<<<<<<====/;::::::::::::::::::::;;<=///<<<;::::.<///////<<<<<<<<////<;;;;::::;<///<<9889:99999999888999999999999::::999:::9888999999:;<////.<<<<////:889::;;;;;;;:99;//;:999999999::;;;;;;;;::9888:////<<<<<<<;;::99999::::::;;;;;;;::::;;;;<<<<;;<<<;<<<<<<;;<<<<<<.<<===//<:::::::::::::::::::;;<=////<<<;::.<//////..;;;;<<<<////<<<<;;;;;</////<:889::99999999889999889989999999999::9888888999:;<<//...<<<.<///<8889::::;;:::99;//<;::99999999::::::::998888:;/==//<<<<<<<<;;::99999999::::::::::::;;;<<<<<;;;;;;;;:<<<;;<<<<<<<<<<////<<.:::::99::::::::9::;<=///<<<<<<<<<//<;::::9::::;<<<///==<<<<<<<</////<;99::::99999:::::99988999998899999998877888899:;<</<.::::.<<<<//<988899:::::::99;</<;;;;:9999999::::9:997779:;//====/<<<<<</<<;;;;::999999::99::::::;;;<<<<;;;;;:::::::<;;;<<<<<.---;<<<<<<.<<<;;:::::::::99:;<=///<<<<<<<<<<;;:::::9999::;;<<</===<<<<<<//////<;:::::::99::;;;;;;:99999999999898888888888999:;;///<:9999:.<<<//<::::::::::::::;;</<;;;<;:99889999999999778:;///====///<////<<<<<<<;::::::9999:;<<<<<<;;;;;;;;:::999::::;;<<//<;::9:::;;;;<<<<<<..------::::;</===/<<<<///<<;:::::999:::::;;:::;.<<<<<<<///////<;;;<<;;;::;;;;;;;;;;:::;;;;;::9999999:::999:;;</===<98779:;;<<<<<<<<<<<<;;;;;;<<<<<<;;;;---999999999:::999:;////////<<<<//=====///<<<<;;;::::;<<<<<<;;:::::::::999999999:<////;:::999:::::;;<</=<<..;;--:::.<//====////=//<;::::::::::::::;;::::::::..<</////<<;;<<</<;;;;;;;;;<<<<;<<<;;;;;;;::::::::;;<::<<//===<:876679:;<<<<///////<//<<<<<=<<;;;;;;---------999::::9:;;////::::;;..</======///<//<;;;;;;<<<;;;;::999:::9:9999999999:<///<::::9999999:;;<<//==<<<<;;:..</////==//===/<;:::::::::::::::;;;:::::::::::::.//<;:;<////<<<<<<<<<<<<<<<<<;;;<<<;;;;;;;;;;<<<<//=====<+766679:;<<<<</=====/==//<===<;999999889999999888899999::::::9999--;.<///====///////<<<<///<;9999:9999::999998889999:;<///;:::99998889:;<<<</<===////<<<<//////////=/<;:::::::::::;;;::;;;;::::::::9999:.<<;:-;//===////<<<<<<<<<<<<<<<<<<<<<<<<<<<<<////======:+666679:;<<<<</=========/==<<;98875556668888887777788888877777799-;;.<<///==///////////////<:889999999::99999988899:;<///<::::9998888::;<<<<<</===//////<<<<<<<<<</=/<::::::::::::::::::;;;;;;:::::::99:;<<;;-.<===/////<<<<<<<<<<<<<<<<<<<<<//////==========<<;8666999:;.<<.<<//=====///<<<:97554334566877777777888888777777899::;<<////////<<<<//////////;9668999999:9999:99999::;<////;::::999:88::;<</<<<<////<<<//<<<<<<<;;;<<//<:::::::9:::::::::;;;;;;;;:::::::::;<<<;--.<//////<<<<;;<:::::::::::;;;<<<<<.//=======/<<;;9999:::;;<<<.<<<//////<//<<:9755433335689987788899999998888899::::;<<///<////<<<<<<<<<<////;96679999::::999::9999:;<==///:::::::::::;;<//<<<<////<<<</<//<<<<<;;;<<//<:::9:9999:::::::;;;;<;;;;::::::::;;;<<<.--.<<///<;;:::::99999987999:::;;;;;.../==////<;;;;;::::;;<<<<<.<<<<<<<<;;<<<:9775443333568999999::::::::999999::::::;<</=/////<:::<;;;;;<////;97678999:::99999999:9:;<=///<::::::::;;;<////<<<////<<</<<<<<<<<<;;;<<///<;::99999::::;::::;;;;;;::::::;;::;;;<<<<--.<<//<;:::99999888888777788::::::....</<<<;;;;;;<<<<<<<<<<<;;<<</<<<<;;;<<:9775443333568889999:::;;:::9999::::::::;<<//=///<:::::::::;;<///;97678999::99888999999:;<<//<<::::;;;;<<</////<<////<<<<<<;;;;;;;;:::<<///<::::::::::::;::;;;;;;;;;::::;;;;;;;;;</<;-;<<//<::99999999999998888999:;;;;:::;<<<;;;;;-;<<////<<<.;;;;;<<<///<<<<<<;:986443335567788999:::;:::999999::::::;;<<</==<<;:9:::::::;<<<<<;:77799::::998888899999:;<<<;;::::;;;<<//<<//<<////<<<<<;::::::::::::;<///.::::::::::::;;;;;;;;;;;;:::::;;;;::;;<<<<;;<</<<::999999::9::::999999:;;;;::::;;<;;::;;-;<<//....::;;;;;<<<</////<<<<;:86443335677788999:99:::99::9999:::::;<<<</==<<;989::::::;<<<<<;:9779:;;::998889999999:;<<;;:::;;;;<<///<<<<</==/<<</<;:8999:9::::::;<//<.:::::::9:::::;;;;;<<;;;;:::::::::::;;<<<<;;<</<<::988999:::::::::::::;;;;::::::;;;;:::;-;<<.:::::::;;;;<<<<<<</=//<<<<<:864335567778999::99::::::::9999::::;<<<<<//<<:9789:::::;<<<<<;;:99::;;:9999999999999:;;;;;::::;;<<<///<<<<</===////<;88779999:::::;<<<<.:::999999:::::;;;<<<<;;::::::::::::;;<<<<;;<</<<:9977789:::::::::::;;;::::999::;;;;:::;;;;;:999::::;<<<<<<<<<<<////<<<<::86535556789::::::9::::;;:::::::::;;<<<<<//<<:97799:::;<<<<<<<<;;;;;;;:99999:::::::::;;;;::::;;<</////<<<<//======<;:977789999::::;<<<<.:::9889999999:;:;;<<;;:::::::::::::;<<<<<;;;<<<::97667899:::::::::::::9999999::;;<;--;;;;;;::999::;<<<<<;;;;;;<<<<<<<<<;:8855556689999999999::;;;:::::::::;<<<<<<//<<:8778::::;<<<///<<<<<<<<<;::::::::;;;;;;;;;:::::;<<//=///<<<<</=====<<;:777789999999:;;<<<<.::8888999999::::;;;;::::::::::::::<<<<<<;-;<<<::976668899::::::99:::998899999::;<<;;;;;;;;:::99:;;<<<<;;;;;;;;;<<<<<<</;:86555689:::9988999:;;::::::;;;;;;<<<<<///<<:8778:::;<<<<////<////////<<;;;;;;<<<;;;;<;:::;;<</====//////<////=<<;:9777789999999::;<<<<.::8778899999:::::;;:::::::::::::::<<<<<<;-;<<<::976678999:::::999:::9888899999:;<<..;;;:::::::::;;;;;;;;;;;;::;<<<<<<<//;:8666689::::98889:;;;;::::;<<<<;;;<<<<///<<:8779:::;<<<<//==/////====////////<<<<;;;<<;;;<<<</====///////////=<<;:9776789999999::;<<<<<::877789999::::::::::::::::::::::;<<<<<<;-;<<<::977788999999999999999888888889:<<<<.;-9999:::::::;;;;;;;;;;:::;;<<//<<///;9988889:::999999;<<<;::::;<<<<;;;;<<<///<<:8889:::;<<<<//===//=====/////////<<<<<<<<<<<<<<<<////////===/////<<;;:88788899999999:;<<</<;-97778999:::::;;::::::::;::::::;;<<<///;-;<<<;:987788999999999999988889888889;</==<:999999::::;;;;:::;;;:::::;;<////<///<;:9988999999999:;<<<;;;;;;<<<<;;;;<<<///=<;:999::::;;;<<=>>>====/////===//////<<<<<<<<<<<<<</////////===/<</<;;;:988888899:::99:;<<///<-:977899:::::;;;:99:::::;:::::::;;<////<;<<<<;:9877889::99899999988888999899:;//==<:999999:::::;;;::::;::::::;;<////<<///<;:999999999999::;<<<;;;;;<<<;;;;;<<////==;:999::::;;;<=>>>>====/////===////=//////<<<<<<<;:::::::..</==/<<<<;;;:998999999::::::</////<;::99999:::::;;;:99::9::;:::::::;;<////<;<<<<;:986788999988899999888889999::;<//==<:999::::::::;;;::::;:::::;;;<<///<<<//<<;::::999999999:::;;;;;;;;;;;;;;;<<///===<;:999::;;;<<=>>===///<<<<////<<<///====/<<<<<:9998888999:<<//<<<<;;;;:988999999:::::;<</////<;;::99:::::::;::999:9:::::::::::;<<///<;;<<<;:98668899998899999988888999:;;;<//==<:9+9::::::::;;:::::::::::;;;;<//<<<<<<<<<;;;;;::998899::::;;;;;;;;;;;;;;<</=====<;::::::<<<<<==<;;;;;;::::;<<<<<<<</==>=<<<<<;777777788899:;<<<-;<;;;;:98889999:::::::;</===////<<::::;;;;;;::999:;;;;;;;;;;;;<<<<//<.;<<<::997778999999::99999888999:;<<<<<///.99999:::::::;;:::::::::::::;;<///<..<<///<<<//<<;:::::::::::::;;;;::;;;;</=====/<<;;;;;<<<====<:8889999999::;;;;::;</===<<--98666777789999:;<<;-;<<;;;:9999999::;;;:::;</===//////<<<<<<<<;;;:::::;;;;;;;;;;;;<<<<</<.<</<<::977889999:::::::99888999;<<<<<////.:999::;;:::;;;::;:;;;::::::::<<//<..<<////</====<<<<<<;;::99::;;;;::;<;;</=====/<<<<<<<<=====<:8555688766779::::::;<//=<<:96666678999999998:;<;-;<<<;;:999999:::;;::::;</===////=========<<<<<<<<<<<<<<<;;<<<<<<<<<<<.<//<<<:988999999::::::99998999:;<<<<<////.:999:;;;;;;;::::;;;;;:::::::::;<<<...<</////==========<<;;:::;;;;;:;<<;<<</====///===========;855556686666799:::::;;</<<:9866667899999::988:;<;;<<<<;;:999999:::;;::::;</=//////==================//////<<<<<<<<<<<<..<//<<<::::::::99::;;::9999999:;;<<<<<////.:999;;;;;;;;::::;;;;;;::::::::;;<<.;;;;;<<</============<<<<<<//<;;<<<<<</==================<:855566887777779:::::;<<<<<:96666899:::::::989:;<<<<<<<<;9989999::::;::::;<//////////===============/==////////<<<<<<<<<<<//<<<;;::;;;:999:::::9999999:;;<<<<<///<<;999:;;<<<;;::;;<<<<<;;:::::::;;<<;:::::::;;<<////==============/<;;;<<<</============///===;87666777888778899:::;<<<<;;:766669:::::::::999:;<<<<<<<;;9888999:::::::::;;<////<<<//============////====//////<<<<<<</<<///<<<<<;:;;::999:::::9998889::;;<<<////<<;9999;;<<;;;;:;;<<<;;;;:::::::;;<<:::9999:::;<../////===========/<<<<<<<<///=========////==;:86667778888878899::;<<<<<;;:766679::::::::::99:;<<<<<<;;:8778899:::::::::;;</<</<..<//===========/<</====///////<<<<<///////<<<<<;;::99999:::::9887889::;<<<<///<<<;:999:;;;;;;::;;;;;;;;;:::::::;<<<;::988899:::....<////==========//<<<</////==========//===;:87667788988777899::;<<<<<;:976678:::::::::::::;;<<<<<;;:97667899:::::::::;;<<<<<<.-.</===========<<</====/////==//<<//////==/<<<<<;::8888999999987779::;;<<<<<<<<<<<;999:;;;;;;::;;;;;;;;;:::::::;<<<;;:9866899::----;;<<</==========////<////================;:87777889988777899::;<<<<<;:977789::::::::::::::;<<<;;:::75567899:::::::99;;<<<<<<.:..