................''''.'''',;ldoooodoooooooodollcclccccccccllllloolodooolloodooodxxxkxxdxxxkkkkxxxxxkxkOOOOOOkOOOO00OkOOkkOK0KOOkOK00O00k0K00KKK000OKXK000000000OKKKK0OOKKKKKK0000K00K0K00000OkkOOOO0OOkOkkOOkOOkkkOOOOkOOkkOkOkxkkkkkkkkkxdxkxollldxooolodooll::ccllllllloooooodddxdddxxddddddooc;;;::;;,,,,,
................'''..''''',,cddddxdodxddxddooolllllllllllllooodddooddooodoxxxxxkxdxxxdkkxkkxxxkxxxxxxkO0OOOOOOO00OOOOOOOOO000OOO00OO0KOK0KOKKK0000KK000O000K000KXKKKO0KKK00000KK0KKK0000000OkOOOkOkkOOOOOOkk0OkOOkkOOOOOkxkkOkkOOOOOkkxkkOkOxdxdodddoldxdoollccllllcccllccllccclooddoddddxxddl:;;;;;;;;,,,;,
...............'......'''''',;coxddddddxdddoooolloooooooooodddddddodddddxddxdOOOOOOxxxkxkkOOkxkxxkOkxxdkkkOOOOO00k0OOOOOK000O0OKK0O0K00KKKKKK0K0KKK00000KKKK0000K0000KKKK00000KKK00KK0K00000kkOOOkkOOOOOOOOO00OOxkO0OkOkOOOOOOOOOOOkkOkkOOOOOkkkkkxdxdooollooollloolcclllloolclllooooddddddl::;;;,;;;;;,,;;,
....................''...''''',;ldddddxdddddddddoododoooddddddodoodxddoxkkkxkkkOOOOOOOkOOOOkOOkkkkkkOOkkxkkOOOOO0OkOOkO0KKKKK0O00000K0KKKKKK0000000K0KKK00KKKKKKKK00KKK0KKX0KKKK0K0KK000000OOkOOkkOOOOkkkkOOOOkkkOOOOkkkkkO0OkkO00O0OkkO0O000OOkkkkxxddddddoooloodolllllloddooooddooodddocc:;;;;;;;;;;,,;,,,
...........................''',,,;ldxdxxddddxdddxxdoxddxxddddxdddxxdxxdxkkkkOOOOkOOOkOOOOO0OOOOOOOOOkkOOkOOkOOOOOOOO00000000KKK0O0KKK00KKKKO0O00K000K00000KKKK00KKK0KKKKXXKKKKKKKKKKOOOKK0OkO0xkkOOOOOkkkOO00OkOOkkOOkxkOOOkkkkOOkOOOOO0000OOxxkOkxkkxxxxddooolodddodddodooloddoxxdxxxol:::;;;;;;;;;;,,,,,,,
................................'',;cdxxxxxxxxxxkxxxkkxxxxxxxxxxkkkkxdxkkkkk0OOOOOOOOO0OOkO000000OOOOOO00OkOOO00OOOO000KKK00KKKK00K000000K0K0000K0000OO000KKKK000KK0KKKKXXXXXKXKKKK00KK00O0O00OkOOkkOkkkkOkOOOxkOOkkOkxkkkkkkkkO0OxkOOOKK000OO000kkOOxxkkdxdooddddxkkxxxddoodxxxkxxxdlc:;;;;;;;;;;,,;,,,,,,,
..............'..................''',;coxkkkxxkxkkkkkkkkkxxxxxkOOOOkkkkxkkkkOOOOOOOOOOOOOkOO00000OOkO0OOOOkkOk0O0O0Ok0KK0000KKKK000KKKK0K00KXK00O0O0KK0KKX00KKKK00KKKKKKKKKKXXXKK0K0K000000OKOOOO0OkkkkOkOkkxOkkkkkkkkkxkkkOkOOOOOk0kO0000K0OOOOkkkOOkkOOkkkdxxxxxxxddxkxddddxxxxxdlc;;;;,,,,,,,,,,,,,,,,,,,
.............''....................''',,ldkkkkkkkkkOOkkkkkkkxxkkkO0OkkkkkkkkkxxkOOOO0000Okkkkk000OkkO0000OOkkkO0O000OOO0K00kOO000OO0000K0O0KKOKXK0KKKKK0KXXXXKXKKKO0KKKXXXXKKKXKXXK00O0OOO0O0O0OOOOkkOkkOOOkkkkkkkOOOOkkkxkkkkOOk0kkk0KKK000OkkkOkk0OOOO0OOOOkOOkkkxxxxkxxxxkxxkxlcc:;;;,,,,,,,,,,,,,,,,,,,,
.............'......................'',',:cdkkOkkOkOOOOkkkkkkkkkOkOOkkkkkkxxkkkOOOOO00000OkOkOOO0kkkO0OOOOOkOkkOOOO000OO00000kO0KK0000KX000K0KXK0KK000KXKKXXKKKKKKKKKKKKXXKXXK0000OOK00XOOOkkOOOOOkk0OkkkkkOkxxOOOOOOOO0OOOkkkkOkOkOOKKK0O000kxkOOOO00000OOkkOOOkkOOkkOOOkOkxdoocc::;;,,,,,,,,,,,;,,,,,,;;,;
....................................''''',,,:lxkkkkOkkkkOkkkOO0O0OOkkkkkkkxxkxOOOOOOO00000k00000OkkkkkOOkkOO00OkkOOOO0OO0000kkOOOkkO00KK00O000O000O00KKKKXXXXXKXXKKKKKKKK00KKKK00O000Ok0OOkkxO0OkkkkOOxxOOkkxkkkOOOOkOkOOOOkOOOOO0O0O00000000OOOOK000OOO00OOkkkkOOOOOkOO0Okoc:;:;;,,,,,,,,,,,,,,,,;;;;;;;,,,
.......................................'''',,,;ldkOOkkxxxkOO00000OO0OOOkxkOOOkkkOOkOO0000K000000OkkkkOOOkkOOO0OkkxkkOOkOO0OkOO0000K0KKXKK0OO00000OOkO00K00000KKKKKKKKKK000O000O0KK00K0O0OkkOkOkkkOxxxxxkOkkkkkOkkkkxkOOOOkkOOOOk0kOkO000000O000O000OOOOOO0O0OxxxkOOOkkkdoc::;,,,;,,,,,,,,',',,;;;;:;;,,,,,,,
........................'...............''',,,,,;codxkkkxkOO00OOOOOO00OkOOOOOkOOOkOkkO00O000K0OkO0OxOkkkOO0O0OOO0Okk0OOOOOOkOOO00K0OK0K000OOO0O00OOO000000OOO00KKKK0K00KK00OxOOKKKK0O0OkOxkxxkkOOOxkkxkkkxkOOOkkkkkxxkkkkkxkkkkxkOOkkOO0O00kkOOO000OOOOOO0kkkkkOOOkdoc::;,;;,,,,;,,,',,,,',',,,;;,,;;,,,,,,,
..........................................',,'',',,;:codxkkOkkkkkOkkOOkkOO0OOkOOOOOOkOOOOOOO00OkOOkxkxxxOOO0OkOO0OOxOOkOOOOkOO000KKO0000OOkOOOOOOOOOkO00OOOOkkOOOO0OO0OOOO0OxkkOOOkkOkOkOkxxxxkkkkxxxkkkkkkkOkkOOkkkkkkkkxxkkkkxxxkxxxkOkOkk00O0OOOO0OO000OkOOkkdc:::;;;,',,,,,,,,,,,,,,,,,''',,,;,,,;,,,,,,
