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