RRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRBRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRR
:..................................................................................................................................................................
:.BRVRWWWW#####W#WW###WBW#####W#########WWWWWWW####W#####WWMBBRXVYt+===;;;;;;:;;===+itYVXXRXMWXXXV+:.,:;+IIVRBMMMMBBBM##W####WW#WWWWWWWWWWWWWWW###W##WMBMMMMMMMMMM.
:.RRVXWWWWW###WWW#W###WMWW#####WWWWWWWWWWWWWWWWWWWWWW####WMBXYIi+=:,,,,,,,,,,,.,,,,,,,,:;;=+tt+tI+:,:,:::,.:YRRBBBMMMWWWWWWWWWWW######################WMMMMMMMMMWB.
;.BRVRWWWWWWWW##WW####WWWW#####WWWWWWW##WWWWW#WW##W##W#WMBXYi=:,,..........,,,..,,,,,,,.....,,,,,,,,,.,,,,.:iRMBBMMWWWWWWWW#WWWWW#######WWWW####WW##W#MBMMMMMMMMMM.
:.BRXBW#WWWWWW##WW####WWMW####WWWWWWWW##WW#WWWWW###WMMBXYi=:,,,.........................................,,,:+IXXBRMMMMMMMWMWWW#W###WW##WWWWWW###WWW#WWMBBMMMMMMMMB.
:.BRXBWWWWWW####WW#####WWW###WWW######WW##W##WW###BXIi+;,....,,............................................,;+tYXBRMWWMMMMMMW######WWW#WWWWWW###WWW##WMMBBBBBBBBBB.
:.BRVBW#WWWW###WWW#W###WWW###WWW######WW###WW##WWXi:..,,..,,................................................:=tYRBRMW#WWWBMWWWWWW##WW#WWWWWWW###W#W##WMBBBBBBBBBBB.
;.MRVBW##WWW######W####WWW##WW#WWWW#####W#W##BVt+.,..........................................................:+IVXRBMWW#WWMWWWWW######W##########WWW#WBBBBBBBBBBBB.
:.MRVBW##WWW######W####WWW##W###W#W#####W##RV=................................................................=IYYVRRMMW##WWWWWW##WW##WW######WWWWWWWMBBBBBBBBBBBB.
:.MRVRWW#WWWW###########W###W######WWWW###M;.........,........................................................:tYVYVXRBM#WWMMMWW##WWW#WW###WW##WWWWWWMBRRBBBBBBBBB.
:.MRXBWW###################WW####WWWW#W#WI=.,,.,:,...,.........................................................:+VIYVXRMWWWWMWWW#WWW#############W###MBRRBBBBBBBBB.
:.MRXBWW###########W##########W###WWWW#Rt....,,,,,,,,,..,,,,,,,,,....,..........................................,;IYVXBMWWMWWWWWWWWW###WWW########W##MBRRRBBBBBBBR.
:.MRXRW###WW#######W####W#WW#WWW#WW#W#B;.....,,,,...,..,:::;;;;;;::::,,,..........................................+YBBRBMWWWWW#WWWWWW#WWWWWWWWWW#####MBRXRRBBBBBBR.
:.MRXRWW##WWW######W###WWWWW####WW###R=....,,,,,,,,,,,:;+itIItttti+==;::,,.........................................iRMRBMWWWWW######WWWW#WWWWWWWW####MRXXXRRBBBBBR.
:.MBXRW############W###WWB#WW##WWWW#B;...,,:::,,:::=itYVRBBBMMBBXXVIti+=;:,,.......................................,+RRRBWWWWWW#WWW#WWW####W##WWWWW#WMRXXXRRRRBBBR.
;.MBXBW###WWWWWW#W######WBW###W#WWWBt...,,,::;=:==+IXBWW#W##W##WMMBXVYIti=;;:,.......................................+XBBWMWWWWWWWWWW#WWWWWWW##W#WW##MRVXXXXXRRRRR.
:.WBRBW#####W#WWWW######WBW#####W##Y:...,;;=+ittIIYRMW#########WWWMBXXVYIi+=;::.......................................;XBWWWMWWWWWWWWWWWWWWWWW##WWW##MRYVVXXXRRRRX.
:.WBRXW#####W##W##WW####WBWW###WW#WI...,:i+iIYVXRRBM#####W#####WWMMRRXXVYIti=;;:,.......................................tWMBMWWWWWWWWWWWWWWWWWWWWW##WBXYVVXXXXXRRR.
:.MBBVWW####WW###########MW#######W=..:+tYYVRBMMWWWW##########WWMMBRRRXVYItti++=;:,......................................;XWWMMWWWWWWWWWWWWWWWWW#WWWWBXYVVVXXXXRMM.
