BM6P6(@ QQQMMMGGGCCCBBBCCCCCCDDDDDDDDDEEEEEEDDDBBBAAA@@@??????>>>>>>>>>??????@@@CCCCCCBBBBBBBBBAAAAAAAAA>>>===:::777666666666777666777888888888777666555666777888777555555777888888888666555444444444444555777888999888888999:::<<<<<<>>>BBBHHHNNNTTTXXX[[[gggvvv{{{iii\\\OOOPPPQQQRRRTTT[[[eeelllyyypppfffSSSGGGFFFEEEFFFFFFEEEBBB???CCC@@@>>>>>>AAABBB@@@>>>======>>>???@@@@@@AAAAAAAAAAAAAAA@@@@@@????????????@@@AAAAAABBBBBBAAAAAA>>>???@@@@@@???<<<:::888;;;;;;;;;:::999888666555222222222222222222222222333777===GGGVVVcccddd___aaafffttt{{{zzzyyyyyyyyyyyyvvvtttsssrrrrrrqqqrrrssstttuuutttsssssssssuuuxxx{{{}}}||||||}}}}}}}}}}}}|||{{{{{{wwwddd^^^WWWRRRQQQQQQPPPOOOUUUTTTXXXaaagggmmmyyyxxxooobbb]]]WWWTTTOOOIIIIIIKKKPPPYYYeeesss~~~vvviiieeeWWWKKKKKKQQQXXXdddnnnzzzmmmfffdddiii|||}}}xxxtttpppmmmjjjhhhhhhfffccc___\\\[[[[[[]]]cccpppsssccc[[[WWWQQQOOOSSSVVVVVVXXX^^^___bbbggglllqqqvvv{{{nnn[[[KKKCCC======>>><<<;;;===>>>>>>>>>@@@DDDHHHKKKLLLSSS[[[hhhxxxnnn\\\HHH@@@???===;;;:::>>>===@@@EEEFFFFFFNNNZZZ```YYYNNNDDD>>>===???BBBOOOSSSZZZfffzzz}}}tttsssyyy~~~uuurrrrrrnnnkkkkkkiiijjjkkkllllllkkkiiihhhhhhhhhgggfffdddccceeegggfffffffffeeeeeedddddddddccccccbbb```___^^^\\\\\\[[[[[[\\\\\\\\\[[[[[[ZZZ\\\[[[[[[ZZZYYYXXXXXXWWWXXXWWWVVVVVVVVVVVVUUUTTTRRRRRRRRRQQQOOOMMMJJJIIIKKKHHHDDDAAABBBDDDEEEEEE@@@AAABBBCCCCCCBBBAAA@@@>>>===<<<;;;;;;<<<===>>>AAAAAAAAAAAAAAA@@@??????;;;:::888555444444555555999999:::;;;;;;:::999888;;;;;;;;;999777666777999777777777777888999::::::;;;;;;;;;::::::;;;>>>@@@CCCFFFMMMVVV```jjjqqquuu~~~{{{pppeeeYYYQQQRRRVVVZZZ]]]bbbmmm|||uuufffccc^^^OOOGGGFFFEEEEEEFFFDDDBBB???CCC@@@>>>???AAABBBAAA@@@======>>>???@@@AAABBBCCC@@@@@@@@@@@@@@@@@@@@@@@@AAAAAABBBBBBBBBBBBAAAAAAAAAAAAAAA@@@>>><<<:::999;;;;;;::::::999777666555444444333222111111222222222555:::DDDSSS```ccc^^^\\\___jjjyyy|||zzzyyyxxxyyyxxxwwwuuuuuuuuutttssstttuuuvvvwwwssssssssstttuuuwwwzzz{{{}}}}}}}}}}}}}}}||||||{{{|||xxxfff```YYYUUUUUUWWWYYYZZZaaaaaafffooovvv}}}wwwkkkccc]]]WWWQQQNNNKKKHHHJJJOOOYYYdddsss~~~uuugggWWWOOOJJJMMMVVV___mmmxxxrrrffffffnnn{{{wwwssstttkkkjjjhhhffffffeeecccbbb`````````___^^^___aaadddoooyyy}}}yyyyyyoooaaaZZZRRRMMMKKKOOOPPPOOOQQQUUU\\\```eeekkkpppuuu{{{~~~~~~jjjYYYLLLDDD>>>>>>???>>>===???>>>======>>>AAACCCEEEEEEMMMUUUcccuuuooo]]]III@@@???===;;;:::<<<;;;???DDDFFFHHHQQQ[[[```YYYOOOEEE???>>>AAACCCMMMSSS]]]mmmyyyzzzxxxuuutttpppmmmlllhhhiiijjjkkkjjjiiigggfffgggggggggeeeccccccdddfffeeeeeeddddddddddddddddddbbbbbbaaa___^^^]]]\\\[[[ZZZ[[[[[[\\\\\\[[[[[[ZZZ[[[[[[ZZZZZZYYYXXXXXXWWWWWWVVVUUUUUUVVVWWWVVVTTTRRRRRRQQQPPPNNNLLLIIIHHHCCC@@@>>>===>>>@@@@@@@@@>>>???@@@BBBCCCCCCBBBBBB>>>===;;;::::::;;;===>>>???@@@BBBBBBBBBAAA???>>>999888777555444444555555777888888999999888888777777888888666444333444666777777777888888:::;;;<<<>>>??????@@@CCCGGGNNNSSS]]]dddooo|||zzz{{{}}}wwwmmmccc[[[WWWUUUUUU___fffnnnsssxxxppp```UUUXXXYYYNNNGGGEEEDDDDDDEEEDDDAAA???BBB@@@???@@@BBBCCCCCCBBB===>>>???@@@AAABBBBBBCCC>>>??????@@@@@@AAABBBBBBCCCCCCCCCCCCCCCBBBAAA@@@DDDCCCAAA???