// MMMMNMMNNDDNMMDDNNDDMMD8DDNMDDNMMNNDNNDNNNNDNMNMND8ZZONMNNMMMMMMMNNNNNNNNNNNNNNNNNNN8OO8OOOZ$ZOZZZZOOZZZOO888O8888OZZZOOOOOOOOOOOOOZZOO8DNNDNDNDNMMMMMMMMMNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNNDDDNNMMMDDNN
// MMMNMMNNNNNDMD$ONDDDNDD888NNDM88MNNDND8NNNNNDNNMND8DMMMMMMMNMMNNNNNNNNNNNNNNNNNNNNDD?ID8OOO8OOZZOOO8ZO8OOOO8D888O8OOOO8OZZZOZZZZOOOZOO8D888DDDD8DNMMMMMMNNNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMNMDDNNMMMNDDNN
// MMMMNNNNNDNND8DMNDD8DDD8888D8O8ONNNDNN8NNNNNDNDDND88NNMMMNMMNDDDNNNNNNNNNNNNNNMMMNDDDODDDOOZZZZZZOOO8OOZOZOOD888OOOZZOO8ZZZZZZZZZOOOOOOO8888888O8DNMMMMMNNMMMMMMMMMMMMMMMMMMMMMNMMMMMMMMMMMMNDNDMMMDDDDD
// MMMNNNMDDDMNNNMMDD88DMMNOOOOD8OO8ND8MM$$DNND88NDDD88ODMMMMN8O8D8DNNMNMNNNNDNNNNMNNNNNNNNNN8$$ZZZZZZ8ZOZZZOOO888888OZZOOOZZZZZZZOZZZOOOOOOOOOO8DO8DNNMMMMDDNNNMMMMMMMMMMMMMMMMMNNMMMMMMMMMNMMDDDDMMNDDDDD
// NMMMMMNNMMMMNNNMN8888NMMOOOO8NOOODD8MMNOZ8NNOZ8DD888OOMMMN8ZI$88NMMMMDNNNDDNNNDNNNNNNNMMMMNN$Z$77$ZOZOZOZZO88OO8O88OOOZZZOOOOOOOOZZOOOOOOOZOO88OO8NMMMMNDDDNNMMMMMMMMMMMMMMMMNNNMMMMMMMMNNMNDNDDMMDDDDDD
// MMMMMNNMMMMMDDNNND8OO8DD8ZZZZ8OZZO88MMND8DNNNNDZN8ODZZZDDD8OO888NNNMNDDDDNNNDNNNDDNNNNMMMMMNDOZ$?=ZOO8$$7ZO88OZO888OOOOOZZOOOOZZOZOOOOOOOZZO888OO8NMMMND88DNMMMMMMMMMMMMMMMMMDNNMMMMMMMMMMMNNNDDMMDDDDDD
// MMMMMNNNMMMMDDDDNN8OOOMNDZ$$$$DZZO88MMNDNDD8MMNON8OOMO$$8DDDDDDIONNNDDDDNNNNNNDD?ZDDMMMMMMMMNN+=8DD8DD7I7$O8O$OOO8OOOOOOZZZZZZZZZZOOO888OOOO88D88DNMMND8O8DDMMMMMMMMMMMMMMMMD8DMMMMMMMMMMNNNDDDDNNDDDDDD
// MMMMNNMMNNNNDD88NN8OZZN8DO$$$$88$Z88MMNDMM88MMMNDN88MM$$ZDNNNNMD$NMNDDDDNNNDNNDO=ZMNNMNMMMMMMN8$Z8NDNOII?7O8Z7O888OOZOOOOOZZZOZZZZZOOOOOOZOO88D88NNNNND8O88NMMMMMMMMMMMMMMMNDDNMMMMMMMNDDDDDDDDDNDDDDDDD
// MMMMMMMMMMMNNDOONDDOZZOZZ$$$$$ZO$ZO8MMNDMM88MMMD8M88NMD$$ZMNMMMNNNMDDDNNNMNNDNNDNDMNDDNMMMMMMNNO?I8NNOI?I7OOZIO888OOZZOOOOZZZZZ$ZZZOOOOO8OOOO88O8NNNND8OOO8NMMMMMMMMMMMMMMMDOONMMMMMMMNDDDDDDDDDDDDDDDDD
// MMMNMMDD88888Z$ZOOOOZZ$OZ8Z777$8$8O8MMDDMM8OMMMD8M888NNN$78NMMMMNMDDD8NMNNNNDDDNDNNMNNMMNMMMMMMN88O8N8?+I$OO$IOO8OOOOO88ZZZZZOZZZZZZOOO888OOOO8ODNNMNDOZZONMMMMMMMMMMMMMMMN8O8MMMMMMMMDDDDDNDDDDDDDDDDDD
// MMMMMND8888OZ$$Z$$OOZZ$$NDD$77$88N88MM88NMDOMMMDNMD88DNDMZMMMMMMNMD8DNNNNNNMMNNNMNNMMNNMMMMMMMMNOZO8N8I?7$88$IOODNNNNNNNNNNNNNNNNNNNNNNNNNNNND8O8DNNN8ZZZ8MMMMMMMMMMMMMMMMDO8DNMMMNNMMNDDODND8DDNDDDDDDD
