaeacccbadbddebabbcecdadbadabaebaecbadacdebaeddeddecbcceabccbbbddbeadeddabdeeabacceaaebacdbdbaacbadcdcddeadbbebdceeacecadbedabccadabcbaeccceedbebbddcddbdaecedddedeeadcddbecbcdeeddebbeebcaedeacabaaeaaaebaabdbaaedabcececaccdcaebebccbbeddcaedeadabcaaddcacebaddeedccabbbcccdecabdaaddbdcaadbbcecaececcdeebaabceaedecabdedbcddbeecacaacbecaecbdbddbdcddbbaccbeeadccdcdaaccecbecaaacaacbdcbbdcbbdbeddeccdedabacddceabaecdeeecdaaaaabcebbbecccdcaebedeaecadecdacbaccbabedebacbbacdbbbbbebcbcedadacdebaadecdaeecdccbeeabeccdcacdbadeedadbccaddabdcdecbaeddaeabacccdbebbadbeeaaadcbaaeacdbdabeabbeddbdccdeaeecbcddaaddbebbbcadbdceddceabcaacbeedeaebdcaeeebacdccddeedabebbcddbaacecaeeeeacedaeaaceaeecbbdaaaeebeceaeaadbacbeecbabaecaeeecadeecedebacccdbeecaedaedededaeceebaeadbbadedbbadbecaccebbacadacabcbddebbdbdceedaadccbcdddccaecedeababebedaaaebeedceabadbeacdeeaaecaadedcdbdbdeedbceddaecbacbecddacaabebbcbcbddcdceeccdeebbdbccdedebaeebdeccbdaabcdeebcccdededcccdedeceadcbdacdbedbcbeaddcadbbaeeaadbdcccadcccdaccccdaddcbbdccceaaecbdbedaccbdabaaecaaeccecdeccabbcabddbdabcebdbedbaaadeaeebeedceabcacbeeeaecdedbcdedaaebeabedbddaaabadccdbbeeedcceacddcdedbcabaccacebacbbeeeecedbbbbabeeacacbdbdeecadbddbcbeeaddaadecdeececcedaaabaeaeaccdaececddbceeabdababdbdadeabbcdbdaaaeaeccabdcdddbeaaccedbddededdccbcceeeabeebacdeeddeeebeabbedeaccebaecaabccbccdceccdaaecaedceecbaddeebdacaacecabcaddaadeadceaaabecdebcdedebcddebbcbeecdebbdecbbddebebaeccadebebaccbbecceeebeabbacbeecaabeeaaabadbaacebdecabebcecbdabaedaeaadecdeccecdeadebdeeadbbecdcebbeabcbbbeadbbddaecacccbabdbacdadbeedaacddecccceacbaeecaeaacbadaceddeacddddaeebddbbcbeaebaabbadddeabcdcbcaabccdacebddbbdbeacaacbbeeebdaedaaebbbdbadddcbabbdccdaacabcdcdcdcddcbaeebadeceddbcebcaeabdbcbbeecbaeaecceddbccbccdbecbbeabcdedacdecbbdaeaecabcaacddbddbcdacacccccbaeabdbbcdbbbcaabedcdeddecacaaadeecdbddbdebceadaacedbbaeedbbdaaeddceeabdcdeaadabcdbceddeeecdcedcabdaedbcbdeaddedbbbebbceabccbcccbbceadbcebecedabbcabeebadcecbaabaeeaadaebddaedbabbdddabaeacdcaacaeebecccbbadcdbdddeedebaabcccdbeebabbbdbdaeeededbdbbebcbdababbdcceaecaccaeecadacaacbeeaaaeebaaeaddecaebceddaadeadadcdbcdaeeebcadabeddaccccedddddeeaeebeeccedceacbdcbcdcbbdbaaaebbcdddbaaceddbeedabdbcdddaceadbcdcbceeaeeecabdbeeecbdccbaeaedadcdebecabedecbedbadecccaedebedcdadcadcdcaaeecabdbebbcdbaacebaecaeddadebacdddbbedbdbdbcadebbcaedcaaebeacceacdabbbdaedeeccecaccbadadadbeaeaccabdaedabceaedcdcccaceeddceeeaddedcedcbeacbebaadcabceaaedbbaceecedaadadcaddebbbeddbeaeebaedccdbddbeceddbbcebccecebadeebacaedceccceaceabaaeeaecbaeccbaecabbdbeccddcadbaeaacadececbedddeddabedbaebcdadbbbaacebdbbdcedbcddadcadbadcdeddcaeedcdaeababbabaadddcdeededadcebccedcadcdbccdbededebddbbadbebcdcbcdeabddcabbbceabacbaaaeeecdadbddcebdcaabcadcbddddabdbaeccbbbedebadcbbbabaadadabadddedcccaeecbcdcdebaeaccacbebedadbdbdccdaceaacdcbecaaeebadbbcaeccbbabacbebabaaacecdaebcdabbbdccabbcdedcbaeaabecdddecdbdaccacdeeccecbdabaceecdaacbcbccbdecceadcddbededaeacabdeaeebaeecabdbbabceddaeeebdeceecbaaeeeedddbcedbadeaeeaaabcccceeeaadaddedabdbdcbecedaddbddebeeaaecaddebecaacedbacacadbcbaccedcdcceaebbcdccdbdecdcdedcadbecaddcbccbcedcddecdcdababcadaaaebdcebaccceacebaaeeceabddbabedbabaabeacaacecaeeabeddbdadadeabccdbbccabcaebccbedeedacacecdaeacbcccbcbcebbccdcededebcdcbbeeeecbaaeaacaeabecbaacdadbddbacbdcaedcddbeccccaaacbeedddbaaddeecbbdcababdaeaabcabddecbbecbacbbccccbeeddbaacdbeeedcecaecaadcdaeeeccdcdaedcbbcdabaacdaaacedbaddbeeabadcebbdccbbaddbcecabaedaebaecdeaedbcdbebcddebcdacbbebdeeecbcebebecedbcdaddcbbecbaadaadbbdceabcacdedebbdcecdbdbcbdabeebbcdaedcebaeedebeaabaceccbddeacceacbbdccbccdebcdddcbebcdbabbeeddbebcdebacdebbcadbeebaceddadcccaaacbaeccaeeaebecedacacdaeabacaebdacdebcedcadcaebaddeaaedcdabcdcdcceceeeebabebacbaeacdbabddaeceabecaeacddaaaccdacbaaecdcccaaecabacabeebccdbceaccdaeceeaaaeabbdedcbaeeaedacdddbecabddcaabdadcabdcbecccbcceeececacdbdeedeedcadccaeaacceddacaeecabbbcebbccacabebabaecbbbccbdbcbbbeaebdacdebcacddbcaddeaaeeacbbbcbaabdbdccaadceedebcdbedaceeadbaeacecadbdeadcbdabaeededddaabdbceaeedadabdaebabbcccbaabebecabbbbbcceddacdacabddaaceabbbecebaceaaebcaddaaddecedcccbcdceebbcaabacddadccbccdcdcdecabadcaeaeecbaaabbdadbecccaaebdeabacbebebaeceddaadeecddbedceeddadebeaecabaeaaacabeedaeaccbaceadebdaeeaeccabaccbaaeebdecbbdeeececbcddabceaadeaaaeebabbcbbcaabbddeedcaaebeceacebcbddadaecaabaddbcdbbbbccddeabdadaabbecaddbcbaddeabccdbeacdbbdcdcecbbacaababbacedeedcbaaaaecaacecdedaebcabbddcaabccecbbccbcbbaadcebcebaaeceaacdabbbaeadddaecbabdcebabbcdcedadcbddeccedccccdcbbdbecbadeedbbaddbcedabcbbdcaeddadeebddadcbadecbddeedbaadeacbedabdcaabddadcbedacacddecbbcecacaaceabbeccebccabbeececaccbdcdecbcbbccdcadebdbdcccdacaddecebadeabdbdaadbccbdeaccaebbbcdabdcbaccdbcbcedacabeaebaabdeeccbebebbdebdeaeeabbbdadabdaeaabcbaddaacacbdabacdcccddaaccccddecbbcadaedcbeceaddacecdbacccbbebdcadacaecbbccdaceeeddaadcbeaedddadaddeaebcdabaeabdcedbecbbdededaeaaabcdcbceeabdcaadadbaeaacaddebaddbccaaaecdadaeecbbceabbcaebdddccbaedaabcdbbebaeabcedecdcacbecdddccdceeaeaddbbaddcbdebecbcabdeaaaeaedaacabdcdcaaadbbadbeccbeddddadbbacaeddbcbcdaadeccaadcbacabcedbcabdacdecdadbeddececdcbbabcdbbbecbaabecdaeaedcdecacebaaeaeeecbeadccbcabcecbbdbebaaabadabbaedccbabbaaaaeaeaecbcceacdeedabeeeadecaebedddecaaededdaccbeaabcbcadaecbbcacbadbcbddeccecdaeccaaedbdceeeddabebbaddcdbacaacbdeabbaaedceacdaeaabcacbebaacdacddbacabaddcecedebecbedeacbbbbbccacdeddccbcbdcbdeeccbedbabddeedabbbcaeeecddcecadcdeaeebddccdcecdcbacdeecbaeceaeeadaacccbcdabadcbadaeeccaccaebcbdccabaadadeddcbaaecebcdebbdbadbbcbcdcdcbaacbbbdbdeedcaeeccddebdebebecddcdbceddaedbadadabeacecdaaccccddaedcdaadacacccbaeccdaaacaacbaeadadbbdbddeedaeedbaadecbeecbabdbadeeebebcaabdcebdeabaaecdecbaecbabdabddacdcceaeaddabdbcdbebceaaeadbdccdcbadaeaebedcbcbeabaebcbceedbbacbabebdcdacdcabcbeacadadebadcdecbecbebecbbcdedceebcaabddddbbeddcdbcdcadcedbbcddddadadcacdcdcbcacacaadbcdacccecceaebcdedacccebebdbbabddabbddccaadeaeacbbcedccbbdbcbeaaecbbbacadcbaceccaacacaabebabcaddcabdbacecebddcaadcebdbbbbaadadaeadeddabccabaeebddddeeedabaedbbcccabcabddeaebadecadbeaaebcbabddcbbacbcaadceeccbdedaccbcbceeedadbdcebbbaccebdcacaeaebbbcabaabdecaeebadaddcbbedbbcdebbdeebdedcbbaaccebcabcddbaeebeeacdddecddbaeaeaeebbbdbdabedcedeacbcadebabddbddcdaaaaebbddadbacbeacadccbdbbedaedbbaabcabcaebcdccebeebddcabadcecacbbacdcaeccbacbabeabebbdeddedaadcbccabbdedeeaccbbbcbeecbdddcbcceaddeabeeadebebcadaddacddcddbccbbbbeaebcbcaebbcabcaebcdacbdebdbacdeedcecabceccdabebbdadedceeceaeacedbbbaebeedbbdacceabaedaabbaaececdceeabadebbaacccdddaabbcdaeeeaeeebbddbbddecdecadadceaaaeecddebcdbebebdeeddaeccdaaacdecbecebecadaabbacdaebcdceacadaaaddaadedbaeecbecebbdeceabdaecbdbccbbbbabcbdadedbaeeaeccdbcaabeceebcaaeeecabcccbececeebebdcdddaebebbdddaaeeedddacbabeeddcccdccedbabcbbdbdbaaecddcbabecaebbaaccbaededabbccdeadeacaadbceaecbddadaaaaabbecbdeebaaacaeacaaaadeeecebcdadbddbbeddaececaacadcbeecbcccdbeedcaedbcaedabccbeecebdbedaacdbbdbedbeedddcebebceaaecbeeadeacecadceacccbeeabdabacaabdebbcbadebdbccacdaadcacaedddddeabaeeeaccdedacdbbddadbcdbdbbdaeaddcdddbcaabbcbdecbbcdaebebcceabddaaabaeeeaaceaaabdeadaababedcaaaadaabccccebdcdebeacdcdcbbadecabcddacecabbacecbbdabeeacedccadadbeeaeabdedabaceaebeabaedbcadbecbabeecddbedbaaaeedadaacddcbadceadacaddabedaadecdcaedbdeacddddbaeedaacebbdddccbddaecebbdabccddebbedccbdeeeebeccadbbdcaaaddbecabaeaadabcaaacebdbdcdacccaaaeeeebabdbdcaebadebecabbdcbbbccebbbcccecbcdbbcebdbcaceebabaeebebbacacccaebdabeaadeebcbcabbdaadceeeeddeccadedccacabdedbebddacdabaaccadeaecaadcdedacecddcdbbedcebdaeaebeddbaaaeebddccddcbadebaaebeddcaceaccbbbbcbdedaabbadaccbcadabadbaaccddeacbeadcecadccbebaebedcceeeeddcebadecacddbbbdaedceeccceaaccadaeedacbeecbcacdeacccaedddaeeeebacadedbecbabaeeddedaebccbecdedeacccebeacddadadbdaacabeddbaabbdcbccddbdaceeeacbebdbdcebbbdddcacbcaacdedaabaacececbaabadccaacebaaccbeababddbbdcddcbecdcabadbbcedeaccddbaeeadacaaadcbdcaeaebeaaeddcaedceebcdadbcbcdccbdbbadcbddbbddbdacdacdeecabeacbaacccaaabdecdeddcbcaddbbdcadeadecbaebccecbdcabdbdecbdbebadadddabeccebabedeaacaccadeebdcccbeddedadadbacabdccbadeeabdcdbaecbedaceaacbcdedbdbdbaacbcaabdeeeaedaadcdccdbcbbeebaeddaadaeededcdaadbabcbedbeeecdbeedceaadbbdeccddccedcbeeebaebbebacbddeaedaedcdaadaadeecdecabacbddadaccacbceacccbdbedcdaaecabcecabcaaebeaacabbabeeaeacaabebdacedaeebbddacdcbacbbcdaacacbbcbaecbeebbacdaeeecdabddcadcdbbccdbeeabccdbaaaadecebabbbccbeeaeacbbbbcddededabebaaedaddeeeecdecdddbbeeecdceaebaedecebeaaecacccedbaaeebdcccdecbecbdbcacceadbaacdeaecacdcaacaeaabdabdbcebadbebaaaddaccabaccabbeddddabaedcdecbdaddebccbabecadbcbadcdabdcdcadeaeeaeaddddababbdeecdabdecdcddadeeddaaaebeebbbecdaeceaeebbdaddbbcecacaabcbbdbdddcbbcdedbbadecbbedacadcdceacecaeaecccdebcddcddbbeacbbdedcbceaddccdbeabcacddabadbdabdbadbabbaebbddebddecbcdcacedaccbdedbbbcaceababddeabcbbcbccbbcbdcbddbcbddbdeaacabbbcbabaaaeeeeadeadaeedaabaacedacaeadbddddbaaebbdadaaaaebdddedbedceadbccecbdcddccaeacacbdaeecaadeaadaaacceacaccdbeadeccddcdbbabadbaddbdabacedaddccbeeaddaccacebbadebdeeaabadcbaadacdadaecbbecdeccdddaaeaebbcbecbcbdcaccbadabddebdbebcaedbabcbbaedebccdbaacadcebcbbdebcbcbbdbadaeeeadeceeddeccecbeababdbdeabbddccdcdebbdeaaeabaaeecdddacbccadbeeeacccdacebabebeaeceabbcdbcdabcaebdedeccaadbabcceaddcdbddcdaddacddadbdccbdceabacccbdbcbabddceabbbcecaccbadcbaaecbeecbbccbbedcecbcbaaebedbecaedadecdeeabbbeebbcdacbbaebeddaceebaaadebddceabbeeccdcacedacabdeddeecebecbcacdcbaadaebcddacacedbdbeabbaadeddeedddeebebaccabdbcdbadcccadcbcdcababcbbeadcbeceadcdaabaacebeeeaadaceababadebebedeecddeaebeedbcaceaabcdcebdcccdebaeebcabaceeebedbbdddcbcdbaedaedddaecdbbceacbcaacdcaeceabdabbaaddbdcbdabddeabebccddddceadbdecaddbbedbccdacacaecdcaaeeeaaaeecedaddeeccbcdaeeeabeeaeeeebcacbadaebcedcddeadaaaaeddaceecbdbadbecececbbacdadadccedecccbecddbccdddbebabccdeaddaaababcebbdcddbcececddebbaaccbbcbbadaebaeeddbddbadabebdbceeddacaeacdadbddaadadbdecbabcacdbbaaecabdaebebcdeabdebeceecacbdbabadbabaadccdccceadaceaddcebadebaeeebadbdbccedcdddbeeecdbbecbadabeadbbbeeceaddcdbdaaabdcaaabceacbdddaaaaeecbaaecdeebeacecaebdaecaaaadcebedbcaedbbdeedbbacebaabbabcdabebebcadbadcacacbaadadeedaacebbdcebccbbabeabcdeeeecdeccaccebcceaaadacdeadcaaebdaececebdadcdcebecbeaecdddaeedcccbdceacecbeaeceedcaadeaccbbddbeedeaeadaaeceeaeadaccaaecccaeaaabaddcdedbeeccacaeaadcbeaceadacaabceaaebebddabacacaacdecebdcabbbcccaceebaaeceebbbaaaeeecbbeddaadceeaeaeeccbabacdeaecbcbaeaedbabbbedcaadaceaedacebeecadbecaaeededdcaaeacbeaedcbedbaaacdcabbdbcbdcbceacceabdbdabcbcaaedbdeceecadceccdbdbcdacebddaedbddeededeaecaddcaeeaabbedcbceccbededbebcbdbcedceedbeaedcacdbabaabdcdcdcbadbdccccceabaeadbdddeebeabbdecdedabdeaecadecebccacdbcedcacaedbbbaaabaccbccccdacbccbdeedceededdebceaeacaddeebbceebabdccddadebccbebdaeccadcebeadadcbdcbbecbecdbdaecbdcebedcacabccdedeaeabbeebedeacdcecbccacccdcadcdaaeadbcdeaacebaedeeebaedebbccbcabaddbabcdedecbceebddaccbdeeaebcbcdbceaadaeeecddceecbabacbaebdebccaaccccbdeabeddbbbceabbebcdadecabdcaabbbdbdddbaccbcbdabdeccecaabbecdcdccacaeeddcddaadbdbdcaaececebbbbbabdbbcababbdeeccdecbdbcabbcbccbcdeedacdeecabccddeeabaedaadddeeacdceaedaddbcbcbbaccddabeabecbcbccaedeebacadbeecdcdddddceeaaedeaadddeecaeaacdcbdaadeaacceedacdcdbaacdabaaedeaccedaeddaeabbeeebacebaaeaeeaccbaeecceadedbebcbcaeddbebddccabacbbebadcbaedcceabdbabdcadbdcdbcbbbecbedbabaaadcabeebdbcbdeeaebebbcdcebacdceeaeadebaecacddcdeceaedecccacdceabcabdeeccdcbddadddbebeacdeedabeccbeecdccaeeedebbacabaecbaaecbdeecaedaeaaeddaaabbddedbdedaacededbeeabbdacbdacbebccadeadabcbaaccdddbeecbabedadedcdbdbcbbbabceebabdccddeebcacdcceeadbdbeddeccdceaacadeaaaeaaabbcdacbcddebbedeccdcddbbbbcdacbeebadabddcbadadcdabadcccbabeeceaebaeecacadedddaaabaacddbcbceabddcbadbdcdeaddbbeddeaeeadcbcabbaccaacbadbccaeddcccaeaaaceedbcbdeddbbccdbedaeababdccaeecdcdabccdaaaeeeaaaecdbcdcdbdbabcababbbacaaaadcdcecaadceadadcaabdeeadecedcaeddeaccecbdadaeccccbaadcbbcccddbbcadaabacbbbbcdeddbcaabdeaedbaaddabbdaadadadcaacacadbbbbacaaebabdadabadebcbdbcccaaaeeddebcdeaddceeddaeedabcdbbdababdadeadbeceadaaccdabbbadceaeaddaeeceaaedddcebdccdedadedadcbdaebdcbeeaeebbecadeabcbdcdbebacedeebabaeadbeeeaadbecacaddeaaaedceceaeeadddadbaaaebabcaadaceadbebebadcdadabbceaeccadbdccecedbeedacabeceebbbbadbeededecaeaabbdeaabcbaedcaadcbeebebeeaacdadeabbbedbcaecdcdecacaceacbbcedbdeaeacdccdccaadaebbeedcbbedbcacbdedaaacbedeaacadecedececbbdcdbecddcdcbebeeeeeaaddceebedecdbbacadddbccaabddcaaaacbbaeaabadceeeacdcdaebddeaaaccecaaebebaeebdbdcddabadccdabbabbacdedacbbecdbbaaeadbebeeaeeabaabaccdabdaaacebbdccdaaabecdaaeceeedcedeaabacedcdcdaebddbcbcbdcbbccdbbacceeebcccebcecebcdbccabddeeadeabbeaacacbaedabbbaeeabbeebcbdbccccddecbccdedcecceaceebcddaacdabeababbdedcdbbbceaabcebeaddccabcecedacbbdcbbdbbbbdcbbebaedcccecacbacddddbeadaadcaabadadeddeacdaaeabeaebecccadbbedbaceaeddebecbecadaccebeebdaddbeaeddaaecbcbcaedebdacaecdeedeccaedceacbbdeddaeaeeddbbebbcaddacaecacdccdebaabdeebdbbeaaebecadbcdcbecbddaceededdecbccdcddbebeeacdbcdadeadebbdecebdbdddbaccdbdcdccceceaedcddcbacbbcdabdccecbaeaaeacebebebadbeccbcbdedacedaeeddebbdeebcdaebaaaeecaeecceacccddbcbdebabebddbecdabcaabcdaaddabdbcdaaceebebcbabdcbbcaccddeddcdaeeeadcdbcbcaeecebeeddedcddeccccdbddeaaeaaabadaeedbddadadbaecbcccabbdddaeecceeaadbbaddbcabbdeddceadbdccecbceaeddcccdceacdbdedeacaeaeaedccaceaaaeaeaaedbaadbaddeddbcbaaddaacaddeaeacdeaddbaccacedeacedcecbaaebbbbeabceeddeaebaaacddbcdbaceeebbaaacecbaaadddbbcbbaadaedaeedaeccdedbbbebdbabddbadeddddeabdeeeccaaeeccddccabdecbacedbdacbeceeadadbbbabccdaacebeeeebcebccdeddacdcbbeeaddecacebceecceabdcaaeababcdadeebeccadcecbdcdddadbdcebdbcdacaedbcddbbaaabbadcceabebeeccccaaceecdbbcaabcbacbbcaaedddbeabaacccbdeeecaacbecaddccbacecbccbaecbceaddcecccdbcaddcdcbbaaedaaadabccddbadacaeebedebbebddabeabdeaaccdeccdeaedadceabcaeccccbabddacdddcabbeceecdcbadbcbdcddeedcdcebbddadcccdbbbebccbadaaebecbccdacacacbccddaceacdbabdecaeadbeabbedebaecbebedadacacdbaaebdcdebbabdaddeeeaecaebabddcabbddaedeaaacddbacabebcebbbdceceebecaecbacebebbaeadbccaaadccaedcbbcadbbabcbecdebbacebaacbedbbaceaccddabeedcaeedbaecdbcacddeebbcccbebcebedebdeecaecdcaedabcabcdcbebbcbacdddbeddbecdacedbbbeacccedbcdedaedadbacabecacceeecddbcccdbedababddedcdeadcdcbbeebccadbdeaceebedaaaaedcaebbdeeadbeaecbbcaccbeebaaecebeccdbdecbacdabbebedbdbedcbeaceacccbcddaadecdadbcaceebdaeebbebabeddecdececaecdbbbebcdbaeadebdeaabdbdebbcbcbbdebddccebdbedcbdaacbaeddcdabceadaeadbdaeadddabcbaabcbeddedcbbedccdccbcbadbebedadebbbaeceaccebbccaeabeccbbcaeaccadaaadeaeccababbcabaaadedcdbaaddcdebdceecdcddbeceeaddbdedaddddeccbabecdedbabebcccbdaeaaadbdcaebcbcbbadceadcebcecbececccecbcbbacaccdbaccaabebeadebdddbecaebdabaeacbacaccadccbbaaedbbeabeddacbedaeaabaaeacbbecdcddddedbededcdeddcbcccdbbecbaebeadcbbdceebbcabbddcadbbbcbacbbedccaaecbbbcacbcbcecaabdeeadebbeaccecaebdebeceaadddbbcceaecdedccbcabcdaaacddaaabaeccdeeabedcecbabeebbaceeacaababccddeaebddaeabccbcaecdbdcceadedabbabadcedcaeeabceadadcabdaeaeccbcbeccdedbadacabeaadcccccaceedceeadedbeceaeeeceaeddebbacbecccaaddadbbadbbdebeebdabdbeceeebceaabaeccbeacdbbddaeaeddbadabaddedbeeeaaaaeedcdccecddeebbcccacdcbaaaebdcacabdabcbaeaeabdcebcbdceceeccbbcaaecdeabebbccbdbdcecaacedaecbacbcadbedcaeceeeebdabcababdddcdacaebdecbebaecbedcedbceaaaebbdbabeccebbbdedbdcaebedcdacebbdaecaaeaeeeebcdbcabebbedbbdddbbdeadcdccceedcbdcbdcdabbccbadddcbaeaaaaccdbeeebebcbcccebecaaaacbdebabbabbbddadacbabcecbebcceebabbeebcbdcbbddceaeabebbabbbcdddbbdbaadabeebaeaaededdcebbccdeedcbbecdadeeadceddcdacddebddaebecedeabeedbcedaeabeeaeeecedcbcbcbdaddddacbdaecacaddaeacbebccbeadbecacedbcaecdeaeeaccababccebcbedaeddbaccecdedbbbcbbbddebeedcedecbcdbecebadedbcebececbcaeaaddaadcbbcccdeaccebabeeccadcdbeccdaaabddceddeaadccdddcbacceaccbeeeebcadaabbbeccaeedcaabedcbabecbeebaeedcdbcdaaddaeeebbedcbbebabcccdaeddddebdbadaeccdaddaaadeaddadddccadededecaabececdebeeddcdbbcbeeeceabcaaebedccaaaaebdcdaadeadebacccbddddeddebdecabdccebaedcccdadbdcadabaeededeebdceedeaeebabbdaacbdaedddaecbcaaddbebeabcadddcedaebaacabdcbebeeecdbccaddbeedebbcababbadaeabedbabedcabcedcabbdcaadabeebaacaebccaadbcceaeddedadaccaceadedadaadbccedeaddccdcabebdaceacddeaaeaaebaeabdebbacdebcacaabedcabdceddbbcedbeabedcbbcaddadabcebedebdebaacaedbbccdcccedbaadadcbceebeecdbddedbdadbbabddadedeeecaaaebbaebcbceadcdcadadedaecdaceebccababdacdccbdbebceeeacdaaccbcddcdeeeadcadcdabadadacdecaadbeaabcdadbcdbdaeecdbedecceedebdeebbedebbacaebbdadcdcedbadcebaccdbecbcdccbdccadbcbbbabedaddacaeeeacdcebbaadadbdbddebedadbaadccacbddccddaecedcdecdcacaadceecdeabebceeaadcecbbdcdecebddddeddbdbacecadadaecdcaddcdeabcbcdeeadccccbebeadeadbaedcceabeeecbaadbacaebdbcecdbbccbecaaebaeaeeebadbedbabcaeecbaacbbcbabdedbabaabccbabcbccaadeeadbccbbccacdbdebaecbbedcddaaadaebdddbaeeccdaebedaeaccdbebdeaeccadceadececbdeebddddaedbcddebdbaecdcdbabeddeadaebddaceaabddbbeadebbbececaaecdedbbccceadeccedceaaaeddcbcdbccdedecaabacbedcdaadcdaceadccdeebccbcabecccdcbecdeccbeaddddabcbddbcacbdbccaceaadbddbaccaeccaacbacadbaeddaceebbbbbeebedcbeacbebddcddceebcdbeebceccbcacaacdcdbadcecdecebcebaccdcaabbedaecbcddacaddddbcccdbcaacdcbcaeeceadadabaaabbebcbddaeecededaabdabbeddddbdacecadebaeeabcbeddceebaebbecddcccdbbebdaedaadbedbeaaebeedededaaddabbdeaecbaeccadcdcbaabecaeddbbdbcdddaabdaedbcaadddbbdddecaddaeabdcadedeecbcdeaacadccccecbceddceedaceceadccbbeaeaccadeacdeadcedadeadcaececbccbdaeacaeccedcbeddecbddbbeccaaadebcabdbbebdcdaddedcebdaadabbbcceddaaaceabacaebddbacbaedaecdedbbcbceabdbaeabcbcdebbcadaecedcdaeeddccaccedbddcdccbdecebddbdacbdbdeeaaaaaddcaabceabcdbdcdeaaaeddcacdaeaacadadccbacaecaeaeceeceddabdaddeaabcbecaeddabcaedbcccabcbceeaabaddebddadcbecbceaadcaedaaaaacbacbaecaeabaeaadbcabadccbbaceedeebdebbdebdacccbdcdbcaeceedcebccbeabdcabcbabbbadabaeeabbaebceddcbebdaebcbaaabdecdbcaeadaeebdeeccabadcbedeaeaccccebcdccbeaeeaccceadcceabdcbaabebbbaabdbadecdbeeddcdcaebcadabbbaeacccceacaeccedcdbbeececebaeadbdeaabbccbcbaccadbdcdaccacceadddaddbdebaddaeccbccedcbcddcaebbdadecceeddcdecbbaaeecdddeecdaedcbedebdcddaecabbdcdadaddbedcdcccddaeebebbaebcbaeaaadebccabdebdecddbdeeeacabbebdcdddbdcdcabdbdacaeacebbddcdcddedecbebdacadeececcaccbcbebaebcdcdbbdbebeeeebeddabaaeadddcabebadccacecaaabacccaaecebaaadbeeaabbeecbebccadbdabecdcadbdadcebadeccecaacabcadbaaabcecdadaaaedabcbacdbdaeeadbcccaecccaceaadbabbdceceeeecebadecbbbcbbbabbcbbacbcbcaecddecdbaebccabcdbbabadeeeabeaabbbeebaccedacabcedeccebcdaeadeebbeaebdebbcecbebcadbecaccbbddbdcaccecaabadddeecdadaddcdcecdecbadbddecdcdddeeaddbbaccbedecceaeeddbcbbcecccacabadbabeabdccbdaaccadcecadaacdbebcddecbdabddbdccaeabeedbbaddeaeebdeaeeeadbadaeaabbbcdbaabadbecddadbdaeaaedeaedcbccbdcacdbeebcaaddcdebbeebbddebababaedbccbbbbebdbbeaacecdebbbeebacdeacaeabbdcbbecaeacdbaceadccaabbbdbabacbdaccddcdebeceabbdadcccecaceeeedeaebbedadddddaecabadbdaabeecdebaccdcbebbeededccabcbadcaddcabedeaadacdaeaeecaabbcdbbeddaccbebebedceecebeaadbedaaabbaaceaaadbacebedcaebcebccdceaecbaaceedabecaedbbbccdadcecdcbcccbebecacccddcabbdcebbadacedbbbdedeeaaabbaddaddeebbedbedebdeabaeceacabdaeedcaceccadddeacbabccaedbaedddceeeeabcccaccbbdcdceecdccbabadddbbaccdeddaeebecabeeacdabbbbbcdccdbbabbdaedabddbebcdcccbaeadddadabeabeadabbacdddbbcdbeeacebdddcacbaacedaeedaababebcedaceeedeceadaecadaababeaacbaddcbedcabcddaaadeaacdcedabebbbbadbbbaacbabcdbebcbbeadadababcaaddabbaeabecccbbebaeedcaadecebbcbdeaedaadcecdadeeeadbedcedddeebcbdaeaecbaccdbabbbaeddedddcaecbbadeccebeabcdaddaedbcdbcbedacdceabdbbcdddbbaaabccceadacccaabbcdababcbcaceaddabedadccecbadcaadaaddddabbdbebaabbdcdecddeebdacededeaecbabebbdbeeeeedebecadabbddeebacaddadcdddecdcaabaabeabebdbbdbbcdcccbcdabbcceeddbdcbaedeaebddbeecebddedcadbeddbeebedddeedbecbdbaaddcdbaaecddaeeedecbcdcbecbdddeecbebabdcccdaeaddecabbceaddadadedaccbeecedbcccaccaddbebacaceedacebebeabccdcbbdcdcacdbeabdeaaebaecebdeabedadecaeddcbadccddeccecadceebdcdebaedaacedbcbeeeeadbbbeecddbdcacdbbedbdddeebcdcdbdceabeabbcdababddadcceacbbdacbccbadabbcabecbabccaccdadecebedbbcbcbabdbabddbeeacdaedabecceecaadaeceeebebccccbebdadabdaacabeeededcadaaeabdadbaaeedadbceddedeeedabcecbadbcbceabbbdabecdaaeddcdcdcaaddcaeebbdcdddbcadadccbbcddddbbbcbebcbdaeecbedeadbdbcbedeacceceabcababdebbddccbadbebdaababcbabedaaedaaddbebaadcdaecaebcaedbbecbcbcecacbbdcdeddeeeaccdddaeeecaaacbcbdcbecbbecaccaddddbadbdaedadbcecbaeddccccbcdeaedddcebaaaceaeabbbdedecdeabdccbcbcedddceacdeabcbceecbdbdcbabcecceaeadedaaeaacabaabedadedebbadbabbdecedddadebccacddddadccbeabaccbdcddbcbcecbbbbeeabddceaccdbebccdacbcdeaedeaccabdaaadedeccdeeacececdcbdcceecbdbaeadebbdbddddceebdbaeacdaaaecdbdabcdceacdbbcababbadaccaecbaccadbaccaaeabeedbbecbdaabcacaceacaebcbbdaaaadcbaccbebbcdcebeaedadcccbebebceadacbddddabddaaedeebcdcebeacddcddbeeebdcbeadabdbbdcddccdaaeeddaacaacebddddaaaececdeeceddeecbabbdbcdeabeecdbaeadacbecbebcaadaaadaaccdaeacdcddbbeccdcebeddccbceabaedcdabebaaabeaddcdbadabadaeceaaeaedabbdcdebababdbaeabdbdabeabcdbbabebbbbbebeecdaedabeadeccdacceaccbbdcadbcceedacbceeaecaaadbbdbcbeaecdeebdacbbacdbacddeedbbdeedccdbbeccebbedadbbedcebeddbeaedacedcbabddbeeacecadddcbdaeaacddeeabaacdeabbccbaebeaaaedecccedeecdaedacedacacbcaecabbdbeaabbbddebecceacbebdbeacbaeccdabeaadadaaacacbeabcddcdedbbddbaaeeeaeccadebbbcbcedaabacaadcabceaedccecdeeadddcbdeadabcebdaeeeedbacbeccdbcbdadabcacaabcdaebebeddebbbcbcdaaacaccabdeeaddceccacabeccbebacbdebbcbdeeccdaaedacbaeacccabecaadcacddbccccededdadebaeabeceadaeddedadabcdccdbddccccadaebbcbcdbcaedabbabaacdbcebeccbecaaadacebdbaaeaeedcaccbcaadbcbbebcaebdcbebcbbcbccdeddbedaaaadcdeebddbdbdceadeeacdcbcdccbaadaebcdccbaaecdbcbaebeeaeccbdedbabcddbedebcadbdceacddbdadbeaedccedeeabbdbebebdaedaaedecbcbbcceeaedbbddcabcccaedeccdbcdaddcdaedbadeedcebeaceabcedccbdeebdbcedeaccbaedbcedabbaeebbeccbcadecabbedbaaaebbebbcceeddabdacaddcdddeedabbbebadadcdcedabdddebdcbcaceddabdbddbddcabccbdacddabeebcbaeeeccdbcdeacbceddaecbaedcbbbccbbcbbeaebeaadccacbbacdddaeaedbaeccbcbccaaeeecbdbabdaaedddececdcdddacdcbcebabbeccdebeebdacbbbcccabcedecaecabdabaacdeedecccddbbeabcceecdceaecdbebbaaddbdaecabceceaeccdaacdadcceadbabcdbbaaeaaabeaabdebaebdbadbeadbcebdbcdbbccbcbeabeabcdbbebcddcbaabaebebdbbddbeaecdbdcedeebccbccbcdcddadecbbdceebbdeacddbaacbceadcdbdcbdaedebeccecaceadecedadeaddadabeeddbebccdeebcccddacadcadedeaaeaaddabadcdadccaeeadaecbcaddcdccaaeeadcdedbdbeaddcbcbeeaddcebecaaebcdebeaecdacddaccdceebdddeeaceaeebedbcabcbbbacdabcabbdccaddaabbbabdcdedadcaaecdddbdbdecadbcedcacdbdbebaeeccbbddbcbbdedcaabbebbaededdcdddcbcacabdcecebbbdebabbcaddbacebaabcddcdadbeecdcdedeedbebacabaeacaedbedadaadebdccedeabccbabbcaaadebddbeeebcebeaaecaeecabdabdbbeeebdecdaacacdaebadbdabccbadccdbcdaabbbaeeeabcabadbedaaaceaebcaeeecbbdeecbbedeadeeeceaadbebeaeadbddbcbeeacecddaceabaddddbaebddbacccdbadebdcecdedbbaeddcdadaecbeacaeaccdcabddebdabbadaedbaaaaeaceedadbbbbacbcbeeeceabadeabdebbacbacaedaedeedcebdeabdabdddcceeeacadedcbaaacccabaebbbbdddcecacbddebebcdacdeaabcdbdddccebdcaddeedecbcebdabeaceaadbddaacbbccecaecbeceecaeeeaecddddacaabadecbbcddaacdbecdbcbdbddabaddbbdceecabeeadacdaabcbecebeaedbeccdbdecacaacaeceebdadeebbacecbadbedbacbdaeedbbaacddcddacddedcebcdcbbebdebcbbbeceabeeadbadedaeeecdacbbbddecbadbadccacbbdaeebbaaddecbbcdbabddecdceeebeabddddeeddcdedbeaacbbeebecdadedaddcabacaabbccababcdbbddbaabaddcabddededadeebcecbcdaeeeebedbedbcbbdaeadbacdbcaacacceeaeecbabecebadcbadacabedcdadbdaeaacbddbcbecccdeabdbaceececaaccbceeeaccbdeeeecadcbdaaabcdaebcdadbdddccedebabcaaaceccdbabeddbcaeeccadbdabdeebdccaddecbacbcaaddbccceddbcccdaeacbababaeaabdadeacdceadadeebccbacacddeeacdeddddddeeeceaaccbdbadbebaceaecbbebdaceddbebdaaaecadbbbadcbdeadbabdbcbdabcbdaeddeedadbbeeaacbddbbbbeaddcccabbdbeaccaaccbecbdecdeebaabcbcacbebeaddeeeceabbabaaaadcbbdaedcdadbaabeddccaebbeadbedccaacbddbdbebcbbaacebcbcaceccebbebeabebbadabcddececdecdeecedeabdaaeacddddcedccedbcdccdbceaadccedbeabbeacbeeecaeadaedbeeddbbdeaacebabcadabceeecddeaacdeabdcabdabbdcebebbdaccaabbbddbdddeeebabdadebcbebeacedcceeaedeeaababcdddcccacbcaeddbaabbecaabeebdbcaccebadadadacebeedecdeababbbbacbeeacaedebbceacbccbbdbebceddabedacecdaadddbebcebcbabdaebacccdeccbacceccbbdebaccbabcacdbecdecdeadeccbcbcdebcbaaddbebedbedeaebbaeaacdaecedbddabbcbcbdeadeeeedeabbdcbbbeeacaecbbbabbbcabbdbebbabceeedacaecebdacacdacbcdccebbbdabaeadaccdbceccbbacdbceeaeaabebddccbddaedadabbeeddceccaeddbbacddeabcaaabacaecbdccddeddedaeacdccecaaaceddcbdbcdccbdbedabeadbdacdedadbaccadcabbebebceeecdcdbdbacbecadeddbdbccaababcccdbdedadcadcdbbeaebbeabbcdaaeecbccdeaebaeaadbbcbaebaddbcabadebeeebeadacdddbdcdbcbecbbbeabdacbceeaeccaadadcbadcaceedbccbcbdcebeccaadddcbbeaeccceaebaccdeceaadcdbaabaebcdacabadeaebeaaddeecabbcadedbedececabcaadecabadcbbaacebbcdcdbadabedacaeacaaedaeabbebeacceccddbdddddbdccbeeebebedcedbccaacaaceabdabddbddceabbbdcdcbbaececcdebaaedabeedaaeeccecabaacdabadcebbdadcbbedcaedebcaedbdeadcabeaeecbcaaebbdebbbcdaeaceeabbbddbdeeebcdcccdadaeaedadecddcaceedebaebabdbadbcaabcaeeaddbbabeaddaaedaadaebbadbeeabebaddabecdbbbbbcceedcdceacbdecbaeccaebababbaebeaeeacecaaceaedbbaadcbeedbddaedacbdbbaeaacdbecaaeeeadbcadcaceddbeccadccdedebeebeedaebbedaaabaacdadebcdabcbaaceedcddbeacddbedecebcbaaedcececccedcdebaaeadbaccaebabccacaedbdcedcbebccaceabccdacaddccdcbaeebcbdbabebcacbeceebbedddbedccbdabbcccdabeeccbeeeadaddacdeacaedcacccacaedeccdaadbccbccbabaebbabebbdaabbebbabdbeebedcbacbeedcaddabebbdbdedeaebbcbbaabcdbabdeabcaaecbeaddeeccadcdabddaecaaaabeddeaebceebadaeebaaeeabbbbcacecbbacebebacbdebecbedacdbbbaabbeccbbbeeebeaabebdabcdbecabdcddbcaddabcebabaecdcbedbabddccecabeccabbbdaddbbebedddbedbbecabaceceedacbdaaebecdeebbbdabaddcbaddccadacacadecbcbacddcdbacdebbcbeacaeacbabacbdbdbbabcebebbbbccbdbdadaceddddcddadddeddebdcdccaabbadaeeadaaebdcacdbbbbacdecaacdcadaaeddacabdbedeacccbeccbdadaecbabddeebdceebcaadabbdcaccabdceaaceaccdabacedcdabdeaeebcdeddebdaacdcacdeeeccdccecddedeadcdabbdddeeceeeeddbcecddecbadbbbacdeccedddebbbabbbadbdeeebadbaaedadaacdbaeccddbeeddeaeacbceebabcbdabddbaebcedacedddaeedbceedeebbcbdecdedadceeebbebcbdbeecadebedacbacababadaebbdccaebadebedebcadeabaadaadccadcaceadabdbacccbdacaeebbbddcebeeabcbabaaeedaabbedaceabbdbcbcadbeaceaecaeaedbcdeebacaddccdbceddacaabeddadbbbdcdddbbdbdecbaacbbdeebabddddabbbbbabecadbeabaedddeeeaeaadbdceedaaedcabadeceeeaebebcedbdabdcebbdcaaddbcccedcbaeadcdcaacdecebeaddabaeebeddecbadeacdcdddccddbcaccbabdeaedeacaeeaccdbecbedbdcdbbadcabdcceaaceeccdedabdeaebedbbcccaeeebecdeeddccdcdbedddcbeaabbbcbdcaaeaedaacabccadcbcabadcecdbaaeedbdacbadcbebebceacedadbadcbcbcddadbbbecdaeedcecaabaabeebbaabaadacabdebcdccccdabdcadaebaecebbedcaacdebdcaebcdccaaecdbdeabbecceaaaabaaadaddceecadbedcdcedcacdeeceeceadacacedaaadddeddabeebbaedddccccdeabbceeebbcbadebcdccccbececeaceacddbebbcbbebeaeaceceacecbcadacdcaebcdbbedbeaeabeaedaebabcecbddeaeeabbaeadcdcecadbccdcdeececcdededceabeaeddadeccdbbeacecdadaacdbdaedcdacdaebcdacadbabaaecdaaadecadcdddaceeadacedccdbcbbeaccaedeceadaceabedcacecdbbdaaebdcabadadbeaedebbabdcddddebdeedccdadcdacedaddaaeccacbbeccdeebbedbabacdcedbcbaddcacecccecdcaaddadaeecdaabcbbbcbdbcdeebddaeabbceadddeecceacaaaaebdeccbadcdeccedbedcbdebdbcdabccadbeadbccceeaaeabcdeceacebceadbaeaeacdbceeacbaeddecdcbccdddbabdcebacbaacdebcbaeadedabdacbceebbcbabecbbacbedddeabaaabbaeeacddcdbdcdcddbeeacbdeeddccdbeedaacabbebbddeecdaceaedecebbbbacadecddaddeaddcbaeeaeebbabaaaacbdcadcabbcbdaedbaacdcbcbdedaabaeddacbcceedeccaaaebaeadadecedaaceadeabebbdadcebabaccaceabadcbaeebebedccebceeccecbededbacdecdcbeeabedbbdcabccbdbdeebbaacceadbeecebdacdecdeeadaaecdacaabbacebdecaeaeccaaababadceedcdbddddebbceaedcaeddccecaeccddbcabeacdeaeeeecebdcadabaaebaeaeebbdcdddcddadacddddcedcecbadecdaebecbbebeaadcadddbbeeccecdbaabcaccedaeacadbeaeeecbecdbccdceeacdadbdbdeeeccebeedbcdceaddeeeabceedbcaeaaaacaacadcedccdcecbedcededdabbbcdaaacbbcaccdbedbbbcbeeddbbeeaddbaeaceccddebeedbceecaabdbccbdcaaedceacaaedcceecdcbbaecebeabdbdbaacabbbeadcbcaecaebcadbbebaacceabacaedddacadbeeedebdcbabddbceaddedebedabbebcddeadaadaeaeabdddadecddaccbaeebbbdeedabaaabcdcddabceaeecbdaeabacbabacdcbaccdceaacdeaaeedcbcdabeeadedcbaabeecacedebecbeddaccdaeacbcdeecabdcededeabcddecbccccabdacbdcceeecceadddedaacbdcdcaaaeecddcebcabcadbabbbdedbadadbcbecabbdcaecdabadebdcddbcaecdedbdacceeeccebccbbdeeaaabdcaaccbbeeeceeeabaaadbdaebccebcecbbbdabdedbbdccacedccaabaeebadedcdaebceeacdcaceacdedbdcbbdccecacbaccddedcaecaaecedbdadedeaaecdbcaebccdeeaeedabceaccdeeecebdeabddcbdceabecebeddccbcaeacdeaaceecebbbcdcbdbbbdeacccdeedebcddcebdaccadcaaabecedebcbcbacddeaeedccacbededddbebbcbacccaabcbcdcdebcccddeccdeeaadaedccdaceeedccabdedaceececbaecaaeacedeeaeaabdcacdbecceedeabcdabccabcaebcdbcaaeccbadccacceaaabccaedcddbadebbadadacbdabbabdbacbaaaebccbcaaadcbacacdadeadccecbdcdabaabbcceeaedbeaeebcadcecdbeaeeeedcdeadeacacebbababcbbdcdaaadccdcbbcaeeaecbdedececaeeccddccabaaeededabeacebabadebedbaedcbadebacdcacedcbebadaebabadcbcbaddbcdabcdceecddbecdadedbeabcdaebdadbddbabbdccecbbaedebcdbcbabcdeeeeccddcdcebeaebcadeeddcebebcccddcecdeabaddadacabbaedeeabbccbbcbbbdaaeacdcdedeceddbecdededebdeeeadeaeacbceecbddcdcccebddaeaeaaddeccbeddebebedbaacdcadeccaaceeeaeaedbcbceecbdcaaccbacdccccdbbdcedecbbdddebbcdeaeaabdcdcdbbeaedbbdadbcebabebddbebdeccecdcbcdaebdacebecebeeecebdeebcdddaddbebdbcbabebcadcdeebbaeabeddadbeeccecaaadadeabdadddbdbaaeccccbaabbeedcdccdcbeadbbadabaededdcacbdbcaebdceacbaaebcedbbaebbbbacbaaeccdbbadbcbcecaedeababcbbcbcabaeabcddcdecebaeddacedbbccddbbdcdbbbdeeeedccdbededabcbaeabcdeaacbaecbdacaeaaabbbedeccdcbabedcbabcaeccdeedadcaaeedebdbcebeeadeebeeccdbecdacadddcdaaaedcddbaddcaeecbebdbcacaedebeadbdcebddaabcaccdbadceabbeeebbbdcedcbbaeddccadeaabdebbbeddcacdbdadebaacdddaaaedbedbacedecbadcdcdbbecdebbdadaececedbdbaaaaabbeacccebceaddeeebcdcbeccbecdeeeecaabedbdaccbeacadadceaeddcbceeeaaddcbceadebbabbacbedeccccbbbabadedacdaecdeabdaecccbebcaadececadacbddedaaccdcdcadeeaecbabcacedacdebddeaabbcddebdbbbacdccbeccadaddddebcababbbbcbceadcbdaaedbbccaeecddcbecedabecdedacabdcbbcaaeeaddccbbebbeacbacedacabdeebecdebeedeceabdaecdaeebddebdeeadadcebaabdedeebccdcbaabeeabeaababedcaacecbcccadeaecbbaaeadeabbadbaabaaeeadeacbbdbcbabbbdccececcdbaaabdebaceacdabedcbdddbabbdbebbdeabbeabcecbaeeaecdabbbaaacbaaadeaecadaeeeabbacbeacecdcaaeedecebebcdddaedacdbcbcbbacbbacecdbdadeeceaabcbcacdaabeeeaaabdabbbaeeabccdaddcaeeeddecdeceecccbdaeadacbbadcacecdacacdddcbdabbbddcbabacbbbbacededceecbcecebacedacdccbcddebdbbdadeeadbcacebcaabdedebcaddcdebeebdaedbecabadecbbabbeaabeaecceacdbbdbebbcbdbaacaabeadcaebeedcbbabecccbeaeaeddcdbdadaaacbeaabbedbaedbacadaaebcbaedebecdcaebdcaecaeaedaeebcbeacebebecababdbeeeceecceedbbecbbabddbdedbbdedbdcdeabdaaeeeddbacaabbcadbedecececdcecbccaeddacacdcdaecaccdbdbabbbbeeeeeebcacedbdeaceeabcebecebeeceadbbabcbbbdccbddebecddecdbdacadedecddaedcbdedabaaeabebeebcebcbaeeeabbacaebdddecdabaaeecaaaddccceedecdddbabecaaeaaeadabeabdbababbdaebbedcabacedeedaacecebcaabdadadadebeacebddedccbceedccdcceaebebdaaaacbbdaecedbbcbddbddedccddacbcdbdecbadbbbbdddcacebedddecdecacdbeddeaaacebdcbaccbcaaaabddeccaecbdccbaeabddbcbbbeedccadcbddebceccaaaeaadeadbabeeacabaedbeecdbeebeacdcdadbdeaedaebbedabaebaebbeddbecddedabbbcebbacdeebbcabbdeddaecbcbaeeebbcedccbcbcaacadbcadadbabcbbaacdeaaccacbdeaedabccdecdaabdaaebcbcccacaccccbeeedaaacccadcabceaccdbdedabebaaaedbedecbcaebbdabbaeeacadcdcaaebaeebddccedcceaecbcdcddbbbdcdcadebddbedadcbabacbcdcddbcaaaddebabeddecdaaabeddacecdcccdacabaeeabeeacdeabceedbbbeedeedddbabaaddeeeddadbbbddabcdbcdbbbeebddcdaeeadddeeabddbccdcedaeddeeeeebccddebecbbdcbcadbbaaccbaadcdcdeccacddcaaaeecacaedaeeedeaeeccadebabcdddcbecdeaeebbaddcdcdbcdacecdcaadbebbaacaeadceacadebacbbcbdaabdddbaeedbcccaedcadebddebaaeaabdbabdbcebabdbcedceedbddcdadbeeebadddbdaceeeabbddeeedcabeaabdddedcbabcbdbaaadeeeabbaeaddbcdceabccbcabaaeadaadecebdebdcbbdebdceccbebbbdcddadcabedaacdabeaaceacdbdbeaebadbdedcbdecbbbdccdbbebbeebeacedeadbabcaacddbedeaaecccecabcaddabeaddbacabdcaaadaeccedaeaedaeaddecbbccdbbbdadcbaedcddbceddbdedccbdcdbaddeabbcedddeacaccbedbbebcecebceaecbecabbedadabacaaebacedceadbababceebcbebccedabdacbecdcbdeeebeccacabccadbcddbecabdcebaaedcbcecacaedecebbbdcdbcaeecedaebbebbaeadeacccdadbdcdbdecabcddaeebcdabbaedbacddcdaebeeacaceebaacaeabcecadabadceecbbaaeadcbbeabeadaabdacdedeabecdaecdaecbaddbdacadcadabecebdabedaaabddacbcbbaeabdeddccbccdbaccebeaccdabcdaabddebeccaeebbeaebacbedecbeaeecaedcaaccddabdadeaddbbbabcbbebbaddeeccaaeccbdabdbacaaddbbcdcdcdaccbedbbecabdddaaadeaeddbeacabecacbacadbeedbabeedbcdaccbeeadabcaaecccbceddddbeecbdceabbdadbcbcbbdcabbdcaedacacadebccaaccdbeecbdccddbaeedbdabebcaadcaeeabddbededadaedacedabdebeaeedecaceadaecaaccceabaecaabdedabcdedecdbccbccdddaecdacededadcdeaaceadadacbeecadbabddabaaaeaabdcddaeacabbbbdcdbbbebaacdcabaaeaecddbadeccdeeceaecaecccbcdbcbbdcedabbdadeaecaabbbeabaedaaddddaaaadabaaaeacacceededdcaeddeabbadaaeacedaebcbeaeacededaaabcadececcaedbeedeeeacbdcaeeddbbbcdddeeaeabbeeedeceadadaeeecbaecaccbebeddcbdacdebbebeaaebabcdbcdcebecbacabcbbcdcbebdacaebbeebcecbcbaebdecddcdebddddbadacdebebedebeeeaddebbcbdaaabaacedcbdbddccbbebdbabbddcbbbecabbdeeabccaacecbcabddedbebdaeeaecbbeabceebdecdcbcedaeabcebebbecedcedaaecbcedbeecddacdbbecaadadcbcaeebdaceccdaabebaeebadccacebbbbcdbbdbdadadcddacaeeaabeedcbcadaccbdecdcdaaacdacccbbcadccceaeadcdabaccccbabccabacbcbecedeccabbcacdddbaddabecceebedebeaebcddccaccbddedbbcaebeaddedcdaabbceebcdaabaebbbebbbeabceeceddbcaebceccecdaeaecaeadbdbaeacabcbedbadbbdcaaeaeacaaaaccaeeeeecbaacbaadeeccaedabaecaeecceabdababdbeccdeaeaedbebbadeecdbaeabcecbcbacabbaabecaabddbbbeeecaeacbbabdecccccecdeaaddbbaecbaeeadbeecabaaedcadaddbebdaeccabbbbdcebddccdadabdbebecabddadeebcbebedbedccddcbcaddaaebcbccedebddaebeacaabaaaeceddaebebabbadcbaeabddcddacacdccbdcebdaeabaebebeeddcbdbdccbddacdabcdcdcbceedbacdceaaeccedeceedbcdecbacaddddabacdedebbcddedcedecbadbbbdaeaccceaedaabacacaaeccdceabcbecceeabdeadddbceeabcdebdedcabddadcdadddddceeaeddcddbbbccedbceecabdbacacacdacebcbbacaacdbeaabbcdadedeeebebaeeabecbdaaeccaccaaaeeeaeeabedcbaadceedaeccabacaeebacacdaacedccacacbbddccdbcacabcaedeeebbcbcbecbddeaddccdbecbbeedcadecbadccacdcbeaeecadabccccabbceddeecdceaebadbeabcbabbcddbecebedbeebcdaaebeabddedbeeabbcacdaeddbdadeaeeecbdaedcadccebcddaccecedbaaecadedeeecabeccbacadaebacebebeadaeccdbbabeeccedaaacbbebaaadbadccdadccaedacacaeaceaeebbdbabcbdaecbbcccddecbcddadeebaebcedecadabbebbcecdaedeeaccdcddabcbcacabaeaaddaabebddbbebeddededbeadabbceddbaddebaadaaecdabeabaeaeebedbbcaececcbaeaabaecbebdbeccacdadbdcdacadedbeedcedbadadeaaaceeaabedcadcabdedbaebccbdbabbceaccdacbedddaebbdcceccddddeceeedcdababcceaabccebaebccebababbacaeacddebbeaebcedaeadeeaceddcdcbbbaebededeababbebdceaededbeacceecabdebebbceebdbaddbecabbaddcdbcdbbacaeadcbeddbcebaeeebbcbacbcddabececebbcebcbaabcadaccabdeeadddaecdbddcededdcaebaecccbbedadaaecabececacbbaaaaeedacbaedcddebebcedeeccababaeeabebaabbacdacdceceaebaecabcbbedbaeddbabceebebcbacbadbecebbbbbbbaacbbaaeccabddeacccdabdbeabbaaeaebcbacbacbdaeddbdeabdabcdcddadebddccbddbcccddbcbcddcccdcadbedbdddaabddeabadeddebdddbaabaceceabeeeadbcbceaebddddbedcaaecdbdbacbadaedacbbbbeabebdecadecdccadcabededebabcacbadcddbdacccdceccacbcddacddccaabbeeeabaaeadadedcddddecceebdcccbbdcaedadeeacdebdeadebbedbbebbaadddcbddceceaeaadddaabddbacdedcabbeadaceeebdbadddbadadcbcaecbdddbbadaeeababaadeaedebebbdbdebedaeccccdbbabaebdaaaaeccebeabbddcaecaebbccbcdabcccceddbcaacdcdcccbdaaaacdabdebbebeecdaddadceebaeacdeaeddeecdcecdecbdbebadccaabdbedaebcdbedbbecbbdedddaecedccbbaedcacedabcbddaedaaeeeeeebeacdeaddacccdeeeebebcacacdacebacdbedeaccaadebbeaecaabccbadecddbaabccecaaedaeedddecceebeababeccebbdadccddececabadaaedcbbcbbeabadbcacdaadbbdecaebdabacbedbbcadcdbadbcebbadbdbadceeacababaceaedaeeacaebeddcdbbaacbdaeaeddaeadaededaeeccecceddddceddcadceaccbeaddeeebaedadeecaceccaedeedaccccceaddacbcacbbaaeccdecebeaedacceebbcbeeddbbecaaccebdaaeccacedcccbddeeaacdcebdbabcaeceebedbbeecadedeabcaebadccdeaaecebeebaccddaebbeadaeadeaacbcaaeecaaaddcacaacacdcbadbabcaeadaeaacaaebaccaddbbaaaabbebbcbbaabadcebacacbedebcdacceabcbeecaadbecdadabcdceebdaeceeceedbbcbdaaadadbececddbcababebedebbddcbacdeaabdeacddaabbaddabbaeadcdbddbeababaacacddadcaaebbbddddcaccbeebbaacbdabeceeaaababebaecdacebcbbebcdaacddacdcacbeabdabbbcebdeedcbdaecccccebebcdedecacbdcdcbdbadedbbaeeacdcecbddcdccdcceeddedabadaaecceeaceaeebadcebaacdebadbaedcbeaaeaeaaebaacabcdccaeaccbbccabdcedbccddbaaebaebbcccbcbccaeecbdddeedbeaadeabaaecededbcbeabcbbddaaddceeaebbaeceebabcaebcecdeecbebcbcebabbacedaabeeaceceebceebdbcbbdabbdeeecdcbebcedeeeecaadccdccaedeedadeecaaaeebdcbedaeaabedcebeadbbabcdaaabeecbaebcddeebecceeddaedcdeaadcbcabebccbbbedceeabecbbadeadceaacacbdcabacbcdadbcbccebceaddedeedebccaabeaabbcaebaeebacabaaaacdddbadadbcdcedaeccaaebeadaaabadbadbeceedccdcdcecacbabeeadebdeaabaddbdedbaabdbbdbadeccccbcaaedeadbcceecbceaeeabddbcaeeaceacceecddbcecedcaeceeaecadddbcceccabbdceaaccdcdeeadcbdabcedaebacbdadaadacbadedcebcbecdcabdacddceeeecededdeedbcdccacceccbeababcacceadbdccbbaccaadecacbbaaabcadadcbabbbeadaaebcadbaaadacdcbbaceecdaeebaaedbeaaceabdcacbebbebebccbaedcbecdeeeeccbadccabacaeddaecedebdaddbccebebcbeadeabecadabedcaedaaeceabcdecccdcadbeadcbcdcbbceccabccbbebeedaecccaecccbebbccdbeebedadacddaedceecadecdaeadedddbaaaddcdceeecddbcacdeadaeaddaccbecaaccbaadceaaccacbbcaabcebcdcabaadcecabdbbbbadcedaeedabddddacecdccdabecdeaceecbaccddedeebbdabeabdebdcaaadcbdbcbdccaccdeaeacdebeabacaebabcdbbdebeceeddeedbcbbdacaeedecbeeebeaaeacacaccccaeebdeeeecedbdbdbaaeeebbdacacaadbbeeceadbecdedaccccaeabccaaadbccdcedaedeeedadaeddccebacbeaaacabaddabecdabcaadaeecebcedcbadbddaccaeaaeaebabacceacaaadccaeebbaabbdcbecdcedddbcaecbdbdcaeabeabacbdaadeddeaececaddedceaedaddabdebdccdedabdddeabadaaedabcebabeedcaaebeceadcddbabeeacebccdcdbbebacdacaaaaedacdabacdeccdcdabdbbcedabbcccbaedcaecdebdeeadcecadeedddaadbdceeeaacabcabeecdddbacabcbdaacddadcbeebbbebcaaabdebbaccadeaddacbacaddaacecbcbdeeeabcccbaebcaedabaccbadcdedbaebadbaccdcaaceabcbedcccadcbcdccdebaeeecdebaaabedaedeeccdcaacbdeabcedeedcebdcaedbdadcdacebbeabbabadceaaeadeeeabebcacbcbbcdbdadccabaccddddebbdeadadbdddebdacacbdcceecdeacceccbdcdadeececddeedadbabadddbebcddcacceaaeccadbbbbcdabebeecbbcbcdecdeeabceceeaaceeaadbeddcdedacdaaebdcacdcbbcbdbdadbceeaeddddceedcceeabdeecdcbeabbbcadccbcaddeddaebbedbbbbdcaacedaadaebcedbbbeabcebddeeaaedddbcecbeddaeddeabbaaeecddbeaeababebdccadbcebcbdcadcbaebdbeebdcaaeddddbaccdcbdbebcacdcdaeeaabbabeebbcabecacaececaabdcabbebaccaeebabeaadbeddaedaacbabcbaececeeabacbebcadeceeaecdcdaedabadbaebccadaddaaebedeecadeecebaeaaeacacebbabbddcacdaabbbcbebbbacaedcbaccbedceadbbccaaeeaaddecadecaacabcbabaaccacadaecdeccbdeadbdedcedaecdbcdadbdabbbabddcddecbebbdecabcaeedbdccdbcdadeddbecdbdaacdcebaaceeedeebbecaeecdaeacaaddeaaacaccdbeebacdacebcaddabacbceadbecbabebecdbaaadabbeaabdccdaacabccaacaaebbedbdebddaabbdacbbeadcacabaeddadcbbadbaaabceecaaacaaaaabccabddddedcadebbedeabbdaacceebaddcdabbecaacddaaadcadcacdbaecdceebbeceebdecaedacabddeeacdaadadeaabbdeabbadaddaceadbeacdbbdddadbaedaacbbbeadcecddddcaebbeeaecacbbacedbbdeddeadbbcbbcbbcbcacbebedeccadaceaacbdabacbbcadeccebcacadebddbaeebcceeccedadadbbebbbdcbdabbabcacddccbaebbbbbeaabcddcdbadaddbbdbacdcdceaceaedcedcacededaebddbdcdccdcabdedbebbeadedabeaceaaedeaadbbdcecbcecababbeddbaabadeacabcabdcedccebdddbceeaceaeaaaeabcabbcaabcbdcbdcedacdadceeaeedbdbbabaebbdcbebdeeecdbbaaabcdaeedaededbccaabbaeacbbcbbcadabeddadebdceacbecdddbdbbacaddbaebccceeebecccaedbaddcccebdabaeddedeacadaedededcbadaebeaebaeedcaceabedcdaaabedbbaaaecdcccdbbbdbbaaaebabacbeceedddebaaedaaceeacdacadbdddcedccdacbcdcccbdeeaccebeceeceabcbdbccebadeedaedcbbeedabbcaecaadbececeacbbdbeaddeaebbcbebeaedadcdeccebbeccadbeadecebbcbbcdcaabdccbcdbabbeccebedeebdcacceccdbaaadcdedaddacbedcbbdcceeadcbebdbbbcdabceccbbecebeebaebbbececaeaeaadbaabbdbeaadabdedbcedbadcddcddebdbdeeeaaeceddcdbabcbbabdcbcddddcbacaedddaeaaeacedceeaeecaabacdbdcebcabadcccaabbabebeaebceacbaaeabbaabcabceaecdeccdbcdccbddeebcebccbaaeaddbbcebeeeecdbebeccabddcbcaeadaacedbadadacacbaeecdeedbaebeaedcbcbcddcceabbcecaadaadceceaadacccccaddeceddebceadbeeadbecdceeebccdbdbeccbecddbbbbdcdeabdeeabeeeabeeebaacebccddeadcecceceabadccbeeaeaedcccadabbeeeeeadddbbdadcddbeeddeddaeccdadadcebcbaddbdeaccebaeadaebadcdaaeeeeabcbebcadebabedbdbceabdabdccdcaeccbacdaaacdbcaccdeccbdaadabcacbadebddddccaeadeaacabedcdbbcbcaedeacabbdaacbbcdeadccbadbbadebdeadabdeeaeccecbabcaedebacadddccbeabebecaeaabbadacdebcaedcbcaabccaeedeadaeeeaccacaebeebaacdcabbbdadaeccebddbaaccebeeddedeaaabddeaaeaabcbadbebdacaacbdeeaeeaabddaeabcacbbddddbedceebbebbcbdebebeeedeedabacdeaecccacbcdcceccbaceadaabbddadadacabbddeadcdeaecbedcbabcdcbceedcccedaebceebebabcbbedddebcecbedbdeaeeaeaadbcdebcccddeeecaaebacabaddaaebcaecdcbbdbbaacadccccceceaadcdddaeabddcbdaaeeadceeddabbdbedddabccecddaccebcbdedbebddcbcccdbceedbdacebebbeacaeabebbacedcbdbddcddcaabddeaeaaebcaeedeacdaadecbbdbecbaaeeebabdccceedbdedecedbadddbbcbdcabcebacdeddacccaeccdededbacaaeeadddcceebebdbedaaebbaccdebebbacbbbaaeccaddaeedeeaeebcdcbbcdaddeabecdcdbcabecddebaaddeaecaadadbcdceeceaeaedcbdeabcbbcaddcadbbabdeedbcaeddcacecccbbdebcddecdedcbcddadbdabddecabecabbbbbaabbeadddeacaaddcdacebcccdaadccaaddeccadddecaeadcecdccddeedccbbbdbdadccabdbedbccbbaeabeadcededbcabaceddbbeeeceedbdbecedaccbbdaeceadaacaebbaeedcbccbdbaebdaeababdeadaeeceeaddddacbebbbecacebddebddeebaecebdeaacbdcbdcbbaceeeeccabcaccebcbbaceeebbceccabedcddacddcadbaadbdccbecbdbedcedcaacbecddbeceaccdcbbbadeabaaccacdbddeadbebdeeceebeceaeeeeaadacecdeebdcbedaaebcdbccbaddadebedecdceacaedaeecdecccbdbddbcbdbbacccedaedbcbcdcbbcbaecadbaebbbdcaacdcaebcdebadbddaedeeadbeedaaaadbaddbbbddeeaaeddbbbbeaecdceddddccddccadaeaddbbedabcbdedbabacccddaedaaeecddadababdddebdeeaaabbbeabcabcaeeaddbceecdddccebdeccdecbdebbddaadddecaecccbaedadbeccdabdecaceeebdbcbadaeaadcbdcdbcedcaaabbedbeccdacbddebaebcbdbcdbcaeededcccdebdbdbedbbaccdecabeddbdcecddceacbabceeacaeabbebaccedbadabaaacccdaebdebcabbbeebceabbacacbbdddeebddedeaaccbbddcaaadccabaaebbbcabcbeaaebcabacababbaeecdebdccdcaeadaaccdceedaedbeabacebebbddaedccedecadcedbbeeaeebccccdcbebdbbceaaadaabbdaceedcbabbeadcebeecdddebabdcbeaebceddacdceecebbabdeaecddeeeeedacbcecadbaeaccbcbbbbdcbbccadbaadbbebeacbceacbabbcedabcccaedaeababdcadacdbdaeaddbccdabbaceceedecebeeaadacccdaaeeadbdecbecabbbeebaedbaebacacccacdceebeadedacedeadcdebdeddeacabbdeaacaeaccaaceccabebdacaabdddaabbbedddeddcbcdbbedbcbcabcdabdcbbbbedaababdcbcbeadababecaaacaedbabacaababbccabaeadaeaacdcbcabdbdbddebcaebcebbbacbadddeccddbdeaaaedcecbbeddcdcabbddbbacdbaebddacbaebbebcedadddaaedabadbadabededaedbbbeadcaadccdcdcdbdadaccdcaeeeadabdcceabebdeaebbbeacddcbcdaceeecdcbcdcbeeaabbaadbbeabecbbbcdeeeebcacdaddeceaeacacdabdacaedcccbddadddcbeeabcbacebbaecadbbdaaadecbecaecdeaeedccccebcbcbceabbedaecceddacaebeecaeecbabecbbecaaedecadeecbabbadcaedecbdeddadacacaaeacdeaacbaedaeaabbeacbcbabccabeadedabbcddeaabdaceadecbebccaddddbbdbdcaecccdaacabcbebddebbcecdacedeedbcddbdbaebddbcadcbdcecabababddbdddcbbccabdeedcddeedbadccccdcbbedbddbdcebcaccebdbabbbceeaaebdeadaaaeecabbeebbaeaecaaedeacdbddecbbceddeaeedecddadecaaeaedaadaeddeadaadaeeaccdcbeaddddecdadccbadecdacdaabcdccbbacbcbcccdcacdbeaedacebeaecbcabbbebbbacceaedaddaadddaecaedebbcdacaaaddeeeeeaccbacdadeacdccadbacacdcbeaedbbabbcbcbbadaadaebededeabbdcaaadbbddcbbeedeebaecdeebeaedaccccbbceeaaabaedaeebdeeabcbcddcdbedecaeedddcdcebeddbbaaedcbcacbbbceacbecaeaaaeaecaeeeacbcceaabddecdbacededceedeadacadbbecaaeabcbdacabedebacbeebadaababccebabbbadebdeeacaadcaebbcbabbaeddeaacdaaababaeadcdeaabebdcedebcbadcebdabbbedcaeaeacdcaadbbbddaecaadbcbcbbecdecdbddcececcdaedcdedabdcabcebdaecaeaecddaadedbbdeedddbebddcaaabdbcccdcdcdcccccecedaaccdbadaddbbecbccedebbddaebceabeebdacdeadaedeaadccecaeaaeddcceeacdcbccdddbdccabbbdeeccecbcddaeacdacddbdaaeddebaeebcebeeaadcaaeacdeaadadcaabddacbacedaadcdedbaacdecdeccdbaadaacacdcbdaaddacaabcddcbdacbcdebcabcbcdecdbbddccbbcaadcebedeebbcdedcecedacbdaabdbebcaaacbdaddaeeecaccedeeaceebcaceeddcdeaaabedaadcdebbeecbdcccbbcaebcceedaedebcbddbadceeeacdbcacbcaedeedceeeddeecbcebbbedacdddedbeeedbabeddededdccdbddbcbcebadcdbddbbebeabbabbacdadeddacaccadecbacdbbebaabedeeccbdaeaedebdbdbcdabbeaacadebdeabcebbdebdcbbadebbcaeccbccbbbbeabeceeadddeeaebcecdbdbceeedbbacdaeaecdecdaddaeaccebecbbdbabecabdedcccbcebedacbaabeccacbdabedeeceabcbaaecedacbacadccedcceaceaeeecedaedadccdacaeeeababcabccadcebbeeecdededebabddecccbeabcaaddaadcdcebccbbecdacddcbabaeacecebeecebedeeabceaddeeeedbebbdeebcccbdcedbceddebcdeccbbaccbdceabeeaedeecbcccacbcaebdadebabbdaddcdcdaabdabbcbaeaecdbacaeabacbeabacabebddadcccbcbaabbeccbebdabbbdeeeddbbadcaecbdaecdcbbaeabdeadacdedbcdcdbcbabedbcadeeaddadbdcedeccebddccabcccbebbedceecabcdaaadbbbecbedbaacaaaeecabbbcccadddedececebaeaabbcdaeebddadecebeddbbeaaddaedbbbaebaedccdcdebcdcceeacbedcdceebcdadcbdcebcceecaaaccaceeeacbdbaeebcacdcaccdbdccbcacedaeabecacdaecacabbccabeedcbbadabadebbcbeedadacdddeeebdccbabdbdbeaebbcccaecdcddbbcdebeceadbaaeabcdedceeddaeacaeeebedbeeadebadaedbacdbcaacbacccddaeabababeebdebeeebedcdaeedaacdaddbcbdedcadedeabecdeaddaeedaeeccbadbadaacdbcadaeeecdabdceacccbaeedbcbbcebeacbeaebdaabceaeeddcedbeebceaececaeeabbeacadebbacceccbcbacacdadacaebccbdabbeaecdceceddaebcbbbbdbeddccbcadbbbadbdbbdedecadaaceedccccbdcbbeaaadcecaeddacbabbecccdcdbdbaabeceabdeacabeadeaaeeceecbdbecceeeacbbdaddedacedabaddbeebadaaadbbcbbcbcecdcdbcbaaecddbcadbdeedbababbbebedbcceaeccbcacbebecdddbcebadcbbdbceccadaebceacbeacddebbceeedeaacaeeceadcbecbabdebeccdabdcceecbaebceddaaebbdabceabdadeaceaaebdbeaacbecabcacbdbaddcedaedbbcbcebeaeabaeebeabcddccabccaadcedbdeddaaccabddbbbcebaedccbdeaebbcdabdeeaaddcacadbecbcabaedaeeddecbcdbadbbddceeddbcbcccaadbdbdceaacdadacacbdbccdcebaabebedcaaeecdadcbdcacbebebbdccaabcaaaeabbebeddacdcbeedecabdbbcaabaeecdcceacadeabbdebddbadcadbbbbdecaaaebcbabbeeccdcadecccdeaccceeeabceaddecdbbddebabddbbdecbeaecdcbddeeebccbabeaeabdeabaeecabbebcaecadbdadddededeeacecddbccaeadedeceabbbddbeedbbbbcceebeadabeeecdbabcccbdcccdccdbbadbbceaabbabdbbecedaccebdaacddddbdebbbbcaaacacaeeacbbaeebadecbbbbaaeecabbecccacbeeaceaacdbaccadddccabcabbdeadaebeaaabccddceaeabeacaecaebaccdddabbccbcecbaadaacdaaddccbabbceabbcbbbeabaadcaaabeceedcbcebcbedeeeebacdceeaacaaabebbaeebcbadebeebbdddeabcabebeadeedddaadddeccaeddbaaaaeeeaabebccaedeedbbeaeaeaedccaceccbddceddeccdbebaecdcdccaaccddcbebdadabbdbbcebeebadcbbdbddeacbcaaececdeeeddeecedadccdbcbaeadedacdddbbddedcbddcebeebebcbeededaeebcbcceaeceebcbcadcdcdaecaabdccdecbabecabedaabeabdcbbcbbaebbddbedeccdbcbdbbaaebecacbddeadcdbbccecbabeaedaecacaacbdddacbcdeebcebdcededeebebabaaeacabccabdcdeaebdcecbacdaedbaadbaaddbeccbdccdbdbdaebebdcbedaaadeaebcdcdeacdccacccaadcaccebaddcaceaedebdeacadcbcaceddbbcacadaecabdaeeecbedcbacccaabeaacbcbecebcaecaabecabcbcebbdeaeeaccbedaeaccdadcbdadbaaccdbabcbbabdbeeabddcaabaabaaeddcdeedeadadaecbbcaebcebadbdcbaaeeacbaebeceaddcbebaeccbabbdaabebbecbbbdceccbceadabdcdecadebcdcddaceaebbdebbceacabaddeddadbdddcbdaeebeddceabdcebccdadabedeaedcdbccebdebedaccadbedacaacaaebbedddcebecaecabceeceaedddadeebbbecbcbbeeedbaccbeceaaadcbbbebcabcbbcddacbadbaaaebcdcaceadceebcbdcabeebbeddadcacebbccccedeadaeedaedebbdcbccbbcabdccedbbeaaeaeabbcebeaccdadcdccaeaaeacdebdeeacceeeadbbbedbabadedbeaceecccbebaaceccacadecdcacaaaecdbaebadececabcdedbbacdebaacabacdaadbddadbcdddbdcdcbdeabbeadabadbcaaacabaacaabaeabddcdebebcdaddceecaaddeeceaecadddbdddbddecdbddbdbaadbbcaebadcceabcdabbacaeeebacecaeaedbedcdccbaadcbaeeaaecebcdebabcdadcabdbabddeaccdaeeaaebdcecdbdbebebdebddaceecddbddcbecadaeeaeaabebdcedadabaebdcdababdccabdbecbedebacbbadbbdecbcdcaeaadabdaedaebcceacddbacbcebaebaedadacbcbadcebddbbddbeeedbccbbabacbcdebcbbcbccbceaeddadaeceedaecdbddaaeaaeaaedcddbeaddcbadedaddddcdcccdcecabeacdddeabaabdeaebcbeeaeeabedbcdabcaceaabcaddcceebacabbeccaaecababeaeccdcecbcaedcdcaacadbeabebeedddccedcbddcccdbdaaeaaabbbdeeededaddeccceadcacdbdadabeeddbabeebcddbeaddebcecbbbdcaccdcbbbccbcaabbeacacaaceebbccddcadbdadeecbccabdedaeaecacdedebdcabbeaaebeccacbbabdeeccbeeedecaacaeebcdecbdacbdcabbacdabcdbeebeebddbecabeedcddbdbdddbcaddbeeacdacaedbdbdbdaeeebbeecbbedcebaabeedaeeabbccbadcbccebccdbeaababadeabdebbdbdcabaccadbdbeddacbcecedeaeccebddeeeeabaeaebbcaceaaaeeaccddbeaebdaaaadedbccababeeadaaeeeceededabcbebaaedaceaccabebadccddcaecbbcaebecbaeeebebcabcaddbaedbbbbccbbddaedcadaedbaebeebceacdbeeabbbbdcebdabedcbedcaddbdcddbdbdadaacccadcecbbeddeecdebeadcdabaddcddeecdadecadbbdabedecccebebacaecdeccacbecaccebdccecddcdbdaeccebbccbbbbcacaaedeeecaccddbcaebdecbbddcaaddeacebbcbbaecbabeecebbddcbebedeaadabbadbcaedccdbcbeadaeadabdedbeabebeaddccbbaccededebccdcbceeecdabdcaaacceabacdcbdbadcbabbdbbbbabdeccbaccdebeccebcebaabacebedeccaaaceaaceadeceecdbddccebaabddccbbadbdbbeadddbaacadcbddebedeabdadbdcbbcbdbbdbadaadaccacabeacdbedbdadaaeccdbcaddeeacdaecadcaadaceeeacedebadcebbdeebeabcceaaccadecedcdccaebbaeebacdcccaacdaccddedbebbedbcdbddedeabeaebbaccebcbdccdceaabdccceeddccddedccebcdeaeddabebbccdbacdacbaccbdbecbddecdacabcddcadbdbbecacecbcabaababaadabdeabebdeddbcbbdbabeaecbccccbdcadedaeeebcdedcceeacbcaaacedbecbdeedeccdecebdcdbdadabebceebebbcaeaecdbbdaaeaecbaedccaddebbadddccdcabddeaeceeaceeebdeebcaeecdbcabdeaaaeadabcecebecebbbaeadcacabebddbcccdeadbabeaceddbbcdaedaeaeccbcbdaccebeeeebaeacbbebdecbcacabbdcceaceedaabecebdbcadaecdccbbdeedbbeeebdeadbaeaeadeceabbadaedeeddbeadceebccaaddacdeaaeadcbceceeddadceecccdaacceeeabdbdeaabdadbdcbbcbddacecdbbebbddceddacbcededddbdbdbcdeeadbacbdcbdcdbcbbccdbcaeeaadeaeaaedecebbaadaaadaedddeceaccedcdeededdaaeaeecbbccaeaabeabebadeadadabebbbebeaaccbdeabcaddcbecaeedaedbccaeaebcaecbecbdebeacbdbdccdebbcceacdaadbabcdcccacbecaceabebcabcadbbbaaacceaadbeabcbccaedbbbdaaeccdbeccaaedbccdeadedadabddbbebbdeddabbbbbdcacaedbeccededadecdbadbebcdbdcdddaebaebbbdcaabebbddebbbcbeeecbcdcecaedabdaacaadceabedbdceadedbddecbbcbaaacdeeadaebdcdacddadcacecaabdadcedaeabdbcbbcaabcdcaeebbdddbcaeacbbdadebbeadccebbcacededdbbdebbaeddccdbaaacebceacdcccddbaabddabaaeadedcccbeeeacacbaeabdbbedadbbabcceabbabbbacbabedcacacabcddabcebaacadbeceacebddbcddedaaaabdbeeeedaadbbaaccedbbdabdeceacaecbcaadbebacbeaeabccbbbaeaedcecdbcbeeaccbabaaeacbdaacbacecdcccacbedeebbbeacaccdbdbceedeabeeacbdaddcbebdcdcbeccbdedacbceebebececdadeaaacbddacbdaaacbcebbccadcdeaeabaabcbeeebcddabbcabeabaccceeebeacdbdedabddcacebcedecddedeedabbebbdabbaacebddceeedcacabaebaabbdecacebacedcedeeccbeeeecdeeaaebaadaccadedaacbcaaeaccbadaeacaedeaacaadededdacebacaaabbedaeeeeeeacbecbabbdadbbabccceacdabbcdabecbbbdeccdbddeebeaecedcddbddcedaeeedcdebdbaabaebeaeacbebceadecbbdbcbbbeccdcdeaceaeeccbbceaeeddddabaaeedccecaabcadacedebcecbdedabbdddaeeabcbaeaedeaebedeaacaabbecdeecbcbddacbcdebeeaebdbebeaadabdabaecceabadcbabccbdddabaaeadedecacbaacdbcacccabddccbbaeecdcccedecddadabddedcaebbcdadcdbcbdaddbbacbbeecdbcceabacbaedadbdeebeeabcdaabcedddbaacebbebeaaaecbcddbbcbacaecdedbaebebeebaebdeedebacacdeeeedceabbbeacbdacadcceabaeeadbceaebbeedbcebabdaddbeedcaadaddbdccdbcddadcdacebeaaaadebbbdaabbcaaeceebdedbeadddabbaeaaaccccdebabecaeedbaaaeeaaabcacbbbdeccdddceaeebccedcdebcdeebabeeeadcbedbceacbecdaabadccaeabdeebceaaababdcaeeaeadedcccdcbaccdaaedecceedcedddeeacedededcbbbeeabbeebabdedebdeebaeeaacedebcbabeeaddaeceebaabaadedcbabbcbdaaccbedcacceecaaeebedabcdccdaeeebbbdeabdbdddeccbabcdaaceeaddceeddcbaadddedabecbeabdaadbeaebbaeaeaeddeececbddcdaccceaedccedcaaaaaeacebbadcccdbebeaeaaddeebabbcdbbbeebbedcecaabaaeacdbeadedbdeaecdcebdaadedcdbeeeacbcaebedbeeebbebebecdaeeeddcdbcacbedddcbbbeeabdcddbecedebdaedeabdcaebdbcececcdbecebdabccecebbabdacaddacedaaeccaeadebdcbeedbadeeeabdbcdcaedcceeddbcaacbcbbacdacecbbbeacedaedbdcdeaacdccdaaaecbdedabdbcecdccecadebdabdeacceeccbaeedcdcbeabecbbdbcdeaebbaddcadbdaebcecaccbbabbcbdeccccdcebeccaaaadcbcbdccbbbccadcbeccebaecaebedcaaaacebeedbddceeebedabebddddceebeadacaeeabebaedbebcbaeeecadaadebebddebcbdbcceebbbbecadececbddbeedccdaabeaedcececababdceadddecbeebbcbdabcdeeeabededdadeabaaacacecdbcbedbbcaccecbbcbaddeeccccdccbeeeeddeeaedaaaaadbecacbaeaacadcbacbeecacbcdacdadabdeedcaacabbaedecaaebcaedcceaaabeeddbeabbdedcdcabedaededeeaaceddceaaadaabedbcaaebdebbeabbdbedebedebaabebcdaddcaabbcddbbccbdeebbbabedbaadaebcedaceddcccabdacaeaacdddaedbebaddcedcbaccbbcddeeedbdbbdaabbcdcebcacecdeedeeedaddbbacecdcbcccccdeeadaadbbbdccdedddebbbaaddeecaeaabecbbbeecbdedddcabaeeaeabedbadebebcbeededcbbededeccecbecdbecaabecebdacddcbdadbeeaaebecdcccceeecaeadecbbbdaedeeadccbbeacbbcddcecdbbdcceeeeceaaeadecabdbabbdbdceeedacedacebdecbebdbdcaeabbcceadeecaaeedbeebecedaaddcddecddcceddedadaceabbaedbeacdaacdbecddceacccececcedadceeacedacdccddccdcdebdccbbeebbbdbdbaaabeeebbaabbbdcbbeedabadebbeadbdaaaedbbabcaecededcaddcedbcdadbeaebbddeccedcaacbabdaddcdcbbaadceaacbcecbdbebeedbabbbaaececcaaebabaadcabeeeaeccbbdebeaaceedeeaabbdbdecacddababbcadabebcabecaeaceedbcedbbdadccccabeddedbdcddcebaacebeeedacececdaadbcdbcddabccabaaacdddcedabaeeaaadaadeedadedbaaaaacdcceceebaeaacadebaccabaabeeaeaebaaacceddeabbbddbdabacaddceeceaaaedaeceaaeecccdcabceebdceeaeaeeebeadceaeeeccbadcbecadcedddebeacacececaddadebebbbdceaaccaaabaddbdceeccdcbdecbbaecbcddbdacecaedcbacaedaaabccacddbdcacebedaebaddcaeabdcccccadbedcaedebcbebeabeecbbccdeededaedecedeadeaadaceceacebbcadabbedcebdadebbdcecbaaaaacddccedddacbadadedddbccdbadbeedacadadabbdcabbbebbabaedecbcccdbccbbbbcebbddacadecaececcddeeedceeadddebbadbdcdaeeadbcededbeaccbbecaedccbeaecaccccaeccbdbaadbdaeadbcdcbceaeedbbabeebecedecbedcedbabecbbcdeabcbcbbaeccadebedaeceaacabbdbebaababebedbeadceaeddeaccbdeccaceabbceeabedaedadcedaaecacbdddedabdddddbcadaadacbaecdeeeecbcdeeebeaccdcdbceaedecbbcdbbdbdceaaabaabeebdbdeebaecadeeebbabaccedaebbededbbbeacdaebcbbbbecabbdaecbbaeeaddaccbedebedeedbcbabbaebebedecaaecceddcbeaeecdabcaeaebadbabbbaeaeadadeababcabcccacecaadcdbdadebcdbadbdbcbbabcbdabeaedabeacbccecbddeeaebacdedcbeeaecbeccececbebeccdaadeabaccdbacecedabbaceaeebeceabecdedddebdaadedcbccedadecccbddabdabddaedabbaaebbbcbcaaccaedadebdacbadceabccddbdbcceabbcbabdccadebbeceaabdcbadcabbbaaeaaecbbcabcbbdebeeccdaddddbcacbddbdedacdabeaccccdceabddbaedcacbaaaccabcbdeeacededecbceadcaccacaeadcccdbaceaeedbebeceaeadcddeaaebeeabcadcaaccaebdbcaadcdcdabaacabecbcdeedbbbbededaeaabbcdddebceadbebbeeddeaadedddbbebcacdaceaaecdeaedbdbcdcdebbcbecadcaeddacdaaddbaecdeaedbaeaecadaebbcdbbbcedbbbbedadecedaadebdacdaedbeadbddcbedbecbdcbcacebebcacbcdcebdddeedadecccbaeebacceaadbdaacabcecbaacdaddddebabcbcdddcaddccbaaeaecdbabdbececbceebadacbedbbcadbacaeadedaadbabebbdbecebbebbaeacacacabcddbeaebacbaaccaabecbabaabecdaaaaadebdeebcbdaccbbeeadabbcceedbecdbabadbeadeccbaaedadeebeebdcccbccccdccaeadeccdcebadaabcbeedebbdccdbbbacbaeacccacbdeedebbccceabceaaeadaaeabaeaabbeaddbedbeebdcbbbbceedaaecdceccbeebecbcacaebddeacadeedcdcdadbceeddaedcdeebedbbbecaccaccbedddeebcdcdceaeeccbdbaabadddbbbbaaeeaccbccedacedbabedeccbbccbaebddacdbacdbacbdbaaedabcbbeaceebcedceceaadbaedcaecaceebdcedbaadbdaebebedacabaabbaecbedacbdccdbcbddcaabcaecdabdddbedbcecbebeeacceebcdecedcdeaaaaaecedcbaecddacaaccaedcbcebddddabcadbdebbddeccddacbabecacbcabebdecececeddaedeebecabadcdbacabdeceebabbceebbebccbbbadddaeeaaaaedccbeabebeaebbdbeaebaceaeabccdebedcdabebeebccdaacebdeaaeddabaebaacebbbbeebaaaaecceecaeaadbbdecbeccecdeaaecdcccaccddeaabdaedebedcceabaaccbdcbdeccdebcceeaeaedaceebcbccbbcadbaaeecebcedaceccacaeeddcebddaaabbeaacbbbbbebebddedccdabedceaecacebddccaeaacaccdabcebbeceaabcbdbeeeeeeedbaacdceabbeadacdbabcaeadacdeecdaebcbaadcbbeabecadacbebeeaeacbaaccbdacbcdcacedacabdceacddaabdebceacdcbcaccbaeecbecbdbedddecbecdbaadccaecdecaacdaadebaabeacacacabaaddcbdaacaeeabbaeecaeabacecadaecbdebecebcbedaadbdbddaaecbbeddcccdedeadbddedddecceddaaaadbeeecedbcdbebccbabadedbacedccdebbdcbbcaaaabeddeddecdeecbdddcebbbdbbabedcabaaddecbecbeebdedabdcceebedddaeccbeabcdcbddcdcecdbbccdcdccaccbabdaceceadcccbceecbacdacacaadaacbeeaebebebbbdaccdbebaeccededbbcabebecbbaaeacbbdedebbaecaaaebcbdecddceedbaadbdaecbcddaaccccbdbcaadbbaddcdebdabccdbdaddabbebdccdeeadededccbcadedadbedccbbbbddceebaeabaeadaceebdaddaedceaaeddcbadcdccaeacbaaddbdbbbdcadbceebeceecbdebabdeacdeaedcebcddceecdecbebcdcaacbacbdaadabeedaedbcbbcecabbbaabdcedabdedbaedacbbbecdabdccdbaabecaccdcaebbdcceceecadbaddacedaaeebeeddabbaebdacdacdbaebcabdeeddaeebadbbbabadadcdbdaccededebabeeaecbeeecdcdbbbcbcdbaaddaeedbadeecbeeccaeabcceddedadaaaacdbccabababaeebbbcddeebdddbeaecaebdceccedbaaeebadccadeacaeedcdddaceddccadddbcdcadacdccaabebaaebdecdaceadeebaaeebdccebcedeacbddedbbdddbcdbecbdabbdeeabeeadadaacdcdbbedbbdbeadedaaceabdccdecaebbcadddacaeaadcdaaeaaedaabcedbbbcaebbeabcaedbeaddaaabebdebceaebbadcbaddccdaebdeacaaddceedddeadadbcdaacbbbeacbbceabbadcdcbdaadceccabbeecdaaaadbebceeccedcecdcaceeebdeeeeadeebebdadeeeadeabbbbbdabdebcaaceaddabaadecedadeecdbeeaaddbbdbecbaeaceceebededabaeeeacbbedddeebddcdcbeadeeedabedcdaedeaebedbbbdbbbecdaabbbadeedeeedcdaadadaacbddaceecaeeeccbddeccaecbeacdeeeeebeceeddeccdcedddbcdbcabdcddbedacaaeeaaadddbdecebdcbbdbccadbcebdaadcbbebddbebadadbcdecaebeddeabcdbbedabcebcbcaeeebcceabcdabaeeecdeddeeedbdddcceddbecdeeadeebecacbecbaaedbabdeceedecbcaeaebcdbaccbccdbabaceaecdebbccedabcbaacbddaaeddedeadeacbbdabdbdeedddaaeeeaacddaceaadaeeddaaeecbdaeabeaccecbedbdccedacccdccaeadbaeabadcddebddbbcdddadbbbcacbeeaacdbaeebcbeebeccebcedbeeeaeabdebcacddcebdbdceeecbcaaeabeaaecebabacabbbadedbcdeeaceaedeedddbebcacaccabbeebdaabacadbedeebbedceebbbdaddbbcdeededcbbeceaedeecaabcadebacbdacbdadddacabbecdeacecaaccdbadbdecdcbaedbcdaabbdeaebdabadbdececadddceadabcbeedddeeaebdddacaeddcddddaccadeaaeebbddbcdaaeccaabeeeeaceebdbebdacacdcbadeabdaedaddcdbebcacdeacddabddecbaeaacabcdaaddcdcdcdbaecabccdedebdbdceebdeaaabbbabcdebccdcdecdbbcdacabcebeddaeebdecaadbbbdddceaaaeaaddcbcedaaeccebbbddabdaeeedeeaccdeacbdeadbdbcaacccaebeaadaaeaabbebcbbdbebeaecbccccbcaeaeadcabcaaccdabbcddbdeadadaedaddeceebcdbceeceadcaeceaabdcaccecdbbbaeaaaacaebdaabadbbceeebdbdcdadbbdeddadaeaebbeeabccabdcdcbdcdeddbebdbbebeebdcbeeaebbcabedabadbacddcaecebacbedadebedbceeaaacbebabcaebdbeaebbcaebecedaeabcadcceaaeacebadcdccdaeaedeaaebcdecceedeaabcceceebeacdabccbccabccdadeacbdebbdcbebdcbbcbebedaddabbbdaedaeaaedadceedcedadddaddaddcecdadebebcdddebadceceaaacaaaaaeeaedbabaabeceebbebdcaacebbbdbadcbeeeccadebaedbeccddbadcdacdbddabeccaeceeebbcadebbbaaaeeaceabeeaeacdeaadbdacbdcddeadedcaabdddddaeccebbbbbcdabbcdbebcbeaaabaebeaeaaabdaaddedeceacedbaabededdcecbcdddbaebdcceaaadaadaccdddececdecededddebacccdbaaebcebccadedebaedbccacccdabaacbcedaacacbabdeccbaadcdedaacebbbacdbccaebdcebaadcdbdcbbebbeeabcaaaaaebadeecdebaccdedbbacbcadbadcebdcbaddeabddddcaddcbcbeddbbbdadcadaedbebccaaabeacdecebbaacdacdeebaccbadccdabdaabdcaabbbecddebebabcbbddcabcacbcaacaddcebeadbaaccdbabbbeacadbbccddbcecbebaeaedbbaddeabeeaecbccaeccacbabeaddddeeaaccbeeecdeecceaebeedeebccdddbeaecebacadacaeabcedcbadacdbcdabedccbadadcbecdabbdcdccbcbbbaccacbedcdbccbdcbaccceddddcdddaaddaaaccbecacdbdbcbecebdcddcbdbebbeccbcaeeeaceabbceaaeaebeeadbcaaddedbdcaebeeedcbadcaebdeaedecdeadeaaabbabcbcaeddbecbdcaeeccddaeeccabccadbbdddcadcedabaeeecdcebabdedaaaedadbbdacaaecbaddeacacdadedcedaaccbbaeabccbbcbadbebdedecaecabdccedcddecedaddabadbaecbebacbbcaeeebeabcbdaacbbeecdeeeccdbedbbbcdcaaeaaecaedcddbbbaeababccdbaaeeacedbaddbcedcdbbccedbadbddaccddaeecddcdaccedcadabeadeadbcababaaceddbbabddabacaedcaebadceedebaebadacddeadcbdecadbddbadecddababcbaecbecbdedeaeeeaecbaecbcaecaedbeccecaaebccbaedeeeaadeecaadebbaabccdbbebeaccddedbebdcdccbabbdbcdeddbecadeeacbaeabadbeccbbebcabddecbedacecdedbbdcebcceecbedcbabaddaabdeaeabbcadacbbaecabdbeadeccdccbdeeaddedeccebeaedadebbcbaaedeccdebbddaebdccbeaedabcddabccebeacccecadccbdaadddddddcaecaebbabdcebdadcdcdeedbaaedbabdbcebaacbdccdacedbdbeabddbdadbecabacddbbcbbbbdbdbeddaedaccaaeeadcaceadccabdbceebdcedbddeeadbaedaddabccecacbcccbddaadbabebcaaeaabbbebedcbdeecaaddaebaaedcaeddaccebdebcdcceaabaacecacaadaeeebebdcbddbdddaeebeaaacaabbcabadbcccddceabdacdcbbacbdacaebccdbcacaaeaaacdcbeadebddbccbdedebbccebeadbebcedbaedbbdebdbebbbdbbedddecedeeacddcbeedaaebeacdaeddaabcbbbaddecacbdabdcddbadecaeedcbbcacdcabdaeeaeceeadadcbedaeadaebeedaabedbbddacecaabeadcebeceeabddcacabaadacadcceedaecdeaeeacebcabbdbbdcaadacecadabaddaeedbabdebdbeabaaaedaacbdcedcbbccaccdcbdedbdcabdeecaddaeeceeedaebdaeabeeaecdccbeabcdeaeedbebbacebacdecaeceecbebdebebdacedccbaaebbcbcebceebcaaaaacbcadebababaeacccccdecbdeadbaadddaeaeeeddaeabdcaeeecbdcaebacbbbaadecdecbccdcbabbadaeecbbabaedebcbdcddbcbceabeabaeaadadebbcdecebdadedededabaeaccaabbbaeeccbcabbeceaddedbdcbabbbdcdbeabecdedadadeeebeebdedbcdaddedaaacdeabcaebbcbeadaededebbdecedaccbddbdbcadddebadedbbdcdabcbcaedaaadbaeecbceaacadeadebdacbcbcaebeaacbeabceeaeadedcdbaeadaddbbedcbeccaedcadddddaacaddbdcdbdaeccabadccabbbedecdedaddeeeabcdddecbdddadbbbdcebbbccdddcbbcdccaaacddccaebcadbddebdbdeddadaabdacbdbeebaaddaddeebdccbccdaeebcdeecebcdbeacdaeeddedcedaabedadcadbcccbbaccededcbeadedaececcaebdebbeebdbddbdaccecdacdedcdaaaadcdbeaaeeadabebcdccccaabaecccbebadcbaaccceeedcceadaedeaaadbabcebadecacdeaacdecbaedecccdaecbacdcbdeacacabbbabdeedebeccbbacdebdbdaebdcaeaaabbdbebdadbbbebdaeddbdbcebeadbebaedcabaadaaceeabdcbdadeddcdcabedbdbecedaededdaeebececaceabbeaddbedddcddeabccaacecadcbbededbececebebeddaaeedbcabacecccbbbaddedebeebbdbbcecdaacbbeaecacdebadcabdadbeecacdbbcbabdcaabebbdbababdeeeddaedabcdcccaacebcaeeedadacabbdcadebccaaadebbabcacdbcbcedadcaddbabadaceaccdddbadaceceeccdbdcebceecbccbdbeebebededbbceecaedbaaceabcbbaaddccaaabaadceecbcacccbcecbcbaaddeeaebcabeddadbcabebbabacdabadbaadbdcaacaaabbbbacaadecbbeddaecdcdaabaeecacecedacdcedadeabddedadbecaeddcdcbdabcebaaeebadecdccebbcbedbebbadbdeeaddbaddebeeaaaeadedcabbbaeeaeddbcdeaedbecbadeabaeadedebaeccbecaccebbbadbdadaeeddbebbcbbceddcdcbebbadcacbdaaeebbbeccacedecbedabebbdebaccdadaadeceaceeabeebbcaecdbedbcbdadcdeeeeaddbeeeaeabcaeccdcadbdaeeceeedddbaecbdceadeaeaebacbcaaadccddecebbeeacbadedaecbbaabeebbbbcaadaddeadcbeebbadbdbbebbbabbcbaccdebeadbddecbdccdbbcdcabcdbcecbebcdadcccbabdcdcecaccebaaccbaecdcbacabedeaabcbccdacddaeecacaaaeeebedbdcddcbdcbeeedbbccadcdacccabeccdacdbadeeaabbddacdcebadcaababdaaecdebddbcdbeccbccdebbbeaedbaabecceaaecaccdbbacdcbacebeadcbeeaaedcbddddbbbedeaeddcdadeeeacbacdaabddaebeeceaceadebeecccedddeacaabaadddcdeecabcadbeddedebbadccdebccccabceccceabacdcdbadabcbeabeedaddddecdcaadbddeecacbccdeaecbecebcaeaedaadcecdbdcbcacebdaabacabedbdbabaccdbbbbacbacbbcaddbbecbdcabbcabcadaaeeaeabcceecacdbcacdabbdacecbdcceeeaecbaccdbeaedbdcbddbbeeccadccecabebbaccdaedadcdbcacdceaebcccbceedabedcabededaaeedbbcaccbdcdcbdaeceececedccbdacccbcbabccecabcbedebcbcbeddbaebeeeadcdcdbebcdeacebcbaceddaeceeedabbeaeeebacedeeccdeaeacbcbabcadbabdcbdeebcededbaeabaacbdebeacacdcdbedceddedcbedcceaddaabbecbaeeaaaccddedddaaabebaaccacdaebbebdcbaaadadaabbcdedecaebdcdbeaabeaeddedccdeacabbeabbccdceaaaaecddbaccdbeaabaeeeeeeccdeabcbbacbbdbecdaeaccdcdbcaabcddbbaacdddccacccccdbddbdbeaabdaebaaadcadaaecebbabeaaabaeeeccdccdcedadbbacaacdebbbaedcadbeadbabdababbaecbbaaddcdecedeaebdccdebdbeebcbbdaeddadcbeeeadeaecccceebbdacadebbddecdaadeeeeeaebceaacbdbbaaccaaaecedccecadecddacbaddbddabaaaaaacbcbdabeaabbedadebdbcadecddcbeaaeaceceadebbcbbdbaecdcebbcbaaacbbcccadccaabaeeaaeaccabdaeedadbbcbedbdbecccaaeebcbdadcdcaccbaceabaeeddbabbbceccbaaabdcadebcceedddbcaeaebdcdcabebcbeedadebeedeceecbbaebbceadcdaedcdcbaccdaaaebdbbccbcdccddeecdeeaaabedccccdbbdeadbacdecedecebeaacdbccbaeaeeddbdedcbdcacbadbacedbcbcecddecaecbccbdbedbeddccbcbbccbcecccecddaeaebbcddddbaaaeeceedaacdcacaebdecbedccbaddedadbbaeabbebecdcebecedaaceebdbaebbecddcccaadcebddabdaedbcecdbcadbccddbbeabcacceedbbeeecbeebeccadcaccddaacabcaeadaccbcabdeeadcdcadbabdceecbdedbcbdeebbaacccebcababeedbdceaaddeccabaceabceeacbabbdbcdceccacbbebceadaacaaaebbabccaceeacbceabcaebecaccdabecdadbcdecbbbadbcaecccbdedbebbbedabcdbdcdeeccddedecebabadcdeaceaddadbceaceadddeaebebedceaddedaabdaddbdeabecdebcdeacdcbaeeaabccdcaccacbbcbbbaddeadddaeeaccbeaebebdbabdeeeaeadeeacccdcacabeabdabebddabbdecabedaddcdacccdcbcedabdcdecceadbaddcacebcdbceaceaecbbbbdccdcabaeecdedecbaacdebbadcdeeecdedddeaedcaeaaecceedecbdacaeaedabdeaadacdacacdacdbedecabeebecddecececaeeceacadddddcbcbceebeabcdadeccbbacacabdcdcbabbcdecbbbceaabebccdcdbbddadacbededeccdedabbaadbbdedabaaebcdcccecddbecdababbaeddcedccebcdbdaacadccbbbdeadcbccadacecbeaccbbcacbebbaeabbdceaacbcdcabaeecbceacacbaaeebacedacecccacbebeadcaabeecaecaaccbaedacadaebdbdabcaabbadbaaeacaabccbeaeeeebdcdadccaadeceeaddcbbbdacacabdcaebdbadccceddeabdceccbbbdbdddaebeecacaaebeabaeccabbadacbebbadeeddebeeaedcecedcbddebdbdcbbecbbacaaabddbcecedcbeeaaeedcecedcaedeeeaebbdbdaceaaebeaddbabccacdbcbcaabdeceeaebdadeeaebdecebcceeaddaebadeeccdddcdcccaeddcdeaceaebebaebaababcddedccaeacbeededbccedddeeeadaebddaeedbaecbeceeeebdebeeaeebeeecdbbeccebcdbaaeaaacdddbebccedbacadeecccccaddecaeeaeecbcacdabaaedddbeebcabcebccddeddcaebdabeecbadbacedabeceddbadcbdeadacccebdaaabddaeeeeceaaeaabcaceaedcdebbcdcebbaabdeeedccebeeaaeeaebccdbbbbadedbecacddaaeddaddecdebbebebdadcdaeebecabbbceaedbbaeecabaebaebaeaaaaeabeabdeddbaaeedbcaecdeaededbabdadbabcaeddaeceeeaadbbdaacadecdadcbeaddcdccbceeabcbdcdddacddbbaaadaaeeababdeaeeadedebadabacddadeecdbababddbbacdaeadeeeecedabdddacbcddebeaecbdeedeaaaebbaaaaaebacdcccbedddedacdbebecbcecadaccdaaccbbadbebcbeaaaacaeeaeceababacebadcdacbccccbeebedddccdaeeedabbecaebacceedccddaacbcdabedcdddbcbdaacacbecacdeacecedaeeadecebcabccacbdcebbadaecaaaceecececbaaebdaacbbbaebbcdbebaaabdbeacdacdbcaddbceeaaaeeaebcbeaeeaadceccaebeceedbaadbeabeeaaabdeacdcbcacddbbbecdaeccdbbeeeccbcdeeedcecbbaeebadadaacceeebaaedabcbbeaceeaacbbbdcdbeaacbaedcbaddedceadcdbcdddabbbebdbcadbddeabdddddbdbbcdccaeacbeaddbeaacdabbdaeccddcebbebbdccaebdccaacccbdbcececcbeaddeacadcaceacebdcbcadacacaacabccbdbdbbcdaeddacaeeacdbeeeaacbdadabdeddeddeadeaccabbbaeccecaddadcaedceceecbdecbabccdacaceaaebebccbadeacedccbedcebbabcbeccabeacccaecbdbdbdcadaaccadbdacbbbeeeecbadedeccbdedebabbbecddbebccabbcaeaecbecaabebbcbaaeacebaeedadcaaacececceebbcabdbcdeabccebdcbebdebdeebdeecccbbeccdcdbcaacdacadadcebcedeecdbdbccddaddddbadccbbabeaacdaccdaacdabedacaddcaeceddbbbcccceddbdedaaeaeccacecebaacdebcbcdaddaccadddaccbbbadbbadedeeebebbcbabcbdbbcdbeeaebbdcdeeebdddaceeadaadacaadbdccbaeecddbabddaddebdebbeeabdddaeebbeccbceddcdbbaeebcbeeadadbeeaddabdadeeacaaeedcbbddbcaedbbdccecaebddccaaadbbaabebeedcaccbdedebeaebeceddbaadaadbcbadceeeeaebbbceebaadcbedaeeedeccbaaecbcdccbdeebdadadedccbcdddaebdbacdacaaeaebceedabbdbcdaebebaecdeadecdaaadedccbaebcbaddabbececeaaebaccdebdbadaeaeaaaaccecdbecbaededbeddeaaeadaeedcdabbbcceadaeaacdeebecaaeeeccecabbaaabadcdecacadcdabacceaebacebaaeabdedbcedbbeaddceeabcaabbaecedbdabbcceebcdbdeabbddcebebccbbbacccbbbaebcadccecaddaebaaebdbcdcaccedbbebaaddccacaddcbbaaeceaaceaeaeabeceeedaceeaeadccdbaccaadcebedcddbddbebeaedddcaaacbdbaaddbceaabbdaeecbcacbabebebbbaddeecbbceaddcadeececadecbdbebbdbccacccbcaebdacceacbbaeebccbadcdeecdeeeeeabcceaaaabaedcbacccaaecadbbbcadbebaddcedabcddccaccebcbaeabbcaddeabadbaeddadbdddacacedcdedbbeeedbebceaeaccbacbccadeababbbedcedcaadbacbabbdeeedccecddbdecbecdbbbaeaadcdbadedbbeeaaeaadbdeeaaeeddeadcabecbcadeabceabdaebacdeceeddbdaecccabcedbbaaeadedaacecddeabccbeadbabeadedcbaaacebeaeaedbdbbebdcbcacdacebeedbaeecbbcebbaacabbaecbaebdadaebbebddadddaabedcaaddaccdaecbbccccabbdaecddbcdeedcbdeabccceddcabdeaeccddebaecaaddcadcbaacdbcbbdabedcadbbbbcdbdaadbeeeaacdbbddbdaabbbabeaeaaceddceddddeaccbaabdcaacdeddabbbceceeddddcbcdebebcdaeeccccabcddabdacaaaaccaecebbccacbadcebcbabbeebbadeedadceadbbcbeaeecbbbacedabcccbdaaaeabaedaabecbbacabbababcbabdebbebeadbdedaadedabcbeccccddeaececcddcccbdedacacaddabbbbdcaacbeaaebaddcacccbbbbbddacbddeeddeeaabcedebcbccbaedecadbdbebdccabaaaedddbebbcddcecabbbdbadddeacbeaebeccaadccaaedcceaadadeacccecababdadeebedbbcdeebaeeeaacbacdeaddbaebebebbcdcedabdcdcbaecdaaaaaabecccddadcdbadbaabbbeccacabdaecdcaeeebecdeaabccbaacbcdbeaecadbcacadaabdbdcecdbeadcebdceeebdacdaabdacaacabbdcaecaadaddcdbeeddedbadbbcdbdcceaeccbbbbadecbdaadcbcedaeaceececcedaacdccedbbbaaeabaccacbadceabdcecadddcdadceaecbddbabaecbdaabcddbabdbaaaebdcbbbaaecdbdaebdaeddeeededdbbeedaccaecbeabdceddeceedddecdebdabcbebcebbeceebedbdeaddcbccdeccaacbebabeaebccecaebcedcbbdceedcecaddebbdcececccebbdebcadeaabddacceeacadbbedccbcddaaccdbdeebeabbdccaaecaecedaabeebcbddcacceaddaeeebbaccceaeaebeaadabdeebaecaeacaceebcecabaebeacccacebdaacddcebbbadbeccdecbecdacadeeaadbbadaaaabaeeabbebedecbaddcadcedbcaebaceccecbeabedbbeddbaecaeeabaacbeccdbaddbdcdebccadcabdbaeeedbcdbcccdddcacedbddabbbadeddaddaebddbbadcdbeccaeabadedaddbcdbeaaebabdbcdacbdebacceadeaeaaddcbbddddbaeaebbcaeddaadaeceaeebdcbedbcadadabbabbbcababcbbbbeaebaacaddbaeaedaaaebadbebebdcaeecbbbaabeddbcccbecbbbeebcebddbadeabacebadaecceadcecdcebeebbaccceeaeaeeccdceebadddabccdbdadeedbacaacdababcbedcaeebcebbdeaddaacaaeaadbdebcacdcabbdbdcbecdecdbaeddacabccbdbaacaddbaeeddadcdbdcdeddaacbcacccbbcdbddebcbebedcdaebebaaaaacbceaedcbacbbddacbebbabdedcdacebcabdbabdaedaabdcaeccaacebebdadbdddddcbccedabbcbddcdcebacdebbdabdedcddcbabeabacedcbcaacbaabdacddcbcccdbbbebccbdcaeabedecedeaccaebceebceedbcddeacdbabacbedbbabbccebddaacecdebbcccdeeecedbddbaceecaceedeaeaadbeddaedcbaedebaeabddbbcbbbeccbccecabbbaedbbcddcedebbeabdaacdbceaacaddaacbadebaadbabecbadccbbdededbddaddbbaabcbcbeeeaedabddebadedeedecbbebceacbbaeebbebebaadeccbcbcebcecbadcdecabbceebceacbeeccacdbcedbdeebbedaadeedcbcaccedbdeacaedddcddebbbaacaccacaacccebadaeedbacdbedaacccdbebaeacbecccedadbbacbcbadcabeaccaccddadadcccccddbcedbaaccbcbabaeeaddadbcceccbacdecabddbaeeddbcecbdbaadadadeadcebbccbbccecaeccdebbcbeceaaeeabecbceacecccddeeabaaddbceaadccabcdbbbdcedbaccabcbeedbacabccdaeecddbedeecebaebaddedacddaedbbcdbbbdebbaeeadbebdcebdbdbacbbedbddbdcceeaecebacebeeccebdebccdccbaaebacddaddcbbecbbbbaeacbdaeebceaecdeceabebaacecedadebccedbbaabccbbdbdcdccdbbdecbbeddaeeedcaeeedbcbbbeecaabcbabecaacbeaabbeebbabaccadcadeadebbbeccabdcbcaddbdbcedadceaaabaaadabcdbeeecdcdedaaeeceedadeecabdbadeebaebadeccddabdbeeabadaaacaeabbeeacbdabbbabedcebbbeeaadeaceeaddcabbaabedaccadcdddadcceeecdbdacdbbaeabeecbacacbcbdedccecabccbeddacddddeeeeebcaabdceccaeadeaebbacbebaabdebcddcebbababcebcdecadacbdeeabddedbbadccbcdccaaabcdecebaedbaabbebebadeadcbbbebcbeacaaaabbdccacbcebddaddbeceaaebabdabcebbacaeeabdbdecbccabebaadeaeedbabadcdbaecdccabcbabeaceabcecacbccdcdbabeccbcbeddcbccbaedbbaceecadecdeccabaaaaaebedbbebadacedecceeebdceddeddecadadadeadaeecacececabcbccecaeeeddbacaadabeaabbbadabceadbeaedaedeaaeeebddbbdeebdacccadbebedadcabecdccaaeecedceddeebccabaddcdbaaecbaccbddaaeaecaedeaeadadbecbeacdeaedbacbbddcaddeebdabcecdeccdddbabcdbaaeacddbdccededbaddddadcdccbeaddbbdabdddbebacaaccebdedebbdbaeabcdbccdcdaccdbcebbbdeebbdcaacaddaeebaedebbcebaeabcdaceeccaaddadcaaceebddceccdbdaebdadcbcdbdeebeadebdcbecbbcaaabcddcdadbbcdacbbcbadbdcecaebecdbedebebccccbdccacabacdadccecaeeedeeccadebeeaecacedaeddebccdacccbdcbbbbdebbdbaaecaeccaacceddcaeacceabaaceacedcdedbdeababaeaddcecebeaaecebadecdeeadbabbcbcbeaeedcedabededcccdaeeecebbddaebaaddcbcacbcccbbcdbdeeadbcaeebaceadacdaeaedbadaeabdeddbcbaccdcbadbaeeecbcbeecbbccbeaaccbddadcabacbccbaaeaebbcddbdaeaeeabaaaddcbadaadbabbadeecbbececdddbcceaabbbaeeddbadaceaacaddabbbedbcecebaaedeeeaaeadddaaeabeeebdebaaebeadcbdcebdddddabdcebbecbdecdecaebeacdabaeecabaecaaebbbcabcceadcbdadbebbcbacdeecdcdeaecacbecaaaeedddddcbdabcccdbdbbaecdadebdcaebebbdbecceadceaabdcdcecdbaceeceadbdccaaceadadeaeecaecaabceddbedbabebadcebceebdeeeedeaeaaeddeecddbdbeaabdcbebacaaeeeaccdddadbbcedcacdbbddaabdaddecacdaedbdaeccddeeeeaecabbdbacddbdbbceadcacadbacbedebcbddcbdbbadceedecdceeeeecedaaddebdadebadcaeabbcdebbebdeabdcecbcaecbaacdacceaaabdebaaacedcbebdbebabedddeceadcdcebcadaadeabdcdbcbbbadbbbbdebedcacbadbadadbceedbbcdbccaaecececaceecaeeeaeccbcdbbaaeabeddacecdbeddaebedbeccebbdaadaabcddbbbaccaaaebecbdbbedeaabddbdcbabcccdcabbedecaabeccddaaeacaacebadbecbeeeaceaaeeedbacbacaacdcdadebeaaaabdaebdaaaebdcbbddccccacedaccecaeaeeebebbbaedeebddaaceccceccdeaeeaaeabdacbadebabccebdeeeeebcedebaeacabeaaadcbcbeedcedcecccdeedcdceaeaebbbeaabebdbeadeddaceddbaadedeecdebcaecedaecbbbbbbbbdeddebcebedbeecdceaecaabecbbdebceaaacebcadaeceacdbbbcbbecaddbbeeaedcccbaedbdbceabcadddeadbcedaadceecdebbbedbccbbaebbdecadcbcaaabebadbdbacadacdbbdccbbcbeeceaeebecaddcbeabaacbbdbddadadedecabcebbdbadaccecdabebcdacaacbbbbeeababedadacbcbbbceedeebbadcccabeccaddaaaddbcaecbeabcbcaeedacdacbbbecbbbadeeddbdceebdbdceadecbaedaeeeaedbecaaecdbbddaceecaabaebecbabcddecdebcbeeaedebaabecbcaaccbaabadcabddcaeadeadcdcbbcaebadeabcaacbdcbeabbdbddcbacbdbcbedbdabcdddddbaddceeceeecaebbeedbdccdecebccacccddeedabcbbbdddbbacdbabecaeaaaaaabeaeebbebabdeeedadadbccaacbabddbaaaeaedcdcebcabdbdcbcaeccabbddcececaddbceccbedcdeacabadacaddaadebbbcaaeceebebcecaccbecbecabeabbccddbebaaeeadedbeecabdbaacbaeebebcedbbecbdeecbebbaadaeaadbaaeeaeebacdcaaacedcceaeabceedeeecdbaecbadeabeccdebeecacbedabdceacddebecdabcbeddcbcceedaddadcbcddbdeacbcbcbcaebeeecedcbdbacaccdabaeccbeccccaeedddbceacbebedbcddeabbcccdbaecaeacaccaaabdbebaeceeeeedaeaddabacaadaecedbaccbedcdabbdccbaeeaacdcdcbcedccbeceecdcadaecbdebdacbeedbededdcecbcdacceaeeeabeabeaaacddaebcaceacaddababebbdadcbddabdcbcaadabccaaedaaedaeaababaccacdceaadbaababeeecdcdbceebcaddacacbabcabeaeaeacbbbaeecabdbcbaadadbcdbdebcbecacdcaecebaeabeccbbcccdcccacbadbaeadabdeebbdedacdabadbaeebbaaeabdacabaeadbbdcbcddaabcdebccdbacdddbcabcbbdddbeecdabaabdbeeacadbddbceabdeebabcedaeeedecbaaebabbdbcdbcdabccbcbccacddbaadeddcbaaaddbaeaceabdbeeabddbccccbbacbcabacdbcaedcedbabeabdbeccdabaccddeeabcadbebdddceddbdcedbcabaccebbbedccbbdddbbedaaabceeaeebaccabcccdcecdeaacdbaccacdeaedcecbdddcacbbaebaddcadaeebabdbaeceaaedcceedccbeecaacbcdbeecbabdbacbbabbdbaadeccababaccdceecdeaabeecbedaddedbcdeaccbabebcadbaadcacedeceeeeeaaedacdbeabaeabbaaeeeebaedadeeebeaabbbaedebadceeabcdbcdabadcdeaaeaaabbddabbaeabdcadecccebeaadadabaeeacaeaaeccdeecdadddccdccdcbcbcacbbdacacbbbdbecbaadbcaeebbcbdacbcadaedbeecceadeddaeaaaacabbaaacaeeeeedbbbddddbcbccaeeacacdbbccababecddecedeabeeccacccccdebccbdeddbdeabebdaaecdceebcaedbddacedcceadbcdbbcaddbceccebccecdededbcceddcbedbcccccbcebdacbedeabcbeeacbdcbecaeebbbddcbcadaaeecbcccdabaacbbadedccbcacccdaadaaecdcbdabadeaddddcbdaabdbaaacebcabbddeebccbbcdacdbabdcbebaabcbaabedcdceeaebddbcdcbddcbdbbdcaabccabdeacebbadeabbcebcacabdcbcabdeeaebacddacbeebbdcceeddbaaaebbdecbeccbbbddbacdabcaecaacecacdcaedadadbbcabeabeeadacbcabeeaabbdadbbbeeeaddcbbaeeabaeaaebacabbabcabdcdcbcccdddabddbeadaddbbbdcecbceedbadbddddebceccaaebbebaeadecdbcebcbcacbbeeadddddcadebbcdaeeeacbbbbeabaddaebaedabeebbcbaeecbdbbbabcbeceaecadabbbeeaeeddddedddcdaaacedaeaccdbaebeacccdacebaedcbabbcbecaabdedddcdcecebcbcdbbdcccbccbcdabdcebdbaabbdadacbcbadedccbdaaacbaeabebeacaaaeddbdddcecbeaebeaedecbccbbaecbddcaadabaaabdcebdbaaadbedcaccadbabaaddcacbbdecbdddcaeeadeeccbecbbbeedbedeeddebcacdbbdeaecbcbabaadcadcbceacadbeceeadeebedaacbddcacecebbadedaccebecaabecbcebaeabddecdeeebbbbacedaceedadbdeecabaddebcaeedcdbeeaedbdadebbadaacabbadbedceeadeaeebceccbdeccedbbdbeebacbcbbbbabbdbeadcaceeaaeddaadeacbcbeaabacebcbceaebaeadacaaaaebcadacebddbaacecbdeddecacedabdccbeedbdeaddabaaaadeecedbbeadcdedcdaaabaebcceceadbcdbaebeceabceaaabcbdabbbacbacdecbadbaeeecbeabbeaddbbebebebcadedeeadacbcddbcdebbadbcdccedaadeeaebcbaebeedcceaaeddbadbcaddbdbecccabbcccebcbecdcabdeecadacdeeabadcedcccaaccbeabbaceadedadabcecbdbceeeedacacebaaadcceabeddeceacedebbbcceeabebdceddbeccbeebabcacedbbebeecdedbbcdcaeaccbaeccdaabcedcadeddbdcbaaacccbbeacdcdababeacdcdddcabdcbdabdbedaeacceeddcdabddeebbbbdcabdacbabddbadacbccdacbdedcdceceadeaadbeebbebbccdbceddeaaeebdcbebdacdecbbeddbbdeddcabebdcbcbbaceddabcdeecdbdceabcbdeeaceeeaaddebbedbeebecaebaadcbcdccdcbeeeddabaacbadbcbaaaeeedebdecaeaebabceeecdbbcebaaaaccbccebdbbdaddbecaceceebdbbdcdaacdbebdbbedddcdaeeaceebeeaeaceaeeddeeaeadaadadbacdceebebbeeeddcdaadececaaacecaccaadcebcbdbdcdceaacbaecadadedccabacadcabeaeddbbcaabdcdcaabebcbcedbceedaacbeeabaabdedabbcadcedcbbceeebcdbbbbecaadbecbededeaacdedcebaaeadcbdccdbccaaedbbdcbbceecedbbdceedebbebbabaedbacabeddeccdcadeceaaaaaacdeaecccadddcabadebceadecbbddebcacacceeeddecdbcbbdaeaeaedacadcdabbaaaedeeccddcaedebcadacabcabeaadddcddedddbdcdaabaaabebecdcedecdaabacadeaeabeaddedbabeadbcdeacebcedcecaecdeabdbbeaeeeadecdbaedbddadecaebbebdceeacdcbbcbddeacbeaccdbecbdcdecbbaecbcdebccbdeeaabdbbecdccecceaecbdddcebccddebabedbeccddcddccbecaeeeeaedddbdbebbdccddebaaedaeecacbacebaaebcaeabeddabbecdaddbcdedcaddbdcebbacaedcdcdeeccebcdeacdbcebaacdceaaadcdadaedbccedeecabcbaadebcbeecddcadabeeeeaabcbcabceddbaebcbdadbaebdbacbebbdbdabeeedbbaaebaeddadaebaabcbdebaabebbccaaeabeaecdccdbadbdecaedeadaeeccbbdceadeeaaedccecdcdbdbeceedddeeddbeccabeaeecccdebdbbaabebdabbedbcadeadacadccebddaabdbedeecdacdebdadccdcbbebcebdadcedebedbbecdadaadccbdcbaeacbebecceebbdbdddedddaedcdbbdeacdeccedddccdceeaabbcdaedecbdcedaccddecaaeceeebcebabdecebcaaecbccecbcbdccbaeabdadecacebacaecabdcdcebddcaccdcaecebabbdbcbcaeebaebabbaeaecbaedebdabbebcabdeedeceeadaeaeeaeeebcdbccebdbdeecbebdedbdbecbeabdbdceeaecbddedbcbdaeecdebbeddccdecdbcabbbbdbdacdedabcdcdedaaccbabacabaceedbddcebadaeeeadcbaccbedcabeaeaecceaecdcaaeacbcbdbbddddeecddddcdabbdddecddccccbbbcceeaedadecacdbcebccbaedabbdbdaddbabcbbeddcacaddeeeebdcdaecbbeddadeaceddbdccaceacdabacecbbabecedaacccbdecbeecddaadbaebbadcaddecebabdaadeacbeeacbdaadaaceedceacdcbeccedccdebedebadcabbceeecbbccbcdbcbdcabbcdecbcaebaeeeaceddeaddbcabecaaeeedbcaebcaadecebadaeaddeebccdbbcdbcecaeababccaadbaeddcbddbabaaeaaebaceacbadbcaecbeaabaaecbaeadeacccdbebacaaacabbbdaadadccdcedeacddeaacaeebadbeeaeeaccbdcccdbddadeeccededaceddacbbaaedbcedeadaaccaacaededacbcdbaacdddaabdbdaccaabcedcbedeaecbaecdccdcaceccaedcbdacdbcecdddbdaccdedeeeadcbdcdbbbeaecaecdeaddbddadcaabacedaeccceebbaeeecbedbbddbeaabdacdcacdbaacbdbceccdbbeeabdececeaacbacedadcbccadeeaeabdbdeadedadcdacaeccbdeabaeedeabadedbabcbbbbcabbecbcababebceeccebbeadedceadaedddacebebaadeccabaacedbbddbbbabedbbebddbacddbcaccaddeeededddbddbeaacdcecababacdcbcacddaedbdeacddbcddacadaceeecaccdaabecbbeededbeabdeeebbdbaeadcddbbcdeebddeababeacbbdecebadaacceecbdceeaeecddeecebeddccecbcddbebbbebceaccaecaedccebecadadaacbcbeedbacddbcaacedececeecdcdebeeceddedcdbcceaabcdcdbbadaaaeebcecabebabdedcbccacdcedcdaabebeadccbaeeccaaeceaeaadceeaedadabdeeaaeceaecacbdbaecaaecbdceabccbadadebaceabbacabdbdbcbecdeddacdeadcaebbbbecbceccabaecaddebcaaebddbaecabdbacbcaeedbeedecedbadbdbedbadceacbcaecacaabbbdededaccabbbcebacbdbacdceeabdcaccadcaddbdacbcbeabdecdacdecabcebbaacbdeaedacdcddeebedacbaabcccacdcbcbeacccbedcceeecbcadeaaaceeccddadadcdaabcaeeccddacbcbbabecacdeeaecdbbcbdeecdbdcdddbecacabcbdcedeecbbebdbedabddecbeddedebbbdaddeadecddabbdcacbacbbaecddbabdcbacdcdadedebcdbceeebecbddcadbccaccedbcccdbecceaebdebeeadaeebdddaebdedeebedcbaeabdddbbdccadddbacdedebeaabddacecaaeebdeebbdeececaaeaadcbedcacaaebcdaadbeddbabcebacebedaadaeeadedaaddbccceabdedcceeadcbeeddadccbcbaeeeaeebecbbbdcabcabcaaeedcbcdebeecddeccbcbddebadcdbbbdbeecabdbbbdcbacadcaeadebadddaabedaeecbcebaacbddacdeabdaaebacbaaadcebecceacbcebeccecbabddcaaeeeaebedebedbdadaceeaccedcbbbbeaabaaebabcabbeddceeaebededaaeebcaacaecebabecaaabadccebedcaadabdbbeaedecbccdaeeeaaecbcecbcdcbdadbcbbadeebbcbcdcdedaadcbabaaccdbbcbeddbdbddaaceebedccdecbaababcceabaeeebbebadceccdaebddaaeadaeecbdaaaadcedcecdcbaeeaadeeecebcabeceeeacacabbbbbaeacbbbccceaccdbdacaabbedcdebcbbacabbaeaedaaecdbedaebdedccbccdbcaedcdbdbcbbabbdcdeeecdbedbbbdebebeecbacaedebddceaecedecddacdeacdabcbeecdbecbdebbbcdbbdbadcbbceaecbdcccdeecaaacedccdabdacbabadaddabbcbcbaebcdbdeabbbbeadeaaedcbccaceacbedddadcacdccddcceedbbceebbcaaadbdcaebccceddededecaddcbcedebeaeecaacacedbacbdddeccabeaabbdedeacbccabecddaabbebddaaecdbcaaedddeecddbbeebcabcedaebddceecedbbcacbdbceeaceabcdccdbbcdbabadeaebedcedcbbdabebbdaacbccdeacedeaeeaebdabcdcdecdaacddddeacacbcbeabdaceacbdbadedeaceaaaaebcadddbebceeaeaabcecaadcdebdcdacaedbacbedcdbbcacdcaceaacdeacdebadaeecadeccbeeadabeecddcaddcdcccbebcdeddcbedadabdcecaecacccaedabeaabbaaaedbaecacedbbececcdadddbcdebdcedeaeababaabaaddbdcaeddacdedebdbdecddbcedeccaaadaebaacedccbabebccedaadaacededdebdbecdecaceabacdebabedddddeaddceeaecdcbceeaeddcceabeccdeecdeccdeddcaedebdaeaedbbacdcbbaddedbbbbdbcceccccedacdbdcccadceacbcbabbedbddeccdcceacbaacbdeeeecbbabdccdbaecadabcedeadbcabbabdaabdecaedcbbeaaebabedbdbdbbebdebdbbbeeceedcdbbadaebbccadcebddadebbcdbeedcbaccddcccabeceabadecedcdbabbebdeecbaadbaacedecacaaebeeeaacedaacbcaabcbcbedebabcadacdbcdeeecdcdbdbabbdeaeceeacccbccecbbcdacbbeceadcaaeaaaaeaccebeeedcdaeceebaabbbcaebaaedcebddeaceabbcaecbadabceebdaccaeaebbabcecdddebdcbeabbbaedceaebceaceeedbbabdbceaedbeeeebccceeceddbbadceadeddabacabdeeeabdadbddbddeaababebcbeddccbcccbabedbbbbeebcceecaacacadecedbccbbadedaaeacaaeddecebcaadabcccbbeedbddbabceeeceeddaccedaeedebbbdcededeeddcdacbbdcbdbbabbcabbcdcebaebdebcbbbdcbdeaababaeacbabbaaddaeecadcdaccebadbacdaddabbdbacacdbacbdcbcccdaeaacdabbcdadbcaadacceeaeeccbbdbedadbbbaedbaadcbaabcbacacbaeeeacabbdcabbbacaeaababaedacbcebaeecabbccbaedbbbeedaeecebcddaeebaabedccbcdacebdacbbbbdaedabbddebaedccadebdbcbededaaabdebdadbabcaacadcdbbcbceabaedacddbdbcdebdbaceebcdabadbceaeeecbdcbacceedccadddeebdbcebbaabbeeacdcededabcdbdcecddbecddbeecbcbeadaeadccbbadcabccababbecbdebbaabdabdcaacaeecbaebbcbcdcceaebbdccccdcbdacebeeedcdbedcbbbabbccceeecebbcbbbdebcccebbaeedbcedddddbbbabbebaebeebceaaddbacbeacecacaaaedeeccbddcaadddddabdcaaeacdcbeeceebecacbbcacacdbacdcdaebadadceecdcbdeecddcdcececcabbdbcacbebacebbadbebbddaeeaeeedcccdbcadeabeeecaaadbcdcabebacedbddbdbcbbbaecceddccbcbddedcdcdeceddbaecaceacdcdbeaadeaceddbebaebdaabdebccbaaadbaccedbdebedabcbabacbccbceceaedecccaedcbcaaabacbadbabbddbaaabecedacedeeadecbaccaaddcdaeabbdaacdbcdaccaadbacacbeadecddbeceeebbdbcdbadcdbdddbbbcecbaabeedbecaecadcbadebeebdaeeadcddaeceabdccddaadebccccbbcdcaaededbcdebaacadbebbddddaaeeaaddbabbaeceeebcbcbdcabdddbbccabedecddceedeeaaaadaddbdcebeebeecdbeddbbcbaeadcdbaacddbeebebeecaabeacaaedbddeadeabadcceadbdcbdcadbbdbcaacbebecdbedcddaaddeedbbaddecdceacceeabeacdcddeddabedbbaaeeebbaeabeaaebeeacbcdedbbdbaebdaabcdaddcedbedddcacadbddaceeeedcedcaadddbbbecebbbebebddeabdeebcddadcdeacdbddadbcebdebbcebdaaaacabdbceaabbeabcbcbcccaadaaddceeebeddeeccdebbadaabbbcccccebcdecbcbdbeebeddeaddeebdddcddecbecadeaaedcbcaeecedccaddecceeadabbbecbdacabdcebadaadeaadaddbbddedbcecebedbaabdaaaaeecbaeeaaadebcdcddabcdaeaaaacaddcdbeaaebebeeaedacceddeabacaccedabeccbcccbaeeeeaceecacabecacbebeedbceaacbcebedcedabddcebccccabebddaaacebdaebdcdcaaabdecadcaabcedaedecbbcadadabcdbbdacedbdbebaeaebcedebedbaddabbddecdbcdebcbdaabdadeaecaeaeabadaddadddceecdbecbdeaaaacecebdbcdccebeacbddeecdbdeddeebabaebeaadacabeaaccacddbceaabbecadddbaaccdbdcedcdccacaceaaacbcedaabdaddadcecdeededbcacccdcedacbeaaeedacbcceabeabeedadacebeaeaacddcdbadbdebaecbebccdaecbebbeeaaebececbeadeebddcaaaaacadaedcedbceceaaaeaaecbdadacbeeaaeeaeccbddcdacebedeacdaebedddaeeccadecbdaeccaeaebaedddcebcbeccadaddaedebaecdceeebaacebbeaddcbabceebedceecbedbececcbecbaedcbcaebcacabdecdceaeaacecabbcecdceebdacbabacaebcdabcbedbddacaebcbaeaaedddbdcedeeebaabcdbaaeabbeedbbcdadbdbddbccbbeaecbdacbeddabeebbedaaadaceecadaabbeeeaeaebcdeaddcbacdddadaedeccccbbdacceddceeaeaacebcbebdcdcaedeebeaeecebbceceeccdbdbbddadcdebbdaeacecdcdbeddedabdaedecbcddbbaabcbcebdedeabdebaaaceedccdbdbdabbceaeebbedeeadcbecdaecddbbadbbddbadacbcddacdbddbbcdbcbdebdcddcbcbdccaeecaeebaecaccbceeeeedbceccedddadbedecdadeceeccdeedcebacceaeddaaeeeddeabccddbcebbeddaccbaaaebcccceaeeecbeaaaebabdbddcddbdbcdedabeebaccdebbcdedddaaccbacbeeecbeebeeecddebdeeabdbedebcaccadbbdcacedccbacbdaeaedadcebcdadcdbebeeeaebdbdbadcdcccdbbecdadbdebecccccecdddedbdbbcbedccecebaedcbcddebacccecbdbedadbdcdaebcceddbcbccccecdccddcccdabcebdacabbcecbdabbecdecacddcadcdbcdddddebabccedacecaabbbdacbedaeeedbbbcaadbcddbeabedeedbadddcbaeceeaacbaabeedcaaaebeaacbcdbdcccebcdcaeaeaebdebaeaecdedbebedddbcbdcccdcaaecaeedacbcddeeecedcadbdeacabaecdbcadeacbbbdaaebcddbabceeeecddddcbdeeeabededbeeaebeaaedbcecaaecbccdbccdebdededacbddcddeabbbeaedabddcecccbbbdaaecdbeeebbcdbedacecbcadbcaadededdceaabdbeecaddbcaaaecebcdbebdeeebebeeeeacaceeedcdcbebceebcecdbdaebdebbbaddabdadbaedaeccbdedcbbbeecdbcebeecccddccbceecddcabdabbcbcbadcebaabbbdcddaecabeacecbedebdabcdbbbccbbccbbddcdebddbceacbdcddaecabddaacdacdbaacdaaddcabaadcccedcbaccddcbcbeedcdccebddecdcbacceaaeaaedbbaadebbbbcecbebadeecdcccededceecbcdbeebeaabebcbeaeccdcebdbeabaaceecbdbaabbdaedaeeaaaebbacbabbbccddaeeaccbcbcaacecadebeccabdaaeeccdcecbbaabdcabacbbcdbccbbbebcbceadeebbaebcaaaedccaccdceccaaecccdbdeccaddcaecebcdcbaddcbdcadbedbbbcdbecaedbdddebeebeeabcaddaadcbbdcadabaddeabaaaccdeeeeedcaadcbbdeeaabcddebcdceecdccdacdcecbaaddebbecbcabccdacedbddcaabbadeaeaececddeeaddaedbbbecbbcdbeeaadebbcdabbecabbbdeabdeeeeeebbdedbcbbcbdabeddbedbcbcccbedbceddcccdacdeccacababdacabeceabacbdabaabdecccbbcccceaaaecbddaacbcebdcbabdbdccaccaaceaeeecaecdedebcaeebbdbdedddbaaedbcdaaebbbbacdeedadccaaaccebadbcbbbeddccdecceeecdadcbeebdabdbaddeccdadbbabbedcebdcabebcdedebbcdeaeeaedddbbcacbbcedaadeabcccbbcecedcdaeeadcaceedcbcaedcdbeecedeeedbeaecceedcbddcbecacdddebedbdcaaeecdbebcdccddcabeebebeacbeaecccbcbeebedbbbbebbdabacbedadeecceedecaeabcadcceabdadecdbacedadbccadaddabdbbbdaddbcdcccbcdaadebcbbcbccedeedeceeadcaeabdcddadecaaccbdabcedcdbeceeedcedaadaacbaababbdadacdadaeaceabaeebbccebdcdaaabdeeebcbceaddbcaddbebbecdbbedbbacdacdcebbdddeddacbbababcacebcbededaaecddadcdebdddceebbedddcbebceeaabbdedbbcdccededdabcdaedcccddcbcadbbccbdcbbcdeaedaadecdddaaacecbbeacdddacbceaddddcabddccdedbccedccbdcbedbebadeacdbabbeddebbecaecbcdcededbccaecdbdaccdaaeacccccacbbeebcdcdcaeddeabacedadedbabbbadadaaacaddaccddcdcbeceecaeceaaedeadacaaddaddeddcebedcdeaceaebecebddaaccaeebcacaabbeccdacdbdccbaecdecdaabccadbebbaebebcbebbecbcadabccebeaebcecaebdcacbdccaabbbdbaccbeecebcdbcddedecdeccdaaabeabacdceeadbbeaeabbdcadcbababdbaeecaddecbeddcdecbcaccbbeecbbdaccdcedbacccdcebececbabaaebbcebdbeacdebdabbdaeacaabdeddcaecccabeebdbdadebccaedadacbeadddaedbbcaeadacceaddebdeccadedeebecddabededaeeccbcceecbedbadedbcbaaecaeeaeaebbccdeabdbdedbccdbeaecbabeaddececbccccaeaacbaccbeedeedabbdeccbaaeacceeeadcacdeebadaedeabaaedbaecceaeecdededbdcebaceecdebaeeabecceebdceddcdbbdaadcbccaacaceadceaaaabebcccadadecceaadccbebcacdaebebdcbebaaabdacbeacdacedcdacedaaeaebcdbdedcdcdacebeddcaecaaebbabdcbddeaabdcddcedcdceeddaeaacceddddcbebebaadaddcdeebbbbbadedceebabceeeadaecedddebddcbaaebaecaecceeeeabbeaeaceebaadbeddaecabccedaaabebaebcceaebebcddbdbeeabbbbbcbcdedceaadadccbcaabcdcdeddeeabbdedbdcaaecedabbbaabdbdadcbbabcbccadacbbecabdcbdaececcbeddaddeeecadeeadeebaabadccdaaaccdbdcbabeeaeadbcaacddedaaaccaeaacdbbebbdcceaebcdbecebadecabceadbddabdeaadaeabadaaaeacabeaeaaeebdcdaeadcbcccedadebbacdadbbbedcaeedaabeebddbdbcbabadcbccecabeceaaeddbadaeccbaabcdacaacdbeebbeadcaacbbaaedcebccdbccebedbdeccacddcdcecddadcecdaeceecbeacedabcbaaeeaceecdebdbedecbbacebeebbaededcaecceeaecbbdeebbcbabcdcaeeaeeccbbbebdeebdcbacdbbeecadadaeadecccaadbdeedccaaabeeeedadcdaeeaedacdadeebbaeacadccddceeecebedacaecbeeeacdcbbadececddabaceecceaddbdadcebaabaabcabbeededccbeaaddbeeddbbcbbabecbeaeebdcaebbdcecbadbbeadbdaabbecccddaacacdacbeabbaeaaeaedacaebdbecebceaaceacbedebbccaabbeebecdaeeecececaadecccbbddaebddedbbdcbddcecdeceaceceaabcbaeddcddadbcedbcacccecedecdabeeadabeebadaeabaceabadebdddddccacacecaabebcedcdaaceeaaadecebbaedbaedccaeddbacdabaaabbabecdeacccaecbdebeecbbdcedadaebedddeceaebeccccccbbdeeaccdcaebeaecaccdcccdbaaeaddababbdaedcdcdaacbabdbddaabcdbececabdcabbaedcdbddcebcabacccdbeebecbcdddacdbeeccbdcecbebabeaccaaacbccecadceaecbccecdabdedeacdaeaeaccecdaeebcedadaddaaeddeaebddddcbccbcdbbaeadcacadaaccdcbcedbcacbbbadeebddcdadaccccdcbecbedeabecbdabdcebacacbebebabeedbcdbccacdaeeebddbeebebddacabdcebddddadecedcbdadddccdbedbdbacbacddacdbedadaacdabdebeebbecbceaadcdcaeeeeceeadbdeaabbeeccccbbbbececdcaddcdcedaaddaacbeabaccaebeebbaacedaabccbdbdabaedccababdbeceddecbedaccccdacdbbabbeeebcebebcadeaabddabdbeeeabdeeceeebecbecdddcebeccceededbbcbcecbdbaccedbdecedbbcccbbecaecbabbbaebdbcbeceecbbbadcaaebeaeaebddbdcbeedadedeecabdbdacdaaebdbacdeeecdbebcedaddababeeaabadccbeeaacbcbdebbaeedcdbeaceddbdcdebcedacbbdddcbaaeceadaacaccbdedccabecdabedeccdcabaedabcbbbcbbbadcaeadaaeaababcedcdeddeccdaabdeecacdaceceabaaeedcbeeeceedacdbaceedbbebdbbbcdceaacebdbbeeaaaabbebbadacacdebadeeaccedebeeeeccbeceadbdaaadaaeddeadaedcdbddecebdbebcabcccbadedbbebdbbdeaacedadcbebdbbecdacddbadcdaabedabcadcbabaecdbcdbdedbecdaaecaddcdacebdedaebcdbccdaebbbcadcdeedebddbccaccaaecadacbeceedcdbebdcbaaadbecddbeedbaddebbeadbcebbbdaadcdddaaeebbbcddbbddacdcbbdacdebddcdbddabeecdcbeceddaecdedcabdcdcabacadaddadbaeacadaabbeebbceaeabeeebeeddeaeeccbcdebacaccddbcdbdbbbadeabdebdebababadcabaccedebbacbdcbcbeeaeaddbdaebacbeabaabaebabdeeeeadeeededbccecccadcbacbacdbbbcbaeddadadbddaebbbeebbcccdbcbececacbccdecbdcbacaeccabbdbccbccadacedddecdebabcbdeddccccacbccbeadbcebddeadccaedededeccceebdabeaeaacbebdabedeaaccbcbbdabebeebdeaaecddacedecaaecdecaacaaedcdeeeebbbdabeeddddabdbeabdbcdccacacdddcbbabddcdbadedebeeaecbdebbaccbbcceadeddaeaccbcabdbdecddbbbdbdbcecebbadadaddaeacabbceaedadddaeaebcdbdcaadacbaaabebdadceaeaebbebbbaaebdaaeecddbdedcbbedbbebbdaabddaeddcaeceaaaaabaedbebbdcabbebeedaedbecaedcdbdbabdbcbeaebacabeccdbdebcdcabeadebcdeabababeeccadeadadddbcaddeedeeaaadbdadabebcbeccbbaccdbbabaebdbcecebdaccccbbebcedbebcccacacdcceeabeccaeaabdbecebbddecaeddeecadbcccaeeebbeadbabadccebdbbdbbaadecdccbccebcbaddeabddebcbaeedeccecbdcbeaaeedbdddeeecdbaddbdabebeeaecebdabcdeeaaaeacdcdccbdabcacedaeceabbdadbbabedabbcceeebcabbaeecaddcabbcedcbbeccedaaeabdbaecbcaeeeacdaaacebceabaceadbcccdbacbbeacbacddbacabcceebeacdccebdaecdacecaceaccaedddceeadeacdedccacabaccbcdedabdbbcbddedcaeceeeadddccbadcdeaecbdcbdeedbadbaaccccdaceaeeecadaecedbebccbeccdbdaccaccdeeacdccecedbbeeeccedaeeddedbeadddbaaadecbddbeaacddeabedacabaadeabaeabcddacdeeaaeddcbbacedaabadbbaaecdbccdbdccbcadbacadccdcdbcaebeabcbadccbaccbbcdceceeeceacdaabdebaeabdcdabecebbeeabcebcbecaeebbabaaeddebdbcbeddccdceeecaaedddcddbddeacbaececeacddbedbddeecebbceeeebeacedabdcabeebebacdecabaedccebbdcccbedbcaacbecebdaddaeabbadcdbacddeaecddebcdeecdebeebaedebadbcdaacaacdcbbabaecdadacaccecaceaaeebeeeabeabedcbbcddaaeecddbaceebebcadbaddabcbaaeedcdaadceecbdaddacaadeadecbaaacacccbbbadeeeaeccabaedcbdceaecbbaccbcaceedceeeddeccbcdaeaecabadaacedecbdaabcadecdbacdceabbcdddecdeecdedecaecebdcddeaccdeccaedcdbbaaebdaebcbbacaebdbcceaeecbbcaebdadbccdbbbceedbabccbbcababbeaaedbbaadcebdbcdebbccdbecedabbcdabcbcdddccadabcccbdedababcaaebebccdacbacbcaaeecdeadbcabbcaddecabbeeadbbadccebcaaeccdeeeabdeeedebeaccebcaacbadabbbabbeabdcaecaebaddddabaeeceecadbaeabeabecaadbccbeecbdaecaabbddcaaeddbebdaadbaacccaaacacdbcadaeabbdebdacbababaeecaccaecdeeceaadcabecbecbccecabdaaebeeeccaaebcceacdbbeddbaecbecaaccacdcacadddcbbbedbbdadbdccaedddeeedbcebddbcabcdcadeaaedcedcaddaadbaecedbcdcddcdacddaebebcbaabddcabdeebdadcddbaceabcadcedcbcbdcbaeecdacbccbaecacbcdbadeaabddbbdcbacecacccedcbdcbbdabaeebbccdedebacabcedacdbadeeacbcaaadabbbcdbabdbcabdaacebeadbebceaadbcdcedbdcaabdadbdceecedaddbdbbdcbdeaeddeaacedcaadbadcaeeecebaadddcdbecbebddeeccdeaadbbbbdccbbcbadcedacadeeabdddaaddcabaecabaadaeaedbbeccccbbaaecbceaadaeacccbaebbcaccdccceaaceccebedeadebacdaeeddabbbacdabbdcdddcadaaeeaaaebbbdabdbcbcdbbeccadbdbdddbabecdabecaeedbdeabacebcdcdbedddbbcdecceaaeceddadecddebbebdeabaebbbacbddaadddadeabcbcebcecbaeddabdbbcadecabacaaccbbadddaaabdcadedbadacddaaabebebcaccbecacdbbdccbeeaddcaedbedbaabddbdacbbadacbcedaadbdabcddbbebedaeceaddbcbbbbdeadbadcbadabdddcadbdedeeaaceacccbbadecbeccabdcabdebecdebbaaebababcceeaacdecbaeacdcecedabaaabbdbbbaeceeacdeaeeddcdbdedeaaedbacbcaacabcebdeddadbbdceaddecabaedcdbccbeebabddacadbddbbadbcddaeeebbedcbcebabbadebaaabdaaebdbacdedccaebacbeddcdebaeeaedeaaeeaeabaaebecebdbceeeccbdbdccbdaedbdecdbdbbcadbcaaddceabeeaedbbbaaabeecdacddaeaeeabcddcccaeacbeeeeaabbabecbecbcaebacedeeccdedaeaddcbdbaebaecebaedbaadbdeedaeabceacbcbbdbdeaaacdacdcabccacbdcaaebcccbcbedeacabdddebeccabdeebcdcbaadceddaddcabdacbbbabbcebaadabcddeeeaabcaccbabeacaacbbaeedccedaeddecddeaacbabdecbbbbbcadcecabaeccadabeeeaaecaadccaabaddbdabccecddbcddaddcecbdbbebeecdbaabbbcacacbebcbbbaaedcdacbccedccbcbeadbcdedcccedebebacdeebcadeeddccdaeecbcbbecaceaaecebaebbaddedabcacbecacdabecaebaaadbdabcceceeedddaeabaaadabecddcdaddaabbedebaeccdecbcdbbcadadaabccbdabddabdeaddeeaabbebccadacccaadddebceacbdbdceeadaaacbeddebdaecccadaedaecbaeaeaabcdbbdcacbbceddeaedccdbdecaabcaaacbcaebedbaabbaaeadadcaaddbaecddedededbbabebdbdcbcedaaaedebadabbaaddcccdacebdbddbbcaddcedadbebdabdaeccbabdadbacdaebcebecababeeacdcccbbbcbbebeecdadcaeeddeceebededcbedbbbaddceaddeabedcbcbbeabadddaceaccabadbceedeabcdacbdadeeebdeddaabcdaaebbdaceeedadcdbbedbdddeecdcbdcadebadbceaaddadbbdaeceaeacebbeeeecadceaecedcebbbaddbacecacababcbedddcdeecbabeaedcddbcecabcebcdabaaabbbddcabecacddddbdabccebbecdbdbbadcbddbbdcbaaddddcdabaacebccebceebbbcaedacdbceaeceddabbedeaaabdebccdcaaaeebabccaaecbedcdebeadbabdaccededdcebccdcabbdcaeecbeadcdaaabaaceddebadedcacadebecbccecddadadcbdedbcebdebecaeabbaddedbccadbbddcdeaacddbdcdabaabbabdcbaeecdadedecbadaebbeabcbcccadbddcbcbcbcebcabdcdddeabaebeeebdaeaabaeaeabacdebcacebccddacabbdcdbbedadbcebbcdeebceebebbeadbeebdcdacbdceddbaadbabeceaaaadcadabdcdaceebeeeacbaddeccbacebaedcebbacabecaedebddacccbacceadbeeaaecedeeaabdbcddbcdedacabddbddcdcaecbedaedcdcebbbedbeedeadbaabeebbddbbadbccbadabddebcccaeddaebbceaebbeddedaeeeeebdceeadcbceadeeedecdcedacaabbdedecaaebdbadaedeedadcaaeeddebdceaeeacacdcddcbacbbbabaabeaedaabeddccabaaaaecdadadecaabbbdbecccbeebabebedeaaceddbddcbdadadabaebccccaeebbaeddddddebdcbaaaacacdaccbecdaaebacdddeabdcaecabbebdbadceecaedabbbdecbecdccbabecaaeedcaccaadaabeddcebccededeccabbaacdaebabedbccaecacacdecdebdbcaebcdeeeddadbebbdcbadaabaedebddaccabedbcebceeeebbdbadcedebdbdbbdedaeecadbdcbdeebdddebbdeebecedcbcbabcaaaaaababdccccaaabdbccebedadbddbabedecbeccbcaeaeadaebacbbaeccabacddbccbaeeacacdcdccebeedecdadbcbcabbecceceeaebdadedaabdcbdbdbadadecbadeeecbbbcebdccbdecaaeaddebbcbbeacabdadbeeddedbeecdaaddabeadddcccddacbddcaeebcbdeebcadaeccaaadceaccabddbaadccabadebccdbecbcecacdddeaadcdcaeeeaabceadcebcbdaeabcacdabbbdecbeceeecaddaeccbdedcdddcbaaeabaacedaaaeecccedbbbaaddcbbbccbecbbaeeecdacaadaceeeeecbadeeaeddbdbcdcdcdeecdbbacbcabaaacbacbcdaeccbdacececcceccddcceebeadcebadbceebedabedcbbeddbecbcebacdccdaedebabdedbaababbbccdedabdccaceaebcdebaebeeddcbbdeebabddcbcdaceaadabcbdeddcbaebdadadacceededcaebdcddedaacbbcdcbebcbecbaacbaccdbaecaeeadcaeccccedeeddaabadadebdccdebdbdacdcbaeeebdcebeccccacbbdbaebebabaedbdbabeeeeccbebcedcbccedeeeebebabeccedeacdcecdcdbcbaabcbbeeebdcaccdcbcadbdbcbeccedcddebecddbadbdcedbebbaedeadabedbebddecaabbaadbbedacabcbdbeedbdcdabeceaeeaaeaebedbdbaeacddebabbddbaeccdabebaedaecddacadabebaadddeddcadcaadaecbeedecadcaedbbbdebbdacabcbdaeecbcbbeaddaededeeaebcedbbacabdceccabedbbedbcdccbdccdcabeaddcecdacbcdddaceabcacebabdddcbcadaddaebbbcdddeedcacbddeeeaeabcbedadacceeedcaaddaebdcecaceccdbeeeececabcbcbabbeddccecdbeeebcedcccebcecceeceacbcdcaeecbcddbcaebabbacdbebedbaaedaeaccaaceecdaeadacdebeecaeceaaebecbddbbcdbedbadabaaedcbdaabebadcdcaeaaadcdecededdccdbecdbdbeddcbaadceccdaceabadecbadaaabcdecacdaebbeaedbcdacebceebebbceececdadcaadaceceeeddcbccedbcabbebebeaceecedddddcdddeabeeeecbcdadbcbaaabbecdbaeaebcbabacabaceabbadadaedeaadedeabdcecbbbedbcaceecccbbdbeabaadedacaeabdacbcabcbbdbcadedbabedcecedababeecceeaedacabddaaebdebebdaeceaeeadcbdeaceacbbeaacbabbdcdcccadecaeacabcdcbedbcceaabaddcebabbcaeeaecaeddbadceaeceebbbbbbbbdecddedbdddbebeddbacabccccdcabdcdaebdcbcddaacbecccaadcdebdcbbeabebcdceeedeacacebbbebccbadbcbdebcaddecebccadcbddcbbcdacdeeaaebacacbecacdeebadcdbbddeeacbceaecbbbcabaadddedbaaceaecaaadaecbdcdebabeeeaecaacecbcccbbabdbbeadadbbeeaeeaaceaacaaabeeadceddbcaeddbaedaebdbddeedacdaaecdecbeeaceeaabceebceadaaddceeaaeacbcdbaddeceadaceaebeeaccbcdeddcababaeeadaaccbebaabdbabcccceeecceababeadacdbecabcbbaecddeebbccdeccaccdbebcbbccddbcbeaccebeababbaddceabddeeaaeededcbdedeeeebccddaeddebccdaebdcaebbedcbebdcbcddcecdcaebadacdedceaccabccbbeeccdebeeadacbaabaeadeabddccceaaedecdcccbbccbcbbbeebceaecaedcedcddedabadbeacbccdacaeddaaaeccdcdcacacaaedbabacdadbceaeabdbbcbcbcbcbecbaadbbecdceeedbbaedebebeeaccaddbbbbeeeebbbdbadbddaebedebbebeaccacdbadddabbadbaaebaccbcdadbccececcbaddcecbcacbeccdebaabbabbbaadeacaacdbbaadbccbbbaeedaaadadbbbdcadbebacabcdecdbaaadcedbecaabbbbdeccaeccdedbcbebccedaededadeecbaaabdebaceeccbaaccadebbdeeddcdaeedcbeecbdbeddbbacebbccbccbdaaaecaebcadabbeadabaedbdaacddbcdadeabdaeaeacceddbcdbaeccddceeebcbdecbcbbbbaacadadbadcecbbcbedaecdbdcbcecbccbeecaddedbeaecbedacbcbaabbcacadebcaaababeeaedadccdcbdacaeeeccaceedcbdbbedbadebccaabcdabcebcdeeabaaaeaedebbbcddeaeecccabdecacedcbaeeeecddbcaccebdeacabaaadeedbcaebdabeabcbebbeeabbbecdbeaedabaaedcaeeaceaacadbacbcecceabeaeddcabbeeeaceadbcddccbbaecebecacbaddebcbcceabaeeeaacbaddbdabccacbeacabbbaadaaaaddeccaebecabdbbdcdebaddccadebddceacadaceeaeababcdebbecddddbddcddbdcccecedacbecedeaacdeabbcacdedcdcccdaedbcaeebbdddaeccbdcbdcdeccdaaabeaebeaaeaabbbcbbcbebcabeebccbcdbededbebcacdaaebdcdebdecaaeceecceceedecdddcbcdcabcbedbbbeeeeeeedacceabceedcabbcaeacbcacaeaaaabeeabcdedebedabdcecdebddbeacdbaebcadddbeebaabdaabcaedebbccdaababbdcaaaceeddeebceebdaaccabcbbbbbcadadeabbebbdacaceedceadaccdeaaedabaebdebeabcdecedaccebaddddbaabcebcaabaeccceadecdbccdddbceeedeeceacbdccbabdbcbcbabeecedadbeccdacccbaebbccbbeddeabcabeaabdacaeeceeddbcbccbbcaebcbeabcdaddabdbdcececeaaedeacadccecddaabdecbeddabccdbabcadedcccaaebadccddacdabeaadeaeeeccaebbcbbcaebbccbadebaeeedcebecaeaeaacebaeccdedaacacbbceeaddacabdcadadccebcebbdabcabaacccebdaaaeebaedccadddbceaccddbdeaeccadbabbbaddcdcddcddaeedabbbbebbecdaaebbaaecbaaaaeedbeebdcbccddccadebdcbdeacdecdedbaecccecceadeacadacbeeeedeeadceddadacbecaeddddddbdeddebbeaedeeeeedaccabcbcbabecbecedceddcbacbababdecbbeabbacbecbccacebeacadcecddbbccebbcbbbcabaaeacbabcaecacdcbdbcbacebbeebcdbebbcaeaccadbdebaecdcbcebcdccadaaaccceabcdbadbedbeabadaabaaedaadbdadcedceebceeacedddadcebedaaebcbdaeedccecdbcecebeaaaddeeabcddaacababedbadacdcbddceceaedbaedacecdadcdccdbadcbbebcddddbadcddcbeceaaddbeabbdbbdbddecbbcecbcbabbacdeabdebbecdcbeedebeecebdbebeaacbbaaaddacddbddddadbbeedcecdcdcdcaaccbcaceacabceadedbbecabedaeeebadeedcbeecbdbcbcebcccbeebeadbcbeabecaadbaeeadacaabbeadaebdeddabebdbceeeaecbccdddcbbbeacaaccecaccdacaaeeddbdcebecbadeacbeadcedabbebaebaccbecededcbecbbeedbebaebedaabdebebeddbbbebbabadaeecdddeddbeedbaaaceabacceceeccadccecaecbcecbdeeeaabbeddcedaaedeaccaeaabdcdebdcabecccabcbacbcbccbededacccbaaeddcbcddadcacdbdacdeaaeaddbcdecadeeecceebeadcddaeeebbaedbebdedeecddecdcebabdedebdcacbcbccacecacaccddaabdcededeedceeeedabceabacaaecbcabdaacceaaebdadcaeeceedcbebbacbebcabaccbbacaeaeaaccddabdccedaeadbeeebeabbebedcbbdabedddeacaccddceddeebbdaaaedcbaabbadddedebdebdbecacdacebebccebbdddeaeabadabaebaccaeaceebdceccadaabcecebbebcdcdbbcbeacdcdcdbdeceeabcceaaadadebddbdebdbcacbaecdaacecdcecbbcdeecdebedabbbacbdccebdcbbeccaabedeabedacbaabcdeeeaebaadedacdebdbcdaebceebcacdaabddbcececbdeeeccdbdedbbbcdabbbadeddddabcddbbcdcbbddbecdeedbedabcaccbaecdcccebbbccaaaeadcccabacbabeaceedbcbaddcaaaadcbdedaaebabdcbeaccbccbdcdaedceaeadcdaceaccbeaddbabdbdebcebceebaedbbaddddcebcebddadadaaddcdadecaacabcaabdbdcbccbaaebcaeccdcdbeabcceabdeabcadceadceaacdceadecaecdbcdacaeecacdbabcbedecaedacedeacdaadbcaadaadcaabeadcdceacdbeadcdcccdeacdecaabeaeaaaabcbceddaadbdddaaeacababccedbbcedaadbbbcbbacebcdbccaaebcdbbeebdcdcabaeaacebbadecdcbabdabebbdbadeeacbceccdbeadccbbbeacaacbececbdaeeaabcabbbaaedceacdceddeadebabedcdaaebdaebbacddacdedccdecaddceeaeecdddcbaeaabcebdbdccbcceddcdbdcecebbebdcbdbaeedcecbadabaeeccbaebdabbceecddeaebbebabeabdbccedcceacacecdaddcddaccaccbcaebeaeedcaeacaadeeadaccacddaebcaaeaebebeeaccdceaaeeeaabaedaedddeccaeceeaaeacbaeeddbedadcbbedbdbddcccaebddcddadbabcbdcdabbbbcebeaceeecaccccddcaecabacadacbeabeaddaecceabbddeedbbeeecceaccdccaddcecdedabdcaceddebeebbecbbbeeabaebaeaacccceaebcaabdeabeebbcbacccbddebdbaaebeedeeabecebcbbdcbecabcecaacceaaecbadddbccbacdcdccddabbeaaabbadabecdbdaaaddaaaacdebdaccaddaeebecbaebaabbbccacedbaaddcdddddcdcadacbeaeadeaacddeeeeeeebebeaacbebbbceabcbbdedcdbbdbebcdabdabeccbeeaadedbcbadbeeccaeddbbeccdbbadeaeaceeadabbdebceedecedcadcdabdaeacbccceaebbbbadbacdacecaeabcebbedecdbdbedcaacbbdaddcbecdcccdceebdaadedbaaabaecebddecbedbdcccddbadaaceabadeaebedcacaceaccbbdebbebecbecabcecbaedcbebcacedbeceddacaebceaeddeaaaaceeeaebacdedceccbedcaecbadbaabcbbbededcaabdbbdceaabcebdbbecceadcddedccdbbcbeeadeaecdbabcbbecabccdedebeaedebdcccacededaeceabcddadeedecbaceecaddcaebcedabebadeceadbaaadadccaceeeabeddbecacedbaaccbdcedeaaacacabaaddbcdaadbbecaeddbebdcaddebdcdaacbcceedecbaabebdbddcdbabbdeddeeeacedbddeaeeabcebaebcececdcbacedccbccaadeebaceeaaaebbaeaeceaaadecdddbecaebabeeeaaacebadbbcddbeacdcbecbbbebedceebbceecacebbeceacbeaedbedeaedeeeebebecddeddbbebcaddcaabbaeabbebcccbeeeceedbeaebbeedeaebdccedcdadeabadcacbbdebecbdddbeecedbebcbceeaceddeddaccbdbdcabcdccadadcecebddcbbddaebddcceecddaaedcaabddbbdddedaecdaebebebebdcacabdbaaccaecdedbcbeaabebcecbaaaccdabdedababceeaeabecaadaceddedcdddbadcbcdaebddbcaabcbcabdabeeabdebdccbabcaceecdeabaedaadccbccebdbbebbaebaeebcecaaaaccadbdabcbdacaaebcacbdceacbeacdbbdeadbaccbaebbcbbdacdcbdeabbaceaebdecdaecceaaebaebcbdacbdbcceebcdeddbdcdaededaebadbdadcdaccdcebdecebabeaededacedbdcceaddccdccbbbbaabcbbcdbbedcaaedbcbcceebdedcaaeeeeaeadcdbadabcdbbeabadcbabccdceabebccaccdbecbccdeaecaeedadaebaecddcbebceecdcedcebdcdbddcbeeccadbecabebccedadadedaccbdaebedeaacccbabbcdccaeebcaacbdcbdeeaedeaaecacdbbcdcadbcedbadebdaabaaecceecedcadaabdebceeedcaabedceaabeedcebdbebeebbaddaadbceecaebeccbdadccabebcacdebabadadabacaeadcaedeebcbabcaaceeeeeaeabddecceabaceaacdadeccbcdecceeaabeccbbecdaecaacdebebddccacdbaaeebeedbbecedbadaceccbeecbaadeececebebbdcdbcaecbbadabedccedbebdecbeeebdadbddebdaccadbdbbebbcaddcbddaaddadbcbaccdbcabecdadadbcccdadbddaaccedeabbbeedbaaacdebaacaecbbadbebecdebaaaeebcddcadcbabbcadbaccdeccbccccccdccadcbdabaaccdbdbececabcaebaddadedadcbadcceabeebaedaaadceaeccbdeaeaaedaeaaccaccddeeadcddaebcebdcaeadaadadcedcadadaaedcdeadccecaecebbddbdddcccbccabdedbdcacbbaebaeaacbbbebcbaedebbdccedadbcedcbdeebababaeecedbbbceadcecebbebdbbeceaccddecedbeadddcdedceecbeeabdacebaedccaadebddbaeadebbbbacbbcbabebdaadbdbcbabaaabbaeaaadbbadaabcbcebeadaabddebeddbedbcebaddbaebacabbdbdcbbcccdccededcaaababbeddbaaaacaecdaccacbdcaeabcadceedbeeeecbabeaeaccdbeedbcdbcbeeeddddccdcedaebcbaeadabdbdeddeeeeecbbcabdbcbaeedddcecedeaabedceebcedcdcaedabdecaeeceaadeedbcbcacaaeaaaceeebbebebebdccdccbebedcdecadcddbdbaecadedeaddbadcbabdccdabceacbcabbcaccddadbdaeecacbbbebaddeadbddedaacaeabbbdcbcdbedbacccadabaaedbeacaddaeaeddedccdebdaaccbaaaccdbeccedebcdeecccbdeabccdabeccbeaddbdceeacbcdaaebccedacaeecaeeecacbbaedccceddabdeaccecdecacebedecaaabaaceddaabdcabaeabbbcbcdeceebbaedbcccdddabcaacbccbeaeadcdbcddcceebeabdeedcbaceacddcbbadcadeeacdbeedbdebbdebebbbbecdecdabdcedebcddacebbdebbdbebbeedacebabcaceaceaeebcbccbeccddadbadecdabdaadaedccacccbccaabcdeacdcedcddcbcdeaaaaedaebebecaeacadaceebdabdbebadbbccdacbabebceebcbddccdacdadbebbeadadddcdbeddccdaccbedcbbdbabcadaacdecebaeaabbeacacbedbedceaaeddbbaaebdceaaedcadddbacbcdcdeccebecdeacdbacccabceebeebeacabaebbceeabcaeaebcaaecbdaaedabbbbaccedcceebdecccaeadedabeccaccdacacbbdeedededbecebacedeabcedcaeaaceecdabedcdceecdeaedacaecdebeeaddabbbedebdbacbcadccaddedbbceabaecceaaddbcbbabecbdaceccbadceaaabbecdcdceadeacceadcebaddeaadcddecbeedaeaebdcadbcecdacbaecdcbdabbddbeddedcaceeacdebaaccdccceecbbeecbceebdcadbbbddaebcacebcbbeadbcecceaaaaccbacbaeeddeacedebaaaeaedcdccaeeeabcacbcdebbabeeebaabbdeadbaabebccdacdcedecceebaeedbcdbaeaedebebbcceacdedabaeecccededdabaebbeddabccaebccbdcadaddcbdcdbaacecbaaddbdbebdbdebdecaecbdabbbcddeaadcceaeadccedbdcedbacdcadcbebbaebaddcaecbcdcbccddeadadabcaebaeebdaaccbcaeaadeacadbecedddcecdaddcdbadabbecdedbbadbbebdbcdddcdcccaaacdddacaeccbaaeaccecabbacbcddcbaebddaeddbcaeedaccbdaabeedebbddaabdddcacccaabddaeeaccaceedeeebdbbbdbcebdedcaabaaacddcdcccdabaecbeaaeabdedcdbccbcdeadbccbcaabaaecbacbaceeeabadadcbaebcdeccebaabcacaebadecccaadcbabeaadedabbaccaedcbddbeadaeaadbbeadccbbdeaddadbbabdeaedcddcabdadadbcbdcbcdeebdaeaddaeaebabeacbeadaeaecdaecbcecdddccedbbbebddcbecbebceeaeecacecaeadbddaeddadacdbcdddadaccccdedbdeeceaecaacbebccadecbeddbaadceeaecabcbceeebeaecdcadddaeaceaaecdadbbdbbbccdcaaacebbebbacbcdbbaccdcaadacdacdeaebeababaaaeebcbbecdabdbcecedcbcbbcaabaabbdcabcccdebcdbcdaadedecebaddaeeacaadcacecaaddcecadebecaadcbddcdcdbaedebcabeccbcbbbcbcceddeebadbeeacddccdcccabcdaeadcdddecbbdacdabaecbeacaeabdadeadaceabadebceecdccaecdabaaaeaadabaaaeeabaedadadeccbeceeeebeccdddecbceaacbecaccddaebdaeacccacdebddeabdecbecbeeacceddaeecaaaccacdaaabbdeeebcbdbcebcbdeadddeadbebbabdedebabdaaeacbacbdabcacdbdaeadcacccedcdcbacdeddebbeabebddecdbdbeaccdbacdebcdbdbdeeedddccabebadababeccacaaebddbaabbcaaadeeddcaecacedbbbdecebcabddbdcabeddebeabacdcdccebdeeddaddbabcedeceebdbedbdbecedaedabcabdecdeabdbbabcbdabaadeecccbeceacdbbbbdacbeecacdeedabeaebccdeaaeeeeaebedbddceceacbedbaabbaaebedcbcccacebcdccabcaaceacaebcedeebcedcdabaedbeebaeaccaadbbedeaccebaebadbaeccaacddebbbddbddecddaabedacadbcbdecbcdddbaaaaaddbceccabbdedcaabeaeadbaecdedeeaaebbacdbabceadbedbeecbaaaccabbdaeaedaddaebceaedbdacddebabeadecadddeedaeceeadabeecbbdbaacebbabadcabbcbdbabdcdcaacbedcadcdbaccccacbbcaccabcbbeaaedcedacbdebcbbdeceaabdcadbeebbaecacaeedaaacebbcdedbeaabdbbdceecacbadddbebaddebccbecdeaababbebabccbaecdebeeeabebeaebbbeddabccbabdaebaddcdbaeeadccbbdaceacabcdccbbeddcecaaaaeacebeddacaabacedbbcedbeaeccdadcbedbedeecbabdddedadebbdddcccbdadeaabccacdeddceeeaeaabaabcbdbbbebbabbacbccbebecabedadacebacdbcebabbadedbedbabdbabadddbdbeaccbcbbdcbadeebaaceeabaeacceedaebbbdadcdabaeeedbdcddcaccacaddaeaccdbbeadeebeaccebbbdcdbddaccaadadacaacdcbaadcdaadcdcdccdabdcaaccebcbabcbbcbbbadbbbcabbdeebeddbcdcbececbaacaaacebebceabeedcabcecedbadbbccabeceabbececddeabeacbaecaeedecaecdbacbdacecbecabbecaccaaaedacaabaadceeddeecdedbebcebbbcccdbbdeacbbcdcbaddbccecaabeeaebbaaaabbbaaeeaaaabddcdaaceeaebbbaecaecaddeeddcbbbdbbaebdbeceeadebbecdbbcadeddbeadbdbccccadddbccbceeebbecabdeebcacadcbcadaedbcababaaeaaecdabeadddbacdeceedaeeceadcdccdeddbcebecceacacececbdaaebcbcaeaaaaeeeadcabbdeedbbeeebccceccadacaddbbbedebdacccedadedeaacececcddccaeecbedcabbcacaedceeeaeaeabacbaccceebcbcbbceebeaacdccbabedbbbeabddccddcbeaadddcdbdabcbedaacbbadceabdedebaedcecdaecbacbbdecbacbecbbbabebddaaecdebebdacabdcccedaaeddacbddbbaedaedeabcadddbabaacaaddbdbbdcadebcbadeabcdcceeeaccaadbeeaddcceebdbbadaabdbadbcddaabeddbcbebcebcdccddcdeaabceedaccbadedaeedadebacbeaededcaccbbbcccedacbbbbeaedbbecaacacacaddddaebabdedceebacceddcaeedacacaebdbebbcdccedbaadeeeddadbbcbdbbcbccabceebdaeebbebebcdeaeadbebaabcdaabcaaedeecbaaddeddecdacdababbdccbedebddcccbcaabcebdcecdceaabdaabbedddacbebabaadebbeacdecbcddaddaaeaccbbaadeeacdddeeadccebeeeebdbdacabacbcdebcadbadabbdceaededbdedcbacbbeeeaaaeebabcebaaeacdbdebbbeedbedbaeecadacabbbdddadabdadedadaedeccedaeecdbeedcdedcccbbbacdbaeddcbccdeeabedaeaccceecddbecedeaddecbaaeeecdadccedeebdbdaeddebebcaaccddadaadbcaaccddbdebdbaecdecadaeccbaabbeabcdeddeecabecddaedaeaaaeddeedcecdadcededadacdceceaedddbbdbbccaaeaaddcabbceccbadebbcaedcabdeaccbbbcdbabcbdddbbcecdaeeedeccbccdaedabbaeceeddedeeeebabeeeaedbecbeedddabeaabbecdabaaacadbecbbbdcbdaacabebedaedeaebbacccaddcddacdbaaceccbdeaccbadbeedebacabecceabdeabaacececbbcdaeaaedbcdeaeaadadcabecabecbdeccbeedeedeadeaabcbebeabdddabaccbabecbeebbcdbabbaeeaccddcaacddeccdcadbbcbdecadcbadeddacecacababaaeecbdedebeddbaedebacedbdbccdecaeaaaabecdddaaebbbbbeaaaabdddeacaecaccddeaddacbbbeddebbddaadcdecbcabbdabededacdabaacbbbbcaabdebdbaaaccaccbddcdadedaeaddedcebadebdcecbcbbdeadbeeaaddbbbcbcecacedccbeaecbbecebbbcbebacadeabdbacdebaaeaaeabcaabebceedebbeeccadbabbacdbeeddbbaceabceedbaedabeddaaacbcbedaaeddacbedcdadadacdacedcbabccbbabbbdbbcbeaabccdccaacecdbdaeceadbbaebeaecbbdceeddabdbeebcdcbeebabdcaaebccccceaedeaaecdbadbbeababaeccdcdcececacadebeceacadedbabcbccbdebdebecaabeeddceeaeaebbcaaeabbdbbbadeaacdceaeededcbceecbdbcdabdbdabdaddcaacdeeadcbbbdaabedebcbbcceebceadcbbaddaecabebaeadddbacbbaeecaeeccdaececaaeebcabdedddecbadadbcbdaabcccdcebddaaababdbceedecdbaecaacecabebdcaceecaddcaaebeacdeacaaededabbcaacbaaccadcadbedabdabbebeebeeacbedbdedeaddceddedbaeeaddbbeebcecaedcbddcadcaecdccbaeeacdccddadcaeabcdbdcaecdbdbdbdabcccaecddaeabababbecbebbeeeabececadbbbdadbabdbcbedbbcdedecbcabcecccdeedaccedbbebbedecadbbecdabbacceecaeecbedacedbadabcdbbbceeccdeccbcacdaaccedeadceaedbdaebeaaceddcdacadaeaabbabcecdabdbbceddddccccddcdceedbabcbcaababbdeddeedebadbccbdbbddbedecdbccbdbdabdeddedaddaeeababbbaacceaabebebaccbaadcadeacddbbadabecbdeecdadcddeceadaaebbaeeaaebabddddedddbbccaadcabdbbbddcddaadeebbabbeedbabcdaabbaadddcaaaedcebcbbeecabeedcbccaaadbdbcbcabeeeecdddbeaedbbbcbcbccbcaddaaeecabeaececdeebbcbccbabbecaccadaebddbdeddadecbadcbcdaddcedbaccbaeedddabcecaebcecbbdbcceaebdaeaabbddcebdebdbddabdacadcaeceabbcdbedaadbdcdcbdbceebedcdaacbbaaecaeadddacdbddeabeacedbcbbaabcccdecaeedecdbbaeabccecbccaaacbdcabbceddceebdeadebbcdedabddeebdadcdccaaedceedeebeeceebcceaadbacaeadbbaccbbdcdaacdbdccbacaceeddbceecdaaecbeebbbcbedbbbcddabdcaaeabedcecdbcaeecdeceeceedececbdebeeeeddacbacedaeeeaaebedacbddbcdecbeedeadcceccdabdaeeebcdadbedbdaddcdbceccbacacbccbeaabcdeccccbadecaddeebcedaebdbbaceceabaceacaaeeeabbdaadbcbaacbcedecaeadbaddcaaadcaddbabeacabadeabcbdeebdbcdeaeaeceebacdeecdacdbaabdccababbbaeaebecbacebcdacdcdeebacbcedecdabaedddcaaecdbdabbcbbeadabbeeeebbbbbaccdeeaddcbaadcceceadadabcaddccbedeabaeaaccadaccaaddaebaceccbeeacdbebcdbebcdabbaadecbddbbbcccccbdedabacbbaedbbadcbedcbbdadadcdeecacceaaeaacbdeedaebceceaabebdbaeddbdebccbdecebbbbcadebedabeaedcdaaabcdebbacaeeeebddcbeceaaedebaeedeaaaccebaecedcaaeeaebbaedbeacaeebddbbecaadcdacddbddbdbbddddadcaccacbeedabbabbebaaaeedaddcebebdabbdacccdabbdedcdcedeeaaeddeccabbeedcddbbbcbccdbeeabaeeaaeebbabecbadbeaeabbedcbddddbcdeaddceccdbeeeceeebbcbbecedaeacbcdecbeabbcdecbeaeadabbdedecabaaaecccdbcebebebbeaccdaddcecedbdcbdbddbddcbebdbaaceebacdddaeeebddeebcbecedecbbebbadbbabececceecaecaaabebacbdcdbcdeacaedcecbdddbdcddddebaeedeabecacbcdecbebecbbdbbaeaacaaecaaceeceacbadaacbebbeecbdebdceabdababaddcdbadeaaaabcedaebdcbbeaaacdecbcaeeebbaabeddacdcbabdbdeacaadbaaadaecaacaaadebeaeebbcaddeebeecebeedcccbccdebbbdeecddbdcdaeaaecbdcababbdaccdaeeaececbebacaaaeeeecddebbaaaebacebecaaabdcededeaaeddeabeabddedaadbbecdbbadaeaecacabeacaddbddcdeeeeccdedbbdaabeaccceaecaeacdebbddeccbedbcdbeddbcdbacdbdaebccacccaccbededeaccaaddeaaabcebddceeaaccdcbcccebceecaedddeaeecaeabaccbaeeeebbbdadcacdececbbeccdddaeededaabcdbebecbbdacbbcdcbceedbedaccccbeaabdeddaadededbdccaeebebbdeccceaeaaedcdbdceedcbcdbedebdecbabaceccebdcecbebbababbacaebacdddbbacdcdcceebbaceadcedededdbddddbbcbbdedecadcebedeaedebebbbdeacbcbaeebcbeabbbdcaeecebaabedcaabeabbcdadecebccaaaaeecedaacccaeceeebceadcdcbdbbaadbddaaaebdaeaeeabedeacaeeeeeedddceeaddbedbcdaebeadacedeeedcdaaeeaedceeedddddbcccbebddcedabedaccbddbebbbddcbbabebcadeaccbbabaddbeeebdebdbaaedcebadbbadaddceccbddceeabcdcedccabbaceecabdedececacabaadaaebbbbaaacacbdabecaebbeaaaecaceacabeabacbdbbeaeedabedeedcddbabbbbbbdbcdacbacababdbeedadedadccbaccaecdbbdcacdbeeabebadccaedbbeeecbecbabaceabdcdbbbebdadabcedcdaddbeddbdbeebdbaccadbdeedaabaeedabeadbebeecbedbddebbaeceacebbbbebbccaaeeadacebbaeecbeedebcbccbadaadcaacbeedcddeadbeabbececcdedeeeddddeeaeabdeceadbeaaccbdacbcccbcbcadadadccecdbedeecadabbbbabcbaddaacacadbeaadaddebeaddabbddcacebebaebaaecddadbcedcecddaeadacbcbaeadbcabdacaecdbbaacacbbadebeeebdedabaacbbabdaeaabbebcadbcbceeaececcaddcccdddaacceaaddecdbbbabbbbacbbccbeceedcaaedbaadbbceceeeacadedbdaedaeadcbabccadceedbbccdedbdbebaceaaebedecbaebbcedeeddbaadbcdadbbbbeedadaebbbaeecabeeadbebabcaecddbbddcacbbeaaabccaabecabdbcdedabecddddaaebdcdadabebcbbbacebcbcecaaabdbceeccaaadaabaadbdeeaeddeaabdcdcdadccedeaedadebddbacceaccdebdcbebedbeeadabdadedcbbcbbaaabcbdbbadcaeaccdbeccdcdadcbccaecbdbeabaddebcceaacabdcaabdbaaccbcbdcebdcbedbeabbabdddbdbeebbcebdbdcabdcbbeabbddedaaceadbaaeedaecbabdaabeebcabcddbcbeeaceaceacaadebbcabecceaccdbacedeebbeccabeceddceedeaccbcbbebadddcaaedddeabebececebeddbdbcbeaebccaaacaebaddcadeedeeaeceddbcecdaaaadbceaddaadbeaebcbdeececabadbdcdcadeeacbabedaabceeeaeecabaebcdcaeebededbdabeeebbeaaaaddacbddaaecaaaaebecadabcbaaeedcadccdcadcededecaabdaddabccacaedcceacebcccddbdacaceeeddcbbebbdeaeeedcaadeeaeeeacddbbdbbaaeabeccebcccaaccacbcecbcbbcbbdbcabeecebeadbdaaceeeeebdceaceddeebeaaceddcabebadbaeacaecceedbebbcbcbcedbddccbaedcddcbbdaebdcccbddaebdbdaaeccbaceacdbbbcaecdbcdbcaadeedaaeaaebeecdddbaebeecdbdaaddaabcabadbabcedcbaaebabaadababddeaaddbceeedcaebdcacaacacccbbdeebdacbaeeccabbeebdaccccbebcecbcdbdaabceedeacdeadbacebccbddbaeecebaabccdcdeaddadecbacceadbbdddbbdcbecaeecdebeeaeaaebedecccebbbacbedbcbccccdbbdcacadadceaebacbebeeaeeabeecdcddccdeeeddacaceadedcceeddaaddaddbececcceabbcaebecdededeaebccdbabcedadabebabbbaaedaabceacbcccdbacaaeeecbadbbaaabaabbeecabecdadddbbeececcbcbdceaebbcbaedccdbdbdadeeceaabeebdeeaccbbcaaeaadcaadbbcecbacaeaaeaaeabeeaeedaeeceebbbaaddacccedddaaecceabacaaebaadbabaccbbebcaceddcbacbaecebcbcaacdbccbacbadbdddebdecaedacacebdcbcaeaedecddadddddebacebbdbddcdbddabaecabdaacadbdabacaedadbaddcaadeaddccdebdeccbacdadcebbddaebaeeebcdddcceacbeaaccccebbbaaaeadbeacddaecebcedbdaadeaacdeecccbcbebeeebcdcabcceccbaeccdaeeadbdeaaddecdbedccaddcebacabbdbedabbbcdbedbbbcaeceeacbbbdbdadddeaaedaaaabdecdabaabcaccedddedaddecdccedceddaebeaacbceedeeebbeaebbecdeccaabdebcebcbcecadcaddbaabacaececbdbcbbebdaaeeacecadacdaddccdbcaedbdbcddcaaeaeccdcadaadeadddeeaccaabeaebbabedebbdebedebeeeeaabdeddbcadbeecbabdeceadceeedbbcabdbbbdddaabbabaccdccbeadeeeccceebbcaccbaeeebdabcaecdeabaddebebbddaaebbccadcbcdebbbedaadbdddcaebdaeccbeababcabaaebeabdcadbeaeddbaebdebcaaadedeaebbbbeedbbecbacbeedaccceaadabeddebcbabedabeccaedccedddaceaedbdcaadaceecceabadeedcbaddcacaebadccbaaccbcecdadaacaebaddebccacdebbabadaeadbeaadeaacccadbaccbceeadabdbeccabddabaedbcdcebceedbcbebcacccccacecaceaddadaecadaacabdceeccbccadeeeaaacaeddadedceadcadcdacaacbbcccdebaeeaaabadbceccedcdcdecedeaeddebebcbcbeacceeebcdcdbdcedebaebbeceedddbcaebcdcacdbbeecbabbbecdebceadbdebdaecddaabcecbeebbbdcccbbcdbbcaeaabbbecabbecdbebeadeccdbdadbcdecedcccedacddededdecbbedcbddacddaadeabcbcbdecdaeceabbbeabdcedbbcbecceabcdcdcedebaacccbdaedaaccbadcbecbbcccaabbeeeccdeaaceadeabbdaedbedcdadcccedaccebcaaadcbbcdcddcadaaacabbddadbbcaeabadecbbbebdaacbbeddbcccccecdccdededeccddaebaaecbcebbbacabbeacaccedcbbbaadcbbbcaebcaedcebbeecbbbdbeccadeecdbcedbceabbceeeadbacdabedaeccbdaabccedebeddaabbabbedabecdabbdbbaedeaaccddaabcbaeaeeadadaebeaaebcdaeeaaabecedbdbbeababeaaaeaebecbcababbdebabeccaddecabaeacaeabcdcbabdbabcdcbacedaecdceecbdbbdeecaebccceecebecbaeccacaabeceadabecdabdbbbccaabccbceaedcdbcbcaedaaeacedbcedddddcabecbbebcabadcecdeacccddadabbadbceabeccabbaabddedcbcabccadcebdbacdddedbeacacabbbdbcebebdbebbdebcdedaabdabbdbbadcceebcdcdcecadcdbdbcdecdedebccdcabccddceddeadbcebbeddaedebbcbadadaccdbeacdcccbaebacdababcdcdadbbececdedaeeaabcbeeaaaaabecccaedeaceaccaadaaaebcabaeddcaeceebcbcbddccbdcbdaaeaeecedceebeedcbcaaecbbdabdbbbcbeeecdabbccbbaadcbcaedadebcdededcdeccdaecaaceceacbaabbacacdcecdaaeaabdeecaddbebdaecbeeeeaaaedadbaecbecaaecdbceddcacdaaeebbcaaacbcbbbbeeadcaabeddabbcdbeddeabaeaebeaccaedabbececedceacbccbeddbbbdeeaaeadcdbdaeacdedececbacbbddddcbaeaddedcddbdbcdccceeacbbdcccebbbeaedbedbcaaabcecdecaddbbbecbdcaeacbcccebbeeddddbbedeacbbeadcbdadedeaeedadeebaeeebcadcbabaaeeddeccbdabacaaabeccebbadeedbbabadcebebadcdcdceedcdecabdbaacedcccebdecedaecebdabeccbabdedceaabdaedcaeeeecdebaedaecdbebbccbcebceaebdaebcaddcddaebeadbcacdbabccdddceeecbdedbaabeabadcaacaababdcecbdcaebdbdcdecbcaeadcadbebabdbbbacecbdedebeddebccaaddbbbedcabcdaaacbcbdaceebaedbbadacaeebcabceabedbacdadcdcaacacbeaedddcaccebcedddabcaaabecdacecdaccdceebacbbcdeabdbbbebbcadabcbceaabdcbcadbaeedababeddaceebbaaceacdbcaacaececcdeeecdbbaddceaebcdaeadccaadaacdaacceabbcedabadacadcbcbbdeecdbceeeadbaceaaebadceadcecbcceebaeaeaedaadbebdeadbcedcbdcdcccecabbecedeaebcecbedbeaebcdbcaebeaebdbceadcbcaadbaaaceebcccedcaecabdbaaadbadcbdeceedcddceadbecbeabdcebddeeacbcdadbaeceaedabdebcedcdcabaceddadeecaadcaabadceebbebeeaeebdedacbaabcebacdababcbdedadbeaceadcececcaeebeccbbddecaabaccebcedbaacbbaadabedecddedcedeebeddebbbdcecebddbabcddbecdbbddadcbbedeaebeabddbbaacbeaaabbeebeacabcaeecebdddaebcbbebbcebcddecccdbcaeaaaeeacdcdeaaedcedbdddebeacdcddcccabbaddacedbacedaddbebdeecabeaecaecaecddbaedbbeeecbdaeaaaaccedaeeddceaeedccdbeebecaecbdedccdedddceebcebadbbccbbecccaadbdaddbdeecceacebbceeebddbbccbececbbeedacabcbdadeaecaaaacbbbeadbcecbdcddabeecaeedbbbaaaddaccdbaecbdacccdedaaabbbbecbcbdaebccddcbdccbbbebcacaadbdddedcbdaebbdacaadbebceccecbecbaabdcbdaccadbccebeddcacedbbcbbdeaedbaedabbdcabebbadcddebdebabdcdbdeddebebedeaeadeaaacaaebdaddaeacbedbacdaaeeddbebccdacceecdcbeaeebeabcdcbcdaddabbbecbadaddabdbdeeaebeecdacabcebdbcbcabdcacbadebbcddedcadbdbeceeadbeccbdaaaadabeebcdbbddadcbbcedbdcacaebacacabbdaccecbbeeabebcdcecdcacbcaceccaaadbddcceaccbbabbeebebeacabccbbcceeedcbaedcecbdbcacedadabeaeeededdccbacedddceebbcdebebacdbbdbbdeebadecdceaddccaeeceaeeebdccdbecceabaeebacecbcacadcccccedccbcbbbddddaeaaacecdedbbdcabbdcedccdaadbbdcdadcdacecbecdcbbcebbcabeaabeaaedbbcbaeecdbcebccceabccdcbbdebdbcdbeaacedecdbeaacbcaeadaccecbbdadbabbdedabadebdcbaccbeeeebeedcebedacbdecaeddaacbebbabdccdbbbcacadcedeeedadcaacbbaedbbacddebeeabbdcbbeadeedebadbabcdaebebbddaadbbecdceceedcbeddeeebccaaccbcadddcacaebcdbbddaccabdbbabecddeeddcceadbcaecbbebaceabdbbcbcabdeecaadcaceeaaabaecedadcacebdedeeddbdcdbabdcdadbdbadeadddcbbacadbcdcedcedacceccdeacbbedaccbaecadedcaaaddacedaeecbbbeeeaeaacadeacbedcadbbebdbbbaaaaeabdbceacbbbdadecccaacabecdeceeebeaddecabaebadedbaadcbeceeeadeceaacaadddeddebeeacbddcdaaaecbaaadbbcaaaaceddadbddeebdecbabaadcdacdecedbbaaccededaadeecbaeddcbbdbebabcbcbeeedbacdbbcbcedacceaedcbdabacbadccbeabecaeeaeeceebadaebebadeedbacbdbabdbcbeabeacbdbeccdaeeddeacbcebdebbacebbeadcddcdeccbbaeacebeaeeeaacceaabbbbccebebbdadadbdbbecabcbdbdbbabdaceebdeaeeebcadadabebaccedcdacbddebebdeccbdbaabebbcdebaacadeacadaccaeedbbcebacbbcaeabacebcbaccaeadbceeaecbaabaeaceaebbdaabceeebeacdceaaaeedddcdbdbbeddbceddeebcdcaeaacccbbdcdedeabceddaeabdcbdcceaebbceaacdccbabbabeabedcdaebecbebedeedbadcdaaebddecdceadaddbeaaceeceadaaadbabbeeaddccbaddbacacccdceadecaaecbceaddbaceaabdbeecccbcabcadcdaeacbccdccceceddeaeaaadccadcedaeddbaddbbeedbebababbdaecabbabdbeccbcededbacabbdcaddbeccebaeabbaeddccaadecabebaccbddedbcdcadeaeabcdceaaacaccdaeeadabacaddddbcedcbaccbcabeaaabdbebbcebdddcbaaeccedeadcbcaacedcbebbccbbeeeabdcdadabcacbedeedadbdebebbaabbdaedcaeaaacaeedebcbddcabacccedbbaaeabbdbeaacdedebddbcbaedecbbbcaebcaecebbddbcaccebbbebdcecbebaeabccbceeaaadebbdcbadbeccdbcbdcdbcacabdebebcdaeddaaaaabaadeeabecbcdabdbddbcddaebebaedabebbaecbebebedaccaadeceecdceecdacdbcecbebddddcbbdcbdecaccaceebddbcdeebbcdbaeadacdbbcdceeaacaaededaeaebdbdebcaddddeddcbdeedebcaedbdbcdccbabeacdeeeebdbdbdbbbcbddcecbdddcdebbeddbbddecddbceadaecabacdcaadbaaabcecdcdebbbaaecccdcccacecdcaddbbdbecbbbbbdcceadeedecbacbadbcdcddadbcaaaaadeceacbdeebbbedccbddcbebdcebcbdbcbcdaaebdbaeddccacdaaeaecdaeadeedecbedeadaebbcbbecabbcdcadcbddedccdeabadeeacbbceaeeaaceabacbcdadbdcbdcdcacbbdecdbccaaeebdddcaaaaaabecbcabdaebecaacdddaeaaadbbdcabeedcbeeaabbddbddedacbbdeaaeeeeeacbdadecdadcbbddecccdedeacceeabbcaeaebaabadcbbccddcbdceceabbbcbdaedbaddbcedcdeacebbcadeaccdbcabbbbebadecababacbbbccbaaecdeccdbdbcbacbaabbdbdadbdcadcbbebcaaaecadcedbcccbddcdebcebbccdcecbcbeeaccedeaeceeacaccecbdeabceabadadbebebaeeeeccadeadabdbabedbbeabaccccdbdeeabcaddbcebadaaeabddacccadbcadceddededaabadebaacceadeacacbeebbaaacabdaadcceeecdbddeabeeabbcdecddbccbdbacebbdceabcbedcdebddaacaaaedbbdbcabcaadcbeeccaecadbbbebaeababcdabdcedecbebbaedeeadcebedceecbabeddedaabedeacecebaeeacbabbeebadcadadeccbdeeaccabdccdedbbebcecdebbdbdaebcebacbdabbbbaeadddbacbcaecbbdaddeedebbcceadbbccdcddddbcadcbeaeadbccdddebaebecbeeebedcdbbedcaccaadccaedebcbadbaecccbbebebceacebaabcedbccedeaddebdbaacdeccabaeaddceeacddbeecebcbdbdacdcbbeaedcbddcdcdbedadaccdecccaacdbabeadadacaceacadaedceedebeaecbcaeadaabcaebedcebdcadbaadacecedadedcabbaeddcadbcebdaceaacdecceaadbcbaaadddbcebedebecbdcececdabaeceaccacdbdebeaccbdccdcdbaccbebcadadbdcacccdecdecaeeaacdaeacdadebadaadaaadececbceebbdabeebabadddbeebdacecbccbebeebecdaaadebdaaeacedccddeababcdbdebbbdbabecbdadbedddbcdedecddbabbcbddcedbbdcebadaeaacbeaccbdaabccecbcbdbecdacdaadaecccbebdacbbadabddcdeeebecccddccaaccceeecdaeaeaddcecceaeadbcddcbbddecbbaccbdbbeaadadabaaaedcbceaeebccbbddeecbcdeacbaccadbcdeaebccecdcbeddedeeeccbceedeecebbaeaedcdbacdabeabdbdbabedaddadccbcacecbedeaecbbddeceaedabdedaaeaedecdbdeebcdcaecdabbdcdcceecdbaebedbadcbabdbeeacdadceccddcdbbaebccecabdeecbcaabebeccccabdbcbeeacebaddbbcbdbbadabaaabaabcddeaddabaaceacadeccddcdccaacaeddddcbaccbeccddebabbdaedaccbcdceaabddabeadbabddacbeeaeaddbeeeacebcdadeebbaeabcdcdeebbacadddcaadebeadbddaeabbbaecabbaccceccdbcbeddacacebeaeecdddaddebcedeccaeeebdceeacaaabcdacedcadeeabddaadbacebedeaaabdbeedcddebaacddbdebddcbcbceabcbadbcbececbbabbbeedacaacbbbddeeabdaddcecadbdabacdabeaabedeebeeaeabbaebdbbdddedeeadcdcbeddceaaadebceaadbababdadbdbbdcebdbcadbedabccadceeaacbbbddebedeabacadeaaadcaadabbaaacdbbaabcbeaaeebbdccbadbbdbeabbecbeadedadbaeddbdbbdecdecddcebeeabcdbdbcceeaabadaeabdbedaedaddbedddbdbeeebeeabaddcbdeaeadcdcdbeaeaeeeabdebddacaaeebdcbdbcbedaaedaddcecdbbcadaddddedddcbbeabeddedadddaeebaedcdeebdedaaeebeceabdecbccdecdaaabdbebadaaeccecedcceabbcabdadebeccbdaaeeaddabecccecebbdebecdcecdeaeceaaaccbdacccdddbeedcacaecabccecbdbebadeaeadabbcdadaccdcaaacccccecbaacccdabeabacdecacacccacabdacaeabebdeaeaeaeabcdbebbdcacabebdacaabeddeabadeadededccebcaabacaaedebbebdebdbebbbecadcdaceebabaecbdbcddcdeedbcbdccedcbecbddcacdbeeeaacebecccdabadbabaababccddabdadbdcacdbbdccbccdebbceabadecdebbeceabaabbeebceebceabcacebccabaabddcdccbbedcabdabacbdbacaadecbcdaeeecbedebdedeaddcaabadcddcaadbdeeedddedbcbeeabdebeedbccaedbabbdbeebacbdeeedabcddbedaabeadadeebdcebcdcbabbbbdcdbbbdbaaaacadacaacedeabbeacbaedcebedaeeeaebdbcebdbbabeabeeecddcecccccaaaaecdbdaeeeecddedbedeecaeaaccedadbbeaabbbcdcaecbddccccbbebcbededaecadceddedbaabdcdbdbcdceceaaddadbdcccbadcbeceeedbdedbeecaddecabbecedbadaacbccedbeccdbeceeadaeeddaaabdbadecbaeacceccacdacddbaebbbbcbdaadedacbacdaccabdebadcdddecaceaccbaeeabbdabeebacddaeeeeabdcdaaaceecdbdaaadadeebeddccadacebcdabbacccccddadeacdeddcabdedeebaaadeecdcedcbeeecbbedbebbedcacbacaeadbabdceedeeabdbbccecededdaeedbacdddaaaeecdcaeedeebcbedbcbbecebaccbdcdcedbdecbebddeaedbdadbbcecccbdaecaacbbbcbedaecdcdebccdadedebcdbbdaacadbaceecedcaedccdedabdecabadcadabcadaeebacdabeeaacaedceebddddaceacdcaccaccdbedbdcccdbededabadcbdebbebaaceabeaaedaaadcaaebeacedeebaeeecdceeaaebdeeeacdcecacceaddbedddadebddbadebcbccdecccbbdaaabadbdadcbcbdcdabbeeaacadcaecaaabeabccdbdacecbadcbedbecbeebaedcbdcecbcbbbdabdbaccccddbbacbceebbbcdbbeebddabcbbcbbadbaaaeeeacbeaaeaecebadaebbccbcdbbccccabaabdbdbcbddccdbaebbbcdbddceacbdcbecabdcbedbaaeeedadbdeecbacbeededdadeabcbeacddeceedeacaeecbccddcbebbdabdeeacacceeecedbacbdccedcaadaadceeabbeecdacdacdebbeabeecedeceedcdeaedaaaeeaeccaeadbedceeeadbdbbccbadacaadbebcbddeeacbeccebddbbdbebbbeedeccbdcbcedcaecccdbbddbbdbebcbebcdcccbdaedcdeacbceadcdddebbcbbdaaeaeeaccbacbbcbddddabcdaaeedaaddeeebddbbaeeeccdabceddddbebbacccbbbbcbeaaedeecbddcedddebdddbebdaaeaacaedccaddadebeaacdeaecdcccdebeadaeccecbdcbbecbcdaabbccbdaeecceedaeeacaaacdbcbbdebdccadcadedeededcddbbdeadeaeeecdabaebaeccecbeededccecbceacadaacaaebdcdaecebebbebabcadabeebdacbeebadacaecbddbecbeaccaaaeebbcadbddcdbcebdccebebdccddedcdeceaebabeadbbdbbdebdbaecbbcecebabeedeaaebcaddebeedebecdaeaeceedbdebdabeeaedceedacaaaceeeccecbcacdbcbbbcddbebaebeabededdabebdddebcaeebecbeececcecbcbebdaeeaeceedbccdaabbebecbeeaacaedccceedcecdaaadcddceabceccbeecdcdcbbaaaaaaccccecdbdacbbbdbcdeddbdeddcdcdacddeadcedaabcabcbbbbdceaeecbddcdeeebeddeacabcccaedceecacacadaebdcceceeeebccdecebddaceaedaddcebdbcabccbebcdebebdccbaeceedeebeebaaeedbeadbcebbceeebecebeadebecbeaedebebdddccccabbcabdeccebeacaeceabaacddaeeeeedecacaecaebdbeeaeacecdbdddbdddadeaacbbcececbacebccdbaacadaadabdcebdedeaaaeebbdbbdbdecbddcddabeedceeebdedbddbcabdcadeddeccbbdebabcbdacabacebbeeabaecbedcdbdcedeccddeeaddadeeabeebacccceddeadeeaebbccbbdcdcdeaebadbaeeacaeebebcbcbbbddbeecdbcbabacdbaeadceccabbadaddacadebcddbeadcbcdcbbbdcdadbadcadbcacdacbadeadddcceeacadcdaacbdadbcdeacbdabacabcaddabacedaaeabcddddadbebdebddaaaeebeebdccdccdcddaeaeccebbdebccddcaadeddbcbeaeeedeaecebeddddebeeebcababddeabbbaebbcdcceceaebcddcaeabeadbbbccdecebabeeeacadaceebbddaadedddacaedacbddeaecadadddaaacadccaebeeeebddcabcddedbdcdadddabaadadaccaeeeccdddbabaacedeecddeebeacdadeeaacbacaaabeebabaadddecbabdbbebeebaaccbccccbdcedbbecadcdacaccbbdedbecaedebaddcdadebbdebceccbbddcbaaacdaabdccadeebbeadbecdeddabddaeaecacccedcdcbeaecddcdadadbcbaeecccddadcadaacaaddbabcececdedbaadcdacccdbbccedbceddbdceaaebbccbcccbabdbcdedccbeccabbdcaadacbbdebcabdbacbbaddcaccacbeccdcdccccbaababbcdeeacbbecdcbcaddeeceabdeecccebcdaedacbbebedeecdeebebaccbaeedcceccbadbdcaaeaeeecbcedecbcacebdacabcbedbddeabeceedbebeebcdcbccaaebaadeccdbdcddeddcbecaeeccbbaeabeedbbeceeddeaabdeebbedcccbaebbcaebcdeccabbabddabebebccbbdeedcaaccbaeabaacbcbddbddaabcaecacdbacbbdacddaabbabdccbbbdebcbbbcbcebceecbadabeededaeceaacdedeadbceeceebacbcccccaeaaecbeeacaaddcdcbdbcaeaadaecbadbbeebcdddaaecebecebdddcbcaceadcddeeabebcabbaacaaaeabacedacbbbbdaddddbbccdceabaeebddaedeeeddeddbbbecdbebaadbabccdebeddbebdaedaaaebbcbbbcadacaaaabccaeceaebbccaaabebcedabaebccbaaeaaaacacaedcedeaaceebcabcaeeaabdaebaddbbdeabbcaecbdbcbbecaedbbcddeebbaceabceecdbddddeaacbedeecbacddbbeaeccdbabccadbdaacebdccbebeeebecadeeeaeeacbeeceacaaaecbceeeedeceadcabdaedcdedbdddbabeacbdbccaecaaadeacdcbdcbbdbccabedbcaadbbaddeecdeceacabcbaeecaedbdbcbadeeaaeaaddcbbabadeeaaacabaebcdcadaaeeedacadbcdabbadecaecdecbbdbecebedeccacebeaceaeaddabcbddacaaaacddaadabccdbdbebebcbcbeebacbedbbedabeddccbdbbeacaeacbaccaccabacbbadedecdeebeeaaddccbdcbbeebbccdcbdebaeddddabeeeeadeadbbeaccbccaeaccaebcddccbeabbdccbdbbcbcbaacdbaceabdabcdaecdddbdbecadaeaeecbbebebeaedabdecbbbbcedabbdcceabbdcaedeebbaebcadeddabadddccceeccaedcaaecbeaaadbebadecebbacacbeceeacdaeedcdadaccebddccaacbabbdcdabcbecabcaaeedacdbcddceaaddcaedbeeccadddedbcbacebecbedceedcdaeaebccdabccddadcdaeceacdacadacedddbdbcbcaebaecaebaceaebdecabdaacbecdadecaeadadeccdaeaeedbaaecbcccedbcbcebcacbaecedeebacbbdedcedbadcbbdbcbbbaacdaccbecdeedddeccbaaeecbceaebbccecccbddeadcaddabdaeccbcddedeacebdcbaddcabbedcccdaceedabdacbbeeddebadbdcbceadedcddabbaeadaddddaecbdadccbdbbdaaadaeaebdeededacababdeaacbebccabaddaedbcbcbbdddebddaebcebebdaeebaceebdabbbdbabdaedcdcaedbddcacaecddbeecdccaddeaadacdaeedeceaededbcedcddeaadcabcabbdabdaaacdabdbedaabeddecbaaaedbcccaedbedebaccbbcbccddbabaabbeaedaacccbdecdcbcdacdaaeccecaceeebddeddabcdcececccabeaedcededdbcadadeecceddabdeebabddecdededbeadcebccabbbabebacdeccddcebcdcaabaaccceeeadcbecdedceadeddeadbadeeeaebeaddbcabbbdcecbbaacadaeecdbedeadeeabdcedeabacebeadbacdeabedaadabeedeabedaeddedabdbbdbddbaeedcceaecabddebacbddbdadedaceaadedcebcedaeeeacedbeaacccaeaeecebbccdbddeebdcdeedcdcbcbbbdcecebaacddbbaaadbbaaecedecbdcabcbacdbcbbccbdeddbecedabbaeeadbedbaaaebbccbebebbddbbabdaebcadcaddcceceebabaeabdbadebcedeecabbdaedeacabaabaeededaadedacaeabbddaeaaacabceaabeeecbcbadeededeceacadbaccacddabedbdabdeaeaccbccdbaaeebddaedabdbdcebcaeadabaaececcecbdcebdecaecdececbeadaebadbaeaeaebdebacbecdbedeeababeccbdccedbeeaeadbbbbdbecedcbacacbdbddcdadceedecbcbabdaacbbdcaddaadeeaadaddeadeabdddbdeaedcbcecdcdbcbbbdacaedaaddbcdcbececbcdabeaecbdddbcadbceebaecaacbbaedbaeddeecdeeeabecdddadaecabeddebacaaddbdeccdecbccebdcabcecadecdbaddccaacdcaddccbaaaedbbacacebdddcedaadedaccabebcddaababadaeeecaaaecbedacadddacceababdbbabedcededaedbbabbeccdaaedebebceaebddecccdeceddccbcccedeceaddcdabdccabbddccdbbdcbdcceedbaacaebacddacedcabdccbbdaeccdacbccadddeeabbbecbdebadaccacedeebdbdcedadebbcbaadbcbadaadbaaeeecacccabcccdbabaabddaeacaecbccdbcecaacdcdadacecaaeaebeccdbcabbadbcaadcdbbeaebadcabdcdacadedbbadbadcaacdceddbbebcbdcebadecaacaaaeaadbdcdbbadcdedbcbccccbeadabaadaceddaeeaecbddedbebaaeaeaccabaadcdcbadebadceebdddadadddaacbeeebcbccecdeedbdaecccaadecaadaabecdbaeceeeebedcaaacdeebedadaecebdabcdddceeebbbcbcbaaadeeabeecbeaeaedbcdceddabacabbbeedcdcccbbbcedcadecedcadedeaacdccaeaaadaaeeacaacbadcbbabababbabeaceecabebdadbabcbcaccceabceaededdeeccdcbdeccbcbdccdbcabadbdcbddadbebbabbdecadcceacccdaccadbcaebbecbdaaacedaccedcaebcbcaeaaadcadcadcdedbacbddaabebadccaacbacabceeebedcbbdebdeedacddaeabcebabaedbbdeabaeadabaddeebbeecbddbbadbeaebbbcbeaddceebcdaebcecdbcceabaedaebabaeeeadcaddcccdbcaeaedcccceaabbddaecadeadacadabccababbbebcdceaaadbddbbaccbaebcebdbccadaecabcdecaedbebaccabceeaeadcebccabbeecadedcbeeaacbddcbdadaaeeeebdbabcdbbacdbcdbdedcabaeebcdcbceabddacdceeeeebcaceeabbbaedacbeadbbedacaaedabcedabedbdbeebaaeababbcdbaebabbbdeeddbceaccdaccacecbcaededeababbabeaaebaceabdddacdacdbdeebbdedabaacaecaccbaaddadcdbabccdabbeaadabcbeebbaccdbacebcabbdcaddedaedadbdbaebcaaeaabdecdcaeecadbcacbcdbcceceeebaecdaadaaaeedeceaddcdadbbddbdbadeccaecbaeccadddcdcbccbcbaeccadcbdacbdecddccddaaeadcbeceeadedeaeeabddcdbdacaaadaecabcaeceeaaeabeebcaacadecdecadccaeabccaabbeeabbbbbaadddbeacbdeeceaaacabdaabeaacbcedbbeedddccbdebcaceecddcabddcbccacaecabbedccbaccbeccacbbeacbbcbdeccabeaebbcabbbdbacaeaaadeaaaecccadbcbaddaccdbcadcdaaeeddccdcddceacdecdbbeeceababecddedaebbaeebacbbddcbbebeadbedbdcdcbcacebbbbcaadeecaacbadecaaeddddbeaccbdeeedacbbebeadcaadecabeacadabadbeeaacdbbaabadecbedddbcabdbebccaddeeeacbcdaaaeeeddabbdbbbccdaedbeddbeacaddeeecdbbbccbcdaaebabbdbcbeecbcecacbeebbceebdceddeedbccddaaccaacdccabbadabcdeedcededbadaabaeadbbdaecaaebdceebaacebbabdaeeceeeaadbddbbcddcaaabdceaaeceebecdcaeabccdddeacaedcddeeabedcddaccebcbbedaadbcaedbeddbbbbaeaddcebdbedeaaeaeebcacedbbabadceccbaeaedeaedabaeccabeebbeccbbbcbebedececcbebadacecadddcbbbbddedbaedeacbebceeeadddccdaebbdeceeacccadcbdacbbcbddceabeabbddcceddcaabacbccbdbcbddcbecbceddbadbedccbaededaebcdbbbdddedaebedbacaeabcacdaadcedccdedabeaabebcccbcdecdedbbdebecbcaaeaeeeebbbacedacccedeebcdecbadcccdbaeacdacecccbecadcbcedcdaeeddbdeadbaadbabeabbabccedbcedbcbddbaeebbedbdbbcbaeedebbddeccccdeccbedbceadecdcadbacbacddccaeabbceacbebebbbabaaacdadbabeccdbdcbbbedababacbdccaddaebbbdeeedbdcacbaedeccaabceecbdacdbbcbbdecbbbeaddaedbccceceaabcceebbcaaecddeacbcabdadeadcdcdddbdaddbcbdeaabdcdeeedaabecadacaaddcbcedbcdbceabcbbdcccaccebdcbaabeceeabdeaddeccdebbbebaddbbcadbcacdccecaeebbcdcdcebcbabadcebededcbbaccccdccbbaecabcdaeeaaddebeabbdbcdededcceaabecbdaebeaeeadbcdbaadecaabbebeacddaceeadbbdbceeddbebaeecdbcbdbbdabdaeeddccabaececccebededaebdeedceeeeebceebecacabccadedabeabcecacdaaebabeacddaaabacbbbaaeaededeaaeceaabebabbbcbbcedbdbbdedbbbbcbbdabdddcabadbdcabebbcdebbabadacadddbeecaecaeaeabcceaaadcdcaeddbedeaaaebbbdbeedbcedaccdebeecacebebacdbaeacbeacebbbadeecedbccdeedbcbbbdcecadcccabadcdccabeadaeabbbdebdaaababbccddddedcacccdccddaddbaeabcacbbdcadeeebdadacebadaddbaacaccdbcdeadaacdadaaedadedbdededdeceabcccbedbbaeaccdaaccacadabeebaddebeeacbecceccabcdeacaacbeeaeaeecbddcddbadccdabdbeaabadaaaacbbcacebbbbbbedccccdedbbcbecadbeccedabdabeecddcddcdadaddacbdeabadbcecdadcebaceaaacadeebedeacadecbaeecaebcaeebdacbbedbacdecdceadbceecadcbeccbceadebaadebaabcbebbddeebcabccacbeebccbbaeccabdaaaecddeacccceabbececbdacbbedaacbbdbcbcdebaccecdaecedaceadedbaaedaacacedcbddbebdaacaebbacdedeabbdecddaddbebddaababacdcccacacedbabdbbabacdbabbdeddaadcbcdbdedaabeeadccabaaabccbedacdbbcaeccecbadbacccdbcbeebbeebadcbccedbbaecacaedcdadaaabebaebddcaedebedebdebbceeadbcaedadbdecabddeababebdcabeeacbeeaabcbdbcbbceceadaeabaeacbceaaeaeaacdcbebbcbeeddcdeebadccaedbeaeeabdabcaaebccdacadadedabacbccbbdcbcdbdcbdecbebbebbbaeeacacdbdadddecceabebbcbeddbdcbabeaedeaaeadbaccdcccbdecedeedeabadcbccebbcdecbbbcbbddbbcaedeaedadcebcecbbeaebdebdaceaccccedceeddedbeacadbcdeabedcaaaaeaaadaeccdbbbbdeddceacdcedaddddecabadbbaedcacbcbecececbdbacbecbaedccadbebdcaedceaabaccbeaebaedccedebdbbadbbaaaddbdeacdddaaacccacacbdebecbbeeecbeaaecedcedcdaeccdedbcabcccacdaeedbaaabecccbddbcedbdbdedceedbbbdbebeaebcabeceaaaadaacccabcbdedddcaebbbbceddedacedbecdedceeedddabcaeecaedaabcabcaabcccabcdebeabdcdcdcbacbbcaddcebdebceadbcedacadcbcbdcbbacecbbcbabdabebdbebaeedbabbbcdceddabdbabbbdecdcdaeacbacaedecaacaaebbbcabdcebbdaabaaaebdbacbbdacceabbeeeedaddbceeecdeaddbbacbcedaedadcdaacccdeadacaaeedccbeebacecccbcddaddecaeacccbccbbcebeaedbebedbbbcebdcaadeceacccbbaeebebaeacdbcceceabedaaedeabdbaddaeabdcededccbbcebbbebbbbceceedaadbeeebcabbbeabecbeeeebebbeabedaabcedcceadbbebcebbdeaddcedcbbbabacaedddddbadaceaecbbccdedaaecdbaacebddadcadaeedaaedacdacdeabeaddbbbbceaadaaebcdededbacedbedadbbeddceccdadabeacaabeaeabbcbdbbddedadebdacdadddeeddcbecaceeedddaeeadccdddadebbeabcdecebdadcebeccbddcbbbdbedcaacbcedbecdedeabbebbaaecdabcebcddbeeacdeadacedcdcbabacebeacabeadeecdddacdacedecddccdceecedaecdebbccaaeeadaabbcabddeabaedcedacbcbecedceaebcacbdeddacedbddbadcebedabaaceadcedacdcaadebbdaaeeabeeedecccdaeeddddccbbbdeeabceaadaebaacbcababccbdeecabedcedcebbbacbaabaabbbcccebcecbeddbaebcacedadaaedabccadddbabddbecbbacaabdcbcbcabbeeeedaaaabdcaaeddaaeddcdebedeeabcedeadedacaebcbebdecccbbbdbbcddcdcacccbbddababcdcaeabaacaaacecbadeaddebcbdcbdbcbbaceadbdeacecadddbddbcadbeadeabbaebabaddebeaebcadceeaeaacbdddccdecbceccbdebcedbbeabcaacaacebaaabebbacbeccaaadbddeeacccceabcdacdbadcedcbeabcdbabdeccaedacbbcaaebbcdcacbdcdeccaaadaccdbdbaccaebdcacceceeaaaaceddecdececbdddedcaaadebaaddebbbecdaceeeceaacccdaeecdacedbdbbcacaabbaddbbcddbdeceddadeaacdcdbebedbcceecbeaaeababecbcbcdcbcccecdeeadbacbbaeebaeecddaaecccceecabcedecddbeeddacacacdcabaecabcaaeeabeeebadaeacdeaaddcddccdaedcceeeaebdaaccaeceedaaaadcacdcdcdeaecdadeebdcebebbdeeaccebeadacabadcbaeeeaeddadcadabcdcaacdcbeeabbdbbdadbeddcbdbcebaceccdbeecdedbebbbbdacaceeceddaececbbdeeaceaceebadcabcdcbbabdccabedaceeadadbaceaaceebbcdaeeadcecbbdceebbaadededeeaabbdecbaebeccdceeaabdcdacebceaebdcbbdcbaabcdddccedbaebdbbadaeeddabbdeceeabbcabbaeadadcbbdcbadaccacaaceddedbaaabcaaccbccbecadbcaecbdedaabcbdddaeedcccabaeaeabeccbdcadcbbbddedddbdbcbdcebdbadaeebdeedecdedaebeeaccaacdddbcabececebecdbaeecadeedbeababeecedaeeadaeaacaaabecabecdddcbdbcdccabccbaaddccddbeadcabdbbedaebcabaaaaebabedaaecabdbecacadcbdbddbccaeebcebeeeabddbdccacecbbecacbcdeacdacdddcbdaebeabbadbdecddecbbeabebccdcbeaabadbeebaaabcaaaeeddbcccaaeeeeceeedeaaedbcddcdebabababeaedbdbddddaabcdcdbabbeeadeeddedaadebaecbcbcbebadbadaddeceddbbebeebebcaeccedacdbdbdabcbccaaebaacedbdbedbbbcabaedecddabbbdeddabcbbeddacedaecceadebaabbddeaebdacbacacecdccacbbedcebeeaacbbdeceaaedcebabaecaeeaecbceaeebebdacdccbdeaebebdcbdbbcccbbdbcbcdbcdecedbbbaaadcebcaaddaccdbdccbedacbaedbbacceeeebddccdbdbceeacaecdddcebeaaabcbebacccacbbdccbdecebaeadaeebadbbdceaebcebccaebaeecbeddcaabeaaaebcbbbceebbbceaaeabccbbcddaadbebacaddaebcbcaeacceabaaabdbcacbdaeeaeddbcdeacebbedaddceddabccebbbcbadbaddceeddddabbaadbebbeaaddabcbcdeaebdbdecadadaceccacbacdedbeccceccdbccdceaceebdeaadeccdadabaaaeeabbadcdebccebcbdbceabaaceeecddcbedaedadcdacedadccacbcebcccabdbcbebeedacbebebaedaaeebeebccbbbbbceedeaecabeeedbccecaeacbcdebaeddaedcbdddebadbbcbabbdeceebadccdadedbdacecedaeaeabcabcabbaeaabdcabebabbcdeaaeebdabcbcbaedeebbcdddacdeeddacdcecbaeedeeeacdaeaaebaaebdbeeeecbbadadeebaadbbabacdccdddbaeacdaecaacbabbcbaeaeeededaaddaeceecbdaadacecbcecaedbdaaacebcbcdcecabbdaeceedabecdebabcdbeabdbbdbaeaceccdbabcceabcabebbdbddaeebcddbcadadebebdcadaceaaacebcecbeccccdedcecdeaddaaececcebedacbedcdbddbeceacaeaeebaeecdaeccbddeeebebeedeaaccceabddbddaabaadaeeebdbbebaacbedecaebbecedddaddeeebebdeacbeeaebccdcedcbdcccedaecdbbcabcbeabddcaaaaeeebeadedbbccaeebbceadccbdebdadbdabecaeadaadccaadaecacdcedccedaebecededbacccdcecddaedbaacdebbbcddcadbdaadeaddbddbecadcaaddacebaaeacceccaeaebcbbddddaedcccacacaaebbabeabecadcabbccbddcaeeedeccbbccbbdeedcddaebdcdbaacabdbecdcbcbeebeaeedecabbbdccdeccdebbbccabdbdcbecbeaaeddcacddebedcbebbececdeceeeebebccbdacebacbbcecceeeeabacceaaccdeaaaceeaebcddaaaccedcadecebaccaccadcbeabdbabebebccededeaeabceccedbdeeacceadaccbeccbacbdaadeaaddeededbedbeabeeedcdbbabeebbaebaabbccebaaacdeeacebbeaececcadcbeaceccbeebceeaedbedbaebbcbabcebacdcdacdedbeacbdeebceaadcabdaaabeaeadcaecdeedcbdbbcdaeeabccdeaebadcdadaeeeedabdaeaaadaedbaddcdcaabbdbceddbceedaaceaacacaebbabbabdcedabececcacbabcdaeedbbeedadbeedaccadccdddabbbccecbdeeccdaacadaaedccbbdbacacbddeceedbdbdadbbeaebeacbecebaaaacaedacdeaacadbddbcacceaebacaebccdcadeedaaadcdddaaedebdebaacddabadbebdecacebbeddcdedcdcdcaeceecbeaceccebcacbeddbdbeaaeeeacbbbcdcaaabddaedcacbecbdecdddeeceaabbdeaebaeebbeaedadbdcaaddcbdcaabaaddcedbbabbcdcecaeedbcbdbdcadebecdcbdbeaeaebbadabbacaacabbeedddecaccdedbebbabeaecdccccdaacbcbbddbabcedecbdeedbdbbedaebdeddbeacaebebaacbbccdaecbdcbebaadcbbebbaaacdbdabdeadacceebcbabddedbaccaddadabcceeaecccdbcbabeebebbddaaceecdacdddeaeebcedadebaaaaddadceeeaaacddecdacbccaceacdabbbbaccebcdaeeaebddbcdacdeecdbbadceeccebcaaccdccbcbddbadaacbaaedebacececbbbdecbbdebddcecacbcdaadcdedaebdadaeeeecddccdcacbbeabdacacbabecaacedacddeedddaecadbaedcaabbadecdadcdaaeebccecceeeaecaeecdddccaadbdcccedabddceedcddbcaadddcbceadbacebdecccbaaabcedcccabbecccdabecdabaebdabbdaadeecacabcbabdacbcadcbcadaabbdebacceddbcaedccebcacdacdeddeabbbaacbbdeeeaeedbcbbaedccaedecdddaebaddcdecddadbcebdcaadccdcbbbbabacccbeddabaaeecccecabeeeeaebedeaceeaaabcccaebbecacccaeacabcbddecdbcdcbacbdedebcceebcdccaeecacadaeddeedcebcdbadcbcbdcbbcbdbdaebaacdcecaaeedaabecbdcedcdadbbcdaedcadecaeacdbecdaeceaddaecceaedbebbdcbabcecbbaabadabcaaecaddbbabebadcaeeeededdbbebdadbacddbeabdacddceaebedebaaecebcdbedcecbcbbbcccddedaebeacadaadebbbeabbaebcceebdeadcbadaccdceaebcecdaccedbaaaadceabaaeabddccaabbaecdeeccaeccdaebadbeacadaedbbeacaaeaaeaacbddacedbdedbbdeadadbecbcccdbcdddbbedacdcbddcaeeacbacabbbcabebabdebddedbcadaababeeceedadedbeeceaeeacaeddbdedaaecbdbdeaceadbdcecaebccceeebabcabcaaaaceaccadaebbdadcdbaecabccbdadbbadeeaccbcdceddaadaceaedaeeeeeddecabbccdedddacebdacecdeceeabcbcadebddcaeeeeacddacedbebeaecccebececaabbdeabacccecbeedbedaecbbcddcaabbaccbdadcbaeddbbabacdedadeeedadcddaaeeeebcddcdbcbaadbceeadbaaadecdcaebbaaebeaebacaeedeaabebacdccacbaaeaadebcecdcdebeaabcbaebdecbeaeabedabcebaecebbcbdadebdebedcedaddeaeabebdecbdceaededaccaddcbcceecaeebbacbaccdabecabbdabebcdecbbbbdbdedccbbcbbbebcdbdddcaabcabdcdddbebaaebbabeaeadcdebcabddebbeeebacbccbcdeedcaccdbbddabbbeebccdbbebadbbecdbccbabdeeebebcdadedebaabedddbeaeacabaccabaccadceaccbebdceeeccaaddecabbdacbaaeabaddcdedcdeabedaeeabacdeebdecacecbabdddbebddcabddcbecdeaccdaeaebdcaabddaceadadeeebcecddeacacccbbcceeaacdcacceccbdaeaddacdedddeedcddeaeddeccdecdcacbebbdddadcabccaacdcddabddecdbcdaccddcedebcccaedcaeeedccdeccecbaaeadbbdabdcdeabddcaaabbbbcceaabccaccebecbadecceaabbecdeceebcbcaedccacccdecbcebbbcacddbecaabdadaaddededdeaeccbaecacbccceceacbbbccceaeeaabcabecbedebaebddabcbaeccadebeeabcecdeadaedccbbbbbdeadccecbbacebaceaecadaadeeecaabcebccdaddaebeedbaecddcebcbbdecdddaeaceebbeccececbddebcabbcdadbedebebaebcadbcbeaaebedecdcdddedcaadeeaaeaeedcdddeecaaddebebaddedcaecbcbaadacbeabcbdaeaedcdedcaecbabebebadcebebcbeceedeaaeadeccdcabadddacededbebdecedccabcbbccbddcecabdbdbeeaebbceabaecdedadbdaeccdccccbcbdebdccbabbacbceeeccbeacaacaedbadbeccadaeacbecbadadeecaebcddbbacadecbbbdceeeebeeaeddaceeaacaadbacecaeebacececdbdcaaeedbadebddbcaecceceacbeeecbcabeabaaaaedbdcadbbeaecaebeeaeaadadeeadcaebdddccaecbebeccdcadcabaeccebbbceedddeeebcdeccbccebbdabcaabedcaeacabedbcadbddaaadedbcaecdabdbdacedeaacebdcaccdcaeccbacddbabbeaaecadccddebdcacacbadaddcadebbeddadabeaedcbdadedebceecdcadaedeaedbaadabbddacbeeaadbadcaecccdabeaabcdadeedbbcdbbebacccddcacbacdcceebdcbbddeaedbeaddccebcdebcdbbdbecdecbdbedeabdbaecbbacdedccacbdeeacaaaadebaacdedccacdaceadcaeceaeddbbdeceaabeebddbdcceacbcdeaedcbbbcdcedaaacbeddedccecdcbcbabbdcadbdaaccbeebedaeaebdeeecbeacddabbddbbadcaebdecccceaccecdcdccadeeadcecdcacaeaaebbacdedeaabcdbdccebabbcdbcdbcbddbaabdcacdaedaeaaabeaebebacccbdeabdcceededddacbdceccecedbecedbedcbacbecedeadcaaedbaecadaadcbeecdcdcdecdecebcdbeaeebecdebbcaccacdceeabdecdcdcecbdeedcacdcebbcdebeeabbdaddeaaddcbbcaddbbacbeddcbcadaaececbedecabacaceccbcddbdaedcbdeacbccbdadebdceccbdbaaabcdaacddeebdedcbcbadddeeadedcdbccedaceebedbdecacbaacedcddacceeadabadadbebaccdcecdaebeeaeabadaceeaaddaeebdbbdacddabbbacdcbcacbeababaebddcaeeeebbddbadaedbeabcddadceaecedbcdbcaccbcdabdbaedbdbecbcbacdeeeabedbcebbcbbaeeceedeabccecdedebcaaadeacbacecabbddbbebbdeaedbdcbcadaabddbcdbcbeeececdbaedebbcedacecacdbaeceaadadacbecedadbadcacceecbdcadacdbcbecdeabcbacaadebddcadaadccbabccadebdcaadbabededdedbdeacaceedcaeabaecadadebededadeaaadbacbdbeacabeadecdcceedcadaaecbecadebddcbaacdcdbaceeccebbbbeaebcdaeeaaaeccadabeebdaccbabebcdaacdeeccababddcededccceeeaeecaebabbdccdbdeebaadbcebcddebaaadabababbeadebccddbcebeaedbdcedcbbddaeeceadaceadccedabdedeebaeedcdecbdcbecebddeadedebdcdedbeacdeaebbddeeeeeecebceacdaecedaebcdbaeddceeeebdadaedccdecadaebabccadddacdaaadbaaeacaebeaeeaeebddecceeceaaaceadcedbbceebaceeeadddadecddacaebecedbebdacdadaaddabdcdceecdcaaabbeeaebbecaecadeadebdbdeacccceadeaaebadeadaddbbbcabbedbbcecabdddabeadbcabcabdabdacabaecceeababbdabceecdbcaaccbbbbbcabdedacaeeeaabbbaaeadedddeccacbaddbeadbaceedadbdadbbbadcdbcdddebededbcccaacbcbbbbdcbdcceeccecdecccaabedeeaedcaeaebaaabeeedbddacaebdbbdacebcdcbdeebddcadbabcaddceedabaedeacebbeecdcdeaaccbedeaecdbbbaadadcaecadaaadeaacdbecebadbeaaebeaaabedebaeaecebdbdddaddeacdccdcbaeabdeccebaaccaaabaccdddacabbbaceeebaabecacadccccdcbcdabecdaedbdcbbaddbaaedcaaceccebbacaedcbbabceccaaeebaedaedcdbecacddabcdaabbcaaabaabcdeabdedaacdddcbdedecbcadcdcdaaebecaecdecbccbecabedaccecacacaacaeaccbebbdeedcdecccadcaabbbbbeaeebcdcdbebbadbbdaeadabbebbccebbccbdbddcededbadcceadbadeeebceaaedbddeddbddbbcdddeecdbedcddcdadebbdaebddaeddddbdbedaaadedcacdcbebccbaedddceeebbdbbbbeeceeaddedbdcbcdadedeebeddebcaecbeebcecedcdeebceabebeaddcdcbbbaddbbcbedbedabdcdbbcadcbeabbadadeeaedbceaabbedbeccdebcebecaeebcbdcbbcddddcbbeecbabdcccdbdccababcabdcedbeddbcebccbcceeccabbbbedddecaaaddbcadebebecaddbbeebaabceabceeecdbedbdabcdabadaabdeceabebbbebadcaaaccdacaabaaecaabeececbadbbbcbebabebbacdedecdcebdbebcbeccbacaabeabbeedeabdebebdebacadacacecbdccdebcbaeecaadbedadaebbbddccceaebbcbbeecdedcedbebbdbdabcddcddcecdacebcbcdaeaaaeadadeddeaaeceeebbcaeaeeaccbcbdddabeabbaeeeabcbceaeedecdddeaebedabdcdcecaacbdaacedcebddacaacbdaceabedbedbabbccccbacdedcbdaeeebedeebbcabacaebaabdcebbaaddddccdedbcceddabacdcaeabccebadebacdbdbcaecebbacdbedcebbddcdecebcedcadccbdddeadbceeacedcbcbecdcaaebbacdccbdeabdccbdddcadaaabdeeeccdbbebdbcbdcecbbdaeaeecbabededcebbeceaaebccbaeeeaecaabcccbcbdeaedcbcbaddeecebeedbddaecebcedbbbabbabeaceabaaabbdaecdebeedebbaebbcceaabacabbadcebbdcdedddcceceaabaecbadbcbcaaabeccbbbdabeedbeacdadaadacebceadbaccdccbbdebbebbeaaeeeaaedbbecaeedecdecbadbbdacdcebacddecdeddebebaddbeacdcdaeebcdaddbdbbaedaaaecacacaceadbdadaeebdaabdaceddcedbdbceccddddbabebdcbadadebacdddadbcaacdbbcebacbcdecbdccccdadbaedcecbebaceadaccbebbbbedbecdbdccadcdabebbeeeecabceaccbadcedcaabbecbedcaacbcecdeabbaaccdccaaadededbbaadcbdabcdbcdcabedeacabdaceebdddecabebddedaadbdaabdaecaabcbdccecaedbccdabceaeeecddbdbdeadebeaaebdbedbaedcbdaccdbacdcdecdaaadcdcdcabbbcbdeeebbaacbbbcdeadbdbbacdbcccbdadeecbabccbecabdcecedbbaddbbceaddbdaeaddbbeaaadbeaddaccaabcadbbdccbeeedddebecddddbcaceaaddbeeeadccebcbcecccddaecabedecaeedcdcadcaebdacdbacddcaadceebaaabdbedcadbabeecdecbaccbedaeabdcccecceadcebbeecbacdcdbaeabacbdadcdbedbabedececedeeadaeaeadcaebceeebeabdeeabdbceddbeccbebbbcaeecddcbbbabddeccccddcaddacbbacdddbbbedecaccaecdaecabbcdadebadaddcaccbeedbddbcbdeeaccbbbdabdeabeadceddbecdcccdadaccabbbedcbabeeecdcddddecebeaddecbbadcabdbcaecdddbcecebcdebcaeceaebabaedcddaaaaecdabcdbbabbdedaacaaccacecdaccaaeacaaddadbabdcadadcacddedeacededdaeecbbeecadaacdcbcadbebaaebabaacdccbcbbbccaaaccbcaeabecddbddbedaeabddbabdebdbbecdaddccdabeccdcdddeeadcbdecadddaeedcccdcddeacbeddbedacbaabecceabdadadaebdadededbeceeecedabeaaebbbeddbbacaceeeebdbadaeeccbbecdcbdbccccbebdacebeeeaacdaaeeaecdbcdcceeaacabdadabecdabdbabdbceaabbedcabebcaababcaeecdbebccedaebecbabcbdbbcdbedcedcebebdeabcbabebacdbbadeeddcdedccadcdccdeccdeadcddaabdeaddeddaadcbadcceeeddbbeceecbadbaabdbebadcaadedcbbedceddaaddddebcaabdacaacacddcbbedaebaeaaecbbccaaaebeaddcedeeecceacadcccaabdddabdaeeddeedeaecbecbccbbeeeacddcaceeacedbddaaeeeeddcdcbaeadedcedadaeeabedeaaedaabdebeaacbcdebaeaeaadcdaaccbdcdbcabdeeaaaecaeabbedcedcbcddaecdcedcccebdabdbabcddcbeedcecddaedbacdabeddddabbbaaceaabaceaebaadcadbaacaaeccbbacacdbbdedcadaabdcbeddcdbcacbcbabddacababddaedaddacccdcbbedebeccbaacdaceeeebacccecdbbadabcdbabcccaccbeeeceddbebbbabebdceabaeaaacddeedeeccdaaadbaedcdbcaaeeddbeedeebadcebbaebdbaebbbddcaaacabdddecaabadaeaeedcacdcbcddbaddcebbeeddcaaaadcaabdbbbabdebceadebbaabdcaceaeeedceadadbbdeaaadeaecbadcecdacddaddcbaaadbcdbdcbeedddddacaccceaaaadcbddbcbbcbceaeeccabccdeacbcaeebaebddcadedbbcabbebbbdbbadcbbebddbdbbdeaaccaecabdaaceeabaabbaccbeaaaeebaedebacaceabcadbdeeaebdebbdcdeaddcdbddbdacebdedeccbeadbaeecaabcccecccadbeaeddeaeebcccccaaacebbeeeddeecdccdcbccaedeebdcecbccaadecdcbcccbbbcedaeddbaadcadbceeacbadeeeaceedeaaedbbebabccaabacdcbdcebeebcdbbeaeaccdeececacdcaaadeeccbcebaacadbcdcedcadbaeabeeeebdcaeacaeaededdeaccbceeecaebbbcdbdeabacaeccbadcdaebbdeacebebbaacaeabbadaeaceaaeadaedcdccaaecddeadeddabaddadbbebddccbedaebadeceeaceabeecdcebdaaededceccaeedaddaabeadeaaccebadddedbedaadbaccebeddbabbaaeebeeddecebdebebadbbbadecbeadebcddbbccacaedddecbacdbceccdbdacbbbadeaeacbaaabebaebbacaebdbabdbacbcdbecbaebbdecddbedadadccbdaccebadeeecbbeccdebccbebeeacababdbeddaeebedaebbceabccdaccadbdcabbdaaaccceacccbcecdedecabcdebcadcdebedaceedbedabaecacddbddbdbacdbbadccbcaccdcdccbdedcdaaeadeeeedbbdaacedcbbadbccbadcabedeaacaecedeccabadacdeeaaceeeeaedaabddaebcbbadebbadcaeabcbeceddebaabbeeeecbbdceecbaabcaaedebdeaaabadbdabedaeaecdadeeadadcbdccceecbdbdedebeeedceaceddbabddcaccedbeccbbabbeacccdabbecceceedbcdcceebadbdccdcaeddbbbaeaebbaadecdaeebdbcbccbdbeadbaabcabdeaebbecaadebedeaadbcddbbebbaecaceaaddedaeccbacdaeccbddbcbebdcacbeabeccbedaaddabaebcbaeebeabdeeaeedacbcdebeeeebcbbebbbeacdaddebdcbabacaccecbcceadbdccdcdaeeeeddabeeedcacedbeccbcaaecbaaddcbcadbdddbedacadecbcbeecbaabbaecbbdaeacadedaaabcabaebcdebcededaacdecedaebaceddbacbcacceeabcacccdccdbbdedadecbccabddeacadabbabddbcabecbccbdabbbbdbeeabbaccaaddaacdcdbdabbddcbcccecceadbcedbdebbeabcabbcbddebebbdbaebedaacabceedcaeaccaceacaeaecabaaebbcaeaccacadacedabeaeedadbcdadbbceebeececacbaaadbbecedebcbdbbaeceeadaacbbcccaaedabddbaeacbebbceaababaaacecbddeebabedbbabdbacbcdeacdebdcacbaeaecdabadceeabedbaddcaceddacbaabbdaddeaeadcceeabcebecbadccdcccececebebbccccbdebddedaeccbdbbdcdaaacbdccdaaaaccabedbeececedcecdbdeacaecaceabdeabaadcaebbacbecebecbabcaddeacbcdbecdeedccedaedeedacdcbaeadbdceabdbccdeeacdaccdddeaeecdeccdddcbacbecaacebdabceabeeeaabcdbcaaacecbbcbeccadceacbcdddbdeddcbacccbbabdbecceecceaceeacbccecaebaacbccebebabbcbceebcaadbdeaaadecccbacbaacdcecaaabdabbcbeadacadccaaebcbeecbdceebcadaadeebeababadbddcaacabbcaceeebcceadebdcedbdcebddccdcbbbddbbbeceeccabebbaeadedaacebedeaedeccaecbaceaecedcaacbcdeaebceacccddaeacecdcddacbbadbdbdddcbbbbceaadcceacadaeccbeddbbeeceabbccdeebebbcdddaaeeebdbdbdccdabaedeebeceeaaddabaebbeccdbcdebbdeeabaaabbbbaaccdcabdbceecdadaadcbdccaabeccecbddeaacebdabaaddcabdbaeaecacbaaeacaaabcbcabbdbcdaadcebeacaaedbeacaeebaccbabeaebabedddededceedebabecaaeecebbbabcbdddcacbdbbaebdcecccccddcaccbbcdcdadaebebbbcdaebbddaaceaabdabbbedcdbeaebcedabedcabeacbdeacbcbadbddcecaeeecdaaddecdcadbdecbbbdebacdbdbaeabcbeebadeaabddcedcaededadaeadddebecebbcbbeaeddddabddaedecdcdcddbcdeadceadabdaeeaebddcabdeecceedcaddceccbaeeeaacedebaaaaaddcbcbbacadcdccbceddacbaebbdeadbadbcbdbecbdcccbcbabcadcaeacecbadebabdaabbbadacbbebecbbbceeecadcbbdecbcabebaebbadadadbdaaeaeecbacedaadebaceccededeeaeddadbcbceecccbaeccdeaadabaaacaabbedbbbdebbbcaababedceaaddabceceeeccaeadedecaabaecacbdbdcdceebdbeadbebbdcacebbdbbeecaccabbdbcaadaebcaabbbbdbaaebccebbcccbaebedabadeacbddbadbacbdecdcebdabdaededbddaebddaaeadababdadeebcdecdebaeaecbdbbeadeabcceeaebeccadcbaaabcabbbacbecaccddbabdbdeecbebbaccecbeaacdadcbbcbdcdcaceeecbcdccccbecaebccdcdecbceeaccbcbebabdaacbbcccaebdbbcbcccdbaedaedcdadabcebbdddbebbccbdddbccecdebabebddccbcecdddaabcddbbbadccabdaecaabcddcbaedbdaadcccdcbdbbdedcdadeaeaaeebbdddedbccaaebecdbdebcddbbddcbccdccaabdddebeadcaccacaacdccbcabeddacadadcbabdcecdbbeaebaaedaaaaddaedcebceddbcbcdaebedcadccddadbeecbdaeeabdcbaecddeceabbbadebcdaecacbbecaacdceaebccbcebbacbcbcaddabddecadbedbdabacbbccdbdcccdeabecabcccecbdbbcadbbeabcdbdaecedbcbdcedabcaededbcebcaebaaeecbbbceacdaeacecdcbedaeececbcdddccaaccaccdcdcccdacaabcccceccabadecddeeaceccbcacddbedaedeecabdccadacdbaaabdebbabdadecddaeecadeaaddcadcbacbacdccadccecbcaabedeedabdddadbbcbeaaebdeccbcbaeecbcdbbedbaebcceaaaabaabebccbcbdbadbcabbbbdeceebccedecbbaeebadcdcbcdbaedccbcdaeeacbbdadebcaccdbdcaabeadcedccbaebeeaccdeedcddebdbdaeeddebbcbcdbcbaceadcbbbbbdddecbacedcedcedbccabbdecdeeddeaebdcdcecdcdccbdadbecaacbbdeaeddcdbeddaedbadbabeececceabbdaeacbbabdeeeaececbcbabbcdbcebcdbbcdbecbadaaabdceeececbaaccbaaabeacceabdbdccddbeccdbbbeeeccaeddadedcbbeaebdccdedeeeccabbecbccbeccbabcccdbeacdddcddedddcbbcdeddabecacaeccdaaaeeaeaeebbceeeebbeacadabcaadcadeeedddbeabecbcaebbacececdceacacacaababcdbeacaebdccdeceddaeaedadedddcadebbacdddeededadeebbbdccadabaeadccceebbdceabccdcdcaeccceeccbcccccbebbabdddecdbadaebddcbcedcaebdadaeddddcbbbeaaadacecbbcaabbdaecdbcacddcdbebabdecbeeeadbabcadddbadaababebddbdeddcadcaabbecaaadcebecbdadcbadddeacbaecbadaccaabaacbaddceadeebeabbcbacaaaebdcbdeeccecedccaabdabbeaccbeebeaadaedbcddddeddeddecadeeaddcacdaedeeddcaadbabcdeacadcbaddadeebddbccadaaedeabadadbdcddcdecacaebceeceeeabcccbeddebacabbdbacaddbbbbbdcecdbabecaccedabdcbdabacbbeadbecdaaaeceecbccedeeebbddbedeeaddebeadeaceeadabbeeccdbaecaacdeeceaaddadcdabaeecbcaaadbbedeeccdeecacbbbcacdadbacdadbddeebbccbcececaccacddcecabbcbccbeeadbcbaddbbabccebaedadaddaaadddddabccbbeccadbbecacbecbadeceeacbcaceebabdebcedeecacddeaedbacaecedecdaebabbeaeaadacccaaddedbeeebebccacaacdeecbcdaacaaebbedebbadeaeedbdacdabbccdaabbddceaabcbbabbaaabaebaecbdbaaebcccadbcbcbeeadddbedbaaccadaacacdaadddeaddddbcbeaaaeceadadabbcdadcabcebcdcddecaeeabaedaadbdbbbcacdeeecdcbecdaceebaceddbebceeeceebeeececbdaecaeccaeaedeabacdeacdacecdaddbeeeadccddbcebdbdbedeeecaacabeabcbcbaacedcdeeeaaddbdadaddedcbbccaaadadebcaaaadecaecaeaaaaabbbdbaedabdabebedeeaaeeeaacdaeddaaeaaacdbddababbcaebcdbbabccecaabecaadcdcaacccddedbbaeeaeacebabdedaceedebebebedbccaadeabcddaceeeaacdcedaabdcaaeadaecdebbadbaeeaceecbdceaaddeceeaaeaaeccddabaacdbbacbabcaaadeeeeebaeeeeccdcddacadeebabccaedcdedebbabccbdcbcbebaacdedeebdaeebaaababaeeaedeaabbcdaeccebebbdeedbbecdabbcadedbdededcdcbaeeadacdaeeddddeaddbcbcdbaccaebcedadceeaeacdbbadbeacbacbdbcedbaabaeaacaeacaaebabbcadaccbaddaabebddbbdbdcbeeacdababbeadabdcaacdccbeccdddceabbaaaeebbedccabdcdcaacccdbaeaabaedaccdbcccacabaceadeabeaedbbddaaaaacddbadcbeeaadeebbbdacaebbddcbdaddbccddaeebbaddaaccbbceadebebacdddaedbdcacbadeaaadcecdddbbbacedbedddabaadbeedddbeeeabddaaacadaaeeebbddbaedcdaaebbddbdbeebccacbdeccdaeaabdbccedcbecaaeaabaadaacceeeeddbabcaeeeeabddccdedaccbccddceebdbacddeaddccdaacbeeecacaecbceacadccdbdebeaaecbadbcbdadbbbbdaddeabdbadebcccaaeaccedbbebeecdcadadccdeaaccddcbcceacceedbcbeaebbadaedeeeeccbbdcbdddeebedeaababdececcbababcaccbebdeddbeddbadedbddedbdbebbdaeddabebddbabcdbdcbdccdeaededaaedcdbdcabbbebbdbcccbeddbdcebbceecbeecbbdbdcabeddcbadedbaaecddbebdbaebdccbceccabaaeedebaeebadadaedcdbdbddeaaadcaaeadcecbedcedcabaacbaddccbeadabbccccaeeecdccbabdaedcdcbcbdbabeabebbbdbeebebdecbddacaccbedacbebbedccedeaddaeaeabbeddcacdaaddaabcdbddccaabdeacbbcdaeaedcbdecbbdedcaabbbaaacacbbbcbbeabbbcbaeaecbaadbdcacdcdceebdbbbbbadcdacccccaacaddddbcecadbcecdaceeebbeabccabcbddebaedbcdaabddddacaecbdebbbdcebdcabeadeeddbcabddacdadbbbdeeeccbcbebaaadccdebeaabddcddcebdadebbbcedabdeeaadcacaacdacdaccdcdbebbcccbcddecdcaedaebeeaedbbdcadbeabaabeabaccdcadeabddcaabbdadedebbabebdbaacacbaacbcebecababeebdceebbcaaeabeccedcceecdaadbecbaccbadcbbbcdeddaabeddccaecaacaebcaccebddeceacebacccceeabaacdadacdabcadcacacbdbcdaaecbbbcccbebcbcdaacadeecdeccdbeccbcbadddcaadccccecebaadeedbcedaeebbebdcbedcaeacaceaecaaddbddedaaabbeddabdbdebeeaacaeaaeaccdcccabddedcccaaebbaadbabeaeadbcbbaeccccacbedaccebbaaceabeddeabaadccacebcebbebccbbaaeddedbcbcbdecddbdbbdbedbbdaedbcdccbdadbdaeedaabebaecbcbaeacbdeeccbdddabcbeadaddabeddeaaeacbccdacaedbacdacdbecbadcadddddbdeedbcabedecebcdbbbcdcaceabdbbdacbaeacdcbceccdadbdbeeddadecbcbeccedadcbbbeddddcaadddaaadceaeedcacacacbaccdacbdaadcaaaeabebcaadbdceadccdeccadeaecacceedabaeeadcacdadcbdacaeeddcbdeaaeedddaadacaabaeecaedbcbeaaddcaacdebcdcadbdbdcccaaaabcdbcbecbeadeebecddaccdcccedbeebaebbcccaeebabaeebbaadcdddcdbeceeadacceaeaeecabdccdcdaabbeabdedbddacbccceadbdbdabbabaebbccbecdccebbbdaddbacbcabebcaddcdaddbcdebcebdbdbadcabebeebceccdddbdbeaecdedbcccecedbccacabbddadedcaaaedadaadcadeaebeeeeceadaecbbceddbdadaeecdbdbbadadbaeededbbcdabdcbacaddcbcbeeebdeaabdacaaebdaddeeedceecccabceeeecbdcaeacebeaadbbbeceabbeebbaacbdbdcabbdbbdaccceaabeabebddccdcaeacbeeecadcddadbedaecececababbaeacbebebebdbccaeabcbcbceaccbdbbcdaadeeccedbddbcbacbdecaceadddeabaabcdeaecddbdacbbebceccddadabdcdddcabbadbbcaeaeadcbdbdcedbcedecaabccbecedaceddeeebbddebadcabadbaadabebddcadeaabaaebcbacbbabcbaaabaeadeceaeacaebadbdcadacaababdeecdcadbebcacbbceccdccecdbbbbdedbaadeaecedadeddedbacbdecacabddbeaaddbdddccdbaeccdbeaeacdbccadcbeaedbdcddabaecccdbabacebbddbeaaebbcdbdaabedddaeeecaacdabddceadbbddcbdbbaaaeeccebeeedbbcbcbbeecdccbddcddabeeaeaeeaedbbeeceedaedcddadcebccccddccacaadeeecebbdbbdceaadedcbccebcccaacedaeeacebaadcdbdccbdebddbecbecdabcaccbdeeeaaeadbbeaecbbbecbedcdabcebcecaddceeaadaebcadabcccdbceabdebaebddcadeacbeeeacdbbcddcbeccaaacedddbebedcbbbcbecdcbdebdeeacebadbcbeccbaebcecaceceaeddeadcbceededadccdccecccedecdadadcbeeebecaaecadabdbecbdcddeacecdedeabecadadecaabbbacedceadceeeaeacaecebccceeadaaeabcedbbcebabdcbdcbbdabbcbdeaeddcdcaadccdcbdcbccecacceaebabbacdeebddecbacaaebaacdbdadbccedeeebcdaecccebebeaebaedbcceecdccecdcedddacdecccabbdbdeecdaeeceeabeeababbedeedababaeabadadcdddccadebccaecebeadacbeeecdacaedbeacaeeceaddbbeeeaceaddadaccacbebadbebecccbeeddcabeaaecabaeaaadbaedcbcebdeadcadcccdbcccbabacdeecbbddeadbdeebcdcddbcecacbcecbecbacecceccdcebcaadecdccdbaccacadebbdabdcdcbcebcaceeaeebcdaeeebeaceadecaaecadcbcbddbbccbcccccdbceeaabecdabacaebdbbcccbcdaedbaebcdcaedbbaabececabbbccbbcadacdbdeaeeacddabaeaaebaaecddccbaebbabbdcccdeddbeacdebabacbdecaacbcaecababdeaaeeeaaecbacadedabadddcbacceccddbbadcabcadebbcdbeacddcededadbddadbdbdeedddcbccaecadaeaeceadbdcaeebadcbeadeaeeaccbaccedaccbbdeedaaadadeecbdcbabdadbccadcdceabdcdbcabcddaaccdedbecabcaebdbbcecbaddbeedaeeddaeadcceedaaebeadaaeadddacaddecdacacadaaaabceadcdddbdddbddcecbacbeacabceaacadabadebddebddbbcccdadbdadeddaeadbababacdeccaabbcdebccadaeabdcbaaeddebbccaeaaabcaaedadcbbdccdddccabeeecdcacbacdeaecebabcadbccabddabbccbcedeeaeccdacbecbcbdeedceadbabbacabcbcbcbeccbbbddabadacbcaeecbcbeceeedbbbdbadcddecbddaeabbddaaababeacbbdbacbacaaddccecbccaaeeaecabbeceaeceaebabcbdbaddcbcebdebadddbdadecaebeeceddeadbbaaedbebceebeedabededaeacaedcdeebcaaeebeeeabbcaabdbeebccabaebdddaddddceaaecaeebeeebdacdaeedbdecbdccdccbcacabbbcddccacacadecceacbcbadbedbddaedddbebbeeaeedcedddececcbbcbcbbdedeccaaedddebcaaacddaacdeaabbaacdaebaeedabbbbdaeeceacdbdcaeacadcedaccaedadcbdeeadcacacdbbbdceaaabeccbdeaccecdededbbbbcadcadcdddbcedebacbacebdddedebddddabadcadcddbeabeceaccabecacdbbbacdacbbaeadaaecceabdaeacaabdbeeecbbeaebdbebcaaaaaaeeeaccebeabbddadbceeceecedbcccddedebaadbbcdeabdddecadcaeccdeabebeecaeeaccbaabeabeadddeacdbabbbbaceecaceadbbcaeccedecdbeeaceeabdebcdedeadbdecdbbabcabbeddcddaeadbebaedeedabedcdededddaabebbeebaceccdbbaedeabddbaeeaeeabdcbaabcbcaeebceedbddabbaadbeaccdbeedabdecbeabebebedcdbdcdcecadebdcaebbdceeeedbacbaaadcdcbcebcbcacbcaacbbddbcecacdcddaddadededceeedaeadcdcceaaaddcecaebedaaacdaaaeedaaeabceddaeabceadbaeeddedcbdeaeeebbbeabdaddaebeddbdbecacedaedaddebaeddaababdbdecebaededebabbecdbeabadccaecaaccebabedddadadcbdddadaadddababeccdbdcebbdebddadeccebbcbabddbbbdaedaaaddbdabeababcabbbacdebcbdddaebbddaebaeeabdeaaeeeaebbdebddddeedadddcabdeabbdceeeccaabacacacacdedeccbcbcbeabeeebeddebbbbcaebdeeccebadeaecdbdacadcbaaacbaabbdcceaccccdddcdcdcabbedacdebccadbbabaceabecdbbbebddebdccaaecdeddaeccabbdebbcecceddabdaeeadbcbabbbddddcddedebaaedcccabdabececdcbedbadbcdceccbbabbeabababdddbcddedbeddecabeacccaecbcaecbadbcbebeedacdbdcacacecbdedebedacedbbcbcaeeeababcedaceedbaadbddeebabcbddbebdeaedcbdcbcddcbaabaddcacedaeadedcaeddddddaaaedcaadbcdddcdaeebdaebabdbbccdbabcceabeeaebcbdebddebeedcadacdbbbbebccbdbcadabaadaaacadeaebcababceceaaeeeeacddbcadddddeaaadecbabecbabceddcbbdeabbabeedacacaeceeddcbdababeddccbbdbebbdcabcabbcebdacebaeaaceadcceadbcaddccbabcaecdddcaddadedceaecebacaebaedcdbbcaccbededebabeacaabacedeaaccdadaceaaecbaddcbbdbcceedeeaabbeeeebebabbebadeddbebebebcdeaeeccbeabdbeeccbebaecaabeedebaaaddcbdeabeccdebbbdbbeabccaecdbbeeaedddeceaaedeaecceedbdabcceccebcdccecdeadebbdaddabeeeccbbccabddadcdeaebbccadcbdadacaeadadedcdeeebecccdcaccbdbddccbcacebedbbaaceaccbdcdaaebeaddaaddcedacdcebdeeeebbadebbaceaaeddaeacbbbadccaaedcbceddbeabcccdbcabaadedbdabcbcdbbebbabeaccaaaecbbcebabdabdadceeeccedcabaecbcddbbbacadebdabdbaabaedeadbcbdeeaeaeeaadecedabddcdedcbcdbcdbdadeebdeaeaabebddbecedcdbbbbdcbceccdabdebddabaaccedddaabeeeacedddbdebacbdacdcceeeadbadabadeebeaaeadaadaedbdcddabdabcbbddbcedbcddecdbedbaeaccedceeeccbcaeddeacbeecadbcabecaebdddbaadeeabaccbdcecdecaabaddbbeadbcedbdcccaabdabdddecaaacccbecaecceccbbeddeeabccbeeeaecceacaaaaeabcbdddeccbeabcaceecdccabadbbdeacecddebececbebddbdeadbebdcaadcddbcbddbcbabdadddecadbddeddccabacdaaacedacccbecbebbdbcdeededdaecabedebaeadbbeabcadabadbedcbeaceeabaedbbaaeaceddedbbdbdacbecdedaedbddeadbeadecdaeadabccdadcbddadecadaecdadabceddddcaccdeededacecebdabddcdbdedeebcddbddccadcdabbabdaaabbcdcaacdbbadadddadcadaecaaddcbdddbcdaaaadceceeddedeaedeabaddcadcdedebbbecaacaedaabdbedaabbceadaeecaaaabceeacabcabaebdcaddbbbdeabbccbecdcdcaedbdcdaccaaeaabaaaaaebeaaadeadbabadededcaceddcbedbadcbcbacbdcaeeccddbdaceaeecaabeebabdedabddaeacecadcebcebbeaeecbecbadabcaadcdabbdcdabcbabeeebacbaaadacbbdcbddbdaceebedbccaacecdabbddeeeeebbdabcddaccddaccdecececcacddeddbbbbbddbddaebdeaeaadcbabebabccbacbbaecceabbbcedaacbcdbabecaabdcaacdeedbccdabcabecaebbcaacdacaebeccaeecbaecaddeecbbededaabcebbbacdbaacacaacababeebdcbdcbdeebdeedeeecbeabeddaabcacacaccccacecadaaaeeddcadceaeeabeceacddadabadaccadadcedbbcbcaedeeedbbcbaeddabcdadbdedcaadceddebdcadbadeddadddaccaeaddebacaeecbabcebbbedccedbadddbddccdeebbdaceadaccaeedbddcdaddbbabeadcebdeeedeedbdebbcbdccccdebadccdeedaeecdedeacaccdeacebaebecabeaaaecacebbddcbdedaaabedabdcabebdcbabcdcbeedaddbacbaeddcdbacaaeaedecedecbcececdddaaaeebdaceccdbaccebbcddeedbdbcabdadcadbdcbbbccbeaeadcbdbaedaeaacaeceeacebbeacdacbdedcaeebbbedbbaabbcdddeaceaebcedbbcdacceacbabaaaddaebcabbceeeebcebeabbecaadebcdaceecdbbbbbaababbccbcdcccedbcbbcdabeaebdaeeecbdbabcbcecddcbbcaeeeabaddbabededdbaadccdaeddcbebebadeadddcccaaacdacbeeaddccdecbcadcbbacbddbddeddbdceddbcbebcaabbcbabaccedaaccdaeaedeabadcceaabacbadddaeababcadceddaabcddcabcdedaeccedbbeaecaccbdedbcdbbeabacddddcacccebbaaadabadeeaddcbebdcaaddadcbbedadecdaabbbebddbedcadeebdbabaabbbeaccccbcdbbbecacdcbebdeebbdcabdccaacdbeececdaeaedcadadddeeecbcdbaebadaedaaaebaceeceacceecceceeebdbabeecbcebaeecedbceabdeacebaddcdaeaaadceeeeddeccbcbbcadabcbcdcdbbbbdabbcbccceebcaababeaaacdaaeddcacdabdccaabbaebddbeadceecbbdcbbaecaedddcbaddeaacdeedaeaecacebbbcddbacbbdddddddbeaeddcdaacceaaddbcbeebdbadcddedccdaccbdbdeedcedeaacedbddbddaeaadceddadcdeaddccabecbeedcbecaaabbbebdedddbceddbdeeccbaacdceedbebdcbdebeeceacaaaeebeebcacabebabcbcbddaaedeaacbdaceaabaeaddeadbaadedcdcbcbeeaaaacaeebbdcadbbdcacddabdaeadbeccaaebaebeddccaaacdbdbdaabaddeadcbbbebeebbecdcbcecadbbabadcbbabdcccbaaaaceaacadeeeceebeedcabbccadbcccbdceecebbaccacbecaccedeceecadadebaaeecbcadadcbbaccecadbdacadbeceeadceeaaeebbdbeaedbbceababdbccaeecdeeccaabacecebdceebdeeddbbddadacecbdbaecdcdacdaaacedbaeccbecaaebaeabeaeeaededabebbabecceaaaaeaebddcbbddbceeccabdbdeeacececaadbdbdedddbbadcdbbdbeededbdbcebdbceaaaecaabdbccecbbddecbebeaadacedcdcdbaebcbdeebdbbcbcdbcabcccceaaaabdddeeabeccbaadeacaebbebabcbbddeebacbdebebaaccaaecabcadedcbccbaaccdaabebdadeddeeecaeeedabcbcdeddcadacdbdaadcbbaccbadcaaccaedadeaeebdcddccddcaebcaeeaccedbddbadebedbddaccbcebecbdadcdaebbdbbecbacbcdccadecadcdbbdbbdbbdbedbaecebdbaedeccabebdaabdaabeaecdaebcbbcbbddaceeabaacbeeebecbdeaeecddacccecaebdbaabbccacabcdbcaeacbddadbedacedddbbdeababdbbecedcbaabbedaeeeebeaabeddbdcddbdceeaccecbddbbaaddabcabccbcadaeccbeabecaabdaebbbeadddbdadbcadceacaecbbdbbddcdaaebebacebcedcddadbdcedeedcdeaccddbbceaecbeddcabdddaededbcbebdcacdcebdbdcdadeadedeedaeaebccbeaaceddaabdcddbcecddcddebcabdbeecebeacdbbbedbabbbcbdaddacbbbcdbcaadbdbaeacccccdaeccebbadbdaadbecabeacceadabbdaedbecccdbdbbddacecebbcacbeebaaacbeebbcbcccaeeeeaabcebabeacdcddebaeebccbeceeeacdddebedecedbacdeebcbbadeabbcdadadddbebebcebddeecaabdbbdecedacbbbaeccbcbcbadacaebcddadcaedaaecedbbeeacbcbaededaacdaeacbdcaebbecacbbaccdeedebcdecaeeebedabeecaeaddeddacaebcbbeccbeaacebedebdbbdcddbccecbddccaaeaebbcddbebaceedeeeacdbcebbbdbbbbeecdddddcaeaedaadcacacedcdcbaebcacdeccaaacdeeaddaccdceadbbaedbaacacbdeacadabbcbdeccecaeaacbadcdccbacdcacdbdcdaadbdbcaaabdcaabaadcbdbecedcaaddecbdeeaebdcadaebdaaebbcebcceecdaaceddadcadeddddeaddbbbcebbeaacecbbbebeabddeacbddcedbeadbebaaaecabacabcdcbaaaeecaadececbceeeeddebecdecacedaedbcaacbeddbdadabbdaeecaeaeacbbddabaecbeaeaedeeeddaeaadbbddedceccebadeedeecdeaaaedecbeabadbeaccadabccadacebeeadbbbadaeeaccabbeceeccbbdeeaebdccbeacbceaddcccdebeedebadbdeacbaecceadeedeadcdcebccbbbcabacddaaeabacedebcaeaceaeddcdbadcdebbaceabebbcdabbdcdeaceeccaadececbabeaababebebbcdceccabddabdaeebbaddadabacdbbeaaccbcabcdaeddedbaddecebdabddbaadddddeabaabceaaeaeececabaaebdbaeedddccbeaeebceabbccdaedaccdadceccbcbebbbabecbcbdcaadbaeebbcccbddbdecaeceedeebdcbebbecebaebacbdcdedcbdeddddbbdeedbbaeddebddeaedbabdccccdcacdbbadeacaebebebecadaccdcaadbcacabbedaabcedbedcbdbacabeebbaecaeabcdebecaceeedcbcdacceecdeedcdbbedbdacdbaccdcebcbdecdedaaaacedeecdedacddaccadbdcadcdddadeebceedeebdcaeeaceecbbacdbddcddccdadbaadedcdaecbeadceedeaaababdcbbbdbbdaadbdccccadcddabccbeaebdebddebdbedaacddcddddbdaadbbdeadbddcaacabccddbaecebeaedbcdbedeaccbdbdabaddeaacdbeedaccdcdcddacadeeccdbeaddcdebabaaaaccadacbbacacecbdcabdcaecddadbabceedeeaddeaccbeaccebebbdbdabcabdbabacacedbeacedaabbccdbedebaaaaeacbbcedddccaabbcecdbdaaacbbedcdacdedbdbbbedddebbddaddeadecbcbeedcddadbeeacdbecceedcedcabdddbbbbcabccbacdaaebebdabebcccaaaeabadecaaabeddbaaccaedadbceebbebdaabaceceaddeaccddedcdacceadebedcaaccaeaebbdaededaaadebaddbcdcecceabdbbcceabeadecbabcdcddbdeaddebadeececabecbbeaeaeeabdadddbaebaeceedcaaabcbcbdaeddcaadbaacdddedbbedbeedbeebbcdaabdddebbabeddbacdcccaadeebebecceeebbbedbebbeadaadbbcdebecadadbbebbaaecdbdadccadeeccacbccdddcbceecceeaabdedcadcecbbddebcadcbdeedcdeeacdbeabadaabecabcccdcbebbbeaceedacadcbdcdbceacaadccdeeabcacdcacdddbaeebdbaacdbccebbecbebecdbdbdcbacddabcceabeeececbdddaebdcbcbcbadeadbdcddcdabedeeeceecbdbceedebbbcbcbeabbdacbcbecdaaacbebcbebaccaaebeabdbabedceacbdbcbccacaebddeadcbebbbcadbcacaccaebdaaacbdbedacdcadaeaeebecabbeeaddbdbebdabdbadbedaedeeaacbcbdcbbbbdddbebadccacbabdaedbedbaddadadddabedbceeabeaabeaaceacbbcdcaebbbbcaeecbaedbbacedeeacbbabceedaadcebeceebdabdeebcecaebdddbebabbbeacbbbdccceacdbcdacabcecbacbaaeaeddbadbcebeacaacbaddbeeededcbdaaceaccebcacaedeecacdaccdbaaeaddcdcdccdbcbeeccedebaaaedabbcedbaedebacbccdbacacdabdccbcbaadbaddaeeabdcaebebaadadbcddaadecebabdbacecabbeeaddccbeedeeeaedecdcdbbaabaacdbebcdcbecadceccabaeaedcdbacaabdeaeaaaabacbadadeeacedcdbabdbaacdcccedecabdbcddaccbbdbceebedceecebaacbcadabaccbcdebbbcbcdadbbaebcdabcdddaecadeabcecaaaedeaeadbbcbcabebacaeeeeadadddcddabacbbcebeaecdadaaaabbacccbecbdcdcdaaedbabcadceddaeabaedebbadecbacdebbcedacdebceacadcabaeaccceedbeadcccbedbecbdabdaeeabddbddaaaaaedbdeadaeebbeebbeacdbbabbcdcaabcabceaabbbebadbdcaeaceaeeaaabcdcededebbbdabddbdddbdcedbcadbabceaaacccdeedaddcacdebbceaaaeedabededececbeedddcecbcddbdeaaabeacabeeaebccdabcddcbeeccaddcadebbdeebcdccbbdbbeeaaebbaebcabeaddcebdeaabdbddcbaacddbadeaebcedcddcdbacddaeebdbbceebdebecaabecbeeeeeadbeacdabbdbcecbbcecaebdbdeeacacbeddaacbaecebaeecceddabccddebabcccddedddeedcedeabcaaeeedbbaddcbddbaeccccddcaeeaeedaaeededbccbcdabcccdccdbedbecaecbcdddbbadacaedcaeccebbdaadcbdbbcadcbeecaabdeaeeecdaaecccebdadddcecaaeaceaecbceabbbbeaaeceecddaeaaceadbacecbcaebedbdaadbdccdeebacaaddbacdeecdcccbebbdeeeaebcbebebbeecdddbdeedccaeeeeecaceeaebaddeaceadbebdedddbbcdbedcdbdaadabebaadeeeddceedccaddbdcdbcdcabbccdcedceceacdebeccdeabdceeeadbbbddecbceaabebdedaebeebdaddcacaabceadccbdcbecdcacacadcdbcacebababbacbabeeedebcdbeedbedebceaebcbebebddcddbacaeadbdadabeccacdadbcbdabdcaebddbcebcccbcabcadaaccbccddeedceadaaccccdcedbbbccbccaaabeccdcccaedddddbeceacaebdaacaceeceeaedcbbcabedaeaceceeacadbbbcbbcdedeeaccbcaedbedeebccdecaaedceabaceabddbaceddeebdbdebecacdecadcadacdcebcbcacaaaadcabcebbedecaecbaacaebcadbeadecadbeebecbdcdbaadaaaecbeeacdebdbbdeebdcabceceedaaaacdeedeadedcdbddaabeeacbaaeedebcbaeeaaecdcdadaeeadaddcbaaadcbedabbeadeedccdbebbaeacebdaecbdeaceddbdabbcecbeacdcaeabadddcbcccdcdeeadeecdcdaacebaabbbaceeeaaabcacceacabeebdededcedeaeacededdcbcebddbeecabcbcaadeeacabbeebbdbbabeedaccccbabdddcddddaaadadedeedebedbdbeadccebeeabddcdecaaabeedbeedaaaeadccbacedbadbbaebacebaaadbcdbdedbddedeacdccdcecbbbacebaceadeeadbcaebbbaaadbbcacdcbceeddbbeeacbbaeeaecceedbacaddeedaeeccdcbabcdeeaddecbbbbedbdaccebbaaedeedbeedddabebaeddbabeadbcadceedeacdccbccedecddedbaccbabbddeaebaacdabeabacddbbacaaedbdeadcbacaadbdbeeabebaeacbdaebdaeebdeeeeaaedeacaaacbcbcbdbbeeaecdadeeadeeeddbbbbeabacecabadaccebcbedacaeebedebdccabcdbabbadadbebabbcecdcccdbbdcaeacdbedcebebcdaecdcedcccddcdbeedcceceeccdbcecbebdbedccbaaeadccdbeeeeeceeaabebacdbaabadbededbccdbeecacbcaedaeebdadcacbadeeddedadaddebecdeeaceecbcededcaebdcdaeddceddebbabdddaaeaacadaaaecbddaaeadccbbdeadabbadbacebedbcebcaccedaededadabbbeababacabeddabacebcbdaacaacebccbdcdcdeacebeccbaaccedbddcddecbccaacedbbccabbaacbdebdaeecaeabdaccbebdcaeebceaddddddbcdedbccdbcaacbbcecebdadbcdeceaabbaaeedcebceadcbdbdedbdcadcbbbdedbcaacbedbbecceeecbeedededceeceeabcdaaedcadddbbaaeaeaecacdbbdeceededdcaceccdccdbdbaabddabecccacbdaeddedacadcbcbcebcacaebdbeaeaaadcdecddeacaacbaabeaebaeaddbabbbebabeadeabddaadbcceaeeecacbedcceaeabcddebacedebcbaaeecedbeabdaaeeaebedbeabdedeaecabbacddcaddeccdaedbecbccdaeaadebbbcbebdeaaeebaeeadbabbaedbdbeaecacbebbdddaeaebdadcbeccdeecdbaeaeadaeaebdbabbdedcecbaabdadeddbbdadecdceeeeaddccdbcabcaeaeeeaeeacbabddabdbaadcaeddaccadceeaabbbbcebeebbbcbcccbddadaecdeacdabecaabeadbceeeacaabadabbabdebbabebecaadacadeddbddeeccedaecbdaabdaebccbbebcdddcddbdbacecdedddecdadaaccbadbdecdebacdbbebdedaacbedbadcaaddadddaacecebeeacededbcbcdeeecdabbecceaededbbeddcbccecebbddeaaeadaaedcbeabcaccdceebebbeddbeacecdeacabececebcacecedaedeeebbacceeebcbcecbecbaaaacacdeacabeddbceaceebceabdbccaddedddeacecdbbebcddddacdaeeccaacbeddcbacddabdaadebcaedebbccddccbccdbeabbaaacbabedeeedbbbbbebccecbcdbcbccebbadbbdbdacdbcdcbebdedcccbeccadbccbdaebaddadedeaebbecedeecedeadeddacaacadedecaebcceadbbcabebaeeaadaaaeeeceacbccdcbddccbcbaccbdaabededbccbeaaaebbedeeebecdeceaeaaeadbcdbedaeebcbccbdcaeceecebeddcaaeacddceadebaeaebeedcebbedbdaddceadddbbaaeeccaeabdecbbebddcddbbeedccdadedebbccebccdacadeecdcadcbddebdbeaecccdeebbaedacbbacccdadeceaaabceaeaecedbacdabaabceebabeabaabdcddeabbdbedbadcbebdbbedaabeeceeeaaaaecdddbbcaecddabaadecdddbaecbebaebedcaeaaaedeaaebbabeabccdbdaddbbcedeedabbacaeacbdbaeebdbbceacbaebcaebecbddccdbbacbddccbeadecdeaecbebeedeccdbcbdedbccabcbbbbcccedccdcbecbbdeaccceabdaaebeaccdcddedaaaebaacacaddceaacdabacacbdbdadbbbcbaebecdbdaccabbaedcdaabadadaeebbbeccbbbbeedaaebeadcbccbeceacaddeebaeddbbebdbdedaedcbeadbaaaddcdcbaebaebaaaedebdbdabeddadcacbbadbeecdddbbbeecccddedcaadededdcddeaedebddaceccedbddedeceaecdaaeecdadecabcabccabdacbbdbdacbbdebecabbdcdaabbccecddbdddbeacaceeddadcceecabeeeceeecddccdaacecdaccdeeadcebadabeceacdcebcbdbbcdbeadcdceceabddbdebaedecccbdcdcbccaaecdacaacadeabadaeaedaaeeccdcadebdaabcebadacdbdacdbecabeacceccbccdbccbaaebacdddccddeedebcbebdeaadcbcceeeabbbcacadbadeeebdbeabdbeedebdaaeddeccdddbdcceacaeaacbadeebceaaceecddeaedccaecdbbadeaeabcacaacbcbdeabbccaacbcdbecddccaedaeaaeceedbcadabcbdcceaecdeeddaeaacdcdcdcbaccdebaadcbcdcccccbdebcbeebecdbacbcbdaabbdcbacaaccbabbcdaaabddbdbbeeeaaecaacddedaaaaedeeadcdccbbdccabbaaacdeedcbadcbabbdababcbcecbcdadcbcebbbeebbcdccdeaceabaabbceeacbeacecbeecbbadedacbeebceebedabcdddddbbabbbeaedaeebbabbaaadbacceddbcecbaeeebedbecbaadcbeeeeedeaabcecabdcccccdeeeabbbdedaecccacededecdeaebbdbdacbaeddcaeaabcabbcddecbbedeadabbaeedeedcbbdbddceecbbcbccbdeebcedacbcadbaeccbbebccecedeebcaeceaaedbdbacccabbbebedaedbebdccacacacddcaaccecbecdbbbedadbccbbdcbebecebdcdbbceeecbbbddaeabaccdcbdadccacacbdecbcbcecbdabbebdbaaaadbceaaaededcdadaadbadaeecdacdddeeaacbcaebedeecbbebdcdaecdbbcdaacadecaabadcadcbccdaacbccbaadaecbcabbeeccebebedeadeabcabbdededaaccabbbedeedebbceebabeaeecbcadbebdbbbdaaecaeebbedaabbceadcbaaabbeaaecabecbbcbaebaabadaadddedbbeabeaaabbbcaaedebeedaeeacacdebbdcedbcdabcbcbbeadaeddedaeccdadeaaedabaedebbeccdccbeeddeccadcabecaedccccaccedeecaaeeecbabecbecebcadcadcddcaedaddcbbcacbedeabaddecedaaccbbeddabcaddbcdbabeeaadbacddaeeceedbcdaceebecceddcaadccacaabbbeaedccadebbdcbeeabcbccabbebbddadbdeebbbcceaccbbaacebeccdddaaadaeacebcaaadbadedecaddccbdcbcaecebbccbdbcdcaceeedccdacbbdbaadcbbaaaeaaedadddecadbbbedacebdcababccbcedbcbbcccddcddcbeedaebeadddeeebaeebcbcbdababdeeebedebeaacecbedbcaccadcbbceadcececacaabbcbeecbeccdeeedcbebbbdcdddeddeaecddbbccbccadbaaceacbdadadbdbbcacdcdcbdbabdbeaaebabcadededaeaedadbeebedcadbdaaaaadcacddcedbbbceddbeadaacaceddebdcaedcabaaaccadeebbdeddccaccaeececdcddbadcacccddabbceeeceeabbebccbdcbaccceebbddeddccabaacdaacaddbacbcdddcbbccaedbbbebadbbcbeaaedbbacbcabcbbbdcbecbdcaababadeabdebcbbbaceebddaebddcdeabedadcbaaaebadeeedaddedbcdcbbacabeeeaecdabdecececdccaeaadeacbbbbcbdacebddbbeaeabecaeeeabaaaccecbceabcecdbdddacbccdebbbddcbedeceebbaaecaabdaccacbedeeadeecdcccaccedcbeebeeddddddbbbdbaebbecbbaeccaceddcbcdaddcdecdbdcbaccaeadacbaaebbedacebcdeaeabebdceabbbaedeeedacbeabcbcdbadddedbbdaaecebeeadcdacdaceaeeeebaeabeadeddecbcdcacebebaeaebacedaddecaedcdbdaabcebaaacaaadaaabbbeccdddadcedbbececbebabedbeeeeceeacedededccaebccdbbccbcbdeacdbccecdbeeaaadddeadceddeaebdedadbcbeccbbbdceeaecadadebabceaeaedcadbdbadadbaeddcbcedabeacdeabedadeccebbdbdcedddaedddbaceceeedcdbadeeaeecceeddacbdcaeeccdaabbbeebadcebdecacdeecabddbbdaaeccbddcadebebebdaceecbecceecadecebcbceeeaeedbacdaedcebeeedbbcadcdeabddddedbcababceeabacceeddcdadddbacebedcebabeabcdbcdbcdebdcdabeeacccaabbecedbeaeeeaabaaaddeedbeacacdcdedeeacbdddccaccbacbddeabccbcceaecceebdecbaeacdacbeaaaadabacdccdeecedceacdecacdedeaeebadcbdbaabdadcdacbadacbcbbadebbcddabeaeadcadcceeeabcaaacaaebdcdbabacedadebcdaadbdbdebeaaaadecbacadebdabaddacddeaccdeaaadadcebdddddebccbeebabebbddaacaebbbeeacadabeacdbadacabcddcabeeabddbddcdeeddddedabdbdebdeeebaaeabeecaaaacbbbdcdcebdbbbcbcbccbedebbbbdabbabacdbcaedeccbecccaeddbbdacebcbebcbedbadcecccddddddbeddbabdabbecdceadebadacbbccedeacdeeceaaeadabcdddcbeabacebcaeeacbceadaaeddcaecbdbebcceebaeabbabdabcecdebbabecaacbebaaebbdedccedbabbacadbabedbaabbbabeeabbbeccddabeddccddebbcadabbecabeaaadeacabccbbdcaabccbdceacaaeebaaedadbddecadccddeececdeadacacadaeecddebbeaeeacdddadaadecbcbbbceabcdbbaebeadcacebcdabdddbecceeccaacaeeaeecebbacedceecdbcbaaadeddddecbaceceededdebbcbbacdcccdeaebdecbccaabebedeeaeeedcededcabdccbaadacceceecdbcdeacadbdbebaccccbeedbaabeabaedddbcabdebabbbddaabbbcbabeaaedbaaebdbebacaaabbdbcdcaddaadeeecceebbebedccadecdbcbcdadebeddedcecccacbeeaaadbabdbededeadbaadeccbcdeedecbeebedbcecdeccbcebeeaacdeaadbaabcaddebaedaccccbebbebeebecacbccdaeecdcecaaccdbebeeccebdcebdbaecdeabdcbadceecbcdcbbeaeaaccaeacaaaccdeacaabebcabdbddcebaaaecbadeaeccbbbeebbdbcadbcaadcbcdcebebdbacededaeeaabcadbbbcceeebaeccbdaacddedbccddcabaecedcbddbdabbcceceadeeaeeecccaceccbcbadacacadebedacacddaaccbbcaeccdcaabbcaecacaeedbaeaaececdebcbbcbbacdeccbedcbbbebcebabdbedebabbeadcbbbdbedadaadabbcdbeacacbabbebdaaeabaeadecdbeaaaebeddacaaaabbbcdcadeddacaaecdbcadabababaaecababddcedcccaedcebacaedaedcddcbccaaacecbeabbbabeddacdeaabeadbaeecdbaddcacbdddcccaddaeebaddeccedbbddadaaeaceebdaaabbdbabdaceebbdbcbbacabcccacaceadaabadececbdebbbcccebaddadaeaacbbcbeededdedecbeeceeacdabecaeaabdebbeeceaadcaddbdceaecababbcbeddeabccdcaaeceeedabcedbbbdebedeecaedeaceeeedebbadbebadaadcbacceedddcddcaadeebccedbbdeaaecbdbdebcdbbaaedbeaacbcacecacaeadccdacacadacaedcddbbcccbbaecdcedbaacaecabcbeacbabededabbaddaebdedbceeedcdbceccadbcccccebceeeceaccdcddcceddcbdbaddeccdeaaccddebedcaeaeccbbaaeabcddcbbacbcddcdbcbcdedebabbdebcdcbdedcbacacabebcecbaeddbdcdcdadadedaecebaeccdcaededddddbdcadbcdbcddebaecabaeedbecadeacbaceeeddaeebcddaedcacbbdbbddecbcbadcdaeaacaacdddaceebbaaacecabdbdcbcbeccccedccedaacdabdbcebaaadaabbaaddbceedbcbbecbcacddddaaebdededaeebbbcddacbaceaeecceabadcceedddaddddecbcdbeccceceaaebddbeaddacdebaecedddbdeacddddaddcdeadcbeabcedcbbccaeceaeeceeaeeddbcbaadbbebcceaabddebcebaedebdebadccbdaebbadccbbaebcbabcbbdbeaeddcbdedabbebbebacdabdaebddaedceecbaccddbcdcbaabbbebdecedbaecbcdcdbaddbdbeebdedcbabacddacdbbdabebddaaeebabdcdadeeababcabbecedcaebecabbacceaddcaeecaedeaaacceabedbabbaeaadadaadcedcccdbdbceaeadeaebccdbcbdddccbdebaeecdbeddbcaaabbdebcdeedbbaabdbcbbbdbdedebaacebdeedeaaccedecaeabbeceddddbdcebcabeacddddaabaccaaabdeddbeeecdceebeabddbcbcadebeebeebdadeacaedabacdebbedbcccadabcceadadbedaccdcbcbbcedebbacbacecdbceaeabcecbedbcedaacbbcbdeadabccbceacabbaecbaeababecedcedebddecaeaacadbeaccceadacdebddacbacaddcbeaedccaebbcccbecbdaaccbadddceebbdbbadcddacdbcdebcbecebebceaabbbededebcacadbaaaecdcebbaadcbccbeaaaccabdedddbaaabeccdedbdbaabdeaabbedbacdedaacaadaeaddadaebbedabcdddceaccbbdbccecedbcabcebebbbeddcabdeeacaadcadbdaabedbbceecbcbebcacccbeaedcaceacebddaeacaccaceabcbdeabbeebeddcbaedadeaebcedbaeabcecdbeacacceecccaaaaddbdcbcedbcbcdccddbbdadddedbccbcbadaadbccbadeaacddcdabaecdeeaaeaeceeaadcccdcbbdcdabbcaaecddaeabcccebcdbcbbbbdccbabddbbbddbcdbaebcadaedbcaebbdbeeeeccbaededcbeeacccebaabebcacdedcccddaaaccabaaacdcbaecbcbecdeeceeadcebebdbcdaadbdadddcdeccaadccaabeaadcdbabbaaaddadcccceeddbbbccaaddcacebebeaabbeabeaecaebccdbaaeadbecededabaddccbadcdecdeedbcbdeaaccdeeaccbeaedddeecdadaacadcccaceeaeedadebbddebdeeccbddcbdcedeacdeadbedbdddaadadaaebeebeecdcaccacbeacdacebcaeceaddededccbdadccccdbbdacbbeddddeeadacbbabebbcacbbcddeabcceabaccddeceacdcdabbdbacbdacdbbeaaddbeeaedabedaddeecbebccecccadcbbeadcedcedbcdceebacaecdeacebdcaedbacdabddeecbcdbeddecdabdbabaccdacaabdcbdeabdeeddbbbcadbaebadccebeeaecdbeddeecbbedddcbabedebdbceabdbeecaabdcedbabbadeeddabdecaceadcebcdceedbdbccaeaebaacdcbabdceebecdacbdcbeceedeecabcacbeddecdaacbbdcdcacceacaebccdacabcaabebcadbeeeadbdaaebbbedcaeedcacaebeeceacddbbdeeaddaadbceadbcbcaeaaaadedbceacbdccdadedbdaccebedeeedbdadcabdbecabbceaadbeeddecbeeaedbabacccaaecabebbcbdedcdedbbcaadabcabcaececcdbdbebedabaeecbbdedabcddbceaddadbeacececebacdccabdeceaaedbebbabdacdaadbbaebdedaeaccecddbebeaaaacdeaadbebaaeedbcbdaecededccdddcbaeeeeacbdccdbbbaacbdcceceedbacaeabdebceeadaabcaadccbaccabaadeddbbdbdcbbcbcabbbeccaaccaceeccbbbdabcccdecccbaedbeaabeddaedacabaeebbeccbaeadddcddbdeaedcaaecdabbbababaaeddaaccadcbeccbabddecbdbebcdadecaebdceddcabeceeebeebbeeceaadbeceddbbeadadcbecbdeebddeeadccabebebbeaddcbecabeabdcacddcbcebebcdaadaeccccdebbcbadddceabbbcbbdcdeabaecbbabeedcaeebadceddcacadcebceaabbadcebaaecdcbeceaecdedadbaccbcdeaeadeddbbbbddcbedbbebdeedbcbbdaeeccedcddcebeedebcddebcceabeaececdecacbdcdbebebadedcdceccbcbcaeacdeaaeeadcbbaebbeaddddadacacbabecceeacdceaecdecdcdcbdcaecbeecdddaedbbdccebbdcbeabaccceeaedbdeeccdabbdcedbdbbddddaaddaadbdaedbdeaadecaeccadaadbcbebbccabbcbaaabebebbdecdbdbdbadbebdaabcaccecacadcedecedaeecbcdababeecbdeaccacaedacbceccaebabadbcccdaeeaddeacbcbcbaeaacacbcaedbddbcecedcebaceceedeebceeddcebcbcceabbdbaacacdeeccdaabedeacbacebaeededddaddcbbcebdebdadeaeceadedcbabadeecdbacacceecaedccbdccedbbdeaddecababaccadaadbecdbedbdadbbebbbeccbbabcddaddbcaddaeebaebdacaaaddccdeaeedcbedbabdeeedbecebeecdbdaabaacbababbedccdacebdcadaacabdcdeaebabcbecaddebdcbbdbccacbaeedaebbaacbdcdebccadeaedaeeaaabdbbbddcedebeaecbdbbcbaecaeadacaaaeeaabdddbdbabcabcdbddecadedbeceddcbbadabacbabeaebeeabbcabaebbbaadaacbabcebddbdaabaeebdabdedcceceaaeebeeecaadbeedeccabbcdccedcdabeabcbbceebdaccaebccecdaeeedecacdeedabbeccdbebceadcbecabaeadcedeeededbddcacbbbaeadaaaeaedbbcebbcddceeccbecbedecaeceaedcdcccedaabddabddbbbaaacbcbdceaecabdbebdbeabceeaadadaeeaebbcdceadcbbcbacdebedbcdccadacbeedbdacecbeaebbbdcecebcbbdcecbaaddbcdeababdcccbaccadccadbbeeacddcdccabdbabdcbedbdabccecdbdecdaecdabccaeebbccdbaccaabccacceccbeeeaaaabcebeccababbbdabeeedcdeeedcabadadcaaddbbabadbaecdaaabddbbddaaadddadedeaadaeaeeddecaecdbcacdaeecdeaaacdabcddaedbcecaabbcebabeeaeebabebdeecacdaaebacccbededccbcabcdddcacbaceeebcbcedbebedebeaccbcbadeedacbadedeaecadaebdcabbbeedcdcaecdddceabbcbdccccaddedaecdacbccceecacbbdadcbeeacbecbdbdedabacbeeebcdacbebdbcbabbbaaebbdabdaebcececeddebacbedacacaccbaaceccabecdcddddadceabdaeddbeecddbddddaecabdaabdbddbcdebddddcadceeaeddedeeceadddbbadbcedbabedebeabcacbbedaeadbebaecbacbcbadbedbabbcedbecabccbbcbdbcaabebbceecacadcacbeeaccacbceccaacdbeedccebeabcaeaaaccbccceeedbcdbeccdcdcaeaecabbabeddedcadbdddabddaecbbedbeaebbeacceeabaeacdbacbeecddbbddcdaddbabcbebcaebccaedcceedbacbababdbeceadcaedbaacccdeeeaceaaeecdbdcdebcdaddbdddcdcbcadbbdccdabccdadbcadabcaeecebdbedabdedddecacdecacdecdcabaeecbbbdccaccbcbabdeabcceceabbedbddabbaaecebeadcdbcdacbcedddeebdeebaabdaeaaecdbdaeedeacbeaaeeebeebcaeaedbbcaddacccaadeebcbaadbdcaccaaedcceeadceacbcbcbaeeadbedcdacadbedbbbdbdddcecbdecccbeccecdcecaebadccabdbdddcdcecdedddceeaaaeabdcceacecbebbbddaedccacbcebdecdebebdabacceeaeccbbdcbbebecaccaeadacecedadbabdaabeacadbbbaedeeddebbdaeddbaaecbddadceadacddeeddbcaecbdbeacceadeaadddcdbdccdeedabebcdceedbcebaddaccdcebeebcdcbddedcdcdecaecdbeeabcddcedbdaaeadeedcebbcadcaabdeeeabaaabeacdaebcbbabbbcdaaaebeabacdeabdbdedaecceacecdcddeabcabcaaebabbdbbcbeedeecebaceedbbbceebaeaecddcdcacdbdabcbabaddbebbdeaadbccbadebeeaddcedccaadcdcbecccbedcebecbcecccedecaacebceacdcedacaddaecdebaabecdabbccdddeababbeacaccceaebdcebeeebccebebdadeadbceaabcbedbadbdbebacdcbabebdaaacaeacaddbabbbadcbbbebedbdeedcaddaaddddcaaaaadcaaaedcbcdebcbcedabdccbdedebabcbabcabaebecbbcabbcbebccddaebdbadbbcddabdcbdbcaceeaeeebacccddbbcbcadceddbccddebbdddcedadebeddaadeccacaaaeaebeaddbaaedaaddcdccdeeeebbebdedebdedabcaadbbcbdecbbbaccbdbdccacdceebdaacdcaddadeeabaecbabecbdeebaebddeeacdbcdccebbeadddeadbddedecaaccebbeaddabadabacddceebcabeccabecedeaedacecdcadbeeeddaeedbdaddabbbddddaaadbebdcccddbdadbebdbcaacdbbdedbbbdeccdbebbdaecacdbcabbbebcdddaceabddbecaadbccaeeaadabedbadeddaaecacacebeaedcceadbedbbcccaebbcdceabacccaecabcedeecaebebcddbdbabaadbebaadcaaddddbededdedbadbcabdcacdabbdecdabbbdbcdcccdccbaedacadbbbdabebdedcaabeededccbabbecbeeadcabeccaadaadabdbaaadcaccbdeaebeaaebccebdddeeebeaaedddcdecaedbbecdbaeaccaedaaedaaebcacedcceeedeebdadcbcdceccbdcbaaadeacedcaebeaddebaebbaddaaecbdcbecddaeeabadbaababcaebdecbabecbcecbadedecaeadddcbbcdccaecbcbdecddadbddbdcbededacdebacccaaadadaeebbdedddcdedcaaadbaabcedbbeabdaeacadaddcebcaedcabccdadedecbaedcceebdadeacbcdabeeadbeedbeaacbebaacabcdecccaabdecbaeebcabcdaaeeccdababcbbadbaddedbbbbbceeaadccadeecadbcbabceebcaceedceeadccdccbdcbebbcdbcebacecbedabcbacbedcbbdcbecdecdacbacedaeceadaaaceeaabbcacadbbbdcedebdecebbedcedeececaebebdbeabecbddeacaadcaebaeebaebdbeeeeaebccaeadabedeedeccdacbbacdcadaedaddaaebcbdcccedecedbebbbaaebddcebeaceeeaadeddacddddcccecbbabbbcdeedccdaeedadcbceeeedecbcbbaedcccaaecccdccbeccdceaecadbdeedeaecbaecbeeeeadddaaeeadedeebebaedadcdaeeabbdbbaccabbacbdaecbadadabebcdaaccbcaeccecddebdbceacedaddedcabceaebeaaddbdcebeeebebeabcbeaadeaebedbeedbdabcbadebdccbaddcbbacbccdbabedcdbdaeeccaeedcabccebadaaeddedbeccadccdeccdbdbbceeccbcaabadaedddaaaeaebbacaadedacabbaeebbacdeecbedabdcebaaacbaaebcecadcaadeddacabdbddeddeccdcdcbacddbabdbedceeddeacdddbbedaceaecbbbaaacceabbbcedcdcdcecddcccbbbbbacaebbbecadaddcdcedeacabdebaadacdcedcccdabadeeacbdeddaeadbcedaadbeabcaadaebdcceddceadbcdaedadbcbccdbeadbaadddeaeacccbdeedaddbbcabecdeeabedabdeebeaeeddaecebedeebaacecbbbdaabcdecacbbbcebbcdbacebeeaccabcbebcceeaacedeacceabaacddaaeedcbddcdebcbccdceabddccedcbcbccddccbddccccccadbbacebebcdeaebdbdbadabaaddacadeaecabbdbeebaebbebcadbebbbadaaddcddeaaedbeedadacdcdaaeeaeececadcadaccdaeadbdaeeedacceaccdaddccebeebaedcecbdbdbaabeecddcedaccbabeacbaeedcaaacacebcbbcaecdaacabadadeaececceababaabcecddcedebbccdbddccecbaacbdaebbddedebbbdbedadbacceeeaedbeddebdaddeaeecbaacecccadeacebdcedccdceadcaaadaecbbcecceccdaadcdbbddcdcebcccedaecbccbbddcbddbbcaebcebcdceabeecbaeecdcbbaedbbddabdbdbcccceebbbddbbcccdacdcbbaaebebecccecbbdeabcabedbddebdadddcadddababdebaddcbbbdabcaecbceddecbcadbecedadecabcadddbbedcdbdccabbacbdeaccceadddcbaacbeaabbaaabddececddacaecaebdeadecaebcaaebadeeddcecbbccdbedaeacceaeabddddccaabecdcacddecbbbddbcccdcbdbdeaddcdbeaaeddedccecdbdbaacaacbcdccbaccbbbcacecbeebeeabcdecbbbabaebabeebbbbcddcdabdeebcaddeeabcbcaeeceadcdcccacaceaadeebecdecbbacaadeaabbababbbaaedbbeeaadadedaebecddebabebbdbddadebabdedcdaaaddaededbcebcaacaeaaccbdbbadaceccbacecabadaadbddabacdcbecebbbdbcbdcdeceabbdcddcaaeceacbdbcaeddaeeddcbbcdaecacbeecdcaccbcbdbdeeedbaadadaccbadaabaadbcecaeceeeceeebccedccbdcaeabeaeeadcdcadbabaaacecdaebaeeddcacabdabcdaaacedbdcbbdabdcbceddcccbecccbcceceddcbbaeedbabcdbbaebdbdddabadbcababdaaaecadedbcceaabdeadceecebcaeeebbeaadeccaeceddbabbadaaceabdcbbeeeacbeedebddacaeeacdcbeadddedeaddccddeababdebcedacbabedbebaddcdacbdecedbabaebbbcebdccbcbbcebebddadbbdbcdbcbacaccbebccbeeaaadeeedcdbebeeacbddbbadbedabcdbdbaadbcdeccbcbebecdcdbbebbccaaadecccadededcdbaddbdaaaddcdeaacbbeddebcadabcadcdaccbbeadaeabdbeeceedaaebedadeddccedbebbebceecedebbbdacbdcdcbbcbaccacedabbcdbcccdcadeebeedccbdcdaaddceadbaeaccbadedacddccaabbecdddecdedaadcebbecbcebbdcbbcdaacddcadbadabedeadbcebcdaebeaaddadbebebbdcedddbbccbbddababdcccbeaabcbaeacabdaccdbdadadedbcaeaecacebececdaedeeeeccddeacbaceeebccedcbdebadbbdbdbaeeddeaabcdcbcdeeabdeddeabcaaaceaabdcceecdeeebcaadbbcadadaccedebbbeaecceaedcaaddbadabccaecaedaabceedbccbceecaeecbbaabebdacbebcceaedeaadedccbdabcdaeaacceedaaeaaebddbaedceeebcadeecbaebdbecddbeeecdabcbbbbdedebacebdcccdeabcaacaccbcaebaaadbeceacbcdcedacdebaaacbaadddabeedcdedbdadcabdcdddaaececaabdbeabddbcadabeabdabbedcdcedcbbadedddbeedcbcdbbeadcebbdbaddccacecccbcaabcebcaababbcccbbaaccddbbaadcaaaceedaacaedaccbdbcbbbacadeaecdcadbcadcbdbeecdbbcaebcacdccdceeadbbaccddceaeebdacebabbaecedbcaaedebcacabdaaccbbaaaaebdecdacaeebacdbdecbdacbcebbcbbdadaaaccaedbdcbdcacecebacebaacaaccbdcadceabaccbcdcbdcdeeddccaebabbbcccdebbeddaedaecebddabcbddcbadedabebcebbebabdbeacaededcdbaaaeddaedcdeeaedabbabcdbdabdedaecadaeecaeeebbadcaecbbcebcedcaccbedbbedccbbdddacddebacbeccedbbaaceaecabeadeabeaddbcdbdddcaeacaeccdeaaccebaedaebbdaebccccceaacaebbbbcacaaaaedeeeeaecbadaaecadcecacecaedeeadaeaecbdbdbcdbccadbecaddcccebdecaadddeeadadceadabddaecccaecdccbddbcbcbecdbbbbcebdcbcadedbaadbbedcecbdaeeaeabbabdbddcedcebbcccbeacccedcaaeceaeceadcbaebdecababcbbeeeedcedebbbbdeeeeadebbeeceebdbdbcbcecaedeedbeaecddcbbadcaecddeaaabdbaededeaccbdcadbcdeeabcedaaaacbdebbecdeaaebecbddedaedaccdcbcdbcdcbaeaccecdebecdbceebddddbedebbeaadbadaeedaebecdbcbedaadeedeaeaaedbdecaeccadacedbabaadbacaaadcedcaabcddeecbedbabdcbeaabecdeedabbbdcccadcccbbbeebbeadceabaeaeeaebcdbdcdadcadcccbecbabddcadccecbdddbbcadabeedabeaecdaaadabaeaecebadeaaccbdddebdedecebaecdacbabadaaaacddacddacabcbcebeecaadeadbbdebedeedbedbccbdababceabaebeaceeadccebadbcbddadbccdbabacbededbaaaddbbbbdddacbcebdadcbdaacaebbedcddcdacdebaacbecddaacedceaabbaceeaddacdcdcdaadbceabaaaebbdecccddbbacececedaedbcabedcebeaaeaabccddaeeeddedecacabdbacceceeecdaaedcaabbebceabedceeeedaebcdbdcbedbbaddcbebdbebacbedebddeedeeddeceecaebceeedccbddeeebbabbcdedbbbbeabdeedceebdccaacdbbbebbcdaeadddaebddcbacabceaccedbadecdedecbbdeacebbdddcecebaccdeeacacbaddcdbadcedeebedeaaeaddacaabdcadebbcecdbaaedabbcbcbedabebdcebdebcddadcedcbddecabdbbbcdaabcdabeadacebbddddbaaddbaedddaadcccaeceadaecdecebdaecbdbeaccbcaacedcabdebaaeebddbccdbdcaabccecaeebceaaddcdbeadcccbcacbebcebdeaeedacacaeabcdbbcbdadbbbebabcdecccdcdccdebbbecaddaeaabaabdabbabbeadadaadeeeecadbecdabcbbcbbbcdbcdeecdbbaadaebeaceacbdebbedbccddcbedeacbdcdeadaccebbdecdabddbdadadbbaeeacdbecdaeaacdcdbaebeeddcbcbbdbcaaeeedcdadccebadcddcbddbbcebbebacbabcdcadceaebbaaeadbdecceeccebbcdceebcccbdabecedaccacdaedbbebbbeececeebcbeeacecadebccacaeccbbdcbbaeaecbddbeaceeeadddcecdececdcadacbdbdddabcdcbaacabadecddbeeccccadeeeddacbdeceabbcaceecbeedeeaecddabbeeebbbaccccedddeacdadeeacdbaebbaebadbacbbbbcecdbdcebcdbbaaacadbbdcdbaaeabebcbeeeadaedadeeebbababbaaaedcbaaddeaaceedebebcbddbbbbdeadadaedaccdaaeccdecdecdeaabaaecbadbccecbdceebbdaaddbbbcbbeacacbabbccbdbcbbecccaaaecadaddeeaeedcaeedddbbeeabadabcbacebdecbabdacbbddeceacebdbcebbabdaacebdacabedeacacaeaabeaacbebbbcacbbaebcddeeacdbededbdabadebbeacaadbecbeecbaccadbcdcdccacbbacecbbcecbbaacccacdaabeabacaadccbccceebeddadbbcdebbdbdddcbdaebbdcbdaeeecddbdddadacaaecbedabedeacaedeccbaebbdabcaeacdcececebabccbbeeedbaddebbddeadbaecbcaadcddeeecabccbecaacadddeddabddeebdccebacddadececbaaeacdceccddcabaeccbceabacdaeabdabaddaaebdcdbbbaaedcaacaecacabbceeabdccdeddaadebdbdabcbbebdbbceeecebaacbccddeeebedabdcceddeebdcdeedbdaeccddbebbaccdbbcaacbacdaaedeebecadbbeabaededecaeaddadddcdebedaecbdeeddccbbbbebccebadcaceeceecdabbcbbadeadeeedaeeadaedbdacdadbdebedebcdaaebdaebcdedabdaebabceaaaaebddcebaeebddadacdeeebeacdcabbcbaeabeaaeecacacececbaeeebcedbeebeceabbdcbdeaaaeadcbdeeebccdddaddeabbaebccdbdcdaebaaeaedebbeecbebcbbedcebecdaabcadccabacdbdcdadadbbbcbccdcbdceebeaecbcdecacaeacabeecebcdbcbdcdeceaebdccaabcceacdcbbbeccaecdacbdedbdcddcdeccadeeabececcbdbabeccbbbcbdebdacddabdcbccbbbcbdcbcbceeeabeddecacddeacbcabaadccbdcacadbecdeeccacbcaebadabecceacddbdacdecdebdbdbedbccedbbdccaaaeacccaceebabbdbcbacabbeccdbebbbdeceadeeacbecebeaabbadadacddaddcdacdcecbccadcacddbcaabbaaabbcdcdedcdbacacadcaadbddadecabceecabbedadacaecdbadcdceebddecbeceeaebeebeddcaedeeeabababddbacbdbcdeeeccceedbeeedccbdbabeeedcdecdaddadedbacdddcbecbddedeadadedcedbcbcbecbebeeabeeaacaecaabdecaebbaeccabbbbddbdbcdebeeaadabceaeeebeceaebaacdabbdadededcebdadcedbcadbccebacbabacaaadbdebaccaebebcbaebdcbbcadddccdedebcedaceebadcacaabebadaeacbadcdbcbaacaceccbcbbdacebbadeadceaeddeaddecbaadbabdbbebdaabbbebbaacecdcaeadbeeceaebcbcbadebebcacdccdecbdcadecbcccbbaccceaeeacddececedcbdaddbebbaccceceebecbaccaccdbcdbdbbaaedabdbbdbbcccdebeebeadedbcbbbbedbcbbeabdaebbbbbabaadbcadcbceddcdababdbadaceabccbbacbadcecbeebaeeeeeebddacdcceacbacebcebecddebbadeedbaccceecbbabcbddedcbcbabcbaadceaacbbdcddcabdaadaaacdadadecdaeebceeababbadeebbdddcebcdbacbddeadcbbbcdaaeaeebcdeccceeabdadceceacccedbbdeedaadeadceaccbbebddebdbdcdebccbaadadbbedbdababaadbcbdcdcaedcceacddbcdeecebbcdcadaecebadebaabdabcaddaeeaaddddeeabdcdcebbacaaddaeaceeeaeddabebbeecbabcaebbabddaececedebbaddcbabdcdeaebdecabbdbceecaeacbababaebcaeceddbeadbbbeadedbbcbdedccbdbacdaceebeecdcbcddeaebccecbcacdaabedbceccabddddcadaadabebecebeaabceeaeaadbebabbdeaaebeedaabbcddcebcdeacbeaaeeddecaaaeecbebdabecdaedccaabbabcbedbabcdcbcaccbbcdcbcdddbeeaacaedabdbebdaacbdaaaacceecbdabbcbcedaacbccdbdbcbddebacaedcbedebaaebeeddedbedebccbcaceccbdcdeccdedccdbacdedbdebeadaedecccdcdccabcdacadcccdeeaebebdddcccacbecaceaaaadebadeeaaedbbcecdcccddebceacecdebecedccacbdcccaaaecdecebbaedaeccbdabbbaaebcebdcbaeebccaaebaeddbadaeaedbbbccdbbdcdeeeedeecccadceadeadcccecaaebbdabaacebabebbebbdacabdabcacceecacebdccbebdeadeaeaccbdecdaccbcabadedeadcdcbececbabebddddeabededbcaccdaececeacebbdecbbacadcddbaacbcadeebedbcbbadacbeabbeedbaaacdeaddcedeaeebceeccadbbcbbadbbbccbcdeebbddcedbebadddbcdecccbccdedbeeebccaaeaceaebeaccbedaedbabaeaeacdbcbebcebddcdaddcbbcddcdeadaeebeddaceabccacbabaeebaeaacedeaddadecdcccbededdcbcceebeaaccdbdcebeedbdddabbcecccdbbbebabcddaecacbeabbcbccabbcabcbedcecebeaaabdbecccbececaeaacecbcadebaabeadbbcbbccdddcdedeedabacbedceadedaebdbeecbaadcceceeadcdbcddcdddaaeabaebccabccdbeccbadabbbaeadbcdedbdcccbdaacdebebbbddbbabeaedbaecadbabcddcadedaebdcbdeceadbaeabebbbeddbcceebaddcddedaebaeacdbbbdbedddacbcdddaaaccbdbdaceccaccadbddaceeebadbddbddceecdccdaeeecebebbbbcdadacedbdebddbaaeedbbdccadcbcdacecbdbacbbaecbcddcaeacaecbbcbaebaadcddbedbaeceeaadeadedbdbbacdbceaeccdcaeaadbbdbdddadddcacbaeaddeeddbddbccaeaaebcedccdbbcabdadeaddecaaebaddbccbbacdacaebdbcecacddbcccbdabcbdedceaccacdedbadbdeeacdedcebdecbdeedcabeabbcbecececedebdadadaeeacccaaddebddbcdbedacbeeeeaebccbecedacddbedcbedcebdcaddbbdbbeaccadcabdaebbaaacecebbdebddddcacacacbdcccbccaaccddcebbaabbbdbeaabeabcdebabddcebdccbedbdbdebbdabeacdcaaedabcceaedabaecaabdaeacaaededccdadcbeccbdeadbeadcbbdcbbdeacedeedcbebcaaaacdbaaeacebbdbbcacdaccabcdcceacaebebcaaebcabeadedcbbecaabceaeeccccaddeaacabacaaacbeaacbccabbcdcbbaabedecedaadcaaedbcbcadebadeaeeeadcabecacdaeeadadccecbaeacdcaedaeabcdcecbcadebbeadadecdeebedaacadcbeedbcacbdacbcdebcebceecaeabdcadadabceddbbeececaeebeecbdbcbbbbeeacedbbcbbeaccdcacbaaabcdccaeedbbeebacdebabbbacbcadaeddadcddecadcbddaeccaddebddbdcbcbdeaedbbadadbdbdbdaaeabcdcccadcadecdabebdbdbedcdedadddbabdadcbeaadbeacadeedcaaddeedaeddbeaccdacdbbabbcbebdaaddbeaaebeacebedcadaaedaaadeddbdbbcbbebbeeecbbbbcbecddeebadbcdcaadabecddcabbeaadaebbdabddaabdddabedabebdbcecadbeacbcddeeceebccdabcebcbecbeebadadeccbbaacaadedaebeecbdadcabcdabebeabdceaddbceceecccbeceeaabdeddedbebbbeeecabdbaecedaeacccddbcbdceccebbdcbddcaddebdaecdecdddbeceaaecaeaaaadadcbccbeaedddeebedbbeeacbcceeccedcdabecddbdcadacbdbaaccddecedaecdecaededdbdcddaaeaabeccbceebddeacbebccabaedebabedbadddccdccabcadbddcbdceaccddcbdbaacddbabcddbaebabcdecdbcbebbdeccabceccccadaaceedbabeaacbeeedaebbabdceaeedaacbebbbdadddaeccacebaebbabeddcdebdcedaeaebedccacdbdbeccecaabddcdcbedceccbcddbdcbcacadcbeadddadededaedecdecbbbbbcbcaacdcbdadbacbbdddcbeececabaaaeceacebbdbdaaeaeedeccdeddceaabbeebcdddbddaaedcadbeebbacbceeddbbbbbeadabebebedcaeaedcbbdcedccedbdaadbaeaeddeadebccdeebebbecbccdeedadccdbddddaebcddcdbdeacceececaadcabceedeeccbbbcecbbdaaabcaccadbeeceddabeeeabddebcbaebeebecbdaacbbdeadabedaedeeadeedddebccedeaeaacbccbdaabeedbbaeabcccecbebcecdaabdbacacbceddcbdaaddceadabbeceebeeddbccdcaabeeaaaecdaaedbeedbeeaccdbeaddddcadebbebbeedcabdddbcacdbbacbeddbddecebddeaadbbccbdadeedaddcabcbdacabecececccaacceaceebbaddeceeebbbaeeadbaabdebaedbacdacbdabdeccadcadecaecbddbadcbebccadbbceedadbcacedaacbeeaabdcecceddeaecaeaedecbddadbccceadcbdedbdbccdadabbebcbabedcbecdbacdecaecadbeacdaaabdcbaeceecacdddeedcbdeebceaccebdaadbaabcceccaeedbaedbdcaaeecaddeecaeecbcbadadeabceaddbddaecabbaabadcbbbadcddeaedeaeeceebcbcaebdababebbedabbadabccaaadacbcabcaceebbaceecbaebebcdeaabccdabceaeeaabbadcbdadbceaaeedcbcaeeeaaaeeeaabacdaeedadebebccaddecebceaddaeeedeeacdcacdcadccbeabcdbbeabacebcccbcabeacecaaadacbcaaadbdbccbdaadacadaeccecacddebeabdecccababadaaceeecbcabaabbbcdcdccdbeebcceedbebddedacdebbedbedaabecebeaeadeaeaeebbaeeeeaddbdbeaeabcebcaadccacbadacbaaaadbeeecccaaccdeecedababcdceceebdccbbaaaeddbdcdbacaeaabcadcbddbabeeecdbabcdbeececcebdbdedbadcadcaceabbedbabdacacacccdbeecdcebeaddceacabcadeccaadacbebdcbdbbccaebeddddeccabbcdeceabecaaebaaaedcbdaaecbdddcdabeaedebeabceacbbbeedeaaeeaccbcacaecebbaedbdbabbbbabaaebcbaeebabedcccacbecededdeedaddccddeaccbcbcebdaeabebbebdcdcdddccadadcaceaedcaacedaccaddbdcadccbddabdcaaabbcebddbdebdeacaeddccaedacadcdabaadaacceccbebcbcadeaeabedabcdadbcaebaeebbeecebeecedcecbcedeccaeceeecaececbeccaedeeebcddabcacdebedccddeacecbeecabecabddcdeeacaedbcedebecadebbbecbaadebeeedaebbddaebacdcbadedccacddececaadacaebeeeedaebecedecddaeeeddcbadabeeddaacccdecddbbebabeeecdcaebdccecaeccaddecbbccdaeacdebadcdeaebcecddcaccaeceddbbdacddaebddeeedebcbacecdddacdebbecedaeccaccdccccadedcaebbccaeedadebdaeacaaccebdacbeaeceddcbbbaeadabddeaddbdaeebcedbcdeaeaeacabdabeacdaddcdcccccbceedbedadeaaebaecdbbcaaeacebaedbebbddcbbacdccbccbacbaacbaaebbcdeedcdacebbedddacadeaaeeadedecccccabcddbaeaccddbadacebabbbddebbdcccdbedbcabacdceaecbeeedeeabdcaedbbbbebdbdcaddaceaddcadabcbcbaaaecabdaccbbddbaaabbbbeebeeccecbabdabcebabbadebcbcbeedeeceacccebcccaaddddccececcbdebaadeaadaddcdacdbdbbaaccbdcedcdaddaebdaacababcdbecabecccaaeaaecdebeeabccebeeedceaaeaddebbbbadbaaadacebdceeebbaeddbdaecacacbeedbbcaaabceaeeccecdaaebedaadbdecadcbaecbcdbcbbacdcdcddeededaceabeaccceabacbcccbadabbeeacabcbdaabaeaceadbaeebeceabebcdecdbdabbaccdcbbcaeecedaabceeaaebaebadacbcaacabbabccbbaeaacbbdddedbeacaadbabeacabdceddbdbcaaabbccaeccedcabeecdbededbeaadceeccbebbeabbcbcadaadedceccadcdcadeceeebadaeaaedbaecdacaacccbdcaecaadebbbaddbaaedaecdddcaadabbbcacbbabacecbbdecdbeeeadbbeeddbaccebdccbdedabccbececbeecaabacebbddbdbbdbbaaeaebccaedeccebcdcdaecabdaaabdecebbbdbcbeeacecccbdeceaacabeebadcdedbccbcadaadaedaebacaedaaeccbaaeeebceededacbaadddeedbcecdedadcddecbabedcdecbedaacadaeeaaaecbbaabeadcccaaaccadaededbaeedccdcebbabdbcbedbddebcbcbbcbddccaacccdeeaeaadddddaaabcecbeabbeedaecaaeebbbaedbcbeddabbdbebeccdcbadaedcddaececedddcacadcbbdeabcacadbddaccabebbcdbdcbcedeaccbdbebebdacddbddcabebcbbeecbbcecacacdeedeadbcddccdedbeaeecbeebcdaccabcbceaddaadeaccacbcbbdecbaddadcabadaebadbaabccaaaedeabceebaccbabcbdbeddaaecbcdeebadceaabdecedcdeacdcbebbeeabcacaddebacbeaaaebbadcbabbdadbdddeddadeebaadedeabaeedbecdceedbdaabcdedbeceeaceccbbdaebaeeeedadbadbecdebcecbdeaededeacddbbbaddddeccbbcabedbddeedddbacbecdeabbdebbccaebdbeaceeddddbdedcdedacedebbcbdeadaaedacedbdaaeddcacaebbcceabadcdedaceaaccbecceeebdcbadddaddddebcaaabdbcbeadeeadebecbdbcdbcbcddbacdddcdedeabecabaadbceedcabcdaabbbbdbbdcbbceeeabdeddebcdddebceadbeaaebdabcabdbeebbaeceabbaacebcbecabdebddccdcceeadddbebcbabadbabcbdebaacddcbabcdccceddddbccbbabdddacaadbbbadbbbadcdebcdebbeddbacdaecbdcaaeabdecaeeecadeabcadccebdbcddabecbaeeadbbbcbecbeaaabeaadedacaeacccddcccccebacdcbbbdeabacaadaedabeebbbaddeaaeacdaadbaacaaeebabdacbbbbbdcdcbbdaabcdbdddecedcebaaeaccadababeaeebeeecaeddceabecaaedcbebdebeeeadbdbbbbdaabdadedabdadbddcebbaeadcecbeeebbddadedadccdadaecbebadebcaeaaaabddccbaceaecbecdcebceccdcccddcbddccadbaaabaaabedbcbedeeeabbaadaacedeaadeeabcebcceccbdacbaddcbdbbeabecabaddbcbcbaacbbbdcdbbdbbabbadcaceeaececbddbbabbbdaeebeecedcacbccacebaacbadeddadceebcdcccaabdcdecacaddebcaebddeddcaeaabebebbdbcddecddedbabbceacdcbdedccceabaecaaceccdeabedacceacededaaabceeeccacdcbeddbaceebbbadbdeaeddbeddaeeebdeedacbceacbbdaabdbeaaaeeeeadbebbccbdebaceaeaceacdceeccdaededdadaddacbaeaccabceddaebedaccddadeaebbeedcdcbceeedcdbbdaebdcddeaacdccbdcdadaebdacbeababcbdabdceaeddadeabcdeaeadcbebbdadabbbdcabcebabbcebdadcbccccdaccbaacbdceccbabadecdedcabdbaacbaebaaceedecdcdceeabcaaaecbdabaaddeebaacedecbaebbedbcbeeaaedabbedaacbabdeceaabcdbeaeeebcaaabdeedeebcbbcdccaedaeeedbbdecacedaedbaaeacacbaddbdeebcdbadacbabdceaaccbcbddecadceecaeeaeccaeddabccacaacacbaacdbaedccaadeaccbebbdecbbccabaedeccedbcadcddcedcbcbebbdcebcabdcdeedbaaababeeddacddcdedebbbcaabacbcabcdedbececcccacbbeebbcdbdbeacdbcacbbadaabdebeaaaaddecbdeecdaccbbbeccbabbaeedeaaebdaecaecebddcedccdbaeeecbdedbbecddaeeaeaceebaaabcccceeeedeacbdcbddbbcecdacccccadddbbeacdebbcbecbcbebeadeaaebedadceebadeabecedbdbbdcabbcbaeebcbdcddacdaddbddcbacccdbedbddbabdddeacecaeeadbdbaebbabbacabbcdbddaeedcbaedddcdcdbacdcccdbdbeeadbcddaeadcadcecdebdaacbacdadeabedbcabeccaabedccacdacdedaebcebbceaaebacedecebeaceaabbecbebaddbccbdadcbaddbdbbdbebabccdeeaacbcabacedcabdbeedabcdedbabedceabbaabccaaeacecdcdcbbadbacbbcbeaadbbeabbeeedcbccadacbcbbdbdacbbbbeceeaccaadbabbdeccbcebddbebabdcbadadebeccbabbeedaeacbddbbcebcbbdbcebdcdceaaeecdbebcbedbeccacceeacbbbbbaccedadcbcbbecaaceeccdcbcacdcbaaabdadbaadaccecbebcabbbbceeaaeeeacbaacdaaccdcacacaaabeeaaedaaecebabaebedaaeabbadcbeebdcdcceeebeccbcaeadbbcbaadedeeaaedbceecbdbdddccacecabbdabbaadaceedabbdacceebacbdabdaadadccbbcccaacbddeddebabcbdbcbeceadccdccbbcedddacbcebdcaeccecdddedbadadddbcaedbdcadbeebcbceecbdbcbbdebeeadcaeaceddaebbdebcbbabecbaecdbbebecacdcbdcaeaccbeaedeaddcbdebacdaddbaaedccaebeedddbbcacddecdbceeaecebbbaedceacacaaadeedbcabacabcdcabcdcaebaddadbbcaddaeeedddacacdddbbbcddbeaeaedbacadbbabdcaabaeccddcecaccaaccccddebcbddacebcabbcdaacbaacbcbccbcdbcbeebbebeeacebcdbbbeebbeddbbaddeabccdbabeeacdeeabbceedadbecbedbbaeedecadddeeeeececeddcdbadbadccdcceebcdabebbeedecdcbdcecbcbdcadeccacbcceccbaeddbaaddcdaadedddcbbdcacadebaeeddbeadcddbbccbaaebceeeabebadaabdbbecebeacedddaceaacbbcabbcacbdbabdccbeacbccdbdedcdaaadbcccaacddaadbeeabeaabdddabedddebcedaeeccbbbecbaebbeacdecaeaacdebdcbeeeccbdbaecacacecacadccabcacbcbbacbddcccaaecdbadebeadcdeeedddedcbcdbbbaeecabdbdbaacdbdddbccabeacdbedbadcdaaeedadeeaeebcedebabbbaedbdcaebabcceceacdecbacabdededeaacaedceaccbaccedebccabacdeebecadbaddabcdcaebdbeccbecbdecdbccecaaddbbcaadddccaeceaadbabedcaebadadeaddaeaaebcadddcedbaeaaededdceccaeadceeeeccccdbaadcbcaaaebccdbceaeccabbadecdeecdbeaaecbcebaaeecbdcdeceabbbcbcecbddebadbbeadabbdebecaabedadaeaaaaedaacdcdcbbbaebcaabaaedcedbcdcbaadcaaeebdedbbbcdeeecebbdaeddaddabdbcacdabbdcdbbbabbebeccbcaeebabcaabeaaddbbccccddbebccbeceaacedcabacebedeeeedbabcdbdcceaedacbdadedbabeecadcedacccccebbddaeacbbbdabacaeacaacdedaedabeebcbcabaeedeaabcedbccbadbbaacdeddadbebddaeedcaaacdecebccaadcadbeeddbacbcdcedbabcdecadebbdcaacbadcddbadacbbdcdbeddaecebeadcccecabdebdaecaaacaecccdacaabaabedcceaadedeacacbecdeadeedeeeadcbaaebbaecbacbcbadacccaaeacecebbeeebaaceecdbcaabbecabedccceebdaeeeecbedebeeadcbdaacabcaacddbbdddceddabbcaecdeeeeacbdbeecdaacdbaeccdcaeeebddaddaaabdecadaaeaddbabcdbceeedebadbdbabedadddbdaebacadeceaceecdcdeccecbbadaccdeecccedbbeeddaaddacbaaddaedaccdbecddddbaedaaddddadceaeecaadbcddcdbbdebdbccecddcacbaadeebbbdcedbdeadeedbeaabebeaeaeecdababdacbebcabbedeadaaaccddbadacdedbcaabccddbedbbcccdcbceeccbcbbeaeaeceebddceabccaeeeddcbddeebcbadacadbedccecceadadcaccccbeabbadecacaecdbccaebbcabceccbaecaaaaaddccedbdebaebeadadbaecbdcbadeabdbeeaebaebcbdcbdcebaececbeaaacccdeaecbcabacccabbbcceabcedaddadbedeabecebcaeabdadbeeebaecddbaacbdbacddeeccaedaceabcadcabbaabdedceebccceceaabcebeaaeacbdbaeddabbaebdbceacaaabbccaeccdaeceadcaeadebdaaededbaabdebbabbeabeeccdabadbbecdacbdebedbcedebecdadacadedabcceeaebceebcbaeedccdaaadaddabcbeeadbaaadedaaeeceeedcbbbedbbddecabedaabebcbaccedadccadddbebcbebecabdbebdbaeebbebbbcceecccabccdeaedaabcdcbaceceeabbcaacaceedbeaacecedbcbdcdbabecbabadcaecceacadacacacabbeedabccecaaebceebbedbcecbcbeebacebcceeccbcecaecccbebcebabcabecadaddcbdebadcaedbbbadcbbbedddbaeaeecdceeeabdabdedecedaebdeeacceabbbabbbdadcddeccbebabbdeebebbbeaceeaccdbdaeeedcaadceadeceebedeedcabeeadedaeeaceabceccbdadadbeebbdeacbabebaabdcadeacbbaecdbdadbdebbdadccbadccdddebecbaaccabbcadceaedbdacccdaeedcbdcaadabeebeeedaaebdbbdbddabbcdceeebcaadacdddcddceddaceacedcadaebdcaeddeaebbbcbbcecdedeccdaddabcecdeaeabedceccecebaedcbbaecbdadaaedeabacabcbbdaacacadedbadbadaeeacbdcceeddddaddccbceeceaedddccebdebaedeeeeacebbdddccccdcdbebaeecaaadbccbacdeabaccebeacadcbdececcdaeebccabdeadcbdcebbcebbebcdbbbbdcacebaeddcdacbdcbacaabebaaaeadddcdcccccedabaedbacbdeaeaeacacddcaddbbdbcdbcebebdddcbcbacaadabbeccdbaeadeeeabccbaaeabbbddcecaacdbcebebaeadecdddebbaceedddcececcebaeaeaeaececdbddcddbdbaacabdccbacbececbdbeaecdccddebebadecbeebaadceabeacddacebbbbcaaddceeeedcbecdbbaaeeeabcabeeccbdbbdddaadbaebbbccbdceacdbedbacaeccaebeaadeacbaeaaaaaeaacdaddacccaeceedabadaadeabcbdedcbaebceeeceddebecaeeddeedbdccabebababdaebaacdddebbdcebecbddbebebbecdbadeaacbdbacacebbedcadeabcbdceccadabddcbbcdcacbcbbcacbcceebadcbcbaecdbcbddcdccaeeedbeabdabcdbcbdbcbdcbbdabcedcacdbcaeaebecacbcdacccdbeeabebaeedbedbaaacbcddedbccbaccbadabdaeabbdaeaaaaebaceeddeccaddcaaddedcbdbeeececdcceeabdcaaaacdabedacdaeecedeedadbbedecabdbdabaddabdedcaceaebdadbaaebaabbdbbabdeaadecbbdacaceedaaecaaccecedbedbaebdecbddaddbcbcaccdcbebddcdbcccebbbdceaebeacdbdcebbeaabbecaaecebdecddcbbbabbababccdadadbebcbaabecddcdbdacabcecaababbdbebbbabcbccecddaaeacccbcaddceebeebddaeeeccacdaacaabddbcbdeaeaceaeceddddddeccaacccddcbcdbdbdbbeabdeddaedbacacceddcbcddceecdcedcedbbabdcdebccdcbebdabeeeacbcbdcddeacecdabaeacdbcbdcadabdbddeecbbecdbbddaeaddbbcccbaadcbcbebcbccdbaacedcaacccdbaadbdadaaebbacebbbaabedebdcabecabbdbbdeaaeeaddeedebcaeedbaecbbbaeabadaacdaecdeaedacaccceeeaccbaecebbdaabdbdaabcdacbdcaeddedeabbcdeebeeeceeabeebbbcebbededcaadacbebcdbcacedeabcebcbababdbabbbbadddaaaccbadccbcdaedaeccddabbcededbccccacecedcaccbacdeabbbeeaccdaddcaecdbdbdeeddcddbadbeabdcebbceacddeeabcaaacccebebbdeadedeedcadaaadbaaabbbdecbcedebaabbdeedbbbcdabcbbbbcecdcdcccdaabacdeceadacdcbccaadebcdebcacdcdeecaeadeeeebdcabaddbdabbacaddeaadadbcccdeebceeeaeaaaccddeecdbcadcdaaabacabcaaaeedcbcbbdadbecbdddcecacadecadaeadcceadaaaaabeccdbaaedceebbddebbbaaaebbeadccaebdccdecccaeabbbedceedeedadabdeddecbaebcadeedebeebdbcbbebcdcbaccaadaeceecbddeaeeecdbdbceebeeaaaabbeddbaaacdbacccdbdcdcbbbcadcccdebbdabdddbdddcccaadbbbdcbcceddcadbbbbeacddeeebcedaccdbaabcbbaeecebecebaecdcbbeadbaccdbcdddeacbccbdeddeeedebbbaadbaacdeabdbcdebdeddeecddbdccedcacbaaaceaacabeddacceeeedaaeacebcadcadadbeedbbededaeecddecccebeaceceaebeaaadebcdddeabadccbdbcebdceebedeadaebeedebbddababdadeccaeadbcbcbdabbbdeddaecadebcaccbdaeabadebebccbceddceabbedecacaeedbebcabbbdcdedbeabeeabeccbbeaadcebcceddbccedecbaedeecdebadbbbabccdaeaedacdaeaaaaadcaeacdadddacceecdaeaadbddddbceeecdadddeebdcabedadcbabcbbcaeebecaebbcccedadeedebcdabeeedbbabbeebcdbceceaddbacdadddcecaacbcbbcebedededddcddbdeccaeedebceebddaaeaabbcdbdadaeacedddcaededeccceedcdbdbaaedebcceacbebdeddbbabeebeddcdbabccabbadbdceaddeadeeccdeaeeddabaecbbdbcabeebaaabaeacbececbedbbababdbdeebabccbaadeecbececbbdcebcebdabaaebcbabaebedcbccdaacceaebeddacaedeebcadccdcdcddbdeadbdcbecddedbabcbcadababdaddaaeadccbdbccceaaaeddeccceddcdddebeaabecdbdbcadbbcebcecdcaaacedacedddbeeedbaabddbcccddeebaeacbcaeabcdbeeeccedaaccbbddbcebecacebaaccdbacebcbdabbcdcbddeaabdeabdcdebdbccedcbebceabcbeddacbedeccbddabbcecbdbbecbbaddbcbdaaeeadccbabeaabbdadcebdcebbbbabbaaaadcdccbaeeacaeeeecccedbabaeebecbbddeceeddbdeeaedadeaebebbbcbecaddabccdbdaeebcbeaebdeedddacebabdaccdeecccabbbdeaebcbeeabaeeddceabaeabeecbbebdceebaabdacddeadedabccabbccaaeabedaacdaedeaaeedadeebaabbdcbeccdccbbeeecbdcbdcbcaedabbcbbbeabebbaaadeeaaaeddccccbeeaaeeecdbbdbbabddbcabdedbeebeaeaabbcedeeddbaaaaebecbeeecceabadbccceacdbdbdbddaabceddccaadadcabccbcdeebbaddbecdecdaaddeddcedbcedadcdadebdbedbeebbeadccaaedbddacceccdbadeeacbbdecadbdadbbddebcccedcccaaeaddccacacaebbadbddbbdcccaabcaecebeaaabcaabcedbbababbdcabcceacdcededadeedacbdcbdaaddcaecedcebebdecadaecbccccadacbddeacdcdbeebaccceeeacbdceacecaaaaecbcdeebabacbecdaebdbddcaadbccedbcabcebbeebbceaaceaeccdaedebbdeaddaccbaecbcbbbdadcaaecedbaebeceecabacbbbccdaacacbccdecbceaceaaecadbbcdededebbddddedeacaacbeccbbdeecdceeadeacdcaabcbdaaeebeadaacaacedaebbbceaddeedcbdeacaddabcbebcadabedadbbdcdbbacaacaabeacdbceeaebaecdcdcdcaecbcddcadaaeadaededbabcaacdcdaaacaebbacadebacdacacdceaaabcdaadcddecadebebeccaaaaccabdebedeebadaedaacabbacaeaeabcdddeaacdeddedbebdcdacbadbaadcacceaaeabbddeeddcaabaddadabaebdedebaabaeccedbbcccaaedacdddebccdeccdcdaaacaaceeebceddccadbadbbebaedbdacebcabcacebeebbecadbdaadabadcbdecacbcddbcbcdadaccedacadbeeabdbabbebeeabacdbcdecaacdbcaecadbaeacceeeeaadbbcaddbdbcdbacedcbeadaebeedadcdeeecbbcaebaccbaeccbeaaeaedcbacaaedebbccddeabeeedbeeebcebeaaebbdbdcdeaacedecacacaacddacbbadaabbabbbcecacccabdddecbabecbadcdbdaacacbdccaadaabebdbaeaacbadbdcdeaceaceabadbceeaceebcedacbbbebddcebaeabdbeddecdebbeeabaeababaccaddcbcdcbebddcbdcabeecabbaedaabaeeeadeebcdaeedecadddaacbacaaceebabdaccbddacaecadebeabcedcacaaadbaaedabdcbeccaedcaacacecadddacdbeeaaeeddbeccbdabebcacccccceacceaceaeceaeeccecbceddeaeebeddacedbcdecbddddeecdbedddceebebdceecebaaedbeecaacbdceddabbbabedeeeaacdcaadbcbabeccdbddedcdeebaaedccdcebcbdccdacaaabbcdddbaeebeccaeadeaadebeeebdaebcedceeaccabbdcecacbdeaabaecebbeebacbdccbcadccbbbdadbbccbdcdadcbcdecebaecababeddddcdeaecdcabcbeddbbbabbedaadadcbaeaddceddceaaebccddcdcbddeaadabcadcdcbadbcccbbbbeacdbdcccbdaeaebbaedcedacaabcaedabbcedcedddbccbacaceccbdbbdebdeddaecceaceedbccbbadacececbbdbaeabdeeacdbcbcccdeceaedbbbceccccebbdaaaacdeceaeadebccebacddbabcbceabbeaeeccbaabdcdeeaebaabccedeceaecddaeaddcacbcadbcbaadaecdaceddacaaadacecdbcadabbcbdebadddacbcebeabdcabdebdccdbadaeddaadeeddadddedebbebeeaacebdeccdcedbaddecceaedcdbeebeabbaededdaacaecdcbcedacebbbdedceabacbeabdaedbbebbbeadabcdeedddcbcbeebeccddcdeddabdbdcdebdebbcebceebcaaeadadeeccdcbddcaeabdecebccaabcadecadacaecddeaacccaabaebbdddcdabcdcaaabdcadeabbbddbdedabeabbadadabbadadbeeaaedebaadeeacbbdbaaccdecadbdddaddbeddeeccbbbdddeaccdaecdbbbbdabccbecbdbbecdabaaaececcaacaaedccdccccaccacedeaadaebabecacebacdccbdaacbdcbdacaceadcabcbbbbbdbecddaeddcbbaabdcacbadebecceabdbedadcceeecdebabdcdbcbeaaabdcceaabadabdcdddaeadbbcebdcaceaacaadbaccdaceebbeecaccaedadddebbabeabbecdebeaabdaceabdecacccaacbebeceedcbdbbeeabacddabcbdabbccbbebbeddcdbbcadaecabbadeaaedbeecdecaccebbcbedabdbbebbdadcbdaaeadaadccadaddeacaeedacaedebbdeeecbceaaeacaaaddaacbdaabebdceabdbdecccabccadaabcadacceaecbbdbabaecdacaebecacbdbabbcdadeeaadbaeedddbcbaeccecbcabbbddecebdcbcccccadeddbdebaddabeadeecaaaceebadcddbabbbbbdcbdcbdccbbebdbdccbacdaeebaedbdbcedededdcecaebcebabaccededacaadebebebbbcbdcbccbceeaabbdaadeebcbdeacbecbaeebaedcdeaebabeccaaedbabcbbdceabbbddacbebdbbdedbbeeecaabeadcbaaccbdbacbcebadabccacdbbcbbabcacedbddcbcdbecedcccbcecdbdbdeddcedecbdeebacccaeeaebbddabbbbcdbeeeddedbabcecceeadeeddcbcdacbaeddbebaaceadabbbbbbebcdeecebbedceebeedaaddbceeabaeeebdddbbdacebcdadddaaaedcecadeceeabbccdbeeeccccdcbcbcaaabccdbdcaadccacdcaabaeaebccdeaaadaeaaebecbaececddedadebbbbcdddcbededacceadceaedeacbdbeadcaccdeacabecbabadabbddaabbcacbbcbbacbddcdecedbcacbbeaeaddbbcccddaadecbbacbdaccababcaaadcbeaeaaedaebbdddcabdecaddedaeedbdeaeebddcecaccecebdeeccbbaaccbbdbdbbcebecdecdecedceaebecabddecedadcdebdebadbdaadadbddcdbadedededdcedbeecbbdacddbecaebaaebbbbccdaaabbbadbdcaaeeddadeaddeddedebebbaaeabdcaecdecaedaecadbbeedeadeabdcdacbdcbdeaeadcacbedbaddaaeaabddccabadbbacaadbbedbbdececccaaededdebaacdadaabedeaaaddeeddabaacbabebabcadddeabdaaddedcebaeecadadddbebecaacaaabeeabacabeeddcdeaceeecbbdeaddbabaeddcbbaeadbaaccaeeebeeaecdebabcbdcedbdbecdcbcdcaadeaceabcecddecdbbaabcedcaecbdabbabbdeadceaccdbebdedeebcbeceddeddcbaddecdddeedeebaaadcacadabccdccabcbdeeceededbeccaeabbccbccbdecbcaacedaacdbadebdcaaaacacdbbddaaceeebdcebbaeeaeccaaadcadaeebdedceacdeddedccadbedbbcaabdadabcebbcaabaaddabbbaacbbeddeccdcaabcedcbceeeeabcbaacdeadbcabaabbdedacaacaebdbcbdeaaaedaaeecacbddbddebbceccbabdacbcebebcaecbddabccebeacccbabccdcbacbdccdcccdbdaeabbbeeebdbdaedaacbcebbeeeccccdcdeebccbcdccadbabddacdacbccdccaeadcbaaabacbcaaebbcbaeacdaadcdcaabbbeeedcabcadeeabbecaebbcdeddbdddcadedbccbddccdcccdcdbadaaadbcbaabeaebaedabedddaeedcdeacaeaadcabddaabeaaceeaeeecdcdbdebedadebedeadbabdcbabcaacdcabadbabaeeeadbaadcbdcecccebabbccbacedeccddcebeaccceacccdbceebaebdbddcbaeaaedecaddbbeddcdcbbbeeeaeaebbcadededbebcddeecdcccbcacecaeaebdaabcbeadeccedbcacadecacdccddeaaddadbaecbbabbadbddadedbcddbccaeeaadbededaedecebcccdaecdcddbcbdeadcceaabecbdebdbdeeccabbcbbedccdaeddbaebbbebebacecadaaabddbedceccbacedaeceedceccbbabcccdbabeceabbacedaacecbabaaacacaaacdeecbcbdaadedadeabeecbcdeaedeebdbbddeddebbedcebebccbddbcadbcaebecbeeacbbdcbbadeeddaacbacecedeacacebbbcbeedeaaaddbedeaabcaceabeebbeaaddaeeeddeddedcdbdecddbdceddaddcdcdddccbddaeaaecdaeeceabceeabeeebccbacebcbbccabbceabaebaceededddeeebcbccdaaadbaabeadecebebbddadceebaddbcbaadddaceaabaadeedbddecadceceadaecccbcbbeaeedbebeaccdeebdbdeedecaedbdbababdeedebbbaadacacceaacebeecbceaabeaddcabbcbcddaeceeadadcdeacebdaeaeaebdcbabacecbdaacdbecddecaeeebdedbeeddeaadbbcceebcbcaeddabeaebedcebdbbcbaeebdbaccbdbbbdaceaabadadcdeadbedaaccbcceaadcccddcbcabcbeaccdaecabcdecaaebebbdbdcddbceccccdbecdcedbecbcbdaabecddebbdaebbdadeaccdeecaabaeacececaecbeecceaecbdadacecaadaeadeeedcdbeaeaabddadeeabacdbddecddaabecabbacbcdeedeecdbebebdcbdceebbeecdeebadababdabeebbacdaabbeaaedebaadcbeadccebdaaaddcbbeadedaabceacaadbbeeaaebbcebcdbecaaaeedecebbcdccebbaddcbcabbcedabbedaccedcbaeababdcddaccddbbecbeaabcdaeeccbbabeccedbacccaacddaceecdcbddbeeceadebbedbceecdecebdbeabecebacceeacecbaabebacaacdbcbdcbdcbeaeaebddcacededcedaaadaceacbcdacdeddcaeeeccaeeadeccbbeaceddadcdaddbaebbdebdcddbbeeabcdddcaecbbaaaceedeeddbaaecadbbebcebbeceabaeebdaeecbecddbeadbcbbddeecaaddbaeabaddccdcebaabecccebcaecddcbacaabacedbecacaaaeabebbebdacacdeadcdaeeeebacebcadccdbdadabbecceedbddcbadacbdddbeeabdbecaeebbededdecdeeabdaaecceaccacaceebcabedbbacbdaddcdecabdbdedaedecaeaeedbdcacdabcbbbbaccadcebbdcedeabbccbbacbabedbdbadaeaabddbdecdabcebcdebadcbebbeecaabdcdaaccbecedacbaecadaedddecbbabddceaebabcbaabadcdcecbeccecdebdadacdecdaaeedbcebbbdcbdedccacbdebaececaddabbdbccabcbcbeecbeabdccaecedaddebcddedeaeeadcaecebeceaecadbeccccdbdbecacceacbacecdedacbbdbbccccaedadcdeaabcbcabdeaeddecadceebbcaacebcbabaabdedbbcdadcabaeddbdcbdadbadeadbdcadbddeddaacecedceeddaaaadedebcdaceabdadbdeeaecdcaebeeddcdbaecbaabbcecaaecebecedbadaeaabbbdabddbdbaeacdbedcbcabbcbdccedcebeaaebceabdbabbcaebbcedbddccaeecbebecccebcecbccabdeeeaebecaaacdeaccedbdddebdababdaaddbddbaceccdcccaddbdacbcdbacbedddbaacecdeadacddeecaeaebddceebedcbaababbbdbcdcedcdeeadccdbddcacbdbbeabecddadadbeabeebdbdadbdecdabacccbeaeddadacebeddeceababbdebbdecbdbcceeebdbdeeebaaeaddacaadbedaacceacaebcbcdeabbcecacbdecabaddceebcddbadadcbddceacecbaecbeeaacceadcaceadbacadecaeaaabecbaedaeaaedabbecbdaacbdaebbbbdebdbaddbecabeeecdabcebbcaebddebdededdddbbebddddcbaebabaddebdebbebcaebdcecacaeaeaebaaacccaecadacacdbcdacaabcddabadebcbabbdccaaededdeebaedcbdbdbdeadbdacedebeebdbeadbddceaeadbdcadaaeebbbadedebbedaedccbddeebdccebedceabbdedcbaedaaceaaecbbbbaaceaddcecdecdabdebebdaebcaeaccbbaccaeecdceebdccaedabaadeebadbecbbeacddbbcaebdcdbecabeaeaecbaaccaacbbdebddececcdcabcedeccebdeabcdaebbebbccebbaceaddebbacebaadccaebbccceabcabcdaaaeeaedbadceedcdbeaeeddeabeabccedaebcbeaceedcbccaedabaebbbddaaaadebbcabcdabceeeeadeccdebdbecebabcdccbaeedadadcebeeeacbdaebacdebaedbbcbacbaaccdadbcddcbdbeeaabeabcdddaabeedcebaedccbcadacecdecdedacccedcdcceccedeabcebccddeeccbedddcbddbebabedeaadebddcbcbdabeddddbeeeddcbabaeedeabeebbddaddbcdaaccadaaabcbbbadebeebcbcedeaecabedbecdcdcedccedbdacaaadcebcedbedbdeadebaadaaebcbcdddcbaacacbedecaeedaccaadadbddcccaebebbddcddcdbaeebbcacabdceaddadecbddcecedadcebcedcbebeeaddcbcecdeaeadacdeedebbcabdaeacbaceaacaaaeadbcdecaeedacedbdadbabcbdcebbadabdeedbdeadceceebeacddbdcccbdadcecbabbadaabcceeadcdbcdebbedcddaeaeebdedbadbaacccdccbadeacebceacabcabcaaccdcabcaaedbbadcacaceecceabebabcbcbebaedcbcdaaaecbbceabbbedabdbeaceadbdbcabcaedcddacccebcaacadbaacaaedeebddbebcbecdaeabedcebdaecbeebcdeabdcdcbaebddedcecdbbceabbdadddbabbccbdceedcdedbdbeeadaebdceebbcdcaaeadebcecbccebededccdeadbbebdcbedaaddecccaaceadbbddaaadccaebddadcdaaadabbcacccdbdaccbcdeadeaaeadebdcbabecbbccdecaedccbbeddceecbedcbceabdbbdbcaaababbedecbbacdddddaeecaedbccbaedddbbcabadcdbcbcaeaeabeedebbddebacccccedbaecdcbdacadeddeeaaabbbeaecccacacdcecaaabaaaddbdabebcbbdcaceaceeadabcbbcedceaedccdebceecabcbdbbbbceeedecaccabadbabdecadeecdabeeeadeebcceccdedceacccecddcdbdececedcddcbcecbecadcdaddacceaaedeeaeabdebebdebdeeaadbdcebeadcceebecaccbebbebcaaaaebaddecbbecbdaeebbbcccccdabeaccdbeacaaededacaaecbabaaeaecbbdbaededbdeadeacdbceaddbaebdbdeccaebadbdacaeccabaacddcebabdcbedddeabbacebcedbedceceabceddccaeaddadeacceabbedeacdadbddcdaebbdcbdbdecbaadbecaaecdcbabbadbbeecbdaeecbbacddecdaabcacabcddaeabbdcddddaeebbecadcbbacaedcacaabeecdddceebeeacbabeddaeabcaedebdbeeabbabedaeeeacaccacdeabedbdacbbdbabbbcccdcbbeaccddebaacadcbceedebdaaabbaeeccdcaadbddbcdcacebccdcbbeececaadedabeebddcccadbecaeecaeacaabcabbcadbbeedcacdbdebadedcaceaedcbbcbddbeedeaabebeddabaadccbaddbadaacdcdaebebbbcadbcbcbceedbacadcddddbbabdebdcdaebcbaebcdabddcccdbbcdaebeededddbaaeedaaeedbbbeecdebaaeecdabcaedbaabcbbaeccdaaeaecacbcacbbcbaaebadcecdeabeceeebddeceddbbdcddebcaecebeeedeaeeeabddceaaebbacbcdedcdabecdeddccdbcdbdcebdeddbcbaccebcdabbccbbcebbdddddeeabcbceeedbeaaeecdcbadeacacdbacbbdecdbecddcccbccadcbabdbacebcddbacdacaadbecdcbededdacdbcdadaaececbdadbabddbbcbacddbcbeaccbbbbaccdccdaccebbedebddedbdddddcdcbedbddacabbccddbdeceacacbdbdadcbbaecabdaceedcaccdcbecebcaeeacacbeddeaacbeaaeddbaeababadcaeacbdaaaaeacdbbaeccdeabecabdacbaaaebebccccdcabebcedccadeeddeecedcdbdcccbbadaedccabbcdbccbebdcacabbeadebeadbebcceccaceeebeeddcacbbcccbdaeaceabaaddbdbaeaccabedcecbcebbeaccdbbdedeccadecedbedaedddabdcbcdaccbcababecadcabbcacdcbeccaeabbacdbceeeeebaaebceaeeddededeeccdcbaecdcddcebbaacdbcceabebbbbdbcdacbceceebadcbbdccdebceadaebbacccebeeedaddccccebdaacadcacaaeedbdeabacbbbdaebaabbeeddceebbecbbbcadeadddcbdadeabedceabcecaecacdcbdeddbabdccceddddbdbaceabebdcaecbcbdaedaaaeceeceebaeaaccbaccedbabdddbbaeeccbbedeaebaebbedcdcaddacbecabddbacdededdbcabbeebacbeddcaadbeeebbacbbaedcdcedcbebddcbbdaaeaacdbebedccebbadebcbadecbcaebcadbdebcdbbbceaeccddbebdbddcaebcbeabebbeceeaaeaacdbddabeceedadbeaddabceabcebabbcdbeaebaedccbadebeaeaadbbbecacbadedcddbebbbedcdcabbdedcacaeaedabedcbecededacadebcbdaabbebebabcacaadbabeeeecbbeeccdeedeeeacdcabdaeccabbabdcabedeedccdbecedaaedcabdcadeeedeedddeecdbdecaeaeebbdadcaacbadbbaeaeccdbaebccceceaabebcbccbbaedebbcbeeabdabdbdceceacdabceeebacadabccebbbaacacebaecedccebdabbebdaddbccbeaceebcddaaebbbceeaceedcdeccacadbaaeababcaebcceccaecaaabaccdeddeeeadebbcddbbdeceeedcdbdedebecbcbdbcabbaebdeeeaacaaecaecddbaebabececceaccecaaeecdecbcbceaecbdcccadbbccbcdeabedeaaaadcceebdaeadcdacbadeaadeeecabbacabdeaebdebbbaacbeedaaebcbeedcabacaddbdaebcdbdebcbdddebcacdaeeeedebdaccbbcddbdaeddbeccacbaacbbeeacbbdceaaaadecebadecbbbeecbdbdabcaccdcdbaccdcdaebeaebddadacccdceedadceecceccacdaaeeebdcaeadcacaeddbcdbaadbeeceeeabdeececdcdceaedbeabbbddccabcaaababeeecccbeddbcecbbccddeedacdbabbcbcaeaedebaecddddbabbdddbadcecbededbceaeddbdbacdccebdaedbbedeadabcecdcaaebaaebececeacceabbaddcaebebbeadceeacdeceedcdcbbabeaecdaedcbebdccacbcbeadbbbcebbbdaaacaacaacdcddbeaaabaacaecaacbcbedbabbaebeddebcbeeaeaabddabccabbaedacbeeaebeaebeaedbecdababacdecdbbeddbaababeabdebdeabeddbcbaacedaacdcaeaaacbcdbcedbbcbaabaacaededcabebedeedcbdeabbbeaeecccdbbdbbdcbcbddcecdbccbacbdbcbdaccaeddbeccdaabceeaacdaebdeccbaeddccbecacaebeceeeaaaddacdbdabcddaadbeadbbcebaddccebaebbbeeebcadabbbbecbcdcaeababdebaaadcdccacbeedcbabccacabdaeacbcbecdeebacdaecdeeaecebbbeddbebecaadaccdcbcdeabcaacbaabcdbdeddcbdceeedaddddebabbedadadccdabdaabddbadccddcdbdccbadcbeadddeabdbbbaaaabcdebdcceeebabdecbedeccddacebabcdeeeeacdbacbcddceddaeccbeabebebeedeeeabedaccacecabdbecbedaaebddeaebbbbaeaaeeabdcabbccbbdbabcddceebccccbccbdbaebeecdcbcdbcaeacaacaaccabbabceaebddcaedccacdcdaddadbeadccdcccebdbaeccddebcbeabeacbceadebedcceebaedaebedecddecbbeedcccaadbcadaeeabdadadbeeeeccacaaebcceadaedbdbcccdaaccbbacabdbeabddedddbaedeebaedadaabeccaaceeadbcbdccceaeedddacaabaeaecaacdaccadecaeebecdeddedbadbdaddbddaeebcdcdedadabdbecacaccdcbaaeeecaedacbbbacbabdeaaabeedcaadadadeebbcdcedbecdbcebccdacdaeaaedceebbaeceaaacbdebbcddbedcbccbedbcaabdcdecdbcccdceacdecddecccebbaeecdaaadbeabcbbbcddacaeadaabcbaaeecebabbedcdbcdccedabadeddcaccecceaceebaaddaeceaadddceadebcaabcddcdcaaecdaaaccacecbaeaddcaeedbbaeeedbeedebbdecaccdcadcacdbcbeedeceeeecdaedabeebbbacabdaccbbbecddccecacaaccbbbaceacaadaceaccbdeaadedddabbaeaddaaeccccceacbcadaabdddceabaadacaaedbbcdaaabcbbededddcadeedcedaececadcedceecebbebcadacbbababccdaaadedeecdccbdddaaeaacbebdeedcabecccedddddcaedeaddabbdedeceeaedbadbbbaabbbcabbedaddacabaeaedbbcbdbadaadebdbaaceecaaadabdadadceaecdcbecaddbaceecebaabaaecedeebdaebcacacaddeaddccdcaecdcbadadeeeccdacddcbcecaacdddcbdbaeddabebcbddeeaddecdddebebdabcdaeabeaceddbaaeacaeccedaecebdacaadececcbbdaccbebcebedbacdaddadadedacdabacecbebdedaedeacdaeceeeaaebcdcdeecaedcbcecaddbedeebbbdebbcecbdddaceaeeaeaaaedceebecebbaeceabcddcaccbecacedebbebaaeabadccdcaaeacdccaeccadabdeecabcbecbebeecedecdedeeecbadcbaaaadbcdadcecdeaaeccaccaeececcedbdeddbadeddbbeadeaccaeceacaeeabeecceceabaadacbaedcacadccaaecbedbeecedeceaedbecaeccaeccabbeadeaaeeeecadbabeaccaadaccabecabedabeaebcdaadcccccdbdbadbedaebddedacebeaabaddbdabbadbcaaddcedbedbeccbeddbdddcedaadcbaccbacbdaaedceedeebeabdecaedeacabbdaecbecedaaacdeabedbaeabbdabedeaaecbbceacbccedaaeaedbeeeaededacbebeaebaceabbbddbadaddddbabcebcaadbcecdedacbdadbaeebcbedacababeebacdecbeeedccebdbdccaecaabdaabbcacacebbbdbeebabdcbededbeeaddaebcdbaeacdaeedeaedaedadcddcaeaadecdbeacdcdadbddbdbcddecedabbcdcdbcdabbececedacadecebdbaeebceeedbadbedaddedccdcbbbecbacceaecbbdeaaebecbdccbdecadbceabdebcdadebabaecdadcbcaaedccdbacdcdacddcbaeeecccaebccbdcebeeeebedbeeedeaadacebecedabaaeeaabacbccaaabedceaceecdeedccccbdbbbdaaddaecbabecededbcaceabcbeeeebacbdcdeaeaabdbbcadeedbabdaccedbbcedaecabbeabcaeebbeeebeececdeaeaaeddaccddcddeaccbdddddbaeebdcdbadeeaeeecbcbcdcacdcdebdabedebdaccdcddeedcedeecebeadeebeaeabbdbceebdaabbacddbabcececdccbdceddeccdbbdaeeabadaadadecbdcdebbaacedcebbbeadcedeababbcbbaaddabaebaeabbaeacbdccebdaaabeecaccbdcecddbbeabdbadadebabeaabcadcccbaeaaddabecdddbceedcccbdcdcbdbdaddecdaeadedadadbdeabbbbbaeedbdabaaeaaceddbdbcadaacabbcedaddbaeaddcbceccdeeddaeabdbbbaeebbdddacbaadecbccadedbedbedcbedecbcdedcabadaaecededbcdacbccebcadedeedebbdbacbdcdccaeeeadeeeedadceaebdcecceceaaceacbadebbbddbbebcbccacdcbbcdcbeedabcecabceabeedecacdbddbdbcdbcbebaebaddcacbdbcebbeaeeeabbcddcdeddebaadaabbadbdcddaebbccdedaeaebecdebdeaedddbcdbcaaacbcaaabedabadebbbaddaaacaddcbacbdcdaccacaebbecbeaadacaabccdeabbdedecedbabaddaadcdeaaddabbccebeabbdddaccdadbbdccdeccaebbbeddadbeacababaaabbedbbdeebaebaedbbceccebdcecbdccacbabdbbceadeedbadceeadeddedcdeacdeaaaebacdbacebdbebaaddaacbeecacbbedceedecdeccebdcebaabdcbccdacbdcbbedaccdccbdcbaccecaddaabdabeecbdebeecdcaaebcbaadbdcabeaaccbaacccedecbcbbcaccbbdecedadbeceacecdbddbbeeacabecbeccaaedbdddbecbbeccbbeecdacdcbddabaedcdceadedbcbbdaababbdbcdbbacbbabedcbeeecabbeabaacaeccadccedaaeaabebccdacbbdaabaeeabeededdbeeadacacbdacabdebeaacdbcaeeeebaeebdbabacbaeacedabbceeabddaecdcdccadedbbdcedeebbadbbaaedcadecdbcaaadceabcdbdbcdbbceeacdedbebacdacdbcbcaddbbccadbbcdabbcccececcdcaeeecceaccaaaedbebeedacebddaccaacbdaedaebaebdddeaccaebdbebbcadbdceccedeecbdceeabdedbcdaaebdeeebbebebcebbcaccbebddedadedcbabceacaddcacaaceacadedbdaeebcededcccccadaedccacacdaeabbaacbecbebcaddddeaaeaacbbbadcddabebbaddbaddccdbddbecebedbcaadbbcceedcebdcebddbceaceceabbcbeadbbcccdbaeedbabeddcbcbeecbddeaebebebeaaeebacebedbbabceedeaedabcdddacdbaacdadaccaeceaaeaadeaceedebaaccbeeadcdabeaceaaacebcedaddcbadddcccbdcadecadbbbeceadbaebddcedcceadebeaedaedcbcbdaaeacbabbaabcaabeaadedddacaddeebbaddbedabcebdcbcecaceaaeddbdcacbacebddedebedbbbecbdcddcbabbdabeddbbebebecbbcbdaeaacadedebdcebbecccbcacdcabacadabdaadeedcaebcccdbadbeedcaecbeebcceedeabadeaabaebbacedcdebeaeadddaedaeccbecacedecceebceedcdccceaeecaeedabbecddcadaeeceecadeacecbcbdbadecabeebccbedbdbbdedececadebdccbdacceddeaadcbbdaeaaaaaebdabedbdceddeeddbededdcdcabbdeaceaceddeaeeccbdbbaeaceceaccbbdaeaccecbceebceaccabeeccecaadecdebdbabadbbbcdebddebeacebecdecdcaceebebbddaaeaccedeccbbbcbaeaecddeadaeacaeaebbbbdccceccdccbaedeedadbcdcceaddebedeccedbddecaeabdcbcbbdbdaddabbecdbabdeabbddacbdccabbcdbaeabbccdcaceaeaeadbcccaeacaecadaaebbddedacdeaebddeeddeadbcdbdddbccbdbbeaedaaeadccecebdaeacadaecaabebebcbbddaababdddbbeaceacbcabbcacaeddacaabbbcdbbdcceccddedceaccdbededeceeeaddabcbaceaeecbcebeedeacecebbbaabdaaeecbbcecaadcbaabadcabcdaabedeebdbcaddccddbbbbeaabddadabeacbabcbddbaabaccabbbaeccbbbbbeabbedacebaeedabceaebabacecebebbbbcdadeadebeeedbcdbcdcdbccbbecddaacdcaaadeeeeebaacbbebcabadaeccccabdaabcbbaccabebdcabaedeccacbaddeeeecebdddbbeededdbeeeddadbacadbdceabddcedbbeccedadcbbdbbdaccdebddceeeacdaddcaacaaccbdeeadaabeccaabadbbeaabeceaeddcacecddabdbbbebcecaabdcdcbeccdbdebbbebcbdbeccbdbebcaadbbcbecaaebabaedededebdcccecabbecdabbcddecdbceabeebccbaeabadecbabdeabcacdeceaaadcebedacebdcdccabdeeadbdbdcbeeaedcececabdacbabecaeadcaeabdabceacbcbdadaacbdecccaceaabdbaebabacaeadebacaddacebadbbaaababceccadddaddbcbeeaedebacbbedadccbddbaabbccaeaceccbbcaedabdabddadcccccceebdedebdbebbeeeacebaccddcabcccdaecabcbcebaccededdacbebbcccecebadacbdacbbaeaebbaeeebdbcdaddbeababbcdddacccdadedcdbccdaebcebcbecedceaebcdbaccbabacbbcdaedaabbdabcccbeacbabcbdcdcbbbedbabaaaabbbcddadbbcedcacabbebdbadddaacedadcbcacecdccbdaeeebdeeacbbceedbcaacbaccedbacadaabdebaeddcbdaeacddcaeebceebecdbeaacbcbaaedcdbecebcceacccdddbabeecbeeadccaecbdcbaeadcacaabacedecddeaeedcdedacedcbbaebddadedcdaeadcaedcbecddcbccdeeccaaacedcbadcadebcebeeddaddcaebdcbcabcecbcaeaebcaaceddbdabaaaebdbbdceeddcbbcaccaadebceabcbedbdcbaeedebcabbcecdaedcdcddccaeededdddaaddecabdcebdcccdbbeadeecddaedcabcbdeecccaeebdacdeeaecabdbbcbeccbacbccedacaaaedbcccabbebaedbbecbaabcdbbeadddaddaedddaeecbddebeacdadeeeabdeabbdddcbdeacbaebddcdbbcdddadbccbebaadbabbbccaddedccacabcdcebeabcdcddedadccaecbccbabecdcbccaababeddccdbacebcaecbccdcaacbbbbecadecacddcaaebcabdeeddbecdcaedadacebabdedcedbabbebdcddbeacdadcdbdeacddadbdccaababadbddcceaebaaeecccaceedaadecdadeeabdbeebbccbcbeaeadbaaaeecdbbcaaaeeabecdaaaabaeaadcaeeddeedcddadacedceeaaecacccdceacbbdeacdcacaaaedbdaedadbeacedcebeaccadecdcceeecbdaeeacaabbaaabdceeadaaaecebabbbbabbbaacadeebedbddabaaaedcdcdceebaeccdbecaddbbdbcecbdaebcbccaceeedbebceeeaedaeacbdacdcdddaccdcbeeccccbbbabacbeeabeeccedbdbadeaccdbdbeadcebbedeabebbbdeaacedcaedccbabeaaaccebeeadeebeeabedebecebaccbabbddebdbdebcdcedbaedddceebcadbbdecacdaecdedbecabdaacdedeeddbcceaceeacbaacaccebbdaaabcabdaecdbadbedbceeabdbecbceeebeaaaeaadcddbebccabccababddabccedeabaacdbcbccdedbedbceeccbdabeacaeceadcabceadbdabdadbbadcdcdcecbeaaadaaecaacdebceebcecedcdcbddecacbdebccdbdeaabdabebedadbdeededbabdbabaccbebeecdabcadeaaedbcdeebbccdeaedceaeaeaabedcaaeabdadddcebcdeeedbeeccacabacaaeeaecedeccdbeceadbaadbeadbdadddaccbaceadebabdcaddcecaaabacbbcccccecbccacdcdacdccbadbeebbdbcadeebdbecdccedcddbaddcdaececeeaeccdacdcbceddbdbadaeeecadabcadeadeaadedecdededdaeabeaddcabadaabcaadedccdeedaddbaaadcbdcaddddbdbcbaeeaabcbeadabceccdcabaebadaacbdebcdacaaaabedceeaabceccbbdaabdacecabdaaacecedbedabeeeacbadcdeedaceedbccedcceaceacbddbbecaaedbcaeedacbebdaedccdbeeaebbbaebddeecadedbceeaadcaddabcbeecaeecbeeadecbeaabceeabebecabbeeaacedcadcaccecaadabedeebabdbbebbeaadbbedcadcbacbcadedeaeeddedcbdcbddaddadaaaadcaccaebdcebabddcaadaddeaeeaabbcbbaedecdeaaddcbbecbaaadeeaabdececbeabacedeccecedbcacbaacabbbeaaceedabdedcbcbedebacacccdeabeaeabdaabcdbddceddcecbbbebacbcbabceebaacacaeebcdcadacdebadabeecbeeaaaadbdadceeecdedadebddecbabcadaeaededdcbbcbcdeedbbdddecabdcacceaaedcdcedbaaeedeeedecaabbddcaedbceebddecdaedddcecbdeeecebdcdbdadeeeeeadbdaedcabacbdeadcccdadeeeecdbaeeeabbcbccabaaedcababeacceeebacaeabdbaccccacdeedabecadacacdcbceaccddabdebcaeeaabdccdabdaebadebeacbcdcddabdddbbbdabdccabedbeaabacbcbeccbecdbaeebbeaaecaaaebcbdeeabcaeaacadeabddaccacaebbbcbbaadcaadacaceaaaaeebdeadbaaeaabebeaddeddacabaeabdaacdddeeaeeececdcedddbabeabeeddcdeedccddcecbedceebadecaabccccbacabecdeedaeeddbabebbdcaaadcebbedcdbcbcaaebdacdcadcadbebbacaabbebaadeaccceabdedcdbbccdaaadeaeadacdbdeeddeabacdacaeecaabcbbbadcebcadeeccaaebbccabbdbbdeceeecdeacaaccabcbaeeacdedeeccadaddeebdababebbcebbaebeaeaddabeccdedbcaddebdbdcbbbbddaeddbbdccededebebccacabcbceeeecdedbeeaebebbdcceceaeebceaddadcecbeecdcecdceeeddaacbbbdbadbceaeacdbbeeeadaaadadacebbedddcddacabacbdcaaccdeabdcbcadbebebcccddcdccccbbaaeeaaacbecdaecdebedcbdeaadcbabcaedabcddbbcababababdaaaaaedbedeedbbadaeccceedecdeeacecabcbbbbcaceacadecdcdbbcaecdceaebbeaadbdcdecbcaeacddbcbdebadeedacaabedbcbcbbbebcddbbdaeebaaaadcaabdadabcecdeeabacebadaaedbeecabbcaaaedebdbeedccdeedbbaecabaeccddbdccdecbeceaeecbadbcaacbabdadacbebdbaaccdcadcdddcbdceaabebeadddaebbaedbeeecdbadccbbecaadccabaaebeedcaccccdedeceaaeaadecdbecdadccadeadecceecadabcebcdadabeceadceeceeebdaceeaccbdbdbbedadabdacceeeebebaaccbbcacbcbdebbddebbedabdadeecdeebdababceeddbbeddabeeeacabcdcdadadbdeddcbacddcadebcceedcaaedcaebbccaacdcbbbdaeccceeaecaebdcadebcdebcbdddddbebcccacccaebdceacdedaabcbcaadcdbabdceaebcccbcbdceacdaceecabddadaceaeeaacdbebdacedcaddbddaedacecdbaceebcdeccbbdbeccebbbbdcbbbcbccaccbdbdeccbedeedcdbcaaabcdbcddecdecdceaadddbdaacadaecbcaaabbeddcaccecdaeacccddaaeeaccccdadbbcbadbdbdbbdecdbbdbdeadcdcdaddbbeddaddabacedaececeebeceadceeaecbeebcddeaadcedcecdcbddddeacdcddcadceedebadcdcccddedbcebaaebeecabedcedeceacacecaecccbabaddaacbbacbacdebccbebadaabdedcbcdecbccaddeedbddbaaceceabbccedeccdceaaaeececdcecabddaeaadcbeeeebdaeeeebaadedcedebadddaaabbcbabeabbceeaaeedcaaebaeebcbbdeeacdbdebeedbcdabeababbabcbeeadbebcdebebebcabbcbeaabdcbeeeeaaeadbaaccacdaeadecebaaedbadceaddaeaaceeddbcdebcdcbdbadcbcbacaacccdaeebaecadbeadbcaabdbedacaebadecaebacdbdcedbdbcaacbcceebecbeabebecbadcedceaebaaeeaeeececebcdcbddadceacbcbcdbaaebcbadeacedcebeddabccdddcbbcadccdabbaeeeddddecdcaddecedecbaccadedeaddebcdcbdcecbceadcceeaeddadbbadceeacadabaedbbeaababeccaadbcabbdddbdddddeadddddeeaddeecdbeaddbaceadcebdcaedacdadeddccebdceeeabcceaaeaaacbcacdabcddeaaebeeeaeeccbcdaebebecebecccccbcdbeaaddbeedededcdcddebeeceaccaaaddadebebcbadbaabcaaccddecaeecedddcbeeabadacbbcdceaddaaddbeeccdceababbececbabbddabdcbdcceaeeecdaecebceceacdcbbcaedaecebaeaaeedccbecceeecbeeebceababbaabccccdcaecaddcbeabbeeeebeeedbeebaacebdacddcbcccedbcddeccdaeeadbecbaccacdbcacbeabdcceaeddaebabccdacedaaeecdbbabbccbbeccadadcabebdbddddaeacaabacadcccbbebdaddcbdaaebdebebecebbadaeeeeddadabdcaaccbabeddebeaadbbbbdadeaeeeadeaadbebbedccaecddbacdcdbbbacceaddeceaddabdcdbebcbaccbdeaeeedebecddcdeccbbacbbdceadeaedaadacdadecbaeebadeaaadcadaaecceceadadaccbebcdebcddccaccdddbdcdeeeaaceeadccadcbedcaedaddeaedeeccbccbeacceabdebaceeabeccebeaacaaaaeebebecbaaebabddacbbaaaddcaacbeaaceccabdababdcddccdaceabeedcccbcbbbadcbccaeaebecdcecbececdbacabbeeabccdaebadeddebaeebbdbaabdbdebeacacacccbbbcacccdbdbbdcdaaaecbdeadbcaacbdcaddcdcecaeaaedacbbeadeabdbadbceacddceadaeabbdbeddedeaddeaeedecbddcbabccccdbecdeeeecaebcaaadededdbcebdddaebcddacabbeccbacbadceeceaebbbaabcdebaaaeacbecdbdebaabcabdebdcbadebedbaabcccdcaebadeadbdadcddaabcdbaacaddecdacdccebabdeadeeddbceaaeaadecbdadedcddaededdcbdedacbdbcbdececddadeabeeadbbddeceaaaaebcabbecdeeaccaeecdcbdcbaeeebebbbabcaebdbdcdcabeedcacdbdbcbbedacebbacddcecdcaadaecabdadecbdddaaadaabbbabeacdddedeacccccbcedacbbccedcaceeedcbcdaebdebecddaabdabedbabeecdcedddeebadccabddabadbdeabcdcdcbdadceaebdaeaeaadedeecadcbebcceabcbebdcaaccabebeabebaacdcecadabaccaaddaaaacaeebbeaeddbdacbaabbabeaadececbbacdecaacbebdaedacdbcadeaabccaddedeabebbbacbeeadcacbdddadcaacabbbccccabebdacaceecabcbedaebbcbedaebbedbeabdaacbdbeecdbbcddabdaccbcedcccbeecadaddebddedeaabbbcbacaadbbddcdaaacbbdaddbadaccbdeadcccebbeadadedbbcadabddeaaadbcaceacddbbbeddccbbecddaeedaacebddacadbaaddbaaecdabbbaedbdbbecdadecbbebcbeccaacbbebaadcdcdbecdecedeaaddcbcaaaeebebdceecadeddcedbebdacaebccdcccddeccadbaadaeacadddbacacacaaebcdadcabbeacededdeabbddbeaebbbdecaedbbeccdbcbbeccaaedebbaaecbdabdadadccabdbbecbdececceaccaebbccabdedcecccceadbeaeeaebcedbdcedeaedbebdbedaebdabaeadddeececbdeaccabccceaccbadedaedbebbbbdbeaacbdedacbcdedbaceacaaedbbdddacbbeaedbdaaaacababdceacabaaceaeeebbdaeaaeebbbbceccebeaaadceedbbeeaabbacacdebbdaeccbcbdeaddeeaabdeececbabeedbdbbbadcbaedcbcbccecbdceeddecbaebccdcdcddbdedbadcdaaadeebaabdcbbdcecbacbbbaaeebcccdccbdabbcddeeeadcbcdcbbeeddcbaebcdaaedbaabddacecaccaabadecacebdbcbbcdbbacdaabcdbccedcebaaebcedcbccabadccabedacebedbdbcddabdebeacaaeaeaeabddabcabdaecebadbdacbbecbbadceccaebdacbeedccdabdaebcbeedcadecdcbdaddaacacaabcbababbdeadeddcaebbaecadedcadeecbddaecdeebcaababaccecdbecaedadbeceeeccdbbdcdceccbadaaadcabbcbcdabcebeebdbbaaaeeeccacaeaeaacedacaabaaceccdcaaabcaecbeabbaccaeabdeaeeacddecaadcbdceadccdeedcbdebedbdadcdbecaedddccadccecbccccdbdcaeadcacbecbbcbdcaeeadbcadadaacedbdecebaabeccedceaabcaaceaacbaeaecadbceebaadbcdaeedeaadbdbccdeebccadccdababacaebaebcddddcecadedeeabcadddacabdaadedbecaebcbebeaaacadbedcdcbdadcebedbddebdbdcccdddebaebdaedbccbedbcbbaecebdbaadadcaebbdedacadcadbdbceebbeecadcdeeabbeecddaaeecabeeeaceaadaacdedcddceccacddaaedecabcdaadacabccdeceecdebbbbdaeceadccadbceaaeabedadcbebbeccaccbddebdbdaeedacbceaaedbbbbeecbdecccdccaacecddccdbbbbbcaabecbbeddedbcababbdbabbecbacdaeaeeebdccbbebbcabddbdbabaecdbdecceeaecebdccdbbccedcceacacaeecdbadedaedbccbbbcedcbabaccdcccdcdbbbadddbeededcdebacaadbeeebdbcadecbcecdccbbadcbdccacccbebddbdbbabadaeadbddddbcbccccdbcacdadbcaddbedcbcccbadbecbdebaaaadeeedbedbdbbeeaeaeceecaaddbdbedebedcaeceecdbaeccccdebcccecababacdecddbbadacadededeadadaebeedccaadbcbedadebaedbdcbebdccaedabedcabbcababbaabacbecbcaceaecedbbdbbbacbbbbaedbabdadeebecbdbadeabacceebeccbdaedeababebcbcceeaacddeddbcaaaebaddbaeadeebccdacaccdcbebeebcdbdedebdbeabacceeaccbadcccabedebaacccabacbbcccedcdededbaeecabceecdcaeeeabbebdcaebbbcdcceddcccbadebabbdbbabaebaddabcdcdaedcadaadeeebbcdbcdedaabcbacccbcbbaebedbedcabdbebacbcdabaccbdeddebdacdcdecadabeabccdeadaadbaceabdbcdbecdbcadedaeaabacbaabcbaccbceeebecedbadbbbbeecbdaeddebcbdccbebaadcacdecedaedbbbacbdaaadeeabcedbcdcdcdcaeabdedeeeeaacaddaeaedcedbdedcbbcdeacdabcbeddaddbabadaeecccdaeabcbaccbcaaabccecdeaeebedabbebbaecbacacacbaaabddeecbccdcbddedabbbaadacaddcceddeadeeecaaccbebeaadccdcabccbeceedcbbbdebcacacaeebdeaeccacddacedeeedeabaadabcdcabcdcaecaaeaaecbacaccecedadcdadbecbadbeacbbedbdddbcdbaeaebdeeabceceecbdabadeadccacdeccbccbcadcdcbadaccadcdaddbddcebbcedddccbdbccbcceeeecdcdbdeeebebabbdbbeccdccabbbedaeadcceddebcaecceadbedaabedbcbcadbadeaececaccecdbbbddcccecadeddcbaeccddbcaaacbbdacddbeedeebadacaaddaaadddccebcddbbdccdbedcadaaeecadeddaadbbbbaaececeddcededabdbaccceebdacedbbcbbcbbdddcacdcdeaceaadebededaabdbebeccddcaddeaedbecbababdddaebcdacedeeeeeaeadacecaaebededbaadccaaedcebbdbdbacadadadbcbbedacdabedeadaecdaedadcdddaecddacadbaeedecdeeacdaacdabeceaeebcbbcaebabcababedbdebeaddcedebdcaceecbcaaddccdddeedccdebbeceeecebdeeadacabdaceceaebddbbcddaaecaeeceebddeeddaabadadcbdccacdabdeccdadcaedbdabcaeaabddebbdeaecbdebddbeacecdacbaaaadaeacceabaadcaedaaebeabcdcececbcadaeebeaacbbebbddeddbadeceddebedaeddbbbeceeddbbcebaebaabebceddcbadccebebbdadddaaedcacceecbbaaceabccebcbaacebbedddbcccaabbabbedbacdbbcebccceebdbcadbdacacdeedccabeabcbeedecdceecbadacebadbebaaaaccccdbbacdadcedeeeaccbeedcadeadedcaaeeaebbbbddbeeeaebcbcbaedbabbaacaebadccbdcbedbbcccaaaaadebecccdeaaddacbcdaebaeaaabecbcbddecacdeededbcbbaebcebcdaccdbcadedeaeaceebdaccbacdbaabebaeecccabeeebbeaaecdacbaebcdcebdadcddceeadebbbddabaceaeaacedddccaebcdcbdebecbbababeedabaecbeedbbcccaebcacbddccbedaeeabbbaeaaddcbadddaeabcaddecdbeebcbaceacedeececdbbcbddacccdbebdacccdaaededcccbcdbbcbcbeeabbadaabbcebdbaecaacddebadbeadeecdacaccedaddaedcaebcbdaebcccacdbddecabcecebeedadbbbdbccdddcebadaddedeeddecadeaaeedabbbaecddbdcdeadabaceedaebbbdbdedeadcacdeaebbcbbaecccdeccccebebaadaaccadceeddbdedeceeadcbecaeacddaadcdbdcdabbacedbccabceaeacbabaeeadbbdadbbcaeacabeaeabaacbcceadbcaeebcdbeebcddcaccaddbbdeebccdccbabcaeecdaeddbcbdeabcedeeaabbbcddcdeaaccecabbbeaecdadcabeeacddccdadeaecbaeadddcbeddeabaedcbaabdeeedabbdbeddccbacaaeadabaeadcdecedaecbcebdacdcadcbdbbcdeebcdcbedbdaccaceababacabaeebeebebbaabedbeaeaccdbbaaccdaeaaedadabacdbbcdccdbadbbbddcbbbccbbcceeddaeceebaeeccebdcccebcbabaabbebbeebccebebbbcbdcababaaddeadebdbeaaccbbacacaecdeeebbccdccdceaebcadecdeabeedeaebbdbdddacacadebddacaadddcdaeadbcccabaaeadcedbbbecbebceeccecbccececddbbaabdcedebeecbcbdacdaebdbebdceececcdcbaceeeeedadaabbaddddcddaeeecdbbeccaaadacdbcddbaeaccdadaeaabcdcabaedbeecdabeedbebaccabaaccabacadcbaceebecaebccbdcdadaeecdeecdebdcacbdbbedbcceeeadccbadaaedcadcdaebbcceaeacaeeddbacbcebaeececcaebeacebdbbbebeaccaaebabececccacdecadcdeadecabccdcccaaaeebaeaadbaabddbdbeccdedeadacaccbaaadaacdcdcdcacdecebbedcbcaaaababacbdbeeebedacbcebbcdeeacdccedcbddceeeebacddbcdedbedcccadbdbadddcccbdcdabdbcbcacebeccaabcdbddcbecbaeabddeaedccebaecbebeadabeeddedaaccdceeedcecadaecddbedcdbbbadcaccedacebcebedaebcecdcacbaeedaddbddcceebcdbeacdaabebcccaabbecdccceaabbdacccbabbeacededcabdbcbabcaabdddcbdcbdcdccbceacabcceddcadbebcaecbcbebbcbeaeebdaaedbeadeacdcaaabdceabebdadbbdaabcabcdbeeccebaecccbcdabdcebaadebeeabececdcedaeaaeaeadeebcbbaadecbbabbcaebcecbedecbbeccaedbadbbdecadbbebabdeebcdcdcdadcaeabcdcaabecebedbdcecaeddbeeedbcdcabedbbedccbdaeeaeebabbaddecbadcaebdaadecbecaeeedbaeeeccdcbbbdaceedeaedcadaabdabeccdcaacaacadeeadebbeecabbcdcdcecddecedadeadbedbccbdbbbaaacceddadadcdecdbbbcebbaaeacebbdebdebecaeadceedcdbbdeabbedecdcdadcdadeaeecabbcacdacbbacdeeaecdaeaedbcecaabdcececcabbccddbaaacdeacbcacbdbbcaebcedbcacadacbaabdceddaecbcdcabacbcbabeedcaebaeabcdcbeccdeabddaaaedaacebedacbeebacbcebdbcecedaececbdeeedaaedeedbdcdddcbeaabcabdadeedaaadecbdadbbeacdcecddeddcadbbbcbeaabcadedcdbcedbecadaababeabcaadcecdecbaeccbebecceadebcbbbacadbceeeaadaeaeeebeeeececcdcdecabeaaccbbeebcbdccdcdbdecedccbbddecbbebedaadcdeeccbedbebcbdcdadaacbcaebacdaadbeeaaebbacddbeebbbbcccddddcdcccdcedadecbdceccbeebadedeabbcedcbeddbaccaecaacaeaadaabbbbbeadccaddccaadaeedddaaecebcbeecbdbcddeabebcbbdcacaebebeccbedcadbcdeceedecdacecbededaedaaddeebacbdcbabddecacddcbccabeaeeadabcaeecbadaeedecddebbbdccadecabcacaeadbccdcccbbcdcdbabcdeceabbddbbeebdeedabdabbbaabcbdeebbccddedbedadcbbbeceabceaeeecdcacbbacebddccaccacaccbdbddcdebcdceccaaaaddeecccaadadeccbbaaabeeaeadcdeddbebbeaeaabacbbdebaebdeeecdeaeacbdbeddceeadabeecdacddcacbbeeeaecccddadeccdebbabbacebecabcdabaacbdabddddbacccecadbeaceccbeaaaadebaebbeacdeacdcccbcbbdddeedbaedaacbdaacbacabbecddbcbaacbcbdbcebabbbceecadcaeebadddaaacebdddcccdedeeacbabadeeecdeabeadabdeeabeeecadbeebaeadaceaceeceabcebeeacedbbadbcaeeddcacecdcabaadbcabbcdcdaccecbecaebbdabcaeaeebdcddeddededdeacbaacdebeadbcbadcebddcdceabdccdcdcecbacdddaadeedabddeeacdbebeacdeebaceddabdbcecbdbecaadddbeeddabedaeeedbcdacdbcbbdbaebcddbddcbadeedccdeaacdbdbcdceebbabccaceccddacaeaeeeebbdadedbdabadabeaabbacccedaabeeaaceeaaddccdadeabcebadbadbdeceedabecedaeabdbbadeeddccdcdaabdeddcbbbeabdabaaebbddedbdbaecaecdceddaaddeaaeadcaedcdddcdaaadaeacdcdeddedcebceceebcedeaaadccacabbeaccaaebcacdcacbbbcbbddddbeececadaaecceeedcddbaeaebbdaaaababecbabcbbbacdcaaecadccacabcdadeeabeebdebadebeaebdeeeeacdbcedcecbddbdadebcaaeeebccbecbccaecdededbabaebacecaeadcdacccbabaccbebdcabeebdeeabacaaccacacbbbbeddddabcdaacecabbaaabccbbebccdeedabebcacaacdabdcdccebaaacacceaabaaddeddecdbadbcaebaaaccbbaaecaeabdabeebbaaaedbdaadcaccdcdaeadedecbedbcdaaeaaaadbdcdbadeadaccccedddbdbddddadebccaeaeaddebacbaceeeadecaabdcebcecacabeccbebeddddababcdcdcdddeeacbccdeedcddcaededdccbdaeaaeccbcdceeeebcdececdcdcecedabbaaaccabadccbadaeddceebbdbceabcadecddededbcddecdcebaabadbccabcddeaeddeebbcabebadccdedacdaebeccbdddedcdadbaeedaaeeaadeaceaaacdaabbdbadeeaebeaacdacaaaedeedebbcebecccebcedecbceddcbdeedceceeaadbebebbeccdecdacbdddebdadaadaabedcddedebeeeeecabedddbedacbebabeacdeddebcdaadeadecbddceddddaedacdeaeaeecebbbaedbaaddbddabeaecdeeadeaecdedeeadeecdcabbddacbeecacabeecdeadabdbaceeaddcbccabadbeddcbbccacecbcdbdabbcabebaecadcdbbcaaeeabddcaddbeabdaadecaccbbcbeddaeccdbbabbdebdddbcacdaeabcbaaeccadbbbaacecceadccbdbeacaaaddbcebceadaacaaabdedbadcbdabddedaecaecacebaccebdbaaaaabebbceceeedacadbebbadccadebdddeabbcedbbebeadddbcaaadaedbcbaedccdaccdbcaaabbddbecaececbcbaddedbdabaeacacbdbdcddcbacaadaacdeedcdbdeedceabaadebcbdadbdbddebccaaebdebbedbaaabcbedececddcdddabbcdadecbdbcedaecbdacbcccadddaabdddddbdccdacbebeeebbccdaabeaaabcdbddcebddcebddaacecebaccbaccbecedcceedacadaabceebaaaabadbddeeabcadcedcebdcabbcacbaaadceaeccaaabebecacbcdcdddddcababaedccdeecbaacbdddcdedcbeacdcecdeadadaeacaeccbddbdccceadaacedaebedeaedbdecdeadacedecdcadebecbdbbcadbcdccbdbbdcbabbcaeddeeecdcdbbcbdecadaacccadecaaedeecbaacdecbaddcdbdacdccddadddbaddbabdeaadcdcedcedebcacdcbabaadddddbeaddbdddabaeebbbbbdcbdeebeaaddeabcbcdbbaaceabeccccbeecebedebadeeeeeeaedaaedbaeeaacbaebbababbacdcdbbedeacecdabccebbceebaceebdcabeedaedaacabaecedadaccceaddeabedbecbbaebdadedcbabbcececeaccdabdbceacbabecddaebbccdcdccbcbdbbbceadddbacdbbceeaecabceeddeabcbddaabaaaceebbcebedbeabebbebdaeeeaccccdbedadcdbbdcddcbedbbbdcddabbabcadbebcbbacaaccabdacbdabdbdebcbadecaebcabbaceecebcdceadebbcceaeecccddbebecdeedaabddeaddabaaabccddccadacbbcbdbcdbeeeeddeaaeedddbdaedbedbacddcaacacdadadeedadbcdaddbedebeaccadcedccbeaeccdaeeebcbdeeabceaaccaeeaeeababdadbcecbdcbedaccbbacababdcdebbabdbcbedaabcbcdeebeebdcccedeecddeaadbaeedcdebecbbccaadecccabcdbcaeeabccebddabedabccdbbdcaadcaaaebaebbdcdcebecbeaceeddeedbcddcaaaeaedbbdeadcebdeabdbeacdeeebbbdaddeeaaaacbbebebcdedecbbdecddddcecdeddbdcdaabdcbcabbcddbdacbbbeabcbedbaadddaabddeabdedadcedeeeacacecabaecbcceadbaccaabdbcebbdcbdcabeecebddccceddcccddceccdacbdadebbcbecccceedceaaeebcebbbeecbbdbadeaddadacbdcbeaebeadceaebeecadddabaeecebecaaddbeebddadcccbbacbbbeaddbeddecddeddebedacdcbcdbedaeabbcdcddecbbddbbcabadacedabdecdcbaddbebcebebeebbdbdbcbedceeacedbddaebeedcdabaaeacdcdeccbbaaecddaccdccdbdecbeecabadebeabcaaaddcaeeaddebbaeccedeeeacacbeccedbaaeadeeeeaebaaddcebdccebdacedcceebbadebcabeacdebcbabacecbcbcdaadadaacdcbdacebedbceaaaadceeaecaecbbcbacbddaeacdbedebddceeebbcdccdaccedeccabccddcbbeeeeddabccccbbeeecdccbeadbbdddcbabcceeeecaddaedeaeaedebbabaddedcaedabedcdcdbccddaeecccdaddaaebabcbceebaaeddcdcbadacdadabceadcdbaeeeadcadeddaacbbbeabcaabecabbdebdcabbbcbbcbebbcbeaaddcceaabeecddeadcbbbaadecedeccbcbbbeacdaccbdceeaaabddcebcbebedbdddabcaddeadaedebedbadaceadddcaaeadaceabdacddaedbbaaecdbbddaeadedeaadaeebcdadacabcabcaccaecebddedddedbeabccaceabdcdacdbdddaeccaeaaedbadbaceedacceedddebbebeecccbcecebcabbbddedecaebbaecdcecaebaabdcdbbdacecabbebdaecedebbdeeceacceeeeccdebdcceababedcbaaaabcdbaeaaeacbcbcbaaaaecdeacdccecaceddecdedbdbaddceccebabeddccabedadddedccabaeeadcbaeeacbcadbeceddcacceebbbacaaadeddabbddcdbddbbecdbecdbeeaeebcdcdaaeadbeeceabcacddcddebabcaeccbdbaedcbadadbbabaeddbacccccadbbdbdadbebbbcaceadedbabeaebcaaccbbeeeebcebcdcadecaabdcddbdcbcaccabcbbaadacaacbbeacceabcadeccbaaaeabeceddedcecacdaaeababbbdbcbabebeaedbbeecdceaaabbacedabaedceeceaadbcdecdaabbabcbddbcacccdaeeaecedebbbdcecebdabbebacebadcaabaeccbecdcedbdeeacdcbccbbbdcedcabdaaaccbbcabbaebdecbddcddabaacdcbeacccabbebbbadacaeacbcbebecebbccbeebdacecadadbdceadacdcebebaccbabedeeaacebdebdbecaccdededadbcbacddcadacaececaacdeceabcabcaadddaeedecdaebaadbebabaedadbdadaeeebecebdeecbccacddaaeeaabdcdcdddbbbaeeaabadbcaedaeddcecceaaceaedbbccdcccedcbbedebcaecbedabceaacceceeccdaceeaceadedcbbecbaeabbbcccdbbdadccccbddbcdddddbeecccdbbadbabcbcdaeddddbcccdbbbacabaecdbbbbbbcbaadecbebdddaecbbcebeebbcceaebdbbeaeddddecbeadaeeedbceeacaecebaddcdbebeebedaacedabbaadcebcabeecbbdaceddcebbccdbcdcbbeaacdcdcdbeaacdbceedddacaceededecddeedeadccdeacbbdbdbcacadcbdcadddbcabbddadadddbdadabebedecceadbbabbaeeaccaabedbadbebdddebeeeaacbbcaacbaeecceedcccbaedbbccbeaebdeabcecedbbdcaeecbdadcddaecdaadcecdaddbaddeeebacebcbedebdecaeaaebaeaaeebccdebeccdabcdcddacbadabddcebbddeadeabdabceceababbdcceddeebaacbdebaaadacebaebbbeddcedcadadaecaadbbebaddacadecabebedaedddeadeddeaeecbbecbddbabcdceaabcadbadbcccbebeecaeecddddadbebaabcccaebedcbeeeeaabaaeaccadccdcceedaaebaddbbddcceecedcaaaedbbbcecdeeacbddcacedebeecdcaacaeceeababaeadaababbcddedecdbaaaaedeaaccabedaaecbabbbbecbececedeabdabadaaceeabaabcacedeadeeabaecbaeebabcdccbcceadeedadeeacbbadaddcddbbdaddbecbdabbeecaaedbdeedabbabeebcbaabbadeadcbdcbdcddbeabebdddbccdcdbdeeeebeabbdeadedcdeeacabeabedaebceeeebacabbcabdccbdddbebedaabbcdbdaeeebcdacdadecedaabedaebeaebcedaddcccabcacddeacaababbccbddabaadeaebeadeabedbabdeebccacdbecebceeabcbdbdcacccadbbbdcbbddadccaddbabbbabbaceddeebebcccadcdccdcaeeacbbabbedeaddaadddabddadbbdeecadecbbdedadaaabddaeceabbeaebaecadbeeabccbcdbeeeedbdcdacbaedcadbadcccadcdeecdeaddedddddbadbcacbaaaaeebadaabbcbdebbebcebcccbdebdcbdcaeaebbbaebcecdeacdeabbaeadaccdceccacabbddabcaedbdcddcadccabbbecbeddbccbdeecaedeacceeeaecaeddeeddecbbdcecceedbecbcaecceedabacbcebdbdcadceecaabedacddbaedcacbbbaaebcbedcaabbceccbdceebaedceaeeecacbbdbabaaabbbcdadcdaeddeacdecddcdbdbedcbacdbdbbaddebecaeecaeaadedbdbaabadaacaaeedbbedcbacceaedabebdceebadaabdeacbebceeeebbadcceeedbbbbbecbebecaededccbabcdcdacbeadcdeedaaccdbcdbedddedcdaecbcbaaadbdcdddcebeabddccdedddeaebbabedcecbabeeecdaddbeccabcecbbdddcdddacebddbaddabecaabdcdadeddbbdcbebbdadababeccaabedcadccdaeecaadeadbbcddaadadbacbcbebecbcacceabbaabcabecbeaacaebdcabeecdebcdebccaabaababaededbaeeeebeaabdcaacacdacbcebdedbdceaaedecddcecccacdaaecdadadaecabdacdacebadeaaeacabcbaaebdaeceababeaccebbabddbaedeedaeeddeebcccadbbbdbacbdcabeccdeeaebaadaeedcbdeaedaeabceebdedbebddaecaacdbddbeacadcdedbbbdebedccbacadebbcacedeebebbaacbcbcadabcbcaaececdeadecccebecbabdbbebccddcdcdcdaadcadadbbabceeecbadbdcdcbdbcebabdeceedcebceaaaceabecccbcbdecdcdcbecabbecaeebacdeabaacdbecbecdceaedadaeebebabecdccaeeabbcbbcaeabdcedbdacddcedeebddbbedbecdbbacdbecbbaaedaccccbbedaaeccaabdaaaeebceaeaeaaceedeccbadadaeacbacbadbeacecbeaaecacedcbbddabdbccddacaddecaedaedcbecabaeecddbbbbbaeedabaaacbaabedaeebcaccecebaceabddabecccddadcecacebcaabecabcbcbedaddddbcddddbdeaedceeebdbdbdcbbbcbdaebcbbccecaacabcdadadbdabeadcdeeabdeccdbdeedebdacbaeebedeccbabbeedbbbecabbcbdedcbcbdabdcddaadeabbaaedcdbdaacacaeddcaaeaaaeaaedadcacaaebdeddcdabebdceacccecdeacceeccdebdcbdacebbadecddacdabcbbacaaaaeeeaecadebbccaeacbbedccbbdeddbebaadeddcbeadeebaeedadadaddedbbaacbdaccebdbecaedcddbacabadbbebdbbcbedcdceeeddbdeebadbeeecaaebaeabcbdbcbabddceddcdadbdaceceacbeecddbacbbeeacbabdedbcdebeadddacdebedbbadccacaecddcddddeacebaaeebecbbecbadebabbcbedbcadebcbeabdebcbceaabbecbabcbbcbeaabbedddeccbbdebaedadedcaadaacaccbdbddddadeccecbcabbdbcbbeebcdbdcaeabdccacdaccadabacacdcdeeaddceeaaeaeecebbbeaabaccecaaeeebccdcbebbbdeaecbddbcbcdddbecedebddcabecebaaeecdbbeebdbbceedeacaccdcabedabdbdbedaadbcbbdddcebebbacdbbcedbdbbdbbdabcccbaedeebecdabaabaeabeababcceaabeeedbcdcceecdbaeabceaaebecaeccbaeeebebebcacbadaceabdbdaaebcbabccadbccccabdbdadbdedbbecaacbaecbcaaecabdcacaaadacdedebedccadababaeecddeeccdbabbbebecabbbbaeabdeceeebeeccedcddeedcdedabcaddeadeaedebadeebaeceeadceededaeecbabcdceededacdccbbbaeeabcaccbaabdadecdcedceeadbccbcdbadbdaecdaacaaaaebcdbeeacacddcbceeaaadadacccdeccecddbadacbddcdcbcbbceedaacecbcaedcebcacbbbbeabedddddebcbdbcebbaaeeadcdedbebddeeaacbcebdbcebecbeacbecdddddcbdadbeeddbaceaecbebbbddceaaebbbdaaeceeaebccabbbbeadcaecdedaedeadcbcdaadabbbaabddadcddadcdcccbaaecbadbaabadbeeeddbadaeeddcecacadcacabbdbceebdacdedebbebedbeaeaccbcebdacdabadcbdbbadcedbbbbedaeecabcbeacbcbedaebeedecaddaccabeeccbcaaadccbcbbebbbcdcbeaecbabeeadcbcaadeceeedccddaddadacdaeecbdbdddabededaccedceaacacabbbbcdbcaebdedeecbbddedececcbbcacccbeddeeadeacaededbcccabdeceddebbbadbcccdebdeeecccaebdedaddeebdeeccaddeadcdaadeabadedcaeaecabeddeeaeacbeaeadccddbadcbeaeaeadacbbdbebadaaceaeabbceabeadbddccbbdeebadacaadbdeaaeecebeebededbdaacbdeceeebaabcccaaaaeceecdacaedbbecdcdcbddedddaeaeeecddebecadaccabeddeaecbeecbceaebaaeaabcedbcacceadcecebaaaeaaaceaadbbdedebcabbdbaecbdaecdccbacecbcaadcceceaeceecccbdccbccaddcaacaebadddeabaedeacdacdadaabbbdacdeebaabceebddaeaccadcbbdcaaddaaaadecaaaaeceebdbaadcabbeaacccadbbcedbbebbaddecebaabcbadeccadcabdbceedcabdcbbbbeeedebedbbdacbbacaceaecccaaedcbecabdbcbecedeccdaacbbcbebaebadcdeedcabeadeadadeeaededdbbceaddaeceeedecedecdeeabddbdeeeaaedbddcbecbeabccbcaeddecaedacbeeeadbeeaaaeaecaadebcbaaccebcbaedeeeaaeddbabbdecaddaabedceccaabeeaeedeeebdccdeadbdeaebabebddcddccaccddcebddddaceabbccbbcbeeadeaebadbbacacbededadaeeddadbbecebedeaaaecdeebbdacadcbcaaaededbbcbbbbddcdccbbdedaeceedbebedcecdddebcbddddddabddcbaadcadadebbdbcaceeaedccaaebcdcdebceedeabcbeebabaadbbedbaaadeedabdedcbcccabdbddedeaedcacbddebeaaeaabcabadbbacdcaeecbaebaddabbcebcbbeeabecdeaeeecbaedbaedbbeaeaededaceabdeebdacbebbbcccbeeacbbcdbcdaedcaeeebdecccddbbebccebcaedbeeeaeeacbaebcdebcccdeadcaccdcaaacaadbedeecddaedbedebaddaaeacddcddabedabdeeadebbaadbebdebdacebcaceaddcaeadeddadacdcadecdedcecddaeddadbedeabacaaceaacaedddeeebeeeaedbcdbcaebdabbeceedccabccbddadacdeccbdabcabdcccaaedaedaadeedebeeadbdcdeabcdaaaecdbdebcdbbbaaacddcccbeeaddecdaddbcbbcdbdbbeddbbebdacbcbcaccbccabddbedaccacddabeddbceeecaccebbadeeedabdaaacacedaccdadeacbbaacaadbbbbbcececbeeaebceebdacdaaabbdaacbaadeeeebcdeebedbdecccbeaeebdabaadddbcabbaedaeccdccdbbebecbadacccdaeebccecdaadeebccaaaeaeeaeaadceccccbdaedaeecaabdacadeccaedceececdcabaecdedebabcdceaaedadbecebbaeacebebeeeebbacebdabceddbcbebbbbcddeebebebdbecddeeadebabddabdbdceccaacbbcbbdbcbddbadbddcecddcbccbbabecdeacaededcddaceadcaeddccecacabccbdeebeeeacbdbdeebcecddaebedccbcdedadeeabbbdbcdddbdabaaadeedaeaedadccedddbdcadcdcceebbcabeabebbcdccdcabcbdddcaaeadbbaebeddaacccebcdcaccdcddccacacedaaeeadedecadaddcecdedeaadcdecdcedadcdeddbdecdccbadacdcadabdbeccecbacdaabbacaeeeaceeecdacbaceebabdacbbbcbcabccabcbbbadbacadedeceeeabeacdcadbeeecebdceebbeecaccccbacedeeeadcbdbededdbaacbcdedbabbeaaaaecccaacddcedbcecddecbecbbcdbdeebbccebcaeaccbeddacedcdcdecbeaeecdadadaedecdadebacbaeceeaedceacdbdcebdbbaeaeccbabdedbdcbcccbdadbaccecabdcbcaeccddccdaccdcbbceccabdeceaddddbdbdecbbebdbdcebcaecdbaedddaeeaddedadaacbbccebaccadaaadcdbbcebabddbaeabacaceeecbeebdcacedecdadabedadeccddccbaebeaeddbdeeebdacceddedcbcbdbacaeacdedbcebacbbedcddbcbeebdbbcccdcbeadcacddbeebeebbdacdadecddbabacbebeadbcddcbadabadeaabdbaabeeccdeececcbbaabbabdaecaceeecedcaccdddddbcdcbcebeadeccddeebeadabaeedacccddeecbabeccabadbaddbcabebcddaadcaaaaacbaedcbedcbcdccadaccaabdbabbdcaeeedbccaccdccadaeddbcbaaadceaeaceaaacccabddceaeacedcbedbacdbcdeebacbbccbcbeabebadeecdbedceabbabbbcaeedeedcadaeabebecdaebaedebacaeebadddebbdbdddbdbbbcaaebecdebabbacbadccdbcabeceaadbbaacaaecdacaccccdaecabdabbcdcdecedccacaadeccaeeeebdaecbcaecccdbccbbeacabcabdbbceeecdadcebbbeabcccdddbbdcedbddeddcbabcedcdacaecabededdbaeccbbbaeeccbaeaaccbbabccaeddbbabeddeebecedaeededaecbcccbdebcaadbcdaadddccedadadedddbaebcbbdeadddcebcabccddeceaadeedabbededbbaceaebaabddeeceeecdcdcbcedaddaecebdbcdaeeabecdebdbcdaddbadcadaceeebdddbecadabaeeacebdedaeaeebedacdcbdcbeeecacbeadadadbbccaeecdabaebcdacdaccdcdceccaedcabbabcccddaadbccbcedbaabeebabeccacdebbcbccbbdbcceeeddaceacbbddaeabbcbcddcdbeceedacdcbbcdcaccadeebcaccedadbedacbbebeedaaeaeedcecaaaebaddbcbadedadcdbeabceaabcadeebaacabeedbccbbbedadeaddcdccbbcddbbcecdbedaabeacdddcaaccceaecbebecccddabacddcdcedcddbcdcecdbcbddececeeadececbdcaeebbbdedbeaccdecadeeacbacaccaccebacbecdbcbadacaaacaeebaeacbcdbcebecdadcceeadbcdbdcabedcbdaddbdabeececedceddadabccabcadadaeddcbcdadadabacabcadadbcaaeaabadccbbdaccaedbcbebedbaadaeabceaeaaccbceddcecceadebdeeaebedcaecceaabcaeabebebaedddbacacedaacbaceabbbeebdaddbaeeddbdcdeedadbcaaebadceecbcbaabcaeedaedecdccebcdadaeaaedcccecadebebebebabedbacccaeccbbecdaccedebaceebccaaaeccaebbeaeabbeeceaaaadcbccaaeddcedaaddddabadcbdbbcebbadddcccbeaceabcbaeddbdabcecaeddcacaaceaadaeadcbcddaddbcaaebcabbdebdbeadecdcbadcaebddddaaaedcceccbcaebebbacecdcdecdcdccebedddaddcedabddddebaabeddcaacabaedbbaeeceeeddbceecbbacdbaaaedddddbaecdadbcaccebcabaaaecddaccdabcabaabeacedbdbeebaadbaccdbacceedebccabeadeaaebbdbecddedcbcaddcbbebdecaebcddcdcddadbdabbcadaddcedecaecbccdedaaaadcbcddbeebbebeaecbeadbababbedaacdaaeeaeadadcbeabcaeacabcbbcdccbbdacdbebddbbeddbeedbcdbecdbacaebbaceadeeeaaeedaadeacdebbeccdcbabcebedddcdacacecaddbecdebcbbbdedebbccbacbabcbbbececddcdbdcaccddedabadeecdacbcbbedbcaeabebdbdacbbedbecbbcedbbdeaacbcbddebcabbeacbebeedeabeebcdecdbeacaeabbcaceeeabbebdabadccbcaeeebeceebddebcddcaaadceeabadcbabeceddddabcabacdbcedbdededabaecbbeddacbdecbcebbdcebddeecbedccdccbaceccdaaedeeebbbdeaedbacaaebbabecdaeacbcddbeabeccabdedcbdaaaebebbcecacdbdbbbededadeaebadaeceabbaabddbaddaccdceceaaabbebebbeedadacacbaebbabdadbaebccadcbdddcbaeaccadbccdababdbedccaacedbbccadaccbcccbabecdceecdbebbabadacbceddeaaedcbccdbcccdcbacdeebbbeabeeaabeebdcbaacecdecbedbdccbcddeadabaedbdedbacacbdeccbdebdedcbbbeaeddcbaaddbdadcedbbbdcbdeeaaaadeedbdedccacccbbccebaaecacbceacbecceebeceebdedbbebeeddbcdecaedcdddcbabbdacdabccbebbeaebdbdcdeaeddcccbadbecabaedecddcdacdcecbeccecbcdaabeecdebeeaddcaddcebeadeaadcecededaccdabecbcaddccbdbacdaddcabbcacadbaababdcdaedadadccaaaedebbbdbcacccedeaebddabdccdecaeacddaadebddbbbeaccabdcbcaedddaeddedbeadbadacdcceddacadbbdddabbddeebecedaaddbebababdadeebacaccebeedddceecbececceacdebbccabaeacecbbebeddebadbbcebbcdececacdcaaabbccbcbbaeecdcceabbcebadccdeeccaccccceaccceaebebcbeebbbbbdddaedabeaacaedbacedeacdccaadcebcbcabccbeaccdbcdeddecedcdcabbebcaedddcdecaededecdaadbcdaeeeabeebaaeccceaccddabbcbebacabeeddbedbcaedacbbdeeaaaaeedcdedabaaebdbcadacbaaaabcadddccbeaedeadbacdcdcbaeadbdccdadadbcaddcabddcbbcacdcaaeacedcddcadebdbeeedbebbcbbdeeeaeaaabbcbecceddcaacabacccbcdbeedbbcdceeccedbcbddddabadbacbaedbbddcbebaddadeedddabeacdbbcdccceceacebddccadadabbddaabcecbeabdbaecddbacaeabadcbbdedcbaadcbbeecbbbcebbdeaedbddbeaccceaeeecbadceacbdebddccccbbacaadacdecbeaabbeeeebaedcceadcceecaacbedbdeddcbcdaeccdeeabcbebdabadbbbbbaccbeaaceaaddebaaeddabbbedcdecdbacedddabbacbbbacedbacdcdedecabbdbdaddbcdcbedbdeccceeceecebeaecdbeccbbeaeedecbbdadcacaddebacebecbbcceacbedeebeedccedecdcbdccaaeebcbbeceaddcabdaacbedaebebddecbabadbeadddacccaecaebdbdebdaeacccbdaacabcabecbeaadadbeebdadbabeeaebceacebadecabaebbbdceebcbdcbbabecabdbdcdeecdcbbcdcebecedcdcdbdbbbecdbccdcaddbabceccdcaabddbddedaceccbebdbdbacdedaadabceebdbabdcedcececcdddedbdaedaaaddcdeaadaaecabeacaaddaabecabdbbddbdeadebeecdcbcdcacedeaadbbacdcebbddaacaecbacbcabdcdcbbabecdbbaadbcabeeabacdebebeceecebbcbabedabaaedbdaadacbedcdececcedacdcbaddbebbbcebcddddeaaebabcdacadecebdecdacbcbddacbdbdbcbbdbcadadedceddeaceeacbaacdddedaaddeacacaabcbededeabbbeaddcbaabbdbbaeaedaadbebbdebebaaaedbacebdacccecbeebabcabcbaabacdcdbeadddeadbbebdaddbcaeddceedcecbabccadddeebacebbbbbdccbaeddabeeeeadbdbbccacaeaadacadaeddcaaabcbbdaeeccbeabaacccdeceecdebbeeedeebeeacbeeadabbcccbebecdbaebbddaceeecedabbcbbacbabaedbaaeebcacaeecabcaaedcbccdecdbadbebbbbcdacecbeeaeeaddedbdceebabbebecccebdaabaabccbdaccadaccbabcbdaccdebdeacdbdccdbeaaeedbdaebcdabceddcccdbbebbabddceccbaaeabacbadcbeecccacaebdeebbddeedbbedeaabbeeabebededbdbcbcddcadbbbbbbabdbbaaceeaedcebbdddcecdeddccaadebbddabdbceeecdccbdacacccdeeaccbbedeadaacceeaaabcedcbabdcdbaecebcbdeeedacceeaebebabbcecccadacebcbdeaeadabdabdcdbbbbbebbcecedecebbddabaaaeabeebddaaddebbbbededaebabcbdbdedaeedecbbcededcdbbeeebeabbbacceebaedaedddabedbbbdbecbecaacdbbccedacbbdabbecccbdbccddaabdbceaaebecbdaaeeaddbadecddaddbbbecbbadcaedbececbcceacedbdeebcaeadddcdddbedbddaacabbaaddaadcdeecbaabedaecaceaddaadceebecbcabdceccabbbcbaadcccdaeababdecbaccdbcceccbeadbbaaaceadecaeaddeddecbbeaedeecceaecbabbdbcabaaecdbdbbcdcdbbbaeadaeceaebddbaeebddacbbdbdcdeadabdaecebcdceaeacaecbdedbdaaaccdaebdaaacbcbcbcebedaccaececbbdacdccdcbccadececdbbceeaddaceedadacdbcbccdacccbceeccdcdacbcdacbaceaeacbddacddebdabaceecddccdbdbeaebececabbebcbcccdadaebaddcdbebecaddddccdccddddcbcdbdeeebddbbcccaaccdcbccacdaeacdaceabdccdddabeabceecdabeddcdaaccdeabbeccacecbcbcbccbbdeeaaeabaacdadadeccacbcbcdadcbaebeadbccbceebeeddaeeeaaeccbdceadcdaeebcdddaedabbbbddbdaebbddcaedbdacacbacdbcaeeddadeebaeeceebdbcbaebbeaccaaecbbbacbabacaecdacccbdcecedcebdbeaeccaaecbbeeaaaebebccbabcbdcdeceeecbabbdddeeceecdeecbabbeeccadeeaeecddaabaacdddeddabdabcacbdbecdbcececeeeccacaeaccaaeeebbabaccaecdebddaaadbbecbdcddeaccddbcecbeadecacebcceaddeaeabdceddcbbeaecbdedbccdeeddcbcecebcddebeaebdaabebbbdadebabbabeebbdbaeeceaccbbdccbeedcbeedeeeeedddeadcebedeadcbecddadbbcaabdccceceabdbdcebaebeebacaadcdbabaeadebdddacbccabccdbcaaaaebbbaceabecbeceebcbdaecddebcedecbecbcbdeeadaadeaeedebdebdcecbceeeadddaaabccdeccebbbddcbcbbbaeaaddcecbcaeeecbcadadaccbcdbdbaaaccebcddedaeacbdebdceadeddcbdeabebdaeaeecebecabadabdbaaebeedcccaadecbcddabadaedccbcacacdaddcceddedaacceebecbceeeaeeeabacaaeceaadadedaeebaccbacdaaaadbccdbbaadccaceadbbeccaabdabcbabbdeabdedeebbdccddcbaebeabeabdabdaebcadabdeedbbbaebcdbadbeadaaeeeddbeceddddbeaedbdddddcabbdddbccccaebbceccadbcbabacabaaccccbdcddeebdcacadeebcbaecbcabeaeedbceadbadcbebdbdbdaaeaedaeceecdbeeaaddedcceeddeebcecdaeddbbecedaabcdabacdcaebcbeaceaeaccdbaadabdaccddbcccceaeeddceabcdeedbdaaaadadebacbbaeaabdeebadaabcbbbedcbacabceaacdbebebabbddbbabecdaedbadeeeebceededbebbadabcdbaeacecacccabeecaeacaeabdbddaecaabbbcbbdaacdadcbeaaecadabdcdecceeedbadcabecbbabcbacaaacacccdbcbcbbcdbcbedbdbcbcccaebeadbccebddccccdecbadbecdacacddbcdcceaceeddcedabeadabebeeddaabbdadacdcdaedeadebaeaecabcbbaaadbbcddbecdbedbccacddecdcbadaaeebacaaebbdbceebcccbeaddbcadcaebbbbecdcccbaeaeaebdabcaedabbecaeeddaabdbcadabbaddaabacacccceababebddcaadcdcbcaabecedeaededacbccdcedcdccadaaadcaabecdbbaacdabeadaebeadbbcacebaeadaecceaabeccbdacaaadecdecdcdbbbdcbbcbbeeceedabdbebbdaaaabaacacacdcdecedcbccaeeeeacaecdeeeecacbadccccbaacedbacadadebccceaaadebdbabaeacbeacbcaaebbdddbadaaaccabbceddbabccbebdabedccbdedbdaddbedeabcbbcbeaaeedaeeceeeabbcaadbddeecadbedebdbaaadbadeeecddccaeadabebddccddcbcecbcbdeccbeeccabccacaedbccbabecdebdcbeceabeededacbeaeeeceaaeabccecceacaecbdbdaccebeeaadcceecaabbebaebbaddedbabecabadeeccdbddecceeeeacedeeeaecabeeabdcabcbebaaaddaabcdbbdbcacbbddeeccdeeedbecddddcabdedbabdaaadbedccaadaabeeaeecacabcbbbcbcecaeacbacdecedeacaeecbcaeebcacaeebeaaadaccdbcbcebcaceaabaeabceebaaecbbbdbececdebaadadbceedacdcbeeecaedddcbeeecdeacdabbdbadcdbedadaedbcccbcaebecdcdbecdeadbedebccecbeeddbbeaadbabacabcdbbbbcbdbaadacebeedbedddddaeaedbededbbeeeedacebadbebecdedaceaccdacedbccabebeddbbdcbdaaaccdaccddbbaeceeaadeeebdcceecaddbccadcbbcedabdebceddeeaacaabdcbdeecdadaeaeadccdceceeeedaabceaabcdcebeabcabdadebcccedccbcaebabebaaeccbeedbededbcbabccadadcdeabedabaeaccccaaecabbcaebedacdabeaadccccbacbcdeaaabdcbcedbcaadbcecdccdcbceeaacebabababdbcdcbdabceccedeacbabcedbaaaebbeabcdeaecddabdcbbccdddbedebbdebbdceedceeadeaddcbbbcebcececccaecacebabdaddbddeccdaccaaeadbcdebecdbcbbcbbdcbdacedcceebedbdedddcaaacdebbbcccabeceaebeedaaebeabcccecdaacebccbdebedaaaceedaecbbbcccaabdbeeabebceeddceeebaeecaaddcacbdabaacedcbceebeaacebcceddbedcdcbcaaaecaeebadddcddcbddcedacacdebebbeacdeceebcaedddbccecaaccbdebecabceceadcbbecbeabbebaeeacdedaececddbaaeaceadebacaaebceadbdcccbbbbacbebeaccdaadbbacceaaeadbbcebabdabebddeddabccddceedebdbeeedeeecbdcabaaeabbadaddebbecbccbbcbcdcbcbaeccecaeeaeddcacdcaadcdadedcbdbadbcdddccabadbbeecadddeadbcabaaacedadbbcaeccaebedebceabbadeddbdedbccdbaabbbbbeaebcbdccdbebdbacdaabcecdddecdedaaacbdbbadbbeaeeccecaabedeeecbaedebcaaedeccdebbbadbabcadedabedbddaccacbdbacbeeeccacebabeedccbceeabcddccbcaaeecdccaeabcaecaaedeadabcecbabeacdadddbcaabebdedccacbbddadbbabeacceccbcebdcabbccaddbbbacadcdbebacbdeaaeeededcdcddaedaedaebabaacecdddacbddecceaaaabeadcdacdeddcbcedaedeaebaeddbbbaaaedadcaeeeddcdaeabcbbbcdecaabcbbaabeaecadcdbeddceceabdddaebecebbcedceedbdeeebcececdecbacabbbebdccbeabaccadddcaebbbaabbdeacbdaecaaeaaedebbcbaacdeddacbdcabdbdddcbcedddcdabaaedcbdaaebdcdcebbceddebeadeccbebdaabbbacbdaaeccadecbbdabbaadcdacbaaeccccbeddedcacecdddeddcaecbeececaeedadddabaadbaabceabecadacaecaccabaadacebaacdadababbaacabaceacccbedceabecbbabecaddddaeadcaddeceaaeeebbeddeaedcaeeaacccacdaecbaddcebdbeacebdcadcbabcdbcedeadabdbbcbbceedcbecbbecdaecdceabdaaaddabeeeabbbedbeddbddbcbebceabaaabdecbbbeeceeccebbdddcaeaadccacececabeccbdbcdabdcdcdeaadadbcdcabbbadceedeebdccacaadccdabbcceecebcdadcebbadbeabdbdbdcecbdccbccacbaddbbadbdcbccababdcedcdbbdaaeecccbccecbadccccaabbaaacbdceaccbecdacecdbdabeabedeaacacbaaeaabdaeecebceccbcbdbbdaebdccebedbbbeacdabbdcacdcbecbaddcbdbaabdeebccbeaaebbbdeabcdbeceabdbcccabaaadccebbcbbcddcbbcbcecaadcdebcbcbedcacaddaddbbddbbecacadeaadbbedeaccacabededaeeeedeaeceebebacaeebaabdaadabceceeabacedeaddeccdebdcedaeeccabccdcbeeebadbbbccaadedcdedcadbeeabaaedabedbbaaadecedbebeacbbbaeddababaedecacdaeabbbdddaeaaacabecaeceabccccbcacebcbdcecabdbacbadbdecdcccbadacbecaebaccbeeedededceadaeceebdcabbacadadbcbbedbcdacbdbceeacacebcdebbdaaeacdabceccdcdeeaacdaceabcdacbbcbeacecccabcabecdaabadccacbddbaacabeecddbeeadeddbabbcdddcdacabdadadddddeeeedceeebebeaabcbceadecdcddacbccbddbcddeddaedcdcdcadbcbebeedeadabcaaacbeeeadeabbadecaceaeedddcebadccaadacbddaaebcaabcdeecadabbbeebacdcbebbdcebdbdcaeaadcbcddbadbcbaccdadceabaaacdccccbabedddaadeedbeecbcedecbabdbeacebdecdebdcdbbaecaebecdddadabebcbddebabdcecdaaaebadcbbdccabecdaacebdaedeeccdacebbcecbceeadaedcdebbdbdeacdebecdbcceeacbbbcbcddedbcdcabceddebaccaabdeeccdcdcbaaaccecbddcceeaaeebdaacecabdceeabbbcceeabbdbceaaaabbbcbcdcbdecbacaacaebcaaadbddaebeaaeeeededacdbaaeabbcedbbceecaebaeaecedcceaadeccedceaadeaeeaaabbbabbaabaaabdbdaabecaddcdacadbdeaaddaeccabcebccbadccebddeedababcecaaaccdcbececbedeecacaaaccaadddceceaaabebcacabdbabbdcaedeecebacabddccbbebbceadbaaccadecebeabdaacdecebcaeeddcdabddaeceeeeebecebbabcdeedbedccecdbccbbcddcacbbdbceaddecadacbadbdeaccacadcedbbebeaaaebdacdedecbdedbabdbedcabcccecdeeccedaadecccebecdceeecdacdccaaecaedaddcacdbdbccbbabceedeaaadbbbecaddcbadcddcdbebebeebddeecaeadbcdebaedebdbececdbdabbcdbeeacaabdadcdceeddbaeabadecddeaddcdbbbcbceaadeabebddbcbeebeabcacdadaadedbbccdcaabbeaeceadbdaeeecdddbdbaabcadccaabedcbbccdababdbbebedbccccebecceddeedcaadedcdecccbbeaadbadaddaccbcbaeaddcdadbacbbadceeccdccdedeecedaeabcebbbedadadeecbdecbeeeeeaeecdceedeadbbddcebaacbaecedaeddedcceacddddcadabbeaecdceaaabeaaceadecdbaaaedddccaeeaabaedeadcacbaddaccaaccaeabadacecbbaddaeaecaacbaacdbbbabbaacdacdcceecebeeecbadedaedbccdecdbbebdacdddecebebbdeacbdecabbecabecddaecbdebaecdbbeceaaecaecddbedbaeecddcabeeeeddccdceabcbccbcecdecbcbdcaabcccebcacccbdcabddcceadbccbecddcbebedbaddbebaccbadedabebccaededcedadcbabeedacaebaebabcbaecadcbbbbaacdbaacabaaadaceaababbcbecabedaeedabcccceabdbeebabaceacbdcacdceedcbdedcbcaccbecbeabccacaabdadeeacdcdbdcdabcdaddbecdbadbbeeaedcadcedeecccdbbbdcaeabecbdeabaabdaabbcecabcbcabcbaceadbcecccbaaeaadeaadbdeabacecbbddbdacccaddbbccabcdcaaddaccdbbccbeeddddcdebdcceabaedcbaeeabdaaabcdeabccccbdbaeedddaeccbccdddbbccaaaeadececbabaeaabceeecaebccdcedbeabeeebbbeadbdaadccdaaeadcacdacbdacbdabbdcceccededebeaacdebadbbdbdbeeabbaeccccbbacaecaaddadcdcecacceaacadcadcbededceccdccdbacbbcededadbdbddbadcecaeaaadeceaaddcbbbbcbbaedecddccebdeddebddbdebaecdcdbabecebccbcbeadcedbbdedbebebdadedeeeceaddccbdaebededebedcdcaccaebaaeddebeabeabcbdeecdeabcbdcbabbaeaeddcbddbbecbbbaaaddcaacbcedaeadcedccedabddecebdebdbcababbdbdcabcbabaababbcaddbeeeaeaacaecacacdbcaeaccebeddacedaeecebcaebccdcadcbcaaecccedacaaeedcdaeeeccdcaadbaacceedaaaaeaccaecadbecaebadebbdebdccdaadecbbbbeccbcbdaddcecdccddababebaaabdcbebcdcbbbebdcdbdedddbbccdadceeaedcbdbedcedaaeddbadaecebeecabddabebbbdbabacaeddeedddeaadedaebeeababeaeaeddeacbdecdebbbdaebaecaacddacbacaeacdadedbcdcdedadcceeaebaebeccbdeadcabeabbdcaeaddbebadacbacaddbdbbdbbedcdedadedeeacadeeacddebbdbcacdbcbaadbeebadbecdaaccccbbabadadceccedcabaedaaedeecbaddbeeaeaecedeedcdcadaddaebedbeccabddaebdbbdebddddcbcbdbaebcaeebbcedaecbcccbcecbcaabaccacedbdccbeaddddedacdebbbebeceadeddebbeecedeeadacbbacdacabacebdebebbaabceccbaacbdbcebaaaaecdaedebaaebccaceedcdecabceddcaebacebbbedaccedecbbbbdddacbdaeaacbbceaedacbcebdaecbcbeecdcacccaddcdbdebdacdeaeddbdebecdbcedbbcbbcdadcedaceddadbdabbddbacddceaaebeecaecbbcaebedbbdedaebacaaeadeabedcdedeaddebabbbbddddcccbbbcaacedbebeedccaaebdbdcbeecbdddcbdeaebeddedeeaaedaaabdcaebebdaaceabeebeecadbbbdcaaeaadbeaacaaaebeeabeecedcdacaedcdccbbdeeeebdacbedccdbbaadeecceebaebcccdbcdddabccedaabecacdcacccadbaceacdabeaaecabdccdbabaeaccaecdbddeeeceaccbacbebcbcedbaaacaedaaadbadcebbbedddccbcecabdbccebeedabdaceeabbddceadceddddccebaecebadbcaeaadeaddecceaaaaaceddbebdaaaecddecacdacaeaacdcaaaddeeaeededbedcaaceeceedbcdeeabcbddecdbedeeaccbaeddcbcbdcceeaabaccbdccdcbbbcacddaeebbdbbaaebaaacdbcbbedaccabacbabbccabeeddabccbaceeaabeecededeebbeeaaeaddcbccbcecbeeebdbcbbcaccabcdcabbddacbeceabddacadbddcebbacaeabaecbadaaaaadbddaedcacccecccbeccaddaaaaaebdbabedaddbaceacdaadeabeebaecccdeeddceedccaaaabcdaecadbeabcbcadbbccadeebcddedabbcdebeaaecddcedaeabccbaccedcaeacbcbdbdbbdbebdbbddeddcbbdaaecebebdcaaadebeaaeeacdebcdecbbcdeaacbbaaabbbeeadcbeebebabbdeaebeeadabecbabdccaebbdceeeacdcaccdbbbaecacededbabacaccbeacadbbbdaedeaeebbeacbecdcdbacbaaabeccecdcbedcabdccaebdbdbcacdddeeebccaabceeabadbbdacaecbbaecbaeacadbdaddedbcaeaddadeedececbabdaaeedbeabccbdabddebcceedbbdeecebbecdeeadcecbbcbedbcebadcdecabbbaeaaddebccbccddcceaaaaabdadabdceedcedcbedcedecaaedbdcbaccacbdcbeecedbeceacdebbeebbdbabbeaedecebeadbaadaababdcabadababeecaedcdcabecdcdcadeaceeaadbceddacaccbbacacdcbecdbbcdcdcbbcbaaecdeecabbebcebbebcaeaceacdcdcdaeabbedcccbadbeadcedddacbebbddaebebdeddaccccedaaeddaaaecbecabcedecbecaddebdaaabbededbdbdeeaecaadebbeabcaeadedcaedeacdbacbbadbdeaccddebdbbcecdabeceabeeeebbebcdaeebabdeaaaeacccadebcadddcdbbbbbdebaacecaeddbdedacbdaeeaeaddaaecedaddcadecaedabebbaecbdebeeeddaeabaacdeacbcceceeacddbbbdaeeebcdabceaeeeeddcbcebeaecaeacccdccacdbbaaceacdbdcaabdeddceebacbacbcddbcaaaeeeeaceeddacacbbaaedecbcecabaedcebcdcbeacdcceebedeaceabeecaacbbedcaaecbccbaccbdceaaacecbabdbacedccaeddceedeaeabaedeedccceababbacaddaedbeaadbebaaebedabbccdedbaabadcdaeeccaebdbcaecbbbaeceadaaeadbbdeacbcedcadbaaecddedbbddeabcdeaabcbbbaceeeaebbcdcdadebcdebaebbbceaababdbacdaadaaceeadcabaaeaaeddadabaccacbadcbdeccddbacabcadbaeceeaceabaedddbeeddcdbbaebbabbbcbbbdcaeeeababceccbccdbcbcddacbbcdaaebabbacacadacbccbbdbdaabcbebaebbaecbcdddeddcecbbabbaccbbacaababbadbaabeaceadaadcbbcdecacdeeeaebcbdbaadcadbdaaadebaccbaddccdebcceeebbdcebedbccbeaeedacacaaebdaabceeccceaacaccebeeeadaeeadeedbbaaaddeacdabcabbacdceabccbaeccbbacbbeabeeeacdbdaadeaaeeebdbccdbaccddbadbaadcacecbaddcadeacceccdeeabddbbebdabceccdebdaadeeeaddaaceaabedddbbacdbccbababbbeedceeabbeceecdbbadababccecebadeeaebdaeadddceeddecbacbecdebaedaaeeebccecadacabaaddeadcdbeaaacbdcddeceedabdaaedbbbcadadccbeaecccebddaddcebacadaceedeaadaeabddccaddbabbcdcdeceebcabbcadbeaabdcbbecdddbceeddeeeedabeddaeaadbcaceacceaaaabdcbcacadcbdaaebeadcccbbaaeedbbebdaeddbabbcbcdbcceaaadaaddccbebacebccadeecddedcbcbecdbecadeeaadbcdaccebbbebeabdadaeddcbcbddcaeadadeccbccadeeccdadaadcdbbcadacacaaeccabbcebdedaeadebeebceadaacdebdccdebddcdedececaeccdeadeccddcdcbeabeddebdacbabddadcadccbedecabaaebbbbeddbcebcdaadabeccebdcecceebeccdecaaabbbabadabbaedeaebbbadaedecacdcdcddeacccccecdbcdeabaceeaebdaecebeeebcddcecabbdbabbaaebbadddbdacacedeeaebccbabdbbaddedbedbddecdedacdaddcdbdbbdbdcabdccceabcbeacedbbedcdbcaedccecdecacdabebaabaebaddeaaaeadcacbcbecccbeeedebadeeebdeebabeecebeeacaaecdcaecdbdecddabdbbcdaaaddbedcaeaaccbacabcccbbeabceabedacbcadccccdccecbbceadedcbbaccbbcbccabcdbbeddecabaaaebacdedeeeadbacdedeadaaedaebcdbdcbdceaaeceaaecadeddccbccdadcdaacecdbaaeddeacbbccdaadceebceceeecccbcdabebccbbbbdcbccecdceedbebcdbbbadcbceedaebbeebdcecbaadcebebcaecbdebabbdbaeddeccdbaaeceaceecaeccecbbbbddbdddaacbcccaaadadeebeddbabaaeddcabcdedcccbaeaaebaebeccddbbeadeddaaaacbebabcecacbdbddbbbdbccbdddcacdcbaceaddbeacbbaeacecebecaeccccbeddbebdbbeedceaecbedbbdceaaeccdaeccadbadddaadeabaeaabbcdbccceecabcaabccbcaacabeecbeaeacedeebaaaeccbcceceaceededebebcdabacbbccbcabdccdeddabadcbdcecbabdababeaeaddedeaaaeeeddbacdbcaebbcabecbddbadbbeccbecaddacbddaaeeeceebcdbebbbadcbbaeedaabbccabbecabcbcabaedceddeaabeadeeedecbbecebcadbecdddcecbcccbeeabdebaedabcddebccbaadaeceedacdddeeeeaddaedbceabeabadeebcdcdaacabbaacacdbcdedaeaacaeaadeacbdaebdaebcedebaadbaeacbccdadcbcddadbbcddadeadeebceaacdeadecbbbbcbeaabaeebbadabaebaacdeeeddedecbdaaedbaaebaaabaeadaaecbadcbdcaedbacedeecbeaedeccadaceacaaedadebaadaecbedebddcddceaaecebdecbecabadaeaccecbbcaaecccbabaabbcaecabeaaddeeedebacecdededbdbeeacccdddbdbecebdedadabbcbddababcdceeebbbadaaacdaadbbecabdcbdddcaceeedcbddeacacaecdceecbaabdcdecdbacdaabcdcccadeddaabdcceabeeeeaccceedbdcebeaaacdbeaddaeadbebacababdccadbedddceaadcbaeaaeadebaeabaeacbbbadecbbbceddeabacecbbdeaebdeeacadddaccaddbbabedccabdbbddeeadeaeaecedeceeaeaaecccdebecdadddbebeacedaeaeebdacbeeaadeaeccebedeeccccbdadacbadeacebdacacacdeeaebbddbbcadaebccddcababedebeeebdbebdecdbecbdddcabeebddedbdbeaeeedaecadcaaabcdbacdadaebcddcabdebaecceaababdbbabdabdaeaeeccdbaabebeaabdacecdeeeabddeaadddecacbeecaeddeeaadbcdddeccbbdaccdbadbabcebcbcacccbbdebbcdaaebbbceaadacecaccabcdcdcdabeccadaddddecbeeacbdcecdcccabaddecaacacbecdcdcdcedabbaddedddcbbecbddbdaabdcebaeeedbededddbcabceabbecbeedaaeeebbcaabbbebdecaebeedbbedeedeeebcdedeaeadacaeaecaaeddaeccdecbedcbbccceaaaedddbdeeaeccbcddceadcbadbbadcebdbbdbabcdddddcdeaeabacbaedebacceccaaebddeadeabcbaeacedeebbaaceddecebdaccbbdbadbdbbdaabeaedcdababaeabecdcdbaedcceaabcdbcddaeddddebcaeeacddceabcbacbdccddbbededebcccaacaccabadccddbacbadacadeccecaaabdecddbbcbebbdedbbeabccdceedaccddeebdcadddabedbeaebeebbcaeccebbbcbdeadededdcedddddedaacddbabdebeccbebaadbcebececcdebddbaaecabcceaaccdebdaecacebddeaddacbabbcecebdddbdcebaadadbbceebbcebbacacbaaddedbcdcebadecabacdccacabddbcbcbeabbccaabbacecabdaeebecedcbeddbaccbbecceaaeabbdcbbaebeeccbcbcecacceceddbcbcaaabdcacadbbaebddabaadeaddceebdcbdaebeeadbdddebceebbdabcecbbadbecdecaddbddecdededabbecaceacbcaecaeaecdebaeacaecddbbbaebaddcedbecbacbcadbcaddbacdedcbddebbbdabdcacdebacebecbcedaadbebecebbbcbaddabdeecadbdcebebebcebeaeaabcaeccaddbdddeeadecedacdddddbdcdecbcaaeddedbeeeeeedeaeceebadbbdcbadbbcbcecbbaebcddeaadabdcdacbccacababccccdecbdcdeacccddececddbbdeccedeccbbcbeedbeebaedbaeecedbbdaacccdcccbeabcededaeebcdedaecceebbabebdecdebeeaeacdbacdbbbccacbceebdacccbaaceadddedccaeebeadbeaccdeeeaecceecdadebdceaddedbdcaaccebcbeadabacdacdccbbedeeddabebbaedccbebdceeecaacbdeddccacdecccecebdebdbbadbaeeaadeaaaaceedcbcdabcbdeacbbedcaebeacdbddeabbaedbebdedeedabdebdbdbeaeaebadceceeaeebaabcabcdabbacbebaeccecbeddeaabdcacdebabcaeeeddcbbeeddeeaabcbbdeaccabedeaabbbecbedcbaebecebabacaaabbadcbeaddedecbbcebaeececbcceddcebbdeedeadcdbabcbccdcdacbbcaaaaeebbbaadedecaecdeaecdacabdbbcccdbabcceebbdacaedecbcabbaebbecedadecdcceeaebccdddaabbecccecbdbbacdaacaaaacdebecbcbbbcbaceaeeaadbdcdbdecbecaedadeceedaedadecdedcbaaeadadbdcdeacdbdcacabbdeebeabaabbbeceeccacbebecedabccceecddbdeebbeaddbeadcbbeccababaecacbaceddbdbbaebbeaaadadcddccbccbcacceadddadeaaabdecccbedcaebedbdbabcbaeaeeecdcccbddddbabdcedcbeeaccedcdecbeeebbbcadddcbeadebdbdeccdeaeeacbbaabaaebaedaaecccdbceeeceabcedeabeadccedaaecdbbcccdcaedcbaabbededecadabacecdbedededacbcaaacbceabcccdcdcaaebbceccceedabdcecdabddcdebebcebddbbdacccaaebbaacbccdbdaedddadbccddeedabaceccecbdededeacdbebaaedbebecbbccdacddbcbebaedacdbaaeddcbeacdcaccdecebcdabebeddeadbedaaeecedbdbdaebbdbacdaebbeadadcddcadacbceebbbdcebcceaeadaceebabebbceaddcdbdaceddbceeadeeddbbedcbcdbeabaeebcdebcbedbaeeedcbcaeebddcacdbaadecacbeecdddeeeabbebebaeaccececbdacbeecceaeebedacbcddbbadcacbdabeedeebcbedeedbdadbedebbaecdaecbbdecdedcbabaecbedaaeddeadbbdcadcdcbabddedbeaebaedcaadddceddeeeceacbadeebadedaceecacedccddcadebaadddebecdccbadbaebedaddeddbacbaeeeebbcacaccdacaededdedeaaabdabbceeaebbdddaadbcecdbaabccbeeceeababdccadbbaaedaadbaeeeabcdceaccdcaaddabecabebccedbebaaccceadcdacbcdbdeeadacaccebadaddbcbcbbaedacbcadeedcabadbdeceeeaaddeeaecddbcebcedbaeeadadeeeeeeacdbbaabcbecbbadabbaedddcdbecbeeebcedbdeebabbbacbbcbaeabeeeacbdeabcdedccdbaebaeacceebeeeebecdaaceacedcddbdbecbeabcaedacdcecadecaadaacccceabcbaadabccacadbebebbaceabdeaeecadadaadcdcaebbaededcbbbcaeccaaeebebddbeadcacececbbedaceaeeecbadebdcceecceccecaddcebcbacdcbbebcdaadaaacbedecdbdadbeeedbeaedeecdddaabbacdbaceaaabcbdaaeacadaaadbeedddddbbbbaecadebbbbacdaeadbeddcedeecdbaabdbaacdebbcdddbdacdeeeeeaacececeaebeabbcabbeaddaddabccabcaccadcdedecdebcbaacaadbbaecdeddacebcceeedadaaceaebeedecaedbedadecdcecddebeacdbdccaaedbddadcaeedeabdecacbcdeabeeecacedccdeeeebceabedebdddcbabecbbdabcdbedcbdbdbacceebbbcabbdaebcebcdccddbeaddadbedbeebbabacaeaabdebbdacaaeeaacabbccbeeecbeebabebcdbcaebbdabbdcddacdccbbabcbebbaecdccdcacaccaabaaedacedcbedeecbdcbecedabeaedbbedbebcdbbadeaaaedbdabaddecdaebbaedbaceccdabebdbdabaeccddcaacacaadaebcbdaaaeeaecebbeaacdaebabbaddacdedcdadaacceaadbaeaabecaeeabeadbbabaacddeabdccddcccaceabeddebaceabdecaeecbccddababdcdbeabeabcecaddeccecbcebdbdacebdbbabcadedeacbdcdaebaebbadecebcaaadedadeaabebcddccdbeedceeddbcebdbdaaabedaddbcbaeadeadaabaecdeddeebaccddacbdbabaabdcdedcabbcaeeeeacccdcaadcdbcaebeaccacaebeedadccbbccaebddadbedecbaeacbabbeeaacabcdcacaceeaadcbbbccccaecdeddadcdbaaeebbeccecddadbadcceeaeeeabadbbccaadbceacadeccecbdebabeeedaedbbacadbcabacbaeeadedadeedddbbccbeddbacdebbbabbbaeacbcdababcebddbccadbbcddbeeaacbeecddedbcaccbceadcdebdaeaabacaebdbdbbcabcedbebcedbdaddcdadaeeaaadabedeebacebbcdbdacdddbaeecbcbbcaddddceeddddacaebaaeecdccdeeeaededbbceecdecdabeaabdaabbacdedeedebdbaceececccdbdaccbbdcdddebdccaddbebbedbcccaedcbaaebdcedbbbeaecaaaaabdeacaecdceebbababecedeccbbcbdcbdbbeedebceeddcbaadbbdbbaaacbddbeebaebccebeeecccbbeaaceebaddacebeeccabeeeabeeaedcceabebdcaddeebeecabecbbaadadcecebceaccdbbebbbddbadacecaebddcebdecdcdebecbdcedaeecbbadbaebdcbbabdedabecadbeaccedabbbdcadaabccccbbeccbbeaabbabeebbdecebdbcbacacadaeccdbaeadeaedeaaeacdcecaedeeecddcabeeccbbaedcadcccadeeeeedbcadbabccebdbcedddaeebacadcdaeeceeddabeecbbcdabebddbbaecddaeacaacdaeeabeadadcbdbabbcaabdcbcacebaedebdecbdebceedaadaeaabdbaedcceedabdbdbcabcaaaecbeedcbbabdcaaaebccaccacabdbbdacbeacddeedbbabbabcacccaadeabbceaacdeaddaabaacdeaebebdbbaeacadadbbddaedadabebeaeaecabdcecbedacddecdcdcbdbceacdecaaeceeddbcaeaabdeabeccddcaebeaebcecbdbecdcaecddebbaddebdeebbacedddaeaacdacaddaadcbbdceebcbbacaecdabecbedcdecdebccadcbaccedcbceaebcdccbcbdcadeaaeaabeedcededdbecabcbecbbacbadddbccbeeecebcaaacabcbbbcbaeebadacaadadedeaadeeeebcdecdededeadcbcaaecbebeeacabddedccbeddccadbcbaedcdceedcbebcebbeeddacdaedebbcbbaacbdceddcccccbabcddeabbcbbcadaeaceddabdeccbaadedcaedbebceecdacceceaebbebaebaebbebdccbeecacdddbbcaddadcbecbdbaeedaccdceadceedbeabbceeadaabaccdedcbcedeabddecdbecccaedbeeebdecbaedebadbdeabdbbbebabadaedcdeacbccdcceabdedcacecedacbbcbedecbbaeecccabbbecbebacacbeeaabbebcebddaadebaabcdcdacabecbbeaeccdceabecabeccdbeabeedbadaebdedaabebbdbceedebaadeeeabdcaebdadaeaceecbdaedbdadaaecebeceeaedaeecaddbedddaccddaccacccaceaeabecdadddaaaabcaedccbcbeebebaacbdbacccedadcccdbacaadadcbdccaceeabccdaeaabaeecccadabdcaebceaacbcdacddabdecbaceeaddbebddcedaaebadabcaebdecadeeaecacbceccdabbbcdebbcacccaabaeabcbaaeebcedebecaabaaebdcdbcbdbababddacbcabcacaedaecbcaabdbbaeaebdcdcadbbecccecbcebecdeaceeaecceaabdbdedbbabbcddedaeadbdbcbabbabbceccdedaaccbbdcebeaabcbaadcaecbddabeadddacbedeeebebeebebcbdcaebadbcdcdbecbdbcddadecbdebeceaaceeccecadbaadedebddaedadaceadabeceadcddbbbeacdeacceccbcdecdedcdeccbdaabaedaddbaeccdcdabeccbdbacaedaabbaaadcadebadabbbbabaabceaabebecdcebdbbeeecbaccceababccebabcbdbdcacceecaddbccbcdcbddecccebeeeedebabebeebdececdcaeebbbbabeeabcddcdcbacebddababaebbbdaeeacbaacdeceeacbabceddaacdceedcdbcacccadabdaddadbcabcccccdacddddadcecaaccbecadbecccddedbeedbabebcbadbecbaebcbccebcbabaabaaddceccadcaaebccbdbabebdeddeeecceaddcdaeeadeeeccdeecdcbceeccdbdbeddcbdddcebaacbeacecaccdeebbddacabaadbdcbccdceaedbccadbeedaeedbeadebabeaebcbabaadeaccebeeecebeceaeacbdbccaedaccecbcaeebcbedeccbbababdeadeeecbbeeaeabaadacbcddedabaeebdaedebceaecbdababcabbeedbbcccceccbceebacecddbdcaaeceeedcbecbbededcaedbadcabdbccddbcdeaeccccabbbaebcabeeeacddeccdecabcdcbbcebddcdcdecccaecaeacedaaaabdaaccdeabdabbbcbdddbbbdabeddcdeaeeaabddaeabeecdcecabdcbbaaebdeeddaacabacbaaadebabbccdcceeacbbbdbebbeeabecbcddddeabbdccdaedeeabadddecbbdecbcaebbdcbdbeaadddcbeaebacaecbadabcdeebebbbcedcaecaacaabbeebcbcdbcdacdbbdddababbdebdbbebadcaccdaceeacaabadeebadcbddecedddeedbdbbededbcbcacacaaebcbacdbdeebebcebdadcaeaaeaadbbcaadabcadeebabadabebdedcaaaedcbedcdbdbbdcedcbddbcadccccaececedbebbadcbbcecbaeccbbeccaeeeddaeeabbeebdecccbdaccacdddcdaecabcecebbbadeebaacdebeeccbdcbadaadcddbcbcceacbcacaabedccabaaaacadccddaedecacecedbcdbdaaebdbedaeddcbdbdeaeabeacbcbeadadeddebeedbbbbcadddacbedcebdcbccebcddaddecebbcbabdaeccdcacdcdbebabcaeadecdceddabbddbbceadadeccbbbedddcbddbaeebbccdeecccbcddcccaaeedbaadbaadccbeaeaacadedccadaeeeaebbdcbadcecdadecccddabaaccabdbccbcaabaadaaeccadbcacdbcacecccaccabeacbcbdababdaebcaeaacaaddecceaccdebeacababecacbabddabdbdbddebecebadbeaeaddddceacbdbbedbbacbacbabbbccdbbcccbddbcebdedeaaceeadeadadaacdbaeeeebddecebebaaddadcbacceddcdaacedaaeeeebcecddbaadbeadeeaaceedcdaecbebddabdbccbacdbcedcacabbbaacbccccebacedecabedadabeebcaaeeaacedcaaeabbdbabbabebcadbbbdedccbacceceeccdabaebacdbcbecbececdadcdadedaeebeccbbeddeddcbaebebdbbceaadaaebadbcbceacdbbddacccdbaeecceaebeeaaddcabcaeeebbeedabbcaadbaabbeeadeeebdcddbedddbddebeedacaaecdecbdeeeabbabdceeebaedccadbabeabbbacdbbbceedeeabaeecccccabdbbedabdeeebadddccabddcbabbdeddbeacadceeecaceaedddcbceaaaaadbbaccdcacadeedbaebdccaceeaecabbcbaabcddebedcaadabccebdadcebcdcbcbecaabaddbabacadccbacedebccaaeaabdcbabdbbaeedabeeebdcebaaeaaeaecbddadccaeabeebbbbbecbcdbbebeccbdceecdddddbdaaacedaeabbdedceedcbeecaccaeacbbdadebceecbdedaaadadedcedbcaaebcceeedababdbadabeaedbddbdeeebeeadaebccdeabcbabddbeecdeccbaddeeadebccdeadcaeebaaebbeeaaaddacbbabedadeddbeeedbabceabebbdebbaabbcbbcdeaccaaeebadaebacbbbecbdbedbdddcadeceaddacbbbdabbbdeaaacbcaabbcedbaaccabebdbaeeabedccebadcaecaacacadabecacdaababceeacabbdebdbeeaaddedcadeacedbddeacdddeaebdeedaabeeeeecaaebbeeeaecbcdddadcdedaeddebebbaadeeaadddbcbcddbcddabdeaedcbbcbdbaddecdecbeeeeeaeaeedeceaabbaceeccadadebaacaabbbeadbaeaadddacaaebdbeaadbcecdeaaeacbeeecdeeabcbecbceedceeeeeeedeebdeeeecaeabbcbdedaadedaacbebabdebccdecddadbbcccddcbdcbaededecaedddcadbebeeeeccbdccbeadbdbdaeacceddaddecebacddadcedcdcdeedcceadeabdeccbaacaecbceccabbaabceddbeeddaaaecbbbceacdbbbdcabcedeabcedeeadaaacdbacdbbadbbcacdedddcdddcbbcddaaecaadbbcddcdcaacbaebaededbdcebcbcebdbecccdccdcdbbdabcecbbaaaeecbbcbbacedbdddbaddbedcddccdbcdddbebceababbbdebaadaeececeadedebbccdbaebeddcedbedbddbdbbcddeddebadaabbcacaadcedddbadecacceceacedadedbceeccdbbebebdccbdbecccebaaaddedbdeccecabbbbbbbdacbcacdabedcaebcadbdcaeddeceeedeeeeccbeacebbdaacdcbbbdbdaeeaccaadeaeededaabbccdecceadccdbedebcdcaaaceaaaaedadaaabddeceecedbdbacaeedeebecbceaddbbceabdacedbebcccacaebbccecdcdddccaebcdeaadbbbacabadecdebdeecdecbecdceadeeadecededeccedeabbcabbdaeaadbeddebdeedaabaeeadabebaaedebbddceaabaedeeeccadcdcabbebaaeaaebabedaaadabdebcddebeeacdacceebcccaecabadaaadecdddbaccddcacbcebedcdbabdadceadadcacaeddaeabddbabaededddaaebddebcccddabdeacdeececcccddddbbceadaceaabeeedabbbcccdecbbbdecbebcdcddbcbbddcedddaedaaacecbdebabebcdcaacdababbdbdeeddaeeeccabbcdaeeeceaaeeaabaddbeaedeeeaeeadbecddadaeecabecadaaceabcbdbdadebcaabedadeaccdbccabdbddaaabbaebebbebdcaaeeeabcbbbddacecaebabcbcbabaaaaaeedbdeccebeabdcbdcdaabbbedcdcacccccbabecacacdaeacacbdbceddedaaceabddebdbbaddeecadcadbcceecaacceddbbebecbdabbabacccacdbacbeedabccabbdbcebaeaeaacdddbeccebaededbcedceccdcdabcdeeaadeabbdadaeddeddaecaebaedebcdeedcbaebdabedbeceaeaeebdcbcceccebeedbccaecaeeadcbcddcddccbcbebbcceccbcddbaeeccebaabdcedcccccceaaeaecbddebdaaaedbdbabeccbccdbdeebbebaecdcccbdbadddebdeaecdabaeddceadebeacdcadbaecbccdacdcdaecbedbebbdbdbbdccaedbedacddeccaaedabbeecbebebcabdceaacebbbecceecbccccebaddcbdcecdbbaebedebebeaebccbbdecddbdeaddccddaccacdecacbceeddaaedeebdcdcedcaecbaeebbdeabcadedabdcdddeecccbbdbbeebeabecbdaddccbbebcadddadbadcbdcaddbdecddedadbbdebcdebccabcbacaeecedcbebeccdaeedabbbeaeebceacbcaceaebaddedcbdcbeaccbaabbcccababbcecacecbbdceebeaebbabbbaeadddbbadbebbbdbbcecbcbcdadedebeaececabeaedeeabccbdbbdcdbbdaddedddadadaececaceedcabcecdacaceeeebdbbaaadbbcbdccbadcdbaababbdbebeecdcbdbacebaeeebadddbaeedeadbddebddabbaadacbbbacebacbccdacbbeecceeebbeeadaeaaaaeedaceeacebaabcaadbadeaebccaccdaebcdaedccaedbdcddaecdddabdcbbdaecaaaccaddbccededecedadaadeadccbdacccadebadecdecccbbeeeedeaaeebebceccdeecbcecaeeddbcacdacaaacdeededbcebeaaedadeacbebecaeadbdcceeccaecbeaebccdcedbaacacedbeeabeebebddeaedeebceaabbaaceeadcddbbedaaabddacdcceccecdbcbebaecadeedcccdedbccadceceeadddaedaebcabcccacddecbaecadaabceebadeeabcddcdacbebdbbbedbcbacadddbdabcccbcedaaadaabeadbaadedbdbcdaeabbabcdbdcddddbeecdacdabbdcabaacddcbeebbeeebbebdcdaeaccababbecdeedaeacaabddbbeabcdecdbddedaadcbababdebadbabaedbaeaabecbdbeabeabcdccadebebbbbcdcbaccabdaaeebbcaabadececdeebdcebaddacaebbaaeeccebaabececcdbbacbccaadaddacbdcdcedaeacacdbacccadaecaeccabceedbacdabeaddcbbacadadbaaddbbedbabcaaacedcbdaabaabddecdacaeeeebbadbacdbddaadcaabddebbaebcaeeedabeaececddbdeeebecadeaedbdabdddeaabdddccceceeeabdeaeeeaecaeedcaddeecaaecaebceadaebdceabacbceadbbeaaaebdecbebdebdaddbcccdaaabaddceabddbacccdadbbcbecccadabecbeabdabeaabbebcedeecadbcabecbedceacdbabeebcaccdccebcebaeeeaddbebdaddeacecadbeebddececddceaeacccdaaaecebaeadaccdccbbdcccdaedbecbeabadbedbeecababbcdbbeaaceeacebdabeaaeedaedbebcaeaeacadebcededdecbecaeaaacbedbeedbdbacaecaebbebaceaaadaabcacdddaeeecbedcbceeadadbdcbdeeecadbdbcacacdbebceabbaaedeccedebcecdedccbdccdeebddecbbacbedaacbbebccbbcddeadbbbcbeeaaabccacacecebeecbbdcdebacddebcaddbcddcbdcbdcacdccbadeabbddbbdeddccdeadeeadedadceecdaccbbbabeebbbdbbddadcbbeedceeaecabbabccaadceeaabaeedaccbeedcdeedccbceccdbeeacadceebaddeabacaaadeecbcbebddecaeedbccbbbceccbbedeeedeaadbecdbbbceaecbbadedbbacdbbdcaacaabcaebccebdcedadccbbebadcdcaeaedebeebbddbcabddceedceaaeaaebebbceedbeaaddddeddcbbaebcdbdbcdbeacebbaeceddbccebececbddbacccecdcbadceabedededcdabbdcaddecbcabbeeebbdeaaaaeeedbbadcaadbddccdacccaecbdecbdeaabdccbdbbaecaccbdabbacbaaaebcbbacbedadccadaebbaecabceadaedbddbeceeeacadcacdbadeecaebddbaabcbcadcedcdedccebeedcddebbbeccebdacbcceaddcdbeaaddadedcabecdbcaaabdeabaaeedbdaaaeddecddcdccdbbaeecdaacabcbccaabedacebaecedacbddebabeaaeaadeebadcececdedbbeecddaacebaaebbdbebeebcacbcdeeeeebccaecaaaecacbdedcedcccecddaadaadeddadadbdcdceabddcdbdecdedaeabbeacbeaceedaedcacbaeebbcebeaebcbcaaeaadacecacaaebeacbdcabcabddaeacebbabebedaeaeecebedeecbabadbeaebcabcaeddbedabccdbccaecedddbbeccebabaadeaadcaeaeceecbeebccbeeeadecaaadbdcdcbbebebdcacceabbecabaaecaaecbdeeedbabadbdddebcbaaecdaabcbbbabacccddcdeeedadcabcedebeabaabecebaabecacaceabaaaebcddecdbeaeacababbbddbabbebbcdbdcaabadaebbeededceecdcacdeeeacbecbdadaeaaececdddebcecabbecbadbbcccebeeaabdaecadbbcedabaacacddabacdabcabdcaccbcbaeececebdeedeeddbcddabdbeacdabcacabeccbaaaaddaccaceebeedeccdbebbedbebdccdaaaeabbeacbdadaabccaacabaaabddacdccdecaadeaecaedacebecbbdaccdbceadabeacdbedbaaaaebeceabaabdcadccddebabcadddccdeeaadceeccaeababcbbadbbebccdaeebcaededdabeabeeddceeaceabeeaeaebaccddbcebceddadedabdbdadcdebadceaddcadbeeaccaebbbebaaeabadaeeebccdcabccbeccbcbdcacaaeeebedcebddaacaebbaaabceccbaebeaeccabebadaeebcddabbaecedaeacbedeceaacaedbaadacababaebbdccdcadecbadcadbbdadaeaeebdaeaddbcbbadbececdbaabcbdcabcbdcbbbccecdbeadddbecbaddddcaadbdeeaeccaaccdbedabbeaedbaaaeedeaacabcdbedbecdaecdaacebdbdceecceeddcecbcadacceabeceadbaceeacdbddaccdadebcdaeadeaacceddaddcdcdededcedecbeeadbcdccaaceedcaebccdadddbcbeddbbeebaeabccdadcbaeaaedcecdcceadaebccaaecbcdababbcabedcccccabcdaeadabbcbebaabeedeceeaacdabdcaebdbceeceadadaadbdbbedadeadeeeaddddadcbbeaebddbeaebaebbaedbbdbdbcadecbacedcbbdebdbeaeceeeebbebecccaaeabaebedbceaecbdccdbebcdbbaeaddbeeccddabdabaebcaebadcdddeaebeecacaeedaeeaadeeddabdddedcadabebabbadcecccceabecdedcedcbdbbdcebaaeeebbebcedadddbecbcbebdadcbdbdadececcdbcbebccbcdabbdceeaacccddeaadaaecddebecedeabacbeceaceceddcadbeeeaccbaecbeeddacdcbaabcbccaeedbbbdeabbdbbeeacbaadcddebaaccaabddddcaaeeacacdcaeeabadccaaedbabaecbaecbdeeaacdbacdcaddaadcebaabbeeadebadcbccabddcadbeccecaababebabaedabcebacdcacbabadeeeadcdaabadbbaeeaebcbdccaecbcecedebdceddadcaabcadabcddccbcbecccabacdcbcbaabbcbcbedbebdbcacbdeeaebaeabecdadbbcbceeaaadacbcddbeccbceaaccdbcceedabcdddeaabcceebdbdacddaeddcceacabdeebaeacaeaebdcdadbeedaeeddecdabcceddbcbeabdceadbceabadeebddaedeadbeddebddaaceaddaccaacceedcdedeeaaaadabbeceebadbecaeabecbdbbcaeedbaeaeceaceacbdbccedeaeeabbabaadebdebecbeedcaeabcaecccadaaedaabebdebdbcaedbeeadcecaaececeeddedadccadbaaeacbbeacebbddbcbbccbabeddcdeadecedacadcacaeadccdbebaaccebabeaeeaeebbeebbabdeecaaccadacabdbbaeabbabebbcddbcbbcdaaecdcacbaddcecbcdbaaddcbccceaaddbdedecbdbeaadbbdaaececaabbbdddbbeadedcbdeacbabccaabdacaaecdededeceacddcaddeaddaeaedeedddcbbcecabaecacebeaeabaceedbecebccdabaabebedccdbeecdbbcdddabddbedcdaeeaabbbcbecddeccaaddcddeddaeadcdeadaecebdabeaaadaabcbedcadbabeceedeacedaddbadcddecebcdbdaaacbaaacaadaccaaccdeaedebebadbebadbccbeceaaabebccaeecaecebddbdacbddaaddcecaeadecbdecbcdbbccebbedebeaccacbcdbaeddeadccdbadddeebdeceecccddcddebaccdeabbcedaaedbececcdcddaaeacaebbededdececaaaaaddeeeacedbcbebeccbaccbeaaedcabadbbbcbbcaadadebeeeacdedbdbdaeaabcddaceaabaeebdbedbcbaedbeccdcdabcdaebddacdcedeeabecaecaaaddbaddccecebddeddaabbddceccddeebeacedbcabbceaaecbdaecdcaedbeedaeaecaceccedcbecccacabbbeecccdbadbbcecceacaedcacbeecccddaedcaceaebdcadeebaebbdeeaebceedcbddaeebababdecddeaeeadceaeabbcdcccccbcabcdcacbcbddbddadeedaeaddbeabbdccdabaeeaedaeeeadcabdabdcdaacbddbeceadceeaacecabbaecabcbadbbdcbbcadaccbadbaacceaddecaaaebeccbdcbabeccabaacadadbbcacaccbbecedcaeebdabbcbbaddeaaddabddeacebacbbddcebbecdbaababdadaeeebbececdacccdbebcbeeaeadeaddbececeebdbcdbeddedbcebeccacceaaeeeabcbaeadedaccddbacedcacbbabbdccbabdaaddbacdaecebbceedeabbedbbabeccdcbeddbeabaaacaaaeadceeabedbcbbaecaadabecbcbdeddbdddadcebacdbcdbbadadcbbadeaadbcdbddaaaadeaabcbccbabcccdbdedcbabbaaacbdbbbecbeebdedaaaddbbdeebddabaebccbadddecbbcbbbdedbcceebabaaaddadeabaadeeeeaacabccbaadceadaedebdbcecbbaaaaccbdeeeececcdbcecddbbacaeacebbbdaddcabbadecbeadcadededcabaccbedcbbbedecadabddbcebdbaccadbcbaacbbeccbbcbaddedaaeeabdcccbedbdcaaeedacbdeedeccccdadbadcabdedbaebaebaeabcccadadbbdacdebadddebeacdcddaebbccecceecbaeaccacabbdbebcbecabeedcdcedbbbedbceabdccadadcedecddaeccdcebbbacadcaadedbaccbddbbdcbedaccaeeddabbcbdbeeeedbddbeddcbeacedbaacaacccaccbdbdeecbdeecdacaaaacacbadbcebcecddccdbbaebccbdbecdcdaebdbedacededababeadaaebdeccaadedcbcddebdbaadcedebbdbedbdaecbedbdeeeebbdbcadbedcddbeeebccdacbadcaacdaaadcabbdaebedaaecdcdbbcbaebbdacdcdccccadcdabdceeceeebddacddccadddebebbeacdbbeccaabaebbbbeeedeadaaabcaebbcadbbbaeebaaecdbebddedeaaaebbdadeaadcdbcdabdcdaeaeccacedecababbaebaaacbaebbdaeccceacabcaddeaaeaaddcacbcaeeeeedddcdcddebbdaaadebeabedebabecabdabdbaedcbadaaadedbbbdcacaebecedabbebecaeedaabccceacdaaacbeededdddcdcecbbebceccbabaecaedeccacddeaecdbaaaebedeadceaabddaceedcbbcdcededdddbbaeebaedaecbbeeeabdedaabbdebadcceeeaebccbcecdcceecccecbadbeacbeddceeaeacabddadaaaaedcabdbdcddedadacabccdaccceddbbbdacdccaeacecdcabcdbecaaaaedbbaeaaabbbbcabadbebeedacdabacccdebcedeabeedaaeebceaacecaecbbaebcadcabadacadcdbabceecedebaccceecdaacebadeeddcdbcabbbedbbeaaeddabedbebcebedcdcceedbcdababaebccadabcebacceabeccabdaadceabadabeedededdecaaebbddcabbedabccacacaaabdecbdaeacaaabcceeabedbccadceaaeeebaebedeaceccacededbceababdbdddedaacddceddcadacbbacdededbcdebbbceadaaddecdeaebecdaeeeecebdceabcbecaebbedeeecbddaaaabedeaaebcccedaedaeceedcddaddecacdedabdbcccbdbacbbeadddacdcdecadaddcecedeedddaeabcdadaababbadeabeeaeedeecaacdbcbeaeceaeacccbeaecaeeeaceccabdceaaabcecbedbdeeccdedeebcaeebdadbceadcabedabccedabadedaaaddcacedbaadcdaddebecbceabcaadbeabcabbabcdaadaeddeedbabbdacceecadceceaabccbdeecbaeedddbcdadaedcbdcbbcdaabbbcedabeccacdbbdcbcbbeeabacbcddadabaccccceaccebbeaaddcaededacdeedabcabcdaceaceebdddcaaebddbababcbeccbbacadaceeeababbdbbeccbaeacebaeaedbedbedcdadcacccaddbdaeacdbcedaaabedcbbeaabbbdeaaeebbbadcbabadddbeccbbbccbabeddccabedeceeaabcdaaaeeccdeabbccaeeeaeedbeceabcbdbccedbbceeadcebbebdeecbabcbedabaceeacabecceadcaeeedaedecdacdeacbcbdddacbabdcbedebcacebeebeeadaabbbecaddeebccebeebcedbdceecaebeebadccaabaeeabbbcbdeaadccbabddddaededcdbcbeeccebdaeccacebdacbbaebdddacccbbdbeeccdadbaccebcbcddceeeaddddbabcaececacbdaddbdeddeeaaceadbdbdddbeeccdedebaaaecbcaecabeacecaacabbdcccaddedcdbdbeeeebdcaebdceacceeddabecceadebcbebadcabcbeecaaabdbcbcdcdcdccaebcabaeeccbceebebcdecaabceeddcbddacbeadbdeeedebdbcbeaeabbdbcdcbcbbdabbbbeecabdabceeceaecaaabccaabbccbabdeadceacaceededdacdedacbeabbcdbdececcaeaabecdedacccacbaebadebbaabdcabebaeeabcdddbcadadcdbcadeccaccbbaceabeaadceadcbcedbebeeacacdeacbadbccdddabbeeaadbddeecebbbeebbcbacaeabeeaebaaecedbeddaedcabbbeccbdddbbaacdcbcceadbdeacaabbcadeaaaeedeaaebbebddbdacdcaaaadccdbcbdcbeabdeeabebeeacdcbabccabdaacddeababceeedceedbebcedbeccbaabbeeccacebcddbeeaaecceaeaacbdabbddbaaddcbebbecedbbcebeeaaddbaabeaaddbadbdcbaddcabbdebaeedcbbbbbacdddebbccaadabcccbaabaecacaadcebacccaccaaaddaebebabeabceccaaeabccabaaacaaaaeacadbecbddadeaedbacedbcdcecebdbdcceceabdceedabcabbeccabebceceaaeceacaadecebdbecedabceedeebdcbcdedadeaeeceaaaeebbebabdaadecaebdddbdaeaeebdaddcdebabecaacbbaaaceaabacecdbedaeacddacebceeeadeaebecbbccecdacbebbbabcbdecdacbdcedccadabcadeedbdddbddadecaeeebbeacbaaadbabbaadebcebeacabadeaebaabdbcabcadbbaddceeddebbeccdbeadabbdabdeaedcebdaaecadcbbcedeebcabeddacadadbbddddaccebabbebcbaeecbcbeedabccbbecdabadcbbbddebeaceabceadabbcebbaaaacbbcbcabdcececcecedcdedbcadcaaedddcdaedaadcbedaadbbdcbbccaddbdcbabddeeacaedabbbadadcbebadeeedabbbabadebeabbceecbcbbbaebcabaceecaaaaccaddddeddbeaeaadaddeddecaaedbdbaacebdbeeacdcbecdadceaabceed deaacabebbcadbcbaddecadeddeabbabccaceeeebccbebbbdacbaceebcbaeeecbceaeaaeebaddcacbabaddbaaddecceebdecadbbcbababdbababbebdbcecacbdddeceabaceddebdbabdebaedaaecbdbeddeaadccecaabeedaeebbdbbcecdeadcacacaeedccacaedbbdccedaaeadddbcdaabddbdceedbbeacbaadeaedbedabddcebccddaabecaadecdecdacabcaddebbcdebabcaaaeaadabcbbddbabdaeabeccaceebbecedbbbeecabdeecaadedaeebdddeebcdbaddcaebedcadacbbcbecadcddccabbedacacdabacebcddbbbebadbdddeaaccbdbbbecbdbaeebaeaabcddeccbccdcddabddcabcaddcccdcbaeadaadaceccbbacebcceeabeeadbcaeeabdebcacddceabecacbbbbcebbbebaebdcdbcecdddebdeeccaaeaddcecdadaceddecebaaedbbebdaceccdedbdddbcceababdcbcdcdaadbcdcadbcccabccbdededbbcbcebaebdaeeccbaedacccacedbdaacbacaadbddbeaeabeadbbadadebceedbaabcaceaedbdcccbcdcbaeccccdcbdecedbaebcccccbdadddaeacdeacdbbceddbcbceeaecbcbaeebcabaeceaedbcbdddeaabaebaddbcdedccccacabdbbecdeadbebdeecdadebcbceccbedbbbdaaadccbeeaeabeadbbdbcbabdebbdcdddaeeedbdcbcbeabccaaeadbdbdcecdeaeacbbcdeadabcebccbdbbddbbcaebcbbeedbbdcacccccbecaebcaeacccddeebdabbbeacaceddebbbceeeaceaaddaabcccdacdccdbbbbeddebcdbecabeddcadccbddbedbabbacdaddacabdceebdbeebcceaeddeaacbaeebebccaecacaebcceeccebddbdaaadedbbeeccabdecddbeebbcececbabacbcdeedebbbecabedadebeaabdeccbdacddaaceecdeaceddecabcedcbbcaebbbbdeadcabddcaccddebeebcbaaaccecbdcbdcebbbbecbbeadeeaeacaceaecadcceebaccbecbeceaecaccabbdddcabcbcdcebdcabaccbcdeabcaeadbcadddbeebeedccdbeecaadedadeccabeabbdcdbbbeabcaedcbebeeaaecaeaaababcbbecbedbccdbaaddecbaabbdcbbebacdeceeacdedebdeccaceeabcaaaddaaceaaceacedcdbadedbbdaabcddddabcaacdceacdcdbddeddaadcadacabdaaddcadebcedecbacedcdaceceaaadaabdacbaebbdcbaecbaeeeebeccadeeeadcbacaeaadcabeeacabdbdadeccececaeacdecbccdbacbaddcbbabceaaacabbcbecddcbbeecaabcdaeabebecbacababdbbcccbacddadcdebbaecedddaaccdedbdeeeaacdecacdddccaaabbdaabacbcaaaabbddecbbaccdcaedbaddacbaccdeaebddecbddddbeddddceddeddbebbeebdaceeeaecaaaaecabcbbacebcbeeacbecdeddedecdbcbbcabbeeededdecdebbcdbccbbcaeddeccceeeecddaebebebbbcccebbccbdabcbbeceeccdbeabdaccbbaeabebbecdaabbccebddbcddadeaeebcbabcabcdcaabecdcbccebedaebeeeadbdcecadebdeeebeedbabaedecaabbcebaddeeeecedaaacadcdbaedcadcadabcaccaedbbeaaeababcebbedeccbbdbbdcbbaebbcbedbbceacbcacaeceeacbadddacbebbaaacecdaecdcacdccbbeacedbbaabbadacddeeececdbbdacddeecceceaecccbeeddcbcaccaebddbcededcceeecebcaceebadbaeebabbaedeaecdebdeaccccddbebbbccccddecdaeeedecdaceeabbdcdaabbabdebdddbdbcacedceaacddbaabaaeacbbbebbcbbededcdadbbbeaaeedeeadadddbabdcdecaccbaecbeabdccbacdabddadbeeabacbcbcbdebaebdabcddaadedbddbeaaeaceceadddeccabbeddaeccbabbbacddebeeecacbbacecdccbdcecbbdaaedbcabdaabcddebcacaaccdbeedeccccaaebecaebecdaaddbdbaeebeabeaebcabbdebecaaeadbbaeacdeddaabaabeabadcaccabddcdedbdbaaaabddeaadbccbdecdacbcdeeaecbbcdbeedcbbabddcccbbbedbeebcaebccbbabdbdceccaadcaedeacaebcdbddaacedbbeebdcdbaebddbcccaeccdaeaeececdadbbadebdebaeebcdceebbdcbeeaadcdbcbedddcccedbebeeeaaabeabeededcdceaacabbedeaaeccdadebbaaacdeeeaadebbadabccdbcbeedcaeaeeddeadaeebbbaacbdadadadedcbbddaabeeecbddabbaccaabebbbdcadebddbcaacbcaebcaaebadddecdadeccdbecdddadaaabeecbcdbeccccecceccaecdeeabadccebabadaabdcaceeccbeeacaedcbecbdadbababecdededaccaeaeaaeeeeeeedecdbddbddecaceeabdbaeadcbcaaaaecceceeaecbbdddaacacdbdbcceccbbdabbbcdbadaccacddcecdadaeccbebbbeeeeabbaccbdcedabedaddbdbacbeaddaacdaccedcdcceaaeaecbcedbbebcbbadbccabadbeeddabbabbeadbcccadbeaaadeabbebaccddcebadcbcabcacabdcabccdecdcebecacddadddbcdeeeedbeaacebaababeebeddacacceeabbadeeadecadaabdeabccbebcebacabdeeeebecdadcdddbdbeaccedaeecccbbcacdccddbebbeaabddabaacbcabeaddadbdccedecbdcadecdcebbbbccbcdcbebcebdadecebcddacaeeeddaeaabddbedadbeaebdcddbbbdddeadcecdacaabacbaebdaeeaaabacdedcedcadcadbedbcedeedeeceaacecdeabdcaedaaddecadebabcaacedaadaaacadcacbccdbcbbeecebeccacaebedbbbebdabcbbaaebdeccaaadbabedbaccddedeccedcececddaebdceabebdceadccccdddaeaebddedbceaaecacbbcbaaaaecdabbbbaaeeeaeacadacbcbabbebbdcdcbddaabcabcbcaadcbaaeedbaaaaedaddbeaacbaababebcceddbaceeaabdaacebeebdeccccaeaacdeaebdbdacbaedeacecabcaaecdeaaabaccacbbcbbcbbceadececaedbdbbdcadcebbddccecdbdcabbcaececabbecdbedebbcedeeaabacedeaeccdabeceebbeedbdbcadabdbccabadcdbeaeabdedbaaadcacbccdebdedbeeddceeddaedcdcedbbeaecaacbbcbeaaecdcdcaacdccbbccccddaacadbebbaeadecbacdbbaaedcdbdbadbdbebdbcbabbaeaceceecccceabbadbcacdccbcbeeabbbcdaccacdeddebcbccddedbedaedeabcdaddbdcceebbcccecccdaebdceabaebebccbdebeabcbeddcadbdabaaaaacdceedcdeccddbcbaeaabebebaadacdabcdcbcceddbabcbebcdceaaaacdecccdbccbacbeabcbacdcabacbdbbcebccbccacaeaaceebbbecbcbdadaecbaaacbdecceadedcccbdbcbedddacbadaaecaabdaaabadaaaaacdbebdbbbdaacceabbddbabbdcdddedcbacdadceddabebcadeadebdeababebbddaddeaecccaebaeaecaaacdbadcacdacacaaedadbeabceeadddddcbbdbbedaddedacacaacbacadddceaeeecdbdcbeedeaaddddbaddadacdadedbbedcaccebbaeeacedcebddabddbabbdeacdcaaaeeddaabebdecbddcbbeecadacbbeebddcecbaaeccabbbaacababdcddeeeabdaacbdaaabbabcbbcceecbddacbbebbaadbccdbcdeaedccdedbdcabbbbeaaeeaeaeacedbcdbbceab