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