BM66(@ kkkiiiiiinnnqqqlll```UUUSSSVVV^^^kkk|||{{{pppkkkhhhmmmsssxxxyyyvvvqqqmmmtttyyypppmmmkkkllloooqqqpppoooooouuu~~~vvvoookkkzzz|||~~~mmmhhhooolllkkkiiihhhiiikkkmmmooosssnnntttmmmjjjooouuuxxxzzz}}}{{{vvvtttwwwzzzwwwtttsss{{{}}}}}}wwwttt{{{|||zzzzzzyyyvvvsssvvvvvvrrrlllkkkooorrrqqqtttqqqmmmlllnnnqqqtttuuuuuuxxx{{{{{{xxxvvvwwwyyyrrrqqqtttyyyzzzvvvuuuwwwwwwyyyvvvnnnlllsss{{{~~~zzz|||{{{|||xxxooommmppprrrsssssssssuuuzzz}}}yyyvvvvvvxxxxxxtttooooookkkhhhffffffhhhiiiiiilllkkkgggdddeeefff```WWW]]]bbbfffddd___\\\\\\___^^^aaaeeehhhiiigggeeeddd{{{}}}www~~~|||zzz}}}zzzvvvvvv~~~xxxssswww{{{sssrrrsssvvvsssjjjdddbbbeeehhhlllnnnppprrrvvvyyyyyy}}}}}}xxxtttvvvxxx{{{|||||||||{{{yyywwwvvv{{{yyyxxxzzz}}}~~~}}}|||pppssssssqqqsssxxxzzzyyy{{{yyywwwvvvxxxyyyzzzzzz~~~}}}}}}~~~~~~~~~~~~zzzyyysssuuurrrkkkhhhlllsssvvvuuussssssuuusssooonnnqqqvvvwwwvvvqqqjjjeeeeeefffpppsssxxxzzzzzz{{{~~~|||zzzzzzuuunnnllloookkkjjjhhheeecccccceeeggghhheeedddgggkkkmmmjjjgggiiiiiiiiiiiiiiihhhgggfffnnnnnnmmmnnnrrruuuooogggkkkmmmnnnlllhhhffffffhhhtttwww{{{|||yyy~~~|||}}}wwwsssrrrsss}}}~~~}}}}}}~~~~~~{{{vvvrrrtttrrruuu{{{wwwwww|||{{{{{{yyyvvvrrrppppppqqquuuvvvwwwzzz{{{zzzwwwtttkkkooorrrooohhhdddeeehhhjjjeee```aaakkksssqqqiiifffeeegggkkkllliiiiiikkkmmmqqqvvvxxxwwwtttrrrqqqooouuuzzzyyyttttttzzz}}}}}}}}}~~~{{{uuutttyyy{{{wwwtttrrrqqqmmmlllmmmrrrxxx{{{zzzxxxwww||||||zzzzzzuuuiiigggeeefffggggggeeecccbbbeeeiiijjjiiihhhjjjllliiidddfffooorrrpppttt|||wwwssstttwwwyyy}}}~~~```YYY[[[^^^```^^^YYYTTTQQQZZZZZZ]]]bbbcccaaaaaaeeebbbbbbeeeiiiiiifffiiinnnpppqqquuu~~~~~~}}}wwwtttnnnpppssstttsssnnniiifffhhhlllqqqsssppplllhhhfffbbbcccaaa^^^___dddggghhhkkkmmmnnnmmmjjjgggffffffnnnooommmgggaaabbbiiipppooommmnnnttt}}}{{{xxxuuuvvvzzz||||||wwwqqqpppooopppqqqsssttttttsssuuusssooollljjjjjjlllmmmlllhhhkkksssuuunnnlllqqqkkklllmmmmmmooottt}}}ooodddmmmuuuvvvooogggddddddppptttyyywwwnnneeehhhpppoookkkiiilllllliiifffggg___aaacccdddddddddddddddlllqqqvvvyyy}}}||||||}}}}}}}}}zzzvvvrrrllloooooolllmmmtttzzz{{{~~~yyyrrrmmmjjjjjjiiihhhgggiiimmmoooooommmjjjhhhiiiiiijjjiiiiiikkkmmmnnnrrrtttsssooorrrzzzzzzxxx{{{||||||{{{wwwxxxzzzyyy{{{zzzvvvrrryyy~~~~~~~~~}}}yyysssttttttuuuuuuuuuuuuuuuooorrrxxx|||~~~}}}vvvvvvwwwuuutttwww}}}}}}yyyvvvuuusssrrrrrrqqqssstttpppiiifffggggggffffffggghhhkkkmmmnnnyyy}}}xxxsssuuuwwwxxxtttnnnjjjkkkmmmkkknnnqqqqqqppppppsssvvvyyy{{{~~~xxx{{{~~~{{{xxxvvvsssvvvyyy}}}~~~~~~|||zzzwww}}}{{{rrrsss}}}}}}{{{xxxvvvvvvyyy}}}}}}|||zzzzzz{{{yyywwwtttwwwyyy{{{{{{yyyxxxyyyzzz}}}~~~xxxssswwwzzzyyyxxxtttpppoooqqqnnniiilllssswwwwwwuuuvvvvvvsssnnnnnnnnnoooooooooppppppkkkmmmqqqtttvvvwwwwwwvvvpppqqqsssuuuwwwxxxyyyzzz|||~~~zzzuuuvvv}}}{{{yyyxxxwwwwwwwwwxxx}}}~~~yyy~~~ttt{{{wwwsssooolllooolllfffjjjqqqlll___^^^aaafffhhhhhhddd___[[[ggghhhhhhiiinnntttsssooosssxxxyyyssslllkkkkkkkkkmmmssszzz}}}zzzuuupppooohhhlllppprrrsssuuuyyy}}}|||}}}~~~~~~yyy~~~qqqWWWXXXddddddfffjjjpppvvv{{{}}}}}}{{{{{{}}}zzzqqqiiifffdddeeeeeeeeedddcccaaaaaa___ccchhhgggcccaaaccceee```dddiiillliiiddd___[[[dddfffiiimmmooooooooonnntttrrrqqqrrrttttttqqqnnnzzz}}}{{{xxxwwwwwwvvvwwwxxxyyy|||~~~dddMMMNNNVVVTTTTTTZZZbbbddd___XXXdddfffjjjnnnqqqsssttttttppplllkkkpppwwwyyyssskkkhhhjjjttt}}}{{{ssswww{{{yyy{{{{{{vvvrrrqqqsssppplllkkkllloooqqqrrrxxx{{{}}}tttjjjccctttpppmmmnnnmmmhhhddddddhhhjjjmmmpppqqqrrrqqqqqqvvvzzz}}}}}}zzzyyy{{{~~~~~~|||}}}{{{~~~~~~~~~}}}~~~iiiYYYYYY]]][[[^^^kkkyyy|||qqqdddpppooonnnkkkhhhdddaaa___```aaabbbdddeeedddbbbaaadddgggpppxxxtttjjjjjjqqquuuuuuwww{{{yyytttqqqssspppqqqrrrssstttvvvzzz}}}}}}}}}}}}|||}}}vvvuuu{{{xxxuuutttyyy~~~|||xxxuuuwww{{{~~~~~~~~~{{{zzz}}}|||~~~ggg```___aaacccbbbaaaaaabbbdddfffggggggooonnnmmmjjjgggdddbbb```cccfffjjjlllllllllnnnoooxxxzzzzzzxxxzzz~~~wwwtttwww{{{~~~RRRGGGHHH@@@===EEEDDDDDDDDDEEEGGGIIIKKKLLLPPPTTTYYY[[[\\\]]]```cccbbbgggmmmqqqqqqrrrtttuuu}}}___===BBBJJJCCC>>>EEEFFFFFFEEEEEEGGGLLLRRRWWW[[[bbbiiimmmooorrryyy~~~}}}YYYGGG<<>>444444333333333333333333444555333666LLLppp~~~{{{yyy|||wwwsssrrroooeeeSSSDDD///000111111000000111222999@@@EEEJJJ[[[uuuJJJNNNRRRQQQNNNMMMQQQTTTPPPPPPOOONNNMMMMMMLLLLLLLLLLLLLLLLLLLLLMMMMMMMMMLLLLLLKKKLLLPPPUUUZZZ]]]WWWYYYZZZXXXUUUUUUWWWYYYVVVVVVWWWXXXYYYZZZ[[[[[[^^^___bbbdddfffhhhhhhhhheeefffgggiiijjjlllmmmnnnlllkkkiiihhhgggggghhhhhheeeeeeeeefffiiilllppprrrssswww{{{{{{yyyxxx{{{}}}|||zzzyyyyyy|||}}}}}}zzzwwwuuuuuuvvvvvvwwwzzz{{{||||||zzzyyy}}}}}}}}}}}}}}}|||{{{yyyxxxvvvvvvvvvwwwxxxyyyyyywwwuuutttrrruuuyyy}}}|||xxxzzzyyyxxxvvvtttnnn```NNN@@@777666444222111333777;;;HHHYYYhhhppp|||?????????>>>@@@AAA???;;;???======@@@CCCBBB@@@??????>>>======>>>===;;;999>>>>>>===<<<<<<===>>>?????????>>><<<;;;===???BBBAAA@@@???>>>===>>>???@@@BBB???>>>@@@@@@===>>>AAAFFFEEECCCDDDEEEEEEDDDBBBCCCAAA@@@@@@BBBCCCCCCBBBDDDCCCAAAAAACCCDDDEEEEEEIIIHHHGGGGGGGGGGGGJJJNNNOOONNNMMMLLLJJJIIIGGGGGGKKKKKKJJJJJJIIIIIIHHHHHHJJJJJJJJJJJJIIIIIIIIIHHHLLLIIIFFFGGGKKKNNNPPPPPPMMMJJJGGGFFFGGGHHHGGGFFFCCCFFFHHHJJJIIIHHHGGGGGGGGGGGGGGGGGGHHHJJJKKKKKKMMMLLLKKKKKKLLLLLLKKKJJJPPPPPPPPPOOOMMMLLLJJJIIIMMMLLLKKKKKKMMMPPPSSSUUU[[[YYYZZZ]]]ZZZUUUXXX___^^^___aaabbbccccccaaaaaacccggggggcccbbbeeeeee```cccfffhhhiiifffdddbbbbbbiiikkkmmmppprrrsssssssssyyyyyyyyyyyyzzz|||~~~~~~|||ttttttzzz~~~||||||||||||~~~~~~uuuuuussskkk]]]LLL===555000111333222000333BBBQQQuuu|||:::;;;<<<;;;:::;;;===>>>;;;<<<<<<;;;:::888:::<<<>>>>>>>>>===<<<<<<===>>>::::::;;;;;;<<<<<<;;;;;;===>>>??????===;;;::::::>>>======<<<<<<<<<======>>>;;;;;;>>>???<<<<<>>>>>======;;;::::::;;;<<<;;;:::>>>===<<<;;;<<<<<<<<<<<<:::;;;>>>@@@???===<<<<<<=========<<<<<<;;;::::::<<<;;;;;;;;;::::::999999::::::999999888777777777888666555777:::===<<<;;;:::999888777777777777777444666888999999999888888777777777777888999::::::;;;:::999999::::::::::::;;;;;;;;;::::::999888888777888888999:::;;;<<<<<<===<<<===@@@>>>:::<<>>???@@@??????@@@AAACCCEEEGGGHHHDDDEEEGGGIIIJJJJJJIIIIIIMMMMMMNNNQQQSSSTTTSSSQQQRRRQQQOOOJJJEEEAAA@@@AAACCCCCCCCCCCCBBBBBBBBBBBB>>>>>>??????@@@AAAAAABBBAAAAAA@@@AAABBBAAA>>><<>>>>>???>>>===>>>???AAA>>>======<<<<<<>>>???@@@CCCCCCDDDDDDDDDDDDCCCCCCCCCDDDDDDCCCBBBCCCEEEHHHBBBAAA??????@@@BBBEEEGGGKKKIIIFFFEEEEEEDDDCCCBBBFFFFFFHHHKKKIIIFFFEEEHHHBBBCCCCCCBBBAAA@@@??????;;;<<<>>>>>>>>>???AAABBB>>>@@@@@@===???DDDGGGFFFEEEIIINNNPPPQQQSSSVVVYYY]]]\\\ZZZ[[[\\\^^^]]]]]]SSSSSSRRRRRRUUUYYY]]]___```cccfffiiilllpppvvvzzzzzzzzzzzzzzzyyyxxxwwwvvvuuuxxx|||zzznnnaaaXXXSSSQQQRRRYYY[[[___dddiiinnnrrrsssttt{{{~~~yyyyyyyyyxxxwwwvvvuuuuuuttt{{{tttmmmkkkfff^^^SSSJJJFFFFFFGGGKKKLLLUUUbbbnnntttyyy}}}{{{|||~~~{{{vvvqqqmmmjjjjjjlllllliiidddaaaaaabbblllvvv~~~|||||||||}}}|||{{{yyy{{{~~~}}}|||{{{xxxxxxxxxxxxxxxwwwvvvuuuqqqooolllhhheeedddfffhhheeeddddddccccccccccccccc\\\^^^```bbbccccccccccccdddddddddfffhhhhhhgggfffggghhhiiiiiihhhgggfffeee@@@?????????===999999;;;;;;===>>>;;;:::<<<===<<<===<<<;;;<<<>>>>>>;;;888===<<<<<<;;;<<<===>>>??????===;;;;;;<<>>>>>;;;:::<<<===;;;:::::::::;;;:::888:::999999:::;;;<<<;;;999;;;<<<===<<<;;;;;;;;;;;;999<<<======???AAA@@@<<<888999::::::;;;::::::999777777777777777777888888777666555444444444444555333222222222333444444333///111333333111000111333333222222222333333222111555444444333333333333444444444444444333333555666444444555555555666666777555666777888888888666555444555777888999777777888666666666777777888999:::555666777666888:::<<<<<<999::::::999777555666777999999::::::;;;;;;;;;;;;555666777888999999999999777777999:::::::::999888::::::::::::999888777777;;;;;;;;;;;;;;;:::999888;;;;;;;;;;;;;;;;;;;;;;;;<<<<<<;;;;;;;;;<<<======;;;;;;:::::::::;;;;;;<<<888999:::;;;<<<<<<<<<<<<;;;:::999<<<@@@AAA???===999;;;;;;;;;:::999;;;<<<::::::::::::::::::::::::888999999:::::::::::::::;;;999888999;;;<<<:::888888888999999999999999999;;;===>>>===:::999<<<@@@<<<;;;::::::;;;<<<;;;:::::::::;;;<<<<<<<<<;;;:::;;;<<<>>>===<<<<<<===>>>===<<<<<<:::::::::===???>>><<<::::::<<<===<<<;;;999:::;;;<<<:::888888:::::::::::::::::::::::::::888;;;===;;;999888:::===777999888444333777888777888;;;>>>>>><<<<<>>AAAEEEGGGCCCCCCCCCCCCCCCBBBAAAAAA===>>>AAADDDEEEEEECCCBBBEEECCC@@@===;;;:::;;;;;;<<<===???CCCHHHMMMRRRTTTZZZccclllooorrrtttsssooossstttuuuvvvwwwwwwwwwvvv~~~~~~zzzwwwtttqqqlllfffaaaaaadddgggjjjjjjooowwwzzzxxxwwwyyyxxxuuuttttttuuutttpppmmmnnnllljjjfff```[[[VVVSSSPPPPPPMMMHHHCCC??????@@@EEEIIIMMMMMMLLLMMMPPPSSSSSSTTTUUUVVVWWWWWWWWWWWWYYYYYYXXXXXXWWWUUUTTTSSSPPPOOONNNOOOPPPPPPNNNKKKMMMOOORRRSSSSSSSSSTTTVVVXXXVVVTTTQQQQQQQQQRRRSSSTTTUUUUUUVVVVVVVVVVVVVVVXXXYYYZZZ[[[[[[[[[ZZZZZZYYYYYYXXXXXXWWWXXXXXXYYYWWWXXXZZZ\\\]]]]]]\\\[[[[[[[[[ZZZYYYYYYYYYYYYZZZYYYXXXXXXWWWVVVUUUUUUTTTVVVUUUUUUUUUTTTSSSSSSSSSRRRRRRRRRRRRRRRRRRQQQQQQSSSRRRQQQOOONNNLLLKKKJJJKKKJJJIIIIIIKKKKKKJJJHHHGGGHHHIIIMMMOOOPPPNNNLLLMMMMMMNNNOOOOOOOOOOOONNNLLLLLLMMMNNNMMMLLLJJJIIIJJJIIIHHHEEEBBBAAABBBDDDAAAAAAAAA@@@@@@AAAAAABBB@@@@@@AAACCCCCCCCCCCCBBBDDDCCCCCCBBBBBBBBBAAA@@@AAAAAABBBCCCBBBAAA@@@???VVVQQQQQQWWWZZZUUUNNNKKKHHHHHHFFFBBBDDDFFF@@@777:::888;;;EEEQQQUUUQQQKKKJJJGGGCCC@@@@@@CCCGGGJJJJJJHHHGGGFFFFFFCCC>>>:::===============>>>>>>>>>???======@@@???;;;;;;===;;;999777666888:::;;;;;;999888999:::<<<===;;;:::666888::::::999999;;;===???DDDGGGFFFGGGFFF>>>555888999:::;;;;;;999888777666666777777888888999999999888666555555666777888777666555333333333555666222333444444333333444555555444333444555555333111555555444444333444444444444666888777666666777999555666777888888888777777999888888888999999999:::555666666666777888888666666777777777777666555444444444666888999888888888888:::<<<<<<:::888777777888888777888888888888999777777666555444333333222444444444444444444333333333555777666333222333555555666666777777666666555555555555555555555555555666666555555555555666666:::999888777666666666777999999:::;;;<<<<<<<<<<<<===;;;:::<<<@@@AAA@@@===;;;<<<===<<<:::888999999777777777777888888888888666666777777777777666666:::888666555777999::::::777777777777777777888888999;;;<<<:::777666888;;;:::999888888999999777555888999999:::;;;;;;;;;:::888999;;;;;;:::999::::::888999:::999888888:::<<<;;;:::999:::;;;=========666999:::999888888999999::::::999::::::;;;<<<===666999:::999666555888;;;666::::::666444777999888555666666444111111444777999999:::999888777666666777666666555444333222222555666777777777777999;;;555555666666555555444444333444555555555444222111333333444333333333222222555444444555777999<<<>>>???FFFLLLNNNQQQVVVWWWVVV^^^```cccfffhhhiiiiiiiiippppppqqqsssuuuwwwwwwvvvrrrssssssqqqnnnlllkkkllljjjkkkooorrrooojjjjjjnnniiieeeaaa``````^^^ZZZUUUMMMMMMKKKIIIEEEAAA===:::555555444222111222444555999777444111222444777999666666777888999999999999:::;;;;;;;;;;;;;;;::::::>>>===<<<<<<<<<<<<:::999:::;;;======;;;;;;;;;<<<===<<<:::999888999:::;;;:::;;;<<<<<<======<<<<<<;;;<<<<<<===============<<<<<<;;;;;;::::::;;;;;;777888:::;;;<<<<<<<<<<<<<<<<<<;;;;;;;;;;;;<<<<<<;;;;;;;;;;;;;;;<<<<<<<<<=========<<<<<<<<<<<<<<<=====================>>>======<<<;;;;;;::::::999;;;;;;;;;<<<>>>>>><<<:::;;;::::::;;;===>>>===<<<999::::::;;;;;;::::::999:::;;;<<<===<<<;;;:::999;;;;;;;;;:::888777999:::999999888888888888999999:::::::::::::::999999999<<<<<<<<<;;;:::999999:::888888:::;;;;;;;;;:::999}}}}}}zzzwwwuuunnnggghhhiii```RRRKKKMMMUUUeeevvv|||uuupppiiidddcccgggmmmrrrssssssuuuuuurrrgggXXXMMMLLLLLLMMMNNNQQQTTTWWWYYYWWWSSSRRRTTTTTTQQQRRRUUUWWWRRRKKKEEECCCCCCCCCCCCCCCCCCCCCDDDEEEDDDBBB@@@:::<<<>>>===<<<===AAAEEEOOOXXX]]]]]]ZZZSSSBBB000999:::<<<===<<<;;;999888999::::::;;;<<<======>>>???===;;;999888888999:::;;;<<<<<<:::888777888999999666444444555777777666555444555888<<<<<<999666888888888777777888999999888<<<@@@AAA???======???;;;<<<>>>??????===:::888::::::999888777777888888888888666444555999888555;;;::::::999888777666555777666777:::;;;999999;;;777999;;;;;;999888999:::777777666666777888999999777777666555555666777888:::999888777777777777777666<<>>@@@888;;;>>>???===>>>@@@CCC???@@@???===;;;999:::<<<:::>>>@@@>>>===@@@BBBBBB<<<===???@@@BBBCCCCCCCCC>>>>>>===;;;:::;;;===@@@AAAGGGHHHDDDBBBDDDGGGGGG>>>===<<<;;;:::999999999444666888888666666666777555555555444444444333333444555666666555555666888444555555555555555444444555555555555555555444444222222333444444333222111666666444333222333444444444999;;;999999===@@@???EEEFFFHHHJJJKKKKKKJJJJJJLLLMMMNNNQQQSSSVVVXXXZZZ[[[^^^``````\\\WWWSSSQQQQQQRRRTTTTTTPPPJJJLLLQQQLLLIIIEEECCCCCCAAA>>>:::777777777666444222111000//////...///000111333444444222000111444555333111444555666777888888888888666777888999::::::::::::<<<;;;;;;::::::999999999:::;;;<<<;;;999888888999999888888888888888999999888888999::::::::::::999888999999999999:::::::::999999888888888888888999;;;<<<======>>>>>>>>>>>>::::::::::::::::::::::::777888888999999:::;;;;;;999999999999:::::::::::::::::::::;;;;;;<<<<<<===888888888888888888888888999999:::===???>>><<<:::;;;:::999:::<<<===;;;:::999999999888777666555444666777777888777777666666444555777666555444555666666666555555666666777888777666666666555555555555555666777777666777999;;;666777888:::::::::999999|||qqqlllqqqyyyxxxoooppprrruuu|||{{{qqqhhhcccbbbbbbcccfffdddccccccbbb```\\\XXXSSSUUUVVVSSSQQQRRRXXX]]]jjjrrruuuqqqnnnhhhWWWDDD@@@BBBDDDFFFGGGFFFEEECCCGGGGGGHHHIIIJJJKKKLLLMMMOOOMMMIIIEEEBBB@@@@@@AAAEEEHHHKKKKKKHHHDDDBBBBBBCCC===777666:::===<<<:::666666999@@@GGGIIIFFFBBBDDDDDDDDDDDDEEEFFFFFFGGGFFFKKKRRRTTTQQQNNNMMMNNNKKKNNNQQQRRRQQQLLLGGGDDDCCCCCCBBBAAA???===:::888@@@@@@<<<777999>>>>>>:::888666555444666:::???BBB>>>999888<<<>>>===AAAFFFEEEDDDAAA===::::::<<<>>>;;;;;;===???CCCFFFJJJLLLCCCAAA===:::999:::<<<===:::999888888:::===@@@BBBBBBKKKTTTTTTKKK???888666666555444333333333444555777777777777777777777777555555555555555666777888666666666666666777888999999999999999999::::::;;;999:::;;;:::::::::<<<>>>;;;===???@@@>>>======>>>777777777777888888888999555666888:::::::::888888333888======999666888;;;777777777777888999;;;<<<;;;;;;===@@@CCCCCCAAA???===???BBBBBBAAABBBFFFIIIHHHHHHIIIKKKOOOTTTYYY\\\^^^[[[TTTNNNJJJKKKPPPTTTVVVZZZ^^^^^^\\\[[[^^^aaa^^^```___XXXNNNHHHHHHJJJKKKPPPRRRPPPQQQVVVYYYXXXVVVZZZaaafffiiiiiigggfffbbb^^^YYYWWWWWWYYYZZZ[[[hhhmmmoooiiidddeeeffffffQQQOOOMMMMMMMMMJJJCCC===888:::<<<;;;777555444555444444444333444444444444333444555444333111111222111111222222222222222111000000///000000000111111---...///000111222222222333222222111111111111222333666666222111555777777666666666666555555444333111222444555666888:::;;;@@@BBBDDDCCC@@@<<<999888;;;888777999777333111333444333111000000000///...000000000000000000111222333222111111111222222111......///111333333000...333444555666777777777777555555666888888999999999666666666666555555555666555666888777666555555666444555777888888888888777666777888888999999888888777777777777777888999999888888777777777888999999555555555666666666666666::::::;;;<<<<<<;;;:::999888888888888888999999999666666666777777777888888888888999::::::;;;<<<<<<777777777777777777777777777888:::===???>>><<<999888999<<>>;;;<<<=========<<<;;;:::xxxsssyyyzzzsssffflllrrruuuvvvzzz|||{{{|||~~~}}}|||uuuvvvyyy~~~}}}xxxtttqqqsssrrrnnnkkklllrrrxxx~~~wwwuuuvvvlll\\\bbbdddhhhkkkllllllkkkjjjoooooopppqqqssstttuuuuuuyyyvvvpppjjjfffcccbbbbbbhhhmmmtttvvvrrrkkkgggdddeee\\\TTTSSSYYY]]][[[WWWPPPRRRWWW```jjjmmmkkkfffjjjjjjjjjkkklllmmmnnnooommmttt|||{{{xxxvvvwwwwwwzzz}}}}}}wwwppplllggghhhiiihhhddd___YYYUUU^^^^^^XXXRRRTTTZZZZZZUUUBBB@@@>>>???EEEOOOZZZaaaUUUOOOLLLOOOQQQSSSZZZcccnnnjjjbbbYYYRRRQQQTTTXXXRRRTTTXXX^^^eeemmmsssvvvjjjeee\\\RRRJJJEEECCCBBB>>>>>>???AAAFFFMMMSSSWWWWWWbbbmmmlll]]]JJJ===666===;;;999777777777888999777777777777777777777777666666666777777999::::::777777777888999:::<<<<<<<<<<<<;;;;;;;;;<<<=========???AAA@@@>>>>>>AAADDDFFFGGGHHHFFFCCC@@@>>>>>>;;;;;;<<<<<<<<<============>>>AAABBBCCCCCCBBBAAA@@@JJJSSSTTTMMMGGGHHHKKKFFFFFFFFFFFFGGGIIIKKKLLLTTTUUUWWW]]]bbbccc```\\\VVV[[[_________aaagggmmmnnnnnnooosssyyyyyynnniiilllssszzzyyy}}}{{{yyyzzz}}}xxxhhh^^^]]]```qqqwwwzzzxxxyyyxxx~~~~~~wwwssstttwwwwwwwww~~~~~~wwwlllMMMNNNNNNKKKDDD???===<<<888777666555555444444555===>>>>>><<<888555444444333333444444444444444333222222111111111111222222333222222222111111111111...///000111222333333444///222333///...222444333333333222111111000/////////000111111000000000222111222222111000///000111000+++***000555444000...////////////000111333444......------...000222333.........000222333333333333333444333222333444666222333444555666666666666666666777888888888888888888888888888777777888999555777999999888777888999333555777999:::999888777888888999::::::::::::999888888777777888888999:::999888888888999999:::;;;<<<<<<<<<;;;;;;;;;;;;;;;:::;;;===>>>===<<<:::888:::::::::999999888888888555666666777777888888999::::::;;;<<<===>>>??????<<<<<<;;;;;;;;;:::::::::;;;<<<>>>BBBDDDDDD@@@>>>999===DDDJJJMMMKKKEEE@@@888:::===@@@CCCFFFHHHIII???>>>===<<<<<<===>>>???>>>@@@AAA@@@>>>;;;::::::999999;;;===???BBBDDDFFF>>>>>>???@@@BBBDDDFFFHHHIIIJJJJJJHHHEEEDDDFFFIIIJJJJJJKKKJJJIIIGGGEEEDDDyyywwwmmmbbbfffsssxxxsssggghhhkkkppptttsssnnniiiwwwrrrooojjjeeeiiimmmlllfffeeejjjppprrrjjjlllllllllssszzzzzzzzz{{{}}}xxxxxx|||uuuqqqpppqqqssskkkjjjhhhfffeeeeeefffgggkkkiiigggkkkqqquuutttqqqrrrssstttvvvwwwyyyzzz{{{{{{|||zzztttmmmjjjlllpppqqqsssvvvxxxwwwsssnnnkkkiiinnnsssvvvwwwuuuttttttssspppmmmqqqvvvxxxsssnnnfffhhhkkkrrrxxxzzzxxxuuu}}}wwwrrrqqquuuwwwwwwttt|||~~~zzzwwwvvvwwwyyy{{{|||{{{zzzyyy```UUUSSS]]]iiiuuu|||}}}}}}}}}yyykkkccc```[[[UUUMMMNNN^^^uuurrrYYYIIIDDDHHHPPPNNN@@@:::@@@@@@888;;;888888<<<===:::888888;;;;;;<<<<<<======>>>>>>>>>======>>>@@@DDDHHHJJJPPPUUUWWWRRRMMMJJJIIIFFFKKKLLLNNNOOOPPPSSSWWWZZZdddcccdddeeefffeeebbb```XXXYYYTTTIIIAAAAAAGGGMMMJJJUUUcccgggbbbYYYSSSQQQWWWhhh|||xxxnnnlllooommmpppvvv{{{}}}}}}{{{zzz|||lllttt~~~wwwwww|||yyyyyyyyy{{{tttnnnlllmmmzzz{{{|||{{{{{{|||~~~~~~}}}|||||||||sssfffbbbbbbWWWKKKEEEJJJKKKDDDAAADDDEEECCCAAA>>>;;;888444111444888:::777222000555;;;222555555111111444555111555444222111000000000000555222///000222222222333222333222///000333333///222222444666444000000333222111000//////000111111444111///000333444222000444444333111///000222444444222111111222333111000555444111000///000222333333666777555666;;;>>>>>><<<666333888:::888:::>>>:::;;;999666777;;;:::666;;;;;;;;;<<<<<<===<<<<<<>>><<<;;;;;;<<<;;;:::888???===<<<===<<<;;;;;;<<<@@@???>>>>>>??????>>><<<@@@???===<<<;;;;;;<<<===<<<@@@BBB???>>>@@@AAA???:::@@@EEEEEE@@@>>>BBBFFFHHHJJJGGGAAA>>>BBBCCCAAABBBNNNUUUOOOEEE@@@@@@AAAAAADDDAAA<<<@@@HHHEEE;;;<<<>>>???===;;;>>>EEELLLFFFFFFFFFHHHKKKNNNNNNMMMJJJKKKLLLLLLKKKIIIGGGFFFOOOKKKNNNUUUSSSKKKKKKRRRSSSQQQUUU]]]```[[[SSSOOOOOOHHHHHHWWWllluuummm```YYYTTTOOONNNPPPTTTUUUUUU[[[YYYUUUPPPJJJEEEAAA???BBBCCCFFFIIIMMMQQQTTTUUURRRLLLGGGIIIRRRZZZ]]]\\\]]]TTTKKKFFFFFFIIIIIIHHHGGGFFFEEEFFFIIIJJJHHHEEE{{{tttyyyxxxyyy|||~~~~~~|||xxxvvvyyyxxxsssrrrwww|||~~~}}}}}}zzz}}}~~~zzzvvvssstttyyy|||{{{zzzsssoooiiiddd```______```^^^]]]ZZZYYYXXXXXXYYYZZZZZZZZZ[[[```eeefffbbb^^^____________``````aaaaaaddddddccc^^^WWWUUUWWW[[[[[[]]]___```___\\\XXXUUURRRVVV[[[^^^^^^\\\[[[[[[aaa___^^^```dddeeebbb___ZZZ[[[]]]bbbfffhhhgggdddhhhccc^^^^^^aaacccbbb```nnnlllkkkmmmpppppplllhhhaaabbbeeeggghhhgggeeedddmmmnnnpppqqqppplllhhheeeeeehhhmmmsssxxx{{{}}}~~~mmmgggiiiwww}}}||||||kkk^^^\\\]]][[[VVVPPPJJJHHHEEECCCEEEJJJKKKIIIHHHGGGGGGIIIKKKMMMRRRTTTWWW\\\aaaeeehhhiii{{{sssvvv}}}tttxxx~~~ttteee\\\^^^ffflllsss|||vvvlllgggqqq}}}xxxzzz~~~~~~~~~}}}yyyuuusssssswwwwwwvvvuuuuuuyyy~~~|||{{{}}}{{{{{{xxx}}}aaaTTTDDD<<<>>>BBBCCCBBBJJJRRRYYYWWWLLLBBB===>>>;;;===@@@CCCCCCAAA???======???@@@@@@>>><<<;;;;;;888999:::<<<<<<;;;;;;<<<999999777666999===;;;666>>>:::999<<<<<<:::;;;>>>999999999;;;>>>>>>===;;;;;;;;;:::::::::999777666222333666888999888777666;;;;;;;;;;;;;;;;;;;;;;;;999;;;<<<;;;;;;;;;>>>@@@???AAABBBEEEPPPaaalllpppVVVJJJAAABBBEEEDDDAAA@@@CCCBBB@@@AAACCCDDDDDDDDD@@@DDDJJJLLLLLLKKKMMMOOOPPPNNNLLLLLLKKKKKKIIIGGGFFFGGGHHHGGGFFFHHHNNNUUUQQQQQQTTTXXX]]]``````___ccc___XXXTTTRRRTTTXXX[[[aaafffjjjlllmmmlllddd\\\XXX```hhhjjjgggfffkkkrrrqqqlllfffddddddeeecccaaallluuuzzztttkkkggghhhiiijjjnnnlllfffgggjjjdddXXXLLLKKKHHHEEEGGGRRRbbbnnnqqqkkkccc^^^]]]```dddfffhhhiiijjjjjjiiigggeeecccmmmeeeeeennnpppiiieeeggglllnnnssswwwsssjjjeeefff```ccckkkvvv}}}xxxhhh[[[NNNJJJGGGFFFHHHJJJKKKKKKKKKIIIGGGCCC@@@<<<:::888:::;;;===???AAACCCDDDEEE@@@===;;;>>>FFFNNNRRRSSSNNNGGG???;;;<<<>>>>>>===:::888888999<<<<<<:::888~~~~~~}}}~~~zzz}}}{{{vvvvvvzzz~~~~~~yyyxxxyyyvvvrrrvvvwwwxxxxxxvvvsssooommmgggfffgggjjjmmmmmmhhhddddddbbb^^^ZZZWWWUUUTTTUUUUUUTTTRRRQQQPPPQQQQQQRRROOOPPPSSSYYY\\\[[[UUUPPPQQQPPPPPPOOONNNNNNMMMMMMQQQRRRPPPLLLHHHFFFHHHKKKKKKLLLMMMMMMLLLJJJHHHFFFBBBEEEIIIKKKJJJHHHHHHGGGLLLMMMMMMNNNOOOOOONNNMMMLLLLLLMMMOOORRRSSSSSSQQQUUUQQQMMMMMMOOOQQQQQQOOOYYYVVVSSSSSSTTTTTTQQQNNNKKKMMMOOOQQQRRRQQQPPPOOOWWWXXXZZZZZZYYYVVVSSSQQQUUUWWW[[[___bbbdddeeefff___\\\bbbqqq|||wwwzzz~~~|||yyyzzz~~~}}}www}}}|||uuuwww|||xxxppphhhaaa[[[ZZZbbblllpppnnnjjjhhhhhhkkknnnqqqwww{{{vvvyyyyyytttrrrvvvyyyyyywwwyyy}}}xxxwwwzzz}}}yyyuuurrrwww|||yyyxxxxxxzzz}}}~~~yyyzzz{{{xxxxxxzzz|||{{{zzzzzzzzzzzzwwwvvvwwwuuurrrqqqssszzz|||sss\\\SSSXXXaaacccaaammmwww~~~rrrfffaaabbb^^^]]]ccclllmmmddd___aaa\\\aaadddaaaXXXPPPKKKKKKMMMPPPQQQNNNJJJFFFFFFFFFLLLLLLKKKMMMUUU\\\YYYRRRVVVRRRRRRWWWZZZWWWSSSSSSKKKJJJKKKOOOSSSQQQKKKDDDCCCFFFIIIIIIGGGEEEFFFGGGPPPLLLIIIHHHHHHHHHEEEBBBDDDFFFHHHGGGEEEDDDFFFHHHGGGKKKMMMLLLHHHGGGJJJNNNWWWgggyyywwwmmmooowwwyyyvvvrrrnnnccc[[[\\\\\\[[[___gggiiiqqq{{{~~~|||zzz{{{~~~zzzuuupppkkkeeebbbYYY^^^bbb___\\\aaaooo{{{xxxnnniiilllqqqvvv{{{~~~wwwuuusss{{{}}}wwwuuusssiii\\\JJJHHHDDDAAADDDOOO___kkknnnhhh___XXXVVVWWWYYYZZZXXXZZZ]]]aaadddfffggggggggg]]]ZZZdddkkkfff]]]ZZZkkkqqqyyyyyyoooddddddjjjrrrzzzsss^^^LLLBBB???===<<<<<<===>>>>>>===:::999888777555444333222444444444444555555555555111222333555999>>>BBBDDD>>>999444222333444333222222111111222444444333222ssswww}}}~~~|||{{{yyy}}}vvvuuuvvvwwwxxxyyyzzzzzzyyyzzzyyyuuuuuuyyy{{{zzzuuuwwwuuuppppppuuuwwwwwwsssppplllhhhgggfffdddaaa```aaacccccccccaaa___^^^YYYYYYZZZ]]]___```^^^[[[^^^]]]ZZZXXXUUUSSSRRRRRRPPPPPPOOONNNMMMMMMNNNNNNLLLMMMPPPTTTVVVTTTNNNIIILLLLLLKKKJJJIIIHHHHHHHHHIIIIIIHHHFFFCCCBBBDDDFFFFFFFFFFFFFFFEEEDDDCCCBBB>>>@@@CCCDDDBBBAAAAAAAAAAAACCCEEEDDDBBBAAACCCEEEEEEDDDDDDDDDEEEEEEFFFFFFIIIFFFDDDCCCEEEGGGGGGFFFJJJGGGDDDCCCCCCDDDBBBAAAEEEFFFHHHIIIJJJIIIIIIHHHJJJJJJKKKLLLKKKIIIGGGEEEHHHIIIIIIJJJJJJJJJIIIIIIHHHGGGKKKTTT[[[]]]bbbhhhhhhaaa]]]bbbfffeeeccccccfffhhhmmmtttwwwsssjjjbbb___dddkkkqqqtttuuuuuuuuuvvvvvvuuuttttttuuuwwwyyy{{{yyy{{{~~~yyysssnnnnnnwww}}}||||||{{{||||||zzzxxxvvvuuurrrooopppuuu|||~~~||||||tttsssqqqooonnnnnnmmmmmmoooiiidddffflllpppmmmhhhiiijjjllllllllllllmmmmmmpppjjjfffhhhooouuuvvvuuuzzzyyyuuupppllliiijjjkkkooommmlllnnnrrrsssqqqoooooommmkkkiiilllsss||||||wwwvvvyyy|||}}}|||tttwwwzzz}}}~~~{{{xxxvvv~~~|||}}}ooojjjpppuuusssmmmxxxyyywww{{{yyy|||~~~~~~~~~~~~vvvttttttwww{{{wwwlllbbbfffmmmssstttrrrppptttyyy{{{qqqfff```bbbeeeffffffqqquuuwwwuuupppnnnppptttxxx{{{|||vvvnnnjjjnnntttvvvssspppmmmuuuzzzwwwoooxxx{{{qqqfffgggssszzznnnggggggllloooqqquuunnnccc^^^[[[ccceeeccc^^^ZZZWWWOOOEEE@@@@@@>>><<<;;;>>>CCCGGGDDDDDDCCCDDDDDDCCC@@@===666888<<<@@@DDDGGGIIIJJJHHH@@@???GGGNNNKKKCCC>>>MMMSSS[[[\\\TTTLLLNNNVVVnnnrrrrrreeeQQQ>>>444222555555555666666666555444333333333333222222222222222222111111000000//////000333555555333222444666666333111000111222111///111111111222333333222222ooossszzz}}}~~~|||zzzzzzxxx{{{||||||tttsssrrrqqqpppppprrrssssssuuussspppppptttvvvtttqqqrrroookkklllpppqqqooojjjddd___[[[[[[ZZZ[[[\\\ZZZYYYYYYYYYYYYYYYZZZZZZVVVTTTQQQPPPRRRUUUWWWXXXUUUUUUSSSRRRPPPNNNMMMMMMIIIIIIHHHHHHHHHHHHHHHHHHHHHIIIIIIJJJKKKIIIGGGEEEFFFFFFEEEEEEEEEEEEEEEEEEBBBBBBAAA@@@>>>>>>???@@@AAAAAA@@@@@@??????>>>>>>;;;===??????===<<<===>>>===@@@BBB@@@===<<<>>>AAAAAA@@@@@@>>>>>>>>>???@@@???>>><<<<<<===>>>???>>>BBB@@@>>>======>>>>>>???>>>???AAABBBBBBCCCBBBBBBCCCDDDDDDDDDCCCBBBAAAAAA???@@@AAABBBCCCDDDEEEEEEGGGEEEFFFIIIKKKKKKMMMPPPNNNOOORRRVVVWWWVVVWWWYYY\\\\\\___cccfffddd]]]WWWTTTXXX\\\___```aaacccfffiiifffaaa^^^^^^aaaeeehhhbbbgggkkkjjjjjjmmmllliiihhhiiikkkmmmpppqqqqqqqqqooojjjkkkrrrwwwuuutttuuusssssstttsssooommmrrrzzzyyyxxxwwwvvvvvvvvvvvvvvvyyyzzz|||{{{yyyrrrrrrqqqsssqqqpppsssyyy|||{{{yyywwwtttooommmnnnrrruuuwwwpppoooooorrrwwwxxxwwwuuueeeggghhhhhhgggeeecccbbbfffccc___^^^```aaa```___aaaccceeedddaaa^^^^^^___^^^\\\[[[[[[]]]___```aaacccdddeeeccc```]]]\\\\\\\\\ZZZZZZ]]]bbbdddccc```___^^^]]]\\\]]]bbbiiinnniiiddd___]]]```dddggghhhhhhiiiiiijjjiiihhhgggfffrrrqqqsssuuuqqqiiidddeeeuuu{{{~~~xxxsssrrrtttooollljjjkkkooosssvvvwwwyyywwwxxx{{{}}}{{{yyyyyypppjjjeeedddggghhheeeaaacccggghhhdddaaagggvvvuuukkkwww~~~|||ssspppuuu||||||yyyvvvtttpppjjjooo|||{{{xxxvvvuuutttttttttrrrpppqqqzzz{{{kkkXXXRRRWWW\\\YYY\\\cccllltttxxxyyyyyypppjjjaaaXXXSSSRRRTTTUUUWWWVVVXXXbbbrrrzzzsssfff```hhhnnnkkkaaaZZZ\\\aaaggg```bbbjjjiiiaaadddqqqtttssskkk^^^TTTPPPNNNLLLKKKKKKIIIEEEBBBBBB>>>:::BBBBBBBBB@@@===;;;999999555888<<>>;;;===AAADDDAAA<<<>>>CCCRRRRRROOOGGG<<<555666999000222444555555333222111333333333333222222222222111111111111111111000000222666888777222//////111333222111111222222111000...///000111111000000111qqqtttyyy|||{{{yyywwwvvvsssssssssrrrssstttuuuuuussssssrrrooollllllmmmooonnnpppoookkkjjjnnnnnnllliiiiiifffbbbcccggggggdddddd]]]VVVTTTSSSRRRSSSVVVYYYXXXVVVTTTTTTTTTUUUUUUVVVRRRMMMIIIHHHKKKOOORRRNNNMMMLLLJJJIIIIIIIIIIIIEEEEEEEEEEEEEEEEEEEEEEEEFFFFFFEEEDDDCCCCCCCCCCCC@@@AAAAAAAAAAAABBBBBBBBB>>>===<<<<<<<<<<<<<<<<<<======>>>>>>===<<<<<<;;;:::<<<===<<<;;;;;;<<<===;;;===>>><<<999999;;;>>>;;;<<<<<<;;;999999:::<<<;;;;;;;;;;;;;;;;;;<<<<<<<<<<<<;;;::::::;;;======999:::;;;<<<<<<=========???>>>>>>>>>>>>>>>>>>>>>>>>??????@@@AAAAAABBBBBBCCCBBBBBBBBBBBBCCCEEEFFF@@@DDDIIIKKKIIIGGGIIIMMMNNNNNNNNNOOOPPPOOOMMMKKKOOOPPPRRRSSSTTTWWWZZZ]]]UUUSSSSSSTTTWWWZZZ[[[[[[[[[]]]^^^___cccgggfff```bbbbbbaaaaaaaaaaaaaaabbbfffcccccciiiqqqtttooogggdddeeeiiillliiiddddddhhhffffffeeeeeedddcccbbbaaagggfffddddddeeeiiillloooqqqrrrqqqrrrsssfffdddaaaaaaccciiipppuuuuuuooojjjgggdddbbb```aaabbbbbbbbbbbbdddeeeffffffeeecccbbb```aaaaaa```___^^^___```[[[[[[ZZZXXXVVVUUUWWWXXXXXXYYYZZZXXXUUUSSSRRRRRRNNNPPPQQQQQQOOOPPPSSSVVVUUUWWWXXXWWWTTTPPPNNNMMMLLLLLLMMMOOORRRTTTSSSSSSTTTTTTTTTSSSSSSUUUZZZ]]]^^^[[[WWWVVVXXX\\\___```dddcccaaa^^^]]][[[[[[[[[\\\YYYXXXZZZYYYUUUTTTWWW\\\aaadddbbb[[[WWWVVVWWWVVVUUUUUUVVVYYY[[[[[[[[[^^^___```aaabbbcccccccccYYYXXXVVVVVVVVVWWWYYYYYYRRRUUUVVVSSSQQQTTT^^^gggkkkdddaaadddccc^^^```fffvvv|||~~~~~~}}}vvvqqqqqqrrrpppnnnpppllljjjhhhjjjllljjjddd^^^eeejjjnnnlllgggeeeiiinnnnnnllljjjjjjmmmnnnmmmkkkppprrrrrroookkkhhhhhhjjjrrrrrrooojjjddddddjjjppp{{{xxxqqqhhhdddgggeee^^^\\\```cccbbbeeekkkqqqoooggg___YYYXXXWWWWWWYYYYYYXXXWWWWWWaaacccUUUHHHEEEGGGGGGJJJLLLQQQWWW]]]``````___PPPOOOMMMKKKIIIHHHHHHHHHHHHFFFCCCEEEOOOWWWUUUMMMKKKOOOSSSPPPIIIDDDFFFIIIKKKJJJMMMOOOJJJBBBFFFOOOOOOPPPNNNHHHGGGJJJJJJHHHDDDCCC@@@>>>===>>>@@@AAABBB@@@>>>;;;;;;<<<>>>???;;;;;;<<<>>>AAACCCBBBAAA===<<<<<<;;;::::::999999999<<<@@@AAA@@@>>>???AAA;;;999999;;;;;;777777:::;;;;;;:::888555444555666000222555666444222222222333222222222222111111111///000000000000000000000///222555555222//////111111111111111111111111111///000222222111111111222nnnqqqtttuuussspppooooookkkjjjjjjjjjiiiiiijjjllljjjkkkjjjhhheeedddeeehhhccceeeeeebbbaaacccccc```\\\\\\YYYUUUVVVZZZYYYUUUYYYRRRMMMMMMMMMJJJJJJMMMPPPPPPPPPOOONNNLLLLLLKKKMMMKKKIIIFFFEEEFFFIIIKKKHHHGGGEEEDDDDDDDDDEEEFFFCCCCCCCCCDDDDDDDDDCCCCCCAAABBBAAA@@@???>>>??????========================<<<;;;::::::::::::999999;;;<<<=========<<<;;;:::999:::;;;:::999:::<<<>>>::::::999888777777888999555777999888666666777999888999::::::::::::;;;<<<999999999999888888999:::888888999999:::;;;;;;;;;;;;:::999999999:::;;;;;;>>>>>>===<<<;;;:::::::::888999999999:::;;;<<<;;;@@@CCCEEEFFFFFFGGGHHHIIIJJJKKKKKKJJJIIIIIIKKKLLLGGGGGGGGGIIILLLOOORRRSSSOOOOOOPPPTTTYYY[[[ZZZXXXVVVXXXWWWWWWZZZ``````]]]^^^___^^^[[[WWWVVVWWWYYY^^^aaa``````fffnnnjjj```___]]]___cccccc___^^^```aaa```]]]\\\ZZZZZZ[[[[[[```^^^\\\\\\\\\___bbbdddbbbjjjmmmjjjoookkk[[[XXXWWWRRRVVV[[[aaacccaaa\\\XXX]]]\\\\\\\\\\\\[[[[[[ZZZ[[[```cccbbb^^^YYYWWWXXXSSSUUUWWWWWWUUUTTTUUUWWWPPPPPPOOONNNMMMMMMNNNNNNNNNMMMLLLKKKJJJIIIHHHGGGFFFHHHIIIHHHGGGHHHJJJMMMLLLMMMNNNLLLIIIFFFEEEEEEEEEGGGIIIJJJJJJJJJKKKLLLOOONNNMMMKKKKKKNNNRRRVVVPPPNNNLLLKKKLLLNNNPPPPPPYYYXXXVVVUUUTTTSSSSSSSSSNNNKKKIIILLLNNNMMMNNNQQQOOOQQQSSSRRROOOKKKKKKKKKMMMMMMOOOOOOPPPPPPPPPQQQOOOQQQQQQQQQQQQRRRTTTUUUSSSRRRQQQQQQRRRTTTUUUWWWOOOPPPQQQPPPNNNOOORRRUUUYYYVVVRRRPPPPPPRRRVVVYYYbbbccccccbbbaaaaaaccceeefffkkkiiiccciiiyyy~~~|||~~~~~~yyyhhhdddaaabbbaaa___```cccfffccc```^^^^^^^^^\\\[[[^^^```aaa^^^YYYXXX\\\```\\\\\\\\\\\\ZZZXXXTTTRRR[[[ZZZZZZYYYXXXWWWVVVVVV[[[\\\\\\[[[ZZZ[[[^^^```ZZZ[[[ddd|||nnnzzz{{{nnnfffcccaaaVVVUUUVVVWWWXXXVVVSSSPPPTTTUUUXXX\\\``````[[[VVVTTTRRRPPPNNNNNNMMMJJJHHHDDDLLLNNNEEEAAAEEEGGGCCCCCCCCCDDDGGGIIIJJJHHHGGGCCCEEEFFFHHHHHHGGGFFFEEEBBBCCCBBBAAAEEEKKKMMMKKKGGGHHHIIIGGGDDDCCCEEEGGGGGGIIIJJJGGGCCCAAABBBDDDAAACCCBBB@@@BBBEEEDDD@@@@@@>>>===<<<<<<<<>>>>>???@@@BBB>>>>>>??????@@@??????>>>999;;;<<<;;;:::888888888999999888888777777666666888777666666666666555444777888:::;;;;;;999777666555666777666555666999;;;:::999777666666666777777222555888888666555777999333444555555555555666777888999999888777666666777666666666777888888999999999888777777777888999:::888888888888999:::;;;<<<888:::;;;;;;;;;<<<<<<:::888888888:::>>>BBBCCC@@@BBBDDDEEEDDDAAAAAAEEEHHHEEEEEEFFFIIIMMMPPPQQQPPPOOOMMMJJJKKKOOOQQQQQQPPPPPPRRRQQQMMMNNNRRRUUUTTTTTTVVVVVVSSSOOOMMMOOOSSSOOOXXXYYYSSSXXXeeeeee[[[ZZZVVVVVVZZZ]]]\\\]]]______\\\XXXTTTSSSTTTVVVXXXXXXWWWWWWWWWXXXZZZ]]]^^^[[[aaaccc___cccyyybbbQQQQQQPPPQQQRRRRRRRRRSSSTTTUUUVVVQQQRRRTTTTTTTTTSSSSSSTTTKKKRRRXXXWWWPPPJJJIIIKKKBBBHHHOOORRRPPPLLLIIIHHHKKKIIIHHHIIIKKKLLLKKKIIIJJJHHHEEEEEEGGGGGGGGGEEEIIIHHHGGGFFFFFFGGGHHHIIIIIIIIIIIIGGGEEEDDDFFFGGGDDDGGGJJJJJJGGGFFFHHHJJJIIIHHHEEECCCCCCFFFLLLQQQKKKJJJIIIHHHHHHHHHIIIIIIEEEEEEGGGHHHIIIJJJJJJJJJGGGCCCBBBEEEHHHGGGHHHKKKHHHJJJKKKKKKJJJIIIHHHHHHGGGIIIJJJIIIGGGFFFHHHIIILLLNNNMMMJJJIIIJJJLLLLLLMMMLLLLLLOOOQQQRRRPPPMMMJJJJJJHHHHHHHHHJJJMMMNNNGGGHHHEEE@@@AAAIIIMMMMMMUUUSSSRRRQQQSSSXXX\\\___```dddaaaZZZ[[[cccccc[[[]]]^^^]]]ZZZ[[[______\\\WWWYYY^^^cccbbb\\\XXXZZZbbb___YYYTTTQQQQQQRRRSSS[[[[[[[[[XXXVVVVVVZZZ^^^WWWXXXWWWVVVTTTUUUWWWZZZSSSQQQPPPQQQRRRSSSRRRQQQOOOQQQRRRTTTUUUUUUTTTTTTUUUYYY\\\___dddiiihhhcccbbbnnntttlllaaa\\\ZZZXXXPPPQQQOOOKKKLLLQQQRRRNNNMMMOOORRRTTTTTTSSSQQQPPPOOONNNLLLLLLLLLLLLJJJIIIGGGKKKHHH>>>;;;@@@@@@888>>>>>>???BBBFFFHHHHHHHHH@@@AAACCCEEEEEECCCAAA???===AAABBB???===???@@@???BBBAAA@@@>>>>>>>>>???@@@===??????;;;;;;>>>===999888:::;;;:::>>>AAA???::::::999999999888777:::======<<<;;;:::::::::888666999888777888888777444111555555444444444555555666777999888444222333333333222111222222///,,,///555///000111000......111444---000333333000//////111......//////000000111111///............---------/////////000000000///////////////...------...000+++...000000...---...000bbb```___aaadddeeebbb````````````aaaaaa^^^ZZZVVVWWWUUUTTTVVVXXXYYYWWWTTTSSSQQQOOONNNPPPQQQQQQPPPMMMLLLKKKJJJIIIHHHHHHHHHIIIIIIHHHFFFEEEDDDBBBBBBBBBCCCEEEEEEEEEBBB???===??????>>>>>>???@@@AAAAAA???>>>===<<<<<<<<<<<<<<<::::::::::::::::::;;;;;;666555555666777888888777555555555555555555555555222333333333333222111111333333333333333333333333222111111222444666555444222222222333333222222222000111333555555444333222000111111111222222222222888444000///111444555444333333444444444555555555444444444555555555666666555555555555666888999999444444555555666777777888333444555777999;;;======<<<===>>>???AAACCCDDDEEECCCBBBBBBCCCDDDFFFHHHIIIHHHGGGFFFIIILLLMMMJJJHHHGGGGGGHHHIIIJJJLLLMMMNNNSSSLLLHHHIIIKKKIIIHHHHHHLLLNNNOOOOOOSSSZZZ]]]\\\UUUTTTRRRQQQRRRSSSUUUVVVYYYVVVQQQNNNMMMOOORRRUUUTTTRRRQQQRRRTTTVVVVVVUUUYYYYYYXXXYYY\\\bbbkkkqqqwww[[[NNNLLLNNNJJJKKKKKKLLLMMMNNNOOOOOOJJJPPPUUUUUUOOOIIIGGGGGGFFFIIIKKKIIIFFFCCCCCCDDDBBBCCCCCCDDDDDDCCCCCCBBBAAAAAACCCDDDEEEFFFFFFFFFEEEEEEEEEEEEDDDCCCBBBBBB@@@AAAAAABBBCCCDDDEEEEEEAAAAAABBBBBBBBBAAA@@@@@@AAACCCDDDEEEDDDEEEFFFHHHFFFEEEEEEDDDDDDDDDEEEEEEEEEEEEDDDDDDCCCCCCCCCBBBDDDCCCCCCDDDEEEEEECCCBBBCCCCCCCCCCCCCCCDDDEEEFFFDDDEEEEEEFFFFFFFFFEEEEEEHHHGGGGGGFFFEEEFFFFFFFFFGGGGGGHHHIIIJJJJJJJJJIIIKKKKKKKKKLLLNNNOOOMMMLLLNNNMMMKKKJJJIIIHHHGGGGGGBBBDDDFFFIIIKKKLLLLLLLLLTTTPPPMMMNNNRRRWWWZZZZZZVVVYYYYYYTTTSSSVVVUUUQQQRRRRRRRRRSSSUUUVVVUUUSSSTTTVVVWWWWWWVVVUUUUUUVVVYYYXXXVVVSSSOOONNNOOOQQQZZZ[[[YYYUUUPPPPPPTTTXXXPPPQQQWWW\\\\\\XXXVVVXXXOOOOOOOOOPPPRRRSSSRRRQQQMMMMMMMMMNNNOOOPPPRRRRRRSSSUUUXXXWWWUUUTTTWWWYYY___^^^\\\YYYVVVRRRNNNMMMNNNNNNOOONNNLLLKKKLLLMMMNNNOOOPPPPPPPPPNNNLLLJJJLLLIIIGGGFFFHHHHHHEEEBBBDDDCCCCCCBBBAAA???>>>===??????????????????@@@@@@>>>>>>>>>>>>>>>>>>>>>>>>??????>>>>>>======<<<<<<<<<===>>>>>>>>>===;;;:::999::::::;;;;;;::::::999333444666888999888777666555555444333333333333444777777666555555555555555333333333222222222111111222222222222111111111000000000000000000000000000111111000000000000111111//////////////////////////////000000000000//////.........------,,,,,,,,,,,,------......------,,,---------............///......------------......------............------bbb___[[[ZZZ[[[]]]]]]\\\]]]\\\[[[[[[[[[XXXTTTQQQQQQOOONNNOOOQQQRRRPPPMMMKKKIIIGGGFFFGGGHHHGGGGGGHHHGGGGGGFFFEEEEEEEEEEEEBBBBBBAAAAAA@@@???????????????@@@AAA@@@>>><<<;;;<<<<<<<<<<<<<<<<<<===>>><<<;;;:::999999999999:::::::::999999888888777777666444444555777777777666444444444444444444444444111111222222111111000///111111111111111111111111222111000111333444444333111111222222222222111111///000222444444333222111////////////000000000000444111......000222222111111111111111222222222222333333333444444444444555555444444444555666777777333333444444555666666666222333444666888:::;;;<<<;;;;;;<<<===???@@@AAAAAA@@@@@@@@@AAABBBDDDFFFGGGGGGEEEEEEFFFHHHHHHEEECCCCCCCCCCCCCCCDDDDDDEEEFFFIIIDDD@@@???>>>===BBBIIIMMMMMMKKKKKKPPPWWWZZZWWWQQQPPPOOONNNMMMNNNPPPQQQRRROOOLLLJJJJJJLLLOOOQQQNNNMMMLLLMMMPPPRRRRRRQQQOOOOOONNNMMMNNNRRRXXX]]]rrruuu___PPPIIIGGGGGGFFFGGGGGGHHHIIIIIIJJJJJJIIINNNQQQPPPIIICCC@@@???BBBDDDFFFEEEBBB???>>>>>>??????@@@AAAAAAAAA@@@@@@??????@@@AAABBBBBBBBBBBB======>>>???@@@@@@@@@@@@??????@@@@@@AAABBBBBBBBBAAAAAA@@@???>>>======<<>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>===<<<<<<<<<<<<<<<<<<;;;;;;<<<=========<<<;;;:::888888999999999999888888444555777888888777666555555444444333333333333333555555444333333333333333222222222111111111111000111111111111000000000000////////////////////////000000////////////000000..............................////////////.........---------,,,,,,,,,,,,,,,,,,------------,,,,,,,,,---------..................------------......------............------```[[[UUUQQQQQQSSSUUUVVVXXXVVVTTTRRRQQQPPPMMMKKKKKKJJJIIIIIIJJJJJJHHHFFFDDDBBB????????????>>>===AAAAAAAAA@@@@@@@@@@@@@@@;;;;;;;;;;;;<<<<<<<<<<<<;;;;;;::::::999999888888:::999999888888888888999888777666666555666666666999888777666555444444333444333222333555666555444222222222222222222222222000000000000000///......////////////////////////111000///000111222111000//////000000000000//////...///000111222111000000,,,------------.........000...---...///000///...------........./////////111111111222222222333333444333333333333333444444111111222222333444444444111222333444666777888999999999999:::;;;<<<<<<<<<<<<<<<======???AAABBBCCCCCCCCCBBBCCCCCCBBB@@@===???????????????????????????<<<888555000111<<>>@@@BBBAAA>>>;;;999999:::;;;<<<===============<<<<<<======>>>======<<<999:::;;;<<<<<<======<<<>>>>>>>>>>>>>>>>>>>>>>>>@@@???===;;;:::999999999===>>>@@@AAA@@@???@@@AAA<<<<<<;;;;;;;;;<<<<<<===?????????>>>>>>>>>>>>===???>>>>>>???@@@@@@???===??????>>>>>>===>>>>>>>>>===>>>???AAABBBCCCDDDDDDDDDCCCCCCBBBAAABBBBBBBBB@@@AAABBBDDDFFFGGGHHHHHHGGGGGGGGGHHHKKKKKKKKKIIIFFFEEEEEEEEEEEEEEEFFFFFFFFFIIILLLPPPRRRRRRQQQQQQNNNLLLKKKLLLNNNPPPPPPOOOQQQRRRQQQMMMMMMOOOPPPNNNSSSRRRPPPQQQSSSUUUUUUUUUTTTVVVWWWWWWVVVVVVWWWYYYXXXXXXWWWTTTSSSTTTWWWZZZWWWTTTRRRQQQRRRTTTUUUUUUVVVVVVYYY]]]\\\WWWUUUXXXWWWWWWWWWVVVUUUSSSRRRQQQQQQPPPOOOOOOPPPRRRTTTVVVQQQRRRTTTTTTTTTUUUWWWYYYQQQOOOMMMKKKJJJJJJJJJJJJIIIJJJKKKMMMNNNPPPQQQRRRQQQOOOLLLJJJHHHHHHHHHIIIHHHFFFDDDDDDDDDDDDBBBAAAAAAAAABBBCCCCCCBBBBBBAAA===============<<<<<<<<<========================::::::::::::;;;;;;;;;;;;:::;;;;;;;;;;;;:::999999666666777777777777666666555666777888888777555444444444333222222222222333222222111000000000000111111000000000000/////////000000/////////.........------------------------///......------......///------------------------,,,------......------,,,------,,,,,,,,,,,,,,,++++++,,,,,,------,,,,,,+++,,,,,,,,,,,,------------------,,,,,,,,,,,,------,,,,,,------------,,,,,,XXXUUUPPPLLLKKKLLLOOOPPPSSSPPPMMMJJJIIIHHHGGGEEEGGGGGGFFFFFFFFFEEECCCBBBBBB@@@>>>>>>>>>===<<<:::<<<<<<<<<============<<<::::::::::::::::::::::::888777666555555555666777888777666555555555555555555444444333333444444444555555444444333333222222333222111222333444333222111111111111111111111111///000000000000///..............................111///......000000///............//////.........------...////////////...,,,,,,,,,,,,------------------.../////////---,,,,,,,,,,,,,,,------------//////000000000111111111222222111111000111111111000000000111111222222222000000111222444555555666666666666777777777777777888888999:::<<<===>>>?????????@@@@@@@@@???===<<<>>>>>>>>>??????>>>>>>>>>;;;777333///+++---888DDDKKKJJJHHHHHHMMMQQQMMMFFFHHHGGGEEEDDDCCCCCCCCCCCC??????AAACCCDDDFFFGGGGGGDDDCCCBBBBBBDDDEEEEEEDDDJJJKKKKKKIIIFFFEEEFFFGGGDDDKKKYYYkkkzzz|||vvvqqqooojjjbbbZZZVVVUUUVVVMMMGGGAAA???AAABBBBBB@@@@@@@@@AAAAAAAAAAAAAAAAAAAAADDDGGGGGGDDDBBB@@@@@@>>>???@@@@@@>>>;;;999777888888999:::;;;;;;;;;;;;;;;;;;;;;;;;;;;:::999888<<<<<<<<<<<<;;;:::999999============<<<<<<;;;;;;>>><<<:::888777777888999:::<<<>>>>>>===<<<<<<===;;;;;;;;;:::;;;;;;<<<===<<<<<<<<<<<<<<<<<<<<<<<<===<<<<<<===??????>>><<<>>>>>>===<<<;;;;;;;;;;;;===>>>???@@@AAAAAAAAAAAAAAA@@@@@@??????????????????@@@BBBCCCDDDEEEEEEFFFDDDDDDDDDFFFHHHIIIHHHGGGCCCCCCCCCCCCDDDEEEGGGGGGGGGIIILLLNNNOOONNNLLLKKKGGGGGGIIIKKKNNNPPPPPPPPPQQQQQQOOOMMMMMMOOOPPPPPPRRRPPPMMMNNNPPPSSSTTTTTTTTTUUUVVVVVVUUUVVVWWWYYYWWWWWWVVVUUUUUUVVVZZZ]]]XXXTTTQQQQQQTTTUUUTTTRRRTTTTTTWWWZZZYYYVVVUUUXXXZZZZZZZZZXXXUUURRRPPPPPPWWWUUURRRPPPNNNOOOPPPQQQNNNNNNNNNNNNNNNNNNPPPQQQNNNMMMKKKJJJJJJKKKMMMNNNIIIIIIJJJLLLNNNPPPQQQQQQNNNMMMKKKIIIHHHFFFEEEDDDFFFEEEDDDDDDCCCCCCBBBAAABBBBBBCCCCCCCCCBBBAAAAAA=========<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<999999999::::::;;;;;;;;;999999999999888888888777555555666666666666555555666666777777666555444333333333222111111111111222111000000////////////////////////.........------.........------------,,,------------------------------,,,,,,,,,,,,------------------------------++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,++++++++++++++++++,,,,,,,,,,,,++++++++++++++++++,,,,,,,,,---,,,,,,++++++++++++,,,,,,++++++,,,,,,,,,,,,++++++NNNMMMLLLKKKJJJJJJKKKMMMNNNKKKGGGEEEDDDDDDCCCAAACCCCCCDDDCCCBBB@@@??????BBBAAA???>>>???>>><<<:::999:::;;;;;;;;;;;;::::::::::::999888888777777666666555444333333444666777777666555555444444444444444333333333333333444444111111111222222333333333333111000111222333222000000000000000000000000000000000000111000000///...........................000...------//////...,,,,,,------......------,,,,,,,,,---------......---,,,,,,---------.........,,,---///000///...---,,,,,,,,,,,,------------............////////////000111000///////////////000////////////000000000000//////000111222222333333444444444444444444444444555555777888999:::;;;<<<;;;<<<>>>??????>>>>>>>>><<<<<<>>>???@@@@@@??????999333///---,,,---333;;;@@@BBBDDDFFFKKKOOOJJJBBBEEEDDDCCCBBBAAAAAA@@@@@@;;;===???BBBDDDEEEEEEEEEEEECCCAAA@@@AAAAAA@@@???FFFGGGHHHGGGEEECCCCCCDDDGGGJJJPPPVVVYYYYYYUUURRRQQQNNNHHHCCCAAACCCHHHLLLFFFEEECCC@@@>>>???AAABBBAAAAAAAAAAAAAAA@@@@@@@@@???@@@BBBCCCBBB@@@@@@@@@======<<<<<<;;;:::888777888888999:::::::::::::::::::::;;;::::::999888777<<<<<<<<<<<<;;;:::999888===<<<<<<;;;;;;::::::::::::999777666777888:::;;;888:::======;;;:::999999::::::999999:::;;;<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;===<<<<<<===??????>>>=========<<<;;;::::::::::::?????????@@@??????>>>>>>???>>>======<<<<<<======AAABBBBBBCCCCCCCCCBBBBBB@@@@@@@@@BBBEEEFFFEEEDDDAAABBBBBBCCCEEEFFFHHHIIIIIIJJJKKKLLLLLLJJJGGGFFFFFFGGGJJJMMMNNNOOOPPPQQQPPPNNNMMMMMMNNNNNNOOOQQQOOOMMMKKKKKKNNNQQQRRRSSSSSSTTTUUUTTTSSSTTTVVVXXXTTTUUUVVVUUUUUUWWWZZZ]]]XXXUUURRRRRRTTTTTTRRROOOOOOOOORRRVVVVVVTTTUUUYYYZZZ[[[[[[XXXSSSPPPOOOOOOVVVUUURRRPPPOOOOOOPPPQQQPPPNNNLLLJJJIIIIIIJJJJJJIIIHHHGGGFFFGGGIIIKKKMMMKKKJJJIIIKKKMMMOOONNNMMMIIIJJJKKKKKKIIIEEEBBB???EEEEEEEEEDDDCCCBBBBBBCCCDDDDDDDDDCCCBBB@@@???>>>>>>>>>=========<<<<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;999999999::::::;;;;;;;;;777777777666666666666666555555666666666666555555555555555555444444333222222222111000000000000000111000000///.../////////.........---------,,,,,,---------,,,,,,,,,++++++------------------------,,,,,,++++++++++++,,,,,,++++++++++++++++++++++++******++++++++++++******++++++++++++++++++++++++******++++++++++++******************++++++++++++++++++************++++++******++++++++++++******FFFHHHJJJKKKJJJIIIJJJJJJJJJGGGDDDBBBAAAAAA@@@???===???@@@???===<<<<<<<<<@@@>>>===>>>>>>===;;;999999999;;;;;;;;;:::999888777777666555444444333333555444333333444555666777666555555444444444444555333333333333333444444555///000111111222333444555333111000111222222111///////////////////////////000000000000000//////..............................---,,,---...///...---,,,,,,------------,,,,,,,,,,,,,,,,,,,,,---------------------............+++---000000///---------------------............------............/////////...............///////////////////////////////////////000000111111111222222222333333333333333333444555777888999::::::999;;;>>>???>>>===>>>???999:::;;;===>>>>>>======666111---,,,+++,,,111888===AAACCCDDDGGGJJJGGGCCCBBBBBBBBBAAAAAA@@@??????===>>>@@@CCCDDDDDDDDDDDDEEECCCAAA@@@@@@@@@???>>>DDDEEEGGGGGGFFFEEEEEEFFFMMMNNNNNNLLLIIIFFFDDDDDDAAAAAAAAAAAABBBCCCDDDEEEBBBBBBBBB???<<<<<>>>>>>>>======;;;:::::::::888666666777777777666999999::::::::::::999999::::::::::::999999888777666777888999::::::::::::;;;:::::::::999999888888777777666666777888:::;;;888:::======;;;999777777777777777777888999:::::::::::::::::::::;;;;;;;;;<<<;;;;;;===??????>>>===<<<;;;::::::::::::::::::>>>??????>>>>>>===<<<;;;===<<<<<<;;;;;;;;;;;;;;;AAAAAABBBBBBAAAAAA@@@???=========???BBBCCCCCCBBBAAAAAABBBCCCEEEGGGIIIJJJKKKKKKKKKKKKJJJHHHFFFEEEIIIKKKMMMNNNMMMMMMNNNOOOLLLJJJKKKNNNNNNLLLMMMOOOMMMKKKJJJKKKNNNPPPQQQQQQRRRSSSRRRQQQPPPPPPRRRTTTQQQSSSTTTUUUUUUUUUVVVXXXVVVUUUSSSSSSSSSQQQOOOMMMMMMLLLNNNRRRSSSQQQTTTYYYXXXZZZ[[[XXXSSSOOOOOOPPPQQQQQQQQQRRRSSSTTTUUUVVVTTTPPPLLLJJJIIIIIIIIIHHHHHHGGGGGGGGGHHHIIIKKKLLLLLLJJJHHHIIILLLMMMKKKIIIFFFHHHJJJKKKJJJFFFAAA>>>CCCDDDEEEDDDBBBAAABBBCCCDDDDDDCCCBBBAAA???>>>===>>>>>>>>>===<<<<<<;;;;;;::::::::::::::::::::::::999999999999::::::::::::666555555444333444444444444444555555555555444444333333333222222222222222111111000////////////000111000//////......//////...------------,,,,,,,,,------,,,,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++******++++++,,,++++++++++++++++++++++++)))******++++++******))))))************+++++++++)))******++++++******)))))))))))))))*********+++******))))))))))))******))))))************))))))DDDFFFIIIIIIGGGFFFGGGIIIEEECCCAAA@@@@@@@@@???===:::<<<>>>===;;;:::;;;<<<===<<<<<<<<<======:::888999:::;;;;;;;;;999777666444444444333333333333333333333333444444555666777444444333333333444555555333222222222333333444555111111222222333333444444333222111111222222111///////////////////////////...////////////...---------------------------------,,,,,,---///000///...,,,------------------,,,,,,,,,++++++,,,,,,------,,,,,,,,,---------......+++---//////---+++,,,...------------............---------.........//////------------...//////000/////////////////////////////////000000000000000111111222222333333333444222333555777999999999999999;;;>>>>>><<<;;;;;;===888999;;;<<<<<<;;;:::999333111///---***+++444???MMMOOONNNGGGBBBBBBCCCBBB???@@@@@@@@@@@@@@@??????@@@@@@BBBCCCDDDDDDCCCCCCBBBAAA??????AAABBBAAA@@@CCCEEEGGGGGGEEEEEEFFFGGGLLLKKKIIIGGGEEECCCAAA@@@===>>>@@@BBBDDDCCCAAA???@@@???>>>>>>>>>?????????AAAAAA@@@???>>>>>>======<<<;;;::::::::::::999999888555111111333666777777::::::::::::999888777777888888999999999888888777666666777888999999999999777777777777777777666666666666666666666666777777888;;;======;;;999777666666666666666777888999:::888888888999999999::::::;;;::::::<<<>>>???>>><<<999999888888888999::::::;;;;;;<<<<<<<<<;;;::::::<<<<<<;;;:::::::::::::::>>>>>>???????????????>>>;;;:::;;;===@@@AAAAAA@@@@@@@@@AAABBBDDDFFFHHHIIIIIIIIIHHHGGGGGGGGGGGGGGGJJJLLLNNNNNNLLLLLLNNNPPPKKKIIIKKKQQQQQQNNNMMMPPPLLLKKKKKKMMMPPPRRRRRRQQQQQQQQQPPPNNNLLLLLLNNNPPPMMMPPPSSSTTTSSSRRRQQQQQQOOOQQQRRRRRRPPPNNNMMMLLLMMMLLLMMMPPPPPPOOORRRWWWVVVYYY[[[XXXSSSPPPQQQSSSPPPQQQSSSVVVXXXYYYYYYYYYUUUQQQLLLJJJJJJKKKJJJIIIJJJJJJJJJKKKKKKLLLLLLLLLKKKHHHEEEGGGKKKLLLJJJGGGFFFGGGHHHIIIHHHEEEBBB@@@AAACCCDDDCCC@@@???AAABBBAAAAAAAAAAAA@@@???>>>=========<<<<<<;;;::::::999::::::::::::::::::::::::999888888888888888888777555444333222222222333333222333333444444333333222000000000000000111111222111000//////......//////000///......------............---------,,,,,,,,,------,,,,,,,,,+++++++++++++++++++++++++++++++++,,,++++++******++++++,,,*********************************++++++*********))))))))))))******++++++))))))************))))))((((((((()))))))))*********))))))(((((())))))***((())))))******))))))(((DDDFFFHHHGGGDDDDDDFFFHHHBBB@@@????????????>>><<<999<<<>>>>>><<<;;;<<<>>><<<;;;;;;<<<======;;;999999:::;;;;;;:::888666444222333333444555555666666222222333444555666666777333222222222333444555555222222111222222333444444444444444333333333333333444222111111222222111///000000000000000000000000------......------,,,+++,,,,,,,,,,,,,,,,,,,,,,,,---,,,+++---///000000///,,,------......------,,,,,,,,,++++++,,,,,,---...++++++,,,,,,,,,---------***---...---+++***,,,...,,,,,,---------.........---------.........//////,,,,,,,,,---...///000111/////////////////////...//////000000000000000000111111111222333333444444222333555777999999999999:::<<>>;;;999999::::::;;;<<<===<<<:::888666333333333000***+++999IIIcccccc[[[LLL@@@===???@@@>>>>>>??????@@@?????????BBBBBBBBBCCCCCCCCCBBBBBB@@@>>>>>>???AAACCCCCCCCC@@@AAABBBBBBAAAAAABBBCCCDDDBBB??????AAA@@@>>>;;;?????????AAABBBCCCBBBAAABBB>>><<<>>>CCCDDD@@@;;;??????>>>===<<<<<<;;;;;;999888888888;;;=========999555000///222777999999::::::::::::999777666555777777888888888888888777;;;;;;;;;;;;:::999888777555555555555555555555555555666666666666555333333999;;;>>>>>><<<999777666777777777888888:::;;;;;;666777777777888888999999999999999;;;===>>>===;;;777777777777777888999:::777888999:::::::::::::::<<<;;;::::::999999:::::::::;;;<<<===>>>>>>>>>>>>999999:::<<>>???AAA??????@@@@@@@@@??????>>><<<<<<;;;::::::999888888999999999999999999999999888888777777666666555555444444222111111111222333111111222222222222111111//////......///000111222000000///...............///...------,,,,,,------.........---------,,,,,,---------,,,,,,,,,++++++)))))))))))))))))))))))),,,,,,++++++++++++,,,,,,))))))))))))))))))))))))******++++++++++++******(((((())))))*********+++))))))************))))))(((((((((((())))))))))))))))))(((((((((((())))))(((((())))))))))))((((((GGGGGGGGGGGGFFFDDDCCCBBBBBBBBB@@@???>>>>>>======???>>>>>>>>>>>>>>>>>>>>>===<<<<<<<<<<<<;;;;;;;;;666888:::999777555666888555444444333444555666777999777555555888888666444777555444555666777666555444333222222111111222222000222333333111000000111///111555666666333///---000000000000/////////////////////...------,,,,,,.........------,,,,,,,,,,,,------......------,,,------------------------,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,------------------------------,,,,,,,,,,,,,,,,,,,,,,,,------------------------,,,,,,,,,---------.........------,,,,,,------...---------------...//////111111000000111111222333///000000111333555777888;;;:::999888777555555444666777888999999888777666888444444333,,,***:::PPPttt{{{SSSAAABBBAAA>>>?????????@@@@@@AAAAAAAAACCCCCCBBBBBBAAA@@@??????>>>>>>======>>>>>>???@@@@@@??????@@@BBBBBBAAA??????>>>===<<<===>>>@@@BBB???@@@AAABBBAAA@@@???>>>>>>>>>======>>>???@@@@@@===>>>>>>>>>>>><<<:::999999999999::::::;;;;;;;;;666666666666777999:::;;;888888777777777777888888999888888888777777666666777777777777777777777777555555444444444444555555444444444555555555555666AAA@@@???===;;;999777666777555555888;;;<<<:::777555555555666777999:::;;;:::::::::::::::;;;<<<===<<<:::777666666777666555333333333444555777888999:::999888777777777999999888999::::::;;;;;;;;;;;;::::::999999:::<<<>>>???===<<<;;;;;;<<<>>>@@@BBBAAAAAAAAABBBCCCDDDEEEFFFHHHHHHIIIJJJKKKMMMNNNOOOGGGHHHJJJLLLMMMMMMMMMLLLJJJJJJKKKMMMPPPQQQPPPNNNPPPPPPOOONNNMMMLLLJJJIIIOOOOOOOOOOOOOOOOOOOOOOOONNNOOOOOOOOONNNMMMKKKJJJLLLMMMNNNMMMLLLLLLNNNPPPOOORRRTTTTTTPPPNNNOOOPPPUUUTTTRRRRRRRRRRRRPPPNNNRRROOOJJJHHHHHHHHHGGGFFFFFFFFFEEEEEEEEEEEEEEEFFFDDDDDDEEEFFFGGGGGGGGGFFFDDDCCCBBB@@@???>>>>>>>>>>>>===;;;::::::;;;<<<===<<<;;;:::::::::;;;<<<===777777777777777888888888777777777777777777777777999888777666555444444444333333222222111000//////000000000000000000000000///////////////////////////...---+++******++++++---,,,,,,++++++,,,,,,---++++++++++++++++++++++++---,,,+++***)))((('''&&&)))************+++++++++))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))(((((('''''''''&&&(((((((((((())))))))))))GGGFFFFFFEEEEEEDDDDDDDDDDDDCCCBBB@@@???>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>><<<<<<<<<<<<;;;;;;;;;;;;666888:::999777555666777555444444333444555666777999777555555777888666444666555444555666777666444444333333222111222222222111222444333111000000111000111444555555333000...000000000000/////////.../////////.....................---------,,,,,,,,,,,,,,,------------,,,,,,------------------------,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,,,,------------------------------,,,,,,,,,,,,,,,,,,,,,,,,------------------------,,,,,,,,,------------...------,,,,,,,,,,,,------...------------...//////111000000000000111222222000000000111333444666777777777777777777777777777666777888888888888777666999666777777111///===QQQ{{{]]]AAA??????>>>>>>>>>?????????@@@@@@@@@CCCCCCBBBAAAAAA@@@??????>>>============>>>?????????>>>>>>???AAAAAA@@@??????>>>=========>>>@@@AAA===>>>???@@@@@@???>>>>>>???>>>======<<<<<<<<<<<<;;;<<<<<<<<<;;;:::888777777777888888888999999999777777777777777888999:::777666666555555666666777888888888777777777666666777777777666666777777777555555444444444444555555333333333333444444444555>>>===<<<:::999777666555666555555777999:::888555555555555555666888:::;;;::::::::::::;;;;;;;;;<<<;;;999666555666777666666333444555666777888999999888777777666666666777888777888999999::::::999999666666777777888999;;;;;;>>>>>>===<<<======>>>???????????????@@@BBBCCCDDDDDDDDDDDDDDDDDDEEEFFFFFFCCCDDDEEEGGGHHHHHHHHHHHHEEEEEEGGGJJJMMMOOONNNMMMLLLLLLLLLLLLLLLKKKJJJJJJOOONNNMMMMMMLLLLLLLLLLLLMMMMMMMMMMMMLLLJJJHHHGGGJJJKKKLLLKKKKKKKKKMMMOOOOOOPPPQQQPPPMMMMMMOOORRRNNNMMMLLLLLLMMMNNNMMMKKKLLLJJJGGGEEEEEEEEEEEECCCFFFEEEEEEDDDCCCCCCCCCDDDAAAAAABBBBBBBBBBBBBBBBBBAAA@@@???>>>===<<<<<<<<<===<<<;;;:::999:::;;;;;;===<<<:::888777666666666777777777777777777777777666666666666666666666666666555555444444444444555333333222111111000//////000000000000000000000000///////////////////////////...,,,+++******++++++,,,,,,++++++++++++,,,,,,++++++++++++++++++++++++///,,,******,,,---+++)))(((((()))))))))*********))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))((((((((('''))))))))))))))))))))))))))))))(((((((((((())))))(((((((((((((((((((((((()))((((((((('''''''''&&&''''''((((((((()))))))))FFFEEEDDDCCCCCCDDDEEEFFFEEEDDDBBBAAA???>>>======<<<<<<=========>>>>>>>>><<<<<<;;;;;;;;;:::::::::777888999999777666666777555444444444444555666666888666555555666666555444666555444444666666555444444444333222222222222222111333444444222111111222111111222333333222000///000000000/////////............////////////000000------------,,,,,,,,,,,,,,,,,,------------,,,,,,------------------------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------------------,,,,,,,,,,,,------------------,,,,,,,,,,,,------.........---......///000000000//////000000111222111111111111222333444444444444555666777888999999666777777888888777777666:::888:::;;;777555AAAQQQ{{{bbb???<<>>>>>>>>>>>>>>?????????AAAAAA@@@@@@?????????>>>>>>============>>>?????????>>>===>>>@@@@@@@@@>>>???>>>>>>===>>>>>>???@@@;;;<<<===>>>>>>>>>>>>>>>@@@???