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