,,,,,.......................,,............,~~~~~~~~--~~,......................,,
,,,,,...................;;;*==:~,.......~~,,,,,,,,,~~~~--,....................,,
,,,,,..................:&&&&&&=-~~~,,,~~,,,..,,..,,.,~~~-:-,..................,,
,,,,..................~=%%%%%&$*----,~:--,,....,,,,,.,~~,~:;~.................,,
,,,,.................~=%%%%%%%&&!~--;;~-;:~,.......,,.,~~~-;*-,...............,,
,,,,...............,-=&&%&&&&$#@@?*!:--~:::-,,...,,.,~,,--~:!+!----,...........,
,,.................!&&&&&&&$$#@@@&*:;&$;:;!;*;~,,,,~.,~~,:--;+?----:-~.........,
,,.................;?=%%&&&$$@@#&$?=#@@=?++?;,~:~~~,-,,--~:::!?;-~~~~~-........,
,,.................;!*+=%&$$#$&%$#@@@@@=+*:,..,~:;-~,-,~:::;;;??::!!----.......,
,,.................;!!*+=%$$%=%&#####$%=-,,,,,~;+?+-~~:~~;:!;*+=?+=!---:-......,
,.................,;;::;=&#$==&$$$###&?%####&?!=%==;~:-!-:!***+%%?-,,~---~.....,
,,.................,,~:?&###=%$$&$##&=?%$##@@@&%==%~~+::*-*!?+==&%!:::::::,.....
,.................,!+=%&#@@&%&$&&$$$%?=$####@@&%%&*.-*:!!*!++==%&&=+===?++!.....
,.................,?==%&$@#&%=%==&$&??%$###@@@$%=+~.---%!+!?*%=&&&=*???%%%?,....
,..................---!=$##&%?!:;?==?%$####@@@@+:,..:~-$=++++?%&$&#$$$&&&%?,....
,...............'..,-:;!?$$$$*-~~;?%&&$$&$$#####*,..~,!$$=??=+%&$&#&%%%%==*.....
,..,...........''..,---:;+##%!-~~~;+==&$$#######@&-..~?#&%?=%*%&&&#&%%=+*!:.....
,..,..........''''..,,,~~!$#=;-~~~~:**+%&$$$######&?=*%#%%=&&?%&&$$&??;;::~.....
,.............''''.....,:*&$+:-~~~~~~:;!?%&$#####@@@@@$$*+&&&%%$&$#&+:--~~,.....
..............''''''..,~;*?%;:-~~~~,,,,~-!*?&##@@@@@@@#&;*&&&&$$&$#%!--~~~......
.............''''''''.,~:!*=%+:---:!+?**!!!*?=&#@@@@@@@#%=%%$$$$&#$$%*:--,......
.............'''''''''.~!**??&%;:*&##&+**?==???=$#@@@#####$=$$$$&#$$$&=*;,......
.....,......'''''''''''.:!?%&%&=:*&##&==&&%&%?++=$@@@#####$%&$$$&#$&$$&*-.......
,...,,,.....''''''''''''.*+;+$&=~;=$&$$$$#$&?**+?&########?%%$$$$$$&$&*.........
.....,......'''''''''''''..'~=?!,:!!;+??%&+::;*+=&#######$+%%&$&=%&&%!.''.......
...........''''''''''''''''',**-~:::~;*++;-~:;*?&$######&$##?=$+..-;~...........
...........'''''''''''''''''~::--;;:--:--~-:;*?%$$####&&&$@@#$&~..'''..'........
....,......'''''''''''''''''~;:-;!*;-----::;*?%$$$$$$&=%&@@@#$?...'''''''.......
...........''''''''''''''''',!:;***!---::;!*?=&$$$$$&?+&@@@###&+-.....'''.......
.......'...'''''''''''''''''.*?%&==+---:;!*+=&$$$$$$#%&@@@@##@##$=;.............
..,,.,.....'''''''''''''''''':!%##$*~--:;!+?=%&&$$$$##@@@@@######$&=-...........
,.,~,.'....''...~~,..,~,'''''~:??;:~~--:;!*?==%%&$$$##@@@@####$$$$$=?!....'.....
,,,~.'......~::;;:-:!!;!;,''',!*!;-~~-:;!!*+?==%&$$$##@@@@#$#$$$$$&%++!,..'.....
.,~~,''''',;!**%+;!!:*??%-.~:!?=$&%+;:;;!*+??==&&$&$##@@@@#$$$$$&$%=?+*;..'.....
.,~~,''''.~!?$##=;;?*;*=?%%?=%$$&=?==*!**+??==%&&&$#######$$$$$$&&&??*;:,.......
,,,,...'..~;*$###%+=$=$#%$##$=!&=+?=*!++??==%&&&&&$##$#$&$$&&&$&!?%?+*;!........