===<<<:::999888888999999999999888777666666555555666666666666777777888777777777777777888888555555444444444444555555777777777777666666666666888777666555555666777888555444444333333444444555222222222333333333444444999999888777666555444444555444444666777777555333666666555444555777999;;;888999:::;;;<<<;;;::::::888666555555666777777666444555777888999999999999666666555555555555666777555666777777888777777777444444666777888999999999<<<<<<<<<<<<<<<;;;::::::<<<<<<<<<<<<===???@@@AAAAAAAAA@@@???>>>>>>>>>>>>BBBBBBBBBBBBCCCEEEFFFGGGDDDEEEFFFHHHKKKLLLKKKIIIFFFGGGHHHIIIJJJKKKKKKKKKMMMLLLJJJIIIIIIIIIJJJKKKMMMMMMLLLKKKJJJHHHFFFEEEFFFGGGIIIHHHHHHHHHKKKMMMNNNNNNMMMKKKJJJKKKNNNQQQIIIGGGGGGHHHIIIJJJJJJIIIGGGFFFDDDDDDEEEEEEDDDBBBEEEDDDCCCBBBAAAAAAAAAAAA???????????????>>>>>>>>><<<<<<;;;::::::::::::::::::::::::999999888888888:::999777555444333222222777777777666666555555444555555555555555555555555222222222222222333444555222222111111000000//////000000000000000000000000...........................---,,,++++++***++++++,,,,,,++++++++++++,,,,,,************************---)))&&&'''+++---+++((('''''''''((((((((())))))))))))))))))))))))))))))(((((((((((((((((((((((()))))))))((((((((('''''')))))))))))))))))))))))))))((((((''''''(((((()))(((((((((((((((((((((((((((((((((''''''''''''''''''''''''(((((((((((()))FFFDDDCCCBBBBBBCCCEEEGGGDDDCCCAAA???>>>===<<<<<<;;;;;;;;;<<<======>>>>>>;;;;;;;;;;;;:::::::::999777888999888888777666666555555444444555555555555666666555555555555444444555444333444555555444333444444333222222222222222222333444444222111111222111111111111111111000000000000/////////..................///000111111222,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++***++++++++++++,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++------------------------++++++,,,,,,,,,------------,,,,,,,,,,,,,,,,,,---......------......///000//////......//////000111111111000000000111222222222333444555666777888888666666666777777777777777888888:::<<<999888AAALLLooo\\\===<<>>>>>>>>>>>>>>>>>?????????>>>>>>==================>>>>>>>>>>>>>>>???@@@@@@>>><<<;;;<<<>>>???>>>>>>>>>>>>>>>>>>?????????>>>:::;;;;;;<<<===>>>>>>>>>@@@???===;;;999888888777777777777777777666555555555555555555555555555666777777666555555555555555555555444444444444555555666666666666666666666666777666555444444555666777444444333333333333444444222333333333333444444444666666555555555444444444444444555666666555444222777666444333444666888:::777888:::;;;;;;:::999777555444333444666777777666444555888:::::::::999888555555555555555666666666444444555555555555555444333444777999:::::::::999777888:::;;;:::999888777:::::::::;;;<<<===>>>???@@@@@@???>>>>>>>>>>>>>>>CCCCCCBBBBBBCCCEEEGGGHHHIIIIIIHHHIIIJJJIIIFFFDDDBBBCCCEEEGGGIIIKKKKKKLLLJJJIIIHHHGGGGGGIIIJJJLLLMMMLLLKKKJJJHHHFFFEEEDDDCCCDDDFFFFFFEEEFFFHHHJJJLLLLLLKKKJJJIIIJJJKKKKKKHHHGGGFFFGGGHHHIIIHHHGGGEEEDDDDDDEEEFFFFFFDDDCCCDDDCCCAAA@@@???>>>>>>>>>??????>>>===============:::999999888888888999999888888888888888777555555222222222333444444555666777666666555444333333222333333333333333333333333111111111000000111111222111111000000000/////////////////////////////////---------------------------,,,,,,+++++++++******++++++************++++++************************+++)))'''''')))***)))(((''''''((((((((()))))))))))))))))))))))))))))))))(((((((((((((((((((((((())))))((((((((('''''''''(((((((((((((((((((((((((((((((((''''''(((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&'''''''''(((((((((EEEDDDBBBAAAAAACCCEEEFFFBBBAAA???>>><<<;;;;;;:::::::::;;;;;;;;;<<<<<<<<<;;;:::::::::999999999999888888888888888888666555555555555555555555444444555555555555444333444444555333222333444555444222333333222111111111111222111333444444222111111222000000000000000000000111////////////............------...///000111222222,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,,,,,,,,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++*********+++++++++,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++------------------------+++++++++,,,,,,,,,------,,,,,,,,,++++++,,,,,,,,,---------------...//////......------......///000000000/////////000000111333333333444555555555666555555666666666777777888555666888999888888>>>EEEaaa~~~wwwPPP<<<>>>>>>:::????????????>>>>>>>>>>>>::::::::::::::::::;;;;;;>>>>>>>>>>>>>>>???@@@@@@===;;;::::::<<<============>>>???@@@??????>>>===;;;;;;;;;<<<===>>>??????>>>===<<<;;;::::::::::::777777777666666666666666666666666666666666666666666555444333333333333333666555555444444555555666555555555555555555555666555555444333333444555555333333222222222222333333444444444444555555555555444444444444444444444444444555666666666555444333777666444333333555666888666777999::::::888666555333333222333555666666555444555777999:::999888777444555555666666777777777222333333444333333222222222333666888999::::::999555666999;;;<<<;;;:::999999999::::::;;;===>>>???>>>>>>>>>>>>???@@@AAABBBDDDCCCCCCCCCDDDFFFGGGIIIIIIHHHGGGGGGHHHFFFDDDAAAAAABBBDDDFFFHHHJJJKKKKKKFFFFFFFFFGGGHHHJJJLLLMMMIIIIIIHHHFFFDDDCCCBBBBBBBBBCCCDDDDDDCCCDDDFFFHHHIIIIIIJJJKKKKKKIIIFFFDDDIIIHHHFFFFFFGGGGGGEEECCCBBBAAAAAACCCEEEEEECCCBBBBBBAAA@@@>>>===<<<<<<<<<>>>===<<<;;;::::::;;;;;;::::::999888888888999999777777777777666555444333///000111333555666777888555555444444333222111111111111111111111111111111222222000//////.........000000//////////////////........................,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++******+++******))))))******+++)))))))))))))))))))))))))))+++,,,+++)))((()))***((((((((()))))))))******((((((((((((((((((((((((''''''''''''''''''''''''((((((((((((''''''''''''''''''''''''''''''''''''((((((''''''''''''((((((''''''''''''''''''''''''&&&&&&&&&'''''''''''''''&&&&&&&&&&&&''''''''''''DDDCCCBBBAAAAAABBBCCCDDD??????===<<<;;;;;;;;;;;;:::::::::::::::::::::::::::::::::999999999888888999888777888999888777555555555555666555555444333444555555555333222333444444333222222444444333222222222111000000000000000000222333333111000000111///////////////000000000/////////.........------------...//////000111111++++++++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++************++++++++++++************************++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,,,,+++,,,------...------,,,,,,------.../////////.........///000000333333333333333333333333555555555555666777888888555555666666666777;;;>>>VVVggg^^^EEE===>>>;;;888>>>>>>>>>>>>============777888888888999:::::::::======<<<<<<======>>>???<<<:::888888:::<<<<<<<<<===>>>@@@AAA@@@???===<<<<<<;;;;;;;;;<<<===>>>>>>;;;;;;:::::::::::::::;;;777777666555555666666777777777777666666666666555555555444333222222222333555555555444444555555555444444444555555555555555333333333333333333333333333222222111111222222333444444444555555555666666444444444444444444444444222444666666555444444444666555555444444444444555555555666777666555444333222222222333555666444333333444555777777777666555333444555666777777777666222222333333222222111111000111333555666888888999777888;;;===>>>>>>===<<<999999999:::;;;<<<===>>>;;;;;;<<<===???@@@BBBCCCBBBBBBBBBBBBDDDEEEFFFGGGBBBBBBBBBDDDEEEEEEDDDBBBBBBCCCDDDEEEFFFGGGGGGGGGDDDEEEFFFHHHIIIKKKLLLLLLEEEDDDCCCAAA@@@@@@@@@@@@CCCDDDDDDDDDCCCCCCEEEFFFFFFGGGIIIKKKKKKIIIDDDAAAHHHFFFDDDDDDDDDCCCBBB@@@@@@???>>>???AAABBBAAA@@@@@@???>>>===<<<<<<<<<<<<;;;:::888777777888999:::;;;;;;:::999999999999999777777666555555444333333222333444555555666555555333333333222222111111000111111111111111111111111222222000///...---------////////////....................................++++++++++++++++++++++++******++++++++++++************))))))))))))******(((((((((((((((((((((((($$$&&&(((***)))((('''&&&(((((()))))))))*********((((((((((((((((((((((((''''''''''''''''''''''''((((((((('''''''''&&&&&&''''''''''''''''''''''''(((''''''&&&&&&''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''DDDCCCCCCBBBBBBAAAAAAAAA>>>>>>===<<<<<<<<<<<<<<<;;;;;;::::::999999888888999999999999888888888888999777666777999999777444555555666666666555333333333444666444222111222444333222111222333444333111111000000//////////////////111222222000//////000---...//////000000////////////.........------------------......//////000******+++++++++,,,,,,,,,++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++************************************++++++++++++***************************************************************************++++++++++++,,,,,,,,,,,,,,,++++++++++++,,,,,,++++++******++++++,,,---,,,,,,,,,,,,,,,------......---------...///000000222222222222333333333333555555444444555666888999777777666555555888::::::FFFOOOHHH<<<===<<<999;;;<<<<<<<<<;;;;;;;;;::::::777777888999::::::;;;;;;:::999999999999:::;;;;;;<<<999777777999;;;;;;;;;<<<>>>@@@BBBAAA???<<<:::;;;;;;:::999::::::;;;<<<::::::999888888888888999666555444444444555666666777777666666555555555555555555444444444444444555444444333333333333444444333333444444444555555555111222333444444333222111222222111111111111222222333333444444444555555555333333333333333222222222...111444555333222333444444555555666555444333222444444444444333333222222222111222333444444333111333333333333444444444444111222444555666666555555222222222222222111000000111222333444666888999:::999999;;;<<<<<<<<<<<<;;;888888888888999;;;<<<===;;;;;;<<<===>>>@@@AAABBBAAAAAACCCDDDEEEFFFFFFFFFAAAAAABBBCCCEEEEEECCCBBBCCCCCCDDDDDDCCCCCCBBBAAADDDEEEGGGIIIJJJIIIHHHGGGDDDCCCBBBAAAAAAAAABBBBBBEEEEEEFFFDDDCCCBBBDDDEEEEEEDDDEEEHHHJJJJJJGGGDDDEEEDDDBBBBBBCCCCCCBBBAAAAAA???======???@@@AAA@@@???>>>===<<<<<<<<<<<<<<<:::999888777777888:::;;;===<<<;;;999999888888888999888666444333333333333444555555666555444333222111111111111111111111111000000000000000000000000111000///.......................................------------------------++++++++++++++++++++++++)))***+++,,,,,,+++***))))))))))))(((((()))))))))(((((((((((((((((((((((($$$"""###)))000111+++$$$'''''''''((((((((())))))((((((((((((((((((((((((''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&''''''(((''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''$$$%%%%%%%%%%%%&&&&&&&&&CCCCCCDDDCCCBBBAAA@@@???>>>>>>============>>>>>><<<;;;;;;:::999888777777999999999888888888888777999777666777999999777444555555666666666555333222222444666444222000222444333222111111333333222111000000///...............///000111111///......///,,,---///000000000///...//////.........------------------...............*********++++++,,,,,,,,,+++++++++,,,,,,+++++++++++++++++++++++++++++++++************************)))************+++++++++))))))))))))))))))))))))************************))))))))))))))))))))))))******+++++++++,,,,,,,,,,,,++++++++++++++++++,,,******))))))******+++,,,,,,,,,++++++,,,,,,---...---,,,,,,---...///000000000000111222333333444555555444444444555666888999999999777555666999:::999888===888666;;;:::888AAA:::::::::999999888888888888888999:::;;;<<<<<<===777777666666777777888999;;;999777666888:::;;;;;;<<<>>>@@@BBBBBB???<<<:::;;;:::999888888888999::::::999888777666666666666555444333333333444555666666666666555555444444444666666555555555666666777333222222222222222222333333333333444444555555555///111333555555333111///222222111111111111222222222222333333333444444444222222222222111111111111,,,///333333222111222444333444666666666444222000444333222111111111111222222111222333444444222000222222111111111222333333000111222444555555444444222222222222222111000000444444444555777:::<<<>>>999999999999999888777777666666777777888:::;;;<<<=========>>>???@@@AAABBBBBBCCCEEEGGGHHHHHHGGGGGGFFFFFFEEEFFFFFFEEECCCAAADDDDDDCCCBBBAAA@@@>>>===DDDFFFHHHIIIIIIGGGDDDCCCFFFEEEDDDCCCCCCDDDEEEFFFFFFGGGGGGEEECCCBBBCCCEEEDDDBBBBBBDDDIIIKKKJJJIIIDDDCCCBBBCCCEEEFFFEEEDDDDDDBBB???>>>@@@BBBCCCCCC>>>======<<<<<<<<<======<<<;;;:::999:::;;;===???===<<<;;;999888777777777:::888666333222222333444333444555666555555444333000000000000111111111111111111111111111111111111///............///000000---.....................------------------------************************))))))+++,,,,,,+++***)))))))))(((((((((((())))))((((((((((((((((((((((((,,,&&&%%%///===AAA777+++&&&&&&&&&'''''''''((((((((((((((((((((((((((((((''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&'''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''$$$$$$%%%%%%%%%&&&&&&&&&AAAAAAAAAAAAAAA@@@???>>>>>>===============>>>>>>>>>===<<<;;;;;;;;;;;;;;;===<<<<<<;;;999888777777999888888888777777666666444444444444444444444444666555444333333333333333444444333333222111000000111000000///...---------000000000000000000000000////////////............------------,,,,,,+++***.........------,,,,,,,,,,,,,,,,,,++++++*********++++++************+++++++++***)))(((((()))***+++******************************))))))))))))************))))))))))))******)))************+++++++++************))))))))))))+++++++++************************++++++,,,,,,,,,******+++++++++,,,,,,,,,******+++++++++,,,,,,,,,---------............///444444444333333333222222444444444555555555555555;;;999888999<<<===:::888===<<<:::888888888:::;;;999999999::::::;;;;;;;;;888888999:::;;;;;;;;;;;;777999;;;<<<<<<;;;999888888888777777888:::<<<>>>======>>>>>>>>>===;;;:::777777777777777777888888888888888888888777666666444444444444444333333222444444444444444444444444555555555666555555444333555555444333333333333444111111111222222333333333111111111000000000000000000000000000000000000000444444444333333222222222333222000/////////000111111111000000111222333333111111111111111111111111111111111222222333333333222222222111000//////...///000111222222222222222///111222444444333222111////////////000000000000222555777777555666999<<<999::::::999888888999;;;::::::999888999:::;;;<<<@@@???>>>===???AAAEEEGGGDDDDDDDDDDDDEEEFFFGGGHHHJJJJJJHHHFFFCCCAAA???>>>>>>@@@???:::999<<<<<<:::EEEHHHJJJHHHEEECCCDDDEEEEEEEEEEEEEEEFFFHHHJJJKKKPPPKKKFFFGGGLLLNNNLLLGGGGGGJJJMMMNNNMMMKKKJJJJJJIIIKKKLLLKKKIIIFFFEEEEEEDDDCCCAAA@@@AAABBBDDDEEE>>>>>>??????>>>===<<<<<<>>>>>>>>>>>>=========<<<======>>>===:::999999:::::::::999888777666555444222444666777888777666555444333111//////000111222444444333222222111111000---...///000000///...---////////////////////////......---------,,,,,,,,,************))))))((((((************************))))))))))))))))))))))))((((((((((((((((((((((((***&&&###***@@@QQQFFF000&&&&&&&&&''''''''''''(((%%%%%%&&&'''(((((((((''''''''''''''''''''''''''''''((((((((('''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''>>>>>>?????????>>>======>>>===============>>>>>>===<<<;;;;;;:::::::::;;;<<<<<<;;;:::999888777777888777777777666666666666444444444444444444444444555555444333333333333333444444333222222111000000111000000///......------000000000000000000000000////////////............,,,---------,,,,,,+++***---------------,,,,,,,,,,,,,,,,,,+++++++++******++++++************+++++++++***)))(((((()))***+++******************************))))))))))))************))))))))))))******))))))*********+++++++++*********)))))))))((((((******************++++++***++++++++++++++++++,,,******+++++++++,,,,,,,,,******+++++++++,,,,,,,,,------------............000000000111111222222222444444444444444555555555:::888888999;;;;;;999777;;;:::999888777888888999999999::::::::::::::::::777777888999::::::::::::999999:::;;;;;;;;;:::999999888777777888:::<<<===;;;<<<<<<===<<<;;;:::999888888888888888888888888888999999999999888777777777777888888777777666555444444444444444444444444555555555555555444333333555444333333222222333333111111111222222222333333000000000000000000000000000000000000000000000000444444333333333222222222222111000/////////000000000000000000000111222222222222222222222222222222111111111222222333333333222222111111000//////...//////000111111111111111...///111222333222111000/////////000000000000111///111333333222222555888777888888777666555777888999999888777888999:::;;;>>>>>>===>>>???BBBDDDFFFBBBBBBCCCDDDEEEFFFGGGGGGGGGFFFEEEDDDBBBAAA??????===???>>><<<>>>CCCFFFFFFHHHJJJKKKIIIFFFDDDDDDFFFEEEEEEFFFFFFGGGIIIJJJKKKJJJHHHGGGIIIMMMNNNKKKHHHJJJLLLOOOPPPNNNLLLKKKJJJIIILLLOOOOOOMMMIIIGGGEEEDDDBBBAAA@@@@@@AAABBBCCC>>>=========<<<<<<<<<<<<>>>>>>>>>============<<<===>>>>>>===;;;::::::;;;:::999999888666555555444222444555777777777555444333222111000111333555666444333333222111111000000......////////////......------------------------------------,,,,,,,,,,,,++++++*********)))))))))************************((((((((((((((((((((((((''''''''''''''''''''''''((()))'''(((222<<<555%%%&&&&&&&&&&&&''''''''''''%%%&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''';;;;;;<<<=========<<<<<<>>>======<<<<<<<<<======;;;;;;:::999999999999:::;;;;;;:::999888777777666666666666555555555555555444444444444444444444444444444333333222222333333333333333222111111000000111000000//////......---000000000000000000000000/////////............---,,,,,,---------,,,++++++,,,,,,,,,,,,------------,,,,,,,,,++++++++++++***++++++************++++++******))))))))))))*********************************))))))(((((())))))******))))))(((((())))))***)))))))))*********++++++******))))))))))))(((((()))))))))***+++++++++,,,+++++++++++++++***************+++++++++,,,,,,,,,******+++++++++,,,,,,,,,,,,,,,,,,---------......,,,------...000111111222333333333333444444444555888777777888999999888666888888888888888777777666999:::::::::::::::999999666666777888999999999999;;;:::::::::999:::::::::999999888777888999;;;<<<;;;;;;<<<<<<<<<;;;::::::888888888888888888888888888999999999999888777777888999999999999888777777444444444444444444444444444444555555444444333222333333222111111111111222111111111111111222222222000000000000000000000000000000000000000000000000333333333222222222222222111000///.........//////000////////////000000111222222333333333333222222111111111222222222222222222222111111000///////////////000000111111000000---...000111111111000/////////000000000111111111...///000000000111333555333444555444333333444666888888777666777888999:::;;;<<<===???AAABBBDDDEEE???@@@BBBDDDEEEFFFEEEEEEBBBBBBBBBAAAAAA@@@@@@@@@???AAA@@@>>>AAAIIIOOOOOOJJJJJJJJJHHHEEECCCCCCCCCDDDEEEFFFGGGHHHIIIIIIIIIDDDFFFIIIKKKMMMLLLJJJIIIMMMOOOQQQQQQNNNKKKJJJJJJGGGKKKOOOPPPMMMIIIFFFDDDDDDCCCAAA?????????@@@@@@===<<<;;;:::::::::;;;<<<>>>>>>=========<<<<<<<<<===>>>>>>===;;;:::;;;<<<999888888777666555444444222333555666666555444444222111111111333666888:::333333222222111000000000//////............//////,,,,,,,,,,,,,,,,,,,,,,,,---------,,,,,,,,,+++++++++++++++***************************************((((((((((((((((((((((((''''''''''''''''''''''''%%%+++,,,&&&%%%(((&&& &&&&&&&&&&&&''''''''''''&&&''''''''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''::::::;;;<<<=========<<<======<<<<<<;;;;;;<<<<<<999999888888888888999999::::::999888777777666666444444444444444444444444333333333333333333333333333333222222222222333333333222222222111111000000000000000000//////......//////////////////////////////.........---------,,,,,,,,,------,,,,,,++++++++++++,,,,,,------...++++++++++++++++++++++++++++++************++++++***))))))))))))))))))***************************))))))(((((((((((())))))))))))(((((((((((())))))))))))))))))***************)))))))))(((((((((((((((((()))***+++,,,,,,,,,,,,,,,++++++******))))))******+++++++++,,,,,,,,,******+++++++++,,,,,,,,,+++,,,,,,,,,------------,,,------...//////000000111111222222333333444444666666666666777777666555555777888999999888666555999999:::::::::999888888666777888999::::::::::::===;;;:::888888999:::;;;::::::999888888999999:::;;;;;;<<<<<<<<<;;;;;;;;;999999999999888888888888777777777888777777666555666666666666666555555444333333333333333333333333444444444444444333222222222222111000000000000000000111111111111111111111/////////000000000000000000000000000000000000000222222222222222111111111000//////...............//////.........//////000222333444444444444333222111111111111111222222222111111111111000000/////////000000111111111000000---...///000000000000////////////000000000111111000000111111111222333555111222333222111111333555888777777666666888999:::999;;;===@@@BBBCCCDDDDDD???@@@BBBDDDDDDCCCBBBAAA?????????@@@@@@AAAAAABBBDDDDDDBBB>>>AAAHHHNNNPPPKKKJJJIIIFFFDDDBBBAAAAAACCCDDDFFFGGGHHHHHHGGGGGGCCCFFFJJJKKKIIIGGGHHHIIIMMMOOOPPPOOOLLLIIIHHHGGGFFFHHHJJJKKKHHHFFFDDDDDDDDDCCCBBB@@@???>>>>>>>>><<<;;;999777777999:::;;;======<<<<<<<<<;;;;;;;;;<<<===>>>===;;;:::;;;<<<777777666666555444444333222333444444444444333333222111111111333555888:::222222222111000000////////////---,,,,,,---//////,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++************************************((((((((((((((((((((((((''''''''''''''''''''''''""")))+++&&&"""###%%%%%%%%%%%%&&&&&&&&&'''''''''''''''''''''&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%$$$$$$###%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''';;;<<<===>>>>>>>>>>>>>>>======<<<;;;;;;:::;;;;;;888888777777777888888999888888888777777666666555333333333333333444444444333333333333333333333333222222111111111222222333222222111111111111111000000000000000000/////////////////////////////////............------------+++,,,,,,------,,,,,,,,,***++++++,,,,,,---------++++++++++++++++++++++++++++++************++++++)))))))))******)))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))(((((((((((())))))(((((()))))))))*********)))))))))(((((((((((('''(((((()))***+++,,,,,,,,,+++++++++******)))))))))******+++++++++,,,,,,,,,******+++++++++,,,,,,,,,++++++++++++,,,,,,,,,---////////////////////////000000000111222333333444444555666666555555555555555666888::::::999777555888888:::;;;:::999888777777888999:::;;;;;;;;;;;;>>><<<:::888777888:::;;;;;;;;;:::999888888888888999999999999999999999999999999999888888888777777555555555555555444333333444444555555444444333222333333333333333333333333333333333333333222222111111111000////////////000000000000000000000000000......//////000000000000000000000000000000000000111111111111111111111111///////////////......---//////...............///222222444555555444222222111111111111111111111111111111111000000000000000000111111111111111000000...//////000000000000000...////////////000000000111000000000111222333333000111222222111111333555888777666666666777999:::999;;;===@@@BBBCCCBBBBBB@@@AAABBBCCCBBB@@@>>><<<>>>>>>???@@@@@@AAABBBBBBCCCCCC@@@<<<>>>FFFLLLMMMNNNLLLIIIGGGEEEDDDBBBAAAEEEFFFHHHIIIJJJIIIIIIHHHFFFHHHJJJHHHDDDBBBEEEHHHIIIKKKLLLKKKHHHEEEEEEEEEGGGGGGGGGEEECCCCCCDDDFFFDDDCCCBBB@@@???>>>======:::999777666666888:::;;;;;;;;;;;;:::::::::999999:::;;;<<<;;;999999999;;;666555555555444333333333222333333333333222222222222111000000111333555666222111111000000//////...///...---,,,,,,---...///------------------------,,,,,,+++++++++*********************************))))))))))))))))))))))))''''''''''''''''''''''''''''''''''''''''''''''''"""&&&'''%%%$$$&&&((((((%%%%%%%%%&&&&&&&&&&&&'''&&&'''''''''&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$%%%$$$$$$###%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''>>>>>>???@@@@@@@@@??????===<<<;;;:::::::::::::::888777777777777888999999777777666666666555555555333333333333444444444444333333333333333333333333111111000000111111222222111111111111111111111111000000000000000000000000000000000000000000000000.........------------,,,++++++,,,---------,,,,,,++++++++++++,,,,,,,,,,,,***++++++++++++,,,,,,,,,++++++************++++++))))))************)))))))))))))))))))))))))))))))))((((((''''''(((((())))))((((((''''''(((((()))((((((((()))))))))******))))))(((((((((((('''''')))))))))***+++++++++,,,***************)))))))))******+++++++++,,,,,,,,,******+++++++++,,,,,,,,,******+++++++++,,,,,,,,,000000000/////////.........//////000111222333333333555666666555444444555555666888999:::999777666666777999;;;;;;:::999888888888999:::;;;;;;;;;;;;>>><<<:::888888888:::;;;<<<<<<;;;:::999888777666555555444444444555666777999999888888777666666666333444444444444333222222444555555555555444333333333333333333333333333333222222333333222222111000111111000////////////000000000000000////////////---......//////000000111000000000000000000000000000000000000000111111111///000000000000///...---000//////............///000222333555555333222000111111111111111000000000111111000000000000000000000000111111000000//////////////////000000000111------.........////////////---,,,,,,...000/////////000111111000111333444666666555555555666777888888999<<<>>>????????????@@@@@@@@@@@@???>>><<<;;;>>>>>>>>>???@@@@@@AAAAAA===>>><<<999===FFFLLLNNNRRROOOKKKIIIHHHGGGFFFDDDHHHHHHIIIJJJJJJJJJJJJJJJGGGHHHHHHEEEBBBAAACCCFFFDDDEEEGGGFFFDDDCCCCCCDDDHHHHHHFFFCCCAAABBBEEEHHHBBBAAA@@@???>>>===<<<<<<999888777777777888999:::999999888888888777777777777888999888777666777888444444444444333333222222222222222222111111111111333222000//////000222333111111000000///...............------------......------------------------+++++++++*********)))))))))))))))))))))*********))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$&&&'''&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$%%%%%%&&&'''@@@@@@AAAAAAAAA@@@??????===<<<;;;:::999999999999888777777777888888999:::666666666555555555555444333333333333444444555555222222222222222222222222000000000000000111222222000000000000111111111111000000000000000000000000000000000000000000000000.........---------,,,,,,***+++,,,,,,---------,,,,,,,,,,,,+++++++++++++++******+++++++++,,,,,,,,,++++++************++++++((()))***++++++***)))((())))))))))))))))))))))))((((((''''''''''''((((((((((((''''''''''''(((((((((((((((((()))))))))***))))))((((((((('''''''''******************++++++))))))))))))******************+++++++++,,,,,,,,,******+++++++++,,,,,,,,,************++++++++++++.........///////////////---......///000111222333222555777666444333444666444555666777777777666666333555888:::;;;;;;999888777888999::::::;;;;;;:::===<<<;;;999888888999999===<<<<<<:::999777666555555555444444444555666777888888777777666555555444333444444444444333222222444444444444444333333222222222222222222222222222222222222222222111111000222111000000//////000000000000/////////.........------......///000000111000000000000000000000000/////////000000000111111000000111111111000///...111000//////....../////////111333444444333111///222111111111000000000///000000000000000000000111......//////......---,,,...............//////000,,,,,,,,,------------...---+++)))***,,,...---,,,...///000000///000222444444333222222222333555666777777888999::::::;;;;;;================================================:::<<<;;;999===FFFMMMNNNQQQMMMIIIGGGGGGGGGFFFEEEEEEEEEEEEEEEEEEFFFFFFGGGEEEEEEFFFEEEDDDCCCCCCCCC???AAABBBBBBBBBAAACCCDDDEEEEEEDDDBBB@@@AAACCCFFF>>>>>>>>>===<<<;;;:::999777777888888888999999999777777666666666555555555333555666555444444555666333333333333222222222222222222111000000000000000222111000//////000222444111000000//////...------,,,------......------,,,,,,,,,,,,,,,,,,,,,,,,,,,+++*********))))))))))))''''''((((((((()))))))))))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$###%%%''''''%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''AAAAAAAAAAAAAAA@@@???>>>===<<<;;;:::999999999999888888777888888999::::::555555555555555555444444333333333444444555555555222222222222222222222222000000///000000111222222000000000000000111111111000000000000000111111111000000000000000000000000......---------,,,,,,,,,***+++,,,,,,---------------,,,,,,++++++******************++++++,,,,,,,,,++++++************++++++((()))***++++++***)))((())))))))))))))))))))))))((((((''''''''''''((((((((((((''''''''''''(((((((((((((((((()))))))))))))))(((((((((''''''''''''+++++++++***************(((((())))))******++++++******+++++++++,,,,,,,,,******+++++++++,,,,,,,,,)))************++++++++++++,,,,,,---...///000000------...///000111222222222555777777444333444666333444444555666666666555222444777:::<<<;;;:::999666777888999999:::999999===<<<;;;:::999999888888======<<<;;;999777555444888777666666666888999:::888777777666555444444333444444555555444444333222222222333333222222111000222222222222222222222222222222222222222111000000222222111000000000000000000000//////.........------------...///000000111000000000000000000000000.../////////000000111111000111222222222111///...111111000//////////////////000222444444222000///222111111111000000//////000000000000000111111111,,,---------,,,,,,+++***---,,,,,,,,,,,,---......+++++++++,,,,,,,,,------...,,,)))***---...---,,,,,,...///.........111333222111000000000111222333666666666666666777777777;;;;;;;;;;;;<<<>>>???@@@======<<<<<<<<<;;;;;;;;;<<<>>>===;;;>>>FFFLLLLLLNNNJJJEEEDDDEEEEEEDDDBBBAAA@@@???>>>>>>???AAABBBAAABBBDDDFFFGGGEEECCCAAA===???@@@AAAAAAAAACCCEEE@@@AAAAAAAAA???>>>???AAA;;;;;;;;;;;;:::999888888666777888999999999999999666555555555555444444444111333444333222222333444333333222222222222222222222222111000//////000000111000//////000222444555000000000///......------+++,,,............,,,+++++++++++++++++++++++++++************))))))))))))&&&'''''''''(((((())))))))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$%%%((()))(((''''''$$$$$$%%%%%%%%%&&&&&&&&&###$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''AAAAAAAAAAAA@@@???>>>>>>???>>>;;;999777777888999:::888777777888999999888666666555555555555666666555555555555555555555555444333222111111333444666555444222111000/////////333333222111000000000000222222222111111111111000///000111111111000...------------,,,,,,+++++++++,,,------......------,,,///...,,,+++***+++,,,,,,+++++++++++++++++++++++++++*********))))))((((((++++++******))))))(((((())))))))))))))))))))))))))))))(((((((((((())))))******))))))((((((''''''))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))******))))))))))))*********)))((()))+++,,,,,,+++************************+++++++++*********)))))),,,,,,,,,---------......000000000111222222333333444555555555555555444444444444555555555555555555444555777999:::999888777999999888888888888999999::::::999888888777777666999666444555777:::999888999999888777666666666777777777777777777666555555444444444444444444444444222222222111222222333333222222222222222111000///111111111111111000//////000000000000111111111111////////////000000000000//////000000000000//////222333555555444222///---333333111...+++,,,000444000000111111111111000000000///...------...///000//////............/////////............---------......////////////.........---,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,.........------,,,,,,,,,---,,,,,,++++++,,,,,,---......////////////......111111111111111222222222111111222333444666666777;;;888666777:::;;;:::888;;;<<<<<<<<<======>>>>>><<<<<<>>>@@@CCCGGGKKKMMMFFFDDDBBBAAA@@@???===;;;===<<<<<<======>>>???@@@@@@CCCEEEFFFDDDAAA???>>>AAA>>>===>>>AAACCCCCCAAACCCBBBAAA@@@????????????>>>===;;;999888777666666999::::::;;;;;;::::::999777666555444333444444555000222333222222333555777222222222111111111111000222222222111111111000000/////////...///000111111000//////............///...............---------+++++++++************)))))))))************))))))+++***((('''''''''((()))''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&######$$$%%%'''((())))))??????@@@@@@@@@@@@@@@??????>>>;;;999888888999999:::888777777888999999888666666555555555555666666444444444555555555555555555444333222333444666777777666444333222111111111222222111111111111111222222222222111111111000000///000000111000///...------------,,,,,,,,,++++++,,,,,,------------,,,,,,...---,,,++++++++++++,,,++++++++++++++++++++++++************)))))))))(((*********)))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))((((((''''''(((((((((((((((((((((((())))))))))))))))))))))))'''((((((((())))))))))))******))))))))))))******)))(((((()))+++,,,,,,+++************************+++++++++*********)))))),,,,,,,,,,,,------------//////000000111222222333333333444444444444333333444444555555555555666666333444666888999888777777888888777777777777888888888888777777777777666666999666444555777999999888999999888888777777888888666777777777666666555444444444444444444444444444222222111111111222222333111222222222111111000///000111111111111000////////////000000000111111111000000000/////////////////////000000000000//////111222333444333222000...222000///111444666444111///000000111111000000///000///............///000//////............//////............------------.........//////............---,,,+++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,...---------,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,---......//////......---////////////000000000000000000111222333444555555:::777555555777999999888:::;;;;;;<<<===>>>>>>????????????@@@BBBDDDGGGHHHFFFDDDAAA===<<<<<<===>>>==================>>>>>>@@@CCCEEEEEECCCAAA@@@@@@CCC@@@??????AAABBBAAA???AAA@@@???>>>============;;;::::::999888888888999::::::;;;::::::999888777777666555444333444444555333444444333111111222333222222222111111111000000222222111111111000000000.../////////000000000000///...............////////////......------,,,,,,+++++++++*********))))))))))))************))))))******((('''''''''((()))''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&######$$$%%%&&&''''''(((<<<===>>>???@@@@@@@@@@@@>>>===;;;999888888999999:::888666777888999888777666666555555555555666666444444444555555555666666666666555444555666777888888888666555444444444444111111111000111111222333222222111111111000000000///000000000000///...---------------,,,,,,,,,,,,+++,,,,,,------,,,,,,+++------,,,++++++++++++,,,++++++++++++++++++++++++************))))))))))))((())))))))))))))))))***)))))))))))))))))))))))))))((((((''''''(((((())))))))))))(((((((((((('''(((((((((((((((((((((((())))))))))))))))))))))))''''''((((((((()))))))))***))))))(((((())))))***)))(((((()))+++,,,,,,+++************************+++************)))))))))++++++,,,,,,,,,---------...//////000000111222222111222222333333222222222444444444444555555666666222333555666777777666666666666666555555666666666555555666666666666777777777666444555666888777777777777777888888888888888555555666666555555444444444444444444444444444444222222111111111111111222111111111111111000000///000000111111000000///...//////000000000000111111000000000//////............//////000000//////...000111111222222111111000000------444===???777...//////000000000000//////000//////......//////000///......------......///......---------,,,,,,,,,------............---------,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,,,,,,,+++,,,,,,,,,++++++,,,,,,,,,,,,,,,------------,,,,,,------------....../////////000000111222333444444777444222222444666777777999::::::<<<===>>>??????AAAAAA@@@@@@@@@@@@AAAAAADDDCCC@@@:::666666;;;@@@==================>>>>>>@@@BBBDDDDDDBBBAAA@@@AAACCCBBB@@@@@@@@@@@@>>>===???>>>===<<<<<<<<<<<<<<<888888888999999:::;;;;;;<<<;;;;;;:::888777555444666555444444333444444444555666666444111000000111222222111111111000000000111111111111000000000000---...///000111000//////------------......///000//////...------,,,++++++++++++*********)))))))))((())))))******))))))(((***)))((((((''''''((((((''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%<<<===>>>>>>?????????>>>;;;:::999888888888888888999888666666888888888777666555555444444555555666333333444444555666666666666555555555555666777777888888777555555444444444222222111111000111111111111111111111000000000000///////////////.........------------------,,,,,,++++++,,,,,,,,,,,,++++++,,,,,,++++++++++++++++++*********************************)))))))))))))))'''((((((((())))))******))))))))))))))))))))))))(((((((((''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''((((((((())))))))))))(((((((((((()))))))))((('''(((+++,,,+++***************************************))))))))))))++++++++++++,,,,,,,,,,,,---......//////000111111111111222222333222222222111222222333333444444444111222444555555555555555555555444444444444555555444444555555666777888888666555555555555666666555444555555666777777777777333444444444444444333333222222222222222222222222222222111000000000000111///000000111000000//////000000000000000//////...////////////000000000111000000000///......------...//////////////////.../////////000000111111111///,,,---555===>>>666---...//////000000//////...////////////////////////...------------------...------------,,,,,,,,,+++,,,,,,------------,,,,,,,,,,,,+++++++++++++++,,,++++++++++++++++++++++++,,,,,,,,,,,,+++++++++++++++++++++,,,,,,+++++++++++++++,,,,,,,,,,,,++++++,,,,,,,,,---.........///000000111111222333333444222222333444555555555444888999:::;;;===>>>???@@@@@@???>>>>>>======<<<<<>>????????????@@@BBBBBB@@@???@@@@@@@@@@@@?????????>>>===<<<>>>===<<<;;;;;;;;;;;;;;;777888888999::::::::::::<<<;;;:::999777444222111555444444444444444444444666777777666333111111111111111111111000000000000111111000000000/////////,,,---///111111000///...,,,,,,,,,,,,---...///000///......---,,,+++******************))))))))))))(((((())))))))))))(((((())))))((((((''''''''''''''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&'''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%###############$$$$$$$$$===>>>>>>>>>======<<<;;;888888777777777777777777999777666666777888888777555555444444444444555555444444444555555555666666444333333444444444555555666666555444333333333333444333222111000000000000111111111000000000//////000//////...............------------------------******++++++++++++*********+++++++++++++++++++++************************))))))))))))))))))******''''''(((((()))))))))***((((((((((((((((((((((((((((((''''''''''''(((((('''''''''''''''(((((((((''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''(((((((((((())))))(((((((((((())))))(((''''''(((***++++++***))))))))))))))))))))))))))))))))))))))))))))))))*********+++++++++,,,,,,,,,------......///000000111111222333333333333333//////000111111222333333111222333333444555555555444444333333333333444444333444444555666777888888444444555555444444444444111222333444555555444444111222222333333333222222000000000000000000000000222111000000/////////000...//////000000000//////000000000000000///.........////////////000000000000/////////.........---......////////////..................///000000111---...000333555555222///......////////////...............//////.........------,,,,,,,,,,,,---------,,,,,,,,,++++++++++++++++++,,,,,,,,,,,,+++++++++++++++******++++++,,,++++++++++++++++++++++++++++++++++++++++++++++++***++++++,,,,,,++++++*********++++++++++++******,,,,,,---......///000000111111222222333333444444111444888;;;;;;999777666888888999;;;<<<>>>???@@@;;;;;;;;;;;;;;;;;;;;;:::===???@@@;;;444///000333888999;;;>>>@@@AAABBBBBB>>>@@@BBBBBB@@@>>>>>>???;;;<<<===>>>===<<<<<<<<<===<<<<<<;;;;;;;;;;;;<<<999999:::::::::999888888::::::999888555333111000333333444444444444444444555666888777666444444555111111111000000000//////000000000/////////......+++---///000111000...---++++++++++++,,,...//////...------,,,++++++***************)))))))))(((((((((((())))))))))))(((((((((((((((((((((''''''&&&''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%!!!"""###$$$&&&'''((()))&&&&&&&&&%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################============<<<;;;:::999777777777777777888888888999777555666777888777666555555444444444444555555555555555555555555555555222222222333333333333333444333333222111111222222444333222111000000000000111111000000000/////////000///......------......------------............)))******++++++******))))))***++++++,,,+++++++++************************))))))))))))************'''(((((((((((((((((()))(((((((((((((((((((((((((((''''''&&&&&&''''''(((&&&''''''''''''(((((((((''''''''''''''''''''''''))))))))))))))))))))))))&&&&&&'''''''''((((((((()))((((((''''''(((((()))(((''''''(((***++++++***))))))))))))))))))))))))(((((()))))))))))))))***))))))*********++++++++++++,,,,,,---......//////000111222333333333333333...//////000111222333333222222222333444444555555444333333222222333333444222222333444555555666666222444555555333222222333000111222333333333222111000000111222222222111111000000000000000000000000222111000///.........///---....../////////////////////000000//////...---......////////////000000........................---......//////......---,,,---......////////////,,,///111000...---...111------............------,,,---............---,,,---,,,,,,++++++,,,,,,---,,,,,,,,,+++++++++************++++++++++++******+++************++++++,,,++++++++++++++++++++++++)))************+++++++++)))***+++,,,,,,+++***)))******++++++++++++******,,,------...///000111111222222222222333333444444222777<<>><<<:::999888999999;;;<<<===>>>>>>999999:::;;;<<<<<<;;;;;;:::===???===888333111111888999<<>>===999;;;>>>>>>===<<<;;;<<<<<<;;;;;;:::::::::;;;;;;::::::;;;;;;:::888777555888777777666444333111000222333333444444444444333333555777888777555555666111111000000000/////////////////////............,,,---...///000///......++++++++++++,,,,,,---...,,,,,,++++++++++++************)))))))))((((((((('''(((((())))))((((((''''''(((((((((((('''&&&&&&''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%!!!"""###$$$&&&'''((()))%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$#########""""""#########$$$$$$$$$;;;;;;<<<<<<<<<;;;;;;:::777777888999999999999999888777555555777888777666555444444333333444444555666666666555444444333333111222222333333333333333333222111111000111111111111111000000111222333333111000000000////////////000///...---------......------------.........///))))))************))))))((()))***+++,,,++++++***************************((()))))))))************((((((((((((((('''''''''(((((((((((((((((((((((((((''''''&&&&&&''''''(((&&&&&&&&&'''''''''((((((''''''''''''''''''''''''))))))))))))))))))))))))&&&&&&&&&'''''''''((((((((((((''''''''''''((((((((('''&&&(((***+++***)))))))))))))))))))))))))))(((((((((((())))))******))))))))))))*********++++++++++++,,,------.........///000111222222222222//////000111222333444444222222222333444444555666444333333222222333333444000000111111222222333333111333555555222111111222000111333444333222000///...///000111111111111000111111111111111111111111111111000///............,,,---....../////////...//////000000//////...---........./////////000000,,,------....../////////---......//////......---+++,,,...//////...---,,,+++---///...,,,+++...000---------......---------++++++,,,------,,,++++++,,,,,,++++++++++++,,,,,,++++++++++++************)))******************)))***************+++,,,,,,************************))))))))))))******++++++)))***+++,,,,,,+++***)))***++++++,,,,,,++++++***,,,,,,---...///000111111111111111111222222222222111555888:::999888999:::999999:::;;;;;;<<<======:::;;;<<<============<<<:::<<<===>>>===:::777555;;;===???AAACCCCCCBBBBBBAAADDDHHHIIIFFFBBB>>>===;;;>>>AAA@@@>>>;;;;;;;;;:::999999888888999999:::999:::;;;;;;;;;999777555444555555444444333222111111222333444555444444333111444666777666444333444111000000000/////////////////////.........---------------.........//////,,,+++++++++++++++,,,,,,************++++++++++++***)))))))))((((((((((((''''''((((((((((((''''''''''''((((((((('''&&&%%%''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&'''$$$$$$$$$$$$$$$%%%%%%%%%########################################################################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$#########""""""""""""###$$$%%%&&&&&&999999:::;;;<<<<<<<<<<<<888999:::;;;;;;;;;;;;;;;888777555555777777777666555444444333333444444555777777666555444333333222111222333333444444333333222222111111000111111111......///000111333555666000000000000////////////000///...---,,,---......---------.........//////))))))************))))))((()))***+++,,,,,,+++***))))))))))))))))))))))))(((((())))))*********+++))))))(((((('''''''''&&&(((((((((((((((((((((((('''''''''&&&&&&'''''''''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''))))))))))))))))))))))))&&&&&&&&&'''''''''((((((((((((''''''''''''((((((((('''&&&'''***+++***)))))))))))))))))))))))))))'''((((((((())))))******))))))))))))***************++++++,,,,,,---......---...///000111111111111000111111333444555666666333333333333444555666666444333333222222333333444////////////000000000000000333666555222000000111222333444444444222000///......///000000111000000222222222222222222222222111111000......---------,,,------.../////////...///////////////......---............/////////000+++,,,,,,---...///000000---..................---***,,,...000000...,,,******+++,,,---------...///,,,------......------,,,***+++,,,,,,,,,,,,+++***,,,++++++++++++++++++,,,+++++++++************)))))))))************))))))******))))))***+++,,,,,,************************(((((())))))*********+++((()))+++,,,,,,+++)))(((++++++,,,,,,,,,,,,++++++++++++,,,---...000000111000000000000111111111111///111222111000111555888:::::::::;;;;;;<<<<<<<<<<<<===>>>?????????>>>===;;;;;;<<<>>>@@@@@@>>>;;;>>>@@@AAACCCCCCBBBAAA@@@CCCGGGLLLMMMJJJDDD???===>>>AAADDDCCC???;;;:::;;;888777777777777777888888888999:::;;;;;;:::888777222333333444444333333333000111333444555444444333111333666666444222111111000000000000//////////////////.........---------...------------...//////,,,,,,++++++***+++++++++)))))))))***++++++,,,,,,))))))))))))((((((((((((''''''((((((((((((''''''&&&'''((((((((('''%%%%%%''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%%%%$$$$$$#########$$$$$$%%%%%%&&&################################################""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$######""""""!!!"""###$$$%%%&&&''''''<<<<<<======<<<:::888777:::::::::999999888888888888777777666666666666777444444444444444444444444999999888666555333222222333222111111000000111111222222111111111111222222111111000000111222333333111111000000/////////...,,,++++++******++++++,,,------------------------+++++++++************)))******++++++++++++******(((((())))))))))))(((((((((((((((((())))))))))))((((((((((((((((((((((((''''''''''''''''''''''''))))))(((((('''''''''&&&(((((((((((((((((((((((((((((((((((((((((((((((('''''''''''''''''''''''''''&&&&&&&&&'''(((***+++))))))(((((('''''''''&&&((((((((((((((((((((((((&&&''''''((()))******+++(((''''''&&&&&&((()))***))))))))))))***************++++++,,,,,,------...666...))),,,000000000111222222222111222222333333333333333333333333333333555555444333333222111111///000000111111222333333222333333222111111222444444333222111111111222222///000111222222111000///111111111111000000000000111000///...............000//////...---,,,,,,,,,.........------,,,,,,,,,,,,---///000000///---,,,,,,,,,++++++,,,---///000//////.........------------,,,,,,++++++,,,,,,---++++++******++++++,,,---+++,,,---,,,***)))***+++------,,,,,,,,,,,,++++++******+++++++++,,,,,,,,,***++++++,,,+++***)))(((******+++++++++,,,,,,,,,))))))))))))))))))))))))))))))************))))))((((((((((((((())))))******+++,,,------,,,+++***++++++******************,,,,,,,,,---------......////////////////////////111000111111222333444555::::::::::::::::::::::::<<<>>>AAABBBAAA@@@@@@AAA<<<===>>>===<<<;;;<<<===??????@@@AAABBBBBBCCCCCCGGGGGGFFFDDDAAA>>>;;;999999:::<<<>>>>>>===<<<;;;;;;;;;:::999999:::::::::<<<;;;:::888777666666555444444444555444444333333111333555777777666444333222222333333222222111000111000...---------...///111111111000///......---------------------------------------,,,,,,+++***************))))))))))))((((((((((((((((((((((((******))))))((((((''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$############$$$$$$%%%%%%%%%###""""""###%%%'''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$#######################################$$$$$$$$$$$$######################################################$$$$$$$$$$$$$$$$$$$$$$$$;;;;;;<<<<<<<<<;;;::::::::::::999999999999999999888777666666555555666666444444444444444444444444777777777666666555555444333222111111000000111111111000000000000000000111000000000000000111222222000000000/////////......,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++************)))******++++++++++++******(((((())))))))))))(((((((((((((((((())))))))))))(((((((((((((((((((((((('''''''''''''''''''''''')))(((((((((''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((('''''''''''''''''''''''''''&&&'''''')))+++---///)))((((((((('''''''''&&&''''''''''''''''''''''''&&&''''''((())))))******(((''''''&&&'''((()))***(((((()))))))))***************++++++,,,---------<<<444......///---++++++111000000000000111222222222222222333333333333333444444444333222222111111000000111111222333333333222333333222111111222444444444444444333333333333//////000111111000///...000000000000000000000000000000///.........//////000000//////...------,,,.........------,,,,,,,,,,,,---...//////...---,,,,,,,,,,,,,,,,,,...///000///.........---------------,,,,,,++++++,,,,,,---++++++******++++++,,,---+++,,,---,,,***)))***+++------,,,,,,,,,+++++++++*********+++++++++,,,,,,***++++++++++++***)))(((*********+++++++++,,,,,,))))))))))))))))))))))))))))))************))))))))))))((((((((()))************++++++++++++******************************,,,,,,,,,------------.........................../////////000111333444555999999999999999999999999:::===???@@@@@@???@@@AAA>>>>>>>>><<<:::999:::;;;>>>???AAABBBBBBAAA???>>>BBBBBBBBBAAA???===:::999777999:::<<<===<<<;;;:::999999888888999::::::;;;;;;:::999888777666666666444444444555444444333222222444666888888777555444222222222222222111000000111000///.........//////222111111000//////......------------------------,,,,,,------,,,,,,+++***************))))))))))))((((((((((((((((((((((((((((((((((((((()))))))))''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$%%%%%%$$$###"""###%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#################################$$$$$$$$$$$$######################################################$$$$$$$$$$$$$$$$$$$$$$$$:::;;;;;;<<<======<<<<<<999999999999999999::::::777777666555555555555555666666666666666666666666666666666666666666666777333222111111000000111111000000////////////000000//////000000000000111111////////////............,,,,,,++++++++++++,,,,,,+++++++++++++++++++++++++++++++++************)))******++++++++++++******((())))))******))))))((((((((((((((())))))))))))((((((((((((((((((((((((''''''''''''''''''''''''((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''))),,,...///(((((((((''''''''''''''''''''''''''''''''''''''''''''''''(((((())))))***(((''''''''''''((())))))(((((())))))))))))***************+++,,,,,,------888111,,,...000///...//////.........//////000111111111222222222333333333333333333222222111111000111111222222333444444444222333333222111111222444555555666666666555444333......//////000//////...//////////////////////////////.........///000000111000000//////......---.........---------------,,,---...//////...---,,,---------------...///000............---------------,,,,,,++++++,,,,,,---++++++******++++++,,,---+++,,,---,,,***)))***+++,,,,,,,,,,,,++++++++++++*********++++++++++++,,,******++++++******)))(((*********++++++++++++,,,))))))))))))))))))))))))))))))************))))))***))))))))))))***++++++******))))))))))))******************************,,,,,,,,,,,,------------........................---......///111333444555888888888888888888888888888;;;===>>>>>>>>>???@@@@@@@@@>>>;;;888888999;;;???@@@BBBBBBAAA>>>;;;888<<<=========<<<;;;999999666777999:::;;;;;;::::::777777777777888888999:::999888777777666666777777444444444444444333222222333555777888999888666555111222222222222111000000111111000///////////////222111111000000//////...------------------------,,,,,,,,,,,,,,,++++++***************))))))))))))((((((((((((((((((((((((&&&''''''((())))))******''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$######%%%&&&%%%###$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$<<<<<<<<<<<<<<<<<<<<<<<<888888888999999:::::::::777777666555444444444555666666666666666666666666666666666666666666666666333222111111000000111111000000////////////000000/////////000000000////////////..................,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++*********))))))******++++++++++++******)))))))))******)))))))))(((((((((((())))))))))))((((((((((((((((((((((((''''''''''''''''''''''''((((((((((((((('''''''''((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$&&&''')))***+++'''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((())))))''''''''''''((((((((()))(((((((((((()))))))))***))))))******+++,,,,,,,,,444...,,,///111000000222......---......///000111000000111111222333333333222222222111111000000000111222222333333444555555222333333222111111222444333555666777777555333222------..............................///////////////.........