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