=;-==-----;-=++=----;:,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,:::;;;;----+*-
=;-==;----;;-+++++=;:,,,,,,,,,,,,,,,,,,,::;;--------;:::,,,,,,,,,,:;;;----=--+*-
=;;;-;--;-;;;=++*+=-;:,,,,,,,,,,,,,,:;-==+**??????????**=-:,,,,,,::;;;---====+*-
=;-==;--;-;;;-+**+---;;:,,,,,,,,,:-=++++*%%%%SSSSSSS%%%%%?*-,,,,,::;;;----===+*=
=;-=+;----;;;;-+*+-----;,,,,,,,:-+++****?%SSSSSSSSSSSSSS%%?*:,,,,::;;-----==+**=
+-;--;---=-;;;;=*+-=++=-:,,,,,,=++******?SSSSSSSSSSSSSSSS%%?:,,,,,:;;----====**-
++=+=;---++;;;;-+=-====-:,,,,,,=+*******?SSSSSSSSSSSSSSSSS%?:,,,,,:;;----===-+*-
*++=-;---**=;;;;==-----;:,,,,,,=+*******?SSSSSSSSSSSSSSSSS%?:,,,,,:;------==-+*-
*?*+=;---***-;;;==---;-;,,,,,,,-+*******?SSSSSSSSSSSSSSSSS%?:,,,,,:;-------=-+*-
*??*+=+--*+++;;;-=---;-;:,,,,,,;=+******?SSSSSSSSSSSSSSSSS%?:,::::;-;-----==-+*-
+*??**+--*+=*=;;----;;--;:,,,,,:=+******?%SSSSSSSSS#####SS%?:,::;;;---;---===+*=
+=*???*=-*+-++=;-----;--;:,,,,,:++*******%SSSSSSSSSS####SSS?:,:;;;---;;--===-+*+
===**?*+-*+-==+----=-;--;:,,,,,,=+*******%SSSSSSSS######SSS?,,:;;;---;;--===-=**
==+?+***-*+---+-----;:-;:,,,,,,,=+*******%SSSSSSSS######SSS?:,:;;----;;--=-=-=*+
+==+*+**-*+---=--=-;;;-;::,:,,,,-+*******%SSSSSSS########SS?,,:;;;--;;;--===;=*-
+=+?*=++-**---=----;:;--;;;;:,,,-+******?%SSSSSSSSSS#####SS%,::;;;;-;;;----=;=+-
+==**=++-*?+--=----;;;------;,,,;+****?*?%SSSSSSSSSSSSSSSSS%:::;;;--;------=;=+-
+==*+=++-+??+-=;;;;;;;--;;;;;:,,;+***++++?%%SSSSSSSSSSSSSSSS:::;;;-=------==;==;
===**=++-+***==;::,,::;;;;;;;:,,:++==++++?%%SSSSSSSSSSSSSSSS+-==---=-------=;--:
+=======-==**+-:,,,,,,::;;;;;;:,:=====+++*%%SSSSSSSSSSSSSSSSSSSSSSS%+=---===;--:
==+==+==----+=:,,,,:,,:::;;;:;:,:====++++*%%S%SSSSS#############S##S#S+-=-==;--:
+====+==;::;--:,,,,::::::;;;::::-+====++*?%%SS######################S%=---==;--:
*++====;:,,:::,,,,,,::::;;;--+****++**??%SSS%%####################S+-;;--=-=---;
??*+=-;:,,,,,,,,,,,:::;;;-+******%???%SS#S%%???S###################%;;;--=-=-===
*?**+=;,,,,,,,,,::::::;;=++*****?%SS%%%S%???????S###S???S###########*------=-=+=
==*?*=;:,,,,,,:::::::;;;=+++++++=-%?????%%%%%???%###?????###########S------=-=+-
-===*+;::,,,,::::::::;;;;;;;::,,,,-????%S#?????*?###?????############+----==-=+-
-==-==-;:::::::::::::::::;::::,,,,-%%????%????*??###?????############+---==+-=+=
===--==-;::::;;;:::::::,,:;:::,,,,,-?**?*?**?**??S##????%############=---==+=+++
==--==-=----==-;:,,,:;:,,:;:::,,,,:====+++**?**??S##???%############S----=+*++*+
==---=-====+*+=;:,,::::,,:;::::,,,-=========+****%##??S#############*----==++*+-
==--=====--==;:::::;;::::;;::::,,,;++========+**?%#S?##############?---===++===-
+=-====-=---::-=;:;;;;;;;::::::,,,,-==========**?%#S?S###########S*---=====--===
*+=====-=---:-==;;-;:;--;:::::,,,,,-==========**?S#%?%####S++???+----===---==++*
****+====---::;-:--=-;-;;;:::::,::;-??*======+**?S#?*?SSS*;,,::;;;====-----=+*+*
??*****+====-:::;--++-;;;;-;-;;-=+??%%?======**??#S?***-:,,,,::;;;-===--;;-+*?**
?????****++=-:,:;-----;;;=++?**????+-=++====+***?#?**+-;,,,,,:::;;-----;;-+****?