///000111111111111000000/////////..................---------,,,------......------,,,---------....../////////---------------------------,,,,,,++++++,,,,,,---++++++******++++++,,,---+++,,,---,,,***)))***+++,,,,,,,,,++++++++++++***************++++++++++++******************))))))************++++++++++++))))))))))))))))))))))))))))))************))))))***************++++++,,,***)))(((''''''((()))***))))))))))))************++++++,,,,,,,,,---------------------------------------...///111444555777888888888888888999999999888:::<<<=========???@@@@@@???===:::888888;;;>>>AAAAAA@@@???===:::888666;;;;;;;;;::::::999888888777888999:::;;;;;;;;;:::888777777666666666777777777666666555666666777777444444444444444333222111333444555777777666555555222222333333222222111000111111000000////////////111111111000000/////////,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,++++++***************)))))))))((((((((((((((((((((((((((('''''''''((((((((())))))''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%$$$$$$#########&&&$$$###$$$%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$>>>======<<<;;;:::::::::888888888999999:::::::::888888777555555444444444777777777777777777777777777777666666555444444444333222111111000000111111222111111000000111111222//////000000000000///.........//////////////////---,,,,,,,,,,,,,,,,,,---........................+++++++++*********))))))******++++++++++++******))))))************))))))(((((((((((())))))))))))(((((((((((((((((((((((('''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((&&&''''''((((((((((((((('''(((((((((((()))))))))(((((()))******++++++,,,777222///000///+++***,,,---------......000111111000000000111111222222222000000000000000/////////111222222333333444555555222333333222111111222444222333555666555444222000---------------...//////---........./////////000///////////////000111222000000000000////////////........................,,,------------------,,,---------...............,,,,,,---------------------,,,,,,++++++,,,,,,---++++++******++++++,,,---+++,,,---,,,***)))***+++,,,,,,+++++++++*********))))))*********+++++++++))))))))))))))))))******))))))*********+++++++++))))))))))))))))))))))))))))))************))))))***************++++++,,,***)))(((''''''((()))***(((((()))))))))*********+++++++++,,,,,,,,,---------------------------------...///000222444666777777777888888999999999:::888999;;;;;;;;;<<<>>>@@@======<<<:::888:::===@@@BBB@@@<<<999777777888888<<<<<<;;;:::999999888888999::::::;;;;;;;;;;;;;;;999888777666555444444444555555444444555555666666444444444444333222111000111222333444444444333333333333333333333222222111000000000000000//////...000000000///////////////,,,,,,,,,,,,,,,,,,,,,,,,******+++,,,,,,+++++++++************)))))))))((((((((((((((((((((((((((()))((((((((('''''''''&&&''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%$$$$$$#########&&&$$$###$$$%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$>>>===<<<;;;999999999999999999999999999999:::::::::999888666555555555555777777777777777777777777666666555555444333222222333222111111000000111111222222111111111111222222///000111222111000///...////////////000000000000------,,,,,,,,,,,,------........................+++++++++************)))******++++++++++++******)))******++++++******)))(((((((((((())))))))))))(((((((((((((((((((((((('''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''(((((())))))(((((('''&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&''''''((()))(((((((((''''''(((((((((((())))))((((((((()))******++++++111...---//////,,,,,,///,,,,,,------...///111111000000000000000000000000////////////////////////111111222222333444444444222333333222111111222444111222333333333222111000---------------...///000.........//////000000111000000/////////000111111////////////////////////.............../////////---,,,,,,,,,,,,,,,,,,---,,,,,,---......------,,,,,,,,,,,,,,,---------------,,,,,,++++++,,,,,,---++++++******++++++,,,---+++,,,---,,,***)))***+++++++++++++++************)))))))))************+++))))))((((((((()))******)))))))))************+++))))))))))))))))))))))))))))))************))))))***))))))))))))***++++++))))))(((((((((((())))))'''(((((())))))*********++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---......///111333555666666666666777888888999999888999999999888999;;;===999999999888888999<<>>???===<<<:::888777666555555444444555555777888999:::555444333333222222222333444444444333222111//////////////////000000000000///////////////......---,,,---.........---++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++((()))***+++++++++++++++************))))))))))))((((((((((((((((((((((((%%%%%%&&&&&&'''(((((((((''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$#########$$$$$$%%%%%%&&&###""""""###%%%'''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$888999999888777888:::===;;;:::999888777777777777888888888777666444333222333333222222222333444444000000000000000000000000555555555444333222111000222111111111000000//////333333222222000///...------------...///000000111000///...---,,,---......++++++,,,,,,,,,,,,------,,,,,,++++++***)))(((((())))))))))))************,,,+++)))((((((((()))*********))))))((((((''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&(((&&&%%%%%%'''(((((('''))))))((('''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&'''((('''&&&%%%&&&'''(((((('''&&&%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%&&&''''''((((((''''''((((((((((((((('''''''''((((((((()))******++++++++++++******++++++,,,---000111111000...,,,---...000000111111000///....../////////000000000000111000000000000111222333444222222222222111111111111222111111000000000000000111000///...---...////////////............//////,,,,,,,,,+++++++++******,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++******++++++++++++++++++++++++)))************+++++++++******))))))))))))******+++++++++************)))******)))((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))*********))))))(((''''''((()))))))))))))))*********))))))))))))(((&&&''''''((()))***************))))))((((((''''''((((((((()))******++++++******))))))******+++,,,,,,,,,,,,++++++*********,,,,,,------------------000000111111111222222222111111222333333333222222///000222555666666666666777888888999::::::;;;;;;<<<<<<;;;:::;;;<<<===>>>===<<<999666444333222222111111111222333444555666444222000......000333444333555777666444222222222111111000//////000111111000///...---------------...---,,,,,,++++++,,,,,,+++,,,---...---,,,+++***,,,,,,***)))))))))***+++******))))))((((((''''''''''''(((((())))))******''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$""""""""""""###############$$$$$$$$$$$$###""""""!!!"""###$$$$$$$$$$$$$$$########################$$$$$$%%%%%%%%%&&&&&&&&&###$$$%%%&&&&&&%%%$$$###$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$999999:::999888888;;;===;;;:::999888777777777777888888777666555444333333444333222222111111111111000000000000000000000000444444444333333222111000111111111111000000000///222222222222000///...---------......///000000111000///...---,,,------...+++++++++,,,,,,,,,------,,,,,,++++++***))))))((())))))))))))************++++++)))((((((((()))***))))))))))))((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%'''((((((''')))(((((('''&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$%%%%%%&&&&&&%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$&&&'''((('''&&&%%%&&&'''(((''''''&&&%%%%%%$$$$$$$$$%%%&&&&&&'''&&&&&&&&&%%%&&&&&&'''''''''''''''((((((((((((''''''''''''((((((((()))******++++++)))))))))))))))***++++++///000111///---,,,------/////////000//////..................////////////000000//////000000111111111000111111111111111111222111000000//////000000000///...---------......///......---.........///,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++*********++++++++++++++++++++++++)))************+++++++++******))))))))))))******+++++++++*********))))))***))))))((((((((((((((('''''''''''''''''''''''''''((((((((())))))))))))))))))*********))))))((('''((())))))******))))))************))))))))))))''''''(((((()))******+++))))))))))))((((((''''''((((((((()))******++++++******))))))******+++,,,,,,,,,,,,++++++*********,,,,,,,,,---------------000000000111111111222222111111222333333333222222000111333555666666555555777777888999::::::;;;;;;:::999999888999:::;;;<<<;;;999888666555555555666333333333333444555666666333222111000000111222333333555666666444222111111111111111111111111111111000///...------------......---,,,,,,++++++,,,,,,,,,,,,------,,,,,,++++++,,,+++***)))))))))***+++******))))))(((((((((((((((((((((((())))))))))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$""""""""""""############$$$$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$$$$########################$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$999:::;;;:::999999;;;<<<;;;:::999888888888888888999777666444333333333444444444222111000/////////000000000000000000000000222222222222222111000///111111111111000000000000222222222111111///...---------......///000000000///......---,,,---------++++++++++++,,,,,,,,,,,,,,,,,,++++++***)))))))))))))))))))))************+++******)))((())))))))))))))))))(((((((((((('''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&$$$%%%'''(((((('''(((((('''&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&''''''%%%%%%&&&'''''''''&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''''''''''''''''''''''''''''''''(((((())))))******+++******))))))******+++,,,...///000///---,,,,,,---------......///.........,,,,,,,,,---------......//////...---------............//////000000111111111111000//////////////////......---,,,---------......---......///000000------,,,,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++*********++++++++++++++++++++++++)))************+++++++++******))))))))))))******++++++*********)))))))))))))))((((((''''''((((((''''''''''''''''''''''''''''''((((((((()))))))))((())))))******)))))))))(((((()))***************++++++*********)))))))))(((((())))))******++++++)))))))))((((((((((((''''''(((((())))))******+++***))))))))))))***+++++++++++++++++++++*********+++,,,,,,,,,---------...//////000000000111111111000111222333333333333333222333444444555555444444666777777888999999999999777777666666666777888999777777777777777888999:::666555555555555555666666222222222222111111222222222444555555333111000111000111222333333222111000//////......------.........------,,,,,,,,,,,,,,,------,,,,,,++++++,,,,,,,,,+++******))))))*********))))))))))))((((((((())))))))))))((((((((((((''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$#########"""""""""#########$$$$$$$$$$$$$$$$$$$$$######"""""""""###$$$$$$$$$$$$###########################"""#########$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$999:::;;;;;;999999:::<<<::::::999888888888888888888777444222222222333444444333222111111111111111000000000000000000000000111111111111111000//////111111111000000000000000222222222111111000..................//////000000......---------,,,,,,,,,***++++++++++++,,,,,,,,,+++++++++*********))))))((()))))))))************+++******)))))))))))))))((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''%%%$$$%%%&&&'''''''''''''''&&&&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$#########$$$%%%%%%%%%%%%$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&%%%$$$&&&'''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%&&&'''''''''&&&&&&&&&&&&'''''''''''''''(((''''''(((((()))*********,,,,,,,,,,,,,,,------...---...///...,,,+++,,,---+++,,,,,,---............+++++++++,,,,,,,,,------///...---,,,++++++++++++,,,,,,---...///000111222000000///............///......------,,,,,,,,,,,,,,,------...000222333444------------,,,,,,,,,,,,------------------------++++++++++++++++++++++++++++++++++++************************++++++++++++))))))*********+++++++++******))))))))))))******************)))))))))))))))(((((('''''''''(((((('''''''''''''''''''''''''''''''''((((((((())))))'''((())))))))))))))))))((())))))***************++++++*********)))))))))))))))))))))******++++++((((((((((((((((((((((((''''''(((((()))*********)))))))))))))))***+++++++++++++++***************+++++++++,,,,,,------........./////////000000000000111222222333333333333444444444444444444444333444555666777777777777666555555555555666666666777666666777888999:::;;;;;;777666666555444444444555111222333333333222111000111333555444222000000000///111222444444222111/////////............//////......---,,,,,,,,,,,,,,,...---,,,+++***+++,,,---+++++++++***************))))))))))))))))))))))))*********)))((('''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$"""""""""""""""######$$$########################""""""#########$$$$$$$$$$$$$$$%%%%%%$$$$$$###""""""######$$$$$$$$$##############################""""""""""""############%%%$$$###""""""###$$$%%%&&&%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%###$$$$$$$$$$$$$$$%%%%%%999:::;;;;;;999999999:::999999888777777777888888777666333222111222333444222222222222222333444555000000000000000000000000000000111111111000//////000000000000000000111111111111111111111000///...............////////////---------------,,,,,,,,,*********+++++++++,,,,,,+++++++++***************((()))))))))************************)))))))))((('''''''''''''''(((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''%%%$$$$$$&&&''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###"""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%%%%$$$$$$%%%'''%%%%%%%%%%%%%%%$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&'''&&&&&&&&&%%%&&&&&&&&&''''''(((((('''''''''((())))))******,,,,,,++++++,,,,,,---...,,,---...---,,,+++,,,---++++++,,,---......------+++++++++,,,,,,,,,------///...---+++************+++,,,,,,...///000111222000///......---.........---------------,,,,,,,,,+++,,,---///222555777999.........---------,,,,,,------------------------+++++++++++++++++++++++++++++++++*********)))))))))))))))******+++++++++))))))*********+++++++++******))))))))))))***************)))))))))((((((((((((''''''''''''((((((''''''''''''''''''''''''''''''''''''((((((((((((''''''((()))))))))))))))(((((()))************************)))))))))(((((()))))))))))))))*********'''''''''''''''((((((((('''''''''((())))))******))))))(((((())))))***+++******************************++++++,,,------...------.........////////////000111222333333444333555555444444333333333333222333555666666666555444444555555666666666666666666777777888999:::::::::777666555444333333333333222333444444444222111///111333555444222000000000///000222333333222000/////////.........//////000///...------,,,,,,------...---,,,+++***+++,,,---++++++++++++******))))))))))))))))))************++++++***)))((('''&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$"""!!!!!!!!!""""""###$$$####################################$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$############$$$$$$$$$######"""########################!!!!!!"""""""""#########$$$###"""!!!!!!"""###$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$%%%#########$$$$$$%%%%%%%%%888:::;;;;;;999888888999888777777666666666777777555444333222111222333333111111111222333444666666000000000000000000000000000000111111111111000000000000000000111111111111111111111111111000//////......//////////////////,,,------------,,,++++++************++++++++++++************************))))))))))))************)))************)))((((((&&&''''''''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%###$$$&&&''''''&&&%%%%%%$$$$$$$$$%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$%%%%%%$$$$$$###"""######$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$!!!###$$$$$$$$$$$$%%%'''%%%%%%%%%%%%$$$$$$$$$$$$######$$$%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''((((((&&&''''''(((((())))))***))))))(((((())))))***++++++,,,------+++++++++---,,,,,,------...---------,,,,,,,,,---------......///...---,,,++++++***+++,,,,,,---...///000111222//////...------------------............---,,,,,,,,,,,,...000222555777888//////.........---------------------------------+++++++++++++++++++++++++++************)))))))))(((((())))))***+++++++++)))************+++++++++******))))))))))))************)))))))))(((((((((''''''&&&&&&''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((&&&&&&'''((())))))))))))''''''((()))))))))))))))))))))((((((((('''''''''((((((((((((((()))))))))&&&''''''''''''(((((((((&&&''''''(((((())))))***)))(((((((((((()))******)))))))))***************))))))***+++,,,---......,,,,,,---------.........///000111222333444444444555555444333333333444444333444666777777666444333444444555666666666666555555666777888999999999999666666555444333333333444333333444444444222111000222444555555333111000111///000111222222111000/////////......//////000000///......---------------------,,,,,,++++++,,,,,,***++++++++++++***)))))))))))))))************++++++******)))(((''''''&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%$$$$$$!!!!!!!!!!!!"""###$$$%%%#########$$$$$$$$$$$$$$$#########$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$###""""""########################!!!"""""""""##################""""""""""""######$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&777999::::::888777666777666666555555555555666666333333333333222222222222222111111111222333444444000000000000000000000000000111111222222111111000///000000000111111111111000111111111111000///////////////////////////...,,,,,,---------,,,+++***************++++++++++++************************))))))))))))************)))******+++***)))((('''&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$###$$$%%%'''&&&&&&$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&###$$$$$$%%%%%%$$$$$$###""""""###$$$$$$$$$$$$$$$"""#########$$$$$$$$$$$$!!!"""$$$$$$######%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&%%%$$$$$$%%%&&&&&&'''((((((&&&&&&''''''((()))))))))((((((''''''(((((()))******,,,---,,,+++***+++------............------,,,............///////////////......---,,,,,,,,,,,,------...///000000111111///...------,,,,,,------....../////////...---,,,.........///000111333444////////////.........---........................************************************))))))))))))((((((((()))***+++++++++)))************+++++++++******))))))))))))*********)))))))))(((((((((((('''&&&&&&&&&&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((%%%&&&'''((())))))))))))&&&&&&'''(((((((((((((((''''''''''''&&&&&&&&&&&&((('''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&''''''((()))))))))((((((((((((((()))******((()))))))))*********+++))))))***+++,,,---......,,,,,,,,,,,,------------///000111222333444444444555444333333333444555555555666888::::::888666555222333444555555555444444333444666888999999999999666666555555555555555555444444444444333222111000333555666666444222111111///////////////////////////////////////000111111//////...---------------,,,,,,------,,,,,,++++++***++++++,,,+++***)))((())))))*********+++++++++******))))))(((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&'''&&&&&&%%%%%%%%%%%%$$$$$$""""""""""""###$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&#########$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$$$$###""""""########################"""""""""#########$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$########################$$$$$$##################"""######$$$%%%%%%&&&&&&666888::::::888666555666555555444444444555555666222222333333333222111111222222111111111111111222000000000000000000000000000111111222222222111111//////000000111111111222000111111111111000000//////////////////.........,,,,,,---...---,,,+++***)))************+++++++++******************++++++))))))))))))************)))******++++++)))((('''&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$###$$$%%%&&&&&&&&&$$$#########$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%$$$$$$$$$""""""###$$$$$$$$$$$$###""""""######$$$$$$$$$$$$ """###$$$######%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''((((((&&&&&&''''''((())))))))))))))))))))))))******+++***+++,,,,,,+++***+++---////////////...---,,,,,,/////////000000000000111//////...---------............//////000111111111......---,,,,,,,,,,,,---...///000000000///------000//////............///000/////////....................................************************************))))))))))))'''(((((()))***+++++++++)))************+++++++++******))))))))))))******))))))))))))((((((((((((&&&&&&&&&&&&&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((%%%&&&'''((())))))))))))%%%&&&&&&'''''''''''''''''''''&&&&&&&&&%%%%%%%%%'''''''''''''''&&&&&&&&&&&&&&&&&&'''''''''((((((&&&&&&''''''((()))))))))((((((((((((((()))******(((((())))))*********+++((()))***+++,,,---......++++++,,,,,,,,,---------//////111222333444444444444444333222333444555666777999;;;<<<<<<:::888666111222333444555444333333000222444777999:::::::::777777666666666666777777555555444333222222111111333555777666444222222222//////............/////////////////////000111111//////...------------...+++,,,---...---,,,+++*********+++,,,+++***)))((())))))******++++++++++++))))))))))))((((((((((((''''''''''''''''''''''''(((((((((((((((((((((((('''&&&%%%%%%%%%%%%&&&'''&&&&&&&&&%%%%%%%%%$$$$$$""""""""""""###$$$%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$$$$###"""!!!####################################$$$$$$$$$$$$%%%%%%'''(((((('''%%%%%%""""""######$$$$$$$$$%%%########################$$$$$$##################""""""###$$$%%%%%%&&&&&&<<<:::888666666666888999999999999999888888888777888777444222000000111222555444333222111111111111111111111111000000000000111111222333333333222222000111111111111222222222333333222111000///....../////////......---------,,,,,,,,,,,,+++***)))))))))************+++++++++************************+++******))))))))))))))))))))))))))))))(((''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################"""###$$$%%%%%%$$$###"""$$$#########""""""!!!!!!########################$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%###"""""""""###$$$######$$$$$$$$$%%%%%%%%%&&&%%%$$$$$$$$$&&&(((***(((((((((((((((((((((((())))))))))))******************))))))******+++,,,......//////...---,,,,,,............////////////111///---++++++,,,///000///...---,,,,,,---...///,,,,,,,,,,,,,,,,,,,,,,,,,,,---///000000000///...000///...------...///000////////////............***+++,,,,,,------,,,,,,,,,++++++******++++++,,,---,,,***(((((((((((()))************************************************,,,,,,++++++***)))((((((((((((((((((((((((((((((''''''''''''((((((((((((''''''''''''''''''''''''%%%&&&''''''&&&&&&''')))''''''''''''''''''''''''$$$%%%&&&''''''&&&%%%$$$%%%&&&''''''&&&&&&''')))+++)))'''&&&%%%&&&'''(((''''''''''''''''''''''''%%%&&&(((******)))'''&&&&&&''''''((()))******+++)))************+++++++++******+++++++++,,,,,,,,,..................------......//////000000111111222333444444555555444444777888:::;;;<<<;;;;;;:::::::::999888777666555444333444555666888:::;;;;;;888555444555888::::::888888666444111000000111222333444555666555444333222333222222111000///......000000000000000000000000000000000000////////////....../////////...,,,+++************************+++++++++************)))******)))((((((((((((((((((((((((((((((((((((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$%%%%%%$$$###"""!!!$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$######$$$$$$%%%&&&AAA???<<<:::888777777888888888888888777777777777777666444222111111222222555444333222111111111111111111111111000000000000000111111222222222222222000000111111111222222222111111000///...---,,,,,,/////////.........------,,,,,,---,,,,,,+++***))))))************+++++++++************************+++***))))))(((((()))))))))))))))))))))(((''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################"""###$$$$$$$$$$$$###"""############"""""""""!!!########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###"""""""""###############$$$$$$$$$%%%%%%&&&%%%$$$$$$$$$&&&((()))''''''''''''''''''''''''(((((((((((())))))))))))******))))))******+++,,,...............---,,,,,,------........./////////000///---++++++,,,...000///...------------...///------------------------,,,---...///000//////...000///............///000////////////.........---***+++,,,,,,------,,,,,,,,,++++++******++++++,,,---,,,***(((((((((((()))************************************************,,,,,,+++******)))((((((((((((((((((((((((((((((''''''''''''((((((((((((''''''''''''''''''''''''%%%&&&''''''&&&&&&''')))''''''''''''''''''''''''%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&&&&''')))***)))'''&&&%%%&&&'''(((''''''''''''''''''''''''###%%%''')))******)))(((''''''(((((())))))******))))))*********+++++++++*********+++++++++,,,,,,.........---------------.........///000000111111222222333333444444444333777888999:::;;;:::999888999888888777666666555555555555666666777777777888777555444555888:::999888777555333111000000111111333444444444444333222222222222111111000//////...000000000000000000000000000000000/////////......---...//////...---,,,+++************************+++++++++*********))))))***))))))(((((((((((((((''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%$$$###"""!!!###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$######$$$$$$%%%&&&@@@>>><<<999888777777888777777666666666555555555555444333222111222333333444444333222111111111111111111111111000000000000//////000111111111111111000000000111111111222222//////...---,,,++++++***//////............------------------,,,+++***))))))************+++++++++************************+++***))))))(((((())))))(((((()))))))))(((''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################"""###$$$$$$$$$$$$###"""############""""""""""""########################$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""!!!"""""""""#########$$$$$$$$$$$$%%%&&&%%%$$$$$$%%%&&&((()))''''''''''''''''''''''''&&&'''''''''((((((((((((***))))))))))))***++++++------......------,,,,,,------------............///...,,,++++++,,,...//////...------------...///........................------...////////////...000000////////////000000//////.........---------***++++++,,,,,,,,,,,,,,,++++++************++++++,,,+++***((((((((())))))************************************************+++++++++******))))))(((((((((((((((((((((((((((&&&''''''''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&''''''&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%&&&''''''&&&&&&'''))))))((('''&&&&&&&&&'''(((''''''''''''''''''''''''"""$$$&&&((()))******)))(((((((((((((((((((((((()))))))))*********++++++*********++++++++++++,,,---------------------------......//////000111111000111111111222222222222777888888999999888777666666666666666666666666666888888777666666555444444777555444555777888888888666555333111000000111111333333222111111111111222111111111000000/////////000000000000000000000000000////////////.........------.........---,,,,,,************************++++++*********)))))))))***)))((((((''''''((((((''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$$$$$$$###"""""""""###$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$######$$$$$$%%%&&&777666555555555666777777555555555444444444444333444333222222222333444444444333222222111111111222111111111111000000000///---...///000111111111000000000000000111111111111......------,,,++++++***------------------,,,,,,------------,,,+++***)))))))))*********+++++++++******************************)))((((((((((((((('''(((((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#######################################$$$$$$$$$#########$$$$$$##################"""""""""""""""########################$$$$$$$$$$$$$$$$$$$$$$$$######"""""""""!!!!!!"""############$$$$$$$$$$$$%%%%%%$$$%%%%%%&&&((()))''''''''''''''''''''''''%%%%%%&&&&&&&&&''''''''')))))))))))))))***++++++,,,,,,---------,,,,,,+++,,,,,,,,,,,,---------------,,,+++++++++,,,...///.........------.........////////////////////////------........./////////000000000000000000000000.........---------,,,,,,******+++,,,,,,,,,,,,+++++++++************++++++,,,+++)))((((((((()))***************************************************+++*********)))))))))(((((((((((((((((((((((((((&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&''''''&&&%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&'''%%%&&&''''''&&&&&&''')))(((((('''&&&&&&&&&'''(((''''''''''''''''''''''''$$$%%%&&&'''((()))((((((((((((((((((((((((''''''))))))))))))************************++++++++++++,,,,,,,,,,,,,,,---------------......///000000111////////////000000111111666777777888777666444333333333444444555666666666999888888777666555444444666555555555666777777777666555444333222222222222333222000/////////000111000000000000000//////////////////////////////////////////.........------,,,,,,---------,,,,,,,,,************************************))))))))))))))))))(((''''''''''''((('''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#################################$$$############!!!"""###$$$%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$######$$$$$$%%%&&&222222222333333444444555444444444333333333222222333333222222333333444444333333222222111111222222111111111111000000000///------...///000111111111//////000000000111111111///......------,,,,,,,,,++++++++++++++++++++++++------------,,,+++******))))))*********+++++++++***************************))))))((('''(((((((((''''''((((((((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################""""""#########$$$$$$$$$$$$##################$$$""""""""""""""""""##############################$$$$$$$$$$$$$$$$$$$$$$$$###############""""""!!!""""""#########$$$$$$$$$$$$%%%%%%%%%&&&''''''(((''''''''''''''''''''''''%%%%%%%%%%%%&&&&&&&&&&&&))))))(((((())))))***+++++++++,,,,,,,,,,,,,,,+++++++++++++++,,,,,,,,,,,,,,,++++++***+++,,,---...---..................---////////////////////////---------------....../////////000000000000//////------------,,,,,,,,,,,,)))***++++++,,,,,,+++++++++******))))))******++++++***)))((((((((()))***************************))))))))))))))))))))))))*********)))))))))))))))((((((((((((((((((((((((&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&%%%%%%&&&(((&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&'''%%%&&&''''''&&&&&&''')))''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&((((((((((((''''''''''''(((((()))))))))*********))))))*********+++++++++++++++++++++,,,,,,---------------...//////000000//////.........///000111555666666777666555333222000111222333444555555666777777777777777777666666555555555555444555666777666666555444444444333333222111000///...///000111///////////////000000000////////////////////////............------------,,,,,,+++++++++,,,,,,,,,*********************************)))))))))(((((()))((((((''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##########################################$$$$$$!!!"""###$$$%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$######$$$$$$%%%&&&444444444333333222222222444444333333333222222222333333333333333333333333333333222222111222222333111111111111000000000000,,,---...000111111111111/////////000000000111111//////.........---------******++++++++++++,,,,,,.........------,,,+++***)))************+++++++++***************************)))((((((''''''((((((&&&&&&'''(((((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################"""""""""###$$$$$$%%%%%%$$$$$$###""""""###$$$$$$""""""""""""####################################$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$###"""""""""""""""############$$$$$$$$$%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%&&&&&&&&&&&&)))(((((((((((()))************+++,,,,,,,,,++++++************++++++++++++************+++,,,------------...//////...------////////////////////////------,,,,,,------...///......////////////......------,,,,,,,,,+++++++++)))******+++++++++++++++******))))))))))))******+++***)))(((((()))***+++************************))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((%%%&&&&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&&&&%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%&&&''''''&&&&&&''')))%%%&&&&&&&&&''''''''''''''''''''''''''''''''''''(((((('''&&&&&&%%%%%%%%%''''''''''''''''''''''''((((((((()))))))))******)))))))))************+++)))******++++++,,,,,,---,,,------......///000000///...---------...000111444555555666666555444333///000000111222444444555555666666666666666777777444555666555333333555777555555555555444444444333111111000////////////000.........//////000000000000000000000000000000000......---------,,,,,,,,,++++++*********+++,,,,,,******************************)))))))))((((((((()))(((''''''&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#################################"""######$$$%%%"""###$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$######$$$$$$%%%&&&333333333333333333222222444444333333333222222222333333333444333333222222333222222111222222333333111111111111000000000000------///000111222222222////////////000000000111............------------++++++,,,,,,------------............---,,,+++***)))************+++++++++************************))))))(((''''''''''''(((%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%&&&''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%################################################!!!""""""###$$$$$$%%%%%%$$$$$$###""""""###$$$$$$!!!"""""""""####################################$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%$$$###"""""""""""""""############$$$$$$%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''((((((((((((((()))******))))))***+++++++++++++++)))))))))*********++++++)))))))))***+++,,,,,,---------...//////...------........................------,,,,,,,,,---...///,,,---...//////...---,,,,,,,,,,,,,,,++++++++++++))))))***+++++++++++++++******))))))))))))******+++***)))(((((()))***+++************************))))))))))))))))))))))))((()))))))))))))))))))))((((((((((((((((((((((((%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&&&&%%%$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&&&&''')))$$$%%%&&&&&&''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%&&&&&&&&&%%%&&&&&&''''''((((((((((((((((((((()))))))))***))))))))))))************)))))))))***+++,,,,,,,,,,,,,,,---......//////000000///---------...000111333444555666666666555444//////000000111222333333444444444444444444444444333555666555222222444666333333333333333333222222000111111111111000//////------......///000111111000000000000000000000000---------,,,,,,,,,,,,++++++***))))))***+++,,,---***************************)))))))))(((((((((((((((((('''&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################"""""""""###%%%%%%###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$######$$$$$$%%%&&&---...000111333333444444444444444333333333222222333444444444444333222111222222222111222222333333111111111111000000000000---...///111222222333333////////////000000000000...------------------,,,---------....../////////............---,,,++++++)))************+++++++++************************))))))((('''''''''''''''%%%%%%&&&'''((((((((('''''''''''''''''''''''''''######$$$%%%%%%&&&''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%########################""""""""""""""""""""""""!!!""""""###$$$$$$%%%%%%%%%$$$###""""""###$$$%%%!!!!!!""""""#########$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&'''&&&%%%$$$###""""""""""""###############$$$%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''((((((((((((((()))******((()))***+++++++++++++++))))))))))))************((())))))***++++++,,,,,,,,,---...//////...---,,,........................------,,,+++,,,---...///+++,,,---......---,,,+++,,,,,,,,,+++++++++******))))))***++++++++++++*********))))))))))))************)))(((((()))***+++************************))))))))))))))))))))))))(((((((((((())))))))))))((((((((((((((((((((((((%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&&&&%%%$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%''''''''''''%%%$$$%%%&&&((('''&&&&&&''')))$$$%%%&&&&&&'''''''''&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%&&&'''(((%%%%%%&&&&&&'''((())))))(((((((((((())))))))))))))))))))))))************((())))))***++++++,,,,,,,,,,,,------...//////000000///---------...000222222333555666666666666555/////////000111222222222444333333222222111111111333555666555222111333666111111222222222111000000000111222222222111///...,,,------...///000111111000000000000000000000000---------,,,,,,,,,++++++******)))))))))***,,,---************************))))))))))))(((((((((((((((((('''&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################"""""""""###%%%&&&$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%&&&&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$######$$$$$$%%%&&&000111111222222333444444111222333333444444333333333333333222222111111111555444333111000/////////111111000000000000111111///////////////000111111111000000///////////////------............------...,,,******+++,,,------------,,,++++++,,,,,,,,,++++++++++++++++++++++++***************************(((&&&%%%%%%%%%'''((())))))))))))((((((((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&%%%%%%$$$'''&&&%%%$$$$$$$$$$$$%%%&&&&&&%%%$$$#########$$$""""""""""""""""""""""""$$$$$$$$$#########""""""######""""""""""""###############"""""""""""""""!!!""""""""""""#########%%%$$$###$$$&&&&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((((((((((()))))))))))))))***+++,,,,,,,,,,,,,,,,,,+++***)))))))))***+++++++++,,,,,,,,,,,,------,,,---///000000///---,,,,,,,,,,,,---------......//////.........---------+++++++++***************+++++++++*********))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))%%%&&&(((*********))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((('''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%$$$%%%''')))***(((((((((&&&$$$$$$&&&(((''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''((()))))))))************))))))***++++++++++++***(((((()))***+++---///000............////////////333444444555555444444333111111111111111111111111333333222222111000//////444333333222111111111222///////////////000000111222222222222222222222222222///,,,,,,///222222111000000000000///...---,,,///...,,,+++***++++++,,,+++)))(((((()))******)))+++++++++***)))(((((('''))))))((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%$$$###"""$$$$$$$$$#########"""""""""############$$$$$$$$$###%%%%%%$$$"""!!!"""###$$$$$$$$$############"""%%%%%%%%%%%%%%%%%%%%%%%%"""############$$$$$$$$$###"""!!!!!!!!!"""$$$%%%###########################$$$$$$%%%%%%$$$$$$######$$$%%%&&&&&&%%%$$$###!!!!!!"""###$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%000000111111222333333444222222333444444444444333333333333222222111111111555444222111000/////////111000000//////000000111///////////////000111111111111000///////////////------............---------+++*********+++,,,,,,...---,,,+++++++++++++++++++++++++++++++++++++++***************************((('''%%%%%%&&&'''((())))))))))))((((((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%$$$$$$$$$###%%%%%%$$$#######################################$$$$$$$$$#########""""""######""""""""""""######"""""""""""""""#########"""""""""#########$$$$$$$$$######$$$%%%%%%$$$"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''((((((((()))))))))))))))***++++++,,,,,,++++++,,,+++***))))))***+++,,,++++++,,,,,,,,,,,,------,,,---...//////...---,,,,,,,,,,,,------------.........------,,,,,,,,,,,,************************+++*********************))))))))))))))))))))))))))))))(((((((((((()))))))))))))))))))))))))))))))))))))))))))))(((((('''))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%$$$%%%''')))***'''(((((('''%%%%%%&&&(((''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''(((((()))))))))*********))))))***++++++++++++***(((((()))***+++---...///......////////////000000222222222333333222222222000000000000000000000000444333333222222111000000444333222222111111111222000000/////////000111111222222222222222222222222222///,,,,,,///111111000///000000000000///......///...---,,,++++++,,,,,,,,,***((()))***++++++***++++++******)))((((((''')))(((((('''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$######$$$$$$$$$#########"""""""""############$$$$$$$$$###$$$%%%$$$"""!!!"""###$$$$$$$$$############"""$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$###""""""!!!"""###$$$%%%###########################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$$$$######"""""""""###$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%000000000111222222333333222333333444444444444444222222222222222111111111444333222111000/////////000//////......//////000///////////////000111111222111000000//////000000------............------++++++************++++++///...---++++++*********++++++++++++++++++++++++************************)))((('''&&&&&&&&&'''((()))))))))(((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%$$$%%%%%%&&&%%%$$$###"""$$$$$$###"""""""""##############################$$$$$$$$$#####################""""""""""""######!!!!!!""""""######$$$$$$############$$$$$$$$$%%%###""""""###$$$$$$###!!!########################"""""""""""""""""""""""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''((((((((())))))))))))******++++++++++++***,,,++++++******+++,,,,,,++++++,,,,,,,,,,,,------,,,,,,............,,,,,,,,,,,,,,,,,,---------------,,,,,,,,,,,,+++++++++((()))))))))***+++++++++)))*********************))))))))))))))))))))))))))))))(((((((((((()))))))))))))))))))))))))))))),,,+++***)))'''&&&&&&&&&))))))))))))))))))))))))''''''''''''''''''''''''(((((((((''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%'''(((***&&&((())))))'''&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''(((((((((((())))))))))))((()))******++++++******(((((())))))+++,,,...///.../////////000000000111000000111111111111000000////////////////////////444444444444333222111111333333222111111111111222111000000000000111222222222222222222222222222222000...,,,,,,...000000000//////000111111111111000000///...---,,,,,,,,,,,,---+++******+++,,,+++***++++++******)))(((((((((((((((((('''&&&&&&%%%%%%''''''''''''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$###############"""############$$$$$$$$$###$$$%%%$$$"""""""""$$$$$$$$$$$$############"""########################"""############$$$$$$$$$###""""""""""""###$$$$$$###########################$$$$$$%%%%%%$$$$$$############""""""#######################################$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%//////000000111222222222222222333444444444444444222222222111111111111111333222111000//////////////////............/////////////////////000000111111111000////////////000,,,------......------,,,++++++,,,++++++***+++,,,///...---+++***)))))))))************************************************))))))((('''&&&''''''((())))))((((((((('''''''''''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&'''&&&&&&%%%%%%$$$%%%'''((('''&&&$$$"""######"""""""""""""""#########################################################""""""""""""###### !!!"""###$$$$$$%%%######$$$$$$$$$%%%%%%%%%###"""!!!"""$$$$$$"""!!!"""""""""""""""""""""""""""""""""""""""""""""""""""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''((((((((())))))))))))***************)))+++++++++++++++,,,,,,,,,+++++++++,,,,,,,,,------+++,,,------------,,,+++++++++,,,,,,,,,------------,,,,,,,,,,,,,,,,,,,,,(((((())))))***+++,,,,,,))))))))))))************))))))))))))))))))))))))))))))(((((((((((())))))((((((((((((((((((((((((---+++)))(((&&&&&&''''''))))))))))))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%############$$$%%%&&&'''###########################$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''((()))&&&(((******(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''''''''''''''((((((((())))))((())))))***************(((((())))))***,,,---.........//////000111111111///000000000000000000///000000000000000000000000444444555555555444222222222222111111111111111222111111111111111222222333111111111111222222222222///...------.../////////...///000222333333333333111111000///...---------...,,,++++++,,,---,,,+++************))))))(((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%###""""""###%%%%%%########################""""""#########$$$$$$$$$"""$$$%%%$$$###"""###$$$$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$"""""""""#########$$$$$$###########################$$$$$$%%%%%%$$$$$$###$$$###"""!!!!!!"""###$$$$$$$$$$$$#########""""""######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%...//////000000111111222111222333333444444333333111111111111111111111111222222111000//////////////////............/////////////////////000000111111000//////......//////,,,,,,------------,,,,,,+++---......,,,+++,,,...///...,,,+++***))))))(((************************************************))))))((((((''''''''''''((((((((((((''''''''''''''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&'''&&&&&&%%%%%%&&&((())))))'''%%%$$$###"""""""""""""""############################################################""""""""""""###### !!!"""###$$$$$$%%%######$$$$$$$$$%%%%%%%%%###"""!!!"""$$$$$$"""!!!""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!######$$$%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''(((((((((((()))))))))******))))))(((******++++++,,,,,,,,,,,,+++++++++,,,,,,,,,------++++++,,,,,,,,,,,,+++++++++++++++,,,,,,,,,------------------............((())))))***+++,,,,,,---))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))((((((((((((((((((((((((***)))(((''''''((()))***((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""""""""###$$$%%%&&&'''#################################$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''''''(((%%%'''))))))'''%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&''''''''''''''''''''''''&&&''''''''''''((((((((((((((()))************)))((((((((()))***+++,,,------......///000111111111000000111111111111000000111111111111111111111111333444555666666444333222111111111000000111222222111111111111111222222333000000000111111222222222////////////....../////////000111333444555666666333222222111000///...---///---++++++,,,---,,,+++*********)))))))))))))))'''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&########################""""""#########$$$$$$$$$"""###$$$$$$###"""###$$$$$$$$$$$$#########""""""%%%%%%%%%%%%%%%%%%%%%%%%""""""#########$$$$$$$$$"""#########$$$$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$###$$$###"""!!!!!!"""###$$$%%%%%%$$$$$$###"""""""""######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%.........///000000111111000111111222222222222222000000000111111111111111222111000///////////////000//////......//////000///////////////000111111000///......------......,,,,,,------------,,,,,,+++...000000---+++---///...---,,,******)))))))))************************************************)))))))))(((((((((''''''((((((((('''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&''''''&&&&&&&&&''''''((((((&&&%%%$$$######"""""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$######""""""""""""######!!!!!!""""""######$$$$$$############$$$$$$$$$%%%###""""""###$$$$$$###!!!""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!###$$$$$$%%%%%%$$$$$$$$$######$$$$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&'''''''''(((((((((((())))))))))))(((((('''((()))***+++++++++++++++++++++,,,,,,,,,,,,------++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,------...............///******++++++,,,---------******)))))))))((((((((())))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))''''''''''''((()))***+++((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%###############$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&''''''%%%&&&''''''%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&'''''''''((('''((())))))******))))))((((((((())))))+++,,,,,,,,,,,,---...///000111111111111222222222222111111111111111111111111111111222333555666666555333222111000000000000111222222111000000000000111222222//////000000111222222222///000111111///...///000000111222444555666777777444444444333222000...---///---++++++,,,,,,+++*********))))))))))))))))))''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%###############$$$$$$$$$"""############$$$$$$$$$"""###$$$$$$###"""$$$%%%$$$$$$$$$############"""%%%%%%%%%%%%%%%%%%%%%%%%"""############$$$$$$$$$"""###$$$$$$%%%%%%$$$$$$###########################$$$$$$%%%%%%$$$$$$############""""""#########%%%$$$$$$$$$######""""""######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%------...//////000000111//////000111111111111000///000000000111111111222111111000////////////000111000000//////000000111///////////////000111111......---,,,,,,,,,,,,---+++,,,,,,------,,,,,,+++)))---000000,,,***,,,...,,,,,,+++******)))******************************************************)))))))))))))))(((''''''(((((('''''''''&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%########################$$$%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$###############$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$######""""""""""""######"""""""""""""""#########"""""""""#########$$$$$$$$$######$$$%%%%%%$$$"""########################""""""""""""""""""""""""$$$$$$$$$%%%%%%$$$$$$###"""######$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''(((((((((((())))))(((((('''&&&&&&''')))***++++++******++++++,,,,,,,,,,,,------++++++************++++++***++++++++++++,,,,,,,,,,,,,,,,,,------.........------------------------++++++***)))(((''''''&&&))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))&&&'''((()))************((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&%%%%%%######$$$$$$$$$%%%%%%%%%$$$###############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&&&&&&&&&&$$$%%%%%%$$$###"""###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###$$$$$$%%%&&&''''''''''''''''''''''''%%%%%%&&&&&&&&&''''''''''''(((((())))))))))))))))))(((((())))))***+++,,,++++++,,,---...///000000000111111222222111111000111111111111111111111111111222444666666444222111000000000000000111222222000000/////////000111111/////////000111222222222000222333222000...///111111222444555666777888888555555555444333111///...///---+++***++++++***))))))))))))))))))))))))***''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$########################$$$%%%%%%%%%%%%%%%%%%$$$""""""#########$$$$$$$$$"""############$$$$$$$$$!!!###$$$$$$######$$$%%%$$$$$$$$$############"""$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$"""###$$$%%%%%%%%%$$$$$$###########################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$$$$######$$$$$$$$$#####################$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%------......///000000000......///000000000000000//////000000111111111222111000000////////////000111111000000000000111111///////////////000111111------,,,++++++++++++,,,+++,,,,,,------,,,,,,+++(((,,,000///+++)))+++...++++++***************+++))))))))))))))))))))))))************************)))))))))))))))(((''''''(((((('''''''''&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%########################$$$%%%%%%&&&'''''''''&&&%%%$$$###"""""""""######$$$$$$######$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$$$$$$$######""""""""""""###############"""""""""""""""!!!""""""""""""#########%%%$$$###$$$&&&&&&$$$###################################################$$$$$$%%%%%%%%%$$$$$$###""""""###$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''(((((((((((())))))((('''&&&&&&%%%&&&((()))*********)))++++++,,,,,,,,,---------++++++************++++++******+++++++++,,,,,,,,,+++++++++,,,,,,---------..................------,,,+++***)))((('''&&&%%%))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))&&&''')))*********)))(((((((((((((((((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$##################%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&&&&&&&&&&%%%%%%$$$###!!!!!!