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