,,,,,,,+%???????????%SSSS%SSS##SS##SSSS%%S%%S%S############@###SSS##S%%%%%%%%%%%
,,,,,,,;?%??????????SSSSS%SS#########SSSSS%S%%%SS###########SSSSSSSSS%%%%%%%%%%%
,,,,,,,,+%???????*?%SSSSSS##@@#@@#######SSSS%SSSSS##########SSSSSS#S%%%%%%%%%%%%
,:,,::,,-%?????????SSSSSS###@###########SSSSSSS%SSSSS#####S#SS####S%%%%%%%%%%%%%
*********??????*??%SSSSS############SSSS%%%SSSSSSSSSSS####SSSS%%%%??%%%%%%%%%%%%
??????***??*****??%SS#SS####SS%%SSS#SSS%%?????%%%%%%%S#####SSSSSS%????%%%%%%%??%
??????****?******?%SSSSSS#SS??*%SSSSSSSS%%?*****??%%%SSS#S#SSSSS%???????*?????%#
???????****?******?%%SS%%%%?*=+*?%%S%%SSS%??*+**+*??%SSS#SSSS#S%%?????*+++**?S##
???????****?*******?%%%%%?*+=-==+*??%%%%%%%???**+**?%SSSSSSSS##S%???**++++**%S##
??????????????**????%%%%?*=------=+*??%?%%%???*****?%%%S%SSSSS#S%?**++++++*?%??%
?****************?%SS#S?+=--;;;;;;-=+*?????????****?%%%S%SS%S##SS%*+======++*??%
+++===++++++++++*%S###?+=--;;;;;;;;--=**?????*****??%%%%SS%%%S#SSS?+==----===++*
==============++?%S##%+---;;;;;;::;;;-=+*?????**????%%%%%%%%%S#S#S%+==------====
===---==---====*%%###*=---;;;;;::::;;;-=+**???***??%%%%%SS%%SSSSSSS*+=-------=-;
S%%%%*--------=*%%##S+=--;;;;;;::::::;;-=+**???*=*%%%S%SSS%%SSS#SSS*+==-------;:
SSSSS%--;;;;--=*?SS#%+=--;;;;;;:::::::;;-=+**??*+=*%SSSSSSSSSSSSSSS?===-=+===-;:
%%??%%-;;;;;--=??SSS%+=--;;;;;;:::::::;-==+**???+-=*%SSSSSSSSSSSSSS?===*?++++=;:
%%%%%%-;;;;;;-=??SSS%+=--;;;;;;:::;-+*%%SSSSS%%%*=-=*%SSSSSSSSSSSSS?+==**??*+-;;
%%%%%%-;;;;;;;=*?%S%%+=--;;;;;;;-+?S##S%?+++???%?+--=?%S##SS%%%SSSS?==*?*?+=-=++
????%%-;;;;;;;-*%%S?%+=--;;;;;-*?S###S?+===+**?%%*-;-*%SSSS%%%*%SSS?+*?*+=+*?%%?
==+*%%-;;;;;;;-*?%S*?+==------+%SSSS%%%S%S%%%%?%%*=;;=?%%%%%?%??SSS?=+=+*?%%%%%%
????%%-;;;;;;;;*?%%*?SS%?*==--=?%??%SSS#####SS%?%?+;;;*%%%??+*??SSS?+*?%%%%%%%%%
????%%-;;;;;;;;*?%%?#@###S?+=--=+*?%S###%S#@@S*+%%*-;;+%%%??+-+?SS%%?%%%%%%%%SS#
**?*%%-;;;;;;-=*%%%?%%SS##S%=-;;-+*?S?-**?%#%+=-*%*=;;=?%?%%*--?SS%%%%%%SSS###@@
++=+%%-;;;;;-+??%%%%=%######*;::;;-*%*+*%%S%+---=%%*;-=?%+***=;?SS%%S####@@@@@@@
????%S-;;;;;;=**??%%-?@@SS%#%;:::::-+?%%%?*=-;--=?S?--=*?=+++;;%SS%SS####@@@@@@@
%?????=-;;;;;-=+??%%*?##=??S?;::::::;-==--;;;;;--*S?+==+*=-;-;-SSSSS%%%%%%%SSSSS
*++++++**-;;;-=+??%%*=*#%%%?+;::::::::;;;;;::::;=+SS?==++-;;;-?SSSS???????%%%%SS
**+++++*%%=;;-=+*%%S%=+?S%?+=;::::::::::::::::;;=+%S%+==+;-;;+SSSS?****?????%%%S
******+*%S*-:;;;-+?%+;;+*+===;;;;:::::::::::::;-=+?SS*===+S%-S#SS%******?????%%%
******+*%%*=,,,,,:**::,=+===-;;;;;;;:::::::::;;-=+*SS*=-*S@#S#SS%*++++****????%%
********%%?=,,::::*?=;:+===-;;::;;;;;;;:::::;;;-=+*%S?=-*?S###S%?*++++****????%%
********%S?=,;+=--?%?=-=+==+-;---;;--;;;:::;;;;-=++?S%==+*S##S%?*++++++***????%%
********SS?=,-SS%%%SS%%%+==*?***%?*+-::::::;;;;--=++S%+==+%S%%?**++++****???%%%S
======+?SS?=,;**+++%S*+-+++=?S%?===;:::::::;;;;--=++?S+===%%???****+++**++**====
+=--;-=%S#%+,:;;;;-?S*+-+*+++**+-::::::::::;;;;;-==+*S++==?%%????%*-=+?*---;,:;;
***+-;=%S#%+,=###SSSSSSSS**++=-;-:::::::::;;;;;;--=+*S**-=?%%????%?=+***++=-,:;-
++==--+%SS%*,-+=-;;-**=:::+*++=--=--;:;;;;;;;;;;--=++S?+-=?%%%??%S?=?%??%%*-,:=*
=--==+*%##S*:-+====+?%?**-;**%%%??%%%???*-;;;;;;--=+*S*--=*%%%%%?%%++***???=,:=?
