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