###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&'''''''''(((((()))))))))))))))))))))(((((()))***++++++******+++,,,---...///000000000111111111111000000000000000000000000000000000222444666666444222111000000///000000111222222///////////////000000111...//////000111222222222000333555444111///000111222333444666777777888888555666666555444111///...///---+++***++++++***))))))))))))))))))*********&&&'''''''''''''''''''''''''''''''''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$########################$$$$$$&&&''''''&&&$$$$$$""""""######$$$$$$$$$$$$"""############$$$$$$$$$!!!###$$$$$$######$$$&&&$$$$$$$$$############"""########################"""############$$$$$$$$$"""###$$$%%%&&&%%%$$$$$$########################$$$$$$$$$%%%%%%$$$$$$$$$###$$$%%%&&&&&&%%%$$$#################################$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%..................---------------......///000111000000000000////////////111///------/////////...//////000000111111111222....../////////////////////...---,,,+++,,,---------------............///......---,,,,,,,,,,,,---------,,,++++++***))))))++++++++++++++++++++++++++++++************************)))((((((((((((((((((''''''''''''&&&&&&&&&'''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$"""###$$$$$$###"""###$$$""""""""""""""""""""""""""""""!!!!!!"""###$$$$$$$$$$$$############$$$$$$$$$$$$##################$$$%%%%%%%%%%%%$$$#####################"""!!!!!!""""""""""""""""""""""""!!!!!!!!!!!!!!!"""######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''###$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&'''''''''''''''))))))))))))))))))))))))++++++******************++++++++++++++++++++++++------------------------------------------------,,,,,,,,,,,,------...///************************(((((())))))*********+++))))))))))))))))))))))))************))))))))))))))))))))))))(((((((((((()))(((((((((''''''''''''%%%&&&&&&&&&'''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%######$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$#########$$$###$$$%%%&&&'''&&&%%%%%%&&&###"""###&&&(((&&&$$$'''''''''(((((((((((((((%%%%%%&&&&&&((()))***++++++***)))))))))***,,,,,,////////////000000000000333222222111111111111111333333333333333333333333111000000000000000111222444333111000......//////...------///222444444333222222111000000///000000111222444555666555555444666666555333111000///......------,,,+++***))))))))))))))))))))))))))))))((((((((((((''''''''''''''''''((((((''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$''''''&&&&&&%%%$$$############""""""######$$$%%%########################%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$#########""""""%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%$$$###$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$..................------............///000111111000000000000////////////000///------/////////........./////////000000000////////////............///...---,,,,,,,,,---------------............///......---,,,,,,,,,,,,------------,,,++++++******++++++++++++++++++++++++***************************))))))(((((((((((((((''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%########################"""######$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$###%%%&&&%%%$$$###$$$%%%########################"""""""""""""""###$$$$$$$$$$$$############$$$$$$########################$$$$$$%%%%%%$$$$$$###"""###############"""!!!!!!""""""""""""""""""""""""!!!!!!!!!!!!!!!"""######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&'''(((((((((((('''))))))))))))))))))))))))************************++++++++++++++++++++++++------------------------------------------------,,,,,,++++++,,,------...************************((()))))))))************))))))))))))))))))))))))*********)))))))))(((((())))))))))))(((((((((((())))))((((((((('''''''''&&&&&&&&&'''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$%%%#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%$$$$$$######$$$$$$###$$$%%%&&&&&&&&&%%%%%%&&&$$$###$$$'''((('''%%%))))))((((((''''''&&&&&&%%%%%%&&&&&&''')))***+++******)))))))))***+++,,,............////////////111111000000000000111111333333333333333333333333111000000/////////000000222111000............///...------...111222222111111111000//////////////////000222444555555444444444444333222000///......---,,,,,,++++++******)))))))))))))))))))))))))))((((((((((((''''''''''''''''''((((((''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&%%%%%%$$$###############""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$#########""""""%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$------------------...............//////000111222000000000000////////////000...------///000///...---...............//////////////////......------///...---,,,,,,,,,,,,------------............///......---,,,,,,,,,,,,---......------,,,,,,++++++++++++++++++++++++++++++***************************)))((((((''''''((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%##############################$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$%%%&&&&&&$$$$$$%%%&&&###########################""""""""""""###$$$$$$$$$$$$############$$$$$$########################$$$$$$%%%%%%$$$$$$###"""###############"""!!!!!!"""""""""""""""""""""""""""!!!!!!!!!!!!"""######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&''''''((()))))))))(((((())))))))))))))))))))))))************************++++++++++++++++++++++++------------------------------------------------+++++++++***++++++,,,---************************))))))))))))************))))))))))))))))))))))))******))))))))))))(((((((((((((((((()))))))))))))))))))))((((((((('''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$#########$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$%%%######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$######$$$$$$###$$$%%%&&&&&&&&&%%%%%%'''%%%%%%%%%'''((('''&&&***))))))((('''&&&%%%%%%%%%%%%&&&&&&'''(((*********))))))))))))***++++++,,,,,,---------.....................///000111111222222222222222222222222111000///...............//////...------......///...---------///000///...//////...---------......---...000222333333333333111111000//////...------++++++++++++++++++++++++))))))))))))))))))))))))((((((((((((''''''''''''''''''((((((''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$###"""""""""######""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$###############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$,,,,,,------------......///////////////000222222000000000000////////////000...------///000000///........................000//////......------,,,......------,,,,,,,,,,,,---------............///......---,,,,,,,,,,,,---.........------,,,,,,,,,************************))))))))))))************))))))(((''''''''''''((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$%%%&&&%%%$$$###$$$&&&#################################""""""###$$$$$$$$$$$$############$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$###""""""###############"""!!!!!!""""""""""""""""""""""""""""""!!!!!!""""""###$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&''''''(((((('''''''''(((((()))))))))))))))(((((((((((((((((((((((())))))))))))************************************,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***************++++++************************)))))))))))))))*********))))))))))))))))))))))))***)))))))))(((((((((((((((((((((((()))))))))))))))))))))(((((((((((('''((((((((('''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###########################""""""######$$$$$$$$$$$$############$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&####################################$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$###$$$$$$%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&'''''''''''''''(((((((((''''''&&&&&&&&&&&&&&&&&&&&&'''((()))***)))))))))))))))******+++++++++++++++,,,,,,,,,,,,,,,,,,,,,---...///111111222222222222222222222222111000///...---,,,,,,,,,---------......//////000...---,,,,,,......---,,,------,,,,,,,,,,,,,,,---+++,,,...000111222111111---------------,,,,,,,,,))))))******+++++++++,,,(((((((((((((((((((((((((((((((((((('''''''''''''''''''''(((''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$#########""""""!!!!!!######""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###$$$%%%%%%&&&########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&$$$###"""########################$$$$$$$$$$$$$$$$$$$$$$$$########################,,,,,,,,,,,,------..................///000111222000000000000///////////////...,,,---///000000/////////////////////////////////......---------,,,---------------,,,,,,,,,---------............///......---,,,,,,,,,,,,---......------------,,,,,,************************(((((()))))))))*********)))((((((''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$"""$$$%%%$$$###"""###%%%########################$$$$$$###############$$$$$$$$$############$$$$$$""""""#########$$$$$$$$$###$$$$$$$$$$$$###""""""###############"""!!!!!!"""""""""""""""""""""""""""""""""""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&''''''(((((('''''''''(((((()))))))))))))))(((((((((((((((((((((((((((((()))))))))*********************************,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++******))))))***************************************)))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((''''''((((((((()))))))))******)))))))))((((((((((((((((((((('''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$#################################!!!"""###$$$$$$$$$$$$###""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""#########$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&'''''''''''''''&&&''''''%%%%%%&&&&&&''''''((((((&&&&&&%%%&&&&&&'''((()))(((((())))))************************+++++++++++++++++++++,,,---///000111111111111111111111111111000000...---,,,,,,,,,,,,---......///000000000000...---,,,,,,------,,,+++,,,+++++++++++++++,,,,,,***+++---///000000000///++++++++++++++++++++++++((())))))******++++++,,,(((((((((((((((((((((((((((((((((((('''''''''''''''''''''(((''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""""""""""""""!!!######""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$############$$$%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&%%%$$$###"""########################################################################++++++,,,,,,------......---------......///000111000000000000///////////////---,,,---///000000000000000000///////////////------------------------------......------,,,+++---------............///......---,,,,,,,,,,,,------------,,,,,,,,,,,,,,,************************'''(((((())))))*********)))(((''''''&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$"""###$$$$$$""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$############$$$$$$$$$############$$$$$$"""""""""###$$$$$$%%%%%%######$$$$$$######"""!!!###############"""!!!!!!""""""""""""""""""""""""###""""""""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&''''''''''''&&&''''''((()))))))))(((((())))))))))))))))))))))))'''(((((())))))*********************************,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++******)))*********************************************))))))))))))))))))))))))))))))))))))))))))((((((((((((''''''''''''(((((())))))************)))))))))((((((((('''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$####################################!!!"""###%%%%%%$$$######"""""""""############$$$################################################"""""""""############$$$######$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%&&&'''&&&'''((('''%%%%%%%%%'''$$$$$$%%%&&&'''(((((()))&&&&&&%%%%%%&&&''''''((('''((())))))******))))))))))))*********++++++++++++++++++,,,---///000111000000000000000000000000000///...------------------...///000000000000000...,,,+++,,,------,,,+++++++++*********+++,,,,,,***+++---...//////...---+++*********************)))))))))*********++++++))))))))))))))))))))))))((((((((((((''''''''''''''''''((((((''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$#########$$$$$$$$$$$$$$$######""""""""""""""""""######""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%###############$$$%%%%%%###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""########################""""""""""""""""""""""""########################***++++++,,,------......,,,,,,,,,,,,---...///000000000000000////////////...---,,,---///111111000/////////.........------+++,,,,,,------......///------.........---,,,+++---------............///......---,,,,,,,,,,,,---++++++,,,,,,,,,,,,,,,,,,************************''''''(((((()))******+++(((((('''&&&&&&&&&&&&'''&&&&&&&&&%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$###$$$%%%%%%######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$$$$#########$$$$$$$$$############$$$$$$!!!""""""###$$$$$$%%%%%%###############""""""!!!###############"""!!!!!!""""""""""""""""""""""""######""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&'''(((((((((((('''))))))))))))))))))))))))''''''(((((()))******+++************************++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,+++***************************************************)))))))))((())))))))))))))))))))))))))))))(((((((((''''''''''''''''''((()))******************)))))))))((((((&&&&&&&&&'''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$####################################!!!"""$$$%%%%%%$$$###"""""""""""""""############################################################""""""""""""##################$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$$$$%%%&&&'''%%%'''((('''$$$###$$$&&&%%%%%%%%%&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''''''''''')))*********)))((())))))*********+++++++++,,,,,,,,,,,,---///000000000000000000000000000000//////...............///,,,---.../////////...------,,,+++,,,---...---,,,+++*********++++++,,,---,,,,,,---.........---,,,++++++******)))))))))((())))))))))))************))))))))))))))))))))))))((((((((((((''''''''''''''''''((((((''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%"""#########$$$$$$$$$$$$##############################""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$%%%""""""#########$$$$$$$$$########################%%%$$$$$$#######################################################################################******+++,,,,,,---......,,,,,,,,,,,,,,,...//////000000000000////////////...---,,,---///111111000.........------,,,,,,,,,***++++++,,,---...//////,,,---.........---,,,+++---------.........//////......---,,,,,,,,,,,,---++++++++++++++++++++++++))))))))))))))))))))))))&&&''''''((()))******+++(((((('''&&&&&&&&&&&&'''&&&&&&&&&%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$%%%&&&&&&$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$#########$$$$$$$$$############$$$$$$!!!""""""###$$$$$$%%%%%%###############"""!!!!!!###############"""!!!!!!""""""""""""""""""""""""#########"""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&'''''''''''''''))))))))))))))))))))))))&&&''''''((()))******+++))))))))))))))))))))))))++++++++++++++++++++++++++++++++++++++++++++++++------,,,+++******++++++************************+++*********))))))(((((()))))))))))))))))))))))))))(((((((((''''''''''''&&&''''''((()))******+++************))))))))))))%%%&&&&&&''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############""""""""""""""""""""""""""" """$$$%%%%%%%%%###"""""""""""""""####################################""""""""""""""""""""""""""""""""""""##################$$$$$$$$$%%%%%%%%%$$$#########$$$%%%%%%&&&&&&%%%$$$###$$$%%%&&&'''$$$&&&(((&&&###"""###&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&%%%%%%%%%&&&''''''&&&''')))*********)))(((************++++++++++++------------...///000000000000000000000000000000//////.........//////000,,,,,,.........---,,,+++---,,,+++,,,...///...---++++++******+++,,,------------...///...---,,,++++++++++++***)))(((((((((*********))))))))))))))))))))))))))))))))))))))))))(((((((((''''''''''''''''''((((((''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&""""""######$$$$$$$$$$$$###############$$$$$$$$$#########"""###$$$$$$%%%#################################"""###$$$$$$%%%""""""######$$$$$$$$$$$$########################&&&%%%###"""""""""###$$$""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""******+++,,,,,,---......///...,,,++++++,,,...///000000//////.........---,,,,,,,,,,,,,,,,,,,,,,,,...------,,,,,,------...,,,,,,,,,,,,,,,,,,,,,,,,---...///000000///...---+++,,,------......------...------,,,,,,++++++***)))************+++++++++************))))))))))))''''''((()))))))))))))))***))))))((('''&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$###"""""""""############$$$$$$$$$&&&&&&&&&&&&%%%%%%$$$#################################$$$$$$$$$$$$######"""###$$$%%%&&&%%%$$$$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$!!!""""""""""""#########%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%&&&&&&''''''&&&&&&'''&&&&&&&&&&&&'''((((((((((((((((((((((((((((((((((((((((((((()))******************************++++++******++++++,,,---))))))***++++++++++++*********+++++++++,,,,,,,,,******++++++++++++******(((((()))***************++++++***)))(((((())))))******))))))((((((''''''%%%%%%&&&&&&((()))++++++((()))*********)))'''&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&"""$$$&&&%%%!!!!!!%%%***""""""""""""############!!!"""###$$$%%%&&&&&&&&&###############"""!!!!!!"""############$$$$$$$$$########################""""""############"""""" !!!"""###$$$$$$%%%#########"""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''''''''''''''''''''&&&&&&''''''((()))))))))))))))''''''(((((())))))******,,,+++*********,,,...000000000000000////////////000000//////.........------------------------------...///////////////...+++++++++,,,,,,,,,------,,,---------...////////////......---+++***))))))))))))************)))))),,,+++***(((%%%%%%''')))******))))))((((((''''''(((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$######""""""######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############"""!!! ################################################&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$$$$$$$$$$%%%******++++++,,,---------...---,,,++++++,,,---.../////////.........------,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,---...///000000///...---,,,,,,---............---...------,,,,,,+++******))))))*********+++++++++*********)))))))))((((((''''''((()))))))))))))))++++++******)))(((((('''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$######""""""############$$$$$$$$$%%%&&&&&&&&&%%%%%%$$$#################################$$$$$$$$$$$$######"""###$$$%%%%%%%%%$$$$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$"""""""""#########$$$$$$%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''((((((((((((((((((((((((((((((((((((((((((((())))))***************************************++++++,,,,,,))))))***++++++++++++***(((((()))******+++,,,,,,+++++++++,,,,,,+++++++++(((((()))***************+++******)))(((((())))))******))))))((('''''''''&&&&&&&&&&&&''')))******)))))))))))))))(((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&"""%%%'''%%%""""""%%%)))""""""""""""############""""""###$$$%%%%%%%%%$$$###############""""""!!!""""""#########$$$$$$$$$########################""""""############""""""!!!!!!""""""######$$$$$$"""""""""""""""#########%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''''''''''''''''''''''''''''''''((()))))))))))))))'''''''''((())))))******,,,+++*********,,,...///....../////////000000000////////////......------------------------------......////////////......,,,,,,,,,,,,---------------------...............///...---,,,+++******))))))******************)))++++++***(((&&&%%%''')))))))))))))))((((((''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$#########"""######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$######"""!!!################################################&&&%%%$$$$$$$$$$$$%%%&&&&&&%%%%%%$$$$$$#########++++++++++++++++++,,,,,,...---,,,++++++,,,---...............------------,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,------...//////...------,,,---......//////......---------,,,++++++******)))))))))*********++++++******))))))))))))((((((''''''((())))))))))))(((*********)))((((((''''''%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$#########"""############$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######"""###$$$%%%%%%%%%%%%$$$###$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((())))))))))))))))))))))))((((((''''''(((((()))******************************************+++++++++))))))***++++++++++++***''''''((()))******+++++++++,,,,,,,,,,,,,,,,,,+++(((((()))*********************)))((((((((())))))******)))((((((''''''&&&''''''&&&&&&'''((())))))***)))((((((''''''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&###%%%&&&%%%###"""%%%((("""""""""#########$$$$$$""""""######$$$######"""######$$$$$$######"""!!!"""""""""#########$$$$$$########################""""""############"""""""""""""""""""""#########!!!!!!""""""######$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%%%%%%%$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''''''''''''''''''''''''''''''''((())))))))))))(((&&&''''''(((((()))******++++++******+++,,,...///,,,,,,---...///000111222///............---------------------------------///////////////...---,,,,,,------------........................---------......---,,,+++******)))******++++++++++++*********+++***(((&&&&&&((())))))))))))(((((((((((('''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$##################$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%'''&&&&&&%%%$$$###""""""++++++++++++************,,,,,,++++++++++++,,,,,,------------,,,,,,,,,,,,++++++++++++++++++++++++---,,,,,,,,,,,,,,,,,,---++++++,,,,,,,,,,,,------,,,---...//////...---,,,,,,---......//////......------,,,,,,+++*********))))))))))))***************)))))))))((((((((((((&&&'''(((((())))))(((((('''''''''&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########""""""#########$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$############$$$$$$%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$####################################$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%&&&&&&%%%%%%&&&&&&'''((())))))))))))))))))))))))(((''''''''''''((())))))************************((())))))***************))))))***++++++++++++******************************++++++,,,,,,++++++***(((((()))******************))))))((((((((())))))***))))))(((''''''&&&&&&''''''&&&&&&&&&'''((((((***)))(((&&&&&&'''((((((''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%"""$$$%%%$$$###"""$$$&&&""""""#########$$$$$$$$$""""""#########""""""!!!###$$$$$$$$$$$$###""""""""""""""""""####################################""""""############""""""#########""""""""""""""" !!!"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&'''''''''''''''&&&'''(((((())))))((((((&&&&&&''''''((())))))***************+++,,,---...,,,,,,---......///000000------------------------------------............///000//////...---,,,+++---------.........///////////////...---------,,,------,,,,,,+++******)))+++++++++,,,,,,+++++++++)))******((('''&&&((()))(((((((((((((((((((((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$#########******************))))))+++++++++******+++++++++++++++++++++,,,,,,,,,,,,++++++++++++++++++++++++,,,,,,,,,++++++,,,,,,,,,+++++++++,,,,,,---------+++,,,---......---,,,+++,,,------...............---,,,,,,++++++***))))))(((((()))))))))*********)))))))))(((((((((((('''&&&&&&'''(((((((((((((((&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$###""""""#########$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$###$$$$$$$$$$$$%%%%%%"""###$$$$$$%%%%%%$$$$$$$$$$$$$$$#########""""""########################$$$%%%%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&''''''(((((((((((((((((((((((('''''''''''''''(((((()))))))))))))))))))))))))))'''((()))*********))))))))))))***++++++++++++***...---,,,+++***))))))((())))))************))))))(((((()))***************)))((((((((((((((())))))))))))(((((('''&&&&&&&&&''''''&&&&&&&&&''''''(((***)))'''&&&&&&&&&'''(((''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$###"""""""""###############$$$$$$$$$$$$""""""#########""""""!!!$$$$$$$$$$$$$$$###""""""!!!!!!"""""""""#################################""""""############""""""#########""""""""""""""" !!!"""###$$$$$$%%%##############################$$$%%%%%%%%%%%%$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&'''''''''((((((&&&&&&'''(((((((((((((((&&&&&&&&&'''(((((())))))************+++,,,------.........---------------,,,,,,,,,,,,---------------------....../////////////////////...---++++++---------.........///////////////...---------,,,,,,,,,,,,++++++******)))+++++++++,,,,,,+++++++++((()))***)))''''''((()))'''''''''''''''((((((((('''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%))))))))))))))))))******************************************++++++++++++++++++++++++++++++++++++,,,,,,++++++++++++,,,,,,***++++++,,,,,,------...++++++,,,------,,,+++++++++,,,------......------,,,,,,,,,+++******))))))((((((((()))))))))******))))))((((((((((((''''''&&&&&&'''(((((((((((('''''''''''''''''''''''''''%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$######$$$$$$######$$$$$$%%%&&&"""######$$$$$$$$$$$$$$$$$$############"""""""""########################$$$$$$%%%%%%%%%&&&&&&&&&###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((((((((((((((((((((((((''''''&&&&&&''''''((()))))))))))))))))))))))))))&&&'''(((******))))))((())))))***++++++++++++***......---,,,+++***)))((((((((())))))))))))(((((((((((()))***************((((((''''''(((((())))))))))))(((''''''&&&&&&%%%&&&&&&%%%%%%&&&'''(((((()))(((''''''&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%#########$$$######"""!!!#########$$$$$$$$$$$$%%%""""""######$$$######"""$$$$$$$$$%%%$$$$$$###"""!!!!!!!!!"""""""""##############################""""""############"""""""""""""""""""""#########!!!!!!""""""######$$$$$$##############################$$$%%%%%%%%%%%%$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%&&&&&&'''(((((((((&&&&&&'''(((((((((((('''%%%&&&&&&''''''((())))))))))))******+++,,,,,,,,,......---------,,,,,,,,,++++++,,,,,,,,,,,,,,,------------...//////000000...............---,,,+++,,,------------........................---------,,,,,,++++++******************++++++++++++******((()))***)))((('''((()))&&&''''''''''''(((((((((&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$######""""""###$$$%%%&&&&&&''''''((((((((()))*********))))))************)))))))))))))))*********++++++************************,,,,,,++++++++++++,,,,,,******+++,,,,,,---......***+++,,,------,,,+++******+++,,,,,,---,,,,,,,,,,,,,,,++++++***)))))))))(((((((((((()))))))))***))))))((((((((('''''''''%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$###$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$######$$$$$$#########$$$%%%&&&""""""###$$$$$$$$$$$$$$$############""""""""""""########################$$$$$$$$$$$$%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%####################################$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&'''(((((())))))))))))))))))))))))%%%&&&(((******)))((('''))))))***++++++++++++***++++++++++++************))))))************))))))(((((()))***************'''''''''''''''((()))))))))((((((''''''&&&%%%%%%$$$$$$$$$%%%&&&'''((()))''''''((((((''''''&&&%%%''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%###"""#########$$$$$$$$$%%%%%%""""""###$$$%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$###"""!!!!!!!!!!!!"""""""""###########################""""""############""""""!!!!!!""""""######$$$$$$"""""""""""""""#######################################$$$%%%%%%%%%%%%$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%&&&&&&'''(((((()))%%%&&&''''''((((((''''''%%%%%%&&&''''''(((((()))((()))***++++++,,,,,,,,,,,,,,,,,,,,,,,,---------***+++++++++,,,,,,,,,,,,---------...///000000000---------......---,,,,,,,,,,,,,,,,,,---------------------...............++++++++++++************)))******************)))'''(((******((((((((()))&&&&&&&&&'''''''''((((((&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%$$$###"""#########$$$$$$%%%%%%&&&&&&''''''((()))******+++))))))************))))))(((((())))))*********+++************************,,,++++++++++++++++++,,,******+++,,,,,,---......***+++,,,,,,,,,,,,+++*********+++,,,,,,,,,,,,+++,,,,,,++++++***)))))))))(((((((((((()))))))))))))))(((((((((''''''''''''%%%&&&''''''((((((''''''$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%$$$$$$$$$######%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$###$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$######%%%$$$#########$$$%%%&&&""""""###$$$$$$$$$$$$###############""""""""""""""""""""""""""""""""""""######$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%########################"""############$$$$$$$$$######$$$%%%%%%%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&'''(((((())))))))))))))))))))))))%%%&&&(((******)))((('''))))))***++++++++++++***((((((((()))******++++++******++++++++++++******(((((()))***************'''''''''''''''((()))***)))(((((('''&&&&&&%%%%%%###$$$$$$%%%&&&''')))***&&&'''((((((((('''%%%$$$''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&'''((('''%%%#########$$$$$$$$$%%%%%%%%%!!!"""###$$$%%%&&&&&&&&&$$$%%%%%%%%%%%%$$$######!!!!!!!!!!!!""""""""""""########################""""""############"""""" !!!!!!"""###$$$$$$%%%#########"""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%&&&&&&'''((())))))%%%&&&''''''((((((''''''%%%%%%&&&&&&'''(((((()))((()))***++++++,,,++++++******+++,,,------...///*********++++++,,,,,,,,,---------...///000000111,,,,,,------...---------+++++++++,,,,,,,,,------,,,------....../////////+++++++++***************))))))************))))))&&&(((******)))(((((()))&&&&&&&&&'''''''''((((((&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%$$$###"""%%%%%%$$$$$$$$$$$$$$$$$$+++***)))((('''''''''''')))************)))((((((++++++++++++++++++++++++++++++,,,,,,,,,,,,------+++++++++******)))))))))))))))***++++++,,,---------------,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++))))))))))))))))))))))))((((((''''''''''''((((((''''''''''''(((((((((((('''''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%!!!""""""###$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$""""""#########$$$$$$$$$&&&&&&%%%$$$############"""###$$$%%%&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%"""###$$$%%%%%%%%%%%%$$$%%%%%%%%%$$$$$$#########%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%############"""""""""""""""############$$$$$$$$$$$$$$$##################$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%$$$$$$$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&'''((()))%%%%%%&&&&&&'''((((((((())))))))))))((('''&&&%%%''''''(((((())))))******************************************************+++++++++************)))))))))***++++++++++++***))))))((('''''''''''''''***))))))((('''&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$#################################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########""""""#########"""""""""""""""$$$$$$$$$#########"""""""""############$$$$$$$$$""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!$$$$$$############$$$$$$"""###%%%&&&&&&%%%###"""&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%'''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((()))))))))***++++++++++++***++++++******++++++,,,---,,,,,,,,,++++++************++++++,,,,,,------...---,,,,,,++++++,,,,,,---...---+++*********++++++---------,,,,,,,,,++++++******++++++++++++************))))))((((((''''''((((((''''''''''''(((((('''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$################################################!!! $$$&&&%%%$$$%%%++++++***)))(((''''''((('''((()))***************+++++++++++++++++++++++++++++++++,,,,,,,,,------,,,,,,+++++++++***************++++++,,,,,,------...---------,,,,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++))))))))))))))))))))))))((((((''''''''''''((((((''''''''''''((((((((((((''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$######%%%&&&&&&'''''''''#########$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%############"""""""""""""""############$$$$$$$$$$$$$$$##################$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$###$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&'''((((((%%%%%%&&&&&&'''((((((((((((((())))))((('''&&&&&&'''''''''((())))))******************************************************+++++++++*********))))))((()))******++++++******))))))(((''''''''''''((()))))))))((('''&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((((((''''''''''''''''''''''''''''''&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$##############################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########"""""""""""""""""""""#########$$$$$$$$$#########"""""""""############$$$$$$$$$""""""""""""""""""""""""""""""""""""""""""""""""$$$$$$############$$$$$$'''(((***++++++***((('''&&&&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&'''''''''(((((((((((()))******++++++******+++************+++,,,,,,,,,,,,+++++++++***************++++++,,,---------,,,,,,,,,++++++,,,,,,,,,---,,,+++*********++++++,,,,,,,,,,,,++++++++++++)))******++++++******)))***)))))))))((((((((('''((((((''''''''''''(((((('''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###$$$%%%$$$######,,,+++***)))((((((((()))&&&&&&((()))***+++++++++************************++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,.........---------------,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++))))))))))))))))))))))))((((((''''''''''''((((((''''''''''''(((((((((((('''&&&&&&&&&&&&%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%#########$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$###$$$$$$%%%%%%$$$$$$%%%&&&''''''''''''#########$$$$$$$$$$$$%%%%%%$$$#########$$$%%%&&&%%%%%%%%%$$$$$$$$$$$$###%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%############"""""""""""""""############$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&'''(((%%%%%%%%%&&&''''''(((((('''((((((((((((((('''&&&&&&''''''(((((()))******************************************************++++++*********)))))))))(((((()))*********************)))((((((((((((((())))))(((((('''&&&&&&&&&&&&&&&&&&''''''''''''((((((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$###########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###############!!!!!!""""""######$$$$$$$$$############""""""""""""############$$$$$$$$$""""""""""""""""""""""""########################$$$$$$############$$$$$$%%%&&&'''(((((('''&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((((()))******************************++++++,,,+++++++++************************+++,,,,,,------,,,,,,,,,++++++,,,,,,,,,---,,,+++*********++++++++++++++++++*********))))))******++++++******)))))))))))))))((((((((((((((((((''''''''''''((((((&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$""""""###$$$$$$++++++***)))))))))))))))&&&'''((()))***************************************++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------,,,,,,,,,,,,,,,........................,,,,,,,,,+++++++++++++++************************((((((((((((((((((((((((((((((''''''''''''((((((''''''''''''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&############$$$%%%&&&&&&$$$%%%&&&'''''''''''''''############$$$$$$$$$$$$%%%$$$###""""""$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%############"""""""""!!!""""""#########$$$$$$$$$######$$$$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$############$$$$$$######$$$$$$%%%&&&&&&&&&&&&%%%%%%&&&''''''$$$%%%%%%&&&&&&'''((((((''''''((((((((((((((('''&&&&&&''''''((())))))***************************************************************))))))))))))'''((())))))******))))))******)))(((((((((((()))(((((((((''''''&&&&&&&&&&&&&&&&&&''''''''''''((((((((('''''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&''''''((('''&&&&&&%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$######################## !!!"""###$$$$$$%%%############""""""""""""""""""#########$$$$$$$$$""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$!!!!!!""""""""""""!!!!!!%%%%%%%%%$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&'''((())))))******)))))))))))))))))))))***++++++*********************)))))))))******+++,,,,,,,,,+++++++++,,,,,,+++++++++,,,+++++++++++++++++++++************))))))))))))))))))************))))))))))))))))))(((((((((((((((''''''&&&&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%########################""""""#########$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$######$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""###$$$$$$$$$$$$$$$################################################%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%"""!!!###%%%&&&+++***))))))))))))))))))(((((()))))))))(((((('''))))))))))))))))))))))))*********+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++........................,,,,,,,,,++++++*********************************((((((((((((((((((((((((((((((''''''''''''((((((''''''''''''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&############$$$%%%&&&&&&%%%%%%&&&&&&'''&&&&&&&&&""""""#########$$$$$$$$$%%%$$$###""""""$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%############"""""""""!!!""""""#########$$$$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$#########$$$$$$$$$$$$######$$$$$$%%%&&&'''&&&&&&%%%%%%%%%&&&&&&$$$$$$%%%%%%&&&'''''''''&&&&&&'''((())))))((((((&&&&&&&&&'''(((((())))))))))))))))))))))))))))))))))))))))))))))))))))))*********)))))))))((((((''''''((())))))))))))(((***))))))(((((((((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''&&&%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$######################## !!!"""###$$$$$$%%%""""""""""""""""""""""""""""""#########$$$$$$$$$""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$"""##################"""%%%%%%$$$$$$$$$###############$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%%%%&&&''''''((())))))))))))((())))))(((((())))))***+++))))))))))))))))))))))))(((((()))******++++++,,,***++++++,,,,,,++++++***++++++++++++++++++++++++*********)))))))))(((((()))))))))******)))))))))(((((((((((())))))))))))''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%########################""""""#########$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$##################$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""###$$$$$$$$$$$$###################################################%%%%%%%%%%%%%%%%%%%%%%%%+++...,,,%%%"""%%%&&&%%%))))))(((((((((((())))))((()))))))))(((((('''&&&((((((((((((((((((((((((************++++++++++++++++++++++++,,,,,,,,,,,,++++++++++++++++++++++++---------------.........,,,,,,,,,+++******))))))************************))))))))))))))))))))))))((((((''''''''''''((((((''''''''''''((((((((((((%%%%%%%%%&&&&&&&&&&&&'''&&&&&&%%%%%%%%%$$$$$$$$$""""""######$$$%%%%%%%%%######$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$###$$$$$$%%%%%%$$$$$$%%%&&&&&&%%%%%%$$$"""""""""############$$$%%%$$$#########$$$%%%&&&###$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%############"""""""""""""""############$$$$$$$$$######$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$%%%&&&$$$$$$######$$$$$$%%%&&&'''&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&''''''%%%%%%'''((())))))))))))%%%&&&&&&''''''((())))))))))))))))))))))))))))))))))))))))))))))))))))))******)))))))))(((((((((&&&''''''((((((((((((((())))))((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((('''''''''&&&&&&&&&&&&%%%$$$$$$%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$%%%###$$$$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$!!!!!!""""""######$$$$$$!!!!!!"""""""""""""""###"""############$$$$$$$$$""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$########################$$$$$$$$$$$$##################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''(((((((((((((((((((((((((((((())))))***(((((((((((())))))))))))((((((((()))******++++++)))***+++,,,,,,+++***)))******+++,,,,,,,,,++++++************)))))))))(((((())))))******))))))((((((((((((((())))))))))))''''''&&&&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################"""############$$$$$$$$$###$$$$$$%%%%%%&&&&&&'''$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################!!!"""######$$$$$$######################################################%%%%%%%%%%%%%%%%%%%%%%%%000666444***$$$%%%&&&###((((((''''''''''''((((((''''''(((((()))(((((((((((((((((((((((((((((((((************++++++++++++*********+++++++++,,,,,,)))))))))******++++++++++++,,,,,,,,,------------,,,,,,++++++***))))))(((************************))))))))))))))))))))))))((((((''''''''''''((((((''''''''''''((((((((((((%%%%%%%%%&&&&&&&&&''''''%%%%%%$$$$$$$$$#########!!!""""""###$$$$$$%%%%%%""""""###$$$&&&'''((((((&&&&&&%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$###$$$$$$%%%$$$$$$######""""""""""""##################$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%############"""""""""""""""############$$$$$$$$$######$$$$$$%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$""""""###$$$&&&((($$$$$$######$$$$$$%%%&&&'''&&&%%%%%%$$$$$$%%%%%%###$$$$$$%%%%%%&&&''''''$$$%%%&&&((()))*********%%%%%%&&&''''''(((((()))))))))))))))))))))))))))))))))))))))))))))))))))***)))))))))((((((((((((&&&&&&'''(((((((((''''''(((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((('''''''''&&&&&&&&&%%%%%%###$$$$$$%%%&&&&&&''''''%%%%%%$$$############$$$######$$$$$$$$$%%%%%%%%%################################################""""""#########$$$$$$$$$"""""""""""""""#########!!!!!!!!!!!!""""""######"""############$$$$$$$$$""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$"""""""""!!!!!!"""""""""$$$$$$$$$$$$##################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&'''(((((((((''''''(((''''''''''''((())))))'''''''''((((((((())))))''''''(((((()))******+++)))***+++,,,,,,+++***))))))***+++,,,,,,,,,,,,+++++++++*********)))))))))(((((())))))))))))(((((('''((((((((()))))))))***'''&&&&&&%%%%%%&&&&&&'''###$$$%%%%%%%%%%%%$$$######$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################"""############$$$$$$$$$######$$$%%%%%%&&&''''''$$$$$$$$$$$$########################$$$$$$$$$$$$################################################$$$$$$############$$$$$$################################################!!!""""""###############################################################$$$$$$$$$$$$$$$$$$$$$$$$+++333333)))###%%%&&&!!!''''''&&&&&&&&&''''''(((%%%%%%'''((())))))******(((((((((((((((((((((((()))************+++++++++)))))))))******+++++++++''''''((()))***++++++,,,+++++++++,,,,,,---------,,,,,,++++++***))))))((())))))))))))))))))))))))))))))))))))))))))))))))((((((''''''''''''((((((''''''''''''((((((((()))%%%%%%%%%&&&&&&'''''''''$$$$$$$$$#########""""""!!!""""""###$$$$$$%%%%%%!!!!!!###$$$&&&'''))))))&&&&&&&&&%%%%%%%%%$$$$$$""""""#########$$$$$$$$$&&&&&&%%%$$$##################$$$$$$$$$######"""""""""""""""############"""###$$$%%%%%%%%%%%%$$$#########$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%############"""""""""""""""############$$$$$$$$$######$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""###%%%''')))$$$$$$######$$$$$$%%%&&&'''&&&%%%%%%$$$$$$$$$$$$###$$$$$$%%%%%%&&&''''''$$$%%%&&&((()))*********%%%%%%&&&&&&'''(((((()))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((%%%&&&''''''((((((''''''''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((''''''&&&&&&&&&%%%%%%%%%######$$$%%%%%%&&&''''''%%%$$$######""""""###############$$$$$$%%%%%%%%%################################################""""""######$$$$$$$$$$$$#########""""""""""""""" !!!!!!!!!""""""######"""############$$$$$$$$$""""""""""""""""""""""""########################$$$$$$############$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$############"""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''%%%&&&''''''(((((('''''''''''''''''''''((())))))&&&'''''''''(((((())))))''''''(((((()))*********((()))+++,,,,,,+++)))((()))***+++,,,---,,,,,,+++++++++++++++************(((((())))))))))))(((((('''((((((((())))))******'''&&&&&&%%%%%%&&&&&&'''###$$$%%%&&&&&&%%%$$$#########$$$$$$$$$%%%%%%%%%########################"""""""""""""""""""""""""""############$$$$$$$$$######$$$%%%%%%&&&''''''$$$$$$$$$############""""""############$$$$$$$$$########################""""""""""""""""""""""""$$$$$$############$$$$$$########################""""""""""""""""""""""""!!!!!!"""###############""""""""""""""""""""""""################################################***---$$$ $$$&&&"""''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&''')))*********)))(((*********)))))))))))))))******))))))))))))******(((''''''&&&&&&((()))******+++,,,,,,------------,,,,,,,,,+++++++++*********++++++++++++***))))))(((((('''''''''&&&&&&&&&''''''&&&&&&&&&&&&''''''(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###$$$$$$%%%%%%########################$$$$$$$$$$$$%%%&&&''''''&&&%%%$$$###"""""""""""""""""""""""""""######$$$!!!"""$$$%%%&&&%%%%%%$$$$$$#########""""""!!!!!!"""############$$$$$$$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$######!!!!!!!!!!!!""""""""""""$$$$$$#################################$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&'''((())))))***((((((&&&%%%%%%&&&'''((())))))(((((('''''''''&&&%%%&&&((()))))))))((('''(((((('''''''''&&&&&&&&&&&&&&&&&&''''''''''''((((((''''''''''''&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$###"""!!!!!!"""###$$$######$$$$$$$$$%%%%%%%%%######################## !!!"""###$$$$$$%%%""""""""""""""""""""""""""""""############""""""######""""""!!!!!! !!!!!!!!!"""######$$$$$$$$$###"""!!!!!!"""###$$$########################""""""""""""!!!!!!!!!!!!$$$$$$$$$############"""&&&%%%$$$######$$$%%%&&&"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$#########$$$%%%########################%%%%%%&&&&&&'''(((((((((((((((((((((((('''''''''))))))(((((((((((())))))))))))))))))((((((((((((************************)))************++++++++++++++++++************)))+++*********))))))(((((()))))))))))))))))))))))))))((('''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###########################"""!!!!!!"""$$$&&&'''%%%$$$$$$######$$$$$$%%%###$$$$$$%%%%%%$$$$$$###&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$###""""""###$$$$$$########################""""""""""""""""""""""""!!!""""""""""""#########$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%!!!"""""""""###############$$$$$$%%%%%%$$$$$$##############################$$$%%%&&&%%%$$$###"""''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''&&&'''((()))***)))(((((())))))))))))))))))))))))******))))))))))))******(((((('''&&&'''((()))*********+++,,,,,,,,,,,,,,,++++++++++++*********)))******++++++******)))((((((((('''''''''&&&&&&&&&''''''&&&&&&&&&&&&''''''((('''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$%%%####################################$$$%%%&&&'''%%%%%%$$$###"""!!!!!!""""""""""""""""""######$$$"""###$$$%%%%%%%%%$$$###$$$#########"""""""""""""""############$$$$$$$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""!!!!!!!!!!!!"""""""""###########################""""""###$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%&&&&&&'''(((((())))))((('''&&&&&&&&&&&&'''(((((('''''''''&&&&&&&&&&&&%%%&&&'''((())))))((('''((('''''''''&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((''''''''''''&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""!!!!!!"""###$$$############$$$$$$$$$$$$########################!!!!!!""""""######$$$$$$""""""""""""""""""""""""""""""############""""""###"""""""""!!!!!!!!! """""""""###$$$$$$%%%%%%$$$###"""!!!!!!"""###$$$########################"""""""""""""""""""""!!!$$$$$$$$$############"""$$$######""""""######$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$$$$%%%########################%%%%%%&&&&&&'''(((((((((((((((((((((((((((((('''))))))(((((((((((()))))))))(((((((((((((((((((((************************))))))*********++++++++++++++++++*********))))))*********)))))))))(((((((((((((((((((((((((((((((((((('''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###########################"""!!!!!!"""$$$&&&'''%%%$$$$$$######$$$$$$%%%###$$$$$$%%%%%%$$$$$$###%%%%%%$$$$$$$$$#########%%%$$$###""""""###$$$$$$################################################"""""""""#########$$$$$$$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%############$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&'''(((((())))))(((((())))))))))))))))))))))))***))))))(((((())))))***(((((('''''''''((()))***))))))******++++++************)))))))))))))))(((***************)))(((((('''''''''''''''&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$$$$########################""""""""""""###$$$%%%&&&$$$$$$###"""!!!!!!!!!!!!"""""""""""""""######$$$$$$$$$$$$%%%$$$$$$###"""###############""""""""""""############$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$######"""!!!!!!!!!!!!"""""""""##############################!!!"""$$$%%%%%%%%%$$$###$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$############$$$%%%########################$$$$$$$$$########################$$$$$$$$$$$$%%%%%%&&&&&&''''''(((((((((''''''&&&&&&&&&''''''(((&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''(((((((((((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((''''''''''''&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""""""""###$$$""""""""""""####################################"""""""""""""""#########""""""""""""""""""""""""""""""############""""""""""""""""""!!!!!!!!!!!!#########$$$%%%%%%&&&&&&######""""""""""""##############################""""""""""""""""""""""""$$$$$$$$$############""""""""""""######""""""""""""############$$$$$$$$$########################%%%$$$$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&'''(((((((((''''''(((((((((((((((((()))((((((''''''(((((()))((((((((((((((((((((((((++++++******))))))(((((()))))))))*********++++++++++++*********)))))))))******))))))))))))((((((((((((((((((((((((((((((((('''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%##############################"""""""""$$$%%%&&&$$$$$$############$$$$$$######$$$$$$$$$$$$#####################"""""""""$$$$$$############$$$%%%######################################################$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&''''''((((((((((((((((((((()))))))))))))))))))))(((((((((((())))))((((((((((((((()))))))))(((((()))))))))))))))((((((((((((((((((((((((((())))))******))))))((('''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$#######################################!!!!!!!!!!!!"""###$$$%%%######"""!!!!!!!!!!!!!!!"""""""""""""""######$$$%%%$$$$$$$$$######""""""########################""""""#########$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############"""!!!!!!!!!!!!"""""""""########################$$$$$$$$$!!!"""$$$&&&&&&%%%$$$###$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$""""""""""""""""""""""""#########"""""""""""""""############$$$$$$$$$$$$%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&'''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((''''''''''''&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$$$$$$$%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$########################!!!!!!!!!!!!""""""""""""