lllllccclodddddddddddddddddddxdddddxxxdddxxxxxxxddddxddddxxdddddddddddddddddddddddddddoooooddoooooooooooooooooooooooolllllllllllllllllllllllllcclllcclllllccccccccc::,''',,,''',,,,,,;;cxkOOOkkkkkkkkkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxxxxxddddddddddddddddddddddoooooooooooooooooooooooooolllloollllllll
lllllccclodddddddddddddddddddxdddddxxxddddxxxxxxddddxdddddddddddddddddddddddddddddddddddooodooooooooooooooooooooooooollllllllllllllllllllllllllllllcllllllccccccccc::;,'',,,''',,,,,,;;lxkOOkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxxxxxddddddddddddddddddddddoooooooooooooooooooooooooollllllllllllll
lllllcccoodddddddddddddddddddxdddddxxdddddddxxxxddddxddddddddddddddddddddddddddoooddddddoodddoooooooooooooooooooooooollooollllllllllllllllllllllllllllllllcccccccccc:,'',,,,''',,,,,,,;lxkkkkkkkkkkkkkkkkkkkkkkkkkkkkkkxxkkkkxxxxxxxxxxxxxxxxxdddddddddddddddddddddooooooooooooooooooooooooooollllllllllllll
lllllcccododddddddddddddddddddddddxxdddddddddxxxddddddddddddddodddoooddddddddddooodddddooooddodooooooooooooooooooooooooooloolllllllllllllllllllllllllllllllcccccccc:;,'',,,,''',,,,,,,;lxkkkOOOOkkkkkkkkkkkkkkkkkkkkkkxxxkkkkkxxxxxxxxxxxxxxxxdddddddddddddddddddddooddooooooooooooooooooooooolllloollllllll
llllccclodddddddddddddddddddddddddxxxddddddddxxxddddddddddddddooddooooddddddddddooodoodooooooddooooooooooooooooooooooooooloolloolllloollllllllllllllollllcccccccccc:;,'',,,'''',,,,,,,:okOOOOOOOOOkkkkkkkkkkkkkkkkkkkkxkkkkkkxxxxxxxxxxxxxxxxxxxddxxxdddddddddddddddoooooooooooooooooooooooooooooooollllllll
llcccccloddddddddddddddddddddddddddxddddddddxxxxdddddddddddddoooddooooddddddddddoooooddooooodddooooooooooooooooooooooooooooolloooolllolllllllcllllloollllcccccccccc:;,'',,,'''',,,,,,;:okOkkkOOOkkkkkkkkkOkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxxxxxxxxxddddddddddddddddoooooooooooooooooooooooooooolooooollllll
llccccccodddddddddddddddddddddddddddddddddddddddddddddddddooddoddddoooodddddddddoodooddddooddooooooooooooooooooooooooooooooollloooooooollllllcllllllllllllcllccccccc:,'',,,'''',,,,,,;:okOOOOOOOOOOOkkkkkkkkkOkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxxxxxxxxdddddddddddddddoocc::ccccclllllllllloooooooollooooolllll
llccccccodddddddddddddddddddddddddddddddddddxdddddodddddddddddooddddooooddddddddooddoolc;,,,,:cooc:;;;;;;;;;;;;;;;:;;;,,,,;;,,,;;,,,;;;;:loll:;,,,,,;:::;,,,,,,,,,,'....''''.......',;:dkOkdlc:;:coxkkOkOkdlcccccc:ldkkkkkkkkxxxxxxxxxxxxxxxxxxxxxxxxxddddddddddddool:,,,,,,,,,,,;;;;;::ccccccllllllllllllll
llllcccloddddddddddddddddddddddddxddddddddddddxdddoodddddddddoooddddooodddddddddoodoc'.';:cc:,..,...,;;;.  .,;;,.   .;:;'  .,;;;;;;;;;...colc,..,;;,......';;,.  .,;;;. .....,:c:;,...;oxl,',;ccc;,';lxkOx,..;;;;,..:xkkkkkkkkkxxxxxxxxxxxxxxxxxxxxxxxddddddddddddooc;,,''''..'..'''''''''',,,,,,;;;;::::ccc
llccccclodddddddddddddddddddddddddddddddddddddxddddddddddddddoooodddoooddddddddddoo:..o0NWWWNXk:.  :KNNK:  :KNNK:  ,kNNKc. ,0NNNNNNNNKc..cllc,.;0NNK:.   'xNN0:  ,ONNXl.  .l0NWWWNXO:..c;.,xKNWWWNKo'.:xkd..oXNNNKc.,dkkkkkkkkkkxxxxxxxxxxxxxxxxxxxxxdddddddddddddooc;,,''''.........................'''''''
ccccccclodddddddddddddddddddddddddddddddddddxxxxxxxddddddddddddoodddooddddoddddddo:..xNWWKOKNWWK:  cXWWK:  cXMMXc .dNMNd.  ;KMWMNXXXX0c..colc'.:KWWWx.   'kWMX:  ,0MMNl. .oXWWNKKNWWK:...;0WWWXKXWWWk,.cxl..OWWMWNx..okkkkkkkkkkkxxxxxxxxxxxxxxxxxxxxxdddddddddddoooc,,,,'''',,,'''''''.....................
ccccccclodddddddddddddddddddddddddddxxxddddxxxxxxxxddddddddddddddddddddddddddddddo'.cKWWKc.,kWWNk' :XMWK:  :XMMXc.cXWWk,.. ;KWMNk;.'''..'cool,.:KWMMXl.. 'OWMXc  ,0MMNo. :KWWXd.,OWWWk. .dNWW0;.cKWMNl.,d:.;KMMMMW0,.ckkkkkkkkkkkxxxxxxxxxxxxxxxxxxxxxxxxddddddddoooc,',,'.',cllcccc:::;;;,,,,'''''''.......
llcccccloddddddddddddddddddddddxdddxxxxxdddxxxxxxxxddddddddddddddddddddddddddddddo'.lXWW0; .lO00d' :XMMK:  :XMMXc:0WW0;.,'.;KMMNd..;:;;;:lool,.:KWWMWOo, 'OWMX:  ,0MMNo. cXMMK: .dNWW0, .kWMWk. 'OMWNd.'l'.oNMMMMMXl.,dkkkkkkkkkkxxxkxxxxxxxxxxxxxxxxxxxxddddddddool:,,,''.';lodoooooooolllllcccc::::;;;,,,,
cccccccloddddddddddddddddddddddddddxxddxxddxxxxxxxdddddddddddddddddddooddddddddddo;.,0WMNx' ..''.. cXMMX:  :XMMXxkWWK:.'c;.;KMMNo..colllooool,.:KMMMMNKo.'OWMXc  ,0MMNo. cXMMX: .oNWWO, .kWMWk. 'OWWNd.':.'OWWNXNWWx..dkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxxxxxxdddddddol:,'''''';lddddooddoooooooooooooollllllcc
cccccccloddddddddddddddddddddddxddxxxddxxddxxxxxxxddddddddddddddddddddddddddddddddl'.lXWWNx' .:lc'.:XMMK:  :XMMWNWWW0,.;l;.;KMMNd.....,cooool,.:KMMMMWW0;'kWMXc  ,0MMNo. cXMMX:  'ccl;. .kWMWk. .;llc'..,.:KMW0d0WWO'.lkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxxxxxdddddddl:,'''''':odddddddddooooooooooooooooooooo
ccccccclodddddddddddddddddddddxdddxxdddxdddxxxxxdxdddddddddddddddddddddddddddddddddc..lKWWNO:.'cl'.cXMMX:  :XMMMMMMWNo..c;.;KMMWKxddc..:ooool,.:KMMWNWMNd;kWMXc  ,0MMNo. cXMMX:         .kWMWk.        ...oNMWx:kWMK;.:xkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxxdddddddddol;,''''',:odddddooddooooddooooooooooooooo
cccccccloddddddddddddxdddxddddddxxxxdddxxddxxxxxddddddddddddddddddddddooddddddddddddc..:0WWWKl..;'.cXMMX:  :XMMMMMWMWO,.;,.;KMMMWWMWk'.:ooool,.:KWWKkKMW0oOWMXc  ,0MMNo. cXMMKc.';,,;'. .kWMWk,';;;;,.   .kWMXl'dNMNo.,dkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxdddddddddoc;,''''.,cooddddooooooooooooooooooooooooo
