;;;;:::::::::::::;;;;;::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
;;;;::;;:::::::;:;;:::::::::::::::::::::::::::::::::::::::::::::::::::,::::::,::::::::::::::::::::::
;;;;;;;;;::::::::::::::::::::::,,,.......,,,,,,,,:::::::::::::::::::::::::::::::::::::::::::::::::::
;;;;;;;;;;,........,,,,,,,:,:,,.. ......,,,,,,,.,,,:::::::::::::::::::::::::::::::::::::::::::::::
:;;;;;;;;;:,,.............................,,,,,,....,,,::,,::::::::::,::::::::::::::::::::::::::::::
:::::::,,,,,......,,,,,,.. .,:................,,,,.....,,:::::::::::::::::::::::::::::::::::::::::::
,,,,,,:,,,,::,,::::;::,. ..,:,. .....,,,,,,,,,,,,,,.,,...,::::::::::::::::::::::::::::::::::::::::::
:;;;;;;;;;:;;;;;i;;;,. .,,,...,;,,:;;;i;;;;:::,,,,,,:,....,,::::::,:,,,:::,,::::,,::::::::::::::::::
;;:::;:,...,::;;;i;,.,,,,..,:;1i;;iiiiiiiiiiii;;::,::,,,....,::,:,,:::,,:::,,:::::::::::::::::::::,,
,,,,,;:,,,,:;iii;;,..,,::;i11iiiii111111111i1iiii;;;:,::,....,,:::::,,::,:::,,::,,:::::,,::,,,,:::,,
:::::;;;;:::::,,,.. ,:;i11i;;iiii111111111111iiiii;;1i:,,,....,::,::::,,::::,,::,:::,::,::,,,:::,:::
::,,,,,,,,.,...... .:;i1i:,:;iii11111111111i;iii;;::111i;:,.....,,,,,,::::::,,::,:,,,::,::,::,::,:::
.. .....,,,,,,.,:i1i::;iiiii11i111111i;;;:::,:i:i111111:... .,,,,,::,,,,,,,,:,:::,,,,,:,:::::,,,
.......,,:::;;;;;:,:i1iii11iiiiii1111111iii;:,,:;i1i;i111111:... .,,,,,::,,,::::,:::,:::::,:::::::::
...,,:;;;iiiiiiii:,iii11i;::::;;;;;;iii111iiiiii11i1i::i111ii,... ,,,,,,,,,,,,,,:,::::,,,,,::,,,::,:
.,,,:::;;;;;iiii;:,;i11iii;:::;::,:;;;;i11111111111iii::111ii;,....,,,,,,,,,:::::::::::::::,,:::::,:
...,,,,::;;;;;;i;:,,i1111ii;:::,,,,:;i;;iiiii111111iii;,;i111ii;,. .,:,,,,,,,,,,,,,:::,,,,,:,,,,:::,
.....,,,:::;;;;;;:,.:i1111iii;;;::;iii;:;iiiiii11111iii;,:i1111ii;,..,,,,,,,,,,,,,,::,,,,,,::,,,:,,,
......,,,:::;;;;;::.,;11111iii:;;iiiii;:;;iiiiii1111iiii:.,i111111i;,..,,,::::,,,,,,,,,,,,,,,,,,::::
.......,,,,:::;;;;:.,;i11111i;,.,:;;;ii;;;;iiiiiiiiiiiiii,,:;i111111i;,.....,,,,,::,,,,,,,,,,:::,,,,
.......,,,,,,::::::,,i11111i;. .,:;;;i;;;;;;;;;;;;iiiii;:::;ii111111i:,.. .....,,::,,,,,,,,:,,::,:
.....,,,,,,,,,::::,::;i111i;,,.. .,::;;;:,::;;;;iiiiii;;;i;::;ii111111i,... ..,,::,,,,:::,:::
.,,,,,,,,,,,,,,,,,:iiiit1ii:,.,,,. .,:;;;:;;;i1111ii;;;;::;::;;iii111ii,... ..,,,,,,,,,,::
,,,,,,,,,,,,,,,,,,:i1111i;:,,.,,,,.... ..,:::;;iiiii;;;::,......:;ii1111i:... .,,,,,::,,
,,,,,,,,,,,,,,,,,:i111111i:............. ..,,::::::;;;;,. .,;ii1111i:.. .,,,,,,:
,,,,,,,.,,,,,,,,,;i111111i,........ .... .,:,,,,::::;;;:. .,;;i111i;:,. ,,,,,,:
,,,,,,,,,,,,,,,,:ii111111;,,.... .. ..:;:::::::;::. ,,::i111;;::, .,,,,,,
,,,:,,,,::,,,,,:;i111111i:.,... .,,:;i;;;;;;:,. ..:;;iiiiii:,. .,,,,,
,:,::,,,,,,,,,:;ii11111i;,..... . :iiiiii;;:, .:iiiiiiii;, .,,,,,
,:,:,:::,,,. .;ii11111ii:....... ,iiiiiii;:. ,:;iiiii;;:,. .,,,,,
:::::,,,,,. .:;i11111iii,..... ........... .,;;iiii;;,. ,:;;;;;;::,,. .,,,,,
:,,,,,,,,. .:i111111i;,. ............. .:;;;;;;;:,. .,::::::::,,,. .,,,,,,
,,,,.... .,,:;;::,. .,,.......... .,::::::::,,. .,,::::,,,,,,. .,,,,,,
... .,, ,,,,,....... ..::::,,,,,,. . .,,,::,,,,,,,. .,,,,,,
... .,:,,,..... ..,,,,,,,,,,,. .. .,,,,,,,..... ,,,,,,,
.. ... .. ... ....,,.................,.. . .,,,,,,:
... .. .. . ..:.. ....... .....,:::::::,,,,,:::::::::::::::::::,,,.........,,,,:;it