<===========<<<<.///======>=////<<<</==/<<<<<<;:8778999999986689;;<<<<<<;;;;;<<<;99::::;;;;;;;;;::::::::::::;<<<;;;:86667899::::::--<<<</========////========<<<<<<</////;:9888999999877889:;;;///<<;:99889:99999999::::::;<<<;;::9644578999:::::99:;<<<<<<<....<<<<====<<<<<;;;;;..</===>>>//<<<..<</=/<<<<<<;:9877888889876689;<<<<<;;::::;<<<;:9:::::;<<<<<<<;::::::;;;;;<//<<<;;98666789:::999::;;<<////=====///=======<<::::.<<....;;::99:::9999878899:;;<////<;:9999::99889999:::9:::;<;;;::96445789:99::::99:;<<<<<</<<.:;;;;<<<<;;;99999::;;;<</==>=/<;;....<///<<<<<<;::98888667887889;;<<<;;::::::;;<<<:9::::;</////<<;::::;<<<<<</=//<<<;;98666789::988999:;<////==============<.:9999:..--99::::::::::99999999:;;</////<;:9999:999999999:::9:::;;;;;::9654579::9::::99::;<<<<<//<.::9999::::99998888:::;;;;<<//<<;;;.<<<</==/<<<<<;;::::999999999;;;<<<;::9999::;;<<<;:::::;</////<<<;;;;<=========/<<<<;;98766679:9888899:;<///=============<.-99999:..-99999:;;;;;;::9999999:;<//////<;;:99:999999999:::::::;<<<;;;:975558::::::::::::;;/////=/;:99999::::::9988899:::;;;<<<<<;:::::;;</===//<<<<;;;<<;;;;;;;;<///<<.:99878999;;<<<.::::;;<////<<<<<<<</==========////<;::7755689999889::;<///<=====>>===/<;988889::;;;:9999:;//<;;;:9999999:;<///////<;;;::9999::99::99:::;;<<<<;;:977579:;;;;;;:::::;;<///==/;:99999:::::::998899::;;<<<<<<;;:99::::;</===/<<<<<;<<<///<<<<//===<<.998777899:;;<<<.:::;;</////<<<<<<</============///<;:9755568998889::;<///<<<===>>==/<;988889::;;;;;:99:;<//<;:::9999999:;<//===///<;;:99999::999999999:;<</<<;:977789;;;;;;;:::::;;<//===/;:99999:::::::99899:::;<<<<<<.;:98899::;;</////<<<<<<</////////===/<.:9987778888:;<<<.::::;<<<///<<<<;;;/============////<;9755556898889::;<//<..<</====//<;98889:;;;;;;;;::;<<=/<;:::9888999;<<//==/////<;::9999::99::::999:;<<//;:9977789:::::::::::;;;</====/;:98888:::::;:99899:::;<<<<<<.;:9889:::;;;<<<//<<<<<<//////////===<.:99987778998:;<<<.::::;<<<<<<<<<<;;;/============/////<:975555688999:;;</<<---.<<////<;;98889:;;;;;;;;;;<<<=/<;::::88889:;<///==/////<;::999999:::::::9::;<<//;999888999999999::::;<<<//=>>//;988889::::;::9999::::;<<<<<.;:9999:::::;;;<<<//<<<<////==/===///.::98888889999:;<<<<<:::;;;;<<<<<<<;;</=>>>======<<<<<<<<;:9866667899:;<<<<<:999:;;<<<<.;:998789-;;;;;;;;<<//==<;::::98889:</=====/////<;:99999999::::::::;;<///-998778999998899::::;<<////==//;987789::;;;::9999:::;<<;<<<.-:999::;;:::::;<<///<<<<///=====//..::9888899999:::;<<<<<;:9::;;<<<<<<<<<<=>>>=====<<;;<<<<<<;;::98866788:;</<<:88889::;<<<<.::98789-;;;;;;;;<///==/<;:::::99:<//====//////<;::9999999999::::;;<///<-998778999998899::::;<<<////=//;976789:::;;:::::;:;<<<<<<<<;-999:::;;;;::::;</=//<<</======/<..::987889999999::;<<</<<:99:::;;;<<<<<</=>>>===<<::99;;<<<<;;;;:9886668;<//<:8668899::;.<<<<<:989--;;;;;;;;<<//==/<<;::;;:::<//===//<<<<<;:::9999999999:::;;<////;-98777789999999:::::;<<<<///=//;987889:::::::::;;;<<<<<<<<.;-99:::;;;;;;:::;</==/<<</====///<.:997777999999999:;<<<//<:99::::;;;<<<<<==>>>>/<:999889;<<<<;;;;::986679<///<866688999:;.<<<<<<:99--;;;;;;;;;<</////<<;;;;;::<///==/<<<<<;::::99999:9999::;;<<//=<;:9876667899999::::::;<<<///===/<;9888999:::::::;;<<<<<<</<.::99:;;;;;;;;;;;;<<///<<//==//<<<;::976678999999999:;<<///<.9999::;;;<<;</====<<<:86667789:<<<<<<<<:99889;/==<:8556789999:;<<<</<<::::::;;;;;;;;<<<///<<<<<<;;<<<//=//<;;;;:::::9999:::::::;;<<</==<;:9876667899999::::::;<<<//=====/<:98888899::::;<<<<;<<<</<.::99:;;;;;;;;;;;<<<///<<//===/<<;;:975678999999999::;<<<//<.:9::::;;;;;;</====<<:7555566689:<<<<</<<::;;;/==/;:8556899999:;<<<<//<::::::;;;;;;;;;<<//<<<<<<<<<<<<//=/<<;;;::9:::99:::;;;;;;;<<</===<;:98766688999999:9:::;;<<//======/<:9998899:::;<<<<<<<<<//<:::9::;;;;;;<<;;;<<<<///<<</=//<;99975567999999:99:::;<<<//<<.:::::;;;;;;</===/<:744455666679<<////=<<<////==<;:6556899999:;<<<</=/;:::::;;;;;;;;;<<//<<<<<<<<<<<//==/<<;;;:99:::99::;;;;;;<<<</====<;:8876668899999999:::;;<//========<<::::99:::;<////<<<</<<.:::::;;;;;;<<<<;;<<<<<///<<<//<;;98755568999999999::;<<<///<<<.;:::;;::;;</==/<:7444456776679:</=======////=/<;:65579999999;;;;</==<::::;;;;;;;;;;<<///<<<<<<<<///====/<;;;:99::::9:;;;;;<<<//=====//:988765678999999::::::;<///=>>>>==/<<<;;;;;;;//===////<<<.-999:::;;;<<<<<<;;;;;;<<<//<<<<<998644458999:::9999::;;<///////<;;;;----;<//==<:764355778876689-.///=====//=//.;876789999999:;;;<</==<;;::;<;;;;;;<<<<<<;;;;-<<<====>==/<<;;::::;:99:;<<<<<//====/==//.9888656789999899:::::;<///=>>>>>=//<<<<<;;;</========<<.-9999:;;;;;<<<<<<;;;;;;;<<//<<;;:986444479999:::9889::;;<////////<;;;---;</====<:7644578888766689-.//=====////..:8667899999999:;;<<//=/<;:::;;;;;;<<<<<<;;9999--<<=====/<<<;;::::;:99;<<<<///====//////.9988766789998889:::::;<///==>>>===//////<;<//=======/<<.-999::;;;;<<;<<<;;;;;;;;;<//<<;:9864444589999:::9899:9:;</////////<;;;;<</====<:876467888877766889-.//==////<..;:7667899899999:;;<<</==<;::::;;;<<<<<<<;:9777799-;<<=///<<<;;;;;<<;::<///////===//<<///.:998877889998888::;;;<//=/=========/////<<///=>>>==/<<<.-999:;;;;;<<;;<<;;;;;;;;;<<<<<;:964444788999::;:::::99:;<///////////<<<//=====<:8766788888888888899-.////<<<<..;:7667898888999:;;<<<===/<::::;;<<////<<:97555779999;<<<<<<<;;<<<<<<;;///=///////<<<<<<<<;:98877999998779:;<<<<//====/<<<<<<<<<<<<<<<<>>>>=/<<<<::::::;;;;;;;;;<<;;;;;;::;;<<<<;:9755568999:::;;;;;;:9::;<////////==///======/<:99777888998888988888:-<<<</<<<;;::755789989999::;<../=>=//;:::;<//////;;97555568999:::;;;;<<<.<<<</<<</////////<<;<;;::;<<:988999:999999:<</////====/.<:::::::::::;;<<///.<<</<<:::::;;;;;;;;;;<<;;;;;;:::;;<<<;;9865689:::::::;;;;;::::;<////////======>>===<<:977788889988888888888:;<<</<<<;;::75579:::99:::;<</..==>=/<;:;</===///;975555689::::::::;;..<<<</////////////<<;;;;::99:;<;:99:::::9999::<//////===/..:99999999999999;....<<</<::::::;;;;;;;;;;;;;;;;;;:::;;<<<;;986568:::::::::;;;;:::::;<<///////====>>>==/<:97777889998888888888888:;;<//<<;:::86579::;::::<<<</../=>>=/;;</======/;97555689:::::::999:::.</////////<<<<<<<;;;;;::99:;<;;;;;;;;::::::<<///<//==/...:977699997778899---.<<//<:::::::;;;;;;;;;;;;;;;;;:::;;<<<;;:86579::::::::::;;;::::::<<<////<//===>>>=/<<:97778899998888878888888+:;<//<<;:::865689;;:::<<<<</.../=>>/<<//======/;9778889:::::::::99999:</==/////<;;;;:::::;;::::;;;;<<<<<<<<<<<<;;<///</<===<<<:8877788877667789--;.<//<<;::::::;;;;;;;;;;;;;;;:::::;</=<..-8778::;;;:::::;;;::::::;<<<////<<</=====/<<;:8777899999988888899999889:;<<<.;;;;:8668:;;::;<<///<<<</=>=///=====>>/<:888999:::::::::::9999:;///////<<;;;::::::;;::::;;;<<<<<<<<<<<<<<<//////===<<<:98777788877777789--;<///<<;::::::;;;;;;;;;;;;;;:::::;;<===<.-8788::;;;::9:::;;:::::;;<</////<<</====/<<;;:87778999:99988889999998889:.<<.;;;<:8889:;;::;<<///<<<<//=///===>>>>>/;98899:::::;;::::::999:::<///////;;::9999:::::::;;;<<<<<<;;<<<<<<</////====<.<:987677778877888889-;.<////<;::::::;;;;;;;;;;;;::::;;;;</===<.-87789:;;;:999::;::::::;<</////<<<<<///<<<<<<;:77789999999988899999998889:...;;<<<:889::::::;<<<<<<<</////==>>>>>>>/;9899:::::::;;::::::9::::;///<<//;;::9999999::::;;;<<<<<<<;;<<<<<</==/==/<<.-:9887777888888999999;..</==/<;::::::;;;;;;;;;;;;;::;;;<</====<.-87789:;;::999::;::::::;;</////<<<<<<<<<<<<<<;:87778999999888899999999888:...;;<<<:8889:::::;<<<<<<<<////==>>>>>>>><;999:::::::;;;;:::;;:::::;</<<<<<::::999999::::;;<<<//<<<.....//.</==///.;;::99888877899999::::::<<</===//<;;::::;;;;<<<<;;;;;;;;<<<</====<.-87789:;:::::::::::::::;<<////<<<<<<<<<<<////<:98888899999988999999::9989:;<<;.<<<:8889::;;;;;;;;<</////==>>>>=====;999::::::::;;;;;;;;;;;;;;;</<<<<;:::::9999::::;;<<<///<//<<<</==//////..;::98889998889::::::::::;<<</====/<;;::::;<<<<<<<<<;;;;;<<<<</====<.-9778::::::::::::::::::;<<==//<<<<<<<<<<<////<:98888889999999::9999:::999:;<<<<<<<:98889::;;::::;<<<////=>>==/<//=<;99:::::::::;;;;;;;;;;;;;;;<//<<;;::::::999:::;;<<<//=/<<<<<<<///==//<.;;::98889999999::::::::::;<<<</=====//<....<<<<<<<<<<<;;;;<<<<</====<..:889::::::::::::::::99:;<==//<<;;;;;<<<<///<<:98887778999999::99999::99:;;</<<<<<:988888::;::::;<<<////===<<<<</=<;9:::;::::::;:::;;;;;;;;;;;///<<;;;::::::99::;<<////=//<<<.---...