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