// MMMNND888OOOZ7ZZ$$OO8OZ$O8N8$$ZDMM88MM8ONM8OMMMDDMM8O8NNMNMMMNMMMMZIO88DDNNMNDNNNNMMMMMMMMMMMMMMZ$8DN87I7$88Z78NNMMMMMMMMMNNMMMMMMNNMMMMMMMMNN888DDD8OZZ8DMMMMMMMMMMMMMMMMN8DNNNMMMMMNNN8O8ND888DNNNNNND
// MMMNND8OOZZZZZ$77$ZZNMNOZZ8$$8MMMMD8MMOODM8OMMMNDMMD88NNMNMNNDNNMMNNDNNNNDMNDDDNNNMMMMMMNNMMMMMMD8DDND$$$Z88ZZONNMMMMMMMMMMMMMMMMMMMMMMMMMMMNN888888ZZODMNMMMMMMMMMMMMMMMMNDNNNNMNNMMMNND88DN88O8NIZODNN
// MMMNDD8OOZZZ$Z$OZ$$ZNMMMMMMMMMMMMMD8MMOO8M8ZMMMMDMMM88DNMDMNNDNDMND888D8DNDDDDDNNNMNMMMMMNNMMMMMNDDDNDOOOO8DOZONNMMMMMMMMMMMMMMMNMMMMMMMMMMMNM8O88OOOO8DMMMMMMMMMMMMMMMMMMNNNNNMMMMMNDDDD88DDD8ONO+IZZDD
// MMMMNDD8OZ$$$OZ7$ZZZNMMMMMMMMMMMMMD8MM8ZONDOMMMMDNMMDDDNNDMNOO$7?I??+?IZDNNMNNNNNNNMMMMMNNMMMMMMNDDDND8OZOO88O8NNMNNNNNNNNNNNNDOIIII????MMMMNNOOZZZZZZO8NNNNMMMMMMMMMMMMMMNNNNNMMNNDDDDD8888DDNNNO=I8DNN
// MMMNNDDDD8OOOOII7ZO8NMMMMMMMMMMMMMD8MMNZZDN8MMMMNNMMMNDDMNNND8OZ??????IIIII8NNNMNNNMMMMMMNMMMNNMDDDNNDOOZOO8888ND8DNNNNNNN$I~~+????????IMMMMNOOOZZO8ZZ8NNNNNDDDNNDNNMNNNMMNNNNNMMNMMDDDODOOO888DMNZ8NMNN
// NNMMND8O8OOZ$7II$O$$NMMMMMMMMMMMMMN8NMMZ$8NDMMNNNMMMMMDNMMD=~?I?????,~+?I?IIIODZNNNNZ?NNNNNMMNNMNN8DNDOZ8O88888MNNDDDDDN=:~+?I????+~I??IMMNNNDOOOO8O8DNNNDNNDDNDDDDNNNDNMNNNNNMMNNMMN88OOOO88MN8MDDDNMMM
// NNMMND8OOZ8$$$IIOO8$NMMMMMMMMMMMMMMNNNNN88NNNNMMMNMMMMNNMMMNN8:.I?I~.....,=IIII8NNMNMNNNNNMMMNNMMNDNNDOZOOO88O8MNNNNDD~:+?III+:,... =I?7MMNNNN8OO88DDDNDNNNNNNNDNDNNNDDNMNNNNNMMNNMMN88OOOO8OO8DNDDDNNNN
// NMMMNND8OOZ$OO$ZODNI8MMMMMNNMMMMMMMMNMNNNNNNNDDDMNNMMMMNMMNNNNMD???I..~???IIIIIIII8NNNNNNNMMMNN877$O8OZZ$OOOOO8MNNDZ=~+?IIII?????~..7?INMMMMMN8O8OODDNNNNNNNNNDDDDNNDNDNMNNNNNNMNNNMD88D8D8OO8NMNNMMMMMM
// NMMMNMMMNDOO8O8DMMNO8NMMMMNNMMMMMMMMNNNND8OO88O8MMNMMMMNMMNMD8MMZI??.  +I?IIIIIIII+~~:DDD8~+,~?I7?,:?I+?I=~IOO8MD8:++?IIIIIIIIII=. .??OMMMMMMNNDD88NNNNNNNNNNNNNNNND8NMMMNNNNNMMNNNMNDDNDDDNDDMMNMMMMMMM
// MMMMNMMMMMMMMMMMMMMN8NMMMMMNMMMMMMMMNNNMNOOOO8ODMMMMMMMMMMNN8OMMMO??I: :?IIIIIIIIII?++O7=?,.~+777~,.,?O$$$=,.~OD?,??IIII??IIII??,.,???MMMMMMMNNNNNDDDDNMMNNNNDNMNNDDDNNMMNNNNNNMMNNNMMNDDDDDDDNNNMMMMMMM
// NMMNNMMMMMMMMMMMMMMNONMMMMMMMMMMMD$OMMMMMM8OD88ONMMMMMMNMMNDDNMMMM???I :I?III?IIIIII?=I?,..,7$$$$+,,,,ZZ$$$+...:?~?II?+=+???II??: I?I$MMMMMMMNNNNMNNDDNMMNDDNNNMMMNDNNNMMNMNNNMNMNDNMMNNMDNNNMNNNMMMMMMM
// MMMNNMMMMMMMMMMMMMMMOMMMMMMMMMMM$7777$7777ND7II$8MMMMMMMMMMMNDDNNMI?++I,?IIIIIIIIII?7$I: .,=$ZZ$Z?,,:=ZOOZZ7,...~?I?===~=+??II?I,7??$MMMMMMMMNMNNMNDNNMMNNDDNNNMMMNDNNMMMMMMNMMMNNNNNNNNDDNNNNDNMMMMMMMM