===<<<;;;;;;;;;;;;;;;:::999888777666777555333111000000111222111333777???MMM\\\aaa___XXXYYY```lllvvv~~~~~~~~~|||yyyxxxxxxxxxxxxwwwvvvuuutttttttttuuuvvvwwwsssssstttuuuvvvwwwxxxyyy}}}}}}}}}}}}||||||{{{{{{~~~}}}zzzkkkeee^^^ZZZ\\\bbbhhhkkkoooqqqwwwzzzssskkkccc\\\WWWQQQLLLJJJHHHIIIPPPYYYgggvvvnnn```MMMKKKLLLSSS\\\iiixxx}}}nnneeebbbnnn|||qqqiiiaaa]]]]]]ZZZ[[[]]]___aaacccdddeeedddfffhhhjjjmmmsssyyy~~~vvvyyy{{{rrreee^^^RRROOOMMMOOOOOONNNPPPSSSXXX]]]cccjjjpppuuu{{{zzzkkk\\\OOOGGG@@@@@@AAA??????AAA????????????????????????FFFMMMZZZmmmppp^^^JJJAAA???===;;;::::::;;;>>>CCCFFFJJJSSS\\\___YYYNNNEEE@@@???BBBEEEMMMVVVcccsss}}}{{{|||xxxvvvrrrooonnnggghhhhhhiiiiiigggfffeeefffgggfffeeebbbbbbcccdddccccccccccccccccccdddddd``````___^^^]]][[[ZZZZZZZZZZZZ[[[[[[[[[[[[ZZZZZZZZZZZZZZZYYYXXXXXXWWWWWWVVVUUUTTTUUUVVVWWWVVVUUUQQQQQQQQQPPPMMMKKKHHHFFF@@@>>>;;;;;;;;;<<<;;;;;;???@@@AAACCCCCCCCCCCCBBB???>>><<<::::::;;;===>>>???@@@BBBDDDCCCAAA???===999888777666666666777777666666777777777888888777666777777777666666888999;;;;;;:::::::::;;;<<<<<<>>>BBBJJJRRRZZZdddmmmsss~~~uuuiiibbbdddjjjnnnnnnppplllddd\\\XXX\\\eeemmmyyywwwbbbTTTLLLRRRUUULLLFFFEEECCCCCCDDDCCCAAA???AAA@@@@@@AAABBBCCCDDDDDD@@@@@@@@@@@@@@@AAAAAAAAA======>>>???AAABBBCCCDDDEEEEEEEEEDDDCCCBBB@@@???FFFDDDAAA>>><<<<<<<<<<<<<<<<<<<<<;;;:::999888888999777333111///000111333111333555;;;HHHWWW______XXXWWW[[[cccmmm~~~}}}xxxzzz~~~zzzxxxxxxyyyyyyxxxuuutttsssrrrrrrssstttuuutttuuuvvvwwwxxxxxxxxxxxx}}}}}}|||{{{{{{{{{{{{{{{~~~}}}zzzqqqlllfffbbbeeemmmvvv{{{{{{xxxoooiiiddd]]]YYYSSSNNNJJJIIIKKKPPP]]]iiiyyyvvvcccUUUKKKMMMQQQXXXbbbqqqnnndddbbbkkktttfff```]]]ZZZYYY[[[___bbbgggkkkooorrruuuvvvyyy{{{}}}}}}}}}ooofff]]]ZZZUUURRROOOOOOSSSWWWWWW\\\cccjjjqqqwww|||zzzmmm```SSSJJJBBBAAAAAA??????@@@AAABBBBBBBBB@@@???>>>>>>AAAGGGPPP___uuuqqq^^^JJJAAA???===;;;:::<<<===@@@CCCGGGMMMUUU\\\]]]WWWMMMEEE@@@@@@DDDGGGOOOXXXfffvvv~~~~~~zzzwwwsssoooooohhhhhhiiiiiihhhgggfffeeeffffffgggeeecccaaabbbcccbbbbbbbbbbbbbbbccccccccc___^^^]]]\\\[[[ZZZYYYYYYYYYYYYZZZZZZ[[[ZZZZZZZZZYYYYYYYYYXXXXXXWWWWWWWWWUUUTTTSSSTTTVVVWWWWWWVVVRRRRRRQQQPPPMMMJJJGGGFFF???===;;;:::;;;<<<;;;:::???@@@AAABBBBBBAAA@@@???>>>===;;;999999:::;;;<<<<<<>>>@@@AAAAAA???<<<:::777777777777777888888888888888888888999999:::::::::;;;<<<<<<<<<<<<>>>@@@@@@@@@@@@AAACCCDDDFFFGGGIIIRRRaaaqqqmmmddd[[[XXX[[[___aaabbbgggeeeaaa^^^```lll}}}}}}eeeTTTLLLGGGMMMPPPHHHFFFDDDCCCBBBBBBBBBAAA???@@@@@@AAAAAABBBCCCDDDEEECCCCCCBBBAAA???>>>>>>===<<<<<<>>>???AAACCCDDDEEEFFFEEEEEEDDDCCCAAA@@@???FFFDDDAAA>>><<<<<<<<<===============<<<;;;::::::999777444111000000222333222333444888DDDTTT]]]^^^VVVVVVXXX___iiiyyy|||~~~}}}zzzzzz{{{{{{zzzuuuuuussssssrrrssstttuuuwwwwwwxxxyyyyyyxxxxxxwww{{{{{{zzzyyyyyyzzz{{{{{{}}}zzzwwwsssnnnkkkmmmttt}}}{{{uuulllddd___ZZZVVVRRRNNNKKKJJJMMMQQQ[[[kkkzzzlllZZZNNNIIINNNTTT\\\iii{{{rrriiiccckkk}}}kkkbbbZZZYYY[[[]]]aaafffpppvvv}}}yyy~~~}}}tttsssnnndddXXXPPPPPPTTTXXXYYY^^^fffmmmsssyyy~~~}}}sssfffVVVMMMDDDBBBAAA??????@@@BBBEEEGGGFFFCCC@@@??????AAACCCIIIRRRbbbyyy{{{{{{rrr___LLLCCCAAA???