################W##WWWWRt=;;;;==:::::;:.,::.,,,,,::::;==;;=;;;;;:,...,,,.....:;=+i+=+====;;;==+i
################WWWWWMRt;:::;;:,=;::,.......,,,,;:::;;:,,,,;;:,,.,.....,,:,,:;=+ttt+=;::;;=;;===
################WWWMBVt======;;,;;:;:,,...,,,,:;,,;=;:,..,;;::........:;++i+++itIYYIt+=;:,;;;==;
#########WWW###WWWRIi+===+=;:,,.............,,,:;:;:,,..,:,,,.......:;+tIYYYYVVVXVVVVYIi=:,.,:::
#########WWW#WWWWXi==;:;;;::,::,,,...........,,,:,,,,,:,,:,,....,,:;=iIYVXXXXXXRXRXXXXVVIt=:,.,,
#########WW#WWWWRt==;=;;:::,.................,,,.,,,,,::::;=;==++ittIYVVVVXXXXRRRXRRXXXXVYt+;,..
#########WW##WWRt++:,,::::........,,;;;:,,::,,,.,,,,..:;==iitIIIYVVVXXXXXRXXXXRRRRRXRXXXXXYIi+,,
#########WW#WWWV+=:,,,,,,,......,,;;;:;=:;::,,,,::....,;+tittIYVVVVXXXXXXXXXXXXXXXXXXXXXXXVVYt+:
##########WWWWMXi+=+==:,.......,::,...,;;;=;;;;=::....,;ittIYYVVXVXXXXXXXXXXXXXXXXXXXXXXXXXVVYI+
#########WWWWMYi=:::::,.......,:.......,::;;;;:;::....,=itIIYVVVVVXXXXXXXXXXXXXXXXXXXVVXVVXVVVVI
WWWW#####WWWWRYi=:,....................,,::::;:,:,:,:;+tIYYYVVVXXXXXXXXXXXXXXXXXXXXXXXXXVVXXXVVV
WWWWWWWWWWWMRVti;:,...............,..,,,,..,:::::::;+iIIYYVVVXXXXXXXXXXXXVVXXXXXXXXVXXXVVVXVVVVY
WWWWWWWWWWMBRYt+;:,,,,,.......,,:,,..,,,:,,:====+iitIYYYVVXXXXXXXXVXXXXXXXXXXXXXXXXXXXXXVVVXVVVV
WWWWWWWWWWWWRI+=;:........,:::::,....,:::::;=++iIIYYYVVVXXXXXXXXXXXXXXXVVXVVXXXXVXXXXXXXVVVVVVVV
WWWWWWWWMRXVIt+=::,.........,,:,,,,,.,,:::;=itIIYIYYYVVVVVVXXXXXXXXXXXXXVXVXXXVVXXXXXXXXXVVVVVVV
WWWWWWWWXRRYi=::,,,,,..,,.,,,:::;;=;:,,:;=+itIItYIYIIYYYVVVVVVVXXVVVVVVVVVXXXXXXRRRXXXXXVVVVVVVV
WWWWWWMBXYii==;:,:::,,:,,..,,:;;;;;;;==+i+iii++++===;;=++iittitIIYYYVVVVVVXXRRRRBRRXXXXRXVYYYYII
WWWWMBVIYYt+=;;:==;:,.,,...,,:;===+ittitiIIYIIYYYIIi=;;;,::;;====iitIYYYVVVXRRRXVVYIIttt+====;;=
WBI+ttti;;+ii=+=;++;::::,,.,,:;=ittItItiIIYIIIYIIIIttii++i++iiii+++iiitIYYVXXXVYIi===:::;:;=iIIY
MXIYIii+=;=;=;;;:;++++==;:.,,;itIIIIIIIIIIIttti+;:,,.....::;==ittittIttIYYVVXVYItiiii+===+=+itIY
VXYi+====;=;===;;:;=====::,,;+tIIIIIIYIYIttt+=:..,........,:,,;+iitttIYIYVVVVVYti+:.....:,..:=tI
WMYi++==+====:;:;===+++==:,;+tIYYIYYYYYYYYItt+;:;+i;....,tRV+;::=+iiIIYYVXXXVVI+=,.....+XBY=::iI
BVtt++====;;;::;::::=+iit+=+IYYYYVVVVVVVVVVYYItti+=;:,,:+tIi+=::=iittIYVVXXXXVt+:::...iRMRt+iIYX
RVtIi+=;==;;,,,,,,,,:=ttIVYtIVXVVVVXXXXXXXVVYYYIIItiii+i++ii+iiittIIIYVYXXXRRVIti+===;=++;;+IYVX