// MMMMMMMMMMMMMMMMMMMMZNMMMMMMMMM$77777$ZZZ8MZ7IODNN888DNDNNMMD8OZ$8NO==++??????IIII$$$I,,.,?ZO8~=$I::~7OOOOOZ:,..,=7$$I==+???????I??IMMMMMMMNMNNNNMNNNNMNNNNNNNDDNNNNNNMMMMMMMMMDDNMMNNNNNNMNNNDNMMMMMMMM
// MMMNMMMMMMMMMMMMMMNMZNMMMMMMMMMNOI77ZOD8D8NMZODDNMOOOO88DMMND8OOD8DNZ+====++????I$Z$Z7~~=78888=:NNDO,:?ZOOOOO$~+=$Z$ZZ$+??????????7NNNNNNNNNMMMMMNNNNMMMNNNNNNNDNNNNNNMMMMMMMMMDNNMMMMNDDMNNNDDNMMMMMNMM
// MMMMMMMMMMMMMMMMMMNM8NMMMMMMMMMMM$7Z8DNNMMNMMNDDMMD8D8OOODDODDO7NDNNNNI~::::???IOOZZ$ZZO888888Z.ZZ8N?N$,8888OOOOOOOZZ$?7???++====IMMNNDNDDDNMMMMMMMNMMMMNMNNNNNNNNNNNNMMMMMMMMMDNMMMDMNDNDNDNDNNMMMMMNNM
// MMMMMMMMMMMMMMMMMMMMDDMMMMMMMMMMMMDDNNNMMMMMMMMMMMMMN8DDODD8DN8DNNNNNND8~,,:=+?7==$$ZO8ZI+~~~~~,ZZ$$8DD8,~::::=?Z8OO$7,,7??+::,=ZMNNNNDDMDNMMNMNNNMMMNNNNNNDNDNDDDDDNNNNNNNNNNNDNMNMNNNNNNMNNNMMMMMMMMMM
// MMMMMMMMMMMMMMMMMMMMD8MMMMMMMMMMO8DNNNMMMMMNMMNMMND8OZ$$$8NDNNNNNNNNZI8NND$+~=I~..$OO8+::,,,,,,,,=ZOO$~,,,,,,,,:~?OOZI,.~++=~=ZDNNNNNNDDDDNNNNNMNNNNMMMNNNNNNNNNNNDDNNNNNNNNNNNNNNNNNMNNDNNMDNMMMMMMMMMN
// MMMMMMMMMMMMMMMMMMMMN8MMMMMMMMMMZZ$$$$7I77$777777777777$$8MMMNNNNNNNOONNDDDD+?,..:I$I~:,,,:~~~~~:,,~=:,::~~~::,,,:=$Z=:,.=ZZ$NNNNNNNNNNNNNMNNMMNMMMMNNNMMNNNNMMMNNNNMMMNNNNNNNMMNMNNNMMDDDDN8NNMMMMMMMMD
// MMMMMMMMMMMMMMMMMMMMNONMMMMMMMMMZZ777II?I???II777777$$7$$NMMMMMNNNNNOODDDDDD:7...,??,:,,:~??+=??+~,,,,~=??==??=:,,::7?:,.,8DDDDDDNNNNNNNNNMMMMMMMMMMMMMMMMNNNNMMNNMMMMMMD78DNNMMMMMNMNNNNNNNNNNMMMMMMNNN
// MMMMMMMMMMMMMMMMMMMMD+OMMMMMMMMMDZ7I77I???IIIII77777$$$ZNNNNNNMMNNNNOZNNNDDD~7~.=$+,::,,?~7?7?+:=?~,,,++::~+7+I?,:::,I7I~:ZNNNNNNNNNNDDDNNNNMMDDDDNNMMNMMMMMMNMMMMMMMMMM7IZNI?DMMMMMMNNNNNDMNNNMMMMMMMNN
// MMMMMMMMMMMMMMMMMMMMNNDNNMMMMMMMMMZ77III???III77II$7$$$8MMMNMNNNNNNN87NNNNNN?Z7$O8::::::..::. .~=.~:,:..:?. .,?I~::::~ZZZZZZNNMMMNNNNNNNNNMMN8DD88DNNNNDDNDDNMMMMMMMNNMMIIZO+?ZMMMMMMMMMMNMNNNNMNNMMMMNN
// MMMMMMMMMMMMMMMMMMMMMD88NNNMMMMMMMDZ$7777777777$$$$$$$ONMMMMMMMMNNNNO7NNNNNN=$$ZZO::::,~,...~+?,==~:,~..,.~+I:==~,::::ZZZZ7ZNNNNNNNNNNNMMMND8O8OD8DNDNNND8N8ODNMMMMNNNMM?+ZI+?ZMMMMMMMMMMMNDNNNNNNMNMMMM
// MMMMMMMMMMMMMMMMMMMMNNNNDNDNMMMMMMMD$$$$77IIII777$$$$$8MMMMMMMMMMMNNO$888888=$ZZZZ,:::,:::,.?7I=?=.,,::,,.I77+I=.,::::OZZ$?IDNNNMMMMMMNNNNDO88OZ88OD8DD888O87$DMMMMMMMMZII7?+?ZDMMMMMMMMNDDDNMMMMMMMMMMM