===<<<@@@BBBCCCEEEIIIQQQXXX[[[\\\VVVMMMEEEAAABBBFFFIIIQQQZZZhhhvvv~~~yyyvvvrrrooonnnkkkkkkjjjjjjiiihhhggggggggghhhhhhgggdddbbbbbbcccbbbbbbbbbbbbbbbbbbbbbbbb]]]]]]\\\[[[ZZZYYYYYYXXXWWWXXXYYYZZZZZZZZZZZZZZZXXXXXXXXXXXXWWWWWWWWWWWWUUUTTTSSSTTTVVVWWWVVVUUUTTTSSSRRRPPPMMMJJJGGGEEE@@@===:::999999:::::::::===>>>?????????>>>===<<<<<<;;;::::::999999999999999:::<<<<<<<<<;;;999888666666777888888999::::::888777777777888999:::;;;999;;;===???@@@CCCFFFIIILLLMMMOOOSSSWWW[[[___aaahhhsssrrrbbb[[[VVVVVVYYYZZZ[[[]]]dddfffiiimmmwwwjjjVVVLLLKKKIIIMMMQQQKKKFFFDDDBBBAAAAAAAAA@@@???@@@AAABBBAAA@@@AAACCCEEECCCBBBAAA@@@>>>===<<<;;;<<<<<<>>>???AAACCCDDDEEEEEEEEEDDDDDDBBBAAA??????DDDBBB@@@===<<<<<<======<<<=========<<<<<<;;;:::888666444222111111222333222333444777AAAOOOYYY\\\TTTTTTWWW]]]gggwww~~~xxxssstttxxx}}}~~~~~~}}}|||{{{xxxwwwvvvuuuuuuuuuvvvwwwyyyyyyxxxxxxxxxwwwwwwwwwxxxxxxwwwwwwwwwyyyzzz{{{}}}{{{zzzxxxuuurrrqqquuu||||||rrrmmmeee^^^YYYUUURRRPPPJJJKKKNNNUUU]]]iii|||xxxcccTTTLLLGGGOOOXXXdddvvvtttiiihhhlll}}}{{{lll___[[[[[[```eeellluuu}}}yyy{{{yyyfffYYYVVVXXXZZZ\\\aaaiiipppuuuyyy}}}}}}}}}rrrXXXNNNFFFDDDCCCBBBBBBDDDGGGKKKMMMLLLGGGBBB@@@@@@BBBCCCFFFJJJTTTeeeyyyooocccbbbfffkkkuuuuuubbbOOOGGGEEEDDDBBBAAADDDFFFGGGHHHMMMVVV\\\]]]\\\WWWNNNGGGDDDEEEJJJMMMTTT]]]hhhttt~~~xxxuuuqqqnnnnnnmmmllllllkkkjjjiiihhhhhhiiijjjkkkiiigggeeeddddddcccccccccbbbbbbbbbaaaaaa\\\\\\[[[[[[ZZZYYYYYYXXXVVVWWWXXXYYYYYYZZZZZZYYYWWWWWWWWWWWWWWWWWWWWWWWWUUUTTTSSSTTTUUUVVVUUUTTTSSSSSSRRROOOLLLHHHEEECCCRRRMMMGGGBBB???>>>=========>>>???@@@AAAAAA@@@@@@======>>>>>>===<<<:::999:::;;;;;;;;;;;;:::999999999999;;;<<<===>>>>>>???===<<<<<<<<<===>>>???@@@AAAFFFLLLSSSZZZaaaiiimmmrrrssswww{{{xxxccc[[[VVVTTTWWWYYYZZZ^^^dddnnnttt}}}www```OOOKKKNNNKKKMMMPPPMMMFFFDDDAAA@@@@@@AAA@@@??????AAABBBAAA??????AAACCC@@@@@@???>>>>>>======<<<<<<===>>>???AAABBBDDDDDDCCCCCCCCCCCCBBB@@@??????AAA@@@???===<<<<<<======;;;;;;;;;;;;;;;::::::999666555444333333333333333000222333555===KKKTTTWWWWWWWWWWWW[[[eeeuuu}}}pppmmmoooqqqssswww~~~~~~|||yyyxxxvvvuuuuuuuuuvvvwwwzzzyyywwwuuuttttttuuuuuuuuutttttttttuuuxxxzzz|||~~~}}}{{{{{{yyyuuurrrrrrvvvyyyzzzrrrjjjfff```ZZZUUUSSSQQQPPPMMMPPPXXXbbblllyyyhhhXXXPPPLLLLLLVVVdddtttmmmgggkkk~~~}}}mmmfff^^^aaaiiiuuuyyy}}}mmm^^^ZZZ[[[[[[___dddkkkqqquuuxxx{{{}}}~~~~~~uuuWWWNNNFFFFFFGGGGGGIIILLLRRRVVVYYYVVVOOOHHHEEEDDDDDDEEEGGGIIIPPP]]]mmmxxxuuudddYYYWWWZZZWWW___hhhqqq{{{xxxfffSSSKKKKKKJJJHHHHHHFFFIIIJJJJJJPPP[[[bbbbbb___YYYQQQJJJHHHJJJOOORRRZZZaaahhhppp|||}}}wwwuuuqqqoooooonnnmmmlllkkkjjjiiihhhhhhkkklllmmmllliiigggffffffeeeeeedddcccbbbaaaaaa```\\\\\\[[[[[[ZZZYYYYYYYYYUUUVVVWWWXXXYYYYYYYYYYYYVVVVVVVVVVVVVVVVVVVVVVVVVVVUUUSSSTTTUUUUUUTTTSSSRRRQQQPPPMMMIIIEEEBBB@@@mmmfff]]]TTTNNNJJJGGGEEE>>>???AAADDDEEEFFFFFFEEE@@@AAACCCCCCBBB@@@>>><<<>>>>>>======<<<<<<<<<<<<===>>>@@@AAACCCDDDDDDDDDHHHHHHGGGGGGHHHIIIKKKLLLXXX^^^hhhtttjjjWWWVVVSSSSSSYYY[[[]]]eeennnyyyiii[[[LLLIIILLLGGGFFFJJJHHHFFFDDDAAA@@@@@@@@@@@@??????AAABBBAAA>>>===???BBB============>>>>>>>>>>>>======>>>???AAABBBCCCDDDBBBBBBBBBBBBAAA@@@?????????