//<..;:::98889999:::::::::::::;<<<<////======<<<<<<<<<<<<<<<;;;;<<<<</====<..:989::::::::::::::::99:;</=//<;:::::;<<<///<<:9887777899999::::9999:::::;<//<<<<<:9877789:;:::::;<<<<<//=/<<<<</=<;9:;;;;;:::;:::::;;;;;;<<<<===<<;;:;;;;;;;::;<<///////<<<:99999:;;<;;;::::99999999:::::::;;;;;;;</////<//======///<<<<<<<<<<<<<<<<////====/<;;;:99999999999::::99999:;/==/<.:9:99::;<<///<;;:98777789::::::::::9::::::<<==<<<<<;:978999::::99::;;<<<<</<<<<<//=/;;;;;;<;;;:::::::;;;;;;<<</===/<;;::;;;<;;;;<<<///////<<::888899:;;;;-:::::9999999:::::::;;;;;;<//=///<//==>>>==//<<///<<//<<<<<//========//<;;::999999999999:99999:;</==/.:99999::;<<////<<;:8777789:::::::::::::::9:<<<<<<<<<;:989999::99999::;;;<<<//<<<///=/<;;;;<<<<<<<::::::;;;;;<<</===/<;;::;;<<<<<<<///////<<::88788999:;<;;-:9::::::99999::9::::;;;<;</==//////=>>>>===/======/==///////========//<;;;::98888888899999999:;<///<:999999::;<<////<<;;9878789:::::::::::::999:;<<<<<<<;;:9999999999999::::;;<<////<///==/<;;;<<<<<<<<<;::;;;;;;<<</===//;;::;;<<<<////////<<;:8666678899:;<<;-:9:::9:::999999:::::;;;<</===/<<<<</===>>>>>>>>>====================//<;;;;::99898899999999:::;<///.:999999::;<<==//<<<;:98888999::::::::::9999:;;<<<<<<;;::999999999999::::;;<</==//<</==//;;;;<<<<<<<<;;;;;;;<<<<=//////<;;;</////======<<;;:86555778899:<<<::999999:::98789::;;;::;;</=>>//<;;;;<<<//>>>>>>>>>===================/<<<<<<<;::::999::::;;;;;<<////;::::::::;</===//<<<<;988999:999:::;;::::989:;;;<<<<<<<<<::99999988888889;<<</==//<</==//<<<<;<<<<<<<<<;;;;;<<//==//////<////////=======<;:865556788899:<<<::988899:::87789;;<<;:::;<=>>>//<;;;;;;;;<//>>>>>>>=================///<<<<<<<<<<;;::::::;;;<<<<<////;::::::;;<</====/<<<<;988999999::::;;::::999:;;;<<//<<<<</<:9999988787889;<<<//=/////=====//<<;;<<<<<<;;;;;<///===///////////<///======<;:86656688::::::<<.::887889::98789:;;;;::::;<=>>>//<;;;;;;;;;-.//=>>>>>=====>>>===========/<<<<<<<<<<<;;;::;;<<<<<<<////<;::;;;;<</==>>=/<<<<;98688888999::::::999889;;<<//////////<::99787777789;<<<//============//<<<<<<<<;;;;;<///====//.<<<<;;<<<<//======<:86666899:;;;;;;<<.::877789::989::;;;;:::::;<=>>>//<;;;;;;;;;--../======>>>>>>>>>>========/<<<<<<<<<<<<;;;;;;<<<<<<<////;:::;<<<<</==>>=/<<<<;96666888999:::::9998889;<<</////===///<::998877789:;<<<//===>>>==/=====///<<<<;;;;;<///=====/..;;;;9:::<<<<//////<:8668899::;<<<<<</<;:8778999999::;;;;;:::;;;<=>>=/..;::99::::::;;<///====>>>>>>>>>>>>>>>>=/..<<//////<<<<<<<<<<<<<<<///.::::<<<<</==>>>==<<<<;98656789999999999999889<////////=======<:99888899::<<</========<<<<////====//<<<;;<<<</====<<::999877799::<<<<<//<:866899:::;;<<<<//<;:88889999:::;;;;;::::;;;/=>>=/..;988888899::;<<<<<<====>>>>>>>>///////...<//<////<<<<<<<<////<</=//.::::<////==>>>>==<<<<;9865678999999888999:99:</////===========<:98889::<<<///===<=;;;:::<<////======/<<<<<<</===<<:886666666679::;;<<<<<;86889::;:::;<<<///<;99999999::;;;;;;::::;;;/==>=/.;:87777778899:;;;;::<<//==>>>>>/..;;;;....<<<<////////////========//.:::<<///===>>>>==<<<<;986567899999888899::9:;<==//=>>>>>======<::999:<<///=====<-;999888:;<<///======////<///==<;:86655667766779:;;<;<<<;98889::;:::;<<<////<::::999:;;;;;;;;::::;;</====..;:877777788889::::99:<<<//====/.--::::---.....<<<////=============//.::::<///===>>====<<<<;;8666789999999999:::::;<==//=>>>>>=======<:::<<////====<<-,99666668::;<//======////////==;:886656899998899:;<<<;<<;988999:::::;<<//===<;;;::::::;;:;;::::::;;</===/;;:98777778999999998779:;;<<///<;;::8888:::::::::---<<<<<<<<</////////<;:::<//=======>=/<<<<<:98767788999999::::::::<////=>>========//<<<<<//======<;:887655556679:;;///=///////<===//-8776679::9999899:<<<<<<<;98899::::::;<<//===<;;;;::::::::;;::::::;<//==/.;:9988878899999999987789::;;<<;;;;:97667688899999999::;;;;;;:;<<<<<////<<;;</==========//<<<<<:8766678889999::::::9:<////===//======///<<<///=====<.:88665556666779:;///////////====/-8666679::::::8899:<<<<<<<:97899::::::;<<//==<;::;;;::::::::;:::::;;<//==..::9888888999:::::::9988899:;;;;;;:976555566688999999999:;;;;:;;<<<<<<////<</==>>=======//<<<<<:866667888899:::::999:;<<<</=/<<<//====///<<///====<.-:866556788887779:;//////////===<-8665678::::::98899:<<<<;;;:97799::::::;<<//==;:99:;::::::::;;:::::;;<//=/..:98888888999:::::::::999999:;;;;;:9765555566889999999999;;;;;<///<<<<<<<////==>>====/////<<<<<:865568887899::::99999;<<<<//<<;;;<//===//<<///==/<.--:8666788999997779:;;//==////==<-88665678::::::98999;<<<<;:::9889:::::::;<///<<:99999:::::::;;;:999:;</////<-:9889998899:::::::::::::999::;;;;;97655555688899:::::999:;;<<====/<<<<<<.<<<==>>>>>//==/<<<<<;;966667888899:99:99999;<<<<<<<-:::..<<////////===<-:9998878999::::9988999:<=====//<<:97555578:::::9:99999;<<<<;:::9889::;;:::<<///<;:9889999:::::;;::999:;</////.-:988999999:::::::::::::::99::;;;;;:9765556899999::::::99:;;</=>>>=//<<;;:..<<==>>>>/==//<<<<<<;:86667888999999::999:;<<;<<<<:9999:..<///==/===<.:999887899::::::99999989;<==>=//<<:75555578:::::::::999;<<<<;;::9789::::::;<<//<;::988899999:::::::999:;<////<.-99889::99::::::::::::::::::::;;<;;:987666899999::::::::::;</==>>>==/<<;;:::.<<<<//////<<<<<<<<<;9868888899999::::99:;<<;<<<;999999::.<//======<-:99987789::::999999999899;<===/<<:975335588:::::::::999;<<<<<<;:8778999:::;<///<;::99999999999::::::99:;/////<.-99899:::::::::::::::::::::::;;<<;;::87776899::::::::::::;<//=======/<<;;::::;;;;....<<<<<<<<<<<<;98899999999::::::9:;<<<<<<;99999999-.</=====<.-:99987889::::999998899999;<=///<::975335788:::::9::999:;<<<<<<;;99999999;;;<///<<;;;99998889999:::::::;<////<<::99999:::::999::::99:::::;;;;;;<<<;::977777::::::;:::::::;</====/===/<<::989::::;;;;;;;;;<<<<<<<<<:999999999::::9:99:;;<<<<<;99999999::.</=///<<<;:987789:::::999998899999:;<///<;:975335799:::::9:9999:;<<<<<;;;::::::::;;;<<//<;;;;999988899999:::::;;<////<.::999999999999:999999:::;:;;;;;<<<<;;::97779:;::::;:::::::;</==///////<;::889:::::::::;;<<<<<<<<<<<;:999999:::9:99999:;;;<<<<;:999999:::.<///<<</<;:987799::9::999998899999:;<<//<;:975533579:::::999999:;<<<<<<<<<<<<<<<</<<<<</<<;;;:999889999999::;;<</////<:::99:::999999::99999:::;;;;;;;;<<<<<<;;:9999:;;<;;;;:::::;</=====////<<:::99::::::::::;<<<<<<<<<<<<;:99999:;;:::9999::<<<<<<<<:99999::::.<//<<<<//;:987899::99::99999999999:;<<//<;:976533579:::::::99999:<<<<<<<<========/<<<<<//<<<;:999899999999:;<<///==//.:::9:::::::999:9999::;;;<;;;;;;;<<<<<<<;::999:;;<;;;;;;:::;</======///<;:::----::::::::;<<<////<<<<<<;::999:;;;:::99::;<<<<<//<-:::::;;:::.//<<<</<;:888899:::9:::9999999999:;<<<//;;:96553579::::::::9999:;<//<<//========/<<</////<<<;;::::::99999:;<///====/..;;;;<<<;;;::::999:;;;;<<<;::::<<<<<<<<<;::999:;;;;;;;::::;<///===////<:::;;;;;;::::::::;<===//<<<<</<<;;:::::::::9::;<<<<</==<;:::;;;<;;;</=/<<</<;:9779999:::::99999999999;<<<<</=<;:8655579:::::9::9999:;<//////========/<<//=////<<<;<;;;;;;;;;;;<<<//====/<...<<///<<<;:::99:;;;;<<<<;:::;<<<<<<<<<<;:999::;;;;;:::::<</////////<;:::;;;;;;;::::;::;<=>>=//<<<<///<<;:::::::::;;;<<<<</=/<;::;;;<<<;;</=//<//<;:97899999:::999999999999:<<<;</=<;:8655579::::::::999:;</==////========/<</===////<<<<<////////<<<<<<//====<<<<//==/<<<;::::::;;;;;;;;;:::;<////<<</<<;:::::::::;:::::<//////<///;:9::;;;<<<;;::;;;::<=>>=//<<<<//===<<:::;;;;;<<</<<<<///<;::;;<<<<<<</=//////;:97899999999999999999999:<<<;</==<;9866799:::::::999:;</====////=======////==//////<<<<////////<<<<<<</====<<//====/<;;:::::::;;;;;;;;;:::</===///////<<;;;::::::;;::;<////<<<<<<;:99:;;<<<<<;:;;;;::;=>>=//<<<<<//====<<<<<<<<////////===<;:;;;<<<<<</////////;:97799999999999999999999;<<<;</==<<9988999:::::::99:;</=====///////====////====///////=====//====//<<<//==////=====<:::::::9::;:::::;:::::</==/////////<<<;::::;;;;<<<//=//<//<<;:::::;;<<.;;;;;;;;::;=====<<<<;<<</>>>=///=/=======//====/;;;;;<<<<<</////////<:88789998889999999999899:<<<;;/==/<::::999999::888::;</======////<///==////=======//======////=====/<<////////=====<:999:::::;;:::::::::::</=////////////<<;;;;<<<//////=/<///<<:::::;;;;.;;;;;;;;;::;=====<<::;;;<//>>===========///=====/<;;;;;<<<</====///=/<:88789999999999999988889;<<;;;/==/<;:::99998999888:;<//==/===/<<;;;<<<<<<</============/====/=======//////////====/:988999:::;;:::::::::::;<///////////////<<<<//=======//////<;:::::;;.;;;;;;;;;;;;;<====/<<::::;;..//===========///=====//<;;;<<<<</=>>==/==/<:8878999:::999999987779:;<<;;;/===/<;;:::999999889;<</////==/<<;:::;;;;<<<<=========//////============/<<<<//=====/:98899999::;::::::::::::<///<///////////========>>===/////<<:::::;;;;;;;;;<<<<<<<<====/<<:::99::....