.........................................'''''''''',,,,,:codxkOOOO0O0OkkOkOOOOOOk00OOOOO0OkOOOOO0OxOkkkkkkkkkOkkkOkxxxxkkOOkkO00O00OOOOOOOkOOOOOOOOOkkkOOOOkkxkkkkkkkkkkkkkkxkkkkOkkkkkkkkxxdxxkxkxxxxxxkkkxkkOkkkkkxxkxxxxxdxxddxkkkxxkkkxxkOOO0OkkOkkOOOkdolcc:;;;;,,,,''',,,,,;,,,,,,''',,,,',,,,,,;;;,,,
........................................'''''''.''''''',;;;;;:ldxkOOOkkOOkOOOOOkkO0kOOkkkOOkOOkkkxxxxkxkkkkxxkkkkkkxxxkkOkkkxkOOOOxkOOOkkkkkOkOkkkkOOOxxddddxddxxdddxxkxxxkkdxxxkkkkkkxxxxxddddxdxxxxxxxxxxxxxkkxkxxdddddddooooooooooooooooddddxkkkkOxddoc:;;;::;,,,,,,,,,,''''',,''''''''''',,',,,,,,,;;,,,
.''.......................................'.''.....''''',;;,,,,;lcoxxxkkkkkkkkkdxkOkkkkkxxxxdddxdxdxxxxdxxxxxxxxxxxxxxxxxxkxxxkkkxxkkkkkkkkxxkkOkkkk0Oxdoooooooodxxddodxdddxddddxkxxxxkxxxxxxddddddxxddxddddxxxxxxxddodddoooolllccccc:::::::;::c:::::;:::;,,;;;;,,,,,'''',,'''''''''''''''''''',,,,,,,,,;,;;
...''.....................................'........'''','',,,,,:;;;;;;::::cllcccclllloldoloooodddddddxdddxkddxxxxxxdxxxxxxxxxxkkkkkxkkkOOOkxxxxxkkOkkxollloooooolddddooodxxddddooddddxxxdddxxxxxddxxddddxdddxddddddddooooolccllc:;:;:;,,;,,,,,;;,,',,;;,,,,,,,,,,',,,''''''''''''''''''''''''''',,,,;,,,,,,;
...................................................'''',''''''',,,,,,;,,,;;;;;;;;:c::lllcccloododddoddxxddxxxdxxxxdddxxxxxdxxdxxxxxdxkkkxkxxxxxxkkkxxdoodollllclooodxdxooddxxxxdoddddddddddxxxxdxxxxxxddxdddddodddoodooolcl::::c;;;;;,,,;,'',,,,''',,,;,,,,,,,;;,,,'''''''''''''''''''''''''',,',,,,,,,,,,,;
..............'.................................'''.''',''''',,',,,,,,,,,,,,;;,;:ccccocllcccllooooddddddxxxkkxdxxddoddddddddddddkkxxdkxdxxxdxxxxxxdddooxdoooddxxxxdodxkxddddxxxxdoodoooododxdxxxxxddddxdxddddddoooooollllcl:::::c;,,;,,,,;'',,,'''''',;;;,,,,,,,,,''''',''..'..''''''''''''''',,,,,,,,,,,,,,
................................................'''''''''''''''''',,'''',,,,;:::::::clccllllllclloodddxxxxxkxxodddoodooddddxxddxkkkxxxxkkkOkO00KKKKKXXNNNNNXKOxdlcc:coxxdooodxxddololoooxddddxdddddddxxxxdddddooooooloololc:;:cc:;;;,;,,'.,,',,,,'',''',,,,,,,'',,,'''''''''''.....'''''''''',,,,,,,,;,,;,,,
...............................................''''''''''''''''''''''''''',;;;;::::clo:colcccccooddoxdxxdxxxxxooddoodxOXNXXXXXXXXXXNNNNNNNNNNNNNNNNNNNXKOdl:;;;,;;;;:clxocllodddddoddolodxxdxxxddolloooxddooddddddolollollc:;;:c:::::,'','';,,,,''',,,',,,,,,,,',,''''''.'.''''....''.'''',,,,,,,,,,,,,;;;,;
................................................''''''...'.'...''''..''''',,,,;c::lcloc:lllcloooodddxxxxdxxxddoodddx0NNNNNNNNNNNNNNNNNNNNNNNNNNNNK0Okxoocc:ccokkkxdlc::colcllodxdddxxooooddoddddoooooooddoooddddddoooodollc:;;:;,c::::;,;,,;;,''''''''',,'',,,,,'',''',,''''',''...''''''',',',,,,,,,,,,;;,,
................................................''''''..''.'''.''....','',,,,,,:::c:llllcllllooooxxdddxdddxxdxxdkOXNNNNNNNNNNNNNNNNNNNNNNNNXKOkoc;collllccccclo:cdOkoc:;:olccllodddxddooooolooooddddoodddodoooddoddoooddoloc;::;:::;;c,,;,,;;'''''',''',,,,,,,,,,,,,',''''''.''''''.'''''',,',,,'',,,,,;;;,,
..............................................................'......''',',',,;:clc:llllooollooodddxxxxxxdddxxk0NNNNNNNNNNNNNNNNNNNNNNNK0Okdolc::clllllc:::::cc:lodl:;;::clcccclodxdddddooloooolodooddoooooooooddoooodoolloocllc;;:;;;,,,',;,'.'''','.'''',,,,,,,,',,''''.''''''.'','''''',,,,,,,,,,,,,;;,,,
.....................'..............'.......................'''....''''';,,',;;;:cccoollooooodoodxdxddxxxxxxkKNNNNNNNNNNNNNNNNNNNNNKOkddddoolllllcc::clc:c:cloloddoc:;,;cloolcclllloooddoolodooolooooooooolooddddddddoddoodoloo:;::;;c;;;,;;'''''''''''''''',,,,,,,,;'''''''''''''',,'''',,,'',,,,,,,;,,;;,,
..............''......'...........''.................'......'''..''',,;;:;;,;,,,;c::cddolooododdddxkxxxxxx0KNNNNNNNNNNNNNNNNNNNKOxolodxdddollllcc::::cl::::cooddolc::,;:cclocc:clcclooooooooodoooddoooooooooodddddddddddddoooddolc:::cc::;;:;,''',''''',''''',,,,,'',,'''','''''''''',''''',,',,,,,,;;,,,,,,
.................................''..........'...............'..',,,,,,;;;;,;;;;::clclldloddooddxxxkxxxx0NNNNNNNNNNNNNNNNNNKOxlccccldxxddoolllccccclclcccloodOKkdlc;::cc::cllc:::c:loloodddooooddoooooolooooooddddddddxddddxddoollllcccc:;,,;,,''''.''','''''','''''''',',,''','''''';'.'',,,,,,,,,,,,;;,,,,