// MMMMMMMMMMMMMMMMMMMMMMNNNN88NNNNMMMMZ$$$77777777$$$$ZZDMMNNNNNNNNNNNN8DNNNDDIZZZZO?::::,~~~,II+:I=,,,,~~~,?7?~I=,:,:=ZZO$$I:ZNMNNMMMNNNNMMMNO888D8OZ88OD8O8DNNMMMMMMMMZ7II+++?78MMMMMMMMNNNND8DDDDDNMMMM
// MMMMMMMMMMMMMMMMMNMMMNNNN8DD8DNNNNNNO$$$$77I77$$$$$$ZZNNNNNNNNNNNNNNNDDNDDDDOZZZOOZ~:~::,~~=+II?=:,,,,,~~+=I??=,::~:?OOZ$$7?ZDNNNNNNNNNNNNMMDDDDNDOZ88OOOODDNMMMMMMMMN+??????I$OMMNNMMMNMNNNNNND88888DDD
// MMMMMMMMMMMMMMMMMMMMMNNNDNDDOO88O8DNDZ$$7$777777$$ZZZONNNNNNNNNNNNNNNDDDDDN$ZZZOZOO7::~:::::::::======~~,::::,:::~:~ZOZZ$7$$NNNNNNNNNNNNNNNNMMD8DN88NDDDO8DNMMMMMMMMMO+?7~++?I$OMMMMMMMNNNNNMNNNNMNNNMMM
// MMMMMMMMMMMMMMMMMMNNND7~O8$OZ$7$ZODDN8$$$$77$7$$$$$$ZONNNNNNNNNNNNNDDDDDDDD7OZZZZ$ZO~:::~::::::====~~~~=~::::::~::~+OZ$Z$I$$DDDDDDDDDDDDNNNDNNNDDNMNNNDDNNDNNMNNNNNNNZIZ~=+=?I$ONMMMMMMMMMMMNNNNMMMMMMMM
// MMMMMMMMMMMMMMMMNNNND8ZIO8OOI+..+IO8DDZZ$$$$$$$$$ZZZZDNNNNNNNDDDDNDDDDDDDDD$+:7Z$$ZOOI::?~:~~~7+=~:~:::~=?::::=?:~$OZZ$Z~,=IOO88DDDDDDDDDDDDDDDDDNNNNNNNDDNNNNNNNNNDN$?+:..,+?$ZDMNNMMMMD8DDMMMMMMMMMMMM
// MMMMMMNNNND8Z$ODNNNNNNNDDDOZ?~..,+$O8D8OZ$$$$Z$$ZZZODNDDDDDDDDDDDDDDDDNNNNN7:.~+$$$O$ZZ$ZZ~:~~=Z8888888O7===~~OOZ8OO$Z$$,..~ONDDD8ZZODNNNDDDDDDDDDDDNDDDDDNNDDDDDDDDDZ+=....=?7ZDNNNDNZII7Z8MMMMMMMMMDOO
// NNNNNDD8OZ77I??INNNNNNNDDDOZ?=..,?ZO8DDDD8OZZZOO8DDDDDDDDDDDDDNNNNNNDDDDNDD$=..=$$7ZZ$Z$ZZ~,,.,~IOOZ88O?~,,,,~Z$OOO$$$ZI,.,+O8DDDNNNN8OZZODNNNDDDDDDDDDDDDDDDDDDDDDD887?....+I$ONDNND7?II?IONMMN7$7$$Z8D
// DDDDDD8OZZ$7I777DNNNDDDDD8OO7?. ,?ZODDDDDDDDDDDDDDDDDDNNNNNNDDNNNNNNDDDDDDD$+,,~Z$$$ZZ$$Z$7=,,,:?=+++==I~:,,,=ZZOZZZ$ZO7:,~7ZDDDDDDDDNNND8Z$ZO8DNNNDDDDDDDDDDDDDDDDNDO7I. ..$Z88DDDD7IIIIIIZDNM7?II777ZO
// 88DDOOZZZZ7$77?78NDDDDDDZ7=:,........,:+8DDDDDDDDNNDDDDDNNNNNDDDDDDDDDDDDDD$ZII$ZZ$$ZZZZZOO$I?7Z$OZ$ZZOZ7I~~I$ZZZZZZZZZZ777$Z8DDDDDDDDDDDDDDNNNDDDDDDDDNNDDDDDDD$+,,.........,~+Z8NZIIIIII7ZNMM7+I=I7I$Z
// 88OZ$7$7ZZ$ZOZ$ZDDDDDD~,,,.... +........~ODDDDNNDDDDNND8DDDDDDDDDDDDDDDDDDDDOOZZZ$7I$ZZZ$ZOOZZOOZOZIZZ$Z$O$ZZOZ$ZZI??$OZZZZZODDDDDDDDDDDDDDDDDDDDDDDDDNNDDDDNNDD.,,,.....:........7Z7I7777$ONMM$+I?I++7Z
// 88OZ$$$$ZZ$$$$ZDDDDDDO,..,....,,......,:ONDND8DDDDNDDDDDDDDDDDDDDDDDDDDDDDDDOOOZ$?:::+ZZZ$ZZZOOOO7~,.~$ZZZOOOOOZI:,,,:IZOOOODDDDD8DDDDDDDDDDDDDDDDDDDDDDDDNNDDDN+:,,,.....,,,..,,,,OO$777$ODMMM$?IIII7$Z
// 8OZZ$$ZZO8888DNNDDDDDDO$+~,.... .,=+7$OO8NNNNNNDDDDDD8DDDDDDDDDDDDDDDDDDDDDDOOOZ::,,,,IZZZ77ZZ7Z~,.,..=Z$ZOZZZZ$,,,:,,=IOOOODDDD8DDDDDDDDDDDDDDDDDDDDDDDDDNNNNMNZOZ$+~......,,,,~+8NDDDDNNMMMMDI?IIII7O8
