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