.....................''..''.......''....'..................''.'',,,'''',;;;;;:::c:clloloooddddodxxxkkx0NNNNNNNNNNNNNNNNNKOdccc:clcloxxxdddoollcc:coxkkxdxxxxkKXOdlc::cc:cccllccc:ccclcloddooolllooooooolllododddxdddddxdxxxxxddooclll:::;;,,,,;',''''''',,,'''','''''''',,,'',;''''',,'''''',,,,,;;;,;,,,;,,
........''...'......'''..''.'......'....''.................''''..',''',,;;:::;;:ccclloooodddddddddxk0NNNNNNNNNNNNNNNN0kdolcccccclloxxddddoolllcclodkK0OkkxxxkKXOdolllccllcccllllllllllloodddllllodoollolclloooodxdddddxxxdddddoolollcc;,;;,,,,;'''''''''''','',,,,'''''',,'',;;''''';,,,''','''',,,,,;;,,;,,
..........'......'''''''''..''..''''''...'................''.'.''',,',,,;;;::::ccclllolodddddddddk0NNNNNNNNNNNNNNX0xllloocc:::llldxxdddddoollllllok0kxxddddod0KOdoooooooolllllccclclooloodddooooodxoclolllollooddxdxxddxxxddooloooclc,,;;;:;::;;,,,,,''','',,,,'','',,,'',,,;,,,,,';:,,;'''''''''',,,,,;,,;,
......'...''''',''''''.......''..''''..'''...............'..'''''''',,,,,;;;lccllclollooodddxddkKNNNNNNNNNNNNNN0kolcllllllcccclloxkxdddoolllllccoodkkooooodxkOK0OO0000KKKKKKKKKKKKKKKK00O0OOkkxxdddooooddodoooddddxdxxxdxdddododocccc;;:,,;;::::;;;;;;,;;;;;,,,,,,,,,,,,,,;;,,;,,,,c;;;;'''',,''''',,,,,,,;,
.....',,'''',',','''....''.....'',''....'''...........'.''....''',,;,,,;;;;:clloloooolooddxodx0NNNNNNNNNNNNNX0ddollcllolocclcllldkxxxdoolooollcclodxkkO0KXXNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNXKK0Okkxdoooddddxxxdxxddddddddccccccc;;,;;:,,;;;,,::;;,;,,,,,,:;,,,,;;;:::;,;,,,;c:;,;,,,,,,,,,,',,,,,,,;,
....'''''.'',,''',,'''''''......';'''''''..'.........''....''''',,,;;;;:;::cclolloddddddddddOXNNNNNNNNNNNNKkdoddooollllolc;cccodxxxxddxddolloxkOKKNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNXXK00Okkxxkxkxdxddxxxollllllc:c::c:;;;;;;;;;;;;;,,,,,;;;;;;;;;;;;;;;;;;;;:;:;;;:;,,,,,',,'',',,,,,
...'''.'''',,,',;,,,''.'',''''',,,''.''..............''.'..','',,,;,;:::c:ccccooooooddddddkXNNNNNNNNNNNX0xdddddddoolcllod:;;cloxkdddxxxkO0KXNNNNNNNNNNNNNNNNNNNXXXKK00000000O0000KKKKXXNNNNNNNNNNNNNNNNNNNNNNNNNNNXKK0Okxxxxxxxooolllllcllcc:cc:;;;;,,,;:;,,,,;,;:;;;;;;,,;;;::;;,,;;;;;,;:::;;,,,,,,,,;;;;,
...'''',,,,;'','',,,''''','',,,'''''..''.........'...'...'',,,,',;;;;;::c:clclloododddddxKNNNNNNNNNNNN0xddddddddddoolloool::coxxkxxOKXNNNNNNNNNNNNNNNX00OOkxxxoooolccclolollccccccloodxkkkO0000KXNNNNNNNNNNNNNNNNNNNNNNNXK0Okddlclccclllol::c:,;;;;cc:;;::;;;;;;:,;;,,,,;,,;:cc:;;,,,;;:;;;;;;:c:::;;;,;;;;:
'.'','',,,;,'''''',',,'''''''''',''''...'.........,'......''',,,;;;;;;;:::clcllooodddxxkXNNNNNNNNNNX0kxxxxdddddoddddddolclccloxOKXNNNNNNNNNNNXK0Oxxolclooodlldooolllcclooooc:::cllodxxkkOOOOOkxxxxxkk0KKXNNNNNNNNNNNNNNNNNNNNXKOxocccllolcccc::::;;ccc;;::::;;;;;;;;,',;;,,;;,;;::;;;;;;;;;;;;;;;;;;:;,,,,,;
.'',..''',;,''',,,'.',''''.'''''';,,''...'..''.....','....'''',,,,,;;;:::c::cooldooodx0NNNNNNNNNNNOkkxxdxddoddddddxdoollcclxOKNNNNNNNNNNX0Okolc:ccccccloolol:ddoolccllclooolc::ccldxxkkkO00OkxoododdxdxxddkO0KXNNNNNNNNNNNNNNNNNNNX0kdollcc::::cc::c:;,;;::::;;;;:::;;;;;;;;;,,;:c:;::,,,,,,,;;,,,,,;::;;,,;
''''',''',',',,,''''',''''''',',,,,'''''.'...''....',''.''''.'',,,,;;;:;:c::coooooddxXNNNNNNNNNN0xxxxdddxddddxxdxdddoollx0NNNNNNNNNNK0kolodolc:;;:cclloolclolxxolcllccllloollcclcldxxk0OO0OkxdoodddddddddoxkxxdkOOKXNNNNNNNNNNNNNNNNNNN0Oxlc:::colc::::;:::lcc;;:lllc::::;;;:;;;;::::;,,'',,;;;,''',,,:c;;;;
.'''''''',',.'''''''',,,,,,',,,;,,,''.''''...'''.'''..''',,'''',,::::;;:cccccolloookNNNNNNNNNNXOdddodddddoddxxdddddooxOXNNNNNNNNK0Okkkdlccclc::;:clloooccclolxxdddxxxxxxxxxxxdooodxxkkOkkOkxdoooddododddxxxxxkxkkkkxxO0KNNNNNNNNNNNNNNNNNNX0koccloo:cl:::::c:::;;l:;;;;:::::c:::;::;;,,,,,,,,,,,,,,,,,;::;;;
''''..'',;''..''..'''''''',',;;;,''.',,,'...'''''....''';,'''''',;:;;::ccclcllllooONNNNNNNNNN0xxxxxodddxdddddxdoxxxOXNNNNNNNX0kxxxkkkOkxdoollc:;:ldxkOO00KXXNNNNNNNNNNNNNNNNNNNNNNNXXK0000kxdoollododdoodxxxxxxxxxxxxxxxdkOKXNNNNNNNNNNNNNNNNNX0kdlcccccc:::;::::::;,,;;,,;;;:;::::c:,,,,,,,,,,,,,,,,;;::,,,