// NMMMMMMMMMMMMMMMMMMMMMNDDDDD8OZ$$Z$ZZO88DNNNNNNNNNDDDDDDDDDDDDDDDDDDDDDDDDDDOOOZ:,,,::7ZZZ$$ZZZ$:....,.+$ZZZZZ$$?~,,,,?ZOOOO888888DDDDDDDDDDDDDDDDDDDDNNNNNNNNNNO888OOOZZZZZO8DDNNNNNNNMNNNNNNO?II7I7$8D
// MMMMMMMMMMMMMMMMMMMMMMMMMDDND8OZZZZOO888DNNNNNNNNNNDDDDDDDD8DDDDDDDDDDDDDDDDOOOO$?,,:~ZZZOZ$Z$$Z:.....:?$ZZ$$$ZZZ?:,,~OO8OOODDDDNDNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN8888888OOO88DDNNNNNMMNNNNNMNNNN87II$$O8D
// MMMMMMMMMMMMMMMMMMMMMMMMMMMO8DOOZZO888DDDMMMMMMNNNNNNDDDDDDDDDDDNNNNNNNNNNNNN8=$OOZ7ZOZ$$ZZOZZOZ$?:,,,?$OOOZ$ZZZZZZ$ZOOOZ++8NNNNNNNNNNNNNNNNNNNDDDDNNNNNNNNNNNNN8DDD888888DDNNNMMMMMMMMMNNNNNNNNNDOZO8NN
// MMMMMMMMMMMMMMMMMMMMMMMMMMNNM88ZZO88DDDNNNNNNDDNDDNDD88DDD8DDDDDDDDDDDDDD88888,:ZOOOOOZZZ$ZZZZ$Z$ZI7I$$ZOO$$$$$OZZOOOOOO=:7NDDDDDDNDDDDDDDDDDDDDNNNNMMMMMMMMMMNNNDDDDDD88DDNNNMMMMMMMMMMNNMNNNNDDNNMMMNN
// MMMMMMMMMMMMMMMMMMMMMMMMMNNNMM8OZODDNMMMNNNNNNNNNNNDDDDDDDDDDDDDDDDDDDDDDDDDDD$,?OOOOOOO?:,:?$7$77$Z$ZZZOO7??~+?$OOOOOOO~+O8DNNDNNNDDDDDDDDDDDDDDDDDNNNNNNNNNNMMMMNNDNDDDNNNNMMMMMMMMMNNMMMMNNNNDDDDNNNN
// MMMMMMMMMMMMMMMMMMMMMMMMNNNMMNNNNNMMMMNNNNMMMMNNDDDDDDDD8DDDDDDDDDDDDDDDDDDDDNMO?OOOOO8$,,,.,.IZ$$$ZZZZZZZ+,,,,,=$OOOOOO$ONNNDNMNNNNNNNNDDDDDDDDDDDDDDNNNMMMMNNNDDNNNNNNNNNNMMMMMNMMMMNMMMMMNNNNNDDDDDNN
// MMMMMMMMMMMMMMMMMMMMNNDDNNMMNNNNNNNNNNNNMMNNNDDDNNDD88DDDDDDDDDDDDDDDDDDDDDNNNZ?$8OOOOOO:,.,.,=Z$Z$$ZZOOOZ.,::::=7OOOOOO+ONNNNNDMMNNNNNNNNNNDDDDDDDNNMNDDDNNNNMMNNNNNNNNNNNNNNNNMMMNMMMMMNNNNNDDDDNNNNNN
// MMMMMMMMNDDDNNNNNNDDDDDDMMMNNDNNNNNNNNDDDDDDNND8888DDNNDD8DDDDDDDDDDDDDDDDND+=++++$I~+OOOI,,,,$ZZOZOOOZZZZ+~:~+?ZOZ7+7?+==NNMMMNNNMNNNNNNNNNNNNMNNNDDDDDNNNNNNNDNNNNNNNNNNNNNNNNNNMMNMMMMNNNNNNNNNNNNNNN
// MMMMMNNNDDO7=+I$O888NMMNNNNNNDZZZ$ZZZZZZZOOO88888DDDD8DDDDDDDDDDDDDDDDDNNDDD8D87+==?+?IOOOOOZOOOZZZ7ZZZZOOOOOOOOO7~==+=78DDDNNMMMMMMMNMMMMNNNNDDDDDNNNDDDDDDDDDDDDDDDNNNNNNNNNNNNNMMNNNMMMNNNNNNNNNNNNNN
// MMMMNDDD88Z7=~?ZNMMMDDDDDDDNNDD8DDDDDDDDDDDDDDDDDDNDDDDDDNNMMNNNNMMMMMD8DDNMNND=??I?+=?$8OOOOOOO7=,=::=IOOOOOOO87+++??+DNNNNNNMMMMMMMNNNNNDDDDDNNNDDDDDDD8888888OOOOOOOOOZZOOO88DDDDMNDDNNNDDNNDDDNNNNNN
// MMMMNNNNNNMMMMD8OOO8DDDDDDDNDD88DD888888888DDDDDDDDDDDDDDDDDNNMMMNMMMNZ8NNMMNNNNOONZ+?IZ7ZO8OOOZ..,:...,O8OO88Z7?+=8NNNNMMMMMMMNNNNNNDDDDDNMNNDDDDDDDDDDDDD88888OOOZOZOZZZZZZ888DDDDNNDDNNMDDDNNNNNNNNNN
