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