#################################"""""""""""""""""""""""""""""""""""""""""""""############""""""""""""""""""!!!!!!!!!!!!""""""######$$$%%%%%%&&&###""""""""""""""""""###########################"""""""""""""""#########$$$$$$$$$#########""""""!!!"""###$$$$$$###"""!!!""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&'''(((((((((''''''''''''(((((((((((((((((((((''''''((((((((('''''''''(((((((((((((((*********))))))(((''''''))))))))))))************************))))))))))))))))))))))))))))))((((((((((((((((((((((((((((((''''''&&&%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################""""""######%%%%%%$$$$$$############$$$$$$######$$$$$$$$$$$$##############################$$$$$$###$$$$$$$$$%%%%%%################################################$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%#########$$$$$$$$$%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%'''(((***&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&''''''(((''''''(((((())))))))))))))))))(((((((((((())))))((((((((()))))))))))))))((((((((())))))(((((('''''''''''''''''''''''''''((())))))))))))(((''''''&&&'''''''''''''''''''''''''''&&&&&&&&&&&&''''''%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######"""""""""###########################!!!!!!!!!!!!"""###$$$$$$###"""!!!!!!!!!!!!!!!!!!"""""""""""""""######$$$%%%$$$$$$######"""""""""###############$$$$$$$$$""""""#########$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############"""!!!!!!""""""""""""############""""""#########$$$$$$$$$"""###$$$%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################""""""""""""""""""""""""""""""""""""""""""""""""""""""#########$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&'''''''''((((((''''''''''''''''''(((((('''''''''&&&&&&&&&&&&'''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((''''''''''''&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&#########$$$$$$%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$###### !!!!!!!!!"""""""""""""""""""""""""""""""""#########"""""""""""""""""""""""""""""""""""""""""""""############""""""!!!!!!!!!!!!""""""""""""!!!!!!""""""###$$$$$$$$$"""""""""######"""""""""""""""""""""""""""""""""!!!"""""""""#########$$$$$$$$$$$$#########"""""""""###$$$%%%%%%$$$###"""""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&'''(((((((((&&&'''''''''(((((())))))((((((''''''''''''((((((&&&&&&''''''((((((((())))))))))))(((((((((''''''(((((()))))))))******************)))))))))(((((((((((((((((((((((())))))''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##########################################$$$$$$$$$######""""""######$$$"""######$$$$$$######"""######$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%################################################$$$%%%%%%%%%%%%&&&&&&&&&$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%""""""""""""#########$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%'''(((***%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&''''''(((((())))))***)))((((((''''''(((((()))'''((()))*********))))))(((((()))))))))(((''''''&&&''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&&&&'''''''''''''''''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###"""""""""""""""########################!!!!!!!!!!!!"""###$$$%%%###""""""!!!!!!""""""""""""""""""""""""######$$$$$$$$$###"""""""""###############$$$$$$$$$$$$$$$"""############$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$######"""!!!"""""""""#########$$$$$$"""""""""###$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$###""""""########################""""""""""""############"""""""""############$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''(((((((((((('''''''''(((((((((((((((((('''&&&&&&%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((''''''''''''&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$%%%%%%&&&&&&########################%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%$$$######!!!!!!!!!!!!"""""""""""""""""""""""""""""""""""""""""""""""""""#########""""""""""""""""""""""""""""""############""""""!!!!!!!!!!!!"""""""""""" !!!!!!"""######$$$$$$""""""############""""""""""""""""""""""""""""""!!!""""""######$$$$$$$$$$$$$$$$$$############"""$$$$$$%%%%%%%%%%%%$$$$$$"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''(((((((((&&&&&&''''''((()))))))))(((''''''&&&&&&''''''(((&&&&&&&&&''''''(((((()))'''''''''(((((((((((((((((((((((()))))))))************)))))))))(((((((((''''''(((((((((((())))))''''''''''''''''''''''''%%%%%%%%%%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######################################################""""""""""""######""""""############""""""#########$$$$$$$$$$$$$$$"""###$$$%%%&&&&&&&&&%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%!!!!!!"""""""""############$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%''''''&&&&&&''''''((())))))***((((((''''''''''''(((((('''((()))***+++***)))))))))))))))))))))(((''''''&&&'''''''''((((((((((((''''''((((((((('''&&&&&&&&&&&&&&&'''''''''((((((''''''&&&&&&&&&&&&''''''$$$$$$%%%%%%%%%&&&&&&&&&########################%%%$$$###"""!!!!!!!!!!!!########################""""""""""""###$$$%%%%%%######"""""""""######$$$"""""""""""""""######$$$######"""!!!!!!"""###$$$#########$$$$$$%%%%%%%%%"""############$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""""""""#########$$$$$$$$$!!!""""""###$$$$$$%%%%%%&&&%%%$$$######%%%&&&'''&&&%%%%%%%%%%%%%%%%%%$$$########################!!!"""###$$$$$$###"""!!!$$$$$$$$$$$$$$$$$$$$$$$$"""""""""######$$$$$$$$$""""""""""""############%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%&&&(((((((((((('''&&&&&&&&&''''''(((((((((((('''&&&%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''((((((''''''''''''&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###!!!!!!"""""""""#########""""""""""""""""""""""""!!!!!!""""""######$$$$$$""""""""""""""""""""""""""""""############"""""" !!!!!!!!!"""""""""###!!!""""""######$$$%%%%%%!!!"""###$$$$$$###"""!!!""""""""""""""""""""""""!!!""""""######$$$%%%%%%$$$$$$$$$############"""$$$$$$############$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''(((((((((&&&&&&''''''((())))))***(((''''''&&&&&&''''''(((%%%%%%&&&''''''((())))))%%%&&&&&&''''''(((((()))(((((((((((()))))))))******)))))))))(((((((((((('''''''''((((((((())))))''''''''''''''''''''''''%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%######################################################$$$$$$$$$###############""""""""""""######""""""############"""""""""""""""#########$$$$$$"""###$$$&&&&&&&&&&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%""""""#########$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%&&&'''&&&&&&&&&'''((())))))***((((((''''''''''''(((((('''((()))++++++******)))))))))******)))((('''''''''''''''((((((((())))))''''''((((((''''''&&&%%%&&&&&&&&&'''''''''(((((('''''''''&&&&&&'''''''''$$$$$$$$$%%%%%%&&&&&&&&&########################%%%$$$###"""!!!!!!!!!!!!########################""""""""""""###$$$%%%&&&$$$###############$$$$$$"""""""""""""""######$$$""""""!!!!!!!!!###$$$%%%#########$$$$$$%%%%%%%%%"""############$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$######"""############$$$$$$$$$!!!""""""###$$$$$$%%%%%%'''%%%###""""""$$$''')))&&&&&&&&&%%%%%%$$$$$$$$$########################!!!"""###$$$$$$###"""!!!$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$$$$%%%""""""""""""############%%%$$$$$$$$$$$$$$$$$$$$$###$$$&&&((())))))((('''%%%%%%%%%&&&&&&'''''''''((((((&&&%%%$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&'''''''''(((((((((((('''''''''&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%&&&&&&'''(((((($$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""###$$$%%%&&&&&&%%%$$$###""""""""""""############"""""""""""""""""""""""" !!!!!!"""###$$$$$$%%%""""""""""""""""""""""""""""""############"""""" !!!!!!!!!""""""######"""######$$$%%%%%%&&&&&&!!!"""###$$$$$$###"""!!!""""""""""""""""""""""""!!!""""""###$$$$$$%%%%%%$$$$$$$$$############"""$$$###"""!!!!!!"""###$$$"""############$$$$$$$$$########################!!!"""$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''(((((()))&&&&&&&&&'''((())))))***'''''''''&&&&&&'''''''''%%%%%%&&&&&&'''((())))))$$$%%%%%%&&&'''((())))))(((((((((((())))))))))))))))))))))))((((((((((((&&&'''''''''(((((())))))''''''''''''''''''''''''$$$$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%######################################################$$$$$$$$$######"""######""""""""""""######""""""############"""""" !!!!!!!!!""""""######"""###$$$&&&''''''&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$###########################$$$%%%&&&%%%$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%$$$$$$$$$$$$'''''''''(((((((((((()))***)))(((''''''((()))***&&&&&&&&&''''''''''''((())))))(((((('''''''''&&&%%%%%%%%%&&&&&&&&&''''''((('''&&&%%%%%%&&&'''(((###$$$$$$%%%&&&'''((((((&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""%%%%%%%%%$$$$$$#########"""###$$$%%%%%%%%%%%%%%%$$$$$$##################""""""#########$$$$$$$$$&&&&&&&&&&&&%%%%%%$$$###########################$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$#########""""""!!!!!!########################"""""""""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$############""""""""""""###############$$$$$$$$$$$$###"""""""""""""""""""""""""""""""""############$$$$$$$$$########################$$$%%%%%%&&&&&&%%%%%%$$$(((((('''''''''&&&&&&&&&''''''&&&&&&&&&&&&'''''')))'''$$$%%%''''''%%%###%%%%%%%%%&&&&&&&&&''''''((((((((((((''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%'''((()))'''&&&######$$$$$$$$$%%%%%%%%%$$$$$$##################%%%%%%%%%$$$$$$#########$$$$$$############$$$$$$#########"""""""""""""""######$$$$$$$$$$$$############""""""""""""############""""""""""""######""""""!!!!!!!!!!!!""""""!!!!!!"""################################################"""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$############$$$$$$$$$$$$############$$$%%%%%%%%%%%%$$$$$$$$$###""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&''''''''''''(((&&&&&&%%%$$$%%%&&&'''((('''''''''&&&&&&%%%%%%%%%''''''''''''((((((((((((''''''''''''''''''''''''(((((())))))))))))(((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%$$$##############################""""""""""""""""""""""""""""""""""""""""""""""""$$$$$$###############$$$""""""#########$$$$$$$$$ !!!"""###$$$%%%%%%%%%######$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%$$$###"""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&'''((((((%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!""""""#########$$$######""""""""""""######""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&%%%$$$$$$$$$$$$$$$&&&&&&'''''''''((((((((())))))(((''''''((())))))&&&&&&&&&''''''''''''((()))(((((((((''''''''''''&&&&&&&&&&&&''''''''''''((('''&&&%%%%%%&&&'''((($$$%%%%%%&&&&&&'''''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############%%%%%%%%%$$$$$$#########"""###$$$%%%%%%%%%%%%%%%########################""""""#########$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###########################$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$#########""""""""""""###############$$$$$$$$$!!!""""""######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$############""""""""""""###############$$$$$$$$$$$$###"""""""""""""""""""""""""""""""""############$$$$$$$$$########################%%%%%%&&&&&&&&&&&&%%%%%%'''&&&&&&&&&%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''(((&&&$$$%%%''''''&&&$$$%%%%%%%%%&&&&&&&&&''''''(((((((((((('''''''''&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&(((((('''&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$##################""""""############"""""""""""""""""""""######$$$$$$$$$$$$######""""""!!!!!!!!!!!!""""""######""""""""""""######""""""!!!!!!!!!!!!""""""!!!!!!"""##########################################"""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$############$$$$$$$$$$$$############$$$%%%%%%%%%%%%$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&'''''''''''''''&&&%%%%%%%%%&&&(((((('''''''''&&&&&&%%%%%%%%%''''''''''''((((((((((((''''''''''''''''''''''''(((((())))))))))))(((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%$$$$$$##############################""""""""""""""""""""""""""""""""""""""""""""""""$$$$$$###############$$$""""""#########$$$$$$$$$!!!"""###$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$######"""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&'''((((((%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""#########$$$######""""""""""""##############################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&'''''')))(((''''''''''''((()))&&&&&&&&&''''''''''''(((((((((((((((''''''''''''''''''''''''((((((((((((((('''&&&%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###"""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$###############$$$%%%%%%%%%$$$$$$#######################################$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$###########################$$$############$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#######################################"""""""""""""""######$$$$$$$$$$$$!!!!!!"""######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$###############""""""""""""###############$$$$$$$$$$$$###"""""""""""""""""""""""""""""""""############$$$$$$$$$########################%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$''''''&&&&&&&&&&&&''''''&&&%%%$$$%%%'''''''''%%%%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&'''((('''%%%######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$############""""""!!!!!!""""""###""""""""""""""""""############$$$$$$$$$$$$######!!!!!! !!!!!!######""""""""""""######""""""!!!!!!!!!!!!""""""!!!!!!"""#######################################""""""""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$############$$$$$$$$$$$$############$$$%%%%%%%%%%%%$$$"""###$$$%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&''''''((()))'''''''''&&&&&&&&&&&&&&&''''''''''''((((((((((((''''''''''''''''''''''''(((((())))))))))))(((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$##############################""""""""""""""""""""""""""""""""""""""""""""""""$$$###############$$$$$$###############$$$$$$$$$"""######$$$$$$$$$############$$$%%%%%%%%%%%%$$$######$$$$$$######""""""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&'''((((((&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""""""""#####################""""""""""""##############################$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&''''''''''''(((((((((((((((((('''''''''(((((((((((())))))))))))((('''&&&%%%%%%&&&'''((('''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###"""!!!!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$##################$$$$$$%%%%%%%%%$$$$$$###############$$$$$$$$$########################$$$$$$%%%%%%%%%$$$$$$##########################################$$$$$$%%%########################################################################"""""""""###$$$$$$%%%%%%!!!!!!""""""###$$$$$$$$$########################%%%%%%$$$###############!!!"""""""""###############$$$$$$$$$$$$###""""""""""""""""""""""""""""""""""""#########$$$$$$$$$########################%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%&&&'''''''''%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%''''''&&&%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''(((((($$$$$$$$$###############""""""!!!!!!!!!!!!"""""""""""""""""""""###############$$$$$$$$$$$$######"""!!!!!! !!!!!!"""######""""""""""""######""""""!!!!!!!!!!!!""""""!!!!!!"""#######################################"""""""""""""""#######################################$$$$$$$$$$$$############$$$$$$$$$$$$############$$$%%%%%%%%%%%%$$$"""$$$&&&((()))((('''&&&########################""""""#########$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&'''''''''''''''''''''(((((())))))'''''''''''''''&&&&&&&&&''''''''''''((((((((((((''''''''''''''''''''''''(((((())))))))))))(((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$##############################""""""""""""""""""""""""""""""""""""""""""""""""#########"""######$$$%%%##############################$$$$$$$$$######"""######$$$%%%%%%%%%%%%$$$""""""#########""""""!!!######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&'''((((((''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$######""""""######$$$########################$$$$$$$$$$$$$$$$$$$$$$$$""""""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$######$$$$$$%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&''''''''''''((('''''''''(((((((((((((((((((((((()))))))))******((('''&&&%%%%%%&&&'''((('''''''''&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###"""!!!!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$##############################$$$$$$%%%%%%%%%$$$$$$###""""""#########$$$$$$$$$##############################$$$%%%%%%$$$$$$$$$##############################""""""######$$$%%%###############################################################$$$$$$$$$""""""#########$$$$$$$$$ !!!!!!"""######$$$$$$########################$$$$$$######""""""######!!!"""""""""###############$$$$$$$$$$$$###""""""""""""""""""""""""""""""""""""#########$$$$$$$$$########################%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$%%%&&&&&&&&&&&&'''(((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$&&&'''%%%$$$######$$$$$$$$$%%%%%%%%%$$$$$$%%%&&&''''''((((((########################""""""!!!!!!!!!!!!""""""!!!!!!""""""##################$$$$$$$$$$$$#########""""""!!!!!!""""""#########""""""""""""######""""""!!!!!!!!!!!!""""""!!!!!!"""###############""""""""""""""""""""""""!!!!!!""""""##########################################$$$$$$$$$$$$############$$$$$$$$$$$$############$$$%%%%%%%%%%%%$$$$$$&&&(((******)))((('''########################""""""#########$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&''''''''''''(((((((((((((((''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((((((((())))))))))))(((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$##############################""""""""""""""""""""""""""""""""""""""""""""""""######""""""###$$$$$$%%%##############################$$$$$$$$$######"""######$$$%%%%%%%%%%%%$$$!!!""""""#########""""""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&'''((((((''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$############$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$############$$$$$$%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%&&&''''''&&&%%%%%%&&&&&&&&&''''''''''''((('''''''''((((((((((((((((((((((((((())))))))))))((('''&&&%%%%%%&&&'''((('''''''''&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###"""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########"""""""""""""""###############$$$$$$%%%%%%%%%$$$######"""""""""###$$$$$$%%%%%%$$$$$$$$$###############"""###$$$$$$$$$$$$$$$$$$###########################""""""""""""###$$$$$$#########################################################$$$$$$$$$$$$$$$######################## !!!""""""######$$$########################$$$######"""""""""######""""""""""""###############$$$$$$$$$$$$###"""""""""""""""""""""""""""""""""############$$$$$$$$$########################$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$&&&'''&&&%%%%%%&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$&&&&&&%%%#########$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&'''''''''"""""""""##################""""""!!!!!!""""""###!!!!!!!!!"""######$$$$$$######$$$$$$$$$$$$############""""""""""""############""""""""""""######""""""!!!!!!!!!!!!""""""!!!!!!"""###############""""""""""""""""""""""""!!!!!!!!!"""######$$$$$$##############################$$$$$$$$$$$$############$$$$$$$$$$$$############$$$%%%%%%%%%%%%$$$&&&'''((())))))((('''&&&#################################$$$$$$$$$$$$%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&'''((((((((((((''''''''''''''''''(((((((((''''''''''''(((((((((((((((((((((((((((((((((((((((((())))))))))))(((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$##############################""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""###$$$%%%%%%$$$$$$$$$###############"""######$$$$$$$$$############$$$%%%%%%%%%%%%$$$""""""######$$$$$$############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&'''((((((&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%%%%&&&&&&###########################$$$$$$$$$$$$%%%%%%%%%###############$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%&&&&&&&&&&&&%%%$$$&&&&&&&&&''''''''''''(((''''''''''''((((((((()))'''''''''((((((((())))))((('''&&&%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########"""""""""!!!!!!!!!"""""""""#########$$$$$$%%%%%%%%%%%%$$$###"""!!!""""""###$$$$$$%%%%%%$$$$$$$$$#########""""""""""""###$$$$$$$$$$$$$$$########################"""""""""""""""###$$$$$$#########################################################$$$$$$%%%%%%%%%%%%%%%$$$$$$###""""""""" !!!!!!"""#######################################""""""""""""######""""""""""""###############$$$$$$$$$$$$###"""""""""""""""""""""""""""""""""############$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%'''((('''%%%$$$%%%'''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###""""""###%%%&&&$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&!!!"""""""""#########$$$#########""""""######### !!!!!!"""######$$$$$$######$$$$$$$$$$$$######""""""!!!!!!!!!!!!""""""######""""""""""""######""""""!!!!!!!!!!!!""""""!!!!!!"""###############"""""""""""""""""""""""" !!!!!!"""######$$$$$$##############################$$$$$$$$$$$$############$$$$$$$$$$$$############$$$%%%%%%%%%%%%$$$'''&&&&&&%%%%%%$$$$$$###########################$$$$$$$$$$$$%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%&&&'''(((''''''&&&&&&'''''''''((((((((()))''''''''''''(((((((((((((((((((((((((((((((((((((((((())))))))))))(((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%##################$$$$$$########################""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""###$$$%%%&&&$$$$$$$$$#########""""""!!!"""###$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$"""######$$$%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&'''((((((%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%&&&&&&''''''##############################$$$$$$$$$%%%%%%%%%######""""""###$$$%%%%%%%%%%%%&&&&&&&&&&&&''''''$$$$$$&&&&&&&&&&&&$$$$$$&&&&&&&&&'''''''''((((((&&&'''''''''(((((())))))''''''''''''((((((((((((((('''&&&%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""!!!!!!!!!!!!!!!!!!""""""#########$$$%%%%%%%%%%%%%%%$$$###"""!!!""""""###$$$$$$%%%%%%$$$$$$$$$$$$######""""""!!!"""###$$$$$$$$$$$$$$$########################"""""""""""""""######$$$""""""""""""""""""""""""#################################$$$$$$%%%%%%%%%&&&%%%%%%$$$###"""!!!!!! !!!!!!"""#########""""""""""""""""""""""""###"""""""""""""""######""""""""""""###############$$$$$$$$$$$$###"""""""""""""""""""""""""""""""""############$$$$$$$$$#################################$$$$$$#########""""""######$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%''')))'''$$$###$$$&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###""""""###%%%%%%$$$"""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$!!!!!!""""""#########$$$$$$$$$############$$$$$$ !!!!!!"""###$$$$$$$$$######$$$$$$$$$$$$######!!!!!! !!!!!!######""""""""""""######""""""!!!!!!!!!!!!""""""!!!!!!"""###############"""""""""""""""""""""""" !!!!!!"""###$$$$$$$$$""""""""""""""""""""""""######$$$$$$$$$$$$############$$$$$$$$$$$$############$$$%%%%%%%%%%%%$$$&&&&&&$$$###"""!!!!!!!!!""""""""""""""""""""""""$$$$$$%%%%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$&&&'''''''''&&&%%%&&&'''''''''(((((())))))''''''''''''((((((((()))))))))))))))))))))))))))(((((())))))))))))(((((((((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%##################$$$$$$########################""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""###$$$%%%&&&$$$$$$$$$$$$######"""""" !!!"""###$$$%%%%%%%%%######$$$%%%%%%%%%%%%$$$"""###$$$%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&'''((((((%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&'''(((((("""""""""""""""""""""""""""############$$$$$$$$$######""""""######$$$%%%###%%%&&&%%%######$$$%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&'''''''''''''''(((((((((((()))''''''(((((('''&&&%%%%%%%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%&&&&&&&&&&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$#########"""""" !!!!!!""""""##############################$$$#########""""""!!!!!!""""""""""""############%%%%%%$$$###"""""""""###""""""############""""""$$$#########""""""!!!!!!################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!"""""""""""""""""""""""""""######$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!!!! $$$#########""""""!!!!!!""""""""""""############$$$$$$$$$############"""%%%$$$$$$$$$######""""""#########"""######$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&'''((((((&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$%%%%%%%%%$$$$$$#########&&&%%%%%%$$$$$$%%%%%%&&&"""############$$$$$$$$$"""!!!  !!!"""$$$$$$##################%%%%%%$$$$$$###"""!!!!!!""""""""""""""""""""""""!!!!!!!!!!!!"""""""""""" """""""""!!! #########""""""""""""""" """###$$$$$$###""" """"""""""""####################################""""""""""""""""""""""""$$$$$$###"""!!!!!!""""""########################!!!!!!"""###############""""""""""""""""""""""""########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''((((((((('''''''''&&&&&&&&&%%%&&&''''''%%%%%%&&&'''&&&&&&&&&&&&&&&'''((()))((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''&&&&&&))))))((((((''''''''''''((('''%%%######$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################""""""############""""""!!!!!!!!!!!!!!!!!!!!!!!!################################################!!!###$$$$$$######$$$%%%########################%%%%%%%%%$$$$$$#########%%%$$$#########$$$%%%&&&"""######$$$$$$%%%&&&&&&'''&&&%%%%%%$$$$$$$$$$$$$$$%%%&&&%%%###"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&"""""""""""""""""""""""""""############$$$$$$$$$######""""""######$$$%%%###$$$%%%%%%######$$$%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&'''''''''(((((((((''''''(((((('''&&&&&&%%%%%%&&&&&&&&&&&&%%%$$$$$$###$$$$$$%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$#########""""""!!!!!!!!!"""""""""""""""""""""""""""""""""""""""############"""""""""!!!""""""""""""############%%%$$$######""""""######""""""############""""""$$$#########""""""""""""################################################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""!!!""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!"""""""""""""""""""""""""""######$$$#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""!!!!!! ############"""""""""!!!""""""""""""############$$$$$$$$$#########""""""$$$$$$#########"""""""""######""""""######$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######&&&%%%%%%$$$$$$%%%%%%&&&"""############$$$$$$$$$""""""!!! !!!""""""########################%%%%%%$$$$$$###""""""!!!""""""""""""""""""""""""!!!!!!"""""""""######### !!!!!!"""""""""!!!!!!###"""""""""""""""""""""!!!"""###$$$$$$###"""!!!""""""""""""############################################################$$$$$$$$$######"""""""""########################!!!!!!"""###############################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''(((((('''''''''&&&&&&&&&&&&%%%&&&''''''%%%%%%&&&'''&&&&&&&&&&&&&&&'''((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((('''''''''&&&&&&(((&&&%%%######$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################""""""############""""""""""""""""""""""""""""""################################################!!!###$$$$$$######$$$%%%########################%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$#########$$$%%%&&&"""######$$$$$$%%%&&&&&&'''&&&%%%$$$$$$$$$$$$$$$$$$%%%&&&%%%###"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$%%%###$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&"""""""""""""""""""""""""""############$$$$$$$$$######""""""######$$$%%%###$$$%%%%%%######$$$%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&'''''''''''''''(((''''''&&&%%%&&&&&&&&&&&&&&&%%%$$$$$$######$$$%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$###############""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!############""""""""""""""""""""""""############$$$$$$###"""""""""######""""""############""""""###############"""""""""################################################$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$###"""!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!"""""""""""""""""""""""""""######$$$#########$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""!!!!!!!!!############""""""""""""""""""""""""############$$$$$$#########"""""""""######""""""""""""!!!!!!"""""""""""""""###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&(((((('''&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%"""############$$$$$$$$$######""""""""""""##############################%%%%%%$$$$$$###"""""""""""""""""""""""""""""""""""""""#########$$$$$$$$$######""""""""""""""""""""""""""""""""""""######!!!"""###$$$$$$###"""!!!"""""""""#########$$$$$$###################################################$$$%%%%%%%%%$$$###"""########################!!!!!!"""#######################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&''''''''''''''''''&&&&&&&&&&&&%%%&&&''''''%%%%%%&&&'''&&&&&&&&&&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&'''&&&%%%$$$###$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################""""""############""""""########################################################################!!!###$$$$$$######$$$%%%########################$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%&&&"""######$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%$$$%%%&&&%%%#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&""""""""""""""""""""""""""""""#########$$$$$$$$$######""""""######$$$%%%"""$$$%%%%%%$$$###$$$&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%%%%%%%&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&'''&&&%%%%%%$$$"""###$$$$$$%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%########################$$$######""""""!!!!!!!!!""""""""""""""""""""""""#########"""""""""""""""!!!"""""""""##################""""""""""""######"""######$$$$$$######"""########################################################################$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$###"""!!!!!!!!!""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!"""""""""""""""""""""""""""######$$$############$$$$$$$$$$$$####################################""""""!!!!!!#########"""""""""""""""!!!"""""""""########################"""""""""""""""""""""!!!!!!!!!!!!!!!""""""!!!""""""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$##################$$$$$$$$$%%%%%%%%%&&&&&&((('''&&&%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%""""""#########$$$$$$$$$#######################################$$$$$$$$$$$$$$$$$$#########""""""""""""""""""""""""""""""######$$$$$$$$$%%%%%%%%%&&&%%%###"""!!!"""######"""""""""""""""#########!!!"""############"""!!!""""""#########$$$$$$$$$###################################################$$$&&&''''''&&&$$$###########################!!!!!!"""#######################################$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''%%%%%%&&&'''&&&&&&&&&%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################""""""############""""""$$$$$$$$$$$$$$$$$$$$$$$$################################################!!!###$$$$$$######$$$%%%#################################$$$$$$%%%%%%%%%#########$$$$$$%%%&&&&&&"""######$$$$$$%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%###%%%%%%%%%######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&""""""""""""""""""""""""""""""#########$$$$$$$$$######""""""######$$$%%%"""###%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&&&&'''''''''&&&%%%%%%######$$$%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%########################$$$$$$######""""""!!!!!!########################""""""""""""""""""######!!!"""""""""###############""""""!!!""""""############$$$$$$$$$$$$#####################$$$$$$$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$###""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!"""""""""""""""""""""""""""######$$$""""""#########$$$$$$$$$#################################"""""""""""""""""""""""""""""""""######!!!"""""""""#####################"""""""""!!!!!!!!!!!!!!!!!!!!!"""""""""!!!!!!!!!!!!"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$##################$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&'''(((&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%""""""#########$$$$$$$$$######$$$$$$$$$$$$######""""""#########$$$$$$$$$$$$$$$$$$###############""""""""""""""""""""""""$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%$$$"""""""""###$$$!!!!!!""""""############""""""############""""""############$$$$$$$$$$$$###################################################$$$&&&''''''&&&%%%###########################!!!!!!"""#######################################$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%&&&''''''%%%%%%&&&''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""############""""""$$$$$$$$$$$$$$$$$$$$$$$$################################################!!!###$$$$$$######$$$%%%#################################$$$$$$%%%%%%%%%""""""###$$$%%%%%%&&&&&&"""######$$$$$$%%%&&&&&&$$$$$$$$$######$$$$$$%%%###$$$%%%%%%######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%&&&###$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&"""""""""""""""""""""""""""############$$$$$$$$$######""""""######$$$%%%"""###$$$%%%$$$$$$%%%'''&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&''''''(((''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%###############$$$$$$$$$##################""""""########################""""""""""""############""""""""""""############""""""!!!!!!!!!"""############$$$$$$$$$$$$###############$$$$$$$$$$$$$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$############$$$""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!"""""""""""""""""""""""""""######$$$"""""""""############$$$##############################""""""""""""""""""""""""""""""############""""""""""""##################"""""""""!!!!!!!!!!!!!!!""""""""""""###### !!!"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&'''((((((&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$############$$$$$$"""############$$$$$$$$$######$$$$$$$$$$$$######"""""""""###$$$$$$%%%%%%########################""""""""""""""""""""""""######$$$$$$$$$%%%%%%%%%$$$$$$##################!!!!!!!!!"""######$$$$$$###""""""""""""""""""############$$$$$$$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&&&&%%%$$$########################!!!!!!"""###############$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&''''''%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''(((((((((&&&&&&&&&&&&&&&'''''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""############""""""$$$$$$$$$$$$$$$$$$$$$$$$################################################!!!###$$$$$$######$$$%%%########################$$$$$$$$$$$$$$$$$$%%%%%%!!!"""###$$$%%%&&&&&&&&&"""######$$$$$$%%%&&&&&&$$$############$$$$$$%%%"""$$$%%%%%%$$$###$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&"""""""""""""""""""""""""""############$$$$$$$$$######""""""######$$$%%%!!!###$$$$$$$$$$$$%%%'''&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&'''(((((('''''''''''''''''''''&&&&&&%%%%%%%%%&&&''''''''''''&&&$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%""""""#########$$$$$$$$$##################$$$$$$########################!!!"""""""""############""""""""""""############!!!!!!!!!!!!!!!"""#########$$$$$$%%%%%%$$$$$$############$$$$$$%%%%%%%%%################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%%%%""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!"""""""""""""""""""""""""""######$$$""""""""""""####################################"""""""""""""""""""""###!!!"""""""""############""""""""""""###############"""""""""!!!!!!!!!!!!"""""""""#########$$$$$$ """###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$############$$$$$$"""############$$$$$$$$$""""""###$$$$$$###""""""!!!""""""###$$$$$$%%%%%%########################""""""""""""""""""""""""############$$$$$$$$$$$$""""""################## !!!!!!"""######$$$$$$######""""""""""""###############$$$$$$$$$%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$%%%%%%%%%%%%########################!!!!!!"""###############$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&''''''%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''(((((()))&&&&&&'''''''''(((((((((%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""############""""""$$$$$$$$$$$$$$$$$$$$$$$$################################################!!!###$$$$$$######$$$%%%########################%%%%%%$$$$$$$$$$$$$$$$$$ !!!###%%%&&&&&&&&&&&&"""######$$$$$$%%%&&&&&&###############$$$%%%%%%"""$$$%%%%%%$$$###%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%####################################$$$%%%&&&'''###$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&"""""""""""""""""""""""""""############$$$$$$$$$#########"""###$$$$$$%%%!!!###$$$$$$$$$$$$&&&'''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&&&&''''''%%%%%%&&&'''((((((((('''''''''((((((''''''&&&%%%%%%&&&''''''((((((''''''$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%""""""######$$$$$$$$$$$$"""""""""###$$$$$$$$$%%%""""""""""""""""""""""""!!!!!!""""""#########$$$""""""""""""############!!!!!!!!!!!!!!!"""#########$$$$$$%%%%%%$$$$$$############$$$$$$%%%%%%%%%################################################$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&&&&""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!"""""""""""""""""""""""""""######$$$""""""""""""############"""""""""""""""""""""""""""""""""""""""#########!!!!!!""""""#########$$$""""""""""""############""""""""""""!!!!!!!!!!!!""""""######$$$$$$$$$%%% !!!###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%&&&&&&''''''$$$$$$%%%%%%%%%&&&&&&&&&(((((('''&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$############$$$$$$"""############$$$$$$$$$!!!"""###$$$$$$###"""!!!!!!""""""###$$$$$$%%%%%%##################$$$$$$""""""""""""""""""""""""""""""#########$$$$$$$$$!!!"""$$$$$$$$$###""" !!!!!!"""###$$$$$$$$$######""""""""""""############$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&########################!!!!!!"""###############$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&''''''%%%%%%&&&''''''&&&%%%%%%$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((())))))'''''''''((((((((())))))%%%%%%&&&&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$########################""""""############""""""########################################################################!!!###$$$$$$######$$$%%%########################&&&%%%%%%$$$$$$######### !!!###%%%&&&&&&&&&&&&"""######$$$%%%%%%&&&&&&######""""""###$$$%%%%%%"""###%%%%%%$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%####################################$$$%%%&&&'''$$$$$$%%%&&&&&&&&&%%%%%%$$$%%%&&&&&&$$$$$$%%%&&& !!!!!!""""""############$$$%%%%%%%%%%%%$$$########################""""""###$$$%%%%%%&&&&&&'''&&&%%%%%%$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%'''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$#########""""""%%%%%%%%%$$$$$$$$$######################################################"""############$$$$$$$$$########################!!!!!!""""""############$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################""""""""""""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###"""!!! #########""""""""""""""" !!!!!!"""###$$$$$$$$$####################################""""""""""""#########"""""""""""""""#################################"""######$$$$$$!!!  !!!"""###$$$$$$$$$#########""""""""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$##############################$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$#########"""""""""!!! !!!###$$$!!!!!!""""""######$$$$$$$$$#########""""""!!!!!! !!!"""######$$$###$$$$$$%%%%%%$$$$$$###$$$$$$############$$$$$$################################################"""############$$$$$$$$$########################"""############$$$$$$$$$######$$$$$$$$$$$$######"""############$$$$$$$$$""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&(((((((((((((((((((((((((((((('''''''''&&&&&&&&&'''&&&&&&%%%$$$$$$$$$%%%#########$$$$$$%%%%%%%%%$$$$$$$$$#########""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""############""""""""""""$$$$$$##################################################################$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%$$$$$$#########%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$#########""""""#########$$$$$$%%%%%%%%%$$$$$$$$$$$$######"""""""""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!!!!!!!"""""""""""""""###$$$$$$%%%%%%$$$$$$#################################$$$$$$%%%%%%%%%'''&&&%%%$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%$$$'''&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######%%%%%%%%%$$$$$$$$$######################################################""""""#########$$$$$$$$$########################"""""""""#########$$$$$$%%%$$$###""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################""""""""""""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############""""""""""""###""""""""""""""""""""" !!!!!!"""######$$$$$$####################################""""""""""""###"""""""""""""""""""""########################$$$$$$######"""#########!!!  !!!"""###$$$$$$$$$#########""""""""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%%%%$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$########################"""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$#########""""""""""""!!! !!!"""###$$$"""""""""""""""#####################"""""""""!!! !!!!!!""""""######"""######$$$$$$######"""$$$$$$############$$$$$$################################################"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$######$$$$$$$$$$$$######!!!!!!"""""""""#########""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&((((((((((((((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$#########""""""""""""""""""""""""""""""!!!!!!!!!"""""""""""""""!!!!!!!!!!!!"""""""""###############""""""""""""########################################################################$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$#########"""############$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&""""""""""""!!!!!!!!!!!!""""""###$$$$$$$$$$$$$$$##############################$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&(((''''''&&&%%%$$$$$$###&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%%%%$$$$$$$$$######################################################"""""""""#########$$$$$$#######################################$$$$$$$$$%%%$$$"""!!!!!!###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################""""""""""""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!""""""#########$$$""""""""""""""""""######!!!!!!!!!"""######$$$$$$####################################""""""""""""""""""""""""""""""##############################%%%$$$######""""""""""""!!!!!! !!!""""""$$$############"""""""""""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$########################"""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$###############""""""!!!!!!""""""###$$$############""""""""""""############"""""""""""""""""""""""""""""""""""""""""""""######"""""""""$$$$$$############$$$$$$################################################"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""############$$$$$$$$$######$$$$$$$$$$$$###### !!!!!!!!!""""""""""""""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''((((((((((((((((((((((((''''''''''''&&&&&&&&&&&&%%%%%%$$$$$$######$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$###############"""""""""""""""""""""""" !!!!!!""""""#########!!!!!!!!!"""""""""##################""""""""""""########################""""""""""""""""""""""""########################%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$############$$$%%%%%%$$$$$$$$$###############%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''######""""""!!!!!! !!!""""""###$$$#################################$$$$$$$$$$$$############%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%&&&(((''''''&&&%%%$$$######%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%$$$$$$$$$######################################################""""""""""""################################################$$$$$$$$$$$$%%%$$$"""!!!!!!###%%%&&&############$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################!!!"""""""""########################$$$$$$$$$$$$########################""""""""""""############"""""""""""""""#########!!!!!!""""""################################################"""""""""!!!"""""""""""""""#################################%%%%%%$$$"""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""############""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!##############################$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$########################""""""###$$$$$$$$$$$$$$$########################""""""#########$$$$$$$$$########################""""""""""""######$$$$$$$$$$$$######""""""!!!!!!#########"""""""""""""""######""""""""""""""""""""""""############""""""$$$$$$############$$$$$$################################################""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""#########$$$$$$$$$######$$$$$$$$$$$$######!!!!!!!!!"""""""""######""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################"""""""""""""""""""""""" !!!"""######$$$$$$!!!!!!"""""""""#####################"""""""""!!!""""""""""""############!!!!!!!!!!!!!!!!!!!!!!!!########################&&&%%%$$$######$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%########################%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$&&&'''((((((######""""""!!!!!! !!!""""""######""""""""""""""""""""""""""""""$$$#####################$$$$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%$$$$$$%%%%%%%%%''''''&&&%%%$$$$$$######$$$$$$$$$######$$$$$$%%%############$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######################################################!!!!!!"""""""""#########################################################$$$###"""!!!"""###%%%&&&"""""""""######$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################!!!"""""""""############"""""""""######$$$$$$$$$####################################""""""""""""!!!!!!""""""############"""""""""""""""#########""""""""""""""""""""""""############"""""""""!!!!!!!!!""""""####################################%%%$$$###"""!!!!!!!!!!!!""""""""""""""""""!!!!!!""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!########################"""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################""""""###$$$$$$$$$$$$###########################""""""#########$$$$$$$$$########################"""######$$$$$$$$$$$$$$$$$$$$$######""""""!!!!!!""""""""""""""""""##################""""""""""""###$$$$$$$$$$$$$$$$$$###$$$$$$############$$$$$$################################################""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""#########$$$$$$$$$######$$$$$$$$$$$$######"""""""""#########$$$$$$""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################"""""""""""""""""""""""" !!!!!!"""###$$$$$$%%%""""""""""""########################"""""""""!!!!!!!!!"""""""""#########!!!!!!!!!!!!!!!!!!!!!!!!########################%%%%%%###""""""###%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%########################%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$&&&'''((((((""""""""""""!!!!!!!!!!!! !!!"""""""""""""""""""""""""""""""""""""""""""""##################$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$############$$$$$$%%%"""###############$$$$$$%%%%%%%%%$$$$$$$$$######################################################!!!!!!!!!"""""""""#######################################"""""""""""""""""""""""""""###$$$%%%%%%!!!!!!""""""###$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################""""""""""""############!!!!!!""""""###$$$$$$$$$########################$$$#########""""""!!!!!!!!!!!!!!!"""######$$$$$$""""""""""""""""""######""""""""""""""""""""""""############""""""""""""!!!!!!!!!"""######$$$$$$########################$$$###""""""!!!!!!!!!!!!""""""#########"""!!!!!!!!!!!!"""""""""""""""###""""""""""""""""""""""""########################""""""###$$$$$$$$$$$$############$$$$$$$$$$$$$$$######$$$$$$$$$$$$###############$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$$$$$$$########################!!!"""######$$$$$$##############################"""############$$$$$$$$$###############$$$$$$$$$######$$$%%%%%%%%%%%%$$$############""""""""""""""""""""""""####################################$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$############$$$$$$################################################"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""############$$$$$$$$$######$$$$$$$$$$$$##################$$$$$$$$$$$$""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$##################$$$$$$$$$""""""""""""""""""""""""!!!""""""######$$$$$$$$$"""""""""#########$$$$$$############"""""""""""" !!!!!!""""""#########""""""""""""""""""""""""########################$$$$$$############$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$############$$$%%%%%%###############$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''!!!!!!!!!!!!"""""""""""" !!!!!!""""""!!!!!!""""""""""""""""""""""""!!!!!!""""""######$$$$$$###############$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%###############$$$%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######################################################!!!!!!!!!!!!"""""""""###########################"""""""""!!!!!!!!! !!!###$$$%%%%%%$$$$$$!!!!!!!!!"""###$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################""""""""""""############!!!!!!!!!"""###$$$$$$$$$########################""""""""""""############ !!!!!!"""######$$$$$$###"""""""""""""""""""""""""""""""""""""""""""""############"""""""""""" !!!!!!"""######$$$$$$###########################""""""!!!!!!!!!"""""""""######$$$###"""!!! !!!!!!!!!!!!""""""######""""""""""""""""""""""""########################!!!""""""###############"""#########$$$$$$$$$$$$######$$$$$$$$$$$$######"""#########$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""#########$$$$$$$$$$$$########################!!!""""""#######################################"""############$$$$$$$$$""""""#########$$$$$$$$$###$$$%%%&&&&&&&&&%%%$$$"""""""""""""""#########!!!"""""""""############"""""""""######$$$$$$%%%######$$$$$$$$$$$$######$$$$$$############$$$$$$################################################"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$######$$$$$$$$$$$$######""""""""""""############""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((%%%%%%%%%$$$$$$$$$######""""""#########$$$$$$$$$""""""""""""""""""""""""########################""""""#########$$$$$$$$$############"""""""""""" !!!!!!"""######$$$######################################################$$$$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&& !!!!!!""""""###### !!!!!!!!!!!!!!!"""""""""""""""""""""""" !!!!!!"""###$$$$$$%%%######""""""###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%$$$$$$$$$$$$$$$$$$%%%"""######$$$$$$%%%&&&&&&######""""""###$$$%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$######################################################!!!!!!!!!!!!""""""""""""########################""""""!!!!!! !!!###%%%&&&%%%$$$### !!!!!!"""###$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################""""""""""""############ !!!!!!"""###$$$$$$$$$"""""""""""""""""""""""" !!!"""###$$$%%%%%% !!!!!!"""###$$$$$$$$$#########"""""""""""""""""""""""""""""""""""""""############"""""""""""" !!!!!!"""###$$$$$$$$$########################"""!!!!!!!!!!!!""""""###"""###$$$$$$$$$"""!!! !!!!!!!!!""""""######""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!"""###############""""""######$$$$$$$$$$$$######$$$$$$$$$$$$######""""""######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$$$$$$$$$$########################!!!!!!"""###############"""""""""""""""""""""""""""############$$$$$$$$$""""""######$$$$$$$$$$$$###$$$%%%&&&'''&&&%%%%%%!!!!!!""""""######$$$$$$!!!!!!""""""#########$$$!!!!!!"""###$$$%%%%%%%%%""""""############""""""$$$$$$############$$$$$$################################################"""############$$$$$$$$$########################"""############$$$$$$$$$######$$$$$$$$$$$$######!!!!!!!!!!!!""""""""""""""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''((()))%%%%%%%%%$$$$$$#########""""""######$$$$$$$$$$$$""""""""""""""""""""""""$$$$$$$$$###############"""############$$$$$$$$$############"""""""""""" !!!"""######$$$################################################"""###$$$%%%%%%$$$###"""#########$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''""""""######$$$$$$$$$$$$#########$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!""""""""""""!!!!!!""""""""""""############"""""""""###$$$$$$$$$%%%""""""#########$$$$$$$$$%%%%%%%%%$$$$$$#########"""############$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&'''&&&&&&&&&''''''''''''(((***)))((('''&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%$$$###"""&&&&&&$$$$$$$$$$$$&&&&&&""""""###$$$%%%%%%&&&&&&%%%$$$###!!!!!!!!!"""##################"""!!!!!!""""""!!!!!!!!!!!!""""""""""""""""""############$$$$$$$$$#########"""""""""############$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$######""""""""""""###$$$%%%%%%&&&&&&###############$$$$$$$$$$$$$$$$$$#####################$$$$$$$$$######"""%%%%%%$$$###""""""###### !!!"""######"""!!! ######""""""""""""######$$$$$$##################!!!"""###$$$$$$$$$$$$$$$$$$$$$###"""!!!!!!""""""$$$$$$######"""!!!!!! """"""""""""""""""""""""""""""############""""""######$$$$$$$$$######"""""""""""""""""""""""""""%%%$$$#########$$$%%%&&&%%%$$$$$$######$$$$$$%%%#########$$$$$$%%%%%%%%%%%%%%%$$$$$$###$$$$$$$$$&&&%%%###$$$%%%%%%$$$"""#########"""""""""""""""########################%%%%%%%%%%%%%%%$$$###"""$$$$$$###"""!!!!!!"""""""""############$$$$$$$$$"""######$$$$$$######"""%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$######""""""$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$""""""#########$$$$$$$$$%%%$$$#########$$$%%%&&&"""######$$$$$$######""""""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########""""""""""""""""""""""""%%%$$$$$$$$$###"""""""""########################%%%$$$$$$######$$$$$$%%% ######!!!!!!%%%'''%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$##################"""############$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$######$$$$$$%%%&&&(((((('''&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&%%%&&&%%%$$$#########$$$%%%###$$$%%%%%%%%%%%%$$$###########################""""""!!!!!!!!!!!!""""""######$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$###"""""""""$$$$$$######"""#########%%%%%%%%%$$$$$$#########$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''!!!!!!""""""""""""!!!!!!""""""""""""###########################$$$$$$$$$""""""#########$$$$$$$$$%%%%%%%%%$$$$$$#########"""############$$$$$$$$$%%%$$$$$$$$$%%%%%%&&&'''&&&&&&&&&&&&''''''''''''((('''&&&%%%%%%$$$$$$%%%%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%$$$###"""%%%$$$$$$######$$$$$$%%%#########$$$$$$%%%%%%&&&%%%$$$###"""!!!!!!"""##################"""!!!!!!""""""!!!!!!!!!!!!""""""""""""""""""############$$$$$$$$$#########"""""""""############$$$$$$$$$$$$$$$%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$#########""""""######$$$%%%%%%&&&&&&$$$$$$$$$#################################$$$$$$######$$$$$$$$$######"""%%%$$$$$$###""""""######!!!"""############"""!!!######""""""""""""##############################""""""###$$$$$$$$$######$$$$$$###"""""""""""""""%%%$$$$$$###""""""!!!!!!""""""""""""""""""""""""""""""############""""""""""""############""""""""""""""""""""""""""""""$$$$$$#########$$$%%%&&&%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$###$$$$$$%%%&&&$$$###$$$%%%%%%$$$###############""""""""""""########################%%%%%%%%%%%%%%%$$$###"""$$$$$$###""""""""""""""""""############$$$$$$$$$######$$$$$$$$$$$$######%%%$$$$$$######$$$$$$%%%############""""""!!!!!!$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$#########$$$$$$$$$$$$%%%$$$$$$#########$$$%%%&&&######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#######################################%%%$$$$$$######$$$$$$%%%$$$%%%$$$!!!###&&&$$$ $$$%%%%%%&&&&&&%%%%%%$$$########################"""############$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$######$$$$$$%%%&&&(((''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$######$$$$$$%%%###$$$%%%%%%%%%%%%$$$#################################""""""""""""############$$$$$$$$$%%%%%%%%%$$$$$$$$$###############$$$$$$############$$$$$$$$$$$$$$$######"""""""""########################%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&&&&%%%%%%''''''''''''''''''''''''!!!""""""######""""""!!!"""""""""#########$$$$$$$$$$$$$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$#########"""############$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&''''''''''''%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%$$$######"""######$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""""""""###############$$$######"""!!!###""""""!!!!!!""""""###""""""""""""############$$$$$$$$$###############"""############$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$##################$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$######"""""""""""""""###$$$$$$$$$%%%"""######$$$$$$$$$######%%%$$$######"""#########"""######$$$$$$######"""######""""""""""""####################################$$$$$$$$$######"""$$$###""""""""""""""""""%%%%%%%%%$$$######""""""""""""""""""""""""""""""""""""############""""""!!!!!!"""""""""""""""!!!""""""""""""""""""""""""$$$############$$$%%%%%%%%%$$$$$$######$$$$$$%%%###$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%%%%$$$###$$$%%%&&&%%%$$$################################################$$$$$$%%%%%%%%%$$$######$$$$$$###""""""""""""###"""############$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$############$$$$$$"""""""""""""""!!!!!!!!!$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$&&&%%%$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$########################$$$$$$############$$$$$$%%%%%%$$$###'''+++((( $$$$$$%%%%%%%%%%%%$$$$$$########################"""############$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&''''''&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$######$$$%%%%%%###$$$$$$%%%%%%$$$$$$###########################$$$$$$############$$$$$$######$$$$$$$$$%%%%%%%%%###############$$$$$$$$$%%%$$$$$$###$$$$$$%%%%%%#########"""""""""""""""########################%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&"""""""""######"""""""""""""""#########$$$$$$$$$%%%$$$$$$$$$###"""""""""########################$$$$$$$$$###############""""""#########$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&'''''''''$$$$$$$$$$$$$$$%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$###"""###$$$%%%%%%$$$###"""%%%%%%$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$######"""###""""""""""""""""""###!!!"""""""""####################################""""""#########$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%$$$######""""""!!!!!!"""###$$$%%%%%%%%%""""""###$$$$$$$$$######$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""""""""#####################$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!######"""""""""""""""###%%%%%%%%%$$$$$$$$$######""""""""""""""""""""""""""""""############""""""!!!""""""############"""""""""""""""""""""""""""###############$$$$$$%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%$$$###$$$&&&&&&&&&%%%"""###############$$$$$$########################$$$$$$%%%%%%%%%$$$$$$###$$$$$$###""""""#########""""""#########$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$############$$$$$$############""""""""""""$$$$$$############$$$$$$########################""""""#########$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$###$$$$$$$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$(((&&&$$$"""""""""$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############"""""""""""""""""""""""""""""""""###$$$$$$$$$%%%########################$$$$$$############$$$$$$$$$###"""%%%,,,222---%%%$$$$$$%%%%%%%%%%%%$$$$$$""""""""""""############""""""#########$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$######""""""######$$$######$$$$$$$$$%%%%%%%%%"""""""""###$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%&&&##################""""""###############$$$$$$$$$%%%%%%&&&&&&&&&&&&''''''###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&""""""############""""""############$$$$$$$$$$$$%%%$$$$$$$$$###"""""""""################################################""""""#########$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''$$$$$$$$$$$$%%%&&&'''(((%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$###$$$$$$%%%%%%%%%$$$$$$###$$$%%%&&&&&&%%%$$$###%%%%%%$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$#########$$$$$$$$$$$$############""""""""""""######!!!"""""""""####################################""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&'''&&&&&&%%%$$$###""""""!!!!!!"""###$$$%%%%%%%%%!!!"""###$$$$$$$$$$$$$$$$$$###############$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%######""""""""""""######""""""#########$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!###"""""""""""""""######%%%%%%%%%$$$$$$$$$$$$$$$""""""""""""""""""""""""""""""############"""""""""###$$$$$$%%%%%%%%%$$$""""""""""""""""""""""""""""""######$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%&&&&&&%%%$$$$$$&&&'''&&&$$$""""""######$$$$$$$$$%%%###########################$$$$$$%%%%%%%%%$$$$$$$$$###############$$$$$$""""""#########$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$########################""""""#########$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&######$$$$$$%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$(((&&&$$$"""""""""$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################!!!!!!!!!!!!!!!!!!!!!!!!"""""""""###$$$$$$$$$%%%""""""""""""""""""""""""$$$######""""""######$$$""""""!!!###+++000,,,######$$$$$$%%%%%%$$$$$$###!!!!!!"""""""""#########""""""#########$$$$$$$$$#########$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$############$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""""""""!!!!!!!!!!!!""""""######$$$$$$$$$%%%%%%%%%"""""""""###$$$$$$$$$%%%$$$#########$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$%%%%%%%%%&&&&&&'''''''''#########$$$$$$$$$%%%%%%############$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&"""######$$$$$$######"""#########$$$$$$$$$$$$%%%$$$$$$$$$###############$$$$$$$$$###############"""""""""###############"""############$$$$$$$$$&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$%%%$$$$$$$$$"""###$$$$$$%%%$$$$$$$$$$$$######""""""######$$$""""""""""""###########################$$$$$$$$$"""############$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$######"""""""""###$$$$$$$$$%%%!!!"""###$$$$$$$$$$$$$$$#########"""######$$$%%%%%%$$$$$$######$$$$$$%%%######""""""""""""######"""""""""###$$$$$$%%%%%%######$$$$$$$$$######""""""""""""""""""######$$$$$$$$$$$$$$$$$$$$$######""""""""""""""""""""""""""""""############""""""######$$$%%%&&&&&&&&&&&&""""""""""""""""""""""""!!!"""######$$$$$$######%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$###############$$$%%%&&&&&&(((&&&%%%%%%&&&&&&%%%###""""""######$$$%%%%%%%%%##############################$$$%%%%%%%%%$$$$$$$$$############$$$%%%%%%"""############$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######""""""""""""######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$############$$$$$$########################"""############$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%"""###$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%$$$$$$&&&%%%$$$#########$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$"""""""""######################################################$$$$$$$$$""""""""""""""""""""""""######""""""""""""######""""""!!! $$$((($$$######$$$$$$$$$$$$###### !!!!!!""""""#########"""############$$$$$$$$$############$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%$$$$$$$$$$$$"""######$$$$$$######"""""""""$$$%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%""""""""""""""""""""""""""""""!!!!!!!!!!!!""""""######$$$$$$$$$%%%%%%%%%###############$$$$$$$$$""""""""""""###$$$%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%"""""""""###$$$$$$%%%%%%$$$$$$%%%%%%&&&&&&''''''############$$$$$$$$$$$$######"""######$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$$$$######"""#########$$$$$$$$$%%%%%%###############$$$$$$$$$$$$$$$$$$#########""""""!!!"""""""""#########$$$"""############$$$$$$$$$'''&&&%%%%%%$$$$$$$$$%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$%%%&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%&&&$$$%%%%%%%%%%%%%%%%%%&&&"""###$$$%%%%%%%%%%%%$$$%%%%%%$$$$$$$$$$$$%%%%%%#########$$$$$$%%%%%%&&&"""###$$$%%%%%%%%%$$$$$$"""###$$$$$$%%%%%%%%%$$$$$$######""""""######$$$""""""""""""############""""""#########$$$$$$$$$"""############$$$$$$$$$%%%$$$###""""""###$$$%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%##################$$$$$$!!!!!!"""$$$$$$%%%%%%$$$######""""""###$$$$$$%%%%%%$$$###""""""###$$$%%%######""""""""""""######!!!""""""###$$$$$$%%%%%%""""""###$$$$$$$$$######"""""""""""""""###$$$$$$########################""""""""""""""""""""""""""""""############""""""""""""###$$$%%%&&&&&&%%%"""""""""""""""""""""""" !!!"""###$$$######"""%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$##################$$$%%%&&&''')))(((&&&&&&&&&&&&$$$"""""""""###$$$$$$%%%&&&&&&########################"""###$$$%%%%%%%%%%%%$$$$$$#########$$$$$$%%%&&&"""############$$$$$$$$$######$$$$$$$$$$$$############""""""""""""############$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$########################"""############$$$$$$$$$#########$$$$$$$$$$$$%%%"""###$$$%%%%%%%%%$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$%%%%%%########################!!!"""""""""#########$$$########################$$$$$$$$$###############""""""""""""""""""""""""######""""""""""""######"""###"""!!!$$$#########$$$$$$$$$$$$###### !!!!!!"""######$$$"""############$$$$$$$$$############$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""############""""""!!!"""$$$%%%&&&&&&%%%%%%%%%%%%$$$######$$$%%%%%%""""""""""""""""""""""""###""""""""""""""""""#########$$$$$$$$$%%%%%%%%%$$$$$$$$$###############!!!!!!!!!!!!"""###$$$%%%"""#########$$$$$$$$$$$$!!!""""""###$$$$$$%%%%%%######$$$$$$%%%&&&&&&&&&############$$$$$$$$$$$$""""""""""""###$$$%%%&&&########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$############$$$$$$$$$%%%%%%%%%""""""######$$$$$$$$$%%%$$$$$$$$$$$$######""""""!!!!!!""""""#########$$$"""############$$$$$$$$$'''&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$###############$$$%%%&&&&&&''''''&&&&&&%%%#########$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&"""###$$$%%%%%%%%%%%%%%%%%%$$$###""""""###$$$%%%""""""###$$$%%%%%%&&&&&&"""###$$$%%%&&&%%%%%%$$$"""###$$$%%%%%%%%%%%%%%%$$$$$$############$$$$$$""""""""""""############""""""######$$$$$$$$$$$$"""############$$$$$$$$$%%%$$$###""""""###$$$%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$###############!!!!!!"""$$$$$$%%%%%%%%%######""""""###$$$%%%%%%%%%$$$###""""""###$$$%%%######""""""""""""######!!!""""""###$$$$$$%%%%%%!!!"""###$$$$$$$$$$$$$$$""""""!!!""""""###$$$$$$""""""""""""""""""######""""""""""""""""""""""""""""""############""""""!!!!!!"""$$$$$$%%%%%%%%%"""""""""""""""""""""""" !!!"""$$$$$$######"""%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$#####################$$$%%%&&&'''***)))'''&&&&&&%%%###!!!""""""###$$$%%%%%%&&&&&&########################"""###$$$%%%%%%%%%%%%%%%$$$#########$$$%%%%%%&&&"""############$$$$$$$$$#########$$$$$$###############""""""""""""######""""""######$$$$$$$$$$$$$$$$$$############$$$$$$"""""""""""""""""""""""""""############$$$$$$$$$""""""#########$$$$$$$$$"""###$$$%%%&&&%%%$$$$$$#########$$$$$$#########"""###$$$%%%%%%%%%%%%%%%########################!!!!!!""""""#########$$$!!!!!!!!!!!!!!!!!!!!!!!!%%%$$$$$$$$$######""""""""""""""""""""""""""""""######""""""""""""######!!!######!!!!!!%%%'''%%%######$$$$$$$$$$$$###### !!!"""######$$$"""############$$$$$$$$$"""############$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""############""""""!!!"""$$$%%%&&&&&&%%%%%%&&&%%%$$$######$$$%%%&&&""""""""""""""""""""""""$$$$$$############$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$######"""""" !!!"""###$$$!!!!!!""""""#########$$$!!!""""""###$$$$$$%%%%%%""""""###$$$$$$%%%&&&&&&"""############$$$$$$$$$""""""""""""###$$$%%%&&&########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$###""""""######$$$$$$$$$$$$######""""""""""""""""""""""""!!!###$$$$$$######$$$%%%############""""""""""""""""""""""""############&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###"""############$$$$$$$$$%%%%%%%%%$$$$$$$$$############$$$%%%%%%%%%%%%$$$"""############$$$$$$$$$"""""""""""""""""""""""""""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&%%%$$$###"""!!!######$$$$$$$$$%%%%%%%%%"""############$$$$$$$$$""""""""""""""""""""""""%%%$$$$$$$$$###"""""""""""""""#########$$$$$$$$$########################"""############$$$$$$$$$######""""""""""""##############################""""""""""""""""""""""""######$$$$$$$$$$$$############$$$%%%%%%%%%%%%$$$###$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%###"""""""""###$$$%%%%%%&&&%%%$$$######%%%&&&(((+++***)))(((&&&$$$######$$$$$$%%%%%%%%%$$$$$$####################################"""""""""""""""######$$$$$$$$$%%%%%%%%%############"""""""""""""""#########$$$$$$$$$$$$!!!!!!!!!!!!""""""""""""######$$$%%%%%%%%%%%%$$$%%%%%%$$$###""""""##############################"""############$$$$$$$$$######$$$$$$$$$$$$######$$$$$$############$$$$$$"""""""""###$$$$$$$$$%%%%%%%%%%%%$$$$$$#########%%%$$$$$$$$$###""""""""""""######$$$$$$######"""""""""""""""##################""""""""""""######""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""############""""""""""""############""""""""""""!!!!!!!!!!!!"""############$$$$$$$$$$$$$$$############$$$$$$%%%%%%%%%$$$$$$#########%%%%%%$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$###""" !!!""""""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################""""""###$$$$$$$$$$$$###$$$$$$######$$$$$$%%%&&&######$$$$$$$$$%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""###$$$%%%&&&########################$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%$$$############$$$$$$%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$###"""""""""######$$$$$$$$$$$$######""""""""""""""""""""""""!!!###$$$$$$######$$$%%%############""""""""""""""""""""""""############&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###"""############$$$$$$$$$%%%%%%$$$$$$$$$#########"""###$$$$$$%%%%%%$$$$$$"""############$$$$$$$$$########################"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$###"""!!!#########$$$$$$$$$%%%%%%""""""#########$$$$$$$$$""""""""""""""""""""""""$$$$$$$$$###############""""""#########$$$$$$$$$########################""""""#########$$$$$$$$$######""""""""""""##############################"""""""""""""""""""""""""""######$$$$$$######""""""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$%%%#########"""######$$$$$$%%%$$$#########%%%'''(((******)))'''&&&$$$######$$$$$$$$$%%%%%%$$$$$$##############################"""""""""""""""""""""#########$$$$$$$$$%%%%%%############"""""""""""""""""""""#########$$$$$$""""""""""""##################$$$%%%%%%%%%%%%$$$%%%$$$$$$###""""""##############################"""############$$$$$$$$$######$$$$$$$$$$$$######$$$$$$############$$$$$$##################$$$$$$%%%$$$$$$$$$$$$$$$$$$###$$$$$$$$$#####################$$$$$$$$$$$$######""""""""""""##################""""""""""""######""""""""""""""""""""""""########################""""""""""""############""""""""""""###############"""""""""!!!!!!!!!!!!"""############$$$$$$$$$$$$######""""""######$$$%%%%%%%%%$$$$$$#########%%%%%%$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""""""""$$$###"""!!! !!!!!!""""""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################""""""###$$$$$$$$$$$$##################$$$%%%%%%######$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&########################$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%$$$#########$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$######""""""!!!!!!######$$$$$$$$$$$$######""""""""""""""""""""""""!!!###$$$$$$######$$$%%%############""""""""""""""""""""""""############%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###"""############$$$$$$$$$%%%$$$$$$$$$$$$#########"""###$$$$$$%%%%%%$$$$$$"""############$$$$$$$$$########################"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%$$$###""""""#########$$$$$$$$$$$$%%%"""""""""#########$$$$$$""""""""""""""""""""""""###############$$$$$$$$$###############$$$$$$$$$########################"""""""""#########$$$$$$######""""""""""""##############################"""""""""""""""""""""""""""######$$$$$$######""""""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""#########$$$#########$$$%%%'''((())))))((('''%%%$$$#########$$$$$$%%%%%%$$$$$$$$$########################""""""""""""""""""###############$$$$$$$$$$$$%%%############""""""""""""!!!!!!!!!"""""""""##################$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$%%%$$$######"""#################################"""############$$$$$$$$$######$$$$$$$$$$$$######$$$$$$############$$$$$$##################""""""#########$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$""""""""""""##################""""""""""""######""""""""""""""""""""""""########################""""""""""""############"""""""""#########$$$$$$######"""""""""!!!!!!!!!"""############$$$$$$$$$$$$######""""""######$$$$$$$$$$$$$$$$$$#########%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$#################################"""""""""""""""######"""!!!!!!!!!"""""""""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################""""""###$$$$$$$$$$$$###"""############$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&######""""""!!!!!!!!! ######$$$$$$$$$$$$######""""""""""""""""""""""""!!!###$$$$$$######$$$%%%############"""""""""!!!!!!"""""""""############%%%$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###""""""#########$$$$$$$$$$$$$$$$$$$$$############""""""###$$$$$$$$$$$$$$$""""""#########$$$$$$$$$########################""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################"""""""""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$###""""""############$$$$$$$$$$$$""""""""""""############"""""""""""""""""""""""""""""""""###$$$$$$$$$%%%################################################""""""""""""##################""""""""""""##############################!!!!!!!!!!!!!!!!!!!!!!!!""""""############""""""""""""###$$$$$$$$$$$$$$$###$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$###%%%%%%%%%$$$$$$$$$$$$###%%%%%%$$$###"""""""""###############$$$%%%'''((((((''''''&&&%%%$$$############$$$%%%%%%%%%$$$$$$########################"""""""""""""""#####################$$$$$$$$$$$$############"""""""""!!!!!!!!!!!!!!!"""""""""""""""""""""#########$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$###############$$$########################""""""#########$$$$$$$$$######$$$$$$$$$$$$######$$$$$$############$$$$$$$$$$$$######""""""!!!!!!""""""######$$$$$$%%%%%%"""""""""###$$$$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$!!!"""""""""##################""""""""""""######""""""""""""""""""""""""########################!!!"""""""""############""""""#########$$$$$$$$$#########"""""""""!!!!!!""""""#########$$$$$$$$$######""""""""""""######$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################""""""######""""""""""""""""""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""###$$$$$$$$$$$$###""""""######$$$$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&"""""""""!!!!!!!!!!!!!!!######$$$$$$$$$$$$######!!!!!!!!!!!!!!!!!!!!!!!!!!!###$$$$$$######$$$%%%############"""""""""!!!!!!"""""""""############$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###""""""#########$$$$$$$$$$$$$$$$$$#########""""""""""""###$$$$$$$$$$$$###""""""#########$$$$$$$$$########################""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################!!!!!!"""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$######$$$$$$$$$###""""""""""""#########$$$$$$$$$!!!!!!"""""""""#########"""""""""""""""""""""""""""""""""###$$$$$$$$$%%%########################""""""""""""""""""""""""!!!!!!"""""""""###############""""""""""""######""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!"""""""""######"""""""""""""""###$$$$$$$$$$$$######$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###"""""""""###""""""######$$$%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$###"""###$$$%%%%%%%%%%%%%%%########################!!!!!!""""""############""""""#########$$$$$$$$$############"""""""""!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!"""""""""############$$$%%%%%%%%%%%%$$$$$$###############$$$$$$########################""""""#########$$$$$$$$$######$$$$$$$$$$$$######$$$$$$############$$$$$$$$$######""""""!!!!!!!!!"""""""""######$$$$$$$$$"""""""""###$$$$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$!!!"""""""""##################""""""""""""######""""""""""""""""""""""""########################!!!"""""""""########################$$$$$$$$$$$$############""""""""""""""""""#########$$$$$$$$$###""""""""""""""""""###########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""##################""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""###$$$$$$$$$$$$###""""""###$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&""""""""""""!!!!!!!!!!!!######$$$$$$$$$$$$######!!!!!!!!!!!!!!!!!!!!!!!!!!!###$$$$$$######$$$%%%############""""""""""""""""""""""""#####################$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###"""############$$$$$$$$$$$$############"""""""""!!!"""######$$$$$$######"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################!!!""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$"""###############"""""""""""""""############$$$!!!!!!!!!"""""""""######""""""""""""""""""""""""###############$$$$$$$$$$$$$$$$$$###############""""""""""""""""""""""""!!!!!!!!!"""""""""############""""""""""""######""""""""""""""""""""""""""""""""""""""""""""""""!!!""""""######""""""!!!!!!"""######$$$$$$#########$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$######"""##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$%%%%%%%%%%%%########################!!!!!!!!!"""######$$$$$$"""""""""############$$$############""""""""""""!!!!!!!!!"""""""""###### !!!!!!!!!""""""""""""######$$$%%%%%%%%%%%%$$$#########"""######$$$%%%########################"""############$$$$$$$$$######$$$$$$$$$$$$######$$$$$$############$$$$$$""""""""""""""""""!!!!!!"""""""""##############################$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$""""""""""""##################""""""""""""######""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""#####################$$$$$$$$$$$$%%%$$$$$$#########""""""""""""############$$$$$$$$$###""""""!!!!!!""""""###"""""""""##################$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%!!!"""###$$$$$$$$$######"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""###$$$$$$$$$$$$###"""###$$$%%%&&&%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$###$$$%%%&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&""""""""""""""""""""""""######$$$$$$$$$$$$######!!!!!!!!!!!!!!!!!!!!!!!!!!!###$$$$$$######$$$%%%############""""""""""""""""""""""""############"""#########$$$$$$$$$$$$############$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###"""############$$$$$$$$$############""""""""""""!!!""""""###############"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$################################################""""""######$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$######""""""""""""######""""""############""""""""""""""""""############!!!!!!!!!!!!"""""""""###""""""""""""""""""""""""$$$$$$$$$###############$$$$$$$$$#########""""""""""""""""""""""""""""""!!!!!!!!!!!!"""""""""#########""""""""""""######""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!""""""""""""!!!!!!!!!""""""##################$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$###""""""###$$$%%%&&&&&&'''#########"""######$$$$$$$$$$$$$$$$$$$$$######"""############$$$$$$$$$$$$""""""###$$$%%%%%%%%%%%%######################## !!!!!!"""######$$$$$$""""""""""""########################"""""""""""""""""""""#########$$$$$$!!!!!!"""""""""###############$$$%%%%%%%%%%%%$$$######""""""###$$$$$$%%%########################"""############$$$$$$$$$######$$$$$$$$$$$$######$$$$$$############$$$$$$!!!!!!!!!"""""""""""""""############""""""""""""$$$$$$$$$#####################$$$$$$$$$$$$######""""""""""""##################""""""""""""######""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""#####################$$$$$$$$$%%%%%%$$$$$$$$$#########"""""""""############$$$$$$$$$""""""!!!!!!!!!!!!""""""!!!"""""""""#########$$$###$$$%%%%%%%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$######""""""#########$$$$$$$$$$$$!!!"""###$$$$$$$$$$$$###"""############$$$$$$$$$################################################""""""###$$$$$$$$$$$$######$$$&&&''''''&&&%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$######%%%'''(((''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&""""""""""""##################$$$$$$$$$$$$######!!!!!!!!!!!!!!!!!!!!!!!!!!!###$$$$$$######$$$%%%############""""""""""""""""""""""""############""""""######$$$$$$$$$$$$"""############$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$"""############$$$$$$$$$############""""""""""""!!!!!!"""###############"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$########################""""""""""""""""""""""""""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######""""""""""""######!!!""""""#########""""""""""""""""""############!!!!!!!!!!!!""""""""""""""""""""""""""""""""""""%%%$$$$$$$$$######""""""$$$$$$$$$$$$######""""""""""""""""""""""""""""""!!!!!!!!!!!!""""""""""""######""""""""""""######""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!""""""""""""!!!!!!!!!!!!"""##################$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$###!!!!!!"""###%%%&&&'''(((###"""""""""###$$$%%%%%%$$$$$$%%%$$$$$$###"""!!!###############$$$$$$$$$!!!"""###$$$%%%&&&&&&&&&######################## !!!!!!"""###$$$$$$$$$""""""""""""########################""""""""""""############$$$$$$$$$$$$"""############$$$$$$$$$######$$$%%%%%%%%%%%%$$$######""""""###$$$%%%%%%########################"""############$$$$$$$$$######$$$$$$$$$$$$######$$$$$$############$$$$$$ !!!!!!""""""######$$$$$$######""""""!!!!!!%%%$$$$$$$$$######""""""#########$$$$$$#########""""""""""""##################""""""""""""######""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""##################$$$$$$$$$%%%%%%%%%$$$$$$$$$############""""""############$$$$$$$$$""""""!!!!!!!!!!!!""""""!!!!!!""""""#########$$$###$$$%%%&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###""""""!!!!!!!!!""""""#########$$$!!!"""###$$$%%%%%%$$$###"""############$$$$$$$$$################################################""""""###$$$$$$$$$$$$######$$$&&&(((((('''&&&%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################%%%$$$###"""###$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$######%%%'''((('''''''''&&&&&&%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&""""""""""""""""""""""""%%%%%%%%%%%%%%%$$$###""" !!!!!!!!!!!!!!!!!!!!!!!!!!! """"""""""""""""""""""""!!!!!!!!!!!!""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$%%%&&&%%%$$$###"""%%%%%%%%%&&&&&&&&&''''''%%%%%%$$$###""""""######%%%%%%$$$$$$###"""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""!!!!!!!!!!!!"""############$$$$$$$$$#########$$$$$$%%%%%%%%%&&&'''&&&%%%"""!!!"""$$$$$$$$$############$$$$$$""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%##############################$$$$$$$$$$$$######""""""""""""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############&&&%%%$$$$$$######$$$$$$!!!!!!""""""#########$$$$$$$$$$$$###"""!!!!!! !!!!!!"""###############&&&%%%###"""""""""##################""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""########################$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$###"""!!!"""###%%%$$$""" !!!###%%%'''######################################################$$$$$$$$$%%%%%%%%%###########################$$$%%%%%%######$$$%%%%%%$$$$$$######$$$$$$%%%######""""""""""""####################################$$$$$$$$$%%%%%%%%%$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$########################""""""#########$$$$$$$$$ !!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$###!!! !!!"""########################"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$$$$############$$$$$$$$$$$$############$$$$$$$$$$$$############$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$##################"""""""""""""""##############################$$$$$$$$$$$$##############################$$$$$$#####################$$$$$$%%%%%%$$$$$$###################################################"""############$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$"""###$$$%%%&&&%%%$$$$$$######""""""######$$$%%%$$$$$$############$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&'''&&&%%%%%%((('''&&&%%%%%%%%%%%%%%%""""""""""""""""""""""""$$$$$$%%%%%%$$$######""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""""""""""""""!!!!!!!!!!!!"""""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%$$$###"""%%%%%%%%%&&&&&&&&&&&&'''%%%$$$$$$###""""""######%%%%%%$$$$$$###""""""!!!""""""""""""""""""""""""$$$############""""""""""""############$$$$$$$$$#########$$$$$$%%%%%%%%%%%%&&&&&&$$$""""""###$$$%%%$$$$$$$$$$$$$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%##############################$$$$$$$$$$$$######""""""""""""############$$$$$$$$$$$$$$$$$$$$$$$$##################$$$$$$&&&%%%$$$$$$######$$$$$$""""""""""""#########$$$$$$$$$######"""!!!!!! !!!!!!"""###############%%%%%%###"""""""""##################""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""########################$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$###"""!!!"""###$$$###"""!!!"""###%%%&&&######################################################$$$$$$$$$%%%%%%%%%###########################$$$%%%%%%######$$$%%%%%%$$$$$$######$$$$$$%%%######""""""""""""##############################""""""#########$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$########################""""""#########$$$$$$$$$ !!!!!!"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%$$$###"""!!! !!!!!!"""########################"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$$$$############$$$$$$$$$$$$############$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$############"""""""""""""""""""""##############################$$$$$$$$$$$$#########################################################$$$$$$%%%%%%$$$$$$###################################################"""############$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$!!!"""$$$%%%%%%%%%$$$#########""""""######$$$%%%$$$$$$############$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&&&&&&&%%%%%%((('''&&&%%%%%%%%%%%%&&&""""""""""""""""""""""""######$$$$$$######""""""$$$#########""""""!!!!!!""""""""""""""""""""""""""""""""""""""""""""""""!!!!!!!!!"""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%%%%$$$###"""%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$######"""#########%%%%%%$$$$$$###"""""""""########################%%%%%%$$$$$$$$$#########"""############$$$$$$$$$#########$$$$$$$$$$$$$$$$$$%%%%%%$$$""""""$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%##############################$$$$$$$$$$$$######""""""""""""############$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$$$$$$$%%%&&&%%%$$$$$$######$$$$$$"""""""""###############$$$$$$######"""!!!!!!!!!!!!!!!"""###############%%%$$$######"""#####################""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""########################$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$###"""!!!"""###"""""""""#########$$$$$$######################################################$$$$$$$$$%%%%%%%%%###########################$$$%%%%%%######$$$%%%$$$$$$############$$$$$$######""""""""""""##############################!!!!!!"""""""""#################################$$$$$$$$$$$$$$$$$$$$$$$$#######################################$$$$$$$$$!!!!!!!!!"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$###"""!!!!!!!!!!!!"""########################"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$$$$############$$$$$$$$$$$$############$$$$$$$$$$$$###############$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$#########""""""""""""""""""####################################$$$$$$$$$$$$#########################################################$$$$$$%%%%%%$$$$$$###################################################"""############$$$$$$$$$$$$############$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$"""###$$$%%%%%%%%%$$$#########""""""######$$$%%%$$$$$$############$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&&&&&&&%%%%%%''''''&&&%%%%%%%%%&&&&&&""""""""""""""""""""""""""""""#########""""""!!!%%%%%%$$$######"""""""""###############$$$$$$$$$""""""""""""""""""""""""!!!!!!"""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$#################################"""######$$$%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$###############$$$$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$############""""""#########$$$$$$$$$###############$$$$$$$$$###$$$$$$###""""""$$$&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%##############################$$$$$$$$$$$$######!!!"""""""""########################$$$$$$$$$$$$!!!!!!"""###$$$%%%%%%%%%&&&%%%$$$$$$######$$$$$$####################################""""""!!!!!!!!!!!!"""###############$$$$$$##############################"""""""""!!!""""""""""""""""""""""""""""""""""""""""""""""""########################$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$###"""!!!"""### !!!###$$$$$$$$$###"""######################################################$$$$$$$$$%%%%%%%%%###########################$$$%%%%%%######$$$%%%$$$$$$############$$$$$$######""""""""""""##############################""""""""""""#########$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$################################################!!!!!!""""""####################################%%%$$$$$$######$$$$$$%%%#########"""""""""""""""########################""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$$$$############$$$$$$$$$$$$############$$$$$$$$$$$$##################$$$$$$$$$$$$$$$$$$$$$###############"""""""""""""""#######################################$$$$$$$$$$$$#############################################$$$$$$$$$###$$$$$$%%%%%%$$$$$$###################################################""""""#########$$$$$$$$$###############$$$$$$%%%##############################$$$%%%%%%%%%%%%$$$###$$$%%%&&&'''&&&%%%%%%######""""""######$$$%%%%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&""""""""""""""""""""""""!!!""""""#########""""""%%%$$$$$$$$$#########""""""#########$$$$$$$$$%%%########################""""""""""""############$$$$$$$$$$$$$$$$$$$$$$$$##############################""""""###$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$###############$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########"""""""""""""""#########$$$$$$$$$########################"""###$$$###""""""$$$%%%######""""""""""""######################################################$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%##############################$$$$$$$$$$$$######!!!"""""""""############"""""""""######$$$$$$$$$!!!!!!"""###$$$%%%%%%%%%&&&%%%$$$$$$######$$$$$$$$$$$$$$$########################"""""""""""""""!!!!!!"""###########################$$$#####################"""""""""!!!########################################################################$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$###"""!!!"""### !!!"""$$$$$$###"""!!!""""""""""""""""""""""""##############################$$$$$$$$$%%%%%%%%%###########################$$$%%%%%%######$$$%%%$$$######""""""######$$$######""""""""""""#######################################$$$$$$$$$%%%%%%""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$################################################"""""""""""""""#######################################""""""""""""#####################""""""!!!########################""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$$$$############$$$$$$$$$$$$############$$$$$$$$$$$$######""""""#########$$$$$$$$$########################!!!!!!""""""##########################################$$$$$$$$$$$$##############################""""""#########$$$$$$$$$###$$$$$$%%%%%%$$$$$$###################################################""""""#########$$$$$$$$$######""""""######$$$%%%##############################$$$%%%%%%%%%%%%$$$%%%%%%'''((((((((('''&&&######""""""######$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&'''""""""""""""""""""""""""""""""######$$$$$$##############################"""""""""###$$$$$$%%%%%%########################"""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""""""""###$$$%%%%%%&&&%%%$$$$$$######$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%#########"""######$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$############""""""""""""############$$$$$$$$$###############"""""""""###$$$$$$###!!!!!!###$$$""""""!!!!!!!!!!!!""""""""""""""""""""""""""""""########################$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%##############################$$$$$$$$$$$$######""""""""""""############!!!!!!""""""###$$$$$$$$$"""""""""###$$$$$$$$$%%%&&&%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$###############""""""""""""""""""!!!!!!"""###############""""""###$$$$$$$$$$$$###############""""""""""""########################################################################$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$###"""!!!"""### !!!"""#########"""!!!""""""""""""""""""""""""##############################$$$$$$$$$%%%%%%%%%###########################$$$%%%%%%######$$$%%%######""""""""""""############""""""""""""#################################$$$$$$$$$$$$%%%%%%%%%"""""""""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$###############""""""""""""""""""##############################""""""!!!!!!!!!!!!""""""######$$$$$$######"""!!!########################"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$$$$############$$$$$$$$$$$$############$$$$$$$$$$$$######"""""""""############$$$"""""""""###############!!!!!!!!!"""######$$$$$$##############################$$$$$$$$$$$$##############################"""""""""###$$$$$$%%%%%%###$$$$$$%%%%%%$$$$$$###################################################"""############$$$$$$$$$###""""""""""""###$$$$$$##############################$$$%%%%%%%%%%%%$$$%%%&&&'''((((((((('''&&&######""""""######$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%#########$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&'''''''''%%%%%%$$$$$$$$$%%%&&&'''&&&&&&%%%%%%%%%&&&''''''"""""""""""""""""""""""""""######$$$%%%%%%$$$$$$!!!!!!""""""###$$$$$$$$$!!!!!!""""""###$$$$$$%%%########################""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""""""""###$$$%%%&&&&&&%%%$$$#########$$$$$$###$$$$$$$$$$$$%%%%%%%%%######""""""###$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$#########"""############$$$$$$$$$$$$#########"""""""""!!!$$$$$$$$$###!!! !!!#########""""""""""""######################################################$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%##############################$$$$$$$$$$$$######""""""""""""############!!!!!!!!!"""###$$$$$$$$$##################$$$$$$&&&%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$#########"""""""""""""""""""""###!!!!!!"""###############!!!"""###$$$%%%$$$$$$###############""""""""""""########################################################################$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$###"""!!!"""### !!!!!!"""""""""""""""""""""""""""""""""""""""##############################$$$$$$$$$%%%%%%%%%###########################$$$%%%%%%######$$$%%%######""""""""""""############""""""""""""##########################################$$$$$$$$$$$$!!!""""""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$#########""""""###"""""""""""""""""""""##############################""""""""""""############$$$$$$$$$###"""!!!########################"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$$$$############$$$$$$$$$$$$############$$$$$$$$$$$$######""""""""""""############!!!"""""""""#########$$$ !!!!!!"""######$$$$$$##############################$$$$$$$$$$$$##############################!!!""""""###$$$$$$%%%%%%###$$$$$$%%%%%%$$$$$$###################################################"""############$$$$$$$$$"""""""""""""""###$$$$$$##############################$$$%%%%%%%%%%%%$$$###$$$&&&'''''''''&&&%%%######""""""######$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$######$$$%%%%%%&&&&&&&&&%%%"""######$$$%%%%%%&&&&&&$$$$$$%%%%%%&&&''''''(((%%%%%%$$$$$$$$$%%%&&&'''%%%%%%%%%%%%%%%&&&'''((("""""""""""""""""""""""""""###$$$%%%%%%%%%%%%%%% !!!"""###$$$$$$%%% !!!!!!"""######$$$$$$########################"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""""""""""""""###$$$%%%&&&&&&%%%$$$#########$$$%%%######$$$$$$$$$%%%%%%%%%######""""""###$$$%%%%%%##################$$$$$$########################&&&&&&&&&%%%%%%%%%$$$$$$"""############$$$$$$$$$$$$#########""""""!!!!!!$$$%%%%%%###!!! !!!"""$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%##############################$$$$$$$$$$$$######""""""""""""############ !!!!!!"""###$$$$$$$$$$$$$$$$$$###############&&&%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$#########"""""""""""""""#########!!!!!!"""###############!!!"""###$$$%%%%%%$$$###############""""""""""""########################################################################$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$###"""!!!"""###!!!!!!!!!!!!"""""""""###""""""""""""""""""""""""##############################$$$$$$$$$%%%%%%%%%###########################$$$%%%%%%######$$$%%%######""""""""""""############""""""""""""##############################""""""""""""############!!!""""""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$######""""""#########"""""""""""""""""""""""""""""""""""""""$$$$$$############$$$$$$######$$$%%%$$$###"""!!!########################"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$%%%%%%$$$$$$$$$######$$$$$$$$$$$$############$$$$$$$$$$$$############$$$$$$$$$$$$######""""""""""""############!!!!!!""""""#########$$$ !!!!!!"""###$$$$$$$$$##############################$$$$$$$$$$$$##############################!!!""""""###$$$$$$%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$################################################"""############$$$$$$$$$"""""""""""""""######$$$""""""""""""""""""""""""######$$$%%%%%%%%%%%%$$$"""###$$$%%%&&&%%%$$$$$$#########"""###$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########$$$%%%%%%&&&&&&&&&&&&""""""###$$$%%%%%%&&&&&&$$$$$$%%%%%%&&&'''((((((&&&%%%$$$###$$$%%%&&&'''%%%%%%%%%%%%%%%&&&'''((($$$#########""""""!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""############""""""!!!!!!"""###$$$$$$$$$$$$$$$###"""!!!!!! #########"""""""""""""""""""""###$$$$$$$$$######$$$$$$##################$$$###"""!!!!!!"""###$$$""""""!!!!!! ###""""""!!!"""$$$&&&''' !!!"""######$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$######""""""######$$$$$$$$$#########""""""##############################"""""""""""""""###%%%%%%$$$###""""""######(((&&& $$$###!!!&&&$$$$$$##################!!!"""$$$%%%%%%$$$"""!!!%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&""""""""""""####################################$$$#########""""""!!!!!!"""############$$$$$$$$$###############$$$$$$%%%###"""""""""###$$$%%%%%%############""""""""""""""""""""""""############""""""""""""""""""""""""########################$$$#########""""""!!!!!!$$$#########""""""!!!!!!############"""""""""""""""############$$$$$$$$$&&&%%%###"""""""""###$$$""""""""""""""""""""""""""""""############""""""""""""""""""""""""""""""######$$$$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""############$$$$$$############$$$$$$$$$$$$$$$$$$######""""""########################$$$$$$############$$$$$$""""""""""""""""""######""""""#########$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$###"""!!!!!!""""""##############################""""""######$$$%%%%%%$$$$$$%%%%%%%%%###"""$$$$$$$$$#########""""""########################!!!!!!!!!!!!""""""""""""%%%%%%###"""""""""###$$$$$$$$$############$$$$$$$$$$$$###"""!!!!!!"""""""""############$$$$$$$$$$$$$$$$$$############"""$$$$$$######"""!!!!!!!!!""""""""""""############"""!!!!!!!!!!!!!!!"""###"""""""""""""""""""""""""""############$$$$$$$$$$$$$$$$$$#########""""""########################%%%%%%%%%$$$$$$#################################"""$$$%%%%%%$$$###%%%&&&################################################$$$###""""""###%%%&&&((($$$$$$$$$$$$######""""""%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((############"""""""""!!!