~~.....''.~;+&$#$%=%&=$##$%*.'':$#$&???===%&&&&&&###$$$&=&&&&&&&+,??*+=;........
,~........-;!????=%$##%%#=?.`''.&$?*!*+?%&&&&&&$###$&$&%%&&&%&&&%,-?+=!.........
.~......,-*+??=&$#####;&#$-`''''=&;:;!?%&&&&$###&=%=!*?%+%&&%%%&%:.*?;.''''.....
.~...-;*+?=%$#########!##$.`''''-&=??%&&&$$#####++**!?%%~:&&%%%%%!.,,'''''''....
,-::???=&###&$####$%?==##%.'''''',;*?=%&####&+*?*;;*=&&#+.+&%%%%%?.'''''''''....
.:*!=&##&?+!!?$##$=!+=&&#=''''''''''-=%$$&&&%+;!;;!?&@@@$,;&&%%=%=,''''''''.....
,*?&$%*-.':;;+&##$==%++?$?''''''''''';&&$&&&&%+*!+$@#@#@@*~%&%%===-''''''''.....
.~!:~...'.:;;*%##$$%*;*?&%,,''''''''',%$$$$###&%$#$$$$##@$~+%&%===;'''''''''....
........'':;;*=$#$=+!!+%$+~-:~''''''':#@$@@@#$&$&&$$##%+**!*%%%===+.''''''''....
........'':!!*?&$%***+=$%~~,-;-''''.~+#@@@@#$$$&&$#%*-,,~-:!+=%%===,''''''''....
.......'''-***?%$%*++=&$;,~~--;-~,~~-?#@@@#$$#$$$%+~..,,~--~-:*====:''''''''....
........''~+**?=%%+?=&$%~,~~~~~~,~~~-*&&%?+??**+:~....,-~,,~~-:;+==*..''..''....
........''~*+++=%&?=&$&:,,~,,,,,,,~~;%%?:,,,~,,~~....,-,,,~~~,~~-:;:,~;*???+....
..........~!**+=&$&&$&*~-~,,,,,,,~-;%&?:~~~,.,,,...,,~,.,~~,...,~~..-=$%%%%&*,..
..........-!*+=&##$$&*~-,.,,,,,,~-!=&?:~~-,..,,...~~...,~,....,-,,,*##$&%%&&&;..
..........:;+&$$$$$&!,,,..,,,,,~;*=&=!-~-,..,,...-~...~,.....:??;:?@@@@#$$$$&~..
.........~:;!?&$$$&?,,~,..~,,,~;?%&=*-~-~..,,,,.~~...~,.....-=#@@#@@@@@@#$&&&?-.
.........::;;+=%$$&!!!~..,,,,-;=&&=*:,-~..,.,..~~...-,..,.,~~=#@@@##@@@@@@$$&&%!
.........;:;;+?=$&=;::,.,,,,-;=&$%!:,~-,.,,~..,~...~~.~~.,~,~?#@@#&$$##@@@#$&&&&
........,;:::+?%$&+!!~,.,,,-!=&$&!:,~-,.,,-..,~,..~,.-~',-~--!$@#&%&&#$$#@@#$$&&
........~;--:+?%$%+;~,,,,~-*=&$&+-~,~,..,-..,,,..,,.-~..-,~~:;?@#&&&&$#&#@@@#$$$
........::--;+=&&?~,-,,,~-*=&$&=-~,~,..,;,..,,,..,.~-..~,..,,,!@#&&&&$@$$@@@##$$
........;:--;+%$&!,:;,,~-+=&&&=:~,,,.,.;~..,,,..,.,;..~~.....,=@$&&&&$@#$@@@#$$&
.......~;--:!?%$%:~!~~~-?%&&%+:,~,,.,.:-..,,,..,..;~.,-,....,+@#%&&%$$#@$#@@@$=+
.......;:--:!?&$=~;!~~-+&&&=*:,,,,...~:...,....,.-;,.~,~-,,~=@@&%$&&$$#@##@@@#=*
......~;:-:;*=&&&!*:~-*&$&?;:~,~,..,.:...,.,.....;~.~~*$#&%#@@#&&&&&$$#@#$@@@#$%
,.....:;:::!+=$&$=;--!%$&=;~-,,~..,.-~..,..,....-:,,~:#@@@@@@#$&$$&&$$#@#$@@@#&*
,....,!:::;!+%&%$*:::=$$%!~~~,~,...,-..,,.,....,;,,:;:$@@@@@#$&&$$&&$#@@@$#@@@&*
.....:;:::;*?&&&$!!;!&$&+-~-,,-,.,.:,..,..,.,..-~,--~-=@@@@@$&&&$&&&$#@@@$#@@@$?
....,!;:::!*=&&&#?;;=$&?;,~-,,-,.,~-..,,.,.,,.~-,~;~.,!#@@@$&&&$&&&$#@@@@##@@@#*