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