>>>>>>===============999999:::::::::999888888444444444444444444333333///111222333;;;HHHQQQTTT]]][[[YYYZZZcccrrrpppeeegggpppwwwxxx}}}~~~|||wwwvvvuuussssssssstttuuuyyyxxxuuusssrrrrrrssstttsssrrrrrrssstttwwwzzz|||{{{}}}~~~{{{{{{zzzvvvqqqnnnooorrrttt}}}}}}{{{xxxzzzxxxtttrrrssspppkkkaaa^^^YYYTTTPPPNNNMMMMMMQQQVVVaaammmyyyttt\\\PPPLLLKKKUUU```qqq{{{llljjjpppppphhhgggccckkkzzz}}}vvvzzz{{{tttzzzyyyhhh[[[XXXXXXVVV```eeelllqqquuuwwwzzz{{{~~~mmmVVVNNNGGGGGGJJJLLLOOOSSS\\\```ccc___VVVNNNJJJIIIDDDFFFHHHLLLRRR]]]kkkuuu{{{|||zzzpppbbbXXXWWWXXXUUU[[[bbbhhhrrr|||~~~{{{iiiWWWOOOOOONNNMMMLLLFFFJJJKKKKKKSSS```ffffffaaa\\\TTTMMMKKKMMMRRRVVV```dddhhhmmmvvv}}}wwwuuurrrooopppnnnmmmllljjjiiihhhhhhhhhmmmnnnooonnnkkkhhhgggggggggfffeeedddcccaaa``````\\\\\\[[[[[[ZZZZZZYYYYYYUUUVVVWWWXXXYYYYYYYYYYYYVVVVVVVVVVVVVVVVVVVVVVVVWWWUUUTTTTTTUUUUUUSSSRRRPPPOOONNNKKKGGGCCC???===~~~sssjjjccc[[[UUUPPPNNNOOOTTTXXXYYYXXXWWWPPPSSSUUUUUURRRMMMIIIGGGGGGBBB???>>><<<;;;@@@FFFEEEIIIKKKJJJPPPZZZ```___cccbbb^^^[[[[[[___eeejjjwwwuuuhhh[[[SSSRRRUUUYYYZZZ^^^iiizzz~~~lll[[[UUULLLFFFEEEGGGIIIKKKGGGEEEDDDBBBAAAAAAAAABBB=========<<<;;;;;;::::::>>>>>>>>>>>>============>>>@@@CCCEEEEEEDDDAAA@@@>>>???@@@@@@@@@@@@???>>>??????===<<<;;;;;;;;;;;;777777666666666666777777777666666555444444333333666333222444777>>>JJJWWWaaaZZZTTTVVVaaaqqq~~~ssshhhdddffflllrrr}}}~~~|||yyyxxxwwwuuutttsssssssssxxxyyywwwtttooonnnpppsssrrrsssuuuvvvxxxzzz{{{|||~~~}}}zzzuuuqqqoooqqqrrrqqqrrrssssssrrrooollljjjkkkmmmnnnmmmiiidddaaa```YYYWWWSSSNNNLLLNNNSSSWWWXXXcccqqquuucccUUUMMMMMMQQQXXXmmmsssiiiooo}}}nnnhhhfffcccpppyyyvvvtttuuuwww{{{}}}~~~tttnnnssswwwnnniiiccc^^^\\\[[[ZZZYYYfffgggjjjnnnrrrvvvyyyzzzrrrbbbVVVTTTQQQOOOQQQYYYdddkkkvvv}}}xxxgggVVVNNNKKKKKKHHHIIIPPPWWW]]]iiivvv~~~xxxlll___WWWWWWZZZ[[[___ccchhhrrr~~~rrr^^^TTTVVV[[[\\\YYYQQQNNNLLLRRR\\\eeeiiiiiibbbaaa]]]WWWSSSTTTZZZ```eeegggiiilllrrr|||zzzxxxrrrnnnllllllkkkiiihhhggggggggghhhjjjiiiiiihhhgggfffeeeeeeeeefffggggggeeeaaa^^^\\\[[[[[[ZZZZZZYYYYYYXXXXXXYYYYYYYYYYYYZZZZZZZZZZZZYYYXXXWWWVVVVVVVVVVVVVVVSSSTTTTTTTTTTTTSSSSSSRRRPPPOOOMMMJJJFFFBBB???===xxxgggiiioooyyy}}}}}}|||wwwpppggg___[[[UUUOOOKKKIIIHHHJJJQQQZZZccchhhkkknnnvvvsssooolllkkkooosssuuuuuupppmmmiiiddd___YYYTTTQQQNNNUUU___gggqqq{{{oooddd]]]VVVNNNHHHEEEFFFHHHHHHHHHFFFDDDBBB@@@?????????;;;;;;;;;<<<======>>>>>>>>>>>>>>>=========<<<<<<>>>???AAABBBCCCBBBAAA@@@>>>???@@@AAAAAA@@@???>>>??????>>>>>>===<<<<<<;;;999888777777777777777888666666555555444333333333333111111444666;;;GGGRRR\\\YYYVVVYYYbbbppp~~~{{{rrrjjjgggjjjqqqwww|||}}}{{{zzzyyyxxxvvvuuuuuuttttttxxxyyyxxxuuuqqqpppqqqsssrrrssstttvvvxxxyyy{{{{{{~~~~~~{{{vvvrrrooonnnnnnmmmlllkkkjjjhhhgggeeeeeedddeeefffddd```[[[YYYXXXQQQQQQQQQQQQRRRXXX___dddjjjtttzzzgggXXXNNNKKKOOOUUUccc{{{|||mmmgggssswwwiiieeejjjppp{{{yyyvvvvvvxxxzzz{{{|||{{{}}}wwwnnnjjjnnn{{{rrreeeaaa]]][[[\\\^^^______bbbcccfffjjjooosssvvvxxx|||~~~wwwnnnbbbWWWPPPQQQSSSWWW___kkkyyyrrr___SSSPPPOOOMMMNNNVVV^^^gggttt~~~rrrggg``````aaabbbfffjjjoooyyy{{{iii___```bbb```]]]VVVSSSQQQVVV___gggjjjjjjaaa```^^^YYYVVVWWW]]]bbbhhhiiikkknnnsss|||{{{xxxsssooommmmmmllljjjhhhgggggghhhhhhhhhhhhggggggffffffeeeeeeeeefffffffffccc```\\\ZZZYYYYYYYYYXXXXXXWWWWWWWWWYYYYYYYYYZZZZZZZZZZZZ[[[ZZZYYYXXXWWWVVVVVVUUUVVVSSSSSSTTTTTTSSSSSSRRRRRRMMMLLLJJJGGGDDDAAA>>>===~~~wwwpppjjjhhhhhhmmmxxxsssjjj\\\ZZZXXXYYY[[[^^^``````^^^[[[VVVRRRRRRTTTXXXZZZbbbkkkwwwkkkaaa]]][[[\\\VVVNNNHHHEEEEEEEEEEEEHHHFFFDDDAAA???