///============>====//<<<<<<</==>>>====/<:888899:::::99999987789;<<<;;;/===/<<<;;;::9999:::;<<<<////<<;;::9:;<<<<<<<<///===/;;;;:<<<<<<<====///<;;;<////===/<:88999999::::::::::::::;///////////////====>>>>>>>==/////<;:999::;;;;;;;<<<<<<========<::888899::;;..<<//======>>>>>>>>/////////===>>=====<:977789:::::::999888778:;</<<<<<===/<<<<<<;;;;;;;<<<<<<<////<<;;:99:;;<<<<<<;</////<;:8899:::;;<<<==//<;:9:<////==//<:98889999999999::::::::;<</////////////======>>>>>===////<;:999:::;;;;;;<<<<=========<<:877778899:::::.<</===>>>>>>=>>>>=//========>======<:877789:::::9:999888889:;<<<<<<</=//<<<<<<<<<<;;<<<<<<<////<;;;;9999:;<<<<<<;;<<<<<;:866779999::;;<=/<<:99:<///////<<:98877899999999::::::::;;<//////<<<....<<<<<<=>=>>======/<;:9999::::;;;;;<<==========<;87776777889:::::;;</=>>>>>=====>>===========>==/==<;977789::::::::999989899:;<<<<<<</////<///////<<<<<<<<<////<<;;::99999:;;<<<<;;<<<<<;:86677999999::;<<<;::9:<<//////<<<:987789999::::::::::::;;;<<<<<;;--::::::::;;<===========/;:9999:::::;;;;<<==>>>>>==<;9755767778899::::;;;/=>>>=<;;;;<========/===>>=//<<;:777789::::::::999999999:;<<<<<<<</////===//=//<<<<<<<<<<<<<<9986778899::;<<<;;<<<<<:9855789999999::;.<<;:9:;<<<<<////<;:97778999::::::::::::;;<<<<;;99899999999:::.<////======/<;::::::::::;;<</==>>>>>=<<974346677778889::;;;;/=>>=;;::99;;<==========>==//<<98666789::::::::999999999:<<<<<<<<<////====//==/<<<<<<<<<<<<::86555678899:;<<<;;<<<<;:96557899:::::::;.<<<::::<<<<</////<;:9777899::::::::::::<<<<<<;:87788888999:::::..////====/<;::::::::::;;<</==>>>>=/<<9533466787788899::;;</=>=/;:888899;<============/<<985555689::::::::99999999:<<<<<<<<<</======///////<<<<<<<.:::8665555678889:;<<<<;<<<<;:85568899:::::::;.<<<;:::<<<<<</////<<:9778899::;:::::::;<<<<<;:8767888999::::::::;..<</====/<<;;;;;;:::;;<</==>>>>=/<975334678887888999::;</===;:8666689:;<==========/<<<9854456899:::::::99889999:<<<<<<<<<<=>==/=//</<<<<<<<<<.:::8866555667788899;<<<<<<<<;;:86568899::;;:::;<<<<;:::<<<<<<//////<<:998889::::::::::<<///<;:866788999::::::::::;;<<</====///////<;;::;<</=>>>>=/<<97533468888888899:::;</===;:8666668::;<===>=====/<;98554456899::::::::9999999:<<<<<<<<<<=>====/<<<<<<<<<<<:9988887666678898999:;<<<<<<<<<;:97778999::::::;<<///<;::;<<<<<//====//<;;:::::::::::;;</====<;976678999:::::;::::::;;.<</===========<<<<<<</=>>>==<<:85544578999899999::;;</=>=<9866667789:;<===>=///<<;86534468999:::::::9988889:;;<<<<<<<<<======//<</<<<<<::87777887777889999999:;<<<<<<<<<;:9888999:::::::;<////=;:::;<</<//=====//<<;;:::::::::;</==>>=<;97677899::::;;;::::::;;.<</==>>>>>>>==//<<<</=>>>==<<;:75544579999999999::;<//=>=<;986667789::.<=====//<;;85334688999::::::99888889:;;<;<<<<<<</======////<<<<:8666777888888899999999:;<<<<<<<<<<:99999::::::::::<<///=<:::;<</<<//=====///<;;::::::::</==>>>=<;9777889::::;<;;;:::::;.<<<//==>>>>>>>===//</==>>=/<;;:8755557899:::::9999:;<//=>=/;986777889::-.<====/<<;;8533689999:;;;:::99888889:;;;;<<<<<<</====/////<<;;:66666788999999999999999:;<<<<<<<<<<:9999:::::::::::;<<//=<;::;;<<<<<//======//<;:::::::;/===>>>=<;9777889:::::;;;;;:::;;<<<<///============///====//;;;:8755578899::::::::::;<//===/;;9877889:::--.<////<<;;85336899::;;;;;;:99888889:;;;<<<<<<<</==/<<<<<;;::88555568999999999999:::99:;<<<<<<///<;999:::;;:::::::;<<//<<;::::;<<<<<</======//;:999::;<====>>>/;:8778999::::::;;;;;;;;<<<<<<<<<//================/<;::98766788899:::::::::;;<///==<;:9777899::;;;<<///<<<<;975568::;;;;;;;:998888899:;;;<<<<<<<////:::::::98877778889::99999:::99::::::;<<<////=/<;:99::::;:::::::;;<//<<<::::;<//<<</=======/;:999:;</====>>=/;:87799999::99::;;;;;;;<<<<<<<<<<<<////===========/<;::987778888899::::::::;;<///==<;:9777899::;;;<<<<<<<<<;975569::;;;;<<;::99999899:;;<<//<<<<///;:99988888777999999:::9999:::9::;::::<</////===/<::99:::;;;;::::;;<<<<<<;:::;<///<<</======/<;:99:;</===>>>=/;:8789999:::::::;;;;;;</<<<<<<<<<;;<<<</========//<<;::98777888888999:::::::;<///==/;:977799:::;;<<<<<;;<<<;975569::;;;<<<;::::999999:;;<///<<<<//;977777777778999999::::99999:9:::;;::;<//////====/;::::::;;;;:;;;;;<<<<<<<;;:;</=//<//=====//<<;:::<//===>>=/<;;:88999::;;;:::;<<;;<///<<<<;;;;;;;<<<<//////<<<<<<;::98777888888889999::::;<///==/;:977899::;;<<<<<<;;<<<;975569::;;;;<<;::::::9999:;;<//<<<<///97555778877899999999::99999999:::;;;;;<<//////===/<;:99:::;;;;;;;;;<<<;<//<<;;</==//////////<<<<;;;</====>>/<;;;98789:::;;;:::;<<;;<////<<;;::::;;<<<<<//<<<<<<<<<<;:987667888878899999:::;<<</==/;:978899::;;<////<<<<<<:965569:::::;;;:::;;:::99:::;<//<<<</;;964&458998899999999999999999::::;;;;;<<<//////////<<;:99:::::::::::;;;;<<//<<<</=>=//////////<<<;;<//====>>/;;;;9878::::;;;;::;;;;;<<///<<;:::::;;</////<<<<<;;;<<<<;9876678877788998999::<<<<</=/;:977899:::;;<////<<<<;:986579:::::::::::::::::::::;<///<///;963&&45899999999999999999999:::::;;;;;;<<//<<//////<<;::9:::::::::::::;;<<<//////=>>=//////////<<<;</=====>>/;;;;:8789::::::;;:;;;;;<<<///<;:::::;;<</==//<<<;;;;;;;<;:9877777778889999999:<<<<<</<;:97789999::;;//=//<<<;:986679::::::::::::::99:::::;<//////<9633&&47899999999999999999999::::::;;;;;<</<<<<///<<<<<;::::::99999999:;;;;</////==>>=/<<<//////<<<</=====>>>/;;;;:9789:::::::::;;;;;;<<<//<:::::;;;<</===/<<<;;;;;;;;;:9877877788999999999:<//<<<<<;:978999999:;;</=//<<<;:99667::::::::::::::99999:::<//<<<//;9633&457899::9999999999999999::::::;;;;;<<<<<<////<<///<;:::9998899999::;;;;//==/===//<<<<<<<<<<<<<<==>>>>>>>=<<<<::889:::::::;::::;;;</<=<.999:;;;;;<</==/<<<;;;:::;;;;:98877778999999999:;<//<//<<;:::99::999::;<////<<<<;:9778:;;::::::::::99999999;</<<<</<:74335678899:::99999999999999999::::;;;;;<<<<<</=//<<////<;::99888899999:;;;;</======//<<::::;;<<<<<<==>>>>>>>=/<<<<:8899:::::::::::;;;</==<.999:;;;;;;</=/<;<<<;;:9:;;<;:9887777999999999::;<</////<<;:::9::999:::;<<//<<<<;:9778:;;::::::::::9998899:;<<<<<</<:7434678899:::9::9999:99:99999999::::;;;;<<<<;</=/////////<;:99888999999:;;;;;<////////<;:999:::;;<<<===>>>>>>=//<<<:98889:::::::::::;;</==<-999:;;;;;<</=/<;<<<::999:;<;;:99999999999999::;;<<</////<;::999999:::::;<///<<;;;:978:;;;:::::::::998889:;<<<<<<//<:7445788899:::::99999999999999999::::;;;;<<<;;</=//////////<;9988899999::;;;;;<<///<<<<;:99888::::;<</=====>>>>=/<<<:98779999::::::::;;</==<-999;;;;<<<<///<;<<;:99989:;;;;;;:::::::9999:;;;;<<<<///<<;::999999:::::;<<//<<;;;;:989;;::::::::::99889:;<<<<<<<//<:754578889:::::999999999999999999::::;;<<<<<<<</=>>=/////==/<:97778999::;;;;;<<<///<;;;;:88778999::;<<<<<</==>>=///<;:977899999::::::;;</==;:99:;;;..<<//==<;;;:9999889::;;<<<<<<;;;:::::;;;;<<<<<//<<;;999::::::::::<///<<<<;;:989::::::::::::::99:;<<<<<<</==<:7666789::::::9999::99999999999::::::;<<<<<<<</==>>===///==/<;:977899::;;;;;<</////<-:::9876789:::;;<<<;;;</=>>==//<;;:99999999::::::;<//=<;:9:;<<<.<<//===<;:::99997889::;<<<<<<<<<;:::;<;;<<<<<<//<<;:999:::::;:::;</=//<<<;;;99999::::::::::::::;;<<<<<<</==<:8667789:::;<::99:::999999999:::::::;;<///////========/=/////;:977899::;;;;<///<///<-:::9866789::;;<<;;;;;;</=>>==/<;;;::::9999:::::<<//==<;:9:;<<..<</====<;:99899976689::<<<<<<<<<<;;;;;;;<<<<<<//<<;:989:::::::::;/===///<<<;:9989::::99::::::;<<;<<<<<<</===;8777789:::;<;:9::::999999999:::::::;<<//==/////<<<<<////////;;:98899::;;;;<</<<<//<-:::987789:::;;;;;;;;;;<<==>==/<;;;;;;;:999::::;</====<;:9:;<;;.<</====<;:98899976668:::;<<<<<<<<<;;;;;;<<<<<///<<;:999:::9::::;</===////<<<;:9889::::99::::;<<<;<;;;<</====<977779::::;;;:::::::99999999::::::::<</=====<<;:;;<<<<<//////<;:9999::;;;;;<<<<///<;:::9878:::;;;;;;;;;:;;;</=>>=/<<;;<<<<;;:::;;;</====>/;:::;;<<<<======<.98889998777899:-;;<<<<///<;;:::;<<<<///<<;;::::::::::;;</====//////<;:999::::999::;<<<<<;;;;</=>===<:97789:::::::::::;::::::99:::::::::;</======<;:9::;;;<<<<<///<<;:999:::::;;;;;<///<<<<<:989:::::::::;;::;;;</=>>==/<<<<<///<;;;;;;</====>/;::::;<<</======<.987789998778999:;;<<<///<<;;::::<<<</=/<<<;;::::::::::;</=>==//==//<;;:99:::::999:;<<<<<;;:;</=>==//<:9789::::::::::;;:::::::::::9:::::;</=====/;:99::::;;<<<<<</<<<<::9:9::::::::<////////<:999999:::::::::;;<</=>>==/<<<<</////<<<;;//====>/;::::;<<</======<-9766788888899999:;<<<</<<;;;::::<<<</==/<<<;::::::::::;</=>==///=///<<;::9999:999:;<<<<<:::;</=>=///<:97899:::::::::;:::99::::::::::::;</======<:999::::;;<<<;<<<<<<<<:99999:::9::<////////<:9989999999:::::;<<</==//<<<<<<<//==////<<//====>/;::::;<<</=====<.