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