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