-86667787789999999:;<<<<<<;;;::::;<<</==/<<<;;:::::9:::;</====///==//<<<;::9999999:;<<<<;:::;/=>>=///<<:78899:::::::::::999::9:::::;;;<</////==<.9999::::;;<<<;;<<<<<<<;;9999:::99:;<======/;:998889999999:::<///<<<<;;;;;;<</=======//======>/<;::;;<<<</===//;9766678888899::999::;<<<<<<<;;::;;<<</=////<<;;;;::99::;<</==////=======/<;::99999:<<<<;;::;</>>>==////:988999:::;;;;::9999:99:::;;<<<<</////==<-9999::::;;<<<<<<..<<<<<;999999999:;<=====//;:998888999999::;<///<<;:9999:;;</==============>>>/<;:;;;<<</===//;975567888888999999::;<<<<<<<;;:;;<<<<//////<<;;;;:::99::;<//////=========/<<;:9999:;<<<;;::;<///////=//<998899:::::;;::9999:99:::;<<<<<//////==<-9999::::;;;</<<<...<<<<;:99988899:;</===//<;:999987899999:::<///<;:987889::;</==>>=========>>>/<:::;;;;<</==//;854566788888899999:::;<<<<<;;;;;<<<<<////=//<<;;;:::999:;<</////=>>>=====///<;:::9:;<<<;;:;;<<<<<<</=//<:98789999:::;::99:::::::;<<<<<<//////==.-9999::;;;;;<//<<...;;<<<;::9877899:;//////<;:99999888999::::</=/<;:97778999:;<==>>>======>>>>>/<::::;;;;</=///98445668888888999999::;<<<<;;;;<<<<<<<//====//<<;;:::999:;<</////=>>>>>>==////<;;;;;<<<;;;;;;;::::;<////<:997799999::;:::::::::::;<<<<<<////====<9999:;;;;;;;<///<;;;;<<///<<;9779::;<//==//<<<:::99988899:::;<==/<;987788999:;;</=>>>>>>>>>>==>=<:::::::;</==<<:64346689988899999999:;;<<<<<<<<</////=========/<;:::::::;<<<<//==>>>>>>>====//<<<<<<<<;;;---99999:.<<//<<:98899:999::::::::::::;<<<<///////====:9999:;;;;;;;<///<;<<<<///=//<:999:;;</===///<<<::999888899::</===<;98888899::;;;</=>>>>>>===//==<::::99:;<===<<:6434668998889::999999:;<<<<<<<<</==============/<;::::::;;;<<//======>>>=====///////<<;;;--968899::.<///<<:9899999:::;;::::::::<<<<<////<//===<:999::;;;;;;;<<//<<</////====/<:::;;<</=====//<<::999899889:;<====<;9888899:::;;;;</=>>>=//////==/<:::99:;<==/<:86434568998899::999999:;<<<<<<<<<<=======>======/<;::::::;;;;<</===////===========///<<<<;-9645689::.</=//<<:99999::::<<;::::::;<<<<<///<</====<:999::;;;;;;;<<///////==//====<<<<;;</=>>====/<<<:998999999:;<===/<;988899:::;;;;;<</==/<<<//<</=/<;:::::;<==/<:8643456899999999999999:;<<<<<<<<<<///===>>>====///<;::::;;;;;;<</<<<<<<//==>=======/<<<<<;96445568:::.<///<<::9999:;;;<<;;::::;<<<<<///<<</===/<;:9::;;;;;;;;<<<///</=====/////<<<<<<==>>==/////<;9999:::::;<====//<;::::::::;;;;;;;////<<<///</=///<<;;;;/=//<:975556689999999999999:;;</////<<<<////========////<;::;;<<;;;;;<<;:99::.<<=>>>=====/<<<<<9753344589::;<////<<;:::;<<<<//<;:::;<<<<<<</<<<</==//<;:::;;;;;;<<<<<////<//=>==/<<</<<<<</==>>===/////<;;;;;;;;<<=====///<;;;;;:::;;;;;;<//<<<<<//////=====<<<<==//<:9775677789999999999::;;<//===/<<</////========///<<<;;;<//;;;;<<;9**+9::.</==>=>====/<<<:9653345789::;<//////<<<<<///<///<;;;<<<<<<<<<<<</====/<;:::;;;;;<<<<//////<</=>==/<<<<<<<<//==>===///===/////========//=////<<<<<;::;;;;;<//<<<<<<//////==>>>======//<::97667667899999999::;<<//==>==////////=<<:;<<=//<<<<<<</=/<;</<;:9**+9::..<//==>>====/<:97533557889::;<<//////<</////////<<<<<<<;;<<<<<<//====//<;::;;;;<<<<//==////</=>==/<<<<<<<<</====/////====////========////////<<<<;::;<;;;<//<<<<<<<//////=>>>======//<::97766667799999999:;;<///==>>==///////<:99::;;;<<<<<<</===////<;99++9::::.<<</==>>>==<:977555678889::;<</=//////////////<<<<<<<<<<<<<<//=======/<;:::;;;;;<</====////=====<<<<<<<<<<<<<<<<<<<<//////=======///////////<<<<<;;<<<;<///<<<<<<<//==<=/=======//<<<;:9875566778899999:::;<<<<<==>>>//////::98889::9:;<<////====/=/<:9999::::;;;<<</=>>///.:86655789999:::;<<======/////////<<<<<<<<<<<<<<//=========/;:::;;;;;;</=====//=>===;::::::::::::;;<<;;<<<<<<</======/////////////<<<<<</<<;<//<<<<;;;;;<<<<<</////==/<<<<;:987556777888999:::::;;<<</=>>>>>//::98888899999:;<<////=>>==/<:99::::;;;;;;<<</==//.;966667889999:::;<<<=====///////<<<<<;<<<<<<<<<//======>>==/;::;;;;;;;</=====//=>=;;:8888888899998:;;;;<<<<<<<<//////</////////==//<<////<<<<//<<<<;;;;;;<<<<<<<<<</<<;;;<;;:8755677788889::::9:::;;</=>>>>/<:9777888999999::;<<//==>>>=/<;::::::;;;;;;;<<<///..:866677889999::::;;<=====////<//<<<<<;<<<<<<<///===///=>>==/<::;;;;;;;</=====//===;:866666666777788::;;;;;;;;<</////<<<<<//////===///====<<<<//<<<<;;;;;;;;<<<<<<<<<<---;<;;;9877777788999::::999::;</=>>>/<;977778889999::::;<<//=>>>=//<;;;;;:;;<<<<<<<<///..;:866678889999::::;;<<====////<<<<<<<<<<<<<<//////<<<<//=>==<<::;<;;;;<</====/////;;965567766778877899999::;;;<<///=//<<<<<<<...//====>>>=/<<///<<<<;:::::::;<<<<<<<<;::;;;;;<;:9988877899::::9999::;<<===;;:9866788889:::::;;;<<</=>>>=//<;;;;;;;<<<<<</=====/.-9766678889999::;;;:;;<=====<<</<<//<<<//<<//////<<<<<//===/<<::;;;;;;<<////////<<;964556787788999889998779:;;<<///===///<<.;;-;..<<==>>>=//////<;;;:::999::;<<<<<<<<;;::;;;;<<<;:9877789999989999:;<<<<<<;:99877888789::::;;<;;<</=>>>=/<;;;;;;;;<<<<</======/..-87667888999::;<;;:::.<=====<///<//////<<<<<<<<<;;;;<//////<<:::;;;;;<<///////<<<;9645567877899999999987779:;;<<<.//===/<.;---;;;...<====///=/<;:::::99999:;<</<<<<<.;:::;;;<<<<;:98778998877899:;<<<<<<;:977878888889:;:::;;;;;<//>>>=/<;::;;;<<<<<</=======//.-9766788899:::<<;;:::-<==>=====//////<<;;;;;;;;;:::;<//////<<::::::;;<<</////<<<<;9645677888899999999:977779::;;;....<<<<;----;;;----<///<//=/<;:::::99999:;<<//<<<<<;;;;;<<<<<<<::988887777789::<<<<<;;:977777788888:;;;:::;;;;<//>>>=/<;:::;;;;;;<<<=======//.-9766788899:::;;;;:::-.<=>>======<<<;-9999::::::99::;<//////<:::::::::<<</=//<<<<<:66678888899::9999999887789:;;;::::;;;;;;;;;;;;;;:::;;;..<<<;;:999999989:;<///<<<<<<<<<<</////<<;;:997777789:;;<<<<;::987776668899::;;;::::;;;//==>==<<::::::;;;;;<</===>==//<;8766789999::::;;;::::;<<========<;;:999999:::::99::;<//////<;:::::::::<</=//<<<<<:8678888999::::999999887789:;;;:999:;;;;;;;;;;;;;::::::::..;;;:999999999:;<///<<<<<<:<<<///===/<<<;:9977789:;;<<//<;::98887666889:;;;:::99:;;<///===/<<::::::;:;;;;<</=====//<:8766789999::::;;;;:::;<<///<<<<<;::988899::::::::::;<</////<;;::::::::<<////<<</<:88888899::;;::99999988888:;<<<.:99:;;;;;;9::::::99999:::::;;;;999999899:;<//<<<<<;99::;<//=======<<:99889;:;;<//<;::99999888899:;;;:::9999;<<<</////<<;::::;;;;;;;;<</====/<;:876789999:::::::;::::;<<//<;::::99998999:::::::::::;<<<<<//<;;;;::99::<<////<<</<:8888889:::;;::9999998889::<<<<<:99:;;;;987777898888899::::;<<;:99988889:;<<<<<<<;98899-;</========<<::9;;;;;<<//<:999::::9999::;;;:::99889;<<<<</////<<;;::;;;;;;;;<<<====/<;:88789999:::::::::::::;<<//<;:99988889:::::::99:::9::;<<<<<<<<<<<::::::;</=//////<:888999::;;::::9999999999:;<<///;--:<<:8755556899887888999:;<<<;:9988899:;<<<<<<<:977899:;<==========<<<<<<<<//<<;9889:::::::::::::::::999:;<<<<</====//<;;:;;;;;;;<<<</===/<:998889:::::::;;;;;;;;;;</<<<;98888889:::::::9999::99:;<<<<<<<<<<<<::::;;<//==/<</<:988999:;;;:;:::99999999::;<<///<;;<<:97444568999988777789::;<<;;:988899:;<<<<<<:9777899:;</=====>====//<<<</==<;9889:;;;;::::;::::::::999:<<<<</=>>===//<;:::::::;<<<//==//<:99989::::::;;;;;;;;;;;<</<<<:88868889:::::::9999::999:<<<<<<<<<</<<::;;<//===/<</<:988999::::::::::999999::;;<<///<;;<<:8544568999::998777789:;<<<;:98899:;<<//</<:9778999:;</===========//<<</=/<;9889;;;:::::;;:::::::999:;<<<//=>>=====//<;::::::;<<///===/<:::9889:::::;;;;</<<<<</<<<<<:86668889:::::::999999999:<<<<<<<<<//<<<:;<//====<<</<:98889999:::::::::::99::;:;</==/<<<<<:855578999::::99877789:;<<<<;:999:;<<<////<:9789::::;</==/=========//</=/<;98889;;:::::::::::::::99::;<///=======>==//<;;;:::;</====>=/<<<:98899:::;;;;<//////////<<<:86667789:::::::::9::9999;<<<//<<///=//<<<<//===/<<</<:9888889999:;:::::::99:::::</==/<<<<<:76678999::::::9988889;</=//<<:::<<<<<<<</<:99::::;;<<//=////=======//===<:97779::;:::::::::::::::;;;//======//===>>=//<<<;;;</====>>==/<<;:99999:;;;;;;</////////==<;9777789::::::::::::::99:;<<==/<</===//<<<<//===/<<</<:9888888999:;::9999999::::;<===/<<<<:976789::::::::::99889:;</===//<<<<<<<<<<<//<::::::;;<</==/////==========<;976678::::::::::::::;;;;;;</=====/<<//==>>>==///<<<//==>>>===///;:999999:;;;;;</////////==<<:877889:::::::::::::::::;<<===/</=====/////====/<<</<:9999988899::::9999999::::</==/<<<<<:976789:::;;::::::999::</======////<<<<<<<///<<;;;:;<<//===//<<<<<<///===<:766679:::::::::::::;<<<<<</====/<<;<<////=>>===/////===>>>===//<;9998899::::;;</////////===<:98899::::::::;;;:::::::<<====///=============/<<</=<:9999988899::::9999999::::</=/<<<<<<:977789:::;;:::::::::<<//======//////<<<<</////<<;;<<<//====<;;;;;;<<<<<<;:766789:::::::::::;;<<<<</=====/<;;;;;;<<</===========>>>>>=////<:77788899:::;;;<//////<<<==<:98899:::::::::;;;;:::::<<///=//<///========//<<<<//;:9999999999:::::99999:;;;;<///.;<<<;:977789:::;;:::::::;<<<////=========//<<<//====<<<<<<<</===<<::99999---<<;976678999:999::;;:;;;<</=====//<;::::::;;;/==============>>=/==/;9868899999::::;<//////<<<//<:99999::::::::::;:::99::;</////<<<<//======<<<;;<<//;98888999999999::999::;;;;<<//..;;<<;:977789:::;;:::99::;<<<////========///<</////==/<<<;;;<////<:8866667899;<;:876788899999:::;:::;<</====//<;:::::::;;;</==========>==>=//==/;9666789999999:;</////<<;<</<999999:::::::::::::999::;<<////<<<<<////<<<.;;;;<</<;9888888988888899999:;;<;<////..