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