,;;::cccccccc::;;;;,,,,,;;:ccc::::::::::::;;,,;;,,,,,,,,,,,,,,,,,;;,,,,,',;;:;;:::;:;;;;;;;;;;;;;;;;
;::cccccc:::;;;;;;;::::::::cccccc::::::;;;;,',,,''',,,,,',,;,,',;,,;,',,,',;;;;;;;;;;;;;:;;;;;;;;;;,
::ccccc::;;;;;;::cccccccccccccc:::;;;,;;;,,,'',,'',,,;;,',;;,';;:,,,,'',,',,,,,,,;;;;;;;:;;;;;;;;;,,
:ccccc:::::::ccccclllllcccc:::;;;;,,,,,,,,,''',,,,,,,;;,,;;,';:::;;,,'',,;;,,,''',,;;;;;;;;;;;,;;,,,
ccccc:::::cccccclllllclccc::;;;,,,,''''''',,'',,;;,,;;::::;',:::::;;,'',,,,,,,''''',,,,;,;;;,,,,,,,,
lllcccc:cccccclllllccccccc:;,,,,,''''''''.',,,;;;;,,::::;;,;::::;:;;'.'',,'''''''''''',,,,,,,,,,,,,'
olllccccccccccccccccc::::::;,'''''''''','.,;;;::::;::::;,;;;;;,;,,;,,,'',,,'''''''..'''''',,,,,,,'''
llllllllccccccccccc:::::;;;;,'''''''',,'',;::::::::::::;,;;,,'',.','''.'',,,,,'''.....'...',',,,''''
ollllllllcccccccc:::::::;;,,,''''''',,,',;:::::c:::c:::;;;,,'''..''.....','''''''.........''''''''''
oooollllllccccccccccccc:;,,'''''''''',,,;::::::::::c::::;;;,,''..'.....''''....'............''''.'''
ooooolllllllccccccccclcc:;,''''''''',,,;::::::::::::::cc:;;;,,...''...''''......................'''.
oooolllllllllllllllllllcc:;,,,,,,,,';;;:::::::::;;::ccc:;;;;,,..',,''',,''''........'...........'...
llllllllllllllllllllllllc:;;;;;;;;;,;:::::cc:::;,;:cc:;,,'',,,..,;,,'.,,,'''''.....'................
llllcccclllllllllllllllc:::::::c:::::cc:::cc::;,,:c::;,'...',..',,,'.',,,,''',.....'................
ooolllllllllllllllllcccccccccc::::ccccc::cc:::,,:::::;,'.......'''..'',,,,'','''..'.................
ooolloolllllllllllllllccccccc:::::::::c:::::c;,:c:::;;,,'....''.'...'''''''''.''.'..................
lllloooooooooolllcccccccccc::::::::;;;:::cc:;,::;,;;,,,,''..'''''.'''''...''....''..................
loooooooooooollcccc::::ccccccc:::::;,;::c::,,:;,,',,,;,''''''''''',''''.........'...................
looooooooolllllccc:::cccccccccc::::::::::;;;;;,,'',,,,',''..''''',,,,''''...........................
ooooooooooolllccccccccccccccccc::::cc::::::;;;,,'''',,,,,'''.'''',,,'''''...........................
ooooooooooolllllllllccccccccccccc:::::;;;;;;;;;;'',,,;;;,,''','''',,''''............................
oooooooooolllllcccccc:::::::cccc:;;;;;;,;;;;;;;;;;;,,,,;,.'',,,''...'''.............................
oooooooollllcccc:::;;;:::cccccccc:::::;;;;;;,;;;;;,,'',,'';;;;,,,''........'.........'..............
oooooooolllccc:::;;;;:ccccccccc:::;;;;;;;;;;;;;;;;;,,,'',,,,;,,,,',,'.....'........''...............
oooooolllllccc:::;;::::::::c::cc::::;;::::::;;;;;;;;,'',,,,',,,,,,,,'....'..........................
ooooolllllccccc:::::::ccccccccccccc:::cc:ccc::;;:;;;,'.'','',,''',''.'..............................
ooooolllllcccccc::::::::ccccc::ccccccccc:::c:::;;;;;;,',,,,,,'',,,'....'......'.....................
ooooollllllcccc::::::::cccccccc::::::ccccc::::;;;;;,,,;,,,;;,,,;,,'''.'.....''......................
loooollllllcccccccccccc::::::;;;;:::::ccccc:::::;;;;,;;,,;;,,,:,;,''''..',,,'.......................
llloollllllllccccccc:;;;;;;::::::;;,,;:ccccccc::;,,;;;;;,;;;,:;,;;,,''',,,,'''.'....................