-;;;;:977899:::::::9999:;;<</////======////<<///</==//<<<;</////<:8555567789;<;:976668899999:::::::;<</=////<<;::::::;;:;</========>>=====//===<9666789999999:;</////<;;<</<9999:::::::::::::::999::<</////<;;;<<<<<..---;;;<<//;9889998887788899999::;<<<///..---;;;:977899::::::::999:;;;<//////=====///<<<<<<</====/<<<//==/<<:8555667778;<;;987668899999:::::::;<//////<<;;::99:::;;;</========>====////===/:8668999::999:;</////<<<<//<:999::::::::9999999999:;<<<///<<;-;;;;---;;--;;;.<<=<:999:99988778998889:;<<<<///.;:::;;:977789::::::::99999::;;<///////====<<;;;<<<</=>====//===//<-97556778879:;:::97778999999:::::;;<<//////<;:::9999:::;<<//====>>>>====<<<<===/<98899999:999:;</////<<<<</<;999::::::::9999999999:;<<<<//<<;-;;;;;;;..;;;;--.<=<:999::9998778998889:;<<<<//.;:::;;::877889::::9999999999::;<///////===<<;::;;<<</=>>======>==/<-95567999999:;::998778889999:::::;<<</////<<;:::99999::;<///====>>>>===<<.../===<:98899999999:;</////<<<<</<;999::::::::99999999:::;<<<///<;--;;;;;<<<<<..---.<==<998999999889998899;<<<////.;::;;::988999:::::9999999999::;<///////==<<;::::;<<<</========>==/<-95579999999:;;:999888889999:::::;<<<<////<<:::::9:999:;<///====>///<<<<....<///<<:9888999999:;</////<<<<//<;:99::::::::9999999:::;<<<///<<;;;;<<;;<<<<<<.;--.<==<:988889988899999::;<<<////.;;;;;::99999:::::99988899999::;<///////=<.-99999:;;<<</======>>==/<-75779999999:<<;:::988899999::;;;<<<<<////<<::::::::9::;<<//====/.--:::;.---<///<<:988778999:;<</////////==/<:99::::::::999999::;;<<////<<.;<<<<;;;;;<<</<;;-.<===<:97557777799::;<<<<<<///.;;;;;;:98899::::::998888999999:;<//////=<<:8766779::::;;//>>=>====/;976789999:99:<=<<;;:99999:99::::;;<<<<//<<<;;;;;::::::;<<<<<<<<-:988889::::;</==<<::88667799;;<//===///====/<;::;::::::9999999:;;<///==/<<..<<<:;999::;<//<<..<===<;97555777779:;<//<<<////.;;;;;::9789::::::999888899999::;<<<<<///<:855445679999::./>>======/;97678999:::::<==<<;;:999:::9::::;;<<<<</<<;:;;;;:::::;<<<<<<<<-98777668::::;</=/<<::9866779:;<///===//=====//<;;<;;::9999999::;;<//====/<<<<<::998889::;<<<<...<===<-9755777999:</////////.;:;;;;:99779::::::998888999999:;</<<<<<//<:8544446677779:-./>=====//;97678999::::;<==<<<;;:::::::::::;;<<<<//<<::;;;;;;;;;<</<<</<-977777889::::;<///<<<:;988779:<////===////===///<<<<<;:9999::;;;<<//==>>=/<<.;:988666899::;<<;...<====--977788:::;<////////.;-:;;;;:99889:::::998878899999:;<</<<<<<<<<:8544446677779:-../=====/<;98789999::::;<==<<<<;;;;;;;;:::;;<<<<<==<<::;<<<///<<////<//<-97778899::::::<///<<<<;;;999:</////==/<<<<///<<////<<<;::::;;<<<<//======<;;;:98765567899:;;;;;;<</==//<;:::::;;;</=====//<.:::;;;:999::::::::998877899:::;<///<<<<<<<<97544456779778::;;<////=/<<:9999:::;;;;</==/<<<<</<///<<;;<<<<<</==/;;;<<//========////;98888999:::::::;<<<//<<<<;;;;</////////;;;;<<<<<<<<//<<<;;;;<<<<<///=====<<;::987665567789:;;;;;;<</===//<<;;;;<<//======//<::::;;:999::::::::9988888899::;;<///<<<<<<<<975445679999889:;;;<////<<<:9999:::;<<//====/<</=======////<<<<//=>/;;;<///========///<;9888999:::::::9:;<<//////<;<</=/=////;;::99:;<<<<<<////<<<<<<<<<<//===/<<;;::9777776777789:;<<<<;<<//==//////////=======/...::::;:9999-;;::::99999988999::;;<</<<</<<</<9754567999::99:::;<;<<<<<<<;:999:::</=====>==//==>>>>>>====/<</==>>/<</////======/////;98888999:::::::::;<<///////<//===>==/;::99999:;<<<<<////<<<<<<<<<//==///<;::997777777888788:;<<<<<;<<///////////========/...::::::9999:-;;::::9999999999::::;;;;<<<//<//<97556779::::::::::;;;;;<<<<;:99:::;/=====>>=====>>>>>>>=====//=>>>>//<//////====/////<:8668999::::::::::;<</////////===>>=/;:99888899:;<<<<////////////////<<<;::998877888888898889:<<<<;;;</////////==========;;::::;;;:989::;;:::::99999999999::::::;;<<<<<//<:8667889:::::::99:;;;;;<<<<::::9:;</=========>=====>>>>==>====>====/////////====/====;9767899::::::::::;;;</////<<<//=====<-98877788899:;<<////====//==////<<;997777778999999999999::<<<;;;</==////////=======<;::::;;;;:99::;;::::::999999::9999::999:;<<<<<//<:8678999::99999999:;;;;<<<<;;::99:<==========>>=====>>>=>>>>>>>==<</////////=========;976789:::::::::::;;;</////<<<</====<;9866677768889:;<<///========///<;;9876667889999999999999::<<<;;</==/////////======<.::::;;;;:999::;;:::::999:::::::999::99:;<<<<<<//<:88899999999999999:;;<<<<<<;;;::9:</======/==>>>>=======>>>>>>==<:9:;//<<<///===///=;976679:::::::::::;;;;</////<<<<//==<;:9866678888889:;<<<</========//<;9988666789999999999999:::::<<<<<==//<<</////===/<<.-::::;;::8889:::;::::999::::::::999:999:;<<<<<<//<:88999999999999999:;;<<<///<<;;;::<////=///=>>>>===////=>>>>>=/<:99+:::---;<<<<;;;;;9776689::::::::::::;;;</////<<<<//==<;:86667899888899:;;///=======/<<<:876666778999:::::999999::::<<<</==/<<<<<<<<<///<<;--:::::::9779::::;::::9999:::::::::::99:;<<<<<<///<:9999::999889988899::;<<///<<<<<;;<<<<</<</>>>>////<<<</=>>>==/;:9778888899:999999987655589:::::999:::::;<<<//==/<<</==<<:97667789999999999:;//======//<<:9666677789999:::::9999999::<<<</==/<;;;;<<<<<////<;--:::;::97779:::::::::9999:::::::::::99:;<<<<<<///<:999999999989988899::;<<///<<<<<<;<<<<<<<</>>>//<<<;;;;</=>>=/<;:97788877899877677655555689:::::99::::::;;<<</===///===<:9766788899999988888:;///..<<<<<:97667788899999:::::9999:99::<<<</==/<;;;;<<<<</===<;;-::;;:977789::::::::::999::::::::;:::9:;<<//<<///<:999999999999999999::;<<////<<<<<<<<<<<<<<=>>/<<<::::;;</=>>/<<;:97888888999877666655566889::::::::::::::;<<</=>>===>>/<:9766889999999998888:;;....;;;;:97777899999:999:::::999::::::<<<</==/;;;;<<<<<</===/<;;;;;;:977899::::::;;:::::::::::::;;::::;<<//////<;:999999999999999999:;<<</////////<<<</<<</=//<;::999:;;</=>=/<<;;9988888999::98766666789999::::::::::::::;<<<<=>>>>>>><:977678899999999999899:;:::::::98877789::999:99::::::99999::;<<<<</=/<;;;;;<<<<<<===<<;;;;;:9778999::::::;;;;;:::9::;;;:::::;;;<<</////<:988999999999:::999:;<<<<<//=///////////////<<:::99999:<</=>=/<<<;:99889899::::998888899::::::::;;;:;;;;;;;;<<</=>>>>>=<:977789999999999999999;;::::::98777889:::::::99:::::999999:;<</<<<//<;;;;;;;<<<<<===<<;;;;;:977899::::::::;;;;;::9::;;::99::;;<<<<<///<;:878999999999999999:;<<<<</====////////////;::::999999:<//===///<;:999999999:::99999999:::::::::;;;;;;;;;;;;<<//=>>>>=/<:99778999:9999::99999:<;;;:::987677889::::::99999999999999:;</<<<</=<<;;;;;<<<<<<===<<;;<<;:98899:::::::::::;;::::::::99999:;;<<<<<//<<;:778999999999999999:<<<<<//====//////////;;9777:999999:<//===///<;:999999999::::999:9999:::::::::;::;;;;;;;<<//==>>>>=/<::9778999:9999::9999:;<<<<;:9877678899::::::99999988999999:;</<<<<==//<<<<<<<<//====<<;;<<<;:99::99::99999::::::9::::999899:;;<</<///<<;977899999999999:99::<<//////===////////<;9885557999999:<//====//<;:99999999::::::::::999::::::::::::;;<<<<<////==>>>>=//<:977899999999::9999;<<<<<;:9766778999::::::99999888899999:<</<<</=>=====/////=====/<;;;</<<:::::::::9999999::::99999998889:;<////==///;977899999999999::::;</////=//==////=<<<;9864335688889:;<<//===//<:98888889:::::::::::::9::::::::;;;;;<//////=====>>>>====<:867899999999:9:99/////<;:8766789999::::::::999888999999:<<<<<</=>============>=//<;;<///<;;;;;;;;:9999999:;;:999999988889;<//======/;9778899999999::::::;<////===/=======<<;98644333568889:;<<//==///<:988888899:::::::::::::::::::::;;;;</==////=====>>>>====<:877789999999:::::=////<;:876689999::::::::::99999988899:<<<<<</============>>>>//<;;</=//<<<<<<<<;:99999:;<<:98899999888:;<//======/;9878899999::::::::::;<///===//======<<;96444555668889:;<</===///<988878889::::;;;::::;::::::::::;;;</===//////===>>=======<:87789999999::<</=////<;:87779999:9:::::::::9999988899:<//<<<////=========>>>>>//<;;</==/========<;:999:;</<;9889999999:;<///======/<998889999:::::::::::;;<//===///====/<;98666666688999::;<//===//<:988888899::::;;;:::;;;:::::::;;;;<<====/////=============<<9889999999:;</////<<<<:998899999999::;;;:::999998889;;<///</<<<<//==////>>>>===/<;;</=//======/=/<;;;;;<//<;999999999:;<//=====>==/<:98889999:::::::::::::;</===////==<<;9866678888999999:;</===///;:87788899::::::;;:::;;;;::::::;;<<</====/////>>>=<<<//===//<;:::;:::::;;<</=//<<<<:9988999999999:;;;::999999889:;<</////<<..