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