RVIt+;;;;;;::,,,......=YVVYIYVXXXXXXXXXXXXXXXVVYYIttIttitttttItIYYYVYVVVVXRRRXYYttiii+iittIYVVVX
XIti=;===;;:..,........iYYIIYVXXXXXXRRRBRRRRRRXXXVVYYYYYYYYYVVVVVXVXVXVVVXRRRRXVVVVVYYYIYYYVXXXR
RVXVi:::=:,............,YYttIYVVXRXRRRRRRXRRRRRRRRRXXRXXXXXXXXXVXVXXXVXXVXXRBRRXXXXVVVVVVVXXXXXR
RVYIt+;:,,..............,+IIIVVXXXRRXRRRRRRRRRRRRRRRRRRRRRXXXXXXXVXVXXXXXRRRRRRRXXXXRRXXXXXRRXXR
RRRVi:,,..................=t=IVXVXXXXXXXRRRRRRRRRRRRRRRRRXRXVVVVVVXVXXXXXXRRRRRRRRRRRRXXRRXXXXRR
MBRXt:,...................;i;iVXVXXXXXXXXXRXRRRRRRRRRRRRRXXXVVVYYVVVXXXXRRRBRRRRRRRBRRRRXXXXXXRB
XIiii=,...................;t;=YVXVXXXXRXXXRRRRXXXRRXXXRXXXXXVYIIVXXXRXXXRXRRRRRRRRBWMRRRRRRXXRRR
IVIii;,.......,,..........;t:,iVXXXXXXXXXXXXXXXXXXXXXXXXXXXXVYIIYXXXXXXVVVVXXRRRXRBMBRRRRBRXXRRR
IRRVt+:,,::::::;:,,.......:i:.;YVXXXXXXXVXXXXXXXXXVXXXXXXXXVVVVYIYYVIIItIYYVVVVXXRBBBBRRBBXXRRRR
MXItIXRVt+++i=::;:,.......:i:..+VVVXXVXXXXXVXVVXXVXVXVXXVVVVVVVYYYIIttIYIIIYYVYVVXRBBBBBRXXBBBMM
BBBBBBBXVI+++=:;;;;............,tVVVXXXVXVVVVVXVVVVVVVXXVVVVVVVVVVYVYYYVYYXXXVVVVXRRRRRRVIIVBMMB
WWWMMMBXYtitt=:+i+:,............+YYVVVVVVVVVVVVVYYVVVVVVVVVVVVYYVYVVVVVYYYVXVVVXXRXXXXXXRBRXYt=:
MMMMMMBXtiii++=+;,..............;IIYVVVYVVYVVYYYVYYYYYYIYIYYYVYVYYVYVVVYYYYVVVVVVXXXXXXBWWWWWW#M
WWWWMMBRYYIttIt+................,+tIIIYYYVYYYYVVYYYIIttti++iIIIIIIIIIIIIYIIYIItitIVVVXMWWWWWWWMV
WWWWWWMBXYVYi==:,................;itttIIIIYIIIYYYYIIttttIIiitItttItttttitttIItIYVVVVRMWWWWWWWWX+
WWWWWWWWRXXVt===;.................++tttIYIIIIIIIItIIIIIYIIIIIIIYYYYYYYYYYVVYYIIIYYVBMWWWWWWWMV=.
WWWWWWWWWMVIt+:;,,................,=+tttiitIIIIIIIIIIIIIIYYIIIItIIYYYYYYYVYIIYYYVRRBBMMMMMMBI;..
WWWWWMRItItittitIti;:...............,:=iiiiiittttIIIIIIIIItIIIIItIIttIIIIIIYYYYVRBBBBBBBBRXt:...
MBXtiYXRBRXVYYYYVVI+:,.................,++iiiiiittIItttIIIIIIYIIttIIIIIYVVVXVVRBBBBBRRRRXV=,....
iiVBMWWWMMBRRRBRRRVI=:,.................;+=iiitiiiiiIIIIIIIIIIYYIIIYVVVVVVVVVRBBBBBBRRXXt:......
BWWWWWWWWWMMMMMBBRXYt+;,...............::;==++iiiiitiittiIIIIIYYYYYYYVXXVYVXRRRRRRRRRXVi,.......
WWWWWWWWWWWWMMBBBRXVti+;,..............,:====+++iitIItiitttttIIIIIIIIYVVYVXRRBBRRRXXVI;.........
WWWWWWWWWWMMMBBRRXXYIi+;;:................;=+++iiitIIYYVYIiiiitttttIYYYVVXXRRRRXXXXY=,..........
WWWWWWWMMWMMBBBRRRVYItii+==;;:,............,==+titIIYYYYVXXXVXVVVVXXXVVVVVXXXXXXYYi,............