''''...'',,'''''''''.''''',;;,;,,''',,''.'.',,,''..'',,,'''..'',;;;;;:::lllccloodKNNNNNNNNNXkxxxxxxdxddddodxdddxOXNNNNNNNXkdcclodxxxxxxkxdddxkkOKXNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNXKOOkxoododdodxxxxxxxxkkxxxxxddxk0KNNNNNNNNNNNNNNNNNNXOxol:c:::::::ccl:;;;:;;;;;;::cc:::;,,;,,,,,,,,;;;;,;;;;,,
.'.'''..','',,',''''',;'',,;,,,''',,,,',,,,;,'',,',,;,''''..',,,;:;::::::::clcloKNNNNNNNNN0xxxdxxkxddxdddxxxdxOXNNNNNNN0dccccclodxdoodxxk0KXNNNNNNNNNNNXKK0OOOkxdxddxddxxkxdddxO00KKXNNNNNNNNNNNNNNXK0xdddxxxxdxxxxxkxxxxxxxxddxxOKNNNNNNNNNNNNNNNNNNNKkocc:cc::::;:cclccc:::;:cc:;;;::::;;;;,,;;;;,,;;,,,,'
''','''''',','''..'',:;,,''';,''',,;;;::;,;,'',,,,,''........'',,;;;:::c:::ccloKNNNNNNNNNOxxdddxdxxxdxxxddxxOXNNNNNNXOdlc:cccllloddox0KNNNNNNNNNKKOOkdddlloloddcodddolcldddl:;:codxxddxxkO0KXNNNNNNNNNNNX0OkxxdxxxxxxxxxxxxxdxxdxddxOKNNNNNNNNNNNNNNNNNNNKxcc:;;:;;;;:clcc:::;;:l::;;;;;:::cc:;;,;;;;;,'''''
',;,'',''',''''',,,,',,''.'',,,,,,;;,,:,,;;,,''..'''..........',;,;::;;cc::cclKNNNNNNNNXkxxxdxxxxdxdxxddxdOXNNNNNNKkllcccclcclllxOKNNNNNNNX0kdoooooololccloooddolodooollodddl::cloddodolllolloxkO0XNNNNNNNNNXK0OxxxkxxkkxkkxdxdddoodddxO0NNNNNNNNNNNNNNNNNO:::cc:::;:::::c:::cllccc::::::::cc:::;;;;''''''''
,;,'',,,,,'...'',,'..',''''.'',;,,,,,;;,;,;,,'''''.''..'''''''',;;;,;;;:lccccONNNNNNNNXxxxxxdxxxxdxxdxddkXNNNNNNXxlllcc::clccokKNNNNNNNKkdc::coooooolclddkOO000KKKXKKXKKKKK00OxxdddoddolclolooooooddO0XNNNNNNNNNXKkdxxkxxkkxdddddddddoooookXNNNNNNNNNNNNNN0cc::::;::::c::c::c:llcc:::cc:c::;;;;::;,,''''''''
,'','',,,'......','.''',,'''''',,,''',,''';,''''''''.''.'''''''',,'',;:c:c::xNNNNNNNNXxxxxxxxxkxxdxxxxxONNNNNNXOolclllccc:cd0NNNNNNXOxlccccccoooxkO00KXNNNNNNNNNNNNNNNNNNNNNNNNNNNXXK0OxdollooolodoooldkO0XNNNNNNNNXKOkxxkxdddxdddxxddoolllld0NNNNNNNNNNNNXoc::::::cccc::::::clccc;;:ccc:::;;;;,,''','''''''
'',,,,',,'..'',,'''';,''',,,'''...',,'.'.,,''''',''''''..''',;,;;,,,;;::lc:dNNNNNNNNXxdddxdxxdxkxxxdxxXNNNNNN0dlolllclc:okXNNNNNXOxolcccc:ldk0KXNNNNNNNNXKK0OOOkxxkkkkOOOOO0KKKXNNNNNNNNNNX00xooodloooxxdxxkOKNNNNNNNNNKOxxddxxdooddolllllc:::lxXNNNNNNNNNN0c::::;::clc;;;;::lc:::::cc::;;::;;;,,,',,'''''''
,,,,,''..''''''',',;'...'';;'''....''''.'''.'''''''.''''',,;;;;;;;;;cccooloXNNNNNNNXdddxdddxdxdxxxxxkXNNNNNKdoolooocccoONNNNNXOdlooooccoxOXNNNNNNX0Okdollcc:cllc;cloolddlllllc:ldkkOO0KNNNNNNNNXKOdodoxxxxxxddx0KNNNNNNNNXKkdxddoooooollllccc::ccd0NNNNNNNNNO::c:::::lc:::clc:::::c:;;;:::;;;;:;,,;;;,'''',;
'','''...'..'..'','''..'',;;,,....''.''.'''....''''''.',,,,,,',,;::cc::lccONNNNNNNNOddddxddddxxdxddONNNNNN0xddoldoccoONNNNNXOl:clodddkXNNNNNNKOxlcclc:;::llc:lol;coolcodllllc:codddolc:ldk0XNNNNNNNX0kxddxdddxxxkkOXNNNNNNNN0kdddollloolc:cccccc::ld0NNNNNNNNd::cccllolllcc::;;;:;::;;;;;,,,,,;:;,',,,,''',;
,,'....'''',''''......';,',;,..''...'''..'''.....',,'.''',;,,,,,,,,;:cllllXNNNNNNNKdddoodddddddxxx0NNNNNNOdddddodolxXNNNNNOoc::ccdkKNNNNNX0kdloc:cl:cccldkOOO00KKKKKKKK00OOkdddddddoc::::clodk0XNNNNNNXKOxdxxxxxkkxxkKNNNNNNNNKkdollooooollccccc:cll:o0NNNNNNXoclllccc::c::;:;;;;:;;,,,,,,,,;,,,;,','''',,;;
,'...''''''...........,;,'',;..',,''''''....''...''',',,,,,,;,,,,,,;;:cllONNNNNNNXdooooldddddxddxONNNNNNxdddoollddKNNNNNOl:::;:lONNNNNKOxllol:::odkOKXNNNNNNNNNNNNNNNNNNNNNNNNNXXKOkdlcccllllooodk0NNNNNNNKOkxxxkxdxxxxOXNNNNNNNXkdollccc::;;:cc:::oc:cdONNNNNXocc::;;;;;::;;,,;;;;,,''''''''''''''','..',,,
'',,,,,,''.........'',;,,''','.',,,''''.''':;'''''''',''''''',,;;:;;;clllXNNNNNNNkoodoloooddddxxONNNNNNkodddlollxXNNNNXo;:c::cONNNNNKxloolloldkKNNNNNNNK0OkxxxdkxdolloxkO00KKXNNNNNNNXKOxl:ccclololoOKNNNNNNX0kxkkxxxxddx0NNNNNNNNXklcc::ccccc:::;:ll::ccoKNNNNXo:;;;;;;;;;;;,;:;;,'',,,,''',,'.'..',,''''''
...,;;,,''........'',,,.'''.'..''','',''',,dO,,;;,,,'''''''''';;:;;;;:lcxNNNNNNNXllooooooodddxxkNNNNNNkdodddllcxXNNNN0l::cc:xXNNNN0dcllolok0XNNNNX0kollccc;;;clxkxc:cclldxxddddxk0KXNNNNNX0kolclllolooxOXNNNNNN0kkxxdxdodxx0NNNNNNNN0xlc::lcc:,;::clcccc::cxKNNNKc;,,,,,,;;;;;;;,,,'''',,'''''......'.......