????????**++=;:::;-;;--=+++?%%%?=;:,,,-====+*?**%S*=-;;-,,,,,:::;;----====+++**?
-+%%%%%%%??**=;::-===+**++%?*+;::,,,,,:--=+=;***S*;--;;=+=;,:::::;;;;==++++++++*
=+%%%%S%*%???+;:=**?%%%++??*+::::,,,,,,,::,,;***%=;;;-+%S%*;:::::::;-=+++++=++++
***?%%%%??++?+:;+%%SS%++?***=::::,,,,,,,,,,,:=+**--=?SSSSS%*::::::;;;-=----===+=
*==+???*??***=;;=**++=++=+++=;:::,,,,,,,,,,,:;=+-*%SSSS%?SS%*;:::::::;;;;;;--===
*++*??*+*****=-;---=+==+**??*+;::,,,,,,,;==+-:+-=%SSS*==SSSS%*:::::::::::;;;----
*=-+?**=*++**===---===+=+*+*?*=::,,,,,,,+***?+*+??%S+--?SSSSSS?=::::::::::::;---
+==+**+=++++*=+==-=+==+*???***;::,,,,,,;**?%%?%S%?%S+-=SSSSSSSS%?+;:::::::::;;;;
+=-=*++=++++*====--===+??*?-;;:::,,,:;=+??%SSSSS%?%S+-%SSSSSSSSS%%?+-;:::::::;;;
+===*++-++=++===--;+==+??**=:::::;-=+*+*%??%S%?S%%SS-*SSSSSSSSSSSSS%?*=;::::::::
+==+*++-++=++=----;===+??**=:::-+++**+*%+%%?=--=*%%+=SSSSSSSSSSSSSSSS%%?*=;:::::
+-==++=-+====----;;====*??*=::=+***++*%+:;;:;::::---?SSSSSSSSSSSSSSSSSSS%%?+::::
+===+=--+====-;;;;:-===*??*=:-+??*+**%*;::,:,,,,::;+%SSSSSSSSSSSSSSSSSSSSS%%+:::
+===+==-==---;;:;;::===+*?*;:+??***???-::,,:,,:,::-**?SSSSSSSSSSSSSSSSSSSSS%?;::
+==++==-+---;:::::::-==+**=,-****?**?=;::,,:,,,::-=***?%%SSSSSSSSSSSSSSSSSS%%=::
=--=+==-+=--;:::::::-==+**;:+*+++**?+;:::,::,,,:-;******??****?SSSSSSSSSSS%%%+::
----==--+--;::::::::==+***;-*+++++*?;::,,:::,,:-;=************SSSSSSSSSSSS%%%*::
----==--=-;;:::::::=+=+**?-+*++++*?--::,,::,,:;;;************%SSSSSSSSSSS%%%%*;:
--;---;;;;::::::::=++=+*****+++++?+;-:,,,::,:;;;=***********?SSSSSSSSSS%%%%%?*;:
;;;;--;;;;:::::::;+*+=+*?**?++++*?;;;:,,::::;;;;************SSSSSSSSSS%%%%%%?+::
::::::;;;;;::::::=+=*=+**+*%++++?=;-;:,,:::;;;;+***********SSSSSSSSS%%%%%%%??+::
:::::::;;;;;::::;++;*****=?%+++*?;;-;:,::;;:;;=***********%SSSSSSS%%%%%?%%??*+::
::::::::::::::::-+*;=***=*S%+++?+;;-;:,:;;;;-=+**********?SSSS%%SS%%%%%?????*+::
;;::::::::::::::=+++:++-?SS%++*?-;;--::;;;----***********SSSS%%%%S%%????????*+::
;;::::::::::::::+++*===?SSS?++**-;;;=;;;---;;=*++++++++*%SSSS%%?%%%????????**+::
;;:::,,,,,,,,::;+++*?%SSSSS%**?+-;;;=--=-;;;;+++++++++*?SS%%%%%??%%?***???**++;:
:::::,,,,,,,,,:-+++*?SSSSSSS%%?=-;;-=+=-;;;;=+++++++++*%%%%????*????*=-=**+++=;:
::::::,,,,,,,,:=+++*%SSSSSS%%%?=----+*=---;;++++++++++??**++++*++***+---=--==-::
::::::,,,,,,,,;=+++?%%%%%%%%%?*----===------++++++++++?+=-;;-====+=-------;;;:::