$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""""""""#########"""""""""""""""###$$$$$$$$$$$$$$$###"""!!!!!!!!!############""""""""""""$$$%%%%%%%%%%%%%%%$$$$$$""""""""""""""""""""""""$$$###"""!!!!!!"""###$$$""""""!!!!!!!!! ###""""""""""""$$$%%%&&&"""######$$$%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%$$$######""""""######$$$$$$$$$#########""""""##############################""""""""""""######$$$$$$###"""""""""""""""'''%%%######!!!&&&########################"""###$$$%%%%%%$$$###"""%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%""""""""""""####################################$$$#########"""""""""""""""############$$$$$$$$$###""""""""""""###$$$$$$##################$$$%%%############""""""""""""""""""""""""############""""""""""""""""""""""""####################################"""""""""!!!$$$#########""""""""""""############"""""""""""""""############$$$$$$$$$%%%$$$###"""""""""######""""""""""""""""""""""""""""""############""""""""""""""""""""""""""""""######$$$$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""############$$$$$$############$$$$$$$$$$$$$$$$$$#########"""########################$$$$$$############$$$$$$############""""""""""""""""""#########$$$$$$$$$############$$$$$$$$$%%%$$$$$$###"""""""""""""""##############################""""""######$$$%%%%%%$$$$$$$$$$$$$$$###"""$$$$$$$$$#########""""""########################"""""""""############$$$%%%$$$###"""""""""###$$$$$$$$$############$$$$$$$$$$$$###""""""""""""""""""############$$$$$$$$$$$$$$$$$$############"""############""""""""""""""""""""""""##################""""""!!!""""""""""""""""""""""""""""""""""""############$$$$$$$$$$$$$$$$$$#########""""""########################%%%%%%%%%$$$$$$$$$##############################"""$$$%%%%%%$$$###%%%&&&############################################################$$$%%%&&&'''$$$$$$$$$$$$#########"""%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&'''''''''((((((############""""""""""""""""""""""""""""""""""""!!!!!!!!!!!!""""""""""""###""""""""""""###$$$$$$$$$$$$$$$###""""""!!!!!!########################''''''''''''&&&&&&%%%$$$!!!!!!!!!!!!!!!!!!""""""$$$###""""""""""""###$$$""""""""""""!!!!!!!!!!!!""""""""""""###$$$%%%&&&#########$$$%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%$$$######""""""######$$$$$$$$$#############################################"""""""""######$$$######"""!!!!!!!!!"""""" )))%%%$$$$$$!!!%%%########################"""###$$$%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$"""""""""#########$$$$$$#######################################""""""""""""############$$$$$$$$$"""""""""""""""######$$$%%%$$$$$$############$$$############""""""""""""""""""""""""############""""""""""""""""""""""""""""""""""""""""""""""""############""""""""""""###############"""""""""$$$$$$#########""""""""""""############$$$$$$$$$$$$###""""""!!!"""""""""""""""""""""""""""""""""""""""############"""""""""""""""""""""""""""""""""######$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$"""""""""#########$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$#########"""""""""###############$$$$$$$$$"""""""""#########$$$$$$$$$###""""""""""""""""""""""""""""""""""""""""""######""""""######$$$%%%%%%$$$$$$$$$############$$$$$$$$$################################################$$$$$$$$$%%%%%%%%%$$$######""""""######$$$$$$############$$$$$$$$$$$$###""""""""""""###"""############$$$$$$$$$$$$$$$$$$############""""""""""""############$$$"""""""""#########$$$$$$%%%%%%$$$###"""""""""""""""""""""""""""""""""""""""############$$$$$$$$$$$$$$$$$$#######################################%%%%%%%%%$$$$$$$$$$$$###########################"""$$$%%%%%%$$$###%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################"""######$$$%%%%%%%%%%%%$$$$$$$$$$$$############%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&'''''''''&&&&&&'''''''''(((((((((#########""""""""""""""""""""""""""""""""""""""" !!!!!!!!!"""""""""#########""""""###$$$$$$$$$$$$$$$######""""""""""""###############$$$$$$''''''''''''&&&%%%$$$###!!!!!!!!!"""""""""""""""########################"""""""""""""""""""""""""""""""""######$$$$$$%%%!!!!!!"""""""""###############$$$$$$$$$%%%%%%%%%%%%$$$######""""""############################################################""""""######$$$$$$""""""!!!!!!!!!!!!!!!"""&&&---(((!!!%%%$$$!!!$$$###############$$$$$$$$$###$$$$$$%%%%%%$$$$$$##################$$$$$$$$$$$$######""""""######$$$""""""#########$$$$$$$$$################################################""""""#########$$$$$$$$$""""""!!!!!!""""""###$$$&&&%%%$$$$$$########################"""""""""!!!!!!"""""""""############""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!#########"""""""""""""""########################$$$$$$$$$#########""""""""""""#########$$$$$$$$$###"""""""""""""""""""""""""""""""""""""""""""""""""""############""""""""""""""""""""""""""""""""""""###$$$$$$$$$#########$$$$$$$$$$$$$$$%%%%%%""""""#########$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%$$$$$$######""""""!!!########################!!!""""""""""""###############"""""""""""""""###!!!!!!!!!!!!!!!!!!!!!!!!######""""""######$$$%%%$$$%%%%%%$$$###"""###$$$############################################################$$$$$$$$$%%%$$$$$$$$$###############$$$$$$############$$$$$$$$$$$$###""""""#########""""""#########$$$$$$$$$$$$$$$$$$#########""""""!!!!!!"""######$$$%%%%%%""""""#########$$$$$$$$$'''&&&%%%$$$######""""""""""""""""""""""""""""""""""""#########$$$$$$$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$########################"""$$$%%%%%%$$$###%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################"""###$$$%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((((((((((((""""""""""""""""""######!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""$$$$$$###############$$$$$$$$$$$$$$$############""""""######$$$$$$$$$%%%&&&&&&&&&%%%%%%###"""!!!"""""""""######$$$$$$$$$######$$$$$$$$$$$$######"""#####################"""#########$$$$$$$$$$$$"""""""""""""""###############$$$$$$$$$%%%%%%%%%%%%$$$######""""""#####################################################################$$$%%%%%%"""!!!!!!!!!!!!!!!""""""+++111***"""&&&%%%!!!###""""""#########$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$""""""#########$$$$$$$$$$$$######""""""######$$$############$$$$$$$$$$$$#######################################$$$$$$$$$""""""#########$$$$$$$$$"""""""""""""""######$$$&&&&&&%%%$$$#########$$$############"""""""""!!!!!!"""""""""############""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""""""""#####################$$$$$$$$$$$$$$$$$$$$$############""""""#########$$$$$$$$$"""""""""############"""########################""""""############""""""""""""""""""""""""""""""!!!"""###$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%############$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%$$$$$$$$$######""""""########################!!!""""""""""""############"""""""""""""""######!!!!!!!!!!!!!!!!!!!!!!!!######""""""######$$$%%%###%%%'''&&&$$$######$$$################################################"""""""""#########$$$$$$$$$$$$$$$$$$######""""""$$$$$$############$$$$$$$$$###############$$$$$$""""""#########$$$$$$$$$$$$$$$$$$#########""""""!!!!!!"""###$$$%%%&&&&&&############$$$$$$$$$$$$''''''%%%$$$############""""""""""""""""""""""""""""""#########$$$$$$$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$########################"""$$$%%%%%%$$$###%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################"""###$$$%%%&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((('''''''''((((((((())))))""""""""""""############!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""############%%%%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$%%%%%%%%%$$$$$$$$$$$$###""""""!!!""""""######$$$$$$%%%%%%######$$$%%%%%%$$$##################$$$$$$$$$$$$"""######$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$######""""""#####################$$$$$$$$$#######################################$$$%%%&&&""""""!!!!!!!!!"""######---111)))"""&&&'''"""$$$"""""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$%%%%%%%%%$$$$$$############$$$$$$#########$$$$$$$$$$$$%%%#################################$$$$$$$$$$$$$$$"""############$$$$$$$$$###############$$$$$$%%%&&&%%%%%%$$$$$$$$$$$$%%%############""""""""""""""""""""""""############""""""""""""""""""""""""""""""""""""""""""""""""""""""""""""#####################$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$#########"""############$$$$$$$$$""""""###$$$$$$$$$$$$###########################""""""############""""""""""""""""""""""""""""""!!!"""###$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&#########$$$$$$$$$$$$%%%$$$$$$############$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############"""""""""#########$$$$$$"""""""""""""""######$$$""""""""""""""""""""""""######""""""######$$$%%%"""&&&******'''$$$###$$$###############$$$$$$$$$########################"""""""""############$$$###$$$$$$$$$$$$###""""""$$$$$$############$$$$$$$$$############$$$%%%%%%"""############$$$$$$$$$$$$$$$$$$############"""""""""######$$$%%%&&&&&&#########$$$$$$$$$$$$%%%&&&&&&%%%$$$############"""""""""""""""""""""""""""############$$$$$$$$$###############$$$$$$$$$###########################$$$$$$$$$$$$%%%%%%%%%########################"""$$$%%%%%%$$$###%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###########################$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((''''''((((((((()))))))))!!!"""""""""############""""""""""""""""""""""""############$$$$$$$$$$$$&&&%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$%%%&&&&&&"""###############""""""!!!!!!!!!"""###$$$$$$$$$###$$$$$$%%%%%%$$$$$$############$$$$$$$$$%%%%%%"""###$$$$$$$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$######""""""######""""""#########$$$$$$$$$####################################$$$%%%&&&'''"""""""""""""""###$$$$$$)))---%%%&&&((($$$&&&!!!""""""###$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%#########$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%#########$$$$$$$$$%%%%%%#################################$$$$$$%%%%%%%%%"""############$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%%%%$$$$$$$$$%%%&&&&&&############""""""""""""""""""""""""############""""""""""""""""""""""""########################!!!"""""""""#####################$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$#########"""############$$$$$$$$$"""###$$$%%%&&&%%%%%%$$$########################""""""############""""""""""""""""""""""""""""""!!!!!!"""$$$$$$%%%%%%$$$"""######$$$%%%%%%&&&&&&#########$$$$$$$$$%%%%%%$$$$$$############$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$"""######$$$$$$%%%%%%&&&$$$$$$$$$#########""""""############$$$$$$$$$%%%"""""""""""""""###$$$$$$##############################""""""######$$$%%% &&&,,,...***%%%###$$$""""""#########$$$$$$$$$#################################$$$$$$$$$%%%%%%###$$$$$$%%%$$$###"""!!!$$$$$$############$$$$$$$$$#########$$$$$$%%%&&&"""############$$$$$$$$$$$$$$$$$$############"""#########$$$$$$%%%%%%%%%#########$$$$$$$$$%%%%%%%%%$$$############$$$$$$"""""""""""""""""""""""""""############$$$$$$$$$""""""#########$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%########################"""$$$%%%%%%$$$###%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%########################%%%$$$$$$$$$###$$$$$$%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((('''((((((((())))))))))))!!!!!!""""""#########$$$##############################$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&""""""###$$$$$$$$$###### !!!"""######$$$###$$$%%%&&&&&&%%%$$$############$$$$$$%%%%%%%%%"""###$$$%%%%%%$$$""""""######""""""""""""""""""######$$$$$$$$$%%%%%%%%%%%%$$$$$$###"""#########""""""######$$$$$$$$$$$$####################################$$$%%%&&&'''######""""""###$$$%%%%%%%%%)))"""%%%)))&&&(((!!!""""""###$$$$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&######$$$%%%&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%#################################$$$$$$%%%%%%%%%"""############$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$%%%&&&&&&'''############""""""""""""""""""""""""############""""""""""""""""""""""""########################!!!!!!""""""#########$$$#########$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######"""############$$$$$$$$$###$$$%%%&&&'''&&&&&&%%%########################""""""############""""""""""""""""""""""""""""""!!!!!!"""$$$$$$%%%%%%%%%""""""###$$$%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$""""""###$$$%%%&&&&&&'''$$$$$$$$$$$$######""""""###$$$$$$$$$$$$%%%%%%%%%""""""!!!""""""###$$$$$$#################################"""###$$$$$$%%% '''...000,,,&&&$$$$$$""""""######$$$$$$$$$$$$########################$$$$$$%%%%%%%%%&&&&&&&&&######$$$%%%$$$###"""!!!$$$$$$############$$$$$$$$$#########$$$%%%%%%&&&"""############$$$$$$$$$$$$$$$$$$############"""###$$$$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%#########"""######$$$$$$"""""""""""""""""""""""""""############$$$$$$$$$""""""######$$$$$$$$$$$$#################################$$$$$$%%%%%%%%%########################"""$$$%%%%%%$$$###%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%########################&&&%%%$$$#########$$$%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((()))(((((((((((())))))))))))""""""""""""""""""############$$$%%%%%%%%%%%%$$$$$$#########""""""!!!!!!"""############$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$######$$$$$$%%%&&&%%%$$$###"""!!!!!!!!!!!!!!!""""""""""""#########'''%%%######%%%&&&$$$!!!"""###$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%%%%######""""""###$$$%%%%%%%%%%%%%%%$$$$$$############"""!!!"""$$$%%%%%%$$$""""""""""""""""""""""""!!!!!!!!!!!!!!!"""######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$###############$$$$$$$$$$$$######$$$$$$$$$###"""###%%%''')))'''&&&$$$######$$$$$$########################%%%%%%$$$###""""""##############################"""###$$$%%%%%%$$$###"""%%%%%%%%%$$$$$$$$$######""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%#########$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$########################"""""""""""""""""""""""""""############$$$$$$$$$############$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$######"""!!!!!! $$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%$$$$$$#######################################""""""""""""######"""""""""###$$$$$$$$$%%%"""############$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$##################""""""""""""""""""""""""&&&%%%###""""""###%%%&&&"""############$$$$$$$$$&&&&&&&&&%%%$$$###"""!!!%%%%%%$$$###""""""######"""############$$$$$$$$$(((&&&$$$!!!!!!"""$$$&&&%%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#################################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&########################$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''((((((''''''&&&%%%''''''''''''''''''''''''''''''''''''(((((((((((($$$######"""""""""############$$$%%%%%%%%%%%%$$$$$$#########""""""""""""############$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$%%%%%%&&&%%%$$$###"""!!!!!!!!!!!!#########$$$$$$$$$%%%%%%'''%%%######%%%%%%$$$""""""###$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$%%%%%%######""""""###$$$$$$%%%%%%%%%%%%$$$$$$############"""!!!"""$$$%%%%%%$$$########################!!!!!!!!!!!!!!!"""######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$############$$$$$$$$$$$$#########$$$$$$###"""###%%%'''&&&&&&%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###""""""##############################"""###$$$$$$$$$$$$###"""%%%%%%%%%$$$$$$$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$########################"""""""""""""""""""""""""""############$$$$$$$$$############$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$######"""!!!!!!$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$##############################""""""""""""##################$$$$$$$$$$$$############$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$##########################################%%%%%%$$$######$$$%%%%%%"""############$$$$$$$$$%%%%%%%%%%%%$$$###""""""%%%$$$$$$###########################$$$$$$$$$$$$'''&&&$$$###"""###$$$%%%%%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&########################$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((&&&%%%$$$#####################$$$%%%%%%%%%%%%$$$###############"""""""""############$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$###"""""""""""""""%%%%%%%%%%%%&&&&&&&&&&&&&&&$$$###$$$%%%%%%$$$"""######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%$$$$$$$$$$$$$$$$$$#########"""######$$$%%%$$$$$$$$$$$$$$$############"""!!!"""$$$%%%%%%$$$########################"""!!!!!!!!!!!!"""######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$#########$$$$$$$$$$$$#########$$$$$$###"""###%%%&&&$$$$$$$$$$$$###""""""!!!%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######"""#################################"""###$$$$$$$$$$$$###"""%%%%%%%%%$$$$$$$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$########################"""""""""""""""""""""""""""############$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$######"""$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###!!!""""""######$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%##############################""""""""""""######$$$$$$$$$$$$$$$#####################$$$$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$###$$$$$$$$$$$$$$$######$$$$$$$$$$$$########################$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&''')))***''''''''''''''''''''''''''''''''''''(((((((((((('''&&&%%%$$$##################$$$%%%%%%%%%%%%$$$#################################$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$######"""""""""###%%%%%%%%%&&&&&&&&&&&&'''%%%$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%$$$$$$#######################################$$$$$$$$$%%%%%%%%%$$$$$$#########$$$###############$$$$$$$$$$$$$$$##################"""!!!"""$$$%%%%%%$$$########################""""""!!!!!!""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######"""###$$$$$$######$$$&&&###$$$%%%%%%%%%$$$"""!!!%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###############$$$#################################$$$$$$#########%%%%%%%%%$$$$$$$$$#################################$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$########################""""""""""""""""""""""""""""""#########$$$$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$#########$$$$$$%%%%%%%%%########################$$$######""""""######$$$%%%%%%%%%$$$$$$##################$$$$$$$$$%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###""""""#########$$$$$$$$$""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$%%%%%%$$$%%%&&&'''&&&&&&%%%$$$$$$$$$$$$#####################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%###$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$%%%'''***,,,''''''''''''''''''''''''''''''''''''(((((((((((('''&&&%%%$$$##################$$$%%%%%%%%%%%%$$$###############$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$#########$$$%%%&&&&&&&&&%%%%%%%%%$$$##################$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$%%%%%%%%%$$$$$$###########################""""""#########$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$###############$$$###########################"""!!!"""$$$%%%%%%$$$########################"""""""""""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######!!!"""$$$$$$###"""###%%%$$$%%%&&&&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$###############$$$$$$########################$$$##################$$$%%%%%%%%%$$$$$$$$$#######################################$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$################################################""""""#########$$$$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&%%%$$$######"""#########$$$$$$%%%%%%%%%########################$$$$$$############$$$$$$&&&%%%%%%%%%$$$$$$#########$$$$$$$$$$$$%%%%%%%%%###$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###""""""#########$$$$$$$$$!!!!!!"""###$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%###$$$&&&''''''&&&$$$#################################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%$$$$$$%%%(((***,,,''''''''''''''''''''''''''''''''''''((((((((((((&&&%%%$$$#####################$$$%%%%%%%%%%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########$$$&&&'''''''''&&&%%%%%%$$$$$$#########$$$$$$############$$$$$$$$$$$$"""$$$%%%%%%$$$###$$$&&&$$$$$$%%%%%%%%%$$$##############################"""""""""###$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$######"""#########"""""""""##################"""!!!"""$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$$$$$$$%%%%%%%%%######$$$$$$$$$$$$###### """$$$$$$###"""###$$$%%%%%%&&&&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%#########"""######$$$%%%########################$$$$$$###""""""###$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$############$$$$$$$$$$$$$$$################################################"""############$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%)))((('''&&&$$$###""""""$$$$$$$$$$$$$$$$$$%%%%%%########################$$$$$$############$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%######$$$%%%&&&&&&&&&&&&###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$############$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$!!!!!!"""###$$$$$$$$$#########%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%"""###$$$%%%&&&%%%$$$###"""""""""#####################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%#########$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''%%%%%%%%%%%%&&&(((***+++''''''''''''''''''''''''''''''''''''(((((((((((($$$######"""""""""############$$$%%%%%%%%%%%%$$$#########$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$#########$$$&&&'''((('''&&&%%%$$$$$$$$$######$$$$$$%%%############$$$$$$$$$$$$"""$$$%%%%%%######%%%'''$$$%%%%%%%%%%%%$$$###"""########################!!!""""""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$###""""""######!!!"""""""""#########$$$###"""!!!"""$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%######$$$$$$$$$$$$######"""$$$$$$###"""######%%%$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######""""""###$$$$$$%%%########################$$$$$$###""""""###$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$######"""#########$$$$$$$$$$$$################################################"""############$$$$$$$$$############$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%'''&&&&&&%%%$$$###""""""%%%%%%$$$$$$$$$$$$$$$$$$########################%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&"""###$$$%%%&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$############$$$$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$######$$$%%%%%%"""############$$$$$$$$$!!!"""###############""""""###%%%&&&'''&&&%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&!!!"""######$$$$$$$$$###!!!"""""""""#########$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%###""""""###%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&"""######$$$%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&''''''((((((%%%%%%%%%&&&'''((())))))''''''''''''''''''''''''''''''''''''((((((((((((""""""""""""""""""############$$$%%%%%%%%%%%%$$$#########$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$#########$$$&&&(((((('''&&&%%%$$$$$$$$$###$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%!!!$$$&&&%%%######%%%'''%%%%%%%%%%%%%%%$$$###"""""""""""""""""""""""""""!!!""""""###$$$$$$%%%%%%#########$$$$$$%%%%%%&&&%%%%%%$$$###""""""######!!!!!!""""""#########$$$###"""!!!"""$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$#########"""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&#########$$$$$$%%%%%%%%%######$$$$$$$$$$$$######!!!$$$$$$###""""""###$$$$$$"""""""""###$$$%%%##############################""""""###$$$%%%%%%########################%%%$$$###""""""###$$$%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$#########""""""######$$$$$$$$$$$$################################################"""############$$$$$$$$$############$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$###############&&&%%%%%%$$$$$$#################################%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&"""###$$$%%%&&&&&&'''&&&#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$############$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%###""""""###%%%&&&"""############$$$$$$$$$""""""############"""""""""###%%%'''''''''%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&!!!!!!"""""""""######$$$!!!!!!""""""#########$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%###""""""###%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&""""""###$$$%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((())))))$$$%%%&&&'''((((((((((((''''''''''''''''''''''''''''''''''''((((((((()))###############"""!!!!!!"""############$$$$$$$$$%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###''''''&&&%%%%%%$$$######""""""###$$$%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&%%%###"""""""""######"""""""""""""""""""""""""""############$$$$$$$$$#################################"""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%"""############$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""""""""""""""""""""""""""######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$ !!!"""###$$$$$$%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$########################"""############$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$##############################$$$$$$$$$$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$###""""""###$$$%%%%%%$$$###""""""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""###$$$%%%%%%%%%##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&######$$$%%%%%%%%%$$$$$$'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%$$$$$$$$$$$$'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$###$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&'''###%%%+++---***&&&%%%'''''''''''''''((())))))))))))))))))((((((((((((###############""""""!!!"""############$$$$$$$$$%%%%%%$$$$$$############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$''''''&&&%%%%%%$$$###############$$$%%%%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&%%%###"""""""""###$$$########################"""############$$$$$$$$$#######################################$$$$$$%%%###$$$$$$%%%%%%&&&&&&&&&"""############$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########"""#################################$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$########################"""############$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$##############################$$$$$$$$$$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%$$$###""""""###$$$%%%%%%$$$###""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$%%%%%%##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%%%%&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$%%%%%%%%%&&&%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&)))''')))///111---)))((('''''''''''''''((())))))))))))))))))((((((((((((######$$$$$$######"""!!!"""############$$$$$$$$$$$$############"""""""""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$'''&&&&&&%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%$$$############$$$########################"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$%%%%%%""""""###$$$%%%&&&''''''"""############$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$####################################""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$############$$$$$$%%%$$$$$$######$$$$$$%%%########################$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&)))(((+++111222...***)))'''''''''''''''((())))))(((((((((((())))))))))))###$$$$$$$$$$$$###""""""""""""#########$$$$$$$$$###"""""""""""""""""""""%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$#########$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%%%%######$$$$$$%%%%%%%%%&&&""""""#########$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################"""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######%%%%%%%%%$$$$$$$$$#########$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$###$$$$$$%%%%%%$$$$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))'''&&&$$$$$$%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#################################$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&&&&'''''''''''''''%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&&&&)))...///+++'''''''''''''''''''''((())))))(((((((((((())))))))))))$$$$$$$$$$$$$$$###""""""""""""#########$$$$$$$$$"""""""""""""""""""""###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$#########$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%%%%%%%$$$$$$########################""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&%%%%%%%%%$$$$$$#########""""""#########$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%########################"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############"""""""""%%%%%%%%%$$$$$$$$$###############$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$###$$$$$$%%%%%%$$$$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))(((&&&%%%%%%&&&((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&''''''((((((''''''%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''''''''''''''''''''%%%$$$''',,,,,,'''&&&''''''''''''''''''((())))))'''((((((((()))))))))***$$$$$$$$$%%%$$$$$$###""""""############$$$$$$$$$"""""""""############$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%###$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%$$$###"""!!!!!!"""############$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""""""""""""""""""""###%%%%%%%%%$$$$$$$$$###############$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%"""############$$$$$$$$$###$$$$$$%%%%%%$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&'''((()))***&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%##############################$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&''''''((((((''''''%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&'''(((%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&&&&(((+++***&&&'''***'''''''''''''''((())))))''''''(((((())))))******$$$$$$%%%%%%$$$$$$###""""""############$$$$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%&&&'''''''''$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%###$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&%%%%%%$$$$$$######"""""""""############$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""""""""######$$$$$$$$$%%%%%%%%%$$$$$$$$$######"""######$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""############$$$$$$$$$###$$$$$$%%%%%%$$$$$$###""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((()))))))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&%%%$$$$$$%%%&&&'''(((((('''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&&&&##############################$$$$$$$$$%%%%%%%%%######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%%%%%%%&&&'''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&'''((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((('''''''''''''''''''''''''''&&&''')))'''$$$''',,,'''''''''''''''((())))))'''''''''((()))*********$$$%%%%%%%%%%%%$$$######"""############$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''(((((($$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&######$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%"""###%%%&&&'''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''###############$$$$$$$$$"""############$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$######""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""############$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))******))))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$%%%&&&'''(((((('''&&&%%%########################%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''##############################$$$$$$$$$%%%%%%%%%######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''$$$$$$%%%%%%&&&'''((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&'''((()))%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((((((((((((((((((((((('''%%%%%%&&&$$$"""&&&,,,'''''''''''''''((())))))&&&''''''((()))******+++######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%######$$$%%%%%%%%%%%%$$$%%%%%%%%%$$$$$$#########"""###$$$%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$######""""""###"""""""""$$$%%%$$$###'''&&&$$$###"""###$$$$$$%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''((((((((()))((((((((((((((((((((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%''')))******)))'''%%%""""""###$$$$$$$$$$$$###%%%%%%%%%$$$$$$$$$######""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%%%%######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$###""""""$$$&&&'''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%&&&''''''((((((''''''(((((('''''''''&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%&&&''''''((((((''''''(((((((((((())))))))))))))))))))))))************######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$######"""###$$$%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$#########"""$$$""""""###$$$%%%$$$###&&&%%%%%%$$$######$$$$$$%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''((((((((())))))''''''''''''''''''''''''%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&((())))))(((&&&%%%""""""###$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######"""######$$$%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%&&&%%%#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$%%%$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$###""""""$$$&&&'''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%&&&'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%&&&''''''((((((''''''(((((('''''''''&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%&&&''''''((((((''''''(((((((((((())))))))))))))))))))))))************######$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&'''###$$$%%%%%%%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&''''''''''''&&&%%%%%%%%%%%%$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$###"""$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$############$$$###"""###%%%%%%%%%###%%%%%%%%%%%%%%%$$$$$$###%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((()))))))))''''''''''''''''''''''''%%%&&&&&&&&&&&&'''''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&'''''''''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%'''(((((('''%%%$$$"""######$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$###############$$$$$$%%%%%%&&&######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$%%%&&&%%%###"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$###$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$#########$$$%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''(((((('''''''''''''''''''''&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&'''(((((((((((('''(((((((((((()))))))))))))))))))))*********++++++######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&"""###%%%&&&&&&%%%###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######"""$$$$$$$$$%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########"""######$$$%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""###%%%&&&%%%$$$$$$$$$&&&&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((()))))))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''(((((((((''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&''''''&&&$$$###"""###$$$$$$%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$###############$$$$$$%%%%%%%%%""""""###$$$&&&'''(((((($$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%###"""###$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%$$$######$$$$$$$$$###$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((('''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&'''((((((((((((((((((((((((((())))))))))))))))))*********+++++++++######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&"""###%%%&&&&&&%%%###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######""""""###$$$$$$%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$%%%$$$#########%%%&&&%%%$$$###$$$&&&''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&'''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((()))))))))***''''''''''''''''''''''''&&&&&&&&&'''''''''(((((('''''''''(((((()))))))))(((''''''&&&&&&''''''((((((''''''&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&%%%$$$$$$######$$$%%%%%%%%%%%%$$$%%%%%%%%%$$$$$$$$$#########$$$$$$$$$$$$$$$%%%%%%""""""###$$$&&&'''(((((($$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%$$$%%%&&&%%%###"""###$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%$$$###$$$############$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((('''''''''&&&'''''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&'''(((((())))))(((((((((((((((((())))))))))))************++++++++++++######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$###$$$%%%%%%%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''$$$$$$$$$$$$%%%%%%%%%%%%"""###$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""###$$$%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$###$$$%%%&&&&&&$$$$$$%%%%%%&&&&&&&&&&&&&&&###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&&&&''''''''''''&&&&&&'''''''''((((((((())))))))))))))))))))))))((((((((((((((((((((((((((((((((()))))))))******((((((((((((((((((((((((&&&&&&'''''''''(((((((((''''''(((((())))))******((((((''''''''''''(((((((((((('''&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$###$$$%%%%%%######$$$%%%###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###############$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%&&&''''''((((((''''''&&&&&&&&&'''''''''''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''((())))))))))))((((((((((((((())))))))))))*********++++++++++++,,,######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$########################&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''######$$$$$$$$$%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%$$$$$$$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&%%%%%%%%%#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""###$$$%%%&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$###$$$&&&'''&&&%%%%%%%%%%%%%%%%%%&&&''''''######$$$$$$$$$%%%%%%%%%##############################$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&''''''''''''''''''''''''(((((((((((())))))))))))))))))))))))(((((((((((((((((((((((((((((()))))))))*********))))))))))))))))))))))))''''''''''''((((((((((((''''''((())))))***++++++((((((''''''''''''(((((((((((('''&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$"""###$$$$$$$$$$$$%%%'''######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%##############################$$$%%%&&&&&&&&&&&&###############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$$$$$$$$$$$$$########################$$$$$$%%%%%%&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$######$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%%%%&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&%%%&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&''''''((((((''''''&&&&&&&&&'''''''''((((((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''((()))))))))))))))(((((((((((())))))))))))*********+++++++++,,,,,,######$$$$$$$$$%%%%%%%%%$$$$$$$$$#########""""""%%%$$$$$$######$$$$$$%%%########################'''&&&$$$$$$$$$$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$##################$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""###$$$%%%&&&$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$###$$$&&&'''&&&%%%&&&%%%%%%$$$%%%&&&((()))#########$$$$$$%%%%%%%%%##############################$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((''''''''''''((((((((()))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************))))))))))))))))))))))))''''''''''''((((((((()))'''(((((()))***+++++++++((((((''''''''''''(((((()))((('''&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$!!!"""$$$$$$$$$$$$&&&(((######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################"""###$$$%%%&&&'''''''''#########"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!"""#######################################$$$$$$%%%%%%&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&&&&%%%%%%%%%%%%((((((((((((((((((((((((%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''''''''&&&%%%&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%&&&''''''((((((''''''&&&&&&&&&'''''''''(((((('''''''''&&&&&&''''''''''''''''''''''''''''''''''''(((((()))))))))))))))(((((((((((())))))))))))******+++++++++,,,,,,,,,%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''%%%%%%$$$$$$%%%%%%&&&'''((((((&&&&&&&&&%%%%%%$$$$$$$$$#########$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$'''&&&%%%%%%''''''&&&%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%###"""""""""######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$#########%%%%%%""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''((((((((((((''''''$$$%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''''''''&&&&&&&&&'''''''''((((((''''''''''''((((((((()))+++,,,+++***((('''(((***++++++++++++***)))((('''+++******))))))))))))***+++***)))))))))***+++,,,***)))))))))))))))((((((&&&((()))++++++***((('''&&&&&&''''''(((((())))))'''''''''&&&&&&%%%%%%%%%''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$'''''''''&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%#########$$$&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$###"""!!!$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&%%%###""""""###%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%###'''***)))&&&%%%(((,,,&&&&&&&&&&&&&&&&&&&&&&&&'''%%%######$$$$$$###"""%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&'''((())))))***(((((((((((((((((((((((((((((('''''''''&&&&&&&&&(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))************++++++++++++++++++,,,,,,%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((('''&&&%%%$$$$$$%%%&&&&&&'''((((((&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$'''&&&%%%%%%''''''&&&%%%$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$############$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$############$$$%%%#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''((((((((((((''''''$$$%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&&&&'''''''''((((((((('''''''''((((((((())))))***+++,,,+++***)))***+++)))))))))))))))(((((('''---------------......///...---,,,+++***+++,,,,,,(((((((((((((((((((((((('''(((***+++++++++)))(((''''''(((((((((((((((((('''''''''&&&&&&&&&%%%%%%''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$''''''&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%#########$$$%%%&&&%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$###"""$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&%%%$$$""""""$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%,,,...000---(((%%%&&&)))&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%&&&'''&&&$$$%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''(((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''(((&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&'''''''''&&&&&&''''''((())))))***(((((((((((((((((((((((((((((('''''''''&&&&&&&&&(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))***************++++++++++++,,,,,,,,,%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&''''''((((((&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%'''&&&%%%%%%''''''&&&%%%$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######""""""###$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''((((((((((((''''''$$$$$$%%%%%%&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((()))))))))))))))***,,,,,,+++++++++,,,)))))))))***************,,,,,,,,,,,,---...///000...---,,,************+++))))))((((((((()))))))))((()))***,,,,,,++++++***))))))))))))(((((((((((('''''''''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%'''&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%###$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&%%%$$$######$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&...000000---)))&&&&&&(((&&&&&&&&&&&&&&&&&&&&&&&&'''&&&'''(((******(((&&&%%%&&&&&&&&&&&&'''''''''&&&&&&&&&%%%&&&&&&'''((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''(((&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&''''''((()))))))))(((((((((((((((((((((((((((((((((''''''''''''&&&(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))******************+++++++++,,,,,,,,,$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''###$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&%%%%%%'''&&&%%%%%%''''''&&&%%%$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&##################$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&''''''((((((''''''&&&$$$$$$%%%%%%&&&'''''''''''''''''''''''''''''''''''''''((((((((()))))))))(((((()))))))))*********)))+++------,,,******+++++++++++++++,,,---...///......---------......///...---,,,++++++,,,------,,,,,,+++******+++,,,,,,((()))***++++++++++++************))))))(((((((((((('''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%###%%%&&&&&&%%%$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&%%%$$$$$$$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&&&&''')))***)))'''&&&((()))''''''''''''''''''''''''&&&&&&''')))++++++)))&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&'''((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''(((%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&''''''''''''''''''((((((((((((''''''''''''''''''(((((())))))((((((((((((((((((((((((((((((((('''''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))((()))))))))*********************++++++,,,,,,---$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''''''''''''''''''''''''''$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''''''''%%%$$$$$$$$$$$$$$$$$$%%%&&&&&&'''''''''''''''(((''''''''''''''''''''''''(((''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%''''''&&&%%%%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&""""""######$$$$$$$$$$$$%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&''''''''''''&&&&&&$$$$$$%%%&&&&&&'''((((((((((((((((((((((((((((((((((((((()))))))))******)))))))))************+++***,,,---,,,+++)))******,,,,,,,,,,,,---...000111333222111000000000000000......---------///000111///...,,,+++++++++,,,---************************++++++******)))))))))((((((((((((((((((((((((((((((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%###%%%''''''%%%$$$$$$&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''(((((((((''''''''''''''''''''''''$$$%%%&&&'''''''''(((***''''''''''''''''''''''''%%%%%%&&&(((******(((%%%&&&&&&&&&'''''''''(((((('''&&&&&&&&&&&&'''((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&'''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''(((&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&''''''(((((((((''''''((())))))(((''''''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))((()))))))))************))))))***+++,,,,,,------###$$$$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&''''''((((((%%%%%%$$$$$$$$$$$$%%%%%%'''''''''''''''''''''''''''''''''(((((((((((((((''''''''''''''''''&&&&&&&&&&&&&&&&&&'''''''''''''''&&&%%%%%%''''''&&&%%%%%%%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''%%%&&&&&&&&&''''''''''''&&&&&&''''''''''''&&&&&&$$$$$$%%%&&&'''(((((()))(((((((((((((((((((((((())))))))))))************)))*********++++++++++++,,,------,,,******,,,......------,,,---///111222222222111000000000000000...---,,,,,,,,,---///000222000...,,,++++++,,,---------,,,++++++*********+++++++++***************(((((((((((())))))))))))((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%###&&&)))(((%%%###$$$&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&'''(((((())))))'''''''''''''''(((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&%%%&&&'''))))))'''%%%&&&&&&'''''''''(((((((((''''''&&&&&&''''''((()))((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&'''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&'''(((((())))))'''((()))******)))((('''''''''(((((((((((((((((((((((((((((((((((((((((('''(((((((((((()))))))))(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))************))))))***+++,,,------...######$$$$$$$$$%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$&&&''''''(((''''''''''''''''''''''''%%%&&&''''''((((((''''''%%%%%%&&&&&&'''(((((((((''''''&&&%%%%%%&&&''''''((((((((((((''''''''''''''''''((((((((()))))))))'''''''''''''''(((((((((&&&&&&&&&&&&'''''''''((('''&&&%%%%%%''''''&&&%%%%%%&&&&&&'''''''''''''''''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%"""###%%%&&&''''''&&&&&&$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&'''''''''(((&&&&&&&&&&&&''''''''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%&&&'''((())))))(((((((((((((((((((((((()))))))))*********++++++*********+++++++++,,,,,,---------,,,,,,...222555333222111000111222444666444444444444555666888888888777666444333333444444888666333000......///000111111///...,,,+++++++++******++++++++++++++++++(((((()))))))))*********((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$'''***((($$$"""$$$'''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&'''((()))))))))&&&'''''''''((((((((()))***))))))((()))(((((('''''''''''''''''''''''''''((('''&&&&&&'''((('''%%%''''''''''''(((((((((((('''''''''''''''(((((()))((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''((((((''''''&&&&&&''''''(((&&&&&&&&&'''((()))))))))'''((()))******)))((('''((((((((((((((((((((('''(((((((((((((((((((((((('''((((((((())))))))))))(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))************((()))***+++,,,------...#########$$$$$$%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$&&&'''((((((''''''''''''''''''''''''&&&'''(((((()))(((((((((%%%%%%&&&&&&'''((()))))))))((('''&&&&&&'''((()))(((((((((((((((''''''''''''((((((((())))))******&&&&&&''''''(((((())))))&&&&&&&&&'''''''''(((((('''&&&%%%%%%''''''&&&%%%%%%&&&''''''((((((''''''''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&"""###%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%'''((((((''''''$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&'''''''''((((((&&&&&&&&&'''''''''((((((%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%&&&'''((()))***)))))))))))))))))))))))))))************+++++++++******+++++++++,,,,,,,,,---------,,,...111777;;;999888666666666777999:::<<<===>>>???AAACCCEEEFFFKKKIIIGGGDDDBBBAAAAAAAAA???===999555333333333444555444222000...