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