####SSSSSS?*??SSS%%%SS%%%%?%????????%%%???****+++++=+***+=--;;:;:::::::,,::::::,
###SSSSSS?*?%%SSS%%%SS%%%%%???????S####SS%*++==+=++=++*++-;;;;;;;;:::::,:::::::,
##SSSSSS%??%%SSSS%%%%%%%%%%?????S#@@#####S%+-;-==-=====--;;;;;----;:::,::::::::,
#SSSSSS%*?%S%SSSSS%%%%%%%%????%#@@@###SSSSSS*=***??=-----;--------;;::::::::::::
SSSSSS*-*%%S%%SSSSSS%%%%%%????S@@@###SSSSS%%%?%%%%SS?;-;;;;------;;;;::::::;;;::
SSSSSS*-=%SSS%SSSSSS%%%%%%????S#@@##########SSSSS%SSS*;;;;;;;-;;-;;;;:::;;;;;;::
#SSSS%*--%SSS%%SSSSS%%%%%????S##@@@@##S###@####SSS%%S%-;:;;;;-;;;;;-;::;;---;;:;
SSSSSS?++?SSS%%%SSS%%%%%??%%%#@@@@@@###@@@@#####SS%%S%+--;;;;;;;;;;--;;-----;;:;
SSSSSS%+*?SS%?%?SSS%%%%%?%S##@@@@@@##@############SSSS%----;;;;;-;;----------;;-
SSSSSS%??%S%*?%%SSSS%%%%S##@@@@@@########S?**?S#####SSS%===-;-;:;;;;;;---==--;;-
SSSSSSSS%%%%++?%SSSS%%%%##@@@#@#########?+===+*%###SSSSS?==---;;;;;;----====-;;=
SSSSSSSSS%%%%%%?**?%%%%%##@@@@###@@###S?=---==+*%S#SSSS#%*?-;-;;;;----===++=--;=
SSSSSSSSSS%%%%?-=?*?%%%S#@@@@@@@@@@###?=----==+*?%######%+S%*-;;;;--=====++=---+
SSSSSSSSSS%%%?=-+*??%%%#@@@@@@@@@#@##SS%*=====++*%S#####%*SSS+-;;--==+===++=---+
SSSSSSSSSS%%?+*+???%%%S@@@@@@@@@##@##SSSS%*+++++*%S#####S*SSS*----==++==+++==-=*
SSSSSSSS%%%%????%%%%%%#@##@@@@##%S##@@##SS%******?S#####%*%%?--===++++==+++==-=*
SSSSSSSS%%%??*?%%%%%%%#@@@@@@##SS#SS#####S?*?%SSSSS#####??%?=--===++++==+++===+*
SSSSSSSSS%%?*=?%%%%%%%S@@@@@@####%?*?%SSS?++%S#########S?%S%+===++++++=++*+===+?
SSSSSSSSS%%?*?%%%%%%%%S@@@@@####S*---=++=+-=S#########S%%SS%*=-=+++++++++*+===*?
SSSSSSSS%%%?=*%%%%%%%%S@@@@@####%*=;;;;;-=-+%%S#####@#SS%?+=?*+=+*****++**+==+*?
SSSSSSSS%%%+??%%%%%??%%#@@@@###S%?+-;;;-==-*?*?S#######S????*?++******++**++=+??
SS%SSSSS%%?*%%%%%%%???%%#@@@@#SS%?*=---+++=*?**?%S######SS%?%%+*******+***+++*??
S%**%%SS%%*%%%%%%%%????%%#@@@@SS%?*+---?SSSS?*+*?%######SSSSS*+**??***+***+++*??
SSSS%%S%%%?%%%+?%%?????%%#@@@#S%??*+=--++%##?***?S#####SSSS%*+**?????*+-**+++???
SSSS##@#SS%%%?*%?+=????%S#@###S%??**++????%S???%S######SSS%?****????++=,=*+++???
SSSSSSS####SS%%+=*%%????S@@#%##%??**%S#####%?%%S#######%???****?????:;+;=*++*???
SSSSSSSSSSS##?=*%S%%%?%%%#@#SS#S%??*?%??S###%SS########?**?????????*;-=;-****??*
SSSSSSSS%%??+=*S###S????%#@#SS##S%?**%#SSS##SS######S%%%?*?????????*-;=;-=;+???*
SSSSSS%%%?+=+?S##S%%*;*??S##S####S%?+=*%###SS#SS###S%??%%???????????=;+;-;,+?-=*
SSSSSS%%%*+++++==++*-:-*?%##S######S?***%SSS#SSS###S????%???????????=-+--;:=*:;*
SSSSS%%%?*++=+==+*??+;=*??S#########SSS%SSSS%SS###S%????%?????%?????=-+--=-+*;;*
SSSS%%%%?++=+++?%????+*??%SS#@#########SS#%??%#S##S?????%???????????+-??*+-+?---
%%SS%%%%?++=+=*S#SSS?*??%SSS##############???%S##%S%?%????%???????%?+-?%?+-*?--;
%%%%%%%%?*++++?SS%?%%??%SSS###SS##########**?%S#%??S%%%??%%%%?%%%%%%?*?%%*-*%==+
%%%%%%%?*+=+=+?SS%??%?S######SSSSS########?;-*SS%??SSS%%%%%%%%%%%%%%S%%%%*=*%+=*
%%??*???*+*++++%S%?*??S#@@#SSSSSSSS#######%=::-%???SS%%%%%%%%%%%%%%%S%%%%%%%%+=*
%??-;*?%%SS%??*=+*++*%S##@#SSSSSSSSS######S?+-;+%??S+==++*?%%%%%%S%%S%%%%SSS%+=?
