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