ccccccclodddddddddddxxddxxxdxxxxxxxdddxxxddxxxxxdddddddddddddddddddddddoodddddddoddodl'.;kNWWXd..  :XMMK:  :XMMMNKNWWXo.''.;KMMWN000d..:ooool,.:KMW0lxXNN0KWMXc  ,0MMNo. cXMMKcc0NNNNk' .kWMWkckNNNNXo.  ,0MMK:.lXMWk'.lkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxddddddddoc;'''''',coodddolcccccllllllllllooooooooo
cccccccloddddddddddddxddxxxxxxxxxxxdddxxxddxxdddddddddddddddddddddddddooooddddddddoollc'..oXWWNx.  cXWWX:  :XMMWk:xWMWO'...;KMMNx'.'..'cooool,.:KMW0;;d0MWWMMXc  ,0MMNo. cXMMKc;dXWWM0, .kWMWk;cOXMMNd.  cXMW0:'lXMMK;.:xkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxdddddddddoc;'''''',coddddoc::::;;;;;;;;;;:::::::ccc
cccccccloddddddddddddxxdddxxxxxxxxxdddxxxddxxddddddddddddddddddoddddddoooddddddddc..'''.. .lXWWNo. :XMMX:  :XMMXc.:KMMXc.  ;KMMNo..:ccloooool,.:KMW0;..oNMMMMXc  ,0MMNo. cXMMX: .dNWW0, .kWMWk. ,0MMNd. .dNMMNXKNWMMNl.,dkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxxdddddddoc,'''''';lddoddoc:collllccccc:::::::;;;;;
ccccccclddddddddddddxxxddddxxxxxxxxdddxxxdxxxdddddddddddddddddddodddddddodddddddd;..d0KO:  .dNWW0,.cXMMK:  cXMMXc .xWMWk.  ;KMMNo..cllllooool,.:KWM0,  'OWMMMXc  ,0MMNo. cXMMK: .dNMM0, .kWMWk. 'OMMNd. ,OWMMWWWWWMMWx..okkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxdddddddl:,''''.';ldddodoc:loooooollllllccclllllcc
ccccccclddddddddddddxxxdddxxxxxxxxxdddxxxdxxxddddddddddddddddddddddddoddddddddddd:.'OWWNd. .dNWW0,.:XMMK:  cXMMXc  cXMMK:  ;KMMNd.......,lool,.:KMM0,   lNMMMXc  ,0MMNo. cXMMXc .dNMM0, .kWMWk. ,0WMNd. :XMWKdcclxNMWO,.ckkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxdddddl:,''''.':odddddoccloooooolllllcccclllllll
lccccccldddddddxdddddxxxxxxxxxxxxxxdddxxxxxxdddxxxdddddddddddddddddddddddddddddddc..dNWWXxcdXWWNd. :XMMX:  cXMMXc  'kWMNd. ;KMMWKkxxxd;..lool,.:KMM0,   'OWWWXc  ,0MMNo. ,0WMWOloKWMM0, .oNWWXdcxXWMNd..oNWWx....,0MMXc.;xkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxddddddl:,''''.':odddddoccooooollcccccccccccclccl
llcccccoddddddddddddddxxxxxxxxxxxxddddxxxxxxddxxxxxddddddddddddddddddddddddddddddo;.'xXWWWWWWWXx'  cXMWK:  cXMMXc   cKMW0; ;KWMMMMMMMXl..cooo,.:KWW0,   .lXMMXc  ,0MMNo. .cKWWWWWWNWM0,  'xNWMWWWNNWNd..OWWNo.'c..xWWNo.'dkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxdddddol:''''''':odddddlccoooollccccccc::cccccccc
cccccccoddddddxdddddxxxxxxxxxxxxddddddddxxddddxdxxxdddddddddddddddddddddddodddddddo:.':oxkOOko:'.. 'oxxo,  ,oxxo,   .lxxd, .oxxxxkxxkd;..cool;.'oxxl..',..lxxo,  .lxxd; ...;okOOxl:lxl.  ..:dkOkdccdd;..oxxd,.;d,.;dxxc..lkkkOkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxddddol;,''''',codddddlccooolllccccc::::::cccc:c
cccccccodxdddxxxxxxxxxxxxxxxxxxxdddddddddddddddddxddddddddddddddddddddddddddddddddddoc;''''''';cl:'.''''....''''.';,.''.'....''''''''...;looo:''',,,':ldl;;;;;;,,,;;;;,';c:,............,;'.....''',,''',,',',okl'','''',lkOkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxddddol;,''''',cdddddolccooollllcc:::::::::ccccc
lccccccodddddxxddxxxxxxxxxxxxxxxdxxddddddddddddddxddddddddddddddddddddddddddddddddddddddoooooddddoooooooooooooooooddoooooooooooooooooooloooooddxxxkkkOO0KKKXXNNXNNNNXX0kddoolcc:ccc::::::::::;;:okOOOkkOkOOkkkOOOkkkkkkkkkOOOOkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxddddoc;'''''';lddddddlclooollllcc:::;;;;::ccccc
cccccccodddddxxddxxxxxxxxxxxxxxxdxxddddddxdddxdddxdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddoooooodxxkkOOO00KKXXNNNNNNNNNXKOkxdooolllcccccc::::cc:::clk0O00000OOOOOOOOOOOOOOOOOOOOkkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxdddoc;'''''';ldddddolcllllllcc:::c:::::::ccccc
ccccccloddddxxxxdxxxxxxxxxxxxxxxdxxddddxxddddxdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddoooooodxxkkkOO000KXXXNNNNNNXK0Okxddooolllcc:cc:::cc::::::cdO0O00000O0OOOOOOOOOOOOOOOOkkOOkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxddoc,'''''':odddddocclooollcc::::c::::ccc:ccc
ccccccloddddxddddxxxxxxxxxxxxxxddxxxxxxxxddddxxdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddooooloodxxkkkOOO00KKXXXXXXXKK00Okddooolllllccccc::::::::::coO000000OO000OOOOOOOOOOOOOOOOOOkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxddo:,'''''':odddddocclooolllcc::::::::ccccc::
cccccclodddxxxdxxxxxxxxxxxxxxxxddxxxxxxxxddddxxxxxddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddooolllloodddxxkkOO0KKXXXXXKKK000Oxdoollllllccccc:::::::::::ok00000000000OOOOOOOOOOOOOOOOOOOkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxddo:,'''''':odddddoccoooollllcc:::;;::c::::::
cccccclodddxxxxxxxxxxxxxxxxxxxxddxxxxxxxxxdddxxxxxdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddolc::cccccllllooodxkO00KKKKKKKK0Okdollccccc::::::clc::::::ok0000000000OOOO0OOOOOOOOOOOOOOOkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxddl:,''''',cddddddoccooollcccccc::;;:::::cccc
cccccclodddxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxdddddxxxdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddool;,;::;;;;,,;;;;:clodxkkO000KKK0Oxdllcc:::;:::loxkxdlc:::okOkxxxxxxxxkkkkOOOOOOOOOOOOOOOOOOOkkkkkkkkkkkkkkkkkkkxxxxxxxxxdl;,''''.,cddddddl:clllllcc::cc:;;;::::cllll
cccccclodxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddoooo:,,,;;;,,,,,,,;:::clodddxkkkkkxxdolcc::::clodxxdddoooc;cdOkdolllllllloodxOO00OOOOOOOOOOOOOOOkkkkkkkkkkkkkkkkkkxxxxxxxxxdl;,''''.;lddddddl:cllllcccccc::;;;;::cllooo
llccccldxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxdxxxxxxxxdddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddddollllc:,,,;:::;;;;,;;:::::cclllllclloddddoooodddxxdoooxkdodl:cxOxollllcc:ccllodOOOOOOOOOOOOOOOOOOOOOkkkkkkkkkkkkkkkkxxxxxxxxddc;'''''';lddddddl:clllolloolllcc;,;:clloooo
ccccccldxxxxxxxxxxxxxxxxxxxxxxxxxxxxdxxxxddxdxxxxdddddddddddddddddddddddddddddddddddxdddddddddddddddddddxdddddddddddddddddddddddddolcclll:;,,;cloll:;;;;;;;clodddoooodxkOOOkkxxkkkxdolloxOK0Oxo:ckOxollllc:;;ccloxOOOOOOOOOOOOOOOOOOOOOOkkOkkkkkkkkkkkkxkkxxxxxdoc,'''''';oddddddl:cllooooooooool:;:clllllll
ccccccldxxxxxxxxxxxxxxxxxxxxxxxxdxxxxxxxxddxxxxxxddddddddddddddddddddddddddddddddddddddddddddddddddddddxxxxddddddddddddddddddddddddolcoddoc::cldxkkdl:::c:cdkO00OkkkkOOOOOkkkxkOOOOxl:ccldOK0ko:lkOxolllcc:;;;;clxOO000OOOOOOOOOOOOOOOOOOOOkkkkkkkkkkkkkkkxxxxxxoc,'''''':oddddddc:cclllcccclllcc:::cccccccc
ccccccldxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxdddddddddddddddddddddddddddddddddddddddddxddddddddddddxxxdddddddddddddddddddddddddoooddoooxkkkkkOkdoollloxkkOOO000OOOkkkxxxxkkOO0OdcclooxOOxc;lkOxollcc:::;,,;lxOO0OOOOOOOOOOOOOOOOOOOOOOkkkkkkkkkkkkkkkkxxxxxo:,''''',:dxddddoc:ccccc::cccccc:::::ccccc::
ccccccldxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxdddddddddddddddddddddddddddddddddddddddddxdddddddddddddddddddddddddddddddddddddddddoooodxOKXX0xodxdddoooodddxkOOOOOkkxxxxxxxxkkkkkxddkkkkkxo;;oOOdlcc::::cc:,,cxO00OO0OOOOOOOOOOOOOOOOOOOOkkkkkkkkkkkkkkkxxxxxo:,''''',cdxxxxdoc:cccccccccccccccccccc:cc::
ccccccldxxxxxxxxxxxxxxxxxxxxxxxddxxxxxxxxxddxxxxxxdddddddddddddddddddddddddxdddddddddddddddxddddddddddddddddddddddddddddddddddddddddddoooxkOKXXKOolcloooollllodxxxkxxxxdddodddxxxxxxO0KK0Okxo:;:d0Odl::;;;:cc:;;cxO00OO0OOOOOOOOOOOOOOOOOOOOkkkkkkkkkkkkkkkxxxxxo:,''''',cdxdxddo:;::::::::cccc:ccccccccccc:
ccccccldxxxxxxxxxxxxxxxxxxxxxxdddxxxxxxxxxxxxxxxxxdddddddddddddddddddddddddxdddddddddddddddxddddddddddddxddddddddddddddddddddddddddddddoooodkOKK0kl::ccccllllooddddddddooooooddxxxkO000XXKkdl:;:okkoc:;;;;:cc:;;cxkkOOOO0OOOOOOOOOOOOOOOOOOOOOOOkkkkkkkkkkkkxxxxo:,''''';ldxxxddoc::::::::::::::::::::::::::
ccccccldxxxxxxxxxxxxxxxxxxxxxxdddxxxxxxxxxxxxxxxxxdddddddddxdddddddddddddddddddddddddddddddxdddddxxddddxxdddxdddddddddddddddddddddddddoooc:::cloool::cccclllooooooooooolloooooodoox0KKK0Okollc;:cll:;;:;,,;;;;,,;cccllldOOOOOOOOOOOOOOOOOOOOOOOOOOkkkkkkkkkkxxxxo;,''''';lxxxxddddoooooooooolllllllllccccccc
ccccccldxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxdddddddddddddddddddddddddddddddddddddddddxdddddxxxdddxxdddxdddddddddddddddddddddddddodol:;,,,;;clllcccccllllloooooooollooolllllc:ldxxolllllccldkd:,:ol,','',',,,,,;;;lk000OOOOOOOOOOOOOOOOOOOOOOOkkkkkkkkkkxxxl;,''''';oxxxxxxxxxddddddddddddddddddooooooo
ccccccldxxxxkkkkkkkkkxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxdxxddddddddxxdddddddddddddddddddddddddddddxdddxxxxdxxxdddxdddddddddddddddddddddddddoool:;;:clloddolllcccclllllllllllllllllllcc;,;;;::cclllllok0kc;:do;,,,,,,,,,,,,,;lk000OOOO0OOOOOOOOOOOOOOOOOOOkkkkkkkkxxxdl;,''''':oxxxxxxxxxdddddddddddddddddddoooooo
ccccccldxxk0KXXXKKKKKK0000OOOkkkkxxxxxxxxxxxxxxxxxxxdddddddddddxdddddddddddddddddddddddddddxxxxxddxxxddddddddddddddddddddddddddddddddoooolc::coddddoollcccccccccccccclllllccccc::;,,,;;::cllloodO0Odccdo;,:ll:,,,,,,,,;ok0000OOO00OOOOOOOOOOOOOOOOOOkkkkkkkkxxxdl;'''''':oxxxxdddddddddddddddddddddddooooooo
ccccccldxxkOKKXXXXXXXNNNNNXXXXXXXKKK0OOOkkxxxxxxxxxxddddddddddddddddddddddddddddddddddddddxxxxxxdddxddddddddxxdddddddddxxdddddddddddddoool:;;;;:cccc:::::::::::::::::ccccc:::::;;,,,,;;:ccllooodk0K0olxo;,cxxc,,',,,,,;oO000000000OOOOOOOOOOOOOOOOOOkkkkkkkkkxxdc,'''''';loooooooooooooooooooooooooooooooooo
ccccccldxxxxxxxkkkkkkO0000KXNNWWWWWWWNNXXK0Okxxxxxxxddddddddddddddddddddddddddddddddddddxxxxxxxxdddxdddxddddxxddxxdddddxddddddddddddddooooc;,,;:::;;,,,,,,;;;;;;;;;;;;;;;;;;;;;,,,,,,;;::cllooddxkOOdoxo;;cdd:,,,,,,,,:oO0000000OOOOOOOOOOOOOOOOOOOOkkkkkkkkkkxdc,'''''.',,,,,,,,,,,,,,,;;;;;;;;;;;;;;;;;;;;
ccccccldxxxxxxxxxxxdddddddxkO0XNNWWWWWNXXNNX0kxxxxxdddxxddddddddddddddddddddddddddddddddxxxxxxxxxdxxxddxxxxxxddxxxxddddddddddddddddddddoool:;;:ccc::;,''''',,,,,,,,,,,,,,,,,,,,,,'',,,;;:cclooddxxxxdodocclxxdlc;,,,,,:dO00000000OOO00OOOOOOOOOOOOOOOkkkkkkkkkxd:,''''.......'..............................
ccccccldxxxxxxxxxxxxxxxxxxxxdxOKXNWWWNX00XNNXK0kxxxxxdxxddddddddddddddddddddxxdddddddddddxxxxxxxxxxxxxxxxxxxddxxdddddddddddddddddddddddooolc:;,,,,,,'''''.''''''''''''''''''''''''',,,,;;:clooddxxxxddxxdodxxxdoc:;,,;:dO0000000000O00OOOOOOOOOOOOOOOOkkkkkkkkxd:,,''''''''.................................
llccccodxxxxxxxxxxxxxxxxxxxxxxOKXNWNNNX0OKXXXXK0Okxxxxdxddddddddddddddddddddxddddddddddddxxxxxxxxxxxxxdxxxddddddddddxxddddddddddddddddoooooool:,'..............''..'''.........'''',,,,;;:clloodxxkkOOKKOxdddddddolcc:cdO0000000000OO0000OOOOOOOOOOOOOkkkkkkkkxdc:;;;;;,,,,,,,,,,,,,,''''''''''''''''''''...