:.MBRXMW#####W####WW#####BW####WW##..;+XRRRBMW##########W#####WWMMBBRRXVYYYIiii+=;:........................................IR##WWWWWWWWWW#WWWMWW#WWWWBXVVVXVXXRM##.
:.MBRVMW#####W####WWW####MWW##WW##W..iRBMWWW###########W####WWWMMMBBRRRXVVVYIIti+=;,........................................+WRW##WWWWWWWWWWWWWWW##WWBXVVXVRVYW###.
:.MBRVB##W###W####WWWWW##WWW##W#W#W+.tMWB####W#WWWWWWW##WWWWWWMMMBBBBRRRXXXXVYIIt+=:.........................................YBBM#W#WWW##WWWWWWWWWW#WBXVXXRMRR###W.
:.MBRYB##W###W#####WWWW##WW###W####XiVBMWW###WWWWWWWWW#WWWWWWWWWWMMBBRRRXXVXXVYYYt+;:........................................=WBVMW#W#######WWWWWWW#WBXYRMWWWWWW#W.
:.MBRYX#W#WW#W#W#########WWW##W####MRRBW##W###WWWWWWWW######W#WWWMBBBRRRRRXXXXVVVYt+=:,......................................,M#RWWW##WWWWWWWWWWWW##WBVXW###WWWWW#.
:.MBRIX#W#################MW###W###MRBWW###WWWWWW##WWW########WWWMBBBRRRRRRXVVYYYYYt+=:,.....................................;W#MWWWWWWWWWWWWWWWWWWWWBBMW#MWW#WWWW.
:.MBRIVW#WWW######WWW####MWW#W#WW##WRBW####WWWWWWWWW#########WWWWMMMBRRRRXXXVVVYYYIIi+=;,....................................tMMWWWWWWWWWWWWWWWWWWWMMW##WMIW####WW.
:.BRXtVM####WWWW####W#W##MM####W###BBWMW###WWWW##WWW##WWMMMMMMMMMMBBRXXXXXXXXVVYYIIItti=;:,.................................,R#BMMWWWWWWWWWWWWWWWMMW#W###WVRMW##WW.
:.MRVtIB####WWWW#W#WW#W#WWR###WWW##VRMMMWWWWWW#WWWWWWWMBBBRRXXXXVVYItiiittIYYYYYIIIIItti==;:,...............................i##MMMMWWWWWWMWWWMMWWMMMW####BWWWWW###.
;.BRVtIBW####WWW#####W###WRW##W##WRtIVYXBRRBMBMMMMMBBBRXVVYIii+==;::,,,,:::;==+ittIIIItii+=;::,............................tM#WMMMMWWWWWMMWWWMWWWMMMMW##WMW##W#WWW.
:.RXVitRW###WWWWW#WW####WMMW#####Bt..::=iiiIYXRRBBRRXVIt+=;:,..................,;=+ittttii+==;:,.....................,....:BWWWMMMWWWWMMMMMMMMMMMMMBBM###W#WWW#WWW.
:.XXYiiXBWWMBMMMW#WWWW#WWMBBW#WWWY=........,=tVXVXXVYt+;,............,,:,::::,,,,,:=+itttttii+=;:,.................,,it:..+MWMWMWWWWWMMMMMMMMMWWMMMBBMW####WWWWMMM.
;.XVY+iIXRRXXXXRBMMMM##WMBXVM#W##V+++=;:....,;+IYXVYti=;,,...............,,,:::;;;;;==+iitIItti+=;,..............:,,,.+I=.=W#MMMMMWWMMMMWWMMMMWWMMMMWWMWW##WWWMMMM.
:.VVI+=IVXRXVVVYIYIYXXBBBVYVBM#WWRRI+;:,,..,:;;iIBYVIi+;::,,........,,,........,,:::::;=ittIIYIIt+;,.............:;;,..VY..MWMWMMMMMMMMMMWWMMMMMMMMWMM####WWWMWWMM.
;.YYIi;tYVVVVVVYYVIVIIYXXXYVXRMMMRXt;....;+:,..;tMBXVIt+;:,,.......=RXIt+;:.......,,:;+ittIIYYYYYt+;,............:;=:.,Ii..RWMWWMMMMMWMMMWWMMMMMMMMMYX##W#MMMW#WMM.
:.tIti+iIYYYYYYYVVXYYIIIYVVXRBBBBRVYi=:.;tMVV+..iW#MRVIi=;;:,......iMBVYt+;,....,:;=+tIYYYVVVVVVYIt=,...........,,:+;,=I+..RWMWWMWWWWWWWWWWMMMWWWWMMXRWWMWMMMW##WM.
:.+++iitIIYYVYYYYVVVYYIIItVXRBBMMMMBBYt,+IWYYi:,IW##MXYItii+=;;;;:;iIYIi=;::,::;=iiIYVXRRXXXXVVVYIt+:,....,,.......+=;i=...X#M#WMMMWWWWWWWMMMMWWWWWMMMMMWWMBM##WWW.