lllllllllllllllcccccc:::::::::cccccc:;clllllllc::;,,,;;;:::::::::::;;;;;;,',,,'.....................
llllllllllllccccccccccccc::::ccclollcccllllllllc::;;;:cllllllcc:::::::::;,;;,'',,,..................
ollllllllccc::cccllllllllooollllclooollllllooolccc:cllllccccc::::::::::;;;;;;;;;;''''''.....  .... .
olllllllllccccccccllooooooodddddoloooolllllllllcccclllccc::::::::::;;;;;,,;;;:;;,,,,,,,,'......     
oollllllllllccccllllllooooddddddooooollllllllcccclllccccccc:c::::;;;;;;,,,;;;;;;;;;;;;,,''......    
olllccllllooooolllooooodddddddooooooolllccccccccclcccclcccccccc::;;;;,,',,,,,,,,,,,,,'''.........   
ooollllllooodoooooooodddddddddoooooooolllc::::cccllcclccccccccc:::;;;,,,,,,,',,,,,,''.............  
dooollllllooodddddddddddxxddddoooooollllc:;,:cllllllllcccccc:::::;;;;;;,,''''',,,,''''''''''''......
ddooooooodddddddddxxxxdddddddddooollllc:;;:cclllllllccccccc::;;;;;;;;;;;;,,''''''''''...............
ddddoooddddddddxxxxxxxxxxdddddooollcc::;;:cllllllllccccc::c:;,;;;;;;,,,,,,,,,,',,,''''..............
dddddddddddddddxxxxxkxxdddoolllllloc:;;;cclllllllllcccc:c:;;;;;;,,,,,,,'',,,,,'''''''''.............
ddddddddddddddddxxxxxxddoolcc;::::c:;;:ccccclllllcc:cc:::;,,,;;;,,,,,''''''''''''''.................
dddddddddddddddddxxdddooooolllc:::;;,;cccclllllcccc:::;;;;;;;;;;,,''''''''''''......................
dddddddddddddddddxdddddooooooollccc::;ccclllllcc:::::::::;;;;;;,''''''..............................
ddddddddddddddddddddddddddddooooolcc:;,:::::::::;;;;;;:::;;,,,,''...................................
ddddddddddddddddddddddddxxxddddooolc:;;,,,.......';;;;;;,,''''....''''..............................
dddddddddoooodddddxxxxxdddddddoooll:;,,,,'...''..''',,,,'...''''''...',,,,''''......................
dddddddoooooddxxxxxxxxddddddddoolc;,'.,'''',,''.......''....'..   ......',;,,''.....................
dddddoooooooddxxxxdddddddddddoolc;,;;;;,'''''.........'... ...      ......'''.......................
dddddoollllodddddddddodddddddollc:;;,,,''............''....   ..     ............................'''
xxdddolllllodddddoodddddddddoollc:;,''..............',,;;'.   .      .....'','''...............'''''
xxdddolcccloooooooooooooollllccc:;,;,'..........''',,;;::;'..        ....',,'''...............''''''
xxdddolccccoollcclllllllcc::;,,,,,,;;;,,''''''.''',,,;;;;;;,,'.......'',,'''''.............'''''''''
xxxddollclloollllcccccc:;;;;,,,'..'',;;;;;;;,,,,,,;;,,,,;;;;;;;;;;;;;;;,,'''..............''''''''''
xxxxddolllooolc:::::::;;;;::;,'....,::c::::::;;;;;;;,,,,,,,;;;,,,,,;;;,,''................''''''''''
xxxxxdoolloollc::::::;;:c;'..    ...;cllcc:::::;;:;;,,,,,,,,,;,'..',;,,,''.................'''''''''
xxxxxxdoolllllc::::;;;cc,.....     ..:lllc::::::;;;;;,,,,,,;;,,,'..',,,,''............'....''''''',,
xxxxxxxdolllllc::;;;;cc:.......    .'cllcc:;::::;,,,;;,''',,,,;;,'...'''''.......'''''''''''''',,,,,
xxxxxxxxdollcccc:;;;:lc:,.''..    .;clllc::::;,;;,''',,,'..',;;;,'.....''.'..'''..'''''''''''''',,,,
xxxxxxxxxdolccccc::cccc:;,'......,:cccllcc:::;;,,,,'.'''''...,;;,,''..........''''''''...'......',,,
kkkxxkkkxxddolccccccc::;;;,''',;:cccc::cccc::;'.','.....'''....',,,'.............'''''''.........',,
kkkkkkkkkkkkxdolccc::::ccccccccccccc:;;ccc::;;'..,'......''''...................''''''''''''''''..',
kkkkkkkkkkkOOOkdollcccccccccc::::ccc:;,;cc::;,'..,,'......'''''...........'...'..',,,,,,,,,'''''''.'
kkkkOkkkkOOOOOOOkxdolccccccc:::::ccc:;,,;:::;,'..';,'.......''''.......''''''','...',,,,,,,,,,'''''.
