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