;.++=+tIIItIYYIYYIVYIIIIItIIYVXBMMBBRXYii=I++++IB##WBXVYVYItiitii++=====;:;;==+iIYXRRBBBBRRRXXVVYYIi=;::;=+;,.....,;;=i,...XWMWWMMMMMMMMMMMMMMMMWMWMMMMWW#MMBMWMMW.
:.++iIYIYIIIYYIIItXVIIIIYIIIIIYVXRBRBRRVIi+i+tVBW##MRRRRRXXVVVVVYYIi++==++itIYVXRMMMMMMBBBRRXXXVVYIti+==++i=;,..,.;;=;i...=RMMWMMMMMMMMMMMMMMMMMMMWMMMWWW#RWBRWMXW.
:.itIYYYYYIIIIIIItIIYYYYIYYYYYYIIIiXBMWMXVIYVBW###MBRBBBMBBRRBMMMBRXYIIIYVXRBMMWW#WMMMBBBRRXXXXXVYYIttiiit+;,,,.,,i:=i;...YMWMMBMMMMMMMMMMMMMMMMMMWMWWB#W#RWMW#WMW.
:.IYYYYYYYIIYiIIYtittYYIIIIIYYYYYt=VM#WWMBMMW####WMRRRBRBBBMBM####WMMBBBBMWW####WWMMBBBRBRRRXXXXXVVYYIIItV,:.,+;,:::It...:BXMBMMMBBBBMMMMMBBMMMMMMMRMMVW##WMMWW###.
:.tIYYYYIYYItitIYYttIIItttIIYYIIIY+RWWWWW######WWMBRXXXXXVVXBMW######WW######WWMMMBBRRRRRRRXXXXXVVVYYVVVIX,.;i++:,=V+....VBRBMMBBBBBBBBBBBBBBBBBMBMBMWMW#WMMWMMW#W.
:.ttIIIIIYVItttIIIYItIItttIIYYIIIYiXW#WW##WWW##WMBRRXXXVVYIIIRWW###########WWMBBBRRRXXXXXXXXXXXVVVVVVVVVVV=.:;.;XYV=....=WRRBBBBBBBBBBBBBBBBBBBBMBMRW#W##WMW#WWMWW.
;.ttttIIIYYIIItttIVIitIYYYIIIIIYIIiX#WWW#WWW###WBRXXBBBRXVIt=iRWWWW########WWMBBBRXXXVVVVVVVVXXVVVVVVVVVYY,,;VX==YV....=V#RBRBBBBBBBBBBBBBBBBBBBBMRB##WWWWWM##WVRM.
=.tttIYItIIIYYYIIYYYIIYYYYVIiiIIII;X##WWWMWW##WMRVVXBMMBXVIi=:tWMWWW##WWWWWWMMBBRXVVVYYYVVVVVVVVYVVVXXXVYt.;=IYI+Y....=VXRRRRRBRRRBBBBBBBBBBBBBBBBBMW#WWWWWWWWWXVX.
:.YItIIIYYYIIYVVYYYVYIttYXYIiiiItI+XWWMMMBBMMBBVVtIIYYYYItt+;.=BM#MMWWMMBBBBRRXXVVVVYYYYYYYVVVVVVVVXXXRVI+:=+iYX+,...=XBXRRRRBBBRBBBBBBBBBBBBBBBMBBMWWW##W###W#WBR.
:.YYti+tIVXYIYVYYYVVVIiIVRVYYIItt+YXMBBBBBRRXYIItt+==;;;;;;,:,iBBWBMBBBRRXXXVVYYYYYYYYYYYYYVVVVVVVXXXXRVI=+iiit+,....=BBRRRBBBBBBBBBBBBBBBBBBBBBBBBMWWWWWWW####WWM.
;.IIItittYVVYYYYYVVYYYYYYYIttIIIt+=IXMBBBVXXXXYt+:;:,..,,..,;+IXRRRRRRRXXVVVYYIIIIIYYIIIYYYYVVXXXXXXXXXVYtIII:.......;XMRRRRBBBBBBBBBBBBBBBBBBBBBBBMMMMWW#WWW##WMM.
;.IttIIYYYIIIIIYYXYYYYYYItiiiiiii=..t#BXRYXXBMMVi.::,,,::;=itYVVXXXXXXXXVVVYYIIIIIIIIIIIIYYYVVXXXXXXXRXVVYVYI........:tXXRRRRRBBBBBBBBBBRBBBBBBBBBBBMMMWW#WW###WWM.
;.=tIIIIYIYIIIIYVVYIIIYVVI==:::,.,..;BRYVVXXRMBYti+;;;;+itIYVVVYYVVVVVVVYYYIIIIIItttIIIIIYYVVVXXXXXXRRXXVVVVI........;tVXXRRRRRRRRRRRRRBRRRRRRBBBBBBBBMWW####WWMMM.