---,,,,,,*********++++++,,,,,,---(((((())))))*********+++))))))))))))))))))))))))''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$'''***)))$$$"""$$$'''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&'''((())))))***&&&'''''''''(((((())))))((('''&&&'''((()))((('''((((((((((((((((((((((((+++)))'''&&&'''((('''&&&''''''''''''((((((((()))'''''''''''''''((())))))))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&&&&'''''''''((((((&&&&&&&&&'''''''''((((((((((((''''''''''''((((((&&&&&&&&&'''((())))))***'''((()))++++++)))((('''((((((((((((((('''''''''(((((((((((((((((((((((('''((((((((())))))******(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))************((())))))+++,,,---......$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%$$$###$$$%%%&&&$$$$$$$$$$$$%%%''')))***((((((((((((((((((((((((''''''''''''(((((((((((('''''''''''''''((()))))))))))))))))))))))))))))))))(((((('''''''''((((((''''''''''''((((((((()))((((((((((((((((((((((((&&&&&&&&&'''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%$$$###$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''(((%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&'''((((((((((((((((((((('''''''''))))))))))))************)))***++++++))))))***++++++...111000......000333111111,,,---444333777FFFGGGAAA>>>???CCCGGGPPPXXXUUUVVVUUUUUU[[[eeekkkjjjnnnqqqqqqkkkaaa]]]___dddaaaZZZRRROOOJJJCCC>>>===FFF???999555444333111000...)))&&&'''((((((,,,000++++++++++++******))))))))))))))))))************(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''((((((((())))))((('''&&&%%%&&&&&&'''(((((((((((())))))))))))((((((''''''''''''(((((((((((((((((((((((((((((())))))(((((('''''''''&&&))))))))))))))))))))))))''''''''''''''''''''''''''''''''''''((((((((()))((((((((((((((((((((((((&&&&&&''''''(((((())))))&&&&&&&&&&&&&&&'''((()))((((((((((((((((((((((((''''''''''''((((((((((((&&&&&&&&&'''''''''((((((''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))((((((((((((((()))************************+++++++++,,,,,,---------$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%$$$$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%&&&'''&&&%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%''')))***((((((((((((((((((((((((''''''''''''(((((((((((('''''''''''''''((())))))(((((((((((((((((((((((((((((('''''''''''''''((('''''''''((((((((())))))((((((((((((((((((((((((&&&&&&'''''''''(((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''(((%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&'''(((((((((((((((((((((((((((((())))))))))))*********+++)))+++,,,,,,+++,,,---///444777999999666333222222888===;;;;;;===888:::HHHJJJJJJNNNXXXaaahhhpppxxx|||vvvuuuzzz{{{yyyzzzuuuqqqooojjjfffhhhmmmaaaWWWNNNKKKGGG???777555///---///444333---(((''',,,,,,++++++*********)))************************(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&''''''((('''''''''((((((((()))))))))((('''&&&&&&&&&''''''(((((((((((()))))))))***)))((((((''''''(((((()))(((((((((((((((((((((((())))))((((((((('''''''''))))))))))))))))))))))))'''''''''''''''''''''''''''''''''((((((((())))))(((((((((((((((((((((((('''''''''((((((((((((((('''&&&&&&&&&&&&'''((()))((((((((((((((((((((((((''''''''''''((((((((((((&&&&&&&&&'''''''''((((((''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))(((((((((((())))))************************+++++++++,,,------......$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%&&&'''))))))((((((((((((((((((((((((''''''''''''(((((((((((('''''''''''''''((())))))''''''''''''''''''''''''''''''&&&&&&&&&''''''(((''''''((((((((()))))))))((((((((((((((((((((((((''''''''''''((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''(((%%%&&&&&&&&&&&&'''''''''''''''&&&&&&''''''((()))(((((((((((((((((())))))))))))*********+++++++++(((***+++++++++,,,...000///222777;;;>>>??????>>>EEENNNNNNKKKKKKHHHNNN```gggggglllwww}}}uuusssuuutttqqqrrruuuzzz~~~|||yyyrrrrrruuuwwwvvvxxxpppgggiiifffXXXNNNMMM@@@888111///...+++,,,///...---,,,,,,++++++++++++++++++++++++++++++++++++((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&''''''(((''''''((((((((())))))))))))((((((''''''''''''(((((((((((()))))))))******))))))(((((((((((())))))(((((((((((((((((((((((())))))))))))(((((((((((())))))))))))))))))))))))(((((((((((((((((((((((((((((((((((())))))))))))(((((((((((((((((((((((())))))((((((((((((((('''''''''&&&&&&''''''((((((((((((((((((((((((((((((''''''''''''((((((((((((&&&&&&'''''''''(((((((((''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))(((((((((((())))))************************++++++,,,,,,---......///$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&''''''''''''&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&'''(((((()))((((((((((((((((((((((((''''''''''''(((((((((((('''''''''''''''((())))))'''''''''''''''''''''''''''&&&&&&&&&&&&''''''((('''(((((((((((()))))))))((((((((((((((((((((((((''''''((((((((()))))))))''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&'''''''''''''''''''''''''''(((((()))(((((())))))))))))***************+++++++++,,,,,,,,,---------,,,,,,...000---000666>>>EEELLLOOOQQQQQQ\\\]]]YYY\\\```nnn~~~|||yyywwwzzz~~~zzzyyyxxxpppwwwxxxkkkccceee]]]PPPBBB999444000111444///...---,,,,,,,,,------++++++++++++************((((((((((((''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''((((((''''''''''''(((((('''(((((((((((())))))))))))((((((((((((((((((((((((((()))))))))************))))))(((((())))))***))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((((((((()))))))))*********((((((((((((((((((((((((***)))))))))((((((''''''((((((''''''''''''((((((((((((((((((((((((((((((''''''''''''((((((((((((''''''''''''((((((((((((''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((()))(((((((((((())))))***************************++++++,,,---...//////000$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''((((((''''''&&&'''''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''((((((((())))))))))))))))))))))))''''''''''''(((((((((((('''''''''''''''((())))))''''''''''''''''''''''''&&&&&&&&&&&&&&&'''((()))(((((((((((()))))))))***))))))))))))))))))))))))((((((((()))))))))******((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''(((((((((''''''''''''((())))))))))))))))))******++++++++++++++++++,,,,,,,,,,,,000000000///---...000222<<<>>>AAAGGGOOOXXX```dddbbbooosssssszzz}}}vvvoooqqqsssjjjaaa[[[RRREEE999333111000...,,,++++++,,,---+++++++++******)))))))))))))))((((((((('''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''(((((((((''''''((((((((((((((((((((()))))))))***((()))))))))))))))))))))))))))))))))******************))))))))))))******************************)))*********************************************)))))))))))))))))))))))))))))))))************+++))))))))))))))))))))))))******))))))(((((((((''')))(((((('''''''''((((((((((((((((((((((((((((((''''''''''''(((((((((((('''''''''((((((((())))))((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((()))******************************+++,,,,,,...///000000111$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%$$$$$$$$$%%%&&&&&&&&&'''((())))))((('''&&&&&&''''''''''''&&&%%%%%%%%%&&&'''((((((((((((((())))))))))))))))))))))))''''''''''''(((((((((((('''''''''''''''((())))))'''''''''''''''''''''''''''''''''''''''((()))***((((((((()))))))))******))))))))))))))))))))))))))))))))))))************((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&''''''''''''&&&&&&%%%%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%&&&&&&&&&''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''(((&&&&&&'''''''''(((((((((((((((''''''(((((()))***)))))))))***++++++,,,,,,++++++,,,,,,,,,---------+++,,,---------///333777DDDHHHNNNUUU]]]hhhvvv}}}{{{zzzppplllggg\\\RRRMMM===:::666222///---,,,,,,,,,,,,,,,+++******)))))))))))))))(((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&'''''''''((((((((('''''''''''''''''''''''')))((((((''''''(((((()))((((((((()))))))))******((())))))************))))))))))))*********++++++++++++************++++++************************************++++++++++++************************)))))))))))))))))))))))))))*********++++++++++++))))))))))))))))))))))))***))))))))))))))))))((())))))((((((''''''((((((((((((((((((((((((((((((''''''''''''((((((((((((''''''((((((((()))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''(((((()))***+++************************+++,,,---...///111222222$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%$$$$$$$$$%%%%%%&&&'''&&&''')))******)))'''&&&&&&'''((((((((('''%%%%%%&&&&&&(((((()))(((((('''))))))))))))))))))))))))''''''''''''(((((((((((('''''''''''''''((())))))(((((((((((((((((((((((((((''''''((((((***++++++(((((()))))))))*********)))))))))))))))))))))))))))))))))*********++++++((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''(((''''''''''''((((((((((((((((((((((((((())))))***))))))******+++,,,,,,---,,,,,,,,,,,,------------)))+++///222666===DDDIIIQQQZZZdddlllsss~~~xxxxxx{{{qqqiiijjjssszzz|||zzzsssllllllwww|||xxxppphhheeeRRRNNNHHH@@@999444222111///......---,,,,,,++++++))))))))))))((((((((('''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%''''''(((((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''''''''((((((((((((''''''''''''''''''''''''))))))(((((((((((())))))(((((()))))))))*********((()))***+++++++++******))))))*********++++++++++++++++++******+++++++++++++++++++++++++++++++++*********+++++++++,,,,,,*********************************************************+++++++++,,,,,,)))))))))))))))))))))))))))))))))))))))***************)))(((((((((((((((((((((((((((((((((((((((''''''''''''(((((((((((('''((((((((())))))))))))((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''((()))***+++************************,,,,,,---///000111222333$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$%%%%%%&&&''''''((()))++++++)))((('''&&&'''((((((((('''%%%%%%&&&'''((()))))))))((('''))))))))))))))))))))))))''''''''''''((((((((()))'''''''''''''''((())))))))))))))))))))))))))))))(((((((((((()))***,,,,,,))))))))))))************)))))))))))))))))))))))))))************+++++++++))))))))))))))))))))))))''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&'''''''''((((((%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&'''''''''((((((''''''''''''((((((((()))((((((((((((((()))******))))))***+++,,,,,,------,,,,,,,,,---------......111444999@@@HHHQQQ[[[aaalllvvvyyytttvvv{{{|||tttxxx~~~{{{{{{wwwiii\\\fffaaaXXXMMMDDD===999666111111000///......------))))))))))))((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''((((((((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''''''''((((((((()))(((((((((((((((((((((((())))))(((((((((((())))))))))))))))))************((()))***+++,,,,,,+++***)))************+++++++++,,,++++++******++++++,,,++++++++++++++++++++++++*********++++++,,,,,,,,,******************************************************+++++++++,,,,,,,,,))))))))))))))))))))))))(((((())))))******++++++******)))(((((((((((((((((((((((((((((((((((((((''''''''''''((((((((()))(((((((((((())))))))))))))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''((()))++++++************************,,,,,,---///000222333333%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%&&&'''''''''''''''((((((((()))))))))(((((('''''''''&&&%%%%%%&&&&&&'''((())))))))))))))))))))))))))))))''''''((()))))))))))))))))))))))))))))))))))))))++++++++++++******)))))))))************+++++++++***++++++,,,,,,++++++***,,,,,,,,,,,,,,,+++))))))+++++++++************)))************************'''((((((((())))))******************))))))))))))'''''''''''''''((()))))))))((('''&&&&&&&&&&&&&&&%%%&&&&&&&&&'''(((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''%%%$$$$$$%%%&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&'''((()))'''((((((((())))))))))))***************************)))((()))+++,,,,,,,,,---,,,---//////...000333333DDDDDDJJJiii{{{}}}nnnhhhwwwzzzvvv|||nnnfffnnnxxx{{{uuuggg```ZZZLLL>>>???444,,,,,,---++++++...---+++)))((()))***)))(((******)))(((((((((((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&'''''''''$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&'''&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((('''''''''&&&&&&&&&&&&&&&&&&'''''''''((((((''''''''''''((((((((()))'''(((((()))))))))))))))))))))))))))******************)))))))))))))))*********+++++++++,,,,,,,,,(((***++++++******+++---***++++++,,,,,,++++++***////////////...,,,***(((---...---,,,+++---///111000...+++************))),,,,,,,,,,,,,,,---------,,,++++++***)))*********))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((''''''''''''((((((((()))(((((((((((((((((((((((())))))))))))))))))))))))(((((((((((((((((((((((('''''''''''''''((())))))(((((((((((((((((((((((((((((((((((())))))))))))******))))))((((((''''''))))))))))))******************+++++++++,,,,,,,,,,,,111---,,,000......888%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&&&&''''''''''''((((((((())))))))))))((((((((('''''''''%%%%%%&&&''''''((())))))))))))))))))))))))))))))(((((()))************)))************************,,,+++++++++************************++++++++++++++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,++++++++++++++++++++++++************))))))))))))))))))))))))((((((((()))))))))******************))))))))))))(((''''''''''''((()))))))))(((''''''&&&&&&&&&'''&&&&&&''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%&&&'''''''''''''''''''''''''''''''''''''''''''''(((((())))))))))))))))))))))))******************************))))))***,,,---------))),,,///111222555;;;BBBHHHYYY^^^jjjxxxoooqqqmmmmmmzzzvvvqqqwww~~~uuunnn___QQQGGG???:::999666///+++,,,+++)))((()))***++++++******))))))(((((((((((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&'''&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((('''''''''&&&&&&&&&&&&&&&'''''''''((((((((('''''''''((((((((())))))'''((())))))******))))))))))))))))))*********++++++******)))))))))******+++,,,,,,,,,,,,---------,,,---......,,,,,,---...///////////////...---,,,******++++++******)))((())))))************+++,,,(((***++++++*********+++,,,,,,++++++++++++******,,,,,,+++***************************************************************(((((((((((((((((((((((('''''''''((((((((())))))(((((((((((((((((((((((())))))))))))))))))))))))(((((((((((((((((((((((('''''''''''''''((())))))(((((((((((((((((((((((((((((((((((())))))))))))***)))))))))((((((((('''))))))))))))***************++++++++++++,,,,,,,,,,,,111......333000000:::%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''(((''''''&&&&&&&&&&&&'''''''''((((((((()))))))))))))))((((((((((((''''''&&&&&&''''''(((((()))))))))))))))))))))))))))))))))******+++++++++++++++************************,,,,,,++++++++++++************+++++++++,,,,,,,,,++++++,,,,,,,,,,,,++++++,,,,,,+++***+++,,,---...,,,,,,,,,+++++++++******)))))))))))))))))))))))))))))))))))))))*********++++++*********)))))))))((((((''''''(((((()))***)))(((((('''''''''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''###$$$$$$%%%&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''''''''((((((''''''''''''''''''''''''((((((((((((((())))))***+++*********************++++++++++++++++++++++++******+++,,,------......,,,000333555999BBBNNNWWW^^^kkkssswwwlllmmmvvv{{{yyyvvvzzzwww|||rrr[[[SSSJJJEEE>>>666000...---+++******+++,,,+++***))))))((((((((('''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&'''''''''%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''&&&&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((('''''''''&&&&&&''''''''''''((((((((((((''''''((((((((()))))))))(((((()))************)))))))))*********+++++++++++++++************++++++,,,------------.........+++,,,------+++***+++---,,,,,,------,,,,,,+++***.........//////000000111......000111111111000///,,,///333444222000000111------,,,,,,++++++******---,,,,,,+++++++++++++++************************************************((((((((((((((((((((((((''''''((((((((()))))))))(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))'''''''''''''''((())))))(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))(((((((((((())))))))))))************++++++++++++,,,,,,,,,,,,---111///111666222111<<<%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''((((((***)))(((''''''''''''''''''(((((((((((()))))))))))))))((((((((((((((((((''''''((((((((()))))))))***************************+++,,,,,,------,,,,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,++++++++++++++++++,,,,,,,,,---+++,,,,,,,,,,,,,,,,,,+++---,,,+++***+++---///111---,,,,,,,,,++++++++++++************************************************+++++++++*********))))))((((((((('''((())))))***))))))(((((('''(((((()))))))))((((((''''''&&&&&&''''''''''''''''''''''''((((((((((((((((((((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((()))))))))''''''''''''((((((((((((***)))))))))))))))******,,,,,,++++++++++++******++++++++++++++++++++++++***+++,,,---,,,,,,---...333555777;;;GGGYYYjjjrrrxxxuuuvvvsssbbbWWWPPPHHH???999111///,,,+++++++++***)))))))))))))))((((((''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((((((((((((((''''''''''''''''''((((((((()))))))))'''(((((((((((()))))))))((()))******++++++***************+++++++++,,,,,,,,,++++++++++++,,,,,,---------------............,,,---...---,,,+++,,,---,,,,,,------...---------++++++++++++,,,------...---,,,,,,---......---,,,------.........,,,+++***.........---------------...------,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++(((((((((((((((((((((((('''(((((((((((()))))))))(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))'''''''''''''''((())))))(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))((((((((((((((()))))))))************+++++++++,,,,,,,,,---------000...111666222333BBB%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((())))))***)))((((((''''''''''''(((((((((((()))))))))***(((((())))))))))))))))))((((((((()))))))))))))))++++++++++++++++++++++++++++++,,,---------------++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,------+++,,,,,,,,,------------,,,,,,,,,------,,,,,,,,,---,,,++++++,,,...000222------------,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++*********++++++++++++************((((((((((((((()))******))))))((((((((())))))***)))))))))((((((''''''&&&''''''''''''''''''''''''((((((((((((((((((((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((())))))*********'''''''''((((((((())))))+++***))))))))))))******,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++---...---+++,,,...111666888;;;EEE]]]zzz|||zzz~~~wwwqqqfffSSSBBB555111---************)))))))))******))))))((('''((((((((((((((((((((((((''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%&&&'''''''''&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((())))))((((((((('''''''''((((((((()))))))))******(((((((((((()))))))))***)))******+++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,---......---------............//////111222111000///000111111111111111111000//////////////////000000000000222000------///000000///333000---...111111///------------......////////////......---------------++++++++++++++++++++++++++++++++++++++++++++++++))))))))))))))))))))))))(((((((((((()))))))))***))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))'''''''''''''''((())))))(((((((((((((((((((((((((((((((((((())))))))))))(((((((((((())))))))))))((()))))))))************++++++,,,,,,,,,------------///---000555222:::PPP%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((())))))***)))((((((''''''''''''(((((((((((()))))))))******(((((())))))))))))******))))))))))))************+++++++++++++++++++++++++++,,,,,,---------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------......,,,,,,,,,---------......,,,,,,------------,,,,,,------,,,,,,---///000111......---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++,,,++++++++++++*********))))))(((((())))))***+++)))))))))))))))******+++))))))((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))*********)))'''''''''(((((())))))***+++******)))))))))))))))******+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---...---,,,///555:::999AAAKKK[[[vvv}}}zzzyyydddLLLBBB<<<444...++++++++++++)))***+++,,,+++***)))(((((((((((((((((((((((((((((((((((('''''''''''''''&&&&&&''''''''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%'''&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&$$$$$$%%%&&&''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((()))))))))(((((((((''''''))))))))))))************((((((((()))))))))************+++,,,,,,,,,,,,+++++++++,,,,,,,,,------------,,,,,,------...///000....../////////000000000...000111111000000111222000000111111111000000///555555777888888777666555666333111222444555333000555333222333444555222000------........./////////000//////...............,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,))))))))))))))))))))))))((((((((()))))))))******))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))'''''''''''''''((())))))(((((((((((((((((((((((((((((((((((())))))))))))(((((((((((())))))))))))))))))))))))************,,,,,,,,,,,,---------------///...000444666IIIjjj%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((()))******''''''&&&&&&''''''(((((((((((()))))))))*********(((((()))))))))*********************************,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,------------,,,------------------------,,,---------............------------............,,,,,,------------,,,,,,------....../////////000............------------........................------,,,,,,,,,+++++++++,,,,,,+++++++++*********))))))(((((())))))***+++***)))))))))******+++,,,((((((((((((((()))))))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''))))))***))))))&&&''''''((())))))************)))((((((((((((((((((((()))***+++,,,------,,,,,,,,,,,,,,,,,,,,,,,,***,,,......///555???GGGIIIZZZlllxxxtttoooqqqlll___VVVHHH;;;333...---,,,***+++,,,------,,,***)))(((((((((((((((((((((((()))((((((((('''''''''&&&&&&&&&''''''''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&###$$$%%%&&&''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((())))))))))))(((((((((''')))))))))*********++++++(((((()))))))))************++++++,,,---,,,,,,,,,,,,,,,,,,,,,------------------------...///000111111111111222222222333333111222444444444444666888999;;;>>>BBBFFFIIIKKKLLLCCCEEEHHHKKKLLLKKKIIIHHH@@@??????BBBEEEDDD>>>999<<>>>>>???AAACCCPPPSSSZZZbbbjjjrrrwwwzzznnnqqqvvvzzz||||||zzzxxxhhhiiilllqqquuuqqqhhh```cccnnnwwwrrrbbbTTTPPPRRR<<<;;;:::888666444333222111111000///////////////------------------------------------------------))))))))))))))))))))))))))))))))))))************))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((('''''''''''''''((())))))(((((((((((((((((((((((((((((((((((())))))))))))'''((((((((())))))******))))))))))))************,,,,,,,,,---------......---111111444999DDDlll&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((''''''''''''((((((((()))))))))))))))************************************++++++******************------------------------------...///...---,,,++++++---...---+++,,,///333------........./////////222///---.........000333222...---000333111///------///111333333111...,,,...222222///---//////---...//////...,,,,,,...000...---------......///000***++++++++++++******))),,,+++***(((((())))))***))))))))))))(((((((((((((((((())))))))))))(((((('''''''''''''''''''''''')))((('''&&&&&&&&&&&&&&&(((((('''&&&&&&&&&&&&'''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&'''&&&%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&&&&&&&'''((((((***%%%%%%)))***(((***///...(((###"""&&&((('''%%%%%%&&&''''''((((((''''''''''''''''''''''''''''''''''''''''''((((((((()))))))))))))))((((((((((((++++++++++++++++++,,,,,,000------//////,,,,,,///111000111666BBBRRRcccooozzzvvvqqqmmm\\\OOOAAA333+++***+++///111---''''''+++))))))))))))(((((((((((())))))(((((('''''''''&&&'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''&&&&&&(((((('''''''''&&&&&&&&&''''''''''''((((((((()))((((((((((((((('''''''''******)))))))))))))))***,,,------------,,,++++++++++++,,,...000000000...////////////////////////111333222///000555888777888===CCCGGGHHHJJJMMMPPPQQQ]]]fffaaaVVVTTTbbbqqqvvvsssuuu|||uuueeeZZZQQQCCC??????888;;;666222222555666222---000000///---***+++---000///000...,,,,,,------++++++++++++************)))+++++++++************)))************************+++*********))))))(((((())))))))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))''''''''''''((((((((()))))))))(((((((((((())))))((((((((()))******++++++,,,,,,,,,,,,------...///---///222666<<>>;;;===<<<888666666444000555111...///444444000+++///000111222111///---,,,............---+++)))((())))))******++++++++++++*********))))))))))))(((((())))))******))))))(((''''''''''''''''''''''''''''''&&&&&&''''''((()))(((((('''&&&&&&&&&&&&'''%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&(((((('''&&&'''(((%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&'''((((((******...666;;;===AAAEEE111---(((&&&'''(((&&&$$$&&&&&&'''(((((((((((('''''''''''''''''''''''''''''''''((((((((()))))))))))))))))))))))))))))))))+++++++++,,,,,,,,,------///------000000///333888888EEE\\\www~~~}}}tttppppppqqqsssrrrlll^^^BBB555******///000,,,************))))))))))))((())))))((((((((((((''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''(((((((((''''''''''''&&&''''''((((((((()))))))))(((((((((((((((((())))))++++++************++++++***++++++,,,------......------,,,,,,---...///000111111000000111333555666@@@IIISSS\\\gggttt|||~~~kkkXXXIIIAAA>>>;;;999666333222000---+++---,,,+++---...///...---,,,,,,,,,,,,++++++++++++,,,,,,,,,+++++++++******************************************))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))''''''((((((((()))))))))***))))))(((((())))))***(((((())))))***+++++++++,,,,,,,,,,,,---...///000111555666@@@ddd''''''''''''''''''''''''''''''''''''(((((((((((('''(((((((((((()))))))))))))))*********++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,------------......//////000000000000+++---000111000///000000...///000111333555777888999;;;::::::===CCCEEEDDDFFFIIIKKKJJJKKKKKKIIIEEELLLJJJGGGHHHKKKQQQWWWZZZVVVYYYXXXTTTPPPLLLEEE===AAA===888777999;;;999777888666333111//////000111---......///...---,,,++++++++++++++++++***))))))++++++*********))))))))))))))))))******)))))))))''''''''''''''''''''''''&&&&&&&&&&&&'''((()))***(((((('''&&&&&&&&&&&&'''%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&'''(((***)))'''&&&&&&'''%%%%%%%%%&&&&&&&&&&&&''''''&&&&&&&&&&&&'''(((((((((***...555:::===???AAA...+++(((&&&'''''''''%%%&&&&&&'''((((((((((((((('''''''''''''''''''''''''''(((((((((((()))))))))))))))***************+++++++++,,,,,,------......222///...///111444===GGGOOO^^^xxx~~~www{{{|||yyyuuu```MMM999111000///,,,+++++++++*********)))))))))))))))((((((((((((((((((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''(((((((((''''''''''''''''''(((((((((((()))))))))(((((())))))))))))******,,,++++++++++++,,,,,,---...............///000000(((+++///222222222111000222333555999@@@IIIRRRWWWppp|||jjjWWWMMMLLLHHHAAA<<<999777444111222...,,,///000///---,,,------------,,,,,,,,,+++---,,,,,,,,,++++++++++++*********************************)))))))))))))))(((((((((((((((((((((((((((((((((((())))))))))))(((((((((((((((((((((((('''(((((((((((()))))))))***))))))))))))))))))***((())))))******+++,,,,,,,,,,,,,,,,,,---///000111666:::???SSS'''''''''''''''''''''''''''''''''((((((((())))))(((((((((((()))))))))***************++++++++++++++++++++++++++++++++++++++++++,,,,,,------------,,,,,,,,,------.........000000000/////////000000...333888777333000222555777999;;;>>>???>>>===<<>>JJJSSS]]]jjj~~~oooaaaXXXUUUTTTJJJ>>>666777777111...///////////////.........---......---------,,,,,,,,,************************))))))))))))************))))))))))))))))))))))))''''''(((((())))))******))))))))))))))))))))))))((((((((()))))))))******+++******))))))******+++))))))******+++,,,,,,,,,,,,,,,,,,---...000111222555;;;TTT'''''''''''''''''''''''''''((((((((())))))))))))(((((()))))))))******************+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---.../////////......//////000111111222/////////000111333555777666777:::BBBMMMVVV[[[\\\\\\gggzzzxxxpppaaa\\\SSSJJJCCC>>>;;;;;;777555111...,,,---...///---,,,,,,,,,,,,+++++++++)))******++++++******)))((((((((((((((((((((((((((((((''''''((()))******(((((('''&&&&&&&&&&&&'''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''&&&((())))))'''&&&&&&'''&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&'''(((((((((+++***&&&&&&))))))&&&'''((((((((('''''''''(((''''''((()))))))))))))))(((((((((((((((((((((((((((((()))))))))***************++++++,,,------...,,,,,,---...///000111111111666AAAOOO^^^pppzzzxxxsssuuuzzzrrrbbbPPP???444000---,,,,,,,,,,,,+++++++++(((((()))))))))*********((((((''''''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''%%%%%%&&&&&&'''(((((()))'''((((((((())))))))))))(((((()))))))))*********))))))******+++,,,,,,---------------...///000111///.........000222555777888===FFFOOO[[[kkk|||}}}yyyzzzlllZZZKKKGGGBBB666000000000000000/////////..................------------************************((()))))))))************))))))))))))))))))))))))'''''''''((()))*********))))))))))))))))))))))))(((((()))))))))*********+++******))))))******+++)))******++++++,,,,,,---,,,,,,,,,---///000222333<<>>MMMJJJNNN^^^vvv}}}pppeee]]]YYYWWWIIIEEE???888333222222222---------,,,,,,,,,++++++******++++++++++++******))))))))))))))))))))))))((((((((((((((())))))***(((((('''&&&&&&&&&&&&'''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''###%%%'''(((''''''((()))&&&&&&&&&'''''''''(((((('''&&&&&&&&&&&&'''((((((+++...---'''''',,,---******++++++***(((&&&'''''''''(((((()))))))))))))))))))))))))))))))))))))))))))))))))))******************+++,,,,,,---......,,,,,,---...///000111222999BBBSSSgggzzz~~~xxxmmmWWWCCC999---------,,,,,,,,,++++++(((((())))))*********+++((((((''''''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&'''''''''((((((''''''''''''''''''''''''%%%%%%&&&&&&'''((())))))'''((((((((())))))******))))))))))))************))))))***+++,,,,,,---------------......000111111000000000222444888<<<>>>OOO[[[lll}}}|||hhh^^^RRRBBB888777000000000000//////////////////.........---------************************(((((())))))*********+++))))))))))))))))))))))))&&&''''''((()))******+++))))))))))))))))))))))))))))))))))))************++++++************++++++)))******++++++,,,------+++,,,,,,---///111222333>>>JJJwww))))))))))))))))))))))))))))))))))))************************************++++++,,,,,,,,,---------,,,,,,,,,---------......000////////////...---+++666...+++000444222111222555777999===DDDOOO[[[ddduuuvvv|||wwwaaaQQQDDD999555888...---,,,,,,...///...---------------------,,,,,,+++******)))))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((%%%&&&((()))))))))((('''&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&'''((((((((('''&&&&&&&&&&&&'''((((((******)))(((((((((((((((((((((((((((((((((((((((''''''((()))))))))))))))''''''''''''((((((((())))))************+++++++++,,,,,,+++++++++,,,------+++///222000---...555<<>>;;;666222///---,,,+++......---.../////////...++++++***)))))))))))))))***)))))))))((((((((((((((((((((((((((((((((((((&&&&&&((()))))))))((('''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&'''((((((***))))))(((((((((((((((((((((((((((((((((((((((''''''((()))))))))))))))'''''''''((((((((())))))************++++++++++++,,,,,,,,,+++,,,,,,---...***---/////////333<<>>888666444111...///---,,,,,,------,,,+++,,,+++******))))))************)))))))))(((((((((((((((((((((((((((((((((&&&''''''((()))(((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&'''&&&&&&&&&&&&'''(((((())))))((((((''''''((((((((((((((((((((((((((((((''''''((()))))))))))))))''''''((((((((()))))))))************+++++++++,,,,,,,,,,,,,,,,,,---.........//////000333;;;GGGPPPYYYbbb{{{ppp^^^CCC...***......***++++++*********)))))))))++++++******))))))((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&''''''(((((((((((((((''''''''''''(((((((((((())))))))))))))))))))))))((((((''''''(((((()))***((((((((()))))))))***************++++++,,,,,,,,,+++,,,---...///////////////---///444777777888<<>>444777444000///111111000...------,,,,,,,,,+++++++++++++++++++++++++++++++++))))))))))))))))))))))))((()))))))))************))))))))))))))))))))))))))))))*********+++++++++************)))))))))))))))******++++++,,,------,,,000...///333111999MMM}}}************************************++++++++++++------------------------,,,,,,---------................../////////000000---///111111222333666999<<>>???RRRvvvyyyhhhOOO===555444333222...------------,,,,,,,,,************************))))))))))))))))))))))))))))))))))))************)))))))))))))))))))))))))))************+++++++++(((((((((((())))))******)))******++++++,,,------...111//////555EEEttt******************************+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------.........//////000000000000111111111111222555<<>>RRRffflll___LLL???999666222///.........///...---++++++************************...,,,)))((()))******))))))))))))(((((((((''''''(((((((((((((((((((((((('''&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((((((((()))))))))))))))))))))))))))******++++++++++++++++++++++++++++++,,,---...000000111111111;;;XXXuuu{{{yyy{{{xxxqqqkkkvvv{{{qqqppptttzzzRRR999***///333+++'''+++++++++*********)))))))))'''(((((())))))(((((('''((((((((((((((((((((((((((((((((((((''''''''''''))))))))))))))))))))))))''''''((((((((()))))))))((((((((()))******++++++***+++++++++,,,,,,,,,,,,000,,,+++///111111111444:::FFF^^^||||||rrrqqqwwwbbbFFF;;;000---111333///)))...------,,,++++++,,,,,,,,,+++++++++************))))))))))))))))))))))))))))))))))))))))))))))))******))))))))))))******++++++************++++++))))))***+++,,,...000111///222777777BBBooo))))))*********+++++++++*********+++++++++,,,,,,,,,,,,,,,,,,------------000///------111555666555777666666;;;FFF\\\}}}iiiSSSDDD<<<888555444111000111000---******+++++++++******+++++++++000---+++)))*********))))))))))))(((((((((((('''(((((((((((((((((((((((('''&&&&&&&&&&&&''''''(((''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((())))))))))))))))))))))))))))))))))))***++++++,,,,,,++++++,,,,,,+++,,,,,,---...///---000444666<<>>^^^))))))*********+++++++++***++++++++++++,,,,,,,,,,,,,,,---------.........111//////000222222333333777:::EEEZZZsssuuu```PPPDDD===999222...000000,,,***,,,,,,,,,++++++++++++,,,,,,000...+++******+++***)))***)))))))))((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&'''((()))''''''''''''''''''''''''&&&'''''''''(((((())))))(((((((((((())))))******))))))))))))))))))))))))******+++,,,,,,,,,,,,+++,,,,,,,,,,,,---...///000...000333:::MMMooowwwzzz~~~yyy}}}{{{mmmJJJ---'''///111+++++++++++++++************(((((())))))))))))((((((((((((((((((((((((((((((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((()))))))))***))))))******+++,,,,,,,,,+++,,,,,,---......//////111333555555222666GGGXXX{{{ooo]]]dddxxxxxxiiikkkllljjjiiijjjgggdddeeekkkooonnnhhheeeiiimmm```kkkpppvvv|||tttvvvzzz]]]DDD666444888<<<111000///...------------,,,,,,,,,++++++++++++***************************))))))))))))))))))))))))******))))))))))))******++++++************++++++,,,,,,,,,,,,---...//////000222333GGGzzz)))************+++++++++++++++++++++,,,,,,,,,,,,---------.........//////111000000222111///111666<<>>JJJ^^^sssvvv```NNN>>>999444,,,,,,111...---,,,++++++,,,---...---+++))))))***+++++++++*********)))))))))((((((((((((((((((((((((((((((&&&&&&&&&&&&'''((()))***''''''''''''''''''''''''&&&&&&''''''((())))))***'''(((((()))******++++++))))))))))))))))))))))))***+++,,,,,,------,,,,,,,,,,,,------...000111222666===GGGYYY}}}uuu|||sss}}}vvvsss}}}yyyWWW999---,,,---,,,,,,+++++++++*********))))))************))))))((((((((((((((((((((((((((((((((((((''''''''''''))))))))))))))))))))))))(((((()))))))))***************++++++,,,---------,,,---...///000111111222222222666BBBUUUqqqrrrbbb[[[YYYVVVWWWXXXZZZaaakkkpppnnnooollliiieeeaaaaaacccgggffffffeeeccc``````aaacccaaaddd\\\XXX]]]]]]ZZZ___]]]\\\[[[^^^fffooouuuxxx}}}qqqXXXHHH@@@333333111000///.........------,,,,,,,,,+++++++++************************))))))))))))))))))))))))******))))))))))))******++++++************++++++++++++,,,,,,...///111111444888@@@ggg)))************+++++++++++++++,,,,,,,,,---------............/////////000......111555666<<>>222+++---333111,,,,,,...///+++)))***,,,...************************+++++++++************)))))))))))))))))))))))))))******+++++++++,,,,,,,,,...,,,+++,,,---///000000111555RRR++++++++++++,,,,,,,,,,,,,,,------......///000000333222222222222222222333333777888EEE```{{{vvvppptttyyymmmfff[[[VVV[[[dddfffbbbdddbbb\\\WWWYYY___cccccc^^^]]]```gggiiifffbbbbbbeeejjjqqqvvvwwwvvvuuuuuu}}}lll\\\RRRDDD999666...111111---,,,...---+++++++++++++++++++++++++++***)))))))))(((((((((((((((((((((((((((((((((((('''''''''''''''((())))))''''''(((((())))))******(((((('''''''''(((((()))(((((((((((()))))))))))))))************+++++++++******+++,,,------......)))222111...222222777DDDbbb~~~aaa```yyyPPP777...,,,,,,+++***+++---------***)))))))))(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))))))))))))))************))))))))))))************++++++,,,---...//////000//////222555444333666<<>>555///------------------------+++++++++*********))))))))))))))))))))))))))))))'''''''''''''''((())))))''''''(((((())))))******++++++***)))(((((((((((((((((((((((()))))))))))))))************++++++++++++,,,,,,---...///000000...444444???^^^~~~{{{wwwtttttt~~~KKK999+++---111...,,,...+++++++++*********))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))*********************+++++++++,,,,,,---...///000111222222333333999MMMlllwwwdddbbbtttzzzuuuqqqkkkbbb[[[[[[___XXX\\\cccmmm{{{~~~tttlllQQQ>>>///...000---+++...,,,,,,,,,,,,,,,,,,,,,,,,+++++++++************)))))))))))))))))))))))))))******+++++++++,,,,,,,,,)))---000000///111666;;;]]]............/////////000000000000111222222333333000777???GGGYYYzzznnncccqqqkkkmmmmmmgggiiioookkkxxxyyyrrrqqqpppiiibbb^^^aaacccfffgggfffdddccccccbbbbbbaaaaaafffrrrpppWWWKKK???222------------------------+++++++++************)))************************'''''''''''''''((())))))&&&''''''((()))******+++---,,,+++)))((((((''''''(((((((((((()))))))))))))))************+++++++++++++++,,,---...000000111...888<<>>KKK^^^rrr^^^^^^hhhhhhoootttooogggfffppp{{{xxxtttvvv~~~~~~~~~|||yyytttoookkkiiiaaa```eeecccZZZXXX___~~~www^^^NNN???111---,,,000111...***))),,,+++++++++***)))))))))))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))((((((((((((''''''''''''((((((((()))(((((((((((())))))))))))******+++++++++,,,,,,,,,111---+++---...------000:::---EEEqqqppp~~~dddcccwwwbbb>>>111222111......,,,,,,,,,+++++++++******))))))))))))))))))))))))))))))))))))))))))))))))++++++******************)))******++++++,,,------333///---///111222777===HHHkkkyyyuuuvvvsssoooiiiggghhhmmmrrrlllSSS888---...///...,,,...---,,,,,,++++++,,,,,,,,,,,,,,,+++++++++******)))************+++++++++************+++,,,---...,,,333000---222555<<>>EEE[[[~~~yyysssjjjdddhhhpppkkkoooqqqnnnlllsss~~~tttoooqqqnnnfffeeekkkhhh{{{ttt]]]JJJ>>>222......---...000,,,,,,++++++******))))))))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))(((((((((((('''''''''((((((((())))))(((((((((((()))))))))******++++++++++++,,,,,,,,,000,,,+++///000///000333777>>>aaaooo~~~nnnvvvSSS666555555000///,,,,,,,,,++++++++++++***))))))))))))))))))))))))))))))))))))))))))))))))++++++***************************+++,,,,,,------...///111333222111888AAA```yyy{{{xxxwwwuuusssrrr}}}hhhJJJ888333111000///...------,,,+++,,,,,,,,,,,,,,,,,,+++++++++******)))************+++++++++************+++,,,---......000---///555444:::LLL|||---........./////////000333111///000333777:::<<>>777222111//////...---,,,+++***)))************************))))))))))))))))))))))))'''((((((((()))))))))***(((((((((((()))))))))***))))))))))))************++++++,,,,,,,,,---------...---...000000///333888EEEbbbuuunnnzzzVVV999111...222---------,,,,,,,,,++++++******************************************************++++++,,,,,,,,,,,,+++,,,,,,---......//////222222333999EEE```zzz|||```JJJ999222111000///......------......,,,,,,,,,+++++++++******))))))*********+++++++++++++++++++++,,,---...//////---///777555111WWW......///000111222333333222666999:::AAAUUUuuuxxxmmmjjjhhhlllvvv}}}sssooojjj~~~iiiXXXIII;;;444222000000///...,,,+++******************************))))))))))))))))))))))))''''''(((((())))))******((((((((()))))))))******)))))))))*********++++++,,,,,,,,,,,,------------///......000///000666>>>TTTooouuu||||||jjjBBB000000111------------,,,,,,,,,,,,******************************************************++++++,,,---------,,,,,,---......//////000555111333CCC^^^uuurrrvvv^^^FFF555---000000///............///,,,,,,,,,+++++++++******)))************+++++++++++++++++++++,,,---...///...///111555444888hhh...//////000222333333444666999@@@KKK```yyyhhhcccjjjuuu}}}uuucccnnnyyybbbKKK<<<777111111000...---+++******************************))))))))))))))))))))))))'''''''''((()))*********(((((()))))))))*********))))))*********+++++++++,,,,,,,,,------------...///......000000333===GGGfff~~~sss{{{}}}xxx~~~NNN333333,,,...------------,,,,,,,,,******************************************************++++++,,,------...---------...//////000000777333<<>>RRRyyypppnnnkkkllltttyyyzzzgggXXX>>>444333333***(((---,,,+++++++++************)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************)))************+++++++++,,,,,,------------------333///000555555999LLLccc}}}uuuooohhhdddccceeeggggggjjjooouuuyyyyyywwwOOO111666222111////////////---+++++++++++++++++++++++++++***((('''***...///+++&&&***++++++,,,,,,------...000444333...+++///222222555IIIqqqqqqmmmzzzoooVVVJJJ999888444//////111///+++...------,,,,,,++++++*********+++++++++,,,,,,,,,++++++,,,------......///+++---777888555SSS---///111222333666888999@@@PPPsss}}}rrrnnnyyyxxx{{{~~~zzzVVVDDD;;;888111000222---++++++++++++************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************)))************+++++++++,,,,,,,,,------------......,,,///444666@@@\\\xxx}}}~~~yyyqqqjjjeee]]]XXXVVVWWWWWWUUUVVVZZZZZZ^^^eeemmmttt{{{{{{sssyyyZZZ333111///---,,,,,,------,,,++++++++++++++++++++++++++++++)))(((+++//////,,,(((***++++++,,,,,,---......---...///000111333666999EEEgggpppllljjjXXXOOO>>>111111333000...///...------,,,,,,++++++*********+++++++++,,,,,,,,,++++++,,,------......///111---222555;;;bbb,,,///222444444666:::???OOOrrr{{{tttrrrtttwwwsssXXXDDD:::222111111))),,,+++++++++************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************)))************+++++++++,,,,,,,,,---------......,,,,,,///333777IIIooo||||||uuusssooommmoootttzzz~~~{{{~~~~~~}}}~~~|||zzzzzz||||||zzz{{{zzzvvvxxxvvvsssqqqqqqsssvvvxxx}}}~~~vvvlllccc]]]ZZZVVVRRRPPPPPPOOOKKKKKKNNNNNNQQQVVV[[[aaahhhpppuuurrriiitttsss@@@222111///,,,,,,,,,,,,***)))++++++++++++++++++++++++,,,***))),,,//////,,,)))+++++++++,,,------.........+++---444555444999BBB[[[uuulll{{{nnneeeGGG111222555...,,,222...------,,,,,,++++++*********+++++++++,,,,,,,,,++++++,,,------......///444...000444BBBnnn...000444555333555>>>IIItttuuulllnnnxxxqqqTTT@@@111---...(((,,,,,,+++++++++*********))))))))))))))))))))))))((((((((((((((((((((((((((()))))))))************))))))*********++++++++++++,,,,,,------.........///000111333999QQQ{{{mmmsssvvvwwwhhhddd___^^^aaaggglllooovvvzzz~~~~~~{{{yyyxxx{{{|||}}}|||yyyuuurrrrrrrrrvvvwwwwwwyyy{{{zzzuuunnniiidddcccbbbbbbggglllmmmqqqvvvxxxwwwuuuttttttyyy{{{{{{{{{~~~zzznnnbbbZZZXXXXXXUUUQQQPPPRRRQQQNNNNNNQQQOOOPPPPPPQQQSSSXXX^^^bbbpppwwwyyyfffiiizzzSSS444666444000...---,,,***(((+++++++++++++++++++++++++++***)))+++---...,,,***++++++,,,,,,---.........222---///555333///===RRR}}}nnnvvvoooUUU;;;222000---,,,///...------,,,,,,++++++*********+++++++++,,,,,,,,,++++++,,,------......///111///333777EEEmmm111222444555333888JJJ]]]sssoookkklllwwwlllPPP666---///---,,,,,,,,,++++++++++++***))))))))))))))))))))))))((((((((((((((((((((((((((()))))))))************))))))*********+++++++++++++++,,,,,,---...//////000111222555@@@[[[}}}XXXnnn~~~tttrrrbbb___[[[ZZZ\\\```cccdddgggjjjmmmnnnmmmlllllllllkkklllkkkjjjhhhfffggghhhfffiiikkkkkknnnpppmmmgggddd___\\\[[[WWWUUUZZZcccjjjmmmrrrtttsssqqqnnnllljjjttt}}}uuuiii^^^ZZZ[[[___YYYUUUTTTUUUTTTRRRRRRVVVQQQSSSUUUWWW[[[```gggkkkxxxrrriiiqqqddd555666333000...------,,,+++++++++++++++++++++++++++)))(((((()))***+++***)))+++,,,,,,------...//////111...111444000222NNNnnntttsssiiiRRR888---000111,,,...------,,,,,,++++++*********+++++++++,,,,,,,,,++++++,,,------......//////000555888GGGrrr333333444666777DDDcccsssggglllqqqxxx}}}~~~aaa@@@000000...,,,,,,,,,,,,++++++++++++))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************)))************+++++++++***+++,,,,,,---...//////......000999KKKiiijjjcccPPPrrr}}}~~~xxxmmmggg^^^[[[XXXWWWZZZ```gggkkkkkkkkkllljjjiiiiiikkkmmmrrrrrrrrrrrrrrrtttxxx{{{yyyzzzzzzxxxyyyxxxqqqhhh```\\\\\\\\\XXXVVV```ooo~~~{{{|||}}}tttkkkfffeeehhhllliiidddaaaaaa___]]]^^^bbbiiinnnvvvjjjbbb|||FFF222///,,,,,,---...//////++++++++++++++++++++++++(((((((((((())))))******,,,,,,,,,---......//////---...111333555EEEmmmsssttt|||~~~iiiEEE222444555......------,,,,,,++++++*********+++++++++,,,,,,,,,++++++,,,------......//////111555888OOO333222444999@@@VVVlllcccrrrzzz}}}sssRRR===555---------,,,,,,,,,+++++++++))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************)))************+++++++++***++++++,,,---...///000///...111>>>XXXvvvyyy___]]]eee}}}{{{|||xxxnnnfff^^^\\\ZZZ[[[bbbrrrzzz^^^]]]bbbfffeeejjj~~~zzzxxxxxxyyy{{{{{{|||wwwsssrrrrrrqqqtttyyyooo[[[kkkbbb555222///------...//////++++++++++++++++++++++++((()))))))))))))))***+++,,,,,,------.../////////,,,000333555AAAaaavvvpppzzztttqqqrrruuurrrqqqpppqqqtttyyy~~~zzzuuuRRR:::333333111...------,,,,,,++++++*********+++++++++,,,,,,,,,++++++,,,------......///000000444===^^^222000333;;;GGGdddoooeeennnwwwvvvxxxeeeMMM>>>111---------,,,,,,,,,++++++))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************)))************+++++++++******+++,,,---//////000222000333CCC___|||kkk^^^eee{{{qqqdddcccbbbeeesssyyymmm]]]___gggpppuuu}}}{{{|||}}}xxxaaabbbqqqvvv>>>:::555111///...---,,,++++++++++++++++++++++++)))*********)))***+++---,,,,,,------.../////////000444555888LLLtttqqqbbbyyy~~~wwwmmmddd______aaa___]]]\\\\\\___dddjjjnnnqqquuurrrmmmwwwYYY@@@000...333......---,,,,,,++++++*********+++++++++,,,,,,,,,++++++,,,------......///...///555CCCkkk333666;;;>>>RRRqqqdddooo{{{~~~|||www~~~aaa@@@888000))))))111111)))''',,,******))))))))))))******)))))))))))))))******+++))))))))))))))))))))))))******+++++++++,,,,,,,,,---------------...000000---999111CCCuuudddmmmooowwwpppeeeffffffqqqyyyooo___ooozzzzzz|||vvvssszzz|||}}}{{{yyyzzz~~~jjj^^^```|||TTT666000555---///444,,,,,,++++++******++++++,,,******+++++++++,,,,,,,,,+++//////++++++000111...444333222@@@iiiyyy^^^www}}}vvvppphhh___YYYVVVVVVTTTSSSOOOMMMKKKMMMQQQSSSSSSRRR\\\^^^fffqqqvvvzzz~~~~~~wwwtttwwwxxxvvvvvvzzzvvvwwwyyy{{{{{{yyyuuusss|||}}}~~~~~~~~~|||yyyxxxuuussssssssssssssszzzpppyyyjjjRRR666+++111...///000///,,,+++***+++++++++++++++++++++++++++,,,,,,,,,---...///000111)))555555CCC|||444444:::HHHfff~~~eeeeeevvvwwwTTTEEE:::///)))...000+++))),,,******))))))))))))******)))))))))))))))******+++))))))))))))))))))))))))******+++++++++,,,,,,,,,------------...///000000000:::888HHHnnn}}}iii~~~yyysssnnngggmmmzzzzzzqqqbbbjjjvvv}}}vvvrrryyy}}}|||wwwzzzlll[[[WWWiiiSSS555///555...***///,,,,,,,,,++++++++++++,,,,,,***++++++++++++,,,,,,,,,***...///------222333111555666>>>WWWmmmzzzyyymmmeee___ZZZTTTMMMHHHFFFEEEEEEHHHFFFEEEFFFIIIJJJIIIHHHJJJJJJPPPZZZ```dddmmmxxx{{{yyywwwwwwyyyzzzyyywwwvvvvvvtttqqqssswwwtttooohhhccc```aaa___ZZZ[[[___ggggggfffeeedddeeehhhjjjiiijjjlllnnnooonnnmmmmmmpppooopppqqqmmmjjjlllqqqiiitttvvvqqqZZZAAA444333---.../////////...------++++++++++++++++++++++++,,,,,,,,,---...///000111333888666LLL333:::LLLjjj}}}fffdddrrrvvvppppppuuu{{{xxxvvvbbbPPP>>>...---000---************))))))))))))******)))))))))))))))******+++))))))))))))))))))))))))******+++++++++,,,,,,,,,------------...///000111///444===MMMeee~~~{{{yyyyyy}}}zzzwwwsssnnnkkkfffqqq~~~xxxqqqgggpppxxxttt}}}{{{www```SSSWWWppp[[[:::...666111)))+++...,,,,,,++++++++++++,,,,,,++++++++++++,,,,,,,,,,,,)))---000//////333555444333:::PPPwwwqqq~~~uuujjj^^^WWWNNNMMMJJJEEEAAA??????@@@@@@??????@@@AAABBBAAA@@@BBBAAABBBGGGKKKNNNSSSXXX```eeejjjllliiifffcccccc[[[ZZZZZZ[[[^^^______^^^______]]]\\\```eeefffbbbaaa`````````______eeelllsssuuuwwwwwwvvvxxx}}}~~~|||~~~rrrjjj~~~hhhRRR???333......000000000///...---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---...///000111333222888\\\888RRRvvvooodddcccttt~~~~~~~~~~~~|||{{{xxxttt}}}||||||}}}}}}zzzwwwpppiiihhhkkkmmmoooooommmppp{{{iiiQQQ888...///...+++)))+++******))))))******+++)))))))))))))))******+++))))))))))))))))))))))))******+++++++++,,,,,,,,,------------...///000111///000AAAUUUggg|||vvvqqqllliiigggfffppp}}}yyyrrrmmmkkk|||xxx~~~lllZZZSSS```pppHHH///444666---+++222,,,,,,,,,++++++,,,,,,,,,+++++++++,,,,,,,,,------***---000000000111444666555IIIooo|||yyyyyy|||~~~|||{{{zzzwwwuuurrrqqqppppppoooiiifffiiioooooojjjeeekkkhhhdddaaa^^^XXXPPPJJJGGGEEECCCCCCCCCDDDCCCBBBBBBBBBBBBCCCEEEFFFFFFFFFKKKHHHFFFGGGIIIKKKMMMNNNRRRZZZcccggggggeeegggiiiqqqrrrtttxxx{{{~~~~~~}}}xxxddd|||xxxcccHHH222111000000000000...,,,***,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---...///000111111111>>>mmmJJJxxxdddeeefffssszzzwwwvvvuuuuuuuuutttqqqnnneeeeeedddeeeeeecccaaa___ccchhhjjjgggfffhhheee```dddbbbbbbdddhhhkkkmmmmmmooojjjffffffeeeeeejjjqqquuutttooogggdddiiinnnppp|||}}}{{{aaaCCC222...---,,,+++++++++************++++++)))))))))))))))******+++))))))))))))))))))))))))******+++++++++,,,,,,,,,...............///111111444333HHH]]]qqq{{{ssskkkeeeaaa```fffnnn~~~{{{uuupppnnnooo~~~|||ssscccWWWZZZttt[[[222...777111,,,222---,,,,,,,,,,,,,,,,,,---++++++,,,,,,,,,---------,,,...000111//////333888AAAeeepppeeeeeeZZZYYYXXXZZZ]]]^^^]]][[[\\\[[[YYYYYYYYYZZZ[[[\\\XXXXXXXXXYYY\\\^^^]]][[[eeebbb___^^^^^^[[[TTTNNNNNNJJJFFFGGGKKKLLLIIIEEEHHHIIIIIIJJJKKKMMMOOOQQQNNNNNNNNNQQQWWW^^^aaabbbqqqzzzvvvrrrgggpppQQQ666222000......//////---+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---...///000111666555EEErrrhhhmmmbbbsss{{{}}}sssiiiccccccbbbcccdddffffffdddbbbXXXZZZ]]]___aaacccgggiiipppyyyyyyvvvuuuuuuzzzzzzsssqqqrrrssswww||||||vvvsssqqqllleeeooorrrxxx~~~~~~tttTTT;;;///---......++++++************++++++)))))))))))))))******+++))))))))))))))))))))))))******+++++++++,,,,,,,,,............///000111111555999MMMaaawwwsssyyyoooeee^^^[[[ZZZ```fff{{{~~~zzzyyy{{{}}}yyysssqqqrrrsss}}}~~~wwwfff[[[XXXfffppp<<<+++555222***000------,,,,,,,,,,,,------,,,,,,,,,,,,------------......000111///...555>>>TTT|||wwwfff______dddiiijjjlllooorrrtttsssqqqppppppqqqsssvvvzzz~~~yyy~~~vvvqqqyyyyyyiiiddd___]]]]]]\\\XXXTTTPPPPPPOOOOOOOOOQQQUUUYYYQQQWWW^^^fffrrreeeyyy{{{^^^GGG444000------///111000...,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---...///000111111222DDDssstttjjjttttttkkkbbb\\\WWWVVVVVVWWWZZZ\\\]]]\\\[[[UUU\\\eeekkkqqqyyy~~~sssqqqppprrrwww}}}oooMMM666---...000,,,++++++******++++++,,,)))))))))))))))******+++))))))))))))))))))))))))******+++++++++,,,,,,,,,............///000111222555EEEZZZiiiwwwnnn~~~xxxoooeee]]]ZZZZZZ^^^ddd{{{|||zzz|||}}}xxxpppnnnqqqzzz~~~kkk^^^XXX[[[zzzMMM///444333***///------,,,,,,,,,,,,------,,,,,,,,,------------...///...000222111111;;;GGGlllyyylllxxx{{{sssnnnnnnooogggfffddd```^^^aaafffkkklllwww~~~tttppplllooobbb>>>777000...///000///---------------------------,,,,,,,,,---...///000111+++333NNNxxxeeelll}}}}}}qqqeee]]]YYYWWWUUUQQQRRRSSSVVVXXXZZZYYYWWWVVV___jjjpppuuuzzz{{{}}}~~~|||]]]<<<------000,,,++++++******++++++,,,)))))))))))))))******+++))))))))))))))))))))))))******+++++++++,,,,,,,,,.........//////000111222:::UUUjjjwwwvvvqqq~~~yyyqqqggg```]]]^^^fffkkk|||}}}~~~xxxmmmjjjmmm}}}}}}rrrbbbZZZVVVlll]]]666666444+++000...------,,,,,,------...,,,,,,,,,---------......///...000333222444@@@OOO|||tttxxxxxx|||zzzwwwyyy}}}|||~~~}}}tttsss{{{vvv[[[{{{vvvIII@@@666000......,,,)))------------------------,,,,,,,,,---...///000111111>>>aaa