:::::::::::::::c:::::ccccccccccccccccccccccccccccclllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllccccllccccccccccccccccc::::::::
:::::::::::::ccccccccccccccccccccccccccccccccccclllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllccccccccccccccccc:::::c:c::::::c:::
::::::::::::::::cccccccccccccccccccccccccccccclllllllllllllllllllllllllllllllllllllllllllllllcccccccccccccccccccccccccccccccccc:ccc:::::::::::::
:::::::::::ccccccccccccccccccccccccccccccccccccccccccccccccccccccccclllllllllllllllllllcclllccccccccccccccccccccccccccccccc::::::cc:::::::;:::;;
;:::::::::::cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc::cc::::::::::::::::;;;;;;;;
;::::::::::::cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc::::::::::::::::::::;;;;;;;;;;;
;;::::::::::::::::ccc:ccccc::ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc:::::::::::::::::::;;;;;;;;;;;;;;;;,
;;;;::::::::::::::ccc:ccccccc:c:ccccccccc:c:::::ccccccccccccccccccccccccccccccccccccccccccccccc:ccccccc:::::::::::::::::::::;;;;;;;;;;;;;;;;;;;;
;;;;;;;:::::::::::::::ccccclc::::::::::::::::::::::::::::::ccc:::c:::ccc:::::::cc:ccccccccccc::::::::c:::::::::cccccc:;;::;;;;;;;;;;;;;;;;;;;;,,
;;;;;;;::::::::::::::::cccllc:::::::::::::::::::::::::::::::::::::::::::::c::::cc:c::::cccllllcccccccllloocldoddxxdddolc::;;;;;;;;;;;;;;;;;;,,,,
;;;;;;::::::::::::::::::c:cc:::::::::::::::::::::::::::::::::::::::ccclcc:::::cllc:clllooddddooooddddddoxkooooddddoooooc:;;;;;;;::;;;;;;;;;,,,,,
;;;;;::::::::::::::::::::::::::::::::::::::::::::::::::::::cc::c:,,;:::::;;;c::::::::ccooodxddodxOxdoodoxxoxdxollcc::cc::;;;;;:;;;;;;;;;;,,,,,,,
;;;;;;;;;:::::::::::::::::::::::::::::::::::::::;:::::c;;;::;;:::;',;:cc:;;:c:cc::c:clcccccooccll:lllddooloolllooolcc:,,;,;;';::::;;;,,,,,,,,,,,
;;;;;;;;;:::::;;:::::::::::::::::::::::::::::ccccccc:cc,,,;,;;,;;;;,';;c:,;:::;:::c::c::::::clccc:ccodolloxxdk00kxdolc,'',''',:c;;;;;,,,,,,,,,,,
;;;;;;;;;;;;;;;;;;;::::::::::::::::cllcloodoooll;,,'',,,,,,;;;;;;;;;;,;l;;:::;;;:::cccccc:cdk0Oxooddcccc::clcoxOoxklcc:,''''',lc:;;;,,,,,,,,,,''
;;;;;;;;;;;;;;;;;;;;::::;::;::cldxdodxdllllc;,,,.',,',,,,,::,,,,;;',,,;;;::::;;;;:c::c:c:;:clodolcc::::;:::c:::::::cc:;;,''''c:;;;::,,,,,,,,,'''
;;;;;;;;;;;;;;;;;;;;;;;;;;ccldOO0Odoodxoc;'','..'',,,',;:clc:;,;,;;,;;:;;::;;;,:::::;:cc;,:ccccc;;;;;;::;;;;::;;,;;::;;;;;'''c;;:;;;,,,,,,,,,'''
,,,;;;;;;;;;;;;;;;;;;;;:::ooo0kdxkkxxdc;,''''..',;,,;;:lcloldolololldoo:;;;;;;;cc:::;::;;;:::cc:,:c:::;;;,;:cc;;;:;;;;;;;;;,'cc,:;;,,,,,,;c:,'''
,,,,,,,,,,;;;;;;;;;;;;:ccllod0kkxdlc:,'',......';;,,,,,;;:c;cccollcldlooc::;;;:::;:;::;;:;;:;::;'::cc:::;;;::;::;;;;;;;;,,;,',::;;;;,,,;xXNXko:,
,,,,,,,,,,,,;;;;;;;:cllldxdk0XOocc:,''.........'cl;,,,;;;;;;;,;c:;;clloollc;;;;;;::::::;;,;:;::,,;;::;;:;;,,;,,,,,,,,,;;,,;,,'.;c:;;,,,lxOOxoc;,
,,,,,,,,,,,,,,,;;;:c:cloKNNOdoc::::'.........',;ldllodoc;;;;::;:::::;,;c:;;;;:c:cddoc:;,;,;:::;;;::::,;;,,,'''',,,,,,,,,;;,,','.':c;,;,,;;;;;,''
,,,,,,,,,,,,,,;:::cdllxOOOkxdolc:;''........':lolooodklcclllcc:;:::;;;:c:::;;;;;clco:;;,,;;;:;;::::c;;,,,,''''''',,'',;;,,,,,','.,c;;,,,,'''''''
'',,,,,,,,,,,;;::::coxOxxxkkdlc::c'.'''''...::;;;;::::;;':c:,',,;;;;;;;,;::;;;:;;,;:;;:::;;;;:::;:lc;:;'''''''''',,,,,;::'',,',..'c;;,,''''''''.