>>>>>>>>><<<<<<<<<===>>>>>>??????>>>============<<<<<<<<<>>>>>>>>>???????????????>>>???@@@AAAAAA@@@???>>>>>>>>>??????>>>===<<<;;;:::999888888777777777777555555444444333222222222///...000333555999BBBLLLXXXYYYZZZ[[[___kkk|||wwwqqqooorrruuu|||}}}{{{{{{zzzyyyxxxwwwvvvvvvvvvwwwxxxxxxwwwtttsssssstttssssssuuuvvvxxxyyy{{{{{{~~~~~~|||xxxsssoookkkhhhiiigggccc```^^^^^^^^^___]]]]]]\\\YYYUUURRRQQQRRRMMMOOORRRVVV\\\dddlllrrr}}}tttgggXXXNNNJJJMMMVVV```uuuoooeeeeeevvvzzznnnfffgggvvv{{{yyywwwwwwyyy{{{{{{{{{vvvzzzzzzuuussssssuuuyyy|||zzzqqqiiiddd``````gggtttpppaaa___]]]]]]___bbbddddddaaabbbeeeiiimmmqqqtttuuuzzz}}}oooaaaWWWPPPLLLIIINNNUUU```nnnkkk^^^ZZZXXXWWWZZZbbblllxxxuuupppmmmmmmnnnrrrwww|||uuummmmmmnnnkkkfff```\\\ZZZ^^^eeelllmmmlllbbbbbbbbb___\\\]]]bbbgggmmmnnnpppsssyyy|||zzzuuupppooommmllljjjiiihhhggghhhhhhfffffffffffffffffffffffffffffffffdddbbb^^^ZZZXXXWWWWWWWWWWWWVVVVVVVVVVVVYYYYYYZZZZZZZZZ[[[[[[[[[[[[ZZZYYYWWWVVVUUUUUUUUUSSSSSSSSSSSSSSSRRRQQQQQQJJJIIIGGGEEEBBB???===<<>>>>>???@@@@@@??????>>>==================<<<<<<<<<;;;;;;===<<<<<<;;;;;;<<<>>>???>>>>>>@@@@@@@@@@@@>>>>>>;;;<<<===>>>>>><<<:::999:::999888777666666666666555444444333333222111111...---000333555777>>>GGGXXX\\\^^^\\\\\\hhh}}}}}}xxxwww}}}|||}}}|||{{{yyyxxxxxxxxxxxxwwwwwwxxxxxxwwwuuuuuutttuuuuuuvvvxxxyyyzzz{{{|||~~~~~~}}}}}}}}}|||zzzwwwqqqkkkggggggeeebbb^^^\\\ZZZZZZZZZXXXXXXWWWTTTQQQPPPQQQRRRRRRVVV[[[bbbiiipppxxx}}}~~~eee[[[PPPKKKLLLTTTbbbpppvvvggg```dddwwwqqqlllkkkqqqyyyxxxwwwxxxzzz{{{{{{{{{vvvxxx||||||yyyxxxqqqooojjjccc]]]ZZZ[[[\\\\\\___dddhhhjjjgggbbb^^^______eeerrrttthhhfffddddddfffgggggggggfffgggiiilllnnnqqqssstttzzz~~~xxxaaaSSSKKKGGGFFFFFFLLLWWWddduuuvvvkkkhhheeeggglllttt~~~|||~~~wwwwwwyyywwwtttjjjgggdddffflllpppooommmfffggghhhfffdddeeeiiimmmtttuuuwww|||~~~{{{vvvrrrpppmmmllljjjhhhgggffffffgggffffffffffffgggggggggggggggffffffdddaaa]]]ZZZXXXVVVVVVVVVVVVVVVVVVVVVVVVYYYYYYYYYZZZZZZZZZ[[[[[[[[[ZZZYYYWWWVVVUUUUUUUUURRRRRRRRRRRRRRRQQQPPPOOOJJJIIIFFFCCC@@@>>><<<;;;fffXXXSSSOOOOOOOOONNNOOOQQQTTTWWWTTTXXX___gggoooyyyppp\\\RRRMMMKKKJJJMMMJJJFFFDDDCCCCCCBBBBBBAAA@@@???>>>>>>???@@@AAA@@@@@@@@@???>>>>>>======<<<<<<<<<<<<;;;;;;;;;;;;<<<;;;:::999999;;;<<<=========>>>??????