==--;-=%S#S?:=##SS%%%S%%?=:*%##S##%*+==-;;;;;;;;--=+?S+---+?%%%%???????**++=::-=
++**=;=?S#S?;-=-;;::-*=;:,:*S%?%%=---==-;;;;;;;--=+?*S=----+%%%%%??%%%%%%%%%?*??
+++=;-=%##S?;-++===+*????++?S?%S+=+**?+-;;;;;;--=*?**%=-----S#SSS%%%%%%%%%SSSSSS
=====+*%S#S?;+##S%%%%%%%S#%++SS#%?%%*=;;;;;;;-=+??*+*%=;;-;-?#S%#SS%%SS%%%%SSSSS
+=---=+%S#S?-=+=--;;;++?%?%S??+S%*=;:::::;;;-+?%??*+*%=;;;;;+#%%S@#S%SSSSSS%%SSS
====;;=?S#S?-=++====+?%%??%@%--?*=-;;:::;;-=?%%%?*++??-;;;;-+S%%S@#S%%S%SSSSSSSS
+***=;-?##S?=*##S%%?%%??%SS?+--*?*==--;--+?SSS%?**++*?-;;;-=?%%%#@##%%%%SSSSSSSS
==--;;-?SSS%=++=-;-?%??%S?;::;=**??****?S#SSS%??*++*+*-;;;=*%%%%#@##S%SSSSSSSSSS
++++++*%S#S%++?**+??*?S#S*=**++?***?S##@@@S%%??**+=*=*-;-=*%%%%S#@##S%%SSSSSSSSS
+=--==+%S#S%+*##S%?*?SS*=+===++??**%##@@@@S%??**+=++=*--=*%%%%SS#@##S=======++++
++==--+%SSS%**?%SS%%S?*++=-;+%####S#####@@S??**++++==*==?S%%%SS######;;;;;--=++*
++++==+?S#S%**=;;+S#%??????#@@@@@#S#####@#%?***+++==+*+?S%%%SSS#####@?+++**??%%S
+***==+?##S%*?*=+=%*++++?S#@@@@@SSS#####@S%***++++=++*%S%%%SSS########??*?%%?SSS
+====++%SSS%*+=++-;::;-?S@#@@@@SSSSS###@%%?*+++++==+*%%%%%SSS#########*+*?%%%%%%
++++++*%S#S%**%%%?????%SS@#@@@SSSSSS###%?*++=+++==+?%%%%%SSSS##########%??+=+*?%
+=-;;;=?##S%*?#S%??*?##SS@@@@SSSSSSSSS?*+=-==++==+?S%%%%SSSS##########@@#?+=-=--
++++=;-?S#S%??*=-;;-S###S#@##SS%SSSS#?+=----=++=+%S%%%%SSSSS##########@@@@S?+==;
***+=;-?S#S%??%?***S###SS###%%%%SSSSS*==----=++*%%%%%%%%SSS##############@@#%?+;
===---=?S#S%?%#S%%S@####S##%%%%%S%S#%*=----===?S%%%%%SS%SSS################@#%+;
**++++*%##S%??%*+%@#####S#SS%%%S%SS#?+=---==+%S%%%%S%SSSSS##################@#*;
*+++==+%S#S%???*?#@#####S##@@#SSSS#S?+=---=*%%%%%%%SSSSSS###########@@#SS######*
+==--=+?S#S%?%SS#@@########@@SSSSS#%*==-=+%S%%%%%%SSSSSS###########@@#SS#######@
++++-=+%S##S%**%#@#######S#@#S%SSSS?++*=*%%%%%%%%SSSSS%S##########@@#S#######@@@
****+=+%S#@@S%###########S#@S#%%SSS?++*?S%%%%%%SSSSSS%S#@########@@#S######@@@@@
+++===+%S#@@#S##S?*S########S#S%SSS%%%%%%%%%%%SSSSSS%SS#########@@#S#####@@@####
******?%##@@####?%??%@####@S##S%%%%%S##S%%%%%%SSSSSSSS#########@@#S####@@#######
*+++=+*S##@@@@@#?S++%%###@#S##SSSS##@@@@#S%%%SSSSS###@@######@@@#####@@#########