becdcaecbdceeaaeacbccecbedcdbecedeccbbdcdcbadccbbdebecabdddacacdcdcbcacbcacbaeaadceeddecdeddccecbcebdcdbacaacbdbeeeecceeeccacacdecebdeedeaeedddecbdaababeaacdcdbddeacebbbddbedccabaacdedbbaaadedbdabdcbabbddbbcbcccaaeabbdcdccdcadddddedcdecbedbdeaabeabdacecbbebcbabbaebcceabddbbddcedcccdacbceaebcbccbadcabebecedcaecdecdeabbdeacadedbbebdceddebadbbedcabcbeacbbbabdaaeabddababbaeaaccecccacdddedcdabdcbedacaddddcbdbdceadaecbdddbadacadaacebecbdeccaaeaddbebdabbcababdaebebcbbcdbbcaecebaabaccbabcaededeacbaeebcbbcdbdaedecebbacccdbaabddeebbbdaeadcaaaaacebbdedccedaceedbacceccaaaedaccdccaabadadbeadccbededaaeebebbdcdbeecdebececcdddaecdaeddbaeeceadaacaadcdaddeeedaaebacdbaebaeabcccccaeabbaceeebeccaaecaeeadcdbeabdadecedadceacbdbbddbcdccedbbaadababceeddcbbeaebaaececccdbbebdcdedbeceaeeeedeaadcccdcebebceaddddaebadbddbcebbcdbaccedbaebecacaaaaccdcabecebdcdebcddddeeacecbcbbddacecbcddacbbcdaeeacddcebeebcbbabdedbcbdcbbaeccaecbdeaacdebbdabbcdceeeeababbbcdadcabecdcdeeabacccbcadaecabccdbedceedcbadbdcbcecedbceccdcbcccdcddeaaddcebdcbcadceeabadccadcaddacaccbababbaaabaabbbedeeecaaddeceeebedcdeaedbdeaceebbccccbabbcbaddbadbddbddabccceebbaacebaaecaabcaedcbdddeadbaebbbbedcaebabccdcabeccbbadaedcbebbaaeaadecccaabbbcdbecabdeacdcaecabbdbcdaedecbdcdbaecabadaaceadeadbdacebeeeabbcbbecdeedabebaaeacdeaebeedbceabeecddcbdaeacecaceaebecdcaaedcaceeaeeecdcbceedcadeabaadabceceaaacdedcbebdceaabaeebecdcdbdeecccadceaabebbaceeccaedeaddcdedcebdbacbaedbbcdedcdebbcebecdeddeaccbadabbededeeacdebecbbbdbbebcadedecacddaaddedaebddcebbdeaadcecbdaeabcdeceaaceedeeaeaebcaecdcaadbacaacedbaaabdcbaeddccdcadaeccdbabdebabbccacabceeaabaccaecbcabedbabcdcacddadadcadbedcbdbbbaaeedaabbaaccaedbeccddeecbeadbcdbcbbddbcabbcdbcbbabceaabcebedcdededeadacbbebebdebecbadabcbaacccdcbaaacecaddbaaeecdbedcddcbebdbbbadebcabccaabbbdabadbabecbebcdbedbbdbabedddcdeedaebceedbabeaddadedeeaeeebccbeebcddedacacdcaeecbbaedcddecadaceddcedabcbdadcabceccbbadedacdddadedcedbeddadbceeedbedacbeabdbacaebccebebbbcacaeececdecedceecdeccdaecbdddedeceabccdddaeadbcedaceaebadacdaacabddedebdbdabcbcccbdaedcbbacedcbdddceabadbedeeecedadcabcbcccadbacdedadacbccdadeedbcdbbaecaceeccbaccebddbeacaddaaeecbacdececadeeabeddcaabaddccacdedccdccebcbdccaaecdcbbaedacdbdbaccacabebdcadbdedbdacadecceabbabadadeedeaaddbccccacdcadbdeacdbbbcbdedbbbdabcdaddecdbdeaeeebbeeabdabdbbcbaaaedbcbeacbcebbabcccdcdbcedbeedddbccaaecdeeebeabbbbabecbebcbddbdcedcdccabaddccddbbcdeebbdaebddddbcbbceedbeacaededbbdaaeaddeaedecbddaebaadcaaebdbccccaeaaadabbccaaebaddaddbdbdceaabcdcbedbebeadaecdececbaaacbececdbcaceeaecddcdedddcccecdbbabdddccabbddeebbadceebccacdbebddadedacaecbebbbdddebdedeabdeceaceacecceaeacaebecdabbedecadbaaecabecbccedcbbcebbcdaebeaaeabcceeaeadccbcdeeebddbadaabddabbeabccadaecbaeaadbecabeaedaacceecdddacedcdebdcbaaebddddccedaeaedaeeadaedabdabcedbcdcbdbbeadbacaedebdcacccdcdbbeedeacecdccbdadcdbeaaaaecaecdaacbaaabbbdbbcbcecbdcbcabaecedbdeaecedacdabadecaadabebcddcaeadcebaeacdebcecdbdadeeecaeedebcebcecebcebdbebdeedbaabceaacdbbbeaedaaeebeaeeacbadbdaebebdecbbedcccbcedaddeaadaadbaadedddbceedbdbeaacecbcabcbbabdcdbebaacdbdecadcaebdabacbbeedbcedeaaacebcababeabcabacddaeaccbcecacabbcaaceacebdabeedbabceaaececddaeaccdaededbdaaeebecddeaeddabbbdabbbeecaddacaedbdbdceccbebcaeccaddaaaaabebeadddebbbbedcebdbdaadcdedecbcbebbbcbcaddeccedddbaaeaeeedbcddbdddbbcdabcbdabbedacbcaceebbbbeddcebcadecdaacedbeaedceaadddeeeeecececdecacccdecaeabadbedeeabbcdecbadcbcdcdaccaacecadcbceedaeeaaceaddbbbbaceadeacbaccaababdabdebebddececdaabbcbccabaebbbeccbbbddddeabebaecbbecceabaebdceebadeadbdeebcaebddabcecdbccccbcebedbebbecdeadabeecdabacededeccadcedbaeddccdaadeaddcaecdadccbdcdceeeeeebedcebbbedeaebbdaeaeeedaaedbebcdcaeeddbabbadbecacceceddaebcebedabbdbeacbbbaddacceedadacbceaaebaabadcaabebececaadbdbbaedaacbeceadacacddaeaadbcbbeddcadebeeaabbecddebaeacecebacdadabeacebbaaeedeecbacaddabbecbaebadedaeabebcbcdebccebaacbbeaccaeeadaedebebeadebdadcbcaadccaaecbbcceaadcbedeccceadecabbdeabdacccbdcddeceecadebbecaeaceecebbdbcedbebbebadbccbbeeabedbcacdbddabeddbddaeaeccbcddeeebeaadcccacdbdceabcbcaeccdbdbedcbdedceadebbbbcdabbebcdcedbcaddddadbebbbbedbadbcceebedaeaeacacadaeddecdaaebacdabeabddacccbeeaebcddbbaeecacbdcabaadaedbdbbacceadbbddecadecedcaddcdcaedbdbdacbcaceabcbbcaaeddccdceeacccdebcceaccbcbddbdbdaebbdaddeceeabaabdddbcabbeceeddbebacecebaecdbdbeabaaedabeadceeeadbccabccddaeeeadebeeebaeeedcdcdeceddadbeadbbceeabeaaeaadeedccecdacabadeaacacbcdaedeeeabbabbeccbcbebbcadeebadacdaddbeeccdaeaebecbbcacbeacaecddadbbeaedbdadaababaaabbeadbebbcdebaeebccdcddcaddeaebccaccabeeebcdedadbcdbdbbedaaaeecdbbbeccebaeceeacbeacebbcbaecbdadceccbcdaeacdbcdddcbeebecbcbdcbebcedbabedecaededbddddadebddabdeedeebbcaaeecbebbdccdcbcecedebccdeaebcbccbccbeeeacdbcecacbccabaababdcbbceceaeebadaacebaddeeacbbddbecbeeacccdeddebdcceeeddebadbccbddcedbbecdacbbeaddebeebbaadaaaabecabccbeadcceccacaedaedacbddcbebdbbeeadeaaaeedcdbddbddecdccdbecbaaddccdedcedaceadaedaabeaecdcececadbaaaeedcbaecddbeaccebbadbcbeecadbabcceeadcbabecbecbacbbdcdeedebaadaabaadddcbadabbaeebdedaedbcebeecdedcabbecdbeebddaecdaeccdaaeebecbececdebbdebdeaddaebeecbdedeaabbabdcedabaabdceeaababbbcedcbaacabcbecbdddebdcaaebddbdacaaedbcceaccbcaecaedbeddbcebcdabcdbeeabddeceaacbdbeacebcbbedcdaaadedeaacedcdbeeaaaddeadeaeacaaabebbebebcdebabeabdceecebeaddbdacaebeaedcdbbecaddcaaeaaabdeadedadddebeacadeaacccecaadaebbddeaccaaecbaebcdcddeeebdcecaaddcdacbcaabdacaebdaaebadeaacaeaccdcbeabeaceeddccaabeeeaeebeacedadddddcacccbebaadcbacddeacacdebacbbbddcaccccddaeeeaeeceecccbbdacbbbaeccadedebaacaadcebbcbbcaecebcaaaccadddbdedbbdccacbeddcccdacedbcbdbeaeeecbaadaaabcbecccaeeeeedcdbeacbcbaedceecbcdcbabadbbbcadabdeeabdaebceebcebacedbeccedddbeacaccdbadebcbecadadedcabcaddaedeacdabedacebbaeccaadcddbdbbdeacabcccbeeadbdadbcaeedbdbaceaacedaadeaaddcadecadbecbbceecaeccacbaabaddbeebcaadbdecdeacaabbebdbdcbebcaeaeebeaeddabaecebdedaddaccbcabbdbacaacabeababdbbddababdabdababbccbeeeacbdebbebbbbcddebeacadaabadbbbeeebeaaececdbdecaedbbacaecadbebccbbaaeceedbedbabcdbbbbbeddacaebeacbcceaabccedaabbeccbceeacbebaccadddcddadebadadeeeaacbdcadecbddadddaababbaaededbcbedcadcaeeecabeaabdbddedebdeacbbaaaacaaddaeedabcccaadcbbcbaeacbbbaccdaabeacbdedecbdabacddaadadeedabdbacbbabdaaaeccaadeccdbddebdadecedcdbdcccdedbeedbcddcabadebbcabcbedaecbeddebaaaaeecbdaadbbdaabbceaabcdededadcbcadbddebddaeeeecacadceedbecddeebbbbeadbcedcbabcaddecdbeceaeaaedbacaddabcdedccecaccceddaebbdbadebbeaaabecddbdcbaeaceecdeccabaddbcedbcdeaacacadeaebeeacdbccbcedabcaaceaadeaaceccdadbbeebbbaebedcecdccacbaaecbaddbdcbbdadaddccedcbbbacbedaabcbdbccdcbbcededeaedaaecbdadebbbadcbadbaabcecdcacadbbdebdbdcbdecdebaaeaebeaaeaededdadaadbeeaeacedccdccceeedbcedcabeaeabcdaadbdebaeccdbbcebaedaeceaaebcceeeddecaacbaedeaecadbddedcddadedbbbacdceeeedaebcaeadaccbdeaddcbabbaecdeeaebaddebbdeeeccddeeadbddedbeccecbccbbecbadacbdedbddbaeeaeeaccebbbbbddedecbaedeadecdcebecedbbedebcabcabeceedecadddeababacdbbadcaecdeddcaedbcedebaeddadbaabeccdecbbddbdededadbedeeeaaadaaacebdeaabecbbaebedeabcddbecabdedadadbbeeebcdeacacccbbacdcdadcabeaebeeaddeecebeadcbcbccccceedeacdcdaaebeddeacbbeceabeaaedabbeabdabacebddceadcaddadacacceaceebdddbaacbeebadcaaeccdcbcbeeababaceebedaeebcaaacbbcbedabcbbddeedbeaccbcadeaebaeedbecadadaabbbdbdccbcbdabbadeeaabdbddabecbdbeddbaeabcabeacddceeecedbbdbbacabbddccdeeecbaddceabdeebbadeeeeaceaedaaabdacdeecaaecbcadcdddcccbdaaacbeaacbadceeecabebcadadbcebbeaccaeddecdeddeadcccecdbcadbbbceeddebecadeeacadbcebbbecaeecaedeaacdeadabddaccbaaadcdadebabdabcedeeebacceaddceedcabedaaabebeaacccadacaaeacabaaeaaacabdaeadbdacdcabbcdbeeaadeedcebcbeceacbacecbcecbcbdbadbeccceceadcdddaeecaaddecccaebcdcadcabdedabbcbedbeeedeaababcabeaceceebdaebdddddbcccebdcdebedcbbacabbecaaddabcdababdadaaaebecbeaecbdaacaaddbbabbeddcecddaeeabaebddabacbcabedaacdecdaddaeebcaaaacdaacaaaaaaabcbdadeddceecceeedcacadaeebbdddaeacbbacdbdddeaabededdcaaabeaacbebdadcdaebdaeacdbecadbeceeedbeaaeacddcedabdbacbdbbbdacebaddcbaadededeabdedddadbaacddbbbacddddbdbcbbeeceebcbacccaeeddbebeeeceedcbadaebbaeabaaedeecbbeddbcedaebcbbbcbcedabbebaeceacbacbdaaeecbadcdacdbbedaacedaedbaddeebbcadbeeddbddecadcbaaceccbbebaceaadacbdaacbbabdeacaecbbbecbdcddbdbecebdeededcabebcccdeebaaddcbaaabdcceaccbecdbdbacbccebbadeeccadeaeeebeaaacadeccaeeddcaeaaccdecaccebacacbbbdceeeccdeeabcbaadcecaaddbbbecadaadecacbecdaacdacaedbcacceccaccccadaccebedebeddbeaeeebaabbeadaabeeddcecaaeeeaabceaecbedbcadccbabdedbabdcaeccdbcdebabcbadceaaecbbddaadcbbbbaebeebeadaddcaecbdcceeaddebadccacadceabeccbddcacbdccecadaccabdeacbdcccceceaccaeddbcbadabdcbaeddeacebaaadacebcbcdbeaabeeaceaddaccdabecdacdcdbbbebaeaddecbceeeabdbedbaeeceacbabcbedbabeacacabdadebcbcadaadebcebccadbcddcdaeddddeebdccccebbaeedaedadadacecabcdeadceeacdadccecaedcadddedcbbbedeaaabbcddcdeecdecbceaebcdcdbdbbbceddbbaaebbbbbadeaacababbeddcbaacabeeabedebceececeeccbbedadcbabaccddcbebcdebdbaabebbecacdaaabedcbbecbceeadeededbcdabedeedbbccbadbddbcaceddebeceeaadaabbdddcbecbaeaebebcaebcbdebacacecaebedadbeceebbadaceebbcacbaccabcddddebccbccbadbacdadedcbbecebedabaaaacadcbbcdcabbabaeaeebbedcdccacdcccceeaabdcbbabcbccbcecedbececabdebbccdbaaebedaecdaddeeccecaabdacedbcbddabbcdbeecaaaecbebbecdececbcbcbcbececaecbeedcaebbbebaacbeceebbcbccbecabdedeaaaeebcaacddcacabbaebcbcbcecdadeaecdddeeaaacbddaeedadcbedbaceebecbdadccaaadcdbabbdbdaddcddccccccaabaedaccaaedaeabaaebceabbacdeedccbbddeccbceebdceaeacdbeccccdaceaeadbbdacceaedbceadeddcebcecaaeddebbeeddbbaedbecbadedcddeaacdddceabdeddbecdcaeaddddacddbbecbaeeebadeadbcdaaabceebadaaaebaeeddbabacecdddbdecbcceedbecabebbecceccbdccbaabeacbbcebdcdbbdbcdeaaccacbaebcdecbdababcecacabdddbeacbeeeadbceeecdaaeecadeecaceaaddcedbbaabcdbeeecacceeabeecdcabecdeeedbdaacdebddcaeaddebcbcdcacedecabdbdcbddbcddbbbbaebeecbbbbbedaebdbadebeadaabadcbddbcaeeabdbbedabbeebcecacacdaabcbcdacaeeaeaebbdebcdeddebabcbadccedeaacdedbbbcabdbbaeadeeccedcacedbebbaadaaacaaddcbbabebbcdddddcaadbaaedbbaccbbdacddaceccaaaebbadbeeeeebceabccbbabcebdaabdbecadbbbaaaacbbdaaebdadeaecebbaaecaebcdeecaddddaeccabbabdacaccedeccdedeaebadaabceaebeeabddcedbebecaeaeaaddceecbdcdbadcebbeacdedecaebccebedbaeeabddadecaceddddaccbcedcaccbdedbbbddccdacceecdbdbaabedbabbdddbadddddadecbaddccbabdaddeeaceaeeaadaabacebdbcbcabbeacddeeccaaebaebdabaacedcaabbcbabcccddadeebbbbacdceddceacdeaacbaeebaecaabdcaccebaadabcbdedaeddbeebeebddcecedeadacdaebbaaecabeacebbbdaebabccbedaedbcbeccecdaeddbceeddeddccedddcabbbdeaecadbccdbdebbcebeccecbadabccabacbecaacbcddbdbddcebbeeebceacdcccbcebbaadaeabbaccdaadecdbbaccecaebbebeaeeadaccbadcaedebedbecbeeceeebbaddeadbabdebaebccbeccadcbeedadaadaeceabaaccdaeadcaeceddbcbabdeddcdbacdcccdaaeebbddbcddcaddcaadcacaadbabceecdabddebdcaeaaecaecacaabdecdedcedacdabaddbecebeeccceacaebbdbbaeaecbbbdeeadaceaebbbecdaccdcdecccdebddcaccbaccabebbcebadcddadbdebedecdacbcbcaddeebedccddbbcbdbbebbdebdecdbbbaedccdbcdcdccccabceadcceebdcdeaddeeebecdccedaeaaeccebbebbddebcacdedadcaceedecaacbdbdeabbdaaceacccdcccbacdaacccdbacceebbadbedbedbedcdabacabdaacecbaabccbcbebdddddaadaaabaabdadceebcceabbaadaecbedcbeebadeccaebebbaeeeecddbaeceebaaaacccdeababeadaacababcaabcbbbebaebabaaebdcbacddbbdaaacaecbbbeebadebbabbadbbbadadaaedddaebccddabddbcacadebecaeebbacacbbdcbcbcaaaeaedaaaaaddcabbaeccadedbaaedebedddceaedadbcacebaaaebbcdbecdbacaaaeecdeedebaaadceedeebceaaaecebbcbbdcdeaddcdbbaeadaabdccbacadbcebcebbdbbcbedcbacabdaacbabaaadbabebbebddbcbbdbcbbdeacbabecaddbaeebbbcdbedbeedcadbbcaecaebccdedecdcbadebdbdcacbccaccceebbdcceedbcbdcaacbdeeaeeadcebcbdeceeabcdaaabecbdedcaebddbdebcddabeebdbacebecbdadebdcebacedabededeebcdcebdecaadaedabdddaadddbebdcbbabdccdaaeaaeeccedbcbacaeedeabcedcbccccaacbcbdccadabaecbddeacbdbaeebcaebddababdbcebbdadbdaabeebacddcaaccdbddaebbacbeadbcdebcacdddecccbbecbcedcdaadcdabbdccecabdcdcdbbdecabeeccaccaeedbbdacaeacacecdebbddeddcbaaadabeececbaedbdeeebecccbdcccaabaceedbddbeccdaabcbcebcbcbcedebcbedccbebddabaedacbadddaeaebeccceeeaabaaececedbdbdcebbcbbaeddbaeadbdeceebdcdbdbbdabdccbaddcacccbbdbaccdbdeceedeeebccedacbdccbacabecdddeebcaedadacceabecabecaabbcdadccebedbeadcabcbaeddbcacdacceabbaaebbdbecdeacdacadddacbcdcaeaccdeaebeebecceccbaeedacbaabcbedddbaadebdaccecccccddadbababacbecadaaeeeceddbcaebcedadadaceacedcddebdbcceadaacaedbeecaadccebacaecdcbccaabacdabcdbeeaccebdbeaecedabbbddebdebebdcaeaadbbbbeabbaeedebbabdaaacddcbedbaebaaadaddcecbdaaabcdebaabbceacbddabecdeabcacdbbebdeeabddabcbedadcbcaaeddebaebdcecbedbdbddaceebaadaabdaaacecaddcaedcaddbadddceadbbdcececadeacbdcdbcbadcacbeddcdebdaceadbcebcaaabeebbedaadedbebaedacaaceeecccbcddaabeceadbebbaaeaddceacaeeebbaeccbdddaaadcbbbcbadeebabcaeeadaebebabceeacecdbebbeccdbdecaccabedbdaedceeaecdaacccedaaeddbacbdceaaaeebcddbdadcbececddbbcedbbdaeecdceabcbaebbebabeaeaaecbbbeaabadaadcabbadbccbdaabdabacbaeaacccdaccaebedbeddebdbebccbdacbdbacbaabbbeedabdcdcbdebdcaddcaaacedceadacabaeabaddccecdbdacccebdcdedbddccdedaebddbcbccdaeedeaccadcbaeababeadccadbccbdbbbeeebeebacdcccbcbaaeabacbbbcadebeccedbcdbbdccbcbdbccacecbccabbeecbcbdaddedbebddbbdcdbabbaeebdeeaedcaaecabdcbeaaecbdbbaacaddabbebdebbabaaccdbacbddbceedbeceaabeeaecbdedccdeecbbacaceabdbbabeeedbdecdcedeabeaccaacbedbeecdbcbceecdcceeadcbebbacedeeebadaeedccbedbdaacbbcaebcceccebadceaaddbbbbeeecdacaebbbdecbbceeededdbdceacddaaaaceacabcdbeacddaeeddbacacabedbabbbdeaccdcedbceeaeedbdccccebcacdcadcbaecccaedadaccdadceeeaabbbdbcddcdacdbddacaedebedbaacceddcdeeaacebdebabbbbebbcccdbbacaceddecdaeebebedadecaecbaeebbececbbabcbddcbccebedcdedebdbcbadacedddcddbadececeacbdebdaeaccbebaacecdaabceaebccdaddbbeabceacebedbbebbeaadeceebaeaadcddededadacacaceaebdebecdbdbeedbdcbdddeedcaaabacdbbcdcceeaacaababcbbdaebabccacdcccadcebccddeeaaeaecacaeedceceedaceceeccaececcbacdeedcbedaceaeceaecadecbdeebeacecbdceadbeebdddebaaccacceedadbdeabeecbadbceacbdabeeeedcdbaceecaceeaaddccbdeabbebacdbdbcdabebdadccecbceaabeeccdcdbbeaebbababedcddeddadaedbdbeeabdbeaedbebccebaacecbdebcebcedaeaaecaadccdcdbcaeedbeaebbdacabaeedadbcdcebabacccbeeceacbedbeebeecbeeaccbcaabdbcceacdccbbbbaeeccdbdcbbaeeebbddbdeaeadeeceaebdaccebdceddbedaacadacacddecacddbabaadbeeddadaababceacebdecededdbcbebbeddebdeaeaacbeaccdaddbcedaabcdcedbabbbaedbcdaabaecebbcddaaeeeccdaadacccabeaacdcaebeeacdaecbdacaadbcbedbbccaaccedaacbbbecdddacbdcaeaaecadbdeecbacdcaecaecadebcddecbdbaabeeebeadcbabcdbdcbdecdbecbabceabeaedbbbcdeaeeeaceeaceccdadacbaddbadacddecaeaaaeeaaeebcddeadaebbaadbbbdaceebdbcabaaeeaeabcaebedcbdcdcbcadcbbebdcdcedcbebcacdddadaabbacaacdddbcddbdbdbeddaecacadceccbcdecbbbcedecaaadceeddbdbaecbecbaabebcdbecebbeadebaacbbaaccbdabbdcaabedddbcabaadcdaeedbadceedadddaadabbbeeedbdeeaccdbbccccbcccadacbdbaacecdcddcaecabebacccaedccdcccdddcacdaacacdbeeaedaabaeeddbddbbeeeebaedabaeaadcecccdeedcedbbcdcdcbdeeacddbaaabebbceaaebcdebaeeabcaebaddedcbeabcaadadaacccebcedeedaecbecddcdcacbcdbaeaeebcaeceaddbaadcdaaecbbddeebceccdbaeadadedebecbecceaeedeebcbecceaededbbecedaeedceacbbdcedceaecaeedbbccaddddcdeacacddcbcbeaddbdaecdceedaedaaaededdcbaddedadcbcbbeaeebecebaeebccbabbeaeeddcabcceecbddaabbccbcbaadebaeaadccaabcebccbdbbdabcebdcaaeacaecbdbeddaecdedcbdebecacbaeaddddbbdddabeedecaebedcccaceeeacdedbdbcdadcbabddadaeaccdebbceedbadbacebacaebeaeddccacaaddbcbccdeeadacdbecdbdbdbdbcadacceddccdeedcbedcdeceecacdeaddbacdaccddedaaebdaddaaacbbeeebdddeabbadbaabaabadaebebaadaebccbeaeeaceebacbbabbccccddcddccbdbbeeabbcebbbeccddbcaeaaebdbcbaddcdbaaaaeabacbabceaebbeceedabbcadaeecbbdbcaadcdeaccdbeeadceaeebcadceaddbdbddacbaaaacbcdbaacabbdcbcabebbdecbddeaecdadbaebbcabbacccbeeadddcbdcaabbcecebdbbacbceeacbacddeceabedbcdeeaccaadbcbaabddebdbddeddeeccbcdbeeaadadbdaccddaecbadeaecceedeccbcaeebaccaedeaecdeceaaecdbcceedbdddbcbdcbcdebedddbebcedabceecdcedbececaccedceeabdeabceeabedaccbcebdabbcdceeeadecdddecbecbaeadcdcbbbddbccbecceedcdedbccacccdbbbacdcdbbdeaecdbadbedadbeacaadbeceebadabccacecceebddbacbbeeeabcdaecdbdebddeadadcdedaeeeeacedebbaccaabdbbdcbaaabdbaabeaeeeedaaeacbecadeeeaccbdbccbbccabccceecaccdaaddbacaedeeddebaeaddbcbbaedebbdcedeadbbaebeaeeadceccdaebacaaebbcbaaeecdcdbacecddcdbbbbaaacdacddecabdacadacbddceddeaeecaaaeacaebbcbcdbaacceaebbcebbcdddcddddadccecbddeebddcaabcbebebdedaaadbebbbbacbecdccedbbecbceeccaaabbbcacecbcbcbccdbacababcaccedcedecabadccdecdabbbdaacbcedaebedbeaceeebbdceaccedadccdcaedaaabadbcdaeecbbdabddddceeccbeacdbebcaadcbdeebbcedeecccddededbccdebcbeeacbbcaeccbcebebedbaeeebbecbdeeabbddbbeeedbeabecccadeecedbbbbccbadeebdebdbdaeaeadcdcccebccaeaebaeaacbebadceeeaaecbdddcebaebeacbaecacabcebadcecdeeaaaacdeccabdaecceabbadbebabbceccedecbbebdabaaabdedcbeadcccebdecbcdadcdbcdbbceeebaaaebdeddeaebbadbcadcdccebcaeeceeaeaeabaeedadbdcebbdddaebebbbcdeccdebccbdaabbbcacecebcebbccdcdadeddebbbeccacaeabadacecdaedaadcbebdbcdbeecadcaeeddccbabaaaabcaedacecbebaacdbcaebecaaadcacbbabecaebdddcbbbcceedcaceebdadceddeccecaceabcecdaaabdcecdabacebdaaecaeedeccebceecbdbedacdbdadbaebabeecadbabecdadcebaecbdbcdceceadeedbdcbababceabaecabccbaabcdeeababecaaedbedccaabcbdebcaaaabbbdcaeacadecabaceaecacceecaccbbdaabbadbdacecaabacbeeceadcadaedabdeeeeaaebecdaecbaaedcadceabebcabecbeacdeceebecaeabcacedeebbbaeaabdcebddcbcbcbbeecdcccdbbdbdebebbbeebacdbdaedbedecacaeccbeecbdaceaeebcaddceeabcbeaddbaebdaacacdbacacadedcdceecdabbeaaeeeddcacadaaecbeacaeacdbedcdcbaabbaabbadcbdddccedbabbacbdaaaecaeaeebecbebeeedcbccceccbdaaceeccaedbbcadcbecbceddcdbebbdeebcdddedbdecbcabbcbaaababcbbbbebdccdddeaccacdbeecabeeecdbaeacaeadeacdacaccbdcabecbadecaaaacdebdbecddabaddddbcadaaebaccbeadccdabcaebddbbacdbcacdcbeaccaccdbabeccbaedceeadecabcdecacbeddccbeeccbaacebbbaaccbbddabecbadbdaeabdbbbcebedcccddadcabbaddabecbabadaacccdecccccbbdcbdadcdcaeabacbceebabcebedceddaaeebbcebcaaabedaddddddbdcaaedccdbddaceadcabcabbcceaceececddeecdcecdedbcadecdebabadbadcacaeededbecaddbaaaebcbdbecbedcecaeeedaabaecbdbccbadebaabbdbbdcdeaecadabebacaedaadbaebeadbdbccbbbcdeedbacacccbacebcecdaacddbeabbaeabceacbedcedebbbecebdeaeaeeacbaacbcdbbbedadbabaedbabcecceedadaabecabdebcdceebbbcdbeabadcccedadbcadbbcacbaacaddbcadbabdbcabaaeeeebdabbbaddaeedeaeabcedaedcabadcacecacbbdcbabccedaabaabebeeddecdbbebbbddaaaadbccddeddadedacebcacbaddbecddcaeddbdaaaacdeedceceddccabcdbabacaddadecadeeacecdccaeeaaedeeccacbecacdddceededadbdacebeabcdcdaacabbdebeebddcaeaceaaddcebaccdccdecbcccaadacbaddebaaaeebabadaedaddaaddbcdaecbaeadbdcaebabcaedddabbceeadadbcbcdbabdadecacdeadeaeceadceadbedcbabccecceddeedeedaebcbdaccdaeeeaadeeebaabeeeacabecccdecedadbeaabbddddeceebdcdceedceeadeaddadebebcdceedabbeddedacecadbadacbbcebdbdcdaaacebeabdaddbadabbecaedaebbedbdeacabdcacdeebceabceeeedeccbddcddaecbcdebdddeedecdbebbbabceedeabdabeedeadedeabccaeeceaeadddcecaaacccbcdbcecabbccdccdceadbbdedbdbdaccbbdeededcbcbbadbbbddeaddadddeacbeacdbcececdaddaebccbcbeeadacececddbcdeaedddaecccdccdebeccbbcaeebaaccdcabcdacdeddaabeadeceddbaaabcbcdededdeaddaddbdbeaaedbebeecabdbbddbaaadbbdabbddeeabbdabbbedbecdbbdedeadbdebbccecdecaddcebdcebccdbabbbeceabcadcaaddddbccdaabdbacebebbbdaeacdbbedcaddbabaeddadedaecdeeedbecdccbedbbacaecebeebabaaedaaaddceacccbcbbaaebeeabedceccbedadbbeedeebbbbaccdeedabddebdbbadbcbbbebabbaecedcaebcedccbabdaacccaeecccedddcbdbabeaaeebbbeacdceaeaaebcbacaddaceeececcdcecdaccacedcdeaebabccdcebcceabbbccbecacecbeedbecbcaccdbbcbebceedddedcbedeaeeebdceeeacbdcdaaaabdcaccdcbebbdebacdaeadbaacaaabebbaeadcdddcaeeddbbddadebedbdcbceabcdcedccbdecdaaadcabacbabacbabcacabaacebcaaddeaeedeabaeeacccbbdccaeeaabdebbebbeaebbbadcdbabbbadbbedcbccdacccdeaedcbdbdaabceaaaebaebcacbdaeabeaeacadbcbcdcadbeeacedabeedaebdbeedceedaaacbcdaeaaecbcbbcebbccbaaaeeeacaaacacceedbaaeaadacaebbacdaeabbcbadeeccbecabadecedcebaabcacebdcadcabadcebcbcecbdbcbccddaddbeacbcdcebcdabcecedbacaaabeebedcabaddbedceadaedabbddbdabeaadcbacdcceaeecccacadbbbeacaebddcbdcbedbbceacadedbbbddeadaadcebaebddcabbccacbadbbacbbdcededebadddeeaaddabcbeeccecebaadbccbeaeeeccdaaaddeaeaaacaaedeedaaddeeaeedbbbeeaecceeeeccedcccacecdccabdebedcbaaccbdebeaabbeaccabecdaaebcbececbecaebcdbcdabeecaabcdbcaabbcbdaccbcadeeabdcabbeccbeeeebeababbcbeeaceaebbeaeebeabeaaecbadbacbcecdacedbeaebabbceaeeccbeedacbecaccbcbddbbeeccdeeecbbdcecbecccbdedeccdeebaacaddeaebcbedacabcabaaecaaabadeaebecedbbcbbeadbeaaabcdceebeceeabcbeceedcebccbceeaacedebabbecacccececbdbcbedacaecabbceecacbcceabbdcbdacaaceebdeaeaaaacaeccadbecdeaabbebbdedddeadedabdcbdcbcebaeabeedabccebebbcaededebdbbdcacddbdaebacabdaadcbbdddacaadedddedccabeeddceecceacbcdaeaaeaccbbbdbbcbbeabbeeaedaaabacccebbbaecaccccebecbceaaeeaeaeacabbaecaccaedaecadebaecedaacbdebdebecabbaceebeccddebeebcdbdcbbbadedbbeddbadcdabbeeadbdbddecbdbbabceeecccbaceddeabcaecadeaaaecedadaebdadcbdcababaccabebcdedddcbbedceccacbcaeebccecaeccadceedcaeaeeceaebddeacdccdeaccbedaecadedbcbbcbbbbbaceadcdedeacaeecccacddbdbcdcebdebadceccadcaebebbeddcdaccdbacebddacbcceeedcbdcccaccdbbadbcadcdeececbaeacdabdacaaecceedddccddbebbaaddaacccaddadeeedbbedceedabebbbdbdcceeecaebcadeccacbeadaaaabaeddaeadbccedadcabddbcedbccdeadaddbabaacebabeebbaddeeeeababccdadeadceeddeedaababdcbcbedacbabcceebeedcbddeccbbbbcaedbdedbcedacbbbaecdcbcbacbeaadcbaadbcaaacaaaadddcecacecdabbdbdabbeaebadcdeedecaabdabaeebeebedaaabbbbbebeeccaacdebecedcdbcedeebbadecbaebabbbaeeddbcdecccdccadbdabeedadecabedabaeeaadbcdeeadabbdeebcdbeceebbececdbcbdaedddeddeadbaccbbbcddddcecdabbdcdacdddddcdededddeeecbebcbedbcaeebcabbadcadbeabddecaaedbadbabebeccabdadbabbbbbdbeecbabbaedebadababdccbcceecedeeecdddcbbbeaccaaeaeebcaaecdaeeeceddaebdaececcdcadddadadaececdeedaeddaeceddeceaccbdbeebbbaaaaecdbcbabbcbebcccdeedbdbdbaabdadebbddedbaeccddbbdccbbdcccebceadaabbebaaddbdebcbcbaacabdbedbcbdacdadebdbecbabbedbbacccbacaeadcacbcdbaddcadcdcaadbddeeebcbddccbbebcbcaccbaabcaddeeddcabccbbedccaddabaeddebccaabaaccddecdeecbdbcaccbcdccbabaaccedbccccecbeceecacbebdceebaedcecdbaacebddbeaceebceecdeacacdddbeeacebbaacebeedaddddbbcdcdeaddeaaabbbeeedceaddacdbbcbeeddcaacccdbddabbcdecddceddbbabaadcbeecdbdbaaeaebeeecaebbbcceccbebdbbcbaceceedeaddbdcbddebebeedcdedbcacdbdaabdbbbdbabedcceeabbebeedabcdecbadebbacaceabcebbcebaadcadeecbabbbbeaeadbaadeaecababcbbebddcdbbcebccecddcceaaabecccaebcddadcbbebacdbdeceabcdacacdecebbdeeeedeeaabbbdcceaabcacddebaceabaedcecceadbddeeccbeadbbbebbeeddedbeddedceabccbbebbdeecaaddbbcdbcbccbaecadadeceadedcaaaaaaaeadaacbcccbcecbcdbbeaeabbdbdcaacbbcaeceedadaddeabaccaccacccaecedbeeeebadaddbbeedbaebbcacdccbbdbecdacccadadedeeeebedbcbcdaadebcdccdddcebddecbcaccabeebbcbbeaadcbeceebdbdeaedddbabbedcbcbaeeeeccbbbccddbdcabeacdedbdddaebccddbbeecdddddcbceeabcdbcdcedcdbacbdaebddedceeccccdeeedeaebabdcbdbbbabaacceedeccddbeccaccebbabccebcbdcdacccacaacabdcacedecccadecdebceecabaddaeadabdcbaeeeaddebabceeebbbbdebaedcdbdebccdbadabbcdceedbabdaedaedbdeebeaeeebdcadebccddebccbeccdadacaadebddbbbbbbdceccdbccaedceacabaddabdebbbabedaacbdddcaeddaabdeaccacebcbcaabbddcdddaaabdbbedbcaabccbccbbcacedecabbabdabedbcecadcdceaaabacebedbbdbbbdcebcecaaaadbdaebdaebceecadeacbcadddecedcedccdedbceaacadaddccbbcbbbeaceeaebadbcdcdaaedeadaeacaaddaaaedcadcbdadebddebcaaebdbbaaaecdadedcaecdabaecabcdadacebdddcecadacebadccceededddaacbcadcdceadcaebcbbedbebdcbbacedbbbaacceeabdceaebaabcabeecabcadbaedabeaceccdbeecaaeeebdbeacdeacadbadbacaaeecdaccdeddabedeccbebccbddaddecbebdcdbcaecbaeeeaedcabdaeabbdaccdbdddbadbcbdadbadbccbcbabaccbbcdaccdddbcdbadedeaebaeebacabcdbabeebecccaceaababdccabcaceababeaccaeababebeeebddeabcddddbcbcbeaebaeaebbdbbedcdadccacadeceabedacbecbbcdaacdcbccbdbaecaaeebcededeeacabaaccabdaddeeddcbecaddadccbddcdaeabdaedabdbcddbcdbbcbdebeadaddabbcddcbbaecdebeeaabdceeacbacaceabcdabddabcaaacdababddbcaecadccbcbbbeddedcedcbccccecbcecbbdddedcddccadccdeabccaddbcbbbcbcddbedddbecabdbacdcabebdaedcaaabccbcddabeaaeacdcdbdadbedeacedabaaaedddbecabdbadddbeccbdddabcbedbdddaaccaeedebbeeabaebbbbddbcacceaebebdeeebcaacacabcbeddbeaacddaebabcadaedabbbdeceddcaedccbeecbddcbcaaaebadcadeddebaaddbedbcbadddacecedeacbabbbadcedbaaceadbddbddbcbcbdbdbebdceccbcdeabccbceecbceeedaadaccbacebadadcaeebddcbaabeaaabeebdcacdaaadedabedbaebbcdbadcccceebacdaedccecdccbcbecedbbceaaedbadeddabdccbabcbededadbbcacbcaaabbbceddeaaceabcecbbbbeccdaddbcddbbacccaddbdebaadcdbcecebdbcedbedccebaaadccceeccebdacabcccaddaabedbcbbeebdccadeedddbebcabedcaebadbebccccbeccedcaaadebccdbabdcadabebdcebbdbbeadbbdeceaeccbbdeabcebbdbebecebcdadebacdecceccccacdacddabdddedddaebecabcdcdceeeedbcbadbcdabdebbeeeebeaaaebcadacaaacccbcaaeeccaadbdccccadcbbcaaecdeaceceacdeecbcdbceddaaebddbdaecddedcbebbadbeceeedecdeacaccccecaaeadbbdacaebdcdaabdbaaccecbccaccbacdedaceacbebadbdbaccbcbbdccbacdbbacbccdbdceecdebaabaedaececaceddeebdddebdebcdbaacbcddaebedebaeadddabdbbbdeeccaeeebdebaeecbeeadaebcbacdccbeebeddabcbaeebadbaebdceddbecaebbdaddcdbbbeadeabaeadeadecebbaeeebeeacdaeacecbdaadbcecebcdebabeaabaadcdbabdebbbbddedbaababdbaceaddbeedaaabeeacdbecaeaabdbbcbbcdbbaccecbddecaacbeeccceccdcbbedeaaaddbddbcdbddacaedbaaebdcadecabaeebbabbebeecaedcbcddacebbadeddcaacadabbcbcdcbedcedddcebedacaabaddebbcabaaebdcdabeecbcceadaedaadacadbdacdcbedbaebeeeccabeaacebecaaebbdcaddedeaabceeabecccbadebaddcbedebdddcbbaaadbedabecddcceaaeecaebabcadcaeaebecbdbecbcdacacadbbbecebecbcdbdddacccebcdbdddccdeddcdbdaaecaedcecaacbcdcbacbdbccbcdaabadbadaeebcbacaaeaacaadbecaabddaaeeedbdbbbbccccbaeedbebbadbbeeebcdebbddadedcdbcaccdcebbabdebeaedaddaaeeccbcdcbbdccccdedaaadcdacedbdbebebbbbbddcdcaeccdbdaebdadabdeabdeaeeadeddccabdbdedeecdaceaddbaaacaedeccaccdcdbedbcaceeeecedbcccaaeadabacdbcddcbebaebdbbbdedadaecaaaebcacdcedaeecdbacedabcccceaaddbbbcdabdaceeabceaacedaedcaddcaaabdecbcacebadeedcabadadcbaeebaeecaccebeeceaccdebeeaaadedcdaaddbbcbbdbaecdbeaaaaedadbacccdaebcebcbbdeebdadaccbedebbedccedeecccbabedcaeacbaccabadbddedcabdabbeebadabebabaeeecbdbaadbebccaedbeaeaaeadbdeecacdacbeecbcbaaddcdeddaaebaebeeacdeccbdaabaddaeabbcebceeeeddcbdbedeaaceebcadbbeabeececaeaaadbeecdcbbcaebeecbdcbecbadabcbaabdcaedaabeedaeceddcbbcdacdcccdcaadaaeacbdccdadececaeecbebceacaeaecbdeaaabbadabeaeaaeabaedbccecadeaeaabcaaaddcbadddcdcabbdadceacddaaadedbacecedccddebbbecbeededbeeacddcdbdeeddadddedccbabcbdeecdceeaccbcbbbaceeebaacddcdbcecebaaadbcbdcceceddcdcbbdaebccbebbbbeaecbacceddbbdecbedebacbceabcbebdaedaedaabbbbeceebeebaebddbcedadcbadcabddbdadabccdaccbcbeacbbbacccedabbadbcecaecaeedbebacaebedeedebbbebbaaadcadeaeccdcdcbeecedabbcabcbceaccceadabddbbdddcbadeaedcabaccbebdadadceaaadeabecdaabddabadabadbeadadbcaceeccddbebedebdcdbeaccbadacdcaecedaaedbaaaebaadbbbbbdddcbecbbddbeeecdbbbababbbdcebeececdaacceeaccbcbebccadcdbcbabeedcdeceabbdcdaecdacbbccecdebbbecbbccdbabaeccbbceacadecdbabacabaeadbbbeadcdcecabcaecbdcbabbdcbbbaebadbeaabbbbbbceaaccaedeadbeaccbbdaccdacaaddaddecbdeaddcadedeacebceaecaccaecadedeeecedcebdeecadbcbecacebbbbdbecdbcdbecdacceabdbcdaccbcddcecdcbacecbbeacddddadeddebaaabbabcbcacdedbcbdeadecdbdbedeeedcdaddccdeedabddeeadaceccecaeaddbacddcdeedcabededcbaecddddbbcabeebebcbacbeeebeecccdbeacdccdaacbbcecdeacaeeabbdcdedbbecebaedaaceaecaadacbccbaedccbeadacaacdbabceabeebdccccecdbceaaebbabdbcdadcabeccbcbbadabebdbecabbddadadbaddaecdaebedcceedbbeeaacbcdcebcdcacabcbcbbbcaedcebbcbeadbececcacddbdadcbcbbbceabdbaeedbeddddaedbbcddebbebaccebbadbdababdaaeacabcbadbebcdaaedbceaecaeeadddcedaacbdaadcdddacdaccbeeaedaaecccccdebcbbdbcdbbbedbdedbaeedbeaabbedddbaddcebecddeebcccccedebccbddcadcaecbebaaacddbdecbabaecdadbdbbbbdadabbbeadcbbbddeebeaceabbeedcaedbdcbcdaeedeacddbeaeebdbdbeaacdaeccdaeabababeceadeebeccbcbdaaeccaebedbbbcedeeaaddabbdacddcddcaedabbbbaacdeeceecdceeceedddecccddcdedeacbabadcddccaddaedccaaceeacadcaccdbdeacbbdcaeddeadeacadacabcbcabbbaeececaabcaadecdeedbcddecacdbacbbcecaeeeecbbabcebcddcebbaddaeaedbeabddcceaddcdeabaacabcddaeadcdcacbecdbbceacecdeeeedaebddeaabdddcacdccacbebcbbbadbcedbcbedbddbeccaebabdeebecdbbcccacbaededcabbdbdacaadcebdddeddbbadceaacddbeceedaaadebcaccbcebabbccdcdaecdaddeedeaeabcbecdbedbdbdbbdedbbdcbdddccdbcbaaaebbececcbdbebbaaecdedcdeeaccceaaebeaabcdeccddaecaeedbbaabdaceeddcbbaeeadadcacdcbacbacecabcbedbcebbcbcaedeaebadbdebaaddbaadabbdcddcacedecbadeabeaadcecdebbaceadbccabacecabdbabcddcaeadccdbeddddbdccaaecdecabbbdcccacbeeccaebeabeddacdaaebbaebbccebcaabbddaeacbaaaaeccecedbcacacbaedbcdcceecdccddeeacaebdadeabceedcacbdccbccdecbccecbcbccdebbebbebdcaacadbcaeaccbadecabeabdbecbddcbebdbbaeeeaaeceecbccaacaacaaaeddcccbaddaeebebaecdbeebacddadcededabdecbbcbdddeadebaaaeebeedbbdbadceeabbacabebbedbeaaaebcdedbddccaeeadbbdbbeebdcbbcaddaccebdccebdcbacdecabeebdaadeeebbcdedebebdcdaeadcccdbbcbcdbbcababcaeabdaabceebaaaaecbeedabaeeeebcadeebdaeadaabaecaecdceaadeccbedbebecdbebecbdaadebcddcabadbbcbbcdbbdebbccdaaddcceddeedbbdddcaaebedbcbbedaebbdbeeebadebcbdeadbeadacddabbeeabdbeaccebbddabaaadcaedbbcdebbbeaacdcebdadbcbbedcecedaaecbebbeaaeebbeebcaceacadbababbcdaacebdbaaaeaaabbaadabedbccaebeebbcaaaddbadbabeccccbadabaecbdeceedeaddcbddcecbaababdecbdcaaadceebcbccdebbeaeaeaacbacbeeccdbabadadcbdddddeeeaabbcaccedcccdaaedccaacacabdaecdccdcbbbeaeddeebaecddbcdbdaabddaaacceddccaecceaedbebbbddbebadbebecaedccbcccbaddbeceaddebbededdaebddecbdecaacceacceeebbebeadebedbbacdacedadcaaaaabcbcacababeddabaedecbbdcacbeacdcaadeaadcdeceecdadaaecaaddeadbcccdddceccddabdedbbdecdbdddccdcacccccadbdaabbbceaaddaddbaedeecddadabeeadbbadcdabeabaebcbaaadcbcdaaeabdcbbaacdeeadbecbeedebedbcdadededbaabacdcdddaeaabeacebbacaccddcaeccbdcdedeecccebdbcadcabdeeebeccbeebdcbbdbbebdbcbcbbbacbadeaaacaecaedbdacbdaadbabddadeecdbecdbdbdadcebbabeabaeeaeecbeedebcebeaebedcecaecbadbbdbbccccdabcedccabbecdecccccbdcddadeeacdbcaabddbeabcdcbcabbdecaeadcbdcddcdcedccedecbcaddbddaccabdeaabdedecbadacbededecbbaebddbaaceabeececdabcaebcdcaddbabcbedddecededbdaeeacbacaecaadccbdddecbaeacadebebdaddcdcaadcbcdbcdaacecccedadcbaeaebccbbebdbbadbcacddbdbcdbdbccceceecccebcedaceeebbceabbddbabbdcbeecbdeeadddceeedbbabbaebcbdbabcabebecaabdeddcdbdbeaacbcedaaccbbceaadbdeabbddcbacddcebbeaeedabcdcebabbebbdababcdeecdadeeabbcdadebcbebdbdbbdedddaabaedbeededdebcecebeccbcebbdcdbdcceeebbdaaeaaeedcdebadececbabaeccebddcdaebeaecbeebdcecddaccdbeebedbccdbcdceadbceccbdcbcdcbccadaebdcdedeaaccaecbbcbbdcedecdebbceacdcbaacacecaccebeaacdbacaeadebbeaeeaabeceaaaaadbabcdcbcbceecdaccacaddbcebbdcdeabbabdadacbeaaebedebcaeaacaeecdeaeaabbaaeedcbaecdaaeecbeebdbbbdeebcbcbbdedcabdacadabbbbbedbbaaeadadbabeabcdaccddcccdceeaaacaaebedadceadbaeaebbccdddaeaadbcdddebedddaadeacaccacebbcbcaabdbabddbcccadbdcedccaddabceaeeebbcbcebbdcbdacbbcadeeeadcdcdaecaabaccddddababbbebacaeecedebadbaacbacedbdebeeceddeeaaeeabdecccbccedbabcdbababceecceddaddcaddabaceedbacaebecabdeecbddeabcceceddbaeecdabcbbabaabebaaabbbbcdeddabeedeabdecdbeabecacbcdcbabecccbaadaeddaceddbbaceadeedaaaedbbbeadaeeedecaedeacccdcacbecdacccedddaccbbdabcdbaacddbcabddacceedcaaceeeaeabecceadbbcccedebcbbebdaabaacdeeedbaeeadcacdeecddcabbeaddddaacbaddcebceddbebdcccacadbabddeceecadacdeabcbedbebdbdbeaccabcebbcebaaccbaababdbedeeecbedcdcbcebacdabeccceebccbebeaecaeeaabdceeaecadaddbacaadbdebeebdbbbdcdddcccdabbcbadeabadebcdedbcbedeeebdabbdcadeeecaaaadecabacadacaceaebdadedaadbaacdaaadbbcbcabbcdaabdbbcbebadcdceeddbbdacbcbdaadcceaabcccdaebeddbcbaeaccbcadddddadcaaadeacceedeaecbddbccadbdeddbdeccebdeeebaceeddbbacbcbebdcddaddedbdaddbabcbdacaddbedcadccdcedbcedcacaeaacabadaccedcdcecabcccabbbacacaaaaadbbecccbecbdcddbaecceecbbadeaadbeaceadccaabcbbddaccddeeddabcaadaebedbbbeeaebdbbddbcdabeebacdbccaaddbecebbdddbebabecdabcaeaaecccedaacdaeeedbadacddedcdacbedeeadddbcbecaeeebbeacbcbadbadbaabacdcbbabbcbacaddbaedbdbaddeabeaaebaccbaaddebbecbaadeecbcedaeaabcbbcbdaaebbccdddadbbcaecbbdabdcecceabbbacededaadddbacececcebccbdbbbedeaadbaeedaabdeaacbdbbaecdaaecdabdbbbcabecbcdecadacbaddedebdcccacbdbeaddebeeeebbbdbeddbeceecadddbecaeebbabedaadcaabdcbecaeebdbdbdbbcceebcaadaddaeddeacdadbdbdeaaecbaddbcbdbdbabdbddaeccbebdbbeedbadeacdcbdecaacebcdbacbcbcadccecbbcdaceaccddbabbbbedccabbebedabbadccecceccccbeadacdbddecedbbeedadceabcaceeedebbeacddbebcddbaceccadddcbbebccbaaecaebbcecaadbabeebcdbdaacadcadebedcccbcddebdcdddebeadcbaceadeabcedbecbaeaecbebdeccddecaceceabedbdebdcaceeebcdbebebaddacaeddaeaedabecdaaaeacbdadbdedabeeebbcedbceaceeeabcaeebbbabcddcccbabeeebaebedbaebcbbeeeceeecdabaeacecbddeaddecdbcabccbbaddedacbbebaadbddadeeabdedbacacbabddebcdddbaeeebaeaaedbadcabeacacaeccceecbcaadbbbaadeeccecababdcecacddbbcaabcccdaceddbbbadebcadcebbddeabecdccaadacdeddedcceeceabbaedebacdaeacadcacdbeebaececeaecceaedbaacdabbcacdcbccbbddccabedabbaadcbeeabceebebaeccceeeeeeeaeddbdccdaceaedccabddbabbbecdeddabccaccbcaccedecadbdddcdcddbbabbccbbeeedbebebbceaacbbdecaeeabecdeebdeeddadbcbdbcbccadbeecdbaeadbbbaeadccbbcaabdbdbcbbceaabbccbdadbdebaddebcbdedadaecbaacbdeeaccbbccaadbaceaddaceecccdbcaedeedceddccddbccedaeceeccbcceeebcbebbeacdacadebcadbecbdcbaabcbbccbeddaecdbccbdeaeeaeaacceaedcdbcbaceaeeaadadedbcaddacbcbbbeebbbbdecdbdcecbacdabcbddaabecbdbadbbacedeccbddbaeacdaceccedbadbbabadeebccabeaabedbaaacedeaebecadaccdbbeeecbbdaeaaeddabbeddadaeceaeaaecbdcbcbeaeabcbcaaedcbdbcaaaebcddceecdebadbbadabeebecdbecedecacedacbedeebacdadcaadebeadadbeecdaeaaeceeeaadeacddcccdccaeeebbebcaddaecdbcddccdeadbaedecdabedebcdabcadebebcccbbaecaaeadbbbaaacaaeececbceeebabebadcaeacddedbdeedaebeeaadcaeeadcbedadeacdebacaddaceedbaecedebaabebebadeecebddabbeecacdaaaccccbdabdabeaeccedaaeecabbdaebdbbeabebeecdecccaebdccaddaaadcdbeaadbcacbbcecbebaaddbbdadaddaccdeceadbbadbceecebcdbcddcddecababcdbbeadbabdcebddacbadedceccedeecccceacbabeeecaddcaacbeacdcaeddbeddecdccbdcdccaeceacdaebbaedcacdcaacdbbecbadbbebeeddadcdbecaccbaddaeacabebceddbeeeeeeececcaddcbeaacbeddeacccbbeadbaeebedcbdbbedcbbbaecbccbadbcdbbcddadecaaebacededcacbccdbcedcecadbcbdacddedcaeceddbcecbebddbcbaeaadeaebcbdadbbedeeacbacbcdacbadeecdbadedccadeedbaaeaaaceceececdcdecbdededebccdeeceaacdcecababcceeeadcdcacebaccdbbdedebaddabacacadbdacacacadebbcadedcaeaaecdedbbaeeeaeaacececbcdabedacaabdabadabbecdedbbeceedccedbcbdccdeabcedcbebbeabacbceadbedbccaebbcadebbadbeccbdaacaadaedcabebaecbadccdaeaddcacbbacbceedaeebeaaacaedadebeeadeeaadcdcabedcadedaacaaeccdedbbecbabdabdabbadacdcaccdebebcdebbddadcaeaeeabeebbdceddcccbaebbadcabbcbadabccdddeebcceaddcebedcdddeaaebdbdedebeeadcdeeeebbeadbcdbcedeedacabdbecbecdbaadaacdbbeaeaadcaeccededbbcecbabdcbdaccaeeaadcdeaedebbbeaeaeeddedccbacabebeedaaccaecaebdabeddcdcdabccdebbeccbddadbdeddbcbbedabbdeebdddcdeaeecbeaeccebcccbbadbeaeacedbaaccbecdbbbddbeccacbccaebbedceedacbbdbbebaaedecbedaeaadeeaeaceedbdeacabbdbcabaedaeacaeebcdcbdeeeabdddeceddecbbdacdddccabcbdebecabebcccdaaaccebdccdcdaaabdbbeceadcdbdbbbaeaaabcecdbacbdaaeccdaaddebddbbdceeaaebcbdeaebbcabdeeebaadbabdbdadbdbabcadedeedcbbdacaaeebdbeeccdddcceebdbbadeddecabecddacacbaddbbbdbaadbbbdddbdadccacdeeeaebcbdbadededadaecdadcdecbdcbeecdacadbecdbbcaedcbaaeddbedecacadbbceebcbeaeddccdbdbdddbedcbeabbebedcbcabbeadaedbabeabadedabbaacaeebadeceddccbbdedcabecceacdeccaddaeabbcbccdcbaabdaedadaeabdcebbacceeaacceaeabeebdaebdcebaadeabbbecbaaeeabddeaeeeababadedaabdceebebddbadaabbabbacbcbbceddeaabdcbbeeecacadbacbaaddbbcaddcdebababaebbcecdbdaaacbdcaaaebdbcecceaddceebdbcddaccecabeedccaeaeaecdadbceaeaccbbdcbeaadddabdbdbbcbdcbaedcdecaaaeedabccbdbaeacddaaddeebcebbadeacadbebabeddddeacdbeddedbdcdecbbdaddcebcbbcbeadebdaeadaadeabeccaedabadaadacdccbdecedcebcdedcbdcceaceeaaccbababbcabdeabcdabbaadecebeadbcceedbbdbdcaeaaadeaecbdddeddeececcbebacdbaecaedeedabeaececeeeedcbdacbcdbaaccedcacbecabbacdeecbbcbcbdaabebbcbedebbedbbcdecbceddacedbcceebbbdcabeaeacbaaecadebecddbbeeaabceaedeacadbbdabaddcddebbecddabbccebaaedaaceaccdbeccaadedcbddabdbdeadeaddabdbdcdcddeebeddaacbbbdccaecbcaaabbbeecebdbbeebdcbbeeacabbecbaabeabbcaacabebdeccaceadccabdeceacbaedaebaadbcbccddedbcabacceebdebdaccceeeedadedacdacbedccedaabeaabceacacbdcdeeecbdacadbbaabcecaedadeecaacbbaadcccbbecbdeaaecaeeeeaabaabecaeeecdedcbcacdcaaeabacccdacaeddabaeaabaeeadebdaecaccebacdeaadedaecadeddddcdccebeddaddbcaccdaedbeaabddabdeecacbdeccdbadacacdbcebccdacbbadabdcadeeabccbbaaddeebccbeeebedcbadddedeaebeaadaddddceacccbebbcbbdddabcccbdaaaaddadbcbaaacadcabaeadaaabbaabbbccbbaccdcbcdddaedacebddabcebdeddeacbcedbdababbabbbadddacdebaaebeccadebadbcbcdbceceaccbeabceddcebbaaedbbcebbebeabbadcaccdbddcdaecabacedcccccdbcbdabddadedaadeccddeadbdbeddebadcbadbaedbacebbebdcbbebbdeecabbcbaaaabacbdeadcbdacdcbdcacbdedbeccbdccdadbadbdcaeacbceaceaabbdccbbbaccabadebdaeedaaeebdccbeabacebcbaeababcbbbbedbbecedeaeeecabaabdbebaabeadbacaadceecdccdeaacaceabcbdedcaecbceeeeccceecdacedeadddbcbacaccbaddedcdeabdcabcadaabcedbecdacbbcaabbdeacdbabdbadbdacbdacbbdaeaabebbebdadbaabdadceeebbdcebcdbcdedbedacbcabbdaaedceceecdccbacbddbdbaabedbdcceccdeceecadabbabdccdcccdbdbeacabecbbcdabecbdcaecdabbacadeceedaeaadcbbccbcacdbbbdadaddeeabaddebabebceebbccabadcaedcadbdcabbcccdddcdbcbbbedccabdbccedeaaccceeceadaccacaadacaededabadcbdeecddedacacdaacbaadbebeedebeacaebceadebaeaacaaaeeebacdbeccbaedbecaccabdedccdabcbbcbdbcdecaedbeedbaebbebdbeabcaeecdbeacbaccbaddbaecabbaabdaeacbccdabeaecaabdeddadaeddcabddccbdcdceedeebecdecbccaedecdeeeccabdabdceabebadaeecadaddaccdcebeeadccddeabbdecbebbedccbcedaedccacedceacbdcabbebabdebdecdddcccbedccdcccbbbaceeccbaacabdddaabcbbcecebcddbaadeaedebaeeeecccaaaabaccdadedbdbdaedaedcddcdbedabeaadcdbbecaecbaecacacebbaedeaaadcedaeecaceedeaabddbaaccacddaabbcabbecbcabdeacceddacbdcdcaecbbdbcabcecbaabbbbabebeeacccdbbbcdbceddeaceaebecaeaeaaadbdcbdaaaceeceaaabcbbdccaebbbaaedbedbeedbeeedeaedbbceebceebbceaddbceadbadeecaedebcbebdbacbcababbeeeedbaabcbcdabaebdadbeeaeebaeadcdaddccebbebbdeedaaabebabbccecededacebadadbdbdbdabaaabbabdeabeaaeaedacaacbebcdadabeaeaadbebeaaadcebdaadbadbbcabbdeaedddcdeebbbceaccddcacbaececbbeaddadeceddbeaceadabcebbeaadcbbaebbebcaeeeecdbcebceecaaceedcdbbaeabebadcdcdcdddceaaacedeabeadcbddaebbdbdaaccbbbeebeebacebbaadddeeddeceebcadaccaeceeacedeadddebbdebeaccdbbbacdadabbdadbaaeeecbeebbbdbcbdeadebdebdbeaaaabbbbceadacedbddaacdaaccdeceddecaecaedaaaeebccdcbabccbbecbeeeedadacdeeaacadcceebeebadbcdccbccebadbbdacacedccccbbdcaecdcedeedcaccadbbaccbedbbdcdbbcaabceadaeaebdebcadaaabdeacacbedcedecdccaccaadacbeebeabbebebbdabcdceebedbcbaeaceaeeccdeeebdadacdeaedbdeabdcecbdceeabcccdbdddecdeebccabddedbeebbdaebdceaaaeecbbebbadebdccacdbbececeadcadabcccbddebbedaeacbeecbccaedacebcbebcecdeedacbbebabdbbaabeecddeccaccccddceaaebedddbdecbeeaeacdebdabcaccebcdeeacddebedcebedbccddcccbacecaabebcdeabbebcceacaeebcedddcebabdaabaebbcccbabdddbddcadeacdbcbcdaaecbedcbeaeeadabacbcccacabedcaaeaeccaaddedeebdedacbaaadbdaccacedeecccaeebaeeeccdeebbceeeedecadceaccacecaacbbdcaeecbeeeecabdbbeeabccbcbaeadceceeeccacdaaaaaeaecddacadcdaedbaccddeaebeaecdaecbcbcaabbebbbbadbceabbbbddebebdbcddbbadcbdbeddecbecabdcaccdbbcebecbcbeaeccdeeaebdeaadeceadbacdcaabdcecdabbdcddcbcbeddeaebdccedebacbecdaeabacaacdaeddcccdedbedcedacaaeeeeedabcecedbcacbaecaaccbbbdbbdceacbcdbcacecbcaeeecaeabbceecacaeddbaebbbabdedcbecdbdedaeddaeddcbcedabcdeabcbadddcdecbadabcdaaddacdaabcbcdcebccbcdeedaaacedcdddbdadaaddbbbdaaacbadbbbcdadddbeddceaeeacacbeaccececbacaecededecacaadbcccacadaeabaaaecdcdedaacadecdbecebeeaaaedbdbbdcecadabcbaaaeeccbedcaecaacedebedacacecbdbeeabbedddaeedebacbacedbabcdeacaedcebabdccdcbabecaeabdeccbcedadabedebcadebbbddadacaaaececaadbbaddabcdaccccedabddbbcacccbaeaaebabeeddecbbebdaceddbaabadacdbeeabbeabbabdbbdccedaeaabedcadbeaceeeebccdddeececbeaabceceaaaccbaabcabccaaececccdcbeeeaeaacebeabaeabbacddceadacdeabbbcdbdddcaabedaabceaedecddadabececadeacdcdbdeebcebeabdcdeaacddeeaceccbcbcabcadccaedceaedcdbecadeacaaaddedbadebcabdcebcbcabcbdcbbaebabeaccccadebcdacceaeaeceacbbbdbebbbbbbcabbdbedceedebedcadacbccedacbebcaeababbebeedbdcdecaaaebbeddeeeebbdcbadbbaeaaaecbccbbebdecaeaebeebdebddcdabcbcaaadeecccadbaeeeadbaeebbbdbbaeadddebaedaebbeadddceeddececedcdaadcabadadeaacbdcdeeaebcbbeeedcccebecaaaccdddbcdcecdbaacaabbdbabcbcabdaacbbeebadeadceaddacbdeceebecabccccabccedaeabeeaaecccbcdebabbccacedabbbbebdababdbcdcaabaabbeceecedbaeecaacbacdceedadeeacaaeabadeeeccbbaeedbbbbccdacbcbcaaeaeeaddeeedddadeedcedadaaaaddceccbccdbeaacecdedceacadbccbddcccacbaeeeaadbecbdcbdeaaeccddaeeaacedcdbaecdecdedaccbaadccdbcccceebccdaeacecebcdecbceaebadacbabadbcaacedecbbaddeaacaecbadeecdcbcbedeeeebcbbadbcbccbbcdbcaacdecdbddcebcbebcbeebdcddcceebecdbddcdcbddaedecadbeaeadcacaceecdeaadeceedbacbacaadececdcdaaedecdbbeeebeeadbbbeebecdbcbdbceddaaeaecdbebbcaeaeedccddbdddceacbcebbbdbbaccdceeabbbaecadbbabcbcbcceddbbbbeeeeacebebeadcdadccecabaadcbaddbcebeebbeecedbcdccccaccaabbaaebaadecdcdbcbacccabceaabeeeacdcbeeacbbbcbeccedbcacbdcbbebbecedbaadbbdddcbceccbcabadaadcccdbeaacbcaeabcedbcbdceddaeeedbdccacbdcbaccbdceeacbbceeeacedecbbbbcddedaeddaadbdabceaedbeaaecbbcbadecbaaaaaceacdbdaaebcaaadbcdccadacddbbaecacbdceecacecaecaeeabdccecaabddcbbaacbbdebadecdadebabbabbdbbebadecaccadaeeededdacbdcaebcbdaeaecddbeeaedcacddbadbdbbdbaebeedcceecacdbbeaabaebbaaebaaebceadeedadecbdebdeaaadbbdccbaacdcbdebdcabceaecdcacedcabdbabcadcecbeeaeeceeccebdeacbcdeaceecaeedbbbebdaadcbeeceabdeddccaddbdcceaaebbacbbcaacdabeccbdaedbbdaebdcbabcadbcaeebdebaaaeedaaddecdceaeacdbaeddbbdceadcddaecdbecadaeeddebeebcadcbacddbcadeeddccdbedcaabcedcecaaacbabbaedbbcdecdeebcaeabbeccaaeceededeabaeeeedabcbeacccceedadcbdbebbaaebadcacbbebbcebddadcaddbaaaaacbcbbeceaebebecbdcebebdbbbbdbbbbeebdcbcbaeaaebeccbedbbedccceabcedabdcaeccbbbebccbdaabbceaecddaaeebbdecdbacebcbbedceaaceddedeedaedddedaceabecbaeeabbeddcabebecceeaeeabbbdbcbbacdeacccaccaccbebdebbdbbdbdebcbbdbcbbcccabdceecbccaaaedbbaeccbaececcdbeacddcccbedceadabcaaeddeadaaccbaccaaeddaddbadddaaecdddceacdbdeadecbdcddacbacdeacadecaebcbccdccdccadeebbdebcbaacbaeacdcecbdebccdbecabcabddcddccccaeecedadacbebdccccbdebdaabcdcccdededadbcabbabcbabbdcbcbeccedacebeedcacdaddcacaacbbdbbddabaddcaadedbdecdeccebbabdadaeeccabdbeddaccdaabecdbcddbaeaedbeacdebebbbeeeedebeccababbaebebccceeecdbdabaedcaeacecbcddcceebeeaeeaabbceebebabdcbdaadccaacbeeddbdceddecbbadebdeceddbdabdaacbcaceacbcececceacdbebdcdcdbbdaeeeaeebecceddeccbaceecebbaecdcddbdadbebededbedbecbecbaddbdcccbedeadcdeadedeabadbadcbceeceecdbbaceaaeebadcbcbdacbebedccabbbbacebbabcadcbabdeaacabbacdedddebdbaacaaabccadaccaeeadccaccedbbeecabaaaaeebbeecadbabccaeddbbebdecccaeadacbecacebeecdeeaeacadaacbbeeedceabdaaceeaeacbdecceddbbdadcbabdebeadecdbaceacdeddbbbdccdddacaadbcaebcadecdebdbcadcadbacceeabecbaeedbcecedbacdccccebcbabdcdeccadceceadebeccebbdacdaecadaeebacbdccddbeeaceebdbaeddebbabaeddddaebedacedacddbddccdbcdbbbbbbdcecdaddaeedccbdadbcdcacccaecedbaeebaacceedcacbeebebbeadcaadbdcbbecddaadddacaebdaaddedcbcceaaaecdaecaacccabdbadacadedecbdabccbeeddaaadcaeeaacbeeacacebbaecdaebcaceeddcacdbaedaddbeeaeeedaebeecbceeaabbaaabaaeceacdddcdacbddbcedabdbdcbaceddedcccadbcebccaedcbddacecbbaeedaaebadaeddbadcabdacbaaaccecbdaababadcdccdadeccaacceeebdeddcaaeddddacaaecbdadbaeeedccbeaceecbcebaebebcebcaccdaaabaaaedbeadabdeedbcecadeadbaceaaadabccadeaddaabdceaebbcceceacaadabeebeaabbadbdcdbbdadccebdaaabaddddbdaaededcaccebebdadeedbacdeedcaeddeaeaaacdbdcbdebbebbbbbececeabaebeaeeacdabbcbceeaedcdcdeedcedcabaebdaaaadbedcbdbbdaebdbabdaadbbbbdcdcceaadcaeececdbdbedbaacbbeedcadcbbcebddcecdcddbcbcaaeeeebcebeaecdedddadbdcbdcdccccdebcbababeeacdbceabcabcdcccbbddbcabcdcabedcaabeeacbaeaaecdaebddeaebbcbeabcaaddcdbdebbbcacabcbdddebecddedddcbeecaabbacadacaaaacdaaccccdbeccdaccabdacebbedaedaecccabbebeedacbceebaeebddcbedbaccbabacadabaecdabeadedaeaaccbceeaaabbacebeababdabedcabcdbcbeabbbacddcddcdeedadaadeeddeccdceecacecaaaababaabebbdeeaeceaabbbdbedaacddbaaecceecacaceebeccbcbbcdaabeeadaceaaddeddadedeedcdcdceaecddceaaaebbdcedbeddaabbecdbddccdedecaebebdcddaceedbecddbebbeaedbcaeeaeadebceeacbeeadeabdbcabbeeecebadedaabebbceeacddaeaaddddcbbeadbeddcaedbaeceaddbdccbceaccbbccacdcbadaceacedcbdddbedbedecaddaeeccbdedbeadeebddeccbaaceebdceccbaecdceddaaaabbeeeeddecdaeebdbbcbddcbcebaadbeeddbcdababaabacaedcdabadeadddbccecdecbbadbcbbcadbcadecbbadcdbbccabaeddbbceeebadecaedbaaaedcaaddaedebbcdddbbaaceedcbacceacadaadadccbeadeacebbbaadbbaccdaadcbdbdccdceedcbcbacdbbdebebebddeddaeabbccdbaecaebedbadeabbcebaecababcbdeddcbbdebabbcaebacbeaedababbdbcaadbbedbcabdcbbbeebddeeadeaabeddacacadaceebbdccbaedbcbdbbcbaeddcaacdcbaacebdbcccabdcebabddaecacbcbebdeabceedbedaeabbeedaccbbaacebdbbcbcaedacaebcaccceccaceeacdbceeeeecaaadabecbcaaaeededabbbbccadaceccabcdcedddcacacbcabdadcecddeeebbeddaecebbddaeebbceadcedbeaadaddbcceeaecbdcecbbacdbacecabeeddacdebcaabcaaddeebadaacdadbbdcaaaedadcceebadedebbcdabaaaaccbbbbecdabcaacacabbaacaeeeaaadebcdaabbecdcaabdecdbbccacccdabeabacdeebaacbdcddaccaacbaeecdacddaedcbbdcababedbcababeedbebdbadabedaeaccebccdaadabcdeddeddbeceadadddbaeccbbbdbadaaaacccadbdadecabbccdccacaeabbecaeadadcebeeededddbadccddcdbaddaacebaabddceaaddacdcabbcadceaddaaedaecbbbbacabddedcacaacabaaecdbbceeddeedceeebebabdabccecdeaddadbcdaadabaddbacadeaeaddaaacacbacaebdabdceeebadbaadcecaeddebbacebbbacdcdcecbaabcaacdaceddbecaeceeacdbdeaaabbbaebcdedaceddcdeedcabeeaeeadedbedeabcdecddeddedacbedcadbaadebcbedcbbbcbecabacdacebddedaababedebadedebaabcbebaaadeecdadaeeeedecbcdecdbbdeedebbbadadebaaabdaabadcddbeaeddcabcddbabdcecbdacdadecbaeabcabeaeadbadcdbaceadcceeddddecdadaecebcdabdcbdcaddbabcdbadabaaaecdedcdebaeedbebebeadcbcdcadeeabddecaecaacaceadeeccebdeeecbdaaedeceebdbaaabbcecbabbaacedebeebcaccaecbcebdcaecdcdcaabdaceedbaaeabcedaadddabbdebecbabaebcdbeaeacaaddabecaaecadcacddcadddcbeabdcdabeceadbbcbeebdaebaaceccbacaeddbbeceaecdcebececbebbddbdcacbdacdcacecddbdaaabeadaaaedcbeeececbabddcecabcdecbbddebadbccbedebcaabbbeeadbeaddbddebeecbeeacceadbdbbdeaabadacaccbecdbedeaaaebeaaacadecbcddedddbcedabcbcbddccdcdeddaeedaaeababeeabbcbcbeebcdeebebaebdbedcbadeedaeaddccbcdaaabacecdeedcbaccedecdcaaabdedbaeceaaeadabcdebdedbbecedaaeedbaaaceaedabebedbbecdcebedcaccbbdccdeaedbedcaacbcbecccadaecdcdbccbbeedbcbeacdebaceedbebdcbadcbcaaddbcedbddcbbbbbeceececbdbdaabdbdcdbeeabddeceaeadcbeeaebadbbbaeadabbeeadadcebadadeeacedbabdaeeaadabecaeaebbcdabdaaaddacabcaeddeeadeacdbaaaebdebdcbbeaedbcbceedeebaeebecdedcbebedcecadabeaedbdeaadecaebcadebaebdcedcddaecdeaadceaedacbcebcadedbdaebbabaabdbcabdcddaecaaebeeebddbdcedbbbebbdbaaaacdcabadeeeadbdbeecbbebccddceebcabdaeaaedadcdadbcddddaedcadbbaabadcccceeaaebddcdbeeeaaedeeacadcabdeeabaacaddebcdacbecbdeeccebacbebceccbaecedaeadbcacaeadbcbcbeabaaabdbdecbcdceedebedbaabccdbdabdcceabcddadbeaddbcbdbaeadaecebcbebccccbcdeedaecbaaaeebbcdbceacebacbaececebacbaadccedbedaeabeebaeabbceaeaadbeeddbdbeebbabddadcebbcdebbaecaecdececdedaeaebdaddaebbcedaedaddddbbaccddddabbcecaeaeecdaddececbecbceabaaacabaacbbbdadceedeaabcdecbcbbcecdccccbaaedbebeedebddddbebccbbccdaaacbaacecdbbacbbeedaebbdcaabcbebedeecbcdcbaaddeceecdeadebcadabdaadcbdeedbdcbeaeeaecebcdcdacbaaebdecbaaabecbbcdaaacabccaaedcadebaadbcabeeaaeebbadddeabedddaacbbcaabdebacccccecedecddecabebadeddbebdadbcaedcecccdabeeebeaccbbebbacadedabcdeaabadddccbaaecadebadeaddecbcaaacedeaedccebbdbdaecceeaebeabecabaaaaddeecdebededddaabdecdadecedbdcdbbceaeaaebdcacacddbecbbacbadcabeddbdaceccdabecaadbacebacbdeccaadbddbdaeeebdadabeaacabeecdceebcedaddaecdddceccadccebeecdeabceededdecaccbddbceedebbbcaeceaabedbbcacdbaccdbcdccbceadedecaecdcecedebdbdeccecbaecdddaaeeeaacadeedcaadedeadebeedecebbadaeaedaecacbbcccddaadabecdedebacdeadeddddcbeecaaaaedbdcbdccdeecbcdacabbceeacaeebadeadabebeeabccceeddeadcedadebdbeececedaeadacbaeadbbedddadaddcaedebdbaaabbceecdbadceeaccebdceadbcddeddadbdceeacbeadebeddaaeaeeaabbeeaeebbdceacdbeaddceaddcbdabbeadeceeacecabbdedcbadbbabdeaaccbcddbbecdeadcabcabaaabbcdebddeedcaeeccaabbeddcdacadcdaeabbbbaecebaecdacdeaebcccdeedbccdcdabeecbeeccebccedbecbadbdccaaabaddddabbedcdaccccdccdbdcddabceccecddeabddbdbcdbcecaecaabcdaaeceeecbaddaebacabaaaabdacacabddadcdecceddaccebaceeeebcdeddacebceededdedadaecccdaacaaeeddeeccbececbdbaddcaddebcbaacdcbededacbebaeeaebcaacaaacccacbdcedbcecdacdeddaaeeabaedbbdebebacaddddbdbebcedaceedbabeeacbedacebdeaeeceaecbdadcbaabaddcacebbaabddbaccdddbcbbebcebdaadceaaccdbbebaeeacebcabadaecaccbeaecbcdeceebaaaddcabadabbeaaaeececcaccbcaadbbcdeaecdbadaddeddecbcdbecaeabecceaceacbdcdcddcdcdeacdebcccdaecbacdccdabebabcadebdbbbacbdbbbceaadccaadbbecacaeceeabdcaadbdceabacdeaacebeedcbabbdeccaebdaaddaccdbbacadeacaadbeaeaaddcbababaadebcbbdedaabdecceceacecacdeacdcbebbebadcbadbaebbbeeebabeabcecdcaecddbbbabadddbdccebededcccabdaaaebbecdeacaaccdaedddadbbaadcacaaaeddaadaecacaabdbdccceedbeebbeacbecadecaecabdaccdcebeacdabccaedacccddaeacccceaedbdeebdbacedeebeacceebbaeceadbdecbacedeeacdcacbacdeceebecbbececdadbbecdbcaccaeabedbccebeaebeebaaacebeedaaaecdeeedcdddedaebabbabeadccbabbcdcaeeedaaebceccbceaebcdccbbebecbedabeaedbebdeebeaaeadedbaeebdacbcddaecedeeebdcbcdbeeaeaeaabeeddbbcdadcacdcadceedaebdcacabeebbacabdbbeddbacbcaeacaebdeebcdaaeaebdeeaeabadedcababadcbeebeacbecacadddebdaccacadaabdcebedecadccdeebbcbbdeebcbdabdbddaadcadacececbadccdddecbaedddaecadeeeaadebadeaecceaeadbbaeddbcbeabeaddbdbbcabcadbccbbbcabaebcdbbbaacdabdabddcabdcddaacddaaadadacbadbcdebbaababcbedaeeeddcddaddceeeedbaeabbdbadecdcbebaeddeeaeebcdbebbbbbadccceaeedbbeddabedcacebcaddeaaadbccdacbdadaadadcadeaebccdebebaaebeedebddebbbbebaebbbdbccdcccacebdebbebbbaedbbbbabeaeacdeeacbebeacddbedbcebaeceecbadbbceadadeabaeeeadecaaabcecbdedcbbdadaebeabedddcdcbadddebeececcaedbacdcdcacbdcedadeeeddedecdeddcbedcbddcddabdebbacceccdcacecdebbbedaeebbcceccedecddbadecedecbeceacdeecababdeebcbedaccedadecedebdaeababdadbbbaaedbeebcbadbdadeecbaeacbaabebebbedacdebadbdabdacbcddcdeeeaaebeedeacdcaaecdbcceabbaeadcbccbabecedbadacdbdcedbaabeaabeabbadeabdcaceaadaacaeadbbcaaedbdebcdbeebeeedceeaaddcaaddaecedcccbddbeebceddcaccdecdceccacadbbbaaabecebddeeadbeecebbbedddbbeddebadcadbabadeacbcebaecbebdeaeacadadcabdcacceabadcdcabeebdceaababaceaecaaccebcdddaaceaaadeccebecdebebdabcbdcbbbcdbdcaeaedbadcaebeeccaacdbeaacbaacdcbcebacdbcbeedebdccedbacccccacbbbeaceedecdeeadecbccbcbeaadebaceeddcbdddeddcdddedacddebcbabacdbecdaebabbaeedecbcbaddeeeadcdaadeacdcdabddbdbeebaeecedcedddeacbcacebcacadcaabcabcbdaebdddcccbeeccdbbeaaccbedddabcedbdeaadddecdcdecdcbeebeeadbbcbacabaaadedebbdecbebcdbaeabeaeddbcbaeecdeabdebaeadacedbdabaadccedaccacecbdbbbccbadeaccbbdcecaacddedbacdbececcdaeeeedbbbbbaacdaedecaaabddcacabcbdbcabbaaccecacadbacabaaacecadedeabcbebdccbbaedaabbdadeccaabdddccabeeecdadccccdabeacddeccdcddaebacadbaeedbeabebccbeeeebbdeebeecdccaccceeedcaaabcedaaeebecdabadbbcdecbdbdbbddbcdadeedaaebdabbdabaebbdeceaeddbdbeeababbcbebdbbdeceeeecccbdeecebbbabeacebbcddcbddeaddadaaeebccbccdeeadcaabbbadcbbeeeaeabdbcdeaaceaaaccbadbceceaaadebabbbeecdaeeeaddedceebeecedebdaabcbccacabdcaecedabddcacaebceabaceabbaacdccbdeeecabacababdadaedaabdcebdcdebabbcbbcccbadabeaaecdbebeeeeaadbadebaacabdddcdbacbdcdddbdbbaaaeeabedeebbeadcbdddbcedeaacdacbabcdabeecaacacbcdcdcbdbeaceeeacbdeeeabaaadadebebbbedeebebaebddbbdacbddacbbcbdbdcaacbaebeaaacccaecdeeeedeaeaecceeadadaeacdcdbcceababeeacccdcbdcbcaaddedbbebdadeadddbecaaeedabdcedbacccdadaddcdeaacddebeabdabbbabbdbbddecdcdbeccaeadaeddddcacdceeaaacdcdeaeeaeeaedceccaaecedcacbddecbdeddbbbeadaacdbdeccedeaabdddaeaadbbbcedadbdeeacedcedeedbbbcbcddaabaeccaebdcabdadabcaecaeadacaddbdaaaebddccbaebdddebbbcbebaedeebcceacdedeaeddddecdcebeededeceedcabccabcbdedaedbededeaecadacddddebabedcedcdebedbddbbeecacaccbdbeaeedaaabedbcbebbddaecbeacceebceecdbdbeebbdadecacadceccccbeecccecbaceaedbceabbbeaddeadaccbebebbeaaebbeccbbaeecbedbdcadbbcacecacdabecdccecbcecbceaaadecbbacadbbcdddbcdcccdacbaddababddecadbbbcaabacedbddbbdeabeeeeeaaceadedcbdabdebebbaddeeeaedadeeaabedcbbabbdbcbebdbacbbbabdebebbbebdccacbcdeeddcacccaeccaddcaaddccedcebaeaedcaadbdacbbecddebbbdbdcebcaaeadbaeabeeecdceaceebeceeaccddabccadeeeabdcdcebdbecdbedaaadabcadeeeeedcacaebecbbcbeacdabcccdeadeddebbcbaaccbeddbdceedbbccaeebacebbcdebddcdbbeeeaddcdeccdecdbcbecabbdbbedbaeabaebaeeeeeaebebedbdedcbabbbaeebbcecdeedddaddedcdcbeceedaebcccdcdbdbeeeadeaeaebcaaecdeaaabcedbcdecdcceadceddaedebaeeedadbaaaabbbbbbacecebbdeedbbaaedeacbdaebadaaeeecdcdabcadccaaaddcaaebddeecddcbeabccdbcdadecdabaadedaeaabaddecdcbbaddaeaabbddcceccbccacbcceebaebedcbbbcedecedeeebdecccbddedadcedaadabbbcbbaeeebacedecabbbbbcdcaaacabddcecebdaecddcdacbbdceaebcacddaaabeadddcebeabdceaceceadabcbbdabadaecdbcbddcacaaceebbadbceaededecbceadabdcecdcacacbccaecedcccbeceacbcebadeedcebbdddaeaaecabaedeecebebcccaedbccebaecdadddacadadeadebaaddedbcabdbabcdbcdbdeaaadbececaedcaddbababeddaeddcdcabccacabeebeaacacbcbbdcadcddacebebbccaaabbbdcbadcebcccbbaddecbdbdcaaecbccdddbcbceaedcbcaedbdecbeddcbebedaabbbccbcbbbbecabaccebbdbbebdddbcdbbcbbecddaaadbceecddbecaccbbadaaabebbbcdbabceadbbbdaaccbebececdddedbcedeabeebcbddabeeceebcbdeabadedcbaabecbecedaaadccebdbdddedbcaddccddedecbbdabbdaaebdedcabaeeddccdaabcacaddcdbcaeabdaecdeacbedeadeebdbacdcdccbaddecccacdedcadbebaddaadedddadebabeaedcdddbccebbacdbcbdeeebdaabddadeeccbccebbbcbcddbdbecedcbdccdceacacadeacdcecacbabdaddeccbaedeecdbcebaecccaddecbedecddbbbebaebbacbecacddceadadacbaaebebcdbbcbeeabbdaddcbbacbaeebebbddabcddbaebbcddaecdcbebaaacdabdcadabdcbbbbadbeccbbbbbabdaeaeccacccdaabeddccaeebedcbabbeccccdbadaecedbdcecceabddbaabadeeacbeebdcbeaaaddebbdcbeeccbceedbeeaacbbdeeeaaebcccecaaeeaebadcacddaecaaacdeccdadbdbebceddcdeacebaacbcddbdbcbdedecbacaebceacbdcaeeadcaceeeceacdcadcbbdddadacdbaabbcccbdbebdadeddeccacaacddccacdeaaacabadecddbdeadeabeebecedaedeaabcbdbbadabababeaaccacabddaaededbcccbacdcebbdabeeabadcebceaccaeddaaccedbbeeecbecddbdddbbcbceaecdadedbacdecaeeebddadbddaeacdcaadccdeebccecbbebeecaeedcadcadbeecebbacbabdbaaeeadadbacbbcdecdeddacacdacbddabbbaccaaccaabcdaabaabeacedeeddedbcceeaebeabcabebdecdecaabeebaabacacabbecbbbddeebcbcdedcadbdecebcaeddeeadacbeeabcccebaeeeebdedceceddedeacddcbabeccdccceaedadddaeccebeecaccaebbedacecaacabedbaddbeabceaebaabacebceccbbbcedecbbecadccdbeeccaedbdbddceaaedbeeaccadeceacceeabaeebeeedbccdeeaebbbceeadbbbeecbbeeeddaeddccbbceeebdaeadadccdeceacacddceeccdcbebadadabdadddeebdcadcdcedaccdbdddaebaaadcabaceebeaabbdececcdaddbdeceedcaadcededccabeaebeecceccdcaadbcbdecabaccacaedcbbdbdcbaccbebbdcbeddbcbceebecedcaeeabaeebbaaacaebddaaabecbbcdaceabaaaeebbeeaeabddbeddceabaadeecebccdacebcbdabcceedaacdcdbacdbbadccbeddcaaedeeadccedbbeddceacaeceaeebebdedbbbdcebeddcbdbabcddecacbdebccadbdbededadbbedaaaeceeaaeaadceadeaedcedcadcdccccaceabbdcbcbcebeddbcbaaebbdeeaadceddeaceeabdedcbeaeccbacbdbecccbbbbaebaadceeeddeadcecdebabdbcebcedcabccbdaedecdecadacabdcbdeacbcdbeeebdaedaeceeddddccedcccbbaaecaaedebcaabdeebcdbbbdcaeaccdcbabdadaeeccadeadcaeceabaddabccbecbabaaabbceddbbdbcdbdcbceedcbedbdeaabbddaaacacbcdbdaedacbedeeeabbeeacabbdeaaacbcbeddbccaadccbbedeeaeddacdeeabadeedebccceccecbcdedecccacacaabdbdbbaceaabdbadcbbabdbcceabaadeabdbeaaaaacecacebcdecececcdeedcedbebbdbceaaeedceadbbbcbaedaeeaabaeabeeddebbeeeccabdecabddcceedeaddbdeeeccdcdbcedcddacaeddaadbbdcedddbeadbbbebbabeeabaeaaabcbabaeabeecdddacbeeaebcccecabddabbebdedcaabddbadbddeabddabebdbcbaeabadcdaaadeaeaaecbbebeaebcbbcbbbaaebcababcabbeeebcccbeeacccacbcecaeedceabdbcddbcacaebbaddabbedadaddccaeecdeaabecceedaccbcaabdbddaedcadabbaccdbaceabbebcadaacbaaadaddbcccdebdbdcecabbbbaceebabbcaeabccedbebaadccdcabdeeeedadeecedeebbcedddaecbcebecbbccabdcecadadececdbbccaaaeaddacabebbecdbbadecedacdddbcbebcdeebababdcbdeccdebbdacebabaeaddcadadacbebbaccadecdaedaaceedccaecbababcceedacaacdbcbcaddbeacdecebaadbdbcdcabecdecdeeabbabeeecdaaedbcebedaacecbacccbedaddcdbabcccdacabaaabeabdaccccbdcdbadecabcaaaaeecbdeecdaaeccebacacebacaadbbdbdaeeecaedddddadcbdaadadebdadabaadcbaaebbbaeaaebacdbacaedbbeabbeadebcdbcbdbabbbdeeaaedeaabbecaaaebbabdecbbdaedebaebaedcccccdeedeacceacdecaadaadcdaacdababaedaeaacaaebcaaecdbdcadacadaaddcedbddeeebdeeaadcbbbaedeacdeaabacddacabebbeaacbccecabdccdabcecdcccceceabedbcdcddbcdbaecaadcaecacddadbdababdbdbcbadbababadbdcedbccedecadaeecbecdcbcaaecabecabcecdbbdacbbdaaeecabedcbeaaddeedadecdcaaaedacaaeecdcebaebbdcbcbebcdaababbaccbabcbedeaeccedeeebbbccaabadcbbddeeacaddeadabbbeadeccdaadebdabeecceedadacabedecaabcbaecaeaebcbebaddcccbebceeedddcdaedaebabedeaebababdaaaecbdbaebbdacdbceadbeadbecdbdaecccdccacacaaaababbacdcaeaaabddbddbcadecabddedccdadbbabdeebedecddbebecdbdbaaaeacbdbbbadbaaedcaaebcbdeeedeedecacaaeacaadcbddddcacdacbbcaebcacddddcbaebadacdbeabbdbcdbcbedebaccecabacadbdaadbebadaceaaedbbeaaecaacddaedeacebeaadadabcecaccbcbdbaccddeccdaeecdddaecdeddcaabbbcecebbbbcdadddeebbdacbadedaeacebbeebacbeedecabdebbcbeeaebedacdccdaaaaecedbceedbecabbcddcbdebcbcadcdadbcdccdccbadecbbbbabbcabecccbaddebcabbeaeacbcedaadadddcdabdecbaddcbeddcdecdadddcebcdcdccddadedaccaecbbecbbedecbdcadbaeedaeececddebaedaacecedbdaccbabecbdcdebdacbedaeecedcdbddcdedcdbebbbebecbebdbeccedebbabdcdabdadbeaaababbbeeecaecabdadccacbddedbebaaceedcbacbeeeaeeeaacbacccddcddbbbdccaadccabcadccdcabbedaccbbcdbbeaebccbcecbdaaceacdceabbdccebacdaeceeeaadcddbebeddeccbdaddeaabecbbbcacdccacabcdccabeecbbbdbabadecdbabbacdecadceceaeccdeabdeadaaedbdeeadacbebadadebbbeacaebbcacbccbadbcebdbcecabccabedbcdebbaeeadbdadcceddbabeeadedeeabecabebbcddcbaeedaccdaddeadedcacbbaaeacebcdcebdedcccebcdcdebcdeaadbccceceebcdbbaadbddbdbebacacdccebebecdadbbbcacbacbcbaeeeeacaebdcaddadbebbcbcbbeacbbcecabbcedbeaecaaecddaeddddbaddcdbbceecdabcdadccdaedeedbcecdeddcccbeccaaeaaceeeeaceaeddceeaedebadbdcaccceebebdccabbeccaeaabecacceabdbccaabcadebbaaecbaeeccaacdedcbbdceeaedcbddeccebededeadaeaccbaebccadceeacdeacececcdbbaebcbdecdaecaddeccedeebcdedadcddbaeeaebdbebebcdedcbdccbbddedbabdddedcbbbacbdcbbdeabadaaaebebacebbadbdcaebcbccdecceeddbaeeceebbeeaaccebecdbacaceebaeaeaadbdaaccdecdccbbeeaeeadbcacabaeeecebbcadedecbebbaaabcabaaaaeedbbbedbaadbeeaacbcedcbbcacacdeecbedaddeedeeecaeccdcbeecbaacecedaccecdbedaccecdcacacadbddcabcedabbacadbebbbaddbabbeceedacbecdaccadabdaedeaadcabdcebcecdabeebabacdeebdadadbeedccdecdbdaccebbceaaebbbcecdceaadbbcbbdadbdaccdbaadabdeeddeddcacbeeeddecdcaceeecdcdadaaecbddcadcecddedcccbbbddeecbeccacddccaaaeacccbaacbcabebdbbddeddabdbbcddcccdeedbdeadccddaebbeeecabbabaceddaacdedddeeadbeedeebddddaacccddcbaacdcabaaaeedddcaacdacbcebaecdaaaddcadaaaeeedaececeecbcaedceebccdbccdbbaaddccabadaaddacdeeedaedccdbadbbeeebeadcbbddcebacbebedccbaaceebecdcdedaccbddeeeeabbeaacecdedccebcbbcdbdbacdadacededbbbbbcaaacbecddecdaacbbdadbedcbebbbdbdbeeadbceeaacbbebecaabaeebccceedbdcdecacdcedbdbdbceeadecdcaadadaabcdcdbcbeadccdcebabbdbeecbbadceacacbbcbdaeacbaaacbdcbcadeabbbdaeeadcbcbaceadadcbeecbaececdcabddbddddccddddbbbdbedeadecceaaeaedcdcabdebedbeecacedabbcddcccdabdeabbbccbcacbbbeabedddbcdedcdeeabdeecaeeedaccdaeacadedabbbceceecccedbaeeaadcedbedbabbeaeacddaeddbeedbdbbecddccecbabeabcbececeaccadebaacaccddbacddecdcbeeddeeaecdbccabbcddaebdcdceebbbeaeccdacaccbebbbaecbcddcbdabdbaccdaabdddbccaccbcbbeabdaeeceddceacdaaaebdbcbaeadadbddaccaaccecbebccddadabadcadacadeddeaaceadaadaabdcadddbeaeadddebddcaadcebaaaabccdddbbecdaecbebaccbaeacccedabbdbcedaccecdcdadebdaeebedcbdccebaeedecededabbaadcbcabbbacbacbbeebeccccbeeabcddbdeaecdabaddebabeeecbbdedddeadbebbcbeaebdddcbdeecbdccdcaecaaabedeecdbedbaaeddccceadecedbabbbaaaacdcbcaedbeaadcbdccdcedceccadeccaaecaabadddcebceebadaceeceebeebeccaaddcaabcbeaddcbabaecedbebadccdbecdaedabdeadcaddbbecdcdaaeddccbdddbaaadcadadbdabbcacceabbddcdbcaceeeddbbdcddeeebebdebabcdcebbaeecaabbdedadacbbddcbbdcdbdbbbdaadcdbeadbeedaaaecdcbcbecbcebdbceecaddeddaeeebaababdaaedbbaebdbdeaaeecadbeadeebeeebdeaabcedeeabaebbaeebbaccdbebaccbcacdddabceedacbdcccbdbcaddcbcebcabadccdabbdbbbecedcccebaaeebbbbcacaeebbbeabdcceebbbdbcdecdbeeaceeabaccbeddcedaacacdbeddaedeceacdcceebddcabbeeeeaccdceacdddbbbcbbecdcbcdcaadedbecbcedededdabceddecceabbeaebdcaceadcabebdeceddacdeaabdecbaabdbceededdeeecbcaacadbccbcdcbbadbdebcbbdacbaaabcebaaeecacbaaebaacadcdadeadeeeedebbdcccecaccdcbdbabcceeddbeccaaccebbbdcceebacebcebdcaabedeacdbdaeccebbcabbbeeabaecdeebebbcadcdcebbddedbccbcbddadeabebaecddcbecbcbaabaabaeddcacdebbebbcacdbddbccdcceaceaebabacedbdeddabdacdabbdbdcadbcaeeecbcddebbdcaabbebddbbadececaededbbacdabddddaedaddaacccacbddbccbbeebaabaceaedcbbadaedecdaabdbdedcdbeecdeacdcebaecabbedadbdaebcdcadccaaaacdbdbeeadddadaebabaacceeaecaedddbacddabeaeebdbdddeaeedeaebdeedcaeabbbacbdedaceabddecbcdedaaddbecebabcdccbcdcecabdacedeececdcebeeaeeacbeeacadccadbdcbcaaaadecbabdceebcddaecaeecaaccecdbaceecbdcbddddacbecadbaaeabbbecbadadcbdecbbbbabecdaaddeabebaaaceaaecaaacdbaddaeededdabbaaaabaecebeececbdbcdaaaaacbcceddbecbdebabeaacdaccceeddeaeacbbcecbdeeaeeeddcbebbaddaecbeacaccadbdbdcddbbbcabaabbaeeadcbddeabdeeacabeecccaabacceeddbecaebdddbbbccdbacbabcbeedbdabddbdecbddccbeceedcbabdadabdbbbecbcbcbeeaaeecebddaabbeedcedeebcbaacadaebeaaeacbbaacaaccaddedbcebdeeabcdbadcadbedaddedabdeabeedbddbbaecceaedaaedbdababcccebbaeaecdbcceabaecaacbccdedeadbbebaccdeebbccceeacdbbdbcabdbcaeaabebccdadcaeacbcdbbccbdeddbceccdedaddeabadadbeaaacaaddebceadeecedececdddbcbedecddbbbdeeeaaabddbcbcdeabcecaeccaccbbdbbbddbbeaadddebbededaabbbaecedcacaebceddaaeaeaedaceccdeadceddedeedccbdacbbacdaaddeadaacddeebacdeaecbabededdbebcdcadebcccaeececbdabdbbeebecdecaaadcdcdeacebbdaddacaaeccdabeacbaccbeaeacdbeddacceabbbaadaabbdbdbecaaaeadebcdecdcdaeeddecedabddededecadeabdcdacecbeaebdcadcdcbeabbaeadeeadaceabadbbcedaeedcbbceceeebcebabcbaadceaabecebbedcaeecabbbbebdbbdaacdddedaaadabcccddebbaebbedceeccbcbdacdbdbaeeebddedccaeebbccdaeadaadaacebcacedeabdcdbdeabeeeedceabaeaeaaeaacedecaaaaeaacacbddccebdbaeeaeabdccabcacdaccadaebacddbcaabbcabccbebabcddddaeebeaebaadeabdebddbdaaebcecebeaadebcecaabeaadaebdacadaeeeaabaceeacabbccaebdeadcaeebdddcadecabcbabecdeebaddedaceaeeedbaabdedadaedbbecedeacdaaaadaebedcdaadecddecdcecccbbeeebeddccbacddddadcbecbedcbdcaeecdacbbdcebdabeeecbdaebdbccccbddebdcdcebedeeecededdaddccbcddeaeaaedadacbaeebeaecdddcbdacbdcddccdecebceaccadeabeeaaddbcaeeddbaaecdbcaecdbaaeabebcdcbecdeccccabacbabdcbabaadbdcdedbbcabeaecccbcdeeeaeecbaeccacaebceacebebcbbcbbececeeadbcbaecaeeeedecdbdebaacebbbacaccaaedbadebddccaabaacabdabcdbdbbaebacedcbedecbecbdbabdadaebadcacdddacbcbdccabcaadcecdacccaecaeebbededcabcbabdcdeaecbaeddaaecadbbbddbdadedaeccdcecdbbcabeaecaeaecddeedceaeacdebacceaceaebcbbbacdbadebbcbaccbaedcecdabedddcdebbecdceecaadaccdeebdbaacccadadebccbdecceccebeaeeceaebbebcbcdbbcccdddeaccbdbcbabdcdcacaadedeccaaeadeabcecdcdddeddbbbccacbcaceedeedebcaedecdddbbacbbebbecbbbedeaaaaebceedebecccddbacdbdbcdcececacdddaadcaacaeccadeaceeeebcdadccadedebcdbbabceceacdbdbdedabaeccdaeeebdcdaaaddbbadcdcabcbbdcbecdddbddceeeccbcdcccacceabcdccbdcaeaabbabecdaeeadeadcbbbabaedecdebbdbadaebdadbabdcdbceedadddcdabbcadbbdcaaeadaaeecaaebdabcbdcabdbdcacbabaabcaecddcdeaebceaeaabcaaebbbadcdabecccecdadeccbcdbcbecedbccdecdbecbccebbbbaacedddabccceedebcdaebdbcccbaeeccabcacdddabeccaddaecadbaebbacdabeaedebbeccbbbadabaeebedbbbeebbbeceacdbebaadbadbcceedcbceabddcdacabacdccdacaceebdeddcdbeeecdabbdaaabedaedddcddebcdbdaeebeeddebdccdebebcbeeecceacabebedaadbccddbebeccebaddcedadccdacbaaacaacedccecceaabadcbcadcbecedacbaeebcbceabeebacddcbcddbcaeabeaaaddacaddeceddcabbedeebacadbabbeaeeeeadcacaeaccabedadaacbccbdedaebbdcdbcecaccbbbeaaebaadeebcbceaebaaaccebabcdcbcbcbdcbeccddaebddbcbcbbadcceacceceaedaebcdebbbcdaeabcdcdbdcebebecacdbddbcedabaeccabacbadedeaeebcbdedaceadcdacedaaabedaebcbdacebdeedaaeedcbbcdbababbaaeecccdecaaceaddbbeadedcaeeeaceecadacecceccadacbdebadcedcbeaebdcadbaedcdeaddaaccdcabcbbeebeedccaedbcadaadceaeceadbcbaaabdeadcccacbedeedccaccbccbdabeabdddecaaecdddcbbedaccccceadabdecddabccedeacbdaacabccebbdccaadaecaaeedcaaadddbabcbbdcceeaeadaedcacdccbeedbcddbadceeeebccddecedaeebbeacadeddddbdbbbbedceebebdedccdebeebeaebcdcddbdeebeaecdacabebebedcaddcabdeaeabcacaadbaeadcbbdcdbcdecadecaaaadcbabcacbcaadaeaabebeddecbbacaccdebdbcabadcbeadbddbeadcadbacceaeaaaaaaeacdcdbeddcbeeeabaddecebcbdabacaecccbabaeedccceaebdbccbbcbddbdeeebdaeedceadbeecccccdddbddcdbdecdddcdbeeeaedbaaecaecccbbcdddeccbdbdabbbbbacdbaccacabbccbbbbbacbcedcaabcdabebeeaaceaddecabeebcaeabebeebbeeebcbdbdaeccadebadeeaeaecbdbdeeaaadbbecaacecdaceebcbaedceeeadbeeddceddbabdcbcbcbdeabaabacddaaaccbccecbebabbccacddcdeabeddbbcaadbeddeddebddadeabdecceaaebaebabeaaaedbcbedbbddaddbbcaaabcebddddabecdedbcbeaecdaccbcbebceadccdabcebeecacdedcbaecdaecabdacbedbccdbeceaccbbeeccabdacababddbedcaeedebecaeccbeeababcaadbddcccdecabebebcddcabdccccbabccdccbedbeabbcbaabaadcacdacbeebeaccbdcceaaaeccaddaccdbaacacbedbdbeceebeaeaecedaadcebdeacabaaaeeeeeaaabdbaedddcbcacdbbeddbabbcebbdbacbeeaacebbdbcaaadeeeaedaaaaddeceabcaaddccdadcecabdbebcdcaebdacadbeadbcdecaaddddaeddedadacaeebcceccaacdeeecdebdcdbdbaeebaacbbcbdbcebaabacacaacabecaeeceddacddeaedcbcbaabcaedecececdeeebadedeedddbbccbedcedadbbbcaccbcedaeddaabaacccdbcabadbbecdccbaeddedbdaaaacaaebdbeaacaadaeacddcbceecdcbddcdaddcaeeaacdeadbcdbbabebecbebaaaedbdcaabcbebcbacdbbbebbdbdececdcdaaaebaadbecdceecbacdeaddceddaaeeddeccdaddcececcecdabedaaadebccdddecbddbcddacadcbddeacdabccddaeababacadcaeeabcdaadcaddabbdabecaddadbbdbdecbdabcbaccbabcecaceadbacecaaabeeccdccadcdccaddccbcdeebbdddcacdedbacadaacadddbbbebdadbddaedeccbcbadedeaeaacccedeaeacccdecdebaaedaabdaeadcdbcbcadabbadaeababceddadedcbcdadecebbabddeddccdbbaebbdadbcdcacbbbbadacdcdbaacdaabdcbeeebcceeccdeabbeccccdddaceecebbdebbeaaaebddcdbceadceadeeebcbbddbbddbcbebbdadbaacaecdceaaedcacdccbaaddccdaadbbbecbdabeaceeddaadaabbbccdbdcbceeaaaecadbedacedaabdeeeebbdbedaaeebaedadccacadeadcbbbeaedabbbcabbdaebdadacccabbaecaabbdaedeaaeaecddebcdaadaccdadcebcdeadbebbcdeabaddecbbebaccebdaabdcaecbbaabddbceaddbbbdcdeceacdbbaebdbdceabeadddddcbabaabeddbbcabeedbbadddaaacbcacbceceadcedbcdaacdcacccddcadbdedcdecbebcddaaaaacbbdcccdbcecbbdcccabebeeceeebceeabccacdbbadadeceeabaaeaebbaedabcbdbebdcdeeeddbadabaccadddebeadcbbebbedceaeaccccecabbbdacebbdbaaecdadeecdadceaddcaabbdcaeccdbeebcaaedcbdcedcaceceebdeeaeedcdcabeccadaddecddbbaeabdaacaaccbddacbcddbbeedeabbdebaadabbadebcbbbeedccaceabdddbebdaeeddacbeecbabdddeceaddeddbcdeccecbccbceeaebabecebacbeceaeabbcdedebdceacbdeacaaabdbecdbeeaacbecadaadcdcbdeecdabdaeccebbdbceebebcdcabecbadaeddccdeacdcceacbadacbcaedcedeeeeeacdeeceacbddabeedebaaacebbabbcaabceebcdadcddddcdcaedeadebceaeeebaceaabcebeabededdacdcdbcaceecebcbbbcbabadebbeaedbbdbbdeecabadabbabebecabdbbebeabbbcebbdadddaaacdeaacddcbbebbddecedcadecadebeaeebbebbeeddebabaaaebbbedcbdcddbeedeaedacbbbeeeeecebddccbdcbddbdbddbcdbeedcaacbebcbabcadaaeccdcacebddeceededcedbecbbcaacdeccdbbdeaddcecadedbccccbeaeeddbdccbecacddecacccaeebaeeeabeacbbbcebeadbdadcdedeadaddccedecedaeabebeccccaabecadddbbbdbbebcaeeeaeaddeacbdcbbacbdeabbcddcbacedcbaaddbeacaeedebdeacecaadccccdaccccdbaaabacabaaacabcbcddeedabaeaaaeddbdadacddcbcbaaaadcabbcbcbdcdaedcbeaeabadccaeebbbcdacaeaeebaaaddecabecabbdbcadabbaecebcdacbbaeaacacbcdeadabaccebbdcccacadaeecdbbaaabbeacbdceebbeedadadbebaebdcdaedccdcabdcebaebeaaaaaecabdceeebaacaabeeceedbaaddcdcadecedbeeceaaccbececcacecddccdaedcacbabbdbadadebccbccbdaeddeadadeccebcdebabcbebeadeebecddacbebbdeebbbbbbddadadacbddbaccccdbecdddbddedbaaeececddbabebbeaadddbdebaebdeadcceaccdcdacdabccddeddceeecdbbabebabdcebbebaaecaceeeeccbdbaabbabadcbbadbeabcaecbcabbcbcdabedcdcdaabcedbdadcccdbdbeabaacebacbcacdbaccecababcacccabbaacddadaaeededacbecadabcadbeaedbbccaaceabcbeddbcbbabddbdbcebabbbaedecbcaaeedcaadedbbbdbecbcbcacbebeeabaebcaedbcdeccaddbdcddbebaabeaeebdeadeeebabdaaeecdbbbebadbbdbaaecebaddceabaabbaebbacdadaebdcacceabaabecddebddeecdddebdacccecdbdcbababdabaacdaeaaddebdcdeeeacbaebaadaeebedccdacddeaacdeacdececbcbaeadeebacadbdbcebbcaabddbdddeaaddaccccadbbdeabddceababaabcebedbdaeceeeeacacccecebecbdacedacedacabbdadcdbeaaddecabeabeedbacbcddacdebdaedebaabdecbddacddacbaecbeadcaeeeeaeaddddeceaecaeeedbeacaadeadeeebedbddcebebddaaebbdbeedcbeeebdbaeedaaaeadddadcaeabddaaaaebcecbabbdbaababeceeaabdadcdcedcdcdeadbccdbbbbcecccdedaddaabcebabdcacacaebcbddbababaeedddadbbcbbdceeaeababaaeeeaedeadbddddeecbaebaddedcbcbabdaababaecdeeaebcbabcdabdebddeacbbecacebbdacbbbebaccdeecdaacdeaabeceeebdbdcecdbabdbdddbcececbbdabedadddeceabcedcaeaadeaaaebeacbbcccecaddbcecceadaababaecaadbabdcbacabaccddeddbeebdcadedeecebadebdeecdcbbebdbbcdbbbcbbcdecadcddaaaeaaabcddcaacbaaebdbbceedacddeeddcaddaaceeceeabdceeaeabeeceebebbddccecebcaaaceecbcbaddeaedddadaaaaaedbbabbeaebcacdabceaccdccdcedadaeccdeeaacebdedcdcaccdbaaeacccdcbdeecadeadeecdddabbddaabcbccdccadebebacaaceabecdaedaccdeaceaadbeeaececbacccdaadedaacccccecbeaaaddadaadeddebebedaeeadcbcdeecebcbdbdcbcddebddcddcccaddcddeecbbbddbeaaaeaaaecdeadeecedddaacadedacbdcccabdebcaedabdbdbaebaedbdeddaabbccdbdbebbabcbcbbecdadbcecaecccceabeccaaacedddeccaaacabaabcdddaadbaaddceebbededceddaceaaabbccbdcdadbccaacdcaeeacaadbbcebdedbabaccdcbbbcbcbdbecbedadaeaddddbeaaacdebaadedbbaeddeddbaceeaabbcdebedbdbbbaeabdddbadbbeadcbbcceecaceabdecabcedbbceeaceabcdddbadbcdaeebdeedededaccedcaebbbdabdaaaededdbadaedcedeeceedacceacbdecdaaaececabeabddddadbdacbccdecdddbacbadeabdcbcadcedbdbdcecaedddcbbcaeeccedcbedddeaccbdeceaebbbbabbecedbbeabdabcbccdedadeaccbadaddcaebdedebbbbeeacaccceacebeaabdbcaeaabbadeeddecbccecddadcececcddcaacebbaebbbbededcabadecaadbbdeadecdaedeeabedadadeeebedcebcbdebbdcdabedeecbbeadacaedbadbeebdddbcbdbbdedcbbabaabecebdedcdcebeedcdddaeadcdacccebacedaaededeecdadaceddcbdaabcdabacccddccaebebaeddceecadebaaebdaccadadcccbecacbcabcdeebeddbdbaccbdacddccebeeddaaabbcbaaaedcdebeecedbddaeabdcedceccddcbeaeeadebebaedbebcdbcdaabbcbbeadcbebaedaeeddcaddceebbaabbadeeadcaebdceabcbcdedecedbbadaceabcedabeceeddcdccbabbdedadababbadbeccbddbeeaeaededcccbdcbcbdbedecadadcdcaaebdcbebddaabaaedeeecdabdbedccebbccddbaaabcbecdbadaabddbdaabcabebcecaeaeeecbbaddccbdebbabbcbaebdebbccaabdbcdcdacbbccdacacdeaeccbabecbecaaacbbbeaaaeecdadeabcbdccaedbcbddcddcecaddbacaaecacebbececeadadeadebcbacaedbeeddaccaaabeabdadbabcbebedcbdeeaceeacceacaabdcbbacaecbeddadaaeebadedbeabbedddacbbeeecdbabdcdebbcceaacbadeecccbaaeadceecbcaeabcbdeacbeadcdaedeedbdabdeaccbcdbbebbcdbbbcecaddededaadcbabecaaacabeddadcbcdbedaaceadeebadacbacdbbbadaadcdacecadedcaedababddbaddbacccdbdbcbccccbddcddcbabdcbbebabcbecaabacccbbbaedbeadeddcadcccedecbedaaaaededdcdcaebcbcccebdabcebadcbddbaeabdecbbdeeeadddcbacbcabcdceeadcedaddcbddcecbaadccccbceeeabdabeeacbddebacceadeececedaabdceeebbeeaadbbedcbccbbebdabcccbacdaaccaebddabbacadaddebdcdabadeebacacebacebdacbbbdacaddadedccbaccadcbdcdbbadbaedadaeadcdddaaaabaceaebcceddeabacbacdeedcbcdabdcbcccaaccbcbcaadeeadeccecdebdeaccbecadeedecdbeeedecabbbeabddcaaeacecdadeccdbbaabbdddbecccaaacdbdccedcbaeadbadbddeddbbbdecaaecbbbbddcedbadaddedbababdaccbaadcdbcbeacabbadeeecbccccaaabddaaadbaeeabdbabeebeccddadaadcdeaabeadccdcedacbddedebbedcdbaaeceadeebdcebbccbacbcacebbaecebbcabceacccbdbcbdecbbcecebaaadcaceeeadadaeabbdadaadaaadbabbbaaacedadccbeadeebbaabcdaadaeabdabeeedcadccccabddaeaaedeaeebccbadbadaadccadcaedbaddeaedcaeaccacccaeccaaebbadeedbbedcedcbcecedcebeadddeaceeaeacdebdaabeaddbaeaddccccecaddeaedbaacdaddceabbbdceabdddadabcceadcecccebceeeebedaceaabccddacaeddaaaeaebebdddadbdeeecaacbeebdddaadebddadaededbdceeabeecbbedbbadbebbaeaccceeccdaeabdeedeeddabdcbdbdcebccedacabdeecbabcdabceebedeaaccbcdedadcaeeaadacceadccaeabdebbbabbbcddcabbcbeabaaeccadcbdadbeaeeadeaeabdbdbccaabaccaccbceabbbeabcbbbdecbedbecdcacddaddabecddcebaceeccaadbededbcaeceacbaeaabdbaeabbeacedccebeaddaadbaeaceabcddcabceabdcddceccebeebddadeddcbcbccccbeddceddbecddeddbdaeecbdebeabeeceaccadeadaacbdaebabcebbdbacbeabcbececebaaebebedbebcccaccecdbdbecdcdaebcbcacceacadccdcdcaabdbbadacbcbbdccdbcbdccebeeaecdacbcacdbacabbcccadcdeadeaebecdbadbcdeecbdaaecedabdaeabbaabdeadaecdadabaceaddcdcddeeedeccccbbeacdeaccdbcbeabcbabbebdddbdccadbcceacceeeabcbbaedadedcdaedcbeeabbdbbacecbbcedddcccadceadbbbbeeaacacdebdedccbdddddbabebcaaabdaaacededacbccbaeabbbabbbecebabaaacacecdadadaddadabcaecdadcbaaeacaacadbbecbaeccbbeabbabbececcebeeecdebcedaebeaddcadeaaebcbbccbececcaedbeabaabdacaacdbbadddbdacdbcbddddaedccdbbdedcdcaeaabcddbbcbebdeadaeceabbcbaaaeedcddbacadeebddbbcdccedcbebdaebeaabbaeadaceaebcdbbaebeeedeeeccbbcdeaebacdaadcddbbeabdcedeaddecdcaebcccecdadcedeacbabdecdcabbaeccbebcceedceddbbdaeaeeedccebddcdaabdaedcadacbddbddeeaeaebeacdeecececbbcccdcdaebecbeeceddadaddcecadaacbdeedbaccbcaeeddaeaeccedaeacbaedbaecdadcecceadddaebdebdcccaceaebabbbadaaaababdccdadeccbedeebdddabdacaceccecabaddebccbddcabaceabccbaeaadbeabedecbbdeaebbabdacaceecdcadbaccddcadcbcabeccbdbebeaadeddcecdbdccecddcabacaeededecacceccecdbbceaddadedbaedaadeacdbabbaacdeaadacddaeaedbebebacadbedaaaeeaeacbececdcaeabccbadcdcabccccedbbbddbcadaeabddaeedcceecedccededabbeebaabbddabeebbcaccedccdaacbdacdabbabaedbbcbecaaebbbaddbdbbcbdddedadadedcddadebcbebabcdbedeedaeabdeeebcdcccacdcbaaaedcadaeabdeebddccdabeebbdeaedebaeacbceebeecdceeccbacaabbebdcdbdbadebebbeadcbadccbbdcddaecadbcdecbedbecaadbeececcccdaccdcbcbeeadedddebddbadecaacdaaaddddedcacadecaaaababadeadcedabeebcedeecbdeabcddeccaebebeccebcbeeeaaeaaaaadbaacbeaebaabbdceadceceedddbbbddbeeaeebedbbeeddbeabddbbbccdddadbbdbdececadcdbaebacaebbabecdeaabcdcebcdbeadaebdceceedaeedcbcdeeaadebdebbecaeaeadaadbcbbebaeeaeaceebeecbadadcaaaebecedbecdcdaaecadcbdaedadeddaabeeaebaddcdacddcdaccddeaebbeeabeecbceabbaeeabcebecebabdeacebdedebedcdadeebcedacccbacbaaddebbdeeeceaabadebaeacedbdeadecbaddebaaaaabbdeeacbaebbadeccaaedcadddcceaacbebcacadbcedcbccddddceebbcaacbebececdceeaabddaabbeedcdabccecabbcdadbbddddcccdcbecbeababaacaabbedacecaddecbbacddcccadddcdaeedddcadccecdedcebddcbecaeceaabcbbcbdbaaeaebcaabddcaedcdbcdabaecbecaabbeacddeccbcddeedbabddaddaebcccdecbcdddedbbcabdabebceadcaeeecaccacaadedbeedbbaeeecdccedaeadaeacecccebbadabcacbadedabcabcbaccddbebcaccceeeeedbacebbaeeeacbceaabbddeeedaaeeacdaedcbbaeabccccdaaecccabaaedeaccbdabebdbbacddebeaebccdbddedaceedecdbadeadabceaebdbdcbccbbcaaeccddaccabddbeebdaaeecbabccbaaceabcbaaadccdeadadedadeeeabaaeacaeecdeebedaaadeacecbadeebcabddbebbdbdacdcacaebcbacccbacacddaeaadabccecbcceaeeedadaeeabaecdedcceaaccadebaecabeeadccadabddecddeadecbadbddaddadaddedddacacbbadddeaecacddecaceadebddcdeddaddbddaabebccebbaabcacebacdcdabbaadcbebebdbcdbdcdababaeeaadcaeaaaaacaceaaaedecbeeedbbcaaaccadbdabdadbabeadbbcabcbbaeadecbbecedccebccbbabdceeecbedccedcdeaabbbdbcbaabaecdcaeecebbddcbccaabcadcaeaeabbccaccaeeaedaadbcceddeadcbaeeedaebaadbccecbbdabeabdecadbadbccbedccbdecaeccdbaceaaadbbdecccdcbaedccbadecccaadacedcccdeecbbcdbdedbcccdaacddabacabacdccaaebbcdaacebcbdabdbccddeadebaaeeaccbeeaeaddbecbbdbeedeaeedbebbbeccaeaaeabdbcdbabbecaeddebceecdcbcdbcbebbbcaadaeabcacededadcaeaabebecedebbceecedcccdcaaebcbdadcdbaeebebaebaeaadcaccaddbbbecdcbccdddabddebeaadadaebdbabbeebbabcccebcabbbdebcabacedcbdaecaacbedbbdacdeabbebebaacacacaaaabaaeaaececcbdecacaadacdceacbcaeeaeaceecaacaaddedaceaeedaecccdecaaadddeecaccdbeabdecabeaebdcceacbeecdeeabaeedededccceeaddccbcaacdabeadcbdaebadecdadacdebcbadcccbdcccbcbbeeeedddaabebdcdeadeaadbbeebbbaedbbbebecdadcbdcebadcabeadebcebbbdedcabebaebdecebadcdaadabdcaaeaaaddadcaeedcbadcddddeeaacaddeccececebdedaeabaabdceccdeeebecbedaccddbdbbdcadcedbbcadbbecbacabdeaacceadbdebbadcdeceaedacaadeeddcdbdeebbdcebbebebabcccdeabddeddeccecacaeadbcebcecbeddedacabbcbebeccbcecaddccbddbdedbdaeccbdadbeeecddeaeacecaaccbedebadebdaaedabbdaacaeacadedebddebdccbaeccebbebbcbbcbabaaadbceabccaaebbcdebabaadeeabeccddebbecdadaddbccbebbeaadaaccdeaebccebeeacdedacbeecccadeeaddcdabaabadeebaedebeccccadcbdaebebbabadecabedccedcadaabdcbacebabcbceebedceadaabedadbbdebddccadcdbdeedccdaedbccabdcaabdbabbdebacabceebcaedcebdddcdebbaeebedcdedddeebbabdcdeacbecebacbdaedabcdcdcbcbaddaaccbcbbebeecbdeaadacbddbcdbbcbbcacdaeccabeedeabeeabddbddceaeeeebddddbedecebbedebecdbdbedaedeedcbdcedeaadadbbdabccddbadbcceedbeecdeccdadeeabdbcbddcdacacccadbcaebaaebdcdccbbabdebdcaaaacdaadcacacadcdacceaccadecbebdbeacdbdcdabedbabeadbecdcaecdbaaceaaeaeedbdacadbeebabbcddcbcebabdcabbbedaaaceeeadeadcadbbcecdaebdbcbaccadbedabcdaedecaddacbcabacdcdebcdbbdbbbbbbcdeddaeddabbccbcaaaceebdcbddbebdaccedeaddecabbcbabbaceabcceacaccdcaeccaccbcbaadcbababcaeeccdcadcbacbdddaddeddeaacdadceaddbceabddddaaaaddcdebaccaedebabdebdcebabbaccadaacabdddeecbdaaebdecabbeedebdbeaecdbbeedceacebdabecedceccdcaeaebeeeeeeedcdceceaaacceeeceababbbdeaecedcdbabceaebecaddabdebcedaedaaaeddccaacdbdaeacecaababbecadabccdddbaaabbaccaebcbadbaeddeddbccaacbdecebeaeabaeeaeeecabdbdcbbedbbececccdecdecbbaeccdaacdeceaeeeabdbdceecabcaedbececeddbadeacbbaeeebadecacbecdececacdebcdeeadcdcdcecabebcdeacccebbbecebaddedaedccadebdabadacecdbebedeaedcaaedeebaddbceaebcbdabebbedecceabbeecdaabaaceaabcaebaaeedddecbbcbbdabbcabbcbacdcbcbdedabaceceeedbbbbbdacceacaacbbabdddaceaaacdaeeedbbacebbebbccceccdcddebacadcaebeccabaddeeaebdecebdecdaebbecbdcdebbcaabbbcedceacdeeebbbbbeaecebabceaeaaecbedbacdabaeaebcaaaadbacdcdebddaebbbcaedbccddeeebbebcdabdbdcaedcceeddcaacbdadbecdaecbbcecedecbadbbeaabbbdaadddddebdbdeeedadbaadadbadcceedbcabcdacadaeeeaeaaaebbcddbbdceebddedaaebaebcacaeedbceecddbaabdaaebeebbccaeecccbddccaedcebacbeabeaaecacddeaaebbadecadaabdbbbedbddecebbbdcebbadaaabacdddeeddccabdbdbeeecdbbaceabaceccaebdabbbdcbacdbeddaaaaecceccbeedebcdaedbcccbccecbbbbcedbeabedeabcbcaacbacacdaaeabeabdcacebacddbececaddbabcaebbebcedbdaeecadaaaccabddaeaacadccedeeeacbbbbbaeecbcaeddcdbedbbaacddeaacbeebdbbbacaaccecdebcbebeadcabcbbeddeebcadacbdcabaaaedeeebdcaedbbabaacbcabeaadaabbcbabccbcaceabceeacdecbcaeaabbcddbedaabedadeabbbeeaccbeecbeeddcbbebcbeedeedeecabdeeeadaedaeeaacacdedcbcdbabdaceabcededebaaeeacbdbecacddbceeaacccdeebbbccccdcedebccbabcecdceaaebdcbadecbacbeccbdedcbeaecaecdcabbbdaaaaaeccbdadddbebcbbaacaedceadbceabbcbebeabcdaedeeaaebeddbccebbedcaadebcebebeddaabbabbbcbdbceeeaddbdcecdcdecdabddaaabeedcaaacabebddcabbdabbcebcbbeedbaaebaeaacdbeeeeccbeaeecdbeddecaeebaddcdedadddccdeeddbdbeacaaeceaabbecdbadbdeabddddbdecbaeccecbdbabdcaecbcedbeccacaaeacabdacdbbadabecddbaceadadaeaeccbaabaddeceacceceebddabacbaaecdbdeaeccaeecaaabbbedebdcdeeedbcdbdbedddeaabcacebecebacbbcaabbcbacdccaacebaededabcedeebcbceabecabeebdcadceccbaccdaedccdbdacacacdbaaceabdbacbacdaeecaedcecabedeceacbccabbeebdcaabbdecabaddecbbedcbacbcddbdcddaeecdcaeacacbdadcbbadaebeaaeeabbecedadabdedaaddbdccdeeedacabebbaeeaedbebdcaadabecbcdaebbcbbedbecbaeeabccacbaceacacceebecdbadedcedabdadcabdbeccdbdadabcecbeaedeebbdadcadbccdbcedcadbdeaeabacdeddbabeabcdccdbcaeeaedccebbebbcccdcdbcdecebccdcabadcddeddebbaeabdcacbabeddceccbebdbbabdecdecacaadacaeeedddacacbbcbebeaeaebdedbedccbcccedaaadeecabddadacaabbdaddaadedeecacbeaaecddbdbcaacdbdbdbbeebbbecdbeccdaceccecdeaedcdacccccaeedcebcebdeddadbcbcaedebaccacddaeaecaedccdcacbeeeaeedebbeeaacccaedecaddbdbccccbacebabdbbecacacbcabcdbebddbaedcbcbbdabddaabeebaecaebaddbdbcecebaacddbacecdabcdabedadebaeaabcbbecedbcaacaeaebadbeadddabbbcdadeaeadddcbbebbedbbaaeeeecccaaaceabbddccaceceadedaaaeebdbcbabbbcceacebbbcadacabbcbdebcecabcdeecbceeeddaacadedeaadacedeeaedcaceebeadcdeeecbedccbabdebbdedbbdbbeaacdacaceadcddddaddbdbdeacbbdeeccccabaeeaccbdcdcdbccdeaaeccdcaebeadadebebbbecdedeaeeeaeddcecaccdebbcaedededbbdcecddbaedbdbacaaecacccdadacbceecbdccddeaaddbbaaeaaebddabecdbccbcebcbccbbedcdbadedccccdbdeedaacaedeeaebbceccbdadcceadbbbececacebcaecadcbaebaceaccccecbdbaeeedceaeddbaceaabcbbaddeeebdaddddeccaeeabaaaececdaeaeecccaaadaabbcdbbaacabebbeaceccadccabebbddbeaaeabcbeedaedbdeceeececdccbaabbdbdeaaaedcbbebbeabeeedbbaeceaedbccabedbeccdacbbaacaeadcecdcbdbdecabeeaacabcebddddeeecdbedaccccdbccbcaebaeececbedeeeedbdebabbbddddebccceeedbdedbbbdacacebdbeadcececdeeebdbeadbedbeeedaaddabedbacabedaaaaaaeeceeebbeacbdecacbdcddecebbeebcaaddbdedeccededdaccbedbaaedebeceecebbbeabccdcddbedbdbacaeccbbbeaacceadccdadadddbbcacaedaebeaacbbdcbeadceeabbbcdccbadbeebbcbcdabccaaaeeacccedbbdcdddddcbeaaaecaeaeebbadcecbbedabaddbbbbedebebdabacbeedddeebadcbacbdcbeaaceeeabcaceaebaedccaeecbbaebabedaaaeceeccdbadbbdadccbeeecdeaaeabbbdcceaecadadeedeadabcabebcaaacaeaeeebccaaddddeaebbdcaddeeccbddededadcccadedcbeaabeccdaacacbbeeeebdeaccdbbabeaebbdcedabcaddceaacacbbcdcdaadddedccbebbcbebbbbbecebaccbaeccbebcbdaeddccccacbaabcdebecdcbaecbaabbdeaeddeccdacaecdcbcacbeabaaecebcabcedabdccaebdcbccdaceacbacedeacddacdeabeaaecaddcdeeaedbcadebedccacdbeededbccaabaebddacedaeabebebaacbdcaeebaceceacbebdacacdccdeceebbdabccaaebbdbbedddaeccbdcbcecaecaeadcadddaddeccdeacedcdadbaddabcceadbdeddaaeeecbcdacbcaeadecabbeacbedcbaeacedaebbbbcedaedbeebbdadaeccabcadedddbeecddeceacabcebdeeaddacddeadcacbadadbcceecdaadaabbddebecbbabeaaaebacededcbacabbdcdbccbaebdcdabdbbaeabdaadeeacecddbbeccaaeaccbbcedbcaedcaebedeecdbabcdddebdacebecbbbbacdbceabcebdadabdeaaaecaaeabadbeeceeacbbeedebeccacccdbdcdbbddebdeccdbdadabcdcedddcbddaacbddaddbdbebbacdccbeadadecceccabedaebbaabbbbebeadaaadabdcecbeeeababceceedbddaeadbcbdaceadadccbdadeebadeededdddccdccceedbeecbaccacebbccaebbedcbebbceaeaeceaeaacacdbdeadbeeaddbddecaeeedbbaceaabdcdccddcaebbbcadceddebbceedaaacbdbabacecdacccebdcdaedadaaeccedaccaedaebdcbadbeabaedbdadbdadbdbdcceaccdccdacddceaccaaecaaedebbdadbdbaebcbdedcbedcedaaabeeecedbbdcedddabadeadcddadbbaceeeaccdceaaaacaeecaccbceddddeebedceacbebdcaacdeedabadbebeedaddbddddabcaecdadaadecdaaeeaacedeacbeeadeaabeaebbcadbebabdabeaccdbdaeddabdcdaabccbcacabcacdaaccadcaabccbbcdaeadeddeacdeaacabacbebaccbcbabedcaddbdbbcdbcbaadbabdcccecaaaacdadcdeabadcdaaaeecdabdcabcdaeaecbbdbdadadcbccbcbbbcbebacbdbeecabacabbabcadbcebadeebbcecdbeeedbeddcdacbdaaccaabcdddacdbaecbdabcadddaccbbdcddbeceecaeccedbdacadaebbeedeebebdceedbcbecbaedbdccdbccebcddceaceaaccbceeeeecadbcdaaabdaaacabebbdebeaddadeeedcacadcbbecdadcbedeaacccbdabcceddecdebeedbceedcbaaabcbaadaeacdcadbabaadbbbcedccbeeecdaaadebeccdbacdcdedccacebebacbdbaeaeedddececdbdbceacbbaecaedebcabdbbccbcaaeeadabeddeebdcbbabdebbdedbbaadebcdadaeaddcabedebbeedcadbdddceddbbeedeeebbdeedacbecbbbabdcceacecaacdccdedbaecbdbecaebbcacadecabaeabbdcbcabddeebcbcdedacbceceadecedbceaddbbabdeaaabbdcbbbaadebcdadccabeebdadbbaecbaaccddeeccbcedcbadbdccdcdabcedbbdbeacbddeaebaeecebbdcbbbeeddcceaedcacceddbcacdeeceeabdeddaeadbccdecceddbcdeecbacdabcdcbcdccddddacbdddbdbcbdebdeeedcabcecbdedbcddeedcaebcedabeebebccdbbcbbabbcdedaddcecdacdabaabddbacdcdebaeabdcabcbccebabdcbddbbeaccbdabdcdacdaacdeadeacdabddcceeebdacceecbceabedcebbebbaaeeeebcdaebabaceaebbadaadccbaadedcacedddebceeedacedaabecddcdecbbebedbccacbcaeccaaebeaacabeaceddbeabadaceeececadcceabbddadcddbbedcadbaccbcddbebedacddeecbaddcaededaaeaeeeabbaaabdaaabcaecadcbcedbcbaceebbedcbedcdddcabaaaadbadadacbbbadadbcbdbeedcdcdbadacaabdadbbdbdbddeeddaebbedbcbcbbbaeaebdcbbbedbaeddcbcabeceabbddacddebceadadabdbaeedbeeeadebcaddaacdacaaabacbdddbdcebbbdeddddbddedabebbabcaebabccdadedadbbccbcdaeabcccabdbadbceebecaabdedaeacdbcecbccaddcdadeebbeddcecbdaaceeacebdedcccaacdebdcbadddeeedbcbedabbaeaadabbbbaedbabbaabdadcaebacccaceccaccaadbabaddcbbcaeaccdcecdcaedbedbcbabaeccbccebbbcbaccdedddddadcdbcbaeccecabcaaddccadccecaddecbdcabecaacbddbccbebccbddabaeacdecabaceddacaabbcacaaabeebcbccbdbcbbabdadcaabccbdbcecbbaacebeabbcedccaddbaddcbeebeedbacdebebbadeadadccbeabaccedeeabaedaaadeaeeeeeaaeedeeaadddcdadcecdbcdedccbbaeeedacdebdbbbdaeeeabaaedabbcaadaaedacecdccaebeaacbaeaccabdbddedabadedeeabdbecaeabbdecdebdbccacecdeedbadadcdbabbdadeddaddacdabaebbcbbddbbdccdecdddabaeddaaddbcadcedccbdceceebedadbedceaaacdbcbbddcdedadddeeeddaeaccecbdeeacddbbabbcbbedecebaaaecebbeeeabdecadbcdabceaaeadcacebcddcceadabdecaedccedbdeeedacebedccaadcbaeddcacbbdcacbbeceddeddbacadcaeeeeeeeccaadaaebaccadbdcdbcaaedbeabceabceddbaabcdbdbabbbedaaceccaecdcbdeaabebeaccccecaceededcacebbebbecaeedecaeaccdcebaeecaeeedeebaebdabbddcceedeeebdaeaabeeecdeeccaabbaabcaeeaceadbcbdcededabdecaacdeadbacaccbacaccbbcddbedceecbdcadcaacdebddbbaeceacdcacccdbaeaddcadccacabbdcbcacbbbddbdacdceebccbbbcecacdaacccbaebcdbeaccdbaecddabceaaeeeddebecededebbdccdeebbebcdaccacedddebacbacbaaeeecabadbaaedcaddbbaadeaeedbeabbbcdbcdbadddcdbcdabdcebabbebdabbdedbbbebcbecdaebdacccbcabcdddbcbceecbcabcadbbcbcbadcaddaaaedaedbbdabdadeccaaebabdddaaaababadcbdbbaebdebacbbeabbbeabbbbddcebaedaeccbdcdeeddbaaebadebebaccdbbdeeeceecacbdcbcbcabecaeadbcaabddcccbbdcbdcbdcdbceacadaeccaaccedecaaccedceebeedddebbaeceadcedecdbbacdcacddaeabadbeadbcacddaedddcdbdccdebdaccbacabeccdbbcbabdaabdbbdcddecaeddbdacbcbeebdadcedcbbaddebcddcbddceebaeddaebdcbdcdebbdcaeceabbccdbccbbeddcadecabaebeceeecbdbabaedebaecbeddbecbabbabeecaeddcbadceceecdaabbaddcdbceaceccddbcdbdeedaecebecacecececdadbbbbecbaaddcbeaeeaaedddeddcebcadbabeaebcbeeeeabbbaaedabbccbbdeaacebcbedbddbebabbbaeebeeeeebbabbeabbdbaadcbcacceaaddddbacdebedeeebcacacccadaeeacdccadbcbaebcaacabdebbadeadcddeddcabadceccaedbcacebcabbbcbcdcccbaeddeaacabbdbeccbeddebbeecbbadedabdbcddeeaaebaeebaadeeeacadcccdcebceadebeeaeabdcbcbccceeadbdecdebcbcabbceacedaaabbadacceaebdcaaeabaeeaadeeeadeecedbcadbadecadbcceedbabbbeeaccaebcacbbdccdebdaeaadaedbccabaaadedebabcdaaaabdeaccddcabdadebdeaeaceddabaabddacaebbcdbdaeceabcceabecbacbcbeabedeebdabdddaccceeadadaaccbddbdcaeebbbdaedceeaadccceebacdabbcbaaaeaebbecbaaebebbcccdacacabddeddcebbdeacbacadacabdaceeedbbdaaecabaebcbaeceeaadeabbaecbeddaadaaccebbebdbeadbbdacebcbaacbbbeaabdacbcdedadbaeedbbdabbbbaebebbaceccbbbaebeccebdeeaeeeabcbebeaeedbceaddadccdbdbaecebbdcbaacdedaaddaabacbcbadbbbeedcbcddcdbceaaeebeaeaecdabcedeacbdedabaccbcdcaabcacceddcbbaabeaacecbbedbddbabadbecbadecacebeabaceecdebebedacabbccdcaeedbcecdddbbbdacabbbdeeebceebbcbeaaaedaedcaebccbcedacaddddaeedeedecccbbebacdedccebbdaededaebecebbacdbedeaddacaeaaecacebbcbaacadaacebacadaebddbadaecbaebaadedacaeaecdecdeccbabaadcccdaaaecedaaeadbadbbddbabdcddacbbeaccdeeeddeaeababeebddcdaaaadeedbacbcccbacebaccdabcbebaebddbcbdaadcaaddcabeaaebadbabbdeaabaaccccaedbcadacbacecaadeaccdeacccaeaaabcbeededcbabbddeccabbdaaeeceedddbeedabdceaacbecbeabeddddabdcddddcddebcacaebeaccabecbcbddcecaaadcddcbcdcaaeaddabcdbaeeebcbccaacedabbeaebaabbbcabccbbabbecddaceddeaebaaeedbbcddededccccaabebcceebaccecbbacbcceddbebcdcceceeadeadcbeadbdcaaadcbaedbdacdaebacbdceaaccbaadeeddcedaacabbcebdabebdedaccadaadbcbeddcdcdeddeaaecaabedbdecadceedaccecbabcceaeabeaeebebdcdcbedddaeebdedccedeacbdaccccceaebdcccdaaddeaeaebbdbbecdbdcbbcdcddccebdaaebbeeabdcdecaaadacaececdaceacdaedaedaceddcccbdddbdcedbbbebaaeddbacebeaadededcccdceaababecdeabacaccadbecbcdedccbaabbbdceaeabaaeeddeaaddcadbccbbeccaebdacddbacbaedaacadbcddbbecebadcdacdbcdeaabeacdcdbdcbdcdbeacbaeacbdaacdebbaedabcaddcaeaecbbcaeaccecbacaddbdbbbbecbeeadcdbcbeadeebabdcbadabdadeabdbbadbdcdabeceaadcbeacadbeedcdebcdccaedadbcacecbadbddbddcaaacdaaebcdccbaddbbbebdbcbbeeebedcebdcbaeeceadcdcacbbdcddaabeabcdbeaeadbaeeecdddaaacbbbabececbbdbbbadeadaacbdcaacccdaaddcedcdbbbabaddaeabaddbcdaecabddacabbeccbbdcdbcccbeebddadbaedbadcdccababaeacedadadbbabbbbcabadeebebbcdbbbaecbbaeabbbbbaaeacecbadcdcbbccbbbdadecbdcdaacddbbaccaeaedebeabcaeceecedeecbcceddddcbcdababbecbaadbcdcdcdccddacbaeaddbcacdcaacbbeccaeecaacdbbabebcaebebbebebddecdcdddabacbdcccceedcccceeacaaabceedabcbabaccdbebdadaeebddcdacdcebcaaacbbebccabbadedeeddebceabdabdddceacbceebccdecedceecedbbdadaadbcdeedaddadeeabaceeceaeadcdbadbbddeebcebadebddacbedcaeaabdedcaacdcbbddeabcaacccbeacdecdabdcdeeacccbabddaddbdeaddebdcbdecbeaeabddabdcbddacdeeebdadcdeaaeebcddceeaceeacdbccbeecbcceccdbbbcebbbaaedacaeeacaecbebaceadaaedcebeddecdddcbeceaecbaccaabcebdbdaabbbeceaaceedbddbacddcadcecedeabdacadcbbeaedebeaaceaeeccdcdcdbdbbaeecedbebbeebdaaddbbdedabdcbdbebcbcacbdbeabccdcdbdacaabebdeeceddaabacabddceeeebebeedcabbdebcbadcadecaaceddebbacbccbebadedabdbbdebedaedbccdcbaeaaedacaaaadbcbebeddbddedecbaadececccbdcacecdaccaddebccdceededdcccdcebdbeebcbedcdeabccddcbadedecbeddddddebbbeeeeacacddacaabbdecadbaababdbebebcbaaedcbccecaaacbcbadaeabbabdcccedaceabdceddabbadabbbaecdbddcaaeaaebbdeaebadcecdbeabeaacaedbacccbcaedccbcedeebecdccaaabcadcedcbbddcccddaeeeedcbaedeecbcadbecdcdeebbedbbabadcaecaecadddcbbaccddcddaedbaadbebdecbeedcdaebaedacaaddceeddbbaecacbbaeceeccdacadcaddceddbcdcdebcdeaacacecabccadcebeebdbcbaacdecdcbdbacdabcaadaccdcacecaebdbabadbccdebaadceedcceeedededeadeaadbadbdcccebcecaceecceaaddababbbedaadecbbbbcbcebcccabbccecbcacaedddcacdacadcbaaeeadeecbdcabbbabeebeabedeeeddbaceddcbbeedeaceeadeccaddcacdaaccbadebeaecddeecdbeabbbaddbcbcbbdaaddaceedaebcbacecccadbceaedcdeeacebeaabaececdcbecaacadcbeeccddaabbbbcedbadbabcebcbcddcbcedabaecbbeedadcaedebedaaeecbcaaccbecdcdccecedaadcbbdaadecebdcdcddecceeddceeaabdbcebebbbccddbaacdeaadbbabcdbabbcabccedeeabceeaecdbebebcceaaebdbcbecbedbdbcdaddeaddeaaebcebedcedcbecdcbdbbbdceeaeeeaedacaaacdcaecaadaaacbacecaeeaccbdceebcacecbdedbecddeeabaacceacccecdeedacaeccaacbcbddeabcecadebdceddecdcababddddcccabceddaaaacbaacdeaacdbbdbccdcbceaeeeecbbecbcccbbcddaeadcbaceabbcbeddaaabcceacdbceaadaaeedceececbcdceeedeacebebddaccebeaedacdbebaedadbaeacedaacacbceacecacebacbbdabbdcdeacaaaaeacaecbdeecbeddabaeacaddccbbdcaddbbaabcedbbceebebebcedaddcabddceacaccbecabdeacadbceadbcbcbaebdbeedbbebabbeaceaaaaeabcbeeeadedddaadcdeecdabcbdcbbaddcbcecdacdddddabcaaaabbcbeeadceeaccdaaebaaedaaccaeeceebdeebebdbbdadbededebbebcaeebbddbcccadaecdcbcbeccebbcdcacccbbddeecdbbbccbcddacaeceecdebcbddcdbadaeaaacadabccccbcceeebedabdbcddccbdadaddaeabcaabbdbbeabaeaaebebbeaadadccbeccbabbddcabcbeeacdbabccbbaeaecdccdeeddaacdddaeeeacddcaeebaabebbdadbdaeeceebbcaeceeaabbbcebdbdbdaddacbcdcdbcacdeddeddcbeeabbbdceebabaabaaaaeecdacebdcbeedaddebceecbddeebeaddeddbbeecbddceddabbedcdaeeecddeddbbeabbdebdddceeedcbedbebaedcaadedddeacbebacacebcacdcdedccebebdeceeacdebdebbeedacedadbebdccccddedcddabacaeabeeddaaaeeadbdabbadcdbccacbbcabccaddbbddecedadbeaeabebcaadabedaacbadbbeebacbeadeaadedbabeeadaeecabeececddbbcecedacccededcdcdcbecbdaededdaedeeebdddddadceadebaaabcbeccdedbddebabbcdaaaadebcbaabedcdccbedaddcbceacdbedbeceecdcaccbecaceadedaeadbcdaadecabcabbbeeebccbcaecdaeceeacdadecedccbedbdbdbaccddbadbcddcdaaddbeecaddebeaddaedcaedbdbadbbcbecddcbdcbcadabcbbecbcedcbaeeadedededbadbeebbdebcadebdbeabbeaaddeeccbaacacaeebbbeaaaaeddcdbbabadbdbebbddcdeeaabbcdceeccbeabeccbedcedbbbcaaaaeeeededdddceebeeeeeabaeedbdbbbbcaeccbeedeecdbddacaeabeacdceeaccbcaacbcbaebaacaadebaebdabaabaaaacddaddcbddbdcbdccdbcdcedeeedaacacddabbceacbbebddaaeecbceeeecadaaaaeaaabbbbacdbccbabdecabbdaaaebccbecebaaddddebadeabbeadadadbbbdbdbaeebabeacceeccdbeddeabbeccdececdcaecbddecbaddeedcacbdaabeecaebdcccddecdddabcaedcabacaeaebddbeebcabcdaedecdcadaccbaacceebdabbbecdbbadebbaeecbcccccbbdcadeaccabaabbababbbbcccddadbeaadebdbaabacdebcddddceadddacbaebeadadbceccbaecdabbbeabaeceeccaeeddebdbacbaebbbadcdbccaceddadcddadaddacadeaebdcddaebddccecbeedaeadacdabddbcddcbecaaeebcecbaeecdbaeaadbccbbdaacecbcceeadeacdcdcccbaaaebddecdddcecddbcaaeddeddceecbbbebdcadcaadcdbbdacbecedcbceedbceebbeeecacbaaaaedcaecdcacecbcdeabccaaebcaceecabaecbeaaebbeecbbaeadabaabeceabedbabdeabeecdababeaccbbdecccbbdddcdccacbcacaaeccdedebeccbdaaaaecedcaccdaedcaadedeadadbdeabeaaedabdecabacbeaedacbbebccaaaaaabbbcdeaaedebcdaceeaddbbbbeeabaddccddeaaaeeedcdebdbaeceadbdbaedcaeabbaceeddccbcbcbedeeedddedeedbecdeaccbaebbcbebeaaceeaabbddceeacaedccdbbdceebeeaabaadbdedacccdcbeeeecdddbddbecbcbecdebeeaceeaceabdadceaabbadbaeebeebddddabdddccdeedcabadadbbadbddeeddecdacadbbdedbcddeaedeeeaddbbbcddbdddeddecccdbdbabecceecbdcaabaccaeebcebaddbecbcdbbecadbcadbddbccbabeeddebaeacbdabdeceedabbeabaaaaacbcbdddaaceddeabecbeabebbbbabaccccbadbdaaaacbdbbbabedddcecaceeedeeaedaccabecbcaabadaabbaaaebbdeadcdabaabdecadaebeaacbddbecaeeebcadeccadcaaadddcdcccadcebeceddcbcdeabaccbdcbccdbacbcacdbaddaaceebebededcdceaaacebbeeebcaececacbebacceddccdcaeeedcbabdbadbdbbeddeaabbdbdbbccbbbdbdbeadddaadaaaddcddaddbccbdabcbdbcdbbeaaebdcdebcecdebdbbdbdaecdcaabedddbacbebaecdeeececeaebbaaedcedecaddadcebdddabacbcaecaeadbcebacceeccbcabdacecddabdeabccdddadaeceedbcbdbbdeeaaaabedabdadacceccdabaebdeaddaeeaaddacceacdbbadadebaaddabbaacadcdcbaeaacebacbbeddeceecedbddeceacbedabbecebbbdededbdeedecebebdaeededbadddcdecbbbcabdbededccebdacebeaccbeceaeedeebbeacccccaeacbaebdbbabcaedcdbebdcbcbbdbcccbbcbadbdcdaedeabaddcaaebcabcdaddcbbbaeaebdcdeddceeddddcbebaccddeadedbdbceecaaeaaedbbebcecdbcccdcedbadbacaccaadbaadcedadeacddbebddaaaabedaedceecabbdaceaabecddbbbedbcddacbbabeccbadaacbaddecdbcbdbaacbabdedaadaaabbbabbccecececdedcbcecbcbddccaecbbbeebaeaeecdbeacbbabaaaacddedbdedebedeeebddbecbbdbaadcbdedeedbaeededeaddceedccdadeaabaeedbccdbcbbcddceceadedacdaebaeadaacdadaebbadeeebeecdadbbdecbbedbacbdeaaaacdbbacaaeeddbddcdbbcbaaaadcebdaebbbcabddbddedeeaeaaeebcaebaddcdbdbeaecebaeabebcababcebababaaabecebacedceaadeeaaacabeaaccdebcabcaedbcbacddeccdbcaacdbbdaccbcdeaeccbeebdddaddbcbccabecdedcbccbdcdcbdddecdcebdeacbaaddedacbbdeebeeacaeeebedcceeaebdaecbcbcbbbbbbadacaccbadacdcbcaecacbedbdbddadacddebbcedddbeddcabbeedcebcdbedadccbecbbbbabdceebebacdcdadedbeadabcbcbdaedabeeddcaabbbabdeeebdbcdeadcaeaaebbbddddcbdddceceaebddacddabcaeebdabdcdbcaddaebdddadebaaaeababcedaaeeaddeadadcabbdaeccbacddbaddaeeecadaecebaabaeeabcedbceacacdcdbcabcceeeedbedacbeadaebdedcbbadbbddcebdaeccbabedbbdbcbedabceebaaccebcdaeacebcbcebbcabdaaeadeedebdcebaecaacebbbacadbebddecabedbeaabdaacaabcccbcaccaeccdadeaabebcadbaeeaeeecadacdaeddbebacbacbaeaeabcabeccbcacbdaadecbacdcaadcbeeebbccdcebcbaabdbdbabebecbceecbccbddcddadebccedbdbaebcaeebadcdcbcdcbdadadcdbcbbccdbedbcaedbaedbbbbdbaaebadadbbccaaeabaabaaadcedabebcebeedebacaeaebabadbdabbecabcdaeabeecacbaeaeedcabaaaebacacdaeeeedeedcbaedaceedbbedccbeccbaaccccabeeebaaedecabbbbaaeeddeaadeccdcebacbbbbcabbebddccccdbaedaeeceabacbaceaaeacedabdaebebdedcaebacbedacaabedebdcdaeceaacaaadbcedadccbadbeaabdebaeecdaebeaacbaadeabeeceeebcaecbdeacbdbadbccaaadcaaaaccbeeececcebbeebbeaaadeeecdbdaceecaccecaabeebbacaabaadcbabcbcababbcecbeaedbbcedddceeaaecddbcebbeeacceeebbedccddcdddadaaedbbdabbebddcbababecaaeebbdaedcabaeeaebcbeaeeebcccadebeeeeaadacdabaceacbeecadeabaddaeaceaaabacedebddeceeeddedaccacebedaceadecebdcbcbbedaebaaabbcbaadbcebcdddadababebcdbdebaabdbbbbbcbbbacdbcceceabaedcacecbcdbbecaaebecaebacbcedbbcadeaeebcabbbbecacabcedaebeededcddceaeebaaabdbccbcecbbbbcdbcecaeaceebadebbbbdccdccaacdecedecedbaacbeddedaaabacddcbbbedcceeaacbcdabbbdadcaadddaebbdccbddbaceebcbbdebecacddcacecbaabdbcbcbbdaacbebeaedecaaecabcbcedcaaadbdccebbcadabebaaabbcaebacabddbacdaaabbdbaecaccadaeeedcbedaecdcdbaececddcdccebcbbdaeeaccacedbdeabbcdddbadcdcacdecebadbdadcdeaddaccbabbecbcecaeeadddccddbddcaeecebbdaacbaceccebcdcddecdcdcedbcabaeaaadacaacaabacdcceeecdabacecbdbaddaddbdecaaaddcabcecaeaaaeaddadecbddbadeabccdcdedddceebcbebdecdbaeaddbdceacddcbabecababcbbdededceaaadbeceabacbeceeebbdbbbceaceaeaaecdbdeadcbaabaaccdaabecbcebdedaaacbabecbcbcacacadccedacecdcddccbcbaaabbacbaeadacbeaabdcdcaeacadecccbdcaebadbcceabdedaadcacbdacaacbedecbcdeecacbcebebeddabdcdcabeacebdcbaddbebbeccedaacadbcceacadaaaaeddbeebddaeecebcabdcacccdddcacbabaadcdaddacdacdebaaebaaceeaadeeedeaccdbedccaeaddcbdadceadbeabbcceecbeadaccdebbeceeabcecbddbeaaedeeddaaeabcecddcdeacdcdacbaaecacbeccddbdddaacecdacebbcaccdddcbecbcbccebcbaadcadcaeedecccdedeeedaaaeaaadecaeabebbdadcdbdbabebcdeceaebdbabcdeaaddeabedddeceebbdddccaecaddddeadcdbebccdedeababacddccecaccadbecebbebaaecbdddebeeeddcadacabedebeedbdcbebadcdedcdbbddedaadaabdecaccebcbbaacececaaaebdcccbdbabeaeeabcbcebaebcaaabedeeaeccacdacedeaeaaceddbbededdbadaaabaaddeaabbceacaabcbacbbeaecbeadebaedddbdccecdecbdbecdeddedccbebababdebdbadebbadebecccdbbdadaeedecebccbdcadddaaebeaaccdeceebccababbacbaecbaaeaebaceecebaabddcecdbaeaacccadebaaaeacaaeebdebbdccbbedbaeeaaaaebbabdacdaabedacaeadcbabdecaddbecbecdebdeaaaddaebeecebdddcdccecebeebeaadddbcddaadeaecdeddbabebbaceabecdedcbdebddcaeceaebaabeaabcedbedbacdddaccedabdccecbcedcaaccbdcebdebaaeeabcacacdaebdcbcabccbcccdecabdabdecebdacdbaeedeabcaccaeddddebdbeeaeedccbdabdcdbeebaebdaecdddbdcddeabaeeabcccdbdcebdbdebeeaccedbeacdaddcceeaedbaedeebdaacbcebeedacebedcbbedbbbeeeccdedcecdbebddadcdeeecaacabcbbcceeacaedeaadaaadedbdabebeecbedaaedccbcaebadccbeaecdeabdcaceabaabaaacdaebaaadebaddbdbeaebaaddbcaabcebececedddcbbecbddbbeadbbcbeccdccdeadcadeaaeccdbabdccccdcbbaeceacdecbadceabcccdeabeaeabcdcddeeddcadcaaeebcddbdbadbceaabdeacebbcdcccbccbcabaaeddebebebecabdeeaacdeddbaebebacaaddcbceeeabebdaaadbdcebebeaacbebcabdbbbbccbbadbeededddeabedbecaecabccaceedcdcbaeeebcadcebdbdababccadccebbedaaacacbbdddddcebdababbcacaadbedadebdbbecadeeabbdaecdccdcaecbacabbbdbcbeaeabdeedcdceaebabdecddcecbddcbaabdcacbbaeedbaddbdcabadbeccbbeddecdbdcdaaadabdbbeeaeeebaadcaadacebceeeedbadbeaecbeccaabebbdcabeabebbaceedadcdcccdacabbcbbaabecdcccedeaecbeaaaeeabeecdddcbbccbbbaeaeeabaadbcbcecdccbeaadbdcadcbcacddcbcbacdbcadbdddcecdedcbaaadcbecbecedbaeadbeecaabbcebecadbbebdbdadedeaccbebaabdccbeeecbaeadbbccaeadcbbdaeacbbdeadbdbabcbedcaccaaabebbaaedbccbdcbeaeebaaebebbaaecbdbcaadeabcbacacebcebdbdaabdeeeaeebeeabaabbbddadbadbbbcdaabccedabcceeaeaeaedcacdcbceebbadcaccebeebececedccbbbabadceabdccccabaaadbbbaacbbcdaaeaabbbcaadcaaeedaecbdebcbbdeceaaddbecbaecdcdaecbceddbedacbdeccbebebcddeaebdadcedbbcbeeaeddceceebbbaecabdeedecabceabcaccacbadaecacddccdcdadceddaaecadabbebdacebbbedcbbddbacedebbceceeabacbaedeeadcdbbdacdbceecebaccdaaaddaecdaeeaccabddacbadddbaddbcccbdcaebadedeccbbaeebcdaecabadaedaabebacadebdddadadccbcebceedabcedacededebbcedeeccaeaadbabaabaaaadccaeadcaebeddaaacbdceebeebddbdbdceaaccadecaadaaabbddecdaeaabadbababdadcdccaaccaddcccbcededbcccdcbedbceadaabaeaadebebbabedbbccddccecccceaacbacbdccddbbeeeebcdbcbbcabcbaebcdadcecdeacabebeaaaccdecaedbbbeddcadbccabaadccecbbcbebeccebeaaedadcabccdbdbaeedccadbccddaaddcbbcadbbcaadeeaacacaadddaeceeacedcbadcecdbbdbceeadaecbabacbadbddbdecabadcbdeccebeeecbabdeccbdcdcdcaacbeddaaeadcdaccbeeedbaaaddacccebbcdaacebaedaeeacbcdbbecacaecacdaabddbadecdccbcbdccaaaedacbbbcdcedbeeeeabeaebbecdadcdbeddcdbbabbdbdddbaecaacecaeecccdbbbbabceeddebcddabeedecaebbecddbdadcceadccdcccdbddbadadeabceecbdcebeadcaaaedaadcbaebbcdbcdbcdecaeabedadcbceaabeacdedeabbaaccabbabdbbedcabecaaebacbeacebaabbcdedeaadecdeabeaececddacbacbbbeaeacdaacbaacdeedcbadeaceabacdabbbceaebaddebaebbeecdeeacecbaaebebddabeabccbbbaddcaaccceceabdeeebbaabdeddebeddbeddcdddddcccdbaedcccaabcdbadcaaecddbedaecababeddacbedadeddaadbdcbeeecbcaaacbcbcbdbbbbbeeddcddaabedebdbabbadacacdddcabbedaeadadebbcebbbacbcdcceecaadaeccbebdaeecceadedadbaedddedecddeddaaaaadbbeabadacdeadceaeeaaabeeaddadccbdebbbcbdedccdebdcbeeadcecaaedcdeabddeebddbedcaedbaeadbbcccdceeaeecbaadeabcaedcdedaeecabbcbbbedeaabbebcdbbceaecebebedbdcaebaedcaccdacbebeaaddbddecaaadcabecdbcbecceeeacbdacdccbecacdaadacccaeadabcedadcbdaaadacaacbddebbdbbadccbdadbbbdaabecbacbeedddcedebceacadbcbbbbdbddebeeedbabdeeadaebdbbbdabccddecadcaaebdddeccaceebedcaaaaeabccdeaeacdcbeaaebcebcdaaadecccddbedaaebbdebbdddbedceaadbeeeeedbbeadacadcdabecedcbddcaabcedaedeeabecdeaeabcacaeaebdedbedaedbececdecabdebcdedabadcadcebdecbbadcdbeeabecaaeeddabecddcbdeebeccebabbaeadadabbecbbecabcdbaeeddcdcdeedecccedbdbdaccbacdaaebcaedddadcaeccbdccdaceccbedecbbbdccdddbaadeeddabeeabccdbbabdabdaabcbdddeaaaecedbbacbacacbedebdbddbaabcaddebbdccbabbaebbebdbcddaecddbcabbdebcaebeccdcadecceaedbbcdddcebedbaddeebbaadddbddcedecbbcccdedbaaceecdbedbeeecbcedddcaeddedccedeaddbdcaaeedbcebdcbbeadcbdeadcaaceddcbcedcebccbccaccaedccbbdbbecaabaeceeebbbaebbcaebdedbdaaddbaddbdaeedeecaaadbeadaacdecbdecabaddabbbabcbaadbdbbaabbeececeaebabadaaebedbcadbaeedadbdcdbbccdddaedbedeecbbdccbedbdbabccedadceadabddcdabcabcddcdedabeddadaabaadeadbedcddcaabeaabaacabebeadbdbbeadecabcbcbbdddeeadeedaadcaebccbccecccbbbcdbebabeaedadeddbdcdebdcacabcadbacddbddbbdacbdceeeeeabdeccbcebeddacdbdacbaeecbabccbbbecebaebddacedadddcebcbeebeddcbabdbbacbdeadeeedecbedbddabeaacaebebbdbeaeceebbadbecdbceeeeabeeceecbdaaccdcdbdbbcaebcdbcddabdeeaeeaaebbadbecadaccbaebabceadcdedbaceebeadaacbeacaccbeddccbbabedeebbcdbadbdbadbacabeacabbadcccaaebabedcbbbabdaecadcacaaceceaccbbadbebdeabcaaeddadbccaeadaecddbbabcbcbdddcbbccacdcaecdaceebbecedddbaddbaeebcbcaacbddccabcabddcdeceeeecdedebcdbbaccccddcedadebcbebebcbecdeeedebadceedaaecceebcbedacadbcbcadcdddcadcedbdbbddceebbbbdcccbabceeebedbbaaeaeadbaaabeeaabacbdddbabaebccadaedccbdebddbdadcbdbbcababedecabecedaddbeadbedadddadddbadeedcaebacbedceebaedbccceeceecdedbabbeebbbbdcebabdbeaebeacebbcdededcedcbdbeacdeaaeecdddacbadbbaeccbddeabaaebdbdedeebcaddaebaadaececdcdacabdaebedeedeedbbbdabbcdcceccbbdccadddcadabebcbbdeeeabdeecddaebedaacaacbecbbeeacddebdbacbeaeaacbdddbdbccadcdaeacbeacebdceeaebdabbcbebcaaddaadbaeacdadeaababbceacacdbbeeadacecdceabbadcaadaadbdadcaeccbaaddbcedeeccaddbbaecbabbcaaddaaadaceedeecaddeaacaadbebacaecdacaecdaecaabdabacceeacbebabcebedbabddcccbdbbdcbbcccbddeebbdbcdbddbdeacbdceeedebaccceeedadededdebdcbbdadecabbddbbaadaaddbbcadcbedceccaaabbaabdbdadaaecdddbcedbaaccedcecaadaabbdcecdcbedbdadbdccecdbdcdbaadabddeeaeccddbcddebacadecebbebbaaeeeaeaabbddbaaadcceaabaebadaaeadedaaebadaeabbeceacabcbaeccabcaadecdceecbebacaadebddbbbcedcacceaaebadcbdbeedceaabcadeaadabdccceaeacdeadcebaeeddcaeadebadadbaeadcddacebbdebcbaddbcdaddabdbeaebdcbcbbacbbebebddadadadedecedbddddadccebdeccbacadbdaccdebaccdbbbbadeccdacccddbbaebedaaceecbdbecbebcaaaacbdbbaaaecedebdbceaeacacedbddecaabbcdedacedcdeeecdcbeeeaeaececaecceeeaaddbeabbdebabccbdbbbdecaaabbadecccaeabcdbdcbdbebedcbcdbdebebcabeeeebeecbbbeabbceccaabaabdeddcdbbedadceadaecacdbcdbbdadeceeccebdbcabccebcddebbeebdccebdabcecedadacdedbeaddbeddeaecadaaabdacdeebebabceccdbcadbbbecdbdbcdcadabbbcdabedbbebadbecacebcccdeeebdeaaddabacbecdeedeaccabadebedaeecdbbabecceebdedbabbcddedbacdcacbcbaddaeaccdcdabacecdbbdeeaaabadabdbadccbdbbaadaccaceadeceacddaaaccdebeabeddadadeeccbdcdcecacddccacdbbdebbddababadcaceabeaccbeccccabdeccbdcbdecedeaedbeebaaabeebaddeecdebeaaabbdbceadedaebbddaeebaecdebacebccdeaacceedddececeedabcbdcdeeaceddbbccdcdbeccceededeaacceedadccbdddbeebecbebdedbbdbbabadcaaaebcadbccbaecaedacdcdacbeccaecdbdbdaacecbadbdcadcadebcbacaedebbabbcdcdcdcddbbcceaabbbbcaccdedcacedbdbdacdedabdabcebbaeaeaaeecbecbaeedbcdcdadcbacdbcbeabedcbaddeccacedecbceabbbeabadbbcebcebcacacdabdabeecdcdadbdeaaaeabdecacbaebceecbcecdacccaccccdbdabeaedacbaaeadccaeeeabdddedbaedeeccededbdadceecadbdbddecdddeaabaaadacbbdbeaeeaabdedbaebddeddabaaadbeccaccdaedbbcddebbaedabeecdbdaacebbcdecdaeecedbabaebaeecdddbbeebbdeeebadeadaaabdcbbbacebadbccebaebedbebadcabbbdeaccbbbbceccbaeeaedbbdabaecabdeaddbeccdadaedeccaceebaebceeeecacbbeabadadcedceadbaebabbcaebebacebdbeabeedeeaaeeaedcedcaceaedabeeeceebaaaecebcdceeabbaebddabceaaadbedcdbcbebaacbeccbecdaacbbaeaeabaedeeccbcbbcdeaacaeedabbbaeeccbabbccedbebaedebeaceabcbcbdeeaaadbdaecaebeeabadedaaecaedecaebdcabedaacbeacaebeccaaccdabdbbeeaaddaaaabcaeadccecdabcdaabcdedbbceeedacacbcaadaceecacdbcebeaabcdcedeaacacaaeebcacdedbeaecedeecbedcedeeadacebbcaaabeadcddebbddadebeacabbadccccbbacdeecdaebecccbcdcceeabdeabadceeccdebeaeedcdcceadcbbeccedaeccdedaccbebaedbcbedcbcadabaecbeacbeceacedddeabddabbaacaabceeebdacedaeedbbcecdbadbcedccecadbddcabceeacbbeccbcbceebdedabbbcdacbcdaaaabcbedbedeaebecedcadedebaabacdecbdacacccbeabbaeecbbdcbcacdcaadcbedaebaeabcbcaeccedcdbecdcddbecbaddcbababaaecdecbcaedcedebdeeabedebeeadccbdcbacdadaebbeadbdcaebddebbcceccddbccacaedddacaddbbcabcedaaacbaadacbcccabeeebeaeecdadacbacacaedceabeeecedcbabbbeeeedebababbdebcdaedaedeebbdabaeabcaecdbecddcdcaaecdadebecaddeceaacbdedceeeabbaaaeedccedabeceadabbabdbacdcebbdcecbacecabdbebaedbcddbdaecbcaabcdbbaebabbedebeecbaacdeeecaabbebddbdaeeaaadccbeddaeecdaaabacbaecedaebdddeccccbcddcdaddbeaddebdcacdbccacbcaebdaddcabbabeedcabddabcdaeaecedcdcdddbadabceeaedccbbbddecacbaddcddbcceeecdbebcaadecaccaeddcebcdedebdeccaaebbddeabdedbbacccdababcbcbadcaaabbbcedcdadeadceadbaaabddadcdcdeeddccaabeeccdadaacdecaebcddbcabddadeaededaedacdadcaadcecddacbbadabdccadddcbdeaadedbbbddaaabeacadabedcadbdcbeacdaebeedeccaadcdecdbcededdabcaedbbbccaedcdceaedbbdeadaebddaedadeadcaaedbbeeecdddeceaeaacbacacdebbacbdaaababaccaedbacceecdeebdcebbecdcaeeaabeaacadbaedbeabbaecededacbedbbceacaaddacabbbbdacaedccebccebbcabccdebdeaeaeaeccbaaabbdccdacceaaedaeedcdbeadabeceeadddbeddaeacbedeeabaacbbacbdaeacdbaeaaaceacaaaebeacacbbacceaceeebdcbcdeedaacacaaeeaabdbcdeaeeaaccdeebdbabdcabcccdcbdbcdbaabbbabbbebedeccdbdbdbddcdeabdbceedbcabadddbebbabdbabceddbccdbcccccacabedbeaeaccbebecdaddeeacaeebdceadedadbddadcdebccebcdbbdcebcdaeacbceacdebdeacaacccebaacebacbdcaccdecdadeecbcebdcaaadeceabaccaacbadeccacadbdbaecbaeceeecceacaedcdbbaadaeacaccccebaeecaaabaabbbedaecadaaeaacacbabdccdbaababaeecabaceaccaadadabeadbdaaedeeecdeecdbabccaebddcddceadcbeeabeceabaeddbdacdebeccaeabbbedccdbcdbdddeeebbbcbeebdccdebcaaadddaecdbeadbcccebaaccdcaeaeedacbebdccbacdaeaeccecddeebbbaeabcecbcccbbadaecdbdeeeabcebebbeceedeadcbbebaebbeaedcaaebbedbecbcbddbdadedadbbacdbdaccacdcecdcaaceebbeaecddbdeccbcceddcccecadcaeabbceececdaccccdcceebcdddcbbbedeceddaacbeaddadaaebcaedecdedcbbacbaccedbbbeeedaccbecbacebbcdbabbbcaaeceddabdebdbdddcebeedbceddbcebbdaeeaecccbbbadadadacebddeaadbcaaebeeceddeaaaaabccadceadcceaededbbcbbdaeccecaeaaebdbadddeebadbabecdcbcbedeadbbbebabeddbebeecbabdcbbbbcbcbcdedbecacacacbaceddaddcccbacbbbccddddeecdbabeeebbacaecaabdeebedbdaeebededacbbbcbdbacabccaeecbceabbbccdaacbdddebcbbbcbaceccbceeeabdcaedaeeabbbdaddcaccabadcabadeeacbcbbadeeeebeccbddbbbebcdccbdccddbaecdadeabbeacadeedeeedbddbbeaaecbdcbbaacdcddaeeebceaddddeabdaacedecbdbbceedcacdadbbbbbddebdabbaadccabcbdbaedbaeababbbeaaedcbdedbeabcebdeddababdddadbcadaeedddbdeddebdbaccddebbaabbbaaedcacbbbadeccccaceaeaccbabaeaacddedcaeecbeccacdcdeedeebdedacddedeebeabeacaddeaedcddaeeceaaceaeaeedceabbaeddddcbebddebbcabdcbddabaccbbecbcacbbbccdabdcedaedbacabebcdadcaceabbbdcebecbdadadaeabdaabceecddcbebbdbbdabbddbcdcddecccebebbecaadaeebaaedbcdbbdddbbebaabbbdaeabbdddacccabcacbbedecaebdcabcbecbedaddddceeabdccdbbaabcadaeecddbdecbebcacacdebabbcedbdadadbaaeaebadeddeececbdbbeeededbcdbccecccabdbbdbdddedccbababddcaeaedecbcdceeaebdadcceaceadbdcdbabeaddbbcbbcceadeeeccbeedecdeeaededbadbecdbbbbdcbecdcbaedeaecadbadabecadcddabcdabedcacdbcaecbeaeccbbcccdbabccddcbcedeaecadceeebcbdcbeddbebeadaecabebcebaadbbdebaddcebcceadaddceadabccdbccdaceebccaccbdeaeddccbbeabdebaaeacbabacaabadbcdacbbbdcebecebdeabdccceaddcaebcbddbacccacbabeadbeddadbacbcaddcbeedcdededaabebbaecdeebedaadceecebcedbacbdecaacdceeaedbbcdcbacacadaedecdceeccadaadaacaaebaadcbebdeccbcbeceedeabaaaeaeedabdcbaeecadebdebacdeaebacbecacaddaaaeeabddedcdeeadacadebeecbeaaedbdaebebdabbbbbddaebbadebdceeccedbdeccccbedebacceeadebdcbcddcaebebaecceaedaccbbbeaddecdacdbddaecdebdaeaaebddccbbcaceccccdcddbaeeccdadeaceabbcbeeeabcebcabacaccecaaacdaddaeeebbbacdcbbacaebdeaddcebcebddbeedcbbaebdadaceadceccedacedbbcaebeeabbdbcedcedecadecbedadabdedaedabadadeceedaebabdcccbdaabecbdacbbcdadaeaddbdebccaaaaeeecaacacacbdcdddbddddbdeadcbcbebdbbecabcbeaaabcdbceeccadecbddabaedcabecbebaeddcaeaeeacbbcadacabceccabbaebabadadcadbaaeccdeaedcebbeccecacddbaacaeaecaedabcabaacdbdebdeaebceeaceeabbdbddcacadadceddabeddbebaadbcdebcccaaeeaeddcedceaabaabededddcebbbeccabbecaecaaabdbcabbcacbdcdbaeebaadbccadbdacdcccaaebdeeecdaecaccbaaebadeecccbbbedebecabdccaeabdcaeaebbadcedbbdecceaaecdaaaadccaecbcbdbddacdcdaeaeaacabcbbdbcecaccbdaeabddccebddedbdcbebbdecbcabaebdeebaeaccbcdadaccecaeedecddcaacbcbaccacceceadededcdcdecbedddbaaabddadbbaaebcccaebaeebdddddbbdbdccdaeeeebcdeabcaadebdcebdddceaaedeccbdebecdcceedbccbddaeddaccedaecbeabbbdeaaeaceecbdaebcbaaaaaaaacdacebacdaddaadbbacacabbdddcbccadccbebcccebcebecaecdceeabacabadcbdeeeaecbccedaccadaeadcaaddeaacabedbbbaddcbeeebccdacdabddbdcbdbbecbdedeccecdacdadaabdaddcbaedcebddedbcdccbeaabdaaacddaeeedbebeddeebbaadcebeadebeaccbadddedcdbbecdbddaabebdadacaccbedcdaacbbcabdcbaaedceecdbaddeabbecbdbeacccaaaaacabcddedcdbcccdabdacaebbdadadaebeebadcbdceadababccadeaedecbaededdbabedeaeeedeeecdbebecdaaacbcaddeccebcdeccaebdaaddddacdeccbacccececbcbdaabddcabebadadcabecedcadbcddebddbadbbbdbaacbacbdbaaeaaebccbbbadaebebdecedadcadacbdacbebdaebdcaeebcbebacabdbbccbcececdaadbedcdcedadcdabceeaceddaccceceaaedacebdaeaceacccecaebabeadbddcddaeedcabbedcedebdeedeecbbebcdeddbbddbecabbbdcacacbbebbbcbaacecaaebaabddbaeceabdebbdeadcaceccbedcabdeabccbdceddaaccaceeeeebbcaebcddeaacecbdbdeaeadaddbadcbeceacdeacbdcdcdddabcacbaabdeccdbbdadeabbcdacadeaabacbbeebebbeceedbeedbdaeccdaebaeecaabadbcadaacccadeeaccbcbcaacbaaaedaadbabeddddbdbdddceabacedddddccddacbbcbdabcdbabedebbeabadddacdaaeebbcabaccaddcacbabdddbaddbbdbadbaeeeccdeaabaebbedcabaaeeedbcdbaaeabaaacaeeacdeabcaccdbeadcbccaccccededeacbcbddebdbddaceedaacbbabeedecbbdbcadcedeeeeecbbadedcbeabbacdedebbcdbebcbadbeaddeddccecbebaeaebbbcabaedbedcddcbabbdddadeacaaebcaeedaaabbececdadaaecbebcdbdeeecbadedeeaabccdcdcdaccacabaadecdedcceaecbebdcaeebedcbeadebaadcdbbedaccebecddcebccaebdececceabdaaeaedbadabdeabedadeebeeacdaedadcbaadcbaddbeeaabecbbbaaeaebadbabcabcabbdddeabebaddaddaaebeddcecdeeecebeabdaacbbcbaaaacbbcadadddbcdcbecbbcaebdedbddcddbceaaeaaecdaaaeaccddbdaedeebbeeeedeaadaabbceededcbbddadbaceeeeadcbcecabddcaacddddabcdecaaeeccbbbebdaeadbadcaddecddacedceecdedbeedbcbcbedadbcaadaeccadeabdddadbabdeaabccbbabcadaaabacbedcaddcaeeccaebcbdcdaceedccbcedeacedaaacbbbcbbeeddcabcdcabbcbbcebcbdbabeeedbacdcdddddcebadadeeeddebabadebabececccaecadcccacdbcaebcdddbeadceaecbabebdcdbeebabcbcdcbdccebedddbbcdaaaaabeadeddcddbdcbebedcbeabebeeaedccbddabceedbaddbeccaaceedcbababaaecbcddebbbcddacebaadddccccadaecadeeaebccdbbcbdaddeeeedeaecbdddcecedcccbcaadbddcbcebbdddcdbcecacdebdeceaecbbcaaecdaeaebebbbeabebcddbcddbbbdcabaadaeeddabadbddaaeaceeeddebedbabaddebbeaecaacaedbddaadabbacaacabeadabeddbcbcdadccaebdaeecbdecebcaaadaabebbedecaeadbbcaaabcdebacdecddcdaabcdeabbeddcbdededbcedaccbccdebdeddacbeccdaeddeecdbadbcabdadddbecdbdbbaedcbcabecdeeadbcdcbbadacddaebecdddbeedbbceecadcddedacbdabaaddbeccbacabcbcaacddeccbbccdcdbdcbcccbbeedcaccbaeeaeebeeeceaccdbebaabddbcebecbaaaebbcebdadeacdcdaaccdeddaecaabebddcbaabdcadedbceadeacbabdcbacaeacedeeeccdadeecaceabaacebeeeaadcabecdaccaecbbbeeadbcddecbdcecbdededbdaddcdbddeceaadeaedcdaeaeeeccacdbdcbaedbcecacdacbbcdadcdcceedccddcaaacaadbbaadaaabeececdcdbdcbbbdaecccbaeadeadacbbddacbaeccedcbbabdedcadcedbacdabebadbccadddccdebbdeceaeecedebddaccceceadacccbcdcdcedaecdbcddeaddaabddbdcdcdaedcabbaebaedaeedacaacbdbdcdecdaccabddddbaaedcbdaedccedacecddeccedaecdcbceaccceadcdeaebaeabdbbcbdeaabcaebcacecedeeebddecacebaaaedbbedeebebcdadbeaecaeceaaedbcdcecbecadcdebacdbccdeadacacbdaeeacbdadabcacbdaaaaecabbbecdaceeaacceeebdadacbceccadedbebdeceabcdeddbacacdddddddddeaedaaaddaacdbacccbeabaecadeebdcdbcaeeacddeeabceebdddababedddcdacbbeeecaeabddbbbadeabacbbcdeecabbadeabecbaeacecdcddbccaabddacdebbadcbcedbabaebcaacdbdcddbacebbaacedecaebeabadbbdacecaadacdadaedeaeeabddddcccddadeccdeddacccebcdaeaacabcdbabadddebaedceaceecaccbebeadebabbaedaabccaceeacecbcbeeebecadbeecddcceeeccbcaecdddbdbabcddeecddcddeeeaadabdbbbcedbeeabbabacabedabddcdcdabddccdecbdbadcebdbccbeccbdcddbeaedacddadbdabdedcbeabcbcdddbbbdcccdeeceaabaaaaccebcbcaaccddbdbedcddbccdcccdebedeadbccdcdeadddceeaaacacebacedcaaaddabcccaeeeadecbcaecabbabeaccdeacecdeedeccccbcdeccacecdbbdaeaecaaabbcecbbccdedbbdbbeacdccdacddcadadcdcacbeaadecedbabbdcdeccecbaccceeabbcadccdededbcedbbeebdeccecdcebcabdebeddcbebbbebcaeeedbaeeacccaacddbdecdecbaceadceeaaadbbbedaddcecccebeeddadacaebdabecbdcbcdbdbbdbdddbdeadcccdccdbceeaebaaaeadedccdbdacdabaaadbeaacdabbcccddbecbadacadcbbacebcccbacceabbedceaeecbdbecdecceddcaedebcecdbdebbdcdecdedbdbecdaaeacccddaedbaceeedeaeebeccadcedbbdeabbdccadcedebeaabcadbbebbadedbbeeebdbeaeeeadbbabadbeabacddadebcbeedeaaddaeeaeebeddddeeebaecccbccadcdbeddddebaaedcbdbcecaadeceedeaaaebebddbabeeebadddeeeaccebceeabccadbdbeacdadbdceaabccddbcabcbabdbbebeccbdedaddcabaedcacdeddaecacaceaaeeedecebcaeaecaaabceaaebebbbbbceaaadcaabdebabcdedadeaebadeebaadaaadadacbecedaacbbcdebaededccaecddaebecabcdeebabeaebabeeaadbcdcddbcaedeeedbbccecdaaeaaaacbecddbcdbddeaeabbbcdecebadeedaedcaaeadeaeebccbaebeeeedadbbeeadedcbcecceedaececdbeaadeacabcaaaecceecccddaebdacccdbaaaceaededcbdabbcecdbaecabaeebccdccedeccbddaccabbebabcaebacbdabcecddecdacdbbedcbdacbdadcaeceadbbebbecabccedabcbbcbdeceddecdcaeceecdcceebdcbcbdcebbedabddccbaacaedbebcbaebdcabdbaabbaaebecbcbdcbabacadcccedceadeeadadeecaabeceecbeeddeaedadeadcedcebdbbbcacadbbeebeeacbaaebaddcbbbcdedddeecdabbabecccecaecccdcebcecdbccbdcdcadeaabebaaebedbbdaabbdadecaddbaceebeaeebaadabedbcececedbbecdcbbdaccbadbaaeecbdeeeeaaecbcaeddaabccbceeebececddcbcbbdaebebdbcbeabcacbceebbbdccddcebecbeadbdebdadcbbaebcbaacdcdcecdcdbceabceddcdbecdedcaebadeceaebbbaabdeedecebbaacadabaaaabedbbdadeaacdbabcbeadbadcbedaaededeeeaeebeebddbcccdaabcabadaeaabcabcbbbeceebdabeeecdabbacaaecdadadbcbdddaddabceabceddbebcabccdbcddbcedbdbcaabecadabbbeaaecebbeecebccabbdbdcdebabeedebacbccceeabeaeceaacebccadccdcbedbadceeebaaadbdebecbceebbbbaadbedcecbaeabcaebabdcecceceadeccdacebebaabedadaacadadbdeccdaadbebbcbabeeadddeabbebcacdaabdebabcebaaabddeadaeeebbdeccdcddbacdaeadbdaedaabcbbcddeabcedbdeceebbdbaabbeccabceeddcacaebdbabeaeaddbbdabecbdbcdbbdbeeecdbbebeaeeeabcbeaecaedaedbeabccdaceedaaadbebeabcbeccadaabacaddaececbcddeecdcbdcaedbdebbedaecacbcabcddedcadaceeedcbacbaddbcadcebcdecbbbccacaaadbecebbcdeccbbedcacaeccecddecbeccccecdaaadbdeeddeeebdcbbcccecbacacddbecaeaacedbecacbadbdbadaeababdcceaeaacbbcdddeeeedecbcdaddecaedbdacbdebdbeaabacbaebadebadbcbeababadacebdccabebaabacedddbbdaddaaadbcbaecabdbeedacbeadacbbcedbccccbdbcedaeeabbbacddbbdebdbabcbedbabeedcceedccccbcbebccebecbdeaaaabeadbbbadeaeadcdccaeebeebaecaecaaddcebadeacabcaddaeacabeabedadceaecadddbccabbeeaadbebcadbcebcbedbeeaddeeeaabddbeadbcaacdddcdcedaaaadebceeabcbebebcdbecaedeebdbcbcaaccaeccbcceaeddaaabacecbabebbaccababecbececedeabbecdbbeddcdeabddbbabbecccedadddabbcdbcecdaeeaacaacdaabdcdbbbbdedbbbabcecbbdbbcdebcddccbbecbcbdaacacdbebbcadcaebbebbccbdaccacedaaecbdeccdcccaeababbbbaeecbdebabcabdddbbdcbbadebeaaebccaeaaeeeaddaeedcaddeabdcabaedbbedcbbcccdabeccbedaddbddeaebbaeadbdbbdadcbedeadabddcebbcdeabaeebdeacaedbeccdaabbbaebcdceeccbbeeecdabaaeaddddaccdeceabddccbdecedcaaeaedbbebacdbadedeacdadacacdcbabcadecbbaadcbdcdabcbbdabadbaeabebadcbadedeaddadbceceecedbccbcaecaeedecdcabccdaacdbcaacacadbebdddbdbbcededcdbeacdbcddebeebdeddceddbcddadccccdcdddeccddbadcbbababcdacedbaeadebaccbcbeeadaedbeabcdacbdeedbeaceadbeacceddedcdecdabdeeaebaadbbedabaaabebccccbcdddaccdddaedbdadddbccecdabdcdeccebeedbbbeadbabcbbdcabebeceaceacbadbcabaaebaeccebaeabeadaddbaabaddbabbbbebcdceedbcccecbacdccdbedbecadbaaadcbbbaeddeebdccdbccacbeacbcabccbbdbbaecbdbaedaaddaabbeadbeaaebbadedabdacdbcbbcecebaedeadaeacceceedebabebacecedaeeaacbaabbeadecccddbccabbdbeadcedbcadbaecbaeacaaaddaceabadccdbdedbabddebbeceaabbccecddbccdddbbddedacecabcdbcdedebacdededebcebdbccdaaabeddbbdebebdcaebdddececadacbbebbeaeeeadeaeadbdcceedecddebebacccecceeebebabcaeaecbdabedcbceebbabcceaaeaeccadbbdaacabaaaaedbaadeaaaebedceaeaedacceececbecbaeaabeedabeaebdcbceaacedcebadbeadacadbdecbbadcbeeaacbbeecceedebedcddcebccabbedbceedaccceecddccecbbecaedbdadcdbecdbdddabcccaecaebaaabecbbecdceaceedacaebbeabeacccebdbcbbaaeacadbebebcddeebbebceabadccbdddebbeccaacaeaedebddbddebdcbbdcdabdaecaebccaceabbbedebceeabaebddaecdecbaedbacdaebcceddbbdcbbececeadbdbacbdbadbedcdcebbbaababdeeabbceceeaaecdbcacadedabeabcdaeccccbdabbaaceecacadddbccdbcdbbaeddddbdebeecddaccccdbdccdccbdebdecdbbdbcecaaabababbbebacbcdabeadaeacbcdeeacecccddeedbdaebeeecdccccbacddbdddababcddeaaaaeeeddceacadaacbebabddeeecbeaecbbbbacaddeeceacdbdbccdedaeecabcebedccbdedacdaecdebedecadcbaaecddaabacdeaebabbeacecbabcbdccecabbbdbeebabddecaecbebcbbbdbaaddbaceecbecbddadebaeabcccccedccedaceedcaadcbdbbcddaecedaeaebcacdeeddadbbcedcaaeacbaabbaadcedbbeaabceaccbeddeddaadeeeecccbebeaeddeeaedaaaecabaaebbddedbecbcdeacbcbeaddcbaacbacdbcdceabcaececdebbccbeadaeebbdadcccdbeebadddddeeebdceaabdbaaabdebeaeacccedebaecacbcbeebdeaeeedddeedeccddbadadeebcccecabbcacbcacebdeebacaceaedcaabcdcecbaeeaeacacceacbeabcbeddaabbdeecaaccaabacecbaaacedaccecaaedeadbebdccbbbeceabdacaeabbcdcedabedbdeccbdbbabaabeeccbddcecaaeeebaadcccceebcaebbccebeeadedcbbaaabcbacbdcdecbdabdeccedbbaabedccebcabcdcadbcdcbddebcdcdabeebdbedcdcaecadddebcadebebdcdccabecebdcecabcacaecaddccddccdeadabadbeeeeecbddcaebaacdbddedaeeeaecadeeacbebbdacedcacdbcedcaaeaeeabedccbadbacbecabeaaedadaccdbeeabacaceceedaaaeeddcabadebbddeaaceeeababababdecdbacdceedecccccdbeddcdbadbebebecbbebddbbabceeacccbeaeceedbaeeebcaadcaaccdbccebdcceacbbecaeddebdadbcaaeeeeedcbaaeacbdeadebdcabebeaccaceadcbcbddedaeaeabcdaddededcaccdadaaeadbdbbbbccceaadcacbbbaadacadcdbecbebbdedcccaedeacdbdbebaeaaacaddaecbcaaedacdcbeebabacebaceaedcadaecccaacedbedbdaacbadbcededeaeaedbbddbacaecccaacabdcadaeaaeebbbddebcacbcaecacdbdecdbabebcbeadeccdeecebddcbcbbbededbabcbcedccaebccadbccabbecabdeddbaebeeeddbbecaceebdbbadbaddeeaddddddbbebcaabadcbdbecadeaedeeabbeeacaedcbcbeaeeadceeeccdccbecbaeddbdcaeeebeaebabcebccbaadedbaccccccedbdadcddbdcbebeeabccbabcdaaecbaecdeeadcdeacbbcedeaeebdeaddacebddacbacbcaebebcbaebabddedaaeeebaecebacbabbcbeaabdeddeacccddaadbebccdedbaeeeddadbcddaeeeddcddabceeadabccaadbbcaddbeeadacecdadabadbecdddadeebdebbcdceddcdaaaedababccacdbadebbabebddbdbacdeadcecaceabadedbeabcaebcbadcbbeabddccebbdbdddecaedecadaeacbdeeceacadadceeaaeaadcbaabdddeebcbeebcabbecdeaaaaaeaacebeadbcddacebbcebaacedcdbacedacddebdebedcbbceebdceeddeacadebdceadeaaebbaeadcaacebcbaebccbeacdbabaccdaccabdeaeebdbcecbeedaaccdddbdaddbeabaeccddeecbcaacbdaaeeacbdeabaababececcecdaddccdcaaebaeebbdeccbaacbdcabbbbbdceeedeeecbedaebbcbcadbcccdaddedeeeebeecaaaabadaeeecdeebacabcdaecccdecdacbcaecadbecdeadbcedcababaaadcddcadccbcceebccaaeceabedeaedecbbccaccacacdcdbccabbaaaacaccaddaeeceeaacedecabdbbaabbbccddaccaaecaabeabccbeecdadaabdaedecadaeddcaaccddbdaebaecaadcbedaeeceedccaeaeaeaeabbbeeaadacccdbbdeadaeccbbcdbaebebbeecbdcbbbabeeacceedbddebdebebeeceabeabbdcbeeebeadcccddcadcdedaaebcccdbccacbcaccdabccbabebedebcecdbbcbaaedeaebbddeaddbdecbadeaceddaeadeddccbaebbdaabbaebbecbacbdeadeedbdacbabecebdabaaeceabbeeadbdcdddbcbbabdcdcebbcaecccdaecdedccaabbdccdbbdaadcadcbedcbaacbcbcecbecddbaeecccbdeaebceddbcdddcddccedbcaeecbdbebdddbaecdedceedcedbdccdebdcdbeccdeececedbdabaabddbbecadecaceebdbbcceecebcccecaadbdeccdeaebabbaedaddecbadbedddaeeeecbbddedeeeaeecabecbeebdedebdaaeecddbdeeaebdccecccaedeebbdddddbcaecddedebdbddabcdeaaccaacbbdcaaebaddcbeabcbeddaabbebedecbebcaaccdeccebdebbebeeaaedbadcaaadadaacaeedcbeabccedebaacbdaecbbcedbadaaababebdaaebdeacaaadeeceedcbabeddeadbcbdcdcedeeeadcadaaabbcabcceccbacdbdcedbcabbebacccbbdeeaedebdecadceaaedeaceeebedaecaacabdbdbbaebdccbeebcabbebaeecebccebcccedbcaaeeedcbacacddceaacdeaeedebbeccdcbcdabbdcbcbecdaaccecaeedbecaccadbbbbebdcaaadcaebddeecaccbcaabbbdadccdaddcaeaaddedecbdaabbdaecaadeaccbdeccedeaeeeaaecaeecebabbcadcaccabdaadaeabaddcecdbecdecaeecbbeaceadcbdcacdeeeedbabacaaeddeacbeddabdbabcacbbdeaebddadadccadaacaacbecdedaabacbcdebbeaddbcbceaeacbadcbbedadcdcacddcccbcbaecaeedcdedebdbdeccbadddecaaeaebecbbeabeabbbaaaaecbbdedbdeabedeaedbecaddaeacddaabdbaeaacacdbaaeddcbedccaadcbaeddceccaceadceccdbedbacdacedcdacdaddeeaaeadeccbeccaccedcbadadccbeecabbededbaaddbeaeacbbbaeeadbcabdadbccbaabadaeccaaceebeddbdeeeddccbacddaeeedddeecabcccdbcebeceebdbeceaaeddebaedaacbcdcdbeddebbbabebbedbcaeecdcecbbaddbaadabaccebcbabaabbedeadceaadedcbccebdadeecdcbeebbaddbbebbbceecbdcbcebeadddeeddabbecacdbdacbbebabbcbbeeecdeaababbdccaebecaedaedcbdbecbdccdeeddcaaeaeeebdbebcdacedadeddaeabaabcebcbdccadcceaaddaacdacbdadecebcdedebcecbdbbeebeedababadbaaddbdbbbbeeeaacecebbbdacdacacdaceccacedaaaacccccebabadabdadeebcaaadcddeedbdaccaaabddbbacdbceebbabcbecbaeaeeebaedebbddedbadddedcbdbabebbaeaadeaacdaacdcceaaeebaaaddabcaadcaedadaebdeadbdcceabddebdcaceccaccadbbdbecdbacabbcebaeeecebbdadabbbbacedcceacebeacaacaeadbcdabddadecdbeacdcbeeeedeccaacddbabaababbaebcdadcdabbbbaebaaaabbaecbcbbbddbacddaadeebddbddedacccaceedaeabdbdccdeeddadccaddaacabcceaaccaeaecbdeaeeccecbcbeaccecbbabdbebebcdabaeaacebbebddcbccdaadcebbcdacebbdadcbeebbbecbbedcecebeececadaddeddbbdeeddbaabbbcbaededeeedaeecedadbbaaebbcbbcbdcbceabddeeebabcaccbdcecbcddedebdceecadbaaebbcbcecbabdceabdebaedcccbdacccedebabdacbaaabebaabdcdbcabadcecdbcbbaecbecebebbdbaccbccabdeedcbedbdadaecbacbdcebaaaacebaabbdbdbccdedbaaaadeabceededdabbddbcceccadbabcbaccedcddaebcbaaddeeacceaaecaaeacabaaedcadabebcdebdddadadcebccbecbeebdcedbbdabdcacccdcddceacadebbacdbbdeacaedcaeebaadececbdbaedbbbbeececaacbccaeceacceadbcabceebeeeacabcedecbdecebcedbceccaaebacdeeabbbbaeededbdbeeddaccdadbaadaebbbdbcedadceeadbcbdaeadaabeccebcabecddcbaebdadeeadeedcdaaaeceedecebddccaaccaecddebbadceeccddcbecabbeeecebaaeacedeabcbddabaddceeedbcbdbeddbbeacddecdbbdaecaecdcdbbedaebcdacecebdcddbaaccccabaeabdabbdedecbdadaabbaebabdbdbedeabdabdbacbabaccdebbdbcccebbceebdcdecbebdceceddadbddabeccbebaeaeabdbcbbdadbcdbcabcccbbabecbaceaecdbabcbbedbdeeacedbcaddbbdcbeacdddaabdceddecedabdcabaeebeaccbadecadbebdadedebbdbcbccdbbcceebdcaeacddbeedbcacacbaabeddaacdcadbdabdeaeecdbcdeadcddeadabecdbbabdceedeebbadaeddebdbbdabbdedebccaceaccdabdededbeeabddadacbcbddbceebbabbccacebecdcbbacebcebbedcbbadbdbceccebedbcaaaecbaacbdeddaccedaddeacdbacaecbdeedddbdadeededadabcdeaaecbbaaabebadeedaebabdcabddcaeebbedbbbbbdeededbcadeebedaabebecabcdeeadedccbaaaaaadabbeeebcbecbabebebccadeedbdcedadbabcedceecabbacedbdaddbddeeacbeeceeeaeccddbcebcdcdbacaedbeaabdcedbecbadcddcebdcaececcbebddccecdeecdddbeeaaadcebccaceccbaaebebbeecdebbaaaeeadcbdcccddbeedcedaedabbccdedbdeedbaedcbacbecacdbbcddacacddeeacdaacadbbbddcdcdcdbcacbabdbabcabadbeccadaccaccadecbecbcbedccebcbbeebaeccbbcbcadecebabbbedbadbeaeabcdabebbcaebcdddeaeadedaddbdadabdbbbbeadbccbabbbaededeceabeedbdaebdcebcaecedadedeeecabcbacecbbcbdbeededbeaaaadcabacbbebcdacdcaadaaaabeabbcaccaddaebbdedcbbbcebaabeaeacceebaaaeeaecdeeddaaceecacceecddcdacecabadadebebcacaeaaebaaeadaaceaaaeedccaedebdeebabaaebadccbaeddeeecdddbdeaedeccebeaedeeaceeabbaadceebeebbddbaebbecccdebeacedcdcceddbddabcbeaddedbaedcaaeaaddddbbaceeeebadcedeebeccccbeacbcbbbeeeaddacdceeaadadbbddaececaccbabddeeddbbaaebecadacacaadccadabdeaaaececdcdebabdecbabbbbebdeaeeeabbbcaccbeceebaababdedaccbabeedbbecedddbdeedbceabecdbacebdddbdebeaadacccedddccdeaecaabeeeddbbcacdbcabacccedceaebccadbeeeadaccaadbdcebdddcabeaeedeccdbeadcbadddedbeeddcaebedbdeedbabcdcdeddbccaeaeabeedcddacdebceaabeaeebeaecadbdecbaddebbbcdbaaceaeecddeeaddadebaebabaaeabaceebecdaaeedcaededabebaabbcccaaabdddbaddeedddbecaddcbdccbaadbbbacaaacaaabecbbddebdccddddacaacabdeeebdddcebddbdbecdecccacaadbecbcdcdadcddeddbadcbbabcacabddaaeccddbeaebdbcacddbeabcebddeaeddadadccbcedabebbdccdeacbbdebbbaaedaaebbaadacddaeebbaabdbbdceeacadedeabbebbdcbcbdedeabbcddeeacdcacbddbcdbdbaddcdcdacecebcaeedabbcdeeadaccbbbdbededbcddebaebeaaadaaceabcbcabbaedccedbaeaccceaeccbeaaabdddbddcdcbdceddcbcebebcaaedcdeaaebbbadadedcaecaaccaeaeeaeeabeaaeccbdbaabdacaeaaecbebaedceddcecebeabeeadddeadbcabededeecdeceedeccdbecebecdaacecbabbabaadabccebcabcabadadbceeeabddebbacdeabcabddbadcadabadabdcacaeedecccbaceaeeadeaedeebeecdededcdaeabadbbacadcedabcadddaeccaeadbeeaddbcbbbacdbaadcdbdbadbeabaccbbcbcaebecebbbceadddcbcedddeccabbdadeeebcadcedadeddaaceadbaddcdbcdbaeddabbdcbbabcbdaaecbebceaedcaabecaebdbedaecbebaacabdaddbaceaacebcbaeadcccdbededdacbabdeebbccdbbcecacadeaddaedcdbeeaccecebdaedaabeaebdcdedcaeebdceeeebbeeaddbbbcbdbaadbebdaabaeccedabaadabebebcaeeadabaacadadbabdddaecdeeeaccbbcbaceeccbadbcbbeeacddeebbbdeabdadaadeddcdbecebcacbeacaceeabcaaaeedeaedccabcccedddbcccacaeedbacaadcddeeaebeebcedbedcbbcdabadeaebcbababbccbbbcdcedeeddbdbdaeeddabbbabecdeadadbeeaeeeeeaddbcecbdbcacbedebcceeceedeebeecebcdccabdabbcbdccccabbbeaeeeaaabeaebcaeaddedaaedcadbcadbeccbdebadebcdbbbcbccdedeabeaacaedbedccdabbaddceabdbeebbceddadbcdbcbbcddecdaaceddbecbdebadcecdadacdedecbadebcbddaceccbdaaeebcbeedccbcbabeeceddbeaaebdcecceadcebcaeacadeabacaebacebaacdcaaebbceabcecbeaebacaacbdddabbbdcccecaccccaddbccbccbdceabadcabbbdaadcddcabbdbacebbeaccacceddeaeabcbabeacdeecdcdbecadbdcdbeebebcaccaccaeabaaaaddccecbdeeccedcedeabdcbbcecabdcdbaddcaddcacddcbcaaeaabcadeebccccdebaecbdebadbdbcbcbdbabedecbbdddaebababadeeedaaddbcbebcebaebdacbedcbeedcdcecdaeadabcddcebdbcdcecdceacaeadccadbeeecaaebebdaddbcabeccdcdcabedcebbdaeccbeaceddbacbedbeeacedecdbcbccccddeeccddcdcbbeccbadaaeeadbcecccbcdebcaadbbcbadadbcacdbdceeeeccceeddebdcbadeabbedebccbeedceddeddbecdddedcaccedecddedbeedadabadbbcdacdbccaecdbacabdcddddceabdcbeddcacdeaaecbecbeacbdbdebbdeebdebcebdacdbbaaabcaedbcbdbdcaeaebabddabecdaaeedeaaeceeceeadbceebbbebcbaabeeabcbbdabcebddcbdcdbdddcbaebaabcdbacddddacedcbdaacaaaaecccebedeadbddaadececbcbaeaecbddccbcecddcceebabbcaaceceabdaadcccdcbddaccdccbacbbbcececeaebccadbdcbbccabbcddeebbceaeccaccaedeadaaadcccceabebadabbeebdacceeabcbddadccdedaacedeebdecadecdbedaaebadacbbeacbaebadbcddaddcecedbacaeadcbeecbcbcacaaaceeabcbdaebbdacadbeadbaccadacdbaebdaeeecdeadebadbceeadeeccbebcbcbdaccadeeacececadbdedaaaedaaebbdceccdedaacdadcbbceeccededaacaebbacedbccdaceddcabbccabcdabccadddaadbaceeaabaebbabdedbaccdcdabadebabddccccadbdcaecaebeddbbbeaabbcdcecdadbddbbddebcdcbccedadcbbcabcaaedaddaeeabbeadddaabaebcaaeaccbccbddcbbbbaddaaacbedabeabccaecadcaceeadeedcbbcdddbbbbbcbceeaaeaadaabbabdbbeaecedbabcebdaeeaabeceeaeedeaccbebcadeebbdceeddadcabcddccbbcdadedcadcdedcabdacddadecbcbcbaceaebbbbedbbdacccebcceeabbadecaabedabecccbcbaebacdececcdebaacceedaedaaecbbdbedcbccdcbbccadedebacacbacebcccddddacaebbdbcddeabacbbaaaaceecaeebdccbdbcccabeecaeaaebecdcbccadbcebbadddebecaeddedccabdbebcadacebdabcbadecbcecacecedcdacdceddbdeaabaccbedaccacacbdbbacbedbcbaebbbaaabcebdecbedebeedaeeacdbeeecaeedbbdddaebeaceadaacdbadcacddcdccccdbdaadeeccecaeaadeeeabbdaeddbdadeececaadbebadcabaedebebdbcacccdaebbbebcaeeeebcaeccbddecdbeecdacbebbeadbdbaaddeaebaceababdacbaacebecbaecebbbccbbbbccdcedbbdeceebaaccecaaacddbbbdceabecacdaddaccababccdecacbccaceaeeeddacccedaaadcbabbcbcedacddebbabddeacaeaebbabbbdebeacdbcdedccdcdeabdecbcdaabccbdccecbeccadcdbcabdddebebcbaecebaacecdeedededeeadbecddeedacdecbddbdeadcbddcbbaadcdbeaeeaccbeebededbeacaccbdadeaddccaaebbeaecaceeececaaaeeaaecbebdacdbddbeaacadbeaaddeaacaaeddaacaccabaedbbcedebaaeecccdeebedbbaeedcbdeddacbaaeeeaceaeecedbecacecdebbbbadecceecaadcedcaabecaebccbbeccedcdecebbdddadcaadabeacbeddeaaeabeceadadcecdadaccddcaaabcbbccceedbdbcaabbcbccdcededdabcbdaeaadbededeeecaeddcaedebedcdcbdabdaaabdbbceaccbacccdceedecbacdcbabdeaaabddadeaaabdadebbaadeedbecdbaeaaddccaacecdebeeceedbbabedcdbbeaedbbcdcaebaddbaddddeccaaaccdabccabaaeaabeebddaaedaeaebecabddedabdebddbdeacccababdcecbaebaaccbcceedcabdbcbceebbddbabebbaeeebaccecdccaeadabecaeabaccaeadccedebebabaceeccdebaddcccebeecbbdaaccddedececceaaacbdacbcbbdabadaabcedbecadcbbdbddedbbdedccebabbdaaadabcdbcdacccabacedaceeccdadecdcbaaceacecddbbddbbbbcaddaeaaabecdbaededaabbeadecaecdbbabeecacceebcdcceeeedbccadacddcbacceceecedeaeeddebadcebadcbeaadecbcccbaddaeaecadbcacccedbbadcdacaebceaecbcdccdccaebdbdddbceeabecbbbcbbcebadeaecdddaaeaceaabdcadcbaaeacbacdeecabdcbddaadeadbcebdbbbaedbbdebebebdbcadedacbcdcaedbbedaccacbaeddbaaadeeddcbbedaabbbccdecdcddbdeadeedebebeddaccbcdeccdbebeecededabcbbdacedeebcccaecedaebeacaecbaabddccebbbdbabeeeceeeeedeedeeabacedeceabbdddcacdebaaaeedeadcedbdcbdaabdebbaccbadbaedbbebdcebbdccddeecbacadadcdaccaacbaaaaebaebacacaebcaceabedbbcadeeceeadededaeeeaeeedeadecacacaecedddbecddcbdbeaecadbdbbbcbebbcdbbeacedaaacbeeaeddacdbcaccabdccbdacdcbcbcdbdddacbddabaeebdbadebaebbdabaddecebcbcacaeedccabebbcecadeaccecabdecdbeeeaccbcccdadecedeeecbadaabeebdabccbabebddebbacddbccedcbabcdcacecdebdbbdcbabccedadaccaeccccebdeabeddebaccdceddebaadbbdeaabbedcbeabceeacbdbbeecacabdbabccddaebdeacaeeaedeadaaccaeeedbecaedbaaacdbbedabacbacaebdedcbdbadcbdacaaadbbeddddedecbddbddecbcdeecedcecdccbeecdaeceeeabcddaeedcdeaccecabeebbebdadedbebcdbddabeeabeacbcaebdbeecbcacebadedebedececbbcdaaabebcceceabbadaccdcadcbcaeecbaadcadbebacabbdbecddebcaecaadacbbbdcebcacddabaaddeaecdceaadeaeedebacbeeeeaabedcacbbcdbbeecacbccddbbcddcbdedcacdbddbdceddebededeecbcaaecaccdceebddddbadcdeeeacaddbcadabeabecddcceaccadecadeaebeacdebeeedeccacadbecacdbdccbedeeaadceceacadbcdeeeecebcbdccccbdceebdcaeebeaadbaadebcaeabbaeeccbbcacbededdcececaccaaccbccbadbecbcacbecbddeacaddecbcabaecaeaecbebceebdbccbeedcdeabebadecdbaaeaebdbccadcbedababdbdecdaeadcdedadebdabaeabbaedaebcccbcbaceddabbbbaaaaeaccdacddddeccebeeaaeeaccdcebeeeabcbdeedaebccbdcbdccabadadecadceecdcecbbddbabadccecacceeeccabdaecbcaaeadabeaebacdeaceaededeeebcdedaeadebdedabceddebcbdedceeacbddcbcaedccdcbaddcdcbaebeedddabdbcbddcedbbbccccccdaccbdccecabedbdcdedabbdaddacdabaedbcceabdbdaedbdaeceaabaeaededddaedabbcddebeebbcbbbddebcbccececbbcddbbdbeecceeddcdddcaabebdecaaceaebebcacbedacceccaececaeeebedbaebebbceedaaaadbccecbbbdeeeaeddeabecdcbabebcebdbecdeaacbbdacaeadbbaddbcdecdeeedcbcccadaddcdbebdddaccddcebcccbdaadaaedcbaececaeaddceadeedcdceaaedcaeecaaecdcbdcadbabdeacebdacbbdbeaeeccaceecbbdedbdcebcbaddaebebbeabddcbabddabdaaacadadebadceeaccabdedadbcacdbdbdcabbddebccdddbadeceddcbcbcdbeceddabebcbaeabadccaaaedbccacaebcdbbbacdeaceceadebcbcecbcbaaeeaeededceadbcbbdaaaaabcccaedcdcbcbdcaccbbbaebbaeadccceaaabaacaeaaacbddaacaceeacdcbacdbcbaabadeabcaabbbedccdbcbdedadecbccbbbcebdaebedcdaabbbabbeccacdaccdbceacdedacdbecbeebaaaccdbccbaadebebccebaeeecedecceadeeadcbdeaaacbadbddbedeeececaabddbaecccbeaebeaaebebcebcedddeddbdbdadadaeacebabbbcabecbcddcbabbbbcedecceecdbecdeabbbceabebeeadbacccebacdabedadebedcdbacabdcedaabdbedecaeaeedabcaceccceceeeaddaacccdceeacabbeebdccbdcabaeabdecbabecaeceeccdaadccdedabbccadcabbdabeaccbabcaacebddebebbcbaebadebbbdeeaaceddecabcabaddecbacdecbbaceceadaeeccddadaaacbdadaabeddabaaecdbeacadbcebecadbaadadbddddadedeeacceedcaddeaecdcbbcdcbcaccbeeddecdaabdbeaaabaaceceeeabacdecebaabeaecabeceebecabbcdbaabbcaddcdcedbceeadedbaebdcbbccaedbaaedadcbcdbedaadcdeadbdceadcaeabbababdadcbdecbaaaedabeaaebedaecaecbdbcebaccdaecadadecbdceecdaedbaebdbeddbceeaeabcbbeecdacdeabebecbacabadbdedeabcbddbcdceecccaeabcaddddbdeedeedebedcbbbadaedabaeccbcadbecbacccdccdbcaaccedcddbdaeecdcbaaedadbaaaddbcabbcadcaedcbddecdbcbbaebbacdbadcddacbcecaecbabcccaacaeebbbedbbddccbcdbeebadebbbadaebdbbacddeedddeeeadbabbabaceabdabbebbeecaedbdcabbbbebdbeceaaedeabdbddbecbcdaeddeaaccacbcbaeaadaadcbceebdaeddcbecbcbbccadaecbdbebacaadddacbdeaddcaeddabcccacabddaddcedcdaedeabecddcdcccdcececeaabecacacddaaedccbccedeabaabbbcaecdcabbdbceedbeedcaadcabdbccebdebebababdbececeedccbabadbebedbabcbeccbeccdccedaadbdabebabacbeddbdbabbddbeabbabbceeecdabcadadacaebeedcbdacdcaeabebcaaacccdcaaddcaababdbadaecaadeddbabdbdecdebeeacdcaaaeabeacbeccaaddadddbbabbabddadaeeeeccabdddaebeceacdcaeacadcdbbaccdaacccbeedbaeeaaacabbcebdeddcaeeeddbdbbcbdbaabbdebabbdcceabdebaedcebdbdcaccecdeaeeecaeeaaaadaccceeaaadcceceadeeadabeecdbdbeeeecbdeceadeedadaeabbddcedcdbeaeeabdcbaabddcbdabcadaaeabccdeaaeceeceaaeeeeaddebaacedcdbecbbdadaecabddeeaabdeacbccebaeadcaecedcdcaecdbebcabaaadcbeaeddbecebbdabaadbdcceadbceedabcbaaebcbaaaadccbcadeabaaebabecebcbcecbdadecddadbbdadaacecaeccdabaaebccbbabacaaaebdadbeeeedacdbbabbaddcdaeacddddcacaecaaaeacaadcbabeaabebacbbebbededaedeaeaaeeaddecbbeeeeddcdebdaaadcacebaeddaddaedaceedadbeaeddceeccbbaebedcceadbcdcbceecdadeedcebcccaacedadedddceacdedadcbbdeeebedcaaebceadaeedbbabbbedbbacbddbcbeecaebeccbecbedabceacbbaaceabbbeaddaeddddbabbddedaecebbcebbbabcedcbcccddeddaedebcdecdbeedcdecebeeeeadedbeebcbeecbabdacbadcecebdaedacebdeabcdcddeabbbeabacbdcbbdaabadadbcaeeccebceedbaadceaccadababbcbccebacbebaeccabcacbbadbeccbacbbedaacccbcccccdaeaecbebedccedbdddbccbbaaebbdedcbbaeabcddaebcdebdedbadbeceebaabadcdceabbbdeebccedaaceaccaecaaaebaeebdbcdcececeacedbebaadebdbacaacbdbcdcecaadeabceeaabaaedecaceddebdbddcceedbcecbcdbaccdcceacacceedeccacdccdbedddbbceacbbabbbbabedaaaddeaadbcdaedddaaabbbaaeddbabddaabddeecceecddaebdedcbcadeedbdeeacedcaadaedddbeaaaaebcecbeddbcabbdcedaceeaaacecdddcabbbcbdebdeebbcebddadaaabaeaebaacdaceacbbbceeedebaccecaddbbebcedaddeabdacddbccbaeebcabdbdcebeeededaaecbeaadcaaeceabdcbebdbdadededcedddcceaaeddeececacbabaeabddaccdccbeddedbbcbbbddbbaadecbbdcbdbaebbdcacebebabacecadeabdcdcdceabceedacbbeedbdaeedeccaaaebacbabbbcdecbaecddcbbeddedaaccebcbdababdbeaaccddecddddabbdececcaeaedccbbadbadccdbdcbcccacaaecceecbbbaceddbccaddcceeabeaaecbaddebedbabbcbaaebbdddeadacdaebecacdccdeabdebceaddbcccbebbbaddbaecadeedaccccbdecadeebdcddecabebedcdebbacbaedccbaddecbdbcacbcdaebeaaaadabbececdbceaaebedceeeeaeaaecbdaadbebbbbcbdadbaadeeebeeeeeabcdbbacdeedadbbcbbcbacdaccdbdeaccbddbcdcdaccdaddcacebcebbeadddabdbbcdccdeeabddacaedebddeeeaeacdbcaeddaabcaebebbaebeaaacdeedeeeccdcdcbbbbcdecadbaaacdabadbaecabbbdadaeccacdbacdedbdbdcdaaaeeeabbdedabeadebeceabeddbbacdaeacdedccbaeceaeadcedacecebaeebdcebadedeaddcbadbaddbdaccceebadaeaecdbcbcdbdaeedbdbadcdededadacdeaaeeccbddeedeecacaeedeeccbbeaadedeaebbbbcecbacedeecbdccaedbcdbbaebeaadcabdbaeabbeabcbeabdacbedbbcbbacadebaeddecddbbbadeedabcaadedecbaeeeeacebcedbecbdaacbcabadecccaedecbeabdcabecaaaeddccececebbbdcccdbcddbaebcbbadbbabbadbceaabdbcceaedcdbddeaeaebdedaaebbdbecdacbbcaadbcbdceeaadbbeecebbecdeaacbeaaacbcccbcaeacaaeddbceddbceabeddacbadbcedcdbdbabeeacabaeeabcccdeecabacdcbcaaaeccecaaeeaedcdddeaacbcebedaeddbdcbdcaacdceecdedaeedccbeaeadaaceebcaabcbccabaebdadaecdadceeabadbacaecbeabeecceeeabbecebabcbeeaacbcdbebdcaeccaecddabecbeaeeadcccebeabbcabcbaadccbcbededebebddcecbeaadedcddbcedebeebbebdbddceceebdabcddceadcedacdbdccdebcadecedabbddeccdcdceeabbcdcbbdebcdaacabceebbbeeaeaabbcbedcaeddedaaaeedeedaedcabcccacabeaddebceeebbcbabcddaabcaeabdeadbaccdcabebcedbbbebbcabbcbddbccacdebbeadebaabeececdbbacadedcdbedbebbcbcdedeabcddaedecdaedbccecaeeddbebabaacedbdaebdddceeedecceeaeeaacacbdbaeacbdbcbaeadaccbdcbcbcbcceebbaaadcbaeacdccbaedaaeecebacaebdcbcbcddccbddcccedaedecebbcaabaeabedeeeabbacbabdceaeeacedddabdbeebcecceaebceeeacacabcdbdaecaedbdebdbaceeeacdedeaabdedbaccbcadbbccaeaebabacccaebdbdaecdeacdcdbdaaeabdbbcccaececececcaaeeaeededdabbdaedacdbdbdcdbadbeaebeccdeaacbbedcedcdeaeeddecbcdeaeedccbedbebceeaadcedaadeabaebbeaeeabbeaebbedeaeaedaebdbbdbebddecaddacaaceadeaebbcadccededdeccaeddebaebeebbecabccaebbcaaacbcceeceebcbbdcaedbbdbadbaacabbcadebcadddacdadbdcababddabbdeacbaaabbeececccccdcbbdcceaabdcdabedcebbeeebdcbedccaadeeebbccdecaecbbecdccadebbbeacdeedaadbbaceaddbbaeccaeadbaabccccadbbdeddaeacddebcacbabbebebcbcdbbaaabdacddeeabbaccddeaacbbbcbecbbacebecdccedbbbdbdaccabdedccbdcaecaedabdbbaaceceeadcbbdadccddadbebcdbcadaeedaadaeecadcddaaddabcedeceacddbedeaecedbeaeaebbabeaeabbcdcbdeaeeabcacebcdecadaccacbaccebaaaddceacecddacbbdadbdedecdbdecceacbeabedeadbdebbdcddcccbbecacdbcdddadddbbaeaddaccdbdbddeecedbeebabdebdadeeaeddeccdeddbacdedadbdaeedacadbbbdcbeacbcdbcbcccbeeddebdceccabaceeaeecbadedecdedabbadebaddecdecbdaeadeedcbbdcddadadaecacdbeebbabadedecdaeecedcedaabacdecbbebedabddadcedccbbcaebbaeabacbadbdcbebccbeaddcaddabaebcacaaabeebddaadaddeabcecbbedabedcdddecaccedaedecaacbabbdceebbdbddaecbadcccdbabceaceaacaaeccdbbcbcbaaaccbadeddedaedaeeddcaedeaaebbdcddbaedccdebececdebcbababbecbdeeabdbceeececdedebbeecccbbbbdbccbdaaeccebbaabbbecccaeeabdcdacdbabacdddedbecaaeacbdddcaeaddecddcdccebcebcdaabcaeaaabdbaebaddcbeddbdbecdeaceaebcadbbacdedbebdbbdeabedceacbccbceacdcdcdcbebdaebeceaeaeebeedaeeecdacecebeabddaeddeecbabcdaadddbebdbebbddaeecaababddecdbcbbaebabebecadcebaabedbdabaceabddcddebcbeecaccbdadaaecaaddeebcceedbbbddcbbecabceacbdcbdddbdcdaeebcabaecbdebdeacbaededbccbaeecabcaeacdcdddebedbdeabdddcdecebeedaabecbedaeeedadacddbaaeddcdbebaeeabdaecaadbcbedbedbccdcdcceeaeaddecdaccaeaedbbddbbdbdbdbbacadbeecdaeabdeebcedccebcdabceacbababeaaceaeccdebeccbeecddbeebdbbecabecbadaaabdedbccdbbaacebedbbcabbaaadcadecaadbaddcdeedcadeebcaadccbbadddbacbedcbbcbaaebcebcbcdadeceabebdacbecdbbbbedadadaaeaeaadeccedcaccdaaaceadbbcbebbacabacbceabccaabddabcabeadcaedecddbabbedcaabcdadbbccebdbdaebcecddceeacaabeebabcdbdabeecaddaececbbdcaccecaaabbebdbddaeedbcdeecababccbcedaceaabcebceeeeeeeeeaadedebddeadadecbaeabcbceacadeeeeacddaadbabddbedbbebddbecadcbdeaaaeabccbccaaedaadccaadbabcdbbbddaabbaedaedeeecebeccbecababbacdccdcccbceeaccaacdaebdaaceecabebaeceaaddebeabcddeadebeaedbbbcadbcaaeacabdaccbabaaebcbeeddcaadceeeaaeacdecccbbecabaebdaebdacbbdededdebcedcdabebbedddcccebccbecdacbccdbdeedaecedcebaceccbdabccceacddddadbaeccbbcecbccbcdeaabccedaddeeaededdaecbeeaeaddbceadcbacbedaeeabdbccdeaeaadbdbbbaceddebaeadcdcddcaacbebabededadccacabbbdbacccdbeaaabeeddcbbebdebdedeccbbcbeecbabeddedecedaaaabececcadbeeadbbdabcccaeeddebaecbebdecbebcaabcacaadbadbdaeceecabcccdaeeeabbcddeecbcdbcbaedbdbaaedbdabdaadddeadbddacdeeeeedbcdcbbecbbcbdceeadceeedaacdaebdacbaaabeededecbddceedaebdeebaddeabdcabbeacdcdcbbdeaedaaeadecedccabeddaaaccacebdbeebacededabecdababeeedbedddbacddbbbcdccebabaeedcdbeddedbceeeadcaddbabdaaaebcdcedbcdceabcbdcbccbbcadeebeeaecdcabbbbbeaceeebcccecaebecaabbacadbcaededcdaddaccdeebcbaceadaedbecddaaabbebabedcabbdddeeacaecacbeecccccbabdeecbecaedadaaadcddaebacdaaaddcecaabaeeaabaaddccdaccaaaeecdaddbedeedeaaaadeeeadebadbdedbbebcbeebdcedacabbadccaecdccbdbbacddbebdbacaadedadbbaaededcbaedebaacabbcccccbebcbcaeddeadadcabbddededdebaadbcdaeeecdadbaaecbeebcedbababbdacbaaabcadbbcaabcdcaecbbbbeebecdbbcbadaeadabddcdcadbadeadededccadccbddceddddabbeaebbcbcaedcdaaaaaccabddbabbebaaaecaccebadcbdbadbcbecbedcecaaddbbaaecedadbdbeddcdadbabebbcedacbbdbedaccdcbaddcceccebddeecebcacacbcceeecddcdecdcdaddeaabbcbccdcedcebbebadbcdaccaaedbeaddaccbaaaccedbcdeebaabbabedabeeeaadaacaabeabbebbddeecebccccadeedadcebaadabcaccabdddeebedccbceadddeddcebeacbabbddadedcacdabaaacaaedbbebbcbabadacbcaaaeebaaeaaeeebaeebcdbedddddbedddbdaeebecdaedccadeccddbcaacbcceacbddaaccdeeeabacebacceccdadaacedbdbedddaeaddadbaaaecadbabcdadbacedebeaaeccdccdaceabadcedccebbabeeeaacacbbcdebcaeebccbeebbbbdabbeaeedbedddeaceeccbcceeebbadebcecddeaabbcadcabeeabbaaaabbbbaeeaccbaedbecdddaccdcabcecedbedcbcbbbbadebbcbcedeaecceeccbeaeebebabecaabaceedaebeddebccebeeeddaecebbadacedcbdbcbdbdbcabcbbebdbbacbadcbaabbabdedcbbccbcbebdeaabcbaddaacdececeabacedcceeaacaebdebdaeedcecebdbbadeeccdaecdeccacbcacaebcceedbceacaadcbbebacdeddaeeeaaccaabbbaaccedebbabcbcaebddacebcddebcdeaebaadededaccbccdbbbcdbecbbbbeadcebeedcacdabcedaadadeaaebddeceaabbccadebbacadadecdebccaaeaeebcacacabdaaabaaeeaadcaadeacbcbacaacdececdcebdacdcecbcabceecddbdadbcdecbecdbedccbbaebdbaccedcaeacdaeecebeebbcaddccadaadecececcbecdadcccbdbcbbdaacbdecadccdddcaecbbecbceabdebaaeccbadeebaaaebcaecbcbceebabeaaadeaceceedbdbbdccccbdbbbcdebabcabdcabdebdbbbcedcdeebbcecbdedbbdacbcaedcabbbccedcdebdabecbbeaccbedcdeabcdbbcbceeeabcdeeecdbcebddebbaecdcacdeadcccebcaeceebcdecdccaedebaeeedcaabacdcdeccdaccdaaaacbdabcdecebeaecbeecdaaccaedccdeeeeedabcbeddacbcbdabdadcdabaaacedbccbcbbdcebdeebeaecccbdaecdbdcadaeebeeacacaacdcceebdbcaccedbdbeadddbedabedeecbddecaaaddbdccadbacdbdeebbbdccdeddedcdddaeeaedabcdccebbaaaeacbeacebadacdaacdbabebbaabcecadbdaacdaebdbebebeaecbdceccacbcecaaaebabeaaadeadbbceacbaaabcbedbeccabeccacdedcbdddaadbbacdacbccaaeebbdeacbbecbcedebccdabecdbdeaaddeadcaecadcaccbddcbebbabbbdeaadebdaacdddacddecdbddccddebbbadeeccecdadcacbbceeceeaabeecdabebcdebcdbaabdbbdbaebbdddbdaddddcaecbcedecbceccdbccabaeaddebeeecedbededacbacebbabcadbdcecbebdbceedddcdaccccdcaadeabccbdcebebceccbcbbeedbeceeedecdbaedeaeceacabdecedebedeccadbeebabbbedbeaddbeeaaacccacacdbbadbdebeebaedbcbababeadabdcaceeccabccdceddeccdcbbabddecdadedacaacdebbebdacceaaeeeddabdeaeabaeaabcdecdbcaeceeaddcacdabdbcdadaecabbebddadcaecdbcacabdebedceecbbaacaebacbddcccadcaaceadbdcbbecdabdcdadbddcacdcebdeeaeeacbceabeabdeddcaeaaeedeabbeadabdcdbbbdecebebcdbdeeacbddcccbaedcedaeedbabdabddabadcaddcbedeedddedcceadbdddaedbdacadaddbecbacebdeceeaebdccbbaeaaedcacaeeccdaddeddaceeacadcabccbbbcebeeddaecdccacaabcecdeeceecdbdbaabdbbdedbbeabdcaadaabcaececdbebbbeaadedbeabcdcbabadacdaebbabbaecadeebecadedaebeaaccdeadddcedddddabaeceecceeeeabdbeaaadacaaeecdbedbbcaadaeebecaddbabccbebacbbddbddcebcceddccbbaadbcdacbbdbabbcdbdececdbdaacccedcecdbecedbbddaeebddbebebdeeeeaaaadccceeecbabbedadaacccbdccedcedeaebbbabdadbbaccceabdbdaaebabecdbbccbdeddccddebcdcecebccdcddcebecddcdbcdcaeeccdcbbecddadadeaaadbdedbdaadedddabecbddceadeeaeedaacdcdedcedeadaaadcebdbdddecedddbecebdadacddeaceceabcabdabdabaadddbddbdaecaeeeacbcaebbeedebaecadebebedaeacdbeeacadeccdadaeabcdadebaddceeeeabcdcdcddcdbcabeebaccebabcbcceeedecddeebececddedcbcbaebeceddcbaeedcdadcdcdabeddbbcaadcdbbbaabdbeeaacabdececcbbaadaaedbdddbcddacccbcdddcbabcbbbeddbacedbcbbddeeecdeaccbcaacdddbedccccebcadcecaeddeeabadedbebcbabdcedcbaebcdebdaaccaddcbebdccccebdcdbebdddebaebebaaccdcdcadadecaeeedabcaabadadbccbeabaceedbaebdbbdaedeeebabbccaacdbeddeaebcaabbaaddbcaacdeadbcbaaebbaccaadceecacbcbbebdbeceeaaccedeccdabbbdecdacebcabbbaaecddddbadeddecbdadccaeecbbbebdbacebeeedceaeccedebdeeaeeaadcccdddecbcbbdbeaeedccdbaedcdcebbcacedeeadecbbceaacbabbaeebeebedecbcdcbccebeccadbebceeeedaddcdbcededebbeacdcecedbcceeebacadebcaedaddceaeadddcdeedcaaaddacdbdecacaeecbdccaceccecbcdccacbdeecccbddeaabbbbeecbddecaccbacaccdecacbeaaabddbbeaabaaddacaeecbceaaaeddcdeeeebcebbebaddebbedcbcabdbdeeccbeebadbeaecebacacccaacbdbadbbeaecaacaeceeeebcbdaeabadcbbecebaaacecddccbeaaaddccddcaeabddbdcdedcccaddcedeecdccbeaacceecbbbddddddcdacebcbbdaeeaaddeeadcbadbcbaadeeedabccdacbbabeeedbbdcecadbcbcbdaabdecedbbacbaeebdabbabbaeaedbbeccdbecbbcbaceeabdeadeeecbcdbbaeabdeaeacbaacddbacaeebabcaaadcdbadcddeadaaaedbeacabdcbccdeaeeadcedaabeabecaceabeccceedecdddbcabdacdebbebabdaeececccabbdeadbbeaaaeabcdbeeeeeceebcdcdbbeeedbecbedccdceacceebbbedaadbbaadcaeedecdbcedebabeeedaacebecaeccaeeccbadbccacecabaacaeddbabdedaebbecedaeceeceebdbaabaccddbdacabebbaedbcabaebdcabbbdabddbdbcbddbecacaacdeedeaebdbcbdeaeddaacbbcdbbadecdadeaaaaebdbdbaedcabbacddaaaedecbabdebdeccbddcaaaccaaaaaebaadbeceecdbeeceededcaabebccbdbcdcadcebcebddeaeaeadcecbdbeccbcbdabaacadcaceabacccecbcebdebecdddbdeccadaecdebedddbcaddddecaacbeceacecadedeecabcbeacdeaeabedcccccadbaaddceddddcaddeacdcbdcdcaedbeddececabbcbceeacbddcacdcbecddcabeeebaabbdcdbeaeebaedcbddbebeebbdadcbbbcacccacedbadbbceabebacdcebcceadbbdeddcbcdbbbdbbdcccedccabdabaebedaabecebddebeaecdbddeecaaccdccdddbbaedbeebeebeacccadeaecbcdebdddabaddabbcaacddaccbaceacbacadcdaadebdbadbdabecbdacddecbadacaddbbccaedddbabdddddcadaadcebebeecbddcddbaaecbcebdeeccbacbedeecdbedbaebbdbabcdbbbacceadbaeeebdaabbedceaacbbaddadbeccaebebcddbcdcccddeddcaceeaabcdbbabacdbebcccdeadaccdbabcbbbdabbabcdbccdbbcadddbadececcdcbdebddaddaecbdabaadbecdedcccecedaecdeabeecbdbbdcbaceabddbeaadeaebdedaedcceccbbabdddcdadbdccdaaaadebbadaaebeeebecaebbbbeedeecbeeedeccecbacdbaedcbecaadcbabccebeaadcbcbbdeeacccaaeedeeacbdeaababeacaebebeddbbeeaaabacbbeeddecebebdcdeecbdebdccebabebcbadabdaeadcdddbacdbaaacceadeebccddabbbddbccbcbddecdacddcabdaceccaedaadabaacccbdddecbcdaabcbbebceabdaceedbeecbaeebcbcacdacaaedabbdccccbacbdcccbbbbcdadcbadabbbbbbaecddbbbadbccadadaabceacadbaaabeaadabeacbebcccedcbecccaeacceeeecabcddaebbbaadeedabbeaaaaacbedeeaababdedeecbbcaadccaebbedeeebeaeccdaaecdbdbeeeeddaaadcbabdaccddbbbdccbbedeadaabcadbcaeddbedaebbcacccdaccaabccadeaccbaeeddbcbbdcadebcbcdaadbcebacadccaeeeccdceaedeabebbdabbeeeccbbdaacaebcbcdebcdababaadcaeaadddeedccdededcdaecccbcdbedbaacbdebecadcbdddcdacbaaaceccbdebdeabeacabbbdececacbddbdeadedccddcaddbebcbbeddcbcccedcaaacdeedaeaadebecaeccbddbbabdedeaaadbdedaccdadeebecedeacbadbccabbeecadddddbecccaaeabcbeeababeacdddeadccddeacedeaaceaaececabebecacddedbbccebeacadeaebebaaddcbceaedbcabeebaebaedeaecbbeabbdeddceedcebdeadaecbbddaebebaecadcdacadaacbcedabcedeebaaadaaabbbbddbdbbebcdbdcebccbbbbabdadaaebedddacbdccabbbcabeecbabbebdbbbdacaedabdccdebaccbabeeacaaacbbadacbbbccdebbbcdcedcddebcdacdcaccacaeaadcabdbcbaeaaeebdbaedddaadcbbccdeedaacebbbdeccdbcbcedcebadedabdbbbdddedeacbcecacecbabdceecbdaabeaabcdcbcecccaccdbbdebbcbdcdedbdebbdadeceedceccaceacebeccbadeadddbaeeacabeedbbddadebddddcbbdaddbedddcaaceccddeccbcecbaccbabbdceccdcccdbadddeacdcccdaccbdcaecdcdceabeecdcbacebedcbaaebcecdccabbdbadbddededadacecaadcceabdcbcabdecaccbcdbbcdebcbeebeceeaaaaaeecebcbacbbbcbcebaadaabcadaebbabaedbccceaecacdbddddceaebcdaaabbbdcdadbddbdbaedbbcedaabbdaccceaacddddebecaddacccebaccddabecbacabdabacbbbbcabceeeebbebdcbeaacbebbbcbbcecebaaeacacbacadcebebacbdeaecbcdabeaedaacbcadcdcbeeebcbceeadbeaedeebecddbacdabebecbedadbcaceabcabadeccdecadebaaacddcaebdcdaebcebedaddaaadacbddabcecdcaeceecacadcbbddceeccebeaadaedbaecdcceaceedaecbebacccabeeddedcbdeabaceeebaabcdeceacaddacabcebbcadadeddddbbaceadcbbdeaaaeebdeaabeccaabeaebaccabcccdbbaacabcaddccdccdcbdeaeeebaeadbaabeebaddeeebceceebabdbacadeccaeaaecacacdbaecddcabdacddeecaedcccbbcabcebcadbaceacbeededceccbaecdddddbaebcadacdcaabcbebecdeccbaebcdcedaddadbbeabacaddddaabdbceaeaaababdbebbdcaaccbacdebbbbaeebbccebeeeacbbbaedccbddaeacccebeedabcccbbeaeacbbdbaddcbaaabaebaaceebecdddecbcedbdadeaeacaacddbbcdecceabadbcbeddeadcedadaddeebdecccaabcebceedaccbbacbeaabcebdcdebbedccdbcbaadaeaebdcecbdabeadeeaabcddeeedcceebeabebeaebecaecbabbacebccdaceecceecaeeccadeaaaabdcdbaaecaeddbaddadebbccececedcceeeddecdaeccbcbeeddcbcaabbbedcebdddaddcadbbceebcaeadaeabeeabccdbdcbeaedadaeccbccdeeebdaeeddccebacadeedccceeeeabededabceddedeadebcecbdccaeebbaadccdcbddeabeceabedbbbdbccbcdeeebeadbaaaceeddabacdeeedaebdabcacccbbdceebdccbbbeeebbacacdcbdbcbcadeeeadcbeaeadcbeebbbaedeccbeedaecdcadcceeaeaaabeededccddcbbcaaebdecebddccbebbbcdbccceedaeddeaaecbedcbbccbaeebcddeceacdecaaaeadedccdaceaecddddcecdbeacadebcadabaedaacddceaccbbabbdebeaeeadedcccedabebbcdadeccbdceccbccddadadcdddccecdcebddbecaedacddcbaedeaeeaaacbeaeaaaabebabecbddcbbedebbceeeadebbcebdedbadbbaadcbcdadbcbccbcaddaacdebcbbcceedeabeabebdbbeddaceaebedccdbaccddccabdcdbeeeecbedabbacaacdddaaceaaddabdbcbdbdbddebcaececaecaeebdbecebaacadbbacaeecacaccaddbcccbbabbdbdbcacebcecdadabbbdeabaabacbcabeebcddcbcbcbdddecebcddecdaccdbabcbdadccdacdbaeeeeabbbacdecacdeacaeccedceedaccbebceebadddddddcddddbeebbecdbbdbccaeceedaedbecbbaeacedaeadcbcdbcdddecedbaaaebeedcddeabaebecaacedabceadedeadddcadddebebccdecebbaeecbeecaabacdaddaccccebddaaaaaabaddebaedebdbcdabecbdcbdaecddacedbaacbebeadceeddeddbbaecdddabaeadbcccdaddabdaecccbcecedeeaaddaacdddabaedeaaaaabceacacbacbeeddbbcbbbcdcbcbcebbedcbcadedeacdedcdcaecdccdbeaebcbdcddeabdacceddadebeacaebedecebdeeaeaaedabeacdddeebcadedecceadadeccdeebbeebcebebebdbcaeddacbdecbcaddacaaeaadcccadcacbcbedcadabebeeebbaeecdbceedbbdebaedcdbbcecbaedaedadbcbdcccddecbeabaadabdaadacbdbbdabeaebabbbeeaebbbcdbccbcbeaabcbdabeaccabddebebbeaacdedbcebcaaceddbeebbacddaebcebbabcdbebdbceeeaacdadadcbbbcbddbdeedbbccaccdaebccdbbbcdcddddaabebcbbaacbeecaccaacdbbbebcedabdadcdbccbabaacbbbbaadaaaecbbccdabaadaedebcbcdeddcbbaeacccabbdccadbaabeddcabcbcdcdeddeeacecbbddeacacddbebbadeeecdcebeeabaddabcbdaeaddddccaeeccadccecdedccedcdeceeaedeabdaaeedcbccbabdbcacccebabebeaabdaeeedddadeaeaedebbadbceadcbeabeacbadcbedbcebeeeecebaecdadbebaccccdbcdcbbcdaebadcacdcddeaddceaaebdceaacaabcacdeacebadbbedebeddaadeeeebbbbecabdceeccdebbdaaddaeedceccaaccebedcdccbdcceeceeeeedbdeddaaadbebccbbceebdaedaaeecaaaeccceccbbecadeacacbbeeaeaaceacbcbbcaeecbdbeeaebeaebadaddbaaecdcaeaccbaacdeecdebccceecddacddebbececdaccdeaebcbdaacddebcbebebdabbcaecabaebdbbdddabedabbdecabcedeccabdaceaeecebcbdeadbedaaabedeeaeeceddcecbbecebbeccebeeccacbcecebbdccdeaeaaacacdbdacbbaeebaeebeeebadadbaedadbaceabadbeceddaeeebcdbbadaadbbdcbebdaacbeacadbaddbeedaadbcbeceeeccbedbdaabadaecabceccaddbaecbdeeceeaeaaaaebdccdbdebababcdabadbebcbdecacdaddebaeceaadedecaccedaceadbadaaeeccabceaaeaeecbcbcdccaedbbdcaaeeaceaaeddadabaeebeeaeaabbeabadbadcdbbcabeddccacbaacacadcaaedcadcecdecebcacdbedbebebbdacccbbdcebabccccccaeeaaadaceebabdeddeaaddbadcaaaacebbcdcaadbaebaceceabdebbedcbeabdbccdedaeaadabdbadeeaebddddcaebcacdddaabeeecbbdaedabcedecabeceaadbeabbacedbbedaeacaaceeeebaddaaddecababacacadccedbacacdaceccacedeadbdececbcdcdedadeeaccceeeceaeaaebdeeceacaecbdebbaeddcddcdccbcdbdaaddbadabceebabadaccddbbedecbcaccededeaacbddeeaedbabeaeddddadedebeaccacdadadbedeaccdaddbdccdddeccdadcdbaddababecbddaedccdcdcddaceabecdbacbbcccadebcbcebaaedcdaecbaedcbdeecacbdaddbebcdeedddeceedccbeaeeebcbdbaceeebdcdcbaecaccbebcbaaabcacbbdbbdeedeecbbcaeeacecbeceadacddeeeeedbdaacbdbbcbcaeaddaadeeebdceedbebaaeccebbeaaaadaeebcbecddedabcbeecdabdcdaeebeacbaadaeddeadceeeebdbeeabcabbebcaabadaeacabcbbbebdebddcdeddabdedeebedeaabedecbedddecbeabceedeebecedbdaedbabcdedbabdcdbbecdbbecbccacacdabdcadbcbcedbaeebcdcddcadbdcdaaadeddaadbcbedccecbbdacbeeebcabbdaaabacaeabbaabbbdcccbbcdbdcddddccebeabcceadceadeedadcaeaddeeebeacbdadadcbeeeeacbaaabceecbdabaaaebcddbaebbdcbcdabbcdabadcdeebbedeccbeabddcdddbdbeaacdbadbcaaeeaeceaaeeaeedaabbbeeabaceadbbbeeeccdbdbabbdecbcbbeaddeeaeabaeedcebbeedbeaaeeebebeeeadccbabaacbeccbeaddcacebbeeecdcabeeeccbbadcbbacbedbbdaaddabaaabeaeeccceeaceaabcadecddbcecaabbebcabadddaabaaeeddadcededcdcedcdeeebddbcabaeacabbceeddddddeeceacacdeccbbacdacbdddbbbbdcebdbabccaacbddcedbbdaebddabaddbcbceaecdcbececcaacbdbddeceecdeddcecebdaccbbeeebceacbbacdccccaccaadbaceaecbdadccaadbadceadbdeddccadededbdbaddcaaddddbbaacbddccadcbeeedccbccceceeaceaedcccdeeaedaedcbbcbebedceaaeabdbdeaaddcabaabeadbdcaadceeeacbcddadcdcbcbeeadeecbbccbebdacaabccbacbacadeaecdbccdbbaebcdbcaebdaaecdaebcabaeaeaecbcbcbacaeecebcebaacbbadabeaaadeadbeebbcaaacddaaddabebbadeaecdceeebddcdddcdadddacedcadbadadecadadececeededddeaebdcbabdedbadeaddcdacaeceedccebacbcdeaecdecaaeeedeccaddbbeabedacebacacabdaebaeebbcdaabeadbeeeebcddbeacbaaacbcaacceadbcdebecbcadccebbdaabbaebbedddcecedcaecbcdceeddecdbdaeddaccdaddcdcdabbccbcdaaddbbeececbcabcccccdbebcadbbaeaaddbdbadcdadddcccaebcccebabaabededebcbbaebedcedddddeaeeabdcbaecbabdccddbacccdddecaabeabceceeecdddddaabcdbcaabeedddbbceceabdbaaeceddbeabddedabebcccaddebcebdeaecbdcdabdcaaeabdbbabccbadaaeaedadcacbeddebdbccbcdceaecbcdbadedacaebbdeebddeaebccaaedebcedcedaaacabddcacbbeccaeebbbbcaeeacbeebacbaaaecebeadbaaecedbbbaceebebbaedabbacebbbbbcdbbbeaabbbecccbbcabebcabcdcdcceabdddaebbccbcecedacdaebacbdaabbbbbeeccdcccceecaeaadbeaceadceecacdceebadbddccabcebadbcabadecbddaaaddaceaccddaaececbcaacadcdbbaaadbbabcdecdeebbdaddbbdadcbcdcbdaeebdedeccbcaabbecbecbbadcdaacddeabaedbceecbeabbbaacabebebadadeaacdbcabccbabaecabadaeadddbebbbabbaacbadddaabbbdaeccaacceacdcabecddeaabaeccddaabedbbbdedddbacbaabddaabebaddcbddaabeabbcdeacebeacbceedcdbcadcccddcdaaeeeeeeaeaababeabdcdbeadeeaddbbcccadaaadadecaabddbccbebadcaeecdacbadcbdccebaebaaebbdbadcccaddbedaaddbedeadbacccddecdeeebdaeececadcadacaeabdbaacdedbbcdebaecbcaacabcacaeeecdaddbccacabccbeccbeedaadaccdabedaeaeceaeeedceaadeddbeecbbecdceedddadbbbbeadcceabbaaaecebaecdaaacabdbddbcedeedaebacbbdddcbeacbeceedccdedcedbeebeddbdbbdaedeaebbbcababcaadaebdbbddbcddbecaedbbeebcbdcecabbedebccecedecdedabeedecdddadabaacccaedcaeeeeacbbebaaeeadcecdcaacdcebdeecbaccbbacdbebceedbcebeeaebdabdddbcbacccccceadedccedabeddadaeabebccacadeeecaacedbaccdbacbedbebdcaecddceacddbdbddebeebccdcaddabbaeadccadbdcbaaccdaeadecbcceeccdcdbbedadeebdccbedbaeaacaaabeedebdabbceebeebdbeddbecadbabbaceadeaddbaccaabacabecbdcebdabdeaecddccbcdadacadacabbeeaddaadbeaaaeadebbaddedcabcbbaaebbdeebceceabdabbceaceddeddebddcadaedabccdbededcaaebcadbdbaebbbabebcbcccedabaeeaddabdacadcbbcbacbdbcaacdadbecbaecceddbbcebbcbabcddbcbddbaecbeacecaeaedccdebbccebcdcbababbcccccebdddacaabcccbdbabcacadeaedcddeeccdbbbbbbabadcdbcdedebcebaaaeceabcabbeaabdaeaadbccaeadddbebddcdeadbdbccaceabaccebceedbccbbceeaebaeceaccbecedcdaccbeeadebcbbdbddeaaeeddaeddcceaccaeaadeeeeabeadabdcdcecabddbabccdcacadebddeeebccadaadbabdccecbeacebbdaddaaccabeddebdbbccbebbeaccbedccebecacadcbccdedbcdeababdcacbccdedeedbbeaaadcbccaaccceaabcaceceadeecddbabebdbcbbbaceecabbaadbbcdaaccbdeedeabdcaecbdacabdcdceabbbcaacadbaaeaeeaaaddeaecadcceeacabaedeadbcaaeaabedbbeabbaeaadeeaaebcbededdcaaabceddbcbddeceaeaabbddbcaebeccbbcdbdcaaddcabbdbecadcdbeaaaadeebaaacbdecdbcbdaeebaeaeeaeccaacacaabbdeddebbbecebdaedcecbedbcdaeacbdaeaaaadcdcbceaeadbccdacbadecebdabaedbceaedeabdadeeaccdbadedacdeaabbbcaaccecbbecdeabdcbacdbedcbcceebacdcabcccbeeddadbacccacddbdcebeebeaebddcebbcdeeedbcbddbeecdbebeedecaddcabedbebaeabbadabcccecccbcadeabdbceaedaaeaebbcebccabcbcbcdbdeecaeccedbdbbbaddedcdbbddbdcceeabcadbaceedaadeedaceaddbbeaedaddceabbbccbbaeeeaedcabbccccaedabeaecebbaaaedeeaadbbbaebadadaeeccccdebcecbcdcddaaaabaeacbadebdeeecadbdabadeddbceecaabbdadbedddcecccdaeeabbbeabcdeabbdbeceaabdadedcaebeeaddddcabbebdacadeecedcceaddcaaebacbdeeedcdeeaabcecdbaccaedbebbeedcbcbebdbbdbdeedccebecaebcbaeeecdebeddadcddcdaeedcbecaeddedabcbedeecdcebeeeddaaaaceedecdcbaadaecaaeadeaddbbedccaaebcdcdeedddbccdaadebcadcedbeaecbddcebdaededbcccebcbbabebbacdcaeecbbccecceaedeabbebdeccddcebcddcdadcbdbaeedabddcbddcededbbabdbbadebcadaaaecdbddacabcaecaddadacbabdbcecceaccbeaabebcceaabcedcaceebceaedaaabdaaeceddcdccaaaeaaadabdcaeeecacbdecdcbeebcadccdacebaaeadbaabbbceacaacbebccbddbdaddaeabdeecdeaacebeceddcdacbdedaaecbedaccccaacebdcaddbaccdcbdacdacbaabeccbeecebbdbedaaacbcbcebacabeadbceabbbdcaaaadabbcdccdaeaddbbaedaacebadedabcdaeeddbccacadacecbecdecbecbabcbbcbeaedabeedbbbcabacbdbdabdeaabbcdecadbeccbdaeaeccdcdccbcebaccbedbecdecadbeadbadcebdadeeabcdeebacddebacabcdadbaacadceaeedbcbabadebaacbedadbeaaccdccedebbbedbcacddbebbaabbccdedadadaddcbbbecebbbdbcadabdbaddddebdcbbedeccbeebeecbcbaeeabaeeaeaeeebdadadedeedababdacacedaeaadaddddcdcbecdcdecccebeadbecdecbedabecedbaabacabaddaabaaedecbccddbaddeeabeadabeeebcdebbaeeadcaacdbabaaaaabddbbacaacccadbdccbeaddaadbaaceecbeeadbdcecdeecddbabecddbacceceabcaeeeaadccceecdcebedbdcddceaeebdeaebcecbbddcbcdaaaeccdecdbdaeceadeabbdcdeedaeabddceaeececeddecbbcecddccedcdaddcdceabdcddbddbcbacddcbedbabeecaaebecabcbaddbcccaaeaeebbdebccddadceeabddececeaebdaccaabbeacedcecdbcaccacbbacbedacceccecaecbabcbccbacebbcbaadbdabddcabdeedbbabdbaecbcaecaaceeaedeeaaecbdadbaedbdbdaddebedcedbcadeeacbcdbdaeceabbeeecccbdbbeedaaaddccbdeedbcabecabddcbdbbbddadbbbdbddbeeddaababaaebaecadaaabacceedcedbcdeaeaeebeecaaedeebaeadaccaebeedcdeceebdcabaadebebceabdbdbbeeeebcdacbddcadcdacaadaaecbbbcabcccedadaeabeababdceaaabbebbaeacaddabddabbcecbccaaadbaebccdabeaabeadeeacccebaedbedaebeaaadcddbabdbeabccbccbabcededdbbeebbbcaecabacadeebcacbabdddaddbeeeeabadedcbdccceebddcccdaaacbbecbadabbaedddecabaadcabacaccaddebdeddaebcbeaaacacadbbdaccdbbaacbadbdddadcaccceeabbceeebaedddebcbbcacbdcaebbdedcbccbcabbbaeeceeecedacabeeadcbdacecbaeedbebedcaccedddcedbcabeecddaeeadaccbdaaceacbbcccacbeaaebebeaccadcdeceebebaebbbbdaaebddddebbcaaaedeccabbecdcbecbaaeaedaecebeaaeeaaebcebadbdbceabedcbbeedccbdacebaeccdbdccabaceadbbcaeceabadcebdcabeeeaecdecadddcebbbceecaadbceecadeaaaceeaedcbdddedbaabddcbecedebcceaceabbadaeeccddbabbcaeadbddbcbeccbececcbeaaecabaaccddebacaebeeadabcaaaddbeabbcaeebeccccedbbbdeddebaedabbccbdacacddebdcdabdcbcccddaeeeeebccaedacebceeddbadddbbeaeedceeacceebdbaeddcdcaeacddaabccddabbaaccdeceebddddbdadbdabcccdeceeaeeeacbbeabacaecabcbbceadecccdeacbadedcdacbdeededaceabaaecbabcdebcadbcacaddaebdbcecbbdcdaddacbbebabcaccbbebeddcdababeabdaaabbaaebdbabbababecbbeeccdaeceaadbeebcadcedbeeacdecedcaececccaadcaedeedddaeabceaaddadbcdbebbcdcbdcdcddcabbdaecbcbbecdabcdcbbaabbddeedccedaddceedacaaedccbbcbcdaecceacbaecbdeaabdddaecadbbabdadaeaeaedccadaaebebbecdcbebdaabbcbabbabaeaaccaedcbeadbadbccbcdebccaecaccdcbbacdacbcedcacbbeaeddcabdbaeebeceaaceaaecdebbeeecaddbccbbbdacdabdccaaceedabaebebabcdceedeaeecbccdbeddccebdbdbdceadeebeabcedeaadcadeeccdbaebbacacecadbbbacbaeccdeabcdaddaeaabcdacacdcedbeeeacbcbdcbaeddbceaeeaaebaecaaadcabcacbdeddbeeabdddebecedebcacaababccdeceadacebaaebdcddbcededdacaddacbacdaecdcbbaddedebbedcacbaaeeaaadcbeedbbedadebeaaeacdadcdaddccedecdeacddbbdcdbdccddcacaebacbbadeacacaeddbadeaabbbdadbdeeccbdbacacaeccaeccbceedeaacdabdadaecbeadadbebcdaedbdbacebbbeeeacdebcadddeeebbcacdddeaadacccddcebacadecaadcecdadeeddebbaaeabebecedddcadeabbceeabebabaebdcedaaebccececcdadeaebbecccebddbbaaabacaddecbaadecdeccddcbdaeddebbbdddcacbbeaabaadebdecbaaeddbeaedebebeccbeaacdedbbdbbebcbaebdcedecbbbeccbbdccaaaecdbedaebdbecaaaddbaaeebecdbcceacabcdaeccabcdabcebddebbdaddceecaeabbbccabacaacadeecddcceaacdabccacddedcedbceceedcceaabcccdbceecdecaebecdbbdcebdbccdaecacbcbccaadabddcdbdddadcecdbaabbdbbbddbbcbbebcbbaceddbcbdcbebaddcaacabbadeccdbeaadaeedbbcccebaddebeceddcccadcddedbaadbedaedcbaeceacabccaabbeecbcdecbbacecbaaddddeecbbaeeadcdcbeecdceedaceeebecabbbbccceaeebccbcbacebeabdeadbbbbbbbccaaaadacbecebbabbcaabbcdedbadbcbaeecbabbccebedbebbbbebaedaaceedbdccacbbbaaedceccaadcbeeceeadbcbdbbaebdbdecdedaeabadacacdbdbaddedccceacabddacdcbbbeccbbececcdbaccabbcabcbbaccdddceebcbdddcdaddeedaeebeccaabeecdcbceeadbbaccbacdebcddbeecabeacbebaedbaabacbabccedbaecbdeabbecadcdebbcdccdecddabbedaceedbeddddbcdeeaaaabcaaddddbbcabaedebabbdeddeedabbbacdcaadaebbeecadeeeaaeabedabceedccddeaebeecccaadacbaaddbecaabcecadadaccbebebceacdaebbdebcaddacabbddbceaecdeadaddebbccdebecbeceecaeeccabedacdbdcceddbedabdadbceddcdabaaeceaebeacaedccccbcbbbcbaabdcdddcecdbededebdacedccccbbbeacdebacaaedbdbccebedadcbecbceebdadebdbabbcdaadaabaaedbabadcbdddcbcdddccecedddaeecceddabadbdbcacdbdedddacaaaeeadecaadccccdddcbcbddadceccbbaeeeadacabcaaacaddabdccaeecadaeccbecabccbdacdbbcbbadcdcccccbbbabeecdbedabebbabcecdacdcabbcebddedeabdbaababadaaacddcabdcedbedabddbbcaeacedbcccaeebccebcadecdbbecccaeaaecbcccebeccabdedbbecdaaedecebcbcdaaebcecbdcaaeeccedbacecdbceddccaaebaeebbceadaadabebaccbbabadbbccceacdcbbcecaccdbdcbdebadbecebbaeccdbcccdedabceaaecbceccbddbbbcaeddcaeadbcbadadbabeeaacaeecdbebecaccbbadeddacbcbeadbebaeabdecddccdcdddbeecccdbabeaaabbbeeccccacceedbccbadcccdbebccedcdcecbaeadeedecdebbeceaeeddbdcbcecaebeaccebaeacecdaabbacdbaeaadebbcedbeaadbdeccaccbadcecbeddebaeeaeacbcdccadbbdbaadddccbebabeeeadccadadcbbcaddbdcceabcceedbacdaeadbceeedcedbabceccbbaabebccebdbbbabccedebaeeaaceccaedbcdbbbccbaaddaaceaaaaadbdbcbeabaaacbaeedeadbbadbeadeeededeabbccbccacdabebbbccdaaaaeaadbdccdaabcdaabdadaeaaaabebaeecbcbecedbcdcdceececcececeebcceeaeadbbaadcdabaacbdbdeaaadeaaaebceadceddccaebdddcccdbdadbaedabaeddbebcdcbecbddeacbabbaeccdbdbeacdcaebedabaadbbdeddcceabbbaaabaebdbdccdecadacbcebeebcbcaedacacbbcdcdedbbecabedccdabeeceeddaeebdebbdeecabeedcdbeecbdbacdcadbcdccccdeaabcbeabdababdcdbcdddcbbbbababebcaeddaddbbdebbcbabcdbabaaaebdadcaddaceceaaeeadaeabcecaacabdaddadeadbbceaeaacaceecceaedcceaeadccbcdbacdbacaabdeebabdcbadcbbaeeeeedbabddaeccbbcbddddcadeebaaaedcddebeeadaebcdbcdcbeaaeacdaebdecceaaedadacbeecedbaccdaedcdcededdddaeaeacaacabdbceaedaaecadceadaabccbdcdebcedacedbceaabaebdcdceedbeacdcaaccaddeadaebecaabbcbbeeccaedbcdecdbacbcbcdeacadbebeabadbcabdaceaccbddeaeebaddabbabbbdbaceadedbdeeceddbabcecaddbecadabdacbddecaeeccecdaccbaedadaccecebccdeceeeacbddaaadceacaaccaaceadaaadbbcabbcbecbbcebabbaccacabbceedcabbdbdabbbbdadedeeeeeeeaaeddbdebeaecbaccbcccbccaeccebbcdebabaecdccccbeecbdddceacddceaccbaaeceadacbdececadcbeeabbccebecadcbebebdebaecaaedacdededeccacdeedbaedeeabeadabacceeeeaadadcdeadabadcccddcddaccaadeaaeeecaabedbaceededacbedabaaecbcaadaabdeecedccdaeecaeededbecccebccbddbcbebaaadbdbbcacaceaceacbeabddaadceaaaaaacebcaeadbedddbcbbacbebbecaedebaedeebcddaddaecbbbababcebedbecdbddaecbcebcaddeecbedeedbabaaceabddbddbdeebcbbadeadbbbbedbacadaedaddabdcbcaaddcacdedeabdbebeaadccadbbeeecccdbabedcabaaeabdbddeadabbecddbaacbcecbadbacbacbcbedeadeddcabadaadccbbbcdbabaeceebcccadbddadbbadaecaedbaabbadcbbaebedebbabdeaebadeeabbeaacccddebacadaaebbbcaecbbedddbcecccdecbcaddebcdebbbdebaeecdabdbdcedaeeaeacebceacdadbdcdbedbabccbebbabdaeddeceaddabacabdbabbbdabeebbeecaadddaaddedbbdaeedbcbeacdededdbdeabdccdedeacdeadbeccaacaceccbceaaabcaccbddedcdabceaeadbdbdbdaaeccbdbedeeeeeeeabbeaaaeeeeddaddacbaaddebbeeccaeeddecdddbcbbdebddeaaacceeecadbeabcdcecbdddcabcddbabececcabcacceacdaebdacaadaeadcbccbbcacceaedebcdcaaadabecebddaeecebcabcbccdaddcbaebceddaeeabdacbcdcecddbaccddebbacbbcdbecbbbcddacdbeecadaeadeadcecedadddcbaaadbaaccabbebbaeaeacbddbbabbdabbebadccacaadbbedaedbdedbdccecadabccaebdaeecbabceddcdceacaabbeacedeeececedccbbcadadadddbcddbdcaccabeaeecaddcdbcbdccaacdaabdbccecbcddeeeabdabddeddaeaceeacceccaedaeeceabaaacdeceadecbdbacbbcbcedaddbbdbcbeedcbddccbcdeeeaaacbddbcaccdebdcedbcdaebedeeaddeeeabccacbcaaccdcbcbebecdcadbdaeaeccaeeeadeaebaaeabeeadceccbdaaabccdceddcaedeaacbbddeaeaedecdcdbeebccbcbceacbbbebdeecbbadbbcaeaaadeabcdbbacdaabaeabaeeceaeaccebecbccebaecbaaaadcdaeaaaeaeeaadeeceedeecbadbbcdaeeebbeeadcaebbebcdcceeaecddeeceeeeccbaabdcceddbadedebaacaccadceccaebddbcccadeaaeaeadcbbcdaabedebdbbccaccceeadbedededccdedeeeabaebccdeabcaebdceeaceebeedbebaddecabcadddeacebaccedccddedcddcaddadeddcdbdaedacaaedbacdaedcbeeeabecebcabbccccaacebdecdaccdadcdcebeaaccecedcbcedaacdcacdeadecebaceacaceaebceacdadccbcdbbbadacedaaccbaeedcedbdbecccaeaacacadaadaccceaaecbdeaaebbddedbeedbadedcebcdbcddcbcbddcbecbbbbcebabeabdcbdbdddebcccebaceabcbeaacaeedebbeeeaddbabbceeacbaedccbccebdbcbcddaccdbabdacadbebbebcebdeeaabdebcccccbbcdedbcaeeaecebbeeeccabcaebdeadcbaadaadddeeabebdcddacacbabdaebeaaeeadceccaeadedceaaabaccdabeeaeaaddccdeebaceaaeebaaaaadccceeadddcedbaeaacaddedcaeedcbabaeadddeaaeaceadadcceabddeeecbcaeacaadeacddeceaeeeecccccdcaeeddcbcbbddbaacceecbecdbeacaacabaeeacbceecbdcebbdeccdcedabbddeceaaccecaecdaaaaaeaecbaaeeeaabedcceccaadcddeedbdacccdaaaecdeabceeacddbacbaeadbbcccdadadacecabecbceabdaaebadedeaedcbabaadadbddceeebebcadcacabcbbaacdccaceacaeebdaabaacbdbacdcbaacecddbdacbccbaedcecaaeabbbbaaabeadbbcbbdcbddebdaaaeeeeedbdbabbececedccabdcbcdaaacaacaacdebcaaadaedadbbecdaaabeaceeaaccceacdaceebdebabdcedacbdeddeebbbdcdcecbceaceaaebacbaebabcdceadcdadadbbdacdadbdcbdcabccbaecebcdbcebdabbcdbbddcbeadabdabeacbacacabdacccbedbcebdbecebeeeacbeddadbadeacbddaeabdbabbbedcbbecdecdceecbbbcbcaedeabeaaeecbdeddecabeeacadeeaededccddadddeaddeacccbeeacdebeedbbceaeadbdeeaeaebaeaaecbbcdcaebdbcdabedceebbeeaaacdaeeecedacbdddabcccdcebcebaebadcaacecbdbccbeccdabeabceadebbebeccbbaadaaaedbcddaeabbbedcaeaaaedecbadeddabadabbbdbadbadbaacbaeaccdddeaedaddcddedcccdeeddacabedecebcbdaccbddbeddbccdadbebccedcbbabadcaccdcdecbbaeaedbecbbdaaabcaeebedadadcbeacbdeeaaeedebbbeabadabccdedddabbbadbdaecabdaebbdbdeddedcacdbabdeddeadcbccadaedadcbaebdbbadceecebaabbdadecaedccbdbecdddcdddaddbbeceaceccdbaaaacddebcdbaedeebdabebebdbeaddcedecbaabedbaddbdeaedaddcdacbeaacbdaaeaebabaeecdcbbabcaddcabbaedcaeabcdceeeddaccabbecebbbcedbbbdcbedcebbadcabdcdcddbecbdddbeccccaaeccdccedcbacbcbddeaaceeadbccaabbccbaadadebabcaeceaeeaaaaebecbeedcecdacbbebbdacdacdaeaecedbeacceadeacebaccbbabcbdbbeadbaaabecdcbdccbccbdccbadebcabcceebccdaaaeeacecbbbebcbcddbdccadbadccedadecedcedcbdccbaebabbaceebeadedcaccaccebadbcdaeedbcdeabdeabdbeeeeaaedcdeeaadbccaceacabdeeaceedeeacbdaedeebbaacdbebcaeccbabdaaacadeaeaacbadceaeaacddaeaeaeacbcaaaadcbcdcaaacdeebacceaaedeeaeebacbeacedcabacdbbaaedecacaadedbdaadbcdbadcbeecaacaebcdebedcedbacbdaeaabbacbbaaccdbbdcacabdaccccbeebabddaccddbdebdacacbcdbcebabaaabdcecaadbcebdeacdccdbecebcbecddadabedeadaeceedcddaedeaaecccbaebeaecaedeecaeadeaeccbecccbdddeacdadaddccabcbedbbbbaadeaecedadebaceddbebecdcabceacccacebcdeaddbceccbceedbdabdbebceccadacbbadedbdaaccabedbccedbcacacdedbbececbbcecdcdbcdeecceaebaddcdebbbbecececeaaadeceecabaeeadcdbebebbceaeeeeacabedbddaaababdaedbeaccadbbaddeecddaccabbdccaadedeaccabccdddbddeebceeadedddabacdbeceebaecceabbebcecddcceeeaddbabcaabdeddbcdceedbeabadabbacceeecadbedceebeedeeecbadedecceddbdeabbcaadacdacbbbdbadabedaeccecaedcecccabebecacdaceedceccacdecddddbdadadeadacdcdccccecbeccedcaedebabbbededdeedaeaeebbbdecbbcabcbacaaedbcaeaccedeaebaadcaabaadbbcabeccbcbeecbaceccddeddddedeeccdceacaaeaabedeeaecabbcabcaaecdbdeaadeeadccccceeddeabcdaeeabdaacaeedebbcaadaecddcadddeebebbbdcebcbeaaddeecddcbebadcdebcecbcbcbdbeeccebaececcdcaeccdbdebddccbaccbdaaeedadecceeadabdbbbbdbbddebddccccedabadaeadddeabeecbdaaddeabeecabbdeebddbbeaeeddadeaaedcedaedcadcabcbccebeecbedceeebadacecebdaaebbbdaecedabdcbbddbcdabccdbebbddecbbbeedbcbcabadabbeaacadcabdddaebceadeaeabbeadbddceebdeaecccbedcabcbddcceecbdadedbebadcdbbcccdebbdcdabeaeedbceeddcddabeebeadbdbcccaabadebccecceceeeacbcbaebbeadededcdadadcacedbccbbcddacbbaededabdedcddebdcebedbebaaabddeadddaaedebdbdbbbedbacdbedcebdcaebbbcdbbadbeeaeceaedbdecdcadcbccacbdbbedeabecdaeeceabdabaaebcebbacbacdbdbecaadddbcaabcceabebbdbadcbaddedbcaabaedcdcaacdcbdddbbabcaccdbceedbbbcddebeccabeddccecccedeedbadebacabdcddcdaacdeaeeadaddcadaabeddceabbcdeddadbdacdbcddabaceedbddebdbccdeeeaeadcdedabccdbdeaccddddbabaecedcdabdceeebcccbbbdeeacecdeedbebbbdebbcabdaabaebccecebcdebaecaaeadedbeedccabaecbbbdabcbccbbacbdeaccdaeaedbccccddbebcacdccddccddaddacadbedbeccdbeaeeeaebcdcebecacdbdebceeacbbbbcbccbebcdabedcbaabdabdadcbbebedadcadadcebadaeacabebabdbeaadcdbbeeeaebceddaacddcbaaaadcaabeebcceaabbccaeeccbcbdbedabbccbcebcbbdcbcedacbcedbdacadecdcbbadbdebcecececdedebcdebabaccbcdbbabbeadaeddddbaeaacbcaeaacdbdeccdebdeeaedabaeceabdccbcddbceedddabdcdeaddddbeedddcccbebcbadddcedbacdbdaadddeabbdcaeeecaacaceccebacddeadcacabebbcadeacbdaaaccbaacdecadaceaccdeadedccdabbbaccacadcedecedbdddbecaeaaeacbeebbeadbbbacdecbbbaecdcbbcbdeedccaaceddcbceaabbbcebebbaecddeebbecbcdcbbdbdcaecdeebbcdedbbabaddbedaabdccaacbeabebacdeedddbbcdadbabaadbebebededdeedbabbbeddbacdaaceeecdedadedeebbbecbceaabbeeebeedddaabbbcecadcdebecaeadeacdcbbbddbeddcabdabbaecccaeebaebaebddccdaedecceadcbeccadceeeacbedebedaaddceebededdaadadaadaeeeeceebeddabeabaebddddcbcbeeebdbbecbbcdaeaaddaeaeacdccebaabbecddadaaccbcbabbaccadceaacddbbcbebdbbddecaaabdbaeeeebecacbecdcceecbdcdbbdbbcaddbdebbeeadebaededaacebadccabeeaabdcbeadddeeaccbdebbdbceceabecedbbaaeeeadbddcdcbeadacdacbbaeedaaeeddaacedaacbababccacabcedacacbaacadcbeadbbbaeabbbbebabeaaaaceaeedaceebebcbeeacaccdddbecadededdccaebadeecdaaddccaabaeeecdeaddeaabccedcbbbbdeecbbbbecaadabebaedeeddedbdbeacbdaddacecbddacdbdbddbdadddbcbedacdbbebabadecdaccbdadabedcbeadcbacaedadaddeecacedaddebdbdaaaebedbedccbabebacbabbceadcdbcbebcecacedddaedbadccbeedcbbaabeebbeaecbedbbdcbadcdedbdeaeaedeadaebeceacdaccebdbaaacadceaccacddcdcbacdeadecebeaadaaacacacddcdecadaeeecabcaeeeaadddcecdacacbaabbcddedacceccbbaaaadbceaaebbedbbbdbadcceeedbbaacaacdcadecdccedeccabaedcddadbdccbaebdbabeeeebccaccbeaeeaccaceebbdbdeaabbddbacbbeddddebeaaabeebaaecebececbceeeceedaaadbddeacbcecdaedabaedaaabcebcaeebeaaabdacadcccedaccecddecddbbbeaebdacbbceeeeceddddcbcedaabaeadebeedbeaedbddcbebeddbdddbcddcbacddeecccdeabcacebeddeaccbbbcecaebadcdeeeeddaccebbceeeaceeececcecdbbacbabedddbcaeacdcaecedaacbeccacecabddddaabeabcaebdadcbcaeeabdedcbdaaaeaaccabdadceabdaeddaecddedccacbcecdadceacebcbdaacdccbbbdabebadcebdbeebcaebedcddccebcaccaadaceeecebdbaddadabbbbcdabdeeeeeaabcdaabbbcdcbdcedcacadacbebdaeaaeebdddaabbcedacaaaceecdbedbbeaddeebdddebcaaeabbbbadaaadcaaaecedecdbbdacdecbeccbecdbededebbadabceacabeceeaadeaaaccaeacddcacccabebeacaabcacaeacbbdcbcbdbdabecaebabecacedbddeeebadcacbaeadbbbbbeaeaccceebcbaeedcbbcbbaacdccdccaeecbbabdaeaaccccedbacdebbbccbecdcddccdeecbabbcbedeeadeabddebccacbeecdecdcbbcaceeddcbaccccceacdcaeddbaddadadedceddddcdecdbddbcdecdabcaddedceececddccecbbadcebceaddeceeebaabceeadbbcaeeaeeabbacadbdcaccddbcdeacacdcceecbbcdcddcccbbbdbdbbacacdeddbebdeeededcdbdbeddbaabbabceadccdbdeecdccabbadcdeebbaaeedbbaaaabccdccbddddeccceebedceecdbbaadcecbdecbaaeeadeeaebaacdebaccaebecdebaacaaacbbcbecbddddcbeecaeaadabdabdeddddcaebabcbadccdacdeaeeeaaedcbbeacdeabacbeebabeebbbacdbebceabeecccedecccbacaaccaacdcdceecacaedcadaeacebbeabcbdaceecccacbbaccecbdeecbeeaadbbdabcbebbecceeaedccdcdaeabbeceaebabaedaeabdadabecababaebcbadbeccedddcaaecdabbebadaabdadaaebdaceacaeebedeebdbebccbbabbddcacbdcdabacdabcadddabbcadcbecadddabeddcabaedebabebecbdbebeabebdbaecdddbeebaaeedbaaeeebaeebddebabcbbdccaeebedcdcbcdcdedcedabcaaacebdecdecbaebcdcabceaabebdccddaabaecdbeaebdbdbcedbcaaccedccadcdcedbeacadeecaabccbccddbbaecdcabbdeebdadbcadbdcdbeacecddaebaacedcdbebdabdcebedebadeceaeebbcbeddaedcdcabcbdeacdddbebceeddcbacdedaeecdeaaebdaceeddeecadebcdebcaceaabdbbadedacbbbabecbedeabeebdabbbdbbebebcabdddbbecaeedcababcedacabbedbaeedadbceddbceaebdeeeddebacdcaeeebdabbdeaabebacdbbceaebecbdbdabbceddbdeedcdedbbcdeeecddbbcabbedccccadcaaaedcbcccbeccaaeedcdbcebbcbbaaadbaecbcdbeeeddeaedeeeecacecdedbcacdaacbbbaebecadbaabeeacbbbdcabcacadcdeaabecaacbebbadddbbbbcbbcdbdadedebabbccebcdddddecaeedebcaadcbcbdcabdbcededdceaebbdccbaeeabedbdecebdddbdaecebeccaacadbbdbdccaedeebcbbabebebcabbbebbbbaecadaaceacebbbbdbaddcddabadccadebeadeadcdeabddcedaacbecacdacacdccacaedbcbbcbcccebdbeeecdeecbeeadeeecdcdbbadeabdabeccdbcddeaebcceecbacacddcedbcbdeceabaedbdaebababebceebdecbdcdbeddbebcdeaabbeaccddceeecddacdaddcbcadbabdecbaebaeceaeebacdbbddcdbeaebbbeceeebdcccdbacbaadbdbaddcebabccdeddabdadeddccadbbdebceccdcaedeccdccdbcbdbbceebcccebebbbadedaeabdbaeaecebbbdcebccabebaaabdbeaaddbacbdcdbebebecacdeadadbcaeedbeddbdebeadeacecaaddaadbeccebadeeacaceacabeeaabbdddadbeecbbcbedbecbbcdeadccadabeececedacdaeddebeaabcdbecbebccabdacddbdddddcabbdabeacbccbeaecaeacbbdacbbbaeddcddbdebebaeecddeadecdbedaeedeeebccceceabeccacadadcedadbadbcceedcdaeaeaddbcdbbeceaababeadedaaaecaaccaeccededecbeededebebedccbbdaeabedddccecabadebebbbdaecbcdbdecddcaccdcabecabbdebbedcbbdebcaededcaabdbbeeecaabcadbbbddababecebecebdcdbecbebacedaddbeedeacaccabdaddaeddbaeaddeeaceaccdebeeaeeddadcdbacbeabddaddbecebeadceadedcdddddeedcdaeaeedeceedcbaaabaeeaeceaabccbecddabaeddedaaccbcdebddccababbdddacbdbdbabeaacdcadcbbaebbceddcdecdddabcaeeaadccccadbecbebeebddcbebbbccabdceaaebddcadbdaacebedabdedabdabccdadcbebaabebbcddbaaeaabeaaaeccaebdabadceabccbebababedcdadaccdbeaecebcabddbcdbeccbadcccddeaeceedeaeeddebedcaaaacecdabaceeecccbaeeacaacaceeabaabbeccabcdbaeabbababacdbeadcdccccbeddacadbbdcaaaedeeccdabddbdaaeccdbbbdebceacaccbaacecddabbabaceaacaaecdaceebcddcaeadedababbbbdcbccacddbebaaeeaecabcccdcdbacbbbddbadccecbcbdcbcebecaeddabbceecbabedadbddbbdbadeedccbabbeccebeaecbbeeccdeceeedbaadacbabadeddabcadacccaaabbdaeaaeaeeebecbecacacbcdadccabebebaaeebedcdccedbdedcdeaedacacdebddebcbdbdaebcaebabbdaaaadcdabccbaddaaabeccbaedbceaecdbaeeaedcaddbdeceadabbbebaaaaacdddeddbabbbedaaedbeceaeeaccdbaeeabdbcacecceeabbcadeacadccceaceaacbdebebeccbaecaedadddedceeebbbceddabbeeabdeceedeeceebeebeecacbccbcbebceedededabcabeaeedaddbaeaaabcdccdcacedaebdadeebadecbbebcbebdbaabbadcbeeeacbcdbcebcbdaaccdeaccadecdedaecddddbdaeccaddebaaabecbcadacdedceccdceaedcedbdcbaeaddcdadadddcaddcbecebecccaebbbdccebbceaecacbebebbaacecaeececdcddbececcdeaddacbeeeaeebbbcecbadebacbaeececbabcedcbcccdbabdbbbddaedcbbedebbcbcbeaabdbdeccddcccadbedeaeacdeebddaccdeeaddbdddcacaaaacabbabcecacbadecbeceadccedcbbbaeabaeeccbeeeadaddaeadcbbbbcdbeaeccacdeceecabbacdeebbeaddecbddeebacaabcdebdbaedcaddacbebeaedddcaacbabcbdeebdddedbbcbdeccbbdaacdadcaddeeeecdbacdcabcdbbddadcadbaacebceeedaedeeddcdbaaceaababecacbeaaaadabdbadcdbeeceebbabdacddaadbbbbeeaceaeaccdceacdeccacbebdadccbdacacceedebbdcedeebecbaddbbbdaedbdabcbebdaeabeecdeacecbaeccbadbbebebebacedcbceaadaeaedcadedaebbcebbbdbdddcdaaadacbceeaedaaabbacadeadedccccbcaedcbcdaacdcdeeceedbdedbeabdbbacbddbedecdcabbeaaecbbdeaeddaeecdaaddcdedadddcbcaaaebbbcdeebbadedbcabaddcdcccdabaebebdaecceadbdadcbacdbdebcbaaadeadcbddaaddebabbdecdadacedddcbabcccacacacdabdcddbedabecddeddeeacbeaccbcacdebacdaaeeababacdaacdecaaeebaeccdbeeadbaccabceddccaaebddbadbddcecadeceabddbaadccbadeccbaacdedccbeddbeececcddeeaaceaabdbdaeceddddbaccdaecededbcacdccadebabeaccaeddaaddabbcabebceabaadeaaacdbcedecacdabcbdaedceaeeaabaecddcdbcbcacbaccccdeaebdcccabddecabeeddcaedecdddadcedebbcbadcbccaaedcebeaadbcecceaeeebbbeceaaabbdedbbeacdbaaecebecbbcbbabacddbcbeddcccaabaabedeccbaedaaaaaeaccccebdcdedccebdacdceacdcaccadbdcdbadaebabdaedcbeebeeebcccadecceaedeedcaeadeacebeeabbbecddedcdcdaadebdecddbeadcbeeeeadcabbacececadceeacacdbdacbbadaacebdabcdcbccaebacabcdecabbdcaddacaeebecececaeeeddacadcaebcbcadaabbbacccaeadbebbdaecbedabdbabdcdbedcacadbeaeaededdddcececdadebcaebbdaedcdeaaedbdcdbdacbadbcdeacebdbcaeadceeebcdadacbabeaedcdbbdaebcedcdbdbeeadbccedcdbeeedececbebdcaabcaaecdcccebbbddeabaedebaaeaecaabcadedcabcaacbebedbcdecadeababbebdaddaaeabdddadcddcbbeabadeeeeaebaeceadacdedaaaedceaebbeeeaddaddcdbbdcaeeabcdbabbbbddcbceeadcbcceedceecaadedcabbbabacdeababedbbeaeceaadaacdaaebeaaeaaddadaaacbcbbcdaeaccabaeabcaaabdadeaedacbcbebeeedeebabaabaecbbdcbedeadbcbaceedadeacaeacdcccbacdeddcdecedbaaccacedecbdeedeacbcddedbdceccddbddcadeabeeddabedacaaeaedeacebaceeaddbbbbdebeadaccccbbadbcdeaaabbeddcbbabbacdcebdedbacbaddbebecbcadacdcacaeeaeabcceaababbdacbacdaddbcecaeecebbdaecacaebedbeedecdaaddccbeeccbeaacbaeecbaebebacdbeebdbcdcebeecaecabcaccdeacebdcbecebcdabdccdababbedabddeeddccbdaabaecbacabdaecaadeacadebaadceabbcdbddedbcdadbeeccaaddbbcddddcdaddddaacdbddadbedceeedededaecbcebadadaebbecbacacadcabbaaadecebebcddcccdedcddbcabbcadaeedbbdccddadabeabccedcddaedaddbdbddaadecdbadbadeceeabedaeaacbbbbadbeedadaaecbcacedcaadccdadbccceacbeeabebabebbbddcaaedbaededdedbcbeecaaabbadceebcebcacccdcbddcdadcadebcdbdbbdaaeabcbaaeebecadcadcaaadceaeecdceabbeccabceecdcdaceeddbdbbadbaebeabddbeeacceaaecccbdaeacadaebeedceabebcabeedaceadbddeecacccbdadccbbaaabeecccbebacbeadaecdacdbcbebcaebddbaccbaaccdbeabcdadcdadabadababeeaebeabdceceeadadeadcbaccddcbcbaabdabacebacabcabacabcbaababcaadcaedddacdeeebeaeebebbbeedabadddceaddcdbdabaceeaebccdacbbaecbededebcbcabddbabdaaabdedbacddbbadecedeeecceccbdaaacbaecaccddeeaaedcacdeecbaeadbaacbbcebabcbccaebecdbbdcaaaaeebcaabcddecaddddeeededebeedbebaccebbabdbaaeeadeaabaccdcbceacbedbbdccbebdcacdebadebbeacbaecbecebacbbddcacebebcecaaedbaaccbeacbedeebeeaaebcaebdddebdbebbdecaebdbdacaabcceeddabbdcbcccaeeedacebdbabbbcadcbdeeabbccebcbbebcebecceccbcaadedaeeaeeacdbecaaebceadceaaccabacebebaaaddeaaedcceebbaeeacebebddecadedacebcaccbacaacdbcdbddcdecccbcaaaccecaeaedbabbdcbeaeeabdcbeedcbbcddebdbecabbdcccaddbcbdacabbabbcebbcbceddedacceeedbedcebdbedecbcacdbbcedcceaedbcdbbcccdabcebeaadbcaeddeaebadbcccbdeebbedaabaaccdbeacddcccedcacaddbbaceddddbabbbcdaddececdaecbbcbbbddeedeeddbacabbceaccbdeeeceeaeedceaadcbaeabaaebeecbaedceddcdebebeabcbdacbdacbaaebedadababbbcebbeaecdadbecbccabdebdceedccbeeaaccbadabdaedaebddacddbdaedbcaeadcbdcecebebedddcabeddadddbaebdbbdaaaddcabcbdaaadeeeedcceecddccacdcceeedbccecaaacbcdabdebcbbbbdcbbddeeeddbccddaccaeaeacaccbecbbadcbbecdccacaabbeccadaccbdaedcccaaecdccdbcbaabbebeabbadcaeabdadbceeacbbbacccedbaacdbabedddeadaeeeabbaebddbaedadaaebcbdadebdbecdbbebbdbacdddeccecbaecceacbdabaaccbcacbedbbebedebaaabbeadbdebbdbcbedeccadedebdbedebbcaebcaecaaeababcacceadedeacadbeebaadecceeadaacbdcdaccbdddedccecabdcbaeebdebbdcedccacaaacdbceeabbbaceedbdceceacdeaeddadaaaaaeebaeeddbcbbddecdddcbbdbdcaaceccadcdaeadeeebaaaccecccbebeaeeebceddedabaeadaacaaddebddbaeddeabaccddeaecddaaecdeedbaeacdddaabaecddabddcbdcadbcdbcbcadbaebabeadbeedcbadddcebbabeaabedeecbdbeedcebababaedbebceebdbadeecddcbccceaeceacabacbeedacdaecdeaeaedccaadacebcecbcceadbbdbadeadcecdedbdeceacedbdadeaaaebebcdadedadcbcbaddeeacecdbcddbaaeebadeedecebbbebcbcdebbccceccbdcaeddbebacaebbeeaeabbaddebbbaabcbdeadabaecdcabcabdcdbadedeabdaaaebecaedbacecbcbbeecdccadaabbaabcccbaedabcaabacbeaabeddedacaeeacbdbeebccccdbccaebdeddbcbbbeeddccabbcacdcedbebbcdcabbbaaedebbbcacedebdcaeaaabaccaacddcdcbbcbcabaddbdaadbdecbebdcdbeeacadaedacedbbabeebbadbdabeaaacbbccaecaccbaccaacacebbedbadbdacdaebebcacbebecaccbdcaeadedccedeacadaacdabebdadadadecacbbbcdeedcbdaebcaeddbbddaacedbdcdbabecdbbdaaaeaccdcddedecaadabcddabcaadcabcabdbdeadbebeadaaecdbaedabbecdaaabacebccdacbbbcebceebebddbeebbbadceeecbebddebaeadcbcadecbcacddeccdcecbbeecaadbadbcdebdaddddcdeceaccbbddaedaaebaacaebcdceeeaecaacdccebebeedadebecbaabebdabcdacbbdceeaceddedbdccaaeacdeddeeecedbeccaddaeeacedeeeeedecaeadeccecaebbbeecbbcdcaacadacddcceecbecadbdecbabdcabbbcbbdabcdaecaabecacdcebddcacbdceeebebdbcbcdecabdceaeddacdeabbabaabdaeececadabbeeddcbedabbbdceecccbbdcacbaedbdecebcdceaebdbcdadbeaeaeaedbccddeddcacabccdeadeaccecdccdabebbaedcbcdaeddbbeabbebeedcaeeadcbcbbebcdcbcaecbdecdccdddcbaeedabecbedcebaaeaeddeabbeedbbdcbdeeeededbbddbaaaaaeabeabbaedbddbcebacaaeadbdbbdcadadaccdbcbbcbcbabaebbbbbecebaeeceeddeacabddcabaedeedadaedacbbccbcdacacdbadddccbeebabadbacbdaeccdbabddaccbbdbeccbcceabccaeabcecdeaaeccebeeaeeddbdecbdabaaadaaeaedeedbebcbdbbeeaccbddecdedcdedbaddedbbacdbcaecccdbebdeecdcebcdbcaddbebdaceabebdbbbcecaacdaaaeacdeccddcbcbbedaecabbceaaaacdbccbecccdabcdaebeedccedbedabbdcabacbcbebdcedebacbedabdaebbedddccccddcccaabbbdeeeceddaeeeaeecbdcddcabecbacecbcadabcdcabddcbcacbcdcaeadcebceccddaaabbcddccecedadddddcbceecbddbadeacbcaddcdaeccdbcecbaeaeeddabdcccceceecdacecbbcebcedcebdbdccbbdbdaaacaecaedaededacdbbdaebaeeecbacabddccccdebcccdadcbbbeddebaacddaaeadedcedebacecaeeebbddedecdaaaaadcecceeeeebccecbeddebaeeabbaaedacbcbcacbaeecdbbaaabbedecbeacaececbbdaadedededabcbdbceebeeceeaabeceeecbacdbcabecabbcacdaddddceeecceaccddcdbeebedacbecbbabccdbbebdadccaedcbeeaabaaebdacdaabdeecdeabeaecceaacbbdbceacbaecbaaedeeebbcedccaaaaecaabeacccadeaeacdaeeadecbccddbaceeaddbddddeecbcabddbeebaedabdacccaebebcdadcedeecaebccbaeddacbbbcbbcbedebaeceacdbeecbccaccaeedcbdeebbaaecaabebbebbbaaabedcccabaceccedeceebedbadecacbaabccadbbcccdadbbccbeebcabceddbbadecaaaadaebbbcbbdadeeadbaadeaabeccbdcaababebcabceeccaeaeacdaaabccbbdbceaeaaaecbdceaebadaededbceecccbaddacacaecdedaebeddbbebcedabccbcdaeaabdcbcdeddcddccecacbdaceeadcdebeaddadceddadcaaddacdacdaabcacacbaabdbbeebadcbcaaaaeeadcececebdcbabeadedbddecacadaebaaeceedeacdddebbdcabaacaadeeddcbdcbbdacbcbcbbcecedaaaeccbacebadbaacdeaecbcccabdecdceeceddaabebdebedbbddacbbcddeedbcacdbecabbddcceacacacebbdacedbccadecceabacdbcaecebcadedbeaadcabbcabbeddcdaadcddeadaabacbecbadbedbcddaaebbdddbedcacddcdacabdcbcaaceebddcebabdcbbbddbacbcbdbaabadbaddedccbaaaacaaaeacaebbaeacbaebbddbddbcdddcbcceaeeadbbebdddbcdecabeadbdeeeebcdbdccabcecaaabadadabcbaaadccaceccaadcaaaaedebbcddeabccbccadbabdbcaacbebaccdbaebadcbdecacdbedaeccdcbbaebabeddbeaedbdaaccbccabcddccbedecbbcbcadaaaebebaabdebbeaebbebacdbeeddcbeacacacbaaceebbedcdbadeaacdccdaaebedecbdceabdedaebadcacdddebabbceaebddedebaecbdbabbcadaccdbdcdeeadbadebdeceeedcaaebdebbeccdcaeedcaaeeddbbabdcbeedeeaeaaababebecabadeeebadabaedceeaeeecadabcaaaecdbeaeaddcacdadccdbecadecddbacdaecddadeddbcaeacebcecccaebdebceaeedabcbcacdcacbcacaddaedeabadbacaaadacbbbaaabadddaaadcdeeceabddaeccbadabbacddbbcbbbdcaebbdbadbbbbcabadaaaedbdeedbdaccbdeddcdcaececbaecbeeebedbdeeccecadacdecdcaadacaddedecacebaccdcecdeedaddaaccaecceaebacaddacdadedebbdeacbdccbdbbcedaedadeaeacacadeebedeecdaeabdeeedeeaeceaabbbbdbcabbaabadccdbddcdacadaaddbacdbacccbaeacaabdbacdccbdeeabbbadcdcabeacccabeadcebaadcdacdadbeacecaaaeaabcdadccedaabacacadaccddebbeeabedeeaecdbeddbacdeccabdddddaabebbccceabbababaeaaaadddcecdeaeddebeacaadadaebadaaacdacdcdbbccbedeacaaccbcbacbaddbbadccdbdeccbacaadadeddacaacdaeaacadccbcabdbededcbcdecbdebabdcddeccdaeeceaaebdaabaaaacaaaeaedebdedcbaecbcadadbbeadaecbdcaeabcecbaedebceaccbceeeecddbbbeccababaeeceeecbdeaeaeedbedbabddccbabaeadcbddbedaeedadccbdabecacbedcaedbbedeacddcdedcabcedaaaaececadaadceebabeeedbdcaeaeedddecdaccbaebcaaeacaaeccdaaaabcaeccbedaadaeebaaeebedaaaeaadebdedadcbeecdaeebbdaaedaecabdbdedbbdaadababcecdbacbbeaccaddbcececbccbdadecdbdeadabacbaaaedabaeaccaedabcdcdddbcecbcdcdacbdedbebaaaeccedbcceeaedaaeadeecbcacbaeceabdbbdeaabecbcadeebabeaedceececdeeebbbdbaeadebbabcecedcebccbdbcbeebeeedbdcaadecbbccabbebecebceadcbcedabdccbdbadebaeccdaddcccdcdaecbdeececddebcebabcacbeeadcbadacabaaaebbbebadeabeddcbbaeccbdbaceddaaecccbcbacceabbabccdaacbbcaadbbcabeabcccdcaddaaacadcbbbbbbdedcdbcbaaabbaddbcdaddaeeaddacebcddacdbaeabacaeacaaceceecadbacbbddbebcacdadbaccaeaebdacadbedcccaceaabedddebbaaeabdbdbdaededcdddadccdbbdecdbcbadccecbebcaadecbdbeddecebdebaeabadbaaedbeaadbdadabcbebdeabdceaccaacebcaaedeabbabdeddedcedbcdcebbcbbdabedeecebdccddacebcbbebedacacededaaecaccaddabacacedbdbdddcaedbcaaadbbaadbaccabdaaeeebedbbbeaeaaedbdcdaebeceecaccbedaadcdebeeaabeaedaacebdaaabeddcbcacdbcabcabbcbcbbcbdabbcddcddeadbbacddceaabdacedeaaaebecdcdaadbcdeadbaecadabadbabaedaabdabdadbcccdecaeaecacbecedcbbdaaaddeccbebaaccdcceaedeaededcaabdbcabcdebbaedddedceeabbdcbbdbadddabdebdcabeaaccebcecbeebccdbecbdaaeceeceaaddbbbecaddbadecdceacaddbbaccdbcccbbbbcdbaecdadbeacbeecacddadccbacabacbdcacadcbbdebcbeceaeddcabdaaeebdbcadeebbecebdecdcadaccdbadddebbadeddebaeeaaabdeeebeaecdbddadbaaabedbbacbceeacdaceabbddcccdedeccbbdedcbcaabedadcddcaaaedbcbacbcdeeeabaaaceaedbedbacabcaecbdedcadbdcbcbacceedcbecbeccaceadebcdedbdedeaecbdceeeeeaddbeecedbecdcbeedbccbdaaecadccadeacaeaaedaaddcbcadddbcdcbdccaccacdaaedeeebaaabdeddcccacabeecbecaacdcdbbcebedbbdbaaeccabeeaebbeabbadadcbebacabdaacdcdcdeacbcebdceaaccdcbdcbbdaeccbccaedcbcaabdaaedabddacbbbbacecdecbbedbbcdceabdccdccebdeccebaeaceaecbedbaaaedccbebdaadeebbddbbbeaacccdabbcabaceacacdebbddcbbceccbbacccedcdabdccadbbcbabddabbbcbbcedeacdeddaeeedcdeaaccecbeaadabddaecbddcbacdcadcdeccecdebbdbebeeaebacbccdaabeeabedaadadcedadecdbdacccdabeabeaccacdbbcaaccadcaadbadcbebbccecbcbacebbebcbecbcebdaaeacadbedabaeabdecdebaececeebabaecccbbbbbbbaecbaecbeecceddebbacaaaadbcdbcbecaebbebdeacadaedcbaacaceebddeedaccceaaeaebdcbcdddadbebcebbdecddbceacaaecdbeddeabeecccddbccdeaccccdbcebdacddaababcbcabdaecedadecdacceeaeddbcbadaeeebacebbccabebaddedcececccadcbcecaeabeadbadecbabdddeecceaecadacdcdabbdcaeeabdbcceddeeceabaceccebacaababbecaccdeedddbdcbceacecedbaeaddccbcaaaabbbeeacabebeebadabdccdadedadcadbbadcecceeedcbdbdbdecdacbdcbddaeebabaebecdcbebecbecdecbedbeacaeaccddabdccaaadedeedddeecbddebebceeecabccbdebeeecabebdaaedcbeecbbaeeeeedecbcddaabaedabaaaeacedededeaaabbaedcacddadccacaeaceedbdbcbaabddaabcdeaedcdceaaacacbddedeaadcdbebdaaeddddcabbceccaeebbecbdaadcceaccdebacbddbbcacdedeaeaddddebebbbccadcaaccaaccdbeeaeecdbaedebebbacbcdcbedceeecaaceeadbdebacbadebdbedebeecbcdecadbcdacdcbcaacabcadbbecdcddcccdaacaebeeaceeadebdeadbdaceabdadddbcdeadaebaabedebeadbbceeaabdebebeddcaadacaccdececcaaadbeaeddaceeaaacaebbdcbdebbeadcbdabdddbbbeaddebaaecebababccecdbeaadcbebbcedbcaedceecbacecdaaecccaeeabecdcddcdbbcdbdbdaeddebbddabdebabdcaaadaaccebdaebbbcbdeaebbedbeedadeaaacdaceebedcaedacbaedaadeadbacabbacbdabeeeacaaaadecebddceaadaecbbedebacdedcaddadeaccaaeabbaaacdeceaebebbebbdedcecaebcabbcdddeeaaaaccccbbcebdbedcbaebdcdbbbaddceddebcdbdceaaedcbddbebbaeecaaaecbcdbeaebebebabbeacbebcaddebeeaaeeadbceebeeaceabacbeceadeabeddebdeeccaaccceacbeceabeebaebccabbcedbeadcadaadeddcdecaabbacadecbcdbbcdabedadddcabbaaacddbbaeadbbdddcdeaececcbbdaeceeaadddbedbcecdecabedeeebaaaeaedbbcbedccddaaecdabeeddacaedcdaaeddcbadcccccebdecddbacbdccaaabbdcbaeedebeacdeadbdcebcacdcdeacaadcbcaabbaaaeccdcedaaababecedbbcabbbddbadbabcbcebebedbbdcdeeacadcdacaabddbdbcbdbebeeceecccebbccaeebacddaadeddabdaecedcddaaaaedeadadbbeaaccbcbccebddececadeeadabeedbcecebbababacaaedadeaddaaccdeadacabcecdeabbcbeebdbdbddbbcdeeccacedabdeeedaeebacddecdacbbabbcabaeeeddccedddcbddeeebeecbdccacdeadbbdcbbcdbdaceddbdcaaabecccdeebaabcceebebadaebedcabdccabedcbaddecaadbcdbeaeadcedddebcbeeebcebeabdabceccacbceabedccbdbcacecebadaaabcdddaededebecbabcccadadddaadaaededdccdaacddbedeeaabcceebbececeddadaecbeeecacbdecbdadadcdadeccdecabdadbeadceaaedeadbacdcbbdeeceddcbbddededbaaccecbdaccccadcdedcbbbcaceedcbdddbaaabeaabdaaeaeabcddcdabcbecdeedbaadbccbcbcabdcdcddceaacdbdaebbaaabcadddedbdbcbcbbadcecdeeccebcebccaeebcbdbababeacbbbbcccdcdccdeedbaedeaaecaceabbededadbdbbaceedaedbddaebecacadebaeedcdaabcdcedbcbaeaeccbedebedccadbcacbbabaeaddcedbbcccacabaceeeaaebdeadaabbacdcbcbaaaaaedcbcaceabbcdacccdeadddbbcddeeaebdececdceeecdacdacbcabbadcceeeabbcdeaaeadddaeaedadbdeedaadcbccadbaeabcacaedceccdeecbaddaaddcbedabaecbedbaeecdacbbaaeeddddedccceeecedbebebddbccdceeecbbdccdcecbccbdddccabeddebeedcceeaaeddabaedacbaaceecdbecdacacaeceddbcbbabaebeecacaebcccbcecedbdebaddeebcbabedacecbaaeecaeddbdecbbabdcbcedecbabccbcccdbddcdbebacdabeedaceaaaccadbcaaecbbeadedbabbcacdedbadcbeaabcbacdbeceaaabaebeebeecccbceeccdcedecbebabebedccbbebddaadacdeccbcebcbbbacbcdeececabecabaabaebeaabcbeedeeddcbddcbaadabceedccbadcaabdcdeeeeedddbcdeecbcebecaacadbcedaabedeeeaedaecbdddbdeacacbbebceeaabccaedbceabbeddabaaadbbaebadedbbeedebaededbeaddadddecdcdecbeaadcbcabedddcdcaaddbccaacbdcbcaecdcdcdecdaacbcaaebcbbbceecbabebdcedebeaaadcbaaddcbeeeeabeeeecdaadebcdaeeddcdaeeaacaedeeacaeaaaeeeedabaaaaaeedaecbcbeacaaeaabdcbaccbaaedbcedacacaedabbeccdcecbaaacdbddacadeedecdcbccececbcbeccbbadddcecddbcaacaabdacebdbcaeeaddcbbddcdebabcccadeceaeacccceeecbecdbbcbaaaebbceeadeaeaebedaacaccaeaaecadddbeadbedbecbcddcaecdcaeebeecbcacbbdabdcbbbbcccbddabbdbdeeadebeecebcbbccdeedabcaeaebcbdeaddeaadacedbedcbaabbdaeddaeacbdabaaeaacbcebadcdedbdbabdadaababbbabeeecabaeebdbbceebecbdbeabcdcedbbcabeaecedcdeddcbcecceeacddbcbaabeabdaaaccacbcbecdcadceccddcaceedadbaabeedadccdacbdcbbbdbbcaaeabadeeadeeabbddbcbebbbbbbaeabaeddbbbedeeebebeaeddbcbabeebbdcaaccabbbbaababbbccabbcdcabccbdcbbeccebaacdcdabcbbbaebedeeebdeccbeeeceedcdbeeddabdbbadedccdddcbaadedcacbeeceecbccdaeccbbcdddaaccaebacbecbdddabeaaecaaeccecabacccdcadbcbeedddededbaccdcbcddeeaeccdbeeccdcacbceedacdcaabddbabdeccaaebbacadcbebbadddaebadedddedadbbcedeeeddabbdcaeccbcbcdaceabdadebcbdaabadebebeadddaeaedcdaadeacadedbeadcaacdaeabdcacdbdcdacbadeeeebdddececdccabeceebccddbeacdacbdaeecaabaeaaedbebacbcadddcedaaebdcaceebcbdbebecbeebbdacabeeedcbeeddcbcdabcacedcdbadacdceedcaccacbddabaedbbcaadeadbddccaacabecedaaeacaeaaadaccbadacabbbccbabeacbecbbcaeaddcecdbaabbcdbdeddecccaabaabeaedeeaabdbbeadbaeeeaeacabedbcddecceccdcdccbebdeeccaaabeddcdcaeeceeaecbabbbccdccaaccabcdcdbadeddacdeddaedbcdeabbcbddbcdecbbeacbaaeababcaebeacbcecbedbcbeddbddbaccaeaaadbaedabbbebeeeadadcbaaeaccaebcddebecbeacebdaaacbdaccbdbeaeabaabaebcaacaabcdcadbebccecddbeabeabdecbadeaababeeadeabdbddeebbccaccdabbcbbebadaaeecdecaaecabddabceceadadaddacdadebadedcebcbaccccddedcecbcdacbecedaadedbaecccbdeecccaebbcbdaeabacedeedbcbeeaadeeedacacebcecaccbaaedebbaecedaeaaecdbeeddddccadcdedeadacddeeaccdccbcadbecbdcddccddbbcedadbaeacdaecbcdaddbabecbdcacbeddeabdadccbebddedcaaacaadecbbaecedcdeebbcabeabbbcbaaaaabaababeceedbeecceabcaaeaeeeaaaceabbccbdbeedcdbdeabddaadbbbacbcbcbebaeeedccaebedceedacdedbacbaaceaaeeceeccecaacecedbcedeabaeedddabdeebaadddddecdaacdeaaecacdddddaeddabbbdeadeadabcadeeebcaeaedccdddbdaaaebaabecbcdaadcadcddeccdcebaadecddabacaededabecbecadbccaecabbccbaaebcadeceddecbdcabbaecbdddabccebadaeedacbecdeebcbebdbbaaadebddbcccabcbedbceebbcdecacdbddbbdaeeebebabebceacaddcbebabadebbcaaccccdbaeadaadcccadadcbeaabecdbedcaaccbccbecdadcbaacbdbedbccbcedeaededcadcbdcdceadcbbcbbdeaceabbaecbbccaddcdbadeaddddcccdceabecdedaededacdaedaabbebcdadadadabbdeaceaaadbcedcebdbcdaadbaeacccbdbdaeddacdacaebcddedbabcbdcbaebabaeeddbcacbebbdedeeeedebceedaaabaceabaeeeadaeeddedbacdbeabddaaababcebadcdedbacdebebccaabceeedccbaeaaaaaddacebcdccdccdbeacddbebbaecddccdeaacbbdbcdcbbdadccdaebbdbcaedcdcbdaabdcbddaacbbebaebacaabeebbbecdceaebcacaadcaaecbdedcabdeceeababeacddcaaabbbbeeadccbaeeccdeaaebcadcebcbddceadadabddeebbabdeaecaeeeecbedcbcabbcaaeedcbbdddcbcedccdebdecddaebbbbbccebabebcbecbceddbacaaccbdcceabbbebccbaecddeebebeaccaacbadedbedaeeccbebeddbaebbdbedbedbacecaecbceaadabbacccbceabccdbcccabedcebaebaacebadbdccacbbccebdbabceebdcecdccdbbbcaeaeaabbcadecbbedbbcaadaddcbdcddcdbacbaecddbbbeebbcbacabdbbdedbbcdaeacdbbbaddcdaacdaabdebbcdebebdadedcaaaedcaadccecacddccdebbbdcdbceceecbaabacddcabecdcccaeebeceddbadcadabaeadcecacbceaeddacceacbdcddceaeabdacdadeecabdeecbecbcdeeaaeedabcecaabcbeebebedabdaeeddabbdadedcedccceeeeacaeacaedbcccdcaebbdccdaaeacdcedebcabeaecccacaeacbaedbadcaabebedbeeebbcdcadeaaaddcddbeeccdabcbeaedabcedeaebdccbccdebeacaadebcecabcaecbaddaceaadacdaeccdeeaceddacebabadebbcedbbadeecdedbcdbbddcdacdcccaedacacebbddaeceaaeddeccccdccabbddcbdececbdbdebdaacbaccadeebcceeddacbdbdbebcedcbeaaadcaabbbacaeceadbecaecaabadccbdbedcabebbabcabdcdbebeadbdedaebddeedeeacaecbadbeadeddedeebdebebdaadedeadaadcbbbbddbdaabcddaddadbacecaccaadbcbbbdebcdcaadbdbcecbedeabedbddceaeebbecceceeacccbbbbebdbbaaccbdaeccceabaaabbdabaebdecadeeddeadbaaebdcaeacbeaacdaabeeadcabeceddaaebaaebaedbbddbadedcbaabbdebadaaeeddecbacdbdcacbbdcbdecedeccdbbabddebcebbbcaceeebdeeadbcbedeaebbccddcddeeddedaceedebadebacccddbdebabcebaaacaedadceeccacbadbebbbbaaddcceeeacdcacdbeadedcdaebebbccedcbbeddedccbedbceebaabdcdcabecccabddceebdaecbdbdbdcaaababacbeedaaaecddbedeeaabeadcadccdbeddbebaebbaeccdaeccaacccdbeedaeeadebdaccddecbbecceccbdacacebbacdababbbabdcbdbdccccbaeeccacdedeebcdabdeebbbebbeddeaadcddabeedbbbecbbbccdeebebeeaeceacbececdbdecccaaededdbeadcadbdaeabebeeaeadeeedccbdbcaedcdeacecddecbbddbbccbcdceaddecabcbcaadbacaaacbdebceeccddbdbdedcbdbdcbaceacedddcecaceddcddeaedbcaecbcbbbebbcacbadaaebadacbbddbcebbedcccbacadeedcdbbdcbceabccbcbbddaaebecaccebceccbaeaebbaaeaccebddeaadcacdabbbaadaebebeebaacdbecbdbbdccabebaadceaaababdcceaacdddbcddbedeceadecbeadcaaececdcceacababbdeccbcaccbbabcbabdccdebebbbecdbdcccabdbbedcdadeeeaabcaacbbbdeeacdbabdbbdaebbbacdbaabcaddceddbcbdbbabbbeeceabeeeabdceacebcccabeccddeddeedbcaacdcbcdbdccebaeddebbbdbdaeaacacebacaaeacddceaeccbabecddecbbcedebdecbcccacbaaacecaccaacdbaceebdbababccabcdeddbdbeedaeaacdeccecccdaadcbbadeaebebeaabbbacdbecebccbcecdaceaedcdedaaeabdbccdceaaadeeecaeeaddebccaeedcedabceecededeababbcbeceaeaabbaabaedceabecababacdbaddabbdadebdeedcdcbabaacdadaaeaadbdadacbeecacdbceddecdcacbbbacbaadcaeeeceaaedbadbaecbbadbcdabaddddcaadbaaaceddbdbbcbdcdadecbebddbcaedacbdbccecddeddbaabeeadcacacceeeaeeeddaecccaeecaccabeebbebdeacceaaadeadcacbabccbceaedcbadddbdacddadcaececdacecdcdecdbcbeeceeddccedbcbecdaecddaecbbadbaabdeedbbbbcbbecbcaaeeaecbdbdeadbccbebdceadaeabaacdaadabdbececbadaedcdbbdceadcebcaddeecaacecaeeeadadecdadaeeddddadacdadbccdeebaddaadeaacdadedaeabcdacceacecbbdeccdebeddcebacdccbedeabecbdaeedecaabccdaabadddeeadebbeaeaacaaebdacbddcacaabceebbaeadcaddddeabacbeadeaaabebaeebbaebaaeccbecdcaddbbdaebcbbdddaebeacebdbcbecdaadcecdaaeabaccbedbdacdbebbcbcbbaecbecdedbcaeaeeadcebdbabddddbcdabeebbcddcabeccbcbaceedabecbeecbaddeaecbccaaaeddaedabcbcebdbedeaceaaaabadbaadcccedccbaeaabaaccaaabdddaeeabdeebabceabadddbbdaabaeedeccdddbdbddccedcbdceaedbaadabcabebcacacecddaeedebbbdaacbededddbcdacceebabbccedcebcedadbddceccbabdebadedebddabebabcdaaaceacaededbecebaeaaecddbdcdecebeabdabdddbbcdcaedececcedaebeeedbcbaccacbabbcebeaeadebddebdcbbbccceeeebbeaecddbbecdcbbaeddeadeedacbebabdeadaeaabddcebeacadbdaabebddbdedbebabbccdecdeadedbecedcacccadbabbbbbabeeacdebcdbcbebddaeebbebcbeeedcbcbcbedeacbaedcbbedababeceecdaacccbdaaebabcececdadeacdbcbbcedeccbcacaccdecdbdccaacaecabdecbeaaadccdacddcaadacaeebcdcbbddeaceceaeebbbadcdcebbcdbdadaeceeaeaecacccdcdbeaabbdddbeebdbacccaadeedceeacabadadbdcacbdcbcbebadbeebcdeacceaeeadaaaadaeecebeeeaeccbbdcdaddacdcadddceccacaecbcbacecaaccbebbcaedbabeebcecbecaaecdebddabeaadaddbbdbcdcdbbacbadeaeaaaaabeeadcbbebdbadeedccceabedbebadaceaebebbabadbdaadcadeedddebbbccddbbaceabdacbddedacbdaabeedcedaadbdcddbcceeadbcceedbcadccbbaecdabbdedaaceaedbedaeecaebebdaaacdebebdcabdbdcadbbeebcaaddcacdebaccbabbeedccabaddaccabebebabddabbeabacdebbadaaccbaaceacaddeadaeecebbbcbcbaadaaeceedeaededadcceaceaccbcdcadeedbabebbeabcbaeecebedcbeceadcbdbaedecabdadceeddaaebbbadabeadabdabdaceeaeebdbccabcaecdcacccaeabecabdcbdeadbddcaebeddeccbecaeabeddcccaaebabbcdadaadeaecbeddcebaeaaccecdbcedaabdcbadbeceebcbebedbdebaeddaabaccddbbeceedabbaecaecebbadbbabdaabaeeeebabbeebabecabecbdbbccdeccbcaaddbbeabeeabdbeeaaadeeabcecddadeaeaadbcedbabeaebabbadcbbcedaaadbacbbccdbdbaabbbcdbebbcddeebbbaacaacbebdddddcadcebbabdbbbceaaebcdadaecebadebcbadabdcbddddbcdbeadceeabcbabcbdaabaecbdacdadccccdbdebccaccdbbcabaedeaeaeaedaccebcaeabacdbbecdbddeceaaaebaccecaadddcecebebeeebeacdcedacdebcaddcbebebabedeebcebdbeaeeeadacbdddbacabeecddcabeaacebddaeedddadacccebbdedbdebbabbeadbbbddcaeceacedbbbedacadedaacedaecbacabacaabdabbcacacdaecedbeecdacddbcabbbdacabdbdeadeeccebbcaccdbceeacdebbddaeddadbaeacccbcabbebbeddaaaacdeaeabdcdabbddaccaaacdecaddcecdcabccdcdaaacbddcdcededcdeeccdbacceedeedbadabeabcdbaedbddeacdbdedcbaebaebbeeabddcbdbdddeceedeaddbebcbcabecdceabbcbecadcdecdcceadabeaedcbcaeadcedddeacedcaceadbbbceededddaebebeadcedadabcbdbcbedbabebbdecaaccccceecbdccbeccbebeacdeddbbcdeacbddacbabedaabdcaacedacaabcaaeceeeccbabcadaeddaaccccaebedbabcaabccaebbdbcbeeabbacbceccaaeceecdaaeedbbadbbcedadbbcaacabcabcbaebccbebaecbaccceaedacdabebaddedbbbccccedadcceadcecdddababecbdecceedbcbedcecbcdcabcddddcabdbceaececeedadabaceddedacdadbcadabeccdaaddeebbdaaccbccdedceedebedeaaddacbdbedacbdeeaebbeeecebebeeaedbcddacdadcdaecacdcaebcdcedeeceecbcdecbbaddececebeeacaccbdeedcbcaadcdeabcdbddbcaaaebccebaaeecdbdddddebbacccadbbbabeaaecebdaebcbabacdacccecbcadbecbacabecccdeaccaabedabcadbaadeaebbebebeeecabddebddbaccccacacdceeacbaaeedadbdaebcbcddbeecceaceadbcdcdecbedabbebeadecceecdedceddcabebbebaeacadbadbadcaededdedacdbbcddbadcabaabaeabadabccbebaedadeedeecebcceccdccdcabcceaddaedbdabacbedbcacccbccdebacedeecbbbebaadcbddbeccdaacacddbecddcaabbbddbdaaaaecedddeebededcebcdbacdbaeaddbdeacedceceadccbeeadceeabcbceddcdeddbbbbbccdcbacddbbacaeacdeccddeeabdaaabacacbedaaedceeabdbbdeeabeeddaaadaccdedddbaabddaadabcecaddbabbdaedabaecbdcebcbdbbeddadebeddcedbbcaccabaaeebcebaaedbbbbededddddebcadddbdedcbaccbccdeccedccdadebbeadbecceaebabaebbecdadebdeccedcbcdaaeeacdeabbbcacdcaadadbdadaedbbdedcbaedcdbedbdeaaebedccdbaaabdbebabbddacebbcdddccbdddcddaeaaadeecdcbdcecbdccaebeadcbdbbbdecdecdbddcccebaeebadbecdedeedebcadaeddaaacbebabebeeceadbecebccceceddddebeeccdcdaadbccbbbceccedabaecaaedddaddbcecedacdaeadeeaadceeddcbdbcbcaecadeacacaeabcaaaeebcdebddadcbecdabceadbabcdccdbdaeeccccbdcdcddbadcbcaadbcccceabaebbbceccdcadcceedbaeaabceeeccaaedceddceeeaabdaadeaedebbeddbbaebbebbccbaadbeaddacabeaceeeeacedceabecbdabacaeabadeddcbeaccacddbacddcdaadeacacbeedaaddccbbedcbaddddcbebbbaadbeddebdddccdbdeaddcaaedadabdaddaceeedbdadaededaeedeeaddaedcacaeebbecaebddebebdddbaecbcabebaecabbadcddbdbadcddddcbdebbebadebcaeeccddbddadccceeccbcbeabccadcedcebacdabdebcddddadbbdaabbbbdbddbeccceccdbaecdcebaebdcaecccebbdededccebbbccabcbbecccdcbddecdcaedcadbbbaedcecdcbdbdacddcacecceaceedcaaebecbecaceddacaceeadeddbdbacedcaabdcbbabddadeaabbeeeadceaadddbadababaeeebeaadeacacbadabbaccdbcadcabcdebeddceadcacaeccdabebecaceeeabacaebcedbaeabaeeabddccedddaababeccdcdccbbeecbdeddddebacababeaceaedeaececabccacdcadcedbadecceccdcbbcbdaeadaadeabdbdadcbbcddcbdbaebdaaeeabeacaaedacdeccdbbebcedebbeabaebbdedebeabbcacbcbdbeaccabadacaddadaddbedccdcddddcdddacbadedaccacaeeeaeccbbbbacaacdbcdceaedbabadbdcdebdbbedbbcddacbdcadbdecacadeaecacdcdbeddeddbaabeeadccccbddecdcadcddababccdacddadeaeeadacbcaebcdacedeabcbddececbdadebbbccdceeaeaadcacddeeeadbeacbaadabcecdbaabeceecabeaabcddcbedeebaabcdbbbacccdcabdebdbddceeeaaacdaabeeecbedeedebebacecebacdcceabddecdccbddaeebadaaedeaacebeaaeaccbdabeddddacebbdcdcbaeacbaebeacabeaacbdbecacbbbeadcacaaadaadddccdaaaadcbceadaccedebaabdbedddacbbeaadeeacdaeccaeeccaacacebacbddbcdceedbabcdbdbcaebdcacdccdcaedbeaebcadbacdbaaedeeabaecbaceadccbbbbdeaceacdcaadcaedeccadcbeebccbddbdedbbcebdddeecbcbcadaaeecddbdbdcbbcecbdaaadbabecddcbeeddcccaeecbadeaccbdecaeeceeecdabedcebbeeebbeceadeeddedcddceddcdcdddacecddbbadcdaabccbbddaebecedbbadcedbbbebcebedeacbacadcbaabdcaccbbbcbaecdcbacadccaabaccaaedaebcdacedaedecdcdaedbdccdcebcacdcccaaddcacadeeecbcecddceccdabaecdedcbeeddeaedbadcbcbbcaecceaedcdbcabaedecbdeddeebccceccabbdcadadededecbabaedeecdcccdacedccbcbebebeedbecdecebbeaccbaccbaadaeecabcaacceebacecbedabbcaddaacdaceedaaceebcaedceecdacaebcdaaecebdcccaaccdaacccdbaddbdbabebdadbeaacaabaedebbbaeacbedaeaecacbbecdceecbeacbdbaadaaedbaaeaebbbcaedccabecbdededcbdbbdcbddcecdacaecceeadeebeabccbcbebadeccceaeaadbbeedeeeebbaddebbdbdebdadbaeeccbdeaccbeecacbbadeacddadceebcddbeeabdcadaceeeebeaeccbddbadbacebceadacadecbbbcddbceceeecbcaedbabaeecaeedbbbddcbdcbadcddbaadbabcdecedbeeddbbeaaacbdadaceebdeacadcabdcddcadebbbecebabbbaeeadbcbdeadebbccddaadaadedcbceaeedcecbddecbaaedadcdbaaeacdcebcabdcdeeddcbdcaadbdbdaeaccedbabecdbccedbcbcbcbaeeecacaeeeedaaeeadeccabddaadaaabcaeebdebbdaccbdeecbbbdaecdaeccaeedddedbccaedccaaebbccdcbeacbdcbbcdecadabeceddcbcdedcedabaecebabaedcdcbeebaebaebaacbccddbeebdcabdbbeceacadedecdacbbdcbcbdcbadcdadacacedcdadedddeaecacaedcaeacdeeebbecdddcdcbbbeabbadacacceecaaecbccaccccdddabaecaaccadcccccbabadeaececebacbbbddddcbbcbceccaabcbdcbbdbbeedcaedddcdadaeeddbdadceecacdbbeadedaadaccdeadcdcaababacbbbedeeebbbecaaabadddaaacbeedddbaecbebacaddaedcdbbabdadadbaaeceaadddbdebceadaddcdaeaccdeddebdbdbcbbecddaaecceeeabaddcecabecdacabecdddceabdaeedddcaeaabadccbdbeceeaedddcaeaacdabdcbbedbddabcbdcebdcadbdacceadebadebbdababbaaeabbdbdaadbbaecadebddacabaeeaacdaadcdddeeccabdceaeecaeebaaeedebadebdaabcbdadcabcdedbeabaededbeceaddcbebdcadabcbebbebdebbaadccddbdbeacaedcdaddaeeddaedeededdeabaabcacbbcdbdeacaaaaebbdbdbeacbcdbabdcdababaeaacbcdabecdacebbadbcbaeaeaaeaacaabcbdaecaabcdbeeceeacabedcaccbadcdcdecaeddddbaaccdabbcddaecebacdccedcadbcebbdecceeecbaedbbeeeacecaebcdebadabcddbeedaecdbabbddcdaaebbcbedaaeeedcebabadbbebceccedacaaeecaaadebdddbdedeebbdccaddaebedcaccbeedcaadadadbecaccdadbccaaabdeecbebbbdacbaebecacebaaaaedcdacebacceeebeecbbccceadcbdebeacbdaaacdbedbdebdeceebdebacacdabcabdaedaeddcbacccebbadeedbbeccdccccbcacccbadbdaeeeeaebdedceceaabeabcdbcacecacdecbddaaecebdebdeccaecaeddcbdcceadbccdbceccbaeabbeecdeacdcbdeadabbaaedbdceebcdddbeddddacacecdbeaadabbdcecbbcecdcdbcdddeddbcdebdbddabccadeacedcbebbbdddedeaacecdbccbdbbcabdcbdaaadecbdbbaebcbbcdbdaaccabcacacbdbdbbadbabbbedabcccacdbaaaabeeccaebaceabbdeadebceeceedeecdebdaddadebbbadcedcdcdadcdcbaebddabdcdcceeedecbddabbceeeaaddeadbecaaddeecdbbbdedabdccceecacbbadececcaaedecebaddebdcbdeeccbccdebedcaabaccabeccaeedaaddedcceebcbedaedbcbcbaedcbeedbabeddbbcaabecbeabddabbbabdeaaaebccbcdccacaaeeedadaebdecddbdeebadeedbdccbbdccaadbdcccbbbbaeedbcbdbedbeadbdadaeeaabcdadebdccecbcdcbbeaabbeceddddececcdcecbdeeccecdddebeeeccaebbbbdbadcaaadebadcbbcbeebeadddcdddeaceebccdbedeecdeabdeeceeaaacbccdcebbcabcadadbcabbbddeaebbdbdbdcadbdaaebadedabdcabeaccbabcacadaaecbecddecbdecedebdabbbaceebbcadbdecedecbeccecdaaabaeadededaebebbbecacddaaaecbbeedcadbcbdccbbdeeebeeacbdaaabadddeccbabacabccacbbcbdebccbedbedbeacccceaecdcdbcddeceaadaddbecccaeccaaacbcdbebcacacdbddeabdadbcbbdcccebdbeccecdadbeaabeaebacbbaababdabeddadceeccbdadeadacacedcaecacaeabaaddccebdcacbacbbccbbdcecbcabcaaabdababcbbbdbddddeeaadaeedbddcebbdacbbddaabdccecedaaeccdeaaeeecddebadedcdacaaadbdcabccacbecbebcdceebacaacbdaddcccdebecdaacdecaabeaeeaedcabdaaabaeeeccaacabbcabadadabaabdeedddedbddaebabecabbeabdeceabddeceeddababaacaddeeeaeaecccddbeabbbdeadddaaadddddebdcbbdcbecaeddcddceadecebcaaebedeabdcecebedaacbcadcdcebcabdedcdabbeeeddeccbdeebaebdaceacbeadceecbdcbeabacadccccdbbeecacbeeadddeaceeebacadccbacddbcaceddddaeeddcdaababdedadbecdaacbdecbbcddecadadabcddcbbadacbaecadbedbbedebcabcbecdacedecbaaacadbaaacdbabbddeddaeaebcaabaeaedccbeebeeeaedadedebdebcdeaeebdcaeecbdadcdeecaeeacaabadcadebcdcdbdcaeebcddebdecbccddbdedddbbdeebeedeaedeebadceeeceaecaebeacbadccaeaeabddccecedbccbabeaaacaadbceaecbcabcdcbbeabdbedddbdcdeedeeccbddaaecdabbdbbdaedadbbaeebbaddeedbccceedbaddaecccebbeddedeaebdedaccebbcabdccbbadbedaadeeccedbacaceedebaadbacdabaecabaccaceaceebeeaddedcdebaabcaeeadcddedadcebbbdeabdadaecdbeaabecbccacddbbaaeeebdddcecdbccceabedbebdcaeeccbebedaabcaeccacccdbbedeaabeeddbcadaeecebdadadadaccecdebbdaaaadaabdbaeaacdbccdccdadbeadccebbaabbceebdeeaabeedacceeaaeadbaaddaeabdcdecbeeaaeecdbedbceceaadbbecacdeeeebbbdbeaececddaedcbacbabadcceeaaceabeadaeabcacedbbdbaaeaddecdbbbacacbeecadebdcddcebdaddeabdcabbacbddadcdedbcddbaedccaedeaaabceccecceecdaccaecebbadceeadcaaeededcbebbeadddcbddbeacaacccbedeccbdceddbddacbccbabccebcdecdbccdaaabdddecaabcdebbeeaeeccbabddeceaedaeecceeeccedebddcacbabcbbbddabcbdedaacccddecdaaccaccdedbedeeedeecebcbecbdaacaaeaadbeccacdbcaaacedcddeaacdedbaebcaacaaacecdceecdcebdecdccabbdadbbbececbcebccbbbdcbbeaeeedbcaddaaabecabeceecbcbaacbcadedaddebdeaeebbdeabdcacdbabaecbdcacaaddbaedbcdcddebdabbeddebbddebbeccedaadbdecbeaebeecccbdcddcbadbcebbacabecbbaaecadbcdacaecdbaaeadebeecbbcbeedeecdbecebbbaebdadbddcacdcebcaeacebdcedbacdbcdbababbdbeacacdeadaedcbebbedbaedebbedbeadabececdeadcbabcacbaacaebdcadcbcdbcbcbababaecdbaaecbcedaebbdacdddebdbbcadebadccbabbeaacbbccaeedbcedccdcabaebdaaadcadbbcbbcaadeeccddbaeddcbbecdcaaeceebbbcbbbabeeebeeacddbbaecabcbcccdecdadedacdadbdcccdababcccbcabdebdbdbadbcaaeddcbbbdeacaddbdbcadeadeecbbdaebcdeaaacedebdcedaeeddbabaaebdadaddbdabeebebdcaadadbaabdbbeaaaececceaeabcebebeaebcdabbceddaadbbebbdccdcbbeccdaacaebccadbabededdeebceaaaeceeeeabedcdabccbacaaebeaebbacaaacbbdadeaabacbdcdbaccbcecddbaaaccdeabecdadcbecbeccededbceccadbacdcebdbecddcabacdbbeddceaaeebdeeeaeaccadecdeeebbdaebceabdcbdadbcbadedbbedadacaeeaecebeddecccdbabbacaeedddbdeabdcceabecdabeaaaaabaaaddaaeaccecddcaddaaabddeeeaeeababeceeccbcdcadddeddaaddaccbebdeaabecbaccecacceccbadbcbccdbacadbdbbbebddedcebdadacaedadaaecccebbecdbebbdeaabedebacdbeaaadaabcdbeeabaccaeeeccbcdeeeaebccdbbccdceccdeeeacceaddaadadaeeeeeeeeabbdadceeaabcadcbcedddbadcecaaeedcbebbecacecdaadbbcbdcdecebdcaeedaeeeecaacbdbccceaabcacacaaabbdbeaebebdedeaaeeedbbbdbbddaddbddbbebdeadaecdeecaadecdadaecbbebcbaceabeddddbccccddbcbacaaebedaeebcbaadceaedbcaedbdbaaebbacccedddbbeedcdcddcceacbebedccdcdeebbaebdddcdddbcdeeabdacceeadbcedcccecceabcbbbcacebcbcbababcacaaeaaedcaacbbceebbebaadecbdbadcccbabcbbaaecdecabbbbadaddcceebaebdcccaabeaadcbdaeceabddeaebbaaeccadeaecdcdeddbadccdbeddacceeceeaaabddaabaacddbaebabebbbcacdeadebdadbabdcdedddeaabecccdeebeeccaabaabaeabadbcdbddbabdedeabbbeecbeadcddebbbebbcbdbcdbcaedabacddaebcdddecceabbbdebdaaeabbbcbbeabdbcbbbdabeecdabeadbecbeeecbcbcccacaceabdbbdddebdecbdabbceecedbbcecbcbecbcdeddeebbddeebdaeccbdaddcdcaddcbeaccdebddddcacaababacbcadacdbeeaeeaacccdbddeccacbdbedbaeecdeceeccaadcabdccbedeecdaaddccbaeacdabcedacabedbcaedbbcdcaabbcedcdbbceebdbadadcdacebbccbeebaececceccbaecaaabccaebaebcdcadccbecaebbceececbccaccbbaceaccddedadebaadbdcadcbbdcbebccdbcacdbaecbecabdcdeeedeeaaddeacaacccedaddcadbabaeedaadabcdeebacbcddebddaabdcddcdbbcdbeddaeeabcedebbaeeabddcdadbabacecaebdaaadbcddbadbdeccebecdbbbcabdaecdbecedcbdedaaaeebdcebddddbdeeaedbecbbecbaedaeaedcccdeccddadceabeedaedbadcbedabaadcbebacaaebabdebcadccddeaaddbedcacaebbabcadeadcaeedaabcceedbdbecbccedcaabbcdeeceecaabccbceccccedcebebaecebdbaadcccbddbacbebaadadbecbaaaadccabceceeaabbedbcacacbebcceaabecebebcdebddcddcbdeabadcdbcbdaabdceabedcdacedcadddaacbeebcaeedbadcadeddeccaceabeacdacaebdaddaedaabdaaaaeccebadcebcebcabcbebbecdabdaaddbdcbbeeadbeddacdebbaeeddeacbbcbeeacdcacccabedadeceaaeedbccdcbddbaaececcbcddbbbddacaaaebcdbebbbcadbbeeebbaaeebabdbeabbdcbdecddeccdcccaeecdacbebcdeaacbbadeebaaebecbaabcbdddeebaccdadacbcacccedeeebbdddcaedecbaaecddabdeabdbeebebacdbbcdeebceccabdebebdbcaddbcbbceaeaedcdbbddecbddcdbbebcdabaacadaeddbbbbdbacacaadddaaadacebacccaedceeacacbbabaaeaeaedeebcecdbbcaacebaaaeeddbbccdbebdddbcbdecdbdebdeddeecaddddbdaabaecdacbebdebcebbecedadabbdbecedddeedccbddeeaddbadccddcceecadeccaacacececadbbaecdbbeaddcaaeaeeceadbeebcbaedacbbbecbedebebbbdeeabceeaabcadecebbbcddebdcdedebdbebecbeeacbcbcaeddddcdedeacecdccbcdcbcdddbadebaddcdaebbeccebddabcedebeabccccbaddbbaeaeabdbeebcebdababcedbbbadbaacdabadbaaaedbdcaecbbcabbecadbbeaeedbdddcadecdddaaedbabbaccaaedaabaededdaedabbaeebdbacdcbeebcbacceacadcaaabddcbceaabcabdadccbdccdecdddacbaaddcadbcdacadedacceeccbedcececbbdabebabeadbdbdbdceccccbbbcccaebcaeaddcdbaadcdbaececbabceddedddeeabdaebbdbcdddbeaaaebddeebaeebadbdddcdcbbdbbacdcbcecaaadedddadcdaaccbdbadeadaaedcaceaadbdacebabeabdceccacbcacddceeeddbcdccebcbdabbbbcbaedadcedcccabaecadeeeaceacdcbebcdbcaebbebbaceedabbbcacdacecbdaeacbaedbbbadbcaceebdebbcdaeeeeadbbeccecddddcdcacddccccdcdadebcdedbbdacbbecacddbadabebaceeaeababbbeeaedbcbccabadbcedbeaebecccceccbedcbdecceadccccecbccdeabeaddeeaeadcbbedcacedaccdbeccebcceacdabcddaccccdccbebdeacaccdcabbddaacecdcbeccccaeeeaaabaecdcabeabccbabcdbcbbdaecebeceecdeebbecbbccccaabaadabbccdbdecacbbdbbacbaceecbcddeebccacbeceaaedacbabcaedbecbeecececcdaaaceacceddbdeddcbbaeeecbedbeadbaeaaeecadcacebbcedcccabcebcabdaadaeadceabddeebadeedcadaeddadcddeedcaabaaaceddeedeccbdbbecabbdabddacbeddacbccaeebccabaacdcbabeacccacaadebaddabbcecababdcdacedcdabbbdeaaddbddacbcdceadbebeaceeabedcbdacdcbedbcdcaecadaebcebaeaecdaadbaddcbcabebdacdcedceabadcebdebbabbbcadadeaedabdedadceadbeabbaeedebeecebddbcbaeccdcecddcbdbdeeccbecdcdbcbaecbeadabacebbcbcedcdddceacddcaecaebaabbebcddaebadabcccdeadecdddbaacaecdbbbdacdbaeaadbbadaebabeaddaedabebabdbeccbaabeebaacdeeecaaaaaaeebcdedcdcaecbabbeeaedcdcacbebaaccbeecadaaaeaccedceeaeccabcbdbbcedbaebcdcdcaeedeacdcadedadebadbacccddcbdeaddbccdbddbedacbccdebbeabbcbebbaabeebccbcbccecebedcacabccbdcceddccacccaebaceccebbdcbdbbceebedabaeaecdbacccdbacbbbebceaacddbcdaadbebbaadadbaaebcceeadeddbedcebbececbdbdddeeebcdceaccdbbceaabcadbcecbadabebaeecddcaebebabbecebdacddbecdaeeaddbdddcadabcbacccedbcebaeedeeeaacdbcaabadcacacbdbdaebbbacadcccdddbbcccacbcceecddaacdceeccdcdbdcedbdeaaddbbeacddaacbbebadecabcacbedeebdcecbdeeacbbcaeebdbaeedeaeabceedacadbedcceacaecdadddaceadebddbedacceeeebdaceeecadadcbdabaabbdedbdecebbcaedadceabbdcadaaceccccaddacddacddeaebddddcebaddeecdacceadacbbdbbebadbacabdacbaeeeeabcdbaddaaecbbcacccecccccadcdaeedaacebdcccbcedaeecaaeecaacaacaaaedeceeeabbabdbbbceedbdeadabdbaccbdccabdaedbeebeeaaaebdeecbaaddbeebbaccdcbadbecbdbcbcedccdabbcacddebeaebeebecdedcdecbbbbdbceeedddbcdaaceaedcdcbbbcdebeeebebdecdecadbbbadbdcbbdbbaabbbeeeceaceabaadaaeeccccaebbdddcabbccbdcabdeebcedaddcbbdebdcacbbeadcbaedaedaadebadadeebdeeeeaacedccdaebdeaabddcdaaaebaabcbbeddaabdecbeeddebecbeaeaeeebbaeaedeaeadecbbdecbebecccbcbabdcbdddccabbecabdaedddccdebcdbddedbcbaacebecadcacaaacecaeaeaecbbadcddcbcebcecbdddbceeecdcdbacdaebeceaedabacdaeeeddcaecbbdccecaaecaecdcebddccadbbceaadcdacbdebbceaecacbacddcbbbaaeeeaebbdeecddebbbdcbcaccdbeabcbbbabcaaacbddeedeebddcaccddbabccccaaadeaebeaeadcedabebaeedbeeedaceedeececddccecdccbbeadaddcaaebaaeaceedddacbeabcdedbaecbacbbceddcabbaedbdceacbdcccdbedcaaaebdcceceeecaceccecbddabbbbaadbeeeaceaddabebbacaadecbaccdeebdcbdacdbadbdadeeddaadeceddcdbdaacededcebedeeaabcceddaccedccbdcceabebbcebbbaebbabaabaeeebceaecdaadabdacdeeecabaeabbadcddadcaacaabdacbccbcecccbddeadbaebddceacadabecabddacddccbceedaaabcbbececbbabedaececaedebbeeabdaabcaeadcbdccaddbdabeccbbdacdeecdebebccceebdbcddccaebbbcdbbacaeaaaddadeaeecebadcccebbaebaebadabcabacdeeeeeaaedaceaaabddedebabbdcaabecceeaeaabdddddcedddbdaacdbbedecebcdcdbdbcadcadccaeeaaabcbebadbbcdaceabcdaaadeadbedececbeabeadbceccbdcceeecbcdaaadddcbabceeabecaeacccbcdebbdececbbcacdcabcdcaadeaeaddddbabecccedebbaebdeedeececcceceedabaceabedeecdcbdbbedcaadddeadeeecdbccdcabecddccddebacdaeeeadcbeeeaecebecccebcdecbcbaabcedbddcdeacebaaebcbdbcbbbcdaaacebcadcbaadbababdbcdeddabababbadbcbeecebeeddecebcedacaebaebcdeaccacddaadcadadcdddcdbccdebecdbebdbaeacbbbdcbacddbacedbaaaabcabdcdcdbaadeecbebcaedbdbbcebccadeebadaccadbceecbececbbaeaebebbdaeaccadeabdabedebaeaadeeadbcadecdceabebbebacdadcdeeacdebaeeaebbccdbcdadceebbcebecbeacecabebdabbaaeddbcaabccdbdcaddebabbeaedabaedceadddbacbbbeedbebbbedcdbdbcebcbdbdacaacebedcaddedadccdecdabbacbaeabedcbdcaacbecbaedbccbadeccdaaccdabcdaceddcadeaebabbdaebbeaeddceebceeccbdbcbccbaaacdabdaeabeaaccceaacacebbbdcdbdaddacaeaccbbabbbcbcdebbdebedaececbdebcabaeaadbbdeeaecbddeebbebeaeaaebaaabcabdeddeacaeeeaeccbcecebcacaaebaeebebdcaedaebcdcbeaacccabbadbaeaaacbebdddeaccdbbaaeeddbcccbcecbdcbcecceddecbdcbceecacddaccecacbbebaecccbacabcbedadcaaeddcbeaebbcdbebddbeecbbddcdbcececaaeeedcecddabaeccaeaaebeceeebbdbaaceeadcbbcbcdbcbcbbdadbaceeccbeaececaaeadaeaacbddeeaceedbcebbeadddebbbaaebcacbaceacebddeeaadeedaaeaebabeabbbecedbabbceddaadebeabdebedeacaacaccdadbdacaeacbbebeacbacdcbecebbadeadbcdacadcaccaabeededcebaadbbcbbaacecabaaeabdcdddaadcdbaaeccdeebbbaddcbaeeaeedbceeeceadcdaabbcddaaadeaeeacacbbdddcdcadceaeeadbbadadecadaceabbbcdaacbedcbccecebecaacddcdecebcbeceedcccbeaeedcabecdeeebcdcedaebdcaebcbbecaeecaedeacdcecbccbccdcedaebaeaebccedaddacbbbaceaadcbacdddeaedcceeccdcabaecddbcebcdeabcdadeeaddaaedbbdbaccadeacabbceaecddceeadbadeddbbaaacccbebecbbecadbebabddacbccbadeaebddcebcbaadbaaaabaaceaabbccbdaddabeeebbbecdcceadacdebebaedccdbebacceeecddbebcdbdecedccabaedbdacdedcccddddddaabccaaebcceddcbaaeccbaeacaecdaddcadaacddbeaecceddbaceabdbaacecdaceccbcceabbdabcbcecccddecbaddbdecabbecaebddbebdecaecbecdaacbdacacaceebbbeeecdbcdbbcceddcacadaabbeeebdcdeeddcdcbeadbddccbbcbcdaceaddadebceabcbcdddcbcdaebbeebbbeaadbbebaeedbddeedabeecdddbbabbdaebddededbedbbdacdaabbbbabeddbebedbcdbdbbbdedddcaecbedabcbeeecabdeebdaeacaeebccbecbebbcbaecbaeeaddeabeeacedabdbeaedbdbadccadadbebaddbbceebecebeadcdeabeeacdbcaeeadbaeaadcdaaeabadbaebecabdbeaebdebbcebabeedaaebdcecadccaccdecebbbeaeaacdcdbbccdacacdeabeedddeccababccaaeacaedbbeebbeabeddecdbdecabcadcaadeaeedeeedcbedadbeaeedeaeedacdddabedbdbdaddcabbddbbdbdbdbbececdedbeacedbddeddebdaadebacaeddecbbcbeaecbaaddeaabdccccedcbbacbecdeaabcabeceacebbacdaddddacebdabdebbaaacbddaebdcadbcceaacdedbabddeecedceeceedebcceaaaabcbbdebbbcbbddacccaadbbbedeebbebabadbbdeeccddeeceeaeacdbecaaecbececceceebeeaccebeaebaebdebdccaaaeedacdeddcdaebdeeceacebebaacdbabbdedbaebeeaabebcbdecebcdebbabebbcaaadbccabdeaddacccbbaeeebebdeadcddbedaabacebadbacebddbcbaddaecdedaaadaeaacdaaabdabdadadeddcaaabdedbaccceeaaebadaadbeddeadaacdbaaabcdaccbecbdecebcecebdacbccdeddaeddeabeeebddaaeacaebbcdaedbaaaeaaeedabedabcacdcdeccddadaebebdbecaabcebdaeccbdeecccbdadcbdbcacdbcaaccbceeaedaebccdecabaaadbebbcababadbdaaedadedbedaddbdadbcbeabcedeeaececdcacdbeabdceeaebcbebadeaedabdeeecdedbecebdadcdddccabedaccdbeedcbcaaedcbdbdacebbbeedabeaebeeebacbadabddccaeceaedcebaaacbdabcbbecdcdedddbbeabaedcecadcaecdaacbceaacdbdcccdceadacaecbabddbbceedacdbccbbaaabceaddeaeeceadbaeabecaaaecabedbdedabcdbbaeebadebdbdaedcecddcaeeabcbbebaddcddddcbabedbdcabaeeaeeaaaddcddcbecaeaabceedbaeeebdccaaaccdcabedcddcacadcccbcccbbecceabdbdabbabbebebbdbdbacbdabccaedcdceaeeebddccececcdddaedbcecbbabedaecdbdcbceadbabcebacabccbdcccaddabbabebbacbdaecbeeeacbbcaddcbebcdcecbcaadaedcbabeaaaebbbacecbddedaaeacebbdeaabbddddaaadaaddcededdeccbcddcaeedaebbdceaadabdcacacaaddeaecbcecaecdceaeecbbeeabaadeabedbceddedcecdebbcdacdaeeccddeecacbebbaebeaaeeeabebcabccdcddcaeecaaaceeacdacbeabcadaeaedeeeddacecaaaabcdbaceebdceaccbacadaabeaeebedbeeeadaacedebedceeccbecebcaaaccaebecacaacbaececedeacedebbebdebabaccdbcdeedaedaeecbddedcdceedbeacbcbdceebadbcbcdeccbdaadbbdbdaeecbdeccaacebcccdddbaeadadbdeedeaebbabacbdecbaacbabecbcebbeeecbdbcbdcbbeebcabeceedecccddcedcdbecbedbadebaecbbebebdedebacdeabdeadbceceabacbadacaecacadcbaeadeabeccebbcbecdedcdceadeacadacdbcbadabbbebbbbedbebecedbecbbbceaacdedcabbeaeedccaeebdbeacdccbcbecaadacebedeabebdbedcaedccdecbeddecaabdbcccccabaccbbaeecdaeeeaeababdaabedcbdcdbbabcbabceeeadbebebbdedebbaccccdeecdcdbecdadaecebabdaecdbeacdcdaedeaaacdeccadbeeaaedadbcbdbdebeeccaaedebabdcdbddacacaadcdeadbdebbdeaebcdbaebdcdddadccbddedcbddaccddbbddbddcaceebeacdadcaebecdbbdbeedcdccceadeeacbedbaeaeccbcbebbacbaaecbcecaaeddedcbeeaedeaeacbbebebdbeadbaaaabedcdbcdaaedaccedcbbebecbbadbbaebdebedcddcbdeebbabecdbcedadacddadaadaaceeecaedebbdcecabdcdddaaadabceadecbeadbdcbadadcbddadeaabdacededeeceaccaebeaaacbcdeeacdddaabcdcabbcceadbdcddddadcecbacbdeaecccaddeededbcdabaebaacbeabddadaecdbeacaeadeadbbbddcbccdbecabdeabceecebbcaaddaaaaaacbecdcbcdddbddbcdabbbaeaadecdcbadeabceebbaabdaaedaccaeacbcbeecabaeebeabdaeeddaaaaecbeddabdbdcaaebbaccebdbaaddeeacebbdaaaccebceadbcdabbededbddddebadeecceaabcbebbcededccdeedddaaddecaadedecbaacdcbabdbcaceacbebbcdcebaacecbdcaedacbbdaebdcceadbababcdbbecdadbedaadeebdbcbbbbcaeeddceedeeaceebebabadaaadbadacddacabceacddcaeeddedeceddcecaddbbacabecddbdabdaadaaddbaeedbbdccaaaabcceaeccbecbeadcacccaacebecceaeddcbbdeebacabebcbbeededcdeeddaaaabdbaedadbaceeecdcacedbabadcebcdeaedaebccaabaabdcebbaeaddeeaacdbaeaabcdbecddbeebbceadececeedacbeadbdaecdaeddaceebcaecaadeeadabadccccdeeaadbdbcbaaedaaeadecacaccbdedebdccebbedccecdbeadbadadceccddccacadebbdccccdbeeeacaecdbbaaaeadeaadcddbcecdacddacceeeadbddcbbcdaeaccbacdcbddbabacbcbbcbeedcbeeadbaaebdcbddcebccddcdcaddacadccdadcbeedebdaeabbcceecdebccdacddcedbbdaebcdcacdebdaadbcbeaabbeabbeceddbceaeaedecbccccdeecbacbccedebaeccaccddbededccaedecdbddcddcbababcdebbbedceaebeceaebeeecbbecdbbdbbcbabeaebbedccdabeceadcadedbdacaaccaaabebbaeabeaeadaaeecbbbebeaedbedaadaeaaedbbdddcebaeabdbbbcaacadabceddcaeaedbccbabcaeedacadcaecdeeddaabdecbeeeedaebceeddeaeacbaaeedbedddddcddddbadaabbcbddedcbaabdddedbeedaaddbbdeeaadebedcceacdbddeaddedadbbcadebbceebebcdeecaeddbaedcecdaedaadeaeebbcbcabbdbcdacedacedbbeebaedaeabbaadbbbabbbbaeabbcabdcdbabaaabcabdccbcdaeceacdaaecacedcadbecebedcbaccbcdebdcaeaeaabbdecbeacaeabadeadbdbccaacdadeacacadaaaedcbbccddedeeadedececdccbbbedcbeebbeedcaccceebededabdbcdcacbbabcbdedcaaddbbcccabbbdcbabbeadacebdacaadccdeddcaddcbcccceddbeecbeadaccecadadacdebaebeedbbebacadadeaddedeaabccedcaeeecedededccbcbcecccceaeedaaacdabddebaeedbcbacbbbdbaccaaacecdbeebbeabbabdecdbaadcabbaaebecadcddbdbdaadbcabacedaebaedcbcadaaacceedebcdbdaeceaeaadeecbdbeeadcabebdeabecbebabadaeecbddbbebebabbddcdcdbddcadcbecbabeeebbededcebbbeecbcdddbbdacbdadcceeacdcedbecabdaeedbdabcbaceebdbacddedacccbabbdddceeaabcddcdedacccabcbbbdbdacadebbdbdaeebabbbddccdaadadcdecdebddeeabeeacaaaedbccadceecbbacdaecadaecacccdbbccdcdedaddeebebdecaebedddccddcecbaabaabcebbaebedbdabcdeceececebbabaaccacdaaebadbaaccdcbceacadcdebddcbdeabccecceeeceaadabdbeebacaddbebacdacdddecdabdbbdbebbbcbaeebbadeddbeebbebbaccbceedeeeababadbedcadbbdabdccdebbeaacbbabdaeeaacccbdeddceccbcecdbacaabadddecdceeaadacceecbbdbdaecedabeaaeabadaebecdebbebedacecccdecdabeebdecbceedadedacdcceeaabeedbecdcdcbdeeecaceeadcbdbacbbbbadbdcdcacebbeeadeacbdaacccacbecdbbbcaeaaacbeacbdcdaebdbaeddbccaeccdaaababdbaadaecdebebcebdecbdeabbdceaaedccebbbaabbadceeeabcceedbccdebeecacccaedccdcaeeceacdeaeccecedbcebabcadedbbdcddbcaedeadeeccbdbeeddbeabbacedabddedaaabbbacbcdedbdcdccbbaaccbcecbaeacdbeccdcaacdecddaaaaecebadbbbdbbbcabdbcaecdbceccbebabbdabedccccacedddebdcdacecabcabdcabddccacbabbeeaecebcaabebeadbdeaaeadddeccadedddbbabebdaecddbdaddbbdbcccaebecdeddcedddaaabbcdadbdccacadebceceadadbbdadcaeccbeadcdcccebadaabdabccaeeedeacaacccebaebabbccdbbdccbbeeedcbbedabbebebdbdccacbeebbbeaedebeadcabdaeabbbbacdebddbcdeadeaadcbbabadbbdcbdccaabdebceabeadcddbeabdceeddaeddebaecdcdeaeecdbebabaebcacebccbedebbeaaaccbbeaacdceebeabbbdcaceeaebcddeccacbbbaeddaeebcbdbedecdbccdebaceeebbdcbecdeddbaadeaaeecabcaceacbaaaaaddeabedadddddbdaacacedcdbaececedcededeebecdbdbbbcecccdebdbdcedaaaecaebbecdcabbeeecbcbcaabacdaecebbbdeaedbbaeccedbcbeaacdeaedbaaaaeccbeaaacaacdeeaddcddbaabedccabacddeecbdcebdbbdccaeadcceeeabcbcedbabbbaebaccbaceceebaecaacdedaaecdcadaeecaaedacbeceaeeeacadbbdccecbadeadbcaaeeddbebebacbacacdadccbcceadbdccedacabcaeceecccbaaacdddbbacececebbbeeeebacccedcdcdabeeaceeabcdcdbcedccbabadeacbdacebbccecacaacdabdecebbaeccaddeeacdeddacdbbbbbabdaeaaacccebbdddcceebaaaebacbebdabcbbdaebecbcccdeebeaebebddbedebcdcbeeabccddbeabcacdbcaddadbbcedbeeeecaabeecadabaeaaadabdaedbcdaeecbbbbddaaedbeeccdecebdabcabacaccececebddbdbeeabdaddeeeecaeabacccedeeaccddbcdebbcceaceaaaaeaaeebaaddcecdebabccaecadbccacedcabbceaedeedcbbddacbeadccdaabbeadaaeceabbececabedbdabbbddcecbcbedcbcadccdccacebecceeeabebcecdeebdcdcdccceecacbbcbdabebeacabcaaccdccbaacecccedceadbccdaaaedbadbcebadbedaeabbbbaaeaeecadecaddbedcdeaceddaaecaeabecbeccbbcdabbcebadaabedcaaabeebeddedddaacdabbebebccdcddebadbdedbdbccbacedebbddccaebdabecbbeaebcedcbbdbdacccdbbdcebadbdebcdebdeaaebceceeababbadbdccbdbcbcdedeccbeecdeddabdebcdcacccabdbccdaaaecbccebaecbbdabddeacacadbebdbbdadadabeeeaeaecadcebaabbeeabbaabdadddcaebcbbbebdecbeceeccecabbebddebbaaeaadbebacbdbaccbdbcbcaebdbbdaaedcbcdcddbbecdcabcaaaaedadaecdeabebcdebeacedcbdceacbcaddacaaceedcddbcceceedddebecbaebbbdaddbcaaebccddadddeccebaecdcbbbcecdaeeecbcdecdbbcabbaaeccaeeebedabaaddcdebdebbceddadeebcdebcebaeadacbdbadadadbddddaeeceebbeacdebaeababeaebadeddaebaaaeaaceddecbadbbcedddcddbdedacdbaeaeddbeedecceaccceccccbbeddecbcdcbbaabebeaacecdebebdbaecbdddcabbbababbcabceaaaaceebeaaecdaaebadebdddeeeaccdaeddbbaedbccaccccaeeaabdcadbcbcedebaadeabdaadedbcbcdedbbeeaecdbddaebbdacebbacbabcaeadecdcdadcabceeceaecebdceadebdeaadccebdaeeebbbaecceabeeacacebaceebaebeddaeaccecdaecbebbddabeaabbbbdbedbddbbabddbbbbcceedacccbaacaabdaabbabaacddecccbcbeeaaadabbbacbbdcacccdadedeebcecaecbeeeeddcdcbbdbaeadabcacdbdddaddcaaabaaaacaebbcdebeaceadbbbbadcabbdababdbaaacbbbddeacbddebbbedcdecbcceabeddddacbccacacadaedcadccaabbdbbdbdccbdaedbdcdeecacbbcacceeaccbbbadddbdbbbadbcdcbdebdbacdabbeaadbbbadababbacbbcbccabadccabedbdbbeaeadadcddcdbabbecccaebeebebcaccbdbbbaebeebddcccadbebeadaadacbbbaeeebeeeeadecbbaeacbdccdeabeeadcdbdeebeeecdeccdbddcddaccecaabbdbdbbedadbcdebabdbccecdbcbcbaeddbcecbdadddecbbdbeececedebaedacacdeaadbbacecddedcabebbacededcdaecabcddbabcbcbdadddbdabceacddaeaaecbcaedcaadddaeabaabddeaecedcebcbbadadadaaebeebcbaeaabcbbcaaceaeccbbeacecdebbdcbbaeeaacbbeabdcaebccaeecaebbaaebcceaebcddaaccaccacacabacecacaacdaedadbabbebedcadceebcbdccacdecaaaadaacdecacddbeecbdbcccbcaecebdaecbabcedebececbaebbdcbbcdeccadaaeddcabebebbbeeedebbcecaebebabaacbaaaceeacadabaeeaaebbdbbcddbaccaaebbccbadcacddbeebdcbeebccaadbbdecdbdbadbdeabccecebedbbadbacaaebdeeedebbdcedcccabedbcaddeddaebaadbbbcdbbedbccccdececccbabbbdabebecbbecabebcdcecdbdadadbdbcbbcacaeecdbdcecbaaebddcceadeaaddcbaddaacbdbdedcbeebebdeaadebecdaeceadaddbddcbbbccbbbeebeeaddecebbebedcabbddbdaaadcaaebcbeebeccbdadcaccaddcdcebceadacaeadcdcdeebdbccddcddcbcabebacdaaacecdbabbabebabbeddeebdebebaebcddddcabaeaedacbbaeeddbeeaddeeebddccdeceeaebeececdaddadebbaaedabadcedebaeabedbeceeeddaaadbaeddcccaeacdcddcaceaadeaccbdcbaeacaeacbacdcbdddacdcaaadbceeddbadbbababecedbaddcbbcceaccddbcdcbcabccaecacbcbceebbedcaeacacbccbcabbebccbcebcadbccaccaaddccdbeaadaaddbcbebabddadaadaebecacabbaedeadbcccabaccbcdacbdeaaedeaadbbdddacdcadaebdbeeebcbdbbdaccbeaeebcaacbaeaaaaeadcbdebaeabddaadeeddcbeabecdccdcabcbdcbeabdcedbdecdcdbeceaeeabcebdeebebbbebeeaecdadaaabcdcdebdeeabbdbcbdbbeecacbebbadbdecdcadedaebccbaebccaaadccaabbcdebaabcddaabcaebbadeedbeebdedbdabbcdeaeddcdaecbebabaebabddabdeeadcdbacbebceaabdccaddedcedeecddbeddcbdceecbcebbaaadbaebbdacbddabdcadbbedadcacdeedabcbdbbccbbdcdcbbceacecdadbcebeddcaddabcbdaadcdeeeeeceacccbdabaeaadeeddecddebbcdcbcaddddbeedcddaddadcbeaccaadedcdbbaaceccadaaaabaddebaeccbeededabccbeabedaacdcbdddaadbadddbceaaebbbddcedebeaadcecccdcbadaebcdcaaaadaaedcdedccbceeabedcdbbaceaaaacebccebebecdbebbdaacdecbdaecaccdcaccabecbbeedabbbedeecabdcddeebdebabbbbdacbeddadbabcbdbebbbacbeaaceadeabeeadecbaacbaabcdcbbceedbaebdbdaccbcdedeecedabbebeedcdeaddeddbbbbbceadccacedaecedebbddeccdcbbcdbbcdcaabaebdbbdddedaaccddaadceeccdcbaebacccaaebaedcbeddbaddbcddabdebcdbbbeaeeabbabaaedcdedbacebebddbdeeadbeccdcaaceaeaedccbaeaeeebaadadababecbecaadddbeccbeeddaaeeaeccedcccdadbdadadbccdebabdcccbbbaabbbbbcadddddbdccedcdadccebdaddaeaddbadeabbcceeeadccbaebaabebaaecacabcebaecdddbcbaacecdeddeacbbdebbcabeccbbcdddbabecebdebeaaedbdeebcecebaacdcdddccaccabbbdaaebedeaedbcacebedbdeebceeedacdbbaaadeacaeecbccdacebeceecbabcaeceabdaeabdabdeccecadabbeaedcbceecdbeceabddadedaadadacaeaddeeaaeecaacaadbedcebacedbbedececbccacbccbcaadbdaecbadcaccdabbdaccbedbccadacacccbccbdbcdedccbbadeabdccbbceeebcaeadcbdacbcddccabcbecebcccbbceaecbadeedbaacacaeddeecacbcccabcdbcecddeeacdcccbbebcdaeedbbcabeedecbedbadebaedaccaccbaecebadbeacaacdbbdcaabcabebdebedbdaedadaabdcdcbacedcaadbeccbbcaccdacdecdecdbdccecabeccdbbaadbceceeebadbddebcedadbbeeaaebcceaabeaeeceadbcaeeaadcabecedcceddcabeccceadbbbdbdcbabcebdeacabcdcbecbcebbebbbceadcdacccbbbdbccebdcbdccbbcbaeabccacbeddeaaaccdadceeeecbcdabdaddedeecadedbcabecabdecabeacdbdbbdcecdbabaabadbdcddbaecddeedeccbbbbedabcebedaacdbddddcbbbdcaabdceccbbbecaaceedcbadaabaeccecdbbbedabededbdaaececadbbbcaadbbcaaebcaeeaedacbddebeddbadacdebdcbdecdeebdceaddcbbcbabaeeadecebcdbdecbbacedbccabbeacbbeadceaabaceedaddacaaaaaacaebbbcbedeabbedeedeedacebbcbcbbadddcbedeedbebccdacaeeabbcddeddababacedbaecdeadcdeadabdceeddbeeaadbecabbbbbcddeceedcbccdebabcebccaaabbdbdededcdabbadddabbddbbeecdaebccadbcabccccaadeacccbeceaaccadbccddcabeeaaeaadadaccbdabbddbedddaeceebcdbbdeaabdbbabbdacaddbacebceebabecdaadcacabaabeadcbcbbdcedecbdaaccdbdacdbcddaadbbbccdacdbbbbbeebaccecdadcaddedcbbbdecdaaebbceedbaeebbdaeddddebecbdcccabbaabcabbacdcabceadccdedacccdabccdcdaeaaaddbccccaccbeaadacabebeeceeaeddcceddcdcabdcacaaacaeebeeabaeddcacbabaaadedadabbedbcecebbeabdacccdaaebabdeeedaedaeecbdedebececdcecedccacbebeebbaccbaaddabcdcacddbeabbdacceabdacecaabaddccbcadcecaeecbeadcaaccdbcddccdbebbaeaaedccbbaeceeecaaeaaeddecbbdeadeeadaaacdaecdbeecbedbcabbccddddcdbedbecbdaebcebdcddeedddeedccbedaddeeeaeccebcaaeddbdaadeaceacaddceddaadedcccbccaebbadebccccabcbcdabebacbbacebdaebcccacbcacbabbcabdaabedeecbabaaadaaedcedddeddaebaaeebecbebceacdedceebcbcdbeebbabedeebeeedacedbddedecdaeeeddddcdbdcededacccdabbcbebaecccedbabaeccabaaebaceceeeecacecddadddceecebebacccbcdacbebaebbecdcacabdbeadacebbccaaadeacbadeeccebbbccbcadaaebcadaedddeacbbdddbacabeeceebdbabebdccdeabeceaacaccdabdabedcebacecbcadcaecbbbcbeeedcebbdccdaaaddbaddaaaecceaaebcbccabcdbdbcdadbaeabeeeecceebaeeebaddeeaddebbbcccdbbebddcbcbeaeadbdccabccdacadcecededcdeaeaeaeddebbdebcdcbabbdcbdcdddceaaebdbabbdcceabbeccdcabaccebdebaddcdabbdcceeeaacdccedbadcdeaddacedbbecdaeaddcdeabdbceaedaacbedbaedeaeebdeddadddaebcdabbebbbbaecbeadedaeccbdeccbdcdeeaaaddcbdabadcbcbbabcdcecbcdcabcdcebeaeeeddcbeecdaebbcbacbaaecdbcaeedaeeecdcaeacadeebceebaeaeebdccedddeabeeddaccdaeddaedabceeaeeaddcbbcececeaddbeecacdbaeaeebebcaddbbdbdabcdedbccaabdddbceaaeacdabcaeceedcadbcdeceadbcbaeaadcacdadeacaeabdbcacaaedceacadccccbdececeabedbaabeaecceeabbacdceedcdecdcddeeaddbcdbbbdcceeaedbedecbdebcdcbeebdddbabadeaabdbabecccbeeecdbecabbbbdbbeeeebbddbdbceabccbbeaaacaceeabcaeacaddcbebdeeddaadbcbbcaaebbbecdccbcdeacecceaaecdabcdbeddbaeeadebbbdcabbbedbabdbcbeebbedaebbeceabecaaebacabaebdeabbcccedacbacddbbdbcbcdcedccddbaedaebaaceaaedbdbdeccbebccdbabeeadebabeaecabbeeadbadeaddcecaaacabbdebbaeadeaecebbecbedecaebbeaaeaecedaabbceecdaadaeadcbadecddbbcabdccececdcedaaaddeabdeadbddcdccdbbbaccdbcdbabbddbbbbeddccbcadcbcbdacdeeadddbedbadcdadcedceeccaeeadbcbbdcbcacaacdbbaecbaeacbeeaeddacbddbeedacddcaedcdbbabbcddcbdaabcdacdacaaeddaacecbecadeeaeddeeacccedceeaaecbbaadcceedcbcaebeabcabddbebbcbdbccdccebbdedbdebceaeacedaadeedbcabacdeecaaeeceabdadeeaebacedebcccdcbbebceaeaebdebebecdbddccacddeebcbacacbebbcaeddcdddecbdeabbdebeaeccdbadcecbeccebbdacbbdabeeecadbebbdddbdceadadddaababcabedbbdbabbbbbbbbbaaeecddbcadcaebcbddaeeacedbaaeaeccabbdcbcbcebaeaceccddcebcbceabcabebccabddddadbabcaacedacdbdaeadebdedbacdcbedaceaaaeeedaadcecbeabddbccacebacccddbddaaceeadddeedaedddccbecdeddaebcbcacdbecaabbcbeaceccbdcedabdbbaccacbeaeadbebbedbdcdeddbdaccbbcedbedbeadbedaedcbdbbaadeadaecaabccdaecdeccbbabddabeabcbabadbadcceecabecdbadccedaaedeeedacddaedebccbabcdacdcadedaacbdbdbbcbddadbebebbbabadeadaebeecaecddaeeecbbcddeeccccabdcbbdaaedceaabdaaeaabceaccbdacdbdbeebbcaeeaadbbdeedbcbadeccaabedceedccdcaebcaeddaecbcdddbdebeedacabcbbacbecddeaebcdcbbbdbdebbcddecaedaadceeddcbbbaadcebdedcdceaccdbebbeccaacebeaecadacbececebdaacaaecddbcaadcecbabaacceecaceaccacdcbedcbccbbeacbdcbecacbbbeecadeccbadadeaccccdedbbbadeadadabeacceeeacbaaecdcaccebdbaccdeecbbbcbecddbdcaaecceedbacddebbeceedcadeeddcddebcacdcddbdccdbcaebdceeeaeeeaebaecaebcbdcdaddebdaccbaebabcbccebaaeebabcedcbbbdcdbcebcdedddabadeeddebeceaaeeaacecdecacaaabeabbcdcbabcbddcbddaadddcaeabbeabdecdbeaabddadecdacceccacbcbbcebaceeaeacebadcdcadaaedbccdcadaaabdbaccadbbbcbabadaacbebebddbeeebbeabdcddeabacaebebcdddcdabcceeceabaeddeddaceecabeecbacdecdcdaaacdcddcddbdbdcdcbecdeeebadbbebccbeadecbacbcdcaabddcccadcebdaccbdeccceaacdeaabeacbcdabdedcaadababedabbdeebddeaeecedbdcecacaeabbbcbaebcebabbacceaceeccaeedaadceadabbbbedcceaaaacebeabcbdaadeccebbcbececaabbdcbaccdccddaeceabbeaadbcdddaabbeabdaaabbcdddbbdbbddcbbcbeacdecdececedacecdccbbeebaaadaeceeadaceceabadaabaaeeeeecedcbadacdabcecaeaccacbdeddecdddaabeeddadcacdacedcaddcdabebccbeebcacdeeacdbdcbdeebaeccedecbbacabdbacebcadabdcbbaaceacaaebbbbedbcaeebbeaeadeaedbcdbcaedbedbdaeadaeeeabedebaccbedddccddeceaaeabcaacdcacbedcdaabcbccceeceddbdbbdbeeededdeaeebedaedbabbccacceddebdceabeecbaeaaaeaeedcdaebabdabcbaadaabbccecaaadbcceabbbadbbabedbbebbdecedddedcdedaddbeaddcdeecadbecedcacedbecdcccacaeeaddceccbdadeececeeeeacaeadedeacbddadeedbdeeabdddbaaaabbceaeddebeccbeecddebbeaddebbcdedcaaaddcbeadeeabbccaabacbdbdeabbecbdbacabebdcecbcdaaaeaccbdbebceceaecdccaeaadcaeaadbeaecdecedbbadaaecdcdcbcdaddcdbabaddcaaeaceabeebabbdadaeedebbdaedcbededbcdbececccddedcdbcebccbadacbcbbdbbcadaebadddbbdeaabbededcdbbacdeadceeabceeacdbbdeeadcacaccbebcdbbbcbbacdcdedabbebeaeabaeceddeebcdeecdaceadebdcdcbbbdadaadaeaeaebdbcdbdabaaabddcedddadcbdabbcdddebdbedcbadaaddcdecdadbaadbabddedcaacbdbebabbddabedcdccabcbdcbdbeabdabdccadaadadeccacabcaecaddbaeceaabaeddbdeedcabdacadbdeaddeceddecbdacbcddbbbacbaeaebbebeabeabdeedeabeedbebadceecddaceeadaebecdedadcebebcaeddebeabadcbdcedddbbbedeeedbccdecccdbadbabeeedddbdeccbdbdbbcdeeacaecccebaaaaccaacabaaeabdaedadebebaaccacdceadbbdcacdddeadbadacecbceaecddcdbdbbaaacbebeebdecdadbaebaeaabdabcedcdeaadcedbebebcdbedabebbbdbdcaabbddbdbbecdcbebeecdbeaadcdbaeceecbbbecbaccebdeaccacbacebaaaddcbcdccdceeeedcbccccbbcdaaebcccdbebddbcabcebebedddedcabecaebdeabbeeadeceeeeccdcaedcccecaceaccabbeddcacebcbabcecbceabcbceadaeeadadabeccbadaaaabedabbceceacecabcaacdcabedcdbcdbadbdcccadbecadbeceaeebacddbaadeeeedbeeeeaedcadaecadddcaedbebceaabcdcaeeeeabdbcbbddceacdaadebeebebcdaedcebccceacdeebadedabededabadadedbdddaacaeebcdddadaeeeeddcdcbddbbedbeaaaadccaecccbcbdbdddcaeaedaebeeaceddabddeebbbdeabdbdeeecdcaedcacdcdaceababaeedceabeececebddeededaeddbeebbeadecbdddacccacdcbaebedabaadecedaaabaaecaebdcecabecaadeacceeeabdaaaddeceabddbdaaadbaeaaeacdcaabccccebabadaaaacecdbebadecebccdbedbaedadcadecaebbbebcbdcabcccbddbaeaceabdbdeadcbdcdbdbbbeaecbcceeadabaedccdceceebdcaacdecebcdccbaebabeedeebebadeebebeeabdedcdcbcabdbdbdcccdbdaeadebbeeadcbcdccdabbbceadbddbeebcbcaedadccbcbdcdbdeaaacebeebdbaeadcccdcabeebeacaabebaabbbbaedbebeacadecbcbdcccbcaacdcaecdacdaadeeeceeeadadabbdbeeacbaccedecebbecadcebcbacabbcaeaebbcaeccdccdccddaaeadebebcbaecedbebeddbcaceadaddcebaeeaedbaecdddcddeddebaabdbeceabaccdaeadaddabceecbbcbbddbcdbcdcaddccdbceaabdbddeadecacadadbcdbaedececcddcdecabcabbecbdbcadcabbabeaabeecdaecaaecabcbceaebacadaecdbccecaeceabbaeabaeebcecbcabeecbcbbeddeceabceeebdecedeecbbaaddcdcbeeabdbddaadabedeabbbbaedeabbbeadecdaecdcaeeeddacbebbadedabbacbdedbbdadccbddaeabaedccdaecedeeeacaddbdcbaeacaabecbbdcabeaccdecabbcbdeeceeeabbabbeaedadcedcaccabdceeadceedbecdebbbbcbadbdaeeacdcedbebdeacabeadeabecacdeeceadbdaecbcaabebedddecbeaceaabccdecaaaaaecaacbcaaaddaccbbdbbbebaadccddcabdbdbbdacbddccaeaebdcbbcaeececdebddacaabbbaccadeccdbeacaccbaecdaeedaaeeceaabceeeaebedbeecdddcbbdbebacbbbbdcccccbbdbabebdcdabeacbaccbcaacedaebebacacdadbbabaaccdbadebbaadcaeecadcbebaaedccdcaebebeecddadededaddadebdcaedcadbddeabdcecabddedacdebacbdacccebaadababeedccdabacddabbedccdeedacacceaabeecbacccacdebbcdcaaedaeeabdbacbdeaadceacdaadabbdbeecdbbbdbaadbabcacabeeddeedcdbebbeabececbceccdbaacdecaaabeaaddceacbadedbcabbcacbcbaadddcdcaceaabbaaebdebdcbcceeaabbbdcaadabebbcacbeaedeaadaddecdeadedcbbcdbcdbdeadcabcedaabacceddacebaccdbcecaadbcbbdaceacaacaabddaaeccaebaaaddcbadecacdbdedbcecdccbddaadcadabdbbebbecbeaeeaccbddeddaeaebdaddbdacbcacbbbeeaecbeeaeddcbebcbdababbbadeabbebecaebaadbdcbabbcbaceccceddacbedcabecadecbdecccecdbedbeceecbdbcdaccabadecaecaaacedaeabdeeecdbbeecbbeceedaddbdadcbacdebaadebcaacecdcdaddaaeaeecbccedcbbeaabadbdbcbaebbdcbdeeebbebebadcbdadadcaeaabecbbdeddbecaededaebebccbccdadeaaadaedceacaeddddbedceeaccaecceeadabebeaebdabbebeacedcaddecdbbcddcabcdccddadeebbbcaccadaabbaedbdcaeebbaacbacbddebaaeddebaedecabcdbcbaaeecbbddabbdedddbbeeaedcecbebccacdbacdbceabdbcabedbaedcbdeaabcaaeceebcacaacbdedebadcceebececbdacbbddcdbadabaeacccdeaaceeebbdeecdeadcabacbbdadaadecdeececceadbbebcecaedaaedabaeacaadecbbbbedaabbdadadaebeedeaccbaceddadddcbdccbadcceeabebdeddedbdbcddeebecbabedacdbbeadabadacecdbccabbabdaeeabbcdcaaaccceddecbdabedaaecedabdbbabaaabcbdbddbedcdcaececbaddbececcdaebadaaddcdbadebdaecaeaedcecbbddebaecebadaaaeaebdbdeaacaebbeebcbcddeecadbaedcbcabbdcadabcadcbbacaaabdeabbeeecebaaceaaebbadbcecbdcebcabdbbbbbacaebdabeeeabadcbdabcabedeabddededbecdadededddddcbcebadeeabeeeeaaedcebaddbcdcceebdeaaaceedbedecaedeadbdbebdedbdebdcdbaeddbacaceedcbbbdbabacadadaaceddcddcbdcabacacbedaaeaadeddacbbccacbceebeccadabeaceeabedbcbadcdbaebeacdbdbdaeeeebebdbcddcababbcaecdaeaebbbeabbbcceabaeddeadadabecaabeacbbecedbdeddacebbeeecaaacbdadeaadeaedebdbadbbaadbaeddbccdddbacacddbaaabceeaaaabeeaeadeabdbcabaeabadbcabbeedbeaddcdbbdcadadadedcccddcebdeedccaaebaceedbddeeeacaeebdeceabaedcaeceabeeeeeadaacbeeccbccadacdcaebecaaddecadbebcaeabbbbababcbeaabaccaaecaadbddcadcdaadaacacddbcdcdedcdbeacbeeaadbdcebeaaebbbcbeecbcaeabcebdebbacbecabceeaaeaaeedaeddaabbadddcebaeddbaeeaeabedeebadeebdabdbcebbedadbaceeadcbeaaeceeeebdadeccebceddedbdcdcdecededcbebbeddadbaadaedcdddababcbeaaeaedbabdccabcbeaccceacdebadadbebbaaebbeeadeeeccadbacedebadcdcdcabbceeeaabdecbcdcddddbabeaedbcbbdcabaacdcabbdcbaadacdddbdaececcddadddecaacaaebbbbaadcabcddcebdddbbcddebdbebdcceabebdbcddaaedcdaceddbbcecbbeedbbbceadceecaeadaaaedeabdbbdcbeeddbbcaaeaeeeaccdeaebaaaeeccbeeccacdddeecbbdeaeabbdbbebaddebbacacdedeedeeacebbecabcbdacbbbecaccbcbeaaebddacdedbeaacbcaacbaeabcbdbceddcddbebbbccbbeccbecdcdebdcdeddaebddaebbebbdcdbbcabddecbabcaccddddabddddaabedcbadacedabebbbaaceddcdbecdebcbdeceebacbdecbeaabaabdabeaadbbbbeaddccbedbceabedeabbbaceebcacdddedbcbbabaeabdcdbcabdcceccabdccbabdceecbadbbbdbabadaaeccdeadcbabdcdaebbbcbadccbccbcbbddadabbdabacdcdbabadbacbcdcaeeeadebbcaccebbaacdbcdbdbcdbdbdbaaccbaaaeadbaededcebcedcbdcbcbccbaaabbecebccacececbecdadbeabdddbbcedceaadaecbaabcbbbbeedaacdaedeccdecdddbeaaccdbbacccbaacdadbcaadaabdbbecbabbbcdaaedebdcacadbbcebcbdcccbbcaecceceebecadbccbdddcbdabecaadadeaaedeaabdeaddddadcebdbabbaeeaeaaecdedbbdbebcdeacbddcebbbadeeaddeacabbacebbeeedabbeeaacaddebaebbbaecbcbbaaedaebcbacceaabcddebedcccbaedcaadebedacceccccaaadaaaebbbeabbdbeaccacabddadcecadeaecebcedbdccddcbddedabedbadebdaaadaddadbdaecadbdeacbbccdaeaadaaccccaddbeecddeecbdcabdcdacbdcdaccedecccaeaeeccdaeeeccddcecacdecaaabaabbbbececeaaaabdcecdcddabcbdaadbdbccceaabacaededbeaecccdaabacbeeeccbcbabaaecdeaccdbdcedbecbcccacbdcbddcebabedecbcddebddbeebcbabecbaaeeecdbccadebcceaaabaaaddbcbeeacecbbdcaebcddaaeddaeeeaaecbdacbceaedbddbdcbdceacdccabaceaebeecddcdaaaaeaedcbcdabeaabccdaacbcdedeecedbdebeaabaeaaaceaaebedaecddddaddeabedbdeedddbdcbaeabdacebbbddeaeecdbadbeecdbeebccaaacdcdedeceeecdaddebdedaeceebeddbaeccdceeecedebabcaadbeacedbdbdeeaabeacbceaaeeacccebaccacdaaaecbcbddbaaeceebeeebedbaabddeeecdadadaabebcbdbeeacbcdcadebbbeababadcededdceaebdcedeccdbadadceeedbbdabcdaaacddacbbcbaeeaaabeddeebdcbcbcbbeacdeebaaadbbcedcaaddbdbbaeaeebcbbabdaaecceabdceebccbbabecbbbeccaaaadbcadbcaadecebcaeedbbbebbdbbdcdbdbcdcabbbbbcdeaeddecbaabdabcbccbedaceeadbadbaadcdadcbbdecadcdaccadebcdccdababbddceaaadcdabcccdcaeacdeaaaebabdbceacbbbcccbaaaaeceaddeddebcdddbbcbacbecaeeddaaccecccbdcbcaccbdbeeebbbadbcaaebaceebeabcccabecdabdbbebeeaacaabeabbcabcbdceeecceececcebeacbeabaaeeeaecbceabdebeceeabdecbdbeeaeaedddedabdccdeeaabaedeabaddecdadccabebedbbcdbbaedaeabbbeadccbdddcecdccceaceeddbebedbddabecababcbdcabdeeacaebaababcedecdbedbeeccdeeeeadceadcacebeddcebaeabacceabccebacdcacbadabddebdcbdcbcebebedddcbcdccaadddbccaecdacbbeeaaccacedabbddededebddbacbdceaeabaedddcecdadcebdabddeadbdcddaebadcedaeedaababbbbddabbcdaeeaaaedebaeaebeeaadbacdbbebdadddedeaabeaeeeebbceeddceeecdaebbaaceadeeaacaeabeedaebdbeaeeacdceedadbdddcbbbabdacdeaceaeadebcbeedaeeaaccddeaeddedeeabdabddbacdedbbdeaceacbbabbbbadbbeecadbebabddaebbcedaaedebdbebacceeadadcdeaabbececdbaceacaddcbacbaebdcdeddbeeddaebecbbadebeaebcecbbdacbabeeedbebddecedebdbbdedbecdcacdaeadcbdabacacaecdaacaeccaeaabbacebabdaeeceeacbdccdcddccadceccbccdadcadacedaaadedcbcbdeddaceaabeaedddbcbcbccaeadddbadaadbdebbaebabedbddccbdbcaecddceadecabdeaeebeceecdebceeeeaeceebdcbdccccbbeabcbaeccebcebccadbcdccaaebcdbecdcadaceacbadacbebcaaaacedabcbcdcddbdeceaababcabadcadedaedbbdabedbeedacbaecaabeadcbdcebbecaabbdeccdcccbadeacabeeeaabcbbebebcdeebbcbecedddacdadcbeaeeaeedbdbebeddeeebecaddaaedecdcaaeaeebabccddcbaeaedbabdcdedeacadaebdccdddbcbbdbbabdbcdeadedbbdbbcededcdbebdcccdcdcbaeacbbababcebccbaacaabdedcaccbecddeeebbaedbeecbdadadceecdddbddaaeaacbddccdacacbcccaecdabacbeebceeecccdedbdeccddcdabdeaacaeabddaeacadaecdebeeaadcedcadedceecaabadabadbbdeeaddacdbcaaecddbeaeeaccdeaccbcbaecadecdcedeeeeacebadcecddcbcdbdebbebcebdaabaccbaebebeaccbcbdecebddbddcebecbcdbdceabadaacaeeddeebdaeabcaedcbeaeadcedbabddddbadedcccddecabbecdaaaedbcceddbcdcbbcabdbceaadaddceebadaeaddbdeccadccbdaccddbebbbabbaceceeaeeecadcbeaaeecccadcecdabdacebbaeebceabbaebbbedbcbedcdaabbcbaadacbecbdbbebcbdcbadcbbecebebbcdeecadcddeeeebaddacaeeaeadcdcceabdbdadbacaecedddebedbdceeeacabecbdbaaaadcbaabacbeebabeeedaeceebccbecaaedbcdaaddabdeadbbdcecaedebaedabedbbcbcbecdaabbeacaddebebaccbbcabcabbabdcadcdbadbdcabedaccdbbcadcaccdadcccddeaddaeeabebeececdaccbadedaebcadcbbebdeadddeeedabecbdeedcabbbddabaddccaecacbaadbaeadeceaeeaeeedbccceeeecdeccddeeacceadebeecdcdbdccecbcabacaaddcbccaeeecdeeaabdcabdbbbdbeecceaccaecbdeadcabbdcdaecdccbcaedbdacbabbbcdcbdbbdbcddcebcecbabaaddbdebccbabacebdeaaeadcaaadcceeaebbbeaaaeddbaadddcccbabeccadceabcabebbdcbbbdcacdbeccedacdbccdaaabdbbecbdaaaabdacaccbaccbedbacbdceeccdbdcaecdbdcdbbaeeebcbdcacbdbcadeabecdeaaccebadbbbcabecebaebcbaedaebdeeecdeebccdbbccadedaedaccceecedcddaeedeeaaabbbbbceebeaaabeaeaeaddbdaabebabdcdccaebadbebdbddacabcadbaddbbbbdaaaadeceecdbcecdccdeeaaaebebebabdeabcdceeeeacadbbbedbdceaeadebabdeaebbedebbbedacdeeaedbadadbbcbbbddccedeebdcaeaecbdddaacabddcbbddbcdebbcdbaecdcececeabbeebbbbbaacddbbdbaacccbeabbabdbbbccabbbceaadadaecaabdecbaaaaedbccbebebdbddcaacdceeabdedcbdabbcaacdccdddbaabdaddbdccbbbcdebdaebdeeaebdeaacaacdddecdcdbcdbbaabbbccbedcecdceccdceacebbaedaceedcbcaaedbddcededbcccdccabbbceeeccceddbcbbbeadaaeedcdadacbddbbecbddaaeccbcabeaadeebdabcceeaeddbdaededbaebedbabcbdecebeedaccbcbeeaeababbdeedadcdbbcadcccacedbcedaabdacebccbbdbcbbeedcadadbdebdccaddddaabccaadbbcababddadddcedbdaddaababdbaabbbcddeadaeaeccdccadeaebaceeebadbaeddabbaeceacdbbabdaebdedaadacbdcdaddadbcbaedacdccdabeaccbecdadcabddbcddabcccaacadcaebbceebebbcbcdbbbbebdebeebcebdcdeaadcceeecadaeeaaeebadceccdddbbbbecceaaacddeeedacbbdebbbedabdbcdcaeaeaebbccbddbdeaddcebeaabbdbcadaadbcabbcceabadbabdcdaeacbcdaedacebecbaeabecdbcbcbdeccbddebbbbbabecbdbcebecaabddaadccbaceccedbaedccabacbcbeebcdeeccadcbebedebeaccbadbebcebecbeebaebeedacceecaceabaeabaeccacbdbcddabeeaeddebccbcabdbdceeeacedeeccebaaaeadebbcaaddccaadaaaecaddbebbcdcbedeeaadbcdcbdeebceacaabdaadacbbbeecaecddbaacdabbbaeadacaecaacdbeedbaedbdaeaeccccdbecdaebebdbbadeacdbedbceacdcebbaccacbbcbcbbebdbbaddddbaddedcbeebcaebeeddadbbbecbcbddaaeebaebbebcbeceebbcedcacbaeabbdbadaacdecaedbcbbaaeacbadcebcdbcdeabdeaaeddcbbbecacbababaedadabecdeabecebbbcadbbeaabcebadeaedeeeddceacaabeacdbccddbaeaaabcdccabadbbeccadbeacaecbcececbbcaabaedabadcebceedadbeecbeaabbddadcabecaacbbecbeebcaeeeddadbbecaddeebbcdceaadddbaaecccbbdecdabcccabdbebbeacdadedeecbbecebdcbdaaeaeaeccecbebedccacababdabebcababdcabccecabcbaecbaaeaecbeacaeaedebcbcbeececacdaccdcccddcbcdbcddbbbdbcedacdabacceadbeebcaeabedeeebbaaaaeeaeacdabecdcaecdceaacddcbebeeddedbadeddaadedcedeeedcedbccdabdddaaeceebaeeeedcabcbbbabaeabadccbadbdeaaabcbddbcbbdbbccdcdeecdcdbcedabcdabeeabdeeeacbbbbbbdbeeabbdaeebdbeadbbbabeddceeecdeeebcceacbceedabdbdbddbebdbeaabdbbbeebccbecdbdbdbeaebbbbbabccabeadaceaedcbbedabcaaadccabadccbbcadacabbbcaeeacbbdcbeadbdadcebbdceaceedeacbeceaceeddbcbbaeddebcdebedaaadadacdeaeddcacddceeaadeaecececabeedabbdccbeacbecbcebabedececcadabcabceacbbedcceedbbaabeeabcabaddeeceaacaacabddddccecaccaacbcececbbeacaceacdabaeedeaebddebcccbddbdadeecddcbccecbcacadddddbaeabcadacedbedaaebcdcdeedecddcabeaeedebbaaedabeededbecbcccabbeccaebedbceabebaaabaecabcdbecebaaddbbdcbcbdaeaeeacbcccdaabccacedecbdabdaddceeccabbcbcdedaddadacbeaaedeaeeccccddecaeaabaabcecddddeeceaeecdccabaaaeebdcbbccbdbdaecbeaebaecdaaeabdcddbedbdeaccebbccaadddbcdacbebcabbbaaeeaaabcecabccdeeabcdceccaacaddcaecbbadacbdccdccacbdabeaccbbcadbebccdbbadaacaabaecadcbdceccaabdbdeddeaadaaddaedabcbeabebebecbebdbddddbccebbbbceedeaacacccddcdbdbbdabcbdedcaccecccceaedbcbbadcedadebcadcdcebceebabababdaadabbdcdededbdbeccabeaacadebcacddadaeaacdcdadcebeedcccccacddeedddccdadadcdcceeebcbcbbedbdbbadbdcdebbcecbdccedecacbccbdaabbbebdbedbbaadedcbdbcdccbdeacccebccdeadeccadbdabeaacdaaaebeaeeeadccddedceedacebdcbeabacedbceeadbcbbdaedaccbaecddcdcadeaeeedaaaeabdaceedcbaaeeeeeddbccaadcbccbbcbecdedcceabcdcbedabbceceeeaccbedadeebeddaeaabeabbbbbdaddacbdddcbacebddeeceeeadeebcadbcbcaabaaaabddbbbbdbdaccbaebbeccdecddeeedcbbdeabebedadacbbcdeddcdaccbbdceecaebcededddcbdabaddaeecabdbbabddcdecccacddcbbdcbadccadecabaccdceedacbbebcaacccceebddbbbbdcdcdbecddaaccdcaeeedebdeadddecbecacedddbcacbecebdcaecdcbedbceebcacbdeaaecebeedbceaeceadcddcebaacadbbdcebecebacacaadbcdbaecbdbdbbdcddacbaabbacdabcadcceeaaecbedaadebedaccebcbbcdbdeeecaeabacdccbeacacabbbadcdabebbbddcdbcdbacbbeddddebceccabdeaebdacadbadbeacaaeacacbdebdbcabeacdbaaaeadccaaeceabbdeadbbcecbdddbccddbbaaaeebeccecddbddabddbeccbdeaaaecddccabbdcdbcdbbabedcdeceacbeeeeaaeebcacbbabdeaebaceadaccdcbedbdccceaeeedacaebcccecbddaaaceeedeadcadbdcbbdacaacadddecdaebcacebbdddececbccebeebeecbceabddbabdceebeaabdaaccbdedeecddaeeebedccacacdccdbecdcdccedebaaedecddeebebdacceddbbbaaaccbcaddcaecebdbedecccabcebabcaaebbaeeebcdccdbedcdcaebbeeedabceeceecaeecbbeacadabaebcacacaeecbdeeeaacdccaddabcbabebdcaadaaadaaccddbcedccdbcdccdecebabdadddbecbadeaabbbccabbceccceedebabbaecaededbadddeabddbedddeeddbeedadccabebadcebcbabccaeececcecdebdeebdacddaedcacebabeedeaadebaeeadbcaebceccaabebaacdccbaeeaaeeddeacdcdcdedbddddaadacaabcecdeaebecaceaaebccdbedbeaaabdadbbbacecbaccbddadccceacebbaacacabccbdbddebdeaecaacacebcbebbebdaaebeecbaaaacbaeedbdbacbbdbecadbcbaabbabeaebbcebcaeccdedabaecabcbecbcdebcadebcacdcaeaeccddccabbaccaabbadbceaebaadbbdeaecdeecbccacaedcdaeebeaacaccccdbdccccddcbdbbbdaaeaabdddcdddbddeeaeabcacddcabddddbdbcedebbeacebeabeaeccbbbdbadbcbbeacaecbcceedacdcaaabccebdedcccacaeccbadbedbaeedbeeacedbbbceecacbbdadaeaebbdeeadddcbedcebdaeadecdbcecbeecadceeedeeacbbcebbceaaacebbccaabaaeaeaddedcedccbaceeeabbbddcedadcecdeddedcdaeebbbbdbcaabcdbcddbeabcdaddebdbcbcdaebcdebddaeddcedaddccbecbdcedbabbedabeeaabbadcececdbacdeaebdecbddceaaecededbddbededddddaecebcdebddbdecbedabeeedeaecaebbdceaacddbdeabcededbbeeccdaeebedbaaccebccbcedaebcdddedacbabebcbbeabebdacaeeebbbdacbddbaecccadecdaecbdceabadbedadcbbaeebeabbcadddaedcbdbebbeacecdbeebedbbccebcaabddabdcddeeacbbaadccabcccbecbaadebbdaabeabceeabcdcdbacabeccaacbcdcaeaeedbbedccdabcdebeaaaeebbaccadadbcdcdcacaddbbaccaedeaabbcddbaaddeaebcaabebdabddaceabaaceebeddaabddaaaaaaaeddaccacddaeecebceecaebaababaebaeabeeadbdbadaaeadabaaeeaddaebebcceaadbbbbabdbaaeeaadbaecdaadceaecaceeaccbbccdaebabbadaabdeaacedcdacbebdaeccceebaeeeeaebaeeaedbbdcddaeeadeeadbddcadbdbaeeeaccabbacabcdbbedbaceaedecaecbcabbbebedccdcceabaaabecdcdabdddeeddbaebddeaedbedacbadadedbceaabacbbccacecebaccedbebcbebebeedbabcbdaecccecdadacbdccddcdccbbeeeddacebdadaaaadddccbbdadaaaaccabccbdebdeaeacceabcdaadebebbdccaedeecebbbeacabdabcacbddacadcacbbccddadcccecabcedcddcddcebccabbdeaaeddecdcaeceaacdbadebdbdbecebbabebcebaddaeccbddabdddedbdaaebecbbabaebabcecabcdeacabadabdcbdaacddcabeacdeaadaacdbeaddcdaaacddedbcdabbecdeabaeedaacddaacaeadecdbddacdcecacabacadabaaebaebebcacbaaccceabdbcacadeeeeadaedadcdbbadbecaceeddbbacebbcebbeedceaaecedeaaabaabdedbacacdaeaebabccaabedebbdeaecadddaeccdcebbcdadabcabccacbecbaeacdbcbcceddcdaeddcabdaacddeacaccbcdbceabbdeccbccaeabdebbeddabbccdcdaaeaeedbcbadcabaeedbbcbdbedaccccddaceabaedebcbbecbebdcaaabeacbaddcebdcbceacbdeecabeedadaeedaeaaadcdddabaaccedbedccdabdaeeaccdadbebcaedcceeddcebbedbeadbdeabaeeebecabbcedaccececaddacebebdcaeaadddecdecdbacacdaaebaddcdcabcbadaccecddacdddaddabcddbabcdacaadbdcebcceadeddbcebbedbceebabaeeaacbbeeacaecbdacadadaeadeabcaabcaeabccddbdbcedecdbebdcaaacccccadadedbdceeedbddcadceecaaccdecbaadcaacbaaaebedeaceddadaceabacbebedabbddebdaecaedaeaecbacceeeecdddecaaadadcdaceabdeecdebbeedeccbdccaeecebbecdccceddbdbccdbabdebbadeddedbdedadaaeddadaddcaabcaebdeeedcebcedecbdbbdbaedacdbecdaaeadebbbaebbcdaeddabbcbabcaaadcccecddbabdaddbaedbddebbcddabcaddaabeeabadbdbdcdbebdbeecbeedbedaeecdcbabbbbdeeaccbddcabdeaeddcceeebebeadccbddcaadcbcdabcccdeaadcbdbecdecbaaebbcdabeebaedaabdddbabbdbdaabdcacebddceacbcbcbccdcaccdacaddbceecebeadedceebbccbcadbaaeebeeaebbdbddbddbbecabcbddeaeacbddaaebeddbbaeaadadaaebdebebcedcceabaecbbcbaccdaeccedbaccaeaaecdbdedbccaeccedeaecbecadcaadaebdcccceabbcbcbbddedeadcbddeaccbbedceaaaceaceaaeaaddbaaebaecbaaecdeebbaeceeccecccbadbecbbdecededebcaeadbbebddbbddacdeaecabaacabbdaceecdbeadececedadceebaaaecdeeecabedeacdeecbedddcaeabdecddbdaaddccbeebaedccdacacbcabaaedeeeededbdebccdddecdacdcabaaaaeddedbceaabddbbdcecabcbcddedbdedcbabbdedebbedcbaeddaabeedcdbdbdbeeaabecaaebcbacbddaddaeecdedbcedaeeeaebcacecbdebaadbcbaaededabeddbdddcbddaabeceedbeccdaacceeccadbcebaebcaecbdebaadeaecbdaedebacaaabbaaaabeeacedcebdcabceccaacbadccaaeccebaaedeabeceaddaaccbccadbecbedbcbbcbeaeeeecbdbacebeabebdddcdaceccebdabdbbbebdbbaeedceeeceeaedaeddbcccaaaadabcadadaccabcaddcdbacecedbacaaccddbdacacacecdddceddaddeeebdbdcddecabccbcdccbabbdbbbeecbaabeceaeaabbebbebbdacbdcebddadcdeddbbccccabacbccabacbabbabadabacdeaecbeeabdaadeeabcabbabcacdabaaacaeeaaadaaceacabaeeaceeacadebddabdebcdbdeebbabaebdbdcbadeebccabccdcbacdbeeaaecebdeaeddeebbebabaabdddcbadbadbacdacaadcabdeabeeeeaabcccceedeaabdadedabddcacbbeeccadeebbebebeaddaddbecdceddebceaaadaebcaebdccdbdecadcaabbaacadecceacbacaaccdeaabddbbcaabbdbbddacdadcebcbdbddbabdcaaadaeadadbdcdcbdccdaabecaecdabedbecaceaaadedcbedbbebbccbaabaaaedbebaaabeabcacccdaaabedabaedeebcbaabaadaacbbcbeaccededaaecadaceacaeaeabcbedddbebbccbbbccadcbbeeaebebbabbeaadceedbdbeedabcdceaaecaabebedbdddcbbebcddcbaecaacaacdedacbacaeccadaaddecebddcbaabeeedbbcebeaccbbaadacccadaddeceedcedcabeecdaadacdbbceedaaeccdbeeeecbccdebebdcbccceabbebcdcaedbbdbbbbacdaaabececadaaaaebecebdeeeadbcecceeebaabaccdccccdcaacbecbdaddcaccaccdeebecedcedbbddbbbecacecdabcebddeeeaebcbeedccdcedaeddeeacbeedabbedaeebbcacddeccadbdbebcbacbcdeabadcbecbcdcacdbbedcceecbbbbbebbdaebcbcadaedbbebbbbdacceebdcdccbeaedcacacbecdaaccbbebeccebabddbaceacabaaeebdccbeceacbbecdeecaaceeabbdcccabbdcdbcbdabdcabcccbdbbdcaeeeaddebebdebbabacdedbccbdaeeebdabbecbbaceaaddacdadbbdacebdcadedccaeccddaeaaeadbdcddaddabbddbdebddabacbecdcbccecddaaebdaddaddebbbbbadbbbacdacdbceabaccebaaccbcdeaeadbbadddccbbccceaaedebcdeddbcabdaebbdeecbdddceacebeedbeeacbebaeceeebcaedcecaccebceeedccbaccedbdbdeaabacccdadbdeaeaeacdcaaeadccaabbcbbcbdeedccebcabaceaecbedbdeabecabdbdbbbbbacbddaeaacedbecceeacebaeabaecccddbccecaedcedbddbcdabccaeeadeccdececdecaccaedcbbbaedaaacadebecebcbddddecdbedceeddeeeddcaaebdeadaadbceddbecbbbbcaceebcddcecceecaabbeeabbadabcabebcbdaccabccbebacbcddcaeeecccaeccdabaadbedaecddedddeedcbaeabddbeaccbcecacccbadadaabbaaddeaaceccdcccdceebdcaabddbaabcccecbaadbbeaddcbcedcbdcebabdccddabedaeebbcedcdecaecebeabecceeeacdcadbebaadacdaacddaacbcdedbbbcccaaeaecbaacbacaaeabdabaeaddcaaeccdbdcadaadcadcdcbccdbbecababcbccabeddddbeeedddcebeaedabacabcdeaecedccaceeddaaceedbbebcbceeaedddbaddeaadcdbabbcbbcbeacaeaececadcaecacdaccaacceceecbacdbadcebbeabeccbdcbcaebdedeeaabcaaabccdddedeabaccaeedbbddaebbacecaaaabaaeeaadaeacdbcdaaddbbedabdbcebacbbedeccededdebddabedcadcbededbdadbebdeabdbdbeaeaabcdcabdaadbdbbdaaacbccccebebdabcdbeadcbceddcbadbaddbdaecaddcebbaadbabbadcebbdecddcaeeebaabbbdeeaddacddbcabeccecdacbddebbddeacdcecabeeadcbcdceedebbaacebdeeadcbaaeadcebecbecaeebaabecccbccbababadacbbebecccdbcbdecbcabbdaaebebcaedaebaabbcdedeccddaeaaebecebcecedccbbabdabcedcdacccecbdebbbadbdedacebbbcccddcdaedbebedbccbedaecaeacbeacacececceddebddadadbcbceeaceaaeacaccdadaedcdcaeeabedecdecedecadacdacdbacadbcaaeccbabadedeadaaebbccbbdadeddcdadaeaeabecacddcdddedcaaaedcadcbdebaecedecbcccacccdbeceedaebeccbaaeebbebaacbbdaeabbbdaaadeaacacbdceceebaaddcedaecbbacbdcacbaaadeaeddedaeabccbaababcccceaeaeaeeeaebeabdadacdcdcbaebabaeadebbeeedcaaabeadceacbcaabbbdacbecabbeebbbbcacecccbedbacaadbbbbdaeddddacbebdaddbaaabdcbcaccadedcaedaaebbdbceeacdcddbbcbedbaecedceacdddbaaebeadeecabdcebecddacadadaedbeaddddbbdbbcbcccbadecbbcceeaaecabddabdaacbeebcddcceedcaeeaceeeacaadacaadbaadeedddaeacbbbbbbbaeaaaaddbcdcbedbebadecbddbbccbdaaadbdbccdaabccdccbbcbdbdedeaeaeaccdcbabebacceaddeddcecabbcebacadebadcaaabdababbabdceedabdadeeabeacedabdbdbddaaeecbebcebdeddeedbacedecabdbcadccdabdbebeebbbabbdbddeeadcaedbcbdcbbecadddabccdcaaeedcadabdbcdccaabcaccedaeeecbebeaaeeabecaaebddccaadecdecedaddecacccdeabacccedcdbccdabaebedbabbeaedaddbddedcdcdbccadbcadacedbeaecdcdabddbbddcbaceecbdddbebbabebedaeaecebcbaecdebcaeecccacbdbbdbeacbbabdbbcdeeacbaebaddcdeabcdaacaccdeeaceceacbdcadbbedbeedaaceeaadcebaeacabeeadbbcccebdeaaeeddbcebaccccadcaaacaececacbbadabadbbdbdaebcdedebdeecddbecdcbccedbadbabeddbdcbbbebbeacdcdbbdcdbaedcaeceeeeedebcadaddbedccddbbdbddabadcddeaeccddbdeebeedbebebaaecdbbcecebdeacabbcadcebdbadcbccacccadbaebeceaebdebbdcebedecbbcdabecadceeabaaceaeaaadeeebddacbeeacebeaddbcddcddcdbdadbabbdeceadadceacccdeedceacaacbacececaecaceeedaebeccecaeaaecaeeaddddbbdabeaabddaeddbebdcabacacdedaabedcabcbacceecebbacebccadddeaacdaccaaaacebcbcabccbccbadbedaebdadbcbbdeadacebdbbddebadbeddeddaeeecdeeebdecbaeedbeeaaecedcdbbddeccdabcaaecbecbcaeedbccedbbeddbeecdcdbceacabdccdbadbdbeabbdaaeebbdebbddebdcbdcadbacdbcdcebcdeaeeacacccdcbcdeecbddaeaadbcdabbdeccddacadcedbecaabeceedbebcabbbdaddbddbadcdaeedeabdedebbbcbdcdcbaabcbddaeddeaadcdaacaeadeadcecbacadccdaadeeccddbabddeeaaadbbeadbdeabddcbdbadecacccdacecbecbaacaaeecccedecadeecedebacdecaeccdbaedeeeedeabdaeccdaadaecbbaceeeecdacddddadeeabcabdacbaebcddbebdcccddeabebbbedcbaeadeaebddddbebdcccbcabbdacdcdcaceadeabacdcacabababbdbaddccebaecebdaaceaceebdaddecebacdbaabebaebbeedbbcabceadaaacdabdaedabdadecbaebedcdbaaeebcaddabeeaeecbcdabceeedbbadeebecabeaaadbdbebabdbacabbdbeadadbdabcaabaebcebbbdebbbcccaebacecdbddeabaedededecabacadecdaaecedacbddbaedcbedcbaebbabaeacedeacceacedeaabaecddabdbbbdeeecbdacbdadecaaacaeeeaaecbbebeedcabaaeddddddaacdabbcabadbddddedbccdcaecedcecbaaceecaeeaaadcababaccedcbedccddeaeddecedbdaeaebecceeacedbacdccdbebededbbbaadcccbdbcacbcccddccceacddabcdaacdddecbecdaacabebddccdbabddadbabdbbccdabebeecbcbbccbdeeebecebbedaabeeedadbdcdbaddbceddeeeadebcbeaceddaaedcbaacebbeaaacbaeeecdddeddabcbccebdacdeccedaadbccdaeaedaadbbbabcdbadbdcbbcdaebbcbceaadbdecaeeababceedddebccdebeabbbabbaedccaccaccbbebdcbdcdeadcdbbedeccabaabdabeceeaabbaedecddbeeaddddbebebcacdcdcbcbccbbeeadbcdadbbcbbdbcdeeaaacdbdceebedbcebedabaaecaebbddbadbeeceeacedecdceccbadeeeebddeccaabaabbededaaccaacabadecabaebbacbacedbbcbecbbdcabbdcaaeceaeaeacadbddbdbbeeceaaabcaaaaeacbbecbcaeaedcdecbdcbdcbebdeabeacebacebbeebbcedacebcaeacccedededddcecabeccddecceaeeecdacccecedcdcdabccdcecaaeebadcbadeddbccecebeecdbdaadaaabeaeadbdccedceebccecaedbbbebaadacbcbcdedbeebdeeedbeeadabbcabaadeacabebaaebeedbeecdcdeebdeeedbeedebcabcedebbdabbaadeebddaecdbadebdbeccdaaeaeeddceadacacbedebdcbaedaabedbccdcccbcdbaaddaedbcacbceedacececbacecabbbddacddcdbeeecadcadceacecdebbaebddeeaccbedecaddaeeabdaddabdecddbbbebcddaaacccaaaceeeeadebbbeaeaaaabecaaeaecbcdbdbcbcbbdaabccbddecaddaadcbaebaeeddaccaecadaeacdbbdacebbaeecdebceaaddbddbabeaaedadbecddddaeedecacbaddeeadcdbeaababcdbdceecdabbedccdcbdbbebbbadbbeaebbcddcdcebcbbebbaddcdccacaebeacdaadaedbcdaebbeabcbbbcbceeeecaadeeedeccbdabcbaebeabcadcdaaacedbcaccaaebabbbaebdcabaacadecbebcbdbdbdbdddcecdebaaeeaebbbbdbcdcbcedeaddcebccaaebbcbaccedeedcaeacbacecebeabadbddbcebbadcaacdccedcbbadabbddedabbbadddeadcbbdbadcbceaceaacdadceadccddbedeceebaebedcbdbcdacbebaeaabbdccadabdddecaaedcaeaddeddddabcbaeebcbdbcbecddbcaeebaacbedbebdbdecedebeacebbbaabacaebdaeabdedebabbeecddbbcebdebecdeddccddaeedebbdbeebacecccadabbaaacedbbabecabaaedcdaacddadeeadeeabebaedbbecbcbdbadbeadbbedaceabeaecbecdddeadbbacdecccddaaddecadecaebbcdabbeeabcbbbbbbedeeccddbcdbcadcbcaadbebbabcaaeccbedbcaabbecabdccecdbeeacbebacdbaabcddeeebeabdcdaeececccbadcbacacaaecacebabbacbacecdbbbbbedbedbeddeaacbebccdeaeedcacdedbbcaeeaebbdecdbdaaeebdbddbebcdacadbcaaedcebbcbcbaacbbbddeddddeeaecedbdceaccecdecbeeaeeceaaebeaccbdeaaaccccbbceabbbcbdadcaadedaeeeecedacbbeadddeebaccdaaadaadcbbcdcdcbebbadadedcacbdcabbdddceaabdbebabebdbaabbdddddccbcbbbbbabbcdceeaddbeeddbadbcbccdacdabeeebdcabaaaeeababbcabcbadbaabbdbecddaeabaceebdadcadacdcdeadbdcbbbcacccaebadebbabdeaadabdaeaabbcbdcedbceeacdabddbcbcacaecaedcdceaeeeccaebeaddbcbedbbcbcacadeecabddbabcbdeeddaadabeeabbebaaaccbbebabccbddbaabcebbaeebebbcdcabadaeddcdaacceabebdcebeccddbbcebcedcdccecadbdbbdacbdeacccdbacbadceecadcbcddccdcccdeceeaddaacecdaebeddbbbdacabaceaecbedaceccdbcbeecaaaaacaccdbddecadbbbcabcadcbcceddedcdbcccbbbeacaabdaedadbadebebadeabdaabeebcddecaebedaadebbadcdeeaceaeadeddabadaaabdeebdbcbbecbabadabdbeadecbedebecddadcaddcadbeddadeccbbccbdecbadbdecabececaabdececdedecbcebeeceadbaccdcdcdedadbaccccacadbeacdbeeeecbabbbaccacbcdedeaccabdbcbaadbcedbbcecdbbeaeaadaebdeaacbcbdcdccebedeaaededceecdccaeeeadacedaadbeabdbeedadebbdedbbceadaaedddebebaccbcbcecedeaaccecedeedbcdbcbedaebdacbabcadbbdedcbccccbedbbeeecdcabeebdddeddaecdaeabababdceaeeccabeadbaabbdeeeabebdbccdaaadbccdacbaebccebbebaacbdedddebadcbdadeeabedddddbdacceecceecdeedcaccdabcbdbcabbbcccadbdededadcaeaebcdcdacbacaccacbbbcabeecadebcaaccaaabbcbcecdbbedeeaaaeacecbedcdabcdddcbdaabbcbdcbbcdeeacbdcaccbdaedbadbebedbcddbcbebeebedaececcadacbbecbdbeceabbdccbebadddeebbbabdbdacdccbabaeaadbbdbbacddbdbddbcacdaeaeeceddddeaceadeaaddaaeeacececeeabaaeceececeabebbbeeacbecccdbababacbabeeacceecdddaacaddbaddbddbcadddcaeecbcbaaebcccaeddbacabedeeceabecadeebcddcecbdddcdcbeadecddeebebbeecacddedabcdbecdebaedccdaebdcdeeaacdcebcababbdcdcaacdadbcaaebadbcebabdcdabedcacdaabdadbcceebaeaceabedcaceecedcebecabeedceacabcbdabbcddeebebbcbedaebeebecaaeedeaddbebcecbaabcecaedaaebebcaccbaaaedcdacbdcddebbbdecebebaddaeccddbcecceddeeddebeccbbcadbedddcecbcbbdaeabddbcdcaeeeeeacbecebceaabcbebedbaebaabdababbbddcbaaaaeddbcaccebcccaacecccebbcdcbbbacedbeeabbaeecebaabdaacaebceaceccdcaeceeeaecceadabdbcededddccecdddceabeaecbbbedbccbedcdbbcbaedabceabceebcdcaabeecebcccedbdcdedaecbceedbccebcbccabbadcaddddbcbedacadbbadcbbbcbbeedcdaecbebecaeedcabcecddacccaaccbcabddebeeaacadadbbbbdacaeccddabdddcdbbecdebaedcbbaeecedebaddbbebdbdbaddaddebeddbaadeadbecdebcbbcbbbedeebccbbbbedbdceaabddaebebccadbcbdbbcaddacaccbadcacceddcbcbebeccecedebaddddcdadedccddcaccdeecebbabacbcdaedddbeeacadbbaccedaaebaacccddadbdbceadbcaeccecbdebcaacbbcdaedabdeeddcaebeaadcabbeccebadccabebebbeebbddceabaebccbcaeecabbbbdaccccecadadbcbcdacccdecdeadacadebbcbaeecceaccddcbcabbadbacaedbaaeccdcdabccddeeeddabeeabaeeecbabdadaeedbebcdaccebabecabddeeaadcaabeddbdbaccecacccedcabebebcdbbbbebadddecaddaeceeadebdbeeaacdccecebcbaddcbadcaeececeeeedcabdeaddcdaebddebaedebddcadcbbbebcecadaeaadccbeaadcdbccdeadeebbbecddacdeaeeeaccbeecbeeddbbddecaddcaedcceeaebccbeacdedbcedadaccebcecbedbbdbeeeaadecaddcabcedbcddbaeeabbebeebadbadddadeabbedaddddebadeeaedadaacbecaeccebddebeaeabaeaecedcdecdbddcbbbcaacdcadebcdcaceeeeadbbaadcaeeecdcddabacedcccdcebbdabaddddabedecbcbcedaeedccdddcceeaecececadcceedbcceddbbdebbbbeebcaacebddbbaaedeacdaabcadababeecbcbddaceebcbdceadcadecbecbabebebbedacbaacababaadecdadaebeaecabbbbeaeecbebbddeaeedbcdebbebebabacdeeddebcabcebeedceeeccaeadeecddbabeaedabccdeedcdecddeeabdaabeaacabacaeaeabbbbceacaeadebaaadbdcceecedbbccdaacacbeadaecccdbbedaaeadcccddaaaacceaadadadabcaeddaaedebebaeeccdaacecdeeeeeccddddecdcadbbebcdabaaecabbcdaecddcabdbccaceaacbbdecbeaeebdbeaeaeccdcbbeaecdeaebadacdbdbddcebeeedbdaaabedbdebdcdcbcbcabbebcddcbdcddebecabcecbedaaeecbabccdbacccbeaebeeecdeddebdcedadebebbadeeeebdcbedadbabeaabbdcbedccedaaeaceebdaeeabdaaccdcdcdeebccaedeeaeadddceedeadddaabbceacdecaebbaddbdebabccececedacddcebbbccacceacbdbaecdecccbeecebdbdebaaeddaeeccdccbebdeaeaabbdbdcbcdcbccdeedddbebceddddacddababedcccedacaaabaccedbaebceaddabdcaeddaceeeaeadcbdccddeeecdcccebaccebbeccbccbcceaadeaeedebacdbdabceddadbcccebcbebaecdbcbeacbdcebddacccecdabdcbdeeacadaadacecabecebaaedecedbcbbceabeeacccbcdcebcaeeecbbeceabedddcacadeacdbcbdaacaabdbddcdaddbcbbbecbdccabddaeaaedeacccbecebddbccccedadbceabeddbccaaaeabcdedccaadaebdecdacaddabbbaacbbcecddaddcddececaaadaaabaeccdebbdaddadbbcedaacccccedebdabeaabadcebaeedeaadbaebeccbbcaabbebdecabbdbbbbdccebbedacbaccadbcecdacecbaeecdacccdbbccdacabeeeeebeeebbecdbbcebdaccbdbdcdbbababbacdcaadeddccdcecaddbacaebdceeaeaaecbbaecdabdbedcaaeebbdbaaaedebbecbedbdcdcadddecbedcadbbeaaeaedbabaabdeedecebbdcebbbbbdededaaeaecbdcadcedcddedaebbcbeadaaaccebaeeaeadecddacdddccceaddbdbecaacccabbdceeacbecacdbbcdaddbacaaccaeaabaaeecbecdadebabaebbbddacaaddbccceaeaabebaeecacebbdaddbaaaaaeaddbcbececbeeacacbdcabaaadecaedbeaddddaaabaaabedaabadabeecdbbeabbdebabbddababddccceabbcbaaceebddeadacaddbedeeebeacdecceaccbdeedbceabdaacaebbccddeaebeceabbcbebdcedabdabdbdddeadeecedabcadcecceecdbcdaebecadbaaecbaadcceeadcbdbccbdaaacacdbcaeadabdbaaccededababdaebaecbcabbeadebacbedadbedebbdddadbcadbccdbeaadbcedecddedcccbaeeebbaebbcccadaeeccabedbcceceacdbdbbcecaaeabeecbedadedaccadbdeaadaadcebbcbcbccadbbdbececeabcbeedbcbacbdbcabbaaeedabadedaeabecdceedabdecbaacaeeaacbbbcdbcaebdbdbbdbdaeaeabcccaeebcddccddaddaddbddbcbeebedeecdeccaaecceebacaabacabebddadcaecbdddeecdcdaabacbeeeccccaababdcdbcdbdcdeaeedebeeccaaebbdedccdedddcbceabacbbecacaeebbecdcdbedbeeababedccabbadaecabcacecdebeceabcbdcceaaacecaeaededaabdeaccaebccdaeebeacaadbdbadabbdacadeebbdedaccebdcecbacccabebddecbdaebdcdeeaecaacaddedbabebcbcbaeaeadebbddcdbabdcdcaecdaeabdcabaadecbaecbacdadaedaaadceacceaabccbccadebecbbbaaadddececcabadaddadbadebeecacaddbeacacddeaedceacedbbaeebdaedceeddcbeeeabdecaaddaccebebcabedaddcabebceeeeccebaaaeaebbebacedcceecddbcabbabacdaecbbabaadececceabccaceeeceacbeceabdeaccdaecedcdadbebdccceeaebdddaaecabdecaeeeecabcbedeebcebdeebbbabcdebcaacbaecdebabaeeaddcaeabdbeacccbdbcbdabecebcaccecbcccedcbdedbedaabeabdbaecdddcabbebeeeaeddaccadaddebdbecdeacbceaaaadebeedcdebabdbceeeeccdacccaebbbdaeaceebadeecdacadacbaddabbbaddcdadaaccbbaeddceaaecbccceddedcadbaecddedcbeacdccbcddadcbeeddddcbceeeebbbaaeaedbabbebaaabcbdaeacddbecaeccebbabeedaabedddcaecbabadeaadacbbdddaaeebecbeeabcedddddbeacdbaceeeaacbdbaeaaeeaceceaeeccdabaadacdddebbccbcbcdbbdacbccbbeacedccaccbedddacdcadccedabadacdbabeeebeeeaaeeeebadcbecabaaaacbebeeccbbdeabbbebcabebbbaddaacdadedebdeeacddececdcaccecddcaaddebbecbadceddbabbdeedddbcaedbcaceecceeeccbccadcddbaaebebaeaadbdaecbebbcbaededdbddcbdbebdddbcacabcbaeaacaeebddccdbaacbbaaedaecbbedeabcedcedcaabedddceadeeabaaccaeaddcbccdbedccbdedbbeaedbccbacdcbbcccccdebccacbdcadecbcddaaaacadbdaebecdeeadbbcdbdaeaedadbddccaacdbaddcaaaedcbdccadeadeaeddacdbaecdbacdbecedddabcaccbeebcacdababdebceadcececdebecdeadddaaadaceeeecbbdbcecdaccecacdccaeeebbecbbcecdbebadcacedaeeddbaedabbbbdcdeeedcbaceedabbeddeabcaadcddccdcbeedbccacebabcdaeceeabbeadacbdbbadcdaebeaabadbecdccaaaecbdcabcecbbdcbdacedbcadeeebcedabedcebdeaabceeaabcabebacacaacdecacbeddcbdcceceaeaccbcebdcaddadecaebeceddabbaeebdcdcaebabbdeceebbabadcbabcaddcbcbdbacbbdcacbdedeedbceeddbdaccababaacaedcceabdbecabdedaeebecacbeeabcddbaccddcdaddbdbadebbedacacadcdbaeadacbcbabbedcbbdbcddecabdcdcdabddceadcaecceceddbceddecdccaeebcbabcacdeebaeabaccdddbddeddbedbaadaebecdccbdeddddcebdcbccabaaaeeabcececadaedcaeceaaeebaaeccbceacbaebdbbeadaacbdedaebdabcebbaebbbdcecbbdcdaeaddcbbcabcbecbebdbecedcaecdecbaadebbdeababedaaaecadecceadccabddbcdeceaacdeceddbebcddbacceaadaddedddedbbdacededbcccbeaabebaeebaeecdcaabcdbcadeadaacbdcbbedabbeaebbceddecaaccdbbdbbcebcecaadbdedbceeedeacaebeebbedabedbeacdbadcaecbbadcacedcaaeecdcdabccddacadcccccbbadcbcddcdaaeaeebabaaecdabedaacbcbdebbecaddcaedbacedacedaaedbedecdaaeceebaadebecdbdbacaeedacedcaeddcddeccdbbaaceeebddcaedaabccacdddbdbaacebdedcbccacadeaacaadbeecdaaedeabccbbaabdbdcccdedccbdebbbabcebabcccbcddbcecdcdddddaadedcdedacbeadbabcebcbdbbcdbebeeacebaddebebecaccceabebceccbcbdccbcbabbaaaaeeeadcceeabdbbcadeddddabecdcddbaebadabeadaebccdedededbeacabeeeaacdabbecacedddbdedbdbacaccebeddbdceeebdedeebeddecdebcddcededcacbdbededcebdedddcacbbaceeccbcebabbdbecabbcebeeeacbebcbbadcbdbbceeeeebcbccebcdabccadebcccbbddaebddcbedcbbdeeedcbcdbcceeeececeaaabdccbbcadeaececedbddabcecaccbaaecceddbaabcecccdaecccedaeeacabacddebcbbdecdcaedbaeacccbcddaebebdabbaaccbbceccabdaddebddadcecedbeceeedcddeccdaeecbeaacaceeccbaeadeaebcabadbaeaeecdcdecebbbeadeedabdedadbabdddadbbbebcbbabdcebbedecabeaabcabeacaecebaddaeebdbebdbeceadcaaaacaaddcaddabdeadcadbbcebecaadcecadceedccabaddddbabceaceecedecaabcedbdbbbccecdddbecabbabaeedceeddecbebbececacadeecadebecdecddcebbdaacdbedbcedbdeedddceadebabbacbdeacdecbcdabdcbbdadadcdbabecdedadeeeecdcdeabcedebaeabcabbdbddcdaaebcedeebdaeabdadddaececccbdcdabaeeeebbbecbcebeeeddbbdceeccdbdcecedbabaddeceaceadedecebeedbebebeaacbbeecbcbeedcdeaeceebceacedebebeabaeedacdbeabedaeddaebbaeeccedadaedaddcbecbcbedcabcadccebcbceccaecbcaedbceadcebecdabdacabacbbeaeeccbebedeedbedebaeadeaebcdaeadceeddedecdecbeedcacccdeddcabebacaecdbbedddbbddcececbbacbdcdedacbdbdbacbcbcddeccdbdedaebcdcabbdaaaecbdcceeadbcdebbddcacdbeadedcdbceeccadbbbeeabdacacedaccddecbaecacccbdacbacadbbdacbbacccceedacddecbcebeeabeccabbedacdaccadeaddddbebeeecdbedcdccbdaaabadbaaacccbbdabdabbcecccbbcddeabdcceebcbdeecbbeeaaababddcebcbbeecadebaaedbdcadcbbeaabdddbadcdeecadbddbedbdbddabeeeadbaeaccceecccaadaaeddedcdcecddeaedababcdbdbdaaaeeabaedbdaeeeacdecceecaddacaeecccceadeaacdcadccebabecbedaedebebdaaeeecdaccbcacdbbcbddceacbabddcaaabdaaecbabcaaaabbdbdcaabbdeccaddcbbacbaecddbccbbbceacebbcadbebedbaebebaebdbaeaccbcaaddbacdcadbddacedcdebbeadeeadcbdeedeeeeaadcceddedeccbcbabdcadccaebdcdecebbdceecdedddedaecbbadadaedaedbaeeabadadabccaecbaaaabcaaaedcecabdaabecdecdadcebaaabcadedabdcaacdcbdaabbaeceaacbbdcebeeacbbcebebaadacdbeecacacbcebdbcddcccaeeddabebecdddcaccbbdbabdbbedcdcdaaeebcebbeaacbdbdcbcccbceacbebcedcadaeabbeddabdddcbebadabcabebdeeedbebbecdedccbbedddabbceeebccbedddccaedbaccbdbdeaeeaadadecabaeaeaabbcebccccacdcccaaeabbcbaacddeabeecebdaccceebbcbaaedecbecbbbcbcbaebcbebdddcbcaedabadcccceeaaaecaaebeecdadabbebaabbbbbeacedbbaceccdaeecbcabaeaccdaabcddbedabcccabcaaaadcdaeaadbeaebcbdeadeebcdcebecadedebaaaccaceebcdbebeeedecaabeecaebdbeadbedebaceaeebddabdabbadadcdbaabeddeecacadcedeecbeddceaecccecacadaeaaaedacadbebdeaccedddbabddecedacbdbcbbcdddcbabcccabbecededadedbbdeedeeaaeacdcbebbbedeccdcdebbaceebdeedcdcdbdebbeabccdbbdbedbbdbabbdbabcebbceccebdeddeccebadadbccbdeccaccaeebacaaedebabbeedeacecdbadebdaecbebebeeedabdcedaebccedbaeedaacccdadaddbcccbbdbeaaebbbbbcbbbabaabbbcebadeeedbeaebbbebbdcedeabdddebebbdbcbaebcccebdedeccdabcebecaccebabddaecdbbbaacbbebdbebbdadbedcbaeebaaebdcacbcdbcaaebeacdcdadaadcabdecdcbbbdbaacbbdedaebcbeacecaadadeaaaccdeaaabcbaadcbeebbaebebbcecdeeaeaaccabdddbbbcabeeadecbdcbddcedebeeaaabbddedcacaeeceadcabbcdeeaadaaabdbbcbccaaccacecceaedbdbedaabcedebcdeedaededaabbeeedadbeaededbeeaceaaeacbeadeaeacccdaabbeebedcebededbdcbabeebeedddbdcaccbbcccedcdccdbddbbddbbabeacadccabecdbecdbabadbdcedaceacaaddacddaaddbddeceebdbdaedcccbcbdedcabbbbaeeddcdaaecbbaebbbceebeadebcdbbaaaaccbccaabadbcbeecdbdbcbcddecbdccaebddbbbebedebcbcecaeaabcbecaeacbcaadebbaaddeeabaabccececdeedeeabbbcbaeaabdcbebeedddcdabcdcceaecbeaddcccbaaaebadbbbadedebeecdcebcbedeebbccdaacbaebaaaeaaadcedbaabddeadbeaacbbcdcddacedeecdcedcaaeaadeabdcccacabcdeceeabcaadcbdddeceecaadeccaeecaddcaadadeddbacdaeadadeccdbabeaebccebbaabcaeecddbedbccdadaebbcbeeebaccaeabdaeedcdeebdbdeebdebddbacbbaddecbdbddcdadadedbeeddecddbbbaededeadbaeacbedbdcdbdaedcdecddaeaabbcdedbcaaedccddaeaabcbabeeaacedaedaaedcbbbbcdbdcbcacddaadbcddcecbbaccdbddbddabbbcacbececdcaeabedebbadceadbccaeeceeacacbcdedecbedccdbbbbabececadeaaaaaeecdedcedaceeeecaddacaedbcbabcbebddedceddeaababcbeeebabebccebcccdcabbeecdcadabedecabcdbccceadbbaadcbcacbbcbdebcdebdddecbddabccebccbdcceeeabccabecacbccbbecdaeeabcaacabcadcbbaeedcbeacbecdbaedbbeedcaebedbaadbedcebdcdeedacbecbbdcaebebbeccbddcecebdeeaebbeebeaddbbaceedeebcdcbedccdebabdbbdcbddbbdcbedbedadcbcecbdadabacbdcebaedbcacccdaccbcdecccccabccadacdccbcdbeaaddabbaceeeaaecaeebbdceddddbabdaaadccbcebdbedcdddeeecdecacacdeacabbacaecacbeaeebbaceaececbdbbceebbadddedaccbbdbeecbcdeaddcadeacdcabebcbdaeeededaadabcdbbdbbedcccbabdabcaabadbbdaabdcabacbaeabcbbdcadceadaaccbbecebaedddeeaddabeabbceaecbeaaeabdcceaeadcaccabdbeaadbdbeaddbebebbebddccedbddecbedebebcaeeecbccebaddebaaceebaddbbeecdbdbcaeadeedaecddccaeaccbaeeabdcdbaeaaccbbaaeaeedddceebcddcbdeacceacadcaedeeddaeddddacebdccbabdebbeabaeecbdeccebcddbbccdcdbceebbeaaabdcccddbbdcbedddedeabbebbeedeeecbccbcccddeaadbbcabcecdeacedddbcabbedeccadeadaddbdbdbbcccdcdabedecdeaaaabddebecdbcbbdbabeedbdbcaadbcccdaecabadbeeacdcccbbcdbcaabadceddadaaceaadeaebabceadabedaedeeddeeaedeacdeccecdbcdedbcbedcceedbaeeacecaeacddccbebeeadaeabceddccdecacbccceeaeaacbecbacbabebdebbcdbcddebdddbcacdbddbecbaaabdabdaeebdbaaaadcbecacaabdabeddcbcbedbededbccdeedeedceaeabddbdaadccdababcbcacbdecedabaccbadeccddbbdebeeaccddcdadecaddcaddadcabeceebecebdaabbecebeeddbacbdabdecccceeecddcddadebddaeecddbcbbebdbcdbdcaeeccbcaedaaaedceaecaddccaeaddbbccbaccdcbcdbdcedaaaedebeebebddadcbadbdadbabccbbeeedceadcabbeeedcbcbadddeddccedaececdbecccdbedbeeeaadcedeaddbeacccabacddebbadccdceebbeaadecaeccccddcbdcaedcedddccdddcbcedaeeedaccddaadbddabcbaeedbaacbdcddcbdeecdcaddedcddaebddeeceaacdcecdddcaaacdeabdaedddecaaadcdbdaeabcacaddaebccbedeaebbaccbbadcbaaddcebabaddadaaceaaaccecedbdddebcccaebdebaaabbdcdecacdcaeeeddbaacbaaeeeeacecbadabbceabdcbeeceaabdbbdbddeecabdbcdaceeecccadedddddbacbadbdaaadbeaaccbacdeeecbeeebdbbbacadbbadabbaadbdbebecccdbcacbacaebeabedacdaccccadddddcbbabdccacaeadcbcadecbcbbaeccbcaaecbdaecaaabaeaebecdeabdbeddaaeeabccaabceeedeaadddbdceeaacedcbaceadabddbeddceccecbcebeebcecccdacceacaebbdaccaeedbdbdcdbbbbcdbcdbbedcbccccbecdeeedabcdebdbccedaaecdbcbccedbbbdbdbaddbceeebbeacbceeabbcddedcedcaacbcbdccdddbadabbaaabedceceeabaccadbdcabceeebdcbdbebdacaeacbdecdebbabccdaeabbbddbdcacecdababbabdadebaeeccecabaaacdbacbaeebbdeebecbabbdeabdcdaabdedededcdbdadeeaecebcddadeccdbccdbccdeaacceccbceaddaeccabaeccceddbadbcaddaababbdeaaabbceaaadbabbdccdececdaebbacecdcdcdedacbbddedabdaddebdebedddeadbcdeacbacebaababdaeccdbbcbaacaacebabdbdecadebbbbcbdedeebbbbbdddbbeebabaaabcbdcbbdbdcecadaeeaedbaacaadaedecbcccdabbbbacbeebcdeabcddadadadebebdcdbedcbacbdebddeeedecbaeeabdbdbddbdaaebbeebeaccebdcddcdcebbbdaeabbaecccaeacebcabedddbadddeeebbddeeeebceaeeddeecaabbaedaaeacbabaeadcabdbbbbdaaceeaadcbdceceecedbecbadcbecacbaedebeeabbcaabbeecacddcaeceebababedccdeabbcdbcdccedddddaeaabaedddecbbeaeabaaaeeaabeabcdeccaebecdeaccadadceecbacddedeeeeeaebbbaeceaecbdaaaaaceaeacaacbebbeceabbddadcbdcabdbcdddceeadcdaedaeedebabbedeaebeeddcbedaedabacaaebeeccbcaccdadccbbcdedeaecebeaddccbabdbeebeabdaecdcacadbeeacecdeaedabdaeabbccceaebbadeaaaeaeddbcdcabcceaeedaabcecdecaeccbeaccbacdedccbadbebaaeeedaadcacedabdadddeeddccbceacbbeadacbeceaecaabacccdbddbbacadcecbabdbebadabaeaacceaececabdaaadebebbcbaceebcddeabceabaebdeabcdaabaebbbbadceecbeebcdbcddecdbcaeabbbebedcdcecdcedccdaaabceabeabcdccbbeaaacccaedcaeecebbbaaadddcaebdebbaeebabbddbedbdaacbdcbaebdbbbabaecddedbdedbabbcaddebbecdcaebebadecbedaeeeabbadaeaacdbcdeccbabdabecdbaeecebcbdbaaccbacdaeceabeaaebacbedcddddaabaaaaeabbaeadcbaaeeaabbaeecdbcdaceacacbacabccbeaeecdedadabdccbadaaeaeacddbaddbbcebcebdebdcebcdbdcaceaaadcceacacdadaeadcdeaebeedcedebadcabeaecdddaabecbeaecddeadbcdbacdbddbaadeabdbdaecdbaaccacbdcbaaabdbdcacdbccaacdcebcacababbaeddbaceceaeeaeebebabcccbedbdcdabecedcdeeabacdbebddeececddaecbaeceeebcdeabbadbdddadaccccbeaacbaebededbdbdacdeebaccabbcbbabdddcacedabecdbaedcdaadcccdcdcdecbdbccdebabcaceaecaebcbdaaeebcbdeaecbadebdccccddbedbcbecabdcbdacddaaebddcccccbcbbedcaebbacbacebeeebebbeaecbcadbdadcdababbbacceedbcccccadaaaadbbaceedebcddddaabdbecacdcaacdccebbeaacacbdadabacdaabcceaacbabdcddecdcbccbdbeadaaebeaadccbbbdcccceeaabbeaeccdddcdeecdbebabdadbeedcdacecebcaaedadecedbcedaaacacdceacdacddaebeabcaceddbebcdbadecdeecdceebedceccbbdacdaeebaebeeecaaadccbaceaebaaebeebededcbbccbcbeaabbbdbdbacdbeaabbceceebbceebdacebaaddecdecabdcbdaebebbbbaeaeeeadedbccaeadbdbcdbeecaeddaddabadacdeadbdecceabbadddacadeaaeeabdadecadbaebabebceaaaebbbecbcbccaedeeadecaadedbcdadaacdbcabadaaeecdaeeededdeedcdddeacccaaadbbbebdcdbacdbbdedebbebaedaedeabdbebdeebedbdcbebdeabebdedbeabcdcadcdaecabaaabbcbbddeeeaaceadbeaabacceecddaccdbeacceebbcbdeecbeccceddeaebdaebbeeeaedddeddbceaddebddabbaedbaabebaacababaaecadddceecadacddedadedbaadbcdebccedbaaccdedcedbceaaeacadddcbddbacdddbbabcabbeacecdecebaeaddabaccceaddbbebebdccaacbeacebeceaaceacdbdbcdbeaebdbbdeaaaabbdceccddddaadcdcadaaadbeabdcbebbaebeeeeaaaeccdadeabccbcdbcadeadaedbbdecacceaacacedadabcbdaeacbacaadbdeddaedbbaaebbdddbeecbccddecbdabedeaebabbaacecdbdadbcdbaebbabcbbbadecaccdbabacddcdaaacabeeeccaadeeccdbbcbadbedaaaaecbbeebebdbbceccdaebcbddebacebbecbebdacaeabbdabaccbedbddadeeebccaaddaaabbdccecdaaaedeaebabeadedcbbdaeeccebdbddbcbbdaabeececbedbbbdecabadbedebdaadcdeadabdddbcedccbcdabdbdadebdaaaecddedcdceacdbedecbddaabecaddcadcbbeeddacccdcdaeaacbedbedebdbddccadedaccbdbebeccddecbddddccebaabeeabeededeecdededccccecbacbbaccadeaecdbdecacceceedcbccbdabbcbbccdbebeabaabbeedbbdcbddcaebcadaabeaedecacecdaddaaddabbccbdcebdcabdeabcddecebddadeddababcceddeceaabccbbaadebebaababceabedbeabeaebeceeddebbbebbacaacbbdbbbeaddaeadccdecbcaabdeecdbddcecbbabcacabababdbdbaeedcdacaaedbadbcaeaacdedeaddeccccbcbbadcedbbcbccccddaededeabeebcbabccccbbcbedbcaaadaaebcaaaaccdaddecbcaacbbbcdebeaacbbdccaaeddcddecdcebcaeeecbabcddbbacdadbddddccebabbbcaddabecaccbabbdcebdceadceacaeceabcdcdadbbbceeecaedbdcabbcbedbbedccddcdccaacddecedbdbdacdedbeceebbebadcaddeebabaabbeaacebccbaaebbaedbdececdbdecacbcadaaacaeaadccbbcdcbbedbbcaecabddceebecdadaaadedccbedadbcbedeaecbbeccedddcebdeebcaccebcabbaaadaceeadbdabbbddeabbcdcbaceadbccceaeecbaeadcebacbbceccacdcedeaeebadeacedeabcecacaeaeeecaadbadebacadbecabdaadeaedaeeccdbecdadecbaabdaebbacdaacbbaccbbcccceeddddedbababdeaeddcdeddbddcaaccdbeacbbbeaaeecbcacacaecdcccbabeebcdbbecdddcecabcddeacdcacacbacbaccceecedcceadcaaeceeeacdcccaebbecceaabcbdbceacdeeacadcbcdcdbdbbeadcecadbeddcdcbeebaccceabdbeddadebcdcddcdadcebababddaebdcdbeceddbbdaebccccbebebaedebeeddcabcddcbcaccedababeadedbeacdccbcaabbaabacdabdcbaecaedabadebdacaabeaedcbacaeabeeedceabcbabbbcecdeadcacdeedcdeccbeddedbeaecddbaedbbaebbaccbceacbbbabdecadebaaedcbbabcdabaababeaecdeccbdccbbeacacddcabccbdcecdcbeeeedaaeddbcdaabecaaecedbeddaecbaaeebcebdccadbbaaeedcecbdabcecbbdbcdbeaeaeabbdadaeeebbeadbdedeebbbdacdeeebcbbbeaacadcabaabcdedddcdbbaecbbcddcddadbceabacbaecdacaeccdcbebbbeedeeddaadaddacdcbdacaebcebdbbbbdcebccabdcacbdcbeeecdbcdcbdbebccbcadebcbbcddedbcbdecbdecedaabccacdeceacdeaccdccadbebdceeeceadaadbbdadabbbaeeecdcdddeebdeeebdcdebecaebbbeceaacedbadcceeabcbabaebcdabadeeeccdadaacecbadceecaddbcbaeeeecedccdddeacaebccddcbbbdadabaaaecadcbebedadbecbccbdcaaabedaedeaccbddebebbddcbebbeebbdaacddbeebbadcdaeddaeaccbdcbacebabbdedcdaeeebbdabbcdbaadbcebaaedaecedaccbabeabaecdcaedededccebbeedcaecbebddeaccacadddeebecdbddbdeadbeaaececcddccaebedbecbaedabdceceeedbadeeacdeadaadcddabccaccbecadcbbaacadddabeaaeddacbdadbccecddaacccedeeebebdcaaaacadeabcbeddaeebbdccaeaaccdbdecbcccacdcadbcbaaeccedadbdbbcacdeeddbebdedecdcbabebeabbcdcbecdebabccedaebaecadcbecececccececccaaebcdcceccecadeeabbbcbeecdcbeadcdacaeedddbecddebcbbeaceadeeceecbecbaadbebdbeedddbbaeadbeeabbccadeabebcdcebdcecccaeadbdedbeeaccaecaeacecddbcebedaedacadacdaeccdecacbbacabedbcdabccbddeeeabaacbeeacabcbcdedbceceedbadbadcadbecbeabdebceecbcbbaaccdecedabeeabbeeaccbaeebbcbebeddeababddcacdcabddaccbebeecdcecdebcceaddabdddeaeeeddebceeaaabaabbdedecadddeabbbdcebccacabaecaddabecdccebadbcbdccdadbacddccaadeaccecdccccbbcebbcddcadbaadadbaedaaaacdeeebcaeacccedeccdbeaacbcbbcdbcdaabdbecccebdcbbacdbacccdbaccdcdedabbabecbbabedccdecdeecbebdcdbcacebeaebddddcdeadadccccbbceedddcbcededbeaeebddcebaeeeeaebcadecaabcbdaccbaecceebbdbeacdaaaabbabcbeecdbdadebcdbcdaedcaecceaabeadeacbedbbbeacbabceaaebbcdbebabedaacacceebcababadbedccdbadcdadacebddddbccdedaebeeebbacdedcbaabacedddebdbbabdeeaadadebddbabbcececadcdcceabbcabdcecdebeceabebededcdaaddbdbedbedadeabbaabbeacbcdabcaaeccedddebdcbeecdedeeeeadcdeddceecdcadbaebeadccbbbedaeddeeecaadcdabacadbdadebdbcdeeeadecaadcecbdcadbdbaeaabacbceabccaecbceeceaeddcddcaebeacdccdecebeadcbbbedabceadbbbbadcbacdecdeeedcbddabadaedacecaedcbedecdecccdaacecccbbaabcbeadbdcdeeaeabdeeddbdaeccbababbbdbcacebdebbadbbbddcacedcbdcbdcbdcedebddbcdacdaebdbbbdecacaeeeddbdbdbeecdcbdccabacdaecbaabcebceddbbdcedeabbbdebcbebceceededccaabceccabacddbbebaccecaccdebcceeeabbdaababcbddbbbcbdccdadeedddceaadbeaccebacbdadceebeeaecacdddbcbecabbeaebdbccbbeebeabdeaeeacdbbaacbdeadbaeacdeeebbacbdbadeebebadcebadbcdccddeaeaadbebabebeecabdcbddcbadbacdbdbccdeacadeadbbaaeeaebdddbbeccbabdbcbcdbacbdaeddceacbdcccceaddeadcbdcdcceecadbaaceccdbaceaeeeebebaaabcaccdcbddcbeaddcaebbeedebbcdeebeaccdedbacaaeccacadcdaddeaccaacbbbaebccdccebdaccdaceabaeecdeabeecbaaaeabbaddecdeceeaabadeccadacdcbecbdcaaaabdecdadcaadceebdcecdeedabaaaebbdcdacdecdeeadebdbcbaecaacbbcbcdebebebdacdebabcabedbccdaecbcccccacaeabdeaaadeecdbbdaececccddddbdeeccdcbddbeeaaaddaddcecaedacbccddccdeebdadbaddcbbaebaeeaceaaeabcceebecbbdbedcbceadacbbdaadbdcdabaeceddbccdabcbbbcdaaccdaddcdcaedaccddebebdcbbecbdeaebddbbdebcadbbacebcdccacaaeaecbcbabbaadddcecacdebeececbeceaaddbbbdcacaeececedaabcebeaceecadebdbcbaaaeccecebacacebadbddabedeecedaedbcbddcaeeadebdaeceeeadccdaddcabcceceeccaeaabaaecebebbbacecdecdcbebccddcceceaadedaeabeedbabddbbccabaecbbeddcacaacaaceaddcadeccdddbacecccccbacdbeebddbccddbeacbeeaabaecddcaddddacaeeceddabbccdaaaceaecdeabcbcbceacdcaaabbbdeaeedabcbccecaacbadbbbcdbccedeeacbabacbcacbdedecaeeaddeadeacbaaccbedacdbdccdbebeaecbcdcdacbdddbdcccbdcbceebdcbaeaaaaadaddaecacdedeabcdbadbdddccbadabeacbacabdecbeedaacebdbabebcacecddcebdddcdeeadeecbebdabaedbcdaccdbbddbdebebecbdbaaadcdbbabebcbdaeedddcaecbbbceaadedcdeacadadbdecdbdebbccaeeedbaccdcdeaeddadedcdcbbacbdbbcbdcccccbdebbdbbdcabddeabaadcddebeddbeadababdabbddaedcbebbccacdaecdccdbeaadbdcdaeddedacdcbeeeabbceaeaeeccaecedcdaccdbabcbcaccdcadbaddcbdcbdeebbeabbedcdbebbebcabbdbcbaddcbbbbcebbeeeaeaeeedccebadccebdaabbbedaeeeebbeeddbbdbbbdccebeebdcabeababebeccdceabaaeebbacaeaeddddbcdeebbbcecadaeccbeddaeccdadbdbaedbddbdbddbbdbdcedcacbcbdbebabeaddccdbeceebeaadeeadeedaebbdccbedbaeacdaeccacdacedbcdeabedeaceaadbaabaacbeedccaedbcaaaebbcccbabaacedadaaaacebdeeecedecceacddbdbadceccaebcdaadeacbedabbaaeccecdccbdbbdebadbacebadbbbebcbdabbdacaadcbcdceedacdaadcdccecbcdcbbbebacbdedcaededabbcbeeacaaaabeecddbeccbbbdddaebebcbcdaaaeababacbdabbeebdadbdadbcecaedbcbebcbcecaadbcdcccabececbdcecedaeeadedabcbdbeddbebdeeabadcebdeadaaddddbbeeddedcdeddeecaedeabeacbcdcbecabaacdedeeabacdddbdeadedbeeabbecaadbaddaeddddaadddbbdeabbedebeabadabdeaecdaacbbbeaedecbcacaeddbebddabaedaddedebdbabcbeccddbacaaecbdeadabaeadbbbaebacecedcababdedbdadbbaaccaebeebdacecaacecbeaddcdbbdceacbadaaeabdcbebcbbcedbdaeccdecaeccbadaaebcdeeceeebeaeebeabbedeebeabdbdebdedcaaebcdaabecddbabeaabecbbeeaabedbbdebdcaddcacebdeaecaaeabadbedccaadaeccdccdeeabaecaaceaeedbdeecedbccedbdccecbabacdadddddccbecbedbaedaabbdccadeccbbedddedddaecccbcaccbdcecaaacdeebecdebbeccaeacbbcbbcdbbdcbdcdedbeeaeaacadeaceccdbabeebdebceaacbaddaedccccdaacadbabacaedebaccccbecebccbdbcecedbbadeececbebbcdcbeddbcebebcceceeaeccdbbdaadaabaeedddbeeebbbebaeecceeacedebebcdaaecaebdbcaaebaebbdeeecbbbdaccdbdbeebbaeeddcacddeecebabccceabdeccabdbbbaecebcaddaadaedbeaaeabceadeadceeaabecdbbaddbccbaebeabbbacdcccbdadadbbeeeeabeacbddcbbcebdbaebbdcaebeeeaeecbaedeeebcecadccccdbcdceadcdcdddaddbedbcccaceddbbbddcaeebcdebbddcabedbddcbcddeaeceabcdbdbdacececaeacbcdcdecdcdabedeebbbebeaabeddbdabebbababeedeeeecaebeaadebaadcddbcddeebeebdadbbeaecebcceddbddeeaecdecaebdeecbececbdbaaeaebdbbcccceadcdbeceaaccdcbadaadaaaeceaaeebdeaabbebdddddcebccccbcadadcadddbcedaebdecedbbbeaaacacdbcbcceeddabaccccceeddaacbddedaeaddabacdbdbdddceddccadcbbddeabeaeeedcbedabdbdedbeeddebcadeecbbadeccebdeedbaedcccaecacaaaedecaaeeacaedcbbedbebbecadaccecdebcadaaadecbedecaddbbbadaceaadacecadadeadcbeabdcccabadbbdbdbccaedeeabebcbbadbecabaecdebcbdabbddcedaeecacedecbdebabbcecbcdacaaccededccbcdccaeeeebeadccbcdeeebdddaccacbbdcbadadaecbeaaddbdceaaddbbddaddcabbeabdebdecbbcadcabdceabcebbebcededcdedccddccbddbedecabbceadacdececccadacbbedeebedccaadcddaeebcccebcddbceedeacbedcddddadaddbeecdadcdcadedbecacaeaaedccdebeebdacaadedecddaccbadcdcaaddcbaeccaceedceaeebeedaedeceaaceaeadccabadebabdcbdeedeabdbaecbbcebaddaecaccbceadddcdaaaaceaccecddeaceeddebadccdcccdddcabaecaedbbcbcbadedcebaecbebbdbddcaecbaaedebaaabdbdeabecbabedeadadbbbdebbcdbbedededacacebbbcdbbddaeebadbecadaecedacacbbbbceaabebecdeddadaaabaacbdcecbeedcbacbbabeaacaacbbbdbdadcddaaaabdceedadbcdceeeeccaaddbccebbdddbcabeeeaebadbcabaaadceaeaaaeaeeecbbedcabaeddbbbdedeacdaddbdeccdbeddadedcecbdddbcbdcdaaeedcabbdcedbdbdabcdbbbceacacbbedbdaecdaaacccabccadceabaccdbbabcdbaadcccddeebddbbbabbeaedaeecaddabbbcaeeeebaebbacccdddadcbcedcdebdaeaadcdcdcbdbceaedecdaecabcadedbaebbbacbaeadadabbecdacaecaebeacbccadacaaebbbccadedabdebdcedbcbedccacabbecdbbddbabcddaeeccdbcaadeeebeebebcdddbacadbddceccadebedcbbdecdaaadaddceebaabcdeadaebcacdebcccdbedadcccdcceccebaabdcadbbddbcccbdbbccebbdaaadeadbdaaaececeeacebddadaccccaebabacadbcbabaadbcbadddeeacbeecaaaccebbccecbddaccdbaabdebcdbdcdeeacacbebadbeecbedacdedceeeccddabcddeabacaddacdabcaecdedeaccaebcaebadeceeaedcdabcaadadccbeccdabaadaabbbdcbbedccaaacbbebccedcdcabdcddcdebebcadbcadcaaaecabdbdcbebbeabaccdddccabddebdbabcbdccaeddbaedcdabdcedabdbedaeededaadeeeaabaacacceadcaccdcadaaccedddbcbecebdcdedbecaceccbaedccdaabebccebebbbbaadceddbdbecedaabdebeadcdedecacdedeacededdcbbebbcebcabcaeceebdcccdcbbabcbedadcddcaacedcabacbbceaeeeeddaadebaacbbeacebddcedcdbcbabdceebaebcbbeccbaacaaaeabecaeaaeccbbeeaaaedbadeaebacaeccbbecbaabbceabbaaabdaeadeceaacdcbadccdddaaadabcbacbbebaddadbaaabaeeababcebaceadeaedbdedbcaadbcbbbbacdbdaeaceeabababbbbaeebceadcdcbbdcdbeebdeeabcdbbeadbadbaddadcccdcdabbaacdabdddeeedccceecebccdebdacdeaaecdebbbcbaabadaececbccceddaeecadabbedadccbaeaaeaebdcbcbccdbdcdeedbeecdbacbebbadedadcdedbcdedbeaaecaddabcadecccaadaadcdbbdddadbecdccaadadeabbccaeedacecaeeddbcabebcabaceebcbedebdbcedcebdeeabbeaeecdcedbaecabeddabbcabadbdcdcbdccdeeabccbdcceaeaeedcdaaadcbccababbbdabbddbaeadcdcdbcbceabbaacbbeebedeeedcbdbceaeeadbecdeebbcabdbceacebeeeebcbdbdaedacbecdbbeebabbeecbbbdbcceeedeadcbbbaddcebadabaecccbeacebcbddebddcbeeceebdedbceaeddeadbabcbacbbabceddeecacebbceecbebeeadbbaabdbaaddcbabbbbacacbdabeebaccceaabdbcdacebcdbedccbedbbaddacbcbbacddeedaaeaceabbbabbbbaabeccdbaaeedbdeebdbbbdbadecaeedbbecddbcecdbcadbeadcbeeeadadaedccebbddcacebeadedddabecaadbddbeddaedbaaeccaecedcedeaaedcaaeddaedaccbcdcedeadedbdebddaeaeeacecacecebcccecacbceeebaceeaaebdbaabeeaacbdcddeaddbeecaaabdceeaecacbceadacccaaddcedaabcdabebaccbdeecbcecebcbedddaabddeaccaeebaecdacbadecbcaaeebdcddaededbeaaadcddcaeaacaaabcadcacccedecadeecccadbbadaececbcececccecdbcdacdeadededbebccbcbdeacabbccedbbadaecebbeddbccccabbcaacccedbcaeecdcbabeaecdeaeddceabbdbbdcbeacecaaccdcdcedaeceecaadddbcedebcdcbcdebebebeecebecababcdeaceccdbddeaddcddddbecbebecbdbcbeaeaeebabdeeeaabbdebcbddbdccabaccbcdeceeebcbbdaeeaebadeaaddbaedbbabccedebdbaebcccbcedaebbeddaaadaaccdabeecdbeadabdddecdecbcacddbabdbaeaaeedccbaaadddcbbbbdebbcaaecdecededbdabaddcabaaaaeeaccaaccedabcdacdecccaebaebcdbcebacedeeedaeeabaeeebeeedddcbcdccbcacedaaceecbadbdaaeacbccecbcbeeeedeadbdceeceacdebcccdaaadcecdcbdecdbbdeadceaccabdaabeadeacccccedceaadebacdcddddbeaaaccdadcbbbedcadddbcceaacadeadcaebeabccbcbcaedebdcdceabbcddcdaebaeceaacdcceceedddcadadebaededbbacebbbccaeccdceeedcecebcddccbcbcbcaeadeeabcaaeedebbeceabecaaaacadeedccdccaccabbdaabedceedbbcdbdcebdddaccaceeabdddacacddaeecacdeebecbddaacbeccaeabcbaabdecbdbdbbeeecedcebbbadeabdbeebbebcecaccdceaccebdeacccaabdbcbaecaecddceabddceabcbcaaceaadceeedbaaaaacbdaecddecccaebaaecbdebccdedbadabedcadebcdebbedebbdbcecbdbddddeddcceedadcaccaaeadbcdcdbdcedadacdbedabbbcbbdcbacadeaecaaecaecddbbaadaecceeeaaeeecadbaccdadccacdedbedebaabecaaeaddcdaccebbceccbadaeecebeaecaadcdadcabedeedeaaaaadeccecbcadeddacabcceaecddbebceeebaeabcbaeceaedadacabebdeebdaddedddaddbdeaeabdacbcceaadabaeeedeebcacadcbadedcceaaebebedebebbbacbbebeccbbabaeaacaaebddeccebedcaecccdbdadbcbddaabddbecaacacdcbcebcaaadacbcdcedeacbebeecadcbdcacccbeccbdebbeabdecadcabcecdaebbcdaeddbdeeeddaaaabbdcbeacadeddeaadabebbbaeabdbeeceabbeabbbcdedaaacdbbcdbbdbedabdddbebeccaeeecbecddedbaabaddcaeebacbecbddedbdacedbacddedeacddcbceeadaacdbbcbbaeacedcbbcdabeebdccaaccaedeabbdbecccbedcbdacdcbaecaabebddeceaadebdeebaebceeddaebbedcdaeaeedbaaacdbaaadcdbcdedcbcbcaebeeaebddbceeecacddcbbecaeecceeeaccdecdbcebddecacddcdcbbeeecbcaddeacabcccaedddbeebedeaeeecdabbdcbdceaabbccaceddbcedecbcbdadabeaecbbecdcddbebbedaeeceabaadbbadceedbccccddaeedaabadbbdadbceaebadadadbdcdebdbdaaecdebaeaeecceeecddbadacbabcdeeebdebcedabddcadcadecceaacddcbccbbeebcadcecdebacebeebccaeededeeadcccceddbadccbebbabbcaecceecedaacbededbeaabdddebaaeabecdaedcbeadacbbcecbbacddcdeeaeacdddcccacceddadcaeddccaeeaccbbccbccbacecadeaedceececededcceebaaeeebeabceccebebceadddcbccabacbecbbcaccccbbeacaedbebaeabdddccedbdaeeacbecbcccaebabdeebbbdecccabdbebcbebaceecaeaeabedbaeccbcdedeeceedebcacaccaaddaeecbdeadbdeaacadbcaecebbedabbbdbaabcbcddbbbabadadadeedcbeacbdcccaaadbaaaabdbcbbeedcbcdabdaddccbbdecdccddaeeeaebdcebddeeaaceaedbdbdaaaddaedbedbdcabaaaacaeadddbaaaecdaaaedbbddbebdacdbdcdeccdbdccbcbedbabedcebdeadbbddcbdabbdbbecdeadaeedbdcebbacbbebbabdceeabdbbebaeebbbaeecbdcedcabdaeebdcbcebbdbedbecaebebddeabedeacdadaccbccebaeeecacbaebdbaacbdaebadedddebaeacaaacbdcebcbaececdbbbcdeaaaaadcedaddedeedbadaddebcbaecbbeccbeceeddeaceaabcadeadabcbcaebccbdbaecdeabadaebdcdcaebbcaebdbcddeacaadadaedcdcecabbcedaceeabaaedcaaeadadccedaaccababddddbcbdaabeacaaeabdadabacadcdccdcdbabeabadebededccbcecabbdebbabccbbeebcbddbbbdeddacebecbeaabbdacecacceaecdaabbbacdcccbacbaeccacddacdbccdadabeeceeaebedbcbcbaccbddebeebdaeeddcceceaaaabecbeeccedceebcededebedbcbecdeaadbdacbabbeaacbdccacbecdcdacedbbcececabeeddbaccdedbecadaeabcabdadbbebadbedeccdecccdbbecaebabddedabddcebabcdcbebcecdcaedaeedeeadcededbbadaeaecaadbabdeacbbebaceeadecddcaebcedaabcbebdeddceeeaeabdcdedacedbbdebedcabceebacbdebdaeecdbeeeedbbebaaeeebaaeccdebbbceccbecbbcdaccacbccaabbddeacecaaceddbabcdadbdaebebeeebbbbbdbaeacaecebabeccbdccaacbaecbcceaddbabebcdcdeccdbaccabcccedadabccecabcbccedcddecccbecdeedaeccacaeebcacaadabdedbddededaddbcdadcbdbceccdbddbbdedeedaaacdbccdacabbdabacddbaeaaebcaddadcbdaebccedbaaaeabaaccecababeecaedbebdcacabeccdeeababebaeeacdcdcdaeaaecaeaaedcaabdcdaccceebabaabcaeedbccaecdeedababacaadaeadcdacadcbceacebedccbaecaebcadaecadcdbedeaaceabccbacceeeccbecdedddebddaceecbabadabdbcdeedaeebabcdabbcdbcccdabbebbebcbdbacdcbaadaabdbbbbadbbdeceabdabdccddcadbcacddccccddaacabdcdacbcddecdbdeaacacbacaebbccbcdeacbebddadcdbdebccaedbaabeabdceadaaecbecbdebcbaddddceaeabeabbaadbdeedacecdcaacdddaddcaacacaccbaceecccdbdeeaaeccaaedacccbcdbaaebadbadbcdccabaeadeaecbaadddcceedcccbbecedbcddedeabdcdddcbdeadedbcbaacdcbacacadacabdccbdaadabaeceaaedadcecbcbadaacdcceacebcbedcbcbaddcccaceaccecdddebeceebbeecaaeecadaadeebccbdbecbdaccaddedecddebeebdbcedbecddaeededbbdbccdeadcabcaadcbbeebbbcadadbdbabaeabdecedecaedcdabdebbbccdcbcccbbaaacbddcabdcedcebbbaeeeeedaacadaaabdcabaaeaaadbacabbaedaaacaaecdaeeecaccabedececbaecddadebdecdceaedeeadbabbdcdddcbccdbeddaeaddcdceaaeacdbcdbaeaabebdaceaceadaadeaddbaaceedebbdbebcadcdcaebdaebdadcbcbaacaebceebccdddbaecadcedaeaedaeaaaabaddbcccebbbddccbbdaedcdbbbccbdaedeebeedccadaaeceeedcbadceadddbccabbadbeabbabadbccccaddeaaaddabedbbeedccacbdcdaddabcaacbbeededebebdbbeeebebedadedeadabeeadaadceabdceabebceddecdbabccbeaedbbdeedbbccaabcbeecdabbcccaeaccadbeadbabbeaacaeccdcbeddeaebdcecdaecabedadadbcacedaebdddaebceecadabbacdabeacddcabbadbacebbbeadcedcedeacbbcbcabbdcaadebcdbdecbcaddeddddbbbeddbabbeeaeaaccbadcceaedadacebcdbacedaddacbbddbbaebebdcbacaecaebdaaabcaacebdaaedeaadbbbeeccdabbdebbbdecccaeecaeaecadbabeacccadcabaceaaeeaabcedddedadbedeecadcdcacacbbaddaeaeccecabdccaceaccabadbbcbbceccbbaeedcddebbcedbbeadadccaeacbbadcceeabcaaccbdbcbcbcdccddedebbedededbabeceeabdbcdeadedbddbcbeecacadcabeacdcbcccbcbbecaedbbedcedcddbceabddbdaaadcbeeeadabedaddbeddbccdcbbbbaccdbbbdacedddacbbabdbaaaeecbcdaacbaeeedaebddaebbaccdcadebbcccaebddbdecbcaaaceacaabacceedaccaebbcdddaedababdcecebcbbcccaecedccbdbdcccccbcebdeaacacedcacbceabcbcbdedccbaddcaecacdcecdaabbcebddaaaaadccaacebcbeccbdeeecdeabcdeeaaacaebeaddccecaddaaddacebeddcbacececddcacdecabbeaccdeddabddaddeecaecbacbbeecdcabedeaeededdcbdbbeacdbcbbdedcabbeaacdcadbacbbdaecceceabeaacaaddbbcedcaadbdbbddeccaaecaeecbcbbecbadababcbcdecbedcabebaacebccebdccdebdaaeeceacbcdaeaeadaacbcdecbbbacdbbbccabdbdeebeeabbeecddecdcbaedaadbbdbddabcbcbdebaacedbaaabbbdbbcbdeabcebbaedebebdcbadbedccecddabbaeccbbeeeebdddeaadecaeecabeebaaccacadddcaacbaecbcbbceadbcddaeadecebaedeebeabebcbbbbeddaecaccbcabbddccbaadeebccabeebbaceabacdcceaddbabdcaebcbabcbcbaadeceeebbcacbceceebddabddaaccaaeebdaabdecbabdeaccbacadebedaabbcccebdadaadacaeddbdceccddabeabcdbeaebcdedceacecadababcbbddceabdcbcdbaabbebcbeddcaededbeadedcebeccddbbabcdbeedecdcdceebaabdcbbdddaaadabedaaeaaebacaccbbaedcbdaceececdceeebeeeececeeebbccaeaaeccbbbcdeeccddddcdebedcdcaaccceedadaaabcacecdedaadadeadaccabaceeadcaccadcaeebebebcbdacaaaecdedacdabdadcddaaececdcaaecacdbeddcadcbadbeedcdeceaeceabeedacccdbaccbacebecbdcedbeebbcabceebbceebadbeadacdccdbadaadeabccacbebddebeadbcabcedaecccdcecbeadbaaeeedbeedccdbbaecddcaacbabdadadcdcddccbdaebcbedccabeaaacebeaaabdeeecaecaeebcceadccbcacdabceececbcecbdddadbbbdbeaccbeaabeecbaaddaacbcadabcaaeadbacbdddeebaccebbcacadbdbeeaecdddbedcdccbbeabaeedcbcdeccdbddabddcecacedceedbcdaebcbbdaedbdaaebeebbbbaadebcdceeeebeadabadeecbccbeababcaadedeccccadebcbceeabdaeebdcebddaaadaedeebcabebcabedbbcaecedbcbecabaedaeebbecbacaabdaceadcaececbaccbbccacdbeecdcdddabbcbebeddbceacebcbdbeececdeeeaddadeeaacabdbebccbaadbcdcbbbcddacabaedcebbdbecbbeadeeebdcdaeaeddaabaebcaabbdcbcaaedaddaaaccdbdcbdaacceaceccdaaaccebeabeeacdebacccabcbcabcebeeaecaebdaaeaebccbabcaacbacaccbcaecbabaddbbdacacbcaeeededebebeaddddbecbdcbbcebeedcdcbedacbbbbedbbdddaabdcdbcbdbcceddedcebeedcaaaedbacbeadccbcccacaccdbcdbcccdcdecebdeededbbeeaddbabebdedaadedebccbbcecbbacbadeaaaabbcaaabebddcbeccdaabaedbeeadaeecdcaabcaebcaebddbdeadacaddaabeeeaccbabebbcedeaadbaaddcecebcdecedadabcdceadedceecaacedecddbdeedbdababbebdacdbcceaaddeddceeacaaebaaddbebacceebddddaddeccabadcaeabceaecbbbccabcdccbaedeccdaccdbdcbccbebcdadcedcbedbacedaddadcabccdbdcdaeeebdadbeeaaaabbdcaccaeeadeecebabbaedbcdadddbccbcdddeabadcbdeeeecbcbcbadaacbaaececccbbacdbbdebeeebbddbdbcbaadaddabbbbceeaedacebcdbbadcabeeaaeedbacbbbccaceabaabbeecbdccbeaecbaabaaeeedacabaacbbabbdcdbabdbdddaedaeeecdaaeeeddeabbcdcecadcbadddcedeaaabebcbedbbebbbbdbaabdedcdbecbadbddbdadaaceaeacccacacbebbbbdaaccadbaccacabddacddbcaaaccaddaceddeaecdcbadaeedeadddcdecebbbebedcbeaaeadcdbbbcdaeeabdeddbebcaabeadbececdbbaaddbedddcbdaaadacdaabbccddcdcaeeacdbbddbadecdceddabcabcaaaededdeccadabbaeedadcccecaaedbdacdceadecaceeeccbaecbdbdccabeccdceccaecddbeedceebaabcbbbdaaecccbdbacabbdbedccdecdebbbcacabcacdaaeecacbdebbdebbcaecdbdbbdbcebbeaacedeebcecdcebcebeadecadeedcebcaedbcbbcecaeadabecbcbbcdebebeddbabaeaeaeecebedbcbaabcaccbdadaeebbdaccbaaadcbadaaddbbcbdbbbdbdccacbcaebcceccaaeadbddbddeaadcaeddcacbbcebbdccdbaaebeabbaecccceacddaedebdaccecdebcdabbcaddbadccdcbbddbabbdcddabdabeceaecedbdeaeacdbdeeabeabbddcaeabaaadbacaadacbcadcaeeaaebdccacddebebaeddbeceecdeeadddcbbaeecebeaccdedbccaebcbaceabbbcadaeeededdcaedbabaaacdbbddcedddbeeebcddcdbeedceedbedaabedbbaaedadbeccaeaccbbecddbbccaeaebdeeceedbcedbcbedaaeecdaaedcebbcdadebdacbddeeabdbcbebceebeaebaaacabeccbbccacaeeecbbbcaedadbbdbbabcbbddadebdddadaaaaaeadbedccadecddacbcbccdaebcaeeabdeeaeaaaeaeaaaecbeeecdbcabccecbcdccdbccecedbbbadddbbbbedbeccddddccaedcddcdbeeeebaedddcabdeecaaebddecbeeeeecbaeaeeadaeceebcaadeabddadadecbdadecdaedeaecbeeebcbcdabaceaaaceeaacacebcacddadbdeddcbbdadaeecceaeeadaaabaecccaeebebeceeaaedcecdacaccceccbeacbdddcaaccdacddaccdeadbaaadedacacdbadbeaaedcbbbedadaccbbeacbdebadaecbccaceecdeeabcdaabceadaabddaeeddedcbcbedabcabecabbeaecbdaeeebcdcaeaecececedbcbeaeaddeccecdcdaeacabdbddbeddbacaaccacbabcdccbadcbecdcbdbcdcedebbdbbaccdaaeedbaeacedbadeabaecaaebadccabddcebbccecbdeabbcebaccbacdeacdccbbddddeeaadeeeddcacccdccbcbddedaacebeecacbeadbccaaaebacabebbdbbebacdddccdededdabebcbccdeeceeccbbddcdccbacdaebddcaccbbaecdaabbdaccbabaecadecdcbdbceadcdacdaadebacabacbeacaadccdadabebbacdecbeacaeeaeebcbabacbddebdeaeacedbbeaaeacbeceeebeeddbddcbdcbaaccecacddbbbebbdcebcaecebecdacecdeeebbbadeaccabeeacabeaedceedcdbbaabbacaaccdbecdbdcedaeddeedaabdeccebcadedcaeebbcdeabceadbbcbddcccebcdedccaecddddaaacececabdeeeaeabdaadbbbcdcedbcceeeacebbcaeeeaabedaeaacadccabbeacdbccbeeeddedbcebeaacacaaabdcececeeebecdedeeceebdddaabbdeaabeaedbcdcaedbebcddcaebedddcdcaadedeabeedceaacdcbcddaedcdcaeadecdbcceabbcacebaebcccadaabeeeaceddededcaceebdeceedaecacbcdccdddebcdaaedebabababbdebcddbaeadbbbceacaebdaebcbddecbdeadedceeaeeadeeabdddecbdacbbebcbcbadecbeededbeececdedeccabccbdddadebacbbaeeedecdecabbedcabcbedaedbddeebceacbcbcdaebbcabcecabbdbdebcaeebbbedbaeacabeaebadeedaaaaeceedeadbbcbecbbedeeebabbeeeecabddbecdadcedcabbaadedcebeddaebbbeeaacacaedcececccbeccbedecadecedbcdaecddacabdeeedaccaeabbadbaeacdecaabbadddcecebcbaeeeccadbcdacbaaeeebdeeeabaeabacacebeacacaeadbdeadaadbcddacbddcedaaaaebaaecdcedbcbaddceeeceaaecdbcbbabebeddecdedbdaaecabcedcecddcabddebcecccdbeeacebbaadcaaecaceabebdaebceacbaadbdaeacdbccbecadbaecbbecbdebbcbacaeeccabbbabbccbccdeaeaeebeedaeebcbbbeaaddacdadbaabbddedddeaecdbcecaacdbbacdbedceccadadaeedacddebecdceaadddbbdabbdcacbeacbbbdcccdcbbaacbdaddbacbbdcdeedabddaaeedebdcdebabadecdeacaebebcecccdabbdaaceedaacdbceaabbeabcdedbdddecdddbbadbbaaeedcebcedbdaeaabadeedeaaeecaeecaabdadabdcbcbadedbabcaabedaadebeedececbebebcabeaacdeeddbeddbaeceaeddebccdecedaabcecadbeccdcabddedcdeceebcdddcccedcbaeaceceedaddedcbcedeaeabbcdcadbaebddebccbbdaeeabeabaaaadebdddabeedaddbdadadebabdbdabeaaedaecccdedeccedcdccbdadebcddaacededccaeaeeeaaebbdaecaeaadbdeccbddabbaaaeddecddaaedadcadbdbbecbababdaadaabaabebaceaeadeaedacadcedebcbccdabaabeeaebcddeeacacadbceeccacccebedeabebbbaabedbacedcaddcaecadbecddcdaabddedbcbdacbcbcccbadaddcdccebedaccebdeaddababbcbbeaeabbcbbacdbebeecedeedadecdebacbaaaaccceecdcaccbcabddaadcaeceebaaacabeadecaaccaebadbccabeecdddeaeaeaebbdbbeeabacacaeebedbaeeddecbeacbeccdbbbacddaecaaaadceacbbadeccadbeddabaccacbcaebebbbdcaeeecdebcdeeaaeedaaaddbadddcbcbcedeeceacbabeacbbebbacceedecbecaeaaddebabaabbdabbaaeddeeabaeceaeeaadeebabdaabbddbedcbebccedadebceabbceceaaabdeeccbccdddebcacaabbcebbaadedceedacecdbddcddcdcdeecdaccdaaedaeadccdddeaaaacbcceeaecdccadedececccceebbdadccdacaaeabddbdbbbbabccabbbaacdebbcaaaecdecaacdecaebbbacbababacbeacdbddddeedebabeabebbcbaecaabdeecaceeaacdaaeecaddadaaaaacaedcdddeeccdabdebcbababaadcdddccabceeeeeeeeebebbdddaebaedadadbccdedcdbedeedaabaabdbaabbaceecaeabdeeaeaabedebacbaaedbedbdbbedcbabeddcdcecdedbdeacdcaecbbacdbccdbdcaddcdaaeaeeecabdcddcecdadcbcdedddbbbcaecbcadccecaedadedebdbdacbebeccaddbbecbcbcedcddbecaededbdcbedbeeceabcbaeeacbbabecebcbebacadbcebcabbeaedccddecacdceacbdecdcebbbabbbcebaadeeacedcacaaecbdabccbabbccbdabcdddcadcbaaaddadcdddaaadbaaebdbdddebdedacaebabadbdebcebabedceaecaadaebbaeddedeadeedbebccecadaebaeedcaabbbaabccaedbeadeaabbceaabdcdeebdecccabaecbcccddeababaadaaaccecdebecdbbeadcacedcdadadddabdebabcdccbacdabceadbcebedabaebcaabaedeacbabdddacbbbbbdcbcaceeedaedcaeaeaaedaaedcbaaeecdaecdceaddbbaedacebbbaaeeeabdbdaebadaecaadacdbabedecdaddaabbcdaebeaeceacaadbbaeacdadacacddeadbdacbabbbaddacaedeebaeebcecabdeaabebbcecdeaaddccddbdbcaaeeeadecdbccdacdaecbdecedcbeccadeaebbdcbcccdabaabcbcddcdeebbdabdceceecaccbbcecccdabacbcedaebaccebbbccacdebdcdbabdacbdebbbaccabdbeccbaeaeccaddbddaaddebeadccaadbaeebabceababeddabbecdeacdcedabdebecdddbaacabcadadcecaeaeabceddeadcaecdcabcdabdbbbbbeaeeccbdeabecccbeccbeccbbaaadebbeccedecaabaecdbebddbbaedaeedcbcdecadecccbbcbebecdbcbdbdddabeecbacbbebddccaaeacedeeaccbccdaddccbeecebceeacdadecedacbdcceaaddbaeaeebbecccbdceedbeddaaabceccacddccbdddaccadeaecdcaeedaeaadcecceedeaacbadbdebbecedcccbaabcebbaabebedadcdcddcdacebacaabdbdebadedecbcabaabededdbecdceeecadbeedaacedbbaebddaeaddebadebbebeeadccadbdcceeeadeeaaabeaacbceddceaccbcbaddeabcebedaaadeeeaceebbadabaedacebbbcabeabbdaaebeaeceaecbccdcedeceebaebacccbaeaebeadadccddcbdcdbddbbbabeddaeccdbcaadddceaabeebcdbedaaaadaebebcedccbaaeabdeebbaadaaccdcadbdadbbbeecbabecccaeaeabbbccbeabecbabeabbcbceebacebbbdcbcebdcddeddacdebbaaadaedbeebbbdbdaaecdeacabceaecbebaccdecabbdaadbbcaacacaeccabaecebcdcaaaceecaecebbcacdabcebbececceeaaeadbedebdddbbdbeeccdcbdbadbaeebcaabdcececeeeabadcdaabdcccecddcbebedbdcbaaeaccacacaeccbaebdaedbbaababbddeeeaeeadbbbdbcecdbacaddbbebdebeaccbdccececdebdbaaedbbcbccdbbdcdeddeeabbbacdeddeeecddbacdccbdcbbdecaaabaacdaccadcccbbbdccdedbecbdbcdcadaceaebaabdabccdecdedbedebecbcdcbcbaaebcebdbcdacdcebadbbadccdcceaacbdcabaeeddbdeaabccdacebebebadbaaeacdcedcddcbcdaededccdcbadcbeeaaabeddaaeacadaadcbecccdbcebabeeeddbcceabbcbccbbddcacabebbaedceacdaedcaceedcdcaecdcceebecedcddeccabbbddcaeccddddeeacdecaecbbebbcbceabebeaaaecbcdeadbbdabaabeedcccceaacdecbacdbebabaadacbddaeceeebaaccbdeebeeeabdedabcacbcadaeaeececaaeebaeadddceabcaedcedecaadccbabcbeabcdcedecccadeecdccdaaedbdbddddecbdabeebeeedddbdabdeceebbbbcdccadccacdcdacdddbcdccaecaeadbdcecebbdabcebddaadeaecabebbcebcdceaceaebeebcadaacecdeaeebcceacbaaebbdccacebdebbcbdecbcddaccbeaecacbcbbcbbabaddadcbabdaedcdaebcaaabddbccdacabdeabeccdddcebaceeadacebabbdcebebbadeebbedcceadaaaeccbbcdbdbccaccecbaedcbbcaabbdcbddddedbbceedcccbeacbbcaabbbcabacaedbedadbcaeaceabebaaadbecacbabbcacbededaddcecacbdabbaeeacecdeccbddaeddadbabecaadeaaadbbebdacacbbdbecbabdabeadaaaddadaccbebbeeabbeebcadbbcadbcedccbaedbeedbaebcbcdaedddbcebbeacedacabebeaecedeceaeccadbaaedbedbbcecbdcbeeaacceadbabcedebdeacdabebacbdeaacdbeecbacaaccbdceeacececcdceeaecededecaccdedecdeaccacaaacccbddedbccaebaedbbaccceccabdeaadeabedbccaedeeceaeebaaaedcbabaceddddbedbcdabddbeadebbcdbdcbaacedccbcebedbbcecacdebbbeebdeacdbacecaccbaabacdcceaacebceceacebddbaceaddcdcadbcbcdbecddcbacebbdeabcddaccdbaeaadacbcdcdbeacaaddaabbaabcecaabdbcaadabcaddeeacdcddcdcbeabddbbacbeababaddedddeecabebeeeedebeeaddcabdedcdabcbbacaacbbdaadbaaebddbebdbecaedeccacbbceebaccbbcdbcaeadeedebaaadaaecccbadbddbeaaaedbcececdbdecccdbddeacebeceaeadcbeedcbadebcadebaacecbcaacdadcdeadebcebbabecbacdecaddedbbeaaeabdaacebeabccadebaebcceadadddeeecbcadcadedeedeebcbbeaaacdbabaadcccbdbdbcbcdddbaacdaabbaedbecdbbbacdbdddbdccbadababceddbebaceaeccccbbdaadbcbbccacbdedbcdeeaadeacecceacaacdcbbbbabdcdacbcdcdcdabedaeeaeddaebeeebccdaacdcbdaeabcaecccadecdbdebbcadedceebcecdbdbbceabcceaaeabdcbeddaeebeedcedeececbbbcaadaeddaecabaddebcaecadaabbeddbbbddbebbeadedcadbeecadcdbbceecccdecccacaabdabbcdcdcdbdcbecccacddacaedbaddbbbbbbcbbbadbbcebdadcddcaabeccbcbacdbaabddecdedaeacccecbdcdcddecdeedbbdabdcbdaeccbdaabaeaadbdbebcdcacadabdebdcbccadaecaaadcdaedebeadebbaccebcaceabbacacbdcbaacadddcbceacbbbdecddcaccbacbeeaaabcecadaddebbddeecdcbccabcdbaddaeadacaeeedcbddaeaebeadbaaeccaadaebcbcccaeadadcdaedbdceeaceedddbecaacebedddaceabaaaddcdbceeddcabbdadaaecedcceaceeccccaebcbedaaccdacaaaecdbdbedecdcdebbbcbbbbbdcaaeceaccadadeeccbcbdabebdabdeadbacdaaabbacbdeaacdcedbcceebbbcccadceaebcecbdadaccdeadceadbeabedbedaaeebcdcdececabacebaaddadeecadbcdcdecdeeedbebdcebbaaebeaacaadcadcccdeaeeaedaebdbeacdbcadddcccbdcddbccaabaaadbbbbeadacceabdcbdbabacadbeeceaeadcaeabcbaeaeadbbbdaecbeedbaeccbccbeebaebebeccccadcbdcdaaecaebbabddbacbecceceedcedcbcbdbecabbbadeebdbbdeaaebdcaaedadcacebdabdeaeebaaaadeceeaccbccaaabaecabcdadedceceacebdbededecebecebddbbebccbbadcbedddaedebcdeadbbeeaecbacabacddcadbdddddabbebbcabebdbcbeedddcbdacdcaeacebedbbdecbecbabaaacacdcbbadbaaacadbcebabaeaedaabbdcdedcdabeadbdaeeeccedbeceecbceaabbdbacbbedeaacbebbdbcbdbcebdcddaeebeabdecdebacabdedcdcecbadeacccbbaccecacebacbedabaedeeeaeebeabdbbadebbcbddcacddeacdbadadcbecdaabdadacbecaecaedebeaccaadecdecebaccbcabbbeeaddeebaebbcedbaeebbceacadebcacacbcbecdaceabecebacddeccddceaeaeebebcdbbaacbaaaaaecdcbacdceddcbabcacdabcdcabcabbbebeeaaeaeecdcccaeacecbceeddadededcdedcbeccedbdaddcdbacdbcaddbcccedaccdeaebedddabecbbcbdbaecaeadcddcabccddaddcaaaaeadadcedbcebcbcdbadceeebbdcaeebbbacaaeabbdedaebadcbdceabbbcdccdaaebdbdbdaebacadbcacccbcbaeaceeaccabddcabbacccacaaabcabbcebebabbbeaccdeaadebdaeeacbbbacebecddabeadccacaeadeacbaabbabbadaceebcbbddaaeabbbccbdbdaaedaccebeabbcedacdccdcaadcadeeddcabedabadacdbaadaeeaabddcbaacaddeaddbbdcdabbdeecabdaeedbebbeeaacdcdaccebabccebbdcbbaabbeebdbcbbbbeecbbebbdecaedbddcbbacedecbadeacccaecaeeedeedeacecaabebdecedadcadecdeabeaeaecaecdecbdccdabeabcdcabaddeebccbbeeabdaecceeddcedeaabddeedbcdadaadccceacabbcbcebededceddedddbcaebabceccebeabdaebcbeaecdacbdcecbadbabcddbabecceccdbecaeabccbceedececababebeddecbeaebdbdbbdeedeacdddcacadbdbadaebeabdbaeaabeebabccadedbcdaeedcabdecbebacaeeeadaecdcabdcacddaeabacaeadcaabbeadebcdebccbdabeadddcaacdbeeadadbebbbaceadbeaabebdbecebdbecaabceecdeecaaadcbdadaaeedacbcbeebbdcdbecdeebabcdbdccceceecaeeedaceebeabadcdedceaabebcbdadedcebbdebbbbcbcdccebbabccbdbbdceeaecdadadcecceaebddbbceeceaaedceebebeabeeedbaaabedbaaeebbbdeeecbcddaaaabacbddbcbbeedeaedcbacddcaacebeeeadecabecccdacebadceedeecccccbeeaaeceedecbedbdaecacedbededccccdedddbdebcbbeeedecaaadddacdadcacadcaabbedddbdebcadccebddcaeccbeaadbdeaadbecccbdccccebedbcbebeccccacacbcdebccbacceccddcbaeabddebddadaaabebdbdccbabdcbbcaaeabbbbadcccddbbdebecddbeecaeebacbeecbcceebbbceadbabecdbbeccdcceeacaeabbbaabadeeeaaeebcadeeeeedaabaaeecbedbceadacdcaebdaabdcaaaedccaadbbecbdaeeedecebbacaacbeaceddbddbeabacbcbdcdaecdcdbdbcacaebbadcbcaaaceacaaeaaabbddaecbbceccaabdabbbacebababbaebcdaaabadbdcdbcecbbabbdaabbedbecbeaeacaaebecdecedceedadebccabebddbbdecbdabacdbdaaccaebaedabbdecdbcebaceccceeaeaeaddaaccadbeadabceaceeeabdaaceacecdadeebbdbadaebdebabacecadbbecbdbaabeedddacbaeaabebaeaecadbeacaccaacbeddaeadbdeabadebddbcbdbaceddddecaceacedebdedebddeabaaaeebdcadabaddcbbacdbeedeaadeabcabeabaeeaeeecebcccbabcddcaebcdadddaeaaedeeeabcdaeccccbbbaddcbdbdeedbbccbeacdcebdbaacababbdebceededceaadebdbaeeeadbaebcbeccacabcbedbedabdbbbceeacebccddadcebbaaaeeeeaeacaeeceecababeabeacaabeadacabcddcdeeccbbebecacdebcaaccbeeccadccceaaadbcdbaaacaaebeecebabeaccecccdbdbcaebdcedceedddcaeecacacbbdaedbbbbdaadcbeeeeeccbddebcddebaacaadccbedcdebebaeedaadbecaececdddadecbddaeeeccdcaeedddadcdeaeecaecbacddbeddebbcadecdaceeedabaebeeaeebdecbedbdabeeddcebbeecaeebcccacbaecaeeeeadeaeedbbdaaeedebeedcabceeabdbeebcecebecceecdacaedaaddbaaaadbcbeabccbcbabcbeeaaaecccbecdbbebecbdadaddcbbacddbdeadebeeaaedeeeceebcbdedaddceacdaecbecccebececcadeddacbcaeaacbcccacbaecdcacbcabcadbbaababaccbedaeaaeeddbcbcaaccecbbebcaeddbdbeacbdbdeabbbabadcbbddeeaaceeaaaacdbeecedbcaccbbedcddecbbceeaedbeaadaaeaebadaaeccabcddadbcecceeceebcbecabbebcdebbadebabcebecbdaadbdbccaeabeddabeaecbdaaeaeaededbebaacbeaeeccbbaaaeeabaecdecebaddecbacaacbdedceecbaeaeaabbcbcebaaadbccecbeccbcedbaacdaaebdbaecbebdcaaaecacbaacababebecedeaabbebbaacdebcdbeceaadddebdbcababecbbabcadadadacdadadbacaaeeccbcbddabadcbcdbbaaacdcaaceaedcbcabddcebcebbaeacbbbcaabcabdeceecbcaddcebdceccccedbdccebecbebbabbedceecababdbbadedddeeeeadbcaaceccceddbeddbaccbcedeebdacecedbaaccebabdadcbcaaaaabdcaeadbeccceebcebdebcadadeaaacdbadddebcceabdeedcbcebeddcccacebbaeaaadceadabcbaaeacdbdaaaaadadabbbdcbecbcbdcbaeeabbbbeaaddabecbbabeaadaaceccccececbbdeaadaccdbbbadbcbeaeaeedddadcaadeaccccebddeaebccddcbcedbbadaeaddabdeaaadbdcdbbdcceecebcdcaccbcddacdcaaaddebdeadbcabbeddaccdbaddebeaaedeadbbebcbeeaddcaaabcdaededaddbcdbeacdeccabbaabbaeabadcadeaedadbbdbacebaadabcbecbdeaaaddbaacdebcbcaedbddbecccddddccabaecababbcecbbbeabdacbaddeceaadbebdebaceaddabdacbdeaebecbbabacbcbbdecdcbcdccaeeebdcedebdedcbceabecbdceadecdccdedceeccccdbbceceeecdbbeebbaedbabbecdebeabbcedbcdbbabcacbdeeeccbdaddacdcabdeaceaddacccdcdbeaeeebdbeacedeeeecbbcbcabdedbcbaeadcedddabebedcecddbeedeeadabeeabbbcabbcadacbaeaaceaaabbbccdaeeeddaaacaaedbddeeddeeaaaedcccdecaaebaadcdcccdecedcbbaceaabaadbdebdeaeebddecaaabddacdeceeaaceddbcdcadbdecaaeecdaedddaeddbdaeeeedeeaeabbaddbcdbdceccacebcaecacdddbdcdcdbebcebdbdcdddccdbaeadcbbbbbcbbaeaccdebbeaccededcedecbaceecadeebcbecebebaebbcdbcedcabdddecdcdcaccdcdeaadcebebcacaeaedbddeabdecdbbeebdedbbbdeddadcdbecadbcdbaabebeeabbbbaaacbbedabdbebbdcbdaaeccdcabbbedbbdbeddcddddcedeeadcacddbebddcacdebbcadaddbbeddcdbbaaadbaadddadeeabddadaecdcccbaddaebedececdaaaddabdcedaeaccebeddccacbaceecddecbbbcadeaacbebbaadccbbdcdadeaeceeeaadcbbadcbdbcdbebecbaaaadececdabdddbbcdbecdeeacebbedeabeceeededdbabbdbcbbebcedcccaccecedceeeecdecdaeabbededaaceebaaadcbabcedbecdddaecbcebedacdaddbeabeeeeeccdabaaeabcbaecdabbdcbbcbaceceecebabeccadcabeabcbaacddcbbcdaddadaeccdaecebecaceaabcbecdeebabcbadeedddbdbeeebabddddacbeddcdecabdedaccecabadaadedbdbcdaadebdeddbceacbacabebcaddeabdadabbeadedbcaaacecddccbadbcecdaebeeeedbabaaddaeeebdbaeadcdeccbbebbbccbcaaeeedbbdbaeecacdeeadbccdeecbedecebdeddedaddcddbddcbbcebabebceceeaacbaaebccbdbeacedddcbccacdcadcacedbdeeeeddedddabaaaebcabcddddbeedbcbbabceebadaaccecbdddddbebaacabeebcdbabddcbbeedaabbbcceacdbdaceaacaabedcceccaccaacccaedbbceedcdbeadbabdeaaaaebbbbacbddabcecaddeeddcaaebdadacadcebabcbcbeccbdecddaaeeacabedceeeaedcadcbbddbcaecbacedebbdaaddaacaeedcbcdeabaacdcaacdcdbdddddeaccccdcedcaecbacbdeecaebcebdbbdbdcbbaadebbbacceccbdcbaaccaaadeeeebebaccedebdbedaeeaebcebeddabbeedecabeabecbacadcebdecdaebbeebbccbeceecbdaeacaeececdabbdecaacebbaceddbcbadeeebecddcaadceaaedadcaecddeeddbdddebbbeedbcbcdbaccadccaaadebabddaecdbdaeccbadbcbeaccccdeadebbcecbebdbaaacdeecbdecbbceeddeabacacaaebeedeacdbdbaebedccbaceccedbbbddddbebdbcbeceaddaadedaceeecadedbccdacaaadedabdeccebcbceeddcceaaccdadcdadcbdeddcbbabdacbdaebccecbbdcccbadcbddebdeceecaeccceebcabcbdcaaaaccaaceeecbbaaceecbababbdeeacedcdaaaacbcbeaaecddbcdcdbaccbdaebbebbebbbbddacbaceaabdcbeaeeedaaceeeeddbeeddeddbcdddbdedcdbaaeabdcaaaeecccdcabecbcebeeacdadaedebabeebbbcaacdcecbeeddbcedcdccddabbabdaebadebecedcbbbcceaccbebbdaebecadcdcaeaebcedbecbebabdcbccbeeaacbdbdecaeaadcdabbcaeccadbceaabddacbddeaadcbdcabbdccbeecbcdebbddbdabeadcceeebedbdbebeaacddeccabcddceecacdcbddbdccdccadebabdbaddbacbebbcaaecbcccbdcccaaabdacbaebaaadcbaddbebbadceceeabacadacddeacdbaadacacdaeacabbebcabcddacabceddabcebcaebdcecdeadabdebcedcbbbaabebdeacabdacddbbdaadbbebbcbcdebecacbbaacbdadeeabcbcebcbcacdcaebadcaeaeecedddbedcdeedabdeacedabcbaaabeddbbcceddaddecebccecaccaddedabcdcbbeaeebdcccdddacbaddbeeedbabdeabcaacdaaaebeabaabaeddedcabbcdaabeaddbcbdeccdeaeeccdceddbedaedadecadbdecabdbabcdccadaceaeacaedebaccdeaeadabdbeadaeedeaaabbbedadbebeebcabcddaabddebaedbeadddcbebcdeeeadaccebadecdbdddedaadbeebacebcacdceadbdecbcdcbbdaadbdeeaecdcadeebabdaebeceecaabccceeadbbdbeaabeddaacdbccbbbeeeedaddaebbeabaecdaadbaebbdacadccacaceaadbacacabadacacdeccdaebeecadeedbddecabdaccadabedcbccabaceaccadeebccbdcbaccebebaaddaaaaccbaceadbadcabdcdccadcebbaeddecbddbcceaccbcabccbdbbeddcdecedaeedabaacbcddbbdedddcbdcbaeecbdcdeedcdcbeaeebecbbaeeaceacaccbecdbadacdedbabdcdacedccdeadabdeeadaccbeeaabaceeedacbacedcbbacaddaddacddcdebdebdaabceaedcdebdbebbedaeaceacbabaabcbdcbadebcbabacdbccbcdebceebddeceeaaaacaeaecaadcddccbbeacddddddeeadbcbebeecaabbccbcabbebbaaadddcbacdcdedcbedeaebabdcbcdaedbebdbacddedddaeeadabadabbcaeeaacdbdabeceabecdaeedbbdecbbedcbeabbadcaaebeebbdebddcebcbbebbdedcceeaeaceaecabcacbaaccbccccedcadbbaccdeeceedcebeeacddeeccbedceeebddaaceadadebaaedccceacbbbebbcdebcbbadcbbebceeecedcadcbdaaeddbebceccacdebdeebeaadbceeedacececcdbbbbdabdbbeccaecbadddabaecccaddaedbaecaeaeaddaddcebaededdeaceacbbeaedceacddeedbcbaeeaabdaedbaeabebadaebadaeaeabcbadaaeabaaedcdcbdbebcabeccccbdaacbaacdabbabcdbcbedabccabeeacdbeddbdbdecebcaadcbdebbbdbbbbaaedecabaacadbcbabcddbeddceeccbcbecddecdddaeebcaebadbaacaededceadcdabaeedbcccebdebcedabeaeeebdbeedaeccaaaedcdbacadaebeddbabeebddebaebbcdbdaababaacabbccedacbdabcbdadededbbaadbdbeeaabebaebdeebdeaaecddccccddbdcdeaeccbcbbdcedabaaaacbbcebcdbaaedccddbeebccbacbcbcdbacdabcccaaeeeecdbecacebadbebeaeccedacdbdaecaeacdbaacaeabdcbeabeacccbaecaabecbdcdadcabcaaebcabbaebecebeccceceaaddeaaabbdecdaddeacbcccdeedecaecedebaeacdeabeedacbeacccdabbaadcecdebbccabdbcaabeacadccccedeaacedbadbbdaadceaacededddddbbeedaeecacaadadeeebeececadabbcbedbeeccaaeacddcdbeabbeeceeddcbbbceedcadcdeebbedabdbbaeedddcbebaeaecacddceeaacedceccdeddeeebcaeebbebabcdabbdebadabaaacbbdbabecedadbcdddaedbcaebcbecdcdceeabebdcecadcccececdddbcaccddbcabaaacccabbeedbbaacbcbbbacbdcbccaaacabbcbdddadcdcbcbdadebabcdbecaedaecabddcbaacebbabeedbabcacbabbcadcbdeceeedaaedcacebdedbeadbaadcacaecbcabcaebdcadebdcdbaeeeecdcbddbddcdddaececbabddcacaeecadeaaeadcceebbeeccbaabbceadaedcebbaeabecacaceebaedbcacbcdecccbbbaceedcaeeaacbaeabcccbeeeeccacebddaedddababdedcaaeadbddcbcdaddaceecceebeedabaecdbbeedcedbcdaabedbaedeacddbbacbebddecdaeceacabebdaeaeeeebddccdeddbacabdeeacaccbaabeeaadebedacedadedabbbcdccecbedacebdbeebedbddcabeababedaddbbeddadbdebbbdaaededdceaedbeeabbedccdeebdbcaabcaebcdbedcebddbbbceabdaeecabaabbaebacbbbaccdddeecedacdddedaaababaedeccedaedeeadbadddaeebadacdbdcedadecdbedadbaccecacbacddeaaeddcebaeebbeccbbcbbdaddbadbcacedecbadddeecaaecaabedbacdbaddeecaabaebadaedcdaaedeeeceebebbacbdeaedbaebbbbacdcccedccaeacdbaceedddaddbacccbccabbddcbdebdebeeadaaceddcceadecbeeecebdcaeaabccdaaeabbabcabbdcabeedabaebddbcdedcdbabaadeedadecdacaeddcccedcebcdbaecbdacbceebbeceaededadcccbdcadedaaecebbeaecbebdcececaaedcaedaaddebddeccedeeacacdaddebbabadcebaaebbddceadeaceeedecdaabcdeababdceadbceaaabcddaeeeecdebbedbbcbbbdaebacaaddcdcdeabeacacddbabbbbccceebadabbcdabacdadeabaaaebeddeadecddddcecadeceddcbcbadeaedadcbeedecbaadeaceeeabadaeedebeaeceebdaebbaabacdbdacbdddddcedbecadbadcacbcccabccabeeabecccccdccccedccaabbacebeaaaaeacdcdccbacaccdeaebbccaeccccbeeacacddddbacaaceeedabceeddedcdadaaeacdaceaedeececadcccbaccadacdaecabbaebebebbedcebaaacaeebcdedecabeedceecabcedaeecadabcbdbcccaceadadaacbdecadeedcadbedacbabccbbcccbdaacbaacbecbaeeaecbceaabdecbdcaddadbeecbacadbcaceccdcbabdaededbaddabbebdabecddebaaebadedaeaeddcacdbacdbbabcabacececacddaddeedeabcecbbebccebbdacbcadbdcdcbadaeddaeacaabaaabcddcaccbebaccacdbaabddddedebeceaeeceecdcbdcdeabbcedcaddaadbbecbacbbeaeecbcdbacdcebcddabbabbaaecbbaddcebebacecadddaaeecddddeccaebdaaacdbddbacecaaabebdcdadedecceedbbdbaaaadddabedaabedeaebccabcaeabacaedeaabebcdddcadeabcacaeebdacacbbaddbcceaecdeaaabbabbcddabaecdbebdaeaababbaedccdabdeebbbddebecadedcabadbdaddadbaceadabeeaedeebaabcccacaebdcacbdceabccbddabebcaaebacdacebbecbdbeaebecceedecddbbcedceccdddaeedaaedcecebcadcbaabdbecadbbedbccdbabebcbbccaaadedaedbeeddabcbeaebbdcdbaeadcebcdeeabaaedeaaaabeeeabcecabeccdbedacedddddaeebdedcddaaadcbcdcbcdcacedccaecbaecadaccedadbedbdbedaddccedeeaecacbdeedbeddeacdbbeeebeaacddebeebbcdbcbbaaaaedbaabbdbcdeccbbdddabdddcdacbeecbacdaebddebcaaebdeccbdbcbecbbeabdadbcdceadbcbdcbaccabeeadeeaccdedbcbbdcdcacdeccccccdcdacaeeedbaeeaecabbdcdaacddcbabcbaededbeaabddbbbcdbdadceacddeddebdccaedadacadbbeaddcbbaaccedadebbecbbaaeecaeecaceabdedbbedabbcdbeaddbddcbddaadcddeddddeabccedbabdbeecdacddddbbdeedcabacaaddacceeecccbbbaaababdcdebdcdbdbabcaeacdbbeaeeaebadcebabbcdaadcedcacaebcaabebdbeacaddeeeeccddbbdebbbcadacbaceebbcedbabdaeddebaebcdbcebedcbeecedcaeeebbeedccdecacabceecbeadacdaaddcebacbcddacbbbadcabbcbcceeabeabcedccadbbddcbceccadbecdadcdaaadbdececaceddeccbdacdcaaebcdedeaaebbdaebaeaeceddeebddaeacbaabcdcdadbcdecadecbdeaaaddeceedbabbdadbcaccbcecbecbdecaadadcebbecdebccadcecbbadededcebdaeaeeccbbecbeadebaaddceedbdcbeadaeeadcbdeddbbdeccaedccacbcaccccbeabdbedaadaecbbeabbdadcacacceaebeaedcbaaeaeacecdeeecaeceedeeebdedeabaebdcecbaaededcdcdcceecabcaebbcedbeaaabecdcbbaebabaedccddaceaeaaedcecebcdbaedeebbddececcdcabdecebeacceeadeeaedaeadbccdedeaecbebccabbdaaeedadcedecabbdcdcbbbedccbdbbededebebceddbddceddecdadcedeeeadccaeebdadaceecbbccaacbedadcdccededbcbaadabbaebaeeaeecaaaddacececdadcdcdbcddbabaadeaadcadbdeeeadcebaeecaeaeaebddadcebdbeeceaabccedeabaeaecdbbecacabecbedcceadcbcbedeccaecebeedbcbcdecbcebaeaceebbedcbdcbecdeaadeabaeabbddecedbdececaeececabbabbbdbdcadebdaddedeeacadccacbbdbdcecbbebddbdaacabbecbabbcdeadecccbacbeedbcdbcdcdcabadccbcdcbaebbaedbaadcbbaabceacadcdaacabdbeddadecddabcdddbbeaaebaadebcbabddeaedbceebacbbbbddbccabcdbbccddacaecdcecccabbebddbbcbbbcadabbcdcecddabeccdbabdbaeddebbadeabcabaedabacadaddacecceaedcacbcbdadaaeddedabeeadabaccbeccdddbcdedcdaaaaeabedacdbbacdbabbdeecbabcedecbdceeaeaccdceeecacdcacadbbaecebcaeeaeacdaebebbbaacabacdcecdbbbebadbbdabcbdabebadebbbbeebcbbecddeebbcbbadddbaeeebebbddecadcbadbbeeebcacbbbaedccdedbabcacababcdcedeededeccbbbedbebcadebaeacbacecbbbdeabcdccadaaeabececcbdcdecccdeaceddcdadaeadccbbacdedaabebbbabbaaaebddcedeebcbaeaeecedeaeeceebedbdcceeedadabadecbadcecddcbacaeababdecdcbebebcdcacdddddecbcadbabcaacaaccbadbaacbeabadddcedddacbbbdbedbbaddcdadbcaadbbeeccdaeabeeaabebbeececcbbadbadcebddadaeeddcdcceaebcadbceeecbaecdddceaeeaebcddeeadeebaddbbebedebacaeaddaccbbaaeebadbcacedeccaedbddabecedcbabebdeccbdaebddbdddecbbeaeeabbbeebdcadbeeaeacaeebcaabdbddbeedbcbdaabdebebcacbecbeaeadeecdbadabcdcdeadceeedcacaaaccabeaccbcbadebbbbdbaeadaeabacddcbacccdbdaadaaadbdadcbeadaeabdceddcbadebaedeaaebddebeecadccadacbedabeedddcdaaecbeeacbddeecbaeabadadebcedbddcbddcaabaccdececbeabdcdeeedaabacedaadbadbeddbadbacbacaeccbbabbbdcbadbeadacbceeaaadeacdaecbddedbbdddaceebaaaabebedaeecbbcbacbeaaeaacccdececcdecdcbcecbadedcbbbcdeebadcabadbcdedebdbbaaccdadacecabdedcddebdaacedddbdaecdaeaadadcecbdcadcadbbcddebaaeeaaaeeeaacebbaecccceeddeedbacdaddbabdbabbbeebbcdccecebdabaebecabbeccbdcaedeccccaddcacdcacbebbadcbdbcccbbabcdebbebabaccbceddceaebdaaedadacadccaeecaaccaaeadbdadbadcddeceecaeeabcaddaadadbeaddaecebcccedcebcabddecacdcaacdddccaccbebebaaadecbbdbaacaeeeabceaedcecebccdebbdbbdcdcaccadddbbaeeedaaecdebccdaececaedbdcdabccadeaeabbdddbcabbbbbcdaeaaaedbbcddccbebdddcbabceaedaaaeeeaeadeebbbddcabddbebeacaaddaacecdaaadccdebbbccdbbbeeabcaddaadebceadceaaecbacbcaecededdeccedbbbaacecddcccbcbabadcaedcbcbdadcedeaecbababcbcbaddbeadeeeddddcdcedcdbbaaeaeccebeeceeacceadbdeababdeaeebbbabecccdaabdebbecaecbebebcdebbaaadebecabdeeaebdcbcabddccaeccbbdbebaadaaaceeddbabbdaedadabaabdeaabcbbadddeaeeddaaccdccceecdadeccceddbbcbbbeecdbcadbabeacdcddeacabccceeeedceeeeceedaadeeadaddeeddebbcdddceccbcecbbceeeeccaacaeceabbadacaabcaaecedececaceaaddabdeebdbbceedbeebcdeeadccdceaebecdceaadabaaaecebceacdbcecebdbbdecccdeecdcbacecbcedaddedbbdceaeddedecdcadbdcdaaaacabcededdebacadaabeaaaaacbccaddddaaaaaacabaebebaeebdeaaeebddacdddbedcedebccedbbeeadbbcecabeacebcdbdbbecddeeedbccceceeadaecceaabdccacadaacbecddcccebcddbaeaccbdcdabcbcddaebdaddecbcacdadbbaababbcddabecabbaaedbdbebbeceacadbbcebedecbacccebbbabdbcccaeabdadcacedbedecddddaceccbaebcbbcbeaddbcddedecddaadcaacdaabedecbcbcaeaabbcbeededbcabaeacbacdeccbcabcebcddedcaacdaadbceeebeababacecdaaedadaececbaeabcbaaaacabbcbdbedddbeadaceaddbdeeedaaaabecbdccbadbbddecbbdddeadaaababbdadbbcccdddddaadeeecedebddcbaeccdabaceaabdcaedabddcbabeecaddddaeaccceeebcabebbeeebedabdccbadbceccacbbedcbbaecedcccccdaacbecbaddaeacbaaeedeebedbaebbabdedaacbbabadadbdcbbaccdeebcdedadbdcdeecceeccbabcbceecadeeabebbccadecaebbeedbeeaaeddcaebbbddddeedbecceddeebebdcdcadacacabebadaaabbaecadbaadbdbeaadeebdebdbacabcbcacdccebaceabebceaaabbebeebcbdccbbdbbebabaccebcbdbabbebdbbcbadadacccdaebbcdbbeedcbbdcecccaadaddeaabdddcddbcceabcbcdcdeaeddaceccbeababeeddcabacabaabacaaedabaedeeebaaaacdceceeebebddbedaaaebceecbdeedadddebbeababaaccbebaadacadedbeccaabadaeeedccccdacdcababbebcacbdecdcaecbdeabccebbdaebadaccceddcccbbcccacbecdeddebbccbcbecdbadadbaaaacaaddeeebccbcbdedbceceacbaadabcbddbceeebecbdebacdccaaecbadddbaebcadcaadccbabcdcdcaaeaebddadabddddbecabeddadbebaddabadbccedcebbdebbadbdccababdadeededcddabcebcdcaaeabebdbdcbdddcadacbcdbbeecaacadcbdddcbedeadebdbccdbdbbedddedebcedbadcecdbaaadcedbaeecedceaccacabdbeaaeeadbaecbbedbdaacbcdcceedceacebbabbdcdccdddbaabbdeecabdcacbddadbdeaaacaeacccdeebbbdcbaaeceddabcadbabceeeaebaeeddbedbeccadeaeedadebacbdbebbabacdbbbbaccbcbdacdaeebacaacebbebdbbcbadbecbaedbaceacdbaeededacbddabcedadeeaacaccebbbabeccdbdaeacaeebcddddceadcaacccdaeadeebbaeceedaadadcccbdbdaccaeeccdbddcdeedcdbebdaeddeeabecdaeecbdcbabbcbaaceeaaedacbdcacadacedccacededccdbdebccdbaccaedceaacdadaeaebddcbdebbdddbcdbcdccabdcbeebcebedbcbbcadbabeaadadedadaeedbebceaaaeacaeccebedaccaedcbdaaacadcebbccbcdbbaabcccecbdddbdcabddecdbdccebededdabeccebbcecedbdcebeeddddaccaddcbcdaadcedceddaceababdbdbcbaedeecaacdadaeeaaacadabdbeacecdedabdacacbdadaeccdaacaabedbedbdecedcbeebdddceabbeddbdcaddbabeccdabdabdcbceaaeebbdadeabaecdeaececeeaeddacbaebeeedbacaddeeddeddcbdcecddbdbcdbeacbecaceabdcdebdabccbecdabcadbbdaeaaaaccbababdecbbdcdaebecdacbdeacabdbeceecbaaceebbeccbedceebaadeadbbeaaeeddabddbbeadaaedcbbceadaecacccacbadccdeeeebcdcdeecddddddabacaecddebdddcbcbbaaceaabaaceccdceebeaacdbbceeaaddcbebcdaccecdeeeecbaaebaaebcccddacdccdedeceeeaaedeeebadeeccdbeceddaeebdeccdadeeddbabadaeaedbadecdaaecacdbdbbeccdadecddcacdaeededddbeaedccecdbeabbabacaabeaaaadadeadededbcdeeebbbeadcceddccceeeaccadaaaddbeeecbbcbcbcebdaeddbbcaacdbbcbbdcdcedbcbccddbbcccdeeddcbedaaaebabaeedaadecaedbecddbeeaebceecdccccbdacbdbbccbddeadbbddaaeedbccdddadaaebdebbaaebdebebbcaeceebebcbbdaabbbcbbaacadabbebbbaeacbdcbccddaabdbddddeeaeccbbbdebecbaabdecaaebabaaecdceeddbbdcddeceeadadcdbececcaaeddaeaeeaaadcedbbebbaceceabacccedcdcdeecadceaaeabbdbcadddacacceeaedccebaaeadbbccbdeacaceddcebdceabcebbeacebedcadebdbabadbbddeababecdcdceeecebceeedabeaedbabababbebacdeaedebebdeccaeadaacbacebcaecaecddeccceaccbdebbaccbdaddbdcdecbdcdbcadcbcecaeccbeecbbcdedbebeebddeddabaceccacbcadcbcdcedaaddeebdbcbbcecaaeebecdeeecebadebdbbeebdcaabdcaeacddedaccbacdcbeceabceecacaaeccaaddecbbcdbaceadcaeaeecddbdeaeecaacebabdcededceaacbebdcaedcacabeddeaccceaedeedcdcbcaabdcdcbbcdbebaabeebaeabdebdddadaddcdadaacceedeabcddeceadaacbedcbaccdbcadbcbbeecccadbcdebadaaccdddcdbaeeaedcdcccedbcaaeceedbaceacaedddadbaacbdadbeceacddbbdeecdaeeaebbeaddeacdbddacaaaadeceaddcedcabcbdededeeacaabaacaeedadecdbabecbdabaceeaceaeaeadbadbceceedbdaaabaedebebedddcaabcacaabeeeedbeabbbdccccacaadceaccbcaabdbaabedddaecbdaedcebddaeaebbeebdeebdaaccccbbabacbbcecdcedeeaaddccebcadbddcbecaceccabacddbeedcaaeeebdbcceedbeeeddabdbdebeabdebdeeabeadddebccbebdeaaedbddaedcdceaddbbebacdddcabceaddbaccbddcbedaabdeaadbadeabbddadbabbbcababbcaeddcbccbeaeddbbabcdadddeabadbdddcacbddedacbcaedabdacadbaaddbdbaeadbcdddbbbbebeebadbedeeecdddcceaccbecbbaccbbdddcdecccaedccadedebdcaeadecadaaadbbaddbcbdecbaebcbcaeceacbcdadbdbbaaccebcaaecbdbdccedadbbadbadaabbadddbddeabddbdcbcaccabedbcccddcdaaaaccebdddaabcedbbaabdcdeddadcaedddeecceaddedcacdcbbdacbebbacdadcadcddceccedeaeddaaadaebddebebaddedbdccbcdedeedcccdaccbdcbedeeebdacbcbebabeaaedabbecebaadcedeedddeaadcebcaaedbeeaedccabceaccdeeaeadbdbbcdcaaadaeaadeacdddddeecaedeaaeaeecbecdecececbbedcabbdacdeeaebaabbaedbbacbdadabdebadbdacecddcecabededdbabbdddaaeeeeedcedbcbceabddebbcaecbeedbbbecebedacebbddedcecebddaddccbededcdddaedecdcdcddcadbbddaacddabaebbbdddeaabbaadaeccaedaeabebacdeaabdedccccbddccdacbbbabdcbaebadbdebaebdbcebcaebcdbecdddddbcaaaddcaeaeabaeecacaaaadcaeaacdaaedabeaacedccbbcadcadddadcbabedcbbddbddebddebebcbcaceacabaeebaceeacbcdbbebdbbabcdacdcbaddbeaccbabbbdebeeebbaeeecceecaddeddaecabbbcbdadbbabcbaabbaebeecddbecbdcccaccbeacddabecdeabdedbdebcceeaedbabeadedeedeebbcecababcbeadcadbbcaeecdebeabadbebacbaaaedcedabeddaeedadceceaebdcdcceaeaeddcbdcadcbdadaceccdebcccedbdbeaeedabacdbccedebbdebbeeeaebbaabebceddbcedcecaccbdedbaccbccbcbaaaddeaaeacdacdcacccbceeeddcbbcddddcdbaaecdbabccabaddeebaacdecadeeedcdbcdbcccbaadacabbddccedeaacdebbbddecddaecbcbaaeceaacadedebdcdeddaaececaebaabeaccebebaebdcccecebeeecbacaeddbbcabadddcaccecbadcedbcdcacbbaebbccaebcceedddababaaddcbeadecaacdeacdaebcdcdcbbccbcccaebdcbddbeaceeaecbdaacdddcdcddebbbcaceacbeecccbabdecacdeebbaaceececdecbcdddbcaeabcdbbbcdbdecadaceebdcddbebdcdbbcaadadbdbdabdeacbedabcebebaeeddadeccddecbeecabeecdddeaedbbeacdcbcaacdcdebbbeedddceaddededccaeaeecbcbaecddcaeaeeaedeebcaaabecedababaebdebcccbcdeccebdbbbacadededbbcabceadedccaabadcccecdacdeeccababdabceadecddbaecdccaddeeeaaaaeccbbbbbabacdaecbddabdbaedcdeebdcbcececddbddabbbcbbedbbcaebaaaecbecdcaaeedadacadcaeecabacecbbaccaddcecdeedccebaeddbcbdbedabddcbeddbcebbdcaaebbecaecabeecdbccbdeedbdeeedeecabbdcadbaedbbddcecbbaaedcaebeceaaacabcdbcdcdedaecedeeaabdcebebcdebecaecebbedceabebdaeeeacadebbdecebbcdebebddeedbccedbddcababaecaadecbddeadecacdecedcaccddeabbaadaaaadedeacbbeccdaccbddaadaecbebebcbbbbcadcdbcbedbeddecbbbbcebcaceadcaccebdebdbcbebcacddeeaeeaeaeacdccaaeceedcdecbcadacbbccadedacebdedcddebadeddcbaacaeadcbcbdaadadbeacbeeeadacdbddaacdabebbdeeacbbeecdaabaacabdbbcbaedaccddadccacddddeeecddedadadcccaccaebaedccbbbaabccbbaecedcadacbaeacdbbcebadaecaedadcbeaddbaaccaabaededaeedbeabcaddadcaeebbbaebabcdadbeddddededbdcbeecedbcabebcceeaaceaebaebddeeebdcabddddadabeddbdebaadbceecdbdeabbadadedcbacddeabcdabdaeccdcaebddbecddaedcebbcaadbbcaadbcecdcdcdccaeecdcccabeecaecbaaebbbaddaacaaedbedeaebdceecadeaeeeeababddbdedbcceeebbddacbdceebcbcbdeadcabcccdcbdddcbeadbebbaebacebdddeacbacbdbeecdeaaadcbedddbabdddbedbbbbaabaceacdbbcbdccbabdbddacdabccdcbaadbcbacccdddddddadeacbbabcdcaecbbdddadabbdcbebaaedcccdcbbbbebcbbbedccbaeaabcdbceecebdbebccedcccacddbedbbececaaebebbeadbdebadadbdadedacddbdbdcaccbdbcdedadacaecaadccebedeaedaaacdbdbdededecacccbccbaebeeacdcebccedcbebbcadbccdbaabeaababeccebbecaeecbcbbdadcdbabcddbbdabceceedcbcaddaaeacbcbbecccbcdbaadeedbeedaedbbeaeecccbcbbaaedadeebadbbeeadeaeaeebbceecbdbbeedcdbdbaeeacddcaeccbedeeecabcacbdeeeabcbdbcddceaabbacedaeebecdbbdeedbaeababdbeabcbcabdbadcdebdaacedacdabeadbbadeddebcccabcedacdddecebedbbbcadbedaeeeddbcbaaaaebecbacaaeddacdcaabbcadcdceceadecdeaeeadabeedceceebcdabacebbebcabebeeeacbcabdebeaeeebcadecdcabbddbccecbbcdddbeecaaaebedbbbeebeaadcbbcdecaebdecdaaabcccbbdeaceaaebdaeddbaaeeddceeabdaddccaececdebedeeeedbccbbacabbecaabcbaaaadeacceacaecceddbddecaedeeacadadababdcdaeccdeedcdabdceeaabcdaecadddcacebdcdaeccdabbcaeaacbbcdcbbdcacaddcdbbacbbecdaadbeeebaceccbaecdaacdbacecdebedaceaacacbeeaacbcedeebcbcecadbceacbcacbeddcacdbcaaddececdaddcecdeccaadeebcaddbdacddceedeacbcdaeeecbdeaeecadbeebdddcdbdabdbabbbbecbbaebecceeabacdeaacacedbcbccaeedceedbadecddaacdbcaedaecacdcaedbddedbadbbccbbbabebbcdadbcacebbeeaccdaabadbdaebabbaeedecadbadeaaecaebdcdebdbabcedacbbeeccbceedaaedacedabeabedaaabeddaaaacbdebabdbdbbcddbdbbecbbcdaadabeecbadbabacbeadabccdcadbdcedbeededdbabeabaaddbdedcaaddceccbabaaacbbededadcbaeaddabeabdadaabecdedbebeeacccbebaacbadeaaceecaddcdceecdbbacebeeadbdacbedcadaecebdedddcaeeaadaeddaabddbbeebceaaddccbeabdcacdebceaecdbabadccbabaccdecbdeaecdecbcabbeabddadcbeaebcdcedeaeedaaacadadbdbeedebaccbeeeaaebbeaacbaedadeddadceddedcbecadebbbdcabdbdbacaabdebadeaaaabceaddbcbcbacecebcbcccbbcceaaccdcadbaaadbbebedceecabadeccbeabceaceaeacbedbedcdbddaebadacceccaecccceecbbcdabccaebeaadebdddbdbdbaabdcbbbbdebcbddeacbceddabdaaadcedbccceccecaeeabbddddaeadbbaebedbbccbccceaccdccddcebccdaaecdaadddbceecaacbcacabacbacecbdbccdaaacaceedeeddeaaecaedabdebbccdbcbddebbebedcedbdaeeccaaaebebedbddabacedededaededebddbcbcadbbdbaaedaabeacdacbcedceebbebbdcbebedcbaeeaddadccecadabcadcdecaebbaaddccedebdaeeaacadeaeeaadceaeebeedabdebbbabdeeaccabdbbcccccdecbbdecdeeebddadabcedeabceddccbbecbaaeccebcdedbcbbbaacdbaacedcbccbdcaebdbbadceaaaebedcbbddcdabaddeebcccbbeeedeaededccccedaccbdaddecbcdbebaeaebacecbabacebdadaececceaaeecbabccabebbeeccdcaedadbbeacdabeacbecbaadadbbccbcdacdeedaebedaedcdacbdbeaddedbddaadedbeadddedcacbdbeadadabacdddcbbdcdebeebabaaadbbddcceaabaedadaebddcebedaeededcaacedbbbccbddebbeacabadddebbdcebbdbdbdbdbccebadcaaecbbcadaeddacadccdebdadddebdeeedeeaeccbabeaaacdaebabbeeeccbaedcaedaedaeeeebbbdbcdebecbacbdedcaeccdcecabedddbdacaccebdbaabeaccecdadebcaeaddbbaebbbceeebeeadbedbeaecdbadceebbabccabdbdcaccbcdabcdacdcbabbeaabcbbeaaecbabbadebdbbaacbebbeaceceeecaaeceeacbceddaccdbecaececaadebbdeaedebaebbceeeabececbcaeddeacaeaeeedacbbdadaaceacdecdcddddaadbeeebdbeccbcabedcbdacbdccbcbbbbaabecbdacaeaccacdddbebadcebddaeadceaebabdccceeaecbcbadacdaccecceebdaecbbcebbadaecbdeaaaaeccabcbecaebecbbddbcccbdbaacecedebddbcbdceddadbdeadcaddccbabccbcadbdcbaedadcbdeeabaabdddbbaeacdabbbbccdecbaaebbdedbdeeebbdcbdceadababeeeaeaaebcceddddbcdebddedbcbbbcedaceeacddbabcacdbedeecaabeaccccebacebacdbeaebdaddecddebecbccaaeadaadaecdcdadbbcddeabdcdeaaedecedebaeddeeadecedeecccbdaeddcebcaedcbeecbaaecceeebdecbaedadadceeadedeebacabbeebcbeebcebdcabaadbdcecdadabccbaebeaaaeabeeabcbdecdccaeeddcbcadbeeeaccdedbcdeaacbcecaaecedeaedbacdcaaecaeccccbeebeaaeeaaeceddadbadecdcadbbbbaaeaceedaaeabbcceebdbdccccedbbeeabbdaeccbddbeedadebadeecbccbaaeeeeadacdbaccaabedddedaedecddcaeaeadcdccaaeebabadbdceaeacaccbbeaeeeeaccadccddbeccbabbacdeabdaeedbcdcccdbcabebacbeaecdcdcbaacbaaaabacddcaacabeeeadeeaadccdaeabedcddaebdbddcbabdedcabdaecdcececeddeeedbabeeabcbedaaaacecdcbbeddadeabaceecceaaaeedccbbeaedceaabdaeaaaecdaaeaddaaacbaeddecbbcdecdeebdcecabbbecbebdaeddcccbdaadddeceaaaaaaaabdbedaecdbbedadaedcacebebcedecdebcdbbdbecddcbbdebabdeaeabcbedaecbbcdabdaeeabccaaadcdbddbcdcdbbdcadbecdcbcbaabbacccdacdaeaebcbdbcdbacedebbeccbbdaaeebcdddaaabccaebcdabdeddadadeaeaeebbacababeceacadabbcebdeadabbbeeebeaaceabbdacbceabedbdccdeaacbaebbbabebcdcbecadbddaccaeacaeabbcbbbedaedccbeccaacbbbdecbadaeaeadebbceadeceaedecdbbadaeabbcdadaebbdababaebbcdacccaddcdeadedededeceebeadbaedacaeccbdacdadacbadbadaedecbdedecdedcdbbaecedcbceeabeadadeebcadeaabaeaececbdcacbdbbdaecabadbddceadeacbcbdeababebdcbdbabacaabcdcaeedeedddbbaebadbcdceccbdddcdddceacbaaaabdddcdeeaacbcebcbbaaeadabccacaadcebcbecdaabdbacbbdedcdbdbbbebdccdaadaaacadedcdaeadbccbaaacbccbaabeeeebecdbbbeaccaeeedeeddbacbaecdbcbadaaeaaecedacdedeedadaaeeddadaacbdaadecbacdaaaedadaadaddbacbcbeedaccadecccadcabcadcbbbbbdaeaccebabadeaeaecbccaacebecdacbbdeabdbbbebbebeccdeacadcbdceabdaaeabdcdecdbabccadbdaacecdbacedcecadaccaabcceceecdddcbccabdbdbbabedacbecdabacbecacbcbcbeaaaddbccaadbeccbebdacdecdbaaeeedadedaeacdaceceaecebacbabeeecccbadbbbecceadcceddbedcedadbaceeedacdaabedaebdcecacedcdeabacaeeacdbdeeadaebadadeaedcbbeabeeaabdecabdaeddbddcacebdacbebcabebaedbcddbccbdcebcbbcedcdaeaeabdecacedddcabccbacaceadeeadcabcaeebabdcebadcbbaceeaedcaeecbeecebdecaadbbdbbceddcbdccbcacaedccceadedaadaadbdbeaceadcaabcaeabcbabbcdedbdbbddaaadabbecebdeaaaabeecdbdccbbaebecadaddebbdeecacaabbdbbbdcdcabdeacbcbdcceddbcabdbebabecacabcbbdeedbaaeacbaacaeedaabcbededeccceaeaebaeaabadebeeccdebdcbbbeeaeececdbbdcebecbacacdbacbebcaaeacdedabbdaedbcabaeabdcccacaecccbabdcadebbdeebbbdecebcaaeaeacbedcdebecceaeabaeeddaedbacacdcaabceadaccacdbbdceddbedebedceeecabecaabaadbabababbaaabddedcdbdecacdcddaccbbbabcbbacbeeabaadcbdbbbaecbaccdebacaddadacdeaadadaceaccecebcbededeecbbdbaebdbaaeeecedcadacdecacbbdceeeeabaedbbbedceeedbeaaeeeaedbaaddbcdaaabeddadeddcabddcacedcaedddebaabbceedcedaecbddebcdaacbbecccadadcacbbeababbbbdacaceeaeedccddcbedbceacebccdabbedcebabcddcaaaacaecdccdceacceaaddaedaedeeadedeadccdbcdddbdcabddedacccabeedbbabeacaedaedacbddacdecceabcaeecadcccebacdbeaedcdeeacedddccdeedaaadcccbdcceaedecdbeaceedbcdabaabdbeabcbeaecaedceaacacbacedabeebadaeeaaedacbedecddcddcbaeeebccaccccccbebbcbeceecddcabacacaeceaecaeedbaccdcedbaabadebcaaadcadcceecbedadcdeaedaadccaaaaaadbdcaceceedccccaecaccadaaebdbecddcdcabceacddacaebacadcdbebaddbbcebadecdbcecdbaeebebadbacaddaebdaeeabbcbbdcccbbbeddabaddabceeecceaecebadbebbbeaaeaeaebdecdccebeedeaddedeeabbaabdbbbceaeceabbcecaeeabdaeecdceaaaededdcceebeebadeadccebbabcdaeaeaabebebbcabcadcedccaadebcaeabccacedceeacdcbcaaeeaedabcccecbdedbddcbcddeeeddeebdaeecbeaccbbbabcaaedcecbbbccadedeaccbacbaabcdedaaacaccbbabbebabaeeccecbebdacedcdbbcbcddcadcbcdabcbcabededdbcabccbccacbbbabeddeadeadceeebdeddbedcdcabbdabaeddbbcbebbeabaebdebcbaccdbdedabbbdcaabccbadddabbaeaedbeabaeedaccddcdeebaeebdebaecdabbebdedceecaecdaeaaebebccbacbeccacbeaacecabcadbebdbacaadabedcccbcdcedceedceedeebcceeaabeccaadeccacaadaebbebeedccaeacaaceccccceccddddbbedaabbcaaabcbcaceadbbdecaabaecdecadecdadabadcedecaedcbcdccbacdceeeaceedeaaaabcaaebeabdadbcbaabbadbcadbbdabadbaceecebdccaaecedcbbecccaebceadaadcdaaedeadeeceacbacdaeedbadbadabdeceeccecedabbbdabcadbadbdadacceaeadeceabbedcbddaccebaecbbaadccdbabdbceecaddcabaabadedebcaeccaebecbeeebcbcaccccadccaabbcaccacabcaeadcadacebebbaebeabeeaadbdbdadbecabbdceacaacdecedbcbdababbeeecadadcdeeedbaceebccbbdeeacbcccaabccaecbbcaadcdaeabacebeeadedccbbcbaeecbccadabdaaecabddcaabaecdbabcedbcbaceaddbcdbddacaacbddddbdeeddebdaeaaabbeaacaedaacaedcbacdbceeaecaccccceaedcbacedecddbecbbbbdbbbabeebcdebeaeedacaecbdbdbecabccbbbcdcbbcbcbbacecadcaacaaabdbacadbdcddbbcababedaaccbbadeaddecdeacdcaedaecbebdaaccbddecaccaacabdadaaecaebbbbeabedbcddccdbdbbddddccbceedaeacebeadcabeadbeeedddcbcaadddbecdeccccccdaaedeecbcacdedbaeecdeabddbddbccdddedddbdecdbeeeaebdecaedcdccacaeaebedbdbecececddabbadeebeebbcdbabdbdddeeecdeaaeebaabbebcadddbcadeaecddceadabadbabecacadceacaccadadcaddabdbeccadbbbdbbdbbbddceccddccaaadeabcadbcdeeadcbdeeceaacbeeeccecedddccadaacceeebcacacddadbabdcacdacbbbebaaccecbecdbeeadabaebdbdbcbbabecaccceceebeedbdacccdaddacdcdcceacaebdadbbcbadeedcebccbcbbdcbbadddbcaebebdbcbacdeedaccedcabedbdaebbbcdccdeecdbceaabadbbaeceadbceecbbdccacaccdcebeeeeeddaaaeaebeddabddaddbdedcbbbdaaeeadcaeebabccdddaedccdaceacdccaedcadbcddbaabeddaacaabaaddcdeddacbdeeabebedecaccdcabcdbccbabeecbccccabdedebaeddcedabccedcecddbdbdeaeccdcccaeebecceebdacedbbaecaeeddbcbceaeccdcccabdbbbeddededdcdbecbddeeddcacbdcceebececddddabccedabbdbcbaeddbedaecaeedaedabaaceebdcabddadedddcecacbdceebeadcdcbaeeecaecbceeeaeaeacbceaaeeebdadabbedcbdaecdbdecaeabaeadbbaedadaebdaadacadcdbeedcdbccdcbbabdeebbcabecbdededeebadbadbdbdebdaabbaeeaeccdcabbbdbaaebcacbcedbadaeacabeedaabcebddaaeedbeeaeebcbcadacdaabececcdebdbbccecacebbbdecccedcdbbedadbccaddbceecceabebadedddabceccbeadceecbcdcadbbbccbdbcbedeecbecadaaadebbabadcaaeedaaaadacbebbeddeeadbbbdeebceeecbdddeadbbbeaacbacbbbaadbbcdaaeccddaccecdcddedcbdbebbeceebcaecaaeaebaedecbeddcabaabaebdaebbaddcbaadaaceaedacdcadcbdccdaaebaadcdecbeadbcbcadaeadedddeabddeeeccadecdbddaebbccbdcaabbcbeeadeaddbdaaabdedddcccacebebceccbdcdcaaadaeaddbdadabdebbcdebebabaaadeaaeadbdcaaccabddcaeedabdccbdbdcdbbcecabbecbdeaddbeacacdcbdaeedbdbeccdeaddecdddbedbadbbcdddcaabcebaeacecabebabdbdbedaeddccaccdcebdcecdecabbbacbacdceccecaaabbdacdecbecacdcdecadeceaebcebdddcceebacababeecaecebaaeeceeaedebdcccbcceaadeedacabacaadbaecabaeaedddaeaaecbddbbdcedbebdddeedcdadaadedcbbcbcecbaebaaedcbbdadebdcdccaeecccaeccacdedbcbadceedcbaadcaaccdacaebccadeabadeaddaeecbceabebbedbeacccaadecdcbecdaabdebebddccebcabeccbbdbeeecbeacbeabceeeccbbdbaceacbeacaabbabcabcabdecacdaddcbdebeabdbeecadbdceeadbeabeacdbdbdbbcecbcdbeeebdebdbcedeabdbabdbeaeabadacbaceabadeceadceddcbdbcbadcbceaaeabaeeacedccbbccaccdaebcaeedebddbbbaebadedbdabbdbebbbcadadaeeedcdcdbccbccdaaebdacdbdebbdedeacedebdeaeeebabbacbbeacdbaaeaebbdccceeaaddaeccdacdbeeeecbbdcaaceaccbabbeadebcbabbcebdeabebbdbecadcdadedcbddabcbcacaabeeebbeceaaeedddeabaacacebdbaeeaccededbbdddceedcaceacaddaddbcdaeaababeeadebedcebdceddaeaebebcddbabdeababcdceebccddcdddbabcdbdacbeddaeedbdecbcedddaddbecbbabbdeeaababddcebecebcdbcccbaaaabbbabcdceaabdcebddbdabeeebbcccedabeabbbccabbeacebdaedaccbeeeabaadddabadbbadcdeaccadcebeeabeaaddddbbadaddaecbdaacaecaccaedeadaabebcbadddccaacbdadacabdaddcbdaebadbbedbdaacbceadccedecaadceaebabdaacaccadadcdcceaeaadddddbddeadeabbdcebdbccdcbadcebdedcaaacadabcddedaacedabbadbeddebbbececccbaccdcdaeacbcccccbebecdddaacccbdbedcabbcebacebdaadbdbdacaaedbbcbeeedbdddbedbedddebebdcadcdedcebeadeaaadedcdedaaaaaeabdceedeececdeaceecbcadeedecadeddaacceacdeabddecaedbcdaccdccacebbcebcdbdadbaaeacdcaaceacaedacbbcabaadcdacdeeddbdcccecdbeadedadbadcdccaceaeebcaadbeecbcdccaebbbdadeebcebcdedbbdaacbabcedbbaebcadedddecbbddadaaaaadaeebedaaeaabbebcdadebebdecebaeabedacecddcddeccbbeecdddcedadeeaebdddcdeaddacadbcacdbcbadadeacaecaababcecbbdebacdadaacdebababbbececdbabdeaedeebecceaaacecccacedeaaedebbabcacedeccbbdedbeaccecddebddaadabbecbaecdbbcccbddcaeedadecebdddcdbdbbdaacedaebdceabbccdedbcbbacbbaebcbedebcccdaebaaaeeedecaddccedaacebcbabaeaddecabebbaeaeabcccbdbedddaeaacbcadedeebeebbdeddaaecebecbedeedbcecabacdbaeedcbaddaecedbededeaaadbaacbdcaaebecdeaccbbddeacbbbdedeabdcedebdebbcecededdbdeccbeddeaadaabaabcbeacadcccaabceddabbbcccbbddbdbedbbdeaacebadbdcbabbabbeecbbebcecbdeabaaabeaddbcabdaecdebcaeaccbbcdabeacacaeebdebdcccecceabeebbdddaabbddaceabdcacecbdccbadddddbdcccabcdccddbaccacbdcbbcaecdaadebcdacdedddbdbadaacabcdacecaeaaccabedebecdbdbdbbabdaccadaabbeacbceebdcbdaeabacaedeaaacdcbaadcaacaecaddaabcccbdbeedaeaceaeabbbdbaecaaeaddddeadbaeedbcebceebbbeddddeceabdbcaaadacaddbabbcbbdcdeccaabebabdddeeacebbabbabcedbddddbcccdcdedaecddcdecababdcaaddadccdaddddacceedecdaeaeaaccadbebedaaaadbcbadbdbaccaaadcadccaeaacbaaeaecdddccecedaeedbbdcddbccaeecbbcebbcedacbbbceeaadaaaedeebbdbabedabcdcbcadaccdebcdaaddbaacccaacddeadcccbaacdcaedeacdacbcdedadeacbdcdecddcaeecddbcddccaeccceeeeebaedcdaebbeccbbbcbadeecdceeaebcebecbdaeadbedebbadbecbebccebdeddbdcbddeceabaebccdddeddcacccbcecdddbbcdeabcaaaeceebbdecbaeaeeedaaddcbceddcbdacbbbebcdbaacccadeecebbcdbabbaabceaeadaeeaccadbbadacbeaebeecbacdbdedaabcbbcbebabbabebeccbadabedbdacbeeececaccbaaecdddbebbbcecddaaeacdcbcbcebcecaaeacedaceecbaaeaadcdbecadeebbdaeebeebaeaedebebddddaeeccbcceebabdeeebaaaabcadbdaebadcedbdeaecbeeeddebaaddcedcadedecbabdcacbdbdacbbebebbbdbbbaeceeacbacbbedcccbbbcccdabdecdedddadaaecbecaebcbbbbdbbcecdcedddabbdedbceebcebbaceebaaedcabceeaaabedebeebdbdcbbdebdebacbbacebbedbaeabcbdaeadedeeadcacabbdeeebcbbdbeceadabdcaaacecacdbbacbbceacadecebdeebdccaaeabbaeeaeeceaabeabdccbecdbacaaeabbcbceecabcdaabdacdddebbaccbbcdacbeabbeaaaccdadcbeddccdddcdecdebddbaedceccebdbceeedbecbbaebeacaccaaecdaaaabebcacccdeceecbcaccaeabedbeddaacadbdaaeabbceddbbceeedbebeccbaacedacedabbcedeceaedececbbbbbbcbbdbecbbdeaedcdecdaecbdbceedadbaadbccdddedcedaeeadacdaeeedcdeccbdbdbecdcbbbeebeeaeeccebabdcddbdebccbaddeccccaaaeaaadeecaeeecedccaeaaeedcbaabdaaebbaabbbeeeebccdccacbadcdadaadaacebabeeebebebaeccddaacdcdaceaaddcdbbcbedcaceaddbebbdcebaaceaadcbcbcacabacddceeeeceababeacddaebbabdeecdcbdcaebaacbdecadddeacceebabeecbbacabcdebbedcacadbcdeededcbcacbccecbdbaaeadbebeacbecddaeeadbbaebaaecabdcdbecadbacccadceacebbeedbcdcbacdcceedaaadddaeeeedeadddeecabbcaadaaacdaaeaaedbabbcaeadbccadaaeddcdbcadbdbabdacdbaaacdbdccdaabccaabbeaddbebcbbcebebedaabcbdadccdbcabeebbbcccbbeeebcceeceacabecdebedadabcabaadabdaaaececacdacbcdadbcacbbdbadbebdaaecbbcddbaebabadaeabaaeccbcdaeceebcbbeaebdeeddcebaceeadcdbdcececdccbddbababcadddaeacdbdebdacabeadccaebebbceabcddcbaccebababcebaebbaedebcbabaebddbdadcbadadabaccceaaaacaaebacebcedcdddcdedcdadccdbbddcedebbeebbadcddceabadccaeadeecccdacacebcceeaecdbdccdbceadaabbcbaacecadbbcbddeecbecbabedeadadecbadbecabcdaeadaebecdaeeedcddacdbaaebaadebdceecaaccabcbcdaebcdabcabdeebdcacbecdabcbedccdcbbddcdbbbddbeeccaabcdadeedadcededaddccacaadcbbeaaabbbbbaaecbcadaeecaacaacdddddaccabcceecdeebcbabdacddddccdebcccabdcccdebdeabacedcaebcdbeedbaaeadebadcdbcbecebeadecddcdbceaecacaeddeabbeabdacbbebeceeabbaaeddaecddcccbedaebeceecddcabbcacdaabdadceedccddbddcbdacebcedbecddaabddabacbaebebacbcebaadbcaedaadbbbccaceedecdceccdbadededbedcddcbbbaceecdcaaaccadbbaccbeeaeeeaccaabedcdedecabbadedbdeaadbdaeadebebeeaddccacdedcbaaeaabccddcebeceaaddededccaedbbedcbdebdaddeecaabedaadeeadedbdbddcecbadbcccaeaeadceeacbbceceeaaccccdcdaaadceeababdbedceabaaabeebbdaaabccdabcdbddadecddababbbedddbbbbacceeccdeeccbcabbecbbbbbdcadeccebbbcaeaeeabbcadaaaabddeaecabccdbabdbdcdcaaaadcecbcbebbeacedcaaaddeadedbdcadbdecaeeaabcaebaeadeaeacdecadbeabeacdbacaeddcecadaccdeedaecceeceeddcaebaaccdebebdabeeecaadbcccecececaeababebcdbbbaabbbdbedbdabcecaddebceddcbecebacaaeeeeddcdeedccdaeebcabbabcdaaacaeacceeecadccccacabdbecdeccadecebaeadecabcbeaacebdddbadbbebeadcdaeeccabbcbcaebcbdeeacadecaadededbeeaddeacaeeacbbbeceecaeecccbddddaebadeabacdbcecedadeaecdeaaebdceaacebcdaccaaaeaccbeadbcaaebbbcedccbbeaebecbcdeebacbdddcebbccebcdeaeeebbdbceebddcbbaebeecdaccdacdeebdcbcdcdcbcbaabcadcbaabbcdcacaededabaccaecbdbbeebddeaeecccdeebeeaebaddbdeaedaccedadceedddcacaacdeebedcebbadaabadcacceaccbbcdbbcbbbabbacebaeeabcbcebbaaddaadbcadddbbccbbdadedbbeeeaacdcdebdcaebadcecaedebcddbebeeeadcbcabdacccbbddcbdbececeabbccbddcbdbedecdcedaeaacebecbbdcebcadbbbcdaeeeabacbadaadeabdbbcbddebbccaacaabadebcadddcdccbcdcaedeebbdebbecdddabbddccaddcdcaeabcbcaebaddddaecbccbdcbbbbaabcdacebcbeaabdccddcacaaeabadabeecccabebeccdaedabebeecaedadadbbadcdbacaebdcdbbdabdddddebabccdabaeaabcbdbbbdedbeeacacceccaeeedeaaeebbddacbebdbcbacadadadebaadbdecbbedeacceeeeecabeddeebaaedebeaaeaddbdebaaadbaecdbbeceddaaeecdeccaddacdcbdbdcdaebadabdabdcabdeddddeddcbcbeeebbcebdccdccdcecdddedabbbcddacaabbbcedceeecbddaaccadcbedadabdcddabedbadbaeaccbaebedcbacbaecadadadeacbcaacecbedabdceaaabcbedaccdceecdbcebdabcaadccbdbceebdecddeeaaaeececadedbcecacbdccecbccececadcdaccccabadcdcebddaeaaddbbdcddcdeddaeedeedcccdadedeabcaecaacecacebcbbcedcacbcdeaaacadcceddabcabdbcebcacdbcddeaaeaecbbecaeaccbacbbbbdcbaacaadadaacbdcabdacdceabebeaececededaebccaccdbcbacbcdebdbadeeadaaeeeccddabbcebbdcecaddeabecbeedededaacbaebdcddabcbbaddeddacdaaacaeaecdbaeabdbaccacbcdcaceeadedcbadaebbadabcaeaeeaadbebddccddcbbeaabceadbdebadaeaaecbbadecceedceddadcaededccadbededaeadeddaeedeacaedbdacdbacbbabbaeebeeacdcbecaaedbecaddebeddaebacbadbedaeddceabbdbccbbbcbccaedbacabaaecacdabdbbdaeabeabadbbdbeccdbadcadbdbbcdcddbcecceebabbbdcaaecccecadbecaadeccddeadbabcaadcedaebadecaeadbbeabdadadcbaceecababcadcaabcbbecdbddaabebeedeebdbeaebdcccbebdcabbacbeeeddecbabbcddeeddeadaccdacacbeadbdeedddabaaaddccbbacbddeedabeabaaaaaeccbeececbdcbebbaaadeabddacacdddbcbaaedaeebeeecebebedccaedabaacecacbbcbdeaaaebddcdaceaacdcbaabdbcccbeeeccdbedbedddbcadecdbcbebaebcabbddabecaeedbeadeddeeddedaeabdccbdaeedddbbbbdacddcebdcaeeaaaebaaceebeaabcebdccaccaeceececeedcdadeddbbdeecdcecacbaabebdbdaddeeeceadadcdaecceabcedadadccbbeabbcaaeeebebececdeabeecbeabbaebbcebdabdbcedcaddeebdebdcbeaccddcaaeeebeddbdecabacbebdcedebdcebcdedcdeeebcdcebccbeaacedddeddccbdaeebcadceecdbaccbdcdbabcaeacbdecccaaeeddddcceedcbecdeccbabaacccdabbbbceeaeedebceeddbdecdaccabdcdcacbbdabcebacddbbadbaaabacdedaeebeaebaeeacdceabacdcccedccaeeccabdbabedbadbadbaabdecacbeddeacedebeedddbeabaceedebbdedecaecdbdebeadebdadeddedabeaebbbcdbccbbbeabddedbecaebebadacbedddaeecaacacddabeaaecabceecabaeebbecbcdecceededabeccbeaedacabcaaddabadcecbaaebecaceecbcedbdcdcdeddedebccabecaaccededaaaacdebdbcaccdbceedcedbdddedabababcbceebabbabecaeebcabbaedbbbdbcdcbabccdeecabcbeddceecdadcdcbddbbcdecaacddcecdeccebebdbbcddcaacddebcbadbaaaadcedbcdbdeddbaabbaaaeaceabcdbcaddbebbcdbedbebbabdedeaebccbddbeddeabceaceedbeeebccdaabdccedcbdacbbcedbbcabdbccdddabdbaeecedcdbebeaaacbceabedeabcebeeddddcdeaedabeebacdbcaaebadcaaeceabbababbaabbbdaeabaccdabcadabeeedbaebececbbadbecccecadbecbebcddebebbbdabecebedabebbacbbddccbecaeecbbdeadeabeaeecebaccadcccccdbbdabdcbeabbeadaebebaccbbeaceccddadceacaeaecdbcddeddabdaeeeaadbbcbeebeadeaedbdcccbdddccdeacdacdcbdcbdeadddaebbeedecbdbceddcdaecaddcaecedbddbcdcbaaaddecadacaebadddeedbccabdcadeedbceedaeddbdddadcbccdddaebedabeabbcabcdcbeeccecddcedddccdeebcedbbabaaaccdccddcebbbaddadadecaaedcddcaedabbdedcdbdddeacbabcdcebabaebdeabbaebeeccabbeacdcbaedcdcadcddcecaccabaeadbaaeeceecaaedcaceedeadadaaaadbdaeccaaacdbaeeeaaabbacebbebdcabbcebdbdcebdcdbedddacaeaebdbabbdacbbbdacededbdbaabaebabbabbaaddccdceeddeadbdccccadaeabdcdadcabcceacacecacadedcbbdcbddecedadedcabdccdbacddacdebeadadecbbdaeadaadbeecebbeebebeebbdcebbadaddcacaaccedbbcdeaceedbebbdacacaecbccbdddbcdbacebcbaebcdeadbaadabacaceadaebaceaaebacdabccdccbaeaeeceaddebbaecccbaccecbbdacbecaceaaddacbadcbceedabdeedadaacccceaaeaceacebeadebedaabdaecdbddecbaccccbdcddbddddddbbedcaeaadbbaadedebdcccabaaaebccbcdbaeedeacdbeeececeebcedcbdbddbceacbbabecbecbaebdbdedaadedacabcacaeecabeaeabaeccaedceaaddadeadcecbcddcdebaedcccaabbecdbddacddbeeeedecbaadedeecbeedecbaaeebddbabdcbdacdccebbabbcbadcedabcdbebceabdcbcebbedececdacecbbdedcbccecabbbcddcceaababeceaaceadcaddacabeebeeaaeaddaebacdbcabeeaeaeedbbdceaacebcadceabdebaaadddddbdabcdaabeddacddaacdabeddcecebddaccadcadeedccaabddabdbbdebbbdedebecdbeddedccdcbcadabeeeaaeecdaadaaddecbaedbaecbdbaddceebcdabdbdcadaccecdedcebecbedcaacdaaddbaccaaecbcecbabdcaebbbcabadadadebbdbdddaeadabebabeeddeacdaeaeaabececadaedebcdbcbedddbeaaeeccacabdedbddbeedbbbadaceacedeeabadebbdcabedbbdbccbdabaaddecadcaeabcbcbaadecbedaabcaeccbbcddabaaedecddcaaaadccbbdedaeadadedbecebabceccdaaebbcbbdbeeeeccbeabedeaccebcbbaeecbebabeebbeadbdeeaedacccacaeaeeddeacdebcadaaeeecceecaddbceaabddbebabdacebedebbebabbbeadaaeaebeecabadaadbdbdcaaaabaeabcedbedcccdaaddcedaededdbbedcdecdedbcbaabadaeaceeaaedbdeaebabbdbdadeaebdcdeceebeecdeebaebcdacabeeecabbbdadeeaacababbbadecddacbcaabedeeebcccacbcdcdacbdeebddccbcbdcdecbdbdbbaaeacaaeadcddccecabedcabcaebcdbeeeeeedddadadabbdebddcdaeadeddcceecabbdeccedeedbceeadbcdcceacadbbbdedebacdebbceeaccaeebceebcacbabbabddaebccbeaccbcbddacaacbdcecceadbadddedacacdababebcddaaaaddabadcaacddecaebebeeaedecbccdcbaddaaedddacecdcaceccbcdebdaeddceebedbbecebdbcbddaadccedbbbacbaadaecddcadbacabcaedeabbcaadadbebbcecebdbbbcbccbbbcdaaecaacceddbddbdaeaaacecacaeebeeebdebaeaeeacecdcbdecadcacceddedadaccedbdeeedbbbadedcdabcdeecbabdcabadbecaebaedbeedeadaceddbabbcabbdcbcbdebbeddedabccdaeccbebdbcecceaeeaaebceacbadaacecaccdaeeaccbacaaceedebdadeaeacdcdcecbebcaaceddaddddecdccdaabeccbcddeddceaacdedddcedaabebededdeccdbddbeebceccaddddcaddadcadccecaabcaebacecedcacdbdcdbebccbdebbcedacdddbabeedbaebcaebbddaeccadbeeceacdbdddacabacaacedccddbbeaeaedabcaeedcdddecaabacbedccbcbeabeebacedbcbdcebbbbaeecccbbdcdacebbeadebeaeddededbbdaabdeaaedbdcddacabdcecdecbaccabcebcbdcddcedabbbaaeaecdddbccddaaddabdbeddeedbddcecbdeacdaaaddbdeecacedbacdebccbcbcaaebdbcedbeeadcdacbbcdddabeaacbcbdbdbeeabcdbaaedbabcbcebedabacaeeaeebcacbebdeacdbaadadbbbacadcbedddedebacecbbaddbacaceebceecdcdaadbebbbaecbbeabedcaddbcddcabedededbeeecdacedaedececbaeeebcebdbcaceadbbbbbecbcadedcdcaeeeacdeecdbaaeeaadddebcabeaecbbeccecdbaecaedadcbddbeeceeccceaddeebebaabecadcaccadeacddcabdeadcaaeaddbdacdcdcdddadecccbdaadaebbadcecebdbdaabeaaacbaaacbbceebdacebbddadbaaeecdeeabeecdbcaaddabddbcdeaabecebceacaaaeeddcabbebcaedaceeaacadabacbcecdececeebdcabbcdceeaccccbedeeaaeaabdccaaaecedcddbbddddebdaceaecaeedeeecbaeaaacbdadbcaeadcdaccbcabaeaaddaadbeeededeccedebaccdcadaddaccabcebacbecaeededadecbbbdccbecbdcdbcbdacaaaeddbaeaeeaecccbcadededbadeaeecbddabaadbbaabdbbacdbeadadbdedcebedddaedaceddbcadbabacedcbacaddcceaadebadbccdcadadeebdabdcdbdbcbbcbcedebadeeedcabdeadcbcceaeccacceececcaaababebebebdecaceecaeeeadbadcabecddeaadbeaadeceacaeedccbddbaaebaccbcabbebbacebadbeabcedcbdbbbadacaceeddbbbdcadbadceaceaeedbbabdeabeeeeddbabedcdbdaccacaeeeddbeeccdbccdcbabccdaccbcccbaaceccdddddeebaabeeacecbeebadebbdabbadedcebaabbbaebcbaecccbcabdadbeaeccaebbcbbcecbcbdddbdceaaccedcceccceaaaeecceeccdbcaaedbcebcbaacccdacccaaaddcdcabddeaeaadbbccbecbcbeacbbcdadabeeeaabaeaeaacaceaaecadbaebbdbabdcddbabcedbeedcedeebeddadedcecbedeaebcdaebcaeccebebbcebbdeeeccdadcdecbabeaaedccdecbabdbecdddadceaccbdaadebccddedebcdeeaddbcecebbbdebddbaedbeadecdddecceddedcaeccdcdabecbdeadeabaedccddedeeeaceeaaaabbaeceeedecedbdebcdbcecdacaeacaccbecaecacadccdccabdebdeecacbceacddbbbabeeedaecebaabaeebcdaabbdbcabcddebceecebddbebaabdccebdabdbdcaaeddbdbaebedbceedeaaeececabaebcabeabcbddecebabdecbaecaebaaebccdaeaebcbaecdbeebaceabccbebddcdddcbeccbcebdcccabaaabaabceeccedbbddddeababdedcdaebabbecaeaaacacdcaeeeeeececbdacdbcdbbebeaceecebeddeabedceaaadedbdbbedabdeddddbdacdbbdcacbededaedadceadabbcedbedabaaeceeaecacccaeccaedbdcccbecadbaddaabcbcdbeaaabeecdcceadedcacdcebcdbcdcdbdadcbbceecdcdaceedcaaaccbccbddadedeecaaaccacbaedeeedcbebdeacbbddccabadeecddcbacaaabceaedebeeccedcdddaadabedcbacbecdddbbeeedeeadeedeccbadecdcbabaceedbbdcacbbbbebedbdaddbdbddedeebecadabdabcaeceeebaeecabcdbbaaddbddcebaacabbadadaceecebbaaaadecaedbddeebccbdcadaaebbebacdaabccdcdadbeaddbabdcbbeeadecbcbdadecabbbcbdbdbdbccedcbdbdbcdeaaacddecbaeecbbbeedcdacccbacadbdabbaaeeddcdacdeaecddecaeecaaceaeabbcddacebaeceadbbcadbcbbbbaddcaccaadddeacacdccabdbeecbedcdbccccccabdedbadddbebacbaabaccebdcebabaebccddbcabcabdabeceebcaceedebddeedccaecddcdebbbaabedaeacbcaccebaabcdcdaabeabebacbabddaaadceacaebaaddaeecdedbdcacccddbabddcadeabecaaabadabeeedbdbbeebbdbecaddcdccaabbedecabcbaccebcdeaddecaeeebdcecbdadcaabcacddddeacadcddeebcabeedebabecdedddedcabaedecedceeaaddebabcebdddaacbcdcacbeeaeabaebceaeecacbcadeaaceeeaecbabbcdbecbaedeeaabcbcdeeddeeaacabaecedebddcccdedcedcadedcdbcbadacdbdddebbdddecdbccdbdabaecdbdadcbadcbebbcdedebccaedeecaebbbadaaaabbaeabaaaceaddeeececeebaadddcdbdadeccdddabbeaabcecbdacdbdaeedacdedebeccdaddbbeacccdbccadaeeceeedaaebeabceebdbbaeecdcdcbddacbddcccbaedddbeeecedbedacbadacedbcaccceedcdbdddbecdabadaeedaceebcddeedcadcacccbeedaabddeaaeabdcceebcbcbacceeabaccddebebaeadddbecccabacdeeaddecdecbadbacdaccaccbbaecbdcdbabbddbbcbeecebbdbbcaaaadeabeaebcecaeecbceacacbcdccbcdcbceeaeacadedceabcbacbbbdcccbebaaabeeadedeeeabedbccccecbebacdbcabedbeaddbeceaddbadbcbacaeeddecbaaadecdacdaeccacdaabbaacbcbadcaeacbeddcccdacbebdececbdeadceddaeadececbdeacbceeeecbebbadcdeeddbbeacebcbeedbbdaccebeedaadacaaebabedebaeecbbcaeadbabdcadebcbeceedaabaabedeeceeeacaceeecdbeecedbaaeeedcccbedbdeebbedbdcddbbccaaccebaceaabaedabeccaeaaaacbabbaeabcceeceabedecbcababbceeebababeaaeccbaadadcaebcaaabdbbdabbeabdeebdaeecababcdeeaaeeebebaaabebaeeaedadaeeadebaecccdcddbcaabbcaadedaaedbedebcabbcbaabebbaebdbacaadeedaceeddcdddddeedeeedecbcbcabddbadadaecccddbacaacaddddddccececcccbbbcacebcacaacddabdbadabcdbeadeceacddebeaadcbdcdccadcabccbadaadaaddbcbbeeedbebbacdadacabacebcacedbaeabcbccecabeabccbeccaadeeaaddaadcceebabeaaeeebceecdecaeacebcbdbeceaaebdacbddeecbaccebadacaecceeaccdabecccccceddebccadcbeceecbcebaedcbedaecbececbecdaaddcddecbbaaddebeacddcadacebbceaeabbbcccedcdadacdeeeababdacbbbeacdbdceaccacdceeeadabeedccddeaeaeadddededeabceebedeaaaadbeecbabcdccdcabbdbdacaeeeaaddaecdcdceaadeadecaaedcedeebeccadccddcddcbdcadeeacccbaebedcdaaccacccadcbabadcdeaaaddeabdbcaecbaeeadbbdaabbceeadabeedabdbaedaeadecadcbeccbabecebccbebeeeceaeeccdaabcbeccdececbabaadeaedcaccdddbddaaedddbaecebecdcedcdaddaecaacbeebbdaedebeebdadbcdedddbccdccaaaaddebcabdeccbcebdcbdaddbcacceedcdbdbbdceaddbbadccedbeaacdaaeeeaacdaacdaddccbadacbaaeaacdcdbabeecabddcaeceebcdecdaaecaddcdbbcbacbccbaddbbcabdcddadbdcecbdadbbecaacbaeedcbbdbbedadeabbbcaccbeddebbdcacbddeddcbbadcbcadcaeecacebabddcdccbabbbeaaabdccecdbaebbccaeaeeaadbdacceebcaaddaaecededcaccceadaddeadaeaceebcadedcceaecccbddacbeaceabdddaeedeeaccaabcaadaedbecedbebcaccdaddadeaacceadcaeaaebbaabeddebbbcbdeccdcbacadcdaacebdebaeecdceeaccacabddbacdacdebabaebaceaaabdaaacaceedbbcbaaddeaadaaadceaedbcbceebabcbcaaadbbdddcaddabdceeecbbcceecceaaebdcedbbeaccdcbebddeaebbacdcaaebdddababdadcebbbaeabaadeabcdceeaecbdedebcceaeeceebceeeecdeccdcdccecdaaadcddbccebaadaddedacebdcbdabeecdedcddccaacdcacdbdbaabeeaccaecbddbbeadadbbcbacdedbcbcebbccbadddbedcdedebebbbcedbbcbdeaadcbbedadeabdaceceaebaeebddbeeaecbdceebcdaaebcaaabeeedcdeebeaecabacedaaccceebdaeeeeeeedbeecddbdcecdeaabceabdbeebedadedeaddccdaaebebdddcddaeaeadbdadaebcbdcdedbdecbcecbdcdebcedcaabdcbacbacbdbcdbedeaeccaebcbdcbceeaecbaedbbecdabedcdadecaaecbaadddebbdebbdbcdbbccacaeedbaadcaddcbbcecbdeeccbdadbeebeadcdbeacdeccdcabeddababcdebddadeebbddcaaeabdebabacebeebdcbdbcddaeededcbbcccbcaeaeaeadcccdecddeedecbaccccabdeeadadeacddddbcceaaccedbedbcbdbacdaaedbceabbeebddedcdbcdbacbcdddeaaceadabcbceebeebaecebccbbcdbcaeaebeabadababbaddeaecaaaebbbcceeadedceddddbadeadddddabcbdcbedaacdebecedaddbcbdedcbceacdbdcdcabbccecdcccebcaabaeadaaebdcdeddbcbaeecbeaddbacdadacaecdeddcbbaeceeeadbbbabbaedbedabeeedecdecdaaebebcecdeebcbabeadcbeabaecebeacbebedcadbdbabccceddcceddeaecdaaadedbeedadceadbdabcceaebdbcccaaadddbdabbddcabbbecbaabdadddbbddbcdecadcdaeaabcdbccaebceebcbcdbaeeceadaecabddbdaebddeadddcdcddbacedcccacacdabcaebebbbcaaccbeddbbebebedeaeaacbaecccccacdbbcbddedcebabbadccbbcbbcaeedadabeecdbaaeaabdbbaebdbdedadbaeaebacdadddbcccbdacaabdcacadeabbbbdddacdddaaececdedcbacdcdaaeacaaaedeaaabedccccbbcacaccaddecadeebeeabcddeeccbdeaeedceaecceaacbcedacadbbeaccedabadceacdbcedacaecbbbcacdabaeeddcbabdaeccdadedacddeadcecbbaaacdacdecddadaaccebbbcdddbceaaddceaacaddaaddcecddcaecbcaecdcbcebabeeeebdbdaceebccdaabbecdccbeebeaeeadbcabadbeeecaeabdbebbcacbceedbcabeebecccaacdaccaedbaaabecaeeaeabeacdbbcaccecaedecccacdcddbedeaecadeaacaeaaedeabadccceccdbaccdeedbacaebabdadbdaebbcecdaeccaadedeadddeaddabedccabeabdbbeeeaeadcbbeeeadcaadccccacbbdeecddceaaceedcbbdecdbaebbacbccdedadceecedcdaaeccabeecebedbabeeedddbceceddbebaedaaacdbddccebecbeebdcededcbedbebedebbcbdcacaeaeceeaddccebbabeeaaeaeaebeccdbbbadacadaaeebdceaeadabeadbaaeeaeabdbbacaaeabeabeabcadeacdabcadaabeebddbcbecedbaccdcccaaddaccedccbaceabbcdeedeaaaaeecacdcaddeacaabdbadabcdeaededdbacdeaccabdaaceecbcececbdcaaaededcdaabccaccacedaddbddaedcceedcbacaccaecececbabecbbdbceabbaeeadcbcaeeecbaccececacbacdbbccccadcbadcecdbacbccaccabbcdaeadecdecbdbbbaadacccedbdeddaedcdecabcbeecbcacdccebaedcddeeddadeebcedbedabbcdcadcdaebcaddeadddaabbbadddebeadbcdedacbacdbdbbadcacbcaccdceecacabaabaadbbcccbddcbeebaedcdcedccebadbaeadabbedbdeecaecaadcbbadebdebedeacbeceebeadbccdbcbeeabbcadedbeddccdbecccbadcebdccabcbedbbeabdacadabedabdcecbeaddebdccdaabddcdbdceabaaeaabbadcceacdabcbcddecbbdeeeddccebbeaebdcedbcbcddcdcbdaecbabaabccedeebcbdcdedadbbcaeacaddcaecccbbcceacebabadcddebedadbebedcbacdeeeedabdeccdabeecaccbddddbcadbeabeebacbcedaabadeccdedacabcccacedeadddaeadecddbdacebdabdceacebccceadedcdbeadabbbacbbaadddcbedcaccedccbdbbccdcacdedcdadcdaeeeaeeadbadaabcadaeceedbacaebbadaecbdeeebacbbcecebacadceebebcbabbbddeacaedeaebeeaddbdbcdbebdecdbbeccdaeacaccdeebbbecbddecadbecccacaaecaeaaddeaacbabebbcedeeddbeedcdeeeeeeccaebdeaaddbadbcbbcdadddbedcaecdbadebcaedcabadecabdaecebeedaeecbaecccadbbdddccabedacabdabaedcbcbbcbddaccbcccbeecdcaaeeadddcdbaddebcdebeadcaeaeabecbcabebcabcededccbeedbabbccaebeaaaaaecdeadddddebecdceacbcdbdcadadeceabedcddababdbebdaacecedddaaedbeeadaedbcaccbcdcceeceecacbdeddecdbecaaabddadacbabceaacbdabcedeaccecebbbcbaddcacaebebacccabdcedaacadcecedcaeaeccdadebabedddceadeeeacbcdebcbabeecbbbdeeddbedeaaeceadeccedacacebddccaeaecbaceceebeccdadcdacacadeddeedddadadecbabdeeaaccbacbcbacdccdcaadbacdeaddcacaaaeedebbeaacbceeabbadeebaccacccbebbcbddddadaecdaeadcdcdadbcaddabaabcedadecdadbddbdbbccabcaaadcabcdacababccececcbbccdcdaeadabbbeeceeaedbedecbceaecbebdddddaedbdbdcdaceadecbecaadcaddeeedeaaddddbccbabbddcacacaddbacabaecedceacbccedcbcbcaadacebeedcadcdaecdbdbecbeaceeddacbbdecddaacebccabeabedaddebdadebadedcbdbadcaaeaddbbcedcebdaebcceaaaabdadcabdebbdabaebabbceedeccceacdddcccdbccebeabccddccaaabeabedbabdcadaeaaebbbdccedeeadabadeccceeeeececebcddcedeabedaeeadbebddcbacabacedbaacddcbebebaccaaebabcbccdcacbcbdbbbaacebadcedccedbacbecedaaaedcaaedebcaacaadaacadabdbdbacbdccbbcbeceddcbbeadacacaeecbcaebbddbeeacceeebeecabeaaccbeceecdadbeccbdaacabddbddeacdebbdeceaeaedcecaaaedbadeccbeadcecedabbcabbbeacbceebdabaaeabdecededcebbebeeebabebcceddadacdaedeabbdcdbdcdaedaaadaeaacdcccbaabaacacdceeebdaaeebcebdebacebbedeaeebcbddaedabccbaaccbeddbaccdeddeeeabcabcbbbceacdbadedeeecabbcabaacbcebadaabdcdcedbaaccbdbdedccececececbcaddbdaadbdcbcababbdbaaaaedcbcedabbaadcbeccbcdbedadebcedecbbccdbacccdaaacbdccccdbcbdbaeddeabddacddedcbabdcacddacdbdebddecbbcdadccdaedbaadedbdebabbdaabebdbdaeaceeccabbbcaddaeadbcabecddbdceeabbcceceabaeabbabeadcebcaebaabadcdcabeecaebcdcedbdaeebdaaeaebbbbceaadcaddcccaacbdaabdbeebaacdadddecbebdeadbcbeccbbacbbbbbecedccecbbdaecdceaccbecaecbaedeecddecccdebeeabaedbdedbebddadbcadecbccdaabdaebecabdececdebccedabbdecaabeedbceabcedeeebedadeccaeeaddceaaecddcbaaccdbbeabbdedeabadeeeeeaebdabadecbdabbabbbbbeccadacdadbcbcbbdbdddeacecdecbaaecbbbcddbeadebcaebeccacaedacbaadacddbeeaaeacbeaddedbeaabdabdddbcdebbccbcbbbbdbcbecceccccbabeccaaaaeadedadaabacdbcadcceaccdbceabbecdebeeecbdceaaaeedceddcaaeebbddbddbaecdebddcadadabcbcdbdcedbeecabbcccedaebebebeeacdedcebeebdaeccdeceacceaaadadaadbbdbabcbdaeccbebdaedaabdecdabccbabdadeceeaeebaeeaaeeeaddadaedcedebcbabedeeaccedaadaccdcaabcbdeecaddceccbacccbcccedaeebcedcebdabaeedaabdcbdcadacceaabadbdebeebdeecbeecbbdaaccdebbacdacdcbacbdecdbcbddcbeddecccdcdeccecabebdecccaaebeeeceaddebeaaeadecabdabeaeedcceaaaeadecdcccbceacabaebebdaccadeddbbecccceaabaeaeddeabeaebbdbdababaeebeeebccaeedcbcccababeebcdeeabdecbcecdeaceddcbdbbbacbcdcaaabcdaaaccbdeceebadebdbaeedbdabbedbdbccaaacdcbbeccbdbabdbceebeeebddbbceddaecacddebacaebadeeddeddcbaceeeacaaacdeacddbeabdddecebccecacdbdabeabbbeedbdadacdeeeccceeabbbdedbdddecbddbecaeaccbababbdceaaebbdbceabcbceccbdbcccabddddddebddbbacdecadceaabddccaaeddecbcbebeebdacadcabdddbdacaacaecdcaeeaeeabdcbceaedcccaebeddbbcdaedcedccdeabbadaeeedddabddeaacbadbcabacacebabacecdbdbeabcaeacdabceedbcabbabdaedeeeddeebeddedcceeecebdaaddbadedbbeddeeabbbcedbdabbbadeacecbaccbdcedeabdccebebadcbcdbdaaabddddbeeececaccececaccbdcbddbccdcadedacbebedcceadcaaabcdeadeccdadbbcecbaeeddadcbecebabcaaebddcbdedbebaeebacdaabcadaaccdeebbbaacdebecedcdbbbababbeecdcbeadabeddbededacbaceabdbcaddbeedceebbcebcccbbdcbcdceeeedeaacbccebcaaaadebbaedcdceaaedbaceccddbaecabcdbedccaeeebacabdbbdedaccdecbaaeaceeccebabdaaebcbecabcddacebacbbecbddbecdeacadaadceceecebeabaeccaeaeabcecbdcceecbececbbdceecbeeabbaadeddecedbbddcaeabadabbceadcbcaeeaccdcededcabedeabcdedcedabecaeaaaecdabbebdbeddcbeabebbabeceaaaceeadccaaeededabbaecccdaabbeccacedcadbdcdbdaaecccdcdeaddaddeebecacaeaccddbbaccbdabeccdecabdecaaebbbabdcaadeeadcccdddeaedebdbdcbeccdacdabeacbedeeaacddcdabaeeababbebbcdcaeeeeecedbecacccabbedebccdddcebccdaddbecaedbaeeedaaaedddeabacbcadacacbbabcbeedbaccdabeedaacbbadddcadddaabbebcddcbdbeacddaeccedccdbbdbbdcedeebeacdaeedaadeabcabbbcdbdaaaeddcbabaceadcdeddcdedcabdbacbeaacdbbdddeaaedebdabadebceaeaeacccbddbecbcadedcdcddddcbeccdbbacbeaabddacadaaceaccbdeeecddeaebecccbcabdeabbbeadacaebbbcaddbeeeedabebdddaaaedbcadebddabadebecbeabbdaaddabcabdebcbadbdbddcacbebcaacbabaacbbbaeacddbbbddceaaadcedecaccddeededbaaeadbabeabdceaecabbaaeabdcbbbaeedabbaebcdbbbdcebbceaddcabcaeabddcbaedaeabceeacddbdecabcedccddceacedaaaadaebcccbbebdeededbcedeadcdacadddbbbbeaddadcdbadbebbdbddbeaeacdbaebdceaacbabbacdecbdbdcbacededeadeebdecaccbeacaacabbbadcaedbddbcecccdeadaccdaebcaedcdeabdddcdededbcdebeebbdacbebbeaedeaceeabbbddcecebabcedbedbdabeebbecdceedecacdbeacdbbbbebbbceecdaebbdbdadbcacdadeddabdcdcaddcebebcecaeeacaeedbccbbcbdadbecdebaccecddecadececdcedacccbddeedcebbedcbadeadcdecadccbcabeebdedcdedabbcdecabadbedcccbdebabdcebcbbdbaddecacdcccdbeecacecedbebcececcdeeeadcbbceecbbdccccedbcecadabbacbbebabebebeeaccdeebbecadbeadcbcccbdcaeacededbbcacabadccacacbdedabcdaecaddabaaecaacadcaecaceacdabaebaaccceeeebaadbadabddbbdccedaecdedddcaebcbeaecaecbaacdaceecedcedbbcbabbaabbdadaaaccdbdeabbadaaeabdcdcbbccbabbeacabedebdaededbbceccddbaaddeececeaeaadbcadedbbaeadeacdeaabaebabcecbaaeacceaeabdbbdbacbbadadcbcadccaeceadcaececaaeaaaccaebabbdbbbddbaebeaaedbeedacebebcdcecceddccedcbaedbcdeabdbebeebdeecedcdcccaccdcbedcecaccadaecacaaeeadbcabcbbecbaacdbbadccecedabadadbdbacaabedacbabbaaadacbceeabdabbeaaaaceccdcebabcaceeaecbacdbcadecccdedeeccccdeabcdbdcaadccabcacecbbbdcaadceeababeaeccaeabddcadcddcabcebdbecaceebeeddbdebcbabcebbdaaeacbdecdbdcbdecdccadcbedbbdbaedeccdddaebcaecddbbebdedddbadabaeaacddbababbcddcdbaeeebdedaaebdaeadeadadcabdcecddcdbaaadbcacceddbbabcdcbdabcacccdacaeacbbebbbcdeececbceaeeedcbdadabddbebdbddcadeecdcaaeaadabccbcaeaceabebcadeadcbacebaddcbaccdeabbbdddeaabdeaebcacceecdbeddabecbbbdacbdbebabecdbdcaadbeeceacadcbbeaceadeaaeeaeacabeeabceabcdcbebecedadbccdebdbdcddcecdceaddebcceedaaebaaabebebcaebbddceeeadacbbabcdacbdebeccabaeebcddbadebcdaccbddacbeddcccaaacaabddcceebccdccdaaeacbcbedcaadcaecdbebdceaadaaccbebbdcdbdbebbdacadccdbdbabeaeddecacceaddccdedecdeedcdbedaeecbbddaacaceaecabccdbacebcecdecbcdebbadbcdddaadebedabbcabadecebedeacababeadbbdbedeeaededeecacbadeeaabbdeeadebbdaadacbeacbcadecbbbbccaddedecabedddedbabbaacaccbddcbacacaaddcbcdacbadbdeebdaeaebbabbcbacbdbdbeeddecaaaaeeccccdcbaaedacebbacbadeddedbbaeccaddeaccbeeebaadbdbaeacbcecddcccabaeebddebddebeeccddbabedbdbdeeabbcdadabdddabeadddbcebaededdbaeeaaaacdbaaaacceedacedeacccdeadaacbbdbecedbaacbdeaaaddbeceddcdeeecbdeddecddceaaaaddddcaabccedaddceabbcbdaaedcdbddecdaebcbdcaacadecbeddadbdbcbdbcbdcbeddabaaeceedeeecacaaadbaabcdeccbadbedcbbbdbbdebbdeabbacabcaebbaccecabcededcdcdeebecadcbdbadadcddbbecbdccbbcdadacdabdddbbcbabcccbadadcdddcbdcedbebaecbcdeeeabbdcdacababbdaadebadccdeaecbaddddcaacbeeddedcbcbccadedcaeddedcaadcdaecdbaddacccdebccacaebcadeebebddbdeeadeaedbeebcddcabacdaeaeebaebacddebcbabaecbcbbdcaecacbdebdabeacadeeacabedccebcdbdbdccbdbceabaeeecacdbaeebdaadadabbcbeabcbceadbddecbabacaeaeabbecbeebdeaeabaeaaadeadaaccbdeaadcdbebcadadebbccdacebadebddaaeaadaddbeceebebeaabeacaacaeabcccbbeabbcbedebecaecdddcdeeddbaccdacbeeaaacceaadeeccdbddaebeecaacbedadcedcdacdddbdddccdaecdcdbdeccedaedeecaaeebbdaaaedbadcbbdeeecacaeeeaeaccbaccbdaabaabdbbabbaededacadbaccdaadcbaeebaeaeeadeeeddbbbbaeadbeeedeeeaeeeccabdedcbdddecddacadcbaddbacbebcadcdcedacaccddaaeaaaddbbaeadeacaeaddacddaaacceabbcdebbbedaeacdcbdcdaaebaeccacacdeaacebcaeadbaabecaaaaeaecddeabeddbacddedacadacdcdbaacdcaaebaaeeeddacabbabcccecbcdeeaabdeeaeebbdbaebaebbeddeeeaccacaccbabdacbabbdeddcadbccceebebecddddcbeaedaaaedbcaeeadadbdbcadcabdaedebbccdccaebabbecabadcdcbbdadddbdeebdedcadcdddceebdabcaadacbaacaaeabebeecbcceeaaaeaebbaeceeccceaccdaeaecccadbcddeeeacabacdbcdeeceacbceeebeadadebbeeeaaacdbdbdeabbccacaeceabcebdbcebeaebcdcecccaeaababeecebbebdbcedcdadcecaabcebeecdcdadecdadebdcbebeabceeadecbcaebebcdabacbcabaedcededcdacddcbccceeadbdccbaecabcbebcbabeeebbaabeedeeecbbadcedccddddacedbccbbcdeaecedccbadaeacccebeecbbdebdbdebebddeaceaadebcacbabdddcbcdbccadabdeeccabcecadedbdcddedbaddeacdccccdcdacbbeddacadbbdbacaddbbabacabdbadaedabceddaacceebaaacaecbdeecedadddeeecddaadeeaaacadbacdabaabbbbcddabbeebaeabceecdecbaebbbbbaeccdadbdebdabddeebcbabecccedddeecdebccdbcababdbaaaceadbbebdcabeabddacdcecccddeadeeaaaadbcbbabdeeaabcceecbceccaeaeecacaadadeccabebbeceedbeccdaecabacedabbcdbceeedebcecaddabcdaddeaebebcbedeaecebdbedbadcecbacbccccbdcecaebcabdecdacddbabcadeccacbccceeedeadabedddccaeeaadedadacdaadacbaaddebbddaddacabcadeeaccbbaebbecdbabaecabbaceacabbcbacecdbabaecbacbeebbedbcabbedebaacdabcdcdccbeceddcecdbbecbbbcacdaedbaedaccaacbeebacbabcdbabadecdacbabbdbcdccbecaaadaddbdeaccbdecbdbedbcdaaacbbceeeabeacededcabdeeeecacebbdeaabddcddbaecbcaaecbcdababedbbebbebbbbdecbabbbdaceceaccdacdddabbdcbbbbdbbeeceeeacceedeceecacdbdbbbbcecadcdaeeeacdaacbebeeeaeecccbdaaaaedbdceeccbdacbeeeadaecccacacaeabcdacbdeecbaccdaebaeebdacecceccbabeeeddbccadeeaaccccbdbdbecdbaeacbeaaadbbdadbaeeebeaaaeacabbadbadbeecedbacabecebcbbbdddbeadaabcdaaeceebecacbddccedcbdbacddaaacbcbdcceacceceecdcdadcdcdaadddaccdbcbacecddebeceadbaceabbbbaeaaaaddeceeedbeabddaebaadeaaacbdbaaecccddccccbdcbeeeeaebdcacbabdecdedccdabbdccdcbadaaaecacccaebeddaccdedcccbaabccddeddbeccbdbbbdcabbbeadcadadedebdaaaacedcdbddaedbdeaedbacbddecebeeadcdedaeddbecddededcedbaacaccddbaeecdabcbadbdeedadecbdbbaeebbdcdceaaeaeecbedcecdebdccdcceccaebdaabbdddeaddeabeebecaaddeeceaecceeaaecccbaadbecaeabebdbaddcccebebceceadbcbcedaaeaacedecaaaeaebadcdaadcdaebababdddddaeedbbcaddeacddecbbbaaedebabaabdededdeceabbddddebddebbcdbcbeeaeccdccbdcddccbdaeadaceddabbdbddceadbcebbdaceacadbbbcddaacbdcdaacdeeadbebdcdcaceaccaddecebbbbeaeabbddeccbedccdedbcceaeaababedccbbbdeccbbcaacbeebbdcaecdcddeabcbcdaebcababababaacccdbaccacbeddeeaabaaabdddabeacabebedbcdceaccdeceebcabadaaaaeccccddadeacebcaacacacdcadbeceabebabcdcdacbdaeeeeeacebbdceaeabecdddeadadeacbdabcbceccddeeccaedbbedeadabdaecdeedabeacabbdacdacbacabddcddcaaacdedeeacacaaabaaaedcbacdececbdadbdeacdeebdbcebaeeebbdbeeebcdccedaeaaeeebdaecbaaaeaadaecaccdeebebaddbddcddccadeaedeadabbdbceacbcdeaaceddeeabbcbbbeadedabcbcdedeeeeaecbedceeeadacdcabbdecbeedeedeecaecdebcaebbbabbaabeabddabcdbbeaaaaccabdddaccabdbbacadaaccedacaeaeedcccbeaadbdddbaddbaecdddeabdaadaebaedbdbaabaeecabeeacaadddccccaeceecaacebedbcccacecaebecbebeebbdcbcdbaeaacbdbedaaabdcabbddabcedbaeebbebcedbeacdeebdaaabdebbeaddccaceddbcabababccecbddceeedaacdabcdacedebccabcbddceadeecaaeaaeeeacedebaddccadebacadcacbccdedddeeecdcbedbadaedeabeaccbbeacabbeaecbaabeaabaedeeeecddaaaeccdebcedabedcbceddbaeacdaeeccaccaceaadbcbadbdeedeeabeccedaaaeeccbccbccceddaddddaaacbbcabadccdbbccebecedcadadbcebeaaadcdedacbbabcccbcbaceecbdecbababeeebceccecaabddbbabccabcececbaecaadcadddcdcdddebeecedeccdddccdcaeddceecbcbbdacaadacadddaadbaeaeaaebdcadadbacdcedccedabbbedbcddeeeaaceecebbbedebbcacdcbcedacbaccbebbeeecdeadcabadabeacbbacababccacbcaadcecaeabbbaebaebcabedcdeaecebecbdccbcdddddcedceedbcdeeeaebadacdebeaeecbdaaddabeecdacecacbddcedcabdbdbddbeeadeccaddeadecaeedcddccebddaebdddebadeaeabaeebacbcdeaddbdcddeceaddccbcbaecdedddeacabdacdeebdeabcdcdebeecaabdcdececaadaeeabacabcaaeeacedebaedabaabddbdbaccadecbbdbecadebebcabdecdeaecbbcdbadeeedbeaccbedbddabaedaedecedccbedebaaaeebdbccdbecebeabaacaddaeecdaacadbeebcaccecebbacdbdedddddbcadbddebbabecdbdaedcbddaeedadbddddcdceedeaacaebbedadededcadbcdceeceeaaacdbabbbebebbacbbebedbacbbcabdaccededcdbccbccecdbeddaebaaeddeacdacabeeacbacdacadcdcccbaabbaaddceabadacedaadcedcdadcdecbcadabaabbcecbebaeeeadecedaaebedaacccccbcedccacaacedceaddcdbcbbaacedacbdccbeecaabbededdbbaebddbddebaaebeebebbbdaeccccaaebadacdbdbbeaedcddacbeddaedcacbccdeebdbebdbbaadecdbabececebaceacdaabdaddaeedbdddabadaccbdaadebbdbcdaebecabbcbebdbaaaaecacacbdcceeabbddbbecaecddadcacdceebacaadeebbcdecbaebabbebccadbdbcbaedebdadadcbeacdccceeeecbecdddcdaeaeeaeeaecdeaccedeeedaaccccbbdcaaaacddabbdbcdedecacccaebeedabaedbebaabddbeabebaceadacbcaebbaccbdbcdccacecaadaccbadaccabadaceabebdbcebdcaeebaeedaccbbacebdcabeaedcdadbdbceccebecbdeeebbebcdbdcaebacbabecebeabdcbacbaeaebbddceaeeaddccdeeeedbbaadceeebdcddebbbebdbbedbcaadbacedccedccadcbcdbbdabcebcbabadbebacebbdaacddceaaeaccaedcdedaceeaaaecacdedbbbcccbaeadcbbdaebadaecdebdebbcdbdcbeceacdebedcbbcebebacdcbecbaaaddccedceeddcbdddbedbdcbabceeebdedccaecdecbcaaebbeeeadcaaecabadbcccaeaceadcddeebddbabedcbdddeebbbbbbcddbebaeebaaceedbdbedbcdcdddbeabadaeeedadccecdbaaccaeecbbdcccbdaaacccdeacbbccabbedcbdcaaddcbeaaaadecabbccaabeedbddecadbbbccacebbabcbabbcdaecacecdbbcbeebcabadbdeebebbcddbddcdecaadacedcdbedcbdeeddcdbcabaeedaabbaeeabaccecaadbacddacaeedcbbccaaaddccbcbbbbcbdaadeccddcceedeeaaceaddbbdddecccdaeddbbbccbbcdaadeaedbbceeddaadddcbcbedceecbebeccdbcaaabcbbbdbeeeeadcdddadbaaabebaecdcbddcddcecaaebddbbcabebccdeddabeaadbebaaebbecbbeddddacaeecacbadeecbdabeacdeebcccaacdceeedbaaeadadacaedcedcbcbdcbdddbaabeecccbddaaeaacbbdebecdcbedbaaebdabdcdaceeeccbbccbbbccbadcedeeacbededeeeeaeacbbbacdedcbcbccabbccdaabededbaedebacdedbeebedeabebddccbbedbcadebacdeddaebbcadbddacaebedbacaccabdeccccecdaeadcadbdabbbecbdbebacebeebdbedacbeecaacdeceeedeaaadcabeddacacdeecadaacdaedeaacaccdeaeeaeecbdbeaeceedbcbdddbebacacecabeabeeeeabebbadeceaacaecadbeddcdbcdceecdcabdeaacddbdccdcdbacdbbcadeccbeedbaddddccaeceaacccbdbdacaeddabcdabadbcdacdaaeacdeaacedbdaadbbbbcdedccadbeeaaedbccccbabdaddabcddeaebaeacdcdaedaedebebdbdabcddcdabdeeeccdcabddaaaeaeaacddceaecdedceeebdcabadbdbcbabbeaedbbeaccccbaadaccaaaacacbcaeccdddcacbaeaddedabbedccdcebabbcdbaedbbebadecbaaceeacbbebdebabcababeedbcecbebcaadbeeddbedabeeccbccabedcaedabddeebdbacdcbbeaebedadcedbcbdaacececbcbcebbbceeebbdbdbbeaaceaaededeacdbcbccdbaeacedcbbbcbdacedeeeecaeeeddcaebcbadbeacebdaabdcaccdaeecaccecbeebccdcbdbdecdbcceaeecbedbeccdbecccbbcdbeeeeaacdeedcdbedaedbeddadecaccdecaecadaebaddaebcdcdcbeaaeebdebaaeaccaababbddaacabaedbededeecbadacccaebeddcaabbdbacebbecdbcaedcedbaddabbceabbecaebaaeadedadabcaccdabdaddebecadbcbadcedabccdaebeacedcabadcecaeadeccbbaabebaedeedaedeaaeededacaeebabbedcaccbbccbccebbdaacaedccadadebdebeabcacdaeecbecedbedbbeaeadcaaceccecbeebcbcededcbcdadadadaabbbbdbaacccebdbdadecaccecedbdaceaedceaedecebdadedbaabbbdeebceebcaaaeeeaeecdaedacecdeaeccedbbdcbedbdedacdcdaaaadadeccbaadaeeccaacedcbbccbbbabeededdeedaeeccdbbbacdddaddbbcbeadadaececbbabebadeaaaabdecbbeadcbaeadabdcabcabeaccbabcdcecadeddbbcbcdeeaeeadbebdaaeacadcacadbaccaacaeabebabaecbdedbaaadbcdceedbcadcbaaeedcebaeeeabbccaddbaacececbbaacebacecaeebdabcedbabbedaebaeaeeecbcdabcdaacacaccbdeccbabaaedbabaeaecbebdabaacdecaeeeccdeabbccccedecabaecbaaebbbcdcbceaeabeecebeedbbdbddcdeddeacbbacaeaeadbdcbeccaaabcdbcecebabddeeddbeebbcaedeccdaebcdcaaceedddbbeddbabdceadbecbaedddeedaaeccdacecedaaacdedbabddabcededcbcbeedaeabdebbcccbbaebebebcccdbdccdceebcbdddebcebbcaabccebadcccdbedaceababdbacccccecadbcceccdaadcbcbeabdaecccccdbaeecabedacebaaaeacbeaddbdbaabddccedaaabceadadeecedebdbeccacdceccedeeebbabbadbeadbddacbeecbcaaeaedeccbeacabaebabedebdebdbcedcdbdeddecbeddddcbcbabacaacedcecebceaecbededcdccaebbedddeebaeccaaceaaeddeabeebbdbeeeaebdedcbaadbabdebbcedddcceeceebbecebaaacecbdebcabbbdeeaccdeeeabceeaedbeebdabacabaaabeeabecdcdcacccababcbbddecddbccececacecdaebbebadeeadbaadecdbceebdadcebaeeeeadcccacabbbcebbeddeaabdcacaeedbaceaaadbceaebdbcdbeebceecddedadbceeceeecacadbcbebdebbbcecbdbdebdcbabdcaadcaaaebeebecadbecbcaadcbcbeeaedabccedaacbcbdaaaeddebedbceabbdcebbdbbaaebceabacebedccbdccbcdabecbcbaebbebabddebaebabdecddbbbaceccbaaebeebaebcbdeeabcbedcbecdaceabbcaecabbabadeeceecbeaeaeceedacadebdecbbbcdcdbededbddddabeadaaddcebdedcceedbcbaeadabeededdbdbddbeddebabceccbdacadeebbabddabedceaaedcbdeabccbeeeedcaededdeddbeaaeacbbcbbacbadcaabeedbbcdebcebedbcebeedcdedbbcbdddbdcdededeeedacbebaaaaaaddeeadbaeabdceaeabaaaddecdedeeaccacdabbebddebbadbcebaccdbcedbdbcccbaaeecbbbbeedebcaaacdeabcdaaaaedeeadeeabcdabecbcbadddddadcecbdcdaeaecddeecddecbcabbdbeedbccbaaaaddbebdeeadedbebbcddbdcbcebaceabebbbaacbccabdbcaeccabbadbeecdacdbdebcacdeeeccebbaeceadaaadebdcaebdbcdbbddceaebcbbedaeaeabeadbbcbabdadcaeddcbceeddacbcdbadbeedecedceebcddaeeaabdbcccbeddeebebacabccbabcdadccccebaceadcdbcccddbeedcceaddeddecccebeecedccebcbbbdadeedbecccdaadcaabebedcbbceeaebebccadebdcbddeebbaeaedddabedbdcccedddcaedccaecededbadbdacdbabacbbbddbddccedbbecccdbdcbbdebaedccebebecbcdacbcddbababccbccbecdadbecbcdcacccabeeaeeaaebdcbaaeceeceeaceeecbdabdaaabdeddedddbbcbdabeddcccababbddaddcebeceddbacaabaeaedddeabdeacdabdebaceecacdeeeeeabebbbcbdbbedcbaaccabebcedaebebceeebacabaacaaaedabedaeddbcededcacadadcaddabddeabeaaeecbcdccbbaccbbbaddbbceeedccebebdbebbbaeedebabdedddeaadecbcecddbbabdeddbbbcbecaadacabebaacaddddeeecadaeabcdaddcecacbcaeabcbaabbbbeadeddcadceabadcbacbdcdbbbbeededbbddebacbceccbcebaedcecbdceedbdeecdbcdecaedcbdddadcdadacdbcedadddaedceddaceecaedbbbcccaabddacecedbeddbdcaeacacddddbcaecabcabdeadaccadcaeaceaeacbacaebeababbeedbabcaeaaedbeebdbcdeacddcaddccadebcaeaccdebbadecdadbbbbdbdbdcdcbdcabbeceeebbceadcccccbeaedaaaabeceeeacaaceebaaaccedbbedacbdbacaeccaccecbbeaebcaabadadcdacecaacdddbdbebeeaeeeaddaccebcedceeccdabdaecdaebdaabcdceecbdecedddccbeaeaaeeaceedcacbedcabccaaeebdebaebcacbeacccceceddcbcaadedbbdabdbaeabccacdeaadeaaebaeebccaeaebccecceeaeceadddcacdcdcbadbeabcdeeeadddeedebaaedddbadacbeeadccdddbdbdabaeacdadadcbaabdcdbadcaebcdddabccceacdeedeebeebcaebdddeeacebbdaedbedeaedbecadbaddadccdedeaebeadbcddbcdacdaaeaabadcecbdddebecbbbebebdaaedacddeddabcaeebabecabcccbaeabdabccbbaeeddeaddbceeccecbeccbebdadcbeabebeaacacbcbdabecececadacacaeaccdbbeddcdcddbecaeebcbabcdeadcddddeabdbaecbceacccadccaceaebecddedeccbebdaccbbbdcbdcdaddbbacbccaccaaebbdeaeebbcacaddacabbbcedaedbdaaadabaedbcaedcedcaeaecaabeebaeedeaceaaaeaceeecbeaabeaebaddceebcbcedbdbeedaddabbbcbabdabcabcedeaaabeeacecddbbaaddbdaaabdacadbdceeabccaeeebccbecddbeeceabbaacddbbacbbaedbccceabacdeadcecabbccebaecdacddbdaaabcacbacbcdeabbbacbbdcdaeaedbdddceebccbcebecaeabbbcdddadcbacbaabeecebadccecaacbaecedabebcdcacebcceeeacbaebbccabdccbdacaaebddcbabeccdaeadeeaaddcadccccadbbdaaaeccbedbaccaeaecbbbaadebcaecbeaacabebaedbdeecccdaeabcededbabeecceabbabeaeaebaadddaabceaeaedbbdccddabdddeccdcacdaabcdeadbcdaceabcccabbeecdedcbbbeedccdbdbcabbbbecdadeecabcbdebccabcdeeaaeddaeeebaabbebaccbbaedbabecddbeeaedbbebcbdaebbeebbceaabcbbecaacceecbdebcaebcacaeccdaedacdcdcceeebadeeaeceadadadbcdaebeeedebedcddadbaadbcaccabbcdcdecacbeeeeeacaedccabaddbaedbcceedaebaeaacacadcaababeddaccdeabbabecececaaaeaceddedeabebabaeedccbbaeaccadcccccbedaabcacbbaeaebcadbcaecaccceabbedaabeaebaeaaedeaadaaebccbbaddcbcccdeaebaebbaddaebbbecdecabaebadbbabcaccdbabdebccdcabcdedccebceeedcbdcedbbabcaabbbaeebbdccebcdebccedebdbdabdbaabaeabdcddadddabecbabedbaaacbeaaceeeebaaabdcdcdeddcedabedabeaacbdddecadaadccaddbbccaabbcaaaedabaadabaaaccedaacabeaabaeabbdadbbcceecbebadcacaebcdaedaabeeaddcdeaebdaadcbebdabbbebdadbeaaeddeaeccedbcdcebeaecabbdeeebddbdcbbdcacebcdacebabbecdccecbbedbedcbbcbdbbbdabccaeaaeccebcccbdbdcebcadcecebebddacaeacacbbbddcabeaadaaadaddabccbaaddaeeddbeeebbccabdbeecebbccbbdbaceabcdbeceeeddcaedbbcadcececebadcaeaabddaaecabaaacdedacdeaeddeebadbccccdcdbdeadcdcceebccbebeeddbdecadbbacbaacdbebadcdcadcadcbeaadcbbdaacacaaabdedebbcbebacaaecacbcbadeeddeebaecaeaecabaeeccadddcbaaaebbcaacecaccadaebceccdaacaddebbdebcbdbbeceaebcdeacbcbcdbaeeeedcebdbeeacedbbaebcdaeaecadbaeccbdccedccaaddcbdeaaceeebdcdcbecbaeabbaacaacccadeaccebdaaaddbcdceedcceddccbccabdcdddaebabbddedeabdddccacbcacbcaaedbdeddaacecaedcdeecaddaadeaaaaedaeaacaeeaecbbdbcbeacebeddbeadacbcedeebcdbbeaceadadcadecdaeecddcadbadeacaabdcabedabacaadeaaaaaaabbbcecaeadbdbbeebbeeeacadabaabdbeeaedececdddcdcdeecebddbebdcebdddbabebdddbbdeaacebabedcbbceabddccecaeddeeecbbaedcceadadadebcbbcaccaceddecceadaeebcacdcdcbeccdcccdccbddbaadcacacabaacaedacedbaaecdadbabaddadbcccbbacaacedccecaaaeecbecebcabedaededaededcddcecdcbeeeeddbabeddbebbcacdbcccccddcabecbcdaaebdcddbddcceebdddebbaedbbcbcdecceaadedbeaededebeabceebadedecccaddecbbcecccdeecbbecddcbabaddbccedcacdeabbacedcbabeaabeeeeeeedaecbcdaedacbaddbebccdbeabcdcadacbdedcbeecabcadaaadaaeacbeceebbddedacdddedababaeaaebeacdadcebadbeeabdbceacecbdbebdaacbdcbdcbeacedaddabdccaaddecadccedccecabbdeeecdacdbebabdddacdcaabbdcaaddeecbeccddaecdbcbbdadaaeedadeeccaaabdedededeccdebabdebbbdaabaddeaacddeecdbdeededeeeaeccdcebceeabaceceabaaacedbcdeaebbdeaedcbddceabeadaadeceaabcedadbbdccabaedaedaccbdeabacbcccebeeaedcdecadbbabeaaebbdbaaccacbaeebacbbedacbeeeaaebeedabbeecccbaacbdaceeebbbecababedccdcdbcbeeddcbeacabdbadecceedeacbcaaeceeebceebddeeecabeaaeecebbcbaeaceeaecdbdcedbdabbdbcacececebddbdeacacdbbaaacdddaccddabeaeddcdaeceadbececbacdeeabdeebabcadecdbacadeeabaaedccdbaddabbbaceaaacccbedaecbaaabecdbebedaedecdbbdcccccbacdaadccebdacedacedaabacdbceeccebcaceaededdabeaddcaddebdbbebcedaaacbadacbadbdbdabcedadcbceccbbeabbaadbceaaaeedaacdbadabbcdabcebbbcddbedabdcbdbcceeacbbdadcceabbbcbeeedbbaebeacadccadbebaccaeacbdcbaaddbbbbaebdeaabbbdeeaeddcdcebdcbcbedbeccaddcaadcedcacabebabadebacbebeecabdcaebadedabdcdbcbdcdabeaacbaeaecbdcbabaebdbeecccecbeebdecbabeccedebedcadaebdeddaaabdbceaecedcccaabcdcabcaedcbeddadceeabddadcddeecacaaacaabbcdcccbdbaccacaaeabedcccbdebbddbdabbaedcaebcebebeeeaadeeaaebdebeadbcdedcdeadeecacbaaeeaebedeebaeebbbecedcecdccaaeaabcbaeeddeabcddcbeacdbbaaeaecdcdacaedcacedbedeeeccbcabeaaabbcaadedabaeddaedceaadaeddaabaabbacccabcaddcaabecdcdaebcddceeeaedacdaddcaeadeeedceacaccdddeaaeccaaceacedebdabeeacedccdedaebaadebeacdddccdbbecccbeedbbeebedbcbdcadededaeddadaabddaeabeecddbcbbadeecbdbcddbbdaeccaedbddaaeddbaccbacceecbaadcaaeeabcdabdcacbacaacecaeddaadcaecbcaaceacbeaddcadbddeeaeeaecedbebdeedbebccaacdbbbdbcecebdadadbbdacaeaacabbcacddccddceeddbaaaacdaeeacebcdaddabaddadbadebeeedccaedebaaecdececcdaaddebeceabecbbccaecbdbeabdababdcdceebdecdabcbadcececdaabadeebedccdbcebbdaceecdcccabeeeaececddeaccbdebeaccaabdbccaeadccbdbbbedbbdbcecbdeccbbdcccbebabebaccecabbeceaeddecbbdceacededabaeadeaaeabdbaaecebeeebdacdcaebbaabbeedddaedeaabedaaaccdaadcbceccddaceeeacbeceaeeedbdddbccbbdaeabeeddeedebbbddeacccbacabbdcecaddacdadeeeddbecaccdcadddbaeeaedbbccaceccdcacdacceeeeabcddccdbdcbcebcdaeedbdbbdeaeedbbbccdccdccdedaddadbbaddcddbcbabbecaedadbbacabaeddcdbbadaecadabcddeecceccedceabeabddcbcabdadcecdadbcaddbaeadaeaabccaacccebddaceabcdacdaccceedcaccbbabdcdeceecddbdeeeebbeebbdcaabbcdecbbdebabdeccccbcebeaddacdceeceacbcccedbdbbddcceeceadcebaaddeebeabeaabecbeacdecbaedaaebbadeccaecaeeabcacdaaebbeacccabdacbdbabedbbacaabecabdbedddeaccdbacaecbadcdbaeeecbbedadbeaadaedcdbabedcdbdcadaebcaedcccbdbeaccceaddbcadaecbdababaeeabccdeccdceaaebaadadabceedcbececdcacbdecbccbcdcbeaecedcbdbeacdbaabbbdecbdebddceebbaccddecdcadadeceaeeaeaccbcddaebddccbdbaddceaeaebbecbaeecadaddcedddaaddedaaabadeeeaaeaccddbaacabccaaadcebeceaaccdeaabebaabdbeebbaacbbcbdecbcdaecbbdceaeeeeeeddacdeedcebaecbccbecacbbbbdadcbedcbbaadadccbcbccbabcdbdddddaebaebedebcacaaeeeeedadecbeabacdadaddeddbeabaecbdeaeddaaebcabbcaedaabaaaddeeacebcbdbcbcaeaacecaeebcbdeaecbabccedecaaaeddaeeebeebaadcacaedbeecdecaeeaaecaccabeddacebbddcbeeaaeeaecddbdeaaabebdbcedacabccebeadeebbbeebadaabcdceaebabbcebcbbaedacbdacababcaeaeabbaaaedcebcabdeeaebbcdbccbdbbdabceebeaacecacecbaecbacdeccbcaaadccecdebaaacecaadcedbceeeceacbaeaacdebadaedbebcbbcaaecadbbcdacddccbcbdbebccbcaabeacbddaeccbedbceddcebdbabdbeecbeebebaadddaaaceeabebcbbcedbcaabaceaeccceaedecbbbcbebbcadaccdecbceaeeceadeadbbaaadcbabbdcacaaecebccbdadbddcdabacccdeeeddadccdeddcacbdbcddeebdbdebbccdadaaaaccabcededcecbdeededccaccbdebeeeeaebedeabdcaeccaebaccbaabccacbdabaeadbdbdcbaabddaeebceedaebbdcdeeaabdbabcaaaaabcabebddcacbeadcdcabbcccbceededadccaaaacceccedcdbabdacdaeaaeeabeeacedbddeaeceeddddbbbbaabaccacbebcaadacdeecabdbbbbbbcedeadcdcbaddeedccaaaaebaddbbabacabeecbbaadcdbaccbbcadedddeabdbeeaedabaeedabddcdaaecbaabdbbdabebcaabdcbddedaacebbdddeaecbeceedceceadeddcacadbdabdaecedaeeabcdbedbededcecccdacbedcabaeaddeecacbecccdbebcaccdabebecacbecaabebadcacbaddcbbcdbbdcbcadebddaeddaccebdbcbcaaebdcaeedbdeebaccaaedbbbbddecdbbaedbeccabedecdbcedbcabddeddeeeacadbbbcddbaebbecbabebebaebcecaeabcceddebacdbbabbaeadadebcdceaadbdadbecadceceebaeedccdcacbadebcebcabaeacddbabbacbcbcbcaddbccaabcbdcaaceddadeadadaededadabbcececbceaedbeecdeeaddccbcddbaaceccebcbabdbbceeeceedbbdcbcdcedcaecaeaeebeabcbddcdeeceaebcdcdcbdcedacbddbebecbbaaeadbbebecbebbdaadacaeaecaadcdbcdbcaaabccababecaceebbeeabccabbbacaccdeecbcccecccaceededeacccbcdbadddaecabacbdadbeadacccccdecceaabeecaaacaebbccdbbdecdeacdbbbaadaeeadeeacaedbddbbbbaeeecadedbeaedaadaccecbeaeaebcdebaceadeddbaaebcbadadbbcacbdbdaebceecccbacdbaadcbccaaebbecadeeddbecedabebceaaeaebecddcdabeabeeaedbbababbbbbebacbbcceacbedaacddcecedbddaeecbaeeeabbcdcccaeabcbdaddacebeadddaeeeaeacaaddbeadadebbeddccdaaeedcaeeabbcaaedddcaabcbbedbcaecedabccdcbccecddddecbbbcceecdebabeadebdaceaebabaaacccbdebeaaaecaabdaadbbabeadecbbdeeabeaaccedcdeecdedeebdcaeabbbebeadeededbadcdddbadccadeecabbaadbbedaaeadeadaabacdedbbcdeabeecdeacdbbddcaeecbacbbecadbdcaedaaeeecdcbdbddecdeeecbdcbedbbdabdecceabbcaaaecbacabaeecddcebadaccbbdcadcaaccdcaedbeecbcbcbbcbcbebaaabdaacbcbeccaaaeaceccbeebadceaacbeebedccbcddacacdceebdeebcceecabbbddcdbbcadcedecbebebbcecabdaadebeebecabebecddbdcceddcbddcdbbdcdacabcdaecacaaaddedcebdeebdbdbcddedbddecebeaaacdccaaddeabdaaaccabbeccebdaadcecddbcaedddedcdcecaccabcccceaaddebacdccabcdceeeacbadbccecbcecbeabaaeecbceedbecbaccaccaeeeadbeecaeaedcdccdecadaaceecaeeaacdbacbddeebccddbcaedcacdcbbcebcdedccececdecaabccbdadaccbaedbaabecbcedadccbdeacdcaedccdecbecacaabdbabbaddcdabbbabdeaaebddacdcdbdcedcddaebdaaaabdeeccecceaccbbcdbbbaedabbcbcceccdbecbecbebdbecabebebaddaeaedecdcdebbcbcedccdceddbdaadcdbeabceebbbcaddaaabdaadcebecdeabbddbabbdbbeebadabddedeccbeaebbbbaabdbbeabacbedbecacdbccbcbbcdeadabdecebbdbaaadacbbcdbaecaabbcddbcbcbbbbaebdabaeccceadebcdbeaacbaebaeeaedadedbceabaaaabdddebaabbdeeadbeabccebbebeeebeaaadaaddcaeadcabaeedceaccebbbaaccedebccedebdeacbddebebbdedadbbdeaeeabcbdaaedbecdaedcceaeeaaaaecdaaabdbaadceeddbabacdeebdbcbeccbbcebdebdcbcaecdecdaccdeebbdbeeddddcceeeabadcaeedeaceadddaaeeaccbaaaacdcddddceeaeacacdeadcbbdbcaecdbbacbcbadebbdcdcbadeeebbbdcdbdddeecdebdeeebbdaddaadbcadaedaadddcbbbaabdecbebdaebeadceccbddbbbaebcdaaabdaceddecdbbacaeacceceaebbeccabbbeeadbeaaccbcaedeeacdceceedbcecbceaadecddcaadbbbcaceabdcabbbdbebeddacbadcecaaebcdadabddabdceacaddbcaecddacdedbabdccedceebbbbccadbdbcacccddbebcdedbeedabbbbdbeccdbbdeabdbbdbcaddddbccdaadcccbdbbcaedabdbdaaeeadabbeecdcddaeacaacbeebcaaeeebccdddecadbadadacacdcaaacecebbcedadabbcbabdaebeebbeaaeddeacdcadeadececdbdccbcadaededcabebadbbabceecaabaacaecaeceabceedceabceabedadabcaacbeeedaadceadceeabebdccacdaabdcccacbcbddadcbcebccaecadaaceeddeaaaeaedbabcaeaceededbcaddbbdacbaeecabddadcbdacceccacdbecaaddabecdaebaceccaebebcebbbcbbdbcdbbceaddbdbabbcbddcbbccacbbeeceadcedbbcababacdbdcbdbadeabaebecccbddecccabbdbacaaecbdcdbbecadaebcbdbbbaeccceebbaabcbbbeccaeadadecaccedaacacdcdcbcadaeedecedacdcbeeaabadaadcaeaceaebbdabbedbeedbeeeebaeabddeeeebedacaedabeceadedaabbedbaacccddcceeecaaaeaeadcbbbcaaeddedecbdedbbcceedacccdcbdccdbdcedbddccaccdabbaeadbaacdadeddbadebacecacbbabcaaaaabeedbabdbabdeeabecbeadceaaeccbdeaecbedccdcbdebaeaaceaadddbaebdecededabdbbddcceccdcdecbeedeebedcdcbeabdecaedebccacedeebbabcaaabcdbacdaaccbdaddbcededdbacbebccbaeabddccecbadbecacbbaedebabebbecebcabecbabbceccdbbdeccbecaaeecbdccedddccbeaededbadeadcacbdaddebaddaeecbbbededdcbceedaeecaacacebbebdbeddcacdeadaeadbbdddbacecaaeadbdddeceddbedabaccabacaddeadaccdaddddaeedaadedccbbcdceedbcbabeaebeecadbecbdcceaadeeddedccddeddeecebebcdaebbdaceedaeaedcbeeecbaddceaabececddceaeeebacbdbadacdbedbbbcbdabbabcbbbdcadabccbabcceebdcbaaedaaeecbdbabdacacbdceadabeaacbedcadeaebebeaeeeccdbdbabbbebbaadadebadedabeddbebdebbdecccccadccbcdbddecbdcaebddeeebbaadbebeadcabccbabeeaecedecddcdddaccacbceeeaadececeabaaceceaabcbbddacadacbbdebbddecdeceadabaadacbcbcecbaeddbddbaaebedebecdcbeecbbebebaebaeadccccaaddbacdbaeaecbddaecddeddeaeddcaddebbacaabeabaeadeaedddabebeccbdecdaabacacabceebcecadccdededcbdddccbaeedbaeebcbaccdaecbdcdebdebedceaeeeedcaeecaedacabddebedceaaebaeccdcaacdbaaaaccddbbbcbaecacdaaacbbcdcbccddccbeccadecdbdcccdededebaecebeceaeedcdbabcebbbebaceabcbbccdddeaacdeadbcaebbdceccbeebaeeaabadcaabedccacdabbdbebaecbcacaeecedecbeccabadaebccaeeeaebcebddcabbedbdeeeeaddacccaaeeeebbcbadccdeaeddcdebdbececdddabdebacaacbcecebcccecbbdbadcbeaadbcbdebdeaabedebbbadecdcebecdceddacdbcdbeecbabbbdcdccaebebcecbaabbdccadccbcaeeaeddeebbbdcddddbccdcbaccaedbbcaadbcecacddebbbebecccedceadacccdebaeaeaaecccdddbdcaebedebacbdbcbdbabdcdccddeeabebbbcaacebebcbcccaebbabdcadcbeddacbbdedeadebdbdedebcbcdbbdbddbacdbcdaebebdaecaaaaacddaceeeddccbebededaeedbbdbccdbacecbdaabcacbccccdbcaeedbcaaabadabccbdeddaacbbddbbeadcdcececebdeaaaacbabecadbbceecdabbbdeabaaebabbacecdaadbacbcdbdecbbeebdbabeaaabbaeaecbbeadeddcadbddabeedbbaeaccabbbbedceaadbcddbdcccaebbecdacdcddddccaceeaaeaebcccceeedbebbbddbaccaacddeaecccddacadeabebbebedcaaddabebeaadceaaccaaacaceaeacebcabdaaebaebdcddcaedcaacaabecadedbbcbccaaebdbdbeadcceebdadecbecabbaaaeacaadbeabeeddaacdaebccedebcccbbacbacdecedcecddbdedcbaadaebdcebbedccaecacebdbccdcaecacaedaaebbaddabdaeddadbcecbdbbaecadbebcebcdccaccaaeeeceeddadccaeabcaecadcacdaecbebebabddbaabaedbdaaabbbecdabcbbcaccecbdcebeedcbcdbaacbbbbacdbbacaceadababdacceddecebadabcacadbceececcecbaeccbdcbabaabbeacbcaaccbbbcaaeeacaccacedcecaaeaaccceaaecbecadcdeeedebbedaaeddcddecbbacbcbabcdbbaaedeaeaeaeccabcabaedbbdabcbcabaeceadaabaacbbacadaeaecddaceeddedabaddaabaddaaebdaccabdcebdcbdaabdeceddbbbedbedcdaaabccedcdddeeecbccbabbcabbdacbaddaedcdedcbbceebadccbbaddbadbdbaaedecccbdcbaacccaedbcadebccabdbccdaabbcaadecbeebacadddcaadabeaebaccdaebaeadeacbcececaaddeadbceaccaaaeecaadccdbeabbaccbaadddbdaeceaedabababaabaacadedeadaaceeddaadddababebadaedbddedeabadbaeaccbbcddedecaecbdccbecddaedcbbabcabecdeccddbadbdbebcdbdeaedbeecaaabcebdaacedbaacbeaceabcdbeccddebebabedbeeccdbdebcdddeaacbbaeccccbeddbbabaaccbdbeedbbaebbaceedecdedacdaadeeacaaabccbdaedebacecbebadbebcbdecbeecebbbdbeabbcceeaeeccdceebdebdedbbebadccdaecebeaeeaccaedadbeadaaabedddddacadbddbedadbbeedbecabbbbcbcbbadbdbbecdeaeebbcbebeaaaaeeaacbeadcbdebceacebadddccbacbaadbadeaaeabbbadecebdbeadaebccbadebdbaccbeeebcaecbcdabacaeadbcdccaddecbbbcddbbddcdecdcdbcbaeccdcdaabddeedbaedaaaebcbbccdecaedadedaedbbacdcbbcbadbaaccccaeabcdbbaaacaaeceebccacceddcadddadabedbcdebedaececdbaddcaadbaababaaccddabbaeeddedecedeeaeaecabbadeaaebcbecdccdeecbbdaadabeacdadaeccaccaadeaeedebbacabababdbbedbddeadeacbeaeaacaebeaedcceaaddeddacecaeecebbecceddeacadbddaaeadebdbccaceedaecccbabeacbecaaecadacccabdaabcabbbdedbecaaeebdecdbbcdebeccebaacebbcbceccbccdabaddceacccdacccccebbbbdebdaccccdecebcaabaaababebedbedaccccccaceceddcbacbcbacdcbbeeabddcbdebecaacddeebdacdddbadaaebabdecbaeadebcdaeaabcebdcbabdaeadaeadaadedcebcdadcbacbdbdeeeabdabceeababedaeaabecbdaeecdceaadabebdeedaabbbbbecabdcdebbddaadcbecebadabcbabaadccacecdabdaadedccaeeebaeecbebdbaceddaddceebaeeebceaecdbebcaeecceaaaccccbccacdccdadecbebcbadabbecebccdebecdcbecaadebeeeaacebddaacadcbcdcdbbcbebaaeebcbaccabaaabbdeadcbeceaabbeebbebabeaeeddebeabbbbdeecdeabcedadcadabecebecebdbaaeeeadadebdcaeedcaaeacbdadeaeebcedecccbedbcbcbebeeccddbadbaccaccaabdadaabaaadbdebaeeeebcdeeccceadceaadbbadaeeedbacbedaadebeccdbddeddaedcbaeacdaedacaeeacccddacebbedceadddeaccbcdabdbdeabeccdedcaeeaeadbabeddddcbaccaaaededdceacddbccaeedecabeebbcbdadcebdccaaaaeeadadaecccbcabcaeadbaaacdbdecdeebddedbaebdcdcacebbeedecdcdbdebbbbddbacdccedaeceecbdcbccbaaddddaacddabbddebccdbcbbbbbacbcccbeabcccbeadbbadebeacbaaedaedeebcbeeceeabdaaeeeaddddbecddacdecaaaeebcddccaaceaabeeeaabecdbeccaaaadddccbdcdcceeaebacaadeabcedbcedbdbeaedcddcbcdddddddbeeeedddbadbccdebdaabecadbaedcdebdcdaeeaeedeccedcaacdeaddaaebbceccebbadbdcdbbacebdeddaeaacdadbacbbccddbedcaaadbeebdbbbcaddaeccdccccaccdacacabddebccbcdaadecdecaaeccaceedcacadeddaaeaaaadacdbbcbdacbadaaedecedebbdeecbcbdcbaeabdbcdbbcaaabcddacccbbaaddeccaeecdcaaeaacaebbeebdceaeeaccbaeadacaddcdddbbbccecbbbbaceeaabecabcbdabcacccbdececdccbbcddbceaceddeceaaaeaacdeddebdacddcbaaaaacddaecdeaaedacedcbecaccdedebcbccbdbecdbdceeababeacbcaddedbccccaaeeeacdccaadabaeaebaadeccceeeccebdbacdcaadbacbaccdcbbbeabddceacbabaaceccabedeecccdaaabcaccbcdcadeeebecbdacecedbdeddbcbdeaccbecbacbceaedebaddcdcebedecbbcddaebccebcdeccaceacecdddacbabcccdadabcdcdbeecdcbbddbdbdeedabcadccccaaeedcdbabbcbeaaeecaddbecdcbddcacbecaccdcabcaaacaeaebabcdaeddcceaaeebbbaeceddecdddeebbbbeceacdbabceddddcddadecaccaabcdbeddbdaccbebdabaeebeeebedccebdaeeaaeadbeeadccbcccebaeacbdecbceddbaabcadbeacaebacbbedcbaddcbaaebcbceedecabecdbbedeadbadcceabdcbecacbabacbeebcabcecddeeebceacacbaadcdaaeebdbcbbeacbddeebdcceabbedaadeacdbdcdecaebcbbaeacabebbbecaecebabeedcbecaabedabecaeecaeaebdeaaebacddeccabeeedbbecbddcecabebccadbdabaedccccbbaaacdacdccbcceeacccceaecbaaeaeaacadbddccbadcbbbcabbaedaacdcdbbddebbcdcabbcabdcdcacaddbcaacbaaaaeebbdbcedabaddddadbcbaddaecbcddeaeadbacaecdadbeccbcdebedacaccdaecbdaebaceedacececebcedbecbdecedecbdbcdbeeaebccdebeaeaebbdbdbceaecdeacedcdcdecbeeeeebaaebdedcdecaabdcbbdacbdacbcecbebbbcbadeeadbdcdcbacacdadeeadcbdaeccaabadbabbcebcbeeabdaeebcbacddecdcadccabaaaaeabaeeaccaaddbaabeecdeacbdccccccdabbecacdccebbacceccdcbacdbebacaedeacccecdecdbcadcbaeeddaacbceadbdbebacaaeaadcdbadbcbbcbebaccbaadadcbcababecebbbdbdbadbadecceebddeaebbecbcebdcdcdbbadadceaeeecebceaeaecaaaadaddbacbdeebcdbdcaeadbceeaaedbccaabdaabcbceaddbdaccdaaecbbdbaacaedbcdaebaccedadcabaccdcdbcbcceebdeddbebcabadebbcdcbbeeecbdcacceaaeccbecabcdbddacdbdaebbbbcdadaedecdedeaeeeaddadedcdaddbddceedbdcdddabeebaabeacbdbaeacaabedccccccbbccaacaabaadaebbecdbcbadbdbdaaaadccaeebdedbbadcdeecceedcceebddecebccbddbcbcaaddaceaeaaddbebceaebaebcaccbdbcdbbabccceedbedadeeaeddacbebecadeacabecdacbaeecccaebddddedbaaddceaadeabaecececcbabaaaeddaabbceaecdaecbaeecbaeebbbdeaeaececacddadbeeccacabddcdcadcdaadaaececcabccbbeacebbdcebdbaaeaecceecbcaecbeaebdcbccaeeacbdeddddcddbccdccbbcadbddbeccababeeddccbacceaceaccaeaedaebeeddddbadceaeebaebbbaddddaabdeacabcdeabeaadacebceebacacbdecdaccaaecbacaecbbdcaccedacadabebaeccbddbdecccaddccbedabdbdaceadadbaebebdcaabcdeebdcacbdaeaedabbeecebdacaaadeaeacbddcdebdccdbccbeaeeeeacbddaabaebeadedebcbeabcdbbeaacbddcaeeecbbdbdeaeededeeddbabebeaacebadcaebaddaeadddaaeaaccbedccaacbcadeaacdbcebbcdabeeaeaeabceabadcceadadacdbcbdacaeebabbcaecdcaaeabcaddcbecebdccbbdbcbcbbabddaeddcebccdbeddaedeaadcaaecbbeedaceacdcbbedceeecedbbaddaacecddebbbcbccddedababbcaeecddcbbdddecbdadaaebebcacddedbccddcbebdbceeadeacbecdbeaadbadaecbddbcebecdaebbebdacabaecebbaebbacceaaebbeeaaebcedcdacbcbabdecedbdbeecbebebcdcbdacdbababcadadeabbceceabdbeddbeddccebcbcdceabecdcbcbabedcdbcabecaadcdbeeccbcbcceedabceebbdbddaeceeaceaddecdacaadaebcbbcdcbbdacbeeceaadcbcecaeaeccbaceadebeebdcacaaebebaddccbadaccdbeabcdedecceaddadebabbbbecbcaaabceeaaccbeaabdaaacedbedddccecdcaabcaeecbdeeceeaecabdeecceeceeabcddeadcbbdbaabebeebbdadebdedeeedbcbcaadbbcaaddecdeddacacebcdcedacccdcedcdcdebdabdaeecaecaeeaccaaebdcaacbdbcbadcedcadbbecaeabceadbdaabdbbdbcbdabbcbdaacbecdebdabcedbbbacbebbdbcdecadeccbbecbabcabaadecdcecbacbddebbabdaccdaaeadaebbbacecbdcdcbacedbadadddbaddeebecbccabdeacdbccbbdeaeabbedbbbcecbddabaadddbdcacbcadacddcbbeeeaddceedebdececeaabebabbdedacddceabcbcdbdbacadeedeabbdebbdeeececceaaabcedcecdbdecdcbcccbaaaccdcdccbbececddacdbaeaadeedcedddaebaaabbcdddaddccccbedddaaeabbdbeccceacdaddcbeeebddeedecbbdddcdcbceaccedcdbdcbecdecdebbebabadbccdbdcebecacbddadcacaedbaadebecebeeadddbccccadcbdaebcabdcedbaabadaeeeeaecadcaeecacdbcbadecdeabdaeccbbeeeaddbbeebdeedeaebebceeedadbabbdddbbbcdedcbbbbaedbdbceecaaaacabaeacbbbbebbebaadaacddaeeeabbdedbecadbdeccdeccabebaaebbabdecdadddbdabbdcdebacbabdbbacceccbadccccedbaeeebbabeeecbdbcecdacebcbeecabedceddeaededccbbebebedbbcdeadbeebcbedebaaceaddbccbdbeadabebeeeeeaaeccbdcddeeebcdbacccbaadabaadccacdacededcacbdcdedacceecacbadebdaaccbcbdcceaeebaadacaeceeacededbdccbdcadbcaaacbbcebbeeddecdabcabeabacabdbaeceeacbdadbdbbcedecbeaebacabeeeeddedadaabbebdecaeeaeadbdcaaadeeadcaeddabadcbebcbceabdedbcbdeaddebbabecdcdbebdbceedaccbedacbdcebeadacedbcababddbbdcddeaeddddeebceaacdcbadeaecdacbcbddabebddacaeeaedcabebedacbccbcccbcdebaeceebecaccececbadaaebdeaddbbddeacbeceaadbaaccadcbabedaadacacccaaecacdddabbddcbdbdebaeeeeedcbedddccacadabccaceccaacbedadabaddcedcbabecedcdbccbbdbbcbbdaaaabddbaaececaeebacadebccbedaccbaadbdeeeeeaececcdecaaeaebccadedebbceaddddedbcedccecabbdcedbedbbcbbddceecddebbcbbbaeecccebaeecdedadddddadcdcddcdcbebcedeceeedddecdddabedebbadccadddabcaacaecddbdbddabddcccbedbdccacebaebadeabcdeaaddbcededcdcebcaadacabeeeecddaddccaceedcdeeaaaedabcbaeeeceeaddcadadbbedcacdcaeecdbbaeabadbebccbacdbcbddabcadecadcedcbbbeddceaecaabcbcdcbaabadcecbbeadaacebedbababccaaaaecdeedcadaceacbccdcaaeebdeeabcbacccedabecaeedbcabbcbbccbebcddbaaebbcddbebeadcabcbdabbbacdadddeecebeacedcaaadcdddbeacdaddecbcbcbebeeacacbecdbaababeaeedebcaeacadbadcdaccacedbadbacaceecdcaedadcccedeeaeaaeedddcebddeacbeeabddcdcaecdbcadaebabaddebaebceedeaaaaadeecbcebaabebcaceebcbecabaeacadbdeaecccdabdbeeaabadaecacaeaedaeabcdbeeebbeeeaeaedecadbbeceebeaaecdbcddaeebebdbcadeddeeebaeecaccaceecaecbebedadbdbbeddebbeccbbbabecdbeaadadecedcdaacebedcceabaeeebaccbdeeedddccdedccadceeeaaabbeacedeaeedddebddcecabebcacaeaddcadddccecaebdbbbbdabaaccaccdecbeaedaacbdbcecbbcbcbdcdbedcceedaedbdabbcccdaaddccdaeccdddaddbebcedbdbbebaabadcadccacbabceaedbecabbececdbaccdaadaedbedcacdacbdcbdbbcdedecdacceaabaabbebabcadcbbeddababcebecbcbeeadaacdadababbeebadadaaebecbeaadbdebbbdcebeeaeabbdacbceedbbbddeddbdbadeaaedcbededcecdccdedaedcbedbacadbebdeccbbebadcadccbdbdceaebcdcdddedcceeeeecaccbceebdbbececdabcaadddaaaaceaaecbbdcecddeeadcaeeebbaaabbebddceeeecbadaddbbeedbdcbbeeedcdcaaebaedbcbebdbcbbcacabeccedacbbadcdaaaedaabedacaadbcaceaeacddacaccddceaceccaeeacbadbcebabbcbbacddacaabeaeeeacadcbeeaeabcedcaaaecdeabecbcaddaecdeacebdbbeeeacbaebcdddbbaabdbdbdacacbeeedabdacaaacbdeabdcddbadbbcdaccadbeddbabcbbadbcceceadcadceaccaadeeeddbcdcdcbcbdcdadacadeeaeeebaacdcbabdbdceddebabacbebbaeebedacbaacbccabebbbbbabcbdaeebddbbccccbeedeeebaddaadaebcceaabddcecaccdbaaacbdceeadbcddbcdeccbaecbcaabdeadebabdcdaeceddeeebeadcbdeccbcedcecbddeeedebbdadddecbeebbeababbeaccdecdacebababbeceadbaaddcaabacebccceecbabdecddeaaaeeacbebaedadbcbddbbcedecdccddccacbeabdbbdcaeabddeccecaacdadddadebebbdccabbebadbeaeccecacebaddadeaababbedbacdbccaaaacdecbebcabceacdeaddcaddaadbeccebeaeceeabaccbbdebbcdacadadddaadccbecbabcacdeecdcadaeeecedcdbedaddebbaacebedbcacdbcaeedcadbaeacabbaabeebddaecdceadcbadbdacbdcdddbabbcddbbadbabdedebbbebdedbecbedaadccedbbddcbeadbabdbaecbaaedddcaceaabcdebbdcccccddeecdeccbddaabbdebdbddbcccdecebecbbcebdbccbbbabcecbeddeedcaddcbecbcbcecacddbdbaddeebcceeeaadeddcaeeaddbdbdeddbbbaebdaadeedcadabccbbeacbecebdcdcadbeaeceaeabeaadabeaeddecceaecdddbabdeebabeabbaacaebaccbbbbaeeddbeccebcbbbaaddaacdbddeddeecceebabdbcbdbbaddbbedadcddcbdecaeaebaedaddbeceecedcdedacaaeeedebcbbdebdadadebbabaddcaeedabccaacdcecedaeccdededeaecddedccecccdaacabebadeaacebdcabdedaecbcceabedbcacbdebecbccaebeecbcbcbbdecceedddbcabbadeebcbcbebebedcbeccaceebbecadddcbddabdbacbacbbbaacbccaceeabadbeccceddacbabccdeaccbdeccecdccbddeccbebabbabaedaccaeacbccbdcadbdedebedbcbecbcbcadcaaadcbeccddcadabaaaaececceaecebebecbbeedabdcaccabdcdcbbbddcbdaaacabcdeebeedddadbabcddabbdacaedbabcacbabadbddabbabbbddbbbdccadbbbecaacceeaeeabcaaebbecededdebacbabccdcbcacdaeeadebdddaeedceabcaaaadebbebadaabdaedabeadeccceeadcbeabadedaacedbbbccecebadcebacbbacbbecdbeaedaeeaecbcddabeabdeddcbbaeeecdddeadeccbaecbdbcdabadeabbdeeebaccdaabcdbedbeeabceacddcabaacaaeaaecbbadedbacaacbdaabccdaadeebcbdbccccedeaeedebaeaedbdcaebdeebdaabddcaaeedecdeccaeacecdcbecdbacdedeecdaddbdaadbcbaedeeababdebadbcdcdebaaecccedbcadbbbdbaeeaeaadbeecdbaacbacccbceaccabeebabeabdceabdedbdeecbeecaecdbedaaacdbdcbaacebdaebdbcedcebdeacdabdccceededebbbececdaeebdaddceadceedbdddecadabcdcbaaceeeeacbedecbeecbbedbeccbbcbcbeaecebedadccdddadbdcbbacdedbbbccdbaccccaedbccdbdbaecaaaebaaecbbdaabeebacdacacedadecccdaceaceeabeaddcdadccaaabbabbbacbbedceaaebbccdeecbecabdaddcdeaaeebcedaaaaaeabcdabbcbbdacbbccceecedaacacdadbbcdcccecedcbeeddcebaacdddaccddddbdaceadddceeadcebbabacbbdaadabdbbeccebdcecaeedeebadbbeaadcdcaecaedabeceaddaacaaabcaaaeebedcbcccecbbaebbcdddecbeaabeccbeedeadeccaebabcebcbdaedcdbdecebeacebbbdbbeeedadcbbaccbadaacaabdcaeeaabcadcdbdbcadeabeabaaebabddcdbceccbdeebcdbdccecaddabbdeaaccdccedeeecdbabccaadaccebacdedbeabaabdadacdadaadaecabdbdaaebcbcedbcbabaeacebdaceaedecdbdecebdedbacbccdbcadaaadaeabacebaacccddbebaaebeeaccebebdbaeccddecabeeeaceacdbaaaecbbdbcdbceedabbadebcabdbadcbceaccedcddedabceeeebeacdeadcacedaabcaecdecabbacdcbcbccaaadebcedbdaeedeeddeebaabeedbbaabbadbcedecaeacbeeececceeadeeeaabdedcbddbbbdaedadaabceaeaaccdebadbcceaaebcdaaedeeccbbeeceeddebceceebcbbbcadbcaedaadbecbeaebeceedaebbebedadbcabcaddebdacedcddadcaacbededbcbcebacebebaadbbcbaedeebacedcdddeaaddeceecbdcaeeabaeaaaeaaaaadbeedccedaaeedaaeaeedadabdcbeeacdaecaeccedaaebbcedcecababebcdcacbeedebaccdccbcecdbeaceebcaebdeaebddcaebbacacdbbbbeededaeaeddccbedbbdaeaaedbbeaededeeabdcbccceadeebcdbecabecdbbdbbaededdedeadbcdcabeadacdbdbcaacecaccdbaceadaadbeeedbbcbbcacbaadddccdbaedebddeeabbbdadecdbaeecbbbcecbeabceccabedbbbbddbcbbcadeddbaacaeaecabeeecedeedaabaddccdbbaeacdadededecabeaaddcbccbbbdebdbccdeabdcecacbcdbaddabdeaaedbccadcacddecdccdbceddcecaedaaadeebeaddcbdcdbcbcceedaacdceaddabcecebebdeeeabccdbecccdebbbacbaebcbaaebccdbdbdeddccdddbbcddeaedbddcaeddceadbdbceaebbdabceaedbccdddcaacddeccacbbabbcbbbcbabebedcceebbdbceceeaceeadaabbecaaaedbbbccbcbacabdcebdadcdacebecabbbcdceebeecaeababeccaabbbcdacbdedcaaedccaabebbaeceebceddcadacbadcecedcccbbccbceadccebbbaecaedbeeddaacbbccaecccecaaedadddecbcacdaededddbabdeaaecabbeecdddbeeccaeacdeadadbebdeacaeeaddbebebddcbbbbcabdebdadecbdbceebedaeaaacccadddcadaeceddaddcdaacddacebebdcbcdacecbeacededeecbbcabdcabbceabdbedcdbcaaebdaddccabacadededdedcdbddecacddebcbaabeeacbaeccdeaeeaabdadccccdbdcbcdbccbaedbadedbccedddcbecbbbabccdedabdcdccbaeebaabdabdaebeabaabecadeaeeadeaccdbaecbacabbcebdcbbcdeaaccacbaeebccdbdddccaacceddcbcaabaabbbedcaabbaeecbabdacebecedbbdeceabeaaaacedebebbedbeabadadeabdeeadeaaddaeebecbecbcdbbbaceaccccdbaaeacecabdbceabcacbeceaccbcaecaeceadaebdaaddcbadeddbadcedadaebdbddbaaaebbcdcadcdebbdaebbaebbcbcabeaaaabaaedaeedcccaeadcadccbaabadbdccdcbceebcacaeaaeaeebeaceebdbaaadabbdeeadbaedaedccbabbbcbbabaadecebbbebaceabcdcbeadedaacdbcbcaaddbeeadedceecaccceaddaabccdccbcdcbedeecbdcedaecbdbebbcdbaeeeaecbccbdeaaddcabeacabbdedecaceccdaccecebcdadedccaccaecedbcbabccdeecbdeeebeaebacbbcabbdaaecceacdaeebccaaebebdcebbcdadcdabcdddcccadbbeddabadbccbdeebbeeabdbcdacdaebbbdecaadaeceaccaebededdadbbdaeeacdabdebeaeecdaeebababecbdbdceddcabcacdeeecaebedcaebeccaddbcedbceeddbcacacbbebeabdebecccdcdeceeabedccbdbcbedcceccabedbdcebeedacddacbeedaeeeeebadecdbcbdbbddedeceeecdadeddabdeceaebaacbcbddbdeaddbbccbdeaadceecceecceeedcbcdeedaedceddcdabbbdaaebeebcdbadeaacdddacccedeccacbacccdbacabbecbcdadeeceededecadceeeabdadaadababeceaeadaadcbedeaebbaeccaaecceeccebedcaededbbcabacbcedeebebecaaecdeedcaaacacceebeeaaddabccabadcdbbdcdeeddeaabcdcbadbbcdbaecddaaeccccaaecacebdbbbadabaaddbeadecedbddaeebeeacbeddaaddedeaadaacccdacbccbeabcbaacdecdbbbadbadcecccbceeabaacaebabaadcdaebcecedceccbbcccbacbebdcbdaeecceaacbcdbcbcdbeeabbdacaeaedebcceaedebcaaecdaaddaedadacdbecbecdebadcdeeeedabadaceeddabebbdecdeaedecdceaacdcbbccdbecceeaecccccdadaadbdbbecaabceaeccaaddecdddaceaeaeaaaaddcbeabceacaeadaebcabacbdaecdaabcabeebdccdadaebebbbdceeeacedabdcbcadbedecbabebedbcbaeeaabcacbddadcdcecbededbceabaceeeaaaabbbeceaaeeaacaebdebedeacaaeeeceadcabccbaeeaeadabdeaecbaeebbdbddbcaccabecccadbaeceaeebebccecdbcabedecbaeeddcaaedcdadcecacecbcbdbddecbaabeedbdadabcdccecbbedceabdbaceddccaeeaccdeadabaabbecdedeccabcbdadcecccbebdbadaeeebedeeccdbdcebcbdedbeacbdeaacbcbdebaadabedaacabaecebaabbebbedebcacbbbdadcecdeebebbbbcdedccecbbdddbdccdbbebbaabdcdbcdabdadedeeaabacabcccbeeaceaeccaedecbdcbdacbeceeddbdbbdedbcddeecdcdacdadcabdcbdceaddaddadddadeeaceeccbeeccdcceceaacddcdaaeecbbadbadcdbcaccbacddeeaddadaddcdbbbddabdecbacecdbdcaeeaeebedccadaaccbaecaceddacdddaebedeccaeacddaaaeccaedebecbccaaecdcdecdcbbbbbdcedebadedaedbcbeaadbdadbbccacededaacadeccbdadaacacceaceebcdbaccadbebdecbadabadecdececcdaeeebadccbcaebbdbcacebacbcdcaedcaccdbbeebecdeaebbbbeceacbbeeabbebedbdbbcdeeedddaaaabeeeddccdaaebdbedecbddadeedabdebebbadeeceabbabdddeecccebaadaeecceacbcebdedeedabdebdeeaecadbcacdceeedbdebcacabcbeeccebbcaabaeebbedcddbdbedaeecaeeebccdddeeddadabbeadabbdcdbbaeabeacdddcebbadbdcdebbebaddcdeecdeeaeedeceeebdbbdeeadcdbbcdaddacbecbacaabdeebddedaedbebabbbbecaccbaaceaebacebacbecbdedbeceabaaabceedaecdaccedbcaebbecbbcaebcbbceececbebeddcdbdcddeebbccecedcadccdaccdbbdceebcbddaceceecbcdadabacbadcaedbcaddbedcebecedbebaddaacdbbedceeceecceacdeedbcabeddbbddacbdaedeeaaadeeedcbcbedeaeebdbeedbebadbceaacbdbdcedacbcceaedbbabbbeeceaacdebeeabedbacbcadbcbabdcaacbbcbcebbedaaaceaebaceaceeceaacebeddeaadaccdbaadeabddcbaacddedaeddbdebecebbacabcbebecaddcaecabcdaedbcccccdbadabcdaaadbdccbecdeecdccbeababcdecbacecadebadccacbeaaaaecbadabbeecabaddccadbeccbbcdaacaecbeecebbdeabeecdbbacacbbaaebabedbddcebdcadecddeacbeddbbbcddbbbceebbcaadedbabcaebabadacdcceaacaecbdbeaadeadaadbaaeaeadacaecddeddcbeadebedeaaecebbeeeeedaaddbbdeecceddedcebddedaaaabbaedadbeeedddccbeebbcbeaeacabdcdbdbdbdacbbabcbdbeacaaeddcbdadabedcbddacebeeaebecacbaeeacdcdccdcddeebaeaecbcabdaeedaecacebbbedaccadeadaaeabbcaecdccaaeecdccaebbbcccecaebddebbabbebbeebbdaedcebbcaeecebaadadcdbbaacdecbddcdaedbdddcdebaecbcdeecbabeeaebecddaacdcdcbbbaedcabadedcddacecdacbeaaeecabedcdcdcceeadcbceaaecebeacaebdacbceaaaeeedcdbcbbcecbbeedbcadddccbbdaeeadeacbcacddbaecedbddaebdbccadcdabaeaddbecdcddecbeaccecdadeedddacaabcbeaadeaceaabddbdeabdbaceadddeadbccebadceaaccbbacbbaadceabdbeccebdabdbecbabcdbbeddeedaedcdbbeccabddeacccddebadeaeaecdaabbbaebbaccecaaabdcdedeebbddebcddaedbedccdddbcabacececbbccbdbdedbacaacdeabdeccaedecedcbbeeaecdbcbdacbdecaebeddadbdbdeeecacdbadadabedbddaacedccbbdcaacaacbeddaedbadaaeedeebabdadbdddeebbadbbcaeecedbccaceaceebccbbedddccebacaaceaabadaabdaebaadcdbcebbdabdbdbbcddaaacbaaeaadaecaedbbaaeddabadcaaadbaebbdcdcecababeacdcbbddeeacbddabbeebdceebbdedcccaddeaccdaadacecabecebdeeccdceaceebdacccccabedacccbadebdbadcdbcdcebddebcbbeedeaecdceebdbeadecdccebcddebcdaaeebdbceebbacdaacbdbcbeaabcdabebdccacbecdedbaabbbeeaaaeaaabdedabbcbebdcbcbaabbacbabcdabeadbacdcdeeececdbeabbaeededdacbeaebecdceacdaccddcbdcacdceeccceeaccedccbbdddeebecabdcbeeadcadcbeabecebeccbbceebbecccdcccbebdeeaccbcacacdaddbbcebaaddadccebccaddbdccdeddcddcceceeaebeccbbebacbcecacaeabdeedddbbeedaededcedbecebaaadebccabcacaacddeacbeedeeeaccecdcceceaceabccbbdbebeeebaebebdeacbbcbbddaebdadeddcdcaaedcacdbbedbddbbcddecbadcbcdeebbacbddcbbabadbbcdabeecddbccbaccedcaaaeeebeeeaccdaceacdebabaaabbaeaddcdebbdbbdeaaebcccbaacbeeadeaeaeeaadaddeddbcdbdbcbccbebaabbbcbeeaceeedcdabbddabeddbbbdddbbddebcdbbeabeebceabeaacceacceacbbadbcadbeeeabccbdeaeaeceabeabeeaccceebacedeccecacdbcdeecccacbcbcacaaaadcadedcbdbbdcadcaacedadcbccaaaeaceceddcabbeceeedbddadeaadbebddeeeaecaebaedbccbbdcaeabcbeebedbabadbbdadbeadaecabeabaddcdcbbebbceabeecbeebbedeebaebbdedbddceaabaadceabcdebadbbaadedcbcbbabbbdaedcdabbcdbbdcabdbbaebccbdaceadcdcccbcadccbabbeeecceaeddaccebdcbeecbcaebcdcaaacbdaadcceecccdbccdbcbbdaaeeeecbaedbebeaaadaebebdbbceebcecbcebccbecacebbdeadeacabdbbbabbbddeedcedadbcebedcddecacaeadbccdeebeabddeeeeaaeaadccdecbddedcebeceadaedbbbebbebdeadbdbdddaacdeebbedbadaaaeaebeccabeeebbceedcedceeddcddbceadeaebababcdbdaedaeacecbbddeaddeebaadacaaabcbadbceadbededbedeeacdacaabadbbdddcaceeaecdaddaacabbecadbabdebbdecdccdcaaceadeaacbaacceeedbdddbecaebedeabebccddccacbebbddebcdecacbbbdcedebeaccedeaadacdcdaacedeaadcadaeeaacdbcbdcabccdadcaacadcaebbcbdbbeabbccebddedaebaddccedbabbeaddceaaccedeedbbebaccecadddbbedadcddbedeabccccbddadddeaedbebaecdedaeeeccaccbcccacacdebeecedabeecbeeeedbdeccbbebcdeeecdbeadcbbadbceaeedccebdbaededbacedabbddcccadeddccecacdeedbcbddaeedecdaeaedddebbcaccdacbdeedddbddaeceaaebbdedadadbaccecaacdcbbeadceacdddccbbcdedebaadddcdbcdddaccadddcebcaabdaaaabadeaaddeacccdcecebaecacdeedeabdeaccecbbbcacadaaecaeaeeebdedcbcedababceeadccdabebddcebaadbceabdbcdcdcaabbaebacceaddcbdaddabdedbeaeaccdeeecbeeceeddaeebdabdbdbbbeebeebdaeabbbebaaecaabddbacedbeaceecaaeadbaccdabcedbcbeedccaddaaeccdeddcdeeabdcbecbdceeaedbdbebaaecccbecccddbbecaeedebbdeaaaeedaaecdbadecceebeadbcbaabdecedacbdddecdcaaaedeeeeccedaebdbbdadecaaabbdcabcdddbaddcaadedbcadaebcbacdcceaccecadcddbbbebeeaedeeedeeaedaedaecebbedebcaddcdcbdeddaedccddaabcddceaadbcbaabaeddeebacdeddbbdddceeaeddabbddddcbecadeebabbaaebaebddecdaccdcbeaaecdeeaceadddaecbedaadcabedccecdadbabcddbcbcaeebccddbdbdcceaedcabdbedaeaaaceacabdbcdacbbebdaccaadbdecaddccaaaddbebdeceaccacaebddaaedadecdabbbcdbccaaeddeecbcceccabbbadedbbebdadcdcddacebdbadbbabaddcdbbadbdbaecbcadbadbcdeebcabeccaddccbabaeaeeeaebcccedcebeacbcecbcdbeceebabecbbdbcebeddccedaeecdeebbcabdceacadceccbaddcadbdddabbbdedaedeeabaeccdedebdaaadcbebcadebcdbbcaedcddadcbaedebacdddeedccbdebabdcbdceecedaadbaabeeaccbdacddebaaaebeaedbeacdcbbeebbccecacaaaeabcdbdcbbbdcabcccacaababdcaeecaeecccadedbabacbeaaddaeecedaaceaddadcaedadaaebccadaaaadbbccadabbaccabaabdbcddabedbbebeeebdabadcbdeadacbacbeccaacbaabdeebecdecdcadaaadecdbeaecaabcecddbbecebcaccbaedaadecdaccaadaeebddcbdcabaedaaaeedbccababedcccdccacabebdadcdaededeebdcddadcebeeccdbdbcccbeeadacaaeacdedaeccbbedabdcaddbaaeebdbcabcdbbbbddedeecbbdaeaaebbcebeeedcaeecebadaccdeaaaccabccbeeebabebbaadbccbebadbacbaabbecbbadeadadaaadeaecdaadadcbdcedbcbbaaaabeebbeeedcddadaacadadbdbabcbaeadeebeaeccbabeeacbababdbbdcdcdadcdaaaaacacaaaceeaeeebccdbbabbebbcbeacabcabcaebccededdecdcbccbdbdeaecececbacaababbdcbcdebaaeeedadaabdaccdccbdceabdcdaaacaccccecaaaadbaabacddddebbbcedbcabbaaaeaccbaeaedccaebbdddebaccceedbddeceabbadabeebabbaddcacbedaeeeddebebdeddacecaedaababeebdacabcdbadeeadadeaadddebaeacaaeeddcbebbdcdaaadebbaebbacedbbbdededcaeecbcabdcecaaceceacdbebbebbdebbccccdecceadacaaeeadaebcbbbabacbebccaeebcbceeeabeaabbccbcbdcadedacdebbdebaedbeaaebadcaabeeebbeabeddadaacceaeabcbcdbbdcdaddeadaceceecceeccdaedaadadcaedbadaadaaddcdccabbaabbebbdcebcdbacdacdbaccbabbeabeaaabeecaecebdaadceadedadbedeaaaabbbeaaeeddeaccaebeeebababaeceabeedaddcebcebdecaadccdbddcdececdaebaccdbbacdddbbcecaaccedddebbedabddabdadaabecbacaeeaacdeccebddddcaaabcbdeabdbbddacacecccedeaebddbecdcabbabaacccebdaadebccacdebbcedadceebacecedaaaebdcccebdeaaabedcdcbbccccbddadeeeeeeedbaadbdacbeddeeaedadcdedcebabdbdbcbcabddedcbcbadccddbbcdeebedcaadaadbcdddaecdedddbcdaeecbcbabaacdeacedddacaadeadbeddddcaacdedeaacaecaebdbecaabddecdededaccbabeaececdabeaddbacbacbdbcbabedeeabeeceaadbcdbdbacaaaabdeabbcbbeeecacbbccaedbadbedbbbacedbabadedddeaeccaacceabeddabeaeeeadcceadbabcccecccbcbcabdabbadeddbdaacbbbddcacaebdcabbbeddabcddeeddaedaabdeacccdbbdaadedeceebcaababdcaabaeeeacccccdbaabbaeedcdbbcceeccaeceddcbdebdaaeeacaeaacaaabbaadbadceebdadbaceebbadbbeddedbaccabccabbaebceaeeddaebdebbdededbceeacacbcbdcdddbbcedceaeaeceabeccabdeeccbdadacbecaeddbdddceacabeceacdbabddccdbcbeebdcaccaceaeceaedbeaabaddbaceedbacabbcababccdbbcabbdbcccacedebdcababbbaeebbedbbebeedbcddddecdadecdaacabcaecedcbdddccbadcddddddadacdadcececcceabacdeadebeadcebeceaeaeccbdddaccedcbaaaecbbdbeecbaebaaacaebbdcccebbccceeaabbcddbecadaaddecabeadbbecbcdbacdcdcaedabcdacebdaedbecbedabaaaaebdcabccddcdbcbbebaaaeadaeabeacdbbaddcbabbcbcecbdddcdbdbadbeceacdeecdbdbbabbaaddaadacdccdddebbcaacceeaebacdadcebcbadeedaaeedbcceeeadecadbbacaceabedaabbebdbccbecdedcaccccbdbabcaeebeaaeacadcdedcbbedeeccebbeaaadeadaaceceebbddcebbbbdbbbcaeccdebbaccadadbbaaacacdeeadebcdeaeadcdacaeabaedcecbcebccabadcbcebdeceebdaddcbccdccbaebabacbbdaccccacbdbadbadddecdeaccebcaecebcaaadadecedccddcaeccceededcbceeabdeacaaeaceedddbcbdeceecdbaceaecbeacaedbedebddabbdccccbdbcacbaaecdddbcbabedcbbbbbcdcdaceaceddaeeaeadbaeaadbcdbbedeeeeedcdabdbcadbaceddbbeebedeeeaadadcdabadcddccbcbeccaeeeedbdbaecdbedddeaaedeeececedabbbdecdedbbcbcdbcdccccbdceedaebceeabebebacbcbdcaeebbeebdeeeecabaecdcaabcbcccddebcdedecdbddabcabcbcecdddcaaecabbccedabddeabeeeaadcedaceabdbbdcadcbedecaeaccedccbbdbbeeabadbccadeeecaadcecdccccebbebcaabbdcabaedcdaeabaebcbbbabcaebcbebcbdacbcaeeedbdccecbbecadececccdcccbdadbdeeddeabbebbcdcbeacaedebdcadbaecebadccaeaadebcaacaabbdcbdebcaeedddcccddebcccbdaccadabbaebeeaaccbdacecdddadaecdecedeeaacdaddaadaebccbeaecdbcccedccbddbdbdbdaaedcebbbbaaeeeabebbddabedaedadedbeecbeeaaceebacdebacbbddeeccaecbebbbaaacbacdeebdaddbadbadbdacdbedcbcbeedcccaaaacbedcbeddeedcaacdbeacaecdeabbaecbceadbecbcccdddeacbcbddacecbbaaabcaeaebbebabcceeabceedacbebdcaedadcecaebeabebeebdcdabececacacbbaaddacadbcacdcedeaeacadabeccacaaacdcecdeeddbeacbecadddbbbdadceccbdedadaecdaadedeecdcaebcbbcaceecdaaaaccdeebebebcabdebddbeebecbcbccedbcddddeccdcdeaddaeecdebedddbccdcddbccbbeeaeceabdcbaaebcecaddadcabaedbeabacbbbbecebabbcceadedcdeddabaceacebebeccedaccdceaadedeaeadeccaebbbecbadeabdacdabecabcaaddeebdedecacaadcdbaecbcbabdeaecaeecaeecadcbdebbeedabeadddbbbbcadddaaddbeeabebcccbbeaadebccadababeaaaeabccbabaaaecddcabecaedcbeccacaddacdbbebecabbbbcaebabedebbbccbedeeabeaeddbaaaddabeaeaccbeacecdaacbdddedbabdddccedcaddbaebbebbadcaeadbebeedbcdeeacbabedbdaaadeacedadbbeebcecbcbaabeecceabbeeebdceedeabdbcadcacaeeabebeeecbaaeaceebeedbbcbdcddeaeebecaaeacaeccdadcaeeeeabbdcddabebedcbeedbcbacdaabadadcedcbcdedeaccaebddaadeaecbbbdaecaccedebcaedecdbcdabbbbbdcadabcbddbadcedbeacbbebaccbbcdbdaebcbbcbcdbabdccacecbbbadedbbcabaedaceaeecacadeeabeaeddbebdbaeeabccdecacabcdaedbbdebbecbabaceabebeddcbcaddeedabceacddcbbbecbdddbacecbcccabacadabdddddcccdcdbbaceaccdaaabddabdbaebdcaddabbeebdacabdebebceccedbebcdeecbedccebcbaddbdabddecabebcdcccdedbbebdeedbeecdcbddaeaabeabebbedccbbdebeaabcadededcdbacbcacedcabaaebbdebcdeeaaceabdeadaccdaeccedddbaceddabaadcaecdbdcdccbabcccbabaccabceacacdcebeccbdcebdaaaadbabccebadbbeadcbdebbdbdabaacaebabcdccaceaebdaccadeccecebcddabddbcebddbeebdeceeaedcaaaceacbaaacbababacacadededaaeabbbcdceadacadebeceaaddbbdecdabacaacccddeeeacabdedbdbadccabdddbdaaeeecebedbdedbeeabecaaaaadaccedbabbbaceaadbcdcececadeceaaecaedbbbceaedabbaaeedcabbaeeebebdebbacdeebdadedbaaddbdbcdcbdacaabeceeacbeeebedaceccebeedbeddcbaadddaddaeaadedddedabbadeddbedaeceecceddaacbeddddecbebedcbbdbcaddbcdcaeaacadbdbbcceeaeeedadcddccaedcebbdcbbdbcccdcabaddbbedbceebadacaadaebaeacacbcedcacdabdeabebeccaacdbcbeabeadecbacedbaadddcecadaabddeaaddebeaaebddcbcceddbdbeceabeddadeadebbdeedbbebdaaeddcbecedcceaeadbbcecbbbdecceeddaedcececbdbaceaedacaceeabceaacbaeabaeeabeebbdadadddabeedccdacccacdabbacbbccbccbbddbbeadeaeceecacceccdcbdccceddbbcbeebadbddacdecaccecddecbceeececadedddbcdbdaaeeadddadecceededeccbcaddaaaaeeebecadedeaedaecedadacaaceaeacddaaecbdddccaaaeaadccdbddaadcadaceccdeecccccdcbbbcdcecbeedcecdadbdbaebdaebebcccdbdccbecdcddcdbbaacbccaadcbdbccddbcdabebbabecbdcecbeebdecddbaaadbeaadeceadeaacaaeeaccbbedaeebbebecbabedaeacdeebceabadeecaeacedbecebdaaecbdacbadcaccbeacaeabbeaaccabcaddbaacdeadbdcadcedaabbcbbaddbccddeddbabdbbbbcaccdceaeacadbdecdedacdcddabeceabbdceccbddccabbdbcdbabccbddbbdbdadeecbaccebecedabcbabaaedcaaaddedaddeebabbbdbeeabdbdcaeeebaecbbbcabdabbabbbcddcaaaaceeaaabdaabadaebaaadbadcabddabdbcdcecedebcacbbdacaeedcccaddadaaadddeecbecdedcddedacbdcbcedebcacdabebbdcebececaaccecdaaccabeabcccbbebeabcdccbabbabbbcdacacdbaebbcddaacabeddcaacadddcceaabdaddedeeabbbbbeeaeedbeeeddedddedcbeceaecbeabeededcedbdcbbdccbeabcebeddaecebaccbcccdecbbaeceaedcbddabbdddcddeaccddeadecbaecdcccddabaabbeebebbcebeccdadddccbecaadadbbceeccccccbcacedeebeacdbbecabbeccecbadbedbcaedeaebeedaaaaecbdcbceeeeaebdeacdccaddccbcabaecabcedadbdeeeaebcdbdabeeaedeeadebaeedeebedececaebceecdbaebbecabbdeacaedecececebdbcabaaeeaabbcebdcccbeaebbddcedbdcaceebabcddeaaaeeeeaaceabebbcbddacbaabeadecbeabbcdaccebadabccaccaeabbcdcabbbbbbcbaeadcedaadbdbaceecbbcbadcaebbcababbeabceddbadeedaaddadbaadeabaacadeebebeeedeebedbacbedcebcbaceecceaedcaeccbecdabecaddcbdbdeccccedaaebbcddaaaadbadadccedcecdcecedbcbddbedaedaddeadcaeebdddacabbeeadcaeeceeaebecadaaccbbebebbbbadbcbbdbabbaedcbcecbcbacddbecdaceeddbdeaebaacecbadcbdeaeddecdecdedbdcaaeeaeaeeaecbeaacdddadeedccabebaccbccbccdbabbbcaabbbddaeadaedcbcadcbeededacbcceccddeebebbcabecadacbadbabadddacbdcaebebecacddeecdbdebaccdabdcacdbebcdaabdebebdebcaaaaccaedaeacbdabdebbdbbceedaccddcdbdbadecaddaaabaababacbbecadcdeabedecbdcaebcbccbbcaceeaabbebddcbbaabeebabbcebaeaacacdaebbbecaadbceabbdcbeacbddedbcebdeaeebdaaaaccbacccccabaecdacecbccaccaccbcdadcbbaedcbbcebbbcdadedbccaaaedbebaeaebbbeaedabbcebdaeaacccbdcdebbcddcdaedaecabaaecaccebeabccabaeddabdedeeedcaddbebcbcdbacbeccecdeadccaedaadeebdbadddccbccdbceccdeadcedeeabbbdbebedeecaedddddeecdbdeaddcaaccabbabdacdeecbaebacaeddaecccabbaebbbdebaabbebbaddeeceeacadedcaacccacdaabdbcbdeecadadbaecdcadbbbdaabcdaadebaedeabadbcdcebddeadbdddacbceecccaeebbcdceeedeabcdbdddccbcbdaaebcadcadbdddedadedbcadedccecbeaccaabdbdecdeaebcbcdbadbbbdeeeaccdbebebcadacebbcbdcbdeabddeadeddebbadadadbaceccbedbebaccaecccdacccceaeababdddbeecadeccacebabdccbbcbcddacebaabbcbbccdddaeecdeaecaadeccabceedbdaddcaecbbdcddaeeeaceedbdadaabdccadcbdbdcebeebdeeeabceeeaecdeadbcbcbcbaeaaceabcbdeeddebdcadeadddeababadcceaccbdacbaacdddbaececbdbccddbaeebccddcdbdbbdeebecbcbceddbeeeeabbdcabdadbceedcdedccdcdddadbcbedbedbaaccdaaaddceaccedeadcddbebacdcbaaadeddaecaccbdeddaadbdeebccabcdddbdcbdeeadddeadbaeaacdaeccaceccdebecceadbbbeaabdcdecaceeedbdbcdadbccbecedceccdbdbaecceaceadccaddeccddbecedebdbccbdeecbbacbaeecddcaaaacbecdeebddaedabdeddeedaabaeecbedcddddcbecbdeceeedaebdeadeaaadccbcdedeabdbdaedaabdaccbbccebadcdaddbadbcaedaabcdcbdbeaebeebbebcdbbdedcedacdbbcaaeceecedaedaeccadadbadddcdeebcccbcbabedeebbabbbeabebbcdaeadbbeedbbcacbcdaaaecdcecaeabaaccadeeeeacdcecbaecdccceedecacdcdcceddecddcdebacbcdedbaacdedbcbccadccedceaccbbcdedbccedbbbcecdbbabeaacabddbccedbeeaaaddccebbabeaaaacaecdceadcacbdcdecebebdebcaaaadcbcdabdcccacaecbbceabaabdeacaaedcdcedadacbecaadbaeceaabcaddbdcdbdadacaaabdebeaedddbdaaacaecebaebbccbdcaadaddceeebeebeccccaabdbbccaaaeecacaecbcedaececabdeecddeceeebdcbedeeddaddcaedeceaaebdaadbadadaabbdccceeddecdccbcacaecaabcaedcdcddcebcacadecbdbecbaedbbdbdccadeddaabcabaedaaedcbccebebdbaedcadbeeacaabdbbdeeccedabcbebabaeaddedaebdadccaddaaeeaeeacddceabcdddbbeceadcdbaccaededdceddcbbeecbeeccecceccdeacabbacaacdaadcadbacdbdabddaedabedacdacaeeeaaeaddcbdbbedeaececcedadbaecddebccaaeeaadceaedeaebacadeabbdaaaedabceccaecedaaceaabadedecdddcedeecbdebccdcabeeadcdebbcbddaecccaeddacccbdecdceedbcccdbcaaeaebcabceecbeeeaedcbdacdebceaadacbddaabbaaadccaaceabdbbccddacecbcaaeabccaabeecacbcceaddbcbeccceebddbededaceceeaeeadbebedeedbdaeababcdcabbedcaaaabbdeaedacbcdaaceaedcbebbedbebbbccedbeccbbcacdbbdbbcccbecbeadebbaaaeeaeeccaedddbaaecabacbeebdaecabbcceddabbdeabbcdedddecbcdccccbcedadddacebeeadedeaadebccbeeeecabcbcdebddddddcacebceaededebcbadeabecadabdcedabeeebcdcdbcadccaebaeddbedbceaadaaeaccceebcaeaeaeadddbccdcceeddaadccdaaaccbeacaabdbbdbdcdabaadcbbbaaeadcecabbeeacccbaecdbaececeadbceaaddadbbeadedcdabacccdabdcaaeebaedaeecbaaebecddeaeeabadcbaacaeccbdbdedeacebddaaacdcccdebdacadaeecddbacbaddebeebdbbbeacdabeebeddbcededbdeebaeedeceedbeeeeabccacacbbbeacbdcbbaebdbeccbcababbedbceeabdaeeaabaccbcbadbaaadbdbdeddeecbcaaaecdaddcbbddbaeedccbaadacadccbbbdcacbbbedeacbcbecbbbedabcddaebaccddaeeededbbadebcbcceeabbecebceadcaddbbdaccdddabaddbdbddceebcadcccdacdcecccbdbbdbaaadaccebaeaabbaecaacaddaceeaaddbdeecaabaccadedbcaecbecbabacdeeecddbcbeeaeeccabccdcdeeecaebcdecaadddaacdbdccacaadaddbabececbeabbeacbdbacbdbbeddebbdebbebccabdbdcaacbacddeecdcaeabecbdbdbcebbbaacbcabadbeaaddcbeebeacdbdecbeebbcddebdbddeabcddccabeaedcdeddadeeedcbcecadabedadcaccddeeaaaacecceecbbeecdebdbacecddacdadbbdccecdadabbeddbdababbeacbebddbedcbdbcccdbeabebabbcddadbaaaeadcedbededbdaaadbceeeeaeaccdcbedbdbdecbceadccbceecdebbbcdbdbecceceeddcbceebacaadaadabaddebbebdacbddbcabecbdaeecaedbdcbcdcdcdcaccaadcbbbbeccaaeabdeecdcbcaebdbccdedcabadecaeabaceeecacbabdbbbddabeaebadbeceddaabacedabdbdecaccdbceccddedcdebcedcceebaeacaedceccbacbaabdcbeceeedbbcbeacabdddedaadacaadabceeabcbeeecdeceaebeddcbeadaebdbcaddbccdcedcdacacaedeecceacdcbdcedecdadcedebadacaabbbbbbecadadabeeabbaebbeeaebbcdeecaacdbaeaebceabaaacaaedadeeddaeeadeadcbbebacceddaccedecdeecbbdacddcebadbaeacddeeabceaeaceabebdbcaccdabdbbcacccaceaeeedcdcbeaecbaddadebadebebbcbbacdebbaaeeebadceccccbaceaaaabaddbcaeacdcdadacdddbadadbdedecddecadddeabcdeccbeaabbebdbbeaeccabedbcdadabaabbebaeabcabcbcdcaaabcbabbaebdbcddadbcbcebaddebebccdeceaebbaccaaedcccbeceaedceabbcadedcacbeebbcaacecbeeacadbceabaceaecbecbecdecdbcdaceeddddedebbdadbbbaeebeaceeeeadececeaedddadcabeaceababecbddbcdeccaedaeacbcbcabcbedbaeeabcbbccaaccedbacdecdcbeeedbabbeeaebdecdbadbcbebdddedbccaeccecbaedabbebbccbbaeaceebdadeddcaebbeeccddbaeaedbdeedcecacdcabedaedeaedddbdddcebeecceceadaeebcbdeedecbbecdecdaebbcacecebbdbeceeaddaeceadbacaabcedebbeeeeeacdeddaadebbccaebaddccebeddcadaddaabecbdbebcdbdeecbababebaadbaccdbeeabcdbdcdeeeadbdccaedaabcbcebbbbbdcdeebacbdbebaaeccaeaeecaabcbeecabeddbdeadbebaeeadccebceceebcdcabdaecbbddcbdecccaeccabceeececbaadcaeeaaaabcababcaebeacacdbabcbdacacdabaeabebaabecacdcbcaaeedacbeebadebccbbcbbaeeabacedbecbddccbcdaedbdadeaacddacceceddeacabeeaebbcbaebccdddceecdedbabdddeacebdceecbadeaaaebddaabaaebeadecceceabdadbeacaecbdeaeaeddbececdaaecbbcbcecbededdeadbaaeecaceaedcbdcaadbbecddacdadacaedbdeccbebbdeaeacdaececdadacccbdcdaecdbadbcebebebeadacadccbdbbdeaadcdeaccacbaaebeeedceeddadaadceacdebcdccaedbedcbeececeddbebaebdcdbadabececbbbaedabcccbbeeaeeacbacbadacbecaeebbdccbbbbbcdecdddacdcecdcabeebbebaebececdddbcdcccbcdddbbebeceadddcdcdeedaeeeacebdcccacccebdebebebdccbeaabcabaeabbceecdacbcccabceaaaecbaaceaeabcabeebeeaccaddeeedcbadadcedbecdacdbacbedecbceadeceacdaceaceddeaeccaaabdccdadddcdbdeeeaeddcaabedadddeadeacceeeacdadadcabcdeccdaaeecadeeaededbabbcddbaabcbcceecbecabcbcdaedabedddcdbcadbbbabacdaddcbcececdeeadcedcdeaeabcdcedeabedaceebbdbdedadbbbeeaebaacbbebcbadbccbadbdcadecadadeacdaebdbdbecededadaccadedbabbeeaadbdcebebebabbecdbeddceabeeecddaeaeceaadbcbbccadbbaebeceeebbdaeecddebcadcdadaacbdcddccecbdcdbccadaddbdbadedabeeddecbcbcbebdcebdebbeeceaaaedddebbdcedccbaeecdeadebeddbddcecbdbcbaeaeeededebaebaeeccbaccabdeedebbeaebedbdbccdcaacbceddccdceaaeeccbdabaebebbceadabdbdadcbdbbeeceedcdddabcebadbdeccdcddeabddbeabbaeccbeddbeaaeaddbbbdacbcbdebcdebeddaeaacacacdddaadcbccdceabbbdbeedacbbcaedcbdcaedadbaedccbebcacbeebdedaddeedbdbbaedbcecbeedcadaabbbcecccdcbbaaddcebebccdbccdcbdebccedaabcceeeceeadcbdddeeabbbbdcdabbdddcdddaedbddeddadecceccaccbececdaccbbceaebaddebcdedcbcddcabeccdaddeaeabcccaabdbcabaaeecbcbbaeacdedbdebebddadddcabcaeabdaacaaaebecdddecdbdcbdccaadcbbabedacacdacaedacacbadacccedccadacdeadcbedacaabeeabcebcbeecddbcbaedebcbabecbbbdbbbabacbeccceceaaeedccaaebdbecccccbdccbaaecdbdcebcbebeddcedbdbcbeebeddadabbddacdbebaacecdeddcbacaeeeccbeadbbabebcaccbbcddbdeaeebbdddddceceebaecbcbeebbdeaebcbeedebdbdaddbcabaaeeebebadaddceababdcdabbcbebaeabddecbabdbeebcaeeddceebebcaddddacceddddddbcbacecdcccaabcabaacdebaeeeeeddedaeddeeeaebbebaaaceabcdecebdeecbabeccacddddcdacbbdcaaedacdeedcaeadedadbaaabcbbababebeeeaeadedbaabbeccbcdbeccaebacadcbaddcaabedacccceeccdcabcedbbbbebebaddebeaddcaadabcceddbbbabbbcdccbabbcbcdacadbbbbaedacbabcacbcecbbcbcbcbccdbdcabacaddeaaabacdaeebeaabdecdbbebaaecdaeedeeacaacceedbdbdcbbbaeedcbbabddecceeaaeceaeaabeeecadccceeebadcdabddaeacadeedacbdaebdaebcecedcaebbeddeddaaedaabbdeedbdaabdccdcbcaedcaeaaddaaebcddbdbbdeecaedabdabdaeaeecccdeedcaaddedececcecaadaaeedbdeccdcbaceceedddccaddbbebdcceadbdeacaacebcdbecdcbbbedbaacdaedadcdaaeadbebebdcccaaeeecdaeeeddeeebadbbecaabccbadddcdabdeebdbedcdbbedacaaeddcdcebedcabbbcdecbdbbeecacccdeeaaaaaadbcbaeaecaeadadeebcabebdadcadbbecbeeebadbbacbeadcccacaedcedceecababbeadeccacebdacdececbeedaaaeecdcbbaabdddcecccaedeebebacaaeeabebaeaeaeeddcbeadbabeecdbaabbcaecbeceececbdeeabbeaeddbbeebdbbcadabdaacbbcbccaaeabdbecebcbcaddbdeccaecdeecdedeabbdabcdebadabdacadbdcbaceeadadcdcbcbbaabdbdebdddaaaddacacadedaeadaededbbedeacbbecaccbeaeccdebeeaaaadbdbeadaeaeedceddeeedbbbdbdbaebedabbcaacdebcaecddabbaaabcbcdeaebdccedbdaeaeecbbedcdeecaeeccbaadadbbedebdaacdbecebbdacebbbddeeccbaccddcdddadccaeeeaeeedbdbaeebbcbcbdadcdeecbeacbccebcbbbaaededdcdbacdaadbbddcedeceaeddbdabeabbcdeddeabcdcbaabdaaedaeacbabdcceecbecddeaebdaadeaabdcebadbcdbbdccecbeccceeaadcdaeeeacdebeabbaabceccbeeddbdbbbdeecbeebdbdebbaebecbbbbcdebabcabebaddaaeabbbeaeebebadadbdabcdabadbcdccdedccadadbadbbbeeabedbeceacbaeeaaaeedebbdddececaaebceabdbbaabaeeecaedcecceaceecbdcececcabcdcbdbcabdeeddcaabedbedeaddebbbaecdabdebaeaedeedcbeebbdadbbcaedabadeaecdeaededdbdebecdbedbeddebbedbaaddcdcadddbcdaeaabbddaeeaaebabcaebdaaebddbaeaeabdadcdbcecdadceedaddeeedaacbccddbebdaccaacaddbdbcaebeebcbaddabaccaebbbcbeabbbaedbbaadbcbeecabcbbaecdebebcbcceedbdaecaccdceadccaedceecdceaaaacdbdbcbddedadedaceaeedabcdaadbdebecccebeadbabaecaecaedcccdaaaacadcaeebabbadabdcabbeabbdcdecadeadbeebebedbaaddeaeacadeabbeaccddddecbbcaccbcbcecadedaddbdbdbceebcbcababeecedcaebccaebaddeeecbdcdadbbededbeabedcdcdabacbaeaecaddeedbbaddaedccbcaccbeccaeacbeaacdceabcbbcbaebbcbbdcbaacacdeabeecaabdedeceacdebaaadadcbddbdecdbeacbdbeddaebbcbcaebcbadacaaadaecddbebbaadacabdbcadcaaccecdcabaecdaccccccaaedeeabcedbdcbebedaceaddbcdcddbdceaacdcedbeddccececcddaceaaaeeaeaebebaadcdceaadceccabcaceebabeecadabeabbbeecababbebbbcccbbedecbcebbeeeebcacaebacbadedcdcedbcbccdecbcaecaaaeddadceddbdbacccddddaeaceacdbccbcabdbcabadbeaaeddcbadacadebebbdccbceddbdcbacdeeebeacdceccececcacbecbecdabcbaaeaaeabdeaaceadbbbaeaeedebebdcedeeadceebbdbecedcabbddebaeeaccbedaddbcddcbebdbedbcdaecebceedbbbdeebceeacdcdbedbcdbdadcdacacaccdceebccacddaddbbbbbdecdabcadabbdbceabbdebaecddacbbaacbbaccedbbcaaddaededddbcaeaaedbdcacecdcddebccaeacaaedcecddddebabbcaededeeebacceadadaaebeaacceaeaeacdebeccbdbabeccbceeceacdcaabbcbabdbdbdaeebaeabccbabbcbacccbdcbababaecaeaeaadaaabacaaacebccdacadceabecaabbcbababdeedcbcdeeeedbaebcdebbdacbbeadedcceecdbeeacaadbedbedebbdabbbdadbccadcdaaecebebdbadbddbcdacbdababbeeadebbcddbecbcccdeddececbaebebebcdcdedccaaabdadabacadddabbbaabbbdbcceeceadbaeabebeceecbaecdbdbeeeadeeeaabbabeebdccbbdecbaccdbbbdadadcbddbeaaedbaebebcbcaddbceeabbcadebdddcacecdcabeaddacecdbaccdcaeddcbaaebccecdbedbabeccccecbabbdcaebcadabaccabdbceeebeddeeeaeaabdcaaeccecaedcebabbbdccdaeeaaeecacbbeeeaecaeebcaeacccdadebedccadcbebaebacccccceaaaeabeeeddaedabecdecadebeabdeecddbccccbebcaaebdbddbbebcdddcacacabcbabaddcbceaaeabeacceaabeeeecdcdbbaddcbdeaedaabcbcebbaddacaedacdaccceeabbbebbbdeabdcbebcadaabbecdcaeaeebaceabebcbdbdaedecacbdedabdbdddeceddcabdcdaabebaebcbebdaaacbcdecbdecacbdebeaeadbbeaaeecaaebdeebdbeececdddeddcccecaeceddabbdccabdbabbcacdcdadcdbdcaddabbbbbbcadccedddbaeaeedeeabdcaeaadabbaecbbeaadbbeadaaaacedaecabeebcecdeedadcebedbbccccebdbabceadbdaebebbcaaecaeeaaeeeecadbdebdeeedbabdbdebbcdbbddedbbceddceaceecdedbcebbbeadcdeddddeabddebedbccdadadaeebebecccaaeceadebddecdcaaeeedacaabecaceceddbedcbcdcaadcbebbdaabaabcabaddaaedcedcbacececccaebbecdccbddcdbbcbdadcebadbbbddddbaebbbaccbceddbcaacebbbccecdbbdacedebcbdebabdaeeeacccdecdbdebaceaadceedeaabcbedbbedcccceaadaeebcddbeeaacdebbdcccddcacdcbeceebdcadbebcebaadbdcddcbeddedebbbbcaebadbcbcdbdbbaaeaaeeaddbdaceaeddceccaadededdeabcddabdaaaacdebddabbdedbddedcdbcbebdeddeadecdcdbcdecbbeadebbcddedaaccbdbbbbcaedddeaeeccdabcabdcadacdaceeaaebbebddeaeecaebabbadbbbacebabbadbdacececeecaaccecbabddbceeebaaacbcebdcacdadbbabbedbceaeeecbbbaaacadcebcbacdcebcbaeadcccdbadcbaddcecabddabababeacbbcedccdbbbaebdaceeadadcbcebaeebdccbbabdbadebddbedacddbcaddcbecaedeabececccbdcaebcdebcccacabeecdedaceebabcacddcbbcebecbbdccddcceacaaeccededcaedbeeddecbcaacbdeecdbeaacddbabdbbbdaeacaeaaeadbeacbebddbaadabccbdabdeadbbbbbbbebaecbbdcdbbcecdadbdcdaacccbddeaadececddbceeceaaaedbbbaaddbeeadeeecdbaeccaccbbccecbdeaabaceadabaccbddacbbbdbeeeeaabecebdbdeaebaacaaeaaaedceccdcddbcbaabdadacbbceebdaceecadebadadbbdceaadeacebaabcadcddebedcdddddeeaceaecadbdbcbcbccbecebcaacbeacabebeebddebbebaaaadbdacacdaecbedcadecdaeebbabdcabebabccdbdedccdadcaceaabdebccdaeabadcaddadacdaeccccdcadaedeedbeedcaaccdaebbeabbbeaacbedacaabdeeedebbedebadadbcddecdacebcaddbccbdaddceeaeabbcdcdceeedbeeacddeaeddeeeaccdccdcedeaebdedccbacccaceebdacbadcaedebadacacdeacbdbadcadddeadeecbacacdceeaccecceacaeebedbbcabaadbeeaeeadacdbdaccadbeeddbbadadcdcedaeadeadabccaebcdeecbacdebdccbcbcdbaadcedeedcddececeaddeebbaebbcceebebbebecdebebbaadeabddbabdbedcaadebbbbabacbaccbddbeadecbacecacabaccbaddadedcadaebedbdaaccaeeadabbadddcdcbbbdcbeebeaaeabaababacaedebdeabadebaeabbaaabcbdbdaeeaadadeaadbbeddedbcdcaccbdbeaeacabbccacdccbdabbbcceacdecddbbcbbcedbaadebdecedaccaddaaeddabdddadebadbeedcdcddacbccccecbeaacbcadecdcacaddcacbeedabeaacabadedbabbeddceccbeaeebbbbebbeadcdeeeeedeeebcaacecdabaaaacabaedaaeddeaeadaaababdcdbdcbaaeaabbdeeacdaadbcdadbadecbbcdbbebccdcecaedecbdbcdacedaaadaeaacbadcaccaebccecbeceadcbbccebdadbbdcddedeaaaedbecabbcadaadbaabebdccbcdcacdbebedbedbaddeadedccccbcbcbbbacdcdbcabbdcaeaddbbdeebabaadeeacadacdeeaaceeeebcdcabecebeccaacbedaadbddedadcbbbdcddbeadcdeddbeaadabaeddcceadedbccbeeeeedacacadeedbeadebededccdbaabdbaeebdcbdebcebadbcccdcbdaeaacddeacdbcbbadddabbdadceddecebecabcceadddaeceacbbecbaeeccdaedcdccacdddcddaaabbedabcbbdbdcdaebeabcdccbeaebccecbddbebaebcadadcebbaeeaedbedaeeaeadadbecedabdeeecbeabdadddeecaabdceebeaeadcedbecccdebcacbdedecabccdaebaadccbbccedeeebacaecaeddeddbbcbacceecaccaebbdacebaddddbbceadbaccddbccbaceaeadbbabcdbadaeebbabbdbbeddadccdadeaddbdabaacddbdbcccbddeababbdcbceadabecdaadaaecbaddcdccecdcadabbabdcbeadcacbdeaebbdcabacdeeebaacaebacbedcdcdededbdaacbbeeadcacbeeadbdebdadceeecbbeaaaddacadcccaacabaebacdededddcecbbacdabcdedebebdcbceeabaacedaaaabddbccebaabbacaeddcddbddceebbccebdabcaaedeeddaabbdccabaaecbbacadcceacdacbcbbabcbaadaeedddaaeabeacbdceebbeeeabdbabdddadddaeddeaedadadcaedcbccbbeabeccbacddeeeeccbcdeeacdecdcdbddddcdabeadcdecaeebabcadcdaaebaaebadaaaeeecbcbcbcbaadcacccbdaebccdaeeecdbddddebcaebbaacccdcacaeebcbaedbaedebbddeeacdacaabadaabbbeacbbbbbdbcbaaddccabdbbbbcbadbbbcdcdddcccbdaedbdebebaebecbdbabccbbebbdbdbadbedbcdebbdbbacabeaccaaccceabbcdecbbddbbdaabceadecddbceeaabdbabaceabcaeadbaabcbacbdadbcaddbdebcacdcacadbecaecdddceabcdaacbdcbccaccdcececcdabdabadddbdaaddeeebdbecbadebddebeabcadedcaaeebcdbaddbabdabbdadcaddadbababdecaabebabbbccbaddddebeadaabeacbaecccaeebbdbbdbbdcbbcbcadbabadaebbdbdcdbdeaadebeaceccbdccadabddedebaebbdaeddeacdbccaeddbbdacebaeeeeebabceecddcddebbdcdcbbccadcbbcdecebabbaeccbdedabdceccddcebadbbddbadadcbdadacadedbadaeceebcaaabbcdebceaaedcaacacebbabbabbdecbaeebacbeceadeecbcdbeedcededbbeebdeceebbcaeebddacaebaeadcbdaadadecaaacbdeaacaaeeedbcbcbecdceeaeeddbebcdbddcdaadaddebbdcddaeeadcacbcccacadceceecdeecddbcddbcdeaaeeadeddeccebaabbbddbadcbddedebaadeebdbdaddeabccececbeddcaaecaecbaddaaacecadaacacdacbebcdabbcbbbdebccdadeaeedceaabccedeaedeebbbeedeacbddabacadacccdccecbedaabaaabbcedcaedeaaeeeccaaeabdedaaccddbeadebbdbaabbaeaeeeaabdeeebcaacccdbcaededaedeabcddbcbcaaceadcbcceaaacdebdacceddceacaabebdcbcedeeacecbbbdaabaacdadcdededaacedccdcdecbdacdedddbbecaceacecaebcdbadadcdbbbaabbeabaeeddbbaeddbbcebbdcabbdedadebdddcaeceadbcbabaccbcdcebdddeceabbececadaaddbdebaeaaacdbcaebadedacdaacacadcbbebdabceecbddeeedbacbceacdaeeabacbaedabeabddabbcbdecbdcdeaddcadaadbabdeabadededabaccbbcaeadceaebbbddbddcdbdaceecaededbdaeeecdbdaceadaadeebaaebdcdabccecebacabbabdcbaedcebabeebedbaeddddceebbebacaeeecbadabecbeddcaabcbcaeacaaabadcadeccdcbaaaebbacbcaaeaedecdedeeaddebdccdbdadabecaacedbcdaaadaceccdabddeceaaedaccdbbaeadeedcbdbccddaadcaccedaccadbcceddcecbbbbcbcbcedbaddeccabeeabbeddbbdecacaeaddeedaededdebcaeacabdbcbeddcececbabddbacbbdeababaededcbdcacccdbdecdebcddedaddbcdddcbeaeebcedaedaccdceaddeddebeedbcbdcaaebdeadecbeceeeedabbdaeaccbbebabeaadccebdbdeeecebadebbbecbacdbbcaceeacaabcaedecbbecedeebaccdadbaaddabacdebdcabeeaeaaddceeeaecdbadbacaddbcadbbcdbbadddbedbccabbaacaaacbabddbcdadedacaaaeebbecbacdccceedaeabbdedcabeededdaabcdacceccdaadeacccabeedbaddbdcaceebeeecabedbbbdacdadeccbdcbadccbaacacebcacaabbddedbcebeeaeedcebeebcaaabdeacbbeacacbdacbaeeacccbdacdcabacdcdbdbbcbcaccccbbbcdadcecebbdccaacdeabeabebdaecdaaacdddecdebddedaadaedbebaadbcdaccccdbdaddbebbaacecaaaccbbdbdeceeaeabddbabbabebacddeeccddbabdcedabeaabbbeaddbcacaebdcdaceacdaedcdccdacaccccdbbdaeebdaaddaeadcbaaeeedddedccdaacedaecaeeadebdabebeecdebdaddcdcbadccdebeeecdbabbcecbbbbcbccbacccabbedcbbaacaebecbbbbbbaecbcaabcceadbdbddcaecdecaabcccdbbccedecbbedeacedeaeaacddeaccacdedbbcaaceadddecdbbcabeededcceecdbbdacdcecbddadddaedaeddbabccdbeaaedecdedeceaaacdddceebaaedeeeaedaaccdadabcadceaeebddbaeaadaedcceaacadbdbeabbecabaadecdcecebdbacccbdcaccaededbaeaaceaabbaccdaecedababaeccabccbdbaedbcbeceecdbcebcaabcceceadcbcababadeeeedabcddacdccdbbebdbeecaebdabadedccbcddaadaaaeadbbbdeaaddeebaabdbdedbbebabbcdbbddaebaeceacebdbbadbabbebaeaddbecdcaacacbaaeacabdaabebccbeeedaacceeadaeabaddecdccaecedeeacbdbacdaceacdeaeeadcdedaeebdbaabaceebaeeceabdbcedcecdcabaeedbaebceeccedeaedbcdcbaeacedeecbbddbbeceeeaedacdabaebbbccaddddbdacecbedaaceaecccddabbaacabdeecaebddbeeeabccaedcddccdaddebdcadaaabcedcbacaacaaeeabdbeccbddadacaebbbecbcdaadbeccceeecdaacccacadbacdeebddddeeabacbddbbeebbebcedccaaddaeabbaacddabadccabbcaecebacbebbcedabdcdebdcabeeaeaabdbedcdbcedbdeeaabcbbceeececcbeaecedbdecabadaedabbcdbecbbddcdacddabaeebacbaebbeccbdeeaaadeeaccdcebcdddcbaeeaebadaabdbbddbccddadbbbaeeacabdbdcbabccdedbecbbeebdebccaaaababdadeeeaeeccddcecddecaedecdbeebeaecdbbcccebcacadcbeadcbebcebacdadadeabeeaaceaeddeeeedbaccdccccdeebeebcaeeacaecdaebbcdbdbceaaeaabcbbbeadcaedabbdeaeaecaacedbddcceadadacdaecbbededebeacbbddbdbbccdadcecacaaeaaebecbdedecebbcdadabeeacbcdeebdabebccbeebaebbceaeecbcccaacbbaaaddcecebdcbedadedcabaccebbcecabbbebacedeabeebeeadbbadeaddcebaadeeeeeeaaadadbcdbbadecccbdbabcbbedcecbbadeebcabbaceeeebeedebdaaccbdbbdbcddeedbbebaaaaeaedcddaddcbecbdbccadaeaeceebdacdcaeeddedacedacbbedddabbeabebbbaddcbbbebdbbdcaebeebcddddeecacaeaaebddadeedadbaaaccaccdebdadddbadcedceddbbdacdeadbbccdaedaadcacbadaaeaaedccbccbbceabdbcbadaaacbdecdbdccbdbdedddbedddbbdeabcdecdcacecbeeebaeeeedeebbddaadaabbceccbaaabbaabadeaeaceccadaccecebaaeedddeadaeebdceeeabacabbaacabbbaddbceacabbcbdebeaecabcabbaedabecabbedcaaaacaacdbcbcadddeaecbcaebdceecddcdcbedccabbcdaceeedaddadbecdeaacbaecdaeaeeeeaadcccdcaabaaeebbaaecdbbebeeeeceecdbcadbbabbbceebeacedcdcadcdcecdebbdaadeaabdbbbaaedcbaaeccbaecbeccaeeeaecebedecebdebbccbaddeccbdaaaeacccdcabcddacbbcbddadadbabbebdbaacaebaedabbaddacccdbedbddbdaccdebedbdbcacdaabeadaddadcdbdedaebcccaadcaccaaedddadcaccacaeecbcadaebabecbaceedadbcbacacacdacdbccbebdcdcbddadbcdeeeabcbcadedbaeeabaddcadbaadbcbeecedebecddeecdccdcacbdccecccdccddacbdbedbbebedadceabbceadecadabaeecadcddbeaacadcabbbbcaddbcbeedadecebcbeeecebdbcdcadaeaabaddccdbbedcbdbbeacecacceaaddcbbddddcacdbbdddeaeecdedaadebadaaeecddbbbebcacdaeaeaeacddecadaeabeaacdbcccecebacbbbceeedbacdecccbdbecdedcdaacdbdaeddabedbeaabbcaaacdcedacaceaddecccecdccdecabddceaccadddcbddceebcaedddebecadabbdcabedcadbedbcbbedabcadcbdeacbcdceadbebabdadcadcadabeaeebcbedeabdeeeebdcaceadeeaeedeedcddeccadadedcbacebbcbebdcdcddaeaebaebebdcccdbbaebbbeadecdeecedbcdbcdbabedbebeeebbceabedddbdbbdcbbddeaccddccebabbaecaeeaaacecbaeeeeaacdcbeddadcdecaecbeaaaccddecedadcedaceccaadaacddecbeddbebceadaadcdacbdbdbaeabebeabacabedbbeadcdbecedaecebbdbdbceedadadbececeabbbbadbebabbcdedabedcbbeedcbbeedbedebdcdbadcebedbccbcdabdaddcedbcacacabbcdcacceebbabacdeeaeeaabcaecaaacbebcdaabdbaaccddbaeaaccdccebbcbadeccddaceacaaabecbdcaeacbeadecedecceaadcebabadadcceececbaceaecdaadbbccecbbadbdeacdbbabaecccaddddbeadaeeaddcdcecbedeeeeebdbdedccbedbeacababeedacadeeeeeeeebdcaabeebabbddcecbeaeeeceacbaedbccbcedeaabcdecddacacccecabdececcdadddeeacedabedabbacbdedcbcabccbeeaedbbdecabdabebacceacdabeaebeecccbaeeeadbbedcebcbcecacebabecbdacaecccabecccebddcebebdacaceeccebaededaeacabdedeeaacabdcecaeacaacbcbbcbcdbbedbceddcdadcbceeacebdbaaedbbdedaeaddaddaabeeacdabdeadcabdaebaeaacaaeabebdeaccbcbedeabeeecaebecdddcbdbdbaccbedcbeeabcdbcabdbdeabcaeebcdcadacbbbdbecdabeaadeaeedabecceddabcecbceeacaebeecedaddedeecddaeeceaaabdeddecddedbeeebdbaecabbebadccedeaeecbbadbabaabeadadbabadababaeeaeaeaeebcbbeceebdcccccdbedcceeeceaeedccddceddbebdbbdabdcddaeacdccaceaecceadaccebeddccdbdcecbecbbbdcebeeccdababdcccccdbcaeabecbadeddeebdcabebdeeaaddbbdedeadcbbbbdebeadbcbaeedcaeabbbeeeadcbcabebabdecaeeeaacaccbbdcacddbebbebccccacddbdbcaddccecabaacabccaedabeeeabceaaaecaabcacbbcabaaeacccdbdaeaacbaedbcecebecbcdcdceacbdcbbadddeabaabdcceecedaaabeebddeeebaabdacddbdbeaddedcececdbcdbcbeaaacebbdbbcdecdeaedbebcedbcbeeabaacabdedddacedaecdccadcacbaebeebebbabaddabacbbaeaacbdceccedeedecbbecbbcdcececcdcdbccabecbcdeedbcabddaabebceaaaecebedbedcbebcedebcdaaabbccbacebdbbabcdccaebabdecdcbccddacbabcbeacbdaeadbeaadceaadacdbedccdbbddcdcbaecbaddbcabcdcdbbdecebbcaeaaeabeeccbdabceaaeceabdbbbcdaebdcaadcbaeabceaaadbeeaceaabadecbaeebdbbdcebcedcabaaddabecadacdbeabecdbdbddeedeeadddeabcaaeccecaceeccdcdecccaeacdeaeeacacdceadedbecbdadebdedaddbbbdedaccdaaaaccecddccbaeeccdbbbaedcaecbbcdcaceeeaccdadddddadadecbecbbdadacceaecacdeedececeaaceaabdcbeaceddcbdddabbedcabeeaebceeeddacababccdacdaddaaaedabebdcceabbeaeedbaaacbdbcbddeecdbdbdbadaebdcdeeaeeeccbedcacbaccebbddeddbdcdabacccabbddcbbdaabdacbdcbcedbcbccaeccdcebdeccbccdccccbcbbaedbbbdccbaedabeaebaeaddeeebaaaeaeaaedeeddbbbecceadebcdaadaacbeeadbeebacbbdccceadabaebbbcebabbbebceaebeecbbbbbbeeaadbedaeebabcedacdaaedabdeabdeeacdeceecbbeaebdbabbadedcaceeecbadaebcebecabcbbaeedbbcbacdcdddddddceedeebdcaebabbaaaabaeeeabbcebdcebcbbceecdbdbecedbceddedebcbbecdebdacacdbadaaddcabdaaeeecdbeaaaeabddddebbddacbccccddbeeacbeceaacdbaccabbdeebddadccadaceacdccbeebaadecacbddadbcaeebdcdaeeadebebdcbbdbeaabbeadacacdbcadddecccbaccaddeeabbbcbecabebececceedeaaddadeabdeedcbedaeadeecdabdabdaaebaeabdddebcdddbcdabecabaeadcedcaeecadcdacabdaeeeddcdbaabbcebcbcbcadacaebddbeeabecbbaaeccbcbdaddcdbeccccdcbdbcbdebbaabdbececeeccecbeccebdbdcaeaaedcebdaaebebcabbdcccbdbdbceececcbdbbcbabbcddcdaeebbddcecabcdcacedcbbcdaacaecbecccdbadecacadebacdeadecaaddcdcdbacdedcaeceddadbebacaadcbaebbdedddcabdccbccdbdeddbdeecabecacacecebabcabbbddeaccacabbbbeaaedcceaaebcaabbdceceebbcadcbddcedcccdccbacacbceddccbcecbabadaabdccdcdcedeadbebdecabcabeceadbbbcbdabcaadbbaeacdbdecbdceccabceeababbcdaeaadcbdbaddcababddeaaeccddbcabbedbbacbedacbbdcbcceebddacdacabbbabacabccccedbaabadcceadadddbcddacaaaeeebddebdaadecaebecaacbcedbbaceebcccedeaecaccecbcbcadaebccdcabcadeceeaaddeeaaecccabbcecceaabacbaeaabaadbbbdbacddbdbdecabcbaecdcaacdebaccaceccedbcdddeabeaedbcaebdabcbdbebececcaabebdccdaccdcadeddadbddecaaebccaacbdbcdacecdbaeedeceaadbaadcddcebcceceedbabdbcbbddaeeaeececcceebeaedecabdcbcbabbaddcbeddbcaeabebedacdecabeeebcaacecdbbdbdcbeebdbbdbecbabedcecedabbbdcdaaceebcebbcaeabcbabdadbadddddaecdacabacececacbecbdcadeddcadbedcddeccacbbbdcabcaddaabcabdabbdcebadebdcacaabaebceeddcdccadedbaaeacdacaaaeadcebcedecabeecceaabcaceebacaacbdbccaaaeaccdbbbbdaaeccacecdddcededeccebdcebeadeeaabdebccdddeeabebaebeaacaceecdebdecdcaceebdacbbaeecbabeaccbbccebccceacbdcbcdcdeacdcaebbaacbbaacccdaeeaacbaadadedbaebbcbccebbbeccebdcbdbedaeeaabbebcacebecbacceecabdbddedcccddaaabbdeabecaccadeeeedaacaadcddcbdcccadaabebebddceeccdddcacebebecebdebaaaeecacaabbdccdaaedaaecbcaedcbceccdaebabbeababbceeabbaddeccaeaccdeaeccceaebcbaacacdebbaccecabbbcbaddebbbbceacbdeadbbaebadbeacadeeddedebdadacedbabbebaacbeeecadebcaceebacabbdacdbbdbdedceecdbccaebabdaeedcacacacedbdaacabadcecbadaaedaebccaccbdaeededbaedadacaccddaaecddebccceaeaaeeaebcebabcadeecacdeeeabbcebcadcbacdeeceeeabcaddddbcdcdadaeddededaddcebadaaaecdcadcdddcbaaceaaaceeeebdbbadcdbeccdeaebdebcadbcaabdbeeacccebabbaedaeceeddbdaccedccbddaedaddcbcdaaaeeeeaccadcbbdcbcdcbedabbdaaadeeaacececaebadbabcabdebddbbaeccbdeccdbecabbcbddcacaacabcaaabbecddceaaccbecdebaccaadadcccecaabcaadbeadcebeebcadbedccececeeddbdaddbabcbedebdbdedecdddebacbaacebdeedcbebcbaeaeeeeaeedddcbbcdccaaebaabbddbeabbdebbaaddccddaeeaeadeabbbcccbeadbcddadccbbacaacccbeabccdccbbabcdeebabdcbcedbbdbeababedcbeddabbceddccdbcabadabbebcadcbbcdaabcddbeaaddbedaabdedbcbaceedceaaeeeebddabadaeeeeccedceadecabbbeccccdeebedbcceebdcaadaabdacdcdacabdedebacecdbddbdccdbbdeaddadbbcdacbaebabbceccaeacdbeeceabebbbaeeabcceeccccddadaecbadbeedbaebaccbeebecaabcddadacbedabdddeebbaeddcccecdbddeaaceadcccebedcbaacadedadedaaacbdbadbccedbeaebeeceddebeedbcedbeedcdebbecccbeaaccbbbcedcbdbdadeddeededadbbddbcdbedaaaebbcaaeaedbabaadaeccabeccbbdbebecdcebacdaacbcddbeacbdeeecbccbecaeeddcccbccdeacdcabacadeeebdddeaacbabeabbedbaadbdcaeeccaecacadaecdeaaabeedbadcdeebcbddaabcabcedebdbdadbcdcaccdabdccbddeddebbdbecabadbbbcdadcdbdaedbabbeacaacabdbceebddddbccadaddbdedeabdaeeebdbdddeacddbeabbdcabaccbaccbadaecdbbcacbceacdcbbbdbeeadabecbcbaecbeeeaebcebcbaaddbcdcbeecceccacecddbecccbcebddedadcdaeadaddeaeddddabcbabbacbaecdbddabcdcebcadabdcaaebedeabaedcbebcabaddddccaeabacdaeedbbebbbbdbeeeccecebbbedbedebbaecaecadacaebbcaadccbbbcabadbbaaeaeccadbaaeaedcbaebbebcdcdacecdceeceddaecaaceccbddeedabcdcdccbecdbeccadcacbadaddcbcbdacaddeebacbcadcddebbebdcbaacecaeabdadecbebdaddeaadaedccddabcdeabcaececccbbedbbbdaddadcecdaddcbacaeedddabbeacbdececccbecdbdcdccbdeedacabbacdbabcdbdbbabccebadcbadbcbdacbbdbdddadddbbdcdadbdcdbdabcabaceadebadebbbbeebacdadccbcedebdbddceacdbaccbdbbecdeedeadedeceaaddecbabdcedbcabcabbaaeccadcecbccbecaebbccedcbdeccbcbdddcebcaabbbddebbbebcacbedccacccebbeecdbccacaabecebcbaaaebdbadebbbabedebbccddbeccabecdecaddbcdccacbecbabdddedcbbdecbccaaeababedbeadaaaebedeaacaabdceceeccbdbaaccabdbcebccabcaaebbabcdaacbcdceeadbbbceeeaedcbaeeaceeabbaaecdaaaaeedddbeaddcabdaacedbcadaabaababdaacadbbcbdbeabcaebcaabecdbcceccdddbaaeebdebcebdebeaeebbbcaccabcacadbeecededdeddddbbbebedbeeddabaeeadeaedbeaadeabcdebaabdabcdeccaaccdaaebecddccacdbabaccbecedbbecacedbcbcaecbbceddbcbdbdbcdcbcbcbeddeedcbaaaadabcaddecbeaadcdcdabcedcebbdbcecabccecaeacaaeaccbbeeaebedcdadcbeedaabdbbaccecbacabbcceeadeeaeddcbaaceeaceeebacacddabbedeaccbacbaaebddcbceabbccceadabaccaaabdedcaedeaccabbabaeaeebcbdbdcddaecdadccddeebdbddbdddadbeebcbaacedbdcbbedacaedcecccccadadabeccbcecccdaebecebececacbbecdeebcccccbdcacbcaeeedbaddcabeddabaacddcadbcdadcdccaecceabdaaaddadadcabadebcaadbbecbeedeaaddadedeaabbebbbdbaadeacabebaeadbaabcebaddabaeeadebabbbcdeccbcaadbcdbdaabbbaaaadddabdeddaceabebdceaaecccaedcceeddedaddcabceebdcebcdedacaaaacceddaeacdbdadebeddcdbeeecbebdabbdeadedbdbedcaabadbdcdbdcabacadddaddabadbedabeeaddccddadaeeaceacbeebbadcdeecbdccacbecdaecddaeaadbaeadcacdadcbedceadecbcceaccebcecdecadddaddcdebbbabdbbdeadceabcacdceadddedebdebceaeaecebacceeccaadeabeacccbbbcaaadecacebacdcbbbeeadabcccceeeccaecdaacccbbecbecbbddcebbebadeaaaeedeaecbbedbdccecabceccabeccdbeccaadbbeedaebacbaabbbcebadedcdbabcdcdedbcaaecdbdedcbdbeaeedbbaeaebbddcbdbdeecececbbedaabeabeaebcbdbcecdedcdacbdabebeaaadeddcbdbaacaeadabcdbaecedceeceeabbadcecaaeedcbbbbaedcdcddaccdccdbedebacceeddbdacabaebabacdddbdbaaeccadbaedaebdcacdadceddaedbebbeabccbeeacebceacdedeaaaedeadaeecaeaaeceaadccbdeadabbbbdbdedcecbcdecdbdcdaecbbdacebaeceeacabeaabaebeeebeedbeaddcbabddebacabbedcdcebaccbadecdbcccdaaeaabdbbabecccccacbbddcaebbeaaccdeecebceeadbebdbedbdeddabbcdbaddacdcccddcbdeabdbeebcdececaacbeaeecedbbbbedbecdcbdbdbbcbbecacaccaebbdbaaeeaceabddacaaceacaedbbbecdabbcddbcdcabaeabedcaeaccadeabbdebdecdebddadaaceabceceedabcbeabaddacabaeaaadeadadcabbabbdbbbdbdaaeaabcedcebbebcbccceacdbeacbabceadbcdbeadbbdacdcdecccddacdbcdceecbcadceeeacbeaedddadeebcdceccbbdaddbeccccabecddddbdeeebaabecdbaecbedaaabceececbcacbbbaeccbaceaddedcecbcceddedaeddcddedbbbdbbaaeddabeeadbecaebbacbbddacccbcaabcedeebbcabcddcccaeeccdecceadbededcbdeeaebbcdacbcddceaeddeabddbcadaddaddbdccdcddedcedeadccbceaddabebddeadcdcbebeeaaaebdcdeacabedadeedbedcacceddcacaeaeacedbbcebabecdcacbaabeebccdddcceeebebaebbbaabeeedaaecbeedddbdbaacedeacecdacdcededadacecdbbddcdcdaddbddceccccccadbcaaebcdaeeccabbbdedabdceebeaeeacdccdeadbbccadecbbdbcbaacdadbddadacecabebddadddbadcacabccdeadabcacceaecdabebdcadbedceaaecebdecacdcebbaadeceaeecaedbabeecdaebcadceedaccbcbddbadcbdcbbececaeaedaecabbdbecbbcacbdbeacbdcaaadaadaedcaecbcdddaecacedcadadebddbcaeaecddbedadecbbdbaceedcdbbccebabeaabdcaaebccecaaacebedbbbbbabcbadabdddeeebaaeecbdcbabbddcaedcacbdaeadabaeeecbbcacceadcbbacdddecceddabdeedadebeadbadbaeadaceeaecdbeddadbeabbebacecddecbecbccdcaccdbbccebaebaaaccdecbddddadcabdddbcbacdcdaabcddabeaebadaebdaaccceeebabdccecdcbaaacdaacacbccebeeaeadbedacbaebadadeacddbdcbdaecaaceeeeeaceaaebaeacbdabedbbbeebbbcacddbbddcdeeadeeeddbdaccdbedacdebcdabdcbaccebcdaaebcabebbbdccaeddbceedeeaabbeceddcbbadabacadedcebdaabaadcbadbceadbcbabcbaccebecccacdcddbecaabcdcccdedaecebbbecbbacdabcebddbdccdaaaabbaaaddbdabeaddcaeebadaaedccbcebbcaeeedbedebbbceddeebadddcbeaabbbbdddcacbcdecdbdbdadaaeabcaeedcaecabdbbedeaecbbaebbebdbeebbbdbeabecacdedcececacabcbdabcdeaaddcdbbcdcedaacbdbdaaaeaeaedbdabcedbdeaeadbbccdbbcbdcaebaccdbdbeeeadaddedcbbdadcbddcebcbecaccbcebdedcbdeeadabebcdabbaebcacbcdbdeccaeabacebdadeddbabdcecedbdcbdeadeacddcccadcebdceacadccacbcdbabcebedcccdcaaebbaebccdcccdbbeacdcaadcddbcdbddeeeccbcbcbdbaaaddbeaddeadaaaebababedbbdcaaaaebdabbdbbbcabcbeaccadbeabdceccbddbcacceaebaadaebdadbcdbadcaabdcbdebeaebccdceeaaaebbdbcaaeedadacccabbaeaacebbeacccededbcebcacdddeecdaadccbdceeaececcaadcebeabbbdebabcabcdeaabebcbcaddcbedabcbebadddbaeeecedadebdedbabddbaaadcedccebcaeeedccacaceaadbcbceddcabedcedeaaeeaecdccedacaddcaebeccaaecccbbabeaadedaedeaaaadedbbcceeedbeabcccadaedddaddcedbababedbaaeeadaebaceeaabdeecadbdddecccaacbaabcbbdcebabdbbbaddbebdeeeeaabacbbddbbcbceabdaaaaceaadcbbaebedbceccbbacbaebebacbcccbdbcaaddbcebbdbbccacdcbeedddaababbbeacbcbbececdaceaebaceacbbbcebcedeacadbdaedababeedbbaebedcdeaddcaccacadcdaadebbbbaeabaddcadebcdbcaadaacebcdecadebacaeddcdddecdcebcedcebdebeeacbeeabbdeedddbecedcacbbedcaaceaabdbbaaebeccdbbdcbeddeebbdbcbbbbcccadaecaaccacecedabddadedadbbeddeddccdbcccabaacbadadbddddbeacadacdacdedbbebaacaeeeecebbbebdbceecccabbbbdbeddcecddacdeeaaebcabbdecdceceadecedeaccddcbcaaddcaadcadeebbbaeeabedddebbaabbcbadeadbaabeaacbdceaedcecaeeabadcdaaecaedaeacdcbdebeeddbeebdeecbeeabdddeacbccbebcceececddbceaadaeadeccbbacdebcedcecebdcdcbaecaacebabccbaceeaaebbbeeebdbabcbeaeadcebdddcdaeccbeeebaacccccabbaeccccadbadeacdcbacacaddeebeecacebcdcbaccdaabbebeadbccbaceadaadeeabaaeeaaeebbadccaddabceaeeeedddabedcbcdbebdcbeebbbebacebcbdddaaceeadaaacacedddbcbccacdcaaeebcdbedbedcaaaaccbdcaabeccdbddcbabeecaaccbddbebbdadacbbddbcdbebbabdadacecebdeabeaccacdcddedbebedcceadbaaacbaedbbdbcedbdceacadedeaeccbcdadddacebaedbcdebaddadaaaedceccceaddcccbdabcaaeddbcedcabcecebbdbcccbebdbbbbdaeebbabcaeadbedccaebdebeeceacdcaecabacebeeccabebcabbdcaeccacebeebdaadaececdddedecdebecacdbbaeaeacbaeacdcbcaabcaabbcddbadcaddaabbcdbbaaecdbaedabcddcddabadeaadeaacebcaccbeccbacaceabeedeeebeeceecbdebcbbbadeaedeeeebdbdaccacbabebeeeceaebbcadedcaaccadebeacecacdebeeccdcdaaaabaabaecabcbdacbebebaacabbdceabacadadeaadcebebedcebccebdcaadabddceeacbaaccddadddaceddaabbcbcedabcbaebbccdaaeaedcecedaaaeacdddccdcbdbbbdebaabdeabcacecdebbebaaecaadbccaaecdaeeacbddddbdcddebebceeacddaabeddbabccdcadecadecdadcdacebbdbbcadbeeaeaabbdacdadbacbdceccbcbeddcbbcececaedbbadcddcccbaabcbaaaeabcddddbbddaccadeaddbdeedddebeeebecaeeeeebeaecccadccdadcebeeedcbedcdedcdebbeabccccecacadecaeaddebcecdcdadeddbaedebeabebecaaacadddcbcddaeaeaaaecbbcaacadcccbadeaabccdbbcaaceabcdcbdaedbcadaedeeddcccadcbcbebdcbbcedaeacaaebcdecacbbaeabdecbbecadaedeaccaaaebeecaedbecbddaacadeaabeadeeaacdccabdcacdcddecabaceaeecaaeeecadcceccebdbadeecdeeeacaacbaeebaddcaecaeceabacddcebababaeeeccbbbbbdedbdcbcedbbaaddaaddeacedbbbecbbdddcadeeaeebdbcbedcbebcbebbaeceebbcadaedcacdcaececacdceddcadebdedbdcaadeeddbadeaddcebdcbccdccbedcbdbabbdebedbebedeaaaaacceabbdacaeeccdcdccbeddcbdebecdbccbcbeedeeadcdececcecdbaecceaadddcbbdccaebeebbdeaebddaccedcdebeecadebcebacbaecdabeeedaaaeedadadeecdcdccddebededbaebdadbceaebcaedebbceacccdebcccddebcaebddddaabeceebaadeeceddbeeaedbabbddeabcbadeddedbebeaaddceabdabeedcdcabcacedceeaabedeababcbdcdaabeedcebbabeacbaaabbedbcaadbcdeedaedbacbadcdcabdadccbceedaaedacedbcbcdebdcbdaadcdcceccbbaccbbdebeebedbdbaceabdaccddaeaebdabeeeeeaababbabdbabbdaecacccaadceadbcbdcadcddceebcabddbabdbaedeeaddecddbdaacbcabbedecbcaccedddbdabbbacbcacbbeccaecceccedadeeedbabdbbbdbaabacadddaedccdbbdbbeedaeddbdeacaeabadccceadcbebcddbeacbddbaedbbadadddebcaeaabeebacadccbecebabebacbecacbbceaacdddaebadbabbeabeaabeaeebadddbdabcacabeadbedcccdaebcdcdcbbceacbebccbbaddebbadbdbadaeadcaaeabcedbdbedcdddcdbecddebdcebdbcdeaccaecbaceecdabcedcdeecddcdbcebcabdbebcdcdabbebbdcddcdeeeaabebdeeaacbceeeeaaababcecedbadbeeeeceaababbaabdbdbcebccacdddbadaabccaaacedbdcacbeaccbbcbbbbebcabdcbeedcbaaaecaaabcdebeadcaaeaecabddecceaadcebcaddbdaddcdcbaddbdceddbecaaebeaedacdcddebddadbdbdeaaddbbcbebdebdedbbbbaccaddcdadeeeebbceadecccdbecbcdbdbccbeadcedeaaeaabbcdeecadacdadbcaabcaeeebcecadcdeaacbeddbceabbbbbaecbccccbbbadebbcbbdbdbecbaddddabadcdbeedbedadcbccdaadeceacceaeaedabdaaeaeddedcdbbeddcaceedeabdbadeebbdbcececaecadbceedbcddecbcdadeedcadeececedbbdaeddaddccaecccbaebdadbdbceacccddeecdbcadabebbbddacabbbeecaecebcdbaecceeebcbdecaccdbddbabbaeaeedbeaeccbaaccddaddebcdeebbeddddaaedbcadbaaaaddaedbcdbabedbedcadbcbeaacceeedcbddeebadbebdabebacdcccccdaebdacbeaaadabebcadcacdceeecbecdeaeeddaadcdabcdeaaeadccaacdbeacebdaaccecdeaaddeaaabbedceaeccbdadeceececeadadeaedeaeeadbdebddadcadeebddcebdcdabcebaddaaaecaedbbeeaabaecaebebdcbeecaadabdebaebcbbedaaababccbacedcabbbeddbecaccbebacbbdddeeaaedcddddccbbdbbbdcceddeaeabdddcbdccadbeeedbebadcbaeaceeaaebcdaaeddcaddeaceceadceeccbadeecbccbbbbebdbccaebaadaebcbdcbeacaaeccddcaeabaddacabacaddbeacddaecaaccebbbeaaedbeaaeaebaecdbdaaeaccecdbbdadabdedabddbdaaecbcbeacecacbeeeecacabebcadeeeeeedebeeccebbbbdddddccdaebbeebacebcdbceeaecbabdcacdcabecabcddeecaacaecdccaeedcdddebdbdceeaeeabaccaebcbacbcbcdebecbdeabacdcabcccadaccedadccedaebcdabbadcaebcedcdaccbaadceeabebbdbcdbadddaebedeadadeaedaacbdeeeeddedcecaeaecacedacbbaaaecbcddedbeedbaedbbcdbedddcbeededccdbcbbabddedbeaaeededbdcdaebaedcbbaeddedecbbdeabcdebcdabbbadacacdbbbaacbceccceabebbcceeeeeebccbeccadddbbeaececbaaceeaabaaacbdadbcadaebbdecddeabacdeaaebaddacdecbeaacabddedbbaddeccecebaededaaccbdebbddceacdcdcddcaebddbaeaecadbcbedaadeceabaacbdbadbbecaaeadaddccbbbaecdbbdebdbdbbaaacbaaebecddecdbddddeaadaaeeababcaaadddacebbebdbdeeecdedaedeccabdddbbeaceaedcbdadaecdadcddcdaaaebdbcaececdddaaeeaedeaeaedccbdbaacaaacceeaaaddbedacbebccdcaeeaecdebdeaacebcbaaceacbdebeccadcbeeedcaaebdacbbcbdbebdbedeecbcaaebcbbdebcdbbabdcbeebbdaddbeebbeeaccecdecdbdcadccaeabbacaeacbbdcaecbbbddbcbaadacddccdcbeccabeeddecbecdcacebeededacaeecdeebebadaeecbbebeaccbadbcebccadbbcddbebaabdcbadeeacdcbedbcaacecaabaacdacaaceceecbdcdeeedeebcacabececbacbcccbdcddabcebccaeabcdaedddeaebeecaaaaededbdaadecacacbabcbbbaaacadabadcaddccaeccceeecdebedbdaeabaabcbabebbeadacceedbacaadeeacdeabcbaabedabbddabeecedaabeaaabdcbabdddaddcaaaceedaceccbcbbadbcdececcdeaccdddbbaeaeecdacadbadaecaeaccaedccdbcaadceaadaaadeebcadbbabeddababebdadedcaecadabcaacaebebbedecdecdbbabaaededcadabecaebdddebaceaaccdceeadcdeadeadacabcaaeecdeabceeeaaceebadebedabdcaabaedeabbabdadbddadedabaddbcbedbbadddecaccdbdbaacacbeeadaadebedaceabcbccabcaaeeecdbaededebcacbeaceaececdbaeeaeaebbbeeabbcdcceabbaeeddeadacdbddcebccdedcdabbeebbdcbebeaddcccbbbecaebaaeebbcbbcbdcaeeccbcbbdaedacdcbbaddabbbbecdedbcaedcedaadddbeacadeeaadeddaecdedcbcdecddaacbbcaeeaaddcbeeddcdbebdbbadddacbaaeaabddbedbdadadceecbddedbedaadadadbdecabdbcedbedbbcebdddbcaecabeecbaadebdecabdaedcddbdddadcdcabbcabcdedcbeaaaddeddbcccdcedabbbbceaacbcddcaebccaddebadaddaeaeedcebdabbceecedcbdcdbdccbbceededccbccbcaadcdeccbdceabeaedbeedcbeaabddadadadedbacbedaeecdebcbdadcecbcbbbdcaeeecbbcdeddeeacecdeceedcaedcbabccededdccbdddccabeeaebdadebddabbcbeeaabaddcccaeddbdbcaaabedeeadebacaaaabbcdbcdaebddbebbcdccbdcadeeedecdedcccbcaeedabdcebabadcccbeeedbeabbeaebdbeeaadeaccadeeeaabdbecbebcccdcdbbdeeeddadabecdceeeedceecbdbcecdabbbdbaabdbdddcacbcdaadeccaebdbccebebbeeaedbddbeebddecbbdcdaeacdbecbadccecaabaebececccddbcbbbcacccbeededdccadadbebcdaaaaadacabbcddbadeeedbddabcdeddcaaebaecddeeecbacaaceababecbdbbeeadebbcacaadceaddacbabedadcacbddebeedccebdbcceccdedbddacecceaaecceaddacabbdebebcdcbbbedaaaaeabbaeabdeaaaaabaadedbbdceaeacadaddcbeaadeadcebeaeadbbedbdebdbddeccbdacaccccbcadacabdcdaabbbebdeebbccbaadebbbbbbacdaadeadebebbadedeadadccbdcaabdecccaceccbcbacdedeeeecaccaeadebdeecadccadbcbdcdbdcaacddaeedaedbbdacaeeaeccdabedcecbcbacacaacccecdcdcbaaccdeeddeeaebecdcaaabcdddddabacaaeacbbbadccbaaeddabbceabcdccaccdabcbceebcdecbccccbdabbeeeeaaeceddcdebbdccdaebeaacbbebebcdceedebadcdccaeacabbbcbedadbeebbeeabacaeecdecbbababaabaeeaadecccddcdccabedbcbeedbebbbeabdbcecbbebecebdbecaeaddccecedbacdedccababddadebedeadcccedadebabbbedbbccbcedccbdbecebacbbdeedddcdabacdcdeddabbbbbacdbceabeeabeeaebdebaccecccdedceadadebbbadebbdeddecccecbdaebdabcdbdbceebabadaebdecacdcaceadccaadcabeccceaabcadbacbdbeddeebcbeccabaaecddbdbdcadbcaceddaddceecdcebcadeededcceedbcebdbdebcecbadecbbbcabadcdcabcbdaabaddeebabeeedbbdbadaecaaacdcdaeacbbbcdddbbecccaadacedabeabbbbcddebdabadaeaeeccaaedcaedecdeddbebbdccaddebbedcbccaaeebeabeeecdeadabaadadeabcdabbecacebaadcdadcbaabbbadeaeabedbedcdcdbabecdbcaebbbabdacadbdcbdbdcbcbbecabcadaaebbceecadbaaccebbcbbdbbbdacdceceabeeecadeeabbdddddceceecaeabdabcbacbccaedbbddebbdacecbbbcdaccebcecebeaedeccebacadeadedccddddaadacdcdcdbdebaeceddeabbcdceeeeeadebddaccabaaecceeebbbeeddbeeacbcbdbdebbdecaeedaececaeeedaaddcadbcbcaaebdadbbeeaaaeabbaeeecddedeecceeabaaabbdaecdcecededeecaaebdeacbcebeadeeeaeeaadbdecdbdcccccbcecdccbccdcbeaecbcbcddceabeacdcbadaeeabeceedaebbdbddaadcadabdebadaeacdbceadeaeabddecceedeecaaccabbcbbeddbcadcaeaabdbbaaeaebcbdcedccdcddeeecbcacecaddddcacbecbeddbbabcadbbddadaaacddbcdcbdabacddcdbaaceaabeeedbeceaabaaeadaebccbbdbedbceabcdbcbdcdcdbcbbbeeeeacaddeaebdcbcaeaeaaccebeeadcedbeddbbceababbbecdcdecabeeccdabdaaceeadbecdcdccaaeddcbceecaddcdedadedeeacaaeabacaabcbcbebbdbcddacbebcbcadeebdadbdaabceecbcbbceaedddcdaddaeabbcedccdbdeeaccadecabceccbacaeebceeadbaeedaccddeacaccbcbabeeaeeadcdbdaceaebabacdaddaecdccdcadddeebeaabbadeccbbbebbbeaaddceeadcbcbdaebccbebdceebbcdedcbbaeacebdeaaceecdebebcdbcaacedaeccceebeabaeaabaacbadbdeaddbcbddaacedbbebdccaaaceaebeadbdbdedeaeceedacedcccdccceceebbdccaaabbcbeccaecddbbaeceaeebaedcbbdadedbcaacbedaaecaacbdcaaadecbdbacdacbeeaaedecbddbcdbeabacadaebabeeececdcddcebeadccebdbcbdeadbeccdddaeadebeebeccbdaadaddbebbbddacaabaeaaccbdcdedeaeccebbecaaeebdabbababcabdecaacbdaadceadcebeebbadbbcaaaabdbcdeebbdbcbedadcbcdadabccddcaaeecabdddecbdcaabceadbababbaabbcdcaceaeaeedbddbceddbccbdcdddbeecbebebebabcadcdceddcbbaebcbedabcddacbbcdacceccabdcdbaedccaceeacabebebccdeabdbaabdbaecddeabdecdbadedbadeacebbdaadecacacbbdaabcabbbdbdeeebcccbbddcecbadcbdebebbeebbcccadaabecccbaccdbbdebcebdbdbcdcdededacccedcddbabcdebddddcdaccbbdeeaedddbacadbbcbdabeeebbddadbccbaadbdaceacbeddbedaecdbebbcdccceecdbbeaccdbbeddcbaadeaedbaedeacedaecaeedadedaceddcadbbaadeaeecbaccbabbadececdcaadaddaaeceedbbbbecbbdadeccdbbbaaacaeeabebdecebbcebbcbabceadacdaadedeedbbbccddeaeeaaebeedacceeabaceeacedeccdedbededacbbddbcddaabaedbebcccbbddabaddaaeccbcddbbadabedceaaeeaadcbcbcbecbdacdcdeeadbedeabacdbacadbeccccdbdacbdabaeddddbbccabbcdaeaadeaceacadeadacbdbcdbbbaaabdabbecbcadbaaecadcdeccaeabcadbcaadadebcbceacdadbcdcdbaadcdececccceddcabdcdedaaeeedcaeabdeacceaaeeebdaaccebadbababacdaacddadaadadeacbbebebcbadbbbbccaecdecbacdeeabacbbcbcbcdbeacbdebeedaabedecbaebebbebcdbaceceddebdabdcbbaadecbaaebbcaaaeebaccdcdbbceeeebaddbdbcccbcdddaccbdbabeacacacacdbdbaabcdaaadbceecbebbeddabbdaadcedcccdbaaecbabecbbacdeededadbdeacbaebddcdedebdcbbadbaaceeecaedbcdaaebeddebddaaeaccddeebeecaccdcabddabaecbdbaceccbceadccbdcdbdbdddecaddbaaecdaaccddeacceaacdaabbadecbcdabbccaddcaaeabcceeebeddcaadecabababadedecadaaebbeedbeeacceabebccebaabeadddbbbddbebbcdbcaceaeebeeecacdceccadcbcdcbebbdeeaeeaacccbbbceadedbcaeadeacbcbacebcbcdacabccaeabdddbddddcbbcedcedeeeaadeebcaaeadedddaecaccabdcbaaeabbdedadcebeddddedacdebdaeaacccaeeeebeeebcbdccbeebcebacbccadebecccdbeeadedeebbcccabbbdebaaceecdceaceeeaacbbadeeaaddddcdbbceeeeceddeddaeebdddeddbbbcaeeddcedcaebeddeededbbccdebcbcbbdbbddeabeddceaecbdeebeaadaaceddaaaccccebdcedeebcddebbaeeabcbcbcaaacdcceabddcdadaadeddeecbddadebddeeacbdedaaaebeebabcebacedcbaacaadbbbebcebbedbedcaadaddcbaedbdabcdbedbdedcebaeecdcdebcacddcbcdecedadbacadaeadcdbceabdcdbaccbcaebaddeaaceeebcddebdcaccdaaabcdbaccecabbdacbbbadbcaebdadcdbeeceebdbbbbbbebabacbeedbeccdabbebedbadeccbccedaeebbaacbddcceedaaabeceaddbdbbedbeadececdabdcdcbacbaedabcdbddedcadccaaeaceebcdecdddedcdcaecdaeccedaeabcaadecaeecdcceedcbdbccbadbdccdeaeeddbbabdaeecceddecbeaabbccecdcabdcdeddbebeaebbeeeccdeaccdebadacbdecacbcbeceaaebeeddeaebeabdcceacdcccaddeedacddbcbabadecabdbdccabebdbeebbeeaaecceeebcdaadbccacdeadddaededadbbebeccdbabcadbeaaaadbaaccccacdbbdededeaeccabccbeeabadbdcbcceabdaeccdeeebccaebcbcbdddadbbeecaddeeccadddcecadccbbcadaadeadaccbcccbcdeecaeeaedaeeccaaceccbdbaacceebeccdccecbaecdedccdcdbbdcdedcaebacbdeeecbeddbcedbdcedabbdbabacddeabbccccbbceecaceeceaaddedbadceeabbdebabbbcddadcbdbcbbbeadcadcdacdddadcaadccbbddeeeceabaddbeabaeacddaadeccdcaeddbaabbddcceeddddeabaadcceaccdeededdbdbbebadcddcacbdcbbcabdacbaadedceaaecdddbddaccaeacdbedecedaadecebabebecebebaeaabaedbedacabeecadabeddccdbabdeeeedeccadacecbaddccccddacbadaabaebeaeeabedebceddaeabaacdbdacbacedbaaebabeecebecbaebdaeecebbeaeaadaaaddcedacbaaeedeeceeccaaceccedacbbeeccbdabaecaadcacbcaacbbedadadebaddbbabaedecceebaabaceccadeabedeacbdebceabaaaaabceedacedbcbbedccaadcdcdddcddcaeabeceadeeaebeccbaaebbcacbaebabbaadccdcaadeabbcaeedacabcecdeeecaecaaceadcedceecddcdceecbdcccddebaacdaedcedbecacdaddbbaeecebaabdaacddeaedaedcedcbaeacdabecbeddecbbbbaecadbaaaceeaeecccbabaaceebcdbbbbacdeabeeecccbcbedabcabdccedbbdbecccbdbdaadededbadbdacadacceedeacccacbbbabbeeaddedaababcaadcceabbbdaeededeeddaaacbeecdcbbebceddacdabaabadceebcdebcaedaaeecbedebbadcadebdebddaeddddbbcbbeaccdcadddbaebdbabbceacaeedbbccdeaecedbadcebbaaceaccdbadceadcebdebeddccbedebdddabeaeaebebbcbbecacebabbbaeeebaabaccabdadbeaecddcadeedceccebadeedaadeededdeeebccebebecdeddacdeacaadcbadceccbeccbacbaeaccccbdeeabeadaadbccdbedeaacdcedcabddceccedbcceeecceaaaceedebceeebcaeaccbddccabdabcccbbcecbdccaddaddebcdcdececcbdbbdbadbcbbdeeaddbcadabaedaeebacbdbedebbbdbcaacbcddbbedbaadabbaccceabcabeebbeaccbccbddadbeebcbcdddebaaeeabddddcdabdcadbabdbacebeecebebcaccbdaecbbaadbcaacceaddaedeeecceadcbcbbaaadabacacaecbccddbeedbbcdebaacdeaaacbaedeaebcacbbbaeedaadccbadceedcdbcaedeabeccaaeadbcadbdaddadacebccebdacaedebbaaaecccdcddaddcedeacecabccdecbebedbaabcabaecbaaddaeebddaaeaedcdbadddcbcddeabbbbcbbdeebeedcdaececddcebeacccaaceceddadcdeebeaecebaebcdbeeaceabceaadcacbdbbcbbeedebaccddbecaacaecbeacebaaccbcabacaeacddceccaacddccaddaeaeaeaadbbacaaecddcddcdcbecacceaceaeaacaaadadbedaedeaceaaccbcaccccacdecabacabaaccecdcecebcbbaeecdcaadbddbcdbecacdeaeadebedeedeecaaeeabedccbecabbcecdacdeccddababeaeebccacbdeebeaddccbeabcaeabbbebbebdbecdabdccbbaabaccddadbbdebcdbedaceebdbcbcdeadcaccbbeebadcedebdabcacbecdabeeebcedccddbdddaaebebbebcdeacdbbdcbaeecdcdbcadbbbedadcbccacebeacdddabdbebcdedcdadabdbdeccbacadcddccecdadecebcadeabaaaecbaabdeaacaeadaeadbaddebeceaecdeaebbaebddebedccaeeebdcadcbdeaadeabeebacbdceaedbdeeceacbdaccbabacccadcbdcebabdbdedbbedcbcebbcccaddbabbcbdbeceddaeadccaaeaaedaeacecbcaaeabdceeacdbdbbaacbcbbebcdeccabdedabdcbacebddbbeacaeddebcabbedeabadbaadbececdbcdebccddbbdbbcbededdecdddddedbdcdebcbcebbdcabecaadbdbcbaadcdbececcdbbbcbdbcbeabeaceaeaabcccadcacdddecaacbedaecbedcadaebbdbaddcdecacbedcecdbeadaaeebadedbaaaaaeeaeccdccbddbecaedadeedececcbebcebccebecbebacbabaedbccbecdedcbabecbeecdaddbaabdddecccdccbceddbdabbaaaedbbbeeabaaadbdcdaebabeecabcbeccdbcedbacbacdcecdbbcdaaecbbdbaccacadcdddcbcebabebbdcacedabcebbbcbadcccddcdacabaaededbbcdeddddaccedbbbddbabaaacddbcdcdaadbcacedcdddaceabbecabececddcccbcaecaacbddeaddbeadaaebcececdedaceeabebdcedceaadabadaecdcddecaeaedceebcbadebbabebdbcacabaebeccdccbbddacbeebabdadbaedcdecacacadeecdcdeaaeacbdbddacdddaedededbdebdadbcbccaaaeaebeabddbaecacaaebaebdaebddeebccdaecbbaacdebceabdcacbceacbccddaeeddbbaeeebddabaebdbeecccdccecccbbabaabdebceabeecebeacadbaeeaacaabddbaeacbebdabedaeeeedadeceacdbebdacabaedacddebcbcadcaeacccdbbccccbcabececdaaebcedbcebcabbacedccbbbcececdcbbeaabdbccebaadeeecbdedbdbcdabacaeeebbecbbcaccaeadbecdeccebdeeecedbccbcdbcbbbbddeeecbbddbdcdaddbddddcbbedddbdddbcceccecccaaeaeaecceaaceddbddccadeeccbdebedeaaacdacbedceabaadbadedcdbdeceddadedbdceeecaedccdeedeababceabbacbabaabaeacbbeadbbebcabedbdadcbacbacabbbdaecbdceaabbbaaeadbdbcacabebddccedebccbbeaceeaacedcebdabadceececabbbdbeacbdbcbdbcddebaeeaceabceebccaadeacdeaeaaeecbeecbeaabbdbabbdecadeacdbcbcabbccdadcabdbeededbdaabccbaebcccacdcdcdcaccdebbcbcaaacaddbedbedebcacbecccebcceebbbcdddbbdadeadcebcbaceaacebebeeeeccdacbbdadaabdacaaedcdeabbebedbdbdeebaabbcdcabbcedebbeccbcbacbebebadddabcaaedacaacedccacbcbcbaccdeededeccccedceaddcadacecceeaeebaededaaadcdecbaacecebeecdcbebeadbcedebdedcabebadedbcbedcccbbceeeceaaeeaceaebadcdacbebacddccbaabbedaedeeddeceabeabbeeeeabddebbdacdeeebaaeebbcbedacababccbebdbcbbcecaebdebdaecdebaaceaaaadadbedbadeaeaacdaacbdccadbdbeaadbddacccadcdeadeecabccbddaccadebecbbececbcabeadaaaabaebdedeeebdbcbeaecabcadddcbbaacedceebcaccbceddcbeaacccebebeddbeabacaedbebdcebeecbaaebaacdecabbadddeecbebadabaeebdceecdbbdeaddeaebddbadceaaabcccbedbdddabcaabcecedbedddacbaeedbbeeeeaadacccdbebdaaeabbdcebcbadeddebccaababbecaceccaaeceabbbbdcbccbebbdbbbeacdeceddbddadbbddddbedbbcbcdebeedebebebdecbbddaeebbaddecddcbeadcadceecddadbbeccbdeccedabbbdabbcbaceaebdddcbbcacdbcebcdaceebbcaeeeaaaadbdabdaabcacdeddbeddadbcaedacceaecbcbbcccdadceccbdadadacceebbacddcacbbcedabcdccdddbccdcadacbebbdaaddadcaaaceedccecbaebddebdccdcebdddbceadedbdabbaacdccedcbaecccdbdbacbccdebeadebcceeeebddcdabeaebdaceaccedbebecdcbccebdbcebebdaabdcaedeedcbbcebaaebcbadaeeddbeddbedeaeddabcbcabbebcdcdeccdccdddccdbdeacbbeecadeeedddebdcececddbcbaacceaedbcdddddecaddcdcecbceaeedaedccdceedbcadbcbcabeeaadeaeebcecaadcdccbeedbccaaadedccaeacabeeebbadcbabccaeadceadecdcaebebadbbbdcaddeaadabbabbcdadceaacbccbceddacdeabacccbdbbeebcdceecebeedbcdecbdcadbebcabeaccdaeacaccbcdecebabcbaecbbceabdbdccecbbccbbadceabebaedcaabeabeebacbeacdaacbbbccdaedbadecbbaaecabcaacaecebaddccabaaecabdcbdadcbedecaeccaeacbccbdbcbcdcabdaadacddbbcadcebbabeebbdccdbbdedcecbbddebeddceeecccdaaceecbacacbacddcbdcddddbcabbaeacaedbbcbdadcebaacbabcbddadcaaddbeedceddedadabcdeadceebcededadabecadceecccceebebbcebedebbaedebeecdaaeceeadbceadbcadadedddbddbdecedbcacadadddceecadbadceacacecbcabdbbaaaedebbeaeedcdabdcdeddaacdacedacbeaeecdecadcbdbdcaaedebaadabdeaeaacabadbbeddeeacbbecbedbbadcdceaeeabaecdceacdeeaeccdaacdddcaaccecbaddadabdbbeacedceadededceabaddabbdecbacccedbdceabdeaabeeceeabaeeeeccececacccbaccebbaedbcbcacbcabdeabdacddaadddecbbdabebbcbeaebaddccedeedebebdcbddedddcbcdeccdccdaeeebdbbeddebacbaabadbbcebdaacbcbeeedcbdcaedbcecdebcceacedcebabbebcecdbbecedbbbeaaacdabedcbdebbbdbcceaccecbadacaeaddddedcebbbeaccedaddcebaabebdeeaadcabacebccedbcdebaeedadbceebbdbdbaddecccddbbeabbdceecabaaedeaacaebaaddedbeacdaacacddedbddbabbccdabbacdaabacebbabbdddcaacaaeaeeaadabdcbdebbdacadabddbbebeceddababccedcbcedaedbacaebdaedbeceaebadeaecabeadbaedaaaeeeededbeaabacdcdddadbdaeaaceddccbaecceddddbabeccbcbcdeecdeedcbdeacecaceebabdcceeaccadacaaedabdcacbbcaceabceebecdbeeacddecccdcdcacddcbdbcbbadaaeaecbbceababccddbdeccceecdcbaabeebdececbbdeebdbadeaedadaecbcedddccadbaddbbcdcbcdebbdedaaecbdbcdceccccaddbbdbcbedaabbebbeecabcabdacadbedbecbaececbcacbdeacdbccaaedadecbeedcabcbcbbaadbeadabaacacbdaeabacabcdebdcadcdbaeecdecadadecbabdababceabebacebebddbcaccbbacadcebecacebbcccddededaeedadcebdbddbdabeccaccbaeaecbacabadbbeedcebdacacdbdaeeeaaecdbeeacddcaaabceabbbcececadcaeceddcbbcdecbdbaebcbebcebdadcddccaceeacbacbabbdbdadceeddaabbccdedbceebedceabbecdcbbdbbcbceeadecbbaabbceeddeecacbceecdcebacccecdccbbcacaadabdbaaccbdeebebeedbeaecaeeccabdaeadaeecaeaabaaeabdcbcbbbeeeaebdbadaccceebbaeacddbaaeceebdeadeedddeccdcedeabaeacabdcdacedeccdebdaedeadccdeeccebdebdbbdbcdcabdacbbebedccdacddddbbbaeaacceabcedbdabbdcadbbbbaabbbeeceddeabcaccdbabdbeabdcecbacabcbadacbdccdccccaeaecebbeeececabcaabcdbaeacccabeecabaebabdadacadadddabbaabddbebaabebbabbeeacadcbaadaceedcdaacedaecccbcbdaebddbcacadeebbbbccddedebeddbdadbdeccdaaccbedcccaebcdcabeaecbeaaeceaabdeaedbecedcebaebeddbebdbdebcddeddcaeaddeccdedcdbdbdbbacbaaecaacdaadcbecebddbeeecbbbdaaceaabbcebcddcebacecdaedcdbcaeacbeadddcebdcadcecbddeecadaeaaacebdcaaadaeabdeeaaaecdbceecbedacecabaedacbcdabacdeecdaebdcacbbadbbeadcabdadbecaabcebcadccedeaaddddbeddbdaabdbbdbaeedbcccbaaeceecdcdeecccdebccdeddcbcacaeabadabbeddecadbeebccbabeeeadccbdaacedeecadbbbdbbbccbadebdabadecbdcbabaccebecdaebaaaccbbbcedcaedcadbdadaddcbaccdccbcebcdedbadaacbaeceddcdbebeeedcdceddebaadedccbbdebaeaababdaadedcbeedcaeddeceecdedabedadcabbadeeecbdedbedcbabcadcadabeaaabaccbbeebaeeddccbaddbdadceeadaebaeadcaebeceeccccdceaaebcdbcbdaccbcacdceecbbddaabeaeaaaceaaecabbdaabcaecaeadeecdcacedbedcabbddadbdaacebbddeeddaeedbeaabdddccbeeebbbdcdaccdacccceddaceecadaacbadcdadcccabacebeaccdbbacebbcedccaecaeccdbecdcebbcbcdcbdcedecedebabddcaebbedabadbdedcaeaeeeebeedabaeccccdeeccbaeabcebdeddadaeeaddedaedcbbedccbcedbccdccabbcbebeecbbaecaeededbadedbbacebccbaedabaedeebebacadbcedbcdaacaaeeeecbaecbdecdabdbabadaaabeaddedabcdacdacdadcadacdacbcccbacadaabcedadadcdaaaeadaddaacccadeddaaeeccddaccbadacbbabadaaaebdacacbedbddecccdedbedbbaccbbbdeecbacaabceededdaedcaecacdbcdeedbbabeabacecbdecbedcaeaaeddddebaeeceaeaddcceebdaeadcbaaaacdeaedaebabadebdcceabccccdeacbdeaebbdacbbeabeaecccddabebcebadcccececbaeabbddaebacedbeddbbebdaeedececaadccceebcdcbacdcdeadbdcadaeebbbedabcadacbdcdbcdecadecbbbbaaebaeccddbaabcaecdbdeeebdccaaacbbebcecedbaadbebdbddaeecdcadeeedeeedbeeebcbecaebeceeaacabdddcbdbcabdaeaecaceecdbacaebdaecccededecbeeceacbcbaceedbaddeeccaedeaadeeeaabddbcedeaeccdbcabebcadbbadaeeccadbcdbaeedcaadaeccaceceaadedabaeadcedbabbccadbecabebbcacaeacaadadecaacaeddbcddecbbcadabeabeccbacccabeaedebecdebedbcecceababcacccbbbddedeccaabbcabddaebcbedadbeceacedcdadcbdbacccedcdaaeaeaebccdcbcdcacdaebbbcbebbddadaedcdabbdedadcbbdcdecadaaddbbbbbcaccbcbadadcabcaeeeedbeeddddcbbaabbddcacaaadceccddcecbccdaedaaeedccbbabeeddbbeabbadbaabddbcaececccaaabdbacaceedaaeaadbbbceaaccdbdbebdaebdaaaddaeaddcbbebbaacaaaaeecbcceadeecbbebcccaacdccdbedabadbeeacaccaaeddcdcadddaadccacddbeeabceaeeedbdbabbddabdabcdedababbdccbbecaaeceabeebbabebceabcbaeadcdcecdcdccbdebeaabaacccbacccdacceecadbecccbaabbabbedacaaadbceeeddebccedceccaccbacebeebbbeaaddecbdebeedcbabcdecaaeceaedbadacbabdddddaabdbacccdcbaaeabceeaaaabaacebdecadedbcaedaadaadcdebaaebdccaedeecbaabadeccaaddbdeaedceeddcbeccecacebccacaebadbcececdaeceebaedaaadaaacdecebddcdacdbeabadbaedcddeaedcdecbccaaeebbbcacdeaccdbbaeacaedcdddacaddceecbbabaeddddeaaeadbcebbcdaaaecaaabdbbcccbddcdaeaebebcacebaeaeabbeaeebcaedaedcccadceacacdceaedeedccdccaacdecbbbcecaceadaadaeeeaadcddaaaecbcdbaabccaadbbcedccedceeaeaeaeccdbeecdaccebabacbadcadeaedbeebaaacaabcddeabbbecbcaedcdabcedccbaaceddcccddedadeabadbcbbecedcabaedecdaaccebedbaddabacbbaabadbbddeababdceebdeddbbcbaedbbeaeabacecbaccdaddbbabbbbbccdacdacddeaecabbbeedddcdaeababbcbcbbcdddedbcdcccbbbcbdcbcdaaaadcbaeaaddcdaedbbdbedcbdcbaaaecdbeadebcdeccdccebdebebaaebeedcbedecdedadbddadeebdcabecbceeeabdadcbabddeebabbaadbdceabadccbbdbaebcdcbdabcbdcbdadeebacbebaeacbcaaaabbcbddadcbddabacdbbcdebcdeabcdecdaaccedbbdcddddbdedbaedaabebdadcacdaecbccebaaecdbceadbdacbdaeddaacbaababacdcdaeddeaedcbecccbbaabbeebbeecdcbadaddaeaedadebdedbddbbeacaaabaccbcdcaecdddceeaaeedbdceaeeceabaaacaadecdbacbdeddaaeeadecadaaeaebdcbcccedeccaadecdddcaecaddcdbaebeebcaddcadaaaaabddbdebbddebcddccedacccdcaaedbdbcddacccacadabdbbabaedbbedcbcebbceabedbdcacaabebacbbdbdaecadbdbbeccbcabeabdccbbbeacaeabaeccbcdaeebaedbbbeccdbbaebcccdecadddeaeaadbdeebcedbaeaabccdbcdebbcadeeeecdedaabcbbecaccbcaedcbccebceeceaddacabddaadbddbccbddbdacbadedcbdeeeaadddbaebbeeecbbceadcdbedbaeabecbceccbedbccadbddbbebddcebebedeeedbdbccdaeeabeecedcbebdaddaeadaedadcaadceadeecbcedcdadbdbdcbecdbddcbacbebedceaebebdeeeeceebbcadeccbbddbadaaebbeaaaeeaebdadecebcceeeaebeeaedebdccebeaabdbdeceaeadbacecddbebadacaaaaddecddbecbaecdbcdcdeddbcdedcdeacbcbeceecbabdccbbeeeabdddecbacccbaecdaebadbbddecaaededecccdeeebeabbdcadeeaccbcaacdcceceddaeccccdebaccdacaedcaadaeaeaaaccebbcbdcdacaadbebbecaadbdaeaadcdaacbeaaaeadcaecbeddadaeccbadabbeabcacebeeabbdebccaabedcbdeaccaabedeacbcabecacbcbbacbaedbebaabccecbedecedbbcddabecabbedeeeadacecebeebdbcdaeacbceabedabedaddabbedeabaaabaccdceddcbbeceeecdbbecebcddccdedaaeeddecebaadbacaaddedebcadacccdceedcceebddcabcdbeabcabeebcadaacbedbbcecdecdeddbdadeaeaeaeeadbadcedcddcbeacaccbcdeddaccbbbaaeedaabdccbaadcdbbbcdebcaccbcdebeeaaaceabbbabeebecbbdbabcacddecbbacabbccbcebdbeccbaaecebdebdacccaadaaeadadeccaccaaddccaddbeaaedbcdabeddabeeeaaebeadbbedcdccaccdcabcdcbaeccadaecacbdcbdecabadbdecdbcbddcbbeddecbadcabaaccbcebdccebbbbabaaaecedbeabccdaddbaebdededcbcbccaddbedcadaeadebedbacaacbeeacbeccaeaacddbeaadacdbdbeaaabddeddbaaaadbbcbecedbdcbdcdcaaecabdbcacbdcdbebdddcbebedddcbbedaadaebedddabcddbeedddeeceedcdeedabccedbdeebacdbaceeceacbddddceecceeadaeaaaeaedadacbcaeadbedecbbcdadaebbbcebecdbcdbddebdedcbbacdcaeceaecbcbaabddaeeaeadadececcbbdedeacebcadaebbebcbbccccabecbcabceaedcbcedbcecabeeebcaecbcbeccaecebcecbcaaedeceebcecbdcbaabebbaabedcbbeceeddcecdbdbabcbccbbcbdaddcdacddbdccebceeaaecdeaeaddabbbabecedaddaceeebcadeabdaadebdabddcbabacecacacedbabcecdeadddeeeebebeecbaebcbcbaeebbebaadabecabcbdaecdeaccccaaaeeeddebeeaacababaacbcebadaeaeddabdeaeebbcacbececccaddbbeddbaccbaacbecdaacebabeaaaaeddaedeccbdeeddaeaebbadebececaeaddddcaedebebbeddcbdeccaedeaedbaceddccedbbcbbdaaeedacacaeecadaadcebacbdabbdbebdecaaaabbcebaacbaebeeccdbbbddbecbbbabaccbdeeaabaecaeeebbecacecadabdcdeadedecedaeeadbececeacecdaabbadaeceebebdbabacebcbacbbbdacddddcbeebdbebebbdcedacbbedcdbbbaecaeddebdcdcdcdbbebadcbeddaabbedccaabdcbbcebbccdebdadeaaebeacbedddeeeeddbeacecaaddbebeeaabadcdacbccaaaccbccdaaceaededcaddedaadabbbdeceeadaaedbdcaebeaeeaeecbedaeeeaacbbceeaadcddcbbcbcaaeedcaccdadeeedcbbbeebeeaecabdacbdccbadcccaaceecbdcadaddeabdbeebeddadaddebdeceaacabbcbeaeacdeabcebdbdcecdcbdbceaebbacddeeceecebcaecacadaedebbcbdbdbaebbaebbaabbaeadaeecbbadccaeabbabdabccccddebcbbeedebbdcccdcecccedcacbcadbadbcbeddccaadeabbcdbbadbedebdddbdaabaaeadaaeadcabadeecceebbbaeeeadeebadacbbacaeadedbebabacbcceabaeebbadeebedbdbceacdcbebcdcbcdbedbdbaaeccdeaaacecebccacadbbcddacdbeacabdaaebedebacbaeeaabdadaceeecdaabcbbdabebecadcbdceaaaccdedddcbdaccebdecbdecbcbdcdadbdadabcbdedaabcabaeedcbacbedcccaecdccbcdcdabcddabbcbaaadabdabdebbbadceeeeabceabbccaeddedebedcaadbebbceeadeaaebaddeddeecacbcbccdecaaecdbbabaeddeebdabaedeedeababebbdcddbdcbbaeadbbcebcaedddeaabedaaadedeecaebdbacbdacbcceacddcabaccddaebaceaddbbdeecedcacecadaedebdcccccbeaeaabeddecdaadccadadbdbcedeccaddabccbdbdaababaaacecdbdeaeebedaedcecbdbbadbeedcabecbaebbccbcbebeaeacaadecccaecaccaccddaecabdddaebeedabaddaeeedeeeaddaaaabbbdedabceaadbebdadeaabcaabcbbbbbbedddcbebdeccbdbbaecbbcecadbdddacdbebaddbbedebceedceaedbdcabdddcedaddebabcdebbdedabdcdadadcbaacdacbbeadebaccdbbeebecbddccabbccebccbedcedbdececadcbbbdbddaedaddbcebdacabcdbccdddeebbeebaabbcbabdaeccebdcdbaabaceadabcbbadabcbdcacaaabbebebdebeeacdebccdddedceceacbdcddbbcecbadbcbedbbaaebcbdddbbbbeecedcdcddedeeabdcbedbbccebceddddbebcdedcdceebedbcbccdaaebbbacebbccbaeeacdbebeeaadbecebbeedbaecbadacbeeaacccbbaecebeaaadbacaaadcddeaacdbcaceacbdaeababadbcaddedbacdcebacbecebdbeeebcabebabddedcdddcaececacdbdadceceaeeaeaedeeddeaacbadcededdaedeabbacebbcabddccedcbbdccedbeeebaebeabeceabbabceecaaeddeaebebedcbaceceaaaeadcbeeaaaaaadcadbaadcabdddbbaedbdaeceaadeaaecadcabccaeabbddcadcaadddbbbeaaacaaeeecadbbdddccbadaeeccebbdacdbeadbccedbaaccbcbabcbadeecdbaeccbcdcddcddbebdedebcdbcecbcdbbbdccadbabdaebcdbbeeedcdcbbaedaeabbbeddedcebaecbbebbbdbdbecdacbceeaeeceedbbdeebabaabbaabadebdddeacdaeccbdeeccdcbeababdbcbeababdbcdadcccbbdcdaeaaabbaaadceedaedbcaddbbeacaceaaebdcbbaebebceabaddecbbaeabecbaeadbedccdacebcbdeddbdcccaacbeebadeecdecdabeacedbdbdcecaeacedbbeadbcbecdddceedaeedbeaceceddddaabbacedcbbdbeacebedacbadceeeabebabcdbdccecaadaabbbaeaeaecabbeebbddecdedaeedaecedbedaaacbccdedddbceacddeeceebbdebaeeceaaaebcdcdebdbadbcdedcabaabeacdecaabbcecedcdddadcccaacbacbeabcdebceccccdceaaccbebbcedbcadaabddbacbbdecddbaecedddcebdecabaaecebabadecbaccdbabaccbeabdcdabecdebceaecdeeabbdeeebebbddeeebdbecccdeaacaceccbacccaeeacebacececebeccaedacebcceedacebdbbbaecbebddbebaddabeddddeeaeadceeacaaadabbcdabcbabbdbbbbaacddeaaceaeabdbbaeeadeebcdaacccaadeecccebeaaedddecbdedbeebcdbcacbcaaadddbcbbccaecbeedeccbeecaaeaeaaeecadddaabeedbedcebbacdbaecaabeedbcbaaaccaeeeedaebedaabbaabcebbbaeebcbcdecdddbbbddcdbbabedccbaaedcdbecadbbaaaddbddbaeccebdbbddabcbadcedadceebbebcbbdcdebdcbbeabbbecbaacedaecabbbaedaaddcbcedbacedabecbbaddeeacbcebdaecbedcbdbdbdbecbedcdceddadbceebdddaabbbbbebbedcaadbdebabccaebddadccbcacaedbcdacacdeddaceaaeccbbcaabddbabdcbcecdaeaddaebbcadaaddbbabaddabeddeeadeabeaddbadedbebdaacddbbeadbaccdbedddbddddacdcbbccceebbabedbdababbbadddaecbdbacacddbeedddeacadbcbadeddeedbcebcddadecddaeabdaddbcbabbbccabceadcaeadaebcababdeddeabcbadeadcbcabaeaecaeebabcaecdddabceabbaebdccceadaadbbbcddedceaaeebedcebbadbadecbccecdbeaebecaaebbcccbdcdebaadcccdbecbaeeccdbaecaddabbaddbeecbeeaaeeabbbbeedcbdaadcccbceaaeebbbbaaaddebcceaebceebdcaeeecbeddcebbdebccebdaeaaacacbddecddeeaccdeabaaabcceaebccaabaaccadeddbbedbdccbddadebccbaaccecdbbddcdcebcbaaabbadedaeaeabacdabeaeedcbabecaceaccaccabeaaddbeccaabdeecddeeabddccdeeeddcdeacccecdbccbdddbdbeebcceeaabbbcdddeedbdcccbeaaacbedcebadeecaeeededbbdcacddadcacbbbbdbccaddbbcacddddaaedeaaaeecbdbadaecdaaeaacadcedcebdcbbeacaaebebcceddcaaaeaeebccbadceebadacddbbbbdcdccdaebabbbcdcbdabbbcceacdbeacdecdcecbebacaadcadbaadbaccecbcbddceeccdaabaaaaaabdbdcadebcdebabbdcaadeedceadbaddbdbcbbaaacbcaabbaeaecbbbcdedddbdbcdbccdcbacaeadccabdeedecabeaadadadebdeeadbbcebbeccaeedcdccdbaeabcdacbedabdacbacdbdedababccecbdbeddeceaaacccabbecddeadcebdebdddbaceabdbbdeacdebeeecdbaedcbeadbcbcaebbbeaaceeabdaacbddecbabbaebddddbbbcccdadeedecebbccddccecaebedcacddbceaecaacccdccbcbbcdecbeceddaecdedbbedbcbcdbdddddebaaebcebcdabdcdeaddbebcccebbbcedbebdcccbaeaddcabaeabdebebedebcbadddaecaccaabadebacacdbcbbdeabeebbebeabbacaabeabbeedeecabaebdcebdabbabbbcdeadedcddbaabeedddbaccedaadbabeabebbedadbdcbbaeeeeaacaedeeabbabdeeaeebbbaccbcbaabcbeedddbddadeaadbbddadcadabcaedebdbbaaeeeaeebdaeadcdecacadeaaccdddcaeaabddadebeddcdbcbdbebadacebeebddbcdadaeeebdaeeeeacecabadabbeddcbebcbeadadecaccddaceecddacdcbcceeaaceedbebcdddcaecaecdeeeaadeeedadddbccadedccbeecedbaaebadbdcbeacebcaeaacaadeaceebecbdaebccabdbedddbbebaeaadbaecedaacadebcabeccaadebbbccbecbeccaccbbdadcebbacccaeceebdeacaeabdeebbdbdeedddceceedeeddddbaaebdacedbeadececaaebcbdabbbaeceebcaacbdbccceecdaeeacabdabeeccdedbecedabdadcbddbedacacedabddaadebabceddacdbbdcbeedecdeadeebbadaebdabaaadbcbcedbaacbaaaeebdaeaadaaaabdeeeaeeaceccdaebaebdaadbeeddecbbcedcacdcbddcadecdaedebbaeccdebebbdbebccbbdaceeedbbbbadeddabaecbdbbebaadbbcdeedeebbbdacbdeaeddbeeccecbaaaaacdeacbceaaebedbbdadbadabcaeebcdacceedacdadcbccaaaeabccbdabaaebbddaabacbaccbdcceadeeebcecacdbececbbdacccdeebebbbbdedaeecbdbdcecabddceaacdbecbddabebbabcedeabeeebbccdcdebaebbcedeecebadadeaabbccdaececcdbedaccbddaaeeccccaeaabbdbcddcddaccbaadaaedceebdbdebacbacbaaebedbaccaddedcbdeccbaeadceacdddbbdceadddcacaebbbbbaecdbebddcdeecacaccbebabdbabdeebecadddccdabcbecaadedcaeeecbebeccceeabaabdaabdccebdcbdcbaecbbaabbdddcbdaabddccdbcbcbecaaeccadbaecaecbcddbcbdadbbbebeabecaaecbdeaceccdccceeeadcecadabeaabaccdcaaacaccbeceaccaecbcececbcdbebbcdaeaedacbbaecddccbcacceeccebadbcccaeabcccbadeabedbbcaebdecbdacccccbbcbcdcdbeacdaaaabdeadcababbddeaccacebdaedcadcbdaccaaddcedaaebdebdebaeebddaceeccaabbdbdcdbecabdeeaadbbcaecebacadcacaaadacacdadcccdcdbbbcdeedcbedeecedddcccadebbcbbabbaaebeccaecdcecbeecdaaebeaacacdbccaecbdddcccadecceebeeacdecceebbaedbcbbaacbceadacbadbcabacddbebbcbccaceacdeaecdbcaebeeecdcbddeecdeecbbbdacbadddacbedddcabdaebadecebeceeeebdaccdacdaaedeebbcdacbcbcaeebcbeaaabcbdcaeecabebcedadeadbbdccceacbdacccaddbceceeaadaaabbeaaaabddecbdcedaccebeadacedcdaacceceacdbbeadeaebcccddecccccbbcedcaaecdccaaeaeaaeecccbcaadcdceeebbacacebcceadeccdbcbabacedbbdedcacbdabccedcecabaebdaaecadcaeadecaaabdcdaddbabcaedeebcbabadbcaebecbcddabdadbbdeebabdaccdeeacdadcbbeeacdacaaaebedeaabcabbbebdababcbaedaacecbbaecdcbdaedadcbbceacbbeddaddbadebccdddebceedaeaccaabccaccbbadccbcaccdedcebeadcbcadebbdcccdabddbbecdcbcbabebdcbcabdbbbaecabcdacbaeecabdeebbaadebabcedebeecdbdcdeaadededebaddaabbbcedeaedcaebcccbbdcbbebbdecacaaebddecbcccbbbbdecedcecbaccbacacebbcadbcddcabcadecdbcbcaacaebcaedaaddcbebdbeabeccbbaecaeeecbdabadeebbbcdbcddcbedbcadbabbeebdabdcdcbabbbaaebcadcbcaacdeaeedbecbbdeeabeecedbddcdbaedbeeceebebbeecadeaeccdbceeaeccbaccdebbeeebcacebcababceaacdaaaceddceebcaeaddcbdaaabcbeaeeabbaabadbccacabaaccdceeecbebdddeceedeccbcebedaccdddacaacdcceddebaccabbbdeeebdbbabeedbeebeabccccbcbadaacbaabdbcacedbdedaecaabebdcaecbadebacbbcbaeddedadecacccadbeabdbaacceebcadebcedbcddadbdbadcebbaebccdcddcdbdeabdbbbdebaabcbbbbcbdeedaebbbadbaaddcebcecadadeacecbcacbdaedbedceabdaabeaddeddbcbddadaebedcaebcededccaecacddcccccbeaeccdbccedaeedcadecdaacecccbaebbaededdbdddccdedabedeaabeaaccdabaeceaeecedddbeaaebadaaeeceabbdcaaceebadedcacdeaebaddacdedcbddacddebeaeabadbcdcadbececabeddbbbaebedddcddcebdcccadecebaacbeeaececbaaaedbdccedeccecbccdbaddabddeedbebecacaabbdaceceaecbcabedcbedeecbecbdccbadbcbecebdadcbecceacceeaeedbdbbbeccadaebbdecbbaeacbcedaeacbbebeeacecebcccdceceabdabdccdbbabdabbacebcbdabbbdcdddbdcbbacbbcaadbdbbeccecbbebdbeaabeedcbebaebaebbdcedceceeababececeeedeaebedddebacdebcbeecbaabbbdcadeecddcbdaaaceedbcbdeaabeabbbcdaeecedccbacacccddcccdbebaceacbebbebacdcbbcdaebdbdaecdbdacbdcbceaccbecbdbbadbdcadcddbbabbcecbcaeaaccabebdbebabdecdcdbecbdcabbedaacdebcedeccbadcebdeceabcaacdccdaaacbbbdbcedbabddabcddeaacebaececbdaebbbcaabbeaddbbbaacddaecbbbccebdaeecabbaebbcaabbbeaabeadeaaeeacaaedcbcadbacaabdedcccbcdecddccadcedcabaeaedcbabbbcaeabdebeabacbccdeccbbdaededddaaaddaceeeabbbbcaedadccbdaeeedebddecbaceaeeccbebedaccaadeeaebeceebdcebcccabdaeaeedbaadaeecedeeeecceedbebbebbaddeabbeeddeaaceeaebaebbdadeaeeceddabecdbebadddaecbdebdceabdaedeedaedabbcabedaaccdbaebbbdbabacecccceeccebcaebaeeeeeeaecbaebacebddedadebbdcdccebddbbbdbdcdbbbeddbbdebacaabcacdbbbadaeaabaeddabebaacdcddeccecaeeccbbadcbbdeaedbbadcabdabaadeeeccaeeeeaddccdecebbacacbcebbcecacddaaebddeebdcebbccddbdbbabeeddcdadebdbbebeebacbccbbabcbbededaeeebecadcdbebdeeeeaeeadcebdcbedbaaebaeebbdaacadaebdeeecbdcdccebbdceedbeebcbceebabaaedccbeadbaeacccbeeddbbecaeddbcebeccddeaabcababbedcabacccbeadadcbdbcdbcecdbaedddaaecbbbbacabaddaecceebbebebbabeaacabecccbccbdaabcdbbdbcbacaadcddecaacdeeadcbabecdabbaacbdaedcadabaaaaadddebeaaccbeebaabaccbbabdbeeececbccaacadabacadaebcdeeacbcedaabcdcabdaeecedcbbdcebaacedabadabdebbceddacdbdaddabbbccadccbdccbbccacbebdaceaeaadddbdebaddddebacaabaabdddbaeadebdedadcbbdbecbbaabdaacbdcedacaeaebbbdacbdeedcbabddacdeebebabeabbdeeaacadbabbcadacbabbaaaaeccddbceaccddebaeaadedceebaacdeabadaadbdbacaecccbaebbbeebbadbaeeedbbabaebcddadabcdccdaebecdeeceaceacacccebdeedeabdcbecbbebbccccbdbecdccbdbcbdcbdbabccaebdbacaccbeeeaaacbededebcadaaeaddcdcaddacbdddacbdcbaadddeccaaabdcbbedbcbaadcacccadedcbadddbdbbcbbeecabdbbccbbecadbedebacbccdaeeccbeabeedcdeeabcbdcdeceadeeeedabbcaacbdbbadcbcadcdcaeeeeaabdaebbeabdaccaeeccaaecdaddaaaadcbcebebbeddaacdacbeabbacdcdbceddabbabecebdbdacdddaecdceeedcdddebcacbcabbdebeeddcdbebdbaaeecaebcceeddabbabbabbaaacaabdcaecdcbccedbaddbcaceddedbbbaceeccebeeceecaceaebcabdeeabdcbccddbdebcadaedddcadeedbddcbabcecbebbdbdceaaacdedcdbceeecbbcccdcaddbabaceaceaccbabcbdccaceebbebaabbaebcaccdeceeedeedcadebbeeeacecdbbaceddddccccaabeecccaccbebaabdeeaedecaeaddabcadabeabadebdacbeedceddabbbaacadebdadeeedbeaadddeddddaaceeeaadcacedaddeddcbdddaedaadbdbacddaaacaaadaacbeedbacabadeadbedaebeccaceacbbddcaaababbdeecadeaddccbcdccddcbcdaabecdccebabedaecceaceecbcaadecebeebaedacdcdbdcbdbdccaddecaeccbaededdcabcdaaebeeddddeabeaecdededacaacedbbbadcbbcbcddecdddcbaecceccccebeecbddecbadcbdcdeeedeaddababdbcdcdbcabeaedcebeacbbbcbdaeaeabcbcdaeccaaccccbeddddabdecdedccbadecbcceaeacbaebeadacebcdecacdbacaacdeeddbcabeebeebebdacebaddbbdecdbcacdcccaedddededdccaddbcebdabbaddbebedcbdacaeadcccdcbdabdeeaebddcddecedbcdcbabcbeceabbeaccedcddbacbacecbcedaeaadcecbbdebaccecdbeecebbbbdbadcbdaeeceebebcabeadbaecbcddcddebbacaadedabdceecaeebbccdddacbecaebbceecebcbbebbdcecedeeedbeddedbeacabaacedeeacdceeebbacbcacbdbeceebcddadacaaebecdaeccadbdacbcbeeccecdcbeeecdacaeedaadbcbecdcabebacbaabbbaddcbdedbdaaababbcaacacaedbbdbecbccadadbbdeaaedeceadcebececcbdedceebbacadcacbbbdeeecbcaeedababacdaeabeeaceacecdacdcbeddbbeeedaeecbbdddbbbedeabcacdcccdaadaacbcbadacdabbabdadadecbbcecdaaacedaadbdaaedcdcceabdacbacebdeedaddeccdaaebdccdbbeddccbaeedcddcaacaeaeddbdbcaaecebcbecaeceaddecadbedadeacceddededdaaacbddbeeebdbadbbcaecbcebcaeddaeaecdceadcbabbdeeadcbbddbadecdbbcdadcdaaaeedbbaedabcababaadcbeabdccbedbceebddbedcdaeabcdeccdbeadbebaddaeeedaedebebcdbedcbddbbecbbdaacabbcebdecbadaaaadddbcdbecbeeddaededaacddcbeeecacdebbaadeecdcddbcbabdedaaceaaabccbdadabeaedbbcedebbeecdaccccecbcadebcdbeaecedaedbaabecccddaebcbcccdcedddcaadcabdcceacdbbccaaaacbeabecdaedbeabcceaeedcdaadddaeedaddebdadaaecccaecbceddbaebbcbeacccecdaacdcbbdceaddbadbbeeadaedebebacededcbccbedcacdedaabdabdeeacabbceeebeddcbcdcaeddcbeedccaeadbadbceeccedbedcebaecaccbaeebabdbedcababdadcaaabbeeceeebdceebeaceebabebdaccbabeeaacbeeecaadbaadaeccebcbceeadacaecbbcdacbadbecaadceddecccbdadaaecbdebdaaedbadbcabcdddddeaeeaccddcbbdbbacbeeaaecdbdaecdbbeccbebcaabdaaacecadcdbbaaebccecbedaddbbbbcadacbabcbbaadadeeeacdacddaaeadabbddacabcedcdcacababacabbebbdbeacedabaacacbacddddcadabbcaacbcecddebcebcddbcaddceecdbccddceeeddcdacbbbdaecdbebaaabcdddbecacdcaaaccdaadbebebeeebacaebeabbacedaeaacaceceaebcabeebbdedbbaecdeadcdaaeedddcabdbccceadcccdadcabeccceaceeadbcccdddcacadbbacebeeddbbdbdbadaedadcaaaaaeddbdeeededcaebdbaccaeeebcdaacebacdaebdcdedecbebccbbcdcececcdebeaaadebbaaaddccdaeeedcccbdccaacbeabdeadcdceddeaadeaebadbceecdeddaddeaecadcacebabeccbceacededccddadadcdcaedddcceedcbebbbebbeeecdcbdaeeeedebbbbdedecbebbbbddedaeaccccdabcabaecdadedbedebcaeeceaecedeebabebacaadaeaeadeebeedadcebcddeebabdbdeddaeecbaaacdadccddbcddacebbbceaacbacebbcbeacbeccedcaddecebbbbeacdbbbdcbbccdbebedcabedccbdddddaedbeadeabacdecaebbbcdbaeecbeedcaecedcecccccbbcaaaeddcedabbbcabcbeebceadbeacacbdaeacabdbbeeaebabaeabdeebbcecadaaddeeabbeaeccdbdabadaacacdebecacbcbbbeabbbeacdeebbeabcadbbcacccaadeceeddeaccecdebedaededbdbeaedbddedcecbcedaaecdebbbdeababddecbdbeddbdeaddddceabeadccdeabbaededdecdacccaaedcbaadbadceadaadaecebbdceadecbddcadcbeeddceaadcdebdacceeebacdaabcaaeecabebeadaaeeebaeeabaaceaeaaddacabccaccaacbabaabbcedbbdbedccadaaedaaadccdbcebdacedeeedbbadacdcbcadebdddbaacdebaedcacbdbcedaabdbcdecddaebaebbebebabacccdaccceeddbeabdeeeadedcacdeddceaeccdabbcebbdccbdedaedaebabddccbdadcbadacddeacaacacabadabacccdcedaaebbdabeabbadedabdeaeedaaecaaecbebdeebabadedacddeedbabbebcbdabadbececabadbbebdeabddaaaaeadeebccdeeedaebcadcdeeeaeddcdbedbedaacecdebaeccebcaeccadbdbaabcadcceddbabbccbbeabadbeaddbbddccdbcdabdbadebeceedaecacdcccdddeacebebadccbcbeebadbdcaaaaaaaebdbeddaaccedadaaabdbdacdbbbabddccecdbdbcdcaccdcaabedbeacaeacbadbacaaadadddecbcedeabbcbedcecaebdbcbeedabbcdeaceeeadddaaccdadcdbdbaaaeceddedbbbdccbacebacbbddacdaacdccabeaabadcdacecbedbebedaeedbeeddcdddabaddbdbacbedcdccaeebdbaacbbddbaccceeabeededcdaabbaaccbbdaedcaacdaeebaecadcaebabebebbaabcaacdaeaaeedabccbaeabaedacedaeebbebabaeaaebacacdaaeeeaaeaeacacdcdecdacebecdbeadbdddbebcabbdeacbeecacccbbbbbabdbcbeaeccddbbeabbedaedbbbbeaeabbbcdbceddebdaabadbbebadcadcbcabbaddebeecbababeceedaecadaebbbbaeeedbbcddecabddcabbeacddaaeeccbdbbddeebedeacaabeaabcbcbeeddcbdddcaeedaeaecbaabddadcadecbebdabdeebdecebecebccebcacdcaedabaaddabeddbacdadaaddeddeceeedeeaadeaedadaabbbdecdadaecbbcdeebbecebdcabbaebedbdeabeaceabaadcaccbeaccbebebcbeabbeebccddabcddadbeaacadeccccddacaaabebdbabaedaadeedcbaecbdedebdcbbbbaedaaccbcecdcbeeadaedadecabbacbccccaddedbabebdbebcecedeedbbaabcddbaaebaacaceccbadaccedcacddbddeaebebdececbbccaceacccebedccbcdbacdedababeacecacaaaebeecedaacdaacaebcbdedccdddedabbdcabaecaabbeaedbaddecdaedcabcbceacdaaabdeacbbcedbbdeceadcdaaaddabbebbebeedbedbbdbeccdaaeecddaceacaedcaeadcacaeccaeacadbdebdbeedbaacdeebcdaaebcabcaaeddddbbdeadeaabaaaebbdabddcceeadcabcdaeaecbdbacdaaeacbbdcccbaecbbbdcdbccbccabcebddbbaaaadabacaaacdeebcbeadabeedbadecaeedabeeecccbebabdcabdbeebecedbeecabbdbbbbddbabaadebebacaeadcabdaeebbccabcdacaebbdddadddbbdbbebbdecebceadacaaaccdcabbcdabbabbcdcddaeecebdeaaeecddeacccedcccbdaebcdcebceaaeeddcedbdaaadabeddcdcacbceadeaaaeabeecbbddaeecdbbccdcdaebdecbaecbabeeeceabbddceaddadbaabcabccddebeedceaeaaedadeeccabbcedabecaaaedaadeeccebaadcbcbacbeeecbaecdadbecdecebedcbebeadbadabdcbedbccccdeaabbcabbbabcebecedbedeaacadbcccaccdedebecdcabcccdbadccaecbdaceaeedcccdeeeabbdeabaacddabdaedbbbdbccddaebaceadcdebbeaebbdbbdbddaceceaabedccbeaeeadedccacbccbbdbdddcbbedbbbecebbcbcbecedddcbeaeabcacadeebddcddeecdcbeeabacddeeeabdadedcbbcabcbcbbdceeeabbcabdaeeeabbacbaebbeaecaeeeeeaccedceceeddbbbcacccccdceebdbaeecdbcdcdddabeacbebcaaabceaadceeecacbaecadaaecaabddccaaecdcadaedcabaceabbacabecabbdbbbddeeedcacbebebcabaaceceddcaadadcabaabbedeecddcaccedbccbacaecebabdecdbeeabebaedeaadbeeabedbbdcdbdaacdccedbcddbbaeedabcaabcdadcdadabbdaacecddaadabbaaaeeeeaccdebbbadaebeaddcdadadedeabbdcadaaadcdaeddabeabaaeaebbbabcabaddbaebdadcacbdaabcdcabecddcedbcecdccdbecbcaaedbabecdcabcdcebebdeececbdcbcceeeccdceeabedbacebaddeaaabadbbdeddceaaabacebdcedbebdcbdebabebccacdaabdacaedcdbaabcbeccbbdeacebcbadabbcdbacdebbaccccacaabecbbbcceebaeccbaaddcecbdddbacadebaadceecaeabebddecaedcdacceabaabecaecddeaedaeddababedaddeeaeedbceaeedcbabbbabbaaedccddeeecaabaddaeeeeadaaebadacadacacedcbeaaceddcabcecdecccaeacbeddddeebeddceabbcdecaabecdcbddeaebceceedaeaeeceedbdbebecedbcedabaadbabeceeebbccacebdcabcdebcddeadaeabdacdcadebcceeeccadacbaccabecebdadecadebcedaabacbebcbbdeccecbcabceacadedddbaeabddeeadbaceeebcbceeabaceabebdedceebedeeaddcdcebbbbccadabedaacaeaceecceeeacaddebedcdecbcabbdebbbeaeabeabcddddbbbdcdcbceeceeccdaaacdceddeecbaddceaaecdaaecbdaadccaebdbaeceadcbceadeedbadeeacceeadccddeecdecadedbbddacbdcebcdcdaabedecaaeaedcddaacbccaeeddaacabadbcaeaaecccdadeaaeeccebaadcecbbdedacdbeddbdbedebbadcaebedcebeecdabcbaeeacaddeaaeabbcbaebbbdbcdeecadcccaedaedadcaebdbbdbdeccebebcdbdcaecaddadddcdecadeadcdcaaaaeedadddbdabceedabacecbdcaeabaccaaadaeaaaaaebccacbdcaceaeecbccdcebbbedbeabeddeccbbcbebccebadcbebeabbceaabaddbbcdbececeecadadedaabcbedddbeaacbcbabcabaecabdeadcedceebbdcdadcbacaecbabebebbbbddbcaccbecaabaaacbeeccaedceeaacdadbdbdacebacaccdbcbcacddeedcddcaaeddedddbdbbcbcdbeedbeadaaccadddbbccdededbedebddcdaecddceeeddbdcbaadcddbcaadcdbbaeaaaeaecabeeccabdaeebdadcceecbbcdabbeadabdbbebcbabdcdcbcadeaebebcdedeaecccbbeeaadebbceddbcdebdbcdaeaacbcedabbbdaadecacebdeadaeacecaccddadeedbcbbcbabbeddcdcaaeabbaadeaeeecebcabbabbcdcaacccbebcacaedbdaeeebccbeecdcedacbadbeabeccbbaabdacecebcbbbdcdbaaabecbaddccadaebcebbcdddaddbdabacccedebeceaaebebbbcabdbdbbedbbdebcababeabebceebdcabbacbacceabedebdcaababdbecdcebecbebdcbacdcadedbeabdcaccbadaaceccbdcbddabcbbbcdaeadbccececaeaeecbaeececadaedeabebbbdeaadecebdcdbddecbbeacdebddddebabeecbdeabceecbabaadacabdcbebdbcebbdcacbaeccaacbcdabaeccebdaccdceecdbebaeebdcbceecebacbbebcbbadeebbeddeeadccdcbccdeeedadcdeedbccbedcedbebcbeabceabaabaedcadddaaeaddbcccbeedacbdddabcaedbecbdedabccbeeacbcdedababbcceddebbccedeabeabcaceadecedcebcdbcaeedeecbedaaacdddcbbeaaabedeedacdccacbeaadbeebdbcedaecadadeabddeebeccbbdbdccceaacecabeaddababadcacebeaddabaaabdccdedeabbdbdededaaddaacbdddddecdecaeabeaeceaedbcacdbeebddaecabcabadeabccedebbdadaaeaecbacbbaeedbcddadabaeadaaaeacbadccceccdccbdddedadbdeabebecbdeccaaebcbeecedaeaeeeadcddbadcbbbeeaacbcbbadeadcecbbabaadceccecbddbbbbabbecadbaecbccdcecbbdebcabacddcddcbeebeaceeedabacacdcebecbbcdecaabcabbdaeddeaecdbebbddaddaaaacbeeeaacccbcccbaeabcedbcddaaeeaeeeacadcbcbceeeacdaeaecbedabdddbeaceddeeaecaecdeacbacaabbcbdecbdcceeeccbedcdabbddbcccbbebdcecadbaeddcebbcbedceeedaccceccaaeebddacbdcbbccaaeadddbdbcdcebcedabceadaebdabcabdddbabbddcdaecabdddcabadeeeecbeeecabacebcddcdacaeabaccbbccbecdaeaecdccdbebbeebeaeebbeaeabeaeeaacdccabcadaddceaecaabbdcacdacbdceebaeadebdcbcacbaeeacabbccaecabddedadbebebebcaaeadaaceeedcbabeaacbbccdbdbabeccccaecabcbeeceacdebbeadecdaadeabeaaaecdbaebbebddedededcdcbecccddcaabaedbdaabdcdeabbbabcbeebebbddbbeceaacbedacdbccdeccabcbabddbcbddddcebbbadcdbcbacdcedcaabbccdbceedceaeaedbbddbeeabdaddcaaacdacabecaceaebcebacaedbbdcdeddacdcecedcbabbaeacecdeeababceebcaaeeeddeaeaebeebebcaebdadaabeebcaeddaebedacbbbbceaabecdeebdadaedadabdbcbbbcbaccececddeedabedcdaaccaaaccacdcecbdeeddabcbabbadeabaceebbdebaeacdbddabcaaabdcbedacebaebdbbbddebcebdebaebbecbdeebbbadbeaaeeacbccdceeecaabadaeeccccccddcbebdecbcbeebacaeedaaccabaabcbabbbacaedbacabebbceedbaaaccbacbabdebbcccddadceddbbecaeeeedbebaabedbadcdcaaccacaaedcccdabedbbabaeddeeecbddbabebababadceeccbedabaebdaddbabeecccddcccdaaceeeccdaadbededaadacedceaaacaedecedcbacccbccebeaddaeeedebccdbcdebaeddeacbdabbdeeaecbeaeeeaeabbebbbcdbdaadebbcdeaaecaaabdcabbcaccaecccaededceaeacbbddbdaccbceabecadcdadecbdcdbbacbdbbddebeccdcebeebdaabebcedcbeebceaabaddecdbebceedcddcebaabaabdbbbbdedcdcbbccabcbabdabcaecbaebbaedbcdecabccbcdddcccebccbcaadbbebaeabaeacbdcccbddedcbcbebdebcecdcbbeceeeeceaddeeccdcccdeaccdbdcaebcdbebddeaeaaeddbdccaeebcbcbababdbadcbcaedcbecaaeabeceedaedcebcbebcccedaaeccabceabbeacadeaddccbbebddbcbecacdedbecedaeecbbadccedaccbecedccabbebbdebbaddceaedadbbacbaadcdbbabedbaabaecaaacccbbcbbbccccaedaaaccdadddcacbdbccaeadbecebaccaedaeceeabcdddcbedaeededbbebbdddeaeeeccbeccabadcbeacaacceccbabddecebbdcddbbccaaeaacbcbdebeeeababccbbbcbbacadbedcdacedabededdbdebbbcbbcebbbbdacbacaadcebebabadcdebecdcbbabedcddbcbbbebdeadeaddbaaceadbeedbababddbdbacebccaedaecedebeabdacdabdcacbacdeaaaaedbbceecaaedcddaadecaebdaebdeaeacaecdddaddccdedddbbdaceabbdddecbadaccabdbedebdebecdabacacaaedaecbacabddbdebeaedbddaecbbeabacacaadaeaceccacaaccdcbcecccebcdedbadebdaceaadedeccacadebcdbccaadccaebaedabedbcedaaadacccbeebbbacaecddacabdbeebebaacbabdebdccadeadeaeeadbaacadeaccedaecbdaebbdceebaabdbbdaaeecebbecacabddadbcbacceebeecaedbeaedcaaacccddbecebecbeecceedddabaaccaecedcdcabdeabdaeebcccdeceecdbbabbacdddeaedadcbdaacdebcacdccdedecadaececbccccececeaecbadacdcedccaaadbcccdbcdceccecaaeaaddaaacabedbcacbcabcecebacbdedaceebbaeaaaaaeccdbeeebbbaeddcdbabbcccbbbdaaeccdbacdaeadddacaedcecabbdedeedcebeadbbbddeebcdeaedebcedddebceeeeeadabaebeecbbeaddebcbbeccacbaceadebacabcebdcbaccddbbcbcdbddacbecbdacaecdbbacedbeddbeaeccebecbbcaaeccbdbbaeccbcbabebeacaaebdedccebacaadcdbdebeaedbdebdcceadbadbebeeacdcadeedeecacacdaacabebdcecbdceadaabeeaacbecabdadbacabddebdcabeceacedceaecdaceecaadbbcaacbedbaceabbadbeeecedceddceedaeccdadabededbbdeedeedcbaebcbcdddcddecdbdeddedaaeacaadceccacaceebdadaaaeebbeadedeedbcaedaedeaacdcabbdcdacbcbabeccebabeecaeebbdcccdcddbdbccbccbedaecebbbaaceabaebaccaacdeacbdbdbaeabeaaeedeaadadddccaaddecbeabebabbeaaacddbeedacabbaedcbcdcaedaacaccaecddaeeadecdbdcedacabedeacddcddbaaaddbabdbadbedececaadbdacaacedecebdeaaedbbdabbcaacbaabcecddbdccbedbcccdabdeabceedcdcbaaeecaedebedbcddecdeedaddeddeecdedccdcaeecebcbbbcdddddbbeeceececbdabbcececcbceabdbaaebeebbdbaebadbdabeedddabbceebadbeedabbeeabdebbbdadccaddaacbdeabdaeeecceceaadbcdbacdaceeeeeeedacccaaacddaabbedacccdabecadbcdcdaeaceaadcedbeecdaaceedbaeaacebbabbdeacdacbedddddecbeadadcbcbcbadaeeadaebcbecadaeedeabacdbdebeecbdeecedeedcdbbdaddeaebbdcabaebedadbbdbebbcaeddacddbeaedaaadeeaeaabbcebbddaceadcddebeabdedcedbcbdbeceebbcaeebdbdaeddaabbedecaeaeabbbababeabeabbceaecdaedbbbabdbeaacbaddadababdbbaadedcbccbaecedbbeedceeedbdcadbcaacdeddcbacbbebdcdbacbaceacdecbdadebbdddeededdcedaedeeabdcceeedacdcbbbceaeceaddeccedbbaadebbbaaeecdecbbaeacbdcadbdbadcbcedccdaadddbdccdbcccddbddbdddeaaabdeebcacddecabeccddbbceeddbdcabecbacebabccbabcedcaccebbdcbacbdeceaadecbeaaedadcadeabecadacdedcaedaaecdaddbdcdccedbaeebcdddcdbcedabbdedadeecddbbbbedeecbcadbaeeaaeabbbabaeeecaeaceceadbebddbcddedbdbbaddddbbcbbbbbeecaadbacbaaeaebdacebdccacccadbdbcacdcabbadadddcbaebdaaeeabcbdbecbadecbdcdabbebddeeeddaeededccaadeeddecdedededecddbadecabdadecaaadedbcbbceabeabebabcdddbbbaaadadabdebdaaebbbdcbbbcdeaaaeacbeecdadcebccbedadebbeadcabeeaebdaecaadcecbbddabbdcebbdebeddaaeacdcbcddeecbdeacdebbceaaddabdbbaddedbdcaacabdbbdbbedadebaaedcdbcddeacadeeadaddcceeecccabdeccadbbcacddbaddcacbccdbbcbabeaaaacbaebedeeccebcbcbcaeeabdbdecabadecdbecdabcbcebedeedcbaaccdddecbeeadaeacedcccbdbeaacacbcacbddadaadbdebdbdcaceebeccdedcdbebbeeeecbceaaeddeaedecedcdacaecdaaadbbcdbceaabeebabdecabdeebdcbeebbacbbbaaecbcdbddebaedebeeabcbcdbcdebbcadbbedadaaaedbedabcadcddedeababcdeebeeccacabcecdbeddabecbcebeddcdaccdccbaaecaeebccedabeaebbdebaeeddeebbdcccddcaacbbacecaedccacaddeadcaadcbeecbcdcbcedaebceddcdacbecddcbcbeccaeaacebddebdacbcdaeeeceadedcebdbecabbececacaabbebaeaedceabcaebecdbedbecbecaddbabceabacedccdecbbaeadbadbcccacecddaceebceabedbccecbbebdeaacdddcdcbeebabceeacbccbcecdeaeadedbbebecbccedaedbaadcdcdebedbabcaddadbdedcdcbceeabaabceddebdeddcccbaebbbbceabcdbbabeaedaaeadebbcbbeddecaeddaeaedeedaccacecccaaebccdcbbdeebbadcaccacdabebeacbaadcdddaaeddedaeabeeacecdeddaedbcbbdcdbcbbbbeadeadeddbdeacdcebbcccacdaabcaccbeaabaecbdbeabceeddcebbecccadaaaeceeacdabbbeabdeeeddddbdaeabcaaeadcdaeabdabcbcebddcdceadbacecadecbdecbdbbbddeacbacabecceadbecdccdacddceccecebbedbbcbbbcdbedaccedceabaebdeebacedabcbccbdcccccdadeaccdbecceebebebaedcaeeecbbeaecbadadbdbabcecabeaeddbaeaabceacdcccdbeacabaeeebeedccebacceeceabdceebabdccbbcdeadbadbbaccccacaeeaecaececddadbbbadcecddaaadbbcaccccdcdbabababecebbbecbdbbeabecccdedccbaedcbccbedddcadbeeadcddddecaabbacdcddcecbcbbddcedcccaacdccaadedaadbadbecbdddeadeacbbdcabadbacdcadbbcdedbececabeaeeeecbcbeacbbabdbebeaacbceccccebacbbeeecbebbadbeaaeaddeeacdbadbdbadbdceedecdccaddddccdbaadcaddcbdcdceebdadbccbddddbbdacaccddbceeceaadaeeacebdeeadccebaabddccccaedcebbabdadcdeedbdeadeeeaabacadaceadbcecdadcacdadcdccdbeebaeebbdbadbcddccdcbbdccaceedabadcdeeeaacbdecbbaabbbabebbedcbaeeadadbbedabeebdecdceaacdbaddebabbeeacdeaeeccddbddcdbcdaedbdccebbadbaeeddceabbdadeeebbacabccdeeaeacbbededddabdecabbaacababdcadddbdbbcdaaaadeccbcddbedebbeaddcdddeabadaacebcbabbababceadebcbbebdebeaceecbecadcbbbeedababdbbddbbaaebbdaabebecdbeabaedebbccedecccaebcdeaddabdabaeaaeaddedddbdcbcacbdaadacbbddaadcceceeebeeaacdebaaeccbcdcdbebbaaaaebeaecababbebbbcdbbadbceeeeabdddbcdaeeaebdbddedcebaddcdebadcdadbcbceeececccdcccbbdacaebccceceeddceeecedebbbccacaaddbbbabceebbdbbcdebdddbdabddaaedbacebddddcbbbcbabadccacadebeaaaacbeedcdcebdbededdbabeaabbbaebbabeaabbceddcebbaaabdbaebdadbaeddbaaecbaebeaabcceadaceddeabccdecacdcabeddacdcdabbcadeeeeeacccbadacadceebcccabcdaacbacdecebaadbdcdbbaabdcbcbdaeceaacacaeaabaddebdcebcedbacdbccaabdebeeceaedebccecbcdcbebbdaddbeeaeedcddebccaedebccacabcabdadbabadccedbabaadecccebbacaceadaadedceecbbcbbdbcbabedadabaaccaababedcaaedcabccebbaddcacbcbddcccbccabcbdceedbddccbcbdadceedcbededeabbacadbadeceaaededcbcdeebbdaacebccaacbdebbeeedbdadccbbcedcbadebddbcadcedbaaceadeebeebebbaeabebccdbaebadbdbedcabaeceededbcebccceaceddaccbedceedaccdbaeaadcbdedddabeadddeabcacedbaabacddbbeaedecaceaadceadcdbbccdecccadbbdbdaacddcccbccdcacaebceaebaebdedbbedecbcadbdddadaddcecdedccdeccdebcdbbdacaaccebcbdbedeedabcdddaadbccabeedaadacdbccdcaeaceebabeacbdcdccbcdacabdabaeeabcceaadeddbaccecbadccdabcbcdccabceebbdacaecdbaaabcaacabbceceaedacbbdccdbeaebdededacdbbeeedcaecedeccdeadeeddbcdeecaaceecbdceeaddaebbbbcedbecebdaeecdbaaebbabacbcaebbccabbcceddebdcccecadbcbaedebedabadcdbeabaddeeedcbdddbebacdcbeadecacbceabdebbdcedabcbaceddcdecccbdaaabbebebebdabcbaaedbebcbaddbbcedbeadceaaacababadecaadedcedaecabeabebdbccaddeecebadaaabcdbceaeaabdbbcecadccadaaeebccdbaadaebddedbbdcabebaacdbccbceecddcedcbebceaaccbcdcccdbaaebbbedbbeeebdaebeeeddaedebdceaadbadeaeaeadcdbdccaeeaeadbcddbbbecdaccbbabadddbdcbaaaddebedabbdebaedeaadbacbbaecedaacedbdeccbbedbeaeaadbebbccebacdaebadebdbcbedbaccdaabedacbeacdeacabeaccaccbedaddbbabdaccdddacacedebdbddaeaabbbeacbccabacceadaaacabdcdbadcdaebdddeddbaadabdcaebcdacacdaaebbccabadbdabdebbceceeeedaeebbeaadaecbdbabaadcdcaabeecebececebacddedabeeecbececcadbccbabeecadbbbbbbcbbecbebabededbbaccbbdedbdbedcbbceddcdddbaaeededccccceaeddecedadcebbddadabaabadedbddecadabedcaacecebcecceddeeadadddbbddeaaccbacdcaeecccdacbabccecaddacbdaaaccbeebcecdeaedeadecdecdaccbaaacedeaebbecaaacaecdaabedbdeacddbcebbdedadeaeeccedcdeeebbdbedeedbbdebacedeebdecbccedbeeacdddeebcaecbdbcabdceaebdeddeebaaabadeaddcececbdacaacdbcbebbbbbcbcaccbabcddcbdaeebdacedcedaabadaceeccdcbbeedccebdcceccbeeeddacbaaaddccdaabdccbeceedecbbdbbaacadaddeeeebaececeaabecddededbeacabebeacaebdeccaabcdbaeebccadaadcdebbcdccdeeabaddbddaaaadecaaabeeabdacbbaeadbbbbacdadbeccacbbadeaedcadabcedbabddadaedacdebeebcdbdcceedbaaadebdddeabeeedccadaeeaeecbecbccbdaebabdeecedddcdcaaaeaadeeccedeedccadddcbecccabadcceeceaacecbdedeceacabaaebddebeebecbeaceeeacceebbedbecdebaeaacacecdcbacbccbdceeddccbaeeaaaedadddbbdeecbccbcaccaeddceceeebadbeceaeabeecabdceeedcdabeedbaddbcdcbeaceeeddabeaeabdceeccedcbabdbacbaedabbabedcebeccaebedebeacdaddbccaceeadecaedcacdcebccadabdbdcbbeeceeeeaeedbacbedebcbcaeedccddddceacbceabcacedbaaadaedaeaebdeeeaddacdcaaeeadbaaaeeaeaabbcaacdeedcbcddaeeaeaddcaadebeaccbccbdccaaeedbacdbdddbcbcacaadcbeecceabbbdaaeeadbddaeddcdeddecceceaceccddabaadacbaeabcadbbeaeddebbbaaceabaacaaceddbabeecbeecacacaecaabdacbaebabaabbbcbededeebcacbeddddabbcaaddceeabcbcdbbeccdcebbcaabbbacdbcaceaecbbdedcaaebbbbcdadceabdaaaacbdcbaacebcaeeccbcbaabadecaaadaedebdcaaccbcebddebecadeddacbddecccedaaebbccabaebdbebaaaaccbedbaeeebadddeddaecaebcbdceaaaccaedcaadadbaeadcecbcbaeadbebecdaabbceaabcadecbbabecddcddebeddbbdcddbaebaebecacaddbbeeedaeeaeebcaadcdddddecbbbacebdebdbcbbdacbbdcccdcdaddbcedebcebecaeeecddadabcaedebdbdbbbecbbbbbeebbdccbcdaacacaeeaeddedccecbddbbdebcbeeabeaebccceddadaeebedeecacaaceecdccebdaedbecebaaeaccdcccaeddeeaacdaceeedaabdeedbbccedeebcdbabadeccdebccbeeeadbdceebcdbbeacadecccbbeeeebaeeededbebdaceaabbbdeedcdacaaeeebabadaaccacdcbbbcacbdaceddadbcaaadceabcccebecadaeaceaddeeacbcaadadbabddeedcacbaacacccebdeaaecddedaddbcadbbcacadaedcadbcabdcbcbeebbdbbdcbedcbeebcbabbdeaceaabdcccbcbddbaeeecdaccaccdcaacbadebabebaeadbebeaaccabbeceddacdbccedebbcdcdbeacddbaaebdbbdececacdebedcadbcbedacadcadcaceeadaaadadcacecddceebebaccacccaaccdddddeabbdcddbdbacdcdbdbcadeadadeccaaaabadcadceeadcedebcbdcdceeacdacbdebdbdccdbaaddaddabeecdaacdecbbebadacceabacdebcdbdcaceadaacceebdcaccbbbdcbbdabbbcbbabebeebbeddccabadcdeceaededbbecacbadcbbaddcccaebacedcbabaeaedadbbdaddebcadbcdddeedeaecdecbeadcdacbbecbbbceabbcaebdeaadceadaadccbdeceaaadaaedcedaacaecdecabbbedcceeaacdeedcabaaeeaeaacaebcabbcbadaacbbbbdebbeebabeaaaeacbabbdeecdbebadbbadbceacdbaacedeebbbabcaadeccebcbaaccebebecedbeceebbcceceebcccdbcbaebccbabebaddadbaadeadcbebacccbebbaeaedeeaccbececcbbeeadcbaabaeabeadbedaebddbdcaabbeacaaddbdbeeccebeacdecedeacabcaaadacbccaaaddacdceeeaaecdebeaccbdddebccdabccccbdccabaecaaedcadeacabbdceaabdbbdadbedacabddddbddbbbadddbbeeabbccaceddcacbcbdedeaccbbcbdbebdbebdcabcdaddbcccabaedabaceedaccecacadbbeeababdceceeaebaeabbbdcdbaaacdbbcabbdcbdaddededdddccaddcbdebdebcccbcbacbddbaadccdcdaacdecabecddbebeabacaeabcedbdecbcaabbbeebdbaeeedbdbdaedcecaeabebceaebbeddadadabdeedddbccdeecdccdccbbceccaabbbdcdeaccdeadcaacddacbcebdbcbcabaabcabdcdbccdabaaabdeedaacabacdbbbbaaceeadeacacbbbaddedacdcbbedeeebacbbedceeccadcdcdbeadebadcdcacaaacadecddababcceabeedbbccdcebeaaaadabeabccadadaebdaeacdedbeeaeedadbccbdcbaabddacccadadcaeccdbcbbddaedcadabbeecdeacaabbddcddaaedbccbdbaddabceccbcbabccddbbddaecdecdacabbbeccddbceaceaddccaacdbcebccadbbecdbcceccabbdadcddbdeccbdcbdaacecceeababcdcdbeaceaaccaabbcaaeaadbccaecebdbaeacbbeaccbdaabadecceedcceceedcaeddddbdbbbcadcbebdabcbedbeadecabdecbbaeceddeebadaacebdcebbabcdaeebdddcdaeecbadebcaaeacbcaabbeedaacddddeacddbcebcbbbdbbddbcbaddcaaadbeeaeaadecdcccbbbaabbecebedaabaedbeccacbeedadebedcadbbcceedeedebedacaccbeddaaecbcddaedeaaddbaededeaceedcbaeccecbaadcedeeccadebaeaeabeabbadaacebebdbbebcaccabebdcdbbbcaeddbcadcaecdaebeaaaeaeccbdaeecdabccaebecbcabeaacbedbcddabddebdebbddcbbaaddcaecdabccccbecaecbcaabcbdbdbadadaaeaabaeeccdbbbaccecedbcdacdeceeecaaccdedcdbabdbbdccecabcebbdcdabddeeaccdcbaacdbdbcebabcabccdcecabdbeedddbdaeeaaddecacdbaeaabdebadaacbdebbcbeeddaedcabbddddddaeadbdbcacbcdacdccdddababaceebbcaddeedaaebabdccbccabebeacbcdddcbbdebbcdbbacedcceeadcabeabbdbdbeaeaaeeaadedccedaebbdcaccecdbbebeabdadccabccdbacbeadbdcccadabcacabdacaecbecadddcedaaccaadacdddcacbdecabebcbbccdddcaeabbdadabdbcddededbcecddbacadcbeddabceeeedbeaebdbbeacdababebadddecbaceecacabbbdbdddcabdbcbecbebedcceadbbccaadaeccbdeedbcdceccbccbdbaededdaeaeeebbbeeedeccebbbabbbdbacdaecdabbdeccedaaceeeeaadcdbacdecddbbdbdabaadeaccdbabbabadcecabaadbeddcadcbaadacbeaccaeedecceebcacabeccdddeaaabdddeddeedabebdaccacbadedaadeabcbccaaaccecededeaaaaddadcedceaacccdbdedabdecccaacdaecebdeecbcabaeaeaeeadeedcddccaabcbacecaceddccaecddbaabbccbdccdbddaaeacceceebccebecbaccaabeddbbeeceadaaaaccabdbebbcaabcbcbebeadededbabaddebbaccbebeeeccbeaeeebdcbeeedaacdadacaececacddbeadbeeccaaabbcebedbebcabcedbccbdbebddeacddebcabbcbecbbedbbeaadaaeeeeebbbbecddceaceaacbacabedeacecbdeacbabceebbacebabebcdabceaabbdcbcacbadccbdaaeabbaadadbcbaceaaaeeaadcbdbdcbbdbaaedeeddaebedaccebbcadbddbaadccbbaedcdabdecbbcdadcdaeadebceedaaecdbdcdedaadbeadabaadddebeacbeacabaabdbbeecdddbebedbdaaebbaaaecccdcdeecccbecacaddccadcbaabaeabebedcabaabeeeaadedcadedbecaabdecbabbcdadcceadeeaccadcceecceecabbcaabbaceedcaebdacbbbbedecaaabdebcedacdeebededeccadeacdaedeeabddcebddbebaeebaabcdbecebbcacbeecceccdbbcdeadcacddcdbdbeacdaeacaabbcaeecbabebdcebeadaabdababcdcabadeeecadbaaedaacebebdbdebcecaadebebcabbaacaadddaecabcdbaeeeccdbdcdcaadeeaaecaaebeedcbacbacedabddcbbecaeecacceeebbdadecccaabcecedacbebdbbdaaeaeabbcaaadcbaecbcdeeaaebceaaaeeddbcddceaddcbbbeccdadcbdbdddcdceadddbbcececcdbbcebcebbabaaaedceabecdddbcbceabeeacbbcbdecdaecceacbcadeccdcbbcdaaecbbcabacacddcecbebcacdbbaacddcbdacceeecebedaeddaebaddecaaeeedddaceecacaeaeebecedbadadbaacddaeedbbeeeaaeeeceeabcadacbeaebdbabadbaaacbacbdabbbdbbbccebbbabceaeedceacecaddebdedccaeebaacaacceaadeadaabbeaaaaabdbdcdecbabeacdccdeebecdaadeeeecddbedddedadaceccedaadeeeabceddedbceeeebcdaedbacdceeaeedcaaacececcabaabbadbeaabdbebcadcacebaceacebccaddbccdbbddedadcbaacdeceeedcebabccaebedcadedecacbcbecbbbbaccabaedeaacbbceceaeadaddeabaddabedebbccbeeddacadbaabeeaceebaabaebeadebeadccacecadabbaeacccebdccdadbeacadebebedcedddbdadbdeedcbabdddcacaabdaccbebccecdbcaeebeeaecbdbbcbcccebecedabacaeeadeaaeecbceaccdddeebdeeaebdbbcbdddbaaaadbebebacbceededcbdcacaaecaeebeabecccbeccdaecdaabbbceacecabaedcdbbccaebceebcceeccccdeedbccccedbbbdcbebcecbbeddcccceccadadababaabcabdeaabaaccebbdddbddebecceeddaeddacebabebdcbebaccdbebbdddbacbcdedbbddaccccecedcdcedaaeedcdeaceeecdbdbabeacbebbbcedcdcecddbdbccbdcbdadedadadaabdbbabbcbadbbeedcaabbcccdbbbbaedbddddccaeaedadcedaadbcccebdeeedaebcbeeececedbbedacebebdbdeaeaedcaeebeadedebcedacebbabcbeebebbaadcbccaeabdbdcccbadcdeaacebddbabbaeeddaebadbabedcbeebdeebeeccdeabecaccdcdcedbcbbdbcbdaebabaebaedbdaaaeadbddbebdeddcabcdcdbabbeaecaabecacbdbeeacdacecaccadeadcaaccbedeabdeeaecabddbdabbbbbbbadabccadcdeddabdcdcececeedabbcdcbeaeddcbcdabbaeadaedeccdebbcedcabcededbdddaaacbbdeabdbaeeabbabeddecdbaecddddccbbbbbdcaeeedbccbdbedeadccdbbadacddebdddceaacedccecdbdbeaacdadcdeaedcceadbddbdaaccecaaeacdabdcbccecebbebddbbadbdaddaccecaadcdccaecddbbeccbeeedcdcdeecdaeddcdedcbbbccbaddeceacecbebcbceaeabbbdbdeacaaedbbcedbadacbccadcddbdcbabeccdbaaaecbcabcecdddeabaccbedcdecebebbacbcccbcbdcececbebbdeaabcaacbebcaddcbdabbdcedbbbeeecebbdabdeececdcedebeeaebbceeeecbbdbacdcbaecbdaaecadbdbacabcdddaccceccdbbeeeacededabeddaacdaaeaadabccdbcbcbebbcaaaabacadcadecadbeacdaaebcdaecbdbabcdccadebccbeabdedcbbcaddeddbbddabcadcbcecacbebebadeeddecababcdcdceedaddccadddcbaaacddadceedbdebcbbeaebbeecbadadeecbceeeabedbcaecbaabcacdecdaabecbcabcdecdeaabeecdeecadeacadeabcebbdbcbccbcbddbaedabadbbcebaedcccbaebdadabbcccaaccacedbdbeceeecbcebcddddcecbaceacaccaceeebddccaccbdcabcdddadabcadeaeccdcdadacaecddeddbdedadbeabaeaeeaededdcedcaceeebecdceaecadbadbeeeaccacacacdaddceecceadadadddccbedaeacebedecdedacaacbeedecedbecceceaabadeeeccbddcdaddabadecdaeceebdcbabbbccabbaeaebbedaabebadaeacbcdceeecddcddbacabecebcceecabbbacbcaccbbedbbececeadaddededdadbaccbbcbdbdbccbccbcbbbcaaebababcdacecaeeebdedeccccdcedadabbdcadeaccbeaacbbacccdabdeaabcbeebdbdebaedaacbbdaabbdcbacceedbeaebacbebdcabdaacdbeddaaedcbcdbbbabddbbaceeeddcecaadbeebdbdccacceaeaeedbabbadebbacabdeaabcacbbeadaedabeadbebebbdbbacbdbbadbeccceeeaaeebeebeeddacdebdeaccebadcceccaecdacbbabdbcdcbeaeebabbdacebbecdadbbadbeeadcbdbbaaddaeebedbbaecceccaeeccacddbabaedadeadabbdaddccaaadcebecbcebccabbcccaeaedcededbbeeedcedecdabeceecbcebdcecddcacbecdbecbcecdbccdebdbbbaaaccabdaeddacbedddecdaeeebcbeecadbacaedadeccddaddcdcacbaadcaebacbcdedcbaddadcbeaeabcdcbacdcadbdaadcbaeccbacbaccbddbadbeecbbaeaceadcbabbaaceeddecbceeeddabcabacebadacadbeacacaaaeabcceddccddcdbcbeeaecdacacbbabdceabbaeaddcdcbabcadabccccdbcbcadbbaceceedcdcdcbdedbdebacbabebaedcebdbcdaacdcaebbcacccaacaebdecbebdadcbecceeecddcacdaeaaadededeaaccdabcdbecddeecbcdeadbebaccaecacebabadbbceeebaeabccdaccbadbcdbadcdecedaadcdadeeecdcecaeadcaecbbdcaacabbccbadbcdeaacaebdecdadbddbdabeabbeeeebbeacbbdcababaeddcabdaaebbceebadbedbaeddcccbcaecabbcbeecebaeaaabebcadbbaaeaeaebdbabbddeddedbcceabdecacdaceddccaabcecadbbaaaadbcbebeabcccbceaddbcebabeebbcacccdbebbccabaeeaedaddbebbcaeccaeacecebbadccaedbdbbcadccacabeabbebeadcebadaabbbbceeebcbabdbcdcdacebdbabcdbabeebaccbedaebbbadbcaaedbaeedecdecbebbbdcdaeeddbaddcbadcebadceceaedcddbaaadddeeacdddedbcacecdbaebbccebacddceccbececbebcdaddbbdcadcadedaabbedceabbeacebdeabbaabdccbaeacbdbcbbedecbcdbdcdeabcaaaabbecaabedeccccbacaedaeabcedcbbaabdcbaeabddeacaedddaddaaacceedaceeeecdedcbbbcdbdaccbeaaaeddceaebcbbeaeabeacbdcaacadceedcbdecaeebcbeecdebadbceacdcedeedcbeebaddcecbeabbadcdcdacadcdddaacdecdedbdebbecebcaaecddddbdcaacdeeedeedecbaadddbdebdaebbccbacdebabeceeedecdeadecdbacccbbdcdacbaababbbabebcacdbdcdbabcaadcaecccdbceaeaaadcdeecdeabaececaeccacddcdcbbcdecccecbebcadcadecbcacdacdddcebceceddacbceeedcabdbebcaccecdadcbbcbdecdaabddceadcaddbebbdbcdcabebeaaaeeadbbbcedcabbedebdcddeabbdeeaccbceedddcedececdceeaaacbdabdaceeecdccddbcedaeebebbcdbdabdcbceecaddabcecabdbceaaccdaabbdacaabcdbcdbacaccdbeeeeaaaaccadeaabcddabecdabdaaaeabcabddcdbdcbbbadaacbdeeebecedcdecddeeedbacdaddaaaddecccccabdccccdbdcbbcacdadcdeededdcadcacabdadbacdabcaaeebeeeecddecccebbabeaceabccaebaebababbbbebececeaabeadadcabcbcedeadbcbbaeeecededaddbdbbebcdacdbadbdcbcdeccbeccbaaeaebcaaeabaebccdebadebeeecddceaceabacdadbccecadeaedecccddeaaabceadcdeadebcbceeddddeebdecebaceddacdaebecaecaddeecbecabeeaddabcbedaaecacdbdadbecbccccbcbedaeddeacdbaccbbdeebdaabaadabacbecbececacedcecaaccddacbeaccecaacbcdaaebebdedbaeebcbcceabaebeacbebabaaddcaadecbcccabddbebcecabbbaaedcbbddbecbcbecacceccceaaecbbdeebceaacbbebcbeebabcbaeeacceaeccbaaaabdcaddbeddcaeeeeaabdacbaedebccceeadeeabcbcbdddebceaacabaadedddddbabbcdeecdaebeebeeadceedbbebbbcccceeadcdeadeeebdeeeecbaebcebedbeeebdcedebeeccabcadeaacebadcadabebedaedceccbcabecebcdceaeaddeecaadeecdadbbabceaeccaadaaaddaaededdbaddeaaacbbaacbdccdeeabdcdbcdacceebccecacedaceedbbeaeacbabaeccdacaadadadbdedceaeddbbdbddeedbeebdbaecadcaebeeacccbbccdeecedbbeaecddaebbaebdbbeeedbecbddccedaeaaeacabaaedbceaabdacceecbebdebcbaabebbdabaeeeeeaccbcebaedddbeebceeeccbdccddddededadacadbeedaccaceedbcadebdcbddbcadeeaedcdeeaebdaadeadbcbdeeacaebcaeadbbdaedddcadbbedeeaccaddddeadadddaebeeaeedebdeacccadedacddddcebaabeeaeceedccbeacbdbabcdcdcbadeceaacecbcaaeecdeaabcbbdeeedeebddeeecabaceebcbedceeaaaacdaaccaeecbbbbabdbddccceedecbacdddccacdaadbeeeeeeedacddbdddbeacdbccbaeeecaebdcbdaacaeaacacccbbbccaeeecddaecdbabadbdbeebccaacacaabadedcaddebaeddbecadeaebbcebaacdbadadcaaaaaecdeceabebeacadbbdeacaeddaabeecaeeeacdcbcabcdabceadecebcabadbebecbcdddacaacebeedbdccbcedecceabaebecceccededecedcebabcbababbedacdbdebadaaceebaaadacabbbcdbcbedceebbdaeabbedadaebaddeabaddeceebddcaedacaddbdccabcabdbbaabebeeaaadeaecaaeeecdbabbdabddbcaccddeaedebdcddcaabbabbabccadcadbebebcedbdceccecadddecbbeebabdcadbbbdebcedbadaaacdcadbbdadeadacaeacceedeceacbbadbdbaabbedadcbdeaececedecbcdaaadadcadcedeabbbaaebaaebcebdddbcadecdadaacbceabdceaacadbecaabcedaebcbecccdaadebdebcabcaaedcadecdbecbebbccecdeebaadddeedddaccaecdaeeaeccaceacabeecbecdecdeadddadcdcabebbbdbddbabbcbbabebcccebcaaadcbacddaceeeeaddaebcbcebbcaccbacddcabddcbdccabaabaaccdcccbaddbdceadcdbeacaaeaebccccdaedeaecebbddeddeabcdccdcdbcaddceccaebbdabaedabcbabadccabeabbbdceddeabeeeedbcacbeeceaddbaeceecaaacdeeeadbdcecadbaeecaddebbdebebcdeabbbccecbcaaaebbcbedbdececbbcecacbccdcdbaddadbebdbebceadebaeddaaeeadddbcdeeedceadbceceebaccaaeaddcaccebdcecbaabbbdebdbccbaaedeebddabecbdcabaaaccebabaaecccdaceabbbeaabccdaaeaaeabcaabcdeccccbbdbbedaeddeadabcecedeccadacbcbeddbbabadabecbcddacdbebdcaadebececdaaebcddbbccaaacebdbcccbbadceccaeeecedcedecadababeaeacaaacaeabadadbedaaaabbbecdaeccbeeeebebadeacdaeabbebbdacedaccceaadacdcbebaccdcadecbaeaeabcadacabcbbbbabaedabeebcbaabeeccacbdadecabcbeeeeabadccddccaceecedcaedeaeebbadeaacadcabeacaadebceeccededeebebbcdbdbbeeacddecbecabdebdceeecdeaecbbbeaeddaebddcadeaddbccbaadcbabdeeacbbdecaabedcdcbabcebbcdeadcebdeceaccebaeeaddeabdcdbdaaeeadabaeddbadceabbeadbbcdacbacddcdbacbadedeacabeadbedcacbbaeabedcdcadcabeaceaaaadbadeedbaeccccbdbcbdaedeccdabaecdcbeeaeadbeadedeedaceadeaadcaeabededcceeccdbbbcabeaedebedbeeecbaaccacccabbbdccaaccdbededdadebcaebaeceabaeeaadcbeebebcbabbbadcaaedbcebcacaaeecadcaeebecacbdabcaaaaeecaeddeddceddcddacddcaadadaddaeccbbbdabdddbaaebddedbbbcbdacecaddebddabcdabcaaeacaaddaacadcddddabdbbeabdaeedaedeaadabdaddecceaeaaddcaabeabeccbeadbbbeceacedeaaacbebbcabadabdbaacddcbeeacaadadbabcdedabbeaceebacaebabdcabacedaaeddeaceaecadebdaabbceebedbabddcbccdeedadcdbedacdeebaabbbecdbcceccaaabcaccebbadbbedcebcededbeddedbceceadbdbdababccedcbceeeacdccccacddcedabdbcbdceadeaecaaedebadcaecaeeeeceacbbccaccbeabecbbeaceacaddcdcdceeaeebcdaaadcdcccabacbebbcddecdbccecdabcaddeaacbceabdeeadadebabedacccbbabcadbaccdddeabdaecbecabccbcdbacaebdbbabbaedebedeaeeccdedecbbeaccbcecdaaccaaaceccbadbbceacbacccedbbabaebcdcbdeeabacceadbaaecbcabadaababdddeedeecddedbeddceeedeaedeaadbdacaceeeceecabcbbdecbcaceedcbaabcaccbbabcaaceddcadaedaddaaaeeadbbbdddabaadcebbdddebaeabceddeceebdbcbadbcaeaabdbdeebdadeaccedebdeecabbaeedbcdedacedecdbadedbbbaeacdaeebcaccdacebecebacbaaebabebabdbebdebecbeedeabedceacaebedbbadaeaddeacbdcecaccbddecbdadaceddaebeeeaacbddbacebbbaedcbcecbeeadceabcaccebaeecccddbaeddcdbcbbdaaeaabdabecbebeaeddeeaecaadaabbedcdeebdcadcbcaeddaaacedadcaddcdbbabecaedaacbbdaaacdedacaaeddddedaecaabadddcbecceceeababeceeeebdeeacbbaaacaeeceddacaaeedebeeddbabeabcceaaebdccdcaeeeabacedebcecddeabbaaabcecdbaddaeeebbbceeacddddecedeaddaacbccdbbdecbbcebcbbdcebbedceacaaebdadadbcebbbaebcbdbdbacddcddddbaebeddbcdebbeecedebeaabcbeddacbebdcbceadcbddbcdbbccdcacbbceaaabceccdabcebcdecaadceceaaceeccedcdedabdcbcdbcaeddbabdbbabaacdebceebeedbbcabbdccccdeebbbdeadacebaaedaacdbbadebaccedbddeedbbbbecabacbeedcaecbeababcabcedcebceccbcbcbcadcacaccdbcbcadccdabddbdaaabadaabdbcebeedbadadacabcbecceaaceebeeecadcbbbbabddcdcdbcceadebededbebeaedcdebaebabbaeacadcaacbceaaeaecbeabebabddbbcbbdcaaaeddbcdceccdacedabdedbcececcbccbebebebececaeceedcebecaaeeeebddccbeaebdedceadccdcebbeacdbedacdabddaacbdcadabeeeebcbabededceadbbebcdadeeceecdedcccccdcdbbbddebaebabdddddcbabdddbcbdedaccaaeceadceeeadedcaeeabecececabcdaccaeedaeccdeceeaaedacdacdacebcaedceaececbbacaececcddddccccacacdddebcddaaabedaeeaedeeaeedadceadaabdbabbdddbbaccaeddedbdbccbabcdbbcededadbabedbebdbcaedcdcabecdebcdcaaccbdeedeaaabdbcbddbbacbeecceeddddcddabdeceeeacebdabcbabababdcceccecdcacaeeedaaeaabcededcaddeaecddceaebadbdedbccaeceabacbccccccacaecccbabdeabeceabceeabbdebaeceeddededbecbdbbdeceaeaedabbbeddbcbaddcaabccdeeaebadbbbaacbbdbdcadbbdbbabddaaaebddadeeedebeccacdbcadeadbbdcaeeababcdebaeebbabceaecbbdccaedbceeeeecbccceeaedbadbaedcedbcdadbecaedaadcbbaaecdcabaacacabbdabeacbcedcddbeccbeddbdeaeddeeaaecebcbacbbbedcdcbdaadaaaadcaacedbcdcaabebcdbaeaebebbdddcdcdbdbddbaeecbaebbcceebabcdaedcbdaddbaabadcdabdcdcacbadadbceabedbdaecdbbbdecbedbdbbcbbdbbbbbadccbeeedbccaacacceeadededeacaebddeeaebaebecbeabcbbabbdbbbabdaceadbeaeacbadcbdeecbbeedbcacedbaeeaadcdcacacdcbccdccadeadacadedbacaabadbabdabbaeebdeecbeeaaeeeaccceecdcdeccdaacabbacceabceacdabedcbecaeacaebbeadcdbcbbcddbaaeebbaecabbadbdecddaaadeaaaaccebbecbcbedbabbeddcdceeebaaabdddbabbbebeaaeabeabdbcbceeadaccaaddebbbbdacdbdeadaabeeeebeabadaceeebaaaddadcbccacdeabcbaabdddcaceacbbddecaecbaccedeedeecaebeaaebceebddabaccabeeaeaedcaccbcacadebbddaddadbadbadebdebcebbcbecebdbdbdbbddcbeaccebbcadadaedcbebcaedabbcbaadcdceddebcdccddecccdcdebcededcbeebecacccadacdbabeededadbccaaddabaebddbeebabeaccbabbabaacbddaceceeccbcbdacbdaacadbeccaadabcdeedcbbabdceebbccaebbbebebadebabcceaaacadabaacccacacbddadeccaadeadcdbceaecddbacdaeecdbdecbcadaccaaedebcaabcccbcddeaedaceadbdbeddaddeecabddbdecaaaecbbddbacacabdadaecdaececcebeaecebaeaccedccdbddceecbcedbbecbceebabbcadabbdbbbcbcbeddecdedebadbdbecbbadeabdeabbeaecddbcadddecaebbdaeedaeecdbabbcadbaceccaaabeabddadccadaaadedacbcaaebadabedbbdeebdbdeabddbcabcbddcceecebbeecdbbcbeedccaaeeaaeecceadbcccadabcaadbcebecedbadbbeabdedcbecdaeebccbbeecacdddeeecbbcbacbbbcccdeeeceeddeabecbcbcdacdaaadabbbedeccdabdddcbcaebebceaadebaaaceddadccbcdbcdcbedabedecbcbedecdaabaeebaaabebcaebcedaddeaacdebeedccebdbbbbccdabaedbcbdbdcebebebcbbedcdbcdbccbaabbcbdcdcbedabbcdcaccdacccddcacedacbaabccbbdcebecdeeaaebabebcbcaecbeaaebbcdacaddeeeebebbadcabeabdaeeddddaaebcaadbadcbdbbebbebaebbdbcddcedebecabcaccbcaeacdbddbbdcdbebabbadaacceaecdccbdcecbcdcecbabeeecaaecacbcbbccccaadbecceecebbcbacdacadcbeadacbbaabecbbecabacacecedadaabbcbcdeccecdcddedaeebadcabbadadbaccbbeccbaabbecccabcbbeedccdaaebddeaeadaadcebbbacbaebebdedbaccceadbdebecaebecaaddbbceacbeeaccdcbaccedadcbbedddedbbbccdaebdabdeccdddaaeddeaddebeeacdebaceeaddbacdaacbeecbbecbcacebcccacbbccceadeeedcbbbddcdccaecbbdbdbaeedaaadcccbbbbecedaddcdcdcbececcebbecaedcdadecacebccadedaeccddadcaccbeebccdaaddceabecbdcbeecdcdcedcbdeaecadbeaadedbbaddacadcaaabaccdbeedeebbeacbcdeebbbabeccebcbdcabccdcadbeddaeaaceadbebbbceebeeecebdeeddbebcdbbebdbbecbeaadeddeabedbbcdadacabbaacbaedbbcadebbecedadeaecdeecbebeabbcaadaecbedceccadccaceaaeecedcddaccbceeadbacccecbcaaaeeddebebbbddbedddecdeedecdeadbdeecaaacdabdcadbcadceadeeaeaeadbbbebacabeabdaeeaaaecadccdbeecceadbbeebdcbdaaeccdeaebbdccddbaaaadabebcdbdaddddecbbeaedbecbaecdebcdeecdbaacaeeebdededeacaaddcccadebbbccddedceebcbbebdbeaeacebbbeecbeeebdaeaeabcdebadbdbcdabebabdaeacaceaaddacecddeebcaeddbdbaacadeeccbbcecaebacadcebddcacadcdacedebcaedcceeacabadceccdcedeeeaaabecdbddcdbbdcdddbeedaaebaaecacccdcdddbabdceabebababbeacebcabadeeccaebcdcbadcdaebdaabbbdcbacaebcbbbcebbeaeababcdedaaccbdebaaedabecebbcaaceedadebbdacdeabbdceeecbdedacedcbdeeedcaadeababbcacedebacacaacaddbdddbcadaaabedddabddbdbebdaecadabdccecaacccbdbaabdaddeceeddebcccdddadaeebebbbeedcbecddecabbacedacabbdbbeabceebddbddbcdeeaecadacacbdbeaadddccddcebacddebcbacebacecdaadceeacdbbdedbbeeadbeaeacebcaccaadbebaccccabbcebcabcdcbadeebbecbabcaceedcbaedbddcbeadeaebdceeeccadddddbcdaeebcbcbadcbecaaaaabdccbaacbaececeeaeabeeeebaacbbcbaceadcdbdabaebcdadeedebdecbbaaccddcdcccdceaaceaaaaadacbedcdeacebbbeeadeacdebcbdbecdabecbaceacaacceaeeaeaeedcbeaaceadcababaadaabddaeceeaaaadaeeadeadadcabedcccbbededcadddadbcacdcbdaedcaeedaeaecabbdcdebcbccdbececadbdccccdeabababdcdbdeabedaccbabdcbacdddaedadbbdebaaddebedbeaacacbdedabbecdaaacdbcddbdadcbabddacddadceccecdcbcdabdcabaedeeebcdcdbcabadbcdbaebecebeaabedecbeadaeaaeadabdeecadddbbabaaabcaeddecdcdbdebaceaacaadebbdbaabaaeeccbcdbecdadeddcbcceeecddbdaeaececadcedeebeabcdbcbdcdeabeeaddcebaddaddadcddbdbcddcbaeadbbecdeacedaccddbbadbeebadeddbbcaabadcacecbdadaeccceadbeacadccbbaccdacbaeccecbbeddbdabdbbbacabddeeecaaceacbcadeadbeacaeecdeebdebdcaabdedcbabcbddeaddabacbbdceedacacdaddbbdcccebabeecbabedababababdebddaaaabedeaecccdeebeaecbcccebcadadbbcebeebababeababacaacdebdcbdaadbdcbadeacacaaadbabcadcbbabaacecdeeecdbddcaaabaabaededadbbdcaccccdbbbbddcbdebadbddebcedbeddbcabecabcdaebaccbbccbeabeadeaaeecabadaccedaebebaebeedccacbeeadebbebebddcebcebeddaadccbccacecaabacaaddecdecaaadbacbedbdedeacadadcbbbcecbcaebeaaecaeacdeddeacaadabeaececeeadbceaeabecaedeebdcbdbbaacecbedacbcdaaabadcdbbaccebccadacdedbedcebbeaccddeecddbdddcaebededaddebeaddaeecceaadecdccdcdbcaccbdbabcebcaecacdaceebabedceaababdbebbdeaeddddcedcebdabeadedbccbdceebaadbbadeadcbbacdcdedaeedccaaedcddccdbbeaedebabcdcebcecdbabadcdccddadadbccbabbbeddbbacdabeccaabcbcccaebdcadbcacbbecacddeceaeaaeacddbbbccdbcceecccecddeaeacecaedeeecbbeeeaaebbdcadbcbaeabbcaecdebcbdeaabbbeaebededbcaccbaedbbddcdcbdabeaeadebbebeccababeccbdbcdedecbacaddbadeacccbdabeeddbdaaecaaedddbbbccdecacddcaacbbebbdcadeecbddcebaaabdacdacbabbecdbaccaeddeadadbababdcbdbdbadaeabbdcbdccaeccadaadaaaddaadacceececaacebeeeedbebaeccbadcbaaceecabbcdcecceabdebcdbececdaedbcedabdebddceedcbdabcbeecdddcabadcadbbaacbbaedecaeeabebdadcdbeddbdacbaececcccbaedddeabeeeeedccbacbdcaebccecddeeabbcaadaccaeaedcbdaeaeacbcceedbdababeadaddaaaeccadebbadeeedebbbccbdeaacacaebbbaacececeaddacdccabdccbecadabebabbcecbabddcdccdadcbbcaadccaadbdebddbeecbaaadadaeeaabadacabcceadabcbcebddcccaaedadceeeccdacbeaeabacdcdbaebddecabeeacdbeeedcdeceeadaeceaaddcdcdacbddecacdcbbcdbecabedcdeabdccbccbacaaeaaedaaeaacbbaedbbacacaabaabcaaaabdbdaecaaeaaceecaacbbedccbdeebebaecceeecbaacadedeeedbcaececdbcbaabbdcedcdedbbbeceabbdcbbaeaedccbebceebeccbcbaaeaacaceabcbdceccdcdbccaeddeebbabeabbdbdcbcccbdaddebebcdcadbcebbaccbcbadbccacddacddecaeedcebeeecbabcddbedbdcaaeddcadccdccebcbbacebdebcdbbacabbaedddbadecebcbcccecebadbdbdeddedbacbbdcabcdbbaabdcaddedbedbeceeedababcbbedebcddacbadcacdccbdcaceddbdaccacbcecaeeddbddadabacaccbdcbdbcaaeacdcababecaccebabddcddeaeedcaaecbadeacbdccdadbaebceaaeadaddabbaedabcdbceabccadcccaaaabedaedbaeeecddcacacccdcaaaaddaacaddcbdccdeaccaebaadacccaaabcbbbcaaebabdeaddeeececaaecadedbccadcddadddadceddabcdbeaeadbbacbcdadaeeaceadceeadbabcdadbceeddbbabcabedbbaceeceaaebdcebecebadbdcbeeeccdcbcdccadcccbccdcacccddceeeccbacaeecceabacccabebeaaeeaaeeeaedeeaedcbdeccaadadadedeaccddddbababbdceeadbccbcdeecdbedbcccedabccdadccbaecbbdddcdceebbededbeababdebeabdbbdbedbdbbdbcaecaaeabbabaaaababdabeaeadaeaaacaeeeaeeebadbebdeaccbeecbbabeaedbbdabaddeecadbdecddcbdeecbbacdcadeeeeabeaccabcddacddecaeebbccababbeadbaebaaadabcdedbaeebecaeccbccdeecaddedaacacaeddeecbabadbddbbcedeabceddaebdeabbbcabcadccacceebcdbceeedacbdcedccedddcdadbddccacddebebdcbdacbeacccababaadaacadaedccbbcedaedbcacccaebbeedcbddadeacbdeccdceebebbebccbddbaebccaaeeeabaacaaccebbdcedeccaaedbddaedcaccabcdbbabebccbceaaaaacccabbbabdddaacbdeecdccdadcdabbedbeeabadeabdcbcedbbcdeaeabcdbcdaaedadcbcadabcddbceeecedabacddeeacaebeebadbdbdabccaedaccbcaedaadaabecbbbedacacbbaeeaeaddcedbbbdacdbbcacbceddaddeacebcabbcceadccadcddaabadabdcbceeeceebceddedaaabbedcaebdebdcaccccdabadbaaebbccbebecdbbeadeaacabebadddcdbcdeacedceaaebbddddabbedaadccedadddbbcadaecedeecabbbcbccbcbbdbaddeedeeedbebdededabebccbeddccccbaccdcceeacaadedbcaeedbdadbddbedcbeaebecacccaeceebdceacdaabaabbdabbeeacbcceaacbeeddecdaacebcacdabcdccaebbddbaeeadcaaabbbbbaeaebeccebecaededdebbdbdbedcbabcbecdabecbabceccbdeebdeaccebdddbccddadededdbeacadaacbeebeacdabaedacccaebacddbdeabebbebedceedbeeedaaaebdeedbedbeaeddabeaeceedccbdecacacedbeaeebcadbdccedadecbbbdddabadccdacebccbdccabbacceebcbedeceabcadeceaccbcdcbadecacbbcecaacbeebacccdddeeebceebbadbedadaaabdeebdababacacebeabcdeeeaeccddcbeddcaeeeeabcacbddbceebedacaeaebcdccebbdebddabaccbcbcdaabccdcdbceedbecebcbbeacbddeceeeadcaccabcbebabaebaddebcbeabdbcadeeccadebecaadddcbbeaadedbbdcdcbabadbaedcabcadcaaceacbaceecaceabacbbaaeceabdaeaadddebccaedcbdaabbbdadceeacaaceaededdddbcabebeddceebacdeecddccadbdbaddbdcbaccbdcbebcaaceceeeeedacaecdadabecbbceebecbecebbaaeecbadbdddeaccddcbaaceaebdbbdabecbeebeabddacadbcdecdebdacaaeebbebbebeeeaaedbcaecaeadbaebbbceaadacbaadcecbdcdeccbdbadcdaddbdcaaadcbeebabdcebabeddeabdceeeccceceeeadceabaabdceddacdeccdeaaacdcededdacacbdeecacccddceecadddaaeacbabedadcbdcdcadedeabbdbceecebaccceabdaccccbededaedebaabdcceeaabdddcbdcabeeedbbeecccaacabbbaddbbdcdbdadadebdcbebbddaecdabdcccbcabdbbbccbedededbdccddeeeccbbebccabebcbbcbdadeaeecabdeeeeccdaabcecbeeceebeeeaeebcddbddeccacecbedbceecadcebceadadbecdeeebcdedcdbbcabecebebdedececebacdbdbcaadaeceedbdbcbcdbaadcaabbdacadbbcddcbedbeeaaaeacbbbdbcaeeacedecabababdebbbecbeebaabbaeddabbdeeccbbcbbbccbaaeabaeadaaadcbccbdcedbcddccbbdebbcacaecbcdebdcdbcdadaaecdcbaaceedbdedeabecbbdbbdccddadabbaebbdcaeeecdadcbbcccdebddebddebeaaedcacbedeaacbecccdabdeaacacbcbaebdbcabbcebadedebaecaadebeccbacacaadabdcdbcabcebadbedbecbdecdeabcbaacedcdcbebaaceededccbedeabaadccaeddccdecbebbddbcaacebcdecbadacdcccdddebdabdbeeabccaedebbceaaaecdecccbebdeaccdedbbecdcabdbadbdeddbebdaeeacccaccbadadabcbadeadbaabdebaeddbeabbcedbddeebdcdbeebcaebcebddccbccbebaededccccdbaaedbaadaddccdeadeeeeecaadbbebaebbceadeeedceadeaeeddddacbecedbeabcabcaeacbaaaabdecacbabbbbccdacebeeddeeadcadebcaabbadaeceecedcedddbcdacadadbbcbabcecbecabdeacabaaeacbadeaebaeadeaceacabdecaaddeaccebcbabbbccbcddedbcbbeedbdcbcaeebabbecbcaeaedeeedbadeaceebeccccdcbbabdadebeadeeeccdccbbbbccadbdabccabdbcccaeaedcabdcadbedeebcdeabecedcdbcbdebccaecdddeecdbceadeccdbebacacbabcbbdbbdaddababccabeccdbeecbcbecadadbaacddbdddcaebebeccbedbebdbcccccdccaeddaeaddbebebbdcbddabdbcaeebdddcdbebceabcebeeaeddebdcabeacdcebeeeacbaabcbbcbccaaeecdcabcaadaeaebdedaceeebeeccdbaaaecadabbbedebcccaccccceaedcebbcadcbdabdededaceecaeaaddbadeedbccccadedbdaceacdcacdeacbbabacadddacdadcdeacbdbadaaaaadadaccaaddccdeebcbabcececbeebcbbdbbadacecceaeddbaadbcccaddcaedcdddacdbbaecaedeaceddbcebdeaccaaedabececcebaccbababbcedbbdceceaeaadabbccbdcdecddbdaebbcbdbabedabddcebbbbdadbdadcddcecaebdcebcbacddadbabadeadcbeeaaebcacebaaadcccccceddbaecdaaceacacdaabdcecadcacebbdbbbeadbddcceeebabccbdbeeeabdeedbeabddbeedbceeaedeaecaebeaddaeebdaeaaaddbcdbececaacecddbebbbaaddceccecdaebceddeaebbedbdcdcabdecaecbeabaccebeecaddabccadacccacbadaacabdacaccaddccacabbcecbdcabbaecdceebdcbbddcaadeeebbdebdebdbedabbcccbedbbeeddebeaaededdbcdccbbaabddeeeddccbaceccbbdcdbddcebaddedbeacabebeecaecacccdebdbccbabdaedbbceccebbeddddaaeceedbbcdddecbbdbdcaabbecbebbebcdcaaabddccecccaaecccceebadeccebdbdbdbaceabcdaabccdaabbaaaecccdbeceeeedaeaabdaebeedeaecbedeedadccbdceebadbcceabbecdcebccceeaadacedbcdaceaeeebadbaedadaeacababacadaabedbbcaeeaaebbbcccdacbbacbbccbbbbcdccaebdcadbbcaedcbeabdcbabdaccbadeabcdaaceeebadbddeabedacdcebddaaacdaeabcccdceccdbbcadbebeecdaaaaabbebbaecdeacedbaccccdeccaaaeadcbacceccaeaaccdceeedbbaeacecadeecbccbacdcceadaecdabdbcbdabdecacbddaaebabdedcccbbbabcdbbdcdeabbeaaccbcbbcaadcdadacadbbbcacbcdcacabcebddcaecadebadacccadcbecadbadeececeeeccacbeceaaeebbdeadcbabdadcccaaaecaebbbecbdcaeaddeeedeeccabdadadececbccdeddeaacbdbaadcbabdaadbcbdcbbaadcdcadbaaaebbcedcedadbcecbbeedabcbdbdbbbcebebbeedbcbcbeedacbcedbbddbebcaacdcdecedeebacbdaaeebbddbaecbbbdedbcdedaabbdeccbccbbecbddeceeabacedbadbccceadabedeacbcbacbabdaeeccdeaeeddedbbbcecdbbdbecacecbceedddcdedbeeeabbceeddddaaaaebeeabdccbbbdccececbdcebabacdadaaebceeddeeceaacddaeedadddceabeddeecedabbacdceeebdeaccaeeaadcaaacababdeedeaeaaedeebdcaddddeedebededddaebcdcbcaedbbdbdcacbaedbddedddaaddbadbddccecadaeacedcdebcebbdddabeeebabdbeddbdcbbedbecbdacaecbbccccdaebaeeccabddaccadeedbacccdbebbeeaccceebebacdeaabcbcceacacecccdcabeebbcdbbdedecabadeceebdddeeacbaadadedcacaccdbbeacbbbbebcccebdcecdccecadcabcabecbaccababddbebecdbcdcdaaaacebebdbccdcbceeecceeabebdacebbbdbacdbaeaebebbedcbbbacebcaacbcccaadabbccbabcdacebeebccdbcdadbddabedcddcdcabebcbbdabaaaeccbcbedcdeabedcacedeabccaaabbceedaaedcbdbcddedaaedaebbdbcadcdaceebbedcedbcceabdaccdecebbacabacccaeceddaeadeedcbbebeadcbadabbaacebecdddadeaebbbaecbecaaaeecebbdacdeaedebdbaeaeddbcacccdaeabacadaecbecbdcadecbeaaabdecbebaecddeedbdedaacceaacbdbcdebedeaabbdcecbbdaccddabeedbcecddeacdcadeddcbeaebeadccecbcccbebddbceaacaccbddacaebcaaaaedeeaceaeecbcceebedacedcabdbeadcdddedabbedbacabedabeddadbaddecddabceeddebcdeededdbaebccdbdacdbbabdadaeeddebbabbeeaebababaceaddaeaaebdeccccabbdeeebbbccdebedbadedacacecdddaaebdceebeedbcecdddaabbdbebadedabbdabbceeebabedbbbbddeddbddcecaebbcaaccebacccbcbaddcccecddbabccdeeeeddebdbdcdbbddbbebbcdaacbeacebbddccdaedcebbedebaeccacdcdbbdeadbdebccbaaedcbecaedbcedcbedacdecbdbaeabdadccaaceadeecaadacecbddccadadcbcebacbcccddbbaeccceeaaabcdeeedeadceccdcadaeecbaaeaedbceaeadbccbbdbbeeddbebdeeabcdacaebdbecdcdaacdbaedebabcbdddacdadcbeabbbddcedabcbadecedacadadbedccdddcdcdcdccaedcdcceeadcddeeaacdebabecedbadbececeaaadbbbbbbceddebdebedeedbabddaddbddedbbdcaabceaabadaadaaddacbecebdbbcdabcdcabacebcadecdbbeccabeccccddcdbecdddbddeddaaeeecbacbebbdaeedbbbaaeceeaaabbcbeececaeaeccbdadabecbededeaaaecddedbbbbbabeecbebedeabdbcbedeccdecddcccdbdeadcedbbadeacbabbeebcecaedddbecdcacbabccbdaecdaaabaddbdededacdaacbccbcabecbbecdcdadaebbdaaaebeedcceeaebeaacaacbddcdbcabeeaebbcaadeebebeeaaaaebadaaedaeaeeeaacbacddbacebcaaecdcadcbcbbbeedaedccdbbacdcbdbcdbadaddcededcbbddaadabdcbdeeadecdcbdbadabdbcbebddbcbdcdebdabbdbdcbbcdbbeebebacbabcabcbbaccabaeabddedacacabceecaeeadbbddaeaecddcdcdbddacbcdeeadbecbebacedaedeeebedaccdbbbacbdebedbcaabbcdddbaadacdbdaebcacdcebecbeeabcabbaaeeaebbaabdbabbcbeecaddbaccaceddcdcadabecccedeaeddddcadbccddbcecbaaabdbbabdcbeccddacebeaebaccecdededaceeccdacdbbacaeeabaccceaeccadeccdbddebcbebeacdedbbcaccacaeabcecebdbcaeddaecaadadcdeebbeecbadececebaaebacaaabddacebbadaabeeedadbedbecbcbcacdaadddccdbdeeeaacbdbdbdccaaaeccadeaabcaceacdbbbdabbeabcedeaadbcbbcabeaeeddbdaacabeedaacbadceadbcebabdeeeabbbacbdbcdbdcadcaeebadabcdeeddadcecccabaaabeddeadbddeedeaadaaaadebaeabdbbbaaedcbeccecbdaeadabbecebccedeedeaceeaedebaaeaabaabdcbceaebadbadeddcaddebaacecadcabeaaccabedebeedbbcbbcecadbbebaaaadcccdbcacbcacecebbceaeddebeeecbceabcadaaccbecdddabaadeaaebceaccbcbebeeaedceaecadaacccecdcdbaaacaecabeebdddddaadcebdaeaadaadbaaabedbdedcccaeceddddececdcdcbcceedcdcedadbbdeaeceabaabebeeababdeaedaceaccdbcaecdeeaccbcedddaeaeeaebdbbdaaeebcceabaadecbccddecabdbedbbaccbebdeeabbddbccceaeeacbeaeeceecacbedcabcbdcecccadabbcceedbcdbcaceadaecdebddaeeeccdcdadedbcdbdecbadcedecbaabacdeebcaebabcacadbedbcdaccbeaeccddadbaadcabeadbbdeeeacabebbbebabadeaabcaadcbaeddaedbdbabebdaedbbccdeaedacceecaeeeccbaeaedbbdbcccdccbedeebecceeebbbabccddcceecaabaacbdcaecbabbaaeaccedeecebbedacceccacdaebabaebdccdaedbabaadeccdcdcdabdcedcbbbedbdacdbcbecdeacabbbecabcbebcaebaaecedeeccaaecbbabeaebcbceadecbbecdcdaececaacbedaeebbbdbddeadadbaeacccacecaeedeecebcbbbadabcdcacbcbdeeeebdaaebbebbcacdeecceebabadaaabdaabedccdbeadaecdacbccceeacbcecceadebdebddabdbaeaaabcdcccbcbedaeeaadaeeddedbebaadeccdaeecccbbbbebedaeaabadeeacacccccaebacccabdcccecebcaeaeadadbebaccacbcbecebaadebebbaabbbedccbedbcaedacabacdabedbcccceabacadcbccdbcdbddebdecbeeaccebcedbcabaaebdabbdedcccaeaecbccdaebbacbaacabaebcdcbbddaeedbdbedcebddabeaeaaecbdabeacadeebcbaacecceabbcbbadeceaeabccbcceddcdaebbeacecdedcaedeccebbdddccdaccaeacdbabedbbdbbddbccddebbdebebeaaabcabacdabcaddababeedeadaccabdccbadaabbcdabaaeccdcdabbccecceddbbecdbeaddbaecbadbcbabbceedabebcaeacbbcccaeeabbbcaadcbeedaeebdcbcbdacbbadedabddebabdebbcdcdeabbbccecdcbccdbeedebadddaaacaaebdcaacdaaedcaaccaedcceadddbdcebacabbcdaedbdbcaedaebdcacdccaddbeececcbebeaddedbbeeeacecedbceeeccddbcbadaeaeceeedddbbacadddadebdeaaaccecceadbbeddcccabeccbaeedcecebcddcbddccdaebadaececccaaebbaeaddbbcddaccbccedddcdcaccaaebcdabacbaccadbabacedbbeaaedbecabbbdbddadaadabdedeaddcdcbccbacabcdcaeccadbbcbbccaabdeeeebcdddacbaddbededdccdacadbeaeedcdeacbaaadbebccadadcccbccbeccdececdeabbacaaeeeebacbbecbeabbdcdedececeeceaaaedaaadabbcaeebbcedaaeadaebbaeecbbdedadbaecddaacbdccccddbcddbdadbecbdaedcbabddcadbeeaaebdcadeadcddedacaedcaabdcdbedcbebdbcbdeeedbbeeaeacdeaabadebebbcceedaadecddebbddeebccedabcadddabacaacadddeacbeaecbababcaebcbaabddaacadbcecdaeaddaedcbddebcdceabccddcaaedecedbdbdcdecddadacbcacdccdedadeabedebaaebcacabbccababecbacebbdaaccbbdddbecbecbccecdddeaddacbdbbbdcbecebbecbbaceaadbbcaddbbdecbdadcaaddecbabacbbeeddbeaaabeddabedbdbdbacdbcabebedeedbbdcacbddbcceccedceedbcdcbbdbaccbbadbebacdeebbccadccbacddceaabdababbcbbbcecedeeabeebdbebcddaecbeceebaeddaeadcceceedadceacbacceaabaeadeabaeecedecaeeaaaecdbccdebcdbbaccbbbbaccdbeccdebbbaeadcbabeebebabeccbebacacdaeadaccbdbcbaceeaeadaddcebabdcdebbcbccbbdedccabcaddbdaabbacabcacbcdcadbaaecceceddebbeebeebcacbcdcbbeebccededaaadbebcdecabbdbeebeedceacbdcbececadaeceabebbbecdcacaeabdeedbdddcddeccdbbacdaccbcdecacacaaadaedccdababeaacaabbaabdeaebceeadabdacadebacbbdbbdceadaeecbdaddeddbabbadaceebbeeabbecceadeddddbdeabdbaebaaeeaacebdcabcaeaebdccabadbccdbddebdaecbdbdaadcdcbddaedebbeabbdaeecaeccaebceaddccebcddbeaccacacedeaceadacebeedbbcecbabcedcdbaecbabddddebedcbcdbacbaeecaaadbdedbababaecebbecddebdaebdeebbbcdcdbecedecccccbcbbcaebebdecbaaebdeceddbaddabaabdaecdcedbeecddbcbcaaebcecaabdcbbaebbcdeceaeaedeadebaaecbaceacaaaadeabcdcebacedcabadbebdebeceeceecaeacccdaaddabdbbebeebedaceedceccbcbecbeddcccbbacbabdbddeaaccadcabadcccbcebaaebcaddeaaacbbabbeaacceedcabeebebaeaceebdecddeadaccdbeabebbeddaddeebcdaeccaddbedebdedbdadcadbcebddcdaabbdaeacaaccaaaaeccbdeddaecabeeacdccdaadcaedeecdabeaaaebbdeaedbeacddceadccbeededbdcceeaecdebaeceaccdecbeeadededdeddcbcccebaccbabecaadeaebbeedebedacdbedbdaebdeaeecdbaedbadbbbbdeecdadbbcaaeaaabcbcaddbcddacacaadcaddcbcdadcacbaddceaabdbbadedcbbcdabceddceacdccbeebbbeddababaedaacdcbdeeaeccdeaeabedeebecedbaddaddbceedddacaddcadbbbdccedeaaceccdbaaabdcacaecdddebccadceebdcceddedbdcbddabaeadebdcbdbacaccdcbccdccebbacdeeeeacbbaadbebabbadeaeaabdaaceebeebaacaaaabcbbcdcaadaeceddabbbcaeacceeeccaaccceaeddbbacaadbcecbbdbebedbecdcbbbedbbeacccbdababddbdaeabdebdceaddedaeaccdccbcbdddbebedbdcccdccbecabbedabbeaabbbedbdcbaaeeeabeaabbbbebcabbbcccacdbeccddcedecabebebdeabdaeacadbcddbcdcbaeabedacaecaaedaabcaccabcacdddebeddbebcadaccccacdecbcbeadadeceedecabbeedadbdbcaeeadeadcdcabdadcaecdaaadbeecbcaaadcebadbabedbcbeaddeeaeeeebeacccaccddcabbdcaccdaceaedbeeadcdadbeecadbbbbaaebededbddaddbecbbbebdccddbadaebccdceccaedaadadebbcacabecccdddeccdaabecbeaecdccedeebcddbcdbdbeebcaecaddabdceebdeadcdbcadcecbaaddacbaeebebcbdcacabbeadbecdcacdadcddddccddbaebebdbabcddbbdbebadebeadacaccdccdedeecdabbacebbbbdbbebdaaebadacaaeeccdbaceceedbeabedbedeadbdbdedcaecbaacbeedcbddaaaeeddeeddaeebaeacedcbbecaecaeeccbdaaccadaaedcbdbccecacadeaaacdccddaeaceadcebbbccbcedeaadeebeeadbdcdeecebabcacadecdccabdbeaebecddedbcedbcacabacedbdadedbdcababaeededdcdaabdcaacbbaccaddccbdaadabcececceceaeadceaceddebbcbdedacbceedcbededcecdcdbaeccebcbcecedadceaceadbacbadccabeaccadaddabcadacaaedbbaaaadedbedbdcbddddddcaabdbdbdddbeaddadcedaebacbddeddeeeabbbcdebaacacdebeaecdaeacbbaaabacbeadadbbeebddecdecbedbbccebaeddbbedbaadcdccbaedabaceabcaeacdbaeecbcecccebadbaabbababadbaceadcdcadeacbebacbedaaeacdbbccbeacbabcceacceccccacddbaedbcabaebdabedccbbabcabaebbbeeeccbdcdbdbdbacaeabaaaeebcdaeeccbedcebccecebbcdadcceceabebbbceccbceeccedeedeadecaacdacadeddddcdbbeeacbebddaccdebddcdedebebcccddcacabbeacdbdaeeddeddecdecaadeabbdbbbcbbbaadadbddedbdcabdddbebccebaedaaebdeadebcadcabeeecdecddeeddccabacdbbcdabaaceeddeaaeaebabcdbbcecdbeaebacdcbbabddcedecebbabecedecaabbddeabebdadccebaaebabddbabebbcedbabdeadabeadbcdccecacbdeabdceaebdbecdbacedeccbeaadbbeedcbeeddeeddaecdeddadbacbbccbdceeadaacdbaeaeaabedcaaeabebabdabbcdbcaecaedbeeaeddcdbbcbdbccedaddcebabacbcbeaceaeaedbebabadadcdcdcadecadbccbeaabeaecedcddcacaebbeddeeacbeddeecdbebdacbeacececbbebbaedceeaabbddaebedaadbbccaacbdbccecccebdabcdadabbcbbedcadbdbbacccddbcaadaaedcbcbaddbbeaeceeaceddacebcecdebedddecbeacbeaabdcbceebbeedddebacdacededabdccddcbddababcdddaaccebdeabcddedeeedaebbdceeaaadceebeadcdeebcdaeadcccacadabdbacedceedbdadbcadadbacebdcdaebcaeedebedeadbbdbcebbeccdcccbaeadecaeddaabdbeebbccaebabedeceddebdddbbbabdaecaadbcbadadbedccbbbcecccceccdbaebdcaddbddeedabcaecbededaadcbddaebecadaadcacbaceaecbdbbaeeaedbceabacbcccbececabcceebcebaabeeabaedaacddaacaacbdcbadddbbdaabaaedbbecbecbbdbaeebeaceeceddccdcbbaebbcbbeadacbbabbdecacccadddcbbbeceddcaeceeaddacdebcdeaececdeccbbbedeccccbceaedbaddababbaeeccbeadedbdaaaacaaedeadaaebeaaceddeabdbdcadbcdbdacdaddedbcebecbbecbbdecbeacdccaaacccaedebddcecedbdbebedadcaddcdecdeddbdecdddcbbdedccbaccedcabbccedeebadeedddbaaacdabadccbecbdaddaaeaebbcddaceeaaabedaededbecdddbeccbbecbcdaeaddbadeeadddbbcdbdcdeadddbbbbeddcbbbacaeecdddaadecdbdecdabdbacaeedededdbebcedbbeecaebddadacecdbbdddebacbccaececedabcdaadbeeaabeaccebdeacababcacadcabbadeadaaaddbdbdbabbcecccceddbecedbcadcaaaadbdcaedeceaebddbdeccebabcaaceaeadbdededecacccddadeaaccabcbddbcddddcdadeaebcbacdededaaedadecdbccbcedecbacdeccbebddcccacacacccdacbcedccedbcaaeccedcdcccadecdedbbaecabcbccedecdccaebbccabbcbceaadcbacbccbbeebdaeeddccbcadeecadbdcbecdcdadcbbcebdabceacccdcdcdccbbbbbaeededbbbaddddbcadddbeedeaecebebabeeeaeaadcbdbaadedeaabedddecaaebcaeaeecabebdeebdacabcabbcbeeaedcbaeaabeeaccbdcddacaaeacadaeccedaeaddaedbceedadccaebebaeebbcadcbbacedbcebedbbdaaeaccddeddaebdadecaddbcacaecbcbdbaaacbbadebddebccceeecbcddcbbcaacbdbcecbbedadbdeeebacaedbbbeceaaadcecceddcabccbdceaabcaddaceecbccebddedeccdecebbedecebbceceacbdbcbeedabbabaeacedcebaccaaaeaceecdabcdbaeeadddeabbdcaecbbdccabadcabdddbebaaacdbdbaaaebaaceccbbbcdddcbeacebacdeddbcbadbdeebcbbaaaaecececacabdadcdcbebaedeeacaaeaebecbcdedecbececbecabdcaeedcaabadaaaadebaeedaecbedecacabbdaadbbabbabdcdcceabebabbbddabadaccdcddeabddcaeadcebacbeecbccaaeccbabdcbcebdeebcddbabcddbeabedbaabbdeabeaddedcbabaceceeebadeaabdecdededaedcbbcaaabbbdaceddcabdaadcecbbdccaecddadacddbbbbccccaaadbdeeeaacebcedaacbbadcbcbbacdacbeaacaecdebadaeadadbdbcaddcbdcaaedabecdbdaebccaadbaaccbbeaeeaddedecdbbceedddebbbbcbdbccddeccadebdadcbedddeaebedcbabdaedababbebcdaecbcecedabdcbbbbcbebaeaeabdeeddaaeecbdbdeaeebbbdaccdbaecebbcecbacdadbcbcabbabbbbeedbaecaebcaeadedbacdcadadaaacbbbcabdaccbcaadecceccaeeaedbadecdececeaeedeabebadacdcccadcabcadcbbbebdedeccecdebecbdbddbceecadbcacabcdbbbcdebcdaddcccadebbcbceacebaebcaeebbeeeadaeddcadadbabadbdccaabbedcdbcaeceaceebbcbaddbdddeaecdcaaaebedeabebbadebadcedbccceecacccdabdbceabccecaacabaebdccbedadbabbacdadceddeebdcbbeceebbdccdcebabcbaaeeadaedcabeadcaacceadebbbebdabaabddbccdbdaccaabbcadcaaccdeddcadebcaabbbdbaecceeeecdacaecdaccabbdbeadedadbcddeadaeeecebaebedbbaddabcbdaddbcdaebadbacaedbccedddaebcecebcbacdbacdadbbecbeccccadddabcaaacaadbebbddccabdbbcecdbcccbbdcadeceacbeebdbbacdbdcbccaadadabddeaedabbdadbceadbadaebddbdbdcbadadeebeabcdedabbdbdcccebdeabdcdddaabcadcbcbcdabbceddceeabaabebeaebadbeaecaaccbacbecaeeddbdcdcdccdbbecedceecbcaeaccbcedcaeeaeadbdadadccaecdacaeecebebacceebaacdbbeebcaebacddccacbdcbaaaadedbdbacbaadceaaccaaecccbeceacaacddcabebddbdeaacdebeaedbbbedcbbaeeebdedcaedebcdebeedcadebbddeecbcaeabeecbdedaaecccdeabccecdabededacccdedcabdacabdecaaaeecaeeddbccbcacecdbcadbedeeceeaeeeebcbccdbddedccbedbebcdabceeebbbebceceaddcdaceeacebdbccadcdeceadaebaebbeebdaecbebdecdbaecdadbbebaaeabdcdbdaaaecaebdeacaacedeacbeadbcabdebddbbadadbaceccabdaaebbdbeddaccdededbbdadcaeedccbbabbabdbabdadbbccdeddaccaeeaebbaaedaecdceecbdcaeacecbededddebabdaeaeebabaaebeaaadcbbbbbdadddcdbceebdabaeedcacdcbeceabeebadbbdabbaeecbdecaeadecedbabecddeebcebabecaacecbcabcbbebccdedbeeaeeddabcddbddbcebdbdabdbbdcbacccebaddbcaedbadcaceaabdeeacaaaacedaeebbcadedaaacbeeeabbbebedbacaeabdabdebdcedacccabccceddcabaaddebcedaabcbcecccbbdbdddebdbabbbaaccaabccbbbaeacabadbdaaceebcbabdceadcbbeeddbcbeaccadeadaabacabacbecedaeeccccdbebaaabcddbaabddcbdeeccabdbceceaaaeecdccbcbbeaaeebabbdeaebbabcaaabccbebcbdbaebecaddadabaeebdaadabbdccaabeddeeababbddceabddbdaeadccbbeebaccdecbdabbabcbcdadeabcbecdbcaeeaecddcebabaeaccbcecdebdeebdbcebdcbaddddecbaecbcadbbcbaabdbeedbccaeababdaeacceaaacddbbeaceadbdedeabadeadeaebacacabcbdebdededddbbacdcbebdabdadaedccaeeaacbbacdddbcedabbaacbcccdcbdeceadbecebdedbaecadbbbabbcbbeecabecbacacacddcbaedcdebcaadaedbaeeabbcdbdaddadbbacdcbbbcbcceddcebbbeeebeaeadddebddadbdbbcecbddeddcdddcccebabbebcdcbbaaebbedcacadabacacbcdecdbdbddaecaebccbedaaabaaeddcbcdbdeaaccacddbdbcceecbabcecccbbbddddeacdabaeebaeebbbacaabcdcaadababebdadedccddceebcebacdcaadcceeaabcabedcecaaecdbeeacdccaebeaaceddeedddbcbdadbebccddecbcbbbeebaabbabbddeadabcdbcadabbbedcabacadceeeecebbaddbeccdecedbbaeeabcbdacdcdacdbadeedbedddcdeadeeeabebbddebdbadcaaeedeaedcdbdccaebebdcadcddeabddabcdaecbbdbadedaadcdbcaaaadbddbdcdecbdabbddcabdeedddaaacebcaedccbcbcadacedaeddedeaddebcaaacdaadbcecbceccadbbaedcddadccbaacaacdacedbeacbeeadcbeacdebeeeeeddbbecadabadddcabdebdcacaaccceccadcedaeedcbbccececcabbcbbdaaddbdbbceceeecbccacddadeacacdecbcceeaeaceeeababdddbccdbadabdabdeeddadeebdecbbbcddddaaaabcdecbcbbdbaccdaacecceeecdababeaeeaeadbceeeeeaaecceaaadebabccdbcedaccddeedcadabbbbeadcedccdabbbdabdbecdaaeaeeededdabebabaabcbdadbaadbeedcbcbdedbbceebdabaabeceadedabdaeeebeacbadedaeeebaecacebcbebacdaeedeabbadebedbaadccbececabdadcdccddccbabcaecdeadaaedbbbcaaddbddeecadecacbaaabedaaaeceaaddeadbadaccbceeacbeeaacccdeecdcecbceebdbceedecdcccbbcbcbcbbdeddeebabdacbbcbadcbdeaebdccaddcdcbaeeeaeeccdbcecdbedbbcaedeedcababbeecbdccabbcacdbbaaabbbbaeadbecbccbdeaabeecdeebdcacaedcaeaabceaccaecebabbbcaebbbeaccadcbdaaceedebbddabbbebcbcbdbccabecdaccabddbeacbaaeeeedadbbdeadaaedbecbcacccecaccaecdcdbccbcccbecbdcedabaaccbacdddecbbbbdebbeecdacedbebbebcbaddebdeedaabaceebccebbeeebddbbdebcacdacceabdedecabaebaabecaebdcdcccbebdaeaebbcdeaccddabdcabaabaccedbeccbbdedaebaebabdddbaaabebbabeeecdadebadaeededecdbdabcbdddabbabbeebdabbdeeacccbbeaabadeaadccdacdccebadbbcaacabbddedadbcadbbecdaddecbbedeeddecbecbaccdacabcebdadeaabebabdbaebdbaedcaabdecebbcaaedaaccaaadbeeaedeeccebbedcedeebbcababbaededcdadabdaceddbadcaeaaecbeecccecdaddadddbbaccbbaeaadebcdaaadacbeeeeebbbcedeadcddecdadddaabdddeeadbbddddbecaadccbcbdeebdaedacdcededdecbbdbcddcbebcebbcacabaeecadedabeebdecbcaddecbcbceaccbcaedeaaeeaadabdaeabdcbbbbaeecbdaaeaedeedcebddedabcecacedeebcdebcdacccaacdcaeddbccbdbcbaabdababdaadbeeadeeceaadcbcdcbacabdceaddabbdeedeaecebcceebebacbaaceebcbdececbbeacecbebaaedddadbdeaedaadbeeeaabccdcbadaedcabaeadbecaadaebacacdaeacaeebcacdaceaccaeebaebcaadabdbaccedabedcceceacdbecbecbcabecebdbdccebbebaabcccbccaaeedcabeedaaaccaabbaedacabaebdeeabceedabeaeeccedecaaccaeddbeaadecceeecceabecbbdddccbacbbaadaaabacdbcdaaadeccdcaaaedcebbbedaaceadadcaaaebecdddaddaecccadaaedbabaeaddadbecbcacdaadedbababebbbcdbecaccccbdaabaeeedbcccdebacdcbcdaeccdabddbdbecddecacdeccedecabadaaccdcbcdbeececaaebeebcebbceacaaceebecacadebabaebeaccdcdcbdabccecdaacacaabdbadcadddcbdcacedcbeebdaccabebdcaaceabbdaabeaacaeaaaaaadcdacaddccbadaadddacbdecbebeadeceeccaaabccccbbabeebcaadcbdcbaeebcbcecbdaacedbcbbbdeceeeebcecabeecaebcceeecccbaedbdcccdeacaaccedccaacbbdeaddeecdaceccbceaecddacdeaedebecaaabdccaeabbadabceaebeeccadcebeddbcceadedcacbdbaccaecebcdbbeecabcceaebeddbeddeeeeeaadddcbeadcaeebbceabeecbeacabaeabebaedbaebaccbdbbedecbbadadedeaededcbeaeacccabdaebadbcbcabececbdbcabcebabdedecabdedaacccecdecabcadbbcacbaebaabcbabeeaaddeabebeacecabcaedebedacdaeaddadeabddebebaeebbcbeecbbecccbecabeddbededcebddccddacebcdaadabaaedcbcceadedccdcadcaebdcadebdcbccadbadbaebeaebddcdadccdaddeeddabedcebbadbabccacdeaddcecbdceacbcebeedccbadeddebcacaacbceadecbccdadcbaddbecccabdacecebaadacabebbcbabbdbadeacadcbabedbbbcdebdcdaedcabadabedcaedbdbcaccbecceacbedceadceaebbbdecadccacbabebedadcaddececececddbbabbacddedcddcbccdcbeddcbedaceebeeebeeceadeeabccdabaeeaccdedbdbebdcceeeccbbbadcdbbbdebaadacdcbdbbacdbeadacbdbbacbaabdbdbcaabbdbbdadbbebadcbdbaaadcdabceecaaacebcbaaeadedcadbddcdbeaeabbdedbadacceeaadbadcebabacdadcddbeceedcadacbdaecdababcbedddabdcbcacdbbcdbcbcabdeeecbdeebdcceabccddabdaadabadccbcaabdbbcecdaacdabedaddbdbebceadaeedbeccceccecbddcababbacabcbbdcaaeedabaababacebaebcceaeccbdebecddddbadeaebbddceaaeccdedacbedccdbaacacddeaedcaceebbdcaadeecceaedcecbeeecddaccaeaaececaaeaeddddcbabbadddbcaaddbcdbadbeaceedabbaddbeaedabbbdceceeceadabbdddedcedebebadaedcebacddacbddeabeedabbccacadcacdcadeadcddccaebdeacaccccaeeeaeeacccbaadcdbabbebdccbceebbeacabcdcaaabdbbeaacabeaabdbdedddbecbcaacaaaadebbecdacbadcdcaecbaadebaeddbaddbeaecdedbcecbbcecdecababaaddecbcdabbdbdcbdbebcecdcdcbdcdeceddecacbaecbcdcccecbbdebedadbcdaeaabceebecadaedcaaccdbebadbaeecebabbcbbacbbeabddcedbbaedaecadbdedeacdcaddeaabadeebcdbbddbdcdeeabbebedaebabbebecbdaadceceaaedddeebbddeaccbaedcbdaccaaadbbccceecbbbedaabbabbbcbabbbceaedbcddaabddbdbadedcadccaeaadbaccececbdedadbaeaccdcbadccacedadbabaaeccaebdcadaabededdcdcdaaeecabdbeacaadbddebdcedecacaeacbbacbccaccaadcbbbddcceceabdbcdedadebdbbeceeccaaebcadaecbedcbdcacbbadcccaadeebddacabddcbbacaabadbaebbbeaaeecceddaebeaecdddbabcbadadedeaaeadbbebacaebabbbaddcbeedcdcdaacbdbbbccddbcdccdaaeecaecccaebeaecbaedcacabdaeeddeccedccdbdedeacbeedbaeeaacdcccdbcaacadacbcebcedebdeabaabcabbdbbbbbbebcacbdaeceabcbeebdbcaeaacceddaebeeaddceaedcebbcaedbebcbaceccdeebbdebecdcaadeaeebaaacdbecedbaddecbbcacccaadebabaacbecbdcbadecababebedeaabdeabceeddecddaedbacecaccadcbecccddcddaacbcbaddabccdaceecbaabcdbadcdadaeecedbedddccacdbaebbaedccdadbcaeebccbabcadeaccebebedbddeeecdbebcbcebbdacadcbbddbcbaadcbddadccddababdaddaccddedcaccdaddedccdbdbdbbbcdadaaebcaaeaecbbccacbbbeaaddbadddcedabddadacbaedaaaccdedecdaeacbebadaebdcebebdeaaeedbbdbcecebaccccaadaddbddddebdeeeebaebcebbeddddcaacaeacdcbecbbbecccbdbbcaddddebbcbbecaaadbcbddadcaceadbbdeebcbeebdacebabbdbeaabecaaeebdeaacbedaddaeeccddcaedaecaebdcebbdebadcecbbebbcdbdedbddeeaeaaacbebcdaddddcbeabcdabacbbbbccdcbceabbaeabdceacaceeecbecacceecbbbbdbdeceeacbbaaaebdbeabbdaecdccbeadadacddbbacaadcbaddaeecadcdceeadceeccedebdecdbadcbacddcdeebebebecceaaedbdbccbbdcdeddadcadacdcaadceaccaadaaebddaabaadeebdbeaeeebeccebcbaabbcbdeabeababececbbaaecacbdbbbeeaeedddeabbacceeeadbedadbacdebaadcdbdcbbbadebbeedcdbedccedbedbaeedcacecebccbaedddcbaccbcedeadcddbddeeeddbdebdbbbcddcbdddbbbebaaecdcddadbeeebddaadbdcedddccbacdaadecdebedbbbeebabeedebeecbeacbdddbcabacabeaecdabbcacadcccadcddebdabdaaddaedccbacebcebecdacababeeeadcedbedbdbccbddeeaaccaccacebbdcdeeccdbcdadcdccadabceccebccdcabdaeeccdcebaabbaaedcbebacdaedbbdedadbaecadbaadeeccbaaadeccbdcdbcddeeeedcdcdddeeaeebaceebbcacaccdcddecaadddbaeaaebccdaeeddbaadeddeadbadcdabbcaeabbecaadbebdecdbadcdadebacecdbdbcdaaeecdbebabcbddccecdabadedabcddedebbcdbbcabecceeaacdcacbcdcdbdcedeebaabbbbceddbceccbbabccbcaebdcabadaaaceeabedceddbcbdecebbcbbdaaadedcedddacacddacebaacddeeccacedbacadceeccacedacaaeacadadeddbcbbcdeeababaedbbeaebeeaebacdacbbcddedacadaedceddacdbeeebeeebddbecebbaeaccedebbebdbadaeebbaabbbcddadbbbeeacbabbeccaecdbaaadaecabddcdebdcbdbbcabcccdeedddebbabdebddecbbccbdbeddbaaabccdddbcceececdbbddeaaaaababbeaadaacceeeadcdaabddadbeaacdacbdaccacdccbbebdddbeeddbcadabebbebddebcaacbdbbaccbdddbbcdccddabcdeeebcbadceddbbadabbcacaeecdebaadbbecbaceceedeebdbbaacabdebecaecabbbabdddecccccadecaebeccdebbbebaceedbadbdcecaaecbaecbeadcadedecadaaeeccddcdebdbedaeacacdecbaebdaeeadcbcacaadbbccaaeadbcedccaebbdbbeeedbabdcbdaaeaaebcbabcaedaabddbabeacaeaebbdeacadcbedecdeddeceaebababdaacacdbdbadddaeedddabacbdbdcbabdaedcdabdabdacacbdabdbeabbdbbebdabeebedeaaebbcddaabecbdceeacccaadcbcadcaaedcbaebabbbceeacceeddcacabbcbcdedaadbecbedabeeeedceddcccadadeeccebddebaeddcadddaedceebedccdebbccdabecaeddeabdbebdcbbcbddbcbecdaaeacbecbdbbdccaceeecbbcecdabcbaaebbbdabeeebdcaccdbebdedaadeecdeabbaceaeaaddaeeaaeeedeaaaedaeaabacbdeeedbaceaadeaeaaaedcbdbeceeeabacdecdadbaaadcbbbebddeaeaecccadbeeecbabbbccbcdaceecbccabbcedabcededeeaedeccbacacaaebeeebdaaacedbeeebbbedabdceecdeecbbcecceabebbbcaeabbdddccbedbaedebaeaaaaaeeabdaeacdaccaeeabedacecbdaaaadbaabceaebcaacebceacccaceddaadcbabebdadbbdbcbeeddcbcdddbddbdbccccbbbcbdcedcdccccdcdccdeadddaccdadaddadeaabdebcdaadcaeaacbaddcceaadcecacdaccebbedccecbcdeadeeedeaceeeeabeecacacedacacdcceadeeabbecbeeebdbaaedecddaaadbcdcbdbbdcabacccdaeaeebeaabdacbcbebbcaadadbeaceabdcbebddaeaeddecabddccebbcadcecbcdbccdeedecaebdebcdebeedceddccccdcddcccdbbdccaeaecbeeebadabbebcabadccdbdbebcdecdcbcaedbbbbccdccbcbeeacdabddebccbbeadeeabdcddcaaaabcadabbdebbecedadbcedbdecdbabddccbaaeecbedbcddebceccbdeddcebadcedbbaaeaebbcbaadbeecebeabcebeccbaceccabcdcccbdbacdccbbecbccebbadcbdaeccecaaeacbebddabcbedebbdaabccbebcdeecabdbdaccdeeecacdcdcbebaadecddbebbcdeedebbdcedbedadcedeecaabdbbabdacbedddbceccdccddcadcedabedaddcecbdbbcbadcbddaabddbaecdceebededacedaeecbcacaecbcbacddaabaadacedacacceaeedbdbcdddeddbbadddccaedcaabdccbeabbdcaaaaedceedddbabbbcbcedabcdcdbddbcecbbeaadabcaccebcddeeeccceaecdacbbadaddadeceaeecaccbbaddbcbeceeacadebadacdcbeaaabeccdaebdaaedacabadbcdebcbecdabcbbdadadbdbdceeacdabdacedbaabeecacbbabcbdcaeeabdeccbdbacdbaedccdbceecaadacedcdcdcdcaadcabdeadaaaacacddabacbddcebbbaacddadebcbebbaaabdbaddebcabacadbabccaaadbeddeadcbbcedcdbdaedaccdbadecdabeaebedeabcadebeacaccddbbbceabbabebccddaacbbcabeccaccdbdaedaddbcddbddddeddabcedaabacdcdcabbeebeddddcbbbaabcdedbccddacccaddacebdadeadaecacbceebbcdadcdedbcacbadcbbedcdebeacceaccddabadabcdcdadbdedccebbbdebddbbbbbbeddacaeccadcacbbaabadcabddeadeccdaccbdabedcbddebeeeccabebcccccadceeaeccebbbaeabcabebbacceadeebabeaddbeaddaeeacbdecbdeadaedecccaadaaeaabaedccccaceacceeeedecedebeadcdeadaabddeadaabdbaaadaedaccabacdbdbeebecabebcdbbddceaaacbbdadccacceabbcceedceddeaeecdcbaaabecdbdeaaedbcabaaaadddecbcebaeaddcbeddcbacaeadbcdedeeaaabddecabbeddaaaaedabccdeaaaebbaccdbecaeebdddcbacabceeabceacacbddbdeaddacddabdbceecdcbaebaababbadaddbdaebceebdbadccdbbbdbdecacacdbcdaddcbbcadeeeaeecebbebcccebeacaaacabbeebdbdbeeceacaacbccdbcdbbecabcaaaddbbedbbbeccdaacdcedcbcceeedbdadacbddeebbbbbbcccdbcebebebbbacbeceeacbbdebbbbadcbacecebaebbecacabbccbcaadbeebaeebdadeeddaedcabdbccdaeebbdcededecdbaceeccedeccccbdaacecbadbebbbdaadebebeebdaeaabdedebabaeddcddabcbcebbedeaaceadbedccedbcbecbdbeaaaaadcbbbdcbbecbcbcecaaaebbacbceadadcccecedcadcdcbceeadbdbbccdadebacdeebabedccbacddbcebacbabbdaeaedbebcddccceecdbdbecbabbabdbabbbedddacdbccbbdbcaaacbcaececbcaeaedbabaabccbebaebbdabbeabcadebcaaddacdbdbcbcbcdbcddabdbcbcddbecaabdaedcdecbdacbabcbbbcdaccbcbacbcbdecbcdacdbebadddbdbebecdedddabedccbbedcedbdcabdaacaedbcabbebedbccbedcedabdcedbaabeeabbdedddbaeacdeecedabdacbdceeccbdeedccbaedceddebecdeeabdbcaeccaaacdbaaddebcaaedddecacaaddbbceabcacdedcaccabbedbecbdaebadedbaacebbeccdbbbdacbbbeaaeacaabbbebbaaddddcccbdcebdaccaadedeeceebdeeadeceacbbdcbaaacdbeacbeecdbaeecdacdbcacddeabeabaededdaecdeccddecbedbbdbdbedccbdedeaacacaccbeabccdabbbcabacdceaddaccaaecccdbbdbedacbdcecdbbcdeaccdaeeabcabaabaceacabbcbddebdeacaebaaacadbabaabbebeceecbbebaecadbedcbedbdeacaeaedccdbcddadccaabdeeacabbacacbbaedcebdaaaebddabbdedcecdadceccdddbdbbacdedeabaeecaaacdcbdcbabcadabeddecccbeaaeabecabdcabadebabdbbaccecdcaedecdcebdedbaedbbbbddacabacdddadddbdeaeadddeeaddccdcbecacaaabbbbddbbeaccdbbaacbecbdeeddbbdcbdabdbeceadacbcadacbcbebdcacbbacabbaeaebedecbabdbeebdaebdbdeccdeabbecbcceeebeeecbababccadddabdabccbeeebdacdcbdbedbcaebdbedcebeaebdebacbccdbeceebccccacceeeddcbeeceedbdddadbdbadecbdedbcdaaacddacbdbcedadcbbdcceeddeeaeddccacecedebddcacadebdcabbcaadedacdaaabeadddedcbaecbecabbeadececbeaeecbcbccccbeeddebeedbdabdcbdadcaacbdbcbbbeedccdcbcaebeecccbaddabdbcdaebadcbcabcbccacbbbdcabdeeceadebcbbdabbbeaeecbaccbdabeeaeeccabdddbecccdeadcbbbacddbcbccecceadbceeaebbacddcadcadadddaeddaaceccddaedbcceacaaeebaaedbdcddcceeaeaacadcbaeebcbabceeebdbabcedebbbddcedaedacbabcdecbeaeecdebdeabdecadbeacedadadbdabadabbcebaeeaabcaaeaaecbaceeaeadcaebecbcececcdccebbcebccaabecaeaaeeadbcabadbdbcecbbccdcdbdacddacaccebccdbebdadadbebbbbeecaebdaddbbccbcbaaeedacaeeddaaadaeaceacacedbeadbcebcaaebbcacbaaedeebaeaaacaacaadedadbceacecdbecbcddadbadddbddaeddcaeecebdeddaaeaaceaadbcecaaebceaabeededaccbcdacdeeddaacaddddecaecadbeecceeabaadeaaecebcacbeeaeeadabadaaedddabbccceacbdbbeeecddcecbbbecbdcabededabbcecabcdbecedebaddeaaccdcbeadcacddbdeacccaacbbeabebcabdbdcabcbddbbeeedebeeabbdddaddcebcadbbdddccecadbdaecedddaaebebeddaadceacdbcdabeeecbbcaebadceaaabbaadeaadbcbccceaabcbdbbeaadbebaccebbbcbacdabbedaceeecbcaebcbeaeaacbbddadbbdbdbcdcadedaabecdbabdaaadeaaebcedebcadcebdcbbabcedbdddeabeebedabeabdbdeddeceadebdadbaeedaedceedeebedcbcbdcbceacdeebbecbabbbaacbcceaeedabadbbcddedeaddccdeccdaeacceaabbcbdeccddddabddaeaeeeeacdadeabcdbaeadecadbcebdceebccaeebdaacceddcddeccaedadadbddccbedbecdeeedcddabdccdaadeedbdadaeaedccaeacebadecbecaecddbecbabddeababaddcdbeaebbecaaacacbeabbdeccacbdaadcbdebbbededadbdcbaadeccdacebcbdeabdccdecabdaecdcadbaaceebbecceabaccbabedaabdacbbeeeaaeeaebbecbaedcbedbdceaecdcaeddbebcaabbadeacdaeddcccabeabacdedbcbbebadaeebceedbceadeaedcdcaecabddeeddabbeecebbcdaadcacaaacabeaeaccdbccecdddcdaabadbbecdcdbbbbcddcacecddddeeacdacdddaadcecdbeeaebbacadabddcebcaaddcbdbdbbbdceabcbbacccddecdcebebdaaddebdebdadabdcdbcabceaaaedcacbbcbbddbebbbdbdaabdeadbebeecbbebecbadebeedccedadcbabaddacebebbeabbabacdbbeecdbecccacebebbcaeabeeaacdecabccebaddbdaddcaabdabbeaaaedaceaceeeaadaebedeacbaedecedeecceaaddadabcedbedccaebadacaeeedeacecadaebbecedbdcbebdacbaacaeebdbeaadceacbbaeeeccaeecbbabbddbcabbccedcbdcbaacaedbccecebbdceedbcbbadecebcdcbcdeadcddabebeddabdbbbcbaaadaabedbdcebadaecbedccecdceabcebdccbeadeeadccbcabccddbbedaaecedccdcbededecbbdbacecacaebecdcceccdedbaccedcececabceabeccdabddecaaaaedbceadbdeeddebdbbaceeecbbcdaccdbcbcbddebccaeedccbbbabdacaeaccaedceaedbbaaeddeaedbbaebaedcccdcacdcddccbabebeccbeddbbedeeacbcedaaeccacecbadddeedaeeeaedddecacabbeeebcbeeeaaedaaceaadbacbdddaeebdceecedbbaabccebecaabebccabcaabdbbaacceddedbcaaeeccaeabcdebccbdececeaaaceecdbcaaebeadccebbbbebaaecdabeaaaccceceeeebdcccddddbdccbbaaebdaedeaacdeaebcecddaedbdccbcccaadccadeecbdaecdebeddeaecbccececeeeeeedaebbeedcdbeeecbeeebabaadbdedabebaaeccaaabbbddbdcbabcbcdeaaabcdbeededeaeadcdadbedadecaadeebbeedebaeaadbcebdebbbbaacdceabddddeebadcbcddaaccddbcebbadcccbdbaeabeaeacecbecaccddbdcebdcecccaeaebdebeaaadbdbeebcdaaadceeecdaddecacebbeabcaabecadadddbabadaccaaecacadceceedaeddebaddbeedebdbdacaebeecddaaadadbeccebdbcdddebdcceacbeeecdedcedecdcdeedaaacccbadcdababadaaecbebbbebdbaabbbddbecbddbcbbddaecabadaddaabeabbeadbddeecdedebceccddccbcaeceddeaaddecbaccaebcbceeacadbddbadaeecacaaddebaacabcecbdbeadeeecaaeddeeeeeeebcaccbadcdbdaaddeedaabccdddeabaacedaadbcaadbbdacebbbbeeeacebdbeabcddbdeeeeabdbdbaebeabaadbdecaeddebedaeacaddabaeccaaddbbcadbaeaabbccadacccbceacdcbeeebdbbdededeacabcededacbbbccadceeaaaebebdacbebdcabbbeecceeabbbeceedcbebcdeacdbeebbabaededadeddcdaaaebdbeadbabddaeccadadeebdbabeecbabdaebdddeadcdedbbadebacdbabdcadabaebacbdeeeeebecdbccdeebccbbccbbcabdcdedbebddcecebaacccaebeeacecacbcdedbaccecdceacbeadbeabbabcdbbaecebbbaccdaedcceeeaadddceeccbcbeebadbcabbccaaacecdcdcddedddedabcebdcaceacceaaceaadaecbddcbbecdabeaadabcabdcdeedecbbeaecacbcaddabbeeeadaecdecddceceacbcceaaaeaacaccdbabcccebdbeebbceeeecaaacceedcacabbadcdebddcbeaadbaeaaeacacaaecbebeccdacaecbcdceeadeecbcacbdccbcadadeebddabdaabcbceaaccaeaecbbaebbdbbeacdecbbbaaebdbeabdcbdecbbdecaccbcacdddaacddcbceeacdcdeddaecdbcabcabbdecadabddcadebcaabdcebecbbddaebcccadacabecbadaaebdbbccdbcaadeaccbdbcedaadceeadadaecedecbdbddadadaecddcedaedbdabbeaadeeabdaedbaebecddbdddbdcccddaaebedadaabdaacacdeaebdecaebdbacddaacdecabbadcbcecacbbbbeecbadccbdceebedbcbcdcddbaaabbdddeccbcaedaccbadccaceaececdaebcaaceaacdcbeeceaddaebcaabbaaeedeadeddaeccddbceecedccbaebdebdecbbcbdcbdcbcbbcdbddadacedaeddabaedaeeccebebceeaacbdecaabbacaaabceabcdabebdcbcdabbebbabeaccdbbddbbcdbdadadcbcabeacabbaaebcedcebedbcadcdbcbdabaecaeabcdadcdcaabaabceabaaacecedcddecebccccddbbbcdacededcadaddbeacdcadbaddcdaaedeadcebcebbdaaabeacbdccceebccdbbeabaeaddbbabdcaabdbbcadddedbdbbdcaacadcaeddbdceccabceadcbadabaabdeacddcddddbedbabecbcadeecceadadedcccaedcbdaecbccdaedceedcadcebcccdbaaeaeaddcdedccacbddaaededcaceaebcaacdbdcaddcadcebeabddbdcaaacccdcdabbddbdcabeebdbbbcadbebaccbadbcbdecbbcebcbbcdbdbdbabecaabcbddbbdbaddecececcecdccbadebacdcaceaddbbeceeedbccdbcbcbccabdebebcbadebaacaecdcebbaacceebbcbcbcdebbcccdadeccbebeedebaadeebedadeaabdddeeaeebaaedecdddbadecbcbacdcaaebdbeaabcaccdabcabcaaaaeadaeedcebecdcdecbeceaeadddbadadcadaccbcdbcbbdddcaacdeadcecccbecebadcbcedbdcdeeedcdabdadeeabbdaaccddeddcbebdccadabcdbeaebccadebeacebebacccecccebeccccacadeaacbceaeceececaedeecaeccdbaeacbdcececdaabaacbddddbbbddbcbebaeeaeccbbadcbcbedbceeeeeadbbdebaccabbbccceedeacadaabaeceaaddceaaceebdaccdacdddeebbbecceecaeaabcbecbbaedaeddaadcaedecaddbdaeadebbadbebaedcbdaaaabeddacbccbabbaaadedadbaabdaaaeecaabbaceddbddebebceeeaecceadcbaadbeadbbaacbdebdabccecbdbeacdcbeadcecdaedeaacdacdbdddddaabaddcadecaaecaddbdacdadbedbdeeecbedeceaecdbadaacddbaaddebdbaabbebcaadcebbccadcbdeabeededabdaedaccaeedecdebacbccbdadbbcceeedcadddededcabeabceadcdcccedddacabccecaaaaecbedbebbdbeacdebeeacdbcabdcdeceaccdaacacbcedccabeadadacdcecaabababcbdcdeabddcaaceecbbdedddedacccbbbbedbcbaaddbcaabbebbbccaabcadbedadbbadabaeaedabbaadbabdcbaacbadcabeddcbdeaebdebcbaecabaaeeccdcacbecaacabaaccdbedcabdccadebccaacdcccacadadceadeedabdadedadcadbacbbebcdbeaccdcbaabebdabcecadeedcbcccdeccebacaceaccbddabdaeeacaedcddeddebcbedeebccccbdebabedcebbbbaaabbbdbbbddbcdcdebaebbbaaedddabdbdaadbbabbccbddedacbecededaccddeececdbeddacccecbebcdadeaeedeaaabdccbcbaeebddabcacbabecdcdababdbebababedcbcdcbeaaedcaaaadcccebeeceeceadbbeaddabbebcebbceebeeacabaaacdbcceaacdaecccedebeeaeabebecaababbbaceabacbccbaabeeaebeaaacebdeddeaadeaadedddccaededdcedeeeddbadbbbdadadaeceedcdceacaacbcadbeaabaaaeddeeebaeeaaaebcbedadddadadedaceeadccbdccdaddbbceddbbdcecccdbaeebaebdedadcdeecccbdbbbbaccbbaaabeeddeaadbeceedcecebecbbebabeeaacbbcecbaaacbbcceddccbbaddeebddeceabadbadcbdeddddbdcbbacbeccdabcaebcdbabbbcabeaceabbcbbacbbaaebbaccadabdbceeedccdeabdcdccddcaabdababdebaedbbbcededdeabbeeedabebbcbdbaeecdbdaddebcaacbcbaccbadeddedaddbeaadcaabeddcbdeadbdebcedecdbbbebdaebbeeacbecddbbdaabceacbbeaaeecdceedcbdcabcdedecedaddcaddceceddcdabeabbebcbaccbbdbbebdddaaecaebdacaeaceddaacedeebedbabacccbceebeedbaeedbdaeeaceebabccdededdaebdbbaabeabcecaadeeddeaaeeaddecbceedbecabceadbaebabcaecaaabeaeccdcbbdbaaecdabcaedabcbcbddbbcabaabbceaedcbcdedcdddeaededeabbdcaedbcadeedcdbcbeacaaaedbccdacdaadedabdcedebebceacceaeaeedbcbdbbdcbdabaabddaeeedcacbcaadccaeebecaceaadcbabeddddababebbdaebcaeebcabeededeedeebeceacaecdcadeebbccbbbdeddebbbedabeeabedcdcdacbcbbadecdacbbaebbbeabbaddecedebeecbacbeaaabbdeeaccbaccddbabaeecbaadebceeeaeeedaceedececeadcbcccdeebecdbebdddaeedeceadeedcedcccdacdcccabbabeacdceddaaccdebbbbdedebeaeaedddbabaeeacbbaedddeaebcacbcdddeeeabcdecbebacaeceedcbcdececeedcbbbacbeedcecabbcdbceccaadabcdbabeeeacccacbbbeabebacbeddedccedabeeabccddeecbdacbbbadcaddbdacacaddabcbeecbdebcbbceccebbceaaccbacaaccaeaaeebcdbccabbbeecbaacbdbbacaceecedcdcdddbcadcebbadbbcdedecbaabeabcaaadddcbdececbebabacadebcabaecbdeabaaccedcbadcbcccabdeccbacabbcdebaaccaeddecdcaeacceeacedeeecedbdedbaaebbedbccadbbbbeeeeabcabdddadcbdeddbadedabadcbaacbbcdebadbceaecebaebcaccdcebbcaeeacbaabbedaecdbbedbabaccdcdbaddbccabeeadbaeccaadbecdacdaddbeabecdccaacaedaabbbdbeddbcaeceacbceaccddbeddddcdbbadbebbbacccbccbeaeaaecbcaacbcebdbcedbcbebecccbcededeccbdadeeaeadaddbdbbddebdbdaedddceebcadaeeadaaeedbcabcdeaaebdebcdbcaccacbeebbcaeaeaeebbecdbdaecceabdcaecdcaaacaaaccdcbcdcbdaaaadcbcaddceaebeccceacbebddabcabbeccedaeebcbdcbcaeebbdeadeceaeceacebbeceaeddbddbdaadddeccbdcaeabceeeabbecbabbbaeedbdddcedeedecbecaeadacdcaedabacccceeadcedaebcccdcaadccdaccaececacccacbbedebbabddacccadaabbcbaabbcbeddebeaeccebcdebccbbbddaededeccaebbbcedaecdbabbeeeaaaabdbdaeabcbbeebabecbaecbdbcccaebcacdecebdeeeabaaacadaacceddebbeddececdbdeabeebbcabecebbaedadabbbddbbdaaddbaeebaabbceeaabcecbddaebadabdcecbbdeeddbccbebcebadcbdbccaaceeddaceedaddacacdaeedaaabceebacbcdbcbbaedbadbddcabbcebcedbbcbccbcdeabbaacceadccbbbadcedebceadbcaedabcaeebbbdebabdbeacddabebdabaeadeebeecdecdceeabadacabeeeeacaedbbbdaaaddebdebbcdcaeedbcddbdaedceddcadcddedeccbaeecdabedebcdadbddadccacaebbadcbedaadeedeaeaeedecadadedccbbceabedcdbbcaceeaaebbdadeedebbebceccccecaebbacaaceeedaaddcdceabddddcabdaabecaabedddeebbaaddddcbbeadecaeebdbbbceaaedcdcddeebdabebbccadebedcdceaaeeacdcacbaaceddaeddeaeeedadcbaedeabeeaeeebbbaceddebdbaeeeaacceccacddaedcedeaacceceaaeecdebbeeaaedcaeebaaaaceeddbcdcaacbedebbecadbbbdeedadceabecbbbeaaacccaecdecdaeecceddaabccceeebeaaadebaddaedddabcddaaededcbbdddaedacabdddeeabdcaebaeeeacbdcccadadebedcbecccccbeccaecabebbddbbaddaecadaaeccacbccedcddedbedcedbaddeadbdcdaaaadbbcbeeceaabaeaebccededacaeeabbcbaddceacceeacbadbeaceaeabebaceedebebbacadaededecadbdeddbdcaeacedddebebbecbcdadcceaaedbbecdeaedacecadbddbcddabdceebbaebdbbcddaaccdbededaabcacddddcaaeacbdedbddbcedcdababbabbbececbcebccaaeeccdedacdeeadbcadcbedceddbbeeddddccdaeeaacdcdbbacccaaadaedbbeccdebecaddcabbbabebacacdcdcebddcebbaedccbbcadbabeeeabcdbbebddabbdddeaadaddcebabdddcedecedcbccdebceadecbddeecbddacdcdcadccdbecdedaadebaddbbbeacccaeaceaccaedecabceccbeaaaeabbebeddebbdaddbebcbcebdaeedadaeccdecbcdcdbacaceeaabacbcaebdacbebbacbcebceacdcadadbaaeeeebabcceddeedaaddadaeddeeaddadcdccddaabbedebdeeaecdacdcaeeeadcdabecaebeebedbbbaabeecbdacaecededbaebacaeaadceaeceecddacaabccabbbdedaaaceaccabcadaeebcedccdedadbcabddbbeaedddeeceeaeddabeaaabeadadaceaaadabecbbcbaabaddeeeacdeeceedbcbcdeaeaeaeeaabeaacdcbdddcecbcdccdddcddcbbbadbaccbceaebdebaeebdcedececbabcadcddddcedbbdbbacadadddbaceedbbdebabdeeacdebdbbaabeaadebadaeeecbcacddbaaebeccbbdddcbdededeaabadbbaeaaddccaeabacbdbcdddeaaeebbacbedabdecabbdacaabaebcaaeddcbadbeedbbecceaedcdbecedbbbedacbdebbdadcbbaeabcebcababaeeaadbbdadecaebccdcecadccbeaaceebbdbadbeaadeedaececaadbccbadebbeccdcacddbabaebbdcceeebbeeaaeacbebbebcbcaeecaebbdbbbbecbdbbeaecdddcccedbadbcaedcedaebaababeccdadadbadeabeacdeeccbbcbbecbdebbbedccdbeabdeceaaaacbcecdbebcaebbcacaccdbcaadcbdcdbdeecaaedeadaedcdeebceeaeddcbeebcccabecaaebdeeebdbdbecadccccdeaedecaabcceceeecbabbeaecbaeccebabacbcabaeadcebaaebbbaaaadbbacbeeaceceeaaacdddadebbadeeaedeeebeacbbbcdbdeaeadbccaeadbaeebcbaeedbaeaccdcaacbcdcaecbacccceabeeedceeebacebadeaabdeecaccacadbdadbceaaecbeadaacbdaaeadecabaabdcddcdedeaeeecaecadcbccaadeebbcbeabcaccdeceaebebcebcbeacaebaebacecdaaecdaccadbdadbbbecccbdddbaeebbabdacacdeaaabbeaeaededdadecaaacaccaadeeabbabccaedaaadcbddebcbcdbedaadacceebdddebebeabdbdeaedaeddadbbabddcbcabedbcddacaacbdceabbabbdedcaabceeebcacbbedbdeaeebddaececbeeccdcdcedbdacebdbddbeccabddcbbabecaecabebcbcecbdcecabddcabaddbaccacaadbdabbbddaeabdbadddbdaaddadbeeceacbbcecbeacbecdcdedbdceedabeedeeabeddecbddeeacdeaccbcdeedcdeddbaaaecbdcbcbcbecdbebbeebeedbbebacedcabecaeeacbaaddbeceecbbdadaecdadbbeebddcebbabeeecdeebddacddebbbedaecabdeeeccaecebebeddeadcddebcdeadccbcceeeddebabaddcbdaadacdbeabacdcbeebaedecbcbccabbededcdcbeebebebeaacbcbdecdcccebbdbccdabbeaadabbdbddabccecacdcbcadadeadbdddedcaaededcabcbabeaeeaddaabebebddccbceececedbdebddecbbbbbdabbacaebbdacddbcccebabcdadddadebeecbadeedbabebbbdacbccdbaddceeedbaeccdacbbcaddbedacadeeebaeccebdeeabebecccdaabcddcebbebacbcbcbebdcabadcedbeccdbdecacbeeadbedbeadaadaabbbdbcaacdcecacebceaaecdaaecacdaabaeeeadecbecabeddbeecdabdcbcddecacecdadbdecddbdddaaeceaabcdabacbeaededaebebabaddaadbecedaacaddbbdbccbbbaccddcadddececaeddeedcebedeecbbcdcecaaaacdacdbbdedceeaadaadbddbdaebbceadadeaecadaadbbeecbbbdbdcddeeeabaeedacaabcedeeeaecbdebbbedbcbbbedbeabcecebdddacbcddeaaaacabbbeaacadeaebbabadabbadcacecdcaacdedbbbbabdbedaeceedabacccaadcbcaceddbcebcaaaecaeceaddbcadbeedbccbccdababacaeceeabcccacaebbecdbdedcddeaddbdebbbacdebeddccadebaadaaebcebbcbceaabaedadbceeeaaabcacdcbbcbecebcddacbabcbdbbedbaebbbcebbcbabacdcdbcdeecbbdbeccadddacacbbbaecbeeadbbdddebebdcadbcadaacccccaedbabbabeebdedbeaedecacababebeaeeadaeccaccebbebcbeaaeddedbcbbcbeddbdbcbbaecedcaaedcabddbeddaaaebeaedcabbdbeededcdeecceaccddcdaebeddcbcdedbdbbbabadaaaedbbaddbebddbcaeabeecbbceabedacdcbdaecbbbcaeaecbbbcbdadcbeecbecbabdcccdbcaaaadcbbddbbcbcbecdabdddbceadeeccabeeadeabdbceaacabadadabbcdacddbceeacbdbbbbceebedbabbbebbececaccaccdcdabbebbcbdcddaaeeebaadcdbcbeebaaededdedccdcdedadecedcdccadbeedbbdcebaeaadceebbacdebedbbeaeaeceaaebbbdeeebeacbdcadeacbbbcbddbaaaabcaeeaebacacdeadedabacbcddedebbbacbabdddadedcbcececadbdceabcacebecabaecaccbedeeabcbaeaddeaebebbddcadeabaecddcabcabccdeaecccecdbdbeeabacacaaeccadceeaaaeecdbbbbccadcbaadcceadebdaadeedbccbbecabacbddbddceddcaeadacdcdceacbbbddcccadbaeccbdddaeebedaabdbeaaabdccadabbdabedaaaebcacdbceeceaaecddeaadbdaaeebcadccebddaabebaebdeccdeacceddaaeadebddacdbabbddcdedccabeedecaaeebdabedeeeccceadeeababbeaaddeacccbeacbebccdeedaadbcbddecdbeeddacaadacceeceabaaaaaebdbaedeecaacdcaacbcdccedcadcedbedcabbeaecaaeeaaacccabbbebdedcabebdeeddcbcadaabeacdddeebdabedeeeeecccebdcaaedabcbdcecbcddcdebdbbdaeaadacdbbaebbbedcddeeabdbbbeddaccdcdbceeaacdbabbeceaaadeeccbaadcadaaeeaaaddcddcdaaadcdebacceadbeddeebdeceadccbcdaecabbdceeabccabaebaaeaeaecbbeaadbeacbbeedbcdbceecbdbbbbedadabcdaabecebbdaeacddbdaaceddedbbddeecedcaaecdaddacbcdacdbacaceddeacddbeacbadaecbcbaaccbcbaeccbccdcaddecceccdddbecceadccbebbeedbadccdebaeecaeaeccbcbecaacaacbcbddaacceaaacadedbaeccbabcdccaeecccebabcdbeddcacdbcbbedbaaabaadddbdcdaacdcbacaddcabaaeaddabebcbeebbbbcadbbddebbeabeaecedbecabcacaebccadcddabccdbdddadaabeeaebacdeabbacddcededdaebbaabbbdceaedaeccdbdadaceccddbdbedabdaeaeceeaadeccbadebccbbbeebbbababdaaadeecdaeeedaaaecaedeecbdaddebbdaaeddbdcebdbaeaaeedddbddaedcaebcbaeeacacebbeecddeccceecbbadbadccbdcddbcbcbebeeceabbaedddcdedbcadcdbabedbbaaddcdcaddcdaaeececbbabdbabaaddeeedebeadbaecabeaeabcccaccedabaecaeeebecdebeddecdacdedeaadecececaaedadecaebbaddebbaeccdaacaccadaeecbaaecdaadbecbdaeabccabcccecaadccdccabdacebbdcacbbdcaecadeaabcaddbdcacdcbcbeeeababebaddeaeeaacedccbdccaaadbaecbbdbddbbebeacacbbadeededcdebedeabadcdaecdaccddcadcdcebcccdcdbacbabcaccceeeceaadeedcacbadcbddeeebcbeaaeacaeebccdbdaddbdeabacbaebcadaeddddedaaaacccedeaecccdcbbbbdcababdabdbeeaaeaeeaadedaaaeadacaebdecdbcbbadebbedceabbbedeeaddddcaaedcbacecebcccacbeecdceacbcccaecedbaedaaaeeceeeabebcddcedbecacdcebdddadebebddecebbbdbebdeedbdcadecddbbdbccaacdacaababcccccdddeedadceccaabcedbedabbbeeceaddbddecdacaadbdddacedabbedaaadcabcdeedcddbdaeebaabdecbdaedabbdecaddcabdcdcbcedccbbaaacddedcceabcacbcabceacceceadeceebbdaddbeedcecdeaccbdaacabadbaccdebcdcbccbceadcacaeddaacbcbdcdaaadbacecbaadebcdcbbdaabeceeedbebacabedbdadacaadacdebbeadeeecabcdaacacdcccccccaebbabcaddaadcbcdddcdaaaaacaebdceaeeeaebeeeeddebaacdedccdebdbbbceabaeaecaadcaacdccaeaeeceeaedaedcbdcccbbcdadaceaabcacebebdaddcbeeccbabcbbacbbebeeebbdbdaaecddcbdccaeabcccecebdbcbbbbddddeebdccabececcbebeecddeddbaabedcdeddadeddedebccabaacdcceacbdbbcbddaebadcecabdbeabeceaaabadeddceebaceecbceabbdbceedaeaabadaceccabebcbabaddeddcecbbdccaadcadcdbcacdbedcaaceabececaabbdeddcaceaddedccaebbaecbbecaacbcedcadcdbeeabccbececceedecbcdbccdabedabedddecbdabebdcadbbacbecebebeecabcbdbbbbeadccababdcabddddacdddccaabadacabcccbdbbdaccbececdbcccabacbbacbdcedaddeabecaabbbabbbeebdecbdaddeeedadaaecaadbdcdcebdebdbbebebdcbeebbeccdaeaeecaacbceacdecbecaaabebbabeaebcbbebcadddaedbbebdaddedcbadceecaebdecaceeededdcdbaaaccdceeebbeecaddaeceddddadedbaaabcebbbdccaaaaccdbdaeeeacebbeedddbcaeadacdcbdbdbccdaeaaabddcaeccaabecdccccebbeedccdebcdcbbebaeceddbcccccdbceceaeabbeccedcccbacebbdbedbaecccadaebbebacbaaacdaaeeabdbdbbcaedccaceeabbdaabdeebaebceeaccbbabdaddadabddbbcbcaacadbcbbebdecdccbdaaadadacddebcbbdedecabbceacbeacadadaebcaacccdddbcbccdbeeecdadbcbcdabadedcebdeebbbecabbcaacadbecdcbdbdbccdeaeecdcddbbedbbceadacbbbacdebcbddcbcdacabcdcbebdacdcedcababacbbabebcceabbcabdcbdadcdaebaaabcdcadadaebdcddddaadbcecbecacebcbcbeecbacedeebabbeecababdeccacdcdaddadcbdebbeebcbacececdbddeaaedbbdaedaebdeacbadceecacabcaadabcdddbaadbdaecebdbcedeaaaeadcdacdabeeccceccacbecabddeaebcabbdddcdbcdbacaebdceaddbeacdadcdbdcbaeeceedcaeeacadaeadecacadbebadacdbbcccceadadacbbbaebdccdcbbbbdbcbdabbaeddcdcddceddbeeddeaeaddacabcaebdccecaabebbeacdbbeabdeaaddebeacabcaddebbcecccdeecacececeabaadbbaadccccdecdaeedbeaacabeabacacdbeaddbcabccedbedcdbcdcbabaeebaaaecbeebeecdcdcbeccdeeccacbdebebebaddccbabbcdaaddecacdaadeacabbcacdeedbccacceebcabeebaadbeeaaecdbecacecacceeecbddccacadadbacedeacbcaccebcdacbacadacabadbecebeeaadeaceedaeaaedddacdcdddeeabedbdbaacaaaaaadebdadedbaeceeecbaebcbdcddbbabbaebcbdabbdcabdedbcabdcddcaaeaacebbeceacdeeecaceabdbaabbdcbbeabdbecdadaadadecbeeabbbeabbedccabbaebeccadddcabedccabeddacbbccacdcdddabadccedaaeccaedbeaacdeedbeecbaecabdceeaecdcbbeedeadcabecbaddecbccaeaceecdcbbbbbecadeadeabebeaeacdaacbedbadcedbbccdbdeadbcacaaaddcddbdbddbcdeeacbddaddaadcdecbaeeaeaadcdcabbbebbebdacbacaeadbceadabedaeaababaacbecebbddecccbbbaababbabedcebbbddbadecbbcddbbdeccecdebdccdecdcbcdabbabcbcbeeeacbaaccacededeaeaedaddddbbccacdbcdbadabebbcaaeaabbacdbddddaaebcbecadabbcdddbbabccccddadacdcaeaccecdbbddacabadbbebeecedeeeecdebcdeacccdabcacaadcbceddbcaeacdcccbeeebdaccaecabacdecdaaaedaadccceaedaabdaaeaeacdbecdbecebceeeaabebbbbddeecdabbdbaeacabeaaacddcdcaedecaedcabeccbdeedeebedbecdbbcbeadbbaecaacaaebcadeabccdebedaebddcaebbedbaacadacbaacbcecbeedeccdbaadabcdaeaecbbbadeeedabbecacedbdadccdcdcdaabbcaccacebdceedbeebaeddcbdbdeadaddeecbedcdbbacddeebecaeaababeebeeaeeddceeebbbbbcbabeddadeecdeebceecabebdbacddaecacccdddabeaedeabdeeabaaabaebcbaaeadcdbabecdbcebaeddbeabdacbbedbedeaddebbdcdabdccabaacecceaaeeedbedcebcedcacadcbaecedadcbcbaadaebeecbdbbeebedbdeacddbacbcdacdbbeadabdbedbeceacebecaabbdaceccabbbbeabdcdbcbccccaaecaddbeddbbaaddbbeecbecddceedccdbbbbdbdaccdecaaeddcaecaeeccdbbdcdaabcabaaaacabedbaaecdadacdeaacbadcacbdedaccadbabcebeeaeaabddceabdaeeaeebadacaddcdbaaaebaccdadebcacbdeedcdebacbbaeabdcaeaebbeeeaceaeeeabdacdedaddebecddebebbdceabdbceaccebecbdaddebcbbdaadcacadbdcabcbcaaaeedaebccccbcabaecbeceedcbaaeadedaabaccbdbadabeccbdaaeecadebbdcababaedececdcddbcdcbdbcaceccbccccebcbcbabdbecdaaadaebbaaededacbeaacbbccdcbebbaebeeceebeeacaeedeeeedbbacedabbceeeeececdecadddeadabeeedeedaaaceeacaeabbadcbbadebeecdbcebbbdcddaebecbceeaceaeabddeedbcdaadabdebebaabbadcccddbecbaacccdabbddddaecebeccaedeedcdccbbdbeeddddadbededbadabccdecabbdaecbbcbebbddbdadccdddededdcacaecedbecbbacbbadebbebaddecddbacaedddebaccccdbaebaadbebbaeddeebebdcbbcaccadadbabeddeabbceadbcbceccdedaeebcedeedbacdacaeebdeeadebadcaccebeaccdadbcadeabdbeeaedddbbcbebeacbdeceabcccceddedccabcbebeeaabdcccceacecdecbbcabbeebecdbdceecedaedebdcbcecaaabadcceabdcceeccbabdbadcccbadbddceeddaccebdaeaebebeaddddaeadeaeaacaeaccbbaecaacecdcedcbbecebdacceddaebdbedceabbddcdddbebdeadcaebcdceabbbeaacdaeaacdbceeadbccdcbebadcdceeaccccddceccdababdbdacacaceddabdadcabbdcdddccbdadcadbbcdccbaaaceaecadaeaebccacadccdebcbabebeaceabaeaabadddebedbebcbadaedeeccabbebdcdbacaeeeecacdbabccccdddbeacbbbbaeadddbcecbadbaeaaeaebdeaddddadeedabbadbdbdcdbcaecceaaebcbaccbddaddeecaccecedabeaedbdcebbbcccaadbccadbebadcaacbeaacaeeacdecdcebcbebbcbbdbacceeebcdcbaccebcddbabdbbbbcccecdedbeebbeaaddcdcddcddcccdebddbcacbccbacaeeebeabccbaadddadeaccbdbaaeebdbceacdababacacbcdabaacdbbeedddabbaecbeacbbaccdaebeccccbdddccddadbddbddebdbeddaaddeabebceebbbceceadababcbdcaeeaeacbacecaebcedaaaeccdbbdeaaaaddacacbcaecdecdebacdedaaaedddbbecdcdadbdedcdacbabdcabddebecdeddaaddbeadebaededcdacddbaacebeaeeeecbbcedbedeeecbbacdbaeddbcebeaccdadeaaddbbacadddceabdccaebcbdbedadceacdcdeccaddacdbdcebaaaebecddcdcdcaeebcbaddabdebaabbeabbabcddbbddcabdccedceaedbeabaccaccedcaecbdbadaeebeaaaaaccebcbbcaccbaceddbebaaaabeabdabcaedceaeebccdbebbbeeebeecbadaedacddacaaceaccdbdabadcacdcbcaeaeeaaccadcbcbecedbdaadaaaaeaaabcabeebdaeeebdeacdbdbedeecbbbabeedbcdbadccbadbbdbaebabadbeccbcdecbdccabbccbcddabbbdaccabeeaeededcadccedadddcccbeceabdcebacadeacabadedacacccdabadceedbeebeaacbcedecbdebdbbbecbddbbdaadadababaeebdecbdadebdccadbabaeaddbebaaeaaeeaadcaaecadcabbdbeceeceabaebbdaeedbbcaeccecaebdabdebcbacacbdcdaccbeaabbbecaabdbcedaadeccadbbcecdbedecceddcdaebbaaacabeaaeecbdbbdaebcaeaececaeddcddabdabceeeebdbecadbebdcdababdccdababdbeebcecdaedeecadcbcdadcbbbaedaebcdaaadaecccccdeaebadcacddbceadbdebeebabbecaadddceddeccbebcaecbdcbdcaabaccbdceedddabcdebcdacbaeaddaaedbacbeaedbdeabeccebdbcdbeabadadbccaabcccdeaecbaeaceebdaeacebebcbbdacecbaccabcdccebcbabbdeedaeaebacceeccddbbcacbbbebacdbacddbbccdacaeaaccbccddaacccdcbbadedbdbebaedcbdeeccdedcbdbcdecebbeaadbbcebccaccbadceadeaaeebcdaccccbbedaecaaddbbdcecbabcedaeedcdcceaaceadccabdeacebeedbdebeabeedcebbddbbeacbacabedecabedbdabcdaaceebddcdddedceddaceecbbcecbacbbedcdeddcbebeaaeddaceaadabdbbbaabdacacdaeeebeccecebacccadccaabbcddecbadcdadceadedccddaeccedbabaaedabbceccebbcbbbdbadcbaceabebdcbacaeadcdecccbbdeccaaeacbeedccedaeedacdccbdddeadcbdddcdceecbebbecebbdbcdeaddadadeedebdbbbaccbbabdecceddaacdbdebbbbecceabbddaceaebdadacdceebececedaecedecbedbadddceeaaadaaeeeacecbeaccacacebedbdaccccadbcddeeaddddeabaddcdcbcbdabdbaaaecadaadbeceecdadeacabaaecaeddbacbddeacacaebecaacebddbddddbcdbdaadbdbaacecddbcedbbaecbaebcbbdadbbadcacbbadaededaeeedbebebadaebebaaedbdcdeaccbaccbdadcbadaddbcaecdadacacabcebdeabeadbbebaeeccbacaeeeebdeecedddaccaabcaaeeebdacdedaebbeaadeeddcabedcdaabaeaaacedbdeabbcaedddceaccddeaacacbaadbdaddddcaeaaaeaabaddecaceebacceabcbbddabdddecebdecebbdcdaadcaebbeadbbccaaacacbdeadcdaeacdcdecbcabeccdebdadbeedaebcbeacabdbcabdbaddccbadaadeaddbbacaceeabdbeeeedbbabcadecacecccaebeddebebcebcbcecacbcabacddaaaeadbcbabdbeabbedabdcdbedccedbddccbbdacdbebbaeabdcdcecdcbbeabeaedbacddeaaedcccecaccbdeaceaddcdcedeccacceaacdacdbcebbceebdcacebcedbaddddacdecdabdeacdddabbbebdbabbeaacbbddbecbacceadbeabbeeacccebcbbeabacebbbbedecccdbaabeacedbdcebedaeeaabccdaddeebddebdcbbedadbdbddbdaedccdceadeaddedabdadabeceddaaccaddacbebadceababbeedededccedbeaeeaecaeaaabccabdeddaebedccaeddbabdddcaebccdcbaeaebbaeadadabccacdceabdcdacdcaaadcebeecceadddebacaeadeceebadbbbaabdddaccdeeccebeebaaeabcccebbceadbcadceacacdddaedbeeebedecbbecedcecceecaabbecabdccadccaececdedcaeaaeebcbdeaacacbbdbedaedbddeedcaccbeddcddbcdeaadccbaececebeeebacdebdecabebebdddcaebebaaabdebebeababccaccbecaadaddeaaccbecccbdcedebaecccdbdeceaaabacccdeaeaaebddcaeebcaaeebadaddeaeebeaaaabeeacbdcedaceeaaccbbaadadbbbadecdcebecabceaecddbabaccebcacbdeecddaebceaecdacadaadeacdaddcecdbeadeadcabbcccadabaadcebebcddcadacdacbbcdcbaeebedacedcabbddaaedebbbdbecebecdadcebdbcacccececaddbcadaacabadbeddecdeeaaaceeedbdbaebecedcadccebbdaebceddacbecacebdeedadbadebcbcceeeddceaabcdddcecdbaccdddcdceaeaaeeacccdbeccdeaaeeddabaccedbabbcaaadbebaceacbebcedacdadbeeecdebdbaaeedcaaabaadbaceeaceaccecdadbecdedebccecbbbeaaeacdedccbdddadeeddedadddeeacdcdbddeeeaaedcedaaecdbcbcddaedcedabcccaccecdacebbcdcdccaedaadbaebddabaecbeedbdebadacecaddeeccecdcdabcebdcacacdeaebdeeebaabbcbaddabddcdcbaebebadcdaedccddecccedcedaacccaabaeeadbbeceeedabaebdeceaeacdeaacdeeecdebaddcacccbacbdbecbaecececccedadeabedbddddceabcadbbcbedbaeeadeabdbdacbddedcddedbedaeccdddbdcccaeabdaabbbacaebcecaeababcaddacaeaedaeaebbdcecdebceeccbbdaacdaabcbebdcdeddcdeaaaeaacaddccddbeddeccecdaacacdacaadaccbdecdebcebdcecccddeceaebdabaacdbccebbbaeaebabeebecddcebeeabdbecebaddbdaabdcadeadabbdaaebeccbbeebcaedcdededccceddabadcadacdbdbddebedcbcbdbeddccadaacccdbeaabbdbccecaabcbdbcceadabddebddccbacddcbddacedbbddeaacddeedbeaccecdeeacebcdabacbbdbebcbbbbeeeeaeebaaeacbeabbabedaadeabaeececaaaeedecadabebddcacedccaacceaaedbcdaabaaebdadddcdddeaccddaababeeccccebbddeccebdccdbbcabccdeaaebddbdddccdbdceabbbdcccedeacacdbbbaaedaeaecaaecedaabcbededccdbaeecdccaeccbeddeebdcaadceccadbdabebdaccbdebdbeecedceedeababbaedddbbcdccaaceabbcabbedaddccedbbcdedcacebbdbeaddeaceeabdceabdececbcacdaddebdcadaadddeaadbebcedaeacdcbebdccbecdabebccbcedeedadadbeabcbeecabadabdbabccabcbaaeeacbdaadacababcbaaaeeadaecbaeeccaadaaededeebeceabedadaddeaedbeacaacdacbccedbaccdaecdbebaceecedaebecaeaecedceddeeccbadccdacdcdacaedbddbbddebcdbabebccdbaaadbbbadcbbbeaaaeedbaacaaecddcbaededbaccceddddacaeaacacdedbabeeaebcaaddacaacdbbeaecbcddeccdcceadacccbcbdedcddbeccdbbceddbeaccebebdcdbbddcddbcdaeacecabdbdeabeebdccbaecbebbcaeddbbdeddeadcccacebedabcebdcccecacaccecceccdbbceedadcceecacbbdcbdbdeeaeeecabbaacdadacebdeecebbcebccedcadbdbedbeeaebeedaeddcbcbecaebdbaedcacbebdcbbdebabdcadecaaadcaeedcaedbcbbbceeaedbccbdacbebdcbacabbeaeddcedebbacbaeccecacdddbedbabadcdbadbcebcceeddebbebebacbadbdeddceccbceddcaeeebacbaacaeeebccabadcdabaacedbbeebacdcaebbdedecbcadcdbecedeacabdaacbdecdddebdbaddaaebbadadcbbbbddcabbeddedeedeeedccbdaaaabcdcaccabbbabdeccccccdacdaebbecaeedadcedcbcaddcbeaababeeedbeccceeeeedadeaeeecdbdacdccaaeeeadacbcacdadbcdbadbadddeeaadddbbddccecdaaddbaebcacabbccbbdebecebceaebbaebcacdaabcedaeebcecedcbcacddcdeebcecedecacadecabebadadadaacecdbbdbcddcedaeededdcaecbbcbdeaceeeaabbbbcccaeccbedaccacdebbadbaedceaeabdaebecdcbdeebcbadddaaaddbbeeebbcebdebaccaabaebaaebbadaeedbdeddceacbebbdaddceccdebdbcbeaebabbcbeccebbacadbbbbdccacaeaebededccbbedaadebebcadebebbcadebcddbbdaedccabdabbddebecaeeeaceaaebaabaedccdbaccdaabbebbddccebdabdcdaadecacaedaadeebbacdaaeabeabbecdeeeaebcacdaecbdddcbebacbdcccdbeadaaeaaecddceeaabaacdcddaaaccdbdbbeababacdeeaabcdecaeaebabaecccdeebeaabeedeaaabdeddbaeccadcabbbcdcedcbdabbdbcecdaeccaebbdeeededbbbbddbdcdadbcacbbaebdaecdcacebeddacecdebeaecadacabccebdddebbebaddeaedbecbedcbebbdeacdcdecbcbcbacdbaeaeaeccabbdcbcbeebedcbceaedbbebedbdeaeddcdeaeecadedbaaccbcbcacdeddbdcaeaebbbceadaddebaecddbcbbbddbcdcbbdcddebadcceacaeaecdedacaaacbdacecdcebcaecbeaeaadcddadabacebebdedadedeeebacdeccedeaecdaaaebaeccddcbbdaabcbeeeaacecebeaacdaededbabbdaabbdcdcdebecdcadacbeddaabddbedcabbcebaacedcaceaabbceecdacceacbedeeeaaccbedadedebebebccaebbeeaeacdeaaaaeeeaebebabbbdeddbbbdedcddddcceacdccbdeaabbacccbaebddbdbecaeecaaabbdbedaadbbbeaabbecadeeeeedeaadbdcdbececaabdeeccabdcdbcbeaabeeabedacbaceccbbbedaaaaacbcdaaeacbccbcedceaaccadbbcedadbbdcdcaacdcbbcdcabaacaeecbcccceabdcbcbbdeacebabadcdebebeeaeececacadeabeaccbddccaaeadbbedcbdadabcececadaaebcccbbeeaabcdbbeeeaedaecebbbbecdaddeacebdedabeeddcebbcadbaacecbeecdabdbcbdedbededabeccbaaeaedebaababcbbaaadadebdbadebdebedcbacaaddcdbddabdcedcdececccdebcabbbbddcaadcdeabecbebbdabbcaedbadecaededadaaceddecedbedabaddcdeebabbdedbabdbdaadeaeceaaceeeecbddcbbbbbeaaecadacddbeebaaaeaacecaaceceeceaeaaabebaabebcabbbccbcddeeecdbedaacddabebcedebecbbceebeddecabdeddabaedeccdedbcbeeaecbeebeaddecebdaeaebebaebaeaecbeceeceeababeaeddeecbacbbbebeeadedabaabdabedbadebaddbbadcdebddaaddedebacabbaeaeaaecddaedbaabdedaadabcbcaecabdcebcbdaaaaecceccbedcebebaedcadeccdadceceedbadebbccbadddeebccecbeaeaceddbcacddabaddabbddacaebbaadbccabbaeecdccebcdbaaeaebddebbdadaabbcaebbbdabeaceebadbbcabbcacaaaddacadabeadcdbbbcdadbbedccdcdbcccaeedeecadbbdecbaecccccadcbdbdbdbccccbaebbdceeccadeddabbdeabaaddeeecebbecdbbebedcdbcbbaedeaeedaaeacaedddeeaabaebbabcacabceedcdcaaecacadcbdececbcecbcccbcadbbcbbccebceceacccddcdaaddedcedaeabbcebdeacbbaaaadbbebaaaedbbdddecdbadadaeacaadecdcbaaccdbddcbecdeebbddcdddeaabacebadeabaedeeaaceabcdbaeaeadecdedadbebeabcdedbdabdcddcddbbdeaacbaedcccbeebacadcabeaddacacdcedbbdcdbbaddabedeedabaaadaedbbbcbaddeaabcccdbebbbecbaecdcdbbbeaeedebdaadbbdbeecbbabcccbaeeecdbcbcbecceabdddbcaccebbcedaeeabbebcdcadeaddaeacebabdcbdbdbddbdecadbecddcbeddcbccaecaccbabeddbcbbcddbdbeebceeddaddcbccdadeccbaecaccdcdbdecabdabccbceebbebdeceedeeeaecbccebeccebcbeeacbdbeeeddaecdbcedabadeaabddbaededadcabeecdccbadeebcbaaceeacbedbedbdcecaaeeaebabededbbaadeebbbdaceedebeccbaaedaabdbdeabbcdeaabcaaadbcbbbecebbbebdbcbbadadebeaeddaacecdaccccdedbdcbdcacdadeddaccccedeebbbaedccbdabbbcccdaacadacedddaadcaccbddcdabbdaebddbecbbaedeaaeaedacaedaeaebbeeddbecaecddecbabbcebcbceadbabbacddbdbedbabbabbddeedbddeabdaceaccadaadbbcadaaaabaaabedcbbdccccbbbdbdccaaaceeeecbadeeecddeaeacdbbebddebcbdedbddaededbeccbcdbbeabebddbacccbcbcddbeababeacbecdebddddcbaedbabdddecbdecddcdebddadededeecedbabeebbbdbebbbdeadbedadbcdeababedbeccddbadedcdeaddeeadcdddddadceabaccdebadbbaccbadeabebbeeaceaddacebeccaabbbbecaaddbacbacdeddcebcadccbabeaeaaeaadadcedbadbcccaeabbbedacdebecdeabdeaecbebdeddccabaddbdadbedbcaaebeceacdeedbbbddedbbabacaeebdcbcedabdbbeaedeadadcdabbebeddbabcdbadacbdebbcdaedbddaabbebadebacbbadcacacbbaaccbeeccbdcabebececdeacdecbebddbaccbeecadbeabdaeeebcabeeadecdbaddaeddbdacdddbacbcbbdbebacdcdeabcddabdcbaebccdcbbcbdbdbecadebbddbcedadadcacebcacdbcdceceaedeaddbcabdccccebededbbccbebbbedbacbdbebcadaecaedeceeaaabbeacbbbeabaaeacacceebbcabddeaabeaacebbdbbadaaeecddcbceadacddbbadddbbacbbccabababedcaccdebdacbcaedbeabbdabdcadbbcccbbbbadbebecaebeddebdaddcecbdaabdddcaabddccedbadeabececaaeddedbceeacecbbbdecedbccddbcadbaddcdbbdabbcebddcdcedceaeddcaaedbddaacdbebeadcbdedbbdeecbebebedbabeadcbcdebeddedbcbdcaabeaecaadeaecbdbdbcdadddccdbabedbeabbdabddbebccddcbacedcbadddbeebeeceabcdbcedabbbaceacdeabeebccbbdeabdaabccaceaaeaaceedebedbbbabbecbbacbddbdddbbecaaabcadddebbbadbadcacbaddbcdaecccbeadeeababbebdbbbbcbbbcdbcadadaaaeeddcbdededbecadadbddbbcdcdadadebbcacbaacbebaadeabcedcbdaaacabeaaccdbecedbecddbdbaeeedccebabaccdccbbaacbbceabbdedcececebaebeaeabdbadcbabeeecbcebecbbdeedccbecbebecbedeebcacacabeecaabccedebacaacadaeeaeeacaeeeddcddccadeadedddeeeeecdeabcbdcdedadcdaacaababaeedeedaddaabaadabceeedaebbacadabcaacdbdabaeeebeddcbdbbdbadebacdccedbdbcdacabeeacccdabadaaabbbbabccddbdaeeebaebcceabeccabdaedeeacdcabceeeebadceebbbaaacdecbdcdebdeebbbadcbedbdcababaebbbebcddbbbedeeeebbdbcaadedadeeaeeadecdcecaadacbebcbbaeeecbcaedddcedadbbbebbbacbdbebdbebbadecabbaaaddbbaeadbeadbdaddbbabcadeeebccadbdbedcbcecddbbdbdbbaebbcbadccecacddaeddeebbbbdcaddcabaccbcabceccbcbebedaeeaedddcaaecaaeceaacccbedeadacdddebaaaaedcaaebbadbeeccdcbaeadcaeaddcbeabbebedebaabbaaddeacecbdceceabcbdbbeaceebdcaceebaccaabbeedbcedbedcecddccaddbdeeeeccdaccebbebaeacbcabcdcccaaabacdcebdabbaadeaeaaabdbcacccebaedddeaccedbbcdbdaeadedeeeebeeabdaaecbdeddbeadbdcabceeccbeabbbaaedcbcddbadcaaaabbeaccccabbaaadbebcaeabeabdabdaebecbcbbdadaeecdceeaabdbdbbdcecbdceeecdebedcecbcceadabedeabdadedadbbcdaddadcdaeddcdbcccdbdabebdaacbedceeceadebcceaecebeeceeeccdedbaedadeaacedbeeaecdeebdddaeebbdbadcddadabeebbedacedddaecbbcacdcdabbeeadaedeedaebcbbabbebbbdeaaeaadcdeccbaaaaeedccabeecccbdbbebadaedcdeaaaaceaeeebbcaadecaceeaaeecaebcceccaecdddbaaabacbeddbaeacbcbcadaecbcebaacebedecdbbcadbdabaeadebeededcabebeebedbdcdebaeebcedbeaaabadcacccedebbdcceeeddbededcdbcceebdcabdaaabececbcbbebaacdedbcbbcabacdcabbceaddbdcaaebaabbcdcacbdecebcbbbbdbbddedcbdecbbbeedbeeaddbdedcbddebdcaaddadbeeaecbedaeceeecaedeecbceaabadebccadeacbadbaceacceeddbedcdeceabeebbebbeabaebdcbeedacbbcacbbebceaabaaebedaecaddecebbdabebaeaecaaaaeeaaaabcebececeeeacdbccbbaddbaacecbbbadcaacdeabdbddbecabdbaccecdbdebcadebbadadccaebbbbbceeacabdbdaeeeaaeedbeacbbccdbbbeceeadcabccaabbebdabbdcbeedeeeeaddecaeaceabbdacaecdbaeedbababeacccededceeecdbadbeeddaeddcbaabbbbacdbbdcedccbeaddddbeceaabceecacbbdeaddebdbcdadbedeebaecbaeaaacbbbeaddeabdbaaacaadbeeadbcbecadacbaecacbbdbbedabcdbbcbdcacbabeadeaccbdabadbdbbebeccacababedcaeccacddcdeabadbcebddadbaebbaceecbbaeeecdaeaccedaceceebabbebdcdeaaedbaaabbceeecdccdbedcdeadeedcecaaaaaeccadccceacbadbcdbbbdecdbaeddcddcbbbeaeabecaeaeeeeedbcdeebbcabcdedacaacdbddaaacedbcddaebccdbaddacbeebbdcabbddeadbdeeacddeeecccaeedebebcdbaceedecdcdcbeaaebadedbcacbdcacacbbacabaabbceaaeaccacbdddaceadecaecdaeeaacadbdadbeecdbbdedbdccdbadabaeedcdabeeeddcbabceceaebadeddbadcceaadbcddccbcebcaabbcdaecdceccdbbeeaeeaebcdddbebeeddbcebedbbcbecabdaceedbeebbcdecddeecbbeecdacedecdeeeeaaecdebccdadabebdbabadaebcdaadeccbdbcadbdddcaecdeedeebbcbddeadebdbbaeebaaabaecbaddeabebdaaaabbddeedecdbccbedaaaddbebbccacdaadaaabaabdeacbacdbcbacaacedeaddaccdbdaeaedcecabeeaeacbcdeeadaaaceeccbdddaeeddebdedcebdacadaedcaadaadedbeccceaedadbdccbcbccadbbdbaabedeceddcedaecbbcddbceabdbacccaadcbdadbaeaebdccdcbaacbecabdbeaddecabbebdaecdaebeeedabdceebaebcbaddeeaaadcdcabacadcdceecedccecabeeaddadedddccbeecdebeebedcbdaebacbbbacabeaadbccbbdeaaaaabccbbdaecddcdbaeaddbdedbbbddeaeacddacbeadaacbaaaaeabebdcdccebdebeeeaeeebaeccbbedcedddaadcecbcdddaaaceacacbadbdebdddaeecedecdbacdbdecdebedebeccdceceedeacdacadbebbccddedabaacadccbdddebbbccaceecaedbbdbeeaeadebebcaaadceacceaeaddabbbdeebaaaebbcacdaedeceddecbacbecddddadeedebecacecceaceabaaeacabadbadacebabbcacadeeccdcdbcaecebdabccaceeccaedebccdabecdaabadeaddedeabcaebaebbaabdccdaceccedeedebcececceeaeedbdcbebbeabecbcacaebceadbbcdadbdecaabbcedecaabebecedcbbebaaacdabbcbaabedccdaeadbddcaedddaacbbaedceeaedecaacedbaebacedabdcbbcddcbebaadddadbceddeceeedadedecaabcbbabbbcddbecacbaaaebecbcceccaedbdbbbdabeccbedcaebdadadccecacacaadeeeebabcdaeeeabecaaadaeebcbdbbaccccdbcdabebbcdccddedabcacaaaaceccdaadeddeabdacacaceebcaebbdbeaeddbdabeddeebdcedbaaccbeadaadeddcadbeabbdadeaadcaacbcbbabebdaebbacacaebeebddbabdceaeececbcaedabeacbeacdbceebdaedcacbeeddaddcdaebbaeeeadddbcdacdcbcbdcceaacdaacbebecdedaacaeeeddaaeceeeeadeeaccbaaacbceebeebdceebabecaabdcdaecdaabdeacdcbecedceacabaaabdceababbabeeacbedecbcbadedbcaadadebacdaeeabcaeddbaaacdbacbcddaeceacadeeeaacbeaceeebbabbeedaeaadeddcaaacdcaadcbdecddeceebbadcddebeddbcdeecbeaebbdeedccdcdacebcddaeecdadcbdddaedbcabdeacdbaeebbddabddcddedcaedadddbaadbeaeebceadcaedcaedeadedbbdabcbcbcdeebaabbacacadeeedcddbdeedbecbbebaaaebdaccdbebabbacdbdbebdcbeadcccdbeaebaadedbceedeadedcceadbbbbccdbbcaaccceecceaddbcbaadbabacebedbebabeaeeebdabaaabcbeacbcbdcacbbeacceababcbacacabbdbccacdbdbbdbcbdbcacbdeedaeaeebcccabcbeeacccbcdbadbccdeaacaebdcaacaadbcdadadbadebccceebedbcdccebecceecbcebecdeeaedaecaeaebcadaabbaeadaababbadceabadedcaebddabbacdcbbaabbdbeecedcadeadcddaedcbabebebdebcdddeaacebeecdcdeaadbbbabcbacceedbbeaceebdbbdbaadbacaedceeecebbedddeeabeaabdaadeacdecaebcacecbcdcbdcaaccddecbcebebbbbcadbadebabccaebebceadccebadadccacbedaedbceeabdedacadedceebacdbadadaccbeadedbadabbdccaccadbecddecbbbdaeedadbcbbeaabdbbcaadbddeaaecceddceccaeeaecbaaceceeedaaebbbadaeebecebaaeddbebbdeaecadacaaddabadcbadbbbbeacebddaecbcaebbaebdaabcdebeabdebcbcebbcaddcbdeeaeecedcdcbddddceacbcdebeecbabcceeadedacddceebbaddaececdcbabacaddaeddccbcdecedbbcddddadddeadeddaaadcdceaaadaebbaeedebddbbbdaababbbdacbeceecbaacbadaadabddaebcccdadaedeacdbbecddaabcaecccedeaacecaebeaccacbbaedbecdcbeebcecdeeeedbabbbdcacdabddbabebcbbdbddeadadddcabbcdadacdaaebdabdbdabecebebadeabccdddecaeaeebcecbdeceeebcddaabaacadcedeebedececadeabacbdebdbecbbeebeceeadacbecbdcbccdeadaeddcacaaebccebbcedddcbeaecededdbdacbeabdbeaeddccbdbbbbbbebbbcdadedbaeebbdbaaaceebeaaebeedbeeddcceeecbbdebdedeadcdbcdeaaddcbdecadaaeedbbaebdcbddaedbddeabeedaeeadeadbbbbbccddadedaaecaddcddabdadbdbecbaeededdbdbaccbbeacdccdcedebdbeabccedccdeaaedbabdaeaecebbdecdcddebeaaddcaeaabdcdeccabcdcececabbdacaabebebacdeedabedebdcbcceaadedcadeebecaaebdbedcedeccccbbeaadaeaedabacbdbbadebdabcecdbcdeedbdaecbbbdbbcdcecadceceacabdcdccecdeebcbbbadaadeedcadaccabaacedbdbabadbceedccbccbeecaaedacdceedadaacbcdddacacccbecaceccdcabbeeacaedcabaaccceaababebbdcdcaeabdcecadccdedbecaecaddcbbebeabaedaeedcbbcbcbcacdbacbcdbabdccecabcdddccaedacaeadeaecdccdeebecebadcdaeabbcadbcbdcecbbeecdbdebccbedbcccabdbddaeedecabbcddebcacecdbaddaeebdceacecccbcbbbdaeeaccaadaebdebcdcdabaacddbdcaeecebedbccdeaabeceadcbeedbdcbadacabdecbbcedcadaeedadedabcbabaebdeeceedaeeaceadaaeaedbabeddcdeeeaecdbaeeaeacdcbbbddadaadeeeeaabadcebcdbbabbbacaadbaacbdaaccbbecddaddbdeaaddabddddbbbbdaebddebddebadbeccabedcaddbdbaddaeccadecbcaaaaeccdbcabeeaeceaccaeccacdcedabaddaadccaabccdaacdedebeeccadeeceebcbaebeacadcccecbaabbddacbbedaaeddeebebcaeacaadebdceddcbecccacadccddecadedadeecbedcacbbcdbeebdcecdacebeeececcadcaccceeececcadeabcbbdceedabaebddbdbeadaccabccecaebcecadccceaddbdacdedecdeadeeeddeebacaeaaddeabbceaebbebadbbddccaeceacedbbbbdcdadeeccedcceaceaecbcaeeabbcccaddedeedcbbaacddedcceabdcdbdeeacdecedaeededddbdeccaedcddbcdabbddcadceceeabbcccbdccabbcecacdecbbdebddbccdebdcbbcdbedecdadcebcdeebcbdaaebdbdabceabecaaadecebcbbccdbadebdcdcdcdddeeaacdeacedbcebcbabbbdaccddadbdcedbeeceaaabeedbdeacddaaeaeeddaebdcabdcccbbabdbbddacdceeadaadbdccddabecedbbbecccaaebabdadebdeabceccbcaeababcadcebeaaaacbcdaacbddeeeacbcdbacedbcdedcdecbbadbdaeeeddadaededebdabcabcbedbcadbbdaacdcdecaedcccccdbadddbecabbbbedbdadddeaddeddddecdbcebcbbbccaedbbdebeecddbbcaaadcabcaccadcbbcdaebcbbceccabbaaeccdcedbebccacdcecceacadceebdbccebebebbcbeeadddbddccaddeeeecdbeedeeceddaaddcaecaabaaecdabbbbbeadbccdaaebcaeebaaccaacbcbadcdadccbdaddeacdcdabcdcdcbecbaaeceaecddccecabbdadbecaedaecaeeadbceecaddadbececbeeabedcedaebaeaecebdababbaedeacedbbababcaceccabdadeaaaebecbacdabccddeabbdbdbebbacbdbcacaaecbbcaccbbcebcdbcedcabbdddeccaaaedbddacbcbaecdabeabedaeacebabcacdbeecaeeadaabeaccbccabbcdaeebbbbdbbebadacabbceacedaddbbabbdcedbaccccecebebcccdbbecdeeecadbedaedecdbeededbeedbbcebdcbbecbaeecabbabccdeebcdeecadacbaaddbaccbddabccabecbbbcbebebbcdcbabedcaeabcacbceddaeaedddbdaababbbbaecdcedddadbbaaeccbbdbeedceabeaedbabaceccaaedddbeaadcbdadebdadbcecbecdccbcaaddedbeeadbecaacdcdbeedaccaaceccbbdeceabbebdecddacabcedbcddccbbcdadbebebebcaacbeceebaecdbbedeebaaabdecbddcadbcdaddcdaedcdbcedadcbacebbebddbbdecdaedacaedccbdadbaccebbeddeeebabacaaaddaacbedabcedaaadeaddcbbeeecdbcedbecacabcccbddbddedaeabdbcbaededaccccacbccaaddecbbbeaaaeebadeaabcbaedacbbabdbeedaabcacdbaaaacbdeeebadebbeececdabaceccabebaabbaeedcbdcebbddbeaeeccbacbcaaadbacaacbbdadebabaeedebaececccdccdecbbcaddabececaecbeceedbbbcabebbaddbedeecceeabeecdbcbcababbdceccdadddcabecdecdbbeebabcedcceeaebdddcecbabcebdcecaeecabcdcbeadceeeedccddbaedceeabedbbeddcdddcbedbeadaedaaedeeeaeccccdcbbeaecaadccaeddecacdcddedaabbbbacceedddbdbeccdacbeeecaaeeaadbdcedeacabdeddeecbdacbccdaeaadbaebeacebeaaecbbdcecdbcebbbaabccccdddebcddcabbbcaaabacacaadebacbbabababeadceeddacedcabacacaabedbdedacddeaabeaddceebabaaaaeddacaceccddecaddcddbeddacdcaaebabbcedaddeddeeebebcdbdbdaacddceeeebcceebbadddcdcececaceebabddaaedeadcecaadbcdecedaacbabadabdaadaddcddccdaeabadeaaeddbaeaeacecbaedaaadbcdcdccaaedeaeaaabaebccdeaeadebadeceaececdeedcecebdbdeecabbbdaedccbddecbbbdebaabdebbcceadecbebdcbdbbecdebcddddbcdbdaebbaabebcaeeedcaaadaeeedecddbeececbcabdaedceccceacbebdcaccbcbddddbdeecdbdbaebaabcdcaaacaaddbbacdccdbaddabdcdcabeddeecdbeebcaabdcbdacddbbccbdddcebbacdabaadeeceddddcbddbabbeeecaabeebcbabecacbcbcdadbeccadceeedecbbeedbebeaacdbacadabdbaeecbdcccececdecbcbacdbcaabebbbabccebabddbacdebdbeadbbbcaacccedcbbbcacbbcdabdabbabdceacbbbaccedbeeccccddebbaaaaaaecbacddadebbacaceeabbdeedcbdadacadddeadaabdaaeaadaccbdebedabbcbecbdcbdbdcdbebbabdbeaebeecadeebcadeaddcbabeadaceceaacadabeadbcabacabcecaeeccdeeedcbeaaaebbebbeecbdaeeceadbdcdbbeebacadcdabadebdedbbecabdedabeceeadbbbadccdbcacbdceebdeaeadcbcecaddbbdedaaacedcecceddbeaeebcadbdebdaacdacbbaecebebdacdeebcbadecddcaddeeeadbccbeeacbedacaaadeeaccbcabbaedacddcbbebbccaeebdbceedbaeacdedddcdebceecadaeaadccaadedbcbecadaeadebeeaccccaadadebecaadddbaedaaebecbebbcceabeaabeebeecaedaabaecacbcebbbccccbbcebcbbeedecbeabddcecabbcebbabadeddccbadcbbceebdbcebdabbddccedaebbbbaddedaebaaeeaccadacceceebbcdeddbededeaacdbeebceeeeeadbbaebdbbecddddecdbdbeabaedaddaebdeaaadcdcbacebbbcdaaaedabbececbbdcdcebaebaeeddddbdabbdeecbadbcadeabaedacebbdcecbbbdaeaccbbbaababbbeddcdedbeaedcdddaaaaababeeddaebdacebdcaeaddbecccdacedcaaedcaabaddecdcbebcbebdebebedacdbaeccbdaccaecdcaebeeddaeebaebdecaabaaecdaabdcdccdcbbdcaebddddebcbebdeacbeebddaddcccdecbeaddaeebcacadeaceedececacddcbdaeaaeeabbceddbcbeadbbaaeecbedbabbbacebaeeabeaccaaaeedcdebcacededbbededdcbeacccbdceedbdeaedacdbbadbedbbccceaddebeeadacbadcaecdbcdcddcaabcbccecbcdcddccdceababdbdcbadcbbdbcbcaccababcbeebadbdaebdaccedeceeedcccbdadbddaeccaaacadabcebccddbccbddcbacdcceabacaaeebcbdcaceecbccaebbdcededaaddbdabaecaeaacaccbeaaaabeddacedcadbddedaedcaecdcedabaeaaeacebbebeaadaaeeadadcbbcaacbaacdeacccacbcbeadeaacdecebcebbcddaeacddeaeacbbebdaeccdecdaeebbbeaadcdaabeceaebecbaabecdbedcbeaceedeeaabcebddbedcbbebabdeaadceebccdadcbaedabcaeecdbdbcdbdabedddbdecdebcaacedceecdcecdccaaccbbcbabdaaddccbbaccccaeaedbceddbaebdcbbbbebaedcabbbebcdcdaadbccddbeabecbbcaabaadadeedaecddccbbecaedecedeadbbedabbacdcceabdacbbcaacbbbebebbaeaaeecebedcebbacbddcbaaebaccccabcdebcabddaddaabbbcbdbaaddaaeeecbcaebdeabaedbedeeabeeddaedaccbbbcdcdedaeeacaabeeebeeddacaecebdcbbbeeeeccaacdedcadaadedcacebdaaddabbbcdabdedddbaaabeabedeadaebccbeaacebeabdceebebadabcdebcbbebaceaedeacdcbaedebacbecbdebcaaacaddcdbadddccceeadaacbcaaeaebbadabedbaaadbdbecccdeeddbcbecacdcddebeceabcabeccdbececbcadaedcbbbeeabccadaaaddcbecdedcbddebbedccdbcaaaaecdedbcdedaddbabbaecbccaaaebdaddaceddbadacdecbabadbbecbedbaeaedeecdadbacebdbddebcabccabcaaaecbaddbeeeaeabaccbcdbececcbbaeebeeaebadcaceecaeaccaedabecbebcbacdbccdcdcbbdddccbcccaecaeaedeecabeeacbbeacecabcaebeecdececccbecadeacaabddcaedcacacdeedadeeebabbaebbaabaaadbacdecbecaddeaaebbaaadcdaecceeaadbcabbbbeccacaedecacbabebbedeceebdbbddcaaaadabcdbcccbbbdbdcbebdddcdcedceccbddacceaaabceedddbcbeeeeeebaadebdebcdeeccebbebbeaaaddcededcbabdcedebaaeaebddacbedbaacddeadcdbaababccbbaeaedadcbcadbeedacaddebedcbebdaceddddbdbbdeaccceadbbaadcddeaaeecceaaeedcbdeedeaedbbbdeabcccedddaacddcededcbdddbdedcbacdbadacbaaebdeabdaabbebabaabcaaebdcdedaabededbebaeeeeeedebcdebbbcabccbccedcaadeacdabbdaeceeaedebcacaaeeaaecbaedcdeabbcbabeebaccbdadbcceaaadcadecdbcadcdaabedbbdcadceebcacaebdcadbbaeddcbcdadeddcabedbccdeaccdeaedbbdaaceababdccebadcbeebeaaccdcbdddbdddbdadcbdbcbdaecccadcaacbdacacbbdaacaddcdbeabacacdadeaaaeabacbdceceeeeeebccdbaaeaeabcccdeeeecbeebcbacdbeeacdcbdbeaebebbcebebceeacededbaebddcadceabcdddccbdedceadaaaeeadbdbecadddebdeaabacdedeabacddccddbddbaabbdbabebeaabeadbbadadeedacaaccccacbdbddccbeeccebdebadeadaeababbdabdedceebcddaecceaceceeceabededccbccadbeebaadceebbbebdcebbaedbecdbdeabbbbcebcaeabedeccddeebbedbacadccaccacdcaecebaaadecccacbececceaaeecadbdadceeacbaebbdcadeadadbaacccbcabacaedabedccebabceedebeecadccdbbbedebdcaccababccbaddaddbddcecbbcdbbdeaaabebbecaeebdaeeebcedccecbddaeadccdbccdaaeeceaebeceabbccacedbadbcecceedebdddbcbdeeadcdabdededacedebcbbddcabeaaedcedddcbbecacedeacbbdccdcaaedcaaadbaecaeaccebebacdcedcbbeaccaeeebdbdcaeeeceecacdabbdbaabadcdcdaddbcbdbcedebedebaecceebeadddcdeaeecacbeebeabecebcbcdcdddccaeacecebeceeddaecdceacdadbbebaddedeacacdceababcbedddadbacaacbccbdcebcceacadaebcabaebbaddebbbeacaaecedbaeebbeabdbeeebbcadaaedbacdbdbbecebabcbedabdccddeaaebceadbecbddadedaeeddedaecddaaaaceecdecdcdcdbbcaebaceaceeecbdbdabcbcdcdadebedaeaadbbabaaacadaaaedccadaabdeeeadbdeadaacaeabeaaaadbbddcdaaedabeebebcaccceadcbdeebbcddeaacabaedeadcabccebeeddcbdeddaaaabbddcebeabeeeabeebcadccabedddbbcacabaeaaebbbcecdbceddbdabacebcacbedaeedeeddbeeaecceaabaabddcadcedadedbcdbbcdaedcdddaaaecccdaceddbdccccacedabbceecdbbebbeacdeddbdbbbcddbadaceabebaecbeaaccdbeadaaecaabaabdadecadecebaeeebaaaeaaeddccbabbdbbaabdceecceacccaeeebcdacacddceceeadbcaaaeaaeceacdeacaddaabcdeeedbccabaaebcceacaedaeabeabcedeecaadbcbdeabdeecceabebaccaecdaacedaaeeebddcccddeebedaddacbddedcceacedbbadcdaabadeaaceeddebaebabaedcaacedddcedeaedcaccdcbbbbbeecbecaddedabdbdaeaddacbacaaddeecccacaabddcadccdeccecaaaebdecbbbbbdcaabbbbbbeaeacdeaababcccbdebcccdeeadcadcedcaeebbbcabecaddbcaaedecaaccecadcecdceccdcbcaecadbecdaeeeeaebaddabbdccbcccacadaadcbaeabbcecebdebbacebabccecceddbbadccbeaccabaccedbbbacaccedaaeadcadabdbdcdbbdadeeeddebaaaccadbeeddeabdaedeadcaaccebdedacdabdaaacedbbedcccebadccedcbaabaeecdaaccbcbcbbaccbaededccbcdaaecbcebbadadcddbcdaabdbaecedabaddbdaeddcaebbcbcddeeedbdbeabddbaaeaabddbccadedcacaeabdaddccccbebdcbdbaabddbdedcacebbcddaaecaccaadbbdeebdcedcbeeeddcadaeaecceeebdbecabceeedddcebdaadccaaedcbbbcedadcccdaddbabcbbbdeeebceacadbcbebbabcdadbecddbcebaeaabebbbdecddaaabbbabeabaeecddaedebddcedacdddadccacacddccdbabbcdbecddaeaaaacdbbbaddcdacdcccceeaaaaedbeacaadaeebabcccbaeecbbedcababbadccececacbdecddccacabacdededbedabacbdbaeaaedeebadcbaccabddaeeaadacacbcedacceadbcecacddadbdeebaedbbdcbbbdbeacacaacebbecebadcceacadcedcdaadcdadecacbbcaadbbeeecccddebedaedcceedbaaaccdbededdacbabeeacbbeccbdabbbbeebcecaceeecaecdceadbcaeedebbdeabebaeedcdcdeedabaedddedddeadbdecccddbbddebecdbdeaeebeabcbecdccdebdcaaadabdbaecbcddabcadcdeceabaddaabdceadacdcaddcebdecddebccdacbddecdacaeedeccbabbcdbbbcecdcabebaabccccbbecdeadedaeccbdeeeaadcdeaeeeeabcddecbebaeceaedeebccbdcbaabdadceededcaaeeeaeaaaccecdedadbbecbdbdccddaccacebaacbdedddecbaebebbbdebdcaecacacedddeebcddccdaadabaabcaabceaedbdbbacacacedeaeadccdedbdacaaaebbacaccdddeecabbcecbdbdcedecdddccdabecdaaaceedccaaceaadbdcbedeeaedbceecaebeebeaeeeeaaeccaadedeadedbddeaeadaecaaceedceaaeedabeeadceedddacaeebbedeaabacaebdbcacabaadeaaadccbbcaebaedbbceabadadddeadeebbbbadccbbedebbddeeacddabdcbddacbddbcececbabbbbbeccdeaecaeccebdecbbbedbadbcaaacbedbbdedcedabdddabbbaaecdedeccdbecaaadcccbadbeabeedbbdddeaaeadaeddddbcadcdecbeecbcdeebcccaeacdbbdebbedbdaaddacccaadceaeaddaeebabcdadcbabddeccaddedbedbecccebdddadcaeeddcacbdeaeceabbecdcdbbecbccbdcdbdcdadbbdbdaceaabdedbdddebaebaeeceeaccbcabcecbbacbadcddaebbbbecccaedecdddbaeeccbeaedbbcdebacaaaabecdeecaaeeabcecbebecaceebecddcdccdbdabdedddeabadbdcaaabbabcbddbdbbcedbdbceeedbbbcedacdebedabeeaebccbaaddedadeedbddacecadcddeeeadadbadceaeecaddcaaaecbcbcddabdbbccddddacbdbceaeddcdbaadebcaadbececcbbbcdddbbcbcdebaddddddbabdebbcdedccacecdbaaebbbbbabccdcaedaadceeaeedbddddcbbceaabaebddcabcdbbadecbeaebbeeadcdddcecadcdbebdabbdbadceeebbeebbddcdaeadedadcbaaacadbbdedbbeeadbeceedebadcabbceecceeeccacebedccaadadebbdbddceaedebdceaeddadeaeecadecdaebadaddeeccddbcdcbdbedbadbceaeeceebcedabeddccdbabadddadaaadcadebeacdbaedcceddebdbaceddcccdacdddeaaeebaecceabbddcecdbddaadaedccbdcedaeeccaabadeaddcdeeacddcddeebecdeceadeacccdadbdeccdebecdddbbeaceeaabbcedcabceaaceedacdedbeaddcecbcacbbabadccaecaabeadcedddbeeccbcedaacdaebeebbcdbeaceeaebdcaacddecbbccbdbddcdacacbccdaaabebdbbaeceecdaaeadadbedcbdcaedcbababeaeadcacabbcebeebbacededacaebdbbadadddceeabbceaacceaeccebddabcabecdcbbceaedadabaaedddebabadcdbcbeeabbebcecebabeecedbbabeebcceeabebbddaaeadedaebddadcbaccbbaceaecdbceaacccbaaecbbdbeeceedadbddaacbdccacbecbacabccbccbaeeadbccbbbaaeaddacabaaacadeacadacadbacadbdadcaccddbdbeedaadbaececccceddebdbbebbdabdabcdcadddeadaabbbdccbebecdecccdbeceacadbeeaaeebdaacdcbbeaedddcacbabcaddcbebcbacabeeecebccabaebedbbacacaaebebddbedaddacaccbcaeceabbadcbeeabedebdebbaabcccebdedcaeeebbbbbdebcbacdddcaceadcedbdeaecadcbaaddcdcdeeeaaeaddcabbbdedadebacdbcbdadedcecadbeecbcddecdaaedcbbbabebbebdbadeadcdcbdccedbaeecaeccbbdabeaccbdbdccaddebeebabeecaeacbbaeccbddbbbcdaceaaaedccabdedddbaebcadaaaceceeaceadcaacabeacdcbacebdaabcdecddbedceadbcbccceaaedcaabeccdadadeabcbadacebcbbaebdadbbeceebdbaedeaebbdcccaedadbecacabeaabbddbaedcedabbbedabaaeebbbbebbdababaabaddcbdceaebaaddcedceebcbccebaabdadeccdcbaeddebcbaeceebcdcdbcaacaddddadcdbaacddbcaddbaaeebaddabdcecaabbbdeeeebbbecbbcbccbdeacbebeaecdaeedaebcdebbdaddebadacabbccccebacedbdeaceaedacecbaabbcbacacabbcbeaaecdaaecdbabbbddcabeadbedbdcaecbbcbecbcdabcabcebaacbbceaebdeaedebdabbadaebddebcebedbbebdeebcebbacecbcbcbadaadeccecbeccebeaedbbcbcbdcdbacdcabbbdbcbbbaeedbdabadceeeaccbecaadcaeaccbebcbceeebdbddcaaaebbceccaaebabdeeaccdcbbeedebddebdeeddaedadddbccbcabddbaddabdeaddebeeccddeedadcaecdabdabcdcdeececacabeabbdbabbdbcacbaabcaaedceacdccdedeeaadabedbdebbccddbededdeeeccaecddbbdccbecbbadcdbbdecdacdcaeaacaacdaddcacccadabbdbdbcbacabbcbcccdbcbcebcecddacdecedaebbaceceeceaecbedecacadaebacbdabbeaddcebeeaecdcaebecdbdbbbdedcadccabeecabdabececbddbcbeccaecddeebdbcacbbaddabbacccbdbaeabceeeddaabbcecdbdeaecdddeddbabbbddededdaccdcdeedbbccddaabebccdbcdcbdccddccbddcddeddcbeedbedbdbccedcbbbeedadbddbebdbabaabcadcebdbebcacbaeebbacadbcaddaceedabbdaabaeeedddbcbdcacaededccccbdaedaeabbdaecaeccccbcaceacabdbacbcaaaaccdecbbeeaecebdaebcabbbcebdbabdcabaeddaacdedaedeaddeddbbeaabbedebdddbcaeaacbbadbcddcbdeccbdedbdddcbedebaebadbbdeedbabeeeebaacbabdcddbecedbecdccdcebbeacbdcbdabbcbcaeddabdecdaddacceddbcdedebdcebbbeddccdcdbebccdeddaeecbcbbabdeacccbeabecabbeeecbebbbcbdacbecaeababbdbdcbcabaeeebabacadbeaecabdedadbdbcdeaccaedddbdcdcabcbbbbadbeadcebbbbbcabaaeccdeedabdbeebaeeceaaceaedaabddaeaabdbedcbbdeaabdbdbacecceadccbedbcbbdddcaaedaccabdabacdacbbdadcadcaebaecbeaccbdcaddcacccbdacaabaacddadacebabaeacdbdeacbbeacedbabdcbecbdceceeeaeaabdcbadabbddcddcdeebedaeaabbecdbddaadbceeeecbbbabbedeeebbacdabbaaadcbeddeacaadedbdbcdeaaddedecdbeddeaaeaccaaecbdecdddecbcadaedecebcaccbacdcedeaadbbddeebddeadebbaebdabeeddceaadebbeaaacbecdeabddabbbedddcedbacddaabeedaacededaaddeedcbedbdbbecbbbaedccedabebacbaabaebcaceccdbdaaaadbccecdebbeacabdddedcdadadccceeacdcdabadecdbccbabaaaadbcceacbaeddceedcdcedbccaccacbbcbdcdcdedaabacaceaaadbcbeddbeabbeeccbceceecccabbdcaaceeeaeecacbbeaaaceaedecdecdeedbbbcbdceeccbebceabeadbaacbdccdcebdabdbdbedaaaaddbabecbdddeaebbbeeebadcdccdecbceeddceecdcccbeeaeeacadcecbadbaeaedaaacbadeeacdabcbacbadacdadbbbeeeaacebaaaaaddebcaaceddcecbddceadcdcdadbaaecddebddabacceceedccddcdbceeadadcbbecccacebdebeceebebdeeebadcedecadeebbaaddcddbddeeadbaecaaacbdadddeebbbdebaceaeacacdceeaccdecbbecbacedbcaeadeeadeabbaaadcabeebcebaceabaeeaaedddabeccceedaadaadcdedeeddcabdadbeacdcdcbeedeacdaebaabddbcebaddcdeaadcaaedaadedabdbeaddeecdacbebabadaeeeddacaabbbceddecaeaeaaaeddadcdbecbabeaaebddacdaabeedbceebcdccecdcbabbbcabddccabcdceccaecdeccbeeeaecaeaadbbcecdecaedbbccbbbbbabaecccbccbaccdaedccbacabeaeeaeecdcbaaaddbbcbaaeacbecabdddccddddbabaecbbeaacdedabdcbacaaeeabbbbbcbcebdaebdbcabdceaeaceccbaedddadaaaacdcabeccdacbbdeecddecaadecbaedbbbdbcecbcadcdeeceacccbccbbccbecbcbdcdcdabadbebcbdcecabbeaeccacebacedadbadeeeddeaadadababcbcabcdceceaddbdeccbcbeabacaebbcdccbcbebeaecccdedbcceeeeaedebaebcacdedcdaaabaedeaebacbddbceeadeeaaeaaccecacceaaadacccbcbeaaceaedebeedcacbeabcdcccbcebdceaeadaebeeabceddbcccceaeddccccbbdaecdbadaaaeeaeebdecaaacbabbcedbdbacacebcecbbcaeccbeaabaedceeecdccecececceadacddddbcdeacbeddbdebeccbedcabceedbedbeeadaeddeecaebabecbddecbedabdaabbacbceabadaedccaabdbcaacdecbeadcbeeddbbeecaeaceabbedbedcdbebdaebaeacbbcbaacddeaeedbadedbeebeadeeaedbaccaedabcbbeabbcacadeaaebbabcbdcbbaccdeebabdeabbdcbeacbaeddaedaeacdcdeadcbacbcdbbdddececeddabdcdaeccbcbabaeebdbaeecdaebaceeccebebaeeadbbabebddebeaeeadeaebaebedaccbadbcbcacaaabcbeccabbebadceccdadcbbedbccbedcadeeeadebcddccddabbcabaaadebbbddbacceddcbdbcedebcaeccaadddeebebabaadccdabcdacdccbedeeabecdddbbcceecedbcddddbbdbccdcbdccdeacecaaeacdaeecdacdacaeecaeacabbdbaacabeccecbccabcbaccdcdbaebdacedbecaccdedceaedecbeeecbecddeebddebcacdaadaaaceeddaadcbacbceeecacbcdbebbedcdddedbaebeeebabadeccdccaacccaccdeadeaeccbbaabeeadcecdadcbdabcbbcdadecedaadeeebebaccaeadbcaaabdbedbddecbeeaddccdadcdbbabeabbeaacbddeeedeaceacedeeddbdeaccdbeadbdaeabadaeeeecdadeedeabedeecbdceadaddedeccaeacedcaaddabecdecccdccecbcdaecaedbaddabeaceebbacaebabbcbecaceddedbdecdaebecebddeecceeeebeccbceabedbdaacbdbaabbcbdeddcaeedbeabebbebbeceabbbbcbddeaeaecbbbcdcbccdbddacbcdeccbdcaeecdcecaebeaabcedacdccebcbceeeaccbdbbeeeaaaaeccdbbecabbecedeeacdecdeaaedccecaeccbeecbbaeceddebebebdcbceddcdaeacecacbbeeaacdacadebbbcdaecbcabaacaaaeeeaaddcaccebebeeebbecbcbccaabdccaeebedeccddbeeaeceedacacaeedeedddedeeddeaecaabbcdbadbcacabdcaddaecacaeaadeadeebcaabdbacbaecebaeaeeeacedadeabebdadaebbbadeedaeccecacaddcadebceadaabadbbcedbbcadccbaeaebcdcaddbddacecdddceababbcddbaedadbbaacabdcdbadeededbeceaccdacabcdbcdbdcaebeaaeadecaaebedebbabdaebeedccbcaadbeaeeaedbcbbdbdbcabadceaabadedcaaccecdbbcdcdbbaddbbbbbaaecacebedcaebcbcaadbdcbaccddabdcbcbdccceeeeaceaeaaabcecdbdbeaeecdcabaeaeacedadbdcbdcacadddadbdadeedcbcaddbdaacaeececdbbdeeabebadaaddbcccbeadccccdbddceaeebaadcccbbaaeeededbcbdedecbbedbacdbbabbdbcdbbecacacdddbddbcbeacceebcbcbadcdbbcedaabbabaabeceddcacaeeaaabebaedecaacabaaeaeedebbbcbddbaaebabadaccbdbaeabedbdbcceecdaeceaebeebeedbbdababbecbbeeebcaaeadabbbabcaabbceacabbcbaccbddaeeeddacebaddcbdedaaedbecbebdaacabbdceacbcceccadddaadebaebabecdacedcdedebdeaaddedbadccecaceadcdcadbdbdedaaedccddeadcecedbaddddbccacbdcabdceebccdebcecddaaebcdcaedbcaebbcdcdcaeeeaacddbebcadcaabcdeeacbabdecaaebaccadadebaadcbecbeaedcccdebcadcdeacbcacddbbddedaceddbddcceaeacaecdaaeaaaedecccaaaddddabcebdcbebcdbaccaeabeccccdccedeedeeccdebceabacddaddeddcccecbcddceaabcddeacdcedacacdcecaeadabcbabaaedbebeeedecbcbdbdaddececeadabdbedaaececbcbcbceebbeeecbedbeadcdddbdeaccaceaedcecdbaeaedaeabbddaebedebdaeaeddbbbbcacdcbdddcaedbaeaacebaebeeddddbeadddceccaaadcddebddcabaebdcecbecebbabbbeccbbcdaababedddbbddddaadaabcccecaeeccbaeccacdbaaceabdbebaaedacbebebaeaaddabdaadaacbaeaeaacccdebbcedbbccddadabbaccbcadaeddccbcbdabddcccedeedeacbbbeceaaddcbbdbcceeacceecdccebebaaaedcbceabbbeaeddddbedcadcaaeaeeaeabbbbcadeeaeedaecdebaadcbbecdecaebbeaebdccbccdeacceddaaeccbeedbeabebbcddbcdcddeaabcaedbbdaeacedebeeaadbaedbdbcedccbcbaddaeebedbdabedaacdbbccbcddaeaeabeacedadabaedaddcbcedebbbeaebdccaddcdcdaeeadceacaadccacedcaaadccdbcababadddbecacadbabbbbaedebcbcbbabecabbaaccdecadeeabdaaecaeacaaeccadacbbabcccbedacccaeaeeceeaeabdeccbebdbbacecadadeeaabdabdebdbdbeadceceaabaddcedeeedcdbbaddecdcadeaabdcbaccbcaaeccabdabebdbcaabbccebdddcaabcecaeeedacaadadddcaadcadaebdeaedddcccdedcdecaacecddbbdccdadbbccedadeddbdaaadeebdcacbdeedddecabdeeaedbbabadcaccabaccbbaeaaebdbdcecadcbdbdccddbaabddbbcccdbbddebccbdbdeabcbdacdadbacdeccceeecaadabacbccbdeeaabaabbdbdbdeabcaeaedebadbeaeaaabbadcdaecaaeddcedcebeddaaaabccaababadcdbdbededaddebadaccccecdcbcbceeaccebedbbadaaccddbbcecccebbcdcbecedebdbdcebaaaacbedddcdebecdabaaccccbedccdebbecedcacbaabedccbecdecbdbcbaededecbecaaddaaaadbdacaaeebabecdbccacbaeebaecdacbcdddbcdcdccdadeeadabedcddcebdebbadacdabdcdccbebbaeaeedeababbdbadccdabeacebdedceeedbbbadabbdeabeedccaeddaaceececbaedbcdededeaeaccbbebeeebcbeabaddccaecddcceaeebdebdebbeaeacbaecaceeecbabbdbbcdbcbbaecdcdacbcdbcdaacabddbdcdccedbebbeeeebcbbdeeddccdddeeeacccaebdabbaeacadbcbaaeabcdbebdecbacdebdcbacabedbcdaaaebdeaedeeccdaeedebcbdaabedbdbdacacdadeddeaadcddeaccadcdaebcdcdcbbabbcbceaaeeebdecdbbcaccddebdeacecddddeaddedddbbddaaabdbbbeddabdadeacbdcddaabdbbbaaaedeacecdeceaecdddbdecdeeabbbcadddeebbcdedebddcaddeedbbbbacbaeaabeebeabaaeadbbecceeddbbbdecdadacaebaaaeaaeccdeceecccdcdaabeebdbbcbcebacebeddadccdecdeeacabaecaacebedbbbdbbeceabeabaeaabeccaadacbaccebdacaceabdbcbedabcbaeecaddeebecddcabdbdddbddacdaabeeedccabcdabcdeccccecbaddbebcccbcbcceecbcaabbeaaabaeeceebcedccadaeedccaaabbcbcaebdcbcbacaeaebdeadbcdadceedadecacdbeedadaadebbcdbbdaecacbbabbdbbedabdebbcbacbabdbcddecdaacacbecaedabababbedceeeabbcbeaceecdecbaecbebdbecceeebdcacdeebcedecbccdaeabceeebeaabcecddacdaaeceddadeabdbeebdbabeccabedcbaeacbccdaeabacedbecacdceedcdcaaccdebbabdecceacbebdbbeadadbebeddbdbaeaecaaddceadcddabdccacaeacbaeccbbdddbeacadddecdbeeecaabbccbddceceaceeccccbdbacaaaeecceacdecadebeebaeabacdcadadacaedcedebdcaadccaaaacceedbbcaedbdadbbdeaedbbbbacdcdaddbeeaedbcdaaecacdeceaceebbdbbcdcaebacacdbceaddabdaeeeabbaaddcecacbebaaacacdbbadbaababecdcadcbcaaabdeecabecedcaeccbacbaadcdcbabaaaacdadaaaccebbcbedaceecdbedcaebdbddeabebedcebbcbcbdadeebceaaaeeebddbaecadecdcedaaaadcbddcaaacdbbebeceeaadcbceecacebebecdacaaadecaeacbbbceebdecbaeecdcbbdccbaacdabccebbccadccbbeedaacadcebbdecdccbeebacdddbebdcdcebdccaedbebddacdbbcbdccbebeddbbebbdbadbcebeecdbecbdeeccacccbaddbeaebaaabceaebabadecdceacdebdccdccaaecdccbdbeebecbabaadeebbbbeccddceaacdaacebddcbdacedeeecdabdacebaaebcccccdebeaceeedbbcebcaeeebaeebdbedeaedbbeacdaeaadccbdbaccceaedebdaaedccbcbeebcccaabdedcabeddcbcbebdecacbccdeacdedcededebaaedbcddebabbeebeabcbaabaeabcaedaeddbabeeeddaddedccbededcbbbaaabbabebcaccdadabcdcdaebbaaebebdaddbbeaebbaddcbdcbaadbbcedcaebcddeddacdbdccacdacecdcaadcbcaaabceccbcecdacdaaacbbccbccaeecdbbecccadccccbbccdeaeabcdaccddadbdaacabdeebbbceddceeedcaebdebeadebacdaaeeccddadbedabcaaddedcdeccdbbebaebcdeaadeaabddeddabdecbbbcbdcdcbecbcbebebcedebebdecebacbeebecebcedecdbbaaadbbaaebadccdaeaddaaaeadaceadebdaadcaccccedbccdebdabebceaecebcabaeeadebcddaebbeadacadbeddcdabadbdedacbbadedaacbedabdbcdbcdccdcbaeaebddaacdbecdddcbebaaceeeedbbdeddbdacabaeebcdeedbdcbbcdcdebadcaeadeaddcebcbebdccddceabbbceedbabdaadeedcbeeaedddcbeacbcbcbedccddabeebdabddecbddbccaccbbcdebeebabdbeccdaaebdeaaebaaedbcececcbaabdeccddbbcadaecebadcdbcbecdebedacccbcbdabdabdbbaabeccddedadbbceabddedeaeceaedeaadbcacceecdaaaeceaddcdbccaacebacbabeaddeadcddddcdbbdaddbbaaeeedeaadabcbcdcddaddabaeaebacccbecbaebadedcbeaeebbceaceaabeddbbacadabcdcaabceceaaacbecacbebadaaedaaeacbcacdedbcedcddeddcddbdcedeaadcdabebdcaaceacaecdbebebeaedaeeecccceaebdaddcbcbdbaecebdcdcabaddbebadbadeeeedeebedaabebdbbdbbedbcddbbbdacebcbabadaabececcdbddcbadcaabbbbbcaecebddbdbdcceaabdabaaadeecacebbaaeedeacbbeaccbddbeddcbbaeceaadcabceaeacedcbbbececcdbedddcccdcdacebbecbdceaabcdbaadadcddaddadcebcaaeadccecbbdcdebedadcdadecdecbccdaadeccaacedecceaacabeeabcebcdbcccddebeabcbedabdebceccedecdbcdeaceeeabbedcdddabdaaaaeedbaaeaaedbaadddcbbeebbebdceacbcaabbcbcebcabaecebaacaebcdbdcbeebeeebdbddccbddeaedeacabbcaaaaaccabbdbbbaeddacbeccadeeceeeebbeaaaeeecdddcdbecbaadeaeddeaedcecacbedbeceddaeaebabbbeeadaedededaabceadacbbacdeecaceebeaaeeeeabdbebcdcbedbacbddadbeddaeedacebcbeddcebbaebecaebdacccaccbbbeceebbdccbbcbcecacdcbdebaeecdceddaddcbadcaadceadeddeacdadadecedebeadcaaecaeaebeeeadbaababcdcdcaebdaaeecbdecbaaecbebaebeaadeceeebdeadbeeaacdeacddeedbeadccaeccaebcbbebadecdbddacabcedcbdcdcacbebdaceedadeedccbabacbababdbebebeaacddddbaeabaabbdceabdbbdbcccedeaaabdedabbcdeeedccebacebacbaabaacbeadaadaadbaacbbcdaeebdaabcacabbecbdaeebdadecdededceacaeceacccbeddbcbdaebbbcbadeddebdbeccddaadddecccabadaabbcadeadbcaaaccecebdbeeabadabbacdbbaabaacbeeceedbcadceeddceddbececaebcaddebebcaecdebbcdccaecadabcbdabcbececaeeeecbbbdccbbedcdabddebcbabbccdcdcabadebbaacaacdeeeaadecabbedeebeadecabdaaabadddaaedddeadedcddebcaddcedbbcdecbaecacebeecbadeeddbedceeeeedbcadcbcdcdcabbbdaeecbcabdeeabdeeadbdeacccdbdccbdeebaececbbcbacbebedeaacbeceaabddbedddedbaadabeabaabaaaaeceedaeaddbadbdbbcbcbaaeaeeccaaabeeabaabdddddbcaedceebdeacedbcddeddcaaddcceabecdedbecbadbcdacddbeeccadabaacdabaaadabdbbcdeebddebbacecbaedebbcaaedadecebddcdbebcbbaddadebbbaedbcdbabbdacadddedaebcddccbeaaccbdaeeddaadedceabddceecbdaeaeacdceeeecbebaeceaaaecbeccccdeeddcaaaaececbdeddcecdeeaaeedcadcaadcdabbedbeaabcbcbdbeeabeeddbccececcbedeabcedcbeeadccbdcbcacbabdadeccaaceeccbceceddededcdeaaebeecbabdcbeaeccecdacedbccaecbaccaccebecbedcbaabcdaeccbcaebacacbbcdeaebeadcaaeeaedbdebeabbeecbbeabcbeadddbdecceebbabdaadaadacebbaaaebadaabdacdcdacbbaeedaccbccdcdebcaedbccedacdaaacdcaadbaaaecaadacdeaeaeeacabeeeaecdeebdccbaebaceedcdebbbdcbcddacdeabddcebdddeeddccecebbcbeaaaceabddbecbeceaeabdabecdeadbadaadcdbebedabceaabaaddebaeeccadcebcdbadbbbbdbcbabbcacdabdbaaecbcdbdddaecabceaaacbecabdbecdbdeccacddbbaaeabbbdeccbaedebbeadeaaabeddaeccbbcaaeedceeccbbebceabaaebbadabccadebeaaddcedadcedddbacbbecdecdeaeecdcedaddcddcbebcdcedeaededdcaccceeecddaedbbaebbcddeacbbebebddbabebbcdebdbabaecdddcbeeacccbceeecddcadacdedaacaedbaaabcccdbebebdcebbaeecbaadabedbdecaceceadcbbeaaaecceeabbcaceecbcccbbbedcbcbbaecddccedbabadeddddadadcdcbecbacbecbedbcaaceceddccabaeccdbebbbaadebcadadacaebeddcadebcbaadcbbebeeeebabaacdbaedaacacadddbbacedcabedcecbcabeeacdabebcccdcddcecaeadbaaceddbbadeeacaecbbecebcdbdbccbeddedbdecbaaaeccaadbeceeadbdeeecebcdcadebcdeddacbbbcdccdaadccadcbdbedabbcedeecaeaabbddaddcbbabdbbbeedbcbcabbdcdbcdebeaddeaaccdabcadddeadcdeebbaddcebdddcdddaaeadcdeacbccaceabccababdedaabbadecbaaaaaeaeaaabecbaadccdededccebbeacdbedeaeddecdcecacbbcddeddbdbdeebbaadcdcbeadeddaccecedbbaaededbdeecceeacddebdaceaccbbdeaaaadbbaeeaccdceaddadabecbdceeaadabaacebcdeddebadaabbebabcbdbbaccaddbaacceacbaadaecdbbdbacdecdbbbcaedaeeaabdbbcdcecebeddbedddbbebeeddebabccdcdedcaebeddbeaecbbbbbccbecbaadacbddbaacabceedbdbcbccecabaacdcbdeccecdaaeccbcbbbccdbbcaecdeaebecbbbdabddccdebeaecccacdcdabecbedabeacacededcabbcdddaadccddaeceeeccebddeaeaaaadaacaeecaaeeebdbeabbabedcabebcbaaebbddebeedbdcbdadeeeaedbbabceacadacabccbbcbabcdddabcdabbcaaaabcddaddebbdaaccabbdabcbecbebdcaeadebcdcaadcdeaecbaacadcabacbdcabbaeeabcedcbaddbbcabbddddcebccacaeaddbabcbcecebedcdbdaaabbdddeedceeeeaebcadcdabccbbaddebacbedeaeebaaaebbbbeebedaedcdcadabeebdbcddaeccdbbbbadeecabadcbccbccccdbdabaabcebaeacecadbdaadbdeabebdaabdededbdbecaabdedaaadeebccbdbccabeaeadeeeacdccabeebddbcbceeaadedcbdbcaaacbecebbccbbdcedbedcaeedaeedebeecedaaeadcbbcaaaaabdbaeeaadebababeebdbdaaddebddcdbdaeecbaceeadbbbeebaecbdebbbdeababbaceeabeeacdcdebbadcbccdbabdeabbcabcbadddbbecbbaebcdaabecadcdeedcdcdeecdbbdbebadcaabceadacadbccdadabeecedcaecdacaeecddcaebcbcbddcbcebeacaedcbbeacdaceddbeeebdaddebdcaceadaddbbcecebdcdececbdeeacbbabadcaaeddcabcbacaeaeaaceaabadcbacbdaabdbadeccdacebeddeeacdaaabecaeecdeadaeceecbebbdcdcebbcaecbaadcdaceabbdbaacabdacdabacacaaebeaebecdeaaebbcaccdaedaaecdbecebbeeccabceedaeedccdcdcccdcdedbcbbacdabbbeaecbbecadeddbbaecabcaebadeeebcccedccbccadadcbbedbbaeebccbdeebebaaceeedbaeaaaccbcceadbecebbaaddeebedadebccaedaaacbdaeddbecedcecedebeeccbbadedcacdccebeecdeccdccbacaccaabbcdbdbedabbbcbbcaacdbdbbabdeadaccbcebebbccceaaddebdbeececceccdebceaddeeeceaedbdebeacacdccdeddcdaeeeeecbceeebcabeebecceadbdeaddaddaeabdecebceedbeabaadbabcbdeabaadedaddbdbedbbddbebdddaacbecacbddccdccbcdbcdeebdebdbbebeacbceabeaabeccaabacbcdabbebdbdbceaaedadadbaacacccabeceaceaeeddeeebebcdedeaacaeaddbbbdcdaabcccebdecbdbbbbdabdaacdbedcdaceeedbdbcebebbeecbddccebdecccabbdbedbbbddeaecadbbdacadeceddedcaaadebeddacaedeaabdedccdeecbebbbcdededddcbeacbbccdacebaaaabeaedbaaaaaabbbbadcdbbabbbdcdebeacadeeceddaccaebacdaadbdbabbcadcadebcaaeaabeaacccbdccdeedaceccbadeedcdaddbedaceaeedccceadccbedaaaeececbbceadeccbacaecdcacdddaebbabeabeeddccedbbaebcaaaecdaacbacecadbdbbddeecabbebcbbaadebccaaecbcdccacbbaeeeededaddcaaacbaacbdbedbcddcacabaaacbedaeaeeceaaceaadaabdadeaccaebecedeadacabddbdccdeabcdebdccdebcecedcbdcbddddcccededdbbaacadadacebbbcdaedcccaececabbceaebbbcdacddeababaddcaceddccdcbabcbacbccacabaedbdebdcacaebaccabcdceedaccebbcbadbebbcddeebaaddcdccaacbceddeceeacabaddadbbeeacbdabbeebcdedbbdaebcabeebaedaadabecaddecabeecdbebceaedadabcdcddbeaeedebebbcbebabceeacbdbccecdaaaccccbaaaaeeaeeabeaeceaeecbdaccdceaaaaadbddebeacbcbcabeacdcaababebdbbbabedeccbbacabbbbdaaaedddeaededddcccaebedbbdbbcabcebdbceaaeaccdbebcbedebdbeecccabebbebaebcbddebcbeedeeecbcebdaeaeceeebeacbecbdbdbdcceeebebeeecddcebdbcceeebebaeaeeaecedeacaacecbecdeccebcbdadbadeaaadcbbbeedbddcddcacabdadbcceedadddadedcbcbcbaeabbdbdabcbbeabaeaaeeebcbdccccedecaddccabdeaecaadcacdacabcbdbbcbdaebbbbbbaddecabedaecedbacadeedabcebbceccdbeebaaedaeaceebcdaccbbbbdadeaabaceeeeadaddcdcccceeaedcbaeddaddcaabddbaaedeccbbadaadbcdeeeeeabdbcdbbeaccaeebdeddcbaddadcdacddccdecccacacdbbcdaaeedbebedabdbbbedeaadaaeeeabdebaccdcccccabddbccabbbbaeecaeccdedeadceabaccaedccbaededeccbadbdabeacadabacabedebcddaebbacddabdeecebcbcecbddebccddccaadbabcebaeddbcaccdbaedbcadbccbabdaeadcacaddaadaeeaacacbacdcaedddbbabaacdcebebeddaaecdeebbbbbecbcaaaceddaebebaeebddcdbdacbebdbddebecbbcccbbabceddeccbebbbcedbebdbedaeaacbceecaceccdcacaecdcebbcbacccceaaaddbcbdbeeeeaeedadcbcccddeedebebdbedadbddecccabdbeaabdceaabbdedeaaccadeccadedbeacdadadaaddbbaeebaaacddbebdaeccddedbdededaabebdcbccacaaceebecaccecaabedadeeeceecdeacaaedbaecedeabdecedcbaebcecdebaaacaecbbbdcbbedebbaaebdbcdbdbceedeeaebebabeeaeadbbebeaeabeedaedcedddcedaadbdcaddaaaeeeccbadcccadcccedcbbabaadbaceaacaedddeebaaddcbcabaebccceeceedcbabdeaabaddcaddadeaacacbdedbcebecdecbddddebdbabcbcedbdcdbadaacebaecbcbedeabebbcedcdbcaebbdeabbdeedaaaeebedbbdbdeebaccbbebeeeebcebbbbecdecadcabcdddbeeecaaebccbdcccbeebabeadeaabcdbecaacbdadbdeeedaebebeaddcbbadadbedebeaebbddaacbabdedeccaebceeeacaddbcabcddeceacdabaebdabaccdaecdddabebccbebabecebacaeeeebcedaacbcabecbadaecbbdebdabacabddbdaedbcbacccbceddacbbddebeebdebdededbedadbaddddaaddbdcbabbcbdbdeeecdbeaadcacbdabceddcabaacceceecaaaeebdebaaacdbeecbaadadbdcddbecacadbebbbcbdcdaaaaabdccbecacbdbcacaabbbaeaddecbcedabaadcdcadecbeebbaaecdebdccaceabedbbcbcecdbccdeebaecccdcccbacbaceaeceacaaaaecaebcebcedbebbececaadbccdecebcaeaeaebdadaedbaddabecdcbbccecaaeecbacdaaaaabeedaebaaadbdaebbdeecabbedeadbbcccaadbecaaddeaaecaadbeebdaceaeeeeaedecddaeccdaaaeaaacddacadbecdedbcdbbabbaabebdcedeaadebecaabdeddaabdecadeaadddeadceeddaedabeecceeadeadcacaedcaaeddbbacdccedebbadcabebddbaeeaeddbbcdaeccccdcbbbabcdabccbaebdebddbbbabededebdcedeabbebddceecedecdbacceaeaaaabbeebbaabdcbececaabcdbdeaddaeeeeddddbcbdabcaadebddabacbaebdceeddbbeaadcebabbdbaabebcecaeeeeeaaceaecedddcdddbdbabbaabbeadebbeebaabdedadeddabeadceaedbdabdcabaeeddeaaeacbcadeccccebbceaaecdddeaceacbcbbbdeaedecbbdadcbeaecdaadbbabcadbababdcadcdaadeeabbcbdbccccaaaaccbedceaabbdbaeddbdaedbcbdddebbdbabacaadabecaabaaabbbacbabcadaeeddbbbdacbedccedeadabbdebdddabbcddceeaccbbccedaeebbceedccbceccadedbcbbebbecadddeaadbdadbbddeccaadebdddbacecaddacceebbceedcdaedcccbaaebccbbbeaeccebbbcccdeeadeaedddbebedbbeebabbdebedebdabbbecbaadceeecaaccebdcdadbedaacaaaddbdcbbdcedcacaccbaabaaacacddddcadcdaebbeedaddbededeacbbeebddbebbcdabbcadaacdcabdbddabbdceedebdaceaaeaaadceeadadccecdeaccadecaabbdaaadbdcbcccecddbcdedbdacebdbbcdceededabbebaeaadbdcaccaecbabeeedbccecbdabecdeebeeaacbaeedacdaeeebecdaeeacbdddcdecaabdcdcaceaacabacececddddeabadbcabcabbadcddeaeccceeededbeaaebaebcaccdddcbbeaebeacaabaaebbbeeaddecaabbeaabbdbbaaddecdbcabcecabcaabceecbceedbabceeebeecbadbcbeabebcdbaeaeaebaccbbeedceadcabbeeebbedeabeecbdcdabadcbbadbaeaddacedbbaababeaddddddbdcdbdccebdeaeecaadecbedeacaceeecdebdddbaceaeadecaedcabbaadaaeeacbdedaeaebceaabaaacaedccbabdabcabcabebaceadecbdcebbdeaaccaeedcbcbadabeeeabaabbaeaddbbbdaabebbeccedaedeacdcedededbbcacecedebadebbabbbdebcececbadaadacbdaddebaddaadcddcddabdcadbecbccdadcbaaceaeecccdccebbeecbdabadcedbaedebbaabcaeaadecadaeccedeecbacebeecaaeaeeddaaeddebcbcbaedeedcdebaccbeacbcdeceebcdcbaccaccecaeaabbeaccbbaebdaabdcdcdbbbebcaedebbcdeceabebdaadeedabeddabbbecadbbaedcadbaabdaededbbbbaedbaedabaacdedbedabdaacbbbcdeaddaceaeaacacbbbaebcebbcacbdbaadcbecdaacabaacebeeacbbbeeaccceacebbdcaecedaacadeabcebaeeaedeadbeebddaccbebebdeeedcbdedcadeccdaaaeabdcbabcdceebbbbaabdaeecebedddbeaaabbecddaabeabebddcebabbeeeeeaabbdebdedbcacebdbddcdabbbcceaddeeecaababacaaeecacccccbcaadeaaedeeeebdadbeeccebceccceedcbbaebdbcacdcbdedeccdeceacaebccccaabaebebdaaeaddeecdaabeeccbaccdbdacbcdaddabbdeeaceeacebbacebddaeeaaabdecdddaacccbaebeabadcdbeccebeacaebddbedbcbcebdabebeabebccacabaddbacbbaaedbeeadaddcaabdeaeeabcebcaeaebbbeeeddcdacaccbeeccaeabadeceeddcebcadddceebbdeaaeeaabbdaddebedccadeccececdbdccebbecbaacebbcabbeeecbcdbdcadbaebcabbdacceccaaecbbeecaaecaeedebadbabacccbbbccdddbbedbdecdedaeacdacbeacdbddadbbedcbdebaaedcddaedacacbbadbcecaecccdbadebabcabbecacacecaebcddbcaebbbcdaebdccdccabcdebceaaaccdbcbdedddbbdaeeaecabbbdadbcbdeeedecdecbadcebcbadaceacdeaaecedebdacdabddbadccdabbceaccecdeccaaecdebbdeeaedabccdddaaecbcacaeeddeabccbedbcaeceaaeaacdebbdbeebdbbcccaaebaaeaaeccaeaabdbdddaaddaebdbaaacecceccceabbcaceeadadebdcacbbbdebabeddacdeacededcceedabcedccceeeaeceeadaabaeeabccecdeebbbadeecbceecdcbdadabdeccdeecebbeaebadcebbedeaebecbbdbdbbbdbebdbbacdceecbdbadceeccceeebcebaddebdcdadbcedeebccdbcacabdbbccbbdadbbdddcbbbbbddbbbbdbbabecdeeaaebdadbcedbcddecbeadecdbbeedccaedacacadbebdbaaddecbcbbadaaebbadeeadddbcdbecedacbbecdebbecccbddddcbabacbedaeaebccabceecbedbcaacbbdaeeeabbcdceacabaaadceecdbbdabbeaaeccebcecaaeccbedddcdbaecbedaecadcdedcadcadadcabacedaacdeadaedeccdddebdeeecbccdbbabcbdeaddcabaeecedebddeeeacbdcdcedbbaadddeebadebdbedadececdabadbbaceecebeccbbbccdbaeaaeaccaccbdcdeccbdbedaceeeddcaacdcdedcabddbecbeececbacaaedcdeacdababeccadacaaaaeeeaddbceecccacbbbceccaeacdbebbbbdcaeaeabdbbdaececdadbacdedbaaaecaadddbaaccadcaaebdaaaadeeccddcebbeedabaaceaeaccedddacbaeddeebddeeacebdddecccbeedebbbaadccdeebaceebebbcdcceabbbdcbeceeabdababcaedebebeedbcdbcebecaaabdbaacdbdeacacdaeeacdcbdbedeacabdcdbcacddbdaecdcabaeabbbacacdaaaaaebdccebdccacbbcacecccdaaacadccdcdccacaceaeebecadddbbdaeaebddaacaebbaaddcaeeebcccaabdcdbeddeeaaaabcbcabaccaddeeecadbcacbaddcdadacdcbccdbbccceaeeeebedbccabbabdbaecdbdceccddaaaabdecedeaadcbeabeadbeabccddedeaabcbcbcececacdebeabcbecaccbbccbccbeccedccbbeebcdaeebadbdbdbddeaddaddbdcceebcbacecdabdeeddcbaeddbbbcaadbebebcbaeeeebcbeecbdbccbeeeccedeebdcedebdadcaccceeeeceeadbaaccddedaeaecadaeaecdcadabbbebaedeaeccaedebcdabcabadbacacccebeebaaccbeedadabdeedcbbccbabcaeedeacdcebbbcbcecdcdaccdedeabbbcddeddbcceabacdbcaecbcdcddabeaddedddcbeeaedaaaeaadbeeacbdcdaaabdebbbaaaacadddedeebcdeccabbddeebaacecdcdebcadbcadececcccceeebdcdddbaecbeaadbdedccceacbabacdceadbcebbebababbbdebbbecccecdcbeaeaabaccedcabbbeeebbcecdcebedbbecdecababdebaeeeaaedecabacedeebbebcbcdaabbccceeccccbeebbacebbeecebdadaecdbbacddcbcbbcbdedeabacccecccdadddaeaceebacaeacbebcceacecddebaaedbbeddddaabdebaabedbdebacdeaeebaaecbaededaceaeaddaedbadeaaaeadaedaebbeeeaabdaacbccabcaebcdedadacccbabeecbeaddebdddcabbacbdbbabcdceccebecbeaadbbdbcadbdecbabcbaeaaccbcdbeaadbeedcdebdedbedcdbabdbbdebbacdbebebdadaaeaeeacedcbebcddbebabbbcbcacdebbcdadbebaaaeeaacdcacecbdebaadaacbcdbccababbecaebbddcbcebccbdcbcdadcddcadaadaeddaaeddbabdcebcaeaaddcebaaacacabebddaebaecbbcacebabedcbedaeaaebacbdbaedbecbaeaedabeedbacadeceabdbceeccdebaecedadbdedeabbabacaeccadaceedeadcbbabbeaaeecdbebbaaebadbabbcaeeddaeecdabcbcbcdbbbcdadcecbebbddedecbbeddabaddaddadecceabaecdaddbbeebdbcbebaaccacbcacccedaedcbcebaecbaaaacaacbcedbccaeadbceebecbebaaeeabcddaeadbecbaaebdebeddbbaecedbeedaabccedbbbdcddbeabacaecdbcbdbaeddbdbdadaacddaebeddccccedecbbcdceceecccdcaedaedcceedcebdcdecddbecdeeeeeebaebadacaeaaecebbdcaaeadcdbdccecbacceeaddbceebcadcedbbabedcecccaadabaeaaaddbbcbebbcaaacaaabcdcacccdbcbdcbccaaecdadbcaddcadceebecbaaeeaaaebdedcdacbedcccbcddaeadbbabcaddeaadedbdcddcabedadbedcedaeabeeddaecbdddddadcdcdcbdbebaccbcdaecaacdeeeeaaaabacdbbdcdaabaeabceadbabecdeedcceebbdadadedeaeccabbaeddaadeabbbdbeaaaadaceaaacbdeccbdbebabdbbaaaaabddcdccaabdaaadbaeccbddeaeeebdcccddccbccedcbcdbbbcaaebabebabeedadcdababaeccaeaedbbcaebadebaceedabbbacedbceabecaeeeaebaacdacaacdccdeddcbedbceeaabbeeaecbbabaaadebeeeebddbabeeabdaadccdbeebeaabacdeecbdadaedbbcabbeadacedbadbdedbcaeedbddedddbadaaebccaccacadbdeeacddeaadadcddceccacbdddbbdddccdaadbaceebdbbcdeaccaeccebcdddebaccaebdceacceabddbbdaebcbadcdbbaaeeadbeeddabcacedebbecddabdbdaecdaedbcddbedcbbcadacabdeaebcddddaeaebebdaebcbeeebbebeaeecbdadeccdedbdacebaaedbaeacbedabeacdaaaabedbbcecabdaeeedcbdaeababeaebeadadecaabeebaeedddaebaeeabbceeeeabeeeceddcbdedaedaacddccadbebcbbadeecedbdeabcdbddecacdecdbaeaccdbbccccbaebcbbdbbdeedaadbcbdaaecbbcbbdbbcdcaceacabcdeccedacbcdaacdaaadaecdcdbdebaeabacbeabecaaaebddadddedceebeaccdceebddedbdabbdecbebaeaacedbabdaecacbedebdcacbbababdbbabbdaacebedcaeddeeddcedbabaccdcadadcddbddbbadecdccddddddaccdeaabcbddbecddbeedcdbddbbaaddeceeebcbcbbbedddcbccedcecaadaacaebbdaeadbabeccccaaedaaeadbecaeedeeebeecadecbccccbeebadbaaecbebddcdbabadcbdeacdbbcaebccedbceedcbabbecebeecbddddaccdeddaabdccbabcacbbaddcbacaababdedcbceeeeebcccdaeaaeddadeaeabaebddaeeeecbeaecccdaacadcdeadcadbaaedbaccbbdaedddcbdeecdcebdbbadbadbceebecebaddcceaceddbcdaacbeecdadabdceadcebdcebceaebcbdcddcbacabedbadbbaaeadccaadecbeebcdccddbdceaccbdbebaaeddadeebeccacccaaaeaaeecadebecdecceecabdadccbdbeabeaabdbcbcaedddbeabeadaabaeccbbbeabaaaadbbbaddbcdcadebdbebdbaeeecaaebbeeaabccabcebcbbcbedebcbbabbdbcccaccebcaecadeebaedbbdcbaaaeecbeacaaeebdacccaacbcdaecdeedaaeedabbbbdbbcaeeadeedeebabdbdebcaccaebaaeabcaebdddbeaadedaceeaacbbbaceaedaadaaaacdbcedaacabacaaeeabdacadabbbacadceceecdcddcaaebdeacbbcacaceebadcaebddbdcebaaacbeecddeddeabebaebcacebbeaedccecddabceccadaeebaaddcaedacebcbbbbaceeceeddadebabddbcbbddddeabadebeecbedbbcbaddbcccaeccceedabaebebbcedcceadbabcbaaeacdcbbddbabbbaadcecbbdbaaedcddadacbebcabbebbadcddbbcecaacbaecabaeccdbabdeaebeedccabcedcbcbebdbbedbebbcdbcdeededdcbbbaaabdedaaaddadccbaedadabaaabcbaabebcddcabadceadaedeabcecebceabcbeccdaaaaddcadabdccdbccebcddcececdddcaaddaeedcedbcedadddbbaebdeebbdbebbacdeadcccdeebcacdcbcdcecdedcebbacdabbccdcdadbeeeeeebecbdbeccedbbbcbadabcabcddddaaabdacadececedbdaebabcdeddcbceadcecbaaaabdecdbdedccbbdcceeebedbdbeeabeeabdddcbbcbacdeacbbdbbaaddcedecddedcaeddbcaaadadcdbabdebcddabaabedcebeaaedbebeaeaceebbdceecebcedbeacebebddebdecdaeecacebbbeacedddacebeeaececcaacbbdcddbdedcdbceaaecebaeeebbbaeadbbbcaecdbdcaaadedecebdeecbaceeabdebcadcdeabadabaabbddcebbaabdecedbcdedeabdbcdcadcdadeecbcacbccabbdbdeaeddbdbcebbedbbbddaabaacaadbdbecacaaccdaddcddebceebbacdabdedbeeccadebccdabcabccaeccebebcecedaabddeeeecedbbddbbeabcbeaddedaaebbbacccdeadbbbdbbeadddeaaddcdbaaaecaebbbdeccdaadbbdcaccacdcdeadeeeedcccdbccdeddaabcbaaebecccbbbbdeebbaabcceaeeeebdcdecbaaabcdbcedbbedcddebcddadccaabebddbbabbecbcddbbccddcebcaebaeddbaeeacbabeebaaaebaeadbabdcdacaabaeacdecdcdbbbccdaccddcaabedbbecceeceebcceaccceddeecbeddeecbcabaddeeababdacdcaccbedcaeaacddbcdadbeaececedddddbeaaadedabdbdcadbbddabaaebeedceeacaeadcbceedabbaaeeecdebbcdddeebdaedeeaabdebbebedeeaabdaaabbaedccbbceebddcbceeaadcabecdeeccbeaacaaddeddedbccacdaedaaaceedcdedadabbecdbecdeacbedbdacaaceacdbcbdebebaadedadaeecedcbebbdabaeeeededebedabeaacccccceedacbbdcdeacbeeeeaaadebcacbeeadcbececabbbbcebdbcbdaacaeddaeaebeabeeaedeacaaaccbabaaddacbacbbcebecdbaaaecaaeddddbacbcecabcdbbecdcdbedecbbadeabbdaebcdbeeeaedbaabebcbabbdbcebbddbebaaddbceabcacbdccbecbdecdbcbdbceaaacacdbbdbadeaecaeaeaabcedeaceabdedacdcccaaaadcaaacccbddddbedbabcecbbbdcdaddbdaaccdeacbcacdbaebacbddddaecebbecaeeecdbbdbddeddaccaaadaeceacaedadeaecedbaacadabaaebabbedacdbcadbdbbaaaaadcbcabbbbcedcebcbeaaeeeabcebeeeabcedbbceaaaabdcadabbccabcebcdcbeaccbeceedbadceecedbceecabbecddbebbdabddbabeabddcabcbdaadaccedaecebabbcbccceaaceaaecbcbcaedbdcdbccaebaeecabdbddeecbbabcaadabceedbacdebdaabcbcbecacdeddccaebbdcbcbbaacecbcbaeccccacacadceadacbecbccaacdaddcdecedeaabbcbbccaecbdedcccddbbbbabceeecaebdccaceedeaabcaaeddecdabcccacadaecdaaeebebdadeedcebedabcedeaaaceceeceebaaddceaecdadcccacddaadadbcddbebbadcaccdbadeaaddedadcdabceacabaacaaaeedcacccbbdccaceeabdaeadbccccccadcaebebbabeadabddcbedbaeebbbeebebdbbabadaebabadadcacadebabebdbdabebadcaaacbbbceeebaabaaddabadcdaebeeeacacabdeedebcbabcbdccdeddcddacecdabceccebabadcbdeaeebcdecbdcccbaaebebaaaeecdbbbdebcacdccdaddebbeadbeebcbcabacebbebbbcbcebdcaaebeaedbeaadcacedeaaabaeacbbeddcacceecaaeccadcedcdcbbccdaaecdecebeebebbddbcbcebedbdbeadcdddaccabeadebbeecbbdbbdaddbabaeccccbceeaabbebbceabcadbdacbecacdabbdecaaaebdaccaccbbddacaeabcdedcadbeaaecdecedbdbccacdddddcdbcccdeddacdcddddbcbbdeccccadbdbaaadeccaecbecacbeacaccdaadadbcbdbabcaeedbcddbaceddcbdbcbadbebebbeedabdcbdbbecbddadbcedcdddaebabbcdaeceabedbedeeacaabbdabbeedcdaddeaccbeebdcdaeedebdebbaabbedcadaabaaacceebaddbabeadebdaadbbbadcebcaaadaeacaedaceededaabbdabeebaabecdebbdaedaedaccdcbbbeeccadbabaedbeebeecaecdadbdaacecabcaaabebbeadadedbeeaaddebcebecbdceeaecabdbedcacebeaacceebdeeabdeedaddaceecbbcceacbccbeabbcadccbcaeeabdccbedadaabbabadeaeebeeeccaabcdecdacdecdaaaedcdebbbeeeeeecadeaabcecaeecdacbaadcbdbddeeeeabddbdcedcdeebceababddabdabdebdcebaedddabececabcdecaddebbeeedadcebdeddbaacdccdaaaecbadbbaababcccceaededbadeacaaaaaedeabbcccaaedbceaadacaacbcbabacbbaaabbeedbeecdaadabdcdcdcdedcddeaaeeddddbcbbbabcebbdadabaaedeeabbbaaacabdbcccceeedddbccabdbedaeaccbdabacccaedcbcebbaeeeebacbeedabbbacccccdcddccbbcbbabadddebabeddadadbbaabadeaebababaaabdbebcbaebddccdcbbacadebcbbbabaedbeebcbdbbaaebebceebaebbdadbeadccaadecadebdaddbbbedbcbabaededbdbbdedecbebecbaaabeaadaadcabeaddbbbedbcbebdbbadbabccccacabedccdaccebaaaeecbddaddedcdeabeceaaddaeceabdddbcdbcbacbcddcbddceaeddedbcdedbeedbebcccddadcbaedaeeccceeadaeecebbcbbabedeeeeeecdbbbbaccedcbedeccdceeeaeedcebdaeebcebceebccaececededdbdacbcdcbceaabbdaddecddbbbdddcbdbcececdeebaaeecdcdbdecdbebcebcddbaeedecabddbacaecdbababeebaadccbdaaaabbdbccaacaccadbddeecebacdaebdebdcbcecdbdabecbdbcbcdbbdcdebeddbaaebbcbacabdbeeccadbeceeeeedeebbddababbcadeaedacacebeadeecbdbecebcaaccccceeaaebdccaccbdbedbaeebccccbabddcbbddbbbbeacebcadbbbebcccdabadbadedbdcbaaedbacdccabcaeebccdcedebbbecddcbcaeadbcebbbccdeedcbeebdcbbecdbccccdbddbcbeeedebedddcddaacbcaeccedbebcbabbbaddaebebedbacbeedeedeabcddceddcbdbeeddbaeceaaaeeecedcecaccdbbcdeadbddddacdedcacadabeadaebdbbdcdeeaccbebcaddecbbceeeceaaacbdcbdbeedaaecacadcbbcceadadcccedecebbcbabbcaedacdedbcbabeecbbdedcbeaedcbbbdeaaebecdcebcbeaedaedbdacbccdceebebcacadebcaabedbeabbbdbaeccedacbacebabddeabdadadedaebdbcbcbbceeacadddcbeedeeacecebacaecbabadabaaeeabeaccdedadebecbbbadaebceaacecaeaecbaecebeaabeebcbbabdddeddedddcdcececadaecdaeabecccbecaeadcbdbcdaccccedacdeecadbdbaaecedaececaaacacdecaacbdaeedeebbbddcdededdbdbeacaecbdbccadedaebdbacdaeecdcdbdddbdccdedddeebcaeaeabcbabbbdeaebcebcdbcbebbcbceacebceddbcaecdaedbddecbbccbdebebaceaceeadadccaecbaedabacebbecbbebdadcecbaaceacdcacadbaadcdcebaedbceedecaabacbadeabdbbecccabbcbeabdeadeebcaabedbbdeccdbeabcdaceacbbddcecdeebdcebeaccadbcadaabecaaeaaceacbbcbeaaaddcacacbdcadebebceecdadedadacabcdeccecdadcdbadaccbcbbacbcdaeecdedcaeacbbaccccebcebcdcbececbaecaeaeedeeeecbadbbcacadbddebdbcebedddaaedabaeaecddaabcadadaaeeeceeddbdbcabadeaaebbbaeeeedbabdcdeadbceccdedebbdebdcdadddcaddbaddaddbaebdbceaaabadbedebbabeeadbcccaededecdddceadaeeecdeaabeeebedeeeecdcedbabcedabbdacbeeeeaaeadddccceecdeebaeaabaecaabcbaaebeeedaddeeabddbbdaadbcdcedddcddeeddedeacebdeddabbddecbdecebcacbebabedcebcbbaccabcbdddadabaaaebdccbbeacabbceebeddadadeeedadcadeaecbbadeddcebeceedeeeedcadaceedacddeabdbaeadbdcdcdecaecddaaacbdcbaeaecdbbeababdebbdaddbdbcadaabcdbcaeecbbcdbbacdcbaeebddeaabdaeebbcaeadccdbeecdcbbdadebdddaddbcdeccbaaceaddbaceeedcecccabdcddabdadbaadbdbceababedebccecceebaeadbebeddabadacebedbdadeaedcbbbcebeeddbddcbeccbdbdcbaccdddeadccecbaaabdeecddeceddebbdbbacbdcccdabeabaeadddaeedaaeecbedeebaacbeceeebceecccabdbbecabacaaedbadcaeaedcaedbaebcaccbebccdcaadedcbadcbaddceaddcdbedcecbcdeaecedceddcdcacceabadacadaebcabdbecedcdacecedcecbeeedbdcdabcceeaceaecbdaaddcacdddeddacbbaaaadeacbeabaceaeddaabadecdcbadbeabaabaabaaebbbcaaebbeabccbdbcebccdcbcecbccbcbddeecebbeeacaeaadebedbadcdccacdceabccbaecacbeebeccbececbddabadbbeddacbbcdbcbadebbbdaaeaeddadbdaacceddeddcbaedeccedccecaedeaedeedbeecaeaddbeebeabebbeceeddbecebcddccebdaeceaedbaebdbadecaabcbbdbbdccdebbacdbceccccdccbeebddcdaadbadcaaeecceebedcecacadbadedbbceaeedadbcddeddeddecdcdddeceeebbcabbdcdeccbebcebeaeaadcbdecadeeaeddceddeddeebcacdbeaccbcbebbacecdebeaadadaadcdbaaacbbbcedbddadacdcaaeebebbbdbcceecccdadcbabadbbdeeabeeeadcbaddaadbbdaaeddaedcecccccddbeaaaaebcbaeabcceeeabddbeedeedaeebdaabddbbaacaaebccacaaeabaaabceecceccbebdebbeeeaddddedebabbabaebdbdeebebaaebcddccbadabbadeeaeacebebcabaeadbddddaebcccccabccdaaaedbceeddbbddbebcaacaecbccadbededeedebbaabaadcaccdbdaebecdbdbcdbdbbddadeccddbcbacbbdaabbeeccacdbecadaaeadcdabbeebbaceadaadaaacadcdddaeceeedacdebddbbbcbebdcadbddbcadaadbeaababbbbcdbccdadadcbdbdeacdceceeadcbbcaedcdadcadeebedbcbacbceccbbcadadacccaeacedaddcdeecddbdeddedeaadbeecdaabeccbdabeabadaeaecbcebabbaacddebabaeedbebddeaacaacecceeabccbedcecaaaceaacccedbaaaceebbccedbccacbbebdcaddadaeedcedebceecdbdebbcdacacdcadcbebdaccdcadebcaedebccecbaeedbbeeedcebeaeaabbbcdaacbdadcdbaeaacaabacbbabcbcedbdbdbaeadceedcbdcbaacceacedcbeecaebadcaaaedaeccdaeecedbcabaddeecadaacdacecaaddbbeeaecacbddddaedabbcaccddeadeccaabbdebaeacbbcacbcacdedaaddebbacbccdeecbccceedaaadaceaebdaadbacdccdcaecabaabbabdcaaacbdadabbcdeeebaeeacccdebebcecbcedcbceaddbbdeceeeaccdcdabbcdcdaebbdcaddbdeddbacaecdcbbedcabdbecaddbdbaceddcdeccbddedcabddbbaebbabbebedcdccdadceecdeadaedacedaccdadecdaedaaebbcdcddcbcdbaabaadecbdaecedeedddddeeecabdbcaadedaeedbddeedbeeacaccccdcbaedaedcddeebccddcccbcaddcdadccdaabcadeeecaeadbcbbcaeececbacbceeecabdcaddbabbacaaaccebaebbcbbdaceddccbaeaeecdedaccdeeeebeeeccabcadaedccbddedbcacaaeddebbdbdcedcbdecdecbccecbeeceaecbadeccceabdeeaebbedcbedcdbbabbebdddecdacacececcbeeecbbcdeedcbddbbbdecbdbadeabcebdecaeaecbcabbcdaebedddddbcebbbebedbcbcdcdcbdbccaeaabbcdeacacceabcabbcebeacdeeebebaaeedcceabdbbcbddddbeadadebaacebaecacaabbdaadcdcedbcbbdedebdadcdaaeeaeacccaecdeeeabbcdcaadaacbddcedbecaaeaabeceeaeadddbdebbdedcccaaabdaeecccebdcbbcbdeaaccbecbeebdeeabeececedcecadabeabeeadbceddbcccccadbebbcdbaddeadeaaacdaabdcebbbcdcdbdecadedbdbebcaddbaeceaccaecbdbccaaadbbecdbdaebebbedceaeabdbdbecdeabcadbbdadddacacecaaeebbabcecacadadcceddebecebdbbecebebededabbbbccbdccebeadabbeaccdeddaeeccadbeededebeeeaeadacedbddcdedbcebbaeaddbdcaebbeddbdecdaabeedbaabbccecdebddabbecaadadbedddeccaaebceeeeccaadcdbdaaaeedbbdadacecdcebabccecaedbaaaedcecacdbbccddebcdecbbdaccbcbdcdbbacdabecceddcdebeccdbacdeacecdecacbaedabbcdccaddbbcabcacaceceeeecccdeededbdcddaecaddacccdceebcdbacdaebbdddeababdbdbdadaccaeddacedcdabebbecbeeaecccdabeaaebdaccbbcddccabdbcbadccdbccceacebbebddeabcaebeeadeceaeedaeddbcedecbccedaeeeaabbbecaceabeaaebaaeadadabdcedcaaecbedeeebdddbcccbeebacaaadbbedaebebeabaddbdaddcbbabecebbcbabceeecdbebdedabcedceedccecabaccccabcddaaeecaddaecddebebbadabdeddaecdbebeccddedeceedacbaccdecddacdbadbbabedacaeeceebacccadeecedcaaceeebabdbacbceaecdabaceedadeacdceeaeeebbbaeacbbeccddbcdecdaedaeadaaecbbdcbcebdadcdddbbaaaaddeaaeaabbadbcddbaddecbaabbdbaabddbeadbbadbdcecaecbebadddacaaebdcadededdebbaadabbebcabdaaecadeeaebcadeeaccbeababaececbdcbddbaeeeeceedbcabbacbadecaaeadccaeeadeccadcbbdbebdeecaaaccaadedeccbeccddcdbeddcdeaddbdddabaebcddabeadcaecbaeadacadceeebebddddebaedaeeedcaaacdbabaabacdebececbdededdbcbbecddaeaadadddeedebddcecccbcdedabebaccbdcebedddaaaaaadadedbcadbdabdcccdebddbdddeeddacceadbbababeeaacbdcdaaaaadbccdcdeeaacbadcdcdcdaddaaecabbcccbcdacacaccceabbadbbedcbccbcdcdaceaaadeebbbedaeabbadcbdeedabdebcbbddecaecddeabebedaacdaaacdbaceeebbaabaccaacdebbccaeeaddeddeaccbbcbbecaeeecdbcaeabeaeecaabbeedaceccbaaebaabbaddaabcaceceadbdadbaceaaedcbaebbaccadbcebcbaabcbdcdddbadacccedecbdaaaadabcdcebdbeebdeacebdbcaeeaecccedaaddbdbeecceceecaecdeacaecccdacacabcdceeeadabbadacbdeccddbbeecacdabdebccddbdbdcaeedbcbeeeebadedebaaaacaaddceedacdaeecadccbaccbecdadceaeababacebeaedebaaadacabdaececbebedbceadcdedbbcaedcdcddccabcbacacdbebcecacedbbabbbbdecdbacbddedbacabaacabeaecdebcbecbdaccddaadcdbbecdcebbcccebbabdbabceaeeccbcabbcdcceeeaddcaadbbbbdebaacdeaeaedacedaedabadeeacdebbbeaccdacebbabaaeacaaeacbbabadbbabbeadbbdbcacbeedddadbbeaeaaeceeaeeaeedcecbaeddaaadacdceadecabbdbaedacdaeebaeccceedbbbabdedddadbdcbcdddcaebdccdddeacdececcacadeedaaceedbabbecbabbcbdbdaccbcecccecbacaccacecbabdccaaeeebaacceeaaccceeddbebeacdbbebaacbdacddebedbddbbdaeccdeedaaeddbcadcecedecbacdcabecabbbaccbeeccdbcdbeddecaadbabeecedcdcdeeedccaacccebbdaaadabbdddbebdbdccdeeddddbbcdbabddebeebadeaaceebabdbbcbadedaaeeebdaadaaedbadebabecccdadeeabecbbabbbaabbdccbcabaeddabcbdbddcddddcbcbcccdaccbdbccdeedebecdbbeaedabbabeddbdaeeeaeececeebddecaeeebcdaeaedbcbeceeeddebacceacdcbcebcdbdaeedceeccaccacadcaadaecdcabaeaddbdbdbacaaeaaddbccddbaccebaeecebdabaddebddaccbcabebbdbacddcbaecaadadedecbbcdaaadacacdaacbeeeddbbacccabcabdeccadccdbaeedbddeaeababdcecabddbbddbdeaeecdddaabcccededdbddebeebdcacebeebdceeddadaebecdebabbaadacbaebeeaeeaedcebeceadddccbeadeecbecaadebebbbdaeebdeddcddecbbdceddbddcaddaddbbdabeadbdeccadecdccbeddaedabceedbeedaeccdccedeeaaeabeaabbdcceccceeebbacbeeecdadbbaaadcacdedbbdbcddcdbbeaeadbbcabedbbdedabdceababcbaadacaabbdadbddddcbbcbbbedecabacdacaebeccdadaebdeaccaddcbeeeeddddedbddcbeaeacbeeeaeedabebcdedaddacabecaacdddaebceadcdceeedcbbbecdabbdeeeebeacbbaeceadebeeebdeeaaccccdebaabcbcaaaeeaaccdacdbededdcbbbddaaddceabdccaceeddbeebbccaedbcdebcedaadbaceeedabceabcbdebaccdeaaacbbbcbcdceacedecddecacbdcdecccccdeaebbaceeeaaedbceeedeabadedbaaddbacacabcbdaccedcaabaacaacdeebdeeadecbdbdacecbcdabddddeedeaeedbbceacbdbacbcacecebeabddabccccaaaeaabcacbcabebcbdabbaebcbaacddaababcebcddaececdeeadcaddedaaeebbbceddadbbabaddceedacecaaeeeddccdeeeecbabbdabbbebdcadabacabdbbdedadadcadecebabccebcabbcbabdacecbbaaaceacaecccbadeaeddaaabcbdbebcededebbcbbdceabdceacddbeebbcbbaecbeaacabbaccebdbebecadcccacedbaecedccabddadadbbcabdaedaaaadbebabcadbccdbeedbbabceaedcabaadcdbecbbedcdbddeddbaaaaaeceacbcedebdedcbccceaadcabbcdcddbeeaeacbcccdaadebbaddbcecdeabababdeebdadbbabcbaeadcccdbedaedbccdebbacdbeaacedcceeedebbddbeedadebcaccddaddabacddaaedbaaccbebcdcaaeecdbcabcabeacaeedaeaadccbadeadadacbdcbddeadcaaeaeabbcdbcbdbaccceeabaeadbbdccbdabaedebbbecaadddcaabcaeeabcbaaebedbabdbeaabdbcccdbaaaeaadabcbaabcabdceebecbbedabeacbaeabdecdaabdadcbdadbccabdeaccceceeaedbbdeeecedcaddeecbadbedbcbcbcaaaeaedbcdceebdadadabdeaabddceecdbaccabccabdbcdcaaadcdbeaaacbedaeecdbcdaaddacceddcdabcbbaedeaececceaedddeebebbdaccbeceecbaaababdbdbeeccbcaadaaabcdaccaccabdcbababebebceeabcebdeabcbdedccbebaacbebecaacbeceeedcbdeecbcbddabdaebbcedbcddeecabeebbacdaeccaaabbdadcabdeaeacedcceeaeeddddedcdcedceeceeadabbdbebaabadccdddadedcdadcecbbcbbebebebecbabaaaaeacbbedaedbddbaabebcdecbecacabcabcbeddacdbbbdaebccbcdcbbeeddacbaaabadeabbbdbdddadebdaceebadedecececadceacaacaecdabaccbdccdeeeebdcaccedbcdbdcdabcecbdbcdcdededcbdbbacadbbabddbddccaadccaeddadcedcbacaacaabbbcbabdbecdebacdadecbccededbaabbdeaeaddcecadedcbbcedaadebdbceeddbceaadddddbdcdaccdebaaebdbdbeaceeeecaeaaecbbcdaecdeddbadabdcabbaeccaaddbbcceadcccbeedceedaaadecbcbbdecaebaadeeddeccbbebdbbeebbbadeacdabcaabbaeebabdabadedcaacecdceebedbdcbbcecdcadebccbdaeddeadbcaecdeeecaededdaeddbdcbbcbbccaababececbaaddaebbaaacdeadbbadebddaaadbebebabedabeaaebdeeabccccdaceecccaacbebbbccbaaecbacdbedcdeedeccedcacadbaeaabcdacabaaeaaccecebaabaeadaaebecebadbdeadcbbdbeabbaabadaedbecddaecedeeadbdbdceadaabacecddbadccebbaecdbcbceeaeebcdacbeaaedaeeaeeecdbcdedecbdeeeddecaccedeeaebdebacdceeddceedceeaedadebdedcaaecaaacdebacdbccaebaceabcaeedcacccbbbcbedceeddcacbddcedecbecadabedebbdccedbeebaadeacdccadedddcabddbbedbecbaebedcdedbbcceabdbeeceaeeceebdbcbacabccedbcbccbdedaecdcbbbcdbcebdeecdcecdddcaadbadbceecacaaaececbdcecbedeacbcacebcdbebdceccbdeabbbbcededabceeedaeecbdebcbabdbbeacdacaaddecebebcebaddceeacebbddbedeedeecedbebbdbcebebcaeebcaabcadabaaaccdedcbdbbbabcbdceadbeaccaecdadbaccdcdaabcbdcdcabdadabcacaacbeaadcdedacacaaebebeadeaadddbcccebeadaabdeceaedcadbadbcdddbdedeabbedcaabdedccedbbdeddabcdcecedcabcaedabecdddabaddbeaceaaeadddabcdcaebebbcecceacdeedaeacbcbbeeddcecceccbaeebaebdcbabcdebecdccaaaceceeaeaaddacbbcbaeeddecddecedcccaeacbabecbadaeabcbccacceeaaecabbbdaaecbbecdbdedbabbbdcaadeeddacbdaabbeceebadbababaedbdbabdceabdccadcbdbccbeeaeeebebbcbeeabdeeaccdebbebbdecbcebeecddccdcacaadaceacadbadeeaacbcdbaeabceaecebecaebdeeeccaecbceebcbccaeaabdadcacbabbdbcbabcdcdededcccecebbeebbecabadeeccabbadebcecaeabcdddaccedbbbdecbadaccedeecececbdcdddceabeaddaaadcdecdecadeaedbdaceaaeccaceadbcbedbbdcdeadbeaadedcbdeadceadebbcecebcdeedaaeacceccbeeaabdadbbcbcccaabcadeaaddbaceaeeedebdbaceacbedbccdcaccdccdcaabbedddabcdedabbddeecbbeccbbeedecddcbcebbbdadeccecacdebbcecaaaeedbaddedeebccecddeadaeababdbbabcecdcbebabbcdeecdaedecbaaabadcdaaadcabbdadaddeeabdcacecedacbebbaadcecededdeddccbbdecbbbdceadacbebbecdbaabaceebbdaeaeabaeaacecabcadcacaabacbdadacccbdaaaabdadcdeadebebabeabadbdcdceabcebeceeecceddecebeaedecbeedddeaecadaeacbcaddbeededaaadceadbbeeebabeccdecaeecdaebcaaeceaabcabddeeebcdacdcdeccdcaeecaddbdbdddbbebcbeddaacdabddaadeeeaeeccbaccaecccedbdbcceddcaedccbbeeadedcbbdabecacacebbabcdeaacedcadbececdbcaabecceceddaebbdbecdcdcdcddccdececebdeabdcbecdeacceddddcecaadeebcdeceadbdcbaeccabddbacdeedaccacbaaabacdeaeeeeecebadababeecabaedbbbdbdbbeeacecebdeeebbdedaedaecaddebacbeeddcacbcadddbbeaadcaaededdaceeebbdecceaeceddacdbcbadcabebeccabadecadccaabdbceabeddbaeebaeacdddcacaecdcdedaaabadedabadcccaabbcddbcebabcacecebecebbcaeedbccabeceecabcddaddbdebedaababaaadcdabdbdbbccbecdddeabeeddacccaeebcadcdabbbcadbedbcbddceeeceabeccdecbeeabdabdbbbadaaebdecdeedabeceaeedbdacceeeccabdebdcaadcccdeccddbceedcecebacaeacbcedadccdcbbccaedceccbcaccbbdabdacbedeadccedebdaddccdeaaaeaadadeaaaebbcbceaddcabebedbdccdeeabccbdaedcddcbaaabbebbdadbcbbceaaaadbdcebadeabbcdadbeaaaececbbdbbdeedbdccaeeebeecdadebebbedceaaceeddbdecdacecaebebadcdaabdcebaddbacecadedddbecdcbceaccdeaedeabecdedbcbdabbbbeeededaaaddbaedbedcaeccabbbebccecaceeabbeedbecccbdbcbecdbaaecccaccecbeaaabdeabdeaeecbeaccadaedeebaceabbedeeaaacdcdabebeabbceeebbbeedceccaceddabddeeaddcabbccaaeacecbabeaaeccdceeacdeacdbdabbebcecccbdacdcdcaddbcdcaeceaccacdcabeaeaeabbccdedabeebadbbbcadaeceecadeadaddebbababeeaecbbccaebbebbaadeacabdecaabebcbacacadcccddbbedabbceebdcbeddccbcaaadbebbdbbecddceaabbdbbeadcecebcaedcedadbbddecaecbdeaebceaecdbeadbdebcbedaeeebaaadbcebcbbacedeccddaeebdaacaaabcabbabddbdddbeaccaabebccaacdaaddcebabbadadcadddaaacbabcacdadbdbaeededcebedcdcbdcdbdbabdcdcabebeeddcddbdbebbaadabddddaedcdadccacdeaaacadcccaecdbceceabbcccbecadeaecbadcaeeecdeeacedbbcbedabcbbecceeaadaedaddedcdbeedbaabdadaeabddeeccedccbedeeadcbcdceecbbdaadcabeabedbaadbabeebbdbcebbadddecbddebddaeaacdcdbadadeecacbcaabccedabbbdecadbcaccabdbcceaeccbaedcbacdebeccaeeeacbbbbedabbaeaadeacdccaecdbdbadbcadcdbedaeededdbbdabebcededdaebebebccdccadabbadebccccdedcddcebbecaaceaeddeaceceababbcccabbaebeabbbaabdadedbbecbcceadeebcedbbdccbddaababcbadbabccbdadaabadbaececcdcbccbaeeadaabbaacbbebdabaaddadebabbbabcdbdcecceccaccedaccedacacdeacdeeeccaebeaedeecacbdedecdbeaebcdddcdcaeebbaaabeddaeabeceabdcacdbebccaabcebeeeeeacdebddbcddaaaddaeddeceabedaaceabbbbabdeadebdadadbaadacddcadabcadecdbdaedddcddbcedaeeaacaaeddaebdcbbbabdbcebebbbeeaaddbbdaccaabdaedcdeaceccecebebedaecceecaeabaabaacceccbedcdebcacbdbddaaceecccdbedbeacaeebcbceeeababcbcccceeecbadaaaaabbbbeedaeabdddccbadcedeccbaddabeedaadaacaacddadbaeabedceccabedeaadbdcdeabddbcacdabcbecdcabeedaecabceacabadaecdcbbbcceebacecebedbdaaebbbbeacbdcaedcbadceadcabbcdeaecdbddcbacbccddbdbebeaddaacdcdaddbbdaceedbeaaeccbbbdedaceddaccbaddbbebeeccbabbcaceabbaccabaabdcaccedcdaeaebccbbaecedeadcbccabccededaebdadbbadecedbaaebcbbdcccdbcadaebcaaddcbbbbacccbeaccbcebbcbeaaebeebbbcdddddbeeeecdeaaabacedadebbdbdbdbcecaacbedcabaddeaedbedbbaadecdbebdeabadeebddbcbbedcbaeeceddebbeeddcdcdeacbcaccbbddccedeebbdaacededaeeddcabecabbbdadceacbdeabbdbdcbdecceebaccbadeddebbeadcaddaaeaecacebdaaeebebceeceeddeaaabcdacecedaebbecdbeabbccabdcdcaaecedaaaeceaeebeebccacceeacbaebaecbbcbcabcdcbcebaaadeabcaebcddeedccdaccdcecdaaedceddabdacabdbbbcedaceadddbdcccbacedaaddccddcaebdccddeabbaaedaedccbbaeadbaadccabcbcdddbcbecccddbbbaacaaedaccceebaddacecaadbaacccdecbeaecbceabdeebaccababadccbdbebcebeddecddcadbdedcbcaedcecddecbbedcbcbbdaebedacccabcbdecedbedbcdabedaacecdaebddcedbadbeaaacadcbecebedcecbdececaebcbdaabaecdeeeaeaaadadadbbbaeeebcdcccceebccbcedecddabbbebdbecbdcdeedebeecdbddceeccedadabbababeebecddaabcddceadebeaeebcecaaebbcacadbcdebaeeeeecdeecbbeaecaebedabedbedcdcdaadbbdddbbcbcdaeecddaaeecbabbeabbecbdcaddbbabceebeabebcccabbeebedbbedecccdddadcbcccceddabcaaddaaccdaabcaddcbccddcabddebddbeddbaebcaadcbecbeaeeeabdddcdaebbecaeabaeaeecdebdeabbabbaebcdbdceeacaedecbadacebadecbcadceabbccecccccbabcbdcbacbdbebececcaebaecddbabecaadbbbaaacbedecaebecacedbaacbabedbcdeaaccdceddcddbedababdabcdaeddbedaddceececbeccecedaaebceaadceecdacaabcdaedceaaadebcddaeddedbeacaebdbdebdaccbeacbabedcccaebbbbbcaacaebabdcbbabdbdcceedadaaaceacdbdeabbeebbddccabedecbcccabbbebabaacedabebdcbaedcabdbadeeeaadbcadaeeeaacdeccaacebaaebadcdcdacedcdcbadbdedacbcababeadeeaddaaebcbcacaddbcbdbaaaccbdaaacbcbddceddddececcdcdccbaacbbadeabcbbebcbbaedebdadbbbaaaddbbbeabddeabbcabbaabedcdcacbedaaeebcdceaccdeeddedcdeaeacaeaccaceeaeedddecdbdccddcaecedeeeeedabaeacbabdabbaecadcbdeeaeaccbdedcdcbdcbbebcebbcdeeccbcdeecbeaeddadbddcbeaeedbbbeedecebadbecbabaeebdaaabdeecabeeadaaabbbcbacecbcccceadeadebcdddeaecdebadecbcdacbcdadcccecdaedbddeeaedbbccbaceedccacbceebccaabbabdbcdeacdaadadccbebbebdaaeceacdeccccbaecacaddadeacebeaecccedaeeccdbcbdeeececedaceaeecbbbbdcddcbbceebdaabcdeacecacccddcbebacdbebdabdbddcbebeeeaaddbcbbcbbbadabbebeaccdcbeaacbeaedbebcbddcbbbbeacaeceeecbbdacdbccaacddbbcbeadecceeeacccacdeacbededbeededabecbeddaedcbeeddbebdbbabbdeacbeaceabecebaeaaaeccbbcbccaeaebcdadedaddcbeadbbcacbdbccabbdcebceebdababceeeaeedcaeeedddbbcdedadcbcadecacecdaaabeabdecbecabcabcbebcdcdecdecceacecbccbbbabaaacacdeacdecbaddaedbaabdadeaecceebcebcaebdbbeddbcbccaabebabaebebcebbdeddeceeececdaaabeccaabdeeaeacebbbbdebdddccdaeadbbaacbccaddabcebbdedddadaecdeeebebecdcaabddaeeeecebbcbabbaedabceaaddddedabeedebadbbebaccbeeabacbcdececdbbbadebbecbccadadecccebbbadaddbabdeedccecdcaadbddceedeeabcbbedeccacbeaccaecbdaaadbbaddbecaabaadcabcacabbaebdaadabcacebecbbdcadaccceddecddabebeeddcbdebcaddabdbecbceaeebaabcbdaaadecdaeeeedcdedbcadaaebaecccecbebecbaadaebbedbdebdcecababecdcbacacaaeaaccdeeaacdbedccbbbcbedbbabaacdbbdddcdedaeaebacdeeeeeebcceeaeadcddadcacdeaeaabeecabccbaecbdeaececaacceeecddbdbceeadbcaedabcdbdceebdeebdcabcbcebdaeabcdcacbeacdbdcbeabebbddbdaeddbbdeddccbaabaebeacbdbedcdbaacbacdeebcadedbcbadaeedddecdadbebcbbbcbacceddbdcabdeaebddbebccdecadceedcecbeaecbeadababdedeaaaecbccbbecdacccbbddcacdcaaedebbaddbaadbdcadbaadabadecabbaadaabaceccdbcdebbcddeabbeeeccdaacdebeabaaeecedcceecedeadccdbbaaedabecdbebdbcddeeabeedcadbabcabebbdabcdabbcebecdbeccecdbdbabdccaeebbdccaeacaedacacecdebaacbacbcbacbdceaabcabedebdbeeccdcbadbaebbdcabbcadbbdddeecccecbccbbcbdcdbecbabcbcacabecaaabaadaddbedacdcaeedaacdcaceaaddedcacbdbdcabeecbbedeeeeaceeaaaccbcebeecabaaaeeaddbdbebbaaacbaeeeebbcdbdccaecceebdddabeaedbcbebaeddbecbeadeeeecddcbccaccdcdedadcaedaccaacebdcdabbcaaccdddddabebdbeecadceeabaaaccbbbbabeadacddcddbdedaaeabadcdbeaaeeecabcddbcdaaddbcdbeeeededdbadbbcbbdcdaeeadbbccbcbedecedbcbeabdcdeceedacbcdebaeabbebdcbcedddbcedeeeeebdebabceabcedabaaaebcadcceebbedbddadeededecaccadaccbddadccbececeacceabccccacebceeabbbaaccbdaabddabcecbdccbaebbddbaabeddbeabebedadbdcdaeaaceecddcbbececdceebeddcbbedacebaaeabdecbdecaebeccedaceadebbbcedceaeebbbadeabdeaecdedcdedcedbdabbbbeeddadededabadcacdbbcaaecadcdbecdaebacbebaebcabccaaabebacaeadbecceacbbbebadabdecddbcccbdcdccdbcccbabaaecbcaebdaadeeaabdbecdcccdeaaeacacbbabbaedebedaadbdcabedaabdbceaebaaeccaeaedaacbbcecccabebbaceeecdbbdbeaadbbcdccabcdbeadeccaddbcebaedadecedebadeabaadadcbacaeddebcebddeccabaaedcdbcdceabcdedcbdceccdbdcbadbeeebcccacaacdddceccdbdcaebcdccaedeeaddcceaadeadbdcbaaedbcabecaebcbeebaecbedeabecbadeddbebaeaaeacdcbcdeadecbccdeceacaeedbabaeaabaeddaceadedbcbbbaeecaaaaacbbceddcbabbadbeabddbbaaebaccecedebbdaceecebabdddbbaeabeceabbbeeaebcdbdeeededcadcabccaebabecaaaaaeeebbbecaeabadaceaccdebeccadccdbaecbacdedaacceeddacdabcaacabaadbbecddcbdbedbaadddaaadeaabaeebbddebeabcccaacbbcebacdaeecceedcacecedcddacaebeadebdecbeebeceebcdeacbebdbbcedbabedbecaaedcbaddebebecdedceadacedeadccaebceacebcdddedeabeadedddacbdbdbbbdbecedcceeddacebbacdaddeebbdbccddbeaceadcaccddebdcceeddcccbbaabbeebdeaccbacacaabababebddbbeaebadbaedbcbddecebebbdabdeebdebbdaebcccbbeddabaadeedadecacebceeecedbccabaacadbcbcdbcbcdacbddbcdceadeccccbbdeeadccdedbaacddaaeeaeeaddddbabbbcbbcbcdbcddebdcdcaddebbaaeedebeecbcbeaedaecdcabccabdcbcabdcedbccbbabbebecaeeecccacdedceceaeeedecabeacadbedeccdecedadbcdddebdececaabecddebabeaeebeccdaacebeacabdbecdebdedcaebeabcabbcdccadbeaaaebceabccaaadaadddbdeaebbaadbdabbbadbcedecdeeeddabedadebcbbadedbedccdbcebdbacaaeecaedbebeceecabcedcdcbeeabbeeaacddbbcacbaddeebacadaaedcccececbeeadbededacaeaaeddaecedbeadbdaeacbeeddccbcbdecbaadcaddadeebbaacaaaadabaedcabacebaddcaabcdbeacbeabccaeacabaaecbbaaacabbcedbcdbacbebdcbbeacddbcedccabacdedcbabdbcabddbbabceadddadbacbdcdedebbebbaaededbeeaeeeccddebecbebcddccbadebdabadacabdabdccaebebeceebeaebbccdcaeedbaebaecccedbeacdcaacedabdebddcdabceeacddbcedcecaeddcabdadabbecbdbaabecebabddbdeadcadadcaadcdebbebeecaeccdcbdbdadccdacdddebbcaabcdeeadabdceadecaccdcadbcacebdcceaabddbeaaaeecedddaacbeeeeadeadecacbebeabaadbbcbcddacddaeeaeebcddbccdaccaeceedbbbaacadebcbcedbbabdcdccdabdeadaeaeeeebeaabeacdaadccdcaacedcdddcbecbbbaeaacbecbeaedabaeeadeaeabbbbdddebbcaadcdccdedcddccdcabecddcceaecadcceabcedaccecacabebacbebeeedbbaadccabababcecccbedcddadcebedacdbaadbbbbbabbdcdabdbbbcbccbbcbdbacddadceadbcdebbcbcaeadcceddeaecebbaeebaccaeaeeebeabdabcaeadeedbbcbbeeeadeaccccbabeebbacbaaabdacacecbddccddecadeeebdbdcbcbbceceabaeadeedcbadceedbdddddaeeedaacacaeacdeabbbbbcddadaecebadbecaebbaaadebabedbbebecacadcdeacdeaddaebebeecbaacaaabbdcdeecebbdddadacacbaabddaecebcecdcdcccdbccecbeceaadcbbaeacabeddeccaeacebdacdcebbccaaebbabddbeecbaabccaaebbdeedbabbddacddabacccebebcbdacccdabedcbdedccdbbadedbcbdccabadbccbdacbabbbaacaadeeeddcccadbdacacbebbdaebbecbcacadcbbeedabbaabbccebcddbeebedeaacceeeeabcceccaedebbeceebdecabbedecbbbadbdceeaddbadeaacabbdabecceebedbbddcddbdcadbcedeabacdeebadaacecddbeecadbdbbeeccaeeeeaedbdbbaadcbabbedeabacddeeeedbabebceeaaebceabbadbacadcaedcbddccbaaecaccdbddcacdabcbdbeccbcacaaaadabdbbdaccdeabcebeecebeaaaaaadbeabaebeaaaecbdbebebdcbaeeccdbeecadcbeacdbacceccbdddeccdabbbbbabaaacaeeebebbeadccdaaaaaaddeeeebcedddaebcedabbdadeeecaeebbcddacbdcdacdddceeacbebdabadcdbbcecddedecccecddcbdbbcdbdcdecebdececdcaaaebbeaedddcdadddadedbdaccbedcecaaadbdcdbaededabebcccbdccdaedacccdbacbbdbeacbbcaaeacccadbaeabdaaebcceeddbddebacccebcecacdeeacecbeacbcacadeacadcdeeacbdcdadcaccedbceeeaddbadecbdadbcabeedecdbbeaddcaebbaadacedceadbdbcdddaabdeecdddabdaeabecebabbdbcedeaaebecebcecceaebcecacbcdcbbeabbceeceeebbbddccaaebbacbaabbebabaeebebcbeeaeacabddaeaaaaaddabbdadaebdedccbdacacbdbdeecdcdadbdddcadecadaccddabedaadbbdadceabddeeeaddacbdabeebaeadadcdaebddcbecaddbeaababcedbaeacabbbccaadacdbabaaeaabeeeaadbdbddeeecceabcdabaebcaeaceadbdaaedceccdabececddcebecdbcaeeeebaceeccbccdacaabaadbaabdbaaeaeebeabdedeccbeecbbceacdceeadcdeccaebeadcecceddaadcbdcddcbebbaedccadccdadadbcabdbbacccdecaecbdcebddcadeaaddceaeceadbaabaeedbedaabecbccddbabbcdedcedbdbadadbadedbdbcbaecaaeeabcaebddddcabeaabeaacacdeddabddecebcdadbeacdcaedadeccbcccbddecccdaebdadacbdbdbcbabebccdaacbacebdebbccbbdaacebdabdaebddabacecebccdbadeacdbcacdebccadacacdcbdbbcdaeebaeeeebdcaadbacbeddcbbcbabddbaaeeebdbedcccbbeacaeaaceccbadbebbeddeaacabbeceddcabdedecabeaeceabdaaaadecadaadbbcceceddcadacbbabeeaedbaaeddceaccbbcdadcabdeebdaeadcedadbbeedccbabdceaebaadddeccdabbcaabdbbbcacdebdbecdbccbceedaebdbdeccdabbcaabacdedceeaaccabedcececadbecaeaecabbbddaebedcbdaddbdcdadccecaebeaebadccbbeacbcedddcadbceadbcaaadeddceecdbcbcbcecadcbededdcecbebcecededcbddeecbccbeebabdcbccdbdbaebaeccccecceddcbeeadeecdebdcbdbbadeeaacbdabaaeedadebaabababedddcecbeceeceaebacdcbacdacadddcdcedebdaaabbceccbceacaccdbbeceebbeaadbedbbceaadeadebcbacebcacbeecacbbaaebeecacebbecebaaeeaaacbedddcdeaaabeaaebceceaabcaabaacddbdebcbadbaeeceeddcaeebcaeeceaddbeacbbddacababccdcbccddbaeaedabdeeacbcdbcdeecacaedadcbbadadebaedbaacddbecbeedbebcbbeaedecdeedadaccbbdadecaaeeacddaeecdebbebeeeecbbbdceddbecbbedaebeebeaebbbaaedeebdbaeeddbaeccecbadeedeaaeaeadbaacececabcebaececbbaabadcddbdccecceedbdaaacdacbaacdabaaecdaccacabacbccaddebedaaeadbbaaacddedbedcebbecdeddadaabdabadbcdeedecaecebeaebaeedadabdabbdddededbbaecbccaabdeaccbcaaaeaeaeadddaebddceabcbcdbcebeccabbbeebceddaaccaddbbecbedaacaeddccceabcebaccacedbaaceaaadaabaacccecedaadebbacebececbddcceeecdabddeabcecadaabdadbaedaaeeebacdcecebccbdcebbbccdcdddbdbaeaadcadbebcebecadccbcdcbeaeaaedbdaacbaebeeaaaacdbddaeecaebbedeeecaeacaedaedcaabbebacaceaeacbebadbbaddabeecedbbaabddccbdeabddacccbdbbbeedbbebcdedeedacbdbbcdebebaeecbdbbebaeebdadcbbdeeaedddbdedeabecdacdbedaabdeedecdaabedeccabcdaabbeadadbeedbaccbdbdbeaecbeddeacedeeaecdaeaaeaeecccaeadabccbcaeadcccaacbbeaddcdabbcbdcbdbbaabaabdabcbbbaaaeadabaebdbadddabdabbcaaebcedececcaddaacaddaebecaddebcecbabecbcbbcecaaaccacccdbcedbaadddddbdecbbdcaacdbddaebdedeccdbcdbdbdcddbbaecaeaeaaddbdcdebdbeddcddcacdcbdbdabdacbccceeeeedabcccccdbcebdeedeabceeabdbbbaaaadabcebcdbaecbbbeceacdceebeaededdccccceceedaeaceabbdedecdbadaddcacaeaaddceccceaeaadabbbcdabbeabaaaceddeedbbeabdaebeccebbcaabaadaecaacbecaeebabccebdecbeeddeceeadcddedbeddcbaaacceeebadedadebeabaaaaaacaeeacbedcddbabeecddbdaacaebbcdabaceabaaedcdcbbbaccdabacaadceabaaccabddcedcceeeaabdddbadeeddbecabcdbbdbaddeadecdaacebcecbabaeededccccccddecbccdbeeabdeaecbcebbbabbbbddcbdebdabebcdbccbdccdebaaaccddbeabceaeddcbdabdaadbcdabbecadcbeadbbeceebabeeedabbbcbdcdaaacdbadeabbcbbddbdacdebecdedacbceabadeecbedcbbcbaabeaddddbadedadccddbabdebbbbabdbdceecdaeeceeadbaeaccddcabbbdedbeeccbeaaaabdecddecdcaeedabaaedcbeeaedeaeeeaebeabddbcbbbdebeecbdbeaebcdeddbdbdeededdcbcedbacdeeaeababaebeaadedcaabadedeecadcbabacdccdacdadbdccacabeaecaadebdeaedebbcdcccabbaabebcaccdbdcbacebbaebeeebacccbdbabbaeedbeeeaceadaabcebdcdadcaacdadbeceadeabbdddbdcbabceeeedddddddbeeccaeaaeaebaabbcdbbddabddcedddeabeaaeceedaccabdaacadddedbeadababddebdeeacdbedbeeeedaacaddebcabbeadaccbaaabcecacedbeececbceebbbcaddeaeedbdaacbcaeabdaaabbcecbeddbdeeaaedbeaecbcabcccbedbbbecdccaeabcaadaacaaebeebeaaadcecdadddbebcbeedbbebbbdacccceecedcbeceaedadedbeacbcddbdecbdaacabbcbcebcccddceedecddbcecedaadedcabbaecbdeacdbaecdbaeccdaddaeabbecbbbabdbbeedebeaebccdbbceeedebdcacdaebbaddaaadeddddbeaabebdbccadbabdedceddbedcecebebddeeacdbaabeaaddadcabbbabecceeeebbdbccebbcabdaabbdacbcdaabbeedadcabbccccebebaeeccebddbbedeebbddebaecacecbdaedddeaeedbaebddbaeaeeeabcaacbcdddaceeeaecbcedbabdaaeecaaaceccacdbbedacbdedacddbcacdbdbdaabdbddadbddababdbbdeacbbededebbddcaddeabeacbcaecadbddbececddaedbcccabeddcdbaccbeabddeeaabdbeaeeedcddcccaaebcdbdcbeaaadccdeedaadededbcbebbeedceddeeecdaeacbbadddaaccaebcebbbdedcaadbeadaccadacdcddccdcdaaababacadbaadaebeacdddbbccacbceeeaddeeebaeeacbdddbebaaedbeaaaabacddcaacedbeabbccebddbbbaeabeccedcddeeceedadbbaaeaeecccdeebdccacedaaebdbcaabbcdddcebbecdcecedcecbcdeabecedacbeeacbdbcaebdbeadcebbedcbedbaaabecadeccdeeddeaadccbcbbbebaeeeeeadddcaaabebaedacbabacbbbcbdaacadcecdcdebbcaccebecabecbaaedceeadddcaedbaabdbbcbacebdaaccbdcdaaddceabbbaadaaaebcadccddacdcbcebabbeeddbaaebddddbdceaaaacabbeeebddeacdbaaababcbdcebbaabcaaadeaddeccaeaedadbaeaacbeadddddedbcedcddeeadbddbdaaaadcccecebadbbbaccdeaedabdcadadcbceedbceabdeecacaebdebcaecabcdaeaeebbceedceabaeaceaaeceecedabeeaccccceabdeecccaaecadcdcdaaaacaaeedbccebddededabbeeaaaaccdebdadaacceeccebcaacdebdaadcbebdceddddcbdadcddeebcccddccdbceecacbbeabcdcadeeddaddbacebaadccacdcbdddddcaecebedbcbbbcecaeddbeedcaabcaadeabceccccadedadeccbbabbbbedbbbaaaeeeaeebaadbabddbabadcecaccdecdedddbecdbddbdaeddaaedcdbcebbbbcebbccbabeadbedeabaceeccededaebbcabcbeebeecadaedcddddbbbdddbadadbabcdddadeeeccebdbdebdeaaeedecedbeaccaaaacdccaceceaacaeaebebbccdadeaabdeeacbaecaadcaeebadeaccacebcddcecbbccedebbbcccbddcbbedbbadcebcbebcedaaeddddebecedbacceabacaccbccccaddcdabdaccbccceedcbddbcdbcceadeaecbabddcacdaecdabdcbbadcbbddcaddbabceeaeaeaaaddddbceadcacabcbcbaeedeacdccccdcceeaeaaeeddaaeeabcdbaeaaaeeddeaabecaadadddbcbadebecdecbbabaadaaadcebdecabeabebdbbeccdecdabedaeeddbcbcecdcaaecdeebbedeecacbebcccbdbadabbbadeeacbcbedbcbcbcbccbbeaeaadccadcddcdaedaaeecccacedaaebcceadedcdbacccdecebaecaaeacedcabbacdcacbbdaddabccbcbbcbacaacbeadeedebdecdeadaeedbccaaabeadbdaaeccdbccaacbededbcddeaaabeedeceacabdecbcdeeaeeacaadeeacdadaecebacdabcaceaadcddbcccbaacbbacdcbacedaeceaecdeaabceaebdddaadccbcbcabebcbdaccbdecddebbbdcbbbacaccceabebaacddbebeeacacdedcddeaeadceedbcceaccbbcdceaadabedcdbadbdaedbcbebeecebcaebebcbcacccbdacedecaedebdcaebeececcaaeeebbeeacecdccddadcbaccecbaadbdbedadabadadcbdecbaddabdeaaceecaddccedabcdaabdddacaedacadcdcccecaeebcebbcccedaddacacedcaabbedecddebddcbbedaedbaadeedacddcbdaabbdaaaabbebccbdeababcbdcceebdabeccdadecccecdeedccbeccaddacadbddcdeceeebaecbceaedaaeabcadeccaeeabbdbeaedbdaeddceaaacdeaddceaebacaaddedaebcadbcbadbdddbadcaedaeadeedababcdededdaaeabbbbcdeedeadadcebaeedadbdbcabeedcaaddbdcccebbebedceccdaaecedeacadacdaeaeebacdaebceebdadaacbccdbacaeacbbcceebdadddaedaecddaabadccebdaaecabbcbdcbdcedbeacbcbedcbdbecaaaeaaedbccaadacbeaeaddcaaedaeebcebcdbdccaaceeedaacaadebdceecdaedaedcdaddedcceaeaaacdcaabcdaddbbcedaeaddcacadacbdcdcdeabacddacacaaaaedaabceebaedcaaebeecaebebbeacecdecddecbadacbabaeabeedaecceaddddcdebeadaeeaeaeadbddeadbaacdbebbeddcccbcbcbbcaeeeaeeedabeaaedebdaddeccabdcbcdedcabeaabeadddacccdadcacdaeaaccccbdddacbdbbadccbebaaddeaebebebcdbdcbdcbbedbaecbdbcdbcbaaebecbcdaebbecaceecabdebcdeaabdabcddcaaeedaacadabaabecceaebecaccdcecaeaaadbbecaedaabdcddedecbecceddabdcdcddabacecbcdaddaeddbcdacabcebaadeecbabdbeeeaacecdcedbeceeddcbcaecadddbadcabadbbdccdceaedbeaecddcbdecabdcacecceaababeecaabddbeadbcdcccacbbbadbdabdeabeaceeadabbcdaaccecaaecabbdbababbdeaaebcbdccdadaeadaaacdbcabadebccccdcbcedcbbbaaaddbbceeaeaddbcbecacecbdaeaeddbdddacddbbedaeecaaebdddecacbeedbbdceaeeababeecdbebdbabcadebceeabccdccebccdabcebdecadcadabbbbccdbcbaeaadbdaebbabadaaecdededbedbcecbbcceaeacdbeebbcbacbeecaaacedcacceacbaaeddecedccbbaacbdaeabcccebebcadccddbedcdbcebcecbecadabdecdbeaaebdbedbabbdcddbaaeaebaebecadcbcbcddcddcaaddeadbcdcadabcbdcedbadeaaedbdbadbaaceaadbeccddaeecadacdbcbccecdedbcedacccabddccbbdaebdcbbbcaacabadbccdeacccbbdabaeaaaeccacddabccdceeaecdcdedcbbdadddabaaedbabbcbadeacdbedaeddcbceccbdbbbbcadbeadecbdedadbeaabeeaadceedaacebebadadabbeeadcbdaaabdeaceebeaceeadeadbacedcbbcadecccacaeecbebbaeedadaddcdeacdeebacedcabcabbaddacbbacbdaeedbecdedbddbbcbdadecdadaaacaeddabcdecaebcbcdeaacabaccdbceeeedcbcedbeddaebbbaaeebcabbebeaccddeeecbddcedbaeeedddcbcbdacdceedaecbceddaacbeeddaaecedcddbdbeececbddaccecbeaeaccdbbabeeadedeeaaeddcbadcdadcdcbeddbebcaecbecdbeecadeccabeeeaddeebbcacecceeaaaccacbbdaddcbedbcdcdcdddeebddedbaabbedeadcbdcbbadcccdeaaacabbeecdaaebbececebecbdabaccbaaecbeacacdcdaaebdbdddeddaeacedbcdeddebdcceeececcbebbbeacdbebacaacadbdecebebbcceeebccceebcaaddbbbbedaadbabedbbbebabdedaeedcdcacbbececbddbcceeebcedeeabbbacdcabbaddcdecaedbdceeeebcbedeccaadcbbbbddaabebcebdbddbbdacadccbceeddedcaeebceeaddbeeecaeaeebeabceabdcbbdcaddcddbaeabbbabceebbcebdbddedeeadaeaeacbacedcddbbbcdddbbdacdeeacaaabebabbbabeeaccaabcecabebccbccaeaaeacacaadeadddbadadeeabddaeedddebbaebeecdddadceedaeaecaadadaebbaadccdcdeedacadebeceedaeedcecdbacbcbbccccdedeeccabcabebcedcdccbdbeceebcabbbcadebcbeabccdadcdbcdadabbeaebbcddcbdaedbdddaedccebbdbccbcedeaeaebabcdcdbdeebbaecadabdcbbcaadbbcecaddcbabeedebceadecdbaaebddbbdbeecbdeaeedeececacaadcdabadadcebaccdebeecbaebbdbeaceddcdddbadebcabcdbecbbaedaadccbbccaeeddcdceceacbebcededaaaaedceedcddbcadeebdeebcccddbcbcccdbbacddcbebcbbeaeceaadbbbadaadccadceaaaabdeadcebbeabdaaaeadbbdaedeecadedbbadbddcacbecebdaccadadbdbababcebdebbcaababdbdeaccabbeeeeeeaadbbbebcdebcaedbdabcadddbccadacadebdebbeebacaadebaaceacecaebeeeddaacebcebddceeddeeccddabacbbeeecdcdcedebbeeecdbddaccbcebbcaabadabdbaaccddcabddaabebeececeedbbeedaeecedcdcdceeedcbacdcbcadeebbaaacdedbcedbccacacaeccadbecceddecebbecedeaaebdceaecdccedeaadcacdbbceeababcadebbcacaacecddddeacccdddcedecbedcedacbcdbbadabbaaccbbbcbedccebdbeccbadddcabcedadaebcdbdaaedaccbccadeaaeccaaaeabddbeaeccdddecdcaeecbbebbcaaebabcdeaeddacecddedceeabaabbedebecccecabbdbcdddbbbbcddecdccdbedececcccccddccabcccbaaaccedddbcdcdaaebaeddbaabddbadcadccebbccbcebbebbadacccabbeebeaeecadabecdbbbcddbdadbbbbbddbedabcbdeeceecbddccccecdaeddbcdceeaadedceabdebccddcceccbecdccaadbdddcedbeeebcadaaddceebeadbdbddddacdcddadaaeeeeaecadbeecacaaadbeadbccbbaeedacbacabbaadbdecbebcabddacecaccdeaeecacaecabadaccdedddcdbeeaabdabceecdecaadeecabdadaadebbbdddceacdaecccbaeaededeaaacadaacadcdddccddecbbebedbdedbaadedacbcaaabbadaceabaaabedabdcaebaeccebaeeedbcdaecdebbdcebeeeacbecddadbdcdddbbcdcddbdbeeadebebedaeeeadbecaabdababebeebbcacdeeccddadaeaacbccdaedccadbadaebbececcbccbaacdbcaedbcbbaccbeaadbddcedaaeeadbabdbaedeabdabeeabbbceedbddbecbaabecccabbdeceedbebdabadaeddadacaadebbddeacebaebcdaebddacadacceeababaeaeaeebacbebdbbbaddeeceaaecbebeebedeebedbccbacbdaccabbdbaaccddbdcbcbaadeaecdbebeabcaeadecaacbbccebdcddaddbebabadbdbdcabdaebecadbeccaaaadecddcccdcbeaacbccdaaccbcecdecbbdbbbaabbccbdecedabaabceeaebcedcbbaacbbcadebdcaebedccbcbecbddbddbcbbeadbcaabccddaebcaacccaadcabdccbdedccdeaeaebbeaadeccbceacdbeacedeebcbcbbddecebebeaeabacbeeeaacaacaedbecdadaeddbadedbbeaeecaadbccdeeeedaadbcaedbeaccebddaabccddeeeadcdebbcdabebcbacbcecddebcdeebadddabbeabaccdcddeeeceecbbadbabcbdbaecbebcaeeebbdaeaaeaebedbbcdbbedcdadbbbbbadccdccbedcedcccabeeaaeaaaadcbcdcdccdddeaddbecdaeddcdaabcbdadddcbcccddadcdbeabaaabaeabdacaebeacaceaebbedeadceeeebdbdceedabbabdcceadebedbdaaebdcebdcddceaddbdcaadbddabedbcdabbabaddeebdadbdbbaeabdbcaadbbaaeecadbebedccdaacbceaceeccabdaadccbdedbaeeaeacbceadbbaeabdcdcbaeccacedbaceccbeeeabeedeadadeadaaaaaacbdbbaecbdadabdebceabdcdcacdbdabcecbbcbaccededbaabcbbbebedeadccaceddbaecebbedbbdecbedebbdcabbabddbdeddcdbcbaeddceecbcededebaecceeebcbbeeebadcaabedacddbcbbcecedadecaabdedebdcddcedcbaacdbabeecbebbacabebdeaaaaaebaaccddcedaeeadccecdadebacbdbcbcdeebbedeaecedcdedeeececacdcdddedbadbacddcbcccebdbacadaeccbbaaccbdeacbbeddddadceadacbbccccbdaecdcadddddceebeaebceeeceecdaaaabaaaabebeeeabdadbbebebeedbebeeddeaaddeeaabadedacadeaaeaddebbcdcdbccddbaacecbcaedaaabbabcebecddaecdaeaeccbaccbaccdedcbecdabcbdbeeaeddaaaebebbedecbeecdadcbcbcccaeabaeabbdacecdeadeeacdcaaddbbbeceebeacadcadeedcbbabedbeebbeaeebadcccbcebddbbceddabececaabecdcddbcccbcecccdbceedebddcabadbcdebbeceaebdddbbebccaadaadaedccecacdcbacecaabbacbceeccbbdedacadbabcbebdccdccaabebbacebbcecccccbadbccaeeabceabbabbbeeebaeacebedcaaeabeedbaebbbeeeeddaebaeabccddadeebdcbcddedabebeeabcedcbbadabacdbeacbadeeecdeabecbaeccacbddebcbeacebeabadebacabdddecbadcbeaeccaeebbcebdcadabdcedeedaeebedcacdcededcbcccdbeccadbceaacabacddedccaeeedacdcbebbaededdedcccedeadbddaaebcacbecdabbbcddababcdbaaaeabaaddbebdbdeaacdceedbddbddddcbbeabdbbaceaeababdebaaaddddcecaebceedeaccacdcabcccdecdeeaaccdbdcbaccaebadadabebdedaddcdbaceeaeccbccedecabecbdbcadbdbabbbabbaaebbaadceacbccbddcacdeaacdcecbdaecbbaeacdbabbccaeaedbbdceeadcdebcaaacdeaaaeadbdeaececeddaaaadcbccaaadeebabdcacbceecceabdaedcdaadabadddecddaceeeeadddabaeadaceadaadecacbbaeddcbceaabcdeecdbebaaacbcdcaedaebcaaabeaecdadacdcceeceaeecbabcddcdbcaebacedcedbbbcaccbddadddeaacbccbcaddccecedeecacbbebbbcdaeddebccceecabbbeeceadbaceeccacdcceebdcbeceaaaddddabaecbbcbddcdcacdccbdcbecbadccaeaeecbdadccdbcbeddaacbcdbeebcbacbeacedddbcaddbdaaaeddebdabaaebdbddcdebdebbcaceeaccaaaeaaaccedcbaadbecdaddddccaaebadabdeeacadbabececdaaebcbabcdeebbeeeedcecdcbebebaedbcbbbaebbcbdbedadcabbdddddeabcceccbccceaecbeaabdcbcbbbcbecbcecaddbdadccaeedababebaeacecbabedbedaceebdcbbbbbddadbbedaadbebebabdadddddadcacdeadedcacbdeeaabcbdddeeadbdacabeeecaddecdcdcecadeddbbbbabdaccabdccbdadabcadacbccbccdecbcbbeddcedaabdcecaddeddebcebdaaaedeaedacbacccabacdcacdeecadcdcecdedbbdceddceddcdebcceccecaecdcabebbebababbcbacacadccccdcabccecedcdbbcbbdaeeededddedaabccdaccdbdbdddbbaeddddddadaaaccdbdbacdabbedeecedbdaaadecbabadddaacbeccaabaddbceecddabcbcadbbaaabedecabdacaaaaaedbeabeabddebbabbbdcaececeedbbbcdbeacdacbdabaececedaaebbbcdadbecdbbdddacceecbebeebbabddaddaecceaeccecaeeacceeddaeeccbaebddbcdeeaecbdacbbeeeabbeccdbaddecedbbddadcaaccbebbdbeccbbbdaddeadccddabddaeacbaeebbddcbeecaccdbcaaebdddbdadbacdbdcaeeaeadabaecdabbaddaaedcbbeceeceaacbbedbdaebacdccecebdadbedadadacbdadaeedceececacaeceadbecacdccadabcbcedceadebeebdaaedcebbbdddbcdadcceeeaedcdcebcdeccdccdccabccbaedbbaebdcccaebcdbbaeeacddbddeababceebaedbeceaacbbcbbacbbdacabbaddebbaebcabadddaacddbbebcaaaeccdadbbbeceabbbaedeeebaaddaacbeeccaccdeaccbcaaddbedaededeeeacdcdcdaecdcaddcacdeacebbcbbaedcaecdabcdebccbaedecaccbecaddcdecbbabaacaeebdcceceecbebeecbcadebccadaacbeecacedcdbeaebbbdddcedabaccceddbcaccadcedadeeecdbdccedeaedeebdbbcacebcdaeadeebbaebcdbeddeadddbaeddbeaebeaaabdcedcdbbbedbceeebbdcddccddbaaaddaccaeeaedaacddbeacdcdecdabeabecaaaabbecadbebaadeedaacbebbcbbeacedcdbebaebddbcacaeadaadeaeccaecedeaddbebbeeeaddbbdaacebbabdbcaecaaeaecdbaaedbcbeacaeadebdedbccbcdccdaaddddbaedbebeebdedcebacbacdbbecaebdbbadececcccdcadbbbaacaaabcececeeebbdbadecdeadbdbcdeedabadebedddeeddbbdabeacbdabddeeeadbccabcabcdbccadaeacbeceacadaaedcddbdbdbacaeabbdcdabcdceaaeedbccaaececbeeecccdcdbcaddbccdddbcaddabaedacaecadeccbaedbdddcdacdbccebebbeedaacaaacaaadcdaecdbebaededaacdcbddcedceadddaebedbeeeecdbcceabcaadcabecbccadabdddceeeadaaaeeaeaddddebecadecaaccdeebbecacbdeeaacecbaeaebcbddaaaacdbcaaddaeebcbcedebabdeddedcadeeaaaddbecbdcedabbbadcbadacecdbabaceabdbceaaaebbecabebbbabdcabededacaeacccdcebadeaccbcaadbaaeaabcddbcecaadedbaecaddbbccedaeabdbdbdeadeebedababccebdaeccbdceaaaabcebededaabceeebacaaadbdeecdeebdbcbdeedbebdbdbcceaaabbcbacadbbcceabdaedaedccaaedbaacdadabdaeeeddcbededcbaebccbdedcbedeebaeedaceecebaacccabcdbdbaccbbadacebeddcdbdaeadacdbbcaaeddbbdaccddcdabbaedbaeaaeedbaaabccbcddcadcabcacbaabcaeecebbbaaecacabbaecacdecceaadabdebcdcacdaeceaedaabcdeacbaaaedeeecbbeaccccbecaebbabdadeaadcdcdddadacbddabebaddeabddececedcebcedebeabcbbaacbaaecdbeeadacbcdcdabcecbeebcbcabcbddeeecbcdbaaeaeccbeedeeeacdbcdbbebbdcedddbedcedbdececeeddbdebadedabdcddebcdabededbbcdabbebbbddaaddcaabbecceceaeccdbacbcabdbbdbacbededaedabededacccdcddddeebdadcdddeabedccdeeabbbabdeeaddbddedacbedeebeddcebddcdbaacaaecbaabcbcdacaebabcdcaedebdaadeabeceeacdbabbaeaeaddabbecdadbaebddebdeebaebaaebcdaececaebbbdadacbbdcdbbecbeeaedbbdcbeebcbcadaededebcdcabbdcabbedddbbdcebdddabacacbaccdcacedcadecabdbeedcaceccdcbdeadeabaeaedbcdccbcabddcdbccdceadeaaceccdaaccccaeebeaadeacebbebbebaebdbbadadecbecaeeadbdcadbbaddeddbcaebbaadccdeacbdecdadbdecceedeaeaecccebcedecbcbdceeddbeeebbeeccbebcedddebbecaabcecbeabdebcabadddcbaecbacecdeebabddccebcacdaadeddababccdbdacecccaadedddeabcdccaecdbebadddbdeeddbddeccddadddeeddedcbbaaabaeabebcdaeaaddededcdbdeebbaeccbdbbdbaddbcbddcabddbaceeeccdbcccdeeeadbbcdcbcdbbeddecdaadabdebbbadacdccbcbdaeacbeabbdbdccdadbecaccdcaabbaddebeebbeaeeaceabaaabedbdddabbccadbddbcecaceedbdeaadcadacaaaaceabbcedcaeaccdecbcecacddccaeecdbadbeececcbcdbebdbebcabdbcddbeabeadaaabcccadcbcaebbaeeeeddcacddcedbaebdddadbbeaabccdcebdcececcbaedeababacbecdeccaccdddbbdcccbbeebcacdceaeeeadecaccccabdceebcadaecbebacbecabaaecaecbcdcedeecaacbeeaceedbcbcdebadabebadcdaebeeacbacdbdebddeeabdbbbcaabacdaaebebdbdddcecebcbeedeacbadbababebbdadcccecdddaeddbdacddebdaeceeaeecdebcaebdedeaaadeebdaceaadccedabaeebcdaaccbdcbbdccaccbdddebdcdbbadeeececddbeeddaacebebabaaeadcaaadacaceeabeeadadaecbddbddacbdbeedebbdecccabbbedebbddaadbdeceebaeaceaaacdcedeaacbbabbddbeddecaaecddeccaecabdaebaadaaceaecebbeabcdecaabddecedabceebdeeaadbcebdaaddbcdcdbbccbdddabedabacacbeebdcdecaddcedaeabbdccbaecbebcdcbeeccbddbcdedeadceacaedeadbcddaabebabeddcbdebcaebaccccabdddaddabdbebceebebcdabddcbbbcaabcbdacbadddbacabcdcdcecabcbedbddddeeadacecbbedddeadceeecdaacccdadbecdcaddcbeaebbbeadadbedbdbdceaccbaddedbdbedcabaacbeaacdbeddaeeebcebeaebbbbbcacebbaacbaaadabaabcaadbecbaddbecadbbcaadeedcdadcabbeccbbcecbadebdbbdedaaebeecbcbeaccbdbcbebaddecccaaaaceecaedbeebeccecadddbacecbadabcaceabdbdecebcedbdddaaacacecebbdbaddaedbaacecddeeacaebedecbedaecbcadedcbdaeececdcdbacbcbcdcebbbdaadedeaceaeebacedaabadedcebcbdeaeddaeeedebbdddbbacecebdaedbedbecdebbdddaadeebdedbaedddabeeeaeddceabdccceadebddadcbddeaecccbedbbabadcaedbdbcacebdddbddbebabdacccacbdcbdcababdaacebddbccbbbccccceabddbcddedababdbdbcbcaebdeacceaaececcccacdbabcbccccecbadeabbeeccaeacbbacbbdeebccbeeeeaddeeedcacdddeddeabcebbeaccbbceccecadecddceadbdddacbdbcbddbbeaaebebcbaededaddeecbeedcdcaeeccdcedcabddbdcbbebdeabdeecdcccaccecebddccaaddeaaacddbbaeeccabbcdeecedacbcdbaebebecbdededadbeeebddcdccadaeaeaaabeabcedebaeabcddddedcdbdcbadaaadbcdbddecbecbcacbcccaddadabdccecedddeccdceddbcdabddacdceecedaddaecbbcaccccbaecbecbadcbdaeeaacbeedcbdaddedeabadbecabbdbddacdcabacbcaabccaebcccdedddaebaaeeacacbdbccbecdbdaaecbdbceacadbaebdaadeeacebbaabcaeddcbaeeeebcacebddbeabbedebaaddbddcbdaabbaacdaddbdbcecdbcebeaabaaaabecbbccdcdaedeadddadcdbadebdbecabbbcabeccddbeaedabddcccddeacbadccbcdbeadeabdececbcdbeeacbedbaddbccdaebeabdedeabdaccabcaacdddaeabceedcbdeeeddcbdbccbbaaacabdcbbeceebbddaebcebacaccbbcaacccdaeeccddcabadabdbbcbbebdeecdeadeabccadcadaaedeceadcabcbddadebacebdebcbcdecbedbdcdaebceedcdaebbbbaecabbcecedabdcadedaaecddbbcdbbaaccbaabddeabceaedbeedebeaaeecacbbedbebcbeccadccdeacadeeadaedddeaacbdaadebeccbebaaaecdddbaaebebcaadbacbbaeeebbeeeedcedbddaaaacdcbbdddacacdaacabeeaedbeadadeaecddceeebdbdabbbbececdcbededceaaaeddaddbbeccccaeebeabbccacbddcdeadabecbedddddedbbbadcbcacedadbcbedbaecbabdbbabdcaacdbecaacbdbcbeacaabbabdddeccacbcbacedcaccedeccbddbcbdaadccbcbcebcdcbaaabdbabaaceaebcebabeecdbecbbeaeecbbdbbbbbdadcbeecaddeaeddddceabcccbacaddadcdabdebdcadeabeedcdeeaaceddbaeaedeaacdbddabeeebcdcadddbcaadcecaaaacedccccbecbdeedacdcbccaeceabbabccadcbbdcdeeeaadedaacbeecbbebbedbdbaabcdbaecdcaeaddddbcdbbebdaedcacdcbcbacabbeaeeacaabbecaadbcecbccdbddbdbadebbdedabbacacbcbbdceebbcddddbbcbcbebddbdcbaecebeeeaeddadcdcdeabdbedcbeaaeecdddbadbdaeedcdeaddcceeebbbebebbbdaebdebedeccbabbbbdaedeacbcecdeeaedcabaabeabddddecdbdadeabadcdcadbabaaadabcacecdadebcdccbedbeecbccecdeabbccbededeccdaacaedccebcedeaadeabeaebaecbecdcdedaaacebcabcecbdaaeacecebdbacaaddcacccadcdabbcacbcaaeabcabcbaddbacecaccbbbebcadbcedabcebeedbceebddebbbcbdaabceddababddabbddcceaebccdeeecceebaaebdddbbeecdaedbbedbebcdbabddbacbbddecbbcaccbeddeacbacdcbedccdeabbbdbbebceadcabebbadeeaadbdeccedddccbbdadecbadbdcdbccbacbadbcbbcdabeeebebbebecbbdbaacaedbeedbbbcdcaadccebcdccbcccaaabcdbcecaeceacbdedbeeadeaebdebcbcdcbdaeeabceceedeeebccacebeddebabaabbeceadeeebadcdbbdbdcdeaeaabcceeeedeadccbaeecccaaaaeadedbccedacdccceecaeaeecbeacecdedbcdbbaccdabddccededeacdedaddcbaaeccaabdedccebeadbaceeedcacdaaaeedabedacadbdbeaababeccbbdaebdeddbbebbaebdeaddacceddbcdedcedadadedaeeaeacbacaeebadbeeccceeeedaeaaccebdabeebdcbbcebdacbcdeebedecbaabbaccccbeebbabcbceccceadebdabdddadcbccabbdebccdcabdcadedbacaaddcdaaeceeecadaacadaaedacacabeaeaeeebecbbbbeececcecabcdecbdeeaeadcebabecbcdbcbdbedbecabbbaacedccdddcbacebabdcebabeacecadbbdabcdaaaacacebcbdeceecaaaeccbbacdaacccbeecaadacccacdbedbeeaadacdecbbaecedbeaaeaebecdebaabcbaddeeeebbebaeccaeabbcdadceececdedacaeaccaeccbcabaeeaadeececbabadbecdedaadaceaadbabecdcbdacaebcdcdccadcadddcbeeacddaedadccbceacaecabeededcaeaabcbebbabcbeacedebbcaebdbaacddebceadcdccaadeabcdebedddcbacededeeadbeeabecbdbcecaccedabcaccbabebecdaaeacedcaeeabbaeddbaadcccdeddcdacbdddebbbedeebebaeabdbedebaeeccceececeeccbeabbbbecaedaabdaccebbadbdbbeadbbcdccddbdceaddaeecbbdaecbcbadacdbaceebadbceceaeeeabeddcccdabdaeccebccbabebadbeceabacbdbceaebccdaacdcaebdabcbedcdbbdbedccdbbeeabdeabdecaebeeececdadebcebcdeccbadbbeacbcbdceddebdbeeecdaccbdebadbacabdceddaaaecbcceacccaadbdeaddddeaacddbdacacddbebdbbcabcaecdaebcacdcebccdbeebeceaeecbdbaebacabeddcbabecbacdccbbaadebaacdaedaecededceecdabeedbdaacaadcaaeddadbedaeeaceadeebcbeadcdcdecdedbbbbccccbccbcedeebbcdcebaadabdcdbaadcbcbdebbcccbaddbbdbaeeebcecaabdedcedacdccebcedababbbeebeabcaccadddecceeeacabbcbcbbcbbebdcddaebadbbcabaebabeaebbeeecdeababcdabebabdccadbcceccbccaeccaeddcdcdbebeaaddabccabedbbbedadbecbcaaaeaadbacedecbddaedaabcdcddcbadadaedcacdbdcecccddcedebbaabaabdcacecaddacbebebbcacceedaaaaebadebccbdcbacbbbcbdabdaedbcaaddcbdbbcdbddabbaecdeeacbacecccecbcceaeecdccddbcdacdadebdbeaeaeabcbecebeacacaecdedaeeaaddedbbcaabbcddbdaccbebaaadecccccbacbdacbdebecbbaacccdbeeeeeedddabdadaadccbecdbdabcaabcacaecaeaeaabbedbdcdeeccaccdeeeddbbdabadabcbbbbebeaddecbaecbabebebbcaebbcdbccddcaaeccabbabcbeaccecdbdbcdecbaeeacdaebdacccdcabbcccbeecdaabebddeabcbceebbadceeecbdeecabeaccecadaddadccceacbebbdcdaccdccedababdcbbaacadcdbbaeeaeaedaaeedcbdaebecdbdecedeeebabaecdddbecaaacdbaaaccdcaddadeeaddbbedeabdebdacbecddddecaebdadcacaadcaacabeacceabaedeeadedddeedabaadddcbbdcbddabebabbbeedadbaceddacbbeeaadabddaedbddadedededeadaddececceaaebcddecbdeeadbebbbaacdbededaeebdacbecedcedbaccebabbddeaaeebbebdcaeeddbddbecacddcbcdadbedccbcdbbbeeadbabcaccccdccdcdadaaeccbdadccbbecabdeccecceaabcdbdbaececadddcddebbcbeebacddcacedbdccbecdcecbcabdbbcccecaddbbcbebeebbaeabccaeaacaccedcbeeecddebcdaeedcbecdbacbcabaeacdcdbeadbbcbebebccabbdabdebdbbadddbcebededaaaaececdbdccbbbbdcaebacbccecdccdedebcacbeeeedebbadabdabeabebabdecdedcddcaadbcbdeedabaaaddadadbdbcdacccddacaaeaddcdcdbebccebebbeaeaabaacdbdccecbbbbbadcdbecdcdacadaddbacbbbedcdaebceabadddcaecccdebdccbbacecedddcacccbaeaebaaedceeaeedcaccbaecacabadcebccbbbdabdbbcbccdeceaaddacbbaeeaebadccdcdbaacdcdabdbacdeddbeadddcebaebbecaeaeebbbdcdbeceeeaecacebbedecdbaaabebbacebdbacdbdedccaccebadedcbebecccceeaabcdaddbadeddaedbeeedbccdcbdcdcdebdcdceabedbbaaaeacbacddeaccebbecebacaeabdbbacccddddbbeaecbdbdbacedeccdcaebabcacdcaaadecadbeebdbcadbccbbecdcdecadebaacceecedbccbaeeadeebbcbdabebabcebedbccdaeabccaaebedcdaadcdbbaeeaadcddaabecdccdcebdaaecaeccdeccdccbdbbeabcabaeeadebdadabdcadccacdcacbacdbaabdedbbcededbaadecaacdadacbacaaebdadceedabacdcbdedaeeabcebeeeacabcebddabadaabdedcdacadcaaccaddccedccebbdbbdaececeebedbddaaaeaddbacccabcdbccdcaaccbdaaadaabacdbedcbddebcbebeddceeeaeaddeaeacacbedbeadecedcbadddeccccecaccabecbceeeaedbaddeebecdcdcdbcaebbeeebaecbbbaaeeabddeaaebddbabccddabceccadddadbaabddecdeccaabddbcedcadeaaccedbccccdaadabaacebdeecacbbccadddbddeaebcaacceebbccbaedababdcbbccbeabebdbedddcacdeccdeedcccbeebcdacebbdcbecaadccceccabcdddabeeebbbeaaeececbacdbcabbcabaddcdaaaaabdaacbdbccbdcdcbaddbaaaeccdacceaddbabeacbbccbcbbbedbbccaddecbdbcbdcaaeabcbcdbbdababacacccadadbaeecbdbbceceabbebdcacddccededcadbaacdcbaedcbbedddadbcbbbbcacaddeddcbdbeaddabecedcbaebddeadabdccdccbacdcdcedcbeeccdaecbcbecaeddeddbcdadabbaacdbdbceaebcdcccbedccaabedebadbcdcaeaaedeaecaebcdbeeeedebbaeabeadacbecabbbecdacbeccbdbebabbbceedaecbcbacbddcbeebbebcbaaeaeedbddacdddbbadccbdddedadcdceaddedaddededcdabadabdcbbadaddabdbcddebdacdbebaadbecbbaabbcdcdcaaddacbbeacedddeaccecdecaabeddcdaaebdacdceddbadecaaedabdddeddbaeeabbbeacdaeeccacdaadaacabbaeadecebabacabdbbaacdabeccabbbabdebaecebcceebeddcddabbdbccbedeadaaccdcebdebdcbdeeedbbabdebbaddbcabacbabebbcdecdeeebbbaebbbbaaeebdeacaeebaeadebeccecdcdceadadeaaddbcaecdadcdddadaceacecbabcbbcbadacccdacadaddccbdedeeadcabbeeccbaadddccbcdccbbdecbbabebdebcccddbeddcdadaaaaabaebeacdaaceeababeebebcdecaaedcbcaddeedcadadedebcddcadcdacceabddceecbecacdeebaabccaccbadcdbbbdacecbeaaedeacaacaacbacdbbbcabaaabeacbaccebaaedcdaedaeeccaabbdebccbedcebeaaadddddbdaabddbccadcebcbaaadbbdcacdeeddcdadaabdbbdddbabeacddeedcdecdabbbbddebbbabdcdbdbacddbddeeedaaebdcdcdaeceedaeaeacceddeaebeedeaeaedeceebbbcabeceacdecdeccaceddedaaddddccbddeebabdbababbccebeebeceedeecaeecbcadebbcaedddcabdecdaeaadeecaebcececbbadbcaeddcbdbedcccacbaeebcdbeddeabecbeaecdbcaccaebcedbebedcaccdaebcdcacbebdcaedcdeabaddccededddcdbbeccceceaadcdedbbbaccaccaedbaedadcabdeaacbabeebeceabbccdbceacdddbdaeaebadebdeaeacbeeaaddeeabdabeabadabcabcbbdeabcecaebdaacccedbeebcdeedaabebeaacbdbbbcdeebebebaddbbacaebddcbecebadccecbbaecbbcadcedcbadbbbbebcacddeedeaceaedadacadeecedccacadaeecbdbcaabbacbaecccccdeaeeaebbceceebdadcabeccceceabddabcbccadddcedaabdcbbdeeabadecbcdecabaaaaebdaecaeacadbbecdbcbbeedeceababdaabaebedcabebdedebadcdcebabcaaeeebacaaebceccdcdabdbbecdbceddbbdbeceecbddabcabccbdbebabdbdaddcedbbbdbeeccaeecdeaaebeeccdabaccbcccedabaccebcedbcbeeaedbeecbcbceabdbcdddacbbbbddbcdbebdacabedbcecbbedebbeaddaaeeedecbbaeddadbbbbbbddbbdbbabaabebebeebaaadbadddabedaccbaecadbecdcadbebcaebcdbdbdbadcebccacbcaebbedcdaebbbbacbdbcbaddabaadbbebbbdeddeaeacbaaabadadcaaadeeecccbeaeaeceeaeaacccdcccdccbcdcbdcbecdcdbeaaeddabdcadcebcdebbddccbdedacbddabeddecbacaaedbbbccdbbeddcccacebbaaeabcecaeecddacceeabaecdaabaedddbbddceaadcdebacadedaebaadadaadaabaeeaaddbdeeebaaecabaecaadeecaaecdeaadbddecebaaaeebadcebaedeadcbaebebdeeaceadaccaecccacbebdceebbecdbeebecdceebbeeabdceabccabdadcabeeeacadeeaecbaadabadecbdabcacddcebbbcdadaebcdeedeaaccddbeceaedecabdaeacaabaccaceadddcddeecacceceeddacadeccedbccbebaaaeddeeadddccddbdbedcdcbeeedbacaadccaadeccdaedbdbbeddaebeacdacbccaccaccbbcddceebeadebdeeabbbaccdcebaceaaebbbebabacbbcdceeeacecccdbaacaacadbecbabdacbbeabdcecdcdaeebeeebdaccceebacacddeedccadddeecdbaaedcbedaadaadbccddebacccbecdeaccaedecbecdacbdaaadacedabcbabbcddcabdebbcceeeedeaaeaeabcdbbecdbaeabbeaddeaaddeaecbecbaddcacbebcebddebecdcacebeabbddcdaadcebcecdeebdeccaabbcbeaaadaedecececeeecaeddeccddebbdddbaeaaccbceebddeccacbadcaaacecbdaccbddaedcbdbcdaaababdccebdedbaccdaaabcbbdcecaabaebbadbbbbdddcabcabcaddedaeeccadbcbadbacbeadebeebeeecaaeddbaeeebdeeebbedaebcecaecdcbadeedabecccbadcbadadceccdcbabbedccbbdcadcbaebdeabbbadddaeddcaddaacacaebccbaddbdcebcbaaedadaebedcecccedebccabbccddbbadedabddeadacceebdbeebddcedcdadaccacedcacbebcaabccebccbbeaddcacadacbddaccedaebbaccccedebcaaeaeacadbeaaccaedabbdabadbabdcbdbccecdeaadabdddddbdbedbdaeaeacaceeddeceeeccdeaaddbbcacaaeaedcabbdeeeeecdcaebadacecbbdcadeacaccddeabadbdbacebebadcaabdbcebecbddcbdaeeccaccadeecaaedcbeeccaeabbddddbacdaceccdcaabacdbceaaaabbaaebcbdbcedbacddadbeabaceecabcbdedecbbcdeabbbcdbeedabdbdeabdacedcbbdcebdcdbcbbaaeebcceeeeaeecedcaaebaaaedbaabedaddadaecaeaeeadbdabbbbaeacabecbbebcdcccbbebcbdccadecdbebaebacdecadeadacdcdecacebaeccdbadcddddbaeaadaccdbaedbdebaeabebdbeedcbeedaeedadddeeccbaaeccebcccbededdeeaeadbbaadebbabeeeadacbaeadeadddaeecaaedabcdabbcabdcabbbedceeedddebabccdbddeaedaeaedcbdcaedbaaacabaeadbecdedabdeabbdbedebddbcedaebecccebbddecdedbadeacacbdadeeedededbacdcbdbceeecaacadcdecbddcaccbacbcaadbddedecebdbdcacddccdecbcceebeaaabadcbdbabdabbaaedeadccaccbebdbadbacdbabaccdabbeccaadececccedccbbebddcacddedaaacacdcabbbecbaecacadcdbdaaabbedeeeecdeaacbdcdacccedeeabcdddbdeaadabebdaabaeebdbaeecbbedbdadccaddbeaadecaeadadceabeabeeccbedbacbbadebebdbadbaaabbcccbaadacbaaddaaddccddbbbdbceaecdcacdbdcebbababacbcedeeaabbaeddabaddecaedbddbbaeaeecebbddadabcdedcdeaabdbeadbceaceadcdbcceebbedabbdaeddcbbbecceabbdccdcbbbaeaeeeacaadcdeaceadcbdeebcccbdadaeabdaaebcccacbeccaacabaaeaeebebcccbcdbcdadeecebedaabeaeecaecadbabeddedaccebbbebbbeacdaabeeaecdecccdacaacaecadeddbecbbbcabadddeddebebcedbbbebcbadeeddbdabdeceadedbdccabacbceeebcdcbbacddbcaaecddedebbdeecdceedacaadebebbccbebecdbebedebceeceeeedeeceadaaedeebcbedecaddceeddeaabebedcbcadadebecddcaeeaabcecdaacacbeacabdccabcbdeceeeaabdeaabacccaaeaadccacadbdcedcddeadddeddeacdaddaadcaeedadceededdaceabccebecaacbeabedbaebbebadccccdeeeababcdeebedaabdadeebcdbcacdceaebdcbeddeecdaabacabedeaeacebedeeeeeceeecdaaabaecbbacbddbdeecbdaebbdddacecdeabbaccaadabbeacacdccbdeecebaceedecabaedbadeccdcaceebbcaaabedbbaabdcebccaaabbbcddebedaaccecccddebcccdeeaebbdeadebedebdbbbdddcacaddbcadecbeadedaeeebccbcbeaeeedcdaaceebcdaccdcaccaaebaeabbaeaaacbcbeeeeabdccacaadacbeccaadcbaeebadbebababeceaaecaddedcbabbaacdadeeabccabababdabedddcdbcbadcbdaedbbeeedccacbcadceadcecabcddabcebeececebaebeddcdaecbdabdeebceedebbdbdcddaedcadacbddadebdececddcbeabcaeaecdcededbeadbcecdeceeaccccdaeebadeddbcbbbebabeddbbaaccbeeadceebcacccdebecebdeccaadbdeeadcedaabebdecbaddeaaeeababeaacbeccebeceadecddaeddeadcacbbbadcdcddacbbcaaeaebecacaaceccdabadeceebbabdaabdaeeebddcccbcadaabaebdbaadeddcbeddbcedccdacaccacbeaecbdbbebecdceccecdecbacabedbbeeacbdecbedcbbdeaecedecbebcdaeebbaabedcbabcbebddaabaceaeebebededbadcdaecbbcacbedaacbdddcebadeaeaacbedecaadabedacecbaccedeaaacaaaecbeacbdccbecaceecacaabaadeddeedaedeababeebaeadbceaabbbaddbebedceeececabcabbaedebbbbaecabeeaadcbeecacbeeaeccdbdbedcbaebeabaedeccbbaedbcbecbacbabacccbacbababadebccebcbacdbcbecbeabaeccecbebceaeaaccdcabbaedbcbdbeacaecbadeabcddcededcdbdacabacdcebdecdeacdecbccddcbeacecabebdbabbbeeccbacbaddcacaceaccdaebcccaecceecacecdabeabadceecededaacbdccaebadeebeaddcabddceaeaccdacaeaeaeaebddeebeaacddcbbcbceaedabcacbdbeabccaaaebbdabecdcadbabbabeadddbdaabecebccbcceadabadacebecdcbaeceeccbcdbcadaddabcbddbaecdaaadbeeaaaecccbceaaeceeccbabbdeaeeacceccabaedbdeabcdecdeceaabeadddbebcdcbeeeddaacbeeeaeabbacbababbbaacddabacccbdecddeedeceddbdaceadadeebdcacbbdceabedcdcdaeeecbdadaaeaaedcbdcaadacedbdaabaaabeeceaccbbecccacdacaaddabbbebceedebaabaaaebcacddecdaeccbbbabacceccdcacbbceadcdeebabeadcbdeabebacddacaadccccadbaabbacadeadebcebdababceabbdeaeacacabeabaaccdeaadaeadddedbabacdcadcabaaccccdaeabeeaacbbcaabdbebacaecaeceddcaeacaabedebaecacabeadebcaeddeadbaeccdeadccdabbadaeeddddaecbddedeeeecaecaccacbdcdecebccdbabecaeccbdebacadebeadaeddcaabdbaccbdebbbadeedcdbbdaceaaccedcaececbeecebbddbabadbccecacadbcdeceecdedbbbedebedddaebcaccbcbbbecceaeaecccbababddadadbacdbdbdbedaeadacaabddedcaabcedaaedbaebbceacaedbbbdcbaaaddeadeddcceabeacddbacddccddbebbcbbaeaedcccbcaccdbdedccbbcadddecaabddaeeabceceabaeebaccdebbbaceecdeadcacdaebeabbeaedcaecacdbadbedbedcddcdaaccbabbeacdecececceaadadaeddceadabdebacbacdbcaceeaacbcbaadcdaeabbbdbcaedbbdadcedacaebebbdcceaeabdeabcabbbadcadcaaaddcddbbabeecebcaeccdebacdbccedcbedcdacbcaadeacaccdebbbbcaacbbdcbebdcedcecdcbaabdeabbacaaaeceecedbbebaebcecabccbcebedeceaaaaaadadceedcaecdcbbcaddcbeacbddeaeccccaaabeacabbeebbeeaceadaebbdeaebaccccebaceaaeadeaeadaaccabbcabbdeabbbacdbcbdedbdadacedebddbcaacdbcdeabdebdedbcaaebaeedbeddcbbdcccecddeccadeaeccdceedcceeaecedcadbbccbddcbabeedbadaaebededacabbeeabdbabdceadccaebcccbcbaeacdcbadcdaaecbebaedcaeeaddabbbadabdceaaaacababebacccbdacaadabcdabeddeedbdddbadebeaabebbcadbbdddebabaaeaaedbeabddebcccccdbaaddbbeebedbcbbabddcabecedabbaebddadebadbbaacdebdecbceebdddebdeaccbdeeecadbaaebcedcbadacdcedbacadaacddaadeabcdebcdcbbbdbeecbaaabcdbcaadcadcbdbebbabceedebaadeceddddedccdcaabebbeceeacadacaabcaceabeabcaceaaddabbcdeedbeeeeccdcdbcabbcaccddbbdcaebbbabecbebcbeddaaeceedccdbecbceaecacbdeaabdbcedbeedeeccaeecdbacbdcbbcaaaddebcecbbbedeebeeebcdbdadcacebdacbbabcaadcaebcdbcdecdacbcdccbbaecbeabbcaeebadadbdcabbaadcabcecccecdcdecdbdaeeabbdeeabbbedacddcbcaeadcdaaaabcbedcbcbbccbdbeaddaadbcebbccbcbaeeecdaadbdebcecbcceeaeededcbaaadaceddeaedcbaaccbaedcbebaacbacabbcadccbdcbedaecbdecccdbedabeaccbcaabdcbbaebbdeeedeabdebdcdecaccddbeecadacdadeabebadddceebdeccbaeeccccdedeeedaaacbbaacdbcaeeaedbbeccacadeacaccbebbceeedbcadcdaebabbecdbbddbdadddcebbbaecaedeceedbcdaedabaaceddbdcecaccecdeaadabbeddabdadddcbeeaedaeecbeebebedaabbaecdeebcecdccdcceedaeccbbdacbeeedeccccddddaecbdaccbedebcccbdcdcecaebebedabedabeaeddebeeeecbaacddcedcabeebddedaacddbabadeecbaceaccabaabcbabceaecbbeceedcbebcedacddbccebbebcbcecabebdbdcdbeecbabcaeacddbecaddaeebcabbababaabeddcaaaecddbcbbbbcdeeebdbccaabddbaeaaeddbbbdedddcbcdcbbcaecebceacebcdebaeeecbacebcdaaaaaeadcecedecbccdcabceddaeebbebebcaebddaaecdaadaabdbdaaccaccecaceebbaabccadaaabaddcbcbcaceeaccbdebadaccbaeccadcaedcdeacbaedaebcebbbebbeabedaecbaedcabecccceaddedcdbbbadaadcdcceeeeddececcbbbaeedbacdbddaadedbbeecbaededdeadddcdcccbaebbcdeedceacdacceaeabedbbedebbdacdaeaacaebaadccebbcdeeacbcdddbbbbaeeedeaeacbadebbaebadbceccddccababbddbceaabdacccbeaedcedccdcaedadeedeaadceecadaedbaeecdbadddadbceacccceabceadbeabaceeecbedbdbcdddaaaebbadaaceceecddbbbcdddddcbecdebddbabaacdadbbbbddbaadeeadcedecaacccaabdddcabcbbcdcbdecbbebedecbaeedcbeeacdecabdeaebbeeabbeeeadbeccbcbdecdedcdbdebddccdacdeddccdeeeeecbcaaececdbbeeeaacebeacdcecdecbbadebaabadcaddcddecaeeddebdbbbabbabedbadebecabbcdaaababcdeeacdeeebacdbadddbceaadeacdcecabaecadbabcbbbbbedebcbbccaeeeceaaabcbbebdeecbedbcacabcecedbbdeaedebaacbbdaeadabbeedecceeaabecaecbeccaaddeaecdddacadcdebdcbbbadacceddbdcbbacdcbdcddbbabdcbbacebaebcddaecceebdaaeacdbabbbcaecdcdddceeabcaccddddccabedadbedcbebabedaebcbcdeabbedacbdaaeabbabaaedecbbdcdccacedcddceabbcddacebbceeadaabdedacbdbdcdecacebedeebdbaebcaecdeacaceadedebcccadcbbdedacdcecbdcabcdacabeebbdbadadeeaaaabbbeebdacdbeacabdcaacdeacdbcabaedbbececadcdbdebaeaaacbebbdaaccbeedacaaabbbabcaeeceecbcaeacdedecedcadbeedcaaddecdadddccaecdeddacacbbeadaccdcbbccdceccdccddebdcebaecbceadbbaeebebbdecccdedecdbcccabaadaceacababcdcabbeccdbeddcdcadebcaceeaadbbceedcdedbbaaebedababedaeeabebcddeedddecddbedebdbaedaedcaddbeebbdeddeacddeaeddabddddeeecdcddcbcedcdeddbabaabeedddeaeaceacabeddbdaaceeedbbbaabcdcabdeceddebbbebebabeeaebdadbcdbaccbbbcdacdddbeddbcacdbccbdeeeceaccededdaebeedbeecaeccddaddaeacbeebcabbdabececbccdaabbbebdeeacedadbeadeeddabbaccbdceabdacadcbdabdcdbdcddbabdeecbededcabbcebabeeeaecadeddddccedbaadaddaebdabdcbbdbdcececaecdecdceebaabaaaedcaebadeeeabdbbcccaeeebbcaeaccedcacceedcbbaaeadaacdcdbbbbbabcdcebccdbbcdbebbaadabeddcaeeeaacadbcecbeadeeabdebcaabadeaacbccddcadbcddbbeabecdbdabdbbebdeddeceacbdcdabdbcdadbbebdbedaaabeaecdabceeeaeacaacdaabedcdaaacbddeccdaeeeaaecaaaadaecdcaabceebacdeccdcedcebdbedeabbddcedbcbcbbcebadeeddcdbeccdbacabbcebdabaceeddbdadedecbcecacebebaecdabaaabdaadeaeaadcccdaaaccaacdbbdaeeacaeedbbbaecaacaadabbdccbbcceaedbeeabbabececbedbbcbebebccbdcaccaebdbcedcebcdaeaeaedbeacbcdccbdceeedcbcdbbaebeeebceaacaeeeeaceccccdeeaebeadcbeedaaabdcbdbacbbcacecbecedbedbcceabacccadaeaacbadbbddeeceedecbeeddeaaedaeecedcadbedbbceabaaccebddddbedccaadbeaabbdbbdcbdcacebdccebdddeadbaabbdbdecbcbbdbdabaeeccabcababcbbbabeabbccbceceabadccacbeccdaabbdcaadbbdcdccdeeeaadcabdeedebeeaebccdebbcaacbaaaccbdcadbaeaeccbaccddedceeecbeceadaceabdcdbebaedceadaececaeaaaeeddecdedbedbbbbacbaaedecaaaabbcedabacddaaacdabcbbdeaacbaebaecdcbadcadeedbcdcaeaeabddeaecccdabcdbdbbcedaddebcaebbeceecaeacedaeaccbccececdacacdddcccacbeeddbbdceaecebceceabadaabbebdcacedcbbdadbddbaedeedcadaeeaddaebabaceeceabeeebadcabccdedabacbcdcddacbdeaabbacaaaceaabceddcadcaeaabbaedadcaceeeceabdebdcbbebccebbebceacbacbebceecbbcbccccabacccebeaecdebecddcdeaadcdabceedccbebbaceadddecbaecccbdccbbdeacccbddbebcaaeedeeaabadeacdedcabaaebeecdccebebcadeebddeceaedbebebacdbeddbbbeeecdeedcceabbabebdadaaeeeecbbededcbacbdadddbeecaaecbcacbecbccbeccedebdacbbcddadbbceacbbdcdbcbbeedbeaddadaccdeadbdcdebadcaaaabadaaccbaebdaccceccdbcdabaeabecacddcbccabedbbdbbbaddbbadcadacabceaeebcaeaeecdabecbabcdcddcbcdbaaadeeaadeccceadbeeaebeaabeddbbcaacceeeceeddbddceccddedaddbbbaaacbdaaedbaddbddccbdbddaeeeabadccadaeecabddccabdbddddedaabeaabdbacdcedbabebdcaaebbbbdbbabbaaeaecbedebbcececbebdaabdeaadbccceaddebbaeadaadddacecbcdbebdceadbbdbcdbccbeeaaebceabcbbbceaececbbddeebbbdacddaeecaabcacaaacbceabcbedcbcedcaaaceabcbeddcbdcaccaceceeeeeeeaaaccbbeeecbdeacaecaeaeceeadbadcbcbcebaebccaebacceddaeeaacedadbdedebccbcbcdabeddbdcbdceaaecabecdddccddacedadedadcaadecadceabdceadabcabedccdceadbabecddbeccbecdbdaacaddaeaeecebacddccbbaeacedabedaaeeebabdbdccceadeabcbddeeeacbdcebbabcdecdacabddebaeddaeebeddacdccbcdbbebedbcbbebcebcecabbaedccecaccbccbeebdbccdcdbaccdbacbbeddecaacccdabbadecdcbbaaccecabbcdaadeeddcbcccddaecdbbebaddedcccacddaabdeabeeaaccdceeadbaadccbddbdbeaaebeabdaeeacdabbbabdcedbdcebedcbeebbbdbccbbeaaadcbaecbeabdccaedaeecebebbadebebdadeeaedddeaebacabbcebbbeeadcbbeddbdabadccdbaaccbeddbbabaecebabcbddccccbbebeeeaadedbdaecbbddcbbbecaeceebeedceabcedbaaaddbeddddbebadecbadcccaedabddeadccdabaddbdbadccbadbdeddadeeedeaedaeccdeaddabbaaadaadbbbcbdceacbededceddbdebedabcaebbdacadcddcbdccbccdbbebdbddadceecbaeacbcedbbabdbaccdaeababbabcedbcdcdbceddbbbeecebebbddbcabbdacdaddccccebddbcccecdbbddeadbeddbceadcecdcacecbccbecebddeabcebcaebceecccbeabdcedebcaddcddecccbdcddaceaececeaebcdcabaaabedadabbdcacdedcddcbdecdcdaaabdddeeeceabddadeecddedbabeaddbeabdddacdbddaaabbabadddccdeeccbcaaaeeaebdaeacedcdaadabdabddacaaaceedaadbbedadeacbcaccdbcbddaadddaeabadcabddedcbaaaaaebaaeeaececbeadaebeabedebbbcdecaaaeaaceccecceeeebcacacbcddddcbddbaeedabaeabbdaedaecbceeebaecbeacbeeecaadecbbadabdacaacedbabecdbbeddedecededbeecacabaebcbdedaedcdbdbceacdeadaedebececacaaddebebeceeddbcacceeabcaedbadbceedcdcebdeeddedacebacebbcdadcbbaacabcacccbbeaeaeccdaccabbbedecdadbdeacbcabecbeaceccaddaadbbeedcbdccaadaeebeaeecdeeecbeabcbdcacedaeacbbaadaedaaeaedaccabcbdbbddeaedaeceaaceadeedabebebcaeebccadbadedbbecacdbdbeecedcbbedababebaaecededebdaceaddeedbdbeceacbdabceaadabbdcdeddcaaadebbcabebcaacbabdeabcaaeecddddecaaaebadedbccceeadccdcdbcabdeccdecebdaadeddbbacdedbeeccbbcaaecbdbeccdeebacbadcdbccadddeccbacdbdaaabcedeeabceccaecebddedeadeabcebbdaadeddcbceaccacebeaaeedeebebdaabaaacedaaadccdbbeecbebebcdbbcbdddbaacabdacbadeeacaacaaebedbbabeaaadbbceecccbacedbbddcbaebabebcbbbbbdecbbeebeeebaeddeebbcbdacedadbadbdaeaedbbecdaabdadbccecacccbaeeeacbecccaacdacbdecccadbebdbeeeecaaeedcebdaddcdecebacedabcdccccedcecebbceadbaabadacbeaacacaddebbaaadddacbacdbeebabcbeadbdbdaccdabcebcdbebdceecabeecdedabdeddedeeabdadbedcbaebdabceddcaeabebbbabbbceeebedaeddabecdacaeadcceadeccaeeedeeacceddcededbebeecedaadeabadccabedbcabaacdbdebbeccedbadaaaecddbeccecdbabcecedebeecaabecedcdcbbcdeaadddccaedeaaedeceabcaaceeabedecbccaaddccabebdaabecddcdacaecdbcbdbdbedeabeedcabcdbeeaecdeecaeebdbbdeaccbabdddcadcebbaeeaeaeeaedaacaacdabdaaddbdcccdddebcdecdaeccdcbaecaacccebdedeaaebaddabbecedecabdecaabcdbceececdaedbbbeeddbbbbbacdacaecddedebabdaaccbbdcbabbeadeeddaabdeabaccbadddaebbcebbadaaaadebeddbcbeaeccdcccdaacccbbbaacaeebaccecdbbaaeabaabacbdadbecadeaaecececceccebdbadeadaedacacbdaeabedbebcbcedecaceecccdcdbbeecddbccdeabdaebcbaeecbbbeceabaedebcdadadecdbcecedbebedadeeaeadddaeaceabadadacecceecccddcdaaeaecbacedeaaebadaeeabccaeabbabdbadcbdabaaebbcccebcacaadebecdbdeeacebcabebadacbccdeacedacaabbcbccccdcbdcdddaabdadcacccbabdbaaadeecceccdadabbbeaceacaadcdbdeeecbaebedddbdacdceacaabbaccccdaedadddadaabcaccbebbcbdeecbdcebcdedceededdcbecbaccbabecacbdedbdddbcadbeebdccbbaadddbbbccebbdcbccccaacddaedcddccaebbacdddabdbbdbecdbcccbbaeebcaabceccaecdbabdaeeceacecaeabdebabeadbceddcccbccecbcaaddacaedbcabacaddbbbebadacccbeaddedabaeedbdedcaccbaeeaccbdadabaebcccbdbddddecdcbcebeaaaaaacedcbedbcdcdbcbdedeeccbbecedaaacacbeabbadeedeaeedeceabacdaebdbddcacbddccababcebeecbaeaeddbebaccbbecbaaadebedbadebedecabadaceeceedcaebcdcbebbcdbccebeecadcaeaabcebdbbeeacbadbcedabbcedaceebdccaaededcadceeecaedcbbdedbbdebcdabebbecceeaccbdcedeebaeddedbedddcdaebeabcabcdacebdeedacdcebcacdcbbdaaeacacdaebbeebcbacaaedbbcaabaadccbadedcbcabedadacbdbbdbdcebbcddcecaeaaccddbeadebeeadaddeebcbbcdbeddbddccbbbbbeeacadeedceebaacdadccabaebdbdaebcbabbeeacbebcddacacaecddbeaedaeeabbbabbbcbbbacabdbeaceaddbeadacdeccaadbababeebdaadecddeeeabeccdacacadccabdebabdcabbcbbbacbceebecbbdedebacebeaccecbebcdaeeecbeddceacddebdacbadceabeeacaceeccaececeaaeeebdeaecbcdcaadaedbacbacdeedaacdabebaddabadaaeaceedbdacceecccacbceedcecddbdeeaedbbbabeebedcdcccddeadcbbccdbadccbbededdcbecedeeeabeacaaacbbbdeadeeeebddccaeeebaeccadbbdadcedbccccccecdbcedaadcbceedecbaeaebecccedcdbacccbbdcedceeedcedeaabcdbdaccddaabdddadcddeebeaebccbdcadacddadbceeadeccdbcaccedcceedbcbdaebcbdddcaaebbbacacebadcecebbbccedcaccedaaecbacdeabdaacdababacbbebeebeddadaedbdbbbcabcebdbcebeedddebdadaeeeaedbcbdacecebacbbcabdddddbcbeeacbacadeacddaaceaabcebeeaebceaeedacceebbebadbebaaccaadcdabadacebaeeadecabcaeabccdedadccbebbbcdbebaecbcabaacabedddbcdbadeecbcbbeeaebcabbdeabeaedbadedebeedcbdceadcaaceccebdedeaecbecdacebdecdedbeeabdedbdecbebbabbeeebbcadcbdecbcaaebacebedccbcecacaccdddcebdadebcdacdaacbaddcbbeacbdddaedbbdbcaeebaaedcbbccacdebabcbbbeeeebaddaadaaeaeaeacdeccbbdbbcdeaceeaabbaeaccccddbcdbabdbecdaaebebcedaeddacadaadedcdcddeadcaeecabddabcdeaeaddacbddcceeacddeedbbacbbaaaeeecddcccdbbcdaaebbedeabeebaeaedebcddbebbcaededdceebbeadecbaebadbdcdcbeedccacaeeeaaadbcccaadbbeccccbbccbabaecacecbcecaeccbbbaaaadabcebcdeadbeabbbaeedbeecbcecdbeeddcaeccbeaedcdceebeedddcbddddeebacadcddadebadeeabeebcbbcbcddacbeaebedcadadacbdacdaabeadcbaecdcbaebadbecdeaedeaeaaeebacedddceeecddecedabbeeeaadaeeeeedcdddceccbabaedbeecbceeaecbeddacbdbbcacbcaebcedebacadbadedeaacbbdaeabbdbccdabbadcdaabacaebbccaaaeadacadebeeecabadaadeddecdedbcbdcabeacdbccbebdebbbbacdacebbdecbdddebdbdbbddaaebdeaccddabcadecabddddaeabababdcbceaaaabaceecceeedbeceedeeadcaecaaadbddecdedebeeccceddabeecabdcceeedbedcaccebcddddeecdbdacccdcdceccaebdbdbbebcdebadcbdaeddbacdabbbbdabeddceecedbaadcbdbcbbeccacdcbeadeaaeeadccbdcbdbbbbdecdddddddacddabeaadcccedebcdcbecbaeadabccababbbcddaecccaaebabeecbbabdadccbbbdabadebedceecbeaaaccacccbecdcadddadebdebadaeaebceedeccacdceeeaeaedacabbddbaebdccdcdebbabaecdbeeaaeadeceddcabceebeacadecdaecdeabddcdabbddecbdbdbecdedeedeccccaaedbcedaaeaddceeaebadcbbbdccbeecbdcccccbecbeddcabdecbbecacbcbebddbebbdbacbacacaabeecddbbbdbedbbebeccacccdecddedeacbcaadbbeadbabcabebaedecdaabaaedccedbdaaeaddcdbbcaddaacecdcadaecddcccbddeaccecbebbcaadebeacdbceeaedccbeedaaededbdedecccdaeadbeadccbdacbadbcccecaaaeebcddceaaeabacaabbebccebddcadddedbabbbabdebeeeecdbebbdcddccceebbdcccaadbebedbeaccebdcdbdddecdabedccdbebadadbceaaaeebdcecdcacbddcdeacceeabdcbbbbdbeecbdbabebecbceedbaacacaecaaddacababdeebacdbacadceaecbeeaaabbbccacadacbededdaaecbddebdeccadcabeaddcbddbeaababdcecbdeeacdecbedbcaacacdbeebbbecaccedebcdecadccbacaeabdddebaeecdebacebdacbcccadbaedacdbbebebccebedbabbacdeddedbbeadeceadbbeaeeabacaacabaaebeececaacaaeaebdaaabebbbbaebeacdcbbbcbedaadebecceecbcdaddadeaadaddcbaabcecadaacbeaebebabaeacdedaaceecdadedaeaedcceecbdcdebaaebbdaabcdcbeaeaadaddbcbabdbcebbcacaebdcdbccdaedabddebecedbedcbdceeebbbbadaddeebabeaceaabadbdbbabbbedebbedaaaabbecddaccaeeeeeaeadeeaecbbcdabdbeccabaaddccaaecaaccbdeabccdcccbdcaddcbcebdecdacadeccdcdcbccbbccbecbccdbbbeabdbddcbaeeedebccccdbabbcddcebabadebdeecaaeadebebcbcdcbdcaeebbeadeaababeadedbcbacaadbeeddebcaebaceabbecacccbaabeebedbdcdcdcebbeceeaeedbdcebbcbedbcaabdccdcbddcceccebeaebabedacebaedabbcbbbbedbcdacbdacdeeacdabeaccdaabccceaadeecbdebeadaadddbdbbcaccccdbabeaaeedaadcebbaebaaccebbddaeecceaebadccdaeebdbdceeeadbeddaeccaeeabaddddadeabceadcaabbeebcceedcddecceabcaecaceedaeabbacebddcadbcedcbccaabaececeaacedcebaebacdbedabbdededaecedceedadbbdaeeeeddacebcbacceeccdecdadbabcdadaccdccccaadcaddebbecbdabacaeeadbbedecacdeaccadeaaecdcbdaaaabcecbdcbecbaadeddbbceecaabbebedcaaeabbcaabccbdbbcedacbdeccddcededdbdeebaedabdceaeedddeeddcbbebdcbbbcaeabaabeabdaabbdcbbadbdbaceebbebcaaccabeccedddcbbbacecbdbedaadaaeaecacdaebaeacadbaacccdeedcaccbdcdcacbdcaabccdabcbcededdddadecaaccaceebcabcedadbedccbeedccabacdaeaaacbeccdceaaabbdaccadaeecebeccaacbaeaeaecdabddcaddceedeceebcbdcecaaccecedddeeaabbeeaaeedbecadedeeabdbeadcaeddeaebbbbddcaddcbbecdddbbddeaaadaaaaeaedcadceceadbcdbcabdebaeddbaecebaaabbbdeacecacdeeeaadcaadaccdddedbecaaebbdbbecdaaeeaedbababadbddbdaabacdedeeebbbbeabebdebddcaacaeecdaacabedeaddebbcdaecbadacbcdddcaacbaecdcbbabdeecceeacaacecdcaabddaabdaeedddababdcdaeabdeacaedcdacbecdceadcaddaebccaebdebecddcbeeeecddebcaddaccebbecbcdbbdbcdedeaceceeaeeaaacdeadbebbeeadaddcddaedaeddcbbcccaaacdecbeabdabebbcbaccabdbaebdcedaaaceeddceacbccabaeaecbebcdbadccecbebcaecaccdadcebdbdcabcaedbdcbbebabbcbbdbadeeccbcaabbebcbeabddccbeeabaccecbbbbaaabddbadeaeacebddebacceebcacaacacbcbcdbdabbcaabeddddecbaadbcceccbceeaabcbcabaaeaedcebcaeddcbdaebdecbecaaecaaaebdbbadbaceaadaaaddedccccbbaddcebdeacedbbbdbcbacdddebeadbeacdedccbcecddcdecdecdebceeacddcadaddcdbcbaebcddabbceaccebacaabcbbbebcecdedadddbbabeacecdbcbddbebbbcedebdecbdaabddacdedbedbddbbccdbaabcaceeeeebeedabdaccdcdbdccbcddbcdcbaccbdbdaedbdadabebadeeaccebaeaadcbaaaeeadceabcbcaabeedcebacacebadcedacadcdcbccbecabdabdaeccccccdcacbdccdaeceadddeceebcdcecabdababedbcaaaaedbbcbcedbdbdaebedbebebddbeeaaadbddaebeeecbcbacabdbeeeceabebeadbaaceabdbeacaabededdedacdaaeabcabccabcdcceacdedaaaedeeddeaebaabcaaeecbddccebeccbedceddbadbdeebdddeaeecaeacdbddeeabbbbebbcbcdbddebedddabdbdbceedbadeeddcbbcecdcadaebdeabdccddddeccdcbceaedcccaebaedadbcedabcdbcaabeebeeedecccadcbaeabbedddbbaabadddbaacbcbadddebbbdbadbbdeabdaaacabebbdceddeeedeeaacabbeaaeecebadbbbabacbdabeedebbcaebdccaedcccdeeaaddaaebaabebaeacbdabcacbdacbaacaebadacebcdeddbceaecaecccebaeeecdbeaaaabceecaaccbbceeaadecebdddebbbeeeebacdbcddbdcedebbeacddbcbabcccddeeaecdeaadcdaabaebbedbadeaeabcaaaddcbcdaaaabeddabdcadbbaadecdcabedbaaadddabbbecababbbbddabadeeccaeceacabceebaacebccdcbaecdbdccdaedeeaddeceaccdbaadeebddbbeaeaaacdcdcaaaadbabacaaaabebebeebeecaeeaeaaadccddbccdbddbaaceeabcbedccccaebabeddbeeaaddacdabaeebeabebeebcdccdaaeaedccededcbcbecccbebdeeccbeebadabdabaceabdeaadcabdcedcdcecbddedadeadeadeeacecccbceadddecbdedbaaebcdecdaccbaceacbbbdccdcdcececdadacbabdeddebcbdcadbaebbbbaaeadceebcaaddaaaaadbabaebadaedaabdbbaacbbcbceeddbbbbeeeddececaeaedbdeceabcebaaedcddbdcbabbcebdaceccbbdcdcaedebdaeaeaaccddecaeadecacdebcecbeacbaaaebebcbccaeddbeadbcbadeabbcadadddcaebdbdeaebebeaacceebddbdddcdcaeadabddeedbebaceccdaaaaddcdaaadabcdababadbedaebedcacddebcedacbdbaabaacbeacdeddbcacadbcbcbeecdeadceeaebcddbbebbcdbbbbdacbeecbdcbbedcabdbbcadaaceebbbecebcccadccbdeceaebecbcbeaceccebdedbeecadbcbdbbcadeceacccbacdeabbcbbdadadeddddbcaddabcadcebdbbbcaebebeabecaedacdaecdabdbcdebbabeacadedbcbbaecabaabadcaeacbedbcbcaeeadcceadbbcabbcbdcaeedbdacddaaddccdeaadbaeccadeabcadadbdccbbccbabcbeaddaecdecaecbcbdacadabbdaddabddadaaacaadadaaddaeccbccaeecedacaeeeaebddecdbcdacdeccacddcaaecbaeddceccadaeacbcdcbcbddecbbdadbdbdaacbaeedeccadceacbabaceebeadaaddcdebaddbdeeceaeeeceebdcadaebbddabcbbecbacbdbbecbeeceabcabceabcdbdaebdebcceceddbeaddbddbeebecbcacaabeccbeddbbbbdbeccecbbaebdabaeccaaeecaabeddaccaddecaaabedebcdbdbeccecdbaebcaaeadccadedaaededbaedbeabcaadaebdeeebebcaeadacbceeaacbdcbdcecbccbcebeaaddaebaddcccbeaaaecbddddbdbbbdedaeddceebbccbaaebecbbdcdaacbdbccabebaabdeebccbcaecaebdaabdccabebbbeaecedaeecdececabbbaceabadbddaebebadaeedaaedaecbaaeaacdacbacbdbccaddcdeebeddddcdaebecbcdbaedddaabaceccecedecabcdcbdacccbdddbddacabcdbeadccccddacacddaacacbaeadbdceabbdddbaceecebcbaeccedeecbdbecbdadbbbbeebadddbadbddeaadcbaccdeccceceabdacbeecbabddbcdcccadcdaaddecbaaecedeecdbbdceaaaaeeabbedcecbcaaeaeccedbacabcaacbecccaeabaccaecbabbceebdbdadecbaddbcdecabeeebabccceccbaacabcbadabadaadabeaadeadebdeeaeeeebdeaeeddadbcddeeeeaebeeeccaeaeaddbebccdbdccbcecedadcdcdedccbaebbeecbaceadecbeadadeddacdbaeacdaaceddadaebddeaabceaeeacdbbbedcaccbbccdeaaadebeccaccecbcdcbedbbcadaceadbdabceebdbbebabaeceeabbaedaabaeddedaccddabeeeddabbacbddbeeeabbeabbecbececbddebadababdbabbbdeeabcceccaadddcdebeacdbccbadadddbacebeeccdabbddccdcbdaaadedbecdeeddadcadbaddcebbdbbbbacedbedbbbecbdddbeeaabbbcbccedbecbdedebebeceaddbeacbbdebeaceadbeeaddcaeaabeeabecedbceddbedcbcdbdbebcccaddaedadbcdabadacabaadcbacdcecabadcbdcedbbbbeebdbdecebddabecbcaededdececcadbdcabaaddebcdccbaaebedeaeddaecdcdedbcbebcceaedeeeeaddecaccccaecceeeeebdcbcacceeaeccedccedcbabceaeeecceedaecabbaacecbebcdaebbaceabbdaedbdbeeebeebdbbcadccdeadacccebbdaeacecbecabbecbadecddeeaabeadbabedaeedcbdecededbeccdbacbceadaceaccddaabdeadceedcaabdbaadeaccbdcbdeaccbabceddbcdbcedccdbeeeccaabcedbbebccecaacccbbdecedbdcebabacaebaeebccebaabbacddebcadbbecdbddcdcbeccdacaaadddbaeadeebaadebaeebaddbeeabeceadccceebceebbdbadabaecedbbddcddaacaaacdcbbeaabdeeeabbdaecbecdabececbacaedbabacccaebacebedaccdaabcbbeddaccbebecebdacdcccccbbadaebbcdaabecbabaaaccacccebedcdeeaaeaecaccdcadaaaaeadbcbcdcceebcddddeedccadedddcaeccaeaeabeadcddadecabcabccedecbbcbcbdecaceaacdeeaececdacebedadbeebeeddaadbdbadbadcdceeeddabebbebddbbaedeedcdcaadaacdbebeaececeabcedddbdcaccbeccacbadcabbaccdacdadabeeedeedbbcdcbdebdabadcadbabccadbbcdaeacecbddbccbbaccedcdbeeebdebddddacccacaaaeebbddecebabeecebdcadcccabeadcebdcbbdebcecbabbecbdbdeacdccdaddeabcaaebebdbeeccdaabcdebdebececdadddbdebabaebcdcdcbecabccdccbcbeeaccddcebeeeabeedbeccaadceebcbbcddabdbcbebedaabbdddccdcebeedeeaadeeebdcccaabdbebcbdcccbeaedcdebcdaccebaececdbbedeaaeddcbdaeadaadceeacadddcbacbeacdedeedbdaadbaadcaeedabbadcaeecdcdcddbddbbbabedddbecbecdebbbeacccdbcecbaecbedbbdccadebcbbccbdceecdedbbecdedabbcaddabbebbadebddccdcbcccaeaaecdeeedddcebbedbceecabcbadbdcacaedbccdedcaaecbdeaedccbeebbecbbbbeceaabdbceeeeaecededadeccbbaabaaacddbbaacceacaabdbcebceecbccdaaebbcedddaaccebabbaebcdaaedbdbdbcbbddeaacadedccbcbecdddbcdcebbaccabadddcbadecedbecbcbedbbaaaadeaebaeadaeeccbeabedbbcacedabdebeabcbdaeecaeddaacbebdeadeccdabeddeddedeadadeaabcbacabbcaedbdaddddedacbdaeebabeaeedebaecebdcabadceccadceccdaaebcbdcddebcebbbdcccbdcaeeedbbedcdebaaeeaeedcebaeeddcbdaccadcdacbadeeebeaeacbeebbaaeebbebceaeedaeeddedecbdddcedceeadccaacbeebeabaacbcbddeeccbdeeabbddabcacaabccacddbacaddbddcdcccaebdeeaceddedbebdeadbddbdecdecccbaacaeeddbedbdddeaaecaaabcccbbadeeabaedcebdbbebeeeebbbdccbdaabaeccdecbdebcedebbdcdcdcccbbdbccebbbeededdeccbabecdebbeeabbaabaebceeeccbaebddaaecdeebbaecbedbdeccdbbceadbbaddaedceeaabcbccbdbebeacdebbccbbcbeeedabaebdbadbaaeebeaaabcabecdccbcdceadeccecdccbadabbecedbdaeebabbeeeaaecaecbdeadabceadbbdbabccabbdbeaeaadbccbbddeccaaeecdbdedcaeebdccbadaccecccaedbcdbbbbbedccabacdacdcedacbaedeecddbedeaebcdbcecaeeabaeadcaedbadecebededeaeeebdcbdedbdcecedecdbbcabecacdddeedcbddbbccddecdcaaabdbcbdbeacabeeccdacbdaedaeaabedeececcadaeedeabbbbcddeedaccceaebcccbbaccebabccaaadddaddedaceecddbcbedcdecbadcdbeeabdbcebcadacebeebebbbadeaeadbaccddcaeeaacddeadeabdcaaeebdaecedecbaadecbdcdedcbdbdeeeceabbaeabbbaeebaacaabecddbedbaccaedccadaebbdccbeedeeeeabbdedddddbeabeecadebecdbcdbbdeaddacdedbddaceadbdddececabadabcccbacbbbdbcceddccabbeebaabbbdeceadecbacdccbebedaecdcbaddeecbacdbcaeaaaebadabdbeebcebabbbceecccdaadcecdbdbececccdadecbecacccadbbdcbeedcabdebcdebbbddcecdbccecdcccdedbeaedebcbdbeadadedbebaacbdabdbadadceaadbcbbaabbaeebdeeababebdaaaabbcdeeccddeccbbebebddeaecddbbecedbdbaabdbbdbeadaeedbbddcaeaecabbdcedbadabebdabeecabbadbaabaaaeaedeccceecedabbeadadaecaebedacbcabdecebeaeebcabeadbdacdcdeddcdcbcaeaaddcaebedeadabbdcbabecaeeaedcadcccdcaedabeeeaadddbcbcbaecebcaebbdeabbeebededededceabcdaddcdcccaceeaacdaccaaabecacadadddbacacbdaaccbdcaccebbcaaabdcbecdbecaaaadaddbcbbaaecddbeadbccbeebbbbcddedbaeeacaabaaaecdcccbcebdbbbcebcecbdbcaacabdacaddaabbaaadeebabdeacccaacbeacbaacdbbaedcbbdbaecdcdcbcebcbbbdcccbacacddbcccdbebebdbbedddaceabccccaaabadcadabaebddbbbeaedabcaebdecacebeeaccededceaebeeacedadbaeecbcceaeaddaaeaeccaceaccdbdccebddaaeeebcddabadeccbddcabceaaeedbdabeeecbbaedaeebadccebdbdacebdbbbeadcdedbbedaadcdeabbadbcaebaddabacbdcadbadacebdccdabaedacdecaaecdcceedcebeadbceabbdacecccacdcacbecacdedebecbaddbccaedeacbaaeebdadbededdddebeabacedddecaccceadadaeecedacbeccedbebedeeeacdacbaccaccacebbcbecabebdecadcdcbeeaadaabecdeededdeadcebbebaadebeacdecdacbdcebbddbcbbbabdcaeeeddaeabedaeeeacbdbeabdbadbaedbbdccdabcedcbeeabbdaeaebacaaacbbcbababcbeceadaccdddceccaebecadeaaebbebddbeaccbdcdabbbcbbacadedddaaeedcebcaeabaeacbedbebbecdadceedececaecbdccaebcdedabaacecacbcabdeaabaebeddeedaabebcdddcdecdddbebceacedabbdeacebbacadeadedacdeeebeacdbaacededeacedcecceaacdbcdaaeadeabdadcdacadeaaaddaebbebcecdcbaeaeaecbeecbbaadeedcccbeebebcccecadeeeceadbdabbabeadaaebbbdeeededebcdbabedbaebbdbeaebeeeecdbccaabcbccaaaabcdcdbeaedcadbccedecaddeabddedbdedbccabddabababbaaccbaeebbacbbbdcecacdaceacadaecbddecebebdabceabeacbdeeacbbadcedcababebdeeeabeecceadaeadcdbebbbdcabbbddecdbcdcdaebaccdcedbcaabbabebacabecdaaeaeacbbaacbddcabeecbabacbbcbdddabecbdaeedacdcabbbebcbedecbbeedcbddbceebbdbeeacacccedaeadaebabdabbbddbbbdecabdaeebdddcbdbabbcdbcaddbaaaebcbccbacecceecdacecdcaecbadebeaaddbeeabdbbaedaedeeabbeceeedcbdaecdeeecbccbceedebcabecaadebadcedabdceedaebbedebddcdebaeeaecdacadabaceedbedddbeadbcbabcadcecdaabccbabdbeacabeebbceaccddeabcdacbebceeacebdabebabcbecdceccaaddebaccdbdcaeecedbdbcddaacabacdbacbaacababbedaecebbbdbebeebeeeccbaeaebbacbecebdccdbeacecacadceaceeacccbaabbebaeecdcdbcacadaacbabbabbabecebdcaeaeecaabccbdeebddeaceadacddadbbbbeedaccdeeeeabcbabbddbbebbeaaaedcdccbdbabccacdcacecaabcddeaabbbdacdcdddbcdebbadeebbbbadaeecbeadbcdbebacbdabbcdcacbbcbcdddaadbbaedeccbecbddaadaccaedbcddebaedbaacdbbaecebbcbcbbcaeccbaaedaeadeaddddbdabecddacaebedacaeceeabbbbcdaebbcddbbeaadcdecdaaadebcbbdedccaeddbdecadddeceabddbdadbabdcdadeecaabebdedcbdceabdccabbdcbacaeacbeecdcaeecccbcdcbadbcbbaaedaeeecaedecdcdedecdbcaadebddbdaecdabbcdbbacbaeeedaaedbcbddddaceaeeaadbccaaeaaaeedddcabbdadadbdedcccdeddaadeeeaaadbcdbaaceaedcaaacdeadaeabcccdecdabcaaaeceebaaeedaeeedbbcacabecaadedcaedecccaaacabaddccaedacdbbaadadcabdecaabccceddbacbccbceeeddcdbebadbaddceedbacbcbdaeadbeaabecddbbdeaaccabbcceeadbcadeeeebbdbadedebabaeaeaccddbeebdbaccbabadddeeecdbbebabeaddbcbddbcebedcceebecadeaacbcdedecbcebbbedceddeabbeaaddccbaabcbbdbbeeecadbcaecacaedeadbeddadececaaabaeabababacbdecbabacdbaaaacddecbcabaaceecabdbeccdbbbdaaddbeaedcedcaedccadabadaedbedbdbbcbbcadddddcbdbddbecebaeeebccddacebbcbedadedccddbdacbebeaebcacaadadebeeeeccccbecccdecdbbdcdacbccaaadcbdccaeaeebabbceaeaccddaadebaaddcacedeeccacaebeabeaadbdadaecaedeacadaaaddbcbcccdcedebcdcbdcbdbdaeccabbeaabecddebdccbcededdceedbcadcdacbececbcacbdcccadeccccbdbbebaadcabedbaababbebbacacabccbedcdecccbbdbadbadddceccdcdeaeababdaaeccdaccadeecccceeeebcabeecddbecddaceeeaccadecedceccbbecdbadcbebeadebdacaceceadcdbdaeadacaccddecaadadaadabbbbcdbedbceeebbbadcebebcbaedeecaedbacaecededcaddecabdeadbebdbabbcdbcbeacecaedcdbdcecbececdcabdecebddacddaeebcadadababdecddbcddcebdaeceeadcdcdddaadebecededdeebdadaabaebdbebbbdadcebcaacacbecceecddedacaedaddedaacdeebacedeecacdaaacbededdacaacaaabbadcebdddeaebecccdeacbaacebcddbbddadbeabdddeeaacadaedbcebaecbaedeeeeabdedeeaacceecaacbebddccaecbadbdccbcccbbeeacebddbdcbaaacddbbbecacdeccdbdcdaddebaacacbdbceebdabeccaaacbebdcbeabbccddacbeececbeaacbadedceedbcbbbdacddbbacbedaaeaaebbbaabddaaccaccdbbdbdeececebcaeecbebedabbedbdcbabcabedaeeaebcbcaaeabadeadecbebcaaaaaedeeaaccadacedbbdbaebeddebcaedbadeddbbecabbebcaeebeccddabcaeedbbeecccbeaeeaacddacdbdedcaaebeabcecccbebaedecdadaacdacecaccedcdecdaaadbbbdcdcbbaedccedcababdcaeaeddecbccbecedebbbdccbecbdbacdddacbbadedebcddeeebbeabeeccccceedaaadddeeeaecddaaaebccebddaceabcdbccbebeaaccecedaeeacceecdadbdedcccdbeabebaccebeecaabdbbdcacacadaabacceabbecedcabaadcacbbbeaaaccbebcbeceebccceabcddcaddcdebbbeaaeaececbdceacedbabeceeeecbedaccbabeebdddbabbeaabebecdaccdcbacececdceecbbdaebaaeadbbcadedccaeabcedceebddadaeecbcabbaedabcabacccbadedabadaddaeaadeacaaebcdbbebacacdbaeadcaeccbaaaabeabbcccaccbedaabaadaaeebbcecaabcbaaeeadbdeacbddccdabbbbacccbcceccdaaadceadbadccecbcdbddaceccbdeaeeedcccacdbebedebcaeeaebaeaedbbcdddccaaacdeecdabececbdcdcbaebdeedeacedaabcbdeebabbcbcacdccacbedadebceeebccbdcccdceadabbeeceacdddbececbbaecaddbabbdccaacdedecaadcdaeebaeeaeceeaaacabeacceedaadcbaaadecdcadbeacabdcabcaadeebeedcaaacbaadddbbaaebbeecbaedaaedccdebcbeeaeceeeeecddedccbbdeaebcaddcddabeaceecacdaacedadcabcbeeeddbbedceeeabbedaeebdcddadacabbedddbcbcadcdcecdacadeccddcdccdbaddcacecacaaaceacbdbceacaabeaeadcddedceeccdacbdaabdcaaaaeedbcaacadcaceddeadceddcbdbbebcdbbcebdaaebdeadabaeeceeaacbcbdcddacbbdaebbbbbeaaebadebeeacebaacadaecaeaadcbebadebaccdcdcbbebbedbcdaaebbabcebdacebddbaacdaddacedcaeeebbdaebdacccddadcabacabebebcdccdacbdaeeeadadabebdadaebdeaabdeabdacaeaebdeeaeeacbdabaddebbcaccaaeecbcbcabeceaceaadadbeebbdbaebccbccdceeebadaedbdcdaccaecaedbaeeadcecdcbccdecdeadebbeababdbbeebaadeeedcbbabeaacacdbdeeebbdaecaadeaedeebcbdddaceedbdddddebcaaebeeaccedcbebbeadedeededacabaeeebeeaadbecbebabdcdaabbccacbbcabcceecdedeadcaabeaddabacbaccebddddccbbecaabadeeedebbccadceeeeabadcaeacdcdcebaeeebbdcaddcaeebadadcbbbadebbaeaedcccacbaeeeaacedbcdcdadbadcdbdeadceabbbeecebcbdadccdcedcaeedcecebabdadeeadeddeddbdeadebdcaacddcebeccabebecbabecbbbdeadaabbbccaccbdddedbbceeebeecbadecadbadcddccbaecddceaccceecbcebaeacbeacebdddbdbbbcbbdcebdaddeccbbdbcdbdcdbbbaaadccebddaabdddbcceececbcacaeeadeedadcaaaeeadaccacadcbebdebaedcaccbabaeaeaacdeeeaccaceadabdccababbecbdadecaacdbcedadbdceedabcebdacbedbaecbbbacdddacadacbdecceaebcdbcedcecdaeecaedcadacaceacaebabebabddeacdaeddededdaccdedeecbbbdcaecbacbccdbabaababcbaccaaebaddaccebcbabeebabdaaaedabeccbeeabadaeadaabdadabacedbedcbeaceebbaecebbeccadcdabaaeeaeebaacdbeeacbecbccddedeaebebcbaaebbecacbddabaaeceddecceebcceaccccacdcadbeadedccbbddabeecdaabdaecdacedbdabccddbadbdedddecadddedacacedcaabbcbecbbdbabeeeaceebcdcaddcddcacdbeaccbbaceeccdcbeaeceeaddaeecdaccdddabbaaebaddeaddebccddddbbabaaeeecebdbdeadceadaeacecbceaecddbceeceabcdebbdcedcbbcdbdadaaaadadcebababcbebdececcbdecccdbcdbabbeeceaaaeaebecacdbbbbdaadddcecedbdcbcabeabdeecccdebaccbccbdecccbdecaeddaecebbdaddbdebabddacbecddcaaeadbcabaeaaaaccbbaeaeccdbbbddddbaeddaacbbbceacdbedeadacbaaeceabedbaececceaaebbbacbeaddddecbebbcdbddcdcedbadddccdeaceaeaeeabadbcebdeacbcddeccbcdbeebdcbbdbeaebccedcebbeebedcbdebebbdadbbcbdddbeacecccecdbbabbcdbbabeacadbeedaededbadadabcdaeceeeeddbddeedcbddaddecccdbeccabddccddbadedabbaacabbbedececebaaeeedbaccaeeabedcdedbceaaeaabacacaeeddeebeaedaddaceccdbededdacdacabadadccbdebdbcbdcccaedeabdaaeddbdebbaadecabcbaeddcddaeecbabacbacedcbabdbeaeddcedceddaeccbddabacccccdcceeadebbacaeecaeabacdbabeeedabebbcdcebcbebeedaeeedcaddeedbabccebababcaeecaeeadeadeaeeabdcdbdccdcccadeaebabddceceddccebcdacddbabcecbeaccaebbabdadeedeccaedccccedcacdabcaaebeecdedcececdddddcbddcbccbdaddaecceccebeacddebbeeabdacbabcebbcbbbeddebdbbdaaaeccdeebedbbcbbccdbdcabeaedaadbcdaacbebddddeaccbbbceeeabddeecdcbeaaceeeaeaaeeadaebbeeeedaacbddecebbedeeceecbaeeecbdbacadeedcbebbbcedeaaecdadeabedcbaeaabdddbbabddddbebacbcceecdecdaebebabbacaceeebededeacbadcddccbedeecbbceceeacebacdcdddaadaccbaeacdcdbeddbaadedeeabdedbbaeacadebeadebaddddcdccaccddbbebeceedabbbbeabcddadeabdceaddaababeedaeadeebeeeeaeadcccbbcbacdedbdacdaedbbdeccdbabbbdadeecdceebeabccbebbecedeadbbbcddabeaebcbdcabedeacecbebdeaedcbcaaabdeebdbbdaaaecdecceeacecdddcaddaeebccbeaebcbedecbbdadcabacadbaabacdadddecdcebebdbebccdcbabcedeccabccdecabcbdccdeecceceacaaceacbeaccaceeecdcadaacdabbedbbcaddabdabcaeecdeabedcabeccdaccebcbeaeabeebeeacbabdabcaccebedbddbcddbebcbdecddcceaabeedeecbabccbcadbccdcdaddeacbddcabdecebbadaadacaeeeeaceaecbaebaeacaeebbdbedcccaeeaadbadedeceeedceaceecabadaadbedbeeadddcdeecaeadcacebbbcdcbdadeadcaadbbacaedccadadbecdabcabbdeeccdbeabaadabcedeacabbaacebcebcabacbcddbabbeedaedecccdbdacbbeeeccbdcaeddcceaddadbaecbcdcceaecabedabaddbddcadeaeabbbcbccedcadcabcbcdcaabadabcbdaebebeeceaabadebaaeaebddecddcabcbbbaeedbdabeddaaacccdbcbebdcddadcbedbbbacdbaabbdecbacebadbcecbccbeeacbcccbabeacdaabebdacecdcabbaaebdaaeebdaaccdbbdcccccabaaeeacaeebcaeaeabbbbaecdcbeedeedcecebaeddbeecadbdececeabacbacdedabebbeaeceedbecedcdcbacaddaeaacaadaeacbdecaadbbdddecdabbcacddadbaacdaceebbcbdebeccaebdbcddaeceadabacaecbccbbecedaabbdddababcecaadddaebbeedaeacdddceaeeeacadbaeaccddbebdabecbdeacbdddbcbdbdebbcbaedbdcbcbcdaebbdadecbbcdbaaecbbcdcbddbdceeaabccbaccebddedbbbebbdbdceeddaecacdbdbbcbedddbacebbbeaccaabbdacccdbdbccabedbedbcdbabeaccececdcaacdedcbcdaeedbcadebbdeacecdabdddaadaddcacebdaccdaaccebcdecdbcdbbceecaeaecebaeeecaeebeceeacdebbaedcbbbdaadeacaccadbdabeecadababcceadcbcddeaadbcacbcaaaaacbdaebdaededccecccbedcbbcecbabedceaaeedccbceeebbaaaacbcddbaeeaebcdddaedabcddbcceeaaceabaecebdababdccdbbedcdbbeaeaaeaeadeaaacbdcbdaeebadaaaadceeeceaddcceaebeceedddabbdcecdeeaaeeccaadbaedbbaeeeaadcaeadacabbcbecbaabecedbbdabcaebeeabbcacadadadabbedbdedcaddacdebcdacdaddcacbacbabcebcddaddececeddeaaadaabcacceabeddadbeeecdacddcdbdbdaeacbeedbcccaddbdaacebadccccbcaedcebdddaaeaebeabbeeeceeeccccedeeaacdcebbdabbacbededadccdcdaedbeaecdededcbcdeceeeeeecbbbaecdcdaaaebddcccbdbccbcaedccbceacbabacbadeaedddabcbdaddacbeaaebadbbdebceaceadebcccdbaadcaeadebadaddbddcaedacdebddaeeebbdeeedeebdeccccedeebaeeeeeebeaaaeeeecadeadbadcdbdcbddaeccdecdcdcdddddbbacceaabcbeeeebcbebbbdecdbbeaebeddaeccbcedcadeeccdacbabcaececedadadecdaeccaceedbcaabcccdadeaedeaddebbadbcebaedbdabebbebcebceeadbddbabadedccbdbcdabedadeaaedadebcbacceeeacaecbcaeeacebaecabdaadbecabdcabcbabcabedcaeeaabebbbabcbecebdcbcdbcbeaebdeeeddabcbaedbbabeeaddebabdbcdcdbddadceedabcceecdedbbbcdcedaadccdebcaeaeceeedaeaebabbbadbbcbbddaaecbbbeeceaaecdabeedddadddddeababbacabbacecbcedbebeccddacbdadcacbdcdbbcebabacdbbddcedeaedcedaebcdcaeaabaadedaceccdddcacaabeeadebceaabcdadabeebeeaaceebdabdeaabaeaebdddceadeadecdaaabbbeabacceacaaadcdcaabaabdbbdcbcaabdecdbbacbebcbecadccaacbebdecdbcebbbbcdaceeddbaddacbedcddeeaeddabbeadedbdebddcceabebcdddedcabedbadeccabcbcbbebaaaabcadebaadedadecacdcbcbaacdacbcaaedeeedebbbdadcabaeecaacbdecbcceccdbedcdadaedaadddddccbbadbeacbdecdaeceadacdcdcebaacceacaeebbccabdedccebacebcecadeebcacccabbaecebadcddbecaacedbdceecadececaadaacbdbdeaacddcbecedbdbecdecaeaabdacaaeaedcbbbecbacbabeaacdeecadeeebedeecaaeecdaceebceddaedadebdedbcadbebbecadcdebbceadebbbcecdececcbceabeebaedabeeeaaebabbddeddcaccccaebebdaeadcbdbdeacdcdbecdabbbedbbbabbccdcbcadbcebbceeaacadacdaecccecddcdcccdcbabedaacccbdbcdeecccbccccbcbeabbabadadabdeaddbbbddecbdbccbdaadddbdcdecbbdbeeedecbaeebadaeaeddaeaaabaaedebeadaaceeabcbcbcaabacccbdbcbbccbbadaccdeaeccecbcabddeedbbdaaddaaccdceccdcbaadecdaacdedeadecbdcbdcceaabadeecaaebbddabbeaebdcdbccbbdabaaaeedabcdaedacedecccccccdaebdbdcbdebbcbecaacbbcbcbdaeecabacaacdccedccddaacecccddeddecbecaaabcceeadaecdcceecedbdaeadeecdebadaebcdcbcceccdbaaaeeaacdddeeebeaceebbacedccddebcccedebdeabcbdbabbabecddbeabbdaeddddedccbaedcdbeaadeeeacdaabcbecbdceaacdeccdabbaaabceacbeceaeeccadccbbbdcedeedbdbbabcbebeaabbcccbcadcbbbddcbabbbabccaedbabcecadacedcbaabaaadaecddeeabadbabbecdabadcdcadbbaadadbcecbdcccabedaabedbcddedaeddeedbbdbebedbedadcedeacbcabcadbebbcdbaeeeebeaaabebeeebecbcebccbdbcecddebbbcdeabddaedebadcdadbccbadbbdebaccccacdcecbeacaeeeadbdccebdedddacecdbdabedbcdcdbbebdbdcbebbbadaeeaecdabbbbdcacbdadebdbacecebdceaaeadecccddbbcdcacaadcddceeeeaaabcbeddbcbceaadadbeeedcceabddbedbcadbaaadbaeeecadeedcdeddccacbdbbecdbbeadadbabbeeabaeedeecaabaacaccdcccdecdceeceecddcebabbddcbebcedbbabaabcecadacadbbeecdcbbbeedaececdadbadebeededbabdecdaeaddbebbdaebcbbcdacaddaeaacaedcdcaacdedddbbddaeaceccccaecdbdecdaeeabcacddaadaabadebdcaacadcadaaaccecaecbcabdbadcbbddddaaabeaeedbdaeeecabcecebcadebacecbbdaeaaaaaaaeedcecdacbbcbbeabaeedbdcdbabacdcdadebadccdcedecaaaaeaeaeaecdcdecbbebcdcaaeabbaeddadbdcbdddeddbdddaeacbabdabcabebdadceecbbeadaddacbabcacebdebcaaaeeddadaddccbdebeadbedeceaaaeecedaabdceddcdbacdddeaebcbdbeaeeccdaeceaaebabbdbbbbbcbecddcbedbecaacdbcacbdaeccbadbdedbacdcbbedbccadcebeddaccbeebadbcddcdebeadeaceeaaebbbaaedeccdceacdbbcbbdebaaceeebecebdaeeecbdabaecbececbbecbaaaccbabbeacabbceedabdacccbedbacecacbbebdeeacbccdaaeeacbdbccbadaedbedeccbdaddaabcdccabeedccddabdbaeacebddbbddbcdadebccecebeddcbadcbbddbdcdeabbeecdddcdddceecddcebcccabecaeddcbcdddcaeedebaadceeebcaddecbadcdbabeceeadaebdbedacbecdcdedceeadbcceacdeceedacedacaaaacccbebcdeaeadebdaabecbadbdcaccbdbedeecdcbecbdbbcebdddedbceaabecdceadcbdebabccecabcaeeebcdcaecdbcedecaaeabbecbcddbdeeeecdcbacaadceaccdacecaaddbedbedecddaedbbcbbedccedbedacddaabaeedddebdcdbcabdaacbbbdecdbaebcacebadcababcddccdccbccecedcbeebecebcbbbcabdaeeedbcacebbccbedeaaceadcadaadcddeabbceaeccaddcacdcdeddcaccdeeccedbcaedeabbaedadebabdcdbadaaeecddeeaabbbacbcbddcbdcccdcaeababdeeecedcadebacceecbcaeeddcadeaecdcbcddaaadcdccbadacedbbeedbbebbdcaaaacdbacbecaebeabebbcbebdbcaecaabdeedbebaadaeeaabedbcddbaadbbbedeeebccebdeceddaacedcadabbebeaeeccbdebeedebbbeacdcaeaccccdbbccdcdeebbdadcadaccaabedddedeabbddabecebadeecbecaabbedabdbebadabccaeaebcebedbabacdcdaededabdecacdbdbddeecdcbdeedabbddbebbdaddeadddaadbddaebeceeebdabadaaebcdcabadddebddbbcadededbcbeeeecabdeaedbebadbeaadaaabbabaebdaacddaedceaaaddddebdcceeadedcbcaedabccaacdbceccccbaccdbbecdccdaeddbdebceabdddcbaebedbdccaadeaebddddeeecdbcebddeacabaedddbadaeeebadeccaeccabbcceedadccbdeeebcbddeaaecedbcadecadbbebceaaeeabababbddcdadedecdcaaadcccdebcdecddcdcdccaaeeedcdaabcdbeecaceeeadbbcbcbdddbeecdbbeadabcbaaadecbabedbccabccbbecacebdedceeeeeeecbedccebbdeabcbaaeddcddebceacdedbbdbadadecbdccadbdeaadeedccddbebddabcaadaacecdcababeccdabadaaeabcaceeeaeadadbbbaabeadebbacaaececaeddccceaddaebacacabebabceaddccbacbbedbacebbeadedeacaddadcebcdbabcdbbccccedeeaceaadccbcbaccacecaacabbdbceaeecddebbabeadbcdcabaaceaeeeaedeabacadbbddeccbbbcbddbebbeaaddacedebaabbcbdcbbecaebddbbaeebedbaebbcecbebeebaebbbdeeeeebdbaeabaabecaadbeeaebeeebcceebadcadddbbcbcacbaaedbecbddabbdabbbaedabcbbbcedbbcbeaddceccceecbebaacceaeebcaeedcdcdacaeedbdacbeaaeebbbedcaaccadcdeaaabadbedaabacabdbdeeaacceaeebaabedecbadbedabbdaeabadadbcbebabdcdcadddeadbcabccbdecaabceaccadeebaeecbebbddccbbdbabaaacbebacdbedcaddaaaeceabbaadbcccbdaeaceddaeababedbeeadbdeeaceceadebcccceadbeeaddaccdaaddeacccaaebededaccaacdacebecdcbdedcddbbbaeaaedcacabeadacdebdcabebadabeebeeabaddebacadcabdabbbccaeceabcceeecabeabadcddbdddeccadbdbeacabddbbbcceadaddceceeabbcaadeeddaaebcabebdcecbedbbebdcaadbeeaceecdebaacbbeaeeaddecaabacbaddaccabbcccbbdcdcecabbadaccbeaacddacbbedaaeaeabdceeaddedabdcaeaebcdeaaacbcacaecdabaddeccccaeecdeabcaabebbaaedaddabdbccebcdeddddadaebdbddbedabececdeebcbaeaecacaebabdadddccdabebadebeebadecbddaecabcaddecdcabddcbebaadecabdaebeebaaadacadbddebaedbaceaceaaeaeeeabcbdabcabaecebdddaedcceeaededdacbaeedeaaabdcbdaccdaddbdcaeeeabbcddceddbbbaeededaeeecbcaceadbedbdabcdbcdbddeeaabdeaedeadecabebdbeadedebddeaddaebdbcdbbeddadceceebddaddeaaedaecaaaaeaaeadedaebbbaecbbedbcadbdedcbddaeddaecdecbaeecaeddaecaaeadecaadbeeddaaababaddcbaaecbdbacdbacbaeecbacbbeceeeabccadbeecaacdcdddbbecacacdddcbddcecceedcacdabdebdcbbecbcbadbddcbbdcabdeabdeddeddcdebeadcadbedaceadacbebedbdcabbdbceeeedeceabaaaababbedbabdbbbddaacccdedabbbcaadceedadcacbbbbebcdcaabadeeaedededcabcaaacceadbabccedebdcdeabecaeecebaebecaaebadedaccededbdebbedaebecaaabccadbaeaeddcceaecaaedcbceddbbcaaddbaeceadabbcacdecbeccbbbacdaccdcdacccbadebeceacacabacaacaeeaacdeabeacccceebaccdaeedacbeeedadacbbdbcebbcbdcadebadcdceacddebbcdcabbebebbddacaeaedeabddedecaaeeadcecaceebebdeacecebaddbabebdcdcdaaaecabbacabeaddbcaccbcccccbcebaeaadebbbabeeeddbebcbccadbbdddbdaebdcceaceeabecddacdedaacacddbaabebaddbccdeedcccbddeddaabaebdeecccaaebdbcdaebbbeaabeddddcadeebccaedaebeccdecbcdedbbbeadaecdcebbeaebeedcbdcdddcebceebbccdbeabbebedcebcacaaecdaeeccebddacbbeaabcaeaababeecccbebebaaccebdbdaeaeaedeeecaccacdecdbeeececccaadcbbaddcbacdcdadedbcacceddbcedcbdaaeecbabaaecbcaceddcbeaeccccaededacabcbaaedbccbcaabecbbedcbaecaedeaebcbbccbccecabbdccddeaaceaddbebadddbdecbeababbabcebcdadeeebbdebeaddccabbaaccbdaddabeaaaebadaaeeebedaaceacdceaeaadccddccceecaedacebaedccdeeabdcaadcabcbaeccccabbdccabdaadcbeccebbcacdcdebcbaabaccddddeccaadedceaaedceaeddaaedbddbacdddebcbacbdddbbebbbcbddccaadeacddabdeaceabedaeaebdbdbbaebaeeaaddaeaaecbcaaedcaadacbceadbadaabdeaddabecdbaebbebcbbcbcbbabedcceddacdaedbaacadeaaecaeadcdccbdabdedadbcddbbeddcaabccdccdbcaaeddeebacdbecdaedeeddddecadccddcbccdbceeabddccaadcceabadcddaebbcbeadeaaddbcdcaddedeadbdbdabbabdcceabebeaacebadebacdcdbaeaacbcaedaaeedbaacbbacdedcddedeacaedadcabbbdaacccdadeabbbcbbdcbdeccdbedaaaeedbedeaeebceabbcaebcaddeceacbcbbbbaacecbedbdeddbadececaabaabdbbbaebaccbbbaaaeaedbdbdeeacdeccddbaccbbdccdbbacaedcdbddcddaddecbeedbeedebddbecabeebbcecabacebadecabecabcbbbcdcacdecebccbdbcbacaecdcbddccabdaabcaebedabddceeddadbddaabecebcdeebbbebbeceacddeaedcdbcbeabeeadeeadbadbbaeeacaeaaeedcaddeaeebcaccaaabbedbcaddcdedadcbecdccbbccdebdeecdaeeeeeadceeddedbcaeeedadabdadceeeeaaaacecadcccbadaccdbabbdcbbedcbcbedecddadbbbaceedeacaacedddcebacbccacaaeddecdcbbeedcecaadbebeebabccceecebdaaccbabcaebebbadadedddcdaaeceeabbbdabcccabeeabaaabdeceaeaaeecdadddbdeceedbaccadceceaadcdbaadebbbeeeaccccabeeecbaacddbbbdeaedececcaadaacdabebabdcddeeacdacedbeccceecabcebbbbeddbeebcbcabbaddedbbeabacabcbcedbcbccadbcccedbdaddbadbdbadddbadbcbceeeedbceaadaaaaececabeacbdeacbdeaeeccbecacdcaebbeacdbeececbbeadabcbdeeedaacdcdaadeecadddaeeadceeeabacebbeeccdcadbddccdabeeaedecbaebeabcccccadacddbdbcaabaeaccaebcccbbcbceedbecdbebaabaddaccbaaedbadcabbadceeeebbeabeeacbccbdcabaaabdeaaedbbbedebdbadcabadbaddddeecacebdebadccbbcaabebbedbaebceaaabbbbdecceacbacbaddedcdcdbabecccddcdaeebecccedaccedcbcecbedceaddedeedcceedeadedeaabbecdbcdebdebbdcacaecabcbccdcbcdcdedeccbdbddbbbabecdbceabddccecdeaaaeceacddbdbcdcebdbabaddecdbebbabdeacbedbceedeabcacccbbcdbacccebebdcaaeeddeaebebbdbcbeaecbbbedbebdabbadbdbeedeebbcdbddbceaecbcdbedbebadcbacebbbbebecccbbccadeddddaecdccbdeaeaaeedabcadebeedbeededbbccbdbbeddeadeccbcaccbdccdaececdbbdeeddeaadacbdcdebdbbbccaaebacbcdabaeccdbcecdabaedeebddddeeabdaacdbcccbdadaaeacedbbdcbddbeabcdaacaedbbddededdbbaccdcaebbdaadbdabbabaecadedeceecbdbddbeaacaaaaeabddeeabbddeccbddcdcbacbdbbeaadcacadddbabccbcbadcaaeaececabcadeeabcaddcaedbbebabecdbbceecabecdddcbeedbcebcbaacaeeaaabbdaabbbcbeadcedecccdeccbbbcbcebecbcdcaeaddcedbcaeabbeaebdbdbbcaabcdbeaddcdadedabbdbdecbbeebebebbebebbaeebbaceeedbbcccacdbbeeebacaecccbcdeadcabbddebdbaeeaebabedecabedaeddadaeaedbdbaebcdacddbebaebecddcddadbaccdecebbdbbbccecdedeebabdeaeccaadeeddeeeabececdcecceccaddebdcdecebcabecaebbaecadabdbdadedcebcdaaeddebdcacebceddaabcddbbdcededbcdacbeddeddcccbacebceceadbddbbaeccebdadecdabecbebadcccbbdcaebeadebddcccaebaeeaccbabbceecdacebeabcacacecadddebebbcabaedadacdbcbddddeaebaacdabbbcaaaaaeacbbbabacbcdedddcbadceedbdaacdcbdaeedcbeecaedececdadabedcdcabbbcdaaedeadeeababdcdebcdbbcdbcbbaecbdbcdaabbeaedcaaedcbdccdceaebebbcaddedcabcdcaacebcbaadbbaebcceabccdbdceceddbbcbccdaaaadabcebaeaabbddcbbeebebcaaedabeeabeddbbedececdeeccdaabbaababbcbbbeedebaebbedebdbbcbaccbbcacceebdaceacdedabddccaabbabcddadecacccccacedcecacbbaedbdecbadebaaadcadaccdacadeabaddcbdaaeccbcebabbdecaecbdddcbeecdececddcbdadbbbeabaadbdcdbeaaeaddccadaabcbdccdccecdcacdacddababadbacdeeebdbecadbccbcdeabbdccbdbcebeccdccabceccccdacdadbbacdaacaedbdeaeebacbabdaddaeecabcdcabcdeaceeebcbeadacbbbaabeaddccdaddcdbcdddbaaadeadedadeedeceddccdecbccbabbeaebabeaecdeabbacdeecdddadddcddaeaabadabdcaacaeeceeaacbbbececbcbbbaaecbabebecabebacbeabaedecacceebdbedebedaeeedeebaceacaecdeaedbebdacadbebbdddebaeeaeebbaabcebcebaabdbdbbacbedabdaaeecbbabdbcdaedaecacabddbedcebccddaaecbabaadacddedcaaddebccbaebedcedbedcabaacbcbdcaebaaddabcdecbacecdddcbdbeecbcbaaabbacddadbbcccedbaebbacecccbbdbbbecbaadaadddbaeebecebebcaaadddadebbddadaaebdadeaacdbecdcadbacbbdcdcebedbdbeaddbabececbebedcabdaebcedeacecdeebaabdaeebbececadadaaabcbddacaddebadbcdecbaacbaadebebdddaecdedbeabcbcadeeeedbededaddaddbccedbdeeddcbaebbbbcbddeacceecceedcbceaeeddabcdacaadecadebebcabcaaecebcccddebcdeebaabdcdbabdeeadbdebcbaeacaaddcecaeadabdcaadccbeaccaeccdeebaeaeebcabedecccbbcdeadcdbdecdbaaeabbbddcbbdeeaebdcbbdaebcbcbbccbbcdbadaeddccadeacdadeccaabbbbecadaddbcbdecccaddeccccbbdeeabbdeeddbcaeccbcbedcdbdaeccdbdcacccadcebcbdcaedcbeedaaeacdeccccbbccacdcdcbdcadddeeaadcdeeedaaaaceaecedcbbbcddadbeadeedbbbbcabbedaacececedbabcadecbdbdaeeecaddeedecbdcbedcebdecdeaccdbbecbeddcbabcadbedadacebcbceaeecbeddeacadaabebdbacdeeedababadbabcadecbccebacbaabceacebceebaecbacceabdddcabbcedcaddeabdcaebbddddbbaceeedeaacbcaceabbbdddaeadcacccdbdeccbaacaaddbddecddedabcaedadadcceacbcaeeabecbebebebcceecdbdacaeabeebadbbdaacceecbbacdeccccdbddccbcaebbcecbbaebadabedcbcdebabdababeabeccdeabceadbcdcbdeebcbedbcbddadbbdbceaddcaddabeedbbbbeedddacdcdccadbdceceeacdacaaeaabcaacceedeaddbbcabceedabecdeccdecaeccdaecaceddedcbededbccacadbaecacebbcebcdaccddaedbecddbaceacbacaacaaadccebabbcebeecaecbbdbdddcbbccbeacdbddeeceeaacdebeebdcaddaaabbcceeabccddcdcdadeabbddcaaebedbccbdcecaaabedbabeadceacbccadeeeababeeaceccdadaeaedacccbddacbddcdcdcedebcadcdbedbdaeacbddaadbbcdaddcdaaccaaeebccdedaaaecdaaacbbdebbaddcdbabebaecabbeaedadcbdaaeeebcaddacacbabccdbabcacbebbccbbcacbdabbbbdeebabceedaececaabdcecbaecdcbdaccecedeadbdbebbabbcbdecbddadbdabebdecacbeaaecaccddedeabbcccaabbbdebbaebcdaedbacacbcdabecdcedccadacdacaeeacabeedcebedddcadaedbdacdeabdecddbcabdbcecbbbcbebaecccebdbdcdbecebeabdcdedcbaebdcdbcbabdddadacedeabbdaadaadcbaebbadccacecddcabbaedcbceeeadbdecedeccebebaaeeedbadaaacaaaebdebbebcdcbceabddabdddecdecceccdcdcbacaaecacbbbabddeccbbbeddebdbedddaaaddcabaaedaaaedeececaaceaeeeabbeabddcbcaebbbcbbcdbaccdabbbcaaeecaddceddcadcdecbbbdbcbacaaaaaaddebbeaebdbeacbbdbbeeddbdcedbadaeceedbdaaceeebeeeadceddaaabaebaaccdacaaaabbdeeeeddebcbbedabcdaddbedaebdabbdaeaeebbcaccebcacaebebbcdacabaceccdccadeceebccddedbccadadcacdbcdaaadeadcbdacedadaaadceedaeecaeabadcecceaeaadcaccbdababdbcbbbddceeddcddaacacecbaabceadabdccdababdcdddebcdeceedaababcaaecdaeaeababdbbcecedcaceebacdaacdabedcbaedeaebbeabbbccebaaecaaceedceddcebabcbdbeabaaeabccbdaaadaebeeadbaeededeaccbedabdebbccebcacdeddcdbcbcdcaddabdddcdecacedbbabbbeadcbdcdcbaceceaecdedacceaeebbeecbadbbbdaccceaadbeaaebcabebaeaadbedbddeadedbdcabcabebdeebdeeebbebbbcbdebebdacaebbaeeaeecaedbeadabbeadceadcbccdbcadacdcbcddeeebceadbbdaddabacbdebdbaedbdecedebdcaedeceeedeabebbeecbabadbeeccceadacdccecebdddcbbeadbcbbceadcbacaebddddaceacccbedbabeeceeadcbabeeecdcbceedddddeedddedccbcabdbdcdecbcaedeeddadddcadacbdcbbbaceeddacaabadebcdcebeceeddbaaccedcdacdbbecaccabacacaeeadbccaddeecebeddeeecbdccdccbceebdbabedcdbcdacccbecdcaedacbbaedecabeeeedacccdbdcacaabcdddaacdcaeceaeaadebaebcdeecabbdbcdcbccbaccebadceeecebeceeeaaacacbaeaeebecbcdaadcabceaaaadcecdebdaebbcaabceceeabbccbbbecbeeddbdecebcbcbddddacacacadbeeeadaecedbdddbaaceacceabcdaadedbbcaebddeebeedceebcadabceababdebecaddbcaebeadadbeadbcbaacabeabaaaeaaddcebaebcdebbdbacdbaaaedcddcaddecebeccbdaebacddabaabceddecbbdbdadaabccbeebcadddeccbecdbceeaebaccccdebabcdeebbaabaccaabbaddabddebddcdebbedadecaccedccdaeaadadcbaebbcccbcddcccdaecdbeecdddbddcaeaccdebadceacdcebcdbeaeedcacddcedcbdcabcceadcaeeebadeccdbcdebaedbbeedeaeccbaccdeeeeedeaccbeedcbdeadeaaabaebecaccaeabaddbebbaeccbdadcbdccbdcbeebaeecbbbdadaceddcadeaccbbadbaacddacaddbddddcbdebacddbdeababababcdedcabdceaddcccadceedeecdeaddaedddecbdebbbcaaceedaeeedcaeddcaddaacdedacecadbbcdbcedebbdebaceecbdababbeeacabdebbedbeedaaecebececdedbaaedbbadcbbebeaebadddeadbcecdbeddcabacbdbdebccccdbccbacdaacbcbdcedbecacbcdccbcdbdbcbdbbdabaeaeeedecbdcbddeaeadedbdcbebacebeaecbcbcbcdedabdcecebaaebadcacdddacdeaccdabbcbceeabbcabbaadeedebeaceacdeedadccdccbabecabeebebcabeaaacdbbdebacaabdbbaabcbcacbabcaccddcdbaebeebaecbbecaebcdcdedbdcbceacededabccdebddedccdadbeebaabebceddbedebceadadbadacbbadcceedbeceddeaddcaeebedbeeeebeecaadccdceaceecaaeacbecbeddacaddbbaccadcceccacbaeadacbdaedbebceecdecdedaedddeaacdcbbabccaeacdbdcddaeacedcbcaabdaaaabbbddccbbaeebabebaddddddbcdabeabebdcedbabdabcaaedebbecccdecebbcdcacedeaadccedeebadcaaccbbcbaabaeccebedbeacedbdccbcbbaecebabcbcdeddbcacdecdecbbdadebecdbcaadecdeabeecebceacbdccebdabdbaaededcedbbeacadedadaabdeadcaceeeacdcccededbddeeeeedbebcbababcdaabbcbbeeaeebeccbecacdadadddedcdaaececaccaaaacebcccededceccebecdebdcdedecaebecbdcebacaabdcebaccedddabbceebdeccbaceeecccbbcaececddbdecceebaddbeecedcbecbddcceadbcdcecdbdebadbeeabccaebaedadeadecbbdebbddcaebeabdaeddebdeadadddbdcbababceddacaebeecbeedbbeaaacbddaddebccbeedcededbbebdabbbacdcabeeeeeaddeceeccbeeccdbabecebeadeddacdeecdebebedeebababbcabbbcaddddbeeacaaecbdaceedcebebbceebbcbecbdacadbdeabdcdbcaedadbbaceadbbbaabedbadbbcabbcbcbebccacaccddbeaabbbadbeeacdceeedbaedeeebadbacaedacccebddceaedceeedadbcbebeaaceeeacbeeeecabaaedaacbbdcbaaaccabaeedbaeaadbadaacdcaaaaddacbdaccbcbbdaecbabbdeeedaccbabbcbbaddeecabdedaabacbdbacbaacaecadbcedaeacedeeceeddeedecabbdbecbabccdabeabcaeeccbaadbbcbbdcbbeadbdeededcabccbbcabecaabacaedbcadeabaeeaecaacbcbbdeadedcdbbbeedebdaaadcadabcceeeaabdebacbcccabcaacbbdbbebbaeacbaeeeabbabadcdcbedbdcacbbeccddaebabcdbcadecacdbdbdedccdbaedaeebbdcecbeaabdedebeaecdacbbbbdcdbebdeedcadaeedbdddacaedebbaebabddeebaebaeaedabaacebbeceebebeadaddecbdbcdadbdcdbbcccdbeedebadbeacdebbabccbadaebceadeacecdabeccecacdbbebecbeeabcbacadeeaeabeceddbdbedcddbaacaeacaadbbdcbedabcbbbcdebccaceaebddcabedeedbcabaeaeaccbaecdedacedadedbcdeeabaecedebddcddddbcececccaebadabcecdeaabcdbbbacacbdddbebaecbcbaebdedbadbecbeaebecabcbcccdebceeaaceaaebddadcaaabdcabbaebedecebbcacacbbabcedaaaabdedceabcbeabcecdcabaecaeabbaeececbbbabcceaddecebadcccbebabcdaecedcdaaedcbeddecdbbbcabbccedadddcadccbeaaeecadcbddecbddebedaabedddadaaeebccdacacdccdbbbadececcdeccadcbeddbabaecccadeaccbbaaecdababacbdcedeeaedeaaceeabeeedbcbdedcbcceecaecedbdebecdbadcdcabeaaeeaaebcbccadbcceebdacabeaeaebcbaebbaeaeabbcecedebdecccddccdcdecaeaabbbddcdbddeaccdccbaebebebaebcdeadabdddcbceadbcadaebeebbddcaaccbacbcdddcbedbaeceecabebcbceceaadbcacedebecabeadcddccbbbbebdcbeecbeaeaaababadddceeebaaaacedcbedbbcbdcacbaceebecaeaeeecdbbebaecaebaedecacabdcceabddaabadbdbbddaaacddeaeaaaccbbaccbeabaebbcedbdcdbaacdcadebebbaaadedbeadbbdbccddcacacdbcaecbdcbaeabeddccdecebebaaaddaebbecdbeeaeacadbdbdbebbdcbbebbaddebcabedddbebcddbcdaedbebdbdcabdabcdcbbceddebccceaaeaacdddddbebbbdcdcbcdbddbabaaacdbdaeaaacabeaadcedcdacadbdcddbeeeeacebaaeaeaaddeadeadbcabadabdabdcebccceaeeeecdadbddccbacecbaaebadcccadbcbdecccaeebdeaeaecacdaaaddebaedaedeccacaccabcdedebbcbdbababeaeaceabaeacaeccdebddeebadadbbcdddceeeaecabdbecbdcacdedabddaeeccdeaceccacbcdeaadddbcadceddcdadcbebbeadceaeabbcebdcadcdcbeabbdebeebcecedecdacebcceaeebebcddeeeedcdbadeaaddedadadadeaeabeecaccdbcaaebcaecadedacbdbbbddbedaaacbadadabdadcddaeadadceeedabdaeeacddcedaedcabeaeaebacbdecbccebaeacddecccabbeccbedbbcdaedeceecdcecdceddbaabeeccdaddeccaaeeceeddcddeaebadbebdaaeaccecbbaaccedebcceeedcdbcbccdadcdaedecebccdabbcdbdcadebaeaebaabdbdbbaaeaabedcdcaaeebcbdbababecdcaebbaddbdaedaadddaebcaebbdbeadaececaabdedbcabdabeccdceadadacdbaaadaabdbddedebebadeddcadccbecdbaecaebdcaddcddecdebdcdcdedabbebecbbcadbddcebaceadcbcabbcacbccbedcadebadcabeadecaccadadbacecaebbaaecdacaecdbaccebdcdacddbecdcdbeadadcbbdceaeeaeaddadbacabaceecdabcdaaadeeeceebcaabaaacbbaabcbbaeccbabadcacddbbdbbcebbdaeddbcbcdbdebcadbaeceddddeaecbcceaedaecdbeeacceccddebaddcccbeaadceeebdedabdcdaddaccdcecebecedcaecabeaaaebdeebceacbaedbdecadecadcabadadeeedbcdeeaabbdeeeeaaadbabacaeedbdbceebbeabacbeeacaccecbacdadacbcaaccbbceacacbbedccccdcccaeccbcbcaaebbcaeaeacadaabaeabadddcecdbcaecdeedbeadbcdeaccdadbcbcbdeaabdaeddeacbbedcebbbeaccbebdbaeceaedbecebdebccdbeeedbcbacbebabccbdedacdccaeabaabedbcdaedeaedeecccdcbbbcebdeccdbccbcadaeaacaebecdccadadebececbaaeaebacbaddcecddddcaeebbdbdddddaccbcbcbbeeeeeddbdcdbeacdadcddcbaaebadcdbdebbecdbeaabeaecbebdedeadeadddebdaeeddcaeeecbcecdacaaccadbaeabaebdadcbbeaeecdcedbebbebdeaceabdedbeebcdacccbdaaadecceceeaeebcebcadcceababdcecbdabcdaacaacdebeeebdbcdeeaabddcedbdbaadbbebbbbbdbadacbccbdabeebabdecaddddeeeedbaecbebbebabdbdadecaccedcccbaadaabeaadabbcdeaccdcecbcddabeabaedbdacbccaaabcacdbececbccbbbebbbdcdccbedabaabbdddbddcdcbaeccabbeaeadbeacddadcaaaaaaaaecdbcddaacceecedcaabdcbdeacceedeeddbcaedcdccbdeaeebaeededbcabdcaabaadbdbdaddeededdacebbedabbddedddaacdddebaecbcdadeadecbdedbeaaadedcadebdacbddcbaacdbdccdddedeeeadbddeebabedaceeddbddeaabcabdbbebbbddbababeeeeaebdeccceeccbdcaebbecaabbbecaadedbccabcedbbdbeebcccabacdcdadcaedbbecdbaadddbeebaaaaddaddecdaacdcbbeaddaedbeaacaeeddcceebcdbeaecddcbdecccacacdacacceeeaaecbaddaeadbcebacbdcddbbeebcaccabccbaabacdaaabaeccaacaccedddaaedeaeaceecdececeacacdadaccededdeeceacdaaaedaceaaaedaeaeacddacaccdbdbaddcbabbebaacdceaedbeedbaecebdcacecaacecbaadecaedbcedaeebcacbabbbcebbadbaebdbcacadecdddeadbaebceeccaadceadbacdcddddaebadbceecdbaabccedebaeaaecbecbacbddcbcdeecdaaccbbcecdddbeaeaeecaeadaabddddbdecccbdceabdaaeabdcdddcbeedbceaaeccdadbbdcbaeeedadbdcbdadbaebaaddaeebdbabdbeccbbebebeccccdaedcbdbaebeedbcaccadccaddedcbcacecedeeeadeeebadcbbeacecbcddccbdaecbadcbdbebeabaaccdeedccbacedabbecdcddadecedaceeddbdcedcccebaecedbddacbbbbdbdedabdecbdbdeccbadadbdbdeaedcbaacdddadeedcbccacceebcccccceeaabdccbaadadbcddcceabbedcbdbbacdcbccddeedbcaaccebacecaedcabecccbdaaccdcbbccbdddcebcebbacabbbddddeedaedbdcddacbdbdcdceacbaabbbdaebaeeadeabdecdadeaadabbeeeacedcaaebdbaebdbedcdccecbaaabdbdaccbbdbbcdebcabcaecbcddbaaabcaceecccedbecdbbadaedaeaddccdaaaedbddddaaaaacbedcbaaccdcecccdeabdbdcdbacccbcedaadbacabeaacedcaaebdadadcbccebadedddaeaebeedcabeccbeaadbdcbdaeccbcbbbcadaddcebeddaaecbeccbcbebcebaeacaadebabdacbbddababaceaabccbdbbcceeabbacccceeaeeebbbbcdecddebccaabecbcddcdecbadeaceabbdaaedbbecaaabbcddebaceabbccabeeedebebebddbaceabdcdbaaacaccbdbabbdbbabdedeeeacbaaacbbbacecebadcbdcdaceebdabeabaeaeccceccbcebccccdbccecdecccaeebedededbdaeabeaebddabceedecbceeddedaececccaedeeaceeabecdabbddaceaebececcceadceaedeccdbbcdaedbbcadedcacbbaeaeabdcbbbdcddeaaecbadacccdbcceaaabaecdbebeaeebacedceddecdcbeadaaaedcdddacdabebaedbeadbcbeaddecadddbcdadabebddedcbdeceedadaebbdebcacbddacbbbdccaecbbebbedddcdbabadbceaecddeadecdeeaebcbddecdaedcbbedcadbdbddabacbdbedbaedbbaeeddebebdeeedeccebbbbaceadaaddbbedcabcadccdbaceaeeceacddababaaacabceceaecbbceeeaebacdeebebbaecadbccabbdabecccbbbddbeedeaeecbaecdddbbedeaeddbaddabbdccdbbbeabeecbaabdcbadcbaeaeaebbecbababbccbeaeeccaaabcebecabcbcaedbebebdcaeadebcecbaeabdecdcebcdcdabbbccdccadaabdeeaceaaebeebeedbdadebbccacadedcaeebdcbcebcbabeedbadaabeeeeabdeabdcbdddaebcadbeccccceeecddabadcacdeebbaeeeaddcbcdddddcccbbdeebccccecceeaacbaebdcacceaaceecbaeebdeacedebaacebaccceeeaccdecaebebedcdbabcbeaaabbcdeabbcdecdacecadadcebebabbebedcadbbdacccdecedbabedbdadbdabacdaddeccdecaebdcbcddadccbecabbcbaeaaaabebcacebbbbdcbedcbbabdeedbbedacedbbaeeedebacbdeadedbaabdddceeddaeecbccebedecbebdaadeddabddabedaadacacceaaadbbbccccbaeddeabdaccbdadbbaeabeceacdeeacbdedaddeaecadbeaabbebbdeeeaaebdaedaecabceeadcaeeadbcaabaacbabeecabbcebeeaebddebbddbeaceacdaceeeccaeebdbdeecabdccdcbabcecceabcbcecdabaedaacbcdbbdbcabacbcdcaccbeddeddeadcadadedbbabddbdbecacebcececabeaceadeadcdebdbaadbdbbecadbcaacbdbdaddabcadbbdbeeabcdddebdbedaeadecdcdbedcdcdccddceccbcceabeeabdecbacacabcdcaeddadcbeabcabaadeeeeeceebdedecdadbceeaabdeecbcceadacbecdacadcbdcdbbcceeebdcbcbcecdcecdcdecabaeeccabebaaddeabacbdeeadbdbaebecabdddcebbabaeacdcbdebbcaeabcccaaddedeadbdbcaeacdaeaaeacdcddecbdadccecdeabeaebccadadcbddceccadaddedeeaceecdbeadcdcddabdeabeadaeeeceedeaebaaebadccbcedcebdacaebabceaacbdddebececbdeeddeaaeeccbacbcbccddbaabbacbeeaabeacbadebedcebebbaeadcebbeacabcababacdbeacdacbdaadceabecdeadcdacbbdbcadbabbaedcdeadcbbcdabecdeabcdebecddbdcebaebdecaabdaaadacaaeeecddbcbaeeaaeebbeaabbbecddedaacccecdaedaceababcacebdbadcdddbbdbceacaabdebecebbcbcbccdbcabddaccebedbbdcedcebcebdecdbecdaacccddcaccbbdabdabcadbaadbeecaddcaadaacaedeaceeeaeaeeeddeeebedceebceaeeedaaababeabbebbddaeceebbeaadeebeaeddaaabbbabecebaebaecadaeebaddaedacdabeacebcbdecbeeebdaecddbabdeaaecacdbcbeebeebecaccddbbadadabdceaeaadcccccadcebdeccadbabacdccebbaaabadabdacdaebcbddcbebdbcabbacaacebeceabadadcaceddaabcbbbacbccadeddbabececaccbdbedaecbedccacccbadeabdecbbebbecccdaebeccebadadbcebebbcddbeabedecbddbbabbccccadbdbaccaddceedebbdcbcbedebeeadebccebbdadeddaaebdeedbcadedddabdbededceacdeebdbdeebacecbacaddebebaacbbaeaeacecabbdbaceaaeadedccbcaabaedddcdcdabdeebcabbdabcabcddceedccdbdddcdbedeebaaeaaeaeabbaacbaadcddacdadcadbeaeebebbbaaeddeeacbbecdbdddaddcdccbcaabedeedbeecdaaecccaebcabebcecabbcdbccceacedbbddddedebccebcbbadcbecbcaaaaecdedceaccaeccaeebcecaeebbaecceaeecadebbbdbcecbbbdecbbcdaaddedeaacdcbdadebdececbbceabcaceababaccdccbbdadebdbaadeabdeabcaabcdadededccebcccaeccbcbbbcdbbcbbbeecedebdabaacadecbbacbdaecdcadddbbbaccabaddcbdcccbdbeeeebccceaaabcbceedebddadcaeaccdccaecdaeeadaacbabcdedccdccceaecbbcbabdcacdedbaaaddcccebaaedcacddedadbacbaddacebaebdceecacdddeacdaeecdabaebcceaebccadcbddacbcbaceadaeadddeeedeacabbcdabeddcaadbabcceeacceeaadaacceecbbdcaabeacdeeebeaddabcebcbbdeddeacddcaedeedabebcabaedbaeedbbedbaeedacbcecbcadcaebccadcaccecceccbbaaacaddbcdeacdbacbdcabaabeedeeaecddbbaaaebdedaddaccdccdcaebceebdecbdddacaaaaddddcceceaeccbdeaceeebcbcdbbccecddcaaacdebdebbeccedbbebbedbeaaaacaacaddcdbbddbcdeadbddceaacdbdddeaddbbccbadceedbbeacdebbacbbdbedbaeedcbaddabebaddaeebbbcedeabeeacbdccabadecdebddcadaabbbacdabdabbebbdbeeacdacddacababcaebadaaecbeccbbacbaeebbbabadcacbbcdbdddcabcbdcedbaacddebbaaabdebaccdbdeeecbbdaabcacdbcbcbadbeeaecbedbbcdcdecbdaeaeebeaabcbaacecbabbacdcbbbeeaeabadadebeabaabbedbcdcceacedcaebbcebdeaebddeebdbdacdbbdbbdacdaceecbacecaeecbbabaabeaddcacbdeadcecceaacaeeeaebeeabbcceaccbabebccdbaaedcebdaaadeebccbadecbdbebeaddbbdbeddcbaaabeeebbbaaecadbecbbddbcceeebcebeedbbeabdadaddccddebcdcaeeccedbcbedbaaaedcadbdeababecbeadaaddeedcaaaeaedcbabaaeebbeeedeaeecacdacdcbebaccbcdcebebdacbbbeaeaeebaccecbeaedbaadaaaabdbecebeeebacccaccccbbdabdaaebebaabcebdccbabcbdcbaaeaeccaeebddedbbadbcebcbdacecdcaeaaeadceabbabbbbbaaacaedbaacedeeadeeaddbdbbeacdaceacddaaabadaceabdbdedeadedccbdccbadbcccecdeebcadaeedcaccebbaadbcbcdcbccdbbaacddbedaccbdeeebbaacbcbbcbcbbacdbcaedbdeddaebbcbdacedaccbdbeedbbaaabdbbeadcbeabddccebdaadcddaccdbbdccaccccbbaedcbceacdacadcadcdbcabdccadeeabbcbcddaebaaccbadcedcaeecadbceaaecccdcbceecedcaabbbbabcebbbaeeeeeebbdbaaadddcbeeabbcbdaeebddceedecaebebbcdbdadccbeccbbbcbeaaddedeeacbcebedcacabeebeabcaceaaadaceaaabebaedbbdedbcdcdddbcaddbcbdeddccdceacdcbeaabeeacadbeacbcbabcaebbbddbbdecceaaeaebadaaabceadcbcacacbdeceddcdeadecdacbecbdbabcadcdaadcbeaddebbbbeedaadcaddbecedbddebcddaaaebecbcbdaccaeccbbdcdceebbcccbbbbbedddadcbedddcdaacaceabeaeaaacbecbbcaeecebcadcbdcaeaeeebaabdceecddbeedabacadedaccdbdbcbecabcbaabecbcedaaadbeabebeddcbabaacacacbdbdbcecdecdbcbabbcbbbddaccecaabbdaabebecbbecddbabeccdbcaccdcdaebbedaebabcceccbebeababddabceeaeeeeaadedebdbcadddeadbabdabeaedddcdadbbaadaebceabdbacadebacccdeddbabceddacedccddeeebaaaaeccddceedaacabeacacecdbaabcdabbbeaeacdcaeecdbbacbdabdaeeabdaeedaabecdaabdcabbccdccceddaebbbcbebcceaccbaeeecedbddeaaadcbabcededceabeacaddcadcaeccadadbbeecadbcdbcabadedacddbaacdadbcdceeacdbbedcedceebceccbaeeceadedebdcbdddccedeeabcdcabedccdddcaddcbdebcededbecbeebecdecbdadedeebbaeddebaaaaeacaebdedddacaeeebcbbebbabdaebddbbbebacaedcabdbbaabdbabecbecbcaecabbeaadacbbdccbebaddeaecdceddbecdcdaededbcabdbabaaeddaaaedeeddcaaadeaacebbbbaedbcdbadeeeecdeaadddeddadaebebbbeccbddaddaadaacdbbbbcdddeeeedbcecbecacbdeeabbdbebeabedbdadabcadeacacdaddaceabbcaacebceeaccedabbeeaaadddebddbbecadaeaabcadabeabcdcaddabdaaadbccdadadcddddcbcdcadeaebbcbddceddcaccbedbdcededbcbcdcbeeedbebadaecbdaecccdaceccdeceddbbbeeebccecccebacbddbceddcbeedadecbaeacaebdaeaceedaebecececdccdbbdebabeedabaecebccabccccedeeeaaaaedebcaaacdacdbccadabbadbbeeabaabdcabeaecadeecacddabeaaeadbbaabedbbabcdbaeebeaedddecbaccaddabbceeeaabcdbdbaddbecaebbeebaacaaaeaebbcedbbdbbdccacacdedddedccdecdddcbaccddaabbecdccaedeecbbdaebddedaeedecacdbacbbeddbedbcddcdaddedecdecbebcdecbadbeeaacddaaeaecadedacdbacebabecaecaadeddeabeccccececdbeecabdcaaaedeecdbcacedddabbcbaadcacedbaaceebbabcbecdbbedeeaadabdecbacaebbcabbeaacacedccddabecdcaadbddecacdecbddcbaaaacaedbabbaacddadcbbebececcdbaaceacecdebedceeeeccabceebdeaacbaccdacadccaaebaabdcbacbecdceaccadaacbeeaceaeddabdebbccecbcceeabaebdbeedabdcdbbdaabcedcecbdcdebaabcaaadeebcdceecbeaddcaadebcbcbdbbcaedbccabcaececdcdccdebbededbedddabbedddcbdbbcbbbbaccbddeaeaaacacacbdebadbaaabdbcdaaabbcaebddbaedacbabcccbcdacadecadcbaababecaccabbecdcbedaceccabdeccacddeeabbceaabceddddbcadadadcbaddddcebeeaecdacaccadaecbddabcacdcacadcbedeecdbadddabccbebaacddaeecbcaaacdeaddacabdabebeabdaadeacaaabcbcdeccceeeeceadbbaccbebaaaadbbddbdcadcdcddecbadbadbebbdbcbaeaaabacabebddcbdacbdddbbecebcabadacebebcacbabacedddcaaccabadbcdbdcbbdaebccdbeeaeacaedcbbcdecbbebcdeeeebadcbdaaaacaabedeadceccecacecaddadecdbebaaedccedecdcbcedeababccddaddbaedccbbeeecdaacadbeabbbebeabadccaaddeeedceeddcbebdcbbacceebeebaabbacbbebacbaeddadabeeebadceaccaabeeadcccddebeadeeebedbabdeaabacbaaccdeceddeaccdcaaacaedacceeeecbbabaedacdeeeeaebbeeaabbbbbdbcbbadebaabaceadaeabedcabdbddbbecedbebddcabdbbebbbbedddecbbecadbacebbebcadcdbadadaebdadebbbdabccdaedbaddcbdcbdbcccdbddaeebecbabebeacbaaebeaecaccceacedcceaabaadedcccdeedaebbcadcbcaecbdcbbbaeaebabeaabaadebcbbbabebaeacaabceacaacdbdbabdadedabccbcaaaedeaddbaaccbcbabedbbbcdaabdcedbabedeceacadbcececeebdcaabdbcdbbdbbedcddecbacebbceaacadbcadbbbdccacceaccaccddcdbecdeceaadadbbeaccebbbbaaeebeadbbaedabecbeeecedcdcabddbeebeaaabcaeaaadcadccbabeeaccaebddeebeccaceebcecbbcabeebeabddedbdddebedccccbdcabcdbabbcbebaababebdddacbecdecbeadcbabddaecacaacbbdebeeeacebabbccccdbedbdccdbdbadebbacbaeeddcccddbecadaedebceededaacecbaccbcbaebceadedcbeebdabaabbaaeccddddcdcbcacbdecbddabcdecdbeabeabeeabcadcabedbdaeccbdcddabaedaccbedbbaebddcadaedeaeadaeeccdbbbcadeecdaecdbcedceaedccecadebecbbdacbcabeecbbaedacccbbabcabbcaedeceddbeccaaadcbcbddddbcaddacdedbadbdeddaabeedacebcaabdeddbebcbbebdceaaeecabacebbabeadcaeeaedaeedcaaeddeeaddceaebcdadaadacedadaceecaaccacadabeccebaeaaaaebecbbeeeeeacddccebaaecbcbcdecacaceaddedeaeabeaebcccedaaadbbbbdaeaedddccbbbdcadacdeeceeeecdcdecceaccbcdaaaeeecbcecadcebeaaeeddddeaabbcdadabbbbbbddeaddbecaaeceeaedadbaedcddcaeabeaaebeaaedaeceaedcdcabccaceacecddaecbeabbadbecbebdbeeeaceaddbaccdccacbeceeececeabadcdecbeebbcbbecddeabbccabceccaeabbcecbdacbcbcdbebbcdcbceaaebbccbaddbdeccaeeebbacacebedbcabcbbeedbaccdcedebcbbcceacbdaabcabebeadcdebcadbcdeaadbebabcceeddbddcecedaedbaecadecebabebeaeaaaccbcdaccdabcadcaaabaacebbeadcdaeeebbaddbacaeadbbaccedbcdeaaeedbcdbaaecacaaeeaaddbcecaeaedccbcccceaebecbddbbdbccacccaeedebbdaaedbcadcacdcaebbcdcabcbecacaebeceebecbcaeaddcacdccbeaccabeeabadbcdebecdeeaadbebaeccaddbaeddaeeddedaabaebececaccecaeebdaccddbcbcddccedbeabdbcbabcddbedbadebbeedeaaacbdccbcdbcebceabaeaabedbdacdbbebbcdebeccabbecaabaaceaccdaeccdbececbbeabacbaecbaebdaccccbaebcbcabbdccadaebadaabbbbdabeebbeeeddeeaaacaedbcdabeaebedeedcceaacaadcdbaaaeaabeaedeccadaedbdacbbddeccabbbedaceabdacbbdedbdebbedbedebbbeeceaadeacaaacbcabceacebdcbedaadebedecbdceceddcddabaaeebceccbecbaeacebeacebbabbebbabeccecbaddceaddcbccdaeaacecebecaccbedbbcbcdcbdcddeadadaebadbccaadbbbdbdbedbecbcccdecacbacabebbdebcbcbabcbdaeadaadaadabaadeabeacccbeeabebbacaabeebcbcebeecbdcaaecaacdbeebebbaecdaaaaccaaaaebdcbdedbeebaccbedbbbadcbeeddccabcbcdcacebaccbcaeaecabcacbaedbaeeebebaaccbeebedabcaddcaeeaececbebeeddaddeeaaccedaaaaeedddeacbaaccacdadeebbdbccededdccacddbdceeadeadcacadedcaddebcdeccdecdebdccebbeccadebaebdcdeccdbcbcbeabecddbceaebdacdbeeeddecebabdcbdeaebccaeaeacadbadbbaaddcadbeccbcaeebeadeeddeeddccccabeaacbaacaadeeabccaacabcddaededadbeaaaeaadeedecccccacbdacbcccddeaabaedaeeaacbbddeaebdbacacacdebbdbceebcacbcbbcdecabeceeacaadcbeedbbddeacecdedaeebcdcbbbdeddedaedceedccaddadddaccdaebeccabeabddbdbebbaccdaaaacedaccdcbacddeedcaaebdcebebcdadbddabcdcbccdadcaabaebaceddeaccecacabceabebecadbaeaacaaebacabcecbaedbbccdcbaacedcbdccddaeaeecaadbcddbeabcebadbdceaecccacebeabceecdababbccbebaebcdecbedbdbabbeddbaaceccbedadbbebadaeebcbecadbbeaecaacbeaeebcaaeeadabacbdecbbbbccaadcebacbbcdedccbaccbaebedbecddccaadaebabaeacecccbcddeaeececdecbeeadcebbceadeabcecbceeadccbbcdecebebdeddbbdbacdbededaaaddecbaeceebbbccdedecccceecdcbddcbacdccbddbbaaabdbaaccaeccbcbdeadebeddaebaedceacbbdbbddeeecaeebcacedcccbaacdaadecedeeeebccbecceaacbddcbdcacdabdcbaceccaedbbbcebeaddeaeccedcbcbdddbedccccaabcacbdacdccbcdcadbebddacaeacdedacbcbedceeeccdacababccebdcabadcbaaddeccedeadededaddaeebdddddecaddecaaccebcbebdcbcbeddbbebccbabaaacbcceebbddeeeeceadcabbacaaecccedcaaccacacbdccdeeaecbebacaacdbaeabcdbceedeccccaadcaaaeddcadcedaceccceaadebeccbaeaddeecadadadbbebeebcdbeacadbacbceaebcadbcdbdabebecececedbdeceddbbabdadbbdccedeacbbddadebdeaeccaacabebcadebddaaaaedcaabbbcdaadabccccdeddddadaecabddeccdaabddbeeaddaeaeadeecdaeeabecbcabddebadbcdeadadedaddcdadbacbdbaebebeeeebbddacbaddaedbccdbadcdeaadbebdbbaedcdaeeaadaddeddcddaccedcdcbddceaeabdbeccebddadedcabedbeeaebcebdbaacacaadbebcacdebeecbaeabcdccdbcbaadaeccdedbaedacbedeedebceadcebdaceebececcdebeebabdccdaacbaddbbcdebebcbbcdedccdddabdacecbcdebcbbacaadaaceccceabcedbdedaddceccdaadeebaccaebbccbcbaeaaebcbecdacedaccecdcbdbdaaebadabaecebabedcabdccdddeccacebddbaecacbabbddaddbaecbabbdacaeebecbdeadcbaecccbdacbcedcbeabdceeebdbcbabbaeaaddaaebaddeddbaaedeaddeadbabcceeadbecdacaddeaebabeddabdcbcbeedebddcdbdaecbaccdaabbbdebebbabdcdabbdcecdcbecbdcdacdcbecacdaaebbcbebebbaddceceabbcaaccaaeabaddcebeebdebdbacaabacebdeeedcdaeeceaacdadbbcbcdabcdcaeacadaaadaaaedeaccdabddeaadcdedeaebdebcbabccbccaaaeceddabbdbcaecabeabbebdbaaacdeeaaeedaadebabadbccacadebbaddbcbabdaaaacccdbdedaeebaddddbbaddedededcecbceeeaaedecedcbaabdacdcbdbecbbcecacedabdadddcdcbdcbcaceabbdddabcebabdaccbcaceccabceeeededbabdbdcdebedaacbbeaedaadbdedbbcaeeadadbaeecdbdbedcbaabaebdacecabcdcbeccebaebdcaebcebdcddadceadbaeedccdededcadddcaeedbeecdeddaadbddaecbcbbcacaacadaebbaedaeccddcabceadbecdacebcbbcceecabeeaeaaeeacaaaddeccdaedeaedbbebaaeaedddbedaeccdecbebcddaaeadbeaadeeeadadecbaacedcdbedcabbcddbdbaecbaaacbcbedacaedeebbdaddaaaccaccbeaedcecbbecabbbaadcdbaababdcbebcabcbebeceeacbbdcbaacbdaaebaabacabbabebbecbdaceaebdeacaadaecceaaadbbadbbaeecdcebdedecbddeebedebcdaaceddceebcbbbcceaeaccbcbacbdbdacacbaccdbbaedaedaaccbcbcebaabadccbddcacdeeaedccedaddedcdabaacaabaeaeaacebbabdbceeaccdddbcdabcbedbabccdedebdbcecdaadededbddbdacdaddbedbcabcacdcdaacecdccdebeececbdcbddbaededcdeeeeaeaaecdcdaeeddceaaebbcbccacbdbecbaebcaccedabedbabebbbdcebdddccacbaccdeecaadceabacaecedecaabbcaedbcceecebcbeebdddeadbbdccdbaaaaccbdeacadddedadabbcdcdebedeceedabceacabddebecbebcdcdacecedaecaaecacadcdebecededdcaabaedbaeddacadeeeadbacadecaeaeddbadedabeadebacbdbeeadaddecaebaecbddedeebdeabadaadcaedcbbdbccadabcbaadebceebdacbeeacbcdabbdedcbbebdccabadaaedddaedaacebbccbcdbadbdabcdebaecbeecdbddaecbbacadbaaeeceedbdaddeecaadecbecccaddccaecbbabbedabacabceaceceabebeedabcccaabdeedbdacaabcccebbdaedebdadeecaabaadaebeecabdbbcaaacdeaaeebcdaaaeaebbadebebcdcbeecaabccbdaddebacbdbaeeaaadbcdbeabbedccabaedacddbbabcbbcaeecbaadddedbeadceaaaadacdcbbddbabbdddcaabccecbbaabacaedbbeacdebbcccddbbbeebdbeaeddadbecdeeeedadeaadcadbdeedcddcaaaaccbcabbebeeaeeeeaceeeecdbadcbacbbaccdbbaeacdbacdeddecbcebcdabdbecddcbebbcaacccbdcdbbdedaacdecbbbdeeadcbbdabadcbaecaddedeadaabdcbbbdeadccdbcebccbedbbbecbdbcecbaeaabedddbcadeebcbcddcdebcadebbdcbbdaaccdaeceaceceedaececbabbcceddbaaabadcbecebddaadbbdccaadaaadddbebabbdeccadceeecaeaedbeaaadedceabeaeabcebabdccabeadceccbadacbeaceedadceaebbbbadebccdcabdabcbaadcdeeebbeeaedabedbebdadbbbaeeebacaedeabacdcebedbbbaaadaebbdaeeddaeadbedcededeaddbcacbaadbcceebcdbaceeaddddcdbccbbcaaaceaabdaabdecbbcebcbaccaceeceadadacabaccdbadebbbaceaebcaeebaceceaaecddeedcacaccaeebdeaaaeceaeeadbacdcddeaceccaddabeebbdbeddcdbeadcceebdbabbdededaaccecdceecdcadcadddccaeddcaabebcdbbeecacacdcdebedeeedeccbdcdeabdeccdeaeaaebcdcdceeeabababbacbbceebdbcdaadbadcdaabaccebecdcbcaabadecabcdcceacedbccaeeabebebcabdbbaebabaaeaeaccdabeaeccdbeadaceebbecdacbbacdabbbcbecabeedddeabeebadacbddabacebaeacbaaccaddaceaacdcccdeeccbeaccdeedbabcbcdbdcccdeaddeaeeabbabeaceaccddcbdacadecddedbeaccdaadabecdcebcbebcacebeaaacdbadeebccadbdabbbdadeacaaacddbaaeeadcddcdadcdbadcebaeedcebbddaeedbdbbbdeeccebbaccebebeaeccceaecbeeccaddbdabbabcceacaeadddeaceaeebdeeccdeccdaaadcecabaabaadaceaaacaaaabbbbbaabbdaebdebeebcbdcdbbbedaecebbaddcccdecacadedbeedeeeababddddddbebcbbcbcccdcaacbededbceadcedaadcbcabbccaccadaabdadebdecddbdebcdecdbbbadcaccaebaeaacebdbecaadacceeeecbddeeaeabdccdccdebdacaabbcbdeceeadabbebdcbebdecadddcbcaaaaaeaeeadaaababaaecbcabbbddedaedeeadcbaaaabdcaddeaadaecdbebbcbcccaebadbabecdcdaacbdaceaddeecbbcedccdbaadcdbbcbdcadebecbcedbaedbadaceabbcdabbddbdddbbdabdcaaebabdadbaaeaecacccbacdccbacecccaecaeccaaacdcdbbbdacccecbbbaaddccdddacadabbbedeabbcdbeedbcbaadaccdeadedabbbdbdbccdbedaeecdbacadaadcbdccbeeecdaeeadcdbcedcbeedcbbcedebdeeeeabdeceeaadedcacaddaacdadddedddbbccacedabdadaeeedcdebaaeddadabdccbaebcacbcdacecdbeeecaeeaebaeaebeadceadddeebeabbcbadedadacebcdbbdebdbaedabccbeeaaeccdacaedecadceabeabdededddaaaebdebacdcdcddaccdedeebeeedcbbbdacbaeccdddabbcdeecbdadbbbbacbebabdacadebdbbdacdbcaddbaeeeeadbcbbeecaecabdcdceabacaddcadebebcbcedcdceacadaeeaeacdabdddabcdbebdbabbbeabdaeaeaadbbdbecacbacbeebedeecdabcbceeaaecedbcbbdccadabeedceeabeecabcccccbedceecceeebdacdaedbcbaadbecaecbcdeedbedebaaaeccacbeaccaececadbdaedaecacdedcdcbddaababdcaaddeeaceebdaedcedddaaadadeebbbbdebcaacccbadacabdcaebebdeebddecdbbbeaddeebacccecbbbecaaacdccadcdbaeeeddddebbcdcdaccdaacdddeaeabaedecbabcaeeddcbcaebadceaeecabbddaecbcbeeeddcadddbdbcbeecaddeeabaedacbdbceeabdbbbeecddcacbbadecebceeacdcecdabbadcdedeccdeecddcbdaddbaeebcaddaabdccdadcaccacbbcbcaaabbaadbdacaeaadecabceebdadbcdabdadebbddbeecdbeacddcbdbaecacadebadabecbaedbbabbbbbeeeaceebabbeacdaadcabdcddadbedbcdeccebaedceecebeedbadbccabbcbacdbaccacacaddeaeabeeceaaeaaebaaebcecadcabbacecccedadeeeecaddddcdcbbdcabdeabacbbceedabedddbabeeceeaeadcdacdcaeedeebdecdabeecadaccbbaebedbecbacdabebddcecdabbacddccabcabacbacecdaeebbeeebebbdcdaddbccbeeddcccceceaacccdbbbddbaeebdeecaeccdcacebcaeebdddbdaaaeeebaeeeebcdeebcdbecddaaedaecedcdbaaddddebccadebaaeaeccaadddbcbcaeedbcddeebcdebeddebeceedbddecccccaddadadddedeabaccdcbbeacaceebcbeaaeadcdbaadeecaddaddedcdcaebccacccaaeaaaeadbaeeddaaabdeccadebdccadcdbbccbeeedacebcebecbabcbbadaddaaabcaeceedbcdeeecddeabcebdcddabacebadbeacacaeccddbbbddeeecdaeabaeeebdaaedceebebedaabbaddbbeebaabddddabedcaaebdedbbacacbccacbaaecbeaaaedaaebecccbcbabbeadecaedbbadddbdbcdabdcdddababadaecedaabcccadbbccaaeadbbdbdedeecaeeeebadcdbaacbebeeaababbdacbcadcbccaebeababbbdbddbcaeaaeebbbcdbebdeecaabbaaddbddeceeeddcdceeadeabadbebeddedbcbdadeeeddbebcaccbccaeadecbbebdebdbdabaebcbaaadddccdaceecadcabddbabaebaabdeededaadddacedaeabcedeabeceeebceaabcbbebdaabacebdbeacedcdccbaccedbcacceebbcbeecedaeaccbcdbeecbabddbdbaacddaebcabdcbcbcceacadddaeabebdbddaececaaacbdacabdaceedaaebdadecbabbbcaecaeaeadddaebdbeecebadcbdadaaecebdccbecbaeaeabeebbeadbddcbdceddabedbddedaccabadcdaecdbebebddcbeaceabbacecddbecbcbdbbadccdcbdcabbdcccebebceccbecbedaddeccbaadbcebdbbeaaabecebaabcdcccbdebccddccebaabcebaabbbdbcbeabcacbdaeccceabcacbdcbccaaaaedaabbeedaddecebdbabdccebacacceadacdbabbdaacbbcdbbccdeeebbeecbddeacabeecdccecbaccadcabbddcbbebdeccbddddaacabdceaaacdeecedaeedeedccdaebebddbbdcccebbdaedadcddedcabbdddccbdbaeaedeaacceebeadbdeadabeaeccdbbeebcccaaeeecadeccbacceccdabdceaeadcbdcaabbccddddbacecdacbeedbdbabbcaabaabecceadecdcccdceabdcccbacbccedddebdacebcecabbeacedbabddbebebedacacdcdeeaeaceebeedabdeedbbacdddaaeccabbcddbeedabaddeccceeeabacedccaacdedcbedacacabeacabaddcadbeddddbdbcebbeedebdaacddbcdedeaeacbeddcbbceadadaeeeeabeebcecbbcacdeebcdeeeeddbcbabaecbeaaaeceabaccbdbbcccacbabaddddbdbcdbaedacadabaddeceeeaddaddabceaebddbbbbeadbbddbcddbcdebbeedaecadaaabcccbbaebbdcdeddbbcdbadbccaeacdbcedaddcebbcaaecceccbaacccadabbcbbdcccbaddadedecdcadeeecdedcebbdabcdedabcadeeadbadeeeeedaededcedbebbbddbededabeacdcedbdcaedbbdbaaeeceabcdaedeeaabddeeeccdceeaaabbaddcdbaebadcadacccdcacbcbdcdddcbaeeebcdbaabbbeabadbaedbbcdeacbaccaeedadacaadeaebcdedbedebeeddedddaaebcacbebeddaeeebbaccdddedbdcedabacecbdaadcbabbbdcebbdabaedbccadcbcceaeeacdcadeacddbcebebaebbdabccdecdcccdaeaeaaaaeeebabadeebadadbaeaebccbcdedbbaceeddbdbeccbdadcaccaadadaabedcacbebbdcbcabbebeddaeebccddeceebebebddcedcbebdcebececeecdbaaceaeaecebebddccceacdbbddcbbedccabcbceddbebcbdbeddcccdadccaacebddcdeabebbaacdbbacacaedccabdddbdbcdddbbeebcbeaaebcdebecdeaddccaedeceedbcbcadebdecaacdabaeeaaabdaeaeebdebbccccdeeaaeebebeacacdaeebcaabedabccacadaabceeebaabebbadceedbbcadbcacccbebdabcedaedbeabeebcccabededeaddeaccbbabdeecacddbbceaeebcccbcbceedceabcabbdbbedceecabecaaebedacedccdeaacaadbdcabcbdecbcbebdddecbcabbcaaedbbdddbbdbabcecbbabbcaaddacabdaabaecadabddcdcdcabdacdaceeceadddccabdbceeebddbdebcebcbcecddbbedbcaaebcecbabdedadcbccbabacdcaaedeadbcacbcedcedacbbbdbdbcebceabdcbbececcbcaeebbbceeebdeeadceebabedbbecddbcdeaaaabecebaaeeddeadbcdacdcaecddeeeeaedceabeeaadbcbccddbdedbbdedeeaabcaeeabcdbebeceacbeadbbdbbdcacdedcbaeeccaebcadbbbcdeebccecceaaededecddacbebabcaedebeddabdbccabcdeaecdbdbdaeabadeaeaeecabaeaeddbbbacbecdeebcbebeacbceebbbaacdaecbccdbccaeebedaadeadcbdbbaaeacceebdbceabedbdcedcbeecdbbcebbbaddacaadbcceadeeecccbcaddccbdebdbedbdadbccdddeeadaeadcbceeeaeebabeeaeaaeccaedacacaaeddeaaedbeabbcdbeedaedbdaccbcebeaceabacbdecadbbbebaeeabcabceeccbdbabdebbebdcdbdbceeeadbbedaceeabedcdacdaaebcbebeadddbbdbeaeabdcbdaecdeeccadceaaaebdacceeceeacedcabedececdabceedcbabcadbcaceecdcbeacebcdadacccdeecededbdaabadbdadaaaabbecdedadddcbeeccebedaeebdccbedbecaaccebecddbdcdeaeaaededeebeaddeebbedbdeddcbaaedaeaaeaabedbdbbacbbbacbeaebecabaedaeeeaccedeadaabbdadbeabebdcdaceeccaebcadaebccbadaecbcdcabdecededeeedddbebcaccdeaadceaeddcedcccddddebbdcaecbeecdbddadeccabddacebbbcbeadceadedbcdbcbeeecadbbcebdcaeddccbdcbceacacbbbccbdbbccdccbaabaceeaeedebcadeabaacbdbdcededbaedadcdebbbbecabddcabeeeededadceccedbbabecdedddccabbcdedadecceccdaeaebbcadabcadccdbedbebbceaebcceaddcdcceabdecadacbbaecdbbdeabeaecaebdedbbbbacaddaddaebbddbaacadeeaaaaeeeebeccecdacadccdbeaceedebceabacabceabbbbcccbecedcbdeddcceaecdaedbdcababbddbcddbebbbccedbeeceabcccacbeecaabccaeceeadbeacecaccddaeaaaadcebedebdcbecaaadceeeebcedadabacabedcaccaabddccdacdbdbbcdaebdeeebeabdcdeaedaccabdeeaeadadbdcdadbedceecaacadeeaceccdadeeabeaaccceeeeaaaabdacbceacebcbbbcaedbccdecddbeeacaeceabedcdbdaedadaedeaecaaccbecdbaaedcadccdcbbacecbeeecdcadddeececcbbaadecbecbcabbcacadceeeeceeddcddbebeacecedababaaccdaabaeaacbabdbbdcbcacbcdaadcdcbbdbccadabbcddaaccdbdaeecddecdeedaeaecbdcdcccaadecebeadcbdaacbaebeaadcabbbebcceecdeeedeebcaacbebaeddbdbbdccbbccbdeeeaceccbcecbaadeacbabdcecaeabbdeadccdecbccabaacbebdececbedddcdbbbcebadccbbadcaceebdccebbbdbebaeaaccebcaaaacdbbbcddcdccacdbbdebcdecbdbaadbbeacaddcacebceaacadddaecbeaeaeededdcdceaccbdecaabceeabdcbeebabcacabdaeeeaccddacbadccaecdcdddcdcbebedebaecbdecdedaeddaacdbaddebbcebaecbeededdcdaacaeaecbdbdaeadcaacabedabeeeadabdddccadcbececebcdaaadcaddbecabdbdabbecdbaccaaeaccedddadbbaaebedbedcebeadbccbacaaeddeebbcbdcdcdabdbacddaabecdeddebdeceacecbdcbaccecaebecdbecbdbcbcebaaeecdbedbbbcacadadcdbbadceadeaceccbdeabbeecbdbbaccebdebdcabdbceebebedceebdbabeacabcabdcbeddbadcaddddaadbaaedebebbdbddbbbaeeabdddebbdadcacceabcdaacdddaddeaeddaaababebdcadacdcaadaeabaceabcedcbadaeededbccbedcdbeeacacccaaaddaeaeaedeeabcddbdddeeecddcedcecacccdcbbccbeacbeccbedaceebcececdbacecaacdabaadcabcaaeaedaadebaccecdecadcdcbdebdcbbebccaacbaecebddeccacbbcdbccdbeccebecbcaaeeaaeecaacacbbebedceeecbcddcebecbdebeeabceececeeabacaecbdaaaeeccbedaabbcaecdddebabececcaedaceaddcdeabddbaececdceadcebbbceeecabceabaeddbbcacbabaedabdebadeeabadbcbbaebebabcebaceaedceddccdeacbeedddecbcbbdceeddcaddcceaaebdeeeaacbecbdeedbaeeacbcebdacabdedbddadcdaeeebaedcaeddcdbabcedaedbaddbcdacedabccbeccbacbeadeabddcbdeddbcacaeebadccdbaccddeeadddcdbbcdecddaecebdeaebeecbcbabaaaaacdaceccacddbddeadddbddbdacceeecedbacddebbeaaecbbaeedcbeabbbccdebaabebddbceaacdedaceebeabbaabaeedddcbdeeacdeadaeadebbcccebaabbaabedeabbcbabcddaddcbdaeceeeeaccaccaddebacbbcdbdbcccbcbebeccbbbeeddabebdeacdacdbbcaeacabcbbcdcdbceeeaccbdaccdebdeeededddabcbedeacbcceaaacebddcbdecdbaddeddaeecacbababdacbaeededbbbcbadedaecacbccdeaaccabaeeabebdebdbccaedeeeeababaedaceabcdcabaabceeaacbccaccbdedcecbaaccbcbeddedbdacdecddeedbcedddcedccacebdedcaaeeabdceabdcbebeeeeceabbbbeeedbaadbbddeeacaaecaecececedbaabdcdeeddcebcbceececeadceccdbddbceddaecaebdeaaaacbcadeeaccebeabeadaaccedabbbdccebabaeecaececdabaeabaebaaaddddbbdccdaacdedccaaceeedcaeaaebddaabeaadacedbcacbbcaeedcccdbceaeddeeabcbaceeecdbeaedbdddbcceeeeedeaabeeeebeaaeebacdecdbbbedcdbebadeeabdaedecaccbaeeedbccbcaadaadcdddbdbaaddcebadcecbbdceaccedbddcdeeaaaedbdeecdcddbccbebacbeccaedcecaadebbdaebeaecdadbddcbaedbeadeeedeecadebcddaddcadbdabbbabbbddecbbbbbaecdeaebdabccbbccaebdcceceabdbebeeecaaeccdaadbbedadcbbeeededbdbdbdeddabcbeaadcbabcbdecbaccbdeeeceaebcbeccabdadccecdaaabbbaaabccdddaaedeeecbbceddccddeaaecaebbddcbbcedcebceabbcdcccebadacdabcbecbababcabcdebddbcabbbdbcbdeccbaeedcdcdacedbebcebabaeebddaabdbeecddbbbdcacdcedeeaeaedaddacbabaecdbcdeeebabadddadecbedbccaecadaeccbabcdcbaeedababdbccccbdaddcdbdeadeebaeaabdaceeecbeaaababbeeeaeebbbdaebecbcccceaeccabdcdbdcddcbabaecbcbecbceccabdddbaebbcbadedcacaceeecebddeebbddccbeddcbccabaeaebaaeeeacadeabbeddddabbdedeeeaacbbbdcedacabadadedcabbeceecaeceaabcebdededbbacaadabbbedeaaeebdccadaeabcaeeacddbaceebddacedacbbedccdbacbdbccbebdddaccbbceadcddbecdebbecdddeaadccbccaadcceaceeeedcbacbaecebddacbbbaceceddeedebbbbeedabeebbebdecddcbcaabaaeaebcaedcdbcbeadddceaabbaeadadbcdddadddcdcdccebcedcdaeeeecaccaacaebceedbbccaaacdaabdaedcbdececdcdcaeecbdcebbbcacbcbadbbadddaebbdeededdbadbeccdddcbbaeadedecdbdeedbaeababbbeaabcadcdaedcceeadbabbeeecebeaccbabceadebbaacedebebaeeeaeabaaccdcbcddeaabdecedebadecccbebaddbedaecbdcedaabdceabcdbdaebcbbedcceeadaeedbebbadbadabcebabedceecebddbcbdbeadeecbbbdbcccdecceeadacdbdceccaebdaeeedadebeccbcbbdbbdcedebddeaeeeeaccdedeedeedeacebdddaceceedbaadcaddeccaedecedbdceccedacbeacdbdddcccccbdddcabacdacdaeaaaabdacdcdaebabcccdceedcebbdcadbdbdaadedbbbcbcadcceeccbbeaceaaedabcacccbaeacaebdeacbbcdbeeabadccbedccabcebaabeabadadbdcebdddbdaeddcbbaccddbeeaaecdebeddeaaeccddcaadbecdaeadbabdadaadccadaceedabeeaabaddceeeddcdaecbbbbeabcaececdceccbcdaaeedbeaaedbbcabacbedaedcdbebaaaecdbaabcebeaacabbaebccaddedaacccdbaddebdadeaacedaecebabbecebeacdedbbebdcdbcbbecebdebbbcdcdeeadddcadeaddcdcbabddaabdccabbbeabeaaeacbdaeaacebccddcddbaeacacbcdaadcccdeacbdebddbdbdaacddbcdbaebeceebdedcccbdbaacbcddbeddeddabceaaabcdadaceaacceeecbecdbabaadadbadcdbbceddceeaecddcadcceecbcceeccbdbdacaaedebdddecbebbcdaeeceeabededbadcccacbbdceddcebdbcecaccaccccddbbebbadcaabcbcbacddbdedbcdcccecacdbdbdeccbbcdeeeadeacaceedbeccbcbadcaeaabdcabaacceecbbdcbdabeccbdbccbaeaecaccbcaadbbeedabeacbbccaccacbdcccbcceabedadebbcdcdaeababbcebbebdeeadbaabdbdbbecebccbbdbcedcedddbcdbaadacabdccdecbdaddddbdbacdaaeebaaeeccacedaedeadacdbedeeeadbadeecaacaceebacdddbbeaebbcecdadcebeeacaccddbbccbaceadbaabbcbaeabaeebaeddbbbcbbcdecdabbcaebdcadabbacacaebbcebcbcbcbabebbbdddedaaceddcceaabaeabbbbeccaacbcbabeecededcdaaebbcacdeddccbbeccdeccbcadbeddcdebcdecceaaaeeebaebdcdadeadaaedaaacbbadbcdcacbececaeaadbabbbccebdbbdacdeadaecbedcabdcbdcadedbaaabddaebaadcccebbceebccbeccaecdbbecdddabbdeeaabeedccadeddaedccdadcddeacbcbaeaeabaeeaeaebcbacbebbaccbdcebdebccdcacddccdebcbcbabebdaaaedecbdccccdcbdbbdcecbbaddcccbeccacbdbedcaacbcdacdbcdaeeaeabacadceddbeedcbdcdbcdeedcedabcdaaebabbdebdbcadaededededaeabbdcbcbcbbcadbdcaaacbdebcdacecaaacedddebeaeaaebbcccacbedcdecebbcbdcdaeecaeaccbcdbeabdebeeeaeddceaabdabbccdadcededabbeeeacacccbceebeddcdebacbebdadeecadaaceddbcbbedcededbdccdeaeadeedaacdeabaeeaecaeadcbaedcaccdeacbecbaedeebddcddacbeedbdeacecebecaaaaddbdbbceddadbddedaccebcddbabceacaecceeadaabdcbeebadaeceadccadddeccccaeebcdcdddabbacccbccdbccbbedacbdeeedbceeacddecbcdaeeecaacbdadbbaddebbbdebebddadccadbadaababcabbcacaedcdceaddacbbeddbdaacaecaabdbbeccbbdcdceccaadbbedeabdaaceaecedcbaaabcadedcadacbedbceadedbabbeadeedacbadcecdddebebdcecceaeadcedbbebecabeededbacedaecbbdbbbeabdbbeeaeccebcebeaecdbcbecbdabaacddeecbdeaccedaadecbcbbccdedabadbaecdecbabcdbaddabcdcecaeabcceaccdecdbacdcaeaacceaddebadacadcabbeadccdeeeabbacdcbcedccbeaacaedcecbcbcbcaceeeaaeacaabcccedcadbaaadcbdbcdeabccedcdbbeeeaeeccbedcbbeccaebbccecededceabadcbaaeccaabceccddacdadabdebbeccbeaeecabaacabebdaadaabdbdecedcbcccdbcbdcadebcaaaebbaedcebaaecbebbcdcbbbddecbddecabadacbbaddcdadcaaecbdccbcaceabdeeacdbddccbbdbbcdababeabdbdacaeccabedeeeacdaaeaaecebcaabdeebcdbdacacbcdcabacccabdddddbebcdcdebdcedebeeeaebdaadcbadaadcceabbeabbcdcbbabecbccbedebbeaebcbadcaabceeadabbceecaeacabcceabcdceececdbebeabbaebaadbddabddeeeccdcbceaccdbcebbeadecdaaabdaeabccadbeceeebbbbbdbdeeabcbcccdaebbacdababccebeabebedecabedeabddbbebddddebabcbecdabadbedcbdaacbbeaeedbcadbbcbdeaecabbddebbeeaabdeebceaaacaddbeaaccadadbdcddbdabcaaeeddcceaaaddbceacedeeceddcbabdbcedecdcbcdcabccdaddaabadaaecddedadbaabdbeaaebcddaeaecebcaeedcaaceacdbdabcbcdacceecabaeaaceabecaacedeabddbcabcdacccebedecbedeeaecceaedabcebbeddeeedaabcdbacbccdcecaeedeeecbbaeadeaecccaaaddedbeececcbcdcabeedbedebcacecbcbcbeaecebedeabedabdbeededdcddcadedabdbeecbbedbcecdadddaddabbecccbeceacccddaeacbbbebcacadebaeaeeaabbdddebceacbbbdabdacbccbdbcebbdbaeceacaacaabadeebdabedbdaabceaaaebaadddededadbeaaccccaacebdbebddadedbaecbeadacdeedbaacdadaaebedcddcbbbebededbabcdadacbbaebaacbdddeedebeecaadecbccbbaabedeecccbdbabecceedcaeaabcbebddcdbaecadbcceabaaacdbecedceacdbbecaacacecdbcacccccadacacaabdadceddeeaacbabacbeabccdeadeddabdedeeecccaabeabceecececceabcadcbadcaaebbebdaddacbcedbacdbdecbbebebceeebcabcddcebaabbbeadcbceedcbaddeedacecbcbbdabcadcddaedcedbbbebdadccebcceadbbcddbccaecebcedbaeacaeddaaadaeeddbcbbbbbccdaeabddaeaeaaacbeeaaaedccadecedbaeedbbdaebaadaedbdedddeebbeeeaccadbbbcbccedabbbdadebedcaceebdeebbdabbbaeeaabcdcbedebaaecbadcddbddcdbddeebbebdadbbcabbeebcbcadedecbbcdcedeebacdabddbbcecacaaaeedaaadbbbbeabebdbbbbedbbdcebaccaabeceedddceaebbdcbdbbabccacacdbcabddceababcdccbecbaeeababadbcdcdcbcaeaeacabcdcabeaaeacecddbddbeabcdbaadaacbcecedddeabbaabeaecdceeeecacdbaebddaccccbadbddedabeeedadeebabebdabdecddbaaddeaecdaccadbbeccdeadbeacbeccedebedbcedcccbebceeaaaeccbcddbcdabaedcdabcbeedcdacdcdddebcccbeadacecbdabaddccebdbeaebddeaeeacedccceddaceeddcdbdadaabeecabdccddbecdbccaceceddcadcbeedeeabdebdcddccedabadcdabbabcedaadccccedddddbecececebabddabcbcbedeaedbcebeedebceaaedbcccacdceaebcaeebabceabeaaabcbaeccaecaddaecbdabbadbaeeeaebdbdaaadadabbabdecdeaaaebebcebaeeeccacaeddeccbeaceaddadaedebcbddbadeebddbebbdcccbbeddeddebebeeccaccbdbacabeacdabaeceddbaddeaedaaccaddedeadcebedaeccabeaacbbddebdbedcaaaddebbaaeecbaeddeabeedaeaacdcbdaceaeeaabddddbebbacdeadeecededcaacbaaaddcbbcaebbdcbbcaababdcbdbacececceddabdbcbccadcaeedeeaacdabacaecaabaddbdceccbcebedcdeaaeeeddbdbaaadadeeaebdeeacbadccbceecaabadedebccbbdbbeaaedcdedebbddccabdbabcdaabdacaaeeebbcccebdcdeeddbccccbeaeeedcaaedcbdacedbabecccdcbbcbceeaeedaacbebddaeddbbbdacbcebcddabaccdeaeddccaedaccaaeccaedaddccadadaeeabadecdbcaaebeeecaebbbbbbbbddaaadebacaaabceabdccbceaabebcebedeaeecaeaecbaecccccddedeadabcbebdeaccdabbdeeabcbdadadbccdaeedccdcacedbadacaeaebcedbdddebbeadccacedecccadceecccaeacdbdcbccaacabaccabdddaaabcbabeeebccddeecadedcbdaaaededaaeaacaedeacdcbacdebabdbcdabcaccdcbcdacabedaeaeabeecaebedadebdccbebbccdeabaeaedaeaadbaaabbaceceeeedcaadcaaeaeedbeabaecabbaddbdddbacdcceddcadbeaaebabeaecddcdeaacaacdacabcacaabbbcadbeddeeaddacbdbbbbdcbccbdecdbdbabaadbaaaadcbeaebdcaeddddbebdcaedbcadecadeaebcaceaacbebdcecaeadcecccdeedddacccbbcadaacceececdeabdbebddddcadaeabbcacbcedddacdccbeeddaacaacdcaacddceabeadcddccdebeaeeabcdccdbceebcaabaedcaecceebeedccebadcdbcccecaaacdaaaeeadeaaadacccbdaeacaeeceebabcaddddcadcbecdbddababebebaaeabccdcbdadbaabdecacaeeaedeccaebdbaaaddaecbcebabecdbebccddbbbbbedddddbcdeacdbcccaabaebbdecaeedeabcaececcecccebbacdbadabbdcdcdddecbcdcabbdbcadeaaeccbeeaaacedcaaddabbcadeacddadbaacabdacaacaaacbdeccebcdbebbeeaccabebecedbddeadbdcaebbbbcdadbbdcbcbaebbcddbadcaeadebebddeadedadbccacdccbcbadebeacadcdaebecacadebccabecabcaeceaabaaaacbabbecbbdecadaaeabbeaadaccccbeaecaecccceaecbdedceeaebedcaabceabebeaadabddbbbeebdbaabccadcedebbbbacccbeeceedcbabbcabaeaaadbbbddbeacdececdbcceebcacabceaebcbccbdaacaaeedadbedacaaecbbcddcccabbdcdbdddcdccdeccaeaebbacccecdeeecbbbcbeccccaaeecdbdbcdecbeadcabccbbdeabaaadbcbecdabcadddedaebcbdaddcacdeedacedddcdeeadaddbcebbacebccbbdddcccaaaaabaccdeedcecacddedcedaaedadeebdecbedebaedcadbadaddbdcdeadabbbbbaeabdeccbceebcbcbedbaaeeecbaccdaedaacdadcbbbbeaccdcccbedddacdcdadaebcebabbacaaebeadacbacbbdabbaebdcbdaaadabccebbcdacabecdecbbadabbececaacdbabebceabdaaeabcddbaacdcbbbbabacdebdaeddadedaaccbdadecdbdeaccbcebebebbaeecbdaeeaededaaeccdceedddecbcbdecebeacdabcdcbdecadccaeaeaebcbadbaddceddebbbacdebcadbecaddbeccbadbeaccaebeedcaaeeecbaebeebcdeaededbacecbdeededbddaebdaeabdeaaebceaccebccaedbaabeedeaeabdedcdbddedaeacddeddbadbbeebdcdeabcaadccbadeacedadeddeccaadaceedadaeeaeaecabaebbadbedeaeebddcbbecddcbaaeadbebededddcecdcddeeccdcbabebeeabdcadbbddecebeedeeebedcdbaecddeebacaadaabaaddeeeeeacbbccdeaacaaeaadbddbddbbecbbeebcdebcaaeadbbeddccedbdebdaabbaceaaacdecdabdadbbdcdaaaddeccdddabbdcbcaadedeadeaebceabcbeedecbabdaebaabeadeebaebbbcadadabaebaedceeadbcddccbabeacbaecddebeaaecedaaeedbbddddeddddbaeeebdbcdcbdebaaebebbbaeedebcbeadcddceeebdbdaaaebecbabbecbdeabeddccdcaaeeaaecebbcebceaebdbebbbaaeeeeabbcdeabbedcacbcaddbdcaeceaacabacebcebedcbbacebcecaededbbeabdabcdbceeadaacecabdaacdbaebbaccbeeebbedccaeeddeabdeceecddeeebedebbcabdbecdcadbebaeadbeadbbeeeebeeaaeadedaabaebcaddeebddaaeadcedccbdcacaabcaebdbabbeaacdbacbebaeccaaeaddaaebdcaeebeadaceaacdbcdadaaebaabacbacedddecabdceadddaeecaebccaedaaadedcccebcccdebbcebaababeceaacdbcbbebceecaebdddabdbbceedacebaccdadabecebdadacdcdccddaaddecdaddebbaecacdaaccccdaabebabddcdbedceaeeccdebebcdcbabddbddbdcdeaecacaddecdeaabdaedcebeacbbdbaebdbebddacebdabbbaacceceeaaadbebaedbbddddaeaaddceaaccebcbcbabdabdbcacdcdcedbdbaebacdecbedbaecdaaabaabddcccadeeeaaaddcddddcbbaeabccdeebaeabeaacaceedcadebaabcebdcedabaeddeecdcedbabdaabaacdbdebcedcacbedaacdaebddbacdbaadeadaaebecaabeeacebaabbaaabedbeadabdeeccaadedaecacececcdbadbeacbabaacabdeeeccbeddbdbeeaaaceceaedaaccddccddddceaadcacdaabadaedebceeccdbdadaebdbcbeadbadbadaadabecedadcacbbebddcaecaadebabebeebaeeadedaaadadeebaeddbaceadedbdbdcdcebebcacbbbcabaddbcbbedaaaccbbecaadbaeabedacbeadcadbecaeceaeedadaabacebeecacecdcaebadabdbedcecebadebacaddcdddabaaccdbcbdbaacacdbdbeeacbeebedaacacaacaebbebdbbeecaabbaededdabbacdebacdeaacacebbacbdeadcddbecbbcdbeecbdeeaaddeeacbaaacbaeebbeccaceecdaacdabaeaedceadbecabadacabcadbadaebbdbdbddbaacecdbeddbaaaeeebecabdebaedcdccdbbabdedddbdcadcbdeabbaaedcedbadeddcccbceebdccecddbbdccddcedbbdebcedbdaedeedddaadcaaeaedaaacdebabcdbadedcdddbbdccaecadadddaedebeceeceecbddadcabaeeeababbccadeedbeeecccaacacebeadccceadcdabaaeeabbaebcbaabbecdeeeeacbecdcaaaddcdebcdcdcdbedcbeccdbeabbcaaecadcddabdaabaeadebeeecdceacaeecddaedcaabbedadacaaecdbbdecddaceaabeaeccdedbebbaaeccbecebddeeaedabdbcbdedaaaebeacaceabcebdeeedbdadcdceccbbeaadcecaeecdbedeeeaaadaccedcdbdaeeceedeabecebcaaeaabedaceedabedeacecdabcaebbcbbbadecdbebddbebeaceadadabdbbeddcbecaaececededebeeddddecacacdaedcceceaabacadceaabedebdeebdadbcddaeeebcabedeecbccbdcbbbcecddcddcabddcbbddbaaaabaedaadaddabacdcebacdadaacadcabdaedaeacededbaccbbccacadbcbabddadcdbdcdaebbacbcdabcadcbeaebebacdbaacccbedbccdcaddccdcccdeecabebbaececeeedadeeeedadabcbadcadccaddeaaacceeddbcbcacaaaaeeaedeaabdacaadceebdceebdcdeabcdceaeeacabddaebaceebbccabdbeaecdbcbbaeadbbbcceeeedecaecbcebccaddeacdecbbbbceeedccccddeecaecedebbdeacaabdceecddbaedcacdeebecdddceccaecaeeeabeabbddabecdcddeadacbdcdadabbbdddbeacdedbeccdcebadceaebaadcaceadebdeadacbbcdbdcdaadadcbbeebedcedaabdbcbbecabdedeccbdcdcbceaccdbedaeabdcaecebdaedeedebbddbededccdaeeddebdbabdccdadaabdeacbddadbbdecbdbdeebcbbebddeebaaeddddeeabdedbdddccabeecabdbbabeddeceabaeaabeabdbaaadeadabddebbcabbeadababdaaeecdecdabbdeceeccdbdcdeadceeabebbcbdaaeadbeadbeecdcedddcaddcbabeaceaddccbdbdebbbdbebcaabbbddebadcbdddadaeddeecabcebbccdbbcddebebeebcecaaeebdcaecaadccbacaeceeabccdcaeadcbebdcebaaecceaacbdebaeeeabebddeeeecddbcdedbbeebdecbbbbddccbcbadedeccdcbbcadebbcadeeedecdbcecbaaaecabdcbbaaaececccededcaeabceedaaecacddedaceaeabaaabdbeebbcdcbadabdbcbbecdcbcbabacdecebebbbeeeaaeaabbacbdbbddbeacaeeedddcbcbceaaaaeabbccedbecabaedbeedbbdecdebedaedabdddaeacdbcdcebbecaacbbdebebabbdceccbbecbddaadddedccbecddbedbedbedeeecbdaeaccdeabdeaeeaebdedbebeddaaaedeceabdbaeabddcccbeaabcbadceacbdbddaecdbdccccecbdbedcacdcaebbbeccdadecbddcdaecbaaedaadcdaceeeeeebbebdceabbaedbaabcdabcebdcbadcbcdecbbccbcecbbdbcadedbaeacaacacbacdceaeaecdcecceaacdbeedaccbecbbecdaaccdcbbbbbcacddcbeadbaddecabcedeadaaadeeceadeadecbbdadecbeebaeeacaedaeebeddabbeabaeabaccdeeaccacaabcdaebaeedeadacbddcbbceeabebabebedaaecdddbebbcadbbbddcadaeaadacbdeadbbaeeeedabbcbaacbddaeeecbacdedabdeaeaabbbcebeaccaccaadcdbbdeabcedaecbeabdccdcebbebecedebcabcadbccbadeeaaebddddceeccbaaeccdbdddeabbbcbdebadaaacadacabcebabbedbbccaeccbeeccdeacaaccbacedaebaeecacaeaeacdcceccbbcbddacbbbbadcbabcbdadaaedeeeeebdcaddcaabacbbdcebeaceaedcdbadeccbbebcadcabbcaabbbeeabbdcbdbbdbcabcabebdceeadbccddbbbbbdebabccadccaabbabecaedabdcebaecccaececbbaeedabcdbecdddebacbacdeeebcabedcecdbaaccdecddbbbaccdaaeddcbaccedcacedaebbaeccaacecedcdbeeccceccbecceaacdeaaeddcedeedeaebedaebadbdbeddcdacbbdeebaccbbdcddacadadeeedecacadbbbcedaddeaaeaaebcadddccceaaedecabbbccaacabbdaeaddebcbddeccdcdcadddeadbeeddddeadbbecccdcdebbdaaadbdccebcaddcadaeccaedacdceecaaaecedcadccbbcbceeadeaeabdadcaadaccddbacedddaceebdccecccaabddebdccbeecadbeaccebacedaeeecacbddcaeebebaebbccddccccaddcabcbacbeeececbbbecdbbbbbecceaeadbdaaebbadcecaaacccceeacceaaddcbabdbbedcaabccdcaddcadcabbaaabdceaeacdacdadaddcddacaaccabeddddaaccbaceacceeacceaaecaabcdcaebeecdeebecccadaeeeedecedbadbacbacececcebdbcbaadabaccecadaddcddaacdbdeecdcbabaacbadedbdabadeeaaabdcbaecdcadcebbccbbbbddbbecdcebcceecbdcaeabeaccdeedbabceecdadcebeeceebbbbacabcdabacbcddaebaedddbadabeddaebbdbeeabcacccccaeabcdccecaabdbacdddbddcbcbcbedbcbeacdaadddbcbebddeabeecddeebeedadcebcbedeacbbcbdacecbbabddadacecacbacdadceaaedecbdceebceabddbddbebcaaeaebadceecceaadbabecdddcdebcebadbcabbabdeedeebdaacdaabcabecdecdddceadeeedcbdedaedaabacecabbeacdccaadcdbdeeebdcaceaceabebdbceabceedbcdababdaaccdebecabcbcaeecacaabbbcdceceedadcaeaebabaedbebaadedbbabccedebadceddaadbdceedbececaecbedbdbceaedcdbbbeddbbdabcdebbcdccaccdeaabcecddecdccdbbcbdbdcbdabdbceabeeaacbdaebcbcbeabaeacddaedadabbcbeddddecaeeaadeeceddaedaacebdeecebdadceaecadaaadeacabacbadceeddacdeecedcdbbacbeeeaceeaeaaaedacaacbdcbadbbeccbcbebeccdbbeaceddeadbbcacbabcdbeadbabdeadbebcdabbaeaeccdcedacebeccaacedcaddbccecabcbaaecdebdbbbbeebabedbbccacdcbecebcbcdaccccbbbeccbbdccdabcceecccedebdbbddadebebaadbbbccbdeaddcdebeaeaceccbbbeeadaddcecebeeebdaeecaeabddbdbddbcbacecacaceabdcccecccbcceebbbaeedaaabceedcacabcebeccedeabdeeaccadcedabcdcbbeccebdcedeeabdccebceceeadcccbadacbcebbacbecbeedbaaedeeeeadeecadddcbaceddabaddbcededbbeeccaaacbdaeabbdbbddadddbcdbcedbdbcaeadedccabdbceebaabedcabedacddbdbeceadebcdaebeaeeecbcaeedbcebaecdebdcbdbaceecaedbaadadcecbedbebeaeedacbabbadccaddcddcbddbccaaacdbebcdedbceecbcdadabbdeccccdacdeedacbdbbbaecdbdcabeadebdcdebbbbdaadcebbadddcaebdeeebeacbabcbceabdedebcecbebcebebbccdcdbebabbedcbeabaeaebccbdaadcbbedaaeeeecddedbcbecdaeaedaeeccdcdacbbabadbcdbbadedbcccadadaddcabbebecebecaadddecbcdbbdcaebbbbebbdedcccacabddbeaacbdabdaacbccbcdbbbacedbeebcaeacbbbebeabcbebdbabaacaecbbbaedbbbebdabbdbedccaedcddaaaabdcccaeeaabcbbeddcbbbbaecbbadbbccbdbbcbccaccdaaddeedaebbcdcabcbebdddaeeabbabbcdedecceecbcedaebbeecadeabcababdcaeeaccdbaebebdecdabceadccbdecedceadadcddcedcbdcabddccadcbccaebaaecbeeaeddeeaadcecebceecaedbecadcbbbbdbbbabdaddebeccecbcdcbedbbdedbedcbebbbabeadcecccecdddcbbbacddddbecbabeccacbcdbcceedecbeeeadbecbdbeeaeaadacbdecbcaebbcdcceddbaddcaecedbaaacecededdaebcebbbceecddcacdedeaddddcdecdebecbbdddbbccddeddddbcbdeddadccdcbcecaaceeaadbcaaaedebaadeccadaabaaadbdecedcecdbbddcedcedecccdddacbbaadbcabbaaeeccaebbbdedebdbdabecbddbebeaacbbabaabcdaacbcadaeeacacbbccabbbeaabadaecebadbdbcadeeccabedbeadbbaabcbcdbaeacaddcacbedcaeccbabbbaaaaabedabbeedcdabbcedabbaabccabaedaccbbadccbcdedcbeaeceddbecedecacbbebbdabbbbacbbecbedabbcaeddbbbdecbdeedcadabddbdaedcdacadeadebdbbdeeebaebdebaadddaacededaeebddddddbcadcaebadbddbadbebdcaeecaccedccddaacdacddecdbedacaceadabcdaeadacccaaccbecededddbecceadddebcbdcbabbbdbebdacacbcdaeaeadbcddbeddabdbaeeccdecbdbeabdbddbdaddcccedacebadaabcacabadeebbaaebcebdaaaacedbcaeacdeddbaeabecbdbbdadccdcbaeddaeaedbbdeadddccabbdbdcccecbbedabadddeacdebddeedabaaebceccdaeeedabbecabcadcbedcebeaebdbdabebcabaeccdaabddaabeccdddccaceaeadabbbadacccdebadcacdbddbdbcdbdeaacaaecedaecadcbeeabbbdbeccaacbeeecdacbeaebbeaacacbceeeaabbdcdeabbbbccbdadbbbccdaeddbbeebdbeaaeacaabeabdeddccecbcdcaeaebebcaeecdeecdecadacedebdedbcbaceaacceeccdabdcaadbcdcbbbbddecccedeabaacabdddabbacdeedaaedbdaaceabbedcebceddabaedacbdbecbdedeaeacecaceceadcbcddcbabecbeddacbbcbbcabbaddbadcdaabadcadddabaddbddedbbacaedbaecccbaedcccdbccaccbaaebaacbdcaaceedcedeabcdababaeebcacaeaaabbcebabbadbadccadcccecaeaaeecbbedabaaabdccbababddbdceeeeeecebddccaebcbebcccdbcdceaedcedaeedaaaedbedbcbbbbacbecadccebaaebcebcdcacecdbeccecedbceaabbdcdbdceaaaadeacaacaaeddcbdddaecedeebdbacecdcdabdbbcbecaeacebbdcecceecdabeedbdbdcabcecbeeeaeceecdeadedecddbdbcccebedecdbceedaebeaaddeedacdaecdcadcdbbebaddcedbbdebaeecddeadbacadabdeddcdbaadabecaedaabdbaebccebceabaecadcaaddedddebbaedacadddcbaaeeedaeeaaaeeabcdcecccaabaddededcdecdeebcdedabbdedacebdbbbbaaceeeebdbdcabccabcacadbbecaeadadacdbbaecaedceadbbcaddacacabcdabecadddbdcdbaceeaecaaeedebbebaaceccbeaaabeaebaadbdccddebababeeadaedeeddcbaaecbbecdeecacdabbdbabcebecaeddecabcedcbdacbcbaaddeceecdcbcedddbbcabbddecdbceebddcdebbddedabeddaadaccaeebbedcbcdbbdaeadbadeceecdeeccedeebeaaaeaaedbabbcacdaccbdcbbcacdccbaeebabddebdbbcbddeecaddadedcabacebdbbbcebdacaeebbebdccaccabbaaedadddbcdddccebddbaacbdabeaabcdceddcaeabccebcecbaddacdeababdececaedaddcecabebcdccebcadbaadebaacdebececeebdbdecabcbdacbcedbeaddbeebbdddbcedcadeabccaaebbaeeadcadbcdbabcbabedebeccebbbecbccbeeebbaeebcdbbbdeebeddcbbbabdcadaceccccdeaeaeceeabaddbeeedcadadecdbcbaebcabeabaabeebeeddbedcabcacdbededcbcecdcbccbbedadeeededbceaacacedeabbadebdbddabaebcedcaccaeabacccbeddbaddccacadadbaccadddeeeeeaeaacdbabbbbbabdaaeaccadbbeebdbdedbcceaddcceacacbccddcdccdedacbdaadedbedadeedbbceaecbddaaaeeeddedbbeedccdeeaddaeceeaddaccbbdaecacebeedcaccdecbedcbdeeedbeeaaacbbbbbbeebcebdaabeecabbbabdddeaaeedcbdedeaacbccccddeeebeddeacdebedecdbbbcadccdaededeaddbbcaceacacaaceeccbcecbbdcdeedbcabdccddedccdebaabcaadaaedcdadadccadbbedcbcccbdbdbecaadbdabadcaadcedebeebdeabeeaecddccbedddcbbdeccbaecaababbecacebbcedbcecdbdcdbccbbebceeeabdeecaaecaddecacaddebbdcaeadaacbaeebedbdbdaabbdccddbccdcdebcbdaceccabeeddbebecbbabbcecdddecccadbccddecedacbedebcaeeadbcdabbaaceaacabcdabbeedadcaddebeccabedabddabaaeccddedcbceddeebeebeaacacedbaddebbabaadebaadcbeeedecedebddbbcbbbdbaebbbeecbcaecbeeaabddccdcdbecdbaecbcdecdeaadbedddabdddceacbdeeecbcddcdbcccdcbdecbcdbdaaababebcecbadcdcbbaadcbaeeddcaedeacebceabacbddabbabdbeccbadecedccbbedecdabdbabbaaaaadaaabcbcecdecaecbdbacbaedbbbdbccaabbedaabebcadedbddadacccaaebcdbacaacacacdaadcdcaeceaabeecacacecdbeeeddbadcaccdebbbaaecbbeabbecedaceaddedcdeeeceeaadcdebdcaddbebeaacabdbbeaebebbacaacabcdabadabeebbecdccedaeeeeaabdceecdebdbdabdaaecbbaaddaeecebaeebaeaacbecadebbbccaccbccaaeebdcccdbdbbacdbdbbaaccbdeaaeaeccadeddacaecdddcbdadaccbcbebbaacedcaabcdaebbabeccdabdcabddeebacaeadbaaaaeadaeaeecaaedaebacccacbadcbccaeedecedddeeabadcbecedebdbbcdaedbeadcecacdeabbdaabacbbcbcdcdbbcadddbeceadaceaadebdcadccabddcbdacbbeacebadedbdabeabaabaeabddbdbbbccaebeeddacbececaadacabedbbdbaebdbaebeebecabdbccccdbcdaaabcadbcecdbabdabcbdcdedebacbbbeecaceddddcddedebccacdabceeddacbadcdeceeeeadaddacadababbcdacccdbdeeceabbeeecaddbecebdabaedcdeaaadbcabdecbedcacbabccabeeadaecdecdcabdcdecdeacadabbbccbbcdbbccddcabbcbeebcdaedbddadedcabdcddbeecacedbabdadceccccdaddcecadcaeedbacaebaaaedeebabbeccaebabddedaceedceaeccbdeadeaaaccdeadccadcbeaeebebdacdcebdbadbdaedeabdabcaaaaebeeeecadebeeebdadaeaaddcadedadbcdadaedeccaaddadaaaaeebccaecdaddacecbaadceecaebccddabecdcbbcbbdacaeaeaccdbbaaaeaceadaccdbbdbcabddabbbeddaeececaeddeaacdcccbbaadbaeaebdbdbcacaadbcabbececcdbcdaaaeabeccbdacaabaaaadadeadeeebdbacbeddceacdacabdedccaeeccdbdccecdabcaadadabdabcbbedbecaddeabedddeeacbcceaadbdadabaeacbdcbdaccebeedaabadcedbddaecdcedddacaadcaccdbdabddccdeaadbbbedecedbceebcdddcedebcababddcdabdddbebeeacdbabcadaedeeceedbaecdcbceedceacebdcceedacdebaebdcebdcbdbdadbacdbdbeddbeaadeebccabbacaddbebbccdebcbecdadacbbebbaedceadbcbadceceacccebbadceaaddaceaabeecaebcebcaebacbbcababbaabddabeebbeedebbecdaeddaeaeacddbbecaadbdebdaccaadceacddcbbddabecdcbceebddacaddaacaaeaabcabdbbcadccaeeadecdcaacaedebbcaadedcceedaaedecdebabedbacccedccdbceaccebabcdaeececacedbeaabcabbadecdcdbcdabdbcaeaedbcacaadbbabbdecccebbaadeddeacbdcbaadedecbbcdcabababcabbdeabbbddebcaeabdbebdeceadccaaeeadcdbadcaabbaaecceeedbeadeddeddadbabccbaeecbcaabadabceaddddeaaadaaebcaeabedadcbeecdddeddbbcdaeddeeccdbdaacaeeeddbaedbdbdacaccabedbcdbacbeeeccaedbcaaeadeedcdcaeedcacaeeaabeedbdcbabddbbaebcaebbbbeadcbeabebaaebeaeebaebbacdebaeaeeaedecdebcaccccebdebcbddbebcaecbedaabbdcdddedeacddcddbecabaccaeaceebbceaeceaaaaedccadcddaccbecbecdbbedacbcacbdedecbccaecaadcecbacbdaacbacccbcbdcddcbdabbaaaedcebacacccacadbacebabbeddadebeabdaadbecaeedbeabbbeaaecebdabdeebaeecabeddaecdedaddbaccaacdadbbccbaabbaedecaddedddedacccddbbcabacebbaddecbaccaaaeeaeccdacbdcadedecdcbaecbadeaadaeaacecbcecbbcabcedbabbbaccadcccbddacdebdeddadbddccddaadeebdacacadbacebceeacbeaccbacabbedecaadbcedcaeeeecbcddcccbaecedccaaeedeecdbdbcacecadceeecddeaeeacbcdabcceeaeccebdacdcacabdbebbacedaabacaedcebaaeeddedcbddbacdccbccadcebddebccccacdddbdcdeebcbbcbaddcacaddbeaaddcabbdadccaebeebecaabceedcbcaedbdeeceddaabcdeeedccedeeadcdcabdeaaadcbaceadbbdbaaccdeccabddecbacbaacebcabcaddeedbaabcebeedcddbdeedcdeaebaadcbdaaebcebbececeebebabcdcbbdbacccbeaedaaaeabadabdbcacccdbaedceccecebecbecabdceeedbceabbaccacbedeebbaebacedcccaeedeaeacdeddebdbaeabbcdaddcebcddceecdbeaedacdbeabecccdcdececdcaaccaeadcdbecaeeadaebaebbababcbaeebeabcadbbecbbdbeddbbccabeeeddbaeaeccaedaadbbeaaeabadbeaaaadbceabcaecbeccebdddacabadbcbbbababebdcebddcaaebdbdbbdaabebbbbbdcdccceaddaddecaadadcebaaadbcadddebaaacceaddddbaceedaacdeabbdaceddddacacdbcbcbcdedbcecaeededabeaaaabdcabaacdabcbabbcbbadccaccdaaabddcaeacbabbdeadbeeedededaeebbbdbedcecdaeaadcbedabdacdbbcceaacbacaeaeadcecacedccbdeeebccbbbcddecbbdcbebebbcadeebdddbeadaecdcaaddebcbaecbbdcddbaddcaaedadcecbdabcdbcdcededdeddacebddaadcaeaccbdcbdbaeaddaaeebebdbdedaeaeccdbaadaceaeabaadbeeececaaaebaeebbabaebeddeeeecacacbeeabaedebcdebaccecaabdbceadaeeaecedcecdeacedaaabbaddbebdddbeedbbcdbaeddecbecbddeecbadbeccaabeaeaeecadedeeaebacbbbebcadccdadcbcbbebaadedddccdbdeadcaaaeceedeeeaccaaadcedabdceaadbcbcebecbbabbbacacecdbaecbddbdcceaacdccccdeaedbddacedddbaedecddcddddbcbedcaeebbadabcdeaedebddddaebdbbecdbebbcbdebeaebacbedddbdbcbadbaedcdcdecadabadcdbbdccebeabdedecbebdcacbeebadbbbbabdecceabbbcbdadcedccdabbdecdcbedbcaaadcedbcaabaaeeaaaaabbcebeadedaeddcebdcadcbdebeacaabaceecdecdaaecdcedbbebebbceedddaaabcdbbbbbdbbeedceeddcbcacccaaacecaaebcceeabbdbdcadaabbccbbcadabcbebebbdaccabbcadbeccebdaeacebaeaacdbbabbbbebddbadebdcccdccddbdaeadcadbcdebedcccebedaececdaedcdaeddedeaabbeaddcbaabacbacaaebdadddadbcceabbedccdeadbcbccbdeadceceaddebddeeecbeaadeeaddabdeccbcedaccccdbbdbbeebacbdcbdebbccbeeceedcdbaddbaebcbbedabedcacbdaccdeeedaebbceacacbaedabbcdbeddcbeeeebbbbaaecadaacecbbdbdaadbdeeecdcbedbbdbedccbbaadeaeaaacadecccceaabcceaedccadbaaddebbbdabadcabcdcdebaccabcbeaceeaacdedcdebebbebbceabbdaaceeddacaedcebadbcecbbabbbcbacaecddddebdcbdabddbedbdddcedecbcdbbcdebdadaabcacbdcaecbcddadaecaabeaecdaddbcbadbaaadadeaadebeebbeaededaabbdebadeaabdcecbcaddaeebeaadbcabcabccdaedbdddbbbbecdadaabdaededcdbccdcaacdabbceddbbebeedbaabdaddadbaaeebaddbeaddcdbdeecdbbdcbecdcaadadabbccaadebbcaeeccacaaacbdcaeadaccbaaebeccddbbcaeeaceacabbedacaecaabcdcccecaddccccabcdcdedabdcbeceecdebbaecababdbcaabdaeaebbbdaceeacddcdeeabacbbbeaabbcbaabedcacbcdbbebcebbdecddadcecadbbceacabbacecdacedacdcacbccaaeadbdcaeacbdbeddcecabbaadebdabdeaeebeaddaaadeabecaaedcaabacabaddeacaaedddccdaabecbeeddebbdeedaaddbecdbaedbeecbabeecdbabcdecadebebbceddebedcabacbeddbdadddcaccbdecacbcaeaadebdbecdbedaeddabddbccacccccceebeaecebadcecadccabeabaeccbcdbacecdddebadbebeaeceacccdcccbdbdaececdaacedceeadcbddaebeddcbcaabbbdbdbbaebdadceddcabbbbbbebaebbeabceceabeaaadbbbbbcaebeaedddccbabdaabdadbcaebebdabeecebeecbdcdeaeaaeceadbebcbdcdcdaceaaddcadaaccbebeaaaecccadedebbaecebbdbedbbccaeeedabdeaebaedcbecadaededececbbabedcbdcaaeeeaddecdcbabdeeebacaedddabddebeeeacbbbeddedcecdeeabbdceacaaeadedcadbcdaeabcbaaadbaccaeabbdcecdcabbacedaacddaddddbdbaedbcaebacdeddcaeabbbbabeabbbaaddebdbacdaedccdedabeaabebbcacccbcbbacadadbdeadbcebddcdcabeeddcbbcddbcebbbaceadaabbeaceedcdaeebeebbbbcdcdbaeeeceedaecbeeeabaaeaabddbadecdbedabaaabaabadcccaeaabaabebdbdabbbaebbeeeecbbeadceecbabdbcbcdddbacbcbdeebdcdaeccadceddadbccdbbdcacddeeebdbaadecbbeaabebcaaecbdbabcaccbadeababbdceceeeaddebbdceceaabdccdbcbcadeabbdeeeabcbaeddaaceecedecabdbeccbacecbcdeaebdcaadecedcdacebcaabeeadcdceaeebdbabadcadebbeadaaccbbadcebccadccbcbbdeceeedabbbaacedaabeebcbbcdcecdeaceaedabbbcaeaedeaacceacaaeecccbbbcbddadceebdeddebdbacbccededdaaacdccbdedaebbbedecacebbadeccdcabaacdebcdabceaaecbceececdabdaacabbbcedbbeeddceeeeceddaeaecaadaaaaacadbeddeeabaabeddaedecbacccddeedecddeaddcbcccdeeacbbcbebbdaeaceeaadedeabdcaccdeaebacdebdddeeaecdabbdcedcceababaadadadccbddecaddbebeddaeadbaadabedaadeabcbacababeedabccedbcaadadcebdceaddcceeeadcacacadcedbebdabbdacacceeccacaccaeadecdeceedaecdaacdcecadcaabaecebcedeebecdbdeabccabaaeabebaecadddaddcbeecbdabbadaeccdaabaedbbaedaaeadeceebcddbdbbdeabbdbeccaeaaaaeeaecbaedbbdaeaccebdeaaadabaedbdbbaadbdabbaebcdddcecddaeededcecedbccbdeebbcbaeadbbebbedbeadedabbddadcecdeceadbbabebcebbaabbbecdcedcddeaabedbbeeabadcdedabcdbadddabaabacacdeaeeeadbdcbcaaabdcbecdedbdbebacdaebeabbacaabbbabdceacdddacdaadbaddacebbecabeebbcacdecceaaceddeeddeddeeebcdbeccbcbeaedbaebbbadebcbcabaddadbbaacdaebebdacbacddcbcaeecaacadeddbcebeeedceecdbbbdaedcdaacdcaabdcbaacdadabbccaeeebdcaedbaddbbdcbdeaaedbebcbaebbdbdaedaadeaecbdeedbcacaaacaeaedcbbabcbbecbddbcceacbceaaceebddbceceeaccdccaebcbbccacdccedebcdaebedabeedadecbebcdebabbbcedbdadeceedadaccccedbabbcbebadddabaccbebdbadeaaddabbdccdccacbbaaddcccddacacceeceadaaadaebadddbaecdebbacecaaecddedbeadbeebadedcbceaacdceeaadcbdcbbdcbdaebbaebbdebaacebceccecebeabbccdbdbdecdbbccbcaedeabaecdbbdeebdbcdcdbdedeaaeeccaeddcebdabdbbdbebaaecddcebdeaddebbbedeacdbcabecabdaccadeaecaadcabebcbdaaeadaccedcaeaabacddcdecbcdeedbceccaeccbbdebcbdeddaadbdbddddbeceebbaacdcdbceaccccebeebdabbcabacdbbcebedbbdbbabebcaeccaecbbdbeebcdcbcabaddcecaecdacdecdbcadbcdceacbdddcacaadcaecbcdacaccadeeeeeecbbbcabeaeecbedccdeaacdeeebcccecceddddcacebcbeebeeddedcccdaccadccdabbaaeaacbeccdbcabbabacaaacbabcdaaaddcebacddcebbbbabceccdabedacdbbeeccabbbecacbaddadbdabdadbcbbbdddcdabbabbaeeceeeaccedecdbbdbecaedaaabadabdaeceaaeccdbbbccbacbbaeeeccaabcaeebaccdbccedcacacacbeccabcbaeceaaddeeabaedcabecaeadaaaceebbabaebedeeedbceeeddacecdbeaecadaeadebbebaecbbdbbaedbcdaaecbbbbeeceeaabbcabaeacbedcdedcbeaeaddcaddbcaccabbbabacdeebababbabcaccdbddecebbbbcddcbdecbbaadbbeedaeadbedebaddbecdbcaaacbababdbacdbccbacdeacdaececdbcccccaedcdcbbacaceacecbacddddcadadbcebcdbbdaaaedebeececcaeaaeabecaadececbdbbabbabeabcceebbcccddcaaecedbaacacdeadbcdecdbbeacacbedccbebbdaedcaeaadbcdbcabecaabbbedecdedabbebbccedaebbcdedaabedeecaadbcbaabaeaaaeaeceebeabbcdcbcaadacedeeddeeddcaecccdabcdcbaeccddcceebdcdaababbcdddecececeebabcadadeddbcadcbbaacddedeeebcbbaeaabeaadaaebbbbcdbcdeaabaadbbbbcceceedadbbedeedcabdedeedbcadeeaddbeaddaaeedeeadcedeabebeabbdeaacdbbcebbcabacabdaccacaeeceadabcbdeeaacbbbdecdbaeddceeebadcbbccabdcdedbbeeadeeaadaceeaddddaaadbcecaabceabdbedccbbbaababbccdcededadaeddcaedbacebdbbbadceddcbebceccabaacddcbdadeeaecaaeaeadaddacccdddbcdbbaedebeadcacdbbbbdedbacbbcdecebcdddbbaedadedabedeacdacbdabcdbbbbcdccedecdeccaadccccbbaceacdeeabaeddadabebdcceccabdedbcdeeeedeabdaedcecbeadcabdebbbcdabcbdcbdbecbcdaecbacebbddbadbbccabbdcacedaadaecbeebcdceeaaadadedeaaabadacadccaadeabbdededddcedbdabbdaeaaabeadbbeaebcacbeabccebbcbcddadeccbedacbcaeeedddeaccceeddadabebcabcccbdedaacdaeabdbadceabcccdeabbcdcbadddedccacabbedcdcdeebdcbcabacdbcebbdebbabadacbbccdebcdcbadedcedebecaadbcbbeadcaedaecaeacbabbadcdeeccbdeaeeecdbdaadcaddaedeebedaeebaacbdbbbddceecbebecdedadaabdcbcecedcccdeecbdadbedaabdaaadcaaeeeabadaaeeedececedddddbacabebebeeeeeedabecdddaccbdaeebbbeddccdbeddbebbaadaabbddbcabbcbaceaceeacedddbddbaeadaddebdbedadcdbebcbbccccdddcbeecccadddcabaaddcbdebddcadcecabbdcdddbbaaaccccbecccdcaaeceeaddddcebbaeeabdeebebddddbcababcbeccdaaedddddadaadbcdddebaedcdabeddeadddaabadcabaadacbddbcbeaabbbecccdaddbcedaeecbddbbeaedbdedcbaaadbaeabbcdbaddaeecdeeddbcecdadcceebceedcbdeceaecedadbccbdabbdbbeccacecdebebbaabeeecbbccdbdbbdedaebcbdcadbccccecbbecaeeaaaacbabaebeddebababcbccbcabaaeddeccadcdcaabcaaeaabdbbcedbaacdedeaabdacdacbbddabaaeeccecebcdbbdcdecccbcbccacccbbaddedacbeddbdcbcdadccedadebddebcdeacebbddddcecdcedbacacecbceedbccdbcadbedbbdcececebbbbceacdeadedbedecdadadeabbedbeecebecbbebcbaabeeedcbbeecbdaaebccdabcdaddccaeadbeeedeceadeccaeaaaecbecbddabeacbccdabcbceeddaaecbaadddcdccbdbbcdcdbcdaaccccaecbedbcedccaeeaddaaceceecdcceecccdaacaacaebeecccebddabedaadbedbdeecacaacecaeecbacbdecaddbbdeabeedbedcdbdddacbadbebeceabebabeeecabbeccbdeecaebdeebcbcdeddbbaabacadcccbdcbabeebbaacdedadbcdbbcabddbacadadcddecddbbdbbabcbebeeedeadbceebabcdeabdacbaeededcbaecccdecddaddbaaebccecdcdcecbeddcaceddcacebecddcabadcaaabdcccbceeebabbceaeccbcceaccdaebabbaeaaceadaeebcaabbbeadcddcbcdaaadedadceedaacaadbccddaaddcdcdabbeeddeeccdccedbcdabeecddddcdceeacddacbbedbeecebaabebdecedeccabbdadbbbdabdcdddcecbccecdacaddceaddcbdcddbecdadabbddbcaeedbdeecaadaccbdaddeacecabcacceacdbebabacbcaabdeabcaabddeacdeecaccacbdcedeccebedccabaaececabcdbaedcbcbbbceeacabadbadaabaadecbdbedabecbacccbcececdeedbaacdbbbacacedddaeedcacdcaeedabbcaaeeaccededaeaebcbedccaecaedcaeeebeaadbcddebecaaedeaadabacecbbcebbbadccaedbccdadbebcedebcdbdccddeabacecbebacabaebedcabadecaadecdcedddceeacdebaebdabcbbbbbdbcbdcdabcbeceebaeeacbcdceddbdeebdedeccabdbbedcbedcbccbedaeccbddedeeeecbdaccbcadcdedebdbbbddcebacbacceaaabaeaacddacbdcbbaaaadeededaacbcccbddeabbbeacbedeaeaebeabbeacaadcbecabadbbeddcdcacadddecdbcaebbdbbadaecedadbcdcadbdaceeeccabdeabccbeacadedebbeacdaeedbaadeaaecdcbbaddabbaecbdeddeeadccbbceccbadaaaaaebddbebebebcaddbdbddecabeeaccdecbadbebeaaebbbadcecdabdcebdabbdbaeeaaadebeeedebdcaadbceddbadbbedcaeecdeceddbcebbacbeabbecdcbcbaecadaeabdacadbccbadbdbaecdeabbebcebabadaaeaadcacbccdcebdbdadeacbbccacbeabcecbdbccacbecdaababdebeacabaabccacbaecedbcbededdecbddacebaacacbebbebeeddbedeabcbdcaddedbeecbaaacdcecacabedebabdbdbddaaeeeddeacbdaccaeacdbaddebbebbaeeccedcebdcbaacbecacedcabbcbabbcbdcdeecaeaaaacccebcaacecadddedeaaaaadebbaaacdaacedeabadadabccaedccacecacecbeceaedbaaaecdeceadbedbddebcdddaeadbcbbecaebddaaedbddedbbbcdacbaabaccbcbaeeacdcbabaabebeaaebbdeeebdcdacacbcecddeaacceeebeecbdccacbebbddbcadcdcdbebeaaccaadcdebcaeaacebcdbdaaaceabdaabccdebeeaaeccecebbeecababeceeccebdbcedbcdaecbdcdaabdbbecceebdbdbcdabecccdbbaccdeccdbccccbcabbeebbaaaceededddebadebcdcbccbaccdaedccbccbccbdecbecccedbbdbaceebcdcecbbdeccddcdaeacbbaacedadbbadadcedacceedbbeaaeceacdeeddcbebbacaabedcaeaacdbddebcabbdabbabdeccedccbcdcaceebddbcceaacebdbcceececdecbdddacbeaaebecaceabbdbacedeebdeaeedcbdccdeeaccabdcedaeecbbdadbadcaaabeaedbaebbdebbaaeaaaababbaeacbdcbeeadedddceaddbeeeacaebdcaabeeddcdbdbbecadadacebaeaacbedabdeedadaacddcadbabaadedceddbedcbaabbdabacedeaabacccdcadadadaabadeeecaebddcdcccbcdcdbadbabacbaddeebccaacbeedbcbcbcbdbeeebebacbbcdbbdaacbadeeeeadeddecaabaadadecbebeacebabaedeecadcbdccacececccbdedbeaaecbdbebbabdabdeeeddeebeaebbadabdbbdbdacdbeecdccadbeaeadaebabcbcdcbdbdbeaabaaeaaecabeabaaeccecebcbbaadecdbbbeaeadeeebeeeebeeeacadddaeeddabbecaadacedcadadbdccddaeeaccdbceaeceaaceababadbbaaacbecaadebaaacedddacdadadebcbddbbaeabadaacddcdeedbbaeeecbabccdcabcbadbbeceecdcbaeacddccdcaceadbaaccaeebbdeacedaaebadacabcedbabcbbcebaebdbdccddabddecadceedccddcbcaeddeadaccdbeababeccebadbddeeacaeeaebabddcbccdadcbdacbedadcdcbdecadeccbddaccadabbeeceddcdbecabcacccebababebadaebadaccdaeddeeebbeeaebebeedccdadddbdabbcebddbaeeccdadcdcabddeedaedbcbedaacdcceccdccdaeaddcdabababddadabacbacbbadddaadaddacaccaddddaceaeeaaddbebbbbdccdcdcdaebceddebcaadcdbacececebcdaeadaceeadcdcccabbddbabeeddeddbbcbbdbadcaeabccbacdeeecbebecacaaccbebdeebdeaacaeadacddbaceebdedcaaecddeceabddecaebddccaedaaecdddecadeacaadecaaaccdeacaeeedddeccdedaebcbaadeaaaacceabaddecbbdddbbbaaabaaacdaedaadabbacdedebccddadedebcacabddbbacdcabedebacbcbeaaccbbcadbbbaebadacbbadebcebecececaeabcdabacccbbcdddaedcdadcdceebadeabbacebcdeddaebbbabdeceacabbdcecdbcecdbdcadedccbebeabadaecddcabdbbcdedbddcecccceaebbaededdabaacedbcbbdeabedbccaeeebcedaecdeeebaaaaebebbbeaadbeccaebacdbdcaccecedaabedadcdbaaacbdccecacaeabedbdcecadaadaebcceaebadccbccddcaccdbadedddccabaabccdabcbceedbaabebeaeedbcbdcbaabddbddedcabbecdcaccacbeddeecccdbcaacbabdaccaaaeadebebccededecbeacacaabdaecebebbacecddbacadeaedcaadbbbecbaaeaeebbcddaaabdaceccbedddeedeacdedcddbedabadaeeabbebdcaddbccccacdeeadcccadeacecddeaebcceecbbdeccebeacceedeadeecdadebacaebcacaceebbcdbedcdcdecabbeebccbdedbeedecdbeeccaadbcabecbcdaceeecccdaccadadbaacebdacaecabebebeadbaceedcbaabaecbaeadecbebdedcebcddceccecaebceaeaaccddcabecbeeddcdcebebadeeeaebdddcdcdddaecbbceeebbaadeaedcccbedcdacccaaddadcacecdcacdadeccbbeceebceadbcacbaebdeaeaebbecddaeddabbbdbacddabcbadcbbbbdbddbddedeecabecdacdadcdaecdddeaacdeecdaeecceabddecedccbcbbcbddcbcaddbbaacbadecbcbeebcaacebeccdecdbcbcdcaadcaccacacecabccdadaeacedcdeebacbddcdbbbcaedbacaaadbbddeedceecbecedbeacddacceebadeeabbbddcebedcbcdeeebddeaacaeddaecededeeceadeaedbaebeaabacbbdaabbdbbddccbecceaebdaeedeeabbeceebacacebdbedacacbbebebebdadcdebdaeaeaabeccebbbbaebaeacbaeecaceeddbcbdcebddbebdbadcabbaecbbaaaaadecedbcbcaadecaddbbeaabaecbaabcaadbdcbdedecaedeaabebebbebbedabacecedcbedbebcceabbbdcbeaddcaecbdaedcaceeddcceabeacebaddeacbcabecaebeaceacecaceddceebbebbbddacbdbacebaaabbcabbcbcabeceecccaddbabebbcdeaadcddeadbcaaebbbedebdaabaebabcabaebbddbddcadcdadcceeabababbabaeeedecacdaaccdadbbbecdbadcbdddbedcbcbdeaeacddbdbcdeadbbcebedbabbbcdcbbdebaaebedadabbcddaacecdacbdbacbbebdbaadecaeeceaedbdbcadabadbcadceeceaecdaeebedddcbecbcadbadbadacabadceababedbcdeaddbeddbabaeeecbacecaaddadbaacededcbccaaeeddebaebcbbeaedcdcbbbcaecdbceceadeaecacbddeebaeccceecabadebbbadcaaadbccdcecbddcdeecaaaeacdeeceaedeebdbbdddddcdacdceaadaedbebcadedbcdadccaeddddcddddcedccddccebabceeecdaddddeaebcacedcadddacebedbbdbccdabbdcebeebcacdeabbecbeedddcbaaceadbaecceeedadaddcececebecaebbbbccbdccdeddcddacaabbecbdacbebaccccedbdadcaaceaeabeadeeceadbdebbbbccbddbedadcacbcceebdabdebbedeadecdcbdbddebcbcadcccbceebbdaacdcbcbdaabecbcddbbdcbeccdeeaaeacbdbbceadabebecabcababedbedbabddcaaaededeedcdbbeabceadeccdacdbdbdbeadcbbbdbcbbecbdecaacebeceebecaadddbeebebbddcabebaeebdcebbeeeeedababdecdbcdebdddeddddadedeaeaccccacbcdabcbedbaccabaddaeadebcbadadeacbeebabbceaaedcbacbdaecccddedcabddadbdcaabcecdecadcbaeaebbabecdededecbcabdcbaceeccaabccaebbeddeddbecdaecbecbbecddaecaaaebdbdccddeeeccaeacbeaccdeaacdeaceaaeabdbdeabaddcadbebcdbddeabdebadaaaaebadcdeabcbcaccbcbbdcdaedceecacbbeaedbdbbdacbaedadeececebddcedbebbcdcdbcadeddebdabcedacecebdeaabcedaaadeccdebcaaadbabaceaeeeedcddbdecabaeccedbabdaccdbbecbdbbacaacdadbbbddbabdeecedcecdaaabdcdeebdabdabcbcdeeddbcdccecbbccbacccdebabbcbaaabdbadecdeeadceebbdeeebeaacedbbbdecdeeaabcbaddbaacbbadedcbccdbcbaadcaacccccdceabbdebebbdbedddddebeecccbcacdeecdedcdbcaeebaccbaeabadeabdbaebddcbdbaeaebdcedaabddaccecdaebccdadebaeeaedadeeacedbecdeaaeaaacccabaedacdcdbccbecdccddcbdedaeceeacdcbdeabeabbbedaadbbababeddebddcecdaeabbceaebdceeddcaeceadaadecdaeeeedbcddecedeabcccabddacebeebcbcabbbcdedcaadabedbceabbdbbdadabebdecdedcdebecaadeaadbaadbdadeddbdacaceedcbbcbcbdcddeacdababaaeebecbdceceddcccaeddccdcbcaaaaebedaddbceceeaecdddeecabdbccaeedadbbdaddadeeacdbdabeadadbbddcbddabdcceceedabbdccdbeadddbdbcbaaacddacbddeadcbbcdaabddaeaececdddedcebbcbacbadbbcadeaccebcebacbdabcbedbceeecbbeebdbbddbccdbddaabcecadecddbaabddedceaaeccbbdeebbdedcecccdbceaddabdaceabbdedabdedecedeecdddbceeeadbcbaaacdedaaddebebccccecaeacecedeecadebbcececbbecabbaedddbadcadebcbeebcbeedcaebedbcdabdbabdaceaaaddedadbedededcbddadceebcccdbadeccdebaedbbbaaadddddbabbdccaabdeccbdecaabcebceedcadaecacaaaacaccdaabddaadbbdbebeebbbaaacaabcdeecbabaaaddecabaeaaddacdccdeacccbccadceddcedbddababcecaabccdeeebedcccdbcaeddaebdbcedaceeebbecaceeacadbaddbbdcacdabdbaacbaedaeddbeaaabebbeebaccddacbdddecdaedebdcecabbedceabaeeeabbadbedebeabdeadeaabcbceeccccbdaedbddcacdaddaedcadcddcdedacdbdbdcbdddaaaadacbadcdcbaabbaadeecbabdaabddddecddcacbbdabddcdaebbeabdadeebcbececcbbbbeacccdcadaacecdadaebddaacbbcdeaaddcbabaebbbedecacbecadeeceacccadbdabbecdaebeabbacbcecccdeeecdeaddcccadaedaedddecdbbeccdbbedaaabdeeddcadddeebddabcedbedebdbdddceeacacabbbeceeedecdbbccabccbecaccababdeecddaaabcabcbdacaaebeaddecdcdabcbedccccebacdcbebbaacacbdbebcbddacdabbedabcedacacddbecbbabbdcedbdbbeeecadecabeccaaaeedaedbdccceddacbedccaccaecbaebbbbdcdbadecbacdaccccaedecbadecdaaecdecdadcdabdaeebeadddacabcdebedbdebdaaebadeeceecacdbebbedecebccecceaadeddbebdcdededeeeadcedddcdbaccecbdeaecdaceadcaacebbbabcccdddccceadecddbaebdcddebdaabaedabbeabbaddadedbcebcebddcbcbcbddecbbecbadbcdeeccccddecbacdcaaadedcbeedecdbcddbbbebedeaaddcedaaedeeaeecbdbaaeadbdceebcabceaddceaebbbdeebebaebbbddcaacaecadeeeaacbbdabceacbcdddeaacdeebbcacecedeabedabbdccceeddbccbadddaadadebaadcceebecdaacbadcaedababceedcebaabdceaddccaccddcddccdedcdecddeeaeeceedbabcddabdbdeadbccbcebbdddddeacceedeacbedacedacebaaccdedcbdcdedbeddeecddaccceeadcebcbabaccbaaeddaabcbdedcccbaeacdbabbeabeedacdcbeadaeaaeeebbcaaaaaedccbddeacbcecacdbbbdbdaacaebcbcbbcabcaadeebddcbddeadacbcabecedabbbaabaccdebebeaceebcdaabedededabbaedeceacedceabdbbccabbaddbdeeedbaecaccdbbeadaccddaacbbeabcccaadabaddebaccaeaebebabcecacaebbccadeeceedcdbcdaadeaaaceedbdbeccabcbdcdcacdbacedddcccdebbcbbdaccacdebbadadebdcebeaeaeddcaaedaebceacdebcccedbdbccbbecdddccdaeddaeadbccbbcebaacddaedabdbcdaadebedecdbdbbbccbddcecedbbcbbebedbacaaceeacecacbededaaeeddedaddaeedddebadccdedaceceaabecdcaabddceddaeabadaadbbacceeeecdedbcacbacbddbaebadeddedddbcaedeeadbeccbbcbbcbcbcaacdeebcecceeccbcceeeceacbbaaaaeedccabaeeddbbacbbceecaabebbedaadacbeacbdececceeaedbeeeabcbcbeddeddbbdabbcebebacbaceeaecbcbecbabcebcceedbaccdbdaeddbecccbaddaddbadebaeaedebeebddebeaedceaaabbdbdeaeadddaeabeddceedddaadbedbdbceaecedaccebdeddebbdebacbabcadecdacbbadcabdeacbddabadeecbeacdbcaeaeaabaaedaaaaeedbdeceaeebdbbcecbbceaaaeaadbddbcbceaaeeadcdcaaadaeacecdbbbecedabddcaadeadcddcbaebaceeededdcdcbaeebabeeededacadaacadabbcaeccdbbdcdbbdedcbebdeacedadaceacbcbeaaaeecedcbdbeccbaccabeeadbbcdbdadececebcbcdcbbabbccaeadcbcbecbbcadabeaaeabbebeedebaedcdaccabdedebeceacdcddceabcadddabcddbcebcebddaedcbdabdcbaddceaceebedbeabdceaabdaebaedaddbdbabeacadceecbbeacbeebdecaaccdebeadebeecbcebcbebedcbdaebeccbcabdcabcbcbddbcdccabdabbabeededbccadeadddbbacaacecbbdceabbbccbebeeedbddbbdbcacbaaaeeebdeccdcbccbadbbddddaebaebebabbaceddecaacdaadbddcdbddddedaaaabbdbaababcdcecebebdeeccdcbecebcbdbacebccaecedceecaccaecaecbacbdcdedbabadaebcbbccdccebacabcbccecbaddcdecdaecdaabbbacdcaacbaacaabecaddcbcbbcdbacceddcccbbadbdcbbdeabdacebbbcdeadcbdcddbadbdcbeddbbaccdcbbbaeeccdeedcceacbabbceedcccebcdeecbcbaddadaabddcacacaeacdaecdeebddbcdcacedbdbaebcecabbbddaccdcdeadddaddcedbcdbdbadccccaaeacbececacebabeebabcbceeeabcbaabbccdcaedabbeecbeacccceddedaabedabdccabaaaaedcdbecaaddeabddecddbcebbbaddeaddedabebbacdcaadaeaeddeeaabccaaadbcdabbdacbaaceccedeeddeecbbddbcdcebeddcebacccdbeeeebeaecaeddeeaaaabcabcccbddaeaabebeabccaeecadbdaceabaacadabaaeacecaddadccdacccadbebbcebaebdceecdcebeedddebbaebbbeaccbdadcebeaaeceebeeddebdcccadeeedeacbdbdbbdcdebbadadbcabaededbcaedcccdebbbdccaeeeeabadccddbbcccddaeaddeadadddaecebebeaeebdbebaccdbedbeeabaccaceeedacaccbbeceaddacbcebaebeebbdcabbddeaeddceddaacddccdcebcdcedbebacbdbabbbbecedadbdbcdeccdaaebaaeedaddcdebeacbeaceccceccadeedbebadadddedeacbbcaeddecabbcbbbebbddacbabacadddabeceecbbcccceddcdeacaddcdacbeddbbbeddeceecadadacceeedceabcbbdbdecbdcecbebbdccceaecdaecadacaaabebadeabbcbbddbcebdcaeaeababcdbdddebecacbdabbbcbeaabebdbdbddeceeabdcbbebdcddcadecaabbbeddacecbcdbeaabeadadadcbaaedadadcdccacbaedeedeeecccaaeeebdabeeccbdadbbbeebedadddbeaaaddccdbebbbeaaeedeabddccacbcadabeeccdaddbeeedaadbcbebcaaacdeddecbbaaeecebabacddcbecdbbbabdacdacddcdbdeabaeaabbcdecbcbcbbacabcdadccabddcdecbebebddebdeaabbebaccdaccaacebebcacbdbecbcbecbbeecbaadccebebdaccbbdbbbbcbababcbecdceeaecaeedacdbbeaedddcadaaedaebcebaeeeeedeeddeabebacccdeacddeddecaeeebcedbdbaaadadbccdbbdcacaaedacbadccbcdeacddeacaacccacbedaccebbbcaddbeddaebdeeabcdcddedcacdaeeddddcacbdcaececdcccdeabedccbeaddddcaeddceededaaeabbaecbbbeebbaabcbabcdadbeaddcaecacbddbebcecebcdcddaaceeeedbaedabdedceeedceaeabaddddddecbacceedbdabdbbdddededdbcadcceecbdcaacbbacbabddddeaccaccdebccccaeebbbebececdcbaededcabbadbbdeaccbeecbedcedaabeccecdbddbedadebbcccccbaadbeabcaedecebdbabeebdbaaaacddedbeeaeecbdeedbdedadabccdbdecdaadccdaddcbddeecaddbcbbedecdebeadccecdbbdccdbcbcedcdcaeeccbadbbbcadbebddcaadaeebdbecbbbeeacaebbaedadbddcedbebdcbcbcbddceebeeeaadadddcceeaddbabaabbdebbaaebccdeabdbdbdcdabebedddebeedabebbbbbcabadcddadeaecbeeaebcadebdeabaaddddaddcadbccaedcadabbbedaebdecdeaccedeeddbccccdbdaaccdebaccbcecdeebdccdaeeeceecadccdcccbbceeecdcbcdaeabcdeeebbacaabbcaccebbbddabbaeadccbbaddedbdccdcaecbbbbbaeaceacbdacecaedeabdcbbeabaadbbaebbbdadedccbcebbaeadecaddcaaeeaaebbdeabceabdadbeddabdeaacaaabccccbeddbcacebddaddaadbcabacacccaecccaacdbbeeaececaadddedeabebcaecebdcdcaeecadcdeadedeebbdbaeaceaaeedabcaeaaccaacabbcadaaadecbcaacaecabccdceaebddedbacadaeaebdaaceddbdbbdbaecbdaaabbbaddececdeaaceeecadbeaeacddebdadbeadceaeabcccbcbabaadcaacddeabcdaccadabaadebaabceddbedeabeacbccaeeeedbbdddbaacadcddbeabcceadaddabbdaeeacddcbebaddcdedbeeadcedbbecdabceeaceeabbaddeacdbadebaeacabbaccebcadedbcaababccbddceacbaeeeacdbdbecaeebaebbebedaddbbebbeaebaeaebeaebadbdecbadcaecdccdedadededcadeccaadbeebbdeddbbccecdcbaecabbdcceebaadbaddceedabaacbedeedacbeebeeacdedebbdaeabddbbcdadabdcebddbedeedddbdaecbaaceebbbedbaeaaedcdacdcebcabeccdcebdabbcbeaddaddccaaadacdaccdaacbcecbdebccdbcbececcadbbaadeadabcaedddedacdabcdbbceccccaaabaebdaadacbadbdaedcbbbdbebaacccbbaacbdbaddaebbccaeedacbeacdadcabddbacaedbabbcbbedecedbdcabbbdceadeeceabeaceeccdcdbecdcaccaaccdebedbcdcbaccddaabdeddbabbbcacddeebebabccbbdbbebcaabbaababbaecbdedaaabdbeaabeedddceddccaceeddbaccabcaceecaddbbddbbbaebacddbdcbccdaaaadaebbebddaacaddaaebddeecaacdcbbbedcdcabcebcaaaaddecbcbeabebdddacbdecbcbbeeadaebbdbcbdaddecdddecccdebabdeeadadeabbeacccbcdcddaaadbcaedbadedceaabbebaaedddceceacbdbcedbddbdeedaadbebbecabddabaacacdcacebdeaaadeaebcaeddbbceebacbeebaededdebbbcaddaeabebbbbecbedeeedcaaedccbbebebadbbabccbcbabeedaddaacbcedccaddeabaebbcddaddeeeddebbccceabcddaceaadbbadadacddbadeeaccbabcdceeaaaaaddccdeecaedcdbbcbcdabbbdacceaaacedcdaaeddcdeababaeecbbedcbdcbbcecedadaaebdeedacddbadadedddcbbaebeeddececcbdbaccaccdcbacabecabbbaccebbebbdcdbabccbabdaacacddaaebbcbbdcaabdbdaacaadecdcbbecdcbbcbdedccdeccebeedbaebebadbeaabedcddccbcbdcbdcaaccdbbeedbdadebaaddedabaddcbaeaadbbebceebabecacaccbeccceacedabdeaaacaeaceecabdbcaaecbaddcbcdacccceceadbbbcecebaabacbbabbeeccdaedbedebbbdabbaebceabbaabbdebebaceecabaabdadeddadcababbdabeebeabcbceddbceaeacabcbbcdbbdcbdededaccbccebeebdaebcedbcbdbdeedabaacacbeeaddacabedbeceecceeecddaeaccaacddcdcebcbcbebbcacdaacebdbabdaacddccbbaecbcccabddacaeccabbbadbbcadcabeaeacbbdbdbdcdbbcececdbcdeeeaebcdbdbdcdeccacaebddceacadbbedceceddcabcbebeeabcecdbcbbbbddcbeaccedebddbcdbeeeceeccadaebaacbdcadabbacdaebbdeabeeedbdaedaacbadedeccbbbcceccdeddbdbcebceabeddcdccaededcbccaadbeecaacecbbcdbebdcabbdcbeccbebbacdccdabbdababecbeeceaedabbbecdaccabbecabdbbedabbaabaadabdccbeeebbcddaddccdbacceddeaaddbadcbebaaeddecadeeaeaaeddaabaeebbbceeadcdbaebbdbaeceaeacdaeadbadceebedacddaadaddeeddaceaceebaeaebedddccabedababedadecaeaabdaceeedeaadebbbbbebbbaecbddcbdcedeedbccdabbbeabbeabcedeedceceeaaadedbdcdebbcadacabecddaadadaeedbcdcbedcdebebdccaadebeccaedabbeccaedacedeaaeaaadcdbcaaacaeacedbeedbeadeecdddcaaadeddeeecebbabbcdaccadcbdcdaccdebcaedeaadeccceedaadaebcedcbebcddceececbedacaceceaababadaeaddeaedddbbeeabdeaabaaaaaddcbececacedaccdbcbaeeabbbbbbdacecdeebeceeedeaaccabbbddcbbaabbedeebdcbeebcecabbeaeceabdeedbddbaeeaecbbdaabdbcbcdaecdbeccedbbcedbddeaceeedddababcaabdbbaaedaeaaacdbdbddedaaecbbaecabdbebbeaecabacccecccbeadeaeccdbeebbecbbdcadaaeabdbedddbcdadaeedeabedecbebcaacdcbcbcaeadbbabbeeecbcdbebbaadbedeaacbaddbdaeebaccccddedbebdeddaadaacdedbdcbadebbcedcaedaaceadceaaadaabeeaeeececceeaaedaadadaabbacdebdbeacecabeccbbcadddbbcccaebecabeabedcedaebddaeabacdebdbecdcebadccedbeccdecebaaabcedadcacdbdddaddeabddcddcabeebaececcddaccdbeaebcdeadbdcedababcadbebdacabbaddaceddeebeabbcebabdebeabbbceeddadebdadeeeecaaeeedecebaabdbacdcbcbaceacbecbaaacdbcbccbeceeabebbddddabcebddbebdababaaccbeedccdcdbddbcdcbecebebeacdaedaaddaeedacaddbccabaededdbccedcebdbadcdaeaeeaaadbdbbabbbdeeabbbebcedbcccbcbdacdaceaecbbecddccadeaadecabeeedcaabceaadecbdcebdedecbdacbdccbcbbeebecedaabbcdaeddebdeebeddaeecadbecebeedaeddeebbdebbcbaccadbcbeadaddaaedddcadcadecbccbaeadcebdddabcaadbebeeedebebedccddedebbdaaeaccccecccbaeaabceaddcddceeabccbebccdedaabdbcbeecbccaadceabaeeeeaaeaddaaabecedeabddabcebceddebdccbcccbeebcdbdaaeabcaadcbebcaaceeedadccaeddcacabbacecccabbecccdccdebabeadcbcaeddbecbebcdcbeacacaeaedaeaeeaababaaecdeeaddcabadddbdabccbbadcdedceeeacdcdddbbdaacbaecddcccbaabaaaeeedbedccbabacabbeabcaeeaccdddbcaeeccbaedeaacdcdcedbdbabaadcabdadbadecbbedbeedeabbdeedceaaeddacebcdebaacbeaaeebcebdaabacbbccebeabddcbadceadbdebcceadbadabccdbebbcccbaabccadebcebacbcecccacbbdedbecddbdecccbcbeaababeeeeaddadccebacceeacdaabcaadbdbecccdecbeadacaadebbeeeebcddacdbabedecadddacdcaeebdddaebbbdbeecabdddceeecbceaaeddbbdeacbeeaddeeabcdeaadcdbedbaccdcceacabecdabdcdedcdbcbcdcbeddbddeebeabaabdeeceddccbaeacdcaadddcacabceedbdabbadbaaeeeacdcdeaadcdeaaabedacdebeacdcceecddbececccdeedcecaabeaeccaeaeccaddcbbccaabcdeebeccaadcdeeaeacbdaadedbcccddccccdbcdadabbdbaedddaeecddeaedabdbacaadbabebbcadaaececacabbabbeebcebddceeceaebadbaccecaaacedadedbbbdccadbeaaddeeedcaeecdceaacecdeddcacdabcdcaaadbdcbddbbedccdbbcadaddcdebeaeedcbccaeaeacbbecddddadebdecbaacbddbecbccbdaedcaaacbadaccadadbdbbeaaacedbeacdeecbedbaeeebebddbeddddadbcaaedeadddcccbdcbbbecabdcbceeaecbcabddcedadabeacdeddeaabeeabdcbcaedbedaecddecdbaeddceeebabdecedaaddacdddcadebbbbadddbdebadadeeedeeccdccccaacbdeaaaaaacebbdadaccecbbbbbadabceaccdedcbceecaeebcbdbbdcddbdbcbcdcdeedbaabbcdbddeebbbbbddcedddbbadbbdddbcedeaaeeaeeaecdbecbeaddcddeedaedbbaddbabebadedcebdecebacbbebbaeecabdcebdedcdaedddaedeaeaeaebadddcbbababacdbeaadbebbebdabcbaaaaeebbbdcddeabcccecbdecdcdbdcbaabbcddcdbdebdeabaeaaabebadaaadebeedbbceaeceeedcbacdaeaaabdaaecaebeacdcbdbedcdacddceacdddedddeaaaaabbdcceaeecdecbedcceabcedbecebccddacdcdcacdaeacbbecaebebbcaedbcaaaaebadabebebdbdbacaeeadcebaaeccaaacddbccabeccaaabcdbbcbdbcacdcbddaeeadedeebdadaadddeccbaaacceceabbbaebcedcbdeceedcdbceeaddcadbbeebbeebbecedbdeaaedabeaadaaadadbecceecbbdadedcdacadcacadbdcbcacbeebdcadbcacaeeceabdecbcecdeacbabeddcbecbddcaadecbbccaadaecadceaabdcbbbccadcedcdebaeaaddccedbbcabdbdbdadabcdbadceeadcecbaceedbcecdaeedcaeadbebdeeecadbcdbeedccbcedebaebabedeccbeebbcadbdeccdbbcdbcdaeaebabacccdedbaecebbdaadbaedaabeecbcacadabecbaebdeadabeebdabbdaacbbcadbaadbedaecbedbeaeacebddbaddddedccdabbdbcebbbabacabcdbcccaeaddbcdebdbbecbdabebcebedbabceadaecbedccacbeadcedbbaaeeabadbceadbdeeadcdbadeebaaadabdaaeacbdbeaccacbecdeebcbaddcdecbacedbdbdeaeeecddabcecabaacddbbaabbddbbdcaebaddaecdebbadbbcdcdeacebecebeddbcdaebdaddeeeadcbacdcaaadbcbeecebadcceeadcddcebdabbecdcedbdeecbebcaebddccaaeecabaedcebcaebdbaadbdcdeeedccdcdeeaaaecbccdaadeabceadcebdbdedbbeedbcdcbeacdaebceaeedeebdeecacbedeccadcdbbeaeddabaebcaaedaeabbeebbaddeacaebddbeccecedaccecbdcaabadcbcbddbedcabcaedeccceeedaaaeabbedceacdeecbcdeeacbabdabeeccebabddcadbcdbdedabbabcccabbabbdbceccbcebdeacbdaedabceeebedbcadbbaabbadeccdaceaebdeeadbddaaababbeacebecabbddcddeebeabbeeeeccbebbcacacdceaeebabaebdaddeadbcddecacdebdcedddeaadccebabbdaadbcbedaeeebbdcaaedeeccadcbdacccaaecabdddedbaecedddaadbccdecbebbcbbdaabdeddbabedaeeaadbabeebdbcdacbdbdceadbdebbcceccecadabdccbbbaecdddaaeaeedcbbbedeaedcbbbdcbaeeaaeedadbedadddcadabcbebebadccaecccdcdceecbecdcdbdaaecdcbaecaacaeccbebceebbbaabacdaaeeedcbccccebdadecbadaacaaabeabdebbecdcecadaedbdebeadbebaacebabdaaddeaaebbdacbaeedcaadeadaebecaeaaaadaecbaccbcacaebadaeccaadcdcbcaabbabdebdcecbbceadaacbdbbaaabbaecadddcbdbecdaaeceaaacdbdbecdbeaebdedaceeebeceacecbebcdcbccdecaaecacdddcddedcadbeeedaacbccdbdabbcbaceabcdadaaeddecbdcaeebddaccccbbbccacbcbaacaceacbceebcaaecdeaebcaaaeacbcbbcabeaecaebedddecbedcaddcaebeecbdbccdbaaccdcececdacddecdebceaabadedceccdaeeadcbdedbabaddacabaeabeaaceabceebbdcaecaebbabaaebedcdecdaeaccccabdeedadabaeeeeeaeeaebdddabbdaccdeeecabdbeedbeabbdcaeaadaddaddbaaadcdeccedacdedadbddccbebeddeacedeceabebebdcecaadeaecacacbbaaeddcaedcebedddabedadaadbaecbbddaeceecceabaadacebbeaaaeccecbacdbebebeeaedcceeecccabeedabccbcbaeeceebcdadedaecaaebbdcecaaaadaccdcedbeecbdcdabacaeadbebbaccecdccedcdaddaecdccaaeadccaedacacbaaceaeceaabceaaebbddcaabbcccdbaaededadbcbeaddbccdbdcbeadddcbaddadebecbdbcbddccdbeecbdddaaaecbdbdcbdabcdcadadabdeeeaaecbdaaeecebaabbbabddacacbcbeedcddacebcebddeaacccbedadbaccdedadedeccaedcdebcdebedaadecceedcdcebbeadedcaddabadbadaaebbabbaaeaedaebcccbcaabdabcdddbdeadccbaabbacebdcaadeeabcbcbadaccedebcdbebcebdcdddaaceaeacadbccedceddecabbbdcedeebaacdeeceebabdaeedbeeeeabbddaaeddeaeebbdcbaedcbcbeeeabdadcccebadeecacdbdabaedecccaeadecddedeeaacabbbaadeaddbedbeaeddecdadeebdedcdebbbdbaeaedbcaeebbdceadedebaddebecddebbcdeedaaeedebdedbecddbaaddadbdeabbaacabedabacebaddaddaaceaadbabcaceeeeabdddaccaaadeaddadddcecacecaccdacdbcdaabdcbcaedcddbadcebaeaeeebdeebdcacababaddddccaabcadbabededbecdaebccadadcbccaeeecaccbabdccbaebebcbcaaeaedacddbaabadccbdedddcbdebbcedbaabdecbaeddcdbbbbdcaccdaaedeebaababaeccdbedadcdbdebaacebcaebaeaacacddaeebadbeadbbaaccdcaeedaeabbeeddbdcddccceacbbdececdcabacaadbecdacccdacdbadcabcdeeceedcbeadcaadaebddcbbebeedbcdbcbebaedbcdaeaeddadcbddebddebbdcaceabbaecbadebadecdcaeaadbeedddeddbccabdabaeeabbcaadebeebbddaedaacbbdbebbbeebcbeeaadddcbedcabbecbdcebbbcecdeddaecddddbadaaacdadecdedeceeeadcbdaacecebaccaeddadacaceecdbceaccecadbedadcceaaabbedbaeecdbcdddcdccaeedcbdbccdeecaceadccaacccabebeeedaeebeeeaedcecaabecaedeeddebeaecdecebdebabeeebdcaadbabdeddbbdaccdaecedbeaacbaaeeaaeadadadbceececadedcbebbbccdeaadcdcedabeadeacdededabcddcbecabccccbacdcaecbaecdbbdabeeecdeedbabedcbccdebebbcabccaebaaaaabbeceeddaaebeeccbabaaddcbdcdccceaebcaabceaacaeebacbadabebeeeadaeebebeadebcbbadbeddddcacecebbbedbecabbcddebdbadcddeecddbbdbcaccdeeeebbdeeaaeeabadbcdbddacadbbacacbebbdedbeaaacbeedcecdddcbcebbbbbdbbcdbddedaeeaaacdbaebbebcbbdeccbddabdbecddeaebcdedaddbcaadadbbdaecbccceedcceebabbbdcbbaeaecbccccebacdeaeccecabeadbdecadebaedadeeceabaabccbdcbdabaaeeecceaadaaacebaabaddaaaccddebedacbaabdadbcdeadabccaeedaddabddcbcabddacebadbdbdcbeececcacbedabddceededaadccdeabaccdbcadedccaebeadbdaabeeabcbbbecbeaeeeaebbcbddeacbbbdcaeaacacebbadaddcabbaabbeabbbecedaabbbeceebdbdecdbdcadcdbecddaaacbeaadaebbebaaeadacebdedbbdbebcdeabbebbdabcecddbadebbbdcabbabbedbeaacebcdcdccebadcbbedbcbedacdeadcddbbeccdabeaecbcccacbdebedcebeacabaaebaaaeebcdeaeeabaeadaaadeddabdacdccaeaeacadabacdbbbccebacceababdcbecabadcddbaebdeeeeeeeedcadaacddbdbabebbcbdebbabcacabeedbbdddabcdddccdecedcadadccebedebcaadbbebcdbabaacebbeecdabaacbaadbdeadecdbedaecdbacbebccbdbdaccbdbdaaadbdcceaacbaaaeddacebcaebdaaeeacbbeaaecaeddeadccaceaaadddbaadaeadbbaecddeeaaeecbdbbeadaabeabbcaebcbbdddbbdeeeebeddabeccecbaebabebddacadbbcaeaabdbccdceeaaceeacbbebdbdabebbaebedeaceaedebcbecadddaaebcababeeaeeebbdeeadaaeddeedecdacccabcaebdcbddacccebcdccceebeaebdcccecedbeddcdeeeeaaddbcebdcebeeaaaeeddaabaebabadeaecaeebaabdeebddbdcccdcbbaebdebeaebaeaaccceaeddbcebbebebaecedeccedcddcabeaecbcacbcbcbcacccecadaebabceedceebbaecbbbcbeccbeeabbccdbcdeacdacbcabdbcdbcddbadcbcdaacbbebaeebcbeebdacceacbcdbdcaaaabecdbccddccccdeceeddcbbbedbccaccacedcbadddaaadeebdacbbcadeeaceaacebbccedbdbaebadaebdbddbcccddbabadbcedbabddbdbbbdcbcaecaadebdeececaacbcccedadaecdadedeecaddcaedeebddcaaddddeeebaeedecacbbcdcecbcddaaeeabaaeabdcbbcddcacbadbbaaecaeabcbbceebbedebccacabcdbeadecdeddbebecabacebdeedacdedadcebeaceaaaaaebebdaebeeaeacdaaececbcbcbddcedebbdcebceadcaeabedbaccaedcaaeeadaadcbeacbedbeeacbaeddcbdcceabaadadccdcdadcaedbbbacedeaabdeebccebedbccabdedeacbdadccceceeeceaddcceeedacdacaaabdbebaabebcedbbebaeaedeeaaaedeadbeddddeebbdaeedbcedeaaecedecacecccedbdbdbecbcebebbcaddbadbcabcccbedeabaebebcbeedbbcacbdbdadebeacceceabebceddeadabdbcbacbbbaaebaaabccbebacaddeaabebccacbcdeaeedcbceccbeeebcbdcdccabcbdecbacbeadedbaaadbbecddcaccadcaceabdcbeecdddadeceecbcacbadaceddbcbaaddbbaaeaceabdeabbacbcadabdbdddbcdbcdbbedbdeecabaeaabbcebdeddbdbacababedbededbaccaeceecdbddbccaaabaaadddcddeacdcdaeabaadbdabbedaabdebbeabacbebeacebccccacbccacdabbdcddceedbeaccddccdadbeedacbaeeabccdcedeebbebcbcbabaeccbadabaaeabcedeabbaacddbeebcebdeccebdccddccadddddeeedbbabebbdecdbbaeddcbbaaebeaadcdacdcbbcbcaeccdeedccebbadebcbaacbbccbabadceaacaaedbdabceacbcabaeebcedbbaceaecbdabcbeedbbadeacdaecaebbbaadeeaccaeeebeeadebccaacdaedbeecdabedadbeeecdacccabecccaeededdbbadbadbebdaaceebaacabbcccbccaececbacadebcdeccbaeedbdddcaeaccebabdacedeaabadcbabadcaaececdcdccadceeccbdaccaeeaebcecbccabaeebedbdeebcdaaecbdaedabacebecdacabdbebecbecaaddbbccacedcbbdeacaeaddacdbceccecdbcdabbcabbddedecddbeaabddcbbacdcbbdccedeacbeadddeebebadbbbadbedaacddeaaddcdeacaeeccbaacdccacddcbebdbabbcadaacdbaadaebddcdaeebcaceebaaaabeadbbcbbdddedcaedaededcedaecdedaaccdbcdaeadcbeadceeeddaecdcacbaacededbcacddbbbdacaccceecdacbcdedaebccadbeaabddbcddedacedebedcecdbbdaccadaeebcccdcccededdaeebcadacbbedccecbcdcbeaaceaecbedcccacdbeadecbbaaacecadebddddcebaebdbceddadbbeddcecabbdcdbccaececdeeebcdeacdeccbeaacbbeabddcebcbebeaebdadcaedecbdcbddabcdceceabacadebcebabebdebdabcebeabebabcbabaedebdddbabadacdceddcceeeeabaeacadcaaecbabcbacbccabcecdeddacedeedebebebaabadeebccdddebcdbcececcbeecaaddbaccbcbbbbdaabcadebeeeababcbccedabdbacbddeaadeccbbbcdcadecabababadbbaededeedbbaebcbeaedaacaddeccbbccbcdedabebeaaccceeaabdadbbeecbbddcaeeaadacbeebabbeaedcbbcebcadebccaaccaedeeebeaeebbcccecdccddedebdadeeeeccebeedadeabdbecaedeedcaddbdbcdabedcdcadabbebdaebbddccbcddddaadeccdeaecddabdbcceadeebbabcceadadaaaaddaeaeddacbeeccaadebbedaebebbcdcbedbaddceadbabebcaacdcbdaaabbdbeebedaaddcbbdbaabadbdddabaaacebcaeddbcdabedecbaaeaecbdddacbbbbedbcdabececedaeaedbccdacbbdabdeeecbeccdbdbccedcaadedeaadeddddadaaeeadddbdeacdeababaecbbcdcedcdadeddbeaaebecaebcecadedabebdbcdbdaeecbbcdceccddcaacbedaeebcebcceeeaabddccbbdcaddbeaeadeacbeeecacbddddeaacbacadcadadbeccccccaabeabecdbdcecccbebbceacadaceabaeedaddebaacbbdcabbcccceebbabdebcbeeaacbcceaaddeadaedceedbbceeddbcdcdababcbbdeeadeddcceedaeddebdbebdacababadaabbbabcceaadcdaeeecaccabbeebeaacbebbdeccdeabeaccebebddbbcbecaeaaceabadabadbddbcddaddbcacdbdccabccbdebeaadebbddeeeedaeaccdabbebeacddccecacbbcaebcbecaddabebdeecdaacdedccadabcbccbabdaebaeebbcbbadbbbcabdebedcebeeabeceddccdeadaeecdddecabebbedcdbaedbcacddabcebcbccbeaeccadaaaadbebdadcacccecccabdbdecbbbbbaaccddccdaaebcdeadeaddecbdbacccccaadbaccdaabebaeccdebbeedaaebcaebbbededcccecedcbababcaebaadacabdcbccdbbcbaacabeebbdabddecdcdaadcbdcbdcebcdaadcebcebaddbcaaeedacebeccbdcebeadecadbcccaceddbbcccaccdeabbaceacbdacadeeaabcdbeaccdeceaeadaecccaeaedacadccbbbdcbadecbaeabbabdcecebccdccacdbacdebaceedebdcdbceaccdccdecccbecbaeceeccaebcceedebebeedcbaccaddaaddeabcaddceedbbbddedbeebabedcbbaecddbaecbbdadeccdabaadbcddebbaacadeddcdcbbaeaaabddbaaaabdebbcbabbedceccbaabeacebceccdacdeeecaecddebbaaeedeebececbdababcceddcddeceeebdddcbbeabaabdeebbcbbbaeeadbcebaebbaeedeccdbcebdccabbabeddceedeacceecabcabedbdeebadcebdebdcdaaadedcdcedebabebdaeedaebcdacbbabcedeeacacedbbbbdccceedccbbacaabdaaebcbeeddcdaadbbbaebecbadabbcdbccdaaccabeabbbcbebdcadbbdaeecbaabbadaaadeaebaebccdbdeacebbaecdbdeeecbcebeaadddeadcebcacbcbceeabdacadcdeebbdaaeccbeabcaeedadcceaccdbcceebbbaaddacabbadebeebaeedbbacaecdcdaebebbeccaabeaeaededdebebcbbbcebecbacbacccdcebbbbdababdbaabbacdeaaababcdbabcdaeadacbdcddadbdbacdcabdcaabeabdadaaceedcaeacceaabdddecdbdddedaabbbbaddadacbbdaaabebeecbbdbebabceabbedbddaeeacddececddcbbecbcebabebdeabccbbcaaebcbcbadeccbccaceeadddeddaeaddccdcddcebbbeecdcdbebaebccbaccdaaddcaadbacceddbedacadbcebeebeaabeabaeacacecdbcaaeaddbbbebeecdbdaeebbebecacdedbbdaedabeccedcdecebcbdeabedbbdbeecccbddecdeaecbcddcacddabcbdedacbcedcabdbdccecaeeacbaceabededdeeaccbbcddddaabbbbcccdcddbdebebacccbdcbbcdacddccdcbaababeeeabcebddceeabbccdacadbcebeabdacaeeceabaceddabacebddcedaeededaeededeebbdddabceeabccecebdaedccadbbdecbbeabcecabdedccbaceeaceeccbbbcbacbeccaaacabbeacdabeecacedbcedcbeaaabaabdacdaababbbcdcbdcedeebeebdbddbbcbecbecdeccbaeadddacaccaccbdbacbbeabeeebceddeaedddccedeadaebaeabeaaecccededcbcddddebacacdeeebcebbbdadecdadebdeddbdbeabbccdbeebbdceeecaeeaacceadebabdbdabacecdecdecedbedbdcbababdabdbbcbbcbddebedbeeddcabacbccdaeaedbcedbdccccedeccbcbacceddbdcaadbbbbedbbeaabedddcdddcbeacdaaaaeeceaeaceaaddadaeaaecabcedbdaabbeaebebadcdabedcccbeaaabdcdbddadcbbcecbdeddbeaedbaddbeaadcacebdababcbecbdcaccddccbbaddcbeceadedddcddeedccceeaeceaaeacdbdeccaeeacdaededbccbdcdcaeaddbebeebbceaeabcbcdabbbbaceedabaeaeabeeddebebebeadbaecaceeeaecbaccbdadecacccbccdececbebbaceeedbdcdcbdebecbaedbcbebeeaeedbcaebadacdeccdaccebddacbaadaaaabdbeaaadaebdbcccbccdcbdbdeddadceadaaceeaacdbdddabbeedcabdcedbaeceecadbdeabceeadeebecebbebecddcbaeebeaedbdaaecebdceebeaedcdccddcdeeacaaeebebbeebeededddeadcbaacdaadceaaeeddceeddacbeebcbbbceebddacbddcbcaadecccdbaedbededeadacbdacadcaeacebceeccdebbaccdbedcadabaaacbedeedeccdbedaeebaeebaabcdbbadbbdbcaccdbcebecdddcabdecaacdbbbdbcdbecdbdadbdebdacdeeedbebeacdbdededbddabcccadacddcaeecbbdeccddcdbdaaebeadabebcddcbddacbddcedddaaabedbccaccebdbbdbdbaeebeaaaaceddadccdedacdaecdecececddecddccdedccdaecbabcacbacacdadbeacddeccadaceddebdebdddebaedcbbeebabdeaadccdddccdbdebecabeacccadabdabbeaabbadbedcabcebeedddbbabecdbcecbccadbdacadbdbacebaeeadbdbdceadbacaaeaebacacdecbaaedddddbadacddbecaeceeedeaceeadebaaeeabdaecdbacebeacddbaddedcaabcaebaeccabcbaeeacabbbecdaaabeccdbabdbabecacadaaeedcbcbaaacbbeeddaaacbcbdddaabaedbacbaebccadcbbbdcacdabacebcbcbdadadddebbcebcedeaceacdaaeddaabbdbecbbcccbcebecebbdbebdceaadbaeccabdcbdceeecbbedebddaedbbabedaadadabbcdcaddbbedddddaecbbecbbbabbbcacaaadebdbcadcbabbeabbdedbadbaaceeeedeebbdcebdcaacabeacddabcadcbaeadcadaddbccdbcdcecbdacddcbcadeacebbabdabdeadddaabedaebebbababcaeecdaedbdaeaaedcdddebbdcbccebecdecaceddcdadcaccdecacbdaccabdeabacabceebceacccbebeeacbddcbaadadabeeecdceddaaedcacddbcddcaacdeeaebbdadecbebbdeecbbdacecbbecdeadcabdbcdcaceabbeacbbcaddeaccdeebddcbcddadccaddbeaacedbaacbecaceddcccadcaecdeaddedecdeccbebcbedebbeadbaeedadedccbdccbbbbacddeacbbebaebadcbbeadacadeabacbbbddeeecbedebaeccadeaddcdceaeccebeaabcbbcbaeaacbcaabebecdadbdcabecddbacbacccbabbecdcdcabaecedeedcacabcadadeaecdeedbdbbebdcdeccbbacbbbdcbdbdccccbeeaecaabdadeedebccdbddbadeaeabceeedddeaeabcbbcaccbbbedccedebedabdbccdaeddabcaedbadecaecedacccedabeecbacebddaccecbdaecedcddebeeeeecddbddccabdccddaaaddccedcdcaedbeebeaaeeccbdaaeedcaaeaedadccecabdeddddbadeeccbdcbeacedcdaaaccdbedcadaaddeadaacdaabcecaeaeadeaaedebbaadbacbddddebedbedeacabaeeedabaccadcdabdabbaacababbdeaebdecebdedeecaebbdcddcabdbcacdaddccdcdaebcabacaccadccddcaebeaecbacaebdbdcabeeadeeddeddddbaeeededabdaccbdadcbedbbbdaaddacceacaadabcbbbdbbbbdeaeaddcdabbcedddebacccebdbeeebeabceedbdeddbdcceacdeadeccaadbaadecddabcddecaadecbbbaabbadebdabcacdbbdecadcbcadaaeadebacebbeccabadbdeaeebcebbdaebabbeacaececcbceeaebecbdededaaeeeecceadddcaaabeebedddbacedccbbaacaacbdacaecbdddddaeadceebaedacebebebddeecebdaaabaaadbddecebbebcbbeeaabdeedbeedbabeaddccdacccdabdeaedeeeebcdcaabeccccdbdbbbbdaacaedcbaedeecbbbaecdbdacabcddbdaadcabcabdabaaaaadddbdcddaabcdabbebcbdebbbbeeabaacccdceacdededeeeacbccdbaedecbdbddecdaaddecbbcebbdaaacaebdcbedecbddaaddbdbaeacaaabbddadcaceaadcbddbdcecebbcaebaccbcacdccecbaeedbdaecdeabdeacabbdbdcbbeaeecaacecbedeeccabedbaededeabdcdcbcdddbdabcadeccdcbeacbcadeacdaceebcbbcbcbebddbbbacddcacbbdecbbccecdbdaacabceccacbaaddadecaeabdcdeedecbedeeabccacedbdddcbbddeaaabdabeaaabebdabaaadbcdaaadbdcbdedaecaaaabeacebdbebeacdbcbecabaceddbcdabeceaeceebebecebbdaaaccbcdcdaddbbeeebadaaacebecebaabeecacbccabdbddeabccdcdeeddcbbbcccbabdbbdbcaadbccebedaebaaabbaceabaaebcadeeebedacaebddacaceacbbbdedaeabdebecabbedbbaeeeaedecaaacaeaacbaebdbaacebdbcbdcbbdbacbedebbedebabacbaacebbbcebeddbbcabdbebeaabbeadaeaaccbadabbdcecccaaccceacbcedadcaadeccbdabeedeeaaadadceebedbbebdbcaeccdcdcacaddeaaaddeaedeaedecedacdadeeabeccebeecdeacddebcacbbbceaeccdeebbbddbedbcaadcdbcdddaedecaeecadeecbbbeedbbbecbcccbbbbbaaabaebaeaabeaeabeabaaababdcbcbcacbeabdccecaeeeabbdebbbecbccbebdbcacbadbcdcbedccccadeebbaeccdbbbdbaecabaeecdeecaedceacccbbdecedacaecaaceaddebabdcbebdaaccaabbcbdbeeedddedaddbaacdbcdaeddbcbcbabdadeceebaddecbcbeaaedecaaebcdecbceacaaedbecabcbaabbbcdebeacaabdbbbaceadedaaccbbabbbecbbaccdcaaddebddaebaeadcdaaacbacabaceaadbeeccbecbadaeaceececaedebcdbeaedbcebbeeaceaedbcbededeeecddaadebecbbebddadccbcdcbeaaedeaeeaccecbcdaaecbcdeeacccdccebcbebeeadcaeedaaadeeabeeadeecacacbabdbcaccccbccceececccccbedecabeaaecdedecebeacbececeedcdaaddcadeababbebdacceaaacccaddccccaabddacbbcedbadaadeacdacaecaecedaaeabbcdebaaccaadddbbcccebcadbceddedcedaaddbedcdaccddeddacbadeccdcababcdaeaadabcdabeadedaccaaeedaeddcdaabacaacbcbadcdddaeaedcbabdeedcebeaeeeddcbcdccbbabedadaeacadacceacabbeacbeacbceeeaebaedceebdebcbbbdbdccbeabcbadaacdaacadecbceddbeaebbcaebdaaddaebabbcaadabecccebcadeaecdcbadcbddadebccbbbeabdeeaadedddbaceadaabadaaaebecbaddeabcebdcdddaebcbebbebccacabccbebeaecabbebbecdbeaceddcdacdacbbbbaccebcbdbbedcaecedabbddbacdabcabbbddbaeddbaaaabeabbdcdddeedaceccdcbccaedcabeaaacbbcbcabdaccacebdcdbeddcadcbacdbaacedddcddcabababbdbcaabaadaacbcacedeecdbbddacdbbbaedcabcabeeddbeaddddabaeedacecaabedabcceddaeedeeaacdaaaaeeeaeceaccbacbbacdcbcaddeeeacbaaccacddebaeaaeaaedddabccdcaebbeabebbeacbddbcacdacbadeaaeeeecdebdeabceeccdbdcbcddceedebeacebbddacaecbaeeaabeeacedcdccbdbbbdedbcacbaaaedddedaaddeddcacadebedddccaedacedabbdaeaeeedeadbeedecbdbecbacadeadabbcbaaaaeadbbccdacddcccecdcabbbaddaecbcaddadeeeacdcecbbbcdbebeaacdcaceacdedadeddddcdcebeebdacbaedbbebedceeecbedeacdbbbdbadcddaedecabeacbbbaacabcbbdbcaebedbccbbbaeddaaabbabdababcdebdabaacdeebaaeaebaacbcaeeadabacbbeecaebbdabacedbebdecbcbbabbddbaaecbcbdbcdeeedcdacdbeaaaaabdabceddaebcdbabddceddcbcbeacdeaacbadbbebbebacabbcbabacecacdbaebcdcdeebdaacdabadcabcccceaebcbadbcdbdecbeeceedbebceccabcaaabcebbcccdeebcccaadcebdadabbdaebbcebebcdddadaadedeceadbeaeaecabbadbaddabedebcaeeabaebccadadcdcacdcbacbbbcdaedcbaeadeddbcebeceabacdcbecdaeedbcebeeaecccdeacccbbcbdababdabdbebbeaadcedccbcdedbbadbbaeddbbeadacbbbcdebbebadceacdaecabeaaababbdedcdadeedcadedbdebbadcbdcecdcccecebbeddddecacebaddceaeddeeeddebcbbdcabddabcaddadecddbddebdadcecdedcbaaccbdecbecdddaeeacccbdcaeccbdaebacaebaedbceceabbbaabdbabebaceaceaeddddceadccacabadbcabdabaaeacdedaddbdbbbebaabacdcbddeeccecdbacbaeeeeddcadbbabdeebbceaedaeaddbcbcadceccaeedeeacababdaececeeeadcbadceaaaddeceeebcbaaabbdabeceeadebebbdaeedceeaabebdebcaaeaacabcedeaddeacadcabcaabdedcbbddcedddbdcddacccadbeebbdddbbddbcedebabdddaacebaceecaebecececcaebeabcababeadcdadecdceadcabdabecdbcabeceaddaacaeaaaabedcebcdedbdedabecabadeecaccabcaecbbaaaeedeaabbabcacdbdeedbeaeeeaddbdccaccaeceadcddeccabdcdaaebcceeaceeeecdbaadaabdedebacdeaaccdeabadaaeaabbcdaadeecdadbaeaaaeaddeeabaecabaebcdececeebbabcddcdbbdcaecabceccabbaabeebbbdacaeeeadacaaceebeeedeaaabcccaabbeaaaaddecddbdaeabeaddadadeabcdbeaeedbcadbcecedabedccadccdbccebaceacebadbbecebccddbaeebbadbbceedbedccaacbdbbbaaabbcedaebbcacbadcceddcbcdbeaecdbcdddccaecabbceadbadbdccecbeebdcbbadaebecddbcbcadadeecddddbedccedeaabeebcbbacedcbdccbaaaeaaccecbdbacdaccbedcbbcdbddcaeadeecaedaeeabcdbeadeadacdabdcaadaccbdcbcedcbaccebceaecedbbbabcaabcedeaebdddbcabccbcdbedeacaeadadbddaaddecaddeeeaeadbadecceecbdaedbddaebecebedccadaebcacabacaccbdbbebbacdddecbdadddcdccaccdbabebecbeecdacaebeaaeccaecaecbbddebbcbddcbcbacddddcbbdadaedcbcbedededecebabdeecdaacaceacbeedcbcdaaddadacdcadcddabaecebbceaccbecceabbcabaaeaaeadccdedacbaabbddaadbaddceaeaddedbbcabddacaaedbdbecbeaadcabcabbbdddaadeccecdbdccecdcaabccbcccddedbcbcadedacddaeacadaeeeaaeadcbbcbacbbeddacbecbacdddcedcbddcaecebdedcaedaedddeeaebbeaceacbedbecacaceeabddabeaebcdbddedeecaaedeaddcbcbecdcebbebacaeaeadcedadbcbdbaabeeacecacbcddeedecebeecaddcecccdbebdeacaeddbadaccabbeabbccdadeacdccbeddbeeeddadedcebccbceccecaaadeaacccddcedabbacececccbcceabaccceaeebebabdbcaecbabadddeecddcbdeedeccdccadcebbcbbbeeecbcccdacceccecaecaeecdaadebaddeeaabccaedbbdabededbebbbadeaacdaedeacdbbeacaeccdbbdcecabeceebaedcccbddddddddeeebeddcbcceeedaedcecbacdcaebacbbbccbcceaccbddbcceadabdecdaddbeacddcadcadcacbaaedeebedbccebceeacebdcceebbcaeaadbeabdbcceeabdeeecdececaeebdacbdbebbcaaeabeedcaeeaccabaebebaeaccddccbbdbaaeeecdcbccebeceaeeeddeaebdceeebebebddaabbddeebeddcdecdbbdadeeabcbddecddbebdbbbcdeddbbcadeaebccdeddcbccbddbbcecbbcadabadcbaddddbcabddebadcaeabdccacebccdceccbbabcadabebccbdcdaacacadeddddbecbbeecadddbdbcbaccececacedacacadaaeadcecddddabbcbeaedbdedaeeabaddcedccbadebdddebdbbecccbcccabbbbbabbdecdcababdbadcaaedebbbceeeecbacaaaeaeaeeccdaeeccabebeecebdbdcecbaddcacdbeeeebddecdaedbebedeeddbedcbaccebcbdccaeebbbaadcdbcedbeadadebbbdabaeadecaebaadbdcabeebacaeebcdbcedebaceaeeeedbebcbecddbcddabaedbbeaddcabbebcddadeaaabceeadadbaabbacdcacdbecaecaeaedeccbdceecceeebdabeebdcaeabeecaabbbcbbebdeddcabdacdaacdbeabaadcddacaecddadccadabacdacabaaedbcaecedcbcbadddbadcccbdcdbabaeabacbcaaaacadbcaabbbccacbeeeadacbdabbadbcbaeccdeedbbbdbeacbcbdbaeabdbceeeeedaeaacbbbcdcaaedeaddcdadcccacbddccddebeaadaedccbcdebbadabcccbdcebdadcbadccbbebebadbdbdeeebcbaebebcabcacaebbecaedcadbbbdecbdbaeccbdceeaddaccddeecbcbbbeacbecbdaedcabcaeaddceaceeacadecaedaaacceeaaeddbdacbeeedcedebccbaecedacddbbbbbaddddbccceccaeacaebbcedededccaaeaccaebeadcbeddddabecaadcebcaebaceeebdbacaadcbebcceeeebcebeaebacabacbdcaaccceaedceeacedeccbccbeaeaedbaaaaeccdbdaebcebeacbdacbcbeecbeeeaaddcadcabcecaaeeeedbeaaeacadacdcbeddeddbaaecacbbcbbcacabbcccbcbcbdceedebdcccebdacdedeaaaedcdeabbdaedeacbaeedbcbeacdbbcbaceaadeaaaebbdacbecdeacbaabbdaceadaccdaeecdbdaeaeabdcebceacadecabadcacecbeabecadbdedccadeadeaebdedaaddddeeedbaeaadceaecbdbddeccdadadceeaadcccaadaeeadaaaaadecacecdacdbecbbceeadeecdddcbbeeabecebccccdacaacbaedadeaebbbcbbceaaddbeeecebeabdcaebaedccbdcadcbecbedddececcedeeecdadcbabdedbbddcdaaacbeadcdadbbdaceadaaaaabeeebdcacecebdaccdadaadbeddbdbcbeeccdcddcaaedcabdccccddeaaaeeabadbaabedbaaeabbceadbaebbeadeedcdccaaddecdabccabcacacdeadaabcabdbdcbebacaebededebcecbdbdebdcaeaceaabcdbcdcadaabbcabbeeabcdecaaeaadabacbbcdceeaceabddcaacacbddbbaacbbacdbddaacbbadacabeadaecdcedededadacbdabbccabcdabdcadcbbcdadeacdbebecaecadddaccaebbbabbbececeabdbebacdbbeaabbbeeabcbdbbbedbebbcdbacbedbdcadccebedacecacbbdceedbebadceaacebedebceaeeabaaebbbdeadcbabdcacdbccaacebddaaccbaabbddcebdadedbeecadeeabdacbccbeedeacadacadadceaaedabddbcaceacebadddebcbaccccaebabbcbbaacbcdbecceddcaeddceabcdeadacaccdddeddaebbddeecbdddeeabbacddbabcedaedccccdadcdbddabbcdecdcbeaceeecccabeabecdcddcbbbcddbaaeeacccaaaaebbabccbdddeebadceacbeaddacaabaccdbcedbdccadacacaedacbbecdaccbbdeeccaeeaaaddaeedabcaeaededaadbbcabceccdacceacaaaebceceabdccedcecbdbbabcbdaccadeebcadeedeeecbaeaddceddbacceaadaceaabcacaebaaaeceebbacbbecdddebbebaaaeecbcbdccbcbcbeeccbdccedcdadacdbbeecbaaadcedeaedbbceadcdaddcddbddbcdcccaccccebdecbacddbcdedcebccaceabbedaadaaeaebadeddbdacbadcabeaeeceabcecbbbcccdbceadecedbbdcaaadababcecbaeccabdccbdadbeadbbbadbbcbcdabdaacbcdbcedeedcbcaaacecbbccbbaaeecccddaaeeebbceaeddbdeddcbbbecbdcbcbaebcdaddbeccededaaeddabdaceceacebcbecbaadebbaaaddecbccbdbbaaabeabcedebacdcaadabbbcebdbacacbaaededdcbdbbeaccdcbeccbaddebcbbaeeecceaecbcbcdbcecbebbeddaaeeabadedcaeebacbabbdceeebccbccbdadabacedacdcdaaaeedbcbcebeebdacdaababeebbbacabedeeddededcdcbbbdccbbdaecdbdaeabcacecccbedbbaddacdaaddaabaddedacdecbcdeedddeababcceddbccaabdbaceabbacebececaeabcadcdcdcdaadcceeaaeacbacbddccbccdcebededdbddbcecdabdaceadcedcbabaabdecadebdedcdedadeaaabbcdbdcdcaedddeadcbaaaacaaeacbecaadbacdedddabcaeaeedcaeacbabaceaebdeadeddbabccabcaaabcdcdcdbeadebdeababecaeddeaabaadaeeccbaadcedacaeaecbbcddaedaeddccebcbcbbdeeabeeaabcbeabacccaebdebaddaecbcbacbbcaeaeddddcaeaadacdbcadacdbcadbacdccedcceecebdadebaedaebeaddcdcabeebcbdcccaebcebbcbbdbcabdaaccbdbeabeaabacbbecdceaebbedaebdbdbaabacbbbbbbdbdbedaccccbabbbbeaaeebecaeeabddebaaacdcbaeddcddabcbdabcadcacbbcbacbbdecaceecbadeccabaebbbaaeccbcadcdeadbabadbeccaaccdeebaebceedcdedceddddaddddaedccdaceeededddcabdeaddcdddaeccbccacdedbeceacecbdeddcebcadebeddcdcebebeaacbdecbecebcdeeebadaeccbbcbbecdbeeadacdaecbbbaaadecaddbabbadeadaceedaccebcceedddceacbdbacedebdedcaccbadbeeebccdcadcabcddcceeeadbaaaadcedbeaeaddeabaadadadbcacbecbcedcabeabcebaeeaddcdadcdbedbdaadcaadeadedbbabbcbebbbcbbeeadbbcdcbcebcebaeedebeddcacdaedbacacecebcdbaacaeadbedabdedeebeadaddaebdadeccbcabbabcabaeecbdcdaccddcacedcbcecabdaedbecbbbaedcaaababcabaabecabeccaaadecddbabecbcadccdadebbceccdeaadbedbaecabecbceccccecbbacebbcdacbcabeeadbbeebeeedebacbccdedddeeaabcaaabebdcbaebbcaccccaacdaccdcaddcceadbacacddddeebbedeecabcaabedacebcaeaeecbaadaabccaccbabcbebddacebbaeacaeccabbddcaadeeadbbcbeeeedcdcedbebdbdbddeebbccbeeeacbecebadeabacdcaceaaadcbcdcdaccbedbbadedddadddebbbadadbabbedcdceaedbcbccecddbbbaaeabcaebaebdbbeccbcedacabccaeebcbcbecbbdaeccaddacabbebcbadadeaeeddcaccaadaecebebdbedacbecbbdbacdbcedcdeebecdbcaccbdcebbedaaebeecdabeacdbbadbbccdeeecddbbaecbeedacdcbddeebdcbbdebdbeabcaaebeabdabededbccbbabcbaeacbcdeacdaddcdcdcbedaabeadedbbadeebacabccaadaabdaedbceeabbbbeaecbbeabebdeebebcaabdcddbebaadeabbaecabecaadecebccbcbdababcebbebdabbbcdedbbededeecacdadabcdadcceaedadaeacabeabbcaaccbcacedacbbabbbbeabbdbdbbabedebceabdaccaeecaeadaceebdaaccdacdeededbedaeaaacdadbadcebcacbcbbdbcdabdbcdcabaaaddadbabaddbdeedbbaeedceadcedcbcacedddeebddccdcbcdbabaedadbcbaedebeabceacebcbbdcadccebeeeebdcecdcaaaeebebdabdbbdeedcbbddebcaeabadbbcbcbedbeebdaaedceeeeaccbbbddedcbccdbddacdadccbcbaccbbadcdadedabcdecaaeeaeacdaecdbbbbedcecbebbcdedadbcaecdeebbdeeedbcadaacbbabadddebebbbcbabacdbddbaccccdeddbbcbbcadbbdacbbbacdbdbaadebbbcebdabaadecaecdebaaedaaabeaaaebaeccbeababadcaddacddecbacbaaadedadcdbcbbbddbcbcebededbeeecabdeccdbdcdcacaadddcabbdddbdddbcecaacaadcedcccbbaaddbcabdedbebcebaceadaebeddecbbccbacabdbdacaeeeddcacdeeabdccedeacbccdcabebedabbaceddddbecbddebbeccdeebabddedcdbcaeeaaaaabdcecdbeecaaeecacbddeddbdcbacdeeaadccadaeeebccddccedbacceceacaedeabdbecedbdecadebecddceabbadbdbbcbcbedddaecddaccccbadebceeeeeebaabdebeeebabcdddbeadebdcdebdadcecdbeacacdaebbdccabbbcdadabdcddbaeaaedadbcbadacacebceeddccaabbbeebecdceddebaeedeeedeacadcccccedbdaeceebddabccbbccbccbeadbdebbddcbcbcbeabecddebddccdedddbbdcecbeccddeeaeeebedbeabdcbaabebbcacccabbdcebeeeaaabbcddedbdadabaaaeaccbadadaeebcebdcabeeddabbdebcbacadcbebababeaddeacebadcddbecbbcdceecbdbbeeecccbdedcedaeeaaaceabccdbbbaceebedccadbeceeacbbcbddadccaccaaadaeedcaacabdbacebbeddceaecacacebaaaedeabcdaaedccbccdcdbbdaecbbaaceaeccdaabaceeacbedccaacaaaaedbbdaceebbdcbeeccadcbaccdaaeaeabddebeddbbbaaaddbcdeacddcdecbbbdabcbdceccededbecbcacbacabddcebbebecbadbceeaababeacdbbeeadddbacbbbeebbccdabacbdbcbbdedcabbedecbaedaabbcbbacaeeccdcaadbdbeaccacbcadecbaebaedeeadadadbcaecbbbdceeccabbcbccaeaaecabaabecdacadacdebbcdaceadedeababcdcbcdbbdecbcbcbbceadebabcbbcabebdecedcaabbedccbaeaebeeaecddceaeeaceeeaabbdbedeebadebbebdcadcbadcaeebeeceadaddcdeecebcebdecdbadaaceebeacdccacdbaddedaebdddeabbacddebdebeaccbbbbeceacceebabaeaceebbdaaeabadcaedbedbbdabacebbceddaccdbbcdecbbcaedabaeecedcbeecbadcececbdddbcebcceebbeaedbccaabebcebdcdbdddcbccbccaadebaccaaeeeabaaebeecaaebdcabbbdaadecccebdcebaeceaeddbeeeeeadcbabeddcbeadadecbbdbbbedaeddeeedbebdddeecdeaebbccaaecdeededcddabdbdaadaebacadddeebddcbaaebacbdbbeaecbbedcbddabdaaebaabdcdedecaacddddccccbcdecbedeeabaebbccdbabdbabaaeacabdadedcdaedcdabbceddaecdbcbbbebdaacbabbbddcabbdabebbbcbbbeaeccbebbddbceabaacacdeabeadddbaadcceabccecadebabecadeecbdbddaadaeddccbedbdcebecdbeccdddcebaabaddcccbcbbebcdecbcbcbeebbaaaaeddceadceeeabecdabecabcbccdadcdddcdceececdaaaeceaadeaeaacbcbaddeebeeeabbaecaadabcebcbcdddccdebcdeadecacdbedcdccbceecacedcdeecaaceddbdeabadbbdecbababaadedadedceebdbbecacdbeddeecaabbcbcbaccaaaebccabcacbbabedcabbabacebaadeebdcabbbcbdcdaebdbaaebeacdebdabedcaccabedabbbbaceccccaabcaeadaecabedbadeeacebbbeaecbbbcaedabebcebbbddcccccecdadceedeabecadddddeaebededbececacdcebeedbecebebaacaacbbcaddbaceedbababcdaedbabdddbdceceedebdbbabaccedcbebbdacdabceabebdeecbedbdabbeccbcdeadacbdbcceeaacbcaacacbebaebddcdadbbcaeabdbaababbaebddeacaecccecdeacebeabacdabeacbcabcbcdddebeacbaeaaeeedebebacabbdaecdeeeedcaabedacdccaeecddbeadaebbceeaaaccabebdcaabceaecbeaacdccaecdaabccaeabbeceededeaaeeadcbbccccededdbcdaecbaccbedecbbdbdbdabdbbbcbacaeaedeeceabcadaeaedbabecaebbaaaedcecbdacedeabbecdbecebaeadbeebeedbdaacacecdeccebcdcecdadecabcdacdbdbddddddbdabdaaeecbdddcdbadcbadbdacceccabdddccecdccbaaeabdabaabacaeeebaceaaaadbacebddacbcbbbcebceebddcdecdcdaaadcaccbeaedaccedbccddedcceaeddbeaedebbeeeaeaadecabdbcaaacaaccbdaedaabecaacedcedcbbbbedbdaaabebcdcdcebdddcebceecccdeddaaededdddceabbccaedecbbedabbeecdddbeacabcbeddbecddaeadcbaededeecdcaebcdaddeecdaaabaddceccabbbccbbbbadeccbcacaebcbbaaabebaaecaccccadecbceaabebcacddddbeadaceebeebaaaadbdabbcbecddaebbeaeceeebadebbdccccbdedabacebbdcdbedabdaaeaacdbebdddacccbcadecbbedadadbdbddedbebdceaacbeaeadddcccbecececcaabcdccadaceeeeaebeccebdcdcdabbeecbbbeddbdbbebbeabbccdbaebbaababbeadaaeeaebbdabdcecaebccedbcbabcbbeabcdbdabdcbabdedadbedeebcbabcecdcbdbbbdabcdccdceeacbddadcaccdcaaeaacabbbacbedaedeecaabdedbaebaceceabceccdebadaebebcaaeacedcacdccebeaedcccedbedaaaeaedbedecccbccabcddaeceaccacbeaccedabeaddeedceebcdabbdabaaeebaaceeacbbaceadadbbddcaaeaebccbdbebeabccdedabdebceaabcaeeadceccbebebedbaedbbdedcceaecaedcebacaecedeecdcdcbeaacadbedbaecababcedecaecdcdccadadcabdeaebeadcbcdbebdeccccecdcadcdbcdacedcececbabbabcaebbceaebadababaedcccdaaaacadacbaebacedcceaecbcaabaaabaeeccacadcaaacdeeacaeaaadedceeebcdebbdaeedcdabbbdbdbdeadadcdbdcbebecaeeaecacceebdbaabcddaabddbcdbeacaacaeeaebebbedacbedddaaaaebecaebdeacaeccebadcbcaeaddeebdeeacdbbbaababbacddaedcbcdaaaaecbcacbaaeebcccccbebddccbcdaacaddaebddbabacadceabbbdccdacdabedcbeedacbdbadaabcacebaddbebcdbebceabceecadadbceadcccccbbbcdbcadcdcdcaabeaaadcdbdbdeaeabaddacabbebeaedccbccadbcdbbdbeeebddeacbabcadccaaddbcccadbbbddceccddecbdddddedbbdddbaaceeddbdbadaacbecebcdebcdeeaaddadedbaeebedeebbddceddbdecbdaeacccaeebdbebcdbbeceaddcecbcabaddaeddbebbabcbdbaabcdcccbcdeeaddebcbabbceecdcadaddecdbeabacaebaeaaedeaedbdbdbebbbbabdcebaeecdbdbeccacbbbdacadeaaedacecdbcddacddeaebeaaacdaedcecdcbbeaaaebabbbbbedeeabedddebcacdbdebaacbaadadacdbddebbdbdbdcdeeadbbdcebdcbcdecbdeceaabcbbdabbbcdcaddcedbecbeebcaeeecdbdedcdaaddaedbbaccabcbddbdbdaecdbdedbebccabbbcabacdabddbeaaecbacdddceddddddbdacbdaaababaabbdcceacdebceadeeabecddeebbdaebeaebcbbccabcaacebadeedbaedabddaacbaebbceaeaabbdcdcdbadeebddbbbcedbeebdedbbdebddaabaececdaabaeeccbbaebedabdddabdbaeadeaedbdaacbdeacdddacaeacacbddbcadedeabebccecabadcbeebeabdbdacaaadcdbdaacdeecacccacecdadccbeeaeceecdbedbedbddbdadccdbecbabededeededddeaccebbadbebccadeeacbeeaddecdcbadbbccaecccebdddaccedadceeadeaeaedcccaddbeaeccbabacbacdcdbbccebaeababaedbbbccbbdbebeceedeaecabbdaaceeeabeecabbebaaedccbedaadddcebdbedbbcbeeedbecbccccaccbbdcebaccabeabeecaebdbddabaeccdabcaadabadceebabaabadcbeedbabcceeacbdadaddceeacbcecacebeedcadeadddedabcdecacabeedbccecbaacbdeadbabbabaaaccebbccbdbdadacbadbaebcbcebdadeeccdaeaceaacebddedccabcbdaeabbeeacdeeedcbdbacbaecbeaddccaecccdadbbeaeedeaccdaaeabcdbabeacddcdcceebdcbcedaacbdbacacccbbaedbccddccacebdeecaeccdacdaebbeecaaabaaebcbabedccedebeeebcecbbeebdebedadeccabeceebacaddddccadacaecbccbdeeecdaecbdedcabecacddeeddedcbeaaedceaedeaceebcdbecacacebdaaabeccecedbadeebcdbdbdbcccadbaeecebacadecccdbdaabbcdbbdabcadabcbceecdadbeccbadeccdcbcecbbacbadccabaeaedddbeddedeebeccadbebdcebaaddeaaddabdedbdcdbaaaebadaaeadeaecbabebebebeaeabbdadabbdbececaebdaebcaeaeacaddcdebcbadbcadcbddedbbbaccdeedeeeeaadbeadecccaeaeecdbbdcdedadcbdadbceeeedbacacebadcbcbadbabbdeecbcbedcbbbebedbdbcddaabeebceecdcededabccecbbbbddeeddacdcaecbeabacddceeeecdbdacbeccbccdbebaedecbeaecacbeccebeddeadcdbabeaaacccebeabcccaeaccccdcdbabddcebccadccccbbbedddecdbaeaeddecbdbaeaddebccbecbdeddddaabaebaadaaeeaacaaddaeecbebebaedbdebeabecbeecbdaadaccddededcabbaeecdcbcebedebdabedaddcdabadaeaebabddbdbbedceddbabaedaddabaededddccbcbdebcaaadbbdbbaddebdaeeddbbbbecaebcbaedadacabecbcbbceaceecaabedebdabdaadbabddcadbccabaaccdddccbacaeaaaaeaedccdcebebccbedeccddcddbeccbacaacebadaebbbacccbecacbbdbdabeeacabaeeabcabedbcacddbbbeaaecbedcccadbcbaddbdbbacdcbcbbdcebabadacddabbaeebdcdecebcdabeaaddcdcaeaddbbeecbdadbdcaedbdcaddceaaaceeaacdecadaabeccaeaacaddbaddcddbacbdeebcaebcbdeccedeabbbbaddaebabcbabbceadebdacacdaedaaacebdcebaaadecdacbbcaabaebdaaeebbcaeeaaddbdceedbdceededddeacdeabddbbdeaeeaabaaccbcebedeeeedbeddebdeeeabecdcdeaaadbcecebeadceeceedbceebaaceadcebdedabebcdaadadcaeaaaddbdbbbadcebecbbaddebbddbeaabbacebdecdbbaebceaaeacabbecdcecdacaadcecbbbdceaacdeddbdaaeededeaddccbaacccdeeaebeadddccdeedcabaeecacdeaeecbcabdeeadbabaddbaadabddddaebacceacbabdaecadcecbaebbaeadacabdcbccaacaeabcdcabdbedaebeacbaebabceddeabadbeedbebdabecbdcaeeaedddcebacacdcdbbebebcadcceacaecedcededbeaadcdbcdceebecaadcddbccaabeabdaacddeddbbeeeeeadcdbdabecaabdbeeccdddddaacaecadbcbdbbcbadcedccaccdddecdcabeadbecababdbadcadbdaababeaeaaaebbcdedcdaeedddecaaadedeebdbbebddebaaadcdbabdaabccdedacbcdeebecbdedecdcdebdedccadddeebbeeedaaeabcebecbabdcabbdcacacecbaeedbeacdacdaacedbacddbebedcbaddeabedcbebddbdeebcbeedbacdeadbabbceaceceacecccebcebdeaddddcbebecdbdbaeeeddebebbbdcddebaabadbabaceddabbeaaeaadaaabccdedcadbcaaabebdcedcdcaeaddebacedccdbdbeeebdbbbbcbdeceaeebbbbacebdebaeeecccbbdcedddaecdbaeecdceedbbcddcabebecebedbddebecdbacdeabbbebeabcbbbccbdacacdebdacbcbaeedcecccbabcbeeaabcdbbbbccccedcdddbaebecadacaddbdecceabaaacbcdeddbbdacabcdaeaedabeddbcacdccdacccdedabeaceabaabbddbdaeeedebaddbcedcabddedddebeccaaccaabcddbddcdcbadecdeaaabbacebddcbaacbcdaabdddcbcaabbebdaaaaaedbcccabadacdebcbdeabceabbeebededecdbeddacaabcddbddedbbdadeaaaeecadedddecaedddadaeaedcaaaadabdacaeedabaaebebeddaadbbabeeadaecebebcdcbeaabdcecdcdddabbbaeebbdeddedcdeacbbededecadbeeacaaabcacbcbddcebcceaedbeacaecdddaccddedeabedecbadabdaaacecededbbcbedbaadeabdbebdeeedcaceccdbebecaecbaedaaeeaddbaedbcdacadcdcecececbceaeebeeadadcbadaadddbbbececbebedbddededbcdbabbebceaebebecbeaabeababbcbabcdabcdeddcecdecbaecaacadccbbbeecaaaeacdddaaccbeadccecceeeacbeabadeebabeabaebaacddcadbbeabddbdeecdbdddaeccdccdebedbdeeeeebdddbaaeecdeeabeadaabbddcdcadeaebcbecdcedcaccadccadbbeddaebbbdbaebedcbeabceabbdbabecadbdaacebebddeaeaddbebcaaedbcbdeedddccecdbeabddaaaeebcdadcaebdbceebbbacbdeedbcbceccacbdeddeabcedbabebeebdcdcdeacbaebaedeabaaabdcceeeabebbaaeddcaeaaceebcecededdecebbadaebdbbaabdecedadabacecbcaedeebebdccbabddbaedcaadebdaaceabaacadcbeecaedbaaaebecbddcedabdccbccccbbbcecbeeeeddebadcdeebaabeeddecdaabddeebbddeabdaaeacdceeacdbcaaaeacdbcbcddacdbedccabdebebbeeccaceacaaeaaaebceccaedabcdbbbacaeebbcdaaddccdbeecedbaabcbedbcaeaaeedbaedaceadedbcaebececadbaececaceeabdbbaaebeedddcbeeeabbdecbcdeeeddaeaecbbcdaddbbbadcebaaadebcdaaeadeedbcebbbcadcbdebebccedbedbbacbaeeabecccbbbbaebdadadaabdccedaedddddbecbbacbcadeeeddedccacdebbcceaadeeebcecadbeedbacdcdeddccbcedbabdaecdbabebcdcbacdbcddecbbdcdadacdcaabbcdcbceabbdebbeeebeebdeaecbdbddeeaaaaeeeaddddbbedecabcbcceacaecaccbdcadadcaebaaadaddbaadbeeeabadedcceecdeddcaadaacbaeebccaddacecabebdbcebdbbbbbddddcdbdeddbeeecaccdeeaeedbaacecacbeebabeedebdedabbabbdaeeaceabddeccdeddcabececadbdcaadecdbadbbecdcdcceacdebaccaabeddaccdbddaaecebebaadeeebaabcacaeacaeeccbaadaaebaecaeeeebedbabababdadcaaceccbcaeadeaebbcebeeadceeebadaabeecdaabacbaaaeaebaeebbcbcbdaabdddebdbdececeaaceedbcaedeeabbccaebbcaececebebdeaccaaebabbaadabeedddbeecdcecbedbabbdbccaacceaebabbbacdeeeacacddedeecaebcedaecebcbaeccbddecbdbbdebebabdbaddeccbbaccabebbddaddbdcedacbabcdcbeebdedbcbbddcacdecdbbcdadadeedececeaccbeecbaecceccceacacbdeecbbbecebbeaeaeacbdbabbeceadacedcbbaaaeadcdbbebabaeecdddedebdbedeceeeaaacabcecccdaaedbeaadccaaaeaaaaabdaecbcbdbeaeaaabadddbcdeeebaacaeccbcbcadeadbddeebbaaacddadcaaeaeabcccdccecbbcabaadeaeedcbcccaeedbbebddeeeabdcbbaccaedeeeadeacacdcdcbdeceabeaacbdaedadedbcecdadceadbaebdaccaadedcebabadaeeddeebceeaaecbeddeebaaabbcebabceeaaaaaeedbbedeaccbbbdcaecdadddeabaeebceacccedbdedacdeebdbcaeebdacbdaddcbddaedabcbbdbcedeabbcdccccdcbeccdacabeeacdadebcdccabedeccecdbebabdedeebaecdcabddbdcbddadbaebacbacaddcedceceedecbceaadbebedcedbccdeabcddabaeaabbaeecaddbcbdbeddddcbcbabececedacdaedeaacdeceaccecacbeabcddaecdaeddcaeabcccdcdbdadaecbacbdeccdaeaddbdabbaebaccacdebaecbecebedecbaeaeeeaededbdedecaacacadbceccbcedccdddcaddbeddeddbccbceabbeccbcbbcaacdeacaacabebadcdbbcabaeaccbabddedccdeebcedbbcbacaddebbaadbcaebbdcabceededededacbdaacbdbaaaedcbeaecdebccabbeacaeccabdebcbdbbdbeddecdbbcbeebbcaedbbddaaaccdebaeeaccdbadbcabecbceeaddeccccbebdbeabcaeddcedeccbcbaaeedaadaebaecdbbaccaaccbcccbddebabeceaadeceabcecabcccebcebaecbeadebabbccadecbddbeabdebdddbcadceebcbbcaeddcddddbeceeebdcaacabadcecadedeadbeebaeeabdccdeecdddeecaeccbabadbcadbbbbeecbedeadcbacadebcbcaccaceadaebccdcdadccaaddeddbedbacebddebbbddbadbcbaadaaeecdcbcdcedbdbccaaebcbeebcddceccacaecbbdaeacacbabeeccbbeedddbbdccaddbcdaeaccaaaddacddecaaabeceeaccbaceeeaaadbbadebebcebedaccaadadccbdbbcaebaeadaeeedcdaeedebeddeddbdeabcaedecddaaabcacdddbdcdcdceedebdcaaedeceadeaaaebadbcccddacaacdabdeddcbabcddccccdabdabcbebebadabaadbcbccbeceebcddbbedddbcecabcddeeedbaabcaebaaebadaabcccbcdeeedbccdcaacadbdeaeeacdeaddaddbeabbaadbbcdbbbdadcbdbeaddabbbaeaeecaacadaccbaceababddbabeabdeedccdbdbeeeccabcbeadacaecbdedcbcdbadceaaeddbccbcdeabacaaddbeebabdedbdccccbadcbaddbcbbbcdccdcccbdedcbebddabbebacadcebbbdcabbbeabddeebaeebeadceedebbddbaebcabbdacdcccabbaabcbdedceeddeadbeeedeedeceedccecadddbdaebaebdebabdbaccceebbdcbddaaacbdadadbaddeccebbaaebbbcaccedddceadeeddacbacdaeebecdccbbdbababceabddbcbbabedbdbbceeaabceaedecbbbbcdcabcabecaedcbccbbbddecbabbaccaecddaecbcdededcdbddcdaabbcaedbddcbbdbcaeaacdbcabcabdacdccdbeeddcaadedccaeceacdcebedbbbdcadbeaaecccbaedccebcaebbcbadbbddabcaaadeccebdabbabcbadbdcceddddaeaecaabaaccebceaabadcdccbdeccdcdacceddaececaadeeaebeddaccbaaaceabbdbaaeecbadcccebcaaecebcbbcbeeacebdebbdcadbebaecbccdecbbedbbdadbccdbcaaabebdabbaebaecbadaacdbddbdeccdbabdddcbeecbbbeaecdbedeadbbacdbeabbeaceacdcebdeedbeeddecaebccaaddcecdbddbddbbabaeeaacaadcdbbddbdcececacdebeeaadcedddabaceeabdbdbaceccbaaeaebbddddacebcadcebadaddebbdbcadaaeabeaacaedcbcbbcececaabbdbabedabeaeeabaaeebdecbbcdccbccedccbcbdacddddeccaadebabbedadeccedceaaabebeaeeaecedccdbdcbddebedebddeacdeadecebaadadeddcadcebeedcecabdbaccbdeddbecaddcceaaceaecbcbcdcabebdecccadaccaeaceacbeabdadcaebdddaaecedbbddddbdacbcebacceaaccbaebcdccadbdeeddedceebdbdcadbadaebdeeecaaaeeabacecdaececeeedaaccaaeaddbcbaaaeabbceeeeddbddabebeadeadccdbaadbceacbbabcdecbeebebaacebadeddacaebccadceeadbdcceaeacbcdaddacaaddacbccbebbcbadaadcebacddbddeccecbdacbdbdceeedcabccabeaadabcdeacbcbaebeadaecabdbeceedbadbdcbabacdcbadcbaadaaaadabbdbcaadbadbcecababdbccebebedbedddcdddacdaeeebdeaabdbaaaeeebcadececbedeccdecebceedddbbdbeeecbbbcbaddeecaecebabecacdeaaaedbaedbdbccaeeabdccdeeacaeeedadddbbbbebbaaaccdbcebebacaceeeddbdbaceedeeceeacadbdecbddaccaeeabbabaecbbdcbcdccacdeecdbaecbbaeabedadaeccbbdbededaddceaeedabacaddcebbadcbeaecaeebacaebcbbaeaebcabcebeddcdadcaecdcbeeacedbdcecebcddecdaddaacedcdcaddddaeacebeceaeedcaaedcbdddacbbeabdebaecedcbecbbacabcedaedcacbeeaadbceedcddddcddbbeedbcbcbcbdbadaeaabacdbbebdccabcdaecaddacabacdbdaabdccedabbadcdcecdcdddcadcdedacaecddeabdadcdddcbbcbdebacdeaabeadbbedaeadecbcdecdccbcdebbbeecbdbbcaddbcaddabcedebcdddacabddeecddddebcdecaabedcddabddebdcceaacdbbdabebbbebbbecdcbbeaccecdbdecebaccbaecbcceddcbccbacdceacdcaecbdcecaaabceceecabccdbaccebeecaaeaaaebbedeecabdbbddadbbccdeaaecdededcdaaedecbdacbbcbaaadacdebcbbaddadcbcabccdaaaddaabaebadcdeceeceddeeebdcacabccddcaeaadeaaaabaeddedeeedceeeeaeebabedeeedbbabebddaacdaeebceebbddbedbcacddbeadedaecddcccdacdcbcaacaadccedebdbbccaeedddbbebaaceaecedeeeaddeecaeadbccaedabcbeddaaadbddaaeaaeaaeabbaceadabbaadaaebcacbcddadcdaebbcceeeaaceddeaccbbbabcbaaeedeaeccaaededaaddbadabcdebadaaabaebeaecbccaaeaccebdeccbaddeebbdebaabdababdacabdbaddddccdaabaceceadcdceceecabccecbdecbacacbaccbbcadaaccbbcbbbeaadcaeadebcaaedbebbbdeabcccdcbdccaaeddbdbdccdbdbcccddbaaeeaceecdecbbdabbcadbbcbbcaebedaecbbddbabeedbabdaddeaecdcdebeabeaedbcceaedbbeacadbbecddacaedbccbcbbdadeaeedabdcedeeabdeadcdebbbeabcedcddccbceecbcedaaeaaeedcecdbbdcadabecdbcdccedcbddcecdbdbacceeccbceeacbbaacbeebeaadababdaabbadcbaceadeedcdcaabbcdacacbadeecbddcbcbaedcebaccbbeeebabbebeaadccbbbcacdcdcaedbacacaebddcbabbecbaacacbbaadcabdabacbaebbaddadeeaacddddedbbcccbaabedbaadcaeabdbaaddebdabdddbcacdaceeabbebaababebbeaadbcccbcecccceecabbececccebbaecbabdddaabdcecabdaaedaecbcdbedcaacbcaadbbaedcebcbcdebeccbbceeccdccabccdbbebbeeecdeddeeeedecdadbbaaebbbeccbcaabedcbcdbaddbceeebdbabebabacddaabbddcedadaacadebcbeedcadccdcacdaeedbcdbcbbbcccacceedabbdedbaecbeebcccaaceadeebbcbebaaabaceedbadcebddecebaaacdcebcdbbeedbddbdedbbdcaebdccaeaaaddecdabbcccecebbbecbbbaccbeaaedbaaddabecdccabcbedaabbeddbeadbcecccadeaaeeebdccadedbedacbeeadadacbaaadaaccacaddbaeedeaeeeadedeaacbceecddebdbeddedccdccccadbddcaddacbabdcbdcbeabcbddcbdbddaaeebabacbabcbccebbdbacceaadbdbbacdadddccdbededdeabaeccdbbebbdabcbccbcbbbeeeebceabbbdbdcaebdedaeeccedeeacdddedcdebccceddbebcbbeeaecdeedaeaaebadeabdabeccbcdbdacbcceadaaadeaaaebaecbacebacaebbaddaeacddbecaadeabacacbbccebbdacdebadeeacedddcaaebabacccabcdbcdadbbdcdccbcaaeabbeeddbdbaaeacddebcdbacaeaaabdaccbbeaaaedbeceeaceaccddeabdadbdabcddbdacadabccddccdecabcabdebddeddeababdecccddbadeadecbaacbadeebcecbdccadaebadcbcbdcbbaddcaaebdbbecccaedbaeacccebbadabdbaabaddbbeeaabaceccbebeeacaecccbdbebeaeaacdadcadedaedabddeeedcbbebbdddceeaabdabeacdecabeaccdecceecdddcceccbcaceaadbbacecadaeeebcacabbceacecacddbbbdadbccbccdcdacccecdeaddaeebbeaedeceacaadceaedcccdeaadcacacdcbdabccdbabecdcbdbecbdacbbaebdeeeeabcdcacdabccebdaeebbdcbbedbeadbbeedccbdecabaecdcebdcebbdacbececbacdabacbadcedbeecbdccddeeabcdeadbbaebaadccacdbeccddaebabbdaaeacddabccebccecaebabdabadabdcbeaaedbbecbbaccabdacadedbdccaceeeeeaebbcdcccddddceeaddedcdeccbddadcbaaaceeaebceaecaaadbebecdddcaccdcadcecdceeebbecdeeaddcebcaabbaaebebadcecebbdccbaccdadecaccebbbbadcceeeaecbecbdaaeaecdeecdcbedbacecbebbadeaadeccdbdcbeecddaccababbabadcaecdaeaaaecaeeabbbcabbaeaecdbccdbbababbcdbccbcacdaeccdeadbaecbaccbdaaaaecbccedeaacccedcaebebeacbebaadbcddeebdbcacadbbeaeaedccaedcaacebeadeecbbcdabeebdbdaceaebaaecdbbeeededadeabcdecadaceedbeddecaddaaeccabecebdebbceeaceebbaeaceddbecdbcaadbaaacdeabaccdccaebcdcbbdcacabaebedaacabcdabbcaddbbcacddcabbbcbbbbdbbbbdbcaecadbdaccadccbadebdadaeeaeedecbdbdcecececcccedebecebaaedaabebecaceedeadbeadcdcddddeabcbcaddaeccabdacaceebbebcbcbbbeedaceadbaaacecbadbadeebabeaeadacbabcebeedcedbecbcbcbdcaaebeecdddcdacddcbcaccddccbeeacecddbedbccacbbdecdaeaedaeeaddecceecaaeecbaaacabeedeaaeadecbeecadbbbdbbbaecaeadccededadecbaebeeebbbbdaaaaddbdddadebbceacbaaeecdacebeacbdadeaeadbcbcaeceebededacbbdcdbbadceeedbbbdaeadecebaceecbccdbadaabbddeddbaddbeabeeddbcbaacbbcabbecadabeaaebdcabcddadcbcadbaddbcadbeccecddcbeeaeebdddeddcdddbbabdeeeaadadbbecedceaadbadedddeececddbaeddbebdaeccdacaedbabbbbedaabbcacabdabaeeccdacccebaccadbbccabdbeebadbacacacbbbeedcdceebdbbdecdbbcbadbeacccdbaeeebbadacdacdcaeeeebeaccebbbbebccdeaadcdbeaaacdacbdbbcdbedeacccdeaecdddabeceabbbebebbacdccababbeccebdbaceabbaacdecebabddbecadececdcaeacbcabbccecccbaaeecaececebbebaeadbbadbdbcbddecbdabcabcbcaebbccaebddcabeacbbcbebdebeadceeabadcdbbbddebbbdbedaeedbcdacadbaccaecccbccbedadaccacadccebedeeadeeebebddbadbdeeabeacacadbbdcaddecadbdabaebbaddeadbcabcbcadaaebaadaeecebddcbcbbcadabbdabdebccabebedcebeeebccbcbcbedecccdebdabadeabbcacaaaaadcadedacbbaacbbdcdeddedcddabbbaeebcabdedaacbadcecacdcaaeeebadcebbdedddddbdeaacccccaaeabbdccbbdddbadaaababdceeaabaaeadeadaabcccbabdbedeaadaddddeabcaebbaceadacdaccedaccbacbacddeadcdbeeebcaceabaadaecaebbadecaddddcdedecacdcabcbcccbabcbbceccaceabcdeedeceabcebdbcdaacecbeeeabadeccbadedbdedbddbeeaacdabaabbbbcebecdbcbeccdeadabbaaaddcdedeccedcccbeeeadecceebeaaaceaceebcbeaeedcceddbbebdbbadeeabeabcacaadabbacccacbbbcbacecebbcaeadcaaceddadbeceddadceaabbbedaaacceccdaddcedccdbddedaededadebdbabbbddadecbdcdeecacddaabbbaeedeaeabaddbdeacbabadbadeaecccbcccbecacaabbaebdcbedcbbcdebcbcbbdadedbbbcdaaedaadcdddbabcdbccadedbbddaeeacbbacacecceaaeedbabcaeedbceaaabdebaeeccbadcceeecbbdaadedbbabaaccbedeabecbacacddceecebcbabbdedacdeaabbaeebdbabcabdcddbeebcdbcdeaaaaabdacebeabdcbccdebbdbcaebaeaddadddadeabaddcbacaecdddaddcdbaaddeadebaebddcdbceaaaceaecbdeaecdcdbbdabecadbabcbbaabaddbdbaaaebcbdccabbdaddacbbcacacaeeebdddbdeccccbeabdbbecadebceabacdeecdadeaaaeeebeceebbebaacbadacaeedadeaadbaededcabaecbdebecbeedccadcddcaccebccaaceedcacdccbdccccdededcceaebecbbcaecbeedcacccdebbbbededaccbadebaedceceecddccebacbedabbdeabebddaedbbdcaedcbbcbadbcbecbeddeeeceaebdebeddbbcccedcbdbedcebecaebdabbecabdbacdacddceecbbeebeabcabaabadeeeedecbcbbbeeaeeddcbecdbcbeadbdbcabbbebcaeecebaeecdbeaeaddbdaaceabaedbeaeaecaaadbcccbdbdeccacebdceaaedaaeadbaaecebabaebebaaddccccbabeeceeaabebdccbaddecbccbededaceddcedcbccabcbcdaabbcdcadbacedddddcdbdebccbeaddaecdbedcaacabadedaeebdacecbedcdddcedcdbeddbadcabbeddbbeceeadbaedeeadebecbbdaddddbabeccbeddbedddeccdedbdccedbddabaaccccccddbebebdbebaadbedaddcecaaccddeebeaaedbdbbcdbecaeaddcbebbcbadaaeaaedaebceccaadeabaeebdecccadaecedbbeecbcdcdeadecbbdadbbeccaecacbdeedcbbecbccededeaeaedcebddedebcbadeceebebdeaddaeceecbbbccddceedabcebddbeccdeccbdceeaddbecbbcebeedaeedceeeecdacbeaeeaeeaaecdbeadaeebebdddaddeabddaedbdcddcdbeaddeceeebbaebaeadcbbbddcddbcddbdccbbadabbaeddddbbeaaaeedbadadabacddcdbadadceecaaccedaddabddcacebcebcebdecebbbbcedeabddbbeebdedccabeaabeeaaddddbdeecbabececcabdddedeadbcacecdeadadebcacebbbbbbeddcaaabbbaaeaeebabbdcaaccbcecdaaedecdbaacbbcddbacdbcbbabdabcbdeaabeedabbeadeddebaabeadbecbbaecbacdabecbdecbadddaccecebaaecbebabaeeaddceeabceeacddbabecddaaabcdceceebcabaacbeabdaecdabddaceebddbeaaeaacecedaabcbaeeacebbbbacbcaaeedecbdceaadabeeecbdadcebedeaeebebdaeaeebcdaabeacebbaeaabbeaeeeecdcbbcabeeedeedddeecddeadecbbcebdadecbdbdbcbeebabacbdbacdbcccbcbcaadbadecbbaaebcaaddbddcddeceecbdbccaaddeaacadedebaceacdadbdecbeeabadabeedaabcdcacdaaecbaeacbaecceeacaeecedbcdaccceebbcdabcaadeaaacecacaadbeecedcdbbbdaaaedebedbcedebcdbccdeeeebbaccabaeedcbcabdceccadcdeebebcabaaabbbebbeadbdacccececebaeeadecacdbacbeebaacaaccddecceadaaacebbabbddcdabcacdceaccadaccbcabbaddaaeccaabcdcedaabadadacbdacdaacbeecadeccccdcabcebbebebacaccbeaabbbcbabdcdbdacbedcdbbcdadcbaaabdbbdcdaeaebeeaacceabdabaadaacecaabcaabccaaebdcadceaacdabdecabbbdbdbaccdcdabaccabdbebbbcbcdcccadaaabcbbdcddbecdbddedaedebabbbddbcdacddbabeecbbdebbecdeeeaabebbeeecdceaeadcebcececddaeeeeacdabbecebacdaaeebdaedeecedcdcaacedcaebddbddcdedeabcebdeaccedeccacaebbccaededddbeceebeccbbbbadcbebadebdebbeeceebbddbdccabaeadeacbbabadebeaaaccbdaebdabcbddedcdbdedebdcedabadadcbeebdbccceeacdceebeaaadeaeedeeceddabdeaeeeadbacbdbcedbeacececbcbbdbceebeeecacabbcceaccbcbeccceacebdcdcabbadceeaccbdeaadadaecdaecaceeaacbadcdbcdaeecdcdaabbbbdbbbbddaacabbbedbdebececdbbdaaabdddcdacebabbdeebbcabebdbedbdaeadadecadeaeeadbaebbdadbeacbdcdebaebeecaaeceabcabdcbdebabaaacdcdbeabacacdebcbddbbdacacbaaecbdedeccedacaadeeeaaecaaeabbceccbbcdbbabbecbaebaaabcbedeeeadceeeeececdcecaaeeeddecdbdbceedccacadaeeecdcbbddaeeedbdecedaebedbacceabeeaaeabdbeabbcdaaaccadcbddadbbacbedbdaebebdaeccedebcaedbedcdebecbceaeabedaeaeaeaccbcebabaceeacdacddbcbaeddcbcaccacccccbcccebebababeaaccebaedbdcebbdadbdedeabedebdcabbbaedbcbadcadcadbcbdbbdedaedadccbcaeeadcdabadaedecebaccaebbacbbbbcabcaeeaaaaacbcddbcbbbccbaabeccebbadbaabdabcbeebcceddcacdbeeeeceeaeaeecbbededeccadccdeceabacadddadbcdbcbbcdcdbbecbedabcdaebaeabaecabadbeccbddaadabcdcedaacecddbedbbeacacebeaccdceacedaaccceecebdceaecbbaabbccaabecdeadabbcbeaddcbdbdccbebcddcaeecdacacceceadbdcbacbccccbbdabddbeabbabceceeedaceecabaeededaeaaabbaeaacaecaaadbabddeeceeabbcaedcbdebdeebceeebbdeedcaebedebbbdeecdcebacaceaacdeabdabaebeceeeeccabbcdedcacdcabdcbdddceceeaadbbecaacccbbddabdeadbaecebedcbdbbaaebaeacaadeaaaeaceecbeadeeebceedeacbabcebaeebecdbcbedcecaedcaccacaababdedeccedeceabdabcbdbeccbdbbebcbaaaccbcbcacaccdbbcbaacdacddedabbddeeabaacdaabddaacceebcdaedebebeddaabbbeddccbbaecadcaaadecbacaebcabeecdaaabbceaabbbdcebcecbdeadbbdaebceadbdbdedebbaedebbdddaeabcececcbaeedaacbdeabbaabdbdaebebdbadedaeadebcdeeddedcccbcbeaabeeecedcdcedbceeddaacbbbebeeeeacbddccdeeddecacbbcceddaadeedacceababdabbcccecdddcbdaabdabcdececadbbccdbbbbabddbbcdedcabdcbedcedcaeedebbaecaecbadbdbeeeaedbdaacdeedcbddddeaaebceaebbedaedceeaedddabcbabcebbaacdecdbacdedaebdcebbedadcbddccabbeccaabaadbdbcbabeccccaaaceaaaadbccdeaedaaddcdceaaacadddedbedbacaacdeceadbeacacbacbdbcbeabcedebebbadbebccdacadcbccdacbacbbeeecaaecdcbcbedcedbebcbeccdadeabcdccdcaaebebbabaeabbbedadbabdeadbdcebcaeeddadaabeaacbedcbdbbdaaeaeaecdbccbbbaececbdcadaabdadcddeeebdebabaabadedbccedaeeeaabdedaecbdadacebaedbddbdaaaadcbcbedcbdabeaeeedecbbaeabceaadaaaaecbadbcaacebdbebdbabbacbceaabddcaebecbabdddadecccaaebcaccaebaeabdedcccdbedeedaccadaabcbaeeedacedaeebbdbdacdebecabddebbbeebdbbebdbdeecdadacdcbdeacdcadaebacaecaaaaadddadadcbcacbbddcadbaebaaabdcebebecbbebaaaebccedaabdcddbcecceebcbceeacbbadbdbddecdacadbbbddaedeebbcccbdddedbbbadceecaddebcceaebbcaadeecebeaaabbcaeaedbaeccadebbbaacdacedeadcadbcabddcdbaccaeddaaabbcbbeeeedbdeadeeeebebabdbbbaedbdccbebccaebbaccacebccecbededcbddcdddacbdbbbadebebebcbcbbbeddcbcabcaebbeadeeabcdacaaebbcccbbedaeeeaeadbabaabbaabbdcdeaaeeacbadecccaeeaaacbdbccacaaaabdcdebddedcabcdbbdcdeadcecedaeeaabdedadaacccaaeabbcccdedcacccbbccdcdbdabedbbeeddaeaacbecbebebdbabebacaeadbeaddbcdddaaccaceaaabdaaabdacaacacbbdbeddbeaddddaecddeeeecbcaaaeeebeabdaabebaeabbccebaddacabdcaebccbadabaebbaceeeeabdebddccecdeaddebaabecdbedbeeeeccdbcedadaabddcdbbcbbabeaabaaccaacaaaeaeddcbdceddcaabaceacebebceabdcedbdedccbabcdbeabcadcebccadccbbbccaaeccdeeebbeecbaaacbedcbbeecabbdcbdaabebcbeaacbdcdceaeccbbdebecdbdebcaaeeadccceebcccdddbbedddbebbabacbcabdccbbaebaecdeebecebeaabeeceadbcbbdacecadeaabacdeabeacbaeecdcdeaaacdaccebceccabbacadccaaaaedcaebbdadbebebdaacacaddebdcaedeedabecdaeeebecdacbabdcdadedaccaebdeabddcdbedebcbedcbbdabbdabaacaaaeaaacecceaeddabdbabbbbdaccbdabebcbececaadecaacadaadeecbaaabdaecdcbaebcbdcbcaebdeacdbdddedebaaadaeaacaccbbccbbeebeebedcdacdbbeadbcddaecdeeaadddaccaadbebdaebbeabecdaaaeecdcdccbeebbddceeabbabcaddcedaacdbceeadbeadbdadddecaebaccdddecdcaaabdcabaeeabecebcdbcbbbacccecaadeecdcedbddbaacedbededabeaacdaacbabddbaddbceedcecbddedaaceabbaabdbacedecedaedbcbbabddecbacdeecaceedbcaabdebcbdecbccecadadbaedbadaebeaacdddbedddeadbaaedaadcdbaabbabaabacabbebdbcedccccebbaddaebdaccbbabddeaccdebdbdedbadcbcdbacdbbdbceddbedcabdbddabedcddabaeebbbcabcdcbeecdeabbadbdddbecbaadacddacbaeaddeddebacbdebcdbeedecebebacadcdacaacdaaddccccabcbaeccdcecdeabcacaacddeebdacaeddcabcebecedcbedbbadeaabebaecedeacebeaeedbcaaebcaddeeaedcbbeebbcbbadddbbdbceaceeeddbbacdccccbbbdbbbaacbbbeaecedcdcaedadddaccaceedeceebcecaaecaabcbbecabebabbebebdcbccabaaddcceaabaaddabaeedebddedeceddbdabecadcaedcaeeecbceeadedaebaeaebdcdcdbadeabbedcccccabcbbcdcaeaebaecdccbeebdecacbdadbdecebcacbdabdeebdbaedecacedbecddbebcdeaeaeabcbeacaadddcdebbaceadccabcccaecacdcadecaceeceacdcbbeccbdacaadeceececcbebacbbcccbbbedcbddaedebbdeaaabbedadecbebabdbecebebddeccedabadeacbedcbbecaebbecdccdceceaebebeccecedbadeebcecaadbdcdddeaddabebaedadecaedeebeacdbdbcedbddacccacaedbdbabbdeaadbebcddccedacccbdbcaabdaeddeebeedaaacadeeeedacbcceaacdddbcaaddcebcebeaaadeacedccbcbeeaeeebbbaeedaebedadcdddcbbabdebbcccadcdbccedbeeedadbbedddbcbbdeadbdcbbbbdbdaaeebadbcaebdbabeedaeebbcedaaedbdedcbccabcadebccabaccbdadeebebeedeadebecbcabccddacdececccebbaacbbbebeaddaeababdeaddbabeddeccdcccbebabadaeaabbcccaeaeadbdeaeedbabeeeeecdacbdbedeeaadabdcbdbcbaabedecaadceacddaecdbabbdbbcbbcdceaacabeacceecdacceceaadbeeeadacedcbdadcceeeabacaabeaaaedbdbbebeebcaadcbbbebcdbedbbabedcdbccabaeaeaebdbacaadeeaebaabedcbaeeadcababdabbdaacdadbdcebdecedaebabeeaebcaaaadbdbedbbeaaedbdbabdceebdbaddacdebddeabebddcdadbeebeebeececaeecabbebcecbdceecacceadbdedaacdedeaebacdbeeacdeccaceaabdbdbedcaedbacbcabbbaacacdecacbeecdcdaacaddbcdebcccbbaacaacceaabaeadbdbbcccacdaaacbeebccabcccaccadcadaedbbeebeaeceaeaddeecdaecacdeaadccbdabcacededbaebdcbacbbcaabdccacaadadcadcecbaeedccbccdddacbabbbdecdceeeabceddddbadceebbdaaccdbacecbeccddcebebaeebeaeeaddecdaddceceaddcddebdbcaabeaaeeeebedcacabedbeacadcaeeacebddadccacacbbbbcbeeaddcaadbeaddbbaaedeaaaddddadcccceabbaecabaaadcbbecacacaccceceeeceebacdbbeedcadbceaeadaecacaeeeccaadbbcadaeddcbceceecaedaebadcbccbceabbddabcacaceddddaaceddabeddbcdacbedabbbddcebcedbdaecbeedcbaaaebbbcceebcdbcdbabbbceadceaebacaceddbabdabebacecaeebcaeeeadcadaedededdbbdabbaabdebbeaedeaeaaababcacdcdcedceebbebaddccdccbeabeeddceaacbababaaecaeebaeaddbeedddedebecdabcbecceebdacedbdedddeaeceebcbdadcbcadabdccdaabeacdccabddeaeccddecccebeacabaadbdbdaccacbddadcccbabdeaeabeeeddbcbadddedadbbeabedcaabcadbabdaddbbdacbdddbeadbbbbbdbaebacabdcaeeeeeecaecdbbadeebededbedcbcdedacdeaaaceebbcddcecccaeaaacdaabcabbeaaeccdddbeaeccbabdbacdbdcebbbcadecdbeedbeacbcccaceeddcbdecccebeeebccebcceccacaeeddddabeacbaabdccabcbdaddaabdcbebcbececeaebbdcebdeecdbddcecbcaeaeacdeceebccadaacbcbdacabbcdddbcbdbceccebceaddcecbdcaebccddceddeeadeedbadbbecedaebaeddabdaaceaaedbaaacbddeedaedeeecaeededdcdcacdbdbdebcdadddecbddedccecabbbdddadeddbdeecdbcbddccbaedacccdbebddbbceaceedbadaeedacebacccaacdbdeaabebacedabeeeaaaccdcbbcbdededaeaaaaaeeeaadaddbedbbccbedbaaeabdadedbcadddddcbbbcbeabbaebdbadddececeeececddacabcbbdcdbbebdccdaacbbebeeadcebbbdaaacebbccbbeaeabeeacbaaadbacadadcbdbbedbdddbdeddedbccbdaabeebaebebcbeecbebdddbcbcddaabbdecdddedcdbaaeaaaeacbcdaddaadbacccbdbebdeeaecaccadddaccebeabaddcdeecdebcbaebcbeeeededbbbcbbcbdaeeeaebccaabbdedcdbcbbddadcabdededbdebdccecbdbabbddcebabaaedaaedddaecbbecccdeacabdaaedaaaedecaecccedbddbbeadaceddcbeaacdacbceebccaaddaabaebaeeaccededadbddbbaeeccabbcecebadadcedaeaabcecacecadeddeaeeeacabeddadeecadeaaddecdedcbebacdbadcabdeedaeccacbbdedcdacebadcacbeacaaceaabbaddbcdecebacbcdbbdbaeabadadecdbceeedbbdadcdebeebcaeebabbcbcaecceadabaedbbacacbabaebbaeaeecadddbecbcadbececbdeecaaabddbdaabeaeaaabdaddbecaddaadcddabcbadcbdebcebdadcceeeadeedacedabcecaceadbadbebaccadbbbdaaaadaebedbdceaeebceddacbaedacdbdecedcacdadbdaabdabaabeeadcbaececcdeeccbdcacaedcdcebbeadddaecbbadddebbeabebbdbbacedceacceeeaaedbadaccabbbacabcdbabaaaebdcddedecddccabaceacdaaeaacbeaaabddaeaedadcaeeddabedeaedddcdddedbeddcaecbdccdbdddabadbeddaebbcccabdbacddbceedcbceaddaddbcecaebaceceedbdeaaeeedacecaacedbbdddeaebacacbcecaacaeabcedddbdcdbacaabedaedaebbcddacadcccddcbaaeecddcaadbcdbdadbecbccdcaacbabbadcaaaedacebdcabbdeceeddeaccbbdbadbaadcebcaceeebdeccbaecabdcddaaadcebaebcedcccdbcaceebabeadccdbdcbeeebeaeecdcbbddebeaebeddbeacdcebeecddceccbdeabcdeecadbbddcadaebabdcbbeccdacddbdddeccdbdaacdddadcdeabedcacbddaddcaebadceabaeabcebcebaddbeddecacbbaeccdcddeceecacbeacdebcccdcdcbcabdedadeeebdcdceddccbddeebedaeaeacdbdeabdbbcadddeeccbcbdcaccbddddababcaebcddceaddeccbbeacaadcbbbddebeebbddbaecdadcaebdadbeadddaaaaaeadeecebeecdbcaedbacedbcdbbcbaedbaddcdbbddabbdddcedcccaaadcbeedebecbddaaaccbcecaacdecbbcdacadddcaaeaaeccecbeeabeedeeadcedaebbbceecdbdbcabadabcbdbcdddcceddcaddacacdcabdcbdcdbceddcdaedbcacbebcacacddeaedebccbceabddbddeceabeecdeaaeaeeaadeaabedadbcaeccaaaabaacebebaadcceacbeedcacbaabbeceadadbecebebceaedcabeccbadcbdecbdaaceccbadcabebdeecedebaaabdceecddadacbebecaacbbabdeedebaedbcadbbdaddceeddcbeeabdcadbeeebcbeaeaaadcecdbcdcaabcccceeeaaeecdbbaeacddbbaeecaadadeaebddeecaaecedbcadcdeeacecdcecabedaabdecddbeedbbeaaadabdedceaadbcbbebecbcdeaebecedecebdcebecaccdacbceeaebedebedebeeaddadbbeaddaacedbcbbaecddaddaeaaeedceebceccedaaddcdabbbcbedcbebebabcdadeadaaecbeabbcccccccebcadeacedadbdeddcddddbccdabbcdabaeaadbbeceadcaaccacdbceabecadbbceabbdbadbbaddddecdceabcbcdaeacbeebecaeacecdeccbadabcedeadaeceaabcdebbdaceddeacddacdadaccbaaecdeaadadbcddacdbbeaeadccdabaeadbdccaaceccbcbbeececddcdbaabedeeadadceccdcaeeaaeaaddcdebdeabceedecdecdcacecaabccecbdaaddadeebbbbacceabdbbdebcacccdecdbcabdcbbeddaeeabbbdebbccddbadebbbddccecabdaddaabdacadddcbbcdbcacaeebecaeddaddeabadbeccbecbcdabbaadaaceeaacebcbdebaeeedabebcebdedeaaabebdeeaddedaeeddaebdbdaceaedbabdaacbbcbedabaaedbebcecccbababcecebecaadbdbebadbbbeeebecaaacdadcadcbdaecbbbbcebdcbdbbcadbaabeaebabaecccdccebccdbcacabbabdaacdaeaecdbccbedddecaebbebcdaacadcaadcbceaabebbeacededecdcbcddaecbcdbbecdabbdadbbacbbcddebccccdaabaebbddbcdaacaedbebeddecddcacdaadcbaddeccbeabbbbabaadaaecddaddbcaeacbcebddcedeccddbccdcddddadadebadbcddadbccdaeccbceebeccecbdabbbedededecddaabbaebcbdcacbbccacebdcdbdecabccccaecebaeaacaeadcdcecdaaaeebaadcbbebaaebddabbcceccabbeccbecdabadcaacaebaedcdddeeeeecabdbdddcdeeaeeaaecaadecabbabeecbedaadaedbbedcedaabeccdddaccaeddebccccaddceabecaaabaabebabeddbcebcaedabbbeaebececaddccacdceaaececebcbdbecaceeeaddaacedcbcecabbedcaeadeceedbbbaaeeadddaaabecdadddeadadabadecccaaeeeeabddeaaadcbbdebbacbdbdedacbdbdeecbeeaeaacabeddeedabbcabaebdddaccadcbaebccddaabecbbaceaaabdcecdbbdcddcbbdcbcabeaadbeecbcbbaadbabedbcebedaeaacbcbedaebedceabadcbaaaaddacdbebdbeccddbcaabaaceeabdbeeaceacaacddcaecdadcaeaecdebbadbbecceeedbdbeaabedebbaccddcbddceedcbabdbecdeedaaeecbcacdbbebeedbbebabddadeabebdecdcdacdacecbeeeeedcdadeabecccaecdcbbdbddebbbdbbeacbcaebeabcdddcabcbadbacdadbaebdcccacdabeeaeccaeeceedabdbacaceccaacbcdcacddcccbaebdcdadcecedbeeabcaebddebcdaddacabeeeaceeeaeebcbadcebcbceddcadebbdbbcbceedcacdaceacdebcdbaaaeeaacdcaeccabbbeacbbcbdbdccabaedacdceadcebecbbaeaddcedaadeacabacebcbebbcaaacbecebacacddbabcdbdebbecdbecbbcaeeabbdaeadddeddbeaebbeddaddeaedbdeeccaedebbbddaceacbabecdebbeacbaaccedecbceedcabeccaacedbddaedcbddbacddcdabacbcddaeabbeaeaabaabdbeeaddadbccadabaeccedadacbceebeadaaddccbadaeeeddbbdcddeadcbeaccdbbcecacecbbcabdddceeddaaedbcdbbaddadbdcdcdcecadbbbedecbecebaedcdcababaccbaadcbbcabecbcabbaccaeddebeeceddbaebeabadcdecedbcdabbcbeabceadedebeecbadddcdbbccbdbaecdbadabcbebaeedadcaedacdbdcdcbcaaabbbdececeddbadaeabdceccbddadaacbeacaddbedececaccddccaeddebccdacacacdbaceaaadacdeaaabbdaabddeacdebeeceeddcbddddbdddbdcecabddbdebcddeeedaaacbecaeeaddcdbcbcecbdeeeaccbaeeddcbaaabdbbebdaebbceacbdbbadebcdeaccacecbbeacbcceeaaaeeaaaacddadddbdeabcececcdbcbedbaaaadaabedbdeeccbbedbccaaadbaaaceabaacceacddbbecdeaedebdcecadccebddeaaecbebdcdeeadabcaedacccdeeacaecbbaabdbbbcbbbcacaeeddaadcbebebaaeaaedacbceeacaceeeaeeabbadcdceeddedbecaeeabecbecdddedebebacbdedaceacadcabdcaeeaccacaeebccdadddbcecddbeeeceeaebcdaaddedabddcbbbdaccaecdddacebbddcbddcbadaeeeaeedddaebdbbbeeaeaabcbbdaceacbbdeceabddebadaebacbccbbbedaeeebcbdecebcdbddcecddeccdccadecedbaedaccaeaebaedebdedabceaddccdaeeeaacbeeccddcddcbcebccbbdbcbdecbddacccbadedcddbeebdebeeacdeaccaadaaeaccebebdbeececbabdccedeccdadcbcaeeabbddedcddcbddadcbebbcecdadeedbecbacaddeaaebbabceabaeaededaeadcebeeadcabcbccbaecbeedeaebaaeccaadbdadeccdbbbbababdebcaadbbecacacddcacecddeaecaedabecdbaedcddcbbdbdbcaaddabeacdddebbcdcbddaaedcbccebbbecabbbabdecbacdabcaadeacacacddedceecbbebceeeeeeedcbccdcadbaeebdbcaaaaedebecebedbdccceddacbceadedcceeabbcdebadbdedccccbddabdbabcdecbaeddaecbabebeaedaecaacddcebcaaedbeadedaeacdececcdcacdecddbeaaccddbdcebddeccdebedbcddaaaabebdaecccceaeaabecccddeedeaadbeaeaddbcebebdadabccbdaeddcabadaadecbdcdbbabdbbbdadabececccddebbbddbdccdddbecaaddeaacbbbeebddadebedbaebdabcdbaccbeabdaecddcbaddeedceecbeeeababbbaadddcdbecedabaebcbdebdabadccebdaccedbbaaaaddebaccaaaaaeadccbccbcadaadcdbddcdceddabeecdeebacecadebbeeabaacabacebcbedcbaddebbbaadedcdabcbdaadbeeebedbeadedbbdaebabaeececcdccdeabededbaeaabccbeaeaeacbeecccecbeacebadbbbbadadbbbbeeaaeadaeccacebebaacebadeaebebcebeeeeceececcdaceedcdabcaacacddeececcbbbedaaeaeabcebdbebeadedbbdebadacdabbeaaeabdccdcccedccccddccbedeaedcbbcaeceaaadeeaecceacceceedadcdcbdcaeaebebddbbbcccaaabbcadccedaebbccaadecbabeecdabbdecbccbedcceaebcadcbacbaabbeabbebacdabaabbbcdeebebdceceedbdccbeaaddcbccecdbadebbacdbbbdbdeeaecabcabecedceddeaeddccbbaacdceaeccaebdddeccdeedabaedbccdccdddddbaedcbcebabdaaecbccabcaaabadaabceabdcadcbdddbddbccedecddbdcdcdccdbbbccdbacaacaadeedccccccccccdaabdbebeddacaadebeecdeedcddcadcdeeddceadcecdbecdbdbddbaccbecaebaaacddbbcdebdbcbbbcaebdddcbbcbcdbadccaddadeebcaeecbcadebabceeeaaeeecebcaecbaecbeabbccaeaddedacbadcaadedabcbaaddaaebdedcddccdabdbcecebbaabcbabdbdecebedcddceaadceebeabcdaecadbdcbeabbbbaeabcbcacbaabeeeaeedbbeedebbebdebddbdccdcdededbcbddbbbececaddcdcdbedbdbbdeeddbccadbdeeeacbaacedddecccabbacacaeadcdccdcebbeadcbdaaeeaadadacdeabbbacccaecbcabcacaecdcdcaabddeaedddeebdcecabaedcebacedcbdbbebdbacbdddccccbbebbcdcbbacddddcdebabdbaeeaabcceeebeececceedbbbcaebdeddebcbcbedbddcbadedaadacedcacbaaaccdcbacddaabcedaeadeacebdebbebcdbabdddcccecbccddedcbebadbbebbdbeebeebbabadcbaabaebadcbbbcdcdbcddaddebecdbbadbbacbededcbedddcbebddcdebaddcddabedaeccddaadbdcccddcaeedaeebbccbeceecdaabbaebececebaebdcedaeedadbbddcacceeeccabeebecdddeebdcabeadddbaceaacdcababeaddebdcdbcdbbcceaaedeeedcdceacbbcbcadcedbabcbcdcacedccbedecbdeaedbacdaabdaecddddbbbaddcbebcabacdbddeccbbaebcadddceccdbcebbcececdcdbbaebccecceaaeaebeacdbcabebcacabbcadbecbcbcbcdbeacdeaadccbbaedecaaebdcbecedaaebacccbeeebdabeceadbcbcdbecdbaccaacedcbecebddeabccbcaddcecddeececbbbdedeabbcceedbeceeeabeddcbdcebaaaaaaddbeabcccdceaacbbebaeadbaecceebcdadedcccdbdcbebbabeeeecaaebacddaeadcdcbcbececcaabaeabdcaabdedececebccecdbbedccccaddabddbddadecbadbaecdaecbbbebadbbabecabbdebaecdbddebedacbddcadccbdceabdadbceabdcadbbcadeedbeaceddcebcecedcceaccdcadbbadbbbcebebeacbcbabadddddcdeaedaaaccbcdababdcddcdeacabaddedccbdaedaebaaebeaaecccbcccaebccdeeececbcccaebccaebdceeabbeadebeedccbbeebcdadbbeddedaeebedbacabdbdeeeeeaebaccddadebadcbbaeadadeebcaecebacabbabebdbbcbcbcbdbdecccecdaaacabbbaabecabbcdbbedabbdebaeaeeddbcaedcedacaedbcabbacbeebadeddceeeaddaebaddbacbcdcdaedecdbaccebeabcaeedcaacadeaacedadcccceddabbbaeaedaabdddabaaaacbeddedeaebbbadccccbcaebeaedadddeacadbbdcaabaaeebaaedabacbcceeacbbcebbcedbdbbbecbcbaceadabecceaeebeeabaadcbcbceeaeedccccbaadabcbdeaecedbebbbadeadbdcdddcacbdadbbcbedaaacdbbabbcdbddcedddbccbddadcbdeecccaecdcbaececbbdbaabaabecebbbdaaadacdebadbdadcdabceedbdbaddbabbbbbacaeebbbccbbdeccacdcbcbecdddbcaaeebeaabbdaecbdecbeedadcecccbcacdadcbbcebaedcdcadebaaababaadbbaecadbdbdbdebedddedddadcedebeebaccedaacacbededacecbbbbcadecdaaabaddaddbcebbadbeadaaeebbccdbdcceecdadecbeeddeacccbcdeeabeaddbdcedbccbadaecdaecbadaeedadebeacccaceaadcacabdbbdcdaccddcdddbeedabeedcdcecbabdccdcaeeeedacebcdcacccadbdccccbbacbbcacdbccdccbbebceeeabccdbcaebcdccaeadcddabdabbceebaecaeedceedbbaaedbceceaccccdcbeabaaabdecaeeddeededaaacbbabccaaeebdbdbadbaddebebdeabcbbcbacdbdbdcedaeedceedeecbbbbaedcdecadbddcdcceacbbeeeacceeeeebeaccddebdbbecbacceeabddecccbeaceaeebeddebebedaddbbeeeaecdabcbecbdeecdddbaecccbdcaceaeedddcddbabceedddbbcdbeaaecaacedcaaebaabdeeeebbddbdebecacaadddebeedddeeecddadcbbecedbaabededbebceabceabadebcbeaaccccbebebbaaacaedaebcdeddeacbcadabdacbbecbccadebbeecccdedadadaedebabaaeacbcbdbbeaebddabccceeaaeacbceededdbddceeccbaedebadbeadbebeceeccbedaaecabdeeeabbccbceaccaadbbcddbcaaccadcadecccaccccbdddbeddeeacacdecdcdbccedabcaacceeeceaaacaaeababccbeccebaccedcecebadbeaaedecbebaaccccbbabbedbddaeedbeecebabbcdbdcbaddebeeaabbcbeabdbadeeebbcdbdeecacaaaddcedabadbbdccdadbccdbdecaaabdbbdbeabceebdbdeaabdbccaaebeabaabadedcbdbdecedbbeeaceccacdccebeccadacbeebbaabdabbcadacdcbbdccbdcdebccbbccdaebbbbabebcebbededdceeadbdadacbabeeecacdedeedddeabbecaaecbbdbacdaabacaabbdbeaceccabedceddbbeabadabebdbcbbbaceacecbedddabcbdddadecbbdadceeaaabbeacdebadaeadcebcdacecbbebcaacdcdcadcdadecdecebaeeacabccdceecadbbecaaabceeeebadaccedcddcccbabdeedabebbcbcdedabdbdcdcdeeaeccebdacabeccaadcabcbdcdbeabbeabcecaecdcbeedceaeedebbdedccbebcdcabeaacbecbcceccbebaacadeadcebdecbddcbbbbadbcbeeadbddaaeceecccddbadbbcbbdddacbbdcedebccaeacbadeebcdccbccddbcebccdcbcdaeebedabadebeaedbbaadeedbbcbdeccdcecdadbbdebaceaedecabadccdeacececaccaacaedeedaccdddcabaaebbdddebdbdaebeabceebcecddcbdbcdbebbaadbadaaacecedddabdcceedaabccabaabbcadaeaaddecbcaeacbdbaebcedbbbeaadedceecbbeadacbbcaaaacecdcccdadbdccecaadaaeaadddddbbcdbabddcdeeabddecdaecbccaeedebdcebcccceccbdbacdaeeeacdcbacbebceeebbaeecceddcdcebacdddbedbcababecaeceedbeadecbabbbdbbaeecdbededaceeaecdcedadddeadaebdddbbaaaadddbdbcbcecccdcaadcbbaabcbacdeadbbeabcbabeeccdebdcddacccbaaaedadabbbdebbbaadcabdebecabdcececedbaaaacbccecacdadcebaecebdbaaedbdddaacabbcbccacebbddacdcbeeadbcbedeeecebecccbaccbceececadddbebbcdbddeabdbadcbddbddbacbccaeccdaaabeceeaacbdccacaaeeadaddcadedbbeaaebbdbbdaddcbdaadcbbbcbddcdedaccdedaecdabceebeebbeeabdadbeadbdbedecedcbbaeeebdaaddceeacbecaedacaeddbcdcaabdaabdddeeacaccdcdbbcdbecacebaaaebaadddaacedebdcbeababaedeadecebbceaaebbebebaeadcecdebebebdebccabaccccbdccccebdcadcdbebbadbdeebbcacbcbabbcdcdbedbaebbcdbbeecccacecccbaaacbbeaacbeebeecddaeceddebcdbcdeecbadeaaadcbbedcadaeecbcdcdedccbbbecacccebdaadcebbdadccdebcadabebedeacbabebebdecabdaecdbedaeceaebaddecbdbbdcabdbecdaeebdcbbebebaebacaaecccdeacbaaceaeaeabdcabbadecacedabbddbbdbbedeadbeedcbccecaedaaccacbdcdeebdddaadeeddccdbdbcbaeccacbcecbbdbecbdcccceaddbaccedaaeabceccbdedddbaadbdaeadeddcddccaedbaabaceacaaacbbbddeeddeabbdeedbbeeccceaaeebddcbbabbcbaeeccdeeeecbbcadbededcedbbeedebdbbcccbabebaaebbdebdadccdaacccdbabcedaebebdcddebaeccaccaccccddcaacdaaeecccedcdabcebddeecbeababcccebdbedabeddaedcdbaddaddcbeeebcdcaebcaaaadaabdddbeaadacacedaeadaecbebceadcdbdbddaeaeaaddebecbdebbbabdaeeeddbecaedebeabcaecdccccacaeadecbedbaaebbeaeecddbbaddeddbbecbbdbdcdaecdbcbceababacacabbdebbdbcedadaebddadcadededbcdceadaecedbcbcebdbbbacaeedecdcedeabdaeaecadbcdccdbdaeccbacbeaedddbcbdbacbdadeeecbecebbcdcdeaecdaacaabeccbbddeedcdbecaaceacceabaeabcadeeeaaecaaebcdeddaaddeaebacacddbcdecbabecedaaaedbaddcbedcacdbdcadaecbadaabacbcacbecaddcbccbabbcaaebdeaaeddeceddbecccdbbbcecadebcdcabedeecedcedbaeadacbeebcebbbbaaabbdcbedbecdcdaabcddbaecaaeccbbcdeaecbaacaaedbdedbbdacecbabbdacecdbdbbadebaebaabeabddeadbbddeceadbdabebbcdeadacaddeceeababbbbeabdabbbbbdddaceeedaeecbabaacbcbcecabaceccaadedccabbaabececdbebaeaeccabcdbaeccbddecbdadedacabaeedbdbebcaccbccabedceabccedadeedeebcebaebcdaaaadaaecaeebeacddcdaecdabecedadadbdedcaeddaddceccccbacabbbdbcbdacaabcbaabcbcbecbacdebebaebdcedeebdddccbbdddebecbbacddadbdadbeedcdcdbdcbbbdddadabdbeabacddebcdbdecbbeedcbaddeadddacdbeeccbaceeebdaabebdadccaaacceaeccddccdebebbedcecdddbaadaadaadacaddecbedbbdbeabadbedcadbaececcebddaccdeddbadeedaeaceaacbeddabcccabdceeaccbabeaabbbcaecbbdbdadeabaceadaeaacebcaceecdedbcdaaacaecaeacedddabcabdaaccedddddabcccacebcbeaeddeacebaaeaabebebccecedcddedbabccceaaacabdeecedbdeecbddbcbcaaebbbcaceabbdcabdeeccbbeebaedbeddbbeabbdbcaddceaaccddbcddcedebdcbceeddebdabdccaddaaaedcceeedcadcceebaeddacbcaedbbbddeadaedbecaeddeabccaedabdacdabbbdcbbaebcccccdccdcbbceccebdeaecacadedcdbcaddcdacdeaaecdcceaadaaddaaccabedbcbdccbedeacdadbcccacecdbebbdbdbdabceeebecbbdaadecbabbeecceaecdeaedaebddccbbbbcaedbcbabeeedcbbdbdddaadddcaceaecacbdddecadbcaeccdbdbdbdedebdbeadabecbeecdeeebaedcdcdcdaddbaddeadaaadebeecbadcbbbaaadabccddbbeabeacacbcaaabdbaeaeacaebeddabedabeeadccdaecdeadecabccdbebecaaabecdeccebdcbedeeceebdbaebdceedacbabbeebcbbebdbddadadecbdaedcbbdeebbdaeebbcaddbebabedbabaebebababadecadccdbdaccdabbccbeacebcdeccbbabedcbdeeeccabcbecaeeeaaceacceebbceedcdcdaadbbadceecbeedebeadbdbedbbdcedbcacdeacbccaaeccbebbacabeabbbadcebdddbaaebdceeaaeeccdddcbdaecadbdddcbeeecccddceddaaeecbeedabbcdbddbbeebccbedceaadbaacacbaabbecdacdbabdcbbdabccaaaddcaccddcccacceaabedabbaeabbceaeacabddbeababbaecdbddecaeccdacaebbdeaadbcbcccbdbeabaeddceacacdcebcbcdbedcbcaeebbabbebccdacadcbbabcacceaacbeabaccbabdbdceeaedaadbababedacdbbdabbacdebcdbbaadaedadcddbeadeacbdaecddadccadcddedaadaeedcbedbecbcecdceedbbdceddeaecaadddaecbaeeccabbbddebadbdaabbcbbeccbeadbebbbaebcbecbddddadeaddeecdaeadeccaecebadeccccdedebacacccbcdadccccecbbdcdaecadaabbeecaadeddcebbdccbbcacbbbbdcbbecaaabdcaaeebceedeaebdddcccaaedcbdcdbdececccaaddcdedaababeaaabbdabcdadbcceebdeeaaaccdaaddeceeaacdbbcaccbaebbebbeeeecaaeecedddbabaccabddcaecaaededbadeceedcccbcaccaacacbeaaddebbaeebebbedaecaecbaebcdbabaaaeaeacadcddcecbaddaeaaddcbbedcbbcaaaadacacdaaebcdadbeaddbeeededdcdeeccdddcabebbdbeacacaedbedaceecceddaecdcadcaddceddcddaddabdedacbbaacbedbcbceeeabaabddccabebacbebeaadbbeabddadbabedeccedcddccbcddcdaaebaabcadddaedabdceeaecebeaadccbbaeddeeedbbedabdeeaedbbdcadbadceeddbbdcddbbdeccedcadeebcebaccbbcdadcdcddeeeaeccdbcbcbbdadaeacbabecbebcbeddbeeacadbbbcbdbcebcaeeaddaecdccababcbaabbedbcadebecacaacbbccddacbabcbdcebcdeacacdbedbddbaedbcbaaccbdeeaccbdadedbaeaebbbcccdabebdbadeaacdeceecbddaaebeabceedcbdecbeaeddccacddadabedeebdabeedbceaadabeaedcbceddacbbebcbccbdddadcacdeaccdddbbbccaacecabbcbdeeddccddcdaaabdecdeaddbebdedeeccbbbeecbeecbedbeeaecbabbccedbedeebcbeacdeebccbbacedaeebabdaddeccaabbdadbcdadeabcabeedcebddebebdcabaedcdaecbdebdcbadccbdeeddecaddbcecebdaacbdbabaecdccbadeccacebcecadcedabcaddbcecebcbacdceadebdcdbbdcbacdedbebabdeeddcecccbdabdadaaabbbeeddedbabbcedbdaadcceaeaccdaebecaaeeedceaabeadaeeeaeedceddedcecbcbadacbebccdeadebbbbcdabecccaebbcbaebdddbaebbcaeeebaaeccbebdbecdebbabdbbdcbeeacebbddcbcebccbbaeeecedaedddbedabbbcbaecaabcacbcccbbccedcacaedadceedbeaaaaddcdacbadbceaabeebcbadbeaeadeadaaaedabdabbabcceedacabbaadadebdecbbcaccaeccaaeebbedaecdeadddbdeebdddcaabdcdebceccccddcebcdeebcdabdcdabbacacdeddacaadcddacdbbeedacbccaadaecdacecbacaaaccdcdcacbebacdcebacabbccbabadadcebaadeadceecedaebedaaddeabcaedcebcccabedcccddeadcbbbdeddaeddeeebbaaabadadcaeaebededeeaddaabacaadecaabddabddaacddceadaaabcadedbeccbbcdbaebedacddaaecaabbeccaaaecebdbbdeabddaccdededaeebeccebdaeeedddcdaeaeabdeeacddaccdeccacbabddbacbaeedeebacbaadacbeaaccabbcbdacddcacaebeeababdaebddeccbbcebbadaacbeaebadddaaaabbdcaeeaededbbacdccacecadeaaedeeccbacbddadaeccecabbbeabbbbcedddeaeaaadacedadacdaaaeaccedeadbeebbadabbceeacbbeddbccebaccbdebecdbdacededcaeadebdbcaddbadcaaecabbbacaceccbbeebdceccbdabadcebbcaadddecaaaaabcbbddcecadaccceaaabaddeccaceeecbbacaeceeddcabcdcbbbcaaaaaebcaccedcdddbdbacbadbdcbabebabacdcceabbebcdccdcdcadbbdaadceeaebdcbdabcaaeadbabeeceaeadaeedadcceabaeecaaacdbcceaaaeccddeeddcaeddaceebcbbdedcbccdadbcacdebaeaecccbedeedbecdacdaddcdeadbaaeeddaacdbcbcecaacebccdcbabeabdbbdcdcbaddbeaccabbdddcbddadcccdbaabccebddacccddeeabeadedcbaecaabacddceeeabbeadbcaadbedcdccecedcebbdceadcdcbbbdceaebddcbceabdcddbdabbdcaecdbeecbdabbabedccabbcbdbdedbbedeadbddccaeaeeccbabacdedbedcdcaadcedadedceadecbbabbdeacebdbecaebdcedccbaabceabcccdeacdadaadcddedcabccaeaebeecdedaabdbaaceedbacadbebcbceecbccbaeaecdadeeaeddcaaebbddaccbbcccdccacccdcecdbeeacdaeaedbdccecbdeecbdaeadebeeececbeeededeaddbcdcdcacbadbccddcdedbedccaceacdeaababdcbecaaecbebedeecbcbcccecbcaddbaeddabeeecaacdebbddcecaacecbcaacdeedddedeaaccbbbeeeaacdbdabecdeecdcacbcbdedcebaaaecddccdbcdbabbecaeaebccedbcdecdedbdccabbbddeeaecbcacdedaeddeccdbedecacccedaaecedeacdeadaadcaaaebdaacdeaecbdeeaaabdeecaabeddeecbdbecdbdbdacccdeeeaedcccaaeaecbdadaeedcbaddebdabadcbeceacadacdedaaaedeaaceccdcbacdbccceecaedeecbecabaddbadcecdeabdccadbdcdebdeceaecaebeddecabbbebdaeceadbaaeadaeaebbecdddbdbbdddaedddadbdececacceccacdcddcaabddebdbedabcccdbdabeedeeedaacbdedbceabaeaaebeececadecdcccddedacaaaedbbedabaebddbcdeacadacbecaadeaaeddbbedccaeebbebddbdebacdedabccbbdaabeeaabbdbeecdeaeaadadccaaccceaaacddbabcaebeecdabecaddeeeebedecdeccbacbeceaededbbeacadeebeddcdbcaabcddbdedeaedddcddcbcdaedaebeabacedebcedbebeddbedeadebbbbdecdbcddaacacdabbcadcaaebbccdccadaecabcdbbbdceecceeedeadddddecaeeddabaebcadddbcbdadeeccaaceccdcccbadeebbbaecaccddabedededbadaeaedecccdcbedbbabaeeecacdcbdabdababcedaddbdabeacaebdbbcacbcccecdbcdcaddaabceebceecccebdcaadeddabcbdebadabaccdcdcdccbdaedacaeabdaebecccaebcbeecbdecdececccbebcbedaadbcaeeecacaabaeaadaaabdaabebccdadbcbcbcadaddbcebecdcadacbebecdacebbccaababeacdebcbaaedceccdaebcbebdccadcacecdabdcccbcddaeeeaacdbeeeeabcebccbecddecddbbaecedacbbedcecaacbacadbeaaabadebcbcdeccadbaeebabdbbbedbcaebbcccbdddbdbbebaabcacdceeaddcacccbdecdddcceaecadedeeecdabdadeecebdaebeddaaaebdadeaeabdacdaadaaebeebaccabaeaaebaaebedecdacdbeebccdaaddeaccedabeaebaeaabeeececbaebeebbeaeedabbcebadecdeebbdeddeaeaabbcbebadbbaacedcceeadbabbeecbecdceaecdadbadababacbbdedddaeeecdaccecbacbabcdeecedbaaedeacacaebdceacccbdaceeadabcbbdceececbcdcbeaadaaeabcbabbadbddaecdabaadedacdebdcdeccacadddbeccccceaedaeaaddddaaaaeaadababcbeeecedebcceacebedaceeeceeacbaaabaeccebbccdbcbdaeaedbedcaaaeaacacdaddededbdaeebaeddaebacccccecdeceabbccdaaebdacabdbdedaacccdcbbbbeaeeaceaadebddbacbdeedecdcddeeccbabcaeeeecdcdbcddabdbdecaddabbeecbabceedcabbcdcadabbbeabcbdbbecacdcadeddecaecbacbaaaabdbccccbeacceeaddbbdaddbeeabacedecdccdebccadeeacbdecbcacdbdcdaeeaeaecbabaddddeedceacbaaabbdaeddcddeecbedeecaeedcedcdbeddccdcdcbccbcbacdbddeadcdcdebddacdadbedccedaeccdacacdadabaacdabbccacbcaabeeaceadbdbbdceaccbaeedbbcccaebeaddcbceebbcabbbdacccccccabddadcedcdcecdbebcbdaaeaaddcdecbaebaacebaddecbecabaadcbdacaaebddacdcdbaeceabeedeeecaceeaaedeabbbeccbddebcacbbacdccaaebbdbbdaacdabeaddcdddbabaacbaabdebbccddcccdbddaeadccdccdabcbbdcccebccaaccadeadcdbebbaebcdcbbddeadeeebddddbddbcacdbaccbadadaddacdcddaddddabbcecabecddccdadcdcdeebcdccedacdbaedadeecaebeceaccdddbaebdaeaccdeadaabdaaaebebbcacbbeabbcbddbddbddcbcaadebaebcaddcabddcbeecdceabdbeaaabaddadacbeaeaccabdeecedacdccceaaacdaedaacebbeddbbaeaeaddbeddeebdcccbacccebbecdaceedbacebaadebecaabedbdbeccddacdadedbdacbbdacdebbbeadeedbeeedeaebabcdbacacccbabbabdcedaddeadbbcbebbdcbacbededbdabaaabddadcbabebdceccdeccdecddadeeedeccdcadeebebabaaebeaaeabdbcbccbeabeecebbbdceebaeadaecdbecdeccaeddeecebccdbebebcaddabbcabcbcadeedbbddbbdbdbbecbabbeebebcdecbdccbbbceedeaadcbbcdeaadedcbebbcddceaeaeeaebbcebdeaeceeabdeaecacdbdcbedddcacdecbbeacdcdbdbbceaddaceaaaeccacbdaecbacccdbdbedcabaabbeabadcababeaeedddbbcaddacaeaecadaceabceecadddceeccccedceaabaeeeebdbdeabcebbaeedecabcdadcccdeaacdcceaeaecdeceacebaeaddbcbcdaaadbebcdbdabdebbeacbccdbdaaeebcbcacbebacceaccabddcaccacdaeecbeddbddeebdbcdabedabcedecdbdbdbabcbecedbecebbabaddeaecadacdbbcdbcbbccdcedebbaaeaaebbddedecedcececcdddedebacbebadbdeccdcddcccaaebebcccabebdcbbedeccbeabdaecebbceacbedecbbddcceccacddedeabaddeeaddbcdddbaceeacebdabeaaaacdbdebedebdeedcdccbadaaaacebdbcdddbbdbdeaacaaddedadcdcbadcdcbcabdcacdbdbdaaceecebbabacbddedbaaabdacadbbbbabadbadbccccaacebdcacbabccebeccbddbebbbaeeaaacceaecceadebedbdcdccdccaddcbccdbedeadbcecaeaccddecaadccebbbccdecbddedabdedcaedaabbaacdeceadacbacaabaccadaacbbabddcdbcdceeebdedededdededddaaedaedaddbdbeaccedeebcebaeeadbeaeadccdaacccecdeecabcebbbdaddaccbdaebcacbeccdbcadecccdeeecaacebbebadabcebaedcdaacaeeeabdbdddecdcbcdaddbcadabaddceddeacadaaedbddedcdeeadbecebbebdeedceeceeeabeecddcaabcbbdbdbcbcabababccbeeacbecceaaadaccebcbaaecbdbdccaaebaabcceaedcecceaddbdbbbbbaebbddeedbaacbdacaecbecbdedeceacdeccedaebacccbbaedeabaaacecadaabdacddceeaaccbecdbcddebcadecabdbedebcceaaaedbbddabedbceaebdbbbdbaeeddbeeecaecebeccbadbdeedeaabcabebebdeebadbaacddbcbdecaebcdadbeeccededccbbabbddabbdceaccaebdacbbccbebedbcebbbbddcecbdeabcadddeadddcbeebddeaaaaeedcbdaacbbdbeebbdbcaaddbbbcaadbcccbabadedcaadbbaadacdbceabadecbdbceacddbedccedbcddabdeeaecbaebebddaeacbaadeddacbdebcdeadddcadbacaeaacbedaeaabddadddbaeceeaddbcceebddbdcdeedbabbbedcbeecbccbbdaebdbdcbadceaeadecbbdabacdeecadcdacdaecbbedbdeddcadecadebdbbddbaebdbcdaaedbcaaadebdadaceddcaacadecdabdbeabcbddecdecbdcddaedbddddceccbccbdccdaeecabbecadcbdddbbbbecdeeaaadecebbcdbdedbadbbcadbdacdcbcaccdbbceebdaaccddbcbcbbbbcbddebdbcacededabdeeacedacbbaddbedeaaccbcaedcccceacebeedcaebabddbaecceedbdcedadbdeeeaeddeddedeeceacbdeaabddeacbbdebcbbeaaebcdecaaababebeeeedcacadcabbcbebecbabcdbdceebbdebebeddeadaccaeaabcbaedcbcdaccdbbcaceadedbabbecabbaccabbadadacceeeecdabddeecbabbbccbbdaddeabddbccdadddbbceadbabacdeeddbaeecdbceaebebecbdcdaabcaecdabedabcabbdccdbcadbbcbccdbadbbbaceedcaeeedbccbdaecbdaaceeecddacdadceadeebabddeedcbadeecbecedbbbbdbdecbecadcdbcdacdcbdddaecaecaacbeaecbccacadbaadaecccdccaeacbaddeacceaedccdceeaecbbeeabcabadcbdbcbeedadaecdedabaeaeeccabeebcdebcbebdabdecedccedbbedacbecbeeaccbddbebcceacebeadcedceccabdbdddcbdcabcbabbcabdccbdadaaaaaaacdeabbaddbcdecdccecedbdcbcdbaeaceacdadedebeaeacdeccbaceceeaebbbaebaaedcbdeceeaecaaaeceacdbcdacacadaabbcebccbeebdbcbbcabddccdcaaeeaeaecdcacdbcaedcaeabececbcdcdebdbdaeadaedabbceabedceacacabacbbbcaacbdbbbdadccdbdacceaaaeedeaecabbebabbadbaeadabdeecaadccaaadbecceaeddabbadeceeedccecbabddbbaccdadcaadeddcdabadacbbecbeaabaccedbadacbaabbbbeedcbbbaabddbdaaabddbcdacebadccebebeadabacacdcecdbbdedadebacbadaaadeeacabdeacbbcedeaeadaedcabcddceacbaabeabbdbacdaecaeceebccebbedcececeaebcbcdaccabdabaadadccdccadbaadbaecaeadbbacebcbbaaaccabcaedaeacbadcabeddaddcbeedeadebdbdebedbcbcdbedbddbecdbecdcbdebddeebbaeabdeeabacdcdeebddadbdccecbbdbebbeabeaeecccdaaacaaeeaaeaceaebcebeaaadccbeceeccddddaecbbdeecabcbcccbdccecaeacaeabbecdeebcdceddaabbbcebacedcaecaaceaabddcbabceaeedecdaceecacedceebcdbcceaeaaabaadcdcbcdadeaadceacccbeecbbcddabbeceeaceabebeebcdeebbebabbebcbcdaaeaaaceabdcabbaecbaaeaddbabbcecbabbaadceabdacdcceedaeeeceadccbbabaeabbcceeacdcbbdbeadeadaeeecadecaedcdadadbbbeacbdbbbadccecddbbabacacabeeababbccdcbcbaecebebaceecaeeecdaabdcaabcbbdacaebeedcbcacebebbbaedeaebbccbacaaedabcdbdeaceccddaeadcdcdeedcbaaeeeeadcdeacacaeebdebdaedeedbbedeedaaadccbccdddaacacbcbadecadeacbebeeccaccadcaedcacadbaabbaecbdeaacdcccdcbbcabedaeddaaedcdbdcaeccacedaacaacbdebedaeadacedccccaadacdbbaddddedbabbebaccbdedeadebaebecbbccddddcccbcbeaeebdbcbaabbcdcecaaddccacccbeadddcbcadececebcbacebadeebccbcadabecbaceaaebcccababacbeeedeeebbcebeedcbdeecabadcaebecccbbdeaaccddbcccaecbaddbdebacadbcceaaecdacebeccbaceaccddcccdadeacacddbbeeadaadcadbceadeeabaabbadddeeaddceaeeeadaaeacedaaabababacdbedcecaabcdcbbbdcadaebcacdaabeeedcebdcdceaabbcbaaecaaaacdddbdcbbcbbcadccbceacaaebbcbbcdbdbdccbbbacccddcacadbdddecebaadacabbbedbacacceebaabbecdddcedeacddebeaebbbdddedcddbddecccaadedceabddceadeaabececbbecdcacbcccbabdabecaeebceccacebeadbdccacacceacdbebedaebcdcaeeaccedebbecaaeeaeaeccdbddabebdaeebcebbbcebdaedacbedbcaedcdecdaacaeeeedaccdabcbddbaecbececcdcbaeacecdaeaabbddcebbebbedceceeeddaaeeacdcbaddadcccecccdbbbdcdceabbcbedbebabcdeddebdeeececbbbadaedadaabdccebcedbabccadbdaebedcaabcedbddbdaedceeadbcabcadaeaeecbacadeeccaebccdeabeddacedbdcabcdbbededbcbcaacceecddaacdebdaaecadeabddedbcebcecbbeddeaadbaaaedcadeddcdadbbaeedeaaccbaaeaaddcaccbbeeabacebecbebeccdaacaaaeaaeabeccdeadcbcedabaaaabacbbbebdaacbcabbecbaaabaaaddceacccebeeacbbeacabeacabadebeabcbcacbaeabaabeedadccdbebccadebacdbdbccbebdbeccddacddeeeeaebaccedecbcbeeaeedbbbbbdcadbbeebeeccbbdcdbdadecbcdbebeddeedcebdddcdaabdaceaacbbedabbadebaeeeaaeadabebecacbaccadadbcabbeeacaeabaeaaabbcddbbedebddccbccebbbaebcdbecedeebaeecbebaaabdccdabcdacdacdbcdabebbdaacbcacabeeceeabaeddbbbacaeaccaaabecddabaddeadebeebdcdeececabadadbbcecabadeedaedeaaebdcbbdbcaddeddabadababaeaeabdacecccdcccbceaabdedcedcbaaabeeedbccceddbdeaabbaabbcccbaaeebccaddaabbeaeeabbbeadaaccabaecbcbbbeacabbbddddeebccacecedaeecedecdadeadacaaccacdecbeaeeeaebecadedddabdecdeeeabdceadecedbadccaabcdbcabecadaccbdcdeccebabdddbccbdceaececacbeadbbcededcdbcaceceaeacbeddedebeacabaaeddaedaebcedcbbddadddbcebbaabebebbbeceeccabbbbbacacbbbddbdedaeeabedeaaaddbdebcccabebdbacbbebdbabcbbbdbededccccdaedecbdbddecadbebeacbadacceaaaacbaaaccecdceabdcbdaeebccaededecaeaeeaecdecbabddeaecadbaaeedcbcdcebecacceccaadbceecaedacbabaeabbcbbadbbbcdceadeeeedacedcbcccadeabeaeeacaabddaabcddbdcceceacbedeaddebacdcaddddeeddddaeaecedadcaebeabadeadaeadebeedcddacaeedebacdbdbdacdabedcdadcdeacebecdbecdadcbbcceecabeacabbdcdaeddeeceeaeeebeaedcadadccbcdaaddbbaaaabadcccbcdcdeadeebeabaceabdadeeaedebdeeaaceecbbdcabbcdebceaccedecbbbbeaabbecdacbcbeddaccacbaeeebcececcebbeddceedcaacdccedaedcdecddebcedbaeeeddbecbeecbbaaeadabceedcbceecbbbbcbbabbddcddceeeaceaaedbecbadceceadbaaecdcadcdabedeaaddbacdaacaeaedcbcdaacccbeccdbdcdeecebeebbbddadababbdeccccdaaeeadbadeacedcecaccbbbddaccbeadcbebccaadeedcdcdadeeeacddbddbaeecbdaeccdbbdcddebabecbeebeacbdaabcedbdaeeeaabbcadedddbebbecbbecbccedbdcadbdcdbdbccacdaedcdabcceecbcbdaaeeaeadddbdcbeeaadbccbdceccebdcccdccabbdcebceecbaddebabddededacceeaabacaebadddabccdbabcbdbbedeecbbdbcddbccaaddabddeddadacddeabaceaedaadbabcdddeaccddebeaeaabdbaeecbcbaccadbbecbadcdbeebddaddebcccabdcbeccdabacabebbbbccaddcdabccdcccbcdbeebedabdebeaceacbcaadacbbbeebadcbecacdccbeabadddedeecadaaccdccadcbacaccebadcacabebadeccdeaaebabaaaaaeebaccecadceeaecbabecbddebaceeecebcdeedbdccbeebebeccdbdcdebdeacdddbecdddaeececbcaadceacdbbccbcbeceebadbcadaecebddbadeacedbcaeecaeddbdedcdcaaabbdccdbbaebbdecebedaccbcebcbbcdebceddcddcbccebeabaeedbedadaaccabcbbdaddacebcceecacbaeadabadceaaeeacebbcccbeaeaccacababceaadddedbbacbaabccbcaaadbaedbbabbaebeeedcededeeaccdaccabdbdddbacacdbaccbdeadcaebcdaebacbceadacdedbeebdebcacecedddaabcadcdccbbbcaababecdbbaddbdcaeaebebdbdbbcdbbceabaddebabbcdceebaccdeeeeeceaaeddceeddbeadcbabeccbdcedbedacdcbdacbaceeceebaeaeaddedcaeeeebbbdecdcaddecaaecbcecdbcdeedddeacdcdbdabdcccacabcbddeacaacedcaabeeabccdabdddbaccadcacbdaeebcadccebadebbcdaabeeadaabbcddbdcaedddbbaccaeecbcecadcbccbddebaccadaccbddbcbdbdadeddadccdbedbaebebeeaaadbcbcebaccbabeeaceabcccebeadbbbccebbeedcadabcebbccdebddacdaaddebbdedcdecbaaedcaabdbdedbdbbeddeebcdaadeabcedecdbbaeabaeeebaecdeaceddaecedcacbabcebedaedebcadaaaebceaceaecdedaedebbdedbeacbaeaccacbbcebcbccebbadadacadeeabaacaaedeceddcdddabaeedeeecabacbdbccdcbebdbdabdeedeedeabdbaaeaaecbbeccddaebedcadaacddbdeccbadddbadaaebedbacebdacabacbedaaecacdcddddaaadcbaeeaeebadcecbbdbcbeaebceeaeecddecbdaeacadecebabeececcededeadedadbbdeeacaedaedeeeeedccacebbadaaadcbcebecddddbdcbedebbcbbaabbeccecdceededadbcaeaeaeebedaecdacabbceedbbebcecaddecbeabeecebccbeeeacccbadaebabeacaabecccbbccacbcaebcdebdddbbedcbbaddabceadaceaacabbebbbeceeebbaddbecacecaddbedcabdcdecbacecabedeacacbcdedcbcbcbbbedaaecebdcdebacaaadbbdeabebbdedebdebbacccdccdecbebbebdbbbabadedaaeebbbaecdaccbaebbcaecacadebaedacedacccdeaebaaddecbbecabdbdcbcbdeccccabececececacdaacdcdaeacceacbcbdcaedcececeadddcceaeddbbbaacaedbbbaaabbaaedceabeaacabdecbaaacdeccabcbceabaecccacbbdaccdcdbbcabcedbcdebccecdebcaddbeececebbacbccdaecddadeedacaecbdacadbcaddcdccdbacaecceadeabcedeebdeabaaddacbdeeeacdadabbcddadacdaadcedbcceaddbaeccababbddbababeacbebcaaebaabcadcabeacdecdedbecdebcabeadecbbaadaeeaedabcadedddcdeeeddedbabebaadabdebeacbeecededeeedccdaaaaccbaaddedcbcdaeadacaaacadbdccbbdaeebabecbddbababaccaabddddacaaecabcebadacaeddeeaddadccbbaadeecbcdbcecceeeececabbbebdcbeceaddbbadcebcebaacabcbdecbaeaededcbdbeeabbcabadcaeaccdeaceaaeccbcaadcacdbabdabbedcccbaedaddeaececaeacadeeceacdbeedddbdaeebaaeceaacedeadabebaabcbaeccaebeadeedebeabbecbbeccacaebdadeabbdcdedecbccacaddaecadbbadddbbeccaadadbcedeedbadcddadcaccaddbcbebcdaabdeeececdabcebcaeebeddeebccebeccaccbabdbcdbebcdbddaeabbcacdeeceeaaedcadeedabccecaccbedeadddaacadaccbbbedbdacdebabacaedddcaabaadbecacbcaaddcaceececcaabababadbedbdbccecdbbaebbbaddeabacbeeecaebacebebeecbdeeddcadbeddebeeadbbdcdddddcabddadadebebaeeeeaecbcacbdadbeddcdcabdbbaacbecdadccacbabdeecacadcddcadedcbdcbdaaeadbaaabdcaddcbeadaeacdceccdbeabccedbacecdaeceeebbcbedbeccadcbccdaabdecebaabacabdccbeaddaccebbeeaceaaddaabbdddbaaddaecaddaacbdaebecbdeddbbbeddbceccacaeddacadebaacadbdbbbedbbddbececebeccaeabacaccbaedbcabaddceabddeebeebbeddbcccaaadeecaaaecdbcabcaadedccebeaccbbdbcadcabedeacdcdcaecdbebccdbceccdacdadceedcbdcacaebaecebecbaccbcbdceabaecabbadedccdbbeededadccbcbdbeabaadaecbeeedbdabaeeeadbbebdaccadddbaedcbabddaebbdadbcbddbbddebbbcedcbcbacddedeccaaaecbdeeadbeddcdaadaededdbdcaccbedebbadeecbeceaacaeecdeaecbaabcddbbadadedcdcbccdeeddabcedbddeadeeaaecdedaedabeaededeacdbcdebdaddedcabeadccbbabccabcdddedccabeecdbbcdebbdbccdcbdbbeacceaacaacbdbdebdeaabbddccbedacbdbacdecbacbcbeecbedbedcbaeaddbcbdbcbbedbdeeaeadceccbbaadacabeaeecbeaedbadacabdccaabdbeccaeaebeccebbcdbebdddcdbcdcabebdccceecabceccedbccabeaeddcaadabcdddedcacedbeccbccbbabedecdeccbeeabdddbadcccdddcbbdadbcdbebacaceccbdeaabbbbaeeaeeeddddebdbacdcdcdacacdcabcedbbbcaecbcacbaebebeaddcacbbdaaeeeeedecbeabdacbceecbeeecdbbccedadeccddebdcddccbbcbeccedcadbeddcecadaeebebabeaedddbbeaabdeeeecbedbaaddaecbebbaccbcbdbaccbecdebcbebbcbdedadebdbeeccebddbaddcecbbcbbebadcedaaeebcebaabdaabebbcbabcdbbdaaccabcadecbdaeeecdbcecebedebbbeabeebcceeaebeabbdddbdadddcdadabdceaeddccaeeddcbcbaabedbaedcbdbdecddaecaceeccaebbeebedbeadaeaebdceabcadcedcababdadedcadabaddeacddeaabbddddcbddcedaeddaaacbcdeacebebcbbbdaaadedbbdabaaebceadbadaeabaaacbaeaceeeddececcdaecddebccbbbbdabcdcdcbbcabcaebebddaedecbacbbddbaccacebdeddcbdbebddbbcbcccdbaaedbadacbeeeeaaecaeebeecdcdebcdeadcaeabcdedbbdbbdbdeaddaacdbeeaacaecbbbdaedbcbdbcaeabcaecdeeedeebacddbdcebcbedadebdacdeceadcdcadbeacbecadbcddbcebaaeedbdcdbacaeccabbacaeabbaaeedbdeeccaedeaecadddadacbcaeebdcadaadeaebdeabddecdbbeadaeadeecadaeeaceccdcdacdeeadeddcbeacecceedbddadcddcdcccdeeddceecdccbbdeeebcabdedbbdcccdbebeddcddecacbbdccccbedccccceeecbcaeaceaecaceaceddeeaabeccabbaaaeebceeddacddabacdabebdcdbbdeeababcadebceeceededdeedabaeceeacdeecebecadbebdcddcddaceeebeaccaeddaaeecdddeddedcedcebdacaddadcadaabdbcdbedccdddcaddaacbedbdbbddbdadaaaebdabbabcadaebbcbebcdacebdebbdbdebaeeccccdabacbaebaaacdbedeeceeaddeaaccacbbcdcbadbddcabacccdadaebccabaeaaabdaadcacbeeacdcebddcaddbcbebcbabaaecceacddcacbecbdddabcaadceaaecaebeaecaeddaadadeeddabcdbdadaeabcadcbcacaccededcdeaccadeaecddddcbcbeabceeadedeedecdecaabddcebeccaddbcacbeebbedebeadeaedcdebdeaadbdbbbeddebbbbabeadbeeaedbacdacacbadccebaeabedccabeecedacbdadabaaeccbbddcdcdaebccbbeeabaaeeacbbeaeeabbcdcdacaeeaedbebdbeedeaeeeaacaabcbcacdcadedbecedeaacecbcdeabadcabcebdcebedabaabeeaeecabbedaedddcacabeeccecabaacedbcbdcdeddbdcdebbeaeabdceaaccbdbadecaadcebbeaaacddbcbbebdcdcdedecebeceeceaaaacdbedbeecaedcedcdeddaddcbbacccdcdcaaededcdcdbcecacbeeabeaabaebcaddbcbeacadceebadeaeeaeddcaeeedddacacaaacdeccbdedcbaedddbdeedbdbcbbdbedbdaadeccabeeecdcbebbccbadabdceebdbdcbcbadbebdaacbccacaebeedccddcabbbddedcadbeeacedebbeedabbaaabaebaaeabbeeeeebecbcdcadacebdbcdcabcccdddecaeacbaaceeaadabcbbbabdeebbcdbbcaaabeddedbaecdcdbeeabcdadcaccaeeddeaeccbcabacdcecabadcccdecababeececeacddeeabbacbdaccbccbdedacaeedaaeaacaabbbaaadceccdecabdbebddcebbcdcdccacedeedaabddeacebeedcbebddabbdebbacdcbcabebcddccdabbeecdedadceecabeddccaaadeadacaedecaeaebeacebbaadbeaadbcbcdacdadbcededdbbcaccacdaadbcbdaeaceeacddebddebddaedbebadeccdbbbdcaaeacbdcaebebbcbbbacbaebaebdbcadddceaebaadceadadbebaccbdceaecbeaaacbebcdcdcbadccaddcdcbabbaddccdeaebdceacabbdedececeaebccccceccedcbbbaeaadcecdaddcabdaabadbdcedecebacedcccdbdbdeacdcccedccaabceacecbbbceececeebeebdeeaaaecbddeccdbcccabcddbcccabdcaeaddcaabeaebdbadacaeedccdcadcceabcabeedcbedebaeceaeedcaabaeadcdbaaacaeecaccbaadaeaabdeeccaedeaaacbdbedacedeebcbaecbabbeadcdbcceabdebeedeceaddacacdebcadccbedbcebbaeedebbdbeeaccaddbedcdabebccabcaabeccdcdcbcdecebedabcebbdaadaecacabbabaeaadecdcbbdcacadbccacdecedadcededdcecedcabebedabacaaaebdaadabdeddbaddbaabbedeabccbeacaeaccaccaeeecdcaecdeddbebaeebaeedaebdeadebbcaeedeacbbcbadbecdaacedacbecceecdececbbdcabccbbebbcecabecaabbdcdbeecccbcbdabeacbccddeddaabdebcdcddcecddebbeabebbbaacabebceccbaeceaccbeeccdbdddcedbdddaeddccdeebeebabecdbacadacdebccbbabdcceaededadcaaabbabdecccdcbbcbcbdbcdabbcacbdeeeaadecbedcccdbcbedeedddacdaeddbdeeacddabedaaacbdeeecabaabddadcaceaebbebedaeeececaaeedadbbaaadacdacdabbabcbbadababedbdaaebddeacececaaedededcaecbebccdededadabbcbadcbcccaabbcbabacdecccedbacddedaccceebcdccebaeeeebaabdbecabadaaddeaaaadbddabceddbddcdabcecdcdbcbdbbabbccbdceecacadabeecbabbcecdcccbbcaedcadbdbaecbcdebbdeeadcdbbebcbdacccceaaabeabdaeabdcbeddeedbdbcbbbeebaaceddecabeccdabebbabbdcbbdccdbaebcaaaedbebceceebeadeaeebdaaebceeadbebeeededdadcdadabddebebeaebcadebacadcedcbacccceceabcacedceddbccbbdeeeedeedcaceeabedcdeebbcbacbaccccbaeeabaebeccaadcecdeeebaadcaedbaeadcaccaddbccceaeebdceddadccbabaeaecebccdeedbaecceadeaceebebdcededeabeebbbdabdceeebabaaadeabadcedaacebdeaadedcdcbcabacebaeddcaecebcadcdeaccbbabccbcebadaaececeebdadaebaeacedccbcbccaeebbececdeedbeaabeeeeabccedccededdedbbaebdcaacdcedbdbcdacaaedbaeecaaebcdeebcdaabcacdbebebeccaacaeeedceccbeebeaeaebaceccbbebecbbdeccdedcbedcdeeaceeebeaddbdbebebcddbaedeedeccbdbdaacabedeededecdddbcacddbdedaeeccceeaedadbdeadaebdbdbdeddecacebbcbdacaabbdbbbcaeceaaeedaacbaadbbaeececedecaddabcecbbbccaeadeacecdedccddecaaeacecadbddcebeaeececdaebaaaaaaaacdabbdacbbadceccacacebbcccdddbcacddcceadbbddbebcddcaaccaadddadbbdabbdbaadbcdcdebadcceedccdcaeddedbccdeeeadcaceccedbecdcecaacebacaddaedeeebadbddaedabeddedbdbaeeeecabaadeebdcaecdeaadceebcedbeecadccedaeadcedaaacceccdecddacdcedbbbeeecbceeaaecceacbdabaeedbbaadebbbddaacbbedcbdabdcbabdaabbeedbbeaaccbdbcbdbdbdcabdbadebededbbedeaaddeebbacedcbaadcdacbedeadaadaabcdbeeecbbcdcdbccabbeeecbceddbdebdaaedcdaeaccdedccbcbcbccdcaacbaeaeadbdadcccecbbddbbbdcdddacdbeacadddcceadbbaadadeaadbeaaaaeeeedadacddcebeebaaddddeeedbbcbdaeeeecbeabecebbaebceebaadbaedaaededadbeedebcedcddbceccedeccbebdceeadcdbaeabcddcdcdabaedccbceccadabccadaecaedcaabdbeacaecebacbecedcddbeeadddddebcbedbaabbdbadeaccacaeebaacabcadacadccdcbdadcddaacdbebbbdcceaeaebacaaccaabadabeecdddeeabddbeecaeecbeadacbeccaeadeadcbeedeedebeeecaacedcdaddeccdceaeceebdabebabaeaddcabcedadeceebeddbdbaceebceccddccdedcadeeedacbdbacbdaccecbccbdacaeaaceababbebadcbadaacaaadcaacaedbacbbdccecbaaceaedaedadbaaabddcbbdbbcacdabadacaeedddccadbcbadaedcbecbbdcdbbddadeeeedabeeaaedecdaeeeedcdaeddaaaeedeaadcebacceaddcbddaceddeeecbebceabeccacadacbbdbdaadbbaceecaebecbdeecbdacdeedddaadbaecaddddaeceeedeaeacdcbdeeebbeaeebcbeedddeacbbdeebddddedbdebcaadcbeccdecaaeecbbaeeddcbdbdcbbdaacabbbeaacecaeeeaedceebbaeabbaaeddbabdadbacdcddccdcdcddbbeaccdddaedbcebebcbdddbbeaeeababccbcdbdebddcbbbaadaeaecadcadaebccbaddbeecddbbdccbeadbdccdcbabddabaeeebcebbbcdbeaaedabecadeebcbcebbdabccceacdcacbddbbbdcbdacdcbdecdaaddddbcbecceddacdadaaceadeeabdaceccabbcbccbddbadcbebedeacbeebecabceceeddccebcbcabcabebccaeeebcdacccdccaeebedddaadcccbdcbcebdaccbdddbededdadeebbabdeadcdbdeebddaeadcceabdaddcebcaccdedbddcddaedeacabdcdbeedcacedcaaeeabbcbdddedcabbcacebeecdcbadcbcaabccecebddbaecaeacbbccaedecececdcebcbabdaacdadbdeedcececeaccbbebaccddeaadbcbbeaaeeebeadedddbbcabddabadccaaeecddececeddacbaebabcaecebbaeeceeaddccceadbdcaeececbbaecacdececaedceddbcaeebabceccbbceaedbaeaceaededcdeddedeaaedaadcacbcdeadaebcbcebbeaceccdccebecaabadecbedaaebbeddadacbaeebacbbcadceddcecdeceaccbbdeabebacdddabecccccabdbaeedaebcccdabbeceaeebdaeccadecadbededaecaaadbcebedbebcbbcabbbbadedcedbbbcbddcbbcbeaabaededacdcebadcadeebaabedadecadcdebdedabbdaddeeabdedddcabecabeeccbaadcdeaecadacebeeedadbdecdebcbcedccedcebbdddecddabeedeeaeebcbbedcdaccbacecdceedeccdedbabebecaecccbdceccdbabadbbbaecbccabdbcddcaceadcdceecacdbbddcbbdccbebcabaebbacccedccccdacbbbccaeecadabdccdaebbceadbcbaeeecedcbbacaaebccbddacedacedbecaabbcdcbadcbedacccbbdbedaaabaceeddedbaaccedcaedcdbcbcaaebebbcaccddceceeaebbccdccacbeabdbcddcdebbcbdebcebdaccdbdeeeaeadcebecdabeeabbeaeaaababccdbcaeaebddbbbeaeadbaedacbaacabeebabdeccabbeebcedcdbaadcdebdcccdddadbabeadbbdbecdeecabeccabccdaedbbbbebcbcecaedacbeacabaaedeeddacddebbbcedadececaabdcceeedeeccadcedaeccbadeacbcaadcebcabdaedbdcaacbdcabaebedaccadeedacccdbbcbbcbceaaaceddbadeebdbdbbcaadedcddabaccdcbbeebccbeadcbbceaebdececcecdcdddaccbaccbbcddcadbbccbadccdaddccedeebacababbaddedbedcaadaeeddebabdbaabbeceeedcbcbbccccaecdedaddcaceeabecdaadacaaddbdecbcecaddccecabdadcbebadcdcecaccdcebececcaaedddccaaaebdceabcbadaceeaeeaadbdabeadaeccaacccdccaabeeebcbaeaabdbaddabdacecccebedeaeeedebabdababceeebcdebebaadeacdabebbebbdbaddcdebeacdaceddaeccacedbeaaabbcdbdccaddcebeccebeabeeecaecbcaacabacbdacddebdebdeacbacadcbdceeeccadedbadbeddcdbcbdaceaaabdbeebbddbacaebebcbaabbaeeddeeaedbacbbccaabacdcabededbcbccdbdabbedadddbddaddcecdbeabeadeaadcdadcdbbccdcbccbbdacaeeccccaacaaaadcabeebbcacceebdabdebcedbceebcdbcdcbabebccabcdadccbbcbaebbdcebcebcadbdceaebdaaeeacbbeadededbbdacadaadeccdcecdeabbcaedbbedbdcacdbbacddaecddddedcbdbeababcedbecdaaeeacccecdacecaadceaadadbadaaddaabdeebebdaaabeaabcbebaccadeacdacacacddadedbceebabecacabbbdcedbacdeebdecccedbdadaceabddceaddbbcdabdbbbdabeaebaedbeebbacaaaccedabdebcdeebeeaebebaedacacbbebebeaaeaacbbbebddcbaaadcddbabdddddcabcbaaaccebacdbddaabeaabccbbbcabcbbccbeddeebdedacbdeebababbeebedaddbbdcbaeabcceeeedaeaedaacaabcccacaaddbbeecddacdaadddaadbacecbbbdbddcbdbbebaeabadaacecebedcaeecadaaeebbcebabbcbcedacebcecaeceaebbbdeacbbacdcbdeeeeceabeaaacdcebcbcbeeabdbebacbcebecddaceabacbccbdedbcdddeeeebbbdcdabdeaeccaeddacabcedabedbcdbeabcccbeadaeadbbebbebeccababedbdbdcbdeecacdebabebaeaabacdecdbcbdeebeeeeacdbcaebebebbdeaedaedccbbccebbbeabcccecdabccdbbcbdabaabdcaaabbaeaabbbaadaeeacbadceaccbecbeacbdbeacddbaabaacbbbaaacababaecbdccedadbacedbacdecbdabdebddcdbdbebcccdbabcbcadeeaedceeadbbbcebaabaaddbecbaeecdaceebdbadcaebcadacbbdeedbdcdcdcebbedaedabaddcaeaceeebdceeaacdbadceeaadbeedaaebaeebdeaacedccebcdcbcddaebbbbeccbcbaaadaedddbacdadbdadbbedaebbcaabdaacacbcaccebdaebaebeaacecbdcccebcdceccdcdeddebaebcacbacecbebebcaecceeeaedbbcdebcaedcaadcceceddceeeebabedaeedecaceabcaccabdacdeedecbaadedeedacbeebcbadddeccdeecabcbdbdadcceabecbaadbebbebdccaaccedbebccaeeaebebedacdbdadbeedebbedeecacaebecebaccbaeeadceeeddbebdeceabdddbcbeadeadaabcdadcceeabeeacadcacdbcdcedcadeceebacabdddeaacedadceacaeadddcaadbcbdeddebbdcabecacdaabdddedcccacacccbbcadadaddcecebbabbeeabebddcecaeaaebabacacadddcddcecadebeeaeaeeebcdcccaaabebabeaabaceebeeaeadeadcdbdeeabccdedbcdbeaecdacbeeaabbabeaedcdadeabebadecbdeeadebcdeabeccacdbedeacdceddbbabbcdacbbabdeddcabcbdbdebedddebadbdabbeebcebabcbeadbdebbdebecdccccbaaebcdbbbedddbcbdecaddcceaeceaecdaaadbcabdeddbeceddcdaadbdbcececdbdedadedbabaabdaebdddedcbbbaccdddaeeebeccbceebebbeadbebceeebedbbbbcbdbeaeddaceeadabdccbecdcdaeabedbaceadddebeeeddddbcdacaedcdadeedcbddbcceebbbaeedaccdabcbcbbbbcebceacbaeeaebbebaadaccebeebecbdbcabdaaebdeceeccedaeabeaadbdddbabedbdebdeaeadeddedabdeedeeceebbddcbddacdacceedbcebaccceecbbabebedeccaccbbddcabacdeddcbeadbcbcaaccabadcbbccbadceccdcecabebdaedabaadadbaedbacebcdaceaacbceabcadacacddcedebedeebeeeacdccacdcabeabeaebaeebeaeaecaeccceeabaaaddeacbecaeeadecabdaaddcdbabceedebdbcacbbadebbebcdbdbebccdbaabdbcbeabbdaecdbdceddadbedbeecedebceaddbcbdbecdceebcccadbccdedabacccedabdabbbbcdadcdddcccaddbebdacaebeaeedccbddddcccccdaacbccabcbeedeababbaecceabeaddbecacdbbeceeedceeabaeeeedcceebbcadaaebbbcdacabceccaccebbbcddaebcdeadbccecacbbbdcebceaeabccaecddebcadbbbadcbabbecacbcecaebdbeaeaeccadaadeabacbacaecdcdcdccdebeeaaabcecedaabecbddbabbeaccceecdcbdbdabebacbcaabcbcaceeadbcabbbdbbaeccabdeebbdadcacdeaeeeabbddeedcedaeddacbbbecbcbcedcbbeaddaaebbdaebcbceeaeadaebecacecccdecbcbaaedbaedcaeebaadadcabbbaeeebbedebababdedbababeacdcbecbcdeeeddeaaacecabbcbcdbcaecaabcaebbaabcdccdbbebcdababccdcaaddedabadcdbbedcebccbdebeaaaedbdbcdabebdbddadbcbcedcbecaebeabaddcacccbbabcebceabcbdecdbcababaedccbdbbdbeababcbaedbaaabdaeabcbebabcebbacbeacdeedeabbebacadaeeccacdbbecabcbbeebdcaccdaebbbedebdbdbdeebdeabeeeecaeebeddbadbadcdeddbecbdbceedeedaeaabadbdbebeceaecaddaececddabdadeccbbeceecedcbbbcebedccebcebecececbbbdabbbdaaaeddadabacdaacdecdcbcaaddcbabcdbceacabbebddaaccebbebebabcbdbaeaeecaccdcacbebacadabbdecbebecabbcddebbddedcaaeacdacecbacebdcabcbceebaeacdaddbecdbecdebccecabeadaceaecdddccdaabcecddaaccdbaaacacdbbadecbabcaaaacaedbeddcdaababecbbbaaebdaaaddeceedecbcbbaedcccbbbbcbaaabcdeedcabbadcaaaccdacdccebdaeddcaaeadccedaaadebdedeeeedadedeaaccbacececacdceedceeeccadbdbbdcdbcababedcdbcaeaebbaddcdcebdedabbcceaaeeadeadddcecbdcdeccbdebdbbadebdaeebdceaaaecdceaedaccbcdbdbbacddcddcdedeacadbbbacebcccabaebacaeaeddeabaeedcdceecebdcaceccecbdcbcbebebaeedbadbddaeeceeabdcdccaedaabdedcdcdaacdacabbaaeeabeacebddadedacddedecacdbcebadededcacbeadddbeabcddbcaeccacdbdebceddbccebcdddacebabdaaaacbaddeacabaacaebccbadeebacdaadcdabbbcecabcbdcdbeceeeebebcecbcaeaedcdbadbecbbbcdababccbacddaccbeabaeedeabdccdcdcebdbbddaadceaedddddaeabcddcbeaeeddbadccaadaacbabaddeeceeaeedbeddaadaaccbcbeaaddbddaaacaccaeacbcdaebcbadaebdabaeaacbeeadeadbdeeabeeeaabbbbbcaeddcddacacededbdebcaeadaeaaddbbddbdcaaccebcbeadccbaaebdecbebaadddaceadccedddaaaeaecabacacaeeeadbecacccaacedcbcaedbebadeacdedadbebcdceedaebaaebacbdccdbeccaeddbbaacaeeaacbaaadabacbdbdadebcbeaeecabcdbececeddecbdedeedbadbbcbeeabbbacdebdebcadbedcbddacbddbdcdaacdccddbeeaebcabcbaaabbeebedadceeaeecdecbbbedcbeabcebbbdeebcedbedabddbbdacdecebcbbbbedbbaacceaecedacbebeabeaedeceaebbcaeeeebebbbdedcbaecbddcccdbaaccababbaddceeacaebaaaceabebacdbebdbddeebcecbdcbceacaddaacddeecccbcbbbdedeccaeeabaeeadcaddcdaadeacedaeedadbbddddadacbceedddecdddbbeeedbdcbdaaadcebbdadaebcbbddeeccaadeebbdbdebadaccedbeddcbeaaeeeeaecddbcbbcacaccdacaabbdaaaeddccaddadbecccbdabadcdeaadadbdcbddcabbaadbbdaddadcbbabdbabebcbdcdcdeebaebbbadbdecaababdbceedbeaabcecdbaaeadaecaaedcedabbeceaacbbbdcddabdbeeddcdecaaedbebdcdeeeeecabbbcedaebaedcbdddceecbccceccabcbcceccbcabecdbdeaadcdbaccbcdaaccaadcdccecdaeabdccddaceeebbeaaabeaecbaaddedbaaebbbbabeaabceacebabceaecaabbebdbddecebcaacecebddedcceaceceabdcbdcebddcadcbbaecebcceebbbeccabeedbbcbaebceaaabacabddbcdacddbceaebbdedbebbbcabadaebacecbdceacecebbebbdebcdaddcdcccaebeccbaaecbededbabecaecbbdebeaeedaadbcabbcabbcceadcbeebbdaebacceccaaaccabecdaebadecbbaabdeeaaddabaadbeceebacdbeeadcdaacbbeceecaaeeccacacddbabaaceacbaceeecdadddcacbaadaaccedbabeedcbdbdebeeeabaeedeacbceaaeadacaeaaebcdbacabebdedebdcadecceceeaedbedbdacaceebdeeecbdbccbacbcdcbeebacbbceeedeccddcaaaccdacdceaedbedebbcdeddddacdbbdceddeeedaeabbbeccbeceedaedcceccbbcbdccaebbdddeacedbeebebdacccbedbaeedebcababdbeecacbeeabccbacccaddedabcbcbeaeaccccbacbcceccaeccbbedcaddbccedcbaadcaecdbbdbcdeddbebbcabbdcebaecabeecbaebcdcbbecdbccaeaedbccaadadcaebbcdedcdbabeebbdebecebdceceaeeaeebdadcceeaaaabebbceeaddddaebaeeeeabbceaaccadadaaedbadccaaaeaeacdccbbabcdbbbcdcebcebdccedabbadabaddbddccabdaddeddadaecbbeedecdcbcabdcdbaacaacdcebeabaaaeceeabcdccaddcbbebacbdadbccccdaeaacccdedcacdceabddcdcadaebceddabbbcedbdceaabbaabbaacbecccdcaadeceadcebdeeaeeedacecabccdcdcabcceaaabecaedeceabcbbaaaeaebeadbbdbccbebbabddcbabbeeccbdbbaeaccedcbedeeebcbcedebbecddbddacdadeeaeddbdadcbbaeeaaedaaadbccbaabacccaadbedccbcdebcabbcbceebebbecaaceaecbacaedeabceaabdeedaacaadacebdbcdeaadbdaccabedadaaeccdcbdeeadccecacabecbaeabbdadcacdebebedeabdaaaebadcbcdaedcdcdeedccadbebbcdcdddcebedbccdceabdbbcbbdcdcbabaddcaceabdbaecdbebbaaebbbceedcebbbecdecabdabcecadabeecdcabeebadeaddbbdcabecbcabbbadddcbeccdbddbccbaeccacbbbaaacbdeebaadeecbaccddcedcaabdcbeaebaecadcabaaaeeebddabedaecdecabaaeeecccabeeaeedcaebcaedebdeaceebbabebadbccddeaccccbbbbbcaeeabbaadccabeeabbaaddaccdbccbbededcdacddcebdddcecadceaaeabeaeabdaaceaacecebdeaacdabaadbbbeadcdbbccdababebcdeeaacbcdceacddcaaabaaccdaaceabdeeeddeccbaededbbbcbeecdaebbecddbbccdcbbdebcbdcbbbdcabbdcaebdeacbdddeadcebabaacbbcedeebdbbeeaedbdadeeeecebaeceedebacceadcccaabeceacedabdccccdaedddacbdcebaacbcaaddbeeccdaabdbcadbabdcbcdeaeecbabdbcbdddddebececdedaecbdedbcadbacacbbcdcdcedbeeaebbbdeebbaabedcdbcdeedacbecdeeeeaeccebdbaacddabecadcdaabdbcaedeeedacabadeecebbecddabebbbebcaaadbebbdbecedcdcadddeceabebebabdcbcaeeedceebbaacaadaecdeabdcedebabbddcceaececabccbdcddecddacedadeadbacccbaccedbdabceaeabeeceaeedacbdeecbcdbaddceaeaccaabddaeabaeaddcabeeecbadaaeacbbcdbbbebcebccdcdcdccecddadbacecacedcdccacabcdecbcedacacacedadddadbbbbecbeadbaebabcaaacbbcbbeecacaaecdedebaedaeedcdddbbaaddcdcdbedbdececcccbbeeecdebaacaeedecaabbaabcddbaabeabddedbdcaedeededceadeaeeddecedaababbaaceabeaddbbbddeeebbbdbeebbdcbbcccaebaccbcedababedceaabeaccbabbeadbbaccdeddeedcedcbcbedeaeebccebdbbcbbebcaabbbbabdabedaaadacbbddcbbbeebabbddaeddabbbecbbdbabeccbbaceaccaaeebebbcdaedcbcddbeceaeeccdbcacbdaebabacdedbcadbbdbddaaadbbbddcdbeeeaaebbcbaabdabdcbeacadaadaaedcadddccdeddecdabaccadbabdbcccecdcaadccedceacbaecaadebeebacaebaeccdebaaebcaaeedbbcbecbdcccadbceaabedbccadeddbcdaaaeebdbaebcadceecbbbacadeedecbaaeaaabbcdcbeddedebdddbcdbeeeacbacdbeebeeccaedeeebcbcecbeadbbdeadeabdcaabdabaabceedabccdaddedddbdedeabddecbbeaeebcabbcaccaecdaaedbadebacbacddbebedaacebacdaaddecdbcdccdabbdaebdaadebbcbdcecaabdddcbcdebebbaacdaaacaecabdcbadcaabbdeadcaabdedacbaeabdadcdcdbaedbbcbcdbdcdaaedceebdcbbabbadabbcbbeabedeedaacebaeecddecceececacebdeddcdbbdcbbecdeaacddbdbebeabdecccccddcdaaedeebdebedaccbededeeccdebdaabdbeeedaccaaaaacdaeabbbeeeabeabbebceabbeaeeddeeaaaccbdcedadcaccdcbeedaeaecbdbeedcbbcbadddeccbaacdcbbcdabbceaccdacaaecbdeebeaaabcbcaeaccdbabbbbaaceccdadceacdcaebebbcddeebcbabeaedeeabbdabebccbbedadcadecabcbbaaadeebadabbcaebdabdcadcbebcdbdeddbeadadbecdedeaeadddddecceaabaebceccbcabcebdeeddabdaeebdaccbaeabccccdceeeaebacaaaedadbbbbeccdadbbdecbccdeaecbbccecbcdbdeeebecaceadabcccaaebddbadedcbbbbecaeeececacbabdeacebadbeabbbdaeadacddabebececbacdbbeacadbeaedddaaccadccddceaeaebacccecccacdaaaaeacdbbbeedcacebcbcbbedaadbcccedabbbbbbdaebaddaddbdeadeacaeedbaebdcbacccabeebabbacedcdbebbcebeadcadeeabeccdddecaabacaebebbeceeccbdcaeccbccbaaebaecaaebcbebcdaddcbceadccceceabddbbacccaceebacaecbbabbcbddbdcebdbcbabeaddbbacbaecebacbeebdbcbeebcbcbebcaeaeccdeaeccdddbcbbaebadbdaabeabdccacbaccbcaacddebcebcceabcebabedbededaebbebecceabcbebabceddeadddedddeacbdabcadbeadbdcddedbaccdccabedacbeabbecbababecbcacecdaacbabddabbacabacabaeeabadbabbdedcdabbaeceeaabbcadcadabdbecabdcbeadcbbdcbdacabbaaddbcccebdcbaebdaebacdaabbbaacccdbdbdddcdbbbdbbabcacbccbbabcddaaadcaeecbdeecebbddaddcabadbcabeaadeddddecbdbdcdeeddabaacdaacdccbeacbadcedbbbccbbbeecbebebabdbecabaebedbcabeddeecdcbaeaebccaebaebecceacaabeaacaaaaacccecbbbcedcbcedacddcbacabbcaebaacbaebeadabcebcaebdcaabacddadceabaacabbccbedaadaaeeaaeadcbbcebebbeeedbccabdebacbcccdaeacbcbeabecaebdebbcaaedecdebcdcbdeedbabcbbebeaedcabddebcbbecdcaedbccabdbcadeeceddedeecadccadadacdeaddbdcebbedcbcaddeccbbdcbebccdebbbdaeeacdcbdeacebedccaeeceacbcddeebdcecbaecddcbcbbbdbaccbcaddbdbbcbbeddeacebccddeeadaececdeaccdbccbedeeedebacadadadcecbbdabeeccaadceeadbbdddbaababcabebbeceecaebbdcededbbcdbdeaaacebeccbcdeaccccbbdbdeccedabcbabadbeebcbcabeaeadcbcdbcdbbcbacbcdccebcebbcdabebbbdacadaaacbcddcbbeecdcdbddebdbddbeaadcebcedbddebeceedeaddbdcccabecdbddbdeadebebdaedbddaadaadebeedbeaaebecadbbaeeeebbbeabbdecabbcdadcddaaaabeabedaeaeeccbdbdeddebdcbeddbbecdbdbedceabeabbbddbbbadacceeabecabbbbcaecdbbaeecbededbaaaabeaaddeeadbaadeeceecabbbaccbdaaebdceaabbcddcceadedbecedcdaeeccccebabeecbddaecaddaeebcdcecaadeddbaabeecdbabeecdecdccbdbdcaddcceacbbadedebcaedaebddacebababbdbaedcdececebabadecdebcbbabadeebedcdcedaadedeeaccbdbdeacbabcacbbcaeeedacececabaddebedcdbeaeebcdeaebeeaecbeeaebbeeebabbebdbaebbbbeeeeadbdadeddeccbaeaaaeddaeceaeabaadbcabebaecbdbedcdcecdaaeccecadbbddcbbebeedadbaedcedecdeaaebdcaababcecccbcccedeacccdcaceddbbeebddbeacceebebeabaeeeccbcedccacaedaebbdabcdaecaeabbbbdcdbcbccaadadedbadeabebeeeeaecececdacbbedbaccbbbdcccaeceaceecacadcbcbbdcdccbebaeedbddcdabeaccccccddabdbecaabbeeddadcaadeacebdcedecddbbdbdbbbcaccdceacbebedccbeddacedbabddadeccbceeecdbbbdebacebabedebddcdeccebaeccbcdbebdbcdbcecadbeecaadbbeaacdbaeceaabbbabddceccbbcaadccbbbcaccadeadaebbbeaeeddbbcecaeadbbddaacceaebaaebadbbbbeedacaabcdddaacbdeeabcceeeaebaabdcbeadebdddbbdbacedcabdcadcbcbaddadaaedbcccaeebccaeacaadeacbbdcacbdbdeaacedceabeabdcbdccbeddbebdacaebabbbcabcadcecbcbcaaebebececadbcaaacdcabbeaeeddcbeddcceedebadeabaadbeaaebbadbecebbaeaeadabebcaadbaeeceabcededaecabeeeecdcbaebeebaebdeceacebeccdeddedabbeddaececdbedcecbdddcebbecabadabdcadedeccaceaadcceaeaeeacedcacaacaecbaeededcdebadaacbdaebcbcdccecccaddbaedebcbbecbcdacebedaeadddedbcdeeddacbbacacdbbcaaecadddceedadceeacbcebebadabdddccdedbebeacacadaacbdddbeccaedddccddcdccaaeaaebbaecdaecdaadadcdaeceacadecbdadedebbecabeabdeaecaedaaceccacebdbacbabbbaccabbdddbaaedddbebcbaccdbbbcbdbcceddbadeeabeedabbecbaebeccaacddccabedeebbdecbabbdacceceabeabbadcebbbcbccccdcbcbbdbeabaadaacadaaabdeaedeadccdebebbbabbcadcceabbcbdbdeeeabdcbcbacebbcecdbebbaaebddcdbcaccadeedbdbaaedecdeceedacbadcecbaedecedbcdaebadbbccbddeecbdcebbdcdeceabdabbabebebaebbaddebaddedadbcadceadeacdbbccdeaebbccddeeecadbbadbdbebdcdaadaacaebbeedbceddbceceebaceaaccecaebaaaaadccdeaceebadcdacebeaddacebdeddadddbcacbeecedecbebaeeddbeaaaeebbeaecedcadbceecbaaaedeabcdbbaedeecbedcbecdcbaabbeeeecbabedbcaddedadcaabdadebeacebdacdbcaadedaaaeaadcacccabdedaebebbcaeeaeedbaccbeeaceeaaaedbbaaebbededbedaabbdcbbecabcebaabaccbccaacadbcbeceddeecbaddadacdbbecdcedcaceaaacbbddcdeabebbdcceeaaeeddcddeaccadedbbeceecbeeceaecabcaabaaeceabedadbebbeaabeedbdeceddcabaabcbadaedebcdebdbaacbabbdeadbdbdaadabbacacadadcaccbcdeecdcbcebeebadeecdececdbaadcadcabcaaeebeccbedabbdbacbbacbbacbdbcdcadcaedcddbaacddbbebbacdeddeebbcbecbccceeebccebdaaddccbeaddeaebdbcedeaebddcecbdceeccebececcedacbcdcdedbbaaeeaedcccdebcbecdaeabeddbaeadeddeeddcedcedceedeaeddbacdddbcacdceebcceebaedbbdcddcaaddbcbccebdacadcbebbdeeedcccdcbdbbdaeddedabdccaaaaccbbaadbadeadbeeccaaadedcabadcbadedededddecaecccbabcdcaeaddcaeedcebeecdedaecadddcddcdbdeccddceadbddbededeccaacdcecddccccceebdbbcabbcdebeddbdceeaaccaabebebbcbdabcdcdebdddbbdebcbecccababcebaccecdbcccaecaabcccdbccaedcdbdbedeaaabccbcaeeebccddddedabeadedadcacbdcecabccdebcebadaceaabecaacdbcbbbddcbaeebcdcadebabcadbdceeaabebeeabdacdbabbabaedacbbbdaecdcaacdecbebbcadeabeeabebeceedbcaedaaabaabdaabbdddbbbdcdecacdadcadbcaeaeabedaedabecbbdeeccadbceedbeeabadecaaecbbddbbaeebcabbbcabeddecdaaeecacabaaccddacdebdcdedabbcdbedbdeebbceeedeebbebeebbbbaaadabdcadcbbeaebedcdcdbbbdcecccbbbcececdeeddecbaabaebdeaddbcacaeabdbedebcacbadacedadcbabdcdcdadabdeabeadddcaddeddcaeccedaccdceccbceeaaeacbdcedabeadccdebacdecaddaaeaecbadaedacdbbaddcbedccadecaaacdcdbacdbaeeebdadcaaaebeebebceadbeddcbebecabedcddbaadceabbbacbddbeaedcdadedeacbaebabadeebcdddecaeecdaacbcaeeeaadebdacacbebecabdaeeeaaacaedcddebebdaaeeaaeccedcaecdaacacbeaeaccdddddbaedcabaedeeebaadbeaacbcabeaacbbcebaaeccabbdebabceeaeeaccbdbccbaecabcecbecedaaeeabbccacddccdccdcacdceeecdeeeacddbbdbaadccdeaabcadaecedbedabaddaedebbddcadceacaeeaddabedcbbecaebacbceaebbcbeadecdaaceacdceaddbdecccbadacceccebdacccaedbbbdecddacddbdbebcbebccdcdccadebeaeccdeadebdbcdbbaddeebcdeacabccdbdddecbececbcecbbbadaedcdccdddcceaccacadcebeaccdbaecaeeedcdabbdadccdbddeeabeccdcecbbacdabcdedbcebabaeabaebcaadabebadbbcbddbdbedbeeedddaddbcbcbddbdcaaacbbeddeabccedcbdcdedadacaaccdeaadeccbbdbacccbdbdcdaeabaacaebdcbdbdbeaeabccbdbcbdcbcadcdccccebcaaabccacaceecacaeeeecbbdebdcebdadedcaacebbabbcdeebcebaedeecabeebecaceaecddcbaaeeeeddabaddeacdebcbeeecddccbbdeabeeedecadccadaabbebadaaccbedabcdacbecaaeacbeeebbadeaeeedabcadedddcbecaeeebbceadeddedcedddbccdcaddecbaaaddeccdacbcbedbeccbebedbadbdecedbdcdcbeaabdedcacadcdcbbebdaeaabdcdbcbcaecdeaacdebdbceabbbdbabbdecccecdbcabcbeccaacdbcceaecabdecedacdacaacccccdcdaadacaddceddbdbaaeeaeeedccdcceccbeccedaaacbaeedccdeacecbbbaceecdabaadceadeedaaeadcceddcabbdecdcebacbdccceddedbbdaebaaddaacaaecbaedbaeecaceebdacaeebacadbcecdadcaceaabebcdaedaacadaabdbebaccbdbbdaeecbedcacedaddbcdbedebbebbcedaccbdaaceabcdabaecbbedebbdeabaccdcadcaececeddaccbbcddebceccdcaedaddedccaeceacbcbcdcceabcadcaaeccecccebddaecbecedcbbcccaacbeaabdedabbbdceddecabebaaaaebabedabdbdbabbbcadbcadcbcddbbcceddeacaaaccadccaebeabbbebbcbcebbcacdcceaebabaabdbcebbbceccceddedbbeaadcecbcccdabebccaaddabccbdaaadccbebbcbacaaededacacaaeeacbaaebdaababddaecbbbcbccdeeddaecceabdedccbadeadccaabecdababceebeaebeabeacaeeaedecdceeebadecdddbedebbdedbbbababbaceadbddeaceadebeccccdbceccdeabbceaddbebdcecabedcebbeddcecbabdbcadaecbbbbcbccebccbcaeeacddabcabbeaccebedebeccbcdeececbdddbedaacaadaeeeeddeadadbbddcbdcbbaddbeaeccbedbcbbcddbbaebaacadcdbeadededbdebdeddecbdaebadadcbeaeadabacddadabdcecbecacdceeeeabdcddecbbdeadabcebbeddcbbacaeeccbddcddabbededcbcabaddcdabbecaaaeebdacbbeddbebaadebccacccebeaadebcddabaacdeccdebaccebeedeacbbdbadcccbbeeadabaedbaacdceaaecccedcedbbccdcccdaaadcbacebbbbcbdaaebcabcadcabdeabceaceeddbaaeccddbbecbdabbbccdbabcadecddadbabcecedcacceddbbbbbbbdbeddbaedccdcbeeabbadbbbaeedbddceccdebceaccebebacaacccdceeacecccbeecbbaccddddbcaadacdbceeaabcebaadbbadedbaccbaacabaddedabadaccdeecbbbbdbaadcddebacedbccacdbbacbeacbeabdeeebadbddbcdcebaddeebbccbacddcbbdcaaeaaeedbaddeeedeaeeddeeabebdddbcccdddbbadcacbabdcbabcdeecdaebccbacbadcdceebcdabbccccdcabbccdcbbddbbbeeadbcacacbedcbcdcccaecabbdbdadecddcabeceabbdaabaccbcceadaedeadadabebedbbabbabceadcaccacbcbcaaeeebdaaaddcdcebadddbabeeabcecbcecedceabdddceedeebcccedbecdadcbddcaaebbcadcaedbabbddbbccaedcbdbcbedabcdccdbccceabacdccbabdebcdeabacbeccbebbcdcdbcedcddcddbcdcbdacebaaaedacbdccdaedecaebcbbacdccdcaeaaeccbdaaabbacdecabeaaeeebeabdbbeabcbecbacedeeadabbaceebbdadedaedcbebeeecccaaeaeccaedcbcbaedebdbcabadeacacdaecdeabbadaedacdcedcedadacdbedbecadcbcaaecaebbedbadecedeecddbdcecbeddececdaecdecceecebddbbceabdcaacaabedcadcbadeebbbdbcdabaaeddbceabcdccdaaeabbdbecccaaaebecbbeaabdbdbdecbebcbcdbaaeebbaccadedcceecabddaeeedcccaccaecbabbadabcaadedceeaaebbcaecbdcbeeeeebcaaecaabeebabdaaaaeebdddaecdeeecccdacaecbceedcdbaadaceaeddcadeedbdbdbcdaabecadcaebedeeaaaeaaecdbdaeaeabcbcddeddecddaecdddbdccaebececbcbcdabccebaccdaebdbacddbdacbaabbadceddecabeddabaddedbeacccadebceccdedacabacedbeeaeaeacececeabbebaedaadcaaddbceddccbdacebbccbcdcecdbbabebecdbedebcbaaeabedddbdbeeebceaecebbcddcaacaeecaebabeecdaabedaadbadcadabcadbdbecdcdbaeddcbdaedaabbbdbdaaeecbdcecbccabadedabaabdbadaceeeecbceccbbcaecbdbbedbebabceaecaedcecebbcdeebeccecdedacddcbbabccabcdabcebebacecceabbaadebcbbebbaaaeedceeeaecedecbdeeccdddecadcdaadaecaaadcddadddcdaccbebbacdeeacbcaaddbbaeabadaaabaabeddeaddeadabadeabeeccbadbadeccdbecdecbacbdbbeccdcadacbdecdaeadacaccdbcbabddcdacceccceccdcbcadeadabbeeccebbceabeebcbebdbadadbedcccccddcbdbbeaaaaabbbdccedacbcaacecedbeaeccbaaddeceddbebbacbbabeaebebedcbbdceccbedcdbaeacbdbccabeaabeaebbedaaaaaadeeccdaaacdbccabeabddbaeebaaebbccdcaaadcaecaabbaeeeddcacacbbacecdebbcbebdbcebadbcaacdceabcdadbaedaeedbecabcadcbceaecbdecebeccdddacdcbcbdbccabdedabbbbacedbcdcbacddbecccaaccceadcbdeeceaedbecbbeeabcacbabcceaaecabadadcdccdeaeaeebcceaaccacdeecbdcbcbebdeadccdbaabecacebabbbdaadacedddbacdbdabaadadbbbdbccaacceeddcdbdacbcaaaaedebeebecddebaabaddecbdeaecdccacdcabdabaaededbeebcceaecdbaddccacdedaaadabaddccbbccbaaccdacaceaaceccbadcdabbeeeecacaccbcedddadeebeaaaabcbdabcdbebdecebebabaaecbaddaceedcaaacacddcddccabaacaaebcaedcdecaaddaedcbaeadacacdcbacccbeaabeddebedbbbdbaeddaadeaacbbbcdbccaaeaebccccedbeaccdedacbbebccacdeeabadababccbdcbacdccbadcbbbccddadbbdedcaaccdceccedadacadadaabacaadcbdbadeacaadcaedeaacbadaaedccdecacaeadabcdacccdacdcbdeeddeeebeddabcabdebdeeabdcabdcedcaadaeadddababaaeabdeaeeaebdbbbadaaacecaacabdddcddcdcbdeebecbbcedacbaddecdbdaaecdeecbceabceddacbddaddeadadacaebaaccdcacdaaccecdbbceecdadbaaceaeabbcebccbbbadadaceccccabedbabbbedaacbbadaadccbccddbceddebadcaeccbbacceabacbabcecceddbdeeebbbedbeaecaaaeeebdbeeeebeaaeeddeabddbbdeceaddacbcecbccccbbbbdddccdecaddcbbadcbdddadaedadaeaeedeaccebedaddaeebecbccbbacbceeaebaacabbbeeecdcececeddaabbaeabbdedebacdbaeaabaaaeaabeadbeebcaacedeccadbdcdbdaedeedbeddcacdbebcaceddbcccabeaccdeaedeacbadbcaddcbedcbceceababebcbbaabdcdceebddaceddcebdebdddececceaeeaabbdadecbadaacaabaaadcbebbbabccabbaddbdbbbcbabacdeaababaeaccecdaaecdbdcbeeceeccbcccabedeadacadcdbeeaeaeaccceaaebcccecaecbddbeadbdabdaedbabebdacdbbcbbaeaabaeebdcdedbbbddebdcdceccdcbdccecadcacbbbbdebadcebbdbdebadbedcbabcaedaaaccaeceeedccbadbcdacbcaedaaebecdaaabebdeaccdaceadbeebecbdcdaedecacecdbbadbebdcbacbaddeeddaadacadabbddcebcecdbcbdaadedbdbeebbebabdaeacdbeebbdcdacdbbbbbecbebeebeedbbcbeeccaeacddcdadddddabadbaeedaeedbeabedbaadccedbbcdeddbedbbecdceadebdeabbbedbcbbbbbaaecaddddcbabccadcbecbebedbdbcbcecddbcdacccbbeabcdcacebedbceccdbddebdbdeaaaceacedccbbbcceaccbdaddebeaacbccbccbdbceeabaeccecedbbeeeceeecabcededcdabebbedecbdadecaceebbeeddceddddebabddbdbadacccaedaacaaccedbbdedacceceacbabecaadaaadbaddcddaabbeeecbdeeeeebcdccaeacbbcadaededabebdaecaddeaabbaceedcbdeedacaddebeabdedabcebcacccddaadeaedcdcdbceeeebeecdcadbabdcccaebabdaaabadebeeeceabbbadccabacbcdebecbccbecdddaceccacaaadeceecbdecaecdbabbcdaaebdedeeaceacddecacadbcdeceaedaabbbadcecccaadbebdecaebddaebacbcceeabebedebeedbddccbeddbbddcddeeddecaecaabdeccabbccddaaccabadddcaaaaeaebbbdededeaacccbaedcaaeecdadbabeeeaebceccbbcebadaaabbaceeecbbecdecbeabdbeecdcceaccdacbccceaaaedbcecaaddeecaeaadcedcedddeddcabddbcdaecdedbdccbadaddcabdcbdddbbdabaecbbbdadbeadbaabbcecdbdadaacdbecdddcdddadeeccaacabcbbccbedaddccdccddeccbbbccecceecdacbcaeeeebabeddadaeaeaaabaaabddababdcabedbabdcbebaedebeeeceaeabbbdcccabdcdcdabbbdcdcdecbcaaabebbcbddaaceaebedbecbedbddbcbbeecaacebebbabcdeedbdddaeeccabeeecdeeebadddcebbccdecddbcbcacecacdddcbddeeccbecbcdedcababdccadbbebcecbdedcebbbbaedacedbbecccaacccabaebcdbdeabeaaccbceadcbceacbccddecdbeaaedcaccaaedcedeeeecbcabaeecaedcdcdaadeacedeebccbeebeeccadccbcbdadcccdbdbcddcaabcaecdcdeecabbebebdecbebdadbbaeadeabdddadaccabbebedccdaecdcdbbdebceaabdcdbdeceebaadddcbbeeedceadbbeaceabdbdbbdeceeaadbcabbbccccbcabbccbdabedabddbecccbdeecbeebbbcbdaddcbcdbcdcdccbababadedbadaaeeececdddcebedccabbcebaecebdbadabcccbeeebaabaadbdecbdaadebdeebdbbeedbbaaeccbcbcddebdcabdcaacdcceaebadedaebacdcacdcddabcebddaaececabdcdabdcdbbbdceeedddaddcbaccadceaedbddaaedabbdbabcdaceaaabcabacdcceaecaddacebeeadbcddaababaaccedeeebeeaeeeceeabbdddeaaedebeaaeebbadbeeebbdcddedbdedbaebabccabaeeebbcbaaacecdcadcaedddecabeccccaddcadcabccedbebebbccbdbaaccdbadcbddaddbbbddedaddcaebccccddeacceacaaadadecadceedecdebbbebaddddabdeabdeaaabeaebeacabecdbbcdeadaaccecaaeecbdcaaadebbbcebccbdedaedccacbeddedebedcecdededaabaaceecadbdebddbdaaabceeaaeaebccacdecddbdcbdcaecedbeceeeacdaddbebeebbedbdeeeacbdedeacceeceeddadddccdeeaaaceddbbacbaecedcdabbddbbaeebaaeaedccdbcabdbdbccbebcaaddaecaedcbbcceecedabdaecaedeaccaddbeebebdeabbcddaecdedddcddabdedbeabbdbdadedddbdcacdaebcabcaebddecedbedbaecdecdcddddcedacbedccbabaeeecbdecdcabdeedaabedccaaeaccddbccaeaaeaddbbeccbdccccddbaeaebcaaabdaebbeeebccccccbabedabdadebeecbdebdbcdbcabccbdcdeaabedbddaccaacabecebbdcbdbaeeeddebaebabbbaeceabebabededeebdbcaaeedcadbbcccacdceaeddabddddacdebbecdddeeddbdacddbcaacaeebdecacbeaeecedaedcabeacaedcabdbdebcdeacbebccadedcdedbebbeebaaaadcebceccadbcaceabbaebbddcaeeaccbcaededdeadaaceebdeeddcdeeaeebdbcdcecdccecceaabacadaeeaabcbebaceaebabaebceebceddbcddddceeddbeaebceeceddbacedeeccabdbdabeccddadbcdcccceddbaaaaedcaabcedcbedcaceecbddcbaadabbbdcecccdaacbdcbededbeaccbeabcdccaceddbedddbdcebdaabdbeeaaccdccebbbdedcdddbedbdbbcaadceecbecaddcceedcccdedecaeeeabcdbcededbeadeeaadccbdebabbbbbebaadbdaeaeddceabcceedeeccdbeeadededcceabdccbcbebacaebdbcdeededeceaeeadccbbecaccedacbaeabddbbebdacbbceddbdbddabeaebcbceddcaeeabdecacacdecddeebdcbbaccdacbeeedeaedecddceeaaecbcaaddcbaecdbacccecbeeabeaeceecaabcccebbaadeeaceecaedcabdcadbacedcccdadbadbddeddebadbbcccbdceaadebbaadabcccbedabadccdebceadaeebddbbdcaaabebccacdbbdddddeabbdbaeedacbbeabebdaecededbceeeacccbeabedaccceddceabbeacaccadecbadcabeaacdabededabaadbbaecabebbcccbbadccedadeeabadacddecddbaebcbcebadcabeedbbeaeeadebaaabddecaeceadaaabbedecbddadaacddaeadbbcaabdcbeeeeeeeedcdadaaeabcccacecceeddeeceddaebbbcbaeeabdebbaeacdcddcceeadbcdaebcebdabecdbddbebdcacdbaceecaadebdbcabbbcdbdeeacbaaeadddcdcebeddcceecaebbcddbeccaebcabceedaadbcaaecceeaecebccbaaaebcdeddddcaeaebcbdacaadabaebbccdbdcbacbcaebeeacbadaedebcbedbcceadbbdadcaebbabdcadbcbdbbccaabdbaeaeceabccebaedcbcadcccebaceabcabcdebecebdcdbdbcbacbbbeecececbaadaaceebcebccecbaeecbdcbadabeddbcabceaeaacadbedddcaddbaadedbeceacabdeaaceebcceeecebabaacdbeabbbdaddeaabcacbbdbbbbdacccbecaadbabcaaaebbbdbdedaccbadbbebbcaceaeabcbcbbbdacaaaedbeceeacddaabbabccabdbcbccdcabbcaedccbbccdeaceeecdabcbebbbcaebeceeebededeeaaaddabebacbaecdeeacdbeaceeabaeeaeacaabeadbbdbcceebbbcccbcabdbedeaeaeedaeacdbdbeeedcabaaceecabcccebdbcecdeabbaeadbeedebbcdeecebecebcecaedcadeddecbcdebebccaadadcaccdabaeecccaabdacccadaeacccedeeabeecbbdacbddccdacecaebbadbecbdccedcbeedeeceecebdaaeebddecacabdbdbdadaebbbcaeedaaccceeecbdeccecdaaceedbbcbcdaebbeeddceeeeaecaceddceedcbccdeccebbabebdaadebddbbbacdaebdaacadcbeddbeeebbcbeaccdaeebbecbbedcedeeeecdcadadabbeabebbbcdcaacdcedbbbeadacedabcbdacaeaecdbdebccbcabdeecccddcbcbdadedbcceeaeddddbebddcdcedbbdcdadaabddaeedbabbbbddbcceacbedeacaddaecceabcdacbcadddcbcbbebceaceddbdcabeecdddcceecadbbcbabbdbcdacadeeeedaedeebecadcacaaaebedbbcebdeacabbbaaecdeeedbbcbaeeaadaddbebebdaebbbeadadcbaaebbeaacedebddabdcedcacadbbbdccaacbecbabddacacecaddcabdabbacddcabcceadcaaadabcedbcdbaababdadcdeadbcebceedaabdbacabdcaeabaaaaabebccdbbaaeeaebcadddbaeddbebecdbebdeaabaedccedbdbecbeebdadabbaccddedbbaadbaaecacaebedeadececaddddbdcaabeacccccbcededbbabddeebcaccdeecadebdaccddbaddaddbdccdecdbbcecdbbebaaccebbacdcdcebaedceaaedaeadcacadedddadcbeddaddbeecaeebbeddbacedebddcababdddeeaaecceeacebccbabaceadddbdbdeebcdacbebaceeebbcecaeecbbeaadbabeeccedbadebeacccedeacadeacaeccedbbadcacbabdadeacabdeacdcdbebdbbbddaaeaaaeacdcdbbeadbaedccccbbeceaacbcdbbabdebadcabaeaddbeebecdacaabaaaacedadaccddcaedacabdeacabcebebeaebbbadcbadbbdeaaccbdcbadebdcbedaccabaadeaabbaddacedaebeaeeeacaadceebecdaacbaeeddedacddedccbacdbeaabadccbebebaccaabcbbeeacaecadbbcedbadaedddaceeaebebcbeabbebbdcbacddcdaebbdbacddaccaadcbebcecbcebacdcdaecbcceacadaebbdadeeaacccdaeccbeeeabdcdbabaaadaacceaadaddddebcaacabedebbcacdaebbdbbebdeabdccaedaaeebdcbdcaacadbdbddbeaacaeeadbbbedbbedbceabdebdedbdcbdcaabdddbbabacceedecdaaaaecedececdcbedcdecbccaeadeaabbaeaeadaebbbeecbaedaaeadcdbbaacceedabedeebbcbdbedabaededbeadbbcbaddcaebeedcdcadebedceaadbcdadcbdeeaaebbbdedccbbcdedbdbcbdbedcbbabddbadbaebdabecacdabbbeadbacdaeeaaabcacebaaebbaabaaacdadcbdbadeaeddbebdddbbcedcbbddaecceacbbcadaddbcbbadaebebdbadcedeedcedcdeacdcdceaccaccdbceebdcadbeceacadacaeaeaeebeaebbdcdcaceabeddaaddebacabdccccecdebbededbabeddaeecbbeaeddccaabbeabbcbdbcebbcbaddeeccbbdbbdeacebeaaeececdbbdcbaebddbdeccebadbbadecbedeababadeacdadcedebbcdceeedabaaacbcebdaceddbbdabbdacebbccedbddbceabddaebccaaacaabcaabdbeaabbcdbdaeaecbdaeacbbdabdcabaccaadceedccbbeedeadabaeccaacdabbacbaccdcddacabebddedecacbbbeadddedddbcccabcddeadbbbccbddcedebbecbbbdaaddabcbdcdadbedbdccddccbcacbbcaccbbdbbcecbaeebaaecddaedcacdcabedebbeaeabaddabbecdadecacdbeeacebdcadcacaacbcaccabbdecbcdcdacbabccbcddbdddeebdbadcadeccdbdbaddbcaacabaadccbeccabdbcedebdecbbecdcbaadccaddbeccadddaabceccbcdbeeeabcdebbcdabdabbdeeabdcebceeeedaacaadbaeedcacbaadabeceddddabbdabcdbebaabeeebdcceeeabdadbdabaccbeddaeacbcbbecababebcdbbadbeddebbcdadeeeccdbdedadbbaaeeeaeadaabeeeddbecbcaedeeaddbdccaaadbcdeadbbebdccddcbadebbddeadddeadaeeeecbdbbeabcdcaaacabbceebeabecaedaaacedcdddccbabdbaccbdddecddbecedcebccdddaeedbbdeaedcecdaceecedbdcbbbeeacdebbdddacdaddeaddbbdecececcbbdbeedcdaccddadececebcebceebbaecdbcbacaeadbeceedddeebacbededccdacbdbcdbbcddcdddccddcdcaeaedcecadebbdbcbcbaeeacdbbdbcccdeeacbedbcbeccceccdbcddcebabdccabeacddadaddabcdaedcbdadcedaecbeadababbcdeeecdebcbacdbbcdabddbeedabdaeacecbccabccadccdecbbcaaebdecdbaaddadeeeeadbdcacecdeebddbcaeeededabeccbeeabeeddaebecaadeeecdeaaccabbecebaacaabeacaedddbebcedddbbddbeaedeeadddccdcacbcbbbaecccbcdcdcaebdcaeabddaebcbbeaeaecadeeabdccabeceeaebeceeeedbeacdebcacabceadecdbdeacdccbbbedaeeaadeecadabceaeebbcccdebddcdddebadbcededdabebcbdccacbeebaddcdaaedbbeeabaecacddeeecebdbaaebaaaabddedcdcaaaebeacbbcecbecaedbbdcdbacbbbacdcceebcaeaebadedabaabeccccaaeeacdaebcedcbbaaeeccabcbedbadcacaabbceadcbcaccacbabcbebeadddcbabbeceeeeaadcbaaebaceadcaacaceabdbadeacaeaeeccabcaaabedcbcacbecedadbbabdecdcacdbaeadbebdaeceeaaedebdadcaadeabdacaddeceaddbdaeeeecdceaeceeaebabdbdceaddeccceebeeeeaebdcaaacacecabadeaeecaceaaaddbedbabeaebacdcabdabaebbdeecdccedbeaaaecaacdacabbadacdedabcabbdaddcbeecedccadbedbbedecccecbddcdaeeccdbeceeaadbbececbaaecceacdaabcdcaadadcdcdadcdcbeaaeedabcbcdbeaaccdaeebdabbbcaeeeddabaabcbadceaebdaaacdabcbdbdadabeccdaaebcbabebdebcbaeaccdddeaacebcedbbecdbabedcaaceadddaecaceabeccbbbabbabbeecdbdabacbbdceccbcbbbdddbddeaeddcadbdbccebaaadddeaecceebdcadacabcdcaaedccbccaeccbadaadabcaacdacdcdddecbbccecdaceccecabbbecbceaaeccedeabbdceeaabddddbbcacceecdbcaaedeeecadaeadaeacabddcadcadcedaccdeeaaaaadbcababebcaaaedbbbdceedeadeadcbdcdbbacaaececeecaeacaeceaaeebbcbdbcadeebdebdbdbbbacbaddaecabadeaaedbbbeddaaadceaceecddebcbeabaaacdcdcdeabdedaaceddbcbdbddebcbeedbaeaceeedecebcdcceeedbededbaecdeaedaaeacbbcdbccdbcdebeaababbecedeaeceaeebeaebeccdcdcddcdcbaeddcabcadcaabeecbcdacbccceeacdbcdcbadaccedebedaaadcadbdcecbacedbddddaaadaedadbaaeddeecaebabcbdcdbeedcebecdededdcdecbacecbbedeceeacdebecceeddbccbeaeabbdedabeaedcdeaeabdbaeddcabcebebbbaceaedacabdedbdcaedeccedccdcbcabbedbabcbccebacceeddcdbaacdaaeeceecdcaccdebdddccebddcbaebaeabcccabdcddebbdabeeeacdeecddcadeccaacccabdeabdeaaeebbdbdadbeaaaabcccedebeaeeeeaabdceabeeddcedcbdcbcbecbaaacadebedabcebdedcdedcdcaacddebaeaeebecccdecdccadbbaaaeceedbbccbaccbdceccbdbddceaeeaaddedadddccaaeaadaeacaebaebedccddacbcdcedcddbccecdbbabcebacbbbbeebeeeaeaabbebbbaebaddcdeeabedaccdaeedccebddbacedbbcabdedeceddddbbedadedebebadadbacbbbaceebcbdbbebebacccedbaeabedcdccecaaadacccceedbbededbaddebeddaeeddebccbccecddaddceacaaddcbcaaccaaadabadadbdeadeececbedcaebaeccccabbdbaabcaeeebaecadbcbddbdaccdadcbdcbbcecabaaccdecbbdeceaebdededaaeeaeadaecdabcbebaedddddebaeaaeebdcccecdddebcaddedaaaadceabeaacbeeecddbcbcadcdbbaaebabceabeaaeddedacedeeebdbdbcdcaecbacccebabcbeeabeceeeadaeddccaccaadbdcbccadbcebcdddceceecadcddacccaabedddabbedbcdecacdebaabbeadbcbcebeadcdcdeebbadabbaebbaabcdeabeccabcbcaeadeadcddcccceeecceacecbcdcdeabaecbceeedcaeaeedbecacdcececbadbdcddecdaaaccedcccedccdbcbceaedacccaaaeeecdcaeebadbabebddbdeeecdbaaedbdcbaaaeebabbcdcadcededaeebdcbaebeceadbcaacebddeadebabbcbeadcbedbbebebaebaddcadbdcbddbddaeadcceacbceceaddcdeaabcecacdcdbcadaddaddadbdabeeababececacedaddedeeebaeadebcdcbccbadabebabcbadbdaeacbeabadcebdbaaaeecbabcaadbaaccaceabbdeacadcbbdacdddeebeecbddeeacbdcabbaeacbcbddeedabaecdbbcebcccdcbdcaabbceaceeacacdaeebbaaadcddcbabcecaeadbbcacdbabbdcaedeabbaddcceeccdceadbeadcaabbececddcdedaaceadeebcacdabeddeccadbdbaedaabdcbeadeceabbacacabdccbbdeebbeeecaddcdedacdcabcbbabccaabdacddcbddbeccceabdebabcdacddcbdbacbcccbbabbcbaacaddcbdcebcdaaaaceccbcedbbeceebeddadacddcccaebbcdcdbdbbdebecacedbcbdeacdedbcbbaedbcbdeadecddbebecbeacdabaabaaecbbeedddcbabadaaaeebebeccdddeeeadbcedadaeceebdaecaedcbdcbdacceedcdcccdabebdcacaaedccadebbabdcdedeceddedccccabbdeecdbeadcbddbdabcbcbedaadabcbbdbcdeabaeeedecbebcacdeadcccaacdbbddeabebacbacccadadaeaeebdbcddbbdadbdeddaabdebcaaaddeebccbeedbdaebaeaceaababcedaabbcaceaddbcbebbddbddbdbbeeeeeacdddcbbcbddcaeaeaccaadabccbdabbbbabebcbbceaebcddbeaccadddccaddebddbbeaaeaeacbdbbeaeacecdedcecbecebccbbcbecdcdcbbccdaedcabeaeecbbedccdabadebbcaccebbbbaeccbccbaecbeeecdebcebdeebddbcbccaeccdcbdbdcdddeaebcbecacbaeaccdacdbcbccadeacdbcaecebdeaaacddcaaddbbeadadceedebabaaaabcebadeaecddeaccabcadbbcbaaaebbbbdbeeeebceddaeddcabdbaaeacdeaabadeabebedbcbaddbbcecbeaadbabaaaeecebbccbbdaeedebccbababaaacccecbccaacedabddbecdcaedaaacdceeccaddeadaaabcbededbbbbeedbedceddaecdabadaceaeaabdeeaddcdaedbbceececebbeccdbdeeadbcbedcdedccccccbddccdecdceddebeccbbeababbecceadeaeeecdcebedecbacbbdebbcbceaaeabdcbbdebdbddddaedbaabecdcebbacdaddbdbdbddaecbabeaedaadddecdedcccdbbeedeccbeababdebdbadccaecededeedbeccbeddaeccdaeceeeabaedededdacdddaacbbbaaadecbbcbebabbceaeebceadbdecaedbceacbbbcdeeeadbbbccdabadadcaeedbdeeeaeabdabeaeacebacedcbadbebdcebdeecedbeedaeeddcadabdccbcaaecbdcdebdeadcbbbebdebaddeeabeddadbcebdcdcddbddeddaeedddaaeebcdbadeceedbaedddabdccbbeeebddaedabadcacddcedabacedbeadaddeeedebbaddeededecebcababbdaeeacaacababdebdecdcbcccdddbdacbaceccdddcebaddbcdacedbedcaaeabbdabcdaddbacbcdeeeeedadedcaebdddeeccdaeadaddcaeedceceeebbdaaeaccbddadaeadeacbdbddebdbebaecdcaceececdcdbbeacabebeecaddacebcaccddcbebacababaebcaaabcebbbedddededeaeadadcbceaeebbaacecadbaabaddcdccdbbcdecbacadeeabeadcbceaeedaeedbcbdabacdcdbcccbabdedebcbebacddedadbdbecbaeaadaccacdacdebcaedbbdeebebedabaebdaeabdeddeeaaccdadbbcaedeebcadbbebddbdddddecbaaeedeaccaadaeddceabadeccbabaccccbdeccbadccabcbcccabccdbeeabdaeccbeaccdcacdeacbddadcececeaeeccbadcaccdcbabdabeddbdecdedddccdadcbaaecaaacdbceeeaaabbcdcdebebabedbbbecaacdebcbedcdbadeecaecabaddeaadaebeaccbebbcbdadccaddcadcccedadddbceabdeddedbaadbebbcaedebaccbaccddabebcbcacdecdabececceceedaaacbaeabbbaebdadebddedadaaceedeeaaabdbdabeceeaeaeebedbabcbbbbeababdaebcecaeebcaccacdecacacccbececdaaecbebbdadaaacdcdaabdbcaadaaaeaedbebdecbdcdcdddeabcbabbbeedaadbbeacecbcaebeeadaabddeeeeaaedaaabebeadadcbdcbaaeecaecddbbeeaaedcacebebddaabbbdeeeadbbaaaeacecaabaabdbcaceeddbeaebbbababcaecbaebbccaebbccabaabbeeebebcebabcacedadcdeaadebeededdabebdabbdebcbceccebceacceeabadeceabdeaaedebaceaacdccdbccbedcdedbecdbabdacedacddccdbdddeeacdceaaddadbbdeebbcaabcccbbeaeeaabbcddeabecadebbbeacabdddbeabaaddcdedacdceaedeabdbdbedebcdaddbecaebdcdbcdcdacabedeaedeaaccbdcabacddcebaabcaedbcebbbdbaeabecdbaaedbaeabeeaacacecacebceeeeaeebebbeaeddecdbbabeacaebaececbcacdabecebbaeddcbedcacaccdbeeaaebebcbbdeebdebbcaecdbccdabedbdebedbccebaecbceedddcddeeabdeaacedeaecaabeebdaabebaeddcbcbdbadedddedebeadaadcdddabbedccedcedaecabddcacbbdceacbdbdeaaceaabccaecaabadecddabccaabedaaeadddcebacceaadbcaebdddbccebeaadddebeeccecbdeadadaccccbadeccbbccbebeabcddadcdddabacebdbbaeebdbaaeaaebccdcebebbcaacdbcadbbbabbaeeeeedabaebacaedcacddbcbebdebccbabddbdceadebcbbbdcbeedeaeeebebdebcccbbdebdccceacdaaacecbdcddceeebdaeedaeaaaecdcebddadedacddaacbcabeadbbbededbdeabcdecdaeeabbccabddccbebcccacdbbcadaabdbabadeccacdeaceaabccaccdcebdcdbbacbbdcceadaaccddcedaaedbbcaccebcebdcacaebebeeaabcacaaccccdcbeadaceddcadadddbedaabbddbaedccccccdbdbcdcadeabddedbecaccaabcbbbbcbaebebcbabddaceddedceeceeaebdaedcdcaaccdcbdeadacdcccceecbccdadcdbabcdbbcbceaecdabcecebdccbbcbbdbcddaebeccdecbcabcaadecbabdebceeebaeabddecedbdebaaaecedcbcaaeacbbdadbcbbcbdcaabccdbdbdbadeaebdbaacbddecdaeddededacabcbbbbbeeeabaaacdadbecbbeecedebdbebcaecbedadbabecacbbeeaaddbcdbbcdaedddeebbcecbbaeaceeecdeacbebaddeacbdbaeaadbaadedcddbbabedcecbdaaaeadeaedbebaecbeeacddababbeebbebacaacebdacbaacedeacaccddbdaaaedaebcdadecccabceceeddaaeaebbccbaceddbbebddadcadbbeeebacbecedcddddacebcbdbddcadddcbcaddedcdeabcaceddcbdedecdbceaddbceeddedbcddababccaaaddabbabdbdbedeeadeebbdacdabbddeaebeaabdcceccaebabadccedacbbaaaacdbeaeaababcdbaaddabacdabdddbdadebeeedbaababceeddbdcdacacacddecceeccaeeacacdddcacbbebedacaececedebeddaedbecadceeccaeedeecedceecbdabbbecbcdbebeecebebaeeaceaebaececceeccadbacccdcbbddacecbaddedababdddeabdbbaadebabceebeeacbcabebbddeadbdccbcecabbeadbeedbeabaabcabccedaeebaddebccbeaeacdccdaebdecbaebdbbcebabccdadaaaededdceabdbbeacdeabcbdceceddadaabceebceedececceaeecadccececbedabcccaabcbedeabcecbddeddbbedcbecbbaecbcaeeebeaddbccdcadbedbaaaaaeaccececeeceeaecdeaeebecbeebbdbbcadebaaaeebbcdbdabdedcccddcceecdbbedbdcbccbdacdaecbebbeebeaeedacdbccbeeeccdbabcbccdedbaeebcdadbbcacbdaeadababdcdbdcdacceedcceccedcabacaadabaceedacedbdbadabbabbdbbccaadeebbcecacaecaebaedebdbcecbbdacbcaecbecdceaaaeacbdbecdccebeeebeaaaaedacebacecdcdbbcecbbcebbdaadcdcbcebaaaaaaecaebadbbddcadcebecbbebaaabdeeaccabbdaebaeeeebdecdeaaeacadeebdeebbebbbabacbccdedbdadcdcababbaeacbddadaacddeeedbbaabddabddedadedeebdebadbdeedbbddacedcdadaeaccedeaecaebebccbebbcbedeeaedaabbddbcbdbcccdecaedadbacdaeedadcbebbdabadebbccadbcbcdcdeaedeaecceddaeedebacdcacacdbaebaceeacabcdbdcbcccbabbbdbbbbadcbeedaecdecabecbaabbbcabddacdeccedbccdbcccbcadeaececdacadebabcbdabbebbbbeeabeeabdaacaecbccbacabecccabeabedbdeeeaeceaedebdbabddedadcccbacacabaaaacdbaccbdcddaadccedabbecdadccbdbbaeeebcdaeecbcbaeddcdbcbeacceebbbbcbecdcbccaecaebceadbacddcecaecbbbeedddeaccbabbddcdccdbcebdbebbeabaaaccabcbeecabdeaeeeaeedadadaabbcdbceeabedbeecdbbaaeedaedaeedbbdccbdceccabddececcbddaadcacceddcdacbbedeaeaecaeeddabaeeaeaacaceebecbcbebacccbbcbbdbbaabaeaaacddedeeceadebeabbabdececccadddcbdaededcdcbcedbaddebedcdbaaedadcdceccdbeacbbdcedcdecdedcdedcbaccbcebdeaddebecacdcbbbbddbedbbabdbecbbbedacbdbdddbeeaeacabaaabadabeadadadbbedbcbaeedeaaeaedcabaddbeaeddaabebdcacebaadcaadbbddebbcbdedeecbdacbbdecdedacdceecaaaeacaeaccbccecddbceeadbabceecdbeabbdebdeceadcbddebacecdaaaedeebadaeccdeebdbbeebedbaeeabbddebbdddaabededecceecdeebddaccdacbbdccacdbebdeadabdbacdceebbcaccdbabcecbcdcebebdacacebdcabaeccdecdeccacbcdbabcdbabcadecbbbacebadaacccbaaedbaebbebbeabcbcdbbdacddabdadabebaccbedebeaabedeebbbdbaadadedddbbbceaeccbaeebbaabeeaccaeedeabeacdeebccacdacccbbbcacddadeabeebddaabdecbebeecbdebabaacebdcadeadebbdebeaddadeebcaeddeedceecacecacccdabadceeebacdccbabaebebdadeddcabdeadbedecddccceecbebaebbaabecebbbaeedbbcabebebcadcdecaaabdebdcdabaebbaecbcdacebacebbeebebaceeccaaebecbeabdaaddcebaebacdbbdcdddbdaebbeabbebbccceebabcaecdceedcedbdbcecdeeebccedbcdeeeecaecadedeabbecbbaaabbadcebeeeecacabeabbdceabacebebcdccddebbecccaccacbcaecdcaeeacedeeedcedbccebddcaacacacdcccdbdeebbddddcabebbbccecacdccecdbdabcbbabbccdeadaecdbedeeedbdbbbeacaaeebaebedbdaddeadcdccebaedeaccbeaeddeaebaacdbcbccabeddeeddadacebdabddaaaaabcddeeaddcabbabaeedcadbbaeedeebeaaacaabcaaebdebacdadecceddbadbdeaedeaaedbcddbdabbdbdeecacabbceacacccdaacddabbbdddbeddddecddcaecbccbcadacaddcacabacadcabdddecedbdbeebedebedabaabecbcbcebdbeebbebdebceacecaceeccecbcccbaaaccebaaeecddddaadbdddeedcdccdbbeebbbeddccaecaadabedaeeeeaacbbeaaedbdcdbedcaadcdbeabecdebabcadaabbedbdaabbbaeeeccdceabcbcabdaeabbcaaaebddcdbbaedaeaaeccaebebcacabedabecdeecdbecbeaccdceaaecebbebceaebebbadeacdcdccddaebdadeadbdcddeebecbbbebabcebcbabebcacacbbecddacccaaabbceeccedeedccaedaaddaaebeeaeaaddcbaabbaeebbdcbcdcadcdaaceaddeabbbdabceccadbaacbecdcaeaebeeedababaadbceceadabadccebdaebabdacaaacdaddceceaaabdbddbcaccaabeedeecabbdacceedebceacaeebadcccccecdedbbadcaccecceadeaeabcecdddbcccbdedeebabcadbdecedacaddcaaaddbebdeadadeebcaeadeeccccbecaddbedcaddccbcdaaacbcebbadbccbbebcceceaaceddbeceaddeaaacabccdddaeaaeecddececaebaedecbedaedabbbcbbbedeabddbeabacbebcaaaedabeabaccacaecdcccbeeceadeccaecbaeeaaecdeaedaceaacacadbcbecaaebcddeacaddaabacbabadecebecaaabaadadeeaeeecdbeabadbadcbaaadadadbebdeaabcceedeacdadcbaaeacbeacdadaebaaeeedbeabeadbeabdebadadbecbbcbbadbcceeacebadddbebcabddddcddeaacdabddbeebaeaccaeeaeddeaeeebceabebaeceadabeecccbaebdcdeeacecccacddecbadbeabccadebaeabcabdeecdebbdacddeabedcacbecbaaacecdbbaaaaeccebceecedecebaeaabdbacbdacdbbaebeeaeedbacedacbdbdcbeaabaeaadccbbccdedcdebacaaceeaccbbebcbeeddcaabaeacdabeeabbaeacdadbbcebddccedebdebaddbdeaeccacedebbbedcaeecdedaadedbcdadaccddbaeecdaecabbebdabcadeceecdccecaebbeadeecaaeddbdbeaacecceeebbbccaaeeabeaaececdbddcadebabebcadecdeddedbadabddadecdbbcaabeececacbcacabbbbeacacbedeceeacacdbaceecbeeaeabadecabdeebbbedbcaacebeabeebdbedbdbdcedcabecdbbdabdededadeaaedeabbdcaceaecdeccbceccbdcaedbdaacecbbacadcbacadbbcceacabdcbbcdabbabbccedcbcedebdcedbcdcadeccabacadaddbdbbabaedbabcacaadbbaeecaaacaedabebeabcdedbcbeddacebcadbeacabaadcdaeaedbdeacbceaeaaeacebdadeecbcdeeecdcbdddddddeddedddbcbecabdbbccecabeeaddaaccedceaabbebaedbbedababdcbdbdeeddaccebcecbdddbcdceddbbaccddddcceeddddaacacbebaabaebbbecbbeaababaeedebceebedbbcccabbdddbbdddecbedaeacbcbcebcbbddcbaddcbceebaddacccebaaebeddaadbebbcddcceccddbacdbeceecaadcaeadbecedabcbddebbddacbdbadddadbcbddbebedccbbabbaeecaacaddcbbeecbbadbedeeaeccacadbbdbcadaceecbadbeabbdbabaaaaecbebbdcdadbaececaeeddcaceedadbcdaaccdcdcadaadcdbbcdecddbcbecaecbddeabacabdeadbceecabeecadcaadbecddeeeecabeaaedbcaabdaccaadcacdeacccaccdbaeecbacbbadebceeabceedacabecabcdcaabebabbdbaeccadacbdbedcbcbdbacadbbeeadecbcccaeeebdbcbccbdeadadabcebadceedaeddaedbabecddeebcabdcdccedcabedabadbcaaeacabaeabadeecacdbdaedbecceccbcebccaececadcccbbadbcaaacdbdddcdaecdddddacbbebddeaadecaacdadedadabdaebadcaebaacbabbdeadaecdeddaeadbddadbabdbbdaebcacaecccdbeacdbceddaaedeaeeeeaedbaeaeaabeecadcdbabeeebabdcdbbababedcebdacaccddeadbcabadcaabaaccaccbbdecadeabbbaaeacdbcacccabaccccaececeeacacadceaadbdacababedaceeaebddececacbcdddaeaabbbbccebccbdedbeadddecbdcbcbedbeacaedbceaceccebadcbeecccbbceacaeaddecbbbbedbeeacaebdbaacdeaeeacbddbaeacbbeddeaabbedbeddbaedcdbcabddebdaeccbabebebacdbeaaaaccdddddccdedadadabecbbbacccabebcaecbaecbdcdcbcbdedbbcaccdadcaadbeabddebcbcbecbececdbecabdeaedbedcedddeebaecddaedbeedbabeaaeecddeecbceccdddcaaedbeacabeaedeedceeececaaeaddacbadebaddcecbccdbeaceeabeabdbdacbbbedcdacedaecccdcdcdddadcdabdaeceacecebaeceaeadbacecadbddccceeeddcbcbebdeacdcdacbecacccbbcaadcabbaeaabbdbbceebacbdececedbeaecedaeebedecaaaadbdccaaadedbeeddabedccdddacacedaacdcaeccbcddcaebcbeeacecbeebceabcdecbaccaadddeedddbaecebcbdeebeedeadddeeccecbcacbaceaebadceaebedcbbdaebeebbebabcddeebacedaabcaaabbdaedbdbbdadbddbdbedcecacaaeecceadadddacbbccbabbeaeebdcdbebcbacdbbdbaeeecbdaeaddbaaeecdeadbdaedcccdbebbbddaeaeecaadeacebbbbbdbbbebbddbeccbecbdcaddbccdbccaedcbdedbeacaaadaddeccabecbbeabbceadecabddecbeecaeddbcabdddbcbdcadebbdcaeeaedbbacdddcddecbcbccaeaeacbcababbcaccadecbeebadbebbdddeababdadaceaccdbdbbecdcdbecebdcbabbddbeacdaecbabdabbddbdeaadaccdedcadaacdacbddbbcccdcdabaccdcdaaaabccadeeceacdbdbebbebadccadeadeeabeacbedcebaebbbdcddbabdbbadcebbacdbabbcadbdceeeaadbdaeebbcdbbabdbceaebbbdcdcdcbecdeccdddaebbacdbbdebecaacdadbbbaeceaadecadeaccbcccbdccbbdbeadcdaddcddabdaccaebddaeeebedbbcebbacacbaecebddadcbcecdbddebdecdcbadaadebaeaddeadabccdcbeabbcbadcbbadccecacbdacedbabdebebbadccdbddcbecdcbededaaadcaaeadedeadddaddaccceaedbccdbceebbaadecaeaeedceadbdbaacaaeededecedaeacaaabaeaebedeaddeebddddacbcaaedeeebaabcaeaaeeedeecdaccaadbbaedeaecbaabcbadbacdcbeeedabdcbbebcddecabdaadeceeaabaecdbeaedbeabecebeaebddacebcbebccdcdaebbcccdeaddaeaeddbcbacbdbcadecdabadbcddcababaeccabcbecbceadeecaecddeaebbaebdeebaaaebeaeddabdadcbbebddbbaabdadaceabdbcacdedeeccedaaeabdcaedaedcaecacecdcdbebedcaadcaccaeadbeceebdbeeddbcbbdeecaaadcddbddeedacdbdebddeececaaadaeeabededaecceaeacbcbedbaccadedaeeebebcabeadcbcceccccbbeacbadcdaadabebeeeeaddbcadddecceedadcdbecdbcacdeeadacbbcbebbddaddcbdabcadaacdeaddcbbdaacededecdadcabadccbcdccdbabbbbabecdbbaabadccadbaeaccbdcadacedcdcaedbcabbcaeecbdbcaacbaceaecddaeeeededeebbbcaeaddabbdcadeecdbcebadddbedaabcabdacabaebebbdbaabcadbcecdcedaacbedcdccabadcdecaebaadedaadeeebeedccbbccdadedbebebaecdabeaacbdaecbcaccaeceddabadeadcbcdedeaeeaadacceabeeeedaecbabdcbbcbbbbdebbdcceddaecdaeccdbdbabebbdadbaeadbbbcbbeedcaadaabaadddebacaddaedadbacccebeddcceaedbddddebbdbdbadbbceabcdadcdbcbccdeacbaaaeacedddaacddedeccdebdcabaeceebbbeacaebedbcadacebdeececeadcdccdaeabdeadbebebeedabcacaaeebdbdededbbebbbbebedbebbeebbddadcabceeaaececbbeaeaaabeaaeaabbdcceabdcbcecabbbabdecebbeeadbcebbbbcbeddcacaeebadccdbdddcabcdebdbcdbdeaadaddeeccabcceadcceaadcbdaecdcddccacceadddebbdeaccdcbcadadcbccbaadbcdacbcdbbabcdbbedcdabbbdeeaadadbadcdadaaebedadecebbaecbdadcdcdbaababcccedbddcdcbaaaeeceeeebeebeccabcabbdecaececeacddbcaaececedecccabbcedebccbdceddaedceeaeaeceacabebccbacdaabaebdddbedeceebaedbebdbadeeebcebcaecadadeddabdadacceaaecaecadddbcceabaabdbcadabdbaacbebbbceececdeddcccadceddedddacbbbeddeeaddbdebaecaeabcbebabebaeeeccdebebadcbeadacaebbbaeebebcceecbccdddebdbbcadbacbddebddbdadaaadccecebedcbcdcccaabcabadbbacadcdedccddcbceedbdabbaadbceeabdababdcecdccbecacebdbabeeeedaeeaceccbcbbbadbddadeededddeaebebbbbcbdebdbeacebbaccbecabbebcadddedbcdbeedeaedeecadbedcabeebbedaeeeaadaddcddbbcbaddacedbcbebdcaabccabaeebebaeaedadcdcaddaccdbbebaacabbaccaeebabdcccbcdeeeeddccbbddbaabeaadeccaaccbeaddeeeebecccbdcbdcedebaaaabebdeebbcdccecedabedcccebcbeaacecdcedebddcacbedebbdebadcacdbcabeedbdeecbebbeeecbacbceaeedcaadbeebebcececdeebadadedeebdbedbdddaccdbaaecdbdebecbacecbdbbdeddabbddbdccaaeedebedaccebdacdeaadeecdaabdbbdacccbbeddaabbbaecbdedddeacebbdeaeacaddebededcdeecbaddbebdadebeaddeacbeddaddbeddeabeebddddadcebbbcadadabeddbdaebdecaecccbccddadbaeacdabedceccdbaabdbbdcadecbcddddcdaeadabdedbbdcebdecbaadaccccccaeaecbbeedccdadbacaaccbbbcecadeeabbebeeabdcaedddadaedbaeeccdbaacedccaaedbdcedcbdeaebcdaeededecadebbaeaddcedddcacabaedebbddcababaadbeccaeceeacdcdceddbcbaaddadecaeecdcceccaceadccaacdaeaddeaebdeaaedbabcadedeaceeeebaeeebbadaaacaeeeccccaecbeecadccdaebbbecebcccabbebcaccecdcaeaabdeaecacbaeedbdbaaebcccdebdaceddbbdebedcaaebbbbeddeeeaecdeaaabcdbecdbbbaeecddecaeacadcaedacdbccbeaabdaaeadaebbdabcceddcddbdaeaaccbbbacddccbdaedceeccacbdeacedeedabeceebbbcebdbbbedcaecaaebbbecedacabcdeaccceaedeecabdcbcecedadabadedcbebbeaceccdebcbabcebebdbcccebbecadabccbdddcdbeccdaebccaacdeacbdabaceaacaabdbecedaceaababbaedaccddbdebbedcaddaeeceddbeadabbeccdcabbddddcbddeeaabcabaaddccebeeedabbadbceccbebdeeecbbdbacebecadcdebbdeccbeecddeeccddbddddcddecaaceaabbcddbedaeeecacccadbdededaceaeeebdcadaceabddebecaeeeeeeedebdbbeabeeceebedeeceeabadaceeecaacdabedbddcbeaaaceacdaaceccccaedceaabedbbedcbddebcecceabeacddebdeeaadeaaebcdadbbeaeddbdddcbeeeebadbcadaaacdbcaecbaaecbceaeebaaecebadbebebcdeeebecbbbdabaaecbaceecbabacbdccaecceaddcbebeccbcadeeabbcaedbececdbbacdeaecaecccebdbdbbcedadceaeedeaabeaddeedcbbeaebddcdacacddabaadcbebeaabaedadbaebdacebeaabbbbdbcbacbdaeaceaeebedbaadcbbbcccdbabeeaddbcebcdaebbecaeaacaeabdabddccbccdcabeabcdcdbcdecaeddabbbcdbdcebcabbabeacecececeecebecdbacdbdedbddadbbcebbcaaaabacaabeacbacacdbbaaadccebacaddcacdcbadceddaeebdaaaaacddecaaacaeceacceaacbbbcbeeaadeedecabcaadddeedcbdabadaabddddecdadcadebacbbebdeebaddcabeecbaebeceeadedebdbbacbaccceaeebaebbeccccbcdaecbeccddedbcdeeacdacdbadeaceaedaeacddbcaedadbdcebeeaeddecbeaeebdebdcacceaddbababaabeeaeacceeadcddcddeaadecdebcdedcbcecadabcaaacaddbecbeecebdedebdccdaaccddcbcabccbcddbecddecbcbcbedadebacaadccbcedbadacdecacdbbdcdaaabddccbebbcadabcdbedcaabcdebcaacceadbdacbaebaeeaecaadddccacbaecaedbdecebcccbddacddaaadbdbeadeeacebcadeecdbcceadadaceeaaebcbeeccdccaabeaacbcbaebdacaeadddbbaccaaccaaaeceeabcacedbbebebdbaaeeaeabbacedbaeeecaaeebaabadbddcadcabbaadbcbecdeaebcddbedbcbaedcaaaaedbacbbbdbcbdbdaaeeaadadabbdecdbbbededcdbbedecdceaebcecdecbccebabaeacbaddebbdceeaadbcdebdabecaeceeeccdcdaddbbcdeabdaabcdcdcdddcaaeeabcdeeabcaaebdbebaeacaacaeecebbbabaccaadebdaaddbbaeadbbbddbbcebedccbcadedddceadebabbddceeceecdbdebbeedeccabcccaaecddbcbbeecaaeaaacdcdaeeccabaeecadedceedbacddaeccadacbabcdbecbdadeedeebeaceaaddbadeccbdebbabeebceabacbabaabacbbababaaccebdaaaeddaeaaccadbebbeeceadcabbeabdaddebbddeadcabcecdbbcaabecccceedabaaaebcacdcdbdcceedbeadcabeacacaedbedcdbaddcecbeddbeeabaacdcccdbceebadbbacbdeecdebaaacddbeaeceaaecedbaaabeadccdbcdbbaebebbdadaecbecddbecbeabddaecabebaedeadebdacabebacaeddabcdaeccdabbeebbcbdaccbadbecccaeccbebabbbbdebcdebeeaceeecbedccdcecbbebbaacaabdaacdaceededaaececcabeddcecaeddabcdbeaacebeaeedabddabdcedadacedebbceacebdeacdbaacdbaabdaccdeadbeaeeeadcddeceaddcbbbcdebecbbeabcebdeaecbedeedadbedbbeddabbabdceaccdcceddecbaaebeadbebbdcaebddaeceedeaeabaebbdeaabcceddacbdddeceddddbaabdbecdddbddabcedababddbceaeceecdbeeacaaeeecaceadbbbceaaabaecbdbabacabbedaddebbebaeddbeaadaedebcaedbedbadddcaeeeaddbeaceacabaabacbdabeadcecdcacebcaaabebeeeaeecabbdbbadedbdaaebcdeebcaedcdcccddeecbedaaacedcbdbabddcaceccebaaeaddebbaabacaddbcaaeecabddcabcdeeecabdeadbdaedaabbeacbbaceeaeebbbdbcaabedaeddbebeddcaeacaecaeadcbceddeebcedbbcdacdecbeedeeeaabdbceaeddbeecabdcdbbbbbceaeabebecebabcaaddaebcabeadabceadcdcaeccbcbdbdcbadaadaadaabaceeeddddebaeaccbeacdbddeaedbcbeaaadddadececbdeabcdcccadecccddaebcdaebbcabedadbbedacccbabedcbceecebdbddedcabacddaecddeadccbeeadadabeaaccabadbdedbeeddacaaeecbdbcddaaddcaaecaccbebbcacceaccebadabebcedbbbaeebccdbaadacddeddadcdbcdbbeedcaadbcacecdaebbdebdcacacdcbeecacaacbecbebbaadaccadececdbabcadcccbbcdcbcebcbcadaadaddbceabbbcdccdbbceeadccdbbcebbcdbaeeacaaecebdcddacbddeeccbdbcddedbceacdcdbeacdaacdeccccebbccbcdbcdbcdccadadbeacecceeebaadecdbbbeadccdbabedbbaeeeacdbccadadedccddaaaceecbbadcebadeacaedceaccaeaacaeacadaddacdcaacdbcecaecddebdcccdbcceccbcdeecdeeaaaededbaebbeabcdbcdedaecadededeebeecacdaabedaceecbacecaebebeceddeebedbaedebcbccbacddbdbdbaddceaccdcedecdebcbbaddbebdeaabdbdbcaeabcaeeeeaaedbadbbdadadcebdaedabcbccedcdddceaeaacbebaabcdcabdadeccbdbedbcbceaaddbbcaebccceecbecbeecbdbdcbeeeaaacecdeeeecbdbbaedeecadebbcebeaaaaecbdeedcbdecebbbeededbacadcabbebccaacccadadbcadadccecddbcecdcbdbcebabbbcbeaebcdadbcdaabbcacdecbdebadceebdcbddadbdaedcccaeaeaeedcdcbadadddbceeabccbedecdcdaeddecaedabadaebabaecbccabacaceddbcaddcaaceadaecdecedcbcdcccdaadaeccdceaddabbabeeabdedecbebbdeddbdddcdeeadbebadeaaccacadbbbecbbebacdbdeabcceeabceaaddadbecdaedbcabcbceedceccabedbabadaeeeccadaabacedcbadeedececaadbbedeababcaabceacecceedccedbeaddaadcabadecdbeceeadadaaaededddacdaadadddbabedebcdcdadedebbeaecdeaceedecbaabebebcaaddbeddbebabcdbddbadaeecdbbacaabcbedadacbccecbadcedecdcacaaeceaaaedbeaeeabeedcdddeedaebdeadcdddeadecdecbbaceeccbebdcbcebdbacccbcdadaebacebccbcdaaabeadcebacdceacaeabacdcdcdbecccdaaadabbbdcedbccddbeedbbebdebddeeecdbbeedeedaeaadddaccdedebeaceaeddccadedcbcbeccdddcecaaeedccddbeeebabeacedaceabdadaabebdaecadaeeceeeccbabdabadcdaaacabdbcedcadaadccbadebcbcebaabcaebeccadedaabdcbddebcacaeeeeededbaedaadbbcbbeaacccddcbcddddccdabbbccdbdddeacdaaadeebacececcabbaacebececebaeabcebcebbadaededbaabdebbcadacbaeaedcdaececcbacccdaeaacebcaeaebebbeecbbeabccaccbeebcadcacdbbbaeecabeeeaccaabbacdeabacabadadbeaceddeddaececdaddcdeeebccaceeaccdedecaadabbbedaaadbaebacbbbaacecaeeecdddbdacccecdeedabdcedadaeccebeaaeaeeaeabeaadddecbcdaecaabaedcaacaadbcacccaaacbbbadebebdaccdadbabeddcaadecaacbbcbeabcbcaedecbdacdbeebdcabeaaaacdbeacbbeeaabedeeedeecaabedadcaecccddddebabbedacdcbadcadcaebbcddcaeecabdddabcabdbceabaeedbcbdbcadeeaacedbdaebbbbacccbeeccbbaabdccbcbdcedbdaabedbdcdcaabadcaaeadbbebcabdceeddeccbaedeabeebbaeecdbcbcbaeaaecdccdabedddecebcedacecdcceacbbacdaaabbaddcadbaaeeaabeededcddacccbabdbbcdcbcbebbaddceecedacadacebdebeacbcacddedacacbcbedcadabbbededabbbceaeaabcbebbdddcadbeeebbaedabaedbaacebeaabaaacbdbebdbaceecbaadcdbadedacaadbbebbbdbbddbaacceeadbacccaecbebcebeaaaddbceabeacadbaebbeddbceebdaaebcdeedabeeedcdbcacbbdaeeecaeacbecbbcddaddbaeeebdbeacccdbcdbababeecdcddeddedcecbbacaacddbbeaacbbbbcddbecbdceaadaecbacacbecacabcabcbdbcdcbbeaabeeaacecbeacabedabededededbedbaadceabddabaabdbeadeeeeaabcdbbdeccabaaeaecceceebbcbccbdddddecbcddeceacbcaddcceeeebeeaaaedbcdaecbabbeeaccedcaccceebecabceebddddadbdcccebeeccbbbcecbcaeaadddabeeebcacbacdbceccbdbbaaeeaadeacdedeecabdccbbbcabbdcebbdebeceddedbcdaacaaebddabacdecadcedcecadbebbcbddabedbabeccceccaacedecbdcaccbedcaccbbddecadbeaeedbaceceedbadaacceeacdadbddedebaacdaceebdbdcbebeceecadccabebbccdaeebaaddcacdcbbacbdccdccecbddedebddeebcddecebdacaaceeacccbbeeaaecedadedebceaacdebebbbbbdaaccaaebdbbabbbceeebbebdccdaccbeddbbacadccacceeacebdedbdeddcddcaecabcebecaaaeaaddcbcebcbdacccdaeabebdecccedddddedbededdeeeadbeaddebcebaedcabeacbbbcdbddcdbbbdedcdebaabeadeacebcadcaeabdccacaeadbaecadaebcebeeecaecbacccdcebededabdbbbebbbebdbacddbbbbbceaecdabebdecabacbdebaadaaccaddaccbebcbeeabacdadeaacaaedabbbeaddbbcaedaaedcbddbecbadcebbbadcbadacbecbccdeadededaeabcedecdbcbebcadcabaceabbdcaddddeeceacccecdebccecbdbcacdaeedebbbccdaaeceebecdabeebaadcdcaebcdeecbddcaccbdcbbbeaaadecddccdeaedeaebcadcbdbadeeebcdadbcceededceeeedcacbbcbacddaabceeadbecccbdcebeecbbdebdaaabedceebeeaaabbedeaeebacacbdaceedbaddeabcdecccdcacbaecabdeaadaeebebadedebdebecbeeeddcaddbdbcebcacacecdebedceabecbcaddbadedcabcbddeabdaebceeeeebdccceccaeabadbeaabcedbdecdeaaaddbcdcecbacecabebddedcdbceebcbaeabdcbcbbeaccedcaeedbcbbebedecadeacceacccdbbdaacdabeccedbabdeebaaababaabadadceaeacdeabacdeebbdecccabeccccadeaddeaabccdcadeecbedbdccbcdcbadbbccedbbaceeeecabccdccdeedcbbabcacbaeabaccabcdeadeadaaccebecbedbcedccabcaacdedeeebacbcdadbacccaedcebaedecdeeeccbbdeeeabcebecbeaaadaceaddcdadedbbebbccacacdedabbcaeceecdebedeaaeeddbacbcddeabbdacbdbadadbedaaabceeaedadbadbcbadcadbabbecadedeeaecbacdcabeebbedaeccdeadcccddddbcccaedcaaacdecdcbaacaeebdebeabdbdbedbedaeadacdddddcdeeeabdcaedaaedbddcadccaeacaeeaeaebdcbdbaacebbddadebdaeedaacdcbdeebddcdecdbadccdceeeaddacaacdccedcadeedaccababdbbaabcedcecebcaecbaceadacaeedbbecccacbbbadbacadcdddbcbccdaadeadbaacbdebdceadcedcedaeacaaadecbcbdaeebdbddceeaaecddaadcaadeddaccdadceeeeccceeeadcbbcbccbdddabebedebceddceddcecbbaadedcdadcdaceecaeedbcaaaaacdadbeeaabbdedaeddbecacaeabbdbcdcebdabbebbdeaccdabeacaaedbabaebacbcaacdbcaacbdaaaacaccadbeeaaaedcecdbddeebaeeaceaeccdaadbcecdebdbaaadecacedaebbadcbedcddaebbaccaaebeeddaacaeaaedbcaceeabdacebaaebdacbaabadaeceddabaddbdacceaecadeceeacaaecccdbeeeddbaecbbeaddddebaacbaeaedeaccaddaeeadbedbbbcdcaabeaeaecacaddabdccaacedaadcbeddebadeabedbccbeaabebceebacaababecdeaeaabebcebeabdbedeeebcbcdddbbddededbaeedbbdccdbecbaaaeacadcbcacdaebdabaabaeecbeaacecbcccceeacebcdeaebecedbeadaececadecddeacebeacacdbcacdadcdabbdbaccabdcceddcdcbdabdccddebdbdeddbdbeebaddedacebaddebcbdaceecdedebebebeaabdbcbdabeacbacbeeceabdcbedbbbceeadbbecdceebbebaeeabdccccacdecbcdccaecedaeaaccdeedadecbbdcceccddcdeecbeceaedbceeebcabeceaceecabceedeaeeddddeaaeccbacedadbbcbeacabcaeebcbddcddccbebdbcddaeebadabeabdbcaadadddabadecbbddcdaeabbbebaddabcdbddbacbbebcebcbabbddbdbbbbebddcbbdeaedaeeeebacbbdaecbbaecebdbaaabacaebcaabcabbebeabacdabbbeaeacbabaecabbbeebbaabcadbcadaccedaeceacedbadabeaeccdeacaacddbededbbdbdbaadbbacdcaebededbcedcacedcdedbdbedbbecaebabeebbcabcbdeadbbbcacbaadebbaaaccdbdcedaebbedbabaeddeeccdbdbbcdcbdbecbeadaaadecbebdaddadeeccaaeecdddcadebbeedddbbdcdeadcebddbcdcaabbbaaedcddcebcbbdccbdbedabbcaebeaddbeecbbdbdadccbdddeeedbaccaecaaabdebcdecdcbaabaeaedccddccbadaceaacaaaaedacbadcbaccddddbeccaaaeddedbacdbaddabceaadcaaddaacdebdcaddbcebbeabbdcbeabaecebbcdbdccdbdaeebabdcbbbbacceaebdddbebbcaaacdbbdcbabaddbdcecbabcbaedabdcecbbccebaabcabedebaeddbedededebdbaaebecbbeeaadaddedaeeabeedeecbaedebadcbabdceeeecdedbdbddabedaeeaaacaacdbebebaccbdeeeaeadbaeddaeebcaeeadbdceaacadbdcaedbddadcdeebaaacabedacbbecbaadbedcaecaeabadcddccabadedaccaeabcbbbcaaaacdacabdabdacdeaadbbabcbacbcbcddaeeaadbcceecdeeecbeecedbbcaebbdeaddbdaeedecbeebbbdddbaceedcabcbcaabbbcedbcadccaccddddbecbcdadabcacdbddabebcbdccddeeedeaeddcacbeabedaddcaecceaaecdccddddceabdbbbdecbcccdedadddaadadaeeddeeedbbbebdedcceacaddaacbbccabdaabeaacdedcbeebbbebcabccadcddabccaeddecceeededeabcddadbcdcdcedacceebaeadbdaeaecbabeceadedeccceccdbcbaddaabaadbeaeabbcbdeadedaeacbcdaddbbadbadacdeaadbcabcdebcececbacbdbbbbabdeadbeebecbebacdbabddabceaeebbcbebbcabdceddbaaebebcdacadecbdbddceabeeeacaaabddddbaceedeeeeeddedacedeadacbdbedbbdeacaaadcbccbbebdbcdeeceabddacdabbecbddbeedeccdbebcabbcedbbabcbbddeaecadecbbedcabbecceacdeabadbbcecccaadccdddebeeecdadeaeeedcceaedeaecbeaabcebbbadebedabbbcdbccbbdddcccdeeaedccdbacbcddccaacdbdcadbeadabbceccdeeacbabedeacacaaedcaedcbabbcbbdbbbaccddaddcaababbddacdeabccdadeecdabadcebcedaecaaeaccabccebaabbcdedbbaceccbedcdeedaeedeeedadcaeceaddccdbbacbbdabacecccdbdeccbeeedbbaaadceeacaacbedaedbeeaabbcbdebcacaceacaaeabccaeeaaecdebacdaebebbbceddaaabddecbacedcaadcabaaebeeedeaaeecebaeaaebaccdbbbdbbeaebecdbecddebccbccdbdaadecbaecabebbedbdecbcbeddabeadbbbebeacbdbacaccaeddcedebeacedadecbbdeadceacecdadbadcdabddebeaabaacabeddabdcacbeddacccebcbccddbbaaebedebbaaaeeaecdacbcdcecdeadccaadddeebaedbebaddeeeaabacabbeabecdedcaaddeccebbdbbbaeaaebaadcbbbabebdebadcdcaedaddcddbbbadbeccabdbdcebabdacddedaabadcaabeceaececedcdcedbdeaadbcdaaddbecbaabaaddeaedcedbbcccdcccbddacdccedabbaacccaeadaceabbcebadcecbedcccdecbceadbbdadebbecdbbcbbcecceedaababbebecbcedecbeeecaeccbcaacadbdcacbadcccebaeebdedceaebadebecacadceeecbeccceeeccacdbdcededbbcbccebbabebaecdaabebdaebdceccdabcbbbeacadaacbeeeeeccadbcbaebcaabebebaacedccdaedaedbbecdebdabcecebedbbcabadeabbeccbccbeeaeebdabcdbbdccedeeeddaceeddaceeeaacdcbeeebdadabcdecbcbcbdadacecdabaaadabbcbeacbebcbcbeacaaacdaeadcbdbdadbbaaabebaceaeeccebdcbadbbeededdadedccbceeeabeaeecadbecaadceeaddbbcbddccdedcebcaaebcebadcdcebeecbaddacceecebeacccceaedbeadecdeceddbdeadabeeaecbeeccaebbecdcadbddecdaaecbcddcebdbebcbddadcbcececdcbacaedeacddbcceadbecbcabdeadbbdaababaaeadbaebaabeabdbebeeadbeadcddaccadecbeebaecccaedecdcdbdaaacdacabdbddecebdcabccbacdcececbbedddbbebddabaedbbbddacabcaaccebeabeeaadaeaedabecaeadcecbdbebecdccedeeaacbbcddcddbdacedbecbcdeecdacbdbabebaaedebabacbbbdbbadeddbaccbadbcaedbeeaadaeeceebdaeaccdbecabecedcacdeaeaacadacacadaaabcaacdadeeaabaddbcaeabadacadcaacbcaceceddeebacadceeceaecbbbdebdcbadaecaaadcbacbeaedddacaeeeaceecdbedcedbbedabdcedbebeedabdedbbddcdceeccccececacabadedbbaceaceadcdeddceaccecbeeeaabaccaceddcdcacbebbbcabdbadeabbdbbedcdebbcbedccccdcddecbeddebecddcedebaadaecdeebdbdeccbaeeacddceeabdbdddedebdeeccecddedcebbbcebdecdbbcacddecbcebcdcaaecddcccdcbcbcbcdceababcebaabdabbdaeaccccbaedbdeeecbddcecbebbcbadddddccacaedbceaeaddeddbedededeccbaabdadeccdbbddbadcaacecedbbcdecbbacedbdabaeacacecdacdadadcdeddaedecdaccdbbbeeccddcbeaabcdacaecadcddbaddbcbbcbcddeceebdeeebddcedcbacbabaadddaeeedbebcbdcdabbbedbcbbbadcaaeedaaccedaccaceeaabedcbcaabcdabbbeccebdeeadbceaacdceccaeaadbbbadaabacdbaaaabdcdbcadcdecbcddcbeeabacacddedddeeabdbbbcbddadaabeeddbbbbcedebebddebddcadddddaedbcdbdaeebaaadecebcceedcadcdceebbcabbeeadecbddcbadbceabcbdbadeddebecdcddcbbccabadaeecbeaedededdaaccbbcbcddadacadddcebaeaceeabdaaaaecbacccbbaebdcaeebabeaddcdeadeeeedcabbbadbaeaaaabcbaccdcdcedbebdddeebacedaabcbabcadedbcbcdcdacaeeadcebdcdbaaabdecedbdbbbdacddecacadddabaacadeecabaacbeaebbacecaccdcdabcbeecdedaedcbaeaaebdbbccbcddcebccddbbccabacecedeaeacbabcdcddbceaeacedcdbcebbaabbccaebebacddacecdbdbbaaadbccedaaecbeaddddbbbceeedccbbedabbeebdaaaccdacabceaaddcceadbccadcacedddadbcacbbcdabbbccdeecacbbbcbaddeacddcadaaccedaddacbeadaccdbddadabdeedcaacccdaabcabceeadadbdbeebecdcceeebacbcecedabbacdbcbbaaaeeeccaccaedcdbdacecdbedeabcededeecccdcedaaaaadeedabdeadeabdbcddcadcdeececdddceecacddebdedcacabeeededbdaddcaabaacbdcecbcadabeaeadacbcaccdebaddbcceebdcaebcecdecaccbcdbbddacbeecbaabeeebccbeaddddaacbbbbceaebbedaecaedadccebcecceaebcbacaedcebcabeeecacbedbdbccecdcadaaaaeeeeccdbecdacacbcabeeaadcecbdcddcdeeaeaecdaddeacdccaadeecdbadeeadadbccbdadcddccacdbadceaecadebaadcceecddbcdeadbcedadacbdbdcccdabacbdcccaccaccadabaeccbbcdeadcbcdcaabaececcddacccbcecaddaadadbbedaadddbaeccaaccabeabdaabaeaebcbdebeeecaeebedeeeabbbbcbbdedbbedaaabeaeadeeebabcbcaabbacdeebaeebbddadcaadebdacbddddbdcabdbceebeaabacadbeeeceaeadaabcccabcccbcadbdeacecabedddbaabacedcbbadcdabbaeccebeaaaccdeecbdaeadcbbeebaaedccacccaacebceacacaceabdbdeadebedaeecaecdeaeebedbeedeaaeaceebdbcebbdbcbdaceeabeecdedaeeeddaabaedacedadaacaaacbadeacacabaeaccbcaeddadbddebbcedbdebceecadebcececeaecbdadaabeebedecdaacaddcabbdeceddeeeedbdcbabdddcbdaabbdebbeabdacaedbcedebaeddcddbbaadaacacddbdcdaeeadabdcadcbabecaacdadaeaabddeedccceeabddbcadcacbbabadacadbcdeccdadbbcadaeacceaabbedccbaaceedecbbacdedbddeacaeecceadacaeddabcdbdeaadccbbdcdacebecabbeeeaebaeaaebbbaccadbedddadbdbcbcebdaaabdbaddaddeabccdeceadeacaddbeebebeedbdbddaecbeaeeeecedcaccaaabaaecdebabaadcabcaeeabaddcddacebaedaededbceebcbeeedcededcdacebcaabaebbbccadcebadacdeaceeebecabbecaaeecaabcddceeadecdeaedbadceeceeddaddbdbbcbadebdbdeebcccedecdccbabedecaeedaeabccbadedbadcbadaacdcaeceddadcedddcbdacbddecbbbddadbeaabccdbdabebbedcdacedcbdbdbaeddddcecbebedaadcbddaedbacaeebcebbacaaddeeabadccabceeaaaedbcddeacdcbdaabeeccccdeaadbcbeecaaeadbdeabdaacdaacdcaadeeddcdeaedabcbbebcebbccceedeaccdddaaebcdbbcbcebbbceedccdbcaeddaecdbaceccbedabdeaeabdecccbbbadbabdcbcddacebbacbadbacacbadcdecccbaebccaeecedbdbbbbdeedabaaacbbdaabaadceebaedbcddbbbbaaacbcdeeebabaadabdaadaceeacecdbdcdcdaedcaeabeacecebacedcaecabdcadcdacbedeaebcabbdcdbcacccddcdcaacaeebaaecbcdbeadaeedcbecbaddddeadebadabebdadddaeadbeeebdeacadccaccaacaddeebadbabcaebecbeaabccdedcdeeedadddbddecacaedabeebebedcadeccdbbdadaaedcbbdecaaeeacdeeddbadccbcdbdbaaadcaeedbddeadacaeaebedabcdcabebaaeaddbaebbbbcbdedaceabdeebcaeaaaeaeeeeaadacadeeebcadaacdaaeccaddcebebaadbdaaddcccbdcdbdccaabbcdecacadbecceacbdbadabebbcddadaaacbedcedabecebcebcbbabccddcabeebdccabaebcebbdcdcebccecbeabccbeabbdcadaaedbcccaeddaccecccdedcbbeecbeebccdbaaedeeaabadecacccedccdddecccbaddddeaeccdcdccdbebbecabdeacabaeaaeddceeedabcaddccadcaadebdcccedabcddcddcccbdbdbcdcececacecdeeedadedeaaabedcceeeebeebeceedcdedededdbecdddeaccbbaeabdeeaaecebeeeaaadedbeaecadedcecebadaecaaadabccdceacdaebdabbededbdaeaceadacbeaabedeaaeebcbeacadbcabadabebceebaedcaabcedbddcadccacdacedebcebdebeaaabbadecbeaccaccadbddcdadbaeaaeedcaeebabbbdcabcdcbbedcbeaaeecbabccacdbcbeaededabadabebaeaecceebeebdbbcaaaeddbcaeabdbedadccbbbdedaebedddcdadaadcceabdbaabadcecedecaecaabececdbabaabadebbaacabbdeecddcbcbbcbcddbedbbaceecccdcbdecbbcceeccbadacbecedeeaebdbdecbdacebecdebdedbdaddddebbbdcedcdedbbbbdaacadeebcecaedaceaceecbdcbbcdbebdceaabddebacbbdddcaadedebbcbeecdeadecbbacebcaacbddecbccebcaaeeeaabdaddacedeeceaaaabaccedeabdaeebccadebcccaeedbbcabdeedccebaeaebbbdbaecaedcdecdecdaedaaaedbbdeaaddadcbeabcacadbbcbceacdaedaecbcadbecbddaceebbebdeeddeebbecbdedbcbedbdbcecbebeebccaccadadabcdcdbdbcdaedadeeaebdacaabcedaaccbcddcbeccdebccecdadcecebdeadabaaebdcaaaedaeaadbababbaeeaeaaeaadaebbbacaedabbccddcdeeabebadbdadaebaacdebcacddcdacececeaecbaedecbdbabdedbbacbcdeeeaaadeebccdadbabcbaacdebadacdaeecbbaaaabacbdbbdbccabcccbdbebadcbbebaeccebeaddbbbceccacbcbabbabdabaadaabdedbbbbbaeadbcddacccbbebdddeaaebbdddaceccbebcccdcaecdcecdbcecaacdceddcebceaebacbacbeaabeecdaacdbebacbdbebcaedcccadaaccddcaeaeabcdbbdedebacbabdddabcbaeacddbdeaccdedaddbebbdcdddbececeaccacbadcaabacdeeaedaaacceddbcdddeedabbbabcaeebbbeecccecabbcebabdeeacecccbebedaebecccdcadeedbadbbababbdbccbeeedceebdbebeddbedbebaabddcaabbaddaecbeabedbdeaddadbaadccdaabbeadaecedbbabdbdcebcbdbaadcdebcdcbceedbbaddedbecbbecdbdabccacdbaabacddebabccccbaedcaddbeedbdbebedeedbddbeadebadbdcadadaeaceeecdaeecbbedbbcecdaddcceecbbcebccabeececedabeadbbdbecdbebaceaedabbcbbababdcdddebadbccacbacbecaeebacecbdeeeabdbbcbdeacbaeeacadaaadeaebabdeedaabddeeedcbbbcccdddcebcdecadebcbbedcaabcbaebcbeadadccaceadcabbddaaccdaeddedbecabcadeeeaecbbdecadeebdcbcbeaebdcdecbeddaedecaabddbabebaaddeecbcbaccaeedaadcdadddcbeabebdcebbbbceeeedbddbeaedebedbdcacbaceececaccedeceabdcabdbeddeebbaadcacadebabdecabdedebeadacddcedcbdacebcbeccaaeecdbadeddeeddaeabadceccceeabcdcdcddeaaedcccecbbcdccdaeebaebacccaeeececedaeaaaddedabacebbabacadccaeabccdccdbbecbadcdeedbdbbeaaceadecececacabdaaadcdeadcaaacdedccdeaceeddbacbadcdbdaebbcdacdcbbbeceeeebdacbbeeaacaaedeeaeedebdbcaebadcdebeaccecabdaabceccdcbddccbceaecbaabbebcedaebaddbdabdecdccbdebcedeceddceeccdbdddbdcebbbecabaaeccaeccccbbadeaeddddcceddaebbaaaecccddcedecdabbcceecbbcadeaabeacddaacededbacdbdaeaceaebecabebbbccbabebdcebadebcdeadeecacbacabaebaeacdaaddcdeedcdaedbcdabcadedeeabcbdccbcbdcdbadcabcecbceabeadbedbaebadecbecabbddcaebccebbabaabccccbdbadeedbcbceccaacaeaadabbacaacdaedeecbecdeabbedaacccebdcbbacdbddbacaecacdcdbeecbaceaebddbaaeccedeedbdddaebdeadeddbbdadedbbdeadcebbaabeeebdeabecaddbebabbebabcddebccbacdbdedddeddbcbbbeaadebeebacebacebabebecacaeabdecbcbadbbabacaccaeccdabebdbcdbeddaeebaececcbbedccecaacbddcedabbcaceadecabbbdcdddbeababcecbaecbaeebcaaebcaadbeedeeedadbedeacaaaaadeeabcdbeecabebcbbadccacecbdcbacecabacdcdacbeaaabbaedbabaaccbacdaadcbadbddeeedeaeaaacbbccacadcbccadebbedaacbeabccabbecdbacedebebcebcdeabceeebbeaaedabbaaebcaaedcadbecdbeeebebebccdceedcdeaebeccabdbbadecebceacadbcceeceebddabcbaedddbbecdccdabaecdecedceaeecabeecacadebabaecadccbacddaabbbbacebebcecdaddcceabbcebaceceebbcdeddbddceccbbbadbdcddaddaedbccaabeacaabecdeaedaaecaadccdaecbcccacebaaccbeccaeeecaddeadeaaeeccdabddbadaedcbeabebdbeabbadcecddecedbbbabcebedeaddcbaacaaacdbcbdbbaeaddabdbeceebbbcadbbaacaedccddbdaaedbaaeaabebcedceaeeacbbcadaeebeaadeaeaeaebeabcedcddadbcdbdbeeabdedecebecbbbceeadbdceacbcceacbceebabddcdacbdbdaecbacecebabecedccbbbceeeeeacebbaccbbdbddadbcecadddeadadcedcdbcaeccdaeeabebcdbaaeceacdeaddabeadbcecdbadedecadabeabdbaaaedbaedcaacadcbbabcaccbabaabcdcccbebceceaaebadbbdeadbcadcdeaacaeecddeadbaaeaabeeeddadbacbebadcdbeebededcaebacdddedaedebcacbdcbbbdddddbdcabcbabaabcacbaceecadbdebddaabdecdeedaeceebbdddbcbacbbbeccedaeaedcdadececaaeadacdccadbdacbeaccedceeadeaaabaaedaccbbcdaccadbdceabaadcaaadacaaccadaaaedeabaacacaabbaecdeddddebaccaaaecbaeacbdbdbcaabbcdeababdaaacdaadbabecadaedeaaeccddecbaadadecabbbeccbebeadecdcdbcceccebbcaeadcaeebecbabbdacecbedeebeeabbecadeccabcceecebaaaccaacceddbaeedaddabebdaeeddabbabecebccbabeccccaabaaebaadadeddbdacdeeaceacedaceddbedddacababebdbadbbbdaabcddabbbcdedcccbaadaaedbeeabedcbcddccbdceeeadacbacbddcdcaaaccbabdbecbecbbebdeaccaedeececdcccebbeeacedeadeebbddccabcbadaddcaeacbcaabdddeadbaedebdbcbbddcacbbbbcebdaaadebedadcacadcacdbadaeebaadeaedaaaebdaeeaeacdcadbcbaabcabceecbeadacecdaadcdccbaebacdcaacaaceccaacdabecebaadccebabeacdecdeceddccbcabedcabccbebadebaadbeedbaacadabbdacbbcccdbecaaddbcdccecdbeedeaacaddbadabbaabbacacbceaabeeebddedebdaeddbacceabdcccaebcccbeeddadecbababdededabdaabcaaaebbdcdeabeedaaceecdabebcaeaaedccaebedcbcdddeeeeacccdaeedcdecaaacedacecdedcbbceecbabddbdebdcbcaadbccebeebcdbddecdecbebdedaecbacabddcdddcccddcdedcaedbdeabddbaaedaacabaadbbeeeddccacbcbeeedebedbddccabceeeadcaedeebcaebceebbadcceaebbabddebbedceebcabbbececeacacadacbccccaeeededcedeedcaabdabeeaceebbdabcedddbacadbdeeebebeabecbdabcccdaddaaabebdccbaaecbbcecdeaedaabeddbeddeeecaaedccdcabdacddeabbcdcdbceddaedcddbdbbceaebbbdaedbeacaccdbdbebeebbecbaeeababdceddecdcccceedaaaeebcabedebabddeaabcbedaebbccbdadcbceacddaaadbcbaecbeccbeaeaeeacaebcecccabcbacceaddebceaabdcaaeabdeaceeebecbdbeedbebbdeddaeaadbcdbbcecdbaededccebababcaeeacddcabbdeaeabeabbccbacbedbebbcdebaacdbdacaeabeacaeabeedceedccaacdbcadeaeccedeebccecabeeaabccabbdcaccaeebeadeaebaccaacbceccadbaddbddacaaaadcabcceecbbcaaabcacaebaeebbccbbdbbaaddecebcdeaeaddebccebdceccbeabddeabccdadccdadbcabbcdcdbabbeeedbcadcbcecccecdbcacbbccaedbbdddcbbbaeededdbccdaeeebbcababadcebcceeacaabdbcccdbddbeeddbdddacacebacaacaccaccdebdbeaabbbdcbecbeceedeeadcaccceccaaabaeeeaddddbadeccceceaadbdbcbebcdaeaedcbccdeabacdbcbddaccbaeaecececabcdbbcdcaccbaabacadedcaecdbcecabebecdbaddbecbaebbdcbeaebaeecbedbbacbdaabbedcadcdecaedcedddbaecebcceaadaddaadaedadecaebeacceccdbdbbcaedcbdccdddaacabbeccbbdcedaadbbddceadabbacbcbeecedccbcebeaadceddcabdbeddbdcbaadcebdadccdadcceadceebbeeeaedbbaddedaaecdeceababcadaaccacbceaacbbaeacaaeadabddbdddaaadadceccbabeccddaceadcecabcaebdbccbbbcdcaceedccbcadeabedceeecceedeecdaacaececcbacaccedeaeaeaccadcdccebbbeeaebbdeecaeadddbdeadaeebdecaeabaaddbdaeabebcabcabeeedccebdbccdaeadacdbcccacdaaaadcbcaaadcaccedbbaeebbbcdabcecccbebaabacadecaeeaacbaceecdddebccdaadebaeeeedcabcadbeaeedecdbcbdadcecdbaebeaabdddbedecdadcacedacecedcecbcacabaeaebbbbadeebecbecedbbcabdceccbccadbdeeccdbcaaeacaaaadaceadcdadddcbeecbbcdecabbceecbbbeeadbdbeadbbbbdeebecbdbbaaccbabadeaeebcebabdcbbeabbddedcdbacaebcdbcaacebcbbeeaebabbddbdbdcdbcaaaaaababaaccceababdbaddecbaedbababedbbbcaaadabacaddbeebbebdbbdeddeababbbcaecaeaccccebdeeeaceadedcadccceeacaaacdbadcbedeeabeecaeaacdadeadbddbbdacacbaaadeebbbaeeaababdbbdacceaabaddaacedeecebdeadbbccbeacedeedcadacddcdabcdabcadebececbeadbdaddeaeceaeaaedbebacccbecbbbadccacdcaabdceccaccaedbccdecbaddaadbabcbbdaeeedceebbcdcceecadeeceecdedddaaceccbceebeccaedaedcbbaadcccecbbacecedabccbeeaceebacdeedceaddaebabbacadbdcbcbeeeceaedcdbebddaddcbeeeaeaeeeaacdeececbbececcedbcbabdcdcecccbbeacdcedbbdcebbeadaacaaaebadcadaaaaabdbbdddddedccacaceddbecabcbcabbcecacccbbaccedbedcdceecccebaecabbbcdabedccedadedabcedeaddeccdabddadabbebaacbccaadaabcabaeedccdbdebdbaaabddbcceceeddbaaebeeedabbeeadbadddadddeeeebaadcaaaebdbecbebdceacdcdeaabdaacceeeeaadebeeeeaceacabadbadcdeacbeddbbcbcccecdabbebaaecbadcaddebabbadaeceddedcdcbebdaacebdbcabaebeeeeabcbeabbecaeabeaceebdcebbebedebcdaecaceaebdaeaadcabbbaccdeaeedeeabebcaabecabbdadaceaacbdeaaacdcebdadbabceecbadcdabdabadacebaecbcdbdeddbdbbaedcdcdcbabdedbeeecceaedcdaadbaadbbaddbcdccccacdeddaddacbbddaccbbedabedebdbddaeadababdbdeaacebecbdebcccadecadbceedcbdcbebdecebaabdcedcbeadeeaacaadcebdbeeacaccbbcdaabaebcbbeddddabbdaeddcaabcbabcdedbdabceccaceeebebecaeaecaddcbabbebadcaaddebeddaedeeceebebbeeddadddecebebccdeeababcbbeccbeecbddabededaaacacebcacaebeccaeccdaacabebbdccbcdceebacabdcebbdcbeaaebeaaadaeacbdcbeebebdacabecbdadcaccbbbcabeabbbdeceabcabbadebcaebcdeddbcecadddebdadaacebaebceaaebbcacaccecedeebdcceeeeadaaabcdebbebdacbacaddbbddeadaedddacbbaaacddbedaeabccecdbccbcceedaeadedecaaaceeeececaaedccaeaddcdbabccbbeacbcbadbbecccbebccbdadacaedbaceddcbaebadaaeaaddecbcdabaedaaceeadddddacbdccebedaeddeeeccdececcacaccecabedcebbacdcadeacedabceaedbdeddaddaaadedcccddbcbcbaebceadebbeaccceedaaaddcadcccddcbebadbcbdaddbcadbddddceaabcbecbebdaebadccabacedcbacadddbbacedaabdcaebedbeceecaceecbdaadaadddabbcedaeadaaeecaaedabaacbcecdbaadeecabdcabcecccdccbcccaddcebdacacebeeeaabccccdbcecbdccbdeeaaadbeaadbadbebeceaabcdceaaaceceaceccaccaeedbdacbaadbebedbcebdccbeabdbbccbeedbdbabacdccdbbadabaacadaaeadededcabadbaabebbeabceaaabbdbacdceadaebebcceeeeceeaabdeabcebdbaceebcebadbbbeceadbbdbdaabbeabbecaacadbaecacebaabeedbbbdbbebeacabddaeadaaadcdcbceeaddcaecabcbadecacbacccccadccecbdeccecaeebdceaebabababeacaeebbbeebeceebabcdadadbabdddebaeeaebbecddecaddbedceecbcbccbcabaedecedabeaaceeccbaebbdddaccbeecacbbbdbedaadccbcbedbaddabdccdebeabebeaeeddedddcbdeccaddaadddbedbdcccbabdaabddebacccaaedcabcaceeaddaebcabeebcccadddeeacecededdacddcbdbdbbaaeeceadddcacbccaededaccabaeeddeebdeecebbdcdbdccedecaceccabdaaaaedccbbcdceaecebeeedbbeceebcecdebbbaacaeabbacbadeedcbdcbadcdccddedddedcacaabcdbbebdceecebadceedaededacbedacceaddddbbdbcbaeebbccbabddacbbdcebdaddecbadaacdbacaeaeaaddeaaaaceeeabbbdbbedceaeacdccaadbabaabecbdbeaecebdeccedeaaaebbcaacccacdedccdbddecdcadbadbdedaaddccaacbdeebcacbdeaeddcdcbdceededeaabbccbebbbcaeecddacbebddbdcbbeebadedaeaaebdeedddaeaddabbbcedecbcbecacdbddeaabdccddacababcbeeaddeeecabebdcdcadcdaabaaacbdecbaecbebaecdecbbeaebcbcaebbececddecbabeaabeddcadcbcccaaeeebeaceabdbaeaecebacaaedabdaeaeabeeecabecaccabacadebccabceccbabaacdeaaadcacbdcaceaacababbccbecdeaadceaeeebabeaabbadbcaccbaaceacdddddcdddceabeedeeccdcbabbaaacdabcdcbdacebccaaeddaaebebeccaabcdcaaeceacebaabaabdbdecebcddcdbdccdbbebedaadbbddabebbdbceeadcaabdcbdaacbcdbccabdcbbccceeabacbeabbaddaccdccabeacbcbaccacdebbdceabcbeeddaddceebacccebbbdcbaeeadbabdabeaeeceeebbcebedecacabacacbadcdebdcaeebcdacccabbbcecebbbdeacabcbddaacdedecbcebeaedebebeeeedbbcbacbbaabbedcecbcbcaeccdeaeaceecaeccaaabdecdeddaeadaebdbeabeaeaaacbddebabdabccebaaedecdcebcedaebaebccecdbdedecaccacababccceddbaeeeeddeeeacdbebeaacddcebcbaacaeacacaceabaedadcaaeadbaddccdcdccaaaebecdcabbaacceadeacddcaaaaeeacdeaddcbaacaeababccddabcaebddadeaedccbbcdadacaadcccaadddaabbccabbbbbddeebaabebcacddceebeaebaddabaedacabcaeeadaadabadcddecaddecbeaceecabdcaccccbceddbbaddbdbaaaebdeeeaddebbdeaaaceaacebdacdcdaeecbedccddaedaedeaeaddbbddbaebbbccaaaddcedeeeeacececccdcbdcbbdbdbbabacbadbacacacacbcabbbbbebccabdecacadaedbdaeccaeeedbaeabcdcedbcbeeeaebedbebecbbbccecaeeaccdecbdddceaccbeebdcbdbddbceebcaaceaddadecaebbecbddabadcdebeddbeaaeedbcbabcadbeadaeccecaceaedbdabceaaecaddaebdccdebbebbbebeaeedcdebdbdacddcebbacaaadcbabcedaeddbbcdcdddedbcdddabdebaacaaeadadeabebeccdebcedebabcbccdbceebecdaceebcddcdaaaadccbedcbebdabecdacaacedadcdeccaebbdeeceeaebabbbceaacadebcbdacabaacdcadceecbdeeabddbaaadedcacdcbdbaaacabccdbcbbdbeaaddadabcacceaacbacaccdbabecccebdcbcaaeaddecdeebccbcdcaebaaaeadacbedddccbedaddddeaedbebaecadbdabcebbcebcaddddbeaababaedcacdceaeaddbacaedbacddabaeeedccaaebdcadedeadaabddcdeaedceeabceaecaedbeaeeeeaddbedabedeceaedeeaedcaccadcddeedebdddebdcececeddcaccdcbecbbadbdabeeaddddceedeebaabceecaecabbdabaadecaabdecbebaeedbceaececcbadccedbdbabbbcbbdeabdebaadacdeabbdedcdaedbeceebcedeabbbecdceeaccadbedcddebaeacaaeaababcbecabaccdbbaceaeacaaadbadaeeabebdceecbaaaebaacaacaabbaeacedcaddecdaadbbabccbcdbdbadbbdeedabcaededadccebcbbddebabaaebacbccccdccbadebeaccecbdabcdbbcdececddbaeabededbabceadabcaaacceddcaeacdcdcbaececadbdecadbebeddeedbdadccdacebebaabcaaeabedbedccedaeabcddcddadaaebebdbbbdabdeebadcabedcabdeaaacdcaaabebeaaaaddbddbadedadddcceabcaabedeceebabbdaebceceadebbdeabccbbcabddbcaeccaeadcedcdadbcebeeebaeeeddadeacdceacdddbabeaddceacaadbddcaddddcacbecedeebcabadaababdcededadeabbdbddbddbabcebcccccbdbacdbaaaeddebecacbbacdaedddeebaaeeaaaacdabccdaabdbaedbdbaaeddbdbddaaadabedecedbcbabaddbbaeaddabaadcceedbdcaadddaabeceacaedcaeabdebacbbddbdcebbedabcecbebceedcecacdaecdceebaecabaaadecdccedadecedaebacebddeddebadcaeebaceebbcdcaacdadcabbdcecdaebceecbaadeceeebcdbeeedcdaeccabcaadacbecacdedcbcddbbdacddabccbccecadacbbceadbedeaddcbdbebdadbebeacbbccadbbebddbaebdbddbbddedbaebecbbcccdebdceccbbbabccedcdbbcbcbdedddaddaebbcbeedddddbdddcabeebbecdbeecdcbbbddecdaeeeacbeedbcbdaacebaaaaddaeeabcedbabddceedacceedbdaecccdadddacedaaddedcbeecbeacaceabebbcaeddbdbcadcccecaddbddedebddcebbcbeeacbdbcaaddccaababacccdebcbbcaeecdeeceeaecbaccebbddcbbcdeeebdacedeecbdbbaababcecddcddcddaedddceedceccbbeeeddaebadbccdbdbdacbabdcbcdecedcdbaedcdeedbdbbbcebbaebbbbbcdaecaddaecaecdbcbccaaaeeecdccccbaeecaadceebacdbbdacceabcbdeedbcecbbddaddcdaaecbededcecbcebddcddaaebcdadbcbdebdbabdedddeaabceebacdbbcecbcdccbdeebdabbbdccacbbdacbeadaccaadbaaecbeedeaedbaeedecedcecdcabdcebddeaaedadcedabcebbbccdecbdaaaddbdcdddbeadcedddcaedcadeadecbcbacacdccdaebdbbeeeebbdebdabebabebebabadabeccdeeacdcdbcddcaeacabaabceeccaaaeeeddbadebdcbcecebaddbdeccdacabaedcedabcbdbebbbeabccdabddebedeeabcdacaacbdedbcabcddbdbbcccdbaecedabdbcececcadeabaeaceccbadeecbcedcdecdedbcadaaddadbdacababdeddbcebcabccbabcdbccbecabecbadeaaccbbcaceaabeabebeedecbaedbadadbacbceadcceabcedbadaaadbccabdbedebeabbacecabedebcaeabdbadbedcbddaceccbebbabeadbdcacbebaaddccadbeaaeaaccecbaccdcebceabedaacabeabecaededbacdaadceebcdabdbcdccecacbcbdcbcbcaadcdbaaababbbaaedaaaaadedbceceededddbcdeaadadebedcecceebcdeedeabeaabdccdaaabacaaadcdbddaabbbcdebaadadbabdbeeaeacadeccabaeaeacddecbabeaeaacbbcacbecabeaebedadabacaeddddecdaaeeeacaeccddddecbeeadedbbccbddececcccdecaabdeeacaabadcdaddededbbecbccceddddccceebacdbbadbbdecdbebaabdebcaebabaddaaccbeeecdbdeddaaaeaaadaedcdacccabebcaabecaabecabaaeadceadcbcebedaddcedddbdeacbdccaddaadebdcedeededebbeaabaacedbabbddeacccceecdbaaeacaaecbddacbecacecebebbbdbaaabdaecaabbbaabdbdabccdccebbececcedcdcdceebbcadeedaebcebeeddcdcaebbdaccbaededabcdbcecdadbadbbeeeeedbdadcdeedadeaebdbcbdbecaacbdeebceaaadebcbacdbdcbcbebadddccbeeaeacecebaeedbbeeaccaebeecebaebecccbcebdecacedbcaeabbcacdbdadabddaadecccccecceeebadbcaaaaeebdaececccaeabdddbcacbbdcdbbacebdaecbccedbdadbeebdbcebbaceedddcbdaeecebbbbbbbcdccaebeddaadbbbbacdbcdbcdbdebbdadbedcbcccbbadcbcbbbdbcbbebbdbaaaabcabaeddacccbebcedeeccccaceddbbbaebcbcecdceaddcdedadbdecdadeabbacddbddbedbbdddadcecaceeecdaddecccbdacceadbebdeacabccbdaecadaedebbddbacbdecaeeeccbadaacaeeaecbcaecaebedacebdbdccadceaaecdaaacaedcccbeeecccdeedccecababbcbccaaabbbbecdbdeecccddeccbddeeaabadeccbbdedeedebbeabebeadebdddcaeccbddeceadecbadabccaaaebebabdbeedccdddddeceebbdddacedaccebddadcbaecabaececacbdedbeeabcbadddaaeccacdadcdbcaedeeacbedddbcabebcbdbaaebcceeddbebeceecbcdacdacebbcbbdbbaadeacbeeeeebdddacdacecdebdebeeeadccacdbebbcdaabcbaecccadbcccbeebadceaeaeebebddbbabccedcababcccebeddddccaeedcdaccacaabcdebbedeaacacabeacaaabcbdacbebabbcdcecbebdccecadaeaabbacdcdedcacaecdcbaaaadabacbabeaebddbecdbccadebccbddecbeabcbdeacbcbceeeedcdcddccacbaedadabadcaadacebadccdbbddaddbaacddceedbcbbccaacbbedeccbdcecbdaaeddcaabcddbdbeddaacdbbddccdbacdabdabdeddccdaeeadcdadbdcdeeebacadacbdecdcbbecccedacecbdbadeeaeaeccededcacedebbcbddccecabcebbbaddddedaccdaebbcbeedbecebeaacdeebadbcdbccebcbcceccaaacccaedbecddecbbecddadbbbbcadeabacbadcaaaececcacacdbadecbddebcccdbddbeeeacceccdcebeceaaddbebabeceedcddcbadedddeceadccaedeecacabcbbccaceceabbbecddbbaeceecdaaabbddaeadbcdbbeacdcccceabccbdeceeaaedcaecbdaacbabddabebdbccaeecbecdadddbaaceabeeaaeadddeebcaebbebeaabeebadaaacabecbddeaecdddadabeeecacdacaddedacdbbdeaebadbcdcbbabcabadbedbdcbebdddabbadcebccddbdebdbcdaeeddeebecceadcdcddecaaeddcbcbdcbacecdecbdecbeacacacceddcbaaaabbadcdeabacaebcddaddaeeabddcadcacbeddeecdaeedddcacccdeeecaaecdceaaabceaaaccadeaeddcebacaceadcaeccceeaddedacdbaaacacacabacedcbcdabbcdbdceecebbdbaeedadcdeaadddcacbdeeddbebcdcddcdbdbeedaacdcdbaaaaaaceedaeceedddcbcecdecdacccaaacaacacbaecbbbbedbbbcdebcbadcaaabbedebcbdbcaaddbbbcccacaebeadcebadacbebaadecccccdbadeeeecbabcbbcecdbedaebadbceeaaeaabdebcdcbcacddacadbaeacedaadaaddadecbcbebdeedaeeacbcaaaabeadbedddeacddbbbeceadbbddebceaddcbcacceccabbcddbecaacbccbaedccdbaecebddcdeeecbbbcecadacabbebcbddbbadcebbbdccddddbbbeeadcaacdeadacedbeccdaeacadecabbcdddbabbcbbdeeabacdccdadbaabdadbbadaddcdaadaecdcccabeeadbacedadeabcdcdeceecabdeeededbeaeeddeeeadeddeeccddbdcdeaabbbeadbbbdcebbaebdaceccbdddbebcadbbeeacbbceaadedbceaddbaadddcbadbeeecacacaebcbaabbaadbdedcdcabbbcdcaeaddcadaacaaecaeddcacaeebddbabbcbbeadcacadddebcacbdadcdbceeebdbeaeaeaababbdeadcabdecccdadecbbbcbceebaebdcdddaeddedcacceddedbbbdccdbabdebaabeeaaeaebebbeaaaebbadbbbadebabadcdecbcecaedbadcabedbacdababeddddabaddadcacceaceebcadcdbdbdebebbadeadadbceddadcddbabddabebadddcbacceaddaecddddaedadbbaebccacbbdcadceadcbbacaedddcceeabbaeacbecaebbeacdcdebedbacebbddeeaddeedbabbbdaddbddcbcaeaacceaedbeaebbcaaececcaceecabaecaebedcacdabebccceaaacbbcbbebdebeaddceddcbaeadceeeddaacbabbeecbeacbddcdaaacccadebdcebccadaabaabecdddbececcbbeaacbdabbadeeecacbecbcbecaecabddbdebcedcccaeeeecbabbedcacccebaadcbcaccdeddeeecdcecaddeabcbbbdeeddcbabecbacbccbaecddcaacaeecdadbacbdedbdbabebabccecabacacabbddeaaddceaaedcaeaedbcdeccebeaddbcaecedacceccdadbbcddabecbeebdebcccabbbcddaaceceadcacaacaaebabbcbeeaabebbbbdabcddeceabcbbadddbcacacddaebabdbbcbcbcbeaceaaabbaeaedbaaaedaaebebaaebbdecbbeabddcbcebdcadadbacddedaedddcabccdcddbaecddabceddddccceaabdbdaecddbacbbcbeacedeccabbdaaebaabdebaebacceaeacadddbecdebadcadaaecdecaaceaecddedeaabcaaabcdcbebbcaeecddaadcacdbaeaaeddadcadadaebaecdedebeccdbbdaedceabbecbddcebddadbaeaddcacaebecadcaabdcaabdebedababdcdaebccaddadbecbaaaedddcbbcacaaaaaceeddbdeaaeaeaaabbddeccdbeedcbeeacaeabcacbcbdecddbdcddeeddebdeaddebbaeccacbcdbcebeaeebbeaceedeaeebaddbccccbdeecaabdadceacacccbcdabddcbeacbcdcdcdedcbaebaaadbeabbdeeaddeedadceeeeeabebabbbdaeadbbdddccbecdcedbdaaebaaaabbbbeacbaadcbbdcdadaecaebedbddeeddaecbdaebccbaedcadcccdbbcedbabcbdccdcdceacbceabedbebadcedadcbdaadcbdeaebeacceeaadaadbaabaaddbaeecbdeaaadaaceeecdcdedeacaaeaabcdeaeacacbaeadccbebbabdaececadbaaabacaaeeebecdececcdcacbeecaeebedcaebcddaceebeedaeeedabebddeecbbcadbdcdeeececcbaadaccdbdcdeeeceeabcaedceaeededbdebbbccaddadeccabaeabeebaddacbbbbdccacedbaaaddebcabbcbccbaeaadabaaddbebbecacebdcacebbdcceacbcccacadeabededdbbeeeebcaceeeeaddeeeebacccaddeaedeccbbbeddedecadaacadbadbceeaaaeacccddacacbeaabadbbbdddbeeddbeedbdbbbbbbadcdeacacaeccebbeacecddcaadaeeaedcaabdabbbbcadaeebdeccdcdddcdecddcdabbbeaeaaeeadabcbebeddbeacaccdbdebdbbabbababadedcebbebbadadeccaededdadeacbdebebccbbcebcbabaeadcbcaeadeacaacddcbccbeddddeaabceacadaaeebbbddebbedbecdcabdceadcdddbdcbaddebabebaeaeaeecbcaddeaabbccaebbaddcbdcddaeebbcebaeebaececddeceddabeaebbbddbcdddbecdaebcdaaaecaaaeeadddcdaacedcaccecdbbdbcbdcaddaebabeccacdcaaccdccdeccbdeccaeecdcbabdccaeedaecdaabcdeccbaaedcaeeebebaebecdcaedeeddbebbeaabcaeececcacebaccaaeccbbebebdedcdbdcdabcceeaeadababdbbabdcdeaedcbedadbddcaddcaedddbeebaebbebddebcbcaadccbbcebdbbadeeedbbccaebcbdcaeaabababcedaaddaeaccbabbbaceaaabecbdbecaedaeddaaaecaaebebebdcdecebbabaeecdabbbcccceebaedaabdcbcbddcebdbbceebdbdbedacbbebeecdcabeddeaddcddeaeadcceeadceccceaabbbbbdbdbdbabbbdadbbceeebccdcebdaacccaadbcbebdceccedcbaeedaeedbdabccaecdadbccddaaccadcabedbaacacddcdddacdcbdeceddbbbebcdedebaebbcebcadcaceeabaecbaebeedbedcebcceceeedbbabcbbededabededabebcebebbeacadbdcacacedcecaabceebacbbeadedbbeedabdabddaadddaddbebdbebddbabebbbccdbebbdcdccbceabbadbaaddbcadbabcbcaebacadeebaeebebacaeaedeceebbbccaaecbebcebacddadbaaadeccccbadcbabbdeddadbacbbdbcedceaedeeadbabcdaeccecccddbbadeccecdedbddceeaadbaadaadbaaaacaacadacdbadbabddcaaeeddcccbadbbecbdcbdaebdddcbecbcedabdedceccbddccaaeecaebeaaedceebbaadeacddbbaccabcaceedcddecddaaddaeceedaadbecbddbacbedbaccdeddabddacceecbccedeebedaeabddadbbcaaceedaecdbbadebdebcacdeeaeabdddbbbecaebbeeedcebaaacbbdcdbaeeacceedceadeebccdaabecabdbbccaabdabbeddcdbebeebaacebabeacbdaadeadbddcbdcaacedccabbbbceaeabbceeaceeabeaaaedcbdcdcbeebabddebededdebbceeccddaeacebebdcccaaaabeceeebaeececccdadeaddbddeaacadbdcbcbbeacecccaccbccddccecabdbccecaccaeccbeddbddbadecbbbdcaedcbcedbbebbecdedbecaacdcebbddcaecebabeacbdbdcabaccbddabaeeeccaceddbadaeaaebedcbdaeceaaceedcbdedddbcaacaccacadeabbaaedbcdeaabcaeadaacddacadacedbacecebdccebcdadecedaebbaecbddadadaabdabdcbddadcbbcbbadaeabccaceacceaebcaaacceddaecdbdadceecacaebcaccebbbeaceabdceadbcdedcbeeaccdeecebcbdaeececacbbcacdcabdeaadeadeaadcbbbbeadbaabacaebcccbeabcbacbedcaabbeeaababececaadecdbaaaaaeeeabddceaeedaaeebbcebcaaedcdbeaeaeeacadcdbddddcbbeaabbdabaeccaeeedcacaceecddddbcaebbccaccddaedbaacbdbeacdbececceeabaecbeadbcaeeaaacaeeacaccedceeaebceeddccbeaddbabecbadceaebeeabadeacbbbbedbceaaaeabaebbaadbdccdeeecabacbddedbcecddaddaecccbacadeaaacabaedbedbadeeaccadecaeedbadcaecbbbeedccedddedbdbddbdaeddeeebcdddbaadccbecddbeabcceabababaaccdaabedddcdebceddccddbeaaeecceecbbccaadbdaacbceccceaaedcedbeabcceeaebaebcbecddccaebcdbcdbaaebdbcbeddccaacaeaeededbeaddbccbbcddedbcaeecccecccddcebacbbcbdaebddebabbeeeebecbbeebbcddadadecacdacecaaeadbcccbdbcbcebdcbecdaadabcbebeccdadebbcacaedeeebabeeadaacbaebdabccceccbacebeecdeaabdcabdeabacdeedadaccacecbcdaeadcacaeeeecaebaacaeeceacabdcabdebebdbdccbeadbecbecedcdebceeeceaeccaaabcbacacccbbcdeaeccedadeaaecdeebecacdcacbeaddddaddbaebdbbbaceeccbdaabbcbbdebbdbaacdcecbcabbaceebaeaabbbacdaabaebbebaecebccbbdbcecdabdeceeaaadbadcaaaaaaddacbbdbdabcbcdabcaaadecddebdccaadcbbcecddaadaebccbcbdbeeccccccdbbcdcbbdcddcaceecdcdcccadddaebbededeccebbcccbeeebdecbeaeabccbabdbbcccebeabaeccaeaedddaedcabddeaecadeaadeacddcbacecbbaabebdccedacdcaedeabaddcadcecaddeececdeaddcbebdbaedabbaaaadedbacdcadcbecacbbaebeecdbdadeddddeedeecdeddeeacbeaedaedcdeeaabbeaeeeabeecedbceddcceabdddaaaceabcabedeceddcbcaadbaabbdacbaecebaccbdbdacbdceebebebecaaaabebaebbccedaaaaeebbabcdcbbeeccebdcedbbceebceacdbdedbecbacdcbaeeeecabbaadcecbaaacaaaabbbdbdcbadaccbebcdabeaccabacadcddddacabeabcbecacebaeaddcbeceebcdcbebedecebdabcbdabeddaeaacbbdbaddcebacbedcbcdaabccdeaebebbeddcaeeddcbdbabbbcbaaecacbbcdccdbcadaedcdeaacbeaabceaaaceebdcadccccbabbceadbdceedaecaeddeaaeeebccbdbacacabacbbebebeacecaeccdbaeadbebabadcbdecbbadabbccbabdaeaedbecdedeadddbaadbdeabbcdccddedcbecbbdeaacadadccdcecacedeeebcecbbedccadbaceaaecedeeeaecaaebdedcbcedcdbbdaaebeaacbaeacdadeddaebdeeadaaaddcdccdaecacedcaeddaddddbdbedccabdbdeedcededbebdeedeededdbbbdbcbadbedadbadaaadedbccbddecbcdddbbcecbacebcacceeeccbcdaeddcdcabeadebbceeacaccabcccbacbdeacbddceadbedecbcacdcedbebebcabecbaadaeeabaccebbbabdddcabbedbaabbceeebebdebeeccbbddacceecbadeaebeccdcccdbaadaebceacbaecbcbdceededcbaaecabacaeabebceababacdabedecbccbaacedacdcceaceddaedbbbdaedecaadaddbcbacdcdbbeecbdbbdebcaaabccbcabedeabaaacaeaecedbbdebaaadaecabaecbedcccecaabceabaaabbdcdacebcebbcecabcecaaacbdaadbeeebedeeecaebdddaadbbaccababdaadacccaadccceeecaecdddcccdcbdceccacecbecccecabbeaeacdaeecaeeaaeeaabeeccbaaaadbbabdbeccdeeabbccddcceabacacbeedaeaaddcddceacbeaaddabaaddbdaddbcacecaecdaedabdddcabeabeeccdcabebabceecdabdcbcecddaddbeeccccbdceabceeeccacbbadaecbaddaedbcbcbaeedaecabdcbddbeddaedacbbcbdcdbaeecaaccdbecccdcebdeddeccceeadbeceeadacceebddbbbdeddccabaaaccdddbeedcaecedecbddacccecbebebeeeaecbdedbaeacaeecddbcdbccdededadedddabddebbeedabbcebbcdacaeeebdeabaeebcdaaedbbdccacdbadeaeccdbbbebdabddcdaedeebadcdbecbadddadaebeeecdcccabedcdcbdcccdaabcabaabcbadbdadeceadadadebdabadaebeadacdadcaccadeccccddcceccabcaeceacecbcecbeebeebbdecadbdaeebcaabbceebdcaabbbdbdbbdbaaadabcbadebbbddbcdedacddccabebcecedddccdcdeabeeccaaadecdabdaadaaddabacbeecddadbbeebbdbcddeeaabeebcaedaddbeddcabdaabcbbecdecaabedceddeacadbcbeeacdcaedadebcddeeabbbccbceccaacbadecacbeeccbdceccdbceecbcaaeabcdcedbdbbbcddbacbdcdbdacebdadedbbecddbdceaecadeeceddcbabdeadbbdeaecbbbbbdabdaeecbacccacdedeedcecaeacaaebecaadbeaadbcbadaccbbcbbaeacaeaaecedacabecddecebedccbccbdbbddecdabdadccbdebaeddaecdcdbabbbeadadabbbdceedcbbcecaabbdacbbaeedbdcbebecdabcbcaabebcddccaaedcbdddadeeebbcadabaedcbaecbddeeacebbecddaaceddaedacbdccbdcdebabdeeeaabeeaebdcdceaebdeaccbdebcecdcacaddcaddeecdcbdccecddbdaaaacecacaedeeddbcdbebbcdbcbeaecdccdbcbedeaccecadbaebcbdcacccecdddeceabceebbbecaabececccbeeacabbaabbcbcdbdaabeadbaeeaebacadddeeaaabbdcacbeadeceadcceddbdacabaebaddcbadceeacccbccabdccbebcbbccebedbcdadabdbedcaabcbdbecebdadedabbeecebadebeeededaacbdcdbddadcddacaddbadeedebcceccbcadeebeeaeebdeecaacaeccababeeaadbdbecdaeebabedabacababbedeeacdacceadcececdaadababdacdbaaceeadccdbebececeacdbbbcbdaabeaedcdedecceebacbabcbdebbcededdcbccacabeabdacecedabedaeeaaceabceaaebbbadddeedddeccdcebabdbabccedadbebcaeacecccabacddabebdedebcbedaddeeccdcbeeababebbcecaedaaeaddbacecdeaceaeeeadaaddeceebeeccacebaebeadbccbddbcddbddadbdcaabebdddccdeaeaaeedaacececbeecdabdabedddcaedbcbcaabeedadeebbbccbceacbddeaabadaadbeceedcdaaddecbadcadebdbceecbbbdbcdcbdbcbeddcaadcbdadcbcedbecaccaadeaeaaabbceeadebadcbaedeedeadaabdbedabcedeabbbedecedaaeacceedacbbbbebabbecddbcccbeaebeebeeddecdbedaabdcdcddacbdcccaddbebbebaebeecedbcebabbaeabadeddbabaeeaecbbceaecdebbdaeebbddcdeaddccaddcccbbbecaebaebabcabebcebeddcebcbddbaeacabeabaedcdacabbcdbbbecdddcabcaadaadebecedadabcadbeecdbadcdbdedbcadcacaeeeeaecdacebcbaaaadbcdcbbabbceeecedcccddededbabbdaaccaeceddcabcbdcbdddacebcbdeeceecbdcaedacebbeebddbbabecdcdaeeeebaacdceeedcbbbcebaacaceacaeecbabaddeebcbadcecbdaadcdabdbbbddbdbaccdacebebcabcbbecbadbdccbaaadabdbabccbbaaeaaeeeaddbddaeceecdeceddcdcbddecdaddee
accdbabcecbcdcebebdacacebdcabaeccdecdeccacbcdbabcdbabcadecbbbacebadaacccbaaedbaebbebbeabcbcdbbdacddabdadabebaccbedebeaabedeebbbdbaadadedddbbbceaeccbaeebbaabeeaccaeedeabeacdeebccacdacccbbbcacddadeabeebddaabdecbebeecbdebabaacebdcadeadebbdebeaddadeebcaeddeedceecacecacccdabadceeebacdccbabaebebdadeddcabdeadbedecddccceecbebaebbaabecebbbaeedbbcabebebcadcdecaaabdebdcdabaebbaecbcdacebacebbeebebaceeccaaebecbeabdaaddcebaebacdbbdcdddbdaebbeabbebbccceebabcaecdceedcedbdbcecdeeebccedbcdeeeecaecadedeabbecbbaaabbadcebeeeecacabeabbdceabacebebcdccddebbecccaccacbcaecdcaeeacedeeedcedbccebddcaacacacdcccdbdeebbddddcabebbbccecacdccecdbdabcbbabbccdeadaecdbedeeedbdbbbeacaaeebaebedbdaddeadcdccebaedeaccbeaeddeaebaacdbcbccabeddeeddadacebdabddaaaaabcddeeaddcabbabaeedcadbbaeedeebeaaacaabcaaebdebacdadecceddbadbdeaedeaaedbcddbdabbdbdeecacabbceacacccdaacddabbbdddbeddddecddcaecbccbcadacaddcacabacadcabdddecedbdbeebedebedabaabecbcbcebdbeebbebdebceacecaceeccecbcccbaaaccebaaeecddddaadbdddeedcdccdbbeebbbeddccaecaadabedaeeeeaacbbeaaedbdcdbedcaadcdbeabecdebabcadaabbedbdaabbbaeeeccdceabcbcabdaeabbcaaaebddcdbbaedaeaaeccaebebcacabedabecdeecdbecbeaccdceaaecebbebceaebebbadeacdcdccddaebdadeadbdcddeebecbbbebabcebcbabebcacacbbecddacccaaabbceeccedeedccaedaaddaaebeeaeaaddcbaabbaeebbdcbcdcadcdaaceaddeabbbdabceccadbaacbecdcaeaebeeedababaadbceceadabadccebdaebabdacaaacdaddceceaaabdbddbcaccaabeedeecabbdacceedebceacaeebadcccccecdedbbadcaccecceadeaeabcecdddbcccbdedeebabcadbdecedacaddcaaaddbebdeadadeebcaeadeeccccbecaddbedcaddccbcdaaacbcebbadbccbbebcceceaaceddbeceaddeaaacabccdddaeaaeecddececaebaedecbedaedabbbcbbbedeabddbeabacbebcaaaedabeabaccacaecdcccbeeceadeccaecbaeeaaecdeaedaceaacacadbcbecaaebcddeacaddaabacbabadecebecaaabaadadeeaeeecdbeabadbadcbaaadadadbebdeaabcceedeacdadcbaaeacbeacdadaebaaeeedbeabeadbeabdebadadbecbbcbbadbcceeacebadddbebcabddddcddeaacdabddbeebaeaccaeeaeddeaeeebceabebaeceadabeecccbaebdcdeeacecccacddecbadbeabccadebaeabcabdeecdebbdacddeabedcacbecbaaacecdbbaaaaeccebceecedecebaeaabdbacbdacdbbaebeeaeedbacedacbdbdcbeaabaeaadccbbccdedcdebacaaceeaccbbebcbeeddcaabaeacdabeeabbaeacdadbbcebddccedebdebaddbdeaeccacedebbbedcaeecdedaadedbcdadaccddbaeecdaecabbebdabcadeceecdccecaebbeadeecaaeddbdbeaacecceeebbbccaaeeabeaaececdbddcadebabebcadecdeddedbadabddadecdbbcaabeececacbcacabbbbeacacbedeceeacacdbaceecbeeaeabadecabdeebbbedbcaacebeabeebdbedbdbdcedcabecdbbdabdededadeaaedeabbdcaceaecdeccbceccbdcaedbdaacecbbacadcbacadbbcceacabdcbbcdabbabbccedcbcedebdcedbcdcadeccabacadaddbdbbabaedbabcacaadbbaeecaaacaedabebeabcdedbcbeddacebcadbeacabaadcdaeaedbdeacbceaeaaeacebdadeecbcdeeecdcbdddddddeddedddbcbecabdbbccecabeeaddaaccedceaabbebaedbbedababdcbdbdeeddaccebcecbdddbcdceddbbaccddddcceeddddaacacbebaabaebbbecbbeaababaeedebceebedbbcccabbdddbbdddecbedaeacbcbcebcbbddcbaddcbceebaddacccebaaebeddaadbebbcddcceccddbacdbeceecaadcaeadbecedabcbddebbddacbdbadddadbcbddbebedccbbabbaeecaacaddcbbeecbbadbedeeaeccacadbbdbcadaceecbadbeabbdbabaaaaecbebbdcdadbaececaeeddcaceedadbcdaaccdcdcadaadcdbbcdecddbcbecaecbddeabacabdeadbceecabeecadcaadbecddeeeecabeaaedbcaabdaccaadcacdeacccaccdbaeecbacbbadebceeabceedacabecabcdcaabebabbdbaeccadacbdbedcbcbdbacadbbeeadecbcccaeeebdbcbccbdeadadabcebadceedaeddaedbabecddeebcabdcdccedcabedabadbcaaeacabaeabadeecacdbdaedbecceccbcebccaececadcccbbadbcaaacdbdddcdaecdddddacbbebddeaadecaacdadedadabdaebadcaebaacbabbdeadaecdeddaeadbddadbabdbbdaebcacaecccdbeacdbceddaaedeaeeeeaedbaeaeaabeecadcdbabeeebabdcdbbababedcebdacaccddeadbcabadcaabaaccaccbbdecadeabbbaaeacdbcacccabaccccaececeeacacadceaadbdacababedaceeaebddececacbcdddaeaabbbbccebccbdedbeadddecbdcbcbedbeacaedbceaceccebadcbeecccbbceacaeaddecbbbbedbeeacaebdbaacdeaeeacbddbaeacbbeddeaabbedbeddbaedcdbcabddebdaeccbabebebacdbeaaaaccdddddccdedadadabecbbbacccabebcaecbaecbdcdcbcbdedbbcaccdadcaadbeabddebcbcbecbececdbecabdeaedbedcedddeebaecddaedbeedbabeaaeecddeecbceccdddcaaedbeacabeaedeedceeececaaeaddacbadebaddcecbccdbeaceeabeabdbdacbbbedcdacedaecccdcdcdddadcdabdaeceacecebaeceaeadbacecadbddccceeeddcbcbebdeacdcdacbecacccbbcaadcabbaeaabbdbbceebacbdececedbeaecedaeebedecaaaadbdccaaadedbeeddabedccdddacacedaacdcaeccbcddcaebcbeeacecbeebceabcdecbaccaadddeedddbaecebcbdeebeedeadddeeccecbcacbaceaebadceaebedcbbdaebeebbebabcddeebacedaabcaaabbdaedbdbbdadbddbdbedcecacaaeecceadadddacbbccbabbeaeebdcdbebcbacdbbdbaeeecbdaeaddbaaeecdeadbdaedcccdbebbbddaeaeecaadeacebbbbbdbbbebbddbeccbecbdcaddbccdbccaedcbdedbeacaaadaddeccabecbbeabbceadecabddecbeecaeddbcabdddbcbdcadebbdcaeeaedbbacdddcddecbcbccaeaeacbcababbcaccadecbeebadbebbdddeababdadaceaccdbdbbecdcdbecebdcbabbddbeacdaecbabdabbddbdeaadaccdedcadaacdacbddbbcccdcdabaccdcdaaaabccadeeceacdbdbebbebadccadeadeeabeacbedcebaebbbdcddbabdbbadcebbacdbabbcadbd