'''''''','',;;:::::coxddkxdodollc;....''''''::;;;:::;;,;;;,,,',,;:c:,,,;c;;;;;;,;,,,;;:ccll::::;:cl:;oc''',,'',,,,;,;,;;;,'.,...':x:;;,,''''''''
''''''''',,;;:::::ccckxxxddddllc'.......'',;;;;;;;;;:;;;;,'',,,;::;,''',;;:;,,,';:;,lolloddlc;;;::c::;,'''',,,,,,,',;,';,'.'..;oc:c:;,,,''''....
''''''''',,;;;;;;;;;;:oxdooolc::'........;:;;;;,,,,,;;;;,;;,;::;;,''''''';,',,,,;;:;;;;;;:ldd:;;;;;::;,'..'''',,,''..'.....;clo:,'''''''''......
''''''',,;;;;;,,,,,,;:dklc:;::'''.......'oc;,,,'',',;;;;;;;;;;;,,'''''''',,,,,;;;;;,,,;;,;c:cl:;;;,,''''''.',,...''.....';cl:,''................
...'''',,,,,,,,,,,;;cxdc:;;::,.........'';:;,;;,;;,,::;;;;;;,,,,,,'','',;;;,,,,;,:;,,,;:;;::;;;,'',,''..''...',...'...':d:'.....................
..'',,,,,,,,,,cl::ldolc::c:;;;'....'....'.',,,,,,,,,,:c::;:;,;,,,,,,,;;;,,;::;;;:::;,;:::cxc;;;;,',,,'''..''........;c::,.......................
.'''''''''''',cxkdocclc:c:;,;;,,.......'',,,,,,,,,,,,,,,,,::;;;,,,,,,,,,,;:::;,,;:clc:;;,';;;;,;;,',,,'''.',,'.....,d;..........................
''''''''''''',;OOlc:llcllc;;:;;c:'....',,,,,'''',,,'',,,,,,,',;;,,,,,''''',,'...''..''''',::;,;;,,,,,,'','.,'......cc...........................
.......''''''',:odlllollc:::;,:ll:,.',,,,,,''',''','',',,,'',;:;,''''.....''..........'.';;::;:;,,,''''....''.....,c,...........................
........''''''''':ooolloc;c:,:lll:cc::cc;;;;,,''',,,,;;;;;;',,,,''.......'''...........'..,cddkl;.''',''...';'''..:;............................
............''''''';lodollc:ccclollllloooxdo:;;;,,',,,,',,'.',,'.....'..'''............'..'cdONkc'.',,'''...''.,..ol,...........................
...................'';lllllllcllooodxxdxkkOl,;;;;;,;;,'..'..','......'..''...........'..'..;::ko;,'',;...'..'..:lxkc,...........................
.....................',;;;::::cccloddooookxc;;;;:,,,;,,''...,,'....'.'...'.'.........'..''.,:;;:::;;,;'..',...:O:,..............................
.......................''''',',clccllcclldoc:::::c::;',,',,,;,,,'',,''''.',,,.....''.''.''.;::,;c;,;;'....':odx;............................... 
.............................''',:lcc::::lolccc::ccl::,,,,;';;',;,,;;''''';:,.....''....''.::;;;;;,;c,.,::xl;'...........................  .   .
.................................',:::c:;:oxdlcllllllc';c:;;:,;::;,;:;'.'.;c:''..'......'.':;;;;;;:ddlcdc,..............................        
..........................................':cccoxoccl:,c::;:c;lc:;,:cl;'.,::::;,','...:lolc:::::,'',,,c;.............................           
...............................................':;:cc::c;cllclc';:;cllc;,:c;;;;;''.,,''................''........................ ..            
....................................................''';;clllc:,;;;::;;;,;:cc:cc:;';'...........................................                
        .................................         ........;l;,;:,,;;;,;::,',,,'............................................                     
           . ................... ...                     ..  .... .. ....................................................                       
                         ......                                                 ...  .............................                              
                                                                                        ......   ....   .......