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