OkkkkkkOOOOOOOOkxddc:looollc::::::::::;;,;:;;;'..,;,,'........''...''''''''',,,,,,'..',,,,,,,,,,,'''
kOOOOkOOOOOOOkxxdl:coddxxdocc::::::::;;;;;;;,,,'.'',,,'......'''''''''',,,,,,,,,,,,,'..',,,,,,;;;,,,
OOOOOOOOOOOkxxdl:cdxxkkkxddlcc:::;;;;;;;,,,,,','...'''''''''''''''''',,,,,,,,,,,,,,,,,'..,,,;;;;;;,;
OOOOOOOOOkxddl:cdxxkkkkkkxdlc::;;;;;;;;;,,,','''....'',,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,'..,,;;;;;;;
OOOOOOOkxxdlcldxxkOOOOkkxdlcc:::;;;;;;;,,,',,,,'''',;;,,,,,,,,,,,,,,,,,,,,,,,,;;;,,,,,,,,,'..,;;;;;;
OOOOOOkxdlcldxxkOOOOOOkxdodlc::;;;;;;;;,,,;:::::;;;:;;;;;;;,,,,,,,,,,,,,;;;;;,;;;;;;;,,,,,,,'..,,;;;
0OOkkxdlcldxkOO00000OOkxxxdoc:;;;;;;;;;;;:ccccc::::::;;;;;;;,,,,,,,;;;;;;;;;;;;;;;;;;;,,,,,,,,'..,,;
0OkxdlcldxkO0K000O0OOkkkkxdoc::::::;;;;;:cllcccc::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;,,,,,,,,,,'..,
kxdlcldxkO0KKKK00000Okkxxddoc:::::::;;;:lllllccccc:::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;,,,,,,,,,,,'.
docodxkO0KKKKK00KK00Okxxxxddl::::::::::lllllllcccc:::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;,,,,,,,,,,,,
cldxkO0KKKKKKKK0KK0OOkxxxdddoc::::::::cllllllllcccc::::::::::::::;;;;;;;;;;;;;;;;;;;;;;;,,,,,,,,,,,,
dxkk0KKKKKKKKK00000OOkkxxxdddl:::::::clllllllllccccc:::::::::::::;;;;;;;;;;;;;;;;;;;;;;;;;;,,,,,,,,,
kOO00KKKKKK0KK0O0OOOOkkxxxxddocc::::clllllllllllcccccc::::::::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;,
000000KKKKKKK0OOOOOOOkkxxxdddolc:::cooolllllllllllcccccccc:::::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
000000KKKKK0K00OOOOOkxxxxxddddolllloooollllllllllllccccccc::::::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
K00000KKKKKKK00OOOkOkxxxxdddddooooooooolllllllllllllllccccc:::::::::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;
00000000000000OOOOkkkxxxddddddooooooooolllllllllllllllllcccccc::::::::::::;;;;;;;;;;;;;;;;;;;;;;;;;;
00000000000000OOOkkxxxxxdddddodooooooolllllllllllllllllllcccccc:::::::::::;;;;;;;;;;;;;;;;;;;;;;;;;;
000000000O00OOOkkkkxxxxddddooooooooooollllllllllllllllllllcccccccc::::::::::;;;;;;;;;;;;;;;;;;;;;;;;
000000000OOOOkkkkxxxxxdddddooooooooooollllllllllllllllllllllcccccc::::::::::::::;;;;;;;;;;;;;;;;;;;;
00OOOOOOOOOOkkkkxxxxdddddddooooooooooooolllllllllllllllllllllccccccc::::::::::;,,;;;;;;;;;;;;;;;;;;:
00OOOOOOOkkkkxxxxxxddddddddoooooooooooollllllllllllllllllllllclcccccccc:::::::::::;;;;;;;;:;;;;;;:::
OOOOOOOkkkkkkxxxxxddddddddooooooooooooolollllllllllllllllllllllllcccccc:::::::::::::;::::::;;;;:::::
OOOOOOkkkkkxxxxxdddddddddoooooooooooooolllllllllllllllllllllllllllccccccc:::::::::::::::::::::::::::
,,,,''''''''''''''..................................................................................