// MMMMNNNDD8OO$$$ZO8DDDDDDDDDDOOZZZ$ZZZOOO88888D88DDDDDDDDDDDDDDNNNMMD778NMMMMMMNNNNNDDDDNDDDDNO77I+==~~+II+ZDDDN8IIMMMMNNNNNNNNDD88O8NMMMMNNNDDDDDDDDDDDDDDDDD8888OZZZZZZZZZZOO88DDDDNNNDDDMMDDDNNNNNNNNN
// MMMNNNDDD88OOOZO8DD8DDDDDDD8ZZZZ$$Z$ZZOOOO8888DDDDDDDDDDDDDDDDDDMM8$ODMMMMMNNMNMMNNNDDDDDDDDDD88DD88DDNNNNNNMMMMMNNNNNNNNNDD8DDNMMMMMMMMMMNNDDDDDDDDDDDDDDDDD888888OZZZZZZZZO88DDDDNDDNNDDNMNDNNNNNNNNNN
// MMMNNNDNDD8D8DDDDDDDDDDDDD8Z$$$$7$$$ZZZOO88888DD8DDDDDDDDDDDDDNMN8O8NNMNNMMMNNNDDDNNNNNNNNDNNNNNNNNMNNNMMMMMMMNNNNNNNNDDNNNMMMMNNNNNMMNNNNMMNNDDDDDDDDDDDDD88888888O8OOZOZO888DDDDDNDNMNDNNMMNNNNNNNNNNN
// MMMMNNNNDDD8DDDDDDDDDDDDD8Z$77??77$$ZZOOOO888888888DDDDDDDDDNNND8DDNMNDDDDDNDDNDDDDDDDDDDDDDD8OZZZDNMMMMMMMMMNNMNNNNMMMMMMNNNNNNNNNNNNMNNDDNMMNDDDDDDDDDDD8888OOOOOOOOOOO8888DDDDDDDDNNNNNNMMNNNNNNNNNNN
// MMMNNNNNNNDDNNDDDDDDDDDDOZ$7?=. +?7$ZZOOOO888888888888DDDDDNND8DDNMDDDDDDDDDDDDDDDDDDDDDDDNNNNMMMNOONNNMMMMMMMMMMMMMNNNNNNNNNDNNNDNNDDNMNDDDDDMNDDDDDD88888OOZ$$$ZZZZOOO8O88DDDDDDDDDNNNNNNMMNNNNNNNNNNN
// MMMMMMMNNNNNNNDDDDDDDDD8Z$7I~,. ,=I7$$ZZOOOO888888888888DNNN88DDNDDD888DDDDDDDDDDDDNNNNNNMMMMMMMMMMMDDDNNNMMMMNNNNNNNNNNNNNNNDNNNDNNDDDDNMNDDDDDNNDDDD888OOZ$I~.:?7$ZZOO888888DDDDDDNNMNNNNMMNNNNNNNNNNN
// MMMMMMMMNNNNNNNNNNNNDD8Z$7I?, ...,?I7$ZZZZOOOOOOO88888DND88DDNDD8DDDDDDDDDDDNNNNNNNNMMNNNNNMMMMMMNNNMMNN8DNNNNMMNNNNNNNNNNNDDNNNDDDDDDDDDDNNNDDDDDNND8888OZ$I= ...?7$$ZOO88888DDDDDDNMNNNNNMNNNNNNNNNNNN
// MMMMMMMMMNNMNNNNNNNN88OO$7?+,... .?I7$$ZZZZOOOOOOO88DNDOO8NND88DDDDDDDDDDDDDDDDNNMMNNNNNNNNNMMMNNNNNNNNMMMDNNNNNNNMMNNNNDDDDDDDDDDDDDDDDDDDDNMDDDDDDNN88OOZ7?:....+I7ZOOOO8888DDDDDDMNDNNNMMNNNNNNNNNNNN
// MMMMMMMMMMMMMMMNNNND88OO$7I?, ....?I7$$ZZZOOOOOOO88DDO88DNN8DDDDDDDDDDDDDDDDNNMMNNNDNNNNMMMMNNNNNDNNNNNNNNMMMNNDDDDNNMMMNNDDDDDDDDDDDDDDDDDDDDNNDD888DNDOOZ$?:....+I7$ZZOOO888DDDDDNNDDNNNMNNNNNNNNNNNNN
// MMMMMMMMMMNNMMMNDDDND8OOZ$7I:.....I7$$ZZZZOOOOOOO8N8O88DNN88DDDDDDDDDDDDDNNMMNNDNNNNMMMNNNNNNNNNNDNNNNNNNNNNNNMMNNDDDDNDNMNNNNNDDDDDDDDDDDDDDDDDNND888OZII+=:,....?I$$ZZOOO88888DDNNDDNDNMNDNNNNNNNNNNNN
// NNNNNNDDDDDDNNNND888DDOOZ$$7:..........,:~IOOOO8ND$OO8NN888DD88D8DDDDDNMNNDNDDNNMMNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNDNNNMMNNNDDDDDDNNNNNDDDDDDD8DDDD88N$,,..............,,+ZOOO888DDDNNDDDDNMNDNNNNNNNNNNNNN
// NNNNDDDDDDDDDNNNN8888D8O7~..................?O8DO$ZO8ND888888888DDDNMNDDDDDNNMMNNNNNNNNNNNNNNNNDDNNNNNNNNNDDDDDDDDDDDDNNNMNNDDDDDDDDNNNNNDDDDDDDDD~.,.,,.......,........=Z88888DNNDDDDNMNDDNNNNNNNMNNNNN