....';;;:;;,,,,',;::,''''','...'',,,,;,,,,,ONl,;:;,,,,,,;,,,;;::;;;;:lcc0NNNNNNN0oolllclodddxddKNNNNN0dooddddoxNNNNNOl;:cco0NNNNKkoc:clx0XNNNX0kdl:;,;cc::;::cok00dolcllodooddoodddddkOXNNNNNKOdoolododddkKNNNNNNKkdxdxddddod0NNNNNNNNOocll:;;;;::cllc;::ccclxXNN0:;,,,,;,,;::;'',',,,,,'''....''''.........
.....,;:cc:::;;,,,,;'....';,,,,''',,,,,''''KN0,,;,,,;;,;;;,,,;;:::ccc:ccXNNNNNNNxlllclllodddxdkNNNNNXdxolxododXNNNNOlcc:cdXNNNNOxddlco0NNNNKxc,clc;;;ldxk0KXNNNNNNNNNXXK0Okdddo::odoclodk0XNNNNNKkooododdxdxKNNNNNN0dxxdddddodkXNNNNNNNKdol:::::;;;:lc:;:;:::::kNNO:,,,;;;;::,;;,,,',;;,''''''''''..........
,,,,,';:clc:;;,,,,,''',,;;;;;;;,,,,,,,,;,;:XNNl;;,,;;;;,,,,,;;:c::c:;;:lNNNNNNNNlcloolllododddKNNNNNOdxoldoooKNNNN0llcccxXNNNXdloxxx0NNNN0d::;;:loxOKNNNNNNXXKK0KKKKXXNNNNNNNX0kdldlloooddokOXNNNNXOoddddddodOXNNNNNXOddooooodol0NNNNNNNXk::::::;;;;ccc::::::;;;oKNx;;;,,;;;;;;;;,,,,,,,'''''''''...........
:::;;;:cccc;;;;;;,;'''',,;;,'',,;;::;,,;;:lNNN0;;;;;;::,;,;;;:;::;;,;::lNNNNNNNXllloollloooxxxNNNNNXoododdoo0NNNNXlccccxNNNNXoccllxXNNNKkl::,;oOKNNNNK0kdl:;;;:::cl::codxxk0XNNNNNKkxolodoodookKNNNNX0dxddoooxxONNNNNNKxoooodololxXNNNNNNN0c:;;;;,:cccccc:;;;;:;:cxXo:::;;;;c:,,,,,,,',,,''''''.............
cc::::ccc::::;;;,;,'''''''',,'''',,;:;,,,,:NNNNo:;::;;;,,'',;;;;;,,,,,;lNNNNNNNKoolloooolcoddONNNNNkodddddddNNNNNkol:clXNNNXlcccoONNNNOxdc::o0NNNN0xooolc:,,:clollo::clolc;ccox0XNNNNKkxdodddocoxKNNNNXOddolodddx0NNNNNNkolollclllo0NNNNNNNXd;;;;,:c::lc:cc:::;;;;:lkc;;;;;::;;;''',,,''''''................
ccc:::lc::;;;,'..'........';,''..'',,;;;,,lNNNNK:;;::;,,;;;,,',',,,,,,,cNNNNNNNKlclollldoodddKNNNNNdodddxxdkNNNNXdollcONNNNdccllxNNNNOddl:cONNNNOdc:coddkOKXNNNNNNXXK0kxoc;::cccok0NNNNN0xdooololdkXNNNNXxdddddddd0NNNNNNOllllclllcc0NNNNNNNNo;;,;::;:c::::c:::;;;;;;c;;::;;,;;;,'',;;'''''.................
llllllc::;,''.....''.......''''''',,,,::;;dNNNNNo',;;;;;;;;;;;:;;,''''':NNNNNNNKcccccccolloddKNNNNNdloddxdd0NNNNKdoollXNNNXlcc:lXNNNOlodooKNNN0dllcokKNNNNNXK00000KXNNNNNKOdc::ldolokXNNNNOclodooddx0NNNNXxoolddddxONNNNNN0lllccclc:c0NNNNNNNXo:;;:cccc:c:::::::;;,,;;;,,;::;;;;,,,,,,''.'..................
ooll:;''.............''.......',,,;,,,;:;;dNNNNNX:,,,,,,,,::;;;,,,,;;,,;XNNNNNNX::::;:llcllddKNNNNNxooddddxKNNNNOdooodNNNNOlllckNNNXollooKNNNkllooONNNX0kdlclooollccodk0XNNNN0xdooolloOXNNNXkodooddookNNNNN0ooddooddxXNNNNN0occc:;:cclONNNNNNNNo;;:::;::c;:;;;;:c:;;;;;,,;:c::;;,,,;,,''''.'''..............
c:;,''.....................'..''',;:::c;;;xNNNNNNk',,''',,;''''',,,,,;;;0NNNNNNNl::cccclcccodKNNNNNkdooodddKNNNNOolllxNNNNkolccKNNN0oollkNNN0llodXNNNOodk0XNNNNNNXK0kdllodONNNNXxoolcoxdKNNNN0ooooooookNNNNNOdddddddoxNNNNNNOcc:c;::cclKNNNNNNNNc,,,,;;;:cc::::cclc::;:::;;:::::;;;;;;,,''',''''''''........
........'''...''............',''',,,:;;;::xNNNNNNX:,''''',,.'''''',,,,,;dNNNNNNNd,;::clllllodONNNNNkododddx0NNNNOololdNNNNkoollXNNNOlool0NNNxlloXNNXkxKNNNX00OO0KKNNNNKOdlld0XNNNKdoodxookNNNN0ooolloolkNNNNNOxxdodddokNNNNNNkc;:;;:ccclXNNNNNNNK;;;;;;;;,;:::::;cc;;;::cc::::;;:;;;;;,,;,;;,,,''...........
..............................'..'',;',;,;dNNNNNNNK;,,'''.'''.'',,''''',:XNNNNNN0,,;:cc:ccldoxNNNNN0dooddddONNNNKdloloNNNN0ollc0NNN0lodl0NNNxlldNNN0dXNNK0KKXXKK0kxk0XNNNOdxxd0NNNNkxxllllkNNNNKodllooooxNNNNNOdoooodooONNNNNNd::::;;;;;oNNNNNNNNO;;,,,,,,;;;;;;;:c::;;,;;,,,;;;;,,;:::;;;,,''..............
......................''.......'',,,,,,,,,dNNNNNNNNk;,,,,''''...'....''',xNNNNNNNc:::cc:::clodKNNNNNdddddodxNNNNNxlccc0NNNXodolxNNNXoodoxNNNKlloKNNXxXNNNNNNNXKNNNN0dd0NNNXkdooONNNNkolooolONNNNOoolloddl0NNNNNdoloollooXNNNNNKl:;;;,;;;;kNNNNNNNNxcc:::c::::;;,,;;:::;;;;;,;;;;;::;;,;;,,,''''..'''........