<///<<;<//>>=////<;</=//=======///<;;<////<;:99999999:;</=//======/<<99888999:::::::99:::::;<===/<<<<<<;98867788899999999:;</===//<;977788899:::::::::::;;;;::::::;<<//=====/////>>/<;;;<//==///<<<<<;;;;;;<</==/<<<<<:99899999999999;;;:999999989:;;<</<<//<.::;<<<;;::<////<<///<<</////==////<<<<//////<;;::99999:;<<//////====/<<:9877799:::::::999:::::</==/<<;;;;:98888888999998899:;<//==/<<;9777889999::::::::::;;;;:::::;;</======////////<;:::;<////////////<<<<<<</==/<<<<<:999998788888899::998888999:;;;<//<</<.:::;;;;::::;;;;:::<</<<</////==///<;;<////////<;;;;:::::;<<<</<//====//<:9877799::::::::99:::::<<///<;;;;;:88888888999988889:;;<////<<;:888999999::::::::::;;;;:::::;<</======///<<<<;;::::;;<///==////////////<////<<//<;;:9998888888888998888999:;;<<<//<<<<.9999::::::::999999::<<<<;<///////<<<<<<<////===/<<<<;;;;;</////////=====/;:977899::::;;::::::::;<<<<<;--:::977778899999998899:;<<////<<<:999999999::;;;;;;;;;<;;:::::;<=====>>//<<<::999:::;;;;<<//=====/////////////<<///<;;:::99999999999998999::;<<<<//<<<<<:9888899999999877889::;<<;;<//=/<<<<<<<<<<///===/<<<<<<;;;</=====///=====/;:98899:::::;;;;::;;;;<<<<<<;--:::977778899989999999:;<</=//<<<;:9999999::;<<<;;;<<<<<;;:::;<======>>//<:9999999:;;;;<<////====////////////<<<<///<<;;;::::::::::::::::::;;<<<</<<<<<.:8666788888888877889::;;<;;;</=//<</<<<<<<<//===//<<<<<<;</======>>======//;:9899:::::;;;;;::;;<<<<<<<<;<<<:977778889888988999:;<</=/<<<<;:988899::;;<<<<<<<<<;;;;;;;;<======>>/<:97788889::;;;<<////====//////////<<<<<<////<<;;;;;;<<<<<<<<;;;;:;;;<<<<<<<<<<.:6446788888889988899::;<<;;;</===/////<<<<<</=====/<<<<<</===>>>>>>>>====//;:9889999::::::;:::;<<<<<<<<<<<<:976778889988888899:;<</=/<<<<;:988899:;;;<<<<;;;;;;;;:;<<<<======>/<;977788889::;;;<<==//=////<<<<<<<<<<<<<<<<////<;;<<<<<<</<<;;;;;;;;<<<<<<<<</<<:85456888899989999::::;;<<;;-;<=======//<<<</==>>>==//========>>>>====//////<;:9999999:;;;;:::::<<<<<<<///<<:87667899999888889::;</==/<<<<;::99999;;;;<<<;;;;;::::;;<</////=====;887889999:::<<<</====<<<.----;;;;<<<<<<;<<<////<<<<<<<<</<<;;;;;;;;<<<<<<<<</<<:84457899999999999:::;;<<<;--;<=>=======//<//=>>>>==//========////<<<</////<;;::::9999::;;::::9:;<<<<<<</<<:987668899998889899:;</==//<<<<<;;;::::;;;;<<;;;;;;::::;<<<//////=/=;:88888999:::<<<</=====<<.:98889999:;;<<;;;<<</////<</<<<</<<<<<;;;;;;<<<<<<</=<<:85567999999999999:;<<<<<<;--</=>=========//======////<<<<<<<<----:::::.//<<<;;::9999999::::999:<<<<<<<<<<<:98778889999889999:;<</////<<<<<<<<<;;;<<<<<<<<;;;;::::;<<<////////;::888999:::::<<//======<.::887788889:;;;;;;<<//===/<///<<<///<<<<;;;;;<<<<<//==<<:86677999999999999:;<<<<<<;-;<==>======////////<<<<<;;;::::999999999999:.//<<<;::9889999999999:;<<<<<<<<<<<:98888899999999999:;<///////<<<<<<<<<<<<<<<<<<<<<<<;;;<<<<<///////<;::88999::;;:<<</=======<.::87778888999:9::;;<//===/<<///<<////<<<;;<<<<////===/<<:9778899999999::::;<<<<<<;;;/=====////////////<<<:::99988888888888++**++-<//<<<;:877889999999:;;<;<<<///<<;;:98888899::::::::;<//////==/<<<<<//<<<<///<<<<<<<<<<<<//////////<;;:9999::;;;;<<//======//;:98887899999988999;;<//=>=/<///<<</////<<<<<</=//==>==/<<:988889999999::;;;<<<<<<<;;<====<<<<<<<</////<<:999998778888888899++**++-<///<<<;877889999889:;<<;<<//=/<</;;:998889::::::;;;<///==//==/<<<<<<<<<<<///////////<<<</////////<;;;:99::::;;<<//==>>>>=//<:98899999::::988999:;;</====//<<<</=////<<<</===///===/<<<:98888999999::;<<<<////<<;;/===<..----;;;<<<;;:98888887888899999999+**++-<////<<;:8778999888:;<<<<</===/////;;::98899:::;:;<<//=========/<<<<<<<<<<<////////////////////==/<;;;::9:::;;<</==>>>>>>=/<;:8889999:::;;:98999:;;;<=====/<<<<==///////////<<<</==/<<<:988889999:::;<<<<<////<<<</===.--,,,,::::----988889998889999999:::99+++-<////<<<;9888999889;;<<<<</===///////<<:9989:::;;<<//==========///////<<<<<//==========//////=>>=/<<;;;::::;;;<//=>>>>>>>=/<;:9889999:::;;;:99999:::;<====/<<<///////<<<<<<;;;;<<===<<;;988889::::::;<<<<</////<<//=/<:999999::::9:::9999:::99999::::::::;::,99:</===//<;99999999:;;<<<<<=====///==/<<<<;::::;;;;</////==>>>=<<<<<<<<<<<<<<<=================>>>=/<<<;;;;;;;;<<==>>>>>>>=/<<<;:9999:::::;;;::9999:::;<///==/<</////<<;;;;::::;<<====/<;;987889:::::;;<;<<<<///////==/<:9899::::::9::::::::::999:::::::::;;;::9:;</===>//<:99999::;<//////====///====<<<<;;;;;;;;<</<<<//=>>=/<<;;;;;;;;;<<<<<<<==========>>>>>>>=/<<<<;;;;;;<<===>>>>>>=/<<<<;:9999:::::;;;;:999::::;<<<//=/////</<;;::::::::;<<====/<;;98788::::::;;;;<<<<//////=>>/<:8899:;;;::::::;;;;;::999::::::;::;;;::::;</==>>//<;:::::;;<///========<//===/<<<<<<<<<<<<<<<<<<</=>>=<<;;;;999:::;;;;;..<<///=====>>>>>>>=/<///<<<<<</====>>>>>=//<<<<;:9999::::::::::9999::;<<<<///////<<;:::9:::::::;<<=//=/<;;:87789:;;::;;;;<<<//////==>>/<98899:;;;;:::;;;<<<;::999:::::;;;::;;;;;;;</==>>//<;;;;;;<<////========///====<<<<<</////<<<<<<<<//>>=<<;;;9888999:::::---.<<</=====>>>>>>=////////////====>>>>>=//<<<<;:9999::::::::::::99::;<<///////<<;::9889::::::::;</////<;;;977899:;;;;;;;;;///////=>>>/;98889:;;;;;;;;;;<<<;:99:::::;;;;;;;;;;;;;;</==>>///<<<<<<////==========//>>===/<<<<<<///<<<<<<<<</=>>=/;;;:86667888999999:::<<<<<<<====>>>>>=//==========>>>>>>=////<<<<:99899::::::::::::9::;<<//////.;::999999::::::::;<//<//<<<;977899::::;;;;;;<//////=>>>/:9889::;;;;;;;;;;<<<;:99::::;;;;;;;;<<<<<;;</==>>=/////////=============//>>>>>====<<<<<<<<<<<<<<</=>>=<;;:97555677777888889:<<<<::::<<<///>>>================>======/<<<:99899::::::::::::9::;;;<///..;:9999::99999:::::;<///////<;9778999::::::::;<<<//</=>>/<9889::;;;;;;;;;;;<<<;:::::;;<;;;;;;<<<<<<;<</==>>======///======////==<<.//>>>>>===<<<<<<<<<<<<<<</=>>/<;;:865556778888877789::::9999:::;<</=>>>===>>===========//====/<<<99899:::::::::::::::;;;;<<.;;:99999:::::99::::;;<///////<;977899999999999:;<<<<</=///;9889;;;;;;;;;;;;<<<;;;::;;<<<<;;;;;<<<<<;;;</=>>>>>>============////<;;:--./=>>>>==<<<<<<<<<<<<<<</=>=/<;;:86667899999987777899996669:::;;;;</>>>===========//////====/<<::9999::::::::::::::;<<;;<<<;;99889::::::99:::;;</==/////<;97789999999999::;<<<<<</==<:889:;::;;;;;<<<<<<<<;;;;<<<<<<;;;;;<;;;;;;<<==>>>>>>====////====//..::998::;<===>>//<<<<<<<<<<<<//==>=/<<;:97779:::::9888877777765568:;;;:::;.//=====>===/==<<<<<<//==/<;;::9899:::;;::::::::;<<;;<<<<;98889::::::99:::;</===/////<;98788999999999::;;<<<<//==<:889::;;;;;;<<<<<<<<<<;<<<<<<;:::;<<;;;;;;;</==>>>>>/====////====/.::997778::;;<=////<<<<<<<<<<<</==>>=//<<;:99::::::::999876556655568:;;;:::;;../===>>==////<;;;;;<///<<;;;;:889:::;;::::::::<<<<<</<<988889:::::9999::;;</===////<;98788898899999:;;;<<<</===<:889::;;;;;;<<<<<///<<<<<<<<<::::<<<;;;;;;<</==>>>/;;......<</==/.:887766778::::;<////<<<<<<<<<<</==>=///<<;::::<;;;:;::9987655676668999:::::::;..//=>>==///<;999:;</<<<<<;<;;989::::::::::::;<<<<<</<<987889::::99999:::;<///=////<;9999888888999::;;;;<</=>==<:999:::;;;;<<<<<<//<<<<<<<<<;:::;<<;;;;;<<<//====/;::------.</=//.88876667788::::;;<///<<<<<<<<<<=====///<<;;<<<<<<;;;;::99876677889998889999::;;.../=>>===/;9888:;<<<<<<<<<<;;::::::::;;::::;<//<<<==.,*7899:::99999:::::;<///////<<::::998888889:;<<<<<</>>>>.-999::::;;;<<<<<</<<<<<<<<<<;:::;<<;;;<<<//=====<;:::::::::;<===<;988877788999:::::;<///////////=====/<<<<<<<<<<<<<<<;;::::9777789999988888889::;;-;</>>><<<:86689:<<<///==//<<<;;;;;::;;::::;;//<</==.,*7899:::999:::::9:;<//==////<<;;::99988889;<<<<<<</=>>>.