// NDDDDDDDDDDDDDDDND8OZO=,........,............,DZ$O8DND8888888DDNNDDDDDDNMMNNDDDDDDDNNNNNNNNNNNNNDDNNNNNDDDDDDDDDDDDDDDDDDDDDNNNNNND8D888DDNNNNNNN8.,,.........,,........,.IO88DND8DDDNNNDDDDNNNDNDMMMMMM
// DDDDDDN8Z$OOD8DDDND87,.......................,8DDDNN888O8DNNDD8888DNMNNDDDDDDDDDDDDNDNNNNNNNNNNNDNNNNNDDDDDDDDNDDDDDDDDDDDDDDDDDDDNNNND888DNNNNNMD.,,..................,,,,7DNDDDDDDNNDDDDDNDNDNMMMMMMMM
// DDDNNNN8OO$7$888DDDD,.......................:$NNMMNNDNDDD88888DDNNDDD8DDDDDDDDDDDDDNDNDDDDNNDNNNNDDNNNDDDDDDDDDNDDDDDDDDDDDDDDDDDDDDDDDNMMMNNNNNNNI~,.,................,,,~8NDDDDDNNNDDDDDDDMMNMMMMMMMMM
// NMMMNMMMNN8OIIIZ8DDNI,....................,IDDNMMMMMNNDD8DNNDD888888DDDDDDDDDDDDDDDDDDDDDDDDDDNDDDDDNDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDNNNNNNMMMNNDDZ?,,,.... ........,.:7NNNDNNMMNDDDDDDDDNMMMMMMMMMMMM
// MMMMMMMMNNNND8$I$8NMNZ,.................~$D8DDMMNNNNMMMND88888888888DDDDDDDDDDDDDDDDDDDNDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDNNNNNNNNNNNNNDDDDI~:,..  .,..,:7ONNNDNNMMMNNDDDDDDDNM+D$~DMMMDOMM
// MMMMMMMMMMMNNNND~INMMNDO=:...... ..,=+OD88DDDNNNMMMMMNNDD88888888888DDDDDDDDDDDDDDDDDDDDDDDDDDDNDDDNNNDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDNNNNNNNNNNNNNNNNNNNNNNDO77ZO8DNNNNMMNN7ZDNNNNNDDDDDDNMM87OMMMMMMMM
// MMMMMMMMMMMMMMMNZ7NMMMMNDD8OZ$ZO88DDDDDD8DDDDNMMMNNNNNNDD888888888888DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDNDNDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNMMN7=ONMMMMMMMNDDDDDDNMMMMMMMMMMMM
// MMMMMMMMMMMMMMMND8MMMMMMNNDDDDDDDNNNNNNNDDDNNMMNNNNNNNND8888888888888DDDDDDDDDDDDDDDDDDDDDDDDDDDDNDNNNDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDNNNNNNNNNNNNNNNNNNNNNNNNNMNMMMMM88NMMMMMMMMMMMMDDDDDDMMMMMMMMMMMM
// MMMMMMMMMMMMMMMMNNMMMMMMMNNNNNNNNNNNNNMNNDDMMMMNNNNNNND8888888888888DDDDDDDDDDDDDDDDDDDDDDDDNDDNNDDNNNNNDDNNNNNDDDDDNNDDDDDDDDDDDDDDDDDDNNNNNNNNNNNNMMMMNNMMMMMMMMMMMMD8DMDOMMMMMMMMMMNDDDDDNNMMMMMMMMMM
// MMMMMMMMMMMMMMNNNNND8DMNMMMNNNNMMMMMMMMMMMNDDDNNNNNND888O88888888888888DDDDDDDDDDDDDDDDDDDDDNNNNNDDNNNNNNNNNNNNNNNNNNNNNDDDDDDDDDDDDDDDDDNNNNMMMMMMMMMMMMMMMMMMMMMMMMNNNMMMMMMMMMMMMMMMNDDNNNNNMMMMMMMMM
// MMMMMMMMMMMMMNNNNMMMN8ZNMMMMMMMMMMMMMMMMMMMMNNNNDDOO$77$ZZOODDDD88888DDDDDDDDDDDDDDDDDDDDDNDDDNNNDDNNNDNNNDDNNNNNNNNNNNNNNNDNDDDDDDDDDDDNNMMMMMMMMMNNNNMMMMMMMMMMMNNNNNMMMMMMMMMMMMMMMMNDNNDNNNNNNMMMM8D