.................'''.........'',,,,''''',,dNNNNNNNNNx,''''',''''''''''''';XNNNNNNk:;::::::cllokNNNNNOddoolod0NNNNOllccdNNNN0loddKNNNKdoooONNN0dod0NNXKNNNNNNXNX0OXNNXdoONNNXxdol0NNNXdddooooKNNNNdoolooloxNNNNNOooooccclkNNNNNNx:::;;:;;;cXNNNNNNNXc;;:::;;;;,,,,;;;;;;;;;::;;;::;,,'''',,,,,,,,,,'.........
''''''......''....',,'........''....''''''oNNNNNNNNNNo''''',''.....'''',,'dNNNNNNNo,;:;;:ccccloKNNNNNdddoodoxXNNNNxllllkNNNN0oocoKNNNKxoookXNNN0xdx0KKKX0XNNkNNNkdXNNKoo0NNN0doooXNNN0ddoooodNNNN0lodxolddKNNNNXoooc::cllXNNNNNK:;::cc::;;xNNNNNNNNO;;;:;;,;;;;,,,,;:;;;;;;::::;,''''''.'',,''..............
'''''''''',,,,''''''',;,,'...........'..''dNNNNNNNNNNX:.'',',',,,,,,''',,,;0NNNNNNXc;;;:c:ccloodXNNNNKddolooddXNNNNxllllkNNNN0oollkXNNNOdoodkKNNNNKKKKXXNNXOkNNNOdKNNNooxNNNNdolo0NNNNdooooolXNNNXdddodxxdxNNNNNxllccccclONNNNNNo:::::::::lNNNNNNNNNc,;;;;;;;;;;;,,;:::;;;;;,,;,'.......'...................
,,,;;,,,''''',,;;;,',,,',,;,''''..'.....''dNNNNNNNNNNNXc...'''',,''''','',,cXNNNNNN0;;,;;:ccclllxNNNNNKooooooodNNNNNkllllxXNNNXxoodkKNNNN0xddddkO0KXNXXKOkdkXNNXddXNNXodkNNNNooodONNNNoooloooKNNNNxdodddxldXNNNNOoccllcccdNNNNNNO;ccc:;;:::0NNNNNNNNk,;;;;,,;;;:;,'',,,;;;;,'',;,'..'''''...................
:;;,,''.....'',,;;;,,,,,',;,,',,''.'',,,,,kNNNNNNNNNNNNX:.''.''''''',,,;;;,,cXNNNNNNx,,,,c::;ccllxNNNNN0oooddooxXNNNNOollld0NNNN0dollx0NNNNX0OkdolcldxkkkOXNNN0xdKNNNOdx0NNNKlodx0NNNXooooolo0NNNNkdoddddloXNNNN0clllllccoNNNNNNX:cccccclc:xNNNNNNNNX:;;;,,,,;,,,,''''''',,,,',,,,,,'.......................
'.............'',;;::::;,,'',''.'.',,,''',KNNNNNNNNNNNNNK:'',''..',,,,;;;,,,'oNNNNNNNk;;;:::::lll:xNNNNNKdodooddd0NNNNXxlllld0NNNNKxolodkOKXNNNNNXXXXXNNNNXKOxxOXNNN0xdkNNNNxodkxXNNNOllloollKNNNNxoxdoxoclXNNNN0ccolcccloXNNNNNXcc:::::cccoNNNNNNNNNo;,,,,,,''',;;,,,,,;,,,;;;;;,,'''...''................'
........'......',,;::::;::;;;,'''''....'.;XNNNNNNNNNNNNNNXc..''''''''','',;,',oXNNNNNNk;:::;;:coccldXNNNNXxoooloolxXNNNN0dlllld0NNNNN0xoodddxkO00KKKK00OkxooxOXNNNKxookNNNNOdkxdONNNNdlllllloNNNNXxoddddlllXNNNN0:lollccclXNNNNNNl:;:::cccccXNNNNNNNNk,,,,,',,''''''''''',,',,,,,'..'''''.'''.............',
.....'''',''''..';;::cc:::cc:;;,''''..'''':ONNNNNNNNNNNNNNXl''''''',,,;,,,,;,;;lXNNNNNNOc:;:::cllcc:c0NNNNN0dlcllolokXNNNN0xoooodk0NNNNNX0OkxddolllllodxkO0KNNNN0xold0NNNN0xkdokNNNNOollllld0NNNNOddoooolcdNNNNNkcolcl:cclXNNNNNNoccccclcc::KNNNNNNNNK:;;,,,''''''''''',,,'''''',,'''''',''.''...........',;
,,,,,,,,,;;;;,,,.';:cclcccc::;;;,,,'......''c0NNNNNNNNNNNNNNx;,,'',,,,,,,,,,;;;;cKNNNNNNKl:c::cccl:,;;xXNNNNXOoclcoollxKNNNNXOxollloxO0XNNNNNNNXXXXXXNNNNNNXKkdlcld0NNNNKxdddoONNNN0oolooooxNNNNXddollooll0NNNNNoclllccccoNNNNNNXlccc::cc:clKNNNNNNNNX:;;,'''''''.......''.....'',''''.................'',;;
;;;;;;;;;;::c::;,';cclllcc::;;,,'''..........'oXNNNNNNNNNNNNNKc'..'''''''',,;;;;;;xNNNNNNXkc:c:;::c;,:cckXNNNNXko:clolccokXNNNNX0kdlllloddxkO0000KK00OOkxdlcccoxOXNNNN0xoooox0NNNNklcodooxxXNNNNkdolloooddNNNNNKc:llclccckNNNNNNKl::::ccccccKNNNNNNNNN;''''...'''.....''........'''..'...................',;
:c::::::::cccccc:,;clol::;;;;,'............''.':kNNNNNNNNNNNNNXl'......'',;;;;;;;;:oXNNNNNNKo:;;::c:;:;::lkXNNNNNOoloocccclxOXNNNNNX0OkddllcccccccccccccloxkOKNNNNNKOdoolllONNNNXdllldodddXNNNN0xoolclolo0NNNNNdcclcclcclKNNNNNNklc:::ccc:::KNNNNNNNNN;'.........''''''...'...............................',
cclllllccclllllcc::llcc:;,,,'..................'.cKNNNNNNNNNNNNNk;...'',,,;;;,,,,;;;:kNNNNNNNOl;::;;:::c;:;ckXNNNNNKkxlccclc:cdk0KNNNNNNNXKK00OOOOOOO00KXNNNNNNXOxl:::::lkXNNNNOolloodddxXNNNNOodoolccolxNNNNNKllllcccc:oNNNNNNNoccc:clccc:cXNNNNNNNNNl;,,''''''''..'''..'''''..............................
llllllllllloooolllolc:;;,'...................'....'oKNNNNNNNNNNNNKo;,,,;,;;,,,,,;;;;:;l0NNNNNNNkl:;;;:;::;;;;:d0XNNNNNKkdllc::clcllodk0KKXNNNNNNNNNNNNNNXK0Oxol:;;:::lx0NNNNXOoclclodxdONNNNNkoooooloddxXNNNNXollllllcccONNNNNN0::ccc:cc::coNNNNNNNNNNl,,,''''''''''',,''...................................
ooooooollllooollllcc:,'.........................'''',xNNNNNNNNNNNNNKc''',,;,,;;,;;;;;;::dKNNNNNNNOc;;:::c;;:;;:ccxKNNNNNNX0koclll:;:::c:ccodddxxxxxddoolc::;:c:::cok0NNNNNXklolclloodxKNNNNXxclolldkkddXNNNNNxcclcccllcoNNNNNNNo:::cccc::;;kNNNNNNNNNX;'''''...'''....'''...................................