-99:::::;;;<<<<<<<<<<<<<<<;;;::;;;;;;;<<</=====<;:::::::::;<====/;:99999999999::::::;<///============/<<<<<<<<<<<<<<<<;::;::987899999999998899::;;;;;<=>><<:876689:;<</=====///<<<;;;:::::::::;<//</==.,*7899::999:::::99:;<//==////<<<<;::::9999:;;<<<<<</=>>>/-99:;::;;;<<<<<<<<<<<<<;;;;;;::;;;;;;;<</======;:::::::::;;<====<;:9999:::9999:::::::<</=>>>>>>>>====/<<<<<<<<<<<<<<<<;::;;::9889999999999999:::;;<<<</>=<:8566679:;;<</=>>==///<<<<;:::::::::;<////===.,8899::999::::::::;</=>=////<<<<<<<<<<:::;;;<<<<<</=>>>/-99:;;;;;<<<<<<<<<<<<<;;;;;;;:::;;;;;;<//=====<;:::::;;;;;;<====<;98889::::99::::::::<</=>>>>>=======//<<<<<;;<<<<<<<<;::;;;;9999::9999::::::::::;<<<//=/:85555679::;<</=>>>=//<<<<<<;::::::999;<=/////<-999:::::::::::::;;/==>>==///<<<<<///<<<<<<<<///////===/;99::;;;<<<<<<<<<<<<<<;::::::;;;;;;;;</=>====<;:::::;;;;;;;</===<:988999:::::::::::::;</=>>>>========///<<<;;;;;;;;<<<;;;<<<<;;;;;;::::;;;;;;::::</======965556678999;<//>>>>=/<<////<;;;::9989;<//<<//<;::::::::::;;;:::;</==>=///////=/////<<<<////====//=//=/;:9::;;;<<<<<<<<<<<<<;:::::::;;;;;<<</=>>===/;::::::;;;;;;;</===<:98899::::::::::::::;</=>>>/;;;;///////<<<;;;;;;;;<<<<<<<///////<<;;;<<<;;;;:::;<======<965566677899;<//=>>>==///===/<;;::9989;</<<<///<...::::::;;;;;::</=====//<<//===///<<<<<//=/========///<::::;;;;<<<<<<<;;<<<;::::;;;;;;;<<<</=>>===<:++::::;;;;;;;<</==/:98899:::::::::;;:::;</=>>/;:::;<<//<///<<;;;;;;;;<;<<<</===>>>>==<</////<<;;:;</=====<:865677777789:;<//===========//<;::9999;<<<<<///////.:::;;;;;;;;;//=====/<<<//===/<<<<<<</=========>=////;:::;;;;<<<<<<;;;;<;::::;<<<<<<<<<<<==>>==/;+++::::;;;;;;<<</==/<:9899::::9::::;;;::;;</>>/:88::;;</<<</<<;;;;;;;<<<<<<</===>>>>====///////<<;<<=====<:8666677777789:;;<<<////===>>>>//<;;::::;<<<<</======<;;;;;;;;<<<<///===/<<<</====/<<<<<<<////============<;;;;;;;<<<;;;::;;<;:::;<<<<<<<//////=====<;98899:;;:::;<<<</==/<;:989::::99:::;;;:::;<<==<99999::;<<<<</<<;;;;;<<//========>>>>>=======////<<</=>=/<<976667888777779:;;;;<<//======>====<;:::;<<<<</===>>==/<<<;;;;<<<///===/<<<<//====<<<<<<;;<<//============/<;;;;;;;;;;::::;;<;:::;<<</////====//====<998889::;::;;<<<</==/<;:9889::::9:::;;::9:;<<==<9999::::<<<<<//<<<<<<</===========>>>>>=====/////////===/<:9766788888777799:::::;<<////========<;;;<</<<</===>>>>=///<<<<<//=====/<<<</////=/<<<<<<;;<<<////======>==//<<<;;;;;::::::;<<;:::;<<<<<///====//===<;9888899::::;;<<<</==/<;:9778999:9::;;::99:;<<==<9999::::;<<<<<//<<<<//=========//<==========/////////===/<:976788888877779999::::;;<<<<//=======<<<<<//<</===>>>>===/<<<<//=====/<<<<<<<<<////<<<<<<<<<<////==///=>==////<<<;;;:::::;<<<<;;;;<<<<<<//=========<;987789999:;;;;;;</==/<;:977789999:::;::99:;<<==<999::::;;<<<<<///////======//<<;;;;;<<<//===//////////==/<:978888888877779999::::;;;;;;</========///===<<.///>>>>========////==//<<;<<<<<<<<<////<<<<<<<<///=/<<</=======//<<<<;;;;;//////<<<<<<<<<//=========<;:766788999:;;--.<////<<;9767899:::::;:99:;;<<==;:::;;<<<<////<<<//====///<<;;::::::::::<<//////////</====/:9988888778878899999999:::;:;;<<=============<<..//===>==========////<<<<<;<::::::://///<<<<<<<//==/<..</==========///////=====////<<<<<<<///=======<;:7667888899::--<<////<<;:77779999:::::99:;;</==;:;;<</////===/<<</===///<<;:99988999999::..../////<<</==//;:999987777888899999999::::::::<<<===========<;--..//=>========/==//<<<<<<;::9999999;//=////////===/<.;;</======>>>>>>>===>======///<<<<<<<<//=======<:9766788899:;.<<=/==/<<;:87779999::::999:;;</==<;<<//=========<<<////////<;:9888777777799-...::..<<<<./////;:::998888889999999999999::::::<<==========<;:999-<</=======///==/<<<<<<;;:988777789;/=======/==//<.;;;;</====>>>>>>>>>>>>>>======//<<<<<<<<//======<;:9778899:;<<<======/<<;:877799999999989:;;</==<<<///>>>>>>>>==//////==//<;:9887777777779----::::-----./////;;;;:9999999999999999999:::::::<<====////;;9988999:<<====////==/<;;;;;;;;9866665577:<////====<<<;----:::</=>>>>>>>>>>>==>>>>=====////<<<:;;;;<<<<==;;:::99:..<<==/>>>>>=/<<;:988899999999999:;</==/<<<===>>>>>>>>>=//////==/<<:9877766677778999::::::::::::;</==/<;;;;;;;::::9999999999::::::;<</===////;;966668879:<//=====/=/<<;;;;;;;:8656888879:<<///===/<<;999:::::</=>>>>>>>>>>===>>>>====/////<<::::::9:::;;;;;;;;..<<====/>>>>>=/<<;::9999:::::::::::;</==//<<==>>>>>>>>>>=///<//=//<<::8776666677899999:::::::::::::</==/<<<<<<<<<::;;:::::::::::::;<//===/<;;;:93335666779:<<///==//<<<;;;;;::96556888899:<<////==/<;9988999::</==>======>>====>====//<<<<<::8888667799::::;;;;....<<<<///>>>=/<<;::;::9:<<<<<<;;::;</==/<<<==>>>>>>>==////<<</=//<<<:9876666678999999:::::::::::::;<===///<<<<<<<<<<;;::::::::::;</=====/;;;:9633355667779;;;<///<<<<<;;;;;:97555688889::<<//////<;988889889:<<<//============///<<;;;::::886666667777888899999999----;;</=>=/<<;:;;;:9:<<<<<<<;;;;</==/<<==>>>>>>====////<<</==//<<<:97667677899999::::::::::::::;;/====/<<<<<<<<<<;;::::;:::::;</=====/<::964444677766689::;<<<<<<<;;;;;:975666788899:;<<///<<<;9877899989:-;<<<////=>>>====;;;9888899888655677889988776777776779998899;===<<<;:::::;;<<<<<<<;;;<</==///====>>>==///////<<<</////<<;9888777999::::::::::::::::::;;</===///////<<<;:::;;;;;;;;;;<======/;:97644557887666789:;<<<<//<;;:;;:9756778889:::;<<///<<;:87778999999:::;;<<//=======;9997666777776666789999999876556666778876668;<==<<<;:::::;;<<<<;;;;;;<</=>===========//<<///<<::<<////<<<;9889999::::::::::::::::::;;;;<</===//////<<;;:::;:;;;;;;;;/======/;:76657778887777889:;;<<==/<;::;;:977788889:;::;<////<<:9877898999999999::<<//=//==;:77555555666788888899999999975556679998766689;<<<<<::::::;;<<<;;;;;;<<</=>>>>>===//==//<<<<<;::::;<//<<<<<;99:::::::::::::::::::::;<<<<<<//<<</////<<;:::::::;;;;;;;/======/<:76679998888888889:;;<<===/;;;;;::99999999;;;;<<////<;:988899999999999999:</////=;:85555666666778899998989999998767799::99876889:;<<<;::::;;;;<<;;;;;;;<<</=>>>>>===///=//<<;;;;::::-;<<<///<<;;;;;;;::::::::::::::::;<<<<<<<<<<;<<<<<<<<;::::::;;;;;;</====///<:97779999988899999:;<<</===<<<<<;:889999:::;;<<<////<:988899999999999999::;<<<<.::8533357889888889999988999999988899::::99998899::;</;;;;;;;;;;;;;;;:::;<</====>==//<<<<<<::::99:::::::<<///=//////<;:::::::::::::::;;<<<<<<<<<<;;;;<<<<<<;;:::::::;<</======/<<:97779::9998899999:;<<<</==////<;:88899::::;<<<<////<:98889999999:::9999::;<...::853333579::::98999998889999988899::::::99999:::::;</<;;;;;;;;;;:;;::::;<<//=====/<<;;<;::999999::::::::<///======/<;:::::::::::::::;;;;;;<<<<<<;;;;;<<<<<;;:::::::;</=======/<<:97779:::999999999;;<<<<</==////;:86789::::;<<<<////<:98889999999:::::::::;<..:98853356689::;;:999999888999988899::;:::::999:;;;::;<//<;;;;;;;;;:::::::<<////////<<<;;;:98888999::::::::;<//======/<;:::;;:::::::::;;;;;;;<<<<;;;;;;;;<<<<;;;;:::::</=====/=//<<:97789:::9999::9::;;<<<<</====//;:86789::::;<<<<////<:988999999999:::::9::;<..:9853356889:::;;::::::988999999899::;;;;::::::;;;;::;<///<;;;;;;;;::::::;<////////<<<<;:99888899::;;;;:::::;//======/<;:::;;;;;;;:::;;;;;;;;;;<<;;;;;;;;<<<<<;<<<;::;</=====/=/<<<:9889::;::::::::::;<<<<<//====//<:97789::::;<<<<///<;:99999999999::::::9::;<<;:98655689::::9::::::::99999:::99::::;;;;;:;;;;;;;;:::</=/<<<<<<<;;;;;;;;<<<<<<////<<<;:977788:9:;;;::::::999;</======/<;;;;;;;;;;;;;;;;;;;;;;;;;;;<<<<;;;</<<<<<<<<<</=====////<<<:9889::;::::::::::;<<<<</=====/<<:97778::::;<<<<///<;:99::::::9::::::::9::;<<<;9865689::::999::;;;;::::::::::::::::;;;;;<<;;<<<;:9:</=//====/<<;;;;;<<<<<<<<////<<<;976678::::;;;:::::::99:;/======/<<<;;;;;;;;;;;;;;;;;;;;;;;<<<<<<<;;<///<<<<<<<</====/////<<<<:999::;::::::::::::;<<<</====/<<<:9778::;;;<<<//=//<;::;;:::99::::::::9:::<<<;:86689::::9999::::::::::::::::::::::;;:::;<<<<<;:999</========//<<<<<<<;::::<</////<;976678::::;;;::::::::99:</====//<<<<;;;;;;;;;;;;;;;;;;;;;;;<<<;;<<;;</=/<<<<<///====/<<///</<<:::99::::::::::::::;<<<</===//<<::988:::;;<<</===/<<<<<;;:9999::::::99:::;<<;98689:::::9999999::::::::::::;;::::::::::;;;;<;::889<=====>>====////<;:99:::<<//////;976678:;;;;;::::;;;;::9:<//==///<<<<;;;;;;;;;;;;;;;;;;;;;<<<<<<;;;;;</==/<<</////////<<<//<///<;:999::::99::;;:::;;;;<</==///<;;:999:::;///=====///=<<;:99999::99999:::<//.:778::::9999999999::::::;;;;;::::::::::::::;;;;:988:<==//=>>>===/<<<:::::;;;;;;</==/<986678::;;:::::;:;::;;:::</////<<<<<<;:::::;::::;;;;;;<<<<<<<<<;;;;:;/===/<<///<////<<;<<<<<///<;::9999999::;;::::;;;;;;</=///;;::9999:;/======///===<;;::999::99999::;<///:779::99999999999:::::::::::::::::9999999:::;:::988;<//<</==>===/<<:9::::;;;;::;/==/<988679::;;:::::;;;::;;::9://////<<<<<;::::::::::;;;;;;<<<;;;<;;;;;;:;/====//<<<<<</<<;;;;;<<////<;::99889:::::::::::;;;<<//////;:::9889;/====//<</====<<;:99::::999::;<////:779:999988899999::::::::::::::::999998999::::::98:;<=/<<</=====/<:99::;;<<;;;::</=/<:98878::::::::::::::;;::99<//////<<<<;::::::::::;;;;;;;;;;;;;;;;;;;;;<====//<<</////<;;;;;<<<///<<;:9998:::;::::::::;;;;<</=////;:::99:;/====/<<<//====<<;:::::::99::;<////.879:999999999999:9999::::::::::9999:999999::::99::;<==<<</=====/;:9:::;<<<<;;::;<//<:988789:::::::::::::;;:999:<//////<<<<::::9:::::;;;;;;;;;;;;;;;;;;:;<<//<///<<///=//<;;;