>>>======888999;;;<<<<<<:::888777777777666555555555555555555444444333333222111111......111444555666;;;CCCWWW]]]aaa______lll|||~~~~~~~~~}}}}}}~~~~~~|||{{{yyyxxxxxxxxxvvvvvvwwwwwwxxxwwwvvvuuuwwwwwwxxxyyy{{{|||}}}}}}}}}~~~}}}|||{{{{{{|||}}}{{{vvvoooiiieeedddbbb```]]]ZZZWWWVVVUUUVVVVVVTTTSSSTTTWWWZZZ___dddkkksssyyyvvvjjjYYYRRRLLLKKKPPP\\\nnn~~~nnnccc___ccctttyyykkklllttt|||yyyxxxwwwxxxxxxxxxvvvuuusssrrrrrrsssvvvxxxwwwwwwxxxwwwtttqqqnnnkkkhhhggg___]]]YYYTTTOOONNNOOOQQQRRRVVV[[[```bbbddddddddddddhhhsssxxxnnnlllkkkkkklllmmmlllkkkllllllmmmoooppprrrsssssszzzmmmXXXNNNHHHEEEEEEEEEKKKVVVddduuu~~~xxxwwwwww|||~~~~~~sssooolllmmmqqqrrroookkkiiikkklllllljjjkkkooosssyyyzzz}}}~~~|||wwwsssrrrmmmllliiigggfffeeeeeeeeefffggggggggggggggggggggggggfffeeeccc```]]]ZZZXXXVVVVVVVVVVVVVVVVVVVVVVVVXXXYYYYYYYYYYYYZZZZZZZZZZZZYYYXXXWWWUUUUUUTTTTTTRRRRRRRRRQQQPPPOOONNNNNNKKKJJJFFFBBB???<<<::::::lll[[[QQQMMMKKKJJJIIIIIIJJJOOOVVV\\\\\\gggvvv}}}lllYYYPPPLLLIIIFFFEEEEEEDDDBBBBBBCCCCCCBBBAAA>>>>>>======>>>???AAABBB=========>>>??????@@@@@@<<<<<<;;;;;;;;;:::::::::::::::999888999:::;;;<<<;;;<<<===>>>>>>===<<<;;;777888999::::::999888777555555555444444555555666555555444444333222222222//////111444444444999AAAPPPYYYaaaaaaddduuuvvvvvv}}}~~~{{{yyyxxxwwwvvvvvvuuuuuuuuuwwwxxxxxxwwwwwwxxxxxxzzz{{{||||||}}}||||||}}}}}}}}}}}}}}}}}}{{{{{{}}}|||tttmmmfffeeeccc```]]]YYYVVVTTTTTTVVVXXXZZZ\\\___dddgggooottt|||yyyooobbbWWWNNNKKKJJJOOOXXXggg}}}tttddd___^^^bbbooozzznnngggppp~~~{{{zzzyyywwwwwwvvvssspppmmmmmmjjjfffccccccddddddcccaaa```___]]]ZZZXXXVVVVVVPPPOOOLLLIIIGGGHHHLLLPPPQQQVVV]]]bbbfffiiilllnnnqqqxxxzzzpppooooooqqqssstttrrrqqqppppppqqqqqqrrrsssttttttzzzeeeRRRLLLFFFDDDEEEDDDIIISSS```ppp|||xxxttttttvvvuuuooojjjkkkmmmppppppqqqsssyyy~~~~~~|||wwwsssrrrnnnllljjjhhhfffeeeeeeeeegggfffffffffffffffffffffeeeeeecccaaa^^^\\\YYYXXXUUUUUUUUUUUUVVVVVVVVVVVVWWWWWWXXXXXXXXXYYYYYYYYYXXXWWWVVVUUUTTTTTTTTTTTTQQQQQQQQQPPPOOONNNMMMLLLJJJHHHDDDAAA===;;;::::::iiijjjmmmrrrxxxsssllljjjfffeeehhhnnnqqqppprrrvvv{{{vvvnnnfff___ZZZUUURRROOOOOOMMMMMMQQQZZZfffooo|||yyyaaaUUUKKKHHHGGGDDDCCCEEEBBBAAAAAABBBCCCCCCAAA@@@???>>>===<<<===>>>???@@@<<<<<<======>>>??????@@@;;;;;;;;;::::::::::::999999999999999999::::::;;;::::::;;;<<<<<<;;;::::::888888888888999999999999555444444555555666777888666666555555444333333333000///000333222222777???GGGRRR]]]aaafffvvvxxx{{{~~~|||yyywwwuuuuuuvvvtttrrrsssvvvxxxyyyxxxvvvwwwwwwxxxyyyzzz{{{{{{{{{zzzzzzyyyzzz{{{}}}}}}~~~wwwpppllliiieeeaaa]]]ZZZXXXXXXWWWZZZ___dddiiioootttxxx}}}}}}vvvlllddd]]]UUULLLJJJJJJOOOZZZhhh{{{uuuggg[[[YYY[[[___lllzzznnnkkkmmm|||{{{yyyxxxtttttttttttttttrrrnnnkkkgggccc^^^[[[ZZZYYYXXXWWWSSSRRRQQQPPPNNNMMMLLLKKKHHHHHHGGGEEEFFFJJJPPPUUU[[[cccnnnxxx~~~vvvvvvvvvxxxzzzzzzxxxvvvssssssuuuvvvxxxyyyzzz{{{|||dddSSSJJJCCCBBBFFFDDDHHHOOOYYYfffuuu}}}vvvooonnnrrruuuxxx{{{~~~|||wwwsssrrrpppooollljjjhhhgggggggggfffeeeeeeddddddcccccccccbbbaaa```^^^\\\YYYXXXWWWSSSSSSSSSTTTTTTUUUUUUUUUVVVVVVVVVWWWWWWWWWWWWXXXUUUUUUTTTTTTSSSTTTTTTUUUQQQQQQPPPPPPOOOMMMLLLKKKEEECCC@@@>>><<<;;;;;;;;;[[[]]]bbbhhhooowwwlll]]]XXXXXXXXXXXX^^^gggllljjjgggggghhhaaaYYYWWWZZZ^^^^^^\\\YYYYYYWWWXXX]]]jjjyyymmm^^^QQQJJJFFFGGGEEEAAACCCIIIBBBBBBBBBCCCDDDCCCAAA???@@@???>>><<<<<<<<<===>>>??????