// MMMMMMMMMMMMMMMMNNNNMMD8NNNNNNNNMMMNNNMNMMMMNNNDD888OOOOOOOZ$$7$O8DNNNNNDDDDNDDNNNNNNNNNNNNNNNNNDDDNNNDDDDDDDDDDDDDDDDDDDDDDDDDNNNNNNNNDNDNNNNMMMMMMMMMMNNNNNNNNNNNNNNMMMMMMMMMMMMMMMMMNNNDDDDNNMNNNNOMM
// MMMMNNNNNDMMMMMMMMMMMNNMNNMMMMMMMMMMMMMMNNDD8888888DDNNDDD8D8DDDDDDDDDOO88DDNMMMMMMMMMNNNNNNNNNNNNNNNMNNNNMNNNNNNNNNNNNNNNNNNDDDNDNNDDNDNNNNNNDDNDNNNNNNNNNNNMMNNNNNNNMMMMMMMMMMMMMMMMMNMNDDDDNNNNNMMMMM
// DDDDDDDD8DMMMMMMMMMM8$NMMMNNMMMMMMNNDDD88OOOOOOOOOOO888DDNNNNNNDDDDDDDDDDDNNDDDNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNMMNNNNNDDDD8D888888D888DDDDDNNNNNNNNNNMMMMMMMMMMMMMMMMMMNDDDNNNNNNNNMMMM
// DDDDDD88DNMMMMMMMMMMMNNMNNDD888OOZZZZZZZZZOOOOOOOO88888888DDDDNNNNNNNNNNNNNDNNNNNNNNNNNNNNNNNNNNNNMMNNNNNNNNNMNNNNNNMMNNMMMMNNNNDDDDDDDDDDDDDD88888888OOOOOZZOZO8888NNMMMMMMMMMMMMMMMMMMDDDNNNNNNNNNMMMM
// DDDDDDDDNMMMMMMMMMMMMNNMNN8OZZZZZ$$$$$$ZZZZOZOOO888888888888DDDDDDDDNNNNNNNNNNNMMMNNNMNNMMMMMNMNNNNNNNMMMMMMMMMMNNNNNNNNNNNNDNDDDDDDDDDDDDDDDD888888888OOOZZZZZZOO88NMMMMMMMMMMMMMMMMMMMNNNNNNNNNNNMMMMM
// NNNNNNNMMMMMMMMMMMMMMMMNNN8ZZZ$$$$$$$ZZZZZZOOOOO88888888888D8DDDDDDDDDDDDDDDDNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNDNNNNNNNNNNNNNNNNNDDDDDDDDDDDDD8D8888OOOZZZZZZZOOO8NMMMMMMMMMMMMMMMMMMMMMMNNNNNNNNMMMMM
// NDDDDNMMMMMMMMMMMMMMMMMMMMOZZZZ$$$$$$ZZZZZOOOOOO8O8888888888DDDDDDDDDDDDDDNDNNNDDDNNNNNNNNNNNNNNDDNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNDDDDDDDDDDDDD88888OOOOZZZOOOO88NMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
// NNNNMMMMMMMMMMMMMMMMMMMMMDOOZZZ$$$$$$ZZZZOOOO8888888888D8DDDD8DDDDDDDDDDDDNDNNNNNNNNNNNNNNNNNNNNDNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNDDDDDDDDDDDDD88888OZZOOOOOO88NMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
// MMMMMMMMMMMMMMMMMMMMMMMMD8OOOZZZZZ$ZZZZOOOOO888888888888DDDDDDDDDDDDDNDDNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNDDDDDDDDDDDD8888OOOOOOO88O88DNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
// NMMMMMMMMND8$$DMMMMMMMMN88OOZZZZZZZZZZZOOOO8O8888888D8DDDDDDDDDDDDDDDDDNNDNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNDDDDDDDDD8888888OOOOO8888DMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM
// MMMMMMMMMMMMNMMMMMMMMMND8OOOOOZZZZZZZOOOOOOO88888888DDDDDDDDDDDDDDDDDDDDNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNDDDDDDD8D8888OOOO888888DNMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMMM