:;-++++=+==----;;;::-++****+=-==--==*??%??%%%??+??*?%%**?*++*+*+==+=*+*===++=**+
;-=++=====-------;;;;-++***+-;=++==*??%%%?%%%%*+???%?%+?**++*+?+==+++**-=+===**=
;-+=====+=-------=-;;;-=++*+-;++=+*??%%%%?%%%?=?%?????+?**+++**===++*+=-++===**+
-==--====--------+=-=----+*+--==+***?%%%??%?*++*?%??%?+?**+*+*+===+**;-++====*+=
==-;-====--------+=-+++=++*+=-=+**?????%%?%=---+????%****+++****?*+?****=====++*
==;;-=-;::::;----+=-++++****==**???*???%%%*-===+????%+++=;=+??***+???????*==+**+
=---;::::::::::--+=-++++**+==**???**??%%%%*=*+**?%?****=:;=?????+????%%??++****+
=--;:::::::::,:;-==-++++?+=+**?????????%?+****???*+++*??**+?*??**??????+=*%S*+==
==-:::::::,,,,::=+=-+++*+=*?%%%??????%%?-=***???%%??+**%?**?**?*%%%SS*=*%SSSS?+*
==-:::::::::,:::;--=++***?%%%%%%???%%%?+=++*??%%?%%%***?+**???*?%SS%+*%SSSSSSS%=
==-;;;-;:::::,:::::;=++*?%%%?%%???%%%?***++*??*S%%%%*???***?%%%??%?+?SSSSSSSSSS+
===--===--::,,,,::::;=*?%%%?%%%%%%?????%?**?**=??S%???????*%%%%??*?SSSSSSSSSSSS?
===-=++=--;:,,,::,::;-*%%%%%%%%%%??****=????????%**?%%?%%?%%%%S%?%%S+==+%SSSSSSS
===-=--:::::,:::::::;;=%%%%%%%%%??*****+%*****+?S%?****?*+=*%S%%%%??+-=**?SSSSSS
+==-:::::,,,,:::::;;;;-*%??%%???????*?%??*??%+*?S%?%%%?*=+**?%%%%%%?+=*???%SSSSS
+=;::,,:,,,:::::;;;;;;-*%%%%?**??*????%??%%S%+*???**??%+****?%%?%S%%*=????%#SSSS
-;::,:,:,,,:;;;;;;;;;--?%%%?**??????+=+?%SSS***%*******+*????%SSS#S%%?%%?%%##SSS
:::,,,::,,,:;;;-------+%%???++??***---+??*==**?%*******?????%SSSS##%%%%%%%S###SS
::::::::,,,::;;---=++*%%?+++=+??*?==+*?%*--*??%?********%SSSSSSSSSSSS%%%%S####S%
:::,:::;::::::;---+?%%???*+=+++???+**?%%+---+?S*********?%%?%SSSSSSS#########SS*
:::,::;;;;;;;;;---+??????*++=+??%?***?%?=----+????******???*?SSSSSSSSSS#####SS**
::::::;;;;;;;---=**?%???*+***?????%??%?+------*%?%?*****???*?SSSS%%%SSSS####%++?
;;::::;;;;;;;----=--+???**??????%%%%%+------===?S?%%???*???*????%SSSSSSSS#S?????
===-;;-;;;;;;;;;;;:::;+??????%%%%%%%?----+**=--=?S%%%%S???%??SSSSSSSSSSSSSS%?%%?
-=+++*+-;;-;;;;;;;::::;*???%%%%%%?%??--+?*------=*%S%%%?%?%??SSSSSSSSSSSSSSS?%%%
;=+***++----;----::::::;-+%??????????-=**+-=+**+-++?SSSSSSSSSSSSSSSSSSSSSSSS%%%?
-=***++===---==++-;;;;::::=*????*+=-+--+?%SSS%S+-=++%%%%%SSSSSSSSSSSSSSSSSSS%%*?
;;-==++++--++**++++++=::::;+*??=--;;==--*%#=-*=---++?S%%%%%SSSSSSSSSSSSSSSSSSS%%
-;;::;=--=++****+++=;;::::;=++=;;=*??----+?*+=----++*#?%%%%%SSSSSSSSSSSSSSSS+??+
+=--:;-==-==*+++=-;::::,:::::;;+**??*-----====----++*S*+???**###SSSSSSSSSSS?=*?*
===-:;---===*++=:::::::::;--;-+?%???------====---=+++S**???+%#########SSSSS==+??
