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