ccccccodxxxxxxxxxxxxxxxxxxxxddxk0XNNXKOOO00KKKKKK0Okkxxxddddddddddddddddddddxxdddddxxxxxxxxxxxxxxxxxxdddxdddddddddddddddddddddddddddddoooooooll:'.....'.........................'''',,;;::clloodxxkOO0NWNKkddddddddddooxkkOO00000000000000OOOOOOOOOOOOOkkkkkkkkxdoooooollllllllllllllcccccccccccc:::::::::::
ccccccodxxxxxxxxxxxxxxxxxxxxdold0XXXKOdoooddxkO00KKK0Okxxddddddddddddddddddddddddddxxxxxxxxxxxxxxdddxxddxdddddddxddddddddddddddddddddooooooooool:''.............................'''',,;;::ccllodxkkO0KNWWXOxddooooddddddxxxxxkkOOOOO000O00OOOOOOOOOOOOOOkkkkkkkkkkkkxxxxxxxxxxxxxdddddddddddddddoooooooooooo
ccccccodxxxxxxxxxxxxxxxxxxxxxoccoxkxxoc::::::clodkO0KK00Oxddddddddddddddddddddddddxxddxxxxxxxxxxdddddddxxxxddddddddddddddddddddddddddooooooollcc:,'..............................'',,;;;::ccllodxkO0KNWWWXOdolllooodddddddddddxxxxkkkOOOO0OOOOOOOOOOOOOkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxdddddddddddddddoooo
ccccccodxxxxxxxxxxxxxxxxxxxxdoc:::::::;;;,,;;;::cldk00000Oxxdddddddddddddddddddddxxxdddxxddxxxxxddddddxxxxxxxdddddddddddddddoddddooooooollc::;,''...............................'',,,;;;::ccllodxkOKNWWWX0xoooloooodddddddddddddddddxxxkkkOO0OOOOOOOOOOkkOOkkkkkkkkkkkkkkkkxkkkxxxxxxxxxxxxxdddddddddddddood
cccccloxxxxxxxxxxxxxxxxxxxxdolc:;;;;;;;;;,,,,,;;:clxkO000OOkxxdddddddddddddddddddddddddddddddxxxddddddxxxxxxxddddddddddddddoodddddooollc:;,''..................................''',,;;;;::cllodxkO0XWWNKkdoooooooodddddddddddddddddddddddxxkO00OOOOOOOOOOOOOkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxxdddddddddddd
ccccccoxxxxxxxxxxxxxxxxxxxddlc:;;;;;;;;;;;,,,,;;::clodxkkkOkkxddddddddddddddddxxdddddddddddddxxxddddddxxxxxxxddxxddddddddddooddddoolc:;,,'.....................................'''',,;;::cclodxkO0XNNXOxooooooooooddooooooddddddddddddddddddxkOOOOOOOOOOOOOOOkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxxdddddddddddd
ccccccoxxxxxxxxxxxxxxxxxxdddl::;;::cccc::;;,,,,,;;::clooodxkkkxdddddddddddddddxddddddddddddddddddddddddxxxxddddddddddddddddooddoolc:;,'''.......................................'',,;;::clodxkO0KXNX0xoooooooooooooooooooooodddddooooddddddddddxkOOOOOOOOOOOOkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxxxddddddddddd
ccccccoxxxxxxxxxxxxxxxxxxdddolc::ccllooolc;;;;;;;;;;:cclooodkkkxdddddddddddddddddddddddddddddddddddddddxxdddddddddddddddddoddoolc:;,,''''......................................'',;:cloodxkOOO0KKKOxoollllooooooooooolllllooooooooooooooooodddoodxkOOOOOOOOOOOkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxdddddddddddd
ccccccoxxxxxxxxxxxxxxxxxxdddxdlc:::::cccc:;;;;;:::::::ccclloxkOkxddddddddddddddddddddddddddddddddddddddddddddddddddddddddooooc:;;,,'''''...................................'',,;::codxkO000000OkxdolllllllllooooooolllllllllloooolllllooooooooooodxkOOOOOOOOOOkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxdddddddddddd
ccccccoxxxxxxxxxxxddxxxxddddxxdolc:::::::::::cclllooddoollloxkkOkxddddddddddddddddddddddddddddddddddddddddddddddddddddddooll:;;,,,''''''..................................,;:clloodxkO00000OkxdollccllllllloooooooollllllccclllllcccclllloooooooooodkOOOOOOOOOOOkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxddddddddddd
ccccccoxxxxxxxxxxxxxxxxxxdddddxddooollcc::::ccclooddxxddddoodxkkkxooddddddddddddddddddddddddddddddddddddddddddddddddddddolc:;,,,,,'''''..................................',;:cloodddxxxxxxddolllllcccclllllloooooolllllllccccllllcc:cccclloooooooooodxOOOOOOOOkkOOkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxddddddddd
ccccccoxxxxxxdxxxddxxxxxxxdddddddddddddoollc::ccllllllllloooodxxxdlloddddddddddddddddddddddddddddddddddddddddddddddddddolc;;;,,,,,''''..................................''',;;:cccc::::cccccllllccccccllllllllllllllllllccc:cclllc::::::ccllllloooolloxkOOOOOOOOOOkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxdxxxxdddd
ccccccoxxxxxxxxxxddxxxxxddddddddddxddddddddoolc::;;;:::cclodddddolccloodddddddddddddddddddddddddddddddddddddddddddddoolc:;;,,,,,,'''''...............................''',,;;;::::;;;;;::cccllllcccccllllllllllllllllllcccc:::ccllc:;;;;::cclllllloollloxkOOOOOOOOOkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxxxxdddd
ccccccoxxxxxxxxxxxxxxxxxddddddddddxxddddddddddlc;;,,,,;:cloodddoc::cclooddddddddddddooddddddddddddddddddddddddddooollc:;;;,,,,,'''..''..............................'',,;;;;;:::::::ccccccccccccccclllllllllllllllllcccccc::::clll:;;;;;::cclllllllllllodkOOOOOOOOkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxxxxxxxx
ccccccoxxxxxxxxxdxxxxxddddddddddddxdddddddddddl;,,,,,,;;:cloddoc:::::cclooodddddoddddddddddddddddddoddddddoddddoolc::;;;;;,,,,''''.................................'',,;;;;:::::cccllllllccc:::ccllllllllllllllllllllccccc::;::cllc;;;;;;:cccccclllllcclldxOOOOOOOkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxxxxxxxd
ccccccoxxxxxxxxddxxxxdddddddddddddddddddxddddoc''''',,,,;clllc:;;;:::::clllooodddddddddddddoooooddooodddddodoolcc:;;;;;;;,,,,,''''................................'',,,;:::cccccccccccccccc:::ccllllllllllllllllllllllcccc::;;:cclc;,,;;;:::cccccccccccccldkOOOOOOOkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxxxxdddd
ccccccoxxxxxxxxddxxxxxxxxddxxdddddddddddxddddoc,''''',,,;;:;,,,,;;;;:::cccclooodddddddddddoooooooooooooooooolc:;;;;;;;;;;,,,,''''''.........................'''''''',,,;:cccccccccccc::::::ccccccllllllllllllllllllllccccc::;;::clc:,,,,;;;;::ccccccccccccldkOOOOOOOkkkOkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxx
ccccccoxxxxxxxxxxxxxxxxxddddxdddddddddddddddddo:,,,,,,,,,,'''',,;;;;;::::cccloooddddddoooodddooooooooooooolc:;;;;;;;;;;,,,,,,''''''......................'''''''''',,,,;:::::cc:::::::::::ccccccccllllllllcccllllllllccccc::;;;:ccc:;,,,;;;;;;::cccccccccccloxOOOOOOOOOOOkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxx
ccccccoxxxxxxxxxxxxxxxxdddddxddddddddddddddddddoc,'''''''''''',,,;;;;;:::ccccloooodooooooooooooooooooooooc::;;;;,,,,;;,,,,,,''''........................''',,,,,,,,,,,;;:::;;:::::::::::::cccccccccllllccccccccccclccccccc::;;;::cc:;,',,;;,,,;::cccccccccccldkkOkkkOOkOOkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxxxxx
ccccccoxxxxxxxxxxxxxxxddddddddddddddddddddddddddoc,''.....'''',,,,;;;:::::;::cooooooooooooooooooooooooolc:::;;;;,,,,,,,,,,,,'''....'''...............''''',,,,,,,,,,,,;;:::;;;;;;;;::::::ccccccccccccccccccccccccccccccccc::;;;;:ccc:,'',,,,,,,;;:ccc:cccccccldkkkkkOOkOOkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxxxxx
ccccccodxxxxxxxxxxxxdddddddddddddddddddddddddddodo:,''.....'''''',,;;;;;;;;::cccccllooooooooooooooollc::;;;;;,;;,,,',,,,''''''.....'''''............'''',,,,,,,,,,,,,,;;;:;;;;,,,;;;:::::cccccccccccccccccccccccccccccccccc:;;;;::c:;,'',,,,,',,;::ccc:cccccccldkkOOOkkOkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxddd
ccccccoxxxxxxxxxxxxxddddxxdddddddddddddddddddddddoo:,'........''',,,,,,,,;::::::::ccloooooooooooolc::;;;;;;,,,;;,,,',,,'''''''.....''''''..........'',,,,,,,,,,;;,,,,,;;;;;;;;;;;;;;;:::ccccccccccccccccccc:cccccc:ccccccc:::;;;::::,''',,,,''',,;:::::::ccccccldkkOOOOkkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxx
ccccccoxxxxxxxdddddddddddddddddddddddddddddddddddooc,'........''''''''',;:::::::cccccclllllc:::ccc:;;;;,;;;;,,;;;,,'',,'''.........''''''''.....'''',,,,,,,,,,;;;,,,,,,;;;;;;;;;;;;;;::::cccc::ccccccccccc:::cc:::::c::::::::;;;;;;;,''''''''''',,;::;;;;:ccccclodkOOOOkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxx
ccccccoxxxxxxxxddddddddddxxddddddddddddddddddddddodl;'........'''''''',,;;;;;:::::ccc::cccc:;,',,,,,,;;;,,,,,,,,,,,'',,''''........'''''''''''''''',,,,,,,,,,;;;;;,,,,,;;;:::;;;;;;:::::::::::ccccccccc:::::::::::::::::::::::;;;;;,''..'''''''',,;;:;,,,;:cc::clodkkkkkkkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxx
ccccccoxxxxxxxxxxxddddxdxxxddddddddddddddddddddddodo:'........'..'',,;;;;;;;::::;;:::::::::::;'''''''''',,,,;,,,,,,'','''''........''''''''''''''',,,,,,,,,,,;;;;,,,,,,,;;::;;;;;;;;;;;;::::::::::::::::::::::::::;;;;;;;;::::;;;,,'....'''''.''',,;;;,,,;::c:::clldkkkkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxx
ccccccoxxxxxxxdxxxxddddxxddddddddddddddddddddddddoool,'.......''',,,,,,,,,;::::;;;;;;;::::;;;;;,'''''''''',,,,,,,,,''''''''........''''''''''''''',,,,,,,,,,,,,,,,,,'',,;;;;;,,,,,,,;;;;;:::::::::::;;:::::::;;;;;;;;,,,,,,,;;;;,,'......'''...'',,;;;,,,,;:c:;;:ccodkOkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxxx
ccccccoxxxxxxxxxxxxxdddxxdddddddddddxddddddddddddooooc,'......'''''''',,,,,;;;,,,,;;;;;;;;;;;;;;,,''''''''',,,,,,,''''''''.........''''''''''''''',,,,,,,,,,,,;;;,,,'',,;;:;;,,,,,,,;;;;:::::::::::;;;;::::::;;;;;;;;,,,'',,,,,,,,'......''....''',,,,,,,,,;::;;;:ccoxOOkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxxxx
ccccccoxxxxxxxxxxxxxxxdxxddddddddddddddddddddddddoooooc;'.....''...''''''''',,,,,,,,,,,,;;;;;,;;;;,'',,'''''',,,,,'''''''..........'''''''''''''',,,,,,,,,,,,,;;;,,,'',,,;;;;;,,,,,,;;;;:::::::::;;;;;;:::::::;;;,,;;,,'''''''''',,'...........''',,,,,''',;::;;,;:cldkkkOkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxxx
ccccccdxxxxxxxxxxxxxxxddddddddddddddddddddddoodddooooooc,'....''....''''''.''',,,,,,,,,,,,;;;,,,;;;;,'',''''''',,,,''''''..........''''''''''''',,,,,,,,,;,,,,,,,,,,,,,,,;;;;;,,,,,,;;;;;;;;;;:::;;;;;;;;:::::;;,,,,,,,''''''''''','..'........''',,,,,''',;::;;,;::coxkOkkkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxx
ccccccdxxxxxxxxxxxxxxdddddddddddddddddddddddooddoodooool:,''...............'',,,,,,,,,,,,,,;,,,,,,;;;;,,,''''''',,'''''''..........''''''''''''',,,,,,,,,;,,,,,,;;;,,',,,;;;;;,;;;,,;;;;;;;;;;;;;;;;;;;;;;::::;;,,,,,,''''''''''''''..........''''''',,''',;;::;,;;::ldkOkkkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxx
cccccldxxxxxxxdddxxxxdddddddddddddddddddddddodddooooooooc,''...............''',,,''''',,,,,,,,',,,,,,;,,,,,'''''''''''.''..........''''''''''''',,,,,,,,;;;,,,,;:lc;,,,;:cc;;;;:lc:;;:cc::;;;;;;;;;;;;;;;;:::::;;,,,,,,'''..'',,,''''.........''.'''''''.',;;::;,,;;:coxkkkkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxxx
cccccldxdxxxdddddxxxxdddddddddddddddddddddddooddddoooooooc,'''...............''''''''',,,'',,'',,,,,,,,,,,,,,''''''................''''''',,,,,,,,;;,,,,:c::;,',colc:,,;coo:;;;col:;;cdxdo:;;:c:;;;;;;;;;;;;:::;;,,,,,,''....',,,,'''........''....''''..',;;::;,,;;;:ldkkkkkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxx
cccccldxxxxxxxddxxxxdddddddddddddddddddddddddddddooooooool:,''..............'''''''''','''',,''',,,,,,,'''',''''..................'''''''',,,,,,;::;,,,,:lccc;',:lol:,,;:ll;,;;:ll:;;cdxxo:;;cddl:;;;;;;;;;;;;;;;;,,,,,''....'',,,'''.................'..',;;;:;;;;;;:coxkkkkkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxx
cccccldxxxxxxxdxxxdddddddddddddddddddddddddddddddooooooooolc;''............'''''..''''''''',,'.',,,,,,,'...''''''.................''''''',,,,,,,;lol:,'',:cc:,',,;:;;,,,,;;;,;;;;;;;;:cclc;;:ldkd:;;;;,,,;;;;;:;;;,,,,,,''....'',,'...................'..',;;;;;;;,,;;:lxkkkkkkkkkkkkkkkkkkkkkkkkkkkkxxxxxxx
cccccldxxxxddddxxxddddddddddddddddddddddddddddddddooooooooooc;''..........'''.....''''''''','..',,,,,,,'......'''.................'''''',,,,,,'',:ll:,,''','''',,,,,;,,,,,,,;;;;,,,;;;;;;;;;:lodo:;;;;;,,;;;;::;;;,,,;,,''....'',,'......................',,;;;;;;,,;;;cokkkkkkkkkkkkkkkkkkkkkkkkkkkxxxxxxxx
cccccldddxxddddxxxxddddddddddddddddddddddddddddddooooooooooool:,'.........'........'''''''','..'',,,,,''.......'''................''''',;:;,,'',,;::;,',,;;,,''',;;,,,,,,,,;:cc:;:clc:;;;:;,;;:lolc:;;;;;::;;:;;;;;;;;,,''....'',,'......................',,,;;;;;,,;;;;cdkkkkkkkkkkkkkkkkkkkkkkkkkkxxxxxxxx
cccccloddxxdddddxxxddddddddddddddddddddddddddddddooooooooooooolc:,'.................''...''''..''''..''''........''...............',,'',clc;,;cc;;ldl;'';ldl;,',;co:,,,;cc:;cxkdclolooc;:ooc;,;:oOOo:;;;cxd:;;;;;;;;,,,,,'.....',,'......................',,,;;;;;;;;,,;;lxkkkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxx
cccccldddxxdddddxxxdddddddddddddddddddddddddddddddoooooooooooooolc;'.....................''''..''......''.........'''.............',,'',,,;:;;lo::dxc,'',cdc,,,,:dkc,,',loc,:dOdcc:;;odc;lkd:,;:d0Ol;,;;o0Oc;;;;;;;,,,,,,'......','......................',,,;;;;;;;;,,,,:oxkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxx
ccccclddxxxdddddddddddddddddddddddddddddddddddddddooooooooooooolllc:,'......'............''''.'''................................'',,'',,',:c:ll;coc,'''':l:,,,;cxkl,,',coc;:dkolo:;;ckdco0Ol;;ckKx:;;;:xK0o;;;;;;;,,,,''''.....'''......................',,,;;;;;;;;;;,,;cdkkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxx
cccccldddxxdddddddddddddddddddddddddddddddddddddddoooooooooooooollllc;,..................''''''''................................''',',::,':l:llcc:,''''':l:,,,;coxo,',,coc;:dxood:;;lkkloO0o;:okOd;,,;cdk0d:;;,,,,,,'''''......'''......................',,,,,;;;;;;;;;,,:oxkkkkkkkkkkkkkkkkkkkkxkxxxxxxxxx
ccccclddddddddddddddddddddddddddddddddddddddddddoooooooooooooooooollllc;'.................',,'''.................................''''';cc,':lcokxl,'''''':l:,,,:c:lo;',,lddodxdloo:;;lkklldOx::ldko;,,:lllkx:,,,'''''''''........''......................',,,,,;;;;;;;:;;,;cdkkkkkkkkkkkkkkkkkkkkxxxxxxxxxxx
ccccclddddddddddddddddddddddddddddddddddddddddoooooooooooooooooooooollllc;'..........'....',,''...................................'''';c:',cocoO0Ol,''''':c;,,,:c:ldc,,,colcdxdodl:;;lkdccldkolloko;,;colcxkc,,,''...''''........''.....................'',,,,,;;,,;;;::;,;:lxkkkkkkkkkkkkkkkkkkkxxxxxxxxxxx
ccc:cldddddddddddddddddddddddddddddddddddddddddooooooooooooooooooloooooool:,'.......'''....''.....................................''',;c;',coccdodxc,''',:c;,;;cc:coo;',cl:;ldolol:;:dkocccokxdldko;;:odooxOo;,,,'...............''.....................'',,,,,;;,,,;;::;,,;cdkkkkkkkkkkkkkkkkxxxxxxxxxxxxxx
ccccclddddddddddddddddddddddddddddddddddddddddddooooooooooooooooolloooooooolc:,'...'''...........................................''',,:l:,;ld::l:,;cc;'';cl:cccl:,,:l:,;ll::oxlldl;:okxc:cclk0xldko;;col::dOd;,,,,'...............'.......... ..........''',,,,,,,,,,;;;;,,,:oxkkkkkkkkkkkkxxxxxxxxxxxxxxxxx
ccccclodddddddddddddddddddddddddddddddoddddddoddoooooooooooooooooolloooooooooolc:;,''....................'''.....................'''',co:;lkx;:oc'';ool::oddxddd:,;cddcoxo:lkkloxocdkkl:cl::xOocxOl;cdd:;,cxx:,,;,,'..............''........  ..........''',,,,,,,,,,,;;;;,';lxkkkkkkkkkkkkxxxxxxxxxxxxxxxxx
ccc:cldddddddddddddddddoodddddddddoooooddddddddoooooooooooooooooolloooooooooooooollcc:;,''''...........'''''''..................'''''':looxOo;:c:'',;::;;:clolll:;;lxkxdxolokkoldOOOkl;;loc:ododO0xld0kc;:lk0xc;;;,''.............''........   .........''',,,,,,,,,',,;;;,',cdxkkkkkkkkkkxxxxxxxxxxxxxxxxdd
ccccclddddddddddddddddddddddddddooooooooddddoodooooooooooooooooooooooooooooooooooooooolllccc:;;;,;;;:::ccc:;;,''.................''''',:oxdc,''..'''''''''',,,,,,;cdxkOkdc;:cc:;:looc;,,;::;::codxdlokxl;;ldkdl::;;,'..............'........   ........''''',,,,,,'''',,;;;,,:oxkkxxxkkxxxxxxxxxxxxxxxxxdddd
ccccclddddddddddddddddddddddddddoooooooddddooodoooooooooooooooooooooooooooooooooooooooooooooolllllllloooooollccc:::;;;;;;;,,,,''''''''.',,,''''',;;;;;;,,''',,,,;cxOOxkOkl;;;;;,,,;,,,,,,,'',,,,,;;;;;:;;,;;;;;;;;;,,'.............''........   .......'''''',,,,,'''',,;;;,,;oxxxxxxkxxxxxxxxxxxxxdxxxddddd
cc::cldddddddddddddddddodoooooddooooooodddoooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooollllllllccc:;,'''''.......';;;;:::;;;;,''''',,;lkOxodxkoc;;;,,,,,,;;;;;;,,,,,,,,;;;;;;,,,,,''',,,,,'..............'''.......  .......''',,',,,,,,'''',,,;,,;lxxxxxxxxxxxxxxxxxxxdddddddddd
c:::cloddddddddddddddddooooooooooooooooddoooddooooooooooooooooooooolllllloooooooooooooooooooooooooooooooooooooooollllllllllclc;,''''........':::;;:;,;;;,'''',,,:oxkkkxxxxxl;;,,,,,,,;;;:c:;c:;:c:col::;,,,,'''''',,,'..............',,,,''...........''''''',,,,,,'''''',,,,;lxxxxxxxxxxxxxxxxxxddddddddddd
::c:cloddddddddddddddddoooooooooooooooooooooddoooooooooooooooolooloolllloooooooooooooooooooooooooooooooooooolloooolllllllllllc;'''''........'',,'',,,,,,,''',,,,;lxkkkkkkkxo;,,,'',,,;;;:lc:ll:llcoxd:;,,,,,,''''',,,''..............',,;;,'...........'''''',,,,,,''''''',,;:odxxxxxxxxxxxxdddddddddddddooo
:cc:clodddddoodddddddddooooooooooooooooooooooooooooooooooooooolllllollooooooooooooooooooooooooooooooooooooolllooollllllllllllc;'''''...............'''''''''',,,,:oxkkkkxkxc;,''''',,;;;;::;::;:::loo:;,,,,,,''''',,,''................',,,'...........'''''',,,,,,,''''''',;:odddddddddddddoooooooooooooooo
::::clodddddooddddddddoooooooooooooooooodoooooooooooooooooloolllllllllooollooooooooooooooooooooooooooooooooollooolllllllllccc:,'''''....................''''',,,,;coxxxddxd:,,''''',',,''''''''''',,,,,'''',,'''''',,''..................''............''''''',,,,,,,'''''',;:lloooooooooooooooooooooooooooo
:::::lodddddoodddddddoooooooooooooooooooooooooooooooooooollllllllllllllllooooooooooooolooolloooooooooooooooooooooolllllllllcc;,'''.......................'''''',,;:odxddxxl;''''''',''''''''.........'.'''''''''''',,'''..................................''''',,,,,,,,''''',;:cllllooooddoooooooooooooooooo
:::::lodddddoddddddoooooooooooooooooooooooooooooooooooloollllllllllllllllooooooolloooooooolloooooooooolooooooooooolllllllllcc;''..................''....'''''''',,;coxkkxo:,'''''''''''''''..............'''''''''',,,''..................................''''',,,,,,,,,''''',;:ccccllllooooooooodoooooooooo
::::cloddddooodddoooooooooooooooooooooooooooooooooollllollloollllllllloooooooolollloooooooooooooooooooooooooolooolllllllllccc;'...................''....'''''''',,,;clool:,''''''''''''''''..............'''''''''',,,'''..............................'''''''',,,,,,,;;,''''',:::::cccllllllooooooooooooooo
c:::cloddddoooddoooooooooooooooooooooooooooooooooolllloollloollllllllllllllooooollloooooooooooooloooooooooooooooolllllllllccc;'...................'....''''''''''',,,;,,''''''''''''''''''''...............''',,'',,,,,''.............................'''''''''',,,,,,;;;,,''',;:::::ccclllllllloooooooooooo
cc::clododooooddooooooooooooooooooooooddoooooooooooooooolllolllllllllllllllooooolllloooooooooloooooooooooolllollllllllllllcc:,'.......................''''''''''''''''.......''''''''''''''..................''',,,,,,,'''............................''''''''''',,''',;;;;,,,;:cc::cccccccllllodooooooooooo
:::::loddoodooddoooooooooooooooooooooooooooooooooooooooollloollllllloooollooooooolllllooooooollooooooooooollllolllllllllcccc;'...........................''''''''''..........''''''''''''''...................''',,,,,,,''............................'..''''''''',''',,,;;;;,;:cccccccccccccclddddddooooooo
:::::loddoddoooddoooooooooooooooooooooooooooooooooooooooooloolllllllllllllllooooolllllooooooollloooooooooooollllllllllllccc:;'...........................'''''''''............''''''''''''''...................''',,,,,,,''........................''''''''''''',,,''''',,,,,,;:cllcccclccccccldxdxkkkxdoooo
:::::lodoodddoddoooooooooooooooooooooooooooooooooollloooollllllllllllllllllllllllloolloooooollllooooolllooooollllllllllcccc:,............................'''''''''.............'''''''''''''....................'',,,,,,,''.........................''''''''''',,,,,''''''''',;:cclllclllccccloxkkkOOOkkxxdo
:::::loddoooooddooooooooooooooooooooooooooooooooolllllolllllollllllllllllllllllllloollloloooolllooolllllllllllllllllllllccc;'............................'''''''...............'''''''''''''....................'''',,,,,,''..........................''''''''',,,,,'''''''..',:cccccllccllllldkOkkOOOOOOOxo
::::clodoooooooodooooooooooooooooooooooooooooooooolllllllllllllllllllllllllllllllllollllllllllloollllllllllllllllllllllccc:;'............................'''''''.................''''''''''''....................''',,,,,,''..............................''''''',,,''''''...';:::::cclccclllodkOkkkkOOOOOxo
::::clodoooooooooooooooooooooooooooooooooooooooollllllllllllllllllllllllllllllllllllllllllllllllollllllllllllllllllllllccc:,'............................'''''...................'''''''''''''....................''',,,,,,'''............................''''''',,,''''''...,;:cccccccccccccoxkkkkkkxkkOOdl
::::clooooooooooooooooooooooooooooooooooooooooollllllllllllllllllllllllllllllllllllllllllllllllloooolllllllllllllllllllccc:,............................''''..................''''.'''''''''''.................'..'''',,,,,,''............................''''''',,,,'''''..',:::::cccllcccccoxkOOOOOOOOOkdl
:::::looooooooooooooooooooooollooooooooooooooollllllllllllllllllllllllllllllllllllllllllllllllolloolllllllllllllllllllccc:;'............................''............................'''''''''...................''''',,,;,,''............................'''''',,,,'''''..';ccc:::ccccclllldkOOOOOOOOOOkdl
:::::loooooooooooooooooooooooooooooooooooooollllllllllllllllllllllllllllllllllllllllllllllllllollllllllllllllllllllllcccc:,'............................'.............................''''''''''...................''''',,,,,,''.............................''''',,,''''''',:ccccccc::::cccldkkkkOOOOOOOxol
:::::loooooooooooooooollooollloooollooooooooolllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllccccc;'.........................................................''''''''''''''..................''''',,,,,,,'............................'''''',,,''''',;cccccccc:::::::ldkkkkkOOOOOOxol
:::::loooooooooooooooollllllllloooolloooloooollllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllccccc:,'........................................................''''''''''''''''..................'''',,,,,,,'''..........................'''''',,,''''',:ccccccccc::::::ldxxkkkOOOOOOdlc
:::::loooooooooooooooollooolllloooolllollllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllccccc;'.......................................................''''''''''''''''''''''.................'',,,,,,,,''.........................''''''',,'''',;:cccccclccc:::::lddddxkkOOOOkdlc
:::::looooooooooloooolllooolllooolllllllllllllllllllllllllllllclllllllllllllllllllllllllllllllllllllllllllllllllllccccc:,'.....................................................'''''....''.'''''''''''''''''.............'''',,,,,,,'''.......................''''''',,'.';cccccccccllllccccdkxddddxkOOOkocc
:::::looooooooooollllllllolllloolllllllllllllllllllllllllllllllcllllccclllllllllllllllllllllllllllllllllllllllllllccccc:,'...................''''..............................''...........'''''.''''''''''''..............''',,,,,,,,''......................'''''',,'',:cccclccccccclllloxOOOkxddxOOkxocc
:::::lloolloooooolllllllllllllollllllllllllllllllllllllllllllllllllllllclcccclllllllllllllllllllllllllllllllllllllccccc:,'................'''''''.......................''''..''....................''''''''''.......'''''....''',,,,''''...................''''''''',,,,:ccccccccclllccccldk0000Okxkkkxdllc
:::::lollllooollllllllllllllllllllllllllllllllllllllllclllllllcclc:,''''''';:,''''''',;;,'...',;cc:,'''''''''''''',;ccc,........................................ .....'......................................................................................'''''''',,,;:ccccccccccllllccldk0000K0OOkkxolll
:;;;:lllllloollllllllllllllllllllllllllllllllllllllllllllllllccccc;. .;:c;... .,cc;.  ..,:cll:,..''..;:::.  .;::;..'cc:. .;c::::::::c:;..,:::'   ':::,.. .. .,cccc:'.... .;:c;.  ':::,.  ...,:llc:'. .  .,:::'   ':::,..;::::::::::c;.  .......................''''''',,;::c:cccccccloooolcloxkO0KKK0Okxolll
:;;;:lllllllllllllllllllllllllllllllllllllllllllllllllcllllllcccccc'.,OWWKc   cKWW0;  ;kXWWWWWXk;.  ,0WWXl  :KWWK:.':c:..:0WWWWWWWWWWW0;,OWWNx. .dNWWOl'  .:OXWWWWNXd'   cKWWK: .oXWWO,  .:OXWWWWNXx,   'OWWNd. .oNWWk';0WWWWWWWWWWWK:  .......................''''''''',;::::ccccccldxkxxdolllodkO00KOxolll
:;;::llllllllllllllllllllllllllllllllllllllllllccllllccclllcccccccc;..oNMWx. .kWWNd. ,0WWWX0KNWW0:  ,0WMNl  :KWWK:.'cc:..;OXXXWMMWWXKXk,,OWMNx. .xWWWOo'  :KWWN0OKWWWk'  cXWWX: .oNWW0,  :KWWWKOKWMWO,  'OMWNx. .dNWWO',kXXXNMMMWXXXO;  ............'''........''''''''',;;;;::cccccldxkOOkkxdollllodkkdlllc