%?*;:*?%####S%?*+=-=+?##S#@#S%%%SSSSS#####S%*=-;=*?+;;;:;::;+%%%SS%%%%%SSS%%SSSS
%%?*+??%%##@##%?*+=-=*S%%S#@##S%%%%SSSSSSS?=;;;;=?S%??*++==-:-%%SS%%%%SSS##SSSS%
%%%%?%%%SS#@@##S??*+==???%SS#@@S??%%%SS%%%?****?%%##????****+=+??*?+=+*SSSSSSSSS
SSS%?SS#SSS#@@##S%??++*????%%S#@%???%%%%????%%%%%%#S*??*******+-==-;+=-*SSSSSSSS
SSS%%#@@#SS###@@#S%??*?????%%%S#??***????**??%%??S#?*********?*+-=+===-?SSSSSSSS
###S%##@######S###%?*?%??%%%%S##?************???S#%==+********?*+**+==+?*%SS##SS
###SS##SS####%??##%?**????%%S#@S?**+++++++++*?%##%====+***????+++++?%%%?+=+%S###
SS#@@@#SS##S%????#%?***???%%##S%**+++===++++%###%++====+**???+-=++?%%?*==+;*####
#SS#@@####S%%????%%****???%##S%?*+++=====++?#S#%?**+====+*?%%==++*+=;;-+*+++%###
##S#@#####S%%%??%%%?****??##S%?*++++====+++?##S%??*+=---=+??*==+=-++-;+%SSS%?%##
##SS######S%%%%%%%S%?**+*?S#%?**++++++=++++*S##%?*+=-;::;-+*+*?%??????%SSSSSS%S#
#SSS####@#SS%%%%SS#S?**+*??S%**+++++++++++**?%S#%*++-;;:::-++=%S%%???%SSSSSSSSS#
@#SSS##@@##SSS%SSSSS?**+*????*+++++++++++****?%S#?+==-;;;-++=*%????%%%?*+?SSSS##
@#SSS#@@##SSS%SS%##S%?*+**?**++++++++++++**????SS%*+=----+*%%?%SS?======*SSSS##S
####S##SS%?%%%##%##S%?****?*?***+++======+*?S%%%%%*--;;-+%%%%SS#SS%*++*%SSSSS#S?
@@@###S%?%%?%SS%?S#S%?****?%%????+==+**+=-=*+*?*??+;;;;;-*%SS###%?SS%?%SSSSSSS##
@@@@@#S%S###S%%S####%??****%%%?*?*+?%%%?*=;;----==--==+++?%S###@#SS##SSSSSSSS#@@
@@@@###########@@@##S%?****???*+?*?****??*==------=**++???%S#SS#@#SS#SSSSSSSS#@@
@@@@####%%SS###S%%S#S%??***?+?*=*+SSS?*++*?*+**++??%S%??%%%%SSS#@###SSS%%SSS####
@@@##S%?%%%%%?*++%##S%??***?*+=-=*%%SS?**S%%????%%%%?%%%SSSSSS%#@@######SS######
##@#%?%%?++===++%###S%%??***?*+=+%SSSSS%#SS%%%%%%%%%%%SSSSSSSS%S@@@#######@#####
@@@S+?*++*===+*%#S%SS%%??***?%S%S%?#####SS%%?????%SSSSSSSSSSSS%S@#@@##@@########
@@@?+*++*+==+*S%?%##SS%???**?%SSSS%####S%%%%%%%SSS%S%SSSSSSSSSSS@#########@####@
@@@?+++====++*?%####SS%%??????SSSSS#SSS%%%%%%SSSSS%%%%%%%%SSS#%S###SS#####@####@
@@@@##SS%?++?%S######S%%??????%SSS##SS%?***?%%SSSSS%%%SSSSSS#SS####SSSSS##@#####
@@@@@@@@#S*?SS####@##S%%%?????%S####SS%SS%%SSSSS#SSSSSSSSSSS#SS###SSSSSS#@@####@
@@@@####%*?SS######S#S%%%??????S@@##SS%%SSSSSSSS#SSSSSSSSSS##SSS##SSS%%SS#@####@
@@@@#S#S%##S###@@#SS#S%%%%?????%####SSS%SSSSSSSSSSSSSSSSS####SSS##SS%%%%%S@####@
@@@@###########@#SSS#SS%%%?????%S@###SS%%SSSSSSSSSSSSSSSS##SSS%S##SS%%%%%%#####@