;.itIIYIItVYYYIYYVYtIYYVVi:....,,,,..iXXVVYYVVYttti+===+iittIIIIIIYIYYYYYYIIIItttttttIIIIYYVVVXXXRRRRXXXXYRVIi:...:::iVVXXXXXXRRRRRRRRRRRRRRRRRRRRBRBXBWW####WMMWW.
;.itIYVYVYYIIIIItiitYVIti:....,,,,,...=XXVYIt+=;==;;;;:;;;;;;;;===iitIIYYIIItttttiitttIIIYYVVXXXXXRRRXVVVVVVYYYt+;++iIVXXXXXXXXXRRRRRRRRRRRRRRRRRRRRRVXBW###WWWWWM.
:.iIVYVVVIiitYXIt++iIi+;,....,,,,,,,...iVRVIi:,:;:.,;:,,:,,......,:=itIIIIIIIttttttttttIYYYVVXXXRRRRXXVYYVVVVYIIItttIYVVXXXXXXXXXRRRRRRRRRRRRRRRRRRRRYIVB#W#WM##WB.
:.tYYRYtii++tYRYtIV+;,,........,,,,,,...=WXI+;+++I:;;:::;;;;;:,:;=++itIIIItttttttttttttIYYVVVXXXXXXXXVVVVVXXVYYIYIIIYVVVVVXXXXXXXXXXXXXXXRRRRRRRXRRRRVYVVRRMMBW#WX.
:.tIVMXtt+ItittttIXi=::,.............,...IRVt+VIiYIIttItti+==;=+iIYIiitIIIttttttttttttIIYYYVVVVXXXXXVVYYVXXRXVYIVYYYVVVVXXXXXXXXXXXXXXXXXXRRRRRRRRRRXVYYIYYVVXM#WM.
;.:iVBRXV+YYYtitIXtt+ii+:,.,:;;::,,:;==:.;IYYYVYtitiiii+==;;==itIIIIttttttttttttttttIIIIYYYVVVVVXXVVYYYYVXXRXVYYYVVVVVVXXXXXXXXXXXXXXXXXXXXXRRRRRRRXXVIYYYIItXM###.
;..,iVXYtiiIYYYIIIi=;=+i;+,;=iiii=;=+ii+;+iIVVVRYti+=;::::;=+itIIIIIIttttiiiiiiiitttIIIIYYYVVVVVVVVYYYYYVVVRRXVVYYXVVVVVVVVVXXVXXXXXXXXXXXXXXXXRRRXXXYIIYIIIIR##W#.
:..,:tVIi++tIIt+=:,,,,::::,,:;=+ii====;;;:=iIVXRXYIi=;;;==++itIIIYYIIIttiiiiiiiiiiittIIIYYYYVVYYYYYYIIIYYVVRBRXYtitRMMBBBVXXXXXXXVXXXXXXXXXXXXXRRRRXXYIIYIIIYBWWWW.
;.,:;;;;:,,,,::,.,,,,,,,......,::=;:,,,,,..,,iXWRRXVVYIIYYYYYYYYVYYIIttiiii+++iiiiitttIIYYYYYYYIIIIIIIIIYVVXXRRXYI;IRMWWWMMBBRRRRMRXXVXXXXXXXXXRRRRXXVYYYYIYVM##WW.
;.,::;::,,,,,,,,,,,,,::,,,,,,,,,,.,,:::::,,,.,+BBMMMMMMMMMBRRXXVVYIItiii+++++++iiittIIIIYYYYYIIIItttttIYYVVXXRXVYYYi+V####WWWWBVBW#MRXVXVVVVVVXXXRXXXYIIYVVIVMBWWW.
;.,::;;:::::::::,,,,,,,,,::,:,,,,,::::::;:,;++iXBMMMMMWMMMMBRRXVYItiii++++=+++++iitttttIIIIIIttttttttIIYVVXXRRXVI+XIitX###W###WRBBMWWMMBRXXXVVVVXXVVVYIYYYYtXWRM#W.
:..,,,,,..,,,,,..........,,,,,,,..,,,,,.;VWW#ViIBBBBRRRXRRRXVVVYttii++++======++++iiiiiiiiiiiiiiiiiiiittYYVVVVVYI=YVV=iBMWW##W##MMBXXM##BBMMBRXXVVVYYIIIYYYtXWBMW#.
;RRXBRXRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRRBRBRRRRRRRRRRRRRRRRRRRRRRRRRRRRBRRRRRRRRRRRRRRRBBBRRRRRRRRRRBBRRRRRBBBBRRRRRRRRRRRRBBBBBRRRRRRRRRRRRRRRRRRRRRRBRRRRRRR