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