:::::::::cllllc:;,''.........................'.'''','':kNNNNNNNNNNNNXx:,,,,,,,,,,,;;;;::c:d0NNNNNNXOo:::l:;::;:c:::lx0XNNNNNNX0Oxolc:::ccccc:c:ccllllllcccccodxk0XNNNNNKOdccoooloddx0NNNNN0olcloodkkdxXNNNNNkllclccccclKNNNNNN0:::;;::;;,,;KNNNNNNNNNX;'''....................'''.......................    
lllllllc::;,,,''......................'''''''''',',,,,,,ckXNNNNNNNNNNNXx;,,,,,,,,,;;::;::;;;lOXNNNNNNKklodc::clc:c:lllloxOKNNNNNNNNXK0OOkxxddoooooooodxxkO0KNNNNNNNKOxoclolldodoox0NNNNNKxoooolloxkxONNNNNNkcc::ccc::c0NNNNNNNo:cc:;::;;;;lNNNNNNNNNN0'..............................................  ..   
c:;,,'......................................'''''''''',,,':ONNNNNNNNNNNNXx;,,,,,,,;;:;;;,;;;,,:xXNNNNNNNKOdcclolclollcc:ccldxO0KXNNNNNNNNNNNNNNNNNNNNNNNNNNNNNX0OxollllloododdxOKNNNNNKkoooddooodxO0NNNNNXkdoc:::c:;;xNNNNNNNk:;:::::;;;,;kNNNNNNNNNNd....................................................  
..................................................'''''..'''ckXNNNNNNNNNNNXx:,,,;;;:::,,,;;;,,;:cdONNNNNNNN0kdlooccollccllooooododxkkO00KKXXXXXXXXXXKK00OOkxdolllooooooddddxkOXNNNNNKkododddddxxxOXNNNNNKdddoolcccccdNNNNNNNO:;;:;;;;;;,,:XNNNNNNNNNN:','...........................................        
..............................................................;xKNNNNNNNNNNNNkl::;;;;,;;,;;;;::ccccox0XNNNNNNNX0kxoloolloododddxdoddoddddooooooooooloolllllooddooddddxxxkOKNNNNNNXOkxddddxxdxxxx0NNNNNNOooooollcccckNNNNNNN0c:;:;;;;;;;,;ONNNNNNNNNNK'..............................................        
.................................................................lONNNNNNNNNNNNKxc;;;,;,,,;::::::cccccldkKNNNNNNNNXKOkkxodllodddxdddxxddddddooodddooddoooodxdxxxxxkkk0KXNNNNNNK0kxxxxxxddxkkxx0NNNNNNKxdooollllcclONNNNNNNKc;;;;,;:;;;,,dNNNNNNNNNNNo.....................................................  
....  ..  ...... ..................................................:kXNNNNNNNNNNNN0o;,,',,;:::;:cc:::coolodxOKNNNNNNNNNNK0OxxdodddxxxxdxxddddddxkxxxkkxxddxxxxO0KKXNNNNNNNNK0kxxkkxxkxxdxkkk0NNNNNNXkddooolllcllo0NNNNNNN0c;;;;;;,;;;;,:XNNNNNNNNNNX,.....................................................  
........     .. ....................................................';o0NNNNNNNNNNNNKko:;:::c:::;,;:cllollollloxO0KNNNNNNNNNNNXKK0O0OOkOkkkOOOkkO00OO00O00KKXNNNNNNNNNXKK0OOOOkkkOkkkxxkkOKNNNNNNXOxdddoolllllcxXNNNNNNNOc::;;;;;;;;,,,ONNNNNNNNNNNk....................................................    
.......................................................................';o0NNNNNNNNNNNNXOdl:;;,,;;;ccllllllloolloloodkO0KXNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNXXXXK0OOOOOOOOOOOkOkkkOKXNNNNNNKkddddoddolcllo0NNNNNNNNk:::c:;;;;,,,;;kNNNNNNNNNNNN:...................................................     
         .....  ..............................................'.........'',:dKNNNNNNNNNNNNN0dc,,;::clllllclcllcllloccclllldxkO0KXXXNNNNNNNNNNNNNNNNNNNNXXXXKXKKXKXXXXK0OOOO0000OOOOk0XNNNNNNNKkoodddddooooolxXNNNNNNNXo:;;;;::;;,,,,,xNNNNNNNNNNNN0.........................................................
....      .         ........................................................',cd0NNNNNNNNNNNNNKkdc:llllclcccccccoocl:ccllloloodxxxxxkxk000OkOKKKKKK0O000KXXNXXKKKK0000OkOO00O00OO0XNNNNNNNXOxooodddooooollx0NNNNNNNN0l;;,;;;;;:;;,,'dNNNNNNNNNNNNX:.........................................................
         ..... ...............................................................'',;lkKNNNNNNNNNNNNNK0kdccc:c:::cccll::clcllooddddddxdxxkkkOkkkkkOO0OOOOO0KXNNNXXKK0000000OO000KXNNNNNNNNX0kxddooooooodooox0NNNNNNNNKd:;;,,,,,;,;,,,,dNNNNNNNNNNNNNd..........................................................
     ........................................................................,,''..,,:okKNNNNNNNNNNNNNNK0kdolccccl:;:llllolooododdodxxkkkOkkkxxxkkkOOO0KKKXXNNXK000OOO000KXNNNNNNNNNK0xxxddoddoollllooxKNNNNNNNNXkc:;;;;,,,,,,,,,;kNNNNNNNNNNNNNK'..........................................................
         ...   ..........................................''...............',,'...',;,''',cxOKNNNNNNNNNNNNNNNXKOkxoc:cccllolooodddddxxxkkxkkkkOkkkkOO000KXXNNNNX0OOO0KXNNNNNNNNNNX0OxxxdddddoooooolllxKNNNNNNNNN0l::::;;;;;,,'''',kNNNNNNNNNNNNNNc.'.........................................................
............ ...........................................................'''....',,,''.'',;:;;cok0XNNNNNNNNNNNNNNNNXK0OOkxxddoooddxxxxkkkkkkOkkkkkOO0O0KKKKXXXNXXNNNNNNNNNNNNXK0OxkkxkxxdxxddooddldkKNNNNNNNNN0dccc:::;;;,,,,''';ONNNNNNNNNNNNNNO............................................................
..............................................................................'''....'',;;;,;;;;;;cdxk0XNNNNNNNNNNNNNNNNNNNNNXXXXKKKK0KK00KK000KKKKXXXNNNNNNNNNNNNNNNNXXK0OkkkkOkkkkxddddxddoodkKNNNNNNNNNN0occc:c::;;;;;,,,,'cKNNNNNNNNNNNNNNX,............................................................
'''...................................................................''''...'.....'',,,,,,,;;;;;;:::;;;ldxk0KNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNXXK0OkOOOOkkkkxkkxxxxddddddxk0NNNNNNNNNNN0lcc:::cc:;:;;;;;;;;oXNNNNNNNNNNNNNNNl.............................................................
''''''.............................................................................''',,,',,,;;;::;,;;;::::;;:clodxkO0KXXNNNNNNNNNNNNNNNNNNNNNNNNNNNNNXXXXXXXKOOOOkkkkOkO00Okkkxxxxddxxddk0XNNNNNNNNNNXko:::::::::c:;;;;;,,:ONNNNNNNNNNNNNNNNO..............................................................
;,,''''..........................................................................'''''''''',,;;;:;,;;;;;::::;;;;;;::cccllooddxxxkOOO0O00000OOOOOOOO0O0K0KXNXXXOkOOOkkOOkOkkOkkkkxdxxxkOKNNNNNNNNNNNX0dc:c::c:::::::;;;;,,,lXNNNNNNNNNNNNNNNNN;..............................................................
;;,,''''........................................................................'''''''''''',,;;,,;;;;;:::;;,;;;;;:::cccccclclllddodddxxxdddxxkkkkOkO00KXNNNNXOkk00OOOOOkxxkkkkxxxOKXNNNNNNNNNNNNKkl:::::c::c::;;;::;,;;:ONNNNNNNNNNNNNNNNNNx...............................................................
:;,,,'''''.....................................................................'''..'''''''',,,;,;;;;;;;;:;;,,,;;;::::ccccccccloooodxxdddddxxxxxkxOkOOKKXNNNNX0Ok00OkkOkkxxkkk00KNNNNNNNNNNNNNXOdlc::::::c:::::;;;;;;,,oKNNNNNNNNNNNNNNNNNNX;...............................................................
c:;,,,'''.............................................................................''',,,'',,,;;;,;;;;;;,,,,;;:::::cccccccclllooddoddddxxddxxkkOOO0KKKNNNNKOOOOOkkkkOkO0XNNNNNNNNNNNNNNNKOdclcccc::;:::c::::;;;;,,l0NNNNNNNNNNNNNNNNNNNNk,''.............................................................
c:;,,,'''............................................................................',''''''''',,,,,,,,;,,,,,;;;::::clc:c::ccccllloooolooodxddxkk0OO0KKKNWNNKOkOO00KKXNNNNNNNNNNNNNNNNX0koccccccc::::::::::;:::;;;ckNNNNNNNNNNNNNNNNNNKOxl,''''............................................................
:;;,,,'''...............................................................,codddxddollll:;,,','',,,,,,,,;,;;,,;;:;;;:::cc::::ccc:cccllcllloddddddxO0OO00KKXXNXKKKXNNNNNNNNNNNNNNNNNNNNKOdollllc:ccc:::::;;;::::;;;;:dXNNNNNNNNNNNNNNNXOo:,''......''..........................................................
;;;,,,'''................................................................':ox0XNNNNNNNNNXXKKOOkkxdoolllcc:c:::;:::;;::::::c::cccccccccloddddxxkO000KXKKXNNNNNNNNNNNNNNNNNNNNNNNXKOxoollllllcc:::cc::;::;;:::;;;;d0NNNNNNNNNNNNNKko:,''..'''''...............................................................
;,,,'''.......................................................................,:oOKNNNNNNNNNNNNNNNNNNNNNNNNXKKKK00OOOOOkkkkkkOOkOOO000KKKXXXNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNK0kxoooolllclclcccc::;::cc:::::::;;l0NNNNNNNNNNNKko:,'''''''''''''...............................................................
;,''............................................................................''':ox0NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNXKOxddoolooolollllllcccccc:::ccc:::::;cONNNNNNNNNN0dc;,,,''''''''''''.'...............................................................
'................................................................................'',''';ldk0XNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNXKKOOxddooloooollllllcllollcc:ccccccccc::;cxXNNNNNNNKxl:,,,,,,,,,''''''',''..'''..'.........................................................
...............................................................................''''''''''''',:lx0XNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNXXK0kxdddddoooololllclllllcccclcccc::c:ccc::ccxXNNNNNKkdc;,,,,,,,,,,,'''''''''''''''''''''''''...................................................
............................................................................''...''''.......'','',:oxOXNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNXKK00KKXNWNX0Okxodooooollllllccccccllcccccccccccc:::::dKNNNKkdc;;;;;,,,,,,''''''''''''''''.................................................................
.........................................................................................'''''''',',',,:ok0XNNNNNNNNNNNNNNNNNNNNNNNNNNNNNXK0OkkxdddxxkO0KNWNK0kkdddoodollcllllccccccclc::ccc:cccccc::l0NX0xl;;;;;;,,,,,,,,,,,,,,,'''''''''''''''............................................................
....................................................................................'..''''..''','''''''',,;ldkKNNNNNNNNNNNNNNNX0OkxxdollccllllloodxxkOOKNWNK0Oxddoooollccclccccc:::ccl:::ccc::cccccokxoc:;;;;;;;;;;;,,,,,,,,,,,,,'''''''....'''''''''......................................................
................................................................................'''''.....''',,''''''..''',,,,,,:okOKNXK0kxoll:;,;;;:;;::::ccclclooddkk0KNWNK0Oxdoolllolcccllccc:::::ccc:::::c::::::::;;;;;;;;,,,,,,,,,,,,,,,,,,,,,,'''',''''...'...........................................................
.........................................................................................'',,'''.'...''',,,,'''',,,,,cc;;,,,;;,;;;;;;;::::cccllclloddkkOKNNXKOOxdoolclloccccccccc::::cc:ccccc:::::::::::;;;;;;,,,,,,,,,,,;,,,,,''''''''''''''.........'....''...............................................
.........................................................''...........................''',;,,'''''''''''',''',,,,,,,,;,,,,,,,;;;;;;;;;:::::c:ccllloodxxOKNNKKOxxddoollcllcccccccccc:::c::cccccc:::;;;;;:::;;;;;;,;;;;,,,,,,,;,,,,,'''''''''''''''''''''.....................................................
............................................................'................'''''''',,,,'''''''''''',,'''',,,,,,,;;,,,,,,;,,,,,;;;::c:::::::::cllllodxk0KXX0Okxddolllccllcc:c:c:cccccc::::c:::c:::::::::;;;;;;;;;;;;;,,;;;;;;;;,,''''''''''...'''''''''''''''''............''''..''''..........'...........
..............................................................''.........''''''''''''''''''.'''''''''''',,,;;,,,,,,,,,,,;;;,,;;;;:::::;;;::;:c:llcollodxOKNX0kxxooolllccclccccc:::c::cccc::::cccccc:::::::;;;;;;,,,;;,,,,,,,,,,,,,,,,''''''''''''''''''''',''''.......''.''..'..'''.................''''....
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,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,'',,,,,,,,,,,,,,,,,,,,,,,,,,,,,,;;;;,,,,,,,;;;;;;;;;;;;;;::::::::;::::::cc:ccccllcloooxOXWKkxdoollolllllllllcccccccclllllccccc:::::::::::::::::;;;;;;;;;::;:::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;,,;;;;;,;;;;,,,,,,;;;;;;;;;;;;,,;;;;;;;;;;;;;
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