0
1
mirror of https://git.sb/baoshuo/OI-codes.git synced 2024-11-30 20:36:26 +00:00
OI-codes/S2OJ/1694/data/anc38.in

2 lines
488 KiB (Stored with Git LFS)
Plaintext

adccbcbbcdedecccdbdbeabaeeabebaddeddedceaececbcdddcddadbdcdcbeaaccbcdecdbddeeeacbaadabccceedcebdbecdbadcdddccecdadbcdeaeadbddbccbddcccebeecacdacbdcbcdddedcebbdcdebdddedbddedddcabdaadeedadeddbccecdcacceebddccbeecdbceaeabbeecaeddcababcaddbccabdccccdeeebebbdbeaebdacbacecbdecceebdbaeadbbbadedcaddaccacddeeacbabeccedaedcbeedcdbaaeddddeccdadcacaaeabecabbcaccaeacdadebceecbadcbbcaaadeabbaccbbcaeebcbacedacbdeccbbdeabbcdacceddcecaeedbeeacaabdcdaadacdebdccbcbebbaebadbaeaadbcdabadccdceeabbecedbaedabaaecebcbbecbebcaedcbdababdaecbdbaeccdbecaeddbecceadedbdaedaaebcbbecbebadedcbccbeebcbccceeeeaeabddedabecedbabebaabedcbcacdbacbeeebcebbcabeceeccedeebabcdbaedccaeebbeabccdeedabeaeebdbaecddacadbbebcebebaeadaededcacdedbdcaaabdcccbaaebaadaeeaecbebbdbdcbadcadaedbaecbcbbdccdbbcdadadeeaebedecdcebacbbbcecedccddbbdebaedccaccebeeaebcccdaeddecededadbadddcabeddeceedeedeabedabdcdaaddedbceeedbcebeccbdbeaeddbaedacedcccdbbcbcdcdbbabcbcdaababbcdddbddedacdaaeaceacbddeddbaddabceeadaebceeadbebdabeaeecbbbddabdeaeacbabeceacdabebcbbaedbebcdcbbbebcbeabacebcbccadddbeceecdbcaceaddabdabeeaacabaecdbbcdbddacbccdbeeddbbcbbedaaebbadcebacddacbecdeebecbedccabacdedecdbeacdabbddcbeeecebacacacdcbcdebdbeacccaeebbebebadcebbbaececedcbbaaebdececaebeacbeeababeccdbdddbebdbabaaaaaecaabaeaebdacacccecbdaaaeeeceaddeabadebbdcdebbbadcedbaaaddedcddaccecaebaceeadaeeecdccacbebbbabbeaecbbcddacdceadebdddaecdadbcdbedbaeebedeabddaaeeaeabeaabbdcdebcbcdcecdedaecaceebdcdececbeadadbcbeadceedeadbabbaabeeeeaeadebaddceeeeebaeadeadeabeceecabbaedcbbabcaaabbdcaccceeadaabacceedaaedcdcbbeeadcaaecdccbccacecdeabaadececebccbbbebbabdbcaccebbeeddeaadabacbaaeccddcdaaeaaceaddadbbeebcdcaeeebeabedcebbaacddedccebeecbcebbcbccceadccbdeeebbbaabbbaaceaaabbdabaeaebebdbacdbbccdaddabcaaccdcedcbebeaeebceeedeadcaacbacbadccbeeddddbbbaaacabeeabedcbdddebebbbceebbccacedeaeaaeadceedaaccccebaddabaecadaebceaecabcbeecabbdadceddbaceadbebedeceaebccaaacdaaeaaacadcaaaeeeddcdacabeeeadddbdceaececebbddbdedcdccadbacedcccddeaceeecbbadedbeaebacdeebbabdddaddbcceedbecacdecbdbbedeceaecbdbccabdbcbbaabdeabbdeadcccaccacaabeaeecddcbbaebcabbaaaaeceaaaebcdcaaeaacbeddebecaceaccbbcbeaddccdccdbacdaaddbebaadececabddcdacddbabbeaacaddacdecaeedabedaddaaacdeaecbabdebdbdacecbeaaebbbabbeadeccecdeebeeccadcaddaaebbccbebedccbbebbeebbbdebebebdecbdbacccaaceaabccdecebdbeeaeebeecceaeaddaeeabcacceeceaccabbedeaceebbdedaeacaeadeaabedebeceacbdbadbeddacdebcbaeebcaeeabcedceecdbdcbaacddadbbbecebdeaaccdecbdbdbeaeeaeaedceabdebeeacaacecbdebebacbabbdbbaccdbeeeaacdededecadbbbdaceceebecdaceabadaaeeeceaaaeeaecaddaeceedeaceadddbebedbedeeebaeaceeabbebebdaaabeacaaaabebeabbbebecadddeabeecdcacdccbcbdcabdddccddbbdecadbbbdbecceadedbeaedcbeeadbdbcbaedcedbcdcdbabbddddbddbccaaacceaabeaecaacbedaebaeceadaecadebdebdcbecaceaccecdabbccedbedcceaaacdbbcbcecadbeaeedeeccaadebaeaccdedeeeadeaaabedaadedcebdbbabaacbbbbedeaaaeaccdbadbedbceecdabcedcbedccbdeaedaebabaeedececbcdeededbececaeaeeacabcdeaadbccedaeabbebdcbccacdedaadeebadbdcdbaebeaeabddaecdccecaebdaaedbeaeacdcbdcedbadbdebaabaeeddedabbdecbdccdbedeadbaebccddcbecbbcdbdcaabceaadaaeaccbdddbceadcccbaedcbcdeccebecadcaeaeaddaddbebbaadaeabbcccacccebaaaaeadbceddeadebbceaedadbdabbdddbeaeddccdbaccdbcdaabedaabcdedebdeabbceaacbadbdebdbbdcabaadceadbabaecaaaaedebdcccaadebbacbabbbebeaeeccbaaabdccdbaebcacbadccababecdadaccdcdcdccdddaaaebdcbbdbadabdcdbbdcbecdcaaaebbaecbaadabecaebcdbceeeaeaaebbedaaaeedbdebecabdcbcdebabecbebddeaeedaddeeceeacebeeedabeadabdaaacdddeecabdecebbacbbeecbcedebebacddecabceadadaceebeeaddeebcdeeaeeeaccaaceabaaaccccbeacdaeacdeabaacbeedeecedaabeaeccbcedeaecdccbdcbcebeeaadcecebaedbbabcadbddccaebcebdddcdddcdddbececbaacebcbcaebdbaadbcdebedeeceaaaeacdcbacdbaddecdcdacccbbadedeedcdabceadacebbdbeaeeacbceeecdceaaaaabaddeceadeeedcabeeaddccdbeaecbaeeddcbadddeadccbddaedadeaeeaadebbbdeaeaebcbeaababdbabcaedbaaaaabaecbcbceaeebcaccabcbbbdecedbdcbbbcbabbcccebbcbddcccbdbadcecdcccddddeececeddeeedebbaeadebeeaedaebccbceccceabaaabaeebbaadcbcecabeccbceacebedbdaccaabddeacbdcabaecadeebcbebaaaeddacdcaecbdcbaabdbdcbeaedabeadcbaadddbecbeceebaceaecdbcadcedeeadabaebbdcdcceecaaeabbdeecaeaedddbccedcdecdceaadeabbdeaddbcaebeecbedecbdddedcbcebeebadecebbeacddcdbebcecdccbbdaccbbaecabccdbeeceadcbcbccdccebeaedbcedbeeaebebecaededeabbebbaebdaaaedccdbbdeedcedeecadadceacadbaaeddedaacbddecbddeeedccbbbeceaceeecaedeabdbbaabbcaabbcdebbdbabdbebbccedcddacebbcebeebdebcbaeabcbdceacebdaeededeaaabcbbaecaeedbddbbbcaeacecdbdcdbdecdbcabbeeddccbdddaeaddebebbdbbecdaaecdbbaeacbecbddeddcceccdeaeadbbecbbbaacdcacacbeaccccaeaccbbbabdbbebccaadacababdccacacaccddaceccbededdecaadedaebceadabacbaabbdebacbcbcadedbeaebeaeecacaccdddebaeabcdbebddcededacecdeadddebddaaececebeaebddbbcbcbcedadbeaaecdabedcceacddeceedecaeebcceceaeacddabdeabeccbdbacadbbadbecddbbeddebdabbeaeccbcdecaddaeedeccccaebaadeaabaecadabcbedebebbebcbddceecbdbbcdaecdceadaedbdcdecceddbecbdacaacacdcebacecadebdeebdecceaaabedcdbacdceabdaebdaeddcedcdcdbeaeccceacedecabeaabbedbdaebcabddbedcbbdadecadbeecddabadbecaaeccbdaaeeadaebeaebbdbcaaeadbacaddbecdbaeebadadecbdbdbbbbdcaeddbaaaaadcbbabbdbcbabcbcbeacadaecbecaeadceaeacaaddcccccedebebbcdbdcdccbccdcdacbdaaaddcecebacbcdcecdbbcbacbbccbaacdadddddaadbdbbbdbacbbaedddbbbeaadecaacdeebadbdaebadcbbdcabdcdceadccdeadbbeddbbaccaaeccebdbddddcbcabadbacecbbcecebcbeaedeaaceadcbdcddecdbaaadacebadccbeccaecabdbbcddababbcecbdcbceecbdeeeabeddecbacebaccdebcdecaedcadceeeeabbcadbabeaeebeedbcabedddbaccebdbdeecccdaceddbcbaebacdeedeadebeaddcaddabaccbbaecaeeeccdaabcecddcacddbbcaddbeccaeaaabcabdbbbebaeebbabcacecdbaacecdcaaabecebaeeaecddbdcbaaadbddbceccaeeeebedbcdbaddabeedccbcddbdadebdbaceeecedcecbbaaecbbbdebbaacdaebcdccdececacbddbbaccddcedddacedbbdcbebbeeddabecbccbaaacbcbcdeaeabaaebacaeceaaecddcaebcccbdaddaeeeaaadeaacecccdebbedcabbbbbadabeddbcdcccbdadbadacecedccadabbebacdaadbeeebeeaabcdbdeebaabeacbdbdaaedcdadcddebecddadabbcdbecdddaebbaadecceabcccbbeaddaacecadaecadedecaedaaeeeeecdebcebabadebceacbecddaabdbedcbdcbcceedaadccbbcaaaaceebeadedaadeacbcadddcadebddeabcbacaccdacccbabdabdeacacebadebbbebedaecbcbbdedebedebbebedaedcbeceecadbdcbbcecbbdaaaaaedcdeebbbedbdbdabbdeedcabdeebaeeddebadbdebbdbbbccbadcaebebddeedadaceabdadaedbeaeadeedcbdabacedbaedbbabecdacecdcbbcbdbeaaecbebdeccbdbbeeedcebecbbeadddcebcdcddeebcbbaabbdbdeabebbccbdcbdbeabacdcbcabedadaaedbeeecdeecddeebaaeaebeeeccabbeceecbcbecadbedecddcaaecddcaebacaaeddadccbccdeeeaeabbaddcbddebedaecceedacaacdedaaebdeccaadbddabeeaaabaddcaaceebbdebabcbcdbeddceedeabedeabacccdeedeabadbcecdceaabeecabddbaeaecdcacaaacacddccccbebcadebeedcdedbdeebaabedccdaedcdaaeeeabdbcdbbbeeecaaaaebdedaececdddcebbeaddaaccdcdcaeaeddbddbdaeaeabcbeaeaeeacbdcedbaeedcaeadebbdbbecaedcbdcadbebadabeddbaaceaebaecbdabdcccccedececcbcedbecdddacaeacabacadaedadcaabbdaececacaeacedcbaadcabcbaeebdeaaeccadeedebbdabcbecdcedeebeaabcddbbbdacabdcecccbbcbabebdacbcedabedabcddcbdedebebbdabcebbcdaddedbcaacdeeacdebdedbbddbbcccccddbeccdcecbbcccabedabeaedbcdceecedaacaeaeebeadaeaceeaeecdbdaacabcedbbadaeebeabcdadbddbecdadaedccbdbddecdeebececddedabdaedeeadaacdceadcededcabbdbdaddcbaacbaecebbcacceeeaddebaabebceedcccbaaeededbbebbadeaecdcbccedccaadcceadbdceedddcbaebedecbcacdadeecbaaaccbdebaeecdcbedccaeecdbcddedacaaebaceddeeeadcacabdaeaebdadbbcaeebeabbdcddcebbdcecdbccdcadcdcddaedbbacabdeebeeeccbeebdaaabcacdccebdddbdbbdecbbdababdcbbcabacadaadceaaabdcadbcaccbbecbeccdabceeccecdacbabececbdddeaddbcecadddaeedbececedcdacbbdcbdaceeeadabcaecdbeaecdeecbbebdddaeceadeeabcadddaebeddecaaddcaaddbabdbebcddbdcdecbcdacebcebcbecdcbabcdcdacdedceabbbcbbdbdabdaebebaaadbbbdcdabbcabbcdccabacacebeecedaeddbcaaeabceeaecedecbecaccebdacebdedcdeaabddabcabbaadcadeaabacbcedaaaeabcdbabbeecbbeccbcaebaccccaaaecdcadecccddbbdadbecdbbacdebcbbadcdabdaaeaeeeaeedcacbacaadcaddceadecccbabcbaecddbdeedbecdbdbdbddebcadccbcdedddaacadbeeeabaedddacdbbdeeccdbdcbadccbbeeadbcacbaccaecdcccadcbcadeaacedabcbedcdcecdcbccccdcccdcadbdddbdaeadcabcaccbaaadabedcedbbedbcddeecacbdabdedeabadadddedbeaaaedbbcdeabdddcedceaeedccbaadeacbedecbddaadeabdbabeeebdbcdcadacbcdaacbdcaabaaacccaaccbaadaabccecdbcdeeedaccbcabbcddecbbdacddcabdeebebdacbadbcddadbaabaaedcbacbddaaeaeacabbdecebbbededdcadeabbaeddebadedeabadddbbaaccaacdddcceecaaabeabcceadbedccabbecadbdccccbdabaeabdceebdccbbdcecaaaebbcacacdbaebbdbaddcceeacdcdabdcbcbdadbebddbdccbcedddbcebedcbebbbbcceadaabcadaecebcdbcbeebcacabaedbeeecddaaceadacbbedebbdaaacbbedcedcadcddcaadaebebaadcccbaeedbbaaabedebaeeeddebaaaaebeabbcccbbdcedbdceaaaccdaeceddadbedeaccabbcaddeacdbcaebeeeabaaedccecebabcebbadecbadaaeddaeeacbeeeaaadaeccbcdebebdaecceeedbaacebaecebbeaebaabdabcaacaccaaddadbcbabeedacbaeaedccececcdddccbacdbaeddbacacccbbbcbaddbaeebebcabcdccdccbabecdaabeddeabcdecbebaceeaeaaeddadabbbcabbacdebdacceccabbaebceecedeeaebebbeddabebeccecabceebdaaaeebdaccceeddbcabdcdbadcaeedbbdcdaaddaddededcdaeaceadabaacacadddbdddecaaececaacbceeeddbceaabcacabddcecaabccccdaeeacbccbdbbbababdccacaecbbddcbdbabeccdecebbdaebcadecbbaddeddbdedadeecbcebcebddcaabebbccdcecabededebaddedccdcbbccbbbbecdcedacedabcabbbabeecddcbeceebaedccddbccdaaccdbbabdcabbddcdcebaedeaceeaceecacecbccedccdddebeedbceedbbceddceeaaaaeeddbeecadcbaedbdadbbabdaedddcebeeedccababaeacceabccdeddcaccdbeaeddacebbacdddebeeaccdacaecadabdcddbccddbdaecabdacdccaaacdaecadddabcdcdadcdaeccccbdbeecccbedcedeeddadcddbeaaacabceebdbdeeabdbaebcbaceddabcddaddaeadbcddebdadbcdbdaedddcbedbcaadcbaddacdbaeecccecadddddedddcebaeebeeaacdddacbacbccabeecadaeebabcaadbeaeddaedcdeecebcadacdbccebbecebeedadedabdebadeebdadcaccdeaaceebdeddeeebadbdaeecdcdaadbbccaabccdebbcdeedabceedbbdaabccebdcdbbcddbebeaacccbcbdaedaadbbdcbbebbacacdbdceddcccddcdadcedaeedcabbccbbacebabaeeaacbebbacbdaeaaaddcdcbeeeaecedbbdeabeacdaaebbaabdddcedbcbaadebebedcaacadbcbdddbdbeedacecdacadedddeeebaabcedadeadccbcceddbacbdeccbacdadedadbbacaabecdcddbbdcceedcacededdcaceeadaaebdaeecaaeacdddcbdeabeddadeacdaaeaaaaeccdaecccadbcbecbdadbbcebdecebededaceaeebbbceedeeddcdcdcaedbdabedcabaaabdaadadadbaadcddaddaececbdbcbcebbaddacaeacdbaceabddeeecbbecbebebaacbeadbbaeeeecaacedcabdeddcdbedbdddedebbecaccebdacddadeccecedecbdabdeaedcdbecdbddcaaceabeddbeebebdabeaeeaecacdcbecdbdedceaaebdbbaececbccdddaeeaaedbdecacbbeeecabdbcddbaadaedeabdbebeeeabdacccdaddccccbbbcbbadaeadecddaceabaeddaadcdedecbcadcbeddbadbcecacaccbbcddcbdcdbecacebcadadddedcdddabaccedebdaddbaebcadeebabadcaeccdbbddccdbaebdcaeeeebdbdacadcbddbadbaeceabbceeccbdacdcdecdaecdaccacceeaeaebbeacebdeabbdecedddbeacdadadbbdaeddeaadbaeddceebcbcaaedbdecbbcbdaeaabecceceeccdbbacecdaaadbdcaaddabbdecaeeacdbaadddcdcacecddaecbaebbebdeeecdddbcacecaedaacbdeaddbbcebeacbeeacacdebdbdcecdadccecceedebeeebeabccabceeadbbccebcbcadbecbdeeecbbebbbbdeceedbabcccebacdbccddeaddeeaecdebdcbeebacabebaededaebdbdabbaaddabddaaadbacdeecedacabaacccedcecebbbdedabacaeedeabcbbcdaacbbadecabadecceddebcaceaeabbeabeabcaebecdaeacbebdddcddbaeeceaeeecbbbecdddececdecdcdccbcddbacaacbaceedceddddadbccdbcbdaabddeeebbebdbcbdebaadeeedacbcaabbcbccaaeddbeceeccceeebaddacceabaeacbaabcaacaadbdeebdeedccecaeabcdadabbaeabddedeebbbdbedeadaacbbceeedcbdeebbaebdacbceadbbcbbabccddbebbaececbdcbdbeebdbaeaaaccacccdcebdbbdbeeabdbdeebbcbeeceaedbeeddaacbadbdeaaebcbbdedabeadcbcacedeaacaacadacaccdaaecdadcaabdbcdebabacacebabcbbbebadebdbaacbceeccbebbbdddcceaaddacbdceaedbdbbbadacbdcdbcbeadbcbdcbbbaaadbddadeddaaccbdddeadbaaadaeedcadbceaccddccabeccedbdcdeddceeebcbcacbbbaaccbdccacdcceecedecdcbeaecddcbebaaabeaaccebbacdeeccbadaaaaaeaeecbabbeeddbaeabddbdbedabedbadaaabecbdccacbcaabaeaabbdcbbdababecedcbbcddecddaaacdbaaaeceadcccabaccabcbcacabdceaadcbaaecebaacdacdcccaaceadebadebbcdcdeccacacbedaaeabaddbadddadadbbbdbccdedacbedaeabdcbebacdabccdbecbeeeebabbaddbadebdeaacddacbacaceeccbedcdaadbadeacbdccabdccbbbcceddbeeccbaebebabddcceaeaecbcaebceabbaebbaaababebeddacabedaaddbababbeebddbbeadacdddcbabadcebaebbedbbacbddcbaecaceadbbedccbcddddeeddbcaacbacbacbbccbeaddedeebdccededbadaebdccadbeecbaecaaeabdbdceadbbbddcabeddbdcbaadaaabcebecbdbebaddcabbcbececacabbcdbeceeadaeaeebddcabebabbabeceebadacbedbbbeacbeabbaaabdaddecbccedcbbebaeebdebdacebbcecdbdebadcddaeddcabaabebbcbddddabcadeadeeaeabdccbbbacaddcdcdecaccaabbeebabeeeaedacedcaaaddebdddbeaeaedbebddaacccebaecdeedebccebcbdedbedeeaacddbedaddabcceadbbebaadddcadbbaeddaddeacecbececdecaabcdaecaeddccecadcedaecabaecdddbccbebcdcceadaabcbdabbabbbadedeccedadedadebecdbcdeadbcddebebcebecbaecbbdeacdececeaadaabdaecaaecaaebaeaaeccebbcdaabbacdacddaaecaccabeddbdecaccbaacebccabcdbcaccbbaecebacdccaccebbeaeddedacdcedabbbeadaacaeadbdaedbedcacbbdbdcbedcbbaebadebebeddabdcaadbaedddadeecedbcddcedaadabacecabceebdbadcabecbceacabcbcceabbddddbaeeeeedebcaebdbbbdaececdaedceecbbadccbbeecccbacebccacebaccbddcaebdcabacbccbbceabccadebebddbebecbcecceebbcbebaebadeaeaedcdbdadddbebccadabceedbcdabecdbddeabcebedcbdabddaceeecbdadeecbbdcedeeeeedadeddabbababeabcdcccadbbdaeddeeacedacbbebedceceedbcedbbcababacdeaceacbbebcacddceaebdceebcdcbbdedbeeecaabbebdcbcebbacdebbdddeaccaecdebacedaedabdababebaaecbdacdabbdebcdabeeccccdebeddabadedcebecdaddecabbdbbdceebbdddbacddcdbbecdabdccbcdeeedcceebedddedcebeacdbadccbedacdcabbabcdaddaeacdeeaccabcccedecebdbcabeccbadbbacebeaaeaeeaddacedbcbcbebebeabebedcbcddbeadccacaeaceadadddccbcdabbbabbccebdcdcaabebeedebcdcacbbecedabececaacacceddebaeacdedceaccbbeceaaeebbccaadcddcaeceeabebceabbccedbabaaaccdeaeaaeebeabdadabcabcbcdaaddebeadbceaddecaacbedcbecbccadaeabbeccaadcacdbeedebebcccbedaeccccdceeadbeebbecbcaaaedceeccaedccadcdcbdeaaecdeebdbcbabbbbcaddaaacdacddeddeccebcdcdaaccaadcdeceeaaaaabbaabeacbaadcbccdccdebdadabdccbebeaacdacbbadcbbedceaccdecdaacabceabebbcbdddeadadacacaddbedeaadcdcebdbacccecbaeceabeacddbeebaceddbabdbdbdedcbcaceadcacbecbaaaebaecadaddebecacdbacdeccebdebabecabedebcedbeeddedecccadadddcedbaeddeadedbeaeddaaaaecdeedaccbbeecebcaecdbaeebbbccbdbecbececcbbcaccddaadaecedebcacecbccacdedbddbeeacdecdeadaacadaebeacdecbeeadbbecebddcbaedbdedcbacaaabaaddbdaadaebacdeedddbceabeadcdcdeaecbbcdcdbbcaaaaaabbaeccbdbcdebddeaceadedddbaccdbcedeebbcbeadcaebcdeaebdbcbdddecdeaeaaaceceedeebbcbacabaccdcddebacdecceddaabdceadacaeaebcbebababbeddeabadcacebebbedadcdecbbcaceaadbbddbaebdecedbdddcdcceeccccaeaebacdaadcdbbeeebbdeaabccdccedacddaabbbedeebceeaebeccdabedcbccaebabceecabadbcbacecacdbebacddceedadbaeedccebbaaceebbeceebbdadbbaaebbbbcbaccabeaddbccbbeddaceabaddeacacbeedceabadadabebacadaacbdcedbadccbccedbeeddadbccbecddcacdddccbaebbcacecdcabbeecddeccdaaaacedbaccedecbadeacecbbacecbedbceacdcbecadaecdaeceabeececbddbdcddbecacbdaccbdcdaaabbbdedeabdbeedbdbebedcbceabdbbadbedaadcbdadedcbadbaccedaeacdbaabdebcbbebadcabbaaecdceaeecdeeabdbccbcbedddedabdeabcdeaeccaadaadeabdabbccbaeeabebcaaceedcdaebebcaeacababeacbeaeedebbcbbcaeeeababcbbeacbbebbeabebbedeeeeaaceddccbcbccacbeaeeadaeaadbaedaebbccdadcedaebcababbeccabdbddbdeeedcdacccebbcacddadedecdedabcbdcbccabcebeeeeeeaecaecbecceeabecdecbceddcbdcecdebebedbaacaedbaabdacabaeacdeeebecddbacecbdcabaaacaecabaccaaedeedecdaadeeebecbacabeabeccbbcbdcdcceddbbaacdbbcabbceaddecbbecedecdcdbbcccadaeecabdbedeaeadecbaccddbbeedadabeeedbcebedcdbcbcaedbcbdccbddbcbcbedabdcadbaeadeedcaabedcdcabaeebaeadcaeddeedededbdedbaddeeebbddaceadbdebbadabddeacbdeedebbaddbbdbadedbccbdedabdadecdabcbbdaabaeeabcabdeddabdbbddaedbccbbceccaeaecdddecceaccdaddbaeecebcebddbbebebedeedcbbdbabbddcdeaccdacdccdcebabaadecdbcacccecbeabcceaaeabcbbaacaedcebdbceadaecdbcaabcbebadcdbcccceebaeedccddbddcbcaaebbadceaedcecddeecbeaaeadeccbbbeeceeeabcbaeecbedcdbcbddaaeadbecdeacaaecebdbdcaeaaeacdeceaeaabecddbdbebabcdacdabccadbbbedaadabdaccceadeceeebcdbaceaabbabcbabdbbdcadbbcedaceadcacbcdcdbdcbbdcaacdccdebecddbeebcedbcebbaccdbbbddedaaacdeceaedaceaedddaabbaacadedbacdceecbdabcedccbadccecaddecdeaaeaedabedbaeaeaeaacedcdceeaceeeadedbcddbbaedaaedbeaccacdceabeeeabdeaeadbacaedbbadedaadbbaeebeaadcddceedecabecbcddabdbdcceeccdacbbdeabbdbcdabddcaaecdddaebaeedcdcaabbdcdeecabbddaaaeaedbecdcbcddabdedebddddacebdaabbdbdddaadddceecadbdbcacdacdccbecbeaadbadcccaaeedacddbceedcdcddcadbbaacbdcdabaedadaaccaabebdcbacdecccddbbadbaeeeebabccbeddecdacdaaabaebebdcedeaaebdeccacabecddabdaebeacadcccddddaabcacccbeddaeedeedbbbaeeedaeaaaeeebbadaabaacdbdcccadecdeacebababaaeeccdccbdeccbebbbcebabaeabeaadcaeaeabbeabdcedcbbeccccebcdedeedadedccdeababacdaadbdbcaedcdcebeebdcdbcbacababbeadbdcbdcdcdaeeceaedbbacceedecacdbbaacadbeceecccdcbecdcaadcaaadccadbdadbbecedaeeaeebbdbeeeeacbcdedaeeaaecbbabbdbdabaeceedbecbdbaebcaaadeaaeaaecababbbdabeeaababdcbdcbebdbacbccdaabeeaabccabdcbdcbaceceddbbcebaecbddebbcacebaecacdbbaebecdcbabacacebcbcabedcbddcdedaacaaeaeccadecdeaebcbcdbcbbadedeaebeaacabcdabcdeadadeebbabbbcabaaddbebdacabbdcbcaedabaecdabcaedccacdcbeeaddaedaebddaddaebdbaaebabbaceabddeeaeaaeedcddeedceeeceeccaeccedccbbaddabdcaedbcebadccbccacadaedbcececcadeddcbeaebaebdcdeaebecccdeaabcebbdeedcbdcbdebbcdecdabddccebbcabdddaabacedeedaeaeaeddedbaeeecddebbcdcedadacbdceecadccdcaeeddcceebbbdebbecebaaaabdbacbaedecccdeabaeddeebcaecaceedaecbcbaccebddceedccbabecdebcbaacedbaabbbceaaaacedeadaebeaecddeecdccabbeccddacbbecacceaaccebbbaceeacacedecabdccbccaccdadaeadcaedaaaeedecebeeecaeaeccccbceccacbbbdeedbdababecebebbbbaeacbaebedeaeeabedbaccbbbdebceadabdedabcdaadbeddabecbcabcacbdcbeccbdbbddebeddddeabbcedccddaaeaaebdbdbeceeeaeadccacddadddaaccddecbddebeddeabaebdedabacbecbaeaccecbaadaaabddaccdceacecdabeddeadaecaaddaecaadcedcaceceabdabcadcdadbcaaeacaddabdddcbebcceccdbbcaebeecbddaedaabdcbeaddedabacbcaaadccedbbccecbbacbaddcdabacecbdcdddbbeaacabceacddcdbceeeeadbbbeccddccadeddacaeabbedcaecabbcacecdaccaedccbeebdcbadbeccbbcececcdebcadcbbaabcbaeeabcaadceacdadecdddaedcdddeebacdbddaaaeeabedebdcbadcedccebbdacaeeadabaeccbdbdbecaedcdebebecbddccebcddbdbbbeecbdcdbdedadaacedaacabacccdebeecdedaecbdceacbcddacddddecaedebabbaecaebabcccacdbebebccceebcbdaecbedebbcedcbcebeebadacecbccbcdebadacebebebabeecdabbebbeabcbbbdadadcddaeedcddacebaebbbeaabeadddbbecccbebeccddeeeaacbadaebbdeadabdbaccbbbaddbcadbcadbacdbdcaaedccdeceaaedbdbcedbbbdebcecccbeccbaaadbbddddacddaeeedbbebbabcbbbadecaceccadbbedcecadceaddbcbcccbdbbecedccbabcaacdbcdbbaebdababbecbcceeadbadebcaacbbacecddaaabebbeabbbeccdceadedeaaebbbbbeabeebebdceddecbdacbbeaddcecebbbbddcaccebecbbdadaeadaebbabeaedbebcaadbcdcdeaabeaacaeaacdcadbdcaceddacaeecbdebdccbacccdbbdbecceccaadcdddeccdbabceeacbceadcdadccbacaaaeeecdbbdbaebeebdebaacccdbbadeebeacbcecacbdadbdbaebcdcaedbbacecddebbbeceaeabbabecccadecbcbabcaecbbcdbbcddeeadcbdeeccdcedaaaecdaacacebcadbadeccdeceedbcdaedcaedceaccbbaecaacecbbbdbdddbcbdcddcbdccadaaedccbccdbebadebcabebdbbabeaadebeceedeedbcdebacebeecdcdceecdbabcadebadbbaebecbdabdcdaddbeeedcecdcacdabeeedcddabcabdbaedbebeccdcdbdcadddcadbdbaeeadbaddaaeacecbceaeeabcdaaeeaaecaedbedeecdaddcceeecacaccbacebeedbaecbddbecadeaebdddeedeabaaadbaeecdcaaeacccedeededcdbacdaccdbbbdaacbdecdeddecebdeebbcbaaeaccedcaadcdbcabaecddbbbcbecbadaeeabdcdbeaacceacdbaccddbcddbdecddcdddbedacbdddddcaaeddadadeeebbcedbdabceebeebebeedacddcbacddcbcaecbcddddbaaddaaadbaddeeaaabdbcacebdadcbddecabdbcaadcdadaaadbcbedbbbdeacbdbeaaaeadbabbebeaebbeababeebdccaecccdebbdbceabeacabbdbacebccbcedcadabadaeaccdacdabccdacdebbaeddedbeeebededadaaecbeecceaeaedaccebdcbccacebbcccbcbadcdbcacdccddaddcacbebdadaedaaceabbcbdbbaacadaecadbdabaadbbdcbdbdbacedaeecaaadaedeeaeddaebbaaeeeeeddadabbdceeededdbabcaeecceadeddaebdbdcaeccaeaadeebdadabbdcbddccbebbbadcdcaebcaaaceddcdbecedeeaaceaddcadceaeddebacbbabaaabdbcaccbdeddbdacbdedbceeddbecdaeeeabdbcceccddacedabcccbacbdaaccbeaacbdbdadeceecdedecacacdadcbeebcedcdbabcebbaebbcdcdbaddadbbceaeaaedacedebcceeaecbbcbeebbcebbbcdbcbbabdbbbebddadcdecebdaaaacbaeaedacdaccbeecbddaccebadbeacaacdabbeeeedddbecdeadedaccccaabcaceccabdaabbebedceebaecaccaebdbeedacceecdcebeeaaedadcaeaeecaeebadcddaccdbcecacceddedbebaaedbcdadcedaaaabadcddeeeaadadecaaccdcceecabaddbacddadbaebdbbeaaaebdccaaebcecacababeddbdedcacccddabcebcbeaaeceaadbaebededcecbcddebaeceaeceddeeadcccccdbdcbcbbbdedbeaddbeecddcbdaabeeacdeabcecddcbebdcecbeeeedbdcecdcabeddeebeddaacaaacecdaecbeccbeeeececddaabebddaecdaddeacdaeccbcbacbcaabebcbdaecbecaaddaccdcacdedebcadcbbbcabaadbcbcbcdabebeaccdbaaaccdeebdbdebddbecbbddccaecbdccccbcdbdbbaacdceabdccbdddccdeaebadbcaacecbbdeeddbacaadaabeecceadcbaadaaccbcdbbcceeaaebccceacbacbaeccabeacbdcacdcaccaaaabdcbecedbadaaadceccbabbaaabebdceeededdbbcbbeeaaececceecadadecddacabeeeedeaabaccacececaeaddeebacdceeabbcbbbadcbdbabbbbdabebeecadeedbecdbaeebbdababbaeeacaedddccbedacadcdebebddddbbbdeebcbcdceeeccdadbacccdcdecbbeabeeeedcbdaecebedcccbcbcdbabaddbddcebcbeeaedeaceeddaededaaacdcaeddddaacbbdecbbbaeebbaaddadcbaebbdabdddacdbccecbdedaeabecbbebccdbcbcdcbcadabebbedcdbacadbbeabbcaeadcacbcdaeaaaeacdeeaebcedabaddadaeabaebebdceccddbeaaddeddabbdceddaeebbeaccdbeedddbbccbcdbcaeecbbadaebeaacbbbbbddcdcbbdddcecbdbdcebeaaebedcebababeaacdbdeccbbddaedaeaebecdaeaaadbaecbeeaadaecbdeaebbacebbddabcabaaaedaedeaacdcdbcebddbdcaeeaeeccceaacebdeaaccaedaccbadcbecebabdedccaaaeddcdebbceacdbcdbbeeddaabeacdccdecdcaaeddacdbeadbeacecdcebeeeceadbcadbaddcbbcaabbeaebaabbcddebaebeeebedadaebccedddcccbdeadbabbcccedbaaabdbdbcbeedccdcabbcadcaebdabddadeecbbaebdbabdbbccaaeeeecbacebcadbaabcaaaabddecaebdeaaadbabbbebbbabebaedeeeebdbecadedadeacaadbebdaecbcdcadcaebebdcdbaaccaebedbdbecbebeabebacedacbdbdcabebebbdddabdbeebebcbcdacaebeddaddabceacacddcedbbcdadeceacddceccbcececbbeababcabeddaceadbbcabdbbdcacceacbbaaaccecdaacededdedecadaedeaceddbaedcecbbdcaaeaeacacdeaabaeebcccebcedbbbcacddebeeadacbedaebaddbcdccaeddcbdadeadbacaabeaacbeabaaebdedaebdebedcceadabababdcbdccbddaddbcdbdeacbebacacbcdcabdbbbcabeddbaddeeacaecebcebdbdabccabeddbdadbbcbeadbcbeacaebdbbacacccbdceaebebecbcdccabaeabcdbeebebccabcdadadbdaddeeeaceebdccabbecdbdbdcbcebcaedebdacddecdcddadeeddabccadddcceaceabaaeebeeabebecadbbccbedceaceeaaedcbbcdbaeebecacabcccbdaebbbbcdbaededcceacbceecdcdbecbeeeeecebdcbacacddedecccacaebaeaeeeaaabdbcbdabbcadbdbeccccebadcceeeeadceceeaaaaabcdbbdeddccdeacaaecbbacdeedeedeabbceaecbdaebddbbdbbaaeccbcecbcabbacbbbdbeeeacabddbbcbddbacadcecdbbbcadaeecebbdaeeeebcbeeeeadddcbaeeaeddeccabdbadededeebbbcdbcdabeaeccaaecbcbbbdccecacdeeddcbdadbcddedbcbdcdbdcdadeddaeaeacebbacdebcaeaeddacbaceddadeacbceeaabcaeaddcbcbcccbdabaaceacdabdcccdabddbecdaceaddbbadddebdaebbadceabaebcaabadeecbdcccbbccaaecdbdedaedcabdebbbadbbeecbeebbcabaedeaedbbbacaeaabcecbbbbdeaaabbadaeaeacabccbbbcbacdbebdedcdecebbcdedbbebebdebeaaecebbedabaabbdadaceeebacbcddedbeeaeebcdcecbedaecadbcbdbdddbacaddbdccddddaceedabbceeceaddabadbcdbcbbbacdcabbaebdecbcaddaacbccbccedbedcbceedadeaddccccbebdebeedceeecdcebeeedebccbaaedbccaaaaabddccbdacaddabaeacbcdeeebcbbdcaaacceabcbccccbababeabcbabbbcbebcabdeaebcadbbdcaeaacaabbedddcedccbabaacdaddedaceabcaeaedaacdedebadcbcbdbccdeeeadbaebbdaabdabcbeedaaedbbddcbbcdaddbdbebcdbcdcabbdbcbcbaddabedbaacaddcbdaabdedcccdacbeabbabaecbecabcbecdcbedbceeccecabaeeddcedcecbadecabebecabdaeabeedabacbabedcddbccdcabddecbddcdcddcaceabbcaaeddaabbdcdbcbccdcdeccadebebeecedeaaabacdabddcaeaccaebebaedcdbccccdeceabcdddeebcdadebceecceceacbadbbbcccbabbdaccdddeddebeeadeebddacddeadcecdaddedddeeaeeccaeadabecebaeeedbeaaaadecaccedbdeaaccebceccadeeeaedcabcdbdbcabeecaccbadddabbaaacebddaabedcceabadacdeadeebedaebdcaacadabaababcdbedebacdbcbececbdeecdcacdbaaaddcdeebccbddbddccddddbecccbeddbbacbdddbaddbeabbabcebcedadbbceccadbbdaedbdbeaddabebdaaecabbdaeebbaddbbbabacabbccadcaccdecdbccedccaccdccabccdecbbdccaaebebdecddacdaecdcdcbdbddcddddbbbeeaaadcbececbedeabdccccadaeacedaeceabdacaadadcdaacbeebdeeacdcbdceccecbabcaaaccadbadddacdadcccbdbcceaeebdedcccaeeeecebceecdbadeaebdebddedcacbbdbeddaddcacddedaebedeeeebaeddaabceeddecdecabadbcabadaaedaceabbbcdecadabbaeaeeaeaecdebbdeddbcaadeeeddcbcdeecacecabadaabbbaececdcecddcdbcebebceacbbcbbceeabadeeadddbdabeaaedcddeaaecabaddebaeaadbbbecbcaadccddcdedbeedaaaadabcaeccdaaeecbaeebdeaabecbadadbbddeadeddbdaebeabaddaadebddbdbbdcbcdbebbbedccacbdceacaaeeaacabbbabeddceecdedaadeadddbbbcbcadedaaebdccddabbddbaabdcbbddbcabebecadcdaedcbbdcbeddbbdccdceaaabbaaabaeabdaaceacecdaabdddadadaacedeadddaaeedaaecdeeddbaaedbcbdcebbecadddcadddeadedbdaeeadeedcccaaddcbedbebabbdcebabedaecaedabaceeedccdcdbddeadcdcbccabddddcebeeeccacccccddeedeeabaeecbbadccaceaabcdbbaccccaebcbdaaabccbcdacaebcaacdddcccbbccabbeddbaccbebdabacaeacaedebacebccecceebceabadebdeccabebeddbeaeccabbdaddaeddbccddcabcadaeeaeaacaeeccdecbcaebcadadeadceedbbdeddadbbabdbeddebbbcacddeeeddcaacceeeabcacbedbdcaebecdeecacbddbbaacbdddcadbcdddbedbebdaebbeacccbabbdedcabbbcaeebadbdcadacbdceabbecddcddcededaeaeaecabbabdadbaaabdbbecbccbdebadbdaaebdbaebdddeadbdecaaeceecebaadacceebeeeecebccecddeaaddecdabbeadcecebbdbcccadacedccccbadddaadcaadbeccecabdeeccaccecaedcabeacbaaeaacebedbcdaacdbdebbeebbcbbedeebaccccbbcedadbcddceacaaebeeaabbbceacdbcbccabdadbaeaccebddbdeacdaeeabbaacaabcedaacebdbbbddecceebbddeccdccaedbdeabddcdecadbddaacbccebeabcabbedaabbddecabecbbdedcdcceaceecdcecbddbaccbeabdceececacebbabadbeedccabadcddeaaaaceeacaadcdbbaeeacaddabdebacacacaebcbeedbabeacbbeddabecbbdedadecdedbcdbcbcdaabdcaeaeecdbcddcabccaddeaaeacbeeacaeeadadccbcdadbddceccdbdbbeddbbecacedabcdabeacabecceeecaaccadaeaaaebdbeeadeaaacbebcdbccdaccadddcdcaedacbdbbaeabddacadadddcbecadbccaabedececdacaadabdcedcbeecbccdaebecebdcbebabddbeeeecabeeaaaebcdcaaddeacaecbabbdeeccbcccbbacbaebbdbdabeedacaadadaeccddbabcddaaecbacdecaebaaecbdebaadcccaaeececbdabdeabdaeceecedeeaaadeedceddbddbaacceceaedaadbeceddabdbbcdcebebbdbcabeccbcbcdbbbbdedeabebadbdcadbceaadedbadaebaaceecdacbbcbaedacaadaabcbbeddaaaabdeabcdceecaeebeebaedaeacccbabdeceaeaaaeddcacabedccdcdabeeacbaaadadabaaebddaabbebbedcbbcbbddceaadeddebadcbedacaddcdcabedeeddcbdeebdbeadbaecdbccaaaadadeaacabccecabacebabccbebedecdbbceaeabdebaedcbcddaadeaaddcbaeddcbeddbeacbeaebeeadeccdddbcbabcaebdaaadebbdaebeadabbcaddaeceeeecccabeaebdeebebdabdaecbadabdbdaebcecabbbdebdbcbdadabcedbdeecaeecdebdecacbdddcedbbdbdddcadccdebcdbceabbdebdaaadabbabbcbdccbdebbdbedecbbdbecdeddeaabddbdabbaccdcbeecbcaedaedbacabbcdbcebeadeadbaaedabdbebcaceddceecdbdcdbcbabaaaceabcebbddceaabbeebebddcadbdaaaaeecacccaeddecdbabdebebdaeaabbedbbacbcaecbdeaacdddebdbeabceccebdcabbeaedeebccaadcdedbbcbcbdedcabcdedddecabbebaaebcecdddbedcecbaebedabedbaeeaaedcecaceaebbcbeebdadadacaecebdcdcdbaadcbbccebceedbbbdcdeaebbbbcaecbceebcabadaabaccbbbdbdaacaddeabdcdebbcbbbdceacbacbacbeddaabacabecbabbcedebabecdccadcadbdeceeddedacbccbbddaabdabcdcacbbacededbeecdaccaeabbaeaecddbcadbddeeadbedadbbcdbcbcadcbeaabecbcecbceadcdcddbdcecdddbcebdddadebcecdbbcecbedeacbccecbdcbbcccdecedadbdcccbedaabdeedbacedcedbaacaaebccaccaceabdbdabbbebdadbadabcabecbdcdddaaadacbebcdacaeedebaebebbebcdcdbadcaeccbaddbceeaaccbdccdcbddcccadcdaacebddbdbdeedcddccdeebbcbeecbcdecbaaedabcaaceeedabaeaababadcebbcadaabcdceeedbacbbcebedddccebdddbbbecddadcacceeccabedcecaceedbdbaaaaccdccaadcbdaededadebaaeedbdcbcceacceaaeceaebdbcccbdebbbcccedececdaecceeaceecbbdebccbdececaddcdbbbbaabdceddedbecabaaddbbbceaddcceeabbaacaecaaabccacadaacdedaccdbcbadbddeabbbdabedebeddcbeddabbdbbaaeeecdbdadaceebddbcbcecdabecddcadacdbababadadbaedacbcacdeddbdedaebebdceeedbecadeedaeacdeaebcecaeddddddcedccdadaeecbabdbdbdeeedcaddedccdeeebeaadceabccbddecbddeeebceceaaabdbbdadaecdbacdceddbacbaeabedddedeeeecbaceabbedbeebaeccbeacbcaeaceedaaabbbaadacdeaaddcbbeebcbaeadaeeaccbcccacedeeeeddecbddcdaceaccabdabdeaecaedbabbdabdccaaaabeaabdccadcecaabcddbcaedbbdeecacceadaadacaeaeaeceeaecdedcebbebacddecdacccbdababbbcbaabdbcddbbcdbaaedbccedeacedcdccdcbeaacebebbaecacabadddaaaecadadbdadccccaaaebcaebdcedbebbeaeddceacbdbedabaebabddeceaeebbbccddccaabaeabeededcebabedaaaaadbaeeedbacabebacbedceedabeecadbcaddbedaabdacaccaabbbccaabcdeddddcddebdabcdabdeebddeabaebebdeebbbcbaaeaacebabceaccbdbdaebeacccceaecdeddcdbaadaeabdcedcacacdaadcdebdbeccedebdcabcbadaeabaeeeacddaeaaacddaebeeadeedaceedeeddaeceeadddeabccbeceadacecceccddabbaedeacaabeadddaeaaadeadaaaecaccbbcaeedceebeddeaebbbdececcadcadddbccabadccbaabacadecdbdbdbcbddcccbadbbaedaceaabdaaececdddbebcdabeecabebbdeaccabacbbdadbacabbcbaaaeeddbaabbcbeeeccbccabdaabcdbdecebcbeddebeeaadcccaddcebabcadccabcaabbacbdbdbbccdbdbaddbebecdecdaebdcdddebabcbdacaadcbccccaaeddbeaceceebeecabdbabeebebaadaebdeeebbeedaebbddacbbbcaaadbadedcdbabaecddacebeeacbadcacceababbadaaeecbcbebeaadecdcbcddcdebadaecdcebeadbdbbcacaabdbddeeaacbbbacbaddabdcdeeadcddbeeebacbebcbecbaeddbdaabcebbbeaceaeedcbddbbaaaaddeacedaeacbbadccaadeacdedbeaacaacabaacedcacebbaeabecabeaaeaddceaaeeebadeeaceaeaebccdacaeeeeaacaaceeeebecbcaeebeadebbacebbecdbdcccdddceaccceabbddaacceeabeecccdbcdeeddacdecdbeccbbeccbaeadaaecbcceaeecadccdebeaadeccbbeedeeaaeeabdbaeaaacbecddbeeedebeabebaabeabaceecbcbdadcabccebeadabebdeaadbcdedceeaacabeebbdedbdeeecbcbccdbdbdcebdccadbceebabecedeaebdebadeadadebbaebadeecbeacdaeedbddcccacdbcbadddcecdbdeeedbbcdbebbaccbdbbadaaccddeeedaadccdcbeddebbebdcebaadabadbbdbceeedcdadacababbbaddbadcddedcdeaddbadbcaaeaebcbeccedabaadbacdaddcabcadacdcbdaaebeccdcddabdaccdcaebbebdbbacbbdbbcddceedeadadeedeaccbcabbcedbacaaeedbbaccccbdcacaaebeabccecabaebedbaaedabaeeaedccadbabddaaaceedecbeddbbacbccabdecddbbcecbedebbceadeddeacdedaecbccdeccabebabbbbdeabdcecdeeaacceaddaaecdddabddacdbebedaccedbdabbccacaaaadeaddebdcbaedeebadbebbbebcddbaababbabddbdddcceaecaeeebcaadbcabbaecdabddceecbaedcceeadbbcdbcbbbdacadaacceebbbbbeeaaddababbcaeeceedaaabaeecedbeedaeeddbbaddadaaccabecbbdebbebebcbcdeecaaabeeeeedbaadeccbaebeabdccbcedbbeecdbabccaccaeacbaaddecccdebceebcdbdecaadeaabddbdaaaddcddabbdbaeadaaedccebbdecaddcccabaacbabbeeaebcebeedebeeaaedccbdaaecdbddacaddbadacebceaccdbaccdedecadeaeceadbdedbaaabdceecabeabadbedbcdeadabedcbadcccceaebdeaebccadeecdbcbdcbabdcbcedaaebeeabdaaedcacdbbbcbeceeaeeaadbaeacabeaeedccebdeacbbdbbcbaceebcbbeccdcccebcebeddcebbdddeecbaddcdacbbedceebacdccddabaadeecbcdadcacebaaacbccbdaaecbcacaaabbcabebacdcbedeaccaccddccccbacdeeeedcdcbedddadbccddccdeeadbbdeeaadaadabbcaccdddbabedecbbdeebcadddcceccacebdeceeacbccdbcbeeccdeacbddacdebeddaabeeacbaaedebcdbddceeccdaabeeaeadabdaddaaaadeceaebdcedbabcabceaecdbeeddddcaedcaebcedbeaeaccedcadeeccdbccdaaabeedddaedddddaaadcecaedaebecbbaaaeceacacececebbacbababebbaedebbbaecbcacddaccddeccdadceeedbaedaebaabdbdbaacdddbeaabdbcbaabbbaaadbabdcbeccbebedceadeeebcdedccbeadddddcaccbebaeebbdccdedbeabbaaccbececcccebdddcddaaceaeccedbaceabcabceccbeecdbedcaeadaadeaccbabaedadabcbdabceddaeeabcddbdaadbbdadabbecacadeeaacedbddbdabbadecddddecbeeeebdbbaaaadeaddeaedeacaddcbdbaedbdceaacbadbbbddbacdbceebceccbccadbeacbebedbbcaaebeaecbaacdbabdcbdaaadedaacbddaacebbebeceebcacbbaabbadebcabdcaaaccbbdaecbcebddcbbeedccdebadcdbabbdaceededdbdcbebaeadacbbdbcebecbccdccaeeaebadbeebaececceeabaebbcbccceccbcddacbbccddedeebceeabadadcbbdbdeccddbdcddbdbccdcdadbeddbaeaaedbeeebbebeaedddcdbcebbdbeabbcdddbcddebceebeecbdaaeadbbabbbeadaebcabbaddaccbdddbebdbbbadeecceabebcdedcdadadddedaaebbeceecedacdcbeeeaacdabccaabdaecbccdbeddaddeadecaaedeccbedbecdbeaaabdcaedbeccccacbceebcecdabdabbdeddcdbbeddcecabedddccbbecbbccedbaaaacebaddacccbaaaccbdecdbdababcabeacaeaabcbabcbbedcacacccbecbedacdeceebceadddceeedbbcbeadadebbdcddacddaeeaeabcbdedcbaaaadceecbaecbecebebacebbbdcaaddbdbaeeeaedabececaeeedcdaabdbedcdaaddcdadeeaceaeabbdbebbaacbabdbdccabbbcceeaeacabcdeadabcaccbecaedcaabbddadaddeedacacdcbcaedbabbbcdcabbeceaaecbeeeceabbcdeabeceaeddbeccbeaedeaabdeacdbdebcedcbaaccceedeabacadaabbaeaccacaaaebadabddeebcdbdaedddababcccebaeaedbaeaadaaacdcaebcbaabcbcdaecdabdebaeceadcbbbeedbaaaacabdeddccbdcacaaeccadbbbcbbabdcbaababdcecebabdddbdcacbaeaebcbadedaebaadcedabdeacdabecebdcaceaadedecbdbebedeebceeaddecebdaacccdcebedcdaadaddcdcbecadbaaddbcbcdcbabcdebbdcaccbeecbcedeccabaeaeaebdebdeedccaacddebbeccddaabdededbaeccbeddaadaebedbbbebeaccadaaecdcadcdacdeedbabeaedcaeeabdcdcdedccddcccabddabeadecedddbeaccbdbedcaecccabbbbbebaceeacbaaeeecceaddaabbbedabadbaaaeadbbddaaeeeedeaeaeeaaaacaaccdadabeecebcaceacceeaeaeeabcaccacbebeedbcabeaaeedbdaceaebabdabcceecbdcacbcaabdbbdccdecdddeabdddcbdecbdcdcbceacedbacdbeeaeecadbcadabaeeecbadeccadbdddbbabbbedeabddadedabdadadbcbbaaddadddeadeedcdedecdedceadccccbbacdbdecdaecebccbcdcebdccdceebcbbcccdecdaceddcccaeceebcaadeeeabebcccbbdbeaabbdbcccdbcbdaeedecaccadadaeaedccadcdbbbdbcedaaadebdecdaebbcbaeeeeacddbacdacddaacdecbbeadacbbbbccdecbdbbdbebcecbebebacdebbdebeceaecdbdbdaabddbeecddbeebdcededbdcebeedcacebcbcdcbeeaeaadcbcdadaeddbdcecacdbacaceaaacdecbaebdcdedbbebcacbaedeaaebcdbedbaedcaebedcabecdccdcdddbddbaaedbedbaadbcabdbaabeccccbcedadeadabbdaeccbbeceebcdedbbeebdbcaebdbbccbbedceadcaedcddebdbcbccadbdbdebeebcecabacebbeebeaadbbebbbcedabdbeebacbadbedddeeacceccdeabdaecacceccbcaeeccddcebeaeebcbebbebebcbdeabeaeeabdeaaaaecbedeababcaaaecdabbdcadccdecbecedddbcececdcbcddedbdabedebecedebbbabdedacdadabdceebbdbbbdbbdbaaaebceedcaebaddeaadaeceeddaaaeddadabaeeebedaedebcceecceeadaeddbeabeaddbbbebadcbabedbabbedbabdccaeacbaeabadbbbdcdcaecaabcabbaaabbdedecdaaababcacdcedaceceddaaedcbdbdbbcecbabbbcaeeccceaebecebebcdbdeccaecdeccdeccdcbbacdeecaabaaddccbadaeeaecaaacdebcdabcebaddeccddcbacaebabeeaddeccaaaebacaadcbdbedbbddbccbebbccbbddbbacdbeebabcbcbbbbedbbbcddcedbddcebdbbbdacebbddebbecadaeebeebddcdecbdceaaeeaaadbcaeddabeeeabccdcadebaccadcadbceeddbcaddcaeaebeeaaaecacbdbbecceaaeaadcecdcbcaacaecbbaaecdbbcaebaecedaabcbdeeaaecacdcdcbbceaabaacdbabdceaeecdabbadeeabaebcdececbadcebeacacadedeadececdabdaacedcebaabbcabdbbaeaddeeeceebaaacecabdadcacdeeccbadeeceecbdbeacbcaecedbbcedcbccdbcdbdecddcbddcbeaecdaabdebbaeeaeacecbbabeeaaebceeedbeeadabedbdcbedeaedacebabececbddbcdcdbacdbdacadeabbadbacedbdeccbcaebdbeeacbeecedcaedcbcebeeaedbbcdaaddbbcdaedceadbebaaedcdcdcaaabadedebabeacddecaedeaaeadbbeeedbaabacbbeeedcbaeceeceaceeeaebbacacdebddbbaacbbabadbebddcddeeaadeaabddccbccbbeaebceaedbcaeecbcaeadbdbdbaecebbbbcedbcdecaeaeabcdedceecebeaeacbdbeecbdebedbdabcdabcbbadabedeccacdaedebcdecdecceeadbaeebcecdebeebecbdbcdbbbaecaabbaaecacdcdbcaccecdccaadbddadccbeebaaddeddbdcdecbedcecebeebdedcdeaedcaecaeeddeeabbceccccddebbeeddddebbdadbdeccceabaeecdbeedbeaccccaebeadbeabcbcebbdbaebdccbabaabcdaccecdacdeddadaacacabdadccdbbaaebaedaebaeabdeebbdaadddbbacaeeabeadedaabadeaecbcccabaccbdbdacecaeacecdcaedaecbcbbbaddadcaeceacdddcbebccbcddaeeceadaecababdaaaaccedaaedbdbdcccdbdbbabccbccddcbecaaaaecbaeecbbadbeceaebacdcebcbebccaadecebabedcbeaaecccedaabdcdaaacdbeaccddbedcbebeabbdeecadacbcdaaedeeaecebacbceedccdcbdabcbbddcedabcbaadededeecaaceaecdcbbbecadcbbeadcddaaeacbcbbabbeccaaabdbbaceabedceabbaabcebadbadbccbaebddebbbaaadaedcceebccbecbedbeeeeedcadbcecbccadcbdbeddebccdebcdbaaedaddbdeaeaeeaacddcccdbedbbacecdcccbeedaedaebedcbdcacdcdeebaacaebeedcecbdddbdecccedededabccaacbaaeadbadbbcdeaadeadaadcceaabaabbbeedbbbbedbcdebecacdebbccaaccccaaaacbaaacdbbcdcaacdcddddcdbaacbbdcdddcceaaabeecadedddaadedcccdabcdbbbeeacbeccaadbecaaadbbcdaeceecedadeebdacbcbcbdceabcdcdedaacadcaabeeeceebebecebedaeedbbadbcaabcccbedbdabbbbcaacadbbabedbedabcbdeeebebdeebcbdaeaceccdbdaabbcbaeeedcebebdadedecdcbbedbcabbcaaedcbddeceebecebaaabbeadeecbcedbdaaaedaadedaccccebdebeeaeecebeceabddaaccaeecbbeaeedceabbdadbbacaaabcaeecbcedceaddacdcbacdcebaaabccadddbdbcadabcdacaccadccdebacccccddbcbcdeebedaadadbeaddcaeaebdbcdadbbeeeaedccbbaeeeaacaabaabcbadedeadeceeaadeacbadccdecdbeacdbabeabcddcceaeaaecbdcacbaabebdaadabddeeceeacebdaebaacadcdcccbdcebecbaaedcceccedbaacbdccccacaaedbabcdaddaabcaabeadbdddbedbcccabcddeadaecdabbaabeccbcadbabdeacceeabddecdaeeecebeaabacbaebeaccbaadcaecbaadedbcdaebbaaadedbcdeaaebeeecddbbdeedbecaaadccdbcedccdebbdbcebbdddceeceadeebcaaeacccddedccebaddaebedbebebdabebdcdcedecdcadaabdbdcdaeebabbadbdddbeaccdcdcabcadbaeadbcbccbcaaeecdacbcbaccaeadcaeedaabeedebcbcaeabbabedadacceedaaacbadacdcbedbbaaccebddaecbcccbddbedcdddcceaaacbeccbabceebbadccdddbcdeccaccbcbceddabceaebcedcddbcdacbeddacacdadbbcbabdbcccdbdedcbeedbbbbbecbbeeacdbacdadebecbeeeceebedeceaeecaaeecdaecdbbcabeacecabaebdcaddababcaeccedcbcdddeaaaabbdabddcebddaabadeaaabcdbebaaabedccbdeabcccabacaccbcdeddbeeddacdceadccecccaedaebbebcbdeebabcdcbacecdeadaacebabcbbddbdecbbecdccdadbdddbadbebebbcdaedceccaededaebddecbaeccdabccbddeedbcebaedbebcbdeaaedeabeebaceaaededdcbdaabeebcaedadccaadacdedecbcebaeeaedcbeeddadaaeaebbecdabaeccebecabeabadaceeaddaaabcebcbbbbadcedbebaebddceadcedecadcebdbebdeeaaacdacaebcadbbccbeadcbdedadbccadddcdbacebecdbcaacbaadbbabadcdabbdedbaceaabecabeccbbecdbcbebbacbdaddbccbacddabcedeeedebedeadacadeccecacbebeccecccddbacedbbceedebddbdceebbcdaadcbbdbadeceedaeddecdbcadbcaeddacdeedebeaeccbeccedbacadbebbbaadedcacbdacdbeeedcdeedcbeaddadaedccaccceddbccebacaeadcbdbdbdceadeddedaaccdcbcacceaacadcadcbbcccedeebeabababdbeddbbabcaaaabebceeeecabbadacbaedccacbceccceebebebecdcbbebaadcacdddecbcceabaecadccdbdaedeaddbcdcbaadcadcdcbcacbcdceeaededdaebcaeeebbddbbebcaeeeeedaaaedcdaecaeccaabedbbddabeaceaaadeadcdebdaaaaeddbdcbeadecaabbceeaadbcaaecadccaecdcdccbcedbcdbecacdcabaabbcadeaceebcbcbdbbabbcbeebadccdbcdcecbaaaabccaedcbbcccdccbdcbaacccdbacceeddaebbabddcebbecdeaabbdabacbdcbeebeacbadcebdbbeccddceecacecdeacbebbdaaeeeaedcbddbcabdacbbddbbcebaabeacebbacddcacadbbcdadbacabedbceeacbbeeddceeecdcbcaaeaabcaeebbeecaaccbbacdcadbbccaaceaddecdecbacdcadedcabcceabbeebcecdbaebceaeacbbbccebbeadecbaacbbcecebbeaedddacebeeaebaabcacacabdaceeaceddaacbcadbddbbacaeebabdabcdaaaabbabbebdbbdeaccadaaecccbdbebbadddcdeaaeedcaddcdceddbeeadcabbceebaaeeadbdadbdecdcdbcdaadeddbcddcbeabcaabeeecabcacadbacdcdcbbcaecbddaceeccbebbcbcdaecaebdedcdadeababdadcbbcbcecdeddeeceaeaebdcbbbcdcaaaeebacccbcdcdecddbdabbacbcdbcabeccecdaaeeceeeeaceeaebedddceaeecbcbccededadbedbcdeaeadedaccacbdcbcadabbdcdeccdcecbccbbdbbacdaebcbaaabcebbcbaabadebebeddaceaaaeaeccdadcbeceabcbadcabbaebdaaaecbaebacbcbaddaaddaecaacbbdeaccccdbcbbdccadbeaebcdebeebddecbadbceddaeebcaadbdcdbeeeeaccaabccbcaaddceecddbdbcebeddeeaeeacaacdaedcdadabebbecbcebbedcebdecdadddccbaaccdcbbdbdeaebaabbabbdadbdedcddaccaadcbababbcedadcecbceebcdacacdbedeebdecabbbacedaeadbadcccccacededbdbccccadbbaabdaaceeceedabcdbaeacbeecbcdbeadeebccdaecccebbadaecedcbaadddcbdbcedeeecdaeaaaadaceabedbabadcbaeedabbcdbbbcbdedcabaebeaaecebcdbacabebaabbcaaaaaaedceabbeeabededdcabbbeebdacbedbcbaacbebaabbcedeeceaeddbbecddabbcbaacbabccdcdbcbcccccaabbceeaceabceeadbedadecbbcebaadbaaaeaeecebeddebdceeabeebbcdbbcacacbeaabbbbbbdbcdedcabccbbadcbecdaaeceebeecedadccddacbeedbbeaaccdaadcedbeccdbaebcbecacbbcdadacddbccbcddebcadeaaebaeabbcedbbcaadcccedeacdbcebaaaadecaaadbecbbeeeeeaedabccbaabcbcaeabeddebadeeebcebabebdcdceecedeaecdeabaebcabeeddeddcbedcceaaacbbdcaeecdacdbdcbdabdbcddcbcbaecaddabdcebecadcbebeaededdbbdebbdebedcbabaebebecaecddaeaaeebdbdecabacbaacbaedcbdedcccbcbddcaaabcbddbedddbaaecddcabaddaeeecbabbeacaaebadbdbbddaccacaadbeaaadbdcbdadbeecdaecbceeadabecdaecbbdceebbbdabaedcdaabdcbeeabcebedbadaeaaaeecddedeeecdbecaadbcadbdceeadbdbaeabdcabdbabbddbdecacbabbbabbebbecbddcddbeebbcbcbeceaeacbadaaaedbeecbeedcdcdacdcacabdbccbdeddececbdbccbbccacabeacabcecaebcebdbbdeaebaabcedcedadeeedeebceeedbecbccdcaaebddedaededaabdbcecaeddcbcaddcebaeeecddabcacbdcacbaadacecacecadcbcabadebbcbecdebaababaedcebcccedccccabeebbebcacbbdeedcdccbceedabeecbedbbbababecdeedbbabaadbcdeecbcdeebbeceaaddcccdcdddabadeaecedeebaeaaebdaebbddcadbeaaaeddeddbbbebabeedbcdcaeedaadabedacbecaaaadabeecbaadbdaeddbedbbcbccbceacaabeaecaebabeabbcabcbccabcbeddbeccecaeedcabcbeeeaebaecdbdcaeddbdaaccedbabcebddebaaaedbcbacbacedcededdaaaddbcbdbccdabdcabbceddcbdbaadcaaedddabaacebdcaecabccabcabbdecedcceaceccacedbdecdcebabedcaedbcadabccbdcedddeddaddaabbeececceebbcadeaceeabbbcbaeeeeadbceacaabacbaadeeaaebedeeedbbadbbdaddcdcdeacddbecdcddaeabecebaedcbddccabdeccccdbdaedcbdacbdcaabcbaaebddeddcbdbdcbdbeedadbaccdbadbcdecbdedbaeeabbbbbddacdbadcacbdeedcadcddcebaaebbaccbaedccdbdacceedaadbedaecbaaeddbcbdbaccbddbeabcadcccddadceacbddbaabcdccbabeeccceaddabeceedcecdaaeceedbdddeabaeeeebcaddbbdcaebdceaabeedcacabeaabacbabadbaddabcaeabdcecdcabedbebbdbdcedcacaacabcaeebcbbedcccbdaaebacbebacbadacaccbbbcdbacabebddbebeeecbeaeaceabeaaedebceeceabebabdcdacbeeadeceebadeaadcbdadbddeccdcedbbdbbbdcbadbaaecbebdedadcdebbdaccdccdbeddeaededaebaaabcebebeaedaeccadcbaeabdbdeebccdccccbbdcebceedcededabcccbacaeccdceedbeeddccedacaecdcaaacdadebdeedecddeadccaebcaedcbbddecbcdacebbeecaaabbdcedccdddbdeceeccaceadecdaacdedebaaabeedcaeddbeccbddbaacbbadcececccdbbeedeaababbacbbdccdddbacbbbecbdaceddaaccebcdaddaccbcaceaedcdcdbabcadebecaeeceacbcbdeecebaeeccabccccaacdcdeddbcecedabeeebccebcabbadbabeceddbbedccabbeccabbcccdecceebbcebdeadbdbbdddbdabbbadbddceecaabdaebdaebebeedcccbbdaacaaecdeaeedcdbbecacaaddddeddeaaeacbcdbaaaaeaebacebdedbadedaabaddaaceeebecbeaebdebaebdebadadccdedbddeeacacadaacddaccdccecbaeeeaeacbeceadceccecaaadbbecdcacaedacecbccddaeaeedacaaeadaeeadebeddadebeeedecdcbeabeddbedceabddaecadcaaaaaeeaecddddceabebdceecaeeadabeecbadecaaeaccbbcacbeaaebdcacedbcceaccbbcceabedaeedbcdeceecccecbcdbddbcdbaadcddddccbbbaeeeaddceaedcbabeaadbabedaedcceacaeeeeccceabeebbdaabceceacedaddacaebceceabadbcddccecddbadababccceebcedcddcadcbcdbededaeaadbbbcecedceeaeeedeabcadebaeccbbebdadcdcabaaababbbabddabebdbbcccdeaebadabbcbcdbdddedaecaeeadeeabcacddacebeecdadcdadedebdaaceecbdbeecdcdbacadebaceabaeaadceebedbacadabeadaedcedeaecccdaeebaadbaebeeebeaaceadeeccbeacbdedcebbccdbeeebcadaadaceaeddedaeadbeaaadeeabeaddacbcdbbbaebaaeabeebeedadaadcdceeabaaebaebaedbcbcbbeebcaaebccacedcdbeacddabbedebaaedbedebebdbdbcecdbbdbbcedebccccdeecabcdedaedebbcddaccedbbeeddccedaebedbaaaceecddecbcbcbabbbddcccbcbcbabeecdeadacaeebbadecbccebebebcecbaacbecceeeceddababecbcecdeacaecacdadccdbaadbebbadcadedccbbccaacabecbeeadabeebcbababbbcaacdcaaeddadbeeabcbcaacdceecadaddeeecdbdaabcdcbbdabbdbdacdcbebcabceadbacbcbdecdeebeadededaceceebaaadddeebcdedadcbacbecdaeeccdbdaeadbbcdedabcbbaabaaeeaeceacabbdcdedcacbccaeeacaaaccddbbcbadebcbbdcacccabdbeabeceacecdecaebdbcceecddeaabeaadddcccbdbedbedbcdaeccdaaabaccadabddbbdeecacbeedeaeacddbcecccedaeeaabcedbebbbdccdedbadaeaabdecdcbdeadbaebaddcaecadabeeddaadeceadcabcbeecdbdaaecececddbddbbccabbeabcdebaacedbacadcaedaaabbdcabdccbaeabcbbaaabcbebcacebbeaecaecdababadebecbcebecdeecddbebaddbeeddaedcaeaacdbddccaabaadebcabeebabbceddedaddcdebaabbbeeeabebdcdaacbbabeabbaebbccddbbcceaddcacccceecbdcebbdbdeeeabadddaadacaaebaccadadcacbbabbadcaeececdbeeccdeebeaabbbabbeadbadcecedccaebdbbabdbddcdcccdcbeceddbbcdebdacaeebaaeeeaedabbeacbecbbadbecdaddacaaeabdceddeaabbbceccbeabaebbeeacedbabebcdbbdeccaecaebbadcbdbddceecdebbaaadbaacadadeaacbabbcdeacedaacabcbebcbbaeacddabbbdccedabeeedbdbadaccecaadbaddeeebeecaaabeaeeabecadbbbbadececdcecdddeeddbcaddebaabeacdbbbdabdebeaedbacbccdbdabaeccbbcbaaeedaadbabdbedbdaecbcaeeedecbcabbeabdadbabdaaddaaedebbdeccbceabdadbdbebeeabdbdbcceeceeebcdacadacbdccbcabbdcbbcaaaeedadcaadacbaaecbdcaacdbdbbeacdbcbecbdcbeeacccbaedadbaaddacdcaaecedbbeeedceeecdbbaacccededadeceedecacbbacdadccdedaeccaababecddceeceadababcdcbbdeeccaebdbeedbecdcabeadaeceadedaaecddedaaeabababeeacaaaaeabbabdcaeaaecbddadedcaeccbcbbaabedbbdecdacbceceeebdaeadcdaeadeabcabeebdedccbcccbbbbbebecbeaebdbbcebcecdeecddeabadeedbcaeacdcbdecaedbeadcacbedceabeacdcdecaadbedbcdaecabdacebbbbbaeadaaddeadddcebcccbcceccddaadbcedbdeebbbbbbcdabcadeabbdcacdeddbacdedaceccebaaddebadbccbdcebbaccbcdbabaebbdcecccadeaedeacddbeadededeaebaeadcdcecaebdceaaeeeededdadadeaeaadacdaeaaeedaeabeecaebcadbddaeaacecbdaabdeddbcbcddebedecdeccbeaceedddaabcdddebcaacabebeabcccabdadabebedbadeadcdddccbaccdbbbdebabeebcbaeeabbbeacbdbdeeccebdbaecbebcbcbbacbdbcebcabedddbedbacdbccdacbedaaedeeeaaccdedabebddeeadbdedaabbeabcaeeadbdbcbdaedeaedacbcbdadedaececccaddcdcbeadaebcbebddabeaaebcebebcdadcaeecabeebaecaadcbbadaababbdbbdebcbddcdecbedeceaaaeedbdadeebccdaebbdedbceaeadbdceadeeeebedadabcaacbadeacdacdabcdacbcaccaecadbbbbecaaddcbbaaedeabcecedadeeecbeaabddbceaecdaabdbbbadbbabdccaeaadbcadddbbddbdccabacceaebbaeaddcacbaaadededddaadababbeaedebbdcbabaaaaadebbdcdeacaedaaddccdceedeceacbedcceeabebeadcceedbdddbbaccebcaccecddcbededbbacbebcecaeeecddadccddacdccdeabddcbceccabaaaebdeebdbaeceeabbbaceaabecbbebccedabbedcbdacbdcebbebdbcabcbabcebceeccabaecddecaedbadeddbedddbecabdcebdeabceedcddbecdadbdbacebabbeaaaecdeecaeaabcaeabbbadeddaaebbcdbbbcdecaddcacceeddccadebbdcbeebbbcbdaceeecdbbaeccddccacdcacebcbaccdcebedcdeebbddbddeceacbdaacebdccdabededcebacaeccbacebdbccadeedaecddddedbebacdeacbbbeeceaedbbabededacabbcddadeebadcdbecdabcadddeaeeacdccbddaeeccaacedccadcaedddeedeadaecbbdbedadecddbbcdcdedddeccbdbcaceadcbabbbcecedbdaeadcbcbaddcaadadacaebabbdcdebcabdcdcdadedbdcadbebaabbabaebcdbcbdaebcdeaeeddceabecbcaaeeacadcbadcabdaabcaedddacccebbeadbedcddeebbbcebeaceaebbdbbeaadbbbcddcabeabbcceddeebdecbbbacbbdceaddaacbcdaaddedeacacebbdeadcbebbbcaeecdbcbdedabeabbddddbaccdbbeceabcabedacbadbeeadabaeddbceebbcddbeeceabcdbdacbcdcdaadbabcadcbedecabcdeeeacddcbbdebeacecdeacbadbbdddeeeedacacecbcedddeacebeaebcaababdcbccdaccaaaddadbdcabadcacbecbbbccbdabbbceccbbbdcbaebadcdddeccdcccdcceedbdcececdcdaaaaaabbdecebacedaaeaacdeecddcabdcdaebeeaecbeecaaedbcebacbeceadeebdccdcdacababbeacaaecdaaaaceeaaeaeeceaecddaeacebbdcceddbecaecdeacdaaccaabacceeccebcdabecadbaccdeadeecacebcdddcabcbcaaeaecceaccaaeccbcaebdeabcbabecaeabecadbdbcedccdbbaddbeeccdeaebeacbbbdccebeabbbebcbebcdecdcdebcaebaaabccacbccaadbdbbcebacbcacccddbceadeebdeebeabcbedaedecccedaacbcbdeaababaaeebdbecacbcdcbaadbedcabeededebcededbadadedeeeebccacccaeaebcdecbadeeacadeaceadbdcbaadaedbadbbbebeaebebeececbcbbabcbcbdedcedaeeddbabebcadddebacbeceeeceabecabbbdedbadbabcbbbacbdaddbecebedaabcdadecdebdaaedbcddaadbcdceeedebbecacdbbcbcccaaaeaaadcdedeaddeecaecddcbecceadcceeeebcaadabadecadeecbceaccbcabbebcceedbddcbadcbcdddabcadcaebdebaacebaedabdabbacccbebbdbdceabeecdaebacceaebdccbedcccecedebcadeadbebdaedbcbacadebadabdcdeaeceaaadbdbbbecdcecadaddbcdebacddaaaaeaaabceddceeaeacdbeacbbacbbceaadceabeddbaddeedbeadbaabaabecbadaeaeabddddbededaaedabeeeccbdbacbaeeeaebaedacbaacdbdeccbbecbbcddcdeaeeadcdbaaeacbeedcbddebdecaaccabaeaddecdeaceecddebeeaccecaaecaaaeedeebbaaaeecdedeaaecebaddbedbbadaceedbeebeabdccacdadabeaaebaaecacccdeecbcddaadaecddebcedcbeebecdddeaceccebccbccaddbaaabbecccbceeadcbdaadaceadebbadedbbeaccbbdeebeccadaecbceeceddabcebdbacdedcedbbbdebddbdedcededdbabeabadebbdbcdebcababdddabbaabbeaebddecedcbedebaccbcddbbedbaabbbedeceeeccedadcdaebdbbdbbccdcdebaadccbdcbdbdcbaaedbebdbdccceaabdbbdcbeaedbeabdbaebebabacbcdaeaeecbabadeebcaaaceddaedbebddebcdcaeecbeaeaaeadbededdedbddeecbdeabbcabbdaebbddaecbedaaebeddbcdccdbdadbddaaeadedaceedcccaddaecabedecdabcaaecbaeceecdcdedbcececabcaeaddcadbecbccaeddaacbaeedaedbecdbaedaabeebdacedaacddedcbbabebdbdcdddceebbaaeebdaebcccdaaababaccbeddbeeddadcaedbcceedddadeddccebbbabeddcdbbdbcbeadacaadbbbbccaaedebecdccbbeacedbcdaebedeabcccbbadddbbaadbcedbdcbabeccedebebaedbeaadbceaacdeaadbddcbccddacacaceabecadecaddbeddcababbdcdacdcdaddeecdcbdceebacaccabaebededccebcabaebdbbdbcdbbeedeebeaeaaeaeabeaddcdddbbeeadeacabeeddccaaadadbeadbbeebbeedecaaeceabbbeddbbbbacebecaebebeaaceaaececeadadcbdaebeadcaabaedaceadcebbdabbebbdeacedcdbedecbbbccebbedbeacaaeccebedcccdaecabadececdebdabbdbadecdaddcadacdedeeadedaeddaedcbeabcdcadcbeeddbdbabedeacedbaaebddbcdaaacebeaccbdaeeeabecdddaacbecddabdeabcaeeebabaedbcdbdbcebcaeebcbbbacbdbcdedbbdcabdeadcabeaebeebedccdbceadababeededdbaedbcaccedccacbbcebececabceaadacbbebededeacdbaabceeebcbdcbbcdecdaaaddceaecedaceadcbcadbeaebcbaecdbdbecaaaebdbacaeccabcaadedecedebaadaebeecaaceceadecdddbcbdaeaceadcbcabdaeebbeedbdbcccbbcdcbdbecdeecbdacaaeecccbbadbcaebebeadcdbeceadbcccddbbedbbbaddaccdacbccbeadbeebbabdadbeecdbbbaaadbecadcdeecbeeebbcaceddeeabbacbaebbeaaeeabaaddbdeaccdccdaeacdedadddccdabcddcaebceceecebaccedcedcccecaaecaadcebeddaceeccddabadbbddaededdaeddaebaceceecdeaaecbdeaebddbbdbcabdbeaabccbbadcccabbdcacbccaacbbaabaeacdccadaaccaddbebeecbaabceadbaeceadebcbedbdbaaaaaaeaccacebeeadccddaecebcbeacadecedcdbacbedbecbaebecdebdcdaeedabacaaebaaeddbaabdddccbccccaccbcbceebabaeedebabeecaaaebaabaabeacaeeebdededaeeecaadecedadaecbbbdcbbdeadedbdbbcebacadeacecbabbcccccaadbadaabcaeeecbdaebeeceeeeadabaedacbebeedcacaceaaadaddcdbdecbcdeadcbaecadcbedcbadabebccceceabbaedeaaabeaebbbeabcbcececceeaeaceeebaaccdeecdddabaadadcbbacbcdabbeadceaabbacabdbdcdaacdedaadbbceeedbebeacccceedcecccebeeddedbcaabceadcabaaeccdeabeccceecaadacaaeaccaeceeaabdcbeddcbbaabeebaedadddccadadaceceedbdcbeaeddbaaababccdedbdeadeababacdaceaebcaaecbaaededaaabbdcbcaebbdbddbedbeeacdbcaceaabdabdcbbdaabdbbccbbcbaddcebecaecabebbddbbcaeaaeeddbeaccdcaecdebeccdccaacabbacbebebecaabaadeaadacbeaabaecabdeadabecccecaccccdbdcdceebceceaababeceacddabcccaaadbebdadbaeccdbeecabbdcbbbbaddbeacdddcdeabdcedaeebceeadbeddacddecedbbbadcecaaeeadbaebacdcdadebbcbecededebaacbeebaeebcbababdbaedceacdcaddbdcbaeedceabdbcebabacedbbdedeeebababadddeccddbedeeadbaaeaaebeecadccbcbebdacadebbedceedadaeabacbeebdbedebcbebedaaddadeebadcdebcadebccbceaaddebeecabcddcbdcaeaaaadcbabdabeebdeddbaedcbecaaebaddbcabcbbabeaacbdaaabdbeaabebaeaebaaeccdadabccbdeaacedadaddbdcbaaedccaaeaeedbbbadbdcaebdddddcaacbcaaeaadaeeeacdcacebacecebadeeceedbbbcbacdeeaeeaceacdbbdaadbcbaacbbecdcabdeeeeceeaeecbabdbaaecaeeedadaaceceaaecdebbacbbeedceebdaadacaedebbabaccecacdcaedbcdbebbeeabeedceccaebbaaadbdbcbbacbeeeaecababecbbeddeccddbeabddebbecdabadbbdcbaaceccaaeaacebadcdccadbdaccbcbbbcbabceadacaabaaaeeadebddeabedacdcdecaabbeabaaadedecadecabebdecbdbbeeebaadeceabadedbaaaadbacbbcdbabecacaaceacdabccebebacaccdceebeaabccaeeaeaccbecaecababedcadbcbadcaceacabacebceebedacbdeddeddcdccbccbaaecddaecaabbbbbcbaeecbceedacaedbecebccbeeaddabcbaacddceeddbcabbeeddeabadacbeaebaaaecbebecacedabbddeabaeabaecaddbdeccecceeedabeaddecddbbdadabedadeecbededadaabccbcceaceeecebeaeebdbebdedebecabeaaddeddcdebdbbecbbeedeceabdceeeadbddacbedcecbbcddbeabceccbdcaecabadaeaddeaedabbdabecbcbbabdcaecbbcedaabeeabecdedeabaaecececcbbbbceeecbcdbecdcdbcecdbaedbbeabeacacedbebabcbebabebdeeddcbdbeacedacccadbbaaddbdabdadceedbeaaabadccabedabcdacaaacabaadaccaacdaaddbdbcdabeeeedeadcaddddcacbacaddabdadeaabcbbadcbddaabacaeebcddcdeababcecdeeacabdacabccecddbecabedaccabebedbcabdabbecbeacbbeeaddbedaabacdeccaddcdaebbcadcadeccebdddaabcdddaedbebbaceddbaddceeaaecebdbaecccbdebeacabaceeaddddbaacdadbbdceccaddcdbaaebecadeadcdbadbadadadcdeebadbacdcbecaecdcbeecbebaccadaaccaeaabecdbbcbeaaccacceaceddeceadbaadebcccaadcbaaceebcbbceeadebaadabeaaacdbcaabeeeedbbedebbbdbbebbdaabcdcbbddedddadaaddaeeecebeaebbceacedeaaabeacbaeeaaebeecdedcedeeecedcacaddbeadacbacbbacdabbdedcaececadadaceeadcadbbabdbeedbadcdcebdddaaaeacebbabbaadbcdedabeabcadccebedeedbacdaacedcbddeeeeaacadbdabeeaccdedebecaddecebbabbeecabdbecddbbdcceedcdbccbbbcddacbbeccccaeadedbacdcbbacaacbbbdeadededbcddaaecbbadabdcbddbabbbdeeeeaaaaadddedacbaaabdbddedcbcabaddadbadbbbbaccdcdbadcbebbeaaebabcdedbdaccecbcaedebcaecddebdabbbedeacdceeceeaaeebcbaccbaccaacccacbbedbcccdcdcdeecdccbdabebecaceccdaebecaeedeadacbeaeaaebebbedbeeababedeabcacbcaaddaeedbacbbccebcabcaecbceccceadbacadeebadeecbabebcaecbdabdaaccedbebdeaaeacbbbcaaeececddaeceeabdcaccdbcbdcdebbceaedabbeddbaedaeaeecedbddabbdabaeebeaeceadbadccebadceddcbedbaeccbbbbdcddcdbcdacaadedababeaadcaedeadaeedceebabecbdeceadaccadcbddeeeebcbdcaedbbbaccaadbcbbcccbeccddccadbaccecaacdaecbbcadadceeecbcecdbacebbacdcedadceadabbbeaadddedbcecbbeeeadedaeeddbdbaddbdadccdbcdbaadebbabcccbdecdbcbdcbdaedcababecebeedbcdbaaaeeccacadcbaadeeabacbeceedecadccabbabecaedcabcbeacaeacecbdcdcdebdaecdedacaadebaacebabbaadcedbbdadcacbcbdbeadcbabecadbccbcaeccdcaedbccdecedebbcbabbecbeaacdabbadbebbbdaddbcdddaacbdabdcbddaeecdddccbaacdbcaccedbbbecadbbddadbaeeaaaccaabddddeeacbeadeaadabaaaabeeabbabededebdaabdbeeecbaedacdeaaedccedaecebadcdbaecaadcaadaabdbeaeebceedceabacebbdbacbcaaceabbadedaceabebcdbcaeedaacedaacabdcedbbdaeadaeebeddbeabddddacddecedcecbbabceaadeecdcecdaabedccdccacebbbeaaabaccaceaaddbabbdadeedeedaaedcabceedcdddacadcccccaceedbeccebcaeddbceddbcbdabdbacecbbeeaddedcbceedddabbbcecceaecdaedbbadbbcbbbeceacbcbbaebbbccdbbdddcaeddcdabcbdecebadcecccdebeabbcbccabbaaceedebdbbaaeeaeebaadabebaebdbaabecaceaeedacbddceccbbdddeaaebbdcbdcbecdaccaadaaaebacbabcdaeccaeaececbbedcabbebceeccbdaaeedadcedeacedaedcbdabadddeaaacbabddccaddeeedabdeaadcceedadaeeaeaadbdbcdebaddaadeecccdadddcadeeddaddbeaeaecdbaaceeabcdcbceaceeedebbaaacacbbbcabdbdedaabbddaeebcdedbbcaceaccdbbdecaaadacdccceecadeeedccabadbcadcacbbebacadabbdedebacbdeaaaedcadcdbcccebbcbadcceabbececebcdabececcdcabbddadabeedcededaccbacddaedbadceedabdebaebceeecccdbcbccadcbccdeeaebadaebaabacdcaabebbdaaaaeddceebadbbabebeaaccbbbccbecebbedbbbeacbaebddcbdabdadecbeccbeacbccaadbebaadaadcdddbcbaeecadcaebdecaadbdaecbaddbeebadbcbeaabdcdadbbeaadeeaedeeeebcaaeeecbbaceaddcecbcadcbacbbebeaabdbecddcacddddeebcadebdbbcddbebadcdadceeebbeacacbcadbcedddbdbbabebedeaaaebdebcdeabbdecebeaeacbbedebabcbacbaeeedceebcadcdbbbedbbcaeceeccaaeeceacdbccbaaddddcbaddbbbaadebaaeacaaacdebecceadebdccadabdcebeccebbdddcaebeadabcdbacedaacdddaaaadaaaeacbbcccaadcebcbdcbbaeabddbbdaccdecdcdbeedecaebcdbecbbdbedbdacbbebedaecdbeebbedabdeceeedebcaebeceeeccddbdcbcecdbabeaadbaccaeeeaceabdccebdcdacedcebadeeebcedbddcadebdaaeecabaedabadcdbcdabbbacacecbedbedbbbeadacdcbabeebadecedcddebdebdebaeebceedbccccedccadcbcccbddccdbebdaccababeeebbbbdaecbdabaeabdbeabaebadecbeabccededbeccdcadaeeebcdcedccddaadebdbadaaeceaaaeabbbdbeabacdceacacddbaebcbbdccdebadccbeceddabadbccbcceecbbbeabbbdbdacdeabdcababdcdbdaeadbcdebeeaacdeacceaecccebdaecebccbeecededdbdccebdbbaabcbaeebadeeddcadddeaedcdebceebeccdcbcccaacbccdddcceccdaadaeecebddddcabcaebeecaececddebcdddbddeccddaabaebcecccabdbedbbcaecdebdeaaabaabbbbbbbdeeeaebadeabaeabdbdabceeebabddcbededaababcebabcaeadccbddaeebbddabbcabacccaebaadecdcacddbedecaeeadcacdcdcaedcacbbcdbeaeaaaccdedbbeabaddbdccadaaeebdaddcbabedcdaeaedaadaedcbbaecaaaaccdcacccabdceeadaacccdaceabaceededbddeabbdaeebcdabebceceeececacdcadebbadaddaabdcedaaabbabebeabdadacbceccecdabadcabdbceacabbdecaaeabaecbebecdbbebdbdbadaeedacecaadebcdadceabbcdaaccadabedacebadebdccbcdabedbbaaabbbbadecbbccaacbdddcccaebcdeedebeccdecabcaddaeaaebbdbeddadbeedecbabaddcbbbdbddaacaddddaddcdadccadeedbacdaabaeaaabebbeeedcbccddaddecbbaebbcdcaebbcaaaeccdedbddbcccddabbeddbaebdadbeaeeedbdcbbaeedabdcbbdbcdadeaaabdbeabaaabeeccccdbdacdbccccaadebaebbecdbebdbbaaeeceebbebadbbbecdcdbcaadceadcbaadebceeddbcabeecebcdedaeabeecacedbcdecadecedebadbacadadbacbaadccbaacecaeddbbbeadaabbebdcbacaeebcbaeceabcbbbcdbdbdedacbccbdbbebbaecddebbccabcbaedbbbccbaaeedbeddeebeadccdbedcadedbedeccbbbeeebaccecbdebceeabdeecbebececcecbdcbaeddacabbedbddbebdbecdeadaaadbbecbeddaecdddecbebaeacadbbedddddbacdeaddecabcadeecebeaaaedbaddebcaecaecebdbcecccdbcadbdabebcbddececdbeaddeabcbbabaeebcdcbdccbbdbeabdcedcedcedcedacbdbecbeeeceecaeedcaebaadbdedeeeddbcbdcdaadebcabdebbebbbcecbebcccecdbdbdaeeccaadecccbbbeadaacbebdacdcacbecbabbeddaeeaaceaaeaaebaabcddeebaeabedeeceeeebaeedddbdedccbeeccbcbecceaabecaeeaabcbcdbadbacbdedaddbbdbedacdcddcecabaedebbdaceacaacbbddabbaacbbebedbbabbbdcbecbaeebbedcccaeaaedabcbdbaddbebdbdbececadcaebbbbcbdededbebecbddedbbddeabeddbbbbebaaeededaebdaabbaaabcaddebdbcaccaedcdcaebbdcaeeedbaeebebcececaaceecaedacaabbdaadabdcebdacdddebdaeadbedcddcedaabdbbdecbcadbeceebcebceadcaaeccdbabacdabbbdeeaddcddeccbcdddebbbaabaebaeebecceddcdebddeacabebeddadccabaaeccdeeeebaebdbcbceebbecbdadabdbdcecdbbcbbeaadcceddadcdaaacabaabceacebcdddbdbaedadedadbecdccbaadbeedeeeeacbeecbeeeccbadeddcaaabeaaaccdececcebdbbbccbababdebcacebcdcebcbaaadebbbdbcbcdaabddcabdeedeebaecadedccddbeeebcbacdddcdaecbdcaaccabdddbebebeacdbdaecbdcabccbccceeadbdaeddeddddaeecddbbacdbedbcecedeedcbbdbaedecbdecdbbcacecbabaeceaceaabbacecdaebdeaecdbbabaaeccacbaeabddadcebbdbdaedaabecdedadcedaadaecdacadbbdcddaccbdbeeaebaccdcdbcbadcbedcaadcdeeebabadbcedadbccbcebdaabcaaeededebeecadbddcacababcadcadbbaeeccddbccdcacacceaddedaddecbaaeecccddeadeaadadebdabaedccbbbdeecabdcebbbdeeaaaddbcbcdbaaceaeadcbeaeedaeadeadbceebbbcedbbdbbbdbecbbadecacaceccabdeacaeccecccacccdcbbbbccdcceadbcbbcabbdaddebccedeaeededddcceceebdcacddcdecbaebdeeddbeaccdaccbedcdaeaeacdaecebeeceeccccbdaeeebceedcccabddbcdbcadccdbecbdaedbbeeebeeeedebdddebdbbacbbbeabdeebebcddddddbaabeabddbcedbddabdaaedaeebeaacadadddaadbecbceebecdebabdbeebdbacccdaaadddceeeabccdeadcdedbeddbabeedaacecdacdcebeeeeedbdcdcdeaaabeeeecaeebedaccadebaddacdacccbabdcebbbaaeacaadededcccbeacdadacebebdcbdaedbdccbbddeeddecbdedcaaeabeaaaeebcabebcaebcabbcaaabceeeabccbdbabcbadbdeeebabcbdecaaeaabbeebccdabacedacacebecccceebeaceebaabbbeeadbedbadcbbcbccdacbaededebbaadbabaddaaeadddacacabdcdeabeaaddbebcdceedbaacaaceadabacdbdeeebbbbbccdaeebbeebdabdbeddcabeacbbadbcbbdababacdbbbebaacadbdaeddddaaddcadabdeddcaeeaadecabbbbcecdedadeeabaaaabaccccdbbdbceceeadddebdaedcbeabbcebaaadeddcabebaeacdbbabdedbcbdaaccdeccecdbdcbbabdabeadaeeedaeccaddccbaddeaaabdedbdcbbdadbecadcbcaadacedececeaecbdcaebbcecaadcdbaecbddaeadaddbadebeabadeccbbaaecacaadddaecdbeedcedecebaacdeceabeadbbebceaeecbddbbbadcebdcdebbecccdcdddebeeebabddccbcbbcdedeecceeedcbecadaaceaddbdcbabacdcddcdaecedacbaeabcccbbcaceddcabacbddabcbdbaecbcdcebbaeeacbebadccdbdadeebddddcebcdcdbdeecccadcacbbacebdadcebbbccdcdedbdecaabbbaeaaaebaeaaaabddacdaeaabacdeddbccbbaabeddcbaaceabeadabbcedededccbbaebebccdeceaaceabbededdadacbebaceeaebecabcceccdbedcdeaacddedcebbacebdedebbdabacaaebebbecbdcaacbdabaacbdebbeecddeedbeeadcdaeaebdedadcaeeadbaadceecebedcebeeeaedbdbcceaaedabcbeacdbaedbbaadccbbcadeeadedecbeaddabdcaedebacdcedbcebaccdeacbecececdaadbbdcdbedcebebacbaebbceabacbaaedcbdcaddadcecabcabdeceacbbcbecedaeadbebccedbbcaebaaeaaceabdbdececaadcbebbaaaebccdddeadaadbecaabecbcabebbeacddacabdcbbabccdeaacdbccdbaabcebadaeebdcedceecacdcccbdaddeabbdddaeccaeedaeabacbbdebcceacdccbaddeacdbdaacadabddedbeaabeeddbbbadbedbeedbcedccdddaeadebdacbadaabaaecabdaaaadaaabebaaccbbbdcceaebccbebebcdddeaaddabadaabdaeeabddbcbbabcdbecebeeceeeabcceaadbeccaddeadbadbbdacbeeeadeccecaceacabdbcbcebeaabdeeedeabdabdcdbcabcebbeacaaededdddceadbaaabddcdeeabcabbcabddcdabddeedeeabddaaddcbddaddccdeeccadbedecaeaaedcebcbecaacadeadcbebeeeddcadbebdbddcaaceeadabcaaacbcddbcbbbcceacbcacbaabeaecdeacadeaaeeeeaeabdececedbeeddceebdcdecddedeedbbaedcbeccccadeddaadaadebaadedebdcedacdaaedaadabccecaabcadcbedcebbadaedadbdabaceacaabdbbcdebbeaabdabcacdeebbebdaaeaebcadbaecadcdccebebdbdbdcdcddabdeeaaccecdccdacadacaadedddaeabedaaebeaadebeddeaaacbeebdaaebbdaeabeaadbedadbbedaaebccdaaeaaeedcecbbaadbcbabcebcdcbcbeabdecceeeceeddabbceaecbdddebdcddadbaedcccaeddaeedaaddbcbdaccaccdecebcccceaddcebbadabbaabaacbaedeeeeceadabccaacabbbaccaccdeedcbebbcecbdceeeccbebdececeddbddbbabaddcabdaaeadddbccdaededdcbdaaedecabaaeaacbabeddddcceeceaeabaacebabdecbaabcdbcbdabeeabbaabbeacbcacdbecddcabcaadeccdecbbcdbeaacacaeaacabdbbeebaadbcdbaaaabbbeaacccceebdebcdaadccaebebbeacdbbddcbcbdeadcabbdaaeaaeadadedeebcdedbcadcebceebeabbdaceeeddadbbccdeabdeecbcadccabceecabebddccceabeeaadcbccadeaabceaddccbebcdeabbdbadbecbadbecbcdabdaceaebeddccddecaeccadbcabdceacdcbaeedcabadcbeedccaebbbaebbeccedadbacaaeeaedddbbceebdccebdddbeebacadeeedaecabdccccbaaabccdedcbdcebddbeabacdaebdbbbdccbcccabdeadbccadeccaddccceaebaadeaaacdedceedccaccbbabcddebeedbaedcbdedcccadeddebbacbdbbddcaccbcbdcbbedaeeaedecdaebdeebeedabbdceacdbcdaebbdebdcdbbacdedadeaedeaeeacabdccadcedacbaedecbbaeaededecddbbdeacddaacdeedbdcebbebddababaecbeeabebadcdabecdaacdaeaedaadabdedccbeccbdabbcaeadcdeaccecddceacdaddaecdbbbbaebacbcabadebaacddddeceebeacdcbbebebecccabdeeedcaadebacaaaedacadbdcecddebcbcbeadbeabadbdddecbdbddeabbdbccbddccdadeadaaaccacdabdacbededaaceddaaabcedcdebaabcddbedaecaaaecccedbdbbedcdbeebbcaaaeedbdbaedacccdedadceabedddccbeddcecdeeeadedecbedcacbbbcdbeadadcaabdabaaedcbaabbacebaeacbcecdaeeedbbadcceabbbbdeeebbcbbceeaadedcebbdadcdababadccdcabdcddaddbeddbdbdedebbcedbdbccbdebbecbedcccdbacdddcabcdaceaccdbbdcbcebcccacbbebacdbcbccebbebaadaaeeecdabbcdcabbbecbbbdeabaceccebbcaacabaaeaacbddbaeadaadabbaddecaebaccacbecdcabbbbeebbeaededecaedadeedcaeaebbdaddceebadceaeaceceadacbabbadadadecbbdbddebddccdbccaedeaddeaeecabdbccbecaccddcecbebdbdbdccbdccbcedddcaadaedcecccddbabcabdecabdbbdbbadddbedcbbcdeecbadedebabacecbbaedabeedcacaedbcaeedadaaeecabcebcbbacbdbeecaedcebbdeeadeedbdbbdcddeddcaaeeeeaaeaabeadceeaadacdbadbaedadbdbeddabdbdeecccebecccedeabedcabcdeaccabccdbbbeddbeeaebcbbededaadecaebcecabbebdcdddebcadccecbccacdaddcbcaacadacadbbdcedebceabdadecccceecbbcbdaabedacdedceedbdebdaedcbbdabcabbceeadceeddcecaaedcecdaccebedeadbeeaabbccddcbacbdcaeeabcbaccadddbaeebdaabdcccecebeeccdabbdbeecbeacceecebdeeddacaccacccecbebbcceacdaddaacecceabaaacdbdbeadeebddadeddcadabddbbcbecceabebcbcaaeecbeebcaedadcdacccecccbabaeccbbbeddeccddacdcdcbecbedceedcdbdcdcdabbadebbedbccbddddedbedbeebbdaeeebadeabdbecbcbdddaecdbccadacaeddbacdacbecadbdceccdadebdaadbdbcaacadabcebbdccdeaeceebaaecdbcdeebeacedaeaedbeececeabaadcebaddddeccddccbeedcadecebddeaaeeceecbbedbacbaccdcceceabeccabbaebabdddacebceabbaedaebecacbcaaecedabaedccabaceadbdaabacdbdbebeeeccbaadebcdcdadadeebcccdcbcaaceeaebdacbecdccaddeeadaebaaeeabaacbacacddbecddddbdccaeaeadcabebbceadbdcbcadcaccbaeeaedeabcccbbedaeedcadaecaceaacbbeeceedaeebbdaccecbebacbaecaebbbcaeaabcedaeadecdecaceaadabecbabbcbcaadadbddbaeccdbebcdaaccdbacdcbbdedbeabbbdcedacdacceaadebbbdeecccbbceedccebdddabcdaeacdabcedccbbbaeebacadabacdbaedbeebcebedbadbabecabbccebcdeadabeedbcdeaaddeceddbcabcdcbedebaabbdcdadbbdadceaaebadeddddbadaaadabebbbbddbbcedbcbaedaacceaeedbacacebcdccebadcbabbbecdedbbeddcddcaeeddbabccaeeacabdadaddbcddbaeaeabccdaebccbdaaeadeaecdbbbbbaababcdcddabebbaaacbaeeadceccaacbbcedcddeddabdbbeccdcbedcacebcebdcbdcbbaabbdceeaeecedceaedbcbccebdeeccdcbadeeceaaacbbcdbeadbceadecaccbdddcbcabddebccacdcdcbccbeaecedacddbdcebacbaeeadaccbaadbebabaeaccdedaebecbeecbdeaedebeeeadbdcbaadededdcadcddaacebeeeedbaacedbabedabccddbebcdcdbeabbcdabaacedaeeedaddaccdcdceaedbcccceaccddbdaecaeeabaddcabcaebaebaababcaecbdaedeaddcccbcaeeaedbaedcaabcadbabebdeebeaaecbcaddcadeacbaecbbaaacebbacbccebededcdeeeedaeababbeeacabceddcaaeddbeabaaeecaebeccabbeaccdeedebadcaeaeccbdebbabbcecdeaebbeadaacdeacdaccdbccacbcecddadaabaceaedcaedcbceeaecdcacccbdceadcbdcdcbaceaacabaaecdcdceaacbbebaaeaaeaedbbbeacdbabbbcddeeaecbdccdeadebddcecbdbacadaabcbacaeaeadeedabddebdcbabaecbeeabeaadacabaeabeebdecaaccacecaceaaeeedcbaecadabddecdebadbacabbccadbcaebbbddbeceddcabbabdbdeddecadbccaaabdbdaedbaecaedaddddacbeddacebcbbcaeaadabbcbdbadcacedddeadcaecaceabedabaaebdbacecbececaadebeabcebeaadddaaecaeebcabeadcbdbddcdbbadcdebebdecaebdaccdaaddeedadeaceabbdaeecdbdbaddeadcecabcbbeedcadbadbdbabcaaddbbbeedcbbcbaacdaeaabdabcdaaabcadeeadeccaeeecaceebebacbdadaaaccedccbceddaeaaccdbbbdddaebccdedebceecbcdacbebbaacdbeeedadeececcdcddddebbddbecedbeadaadcaebcddadccebdbeadadbecbebcccddceddaeadbabecaaabedbdcbbdcadcbaebcdddaccbecccabbbbbaedeccaaacbedecabbdddabdadbbccbeebedbdddcdcacaccbacbcebadecbccebcddacacaeadcceeadbedebabccedbbcacceadcedccdededdbcdbbcaccbdadacdcacebdabacddeaaebaaabdcabeabdedbcedddeadbbcceeeaaeebdccdeeaaddeddeeeccdedbceeedcebeacaccaceeddbddeeeeeedbdaedcebbebcaecbbeaddcccacededeebedcebcdcecdcedaacbbdbdcceacdddebdcbebeadbbdcaedecdbaebbdaaacbcedceeaddeebeeceaaedcbccdabbbdecceaebabdebbddcdeabebbeeccabcacdbedbdaadbbecedbceaedabbdcbadbbbeaebcdcaedcdbdeacbebcaddaaccaaabaecbaaadedeebcabacaacadceeaecebaceadededadceaebdbaeceaccdddcadcdeaabbebbaabecababecbbceadbbaedeaaabdcbddadbbaedaebaabaedacabbdeddebeccebcddeddecebdbedbaddcaebdcaedbdcedabaecbcaddcbaecacedaeebbcdcacddcbdeaedccdcdaeadaabcedbddbbecbbcabbbebddcadaeacbdebbbecbcdbdebaddceebcebaedbbaaaadacdaecdeababcccadbedacbdeadcaeeaacecbccdebebeecedcaeeaacdcecdabedbaadddedbebeeeedaaaccbedccdcccebeebdceecdedcdaeeaaeecdaaccccaebddcaacbedddcebcdcbdacaddbecdecbcbcaabebeeaeecacbcbcacabdedeabaaeedbccddccccaedbbebbddebcbdeecbdecedcbddcdeedcaccdadabbeedbebbecbbaebdccadbaeedaebadeadbcebbaeaccabbadccccedccdbeadcbeebeebbcadbbdbdacbbacaedebbcedddacaeaadbcdbbebccbbeecdcbddcdeeebccacbeedbeeeaeebeecdaccccaaabbabcbbceeedcadabaeebaccdbeebacbceeebdaacbbebcbdaeaaadebbaebededbadcabcbeaeeabbaddaceadcaddeceedaeeededebeeddabcbdebadacababaaadabaaecbbbdebbcedacccdccaaeaadcbacdaacdecadaccabbaccbdedcecadccaecadabcdeebbeacddaacaeccdacccdcbeeacdebeeecbceabbebbcebbedacdecdbcaeaebdbddbdbceacccadddddccaeaeaeaeedbbababbeecdedaaeeaaacadbdbebcabcdbadcdeddcdcdbdddadcdcbdbdeeaeebcaddcbacaccebbaaadecadadedbacdbaecbcbecbbdedbaadacaeedeecdbeddbadbdcedcbddebaaeacdadddcceebcceceabbecccddbaebdadeacdabdabdaeadaccdabdaebebadecbaceaadadedaaebdedccbdebcdabeebddabacbbacbaecbcceaecdacaeedddabaccbbcebdeedaecadbeeedeacbbdeadeadaaecaabbcbdacacaedaeaadaededeeeeeaabedbebddbeedcbaddceebaecaebececacdceddaaecdcacccaeedcdebadcabcddaedadcceecccdbeedbeeeddcecbbdddbaacebaeadcebdababaaebcbcbadaabeaadbbdcaaeaaaebacdccddcdadaccbdccddaebdceadebdbbeabadcadddbbaaddecbdcbaecdcebcbbcdcbebcedcdbdddccaeccdeabaebcdaebaabdbadeecccaedccabedaaeeeeebcecbcabccbcddabaabedbdcbebccaebbbdbaddaaacededecbcbaebcaadcdebdeaddbaebcaceebeceedcbebaecadbebeddacaceeeddcedabeadceccaacbadccecedbbeebcadcaeacadcbceebecabecccbdceaceddaecaebcdabacbacecbcedbeabaeddbdeeacaebedceeadbacbabdeceacaaccaddbcaebcbbddeddbaecaeabdbeecdbdbecabacddddcddbdacbdeccbddbeeacdebcecebeecbdbeddaadbcdebcecbaadaeddeececdceeccddcaedcdcdadccbaedccaecbabaccecbacbcdcabadaaddabccbebcbbadedeaaccebdaeedbcaacdeaabaaabababbdcdbdcaeeaeebdceecbbeedbeaeacaaaeadcaebdebdcdaaebbccbdcbbbdeaabecabdabacbeebeedaeaceacecdaadabecaabdaacdcdcedebabdeaadcbeedaadcbedbdbcaeabaedbedabdaaacdeaaaecbbdcdacbbddcbeeebecccebbbdbcbbceeeeadeadacbbdabcaedebaaeeecbcebaebdccbcbdbbecccabecaccdabeeaacecebebacabedaadbbeecdeccbedbeeadaebbadaecadbeccdacdaeddecbacebddeabaabeabbcbebeebbdebeddebdcdaeedbecdaedbaeddbeeadccebbdcedddaededadabdeaddabdbcebceecbcdcecdccaddedecdbadbdeebceaedecbcadbdceabaacbbcebacdcbdbcbecabcdaedbdaedcbeabacccebdedeededccadcaadedabdbeeeabeaecdacbeddaeacbacdcdcbdcdcecaadbbacbbacaceadacceaacacadceeaadaadcbcdcccaacdbbdaebcdebdbbdbadbdabaeadbbaaaaccdcdeaddebaeadbebaabecedadeaadebcaebebacaeeccababddadcbdbbbcdddbdaeabaeaaeaccaecdaaeaedbbabbcaecaaeeabcaecadadbdbecbcdcaebbabcbbddccebaadededaeaedeceadcebddbcbbcadeeedeceddccdbedbabeadececceddedbdedadbccaeeaebaedbabcabacbdbdedabeddcdbceddaaccadaecceaaeaaacdabcacaaacaacdeddeecbbcdadddbeaedbeaeaaacacbbbcedabebcbddebdaadacbcdadceeededebaecdbadbcdadeddcbdeebcdedcebeaaacaceeaaecdccedbedabcbedcdadaaaccddbdecdccccbddbebbbdcbbeebecceebecdcdedadeeadaaccdcabbbabcacaeabbcedecadedaccacccbcbcacbdddcecdbabecceedeaaacabaaceeaeaaeeeadbccadbeeeaeeeccdebcedeaedbaadcbddaaaedcdcaeaecbccabccbbebabbbdcdbabecdbcbeebececbccedcebbdcbccabcaaceeedbbbebbecdccdbccbbadceabeacbcdbeeeeddecccaabcceededeeebdcdbadbecbebeeeccbbeaaccaeccddbdebcdebeeaceddccbcddbbbdccccedbadcbecdbdccaccccdcdbcdccadcaabaddbadedadcaccdcbcbbceddaccdbddeadaadaaddadddccdccacedeadeeceabadbaaeddbcaadeecdaddebbdccabbcbceebedebebecbcdacaceebdceebcbceedccbdcedaadbcccceabdeeeedbceaaceabacdeadebaebbcdaacbcbbebacbeeedeecaabeececcdedbdaedacaddccdcaacdbbbcbedbecadcecbaacbdcadddcadcbcdeedadebbabebdedeadcaeadbbedecccddaddcaaacededcadccbdaaecacabccceaeeaddeaddedcdbbabceebabddbbbbcdebebaeccedceadaaedeeadeceeebeecdebeaecdbbbdcabbaacccccaecddbcededdcabbedaddbeaaeaeabeceeeabeccecedeaecebdaadcbdebecbdcbccccddbedeebbaadbaebbbddeedbeacabecedceedbbbdcacccdbaebbedebbbdaebbaeacdeacedcbadeabbaadbddeabcbeadaebebcdadbbbabcebbabdaadaebbacbcabddcbcebddcbccadcabbdaadccadadeaaaaceaeecdebddebbadaaeebeedadeaaadbaaccdeedcbadcceabbcddbdeeabdceacebcbccddabcddbbeabdbecdbdbdeeeabdbedcbbbdaabacbaecaacaebddacdeedceeccdadddcebdcddaccbbcedebbaddcaaaaaaebeeddbbacacdccccabccbbecaddaceddcdbbaaccccaddeacbeecacabbaecbeddaaacdacdbebcbbceaaeceeeccceaebedbaecccbbeeaebbbdbeeeaaaacbbacebaadcbecddedacbebddebecbaeeacccadcebaddbbcebcdecbdadedebecdeabbaabbabedadaddceeeaccbeaebbeabdecddaacbeaeaadcbbbeadcaabecaeacbdbdccabacdddaeeeaebebecdcdecddedecdedacbcdcbbbbcbeaabedacbbaaddbaabcdddedcebeadaeddddaeeabcabeaaeaabbadeedceaacbaedabacbccedbcacebadddcddbbececdbceeadbbeeacebddacbccaceadbeacddbddaabdebdaeeedeadaabaacbccdeaeceeedddecceacacdcbccbdbacbdddebedbabbaacaecebdbdcbeaddbacaeeaeadececbdcbceebeadadeacbcbdbceccdcdecbeadaaadbbeeeaedeacabdcedbbcbdbdadedacaecddcdbaeabaeedaaabccaeecadebaeeaccbecaeddcebcbbabebbececcccaecacdaddaedcbebcbbbeeedaeccbadeadbcebcdbdbdbcadaebddccdacbbbbdcadddebccbadbcdebdaaccbbcceeeeacddcbaeddcebbbdbddaadebcebdcadadebabcbceebcbebdabaadbedecbecceedaecebaeabdeebeaaeccecabadbdbbebbddcbdcceaceabeaabcaaaddcebdeccbddddaadaaaadbadbbbaceabaacdbdabdbbddaabcdbdcbbacbcdebecabbdbbeceaabdcbdeccebdbcddabaabeaadbccdabeedcaeabbecaeecddedccbaccaabecaddeddabdeebcbdcaebbcecdbbcdbebacdbbbacccdcadbdbecadbebedbaacdbadeaddbaeeeaeaebbbbedcceaaedeeacbcabbeabaeaebedbabecbccbeeeebebcababedcdcbccedbbdcadabeebadeebedabdecbdbecdbaddbedbbcecbbadccbaaadcbdccabeebdeebbdaaecadbeebeeddcdadacaeadccdebacdaaeadedbebacaeccebccaddbccabbcbdbbeecebabbeddcdaebacdababaecadbdaaebdbbddbbcacbaacaebbeddbdecbebbdbcdbcddeccdcdeccbbebbdcaeddaaecaecddcdbaecabccdabadecedebacbbededdabbeeadaeecddddbeaaeeebccceedaeedebceaeabbededeeaadedceedeaeeebbbacedecccbeeccbdbbcdddabdebbcbcbcacaccebacddaecdbaebcaeabecceeaecacadabeaeadecececebbebaaddddbbaacdbaadebaebaccccdceaadddceebedcddccececcbcccbbacceaebccabadeedbbdeecceebdbdbebbcbaaaedddaeaccddccbbddebacecaaaedecedccbddcbdbadccdacdbdbebcbacadcccecebbdbeeddeeeddedacaaecbccceeaadcabbdcebbbebcadacbeebcbccadabedbbeadcdddcadccbdcaccaeceacacabadedddaccaaaebaeaededaaacdbecbebbcdeababdcdbdccbeaeecddeedcecdbdeddbcaeecaaaddedbccdadcbdcdddacdbbacaddcedebcbacccabceecbcedbeaceadbaabebcabdbdbdadbbcabedddcccbccaecdbebdbdbadbaccbdbaccabcedbddcbdecabcddbdbdaaecddeeedecabbbbdadebdacedcabddebdcaddbedcbbcbaabbcceccdeeaababebbddbedaeeeedbccedbecebcdbedebebaadbbeecdbaaebeaaaaeccbdeebeedcebbaccaebbaabaaddbebdbeebccebdbdcaaeacceebadaedadecdebeecaebaccedbcebeebdcdbbaabcdeeddcebcaabddccaacededcdbddbedcdcbcdccbbcaddceacbbcdacbacbbceeceebdbcdeaebbceecdcbabaeeeadddedceacebcdaeacbabdbdaeaeddcbeebebcbaedadeacdebadaeedcdbcebcecdcdaeaaacbeedcdedddccaacecababdbbcdaebbecabbcdabdbbdeabadcabdaeedbbbaebabeaadaaeacaeeacbcadcbccbebcadecccbbcabdbcccdbdccbddbadbecaeaadaacdcddaeeeabdcadbebaeeadbdebdbcacededcdddadddcbeebbcdaadbdeadbedabbeedacdbcbbcdabbcdddeeebcdabdaebccbeaabeaabebceaebebbcdcadebbeaecadebdebebaeeabdbdabbeebeaaccaccbabeaddddaacbbadaaedaccdccedccebcdcbcbcbaecbeddbbddeddbebeaccdbeedaaddaabddedbaebaddacccadbbbaecbdddccebdbcbabdbdeccaebddbedcaaaaacdbbcaeebeaeeaccdebbbaaeebdabdcdbeeeebaeaebbbaacebbbaabeeecbdccedcaedbeeaeddeaddebbadccdcdbabbcdadeaebcdbaabaeadccbdedceddeabdebbceabccdccacbadaaeeadcadacbbbebddaeeebecdcbeeacaceabeadaaeaacccbadccbcdeaedecbcacdbdbdecabcabbeedaddecccbbbacdebeaacbababbcdaeceeaaadcaacdccbabeedeebccadcdeddeadbcdabceddeebcaccaedbabeadbbccbdceabbaddccbdacabdccacdaeaadcbabbbdebbbaeeddcbdbababebdbcabacacabecedccdcbcaadabedbccbdbcbbcecdbdcaecdecbbaacebabcccbbddabcabacacedbeadaccceaaecccebeebdaaeaabdabbddbcbeecebcccdccddaacdbddadceaeacaeaceabdadccaaacddaaeaceebadaababadbccecdcecabbccccabbdadddcbbeedaaaedebcddcbecbeadebaabcbaaecbccbabcebcaabbacadaecdbdedbbbbdbbbebdbdbddedcedcdaecbabddaadcedddcbbbacbbebaacbbdeaabbedaeaeabdcbdeaceabedcdeecdaaddccbacdddeacbbbbddddaacaceaecdadbbeecdabbcaabbedaedaccbdabdbdebcadbcaaedcbacbdccaebcdaeebddcdaeadcddecabbabeeecbcbeebcccbeabdbcceecabebbdbebbbadddbbdbcacebcdaeabcdeaecadbaabcbcbcdaaedaabcdadcebcbbccdcaceedebeddebccaddeccaaeaaeceecdccecacdcaaabcaeacaaedeecddcceddecbcaacebaedeedaeedbccbdadadbdbbecceecabbcbebbcdacdcdddcabbbadcebdaadeabdccdadcdcadeaeabdbcedeeaacceeccaebddaadddabecccaccdeebbadecebebbebadddddeadecdcbeaeeabecccebaebdcebaeadaacecdadcdbededbddbdeebcebadeceeadceeaacedbbbdcaeaeaabebaaddbbbddaabeecbdaaeddbaedbebcaadaecedbbdeddacdbdeedabadcbacecbadcebbbaabcdddcdececbdabadbbedbdbcdbdcccccaeebbbbeacbbdeebececedecedcbdaebbcaeaadabdeadeadabcacdeecdceaecdeacebcebaddaeaeccbccaedceaeedaeaaabddceccbeddcdcbcbeceaebdbaedcbbcdccececbcadacdcecebbbbbbdccadaabaabbbecacebbaceabccabcccebdeddeabaeecdedaedcdabcbadeecaeecbeacbeebceaebbbbddcceebabbadccbdeabbaccdaaaeeedbddcebaecbedeaadedacecedbebbdecdccaebddbadedbacabadbddeeedcacbdebebcbbedbdedbaebcecdbbcacaaaeececddcebbacaddcaccbabbecceebadccbaccacaadceeeedaddaedebdbadecacdcbbaeeeaaceddebedceccabaddebdabecddcdcdecbacccbececdecdddeeeababbadbdddebedebcceebbbdedeededbbaaebbdebdadbeaaabdceeccabdebbadacaaacdbdacdeadbcccdaaddaebbbaadddbccaebbdbdcacacddaabddeeeacdabeaaadcbabebbbceeeccacbcecdcaaaedcaedcbabdbebabbacebbaedeabebcbbacdedcbeeccbdbdacbdecddedbebecacdcdecbbccccdacbcbaaaaaccbbbcacadedcddebaeceabadaedbdeeaccecbdcbcdcaeebdcdeedbadadcbcaedbeeeabbddddbcceeedbebccccceebebacddeabeeccecedebbeceabcbadedddbbbccdabddadaccdeebbeeedadadeaabdbeeadccdcebebbbaedbcedadebeadbacbabaeeaeccbdaecbcadceccddcbcaaeabbdbdcedaacdecdbcdcebcdedbdbeccedaadedcccecebacaddddeebacbddccedcbcecbcabbeeddebbededbcdbcddaabcebdeaeaedbedceebacdcdeaaecdcdceaeaecbababccbecdabddbadaadeaaacdabdbdaabeaacddaacdabbeacedbacbdddcceadbadebadbbebbcdabddacbcbaccadebaddcbbadbabdadebdddaccccdadebdacacdcbaebcedbabaaeeaacedcececcbedbdabddaebeecdeaccebdbbcdeddaecaccbceababbdbdcecddcdebbacaeaaeaceaecedeecedaaeadaeeecddaddaebeeeeeaeeebddadcdbebabdddeccbbcbcbbabcdaaceedddddbaaecbbeecbcbeaddbdeedacdcacbbcccabcdcdebcaeddadcaeaddabbbbaeaacacbacaecdcebdccbeeabaecaccdccaeabadeabaadecceadbeeaabaebebaaceebadeabccadbacedaddeaadacddedcccbacedabaaecddedbeccadbeabbeaebcdbadcecbaaccccaecdbcdbcdcadadeccbaccececedeaecdcaacbdcbdccacecbaadabedbddebceaeaadcceccacebebcecdaabbcdeededebbdbeededeacdaedaccbddddadaadcecbcddcaddeddcadcccaedccbdababbadbeaaeedbbebadedecdaecadbddeebbeaeabbeeecedbdbbcbcdddaacccddacabedbeccbeadbcaecadacabbcdeaeebdecdddaedceceadcbacacdccbaadaadadbdaedddebeaccaccbaeebaeaebccaacabedcceaecbdacabadeddcedcbeecaddcabccdebcacbacbadcccdabeadaddbeaacaeaeadedecdeebdaacdbceeebeecbddbabaceadacbddeccacdddcabbeabececcdbecccdbbaebceededbedaadeecabaccbccdeabecebcbdeddcdacaabcadcadbbeaacbbdddebdcdedccaadccbeabedededddaedbecaebabedeabeabeaceddabadebbbddacaaddacbebacabeaaacbcbeaddaaebdebccaaceeaabeabdcccdabeebceacebdccdcaaccecceacebdbdccebbeaaeececddddccbeebeadeedebcbbcdbbaadebdddebeedeaedcdecbaccecebccbaccebbbdcecadcdbaddbbcaccbbcddcdbdddcaeabcecbceadaaaaaeebeebedddaececdeeeaabadcbcddcabbccdbabdabcadebaabcabeecadecabdcbcacaecdbdaeebebcedaeeaadbaccbbdccaaaaaccddebdecccadadcdbdadededddabebadbaededeecbbbcbaeeeceaecdebeccbcbbeacadcdbaeeeeceedaebacdeddbcbaebbdcbbdcbaedbddbccbddcaabaedcacbdcadcceeedeadbabddddaddcedddbbadbbebeddaccabebaeadbdeaabeaaabaabdeabacbaaeeebeadddedceeacecdcebcceecdcbceaabedeacadeabccebbaebaeaebcdadcebcbaaddecbcecdedbdbeacabbdddecceebcaecaceabdcedecbcccccbbeebaadccebceaededeeaeceeadceadeadeceebbdbcedbadadcedaaeeeedbacdaaddbeacbaabdeeeaeceeebabeadcebdeadedeeaacececacbdcbbaccbaedbccaedeabdceecccdeacabaceceaaeedddaddeecaacaccbbdeceaaceeddabbbddebdbcdacbdedbdbedaedcaaacceeebaddaceabbdaeceebcebdbbaabecbbbeeaeacccabebddaaddbcceddeecdacacbcaaaaaaebcddcebcedacbdacdedaecabdbbaaeacbddbbaeeedbbcecaebeedcbcdbebabacdeaccedeeaaceeadcecebeaaaecdbdaaedbdddbdedcccbbabadcaebaecbddbaadaabdcbdbedaaebacaedecbbadcecbceaebbbcabeccbdbeadadeadebbeacacdadceaeceebeccecddeddecabeeadacbabecbaddbbdbdcdaeacbdbdeedcaeccadbaceebbcbebbbaabaaabedacebedeebdedecbdadaceaedddeaabcdbcebdbdbcabdaacbaeeedbededadcecdcdacdedaedcebbbebebbccdabdddeaabdbeecdaedccdbcdcaccbadabcdecedbdacaddaebcdacbdacddadeddeaabdddbbaebaabaecaaacdaabaabceaecccdbecaaceadcacbcdcebaecccbeacdabbeebadeceeadbdddcbbbcacbcadceaceecacdaeeedebdbeceeaceddaeecddcecccbbdcbaebabedebabeecaddabacaabbedbbdbbebeadaddceadbdbedbaeaeecadcceeebbeaedaeccaeceacddabeadabcaabceddecbcbbbedeeccebcdeeccccddeabecdeaeeedaebaccbddbdbadccecedabddeadccabbdcbeeadccacdeccedddcbdbadbcabacbedcdebcdcbebececdacbbbdbcddbbaddbadaabbeeccbeedeaaadeeebdecaaddddeaecdaddabeebdcabeadaeceabbabdbbaedaaabbdcddabbbeacdeddccccababbcbeacccbdbcecbddebdecacdccecdeabeebcdadebbbaecdcccbbecebedacdedaacbeeabbedebbcaacbdacacbdeaaecaaeebaacbcedccdcbdbdceccbdedbbceadacedaacdaceeccdbedbeedabeabbccaecadbedbdbbadcebabcebeeedcdcbebccaaeccedcaebbbabaeabbbebaaeebdcbcbaddacccdaddaacecbdbedccaaddedceabaabcccebabbeaabdabcceebabdadcbedbccebabacacacaccbacaddebabaebdcdbcacaecadeccabbaaabcaabdcecaddcacadadaccccbabdecacdeebcabbceddcbaceeccbdeadeccedbadcadcbacdcdeeeceeddcadeeddbceecbcecdeededadbcdeeeeceeaeaddacadbdeccdbcaedcaceabceeeddaadceabbccdcaabaeeebccecdbdbcaeacccaedbadebeadabcbebabbcaebddbabcaadceddcdeeeabebddaabedddcdccebbbeaeacddcbacaccabaabbbddecdbdcebebadbbaecceacceeeddcabeeedadbaacdaaabacbdabbbaacdebedaccddbdeccacbaceccdbaedbbbeecdaacaedcbeacbdbabdeacbbceaecceccaebdbbadccbaeebabedceacabccacadaadcadebddadcbdcedceabbccbccecddcedeacbacddcacbbcbacccacaaecadadeeeadcdbcbeaaebdcedcdcebdeadaabaebeaccacaaddcaececdbcdcbaeeaeabdbdbbedabcedebddccbbaaedbebbbebaedcbeabeccaeadbbeacecbebabbdaaabbbdeaabcbceaabeebbeaadeeeaeeeacccedecedbbadcdbeceecdccabebceebbecabccccacbaccbadaeadbbebdeedadbbaaaabbaacecaddbedaeaebdedbebcbeccaeaecbeacdabcdbdcecaaedaaaebbcbeeaeaadceabcebbedaeccceeebdeacbdbeceeccddccebdbebaaeabdedeedededdedcbecceecabdcbaeccbdaaaecdebcabbdabeabcecbdcdcbbbceecdaecdcadceecdeabccbeeccaacbeebbeebcccadcecedeedbadedaaddddbacbbedadcbcdaabcbbdaccdebccadedcacebeedecebddcbbdcbbeeaeedbcbbbdbdacdecbbdedacaebcaaddaddedecaeeccbadaebcbcebeaebdecdaedcbaaacedaacebedaaaeabdccdbccdcdaceaedceccbeacbdadddddacbcceddabcdcbacaeccededeccbabcbbcdadeedacbddabbcadcdddbbaebcdadbbddcdecccbddddbcbcebadeaaadaceccaaebebaedadcdeeddebdaaddaecceddaceedbbbeaebecdddcabeeebdcedeaedabccdaaddadbdccbaddbcedbedcdcdcdabbaddbddeecaacbaadaeacebdeeccdcaaaaeebecaccbcbbbcecaddaeddbbdcadaaeecbeccdcbadcddeccdeeaececceaaabcdbbeeecdaaabbaebaeaebaacccadcccabcbdaeccbddadddcceadcdbaaddceabdecbceceaecbbeccecbaddbddbabdaaccaeedcdedbcacaeacccecacdecbaccedbeaecacbdbaaedaecdcbececbabbeedddebeeccabaccbccaebcdaeaceaceacabbcbbdebecadedcedbacededbebbbdebaececbbbdbbbdbbaebdaedbbbbdbabebdadceeaabccaceaebcadcdbcabbceeabdeabddebebbbedbcabdcebcdceddecbeaabdcbeedddabbcbddaaabbbedabecdaedadccbcdbcaecdcbebcdbbadeccdbbaadedaabeeeabcddbeeaaaeebabbebcacacededaccbeacadeedbcabdaeddbcedcacdecbccebcdeadbbbbeaecacddbbaeaadbbbebbcbcceebccbcccbecaeaecbcaebdcbbcdacdcaccdbecaedcdcacbbdbabdbbdbeabacedabaeddbceabddcdecebacaeadebdedbadabbbeeaeacbaadcecaebccdbceaceceecdabaaedacebbbcadccacaaaabddbeabdaadaadedabceabaeeedddecdacdaaadbdedbeecebecdeeccaeacaeebdccecdbdcdcaeaacbaababdcbadccdacaeacddceadedddedccbbddbdabeebdbcdadbeedccabaedabcbdcadcdebdeaaacecdecdbeacdbedbacdecbadabcebeaeecbaebcdaeaedacececdaacaedecacdceebeabbaeacebbecbdbdcdecceaecbbcecbaacabbbeaadcbdcdddabdbaecceaababeccecdbcceeccbebebddeecbbcbceebdeaeeeeaeebeebeeddcaaaabcabbccdeedcbbccedbaaeababdcaeddbbadaeadbcbbcdeeedeedacaabedbebcacadedeedadaddbebbeeddcadedbadeaceaccbebcbccebadbeeaabcdedaedbbddbdaababcacdbedabeceadaadadceabdddedbabbcaeedabdddabeedacdeccadeecebdccdaaccccbabcdcbbacdcccbecadbeceebacddaddcbecbadbdddadaeebddebceccaeaaebbedaaedcdbedeecbcdeebcecbdcceacdadaaebadeabcabedbeaeebdbcbaaecdbdcccedabbebeadabbbdedbedcacbedaacbbeaddbbbbdaceeebeabaadccbcadcaacbcecaadcdeaccbaccddebdeccdbdbdbdaeabcbaeedcccaadcebaaabceebbedcebccddaaddaecdddeadbbbbabeceecaeadeaeddcddcebeeeacdcdabccaedcdbaeeebdbeeaccebcbaaddaebeacaabbbcedcdcccdecbbcddccebadebaecaceebedcacceebbcaeacaebaeaeeedaeaedebaccdadabbacabdeacddaaedabcebdabadebaedcbdedbcedaecbcbceccddeaccacdcabcadabedabedbbcdebddededacddbdbbcbbcdeaebaebcebdaeaedbaeccedebcedcddebddaebacbcdcdcbeeeebdbcbcdabacdddabeabbcadcabdbacbddaedadedeadaeabeccdbebedecdebdccbddaaebecadaabaadbbbebbebaeebdbccccdaaeaeaebbdaabacccddbdacabdcaccacddabeeeeecabdccdbcbabbdddacbddcaeaeebaadcdcceaceeeaabcaecaacdedabebddeacbacacdabbaaaaeecbcdecacbbcaedbdedbadbabacbedeaeeadcbdabaaebdddbaabbbbebbbbaeaaeabbbddbcbcbeabbcccaeebbbedccbedeeabeeeeeadcacedabbdbaeeaaebeeaabadaabbbacdeababaecaccaecbbbdccabdddbebdecccccaaebdbeccebbccbdddeeedcaacdabceebeeeacdaadababeabbbbabccadcbccbcddebabcecbaecacbbeecaebdcedeacdcaaebaaeadcadbddecacdbbbcaecbdcbbbecacabdeabaddeeeaaecebadcaadbbeacaebeabbbcbedbccadeabecaacebccbedaddecadbadbdeddcdadbdacecdabbadbdceeabddcccdbbdcdedeebaadaeaaaabddcccebcddaedebcbebcbedbcddddcdbcccaaeacabadabcedadcdceeeeedeeeddccadccdabbdbbbbdcbdeedbabbdeeceebcdeededbdbeadbeeeaeccbbcceeecbeabceecdcedccaebecdddaadeadadaecedeeaeacdecddaacbbbbbceccababacaabcbedccbcdbaabdcccdbbcecbecceedbadaaacaceeabdeaaececcdedebbeeeeebabbaaddabdbaaaeddaaedecddbdbbadebeceecedabcacdcbeaeaaedcebabcbbaedebabacbabececaeabbabedbcbecaebabebaccaeaedaddaaeaeedebadbddcccacdedeebcbedacacceecdcebedacddaceaacaddaeccdcaaddcdceeddccadcbbcbcabbacbabaaeabeeceaebdbecacdcaccedaaabcbdeabaecbeedecceedabddedecaeeaaaececebadbdcbbabcecdcdbdcacccbacedbecdbcbaeeabaebdaddbebcbaeaabbecdacddcecbadebbbceccadaceeabbbcbbbdcabbbadaababdadaeaddeedcbcbaabdcbbcadeebebacdeaaedddcbcbccdddabaaacbdcdccbbaddebedeedcdeedeccbbbdeaadaacddedbcdabcaaeceeaaebccbdcaaabeedecbdcdeeebbdacaedcebcabdaecddaeceaaacadcbdebaebaddecdacdebcecccbbcddbdcadaacdedacaccbbeaabdbeeceeecadbdeacccdabcedaeceaeaedddbebaedacbbaddbdbcdcdaacabdddaacbedcbbbdecedcadaaaabbebaaebcdabbdeadbabebcaebcbeddcdbdeecdedccecbeadeeedaaabddaceedcdebbaedeabdcaacaaacdceeedbcadcdddedeedddedaeaacdcbbeedacacaeddebbbddcbeceeaabbcabcadcbdcedebddccbdcebcaaddabdeccebbcbbdbecbbbeddcaabcccecedaacaaecdbdecddaaaaccedbeeadcbbdbbbaeeeceecaeeabbaddbbbdeedbedbeddbdeadedcbbaebbeaecaeccadeeccbecdcdaaeadcdcddcbabdcecccbdecaabbababdcbcebecadbbdcacebcbccbecdcaccdaebabaadedcedebbcebeadabcdbbcbdabaeaabcdcdbecacebbdabdeebcdebeeebaabaddeaaacccabcaeeadcaabbdbbacedcbadbdacbddbbbcdddbdabbcabbabecaeedeadebbdacbcaebbdbbaeedaaaebeedadbdbaeaeccbdccbcbddcdabdaaededebdcddacdaecddecaaabdadbddbcabbaebddcebeeacddbcccacdbcabaddabdedbbdaaeadaaadbcaabdcbcdcccceecacebdecbddeddbecaccadaaeccacbdabbbcbcbcbcadceedecdbdbcaacbcadcaabcaccadaebdaaaecaabdcdcbdbdddbaddecbddedcbcaeccebdacdeeeeaaaccacbeebdbaddaaebcddebbddcaccebedbcaabccbdacadaebabaaaeacaeeedecdcbcebccdccbcbabdbceacbaccddcbcaebcdaaedaeabdbdeceeadcebddddaeecedccdbacbbdeadbbecdbdbadbadebbdabdbcedabebadbaeacaabeabeaacadbdedebdaeddcaacedebddbcbbbdbbdbecbcbaceeeabeaccedbdbcdaaecdeadbceadcadeceabddacaeadbbedddbaacbdeeccceccaeddccbaaeaaedcadecddbebeebdcceacaecdccdaddddeddccbceddaeeccabacceecbcddeeacccebdceceedbeeecdbedeabceedbcbbeaeccdbdddbdecbaecaceedbcdccdececbbacadedbadbacbdddadbccaabaeeabcabccaaadeeedbdbcadbcbcccbaaeebbeddececedeeaeabeacecbbcdcccbadbbdadebbadabeeebedecbcbeebaddcaddeddbbdebbbdbbeeddcaaedcebbdbcbcdccedbdaebcdceedaeedbaadabdbacdcdecdeaaaeaeccebbedeedcedbdcbdadcccdeebddbadeeddeadcdbccccecacaabbbddacbdabeadaddbdaeeabbecebbbbdcdabacaaceddeaeaeaeabaadccdcdcaeedbedabedcdeeedaceccdabdaaaedeedcceddedddbdbdcaebdceecacbbeedebbdeedbaceacceeecedcbbebaabeabaebecbdebbebcbeedccddaadadeedabbbeeddaaddbdddeebacabdaeeadbdebabaadddbbeceabceecaeddaecbbbeebbdcadbddcebbccdeccadbaaaddebcdedadaeadeeabcdcddeaaadaaaacaeaebacddecbcbdddcededceaeaecedaebdcbbdbccdecbbcaeedacecbaaedecedcbabcbbbcdabbccadbdaacabaabebdaddaddadebcecbbcedacebebcecdeecdceaadbebccbdecdddbbebecdedebdbbadadabdabebdcbebeacbcccbcdbeeabbbbaabdbdecdeecbedebaebcaaaadbcebcbaaeecaeebbedbaeeceeacabecbcbeebbcdcaaddaaebcedcdceabbababdcadaacaaeabbbbbaceecbaddacbdaecaccecacdcebaaccaccbccdbcbdbecddabbbbeeeccecacdcababcbbecaeeadaabecaeeccadcebdbacecdcbbaaadbdcddddcbacdceeadcdadacdacbaddcebeeeadaecceaacccacbbebdddbabeedaabccdbabebdbcdebeddcabcceebbadebaabcdbcaabcecedaebecabcacbeaebcbeaaaedeccaeebeadbdbdbaaadadabddceaabaaadededaedbebeebdcdeacaeadbaedeccdedaabcaaebdaecbcbebebcdddbecdeddddcbeaacbeddeebabdcddeeceabcbbddbdedebeecbbbedccdddcccddeedaedbebcececcbadaeceeddbbeddcdbeedbccdeaeccdebedecdadcdacbeccbeceaccbcaeeabeddeaccedaabecdcdebdacddbbdebcecabcebabeaddeabbbaaeeccecaebbadceadddddaccdcdbdeeccedecbaaecbcadceddbaaebccceeddedccebedcdcccebeaeebecabcdaaeedbbadbbddebeddacaacdbeacbadabcdcdcedddebbceeebacdcacdbaddbbcbadebcbbaceebabccedbbcedabaeadcecabdddceddaebccccaeecececcacbebedeedcedbbbaccaabdaebceebcebeedbbbdaeddeddaedadceaadacaccdeaecedcbbaebebdbecaededeaeecddebbbaebdbadecdebbeaedaeaeccbadccdbbaccedddececacbbdbbadebccdcbdbcbbcdecdbdaebbaeabcececbaedabbcabdbaabeaeeabacbdceecccaaabadadeecbaeddaaacdaeabaccaacaecccbeecdeabebbedbcddbebaebbaadeeaddcaeebddeeaeeadebeabcaeeddcbcedbdccbaaedebacecbcdaecbacdaebddbdcacadcdeddbbbedddcdabdaaabeeaaacdaecbacdabcaadbbcedebaabbeeeceebcabdedabccbbdcabcccdbadebabdabccdcdcaaabccaacdcdecaeaaaabccebadebebbbcbcdbcecebdaaebabdabdbcdbdddaeeeaaeaedcbdacbceaaaddbbaedabdbbecdaedcedebbbbbeedcbdebedbbdddbbdbabbebeeaadacedbcabaeebbaaacadccddaaebacdddebeaddabcacbbaaccdccdcbcbaabaeabbcbeeaebdaecbdcceebdddeccaaaaaeeebbceeabbaedcaebbeaeabbbbeecbcadbddeddcececdaedcddeaaebdcbbcdaabedcdccdcdddccccadacededdbacedebaacadaeddcbbbbddcecdcacbbbdadaccdbbdbcaeacbdacbbcebddabecedcaddcdcdcaadacbceeaccaedacdcdbcaaaacccbcedbdcbbbdeaaecaacbabdceaabaedbbebdbedcdbeecbedeebbcbbbdedabddbdadbaeccadebabbcebedbbeeebabadebbabaaccbedcacdbcbbccbcecdbccacebabacbccdaabbabdccdcdcdabecacccbdcaeeaebbcaccacdaabcacbeccbdcabaaeddebacbecceddbcaeeaebeaaddeeacbdbebacadedbdabebbbcdcceaabacebabbdbdadadbabdcdacceceabebabccebadaeacddeebeadeeecadceacbabccacebdedbabcadedeccaeaaddeebacabaeaaeccdecdadeabeecdddbbbaeeeceaedbbaedeecbadecccbcccebdaeddbebcdccadcddcceccdbdcecdeddbcbabbabccbaeaaaacddaadcaedeedaeabcbcccaceaabbacbeddbcccaaedcbecbcbddccddcbbaccecdbdbbdeebaceaebcaedbdcccbeadadecdaabdbedeeaeaadecacaecbeeeacabcdbedddcbcbbddcaeaeabdcdcceccebdcbcdadeabeddcbdcdcadbbcbdaeadaececaccaaaeecaaacabeeaeebdecebabaecaceacaacabeebddaacaaceccddcedbeeeceadbccaddcdbedaddeeabeadebcaebaaedaeadeadddebcbdabebceeccaeadcebedbbcbaeeedcbbdbaceddeeabdddccbbeddcaecacacbcbedaacabddebbdbaebaaedbccebaceaddbceccecbabdedcbadbbdbbbbdddbebaedccbdddedcbacdddbdacbbeddedcbabaeebaddceaeacecddbabcbbaaebdabedaadbddeddbcedeecbacededdcdedcccebadbdbcdaabbbabbcaaebeadbbdddcbaaedcbeccdceddaabdedbecceaceceeccbeedddbbbabaeabedaccebeabdbbabeebdbacddedcdebdaacdcaccceaabebadaebeaadabdbcceaaddacaadccacecebadbbecaaacbcdddbadeaddaddeeceebcdceebeeebdbaebcdbbabccaeedbbeebcebddeecdaeaaaaecabdacdbababdeebabdbcebbbdabcbeaeebdabcbaacbadebeececaacbcacebedabeaccdaebdbdaecbddbbbdecebcdaabcacbcdbadbaedeecdddcbbdaeeeeddedcebdceebcbebdeeaaabcdbbdadbacddcbadcbbeaebabdeebdaacadcdaeaeebedeadeeaebbadbcecbdccabadccdbeddcdacecaaebcdbebbdcddbbbaedcdeeccbadbbadaceeaacaabaccdacceadbebbccacdcdbaceceaddedaaadeccdeeddabcabbaceeddcecbdbacdedbbbdbcbbbbcbcdbbddcaaddeadaeddbbdedbaaadbacbdeecbeeacbdcdaccebdcecbdadedeadadacccbaebcaaacdeebaeacddbabeaccaebbdceeeebbadbcaadcbadcbdaaeeaeaeadeaaccadbcbeaddccebddcecebcccedddaeccccbeadabeecccbcdbdbcdbdeccdaeaaeccedcadcdcbeaabcdebcadacaacdaaaddcdabcbeeeacabaddabdcdddeadccaaddcecdbeeedabaabdddbeeaeaadaaaccccdadeddcbcadceabdcaceddbadeabdaeacdbeeccbbdbbacdbeccbceedceaaaddebbacbcdaccaedabcbaaebceacecccabcceaceaecdaeebcdeeddddaabccabbaaeeccbcbdcecadbcccbcddabcbebbddcdeccabdbbdabdccabaaeacbcbcedeebcdcccadbbdcaddebedabdaddaceeecbabbbddadcddacaccadedabdeedcdbeeedaeeeddbdaeabacdcedbbddedaaaeadabaaccaadececaadbccdddaebbacacabeaacceddbceacbdcaeccbdebcebcaaaccdbcececdcecbbbebedecbbaaecbbbddbedcaaedbebdedcddecaebbcbdeebdababcbbdcbcbccadaacbcababcbacebcaadcdecedaadeaebbcadeeaadbeecaddecccedaceacececcaadcddceaddcabdedeeeeddacdbbbdbaccbeeecbdacceddccbdecaabbddaeeacdddcbddeaabcadcdcdadeecbcbdebcadbbdcabbbbaaedbccaadcbdbadcbddcdcacbedbcbddddcbcbddececddeeabeaacadbedbabcdbedeaccbaacdedaacdceebdaaaeeeebdeeadeecacdaaadaacceabbabadbadbbcaeaaaebecdcbecbaeceebecaadbbccbacccddbceddaddcdedbaabbccaceaeaccbabedaadabbbaeebbaabcccebdeebabcddcacdeedeaedebebcaacadaaadccdccbabcaeccaabbbccbbeaeddaaedacbccabdbdbcceadebeebcddcedeeaceeeddcdbeddcccaddacaedcbadecdcdeabbaebccbaaabedcdeaccaedecabcaaddececdadcebbacdbedbaedbceabcceedbdccedacebadbedaaeebadbabecebeaadeeeedaceabedcebddcbcdcadadcddbedcdaacccbcedccccacbbcaacaacaaedcbdbacebbcabbabdeacbeaceabbcccaaddbbcdecedccbccaadceaedbbbbcacaeaaebeedebbbccccaabbaeeecdddedbdadbddeaabadbeadbddcddaeebdacaeeceebbaebcdbbddadeedadcccaeeadabeaaebabdcaccaeceadabdabbabebeccaaaeacddbaeccccceaacbcadadbbbadeedebbbaedbecedeebabddcceaedbeecbaadaebdbabbadebbaaabdecdbeeadabaeaeabdeeaedccccdbaecabbabeaaddaccbaeeabadaeaeabacccccbeddbcaadadebdbabbdeeaebceaebabbeddabebcedbbcceadbdcbccbaadebadadbccdbcedbeccdbcadbadbcbaabacdaacdcdcaddceeecaaeeeeedaedbbadcdbecccedacbcabcaedceaacaddeaeedeedcbbddddececaeeceacebaebeacbbacadedbabdccbbababcdddeeeaacdddeeeedcdbddeddeeedbcaeccabcedadcbaebcdcdcceabccdbddbcacbdcdceaaedeeccbeeaebacbddedbbacbdadeabaebcaddacdcdbdcaecbcbebdaecdadbddacdeeacccdacbcacbeacdeacaacebeecaacebbaaaedbadbaabaeebcdeebcdaedbeeabacebeedaeccbcebcebbccbcccbceebeaacbbcabadceddcddbcccadacedccdcbbcdbdbaebdaeaedcbebaaeceeaebcabaaeddceddcadcdcceeedadcbeccadddecebccccadabbeebdbbaadabaeaeaaaacbedadecedbbeceedacdbccdccababecebbdbaaeabbaeaddceceedebaeceddeedbbeadeadbaadccbdecbddebedeaddccdccacaeaeaacccacdaaecbaaccddcbccbddaacaaeadeccdbaaaccdbdbdabecdbbedcebadaecedecdbcbdbddbbebceebededbceccaccadaeaaebecacebabbddaeebeccedcaceecdbdeedebdeaedbbadddbdaaaeebeebecdeeaadeeddecdadddcecdaadbbaadbddadcbeddeeaabcecebbaaeaedbebadadcaabeecebbacbaebabdceabeaedebcaacbcaabdbebaebaebecdcdbbeacccbbadbcdedabaabbdacabdebdaaaaddacaadacbadedecaadbaceccaaaddbbcabcbcedbedbddacaddceaedabbeacbdbaabeeadaebbaedaaaaabaaaccbccbedebccaddacdeccbbedacedadabbaabcebdeddecaddeadeaccebacdaecbecbeddeabeddebccaacdabbababbeaacbddbecaabecdbaaaabbebabacadedcbccaceedddbcceacaddeeacddcaebbcdbabeaaaadaeaaacaceacdbbcbdacaaaecedaccbebbacbcbbaacdebebdecaedacbecdcacedadaaedcacbdaacccecbcdaacaceabebddcecaedeeeedadedadabecdabaeebeecebcccacebecdbcedcbbcdcdaaabaeebceaccaacbadaedbedcbeddaeebbeadacaebabccdbbbaebbdacabdbcdbbebebcadcbdacbdbceeeedeadcddbbcdacabcdcabbecebeacbadaeaddcecdedadadaaeacebdeeedbcdeedcbeeaadcadcdcedbbdecbbccedaaedcaeeeededeeaeedaecceebaecdabeedeccabaedcbaccecdaaccacbabacccbddcccceaceecddceabdcbdbadbcdcdedbabbedbacedbecbececdbbdbebddbaabeeaaaadecdecebebeaedabebbbcddaebdeddeebeddbcadacabedddcdcabecdeecbabadbcacbcbaceacbebeacbdecaabeaddaccacaebbbabccbdbbdecadacbacdcdcbbdcdbdddcbdcdcbecddccdbbbdbaaeadbbadddbbadbdcededcbcbbebedeaadeeeeebddcaaeebebbeeacabeacaeebabcceecdbcddcaeabdecaddacecbecebabbaaeeaaddcedeaebaadacddeaecdadddbaadababaecabcbededccddecccdbecacdeccebcdacadaddbeeeabccaebaadbcbbaebbdeebaeccbdddedcdabecdbdceebecbeedabaacbdacdabcaebcdaeeabbddadbbcabdabaccbecebcbcebbacecadaddddbdeaeccdaecaedbcddadbdbedaaccdcbedadceedaebbdbebedcdbbbbbdbaeadecdbedcecabdaaeecbddeebeadaaeaebacccebbdbecbbbcebebdeddadcddbabddceeccceadebbbdeecbaeaacebcbbabdadebeabedbbcadbedceaecaddbecdeaebddceadeebedbaceddccbacbdededbabdcadccdadceaaeeceedaabdbbbdccddcccdcdedeebbadbcecdecbceaedcaabacaadbeabceeaceeaccaadbbabbaccdbabbceaacedecdabbabddccbcbadcdcbacedebebaeaabdaeabbbdbeebaecbacbccaaabbdaadcbeccecbbedebabcbadeabddaaadecadadcadbebaabdaebabeaebbaacdddddaebedadbaecaebddeeebdaddbacdcecaccaeabbcbbeeccecbcbbabaaeaeecbaabbeccccaeddabaabcccdeebecdcebacdcaabdabbbeadcaaebbcddcdaddccebbbadabebbdebdedacbadbdcaccdcbcedecebedabbaddbeecedeecdaeccbaaaaceddccdcdecccadaeddacccadeedcbebdaceedbddadedaeaedbbdeaeaadeadcbdbdebdedabdaceeecddccbacaaaddbddbeeebabddebabecdcacbdcccdcbddaeebeececebdbecbeddcaabbadbdaedaaebbbbddeaaccebbbdbeeebecdbdcbdecbcddcbbcbceedaeebeeaebabaeadabadccadaececdddaeddecdaebedebbeadbbaaadccedbdceecbecbbacadaeebbcacedaadcaadbececddecbddecbaebbcaaaddaacaebaeaedcabaeebcededeabcdcbddcddbebaeccdacabccdbdaadddabdaeaeedaaeedcacacddebcdbccbaecbadaabbbeababadcbdbcecceaedcccbdcabbbdadceaeaceebeebadadcecdcccaccbcaacacabacabeebbddcccbbeacbdbebbdaaadbeddbdbbecedaabacdeebacabebbeabbcccceadeeaeaabdadaccaedbdacbcccbccbaaabececccacbebbdccbdaeebceebdebccaabddadcedcbabbcaacdcbdbbccaddedebcbadbdddedbddbccaecabcbceadabededccdeadbdebdbdbdddddacbbcbbcbeebaabbbcedeeabdeacdecaacdeecdaacbbbecedadddecbceaebdabebdcdacbdaaceedcaeedcaadbdeceedbeeaeeeadbbddaeedbabdceddeccaacaabdeaccaacdddbcdabbcaecdbeeddabccbbbaedbcbbacbcaedabbaeaaeebaceddbdcdccabadaadddbedececbcabddebeedcbeccdebdbeceddbcacdeacdaccdeddbadadcadbdebaedebdebbbabbaadaaacdbeddbdaaacdcaeeeccdeeedeabcacceeceacddddbdbbbdeaaeaeeddceeaecadeacacadeecdcedbbeeeadcbadaaebabbaedeccebcebccddaabadeddecaecdeaeaeeeaeaccababbbabbcedadcacdcacbdbcbcbaaabccadbdcddccacdcaceadbaeaaeeaedecabbbdbcaedadcceadadaccaaccaceeadaebeacdceceadcdcbaadbcbdcddecbabecedcdbbdecdcccacccddcecedddddddebbeaadcbebeccabcdbcebaaaaabcaaacedbecacabaaddabceccbabbeccebdeadcaccdabaceaceadcbdbdbeadbdadadddcbbbaeecedaacbabcceadbdcbbdbacbbaeeeeceabbadcbcabdcbccecaaeceabedbcbabddaadadeedbeddccdbddadcaaebbadbdbbaadadddecadbbaabadeabadaaacddbccdbacdeabbabdaeecbaeabcadacdbbacdaabaaecbcbedcbaeabeccbecbdedcaccbedceddbeadeeeceaecddddcddbceecaedcaddaaedacbdbcdaeebecccbcaeccdbbddcdedeacabccdcedbccdbcaaccadcdbceabeeecdbaadccabcdcedbdbeaacaadbcdaceecbebadcedeabdcbbaadabcacdeeccadededdeddeacbceebcdaaeadaaeccbcedcccbdedccedeccdababbedcadcecdacebebdbeaceceebcbaaaceebdabebaeeadaacdbdebbbdbbbdbbaaebeebdbeebebeabddeddeddcbdedeeeabdbadbdeedccbbcaeaabdbaacdcbacdacdbaacadaceacdcdbacdeedbbbebeabbcceeddbdcecccaadcacddadececcedecededcbcabdaebacbcbdbdeabbadcabdbedaeddadbdcabbeacbacebcdbbecddeddedecabdcdacdbcadeacaedadeecbbdcebbedeaccceaadbecbadbbaeadecbcecabaecbadecdcbddeabdebbecadbbbcecbcdcbeadedaabbcdecdbecbbebdcaddbecddacebabeebbbeeaccbbbabbcbbecdcebaebabdbdcebecbeceaaebdaeeaaebbdbbbbcbbadecbacaedbbaddbeebdabccabbeeaebacccebeeacebbdeedeecbaaaaedbdebeededecddededcdcdddcdbcaacacccddceacaabcdaaabdcbbdbaebbcaaaaacecaddcdabcdbebeddadaadaebeeaccaebabbddcaceeddeaeddcebdbabbaabdaecdacbbbbcdbaaccaeddcbadaedecedbaeecccceacacdeabdeeedebcddaccabcddcacaacbbdddcaabaccdaeebadeccdbbcddddcbcdeebedbdbaedccaecccddebcaceeceeeebcbbbceaebecdeedcbddddaecbeddabdaeeccabecaeecaecaacaddddbedaeeadeddcdbcbbcceddaedaeadddcddddcbbebdcccdcbccbeccaaebbedcdccdaebbcdcddabbedcdedacdbcdedbaaeeeaadedaaccdedacacbceacdbcabedeebcedaaadccecebbbdccdebaebbaddbedbeaabcdedaaeaccbcbeceaeaeeebabeacedadcbcdbeddcaebcbeddbddacadbcedbeccdbddbbecdbdababddacedcdbadecdeacecbddeacbbabbbacbeecdcceacdabeabbcaeccbedbcebabdbedbecdacaaacaaebaadeacddceebaaddeeebadcdccdbcebcaeaeeebdcbabbbaabbeccecdeccdaecbaabbbdcbdadbddbacbbcebbadddbedbbeedbacedadbbabbceaddddeaeabacaeeadcaddbceaaeabdacdeabbeedaceeceebeabacecbbabbbaaaecbdaccdbccddaebbdbddccbbddbaaecddcaddcadeaaeedcadbdbbdaadcacdaaebcebcbabaaabceabdeaaecbcbecaebcdeadbecceccadeecbbdceaecdacbbeeeabbbbdaccbccdcbdcccbcaacbeeabddabeecadaedabbddccadeabcdddebaabeeedbadceabbdabbacebcccacdcbccaadaccdeaabcbcaacedaecbabeeddeabedbeacadbcddddbcabcabbaadeebdbeeeeedbbbadcacaecccaacdddcddadbbeacbdeecbccdadededdeceecdacabeadecddddecdbdcbedbbccdecceaedcbcbaeeadcaccacebaeadeedcdbcedddbdbedaaebcabbdcbeabdadaabddcaeecbbcdbbbcdbedaedadbaaccaaeedadecedbdbdaabeabbdcaecadbbcaebababbbddeddedcccbeaacaeeccadabcdaaebdbddbccabaaadbbbacdbcedbbabcceedcddcddcbcbdbeedabadbdedbacadaadeebdaeacbcdceaedbaabadeaedbbdeaaebaeacaaeeeccdbcbbceecebbaeccddacaeccaabecabcdededabbceceeddebcebaaebcacbdeeadaccedadcaaeecddbcacededaedcabdabdcecaabacbcbcbccacbddbabcdcccecbcceaddbbcbcdbbcbbabecabedeeeaecaabeeeebccecaabbbcceabdaedabecedabbcabbadeedbeaeeceeababceddcbdcaadcddaeaddcebaeeabecabbbcadceebceecdccedbdbdddcbbdcabcedadcdbbccecddcadcaedbebbcdebbccaeeadebaaeaaebbcceeebaeaadaacacebabbbeeeccedeccbebeaddaacacedccaaedecaccbcdbddbdeccebcbdbdbbacdbdbcabdaeecdddccdadbabedeabaceeccdeebdaecbdebeaddecacceedaeabedbbddabcdaedececeaaeeecbddccabaccaeabaebbdeeccdeceebdabdbccdeaeeaedeabbbcedbbceeabdebddebddeeecdaaddbadeabdedbabbaeedcdadacabdebaebabeaedacdbdeaebceecdbaadeeceeeacdaccdceeecbcbaeecdcacbebbdbcacacdceeedadeddebbecadedebadedccdddeeeddbeeccdbcabdbaaedbedbecaabbbedaabbcbbddbddbacdbcbebcccdcdcebaacabddbabbecdebcbaacebecbeaecddabacdaeeedebbedeedbcdddeeacabeeaeaddcbeebbdadeedcdbbeacddcddccbaabbbbaaecbcbaeacdbeabeecbcdababcdeddbdbcedcdbcccdebdcebebbbaddbaeabaaccacbaccaabeaaeebbaebdeccbacddecdbdbaabeeebdadddcabdabeaaecbeddcdddddcaeaadebcddcaeeccdcaebaebabbbeacdaaabdbeadacedbddcdcdbbeecbedbceecbdaebccebcceaedbcebedaaeeadbbcaebabceaddbbcdadbdceecccecebaaceccedbbbcacdebbebdebecbcdaebddaaebbccacacdcacceacecdabadaebadbcecabdbeeabcacecadeeebbaebcebdaaaecbaaebeecdadadadcccdbdeabbdabcccbeaeddcceabcecdbaddeadcdcddbbcaadccedbebbadbebabebbbeedadaaeabbacadbaedadaeacbececcaddacebcbbeaecceaeabcccadabececaaabecdeaededeadbaceaceeddaeceecdacbbbcdcbaabecedbbeedeabcbcbcaaecebecbadbdcbeddaaacebdbcbdeabbdbdcbbaeeedbeaeeceeadaabbdaebecdbeadabebebbecabccbdbedebccdadbeedacadceaaeedabdaeaeaeeaabbaaaeacdbcaccaedbddacbcadeababdcbeeaecebdecadeadcabaebbceccccabccedaceceecbbccceabdadceccddacbddcaadacacbdcdddabaaabaddcabcacbbeeeecbdeadeabaaedecebbbdcbbdeccaebaececebaabeacbbcdeaeeaddcaaceadbaaddeabebcaaebdaeeaaaeabadeeddedecbaaabedceebccaacdcdbbdeaaacacddcbdbadeeabaadbcdeabaaabacabacddcacdbdbcedadddceceeeadcccdacaeaabbcbcccebaaadebeddaccadacceacdcdddeaaebeadaaaeacdcbcceaaaadccbaccdedebcebdaedbadabbecaceeedbdcaeaddcdcbbcabaeedddbaeacddbcedccdeeeaaaddeadbacceedadacbbbbdbaeacdbdceeecadacdbdedcabccbebbccaaaeeaecccacbebabbcbbeadbbabcedabeaeddbeacaaaddeececdeaeebcdbaaeebbdddcddddacbcdabdebeebaccabebdedcbdccdebcbeccceeebbebcdcdedecdabdaaccdaaecddaecaebacdddaddeccaaedaaeccddaabbeccdbaeaecaeaecaeaadadceeedbaeecaedcdbcadacaeeebeecdccaadedcaddebdacbbeadccbdcccccecadecadbcbbabcddadcdcdbbdccabdbbdceacccaecaccbcbcebdceeeaaddcdbdbacbbeadedccaaeaabaababbbdcdbdcbbbaecadabccbeaecedcaabbeaaebaaaaadedadcdcdcbddcceacaabaeadceeeeeccaaccbcedbebabadabcdaaaadedaceadbeedceebbbdeebdecdebdbddadbbdbdcbbdcacbadcbceeceeecbddcacbadcaadcceaeadddabaebeceadddceceeadceeeccbdaaeeebdedcccbecaeddaccecebaceacdaccbebdaddcadaedecabebbdbdeebeccceeabbccadbeabdcebadcebdaeeeadccaeebaebdbebbeacbbdedebccacedabebdacaeacdebbddabaaeabceaeecaedbecabbbaccaaadceedddbcedadabbddbebedbcdedaebccecbacbccbbeeabecccedecddaeeeadadeeceecbcadcdedbededecaddabaeeebddeecaedceabecdadceaaaabbddeccddbbeecceeeacdbcadabeddbadaaebabeabbabbeaeebbebdbaacaecccdecdeacedaaeebcebdceaddabadbdcdcbcdadeeadcabaceeabeaaeadaddaebbeadbcbabdeeecaaeeebeececebdedcdceaabaeddabecbcadcedbccdcbacebaaeaebacbaabcdbecaccdedbdbedbdccbdcdddaebceeddadaababbdccbcdabebdccdabaacedcebadedacedbebddbdcdebcecccdcebbeacddacdbcceddecaaeccaeccaaeaebeaadaecbabedadccaedceaaadbccedbaadcdbbeccbedcebaaaacccababdebddecadbbaebeddbcaeaababddddbeecdcbdcbabaaebaeacabcbeebaccaeedcdbeeaadbdbccdacbdaecebebedcaadbcbccbbbaebdaccaaeabebdadecbedbeeeccdbebeadaebcbbaadbcdacbaebebbbaeacdeebdbdeadcecdbbedcbceaeaaebdbcbcccbbeeabaacccdabbcccaadaadeeceacbeaebecaeebccacaaaadebdbaddeebabacaccbaadadadaacabddcecbbedbdbaeecbddcedcbdeebdcbaacbeddcbacadaeaddcacccbacaedababaddddcccaaddeeadebbdbbeeccaeabeecbaccbcaabebbbeedacbdbabeedbaeedccccadbcdceaccbceeeaccceaedbabbebedeecdbcacbedcbabdcebaeeedbecedeecedabaeaecdeabeabbcecbbdccaebeadaacbbdacdeacbcbedceedeccadeaadeaeccebbaedaccebcdbccdcbbdaaeecdbddaeebcacbdedcbacadcaecbbdbebaeccdeacdcbebbcbdebcddaacbdcdbbadcebbacddecaabeeddceedcabadbcadacabdcbacdbdeabdbecdbdcecaedeebebdeacecaebabceeddcbbcbeabdbbdaaecbbccabeddaeaedcdaddbbcbdcdedebbdddaaaaecddadbeddcaaebdaecbbbdaeabcbccaacaabdeadcdbeccacccacdaaebdccdcbccbbbedbeeeacadaeaeecbadccccaeccbceabcacabeaddedbecaaecbceadaedcaebaceadaccdeedbdbdaeaddddddebbdeeeaaecebbdbadbbadcadadccccdddabaecaaccacccdcddaddaedbcbbbbeeecbeedeeabbabdcbeeacccacccdacabeabcaaeaadcecaeecdcdbeedacedccddbbbcededaccbecddeeeeeaeddcabdcbeeaaeeeaddbdbaceceabdecbdadcddabdcbedebebedabeaaabadbadaedacddbadcddeddacddadcbebdecbcdeecbcccebcecceabdbabbadbbcedbcdbdadbeaebaceaeedcaaeebebaceabeebdebdebedecadaeedbeeabbcaaabebdcaacedccacabbcadcdacbabdbbeaebaccacebddcaadaecccdaeaaadaccbabaedcecaaeacacececbcbbcddadbaccccdababcccecbcacbddabebeebcababecccaedabbdaabaabedaacbeecbadadacaecabdcaacaeabcbdbcceaeccbecdbbeeacecaabaecedcbadccddbdbeeaecadbebdebbabcddabadddbcbcbcebdedcbcacbdccecbdccbaaabcbadcddcacdabdaadccbadcbcccdaeadbbbdcedbebbeabacbaabcdabeedceacdabedadcdbbdbababcaecabadcbcdeacabbdaaccaebbeedaeeacaeaacecabeceedcbeddddbcdcbdacbebceadbdbdeaacedcbaabecdbbabccabddcebccadceacabbbeeabbbcbaeddaabebbcbbcecacdeeabeecdeadccbacdcdedbaacbaaaeedaabbddaddbbabddebeaedceabbdceecbedecadcabeebebbbdaececebbbacdbababbeadaceadddcabdcaaaacdbebcacedddedeadecebdeadbaaecaaeecceabddcdadebbcabcbedaaaaadcccdaabdcacaabbbbcddbcdacebdeaccbebcadcdbddbdbeabdbecebbbcbbbeaccaaceacdceeaccdacbebabecdbdbadaaacccaedbbbeecabdeedbacebcaeebdeaaceabbccccdecccaaededcadbcbcebcedaacbdacacedaccebedaacdaecdabdbadaaacdbaecbbcebbbcdbdabedcaeaadaedaeadccddceadacedbcceeeccecceeecccdaadacdcdaacebcdadeaedeeaceccbeaebeabeacbdbbdcadaddbedddadcdaadddbadebdedccbaaecccecacaeabdaacbcccdacaaebbccdedeccdceeededbededcadeadecaeebdcccbbbdddcbaeeccaacbabecadbcebeaeebcddeebceabaeabecbdddadbdabddddbbcbedececaeebebeabdbbaeabdbcebbdaeddbdcbaddbcdaecccacbcbeedaeaaabcaceabcbeacbdaebdcbddeaaeabaaabeedacdacdaaecdeccacbaeadcebbedaabaaceaedaebaaedaeccbaeddbdaeeaaabcccbaedcecaeeebbcbeadbecdebecdccaebadebeedbdeeeebadddaeabdbacbddeacaaaccdbbdecacbeaaddebdedccbaddaeedebabdedababdccbcbcabecdcbbbcddeadbcbeebaeeadbbdbbcebcedabbadbadbecdeeccdacdcbeacdccecdcebdeccaeabddeacacaecdccccaebcebbcaaebeacbbebdbbcdbbbeddebaccdaacbcaadbdeaaeaccddcebbdcecaaeccbcdeeceaeedcccaebbcabeedbeadeaecbbddceadbedbecabdcbcbbaebcdeaadacdeebaccedcdbcceccdcdaddacdbaaecccebdeddababaaecbdbbbbeaadebbbccdcdcdeacdadbaddccbddeccdaddaceebdeeabedbdaeeabebbbdbdedbccaddcddbeabeeddadadcdeacceccaadabeccbdeabeaebbcdabeabceabdbededbeddaebceeeacdddabeeadbdcedcabeabddebacdebcabcdabcdbdcbbdaeabebaebdaabeebdccceeedeeaeadabadeaebccbabbeabcaacddbceddacceabbedbeeaebbdacdeebdaecbbaccbeeebeecadcdbcdbaebddbbceebccdccbacdebacbebabaaacdcccadaecbbcecabcaabbddccddbcebbeccddbbaebabaccaacdbcceecacbedcabceaaebedaacadcceaaaabcceddbdeecceebeaeaabdabdcdcddecccacaddbbabcecedabdbbbdccaabdbadccddbdbecacceccdeadaebeecdcebdcacbeacbcbbdeabbeabccbdedbddddbbcacebcbeceaebcecadacaececebedeaabeaaceccaeeaddebcbcbdeadbecdeedeebedbdbaeabeacbdadcecdeccaebaeadeddeecbdcdebbbeeddebbaadcdcbccbbedcbeecbbeecebcccecbdbddcbeabcbbceadeacacecebedadeebcbbaaaedadcaabdcabbadcaaadbecaacbcbcbddccdccbaeacdaaaeedceaceccbcbdbccbcecadcccabdedabedbcabeccabccdcbcadadcedadbedccaddddbdabdedebddcbeabcecbcbadaddcecdbaaeebececbecadcedbbdbeaaacdecebbbeebcebeaadadccabdcabcbcdebdedeadbcddbcbbadcedacdccdabbaeceedcacedebddbceccedebaddaececdaeacacebbebdccbcbeeadecabacdbaebbdaebdbeccaaedababaddeaedbadeccdabeaaacdcaeeaabddacccdceaebabcbecbaedebccdcdbeddcdaddddacbeedecbbeddbdcaabbaeceadeaddedcdcedcebccdeededaabeacebaceedaabdeabadeedebedcecacbdccdecacaddbdbdbbbebbcaaeacddadcabdcccaacddedcaecaeadeebcdbedcdbedaeeebabbbdacbaecbabcedaacdedecdddeccdeadbebebdbbbecebdacbeaebabdbbcbaabedeaeeecbdaddebdebbcdddccbabeaeadcabbdecabcadeabcadaccbabceccbcacaaaabdadddcebbdecabaeebcaeedebdbcabaacdccaedbbaaeeebeeecebbedbdbddceeaeadbbbecdabbaeeccabddadebacacdcdaaedbcaececcbeccbeeeacaeaeaccabaddbaaacdbeaabaacdaeecdaaedaeecdcbabcccbebebacbbeecedddaaecddaeabdeccdeeeaedcceacbebceacbdbdcebddddbaababedeeaaacdadbcbcbedbaddaeeaedabcabbcacaddacbcacaacbacbcdadaacddccbabcccbdceedabbcaacbccdaedabacdacabaeeccbbaebccacedacabbaeecbbadabbcbdeaadbaaddececedccdceabdaaaeabdcbeeedabcdddecebbbeeaaeacbacaaceaedbdadeadcbabbaebdeecdabbbccbbcaeceddcdcddcdcbabddddcdecccebeeeedaacddcabacbceaebdaaeacddaabecdaddcbbdabeceaeddecadbcddedcdabbeaadbcdeaedaebbbbedacbcdecadacccbacaebdaadaccdcbcdedaacdbceadaddabcccdbecacecdcaebcbbcebeceaaabbbeabcaebaabbadaceadbccadcaebbddedeedcadbdcbbeabbccdbabeeecbdbeccbabddaedbcddbdbbebdaebaceceaacaeceeedaadecabeecddecdddccdadcddabacaacaececbdddceaaaeaebadaacbcabedadebbccdcbbbceeabadccaaacbadbadeebcbbeedbeadbaeededbdaeaeaeaecdcbecdeadbbdcbaedecbbccbacabccadabcbaaceddaadbeaacecbebdadcebdacebedaeaaadbabbbcaabcbdbddbbcdaaddacebdeacacdaedbaebecaaadeebaaaaeddeecabeacecadeabbcadcaeaacaeaeadceaecbddddbdadaddcbcdedabeaeadeceaedccbabeddbbecedeececaaaceadeaeabacceccdcbbeacadbbadcddebbceaeceecccbaccbdcedbbcccaceeebcbaecdcccbebecddacabdbcccecbbcdbededadacbecaccdaabddabaecbebdcdebbceadeaeccbbccacedaebbacdabceedacbdcecadbdeaccbdeddedaaadacbdadeeecdeabaeceeaadaceabaceacaaacedeaddbdcaaeabbccdadebdaecbcdbccecdaeeeabaaedccadccacaccbbddcabdaacbadccebdebadddeaeaebdcdcdcaaebecebdeeadacbdeecbcdeabeeeeecbacadeecbbedaeedaecdaadcbbebedbdededacecdecadacdadeaeabdcccdeeddeebadcbaceedeceeaaedbeeeeeeabbbaaecbacbecbdacddaecedaedcbbcbbbacacdeacbbdddadebceeeabecceaaacaadadedacbebbceaeabadeacbdabbbadedcadedeeebaeceaccbeecbabadbeccdcacedbaecbbdecaceaacdbaabdecccdcaedaaecccdbccbeddecabbbcaaebbececddecbbdacaaaedebbdbeebeeaaeecbebbdeacdbbeeadabeebdbaccaeeddededcdcbbcabdaecabbeebdbdcceceddcacdabbdcbdebacbaddbdbbccbaeadcbcdeaaabbcdebadbbdadbedaacecebcabedcdcecbbeceacdeaeaeacbabbbbccdadecdeeaebabadeacdcecaeadddbcceedbeeedacaccbaebaedcaecdddedcaaaeeaebbedbdadaaabbccdeadebbdaebeadbcdeddbdccbdcceeccddbcbcecccdaccdbbcdaddaaebabddceaaaedbdbaaeacabebbbbdeabcddacdbadecadbbaeaccdceaedbabeccdecebacdedcedaebebbcecddcdbdacbccdeaeddabebcaeaeedcbabaadbbddddcdaacdcdcadeeeddbbdddcdcdeecdbcbdbcddecdcbcbabbecdaabceaaddccbaccecbeabceadceaadccaddebabaedaabccdbadeceeeddeaaadcdeeaebeabdadaaebccdcdbdaccaeaeddebeddbbbbbaaeaeaebeacdbccceabbadeabcbebcbaddbddbebcdcaaabcebdcedebaeebcbadadedcaecbdcabacbcbadebcacadaacbabadccacdeeeedcbeabbeeaabaaabbdacccbcbddcaccbbcbddaacaaeddccdbbbddeaedebadcbbabaecbccaaceaeeebcbaeececcecbccdbebbeeceedaacaebbdabeacbbededcaddacbeeeaaeeddeccaaacceeabababcdbceaddbbacbedcdaecbedeececdbcacceacadbacdcabebbabceeacceebaeceedddaabceebbcedabacdabbdaceabedecebdbeaddecbcaaccaecacdcdbbeeabdbcdcdedbcedbeeaebacdbacacaebdcccdebdedcbbaeebdbeaeeccccccaebadadcddaabaeeeddecdbeedddbddadbdceabddedddaceccdaaebdbaabacadcaceedbdebecbdbbacdaadbeadeedcccbccceeebaeceddeecbebdeccbaccbebcdddadbbcacdceeeccaadecaaebdcbdceccbdadbcaceeebedbedcbcbadebddadecebdaccadbbacabbdddeabbdabddbdaeddaaadecbbddddacdcbcaeaeaedbeaeddbdbeedddbdacdbaadcabbedadedacdecdbcadbdabdabcaddeacbeddbaaedaeceabaabacdaeedbbdddabcddaebecaccadcecbdabbdaeecdacccccedbcdbacaddbcdecdaebdebdcbaedebcbddddaeecabbaaaeccaaaaddcdcbccedaaedbbccaedcadddcdabbdbdccedbeecacacdbcacebddddcbedbeabeebcbaaeceeabbddcacadbcabececddacccadeccaebccebeaaabcbeccadbbbaaceaaacacdcadecbaebccdbacaebbaaaebbebdbeededddbedcababecdceecebbdccbeebcebcdeabbadcdcdaceacdcaceccaeddbedbecbcaacbbbdcdccadcaebbebebbdabbadbccbaaaeadacbcacdcbddedcbbacbeabadbaddbbecdbbcdcddeecdecceeeadaeecccbcaeaaacedbadccbacdbddccdbcbecacabbeeebabbdaeceedbcdccebbadcdebdcbbacbabcaccbaeedbcecceeebedcaddacaedadbdecdacccdeadcdcbbeedaddbabaaecbeedaaededeecbaeaecaebedaaaabaecabbcebceadeeeeaaeddcbccebdcbcdaaaedaceaeeebedacbaaeecdbadeaccabcbcaecaaaebbaddbdadbacbeabbbeaaceebaadccabdababdcccbdcecaeccecedbaebadececdedaedeedbecabcaeeabaecddeadacadabdbbdbdbbbecadeacbbbcedaaeddabacecbaebedaacabeaaebecdccdadcceebdddaccedecdbacdeebccaeaacdedccedbaddbebcaabbcbadcbdecdecaadeedcaaceeddbcaebabbcbedeedbcdcaaeeaedaeecebaaacadadcdecebaaabbbcdbaabaccdbaaccbaddaaabddbeeceaebcdebcebbeeecacebaaabdcbaedbacbccbcdecdbbbacbcebaaddaeeeebbbeeecdaecaedabebbabcddeeadedbdedbaaaebbdcbecdeaebebbbabcbcceeebaadaccdbbededdacccbdaccdedeaecabedbecabbacebecdcbcabdecceecbdeddbecaabadcbddceecabaebcedddcbcceecaccceebedebcbeeccdeadebcadacbbcbcacbdaaddecddbbaabadacabacbcddcddddcdbecebabaacacccdebcecdaeaddbdcdeedeeddeaadddecbeebbabebdcecdedbeeebbacaabdbdcdecbccdeebdaccbbaeadbaaabdcbeebbcdeeedcbddaedeeebcadddadadddedcddbbebbadcacbeeabeddaeaddbcdaeecbebcdeeadbebacacbadacbdceabedaaccdccedbacddccceadaeaccbbeceaddeedbcbbcaacddcaeaccedbcdecadcdedaddbacaadaedcdabbbbebaabdbacadbecaebdbccdeeaddecdebaacedecbcdccabaedcebeedbcecaebbeebaeccbcbdeebaaecddbdebbabdadaacbccbbdeedeedaddedbaeeaebacdddedbadebdbdeabaecebdadcbbbbedddbabaeadecbdcccedddbccdceddbabdeadbbacacceaedddeeacacebdbdbbbbcaceeebaeedaccbbaaebeacbdacbdeecdabdcadcedcbceadacaadceadbcabcddcadcbddbaceeccdceebeadbcdaecebdaceebcbecceddcaebaecaacdeabbcdeddddaabceaccabacccdeacbaeebaccabaedcccdabaaddbddcdddddabeccaedbcbbdbcdcacdaabeadbdbaaeacddddeedacccceaaeccaaabbddcedecdecabcdcaebcbbeeadcdabcbdeaeabaaecdbcadddacbdbcddecbadaaeeddbbddaaabbbbdbacecedbdeaeceeaaccacbebdedaeaddbaadbdeadccecaeaaeabadeedcbadccbacdebadcbadacededceaadacdcdcdbeecddcaccecdeaebeebbbddcbdcedaebaeadeecaeedeabcbdaaececdbaabcdbaaadcdcacdcdbbcaccdcbaaabbebdeabedbbdebadcecdcabaeadbeedabcadbaacdcdabaccaacbcbbcbebbbacbbadeadbeaabdbeedccaeaeaadceddaebcbcdabdcacbeebecabccbceddccbbcbdacaedaecababedbdccadeeccdccecabcdcaadbcececbdbdabcbcabadeeebaccdadbedcecddaabedddbddecbdebaabdeebeeaaceebcdbaabebcdecccdceabdcebceadeaaeeeabbccecbacebbeeaececbbeedbddadbdeacbdebbeaaaeecebddbedebebaaeeacdabeebaeacbacbdddecccedbdaacadbcaceeccaeadceaddbdabbccbeaadaadbaacebcacabecabbebbacbcecbacbdceeecdbabadccadcbdeeacabcdeaeadddadccbbccccbebebacdbbceadcedaeccbbddcacdddcceaacccbededadeaeeedbabbacdedcbbcebeaebdcbbededeabdaaedbeeabacebaebdaaaaaaaccecbaabddadabbacbbebaaedbdebcaceddeadbccbacaeacabebacdaaeaedaddaeddddbccdaceacedcbbeeaedeabddaadbebcacebaeeacddddceceeadaaceeecbadedaabeeaaaabdbddbeecceaeeaaceedacadccabbdcdecaacdbbcbeeaeaccedbdacadbbdcebaaceddabeecdebddceabbdaddbccbbebabcbdbcbebeebbbeccaaeaecbaadeeacddbadeddedcacaccdcdcdbdcecacdcebeacbadecececedceaebbcbddcbdcebcccbceeccbeaedeececbcabcbccdcceacdcecebadcdeddcdaeabdcedbadaeebacacacaddbaaaececeeacdbbaceeeaebeabaaaaabdbbdecdceeddecabeeeaebdceebbdbeacdccabbeebbebeebdaedabedbeebeabdbbebacdaaebaaaaeabcdaabcbcddcdbdcedddcbabcaacdadbedddcadedaceedcdaccdcdeddbdceebeaabebcbddcccdecddddadedccdbccacbeeeaaccdaceaeedaacbcededdccaccebcbbdabbbebebceabebedcecadaebdddedccdeaaeadcbcaeacaecebeddceddcaabcbcccadcbecbaecdcbcddbddacbadebceadbaeeeeecdcdeebcbcbbdcbedcddaccacceaedbdebdcabecadceeacabdaabeccabacaeabaeddeddeebdeddddadeacdeeabadacddebecdbddceecebbaadecbecabbbbeebaeabdeebeeeebcccaecadcaaaebebbacbebdbcabeaacbddeaebedcdadceeacebdeedaabbacdaaabccacbeaaedbabcacdacbccdccdeaeadcbdbececbedbcbbddbadbaabcdacedeedccddeacbedecddbacebcaeaaadaddbadbcbdceceddebccbacadbdaaeeedcbdbeaaeccdccbecaaaeebdccabddeacbecbddcabcaeaeaccaeadbcbaebdeebcaaabddebdebaebdadaeddeddabbbeceeddbeaacedbcacbadaaccaabdebbbcabadcccadebdcbbbdaddbaccddababdacabceedabaaaeaebaecbaaaecebdcbeeaaaaedadcbdbcabeacbbeadceeaadeedabcebcabeaadceeeeedcaeeeceadecdcaeebbdcdbceebbeaecdadeaebddcbbebddbcaabbaedacdeccecedaecebdbeaecbcccacdebeebcabaecebeccccddebecaeccddedceddecabceddcdbecbceaacdeabbbeaaacbdbddbaceddbceebcbdaabbacecbeedddbaebcacdcdcaabeeeababaecccdededcaddaaebaebbedbaadabdaccccebbaacdeeaeccceeacdcddcdedccbdcbebcdeeabbeaedeebeecbbaabdeabedecbebdbebedaabbcaabaddacaaadadcddcbeeddacaadbbbceccecceeaadbaadecacbbeeeeccabcdabdeacdeabaccbcaeeeececcacaedbabbbebadabccaaadbdbeeeaabdcaedadcabbecdecabecdeabbdadcbaaeddbddacccbbeccaaccceddadeccacdddacaaecaedcacddabdebcdbdccccceddcedbeaedbcadbadaccbeaecdaadbedbeeebdcdaeadbdabacadebbdcaebdecbadabdeaeeabacabceadabccecaedbcacbedbacaabdaaeeaabecdabeddabdddbccdcecbacadaeabbadeeedcdbbbbeaadadecaaddccbaaadbecbbbcadeaeeeeeadbdcdaaabecdeedbebccdcdbecaadbbeeaacabcacbedbaadeadddbddcbbecedceaadeecdbbbedaabcbaeadeddbbaceecdacebbbddbedceeaebceeaceeacebbaccbdddeccbacabaacbbbbbaedeaaebcbabbedaccdccebbbaceabdedcecceaabeacacbbadaeebdcbaeebeabdacecaccddedeeeedbbacaaaeecbbcacaaeceedaebadedbacedbdbcbacbeebdaecdaceedeaddcbbacdbcdebeedcabbdccdbbecaedcebdecdbbcacaccdbaaeaacccddbecadddccaedadabbbabacbacbdbcaddeacaebdabccbddcebbdbeacbcbdebaceadbdabeabdeaabccddebdeeebdbebdaaabaeaabdbeecabdbbbadebccedadacadbebacedcbcbcbccbbdcaaaccacdceeaaceaeadeadabaeabdcbbddeabccedceabdaeeaabceeaaeadbdddedcaecdddcdcbebdbcbdbbddaebebacdecacbcaeccbcccbccbcaccecccecacddddbacbbdaaceccbcedacaadeabecbbdbabbdacbbbcdebdeebdadadceebbeeeebaacedadbceddeaabcdbdcdabbbdceeaedbaaaddeedeabebbaccdebaaceaeeeacbbbccccceeddebcadbaeaccdeecbacbaccbacdaebcdbabdddcccdeadbbedaecbdcdbaaddbdeeccaddcbeacdabddceccadccecbabebbcacdacdabbdeaddbbeedebaceabebdaabdbcdbddaeabdbcacdbaecccdadaeeeabcdedaebdbbeeececccbcacdeecdbbbccaaeeaedbadeccbceeccedadbcbdcdbeeccbdbacaaccbadedcbeeeecbecdcedbdeabacdacaadbbaeeeaaeeedebbddbcecabeeddedcacaacedcbdbcadcedcaecdccbbaaebcbbdeeddcabdeeccddabaeddcccdcaaabbbaeeccbeacdabddcdaababbacdddaaeedcbedbdbdedbbddcaeacecbdbdededcadeceeeebdceabcaedcbbaecbcabdeaedeaeebbaeebaaeebaebcbbcebdaaadcdccaacebedbbedaecdbbcbeabaecaabaaadebdbaedbedcedbadebeadcaceecedcbbacdaebcacacbecbbabdacccabdebbeeebebdacbbdcaadaadadedbbbbddecdcdabbdcecaeccecbeeaebdcddaaebeebbadebbececebaeacadaeeccbdecceaadedcccaeaddacbaaaadadbcdcaeaacbbadadaddeebeeeeccbaeedcccaddeabcadbebeacddcbacebccabbebecbebceadabbdcddabbabcadeeccbeddbadeabccbabaaeddbdcadabdbecebadbbbecbcbdbbacdecdadbacaacacbeecbdcccbaabcccbcbaecedbbadeadadedcbcbabacbbaaadbbdebcacaaeaebbcbccbcdaeadcbabaaaeabebbedeebdbebceeecbcdacadadbcccaeabaabeadebcedddadacecddceeedbcebdedceaaaeebcaeebdbaecaaebebedcaddbaeccbcbbedebedccdedbbeeebcccaadadddbcbecbedbaecdeeaecddacacedbeeecdcacceaeadadededbeadcebdccbacaaadcaecceaeccdceabadbcdaedaacdcbaeeceddebdbbeadcdbaccbeaccecbaeeeceabcdcbecadacadecbcdcceddaaeebeabdeceaaeeaaaeadabcbeaabdcaebeadecdcddddecdadeeedcdebcccaedaaeededebadcbbaedcccbdbececcecedcebaedbadadaacebbacbebababebceabaceecaadebabbcbaedeeadbcdcbcbcdbacceebdaecdcbbdecaabaaeeacbdbddecaeadeadbdbaababdbbdacadcecbcedaebbadbaceeeadaaeceaaadbbcaabaadddeeecddbeacbbcdeacabadbbcbeabaaaebadedbbaceeddadebaabcecdadbdeabcdddbdaaceceeebccbebccbbcdeecabcaaddadbcdedededaeadbdcaddaeedbcdccccaacedabaeccbdceeacdecccaacddccccccbcccbcbedaaabebdcabbdaedbccdbebacebedaeacacdcadccdeecdcacdeaabadcedbdcddeecbdceabeabbbcdecdeceebacbedddaccacdcbdcaddcadbdcbebdacbaabecedaacddccbdceeceaccbdcebbeacdccdddddddddbedaabeeaecaddbcedceeccbdbdeabaeabbddededaeccbcebaaaaadbdaccdabbbaeaeaeebaecadecacacceccdadcdedadcdebeddcdbeedaaedeccccccaedabcadcbeaeaeebadbbaaeccedcaebaecacebdeabedbceebaebbcadaccbadeebbccadadbbbcceeaceecccbeecbaebdcbecddeccaedbeadaeebddecdacdebcccbdbbdbebddbddcccdcabeaabeeabcadbdddcbeedbdddcabbdedcddceeaaeaaeeadddbadaebeecdaceeeaadcadacabbbabeedccadbcdbebdadcbbdaadeeddacbccaeabaeabadeddebeeeedcaeaededdbbadbcabdaddaeebbcbcabbbadadaddcdebdcbadeadacaabcaeacebeacbdbccadabceddadeacaeddaedbaddcbdddaedabedcacecdbbdcaedaeaebebbeababdbbbdbabebcbcadbcdaceeebbcbbaeaaedadabbcddcedbddecadeabcebcdedcdbcaeebadedbdcaaaadcceeeccadddedcdacbcdabeeebeacacedacdeccecbccabecbdcbbebbdabcaadbebbdcaebbbdadaeeabbeceebacbdaeddaeaecabacabbadbdabdacedcaedabecdcadbbabbbbcccabcdeebcedaadaebcbcbdbdbeabcbeebdebbaceddbdeebcaadedcdbbbeebdbbbaaddeedeedcbdeaacacbcdbbbaadcababbbabaebcebeddcbcdcaceddeedeedebaddcebddcbacbcacbcceccbbedebdcbadeadebcdadcbceabbbbccaadeabdcbbdcbbdcbeaecceaddbbaaadcdeacaaabaaabdadeddaaccedbedecadaecbaaebbaddcaeabdcccdabebebaabebdebaabdccddaeedebdadccbedeaebcdebdcbebdcdbcacbaedccaedacabbdabbedcabedabacdeabdceeedccebaddbaacaaeeabcdedadbbeedcdbecaabdccebeebeccaedeabedaecadeabaadcadbdacadeabcbbceaabbbbeaadceebcaaedcbebdeebdacbcbdbdecebecdeabebeccbccbacadbbcdeaeeadbecbbbeeaecbebaceeadccecbdcabbcbedccdcaedaabbccacebaccbbbabdeaddebebdeebcedddaaeccbebcbbaebecaabdeecebeaccdddebabdbdecbeabaaeccedaeeacdcdcbbaadedccedeceabcdcaeabcdbdbaddcbbedeeeadabbbccbabceaaaebabbedbdebbccbcdbceaaceaddaeedadcdcbaecabbdaeabbcabdabccdccbbccccbadcbaceaedacedeaabbaeeecaccbbceebbdbcadacedbebbdaabcbccdbcedabecbeaadaaeedbbbbbcdbbbbbebcbeaaccbceadeccaedaaceacaabcabbceceaadcaecbbecdeecdedcebeadacbbcbbbebdbdabbdebadcdccdeeadcdeddbbecbaedbbbeebaaccbdeadbdcebccdcbcebeecabdadedacdbbdebcbddeddeedaaebecedeeaaeeacbcdbddadedecbcaacdcbaaaaccaeccccebbbddbdaaeceaebaceabeddccebaaceeddbbbcacccaaebeebaadccbdebadddaaacdbbabbdeadaaeeeebddabdeadacdaadeebbebeacddcddeebcdcddbeeabcabecbedbceaaeddccbdcaadbeedddadeadbadcdbdeedbcaedbccbbecdbcdecbcebceddedcbebceaceaabcbddaaeeeceacebacbcddbccaedcedbadceecebbaadabccaeabbebceacebeeebaeacacbddaaebcadbcadeaebaeddbbbbcdeeaaacddaaddbcabeedebdeeaeaeeeeeedddeeedabdeccebdecacbdcbadbccbedddadabddcceedccedaedaceaecbcabbceabacabcbeeddaebddeaaecbaecbbbdebbdedaddbacdcaeaeedebbceabeadcaeeebaeabbaedaedbdccbabaaddddebbdbdaabaeeaaccaecddbaebaeacacecdaaacdbeedeccabecbeddbeedbeeacdaaccceedbaadbdaadedcdddcdeaaabbeadbcdccaadbbcaccceceaaacbaedebbdddccdaaadcbdcacadcaaecddecaecbdbaadccbbaeccdadbcddabccddacbcedacaacadeadcbeeeacabbbdcaeceaececbcddaeadeaadbabeeeaabebbbadbcdbedceeadabcaddeecbbaebdaccddcbceadbcacaeeadecacdebcebaddcbcdcbbdeedbcccdcaabaaeaccdccedeebcccbaabdaeccbcadeadbedaadcccbeeddebdadbddddccebcbbcaaebcebeacaaeededeedecbdbaccebeeacaecaadcdaaeaabaedababcdcbdadaabcaccbdeceeeadcabcededecebacdcecdcbdabaccbdaacdcdcebeeedbaabaedbeddadbcdceabbbddadaaeacbdbebecebeeeaaebdaabaaeaebededdccdccbdccbcdedabcabaadbdeacacbedacebbadbcebdbcddeaedeabbaedbbeddeacebcdadbeebaedcedeeacebaddaeebcdaebdadaeceeadddbbedadedebbbbebabcdebbaedcdcdddbbcebcaacecedaedabacbcabcdcecceddbedccccebdebddbddcadedcceadeaeddeebcacdddaacadccaecccaabeeaeedeedabdcdbabebdbeeaceeaaacdcdeabacedeacdceaeaadacbaacdeeeebccdadaeccbbcecdbccccecdbabddbbecbdcaaeeaebebcabceddabdcebcaadbeedacacdbddacddbecbebdbedcaaecbeeaedaebebaacbaedecceceaabbeebacbaacdeadceebadcbacaacbcecbacadaabedadabcdaaecbbdcddbbedddcaccedbccaeaebccbccaebdcabeaaaeabebdadeadebebeebcebeaddeaccdbcccebbaadacdebecdadbadddacabcbcddcceddadaaceceddadbbbcdeebdaebcebddccbccebddacedeacaedecaeedddbbcecadbbaadedddedbdceaaabaadbbaaacadabecbcaabedaaaceaabeacdccdaeecbdbeeeacdbacccceeabbdaeebedaddbdcebdeaaecaedccbdaeaaacbddeadcadbeccbedcecaccbadadaeaaddceababbbabbdbbccacbcaceebdcbabcbdbaacbecacecbcddbededcdbcbccdeedccdeebccaaecadedcbeaedbdaaddbcbcbbcbeebacbecaceddaaecaececbebecbdddadbbcbeecacedaeeeaebdcbeaebeceadcebedbadbbdcadcdbbedacaeececbededceccbedcbcdabbdbeebbcadebcbbaaadddaccdaaeaabddcedceeccbeadbaccdaebcadabdcccaabedcedbedaabadabadaadbebcaeadcbbeaccaabcaecabdebbdceddcbedeaddbacadbebacbebacaecddeddeebaaecdcecacecebbbdccaedebadebacdbaaebdcacaccdeedcddaddbcaaecaadcccbdedbceeebcbddbaabbeababadcbbbceaeedaadcbeeddcbbabadabeeddeceeecddbaadaacbdedbaddedcbdbdeeabacacaacecceedcecebadddccaeadadaebeedeabbacddecbccdddddcdbaeeeedebbeaceececeadaeaebedaeadabccdadeecaddabdcbdabcdbeeccabbeddddaddcbccaaaabceacbdabdeedacceececdbebdaccedcabdaebdbaadabcccdadcbaaceabadaaccaedaaecedaabbacbbabeeabdcceeecbcbadeaeadbdbbabccaecacbcbbbdedcdbcabeddccdbcceaaceecdecbbaeadebccbeabececdcacbaccbeacdebbeacbdcbdbddaccadbcbcbacaabaebceddcdaebeddbbadaadbeaceabddeaebdceaaeebcaabebacbcedacbabbddeccbbdcbabaacbcbdbedebcbdaadcedcedcabaceceeccbeaaecedabebbdbbeeaadeccbdeecaeecddebecdcaaeceedaebcabadbadbdeaedcaaccebaaedaccedeebbaedddbecdeeaaaeabeaaaeddcbeccedcdbcbcabeaabaadaabeebcdcbaadebdbdaaabbdedbebacaaaebdabbdebaaadaaedebaabebbccdbbdbaddcabbaabdeadddaacbaccecedcabccbdbcbcedccbdebcebedaccecbebdabeeceaaeddaeabcadbaaecbccabdadbcbdeaeaedccdeceadccaeeaaaaecdddbcbccadecaabbdbadeaaebaadaeacceddaaabeeddbecebceaceecbccdcbacceebacaaceeeaabbcbacbbddbaceaecdbbdadadcbdcdccabdddeaedbeabbebeabcdebdabecaeabdbadacadeccbabcbecbeebccacadbdceeabeebedaedaccdbedecebcdcedbbacdcdceecadceeadbaaedbdcaacaebbebecdaeabdeaaeaddbaedecbbbeeacbcabcdceabddbccadeaaabcebbbbddcbeadacaeedbbcaeecdeeccaabcbeabebecaeaadaeecbcaecaceeadcbaeeebbaabbdebbbdaeebeeacbdbbccbdaecbcbdeebddabdbbcebebbecbcdeadecabbdbceeacddaaecadeabbeecdecaceecddcaeebccbddebcbdeceaecadadcaedcecededcadaacceeedbbdbdcacdebbdedecdbacadadebddeacbedcbdedbccbdccbedcdaeeaecbaddecbbbcecdddeabccedbdaeabaaacecaddeabcedecacaecddbaacdcedcaebceeccebbbeeaccdcceaaaebaddccbacdbcddbdcccebbcddedbabcccbadbdadbdacaeaaddbabcaddcbebcecaedceceecddedeabeacdcbceeceddcdedbcabadcbcedaaaabcbacadedeedacaacdacdbbabccceecceaecdacceeceaeaacbdddbbeededebadaceacacdcdddabaccdacdbebdeaaebecaaddeadcbcebecebaadeeebbcbbbaaeadbbebbeedeaaededbabdbeacdbbdcbdabedbcbadcdcbedcbaebbabaaeccacddeabbadbacaecbcbadbeaebabbdeadaccbdeabbcdaaceebbcacabcdeebcbbeadeababaeccadaeebaeeccabeecdccbadcaabdcacbddbdddddbbeabcdaacebbbaddaacebaedceaabdbdbedeeedcebbedbcbaaabdcccbaeccddabaeeeeccacdbdcecbdeddeaceacdbeeacdececceebabbceececbdadadcbadcdaeaabccdadaabaecdacccddcacbdcacdcbeaddbbeaaceabddcbdbbccdbebbaaedaaadbbaeceecdbbaacdebeccbebebdaaadeddcbceaaaacccaaccabbedbacccaedbbaaaadeacdbebdceaebcdacbcdeaaaeeecdabcecccabedebbdddcddcbeeadbaaccbcddadcaaeaddacecaacecaeacddbecdeebaeccacaecabebdababeacedddedaeeeebceccbedbdaabdbedcabbaabaaabaaebcdcdaedadaedcbdbccdeacbacbcebabbddbdbbedcdddacaebbeadbabbdeedadeecdbaecadecbedaadccdbbacbbebccacbeaaeaabdcbacabedcdbeeaceccbbeddadddeabbbebeabcedcacbcbeecedbaaaebcdebbeecccbceaeceabbecedeadcaeadbcbbbadedadaaaebaaceeebaceacdaecdddaeacdbbdebbdebbeeeadeccadeebebbceaeabeddbbbbddbaccbabaebcabadabcbcaeeeebdcbaeeacdbcaddbabbcbeddedadcbaaecebbcabbccebaebbccebdcaeebdcabbcaedebadacbccbceababeabeadadbcadaeaeceeabedcebccbddbbeedececbbdbbeaeaaabbeaacaeddcbddbdaceaaebbabacebdbbddcbeccdcdbddceaadddceccdecbeaebeeedaccdecceabdabcebdbeaadccacebbeeadecbddeababbeedbacbadcabccacddddedccebcccbbaaebabdaccdeeabbbcccaeecdbbbadeebdccdaeecbddaddbaeeabdbeabaeabdbbcccdabdacbacaeebddedeeabcdaaccdaccccdadadbeadaeadeebbebabebaeedeaccbcbcecdcdedebbcedbeeecdacccbebbdadacadbeddaeeecbeceeebeaaeeaebebababbcdcaacbdebdecdddcbbddeecababaccceacadabcbdeaebbbddcacabdccecdbeeaaccbadebbdbbbdcebdecbdddaeceddadceaebbcebacaeddcdbaeadeebeebaacacacddeadccaccdadceaecdbbddaacbadaacceaecdeddedebeaeccdddcbaadcdbeeacbeeadadacebaadccddceedaeebdadeceadbcebdbbbdcbadbeaaaeaaaebeceacceebcedaceaacaeadaebaecdcbccbdcaeebdbbacedbcbeddbdaedebbdbedcdcddaddadceeebaceabadcddbecbabccebbcdcbaebeaaebedbdccdacdccadeddaabbdddeaebababaacbaebccbddadccebeabccebedacaedccdaebebbaeeddcdbeaabeecccddceaecdccbeceeccedbbdadbeeeabadcbdddebbaabaebbdaaeaebaadebebbdbebcdbebeeebabddabccbadccccbbdccaabacebaaccdacdcbcbccdbcaeddacccbbeaeccecbdbdabaecebcbebeadbcaaecdbadcdedccccdcbdcaabcdeeacccbcacccabeaedeedddbbcbdeeeaaddacabaaceabceaebcddebccbdcdcabecdaeeabceaeecaaabbbdbdbbbbcebbcdcddceaccddddbcacbcbeebbebdcbeebdcaedbcedbcdecebcaebaeedbaeaeedbceaabacbeccbeabaeaeeabeaaacdabaaccdabddaadedcadabbddbadabadaabedbddaadbabadcaeeecbcddeeaaaeddecaabadeaedeacbbebdbbeeeeeecddedbeebdbdbdecedcbcdecceaeddacabeebedecbebddebeeaceadeabbaedecdbecdbeecaebbeeecadaccaeeabcbacadbababecbeebcbaccadbaccacdecabdcddedbaccddbaceceaebebaedcceebddcdbbadacddebcadecdabbabdedeecddecedcdbaeeededadaeebabbddbdabdddacdadeedbbeebbddabcceadbccabdadeebebaddcbabedadadbcacabcbaabcbbeedadbbcddecbcdeaadbabadeaabbedbbebcbbaddbdbcebdbcdcabebabccaebdbdebacecbaecdcbababbcbcaaedeccabebbcacccdebacdaabeaeedebdeabdabeceabccaeaeaababaccdaacacbdcdeaecaddbaabdbedbbebbeadddcaebcdcaccaddedaaecbaeaaeeebcbcddbdbbcedbdbcbcdaecabdaddcdabaedcbdcebeeebaadccbcbedadeaddeddbadadaceeacebbbcabcceebeddccdcaceaedaaddbecaeecabbbbcaacdbeaedcedaaebcddeebccccdcbaedaadccadaddcacadaddcbeddddbbceaebebcdeadcaddbcedceebdccbadcaedcbdadcdabbbeeacdedbdccbeabbeceaabcabbeadbdabcdeaaacacaedcaaecaceacddbbeabeadccebdcaaabcddbbccacadaceeabebeaadbcecceeceedcbaccdecdcbccdcaaecbbccdeadeaacdcdbaeccaaceeebbcabadddbcacbbdecdcbdcaecdcceedeacdbccbdddeedbbaeacaebbacecddbaadcdcedeaacdeeaadbbacbbdcbaeaeabddceedcdcbbedbcceebecaeacbccbdbabbaebaecbdeecbadeeabdecaeabacdccaaebeabbeedbeeddeaddcadcdadacaeeeebeebbaedacceadbbbdbdbdbdeadeaaeabbcbcadddedbaeaedceeccecdcaeacabadabecbadbbcbddccdaebdeddcdecebbdebeabebbdcebaecbebddaecabcacaacbdeaedbcdeebccbaacbeeabebebcbebbdbbecbeddedddacbacdaecadceccaebbcdbbbedbcdcbabcdbaacaaddbdcaccabebeeeddcdeedacaddbbabdaaaebdcbeadeddeebabbaaabbcebeebeddddddeeaacaadaacdcaabdabdbedaebaadbdedacddccedaeedddacecdeeddcadbcedbeebbeecaebddceeedbdadabbdadadeaebbeedeabacdedddbcdbcecceeadeadeadeecddcaabeacecbacbbaccbbaecedacccedabeaabcadebdbdbccdcebebadaadccbbaedcdabcaeaadebcdddbbdedabbdcbcaaeceeeccebebcdccacaebaadacdeacaceadedeadeaaeedecccdaabdebeabeacccdcacdeaeaebddeccacdceabbddeedcdbadceadbedacdeeadadaddcecdacdacdbbcdcbcadabbdaeecadaacadcbdbabedeaeaacccedeeceabbcbdcdaededaaaccaabccbebabaaacadbcccdeecedeabdeadcddcacdeceabbeadbacebedbdccbcadcdacaeedeaeaacbbddeacdceaedcedaddaeccbbbcaabcbedacdceabadbdababaedbadecedbbeddcbdccaacbdaaeedeadaedceaabaececcbeacabcebacabbeccbabcbabebbdbacccacdecddbcacccedacbcadceaecaaaddebebdcdddbbeebeadccdbaaececedbceebeadddebeaecaccadaddaceddbbebaecdaeedbbeaaaabaaaeecdbaccbbadaaabcbeadbbaeccececceecbabedaeacecabbeaebddbbbbadbcdbeedbcaeceabeadeaedccadeaeeecdcddbeacbcbcbabeceedcbcececedabdedbabacebadccebeaceacdacacaedeadbeeddcdbdaabebebdebdcedeedebdeccdedcaecddcddeccdcbecaadacaeccbceedbddeeeadeaabeccdaadcebbebeccedccdabeaacdaaadadacedccceacbdbabeddacecacdeacedcadcadccdaaeebaaabcaebabcbdcacbbdcbbebacadccbddeabbbdbbdedbaeebaddabbebbccceaecdcccebcbbcacaaecbecbbacecaebacadeecaedecbddacaacebddeeccddacbcbaaaebbeadeeceabcccbaacedaeeeedabadeeddedabedecacbceccbbbbbadcbaeacdbcabebaabdabdeeeadadbbddcacaaaeeebcadeadaeeeabeeaceddabccbabeacaacaaebddcebabddbdbeedabcededcbacaebbaacbbbccadadceaccdbacbedbcccbbccbeebeaebbabbecbacccbddebeabcebeaaeedcceadabddacaedacddaabddbbaddbedceeacbeaacedbdeadaecbabdbcadeceeeacdacbcceeeddaeaaaecdabbdecadbaeabbeedceabadcceeeeabeeebddbdceaacbedaedeaebcdacccceedbabddbeebbcabedecaaeeacbebbdbddbeebccbdeedaacececbeabdabcebeddaedececcabcbeccededdcedaedadacaabcacbaacdbaeceacdcddedbecedcaacbbaeeedcedeadeeacdbbedbecbceedabadaeccbbcbccdbbdeccecccbbcccaeceaeeacebccdeecbedccaccdaeaebebacdeeadedeadbabccbedeaadabeedbeecaababecbdcabdacecbbceadddadcddbcbadebdbadaecbbbaacceccecbabbceeabeeceddeddebeaabaededbadbbacaaabbceceebaaedbcbecbbcdedcedccaceccaabeddcdaddbaeaaaaccbacdbadeadaedcbeebbcabddedeabdaccdbdaecdcebddedbedddaeacdeddbaebddacdcdbeddacdcadaebbcbaeeebbaeeedcaddacbdcadabbdedccadccedaccbaabebebccddbedeecbeeeacadbdcdbacedacbceabbbdcaadddbaeeacbcdceaccecdedecdcbccbdbaaeeceeddabbecdbeedacebaedcbdccadeaaabbadaaecededabaecdcdbabdaebbacbbaaaceecbccaeeacdcbdebbbddedccbccacceaaeaadaecceabdbbbeaecdedcdcebbadddbbeccaebedceebbbdccccbabbedecedeecbdcbcddeabeeaedaeebcddebebeedcbeaabbaebacabcbaabbdbbeaebdaecbbbecedbddbcecedaadceaeddadedaeabbbbaaddabcbdbebbcdcbbcdeaeacdbcebaccadaeadbbcacacbcadbaeeddedbecbdbaecbbbcdacdedeaabaacdcedbaeeadcaeacddeeabdaaeceabebceaebdbdedcbbdecbbaabbcaabadbcadaaadbcabedbcbbadedcdccbcaedeeadbecedbdcdacccaabdabbabbdeebaddcaeabbacdaeaaccadbaeddcadbcabbecdcdbcdeaaacaccabbecddeccaaeebbcaedbbdbbeadcdbebdeaccdeaddccebcebbbeabddcedacaadbdcaaeebaccacceccaccbebbecdcecbdeeabadceebbaebcddddccdddecaccecabddadbebecaceabececdeedbbcaadadccddbbdbbebddceebbeaeeadaedbdbeabbdbdddcdecdaaceabcdabeeeaecadedbbedbdabeabeaadcdceebeedbbdbbabcabaacbeddedcbadcaddeadeebbdbcaedaebceacabdecdeacebeedebabeaaeceecabcddebdddaecebdabdabcddbdaedbdcddecdadabdedaadacdecbecdaebbdcbdeddcbccdccddaccdebaadeeddcddbbebaaabadececaceecccdcdeebacecbaedaeaeecddeaedbebaebbebdadcaaabcaaceacecbcdadbdacbdbbadabebdbbcdeeaeaddcbcedccedaddecdcbdcbdcedaebaeccccbcebdaccdabeabbdcaaecbaaaaeababdbeeadbabaabbddebecadbcacbeedbecbaabadbbddadccaadaeacdeeddbaeadbacaeacebdbaaddbcaadcdcacdebccedadaebdccbdeaeddceedaeebddacdaacabcbdbadcbcebbdadcbeedebbdbbbedeaccccebdbdaebbcedbdbebbcdebbbcecdccdaabebaddaabbebbdaadebaabeeadcaedbeadeccdadadcdbdeccedddeaccebbcdeaaadbdaccdbacabdcaacacebcbbdcaccdbccbcababecdcddeacccdabaaaadeebacaeabdcedcebdbdbeadbeabecddaddbaaccdbcbcbcaeaaebcdadabecaeebaededeacbbceebbdeceedccabaddbdadeacabedddeccbacbdedbddcdecbbaaacdebeeacaeaceaacbecdaeeceadcdcddbadbdabdacbadeaacbeecdeeaaabeecdaccaccbbaacceeeadedccadacdceabedcbacddeddeadcbbaacdaddeabededcadbccaddebadbcecdebcaeeacebcbeddaddedaedeabdaaaecdeacbbabceccaeaadcdddbeeebbceeadadbbaabecedadebdebaadedebcacceddaaababcacbdddaadaaddeeaaceedbdeaaececaeaaceedecdceabbdcabaabbdceaeebebdbdcbdaedacaebcedcaceeeaaccbdeacdcebccbcacaeeebbabbdccecbcdbaccbbddacaeadabccebdbddbcbeccaaebabbcbbbeeebbdcacebaebedacaacebbceecbbabbbdbbddbeaecdbedeadbeaaacbbccedbcbedebcecaecedddeecdaeeacdeebcaacceeebcccdedcddccdadbaabeadaeaaecaebecbacebcadadbaedbaeabcbeeaadccaeaacabcaeedbbbdceabcaecbdaebccbeebaccabeedecebbddadecbccbeccbbeececeaabbdddaabaaacbacccdaadeabeecbdeaeeccdddadbebbaedaadabbcaccbaaeabaadaaedcdbebbbbecaddaebedeacbcedcdcbaecccbcabddcadbabccbadbdacccadecaeaceacccccedaaecbdbbedebeccbdeccabedaedbdeedcabbdaddeebdaeadaebdeddabbbceabbcaadcbedcbadeddeecdaaeeddbdacedadbabbdaebeedebcdadcdcaeccdddbcabcdabcecaaddeaabcececeeddecbeebedbacbebeaaaaebbecabaeedbcedaaaeaeadabaccbedcabbddbbdcaaeaababbbbaaaedbecabcababbedeceddadbbaedcccdecbdebbddbecaddbadbeacecadaaaecbcdccabaedbbacdbcdecccdcbaaaddddddadacdebbbbdbceadaecbadcebabbdcadadbadeedccccedcbcedbbccebbadccdcccbdcbbaddaedabcbcedeebeecbbdeaacbbcedccabbbdabecaccedeedeacecbbdbcaabbaddbaedadcabdbccbdbeabbcdeeeeeababebeadacedcdaaacdeeacccbdeeabbecbcaabaaaccbbbbdbadbddbbeedddbadcebdabbbbeecbdcaeabebebdabbcbcacabdcbdaaaedbddcaebacdebbcbadccbecdccecedddaedeccbbdadccebcbbbbabacdcddacecbcaecaecdbaaacadbdeeeecbacaedbdedbebeceeddbaabaddbbdcaecbedeaccbdcaedbeaddabaaeeeddbccebbabddcbaceedececaddccdcccbeecedaaedaecdbadabacdcceeebdebbcccdbbdebedbadcdeadebeabcceddbcababbbeacebdcccababaaebaeccacbdcdeabddbadbedcddbccaaedbadbabecdcaadcacbacadebbbbabdcaeecdebbbbbbcbbeacdccacddbaccccdedbcccccceecdcdcdadcababecdcacacdeaaeeabcbccbaecccaaebcaebdceaeeedbdcacaeebbacadaedeabecabdcdaebdaddbdbcdedbddbebddcbedddceabeceaabcdccdddadcdeccacaddacedbebbcbbddadabceedbccdbcaaacceeaaacccbdbabdbdbddccabcbdabaedaeccaabdcaebacabcbbdddcdbabdaeaabdaaaaacbbdebbdebebecdccdabcbcadbbdabbbebeebddcddbacbadebadbdebaddbbdceecbeaaabdbccddbbebbbdeeaacbedaabcaabcaabbabcdaaacbaadabbabcddbdbebaebbcdbbeaeccecdecabbdbbcdeeceabedbddeacbccceaecebebecedabbcbbcecaacbabbdecbcdbecdcbaebdbcdabaacdacceceebbaddebabddcccaaddeccaeeddcbacecdcbdeeacdbadeeccbdcbbeaaaeebbeeededccceeeaacadcbcbeacbeeeaceddcecdcccaaecabcbdaccdaaeaaebcdeaaecbbdececebeaabbcbccdebbddbebcebeeabcdcdbeddebbccddabeacebeeadbedaabcbcbceeebceccababbecbaaaedceddaedebaaebcdbbaaeedccbdddedebeababceecebbdaadccbeaaeedbdccaddcddccdcbbddebecbecabeceaabeaebaebaddddbbbbacdebcedccbdcdadccecdecdbbdacdeaebdbbbabbbdeecabadbdedacdeeeeecceaabeadddaaeeacebcddaaeebbecddaacaaecabcddaecbdcddbcceabcdcddbbdbebeadabeacabdbddaeedddbadaddababdbbbdeebadbcabdecbeacaabceabeabedddacdbabdacbeabdbebdbedbbdbccbddcbbaaadeeaededddbaaaaabcbcdeddcabcbaacebbabdaddeeadacdeedddcbcdbeedadaabaecccacabbbdaaecaaeceabaacacdcbeadcdeceaadccdebebaaeddcdbceaedebdebcccaedbacabdddaeebbebbdbaaceeeddbabbcbdddbceabcaeaccdeaeadaaceccacaaebeeaebbcceadbabbbaddeedbbbcbeaadeccbadbaebdaecaebcbbecadeacccccebdbeeaaddeeedebedcddcbacbbcacceaceccbadaaddbbcaaeeaeecdacbedbbadbbeeaebccbacbaadaedabdaabaccdadccececbaadacececdebcdbcadccabaceddbbbceaebeebbcbddcceedbcbbedeeaeeecebccccedbebbceeaeaabaeedeebbeceeabadadedcebceeeaacdbdcedbbcddeecdbccbddabebabdaebeeaaebeacbdcaccaeceabcaccacbbbadeaebebacbcdbbabdbdabdaaddaabedbcaedadeabbdecabddebbdedcaccbaccaeedaebbeebceededbbdbbdbebeaabceebccbdaadebddaddaaadecdcdcbdbadaaebedaeabbcdacaabbdceaaaceaadbeaceedbeeaaeeedcdbbdcccbcbbddecabbdbaadecdabaceaaeaaddedeadbbdadbacedbadabdcecaedeebeadbeadaebdbbeacadbeaccbeeedadbedbacdedabeacabccdcdaecdaeacaaecdcaadadbabdcbbddaaeeccadcaaaaadebcbbbcedacdddceabcdaaeedcbbaaeaadaeaeedaeebebebadbbdbbbeebaecddceecbdcaacbabdcdbdaeccccbeaacbebcebcbdeecdeaaadbbeabbceacdaebbdcabcabacddddcbccdbeceececccbcaecedddbbececeabbaaceaeaeaadaabcbeaeddadbececaedcceeaadcebaccbbbdbbccbacbecbbcaeabeaddeaeecbaadbbcbabaadacdccacebbeebaacccaedcdedeaaaacccabcbaadcbccacaeddeeabaabeeeabedacbbadeedaeccabdebadeeeedaeeaceadeeccdedbdedaedeebbbcacdcaddeaccbadaedaadbebbdaaccdaabcecebcbbacbeecbeccacccedadcbdeddaaadbbbaeecbaaccbbbacbdbabeaedecbcaeeecaeacadecbeaccddeaaaeccaccceddbbadcbddeaeceedbdbcaccaaeaeaeecebdedbabdebbcacadaeeebebeccbbddaaabcedaddceabcaeaddbadadebecabbceaaadbddddeaddeacebdaccaaeaeabbbbaaecaebbdeccedccddabeabdadaccceaeecbbaeeddbaccaceeaeaeceaedbbadaeeaebebcadcdaaacecdcebecceebcccdddeecaacaeadbacdddbcddaeceeeabecbacceacdcaaecccadeaeaddaedeabbacddabbaacbebaccbddcadaaeaabddebbccbbeebbedeabeaeecbbeeaeeeadbaaaeeacaacadaadeebabcbedaebadecbadedbdcddbeaeeedcecadbbedbdadaedeaabdababaeaeeaddaabeaacbeedacebddbcceabdddebecdabedeededbdaaceadebbbccaaaaeeadaeddeeedeccbebaaeecadeedccedabebbeaabeddedceecbebdabeeedbccabadbddeadebbadabbedbdbabdbdebcbbaebbecbaecadcdceeeeaeadcdcbbabdddbeccececdeabedecedaabbbedbcbabeccacdadcdedeabeeabaacdcecebeabbbdaeadabccaecaadbaacbbbedddebcddbabcddacaeabecddcdcaacdbaaaeadacaceccabbeaddcbeeeceeabcbddcdcbceaaeacdbbebeacaebdeedecbacbcedbbbaccbcedcabaadaeacacdadedddcadbebabbecceaebedceedbcecbaaeecabecacdabdedaaddcbeedbdecbedaadeacebabaeaaaeaeaddbdbeecdacbcdaccaedbdddcedbbccaddcbcbaebbdbecbebdbbaebbedabcceaeddcebdebeddedcaacecceccbccebaebabeddddccaccdccadcdbcecaddbdecdaeaaeadddbccaabbedabcaadcddeeeaadcaaacadbceeeedbceacbdeaabaecccaaeaeaadadaeacecabcbbcccaadbbdaaeccbbdcbacddecaeaacebdbdabddcecaddbbddacdbacaadccccaecbdccabaebcaaeabddbabebabdddeedceebccedceaddebbdeedcbddbddaaecababeabbcddabeacecbbdbeadbbdadbabeebeceacadebbccbcdebbddcabebbbcacdbabcdacbbcdccedddecedaedbabcaaaebebadcabbeadaededebbadeaabbadeaacecaeeadbcbbaeeebabacdddadadeaaceaededbecbdbbdddbaecabedececccbeccadcbcbbdedcaeeccbbcbebbddceddddaabaecdbacddaacabeacbbeeaaedcbebdcbceabbbbecaedeaeeebcecddcedaebeeecdbeccbacaabcbcaadbbbccceceabdddbeaedecacccaedbaedbaddacceccdcccceeecccbabddaadbecccacaebaceeadcabccdacdcbbaaadecbaeebbdcaacecaebecdcbeadebabdbddbeecaadabceddaaddcebeadaeacacccadedcecacbbecbaebddbdaabcdebedcaddbbaebeeabdcedcdcedebcbaabacdddbddbbcebedccbebddbdebbedaaedaaeacaabbbccbcaaccabaeecdccabebbccdddccbceaaeddbbbdbcabebacdaeddacedaceccecaeccececdbeaceeebddaacbedacbaecccabcadeaabadaedbbbecdccdcebcceabaccbcabbadeaecabbaebdecbdaccdbaddeaadbceceecdaaaaebbcbabbdbddceabadbcaecadacbdaeebbeabddeeccaeeeaccbcbdebdcaeabecdcccdcbdabdccccdccdebcdeedecbbedaedcdbcabcabceedcbbaacbdacccdeecedeabccdbbbbedcabbbabeeaeeddcadedaebceaacebebddcaaedcdedabeabdbbaeeabdcadababbbdcbddeabeceecedaecdddbaecaadaccabcbcebcdabbddccddaecdcceabddabbbcdeaccdbdcaedeccbeacbedaaaaaeaabbbdbdeedebaedaeadddcbceccccacadaeebeecdcdaeabbaabcaacddaaccaacbdabeaeaaecadacaeeeeadbdadcbaabadddacedcacdaaacacbcdebececbbbddeaaaaadcbcbababddcbbcaddddbbadaeddcacecbabdaaacddabbaaacbbbcdbceeddebcbcebabccbebaedceabbccebddcebeeccaedbedeaddcbedadecebcbcbabccbcdaddddcbcadccacaedddccdeddaeeadbededcebaeebeabdbcebddbcdaeccaecbcecadedaaeeaceaedebcbeceaecdaecdcdcaaaecbbbaedeaeaacaceaadddeacdecdbaadbebaaacceeeaceadaabdaadcececedeeeececbaaebaaebccbddbadecdcbbeaceddcabceabbacadaceeaeaedceaacacadabedbeddeebddbbadedcbcedbcbddcdcaeaeecbdbedbbeddbdbbcacbdbbceecdcbdabeecdcbacaecaababcebdddbbddeabaeeebeacbaececdeebdbaeebecbedbdbdeddaddabddeadccadbcdbeaebbbecaeeedeceaaddbbcddacacdcdabcacbeceaddbbaddadceedcebdbdaabbdcbadcbddbcbddbccdcaabdaebecdbdbbdddcaeebeaeabddcdadedbbdcdcadccaacbceecdcbbbcbecbabcdacdbdbbdaebbcebcdaedddadbbdcebabdbaaaabedeaeaacaccebbdcdaeeaaacacaeebbccadccbeeabddabbabdcdedeaebcbadecbdbacaaeaeaceccebaebcedbcbedbbeeacdcdeeddbbedcdabbdecdddceaceeeacecbbcdddbbbbcbbebeabdbeedddcecdbeaedcaeebdabcaadbdebdcceecccbacdbacebaaddbbdcceaabbcdbcebedbadaabebecaaddadaaadcdcbaadbeaaaabdbedcebcdacdaddbaeaabbdbcaadacacecbbdabeadaaeedaecddbccbbaadcaaabebeaaccbbabddaaeeedcbcccdabedeadaacdaadccecbcdbeceddcabcabacaaacbdbeebaeeddccbacbbbebeabbbadecbecacccbadbbadcaaecdabecdbcbcebacdcdccedbccccbedadaedacaaeaecabbabccadbcdbbdceadbecaebdbaccccedaebaccacaedadcdddaccbdbeacaccbcaccadedcaccdeececacbebbababcebceaddddcabaedadeceaeacccbbedaeceedddaddbbbbdedcbccbbbabaeabdcacddadcbaaeeacbebaaddecacccdeeeaeebcbdadbeddedbbdedebcdeddceeababeccebabeabdaebeabeedcbddcdbbedeeebbcaaedabeadbbdecbadeabadabeceebcbeeedaaebeadededcaaedbbecdabceedecbadeabccbbccdabcceadeeababacdadcddeeaceecebdceebbebcacacdbdeddcebacdbbdbceccaeeaedeaadaddebdcdaaecababebbdecdddecebaecbdacdbcdebabedaceadbddbcedeacaeddaeadbbdcabcedebdcbaabbccececacddbdbebdbabcbedeabebdedaccbdbadaabccbbaeaeededadbedacddddbbbcedadacadbbbdeeddbbadabeabbddebcecebbdbdcccbdeeedccaebabcdeeedeeabeceacedaeaebedaccbbcbaabeeecdecbceabbeacddebbdbcccbdbbcabaccddbebeabccdbbbcdcbceedcdcecedbdbedccccbaadbadebaeeebabebdcecbbbcaecbedccabebbebdededbaebcaaaceedcbcdacedeedbaceedeeedeaedbcadadceaececbaecdbecabadacebdecaebaaeabbddeedaeaaebabbedddaedbeecdeabeaaaadaaeaddeabecbaaedecdbebbcdbbeedaeecdddaeeaeeecbacddeddbcecbbabebbcbebcabeeccbeecadaeccedebcbdbdaeeeeaaceacddcedaebbaaedadeaedbeedbecbebdbdaebdababcdceacbcaacaabeebebdccdcdacaeecdabcdaebdbceebbeededdeccdaaeeeadbbecbdeeaecbebbaaaaebbaecdbbbcbabeccbcbdadebcdbbbaadaeedaccebceaadceddbdaccabdbceabdabdcdbdbadeabebebaebaacbcdbdabcdbdcabeceaccebecbdeeaacdabacccaaadacabbbbacdbadddbaaadbeacebdebadaaeaeadaaeddcedacedecccdeadbdeeecebadedcbbbaccbcbbdbabcceaeeadabbaaedaebaebdcddebdbbcdbbcadcdbccbebcabdbabebceddaaaeecbebaedeeabdecbdcbbbabbcedcbaeebddbcdcaaebedaadccdcbccadecebecdddbcdaadabddceccbcaeeaadbabdbaadcbebbbeaaecadacaacdecabdacabebbecdbacecbadeecedbbcaaabadbeeabeedbedadbacedebbebabedbabbddbedcbdbeeebebcedcbaceceaaabcdaabcbcabdcaebecbbeaeaabcdbdceedcadacdadccaddaecbcbbadecedbcdeaeaccdaccbbaddddcaeecebecdbdeaedcbcbeebbaebcddbbdeeeecbdacabbdcdddbbababaccbbcabeebddcdadaabbccbaeaaddceacccbbdbadddeddebdecabacaecabecbbbcccdaedecbaeeccacbacdcdeaaecaadecebbadceebeeceeeacaccdbadbdcaecccdcdaadcccececcdddaeddadbaaedcbbbdbdcbddcccdadcbddaddebceaabeebdceeaaccdbedbebddcdeccebeaccedccdcacabcaccbcbadbcecbabaebcbbacbbdddaaaeddedeaeddbccbedaeddddbcdeabedacbdecbdbceabdeabceabebbbeaeddabebcdabdceddaaddcbadcbadbadcecbedaeaccecdcacdbbeeedebdedaebeecddeaceaddbccecaecdcbcbedababcaaecbbedeecbcbedcbbccbdeeccbdcacbeddaaecebdedaaeeecacecedcaabebbecdcdaeeccedebedecedaecbdbcbbadcbaacedccbdaedacedabbecacabeedbadcdbbdbdbaaadadcababccaacbbbaebdbbccbcbaddbeabbdadacbbaebebdabdbbeacedccbecbcedcecbbcaaaadedeabdadceabdeeeadcddababbbaeeedcbeeaccccaebdebcecabaaecedadddbbedccedcadebeaedbbeccdacbeabadebaeecbbcdcccbcbbcebabcedeecbcacbbadacecbcbdcdedebcaeceababecdcaaeecdbeaccbabcbdcebecaeacaeabcaadddeabdbabdedcedcaebdeacbdceccecdcdbddceadaacbabbccaaddadbaadedecdcbdebdbcccabadddcbacdcbadabcbecadbcbdaabeececabddcabeaebcaccdddeeaaeadbadbcadbcbdcebadbbdcdbbcbbedbaeccbacabaedcadbadcbbcbebcbdddcdbdecceccbbceadaddedbeeddaccedbadbdabecdeaceeceacddecddeabedeeacccaddddedcedaabbadcadecbacabeedaeeadabdcdaecccbbdedcbcbacaabcecceaeedbadccbeecebeacadbdcdbccbdedaaebebdeedecdbbeebcadbaabeabddecddabcedddcbeaceeeeedbedbeeacedccbaaacabdbdbcdadaaaeacceaecadadcbebdedebdaebbbadbcececaeeacdbedbdeadabebeebecdbeceacebaccaeadbbeebdbeaaeabdadaeadebeecbabddacbeabdaabdaeadeedccddcbbecaddabbaeedeeaecaedadbecdeadacbeebedccdbbcababcdbdcbcdcbbccddaaacedbabeddbdbeabcadeccedccbecececabedbbdddabcbecabaccaabaebbcedaccecdaacbececddbddeeaaddbcdadabdeebcbaddccecbcedaabcaecbddddbcbcbeeebbaebdcdadcdbbbcacddccbbccdedccdaaccbdaaadaaceceeeaaaeecabbdecdeacddabcacabbeabededaaccebbbadbeddadecbdddabdedcadabceddcbddddcadecbaabeacadccddceebbdbdeacbaaccceeedbebdbadeedceabebedebebaebebbaebeabbabbdcaeaeecadbebebaeaeadcebcabbcbddeccdedcabcadcdacabccceaceeddacadeddaaddeabcbbdaaadcbeddcbdcdbbaddbcaaababddacacadcdcedaebcddaacbbbaebaeaddebacebbabebccaeddebdaeeadcdbdcbbeeeeadeeadaabecebebbbebdcadbccacdbbbebcdaecdbedbbaeacaabbdedbabbbdbaecbeaddecdacbaaaebaebebdcddbeccdededbedeeadcecaceebbbcbecbdbeadabdaeeeddeadaabeadeeaebaaaddebebaabaaabbedaadeebeaeebccbddaaeebeeedbdddbaecdeccbbeccabcbbdaabcdebbeeedbcaacacacdeeacdabeddddbdccccddeacbecbdbcedbcdedcbcaeedddbebbaebabbbbdeaadddccbbdabbbccebcacecaabbadddbdabaaaecacadaadcdadeadaacaeaccebddcbaccacaacbcbcaedeaceadddddadabcbadebbebeeddeaaaadacabebeeaabcececabcceecbdddebcebadacbececabcaaaccdaaabbabcddbdbaddeeacbcbebbabcabcaeecacadaeebaaddcceeaeeccaddcceeaeadddabebdcadbdabccabcccbdeceedecbadbddcbdcebdebbddcbeebcecedaabbcabcaeebebaaddabeacacddcedeadcaadbeecdcadbaceeacacecaaadcaadeccecacbceeeebbccadeeeceabacccaacdacbddaecebceabcedabcdccdbeadcbeebabdaadbdceacbcacdccceedbbdbcbcbebdcdcbcdcedeebcacebabecbaedeadddabcbcaadebdebbaeceebbaedddbabbbbaedadccdabcbbddedabccadccbdccdebbcbeecdbeaacbdcddcacdccbdbaeadadbaadeaacecebdacababbceaedcdcbededccdcbdeedbacdebabeaadbbbbdbcbadeaadeebaabeeedeabcbedbbdbcaebdabccbcdaecbbadddaaadaddeeebbbeddbedacaabbeabbabecdcaacceddeeabbddbecacbecccedacbaacdbddecaebcddbeceeedbcecaaebbcddedcccdaddceeddcbbeecdeaabacacaeabecccaacececbeadbdaccaaeecbbaeccedaacbeeadebbebbeadedadadddcdbadbabbcaedaddaecdecacaadebecbecdbcecdaddcebedeadaadeeeadebeabcebacdabdededabdbadadecbeaaabedddedbbdbddbdbecbadbeeaaeebccdcadbddeedebcdebcaadbebaceccaeddcaaaddbaabdaaedcdabebcedecbddccdcdadddecddbdcceecbeaaaeaaedbebacceceabdeaaeddcccdaaececacbbaeebedbcadcbacbaeedbaeeddedeedcaaccdbeceddccbcbcdabeadbedeedecaddebcbecdceedababcbdcecebddaeaedaeddcaeecdbddababeacabddeaaaabadcaeaeeacaceaedecacaabdddbaeaccbecaccaaadeebedbaeeeccbcbcededdedbbdceceaecedaadeebeeddbeaeecedeabadddabbbccbedebbaaccaadcabdebdeabbcdedebdcecedcaeaedcbbbbadaaecbdaababadbbdbcccbcdceacbaabcbaebdedceadddccbedaedcdbcddccbeeeadbbccdadcbbbcbddadcdebbccabbaacddadbbecdeecdeedccdddcaedeccebadccdaaeeabdebcecedaedbeeeacadbedccaddbcebbacabeedeaabecccbcaaddadbebcadbbcbcbebaecbceedeeadebdaeaacacdedccbddedcbdbcdecacdeaceedeabaecbcbecadbcedeeeaecdcedbdbabcbbedeebbbbeddbbdeadbbdadddccbebedeeaedaeabceeaaceaaaeadeeeeccdeabdcdccabcbcecdebdcabeaabccaddcdddeabbcecbbebabbacabaeedaeeeabbececabbbeacccbaabbbbabcabeaebaeadbdabaceeeaceeecbcbcbeebbecdcaabacadaddeaedebaadeaeebeececbabbcdbeabcaadecacdedbaacdddbbceaebebaeecaeeeeaacbaedbddccaabebcdceedcebdbcaaacbbbaabdedcbccdecabbebabceebdeaeaccdebdaadcadaddeccdcaeeeacabddbdbdeecbdeacceddaaccacbabdbdaddaeecedbebebeaceadbadccdbdbdceeaccabacbacedbccdcedccbcdcbddeeeadabcbbdcedcdabddededbacabeebcddcaeaaaacacceaeeebcaeeeaaeddccebaaddeccaaceeadbbedbccecbaebaddbaaeddcededebebccdaebacabdeebccaeabdcbebeaacedcddecccbaeecbdadeaadadaeadcaaaeecdeadecccdbaeaeecaeaeecadcdaacadacabcaabdeaaededbedbeadededceecbccaeecdebececeebcebeabbbbddcdedcaaebdcdedaabbedaabdcdbdbbdabdcbbbdddaeebbddadebdbabacdcbbabdebaaeceddbcccabeabbddebedacaacececddedcbcecbadbaddbdeaabedaebbdaabcdcddbeeaecddabccbacebeebecdabdcbaabadddecadccbdadbdcbaaeebaaabbcaeaedbdcadebaacdaeaeadbeeaeabbcacdacccecebddeabdcbbadaaaacbecccbbbdecdaebacabaadaacdbaaeacbabaaeacbebbadbdaddedaddadcbdeedbdeebdbeaacccdeceeaacedbdbecdddedaaecadddccacadedebeaaacdadeaddebeacebadcdbdebbebeccaccddacedcddadccbbbbadaaceaabeebaccbeebbbbcccdbbbbcccbcadaaebcbdcdeaedcabaaaceadbaaddbbeabebcdceadebecaddaceeddddcabcbebecbaaacadeaddccdeeedbddeeceabbdeddadcbbaebeddabadecedcbbedcedeecbcabcdaadeeaedaddcacbddbaadabdecdaaabdcdbbccdeecaabbaddeadabedcedcdeeacccdeebdababdecaedbdceeebccdceedeceddeadaabdddeaaacdbbcacdcebddddaebeebebaddaacbbbdceedeeeadedbbeeedbbdabcbbeeedcaaaebaabaaedcbebacbbeadcaacdeedcadbbceacccbabeeeeddbaebdbeacabbbaacaaecdabaceebaadeadacddaaeeaadbabceacedadaacddeabdcdcdedebcaaaaebedcdaacaadcdededabceedcceaadeddacabeadbebaedeabbbbebcdbaebecdcbdbbcecbacbbcbebbdddebaaaaaaacdcbbddecdcaccaedebebaccbabbbdcedbcbbabeaeedbcccbeebcaeecdbcabbcbbdceacebdeeebecedceabcccedbaaceeddbcacdbbdecdadeaadddcccbbaaaeabcbebacdcdbaebdceacbcebbddabdbedecdbbdbabcecdbabcbdbdddbaeecebbbcedbdaddabadaacabcaadcddcaacbaaabddeadebaeeaeccdcdcbcbbacbbbcadcbbdecddbdccaeeaddedddeebebdcdacaaaedabaadbddecdbbdbddcaccddcddabcbacbcccadccabeaaabbeabeadcebbaaddbaedcacbcbbddddeececedcebddcbdccebabaecabeabcbacbbadcbbcceaadabbbcecdbbaedabbcaababbdeabbebcaebebceecaeaadbdeaeadecbbbdbacdcbeadddcbbcbeeccbcdbacebebbdebbcecbbccbdcebeebabdddacedecbddaceaeccdbcccaebdddbacaddeadadbdbebdacbddaddbdcdceaaeeeaebddcceeaeacbcbccdecdbebbdbedacdebaacaedddbeddabecacebcaceeedeecdadaaacbcbaeabeeccebcdddadeadacabeadceddeeeedebbcacdebdbebacdbedacddaaedceceabbedbcdabbcbdadcddbceaaeeaaedcbbabdcbedadcaddeabbdaaeeecccabcebdbebcbaececaedcaedbabbeccceeaddeccdccbaacceadbccdeaeaeebdcbccdeaddaddbebaeaeccdbeccadceedecaccbabdaaeabcaaedacdddeaadcdbeeecbaeedaaecddbcbebddcceadeeddcbdbdceddcaaeadeebdacdebeacaeaecdeeacceebcdedccebacccabdacaebdceaacdeaeeddbddcaceacbcdcebaeadbddddebadadedacbcaeeaddbeeeeddcaeceededaaedbedcceeebababebeebdeadeedebebceeebbeaeacccdcdbbdcadcdbbabdcccddacbbacceeceaabcedbdadaaaecbbcadabcdecdbdabbecabbceacacacbdbabbcaaeddeaeddaedccdcddeaaddacbccdeedaacdcdeabcddbeaddaeaeaddcebdbabdbabbeeedddceaabbaedaeaebdccabcbcbebcdedaccebcecbbedccdecdaacbbdbdbeeaadbddcebbeaceadeecdeebbceedebdcdaecdbdecdcbdadeecbdcddecabcadeccabdcedaeeeaebcbacaccdddabbbbdcedaabdabdecebaddacbbbebbabdeddaccbadeabdccbbdbbdccdbecdcacdccadaeededbbdccbaeecdcbbcbbbbcdedeaebdbabdcbdecbebecaedbcdadedbabbacaccaadbaaadababcbecbeeeaaadbcdecdbaadeeabbaeaabedbebcdebbdddeadccbaeeecbaaddacebdbccbacacdabcdebdcbeeaaaccdbebbbbbecebeeabcbceeedecbeddddcebbaebbddbcaccbbcbabbbacebcebaecebdacdbbdeebeecdcbeddbdbdeceadeadcaacdaaaaddbeadaecbddcbebcddccceceaadcaadadcabdcddbbccdcaacbadbbecbadccbebcddadcebdacbccdcabdacdadbacacdebaeebcbdcceaeccaadcdbcccbdbcdddbccbdeeaddccdaeabeacecadaacddaeddedeabacdebeeacbaaadadeecbbecdcaadbbedabaadceededacebdcccebcebeabcdccedabaadccbbddabcebceedcccbadeeddbeadecbeaccbadddacaddeebcdeaeebcbdccaabceeaeadbbcbbbaabbadcbdccaadebccbadeeebecbddaaeaaeadbdaedbcbababbccaabcebbebaecdeeecbdeeeeedaddecceebecadccccbbecababaaeaabaeeaedcaeeebcddadccdeabcddaaaeedcceabedbacabcaeabacabacadabeeabbdbedbadbcebadedccabddbbceebcebadbbacbbcbecdeacacdbbcbceaaedcabcbbaeabcecedebcbbbcdbdaeecbacceeeeacbeecdcdeaeebcbdbdddaddecdabbebabeccadedaceaedebadebbbbeadcdebeddeedaecadcbbeccbcbebcededdbbebcedcbcceaeaadbeceaceebbbcabdbcbedacabbeaadbccacdebbcbcedebbdbbdbeddeacbbcaebadaaacaadcdaadcbdaaaaccdabecabdededaeecaabbcaeedcdabbedceeadcabedbdeccaaeaacecaeeabdeacecacbcaaebbeceaebddddbdbdbaeeadedbddddddeddacebdbcabbecbdaaaddcbebccaeeecdcaeebbdccecebabeddbbaaebaeccdbecdbadbcacaebbdccaecacabbaedcbcdaccccccbbdebcceacbecaceaaaeecdcaeaecabcbcbeaebeeebbbecebabddbcabcddcdddcbaacacceeadddcbebbdeeeaeccdecebbecbdcebacdddeebedacbcacdbeacaddbddadeedcbadcebadcaaddcbdbdebdecddebeaacacdbbaabeabaedadacbbabbdecadacbaadccdebeaadccecdbceacbbddeaabbdcdadabdacdaeedcdaeeabbabbeceebbebaedaeadacbcdcbbccababebabacbcbabeeedeceaebcdaeabaabdaaebbcbecacabbacceceacbbeccadedacaeaabaaabadeabaadabbceeecbbaddccadbcacabebaabcbadccadaedabaddaedbececbadcabbbdbdeaabbbebddecbccdaaacdaabedbbccbbbcebdcbadbccbdacabbecadcadaddedaadebeecabadebaaeebbeabebbdbdaadabcbabecedacccaddcdcceabecedeccccadaabeadbeebeeabaeeceddaadebdbaaeeadecdcbcdacbcbeaacddadcdabbcdabcdaaedbdbebbcdededddaacececedbcaaebbcaabddaeaabdeaecbaacdddceedeeceacdedbddbaebddabecbccbaddbabdeaaaebabaacedacbebedecaebcecdaaaaacaeaeecadbbecbeceedeacecebbddcaececdeadcccdeddcceddccbadcccaeacbcaeecdeaacbaabaadaeaabeceedecbdabebebbacadbbbcdddeddcebeebeaccadbdccbacadeaeceebceaabeccbcbaebebdaebdeeeacacbccadecceccebddbadaadcdcdaabeecebebdabceacddcecbdbdbadeaebacbdebbceaeaaebadbcbeeaeccdcdabdbbeeccaeebaeeeebdbeacedbbacabaaabbdabdcebaccdcabacbbabbacedbeeeceaaeacbdaeddedebbaedabdaddabccaecbcaaaadcbdebecbdbcdaaeebdcdacdadacddacabdedababbcadeebabacaadedccadadadbacdddaebccaeeedabaeecdacbdcebadbdaaacdedadeddddcaededeadeeabdccbdceaeacebaedbbedeeecaeedbeecccceacabaeedcbccdbdaaeabcdbcaabeaebdaaaaddbebddbbddcaeadedadeceacddcbbddebbaeccbbedecddbcebbbaeabaadcaaceaacbbcaabdcddceabcbacaecebecaeaebbdcecaceeadaeaaceaeadebcdccacebeaabaebceeabbdcdaeabcdeecebdabbdacebbebcaaebbcecedcaebdbddddebbdacbebdaeebbacebedadabaaacececacddcdebccdccaeaceabdedcdbabcbedcadececcceadddaedaccbadeeedddcadedbbaccadeeccaedeadaeeceabcacadaaceaadadcabaaacaeaeabdbeeaeecaeabceabeebcbbaeeacebebeccadbbbbebadcabeeeacdadceddbcdaacdceeebbccceacbeabbaededaeedbdeebaddedccbeaedeebdddbddcdaebeeeebccceecacbcadbcdbbccadaeedcacaabadbbcddeccbebbaccdcbcdeaecccaccccceeeccdaceceddabeeacebeceaccdeaddddeceeabdecacbbaaedeaccccbecbeaeeeceeabcecaedcdbcbcecbcaedddebecdcbeceabceaccabadedabccccbecdbaedadcdeaacccebeecebcccecdeeebdaccaaeebbcdabbaaddaccbbdeadebebbbbedacecdabeeabddbbdaeddbbabebcaebeacaeacbcdaddcdcecbccaacacbbcdacddcdaddecedaeabcebebbbdabaccaceccbedabddabebeeadabeddecbbcaecccddadaededaaadbaabcededecabdbbbababcedaaacabbdcbbcebdedaacecdcdedececbcebcaedacadbccaaadbdabdaadbebcbaeebaeebcbbdccbcdbaedabaeedebedbdadabedddcccbbadaebeaedaebabcddebcdcebaaaaaebecbcdbcdebbeceacddbaadeceaebabdbcbaecacdacdaeceaedcbbcdccdbaeacdbeeaebeeecdbacccecdbedbaccacaacbacaeaabeaddacdebceadbbaecedceedcceeaadbbcbcddbccebdbdeabebaaceedbcedeaedeecedccaaeaabbedbbbdebcdcacbebbdedabcdeeacacbdaeceeedccbcedabbbeeaaacaedcccdbcdacceedcdadcbbebaabbbbdadbdcccdaadbcacbdbbebbadeceeeedbabaaaddcacaecdceacbdbbdacbceeeaeabaaaccaadeebbdbdcdbcabaeeccbadaeacdbeedcedacebaaedddadbdcbeddbedaeccddceddbabdbeddbcccaaccccabddadcdebbbcaadebeabddcaebccbadedddccedddeaaacacbaddbebdddeabaaacdedecbceaaabccccceabeabbbdbbeddeabdebbcaabdddaddcabcaeaededadbadaedbeebddedaccbbbbdaedbdaededecccaccdaddedbdddaaceacecdecadededecebdadecbaeeacaeecddddcaeacdbbcaedccdebbabaeebadeabbbebddacacacbddadecdbebceacbeccdebadebbaddbcadecbdcdeedbedcdbdabdcbbccbbcaecbdbeeeaedddeaeabdacbdcccbcbdebbbeadecaccbcdcdaabbadabbaeebbaedbbcdbebcceeebdbabddaadacaaddeadccaaddccdbbabeeccbecadeaedcabeadedcebbaabeaacbbcaddeaddaddcacabdeedeedeaebabdaaecbdeeebaaaebdbdababdbdaaddcdaebededcadddceddebbdabddbecacecdaaadeaebbeebededddceeeedceddabeadddddecebdabecedeebcaebebabcdeaaaacaadebcbbaceeadeeecbeaaebcdbcddeedcbdbabaaaccccdccaaabbbcaecacdccbbccadaaeabceecbbbaceabecbcbccbcdecdbaadaaeadbddbaedbeaebbddeecdaeddadbdeaedbaccbbdceddbcdebdedecbcbcbaabbbdadbaaddcdecbebeebbcdbdbdaedbadbaeccadeabcabbeaaadaadeeeebcecdaadaebcdaabbbcdaccaedbddbeedcadaadaacabdcabdabaecaccdcbcdbddbbaaebdedbcdccccebeacdacbbaeccceebccebbccdecdccacbcceedeecceadcedceccdebcdeaeacebeaaabdbecccaaecedcceeecbdbabecdedcbdbaddbcadaccbeccbabecbaaeebdacdcabeaedbdbdaceedccdbcdaeaccbaabbaedbcadeaccbaaeaabdbddcaebdeaabdbcacaebddabdebdbcccdebeddcdcbcacecdbacecabaeaebdeeebedebddbebedebaddcbecedaeeabdaeadebbaedcdccbabeccccbaecbedabebabbbcacaacacabcbaccacebeaaadecddaebaadcdbdaedcedccddcecceacecdbaecdcbacbbddecabbdddbeccebaebdededbeacdbbddddddbdddcecacdacdadccbaddccbebccebdaecebadeeecbeeedeabadceabcecedeeecdabbabbadaadcdbcddacbcaccdbcaedeacecadacdddbabbbabbcccebeccbdbecacadcbcdeaddcceeaebeaddccbabacbdceaecccdeeaeaccbebdeddabcaabeadacabeddccdebbabadddbaeaaabdebaaccddbecbcdacdaabddabababaedddccddcaadaaaebeacdaebebbabddeeeecebedbabedaedcdaddaedbccdeaabbbcacbbcdbdadadabecaaabcebbcbcbeebcbeeeadbcadcdbdbbdbddadacccbbdccdebcaecaeacdddbaeccbcedeccbdaeddccbdaeaccadedabedebdedeacabedaceaeaccbebaaecabcbabdcedcbeeaaacbaeacacdccbebabeaedeaaaabcbdcdcecddadceaaeaaedebacabadacedebdccecaccdeecacaeaadaeccbeeeabecedaadbcdccccdbcbdcbcebbbbcdbbecdaebebadcbbbebbdccdebadbccccbaabddcdbaedacdecedceaeadecebeeadaedecabebbcccabbbbceeebeabebdeaeacdccccbbbccdbeabccaeaecdeadabeaccddeaebaddcbdabbddccbebdeebecdaaeecaddeabcdeacdbbeebddedeeeaaebbbcebccabaabdacdedceeacedbaeddecbadbaebbcaeeebcdcaecaeadcaadaeaeaacebcbbdbcacecabbcbaabccbedddcccbedaecbdaaebdbdbaababcaeeecbbecaacadaebcddadedbedaaeceaebcabeeecbacdbceebbcbdccbecbebbbcdedccadbedcdbebaabdcbcacebaecddeababdbaacdadaaeaedddedcebdedeeddbbccbbedeececcbcdcbaaaaaccedcbbdacddecedededcbbbdcbebacccadecebbbebcbadabeddcdccaccbabaeeedadcdecacceceebdcebaccacbacabdeceaccadcabeabdebedeaaededabcbbbaeceebaccbcedaadaececedbdcebbeaaeccbaeddcadeecedabdaccdcddbaedbebbdebaddcabcabbdddbbeaaabaeacdaeacabcaeecacdbbbbbacadaebeecdcbdebaebebebcbcdeecbdadaddbedccdebabeecacdbcabaacbdceacabeeeacaacdcadbbedcacebcbdddbddbabcbbddadabdbccddadcdbedabdbaadccdecccaededeaebaccbcebceeeeaceaebbaeacdcedababbddcecebaccaddeebbbcaaeabadaceeeaacecdebadcdedeadcccdeebccbdeedbaddcedccbbbbdeaeacbeaeaeebcbcabababaebbeaddcbeadcbeacbeaaebdaeadebcabaeeacebeacbbadaecadddceadabeaedabeedeccbbdcbeeeddaadcddcebeabaadeceeeeadcbddbbcbabdebadeaedcdcdecbeecebbdeedbbabcaeccecbcdeadabdedaedbdacaaeaabdaebaeaccbbccaebdaddaabbbbadaddcacdeceeccddbeddadbeeeedacecaceaeaeeeecbcdeeadadbcacbecaebdedbaacbadadecbdbcdcdceecbcdeddaaeebdbacdceaecbbcccdccaeceeaebaaebbbedcacadcdebcbbcebeadbaddaebbcdcedcaaaeacdbcddccaacbdeeadddebacaaeccdadadeedaaadbeadaadbdedceaaaaddebcbadddeccabdaaaaebebabcedbccbdaaabcaaeeebadabeccbdeedccdbbedebbdaddaccaccaacceccbeebbcceaaaddbacbbdadcadbbeadecceceddaadeebcbbddcebbbdbaeaeaaacebcbeadeebdcaeeaddbcbbaedabacecbebdecbedaacbdcadbaeeeaadbcadedcddaeccbddeedbcaaebdcddcccdebacedaabcdecdaabedbbbadacecbccdbdceecaaabaadcdedddbcbdbaabbbcbabedbeadcdaebacbadcbbdbdeacbbbcadcbbeacddcbacdadedaeeabbbabdaddcabcdbbceadaedadccbcaaacabaadcacccbededdbedddeedbccecedcaaecbabbdacaabdddedacebbdbadddecdabdadcbceecdadabeddedabcbddecadcacaaabacbededadaeedecebaaeaedcdeadebceedadcddacaeccbdcadaeededeeecaaadaebcaeebdbecbdaccacbbceaecdedecbbebaadddadbccecbbcaededbbdbbcdbeceadadedaecdccbecaebddaaaeaadcedecddbacddaaccbdaaeacdaacacedecccbdededdcbabbbeacedddabddcdcdabdbcececaecababdcaebecdcedaabadbebeaaaddacebcdacccdaacadacaecbbcaccabebaeddbeccbbeaaeacacbdcbdcbbbadbcaebdecaabdbdcabecdbcaacabecbaedaacacabcabecbdbdedcedcabebcecbddaeaeccaebcecbecbbadaddbebcadaacadbdebcacdaedddacecdcbcaccdedbbedaaecbaaaabebbbcdbbbabcaaadebbbdcbbeaeeddbddcabcbcacdcdddbebcbceedeaedabaebeaaecbedeeedcaebbaedcdcebaeddecdeacbaeacbdeedccabacacacbbeeaeacaedcedbadeebebbadbcabcabbcaaedbcbdebdbbedecabbdaadaebcbadeecdbcccbaecbbbabeadaaabebeedcaccbbeeeadeeecbcaabdeddaadbcccdecbeedddccebcecccbdbdddaabeabeadbdaaaabbadbebeeebdbbabaecccadcedcebebabedbaaedeabbeddabdeaebbbabeccaddcbbdbdacdcaebacedacaecacebbcebaadddebcaddabebebddbcedccaacbebacaeecddbadaeebdcaaaccabcbdbeeaddceadbcdddadabeaebcccbedceecdacebcdaeaacbdcacdaddaddeebbcdbeaacdabebaeaacbdcebdbebcceacdedadbaccccadcdbcdbeaddcbbbccacadcbcaecbebccecbbdbcdadccbbcbbcbbaedbdceabecadcacdaaabdbaedaabbeddcbeecabddcddabdbeaebebddcadebcdeabaacebdcabdcaddeaecadabdabeccdbcaeecadbeeaabcadbbadcddbbdecdaacebdceaaaebcabcaecebddaedcabcedbecdcecaeeaedaaebbebcaababbccedcacaddedbbcbedbddbeaacacceddcaccaeacbdeadbedaebccdbeecceababcecdceadbcaaedebaebecaceccbbedeceaeeceaaebbacadbaabacbceaecebaedcecbdbeadcbadcddcabdaddeccdcaeeccddddebacdadbbcaebdadbdcddadccadbccadeeeebaeacdcceabdceadabdccedaeaacbebaedecceeaadcdaaadcacdbecadbebabdcbcddabadecaddceccaadedcccecebaddcbbebdaabdcdbcdaedbceddcdceaedeceddedbdcaebacbedcabbaecedcabdcdbedabbedceabbabaeddeaddeebdcdcbdeadeabaaddeececddcbaebeeedceedcbeeaaeaacddeeccacdacccccdcbebeddcabcaecaaecbccbbccdacceccbaddeeacecbadbdeeccaecadbdcdaeaeeababaddddaabedddabdbcddeacdaeeabdadeeadecabeeecccacadaecddecbeedddabadadecddbacaaacddabbccdccbaaaccdecebdddbaaebdecbbabdcebbdbaacdaaaabebdcdbeadbeccbabacbeabbbbddddeeccebcaceeaecababedcbaceededaaabbdabbcadbadeeccdeaeaedbcdeeaeddbababacebeedadebbacbacbdeddcedccaaaceabbbdbccecdabdeceaadbaecaabaadcaecbcdeddbbdbdcebadaecadbdedecacedcecaeeebeeabecdcbdaadbbdbcaccecdbbdbabcedbcbdbaccdaccdeadddacaabccbeeddcebbbebbdbbeecdeacdcdeedaaaabbcabcdbaddbbddececdcdeacddbcabcdabceadbeddcebbbaebecbddbdddaaebacebbadcecdcebeccadabdeabcececeaccbacabdcebddbbdccaceddacbbeecbacecdbdceeadaccbdaaccadddbeeccdadcdedeedaadaabcaacddbdadebbdcbaceadebaebabaaebceaecbccadcdadacddeddbbaeeeaceecddebeaeaeecbdceecccbaaacbcddcbeadcdedeedebbdabbcbaeabaeeeeabaebaddebbeacbacddebbceadaddacbdadeaaabebabadbacddeeeaddcddbedbbddaddabcaecdbeadbaceccbbadebcebddcbdcceacccdceeeedacbceaeedecbedbbedbdbceeeeaeeabdeedabeadcbadbdceaadaebcdabbdcaacbdedadeceeaacdcebeeabdceaeeccccadbbcabcddececededeaabcbeccedaceddddecabadbaebccecbbddabaaedadcdaaccedcebccebabeeedbbbedccedddbebcccabceacdcbccbddccbbdcbebcbabedabaecaabddeceeebbddebccdccabeecbbabbdebbbceebacabbaadbaebccbdeadbbcbdbaebdeadbaaaecbdabebebdbacaccbbedecaebaaecbdddabacabccdceaedeadaeecbedadccedeaccbcdbcadcacaeeecbdcedeedcdaeeacbabeaaecbabebaaccdbaacaaadcbdeceedcacaeeeddedabdeadebcedaadecdadbcbcaebeddddbdbcbebaeddcceadadcacdeeadbaccdceabeaebacdecdcabacdeebdcdabbbcabeaccbbaeaadebcdadcaddcdcdebeaceeeeaaeeeaceebddbacdabdedbecbaccbcebbccbceecbbdbeadeabbcaadcdaedeaacceeceacedbebabadaebdcdbaccaaedccbabbeadbbccacebaddeebdecedabdadeaeaaecaaccceabeaaebdbececaaccbebdacbacacdebadbcbccbcaadbcaecceeaacbaebbabccecaaeeceeacaaabeaddbaecddeceebbcdadaeececbeaededebeeaadbeebcaedceccaaaaedebcbcbecddbdcceddcaadabdaeebceacaacbaeaccedbebcddeddaeacddaacabdedbacddeaeadcecacbdcdbeddcbdbbbbcedeaceeabeeabdadedaececadcacdaddbbababeacaaabbbebcbdbcdbcedcabbcdabdeabbdcdbdaaceaeebeabaceebccabdcbcdcdabdcacdbebcccbacacbcedbcedbbaecbabedcecdcbbbdbbadbecaecbaeeeeedeabeaccccddcbbdabbcbbdbbdeabbebcbeaeeaaccecbcaedbcbebddcddaeddeebcadedbedcadceeaecdabbdcdaebeecacaaadcebeaacaebbccaaaaaabedeacbcabaebdbabdebdbebceececebcadcdbbadceadacbeaedeebabdacaeabeecbcaeabbcbebeecadcaedbbceeaaeedceecadbbabbadeabbebcbdbbeeeeddeadeabeadecdaabebecadecadecdacdccedaaabeadceabcddacccbebeaddcadaacbedbbdebceaaaadaeaecabedeeecaeebdbbceacdadcecacdeacacabecdbdaabbbedcedacbcdacaacbedbbaccdbeedcdededaddcbbddbcadbccbcecacccbdecabdecdeebeabdceaaeaccdceebabccaceaddeccddbbaccaeaebeeaecacbbddcbdcadeadbebabaaeeabcccadadacaacebcdbccdcebcaddcecedcabadbdadebddacddcdbbdbdbecdabeaadacccebeeedebdaedcbbecbcdeaaedeeeeccbebddbcabccdacbeaebdbecabdbceacedbecadeeeecddddcddbcebabeaeadabdbdaabebddeccedeeaebbabcbccabeecbceabaebcecabbdccaaccebbbadceecdaebbcbbacbeeeadcebcecbaecbabbdbdadabcddbcebcdceebcdcbacbbeadbdeddcdbeaabdbdacaabcaabcebbddeabbdbccbcdebdaacbcdccdedceeabababbaeecbeaecbabedeaecebadbeeadabceacdcadebbcbdecdccbeebbceddcbddcbdaebdccecaceababddceeceacbceeeaebcdbadaeecadbcebbcbdeedbaebceaaecbaccdacecdedabaecbcebaeabdebceedaaabddabdcdeecdbeaedeaaddadddeabbacdeaeeaadbdacacccbaaadeaaaaacbbaaeaacceecaadcabcadbbcbcaaedeeaceaaddaaecccaaeebadedebccdbdadbccdceabdcbdcbcececdeebcacaaeadadbbdecbedecdbcacbadcaabbeceabbcccaabacbdaaacbbcdeaabbebbbcdebaaedcdcdcbdbdbaeaacdbabddbcecdedddaddeddadcaabcceddbeacacabbcddaedeadccdbeadacbddbeedbdbedaadaaddcedbbcadabebebbaabadeacdcbabaeedebcbbeaadeebecdbedcacbddcccbccdbddadaadaadabcdebcdedebdbddbbaceeacedddbbdeaeeecaebbebbadbaeabcbbacbddabeaabebdbbaedbeaddcbebadcebdebabeceedbaadeadbaabbbaeaedabebbeeaebacbcaceeddbcaaaaacddebeabcbdeecabbeeddedacececccaddddeeebcaabbbdbbcbbbdbcbdbabcaedacdeabaeeacdbaeeebeddaebeaacacbbecabbbebdeabbeabbcdcaabedbabddcedaeeaacedadbaeabdbedcbeaebecaccddeaaeadaabddbbcecbdcedcbaccbcadeeceeacbaebacbcabceedcdeaeeebaaceebaaebdeaaeedcedebabaebcebbecdadebdccaedeebeaadacecdeaebadeeecbecdebadeaabbadccacbbebebbbcbbddedacacedcacebecbabeaaaeedbadbddcbbeddaaaeccbecdecdebabeacbadeddddedacebaeccccdcedeaeabbeccdbdcedecbcbaccccdacbbdbcbdaaecbddaaabdbdddeadacacecaebdebeedadacedbdceaadaaceddddcaeedaecacabbcdbeeeadddbceabaddaddebcbebddcbeabeeeddbbbeedeacdadabcbdceebbabbceceabdacadbbceebceeaadecbceecceeedaeadaabeecaeebadbeabebbdbcdbbecccbdccabaecaabdbdedbdadeeeabadeaadddebaecaebdbbedbbcacebbaaeecccdcadbecbbabdbaadbdaceadeabbdbccdaebadcebeecdacecadabdddcaeaecadbedbceeddeccacaacaeecaaddaacddacdccabccbeaceadbcbdcabbaadcebaecadcdddcceedcecaddaecdbccdeadedadaedcdbaeeeecbbadacaaaaaaedeebecbeaecbeeadedabeadcadceceaccacdaecaebeaebbceeeaacdbcabcbdbbeaceabcbcdcadedecbdbeabcdcdcacaeaaecdcdbeecacdeeecdccbddeeeedddeacacbcdaadeeccedccecdcbddbbdecdbcedbebbbedcaaabeccacabadebcabdabbacedbeeacdaebadbdabbaeeeeeebcaabaebbbbbbbacdbeebcaabaaadadecceecdeeccebaeceecbadabeacabedddebeacbadbcdebdcacebdebdbcedeacddabeabddbcbabecdabcbbdadacddeabdecaeeceececbabdbdaaddabdbccaaecbeeaeebbaacecaabebebecdbcebdedabdecdacdaccdaabdcdaabebaabcbabdaacbaadaccceabaccaabbbaabeecdbacbdceeaceddedbdbeccdececcaaaebebebdecdccbbeacdabaeeeebaeabdadeabcaccbeaceeaaccddcebbeecacddbddcdcadbdabbaaebdcaedbbdcaeeeecbeedddbbbaacdcdbbdddcbbcbedeaacddecccedcaebaecaebaaabcecdddbdeedabadeaacaeeccadacdbcaebdebeecabbeebdaadadcdbbbabdedccecdebdcbeedbaadedaddbeaeceaacdaacddaebbdceabbeabadeadcbaedcaabcececbbdcebaaacedacddbbbcbddeadbaadeadeebbdbdadcabaecacacdadccdcbeabcdaecaecdddbeddeadeabdddeebdaaedebcccabecdcdccedeeddbdecdbadcbbdaaaddbadecceccadbbdcabaaecbbeaeecccedadeaddaeeebcadeccccaaabdececaaddabedbabaaebbcedaddbdddbaebbbdeeabacddeadbddcabcaccacdecebdecbeececebbdcdabdabceedcabbdaebbcebdcdccbbcededacdcaaccdcaadaeabbeeddabedbcbadabadcabadbbbadaacbeadeecddecddeddceacaebacbcabbebbebbaeabcdbeaeddaeceacadaacaaebbdbaceedaadbbebaabbddbcedbebbbeaeaeabecaaaebdeedbbdcadcadacdddbaadeecbbdbbeababdaebeddcdcdceedebecbeaaabeaadadebeceebcacbddcaaedaaeaedaaacbceaecacadabaccdadbadeceaeebcebdadceaababbecebcdebbaaceccbdabcbeaeaebbdaceccceabadbcbadbeacaedcbccdaeeabebebeacccddbdeceebeabbeeabdcbaedccebcbdbbbdddbdeedcbdaedaeaacbdbbdacdbbacdabeebbcacecbccaeceedaeacadaeecdeadbadedeeecbedbcdbcedccadbdcdeeedcccbdbcdbbedebeadaacdbbacbdbceaedaeadbdcdcedabaaebbadeecddbcdbecdbcacbcabddbedadcdbcedaadccadeedecccecdebbccadddddadceebccdaddbbedacebddeeddddcdccbacedccdceddadeedadbcebeceeeabeceacceecbbbcaddbddaccaadaddebdaedcaadeaaddbadbedcedaebacedbeadaceacaececeebbebabddcddadeeedebeabcbbeccabcaadeeaabedcbcaaecadcebebaeaededebdbaebaeaaabbedecbcbbaadebdeedbceeaaeeebebaaaaadaadeaaebbebbaabaebbaaaceebbdbdebbdececdcbcebababbbebccbcbaedeabadeebdddeeaabdebdccbcedaedeabeedaedabceedaeaabcbbacbcabdabbbedcbaadcccdabcdebbdddeeaeebeeecabcccebbaaecccedbaedcadbbdceccbbcbddaadbdcabbbecccdabecdecaeceadadacbaeeceeccbdbaeececaacbabbdcaaebdacdadaebdeceacddeecacedeaaaabbabacecaaacdcadeabcbcebdadabecbecccedeacbeecbbeadebadcebeeddacceadcbcaccbabcadcadaeecaddacbcbbadacadeedbbdadbcbdbbbdebcbbcaaaccaceeaecacbaaeabdbdebeeeadedbdedbcbadcbebccaeabeaaddebadadcacdcebadbbcddbdadbdccecaecddbbcbbeadbcbeeecaeceeaaecdadbaebeaedddadbddaaceeacccbceecadbbbedebeaebcdbbbdeaebbabbddbaabaadcaacdbbccdeeeacadddddceacedcadbcdccbcadcccaecbcadddcedccdcdbebdebeeceecdaedceaabaacaacbabeccbddbadbddbcdecccaaccdaeabdaebcddcbaceabbcddcbbedeeecdacbcabceeddbbaeeabacdcadebcdcaaccddcdccedccdbcebebbdddeaeedeecdccdcbacdbdbacddcacbbadcaaaaecdacdaeeccebacaabbabdebeadddbbbeadddbcdcecececdcdadeaebbcdccccaaaacceadbaddaeabbaccaebbbddbadaedeabccbbecbbebaeababccebbaebcebadccedbbaccedebaeabcedeeccccaeddbdddebbcadeceaeceaebdeaedeeecedeeadabcbdbdbdaebcbaccbddacbdddecceadebacdbdcccdbccebcdecbcaeddbdedddcacaeaaeedcabbeedadeecbecccbcbbcbcadccbecacdadddcdbceecbabedbdaacbbabebbeddbdaeceaddebeccbdabadbbcddbeadabaaaeecddacdcedabaaabbeeebadcdbadacecdbcdbbcdecadedaceaaadecdcedabcdcacdabbeabebacebecaecbdebbcaceceaaeebcbcceddcccbecdbdbcbaceaadedbdcccdbddadadabadbbdcceeeaaebebbcbcbcaadcebccabdceadedecbadddcdaaeecaeeaeaeabceddbeccdeabeecacabedaddbcabcacebeeeebceceeecbccdeaeccbabbaaebaddeabcdddcaebeabdeabedbeaabebcccaededbacbeaaaacaebddbbccbdadccbeddcdbaaddccacbeececcaddbdabbcceebcbbdbedecdeadbdcddddaeceaaabebdbcdeeddebddaaccbddeccdeaeaeaccedeadceeebbebddaaeacdbbcdddacbedbccdbebdceebdbaebedebebddcbadadbcddcdaabbeabcaaddeebeccbbeadbbdedecbbdadaaeedbbccbabaecbedccbdcaceeecabccdcddddbcdabcabaeadedaacccebeaedabbccddbaeabcdbaddbadbbaebdebebbbbcbebaddaabdebeabbaadabdedcbebbbcbedecbdceaacaeadbacbdadadbccdeedcceebebeaaccebccbaaaceeadeaaabeeddaacdeadcaeccdeddcadbaeceaeaaabbbecebbbaddddacbbeabeeccbbceedcadbccdcecbadaebbcecdaccdebccadeeebbcdacedbeaddadebcdecbcdbcdbbeddbaeaaaaadbacaaacaaedacadcbeacaccbebdcdeccddeeeecddebdddbeebdceccaeedeeabecebcecdacadabeaedeeeeacccbeacecbabbdbcacacbbcecbecadbcdebddaaeeeebdaadeaeeeecdcdabacdccedbcadcebbeddacebcaebaeeeebdccbeeeaacaabececbbdcbbbcaeedeecaceeeabeaadaededccadceceeceababaacaeeeaeddeadbbbecadacecbabacbddaccecaccbdacdcededdeeaedeacaabebdaddcabbcebcdbeeeabeabbdaeebacaddeeaccbacaeeabcadadecceeacbccccdeeacbeeabcabedbaccedcdabeaceddeedebccecdcbddaceedbcedcabeebeeadacdaacaaadcecdcacbdaadcbcdeeddbedbaaeabeadbbaaeeebbbecdebecadebacbddbbebaccacbddeeceecbabcbdbeacbabaddeecabccceddaceaaedaadbceeeacdbdcedaeaccdddbdcbebbccdcdccdacbddeedadebeaceebaebbeededeccecaaabbeeaccabcedceeacecacebedecebebbbcadcaadeaadadebdebeeedbeecddabcadebcbebdddcccacaadeeaebecdceecacaaadabaeeeeeadccdeabdaadbbbedaacaccacaaebcbbdaecadeeaaadcbeecebdaeeabadbedcadaebceccaadaddebdbdceeeeccbeecbddaaaccbbabdeeabeaabaebdaccbaadeebeebecaebeeeadccebecadcceadbecebddeeeeccdddcaaccadddeaceddbaceedbdeeeccecddbcddbcddbcabdeeeddbdbeeddabaeedcbdadebcaeeddcbccbacbccbdddebdeeeddecebacdeadaaecadabdeeccbddeeccbbacbcbabdbeebdcdbebccecbcbeaaabadedbddeaacdcdcbedabdeeebbacdabacebddccebdbdbcbedcababcbccbcbaaedbeeacccccaedadbabddbcdcbddedbdbbaceceadbacabcbecdeadcbacabcbdbddbccdeebbabcccddaeedcadecbcbbdecebbaaedcdeececbcecdeebdaeedabbdcacdeaaeebecdadaeeeeeceadcaddddabaedeabadddcdcceeecadeeebacdedcaedaaaabcddcacbbceccdbacacebbdedcbeecbcedcbeeddcaaabbebedbecbceeeceeecbcaeeaacabcebdcadcbcabdedddcabeedbabecbeceddaeaacdbaabadcadeddbdadaceedebdcbddbdbedaebeabdeacbedacaadbeccdbadebadebdedabdbbedaccedbaddeedaadacadecaebecaddcbecabddedcddcbbeebcaaebecdeacacbbedbebccdbabaeddbccedbbbdeadcbbebdebdbbcddedbddcacceaeabcebdaecddadedacaeabcbedcadeecdaacbbebbbbdacceccbeaabadcbdccdaabeeabcedeebccadaadbedbdceebdabeecdbbbebecddbbcdcedccbccbaacbeaeaabebdeebdbbececeebdeadaeaeeadbacebabdcebacabdcedeedcdacebcbbcdeaaeabcceaaadaaaebeacdecacdbddcddcaeacdaeadecabeecaacccccaaccaccedbcebbbdbaadaceaecbebaedbdcebeddcebdcbbcddbcadabadebadeeaddcbaaeaeeaaaceaeeccaabccccdbacaaeabebdcccbbeaccedceeedaeebeebccaeecececaaeeaebcbbaaeccbeadbaeaddeabddddddcadaaebcaccebebabaecdacdbaeedbecbccaccadcbdbbdddedaccebddabdaadccdccabccdabceaeeaceecadbdaecdcdbddeeccccaecbbccbeaaeadeecadedbdddabbeedeadeadacbbadccabbddcbdadcddecddccaddbdcaeabaacbaaeadbceaecaecacacedbdeeeebeaddbdabebcdebbaeccdeaaaaeaeabbabdbaaceaeacceaadccbaabebcbeeabedbcaeabdccdbdaeadedaeebcdcccaecaadabecdcdcaeecceccacaebbcbedecaccbceaebeadaddaeedccdeebbdeddaceeabecccbbaeddbbdbbabaeabbbdaabcbebddbabbdadbbeacdeecccacaabeecadbbaddbaeddedbcabbdacaaeeeaadbaeddaebeedcbbcedaeebebbbcddcaeabbdbeaccbbceabadebcaadbeacabdadddebaadcdebeedaacbdaeaabaaacddcacdbaebedeeeabdeabbaceabadecbadbcacbbaeadebdaabedeebdaabbebccdedbbdeeceecbcdcaccdabecedccbbdebcaebdecadeccddaccddcaeedeacbbbccdebdebcceeceecbacbecaabddddabbebccbccbcacaddbabeaadadeccdbbbcbcbdbedccebcecddaaeeebbacbeedccbcdabedacbdcbeadbaddbbdacddddcbbceddbdbbcceecabbcaeaccadaaeeebeaebeedceedeabaddeececcceeacccadcacccbecabedeaaedcbbdddcbdadcdaeeeebbeeaedcacdcdddcedcbabbddabcebeeaaaceabdeccecaedbeaeeacdadaebeeecacbabadccaaaaeeaceaadcaadcabaeddbcccaedceeacceaacdaecddabbededdebdcaaabacaccabbdbcebbbcbeeceedcdacaaedccaaaedbdcbabbabceacedddcdbeeeccaabbeacdeeebaaadcbadebeeaecbaeeebcacdbacbccdaeecaddaceaacddedbecbacaeccbedbaecccdceebcddeaeebacaacabdaadabcbcdaaebdacabdaebebecabacebecdeddaacddccbebddaaeeccebeebcabaddaddcacedbcccedbddccbaebddcceaababbbebaaadebcebcacbcdbecacecadbdddeaaaabedceabeadbecaeaebbbbdedcadcbcdcedaccbebccceddbacbabdebedceccebedceeddeeeeeeaddacacedebebeddddbeccadedeecadbbdcdcdacecbebeeeddddbacdeedeabcaccedeeaceededbadadedaacddeacbcaecaeeacaabcaebdaeeabcdabddedccccdeaaaaecbbbedccdaaababdbeedcaebaedbaeaeeceeccaaccceecacedbdcecbecbeecdabbbaeebcccbadaddaaabcedbbbbccaeadcdcedadeaadcabcadebedbbcaabeccaeaebaecebdacaeccaedbaaebceaeeccbaabbeecbdedacdbeddcaedebeadbecdedcecaadceccabbdcbdcbeccaaadaadddcaeedccaadcadbaedadcddcabceccdebaaecbcdbcbdececcbebdecdcaaadbddbcdbaacbecababaebaabdbabbbddacabecabceaaeaadacbbeacccedaabeacccccaedbebacceabcccaecdbeebcacbdaaacedcdeeedbbeeedeabcbedcdebccbeaeccdbcabdaedcccbdcdeaceacebcadabdbdbdcdbeebdcccbbaaeccccbdaeadeedddccaceadcbecbcdacecebdaaebabdabbeabedbbeccacdbbebbbcceacddddadbbeabdaaeacbeebcdbdeebccdcbdadbbbcbbeacacdeceddaebceeddbcaaedcdbdeaaabcdadeaecaedbecbcabcbdddaccbcbccedcddbaceaedcbadcabeddbebbcacbecacccbeeddccbbecbeeadcbaadcddccdbdcdeebadaecaabdedcacdedddbbcbdcbaeccbcdabdcaceeedcbcccacdedecccecedcaeddeeaecddedeaadbeacedacedebdbcbbeeccdcedbededabdddbaccabadcbdbaabbaaccddbaabababcdbdbcbcbbdceaaebdbedbebeecdbceeeecedccaeaceaaccdbddeabadaaaedcabbdedacabbddacdbabbedcbcdcbebbdcadacedaebbcbeaaeabaeaebbeacebebdacaabdbbbedbeeabdebecebbdcdecbcaedeaceabcdecabbddaddaeacabebcdedddcdccacabcbecabdacebecdadbbaedaadddcdbaccbebadabdeddaaccbaaacacbbbaebaecabcdeadbdeadaedcdadbeabbabacadaeadbcacdeeaaaecaadaedacaceccebcadaecccbcdcebaabbcdeddaaccbdedeeabdecbacdbcecbaadeacbcabcccaceaacecdedcbaeaaddbaeeaabededceedcceddcdebceebeebeacceceaecaabadcecadbaddddabddbcccecccdecadeadcbdebadaadabdaeedaaaadebdedeacebdbeeedcadeacdccabbdcbbbbdaeeceadbadecbababddbdbbbebeedebbbbababcddcacacdbacbcbcdbaecdaedcbaeacadabeeedeaecdeebcbdbccebacacabededebeebacecebdddbcbbdbdabbbbaaadbbdbaeddaeecabbdceabbadbdebabecdaedbedbddebdbaabddddacabdbecdacaeceedeceeadceecbcebcceeceeebdeeeebbcdbcabdebedaecaaecbbebcbbdacaddbcacaadbdbdaeadddacdebaedcedbccbeedaedbacbdbebcaebeacabdeacedabdbebccbccbddbcedaebcaaaccedbbccbebeeadcdeebcccabdeeeebbbeabedecaeedaeeecabeebdabdcbedaaecedabdcaadeabbcbeebaabaacaedcabebacdcdcedbdccdbdacceadbeeedadccdebebcbaabccacccdeeecdeebdedbdcacebdcbaceebaeeaeceddcaebcccddeedecbaadbabeebdacebabadacbcbbcbdbebbcddbbcadebecbadbbcdedbccdeabcabcebbdbbadadabdbadcdbecbcebedeebcecbabcdbedaaacdaeececdadcbcdbaceeeededcedaabdaacabddeedbadccabdbeaadccebdbbdeebeacdccccaeeeeedccacdebdadadacbabbcbeaeebdebedcbbcacdcbcccbeebacbdebcbcbeeddcbadaabdecebaebadcdebdecdbbaabaecabdadaecccaecbdedbdebadeaadcdcbbbabbcbeabcbbeeacdcadcabcbeacdbdabcbbeaeaccdcddaececbeaedcbaebdceaeadeedeadcdcaccbcdbecdeaebebcedadebabedbbdeceecaabbedaeaadedcbcadbbecdeabaadadbeeadacaaeacbcbbaedbecaaeaabbbaeacdbaebcdbdcccedadceebaddbeddeeebdbecdcbdedadbbcbeddbdbccaedebabdeeceecaedcaabcbddeedbebdadebddabcaccecbeeebbcedabbdcbaadbaaadecbbbccaddbedbadbcaaacecbbaedbdcacbcecbcdaecbaaeaabeecedcbedeedeacddcaddaeaebeddbdaccaaeeaddccddbacbbeededbbbabbbdcadcacbddbceaddbecadedbdaedbedaeebebccdbcdaeadddccebbbbbdaccacddeeceaedceebbceccadabdbdceabedbdabdbddaedcbdbaaeaacdedadedebcdabedbebacdabebdbeebaddecccbabdedaddddeacdbeccccbaaeabbbdaeddeedccabdcdadcddadadacaabbeedeceaccaeabddaaeeaaabdaacbccaacdabedbaeddcdcbecedebceddaedddbcbcdddadceadecbcbbaeadbbccdeeacbcecacbccaceaacbbadcddccbedccccbdddbceacbbddbbeeccddccaddbaebadeeaaedddcbcacbbaacdbadedacaaeecadabddbdbebcdcdabdcddbeadadcdebdcdccebcbbdecccdeaccdbbcadebeebedabeebaddccbeddddbaaceddeadcdaebbecbaebdadabdeebbbbeeabbbedbebeddcbbbbecedabcdabbecbcceaaebabcbdadbabeadedcbcbddaaccdcdbeeabedacccabdaababeaaecbcaaeecdabbcceeaacbcdeeadcbbaccabcbbcdaecdacacdcebcbacecdebdbaadedaceddeacbdaedeeaeaddeeaabedcaeceecedceeedbdddaecaeadeccebdedadbdadeededceabebbacceaacdccdcecabeeacbacaacdcbacdcdaeaebadbeeaacececcdeaacabcdcedabeccdccadcbbbebeeaddddcacedaeeaacdaeaaebaeacbcdadabcccccdcacbdcccebebcdacabdeacbbaceadacbddeccaeaadceeeedccccdaccecabbcdadbdeaaeeaedddadecdaceedddcbaedddeedadceaecaabababcbccdebacecdabcbcadcedeaecabdddebebeceeeddaaccaadbaecedbbadaecceceecbbeaedabccbbbadaedaccbaedbdcddadbceceadabbededaeaaeecbcbdccabcadeedeacbbceaceacdcdaedacdcbadaabecaaaddababacadaaabcebbbdaededdcebaeaecacbaacdecddccddbdaccddbbadaddcdadecddebdbbaacdeebbcbdccbcadeadecbbddeeebdbbdacbbeecaedcbdccabdbbcbccdcbecacbaccdcbbeeedcbedccaeaeeeabdebccdaaacaaeacaccabbaceddaeccaeadaebcebacbdcdebeedeedeaddaedaebaadadceadacacdadebabdeccdebceedbdcbdaebaaccaadaaccaaeddeacebcaeabdbeebaaeaaaaceeeaedebeabdedbeaeabdbaecadadacdbcbceecccdcdebdcbdaceacdcaacdaddcdaaeceaeddaaaaeeacdceaecacebedecdcbeecadeacabbceabcccbedeecebcbebedaedddbbdabdcbaadabaebaddccdeebabacdddbacaaaddaadbeacbdbdebcdbdbacbdccdeedbdedaeeeecaaabebcdbdebbcbcdabcdaaedaadcdbbdecdadbeabeabdcaecdcdbedeeeddbdbbddbadaacbaddccebbaaaaebcceecddcbbedadadbcadadbbddbdeecdcaeaedbcbddcaabeddeaaebbadebdacaacedcadadcaceabcbdadabdbbdddbbaddcdccabbabaadcbecdccebeeaececbadedddedceaacdbddcbddbcaddaabbabdabeeddecbbeceecebcdecedaadddbedeaebccbeeeeadabccaebacdcdbcabeadddaeeeebeadcdcdeabdcababaeebbbbaeddbdcdbebacdebdbaeacabaebceebdcdceceeedcdadaadaaaaedeedcecdbcabdcbeabbdbcbeeecabebbcbdcdbdbeceabebdacedbadcaccbcdccdaadadedabbebbdebbedebdcbccbaaeadeabcdecbaabedcdbdacacebccbaebacbcababaddabaddadcbbbdedaaaabbeadcbbdddabadaecbbabebcebeadeacdccaccdbebebacacbcceeeddedebaaeaaabedadbdcadcecdcdedabeecddaeacecdbecdacdcadcdeceedbeecaceabaaadbebbbdbcabbebccbbacebabddeceaacbceddadddaeaeecbccaadaeaecddcaaacbcdbebedecebbaddecadceeeadcedadaabcadbedecbadedebddcbcedaeddbcaeedbabbdaeccaaeeabcdddaddcbecabbeaaaaeecbddedaacaedebacaacdbdabbcacebdeacbddbccdbecdbdbeacaadaaedebeceddbacadaeaececabebaedbbcadacbecdeeadaaaabbeaaadecdabdacedbeedbebeaadbcbeedcabceeadeeddbcaccaadddcddaedeabcdaeaebbebeadaceebedbeeebaaaeecabbbeeadadbebcaacbaeadaaccaacbddbeeabbdbcbdadecbcbcddbcdcbeeddcdcbcbdbceaeedcacccdcdceeaadedbdabadbdbbbcbabeddaabebbdcddebaadebdccdbccacbedadcaaedbedeeacbaeebcaeeebadcadaeddeaceccecbbcadcccebeeaeebbabaeadeacbebcdededebadbbedbbebabdedeaaabdceaaeeabeaecdddbadbabcaaeaaebeddddcdaedeabacddceeccadcaceceadaacceaddeacabebeddbaaeedcabbdcbeeddcacdcdddaabaabccbbeabddebcaddccaaddbaedbeccacacaacbdbbdeabdeabdeeedebccbcdccacddcacbadcccbbeddddbbbadaadeeeddceacabdecccdbceacdeacccaabbacdebcbecdddbbecadacbbddaaaeeacdbacbeaedccdebecaaeeecdcdcceaabdabdabaebeeaeaabeaddbcadbcedeacbebcedbcebbaabeecdddedbeacaccdabdbecdaaeecdbadccebacbbeabbeeeeaecbbbdaeddcedabcebbaaccdcdededbebdacdcadddaccebddcbacdebedceccecabbccacedceeaeceedbccdccbaaeebcababbebabbdaaabeaccceeaccabdeccbccaadeaebbdeddaacccbacdecbbdcabcccddcdeecbccdbebbcbbbacedebeccaceabbaaaeceeeaeaedabbcceebacecaedcbebdadbdaccbabdbdbabbcaaaccccedcdabaeaebaacedbdcaabedccbcebaccbcbdebbdacdbdebbedbccbcdcdcaacaadbdeabeeabcecdabccaeadbbacabebdedbecdbcebbdabebaeddeeceadaeedbcabbcccbceebccdeddccccacbcdecacaccddeaeacedddbadddbcaeeaaeeeeabaaccbcbcbeacbeeaeebdbbbdebceeaaaabdbdbbdacccacdeabcdcabcccaebabaaedbdcaeaeededcccdcddadbccaabedeadbcdedabbcacebdbcdecaaaacedbaebcaaeebbbeeaceadaacbbeecbdadcdaececaebcbedcadcacadeaaadddeeccaeacecabeaaeeccddbbdcbceadccadabccbdeecbbbabdeddcedcadebbbacaaeebecbcebddeeedcceebecdddeabddbbaadedabebbaecabcbdcccadbedbadebadeeeddbcaaabadacedcaddacddeeedccebedcbdcdaaacadbebacebbdabbccadadaeecadcbcbccdddedecbbabbddbcbadbeeabdbccdbabcccaccdebddcbedbbbcdbedbebecdcabccaabaecbdeabdcddcdbdadbdbabbabddbbbeeabadcccccbbdcbdbbedcedebadcdabaeaeaeabaedaebeddccadcdcbbbbcebcccdeadadcbeadccceceaaaabebeeeecbebcbdabeedddeaacbcaaaacebbadadbaecdbccbbddeaebedeededdaadedbadedaeecbbcdadaadbbebbaadbccabebcadbbdcaaaecdeadcaadbddcdaaeedddcbcbccaaccceecdeacbccbcbaaaaaeceecbebdbeaccdbbaabbbabaeaabbbcdbcabddcacaeeadbeebadcecddcceadebbacbdecaeaadbbabeabecbbacdecceddedbdaccaacdabbbecceadbbaeabbaccebbaaabcdeddaceaeeaeeedeeecbadacbedeeccbedaabebbacbcccedcaabbbbccedebecdadeaeaaeaeadacedeaedeadedcdedeedaeebecbdbecaadcccbaabaaaecbbccdeeaeeaccdcaabedceddbedccdbddddbdeacbcdecabbdcdaedcdcedbeeebaedebbdbeadbbebacdbcbebadaedbaddeeaaeeaadeacadbecaaabbecaadbcadacddbeccceecdaaebbbdeceaaaaccddcaeeaeaabdcaddeccdabcbcbcadbababebdacadaedaeebdbcceceaeacabccacedabebbdbdadaabbeaedbbbdadacaeabdbbaaebcabcddcbcbdebaeddabdabaadececadcaecbdbcadcdccdbeadadbececdcdbababcacbeaedbbdcebcbcccdbbcbdeedacebbdbdcddcdbdaeabcdccbdedcdebeeddaecdedbbbdeeeeecdecadadccbeaaeebdeadadcbaccccdacbaadadeebeacbcdacceacaddceeccbbdbbceaebeacdcecddcbdecdccadeadcabdddccbeceeebdeccdbcacccabdadadddbebeeaecaadbeaaedbcddbdbbbeeadaedacaedeaabdddaccbbbeeabdeaacccadcddbdddceaaebdcbddccedcbacbdddecccddaeabdeeeaaaaabecdaaccaccbcdbabdecdbedbabcbdeaeaeedcdcbeabadecabadcbbaacadadddadbcdcebedceebadbdccebecddddaeecdabceacdbbbbdcaebcdcbcaebbbcebcceccabebcdbdcbecededddaebabaacaaeacaeebaccbbeebceacaaaddbbcadbbcaadbbeccdbdbccabaabaeddbcccbdbabadacceabaceaccdeeedcdcbbceabdddadebdedeecebabaddcaadeccdcedabbbcaddebcaeacbbbaaedeaecddabdeacebbecdaabebecdcbbadcbebdcdbadeaadccdbaeaeccbcedcbabbabcacdbbcbcbebddcaeecebdccdcddaaaacadecbccddcbcbbacebcbbbceedadbedbacadcddeccceaccacedadeccaceeeadcbcdbacdcbceacedecddbacbacbcdabcbbcdbcabbeacbacdbcdaaecddadddacbaeecadcdeabcaecbbdbcecdabcccedbaacabcbdebeccddacdaaeeecaaadcecbbbaeabdbcbeadeadbedecadbaeddedecbececbbcaeadbbdeacadcdedaeddadacbbebcbeeccdcaaebedecdeeaaebdcaadaceeceedddbdedaaadabdceedccadbcbecbadccabeebbeaecccaceddbaedbcdcceeebecebdbbcacbddaeacbddabbbddcdaaadaeeabbeddadaeedaaacedcbccaecceaeccacaadccdbdaddcddaddbadcaecabebbdbbbdacbceceacadadecebcdcdaeccbccedcbecabdcecceeddbedcadcaddbdabdbaaaeccaaecddbaeeccabaeaaebedadececdeadaaededddaeaebcaaededadeeaaaaadadaecaebdcdddaaeaeeeaaeeabcbaaeccbaaaeecaabebaadedbeeaebdadeaeaadedbdaddedadaadbebdcceabbceaceacdbbabbaabbbbcbbcbdecaaccaebccacddaabcdeacdedbbabeeebaaceddbacbddadddaebecddadbeabccbcaddaccdcedadcddadcdcdebdedbacbdbbbbaceeeecbdaccedcaaccbcacadddaaddbceadbddbaebadbabcccbcaaedabbaeeccacbacddadbbebacbcaedbecbabdbddddbbeaebaadaedcebeaccabaeaeddecedbbcacedbcecbdeeebabbdecabdcbbebdabaeaaebddcecadeebceaabcbeaeeadccbaebbcecdceedcecdbbeeaeeacbcbabbacbaeacbadcccdcedccdceeccacabcdaecadcaaaacedededceeebddaaedeeadaccddeebdceadddbbcdcbbdbbdcdcceecaeacdadaebdaddadcaedadaccbbdddeacdbbeccbccadecdacbbbbabbccbdbdabedeebbadebbdacebbbabbbaaceddcdadccaebacebdccaaaaaccbcdabbecaabcddaaecedbccebacbddbddbacadcbceaecddeecbebcbdddaeebaabcadaabbabadbababccdecebcdaccccadbbceaccacbecbbdbbdaabbbdaeebbcaabdaebdaeceadebeaabbecdecdddebdbedbcebbcbcedbcecbadcebeeacdabcdebbeddaadadaaaecabbbdceaadedcaeeeeacbedeccecadeaacbecbaddaaedeeadadabbbdaabedacadbceceebaadbacdcdcceaebbceaebabdcedddddedebcddadaececebccabeccecdcbcadcebadbbeddcbadbaeecddedbcecbddabcceaadeadccbeccdedddeaaadbdedadceccbdabdcbddcbbdbdcbcaddecedcbaadacecbaaddacbeecdddbaaaacbcdccbedcdeacebaeceecccbdeecbabceeddedbbdadbccabacecaadedaabcdededeccbeebadaaacacdeaedecadacdcbcbbcdcbdaccdeeacceecdbdadadbceeeabbedbdddaaaeceddaebdcbedeabeabcbddbaccddccaadbacaebecebaddceadcdbbdecbbcbcbcabcdaeedadcababeaededcddedaeccbeeeaeedddebebbdbbbcddccecadcedbebddbbdabdaaabedbcbdeedcdeedbceedcadeedbbcdbcbaecebaaeeeabdbcdbeebdbebbabadcecebabeccddebcbacadaaddedbdacbcccbceaccdaeabaddeaaadbbaaecedeeebebddcdecbaabaadddddceeadbaabecddbdcaaaceebdeedbaeacceacbcbcbacacbeabeedcbbcbbbddeddbcdbeaceeeeceaccabceaedeeddbbdaecdecddabecebdbdecbbdebdddebdebdbecdecbbeeaceeeaaaedebccecacdcccdebccddebdaededaaaaeceaddcedeadaabbdeabdaaebcadaeaaddaccdecaebcadaccebcaceeaeceacedbddcccddaeaaccdeabcecccaddcbeedaedddadaedbbceebeabbadbbccbdcaccbeedbeadabaecabbccecbbbdbcebbdeceabaeabbbdbdecbccedbcbacdbdeaeedbeabebecababebdadabcaaceadaacdcaeaddcbbcbdeabbeaeccacebcadedbddedbcddddbebacbbdebecceeabdacdcabbadaebbdebbcbcdbebbacaabaadcaaeaccadeeeaecbdabbcdcaebcdabdadaacbecdbcbeaacaecebcedbdccbeddabdcbbadedbccebccebbdaccdeacebedeabdabecadeccddbdabbbbeedbdbaaccbadcceadcaaceedddaebbaaacbbccbbddebabecbbacbbeaeabaaecdaddedcbedcaedbaecdcdabceabeeddcecaeebceaabdceacebbddceadbabebeedeceaaceebecabadcbeebbadceebdeeecacaaedcebaeabcdedeccbaadbaccceaeaabedaaeadaddaedcdbabdcbeaaecdacabdaaedbdceedaaeeeddcaacbbcceeacceaccbbaeabdbabaeecabccdbdcebaeebcbecbcaadebdcdbbadbdccaebdbcbabcabdcdabaccbeebcedbbcdddddadcaeaeabdebbcdebceabbecbbacaebbbdcabaeccdaacecdcbaceeaadeaeebbbccbdcadebbbadbecedcbbccabccbabacedeaeddaeeebabbbdbbabcedaececbadccabaadcddceeecddbbbabcdaaadcdbeaaedcceddcccebdebbeaecbdcaacdebcdcdaaeeccbdddceecabdeacbcabdbebdcaaabeacabdabbbcbebeaaaecccbdcdcccbecbabbdccbebbaeaabacbaebdbecdeedbabaecacbbcadbaeecacedaddecbceebcbecaebdccbdaceccaedcdeecbebbaabcbcadbbcbbdbdabedcebaaacdacbcacbeebbbbccddcdaedccabbaaadbcbdaeeeecbaeddcecaacecdbdecaccacbaadbadbbedaadddcacaeadcabdedcbbebddbcadcdcacddabbddbedbbcdaecadcdababbddccecedddbccedeabceddabccebacbadccebabaadbebbcececcbbcacdbacccaaaddcdacaedeaeaeacdaeeceecedccebbbbddacebebaeaccdedebcebaadcdaceceacecbdbedabceeddababbccbddabecccabeadbbbdbcbcecdcebebbaacaddbaaabedddccbedeedacddcaddbbeedebdeaebdebbacdebcdabdeccaeadcbabebabceebbcedbebbaebeebadeeaadaeddeaabccedbdeabdbdbbeeadcaecedaedebacacbbcceeabdcceaaeebeeceaebaedbcecbcbbebbdbceaaeaabaaeddababdcbadebaddedabdadbeaabaeabababddebeeaeddbecbceceeaecacbbeadbeaebbdbabeabddbeddedaaabcadebecbecaebeedacceecacbbebaacdebaeaaeaabeabbaeaecaabdecececcbebeecbaeaababbddccdcebddcaedeabaadbdbccdbabcdeadeabcedeebabbddacdbcdaccdceebdcddbdeebdacedddecbbecebecbaccaaeaeebedbcbbbaaddddceeecdeccebaabacceceaadeaebabcceeebacedeccaadeebcebceecdbbcddbedddeddbdcacedbeacabacadbbaadaebccdbdecabceceeddaddbeebdbdaabaddbaededdeddceeecbdabdaedeadddebeaabdbcaedcbccadaadbcdbebdabcdadcdacbaeabbabdecadbaaceddaedbcdabacbdbbdaecbebcdecbbdceacdcaeeeecbacbabededddbbdbeddcdcaabdbbdcdaecbbacccaecacdebbedcdecabcacbdddcdceeacbaedebbaceedbbadcbcbeeacdbcbdecdddbaedbedcecbbbedbaaaeaddaebbcbcedeebcddbacdacceaeceacaebaacbaeeedeabacadbdaeeacecdbaeccbcaccababcdabbaaeaedbabadaddcdcaaabbddddceddbecdecdaebbacaccbababbbaeeabeebbceaaeecdbaedcaacadcbccbedaddcadaaccbabcbbeabcedeabedbdbadcbbcebcabaceecbbaeccadcdebeeeeadbecedbcadeceabbbbbcaecacdeaeabedacebbcacadcacdadecdeaddddaabaebbaeaceadcdbcdccaeeebdededbbddbadedaaeadbccabccdcddadceeabcebbecdacdaacbddbdddbdecdbbbeacddabddaebaacdeccbbedbcdcebaddeeabcdaddeaeaedecbebdbccbbeadddebaceddbdecbdaaaabccadeadacdedbdbdbdddaeeabcbcedadbcbbccdbaedbabbbedcdcaccdcdabbecdbaebdaadbebdaecaccadedcecdbbbbeaccdaecddeeadbdbbedbacceccbccceadacecaeddaabeddceaeebbdbbaabccbbaccbcbcbcaceddccaecaeeabedcdcdcecbacbcdccadbddecdacbceaccbeaeeaecacacbdececdedeadeceedcbaabbddebbbdecabdcdcaacebabecdaadeaebebeacaeeacedacccaaaeebccacbbcaacdccdcceddedebcbdbceeccdebeceabbeaceecebadbeebeaaeadceccaebbabebbccbeeccabeaebaebeabebbdcaddcebebeaabdbcdbedaacebebbbbbcdcdeeccbaabdddcbbbceeedcccaebeddbabebdecdcbbbcdbbabcbcbeccdaaddeaadbdaeceacddcbcadecbaeaddcbeecccdecbecabbbccbddddccceedbbbacabaaaceeeebeabebcbcabbededadcedbcaeeceebcebbdbaacecbebdbdcdbbbaedecbcddddceaaadbacdadcddeebcecdebdeacdabdeeaeccaddadaebdaccaeeaddaebcceeaeebedbbcadbcbbdceeddccbedeeeaabcaadcbbabdceeedbbcccecabbeedadcabbdcccebdaabaccddcdebdeebbdcaaaccbedbdccbeaecceaebcdabeccedbccedebddbaaaccbaecadbaacddbdbadcbcbacdeaeebbedadabeaaadadecaaeaadbbadcaeccbcccceeebebddceaeedeeabbbbdcbbbcdaceaebecddaebdacaaaccbeeedbeeceadbcdbcdddadedcacedadcddabebebdbadabbbedaebbcaebdcaceedebaeccabdeeaeeeeacdbbcaaebccedcedbcbdeadacdeccbcdddbedbaadabbdaddedbbabebaacdacceddeccedcaabebccacebcdedababdbbeedabbdcbeabdbedcbacbddcaaaaaacecdcdddddbdddbececacaebcecbebdbcebdeaddcbdccebcaaccbacaebaeeaecddaeaaaaebebeeaecdaacabbaddceeccaadecccecbadcccbaceaabdbdaeceacceddcdaeedededccbdebcabccbdadbdeddcababaeadddccbdebddcaddecdbbbadacdcbbecddcbbeceecebabeeaceebdebcaaddbcbeceeeaedaacddccaaadbacceeeeccedeccdccceabdbaaebedeaaebcaabbebcdedeaeaccddcacaaecadcdebcbcccbdeddbdeebebaebedbacdecbeccceeeedabacadeddaeadacadbadecbdecddcbcbadaadcbdeddeacedcdbdacbcaecbeddbbdcabdebeddbeedcaddcbdaeecdaeaacbddeaeddeeaedbecadedeaaecaadeedababcbcacdcabccdbabadadeaddeacdbdbdaeeaceedaddbcdedbbcaccaeeccdedaedadedecabedcecadeaaabcbaddcededcadcecbdeceddeeedeccccadceabddbbebadcadccbadbdedbedcecabbbddbddcbabbeaeeabadcabceddaeccededabedebdebddcecacbaebbbaabbebbadcccebdbaaaabdaadebdaeeeaeecbbebceebaaccecededcbedcbebacebccabaacdcadaceaecdabbbeeeabeadcacdeadbddaadecbccbcccecccccdadedeccacdddaedecedaddadbccdedeabbbbcdddaedbcbaedbaadecacadedbaacaadaccddecabebacdbecceaaacbddbbddaadeaacdcadbaeaadadaccdcedaaadacbeaadcbdeecdcebadcbcebcdebcbedeccaccdaeeeaeebdeadeecaceeedeceededcaebccbbeaeaccdbbdcdaddebcdedacaaecaaaadaeceacaabbaaedcadbccceebbeccebebcaccacecadadeedbdedbaaeeebedaaacedbdaadbaebdeedbaababcecaadacebeccdacbbccdcedabcddaadbcbeadedbbcacdeabadeadadbcaaccdaabdbcddbedddbaaeacbcabadcbdecbeedcecedcbbccebbddcabdaeabbbddadcbaeeeacadeecaebedccdcabbcbcedaccdbeebebcaaadccacadcbdbdbdcdccdccbaeddcceddaaacdbddacdcecacbcadceacacbcbaaadababeabdabdbaccabecebdebdbdddbcacccbeedaebadacabceadebdeacbbcddcaeecbcedcdabbaadcbbeebdcdabacccabdeccecacdbaacecccaaeedcadecebcecdcbccbaaaabdeddcbcdceccbbbddecedcdecabaecbeadbcdebaecaebebeccacccbabdcecceecbcbaecbccebcdadecddeedaebcdbdeabadbaedcadbccbdeccbaededebdebaceaeececbaddcaddeecebdeedbebaadddacabbabeaabcbadeaaeececacacdcbadbeeddcdabaebaacdcdeadbdebceccaacdeacabcecddbdcacbacadbddcdeaddccbddaeedceacdccecbcadbedeecbbdbcbacbcbaddeecaaccdadcebbebdbceaabeeaddadabbaddaceebaaedcaccddadcacbaddccceeabceeeaccebaaadbbcceeecdbbcdacadecccbbcecbdaabddeeeaccaebbaaecabaaaedebaaeceebcabddeacebaeccabedabdbaddbcdbedcbceddeaebaeecccdedccdcebebcdededabdaaddeabcddcddacaabdadbaaeaceceeaabadcbcbeaedebeaadabbdbadcddbbdcacaeadbdeabaaebcbbcceebbabcbaeecceceadaadbcdbdabecebabcacddbcadccedbdabddccdedddecbddadeeabebaddecbdcedeecddadbeabacccdaebbeeadaebdeabcadccabbddcedbeaeccdbdedeedceeaabcabcacbebdeccbbacbebaeeaaedababadbdbeceaaedccabcdaaeebceeadacbadbdabceacbdbdaceaeacbecdacbdbaddacbabbebdacdebcdacccccbcbdbdcacbbbbaaeddebbbedcceeabaeeacdeceaeaeebcacdacadbadcbacaeaedcbabdcadcdebedbbddcbebbbeadeabdedaccabadceabdeedeadccdaeddecadaddddebbdcaccaebaabbceebdbeaadcabbeebccabdeaeeacbdcbadabbeedbadddbabccaeabcbbbeddddeccebedbbdabbdecbddbdbbebeaadeabaeecbbddbeeebecdceaedcecebbecdeaaadeedcbbddaddddacdccdaddebeeaeacddcccdceaecdcdcbbabadddaecbbdebcebecbddaeaebebeeacabeddeccbecbddecaeaedcbaddaeecbadcbcdbacbdedadedadceaeeecadcabdadcbeedecaecebddabedceabbbbbcaebdccbceecebacceaebeaaabaaaacedbaabccabdadebcccbbeadbdabcddceeceebadaaabbeedbbbadaddbccddcedcabdbeeabbbdcaaedabedbaedbcecccbccebaacdeabbbbdebaccccbdbccadeaeeebcebdcdbcacdcbdaaeebebecedebcabcdeccdabbdbcbbeaccbdcebcbccceabcceaebccaeaeeccdddeaabddeedeccbdeddeabdcaaabecdeabeedbeecdbdabbcbbaadaaabacbadcadbceceecaadbebbeeaeadeaaebcbebbbcbeaddadbcaebdccacdeecbabaecdddebeeacabadeebceecabacecaebdbcacccdaebaaddcedebdbeaceaaaeeececaecdceaacdaccdebaecbaacbedddccadababceeecbcbdeebcadccbadeddebbaaeedddadbbebdddccbeeedabbedcccccedcbbdadebeacaaaccdeccacddecaadbaddbddecedeecbccccebbbccbccaecddaaccbabcacdbcbbadadbdccdadcabdddcccebaaacabbedddacddbbbdaddeddcdadcaaeedbbcadddeeeeeebdabdbdcaaacdaadbdecbacebbecccbdadebacbeedaadcacceeaaeedecbcacaebdaabdebdeadcccbbacccaeeabcabdaaaccaeaebdaceeeacdaddacbbeecceaeeeeeaacabbbdcedeacbcddeedaeadecedecdabaeaaadbadabaabbbceecbadebbbbdebddebbebdcdeceededaceecbdaadaabadebedeccaceadbbbdbaededaddccadebadbddededbeaebeeaaaaceadbbaedaaaccbbbedddabbaaceaeacacbaecedcebebabbaebbeabacaddcaeaaaadddebbccedcabbecdddadeaebbaaeeaedcdccedbcddcabccaaebdceddebdabdbcacaeadaeaaebdcddeecdcaaaacdcecbdaebddacbaaebacecbadcaaaabcebeaccedbbcdadeaadbcaacbdbdacceebdaeecdcceebdbeaebdddeaabbcaecbddbadeeaabebdbdaaaededecaeecaceaddccedaaeeabdbadddbceeddbadaabecdddeeebeceaaddbdabdaaddaccecaacceaabecbeddcdcbcadeadbeaaaeeebdbeeacdeedcaeedddedcceedddecbdedceccddcdacacbddcbbccdbcecaeccedaaadaeabcdebdbbbbabaadaeddaceedbadddccebbccababaeadbaccbdeddacaadbcebbaececbaeccadadbdedeaababdabbdbacdcedddadecdbcdeaaceacaebeacebbcebeedcbeaaceaaebecbcebbcbeddcbaadbbabcedcabdcebadbbceecdacedecadcdcecabcadebabeccbbeedcbebbddaddcbcaacedabdeacdbcbbedeacaaebbcebaddcbcccdbcbcabdcbeebabeaacebcbdcacebeeecdecdcdaddbdaaacaeacadbaeadedbeaacbbbbbedecaeaeddaaecedbcecdbebbdddeeaadaacdbbddebbddacbadcecacddcdaddbcaabcccacdcbeebeaadaabbcbcebedacaabcecacaddcacdaceddbdcbacaacbeecdadaaebebbdcaaebceaabacdeddcebacabccebaebaecbeaeecbceebecceddadbaecabcddcdabbeaabeeddcbaedeeaaddbbbdaceedbcdbadbbecdabaebccdadcecccbaaaabcceebaaabdccdcaacdedcebbbabccdbeecceccbdeeddbaebecdaccbcccabaecebdcedcdddccaeeebdddacdedeedbcbaabccabccaeeeaabbdabcddbaabadebcdeccecaecceadbeaddacabacacbcdebdaebcbaabcbedabbedccddecddcebacbdccdbdeddceaacbccdcddceeebbaadabdedcccacbcbadacadcecadcacabbbbedccabdeaaecbddbbcdaebeeaceccabeeeebbbbbaccaedbeececaeeebaecccececdddbeacbcbcadcebdebeadcdddacbcbbacebeaaeaeabddeacaedaabaadbbbddeeabcbbecabcdaccdcdbebcccbebebdbeccbdecbdbedbabbbebbabeeecbddacdcddcaebbcaebeebcbaeecbbddcbaabceddbaedcebecbbdbacdcbeabcbabcaadadedebecbaedcdcdbbecdcdcdbabbaacadebdcbaacaebdaaeddeeccbaaadbabbbacecdebdedbbadccbeeabeedeabbeaabbabddeabeccabcacdabacecbbadecaeebbceeecdecacacddddabccaebadaaadaeabedadbababbbadbccedebcbdabbecacedeaaabdaccdabadecbebbddaecdeeaeabcbeccadaabecedadeecebceedabaadcbdceabdbeaaadccedbeddcbbadcdaccbaaddacdceddadadaeaddbbeddabeaddabbcaaceaacddcbbdcdeaeaddeecdabbcbbdcdaebbdccbbcedecececdaadedbceccaecbadbceaaecadccdbebdcceeacdcbdeeadedcbabedcbceacdcecdceeaaebbaacecbbdccaadedccacbaacddabbbbacebccdbcddaacebdbddbacbebebcaeadebaedbdccebaaadbbbdebbbceaeeeeaaaecbedbdadcedbccebcdddbeaeeeeecabbebcbbabeeceeeeccaadbcaddbbeeecbeccdeeadebdeaebacdbddccbaecbbeacbbbcaccacacbbcabebebdcaacbaaaabadcecdeabebabcbacbbcbcbebbbddedadcacdceabbcabbadccaecbaccabeddbacccbdcdabadebccebacebdaaaacaddccdddeeeeddbdaadcecaebbbeeccedadccceecdabadadeaeebacbcadbcbbccdecadbcbccaeababedbdebcabcacbbcadecaadaccabcadacddcadebbeebcdedddbbcbdbddeedbbecebcecbbbcccaceeeacebedecaaadbdaededadeeaabeececadbcaceabeaaecbeeedbdcdcacddecdddbebbabdeabeaccddccacbdeacbbebccabbdedaadbceacddddeccbaaddebdeadebdccbabbabcdcdccecdbbcbbdccecdcbdeabaacdeeecbcddeecadeecbccabebddcdcebecbaecabcbbeebdbddcdbddadadaadaaaaaabdbceeaebbdadebadeebeadecbcdaeddaccaacbcaddceecabbaceeceeeabcddaabbadbbeaacacdeebcaccabebbeeabdcebcecdbbddbcacddebacecbbbedbcbaabbcebcdbaacbaeabcadddccebeaabecbbeadbedceeadbbbdcdddebebbcbdbdabedbaabcbccbcccedbceadaebedceacbaeedaebbaceccbbbcecabcdbbadaacaadebecdcbbbabcaddcaaeceddadedeadccbdeecaebbbcbaaadbabbbacebccceeecccabdeebddcdbbdcebbebaecdcccebeeeacdbadccecbbdaaccaadbbbebebaeacbeacaedaeeaedcecadbbcdbdbabcdceadabaaeabcdccbcacccdeaeaadcbbdbbeebedeeadcbdbcdddebdeaecaeabbbbccadbbcaeeeebebebcccddddebbbbedeeadedbdcddcbdcacebadaebbaaebbababacaadebbeeeacbbadbaccbcecccbabcaaaeedadddeccadedcaebcdeeecddeadadbbdcdcbdededbcaccabbcbedadacedddcceeddcbdecceeaaebaadaceabeaaedaebebcabeacdcdebbccceacbabbddcabadeccebbbdadcdecaeadbcacabadceddaccdaebcceaaebaaddaacadbeaebcdeebcadceddaabdaaccadeeacddccbbcececbddbabbeeebebdbeabbbbdacdcbcaaaeacedccabacdeeadadddceebceeddeedaceecebbeeeccdebaeedaaacabbeeacbcddddbdadadeabbddbcbeabdbeadecbcaddebcbadbacedddeaadcdbcdbeabadcbccdabceadceaaeebeaabaeebbaaaabbddeaeceeebcceadccbdeccedbeaadadccabacaecbcedcbbbccdbadbbbbbaccedebabceccacedddcbbcdeaadbcceecbdeecdebdbaddbdcddabbdddceeaedabddccaaaacedcdbebabadcbaabbbaabdeddebddbccdcacbadddccdbcbdcbddcedbeabacbbdbdbbbceaeababcbecbeacebbaebddeedbdbbceedccceaabbcabddacbbecbaabeaccedaadeeceaeaadedabcaabdddacaaccdebaaeeecbcccdceebbeebcbccabddcdadceaacddadeabbcbceecdedaabbabcccbeeacbcdacdbacacceecdbbeaeedbedcdadeddebaebadbabbddaddcdacecacdccbcaecbaddcebbeddccbaadbeabbcbadbecadaaeaadddcebbedddadbadaabeedeaababbbacedebaccdcbdbaabacacebbbdbcbabbaecddccdbeaaadeacaabdcadecdeeaaeccdaceddadccdadbdecddcceabeedceddbccaaabeabeecbdadbcbbebbaecceaedceaacedbdceccecbecdcdacedeceacacbbaaceabcbdedeececdaadbbeaeddbeacaccaeebbaccdbbabdaeaaadcecebbecacbaeeccbadcbdceeeceedebcbbbedabaecbbcdebbdbeeadabeaebadabcdcaabdcebdcabdabaacbcedbeecedcdebacabbebddcccdddcabedeccbadddbdaaeecadceabedbcbadedbceedceacaeaabedeabceeacabdbbedcbdbeecdaedbeacabcdabebceeaeacbbbcbbdeaadecbacdacdbccbebadaabbddbbaebeadedabedcddbbadebbdebdcaeedeabcadaccdebdcaabacbbaccdeeaeaccecebbacaacbcddbbddaeacedbbecdebcccaccdeaeeebeebeeeaaecbbbabdccbbcaabebbdeeacdabaadacebeabebeaabebecccabebbcbabbbbaaceaeecaddcecbbdedccabdecbaeeadbdaabaaadabbdbaeaeddcdaaacdcbbdbacedaeacddcebdcebaadeedadedebdecbacacdcedcaeadccdcedeebdebedcbbbcdceccebadbbcabaeaeabacbdaadebcebdbadbcceabeebeddbacccceaddecbdccddeadccbbdbccabeadacddbdbeeccbececccbdedabcdedbadddecdadaabdcbebbcccebcbabaabdbedbecaeedcacdbeaadddedadbeeacaedbbdbceadcbebaedededbbaaeeebedbdcceadaecaddceecabcddecaecabbbdccdeecbebccbdaadccacbadededebeabebbbbbebdaabbbbdcbabedadcaddccedcddedbcedacaecaddbbdeaebcaceadceedeaaeddaedadabebbaeeaabcabdceebdbbccceedcaeaaaeabeecdbdadbaaedbeacbaedacbdedbdaecebcaddbaadeacddcddaecbeddeacedaeabdbabbccdbcdcbacdbcaaeaccccbbbdcadbabebbdbadceeaddbbacbcbecbeccecbcbbaeaeccccdacdbeccdcdaabadcaaacbdcadddcbeabbaccdddeacceaecdbeabedcbbebeddcceeddbcbeadbbcacecdcbadbadceacdebddddedbcccdeadddededeeeaabbdeeacbccdbcaaebedccddeceaccbebadcdeeadecaeddbcdcaaabbbaaeedbeeceecaebeaceaaedbdcaacadbcceddeddcedeabbbceeeadbebcdaadaaeaadbebcbbbcaadebbdccbbededacbabdddcdedddbabebdecdeabececdceaccebaebecbceeabcdbadcdcceccbeaeaabecdedcdbbcacacabedcbdbcacaaaaadbaebaaceacecbcebbedeceaabecebbaddbddbeeeaacabeeedbdacceedeadbccccdeceddaedaceedbaccbedecdaacbeedbdcacbedbadccedcbdadbbbeacbeceaddccbdeeeaeedecebcdbbbeceecbebdebdcaebbbeedebeceedacbceddbeaadececeaceeecaeededcebbaedcbbeddddeebddbbdabbadbeddcddaedcddabcacdaaacccbaddadabdeebeeeedcccecdabecbcaeabbdbdedcbbcedabaebdbcdaecdeadddbaebdedabdbccbcdcdadccacdbadeebeebeedaecccadaaceadaecbcbdcacdedaddecaeadcacdaecaadbbcdbaceecbbbecacbadbddeddacadbcdcdcaaadcebeacdeedaedcbdaadbabddceccaeebedaeeecdebeacbbaabeedcdeabcbedbeaceedebdaabedaedbdbbabbeedbdedcaebadaadcdaaaacdeebaaddcdbeaaeeddebcaadbbaadcbdadcdbbccadebdbaceababcbdcbaeddbebeaebbbcccdaebaebdbcbebeaccececbecdedcdabeebaedeedeebdddbcecbcddaebdaebecdeceaabaddbebbbadbbcbedbaececebebbdeceaedbabdeebaecbcdabededcacbbecccdbeaaceeccebdddaeecaaacddeaccbbeebacccabeeaeadeecbdaeeddbaccbeeeadceeddacddbdebdcdaeeabbadcdbcdbcbebdebceccebbabcecaabcddaaccbaedcacbadebeabeedeaadacddbeaaedcaacaceeeababcdbdccedabceeacacddedcdbddabbdcbcccebddcecdebddcadbacadaadacbbadaedbadaceadedbbbddbdbedecbedaaceeabeaeadbdabaebebcedcdbedcdeaceccadeedeabcbddeaabccbaebdecaebadaedaeebdceeadcbaddbbabddbcacedcaedaadcaeaecebbadbdedecabbdebbaaabaaeeeacbcceeaebdeedcbcaebbbeeecdbceadaeceacddebcdbbcacadedebbdbdacebcdcddacadaecebcbeadcabdbbbadceabeaeeecbcdeddabbbbdebbbcabacccbddbadbebceccdbdbbabebeededbbbbaccbecdeaeeaceccecdecdaaccaadecadecccedaebcacebccabcbbedaaeaabbdeeebccbaecdddbdcededaacdcbccaeddeabadebdadaebeebcbeacdbedccabeabebdbbaaaaebcaeeabcdaeedadecaaebcdbedaabbaacaddbbcadacdabcddbbcbecaecbbbedaaabdadcaeebeaeecedebeeccbecacbcbcdeeddbeecadadcbecdeaebbaecbdddbbcabddaddaaddcebdecdaebbcceadbdacabcacbeeabccaaaceecabbbaeaedeededecaddeaeccbdadbbadebeccaebbadbabecaddacdacdbdceebebeeaaccaeabedbdceadececeaedadebdceebbddedaaadbeeacdbbecacccbaedbdddcedbaadcccddcbcacccaadaecbdaabecabceeabeaaecaccaeacdedabddceddbabccebdedcadadecbbeceebeababecdbedaaebacdccbbabcebbebccbcbebaaedababbeeeebebbcdbcecacadabcbabdcabeaeedbdcbcecaebcddeadeaedbdbdabdebacdadccddeddabdeccdcaadbbececccabceceadcaccbbbbdcbaaaadbbbbadcbbccacaaccdaecdebdecaceecddecebacababdeaaeacdbbadbbeeeabdcaebcccabdbbbdcbbccebecbdebecedadeceadcebdcddedecebcbbcdbdacdeceddecdcdbdddebbddbaaacdccdececaabedcdceebaacddbbeaadebabacbcccddaaeebcbdccdcaabbedaedadaedddebbdbcbabddebeabdbddabadbaaceeaededddaebbcbcdcabbdccdbdaccebedcacccccbccacddebbdecdbceaebabdcddeddcbdacecbcbecadabecedacebeadccceebcbcadccbbacecdcbdbdebdccdacbaeeeecbaadbcacaeebcbdeecccddbebeddcebbbcbcadedddeccecdecdecbedabdbbcdeacaecabbbdbebbeeabcababaeabcbacacccebdabecebbdeededacdccbebbdceccccaedcccadecdbabedebdccdbdeaeddedadaadddadedccbdbcbeacaaeecbeddeceeececcbdcabeecaaceaabeecedeadacdbeebacebbbdddaaecdeebabcbeaccbbeeacabaeaaddaebdbeceeaabdeadbcbbdacceceeecdeacbcbcbcbbbeeeeababaacdddebabdaeebbeebcbedabaaceabebabadacacbecbcecbdeebacbbcaadbdacabdcdbeabacccbcebedeaaddbcacddecccadcadadbeecbebcccadeaeaadadbececacdbbedadddaeecdeebbcbeeaaabdacaacbcacbbabcadbabcdebcababcbceaedadcaaaebcadbccdeaddbacecebecccdedacebaedbbeccacceedccdadeaabbadaebeaccdbdcbdeebbabdcddebcedbbeeeaedbaceaeeccbadcebdaeababdaedbdcbbebbaaaccaeaeabddadabadbdecbcbddebcedeaecdecccabaddecebaadbbeeccebbcebeeadcdcaccbeaecaedebcddecaddaebeeaaebadeaedbdccacbcdcdecacbbdbbeccccdbaeeeacaccecddaeebcddcececdbbaaebedadbbdacadcacdcaadebdbbcecdabadabeeeadbeccbbcddeedaaebdeadaeececbdbcdbccdcdbbbaebeebadcbdacddaddcadceacaaecdcebcdeadbccaeeadbdceacddbbbadabeceedadcdecdceeabdcaabecbabdbdcdecebaaedabacdeaeeadadababcbdcdaebbbbcbbaedcdbeeedcabbeecbbcebecadcedeeaabeabacaaabdbdbbeaeabdebdddddaaaeaaebbbccacecadbadabdbdbdeddebbdbeebbedcacddecdbabedecaaebeeeecbcbaeedbcdcbdceabbedbcdecddebdecdbbcdadbdaadddebcdacadaedaeccaacddaaddaeabdaedacdebecacbbdeecdbaabebbbdbaeedabecaccbcdbeddaadaadadccbaaaabbbbecdeedabdcaeeaadcdadccbeddbebaabcaaedaccadbcacceaebbaadcecbabbadcccadeeebccadddebecaccaecbeddbcbcdeaecbabebcbbbbcedbaedcacabdbaacdaacbddcbbdeaecbdbbaaecaedcecceebbaddbbeacbbeebdbdeacedcdbbceccadeabebaccadcadcadebccccbccbebbbdbdebecbbeaaaeddbeaaeedacbdabbbdedcbacbaeceeeeaeddcdcebbcbbacaebebeddddcccebbaaccbdccaadcdeaabaebdaabbcacbddebaddaecedbaacbcbddcbddbacbbcecadeeedebcdebcadeebddeeacadddacdcccacbbbaccceabaabcabdbcbbaedcebedcddcbebcaccebeacdbacdccdbabacbddddcedbbdabcdccbcdedcdadcdabdaacbeedcaadbbdcbadcbbbccdeeddaaeeaacabbadcededaecbbdebccbaaacadcaeddcbadceeaedaedaaddaabcdcecabdbadaeccaaecadedaaaccceebceceaaacecccecaeeaaaeddaaadaaadbbdadaebcdcaeadeaaeeaacdccadebaccedececeeebdaaaababccccbdddececdabcdbdeabbceeccbeaacaaeadaaaecbceddcaeacbacbaaabeadcceaaebbbcabeeaceccedceecadccccdbeebbcdcbeebcdbddaccdeaccebbbedadedccbadaecadececacdadcccdedbebeeedddacceeeddeaebcdedbddeedaecabddeddecebabbaddddbcbadacaccacabbbcacbbcabcdcabbdaceabcbccdbedabeaaebbeaeeeaaaddecdedbeedcceacdcedcdeeddaedadcbbbeabaabbbebcbbbddcdaceecbedacdcacbeedcebbbaecadcbdcecebedacccbecabdebdbbdacdaeadbdbaebabaeabeebaaecbacebdeacadabcebbccbeebbdacdbbdaeadcdcccdeaaddbceaaddceacbbdcccdecbccebaccedbcdddeeeeacabbcbcacccabaceaeaaadadeebedabdbdcdbeaacabececbddeadabebaeceabdceeacadcbdaabacadeacebbeccbadbdcaababcbdbedeeedebadadbcacebeaebebaadbdaeccbcceaacaeccaccbcceaddbdbcbeabcbbdbdabdaebeaaadeacedbebddbcaedbebaddceaddaceeadeccebeabdbeebeeaadeedbbcaccbbddededadbadcbedcececcdaacbcdaeebebbbbbceabcecdceedecddabbcdbadcedcaddbeeccbeeebaedbaeebedcbdedcaadbecaaaeaabdddcddadceaacbacbbeccbecdbacbbbcbaecceeccdecaaadecdbbeaddebbbecaeaabacaeaeeabaecabbbcadceaadceeddadeeeabbedeebdedeacbeaeccdbcbaecacdcbdeeddbaebeabbeecabeabbcaaeebbcccaaecbecacbdddbcbaababceacabacceeebcccaaccbccecedabeecdeceedcbebccbbcdecaedcbacadebdadaabaeceebacbcbcdbdbacddaddadacbdeeaedcaddccdacbdedbbddbbacbcaeddabcceebbddaeabccebcbaaeadbcdbdbadbaabbcaeedaddecdaebeddbecbddcedaeadacbdcebdeccbbbdaecccbcdcbabddbeceaaeecadccebdcbcccdecbacdceeccaedacccbcbadcedcdecbeadaeceaedbeecedcbcdbbbccdacdecbadbacabbcedcdabcdceeaaddddddadebdecbccabbdecdaecdddaadcebbaadeeaabaddeadccccacdedcabeacdbcbccbccaeedeadaebaccceaacdaccddeccecebcbbedddcbbbeacddbcaeeaeceeccabeddcaceedcdccaaceebdbaeceaceeabeadcabececcdbdeebceddadcadcdbdbbdeadabaacbddbcbbceeddeecbadeaadbabdaedbcbeaeceddacbbdceeeecbebaddbbbaeaaecabdebccdcdecaadeadeedcdedcedbabaaebecbceddeeacebecadbdaebacdccecdbeaabcbdcdabccbddceaeebeedbbbedbaeaeadedebcbacadcbacbedeababedbacbcbdaeebbdbcaabaaccdabbbebbbbcbebcbadcadbcdcbcebcecacdcecdabedbaecadaaedeacbbdbcbccacccddacceacbeaebcccbdcabccdbcacebaadabaedceeddecaacaabaaaaeeadcbeacdeacbecacbddccadbaacecdccccaaceeedacdbdbeaeaddaaabcdeebabcecaceecabbccbacdacaabaabdcabdbbbbcbcadeabcaaccebcbabbcbeadaaececbbaaeebddddaaebaaddbcedbcedebbaadabaacdacadcaacbddedccedbacaedaedabdbacebaaadedbeccddbdaacaeedceaadadbccbcdacebceaabbdeabcebdebeceaacdabbeeeadedceabbdcbbbebceacdeadcbaadebaacaecddbecbbbcaddcddbcdabeacebadcdaaadbcdaaccaddebcdeabbececcceaacbddeccbeeeeeaeebcadeddacaccdacedbadddebcbbebdbaadbadedddcaaadceceeebedcedebebcbeecaacdaadddaeadcabecddcbaeecebeacbcbcdcabecaadeeeececbdaacdaaecbaebcaabbeaecaeedbdebabbacbeadbebebaaadceccadabcaeeeadacdcdedcbebccbbdadcebecabecbcadaeeaeedccbebddbeeabebaacadbdbecdebcdbbccabbabddbaeadbacdabacbeacdeabcccbcacbdaeccbebbbdabcadcbcceaccedcdddedacbaedecbeabbceaeebaddbedaeabcbacdaebbbcdedccebaaeeadcbbcacbbabbebeecabedabacddeaaeaceeedbebbeeeddbccbdaebddecdcbcbbbcdaddcaedacbadbcdbaeccbadbbaebcbcdbbcbcaccbbbbedaeeabcbbdcaebaccdeabbceadebcaceacdbcbdaedbdaabebdeecbacaddcbaabacddecbcdcacebdbddccabdccadaecdddcebddcdecbcadedaecaaaedcdebcdabddddabebbacbaacdbdadbaaddaecaababedeebeeabcaebaddcdeabeddeabeacdacbcdaaecdeaceaeddbccbabdebdabbcceabdbcaeeceddacacadcceddecaabbddaedcaeaedbabecebdbcbcdeceaeebebebcebdcccdbaecccdbcbceadceeeeddadeadcbeebeedcdcbeabcecaebaedbceacdbccdaaadbabaaedabaabdcaedbebbedadacebabaceaaaecdceebcbcadcebabceededaebdadccedbdadaadbecdbeabbdacbedceadcdddbbeabbaeeaeecceaeacceeaabbbabeecaeadcaccaaedeebebabcabdcbbadbadaeebaacaaeeececedaddeddcbdceedeecaabbcebdeeaabdbacddeacaecdaebeadcceadcedaeeaaeebdbcceceeeecaddbaeddbbccadbedbeaabeaaadebdedcddbdcacbbdabebeecbeaecbaddbedcaaeccbdeeaeecddceacbbcbeecbecdceccbaabdcbeabaabcbeadbacbbaccdabcbacebbacdccceeecccbdebabcacadbbaccdbbeabccdcbedcbbedbcccebddacbbeceaeebecabaebeddbcbcbaacbebecceacdeeaacbdcdbadbccabbdbcdcdedcebbdcdbeceeccbeacdebddcddcdacbbacbbaebabeaebcaabecddbbbaddcddeaabbdbeccdeecbccaeaabeaaecbcdddaeeadabddaccdeccabbbbaeebedabacdbeecdabbeacecaccaebebabdbadeecbdbcddbadbeabccededecdaddecaecbabeadebdcecdcdbaccbdbcccacdbabbcacebacdbacbcecdccbcddaacddbddaaedcddddbbeecdecebbedaceadbbbcabecdabccdebeeeeacbdaebebcbebebeeaceabbcceaebecdcadcecbecacaebdccccdeaaccdcccbdaaccbaabdddeedebdaabdcaadedccedadabebcbadcbcdcccadadbceacabeabbbdbddaecdcedaeceecbaaababddcaabdccbedcdeebdabdeaeaecceadbebcbbdaecaabeddaebacddcbeaedacaecbcabeabeeddcedaabbeccadcbaccdaddbbbbeeaeacdbdcdcbbbacaeeeeabeeceebedadbeccaebdcbeadceaebccdcaabcecadcebbdeaeeeebacacbcabdebdbaeeeeadcebbbacbcdbabcbdadaabccacdbcaedcaeaadcabbedbdcedebedbbddecaddebebceedadddeabeceabaabddcdaedadbeccdabcccbedeacecabedaeedcdadcdbcdbdaeabeadbdabedcadbaeaacabccdaccceaaddbebceccbdceeaebdbeebaeacdbddabaaaaccdeacbdbacbacdadcedceaacdcdcabdbceaccdcbedbeadeceabdaadcbbdbcbebccbecedbcebadecbaccdeeecaccadaeccbeecabecadbdebcbadeeaeeedeedbdcbaaaabadbbbbeadbaaceacaebdcbbcedaaedeaeccceebabaabcabedacedbaeaccddacacdcbddcedddbdcbebbbcceddbeedbedbebdbeaddaeceadeabdbbcceedacebccacadbebbecddddadcdcdbedcaedbaeddcdabddecacdcdcedbeccadbcebbacbbaaaddecadaeaebcdeedeaeeddbbeeeacebebdacbbcdebacbdaeccaddaecedeaebaddccddeacebbeedaccddcdbeccdedebebebdcbcebcedccabdaacdcbcbddeecaaddacabdaaaadaecbdeecaaeedcaceabaeacbbaddecbddcdbdadeddeacacaeddbbbbeedaeccdecabdaddccabdeabebcecedebeedaaaccaddaabecbceadddebcdcbeaeddcbdeaadaecbbebbdceddebabcacdceeddeedbbcdacbaedeaeaadcababeccbcaedbcdcaaabadabecbaaceadbbdadeababbeacbceccacecbbdddacbcadcdebcaabbececcccdeddacacccaddedbccdabdccbbeabbdadeecdbecdecddeaabeaddddadaceebccdbddddaadacbedadeedebbbcdcdcedbeaeaaddeecbdbeeabccacdcaddadcbecaecacedaddcebbdacbaccbddccabedecadecacaeebadbdaddeecadddaeedccbadaedaccaacecebeedadbbaeacecdacaadaccbabceedabbdccceabaebdbbddedbbcecdadbecadcddacddcdcbedcbedccaedbbcccceacedcbddbeaacddebabadbbeeeceaceecededeebceeaddbcceeddadaeadeaabbedaeecaccedebedcbbeeadcdddbadbbbeeedddbaabbacdacabcbacbedbbebceedcadadcacdacaeaddebecceceedbbdaebbedbababbedaddebcbbeccdbddaaadbdaccbbcaaccaabdcccbeeebcabbaaccdbaecedbeadeeaaadcbbcdebabaabaaeaaddcebdeaebcdeaeeeecbadcdabbbbedddaecccecbacdcecdccdcaeedccccdabaabaabdcaacdabadedbdbcaabcbeeeabcdcaccddbbebccddaaecbeadebcdcabeeedadddbdebbcadeeecabddbcaacbaccbbdaddebdedbcbaeaeaadbacdaadabedbeaccbdaaadbcebeecacaeecbedcecadebbdacdcadccaaadceebaecdebcbadcaddbadbecaddbbdcdacacbcdcaaecaadeccebaeacadaebaedaccbdcaddebcdebcbcdcaadbececcdccbadabcdaaaccdcdebecbaecbcebcdcabdbdbddccaeaeacaddaabdbdaebbaddebdccdcecdacbdeabbceddacdedbbebaeceeecbebbdddddacebbcbcadedbaccbbbeddebcbababbebaadadebcaecbaeadabdacedcbeacceececbadaceadbdacdbabedbaccbdabbdeacccabddeadbdaddbcdbabeeddcbddddccccdbdbdabcdebcdaecbedaddbdeeadcceebeceeddeceebebcdadaecbcbbeedadbbbcededdbabecbeaededeabcaadcdcecbaebaedaabcbeadcddbdabbccbbcacadeeebebacccaacedccdaddadbcbeddbecebaeedcaebeccbccecacbccbecdeadbceeeadeadceeebbaecbdbbdbcddadeeaddccecabecbcdccdcbcaebabebddebcbbcbdcaadcbdeebeccddaeaeaaddcbddedcaecbebdbdcbabcaaaaadbcaedccccedebdcdbdadaadedaddbcebcabcaadcbcecbddebadcdbbceceabbeebaaadedaededbdacdadbbdbebeeaadcebdeeedbbababbadecbbbceddabeddccdebabcaeaeacadbccebebdeabeebcaecdbebaabccabaceaeddbcabaedadeeccbdeadbccadaddbaaeacaabbccaedcadaecbddcbebddbdedbebbdebeceddadbbdedabadcaaccbcbeeabceaeacceebcdbddabcbebdbccabaabccadbbeaebbedeabeeacedbdbbcccaddebabddebddcebccaacbddaaaecabcdecbedebbbceccacecedebacdebdeeecabadedbaebdddddccccacecbacddaeddbeebacacddbaeaeeebacbbcecedccaebeeaabdbcbbaaaebcbebeeaedeeeacaecabaadacabbabbbcabeeacaacdadaaddccedcaeeaeebccecadcbeeaeececabddcbcdaaeeccedebeadebdbbbbabebadabbdebcaeeabacaecdeaecddbeabecaecbbdacaaeaacdddbcdedcaedadbcadeaacaaaadddaeebbddceebcbaedaeedaedaaacedcbbaeebbeccbdbbcebdbdadcedebbcbeacedaccbddebedceabdbcbcddacbdebbeeabeadacbaccdeaddcbbeddebdaadacacdeeceacddedebdebcacaaecebeceaabcaeacaeeaedccebbecbedcddcdddccaaaeceaedceebbdbbdcddaeddcbecbdebcccbedccdddbdbabccabddbeebddabedadeabdaeaaaeeebadaccbaeaeeddabbbcaaebbbadbaeeaadeaebdeeacddeabcceeebddbddbcdddaabadbcebdbcaacdbdcabdacaebaccbeddcdcbedecbeaaecbcaaceacaadddeabdbbaedbceddaadccbeecbedeadeeddeabcbcdbbcaceaaecaadaaacbebccedbdadeedcedbbcddabadbeacdcabecbacbeeaadbbbabddbbcdbcdbababbeedacdabdeeebdbbdecdcbaeaccddbeeadddebbeaacbaedeceebcbaadcadccbbbbebbddbdcdcecbacabeaaecebbcbbbcddabebccbaeeaededdeadccabbabbacbbecaabbddcccdbdcccaebdedebaddcbbdeceddedeaecbcbdcbeccdcaebdecbadadbecddccbcecedcccddccbcdadaaebcbcdebcecccaccddbbbcedeadcaccacebbdcdeaeaccbdcbabccbbeaebcaccebcbaaabddebbabbbadebcdeebdbbebbdcacedcccbdbacbcdaecbacbbdeeddcaacaeadcbeadbabaebeaeacaabecbddadaadabbabababdeeccbdceabdbdacbdeddecbddcbecedabebbcdabbaecadbbbeadbccedbaeecacaabdebabecdcdabbeacdbcecdcbeecacdddedbbeecceadcbdbbcaecaebcacbcdcccedebaeceedbaccecadbcabdeeaeabeccccdcadbadadacaecbccebdadaabacdeacedeaaabadedccdcdbcbeebdbabebbbaedebcebddcbabaeaeceedbbbdeaacadceceeeeaceaaeaacccbccddbaadeddeedadeddbaaabbbdaabddaeabaacdaeebeadebeccabeaeaeaaebcccecdabcaeedaddbebacbebacedbbcdcedbeaacbbcddaeacbdabebedecbdcecceebcadaabbcbbeddcabcdedabebddcabcbceeeebdcbedabbbadbdcbeeeeccbeccbdbbbebcadcdcdbcebecbdcbebecaadcbeddecdbcddecdabaeacccebaecedcbeebacacccaabeaebcadecceaddecabdaaedacaadbdcaadcedeaedaebedecbecadadccdbcbbbdabeebabaabccbcdedaecebdcdbcababdaeedcdbadbeaadbaabcaebbdaedbdcabceebadaecedbcdebadeedccbecbdecbbadccaecaacdedeadbaadcbdccebdeeaeecebedaeabeacebbbddbcadbabdeebdacadaaecbecdaadacadceebaaeedbbbabeaecbcbebdabceddcdbbecaecddecacbcddeeedeaebeaeeaebbeceabaadacdbdbedcadacdadcddcabaccbceebbcdbbbbbaeeeddabebcdbdeedbcbeeddcabbdaaaaeacaceaedbdcccaebdbcdeebeeeaedcedeadccbbaedbbedbabdabcbceaedbacadbeccbaacacddbcecadcbeabaacbdcecadeebdcbeceeccbdeedcbaabaeaacabeebeebdcdeebeaddeaaebbebbedabaeacdaaecbbbebdcbeeaaacddaaabbcddedecedaaabdeaabadacbeacdcbebcadcbadedbcbeacbbccdadbabddaadeaeaeeadbbbcdbdacdecaaedbbcaeaaaccbbcdeacbeacddaacaaabaeeedddedaaccccedbdeeacdedabebadadcbccdebcdebbaeaedebabccdcdaeadbaeabbddebcebadadedceccbbaaebddddbcebedceeacdaadceadeceeeaecebcadeeebcdeacdaebeebbddbcccbcdcdeaaeecacaaaeaeaecebdbbcaabbadcbbcacacddabcddbeadecdddcbcbccaeebcddccccaadaccccccbddcabeecaeceebbdadeddbacebbaeccbeedecbaacacbcdeecabcccebaecdeaaceaedecdaebbddcdebcbcabceeaddedebbcbaacdceccededdaeeaabacbcdaeaebbbdbcaeeaeaaccdbccbcbacadcbbecdbdadbacdddcddccbcebeecaadeecbeccddccbcdbabedeceababddaaaccdbaaedbbeedacdcaddceeacbaadaaeadedccbcaedeabdbeabacbaacadaedabcedcadaceecacdcbcdebcacedabbdceebadaeeebcddcebdaceccbaecbddcdeadbdbbedebbbbdceacbcebcababaaebdeceaeeddbcccaecadaedecccacbeacbbcdddacbeebcdceacbedacdedaedbeebdeacbbaabbeddcbceabdddcbcabbdeaceebcabeeacdceeebcccdcaeeeeddcaddbaaddedeadddbddcededcdcdeacaedcdccdbdecacbbaeaceaacccacbddadbddeceabceecdeecdeaaadacaaecbaeaebeaedcbeebeccaaadeeedeadccbedacedbcbaeadaeaaededbacceadaeaedcdbdeacdaaabcceebcebcaeccccadacaebdcaaababdceeeabddabccebeebbbeebbcacedceceabeedccbaceaecdedddcebddccaabdabbcdaebccdbeaedcddeddbbcbbaadebeacecaccbdcbdaddddaddbdeeaadbebaeedeaecdeedaaaaecebbacdecbdbbcddeeeeadaabdeeddbbebeadaadbaacdeaddddcbdbcddccdebacddaccdeddadceeababbdcedaacebaceedadddbdcaebbbdbeccaaeaecaeabdacacaeedecbbcddbaaeaccebacbceecdeaabbebedbaeabaeeceddbcdcecccaadeebbdadcccbdbddcacccedadebddaabaaabecccbecadbcaadeeccebbbaecbdabbaacaeedddeebcbeebcacccacaaccdccdcbaaaceadcecbcbaddddeccebbbadeeceaacaebaaaedaadcdcdaabaedcaeaccbeadeeaddbabacdebcdedbddabeedcaebdeadddaacaddbecadeedddecbebdacedbaaabedcaaabbbdedadebdeaeeebbbddaabaeabcbadebcaadedceadaccbbeceedabaebeecceeadcdeccdcbbabbedcaabbedcddaacbaddaedaecbddeeeecddabaabecbaccbcdebdbcdccadbeacbeaadeccceccdeeabaedacbabbdbbeceeaebcddebdeacccedcbccaddccdedcaeaeceaecbdccadabdbeaeeedebeccdeeacdeaaabcbcbddabdecdadbeaaadcebbabcdcecacdbbcbeadeaeaebaabcbcbbaeedbeecebdeeecbeeaedbcabebacdeaaedbdeddbbeeedebbeedbedeecdeccbbedebdcaeedecacdcaeaddbbeaedddebcdbedeedbbceeccdeecbeeddcdbdedecdcadbceeabbbdeaddcdbdaedacaeabcceedaaddeabbdaddaddacbcdbaabdcbdaddddebbcaedeabbedccabdcaceabbeceedaeedacacdeecdeaccbdbeccccbcbaeeaacdceabcdebbbbdecaeeaacaaddbccdeaacabbdcdbcdaeedacacadcbaaeacccddebadddeecbddedbeadcacebabebdedaacecacddcedacbdadeacecddeecaedbcdeadeeadaaeeeeeedcdbaecccedbddcdebbecbedadedecdccbbeaabadaecebdbadabacabcccccababecddaccedbcdeddcecbddebadcdaecddbdbcacaaddbbeeeeccaeaededeeecebdaddcccedadbccabecacdabeeccabeebbbdabcacaeccbcabbbeaacccebabdccadeaebaeadbdcabaaeccdaeecbaaacaccaddeadcbebbbeabbcddabcacacaacecdeeceedbccadabeaebecebbaadeeccbbcddebeaacadeadadbddccabdbaceecedcddadabcdaceedadbacdbbeadbcdbbbbaddbdabcdcdaacbdbdebccacaadbcccecdacaabaadcababcbecaedbdedcaeccccaaaabedaaaaaabadacabdecdccdbeadbccaaeceedbdeeeabbdececadadeaddbecbbdeccbccddedaaccdabcdddceacdaadadaaedaaeadecccbcebadadaedaadaabbaddeaeebdcceddacdaaabebbdbabdedbcecaeabcaebcaeadecebbdaadadadbdbdeaeecddbebeabbedcbbeccbeaabdbddbdbceabddcceeebaedcdcabbdbbdceccddeabaddbaacededaeaeeccbecccdcccbceaddddcccebecbdaddeaeedabdcddbbcacadbaaeaadbcbaacbeacddaaddedecececbcecbebccdaeceaacdacedeeaeccdabcbcabdddadeddcebbbacededabacccdccccbbacbbcabcdcbeacddbccbdddeeeaeaceedaceeabbeeaccbaaedcccdcdeabcedbebdabcddaeedcbaaebbababbdbcdedabacdadbecdaeeaadadadbabdebdcabcebeccabcdececcbedecebcbccecdeedddedabedcaedceebccaedcebaacbbbdcdeadcabaceeabbcdeabcdebebaaeaebbaedcceadbdebbaddabdcdacccbbdabdeedccedbdeedcecdbedabcbeecdceadbabadabacdbadbdaabddadbddbddabdecadaabdebdcebaaaadcaccdeecccacbbbadeaeceaabbbcbecdaecceccbdeedeaedcbbebdbddebebacccdeedaeceaeeecabeeaabcbecadacbedaedbaeceecbbbbeadceadcdbddddedaaacecadaebddeabbbddbaaaadceabbeceeadbdcbdcedaabaacbabbaebbbbdbeedbedcbbbecbacaabccdbdbdeebcacceeedbccecdaabcaadaaebbcdbdcdcccebaecccbccabeaeadcbabeabbeededebdbcacdceeddeceeabbadeecbbbcebbdaebeebdaccbeeceedadabbeadaaeaebdbdcdcbaedabaddcaebecdabbbaddadebabdddbabcdacdbccdcdecdcbaeedaddddadddcedeabeeebaddecbebbdbcdbabccebededcbadadeddcccccedebdbdabaabadbbadeeeabbaedcaacedacedbdebbcbdcadbabdacdbcedcddadcacebccaeedcdadebaeeaaaedbcaaceadebbeeddaeabbadcbbecaeeddaabcebcdbbeaeceeebbebdbbcbcacdeaabaacbaeabcedcacdececcbcacaedceccbebbcceebbdaebbcebeaeeddddabcebbaabdacedcaebddbeceebddbbdeaccdbdcdebdddbadcebbbaaeeadcabaccecdbbbdcdebaeeeedeaaddedbedccbcdecbbbcadbedbeccccceccdcceebbaceabaabaedbeaccdbbebdaacdedaabdcdbbaaadeccabedebbeeddcebeebacdcadbbcdececcaeecadeaabbeeacebeebcddeeaabecbaabdbbceeaeaabdaacadbbadbaceabbbbededccaecaecdaacbeaacbacbadddabceabcaedceeeaaebbabeeaaceaadcebbadadaddbdaebbdbcadddbcbdcbcabdcabdccaccddccdcbcabccddddcacabaaaecbcaabbdeadebeabecaeccdcdabbaacdbeeeeadbebcceeeaebcbcdeaecbeabdcecbaecabdcacdeebceaccaecbddbbabbecdeeaddcabdbcaacaaddaceaecacaeaeaaedecbebecaeeaaedaadeadddaaacbaaadeabebdbaccdacbceaaebceddecebcaaeadaaaccccddbdecdabdbaeabeebdcccebbcdcdedeaecdaadadccedeadbcabaadbbbdcdbaeabeeacdceaacebdedbdcbadacdaddbabdcdadaeecceaddeecbdeaadbebadbcbdbaaeddddcecaddeecdacdadbbabcdaabcecdebcceceabdabebbbcedbeccbbeeceebadeddcaddbdbdeeedeebeecedaeebebbbbddabbcbbabcdbcdbeeabcceccdbedccbdcbdbaeedbddbdcddebbabecbbaeeedecedabaebecaecacedecbeababededaabcdbbedbeedcdaeaddbaadbbabbadddecbeedebbedbacabcaceddbadccbcebeadbddbddcdcadaebacadababeabcaccacacbebcdbcabdddbeaddaaedbabdacdaeeeaaacaceecbaecadeeabdddcdbaaabeeaadabbedbcddbdadbddcbbbcdceecdcdecedceceabecbadecbedbccbebdbadbadeadecceecbbccbaaeabbdbaadadecacecbccebbcebcecacbccbbebddedaabaededdadbbacddeddaacadbdccdbadebeabacdecaeedcadcaecbecebcaadaeabdbedebeaaeabdeacceaadeecdceacdabdaaebccdadecaaccaaddadbedbbaaddbddbcddbbaeebcbddaebadaceaccdebebcdeacedbdedeedadcbddedcdbcadcbbccdcedbbedeeccbeddbbddcaebcaeaceabaedeecaaeeeddbbddcdeccdcdacbdedaaaacaddeadcababcdcaadaabecdcdaaeeebccbdeebdaaebdcbbacbceaeddbebecaeddededcdccaedbecaacdeabeaabccdbcbabeddbacccdaeebdbeabbedaaeddeacbdbabedcacbbdcabceaeeacacacbdcbacebcadbcccdaccbacbaedabccdcbdeeedeebdadcdedbdddaeadadbebdbbaacbddaedeadaeeebdccccddabbccaebcdebcccbbddecaddadedededcbacbcbeeaebccecadbbbcacaececdbcdaebadbeacdccedecaaabcedacbdcacedbbbeaadadbbacbcdccabccbbacdadedcbcdbbcbcbcedcdcdddddceebedbebebecabedebebadabededbeacabcceadedbceabaecaeceececbdbedaeebdccbbbbbcaaeeddbedcaccaeeaeeabecacdedcdbbeccbbbcbdccacaeaedaaddaaebbabcabeabbcbdbdbbdbebbcdebbcbbbeebeeccccccaaadababcceaaaceccdededecdddadaeeddababdcddccacacbeebbebbcbcadecdaaecccecaddbcebabbbceebdaddaecebccbdcaedeacaeeebecdeeabdbbcebcbdcbaacdeaadadceeaebcaedbdbcebacdbbedddaedaabbbdacbedbcacdeeedeeaeaeaedbadadaddedbaecdbaddedaaebccebbdcdeebdccceddabcdcacaadbcebbabecdabeaeabbadabddbebeecddbabebacbcababcbddeabccadeaccabdadebdadcabcbdeebadbeedbccdedcbadcceeecebdedacbeeeeaccdabaebaaccbdacbcebdaabbebadcdcedebcbdcbbcaaeccdcbdaeaebdecdebccbbeaddeabacacbedecaabbeebbdcbdadecceddecdeabedeeccbacaaabdedaceeacebccdbaaeeabdcdbbedaaaedaaedbaaeaccadcbbdbadcdccbebeecececaeaceecaebcecbdcdadceeadedbbcadbaebaeacbcddacdbecdacececcbbebdcccdcbbeeccceedbdcccebabceebbdddebdbaaadbbbeccaccdabeaabceecbdedbaeeadbcbbadaecdaebadbbdededbbdaecdbbccbccaadcedbadadeedebbeaaeaeccbadbdebdaddbbabdcbcaeeebddccaebbcddccbabeacaaacebddccccbaaedbcbeccaebeeeeddddaccdaccdbdcceadecceebbddeadcdbedeaddcaedbabdadedaddabdaaaaebedcabaeabdbbaebbeaeeebdbeaddceccedaabdeeddebddcccaadcaacedddbbacacaadddabbebcdbaceebcdaecbdabeabaabbcadebcdbbacaaaceceedabeccdddeeedeaaddcabedbccdddbdeaddeeddcdccadacaeecbaecbdbecacbbbdbbddadaeddddeaeededeeaaaabecaaacaccbbbcbeadeadddaacacabbbdecdacdbebecbeedceaecbeecebedbaddceaddeacdcaaebedebcdeddcdbedceaababbdeaabaaeebeebadbaeccbceabaeeebbddcaabbecdadebdacdbedbebecbabcedadecdeaecbbbaaecaccedcaedbedecbddbcadcdbeecbaecceedccaeeacceedbaeebeaaeceeecaecdcbaaeceaccbebeebceabdeccaaaacaadeabdbedadeeebbbaadbecaaddcccadbbbaeadabdcdababdcecacbbaddbeebbabaabadceaecbbaecbcaeccccddcedaeeacebcbbecdbaebeeaadaeadbddeccbcbabacadcdeccacddabaaecbecbdecbeebeecebacadddddbcbbdccebdbdbbbaeeccecdddcddbacbbebaceabcbadadbdbbadadccceaebaeeddadebbbdebeccbbeaeecdaceddbaaacedacecedbacacbeaabbdbaccebacbebcdcdaaeadadbdbcaedccdaabdcbdcbacddabdaeecdaacdcaedabadeeacaacbaaeaedaeadbaacecccbddaccadccbebaaccbeacbbcbeaccaccaeccbecddcdaadddbdddddccaebcbdbecccdcabcbbdccbbcbccaeddbaedebdddacadaababbdceedddeebaabadaadddbdcbdecddcadaccdaaeeeebdeabdbdccbbecbebbbeacbdecbdacddadbaedeceebeadbecedcbeecdadbadbdccacbebacdbcbccaadaeeaabaabdeebbacbcdadaadeccdcaabaaeaacebebabdcadbaccdabbdbeedcdaaceedcbdebcedbbaebbbaeaceadcedbbbeceadaeceaebeceededbccbeccecadddccbaececbabadddcecebeeeadebccebbbadedbeeeabbcceebbdabcecaabcbcaeedeaecbdcedbabdebcbdcecbeeabdaccdcbdbededcdaaaedaebcdabaedbcacdaeeacbdebcdbdbbaedecddeaeecaeaccceaaaeceaacaabdbcdddcbcabebbcdccbdbccaceecbcceeebbccbcdbddedaecbbcaeddebcddcebbedcdccebbeddbedebddbacbccbdeeacebababcabccbbabccccccebbbbdebedadebcebcedeaaadaacbecddadbeaabbecdeeabaddeeabbbddbabcccdeabaecacbdbdaaaeabbcadabababeecaedaeacbdabbedbacddeacaddacbddabdebbcbaceccbeaeaeebcabdcdcddeeabcbcaaccbaaabbccebaaaeeaeedbcdacdedeccaebbdbdeaeaadcaebcdadeadacebeeeaccdbedcdabeaaccbddedaeedabedeeadeeabeccceadcbaebaacdbdaaabbbeccdbcbedabaadbededbcebcdaeddeacacadacdbaaecaccbcccdeedadbbaddedebbadeeddacdcbeaacdeaeeeedaadddcbbddcddbbdeccabeccedbbdcdedbadbcaebdbedecdbecadedabcdcecdaecdadbbbedbbabcaecdebecaddeeacecdadaabdbecdcbcaeaacacbbedaeaebbedbdcebadabedbdaabdedebecbdadebcbadecdbccebbbecdcceadcdcdebabadbcccdbbeedcaeddeeecdadcddaecdeeabdcaacceadeaabbabadaeedadbdabeadbebebcbeedbcececaedceacadedceadebecccdbdebadbccaaacebadbdbddcdabddadebdebdcadaddbedebaecbddddcbddaecbdeeeabceacacdcddaeabccdcaadbaccedcbbddbbaacdbaeaeeabcdaadceabceceedbddddddaebdedcaedaeaabeeaecaeaabbdebcceabcebeadaaacabdacdbadcaaeddddeebeebbaccebbaaeaedbcccadcedadedeccabdceaadecdaaebdcacbdedaeccbdcdeacdcedbaebceddbdbaceebeeeeacbeecabeacddbcbaeeeacbebbeeabbecbbeaeadcdceaaceedbaaeeaccbdcdacbbbbabeebbdaaaacddeaedeaaeaddecdbabeebbcccdcadabbacecdbecddaaadcbbdadedacbaebaccbcbeaecaeacaaccdcbceccaddeaaadacaeedebbadeacbdbaaeeaeacaecaabdaabaddaadadbdbbdbeeebbdabbebbaaebdbcbbecacbcebaeceedadeaeebbebbcbbaecccdcbabbdbadeaecdbccdacbedeaaabbccddccdabdabceaceacecddcdbeedcacbbaedeeceeceeebeaebaddcabdcaadeadacedaaecdeadbddddaecadddedbddcceadeabdddbdcbbbcdaababeedbadcbaeaabeddaadbecbeadebabcedeedcecdaaabdeabbcbaaecbecaaaabaaacabdaebbddacdadccbdccdeaeeeeedebcdcededbadcaedeeeedbedbadcceeaeeadcecebbcdcdcbdeaeecddedacadcaacbbdabacabacbacbbecdcabbcdbbbddeaaeacbccecdacdeeddacbbadbadebcebccbcccacadddbaeccebedddecdeddbeeaaddedaaacbeebcecdedbacbceebcddcaccaeddbbadddecccedaebcaeddcecedeaddbebcddbeecdcbacddabcddebcceceebdddddcceebddbaeaaabeeebdccdbcddeecbaabdeaabeceeacedcaaacbcaebbbcabcadceadeaceebacbbdedbcedebbaaaababadabbcaddabcccaacbcacedeecedcdccabbaaedebeecedcbeebbebebbddbbdbbdbeebeebcbdcecdeeceddedcbbeaedadeedccbddabeccbdabcececbdedbaaeecbdbeabcaaabbddedbaebdeeceddddddccbbedddccdbececedebacbacabecbdaecdcabbbebdebaeebacddedcaccaeabaaccbbdaeacaddceacdcaeedecdbcdddbbddebbebebaceadecdaabdabdaccdcbddedbaebcabdbddebdecdeecabbddbeebacbcbeebacedabbcbdecdcbdecdcbbcbcbabdddbedbadeebeaadacadbdccabcdcbeceaaeeddcbdbbdadedcebeeedbeacbbaeedadceebbcceadbcbbbaadebceacdecbbccdeeebddaaeeacebcdabdeddaceeeeddbcdbbbbbedeaceadacacedcdaebaccbecaceadcdbedadaaeaccdeabcbdddbaeececdecdedceceabeccabbaeaebcbbceaacdaeeeeeabedcbdcaebedbdaddbdaecaabdcbbdcccdaecebbddeecbabcadacaadebcabadccbdbdaabbedcbcacbacebcbceabdeddcdeeaebdbcebdadbbeedbbbcbaccecdcecbeebdcabbcebdcddeaacddbacebdaaecabbeaebeeaecdaabaddadbcbbacedaeedeaedceaaceacdcbaceccabdbcadbcddddcbddcbcdcbaceadecdaeccaacdaaddddeeccddddabccbdaaeeaaecabeddbaacdaadbdaaadcaeeddbdcaeadaddddacbbcebcdedadceacdebdeadccecaedbeabdaaedbcecaceebcabeddaeacebcbdededcecadebbbbbacdbeeccabdecbdebaaabbdbdeceebaaaccabbeabebbbadaecddbadcdacdaabbcccbabedcbdaeebbabbeeededcebdcaddadcaccdbaecdedecdacdaccadddbbeeeaccebdcaccdddddaacaebbbdcecdeedabaaadecaeaaceadbaccabacddbdcdaabdceccaeacdcdbbbecaccbecdcbceecbecbbddaacddedadbaabceaedbdceceaaeeaebcedbcbadcbbddbbedabdcaacdecceadadadededdacbeceebaceaeacecadaddddedbabbeeabcbbccecdcccbbeadbbebbaddadbadaeeebccbababdbcecacdaebdcdedebcedbacaaebdbbdbbdadadceaaddcacadecbeeeccaeccecbdbdcbcbeaeaddaeaacdebcaccbaadceccdbcdeaabebbebacdcebacbeaddbacdeadcaeecacbcdacdabbcaddddbeaecdcbdcbaeaebdbccedebdabdbcceaebacdbedeaedaaabedbaccecaababdebecccbdaeabbccabebebbdaaebbbacbbacdacaaccadedeebabcbecacdcebdeddccdedbabbdddcccadadcebccdcedbbedbebcbdbcaebdebcdbcaaebdeadedbcbabdcbbecacdabbccdeaadabccaddcdeddbadaeaceecaadaedeabdccbdecdcbcdaddeaeecceeaadcaebeaacbeecedeaeeeacdaeadedebcdebedabbedcbeebddeaeadadcaadccebbcbbeaddedacddcebcdaccabddcdbbadaeacaddabbebecdcaccceedbadbececdecbdcaaadeebeceddabcaadbccebeddabbebcacdbebabacbcaacaeeeeaeabcbccecdcebbadccdeababbedaccaccbadebbacecbbadcaebbbcceaeecbdbebdaddaebaaebacbcdacceceeacecedcaadcdeccabeedbaaabbbaccddbbddaeedeeeebcdddbabdbdddaabbaaccaabededdddecedaeeeddddbabbacbbaaecbbcdababbbaacadaddaabeaebcacadbbddeabddebbbbeddbcbbaabdacdcbbdeacbbceadcaeeaeabecddabecccbaabdbbdbbebdbcbbebcacaecdebeccbcadbacdaabdaabddceeadadbddcdeceeaeeecccbcdadabcdacceeeeadbddbacbadadabdeacbecdbecabeedcdceeaccecdacdcedaadeadaadddcdbbbedcdbbabbeaadccacdeaaabedcbeeeeecdcaebcddaddbedaeddaebbccacccdebbcbacaadeabcdbcebdeebedaeebeecbaceaebcabbeadaccaacdeecddcecccbbbbbeceaebbeedbbaeeeedbcbaacdcabaaacccedadecabacabedccdcbddbbdadddbedaccccedddeedaadabababbdccadbbcaddbedebdeaaadbbbbbdedbdceaabbddebaddbecaaadbdcbcaebdcdcccbdcdbbdaeadaecdcbbecdedaceddeeeebbeacddbcdadcbebdeeaeecdabacaacbeedceaadbacecbdecbcebaabaabaccceadeedabdacaaebededececacbcabcaceecbbbacacabbbebcabcdaedacdeedeabbdecdcccecceaaaceeacadeacbceedcbababbdacdaaccececcbdeecaddbbcacaceecabcdccdcacddbdbedebbbadeeeaaddecdabaeadebbcccdacabeddceaeccddcdcdadcabbbadeabebceaacbceadbcbbccecdbcbcccbaccbbdacaebbaceceaaceecedccdcbbccaaadcaaeeedceebdaecaddeebacaeaacaceeddcacceabcceaadadebabbaddecccbeecebcacdcdedcebccabbebceaedaacedcbaacbeedbebbeedaaacdeaeddbcebeebdbccccebccebddddacacdaacaeeaeecbbeaadedacdaebacedceedabbadebceaaebdbecedbeadecbaadedebedddccccdedeebdcedadeeceeeecbacdaaeadebdedebecbdeceeeebdddaebcecadeacdcdcdddaaabecbccecdeccdebadbdaaadabceeaebedcbddbacbcddedccccbbcaeebdacaedaabbcdbceadadbaabeeeacacdbdbbadbbdaacccbcddeddaccaaadeecccecdcbdcecaeadcaaebabcddcecbaecaeeaedacedbabbccacbddaeeabceabaabeeeebcdadcbaeeaeebcbacdeabdcceceeabcacdebcadcccecaebdebacacacdebadaadacabaaaedddecbbceadeeebdcecebbbbbdaaeabcacbedbceddcdccceedecaeaeedbecaddbdcaebdcacdbabccebdeeeadaecbbeeaaccddaceddadeddbbdaccbbccdeeabddbbabeaaaeaacbcabebbeccdbdeebbeaaddbcdacadcedaeecbbaaebbdadbeeeebcabbcbdecceeacabaecaebdbeaaeeecbaadceabdbddbcbaaadecdccdaddeebbccbceebceeceeeebdcedceeabaccdebcccdacbdcabcebdeedadeadaaedcedcecadadcdccdcecadaeebadabbacebcaddaacedcabaadcbbcacedcbabdbbbacdddaceabedcbcebbabdcaeeeaaeccaccebbacacacadecdbecaedbdcbbdbdcbbbcaeabaaabcbdbddadbeabdcaaaaebbecdbcceddcebeaadbaabeebdeadedcacbcacacbadbaeeedbacbdaeaeccbebceceedcdbbdeaceacbdccceaaecababeccaeaebadebdaaccbdceadecdbdcbebaadebbebbdeceaccccbebaedeedddbdadacaeddccebeecbcccbcacdeaabbeebccaecebebcbccacbbddbcbecbbccdebacdbdbdabcbaabdcccececdeaceecaedaadaacdeeebdaeeddddadbaaaabadbbedcbbccadbaacbbabaecabcbbecbcaaaebecaabaededaaeadcdcaeadeeabaadabadbaaadcaccbabccaeccaabedacdcedcbbaabeeeadacbdcdccecbacdbadabdbeaabeaddccbbbcecbdcbcacaceecbeaebaadacddedaebceccecebcdcdabdedcacedbdecbaecebdedecdbddabcbaaebbaeadcecadeedbdcbbbcebadedbddecccddcababaddbacbeebbcececccabcbdccdabbedbedcccdededdddecaebceadddaebcbeceebbeaaccccaeebedaaaabeadabebceaedbbebdecbebdbbebeeeeecbdcdccdeccdaedcceeabccecbcededaaaaadedecbcdcbdcdbbeaedcccdbbcaebbbdebcdeddadaecdaeebbadaedeacabbecabdbceeecdecdadccecaddbebdbaabbdbbcbeaebcdcdeadbabbbadeadeabdbabbedeabcdadddbcaaecaeaebbbabdcbebbceecbadebeeaaaadabaccadebceccaeeacadeeecbacbeddbacadeadbeaeabedcbcedbbdcdeeddbbcbaceebccdcdddaccbddabdadbeecadbcedcdbecddabdccccbedbddbeedcdecdecbcebabccadabdabddaaebeaddacdbaaebdadbdcececeddaccaddeddceebedabaddcbaaddaeaacbcaecdbebeacadddbebdebacddaceeecddaaacabcdbceebecaabdddcdceaadabacddedadbceabbabaddccaeadceebbbcdbcacbeceacecacecbacaeabbbebbeaabaeabeaabecbadaeebbebcddbbbaddeceeccbdcbadaeddceedcdbeeddeaaeacccaaccacbbbeceadbaddabeaaddebbdbaaddceeabdcaedeaaeeeaebaecddbdadceecceaccbebaccbcedbdbecacdccbdaaababdbccbdeebaecccedcdaebeaeeadeedabcebeeeecaeaecbeacbdcabbccedabacbcecababbbbccaddacdaeacebbaeadcacbaaeabcabedcccbeebaddeececbaacadeaeebceecbaedddbcccebcaeecbddccbbdebceceebbeaedcecbacaaebdaaacbcebaadebadeebeaaaabddbecadbbbdcdeadbbdccbbbbbeeadadedebaeebadaebaeaadaddeddeabcbdddddadedcbdedaaebadeabaceedabddcbdeabecbdeaaedeceaadbacdabaabccdedcccabceedddaeaaabdbddeadacebbccdbbdaabceccbaeaaccecadadbecdcccecbcabcdbaccaabeacbacabbdcaeccdeaddbedbeeeebacaaceccabeeacbdaaaeaeccaababaeacaeabbbbdbaaaeaebedbbcacbbcaebdbdddceabecaedcebabbabaeaeeeacaeaceccdedadbbecdeeecdddebdebcbcdbdbcaeaddeaceeeacababceabdecedbadebcdcecbbddebeccaeaaeceeccddecdcbcdebdcdbebedabeacdeecaaeaadbbbcbebccceaaddcecadbeccbbcdbdbdbbddacbbdeeecaabbbbebeedebbaeebbddeeeeddaddecdbcaccdebcceeceeccddddbcddacdbbcebbbcddbeadadcbcdacbecaedaeedaccdbebbebbaaebceedaabcaeabeebbdddcbdbaaedddaacdccbbbcccdcdcaaccccadcbbbcaedadeedecededbeaebaedeabdcbcceecaaebdeeaebacdbeacdeccbbecdcebacbceeaccccadcdaaabbbaadeebbcacadcdccdedcbaadebbcaccdaaaeabaebbcbacabbccaeabcadcacadbebaaaeebabdeeeaaecdddaacecadeeacdaedebbdadceecacddebdedcaccedbeabecdccbcbbeadabeceabcbaaddecbaedaeddebadeeedddabaedddeababdbcadebdbcecbbabebdbbcadbdededcdaadbeeecbaacddaaedcadbaaacecadbcdebebbaceceacedbbbdebedaeddbebedddcebdaaabbddecaccbedcbcebceaaabacabeccbbcaecababeccadaabbaeaacbbaddcdbadcbbddbdadbbaddbbaaeeeeadbeededddacebacdbdeaeadeccbdcadbeebccbbadbccdaaeadededadbcacaddbaecddcbccccedbbceacddcbccaadbaeedaacadecddeedbcacdcebdbcbdccbdbedeeaadebbcebbedddbceecaceabbaabbadddbdeddbaacacedbdecbdedccbeacedcacebdeabaedcbadedeadeacabdaddecacdccaeecdebadecdbeddcccebbcadbacdbcbeecdbaebeadcebdabccdddbabeaeadaedccbacecddccbaaaaddeeecbdeedcaeddaacedcdcaceceacaeedbeadbdccdaeeabddbcaebbdeccdaedeccccaddebcbaddddbcbacbeacbdcaecaecaecddbaeececbaeedbedcbcbabbcdeeededcaaabebcecaeceacdbeebcbdeababcdcadcbdcacccdbeccddaeecbceacaaeecdebbeeebecececdbcacccbdcececbbeeaeecadbaacebbcbbcbdebaaeeebdeaaaebcbddceebcadcdcbedbadbeabcdeaecbbbaecbbbaadbdddccdcedadaceccceeacaccedbdcbbbbceceedebeaadccacdcdddaabdecbcabcbedddcaadcdddeebedeebcdcebbbbbeecbacdccaeabeaaacabbceabadeeedabedcedadaadabaddbdebdceddccbcbbaeabbeaaaecccbacbabccddbddbcedcdebdecdbeddecbbabeddcdbddebceacbecbbebacecacaaaeacdacabeceabedcddbeaaeadadcbccdabcbceecbbddeaeaaccebcdcdcddecaeabaebeecedeececedddbcaceabceccaebeadbdbdedcbeedbacbedadcdedcdacbabcdabedaadaabeadbeaddbaddcdaaacddbeebadedccbbdccbddacbadaabbccebbadecbcabebbeddaddcedeeadbaaeccabcbeaeaceddedbbdecdbaebaeacdcadaceedebdacdadecbdaabdecebbddddcadadddeebcbaecbdaccacdacdcdabdacebaadaaedeebdbeaaaceaabddeaeedaddcaedddeeeccbdebdadaacdbaaeddcbcaededbddedeecbdeedcedeaeedbbbaeecadaddedeacedbeadedccbecdddbeecdbbbbdbbccbbbaecaddcaceeacbdbbbcbdeebcaeabcdcabaeaedecdcdbadbebbbaeabeabaeaeeecabceabedddabcdbbebeddeadcdacbdeedbbccaedeeaceebddebcdecadbddcebcbcbabbbbdbedccdaeaeacccebacbdacedcbaddedabebccebaceaaaadedeadcceedacdbacccbecbbbdcdeabccceddaaccaeebbdddcbdbcadaaeabbbaaebcadaadbdcddededeacccaeaeadabaebeaebbbdcecbdbddcceeddececddeabbdeabbadbabadebceebcacadbcacebbdcbcbaccdbadcbedbbabeceaeebabcadedabedaadddbeabadecdeccaacababaceaaedacecbbdbdebaeeeebacddcdbeebcbeaebbceaeadbebecaebbbabecbeaadaeaedabddbddabdbccebeeadababbdccdddcedbeadbebcebedabccbcceebaeadbeaeacedeabddaadeebbeeeeacaadbcccedbbbabdbeeebaedaeabcedaeacedabcdbcaadcccebbbcbcbdcbdcacbdeabcbcddbccbabebadeacdababddbbebeebcbbcedbedcdbdacceabdcbddadbbacbbaaedbcbbdcedacebddecacdeaccccbaeebbaadcedbdebccdcededabadedaddacbeacddadcacddcacebcdcaaebccaaaddbbdbaccbdceaeaabadabaacbdbbbbbbeeceedbdbacccedccdcbbbeacecaaaccbaeecaaedaaaeedbadbccbcbceadabdccedbddbdbcccbaadbabaabebdaabcedabecbbddcdbbeaaeebceaecdddcbdbeeebcdadeedaebcdabeadaaeababcaacddcbeaabbcabdcaeabdeeddaebebcdddacaccaababbaadaceebdeceadccdadeedccaabcbbccddacdbcaeadaabcbbbdebdccdceeabceddbcddbaabceedadccceaeccccdecbadaadcbabeacecededeaeeedcbdcdadccbacedcacedcabdcaebadaeedeadccadbaeeadccedabebcebeaacadecadcaabeeabecabcbcdcbaedbccddbbdbbeeaccbecddbbdaecbddaabebabdeaaebbeacdeeebccbabcdaebdedcbcdabcdeacddbcbabddbdedcabedebccdbccaeababedccecbcabbadcddeadabeddeedeeadcddeaaeabedadadddbbccdedcbaeeddaadeedceadbbcbceaedebaddcaddaebaeeeaaaccecbbeadeeedbddaabdecbcaaccabbcdbcbeebcddeeacdaeaabbeaeebaeacedcebbddebeedabedcbbadcedcbcedcbbcbeeeeeedccacbdbceaeadcbdcabdecdcaedecdacadccadaaceccdeaaadedcaabaeccacdabcdaeaaeaaacacaadcdeeabebcacbbaadbdeeddeddcacecdccbaaedeabaedaeeebbeaedacadcbcbdbdacdacadaaaaaaebbaddbbadeaeabecdddeceaebcdadaadcacddeccebeaedabebebceeddeeebccdbddcaaaebebbcdadcaaadaeecacdecedeceaaacababdbebdeeebcdbadbaadcccddceeccbeccddeacbabedaaacacdcbaababbbdbabaeeaaddbdceaedaeeecaecbddccbbaeccdccbbdecaaddcaaecbbdbbeebcacecbabaeacdaedebacddbebaadaeecdebbbdbdaceaeadadaaedcadadbddacebbdcaccdeabdadcbeeeccaebcabeaedcddaacdebddebadedeedaebebaaebbcccbcebabadabedcdddddabbccaecadecbcedabacdeeadcbeeaedaeaabdaaeaacececceeddadedceaaecdeaccaebcdecbbdeaeeeecbccdeaebbaddaacdeebcddaeebebedbcdedeadceebaeddbdadddbdcceabadbbdaecbbcbceecbadbdecbbadcdacdbedcabbeacacbbaebedaadbddcccebceeedabbbdeceecbebaddbbaacbbeccddbabdabebaedecebccdeedcbaaabdebcdadcbbceabbebbeccbcbcdaabbbdaaaadeedbecdacadcbaeaceadebbbabaededdcedddeaeccceabdacbaedacadedaaceeaeeabddbeeadcaaabcddedabcdbbbbbcbebaaebbedabceedadaabbceaeedbcacedeceeeddbbeebadbdecdabdcbeabebeabeeddacebbacdaadddebbacbeeeacceedeeadebcadaabcbbaeececaebbeeaeeabccabeadbaabbeebaddddececabadabadeeeabbcacaedbeeceeeaabaaedbecbbbdaacbbbaeaccaaeacbedaaededddccdbdaadaabcabaccdedbbccbdaacdecbbdbababbadcccadedabacecdbededcadcabdddebbacbbbedbbbebcacdaeaacedbaaedacdadbbbbaaaeddadeabecdbecacaaaacbededdaedbccbbaaddbacccceaeebacacdceaebceccceaadbaadabebccaeaecabceddabeccebecacbbedaccebccacaecdedbdceeddabdcaceaaddaabaaababeacabcccdbddecbcaeceaaaaecdedeeabeeecdeedbbeabacbceeeabcccecaeabbeadcecedebbccebeddcbaceaccacdbbadabdccacbeddecaddacbacdaebdabaeeaaaabcabeeadbcddbbdbeedbcabdaabcacbadeacaedcdabaeaceabaecdbbbecaaaaabddebcbeddecabacadbdbbbaeddacadbecdcebeeaeddecaaabbbebdaadeebcdaaaaceedabadcabbacebedcdaaedddeeeccecbcaceebaebdaaeaaeedddbdadbedaeedbedabaceeedbdaecbaadbcbeeeebbbabaadebdeccacaaecabedecdbdbdeaeaeaceeeeeccacdcdbcdcceceedcaadebacebdbaaaecaacbcadceaabcaadddecabceebbbcabbebccdebcdecbddadbddcbcdaebcbadcdebbaedacadeaedabbcdbbaebbeababedeedcddbecdacdcdebddcebcbdaeedbebddccaadbeaeecbbaecdacacabbcccdaecdcbcbcdadcdeabacbaaabcceaabbaacbbbddbabcdddebaaabecaddbcdaaadeeaeadcbdacacdebcbeabbbbeadcdaedceceacedebeababdaceddaebbbaaebadccdeddaedbbcbccebcdedbcddebbdebaabceeaaaacabcbbaedbeddacabddadacecbeaaadaeaeabebcbeabcdbaeeaaabdbbcbeecdddbcaeacecaddeaabacbdadcbcabcbaaebdecedcbdbdcdabaeaaebdceabcbabbacebcbeadccebeaeebdcbeedacdbcebcedacebcaecaadaadedddbbeacbddbddbbbcbbcbacbecbbbeeaecadabdcdbeeedbeeeeaeeadacbdbccaaacbcbcdadbcbeeabbeeacdeaeccabdeababddeaecacedbedddceebeededacbecdcacdcceccdadbedebccdcbaabdbdbebaacdeaaabcdeeadddacaeebaebaccbeaecadcaabdeccccccabaeabbbbddaeeabcdbaebeddacdaebbabddabceaaacdcacceecbbedddbbaaabcbecebdbecbdabcbdcebbdeecaaabcceedcecdcceaabcdadddebddadcbdebdddabccbbabeaadebabaeceaaabaacecbddeedeabcdbedcbecaecaabcaeecdabceaaadedaecbddaedccbbbcdbcedeecaeacddddcceeccabbeabcaccbedbddceadacbcdeabecbebdceabbadbcdebdebddecbaaceebdbeddadaabbdaadbeeccceaddabcddcdbaecadaaabcddbeceedabbdaacabdaddbbccddcaadbecccbbbaabbaedbebcbcecdcdbeceedaceeaeccdabccabdeccdbcccbcadaedeeebdadebbacceadddbbaeaadbbcacdcabbcdbdecadacacacbbabedacbbbabdabcccabeeacbacecdacadacbbdabeccabbabdabaadecacbceaaebedebbcbbcaeedcbcddaecccedeaeeeededcaccbabceddccdaebbaecdeaaccacddedbcbedbacbdebbdcbaacabecdaaccbbcbceceddbeadaddedbbaaebdeddeeaaedcbddebadedeebdeabcbeadddaaeebdaaddcbcbdbeccdabdebbcabaaddbddbededccdbaaccbbaecadbaacbeebadbebaccbaecdebdbbbabaeebcceecbdbceebcdebabcceaddaedbcccbccadeadeaeeedbcacebedbacacadedaaccebabcaddddeacddaeaacddccbcbcacedbbccbacdedbdcddcdbaacbadddaccceccbeccacaeaddbbdceaeaddeccbabaaaadebdbaaaedacaeacccdbbdabeadbeaedbeaedeeecdddcdeebabbeedcebecbcedbaadaddbeaececdecdeaeaddcedcdadabceaecbbcecddeccebdebcaebcdcdbdaebcccbeccbbaaedbcabdeeaacdedbcebdedadaaedeccbccbadceeebccbaeecaaedecadeacdceabdddeaebacaeecdcdcdeadadadacbcbcbeaabedbddbbadcbcebbaeddbeadddcebacbdeddeacbccebaedcbdcccddadaceeabacedadcbcbcbcaeebceebddaeaddaecacedcaaddaeadddeeadeccdaaaddcaecdedddedcaaeaccabcdbbbadeddeccaaaecbaaddeaabecbbceaababdcadbaabccdebdaddbacedcacebdaabacbbecceccbecaaadbeeaaededaabaddbaeccceedbcebaeebbaacacaacaeeadadeebceadddaaecaeddedbedbcbbdbcebcaecbbddecacbbbcadcbbdabeaaacddaadeedeadeceacbebcebcaeeeebdaebccbdacabacccacbcdcdcebdeebeabaaebedcdaaccaaadbadcececccaebcabbcaddadcdeeecbceeaeaadeeacebdeddaaaebedeaebdceedcacacedccbebeaaaddbbecbaebaedadcabcbbbaddcddabacabcecdcdbdeededabccdcabdcceacbcbcbebddbdcddebcceaebaaceccbcdadaaeaaabeaeaacbeacddedddecdceceebbcbdaadebceceeacddbecbedddedeeeddbbabebbaebbbdbddeebbbdbaccbbbcebbbbadbebcdcbddabeecceaeccbeadbbdccbaebdddbcecacddbaaebbeedbbdddeddbeabeeaecbdceaeaeabccbabceedbaebacedaceeedaaadeacabcaeaeddedabeebabcdcdeabedbedddceecadaaeddccaaededccebdebecbddeceebceddddbecaccceadaaeeeabbbbcebcadbacabedecdcddaecbedbebccddbddedeccbdcceecaecaaaabdbebbabddeebaeccacadebbedddabacaaaaddbbeccbabbbaebdceebadbeaeecccadbbeabdaeadbeebaecbcdbdddbaacccbcabcebbadcdeccadebeccaebadddecaebdbbaeecaabbeadbbaeaaeddbcdceaeaabaadeadedeecdaabbccbeeccdcabeecaccbbcbcbedbdcaedccbdbdddecbbdaaeeccbcddbdeacbdedcbecdaccacaaceebdadeddadaadeccebbeedabdaaedccebbeabaddcdeecaddedbaaccbdeacbedbceabdeddcceacbeedcacbccdbeedeebddcdcccebdbdaacebedaedddeecaeadcbaeadbaadaabbecaaceddbabcebdcdddbcbdcaddaabacebcaaaeedccdddcaeeaaaaeacebcbbdecdddaebbaeedeecdaaebbeaaedeabcadaedddbbadcaeaeeaaeeddecdebbcdbbceecceceaeaeadebaebbabbbcbeccbcedcecaaabcecbaacabceaabecbddcaeeecdbbeabdecbedddeaadedcdddaabbbcaaadebddebbaccdababeaebbdddbddadeaebacacdaacccbcceeecbcadabaeaadadaabcdacbbadcbcadceeecbdadbdcdabcadebeadeaedbaaacabdddcedebbdeeaeccdebcaeceecdcbedeadcaaccadcaabaceceededecdbbddccbcbdeabdebaedebdebccadadeccdecbcbcaaabbdcaaaabecceeedeccededbddedabdcacadeaeeecddcbddbdabdcaebdbcbdbaeacaccabbabebbcdbcacaedcdaccacadeadeaceadebbcadeacbccccacedecacdcecaeeaabcadbecbbcbecddcbcbaecdeaeaaddeabaddeabdbdbbdebcebcdcceccbddddbcbddbcaccbddcdbbbeeeddebddebdbdebdaeadccdabdddeecccbbcebcbecccedaceedbdebaddebcbcedbbdacbcecdadacbcbadaaebebdaceeaaeabbdadabaadaecdbccbbcabecaaddeeabbecadeccbbadededcbdccacbadaceeddccebbdedeaeebdcedccdbbbecaaadbeecebeedcdddacbaaabdebbebcccdebabeedbecdeabaacbedcabaabebbebdcceededdaaddcaaacacecccaccdbdedebaebdcacdbedabcdaaceccbcbbdbebadeccdaeaaeacadaebdebddbcbcecacbaceaacaaedbadedddbadbcbecccaaecddbacdccbabadaaebcbeacdcdbcccdadacaeadddacdcddcdecedaaeceddbcadadbaaecebdbcceacbeceaecdebdeceaddedbeacbadceaccaabedcdeeeddeadabcbceddabdabcbcddddccccbdcccddeeeeaabbcdebecadbbeaaaeecdcacedcbbbebebbcccbcebcbdecbcdeaccebbabbdbbaeaaccdbdebbbacdcecccaccddeaecdbaaeaddecddcdbddbcdabcaaadacacebaabacedeecbddaabbeedbacaaceccbbeabeccbedbdbccccecaddaabedbeaeaaadeabbcaccddadadcecedacadcbeaabbdccacaeadbbcbebcbaabbbeddcaaacdeabbbbbeaaeddcbcdddbbbcaccebcaaabacbacaaedcceaccadbbddaeceeaeebdcbaceadeedadccacceecbbcccccdacaeaccdbbbacdbbacdbeedadbeebabdbccdeebceebbacdbbebebebbdbbadccedbbdadccbdaeaddbaadcdaecadbeadedaeacdcdaccccbeedceacecdbecbeccadbeeadedccdbacdbebdbbcbadbabbddbccdbbeaabcaeecebddceeedbddeacbdbabdbbeeddcdacebbcddabbbcdecedebcbeceebceacadcddeeebcebecaccbdbbecebaeecbabcaadaddedbdcdccceeedbdaedcceecbccaceccdacdccdbcbddcbcbdbbadcecaeeabdeeceaeeaeedecedebcbbcbccbccadcdaceedcdcbdeaeaadbcdbcceabdadedbbdabccebadeaadddddabcadcbbedcaebbaeedbeeddcecdeeadababcbddaadbadedecdcaabceaaacaedebcadccceadbacdeabbecaeaecddcceacabaddabaecebdaabeccadabbbaabebbdaaacadeaeebbdaeeadcacdaedececbddaaedbbbcaeabbdeadeabecdaeddbceabeeadbbbbacdabdbdadaaddaaaeeaacbaddddbaededbebddbbbecaadcedbccbeeedecaeceadadabedcdeeadddcaabcedeccceaebabdcbcedabeebabadececdedeeaebdaeacbcbebeddacdadacbccebdaababadbccbbbdabcbccaaeddbebdecaadabdbcabcedecbcdcaebaabacadddcdccbdcbbeeccaaaaeebdacdccaadebcbebbebbdeacddeeeeabebadcadceabaacaeccacbdaaaaccbbeccadeeadacaebebddddccddddeeaacedebaebcaaeebedebacaedcadeccbeecbeabedebbdaaccadbeeeddccedcabebaadbbbadecabbebacbdbbcedbecbacaddaebdcdbcdcbaabcedacdabbbcccbbddcbbbbeadaaccedccabbeeaedaeaadebccbecbeabdbccbbbcadbdbaecdabdabdeedbeadedcdbdddaedacbedbdecdcddeabaeecdeabdecceedabecbddbedeecbaacdeadeeebcceececcabbaebaacccedaaddecdbcaaedcaaabdaeccaaebadcedaabcdadacbeabeeecadddddecbecbcdbeeabcadaedbbddebdbedbdddeadbaddcdbbcbcddbacbcdcadacdeddddaacbadbddaaeaaadbadecddebaacaeddabacececaeaadcbeecaacdbedcdcedebbdeaeceaeccabacccdaaecccadbdaaceedceedaddabbabbabdebbaaeaabddeeaeedbdeadcccddadcaeaacedeeeeaadcdadbaddbdacaaabeaaabdbeaceeddcedededadbccebdebdedbdbdbbadbdadbccaceaeddbeabeeebdebbdeeecdcdedcaeeebeccdbadcaecdccbddadaeebdcbabbacdadaeabadabcabbbdadcdeeaeeeccecbebccecebbaccbbebddeccbbbcdeebabcaadedabeecdcaebbeebdeaaeeebedcdbddcbbeedccacaedbdbdaccccbcdbcbecddebcadcabdcaeaabbccecaaadcadadabceeadebcabaccdabbeebdbcbdecedaacddbccaeccebcccdddbbaeeabadecbacceaeaabddceadedebabdeeeeeeebdeacaaebecedeccddaabbecdbadacbdeeccbdcedeebecddbbdeddabbcedeeeadcaaaedabcabbcdabbeacadceeebbdacbeabebdbecacbdacbebbbebbcbdecdeaacceebaadcbceaababbbaeddeadadadcddcbecabdaabdcbecbdeeeebaeabbeaeabbdcccdbacdcceaeaadbdecccbcbedbabdbaddeccbdcdbbdccaeaeaecacdcaabeebbbeddccceedeeeeebcdaabedeabdbadeabdacaccbeecbecaccdeadbcdeacbcbbcaeeaaabeddecbbceacbdebdbadaeadbdcdccbbaedebccececcebaccbbacacedadbcedbebccbdbebadbaeaccebacdccbebedcbeadecaabbdeabbeaabaabdabdabdaabccdaceaeceabeaaaeedeebdbbbebedaedbcdeaebcaadbbadacdbdbbceabcabcaddbacbbdbbecdadeaddecebdbadebabeedbcecdcccbcdbaaccedbaecadeaedacedcabdadcccaddcebaadedebaedcdabcdddaeecceebbecaaebebddeacbaaddcdbcbbaabbbdaddbacadaddbcdbbcbabdaceeabceddbcedbedbadceceaaddcebddaeaaabdcdddeceddebbbadaeecaadbdebeadcbdcebdccecbeaddcbeddbacdedcababdeabccbedaeeacdcecabaadaaceeeddbadadbdaaccccddbaabdacadaebdacddeeedbbecbdbdbbbeeedececdbdccedbabbcedacdddbdcecdaeebcbceeedbbbadabaaaaccccdecaccbecbeaccddcdcdcdaaeaacbcdcdbecedcadbebabdbbecaaeacbceccdecedeaadacdebceabeadaadbeaecebbacebcaebabbabbbbdbaaaebedadeddebbbdaadecbdaebeaabbacbbeedcbebdddbdcadcaddebaecdceebaccbdecabebeeeaebacdadbaebdddcbcaebabdaacebbcebacbeaadcdceebabeeaadabdcadaeebabebedcacbbaadcabdbdbaabbdabcedadbccbdaeadbbebbaeaaebdadaacceadbbacecdddcbacbcabebbdeddeaadabeedacebcdddecaaabcdcbcdbbcacedbbaeeddbecbbbcbabcbaacededeebeebbdacebdbdccddceabbbddeadecdcbceebddeabbdecbacaddebdbddabbcdcedcabeecdcedadeabadcbdcedecdeecaeeaaeeedddcbdaaeecbacdddbaddebaabdcbbdabcbadbddbaaeaaebcccabdcdbcdbeececdbcdcccaebcecaeceeecceceaeaeadcabdaddeeeabcdbbadcecddaaaeebeebbbdcdbbabccddaacbdbdcdbaacacceaaaaaccbebeaaebaeeebcbbecebbaaeabddcbeedcaeaaecbcedbcabdeddaabccecbcedbcacbececbbabdebbacdcdcbecdbbdeadededdedaecccbddadadcbebdaeaaddeacbdbbcbcceeedcebebcacaadccebbebecaebdbdaabdbedbeeccbabdeccccdaeeaeceaacccbaadbdeabccedecbaecdcbdceecccbabccdedebaeccdabcabdaaceedbbdadcdbaccabacceccbaccecacebbebcddbabbcdaaaddaabdbecabdbdcdcbbaebedababaddaeceecdbcdbcbdaccbdcdccabccaaaabcbababccccccbbcaedaccedaadcbdaaeabdaecaacebebcaecdaceabadbddedadabbeabbbebacbceddaaabbdeecdebadccbddcaacedceedcdcbdbdbeceaebdadecbadcebbcdeeeccbccdbccccdccddbcdebbbdacabdbcdcaecbacbcbedeeacaeaecdeebabbaddaecdccbbeeeceaddcbbecccceddedccaaabddeadadcbddaceddeeadbabdaddddbdcbebbabbdabeccbeeacaeacbdecaccdbebcaacbdaadaaacbdcbebaaeeeaaadecabaddeaeebdcbbeabcaddaecedebecbcecaabdabdebdebcdeceedacbbadedeacbdebcbeabecabbedcdeeabbabbbaceddbdedddeeadbaacdeaeaddabddaeabbdbdababbbededcbaacbbccebbedccbadddcbaebaaedbeebaaebdaaedacaeaaecbbadabccbceebbdeebaeacdbdcdcaebaddedcecbeaebdaabbcadebdddbdecbaececdeacdcddcbbaacdecaecddbeacabcaaaccbbebabdcddebadadcceaabceeeebeecbdaddbeeeaebaecccbbcedeeeeeacbdbcdeaddabeabbbadeccddbceeabdacadbeaaebebebeecbadecaedecbcdcdcaccdcadcbbddaededcecdbbbbccaaebbadadeadcbcbaeecdbdeccadbcdcabacbadbbcbacebdceedddddcdbdecbdbdaadbdaeeaccdaeaaedacebbcebcadbabbbddebcaacdabcadadbabbedacedccaacaababaddebbeebeeebeacddebededcdbcaebeaadaadeeacaedddacbaaaacceacadebacadeedaebbdbacebebcaaaecdebdabecbadcddddbaeeaaaeeedcbebdbbdbbccdabedaaccbcaadddadbeddaddbbbbebaeedeeabeadaedbdeecdebadadcccababbdeadaccbcacddceebededaaccaabccebedaaddbadeddbbeeabdedcdcbbdaeabedcdaadaaccecedceaadceacccdcedebdecbdabdbddaaeacadadbddadbdcdabacbccabbbaadcebeebabcbdeeedaaeebdebdaeacaacccdbbddadeabaedcaecbbedeebabbbbaddceecbdedbbaceeababdbeaababdaabbeebdbaaaadccacaddccebccbbacceeeccdbbbbcbdbdecbeccabceeabbaeeccedeecaddbbbbeaddaabbddaceeabacacebeabbcbcbcbbbebebcddecacadaaabedaaaacabcabecadbbdaebeedeccaabbabbdadcbeecdbbbadebecbdcedaccabaaccdabaeaecaedeaacbdbcedbbaceabcabddacadbdeddaccccaadeeedcdbcabdacecbdcbbebccebdbddbeedbcbccddaebecebbacdcddacaecbbededadbcacdbdeddceeeedaaddeedbabaecbccbbeddeeabaceebeedbdabeeaabceaddedecaaaeeecadedddcebaccadacdbdcbaaadacdeebceecbcaeacbbbcabcadeeadbdaddbcdecccdababedcaabbddbbbbebaeadeeedaacdedcbeedbedbbbcaddedcbdccbcbabddcddedeebaebdaeaddceedeabdddccaaccdabbceeceaddddbcaecadeaabdaabbcbbbdebecdaaceabeaaedcbbbdceaddcabcaeeadbdecdacbadeeacddbbbeebbcdbebebbaddccbcdcddcaaebddadddbebdcedbbaeadccabaecbcdbddbddcebbdaabdeccedeaadebabdecedadadebdcaaaeabebddbccdceedaecdaeeaedaeeceaacadcbacdbdaebcbbdddcbbcedcedecdcacdaabaedcaddbbebacbddcabcedddcbcebacddcdeaecccecbebaddebaddaccadbacceacabddcbdbceaddcebbcdedeebdeecccbeaaeadebeddcbaeeaaaebcdeaeddcabceceaeeadebcdeccddbcdbdcacbacecbcbbccddccbcdeedddceaeeddcdcadbedbeeebaedcbadcaccaabeaedeecebcbdbecebddeeeaeddcaecebceeedcdaddbccbceadaaaadedaecabebbecbdcbadeaddaebcaaebecaaaccddddbbbabdecaeacccaebbdaeebccdcbdaabedccdeebdbbeabacbdbaeeaaaadcacaaeedcdebaaeedbeaabbcdddabbabebdaeebeccbdddacacaecdcbbebcdcaaeacbccbeaacbdabcecbbabcdbbbaaabbccdabadccbdcbcbeadecbbcdebadedaaeeccebbeaaeaceddabbacddebbeedbadebecaedeabeeecdbcdcbccbddbbcdbbceadabaedeebeecdadaadabdeaacacdbcbaaecbcbdebeebbebbaebacdaaecedbbdbadabdebedabedaabcdedabcbbaeaceacacdcaadcccccdbedaadabcdedbdbacccbabdbeecbbbcddccdabcbdcadbbabbebaacbacaededdebdeadebebabeabaecceebcceabdadcdddaaceceaecdddebbabbaddecadcaddddcbbcecbecddaeccecacbbdbdeedebaddcaeecabcdeaccceeaecacdebbceeaadebcccdaacbdaaabbebddacadeccedebcedebbabceaeecabadbbabbebbbabbdebaeaacccaedaeacbdbaeadbcaddedaaedaadaeeaebeddddcabbbebcdaecdbeaecacaeeededdcabcbecbaddcacbdddcdabbaeeabaadaddacdeaacdcbcdadacbeacbdabcdcdbcdcadbddeaddacbeadacdabdebeebcabbeabecaebadaaaecbbcaabdadbaeaabdacebabaebddecdddcbcbeaecbaebdcacddeaceaddeeabacaaebbbebacccccebbceaccadbacadebcabaecdababdbdcadaebbadcaeebdcbcabceaaebccdddabbebceabbcecacbecddabbbbbcabbddedccacabdcccedecddababdeadcadedeedadccdcbcbaaaddabdbdabedacddcbcacbaeaaeccbcebacdbccdecaedeecaeaeaeaebaabaeabdecccaeeddbdcedaeddedacbbaeddbeadbdbeeaecaaeddbeecbdbbebadbeebaddbcabacdadcadccbaabdbccecddbabaadacecacecbbcbccebdebadabddcaaeecaeeaedadecaeecebaaaabcdacbadabcdcccbdceddcadeeabeaecdaeedbaedbeabbbadddbcbacadbedeedacbeedadeddebacaecdcbdbedbecebaaeceeacaadacaababaacacecedeedbbeabadbcdcaabcdcbcceccaacdcecdcacaecdbaeeedeabbabeccbcededdbebedbaeaeadacdbedeebdbdbcdaeeecbbbbdaabacdeadeacbaeaccdcceaddbcedbadcbeebaaaebdceeabacabbdbaddcdadcadceebcedaaceeeeceaceddcdbedeaceabbbbeeaadbbabbacbecedaabccdbecdbccedbabdadccaabcbabaeaccdabdeaaebecbbbabaadcdaebcceebbbedcbbeebaeccbbdcaabedcdbbacaebcacbadbbbbcdcacbceeedcbedddedcaacaaeadeaaaaebabeacecccdcaaaaeebdebaaaaeabacbcddcbaaddcbdbdebdbdbebdbaacabadaeeabeabadacbeedeaeecadbcbeddbaddbaaaabdbbadceceabbcaceaebaeeceedaebeebbeeedbebacbcebddabeaedbaaebcaaeadceacdccebcdaecddeecabeabeabaebdbacceeebedcbedccbcebecbcdcddebbcdabcccbbebeeaedbbcbbabddccdedaaaabedbccbcbbeddeaddaeddaddccebcaebbdaaecacbbeaaeecddacecbbdbbbcbcaebbedcbecdabdbddacceababaabbcbdbdeadecbadacbebbcbdadcbdbebdbbccecedeeedcabdbabeecbebbaccedcdbdaecccbcecdcadadadbbccebeeededceaccddbcbcbeaebeecdebaccdcebbacbddccceacaacacddadebdaacaceedccbbeaeddbddcebebeaaacbecdcdbdbaeeeeaabcecaeebcaadadaecbbaabaebeacacdaebdddbcbcdaacedcabcdecbbedadddeeddbebcdeecacbedbeccebcdceccbeadeeeaaccdecbedccbdeccadbddbadbdadbcaeacaacdbebccdedbdecadabaeabdbbeedaeceeabcccbdbbdacaddcaadcebcaeedcdbdeccaaddabdeadcdeaadecadcdadcadeebdeaabddbbcabbbdadcccdbdcbccabddcdddbbeeeedcbadcadebbeecaecddedbcebcebceebdbcdedeaddbbddaaedeeecadeaeebabdebedddbdabceeacdaceabcbbaedeecebabbabdcdbccceaabeacdaaccdbcbdbcababdcadcabeababeabccdeadcaceadacaacaecbbceaecbdbeedecdebddadbbbaaecaaaacabcccedaaddbbcbdadccbcceeeaecdcabbcbadeacadbacbdedccaaecbaadcaaacedaceadabbbadbeabcabbeaaadaaaedbcbdedddbdbedacaaeceedbbeebeaaeeaceecbeaaeecdcbecceddcbbebccddaddcceedbaaeebedaedeabadeebcedddbbebaecacaaceedbebeebbdcabbddeebebcdbadeeebeaedceccaedceeecdbdebbaccdcbbeeaabbeabbbbdedaabccdcedbccddedbdaaaeebbcbdeccabbbcecdaceeaaabedbeaddbdcdeeddeabddeccbcaaacdbceecbcdeceeccaadeddcbbdbdecadcaaeaaccacbeebdeadbcbacdebceeadaddebeadeaccccdebdabedcbdedadbedcbdbdbebccdaddbbaccadacceadaaadacadeeccccccabaaaacabddbebdcbadbaaeddeecdabbdcebabcabebacecdacdebceabcaaacdcbdaecbbeedabbdaaadccbabbbacdedabaddcdddbebebceeeceaabddcecaceacccdcebbcbadeabacbcbbacebdabdbccdbdaebadbdcdaabbdededddeeaaddbaebcdceeaccdbdbbbecdaaabeadaeabcdeaaecdadcaddeacceceeeddedbeeacaacddcceddecddbdeaacdaeacbddbbbebacedebeaaeedaaaebaacaecaedaeaaaccadccbebeaebddcbdbedebdeecbbeeaacebdddbcedbeebcbdcbcaabdddacbdaebbadcbedcebaeeebbdebdceeabaacdadacebedbdbccbaeedcdbdaaadbaabbcddcacdcccbbdaeccbddddcadaceebedaadcddcbbadedebcdbcbcdcbbabcccabccbcdaacbebebcecccabecaeeaecdaddcddaeecdebedacecccebdebaabcadeddaacdabbeeddbaabcecccacdbdcecadbbabbaabeacbbacaadeddbddacbdadaebadbbdadeebbecdccdacaeceadcddcdadedbbeacebbeecacdecddddbdbcecbcacedcddcdceccbeeebdaadabaebcaeaeddcbeeebccaaecbbeccbcdcbdbddabaeedcebceabeeccdcdedaddecdccebeaebaaeceddaedbebcedadddecddbaacebaedbcccbbcaadecabadbabdedadcadddcedcbaacaeacdcbeccbeaddabccacadcbeeeacdececaebeccddbadebccbaaecdaeaaccaacebbecaceadeaccdbaeaaeeabceedadbeaaedebbdbdbecbecdcbbcbcbceeabbcdeeadecbeddeacdebacdbbecbcaaeaeaeaeaebabdbeaadbdebbdcdddbbcceabadedcededbbbadcceabedcababdddbaccebaaacbaecbedccdbcccdeabeadeccaadbbbcadabdbeccdcddeceaccaebbbaebbbbaaeaacbadedeedeeaeceddabedbadcbdcaabceecbcecdbcddccaabdcebdecacabdbcdabccdbcbddbdbddeedccddbbceaaacbbdbeeecececadccedbedcbebdbdbcddeceabebbcccbeabaddcdcdccdebbebeadcaeededabdadcaaecccceaebceddebeceaeacccbdecceaeacdcccecdeedbcececdcaabacdeedbeeeaabceeeeeabaccccdbcdeecedbabacddabadceeddacdcbdbcaaaccdccedcdaebaeeeeacdaedeceacedebdabdabcaadaacbebdeeedcdebddeeeebeeebebadacaedbdebddbdccbbbabcebbcbddabaacabbaebabaaedcbabcedaaedeeadddaedbeacaaddecbdcddabaaaeceaaeaebbbbbddbbaabccadbbebcebdeabedcbcccbdaddecebbdcddaacbdbbdacccabcbdaedbbebecdeddebdadcedeeacbbcbdeecaeddddaeceeceacaacdbddceeedebeaedbbccdadcabecdbacaaabadbacddadebbcaecdedbedaccaceeacddedabdaccddcecaaeddcabddbeddbebccabbbaebbabbdecbccdebeabeebecccdccdccaeecceadabcbcddcdeebaedabbccceababbdbbcccbbeebeabdccdaeeeedbadacaabadbcabddebddbdabdaadbdbccceecebacaddedebaeddcceecacbecaeacadeabcabdbbbbbaccbaddedeacbdaacbcbbddcbdbdadeccbaabbdeedddbeaccbbceadaeaccebdeeccccdbcaaecebbebdcaaeaebddcbadcccedcdeedeadbcbedebcadcbacccccbddbcdcaebcdddbbcbbbbdaedbdebbebbeaaebedcbaedbdedbcbaecdceeaaddecabddcccaaacbaddacadcdaedcceedaabeddddecadeecbcabebceacbccbdbbeadaacaccbbeadcecaebcabebadcdbcecdcecddbcbccaddccacdbceabaedbdbbeecdbededabbeeddcdbddadcdceaeaebceadbbdaaaaadbeabdecaeaeaeebeecdccaecddebcecdbcddcccabbedcdcacecabebbaeaedabaebbcaaaaabecceedbaedcccacdcbabdeecbaceabbebabacebeabdadddddeeccabccccdaddddebeaceceaeabcabeeddeecbdbddaccadececbeebacaacebdcdbabcddccaebbaccbaebdecbecacbdedaacbdbebbabdcececbcacccaaaedcabebccaebabcebcacbebeabbcadbebbdddaecbbbbebaedcbededcddeabbdeaadeebcccbdccbbebdeaceacccadbddecdbeecaececbadbeaaaeaccbdbacdeaeaecebecaceccdcdaecebdcdedecbdbbaaadecceadcabdabeabcacabacbdccaedacabccceeddcceadbddbbdcbdcabecaeaebbdebbccdadddaadebeccbaeddcecbcbaeadcacddebaccddabdaccdeabdbcdabbbedddceadeedcebdbbbaaeddcdadcecddaeeecebbdedbeecbdcaaaabcadeceaabcaceaeaedcedaacbaccecacbccadcabeadcbaacbeabddbbdbbbecaedababeedaecabebeabbcebbdbadbbdeaddbbeeceaacaaebbadeabbeeadaecbecceccebcddadaabababdabacdeccbcabcdaeeecdecaebabdeeeccaeeebddaccadbdcddcbdabebadddcdbbdacbeaedcabceceecdcebebccabaebedaedaebddbbcdceecaeeaacbaeeceaedbdecdcbcdeebedacbabbcebceddaeeabbcbbabedcaabaaaabebebecabdeebaecbdadecbccbbbeebbdcbaaddbcddcdabcbceecdabdebdceaadbcbcbebcddccbeeaacbeddbaaaeadcbeaaabddacddabedaddcddccbceaedeabcedcaeeecacbceeccdecddeaddbddcdbddbceeddebeddcacbabeabdbdcdbdedaaaceabdedbedeceebcaeeecbececbadabbbbbdadbbabbceadaddceeceddbdabcbabddbdcadadceceebebbbddcbdaccbedeceaaeccdbdbbaeeebbabaadadebbbdcbaebaceebcbecdedccccbccecabcadbceaabcbdaebbdebcabcdebcbcaccaebdbceeeabccebadabcaedebceecaeedeaaddeebecdecdaecbeabccbaaaeaaacaeadedbccdaaceddcaaaaaedbbdccbecedbbecdbbadbeeabaebacbdcaccadbcbbdcbedabdbdbdcbbbeacbcdeeeacbdebbaecddbcdaeceaaaebecbbdcedcdbedddbdaebccdddbcaeebbdacdecccccccaaadbaebacaeabcecaaaaacdecceabaccaedcdebaebebddeddeaccbcdecdebecbecdbcecccccbcdadcdcedbeeccdbbcbacdaeeacdedbbbcdeabeaadeebcddbccadbdaebadacdbcbacaedbaedcdaaaacedebcbdcbdcbddaeabdadaabbaaaeedbbeddbdbcbeeabcccbbbbaacebbbcaedeceaadabcaedeeeaaeceddbcaacedccbcceaabeaacdeebedbceccaadacdadabcbaceddabbeccdbdadcecedabdbbacddbbabbbdaddbabeeabbadecbdaaaeacacdeabddcdeddbbcacbededaeedaeabdadbcebdbecdaeabcedebcdaeceaacacbdcdecdaaeacbbbcceedbbdcdccbecabebdcbdabaedbcdeccceaebebaccecbbabadcbaabbbddaaaebbaeeaccbdbcdcccbeedbcedbbdaaabbdeaeaecacaaedbacbebcebcbcaadecdcaeadebeccaabdbbabebeccdccdaaeacdbeadaadbdddacdabdbcbdccacccddddebdbacabbebaabeebbddabbacdbbadceeedebdcaeddacaaadeabdebccabcbcceceebedeacaecacbbacbdbaaeadebbdabcbcaddeebeccbdaabecbcdecaecbddedbdbebbeeadeebcceeddcababcacadabdebdebceddccdddabebaccddccddadbeadbbdaacdbcddadcadeeaacedbbbeccdabeaaeccebdccbcdbddbdeacdbacaadbeaceeaaeccbdcaeceddacabbcbadbadcecedcacacceedbdaceadbbceabcdecabcaadaeacdacecceecebebbdccedeabdccecedcceaebdcdeceedeeaedbdcceacdceaadbbeeacdcbbadbdebbdecdaabbbebdacadcbbadcbdbabcdcbacccbaaaddcdeecadaebbcbededacadbbecbddbdedceeacadebedcdadbecddceccecbbceebddbbcbbbbbcebadcaaebbdedbaeebdbcbbbedaeeccccbbbabdadceacaeabcdeecccecadaccbcdedaeceecbcddbaedbbedeedaebcccbebecacddebeebcbdebdddabbbabeebecaaaaaeddcaecaddcebadecddeededecaadaeeccbedabdedaacacdecbcbbbdbdaadecaeecadcbdcacbaeaecaaeccbeccacedeccecbbbeecdbbbedbceaeadededbbcdeccabbceebcecbbaedaabcdcbdcacbcedecaaabaeadbeddebcdcedccbecdaaeacadcdadebcbebaeaeddbebabbdeebedbcabeecccbdbceedbebdedbebeaabbebdebdebbdcbaeadcaeddebdacbdebcdecbeaadceeadddbeaeeeaccedbeaccdcbeeeebdadbdbccaadbbaebcdeeaaabaebceaabababdcecbbeaececdeeeaecaeaeebcdabdeaedbaadacbbecbebbbececbddcddbcbedcbdedabedabceebceaaceeceaadcebdabdabdcabbcadebceddcdcaaebbbcadaccccdebddceddbdddcabbaabcddcbbdbbdabdedecdcbbecbdbeabbbeeaabceaccaadccbaeeebdceaceadaaabccddeacdcacabbebeddebecedaeabcadcbbdaedddeebacebecacdbacacdaccddcaaaceeebebbcaccabeecabeaaabcbcbddcababcbdabbeacedbbadebbcabbddeaeeddcbbddbbcdbcddcadaabdcedcaedccbdabcbbbebcedbcabdbecabdecbbbcadcbeddbccebebdeacedeaaddcbdedcaedbaeadacbabdcecaeeedadbadebcdbcaeaebcececeedbaadbdadebceeddbeddcecccabaeceaddcacaeabacddbdaacceeedebdeebacdcdddcaccccecdddbbdcbabdbeebadaddbebdbacdabacbdecdcdabdcddebbdbcbcbdbecbacddaaecbaaebdeccdddbebedaabcbceadeecccdacbcbcbdcabecaeadcdaabccaecdbceccdaeddadcdbcdeeaecdccdebbaadadebceaaeecabbaeacacaadcbaaaabbbaeabdecbaedadabaeaededccdbdbeeeaecbdbcdbccaedcbadbbbacbaeedaeddbcedbbdecacdeebbdcddcddbdecdbdedbaeedeebacacbdbadddcaceaeeadbeebdeddcabbbbdccabbeaeebdcadebdaeceecdcacbdaacaedbeeabaabbdcebddeeceaccaececaddedcebeaaaedbacdbddeccedacdccacbaaabcabdaedebbdceacbbaeabacadcedcdbbdedbcedbaebadbaeebbadacdcacebcccadadcbdeeacbbcdecaaebeeaaedeaacccbcebcacdcaaceccdeedbadbbdcaaacbadabedebcdcaabcbecacceeadedbebdecdcdbabbccccbcecaeababbeccbdeecdbbeceacddacdcaaacbbabcdbaeccdcddbabcbceccdbecebbdbdaaeddbbeaaaabddabcecbaeaaecabaddcdedeaebabcaccbbaaeedbedadbdeabeeadacaeabcccacebaaeecbeadbdadbcaaddcdbabdeebabeccabaecddcdacbaeebbcdaecdeeaccddbdabbbcbbcbdbdbadcaeebaedcecabcebbabcaaaeaedbeaadcdbbebdcbabdebbccedacccbbabbdadbcbadcedeebeecacbceebeccbcbeedcdacadadbcbbbcbcbbaaddceaabbbecdadedceaeceecbddbaaeebeacdbcebadcdedbeecbaecccbbddcddabeebcacdbbdeceedeaebddaaacbeedbadbddacddcbcbebbceebdcaeadabdadbeeedbcddecbaeebaabebeaecddcdceacedbeaacabacccbedabddbecbaeadbadcccccbdbdcebecbaecacdbdcabacaccedaeadeccccdabeedbebbccdaacbecbccbbddcbbaaecddabaaabeebbcccbebbeddebadbaaeaabadbbaaabeebeeeabaacdbceabcedabbccbcabdaaaebeeceacebceedbadbbacbdbcadcaebaeaadaddcecceaabbeabcaddceaccaddaeabedcadcddececdddeeaaaeebadbbacadcdbbeeaaddebeeababadaaaadccacdcbdceeaaadedadacacdaaabddbcabbbdddcbcbbbcbedeceadabbbceebecbccbbdecbcbdccdcecebadceaebdedddcebaeccabcdaabdecccbcbcbebebbcbccdbaabaaacdbabaddddecedebdecccdeecbcceddcdbeeccdbdebecbcecebeeecdccbbbadaddcebbcaedddaeeddaeadebaecbdabaaacbecebececbddcdccceebbacddaccabbcbcccaccaabebadeadcbcdeaabdcadabbcbbedeeaccaacdcdbceaebdccebdcdebaebbcbacbbdbbdbeaadebeceeaaaaaedbaaaebacbdadadbcaddecadbadadcaadacceccabebcdcabbddddbecacabdcadcaaddceacbeaedddbaddeababaabeaeecacdacedcbcedceaeeadbdeeccedcbcccaaeaddeedcbbaaabbabaaaeebcaddebcdbaaaedcbdbbdaddeaeccaacaabcacdbdddaeeaabbcbadeeecbbecdadebacaacecdceeebecaecbdeeecdbcebedaacccdaacddbadcccdebccbbcbbcecbabaebdadccbcbbaeeccdbabddebcbbebbbdcdbcdaaeaabbceaacbacbacacacbcbabecddcbaddbccaecebbdbaadacbcdcdcaaadbbaaccbbaebedcadbabdabbcaeadbeecedecddedeceaecdcdcbabeeddbbacdeabccebaedbadbebcedbdaacdbdeebceaeaedbcaaccbaddeecdeeebbacdacddeecbaccabbcadcdcbbedacbbdaaedcdbdebbdacbdeebebabdecdecaaeedecabbdcabddbcabbccadaddecdadbcdccddaaddbdbacdeceeabdaabddabacbdabbaadccceccaaecdaadceeecbcacccadbdedbdbebaabbbbaaddbcdacbeeaadcdadeeabadeabcecebcbeddecdabeeabeedeaaecaecdecadbcddedbbcbaeadacebbddcbecaebecceaeebdaeacaecdbcdbcdedcdbeaeebccbacaadccbaecadcccaacadaabbeebcedaeabddedacdcacdaeddaaddbeecdebedeeddbccdaedebdacabdeeebbdbadaacabdabaedcdececaaeccddebceacabeddeeddbcdecebccaaabaaaeaeedbeebecabadbacaaccdabbbedaadeeaecbbceeaddaddeabacbeadccccabbedbaaddcbacbeecaeaecceadcadedecaecdeaecccdeacaebcbaedadbecbeceadeaaadadaadbbcdadaecdaabecadedbedaeddbeecbeeacadebdcedbbcbbaaeaccabaaececeacbbbaedbbbdaeeadaedbecbbccdaeceeadcdddbbcadbadecbaadbeeeabcdebbaecdaaabcdeabebadccddcdaeebaaecaaadbadbacccbdcaccabcddcdacabceddaaaacdccbdcdeadacbcedbbcbbaabedeaedbabaeceacdbdeebbdadbbceaecebeecaaeebaeecadbecdadaedaaebadeebbadcbcabebcbabbbeddcdecdcaeddbeaebddcbbdaaddccdbdcceddecdaebeceaeabacbabcdceedbaddddabbeeaecbbabdccccbbddccadbccccdcddaedadabcabeaccaccecdedbbcaaadabecabddcdebdaecddaeadcdccaaddecacbdbdecbbbeeadeccdcaaeceacbececeeeeaadaeeccebbddcdeddabceeaaacceedcbacbebceaddcaaadcbaeabdeebbaebecbcaaedebceccddaccaadcedcddddbcecbbdecdcbcbcdceabaceecceaeddabdabadbcbceeaaecbdcdedccbdbbddabeccacbccecbbcbbcbcaeedcaaceadbebeceecdceadaacaecbbeaceeeceddceeeaddcadebeabbbabdbbceeccadeaababecbadedcdacbbabcdbbaddddecccaceadaddacbbebaeddecdeacbdbcdbeabacaebbdbbbbeccdddbaceebdcccedbeeaacecdabcbdebcacbcbdeccdeaeeaecbcbecbaaeedcccaccccbbbbaedbceedcecdbbbebbeddaabacdcdacceccbcacbdbddcabcdeaeccdbadbbbbacddaaeecbbdaaeeccdbddcbebbebcdeecbeccebeaeaacddcbaaaaddedbadcaaaebcbcebaadacadabecbeeebdedcacceabaecedcebdcdeabbabdddeaacbdcbbbdaecdabeccadacaadeaaecedaaedcabdbdeebaedcdcdebdcdcebaacacdbadcdeebeedbcccaaaaeecbebaececbdadbebcdcecdadcaebabacadcbbceaaeaceeeddaaecaabedaacaccebabedbeabcbaaadcdaecdbbdcbdbdbbbedabceeebbaccccdcebeedeacdbedeccbbeeaadaeeacaeaccecbebdebbdcccaeaadadeeebbaeeaceeedabaeadebeadaebacddceccbebecabddcebdadccbdbeacbadeceeaaabbbedcbeaadaadcccbeaedcedbbaeebbaccdddcbcaeadccabaebbbcbbbaacbcbbdaeacebbecbaaeaedbbaaecdeabeebedbdaccdbacdebbcdcacadbddaeecbabbdbcacbcccdbaddeaaecbecaacbbeedabdedbeddbbbccbaadcbcacbccbeecbdbadecbcaaaeabcbbdbadadbdcecccdcadadcedbdeacaaaceeedaecccaabdbeddbbbeeaeebeeebbbeaeebbbacedacceedcebbdaaaadbcebdeddecaaaadbddbabaededaedbcecdeacacccbdabcaaedcaedcbccbabedabcdacaebecadaeaaadbaecdaaeddeabbdddeeccbcdbccbdddbcbedceeebacdddcbeebeceeaeadbaeaaebacbaecdbaebedddebbcdccceeebebeccebacdcddcaeadbedebaabcdecdcbdecacebdcedecebbaebabaadbaaebcceabcabeeaddddaedcbdebedbbddabbbadcbacdcdaecdcdecdeaebdedcaadecaadceecdadedaedceedbbeabacddaeccdebcacdceacbacbbacdbaacabcddccddccbbabaadcebbadacaddcdabdeddecbeecdcbdabdcabddcebdddceeccdddbbbcdbcdbacacdeeedcecbbceaedcadadaecbeeebdcaadccaceedcadaecdceeceeebaaadceceaabeeccbbaaebecaadccddcbaeeabbcaccccdcbbbbaeaecedeceeddecddeeecaacedbaceeeabebbdddcbadaabacdbadddeacddaeadeedabbeaddcababdbaeacaccaddcaacddeaeaabdaadcbcdcceddcbbaadcbdecbbddbadcacbcbbabeedadcdbeaededddbaccadedbceacecaceccaeaabbcacacacaecedcdecddaebeaadbecaecdebcaecbceebddeebccaecdbeeabaecedacbdadebaabaddabeeeacdcdadeddcbbbddadcabeeaccbbbaebcdbbbebbcecdcbaebeaacbedbeaebaeabcebbebcbcacacddcbaecbcaebecdebebcebcdccbcabdecacbcbcecececcbcdcdcacbabdacedeadacdcacddbaeccecedcbdeedaedcbdddaebbdbcbdacaedcbaedeceecccdebcecedbbbceeebedacbaecaeecbabccbeeaacbecdcecbcdcbbdeedecaaecadadddaadbecbeebbdcadadbbcdbbecbabaebeedcdcbddeaddaaebbddaddacbcbbdcccccabebecccedcddabcbeaddebbaeddaebcbdebcabaebaadbbbaccacbaacdcccaceeebcdccebceabbdeebcdcbaeeaaabaeadedddeddbbadaadcadcecdcadacbaaadcedbceeacbecedcdbdadbcbacdedcadbeeceeebbcedbabdebbdaedcbabccecdbeadacbdbebadbeccdabcddbbbaedaceeeaceeeadaccacadddabecadccccbbdbccbbbadeacdbaecccacddedcebebeebeceaccceabdccadabbccadcacbbccdaededbaacdabaacdddcddadbecaaeabebcbcdabdcaadebdeadbbacacaaaedbddeeacaadccadaddddbeeaedcdeedcaaaceddeaedbcbaaccecdbdaccccebeaeadcedadbbeaadcaeccabedaaecdcccdaacdcdabccedeeebaebbadddebbbbcdcedeaeddaddebccedbeacacbceeacdceeacaeebddadcabdcbcaeceabadddaedaabdcedcccdbbebddecdacbdaddeebbaadccbbdeeabebdddacbbabcaaecabbbdaeaceeabdebbbddcbbecdccbdabeebbbccdedacdedddcaaaccaabdcbdaeceddcbcabecacacdabaedcbcdcdcdeddbebebddbebadebedbbebcebddeaaeeadceaccadecbeebbdedbadacccdecdddcaabbbdadacaebceabbbadbcbbccaacdcaebeabedaddbcbdbaeedebbdaebccaeaaddbdabcdabcedbdeaaddecabadaecadaeadeeedaebcdecadbcbdaadeecceaccedeccacdeecdbcaaeaedaeecceddcdaacebdcedaacdceeaacbacddabeeeeacadcbcbddbbeaeeebaadedaadcceebbdeaddecbaccededddbccdbeebaeacedbcddccdeddadcadbbccaeebddbcbeddcaccbcaeabacabaeebbccceeaadecbaaaddddadbaadedddaaaaeebbeabbaddadcdeeabddedbbcaaabaeadecdeaeeaadbdcdbebbeeeedecdcbeedcdddcdcaedddbacdadecabedddaacccabadacbcdeccaecccebebadcdebcddacddbeeceaceeecacdeacaadcceabbbddbcdaeaddccbedbebcbddeddccdacddeceddbceeaecaaeebdceebababeceeabcbdabbbcdbbabeaccdadccbaddddaabedccdaccbcecbcaabddbbdeacacadcccebbcbccdecdaeadaebedcecdaccbbabbadbeeeddaaecebcabeaedaacecdaecbebbeababeceebcbbeebccceaeccdddaabcccebbdcecabbdddbedebbeedeaceecadebacdecbddbdaeeedaddedebadddccdaccbdbabcecadcdbabccbbdcbecaaccaacbcdbcdecceacccbcbcabaecccaccbebdcbcbabbbbccaecacaeebabdaeadcdbdaccebedaeceedeececacbeaddcabdbdeddecccaeacceaededddcebddbedaccedbcabacdddeeaeceecbbbabaecbbbbaaccedaceebcdcedaceddddaaebcdeecdbceecdacbedbdceedbecacdecaacbaaddbaeadabdbcccdcceabebeadadcedabcabdbdbcbbeeeacdbddddcddbdedeaadbbacabeabcabccacadcdaaddcebdddccdadcedbddedbbebddcaaecbdeeeebaeabcbedadacdbdecedacceddacebccedabcddbbcdaddceababaceebdbdcccdaebccaecbceddacddbddcdadcdadebdaecdaebcaeabaeedbbecedceeadcdcbaaccabeeadaccdacedcceebbaedadeedcbaeaadcbcbceebcaaeabebecaabcaccdebdebbeeedcebcedcdbccbdeaadaecbaecebccdbaeaaaccbebedcbbcdddadddabcacaaceaebccebecddceccbbddbabdcccbdbcbabeceabaaaabebadccacceecdccedebceeaeddbcbdacaaeedacccdeeaeeadbadaeacaedcbeaaedeceabebebeacdedbdbabeadadacaaaadbbbadceaeccbeadccdbdecbeddbadedbaddecacebcdbaeadaebdaabeebaacdaadeedaebbebcebeddbeaebaecaecadeadabcecacaceacecccecadecaacdaecbabeaeceeacddcbcddbddedddcedddcddacdaeadbdceeececceebdaceddaabccebecaadcdebbedbacaaeecabbabcdabbecdaeabdedbeeaaeacccbacdbacabeeaecbacceebdeadaadebabccbedbeceddabacdaeabbddbabdcdbecaabbbcdeccbbcceeeecbbcdbaecbeadcccdbbbdcaecccaabecbdeaaedcaddcdcddabedcbedbedbdeebcecdaaebcedcaaacaebcdadaabdbeaeabaabdeaabacaecdcdcbabbbadcecaebceaacbbbadcbbbbabeeedbeaacceedbbaadbbeccaecacdededaeeeabecaddaeeaaddaeeccbdcaabbacdbaeeaacabbbacbeaddabebcbdaddaeaaededecebacaaadbcecdabbdcceccbecbebecbadacbbebdedaabbcadedcaeadcaccdbdadcbabdbbaeaedddabeabaaabbddbbbeeaccebeeeccbacecaaddbebaadecaebbceaaaaacaebabceacaaeebacceebecaacdcdbccebecbcaddecaaadbbddcdaccccdedbbeabddcedccbbbdddceedbbacdadbdeaaccbdbedaeedaaabeacbccacdbcabddcbedbdccdcccccaaebbeaedceecebaaaaccbdbdeddcdddbadcedeeabcbddcebdceecdeacadccdbcabbcaabecdcbdcdebeeadacddcdabedbadabedabeedcbddedacaaacacdeddaaedebacceeacacaeacbeddbadacdadaeadeeaccaccddbdeadcddcdbcbeabaaeeacedaeecbdbdaddadacddcccdaceeeadcbcdebcddbaaccddaaacbaabdcaccdaeceaaddaecbcdddecaaeababeedaccebadcdccaecdbaabeadeadeccccddaaacdeadedabcdacacbdbecacbedaaccdebbeaccdcacebcbddcaeeaccabccdedeaababacdeaaacbcaecaddeadbaeccccbcaddcadcbadaaeebaabecdbcdcaeecddcbabeedceeabbbaebeabcaacdccdaeaceddcdeddbdaabceededdeceeaebdcacbcaaabbaabbaedcbdcaaadedcdabddabbaecdaadbbddcddbeeaaecccdaacdadebabbaaaceedbbcbbebdacebaebedbacdbbcedbebedbbecbcbdbaeaebbecdbbaeebadbacabcebdabeaecabcaacbcccacadbedeeeccadbbceebbaabaaaeadeabeaddeccbcccddbccdcbdecbbcaceebdbcccadeadeadcabbebbeeedaeecacdeeecbbedccacdedebababaccbbdcabdddcebcbbddddddbecbdeebcaebccccdbabbdeddbeeebccedbebbbececdaeaedcbecbdaeedcaeadddebdbaddbcedccdbbbecddacccdeaecbceadbbbbdbbacbaacdbcedcabaaabaaeebdaaedababceeebbbcedcdecccdeecbbbdedccebcebcbdebedcbddebbcbbbeccdacdeebeabbbcaaacaaeaccadbdbcacdeceababbdedaaccadbcdcbbbdcaeeccdcccabbddeaeacdbdeaeadcddadcbbcddbaeeaabccbcaedbbcebbcabaadbcdebdbbbedbbabaddaecbddadcbabddecdcdaeddaadadbceebcdadaeaecbcaaceedaccecacdeceaeabcbabaebbccbccabaabcdbebeccddbecddbedacccbebdaeeaabdabecaabaaecacedebaccccdabbcacadeabbaeacabcaeaeebdcacaeebadedeeddebcacaccbecbbdcdbbbaaceeceedddcceabddcccddadeaebcaacacbbcbdcedbadddecddccdbdcababdacebcecceebaedeaecdbecbeeecbaaaaeaaaecbaccdbccacecaeeadadeceabdaeedebeabdecbabbbbcddeedbdcbcaaccaacbbacdaadecedccbedeebcecbdeaabeddabdcdcadcddecadaeaeedacdbcddabaaecccdaaceaccbecddbcbbcacacccebdbddaddcdecbbeeadcbccbbbbbaedbddccbeddacbbcccbebabeabeaedaccebcabadbddeaecceababdaadcbcdbcabbbbbbabdcbadadaaadecebbbeeceedeaaecdddeaeacdcecaeeedcccbeabebdcceecccedaaadeebabecbaeebbbaaacaccdecddeeadcceadbedaebabebcbbeacbbdecacaacebdadccaedabacbabbabcbddabaddbecacdbbdacecceebcccedbaccdbcaadcbabababcccbdcbeaaadbccaadccadbeedbbeedbcbdcabbcdacddcdcedbecbaacbbabdccdecaeccaaeaddaebaadbbdabeaaedcccbdebbaacbeebdbddecbbcacabebeaeedbabaddbaadcccabbabaecbdbccccbdcadddebdabdbdddbeeabacddcbcedbdecdbadedaaddceadaaeeebebadacbabadddeadeaaacaebabdeceadeeedccceccecbcddabdcecaaaabbbdcdcbdeadddbaedbdabaccebecdaaccabacedddbbdcddacacdaaaedbbaeebebeeedcdcbbbabdcbbbbaececaceadedeebbcbdebbcceeccbceaaddabbeddbccadcedecdcddeebbccadbdacadebebabbadcdbdbdeceacbeecbbbcbebbeeebbdebdcebbcddcaaeeccebcebdbeadabcaebdaadddaddacbcccbbbdbeedcdecebeedcbedcdceebdecbacdbdcccdbeeaddaddbedceabeeceddcadeadcdcbeeadecdcbdbdbbadebbaadbdecbadaddaececdddaeeeddedabebcbbecdeeacbeedddaedbeabbccbaebdaeeeadcaeaebecdacaebaeecadedaddeacaceecaaebbbebebdbbebecadeadedecddbedaabadebeeaddccbdddddcadaabaeacdcaacaebdeaddcadbbecedcddaccadacabacdeedbaabdbbaeceaebddedbdeaaeeebbaceaeecceadbabecaeeddacbcecbedaceecdcbacdcbaaabceedcabbbdaebedadeebdacaeabcccdeeabcbcbbaedaeaceecceedcdecaeeececeaecbcedcbcbbbbedadebbcbdebdacbcbbeeaebccdcabebccecdeabaadbbdebdaacbacceaeeddddeabbcddaccbceedececebcdcacddeedadbaeaceacdbadccdabcdbccaebdbcedabbecabdcaeccbbaebacaabdaeeddebccbccebbecaadebbdddedadbedadbbadaaccbbecacbbcdbcacddbbdedaaeeddabececaabacdcbbbaecdcbeddcddcbcedecccdebacdedeeceeadadbbbceebaecbeaececccbaddccccaddccebcebeeacbbcebacdbadaeaeeaebcccdddeddaaacbbaddedccabcdecccbcbbeedebdcdacbedbbabbbeeebecbccadbaabaedecaacadccbcdbbdecdbdaaacbdaedaccecadbbeedaeabbeeddacecadeabbceaacedabaaebeeeeeaebdabceadddceedecaeccaebcbabdebccbcabeceedccabbcdcceaebdeadbbddbdeccbabadccdbabbebaccaeaacccbbcdbdaaebdbdcbcdeccebbccbdcccbcccbabbacabddadbeddcbadacdcccceeccddbcbaaedbacdbbaaeceaeccbbaeebbadcdeabaccadbaacbbcebbacbaeaeaddbacccbecdcadbeedaebdddceccaeacbdeedabaebaecaabdccebcdadaeceaccaedcdbdadbbaeabedebecbbeaaecbeaceddbccdedbbeaeebdcddbadceadeabbecadbcebbcbaabceaeaceceebcbeddbbcdeccebddceacdaeaeccbcabaceedccccddbebddbcbbaeccdccbaccdcaacaecedeabacdacbddadadcbbebdadedbeaaccaacbedacadeededbcbadeabadbbcdcbacdbdbebbaaeabbadaebbdddcaecaebbceaaebcdbedcddddcaeadaaaaedaedacbbdbadbcbcccacaaaaeadcdbabcedcabecbdeedeebacbbdeacbbeebaddbbdebebedbadbebadcdcaedbdbcdeeeaceaeeaaddcaadaadadbbdeeceeebaabbcdadeceeecbbaaabeeeceebeceadaccaeceaddaabaceeeadeebebecacccdaacbdacebbeabaeaeececddbebddabcddedddcbaeedcdcacaabbedebaaeeadebdbddbaceecabaaedbebbcacaacbbdbcdcdbbcdcaacededdebbaaadabdcbcaaaedebcbaccdacdaeedeebcbeccaccbbeeacadadeceedabccbcedbbbddcbadebcbaeeacdcbdbdcacdcccabacdcddacabccdadeaddadbaadaccccbadeadbdbedbecddebecbaacaedcbdedebbbaeeadeeddaaaaddbdbedcacbeecdceecaaecececacadcacabeedaebdbeeedcddceaadbbaaaeacedeebeedcddeccdcbeccbbddcecdecdadcdddbacccbcdbeeeececdbceaeceaadccbcacbedecaeeccaadeaddebdcabdbaeeccbcbdccddcddbcdebeceacbebcadcaeddbdabcbddecdcaebdaccadceadeaacadecceadcceaababdadcadedaeaecadaccebdcbeeeccbaeaaeeabeebcbccdcddadebaebebccbcbdccccbaeecbcccbeecdabedebcacdcdebdbadcddbaaccbaeadbabeabacadbdabcebbeaeabdeebcdebceccdceebaacebececdccbbbacbbdbdcccaedbdaeaababbedebaceabaebccdcbbccddaebbeeabebcbaccebaccbaadeaceedaccbccdecdeeabdbaeeecbacbdbdddedaceddccccabdeedeebdacaddaacddadedecceacbacbadcedebbdadddbabdbcbeaeecdcededdebebdadedcdaecaedcbebdbdbeaaadcadadddbdbdbaeecabeaebaabedcdebbcedeabbdaedccaaadabaadebadbcabcddddadcaeeecccdeaabcaeadacbeacbbacbaebcbbbeeadbacbdacccbddabbcdaddbeeccccedccddadbecdaecdcaccdccdeebacbdedadccbacdedbcdaaaacceacedeecebeacbbaaaccbabbcaabeaaabceeaccaaddedebcbccbdbeaeecdecbedbdccabdadbabcdacdbaabecacaebcebdaecdeceedadaaecdbbcdcbcccdecddacbcdeaacbecebecebdabdddcccbabadaeaadcadecbeccdebbeedbbadcaacbabcbbabbbebaaacdeddacaebeccaddbedeceaceebeecedbbbdbbcbaeeaaabbaecedaebcddbaceaddbbcbebadedbceceaaaedaebbbddccdbeadbbccaecdaaddeebbacdbdaeeccabbcdebddadaaaaceacdebdedecbccdaebcbdceeadadbbcedcadaeabdeadcbbdcecedebababeeabcabacbcbcebdbddcbecebabddebcdceebcaeedebbeadaddcbaeabecdbbbdaebabbbabbedbcdceececbccacebbaddeadaaeabebbaacbeacddadbddebaaaaaddbaaeceeaaeabeaeaecbeeaeebaebcababedabcddeccdcaabcabadabadbcdbaceececcbceeaaedbcceccccdeabeccabbdadacdedaacbcebddbaddabceedbaaeabccacbedcdecbcaabccecdbbcbbcabbecbaecddaababcbaaeebececaadaadacdeabbbccabcceebdbbeecdeddbeacedadccedebaedcbcbbcdddceedaaddadcedbaacbaccbbbbeaceacdbaceaaccacedcaabdcdcbccacadcdedeadceedeebbbcbceaedebcddbcddebcdedaccdeecbdadcadcaebccaadaeaddbeebbbbacadcbcacddadaddbeeeabeabdbdeccbabbaeceddacaceceedaacbbdbbaaddbaacddbbabcbeeaeccecceadecdddcbdacecadadbadcccedbeddbaecbdbeeaddabbdaedccccbbbdecddbeedadabaeedaecebbaabedcbceceecdeddaddedebcdbabbabebcaeaceeccddebddeecbecbceceadeccedbaeaededebcdcbdcccdcadcbeddecadbdcbbcaecdabeeeecaaeabccaaebcaddbcdcadaaaaccecddbcaccacedbeccaabbeccabbcedecadbdbdcabdabdccdbaaebadaebcbecbdcdaebacddbdbdadbadeabeabdacdeecdedeaaeccaabceeddecbdbabcbaeddcdeaabbeacdaeadeebbadbabeacecaacdedbacbcadcdeebddeddadeadaabaadbebaaaaddabeaeaaaadebbccbedbcbdadbabbeacbaaccaddbcaeeccecbcbecebdbaecbaccbdabbddbacbdccaebcccdedccbadecbdabdecbdccaacccedaddcaebeddabedcddebeddeedaedadeeebdadcbabaaabeedceadcadccbabebddeccabbdcebaeeaecdadcabbdacebedcdceedbcabaeacbcaabaaadabddedecbeebbcbceaccababaddcdedeaceaceeecdbaeabbceaeaaddbaadcddbaaedabdbecdecadceababdacccacccaaeaeebeadbcbeeabccdcbbcebdddcaadecbddcdcdcdeddecdbddaeadbaaabcaeaebbbbbcaabbcadcbbebaabaecedcecdabbddbdbdaccbcdbecbdedbcedcdcbaaeababdbbcadadbdcddddbabcdaaaabdadcaeddaebacdbacbecdcaabcebeabadadaedcebbcadcdbabedbeedabcdcaeebdddabcdbdeebdaabecdccabcdbcecddadcecddaddadbadeadccbcdabaebbeeeeadbdbdabccdeaececedebaebbeceaecbddaebacbcadbaacaedebbcdbcbaeecedaebbadadbccaeecaeeaebedceaaeabcbeabcaaddbeecaedeeadaeadecbbdeccbdabdbeeabcbcecdeaababeceedebccbddecbbebbcbbdeccedccebcddbecbdeabebbacbbcbdccdceebbadaedeedaaaddbeccbddaaaddcbbddccddecabeaecdceecabebddaaaddbddeaaedcaedbaebbeaaebbcdceedaeeabdbeddacebabceacedadceccbceeeceacbcbcbdbcecadadededdecadbebccbebaacbabbbbdeecdcbdbabdeadeeddedaceecaeddcdaadccddecbdeccacccdcdbbcbacebbaeebdeecccdaeadbbaedceecabceaaecbeadbcbdbacecddbdbcbadaeabdcabaaeaeaedeccddbeadadbbbbcdeeccdacddddeeeaecabbeeaedbbeceebdcbcbaeaebebedaabbeceaadaecaaecaaabdecaaeadbcaeaebbacdbcaecbdaeddaeebdeecceaddbbaabbbacceacbedaccdbcdddebdaaebcaaaaddcbaeccdadbebebdcaaaacacaedbdabbcdcedaecbdeacdcabeddadebcaedcddbddddcadccadaddbdebabaadceeeebccdbbdaabaeceeeaebdbccaccacadcecadabbdaabadeeeaacceadccbddaeeeedeabccedcccbdebdcdcaabddacdeebedeeaaeedddbeebedcaeddedddbbadcadcacdddaeddaacbdaceadddaaaceadaebbaabebcdaeadeaeccabdebedbedceccbbcacdbdcededcbddccbadeecebbccaacdadcbaccebbcbdceaacaeeadccddadcaaeedbeceebdeeecabdaccecdeddcdeebccabdccdaaeeabeecccaabdacdaccbcdecbeceebdccdcbeecbaeaaaadcedceaeddbcabecbadcadeeacadceaedadecebbbbeeebdbeaadaeecaabbbcadcadedaebbdecebeceacaddcbedbccbdcebaeebeabbabeadcaceeaccdaaecaabdedcbedebceaedeeacbbbbeaecddebdbaeaededbbdabeccdaecdcddcadcdbbebacabeddcbdedaeeaaddbdeecbdeececacdcaedbeaecbbbddddacebceebbeaedeacacaaedcadabbaaeeeadaabccbecedbaeadccecadeccbdcbadcdeabebccdbeecadadbabbaaaadcaabaceeadeaccaadbdbcaaedccdabebaeeeceddbadbeedebacaecedabbdaeebaddeabcbdcbdbccdbbdeaddaacbebdeeddcbacbaadbbdaedcaecedeccaebdcdabdaeaadeabbddcbaacbeddcacccddebcbddeeeaedcdbbccdddedecdcddadcebaeeddbebbcabacebeeabcadeadcccaacbddebdeeeeddabbbcedacaccbddbbdaadebbbbebcecacccdbbecbadaddaebedaaeebbeceebaaedacccdbebeceaedcaabcaeebdeccbddbdabdbcabdeadecadccbddcbdebeacbaddddcbdabdedbbaddacedecaadecaeaaeaebcedbceabaacaeeabacbebabacddccadceadadbdeebcaaccbaeeeaecbdcecdcbedeabeababaebaeabebdeedadebdbdeabdaecacacceccaababddaebecbadeadeebeebcdbcbbaeeabdcabdeebdbacebeaeacbeaadcabecacbacaeeeaeeabaabdbbaecebdbcebeacdddeecacbbccedbcadbaebeddbeccadcbbdeeadedeaaeeaadaadbaaceadbabeedbcccecedbdcbdbebaceadbdbddbaacbcbebbababcaababedcaaddbabebddaeacdbedeabebdeaebcdccbeecaaabedababbeeeeabbeaebeacddbeedbbdeadcddadabcdceebaaaccadeabcbcacadadeaccbacaacbbdebbbaeaadeacddeceebaccdcccedacabddeddaaadebbdccdccddebdadedbaeccdbbcebabbbbecdadacbeadaccabeacdddceaabbedecaceabcbddcebdeeabdaececccdddbabdabeabcaadbeaeaacacbbddddbbacabccecadeebcaacbaacadadddcdadabbddadbabeaceddebdccdaaabdcccdccdebecdbeedbdecaeadcdbbbbbcdbdaedadcedabadbeeadebdeadcaeedbaccdcbdedaceccbcaedadaacedbddaacbabddbebeceaecdbebadbdedceebaecababdbaedabdceebccedbbbabedeaeeddedaececbadedebdacbdadaddeceddaaddaadebabedeaddacedcbbeeeeadeecabecbdcacdbddddcbedcbdceadecceaceeceacaebdcdbcdbbbccbddeebcaecbbcaeaaaaedceadecbedccecacbdbbdacdbcecddeedcadcadedddabdaaedcdaadabebacedecdabaccbdcaddcceaaedbebbccaaaaedbedeaeaeecddebededaecccaeeaccdeedcdbedbcbdeddeeecadeeaeeeebbdaabbceedbdeedceedccacecdaacededdceaeabeedecdaaacebdcaecdaaceccbeabcdbedcccabbeaeceeddccaeeeaeaabcebcbeeeecabcbddaaacbbeedcddebeceadaddabdeceebccaadaacbaebdcdadaeeabbddcbbdbaaaedebedeadaeceabeccbdecdaddaddbceebdcbadbdcdccdbbbdadcedcedeccbdbaddaaadadecccacbabcecbbbdcccededecdccbcadcabebabeaccddacdecbbadacadcdeaaadbbedcabaddebcadbacebeabaccebceebddaaabecbeadcedbddccbdbadeeedcbddbebdeccceddcccbecbeaacedbaaedebebdbdedcbbbddebcbecbaabdeaecbbdcbcceeacdeeeeabacaddababcecaedaabedcdacdeeeacbadadbadaaadbceccdaeedeccccabbceeadadedebcddacaebbdbeebbcadebdaeedcabaadaaaebbecbbbccbeecbabaeebcbcabaddabeadbaaeccbbdebdaadcaaecbbcbbbdacaaebabacaddeceaeceaeddeabadbbedebcbeaccccbcccdaaecaacabebddcccdedbbdcbedaeccacddedaccbaeacaedeecbcdbaacdbedbcbbebdceeddcacdeacaecdadebbbadaccddeadbceedbbdddcdccaadaaebecbdedeedababcdceecceceadbbdeadbbbbaaceddecdaddaadbbcaadabadbdbdcaeebcebdcebecbaaccbbbaabacecccabebacdaeebcadaaadebbacdeecabbaaceabbcaadccdecaccdeecdeaeeeaabcddcdcadabecadbdcedaddacbdaccdaaccdadcdcbababacaacdcdaedbabbeceecedeceeeacbadaeabbecddeaeebdbcaecebcbaedddcacedbdbdaaaddddabeebdeecbdbbcbdebdbcdceadaccdebddedbbdbcaaeeeeaaebeaccdabccedccdbdcdddeabcadceacdcceaededaccdcbcdadddadeaabdaebccdaceadccecaccdbabaaadaddccccecaadddbaaaccaceccbaddddacbdcebcadaedcadbeebcecbdbbbcebaebbadadccdcbcccdbcadddcddcabbabaeabbaeaeacabbbccbadceeaeaedcabeaadecedbacadceaebcecceccbadbebdaecaddddcaacddccceedbebacbbccdaabbceaaaaccaeaacdeedbcabbedcaeaaaeacacccbabdcaceabeecccdcabeaaddcbddebabedbcbeddbddeeabbbedcaaacbeeaeecaccabbaaebedbcbceabdbbcabdcaddeadaecaacadeddcdebaacbbbecdbdeebdcadabcebbedcaedcabdebcddbcacbeeededdbacbaadbbbeadebbedcebbbeeddbecebdedeeaddedbaabdccbcdbaeaabbaedadcdcdeabedddbeeedacdcbcccacdcdbedbbcadeecaaddacdededdddacccccebbaceabecdadceecebaadeddcbbcbdeadbbdcebbbbbdbcdcaeadeeeedadbebcdbeebbadebccdadeaebcadebdecaaeaecedccdaacbdcaaccdccbbacaecbbbdadaaddaaaacadaddaebbcdedeeaadbaccdaaecddadaceeacadecedbacdababebdaaebeeacdaaaecddbebaacdccccdbabebbdbabbddbeaccaccbaabedecceeedbadcedadaedebbaccaccbebcbcccaaabadbdaeaeceecabdbaeeaaebdaeaeeebdaeaaeeeaaaccebceececdbaeddeacabaedebbecbcbabaebbededcbbadacbddbaedbbacbcceddbcbdceaadcbbecbbeeeddceecbdeaeedcadbabadeaecaecaebdacbaabbdeadaedbdddabdebadbdbbbdbedbdcadcbcaddabacebdeadbaaaeedddaaecebcbcdedbdbbdceabcbacbdcacbeebeeacddbceeecebcdbdbaeceddbaaebbcbddddaaceaecdceeeadcdddddcebbddeabebbaadbadabeebbbedbaaadeedcccdbeebcacbbebabaeaadbeaacabedcebaeebaecaaaaaaabadcceddebddbdddaebbbbbcedbaebeaaadeedcacaaabeadcddacdabccedcaaeedbabdadbbdeadeeccccaaebedbecadaddadceddbdaedbeeaadcedcbccbeadbcbebedcdcabbaecaceaaeddddbdacbdabadbddbadaeddebdcbdbdadbeaeddccbaacbbbecceddcaaaacaceedaaabdbeceedeaaddbebaacaaceeccbaeabaadceddcdebadcaaccdedcdbdbcaaacabccdbcebdcaddaaeeccabddebdebddceebbccdcbbadcdedadabdcaddbeeadecdeabccadacadadadebcdcaabdbdcdeadaeccceaedddcbabdeecddddabdcbbdeeddabdceeddcdbedeaacaabbaccebbbbdbceadbcbdceccdeecceedccbeadaeddbcbcadeddcbebdbdacaabdbebcacbbcbddebcebaedbbebaaacaabbccacdadbecedabdeceacabacebbbbbabcebbaeebeceadbcdddccececdccbacdadddbedbeeecdccebedcccdbbaeeeecaccdccdcbedabdccabdadbadaacbebdedbcecdadedabdcbdadbbedcbbaadcbdececedcbaecebcbeceebdeaddaabcdcebeaeecddedbdeaeeedebacdeceeaecceecdbbaeebeebeebdaeabbdabbebbbbcbcbdbdbebaaaeeeaaebbbbceaabebeaedadeddabbecadabadaebcccbdbebddbbedbbeadadaeecbdacbaebcaacdcbccdbecedcaaecbbadcbecbeeabdcbabdceaecbaeedecaacbacddaecdbacabcaddabdceecaceeaeeacbdbaaceacbeeccabedbcbceddeedbaeaaacdeeadcddcadbeccbacdcebbaaedacacccdacdbbbeaeeadddbabaaaeecdaccebbacbeebdabbeaccadecbebdeadedaaecebccaccdbaaabdcbdddedcbbcbdddcebedceaabccebbbecaddbcbdedbaebcdbbeceddebbcababbbdeebabaeedbededebabcabbdedbbceebcbdbdecbeaaaacebcbaddccdeeaadcadadcdceebebcdddcceaadaaddadabbadcceeebcacaacddddaeedcecabebdedceceeebeabbbbabbecaecaaeadeacddbdddcdcabeeeceacaccdecaddbbdcabadaaeddecbebdaeabcebcbececdbccddcdbadddceeaeaebcbaadbebaeddecabaddbdcecaadbbcdbbeebbbedabeadecedddcaaddbadcccaacceeabacbebadbdddcbaeaccbccdcddbeabadbdedeadbbbaeacbbeadaddaeccaaeaadadadbccacaecdcbdbeaabaceaaddebadbdadaeccbeaecbdcaccdcaeaaceecdebdbacdacadebcddccaaeaaccdbcbedbeaeeeebebbcebecaabadcdcbdcdaedededaaccbcdcadabbbeecdcaaeebbcabaadccddeabbbeebcebaeabdacdaeeabdcaaccecaeacecaaaaebdddecacabdaccbcaaddaacceabbeeecbcbacecbecbaedcdeadecbecbededacccdbabbbaebdceaccdbdbdbbecbedbceeebccbdaeddeadbcaadacebadacaebbdcdbbaccaecbaabbacddbbabaaeacbeebbebaebbbeddabceaedcebaaaecbdadaacbeedbdecaebcbdbcabacdbbaececddaccbdbcbaeaeecbaccbcabcddddccecabbddeadadacdebedddbecbedbdbaebcdbcecadbdaeaaeadcddcdcbbcbeadbadcbdcbadcabcacddbbdcbdbaceeedddebabdaaeebabeebaddcccddeedcabcebedbcbcaeaababaaadbedbebedcdeebcbebecadcdbdecbcdcabceebcbebdedddbddbcddbadddedacdbceadbeebeabcaeebbdbcebccabbdadeeecebeceededebababccaeceaddbdecacbbaeceadbcddcddcacaededdcbccdaaeeabeeedbbcaacacbecedbbebdeabacabcdddaadcabeedaecccceeaddcaaaedacbcabdceaadecaaebdcaabddcdbbcceedebcbceeecdabeecceebcecabaabcccbaadbeadccedaaabbdebadcedaeddbaacabcabdccdebbeccbaacddedcaaabbebedcdbcbaacedabccddedbecacaaeadbaeacceebabedbddacdadadccaeecdcaecdcedcbdceedabecbabcdacdaddacbebcebacaacaeeddeeabdceedcaeeadbedbdedeeabdcbbbebdeaeadbdbcbceeccbeaeacecaddabcbcddabbbeabadadeaeeecdbbceeedacaadeccbacbbeacaaccbcacaaaacbdbbacccdebaceeecadedbaeadaecceeaacacddbedecbadaaabbdcbbccddebdccabcddeaaeeeabeacdacaebcbecbbbedddbdbbecbdcaceeddcbccbbadecbeaedeccececeaceeedabeaecbacdbcdcccbaabdedcecacaddbcbaeeceddccdcbdcbbcecedadbebdbaeaccaacaabeceacdecdcabddeeaaadcedcecdcadceaeccdbacddedaeeeaddadaccbebcadbecddccddbbbceeabdcebbceccabeeaeedadcbcbdceeeecaadbdadaeaebcddeecccbbceddebacebdbaecdadccbcadbcaeddbdacaaceeddceccdddadaadceabadbbbccaccbdaeeabbdeeadaedbbbdcecccecececcbddebacaeadeeabaaadcdcccbedadbddaabeccbabddbcaaccacdbccedeeeedddbcecabcedeeadbacceeacdbbdecbbacebcaeaabbcebbdaebbcdceeedecbcabedbedcccdaaeaedadbddcacaacbebcdbbeacecbbeaacdecabdbeabdedbbbbaebcecbcabedddeeaedaeecedabcdaadedbcedeeeaceccdebedaddbadbbcbbbaeeabebaeabcebecaaceeaceccaaddeeaebddabbaadcaaaaacadbdeedbbebdebdbcdebedacadcdbadeaeeeebddeeaeecabcbdbaeeedaaedeabdacebedddaedbaeddabeecadcdeebadecdedbccbecbeccbdbecaedbceebadcaabbedbeaecbccbcdeadbeacedadabadadbcebaabaadacdbceabcbeebbbcbebcaabbcaadeabdbbbbaadaaaeeeaabbaeeeabccdeeaacbbbeccebabbebdbbddcdadeaeaadbdebcdeadbdbddcecedbbacedaaaaacebdadedaeeaedbbedcbaadecbdebdeeeaccaecaeaadaeebcdddadbbebcebabeceaddedadeacabceaeccceeecabadcadaaedcbbdceaecbbdbaeebaaeacddeeebaadcaecbbdbebaeadabcaebaccabceedecbadcdeeaeccaeadcaeceabeabedbdadaabceadeddbaedbbabeccdeebedcaaeeccabdbdabebbaabdaecdeedeedbebdababcbeddcdecbccedaabecaaecbabedadbbdcbabadcaedbeeddadabeacbdaeddadcbcadbdaecbddcebdbeecbdbebbeddbbaaacdaadbbdddcadeeedacceadbebbeabceccbebbbcdebedadbaccebddbbaeeaddaeaacbbcbdbecbeadddbeedebdcadabddababdcdecceccebbacacedcddbdbcdedadaabbadcaeacdcaeedcadcbbcccacaeaecbceeedcebcccbcaeaebabedabbaaabbcecebaccddedadacadceddeceaebedcbadadebeeaedbcadabdaebadeeeaacbaeccacdbedaccbdaebdddbdaaaaebdcdadbdbddcdbcadebbbdedbccaceadeabbbdaabdaceeadecbebaeacbecacaacaabadbdbaaaeebbcbdaccdbdaddbaaedadaecdeeeecdbbdedcedceabeadddcebedbccdddbeecbebbdcaebcdecdddebdeaebaaeedbbaccbcddeacaebdbcedeebceccbeeaecbbcbbdabbaadddaaeeceaeabbcccdabbaaddeadccddababcbbbccdddbebecaaecddbeddeebecabbaddabaeacbdaebdbddbbebcdaceaacbadbdbbddecbdaebddcabdbcebbabdeabcecbaaddbebaccedcddeeeebeabcdcdacabeccebdccccdcecadcbaaaeeacdceebbdcdbcadbcebbeeabebabdeceaeebecddeeebededadbccccdbeadceceeeeccdbdddcabdecbabcccedabeeeedaeecdcaaecacebbadeeaedddcbacacabaacdbacbaaebeaceddbcadabddedabbdbccdacbccccccdcdceabacdcabdcebeadecdcacdbcedcccdacebabadacdcddbdacbcdadaedcdacdcbcedeebbdcddcbbcdebcbdcbbbadbdbeeeccccccdaecbabbccededbddccaaabccaeaebadabaabdcddbcdddacdddbeebcdbedcecabdaabcbaaadaeceeedacccbceeceaebcdaceedbddaebcdcbaccaebacbbdebcdeeccdcaaaeebcaeebeeabeccbacadadbccecbbcbeccbeaacacbeedcabddeacbbdbedebdeddcacaacecedacacdbebabdaabbadaaccaebcaeecebbcbaebbaaadeaceaccbaabcebcbccbecebbeeeaadaccabceacecabbdcaddbdbcadccdcdecadadaabcdbeeeebeeacbbedabebbdadbeeadadccabcedabddeaaacaeeceddddaadabedebecacbcaabcbeabaeebbedbdebadebedaacbecabdedceacaddaeceeeedcbeedbaeecbbccdbdbbaeeededeebdeebbceddebaddeecadaccbdbccbadcceceeccceaacddcbdedaadccceaaaaddccaddcdbcacabdeccdacabcecbdcacaecccabeedcbbbddbcdcbabeddbcceedcbadaaabebaeebdcbbecdedadbeacdbcecbddedaaaeddeedecbaebddddbbecbcbbcbabbdbcbbbaeeecacbaadadabeccebdbcbaacddaccabbdcecccadecaeebeabdccbbadebdbdebbedadbedcccdcaceeadcdbcedeacddaadececadeeeebdccbeebbeeebceddcbacabcaadaddaedaaeeeabddabbcdceeacedbeeeceaaecddaadaebaeaeddddaaeadaeccbcdcbdeebabededeeaaaeaeaebbaeecbebbbbdabadbabbaedeeeeaebeabdbdcebaecceaeebadbccceceaebcbebbcdceaeddedbeabdaebadcbedabcacdbaacdebacacbcddbbdceaedccadabdeeaecdeddbadbeabadcadacaedcdaccbcccddeaabadadadbdaaddaebdabcbebadbeeeecdcbaecbdeeebebdaaedbdebabbcdedbbbcaedeadcbababbadbdecddcceebedbabedbbededddbdbdccaebbacbaabebaedbdceeebadbbbcdeddbccabadbbdecbcebcedabceabbbceeddcdabaaaabbddeeeaeebbdceedcecceaceabacceddcdadebbeddbbedacdebabceebabddbbaebdeacbededcabbaaaceebdbaccaedaaebaeeacdcacddcacccebdadcabbaeebccecbcbceeacdeaddbceeeccdbcaccacaddcdacbddcdbeebbadabccbaceedededaedeeeecadaacbceeecbebbaebddaeddcadccccaddbcdceabccaabbaabdecacdadebbdeacdbdccacbbebdcaadaedadcadccaedbbcedeaecddbeaadcaccecdcbaeabdbddebebdccccccbecddedcdbdaccdbeebccaecbacaabdabebdbddacbaddddedadbceaadaaddbbdaaaecaddbcdcbccdaeadbebbcedcbcdcbdacebcdeacbbdadaeeddbdebceeabbabeecebdeaceddbebecdcadebaaedbeccbeacabaaeeccabdedbebeddadaaccdeaeacbbedcdacdeebeddecaaaaacbbcdcbeaacbbebdcbeededbbaacdcacedcdaceeabadeabaebbedecbaadbccdabebabcedeacdadcdadeaacbaaedabacedbaebdbbdedcbdeaabcbebbcaaccbccccddaeeddebeebbceacdddbeeabadedbcdecccbecaadaadabebabeeabcbaadeeaacdeddcbecaeedcbddedbecacccbacdaddcbdaaccabbebabbedccdbecdadaddeceaedebeeeebbcbbceebdacddecbecceebcbbabdacbcedacaadbcaeaabbdbaaedcaeacadbeceeaabbbcbccadeaacddbadebeeedcaecebabdbbbebecbadecddadbcddbddbcdbbbcaaeedddaeadaabebecebdceebceaddceeadecbdcdcebcacddbbdcdccecabecddaddacbceaabcabccecdaeeaedaceabdeeadbeecabcdeccdbeecbcdaabacdabeaaabeddcbeabaaaeeecdcbeeaeeedeedbbeabebdbddacaecedbbddaecbcbecadeacdddadcdeabdcaeabbbddbbacecdebceaeccbdeacaeabdddeadedcbcaeaebeccabeaecedccaeedaaeecdedeccdcaaaeeaabeccebceedebcabacadbcebecacebabdbaedcaeececdbdacecdceedccbbbaabeecebaadcbcecbdebaedbdddcaaaccacaaddbceaeaaabadbbeacdaceabbccecbdadcdabebceccdcedccbadabcddcbbeceddaddbedaebaaacdeadcbabbccabeedaddeadacbecadddcebbcedbdccabbddceccbbaeeecbededdcbceecdaaeadbdabaacdaccebcdcbcbadeeebbccacbbcbabeccedbcddcddcebbddacedebbddbaaacbabebdcbeddbdceadadebbaaebddaaaccaadabbeadebebdcebddecdadceedccbbebdeecaddcbbcbaddcedadbebcabdabebceacdddcdbdccddeeacdbeeecabeadcbdedadccccecceaecacddaddaecdceecdcdcdcbcceacaaecbbadcdedcddaaaccdbabcecbbccadeccdacaeacaeedcaedebbbbadeeddeacedabcbddbadbedddccebbceceecbeeeeeeaaddcbbdccacbabccbccdebcabdbddcaddabbacceecaabbbccaacaecadeaababdaedcaacbbcbcaeedcdabaacaecaeeeabcdeebaedbcdbbcecaecbcbcbabeeabdaedacdbebdecbbdcddbccbcebedcaccabaaacdabbceddcabbccbcccaeabebaecccabeceedbceeddedeaedddbabdceeeaccbdcabdccbcdaeeedaaccbcdbdbaacedabbcbceabeadaeeaeabeecedceaaaabedcddeaabbccabbccecebebaaaacdbdcdecabedceccbededeaadadcacdecdbeabcebceddceddebeacbebcdeecccbdcdbbeebadeadedbebbeadbdcebddbebccebebddbcdadddbaaeedbccdacceedbdbdeebbbbcdbbaceaebbbcdbcecdccdecababebccebbeeaaececbabecbccbadceaeeecabeaadeadebdebcceabcbabeacacecbecbaacadccebebecccceaddaeaabbcddeddeaeacaadcbbcedaddbbcbdbabccccaaecdededdcadccadedbcdbbcaecedccabbebebedccdbeeedeaebedcbeabaaedccdbcbdbecccdecaabbadcccdebeaeeabddacacecbeccbabddadbccabdbcbdccebbcdbbcaecaecabecadbdaceeeabcbaecbddeecceaeacccddcddbbcbcadcdedcbecebeacbcdbceadeeabbcceabdaacddaaeddaeceaeededcbddcbecdddabdddaeadbeeeccccbebceecaddcbaecdabbaabdaaebcedecdacdeaeadedaeccabdbbbdcdccdacbaaeeddeeddeacdecadcadeaaccedecbcbdaccecebcebdbcadbbbdaaebeaaccdaacbeccccdaebebabccccadbbacdacdddbaaecbdadeedecdddabcaecbbacbdddaabdbcbbccaacebecbaeeeeaddcdaadcadcabdbedeabbbcceaeaeccccececbcecbcddacedabcecbcaadbcadacbaedbcdabcbdccdebdaccaaebcaeebdadadbcaddedabddbbcdebbbdecacaacbddcaeceeaceecccdccadababdceddedcbccbccadebacaabdcddaececebadbaacebbccceaccbcddddeaaedcbabbeaeacebcadbadaabdabeecdddcbceceebebddbcceadadccddacacacdababcbdcbcbcbdedeadeaaabdcecdaedcbdabbaaaaeedbeaaceaaddebeceeeecaeedaeeaacedecebeecbebddacaabdeaacecddcaccdabeaadaaaddecdaacdcdceeeabbbbaeaddccadcecdaedaeaaddaddcdbbcbcaeeaedcabddbdbcbaeaadbcadbddaebdcabebebabdbbccdbaedadcdbabbbaaeeaebeceeabcbbccdacceeeeacbeaebeabeceaabeeabdceaeeeedeaacaeedeedbdebebdadadbabeddcaddcdcedddadcaaedabedcbbabcaddacdbecceabccbbbeeccdebcdbccbcddccadbcedcedebceceabcccdedcbeccedcaeddeddbddedbeabbeeedbbccaaebeadceabebdacdedbdbbbaaaaebcbdadcaacddbcabdaebdaadabcbecdbcccccceabbebedbcbaddaacadebebbbcbadddeaedabadadeedceebacdbdccbadddaaadaccbebacaaaedbbeebbcaeaeaddcdddcceaeadbceedacebeebcbebcacbddadcebeaaaeeddaaadabdbedabbaeadadbdcecdadacbccaabeddeadbeaecdadadcccdacaebbbabdeaedbaeddeacecebadaeabcdeebdbcaadaadccebedcadbdcedbcdeeaccaaaaeadccccdccacecadababcdcaddeddddcccaddbadcadeaecdecbbbabbbebdcbebabbcacbaaccacbddcddcaabebcbeedaedcdbbdebaacabbdeeebaaecdedbaebaebabaecbaadcdddeeddebceaebdbccbdbadedbadcdabcedabbddeeeccaebcedddcdacccaeceedbccdeceabcbbceaeeacebaacbeebbbbadcbebebcaccbbaedecaebececaeabddebcbbbddceebcdebaeccdaacbcebebbcaeddcdbcbccbdcaabbccdeeceeadbeebcedcdbebcdbacdcaebbdacbaedbeacdaaaebecaeebadaeaddeaebdeceddcaaddabceadbedbabccdcbebeeacbececdacbddbaaeeaecebbadacbaaeeeedadceecabacdececbdcbccebddaaadebdccdcbabcccccaacbddaacabbceaddbbbdbedbaedecdbebddbdeeaccaeaabeddadbaeeecdbdabbcdcdedaeececcccabcdabdcbddeddaadabdbccbdacadccdbeedacceeaebaadceedaabcdbcbecaedadbacdceaaadabdcdbadedebdcdcabebbdebcebebaeedaddbeebbbbadbeddbabbdbbbddeaeaaedceccedaadcbabdbdeadeabeacbabccedaabacabbdcccbbbdddeeeacedccddabcddbaaeedcaacdabaababeababdecdbaedaeeeaaaeabdeeabddbbcbdeaddaebebebbaaaeddccdcbadbbcbaeccbcbebdadeeebedcabbedecabebdbaaaadaccacbcdbbaaeaabbeeaabbccedcddecacddbdaabaaeaaeaeaeddaedaceddebcdcaabbcdbacdaaceeaaaaebbebbdadbdaeecddcadaadaccebaebabccbbcbbddbdadeeebbebbceecdccbedabcbacccadcacdcddbbabaaedcdadceceadbaebccbcccbeaecdbbecbcdbabaebdeecdceaacecbdcaadeccbdeaedddcdcaabbdcacbbdcecdbdedbeeeaabeebcbeeeeccaeeebbbaedcacbccecacacbeceaeddcedeadbbabdeeeddbdedecdceaabdaeedeccbebeeabcadadccaccadcbeebddeebeecdaeeaacebdeadceddcecbdbddbabccdcdecbecadaabbbaebebcaaddeebeadeaeacbebecbaacddaabeecbdbdaaabbaedcdebbdadabdabcbaccbabaaedcbaceaeebbbabedbbcddbaccbecbabbcedecbbebddddeebecacabdebdcbecbcdbdbacbeddcbcbddceaaaddddcdbebbaedbecebcbadbcebedcbeacbccbdcdaacaebcaadbccecbdbbacaccdcdbaabeddcbbddadebbccdddabaeeabdedcdddbceaedabaedcdedaaadabeddedadcaeadbcdadedbcbabadebbaeebbddebbacaeebbcaeecdbddcabdbeabaadddcaddbdeaacddbaaaeaebbaadceacaaaccbabebcbbdecaadaaddbedcdcccaaebaebadddaebeabaebbdbcadabdadbdbeeebdabecbcacddbbdbdeadabcbaddaeabcbaedddabecbbaccaababbedcaeacbeeddcacbdaeadaaeeebeeecabeeacabebbcbcdbbccdcddaacaccebcbdaadadadaacaacaaadcedeacebadddccaedaccedbcedbceadbbadbcabdcdeccecedeeddbdbebbdeeeabeacceebbbcdcbacedacbeabaeeebceebaccecebdabbeaeaeccbbcbeeaeaaadebedbdddcedaecebeaacebcdeddcbdbdcdceebebbcccbbdbadbcbaacdbdadbccccdacaebbccceaaeaaacbecdddbbdbdedeacabcdabdeccbddaebbbcedacdeccabdbcacadabbeacdcdcddedcbaaedbaaceacdeeacebacbbcebbadbcdabdddabacddccddebbbddaebaabadcdaeeacabdabcedcabcbbccecaaedababadccdaceecaccccccbcecdccedeabdbeeebabaeeecbbbcecccddaeeedccacaceaedacbeabbdbecebcadbaeaccadabbdadaeeebcbeaeebdbdedcdbdcbcebcdecdbbbcbbbdadbcabadebcdcceccbeddebeecbaadeecababbdcbbeedeaceccaccebadeaeaabceecbcaabddebadbdbcdbcecddbeaddbccbdbdecddbdbebcbaebbcbcbbebccebeabcddadeeecbecdbcebcaeecacbbdbcadcbcabcdbeeedeebeccbebaaecdeabaadaeeedbeacaabbabdacdbdabcbebdecbcbedbdebaaaebcbccbcdbbcceaaeecdeadaddbababdbadabaeeaacbeddccedaeedbeaedbeaeedbdaabcdbbeebdcddbeabeedbedbceaddaeecebbecebcedbdacdcaaadecadbdbdabdedaedaddacabdcebaeeecdaaadcccadddaebceabdadbbcebbbcdbbddabcabcbaedacacddadecdacaebccdedeaebedeabcaadbeabbebaddebeebdcdcbddddabaadbbbacedbadcaadcabdcbeaacaddccabdcdaddaeeddadbeaabdcaabadebabbbdccaeeccdcddaaeeeedcabdccbcbcebbcdcaedaeabebbeeeeeaccdbebddaacbcdbccbadcaeaaacbcdbecaecbdbdbbcbcacaecceceaabeeeaeaacaccaccaabadbdbecdebdbaaebdebeddadaeccedbccdcceedbabaeccedbebcbebbbcedcbccebaabecccbbdaaddcbceeccedebdabcebbcdecedbdaabcbdcdccccceedccbbacbabeabceeabeceeddcadcbecdeadeaaadebbdeeccebdbcdecaddecabaccbdbccaeadadbabedbaabbdceebedbbaaaebeddeebaedeaabbdeeabcbcbacdcebbdabeebdbbdedadbdcccceddabcecdbbedebecabaccccaadbebdabaeeedadbedaaacbceabbacacebbeeddceeddebbceacecbcdaecaaadadabdbeceaceceabdeabdbcbbbdbcdcdeebbdacdacdcbcddabaacdbeccadeececcacdbcabcadcbbdabcacdabecacdedabeadebabaeabbbcbbebaecbecbeeedaadbdddebbdbeaeeeeecddbbbdaccecdceecaabbbdddcacdacebceacdbdbbbccedbaecedbcbebedbbdebdbedcaeedbaecbacebaaaadddabcebeaecacebbabcbdeacaddebdcccbaccbebdaacbcdedadcecbddecacbbdaeceeccecdeeaceaaaaeadbabceddbcecabcaaddcaedaebaceaabbaaeecebaecdebdcacecdceaacacdbeeeebacadbbbbaedbdadeeaeddbbaddddcdeceaaedbbcdedcaebeebaaebeccabaadeaebedccbeaebaddbcbdabacaeacedaddeaaebaecbbaeceeedbcbaecabacaadaeeaabebeaacdcecedcdbabeebdadbebaeaacaceabbccebaaaaaddedcdacdbdbedbdcbeaecaecddbeadcdccbcaaaaaccaecadaaebacbcbdccddbdbcaacedaadbcbcdaddeaddaeeaaabbedbeebedbdcddbcdaaeddeaaedceecbadaabeaadeeeabdadbebdeddebbabcdacbebcbbecbedcccddadacaabccdbcbcdaeacacebadbcaebeaeddbcbdaeeebabbaeaacdeadebcaacebaaebbbdbcbddddbcacdeaeddaacebecbbbedddeeedaccbccebbaadabbcdecaddccbcbcbcdbbdadcbedcdbdcbcecbecaeedaaecddbddeebceaaaddbbdbecaadeaadbcaddeedaabccbedcadabaddbdbaaacdeaccacdbabcdbbeabbedababacdaebbccadccbabbeaaaebabdbebdcabcdadecbedbeceecdcbdeabcabbaccdcbeacbeaabdcdbbcceddbdaebaccbeaddbedaaeceddcecaadcdcabdeddabddcccadbeaacdedebdedccadaaaadcdcbaebcbbeddacecbeabbdbdaebbcbdbbbcdebccbadecddeeaccbeabeaecebecbcadbabeceaacdebedccacaeaaddcacedceeabcbecdbcdcceebecaddcebcdccccdeaedeeeaabcbdddebeeaedbbaceebebdcaceaabcbbbdaedbeebeadcadcbdcbadeadcaeaedadacabaadebedbaeaecaccceedccdcadbccbbcdbdaceceeacdecaacaaadadcedbeecaabebdcbbdbdaccbaceebbcacdeaeadccaeacdcaaebaecbbbcacedcebdababeeebcecdadabdeaacebaeeebeccedcaeddeccceeacdbbeadadbaaabbdcadbcdceccdabaebdbcdeaccbdbdaddbbaedbdcbbeadddacceeababcccaeacbdddddcdbabccaeaaeebccedcbbbadbcdabacdddcbebeabedbeacbbccbebcdcbecdcebadeaaaedccaabeeacbbededbacaadaccdecccdbcaeabeeedecbaddbabdbebdbcabdcbdebeacacdbdeebdecdeeaaacdcccbdbeaeeaacebdebcbcaaabdeccbbcbdbedecdeadabbcedaababaecbbccaacdddccaabecdaacbabedbaddbbaaabeccadcbcbbaebdbdaaaaceeebccdaecdaabbeeebbdcedadbecceacbccdbabcecedbdeebbdbacdecbbcebabaecebbbbbcabaaceebcebdacaeadcbddedebbebccbebaadcdbeeddbdbcbaedcbdadddccdcecebdccabbdebcebcabedcabcabdaeeedababedebcbdebaecacdcedeceedcccdcddbadbbcaebecccddaeacceeddeadbeecebcceddaddcdbbcddbadedebcadaecdddeeaeeeebeaeeebcadcdedebaeeaccbbdcaebdacecedaabdaedecddaaceeadaeedbcecdcaaccaaccacbedabcaedeaddaececdcdbcbccaedaccaadaceabbddbaebaaebebddababeebecaabebbbbbaddecdebabbcecceecdccdbcdbdebecccdccceaabeadedbaaaccdaddcdbccabdbdeedeaeaceabaececbecdddabacbbbbaebcaeedceaabbcaeecedacecdcbabadcdcecbacbacdbecbbaacceedbeaccbcdcbdaceaebdcaedbaabccaeddbadaceacaeaeccaebbceebceddcebaeedbbbcecebddceadcbaaaedcddceddcebecdbdaaeceebebddeeddbedbdedcdbcebaeeeaddbcadceedbccbededbbaebadaecceaaabeceebddaeaabebaaacecacebcacdcdcbadcebebcceebeccacbbceaecddadacbdacbeebedebebbaeabccdbaccdccceadaadeacbdeadecbdacdbeecddbcbabbeebecdaeaeecaebacedcbebbdaadaeaedbadceecedaabebdcbdcdbdbddedebecabebcacdaabeaabcceebdbaddabaddbcacbaaaebdceddacaccccdaececeadbeeeeceadbdacddedbabccadcaabddccbdedacaaeeabeaadccdbdcccddeacadaacbdeaaebadddcaceebaccbaeeceddcaccdbadbcaedeaddaadcebdedecdaaabeaecadddbebddebaaacdcdddbdeebedbbdecbacebabcecbbdbbecedeedaababdebaadcdedeeadaaeacbcddbaacbbeedaebcbdcdbdcdaaadaebbadcdaadddcdeaeecdeeceedcaaaeecabaeacbabbdbeddaeebbacdaedecaecabacaabddedcdebceddcdbabdbdccabddeaaecaecabccdedecacdcadccadebbadadaccbcbdcaebaccebeedaeaaebccddeacccdceaeebccaebbedbdcbcaaddeddbabcaaabbceccbcdeceddbedbedccbebceedcdedbadebcacaaabccacabacdeeadcbcbaecccddbecbadcccdedeeccdebcaebabbadabcedbdbdcaededeebeeccabbceccaaedebeeecbddaceccbbbadacedeaacbeebcdcceeabdeeaaecadeccbcbbbdbaebdabbcbdebdecabbbebbadbabaaaebcbaadddeceeeacebeebacdbdadaacbaddecdecceaccbeabadecbcaaedcccceaedeeeabbbeeacdccbcabbadadaaecacadbecedacccccbeeeebbacecaabccbbabaeeeedaeabcbbbbdedddceecbebbcaaaaebebcbccdeabceebcccabbcbdeedcbaadebecddcadacbcbaccbecddcabdeeeebaaaceccedeadeaebbcecadddebdecaaebdbeadadbdaceaabedbbaaaabbcbecddeacacaccaedbaeaaebdcddecbcaaeddeebcccdcbdcbccaadbcabaaeedecadaeeebecabeeeacccdcedcabddabbbbbdadecbdaeaeabeaeeadadcebecaccdabcaccdeaabcddaeeedaddeccabadcbcadacbcaeebeababaaebbccbcbcdbdbeddbabaeaebeabbedcedcdbaaeaebcdcbdbeedeeacebbddebebcdcacaadaadbaddebaaadcdecccbecaabdebbcadcdcecbdeecdaaebbebeeeeadaeeeabdeddcbbeeaaccddaeaeccebdededabbcacebaaececabadbaeccdecdedadcddbdeacabcbcadaaadcebcbdbbbdadeabcdabcecaeadcebadabecceadecbcbceaedbeeecdabdeecaaeaeeabaedcdbebceeeadecbdeabdabcdbddebcdcadaebbccecaedebbbabbaaecbacdcdcabaedcebbbadaaeeedbbbedabaecadaebadedcdbccabaddbeebdecebeceaebedeeaadcedcbcedbccbcdbccabccceecccbddceeaaddaeaccbdbcbdbcbeeebdeeceacadcdecaaeabaacaaeadebdadaaccecaccdecccccecbdceebaaddabececdebbebaeeadaddeddbdabbdecaaaddbccbaeaeadaceecbddeeabdeebdacddacbdadbbabcddddeaeccaeaeaecebceeaaecdabedcceadbddbbebcdbacdcedaedbdebbaababeabdeddedbaebcbdbeeebbebdcbadabcbebbdeeeadddaaabbbbabbaedccbbdacdbeeaeddcbdabaeabaadccbebabbadcbbdcdbeaaebeaeceededdbeedabaaaacdcdabccaccdabbbeabceeabcbbcaaabbbdaacccbedcbabbaaeecadccdbebadeeaebacacdeceeedacdbcbddcdaaaddcbdcbbcbdaaeddadbcdaaaeebaaececbdeedecbddcceaeaeeacaaceacedcddbeeeedabaadeadacdecacdcadbceacdbecaaddebbceeebccdaceabeceeacccbdbabbcdcdddeaebcadedacadebabdcddcbdebccecdbdeecaebcdeceadebaabdeacdacddecbadcdddeddadedaccdeeebedbebebebaedbcadcaaeeeadddabecaeeabbdcddddcbcabeccacaeadaaacaacdeebddaaebbccdabbaaeedecabbcdcdbebeadadecebeaddbabcbbaaeabdbbaeacbabdcaebeecedaddaeacaebcceddadeeccebccaedcceadbcecaaebbeadcaadbaabcbeabeebceebebbbecadceeadadbbdeccdabcacbbccebeaeedeeeddacaecccecebdaacaeecadbedabdceeabbeebddcbcecbeaecedddecbadeccebbbeeceeeeebddcccaeabdadcceebceadbbaaeebdabadaeadeaaacbbebdeeadbdadadcbecddcecccccbadcaeeedacaaeadcdabbdeccdbeebdadbbbcccbaccbecadeaedcbacabaacbadbcbcaeecededadbebebdbabccecdcaaeeeacaddadcddacdcdededdbcadacccdbaaabddbeccccdedcbdabeedbbecabdadbbbbdbedcddbccaddacccebebbccacddabadedcbbadbddcdbcdeeaccbabdeebdacdecaeedcaceccceebaedbbdcbceaebebbeabacbaecdcccebbdaededebdeceeedbddddbadcedbdeaeaaaebceabbdbdadeecaebcdcdbeadaadeabdabcaddbeeadeebcbbeeedadccebdadececaccbccdbedcdceedbcbcaedcdbdeebcdbdaecbecebdbddcdcddccdcbaceedbbdcbbeecbdeccedbbbaaeeeededaecdccdabdbdcacabbbabebeceececbcdccbcacacbeeaddceabddeabaeebaacbdaacbcdadaabbcbdddbbadeebcdacacababcaceebeaeaeedeecbcbaeacabcadbdaacaebeecaaacbadbdcedecccedcebbdadcdbdddbbebdaaadedaecaddedbddaabeacbebdbdceecbdadeebedaebdddcbbccdbebadbaaccbadcbeacabcdeacaecbbaaeaacbbbaaebaedbaaeceddbeaadeacaccdabceaeaeedddbcabddbcdbbbbaeecaccbbcdecbececedccdbccaaadccbdaacbddeeaadeaabedcdaeeeabbdaacecebddbdabaabddeabbccceaaadedcbadbebadeabdcebbaecdbbcdbabdababddabedcccbbcbbaccebbcaddddbdaabdeedaaaabdacebacaeecdaaddaeabacabddbabeaebbbedaebbbbebceccdceedacdaaeadbecebbeeebcdbcebbddddbecebabbbadccabedecbcbeecabcedddbdeabbddaaabddacddabecdacbdbbcbdacedeaebaabeccdeabaecaecbaecaddddbcddcacdbbeacaccbcaadeedeacccdadeaeebecacdecbdbbbbceebededdceeacddbeddacdbbebccdecbaaeadeedbedcbbcdebdaedeaeaadddcbcdebbacbceccdaaedeaedaebcecabbcadeeecabbdccbbaadeedbeadbcacebdcbbaeababbcadbbcdeaceebdddbacbddcddddedbcccdcbedcbacebeeaebbeabaacaaeceabdddadadbecddbdcceaeabcacbdcbbceaeedabebeeccbcbaabbaedacbccbdadaadbdcdccddbeabddcbaedbcbdcbcabcddeecbaeaccaccebcebbaebebdbedeebedaabedcbebeeaecdddcbaedeceabdaebccbecebedbbaebabccdeacebaeababaeaddbdcbdaceadaebadaecbeacabbdedeceddadeccececdadebccacedccacaddedbbcbbdceeabdeddbebedebcedbeeacadebceeecdcdcbaebcdeabbbacbaacdcaceecbeccaeaaaacaabbabcbedbaedceaaacaabebbccaaebbdddaeecbbecbdbaceeeadddadbcacaacadbadcaededbdaeaacebeaeebaeeaddeacdceddeecaceebccaccaddaeeeeddedbaccecbcddbeaeabdbbdddbcebebcabcbabdcabceabcbaaaceadcdcdceccdcadbaaebacdecadcbecceacbeebadeebddcbeaeabbcbbcbeadaddcbcccbcddebbbbccedddcdebcbddeeaabcacddeadaabeacadbdbceedddeeadcbeacbebeabeabbcbbecabccedeaeddccdeddaeacbdbebaccdedebdbceadabadabddebacabccadabaaaaadecdeeabbdaccebbabcbecbdeeeeedeebcdbcdccacaebadeacbaaccaedceaaeeaabbedeccaaccbcaaceeecaacedcddaddbeddcaccbdcccbeccdaacabaebccccdeabbaaebbaeecbbddbecceaecaacbabecbabccebcdccbebdcdbeabccdebeacecadaabcccaccaaceceeaedaddeeedaccabacbecadbeccceccdaaeadbcbbdabcdedadbedaaceabcbdddabbbdcdeacacbbbccabebdaebaaaecbccbbecbeabbdbbdababadadcbcdabbbabacadccccaacaddececdcdaaaeeaddccdeccedbcabaeeaabdecbddabcdcbdbdddcceaaaadbebbccacecbebaaceecebbeeacbcdccdbccccccacaedccbbcaadedeedddabbaebdabdaeeebddabeeaeeebeadbdbcaabddeadeaeeaabcbbdecdabbbbeeeeabbaeadaccdecedacabcadaedccaacdedeaaeecbceacdacebcbdacdcaeeabeccbeedeaabbbeedeaebbabccaeabdebbadcddcebecceaaacaddcacaeabcacceecbeaaaaadebeeaaadbdceaeaebdcaaaeaceaeaccbecebbdaedabaedcceebdceaaededeccadeedeebcaaccaeedeabcabdbadbcbaedabecacedababddedadeedbdbcaeadcbaabbdedaceabecbcceaacebebebdccacedcedcdbbaaedeaceeecbcbaeebbdbdcdbcddccecdcadaceebbadcbceadcadbedcebddaebbdecdeeabddbddadbacdadaddadaaceabebcbbcdecaedcacaabaddbbbacddccecaebdbeaeeeaccbedccdecedbbeadbaadaebcdbabeeacaaeeddadebabbeceecccbceaedebceacecbddcebdbaecbebedbbeaabcdaebeeabcbbacccddbabaeecddedadaaedaecabeecbdcadedabedecdccaaddadbbdaeddcbdedacdccdcddacbcbcaadabeeebdbeeebcebcaeadddadaadceaaacebaceadcbecedadbbbabddaaecdcaddbaeecaceebcbbacaedaaaaedbddebdaddddabcdbbacdcacaaeaeacebbaebddeaaeacdacaacedcbdcddccbeeecacadaeacdbcccecbebbebbcbeecbbedebeebbedacaecebcdcdeaedaeacaccecddaaadceecbbcdbcaccecaedbbbedbcbcbeaedcacedbabadeeabbaedceddadceacacebdaaddbbcdcedbbbdbebdcaaaaeacadcccddbcdbcacdddceddbcbacbdcceaaaaccbecadaeacddcdccaacadebecccdedcbceeadbadebdddbccebeecbbbcecbadbcebeedccaebeabacdaacbbbbebdccacdddebeeceddabbaeaececbceedbcecbeccccabdeedebbadabecbceceabedadaedcccacaaccbdccbddddbbadabeacceebeccbcaadccccdddbeeadcbddcababbbcbaecadcedcaaecebdbebdcbeccbceedecaaceeecddeaabcbaadcedeebadbaebccccbeeacabedcaeaccdeebdeeceddeaeacdbbbbdceeecadbaccaaceeacbdadecdaedebabcdcbbdabebdaacbdcddecaccdabdeaccacbedcaaeabdcddddceaeaaaddddcdaacaaaadbebbbadacdbeaaedcbcbecebdceeceedcaddeebceabeaebbceababccacbabbbbbdcbbbaaedaecacdcebbbbeecbeeccecbccbedeecddaeeadcbbcaddcecdecdadaceabbbcdadebbcdeccbcbacbedbdedceabdceecbacedeecadcaacdeeacaabbabeccdbacbcccddbbaaaaebceddeaaeecedeeddebdbabbaeecdeeacaccceacbabeeedcddecaabccbabdcceaecbabdcbcbabacebdcdbbabbdebebadbbcddadcbbeccececbbecdadbcabdcacabddeeedbcbcadcbbdbdedcacbbedcadebdeaadcddebaccbebaddcaadecababedccbabedaceaececdaddddedbbeaeddebbdaecabdbcdddabcbaaeeddcdedadedabdadebcebbdaddcebecadbbdeeeadebcaceeccaeaedcbeeebabbaddeddebbbcdbdacdadcbacdebeabedcebdedebcbdddedbbbeebecbbeddeceacadadbaeadbadecadeedadbceaebeadbceceebedbbdecaccbacccbaddbbbdaccadaecbcadcbebabcccaaadeeaedcacdaabaaaabdebdaebaabebacebcbbabeabccacbaddbeebcbaeeecdddceaabebecaadcdbcbadcebbadcedacbeecdececeaabcaeaaacdaedcdcbcadaeeeadecdacddddaceededcdbcbeecadddacedbabeddcccadaeeeccabeaacecdbcebdaabbbcabcadaacaeacccdbedcabbbbbececbbccbdbeddcdaddcddecdbceaeedcbdaeecaecaaeabaaddcbbdebeceeebddbdaadedebbebdcacdebcaddccbadbdbbcabbeddedcecebaddabeeabcabacadcceabedbddcecddaaadaeddaecadabeddadbededbedecebaeddedcacdeaabbbcacecececaaaebbedeaebacabdddedbdbceeedbcccbebbdaebbdddeeccdaabccdacabdebdacbecbbddbeadcaccaaeaccaaecbdebbbdedcaaebebbcedbbeadaabbdacadbecbbaceeacecedeeabacddeccddaeaeeabbadedcdadbbabbdbbbabadadeccbcbdddaaabeebaaacddedddabcddaabeeebeecaddbcdeaeaadcaaeaedbcccbdcdcabdbbbbdccceadeedaaeeedecebddcbacebeddbaabaeedddbdaaaadeedaedeaabbeedbcaeedabbcaadccbbcccbededadebaccdddeabbdcabeddeaadaeedbeabbcebebcecbcdbaedabcdabceadbbbeaadacdbaebedabcebaddbaaabaedebacaddabdccbdcaccebcdbcdeeaccbabaeabedcacccdeccabababeddaadbceecededcabdbbceaaaceacceeabebbbeadbeabdeaebdaccdeaeedabbcccedabdeaecbdaaeaccdbaadbbdeedacdddaaccebbcceedcbaaebaeaeceabdbadbcbabceaebaabeebcddeabebdbbdceeccdeacdabaabacdddcacadebdadedbdacdcbaeecbaceaabbabacecaaebcbeeededcdbeccdebcaaecacadaebcabebabbabebeedadccbebccdcccaeabbabbbabacdebecdbabbebcabbecbbdebbaebaaaaadbcebdacbcbaddddcbeaebedcadeebdeceddbcbdcaccbecbecbceadccbaeebceaaeebaddadcbaddceaadeedecaadaebaddedadacaacadcbbadbacedcddaebbbacaaaceacdaacbabbaabcbbbbeceebaabbdbaacbeeececccadeeebabbdcdeeaaacaecdabaeabceeeebaccdebbbadabdadabdadedadaabedabeeddddcadcedecbaadaebadadedbdcaccbaaadcabaecbddeacbacbabececcbbcbbbedcdbbaabbbaedceacedbccdbaaaeebcedcadcabbbdeabbccaaaaccabecececcdaddedabacaacbbccebdaddbcbebdbbbceedeaebebbdcdaeabdaaeaeabbdcdaaebcdbcceabecbaceceebaabbeeddaedcbdeeadedaddaeaeaaacddbcccdddcceaecdcdbbcebcedabcbadbedaeaebaecdccadbacddaacdaaaddecabbedeccaaccaaaeebeabdccddddebaacdddaecacbecebddabaeccaebdcdbdabaeabbaeaedbabbcabdaebcebaceeecbbbbedcedcbddcbceecedaebbdeeacacbcecccdbacecaabbbcedeaadddcabccaaedabbcdebcaebccccccabeaaedcdacabadebcbbcedeedbaedbdeddaecdcbadcacadbaecabcbadadcabadbcecbbacebbbbcdbbacebddedacdbcddceacbbdbcabddbebcdeddeddecddecbccabbceddbeecdebebabeedbdcaaaddbdbbdeadbdbcedadccadaddeceabcabecdedabddeecaabebceebabbdddabacabcaabeebaebbedbdadacbabcbecaebaabddadcdcebadcadcabacaeacbdcccbbebbebadcdeaadebddccdbaadccdaebdeacadecbbeeeccbecedeeaeebbdcadeddddddbdaecbcbabacbbbdebbbdcecbcbbceaedaddeddbeedeaeaeeecbbaeddcacadabcbdedabbeaeebecaebbbbbdebdaecedadbceecadedabcdcbeadcedabbcbccdbcbccbdbbceceaeaedecddebdebccaabedcbcedcceacabbeedeceaccaeaebaabecacbbecbbeeddccddadcaabdadddeeebbadebebaceaadeeeedbcabaeabbdbdddeeeeccbcadadacdbacaeaebadbebaddadcceabbababdbdbcbdcadeeaccdebeeeebebcbcaabbbbadbdaeedbedebabadaeceacdddbacebdaaeedeaebcaceaabbaabaeecdcbcdeaadcddddcadcddecdeedebaadbdcbddebbdddeedbbddacbbabaaceebbbdaebccabdabcceeccbddabddeabbaadbaebbbcccadcdbbabddaddcddadbeeabcbbabbddbaaaccebbeeedbdabbcebabdcdaaaadedcbeaaeedcbbaccdaaebbcebcdabdbaabbebbebddddcadededccdeddedebebedbbcdbdbeebacddaaeeaecbadcaabbbddcedceebbeadaeececcebdadacdbbaaddcebeadccbedadccbecadaaeecddaceebbbccdeeabadcbebdbccadaedeedaeebaecdabaebbaeceeabdadddecceeacbcdcbaceccccbabdabbeaeecbccceaddceceabcbdaedebedcaddededabbceceabaebcabaeaccaeeeaadeaecaeaabbaadbddaebedadeedccccecacdadedacbabecdacadededcdeaebaacbecbccbbddbedbcedaaeaadabacbcedaaebedcaeceebebebadaedcdeaabeccccabadcbaaeaacddbccceacbddacbcaddddbacdcbacceacacdbcddeeedccbdbdaebdecbdbeebadabedbacaeccbbbabddbdbeaeaeedceceebadbaebdedaacdebcbbbacdbdeebbbbddedaebeebddbcbceedabbdddcedacdbbccaeadecbcaabbcecaeadebdbcbbaccbcaaebedbdcedcedccdeaeddacecdeedbeadabbebccedebbdadbddebbcbdabbcdecebabccbbddcebdaeceaaccddeadeadbebabddadcbbadbddbdbabaaaaeabdcdeececadbabcdbacabcabdbbebceabcebebcbdcbcadeceedddbeccecacdabaabcdcbeecdabedbbaaadaabeeaadededebcdbdedddceaddedbeedabcbeecaeeeeaadddedaacedcedcedcebcbedabaaadbeacabcedccaccdcbacebabceeabceccbedadaabaaeedcabdebddbcbcccbbbabbddbeedbcccedaedabbedbbedbacbeaebcbeeababaccaabcbebbdcaddcdaddcdbbcdecaeabaceaebaeddadddceaeebabddeeccbddedcacaaecdeaeddcaaaeddaedbbdacecbcabcdcdadeeadcbaccadccacdebbeaaabbcdbabbdeebaacaadebeecacdaaaaeacbaedeabedabadcececbeddbaaeecaddcadaabeaeabdcdabcacabbccedbcdecccdddbdacceaacadeeaaebdcddaccdbeecebeaddecebcbcaecaaaecabeecbbdcbeabebcaecccdbebdaaaadcdabddbbccecdbbeaaacbcbeddbedddebcdcdeeadebbacebbacccadaabaaaadeeadccddebbabcbabbbbadebddbdeaabeeececddcdcdddecabbecdcddaacdbdcecdccdaebbcdddababbcdcebabbeebeaeccccabedbadecececabbeaedbaabcaeebeddeddbacdbdcbdacbedacecedcedecdebbbedecceabedddadcdcecadddcbbddbebacadddeabcdebacccebaedceaacabbebbdeebaeddceedbcadaaaaddedbbedccdecbcecbaddedebccaaabceeaabaaeaccadeddebaadceecadcaceabaeeeecdacddbdbeccedebebeeedcbcdbeabebdbbeedddddeddbeddbebccdaaadaacecaebecccbdadcdaabeeaadcbdcaebdcccaaeecceabdcacbbbcccbdacaedecebdeeaaeaebdbceeaecacebeedbbbaccccabdcbaaeedbacdbcaeabccbcbaedcbcabdcbccdedebddacddaabeedceeddeececcbcbcbaeaaacccdcabebcabbcadcacccbdeaddecbebedaacaaeecdbecccaabbdbaccbbeaebbbcecabcecbbcabaeddeabbacbebdbcbbbacbcaacdbabadbbbbebaeebeaaadaeacabacdeeaaaaeccbcbdbbdbdabbeddcacbcacecabbdeddabdbdbdaceeebebbcdbbeacacadecaddebcdbcddcbbcaeaebbaadddaaddeeceeaddddbbcbedacccddcebacabcaccceabbcccceabbbabcaabbbbebbeeceddcadaabbbcdccddbbdcdabcccdcbbcaadabecaceeeccddeecbbddebbedcaebeebaeecacedeacbedddbadbeeadbbbaeecceaedcaedebddccbabeabbbaddeabddcbeeaabacbbebdcabacecdaaaaeccceddaadbaacdbdddecebdadebbbaeddcecaeaacdcadccdacceecddddaabbadaecdcebeecdaaaaceaddcededbbeecddbbadeadabceddecebdcaadedbbcaaeaaeebdcbcbacadedddcacbaceecbababcbeeecbeeaedadeaddcbdbaacdedbeeccaaccadbaaeecbadadaceeacdccbccaeaecdadaebdceddaebcadbabadddeeebdbeebadbeebcbedbadbbecabbabbacebacceadbaddeaedbabbaddebdbecdaaaddbbbbddcebecbceedcabcecccdcaeeebeeddebebaacebcbecccedabdcaeabbdaaeeaaceaddceaadcdbbabaccccbadaadabaeccacabebaedcceaebbcddbcaeaadebdbedbcedeedacdacdddaabdcaabeaaadcbacabecbeeceebaebcdbbcceeebcadbadeaaedbacdbaabdcedadcbcbeddecdecddeadddabbaeaeaedddaabbbbaaaaceabdbcedabacddaceaeebaececbabdddaedaaecdbadaacaccdbdbbcdcbeccbcbbebddcdadeeaabaceabaaedcbbebacbebecdcddceeacaeeaaaddaecaaeedcbebaeedccdedeacdddebebabadecacedcccebeeadddbdecdaacbeadcaadaedebaacaceecbaccceeedadadbcebaeaaaaeeaccebaabbeabdcbdceedccabbebcaedbbcadacaaaaaccdbaaccbeaabdbceeaaaeeddbbbecadcbadbecebceecceadebaeebecbacadabbeaecedbbbcabcbbebbcdbcdaeaebaeadcaeeeebacbccceaeeddcceabcaaabbcdcbdcebdbbcebccebcccdadcdadbcebecaecbebacbdecebaeabbcbdeeebaeebddddaddaadabaeebabcbbecdaadaacbdbadeaaeccbddeacebbaaceecdaaaedabcbadceadabdbcdbcdceacbebdbeabdabcaabebebacedecbdbaabeceecaceedcbacacbadcccadbcaccbecdbeaaddeededdcdbaebeeadeccebacdbdcecbbdebdcaabcdacddecdacddcceaeaccedcbbeacddedcdbcaabcacacbdddecaedaceadbbeeeceeeabdceddebcaacdecededbdaddedddcdaacabcceeeebcadcbccdebbdecdadeaecedcaecdbabcbedcbbbccdbababaddadcccedbbcabcbabcadbeebbcdabdbabcbdcacbdcdabedbcaecccdacbebacaecacdaebadcbeaedbaedbaddabbedbcdaeaeadaacebeabedbceadbeeeebcaaedebbecebaaadaaacedbbcdeeadeedbaebebadaadacdeceaedeabaeceebcebaabaaddabeaaccdcaecbbdcddbbcbbacdecacbdaeebececdebbecdeebedacdacccadeacaeaedeeaedcabcadcebeeeacbbddbadaabadcbbbccdecebbcdbabbddcdcaaddcbbbcdaabdddcaacaddcababaecbdeeceeccbcddabbddcbdbbbadaebacbaceceeeaaeebbacbdabaecacbdbecdbaecabbabceeddbbaabccbcedeebadcabbdceadaddbbbbdecbbeaeacedacccadaeddaebeecbbcdebbdccacbbeccaaceaadaeacdeebadbdaeaadeedadededaeaeaceeedababccbcbcdbcccaddddbcdebaacecbcbbdebcdeabeecdbcdbdadcdcbceaebbcabadddecdcbedcdeceadcadaaceeddeaecadaddbccdeedbcebbddaecaaedeabadaccebcacabdaecbbedadddcccecbcbccaaedcacccbdeecacccbabebadebbcedeceaaadeacccccbdedbccadbeebbbecbbcdbbdcebddccceccdcbdeceaaaaccbdedbcbbbeeeadddabcacbdaebcadaddaccecbeabbacdcebdcdabecdcabdcdbcebaedeecddbaaccaebddcdbcaedceadeecbeddbadcdddecececcebacccabdcdbbeababeeeccadaeedecbebeccebaaddedcecacdbbeabdddebdecccedacddeaebbadcbeedeedccbcccbdcbddbddedcedaaeeeaaeeabeaeebbbdcbcdcbbddaaeebecabbbbedaeaaecacbbbddbecdccdbecaeacabdecbdcdaecaedcbcaabadecbadcecceaaebeabacdcecdcaeabbaeeeaaeadcbaaaacedbbdecbcadcdeaedeabbebdcceeccbdadbcabeebdadbcadbbecaacebcbdbbebdbabbdccceecccabccdbabebeccabaadabadbcdddedaaeecdadabacbaababdaaaeeeddbedcddddbbbaacebdcaabaadbdddbbeeececaddcebeebcdbeeccecaccadcecdcecdbacaddeeebecdececebeeccbebaddaddddebeadcdeeacabbbaebaebadcedbcaeadbbdbccbddedccbcabcdcadaecdedacdeccebbacdaacbbaddbdccddaaeeaaaddaeaaadbceabecabdedacbcdaeebdbaddedcdcbdcbdedabdeceacabaaabccdccaadccdacdadeaeeadabaeeeadabbceabddeeeaeaceeadedcdedcdedaedcdeedddecbdeaeedbebeccaadbeacacbdaaddaababbacbcecbccacabeecaeaeacaadaadcaaeedacbbcaababeecbcaaeabdaedabecebceabccabcbbbbceadbecaeaccededdcedcbdedcebcddbdcacbcaebbaaeebaaaedbeedbaaeaeebbcbdececbdbbaeaccdecbdcddeddbbbcbabcdcbccbcbedeeeccaeedebeebbddccedbcdedeacbedbceaabcdeedaeccbcdbcccaabeaadbdbbbbedebdccebeaaceadcbbabeeacdcecbeaaeceaeeebdeddeabdacabdabbdedaccebdeceaabdbbeaaaceacddeeeeeaecbdebadedeceebacdcadbcbeadeeaababccbeeabeaebbcbdadbeabdabbbdadadebecdbcccedacaeaeddaeeaabddadaabbdacdcedcadaabebabbedcabeddeaddbddadeecdadbbaeebadebcaadcbdbeecaebddbcbeddbcaadecacebedadadbeddccccaedbcaaacbebbdaddabcaabacbdcebedeccaaaebedbbdbacdbeaebacdadaeeceadeabeabaaaabdebbbaaadbecbadbebdaddbccedaadbddcaedaceaaacdcabddcbdcbcacedbbbabdeeeddabeaddadbaecacedcdbcebddaaaebeabdacaacaeceaedcedebdeebbcecaddcedeeaeadedcaebaadebbbccdbbebddaacabaaccacaeeebdddaeddbcdcaabebbaedacdccaabeeccbdeceadebaaccbcdceaededbcaacbcbcdaceecbbddaaacaecabdddcaadaccbdbcaccbbacdbacaabebaaccabceebabbeacdbcbaaccdceaacbcaeabdececceecdbaebabdecaccdedcbaddecabbacbebccddccaaeddbccecaddaabbedcadcaceeaaaaeeaebbddedcdeabcebbebdbebcababadaaadcaebcbdeecedebcbedadedcbaccbbdccaaecadacbcbbbcdeeebdacabbcdadaecaeaeeebeaecdcddecbaecdcceeeeedecdbcbdbaeadeabcaeeacadbcdbeabaececebbcbceadddcecdccdadaaceeddecdaabedacecceebbdabdbebeebeeebdedbddecddcaedcceceecbccbeadeebcbeeedeabadbadadccbbeeecadeabbdbdccebadcccaaacdaeadcdcdbbcaeacacdebcccbddedeaebbeecdcbddbeadadcecadcebdbdbaddbdcabddeaabbbdbaeaeedccdededbdceacaadbedeeddbeeaceacdaadbcaeabcebccdeaacedeecbaedbacadeecaacbabeebeabbbbacaeabaedcecadecbacccbdbbeaaaeddababcecbddeeaadaeddbbedacaedeebaeecacaddbecbebebaccccdebbbddcdcbcebbaccdaeaebeabcdaacddcebbddbaaacebbbecabebccddccaddaeeddabdbabacbdecedcaeceddbcdceaedbbadebbdedebebbeeeeeedaddbaedabcdbaadededcbdcdbacbdabeeddadbddeaeabccaedcacbbbaabaedabbceacdbcdddecceceadebbdabebbdeccaeebddcdeadceeadeabacacadbebbabacbeababdebebbbebaadadceecbcdabccbeceeabdeadeeddbdeebcdbbecdddcccbcabbaeedbecadeacaeaabccccbdaadedaacaaaabcaacddededecaaeaabedadbcbcdeacaaacdcbadcdadddacddabdeccceaaccdaccaebedaabcaecabeceecbeccbceebddabbbecbebcceccbbdadddbdecadaddcaaeccdacacdaecbeaddbccededecadaacdccddabedcbadebaddabdaedbeabddccacdbeeadbcdacedaabdcadbbeeecbabdaddebcebacddccbbdeaacebadaeaeabeeeeebabdcdaaeebbbeacccdbecdcaebebcbabcedbdbdaacbadbdceaddcaddbeabdabbddcdedaeceddebddccdcedebcaadabadedeebddecbbcacddcdecaaceeceaeaeedddeaaecabbdaabcadddbceddcccceccbbbbeaaccedeacdacccdadedcbecacacbcbcadeccdaecedabecebaddabaacdddccaaeceddedeecbaabdeebcdcabcdceeadabdebadedaeeaabcacdcedacabcbdcebdaabebedbabccbcbdadddaeddaeceecdacbaeebaabcbcbcccaeebeebccacabbccaaaacecdbebdaceedbaddaecbbbcacbaecedcaecbeaadcdbaaedadcbddecabcadedcadcdaeebcabeebecebdaddaeeddabbbeaaecabdedcceccedbaaabcceecceaaceabedccdaebbecdabbbaeeacdedbceeeeddaccbdccadebcbaeeacadaaaededebbabdedabdadcabccaabacdaaddceeaadcdedbadccbacaececdeaccaaaacbcddbbbbeaebcadabbcddcecaeaccabaddeaacedeaddccabcabbeecaccbdaecaabbaebadbdcbaeedeceabaaacadaedabadcdcaaeddbeacbaddabeeceadbacebeabbbdedacbeadaeaecacbaeccacaebedbacdaeebcaebabbadaccbcacacabaacdeedcdabdceaceebcaeeccecedddadabbdcaaccababacbaceceaddadcececaddbcdeeaceaabacedebbeadbeaaaecdbeeebeddacdeabbdacbabcceedbceaebbcaacccdceceacbedccddecdebdecbabeeaacdccbeccdebcaeccdbecdecbbbaaccadaececcabaaadbebbccdaacdedbdabaebddbbbbeadcecaecdbcdadcabeedeebdddbdabbeaacecdabdcdaeabdecceabcdaedabebcdcacbbddedaeacdebaeeecaedabaadbacbdabaaebaabcbbcaedaebebdcdebacabdccbbccecacdedacecaadcedaacddcbdbabbbeabbbbcdacedbbbdaadceabbbbcceabcdebebdcbcdebdbadedcdbcedaddabaaedcddeabcbbcbceabdadeddaadcddaaccacebdeaeecbbcbcbdecbaaedcccccaebcccccaedacbadbdeebedbcecadcdaeabcbdedbbbdccdebcdeddacabeebccadedaadebcbadececbbeeecdadbebecbcbeaccdddeeabddbbaeaddbceedbdebaaaeddacaebedeaeacedaaaabbdeadbaaaadcdbdeceaddddcdcbebdbccbaaceebeedcdbdbdeedeabbdaaeecceaacdddadcdeadabdddeaaccbbdabeceaebeaedddddcecbaabddaaeeaddbadcccaeecccdcaaacbbdcddbaccdbcddbecdbeeaeaccaeeaccbaadecacbdddeeedbbeeeddeeedcbdecedcecdecceadcacebdcbaadeadcaeaedbaacdeaaaeaaaedbbaededcbbacebeeddcadecbdebeccebbcaaeadcbcbccbeebddbbaedcbacbbaeaebedaadedebdbddcebeabdaedaebdacdbddededebbcabdeeebbacbeacdacdcecabadceebabedeceacaeabcdddbcccadecdcccbecaaceadcdcedeaeeabaaaecccdeadebdcaddeaaadebabbaeddeddabecbecdabeabbdadbbdddbcbadbabadaadbaabebcecacdccaabcbacecdeababcebbbedaeaeadecebebbdcebbebbeeebdebccaaaebdcebadabdcdbbaebbeabcecaaeeeddebdeadbccbeeadcbbeecdcedabeccbdadeececdbadabdacdaaecdbecadbdabcdcdddcdeeacabbebbbecabddeeadecabeeadedcabbaaebcdebcbacbacbeadbebbaaadeecbcebbeccaaaecaaadedbeabddebbecacacacbbeccacabadaedbbabbcbcaeaeeaadeadbccdbeebbceaeaeedaecdddbcdeadccbcaddbbdbabceecdceedeaecebeaaaadcbcbbeeadabacbddaaadbadddcedcddbdacbadbaabdcceddeeaeedbcdccdbabcbadaddeeddabeaeecedadedbeddedeebedaaebacdadeebcccdbecaebcdbeaadeabaddbcecadbaedababcbcceeccdbbebebaabdecdbdabeccbecdeacaeccbbeabccabeddaaeecdeececbeccbdbcbdcbcacdbccbcecadcccaaadbcccabdeabcbaedceecbeaecbccedbadbcadcdeababeedeeabceacadbddccbeaebeccddaeccddeeaceeaeeaceeebccdcaedbebdaaeeabdcabacadabbebdaacdddbbababeedddbeceededddbaedaacaecccabdcedabedcbcbdaadaceecceccaccacaaebadecbbacecedaacbbbbbecaddceddeeaadccceeabbcddeaaccaecbadbdababeeabacaceeeecadecdeabcacaaebcadecccdbeaccaeedacddbbccddeaecadeccbcbaeebdaeaebaceecdcbecadbbacaccedbbdebeceeadbddcbdaeabdcdbdeaadaddcbcdbeaccbdedadbddecbcbcaeaeedaccadebccbcbeeddceacebacabebdabacebeeaecaeeececddcbeaacbdbbdcddbdbacbaecbacdceaecadbddcbdecbcdadcedbdddebcdcbdaddddcaacdacaacabdacdbbbcbaddababadadebedcaedacabaeeaedacdbedcddbbeededebdedbbeccdcccdbdbabedeceebabadbbccbceceeebebecaececcaabedacdbbeacaebacceaaacaabebabdcebbceaccdadaeaceacbaceedcbcaaccadbdddebceabadaacaecbbacdabdcabeaaadcdcdcedabdededccaacecccbacbaebdbbdecbdeebdbacadaeaebeaeecaeabdceeacebbaabedeadaacadcdbbecccadbcbbaecaaccdcbcddbecdbdddaacebbcabbeeeeedacaedcacaceaeaacbdeadcccbccbddeabbcbaeebdeeadaceebebcecbbcbaadbacbdbdacebaecddcaacedabaceaedbaccaaebebeaaabecedaceaaecbcdcaecacbebaebbccbceceebcebadcbeaceeccaeeeacaaeedabecdaadacbdcbdadeebcaebdbdcaedddbaaedeabcadcabacdceeabdbaccbcebaabceeabcedecaeddddbaaacdbddddebdcbeaebebaaccaedadeabdcacbaacccaeceadbddaceddccddedbbabecbedaacaeabacdedecbedbecaeaaadeaaababebdcaaacdeacbaaccdddddbdbdceccdaaecbceacaacaceaacbaccbbcdbdbdbbeaadbaeedabcecebdedacddcadbcbcbdddaecbbcddadcabbebaadabbcbecdbdeebccecedeaaadebebecaeecbaeaccdbadeebbbebdebbddcbbacbebebaacaaceeebabceacdbdbecbcedcacaaecbeecccddceeaeeeceddaebbcdbaacccdcddbaebbbaeebcccaccdcaeccdedcecccbececbaadcebdbddcbaadbbdbcaedebdabcbdabadbdbeaebacdddeacadcbcbdbcaacbbebbcdaaddbcabcbdeeadcbcccadcacbaddbbcdeadbccbedbceeabddecabcaabbebcdddcbbbbadbeeadbacddaacccebbbbcabbeccaeccdeaecbdbcbddcedbdabeddbcdcebecabeabdeadddadccdccbacbebebadaaebaccacabaccdbccdadceeaddaaacebeccbacacceebadbbadeeaaceeabeabddaaaeeeeddcbacebbdbbbbdcdaceedabddaacedbaedecbaecacbbaaddcceeacaededbebebedaaaeaaddbabbedaecbcbaaaedcbbeeadaccedddcdcdcbccebdaddbaaaabedaeaaddcbdcededeedccaeebbbcccacaabdeaccabadaadbaacdecababeaaeaeababbbbdadaebbbacbabdeaacdcbbbeaebcdcabbcbbaeabaeddceddddcbebdcbbaadebabcacbbdbaeedaeacedaedabacdcdadaacbaedccaeadedcdbaacabcebadccbddadbeaddadcbceaddbcbcdddcacbdebdaebeabcdeebcceadebcacbaebececeecbedcbaacbdcaeebdecdaaddcccaedcadddbcedcecebdcdaecadbdeabedeebcbdeecbccecdebdeaccebbccaabdaccdbccddbdcdcdeabcddacdebaecbeecdcedadebabeadebaadedbebdcbdacccaddddcebbbbaaebadbdaaddeabbbedeacbbacadbbaaadcbdebdadbabddddbeeeadedcabecdcbeeeebaaababeacabcddeceeadbebadcbdacdccbcbeeccddbbbdecaedaaacbcbeccddaeabecedccdcbeeaccbcbaacadaaebdbcdccbddcddacbdcaeabedacdbcbdecabccddebcdedbaadddbbbeaccdbbbebecdabdaeeecdedadaedcaeabbbbbdcadbdbaeaebbeebcaeebabbbadcdbeeccdbdcbdbdcecddabaeaadbbadecdacdeeebcbdabeacbaabdbebdeaabaaaaeadabbdcddebbaecacbbcdabbeddaacbeeeccbbceecdccabccecebababbeeddabeddcbdcdeadbccbeaecaecaaccdedbedccbbdeaddddaeddbacebddecedeecaccaaebececccebeeddeceecceaddbeaebabebbeeccbeacdaddbcaaaaeaadccadecaecedabcccdcecaeaceedaddedbeddbeeebcaeeaadaeddadaacaacdbddbdccdbccebbdccdcbdacacadaedadeaccbaabdaddabcdddbbdacdcbebeaeedbaceaeaeacbaedbaaebdcbbcedccbbcbceeceecceebbeadecacdddbdaaebceaaebadaebbebeddebeecabcaacbcabebeedaeaeeccbbdadaadcbbecaddacdbacaeedabaacaaadedcabaaceeadbeaaeabdbddcbaebdcedebacbbcceebebecacbebaebabecaeccaeeaebbabcebeaadbaacecddcbddaabaecacaabcbeeceacacbbdaebdadaecbbbdecadddebabcbcbbbedacbaaebcbaedcbabcabceeebeadeaaabcadebcbaaacbddbbdbcadececbdcbaecabccddcbbaeaaedbdcacaccbaddccccdacabeecceeebbbbdeebecdaddbcadeddbcdcedebbdbebaecbbceeabaddebcedbcebebacebebbcaaeabcccccccbedeaebbbaadddbaddccddecedbecceeadebaccbeeeaeccadbdabacdcaadbdcdeeecbdeeadcbcbbcceacdcbeccebecabbcdbdaeeadecececcebacbabcabebaccaadaddeaeaecbcdebedddcbaedceddacacedbdccacabeccebebcadbccbcbbbbebeacecddbeaaeaecdcabadbbcbddebaabcebeeaddcbbebbceddeeeecadaeeddcdaacccbecaedbbbeebdeccbbbceddebdceebecaedeebccbedccddcddaacbaebacedecddaadcbbeeaeebeceecbbadbabdbcbccdecebadbdabdacbaaeeeaebeadccecbbbcabbadbadaeaabbdbdbbecbedcdacaedcbcbdbbeddcebdccdceddbcedeaaaedbbdeedcacdcaddaedaadbabeddadabeacbbceccccaabddbabcadbadeeaccdaaacdeebccddcdddaaeedaabbacbaeeeedcccecdbaaabeceaadbedebaaaaaadbcddabadcddbbcbcdeebbceccdabeaddbdedcddeacaddecaaabcddedddaadcbceebcadcecaebdaeadbdccdacdbccbdceaceadcecccbbedcddaaabacccbeecceceecaeeaadadaecabdcdcabcbadcaacaaaaebbcdeebcaedccbebadeeeaeecbbebdcadebbcaecadcdbccaecbedbbeebbdbcaceabaebbeaceebeacebaabceabeaccdcaedeaabeadabceecbcaceddededeccccccacaeeadccacdedbcbabacdbcaeceedcebbaccbeeecaedbedaadbcbcaeadaccababadcabcaccaaeebdabacacbbcdbeacedbdbbbabecbecbeeececbdcbbceecdededbdeebecababaccbaceeaabdbacdccbbbceeececcadabadbdcbeacecaaaedbbeaabdeeceeebecbcdccdecbcdacabdaccdacbeaadbeeacedeadbbbddbaadbdbeeebebccbaadbcabccaeaeebbdcdbdcaceeeddddddceeccbaddaaebaadaadaaddaebacbddbbcbcbadaaeaabcdddcbecaeddcbddacebabecbdbddcedaeeadacbbededbbbaabacaececddcabaaddbeaeacecdedacbdcadebbdbbdddcbabcedebddbbceecbdcbabeadeaadceaebacaebbceeeeceabceedeaddcdadacaabbabedaeadebcccbdebebaeadaeaccedbcacbaaccdcceadcdacebdeccadabbeccecbdaabacbceaceceebccbcaeddccbcacbbbaaecadadceeedbdaaedaecedacddbcadcebbdadccdadedbeddcdbeaeddedeeacddabdcdadaeccddbdaebacbbaaeabbbebabeecaddabedccadaabebddacbeeaccccdaeddebeeccbbcddcaeecaececaceeecedbdbecadecdbaababeadedaacddcbeebeededbecdbadbdcadcebecbeedeecbadccccedbecedeebaebeaedcecdeedbeacdccaaebcddebbcbcecdeecedeadaaddcebdccdaaebbddedcaeebeacdbaceaaecbbacdeebaceddddbdbaeceaeabcddecadededcbcdeaddcebdaeecbbaabcadceedebcadcaacbeeeaeecdcabcddceaeddbbadecddbabebcbadcdbddaaaacaebdddedddddcbdebaddedabaacebeacdddcacbadaeececabeedddbdcedabcbedbbbbdaaaadcddedaecbbebbbecadecaddccddddbcdcbbbabcbbbeceadcacababddacbdaedcbcaeeebdeecbaddbdccaadabbdecbeeaacebddecedaaaceaeaddebdedecbddadaacacecddeeaadabecabcdadaaaeccbcebceeebdabddbabddaebaacdeabbbacdadbcecbddeeeccbbedddbdeaaeeaeebacdbbdadceaacaadbadccddecdddedbcdebeedccdbedcadaaeaeaceaceebeadadeaacbaaceedaceaeadbacbacaebbbbedabdaccadecbdcedccacaabcdccdcaeadebacdddcacbabbebbdaecacaecebeaeebeceeeadeeaadcabdecaebdbeceaedaeceeccdcedadbabbbedadedbedaccbacecbeeeccccbcbaaeaddaceadadcdaebcdccdadebdddcececebdbacecdbabaedceaabcdeecebddabecaaaceecbbcbccdbdabbabbdcabecaebcdbbddbedddaebedbbeececebdceaabbaeecbdedcadecaddcccdcdadccdceecbbdcceeabbdcdccaaeadeeeeecddedcbdcecdeaadbeacdeabcebabdccbaacadbcacdebeaeedacecebecedebeecedecbcdbeddcdedecaceabacdddbeeecbbecbbcbaedeebebbacdebaaaceabceeddaebacbdaaacbbdbcbddebbebdbdbbedddbedcdaedcebebeaacdadcbedabdcbddabebecddddcdeecedddeebebdacbeecddcddcbbadacaddacbcaebbeeedabcecbbdddacccaeabaadacaeeccebbdedacabedbcbceceaaaeeabbdbbcecadceddacdeeaaabcacddabedcaebbdedaedacaaaaeececaebbacecabbdeddaddadcbdbbabdcbacabdbebccdbaabbddbddebdaddaaedeadeeedbddadebbddddecaaeccbbbddddbbcebeaeeedcdabcbbbeaddaecdeebabbbdddabdcdaeddacaececcccdcccaeadbddbdbcbdadebaadddddceadcddedacabeeebdaaedeeabccebeeecbcbcaaaaacaceaecbaebcbbabbbceaaeadccbccaacdcbebeabcaecaaeaddadaddaddceaceeaedbbaabcbcbeddbabcccaddeaabbcbecceacbcebaabcaacedccccbcbbcbceaabdbceaebbbbabecbcccebedceeabeebedbeeedacddabaaaabbebdedecbbacdecaaddeacbaeaabaeabeeedaddecaeaadbbeabcadaccccbbdedeacdacbeabababdbcedeaeddaabcecadcccbacdcbcbbecacaeceeeeabbeebbaaccabddaeaeaedbbeddeabbabededcaddcecedcdabaadcddcdbbdeaddaddbcdbaeeaeaddbececeecbadccadcacdaacdaebdeecedbacbcbbadcdabeccebdeaaceceadbdabdeeedbcbedbceccbdccdedaceaeeedcdbcaacbacceceabbebebadaaddeadccacdbecbeaeedaacedbcbaadeeaaeaadcebaeaabaeeaebbceecdeaedabbaebdceeecebdbabecdeddbbcaebadabedceadccabcbcecdbbbcdddcedbeaeadebbeddadacdbccbaabdcbdcdbeeeababdeabaddcadadbaeaaebbaeccaaddedccbbbeecebebddedbdeeaaabcbbbebaecddceeaaddceeedecddaeacbedadabdcabbaccbccbacdcbdebeabaacbccabbccbedaeacedbcbcadbedceeaccdcbecbcacbddbbeeaeaceacbeddaababbbccdeecbeaebebdecbadacbebacbccabeaaececedbbbcdbaeaadcdaecbeedaccabcdcbcddadaedabdcdebaacdcdedcbcaaaabdabbcbddbbecbbaeabeeceeaabceacdcacebbcbacdbedebcddcacccbadaaacebedeecedcaeaaddccbebacedcbcbadbeceedeadeabecdbdcddbdedbedcddadbddaacbaeddeaeeacaacadaeeabbbbecebacdbeaccbbdbdeaadcedcbacbebddabceeaadbcdbddbdabdbabbcbddadeaebabbebaeebeaedddcedabeddbdbdecbaaedcddbcaecacdaddddcecbeedbddaabbabacdbecdaccecbcbdbcbceaaecdceeccadebdaadddccdcabaabceceabbddbccbdbcdaacdcbdacacdcddcabccebecdbcdeedcdcdcaecabdeaebccccdddebebaccaedecdbaceddeadbeacdbeadbceeeabeeddbaabbecdbaadcaebceaaacddcaddddeddadcbedadbdceeedeabacdddedeabaacbbaecbcedbecdedaaebcbeebcbeeadceaddaccbebabcebcccebeabbeeeacddcaaedbabbebedcbdabbdddcdcecbacceabcdbbecdcbeaceddbdceacdaeeebddebbebdbbbddecbabadeadcaaaeeeaecabecbddaadedbababeaccddbbbabecabaaccedcabcaccedaeaaeccbbeccadcaddcecbebccddaceebcdeaddbedaeeeccecdccbcbcebbedaaabbebbbabdcadabcedaeacbebbcbaeedceceadceeebdbabeeadeddaddcaddbdcabbceacbeebcddadececbaddbddcecadcbcbababcbcbedcbeebcbbdebecabccdabcaadccbbdcedecadcbddadbbddcaecdcbaccdbbddbccbdaceacdbcaeadcccbccaeeebeedcdecaebcbdbadaeeaacdeddcdeeccedcebdabadedbdcaacbeaeedcedeabedcccaacacaacbabaaecedebeaeceeeeecbceedcddcdadaeeaadbedbacdecacaddeaaedecebadacbcdaebdcadecdabcaccddbabcbaadeedebdddcaadabcadbccadeadebeadaaaaeddbecaeceeaddbcdcdbcbcbddbbdcbbaecdadaeedccabcdcadaacdddcbeeebedabddbebaddedccabccbaeeaacbabbdbabbaaddabdedebdbbbcbbeabcadcbeaaddacdadaabbccabdeaeadeceebabdeeeeccccdedebeabeecbccbedaadcdebabccbcacabdcdccdaceabaeecddcdabcecaebecdbeabaaaadacceebcecddabedecebedcaeacdbeeceeecebabaebdbacaebadeeebdcbdaddaeeeacedbedabcdabadbbcbbbbbeecdbcaccdbecadcdabaababdcbccdacbebcceeecdcbaecbdbeacaaedcdeadebacacbabedeedbcdabeecbbdcdccebdbceebbabbebbbeacddaacadeeeaeaabaedadabaeeaeebaeebbbbeccecadcedacdcceeaabacacaecdcabbecbaadcedecacbeacbbebebdabbedeebdddddaebbceebdbadaabdaebbcadabbadadddaabcbdddcaebcdbddbccaeeecdcdedeccedabebddabdaaadddeaaaeadbdeabecadaaeceedecbdaadabadbbccacdbbaacdadeddaebebdbcdaddbaadcbcaeceabdcbadddddcacdcaeeadeedacdbabeeeecaadcdddaaaeadedaeaebcebbdebbdabdcdabdcdeaaaaeecedbedcecbdbabbddccaabbdbbacddacbbcbccebdabacbceaeaebdcdccdaddaecdccecceadaddcdebbcaecccddceaddacaedeeaddabcbacbdbdaaacbbbadcecccadceccceeaaabeceacdcccdceaedddbdcdbcaddaeceeebceccadeaaedcddbcabcaadaebbccaeaeaaacddecebacabcaebaeaababecedecbcadeeaddacccadecbaadcddebbbcabecccadeaadaeadbcdecbdabadcbdceccaadeeccdabeecaecaebcdecaaadbdbeaabbbeddebdbbbceacdcbdbdaccbacceaadecbadaacbeabacedacddddbecddcadcbebeeecedaceddddadaddbaacbaddadececabeabbedbaacecdacbedeeebeedcaaabcbaebcbdaaebdcabccecbcbdeeeededdadebabebdaeacdaaddcdbeacdccccedaabadadaaaddeadeceaccaaedaadbbdbdecddbeeaeeaccbacaceecbcacaddcaeaeebceaebbedbcaeadddcccdbecdbcaedeeaedeaadacdcaecbadcdaadeeeaeebccebcebbadeedcdebeebabeaeddaccdaaeabcaceceedbdbabdacaecbcebeaaddbabcaacacceccaabdbddacbddddecaceeeeabcdebdbdaedcddeaccadbdcbabcebacbacdbcbbedddddccaaeabbcddeadaacadeeeaaabacacdbdbecdaedcbcdadddbdadacdebeedcccbeacdbbdbaadddbddccaadebadcdeaaeddeaaddcabacbcdbddececeecdadaacadcdbaeddeaccddcccdbceebddaeacbcebddbaabbedcadecbdcddbbcaaadcaeadecdecbbdcbcceaabeedcdedebeaddcabebdcececaeacdeebadddbaaabbacbbdaedddcaddddedaddceccceebeaeedbcadddeacdaadcbbabbecbddbeaddadcbbcabeabdbcadddeacacbecaeecedcedaccadecbcbcdeaaeaaebdbcbcbebacddcabecbddcccbeddabceaeebebdebbaadddeebabcccccdebecdcdceebcaebcceacececedecedabcdabbbedaaadaacddadcdaedaaecdddbbdbedacdbedcbeccbecabcdcbbcabdcdbaeceeddabcddccdcdacaabaecaecadddaaadbdccceecdabbdeeaeeadbdaedadddedbeacedbbaaeddacdbddcdeacacbdbbaaeadaeceaedceaaadadebcdeabdebccbdcddebaadeddbbdbdccedbacdcdbbcceccccbcbcbebdabbeeaaaddbbcdcbbdbeceaebabeceededadbabdcdadeadceadeebbaebdbceeebedcbcebcaebdcabebcebbeaeaabcacbbbbcedcaaeecbaedceceadeadaaeecddcdbbaeacecbecaccccecceceddbdebcacbaeabadebdacdbbcaebcaeeadeecdccadcaddecccadabccedcbbbbdcadabaadbebcbcbbeccdcaecdadacdacabdbbdddecbcebeeaabaeebbeddccaddaeadacccbaeccddeddbdbeddeebbebedecadcccaadcddbcedbeccaaedbaeacaeeaeaacccaddcddeccbdeceddabdadedcbbbccaaaadebeecceabacaecdcacdcdaacebdbadbdbdbbabcadcaaebadeeacdceddedacaadaedaeaaaebabbeeedbeddceccabdbbeeaccccabbabdccebaadecdddabcddcedbaccddceebedbbcceabbdeeddbdbeebbcbabbcddeadddedabadaeeeeeeceebcbeedbddcbadcacecaeaccbccabcebeddbdbedaeaeacbddbcececcaeabaeedcadeacaacacdcebdcbcdeadcdddacabedacbbeeeadbeadddadcdadbadaceceacadcacbddedcedabdeeaacebceebabedbeaddbddbdacbdeadbedbcbeebdeddcadaaceadebadaddedabadcbeedbcbbcddacbaccbaecdcadeaabdaecebdbddbaccbcbbeebddcbcccacaacddddcabbbeccabaeaedcaeacaccaceadcbeaabaaeedeeebdbbcedcedadadadccdcdedbbdacddaeacadcaceaeadabbdacbbacddececeddeeaeadccccbccaadcebcbbaaddcabacdbdebbabacdbedbeacbaacecdadeecccbaacabdcaedcbadcdccecccdccbceedececbeadeedaacaaaccbdbbbecdeecaddeeaaaaabbabaaecacbadbadbcbdcbbeaecacdbbdeddaadcddcbeecdbabcdeccabcbececbedbacbceebabbedbecaddbbadeaeccbdcaadedbcdeecbaaeaeadabdebbccdecdcdeebacaaabeddbbbdddbedacabbccabaaedabbebbaeeaadceaabeaecaccbdeacaaecbadeebdbdbaaedbeddacccbcbabebccddacddebebdaeacaeeecaedceaecddbcbebbddbbcbcaaeeacabbbbeccbedcbcabecaceeaacedacbceddaddacddaeceadccacaaabbecedbbecddedcbcacaeacedbaccccacaaaddbbdddeeecdededaadebeeabedaebebdcebbcbccbcaeacebbcbedeaeecdbaccdaebeaeadbbaceabaeaddcdabcdcbdbcdedcbbddccdcbbeabdbcbddbabdbadcadedcbeeecedaecbeacaccabacabccdbcbabbcaccbdcedcccebcaecdbddeddedececbbbbaabcaeedaebaaedcccadededbbcceddcdeccecddecbdedabacdbbacdbaebbbbecbdecddeeabedbebeebddcdacbadccbaaeecbceacaebdbcbcbdcbbcedbadcbcaadccedaabdbbdecdaebdabbedbebeaceddabdeaeaccdcbbbecbbeebddedaebdababcbeeacedcdbbddebdadedcdeabeccaaecccacbecbbbbbdbaecaadceaacddabbcceebbdeebbcceaadcdeadbcdceedbaecacdadcaaecdbbbeeedeacbbbeebeeadaeedabebebabdcaadaeccbeadeebeddbadabeddbcdcaaeadcecbbbcdbedbdabeaaccecacbabbcaedcccbcedbaaaecbdeccdebcbcbcaabdaccdaeccdecccdbbcbdddacaeceeccdeadebebdabeedcedacaecbbedaaeaeeeecdeeacabcedaebaaecbebabcdebbeacdabccabdbaccadeadbbeaccbcbbacadcddacdcebceacceedecaeabbdeabdbadaceaaaaadddbeacadbedcbcaddcdccdccaabbddebaeebceaabadbdbbbdeeccabcedaddcceccaaabebeadaececaedeaaebddecbceaabccdeedaedcadaeeedccdeccacbcecccbbaeaddedbecbcebeedbcbccdbbacdabebebeabbaaeccbedcabecdacccabdeaceebdddabbebacceecebaadbbaeadbdcaaacdceeccdeeaeebbbdaeeaecdddadabbaeddaedaaeadcbccdaedabbabbbeebccceabdcbaeabcaadebacdedbdbceaadedecadaaabebccdeccdbcdeaebdeaaedbbdceccdbdadbbbcebabcaccaeeecaadacbadeeaebdcacaeeadcbacdbeccecabedacdaadbdcdacbbedbdedccbadaecaaadbbcbaeabbdcebdeaebbccaebaebcdacccaedcbaceedeeadeeebcadacbcbdbebceabddeecceebababccdaeaeecddddcceecbeaaeeeadebdbecebbccbddeccabadccbdbdedceecadacacbaadcaebbeacbeddbccdbdadcccaeeedbabdcaeeaccddbdbacbbabbdebddaeeaaaaebdedaecdcbeedaaaedaaebcabddbdedacbeaeabbeecbecbcbadcbecaeeaacdbcbcbcedceacdbdbddacddcdcadbbaddebcbceaaacebaeebbaeedeeddaddecbedddadbeedcbcbaecacdcacebdbbbdaaacdababedcccddecabebaaadccdaaaadbaeebcebcedbadcbbbcbebbdbbcebbccedadbbadbcacbcbaaabebeccebadbbebdabdbdbaeebbdeccdbadaebecadcaebbdacddebbaeddeececeeccceabccebaadbbeadbaadccbccddebeaaadebadbecdadaebecbbbaeeadebaeaecadaebaaedeaeecbdbdecbdebaaeeaddeccbdecdababbcbabadbbcaddadcabeaedbacddaaaebbdcaecddeeddbdbdabaaaedeaaeeadddedabdbdbaeababdcebdcbbbcebcedabcddccbdedccdadebcdcdbebecacaaacdbdaaabbdaccdcdbcebabaabedeecccbbeaecadaeeaebbdabacdeeddbacaadcceccbaeaccadcbdcdbcaedaeddcabbaceeccbacdcacedcadaccbdbccedebedbdbabddabdcdcaaedceceabbeeccdbedebcabaeeaedbedadcceedeccbbadccbbddbaeeeeddeaccebebdebadbecdcbadbabcccabaadecadeebdcdbebcaeeddbdbdceddbccacedcbaddacaabeebadbccecaeccdebdadaadebabceabeaadedacacebdebaebdedcdddababddedadccdaaebcbaedaaedcdcbaedcbbdcecadebbdbcebdddbccddeaeadeaeacabbdcdebaeccecadbaeebebcccdcdeabbdedceedbededccccadcbcdabbdeccabbcaecabdebaedbacbeddbdeedaaaaddcbdeaaedecdcadbbcecbbcbbdedabdaacabeadabaaeceadaeddebbdcaabbdebdcdbdcbbeaaeeecbeecddbaabdeccbaacbcaecccecbdaebedaabbcabdbbaadadedbcbbbacbbcdaedbbaddccadcdeecbeccbeddbdbdedcceedbcdddaaddcdcbcabaabeebbccbcaceabecdddbbaedeaeecdcdbdbcdbdadccdeebaeebaeecceddcbdaeccdceacaccadacecaddbeeeadaacacbbadebcadaddcbcbaeddcaeeeddebdaedccddcddeeaaaddaedbabadebaccacbeeaeaccbbdeccccadcaabbaddeebcecdecabaaeccbbcdacacbdadddbdadbcabbaabcdcedcdbaadeebcbeeaebedaecbcebaeceaabcaedaeaeaebacaadcedcddcbeedcacdecbcbcaedbeccdbaedcacbedacabcdeeddccceeaebeabcbeddbcccabeedccbbadcecbedbaeeebbdecacadbadcceabdbebdbedbdbacddadeeaaacdaaaebceaaacebadbaacdeaccbbdacdaadaceaeceebdcdacbabaddbcaeddeabdcccbedeabddcebcdcceaedacadbcdabbdaddcbbbadeeebaceabeeeeabcebeacdceccbbedebadbdeeabddbcdcabdbadedccbbbdbcedbcaebdedeaaabecaadedadcbaddcdeaaaabedcceaacbcdcaecbebdabbaaeeccbaaaddedceddadccccdacbaedcdebdbbdbbcbcaaaeaaeddabdabeeccdccacbeabbcbbdceeacbebabddbdbdebeebbcbcaeaacbceebbaeadeebeeebceeceecededbddbeaeebceceecccadebeaccdddcdaadbeddaadeecebdbbaccecccdedaceccddecdececaeabcbbdbcdaebaabdeddcebbdebbccddcdcdcbebddbcaccdeebbaaeeadddcbedaceedbaeddaebecedecbbbbbddbeaedaedbbbdbaaccebbabeaeccbaacaedaddecadbdaecbdcdebdbcaebbdcbccbbdbcdcaaedeedaceebdbabbbcaeeaaabccaeaecebddeeabaecdadbaeddaecdbdaabaeecacbdeebcbcbabeedededdacdbecedeebdedddcdddbddacbddabbdaaedbbbccbbdbeabccadcaeaecadaedbacdaaebbaacccadbdaebbcdddaecdcaecacdebccccbbdbecedbbedbededbadcccdaabbadaeaadeceecadccdaaadacebdedceecacacedbdabdeebbbeaebbeeacdbcedcbdbbedeeacdaddbddaeaebbcbebeaecdeabacaaabbeacadccedccabadccdecaddebeaacbcbeeceebadecadbdcadaedcbbeccebddcbeaacdbcbcedbabacbedeadbacabaadadcedecccebbebceacceceeddbccecaeaddacecdbdbadbddeadccdacbababeabcddaeadccbeccbccaeaeeaeacdaeadbeacdeeaadacdaeecdacaddabddccdedeebcceddbaddbdeacadaeecddeddaaaccdebcdbecaddecdcbadaadcebdcdaddaeaaeebacddeecabbbcadaddbdecceeabdcebacadadccbcdbeedcceeedddabddebbedabdbbcbabedbaebcaebeabbebecaecbbacedeeacdbcaaedcaccacebdcdecbedebbbdabbcaecacbaeaddcdcbbddcedbddaecbcbabbacbceeedcdcbaececebabbcccccaddbdaedabbaaddddccbebcbeebeeccecadeecaceecceeaabdcbeeaeeadddeeeeaceeaabdbacbebbadaeddbcaacbeadcdadecaccdedadcbcdaeabdaeaccbbbdcbbcddabdaedcddcccacadaabeaadcdaaaddbeebdbacbeecebcdccadeaaacbcccbcadaabadececeabddeacadecccabdbebacabbebdbddebdccebabcccecadccaaadcbbbccddaebbdeeacccaedaccaaeeddceebcbceaedecdbeaeecbdbadcaecbdaaccebcbdaabbccedbbccacedecbccaaedbaadebbbbbcdadebcadcbacddadbdbdbceeadacccddaccbdcbbcaacdaebadaaccdacabbabccecaaecdccdccdedaebbdeedadebbbdcadeeddacbbbdabccbacaeaaddeeabaaabdbbeeceeadbcaacbeedacbeecbbccdedeedbabaeedaaedecdbaadbdceecaaeceadecceabdeeceaabbdddebbceabbdcedebbaebcacadbaebbbdaccbbadbcbdaaebdbdccceecadbccdacbebaecbcacacbedddeadecbbbcbebddccecbaacddcdececcebcaeabdaeadeccaeaeeeddbaddaecbdbeacebbeacabedeecbaeebcadedeebdcdbcbccbeaabddbadaddeddbdcceadebaeacbebabaabbebcedbebcedacdeacacbcbeceeeccdebaecdcaadcccdecebdecceabedebeedadadeeeaaebcbdaebbbdcaaccdaeeceaccdeceeccaaceacddbdcdbdbabceeacddeecdbdaecbabeeecbdccbeaadcdebecbabdadecddaebecddcadaacedeabdddcbbdeaeecceadbbcbabdcabacdcbbeebaecccabcaaceadabbdbedaeedabecaaaddacccedebdcdcaebccbbbdeedbeaeaeacaaccaddeebcebdbcaadaabdccdedaccbebccacbbacbccbecedcddbadeddcbebbacdddaebbbbbccbebdcaeebeacddeabeaccbceceeaaeaaeadedaeecebabeacacddceaddcdbddcdadeddbedddcbbededbcababebaedabbeaabdaacbeaaebeeacedbaadccbcadbdbacccbbcddbcdcabccecacedbadbeababeddcddcbbeaddeadaacbcbaebbbabacbaebdebdedabbececdedbeabeeeeeccaababddccabcabbaaddaadbdaebddacdadadadcabecbaebbadedaabeacaceeecaadceeddedceceebddedaabeabbedceabbcadbeedecedabdaaeecdedabedacecddaccccdedbebbeedabdcacbeebaebedddabbadcbcdbcbdaedceaddeddeabcceaacacadebbcbadeddbaedadcacdaaaddcadcebcbbdedbcabdabdacebeebadcbdacadedbcbbcacdabbbedaadacebbbdaeebccdcabbedaaeeeacccbbdeacaebadaadbbdabdacbdabeccacbabadbbacdabdcaccbdadaacedeecaaecdbeecbebadcacabceadceccdecdbcbdcceeeaeaeaaedccebdaadedbadcbcbbdbcccbdecadaaaccdeadeeddebadeadcedabaaaaddbeddacbdeddabcdeadcabdcbeccbcadcadedeedbeccdcdbbebdeacbadabcbeaaccaaeeeceaccbeadddbadddaecddecebcaecebdacabedcabecceabecedaacadaeecdbccabebcdadcaaaebddaabbbebaaaacababdbceeecddbdddbdeccbbbbbeeaedacbbaaeedccbdaebbaeecaebebaecaddbcccdaabbdcceeadecbcdaaccdcdaecccdcaaaddcbcabedbacccbbdddbdddbedcedcdccadcdcbecaabeceeadaaacdcbcaaeceadbabdbcbdedddabcbebcbdecbddadaebdaaedeaecacdddcbddccbbbaaedabdebccaeeadeeacccedbdbddbdeadceaadbdbadecdbbabbbdbcdedeaebbabeddcdcdeedababaceebdedaaebdebecceebeaebbedbceabcaceadacdcdccebeebcbabbdddaadbdceaeadebecbbeddecddeddecaeaedaabcaddbedeaedadaccbbcdcbacecdbebcadeecaddaceabdedacaadccadcccaaaaeddeadbabcecadeccabcbeadcdaeebaebbaadddceaecedcacdadbcdeddacceebcbabbcbeeabbabcbabeeecdbcdecdceededceddbbdddeceebccecadbbdcebcaebbccbcbadaaedddbbecbaeadeebadbccbaddaeedeecbceedcbdbbddaccadddaabbbadceadbcaecedcebeecbcadbebbbeedceadcccaddcadaaadcbdbdbaddbccbbbbbecedecdaaaababeddcedcadeddebccccceedabcbaeaabeeddadebcbcecceeecdadceecebedebccaccdaaaebcbabbabddbdbdabebeaabaebdbaacccbebebaccccccbaadbdceadaedbccadebeaadadeadaeedbbcaacbaedabeeabbbcddeeecacdecdeaeeecebcbaadeeccbcdaceadabeeedddbecebdcbceddacdacbeaddebebdaaebbdaacbdecdddacddcdbeeecbbbcdebbcaeccedacdabbecccddbbbedeaedadcbaadcbdbabecbacccedeaababdeeedbcddddaeadbccabdceabaabadcabcabbdbbcdbedebadeaecaeebecddbaeabeabedceeeeddcdbaddacbdeaeeaaedbeaeecabcbebbccddbddbadaaeaaaeecbdbbeaaeeeacdcccbeaadaaeddbacecbdaecddbbacbdeedbddabaaacecebddccedbbbaadecaeeddceceececeddedbbdeedadabcecdecdccaeedbaeeeceeceaaebedcabcbcbcebdbcddbecabdeaddbbcdaaebeadadecbdbececcbdccdbcccccdcadaeebaadabaaedcabbbdedeaacdacdecbdbedcbcebbedabbcbedccbeedebbabadcaebecabddbcbcbcdbeccbedbdaeaeebeecaaabddecaedbecbdbbcdedbdccdddcccabababcebeebbbcabbdecabdabeadacecdabccdaacceabbbabcdbcdacbdecebebeaecdcdedcdbceaaaeceabdecdacecbaaeaaccadbddbedebeaceaacdbdeeddabebbbecbddacbaadedcdddaecdcdaeeaaeebabbcdecabcdcbacbaebdbecdeacbeedeaeadeaececaaccbaaeebdababceabebecadcbeccebedcbaccdecdebbeababdcdbebdbcaaebceedebaccdceccabdadedcaedcecceacccaadcdcbbceadbecababdcbcaabcedccbbbaaedbdaeccdccbebeaececeadcbbbdbdeeecedbacccebdcdeaebaebaaaeabedaeeadcccebcdaedcbceebeacdecaedbddbabdcddaadbcaedeeaadeeddaabbdeeaeeabcbaadddadbbceacbeaabdcbbcbbedebaecbbbbbcbccdeebdeaceaebcaacebcbadcdaeadbeccacbebccbbcbabbaabaceddeeecbbceccaceeecbcceccddaeeccabccdbeddcacbabeceadeeeaabdadccceebbeaedecacbddcddeaadceddddadedcdcdeeaeddaccacaabecccaeaeaebbdbbedeaccaeeaaaddbcabbbedecadcaebbdedccaccdedaabcceeaaaecccbbeababeecacbcbadbbdbadbbbabcdeeeedbbeadceeddbaedeeacbccbdeacdaadcbbaeaebdcedbedaaacdcddcdbbdbedaacebaacebecddadbceaaacbaecaddbebdecdaceadcddbecdeeabacdaebbbababbbeeebdaaaaecdedeeccddcebecbeaadbecaacdeedddcbdcabdbebbbaecdbbeaeedcabccdaaebcccbeaabcccbbdecdabeabbbbbbacaaeaedccaaacaeabddadcaadbcebbbbcbebabebaeddbabababdaeecbdceceaeaccbceedabdaeeebdacdcabcdbddadddadbaaecccddebabdcaacdddbecdbbeddebedbaabbcaebdaacecedacddbbdbcbaabbbaaccbdecbaebacdedaacabdabeaebdacdabaceddebdceaddbecbdcdbabcbbbceabedaeebdeabdcbcaccdaacbbeedcccadbbceccacbbeaaccaadcbbbdededbcbcdecaeccbecdeccccaacadcdaacbedbbddeddbaeadbedaadcaedecbeeebeccadedbbedabdeacebadeeaeadebbabbdceadbbbbadaebbacacabccdddbcbbccbecbccbdaebcaacaaeaeabeaebaddaebbeaedbccadcbccaecaccacddecbdabeddbbecdddcbeecdddedeabbcceabdebdbddaaedaeeebbaadbcbeacccaeeaddcbbeaeabadacbcddbeedccdaccedeebccabcdccedbbeeedabaecceddaccccabdccaccedbeeebcbdcdadadceccedbcaaaedeacecaeaecbaacabbbbadaeddbcebdedbecbcdcbebeabcaddedcbcceebbcdcbdeaedcbccdeecbeccaebedebcecadecddcadaaeaddaeeeeeaaeedebeeadbedddcdeeabbbaeeaddacacbacceccdbbdcedbbececbecaddceabdebbbbdccaedceebddbddcccbabedddebacceaebdcebdbaddabcedeeeaebcedbeabbbcbeaadcceccbcdeecbabbaccccbabdbacdcecaabbdeddcaaebeadbeeabdaabaedcbcccdceabdddddaddeeadbaadaddecdcacdceddaadabeaccaccaadacceddececaceddcedddccbacbecbebedbdadeacceaebabdcdcbebcccdceaecacaabddedeedcebcadcdcaecbabeeaaeceddcbdadecdedaeddbbccddebaceabaebeaedcabddcdbcedccababccdebaeeddcbebcaacdaedaccbadbecadbebbdbadbabcddcacdaeddedbbdbbebbedeeadecbbabbdbaeabbebbcdececdcabedebaabebdebbbeacdabeceabeedecbcdebaeeccddcdcadceddbaecbeecaaacaccdaeecaedeeaeceecdaaacbeaeaeabcacbdeccacbbebbbbabbcddbecdbaecadecdaebbedbbdaccdebeddeecbdceabbbebcaeeaeeeaccbcecebdecedaaebeacdbccbcbbcacaceeeebcbdeddbcddeeadceceebbdbadeaebdbdccbedabeabceebeddabaaccbeaaebacededbdebabebbdaadeebedccdaecbeebebeeabbebeeaedaacebbeacceeecacabdecaeddaedaebdbaebcbaebeadacecccdebaabbcaabbdcdbdabcccdabbedadeccdceaacaccadeeedaebabcdeeeaecaaacebbabaaebeaeeccbbebcdcebbebeabcbbcbeedcebcccbbccbabadbbeaeebabbcaceddaaecebbebacbceeadeecaeecebbacecbabcedecdcdabcdeaddbddaaeeaaadcdcbebdccebcccddadcdcaebdebeaddddaacddbbebbeeeeedecaacbaddbcbebcddcddddaccbcaddeaaeedbdbcbdebadaecbeaeedcecdcddddadeeadbabacbdaedbddadcebdeaccdeccbeacbeebdecbeddcebdebdccebacdaababdecdeabaecdcdbcaceebdaabddebdbcbbaddcccadbacddcdbeedeaddbebbeebbcbedbbddcbcdaadcdaadbbaeddbaccbebeccbebcbddceeaedbbdbaecdcddedeabcccabddebaddbbbdbcacaaedceaacedeadbbddaeeecabddedebedeaeebcbcabcbbbddeceeabaaadadcbacadbcbccccbdeeaadbedceacdbceabadceaacdcbcabaddcbacededbabbdbbceeeedcbabcadaaeedbdabdceecdcdecedddeddbccdcbaedeabebcbbbcdabdeaeaabeddcacdaecdabdabdeccdbdcccaeceeaaecccecdbdeabecddcbdbecacddebdbadebbadedbccbcebdccdaeecbeccbacadcbebeeabcbcddbdbddeedcdeebbecdaeedaedddcadbeedbccdececdbbaaedecacbcdecaacbdaacaeeeaeeabcbcbabedacaaadedcecaaedbdbedbaecdceabdbadbdcccdbdeececdbadeaacdceccccddabaecbbeceaadbaaaaeeeaeebabcbbeddeebcecbeccddbaadcddcaeaeaaccdcdbbbccddddccbaeebeaddbedaeacdecccbcccaebcdadaebedccbdebbeeddaecbeeaddebcedaebbebbabcacddedcbeeeeaaadadeaeebeaccbdebeaccdeeadccbdcdcbececdbaecadbeeaeaaabcdceeccbdedddbbedbecaeedaacccaebddbadacedaaaccddacaeacedcabbbdeccadeebbdabbcedcdabaacabeaaadecdeddaedcaeeecbaccdbdecdcbcbaebbecdadbddababaadaedaacbcaccaaccbeebdedccebedaaacedbdacbdbccdcaccebbcbaeaaacdddcbbaeaceaabbdbbbbcdbaaedbeabbabedabdeeddecedcbcdbeeaedadecaadeccbdeabcddbeaabddaeeaccebecceadacabedadcbadcdaebeddbeeeddbbedeecaedccbcdccccbbaaacbacbeccbbadccdabccabcebdbdaebcebcededcdeeeccadcaaccadabcecbaabdaceebcaadcaaeaddccaaabacbecedceabccdaebaacdccbeadadcbaabecaedcacbeddecabdacabbebaadbeccbeceeebbecdadedbcaaceceecdeeeedbbcbdbabacccccdaccdaecccebcabbedabaedbbbdecabbcbabcbcbbadbdceceacadcbebaeaacbcdecdcccebdeaecaabecbeeadbeccabcbdbacbddabcdabedcaeaeaedcaeeaebccdaadcbdecdeccecaadeabaadcebbbbccccecccdbabdacbeabddbccecceaaccdeaabecdadeecddccaccbceddddebbbdbdeeeaebeadbaedaadddacdccdedbdccdecccddeadadcadbdacdbdcbbdcadcdabceeceecadbbdaacdebbdeceaacdbeaceaceabbebcadacadeaaeaddaddcbacdbabacdaebdabaeecdbbcedeaecbbcdedeedaaddcecadccababeaaacbdadabaecacbbaeecaedacdabaedbbaabddcdecbeaadabeecedbdebeadeaeebcceaebccccabdcccceebeebdeccbeebabeedcccbaddabedcebbbbbcadeeaceeecaceaecdbcabcabcdcbaadebbcddbbebccbebcdacdaacddaaadbbcccdaebdcaacdeaecbedaadcadcdbaaabebaebdeabbedacdecabaccbedbdeccadcdcedbaabbbeecabbbcabebcbbbadbbaeebdeabbaeebacdeccedaddbccbdbbdbedebebdecbbaebbbaccdaebadccadedaaedbdddbaecceeeabebcacaadbbbbccdccdbeebcececeadabdcbadbdbcbceedcaeeaaeadadacbebabcdebdbeceeebccbbcdcdcbadebbebeccedbedebdeabbcdcabaddcaaecbcccedbbbddbaedabaadcdaccabaeebbbcedaacdbebbedcdeeaecdcecdaedacedbddddcedaaaedaabbbbbdaaddbaddecdcedecaecdebeebdbdbdeebccdccbbcaadbececeedceededbcaaadddadacedbbcdededccaedaedabdaeaaeadbccaeeceaaebdaaddcdececadcdbcceeabcbceddedaaddacbbadbadadaacdddbdceabeddabcbbebeceaedecadeaebdeecabccacddceeebbceaebdbdbcbdedeadbdeddceecaceeabccbbddceeaebdbebededbbacdaeceadbbaaaedccaeeeedcadcbedabeaddaaaaaeaaddacacdccdeddbdbecdeadbdacbcbaebecdbcabcbcdeaabdbcecabdecdbdeaccecdeecdcadceeaadeadacaebcaadbbdeaeaababbdacebbcccddbdeaebeadaaabddbeaebbeecccbaebdbeedbbceabeaecbecacaddeccccdbbeaeceddaaacbabadcabcbaaedcbebabddaeebbdbedebabdcabacecbaeddecebbedbbbcebbccdabdcbaadbaeabdcceedbddecdbcdacaebdbadcebdbeecdedcdcacccaaaeeccccaceddcdadcdcccdcebeeadbdaebdbaaacdcabcaedebbaeeadbaeeeeaeaebcaddebcdebbcbbbecdbeebccdbecbacbdcacdecaaaebdedcccdbdeddacbbcbadbbedbdecccdcacaaeaebbacdeecbeddbeaecceecabeaccdbdabbbbddcbeeceaebcceeccecbdecbbebddbedacccbdcabeabecdadecacadcecdeadbcabadecaabbeaacacddeabadcaeabaddbdbecdacbacedcabecacadbdaddeaedbbceecedecaecbebdebecbbedaddcaeeabeedbdcdddabadabceceeaddabcdebdadebddbeeaaedabcdaccccaddeabeacaaecbdbacbecbbebddecdeccbcadeeadbeddddccbdccdeeeddbeddacecdebbbddbeeabecdceaebbeeccaddaddbaaacadbeabaedbdadeacbadabaaaeebdcceebcddeeabbedbabceeeddaceedcaddcbabecabcacaacabbdbabcdcaedccbcddcabcbecdaedbdecabceccdaeaaeeadebeaeaeeceaebabdbacbcdeacebddbcedebbcdabeabdaabbcaebadacaccddadebeadedcacabbaabedeeccedadcdddecaaedeeeadccaacacecaaeadeadccaecedaebaebaaacdcbbaedeaeaadeddbecbccbecedeebbbbceadeebacaaddebadacabaaeeeaeedebbeecabbaacccdaabdabebabeabcaececebaebbcbcdacabedbaacaeebcdbbebadaeaecbcbaeedeacaaeccebcbbedccdbdebbacaadbadebaadcedcecaabdadbccbbcbbecdbdaccbeeaccbbbcceccabdcecbccebdbdbedcddcadbbaaeebbacbacaddddcacddbebbeceddaaaedacaedbdebacebadecebbcddaeacbbcbcceaeadeaaaeeccebedbddeecaaddcedadcaeaeddbbdacabadaaddaebcebaabddeedcacdccddaadcaaaecbbeaabbdbcdceacbceaedbbbbcccbbeaadeecacbdacdccbcdbadebbbcbcdcddacccacacbeaedcecaebccabbadeadddbdedaccdbedbecaeebeadbedcddabcccdaabcceaeecccdcbdabbaeaeeeaeadaabeccdccbbbdaabbabbabdbecaecaeecccceedebbcddcbeaacabadceddcbabbbcdcacbedecdabcbccbddbdadaaeaddbeeeeecdeaedcebbacaaccceccbbcbdaeeeeeadcbaadcaeaaeedcecdbdccccabccdbbedcdbaebaaddddcbaaaacddbddaddbcdddcebcbbbdedeedebabddbcbcbaddbcdbcababaaaaaeecddbbaaeaeaebbadaebcabcabadeedbaedceebbcbdeaaceabedcaecaaecdeadbbdaaaedddecbccbbbadddcbeeaadeecebabaedcdbbaeedcabbabbdcbecbcecabdcedecaabcabdcbbaddcabbdcecdbabdbdcccbebbcbbbbabbccbcadecebdebddcadeceaeddecbadedddbcdbeaadeeddcceaadeaccadedcdaedeaddedceabcaebdcedddecccdacaaecabbbaedaecddadcdadbccacbaddbeaacbeaaaadaadbbdbccaeebddcdddeeaacccbccdecaedcadeeacaecdaaecddcbbacccbccecdabbabbedecbcadcebecbcccbccbcaedccacecdacdbcacebcceecaddbbdbcbbecebacadbcddbdddcbdaedabaaabeccdaabedbdddadabcccadcedabaeeccaaaacbbaedddaebccbcdcaebbadabccaecedbbbacebdbcdebbececcedecdbbddcbadbbdbdeebeecadecbceacabccadaecedebedbdcddeadedcedaadaeebbeebbeccbbaaadcacbddcaadebeaeaecbcbddeceaeaeabbbcaaeaebedcccbeccaeecebcbdaedebcddbbbbcdaeabdaeceeebdcaddbbdedaaeedaecddeecadcaacdcabadabebccddbbaacbcadbaacbeaeebeacdeabeaecdedbbcceeaedcaeaaebeaababcaaeeecdbaebceccbaeecabcdaddecdbcbbabdecdedcdaeddddbbebddbeeadaababdcbeaccbeebbbbedbecdaecdcdaababbcccaacabbeedddedaececdbaecadcbedeccbcdcdabdadeaaccddcbcbcdbcccaeedeceebbaddcdbcedbdacdddaddceeaabadadeedcbacedeeccbacbecbddbdedccbabcbceccdedbeebebcecdceaedaddacbcabbbcecdeaaaacdcddcddbadbaecaceeddeebbdcacaecbeeaacecaeaadeeacdddecababcbbedbadcadaeaeebabdaddbacdacdecccdececcabaeeaebeecdcaebbbbeecaceddedbbadececdbcbcacdaaaaceaadececbcedbecdebcaecbaddbbacccbabebbaadceeadaccbadbadcbadebedaabebbcbdeecbaadcdbdeaeeacadcabeadaeacedcebeceecdbbcaaebdedcabddbbeaeaccebeabbbdeeadeeebbedaeaabeaaaebdcadcbacabccbcaecdacdcbcdedbbeecbeaacbbdccccdeaedadbddcedbbbbcdeeddaacdcabbeeeedebabbbcbbccdcebbecaecdbcecbbcdadecdedcbedbcbeacdbcdbaababaaeaaaedcddcadbeaebdcdeabaaabedbccddeaebbcdaacdbacabaeebcddceecdcadadabddcbdbbdbdaaaabcbedddedbcddcecdccdaddbaebedddceccbecaeacacebbbaadacdadecacceccbaddcdcaedcaeceadeccaeddabdeacbdeaadddcddacedbacdebdccdcbdaaaebcbebcacbdedcbaedcbeeaeddecbaeccacbbadbbbbececddbecdebbbccddbbbdaabadebcebcdcacabebaaddcebdeaabddaadabecbbdadebcdebccdaebcdcbcabaedcddeecccdceaabdceadccdabedeecdeadcebbebaebecddbdbcecdaecabdabbeccdbdaeadaebddddeedecaeadbadcaadcddaedbdabaebebacabeddcbaaedeeacbcbdeadaebecccdaeeaeeaacbadbdeeaddabaaabbbedeeebbbddadbecbeddebdccabaedcacbcecbedeaeedadeebcaeeaddedaedbadeadacebeabbcdbcdcccdbcacdadeaedeadaeeccecbbcbdcdbaccdbaadccaeebabdedccbedaaccedabdcdbebbbcdbbcaceeebebeababbcbaaddbbcebbacdcbeaaddcebdebbeaedbbeaddcabeaddaabddbdccbaadeadabcaadbdddeedabbceeadebbbcdbeebbcdebebabacecbdaadebdbaeacedadebdedbbebeeacccdddcbbedabecadedebdcbaeebcaccecbebdacceaebaaccadcdcbcdddcabbaccabeabadcdbeabaecdebebccdaaedebeeabbaecbccdeabcaaeaaeceaddaeaacbedeaeeceadbbbdebedebaadadcabdbcccbadddddedcebbcaeccadedebbbadddcacdebeeabeacbcacedaeccbbcdddebbdcaddaeaacbbaddddadacaacbdeddaedceddbebdadcddbedeeceabbeabbbcaecdeedaecbbcccbecedaeeceaebabdedebdeebdeaadecedaccbadbcbdcdaedcbeebadceaddebbdccecbdbebbaeeacdacbcddbcecacddccddecceadbbacccaecaeaaebbabebbeeabdbceeeebabdccbabaaedcecdecdaadcacbeedeccebaddcdddecbcacacdebbaecaecbccaebcbbbbcdbbcaedddddaebddeaabdbbcaadbededeebbaebacaabcedcaaadebcddabeddaaacdcacabbcadbbbdbaccdcdeadcaccbebceaacebaccdbedebceabebbbdddcdcccaeecbaacdcbcbeaaedddddacadbaeebbbbeeebacdaaceedcdcaeabaceabbdcedbaacbcdcabedcbbbeecbeaaacaaecebdcbcdabdbddbecedecceaacedcbcdcccdcdaedddaedaeacddccddbaecbddacbeceadacbcccbcdceaaaeccabaddaebceabbddecedbaeeaebbddbcccaeaabeebadeeceecaeeeeebbcbabddcbebeeaaedeadcdcbacecddcdebdadeecbabceaadcdaaebedbcdddeceacbebbbbcbacebcadebadeeebdcceddebabccbdddcdbccdabdcbbaeadbeaaebdbcaeccbbcdebcbbbbabdbdcaedbbbecdcdbaccacddacdeadededecebabbbbcebcecdbabbcdabaaddddcdbeadcdcaccaacbebccdebaaeaadcecaeccceccebaeabbededaebadabdadcceadebadaaeeedaabdccbbabbeaecdabdaadaaaeeebdebeabcceaeebacbcbabcceadbcbccbdaabdddcacaccbacacedccecccecbdecbddbdbcdaaccaccddedbeedcbcdcbbadddacbdbdbbebadceeacecadcccabceabdcbdddabecebedeeacbcbbaabaabcbceceedbccaecbaaadbbaebccabaebaceaaecbbdcdabcaacbcbdbdbabccdccbcaecdedeaaeabdbcddbcbbeddbeaaaaadeecbcedbdebdacccaaaaeaebeaccbdcebbbeebcaaebabbcdcccebbecebaceadbeabeaaedccdcdedaeccbcabbcecbeaebbdcaacedddddebadddeeebabdaeccdddebbcaeeeedecceebebbbbeccebcceddeecabeacaabacaaaddedeadaceaccddeddceeaacddadcadcbebcdecedcbcdbceedacbbecaeebcecdccdeceaadeebceabcbdcdcbbeabcdadeadddcddbbecccebebdbedecccdeeabdeaceebcbdccadcdacdbccecdcebebbddcaaeccdacaacdadabdaaccdeaccccbbbceeaddeaeacabeabcaaaedcaeedcaabbbbadeddecacbdbeeaabdcdbdceacbbccccbdddabaadeebeeddadebabcbbacdbcbbdbdcddddbcbeaccaacebabbbeadbdaeeddecbcbdcbebcbbabaeacdcaeebddbbeebbccdbbdbbeeaacdbbbeacbdbdeeeebbabebeceeecacbbcadbbddebdcebdbebeadedacadcbadebcbadaedccaeecaaddabeccaecaddccdeecbcbdacdeaadccacddadeabaeebebadbbebacdbcabedadabcecdebebadaebbbdddebdaaececacddacdedbdddadabdacdccecaadcdabbebceeaeabbbabeccccaedaebbabaddeadbdadcaeaabacdbbdaebeeaeacdbbeaecaddadabedcdaceaddeaecbecbbdbaaadadbcebecbaeebeedddcdcbaaaaddaebabbebabbccadbabbedcecacddaeadecadcaedbebabdaaaccacdaeedcededcbdeaaebdbeddbabeeededdccdccecdcccceeddcbbbdaecabcbeedcdabdadedbebeedccacddbadabbbcecccbbaddcebaddcbeebadebbbcdbedacdbeceabebbdbcdaddcdaeacedaaadacbcebdacbdacdecacabcebeeeacebdccbbdbdcaecdddceddbaabaacadcbcdbcceddcdcceddbebeebceecabbebcadcdcdbcadebaeddcbeddcdbcadbebcabeeabecabbabcdecbacabddbbdebaaaadaddcbcabccdadbaaecdcbaeadbbebdecabeeabdacdcdacaebabeabccaaabaedddcbebadacdadeddbdabaedcacbcdcbedabdadbdbabbeebbedbebabeddcacecaaaabdcbeeacceccdcaedcceeedadebbedbedaeaecbcbdbcaacddcddcdecdbcbbceccaedaedcebebcebbdbdcaaecdedaddbdbcacdcaabecacdbeecdadeacbecedcbabcaabcbdcccdceddedecdbcdbadeeaeaaccdeddeacccdaeaeabeaabdadccacdaddcebaedaabaddceecdeddbdbcaceeaaaaabaaaaccecddeedebdbcadbdbcbbeddcbdaaaeabbbcedbdbacecdaaebbddaddecadeeadedbebedbaaebabcacccceeecacbbccaaacaeabedccbcabcebdeabdbcccbccbbaebeacaeaeacbaaadaeccdacedbaedddddaeacbceeedacccdcbdeccacdaedeadbeacbdbbcbbcebeeacedcbcecaeeedebbbccacaeccdaaacbbebaebdaebceaabeecababebdacacdcaabcaaadeebddaabdadcbccdcadceebcdcaebbadacccdecdbebeacaabaaeddacdabedbddbbbdbbddccceaebcbaccbcaadcedeaaddbdeacdeeddabdbbadebcecddbaddbbdcbeeeecedaceeacdbddaabecbcecadbcceeaeedecdddccbbcccedebdbbcaccacdaccdbabbaaebeededdaeaeebcdcedcdcdbbbdacdbbceceecbaaacedcddbaedadcbcadabeecdcbbdbbbdaebcbedcaceaedbbcdceabdabcccacbaeabdabadcdaaccecbddaecaaadeeddaceddcbddbcbbccdcdcacaaaededbbbcaedbeeedeaeebabcbeeedbbbbaeecabddddaeeddbeeebedebdeddcbcabaabccaacabbaadbacecdeadcbbccbbdcacccadcbbdeaeccadcbcdbcdadaaaabecdeaaeeeabeeecdcbdddececaeaecdbaadbcabaedebecbdeaaaadcebaebedaabeaadbdbadcbbedacaabbaaeedbabaaceaeabbaaabaeadddbabceebacddbcaaaddecbdcbbbbcdcdaedadcececcdeceaecdbedbeecebcadeddeadcbacecaccbbbeeeadccdbccaedaaddccbcebedeabaecdbdcdedbdcdedccecdabbcbaabbaabdaeeaaeedbaeaddabbedbbdcacebbdaabdabddabdeabcdeecbeebabdedbbbddeaceeddbeecaddaccebbbaedbadababdceceecdedceccaebbabbbaeaaeddccbeeaecbcbebcaeacadedeecbdbaecaacdddbaaeeadccabebbdbecbbccaebcedaecdbadeabadddadeeaadbececceaabcddacbdededacbcaedddacbcaaaececaaadcddabebeaadeaddcbdedeecdccebbcaeacdbbeacdcbcbeeebabcdcdeadaaecaedcdbeeaabaecbababebbcaeecabbedbaccbabdeedeeaeaeecebbabdeaeecaaeebdebedbdacedacdabbbcdbabacacdebdbdcaadaedbaaaabaecdebcebddcadcadeacebbcaaddbbceacbceadebcdccabbbdceedbdadacecdbeedbdaccbeaaabeaedcbcecabaabeabddadbaccbceecacdeacbcccbcecccdabccaeaceedbbadbcdeabebbdbeeccabedadcccbdabcbbebcaedaadeeceeeacaaaceedbecdcbbeacedcbecdeeeaaabdabcacacbacaeecebaeeebcbbbbbdebbadbaabddbdcbcdcbcadcedecccdcedbdabaaecdcedeeaadcbacebdbacbedecbaeebacbacbcbdcaaaaeceeababcaceadcbaaabacbbecbbacbbcbcdeadbeceddbedbbeebedcdacdcedeebabedceedbababeebcacadcadcacaeaddcacdbceeeadbbceadbcaeaecceaebeccbdeeacdcbaeecdceddbcececaadecdeadebdacdbaabdaadeacebadcdbcccaacbeededaeacacaaaaeedebcdedbbcabbacebacaabbebcccbeecedbcdeaaabeddbddeeceedcacabdbcbecdecedebeeccebcdaccdaadeaabdadebebaedacaabbbcedaececbdceededabbeebedbdacdeacbdeeaaccdadcddcadcecccabedeebabcaedbecababbcdabeaaddeecabaceabccecedababaededaaeebcddeeaccbdeadbcedabdcdeecabbaabaecdedebddddddacbeedbedcaeaaceeddaebdaeccddabcdcecbccbceadbdbeacdbebbcddebcdedbdbeaaacaadbbdebeaaccdeaaaeedceabeaacccbeeeebdaebecdadcbadbdbdcaebcdddaaeacdabbbdedaedabccccdbacadebaeaadeaeeccbacbdbcdacdeebcdeeceeabacdbacbbbaeceabddaaedeebbbdeedadabdaaebdbabdcceddebbaabbdcebbbaeadadcbbdcdbedaeaceeedadceaadbcbdcdcaacbdbacdeaeccadbdddcdbaccdeaaaabaaebebbdcceeaabceaaadaaedecaddcaaedccdeeeeadacaebbdedecdabddcacecabadabcdcdcdcebabddaadddcbabadbcaedbbebebebeeabaeebcaeabdacdbebbbecedbcaceebaeadcaadcbecddbbddcbeaaebdebbbdcbdbeabadbbdccababbccaeeebdebaedcceebabdabeaedabcdebecbceebbaebeadeedaaaceaddcadebddcaaacdbdbacebdcaebeceadabdddbacccdeeecacaccbeacdecaebdcedecbbcdcdbabbeeebecdbeaaecbeeccbeadacccbaabaaaabccbdbcadddacddeeecbeccecacbbeaeedbedaabbbdaebeeecadcdcbdbeebebecaaacaeadabedaeaacccbdedbccbbccddadaddabcbaaacecdeccacdcbaecedeceadcddeecaadaececdeadadeabaaecbaabcabaabcbbeeccabeaaaaeaedcbeadedddeeebbabcbcacbcdaabccdabdcbaccadcacbccadeeaaadcccddeeaabbdeaebedbdeddeacbceeeebdcaddaebcadddaaecbdcdbdeedeabaabcbdcdbceacbeecececaebbebccabeebcdbbebbeccbdcacbcceceaaacbabacdbbceebaecaeeacdabedddaddedddeaadbaadebdabdbacccccadceccbaebaeebaebabdadacdabcbebccecaaedacbecabeeeaebeabacbaaeccaabaacebebeacdaaacbcbdabeaecebdacbabdeeeecdbebeebbdbaeebdcedabaaacaeababdcdbcdebeebaeebacedebccbeceecdbbdadbedcaedddbbcaddcadeebaaeeadcdeacdccaebecceadbecbadcbcacbbecdbceeceddddedacbdbbdececaaebbdbeddcadabcdadceebdcdcaddebcdadbbdeeebdadbdcdbdebaebeebccbbdabdbadabcceebddbcbcaaccbdaeebaeeddbbedbdeedceddeabbbacbebebececbbddcbeadaebbeadedbdadaddbabcbeeecdcdcccaddadaabcdbbababcdeeabacebadccddbaacacdcbcaecdedecadcceeebcbabeaeecbddbbbdbddcbadeccbeeaeebbeaededdecaaacaadcddbdaabecadaddecbdbbebdcbbbababdbceecbdaecebcededcceabecabedebdaacabdbdabbbceeecdbeaadeaddedbcbddbbbdbeecebabecaadceaecbbdaadaabaceeeaeebbaeebbccebaadebbbcdeccadeaacecaacaaaeabbdcacccddcdabcdcbddeedeebcabdbabdcebebebbacdcedccdedcebcdbdccecacbaadaabdbaccacddcdedadcbecaeaeadadccdaaadccbcdaaaadbddbeadcabccdcbceedcdcbbdcdabcbbdbceabbbddcabecbdddaedeebabcbbadacaeaccdacdccecdecabcedaedeceeaeebabcaedadadccbadaccebcccebadeccaadeddddaebecbbbdbadddbaeeaeaedebcccedbdbabcabebdbcaeddeaadedcebdaabbeebdccadceedaaebbcbbcccaecddaaaeacaddebeabebdaccdddaddbedbecadebcdabedaaebddeeadacaadecadebabeabbedabbaeebbddbdcccebcacbbdabdccddbaddebaebdcdececbcaaaceddabbddcbcbacaeedddedbeddcdccaeeedcaadcbbedadcdddebeaddceeeaeeeeabeacdeabeabebeebaadacecdeaacbecdbeebcbdcbcabaddbdaabdaebbaabebdbcdebdabdcbaebacccccdccecaaccaaaaeaddcadbbbecdbacbeadaecaebacbeceeaccdeddbaccebbbbeeaedbedebeccdeedbdaddbeeaabcdbdcbbecceeddbebadaabaeccadbdcedacedeaacdaacdbedbbecaddbdbcdeedcabadbdeedeecddbaeedcacdaabcdeaadebcceacacdceeeadaacebbaadbbdeadabbdbcecdbcaeaebedddaabeaabdededbeddbccbbabeeabcdcbbedcadbeeaebeacdbdaaddedabdbaeacaaccebaaaacebaacadcceacedbacacddbdadebcadacebabddbabdebcdebbeabadeddebddbebaccedeeacdebdecacebcbaaacceebabeaacddcdcaabdaeceebeeecbabacadaaebbeceeeacecedbdbdbaeabcadebbbbadebdecbcdccbecbbbaecbbcdcdaaeccbaabddabacbbabcaaebaacacbdacedcddabaeebdbdbabdcdadadcadccedbecbbcebbdcebdcecedcecbabedcbdaebaadbbaeebdeebddbadeabbeddbdcbbceeebeecbebbbedbaaaabaaabacccbaeaabbebeaaaabeacbbeccadbdbcbbdaadeaaccaaaaecadabeebacadeddeddcbbdecbadbcbaaceaebeeeadbbabebadabecdcaeebaceeddcaabbdeeeadeaaccbedcbebabdabcdecddeadbdcebdabdbacbdccaaaabeecdaedecaeeeaeebaaabaedbeebbdcebaeceebececaabcceeeeccaadaaebeaecaeebdeeecbbbccbeacddbbbbcdcddcceebcdecceabaeebececcddabbdaededbadbdcceecacdcbacbacaccccceaeeaadaaaecdecbcadddadbabdcaadeeddddbeabdcbcaabebcaddecabddbdceabdcaedebaecebdcaeeeacacabbecdbbddcccdececbddaadcccaaeaadcabcbccddeecacabedeccaecedbccabbeaaebaddbccdecbecebaceccbbaeeaddcbbbbcdcedadecaacdbaedbcedbedccadaaeceacbaeadecdeaeadbacbaadbbaedcdabbbdadcccdacbadddbeacddddcdbdadeebdcaacbbdeceadeaabcdeaceaeaaaaabaddcdcdbbcdcebadeeadabdabcaaceadaccddbdcaaabcdabdccbaeceddeceabcabedaecdecccdbcccdedabadaadbceaeeecabecedbcaccdddaacedbddcdadbdbccbbeecdabaabeebcadebadbabddbdccdceeaedcbdceedbdcdaacedceecdedddaacaadabeeeacbdbcadaddbeecdedadcbecbdababccedbeeccabbaddcbcbebbbdacedbbdbbcaacdbeabadbadabdebbabcebcddcadbeabbbdadaecdacbaeadacaebeeeeeddebdaadeabcddebababacebddbeecaaeacccabcebbebdeeeacacdebcacdccdcacbabbdaaebacbeceaddcbcbbbdadddcadebbeacbddbcbabcaedddebbcedbdaaccaddeeaabaecbcaddccbbedbaeabceacdaaaecddbdbcbcabcbdbbcbeaaedbeaaaaebadcceceeededbecbddaececcecceecadaecbdabebaadccbecdddeebeadbeedebacaddaaeecbaeaadcceccabdaecbddeeaeecceabddcdabeaadcddddadecceddccdacdcaaeecdeeeecddeecbbeaedbcbeddaeedbbedacabbaeaabeaadebbabbececdddedaeeeeaebbaeadcebeadbdbdcabcadddcbcaebedbeeeaaaaadccaeacacaebbbcbceaceaaccceebbbeecdaccaaeccbabcccdbcedeecbeabcbdebaadacaeceabcedacbeacdbdbaaaaeabbdcdadadbcddedebccddebeebbedbeebbebacabeecadbdebcadeaaabdabcdcdbbecbeeceacadcadeceaccbdbacdbdbdbcaecdadadeabadddeeeacaebaeadadeecceceeeadbdcbcaabbacdbaecbcddbcbadbaacdadcaddaeccbacecaceadbeedaaecccabbddaabdcabbcbddbcddbaacceebbacedbadcabccbdeebbbaacdaceeabbbbdaddcdabbbdbebcbbecadaaebbccbeebacaabeddecebdcacddacadecedbcdaecebdebcadacabaccebeaceaebebcdcabbbcaccdbadcecaadcbcbaeceeaeabeaacdbaeeebbaabecdabedeeeaeaaccbdcbeaecaacaacaaeeeddeaababceedcababeddadeeaaeaaecbaaeaaacccaeacaecebeecdddccceedcecadabecbebbeabbacbaccdbcaeebaedeeaecccbcdeccadccadeeebdaadcaacadbabdcdacaebeecdaebaacecddddeedccabecadddedbabdbadaebbaeaecbaaddabeebeddbaecaebcaccdcdbdaddebbbdeeecebebebbdccacdeebeceaacdcbbdaeeedcacebaaedaccecaedcadddeaeaaaeaaecdebaaaccbeecddaacebbdaabbecebaacdcbddcedbdebaddadebcabbdaabadcaeacbadddddbbedaecbebedeeacbdcabedaadebbdbceaddbbecabceabcecedeabbbcdabcedccdecddedeeddbadeeecbaaeecdddcbdbabbdebbedbedeeecacabccdcbecdbaeececeadbadcccebbbcdbeaacbbaaadddaeceabbaddedeacdcdcbdabcbdbbebbbdaadbbdcbabbdbdaebbaacddbddeecbdddebeaaadeebdedabbbbcaddaebbdadeaebbecdbcbccacabbacaaacebacecedbeadbcdcaddbcedcbccbdcbacaebdeabbabeeeebedbbacddeeedbcbbbccaeccbaabcdbcbdccebcbeaceeeeaaedeeabddaaeaaebdcadcaccaaacccbbadcdeacabdcdceccebdecbbededcccdeeebdaeebabbbecabedbceadadeadeebcbbbedbbabddaacbadcdabcdddbeeacdacacbceecbdacabebbcdbacbaacbaecaeceeedaacdbbaadccbaaaecbedeccdedbcecedbdbadbeecbdddaeaaabaceaedbbedaeabaaccceaadaddddbcaddcdeebbecccbadddcdcdebecbbbdeaabeebeeaccbeadeeecbecaaebaeaaebddbbcdabadbaccddcceceebceebbacccedeebbabecbeccbaecdedeaecebebaeaeccecbbdedaeaaccdbbcabacddcabcaceebacdbdaacbecadecacdccaeceebecccbacabddbaebacbadeeabbacedcbadedacdcdbbeaeaaccbebacecdebeabeeddbddcbdabbdbbbaccacdceeecaacdcccebedacceeebeadbceddeabddaaebddaacdecbedecacccebeeaabdeacabccbbbdcedeeeeacaebccecdedccaddcaeccdcbbeecadcddccaaaaeadccbaecbddacbaabedccaeaddbbbbdcbceacadeeaeadeddaebbbdccacddbcacdececceaacdecacebaccabbadaebceadbbecebeadddcbbabccccdcbccbcdbbdccaaeebaaeecdeddbdcdaeeccdbcbccbdaeeaacaeacdcdecbaadbbcebcbdadbaccccacaeaaccccdabaaeccedecedbebddacecadedaabdccbaabcedcedbbcdebccbcdcedacabccaacaaecadaeedbeeaaeaaddeeaaceaecbdceacaeecbcbdadddbeceacccacdcbeddaacbbcbeddebaecebceddebeaeecbeccabcedacecbaedabbbbabcbbbdbcadebdededaebcecdabedbaaceddbebddeecaaedddddedeeaaacbdecaeedabcbacdecdaaadeaceabeddebadccaaceebdbabcebcdaaaeadabeedbecadadecbcbcdcabeabbcdebbbdaebecbaebecdeceaabcdbbabddbecceecbeaceacbbeebdaceedeadebadaeadeacdeceabdbbcbdcacdedcddbceebadbdecabbabadaadceacabcbadeeedcecdbddcbcaabadcbdebabecdcdbdebbdbcdeababcdbcacecbcdaacabcebbccbbdacdebcecdadaacddedcbceeedbabeacaeabaaacbedccceeccaaacacbcacabdedabeaacdcaaadcbdeeacbbeceabecbdabaadbccebedabdcdbcbcbcabccacbbccbecbbaedceeaadddcbedabbcedbbbdbecedcddbbdececebacdbdadebaddecbcccbbebeabacbbeebacebedadccdbbcbedcaddbbcedddbdcacccecaedcdeeecddcaebbebaeadbccceecaeceaebcdbdcdcadceebaadccecbbdabdebacdddddeeedaeaddeadbedaddaeedbdeacbabebcbacdddbcbceccdaccbbcaaddeadbbeedcebcdaadcbedaceceadcbebcdcaabbcbaeedcccbdaedaabbcdeecbadceecccecebeecdebbbebddeecbeaeebbaeaadbcbbedaaadbbedadbceebcdceadbcadcbdbbceabdcbcdecadbdeeebabbeabdcecadcbbacccdbeecbadaeaaeebbbbccdeceeeccedcdceebedbeebcebdbedadcadbabdccbbdbbcbabbdeeeebdacdcdeddacdcbbabdacedbceabedadcebcbdccddcceeabbeaccedaaaaabccbaddadcbcadabdadecaaedebbbecbbdcacbedeadadebebeedecdbccbaecaeabbdaccbecdaccbcbaecddcbbceeebbcddebbebdaeeceaceabcccadcbbeabceaeccdebccbbedaceecebccdaacdcbaaaababdacbceaebdacbdbaecbceaedaecaaaadadebacdaaedacaeebecbceccbcabadcbcaebeaddebccebbcebdbdbbacdaecdaccaabbdabbaaacceabbcbeabeaacbdbddccadedaecadeaecebcdcaceeedacccbcededebeebcecabdededacdeceabcaecccbaedbbbbabcaaccaaaabeddbecbbaebbaaebdbebcbcdeabacaddbedddddeabcaabcdabaddeeebeeacdacebbbcabbecbceccadebaadcbcbdcebebabbecacbebacadaecddababebeecaaeacebcedcabcabebadcbeebbaebedcaeaaabaedeaaccecedacbcaadcccbbdeaaddccaaebcbcdbbeececcbaddccebccacbceacaeacaddbebddbadadbcbbdbcecaeaebdebccddaeebebcbcdbdabcbeabddbcabeaddddbccddaceadacccabaddbddbbcaaaacecabecaaeeebaeabeaadabedcadaaceaabadbaebacccceaaacbceecacbbbcddbecdbbaceeacbadeaaadeddacedbdaeeddaacbdcbcaebbcbbcedabacccabcdcbdabcacedccdcaecebdeaddddadccbbbbeacdcdaccccedeaaebdccbbecbcceacedbbaeacaecbaeadabcdecbddecaaeadeaaaacecbaaddedadbaceddaededdaccbaabaddceddccbbacebaccbbceaedcaddbeedeedcdcdadcebabccadcbeeabbebedbbdbaaadcedaeeeadaedaaabaacdeacbeebdeccaaaaadebecaaaeceaaddadabdccddaaeadebdcbdeaaaabadecdabcaaadbaddabebcbbaeecdadaeaebddedcdcabdabbeeaaabaeaacbbcaabbebbeeeceddecabadaececebcdedcbeddedabcacabceadacddededbedaacdebdbbcdaeaeedcbaacccdebaeeaebcbdeeaacdebaceebabacebecadabeaeccdbaeceacedcbdabccebdbcddebdaaacecadaaedbbdabdddddbcbaabbdcaacacaaaddddaddaaaceabaccddacaecaabaabedecaaceadeccbabacddddecbccbcebbecdecbddcaacebbebebbccdabaddbedacbebcdccdbbdaaabaacabdeaabebcbceabeeaccaedbcdbaeedbaacedaaaededbbbddddbbdbacbedbaddacebcacddecdeeaacaecdeddaddecdcecadbdceaddcddbaeaadbcebbacabdbcceecdcbccabdaaeeeabdddbbdbbbbadbebebaebdcdccbcdbabccbacbaeedaadacbbbdbadbbcbbccdeeeedaebedaceccadbcadadcdbcbdbdcdabcdbccebdaacbdcdbabedebeecebbcdeabebbaabcbdcbaabdedbabccbeaaaeaededbacbceecddeecedceecadbcecbcecabadeabdebaebbaadddeeadbcdeaadcddbdbebdbebbeedcccbdecadbcebcebbdacdaecdaaacddbdcebdaacebeabedadadbbadcabdbbababeaabbaaeeebebcaeedaadeccedabebbabcabcbcdeceecbcbabdebdbbdbecbdeebbbeacdebbadbabeadcabbdbebcebdccbcadcbcaeeeabeabdcaddbdaecccbccdcaeaceaeeebdbddadaeceadacebbdeaeaacdacdbcaadddddedddaeadbcedcacdeeeedccccdeebedcaaaceacabebdeeaccaebaabaccecbebbdcccebbaadaaeedcdbbbedaaccceddeecaeedddacabaedcebedbbedbacceedcbecbbaacbbccadcceadedeaecadbdddddadedadbcdccdecebbcaddacebeacdaacbedaebababacdedebebccceaaecdbacccbacdbabaaddcbacdeeadddcccaabbedeccbeeaadddeceedaaaabeecaaebbdaedcedcdacbbcbbdaecbbadabebbcedcebaadedddaddeaadeabbebeedebebdcdeaedcdccbcbdddacbaaddadcccbdcaeaadaedbceacbbbabbceecdbcebcccbccacaebdeeaabcccddaeaaccdcdeaebbbcedbaeecaadcbececedbbdebbacaddacacdcdbbbccbecbdabcddbcebcacaebaccaeeebbabecbaaeeeaeaedecaadbbbcdecbeeaedaeedbcaeabbdaceeecdcdadcecebcaeeceaebdeeacaddcebbcaedddeebbabcdbdbabadcbbaacdebcaeaadcbdcccbeeabadcabddcdbdccdacabbbccbbdcbeabdbababccbcdbebadacedbbebaadcbdbdaadbdebddcabbaecddeeeceddeeaedabadddebaddceecdbdebddccaedcecbebccbdcbcccbdcabecccabcdacecbeceddbebbbdbdebaeeabedaabbaacbddddebbcaeabeedbedbbcccacdbbaeecacedeaadebbbcbbcbccaadaababaccdcecacdbbeedecaccabaaecdbedcbcdcacbcbecaadbedeecebdcdadbdaaecbaddbaaeaeabbdecabaebbabaaeaceedbeeddabecbcbaaeeaeebbdbabbbceacebccabcbdbbeabadaaedaadaabbbeccaacebdeeaacebbbbbaabadbbdaceeaadcdebeabbeaadbebdeebbabeddbdbdcaacbeabdbaceebaedbcdeadcddacebecdbdaaebedddcbbacacdedadeacdadebebbeebebcbcbbbabcdbdcaeeebbedcaeedacebaeebdcebdbececcedccccabdbbaabcebadcbadebbcdeacacaaeadcbecccbaebdbcbceecdadbededdbcdcebccbbceaadeacbabcbdcedddabdbaedccbaddddaaeaaedbebcdbabaeebcdcdacedbcaaeabaeccebaadaaebabeebbccaadbaddbeaadbdbbcdbdcbaaedaeaacdaaaeabdeebdbabcaecacebcbdadbadececedebbbedebeeeebabaaadabcdcbccdbccdeaecbcecebbabaecddbbdaeaebdbdbabeadaaacebdbcabddabecbceeabdcaddbbcbddaccaddbbeeebbebceccebdcdcabdcebedaeddcebdadabaccabbadbccebebcbdbcceebddcacdcababbeadebbeddecbaebcaceebebacbbbacdedadbbcacbabacacaecdddbdaccaedcaadbbbdbabbdaeddabbbaaddeacaeebdcbceadebcddcaacddecbccdeaccadececcddaadebeeeadceacaaceabbeaccecebbeaabbaaeaeccaabdecbedababdddaededecbecddecaaaaccbcdcbdadaeaadbdedbbdbcaaabedaadaedddddbdacbadbabddccaebaabeacaaeaebcdceedbbbdcabbcadeacacbadcbaecbdacbedeadbcbdcecebcdedccddabeedcdbdabcedcaaaebbabaddddebeadeacdddeedeecaccdeabbadceadedbdbaabeacbdccbbebceacabdbccaebcdebacecdcdcecdebaccbcecaeaadacdccdbadbbeabaeaabcaedaaeedaddadccbcaaeddddedeadecceddbbdadbaceddbeacdbdceaaaccccdaaedeacbcdccddccbebabcbbcabeadebabddcaaabadbeecbdcebcdbcedbdadddecbdbdacccbcededaacaededcaeeacdbededceeedcbedcaecaabbdadebabaaadecadabbbaeadcdeebecaadeaaacbcedbbecbdcbeabdeaceacedaedaeaaddddeaabaeabaadaeeccabcadbbcecbbddbdbdaeedaebdbcdbbedbadbdaababbeaecaebbdbedcabbcbcdedcacbadecddbbbaebbcbecbeacabcabaeeecccebbcdddeabaaceadabadbbaedcadcaaecabcebceaadeaabddeaecbabccacbcdbbacccbbacceedacbaaeaebddeccdcdcddcabcecdadbcadcabbeaedaeacaddccbcaebcedceaacceeaaacbeeebbeddaadccbdeacdabadddebbbdddedbdcddcdebbbbbeaddadcabcaebbeceeebbececcbcebaebcbebbeeebcacabeabacecbbecdbeeecadabbdbbedacaeaacbdbcdebaacbbcceebaabddeaeeedccabecaaeccdcabeecaabcabbebdcddaeacaccbeaeceeadbddbcadadabddabadecaeaadedacdeddabdadbedbdabeddecbcecdddbadacbdedcabbacaddbcbcaecedcadeeadcabbddedabdaacdcbbaabaabcaeebddcacadadabbbcedeeadcddbacbeabbadbedebebcaecdebcaacbaaecbcedabbabbddacbadbecdcddcaaacbbaedaecbddbadeacacbbaebbabcababbbeeeaeaaebacababebbbecdcbbedeacaabbeadbdeadbbcacaddcbaccbeacdbcdeedaddebddcdeddbcdbcbabbabedabdeaaaaeaeebecccbabeceedbcbbedbccdccaddbbbadcdeeaadecaceadbbedaccaaecaaaacdaebceddaaaddedbebebdbdbeccbbcbdebeadddbeeedebdddbedaddebdadaeaecceaecedcbbecbaccdacdceaacedbedcedacbbcdacaadbbacdedbdabaadecedbedcaeeeebbdcaedbaaacbcdebbcaaacaacadbdbcbeccbaedcebcacbcbbebadcdecbbeccaabbdbdabcccddbcecdbaeccdededccdbbbaccaedbebabbeabdbeadcdaaedccbbadeddceeebbbeaaadbbddbbbbabebecabeaadeedceedcbccaeadbcebbaebeadeeddceeeddcbdddeeeecadebabcbbacddbebeccecabdbeeeeaecddaeebaceadedcbcbcecbaebcdcebaaacecacbdbceecaacdadeacbaedebcbdcbaaaccabdeeacdceabcacecadcdcedbeadddbdacbedcccbaeaaeaccbbdabeaddeebabdcdabbbacadbcedccdceceabbaeddecceccbdabacddaecbbaecceddecbaebacadebbdccaaaaeabcebbccddacccdcecbccacedcebeebcbdcdebebbccaccbcdbacdbabcbddaceecccdcbedabdeccaaeeaececcaecbacaeeabdcadabeaabbdecaabbeabbcdbddbcadbdcedcdacdbdceabcbbdecabecbabdcdecacebaadcddcbbdebdacaccdbebadaadbdbbadcbcacbdadbeedccebceddebadcbedbdacaaeadbecdacbeecabbcdadebbaedcaaddbebbdcacaceeabeacbcdddeaebdbbecacebbddabaeaaebbaecaabecdcebbedccaedeacddddbadcabcaeaacabdadebbcbcbcbaaabeacdccecacbdcaaaedacabddabcbdddeabeabdaaebdeceaecdbcadbebcdcdeddbeadbdaaaeccbbbbbebbbaeeeccecaaeabcecaeeeabacecdbedcebeddeccdacccbaabeaedbebeaabaebeaeddbdcaaeeebeaeedeeaeceaabcebcacbddcbacbcebebecbdedbcebbdbbebddeabacaceaacebcedcbeabacacccbeaabeecbcdedcccaebecbaceaeaaddeaeedcaaabeaecaadebcdaabacedcbcabdddaeddbbaedecaaadacaabacaaaceaeddbbddadbccdabdaebccdacbdbcbdbcbeccabdcbddcabebcbecdcddcddaabcebbdcabdcdbcdbeaebbebbcebedccccdadedbacaebdcebecbccccbdecdddbbdcadaedbcdccdbadedcaabbeccaaadeeebaddbceeaaedcaacacbbaecdadccbcaccaceadabbecbceceeccbcbbecdddbbaabacedabdcbaddbadeaaeccbacdedbbedcecddabdccccbaabdbbddbaaaebacbcbedbbbbdddeddcaaaeddeabeebabcceddebdaecabaddacacaacabebcbddeadeacaadbaddbbbaacbdbcbecccecedbcddaeacdccdeeadedcaeecabeceeeedeceaaadecbcbbeeadbebecaceaddbeaddbcdaeabcabcadadaebddacbbbdbbdbaacbceacabaacdccaedbdecaebbecbeabaaaeebecbaecbacebdacceddadeddaecabedcbcdecedecbababaaaacaadbacbadaeebcddcadcadeeedecceeaaadcdbbcbdbbedbaaebebeccabdedeceabdcadbbcdbaadeaacaccdcbedcbecbedcbdeebcbecaceeeabbcbdcbebeddeaeabbaeedcbeddbbedceddedbddbbabecaadacebecbeaadabeebdeaecdabacddadedcadbdbcddbddcedebcdbdcaddcceadbabadddddccbcacabbccabeebeaccbdcdbddcdcecaeecbacccecdcbdbdbbdaaaddccebadbdeaedcabbdbedebbacdccbbbcdcddddbcbdedaedeccbcccbeaabcccbedeacbceadbeaeedcdcbdbcdaeeaccceaceeabaadeeceeddeacedadeacbaabdebcbcbcdedceddeeebaebeeadcdadcddbaadbeeadabdadedacaeccecbeacdebdbaebbaccbdbbdcddcbdbebedcbbcccddbddbcccebacadededddcddabecaeaecaabbbaacbbceeeedcdacdaaaaebdddaabecacdadebebacdcbedabddddeaaadabbeaecddacedbbdcdebedcddeaeeebacbcbeecdcbebaadaceebbdeecabdcccdabdadebaccbbbbdbcdacacdbdceeeabbbadbecbcdabcebbaecdceeddeaaedbcadeddbbdaeabdbcccebdebbadcabbeecbbdecaacdcecacaeceedbeccecbbdaecdbcdaebeadbcaedbeccddbabedbeadaeddacedaaddebeeabbecacbecdbaceeaaaccbdceaaececbdcabeeabbdcebbedddaacedbccdddedeceddeaedbedebdaecbeccabbcaeaceaaddbeaaaaccbdbeedaeedceeebcededbccdeebecedcebebdebbebaacacbbebedbdaaeebddaacaddbbaaeebdbdeccbeeaceadddedacadbadcebaceedcadadcdbaaabddbbeccebdbbaeeaabeecacceaabbbaedebbebdebadccdbadebccddbbbccaaeceaaceaeeebacdcaddbbebbeeccdbabcadbdceecbebbeddebbaabddaedbaceeaeeccbdbddaddaacccadeccbecdbbbaadceceddbcbcdddedeaebeccccadcabbdcacbdcbeeeebdabbccaeddebedaaebcbadeabbaacaabcbadbddadbeeeddbabdbedeecadbedbddeedceeedcdabcbceabeceaaabccdbdcaaeaeebeceebdeeaccaaacaaaeaaccdededdabdbadddebdbbbceedbbcedecbdccbbbeceeabbcadcebaacaeceaccdeaddbdceaadcceeaedddcedabceeaeeebbbaaccceeadbdeeebcdbdabbaeaeaedcbbbbabbebaabcabdaddcebdcbcecacbbbaeadebedcdbcaeaddeedabeeddaabdbccdbabdbebdcbbdedbeaebbadbdcddebbbcacaddeacbbdbcdeddbecaebdbeabdaabdbeeeeebaeecaadaeecbedbeeabbebcbbeccdeaabeccadabbeeeaccbecaabebabdbcdbdaaecacbedeceeddbdcdcbcadaedadecbceeedeeabdeadbcecdaaddaccbbbacbebbdbdeebbbceceecbbeddddbeeacdedcbdebacedcdccadcebadbbacebacccdeaeecbeddabecabccbeaaecbeddacaeedecedceaebcdedbdbbaacebcbecaaadbaebddaaadedeadcdacdbdbdebadccacaeddecdeedcdedbbccdabddaebeecdebbbbdebababecaabcdddaddceaeeeaebeeaabdbbecddebbeabaacaeaccbeabdecdbdeaacbeeeddcebcddddaacdaecbbedbdaeaaaadcaeeabdeadacabacdccccedbbbbcabaabeacabdaedaedccaedcceabcadeadbddadbcccbcccaaabcadccbccbdbeddcdcceebddccbadbcdcceadadbbbbcbcdddddebcccceeddadcbbbdbebeabceaddddccdaecbeebcdeeaeaddadaabbaddaaedccbbbccedaeeadbdcadcabaaddaccbdbaeaabbccaadbcedcaecaadceaaaabcbdaebeecaeecbebbabbdecebebdbbdaeaaaabdccdcedddccabbaadadbedaceeeedaccaadbebdccdbbebdabcadcebddbcecaeecbbcbacaaaabadaadcaceadbeeddbadbddebeedcddcaacdadecacbadbdcdecaadeebdacaebccaeeeacdaabbeaeedcbcacbeeecaeadaaceacbabbbecaacddcddbaaecaacbadcdadaddeaccabbdebcdbaeeeddedbdcbbdbaeabcaaecdddcdcbdaaddcaabadbcdddeedcebaeacebcdcacbacacdedddcaeebaceacadbeecaaedbcddcacaaacbebcdeeddeccbbebbecbcbbaeddbeaaebceaeaedcdaacbbabbbabbdcabecaaebacacedceedbaebbedbabebbbbddeaadebceabacadbecdcecbddcabeeccedcaaeeaddceabecddebdaecadcddbcbbabbbbddababdeccdcadcdbdbccdeadceeecbccebbebaceebbccdceebaaedcacdcdebcadbbbdaaadaccaebaaebbbdceadcbdabdbdcedebcbecbdeedbcabaaddaecbddaebbedbebddbbeaddabcacbdbedddaabacccdcdadcaedccdbcebbaacccddcaebedebaaaecdecacacaabbecdaddcccebcaeddbaaaeecbdcdacceeacbaebbecccbecdecacddcdaeaeddbcbdbbceacaddccdececedbadcbbbaeddabdcabadabababbccecbaeeacbccbedbadbdecaeabcdbcedabccbdaacdbcdacebcdcbbedbbaeaeabedabbaeaaeccbcaedbcaaedbeacaeddecebdbecddacaedaabadeabecdbdccaeaadbaddeeccddaaccbcccbacccceceacccaabbebcdeaeebaccdaaeeadbdbbcdbaeaccaeedebbabecbabbcbcdbedabaebedaaeeaceeabcbaabacdebddcaceeecadcdecdbccebceaaacdeeeedecdeeacadecaccacecccdbdeedbbbebaeedeabcbbbcdbdaacebcbcbaeeaaddedadaaecedecacaceaadcbeccbacebcbbedecaacaabdecdaadcbeccecbbecbbdbdaecacbedcebeadccdabdcbdedadedabbeacedcdeddcdbcccccabeaabbebccecccdccbcaabbddadebeededecbaecdbcdaeeaecdbacbabcebcbebedceaeadcbbbbbeaecdebedacbbeeabadbabcbbedccadebbbdbebaaaabbcbacebceddeaebeacbddddbeebdeacddaecedbcbdecdabeabbbccbadcccadbdbeececddcddbdaeccaceebbbccdaebaedcbeeeeeaacadbcadcdcddeeeecceedcbaadececbebabceaebcdeabbedcdeacbccbcaeeaddbbebdcdaaedeebbcadcaecddeecbedeaeaaeececcddbebcaceecadcaaeeabcddeeedddcdeceecbaebedbeeccebadbcbdecececaccacbdebabcdcceadbddabbcdaeececdbdcebbcbadaedbdacdbdbdeedbacaadbbabcccebeeccccbcbbaceedabeaeecddcebebdceeedcadaacddeaececaceeccbecabdebdacaaeaabaedeecbadadcbacacddeacbeeacdacaabebdcaccacdebdcbeaaabdadbdbdbaedaccdebedeedceddccacebebbecccacabcbaebeedddedaecddabeaebaeadbaaaccaaecdecbceeddeaccdccddacbbbecbdabcebaadeaebdbdbebecaccceaaeacbebeadbaacceacdeabddaabcabcddacadbeeddcbbbdbbdcdbbaccdccdddeabcbcacdbcadadeabdadcbbeadbaebbcceeaecadbcbbeedaeaebbddbebeaabcdadcaecceebdcdbcbceccbcebbbccaaabbededbacaadebecaebeedccaacabebbaebddbadcebaacadcccdecdebadcceadbeebccaaabeecdbcaadeebacecccbcdacbadaabcccadabbdebdcceccdacadbdadaeebeacbdebcbabcdebdbbbecebbaadedeacbdcaebedeeaaedcdeabcddbabdcedadaececbbcebeaadbcdebdbbccacaabcbbedcedcaacddabbbebdaeabdeceebeaadebeeabcaaaeeddcdcdadeeeaabbcbddbdceaaebedbdaebaebadccdbcbababbbbebdccbcdeeedacaabcdbaebcbecbdaebcbebcdaddccbabeadaecccdcaeabcadeccdaecacbeeecaddedebbdeecdececbbabebebdcdcacbddddecabbeacdecccedaadeeddecdaadbddceaaaeceaeaaaababeacdabbcdaaedebbdddeeedccadeebeeccbecedacaaacaeddceabedbcbcacdecbbcdaaabacadcaebbebaeecbacbcbdaceaaeddeacbedbcbbdcadcbdbdeedcbacadecdbabbdbadbbddeaebdddeeaacccbbbdaaadaeeebeaabdadeabbdacaeeaeabdaaeccdacbdaaecdccaccbecaeceaddcaccdcecabdeecaacbcdbbdacccacbdccceeeedaedcdbdaabadcbdceedcccedcebdcddddcacaabadcbadacdabdccddbeddddcccbccbecbccecccabaedcddadbdaddeaaaacbddbdbbbbccadcdabdcaddebbdcadaccccbaecdecaeedaddaceedcabebdeaaebcecadaadccdaadcdbedadceebbeeebecadccbcbaededddcccaacedcceaeadacadccdabbbbbeadbedcebdbbabddbdcabcbcdebadcdbcbccbbaecedceacaddeaaadcbacdbecacdcaccdebdaceeddcbecbadaddabeabcbdcdbcadadaeeeeaabdceaadbdbcdccecbcccbbebcaaeeddadcaabebdbadaeecaabdbbddbabacaebdeeacabeabbdebecaccecaedaadeadcaededeedaeecdebdeeacdabcaaddbeceeccbdececdaeddcacebdeebdeddadecdabaacebdaadabadbecbebcaeceebbeabcbccaecdbcbdadcaaebcbcadbcdbbbccbdccaaababbaebedddeaaebcbaeddcdbcdabdbdcaebdcabebcebdacbccaacbebacadeadbbaabddedabdcabcadbdcdcebcbabcdadeaeaccddcbdbbacbbecaddeaeacaccdecceacceeadcdcbbabbadeabdeddccbedcbaccecbaeebcececceaecedddabbcacbcbbaccecbaecedeabaaedbabcdcecabbadeceecdbcccebcdbcabcdcbedeaccedaabcaeedbcdacccbadcdaaeadaddbcdababaacbeeacaaeaacaadddbcbddcbaddbbcbbdabcbdbbaadedcedcaacabdbaacadcdbecdddaecaeccceebbeeacbeddcccebecbabddaababdabdbbdbceeccaadaeacbabebceaacdddcdebeeedecdaeccbbccdeaecdbbddcebadcdbcecaeedacbbeedecacaeeadbeebddedbaddccdbebebdaadceeeacbeddabdabbcdbbedceedcecdedceaddeacceaacceabedaeeeecdebaeececdecbbadaabbebecdcbecbdcadcbebecbdecdababaabbaecabedacccaedeedccaaacaaecacdcaebeadebceeceaddabedecabaedacaecbdbeacedccacabbdbbcabcbebcdbcaecdecdabcdadccccbaeeadbcbdaeecdcdbadeccbebcedbccdadcdedcbeaaceecdbacdddbdaaaebcadbaebccedeeaecbbcbdbcadbeacbbcdebcabcacedbdabbdeaeaacceaedcabdaacbdaeccdbddccbdcdecabdaddbbbacaccebdddecbaaadcccceeedbebddaccbeaebeaccceddedeaddbcdbaebdbbdbbccecadbdaeedadeaaeceaaaeecdbabbdbaecedeccadaaddcbddecadcbecdcaeacacdddccacbbabbebcecebcbcbaeebbdeaedcecebedccbdbeaabdaaccecebdebaadacccccadcdeaaacabccbacbceaeabaababceedbedeaedcbcebedecacabcbcdeeecedbbedbcaccdbbaabaddcdeddccdcbbacdaceceabeeeedcaaccbedbdeededbcbcaaebaacdecacedbbdbccabcabddabeaebdeccebcdaaebcedaceaddddbaaacadbdaebddcdebedeeccccecabacdcbedeeceddcebbeeeeeaaceeebaecbebadcdedebebcacdceeecceebceddcccddaccceddeabaedaaeaaadaabdbebbdddaedccccaaddebeabdbbecebdacecebabdedaecedabbccbbeccdcaedcdacaaeceaccaeacccbcdbebabaaddbeccecaecedbcadbcbceabbcccbaededcbdaeabeebdeaedecadecdbbcceeaccadaccbeddbadbccdceeebbcdaaadcdddcbabcacecaedaaeaaecdcbaeacecbedaaeaceaccdcbbcabcabdddbabadcbcaeebaceddacdadbdccaceaecbebcaacddcadacbaaeccaddabbaecaadbdaadaccdececeecbceaacbcacddeeedadabdaebeacbeddbddcaebceeeaabceeaddbccedbbeeedaaddeeacbbabdadbdbccdcbebaecaeeecccbdeeacbeaceddabddccdedcaeceabacceadbeebaceaeddebcebdedbbbddaccdaececdbedaccadedeedbbedbddbedcbcbcaabaabeebeaaeadcaeabbbbbecaddcbcdcccdceeedadacbdeebdbcdcbaebeedeccabdacaaddedbeadadccdcdbeeeaaebdabcddecacebeeabcadaaadceddcaecbcdcdbccacbdaddddaaebbadccbbdbbcddbacbcebadcbddeecacbdeeeeeceebdbbccccaccdeecbadbbdebddeeeddcceadcceaaadaddacabdcebbebddbebcdadceeadaaeaaeebddddacaabccdaeabbeacadbbebbdbadeeeeddeeabcdcedccbcbbbbcdabadaeacdebaedccdedceccbdababccbacdceeccedbddcbebdeebaaaabadebaaedbaebdadeebbecdabdbeadebbadedcccabeacccadebddbcbaadcbcaeacecdacaebeaaadabccddbdccaddadaaccbaccaecdecdceabeddacedeedbedadebeabddeaedbabdaaaccbecaccbbcbecedceabbdabcdaddbccaaeeaddeaceaccaedeabddaadbaacaedaddbdbedcedacdbecebadeceaebceecebabbdecabcaebcdbcadcbabddeccedabaeeedeeacdaaacdaadabecbaeedacecdbcabdaacbceeaabedbbbabeededddbeabdbcbcdbceadecdabbcdbdbebbeccaacaeeeedabdacccbdabceaededacbeeecedcdcdadddbceedaabdbdcbceabddabdbacbcacadbebabcaadeeeebadebdbdabebcededbecbeccddbabbdcaedabcbdaadbeaeecacccacbbceebdbdcbdaccbaddaecaeedeaacaceddaebbecbbacabadecdbccaceaaedebadeeaeddcdbbacbbdecbadccbecbaeeedddaaccecedcebebadcaeeeeadcddaddeeccbcededbeacbebdedaddcbbbacccbbebaaabdbeaaccdecbabbdeadbadcdebbcaacccdeceddecccabaebceddcecdacaeadbcecbddaeedaadcdccaebeaaddcdbacacbaccecaeabcadeebbcaccebedaeabdeeababcdbbccddcdbcbadccbbbddeacabeccdbcddeccdcbaceecbbcdceccaebecdcadecbebeeeadaababbdcedcdecacdbdcdaeedddbcbbcdcdbdcecbaebadedcdabedbbdabbcbdaeecddcedbdddaeddeaedeebebbaebdaabdeebeabdbdbbbdabeaddebeecaaecbacdbedbbcbaeaecceaabebeacdedbbcbdeddabeddcaadbeddadccebeaacedacddeeacdeecbadaaedaceabadcabcdeeddadaacebcbeaacdeedbbcabdccebceebaddeabddadeaabbdbdabebeadadbeedaedeeeedaedeaabcdacceedbdbdbeebbacbadccedbcdaeaeccbbdeebedcbbebddceaacdcdbcaacdcecdcceaeccacdcdcdbcbeaaedebabeedbcebdbcbbdeaacdaccabcbaeacdaeadeedaddbbabedcedeebdbabbceebbdddbbdecabbeddeedcedbadeedebeeecbecbacbccbeedbcdccedccadddcebadecbdaeaaaaaaeebedeedccbbedadcedccadcaceccdbaaeeebceecbbaadcddaeacdbeebdbeeccbebcbaeaccbbdaabbdccbdbbdadaccabceacacaadabebdecacdbbaadaaaeecbecaaaadbbabdceccacebecbaddeedadbacdccadacadaccbceaacccbdcbdebdcdecbacdacbdecbabbeacaddaaeeccbeadcbbabdbacdddeedadcabadcaacddbbebcbadbdddcdaebbecdeeceeadccdbbabeeadadabdadadbddebbdbcadaeebeabddbabdeececdcaacbcacdeaeaabeeecbadddaaccddedbbedebbebaaadbdcecbdadbdeaaddaaacdadeceeadeebbbecdbeedcabeabdecddadaabaadbbdcbdeccbacbbaacddbecadcbedbabbbbdbaaccbabacdcdbaecccccdcdcaddaadbddeaaaeeadebbaeaeacaaadaadeabecaddbcbbaecbaacdacceeaaaeaaaddcbadcaabcdedbbebeacabeeacbcbdeaddbdeccdddcaecbdecbddaeebececdbaaecddabdadcceebbcebaadedbbaebeddebaddaeedecaeeddaccaaaaacccdceeabdcdcbcadaadcaedbbbbbebcaadeadceadcbbaadeedecdecdeebeeecceccdddcaedabeeeaaddbacacbbdedbaecdbbcbebddaeedbebbdbceaccabeaddebbaeeecacaaacbeedeaadeaccdecbcadcceabdbadaeddcaecebcaeeedcbaedaaacbbdcccdeebabdddbcadecbcdacaeeacbcccdbecabecedcbcdbadeedbbbaedeceaabedacccaebadddeaebcdbcdaeabadeacacceeddbaadbeacecaaccabbbcdabaaabddacedddaeecddadeedbeabcccbaebbbdcdeaeecdecaaeadcdcaecdeabbccdecaacccddcbacdcbddddcaeababacddbcdeeadedabbedbecdacbcdbbbcbaebbdedddaccbbabebebcdeabcaeeeeecaeadcdbccecedcabcebecabebaeeeaddedcbebecccebacbcebedbbaadcecedbacddbbabaabaeabbdbddcbcdecadbaaddcaaaaaaddbaaeebdacdabceaceebbeebaeaedebadddccaabbbcbcaaeabacdeebcabadbcecebceaacbebbecedeabcdddcbebdbbdaaabeeccccbabeccbabedaeeddcbeaeacabacdbedcdabbecdadddeabaedccbeedabcacbadeeaadaebdaceccdaacbadbddebeaaacadcdaeedcddaabbeaaebeaeedcdecbdcddddcaeaebaabbecbbebbbcdbbeccaeeccdecaccabaddbacaacebceaadbaadbbddccbacacbeebdaabaccbadcddbbaeadaeabecbbababeaebadabbbdeebaacbcbddabdbbeebcbeddacaadbaeccdecccacbbceebabccddbaadebedbeaceedbccdbbacbabbeebebedebcbbcecabdcabbaabebcecdcedcaabadcdbecdbaebeaceeaadaadeceeaddaecedcaeabdabdcecbbdeaaceedeaebebbaadcbeccacbbcbaabceaecdbcaebccebcacaaadcdeaecdcdadccebcceddaecddeacbadcaebedbacbadeabccbdcdcdaceaaaedbcbbcebecabdbaabaeebcbcabcbbeaededabacebddecebcedbecdebeddceddddaaabbaadeaeabaddbceeccdadaddadccaeeaaccbbbcababcaaababdcecbdccaeabbecdccaaddbaaabebbaedbddbbdadcddabdaaadeabbbdcbbeaeebadaaeddccdebaebcbcadcecaacdadeedbaeeececccedcadbddaacccadbbcaeaeeededdceddbbdcccabdddcbbdbbaccbaeeeededddaeecddeaceaadcdbdeddceaccaaededbbbeacabeaaedcedabeddabeadeeceadebdebdbdaacdabdcacedcccecbcbaabacccbcadebadbcecdbbdbacccccaaeceacdaeaeaecccecbeacaaabaacbeddcacddbaebdcecdecdeaceddcbdbeccdbdbabbabbdaacaccedecdeeadbaccaadcddecededcaabceccaecbddeccdcdeebceeedcedcedccaadeedebeabcceeeebecadceaabdcacdaeceecabbcbadbdaedcaadcaeeeeddebacaeadaceacaecbebaebdbdeeaadbeeaecaebacbbcccdbaebccdaaabbeabacabdcdceababdccdbecabbbddebbaedaadacecddaacbcceacbeadcdcabbeeddcededbabcecaacbdacedbdaabeddeceebeeeacaeedbdaeadecceccbeedbedaddbddebdecbecacccdbebcabaabeccdacddbbededaaaaaaaeadcccbdeccdcbadaeebcecceecbccccabbccaeceeeddeaadceeeeadecebedcceedadaedccaaddcbabdbbecbbbdeceaadbeddcbdbedbbaaceaadacaebceedbaecddcddabeddbeadddaeecbddeeacdcadcaeaeaddedaaeccecdbbdbdeabeaacbeabbaaaeabaecaecaceedaacbeabaeccecbebdadbadddebaccedbccdaadebdaaaecbbabeeeceebccaabbbdabaeddaeedacdbedbeecaddddaceeccabebcacecbbacbbddedecbccceecaebebdbdbadaadcaecceceeebbbebbddeebcaceebceeddebbdbccacdeaaeeeccdbdededaaacceeacceebeacbddeaebdcdbddabcaccdcabcacbbaceebabceddaaedaacdcccddabdecbaeeaecaaeadebbdcabaccabdbdbdeeceedeacbbebbcbdedcbceaecaccbadcebbbcdcaecebeecddadbcaeecaaeaeeaaccdbaaacccaacddeceedcbecdcbdadcdabebbbaeacdbdcecccabdacaabecabcdbebdddeabcdbbbeaacbaaabaabecdbdaeaddcdddccbbbbbcdaeddcbacdbeeeaacabddecdcaadcaecddebecddbbeadeaadddaaabcaecbdbebaaabedaddebdaedbdbbeebbabceaeabeacaeaddccdaacbbcbddeeaaecccaaaeaabedcedadbaaddbbbecbeabbbaacedacaddeddceadebabecabdcecdeeaededaaabdccdaeaddbbddbdcdccecaeaaedcacecaddacbdccdaecdddadecbccadbdaddacebdcacbacabeebbebcceebccdbcedabcabddbdededccebdbdddacabbdaaeedcdabeadedaaabcaeebaedceeeacbbbcacacecbbebbeeacbdaaceadbcedecdeddbceddeebbceedcecbccdcbddcbbeebbabadeabeecaaedecabccdbdbbcadcbbddebddadcebabcedabbccecbeaeeaaadbbbeebabbedecdbaecebaedeccecdbaebceeadccbdeedabaebbebdeddddedeeaadaabdededaabdddaeabbddacaeadedacabebcabecaabdbebdeddeeaadeccedabbaaeebdbcbaabebcbaacecbbbeabadaccadcdeddaeddbbbaddcaabdbecdbdedababcaabbccabaeebcadcabaceeceaeeecbecceedcdbeedebecdbdeadacbbcebadbbedeacdbdddabdbaedceeeebbddadceebcbaaebadbadaeedbbbcdecdeedaabeecbbecabaecbbacddcbadedddaacebdbabbcccdbaecebdbdccccabcebaaadbacadaceadecbecdcababebccdaddcbecebaeeeadebbaacbeaeaaaebcdedcaceabdcbecaaacdeddbbbccdbdacdbabadaecbdabcadaddacecaaedbdbdbaccbdababcabedaebeaebbadcbdabebaaabebcacbdaeaaebdcaadcbdbebcecbecbcbdeaadbaabdeebaedacbebeeedddbebdeaebaaeacaeedcdbaaaeddbdadaebeaebecaaecaaeaebadeaccedecceedcbdabbadbcdbdbbceacbdebcacaacacaacecbceabcedcdddddedeaeceddacbccaddadbdadabadeacdcecabeeebaedecdaacccbeaccddecadcdabbeeedccccedeeeadabacdedbebeccaeccaaceceaccccedcaeeebbedcabedcbcaeededaecadcceceedeacaebabcecadddaccceeeabeaaaecdbcedaddaeedddebeecbcbadabbaeaeceeaeecdcccabeadbedabbccacaabdccebdcebdccaccdbaebbeaaabbcecaeddbbcaddaadcdabcebddcecabdcccbcecddcbdbebdbedbecbaddccbaddbaedebeedceaedbdbbeaddacdcadadecebbcbedceadbdbcceabcbabcaabdcaaaedcbddadcabbddeddddddaaebcaccedbcddcdbcccaccbdbcbbbcecdaaceeddacaebccbdaededebbdbaccecacedaecdecdeeeddcaeaebeeeddaebdddcedcbbcbceebdbdecdccecaaeaddadaeeaeadacdcbebdedcacacadaebdbbcececcadadcbecbdbdebabeeabaececcbebeaecbbedcdbaebdbbdeaadcbbaeebacddcbdadceabaccdbcccedbaeadcaadcbbddaebdaddadedbeedadeabbeedebededaeeececadcddeaddbbbaaadbaadabaceddbebacdbbaeeccdcabeaeacdbabccdbcaaacbceeacddbbcbddaccbadcbbdbdaeaaceeaebeddbebceaedebedddeeebbeeebbbaabaaaaacbbbeaaecccccecddaacebbabacdcdaacbeddcaeaadedcaccebcaaeaceeeeeaddbecdbddcadbdbbbcbcabbebcdadecabebcbdbdaaddbeecdedceebcadbeccbedaadddebabaebdebecabcddbebbdecbdeeaaccccacecccbbdabbbaeadbadebabcddadabaccecacbdeeabebaebbaccedebedbabdaebdbbcdbcacbdcacbddcddebaedabbaaaccceecacaeeabbbaddaaeccdebdcdccebcecdbadebaaeebabaeadceeebaaabaedbedbabbbdaebdeddbcbdedbecdbbcaccdbbdcdbcebeeececaacdeebcaadbccdaddcadecbedaabcbedcbabdaabbdeaeddcdbebaaaedcdeebdbccbacadbecccaccdaccbcdececedeceededadedaccabaddeeaaeecbccddcccbcaaacecdbdcdadbcbeeceabdcebceaedeececeebeeeeeeacbbaebebcbcccbceecddacbacbceceddbabaecabacbddeeceebbeeecceebdebdcadadeeebeebcdebbaccdeebebcbdeacaeebaedcceddeebcacdceeebeeeadadebbbdcbedabccadcdaecbaebbecdccdedcacaaecabdeaabbdececdabedbaeadaeabaecbdddcaedeabddbaeedeacbecedbaaaccdbceaecdaacdbacdceeacedaccbbabcdbabbcdbabeecceabedeeedcddcacbdeadeadaaecccdedceedcaaacaeeadaaacadccaccaabbddebeedaebcdebbdacaebeeddbedcccaaeaceceddaedecedaeeaeeccaecbbbdacbdbeaadbceebabebaddecdebbdccdeadddbcbbddbcbdcdbceecbdbabdcaaabaeecedadddabaebacaeeadceedeecdcdbdeceecedbebaeaadacbebeddeddaabbeacbcdebddbadaeeeededdccabadabcdabacdcacaeeadddbabcddbeaaeaabcaeccdeaecbeebedddbbdebbaabeccddcbeabcbaceeacebcacaeacebaaeceaeaebeabbeeebeedebdbbebbbcdcaedacecdadedcedeebadbddebcbbcadcabceaacedaaddaaecdebecceabebcededbbabaeeadbcaacbaeddacdaaeababcacdaaeccdaeededeaaaccecddeaeecdbeacbbcaccaaebdccaebcdebbecdeeccaadbdebacdacbceebaeeabaabbbeaeadceccecdedeebdbddacecebbeddaacaceabecebeedcaaebdbabdbcdedbaabbdedceeeccabeedaaebdbbcbedbcedbeedeeadcdcbcccbeabdbcdeceabbaaacaeeacccbbddbacedcdadbebcbbacddcbeacddcaaebdbdccbbbddebeacaedeacaeaeaddbcceceedaddcdcabaeeacedcacaccccaadcdabbeedadaecabeecaedbabdebeedcbdeedebdbcecabdeabdeaabdcddbecedcacddeabbbbbabdebbbecdddadbdeaadbcabbbeeecccbbcdbbddbabceaedccdeaecedaabaaebbddcdbeabdccdacaceabddbbbebbcadcacdcaeedcbaebebcbccabdcdbcdcbcadccdeabcceabecedbaadedbcdecbdcddcaecccccbebaddeddaebbbaecbadbadceaeeddbbaaecccebcddeebcddbbbddacadaddacaaadbddcedcdbcddaedbdbcebddcdecbbbcaebbedebbddabddcbebbedeedacacedcaeccabebbaaccdaebaadeebdbdeeaabddeadbdadaaccccabaccacedbccecbebdcbdbeccdcadadcbceceebabaaabddaaddbccdbcecabdcdcaedbdbebbeaabececdeadeaebdabecdbceeccdbadddebeecadbcdabdacdbbaacaadceecbacaeeaadebdbccacdcdecdddceeeddbcdbecddabbeddeeabacdecaebeadbceeedbacdaccbbdeadbdbedddcccadaecaaacebbbebebccacedecaeacbeccceceabeedcdbdcdebbcbbaebaedaaacebbddcadcdaaccacdcaedccaddaccecdadbcdaeacbaeccecbcdaaeecacddbbddcccadccbbdcaeeaabdaeceebacccbddaabaacabceeaccabaaacceedcdacabcaaeeeaecebabdcdcbabcaeabecbbcdecbbadbcdcaaaabdbcadcbbaeddedeebccbcdadecedbbadcccbabbceaccddebcecadeabbcddedeaeebcdcdadbdbbbaecdbebbccdacebdacecdcbccbeddbebbcccccaeacecabccacdbbacabeeebacaabeeaddaebdacebbcdcbbbadccebccddbebcdecceccbbacecbdabadacbbccaabbdacbdacaadbebcdaacbceaccdeaadeacceabceecbeaeebebbecbadcaadaccdcbabdcdcccabcacaacaddedcadedbcdadaebeedeeaeeceaddbcbcddccacdbbecbacccdcabdedaddaaadbaceacebecbaacbbdcacdabddbadcebeeddadeeedeacdebeeebbdeabecbedecdcbbccacdaccadceeceebcadebeaeaebeedddaaeccdbbacabddbabadbbccdecbdcebacbadbaacbacebcdadcecebddcbcbecbdabbeaeacbcbbaabdaeeaaccebeddcdcddcbedcaeaeeeaceddebdcdbcbacaeccdccccededbcdabcaedceabbddeccabadcbcadabcbcbdcceeeadababdaabadbbbdccaaedabedecddbcecbeaddeebeebedeceadbecaecdddcabdbedeaddadbedbbedbcbeeecedbcaeadaaeedcbceabaebdebbeeeeaaacabbceeeadbcaceadbabeaadecaddbbaceecdbaecddadbdaedacbdecddbabebccbdabbddddbbaaeacadacbabbdcadceadbcdbbaaceadcaeaaabaeceeaacdecaaceaeadadaecedbebadddaeadbbadebcadbabbeaddcebdeeabcbcaccbccbecdcebaaaecaaacccbcbecaedcadedbbeabcbcbdbdacdbdddbacdabbbdecacbddccbdccdacdaddeddaaeabaecdbddddddabeeaeeeeecbebdbeeebdddabeacacecaccdbaecbeadbdedbbbaadbeaeaeaaecddaddaedebceaaeedaaecebbedaccbeddebadcbadadeebcececbcacbcdbdcdeedacbbadcecacdecdaaeeacdcddcdeeceaadcdbedaecdbcabeeceabaecbbddececdebbbcbebdaaaceecbcbdbdbcedbdaebdbdccbbacedabedcbaddaebcecdccdbbcdabddbdddbdcbcbccbadcdddbcdabaadbddcebbabdccdbcceecccebdcdaaadcddbceacbdcdecaabbdebddeeeeebbbcbcbbcdeceacdbacadeeebdcaceecabdeebecbcedccbacdbebbabceeeeabdcbbecdbbbebcdedcecbbdcdeadcbdddedabacbabcdcdcecacecddabeedbeddbceaadecaeaddddadaedbcbcededecabbcedbaebedabedbaddecdbdcedeccccdaeaadeacbbadddbcdaeabdaeccbaeaabacebbaaedeadbbcebaebcecbbdddbddadaeeadcecaddcaabcdcbebbdaddaedcaceabdcbbbeabbbbecaacacdaacdbbcacadababcebdbbeabaccbeaaebadbbabdaaadadeaeaacabddabccabadbcbaadcebaeccdddbdebcbceebbbcbcdccdbdcbabdccbabcccdceedcdddbebaacdeddddcbdcaceecbdcebeebbeeecbaccceaddddebedceddabbaaeedebbbaeccecbbcecbbbdbbedebeaabeabaabddacbaeaaecebccebbbeabeaabbadcbdcceacacbcededdebaecaaadaddaecadeccdbcebcceebddeaeedcdccbedbaaaaedecdeeebaababbbaebbabcedcbedabcdecddccbbbdadecaacaebadedacebaceedbcdebadbcabbdadcbaceaddcbbacbcddaaaadcacdebcbedcceaddbebeedeccacaecceeaaebeaaaceeacaeeeeebacbbbebdaccbbeedcbaeccbdadacbcedabbecbecdaaabdbbcabdcaaabaaacadcaccabeecbcdcbeeabaaeccaaeadedcecbddcdecbeeaebbbeecdaaaccaeccacaddedeabdeacadceedddcdaeaeeeadeeaaacddeedcccddaeebbccebcbabebbcaddadaacbbaeadadedcaadaeabcedbeacecdddaaaaedacaeeccebebdbbceacbcbccdeaadccebaeceedcaaddebdceabcbdbbcbccaeeaabddacecdbcaeaddcbaacedebecebbaeaeabcbcbcadeccbecabdbabebcbaebbaeecdbdbccdabedeabdabceabeaedecbedeaecddcdcbabbeaabeecaccaceebcabebebccacedcedccaccbeadbbedbdaaccceedebcebaaeacabbceadedcdecddebeecbbdaabcddebcbeecabddebacebcbabbecdbdbbaaeabcbbccaecaacbebacebcadadccbebcddcbbadbbdabbaaccaabcdbddaadaecbacbccecccccceedeabdbdcaeadacecdddcadbdbdcadbabbceedaaddddedddaaeacabcaababacbbbebcdabeecedbedbabacbcadbbcdecdabecacbeceddbaeebcabecaeecccededcaccdaccccbbacecaaeabaacebdacdadaaeceeeadcbbbccbaecdabcedacbbcbeacaacdaeeeebabccdceeaccdabbbadaeabbaceeeacdaceecbeabacadadaedcccaebaabbdbddcacccdececebddaaebdcbbecbdccadbeeceaabedabdcdcabbcdabccdcbcaaadbadeaaebcdeaddcceeebcadacbdbcdeaddbcdbebceecaaeeaaccbeecbcdecdbcacdcbaceeaaaebddddcddebdddcceeebabaeadeabdccddcbdcbdccacacaadedcbeabaabdecdeaeaddaeeccbabbbecbeddbeccaabedaaaedebdacdadedcdebccbaeeadadbeacdebabdbdcedcacdeaeeedbbbcaebdadabdccadbccccbbcbdccbbdabbdadcabdbcaabdcaaabaacdaddbbbaaadddacaceadebcdaebadcbdbdebcbccdaaabaaacbecbedecabbccababceedbbdebcbbdaddcedcbabbadabbbdeaeecdadbaccebdcedacacecdddcebeacdccbdebbeebbbbcdcbbcbdcdabeacdeecdeebadabebecaaaadceccebadeadaabeddecdcbecbcecbccdcbaeceacccebdcaaacdbeaecaeddacccecdeccdcaadbaebebddddaebcbeddbeeceabddeedcebdcbdababacbccccecdcbaeacacadebdabebbeabdecebbddabeadabccdcdacbadaaccbdcacaadebbddbdaebbaaabedceeaabbdaaaaaacbaccaddcaeccceedcdcecbddbabdeecbadedebaaebcbebeaddbecbdabcaeeaddaccaeddbddeaadeabaeccebedcabcacddcedcbabddbdcbddedcbddedceeecbeccaddcbddecedaaabcdbddccaddadcaaaadaddbeecdcabbbeadaedcbdecbeecaccbedacccbcabeeadbdbddcaaccceaededbceaebbeabbecbdceeaecabdacaecebdcbddabdecdbbdbecceaeecbcbebbcccedaacaaacacbdcecceaabbebbeebadeeddbecbbcedbedbeebecabbedebedaddcdccbedbdaebabaedddcedbdbadcbbeeeeeedadbcabebccdcbdabdcbdebeceeaabaebbeabadeacacbbacaebbdaebbcdebbebcaaebcaeeedacaadccacbaedbbecbbccdbbecdcaebbbcceeeaddabdbdebebddcaabebdadebaabdbabadcbcceecdbcadddaabceacddddceacdbacbabaaacaacacacdcebaadabeeebaecaccaedbedccebdcbeeeecebbeebdcacbeeeccdbddeaddcbaadeebdadecdcddecaedaacbabddddbceaeaacaecaaecaaedcccdeadaccebdeaddddcdeeaacdacaacbcbbdedadbddcececeaddbcccbacccbbececaceaacbacebdecbbeedeebaacdaedbdbccbacdedcceeaeabaadccbabbeeecddddccdebbcdebcdbeeecacdabbbcaaabdcaabacddbebccacaaacbbdbddeeaacacaacdeacabacbcbdcadcacbeadbdabadddcdabcdbabcddaebebbbbeaaadeddaebcbbbbbabedadeadbcebcaecadaedccaebaccbaeababbcbcdbbdacacddbbeacbbeebeadadabbedbccddbcbbdbbedaeddccbcabdacebdaacebdeadbcccbceeedaaddeaddbeccccccbbcdbdbbcbdadcaeceaddacbebaedcaabeccdcebbdecbcabedddcaebeadbcbebadbeabdbddecdeddcbccbdcecdccdceccbcbebeeaebadcaeceaeabbaebadbaadcabedbaabaaddcedaeecaadbbebbbbdbbcaadececddbeabdcbbccbaeadebbeddcdbbebeddebbdccccaddcdcebeccddbcbadbbcabaddcaecccdbdeebbeeecddbcaaaebbddeaceebcbbcbcccaaeacaedbccebadbdebbbabaceeddeeaecaddacccbdcdaedddccabdbaccaebdebcbcdabbddcaaacacccbbacacccdeadedaccaebccdaaabeecdaedebbdaaddcacddaadeebdbbcebbbecdbabdbaddeaddccdcdeaaebbddeaeddcbdacbbeddbcacdcadbceaaeeeedabbcbaaebeabbaaebacaaaabcdbeebabacbbcccdadabcccbdbddeeacaecacceaddceabeceeedddceadeeacebcdbaedbbcbddebcbecbddbbaacebedeaedaacbdaaeaaaebaeeeeaddcdadddeabbcdcbcbeebcadcabedeedaebeebacadbdabebdccccddeeadeecdeebddbcbadcebebceecbbcdceddedadcebbdedbeaddadedaebebcecadedeeeacabeecbedeabbbaaaecebaaddebeaceaeadeeeaacecbbcdebbbdaeababbdaceeeebeaaecdcedbbddcbbdadbbdcbbbbabeaadebbebdbadbaeacbbccccbbdedeaacecbdcebececdaaaebbbdcbbddbdbdcedabdcccdeabdbbccdccadedaeaeadbebdeebbadeeddbddecadbddcacdeccdacabaaeebadaebccdbbcdacecccecddbeebdadedbdbdbdddcabaddceeaecaecadcebddbcadeddbbbecddddddbbacabbdccccbaababcaebebcaabedeacebceacebabddbeaccbacacdeebdabcdebabcceaaacabdeaebeaacaeabdbbcdeccadbaeddadceebcebbabaaaccaeedeacbbecccacaaacabcbdebaccddbeebbcdaaebedbbacbdadadeadeaebbebdbbccebadadacceaacbcacdcbbedacebebdeddbedceaaeeedcadecbcaecccadaaabbcbecabcbbcddaaabbedabbcebaedcceecaeedaebdddbdeddcdaceaeaceadddadbbadbdaebdcadaaececdecaebbcdeeeaebebadaadaccdbbaebeeddbdbadaccdabbcabdeaccaacadacaceedadbddbeeddabdaedcabdaadcbbbabcabcdcecabcdcabddbccbcabeebaadcdbabdbabddeebcdcdeeaebcceaabadecadeadedbacdccaabdeeaeedebdbecadbdeedaeaacacdcdaddedabbeabeaeebdcebcdadacbceedeadceaabddbaceebecdbdebbaeecbaebdbbcebbebdccbadcdceebbcbcccedeeeccabeabddddcbeabcecceeccecaeacecbdebdcedaaedcbaeccddbbbbdebabaacbcbdedecaaebdcdcbadacecddbdaeccbbecadaebdbeccbcdcedcabecbccebaeeebadeadcddaeacbaccdeebcabdadedaadbddadceeeacbdddbbadabdbaebaaedcbeedcabeeacdbaacddaaedeacbcdeaedceacdbecabaaeeebdabcdedcddbbbceebeadaabccacdacddbdaeaeaeaeccaddbcdcddcccdbccddebdbbeddecebbcaeddedeaebededebccabddadedcabdadebbcceeabeeecdcdbaddabdeecccceaebaddeebcebacbbaaeeecededdcdcabbdcbcbaadaecddcaedeeddbcedaecacbcbbecbaceeaebeccbcdddbedaccabbbcdaadeabecbcceddccbedbcacaabedaaceabdedddeecdaeaadeaacaeadaabbdcbdeeabcaeeccbaaddbacabbabadbcabeccdbccdabddeabbdeeabbadcbbbbaeeabcdedeeaadeeeabdbdabeadadbacdedcbecbaaeeecceebabaaecebddbeccaebedbbeaeadebcbbebadeadceedaabbdceeabcadddceebbedecaaddbdbcdcccaacaeedabeeedbaeedbadaaccdddaecdabebbebcccebeeaeebebaeaecddcdbacebcbbebbacdadeecbddccabbdbdbdecabdebadeeababeeaecbbadbaddbbdbdeeaacdebdabeacddeecababbebaeddaaddbdcdccbabebadbcccdeecabccaaddccbaeebbbdbbdebecdcdedccdcccbeceddbcedbbcbbecbcdbacadbccdbbddadcbdadceacbcdaccbdbcbddaecbecbaceeccaeaadcdcbaeeddccbaecaeddccaecbcdaceaebbedeaceacecadeacbaeacbeecbdcdcdddaceeeeaeabbabcacdeaaccceceddadbdadedccbaabaabbaeaadedeaeeecebaadaaedabdabbddeaedadebbcceaaccdbcdbadeacbadeaceeccbeaaaadeccabeccbcaccdaeddecbadbabeeecadaecdcedaabddcabaabacebcccaaddaabeeedccdeaacebbeddbebebabedbacebccbacbedeadbacccabaedacddceedaeacbcccbdcdccddebaaccbcdccaddbebcdbbeecbbcecdbeecededeceeeccedabdaaeabecaeedccdbdacabcbdaccccacbcbeedcdedbeeeaadebaedeccbbedcaeeabaeebdddccdaccecdedacdceccacebbbcceccebcbedcacebceceddcdedbbecbcddbbadcbcbdeabddadcbbdbdaeadabcddeabcebebccebcbbdbcecbceaaaccccaacdecaadabccdcedebeececaaddabbebeeeabeabcacdbaeaacdcacecaeabdabeaadeccabecebacdaecaaeecddccbdbbdecaadbecbdadcbebbadaacdeacebbbdebeadadcbaaaeadaaaaeeacbbeaddbaaccedadaccedcaadaedadeadbabcdacbbaeedbebacdbbeddedeedeeddedbebdcceaebcbeceaadedbecbbaedeededcadccecedcccedeceedacdbdabdaaceabeaeacceaaddebdaadedaaacaabdadebeaddccbcceeebaaeedcdaeaeeebccedeabeebedcbeebbcdecedcdeacbaebddeeeabaaebeadebcceccebeebbceccecadbebecedabccabaddadbdbdadeeebbdceceadedbadabcebbbbaadcadebcaebdbcebdceaebdcccbaeddccdddcadbeadeadaddcbbcdddaaeddebbebabcadcaabbdcdabeaccaebbdecbcadabdeccccdeabeeaccacdaadbcdabcdecacdbbbdccddcdadeaecebadbaeedeebaeaaadeedcddadebeeabcaaaebecbcdeaaaacaeabdbdecdddeeadbadbcdbdbccadbbbcaabdbdbabacecddddbdbeddbdddbecaddcbacdbbeacaacaabecddebdecbecebadbcebeddbbebddbeededdcaabcdecdcdccabdaccbbdadccdbbedddcebaaedbcdecbdaecedceeadebcaecbceaeaddbcaeedeaecddeeaabbaddbbeaaeaaedcaacddceeabbeeceeeacadadeddabbbdcacbecabdeaaaeebdaebddbadbcccdaaaebedebbdbadcecbaacabdcbdbcadabedeaaecedbcadaecddebeccededdeaaedabdddaebcbbeeebbbbcbbbdbdbdeabadaceacdeddeaaaeabcdaebecacaeccccbbddeacddaaeeaccdbaadadacccaeecbbbaabdeebeeaccaacaadbcdebdbdcdceaebbcacbbebeeaedeadcddccdcdccadebdbadbcddbacabebaeebbbadbcebecddeeaadcdcdaddaabceddddddaaaaacddeeecaebbdcacddacdbddebdbabcabbdccadedadbdaaededbdacaabcdedcccdddedccdccedcdeadeadbbdbccaecedddbcddbaddacccadcecbedceeacbabcccdcbaebcbaabacbbbcbdacecebcdcccceadbaecbdbbcdcbdaedcdeaecbbaedceedbedeaeacedcececddecadbcaebadceedcdaacbcabdcbededaaaccbabeddbebdeaaadcdebbdccbedacaeecddcdceeeadbdebedaeddbbbeccabeceadccbacababeedddeeedbedecaaaebbbcbcdcecbacaacdbdbbeaceabbbaccddeceedceaadcdedcdedaedbccbdacadeacbbeeaaebdccecaabdedabadbceaddcbaddebaecadcedcaaeeccddeadabeecdbeeeceecceeadebcaabcaedaccbbaddadbcbeadacdacdebadbcadbabcedaeebdbeeeedcaaedddabebcebacbedaadeadbcaebcbdddcdeecacecbdbadddeaebeadcbaebbdcaeadeddbddaabbcaedacedbccedcccbacebaaaccedaadbeabdbebedacaecbeeecbddeecaaaebcbdcdbbadcbeaedddbebcbeabeabdbccbaedbbceceabdbbceddabbcecdaeabaabcabacceedaadbcaceaeaeeeceaceebdecbbdacccddabcdbdceeebabbccbebbaddbbcbcdddcccdaaaecccedbebaeabdcdbccccdadcaddadceaadacbdaabadbdcdccadcecedadcaaebeebbceabedeedcaecabdbaadcacdebeabdebddedeadedddcdacedecebccacdbcccebcadabaadeaebbeddeccebdcbbebbabaebcededdaabcddbdacdaecaadbeadeeadcdcecdacccaabcacddaeddcbadedbbbdcbdeebcecaccaedbbbbadbdeaaabbabbebaccbddeaecdbcdeadceddcabacdddcaadcecaecdbadabebacedeccbcacdabbcdceeaeaaecdbcbabbcdbdadacacedabcdbcccdcbdeaeadaddaddabadebebaabceadebcadddabbddcaeadbaaacbccaaabaaebaceebeedecbddbedeccdcedddcaedcddcebedebdcacdeeaeaedbdbbebddbeddbaeeaaacceadecaaeaedebeeabaaadbdddeebcdbaeaceeceabbbbbeacbacbdeaebbecaecedbbdeddaaccecceeeebdebcbebeedaeebcdcadccbbacacbcdadddaeaddacaecbabbdaeecebbcaeeebeeeccedbdeabcceaddcccbecaaecbbeecbaeedeeabbddabdcdcbbcbdaebabebcdaacadeecaaddabddceadccdaceccccccaebcaccacbdebeddbcdbaacacaceaccbbbeedbcdebeebddabbcaedadbcecbeeceabeceeeaedeedbadbacedbcaedeeadbaedcaeecaebdbabcbbbeaaeedcbaceadedcacdcbedebaebdceeceddacddaddaaaadabcceaaabbdcecaebedcdbcaaeadeedabeabdddeddccacacbccbccedeaeecaedebaaaabbacbbcbaaabcdeabbbaabaeaedddabeabebbaeccaaaebdcaaaeeceaadbdcaaaedeeeddbbbdbadeaaeaecadeceeeeabaecbcabacaebbedcbebcababdbbcacddcdbcedeeedeccaeeeedbcbaeccadcebddbbbbaaaceabaedcbabdbecdadcdecdebcdadbaecdbcbbbaadecddcabdcccccbbdebdddaaaaaaddbbacebcbadcdadebdbaadeadabddbcddccaeddabebbabbcebdeaddeadedccdebeebcbacaedbdaebdbacbecdecebbddabebabcecbcccddddcdbbbbcedebedbdadeacaadccedddadacabbcbacaabacbadadbbecdabdaadddcdbbbaabaccedbcceeebaceecddcbcdceadddbdebbceebbeccbddeaebcabedbdedbdcaecdcbdaeacbccddbdbccabcdabbbbbccaeeaaebddedeadceaaaedabbbacecabccbdbdcbcdeacbeebeedcbdeccacedaedcdbccddeccebcdcaedacabdecccedccbebddcbaebbcdaceedcdadeecebeceebabedcbccbbceabdddaadbceedbbcdbcddeeccececebbceccdbacbedacbaeaddeceddddcddebbeacadeceeebebecbbeaaceaeceadaceadbdddccbcbddbddbeadcddcbdacdadaabccdeecdaabecdcebaccdccddbddaeeabaaedbbdcbecdddecaeabacdbacaaaedbebcdbeabebabcaccecbaaaadedbcebbdebbebdabaedaeabeddeadceebecbddbadacbdadadbcdcdbbcacbdbccedbbbececbbdabeebabeddebacacaceeedbcdcceeaaecdcbdacaabadbdcaedcbabcabbebededdcdddacedbcbbcddcdabbcadabaacceeddaeecbbbbaeabecacaaaeccbeeeadeecbacdbbebdecabecadeadcbccaececbaeebceacbdabbdaecbdccbcbebadaccbcbaeccdbadabbdeacdcbacebbacdedeceaababcaaedbeaeaaadaeebcebdedbcdddecbddaaadbeaeadcadeebdcaddbdbbbebbedcbaeeebebadecdcaadeedccacabcbaeecbadbeadcbaccebdeeecddaaeecadbaceaaaebbdcedebeaeeabaadbcadcbacebbecebbecdaccabaedecedebdbedebeebdabbcccaaedcbbacadbcbbdcccbdbcdeeacaeaacccbbdaeadacdeecdeabcccbdbcdedddcdecccadeaceadadaabedabaeaeacbaaddabcbaccccdaeebeadbccbeebcadacaddcbacdcedaaaedcdedabceedbebeceeaddcbebdbcccdeebbcedeabdbedadbcaecdadedaaaccccbbbbbcbbacdcabcacedadbedbccceaccdbecacecbebbaadcaddabbebaeecbaaeadeceeeaddacbbcbaecbaeecdeadbedbadaacbecbbececbdcceaccaedcaaaaabcdcaeacdecceedeededbaacaadeabdbdeadcdacabbdedaabdeaedcabdceaedcbcdbbceeedebcbcababdeacdaacbccabdaabebadbdceeecdcaebcadcdcaabacdeebeddbceedcddaaaebaabbdbcdecebbbdaaeaeaddaedeccedddaccadccccdcebcedabbccdcbcabbdabcadaaaddeddbbeebdeabccbdebcdaacaeebabcdcdcbebabacbbcebdadccdcdaabeeebcaadaedeeadbdcbbcadbdbbceeeaeebdcbbebcbddbebcaeacddceebdcabaceddcdbebedbacebeddacebcbaabbbdabbeeadeabeeadeedcbcbaabeeabeeadeeebcdebacdbddeecdaaccbccbcdddcdebbaaaeaacabadcccbaeedadccaecbcdbcaabcbacdeacbcbdabbdedeeaaeadeddeaaacaacaccccaeadddededaededecebacdbeeeaaddeccaeadbaecaaceecbbcdceaeaaeebdcddeaadcedbabdaaacaebdedcaaeaaeddccdcabccadaeaacabdecaacddbeaddecbdddbcabbabaabacabdabebebdadbebbdadadeacedadcdbbbeeaeecbabbceccaedddeccdddbbacedabdcbeadbbeaecadeecddabaccbbcedcccebedeedecbcebabbeaedbecbddbbaebbbbdeccedbeadaacaaaaaeecdadcdbeaabaddaebecdedacdebdadddcaabdebcddebedcdecdeccebddbaeebbbdaadeeecedbadaabeabcacebcdebededbbcbcbdbaecbcdccbaaeddbabeabbacbcbaebcbaaebdcbeceddcacebadbaedeeecbaabeaacaceeecaeeaaaabdabbbeabcdaeaeadaebbcbcdababacdeccaccaacabecccaeacceedcaaabeaaaeadadceabbddbaacebebddcbaeaabdcedceacabeeddedbecbbeaedbeeaadedebdddcddabccbddacbcbecbcdacebaeadccdddbdcaaddbdececdceddbddeadabeecdcdedccddcebccdcacbabaadddbbaceeecbebeecaccdecdbdcceebcceabcddbedeabcaaeebdaebdebcacaedeccccdcbbaccdecddddedecaaadddccbcacbedabeaddadcdabeacdeddbadcebbdcbcededddbdccacdbebceeabcbddebacbceacbbdcbdeeeceddbcbbebcdcebbdccececaccbbedcddeabbddeededccddadcaeebecbbdbebbcaacedbcdbbdbaecdcdbccebbaaaaaadcddbbececdcbadccbbaacdaeccdcdddcbbebbbadaececcabcbcceeeebdbcbdedebddebcecddeccacadeebccacdeeadcbecdccdabdbbebbaeebcaadddbedecdbbbbcedebbbaadaedbaedbadbdddcdbbeddbacaaadccbdabddcbdaeecabdaabebbedabbcbcdbedcaaeabdbeeababbebbbdccbacedadcbddaaecebcdaeddaaecbedcbeccaaedcdccdccbcbcdacbceeabdadaeabcacdbbdbeadcecbaabedebaddaabcaccbaadcaeedbcedbeccebccaabcaadbeeddebcaaccddbdddcbbbdaacbddcebcaccbaeaeeaabedcaacbdecaebbaceccacdbdebbebddecbdccddabddbcdbaabddceeaeaeaddacdddddbeaaaaeceeedbbcdeceebcbcbcbbdabaeaceabdededbbaaceaeeccebddbeedeeaedeaeaceebeccabacddbcbdadaebdebdbbcabacbcdeaeaebeebadbeeaddbadeccecceccaeaaadbcdecadccbabeccebddbcbbdccedcaecceabebbedaacebeaadebcacacccbededeeadbbdcaedcedeadccececaeccbeecdabacebbeeeadccacdaccaadededabdcdebabbcbccbdccbdeabbcbaceeabeabbbdebcabcbdedaeeaaeddeedbacdddbdbaebbccddccccedccedccaacabaccecbbaaaddaceadddaaeadaaebdabdeddbaebceccbcaecedbddbeccecbacdacbbcbaadcdceceeeedcacedbaaacaacabccaebddeccecbeedbdecabadbadeaeddebeaecbbdeaacdceaeebebbecceabadcddedebabecdeccebcbbeaecadbdeabdceeaaebcddcdeaeddcbbeecbeadcbeeeeecebacbabbdcabbbcdeadaaeccdcbaddbaddabeeddedcebcabeaceeababbcbbceecddcdbaeaaaceeccbcbbaaeaaccdddcbbacdceeeadaeedabddabbdecbbbebeecadaeccdaebdcbededcbcbeeccebcecdedeaccbbdceeadaeeecdeebecbacaadabddededbdadebebcedccacddbbcddcdceedabcaebbdecaedeecddecdabedddadeeeaccddbdbddcebebbbeacebaccdecebaecdcbeadaaaaabaeebaacbbccedbbdcbdbcdcbdcdcdbdbcddecdeadbbacdcedceededbcdcaceaadbebaeceeacacbeeaaabbdcdedcddcecacaedcaeaeccaddedabedecdbecaadebacadedbaccbaebedabaedadbcadbbaecbcbddcbaaaacbbccaaeabbebaddaeeccddaebabddbceaebeeebbeeaaddebcebbddaaabeddebaaddebdddaaaacdeecbacaebeddedbbeeddeaabdccabbacccecdeecbccdbddbecbabdadccebcccebdabdbaaaedbceebdbdadbbeeebccbaedbeedebbbacdaccceadeddeeacaccbbeddeeadadecebbdedcbaecaaaaddbababdcbeaaadbcddddeecbbeebaabcecbcdaecbdedebaacebbeebaaadabcaccbdcbbadedeaaddbbbaeddecaceedecbaecbecaedebcdbbedeecdbedccaeeaeedbaccbcbdbcceeaddbbcdaceccebbddaedeeeaaaddeacbecaaaecbaeeaebdbdcbeaeddeedabdcccbdcebcaddccccbdeacdaedabeeacccacedeaccdabccbdceeaedddecbdabeaeaadabaeabbaaadcbdcdcaedcbadedbddbaebcdcbbddbbacecdccddbaeadebcacbdbcdeabdcdadeabbebddbddcceaceccddbaaacedaeeccacdbabbdeecadebddbebcacbdaaabadbdddabbeaacaecbeadccedacddbeaacbcababbdeecbecdcdeaceaebcaaceedceabacebccabbbbdceececbeaebadcbcedbadbecbdddabcbceebdbdaccbaddcecacacdececeedbbecabebdedbadeebdccedbcabdadbddbaacbbeacdcaebeeddbbbccbddddcddadddbacbbcecbdbaaedaecbcaaebdeacceeaeebeccaecdcaccabcbddeedbceccbbacccaecabecaceaabeebbdecacaedeaeeedcbeadebdcabbcbdebcaedecbdcbbcbccaecebbdbeaccdcecbaeabddcbbeebacdccaacdaaccbdebcdaceccdbaceeabeecaaebedaabbdebcbeaeabadbbbcaadcccbbccdeaebcbedecaebcdcdbaeedcaaabddceaeaaeaccdbdeebececaacebedaccaedcabdaaeaecdbeaabdccbdcdaddbeeebacbccdebdeabacccdbeaaaaaecbadadbcaecbccbdabbccaecceaeaaebbaadbccdddacdbeeaebcddeaeabaddbbccdccaaacddedabaadbddcaccaaccbddeecdbeaeaebaeddbabcdebbbbabbdbddcbdeaaecdbecaeacecccbedbbabddcbcccadaecadddcbcacebadcaebdcebebabcceececbaaebaeacdebdaeaeacaebabaecadeabcceeceebcdaebbdadcebbebababdbeccadacbedbccbbaeaabddaadcceacabccbedcabdaccdbaeebddbebdcceddecaacbdbdeaabdabbcecbccaccebbddbaadabebdeeeeeebaeeaacbedbccaeedadaabcbeadababeeddbeaecbedcccbcbdedbdaaccaedacbeeaadecbcbaeaacedddbebdccaecbbbdbbdecabceddadddedcbdadcbbbecdbeaaeaccedeaaadcbddeabbaedccdceadcabaddbccaadedbbdedccacbedacaededaabcaeacadbacedadaacbbbeebaacdbeecdbbacecebceecbdedcbbdeadbdabcdadeddddbdedacabedbdebdbcdecddbaeebccebbcdcaedebdbedddbadbbdbcaeebbaacdeecabbdaecaadadaacddccacedcedbcbeeebecdcaeecaaadeedeccdcaedebaeebdcaaadaaacbadedebaaaceecbcaabbbededbceaacededaebddbbdbbbdbeebdccbddaddcabedbeaabeaeebbadaadcdddbaecdceaaacdabaddceddcccacccbaddadacedacebaccceaaeabbecedddedadaeddddbebddbbcacbcbaddebeaeebbcccdbcbaddabdcbebaedbbeebbbaadeaaaebbadaabdadadbbcacecbaaaddcaaabddccaeeceddddbcecbababdbdbecdaccdceedaebeaebcbcadcddeecbaabcbeccbaebbbebecbdeabadeebadadaedaedcebedaeccdaeaddaedbaedadeacbbadaeadbaedbdebebabbaacdcdebdeebeabddbebcdbeaeeaecabbebdcceacaaacdecbbcbababeccccbcabeebcbabddacbaebdbcaccaecedddadacedbcdabcaddcadadbadaccdbdedbdbadbdbbccdcdaebccbbceacdeecdcbcbebebeabdaacddcdecdabbabeddeddaddebaeaebdceceebddedddbeccaadccdddaccebcbedaeccaebeaaccceccebcbabdcbbaacedddccaebbcddceccddeababbbcaeaaceddbcadccacbaeaedcbecdebbccddcccbcabcbedbcbcabedcaadceacedebbeeaabceeddcacbeecbdebedcbadbddaeebddaceeebbdcdcdceebbcaacdadacbdbcecaacceeedadddcbecaeabbedbdbaadbaeaaddadaddccacbbcceccabbcbdcdeaeaddaadbbbeebcedecdbbddabdddbdbdcbedceaddacaeedddcedcbbabedccaaeccbadebcebeecbbcbddbbbdcbbdaeedcdedebcbddbdadbbeccbbeaaabddbcecbaabadeccbdbeabdcabbbbaababededdeabeddaaeedbeeaceaceedddbcdbcccebbaaeebacbabcddbccccdceccdbdeebbdddacaebddeedbeeadbdaacbdecabcbbbebedadcbeabbddeabbbdabdaedaeeddabebcdcceaaeaaacbebeabadcaaebeecdedeaaaedacaabcaeecdbdcbbedbceddbeadbaaeddbbdccaacdbcbcbcddcdadbedabeeebdeaccababeeaabdcaadddecdaeeaabeeebcdcccddabbcdbbadbcceadcecbdbdbedcbabbabbabaebbdaaeacbeceadedbdeddccbeeabeadcedaadabaadadbbdddedcbbcacabeabdbeaaebcaabcacbedbedecebcaacccaccedeedceebbebcbbdacdbebddeecbabacccedbccaeeaecacbabacabebbeaeecebeaddacdbbdcebedbbedadeadbbecdadaeabecdadcaecabeccbadcaeecbbdbaeabedaecebacaaceebeacdecbeedaededbabdbdeeaaccacbdcadcbadecaeccaaacebcdacbebbebcbbaaecdceddcbbecaacbceebacdcaebaccacbadebacbccbceccadaecadcaabecddbccaadcbdbcbdbbedbecabeccbceeaeadbaabeabcbcddccdecebaeebcaebebabccbbceeaeacaadebceaeccbdbaedeebbababbbcdddebdabbacedbdcacbcbdebdeabaedbccbcbadbdeecaeaeaacaaeaeaedabcaabecbcdccbcccecdecdaacecccbeeacadbaacbdbccbcbcdbbaaabddbaeebadcdcaacedcbbdecdbeecbbbedaebbeaccccebccbeeccabeecdbdddebaaeaeaaaacddcdbcbddcbdbdabcabdddcedcdedcacbeacaaacacdebaababbeebacccecadcdcbeeaceedbacedcaddabbdbdbeaaeeeeeddacecdabaecbbcdbaeaeaddccbbbbdbbabadeeeeccecedcdbbdddadaacaccdccddbcdacebebabebeeadeeccddecaebebbaadacacecaceeeccdebeedabddedecadcabcecedcdbbbdeedcaccccbcccddeaddaccccaadaecddbacaecaabacbbcaaacbeaadcdbbcecccbaedcbedbcadbabbbbdbdebdccdaacabedbcccbdddabcaabbcedcdceabbaacaeabecbacbcdeebcebcdcdcccccddecadadedbeeecaebcebeeabdeeadecbdbcaeedebcacbecccaaddaedeaddccbecabbaeaaabeecadbbcdecbadecaaebabaadecaecaebeeaacdacdaaacdaebbcdeedacabadecacedacccebbadaeaaccebcacbdabeaaacacddabbacbaeceababedcdecebaaaaeebbbedadcbcaccedeabcecbadcddeacdbdbecadcbccecdaddccebeccedececcdababdccbbbaabacbdaacedeacdbbabcebeaabebeadbbdcebcdcecaeaceededaacccbbbdaaeaaadbaabcececaaceddaeebbeacbbdadcdeeeedbbadceeadbeadecabbcedbecacdacacebaadcebbedebaecaeeecedecebecabdacaeaebddddbaeaaebbebdcbacbddadeeeadebedcbccbbdddbabbbcbceceadcbedaaeacabeeccdddadbabcadbdbbeecadcdaabadaebdaceebeeddacdeeaabeaebccddabaaecdbaddacdeddebbeaeacabbbdaecdeeaeedcddcdcaceddcaddcdddbaccceeebccbcdaccbecaabebaadaccbeacddacaeddabbeeebcacbcaedeecaeacacaaeabecaeedcdadeceacebbcaabedcbcbcaabeebcceaababaaaddbaeaeebddcabcedbbabcababeeebabcdbeeadbaaccbdcbecaaccedaaecdaeaebcacdaebddacddaeebcdeddcaaadeebccbbbebeabeebbedcdaeedcdacbeaadabbdeaadbbddcbebebcbdbdbdececbcecebaabdabdeddecbccbebeaaaeeaaacaeaddeedbeaabeeabbaaeeaebbecbaddbadeceaccaaebaadddcdedbbdeeeedacaedaabdcddabcdccaccedbeabeaaabcdccdcacbaacaacbdaacdaeaacdbdbcaeabecbbabdccdbbacabdedbedaebdcbdabcecbbdbbbcddccdcbaecdbbdceebedbcaccaeacdcebbdeabddadcacacecdabcbcceadceddaabeeaeeadebeadbccecbabaeebdcdcecccbbbaeaebcdeebceeeebaecccbdbcdaeedccdaacabcdacdbebdecaeebbccabdeccbecdcdbeeacadadcbceddcdbbedcccbccbaebacdcdedacaceadaceccbbddeeaadebababccdceeeadbabbadbcaceaeccecbeeebcdcecddcecdaadbecceabeabaecdabbbadceebbbceadedbdedcbdacabdcadccaebceebebddceedcddbebaaecdcbbdaeaaeeddbdecadaeededdeadeebbcecadbbceebaeacedbebddabdbcaecbeaddcabeaceaaaaeeeedccedbdbcccdbbcabdcebaaedcbebaadededcccccddbcddddccecaecaecddddbebcdcbcedbcdeeaaaeceaccadbbadbedbebddabedabbddbbcaabeebbabeaabeaaeceaaccbddcdeaaecaebaaacecbddedeeabbebaecccceeabacbcdcddeebdbeceadaeddbedeeabeccecbeaacddccaeacebacaabdaddccbdaddbeabceaaacdcadacbcaaabbbeceeceaaeabdbadbbbaadbbeabdcabecadedabadcadddbeccddaaecaedededabdaedbcbbaeeaadbddecdedeaedccadeadbeeedbededbceaeeabedbbeaadacdcabecbaadbddbedccabbdeacadeaeeebacacbaaeeedeacbeabbaaaeebdaceccbadbbecccbecdbaeddcadbaebacaeababdbbadacbdaddbbeadcdcecbcedabeeebbddceaaaaabeecddcaeddbaedadababcccdcedcacdaaeebcaacaeeaaccabeebcdcbcadaaccaeaebeebceeccaaaaaaadacaaccebdbdcdbebebaedcabddcecabebacbbeaceedbaeaacbabeadadccbecdbddaceecceaeabebbaaabdacdcbaeecdeedcccdabadeabcccddcbddcdaeaeceaadceddbdaabeeddeebbabcebbcbbaddedddeaddabcbcbcaceccaeaeccabbcbcbbacbeeaabcdcdbeedbdeeaaaaacdeaebbdbabcdececdcebbdeeaadacbcaadeeabaeccaceadbadabbedbaeaeabdecaddabcbadccdeedbabeaeaacbdadcedaadebcdeeaacedcbbcaaeadcaadeabdacbaabbadddebdababdcdddcdbbeccaccbddacaecdbdbadacabcebbacceccdaecdadecddbcdbbaaabacadeeceeaacdbdedecaecaedbbacbdcbecbccdedcbeccdceeaeecdaabbdcaeaaaddcbdeaebdceeebcabcaccbeeabcccbacdeaedcaacaadbabceeeabeecbcddbcdadabcdeacbadecbeaecdaacccddddeebcaabadacdadcabadacaceddcdbadeaecdedbeaaaedbcacdadcecdbbedcaaedcedcbbabedbdbeeddddedaedcbabaebdaaeeabeccabdebaaeabddadeceaebdddceadbecedeadbbedccabdabecdbbceedaaaabedacddccabbdacdddddcedccbcdaebdcaebadabbdcdbeccdddecddaebeeaeebcdccbbeaeaccdabadbbdaacaeecacbbbedacbddacdebdcbbcdbeecbcebcdebdbedcdaabaddecccbebbcceaadcaddbdbddacdcdabedcbeebdeddccaaeaebeecaecebdeedbdcdaadbbcbbbcaceaacaebabaeedbcdaabccdbbebbedcbcaeebebabebcaeeedeaddabcdcabdcbebcbbeeccdaebadacacceaccbbccadecaeaeaabaddcbabeadecedddabdabcbdeeebcaaaeadcbecbeacededebdddedaeeccdcaaaeabbeebdcbdaecadbbdbdeacbdddabacdeeedccbcaddcbeaddecaebacdccbbcbcdadeacbddbdadaadacedabcedeebebecdccbdecdbeddaeaebcaaebbceadccbdacecabeaaadddeeabbdadaeeadbaddebbceeeabbcbbbcacaaabccdbdbddbaacceabaebbccaceddeedcbaaedbacbaaeaedeedabcebcbdccdabbddadaabdcaacbbbbbbdbacbbcedacdaaddcebbcdaacdacccdaabcaebedaacebacababcbbcbaabeebadbaaaaebabaabdcecececdebbcdddaddbbdeebbeadcbbabaaccbbabcbecaedabdeebaebaecaeccbabeacceadeaeeeebcdcbcbdcaaaddebcedbbadcdeaaeceeddeddccdcadbeadaeeebecdcdebececadbedbbadcdacebdcceadbeeaedbeaacebabdbbbdddcdcdccdaaebaacabdeeaebcbabdceeedbddbcdedcbbcccededecddcaccdbaaddcabedbdbbcdeebdaacaccbbbbadbddceddadecbedbdceaedaccecbdebbdeadadcedbbebbceddadbbeccbcaacecaeeeaedccdbabdaadbbcbcbeabceacabcbddbeacdecebeabecdbadbbcdabbcdbdbbcbadadcadbbacedbedeeecbadecacaaeacebbdecbccbbbecbcaccadccebcabcdaeacbcaeeadecedcaededecacbbcccbceacebcccecbbccadadceedcdcbaaeedbeecbceedceecccaaebbabccdabbcaebecdbdcbdaecbcdaddcebbedcebeeabcaeebacadbcbbbbdedcadacdcebcbdaeeeeddaccccbaabdaadabceedadadeaeaaecebacbbedebbebdbbddcebdaddaccceccdbbdadbbaedaebcbcaedacdedcaabbcddaadaceabcdebcdbcebacacbaecbbedcadbbbbebababbdddcbbddaeadcaddcbeaaaadcabdecadeccbdaaeccddbebbbdaddadcdabcdadccbeadeacbbbcedcbddbecbddbcbaaaaebcbbdbaebedcadcbcadeaceeeeabbecacaccdeeabdaadeebddddbddbabeabddbcdbbddecbaeedbcacadecaaceccbebabadbedbecdacbdaabacddabdebcddabbdbedebbdecebdbbdadbdcbaeedecbeeacbbcccbdeabcbcaeedaeaaadedcdceddaddeedadbdacbeaccdbbeeeaccbcecbcdacccabbedeebabbadededcbceeeecceeecaeddecccaddbdababacbeadbcccddacbcddeaeddababaeceeabcaccbecbadcddaaeaabebececbcbaacadcacceadebbeebeccdbbcddcebadeedbbceddcadcaceaebdcaeddbbbeaddebddcabeadbdaadbbbaecababeaebcadbbeeaeebacdedcdbaccecbebbeaddbcccdecdeaaeeadbaeaabaaadeebcdadaabcbaebedbceaddccbcbaecacbabcdecbeeaccbadaeeccebcdcabbdbdbdeeddbddacceaceabcbdadabddacbeacbdbedadebcebeeecbbeedbcdabeeedcdccdbcdceceabdacdddccacbcaccadedaaaccdcddaceccccadbdeabacabcedcdedaedbbdebbadcaedebdcaedcbcadcaecbebbcabbaebaacbacecbaeecbcaeababedcabbbebedeadcacbbabdacdbeeaaebbdcdceabeacaedcbbbaaabbeedbacececacaedcbbaaeeadaeecacaaebdbecedbdaeabcabeeeaebcbddaedaeeaeaabbedaedbbaaaceebccbbdbdbaeeabdcbcbcbedabbeacabcbebacbbabaaadcbaacdbcadcbeaddeeaaecacaadeecedadbacedbeddebdddbccedccaabababcaeaadcebadddcadbeabaaceebdebcceabddedeedabaeebbcebbbdaadabbaadcdaebcbeeebccacdbbdeabdeabddccebaadbcccdbedbebeedcddcdadddecebcdabddadcabcbdbcdcceeecaecdeccedbdccabcbcedbbededeaaceeacbdeabdddaaebdaddeddcacaadaaaaeecaadbcebeceedcaddaacdccddcedeedeeacaedbeddeedcbaebbcbcbebebebcdccdbabeeddbeddecdacaabebdaacbbacebbbdddaacaacebecccaabbcaeccdbaaedbdceebeabcecbaaeabeadcceabbecacddaabdebbcedcaacbdcbdbccaecacabdeacbeadbeceaedccdcebceeebeaacebcebbaedabbcbdccaaebddecdceabbadeadeccebeddccaccbcedeebeeeaedaaedbcccccebdedbbacbedbcecdedadecbbacbacaadeabadaccedcdebcabbceeeaeeececbbcbaeeaeeeceacbaeeeebdacbadecbebabaeceeaebaebbbbaadecdbbadbbdccdbcaddbabedceaedebdcecdeacaeadcaccdedcaddbadbabeceaadcbdedebaabecedabbcdceddbbdbedccdcdcadddebaaeaaacbbdeccdeeceedaacaceddbcbedecbaddcaaacbbacaacbaabdddaacdaddbdcebccbaedddcdeaeacdcbeacedcecadadebbabecaebdbbbcceebdcbceeceeaecbbdbbebbacdbeecaaabaaadbddabdbdcdbcdcdeddddaeeaebbcbaaeebbaebcbbeacdbcdcdcecddececcaacdbebbacaecebcaaeabdddbcecaccabcedaecadecacbcddedaeedcdadedacbbabacaaabbebcaaacbdaadbbecbadaecebcaaebbebaeeedbbddadedabdeeebcacbeaaecadcaadedadaeebdabdbdaeaceebecadddeeecababaaccabadececceadacbbdcadeeeddbebddbcddeebbaccbecdbacaededcceacdaddacaeadbbbeeebecdbdbedcbaebdcdcdcaaedaecedbdccddcbccebdbaddbaddddaedcdabbcecbedebddcebeeabbaebaaaddecdcccddbaedcaadebbdaaadacbbadeccbaecbbddceabeecdbbbacdedbabeadaaaaccbcedbddeedadcecdeccabbbdeaaaabeeaceaceabbdbdadbdaedeecacdabaeadcccdeebeaedebdabdacdabdddeebbbcbaddddeacdbadaaacdbdbcbaeedadcdebdedadbcbabaebbbbedcdcccbecebddeaeeaadacccecbbccccacbcddabcadebcbeddbcbdccbcaedadcbcbddccdcdeececceadcbebdababdaadadbdebddceaddabbcedaebbdcececcedcbcbbbedcdcaeaeabadedddeecbeaecbebdcdbecedecceedaaaeedeccdbeeadbcbdebdbdbccdabcbadcbdcaddccbbacedabcecbddcebabeeadccbdaabebeecadbaadeacdedebcedeabbbcddaacedeecdcdceeeaedddbebbaeaabaaabeaddddadbbadcbcbdebcaebdadcdaaccbecaabcbaceaabbcbcbdadecaaddbbdebbdadacbccabaababcdadedcddeebbcabebbdbcaabbbebbadecbcceebdbaebebaeabdcdbeccdebcdcaaebceadaedbadaaebdeacdececebeceebabacacaabebeadebaccacaadbbeebbeaaadeeeacccecccceaecdedbdababbadaabcbebecbdccebaddcedecedebcadedaccbdbdacaeabdbeaabcecbbeeaeeadabaeaebedaaedeebebababedcadbaeeedcacbcebaccdceedbccaacdaeacbbbcabbddbcbdbbabadcebdbbcbceedceeceacbdaddbbabcececeabaddedaddccabbebaabdcdbbeecadaeaeccacbbeccabebcdadbabbdeddadadbadbebcbdeaaccdbdcdacbaacadbddccbbdaecbedacedcbdcbaccebadbebdddcddabedddccaedceebaceabbdeeebcbaddaedbdebedbaaabbbbcbcbebeaeaabbbaeabdcddaeadcbdbeddbcbbaccbabcacabaddbacdeeaddeaecdcacddddecccbcbbbbccbcaeeccdecdbebccdcdcdbbcabebdbdbddaddedbbacdaceccebdaecbdbabdabdddaecdbceceedeabbbcabeaccedaebddcdcbeacecbbdbeecdcebadeacabadedacebaaeabacbedeaeccecdcabedeaaebeeebdeebddbbeeeebdbadabccabadeadbceececbecdedaccaeacaccabdcbcbbeececedcbceeedeaeddaabebbcceddbbbcccacaecdacbdeebcbaccccbcddabcaabbdbcaeaecabccdeceabaaccaccddababdcceadcecbeaeeccbcbedbecececccccbceeaaddbcceacaabcaebccccdbbcddbeeaccdacddaacdeeeaeacecaebabdbddbcbaeadbacdcaccbdbcceaebabbebcddeddbedaeaeaabbdedbdddabbcceebdbccedbeddcdbdcacdcaedaecaaeceedcebaaeaebadcbcdadcedcbadebdeeaeeaddecacbeacccdbdaeecddedcabecdaacaccdeaabbccadbecdcaaddaedaacaeecebdaeeedcebbdbeaecdecbabbedbcadddcadcaeceeabebccbcceecdbbcdceeebadeeadacecebccbeebeebcccaddbeaaaedbabdbabbcbdeabedadaeedaaddcdbabdbaebdbceaabadbacaeaacddceddceaecbbacbceadbeacdecdddeeeddbdabbeaacdddddcceadcbdcacacdceeebaccdbdbeaeeabcdadddddbcbcbeecbbeeedbbbedbacdaebceabdbbeedeacedcdddabbebbadeeacecbeddabebcdbadaabaabebbbeaaaaabceccebcabcbcccccdadacaadecedbaeeedcabcddeaccedeeaebacbdadbadabacaeeaecbaaababadbbbdaacadaaddbbcadbcaeeeddaeaebecdbccbecedecceaabbdedbaddccadeaccdbbdaaeeebbadcaabcdacbeebbbccdcdeaacededaacadddabcceeaebeddecdedceabeddcbbdaaecaccceaaddeebddabeebcbdbebdebadabaeeceadbececedeecbbacddedbdaccccdddbbcbbdeeadccddbaabcadcbbdbeedbeeddabceecedcdecdaeecdbbbedbaadaaaebbbdddebdbceaaedabbabaeadbebebbdcaadcdebcedacecaebdeebdbaaecbbdacecdcdeaddabdbcebaddcdbeaccbadabebdedbeeaceccbbacdabadaabccdceecabcdddcebebeddeeabdbcbeaaeacbacabeeebccbececaeaececbbeaadaebceebdaacdaabedeabebdcaeacceccecececcdebacedceacabaaecaebacccaddddedbbabdebaedebbddacadbcedbbdacbeeceaccaabddadbdeabeaceaddeedbbbecdddcaccdabedadbdecedcbbccebbdbacbbcdaaceaeccddacceeaadbdccebbbbecedbbdabadcbebaaeaabacdeddddddedbbadaddbdcbaedbccacdacddabbebeebebcdcbdbddbeddeaeaeddbadeaeebbcecacaadcedaaecceacecbeccabcdceeaeabcecdadcaeddbedbcebbecdacaaecdeedbcdceaedcbbdeeaadccbcbcbacccaceedcddaabaecbbcbcecbbcebdeeeebadcababecadcccbbbdaddbbaeeaebdbbcdabbddbcadbeaebdacceddedbeccdddeecaebdccbbebeaccbddccecdbedecaedadddcbaaebbeedacdabddddccddabbbddebbbdeceaeacdceccebdcdaebbddbabaabdcbabaebcecdcebeddcecbeecdccaadbdecbdeadaccbcbdecbabeedeecbddaabdcabbcedaaaceeeabeccccedbbdecabceccccaaecdadbccaaabcccdcacbacddcedceacbdddebaaddbabcaccebbdcacadbbdbeedebbcccbbabbacccbccbadeebadecbdceabcbcabcedeeeaaeecccceeadcacceddddaabcacecaebcceabadebcabbcdaadccaebdbddeddeecabacadcbaabdabdaddeeecbdebdbbacecaecbeceeebbdcbaabeabeaebedccabaabdcadaeccdadbcbcccdccacdeccddcedeebbdcdbccdebebbbabadbdaeccbdedceeaeaeccccbcadcdaeeadcbeddcacdcbdadadadadceceeadddcbddbedadddbaecdcbbeaadbeabdebedbaeaaeeaaaaaabccaacebaeddbaaeaddbebacbceebeeababcdcbabdddedbabdeeecebacdcecabedceebacebebdcedceedebabbaadcbcacaddcdacecaacbaaccdadcebebbaacbeadcbcbbcbbabdeeeccccbeacbeeacbeaaaedcdaecbdedbabaeeccbbcceaaeeceabcdbbeecdaadecbacacbaeaebdeaaadcbecabacbccccccdeabccbdaaacbbcabcbcdebebebaadbddcbbcceaecebcdaaebacceabcdccddedeeaebbdcdaabccbbcabcdececdebececeebaaaabcbabeebdaaebaeacbcaadceebbabaacbdabedeaeecabbdcbaadbdbbdaaadcbdebdadcbdbabbbacdeabbbabaabebeecaaeaadbacdeaeebbebcbacdbeddaeeededbdccbeddbcacabbecedeeeeabadeeaebececdacddedcadedeebcadcbecbcaecccabdaddbbdeadedbaccbbbbddecaaeddedbdbdecdcebbaeedeabdebcdaccadedbddbabecbadcdccdcadaccdcdeeedbeacabbdeedcaadddcdcbacbbeddedeaeeeddddbdbaabceaeaddbddecacebeeebedabcaeedcaeeeadcdccabaedccdcbaebaadbcddbdecccbeeabaecdeebdccbbacccdebcaabbeaeacaddbecbbdacaaeceecaeeadcdbcadaddbceeabaeccabcbedcbdcbbeabebecabdebbadcedceebbedbddeabdbbbdcbbccaccacdbdbbdbeacebbecaaaeadddbebebababdadacdbbeaceedcaabbbbdaeedcabdcbaadccaadadbcadceeecbeabacbdeaccbbedbdeedebddccacdebbbdcdedaceadadccdecabdadaeccccccbaeccdaeeecdcbceebdaeecaeabadadbddecdccdabbbadcabdbeecaccdeeabdaebeceaccdceceabbacebaccbaedebccdabbbacabbdaecaabadddabccdedaeacadaabebeeccccaeaeeddebcbeadaeecdcdbbeadaeedacddbcdceabaaabaedaacebaacadedeccddccddbccdecebceaaeaceacabdaeaeaecdeeedcbabbabcaaeeabdabecddeacdbcdcaadbdcabdbacebaebbcbacbddbcadcbcbedcdadaeacadcbbcaddacadedaedceeecadaabebbdeacdccbceecdabddeabdcaadbbbcdeadebabaeeaabeabdccbeacbeaaaecbbcbdbedcbebeddabbcdeeacecdcacbbcecdcdbcedeccedadebdebaaaedbbdaecddabedadcdeeedccbecaddbdddaebddaaccbacbbdcaddaebedccdabdeececebbbddbadcbeedcecdeeaeaabbaaaeacabccbbedcddaaacbbeacdceecabcceedeacabacdabaeceecebecdecdeedbbdbaeadbaceebcddeeaedededaeecadddeaecacdbeeedcdccaedceaebacdcdadabcababeaededccccbebeeeadccadeaaecaacaabcbbdedaceddeedaeadddadbadddcceaddbdecaabaaeedacaacbadbdebccdcbcddeabeadddbedcabceeaabadedbccccddbccedaacbebabacebdeaeeeddbcbceacdabacbadeccbbdeaedaddaaddabadaceeccacbebeebeedaecdeaacbdbceccbddccecdcddbcaceaccdbeebdcacbbaecbbedbbedabdeedeaadcceebbaeddcbdcdbddcdbacabdcadecbabcceabaaaaaebeadadbeabcbcdecccabbcebacbdaebadcbcdbddaddbcbceecaabcecccaccdcddbdebcdadaacbbabbbabcadaadbdddbeabebeeacdaccaedccdadbaccbedaeecdabbeaebeddeddadcaedeecccececedbcdeaebebdcabaadbadecbdeceaccbebeaadedeebeabbbedbabbacaeaeabbeebbeebeadbbeecbdeaeaeeedbbbbdeababcdbbbcebdddcdbebedceccbbdebbabddeeebcabebeeeccceaddcccddeeddaedaaadacedaaaeabcadaeaaeeeebdcabdcdaadaeecaaebeadaaedbcdacabaabdbddccbdcaacacdceedcececaecdbabdcccebbbdebabcccbbcddeeaacacdaaacabbbdcaaedaccbbebbbcdaddbdaaaabcbcbbebdcbebeaecdeeabcbebeeebdebcadbeebcbbdbebebaaadcaddbbeadaadacdeddebccceddedeaceeaaaccdbaceddebdbcbcabcedecbaabcaecdbadadbdeedbdbeeecceeeddbadcdebdcedadbbbeedbcbbbcaaeabceaddceeaddcebacdaacacccbceedeeecdbedaabccabedccccdacdacebaabadbcdeaddcdedcdcdbcabaccabeadbcbbcecbdaccbbbeaecadaccacbbebccdadbcaecaddcaceeeadddbcedcedebdbecdacedeaceabdacdbadcadaaaeedbcedccdadadeebddcbbdcbeeeecccabdbeeedeaaaeaebbedbbbcecbbcdddededddcdcabaaaaeabaeedeecbbacabdbadeccdeaacdaadcedeedcbcbbadebaddbceedaabbbdacdceaaceeddbabdcbaccbceeddedecbbadbdebbceabdececacedbbcebcceacbcbabedbecbbdededbcabcbedbbebcdaedabcebcbecaabdedeebacadeeaaabcbdadbbabbaabcddbebcbddaeaaecacacbccbebcdcdbecdccaeccadcccabdbbecbabbabeadbbccdcacacabceeddbdbccdebeedbedaadaadbbcbdadddcaeebcaeaebeeddbedeaecebbddabaabdababebbbbdceebdddebcabddeeeecaebaabcebbddecaccbedecccebeacdceacadaabeddadcbaddabcdcddcecceadbbbaecaeeedaeeedaecdbcdaabeddebbbdbacaaeeadbaadacadadabeecaabeedbccadedecdeaecaaadbcaebeeeadeeaaebaadadceaedeeabeedacedccddbebdbcaacccaebacbbbcaebcdcadeedebabbbcabdbcdeeededbbaaddbcbaacabdbbaebebdecdbabebbceaeebaedeacdeeaeedbeeacaacdaaddccebabceacbbcaeedadcceddadcdadbedaacbdceecebbaadeaceaadcdcadaddacbaceacceabecacdebdadcccdeeadaadebebcbebadeceacaadcacbccdabcdceaeebdcccdeccbddabbadcdebddcabbaccbcbebabbbacdaeceabececeeaddacedeebdcddcbdbcaeceebbeabababaebadaeeacdaaacddddebcddddcedacebcbcbcedbcdbbadabdbaecddaabccaeacdbbecedbcedcbeacbdcabbacbaaebdabbcddecdbabdcecbdcedcbbccdbacdddbbdabadbdebbbdbcbbcebcddbeedbecaabcbbcabebbcdaaecdddeeaddbaebaeeededcdebaeecbbcabebdebbbddbaabdbadcdbccabaedbbaaababcadbbedcacaadeeddcedeedaeeabeeeaddccedbbddabdbecccaccceeeacebbaeddceddebcebbdccecdcedbbeeeddabcbdebccedbebbdceaceceecbcccdebcbbdeaaabcaedcbeacdccdcdabaebcdcaebdabdcccaacadaecdbdbdbdbdcaacdbedacaabaeebcbbdbacedabcceeabddbbeaaebdacabcbdceebccdebddcaabbbeecabaebcbedaababdacbbeddbcebdcaaecdecebbdcbddeeabbbcbcabbccadebbaaddaababbadbdeaeeaceaaeabbdbcceccebeaaadcddcbcebbdaeeacccabccdecebeaeaeaedcacbbccbbcbdedeabbdecbbcadbcaaecaeadebdcddecbcddeabcbcbeccadccededcdbaceaeaedbccebeaacbbaeadabcaabcbbbaddbcaaabeedbacdaadcbcabeaabbaedeaccdcacceababcedaccacddcceadabbdddcadeeeaadbbedeacdadddccbccdebcdeecaacabdeeecbeeccbddeecdbaecdadadbdbaeaeebaebbceacebedebcccbeebaacdedbdeeacaecaaeaededdaadabeeabbbabccbcdebbaeeeeeceeaddbcdaceaabdecebdadeeebcbcdacbbccddddbdcddaaeebbdacaccbbabcacbddbebaceeaddceeddebcdddccbbcabcdabbcbbaecccdeddcbeebcbbddddaeabddeedcacadbcebdaacacbecbcdabecbcaebddaadebcccabcddabbcebaabaddebaacbbbeeaabaaadedbdeaabeeaecbadbccaedebeccbaacaedbdceacddbceccbaacbbaebbccddaaabbcbcdeeaeadbadaeccccadbbdaadbecebbbbdaecdbaeadedbdadededdcadebcecaedbdcadedaaceddccebdabbeadbcedcdddbcaccbdbbdbbdaebeaceeeccbecbcbaaccaabbdcceecdeceebacedbcbddcbebdbbeeddcadabdbbbcedadeaddedbdcddcabcedcacbedaacccceedcdaceadecacbcadeabddbaddbaaebdceaebbbdcdecbcddaccaaaaccecabcdacdeebbcdbccebbedadcbceaeceaabbbdeebbeddcabdceeeceaccecacebdbedabaaeddccddbdbbaadcaaeedbeedbcaccacddedcaccdaaeaeeedadbbdadeaeebecaecbddeabbccedbabccbdaecbacacdeecbeebceaaecdcbcdccbbecdbdcdddbabeeeabaeaacbebdaddbbbadebbcabdbbceddddeaceacceddaccebbbaeddaceeacbbeeebcceaeceadddeedddacddedebdcaadecbaeedbcedbeaeeddabeaeceaddacaceacaceeedbdbeebdcedbcedddbddceeaeadedaceccbeacadecdbcccaeaeaedaaedaeadddaeaeabeddedbadbbadbeaddcdbaaebdecaeeeebcbacbcbccbabbaeecccaaeabeaeebedcaddbccdbcbbaceabdcedcddbbaddeddecebedcbbabaddbecabbaeddadaaebebaaebcbbabbcddabdeeaeadaddbedeabdacceccaddcadadcdbadedaaceeceaadaaddeabbeceeabbcecedcaadedcedbdeeadbcbebbcecbcbdedcececcdbbeecedceddeeabbaedbadebbebbceebebedcbaccebdcdadcbbcbdaddbcceacddacceaddacdbeecedeedceccabacecdaedbcdbcadabbaeaecaeaacedaeebbdbbadabdaaceebbcbcaadcaaecdadabbcdeccabaddaacbddeecabddbbceeedecaacceadebdddbdccabcdbbdcaecdbadcdcdbbebdedadebeabdddedabceebbebcaaddeaccebbccdbeabeeecbcebabddebddaabbdebeeecabeadeebcaecaadaabaacdedacbdbeeedadcbbcceecbbdaceabceedddbedabaadeacddeeadbddbdebecceeabebdacdecaaaceeeaedbeddccdbdeeaeededcbcdddaecbeebaaeeecdaaaaaddaadabbcdaaceddbecedeccdcebeddbeeaaabecaeacacadadaeaeecbeadeaaabeceeacdeedbcaeceabeacddcaeeccecaccccbcbccacceceeaededbeedbebdbecddeadaebebbddcccaedacccaadeebadcbbacccbbadccaddbaaebdadeccbaacaeeebbdabceeedbebddcbaadecdebceacdceddbddbecdabbeebabbbcbcdbaebdddaadbbacdcbcadceebadbeeccdccddedcbaaeaaacebcdbecbcececbdcddbcbdbedacedabbbedbbeacbdcabaadbbadbbacadebcaeabebbabacddbccaddeeababadcbdedcbcdcbaedbbdddecbedecdcdbcbedbeebdaaebedcecceedcaeabbabeddcedacaecabedbdcacdabebbbceecaeabcacdebccdcccdbcaedacdeedbcdbacbedacdabddddeaababbddbdededbaadeabcdeaacdaaccdadeaeaccdcdadededaddadcdcbcbaeddbecedabbdbaccecadbaaaaaeadedaaabbabccacaedcabecbdaaaeababdbabccbbdddcbbaeebceacbebdabbaacebdcbdcdedcaabecceeaeaccccecadedebaddeacceaeeeaecbbbccebeaeeacbcbabadaddccbdbddecbaeedddeddadbccdcdaedbddcebecaabbcdcaedbeeaeeeacbeebbeccbeeeaeeacaaedaecdaacebacbaaaaaedabeedcedaedcdedaaeabdbbedecdddcccebdbcebaadebeaadbebbabccababceccadbdadbbbdeacaaaadbdcadbcddbacdaeaabbdaacaeacbecddcaddaaedacdccbeebbeaabadbdaceaabeaccabdbbccdbeeaaeaccebaaddaedcecebebbcbecdeaacbebccddaabbcdbdeaedaadeebddeaacaacbdcdbbebeadcaacccdbbaebeebcddcdbcbaaeecbbebaccacecddecbccdecdebcddedbebbddbeddbeebadceadbdeaddbccedeeddaddebddcdbcddbeddacacdeacbcbecbdbbaaedadaddddcccbdcadbabbaebeeeeececccebabeeeceddbeceaddcadeccacabaacaeccbbdcaddacaaaedeebebebededbaeaabdeeabedeaabcaaddebdaeedbdeadabccbaddddcecaccbecdcadbbadadedbaaecddceecddeedbdbbbdeedeeccddbabaedbdbddcdcdacebdeeabdbcbbaebbbcebdeeedbcbeccadbcbaaeebaecbcbeeccbceaecbbdebbcaebcbbbdbbaececbadecbaeccbadedeabebdaacabbdcededdccedaceccbebecaecedcdbcecaaeadbeaeaddbbabddcddbcbcdaddabbdbaebabcadbbaebebacebebaacebeabbedddccdaecbddebccaeadedadcbecbdcddceddcdcccdbbdaebebeabcbbeacccbebcccbeecededacabedbbccabbcbeabbacbbecccabdbebbadcdeecadbaaabdadeccebbcaacdeabdbbdbcdebeaacddabdccbebaeeabbacdeeecaaaeaabbcbccbaccbcadbbabadddeedccebeebacadaeecdcaccdcdaeeeeadaabdbceabbdaeccacddbaaacaddecebeebacecdcabeebccdedeebaecedadcacaacccaaedbaacecacbaeeecbeeddddaabeeeabdcebddaaabecceabcdaaaaaecaceddacebddbedbddbcecceedaceecbccaaeeadbeaaebaeebceeccbbbdcacddbcacdcbceececbdedcdaaedbbedbdddbdbdcccdacceecccdedaeabbadedbbabaeddaeeedbbedbcebcaabdaacdbbbdcddbdeebbcddceeeabbadaddddabeaaedcacdcabbceeceaeeeeaeaaeecdcbdcccdbbdeebdcbcbeaeeeddbcdebdeeddcdadbedceedddbbadeceeaaeccaccbdcedeaecdcdbbceeeaadebaccededbebdacabceacacdaecbcdcbebabcdecedccbaecbadbabcdcdccdcbeadceddebcccebadbeedcabcadaaebdeedbabeebbbdcabedbccbeadeaabadaedaeddddaaeedccaeaaecebadbaadeededdddcdebbcbdddaadcbdeeaaaabecabdceebacbbceeeabbdcbbeadcdddcbcbaabbaadabbddcebbbbdebccbccdedabcdebaeccebbcbcaeeceacadcadaeadcabaceaecceaccedacbcdcbedabcebcbcbdddbcbcdbddcdbaadccaaeebdebedceaeeeedebbcdbeaebbaddaaebceddbcadeabcdadbbcbdccacbdbeacaeedbaebcdbbdebccadaedecaaceacbbedadceedcddaceedaabbcbedbcaabaeaecbabeecabeaecdaabeeecceacdbabaaebbecdebadedbbdabdcbbeddbdedaebedbabddabedbbeceaeeaadecdcdadeaeaceecacdcbeebddabebeddacddadeeedeadddeeaaedaeeabeabacdcacdbccdcbacccbdeeecbbecbacabddceacaeebcaaabcaebdabddddedcebaebbaabddbadbcbaccaeaccbbccceaccacaabeebbaaeaddbdecbabacdacabbdabbecabcebccdeadbcdcceaccbbdeaeeaeeabebacdeaaedbdeaedbeadcbbbddbebacbeaecddecbadbcaebdbecbcacabcbcacaebbdadecbdeaabdbadcbeecbbaeeeabdaeaabccaabcdacdabedabcdcecdccccedcbbacedcaeedcadabbaeceedbdeaddbbcedcceabedeeededcaaebdedabaeebaabcbdaebbaecbcabeaddebaabdeacbaddaecbecdeddeadcdbaddddaaccaaecdcbedaccdddcacebdabdeadbcbbcceccaaabbdedeeccbbbaecceccebbbcddcbcbbbbedeeeedebadaedacecdeabceeabadecbaedabdaaaeadacdbbddadbcecceedbedceabaccbeebcabdeeedcededcacbaeecbdedbdaaabaaaaaebebbcdbddbbadaaadceceaeeecebbbbaaabdccabbcbcdbdbeccaeecaabaebcaccadeaaaeabcdbbbcbcccbbbdbbdeddeaadebecdbdecadeddeedadbacebaadeaaaabaacbddadeccceedaceeecaeedabedbebcbcebcbeedacbaeddadcebcacdeeaedcdbabbabeaedecababdbeecadeeabedccccaebdbdeacebcdedddbdceeddcbcdbabeacebcedbbabcbeaceccaccadacbbaaecbaeebbccaecbbceadbeaaeabedceedbbecadadbaebdbddbbdddddeadecddaccdeeabdccddcacadcdeaeaacccdcbaccbbddaacadaddbaedcadcdeeececddbdbbabedbebacedccdcdcdeccadbdabdecedebebaccdbacaaddeadcaaeebbdbedaabdccccbabebcdbaaeddeaadedddabddcbbaaeaddeecddcacbbebcbccbeceadebbccaccbaceaabdddedebeeddabbbbcabdaaebeeebdabdbdcadeaedcececeddaedabedabdbceaeeddedccacddbaeeddbcedebcaeecbeeeeaabcdbbebeabaeebbccecbcceaceaaedbabedbbcaccdbebcacccdcabacadcbcbbebacadedbdecabcacaaedecaecbebaaedaccddddceddaabdacceaddcacdabcacebadbceaddbaadaaaaceadbacecbdaddeeabeebeccbcccbdeadababaaabaaadcbededdcbcecbddacedadeceecccbaaadaadaeadacdedaaeeacbdcddbbcceccdccddbbbaeddcebdaeacccbdbadecedadabadecaebbddbcaeabdccecadebadacdabbeebeeedecccdaeddddaeaccacaccdadadaccceecbcdcceabdaaabadcebeaddaebadacaeccdbdaddbdcdedbcecaccbedcdbbaeacebaebbacdeeeadbaacbaacbeceaadbabddbbdeecbcbbabebeaaadcdceeceddcaadaadbccaceebcacabcbceaeeebeeddebdebcbcabeeccdaecdeebaebdaeceaddaadabcdcaedeecaebebbbbbddacbdbceeaaacbabdebbabaccdbaeaddcbdebaabdedbcacbccbbabacbdacadaaaacabbbedbebeacedbcdbabcedebbccdedacbbaeaaeebddceedcecbaaaeeebbdeedacbdcaaddccacbbeceadaaddadeeacadcadedecdbdecacbebaccdcacabebaecdaaeaaaeccdecbcddcebcddbeacbebbcdccadaeeaacdcebccdcccdddbacbabeecedddbaedcbcdcaebdaaaebaeadaeecadebccabcbebaeddcdadbeeddceeecebaaaaecdcdbcbedcdedcddedcddddbcdcbaeecebcdecceeacdcaeacceddbbbadbeacddaedbeeaebabbcaeeedebaabbbbadbbeedadbcdebcccbcbcacdbbaccbbaadeddbecadbeecbebabaceabadaacedabeedddbcaceceebeddcdebbacccdabeeacceacbcbaddedaebeaebdaebabdcbbdceacabaceeddddedcdabddaadebcecbebdeddbabacadbacccbeebebadcbedecbbadbaecebacbadeecdbdbbcdcaadecccbbdcdeeaaaadaeaeacacaddceeecceaadcdceeccdbddbeacbcccccdbbdaaccbbbaadbcbcabbeaeadaaacbdcbcecadbcaaebcbddccedbadaabadbcedddadbaeaedededeeeabbcabeeabcdbddcaeacaccbabceecacaaecbeadeeeaadaebedbbacbdcedecdacbacceebadcbedbcdeebbcbcdaddbdebcbdbaddeaedecabcabbccedecdeceaccbdddbaeedaeeabecabbdadddecccebaabedbbccdbdeaadbaddcaaceabdceeaabcdadadecddecedcaccacdaecacebaaadebacddcbdccceacbcdaabbbaedeeaecddaabceadeaeccebaedcaeaedbecdbcedebcdaebcaebaecaaecbaceccbbaeeaccdaebabceeaaddeacdcdbadcdacedceecccedccbdbbbbbaaccaeccabbcecdbbcebbdddceeccbcddbcbdaababaabdabbbabbcbaddacaccaccdcccdccbbceabebaaecbcecceecceceadcedabeeedcddcdcececabadeadececeabdadcbbcbebbaaeceaecbceecccbccebecabdbbecdebbcabcaedaccbedddbeacbbedccdcdbadabbbebacaeecaaccdbdbccebdebbeabbdbcaededddddebceaebbacbcebbbaebdacbaaaebebaacbcebbcadeebadadeccebcbcadbcededceecdcceeeaadbeeeecdcbababdaedaeebcdabdbcedaaeaadcaedaadceabecadbbecccecaedadabbecbaecddcedacdbcbddddeeebebddeacbebbbcbcdcbeccaedbabbdeeaacaedcccedbbaabacbedeecdcbdaaeccbdbcceececebcebccbcccaceebeabccacdddceadbdedeedaccddacbedbbacadaabeecadeebecbddbdcababcbceadadbdddbdebeeabcbeaaccbbadcaecabcabdbaecabdcaaacbdeaaeccaeeaeaecadaabcceebbbbdbdccbeedaaaaecabadeecbbebbceccdddbcaabeeabdaeedccecadcbdddacaadaaaceeeccaacadaeaeceeaceababbcbbdaecaeadbdacbbdeaebcbcbedebdabcddbcbabccedecdeaaababeadddbceddededaabacedeabbdcedcbdcbbceacadbccabcdecbeadaadcdeaeeedddbaaaacedaddebdceeeeeecabeaecedccceaedeccaaecadddbabaddeaadababdddbabbcbcbeaceaebddedaeaacacebbebebacdcedceccbecabaddbcceebbaeddabcbbaecacaeddbeceaddcddbaadecbdbbadbacebadeddeedaadbbbdccbbcbcabedebaddedbaaedbadbedecdcebadcadbaaadcabecabbdebeddeecbcedcebcddcecddddaaecbdddacaebcbbdadebcebdcacbddbceeededdceceedecdcebcdbccbdeccbabbeaecbacddcdadbeaaeecdeeccdcdebccbcaaadebbaaddddbbdedacebdccaaddbcacaceccedebaeecaedebcccbbdebaeeadabeccedeebcbbaadeeaadddbbebccdebcaaabcaedbbddedceabcceddddcdcdecccdcedbecabcbabaebbebbaceecbeeabeadebedccdbeacbedcdbbbaeecebdebceaeaadcadbbecdeaccbcbaaaeaedddbdceddbacaeedcbbaaacbabbaceebadaecdbaabddbeacdbdcecedbedeebabbddbdaabaadcccacabaecabbacadebcddaebdebbbcaaeabceadededeedcdeeaebabaedceaeaaddcbacbccacbdbbcdcddabaccaaeacadbdbecacbecceabcdecbececbcdcceaebbcbebecebacabbbbaecadccbcedeaeccacdeccdebeeccabaeecacdebcaeebdabbedbcaccabadacbcebcbeeacbeecbebaeddabbebcebeeaadedeeeacbacecdeacacceaddddbddedbebbecdbaccbdeeeaadcbcaaccebcdaddbdedebbcdeaeeaaaceacdaedceedddeecbeaedcbccbeddbbddacadaacaaaccccabadcbeadcddcacceebacaaedaacbbcbcaabedbecaaaaecdabccadceeeabbedcaeebcaccdededabeebcaecbbddccadddaecdeababdcddadecaeddddcabecdecbaddaccaacedbcbaeacaabbaccaecabdeeeeccdeaeeeedccedeebdbdedbbebbdcabecbadccccbbdaccedcaebbccbcaedbadeecabeedbdbdcbaaadcdcddbbeaeeeedacedbedbeddebceacebceacebbedccbbdaeceaaebdadddaeabcaeeaaecaaecdbcbbabaaacbbbdadcbecacabbeeccbbcedecaceaabebadbebdbddaaacccbddbbbdacebebebcabbbeeddeaacdeaddcccdcecdebdacacabadecbdaaaaacebedacbadbecccccaccebaccbababdbcbbeeddacecdaddbcecdbcdecccaeeccdddbdeacaeacedacaedabcbedabaecdaabeadcedbcadecebbcdcebadaeedcdccbcbabcabedaaedcaaddaabebaeedbbeededbabacdbdbeeebddbdeaecacedadeeeddcbaaaaeacaddaadbaceedcbaacababbaeddcdcaedbbbeebabbcecdaeebedddaecdcaacbdcdaacddcacebbadabadcbeccdbacbebcaaeacabebdcbbccdcdeeecbceadcddddceaddcdcaadeddbaaadeabacbccdbacadeeacbeacebeacdeeaedccabadbbddebbbaaddccecccacbecadacceeadcbdeccadcedbcabdacdaceadaaedebdbbcaceddeacedbeedbaacacdaccaddaedbdedeacbcebcddbaedecdeeeadacaabcdbeeddeaadcddcecaaedeadceaedccaeabbddacddebcceaabaccdceecdaecaeeeebdbbcecdcecdecdddeccacdcbbeabcedecbcddbebbebdbcccbbceddeaddeabeeacddceaaedbaabbddcedbdaaadebccebaecaabbdbcadddbcadacdeeadebbdaeeecccbdadedbdaeacadaeaaaacaaeeebcdbbdbcddddceadaaddbacbeeeaccaaecaabadacdcdbacdacccebcabcdcbecccabaacceddadebbaeeeabdcabebbdcacbababbaabbdceadccbbecdacdbebeeaaceccbcadbaceedcbabebcadcbcbddaeeedeeebdebbdbbbbbabededccceeaabeacaedcccdddabbbbadacbbcbeacdcdbcabacbcbcdedcbadcbdcbdbdeccecabeabceebdecaaaacedcaadbcecadedaacecadedaeeeebcccaeaeaccbbcaaeeebaeadaeeaaecdeacdbbbadebdbbeedabeabaddeccdaccddbceaeedbbbedbbbddededbebbbbdeccbdbeedbaebcedbacdcabaeebebbdaccacdcbababdcdacccbcddacdacbaecadeeacbbabbccdadbeaeacadeedbaebbbcaadaacaceecbbeeebeadecaabdbdcbdbdaddccbcabbdcdcddcaebeeaaeeedeabcbaeacecbdbacdeddccbdceddeaceedebeebdcdebcadabecbdddbccbebdaaabcabeaadbedbbbeeaccebcddccbdcbcdbbdabbcacabaaadbdbbbabcabeeddabecbbaeabcddecbeacdcedbcdddaacabbcacaeddbebbaadadbebbcaccdceabebcdeadbceeebbdbbcceaeaabbaccccdeecbdbbdebcebebdbcbbbdbedaaddbbeddceaabbbadeaaceebdaceebdcaeccaeedbdeeebeeacedaacaaaeccadbeedbcebebbcecdaaceadaabbceeadbbbbbdceaebbadbcaddaebdddbbdaecbacdeaedecaedebdaaaacdecdeeedacaaddcbcbeacdeadeeedcbcebcbaccaceacaadaaaccdaaebbbabcececbedbedbeaaaaeaeeadcaadadeeadcdbedbcdebcabdbebeebcdaebbdeaaecdacdcacecdeeacaadbadeaaeaeaceddcdcedbccdbcaaedbaebedadbccccbedeeebcedadbcdddadbcaaadccdbbceaccecbcddeeccbeedaaadbadbbccdddacbdddabecebcbbeecabbbacbeedbabbeabbeabcdaaeadbdcbcebebaabdbebabccdaecdabebdbdceabccaecdeeeedaeebcbebeecaeecddbbcdbeaaeccdebcdddccabaaaebdcdcbcceaabaadbaabcecdaccceabbbdbeacccddeeeabdbbdeebebeeaedbadeeeccadededabaaaccdddbcaccaebcccdadddccbccceaddddbdbeacababcabacbdbbeeebbdecbbecdbcaccaaaabdbbacdcaeeddcbeabdbbaaadceaddaacbbbbaecebdbbececaabdbceeededeebbadeacdbcadeaedbdaccbdcacaddceebeeaeeeeaaabeebabadedeceaabbddeddadaddadedcadddaabeedbaeecedbaebaabbcbaeeceeaddbbcccadbcbbdeeebbbbcdbaadbeccaceeadcceaebbceeccaebdbbbaddbaabbebadcbdaacabeeacbdcbcaaeabdcecbecccacceabceaddadacedceecaedaedcedcbeadbaaeeacccbbdebbdcceadbcadbbccbbbbdbddbdeaccbbcbeaabddeebdaebdddacabbaceccdebcecabecbcceeedcecadcdceebdedbecbcdebaaebbbddceedeeddaceabbaaddbcbedeadecbddbeeaaabdcbeeccebbabcbdedbcecebddcecbdccdabcddceaacebbbdcabeeebdbbbbaebbbcdacdeabdbdeadaebbdaecccbbccdbedceaeecbcbaebcacbbecbdccdeadbeedeecacbedcbcbedccbdaedadabebcddcdbcaedbedddbcadeaadadecbdabadebbbdceaacebeaddecdddbebcbdbabbcedaadddbedaadadaddbdcabbcdaabcbbecbbccadcaddebdddcbeecebcbedecdbdbbdcadaebadedbebbdaeececdacedebaadeadaacaddbadcadcaecdccccecddaedcccbadaebdbebeccebaebdccaeaddbeebeebdcbbcaacdaacbddceeeeeecdbabcedceddaaadcebebecbbddbbdccbdbeecbcedaaacedddeecceabdcaabebbaaeacdbbeccacbeecacddbaeeaabdbabeddeecadaedeccedeaeaaabbceaacdcdadccadaeaddaddebbcdaaeeddaccbeccbdccedebbedcbbbdcadcaaadedbabbddedeeeadddbcedbcbaeaebcbacbababeeccccebddcbeaeddcdceacceeeeddbbdcdebdbbbcebcccecbdccdccbdeccaeadabbbbadcdcaaaebaaeaabbaeebabeedddcbcaaaacbcadcedcbbbdcdcacedeedbbbeaabccecaaabaebdcbccbcbeedddbcaacbabebcadeeeebeeccbcddddacbdbeddecabddbdcabeeaaabadaccaaebadecddedeeeecadaddbeedaeaeaeabbaeaaaddddaabddcabbebbaebabcbeabbeeebeddcdecdeeecdaddaceacbeebcabdaddcbddeaaaaddbbdaceedeaaedecabccaecdabbababaccdbcccbbbdadbebaebeabecaeccdbddcdcbcebdcaedeceddcbadceaddbeeddeaccdabbddecaccaedbeaaaedadcedabeaaeabdcbadaaddadedaaccbeccbbbddddbbdbdeecaecabdabacacceaeabedcbbdcadeadabcdeeaeebbeddbbedeeaebceabbddeabbaadbedddecbebadebcbbacbecdebacecbbdebacebdaceeddbcdacbaddaebdaaceecdeaaebacdabdbbabbcbeacadecededbddebbbbbdbcddeebebcbaaadbdccdecedbcceecbeacaaaaecddbdeeacaaccacbecbaaacaddebaacbaabdeeebbebabcaecaaacaacebdbdeeebeaadbbdbbaebedaaeaedaedcebcceaebabebacdaadebbababaaacceceeccccaecaeecadcaaaaacdaaadeccdededcabecacaebaeeddeeccdedaaeeaabbdecccceedbacdeaceeecdbbceadacceaedddcdebccebbbbbbaecdabebbbcdbedaabdaeecebdedeeaeeeacbbacababdadecdedaadaaedeaebdaabeabeaaeabbaedbedbdddeacbadccdcccbbeebadbdebaccaaaadaadbabedbedacacccdbbccecaaaeedeaabdaadbcaddbebdedcabceacecdacecedeacadcebddddeaceccbdcababebabbacadaeddbccbabbdcceebecdedeadbccbabdbcdddbeaecadcaacdcdcdbdedacccceabbcdeaeacaababdeaceaebcddcaedaecadabdedadecabebaaebbdbcaddedaddeaecbdcbeabadacedaeccbcecbedacdbabecebccebeaccbbedcddcbdbceabaabebaacecbcbcdcaacbabcdbcccccdecaccbcbeaceaaaeccdaadddeadcccdceddabaabaeedecbabbdeaedbadaadacbcabaeadbdebdbdecdeceeaacedecadbedccdadadcaadeaadadbecbebdedeeedbeaccdabcdbadebdbaeeaeeabebcbcabbaebadaababbaecacebbebdbccaddbaabbddecadebdaddbcaebedeadcabdecbcbcacbebbcccbeadcccbabadbbddbadbbceaedeccaddceaabbabedaabdcdbdccbcceadcdccaaceadacebededeedbbbdcbdceceedbdaacbdaeabbdddcdaeceaeddcbcabdbbbadbaebdebecedaeddbacaeeebcacaebddbdecdecbcdbbebbbcabeabaedcdcdeadbcccdeeeddedebbbddddceabbebcbecaccbadbaecaddccdcbbaebebededceacbabdecdbabeabbacbbdcbdadcbeeddddeebeebcedbaccdeecccabaddecdeddbccdccbdbcadaecccebebcdcccdeebbadedeaeacbadacdbdedacbedcdcbacddaecadeddbbcaebdeabdeeeddcecbaccebcdbbddbadeeedbcecbaebdebebcdadbaacbeadbdaeacaaeaacededecaaeebadedaeaacebebedbdbbdbdecbcdddeeabdbaadaedbaaadaeceaadbadaaaaecaceaccbbaaeddbecdcaddddbcbabbabdabbacadccddcbcecebddecceeeececbabdcddcabceccebdbbddebeaaeddcadbddebebbcabaadebccdbacacebaddebdbbccdedcbbaeedcbbaabcbbdddbbcdcbbcedbacccecdeacdbdeeaeaeedcbabeeedbbaadaddbcaccccedcdeadbcbdaabdcbacabaddbdabbcbecedecdedacbccbcdcdeebceaddbeabebeebdebbcadbeeebdbbaaaeacceabebccccdbabadcdedcebddaccadbeeeccbabacccccdcdabecdedecedaddcecebcccdcadcbaaeddaabececebcbcbbaebabddadaabeeacccacbceaabdceebbbdeeccdededacceeeddaccdbcbbccadeabcadbcebdeeabaedebceadaceeadeaecedccddddbbcacacbceeedcabbceabcbaacdeeaaeccdbadcbcbbeecdaabbeeedbbbadccabaaeceaadcacdbeadadbeecdcacdcaabeccaccbcaaaedcedcadeceeebaaebbacbccabaccdaeaceaaccadaebdabaebcabbdabdacebdbbeaacccadaccadeeaadaededcabaebddaceedaceeeeecbdbacaecaacceaaedbcaabdaaceadebacdecacdadbbdbacdbcbcbeacdcbdccadcacbadbdeddeddcabebcbcbcceabdbadaabdeeceebebeedcbdeeaedddcddaccdbdedcdacdbbecbedddabadcbdedeaccddabaacaceaebebeabaedccebdcbadaeacedccacceeedaddcdedbdcecceaadedeaacbdaddebdecdccdacabededdcdebadddabdcabceeddabcbbbeecbddceabeacceaeaedeeedcdbadaaddbcebbbbdddcedadacddbebcdcdbdeaccdbedddbbebdeeccacbaaaedbebcdeaabaedeaeddbcbdddeadddabbdcdeaccdeadacabcdbceadeaaebaebcddacbcbadabbceadbbabdabcdacacaaddadebaebaebedaadccddbbdcdbcaeecbdabebcabacbaabebdabcbbdcbdadaaacdcbeecaacdabdbdecbedeaddeebdcbadebcbbacbbaaedbabbdbcccebbaaeceeeacbbeeecddaededbbbcbcabbaeccbddbeccaeeecabdcabbcebddcaddacecaebaababacabecdbecccecbcedabeebacdebbecdedccbebaceccbdbedebdaaedeebbdbbbbdeccccdeecaacaadbbbdbcdbbebcbdceaedcbaadeecdedaacaaebbaebbeeacaabebceeccbcbceaebacccedaedbcecaedccdcadebeddbebcbaeecdcbaeeabeaccebcedbcbbebcdcedbaddbeecdaeedaceddaebadadeaeaedaeebaeeeeadcdbccebadedccaceaacbceecaeadcaceaaeeebcdbbeaaaadcbaaceacabeadeecadcdbbabaeeebebdadacccbaccecaddecdecaceaccddceeaedabeedaddbcbaedaeecbcacadecbbcdedaeadddacbccadbadecbebbdddbebcdcbdbceeedeacaccdabdbadadececdcaeddbceeabcbdbaedcadebdaaeccdadabccedcabacdaecaccbeccdbacacdcacadedaaecbedaeadddcdecbcedebdccecdbcaaceaccadbeabeeaebcbcdeecdeeacaabccedacdcbaaaaecedeabbbdaebacbbeeaededadbeadbbcdaccddaaeddcddaaecdbcecbeecddcabadadeddbccadaeddceeaebcedebcbccbdeebdcacedddebedcccccbdaeadbebcaaccbeadcbadebebbccdacebacbddebbdcaedbdabbacadebabebadcedbeddedeecabdcedeebbcadcacebacacecaaadccebdbbddcdcdbbaaddaecaebbbcebeecbcccddbcdbcbdbaacaddadeeacbcbdaedabdecbdebaedeecaaaeaaccadceebdceaeaecbaccabaaeaccecabedbaeedabedcaaeabddccadddbaecdddbddedbcabcdbaeecaceaaebebedbebdacdaadccdcecddcabdbaebbebcaecacdeccecdaeebbedcbceabbebeababecceccedbdaddabeacbadddbccceedcaedbbbddbcadcacecabddbedbdababbaaaabdceeabbabbdecbcdbccdcacdddadcedddbebbeccddcdacdbdcebebddacdddeabebaacdaacedbaeaebbbcbeaaccdecbbbcddaedebbbaacbacbcdddbebabcdccbdcdbdbbedcbeeaccdbcbcebddeddaeaaabbbdbaaaaebdaabdbcbadcbecbdecaadebadcbaaccaecedccdadcdceebcacdcbeeedcdbdcbcbaaeadcbbdedcddbcceddcebdddaadadeadbbcabbcccbdaaddbaebccbeddadaccddcdaccacecebcacdeaaaecebeabddeebbbeddcacceabadceaedeebcadacdbddcedaecadaecddbebbedeadddeeabbaeadeacecbeadbdceecdbbcebbeacacddbeadebbdceebdbccbcbbdcdcadcdaaacceadbedeaacddbbeaacbacbbabcaceeadbadbecdcedeacdaceedccaceaaacdddacabedcddcbeadccdcadeccdcdabaebabeeaceabceacbddbdabcdadaaabdaecedccecbdaeededabdbcdbecddcdcbaaaecedaabbcbdcabeaeddcadcabbebabdcaabdabeecabcedebabcadcebdccdaabacbecdbbabdccecccdeacadacdaebadebeaebdbdaedadbadcbebadcaeecdddecededeedeededacaeeddabaeeceabbeabcbbecbadbaaebcdabecdaedbcdebbcaeabecccedbbdabacecdbbdcbebcbdceaccbcecaabecdcdaebbccbcebdcacabdaeebbbccebcbaaeaccbceabeedeedcbeebccceaaebacebceadceadbebcbdaccbccbdbdbdcbbeeadceeecdebceedecaaddaebeacabecadacddabcbbdcaadbddcdeecaccabdbceabbeaadadacdddeacebdbededebaaaddcdcbacdbeddcceedbeeacedaaccddabccdcaecaaaddcbdecadecaebadcddaebeadbaaacecccbcebcceabbdeddbecedcbcebcbbbdabeaaceaeddeeacaaccacabacdeabebabbebddddbceadcaadabbeeabbdaeddbeeacaabebddbdaddecdbbdccdbcabeaebeddbaecbeedccecaeabecbdeeedbcbaacacbeaaecbbeaaceebbcbbecbbabdadddeeaacdebeccbabccccebbcbecbadcdbccabaceeedbdebddcdabccabdadbbbcdceaccccbeccbebbccdceaececbdecaabcaacadceddbabdacbdedcadeaebeadcaebadbeacdddcceaccbadbebeadeacbcaeccedadddcbbcaeddebaebcdabeaddeeeaebcaceaaabdeaeaaebeeeddcaccbaaaabbeeabebaeadebcedcbbbddddbdbdeacadcedddcdacaaecccaddeaebdcaccacccbaaccddabcdcdddcebdadeababeadeeacdaebedbececbaebcccdcecbaacbbeadaaccddabdbdaacabddcdcabeebacdaaeccaecdcbbbaecdcdabaeecaebbeeaaaeaccaabdeabaddadebbbeacedcdebbbbdbecdccbbbeaaebecaaabcedebaeacbebbeeabcdabaaccaabdbdbdeaaebccdadbebacadbaceaabedeeedaeadcecedcecbbceaeceadeeabcadbdeacedbeaadbddcdbcacaecacbeeeebebddabebabdcdcebdcceacbdcebaadecceddecbddbedbbeabacacabcabbcecebaeebddceaaeceddceeebaeaaeaeeddbddaeadeaddedeabadccddbeebedddcabbecbebabcdebdeaacdbcedcabbbceaceadeddcdbeabedccaedabaaeaaccbebdcaecdcdeadaceccdabcbaedecedeedbbcbbddbeeecabedadedadaccddedcaeabbbecdedbbedceccedbaadeeddbaeaecdabddbedecbaeabbdeabbceadaeabceabcbeeadeadbadbeabcecdcacedeececabcceedebacdcedccceacacebdaeccdbebdccebbeaddedebeaeabeabcecbeececaabbdeedebbeccbaeacbcdcaceeceeeebeecaabecbbcdbccbaddbbbaedabdccbbbbbececbdabedbceeebabbddbbedcceedaacecbabddaeddeddaadbcdbcddddebbcdcbadbbbceeadbcdbeacdbedeabeebcadbdedacaccbdadbdebcdaedadeebdbccdbdadeddabcedbebcdedadadddbacccecaceeeaebedecccacededdbacededdccecbadaeaacbccaebdcbcaadbdadcdbaddceaeabadcdcbeabaedabbeadbcabdecbeeacababdddcebeecacddceeabdcbdaeeeaccccadbcddaaedcccdaecdcdddceeeeaebeeeaeebccbeddccebeceadbaadccedabbddebcecadaceaadbaccdceaebdcdceeeabaeadccabdbdeccbdccedebeadceadacacabcdbcdaaedbbaaeedadeacddaadacedacbdacbbeaebbdccaeacbdcdabcaadddbbdedeaabeadebccdcbdcabeedaadbacdbecaabeebbcedddcbbbaebcbedbbeabbcbbaccccdaebdddcdeebeeedcbbddddecbadaebbddbeeaaeabaddcbeaeaaacdeacabdedceaaeabeedddcbcecbaeeccccdeaeeaeecbdccaceedccacaeedaacadebebeacacbddebbbeccbdbacbcacbbddcddadcebbbcacdeeabaeccecbacbadeaeeccdcbbbdbdaccaceaedddabbcdcbeaeeccbddaeeaabdcceaddbeceeabdcbbedceaadbaaaddeddbbdeeaebddcbceceaedeadbeadcbdecadbbbdeddeccdebaaeacbdebbdceecddbbecdedccbbcbdbedaeadbacdaccaadceeeeecdcdbceaeabdbecacbcaaccdcecedaeebcdcecbcbeccdedbaeaaadaebadeaecccaedabddcdbeecccbbebdadddeedbcabaaabbbeddbbdebdccbeedaaeeedcbbbcddeebcadecebbcaecbcedaddebecbaeccbceddcacdaaaececcacbddeebacacbbccdbcedaebdcbdbcaadbcdbbaebcdacedcdbacedebddaadbcdbaadccacecbaeddacbaebabadabdcbdaeceedebbcbdabeaeebbeaedebaebcdcbaceecabbdaacaaaeebccecccabbabeebdadbadedbdddcbcdeccecaabedecccedcebcbadcacadaabbcdaabccbcbaadbbecabbebceeeeabbcaecccaddbddaeaeceebdadbecaeedbabaddebacdaaadeccacbdbbbbedcbeaeddadccccbdaadbacdedbcacddedaaccdeedadcdadddecdcaeebdcbdaeddcaeaddaabdaebdbbcddbebbddaabcbcebdcbeeebdbbcaedeaeddaadcdadadaacedebebdcceaddddcbcadedbcbadddabddddcabbaaceecccbbaadbadaededbbeaaacbdaabbeebccbcccbecadbaabdbeecdcaacdaeeecdeecbdbbdebbbacbebeebdccadecceaddcccceaaeebedcdcedbcaaedaebababadebbbdacaaedddccbdeeceaddaeaeecbcadddecbbebabcddceeecccecacdedcabbbcddaedecccddedabeccdedeebadcbcdcddeebbcdcbaabacedecddcedddacddadbdaacbcadebdaaeaddcbddedbecebaeabadddedcddccadabeabddbbbdaacacbdaaacbdebcbdbadcbaaacbacaebcadcaebeabdeddaeebedbcdcceadebadceabbdeadcedecdbeebcacdbddecedbdcbdddcddbebbdcedcdbdbdceaccebaeacbbcdddcabbbdabdeaecaeabadddeedadcbaeebeaceadacbccbdeccaeacdaddbceaecebcddebeeeedebedecdcabbcbbbdcebedbcededbdadceddddddceaeebabcaadcdbbeebeccacdeeddcbbcccabedcdaabcbeadecbbabcdbcceeaddccdadceecbadaacbdebcbdeebbcbdcedecbcacbdededcecccadceeaeacdddadddacaadcdebebbdcdcdbbcebecaaabbcceaaccaebbcbbbddbcacbebcaebcaeeadcdbedddaebdcadecccbbdacaeadbcacaeaeaabcbbeecccaaabebbdcabdbdabcddecbdebeaaecedaedcdcadabdddebcaabbadbcbaaeeedeabeeaacebceccbabdddcedeaebcdcdcdaabdcdecacdbdaadbaeddaededbaadddeeceeabaebddbadddcbcbcebeaaaccbcbbedcbccbecbcabeccbceaddbedbaedacbaacdaeabedaaddbebebdbeaddbdebcbddcbaedcbebcbbdabceeaababedcacecbaccbacacbccacedccaadeabacaebcbbaaadabdbaeeecdededcbddeaedabcaedcdededeeeddbbddcdecaabedebbaabdacacbcbadcdedcbeeddbceadcbdadaddceebadcabbbeedeebdbbcebceaacbadddacedbdccabadbbdadeacadaabcaaddedeeddccadcadcceacbbceaededadaaebdbbebddaeeebbbebeddbceabcbcabcacbceeacadcadabacbaaacadcdeaeeddcbaaecaabbcebccaaddadeddbebdaeaadcaaebdccabebaacdaeaaecdcbbeaebebccacdbacdbccaccbeaebcbecedeededdbaaccdeebabcdbaddacdaeabaceeaddcbcdacdbcedbaceacdabcadadeccebdaedaaddcbbbbcacdeccbaebdcbeabbeddcbbacdeabdedabbbdbcddeeaeddbcbbdcbaaebdeadbbbbcbedabdadaabcbaeddcdbcdcbececdbdbbbbbdddeddebeabacbceeecccadadbbcddabccbcddcbedecccbeadbdebcebddccaddbddaacaacdebaddcddeaecdaaeabddacabbbeedbbeeebdcacddbaeeaaccbccdbeeabedecbaeacebbaabebaccbeadabacabdbadeabedbcdcaeacadccbcccdcaedbcbdcbdbaabdaacebdccedbdcbedccddebcdddbddcecedddbaecaebbeabaeeeedceeadbcacabaedcdbcdedacbdccccccacaceddadbdbbebbbbeedebabadaceedbcccbabdeabeecdabdbabdeebaebaeaceabababadacedeeeeecceedbbabdaedbdbedbddcdaacaecdddaceeabbadedcacbedebcaabcdbbcdbaccaceedbcdeecdecdaadcabdabdedeaadcdcbadebbcdadceedebedcdcdeaebbbaeeebadbbeacbbdecdcecabacdaabbcceabacaccdaacbadbcbbeaccdcbcebceeaedabadaccdeadddcbebadadeaceaeadedaacbabaebecbabeeabebeababeadcdcbacacdadedbaeaacadcccbdcaadebdbbccbbdedcaccabaddbddcdaadadccdeaebeccedecabdabaaaacdaecaabecadbdddbaddecabcbcdcacadddcaeecbebaaedacabbaedaccbbdedacedddbaccddadeabbadededcbbeedceaaccbbbbeebdaeaaaebaebadbcaeddbcbadcaeecbdcbabbeabdcacebbcccebecdbcdcbcdedbacaaeacdaaeedebdecdcbecccddedeeececcecbeaccebcabebdedbaeedcddbdbedcedecaeabebbbdaecccbddbcdbdbadecbbdaaacabceaadaeceddcaaeecddebccedeabbdeecbcaebcbbaeddbbbcbacdebcacddbdebbdecbbebcabacbdceeebdbbabbbedccaaacdedaacbeeecebdbeeacbccbbabcbccedeabdedeccdbeeacbeababcdedaebedcacadbbcacceabcdaadeadacabcebcabcddcedbdbaddcacbccacecdebdbecbccddbbaecdabceeedceeeddbccedbbbddcbebecdbcdcaedecaabdddcaacbeadcebcecbbdcadcbadaeccedccdadbdecdacbceaaeecaecbddabcedadcecbadaadebbbbbbcbbadbbcdeabdecbceeebabddbdddceeeddbebdeadcdbcaecaaeacbddeeebccabeebcdbccaccdabeedbdeeecbcbcaabebbcecaacedaaadeeeccedebabebccbebeeacacbbaebbdceedcbccbeaedaecdbbaabcdccdadeebdddbaddabbbccbdedbadcabdbdcbddbaeaedaeadcddababcbaacbeeaadaaeaaaaddbbcadadacabcbeaacddceddaecbeddcdcabbcbacebadabddebbaedaadbaddcdbdcacdeeedbaeedbccebecadaaebacecdbaccbbedcbcedbdabeabeebbcbcbcdddeeecdedceaabeccecddeebacbdeeedbbbaebaeebddabdbdeeeabcceedeebcceeabdbdadedeaccbcebbabeecedcdbececbcddedcaceaedaeaadcdcddacabbddebaedededbeecdccbcbbedbbbdedcdbcebdcdadeadbadadeeceeeedaddcedaacadacaacbedcdccbddabeddcdecbeacceaabcdbaedcabcbdccbbabbbdcaeaecdadebddcceddeacacdbabcdaebadcdebebebebcadcbccbebcbebacbdbbbcbcbdeaeaeeecadabaceebcbeebeceadccbdecaebabebbecddbbcdbddbeebedceaecdeebdecceebceaddbbaabdbcddaabdcaadceacceabadaceeabbdabcbcddadddecdaceaaedeececedbccacaecbebcddadadacbacdbbabccadbdcebeaccbdecdababbabceaaeacbbbcddeecbebccaaaadeebddaabbdebdaecbeadebadbbccadaeaeabdaabcebccdabcabbdcdcaeaeabdadadcecabbbcddbbdcaadeedcbcaacaceacceaeecbdaecbcaecbeedeabeddcbbccebddebbdceccbaacdbcbcdcbdacddceaccebcebbebebeecebbbadaecddcbbaadadabcdaaabdbddccbedbacdbbbbceeabbdedecbaadbdecbcebbdabcbaeabdccebaeaddbabdbcadbbbbbabceeeacddbeebecdecdacabebcedbaecbdaaececabcdccceeeddcdcecdebabccbebdbcdbeebcbacbaeebcbdbbbdeabaaeeecedabebceedcdabcccccbcbdcbdeabdeccddcddadeebaccbaedabecbedbcbaabadacbaabdeedacddbaeeddbdddbddddccabeadddabbcbccaadbcdacbcbcbdebcddbdaeeebbcddbcbcbaeabcebcaaebbeabcccbddecbbeacbddceebeebeabbaabbababaeeeddcddcbbebaadbdecdababbcabaeedbddebcaabdeddacecbceeecadebbadddbbddeeebcdbabecceaaeebbbbcacbedaabeadbbbeaacbdbdcebcdbaccbcdaadcabaaeaddcbabebbebaaaacdddbeeeabddeccbeddbddeedadbdbedecdcbbadaebdebbdbddbdcbbcadbcdbbdabeacabebbeaacaeacbbdacbabcdceadcadccccadeacbcdbacdadecbbedbabaecddcaddcdbaeaaaaaacabbaacacedbaedabcbbccbdbdadbebbdceecdaebacdeeacbaeebddcaacdaebceddabdbcecbdabebdaabacaeabecaebdeadaacaacecebbcaecbbededdbdcadbbccdddeebdeceaaabbebbcbdaaebceaaebcbecabaceebebeeedbeaecbbdcaadbdbadeeedaaebddddaabeeacddbbeebddacdbbdaecdbbbababccddebaddbaabbeadbbcdbeadcdcaceccdbbaebbaeeacdbecbecbeebadccaeedbccaabebdecabadacdeddacaceecdeddceeeeebdccebaadbdbbcecbadbaccaaaddceddcebbdacedcecbecdebbbeabdebeadbeaadcecbbcbdaedceceedbdbaaadbcaaeabaeddabcebeaddecbbccbdeebceddcdcbcaedaceccdeeadaecbbaaeccbdccaeebccbbdacaabbdbcddcbeaaedddecbdcecdbbaeeaaaedeadeeaeabaecaeebcebcbcccbeceebabdaaebecbdececbeacbbccedbcaabaaddedddceadbdecebaacdbcdaedebcdbbdacedcaceabcceeeeaebedaaacaddeaccbccaddcabcbcddcbcadabaceccccbeaddaabdaedcedababbcadacecbedabddecaddacaeddceebbbedbadbbeedbecaecccdadcdbcaeabedacddcabbccabdbaeeeedeeceebceeccaddccbbaccbabbabdddcaceedabdceeabeeaacddcacecaceebbbbdcccecbbbcbdebddeccccdbbceeebdabeaeadabbaaadecdcceddeeaecbcabbdabcbeadadbaeedbcccaeadbdbbcbdadbdaabcdedddebeadebddadababbedeadbcddcedbcebcaaacbbecbcbcaedebadceaceaecdbdeccacbdccaedcbbddcbeedddeeececcaabbdcececaddbebcecdabecaddeeecbbbdeedadcbcaccdaedebdddeebbbeaeaaeaecbabcebdecbebcebeedacaedddaedcbdbbaccceddbeaeddaaeadcbaebddcadadbdaedacdebeddcdaababbdcbdbabcdbbeacadaccdbbdcbbedebecccbeaeaedcbaaeddbadedcbaadbccbbadcdedaadacaabdbebcaeaddbeedaeaeeadeebaaeeaeeeadddbddaaebdabdbddcbacaaedbebcbdabdbdaededeadcaedbacacbbdbcedbcaebbccebaeaccddacaeccacbeaacaddbacdcdeaeacdbadaaceebdecbddceaedbccaedaebdabbcbdcacebdddbacaebaeebdbdbdeecadddeeeaddbeaddcbbabceaceceedebeecddeabddcacaecbacaaceebccdadbdeaabeaeecececcacaacadebddeddddbccababcadeceecabbcabecbbcddcdaaedbadbabdebdeddcdaabcbbaeabeaacccbdddecdccbcccdbaeddccedebaebecbcedaeebbbacaddbecbaeaaedacdaadacbcdecbbaaeacabddedeeebdaabbddaecaebbeadeabadabecbcedcdaccdeabbcaeddaeeebbbadcbdebcdceceadddbbaeceaeddcebecceedabecdaaadeabbbaadcddedaababbacdcaddaaaeecadcbadbdedbccbdcccecdcceaabdedaacceeecccecacbebcadcadecbcdbeaaaceccbadbdacedcebceeccddbcbaaceabcccbcabaaabbadeedccabccdbbeeccbedbcdeadbdccbedcabddcadeabdaabcbcdbaebabdacbaeecbdbcccdaadeaddcdabdeabeacadeaadcecdbdeccbdacbdacdadebcdccbcbdbaabdddbbaaecabddccebaebaaeaedadabdeaeeddebaaebaeacdeaceedabcccebbdadebedaebabaeacddbecacaaeccbbdccbaedacedcecbdeabcbcaaedeabeabbdbaecdcebcadcdadcdaacaadaaecceeeedbebabcbebbaedbaabeddedbccddbccaeccabbbaadddedecddecabbeaaabebaadbcdeecbceacbabddeacedcdaceaccbaeeebeccdbdeadacecdceebdbeaeecedaebbcbaabbccbabecadcbcedaccaecaebaeececbebeacbbeeceabeecebdecbdedbdbbceceeacbeedebeeccbbbdcdbaeecdacdcbbcedcadddbcceaabdecdcbbbcccbcadcdacbdbcedceeabaaacacedddedeebddceaaabdbcbbdaedbedaeeabacdbeabdaeeecabeaaecaccbbecaeceeccddaacccedeecbceedebcacceaeecebbaacdbeadadbeaddebedadbcaebceaceaaccbcdeededaaadaeccacabebedaeaebaeacbbadaeeeddebeedeecbbcdeeebabbdecdddbadaaccbcbddcabdabbbddbabcbcbeeebeeeddadccbaccecadccbbdeeabcbebabcadcadaecbceaccaacbcabbdebeaeedeeccaaabccdbdbcdacdcdeeecbebaaabaaebdaedcaddececcdecdcbcbeebaadbabbddceddeedaeaececabedcccdeaddadadeaeaedcecbbbbdceccbbcacbceaeebaecedbaedaaaabbccadabdaecbbceccbedccceddceacbebaeaaddeaebdacacbebadbcbedbdaebdadbbaedabccedbecdcdccbccadbeaedacaaeeeccabdeabcbeeebeadabaacebbbbdedadcdaecddcdcbcdcaceccaabeebdcacadcebccddadbbcdbcecdbdeedddeddceddbcbaeeadebabecdcbdebaeeeecdeecbaaeedacbdcbcbdedaddecebbdaeecbabdbccaebecadbbacbebedddabbdadbccbdddcdbbacbeecbccdeccacccbadbacaccadaaedadbbbebecaaddceedaebaaccddbdaebcdebdbdcdbaeeaecbcabbeedbadadbeaeeadbdcbeddbcbbbdcedcbccadbbdbcaadddcdccbcaacadedbccaaebebeedaaabbbbaceeabbccaacabdaeedbdbdbddcbadacdcbbeddeeaadcddaeccadcabaedcdcecddcedecaccdccaeeddeebabbecdececeebccedbbcceadaecddebbccacaabacaadedeadaedacedbedcdaeedeeccdeedaaddadbebedccadedaaadaeabaacebedbebadbbbeacbbdccbccabdaceedbecbacceabdaaeaceaacbabddcdaceacecdbcdbcecebcdeddedbedbcccddcdbeddbbaebebcabdcbdaabedbeccceabacedaaadaddeededccdaaeeddaacbbceeadeedecaecceceebcbeccbdeedbbcdceeeccaebaddabcdccebdcccedccccdcbebddcdddcbbdadadbccbcebbaeecddedcbdabccceeaccdedccbcceaeabedbabceaabaeebebddeaebcadbdbccaecebaccdaabaabccaebcdcaebbabbecebddeeddcdecddeeaaadaeccedbcbdabdeecaccbeccbbaeccdeababcdcaabddebbaceedbbeabbdbdeaaeebbababaedeebebabdaaeedcceeeaabdcddccdedddeebbbeacebaedeeadeacbccbbebcedbbebaedcaceccdabbacbbecdbeaeeaeeaadceeccbcdeaaaacbbbccdcccdecaeacadebddeedebdbbadacdebceebeccbbbebbeeecaeaeadabaeacbceceaddbacacdabeaecacbaadcedeededbcccaaccdaadbeadebeedadceecabcacdcaabbacbaacbabeecebcbecdbdbbdaccbcdeeaebabddbeaabccaebcdcabcacdbccddabbcbebecceededabbbbacebababbddaebacedeedadbdeaaacbbceebdcebadacecddadcbadcdbcdacbdccdbadacdaacddbddddddaedaccbcabaccabdbcbaeccebdadaacebeaacedbebbdceddadcbabdbaacabebddeaabadbebbcebdcabcedbaeeacabbbedcceebadeeddedddbeaebdbbbcbaadedbebbaebebedccbaababdceabaaedeeaaebaababbdaabaacdecdeeadecbebeceedbedeacddecbeeeaadabdadeacaabbdcabedcbecadcecdbecbbdebcbbbcccaceeaededaaaeddecccacbbcaebeaebececcbcedcdabedbdbdbceaecdabbbddebdabceaaadcbbccaedbbddbdccdaeceeaddbecbbdeeadcbdbbaadacdcabebcbabdeabddddaccddbbecaccdeedacebedbaaacdcebeeecdcceeabbacedbaaaeadccaedeedcbedaaabebbcceaebbbdaabdbecbcbcdaeebebdaebadaecccdecaebadbcbbdcddadbaeadeeedcdccebcbdbdeacadeadaebcacdedccebabaddccdaddaecbcbbbccadbebceddeedeabbdabeebabeeaebdccddeededdeebbeebdadacabdedaebeaccaceeececdcadccedcbedbbaddeccabaacaabcbdecddccdbdcdedebcaeeddeaeecaaccceebadcdcedbdeeeacabdbcececbedcababedcbdcbbedecbdeebededaedeabebeedbaeadcabbbcaaadeaebdbcaecacdacbbbdbcbaecdbaadcddceacacddadbbbeadadbaabeaeeddbdcdaadaeacdbeccbdceceadccebadccbdbabbaaddbedbbbaadccdebccedbaadcbcaebcdaabcddebbdccaceebebaacebeebeddcacadbcadacddaabbccbdcaabcdcadcddeabedaacaededdceacbedaaacecedbabebbabbeddedbadbdcaeedbdedeccacbeccacedbadecedbececbcbcccaacdabacbddcdcacdeebaedeccdebedeadbccbccadbbedbceadddacbbebedddbdebaaddddcdabebababbecbccacbabdcecccabeecbadcccddddcabaeabbeedabdadedeaeebbbacedebeeeacaedbababdbcabdecdaabadeccabaacebbcdaabacddddecbbdccbceceaededdcaebbdddecaeaacacdccddcbdeeaeccbcccebabcbebebccbeeeddceedbacaabadcecadedccebbecdbcdcabeddcacbcacdebceeeeadaedcdcebdaaceacdeedceadacccebaacecebecaabdadaaeeacbbdbadaeedaadbbeeeeebcddaedeceeaeaecdcaeebebeaeaadcbbeabacceceeaebcbddaebeabbecadedadcdaebdcdaaceabcecdcdcadebceaaabeaddaebdacebbecddddbbbabdaeabbabeebcceeaeceadaedcbdedebcccbaeaebdcedcddcecedaaaadeecdcbdbdaeaabbacddaeaabcddccedeeccedaedeaecedebbaedebedcbbecebecddaedbcbbcbbdaacadceebdcabacdeeacbeecbaecaebaebaaebeecbbcadbcbdacdecaacdabdaceaccecdededeeeeaaaaabbedbcaedaaddbdaadcccbbedddecbbdeaacdeddeceaddcaceccebdeaccbadbacbeccdacccbccebeccbdcbdaadacdddaaaebebdceeaacabedaddbbcbeddaaabecbadabaeedcbcbeceebabdacceddbeeadabedcecdbbbabcbaccededccdaebddecaddcccccbacaabbadbbbeceaeeeacdadeabbebbaeeddbcadedceedadaaabbbaccebabddaaccedaaddabcdaeaaeddedcbebabadeeebcdadbbbbeaaeabeddbadebcecaaebeccebedceddeccebbadbedddaeadbdabcbcbadaedeecbeccaccaeedeeebdbcacbecedeceedcabacaabbbadddddeeeeedbaecceddecbdabdacaaeabceecbdeabceceecdcaecdadebbbcedcbdeacddcaeebbccbdbbdedaacecbdcedbebebbedaceddbddadaacaaeecdebbacaeecbbdcaedadabacaaedcbeddbeebbabbbabbbcdcbcaecdabaaeadcaaaaedcdeecdddbedbdaabbeeebacdaacdbeeaebaedacbbaeebecaebddeebdecacbdebcddaeaaadeccabcdcadbebacabbededdcdbedaebcdbacbdcaeacdeeddcebdbcbebaaaaeceadcbceedbbdcdddcebadeaaaadacdcebbcbbbddeddddebaaebbcbccbaaaeddadadeeebaacddbdccbcddecccceaeacbeaebddebddeabedcdaebebebedecdaecddcaacdbbbddbcdcdebeaddcbdaedaebbcecdaeeaccdadaeebdcbcdebaaaabaabedcbecbaebaadaabbbccbcccaaaecdcebddeadececacbcdbccceadbabaabaceedbccadbdeebeadbcddbedddeeeddecbeedeeacaadaaccddcddbcbdbeeccaeedeadcdedbececbaddbecebabbdddeaebaeaccedadbadbdcbccdedcddacaadcddcecececbaecbddccdccdeacdaedaadaeccaedbadcdebecbbbebacccbaedcddeabcdcbceacecacaeadcaaeeaedcdcabebeedbcbcbbdaeadcbededacdecbbbeadeaadcdecdbedceabadebdebdbdcdacbcdeeeceeccbdbeeaababecdeebcdaeeaceddcbdbadaccbdaabdeebbaaeeadbdecaccccdaccdcdbaddabbebabdaadabdeabebabeeeaacdddbecedbceacccddbeebececdeacccbeabbeeaebccaadeaeaaebdbccbdecbbcbabbbeaebebebadaeedecdbbceeacdaacecceddacbbecacebcddabceaeeabcbebbacbbecbdecacedaddabdccdebbaaeccbeedacccacacdecaceaaadcdadecccbabebdeddeecececbabbcaaddaaccbbdbebaaddecbbcdbdcdcbdbdbaedaeebdbbccccaabeccebadebcbacddecccdabccdabedaceccceacceeedeeaeddeaccedeacacbdbbdbebbeeceabcbdabdaeeedddcdadadcdbaabacedbadeedbeaabacccdeabbdebccadbdecbaaeccccdbeaaabeadbacbedeaadeebecadacadaecbebbccdebbdccbeddbcecdaeceddbccacccbadeecacbaeebaeededcccbaaeaeedbebbdaaceecceeaaaebcececebcbadcabdcaeeaceebcecbdcabacbdbadbcdceecccccdaeaaaeecebbabcbbccaeeaeedebcccdeddaabcaeeaddccaccecbdedcbccdcbbecceacedeaadecedcabeadeccaaaacecbceeaeeccaeadbcdbbdaebccdcabbbcaaacdedeceaabcceaecdedadbcebabedddababdbbcedecbbaebeeccedcacbcbdcdcbccdceeabdbabcbaabdedebeaaddabdceeedbbbbedbeceecabedbdbcacecbbadbaaedeaeaadcddccbbddcaeceeedecaeadecabbaccdcdebdabecedaedbcecadabdbddebcaaeddcdebdcbbddddbecadccdeceddabacacbbabacababcaebaacdceeccbddbedbedbcabccaecaaebadbdcdcacbbacdcceccbedaecaeeaaaeaddeccaaeabaceddeaaeadaacacaebabaeaccaccecbbdaeacddbecdaeacdacdbaeddecdcebbcebeaabdebdadabaeadcbeabbacdbeecbebadbcdceebabcdcbdcedceecebacddbbdbbcaaddddabeeabeadcabdbbcdaedabceadcaedbeebbdeccbbdebbeebecaaddcaacdcbbabeceebdaeebeceddaedadbcbeaedeadbaacdbcabdebbbaeaeececdbbcbddcaedcddcaeebeecededcabcaccbbcdbbdbeeccbdaeecabbceedcaddbddcbadbdadebaebdbdaedcdacaeaabbdecabbddeeeaddadeddeebccbceedceebacaadaddcacebeeebcdcebdacebdacaaaeadedeabbcaeeaebcabecedadedeecdcdbaddecedcaaaeadceeeeadccebeddababcccaaeceaecccdaecbbccebcbaddeeeaddaecbceecbdaecedceeaaadaaaaadbedebbbbaeacabecedddceabebecaadecdbeeedabceaebcabacceebccdaebbcadceecdedaebaccbcddaaddddeecbbbcebbaebbbcbdbaeacccaceeaadbcccbeddddcabecdbbaadacdddbceecccccacadcdbbcebecbedaedcdccaeecbcebbbeebaecddaddeabbbdedadabdcbbedbaededeccbdadeebdcababcebbdbbdacacbacbdccbeaccabdebdcdecaeccaaeeaddddeecaebeddacedbbdbdebaadaaebdcbabcddcaeeaaaeeedcccbdbdcecaddbddbcdededbdadeaededcbbcdebeeddbdcbaeebeabdeeccbeddbadbedecbadeecddcdcbdbaccabcaddebacdcebdbadabcabdcaceaeeccdccbecadeebdeabacbabaccdeccceccbcdedbbceeeddbecbbdccdcacdadccabcadcdedcedddccddabbeeeacbccacdbaebbdaebbdaaaeaddddcbacaebdaccebcceddbacedbdadbaaecbcaacdcdcacabbcebdbdbcdaaecdacedaecaebebbdebbeaeadeabbecdcabedeaabbeaaeaadbadadeaccbdecbcddbdbbeebedeadaadeeadabbabcaccedeccbeddcedbabedbdcabddbccbbcceaabeededadacadadeccebdcdeeecdeabceecdadadddabcededdadacbdccecbadbccbccecebdaaaeaecbdeebbecbddadbbdceecbbeeddaaccdcdbaecebdaeddbcedaaccbbaaaceedccbbabbbddecabedbcecbacdaedcdbcebaecdbdabadaadaecbebcdcaadcabbaeaabcdbcbbcbbeadcbacbccccebebccddaeacdeeeccbdabdabbdeebabcccbbabcdaeeeacdedebdcaadcaabbdbdbcedbaeedadbbdabeaeabdecdcedddaaaabdbcbeabaeddcaacbddbeacdceebdebdaedeeeebbdcadcdcddacabdcbecceaedbacccddcadbeeabdeeedbabcbcbebbbeccbcaadecababacebbddcdabdadddadcadbadddbdcacddbbdabdbaaaaebedadbecabbdedeadeeedbbdbacddcaacecdeabcbdcacbaeadaeadbeaacceedeeadabcdcdacbcccdcbcddbbabedcdaddabeeadcbaddeadaceabaeaddabaddabcecdcbaecbbceccacbbacdabacedcdcacbdbceeccdaeeebdebacedbcbabcaadbebdbceeaabebedbeddbddbdabaeadaedaeedeaecaededddabdccaeabbccbaddedcadeaabbbdaebaaddeaaceebcbcbaeababcabdabbbbccccdabcedaaebcddaabbabaedbceabdccccaddeabacddccdecdbcdebceaeaddaeeebdaaaaedebdadbedcedbadaceddbcdccbcbbcaeacdedbeaabedbebdddcdcdbabbacebbddcddeabcaeabdabeaeaabaaebceddbcaaadbecabbadbecadabcdabdceddcbaecbebaadccedaadbddccceccbbbabdbeddadcbdedabccbdacaddecedcbdabeedcadcbaecdabbaacaaaaaaabacdbbeeedbeabebcbbccdebcedccdbedebaecdbccdaaeaadcecedabcbccbbaccbbebdadececcbddcadcbddacdedbdcccbcdbbcdcaeabaacdcecdacececbadcbcadbedddaacabbcdbddebeeabaabceeabbadabababdaebaccdaeedbaeccaaccdabdbdacdbddadeeedceacbecccebcceacebeacaccbeccddbdabdabcdbedbcdaadcadabcdbceedacbbcbceedeeddbecedabecdbebbabbcccdeedeaceeceabeebdbebbdecbcbbccbaceaeccbddcbecaacddbacaabedcececcbbabbbeaceeebdabddacaaaeddddadcedbaecaeaaecebbeaaacdadcdabadcadcbccccbbbaeeeaedbbccbbdceddedbccedcabbddceddbddddabaadeebcbdeedcdeeeddacdbcbddbbcccaebccbcacbabcacddbacedceedcbecedeaeedcdcbcdabacebecbaaebcbbbeaeecadaddcbaacbdadedacacdbedaceebcdbbbbceeadceebaecbdeaaeaaabcbcebdaececbeccecdbabbaaaaaabdeacbebdecceddebadeedadcdbadaaaddcabacabbccddacbdbabaeaceccadbbdbceaddbeecdbbbecbdebadedabaecbdebcbaaacdeddccedcadacbacdaaedabeccbbbabedbbdebaaeabdeadcebedbebddebcebccceaacbccbdbaeaaddcacdcaddddbaadaeacbcbebcecdceeccdebcbdccdabaaecabbcedccccdbcdecdcadddccbcebeabeecbbabbebadedbeaedadadcacbeabbceeddedebeaeaeeacabaecdadcbcdcaddddaddaeedabbdcdddeaeeddcaeeadcedcbeeddedaabedecacbbedbbabceededaaaeecdddccedebdeddbaecbbddddaeebdaecdbeebeedddbaccadacdcbeeadddebdedadacebcdabebadcaabbdbdaabbccdacedcecdbbcaedaaddcbbdbcecabeebdebeaeacbedcccedcdcedadebadbaaddddcbadbdcabecebeacabedbeeabddbaabdbcddecedaddcdebcadaaccdabacacbedcabbcdeaddadecdbddeedaedccedcecccceedecbdaeeebdbaabbbbbdabeaddaeabceaeadcdeaeccbeeedcaeabccebdedcaaeadeceeadbbbceceaaaebcedabbddcdaaeaadcaccebeebbbbeaeaecaadabbaceedbebccdaabbedecdebdaadcbcccbedbaeeedebecedadedacbcaaacecabbdeeceaaacbcdccdaecbdedbbcaabacecccbbccaccccaaccdeeddaaaaaaccbbcadcceabbceaaebbeadddcedadddbaadcecdacebddddeabceadbcadddacacdccececdcececdbcecaccbeabeccabcdddccdebceadbbceebadedbebdcaadeaaadabbbecdebcdbabececdcedadccbebcceadbccbbabeaacebadeeddbdadcecabeaeabcbbecebaaeeaacdaccbbdeebaebceacaceeaaaddbedaddecabddcebccacdceababbeddeaaebddccaccabceaaddeebebbdcdbccdddadedbeddacccadedaccbaaeadccdbddbebeaabdeadddccdddceadebbabececaddebcccaedaecddbeaeebdbbeacdeccaccddbbbaeccaebaaddedceadaecaabccaceddecbbdeaacecceaecbaeedaeabddeabdbebcadddbbdacbeaaaccbeebebecbcadbdcecceaeddbbbeaecbccecaeadbebdeedacbebdbcacbdabceebaadbdbbbecebeeeceeadcbeceecedebbdbaaeadecaabaecdddacdecddbcaddddbaecaeaeadecddeedecabdddcbcadcaacaadbcbddecbdedabeaedebaeedacbcadedcdeeabdabddaaaedcadadbddbebbeebebbbbaaebadbdacdaeaaddadcedddbcacacabbababadbdcdacbdececbbaebbbebadeceedddedeeacaadbceedabdeadcceacbeeeaccacbebeebcbdedccdbdaebceabbbddbeecbeddaecdbaddaaecdcbcbbcdebbdedcebeccaacbacdbbceaaeebbdebdbcbddaaaecabccdcbabedbdedabddbddebadabeadedeeaaacecceebbebdeaacaedcdbdccdeeaceddcccdcaceececcbcadadabdddbbacbdcbaabddcacaaadbbeacbadebdedbedebcbbbcdedbacdcdceaddadabcdbcabbaadbadcbeedcbcbabbaddaadccbabbadeadcedecebcabeacabcabccddaeabeceedaebeaceddaccdbecbeecdadebeeedeaebaeedbdbaeceadcccaacaebcddcebadabadbadecbcdabcdebceeeaebdebbbeeceeddbcdcdbcbcaccdedccbbccecaaaadbabbccbbeebbecbecbdeddcdacbdcdccbebbbbcdbaeacddcaaadeebbccadccedddbaddddeecbbbabecebaabeeaabeddbdcedcacaaacdddecbbcaabcaebeaeeeebcccdcabeacbeddaedcbbaaaeecadecaadeeebaceaeeecaaccecadbaeadaacdbdebbeaaacdbbecdcdaabceedeaebccccadebeecddbdeadecedaaaecbeecbcbceecbbadddadeabddeaeddebcebabbbddbbabdebbbbabbdebaddeeddcedcddcccdcecbdedbaacecbddedcbebadadbbbadeeebcecabadaddcbdbddbcacbcbcebaeddebbddabbcdaeacaddaeabeaaeacecadccccaaabcabedabdeedbddaccadaccddcbbdcdebaaabdabbccbdccdadbcecedaebbeaacccbcaeddcbaaebaddedabbeccbaddecddcbbbceebccebbcedbeebacabaabbcdebcdbcecababedbbebbdedaecbaeccbceeaceadcbbdabbcbebaacbaaaebbdaacccacbbdaaccddadeacccadbeebdeeeddbbbacbebbcddbcdbeedacacaceadbdddaadabdccadcdaddeeacdaecdedbacceebebccbdcddbdeaeeedcbddedcadccaeedaecdedaacbaacbcaacdaeabdbdbcddebaaaaacbdbadccdecdcbbbdeebdcceeaabeaddecdbbebbadaaabaebcdacbbeadebdbecbeabcdcbdddcaedaccbccbdbddbacaccdbcedccacedaabeeecccdcdbcdcaaadeedbcdcedddecaccdddddbccbcdadacecadaabbeacdbbceeeabcedeedbeecbeaddaeedddaeabebbcecbedddaebbdaceeadcadbedbedcedecaecabacbaaedcaccbccebdaeadbcdbbeeebaaebbdcebbeabbdbdcddaabdccaedabeccceddadaadadedbdeddedbbbeccebdddccdceccdeeddbeaedabcaccbbcaaadacdcceebecedacbccbdaeabbdbbeebceeaccddeabcbeaeceddadabadcadabdbbdecdbdebbaabddbdccdaceabcaacbbcbadcecabebcaecdaddabecbedadbaebdeeeeedeadddbbadebecaadebeedbbbcceadecdbaaedebbabadacaeabccbbebdccbbceeadccbcdaadcbdadbeedaedbaeecddccbdacaebabccdecbaddbbbdebbaccadacbceadcbcbbcebbdcebaccdaacaeaecbcaddadeeadbacebedaabcaadcebbcbdedeecbbdabbbbecbbadeddedacdabcbbbeeddaeebababdbadddccacebcddbaeaaadeabdaeddeabcbbcdcceddbeecbababacebcceaebbacccabeebbeaccabbaeabbeadcbcedbcbbebbdedceedeebceebaedbbbdbbceaaaeaacaddbdbdbbedbbaabdaeaddbbcbaccadecbcbbccddaadcbdcedbbecdcecbccbadebaaaddeedeaebddadcddbbcabcdacbcccddbadcbbbddcbebdeccbcbedcccbbedecabbcadbadbeddbcbaadedabcbeeebaebdeeaddceabedcbbcacbaccbdebdebbddcbadcddeeddddceeaabecbaeacabdaedaacadcdbbeeceadecbbcaebddcddebbbbeaaebebeeacebedcddeeceaaaacdddcdaeedbeecbeeadbaceccddcedbbcdceabaabeaabbadcccbaaaeebaacbedeabbdebcbccccdaddeebbaaaedabbacacaacecdacddcacedabeeccadbbdbaacdaecbcadaabbdaaceaeaedbcceaeedddbcddcadeadddbcabcbadcdcdacaeeccaebeaabdbadcdbbabcccbebaeeabdbeedadaebbabdcdcaeddddecdcdceacacbaaedadcababbedccdbddeaeccbbccadecbbadeebadecccdbdbabbecccdbaeeadbecbbbdbecaebedecdddcbbddddbddaaccbdaaceaacadcbdceabddbbeaebeeaeaeaacbdbacbbceacbcdceeebdeaabaadecbeabcdeaaceabeccebbceaccbcccddbbcdedeedabdebcbdecebadebbcaddababbaecdedaedcdecceceedaddbabeaddaadbccebaedbdbeacddbdeaaeddbadccbaceaebbedaabecddaeaaadeaabbdddadecebdaceaddcbbecbadbaecdcdecddbdacaccacecbebadceaeeaceeeddcaacbdaccdcdaddedecbeeaccabcbcaabdabdecbacccadebaabadeedaedabbcbbcaceeadbdbbabebccadadeeaaabeaaabaddbccbeecacdbbdbadccdceebadacccdeeaedaeceaeeceabcecadaaaeebebccbbdbadeccbdacbbcabacaeebccdabbacddccbcacaeaabeebdcdbbcbcaaaedbaceadedbedebcbbdedaedeabdccdcbeccdccbbadcdccddbbebacccaaeebebaaebdeadabbeeadcdddebdcbcdcdcceededcdebbbbeebeaeedcccdcadcbdedadedceceedecebabbabbddeccbaeeadeeaaaebabdacbccbbbaaeceabcadbeeeeddcdecacebadbeccbaeacbadcaaedbeedddcaebeeadbeecabbbdcbcbacaceabeebccabaaccadebddecebbbccbeeabccdacdbbbbaaadbeebdcbaeadcbacdbbadbbcdbadedaaceeabeaeebcabdaeddbcbacbabdaedcdeecdddaebedaaccedbdcdbbbbbebeeebeeaabbeeaadebaebbccbaccdcadedcddbcaedabdccbbcbccaaaaacdaacdbbaebccebcbbcededccebaabaabeecadcdbeebccdddbdceedaccdababbedadbbcceaabcdcbecadbdccaaccedabedaebbaebdbeeeebeaaaeddadebcdbaacecedabcbeabcbbaceaceebcbeedbebccabebbdceaccddbcaceabacbeaedbebcaeeabbdeccdabdedbdbbedbabcaddadaeaaebccdacbdbdaadebbbbedecdabdbbdabcbcdedaaecceccadcebdabddecbedbbabebaeabecdbdeaccdcbabbbeddcaeaaecaccaeccebceeabdedcbeccaebacecbcdcbaaedaceecaadeacddbcccdbeaadadbeedcaacbaaabdeaeaaaaeacccedcaeeaedebcaededccedaadcbccaecccbcaaeacdabcaaceeaedacddbebceeadbaeebcbbcebddceccebdbadeecbcbccddbeacbedcacbbcacdadcdcabedededbaaecbebdbeebbbddeccdecdcaecadcbdbdbeecbdcadcdaadaaccdeecebadbdabaecdaececcebbdaeacccaebacdccbbdbabedebdeadeeeaebbdabbcccccbbeececaedcddbdedbeecccddddedddddcdcbdbaeedbdbecdabcacdcbdecaeacdeeedbeccedccbdadccaabbdaebdaecacaabdaaeedeeababdeebcceecbdddbcabdcaadaeeeabedecdeedddeacdbceecdcddcddbcebcaabaeadcacaaeecaaaaeaedcaddccadacdebdbddaebeeadeeadddbabdeccabaecadbebdcbccdccdcdcbceccedbaaedeeeaaabdcecbeaacacadcddebeaaccdacbcbcdacececeedacbbeaebbbcddcccbdcbdaeaeeadecdceaddcbbaeacdbaceacdccebaadabcedadbbdebcbadddcceabeeecdcacdaaebccaaebabceecdbbadaaabebaebbeaecaaebcbeceaceeabbcabceceeeccdcdbeaeadaaecdeeacacbdddcbebbabeabbccbbeddaeeccbedaebaebddadddddeaacebdcdeaddbdacedadbbdceacdabadeccebbbdceaecabeaadecbdacaeecbacdddebbcdbdbccdeccabadbceecdecacbbacecbbecbaadbaebdbceaedecabadadecaabcabcadabeebcbbbdeabcaecabebbeeeccceceaacebcebaabcdcebbabaaebecbdeabcbccdacbddcdcbeeccecaaaddcaaaabdcaccbabdebebdaecebcddaceddeababdaeecebaccdceddceebbddcbddbaacdebbebccacddeebecdeaaceaaaebccacdbdeaacdbcdedabacddbeaebcacaaaeddcecdbbeecaaadcabeeebbdccddabcceebdbcdedccdccaccecdadedbdacebcadceaaececdadebcaaddaecaaeaebbdacebbbeedcdccddaabbcaddccddaadaebbbeabebebaaeaccceacabacbccddcbeebeeaebadbacbdaaeaebceddaaabadaddbabcbbcbbaebcaebacadedaccccaddaadeadddeedabcdaaccedbdbcdabbbcabcbcabdeacbcddddbcaecaadbbceedbbcccaecabaacdecaddcdabdcaaebccccbcdeeebcacccaeaecaacbdebbdebdceeeaeceeacebacaabaaeebccebccebecebeaabcbdbadcadcdedecdaabbddabceccdcdbdbecaeedbbacaedebdabeeeedaaeaeacebeecebacabaabadadabdbcaeebebcadcaeedbbaeabbbdedcbdaddcaabebaabbddccacaabcadcbcabadcbeceeedeceacddddbdccabdcebacbebcceddaaadbdaabbcebabcdedbdcdcedaceaacddbcdbdabeaeabeeecbbbdacebebabcadbeeceacabcccdcbbcdabaaaedbbbededadcaaddecdbdacebccaeededcecaaeaeeeaeedbceedccdcacdcdbecddaececbccaabdceaadadcbeadeabdeadadbcaaeacbebecdaeabaaddddaecdacaebeeeaecdcadcddeebabdadbbaededbacdaaebddddcadedbbbabeadebceeaeabdbccdcbcdbaeeedeaecaeabeccbbceaedceebeeadaeeaaaeebdddcceacaaecdbcbcaaaacadbeabbdcadcbdbcbcaecbdbbedbcbcaebeecdadacdabdcbcdaceadbebeeccabbcccdbaaeacbdabcdbabbadeabebbcbcbcceadaedeebeeaeacadecaeddedbcbdbadabcaeedbdcaaccedbdbebbddecaaddbdbbdacdacdbccdecacacbcbbdbeedcceedeceeedbdcedbbcbcaebbcdcaacbccadbedbccbbdeeeebacacedccebabaebcbdcccdbeddaaebeadecbeddbbceabecceeacdaddaadccacdcacbbdabcdedacebdebcdcbecddaedeadcddbdcccececdebccadbecbdabbaaacaccbbaaddeeeabacceddddaacebdaceaadcabeaabbeccbcaaceaddecccbdddaeccddbacabcdbdddedeaaaeaebcebcccabdcbedbedbeaadaacdccdccacbcdaaeaaddeaadcbabeccdcadacedbaedddeeebebeeeedccaabddbbaecceaeaccbadbbbacdbdccecaceaeccaaeadbebdcceddeaaaeecbceaaedbeabadcebaecdcedbbdcbebddbbbbcbcaadbdccacddaebdddcdbdbecddcebaebdbbddedcdbebabeabaccbaececbebeaceeadcbabacedbceeebdeaddcebaeaaeddedbcceeeabebeddaaaedeabebeecbdeeeebbaeebcedccbcbcdceaebacbbbceeccbadcbabaacebaabdbddcaeabeddddabbacaddecbddbacbaeecdceddbccdedaabbeceadeccdadeadccecbaaacaadebaaededaedeacbaeddaadbabddbedadbcececedbdecdaadebabaebcdebdcecdeeeadcaeddcabaaebeaddbebecbdbbaeacbdaabbccaaaadedcdeabaeadddcecdacbccebdabcebedbddeeaaaaeeddeeebddeaebecddbbabbbccccdabeebbbeebbeeccadaeadaaeedbdaebceecbaceecaaedbdbbadaadddcabbacbbeedeacaaadcbacbdbcbaebdddeecbbdadeaedcaabcbeaaebedcdbdbeeeadcbbaddebdabbcaeaddcaeddeaceaddceededdbeccaaeaeeebabddbbecddcecdbedcadddbbdcbbadeaedabaaadddbbbcebadeedeaaeeedaddbebdebbdcdaabebcebbbecbadbababbdebededbbbbbbaeaadcaabccddecbaebdbaccadbbeaebdbddaaebdecaeceedceaabcadbdcecabbbbbaaebbabdcbedeccdbedbaccceebeddeeeeceadaeebaddeedabeaabbdcddbcdbbcadcadbedebcaecbecabaaccbebcedbbcbebabeeacbaacdcdecedeccadcbeedeceadabaeabdeedbbacaaeedbccdcccaebeadabcbabbadbbdcedadcdceeecbcdabbdabcbeedeebbeaaecdebebabdcbeadcbadecaecdbcbbabedbccddacbdcddcacbaaaabdbddabbbecabddedabbcbeadacabcecaddcdebdbbcdeacedaaeebebcacbcaaeeeabdbbebaeeaddebcddbdcaacebbdddebedaecadabeadaabeccabbbcddabadbadebdbeeeaebdcebeddcdcdbabaeabcacaddeabcedeaecabdeaddddcbbceedcbbabecaeecdecbbdeaecdcccbbeededbeddddedebaaabcbbdbcbabaebdbadcddbddbdeddaedbeceedccdbabbbaacdeadbebdbddaeaabddcecbcaedbdddcaadabddccbeeccecdbabdeededeeacaebaeabbadedcbcdeeaeccceecbbdababacaebaaebdbeddbaabeeaeaeaebecbcdeacdcecbeeadbbbadbdebabaabcbdaabbecccceaecccbaecbbcebbbbddccddaecdadbebdeeddaedaebdddbbdbdcacbeebbeecdbddcabedbceccbdeacdeaccbebbcdabdaacbdaebccebddbeeecebddcaaabbeadbeedcbdaeedebabcedcaaceadbbbadceaeccbdeccacdeeccbeecdaaebaeeabdbaabccedbdccccdebaacdadeecdcbcdcbabeebbadbacbdedaddddcaeccbaddeabcecdcaccccbcdbccbaaeedbeaecdaceccbaceeabdbaaabdcdcaaaddaaacbcdcabcddabebadccaaacbcaaedaeeaaebdeddbacdbeebcadecbbeddcecbcdeccbdeabedaabcedabcaedeebbaeeadbbddcadbccdccdddcaeaddadaabbeedcbaeeeadeeaacceaadeddeabaedaadaeabbcecdbcabdbddceaacdeabdabbcedbaeaebdbacebaecaacaabdcceaaceaaecedaeebeededaeddaeeabdcebebcbabdebbcacddbceddecbbddcbcbeddecadabddcedebbeecdeeebcbcdaadeecebebaacebcedbaaeacebddcdebacaadddacbbcccccccaadbdaadeaadbbedadecbaedabcbcabadeaddcabdbdadaddeeebedcaedcacabacdbaebcecbacbbcdabbbebabaebbdcbceeeebcadbaaedcebeecbebbaeeadbbaedadbbbacbebdcbeaaadaecebcdeacadbecadadcbeabbaebebdcdedddeadbbdcceeeacceeabccacdbbebbbecabebdcbcaacdaecbcbceecdededaaebeaacaebbdeedadbaadbeadbbecdbdcbddcbedbabbeaeeddccccdbdcddceceaebdaddabcebebabeceabaceecedceebbcceadddbabbbbbbcdcddcadcacaadbabeacedbdceadecabeadacaadaadeacaaaeacddbacadddacdebbebcaedadbcecacbcedceabbceacdebbeaeadceaaaecacbdbebebabacaddddceaccedaddbcbcccdaabedaeeedcddbdecdbdcbebccebcceecdebbdeddddcbecdaecbbacceacacdabdcaccbaaceeebeaddbbdecdcdeeebcbaaacdddeedebdbedacbeadebbababcadccbededaaeebcaaeebadbaebdccbbabdcbbedcedbaccbcebaeacbcdeaedcdccacbdedaadcccaaeadcddcaeeddcbabbebceeeaadddecbceacdeecbeaacbaddabcbaceedcddaabaddccccadceeeecccdeabeddedceebecebbcbaeadcaeabbbcedebbedecdbbccdddebcdbadbcaebcbccddaccbdededecbcedbdbecdadebeececdbeddbadcebbdaeeeaccbeebaeedcdbabebeadbcedcbdbcacdaebbcadbabdebaadcdcdeccebbdcaaecadabebbcacebadbbcbaeadccbcebaaccdedadccebcbebddaedcdebbbbcacdacdaeaebaaeebbeaedcaaaebddadababaeeebdabdacedeecedceaedaabaddbadeadcdecbbddbaeabedaaabbeeaddecbceedccbdaaaedabecbaedeeeaaaaeaddbeadceaadccbccedcabdcdcddabbbbeadbcbbeeabeeaaccddccdeedccdacdbdcbdbabdedccddaeeabbaeacecabacdeaaaadcdcdecdbeedaccdedcbacedbbcacceaabbabcceadabcaaeeebedeecaecdbdedbccedbeceeebcacaeedddddeadaacebdeeacdedbabcbdbccdbdeaccacbdcdcdcabdccbaecaedcdddbdecbeaecdedbbdedeaaeadcebcbbaeeebeaacbdbbbdcbeaaebbbbacaebbccaadedebbaaecdcbdabacaccecccaadceeeabbdedaadedbedbcecedbceadaeddbcaddadbaabbacdeaedecacabebbdbcbccadaaadcabeecbcecdcbaddbbadcadabdacaecabeadceecabaeaccdcceddcebdeecdadcabecaadbecbaeabbecbddbcccddcaeeadebebddaccededebbdbccbcbceecedbbdbbbadadccdeadbdedcbbadebbbebeeebacbddadccdeedabedcbcdcdceaedbdcbcaaeabeaebdcdaaacebabccccbddbdedbeaedeedeebddcabdedebaeaaebdeadbdcbccbbccbddbbdabbdcecedeadaddeecdebeeeadaeeebecaccacdcddebbaecdabeabeaadcdbedadaeceedbceeacdcedeaeebebbbdedcccbacdabdbeecaccacaabcbbccbcbeabedabddbaddebcacbbdcbdccddedabedaddebbaebeabebaeacdeebbdddaacbedbedbbdbddacacbeddeeedecbbbdebbdaedbbbebcadcddbcbcaedaebdcabddbcbabedcbbcabdceccccedebcccbabadccdadaadcbaddbbcaeeccbbdeedaaeddbdbdceeeabdaadcaaebdbceeeacbbcacccdcdbcbcaeabbdcdccdcbedddbcaebbdcdbbaceaaaaaccbacdcbaddcabdceedbaebddececaaddcadeeeeadeebcebacbcbbebebdebbaaeceacacecbcbcdeddabdcbcecbbecbcbbbabbdbacaeddaaccccaeaeeeaecabbcecabceddecbadebbebcccaddedeaebdcbebecebadcceebbeeddcecccbeeaabcadeacecdacbaddebcbacceccedbcbdebaecbddabbadbadcddcedacddecabbbdcaadabdbedbedbcdeeeebbaadeaaeaebdbecdaacaaaddbebaaacccaedcaeaceeeaaceaaedaeaaeabdeadbeeecbdcbacbaaeccaeabbdeddcddacdedbdbaebacccdbaddebeaedebdecedbbabceedecaaceedbabecaacedeedadadcbabbbcbbeeeaddadbbccacdaecaacebacbaddecbbeeeccebdbedacabbeacabcbbbecddeeaedaeddbbaceeadedddacbbadbabaaaeeddebccedcdbcaadbdeeadebdadabeebcedacbccabeaaeeaaeceeedacaedccdacbebedabdcccaedcdbaebabcbcddadccabceedcbddabbbacdccdaeaacbacaabaccdabdedcbdedbbcbcebebeebddbbccdcddadaaebacdadaebceccaabbdeadecddeedabedecbeeddbdabcadeaadddcdbacbeacaddddecbdeaacaadbdebedadddcdaadcccccebeceaeeadabcadacedadeabdeabcddecccabbaceeabadbbcaeabbdadddadaaccdeccacdececaddbcbbaccaecaddadddadddababdbaacaaecdabaceeadcbbebaeeccaabdccbaaeedcbabcdacaecdbdcdaadcbcacbaeaeeaccedcecdbceacdaecebcdedeaecaaadeaaadeacccaebcaacecbdbcedbeaaadcbecadeecdedceaaceebceceddcdbaddbabaedadebebeaaeaeecedcebbbbedaeadadccdebacbcacdaaddaededabdcbdcbdbdbbecacdeedecbdcdbedeabcabcbcaddeecdeaacacceadadbcdcabbacbaabbadcebddacaecaaaededacbdcedcadccaebbdeacebdeaeaebbeebeaeededcddadcecccdadbeeeabbbeabbcdabacecbadaccdceaccbedcebcccdeaedbcbcbacbbebeacccdceacaededdaeeddedebceaaedcaedcedddabdeceadbaeedbccadabbeccccaaeabaceaedbaaabecbddcbdacebeddcaabeadccdaceeeabcbaaecaaeadcadcaeeeabdbeaaeddcaebdebbeaecbedeacbebebbbeaeddebdebeeaeaeeacdeeeccccbaaebbcdddbebebddededcbbbeccdabebadeccdddeacaceacabecccbdacdccceecdbeaceeeadecedddecbcacdcaaceaeaecccdecdaadabecabeeecbcddbdceedaecbbeceedeeeacdabdcbcacdbbeadbbcbaacaaaecbcdbcaccdeddbaabdcbeddccbbcaecbeebbecabdcdececccdaebcaacaaaabecbbeccdcaeaceddadbdebaeeabdacbaebaaedacaeececcacbcbaceeabbceeeeabdebacddabcdbdceabdaccabbdebcceddeeaacdcccbaebdabaeeadbdedebcabadbbdacebcecaaeeaabaacbcaccacceacdaaeabbaedeeeecbbedcbededcdbbddccbbcdacbcbcabccdebaecabbaddbddcabccbaebdbbebeaacaccecbcedcaadcedbaeaaecadebeadcbdebecacddcebdeaceeeadbdebeaacabdccabccabceadcedaabdeedbbebeaeedeccdbbcdcdceabcbdedbcdcbebbcdcebaddcaecdceeaaebbdebbbaedadaebddbbccaedaeecdabadaacbaeabcccabeacedeaeadddcbcbebebdaeedcaddcabdadebaceadadbcaccedbbaaacdeabbddbbadccdebeaeadeccbbcbdddbdbeeeddedaaddaaedebeddabebadcbddddaedaecbdececcbcdabdbcadcadbaeebccedbbcccdceaccccbbeaedabcabcbaabeeaaadcabebaaabaacebdcdcddebbdcdedbcedebadaccaabdeeeaebbbcbcbecedddcbccebcecbadcaabdcecedbeceacdacddbdbbccbcdceecadadbedebccabdadeddcccabcbeebddbcddbcaceceedaccddacdcabccceeabbbecadeccdaeaddaddbccdedecaddaeabcaedebdaebdccaacaddacdaaaadcdbacbeeccaacbbacbaaccbcbaccbebcbcdcaecebbbaaebabdddeeaadedebdbdeeaaedacacbcbebcbcccacabedeaacaaeeabdaecabbbcaeaaaeedcedeccbcdabbeccccbeaebedcececcdcdcabbebcbbeaeccbbeececaddcecdbbdececebcccdcaadbbbeaacbebcadadbcecdcceccbbddccdccecbecadbccdddcdcdbabaeabedccebaaebcbdacdadbaedabbaebadaccddbcaebaecdceadecddecbbaecbbabcaabdebaeaadbbbddaadddceddccbaaabababaeabaddcdcbceabaeeabbbdababcebdaccaddcbedcbebddaabaccdadbbcecaaabbdcdecabcdadeccdcadccceedbcdbddabccdebecabdeebaceceeedcdcaadeaaaeebaaaececdbdabcdaaeaabdbebaadbbcadababeeddeccedcebececaedadadcdcedcdabaeddcbdcdbaabdecebeeababdadeccadbadbedbeeacdddbddbcbeadbaadcdabecdadabcebeeebdeecbdcebdebcacceccbbbacedbcbdbceacdbaaeeacbdacdbaabeeabaaadcdcaceadeadedcdecbdeebcbbcbddeabacbccbdcbdeedbbbcabdeedacebceacbddccdeddeedaeeccddadbcacaedbecdbdaaecbcddeceabdbbadddececaeeabecbbcddcddcbaedeeccbeeaebebbbeddeedabbeaabeeecacbdcedecdceeedcebadcededddebedecaccddeeebabdacdeedecbaccaaecbebecdecdceabadecddbcdebeeddeccbbacedcdabcaebbabbbdddbeddbacbbbceccccadababacacedbdebebbadebadcacddebbeeadcceaedeedaeaadabbbeaebddbccbbdceaeebcdcdeadcacaedceeccecbecebebddacebbbcbddccdcbeebeaceaaaebacebabaeedbabbbbbcebaebbeadcaeecdccadeabcacccaabeebdaabeaceddbbccdccebcdcdbacdcbeacadddaeaabaebcbdcdeaeeccdbedbaadbdbaecebeaaacdcdcaeecceeedbbdbabbbedeaebbcdadaccbdadebbbdcbdbdbacacddcbeeacdadaebddedeaebcceaeaebecdcdeeabbbcbdbbdcecddeceecceadeaadbbeadedeaccdbeeedcabebaddababbcbaebcccecadcdbdbbdeaebebdcdaacdbdaeaccdcecceddbabdaeecabadaedabdddccadcadabdbcdddddbcbcebebbbbccdbbebeddcbbbcdbebdbeaaaeebdcecdeddacbcadddacecaeecadededdeadeeabcdacbcdccacbceabddbacceeadebcbaecccbedacdddbeeeccaebabceabdbaabceaabccdeccaedebccaccdeebbbbcdbddceabeeaaabdeddacbbdaecebdedeabdebccdbeccddbaceadaaabebeeaccbddeeabbccbceacceedacecdceebbeaacacaebcdbbcecbbcebebacbcaccaadadaeecccecbcdabddebcbdabcdeaeabbecbccacdebcebaeaacaabddbbeeabcdaecebedbeceddccebebccabadbccbbcadebacebdaeecbecabbddbaeecceaedccaaeeceabdcbbabbbeeeaeccdeecdebabccaebbabecbbbeaaeedbababcdacaecacbbeccceabddadddcccecabeadbdcbababccddccaccbeaabaceeccececbacdbddbcabbedabebddccadbbbcecceeddeddbdbaedaeecbbaebbebcbbacaddedaaeeaababbeceeedabcabcccbdddbeeeebbacadeeebdacdcbccaeedaebaeeabaedcceceabccacaacbeedadbdadebabbbdecaceeabeadbaececbaceccdbccdadbebcdcbeeabedcebbaebbaabeddeabcbbdebdceecaadabaabebcabeaeeaecbcdababbcdbcebaebddedbcdebbeadacdcdbeecbabacbdabbcdacbddababaecdaabdbcbeccadbcacabcbaecdaacbeccababaeecbcdbaadbeeedceabcddebacabcdbbaabacaaedaceceacedcbaddbcabbecbeaceaedebeaadaadbbbcccdacdaaddaedbcedbadbadcddbaeadaedcdbccaebbeacdaebddddbccbbbedcebbaebadcacdbecbeabbdddebdbeedcaacecbabcaaaeceeabbbeddbceccbcecadceceeabbacdbabdbcbcdebeeecbbabcedebbebaadcbbdebdaececdaccbadbbeadcdbecedaaacddeeccacedbbbacdddecbbaaeabbcbbeabdcbaecdcdecacbbdcdabddbecacdaceaecbccbeeacbebbcebaedeadeebdebeaaaaedbabceceeabbaaeebcadaabecbcedcabccdedcaaaaaeaeadcaadacdeeabbbbecacdecedceaddbbddedccabebaebecbaaaddebceadcddcceecbcbeacaaaabacdebcebbabbacdcccbddedabbccabdadeabdaaeadcddeddccedbecedccccdadcceeabecdacadcdeaaebeeeeaebcdedabcedccdeadddacbdaceadbbbabdecebceebccaabdbaededadcddcbaabaacacdbcacaebeeecdaaceaabcceecbdbbcedcdbddaabadbebdbcaddbabbbaceeacbbcedecadcdbceccadadaaebeadeddcdccccbdabbdcebbccddecdebcdbadbbbebbecdbbacbbbdeadaccaddabbdeddbdabeaadeeddaeaeeceadcedcdedcbabdedbcceddbbaddbaaaedeacdbababdaecdacabcbeecdcbabbcbbbacecdebdcabcbddeeedabdabbdbbdaaeaadeccbcceedbacdbbeaebeeceaabdeeecccdddbbebbdeaebbcbdabedcdaedcbedbcaadbdabedacbaabdecadeeadcabdcdacaadbeacccebcbcceaceddadaedbcdbabaedbbaeacdaadaaccecddeaabaadadaeaaadecadbebaebbebdcaababdadadaeaaeeaaccdecdaadbeaacaaeeacacedebdbddbccbcadaaccaaebdaddadbbbbaedbccaaaddebdbcbcbcbeebeeacaeacceaebbdddbcccdebdcadcdacadacdedbaebcceedcdccaeedcdaaaaacdcbdecbbecaccbacaebbbaecedaddaadaebdcadadaeedaceddaacecbcddbadcbcbdececcbbceeecceccedbadcadcaebbbaadbbaebbaebddabdccbddceedcbbaeddadbbeceaebbdedaddcdedddddacabbacecaaeddadcabeaacbdbecaeabcecbcbeaaccaaebdbdcdbcaebceedbcbddadecddeeabdaaedececdacaeddadcabbbcbadeabadceabcacacccbdbbabdbbcacbeedabacbbbbacdaedcaccaeebabbeacacbcdeececabacababebbbceedacaaceeaebbcbceebdbcbadddeceaddecbaadedabaccbaaaddddeeccddddebebaaaccbededdcceeaeeaeaccaecbaacbebcdadcbccabbbccbbdebccebaecdceaebdbbdceaaecbababbecbecaadeddbbecaedbadedebdebcbcbeedbeebbccbacabdcecbdeecededaedaaeeeebbecaabbcaeebbbaabecabdcdaccedddecdeaaabdcbeaeeebeeeddcebadaaabceaabebeeccddaddcbabddaeacaacccaaceebaebacbbbededccccabceedbdcdcededbbeeedcdcdaebbeeecadeedecadeeeadccdcdeccdbaeecaeabeabceabacddadadbdcabdadbdbebebecdaacdbcaddedaecbbceedabaddabebcaddedcbeebbddbdecdebabacdddbadcbaaabceaccdabebcedaaabbaaaeaaeccbebaeacacabbcdadbacaebadbcbebabeccddbbeaaeaccacacabcdacdbabccedcccbebcacdadeadaecaecbdcebcddabdedcbcbeedceadeebdecedcdbdecebabdceccdcbebdadbdcabaccaddadaadadebdcdbcacbbdecccaccbbcbcacabbdcaececbdbeaaebbededbbcedeaebdbccbedcebbbcaebcbddcdbddeddacacaecaacebabeaccadcdaeebaedeedaeccbcdbecbcddcbdedecaacddedbecebbeeaaacbbebaadaeacbaeecceccdeeadaeccbdbbdebdacabcebebcaaddbeaeaecdecccdedbbdbeacebbcbcedeebdcdaeeedeebdccadacaaaaaaadaecadaabcaaadabdbbdbcadabbdeaaaecbbbbebaaebcacadbcebbeedcdbabcdddeddccaacbbcbcbdcdaaeeceeaacdedeccaaceececbddbaaacbaededeacbabddaacdaaedeeaedbaddcaaaeedcbbdaceddecbcdbadbdcbdbccdadcdaaebdcededcadaeecaacaacdeccbcbcecbabdacbbadebeceebdbbbeedaaecaadbecbdeecacaaadadebbaabcdaecdaaedcaaacedccbbcdddcacbabdecdebedcbbadbbeacdeebcebeebdbaddeceacbedadbadbccdacededebdaecbaecabcaeaeaadddeeddecbadaccbededeaacccbebebbceacbbeadeecadcbddcccbdcdacbdcedbeecaaeebadbebbbbaacadbdbbbecbbcdcdbeacecdeeecceaeabdcddaaabdbbceccceaabddbceecbedebaceebbbeebbbdebbabddadccbdbdcecbdadabbcadaaeceedbcddaeaceddbaaadaecbddeabedccccdbdcbcbbdabbdceaebcdeaebcedcdcaebeadbceeeedbbcceccdbedbbadabeccabaceeebbaadecadeadcacbeeabaedeabebbaddceaddbacebbdbaedaeaeaeaebcdeeedbcbaeaeceeccbbebbdadcbaaecceadbcdbbbeaabdcbbceeacbddaedcaacedabbeebcbebabeabaaabceecbceaecaadaaeceaeececabddcceedcbbaecbdaebcadbedebeabebcbccdbcdccbeddbbcddabccdcdaebbeedbadaacdaeaddecbadbdedaeaebaaddccadebdcbddcdcbddddacdbcaeabccbedebaecaadbebedadedadbaccecdaaedeecccbbcbadbeecadcebecadcaeeceedccbabcaddedaaecbeacbddacabdacacbceccbddaecadedbbcadbbeeacadadcabdeeabbceabdcabcccbdbaedcecaeacebeeabceeddacbccbbedceababdbceeaccabeddccadcedbeebdaedbddaebbbaecebbacacadaeacdceecadeddcabecdcbdecdbdcdaacaddebcceacdacecbecbbdaaaeacdabccccdcceeeaeededcabeeacdbbceecdcdcbacdaaeddeecabdabcdcabadaaabbdadaddacedabddadeeaedccbccbdadbedaeaccaecccdeedabeacabdadbcbdbebcadcceaebbdddaeaddbbbcccdbcdbddccbebbbaadecccccaecbaedebceabdacedeabdadadceabdbdeccecabccedeacedbecdedccaecceeedaebeedaceceacbecaeaeababbdacdbcecaacdcaddeedeacaaeeeecaededecbcaecbecdedcbaeaaeeacacadeeaebeecceadebbadcdebcaecbbbabadedeeebcecdcbdeebcccdedcedddacceabacecacccacecadeccaebdadbecacddedeecdaeecedeaedaedcbdeebbcabadcbcbbacceacceecedddacadcdeddbcacedeecaccedddcdbbdbaeeadcdbbbcdeabdabeeecacbaacbcdbddcdddacecbdecabecbdbbbddabbdbbecbbdadbbcadbdaaabaadabdbedceeeacbcabcebddcbcdbebedceacadcaabeaccdabaeedccaabaeeaedaaecadbacacecacaddbbdedadacdcadcbeacebbeebeacbdbeddbcbadaeebacccaabecbccacaceaedecdbbeaecaeccbbbccabdecdacadbbdddabeadcaebdbbdadbaebececcdbcbcadaaaebeebcdeedbcabcdaebeeeadacbdceeecbaeecbcceecdbaececbeaceaaaecedbabeebbceeeaaedebcceadabebdedcbaaecaecdacbbcdbcaeecccaebaaceacbbcdccdaddeddaeaecaddbbcbbcecbedaeccbccbcabadaaaecaecccbbcccbebbbddccdbbaeebbcbbccdadbbdbeaabcddedbddccdbecccabbdbdeeecdeeecdeabdbaecebdacbadbaabeabbdcdaaeaeddcabededbdeabedeebccdeceddbecbdcdbbbdeaaeeebeacecededcbacbcadcdeeacbeacbdedeecebbecbadaaddcbcdbbbeeebdaeddacacaaceeaccabbedbbcdaeaabacbcbbdabcedebbdabeeecccdedaadbcaabdacbdeadddecccaaccdaeccaebaddbbbcdccbbdddebdedbdcbbeabadbdeeaeddeacedacbbceecdeacaaaadaebbededccbeecacbbbbeadedadeeadeeccdcdceacccaecbcaddbeedadadbaeddcabcbedcdcdaecaaadbadeedccebcddbdeabedeaeaaaeddebeebaaeadbcaddbaecdaacdcabceaabbbdbcbcacccbcecedceaabaacebdcddaedeebaddecceebeabdceaaebcdcdddbbdbaaeeeacdcdcdceaeaaaccbbaeaeadacadedbcebdcebcbdaabdbbbecdaddbebbdaadbebdcedddaadadcebcddecaaeedbcacacbdbddeebceccdecdecbcabcecdddbcecbcadbeedeeabddadeaccecdbabecbcedabebaeeebdcdeecbebddcdcedbadbcbdacbecdacdecbdcabdabcdbcbeaebdeedaecccdacecdbeeeceedceaedadcebdeecbeaaedabbabceddeedddcccababaaacdabbaddbbeedccddcadecbbaaeeacedcababcddbbadbbaedccbabebdadccebeadcbeadbadbbcacceabddcdeaebcbebeeddeaabeaddeaeceaeacbccdbebbccdabcadeceedecbbebcacdabebaacdebceaaebeddabeeabeecacedaaabeeaabeceecbbadddbebadecebeeccbacbecccbaccceabedddbacbdeabcabadcedbedaaebccaeebbeaddedbbbaaddaddbbadeeeacbdbbdbadccbaddcbeeaabbbabadaabccbedabeceddcdcdaebedebebacccaceacccaadccdaedcdbbedadcabccddcbdecdbdceaabaeeceddeaeaaaccdacccdcbbbbbcdcedaaecbebdcadbbabdbcebbdddedddecaebecddccedcdcbbeebeabebcdeaababdabeeabceccdeeaebeccabdddbaddceaceadadaccdeaedabdbdadceebddaeabeebebbbdbeabbbaeeabeaddadddbadacaebcacccdeeaccedbaddcabcdeecdbcaebdabbabceacdeeaacadaddbebaacacbadbcbacdbadccacccbabdddbcadecbceebabadaddcaadcbbeabbbbddbecbeeddacaeaacaeecbeedaeaeedbaacdbedeedbdadbcbbbbcccbbcbadceacdbdbdeccbaacdddcaecbbebceceebadaeaaebbddaecebdebeddcebeccbadaeaacaecdedbadedcacaadebcbdacbeedaaaacebeabecccaaaaeddeaeaebeabddeecedadcbdcbeeaaadbdbbececaebcecebceaccacdabeabaeeacecbacdcbedcbadcbeaabcecadcbcbdeecdaddecddedaeeccaacddbccdbdbbaaedababdacbebbbecbddcbdeacdacdadcbbaeadcbbcceabecaceabdedcaebadbacbecaabeaabebdcdcbbaacbeccccdcbdaeabbeecbbaabeecbbacebdbbdddecbcbcaeebebcacaddbeaedeadbdabdedacbdbdbedceebccceddadbdbcddcbaaaeeecacededaddacbbccbcbcceacbddaeacacbccbcbabecebdedaccbcaebdcdebdaebcdeededdabdeeedcacaeccedaecedbaaebccaadcebbbabedaeeaebedbebbcbbddbdbebbeddbacddaadeaabaebbeedecccbcaccaaeaacbcddddecdcedbecabaeeccaaedbaebbbebababcbcacddeabcddeeaceaceecaacbacadbdaadeeeaeddbdaedcbbaebeedcbaaacdbeedabdeebdcccbaadacbdbecebecceaeccdbceeeaadeecccdaadeaccaebcacaedbeedecabdecbcddbaddededddbeaddacbbcbdbcdddccccbcaeccbbceaedecddbcdedebadcabbacceacacadcbcdbbbdcceecdbcabbaaabecbbcdcddeddcaeeadcadaabcaeacacdccbbbedbeabccddaabcedbcadadccbbdcececaddeddaeccdebbaaddbacbdecedacaedcdaecacedbcbacbdcaabeaececdcacccdddeedbebebebcecbdaecdedeadcbbbecbaabbebddcedbbadebcbbeeeedcdcaecbecedccabbbedbedabaddaddbdbeccbbbcaaebabbbdcecedabcceecddcdaebceeaaaabbadcdeaacacecadcecbbcdeebdcaceaedbcbebdeecdbdedbdebdbcabeadaddaacecbdbabdedabacbcebdbbdddaecdaaeacbcbdbcdebddcababbbcccdacbdbbbabaddbdcccababdbeeaadadcccbedbcaedabbceaadeaecaacdbeaeebaadebcecbdcdbddeaaeadbadcecebbbaeacdbbaeaecbbdddcceddbaeeddbadecdbcaeaeaedeecedadbcbbcdedcabaaeedadbcbabaaaabdaabbcbcaddbbabcadddadedcbcbcaccacaedbcecbabdaeacbedbdcebcaeaeacaaaaedebeecaebeebddeccccaababddeaaceecaedaedeebdcbbdccdcdacecedbbbdaacbcaadedeebaabdceeabdbdebbadcaaaacebcdaaadaebaaebbeedceeebadcdedbadccdbcacdcdbabcedbcbdcbddabadbccbecadacbccadceddaadaceceaeeaedaeccdcacacacdaddbaabbcceecdaaeaeaddcdeceaabeedccdcdbeaadbeececeaacaedebcedabdacdeeaebaeebeebdcbedccbbcceecdecceebaabecceaecdecdcbbbacebedcadcaeccabcceeaadcecedbaeacebacaaebeacadacdbbbcbbbacadcadcbdbebbebceaabbdbcacdedcbabdcebcceedeabbaccbedbdedbeedbecaebedaeddcbacdbbdcecbcababaeedbabccdeedeedbbdcdceacabecceebccdcbdbeadbacaecabaebabbdbaebbdadbdbcabcdcbaaaaedcacaddcbbdbaebaaacabddbebdecabaacaedbaebdebebdcccddbccbdaeeaabadecccaaeaebdebcddaebdbabaeaaaecdacacddeecbbdeebecbaaecedecdcbecadedaddbecadbdbccecaacacbbecceaddeccdaebeecaaccecbbccaedbdeabdaccdecedddcdebebeeeccdcbcceebbdccbeaabdcacdababdcdbcaedebbaebabceeaedbaeceaaedbdeeabddecbbadabcbddeacbcbbcbbaaaabdedaaaabeebadeabbdcdbdbdadbaeadadcadbaacbceeceadbcdaebdbbbaceeaabaecbaaddbadabdbacbbcddaadeeaaccdeecebbbabbdbabcddbdbdbceedcbebbdebbdcabebcaebdbebcebaaeabaaeaedbbeaeddcbeaecbababacbdbddaadccceeaadeaaaadadcdccacdedadbacdecebcbebeebedabededcabbcadadbdcecadebdebdcabcbadcceebddeeaebbeeaacdeccbcadabbdcddbceebacdedcbaeaeacbdabbecdebabacdbbddecabdadcacaedcdbbdbceaadbdaeeaaeaaadcecebdabeceabcdabbccbcaddaadebbebbacdebaaeeaacbaeacdbbabdebdceecaeddcaeaceeccbbadddbbeeabcccedeedbccaddddcecabeeedecbecabaeccabacecbacdeadebbecacbeebdcdbaedbadccccdbccbbeaeddaaeddebdaabbdadceaadeadbecdebebacdeaaedebadccecaabaedeeebaeceabbebcbbddedbdcbdbcbedddedadcbacbdbeaddccacdadeeeacedabbbbecbecceadaaddaabaeacaaadcddacaccbdeccbccddeccaabbceecaaaebdddcbbedacedbecaceadeedcabbbecbacaaadbeadcbeaabacababdedcdbdeecaeedbeaecdbbcedbdaebddaaddcdabeccaedebcaddbbceeecdbcedecbbeaeecddccceedbbdbdbcdabcecebbddccdbaabdcadedacedbcaedddbabbdeddbeadbabadbdccecbabbdbcadddaadcbababacbaceabaeabaeeabbcbaadddbebcaaacaaaaedececcdeddeadedbbededeeeacbabaebcceeaccdeaebbadaaaeedcadabdedaaaacbdddaacdecaeeeacdbedbdababbbcbadcbecabcabdadebbbcacbccaeeaabbebbbabcdeaabbbedadccbedcaeaedaebbaedcbaacecabccbbadadbcaabddccdeecbacebeceeddcedecdedbecaddaabdebbacdebabbcdccdabccadddaadecbdbaaaaaedeaeeeebbedeececaddbceccdabbdeedeccbbcbcadeecdeceddebabcdaeccdbaaccabedeaeceacccdeeeddecaceaebebbdbcbebbbbdedbebaabadcdcddebdadbbbcdeeeecbbeaedaebbbacacccbcbecbbeeddadceccdeabbcacaebaccbceebccdddedaeecbadabddcbadbaecbccccdcbaeeaedbdbcebbcaadebaebadbdedbebeadeeedddecebcdbbeedbaabdbebecbcbccaacbbceeacabbeecccbdaeecbcacbdbdbbcbcceddcdbccedbbbcdbeccbcdadeabaaebbddddbdabbeecccbccbbbceaeacebabcccccbdcdbdbecaabdcbdbdacdbdeaececdcbadedbcaabddbcedbddcbcaaacaabedddbdbddccadbdececcdbabaadbccdebbcedccecceebedabdaccdadbbedbeaaaabbeebcaccecccbceacbabeaccddddbacbdabcadeaecbaeaabedacabdaacaeecaaacacbdaacbadabdedaaecadaddabadebdcdddcbbbbedacacbebcaeabdadcbbbdaaebdaaedcbacaadeaeddccedcbabcbcacebdbebbeeecbceedbbeccdccbeacdddaacaadbbacebdbdeecbcdceadeaedabeeccdcabdcddeddeadbceaebcabeaeaabbceaacdbdcaecdabeeddbdbebdabeebaaccaabacaceaabaeedbbaeedabadbdcaeadcccccbebbddedeabbebbbeedbbbbbedadeadcaaeedbbaaeabedceabdcccaacaecbecbbbbcdbebcedabcdeccdabcaaeaaadeeaeaabaaaedddcdaadbbacddbdacccdbedacdebebadabdccbeadabaebbcbddeddaceddedcbbbaaaccbaadbdacddaecdbdcbdeadcdadddbaceceedcbdbdeabeadbceebbebdebccbecddedbeacdaeeccacbebdaecaddeaabbbeceacdddaabcccceeabcdeddcdebceeaaceedbaaadbbdbcbeeaeadccebaccecddabdeeabeceddecabbaeddedeaedccceabeceecdecebdeaecdbccaeecdadbeebcabcdddaebadddeceacabeabcedbaaedbeebcdaeecbbededbaedddceeadedbcadeddaccaeebdbecbdacebcadcabaddbdbbabcdeabdaebdaaaeabdcdbaceadbedddeebdbaaaaeddbaabadbacbaeeeadeceaabccddabcbabbdecdabbdababaabcbeaddcaaddebcecaaebedcedaccebdaceedbccedbbdaacccebdbebcdccbdadeebceeaaaaceeabdaadbbabeaeeddadbbbcbddcbcbbdcacbacdeacbcacddbcaeeccddbddebcadbdcbadeeedcdedbcabccebbbbbcbeecadaccbeebdeebbcddecdbbedcdebcdcbbeaddceaeccadddccaaebdabccececbbdeaacbeeacebbebcdadbcacecacdecceceacacbddbdeeadeeaddbddeaecedebcbeecddeebabeccbccbadbecbadbedaaebecaacdecbedceddaebaadccdabedccebaeccebdaeeebddeaadcebeebbeecdbdaeebaaebdecdbbaeceeaabaabdbeccabdccdbabdbeebeeedacbbdcebecedbcaaebeaecacccedbdcedbabbeddebeebdaebbaacccdcbebeaccbadeccdcdaeccbdecdeeaabaedcaeeecebebbcbabcaadeacecadcceaebaaadcbdaaebbcbaecdebceabdcedccabbebcaecbebeabcedbeaabcdbdebaaecacceeeaeceeaddeaaaebeccacadbdeabcdaaddccacebddcacdebceeeeedeeaebaaacecdbceeebecababededaaabbdacccdeccecabecadcdbeaeaadbecdaecceececbeacadcaaabadeeddbedcccacbeaaddddeceadbebacbddadbddbcbcbbadeeacbbeccaadcdaadeddadcebddeacdcbbbdbbeebebdcbdcaaeececcdcacbdeeacedcedabbbcdcbabcbbdaddebcabebabaabbeddecbbadaeacedcdeebdbebcbecebdebccdaceaeeedadcacdddacccdcacdcecaeaebabddadddabcdaadedcbebbbedecbbaeccaceaeecaadadeadeebecebdecbbdddcadebccbaecdadbbecccaccddededceedcbddcbdeaaaedecbeddebbececaabeaedacedbabbebeeaadbcacebcbcdccedeebaccbbeebdadbdecdaeccbccbbedceeedebddeedbaacbecbbaebeadcdebadebccadbddbdcdccdeedaecabbdadadccbdbaceaacdbbdaaddacddecebbadeaddcdbbacaeddbcadbacdceecabcdecdbdccacaccdbddbcdcbacebadecdaabbbbbccbdceddebecbaeeeedddcbeedbcaaccbdadcabbdaccddeaeaaaaebeadbeadceaccbaaeeedbdadbbeebaccddccbeddeddabdbabdcaaaeaecbbddedbadaddbccaacdeeeddadbaaeddcbdbbaeebebaedacbeddaeaebaeedbbadcccbbcecdcaabecdabbbaeeacdacaabbbeeaadeeaeeaceeeececbdaebadeaccaccedaeadeaccddbacedcabdbddcbecbdebcbedbeeeaeedacdcaeddeeacaadccbbccdcddaccbdaccedcdaabdeebcbbeaadcdeedaadaeeaddcaecceadaeadededdacddbacebacedbeecaaccdcadbbaacbecbbceeedcbacdaceededcddaddddcccddadbdeeadbcedccaceddadcdedababaecdcdcaaadebadacbbbcdeebbccabaccbcdbddceebaebbeeeaaddaddeeeddbcdaeecaabdcaccdcedcbbedddbdbabddebaabaaeedddaecaeecbcadceecabcdabacdebdaccedcebcddccbededcacecbebbeececcdacbccebbbeaccadcdddddcaceacbdbbdeedabdbbbcaccdeebcabedebdacbdbbaaecededbddcdcacaecbbeacbaeaccabcdaecebedecbbddedbdaaccaabbdedaccbbadaedaecdaebcedccdabbaabeeaccbdeababedbdeabedcebdbcbccadebababdcbdaeaebccabeeaaccddebdedeccdaaaecacaaddbbbccddddbbdbceadcdeaaabecdeaddecedeabccabdadeddeeabdeccaedcceecddeebabdbeebdceedbcdcdebddbceccacbedceaaeadaeadcbacdbedbbddcdaecebadcbcccedbdebbecaabdedaeabbaecccecbeacaeceaceabaeacbbabbdbcbeeaebabeabaaeecacbdeedecedddaabdccaeebeadccadbadeeabdeecabceacdabbdcddccdacbaddeeadeaddcbacebcebcbdbdedeaeeeceddddccdcdcdebeabbccdeabebeacaeddcbdcadcadcedbedabebadeecedecaecaaadabdacbedbadcececbaecbeecbecaadeeddcddadeeadbeacccbeaebdbdedaaeeeebaddbeddbdbdccbcaebebbdedecdeeadbaceedddbcdedcbeacbbbccebaecdbdbabacdacceaaeebecebedaabaeeebabedcdccaabcdadddbceeaabccaabbcbbabbbdbabbcdeaadeaeadcecbedeebcddbabccbddbbdebbadddedcadccdbccaadbeababdbeceedcaeecedbceedacbdcccacddeededaececcacbceaadaeebccdaacaeceabbccacabdeeaaaccdbddcdbdeebecdecebbaedaccecebeecebbeaacaeabbeadcddaacabaceabbbdabeadbdcdaabadbccdcebdccecaeedceadcbcebabceaceaeabddeedcdaadbedeabebcccbcceacdecaedcaccadbdbceedeeccbbdabdcdedeedabadbaadeabecababdedbbbdcdbcdcecdacedbbddadeceebdbaaeeeaebabedababcbdebdacccdaadedabacbaacddceeaeadecaedcdabbecaddbabecaabeccebeadbcecddaedaadcaadceccaaacdddbcabdaeebceaabcddebdccccddccedceddaccabdbaabcabdebbbabdcadceaaacdbaeacecccaabbcdecceaecbaebbddedadbaaddddaeeaebbeddcadabeaaeedcdededebdecadcebdaeedaaedabbabeaedaebabaacedcaacdaedaadcedeebbcdacbcbcaeddccedcdceccbbbaadceabcdbeecebabdaabccbdebadbdcccabebabdebaebdbcdedeceedceeedabdeaceebaeeecababcbbdaeaaabcadebcbacdedcdbbadaedbbaeccbebaebadbaddcabdeaddccdabededeccbcadadeebdebcbddadaaccdaaeebccadcbaceeabbccebdeccdadcbdbcabebdedcebcaeababdcaadecdbbbbebcbcccecbeaebbaeecbadededbbddaccecdabaecaccacbdeaaccbecbebecdadceddeacccdadeceeabbdcdabdaacaeceabeecdbebcadcaaaecbcdaccaeccebbbeabcdcdededebdcbbbbcbbbdbaadbdadeedbadcaecbceacaabcdabedeedaabdebcbdbeebbdeadacabccdecbbabbbacbdcbedaaaeccacbbdcddabcabcdeddedcdbbdaebadceeacddcdccbdceeebeaaabdbcddcbbecacaecdeaabbeedaaaabdbecceaaeeeededbecdcbeecbbadaebcebdcdcdaebcbbddaaeaceccaeddabbaecaccddbbaedcddeccaebaeaeceebbbddcaabbccdeacaeddbdceebcecdddcbadbaebbacaebbcbbeecacbcaddbedeacabcdeedbdcaaaadaccccdbcebeaabdcbbdbeecbbaacceccadeecccabbbadcaacdddeecbdcaddbeeadddadecdbdeaaeadcccacabeacedeeceadcdedaadeacbcbcacddccbbcddccacbcdecdbaadecadecaecbeeaacdedabeadbebcbdaaadeeaacedcbdbdddcabacbabaedbaebbdaddebdbcbaaeaaeacebabdbcbeedadcceabceadedebdedbbabbbbbbecaeaedbecbadcbabdcceabeaecdacaeddeabccedceceadeacaeaededdcaadadbdbaeccaddecdcaeaebbaebaaccaedbdddcacaaddcbddbbeacbdbccddcddeaabadcebdeaaedcabaabaabddcecadcadbdcbcbcdedcbecdaccebabeebddbbbaabededdbdedadaaaadbdbcaedddecebbdbcaaeccaeabeccaaccebddecadbeacabadedccbceeeebdeeaeabcdcacaddedeeeacddcdedaedabccdcaabdcaedbcccdccecbabbaecebeadccdbddcedcbecdbcecbcaaeddedaacabdedbeeddbaacbbbaddaaedacadbacacebccdeccceadadbdcbbebbdcbddabbcbeeacdbbecbbceebbbaadcaebdcddbcbcbbabbabeddaeeeeaadadeabeadbbcaeacddcedcebbecacecebbebeacbbcbeaedeababbcdcacebcbaceabedaaaedbeabebbaccddcedcdddbadeabddccbccdbcedacbbddbadcaabbbbedacbdedadbcdaeaedbabebeababaababcbbededdacddeacabaaeaecabdbecddeaaabacdcbdcbeabcebccbdeabcbdccccbacbeeaceeacedbebeedaebbbcbabeeddceebdccaddddaeaebcbdbedebceabebacaceeadceebcbcdddbbacccebaddabaabcdaceabdcbbaceeadaccbdcbbeecebdaaebdaadaeeebbaceecbcaaaaecebdcccbcddadadbedbaadddcbeccaebebcaadbadbbcceacdbabddecdecbcdadeeabbaaabaeabcbdeaddeecdaaccdaddeeeceedaccadecedcbadbbbaecbccceecccedeecdeaedbbdecabdcaaadcddecedccbdddebbadbeccdaaaecedeedcdcdaebabbedeaeaceddbeeeabaeaaaabbedebaddbbeabeeedebbdbdddeeabbedcaadbadecebbcebaaecbdeeaedacaeaabedaaaddcccecaecaacdaecbddcbabbceddbcdedebacdeedbdbdddcbddbebeaecbdddaaaebcabeedcdeacdacbaaaeacdecaaeabaeeecccbebceebceeeeaeeabbaecbbeddaddabdadedcdbebceabadcbecbacdbaeebcbbaaeeacaedeceebdbdeabdcedcbcdecdccebeecddbeaedbccaaadaaeabdcabbedbecbecdbcadcedebeebdddedbdcabeccbbddccedcdaebbecbecbdabbbeabaabcddaadabeaaeadeeaddeacbbeebedeeeeaddcdaedeadacbedcdccbdddcdeebeaabeceadecbccaaacbdeecdcadadaecebcdaebedaacbaebccdccbadbddbdacbcebbaeaaadcaeaaddacdccbeeadbbbebdbbaecbdceabaaeabdedaddebdbdacebdcebadcbadecdbecebcecdccdcdecdbddccbadeddcdcdcedcdaebabededdcabedbdcbadcdeadaaddadaedaeceebecbecaacacaebdbeacdcddececdaadbeeaaceccbbeddbbdbbadeccecadebbecddeccccceddcbbeaceaaeeabecdaeebbddecacbcabcdedaddcaccbaeeedbecdabcccaeebbbbadadbebadcadeceeceacedacbecdcebabbaacbdeebdbeecdaaaeecbcddcbceecbeccacdeceabbbeeedeaeeaedbaeabacaedabebadccdaceecaeebccbaaaacabcbdcdeeebebcceccccbaebebcdeabcbbccbccceabaabceabedcdcedcaecaebbaeaeceecebcaccadacccdddebcccaaadadabeebdcbdeecdadabbeecabedcbaebdecdadbbdeaaebdbcbcdeecdcaccabdebaaeeaceaadccbeabbebcacbedabeebadebcbeeebeceeeececdadabbeacbadedbbbbbbeeaecbcabedbebacbadabdcbbedaccecdabbecbabeacddbeacedeaeddebcacccbedabbaeadeaebadbbecbecddecdcabeacebaeeaccbdbccbcbdddeaecabedecdaccaededaecdccbbaecadddebaedebcecddbdbcdabccdacadbeccabddabcbababccdbddbbedebcbaeaceebcabeddecaaebadbbebdbdecddbacebceaecbceeabddedecccbeeababcddccdabddbcacdabdbaeaceaaddddcddbabdedeecedbbeebdbbdeaaebddbeddccdadbacbbeaaadeddeeedeacddecececaedaeaeadbddccaabbcdbcccbbadcdacaedabbbeacebabbeeccdceaeacadbaaebbdaddccbedaadcabacdbbdcdaeeeeebceccdceddceacedbdebdacbdbdaeacadcedbbaebcddeddeedaabcbedcccbebbeabdedaaaaedcbbeaecdeaeedabcbcbcdcebddcaebdbeaaedcabaedebceebbccedeaceaabaaaeeadbeeeeedbbdecedbbcddaeebabdcbbbdcceecebbeaddeaddecaeccabeacccabeaebecdaacdababbeabeecebdbddbcdeccadacbaaeebaeaecdccecaaeceabbaabceccdaaceddebbbedddaeccebaebecadababaabecbdbbcbbbcebabdebbbdaaebedbcccdbcdeaadcacdaccecdeaaadbbbbedebaebeecccaadbcebcdbdcbeecaabdbcdbcbacaddcccdadcdbebcdddaecbddaabddcbdddbedbbcbbdedadbbadedaeedecebdaabaabbdadecdeabbacbeeacecceadcdbdaebebdddeaaeaeebadedaddccbcacbddcbacecbbdceddbedcbcaaaecdcbceeccabbdccdcbdddccbccdaaaeedbadebbadbecbaecbbeecaabaeaddedddaeeacedadacebbecccacbbabddadecebeadeedeaddaaeaeededdcbabdcbabceacabedcbaacaaacaabbdcaddacbbbddacebddaababddbbcaddaedbcecbaddaecababeceadedadabeaaeeabcbeeadbdaebaccacddcdccaeedeadbcbecaedcaabceecbcebbabaeacaadcddcbbbaebebbbacbbaddeeeabbeadccebdbadbddbbcacebaababbdbaccadebcaedcaadcaacbdedddaeeaebacababccacbecaccabccabbbdbdabeaaabcccceeebdddbecdcdcabdedcacacbdbabddaaacbdbeacdeeeaddadeddaebbaaccbcacbdadedbeeeedbbdeaaaaddbeaddcdddccadedceadcceedcdedcdbcbaaeececbcddabdbeccdcadabbcbabbecbedaebccacdeedcbeceecabbbcebaabbdcbacecceaecbdcbabdcedcedebebebebdabcbedddabdebecaeebddbcbbdbbedbaebccadddadeccdeeeebcbaedcedecbcdcccddbcedadebdcbbedbecdadadedbedbacbcdeabcebcbbebcdebeecbebbdcbdeccdaebedbdcebebdeacceeceaaacecbcedccccebcdabbdcabadbeeaccaebcbaccaceebeaeaeeeaaabbccdebbdceacaebbcedcbececbdbdccdebebedcbcaeacadbddabadbccababdccbddbdeedabdcedeeaeebdbebcbecadecddbbcbacdcccdaebbbdcabeedabcbbaccbbdeeececcabcccddabdcbaecdaaaededcddcdeacebabceeacdceebeddebbbbadebaebcdbbcbeceacaebdadaaaabdcbcebbecddaececacddbecaeadcccaccdacceecdadbadadcdebbecedcadddddbeaaebedceebdbbbaceadebccccbbcbacbecebedbcaaaebcaddbbddddbbdbccaaecdaeceacacbdaaecaddcbebeaaaacbababceccbcaabcbccaebebbbbbcddeabdbecdcecdaabaabddecbaaddcaaaddbdbbadbedcaddbdbeacdcbacddaeedddebcdacbdcaadccbeeccaedecdeecebbeaccddedeededbebdaaddaebddedebcebdbaaddcaecbbcdbceebbcbcaceabadddebeeeeacddbebeaecebdcebccbbaacaceeddaececbceadbeadcabbcaeecebcaedaedbacdeaecabaceececbaaceaccddccdaddadbaeccbabcedccababcdddbeecddddadaacccbaddbbdebeeadbbeaddddeccbaaabcbddaaddaeeadbdccbecbebebccbeeeeebacddceecdaaabbacbddbdddebadbcadbccabacbbdcaccdcbadaeccdddedcdcdadceadeecebcceacbabecabdbeabbccaaaebcedaaacdeecebbbccedcbecaedebaeacdbccbdcbbabddaceccceacaeecacdcdcdadaabcebcabcdbadaeceacddbeedecaebacdaebacaddbbdccbabecdaddddcbdcdeaeaeadccbeadcbdcccdacdbcaeebeaceabcdbbeaedbadcbcddbacdcedbaeccceeeeeccaaabaadbdbdbeccadadabadcadadeccaaccaceddcecdaedaeeababddeadeddeeadeddabcdcddaaccacabaedcebadbbeaadedcceebcbbebddeccbadacedbdebceecccdeaacbbbbaecebcbcdbbceaedbecbedeeddbcbdbcebeaecbbadcaedeebeacaabbbceebadaccdecbdbadeeadadccabebdedbbccddaccadecebeaaedbedeabeedacceeadcecdbecaedeaebacaaceacbeedebbcccdddbcedabbbeebcebabaacdedacddcbcceecdbbedbcbabeabdcbdedcaeadabdeddccbcabaccbedcbcdddadddbceecbaeeaaeaddeabedcbdaaacbceebbdaccbdbbcbbcbcabbbdddeeccdebddebaadbaececbedeadedeabbdebdabbebecdababbdabcabbeedbecdcaaecaacdabcebbadceeebbeedeeeccaebedaccdbdcabadedbcdcddaabdebebaacdbbdcdccbadceaceddebbeadbccbeacacecbacbcdcacecdacaededbebecdeedcdbbabcbbeaaadacaaedccdababebcebbedcacecaddbbabbacaacdaedeedccaadddeaececdaedeaaeecbdcaaadbcececcebddebbebdbbcdcacdaabdbcddccadeeeddbcbeaecbeaedbdcdbbdebeadeaebeadedbecaaababedabebbcbaadbababbebaebcacaacbbecbbccbecdccbeeddeecbdbdbaedcccdebdbaebeaeceeccbededaabbaeebeddbcdcedcbaecbcddaceaabdbaadeaadeebacdcbbdeaaebcddbcecdbcceeddaddeadacdddccddacadabbbedaabbdaebcdceecedbdbbacedeedadaacaaecdebeedaaaabdcedeccbadaddbbcdcbcabceaebbabdabbababccbcaadbaddedaeacdceabccecdeaaebdbacbbbcabaadecdebebcbdcaacaceccaecaeedcccbccdbabccecbcaedacceeacedcaddaacdbeccedbebebabcaacdaceaebacaedcbeddbbbaaeeeddcaccedcdbccaaabadbabeebdcdebddbdeacdbaaadbecadabbaebdbeecdabbeacaaadcbbbcbdbbecbcebaaeccacddaececadaedaadaedeedcdadceabcdaeeaeabbbeabeeadbacddddadbcadeaeecabbdeecccccbbdbbcbbebcbdcdecacdeaddadeabaccaabcbdbabbaacabdcddcddbbeabecbcdbaeccdccddbcbbaacdabecdbcdaaeeabcabddbbdbcbacaacbccdecdedacdeccbebbeaadbbeebabcdadaacdbbeeedaeaddebdbecacdcdcecdedaabcdbbbbaebccabaeabbcbbcbaacbceeeeadaeeddeabaaaacabdbdaedbdbddddbcebdbdedaabceadcacdddcadedcaebdadbeeacdaeacdcbbcdabeddccadadbbbaadaecbcbecebdaaeeabcecddabbaeeeaedbbceaedbcddecebaabbcebabbaceecbecdaedeaceddadabaddeeceaadcebdaceedcdbebccdabadaaddecbeccbedcedaadceeaacbbaabbbdaeaaedaccacdadceaeedebccceaacacbacddcbbaabacceedecadbbecbacbddbeceddccabcaccababeebeddbcacddeebbebaadebbdaecdbcddabdcdeecbacddabebbbddedbbedbcdeeeabdccbedaaacbbcdbbdcdeccdccdededddadcbcacecbacccdbcebabdeddcbcedadaaedaaddbcdeacdbeaadbccaebbdbeaebcdbcdbccdbdbbbebeaadededeabdcbeceacdbeeabcbbbaadcaaecbaebedebeebbaedcbcbceccabbcceeecdcaaedaeaaadadcbeacacaaacddecabdddcdaebadeccaeceebdecccccbbeabacabaeccbceecacebeadceebbbcbaaaaaedcaddcbeadbcecbcecbdbaadadeaeacaabeaedbcadbeacceedcdabdaddbaaaacbcaeddeaecbaacddadddabbbcabadbccccacceeebdabdceebbadeadccdaddeceddaddaadbebeccebaacbcecccaaedbbadabdddcbadcecdeaabeedcdcbceeeecaeabecaddaeeadadbebbadbacecdacadccdddeecaaacecdcadbaecbcecebcabdeeddacadecdcdadcddbddcaaeaadedececddcccdddaddeceeeceecdacceabdddacccbedababecbeaeebaceccbecdbbaedbcbcdaeddadaceebbeeeadeddaecdbbbedacdcaecacececedbccbabaaeeadabbeebcbbbccdececeadbcdabddcecbebdeadcbcacbacaccbedecbddacddcdeabdbbbecddeaccaeabcdededbadedcdadcadaccbaebdabdcbaedecaeeaabceaeadcabbbdccdacdabdcbbdbaaaeaebccbadebaadedccecacbaeadacecacbecaeeaddcdedacdebeedccbdaaedbaecacdbedadcbdcdaeddbebaaccaeebeabebdcadeeeaaedcdcbadbbebdccbeacddbaaabbdadadcecddcebedabcdeddadeaeaeadbbeaacdbbdceeddacccdcdabbdcdaeacdedadbbbaadbcaeddcecabdaeccadecaabbaaaeaeaacadeddbbaaaddbedcecbadcdabedddaacabcbabddbebcbccaceeabdcecdcebddaccdbbceaaeaeaedcbbdddcdbeebbeebcedbaaebacddaddcccecbeaacddcaedddabaaacaedccedcdaedededaecedeedcabeaeaeecbaccbdcbebdabccbdbabedcbaeaeddaedcdbbcaddccaeeacaebeaeeebeeadcbbdcabcbddecaccbaeedecebdcaeccbeadbeebeeabebadbdcbbeaaedecbbccedbadabeadaeaaedbecbacbccbeaddecbeaddeedeeeebeebbbebaadbeadcceecbcbcaebdbadebbdbbccaccdddbadaecdcdadabebbececceaacddcecebaeeccbdeeabebddcdcaaebabdaecddbcbaaabbdbeabbadebabacaadeaaeedacaeaeaccecbeebacabaaabbabdeacdbdeaabaedabdcacedccecbcbdbcaddadbebecbaceeaedddedddabdebcddaecccadbaceacdaebdbaabecabbcadaabedbbbaeeacabdaaaddbadbecbcdbcbebceceacabbeeeaabbdccaabbccecdabedeeeeedacadbdbbcbccaabdedeabbcceddddedbbaccaacebbcbadecaeceddbcccbdbdddabeabdbddeebceeebbadabcabdccdedaababbccbbdedaedcbccbcbabecbccadaadcaaaececdddaedcbadaadebabcbbaaaddddedadacbcdaadabddaaebaeeaecedbdacbecebcdbdcadbdbbadcadeababcacabddabbbcecaadeeccadbdbaebdcbaacaceccdcdbcebeceeaacdcbbaacebdeacdedcbacdcaebaddaccbcbebdaabbdacdcadadccdccbcebaaebbcbbeeeeebaedddacceeceaeadbdbacacebbeebeaaeaececcebabcddeccdbabcbaadbeacdeaeddedaceaccedddcadecbabeabeceeaaececbcaedbcabbbadbbeaccdcebccbdaddbcdacddbceebdebdaaacecacbaeaebbbcddaaaacdcabdbdbcccceecccbabeadcccdeddbbbaedcbacdcabcbaeaddaaeaeeadcbbeaeaeddbabedcaedeaedcccecececbdaabdecaeadbcaecdaaadaaeccbaaddcdacdcaedadaaccaceebecbabebceadbcadcaedbbabaccadeaabbdcadbcbadeeeedecededecaecdecaadcabababdeabaccabeebdeedcacadacebdbddcbdbabeaeeebbeaacecedaabbaaacadebedbcdebdacbdadbeebbacaddbdaeedbdcbcaccebbecaadaacacaddececddcbaabcbecbaadcceedeadccdbbcaebbcbeacdaaeaeaeeeedddadeccacabdddaebceabbaecabadcedabcccddccaaeceabceeedcbabdbceaaacabacaeeedabcdddeccadaebbeadbaadcbddcdccaccecbdbcaebbcbaaaebebdcddacdebbaecccccdaabbaccdadadceeabecbddbddeedbeabdabadecaedecbbaeeebbbbdeabaddababceccbaabacaaccdceebebeecaeadecceecdeaaabaddddddecdcdcdacdbbcedadadeddbaeeddbeebceadebacbcebcbdbedbdbdcbaccbedbbdaaedcaadcebabdabddecddadaabbceeccacaedececdcedeebcaedabacebcedcebccbbeadcdbeebbeaceceaabbedbabebabddcdebcacbeccaebbbdcedddecabaccaadbcebaebbeadeeeecedebeeeaeeeeccdbdbdcdabaeaedebdcaadbbacddbbebcecdcadaeabdacadeebdbceecbcdabcbdecdabbcbdbcdebedeabeadaedacebacdeddbcaeaecbdcaebebedaaccaeaaeeaecbdbcebbcadbdcdbcaceaceccecbacaddeaddbacdebcbecbaabdeddaadbcdeaeebbaadcddcbbcdddcaddadadccebccacebeeddeaadddcdcdddebeeaceddeaabedceabaddbbbeeedcbdcdbabbaeadbeceaebdeeabdecddaeaebcecaabbbeceabdbaccecebcbadaaddbcebdadcbddccecebccaeecbaabdbabebdbbbddbecdcbbdabbdbdeecabadbcdebeeaacabcebacdeeacdcbaadecebaebbdbdeddddbdaaeecaedebabaaccdabbabbdecbcaededbaaabebddbaabeddbeabdedbebcabbbebcecadcbabacaeeeaccccdabdccadecaeaecdaaeeebabbbaeacbabcecdddbddabdadabecacbdbcbddebecacaecbdebddeacacedebaccceddcdeeddbcebaacbdddcabadbbdcecdcdeadcacdeaaeeadacaebacceedcdadeeecdbebebaccdaaacbbccecabaebbbccbdcdbbaddcdecbaddeeadaeeaebbaceaccaeeaecbceeecdaeabdacaecabcedbbcadceeebcbceebbcbeeaaecccbcaeeaeeeadebadabdeadcddceccaedcdabedbdbebbebdbabcaaddbdcbecacacaeeeabeeebccbbdaaeacaabbaebeaaceaebdebaecdcbecdaddcacaccebaeaeacceabcdabbeabacdecdddadedaddddeeadacecbeaeebcacabdbadceeabaaddedbdcccaccbeecbabdbaaaedcdecbcdbaeeedcdcbdeacaabdcadaabacadcdeadacbdecddbacaddbbcaeedebbedccceecaeacdacbcebebacdebddbeadcaaddbbcedbcaedbcccabbdbcdcbceebebbaeddedccecedebcdaaabecadbbbcbbbaadbaecaccdebdeeabcdeddcbaeebcaebabadabddddbdbbbaedbedadaddebaebcaecaadeedbdeedccaadbabddadbccabeaacecedeadbebacaedcabecdabdacdccdcbaaeeccdeeaedaddcddecbcabaeebbbcccddeaeebaaebdcebbaaabaaedcdedddbbdcaddccdbcdecebbacceacddeddebcbaddbbededadcadbacbcdabdcbcbbdaaecebedadcdadcccbbcebedbcadcdbcecdddacbecbacedbacdbeaeadebbbabdbadaecbbebcadcceebbcadcdeeadaecbdacddeecedaddbeadadbecaeecaceabdcdcbbbcdacbbeaceeddeacbdbaebeacbacaabdbdaececedadcebbecdcdabbdcbdacdeababeccaeabaabdccadabcbededadabecdbeabddabbbebdecbbeeeedaebedbedcbcbcccbbaecdddcdbdeecaccdecbeedbcdabccaecbaaeddeaaaceedcaebcbcbeededecacabeaaaaecccabaeabdaebcaebcbebacddededdadbadeaaebaaababecacccdabebdddeccbaebdbbaaeabdbeecdabadbaadcacbccbeeeceeadbaeedaeaadccddcbeddbcecedbdabbecbedcdbbdedbcbdedecddcbebaceddebecaaacdedddecbcbbebbcbedcbaaeaecacaadedcbbadbeacbaddbadeccadaeeecdcdacceeaccbeebccacbedcaacbbaceaabdaeeaaabaddbceeaccacdebadbaedcaecacadebcdabdaecbabceecdcbccecebeeabacdcedaccbaaeedcbbacceaaedbedcabcbdecbcdcccdcaddaaedcbabeaedabcdbebaceaeaebdbcbdccbeaebbebacabbaacdcdeaaaeeccdcadaabcebedabedcbcaacbaecdedcdedaeeaddcdeaacbaebccbecaaeadbceababdddadeaddcbccdcdaeadbcaebebedaecdbddeeebbbaddecddabedadcbbeaceacdadaaddcaaabccdcdacacacaaababdcecdebbabeacaeeaaaebcbedcdabbabbdccabdcceacbceaeadeebbadebaaaeecbebecbeaacecbbbdbccaecdcdeadaeadaeaedebbbcbddecccbeecbdaccaaadbedbaebeecebcadddacbeeccbccbceebddcbedabeaebebadeaeecdedddbcbdcabbebececcdccbedabebddebcacecdadceaaabebdcdebbbaabebcdedcecacbaadcdabdecabdbecebddddeeaddedcbbedcbcbeeadecabceeaddcdeaecddddaadbbdcdcbcbabaeccbdabeabebbdbcabdaacbcdddbbbcbccabdacbccccebeadbdccdcdbaaabbaabacaddacdbacdbabdaaeabcebecdcacecbbaaabcaeeedeaaecbbeccebabeaedecbdadaecbbaceacbadbaeedebcebeadaaccdebaaedaedcbcdbeacadaaddadeadccebedeaeacdacbbcbeababdebddeaabdeedeccbcadaacacaaeccbecbcbaadbaddedeadacedcceddacdaeecaeeacaabdeeeabdcdbeaeebeeeccbbbcbaadcecdcedcedeeeebbabedbaceacbebaabddbdaebddeaaddebcdbacbaeadeebdebbeaecbacbcbcceddabedaeacadebeabcacabdcadcccdebecbbebbbccbdcdaacddcbeaaeeaedecdeeaceaaacabbdabcbbeaeddcbbaecdbcdadbeccbdeddccebabbbdaccaabaeddebddcdacbcccbadddaccaebdeccdacdcadcaacdedbcacaeecacdecbbedbaecabeaaeadcadedcaddccadeededddabddabcaceebedbcbbbecbbaddbcaedcbccabdabceeebbbdccddeddabcdadadcbbdbbddeeecbbdaebeebbecabececdbbbbccbedecabbdaecebcedbeaedcaaaceaedbabdabcbdddcdebdcabdceeabbedbbbcbececebbbaadbacaaceeaeecacbdddbdcbacccbcebbedccaeedcbceecdeabcedbadabdabddaedccadccbcbaaaeccedbdaaddbbebeaabccecabededaecdcdaacbdaabddaceeceecbedbdaededddbcebccaedbeeebcbaddcbecdbdadcdebdaaecebbebaddbeabdaddadecaebeecdddcbbadebdabacbdbdebaabaaaccaeceaaeaabbeacddaecbabadceedbbcaebacaedceeaaacdabebbccedcadaddcbbdddbbcddedebbdaddeabbcedeeceaaabaddcbaabeeddbadabaabcedcdcbdbaddcbdcbacbeadcedeeccadaececbdacdeddbabeeabcceaebeeeaabecabcdacbcecaccaeccedbbcdaccecbccdcdabcdedcedbebcaddddbdaccacbcdbcabdeaebbcbecaecbbececcadceadbcaeaabbbdddeeedaacabaedbeecbeacebeeecddeabcccdbaeaddccebcedcaddebcebcaaacecbeecbecdbbadcecddcadccadccacecabbddcbedaadedcdaeedaceadadccdebeecedcadbedacecadadbeeccbbaebacbacebdcbeebbcdbcbcbbebcdedacaaeeadadcddacaabcddeaaceedbdcbcbcccbeddcadcccbbeeeabdcaaacacdcedcbebcbecebbddbcdceddbdaddcecaabebcaeeaccccccadcebeadbdcdaccdeecaabacdababdadcaebabceeaebcbededdbbedeceecbdcaeecdceacadbcbbbaeeabacbdebaceeabdcadbdcbcbdadabadeaddadeecaeeedaaeeeeacbacadadcaaebaaceaadcaabaadbcbcdcbadeabcebeabdbaecddbcdaecbcbcebabaeaecdcadcbbacaeeadecebcddbbedaccaaadbeeecdecdacbbbeccedbdacbddbbeaaeacbdcccdbececbaedbbbdbeecdbbecebacbccdbaeaaedcaddbdbcbcedeecbdccaadadaedbacdaedbdcaedacaacaedeabccbadcadbbebeceddaabdddabdbcacedaebabbcbddaacaeadbcdcbcaeadcaacaccdbecdbbaacdabbbbdabaebccbdbbaadebedcbbddddeeceeeabdecedbbecdcdcbeccdbaacbaedcdccdcdbacedabebcbcaedbbcdeabbeeeddebdbdadbecdbebdecadbbedaebdeeedeaaaabbacbdcbddccbacdcaaadbadbedaecdaeccddddbabdcaccedecdaeeeeaceebabebaceeddcdceaacdcceedbeadcbdaaeacebbbbaaedddddccbcabbadebdeabdcbdaadecaaececdaacbeeabeaedabbbaccadecadccddebbdbcadbadbaadecedbbbbbaccaebeedddecaeabcdcadbbccdadcceabccbecaacaecdbcbdadbdcaabbcecbbcececdcbdbabddcdabecddadaccddabeabaeeccebaddcbbeadadaebbebdaddeeabacebbdbebcddbaddbeeeaaeebbaacceaaeceaeadcbbaecddebecccecceecbeeabbcdbcabaddceaeebccbccedbbdcaacabdadebecdbbddbdecdbbecddaaedeedbaaadebadadbaedebbaaabbcaeceadcacdadceaeeccbabbacdaabcccdadeeacccdbdcdadceacededcecaadaeeeaaeecdbccdebccccebcbcdabdeecddcecabcceabedbcabeeccdaebbacbddecbcecacdebbddedddbddedcccbcaeaecaaaeecaadccaacdbaeecabeddeaaeedcceeeeedcdedacdcaccddadcdddbcbcbedcebddddaebdbaebbedacadeddbadedaabdabbecebececebbaaadceedadcddecbedeccbccceaabdbabaabdddedddbbdcdbadabcbdeebeabddbceaebddbebbdadbbddeabedcbeaebdaaeeebdeabcdddbeeabedcabbceeebaccccdbeedceadebbcbaeccacabaaadcecdbdebaceeeadbcdcdeccaaedbadcbcddebbdbcccdddbaebdbacecebeecacbbbacceeeddaacdddedcaebeaeaecbddebdacdccceeeabdadbeaeaaedcbdeddeaeadcdebbdacaddbbdbdcbddcdcebbcbbaebcbcbabbbadebeddaacccbdceaecbeecbeececbeaaeebeabacabbcabdcacbeebddbabaeaeedebbeddbecbccccecbbbdbeddeebdccccecceeaeaeedbdacdcadbeadeccebdddabeddbdebdaecdccbdabaecabcbedeeedcbcbdcbceebdbedbceabdacdaceccebdeecacbdebbdddcacabddabeabbcaaecacbbaadcacbeecabbebeeeeecbaebcebecdceedcadbcaabaadeebdbbdcbecacbbbecbebbddceccbaeaccededabdddbaacaaaeaaeceeebaddbbedddcdbcbcacaddeeeedacdaddeadaddcecebcbeacaaeedebaedabcabedecbcdcacbaeaeecdcaeecdabbeaeecddbddceddccdccdedbaaeecddcdaedebdbdeebbaaeababebeeedeeeacdaacaabccbbdbdbcbcbcecbceccaccceecaeaedbeedaacbecccdbabbceecaceedeaccbaccdececcbdcdebcbcebebdbdeadacebbdeabbecbccbdcadedebcadedacdededbbcdaaeaaabbdbbeeaddebbeedbaedbecdcaaacddbccbbdbbeacccddbedeebbeceacabecbeddcedaeaaacabdaaedcddadaddddacabaabacaedeaabbadebaeabdbbbaaebecbaaacddaebcdadcaecdcabacbcdcaaebcedcbdebecaebcbbbdcedaecbbdceaebadbbbeaadbedcbacececcdaedaaadaadeaecdbcdaaabcbacbcebcbbbbbbbbbedbddaebcdecdaddedcbebeeecebbadbaaacbbdcbaebbaabbdbdaabbeabcccabaedcabadbabcabdbbebeecabdbedbdecccabcadeadeeeddcacabebdadadeeacecdaaedbebbbbbacdcadabaacdbaadeabcbaaeabbedeeebdbdacebdcaceddeebcadbbaacebbccbdecceebcdacbbebcceeedbecaceaeeadceccccdbadaaacedcbcdecbdbcdbaeddaaacbcedeeebcadadddddbdcbeeeccaebebbeaecdbaceabacbbcccdadbbccacaaceddeeaabeebcdabebcbbcecabceacaceaeecaabaabdebbbcecaedbdbdaecaacacabebccabceabcebeecdceeaaaddbeebacceeeadcdddaccbecbeaddacecedebbcddcbbecaeeaaddedceceaedbbccdbaecebbecabdabdeecbbbaeccabbdedceccbdcbbdbdceddaadbbaedbbcbbabaddcacebcecdaecbaddcbccbbbabadbadabccaadacdcdeeddaeeecdaddbbebaeddbcbceaeebbedabddeddaeebaddeaeebaadededacdccdcceaaaedeccbacbabeecbaadaeeecaddcdacacebaeabcebcbecdebecdedaeeeacedbabaeabeadcddcbbbecdeabeacebdcbbeedceddeaeedabeebedadbcbbddeccbbacdeebedcdbcdcccbabaeececcadbdcbaadbeaeeaedccdeaceeacdeccccddbbcdcebabccdadadadddbabbaadeceeabdeddeeeecbabadeebedbeeeabdbdabbbbaeceecbaeccdadcecbbeebeebabbbeeaeeccececabedbceeaccbdadeabceeadccedbacbadceadbbaabccceddbcdddcbcdedeccaeacabebdddadeacabddcacabedebcbbccadacbcdebdaadcdedaaeebdeccbbbadeebbbababeebcdeaceaaaedbdadbaeddaedadbadbaebcadccedbebedeadebeebcaaedbdcbadedcdadccdcaadcdbbdadebbeaeabbbeeecedbdbddebbbbbdbceacccdcbcccceaaacaeacdeececaaeebeecbddcaaedeeeaebacbeaaddaacdaddddebbeaabeacadcbaabcbdadaacbbcbedcdbeaedeecbcbbcdbacbcddcbecaeddabcdbaccbebecadadcbdcacbcaeeeadececbacbecdeabccabbdceccdcdeadeaecddcdeeaeddeabebedccaacdebeaabcdeebceecebbeceacdaaddadeeecdeeadacacaacaaacddbbbbdbcccebdccbabdcdcdaabeccecdaabebbadadebedaebadaeaceccdcbbcdddaccdabdddebaaddbedaadcdbbcbeeadedaabdccababacbeebdedbcaebdedccaeaaddececadbbeaeaddbcdbcbbecdcaababcaccdbdcdabaacdcbbddaabaeccabacdddcdbcbeecbdaccdeaeadcdbabaeaedecbedbecbbbcbebaeababacbdcdaedcbbcdecaebabcceecbbcccaaabdeebbaadedcdaeeeeecbcdcbceededebcccecadeebaebaceaaabcddccdcebeabdebbbbbbcdbdddaebaecbdeeebbdebdababcedbeccabbddcbcbebaceaeeaeccabbdeddaceaabdceeeecbdeabceccaeecbbecacadbdbcbceeaddcedeaecddaaceabcaeeddcddebbdcdebbbbccbdbaeebbedceabcecaaaeedcaaddcecedcccebabcebabceaebabcaceaebcbaedeeccddaedaccebbcdaecdcabeeaacacdaecccececdeecaaeeebbbabeceeaebaacddedcebbbbbcaacaccbcadcecebdcdbebceaceaddbbceeaabdaedabcaacaaedcaecccaebaccdaadceeaccabcabaeadcbbcacbabbdeaabdeacccbeaeecaebdbebeebedcbeaeaaeeeadbbceabddeeeeddebeebeeddbddeddddcbbbcbedcdaceeedeabdcecbbcecaceeebeececbeaabcbcecacecddbbeabecabbbccddcababcaebdacaedebeebdeaaececdaeaececbbeeecaddbaaaabebbcbcbdbdeaccbcdbcabccccedabebbbedeabdbccdaaabbaadbdaedbeebcdbedddcedcabebddbeeebaccebecddaccedebbbbbccdaadaaadcddbeabcbddacacedcceedababacdbecbbcdcbeccadbbddcbbeacdabcbbbbbeeacacedcdabbacceacdcbbebdcbbeccaaeebbddbcccabbcabdddddbebdadeaeadaebbdbcbddeecddbbabeeedddbadeacadcbbacceaadcbbebebcdecabcbddabbdcedcbbebaaeedacdcdbaeedbbcacdeaaadbdbccdeabbbcceeebecbbbecccdcccabdeabbdbbddedbcccdabedaeaeeadcdcbcdebdaaddcdebbdcdecdabbccdceaeeadcdbddbebeceaaedcbedacaaeaaccaaddcaaabeadadebcbdaaaaebedaabbadececdddeacceedbdddcbecadebccdeacebcebadbbcbdaeeeccabddeaebabbcbbdadabadbbcddaadcedbedcedeacedebbedbbccbddaddddebbedabecbccbbcceedcdcbededbedccacebdbcddbedcebeebdecaaccebbadccacebcccbeaaaeccdbbbeebbbdcaabaeacadccaccabaadabcceaeeaebadcbbeaccdedaccedeaacabbeadebebbddabcdaeddeaecccccacaceaecaeecebdaaebadcdaaaaabceaedcedceaabdeddecaabacccebddbdbbbcaaccaebcbccbecaedadadbbddcedebadeabcbeeddabeacebabecccdceecddbcbbbbcdeeacaeeeebadeecdbbbbdaebbbbbbcdbeaaaaababeebdbedadbaaceeeeadeedeaecedacbeecceadebbbbbacebbeedbebcdeedaedeedbaadceacccabedecdedbdcaeaccebabaeaeaccddadbacabdeeedeaabdbaaedccdcbbeebeadcdebabbeddcedceadaadcbbaebadcbdbbaeeaacdeaaeacddadceadbeaecccecaabaabceaebeebdebbdadcdcddbcacdedabddbdaccccabbdeedbeceabeeebeaeadbcaaecdbcdbbabeddeabccecddacecbebdedacdbbcbdeecdabceecdecccebbbbeecdcbdcdebbbbaddcdabebebeabbbeeeddcbbadebedbcddbbceacabcbeebdcbeaadbaeadcedccbabdeaabacceeddcebddaeadcdedaeaedcacaceecbcacabebcbedeabecbdecdcdeabcabdeddecbdcebadaeddbbdcddbeebbaabaeeddaabeaccecaddcebcbeecdaeadcacbbbebcbecbdcbcccbbbcaebcbcdaeabbaceaaeaecacbaeccdacdaedbbdaedacbbebeacbabcbcecbeadacabbdcaceeeccbedbecdcecccdacbbedbaecedbaabbebbbdbdadbdbbebdcecbcdabecdacadbecbbbaeaecbcedbcbbcccbedebedbbeeccaeaeaeacdceccbaadbccebbdcedaeaddeeaadbecddcdbdcbebeecaddbbabdceeaccabacccaaaacbbbebbcdabddabbacaeedddbdbdcbabdebaaccdebdcacdbbcdbcdcebbabebddbabbeeedeebcdcdbbbaceeccacbcededccebcceceeacddbeeabbbdccddbddbeddbebecceaedebdaaabcedccbbadbcbecaabeccdeebebaaaebcabcecddabcebbccdddadccabbdbcceeeaacbccdbabacbdabeabaccbccbbcdaeebdbccdcaebeecaadbbcedeccdabbdadeabcbbdebaeddabeeaabeedcecbaabaddcecdceacbeeacbdaebbebbaeedbebecaacdebaeedacbecedeacabddecabcabdbebecdeeabdbcbbdcbdbdeebadbedadaecdbdddadeddbcdeddcbebbeabebcbceebebcbdaceeeabddacccccdecdcaedeeccdccebbddecbadcaebbadecaecbdebcaeeddbecaddeacccceabecdaebaabdacdaaebceecbbccdabecbeccbccebeddbaaeccdadedabedcbbbdecabcbbdebcecdcbdcababecccbddddacbdeadcbedaabcdeadbabdadebaeedddaebedbaedddededceccdbcbdecdeceedeacdceacbdeaacecbbbadaeaedddbcdaeeadedeadebbcdccdecabdaeabbcbabedebdaceadedbbbaacceaeeababdaacdcebdaaaeabbedcdadcecceeacabcabcbedddbdaddbcddcdaebddabbbeebabcbccabbedecacededaceeaedebceaaabeeaceebabdddbceecebaabbebbcddaeddebbddbadadadeddeebbbdecaebadaebbcdeedaeceebecebceabcabdeeccacdbaeecdaedcbddbebcbbedcdbcaddbccecddbeabeaadbeaebeaeaeaeddcdddeabdbeeebeeebbaecddaddedcbbdacbeaeeddeebdecebbbededceceaebcdeaeeaebdaadbecdeecbaadbeaaeecbecdebbedbacadcebeabcdcbecaeebdaceacbbbdcdbcaaabccaeeebaaedcedcbdabcdccbbdeeecaaddcdeeecdecadbbecaadaabadcdddbeceeaeeedbbddacecdcdaadbbcecabdacddddabdeaaabdeddaeadbbbcbbeecbbdabaababeabacedbeebeaeedadecdaeaaadecaaacababadcddbdbacebcaeeebdeaeacbcaadaebedebadbccaddbacbacebdbcaaecdbadadbadbbaececdebddeceaeceaececdcddbadeeeeaceeaaeedbcdedadbbbdbdddbdccbbbabbedeacbbdabedaacdaadebcdabceecddeabecbbcbcadbcbcabddeadcbaeaaeaccebbdbbbbeecddbdceebeecddcbccecbdceacabddcacdaacddaecedceacbdbaaeedeeabcebedeedcccabcdeedeccbaebaeaceccdddcccbcedabcadbcadedaddbdbdcbeedadeacbbbcecdacdbbcdccedbdaabddecacbeebbdcbbddbbccdcdcabadaabcddabaecaacdedbebcabbeecabeaacecabcacbcadbacbbdbbcedbcaeeadbeddccaeebabeeedadbbdbddeedaabecacebcddecdbccbbacdabecadcbaddecbbeaedbdabbeeadbcecedeecdeceadacbaaccebbbaeaddaceeecaeadcdbbcaaaaadeabaebbdccbdccbbcacadcbeacacdbcdbedacdddbcdedaadccdbddecdcdabeaecbbacccbaeeccdbddceadedeebaacadbcceabbdacbbccebbbedadaadbadcbbadbceaebcecdbbdbcabddaceabbdecaddeebedbcdddeebcececedddbccddabebdddaebdaabcbcccabdddacddbdcacecbdadeeaeadebdbdeceadeadcdeaececeddcdedecdddceeecabbbcbcdbeccbcedbdeddaddedcaacbebedabddcdedecbdaeabbaedbbdecedcabaaeeaabcdbcabcbaecebdbacaeedaedcbceaebdababdcdcbaeddecaeabdaeadbaccdcaccaeeceeedacedcabcacdbdbdcdbdcbbdcadaeaedceaceececabbecbeabdecdbdadeaeadcbabbabbeadabccbccbadddeecebedcacabcdcdaedcdeeedececdbbcbbaddedbdbdccddeeceeebbacaceededdbccbcbaaeaadcdeadceecbadeaecebcdcdeecbcbeedcbcceedbdebcadbcddabeb