=++=;::-+++=++=;:::,:::;-+*+*???%?*-------====---+++*S*%?*+?########SSSSSS?-=+*?
==++=;:--=+=+--;::::::=+*??**?????=-------===---=+++*%*+++?SSSSSSSSSSSSSSS=-=++?
==+=-:::::;;=-=-;;;;::=++?***??????*------------++++?*+*?%#SSSSSSSSSSSSSS*=-=+++
=====-;:,:;-+++++=+-;:;-=++**?????*?------------+++***+??*##SSSSSSSSSSSS?==-+++*
=====-:::;--+++++++*+=;--==**?*?????=----------=+++*++**?*S##SSSSSSSSSS%===-+++*
===-=;:;==-=*******?****+=*????%%???*?+--------=++++++-*??%######SSSSS%+-==-++*+
===-=;=%%%%????????????+-*%%%%%**?**++=--------=+++++++????S##SSSSSS%*==-==-++*+
===--;+SS#SS%SSS%%%%%?+-+*????*=??**+*=--------++++++**??%**#S#SSS%*====-==-=+*+
=-=--;-+*+==*++++++**+-+**+++*++??*?++=--------+*+++++*??*++S%%%?+====+=-==-=+*+
=-==-;;-+=--++=++++**==**++++*+?????+++-----=+*+++++++++++++?==+-=+=====-==-=+*+
====+;;-+=--*++++++**=+***+++++?????++**++**+*?+++++++++++++*+=+==+===++====++++
+****+--+=-=*++++++**---=**+*++?????+++????*+=+?+++++++++++++*=+======++====++++
=+***+--+=-+*++++++?-=++++++?++*???*+++?????+++?=++++++++++++?**++*+========++++
--+*+=;-==-=++++++=-=**+****+++*???*+++?????+++?--=+++++++++++++++****==-=+=+++*
-=***+--=--=+++++++-==--=+**+++*?*?*+++????*=++?+--=+++++*++=+*******??*-====+++
-=**++=-==-=+=++++=--=*******++*?***+++????*=++++---=++++=+***********??*====++*
=+***++=+=-=+=+++++=+*++*++++++*?***+++????*=+==*----=-=+************???*-+=+*+*
+****++++=-=+=++++++-=+++++++++*??**++*?*??*=-++?---;;--+**************?+-==+*=*
**???*+++=-=+==++++?--=++++++++*??**++*???*+:+**+-;;-----=+*********?**?--=-=+=+
??**??**+=-=+--++++?=--=+++++++???**++**??+:=**+=;---------=*******?**?*--=-=+==
*?????*++===+-=++++**---=+++++*???**+++*++;;**=;------------=******???%+=-=-===+
*****?**++===-=++++***---++++*?*??**+++===:=*-:------------=**????%%%??*+==-===+
*****??++===+=++++=***+--++++***??**++=-=;;*;;-----------=*??*******?%??****++++
*******++===+=++++=****--++++**?%?*+-=-=;:-;-----------+**+=--====+***?%???**?**
*****?*+===+*+++++=**+*--=+++**???+-=-=--:-=---------=**+--====--==+****??**???*
*****?*=--=+*+==++=*++*--=+++**???=+--=;-:=--------=+**=--=+=++-=+=*****??**%???
*******+=-=+*+++===++++--=++*+*???+=--;;-=--------+*?*=---===++==+++*?*???*+????
******=-=-=+*+++++++**=--=++*+*??*+--=:-+--------+*?+=-=+===*+==++++*?%?????+++?
+****=----+**++++++**+---=++*++***=--=:+-------=***+=-+?++======++===????%?%++=+
-+***--;;;-=++++++=**+---=++?+++-*--=--=------=**+++=+??--==+++++++=?%?%%?*??+++
;-??+;-;;;;-=+++++=**+---=++?*+-=*=-+-=------+**=-+=+??+---=+=--=++?**??%%????+*
==??+=----;;;--====**=----++%+--++=-*+------=?+=-+++???=-------+=+**????%????%?%
-=++++++=--;-;;-=-++?-----++?--+*+**?+-----=**=-=*=*??*----++===+?++*?*%?%??%?%%
;---==+==---;-;;;+=**----=++%+-*??**?-----=*+===*+=*??---==+=-=+****?****?%???%%
;--;---=-----;---==**----=++%?+*%?*?=----=**--=+?=*??=-=+==+==*?**??????*?%????%