;;;::llllllllllllllllllllllllllllllllllllllllllcclllccccccccccccccc:' ,0WWK:.:KMW0, .lNMMK:.;0WMWx. ;0WMNl  :KWWX:.':c:'.....:0MWWO;.'..,OWMWx. .dWMWOo, .kWWWO,.cKWWXl. cXMMKc .oNMM0, .xWMW0;.:KMMNo. 'OMMNd. .oNMWO' ...;kWWW0c....  ..............''''..'..'''''''.'',;::::::cccodxkOOkkOOkkxolccccccccc
;;:::lllllllllllllllllllllllllllllllllllllllllccllcccccccccccccccccc:..lXWWx;xNMNd. .oNMW0' .OWMWx. ;0MMNl  :KWMX: ':c::,... .OWMWx. .. '0MMWx. .dNMWOo' 'OWMWx. ,0WMNo. cXMMK: .oNMM0, .kWMWk. 'OWWNd. 'OMMWx. .dNMWO'    .xWWWO'  .........................''.'''''...',:::::::ccloxkkOkxxOOOOOkxdolcc:;::
;;;;:lllllllllllllllllllllllllllllllllllllllllllclllccccccccccccccccc,.'OWWXOXWW0,  .dNMM0' .OWMWx. ;0MMNl  :KMMX: ':c:c:;,. 'OWMWx. .. '0WMWx. .xWMWOo' 'OWMWx. ,0MMNo. cXMMX: .oNMM0, .kWMWk. 'ONWXd. 'OMMWd. .oNMMO'    .xWMWO' ...............................''....',::::::cccloxkkOkxkOOOOOOOOkxdolc:;
:;;;:lllllllllllllllllllllllllllllllllllllllllcccclcccccccccccccccccc:..oNMWWWMNo.  .dNMM0' .OWMWx. ;0MMNl  :KMMX:.':c:::::' 'OWMWx. .. 'OMMWk' .xWMWOo' 'OWMWx. ,0MMNo. cXMMX: .oNMM0, .kWMWk. .,::;'  '0MMNx. .dNMMO.  . .xWMWO' ................................''...';::::::ccclodxkkxxkOOkkkOkOOOkxxdol
;;;;:cllllllllllllllllllclllccclllllclllllllccccccccccccccccccccccccc:'.,OWWWMWO,....oNMM0' .OWMWx. ;0MMNl  :KMMX:.':c:::::' .OMMWx. .. 'OMMWXOkOXMMWOo' 'OWMWx. ,0MMNo. cXMMX: .oNMM0, .kWMWk.         '0MMWXOkOXWMMO'  . .xWMWO' .''',;;'.............................';::::::::cloodxkxxkkkkkkkkkkOOOkkkk
;;;;:clllllllllllccccclccllccccclllcccllcccccccccccccccccccccccccc:ccc;..lXWMMNo..,..dNMW0' 'OWMWk. ;0MMNl  :KMMX: ':::::::' 'OMMWx. .. '0MMMMWMWWMMWOo' 'OWMWx. ,0MMNo. cXMMX: .oNMM0, .kWMWk,,c::::'  '0MMMMWMMMMMMO' .. .xWMWO' ':c::::;''''.........................';:::::::::clodxxkkkxkkkkkkkkkxkkkkO
;;;;:cllllllllccccccccllccccccccccccclcccccccccccccccccccccccccccccccc:,.'OWMW0,.';..dWMW0' 'OWMWk. ;0MMNl  :KMMX: .:c:::::' 'OMMWx. .. '0MMWKxdxKWMWOo' 'OMMWx. ,0MMNo. cXMMXc .dNMM0, .kWMWkcOWWWWNd. 'OMMWKxdxKWMMO' .. .xWMWO'.,lllc::;,'''.........................,;::::::::::ccloxkkxxkkkkkxxxdddxkkO
;;;;:ccccllllcccccccccllccccccccccccclccccccccccccccccccccccccccccc::cc;..kWMWO'.,;..dWMW0' 'OWMWk. ;0MMNl  :KMMX: .:c:::::' .OMMWx. .. 'OMMWx. .dWMWOl' 'OMMWx. ,0MMNo. cXMMXc .dNMM0, .kWMWk;ckXWMWd. '0MMNx. .dNMWO. ''..xWMWO'.;lllc:;,,,,,'........................,;;;::::::::::ccloddxkkkkkxxxdooxkOO
;;;;:cccccllccccccccccccccccccccccccccccccccccccccccccccc:ccc:ccc:::::c,..xWMWO'.,;..dWMW0' 'OWMWk. ;0MMNl  :KMMX: .:c:::::' .OWMWx. .. '0MMWx. .xWMWOl' 'OMMWx. ,0MMNo. cXMMXc .dNMM0, .kWMWk. ,OMMWd. 'OMMWd. .oNWWO. ,;..dWMWO'.;lllc:;,,,,,,''.....................'',;;;;;:::::::::::cclodxkxxxxdooxkOO
;;;;:ccccccccccccccccccccccccccccccccccccccccccccccccccc:::ccccc:::::cc,..xWMWO'.,;..dNWW0' 'OWMWx. ;0WMNl  :KWMX: .:::::::' 'OWMWx. .. 'OMMWx. .xWMWOl' 'OWMWx. ,0MMNo. cXMMK: .dNMM0, .kWMWk. 'OWMNd. '0MMWx. .oNMMO'.;:..xWMWO'.;lllc:;'''',,,,'...................'',,,,,,;;;::::;:::::::ccloddxxoooxkkk
;;;;:cccccccccccccccccccccccccccccccccccccccccccc::ccccc::::::::::::::c,..xWMWk'.,;..oNMWK; ,0WWWx. ,0WMNd..lXWWK:.':::::::' 'OWMWx. .. 'OMMWx. .dWMWOo' 'kWWWk' :KMMNl  :KWMXl..xNWWO' .kWMWO. ,0WMNd. '0MMWx. .oNMMO'.;:..dWMWO'.;lllc:,'....''''''''''...........'',,,,,,,,,,,;;;;;;:::::::::ccloddddxkkk
;;;;:ccccccccccccccccccccccccccccccccccccccccccc::::ccc::::::::::::::::,..xWMWk'.,:..;KWWN0xONWWKc  .dNMWXkxKWWWk'.,:::::::, 'OWMWx. .. 'OWMWx. .dWMWOo' .lXWWNkx0NWWO,  'kNWWXkkXWMNo. .oNWWXxlkNWMNd. 'OMMNx. .oNMWO'.;:..dWMWO'.;llcc:,''........''''''''.........',,,,,,,,,,,,,,,;;:::::::::::::cclodxxx
;;,;:cccccccccccccccccccccccccccccccccccccccccc:::cccc:::::::::::::::::,..xWMWk'.,:;..c0NWWMWWW0c....'xXWWWWWWXx,..;:::::cc, .OWMWx. .. 'OWMWx. .dNMWOo'  .oKWWMWMWNO:. . 'kNWWMMWWXd.   .dXWWWWWNNWNd. 'OMWNx. .oNMWO'.;:..xWMWO'.;lcc:;,'''........................',,,,,,,,,,,,,,,,;;;::::::::::::::::clo
;;,;:cccccccccccccccccccccccccccccccccccccccccc:::ccc::::::::::::::::::,..:ddo:..,::;..':oxxxdc'..;:'..,ldxxxo;..';::::::cc,..:odo;..'. .cddo;. .;oooc,. ...'cdxxxo;........;ldxxdc,. .....,lxxxl;;lo,  .:doo;.  ,ooo:..;:..;odo:..;llc:;,,'''......................',;;;;,,,,,,,,,,,,,,;;;:::::::::::;;,;;:
,,,;:cccccccc:cccccccccccccccccc::::::ccccccccc::::::::::::::::::::::::,........';::::;'.......',::::;,.......',;::::::::cc;.........;,...................'...........'''...............'...........................''.'cc,..'....':ccc:;,,'''''.................;::::;;;;;;,,,,,,,,,,;;;;;;;;::::::::;,,,,;
,,,;::cccccc::cccccccccccccccc::::::::::c:::::::::::::::::::::::::::::;;;:;;::::::::::::::;;;;:::::::::::;;;;:::::::::::ccc::::::::::::::;;;,,'''''',,,,,''''''',,''''''''..'''''''''...''''''''''',,;;;:;;;;;::cclllllllllllllccccccc::;,,'''''................,cooollc:;;;;;;;,;,;;;;;;;;,,;;;;;::::;,,,,,
,,,;::ccccc::ccccccccc:::ccc:::::::::::::::::::::::::::::::::::;;:::;;:::::::::::::::::::;:::;:::::::::::::::::::::;;;::cccccccccc:ccccc:::;;,,,',,,,,,,,,'''',;;,'''''''''.''''',''''''',,,,,,'',,,;:::cc:::::cccllloolllllllllllccc::;,,,,,''''...............,looddoollc:;;;;;;;;;;;;;;;;;;,,,,;;;:;;;;,,
,,,;:::cccccccccc:::::::::::::::::::::::::::::::::::::::::::::::;;;:;;;:;;:::::::::::::;;:::;:::;::::::::::::;;:::::::::cccccccccccccccc::::;,,,,,,,'',,,,''.',;;,,'',,''''..'''','''''''',,,,,,,,,;::ccccc::::cclllloollllllllclllc::;;,,,,,,'''...............':lloooddooolc::;;;::;;;;;;;;;;,,,,,,,;;;;;;
,,,;::::::::::::::::::::::::::::::::::::::::::::::::::::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;::::::::;;;;;;;;;;;;::ccccccccccccccccc::::;;,,,,,'''',,,''',;;;,,,,,,''''.''''''''''''',,,,,,,;;;:cccllccc::ccccllllllllllllcccccc::;;,,,,,'''''.............';::cllooodddoolc::;;;;;;;;;;;;;;,,,,'',,,;;
,,',;::;;;;;;;;;:::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;,;;;;,,,,;;,,,;;,,,;;,,,;;;;;;;;;;;;;;;;;;;;;,,;;;:::::::::::::::::::;;;;,,,,''''''','..';;,'',,'''.....''''''....'',,,,,,,,,;;::cccc::::::::ccccccccccc::::::::;;;,,,'''''''.............',;;;::ccllllllllc::;,,,,,,,,,,,,,,'''''''',