>>>>>>===<<<<<<<<<;;;;;;;;;:::::::::999999888999999999::::::::::::999999:::;;;;;;:::999999:::999999888888999::::::555555555555666888999:::777666666555555444333333000///000111111000666===AAAMMMZZZ___cccrrr|||xxxvvvtttssswwwtttqqqqqquuuxxxyyyxxxuuuuuuvvvwwwxxxxxxyyyyyyzzzyyyxxxwwwxxxzzz}}}~~~xxxqqqrrrooohhhbbb^^^\\\]]]]]]\\\```gggnnnttt{{{|||zzzooollleee[[[UUUSSSOOOJJJLLLNNNWWWfffwwwxxxlll^^^TTTTTTXXX^^^kkkyyywwwmmmpppxxx}}}yyytttqqqpppppplllmmmooorrrttttttqqqooodddaaa]]]ZZZYYYWWWTTTSSSOOOOOONNNMMMLLLJJJIIIIIIIIIHHHHHHHHHJJJOOOVVV[[[lllwww~~~~~~~~~|||yyyvvvwwwyyy{{{}}}fffUUUIII@@@AAAHHHFFFIIIMMMSSS]]]jjjwww}}}wwwsssvvv{{{}}}|||wwwsssrrrrrrqqqnnnllljjjiiiiiiiiiddddddccccccbbbaaa``````___^^^]]][[[YYYXXXVVVVVVQQQRRRRRRRRRSSSSSSTTTTTTUUUUUUUUUVVVVVVVVVWWWWWWSSSSSSSSSSSSSSSTTTTTTUUUPPPPPPPPPOOONNNMMMKKKKKK@@@???===;;;:::;;;<<<===MMMRRRYYY```gggooovvvzzz}}}oooooossssssxxxyyyqqqkkkjjjlllkkkvvvnnn^^^VVVTTTTTTRRRVVVZZZ^^^aaaaaa```___[[[ZZZZZZ^^^eeemmmrrruuuqqqooommmooowwwuuueeeXXXQQQKKKHHHEEEDDDEEEFFFFFFEEEBBBBBBBBBAAA@@@???>>>======<<<<<<;;;;;;;;;<<<<<<===<<<<<<<<<<<<;;;;;;;;;::::::999999888777666666888888999::::::;;;<<<<<<:::999999999888888777777999888888888999::::::;;;999888777666777888:::<<<<<<:::888555333222222222111111111000000111444777===KKKZZZ``````hhhzzz~~~zzzxxxwwwxxxzzzxxxtttrrrqqqrrrtttvvvsssssssssttttttuuuvvvwwwzzzzzzzzz{{{||||||}}}}}}~~~{{{vvvooolllhhheeecccbbbdddeeeeeeiiiooovvv|||}}}xxxqqqkkkhhh___VVVRRRPPPMMMMMMQQQVVV[[[hhh|||{{{nnn]]]ZZZVVVTTTWWWbbboooyyy~~~nnngggmmm}}}}}}|||zzzwwwwwwsssmmmhhhdddbbb```___bbbfffjjjmmmssswwwtttnnnjjjjjjjjjhhheeeaaa]]][[[^^^YYYSSSOOOMMMLLLIIIFFFIIIGGGHHHLLLPPPVVVcccnnnkkkVVVKKKGGGFFFFFFFFFJJJPPPVVV[[[aaallluuutttuuuzzz~~~}}}|||}}}{{{vvvtttssssssooollljjjiiiiiiiiiiiihhhdddddddddcccbbbaaa```___```^^^\\\YYYWWWVVVVVVVVVTTTSSSSSSRRRRRRSSSTTTUUURRRTTTUUUUUUTTTSSSUUUVVVWWWVVVUUUSSSSSSSSSSSSTTTPPPOOOMMMMMMMMMLLLIIIGGGCCCAAA>>><<<:::999::::::LLLOOOUUUZZZ___dddiiilll{{{~~~mmm``````ddddddhhhooouuummmaaa[[[VVVVVVXXX\\\fffqqqwww~~~ooo^^^TTTPPPOOOPPPSSSUUUXXX[[[^^^bbbeeegggmmmmmmpppvvv~~~{{{hhhZZZQQQLLLHHHFFFDDDCCCCCCCCCBBB@@@AAAAAAAAAAAA@@@???>>>===<<<<<<;;;;;;;;;<<<<<<===<<<<<<<<<<<<;;;;;;;;;;;;;;;;;;::::::999888888777888888999999:::;;;;;;<<<999999888888888777777777999888888888999999:::;;;999888777666666888999:::;;;:::888555444333222222111222222111000111444777888EEESSSYYY[[[```lllxxx}}}{{{zzzzzz{{{{{{xxxuuuqqqpppppprrrssstttssssssssstttuuuvvvvvvzzzzzz{{{{{{|||||||||}}}|||wwwqqqnnniiidddaaaaaabbbdddfffiiinnntttyyy|||~~~}}}zzzwwwuuurrrmmmfffaaa\\\TTTNNNKKKJJJJJJOOOUUU]]]gggzzzpppdddVVVTTTRRRRRRXXXcccrrr{{{|||pppnnnyyy{{{vvvrrrpppnnnkkkiiifffccc___\\\[[[ZZZZZZYYYZZZ^^^ccchhhrrr|||~~~|||||||||{{{xxxsssooollllllggg```ZZZWWWTTTPPPMMMKKKKKKMMMSSSXXXcccuuujjjVVVKKKIIIKKKLLLPPPQQQTTTXXX]]]ccckkkqqqnnnnnnpppvvv{{{{{{xxxvvvuuuuuuooommmjjjiiiiiiiiiiiihhheeeddddddcccbbbaaa___^^^___^^^[[[YYYWWWVVVVVVVVVTTTSSSSSSRRRRRRSSSTTTUUUUUUWWWXXXXXXWWWVVVXXXYYYUUUTTTRRRQQQPPPPPPQQQQQQPPPOOOMMMMMMLLLKKKIIIFFFBBBAAA>>>;;;:::999:::;;;KKKNNNRRRUUUWWWZZZ]]]___hhhyyywwwjjj\\\RRRSSSVVVWWWZZZ```cccmmm|||}}}ooo```XXXTTTQQQRRRVVVPPPYYYbbbdddgggmmmpppqqqnnnggg\\\SSSOOOOOOPPPQQQSSSUUUYYY]]]dddmmmvvv}}}hhhXXXOOOJJJGGGDDDCCCCCCCCCCCCBBB???