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