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