===@@@@@@@@@@@@???>>>======;;;;;;;;;;;;;;;<<<===>>><<<<<<<<<<<<;;;;;;;;;;;;<<<;;;;;;::::::999999999888888888999::::::;;;;;;888888777777777777666666999888888888888999:::::::::999888777666777888999;;;999888666444333222222111222222111000111444666555???LLLTTTXXXZZZ^^^bbbooovvv~~~}}}|||{{{{{{|||}}}}}}{{{yyyuuuqqqoooooopppqqquuuuuutttttttttuuuuuuvvv{{{{{{||||||||||||||||||~~~yyyrrrnnnhhhbbb______```bbbdddgggjjjnnnppprrrrrrrrrooommmjjjgggddd___YYYUUURRRMMMIIIHHHHHHKKKUUU```mmm|||tttcccZZZPPPPPPPPPSSS[[[hhhwww|||tttxxx|||xxxsssooojjjeeeccc```^^^\\\YYYXXXVVVTTTSSSSSSTTTTTTTTTYYY^^^fffttt}}}vvvooohhhaaa[[[VVVQQQRRRUUUYYY```nnnjjjWWWMMMNNNSSSXXX]]]\\\\\\```gggmmmooonnniiifffdddggglllttt|||zzzyyywwwuuuooollljjjhhhiiiiiihhhhhheeeeeedddcccbbb```^^^]]]^^^]]][[[YYYXXXVVVVVVVVVSSSSSSRRRRRRSSSTTTUUUUUUVVVXXXYYYYYYXXXWWWYYYZZZUUUTTTSSSRRRQQQQQQQQQQQQPPPOOOMMMLLLLLLJJJGGGEEEAAA@@@===;;;::::::;;;;;;NNNPPPSSSTTTUUUUUUVVVWWWZZZhhhyyytttddd]]]SSSLLLNNNQQQSSSVVV[[[\\\aaakkkwwwzzzrrrfff[[[QQQLLLJJJIIIKKKOOOOOOVVV\\\\\\\\\^^^_________[[[VVVSSSSSSTTTUUUVVV[[[```gggpppyyyqqqZZZOOOIIIGGGFFFAAAAAABBBDDDEEEDDD@@@>>>>>>?????????>>>>>>===<<<:::::::::;;;<<<===>>>???<<<<<<<<<;;;;;;;;;::::::;;;;;;::::::999999999999777888888888999999::::::777777777666666666666666999888888888888888999999:::999888777666666777777:::999888666555333333222111222222222111111333555666===IIISSSZZZ[[[YYYWWWeeelllxxxzzz~~~|||{{{zzz{{{}}}}}}}}}zzzxxxuuurrrqqqqqqqqqrrrwwwwwwvvvvvvvvvvvvwwwwww}}}}}}}}}}}}}}}}}}}}}}}}~~~{{{pppllleee___\\\\\\^^^``````aaaccceeefffeeedddcccbbbaaa^^^[[[WWWTTTPPPNNNNNNLLLKKKLLLNNNTTTcccqqqtttfff[[[VVVNNNOOOQQQWWW```nnn|||}}}zzzxxxqqqlllfffccc___[[[YYYXXXWWWWWWVVVWWWVVVUUUSSSSSSTTTUUUWWW^^^fffqqq~~~rrrgggaaa^^^___cccfffjjjxxx}}}jjjXXXPPPSSS\\\ccchhhiiikkkrrr|||yyypppgggaaa[[[[[[]]]dddrrr}}}|||zzzvvvrrrnnnllliiihhhhhhhhhhhhgggeeeeeedddcccaaa___^^^]]]]]]\\\[[[YYYXXXWWWVVVUUURRRRRRRRRSSSSSSTTTUUUUUUTTTUUUVVVVVVUUUUUUVVVWWWWWWWWWVVVVVVUUUTTTTTTTTTPPPNNNLLLKKKJJJIIIEEECCC???>>><<<:::::::::;;;<<>>>>>======<<<<<<:::::::::;;;<<<===>>>???<<<;;;;;;;;;;;;:::::::::999999999999888888888888777777888888888888888999666666666666666777777777999999888777777888888888999888888777777666666666999888888777555444333222111222333222111111333444666;;;EEEQQQ[[[]]]YYYTTTWWW```ooo~~~|||~~~{{{{{{|||}}}|||{{{xxxwwwuuutttssstttuuuvvvxxxxxxxxxxxxxxxxxxyyyzzz}}}}}}~~~~~~~~~~~~~~~~~~~~~{{{mmmiiiccc]]]ZZZYYYZZZ[[[\\\]]]^^^______]]][[[ZZZVVVUUUTTTQQQNNNLLLKKKKKKIIIIIIMMMSSSZZZeeevvvqqqeee[[[TTTSSSLLLOOOSSSZZZdddrrr~~~wwwooogggbbb\\\ZZZVVVSSSPPPPPPRRRSSSUUUWWWXXXXXXWWWXXX\\\___fffqqq~~~uuummmkkknnnrrrvvvzzz|||tttfffYYYRRRWWWbbblllqqqwwwuuuddd\\\TTTPPPPPPUUU___jjjwww~~~|||yyytttnnnmmmjjjgggfffggggggfffeeedddddddddcccaaa___^^^]]][[[[[[ZZZYYYXXXWWWVVVUUUQQQRRRRRRSSSTTTUUUUUUUUURRRTTTUUUUUUTTTTTTUUUVVVXXXXXXXXXXXXWWWVVVUUUUUUPPPNNNLLLJJJIIIGGGDDDAAA>>><<<;;;::::::;;;<<<===iiijjjiiieee___XXXTTTRRRRRRXXXaaajjjmmmiii]]]TTTQQQMMMHHHGGGIIIMMMPPPSSSRRRQQQRRRWWW^^^```]]]YYYYYYTTTPPPOOOMMMKKKMMMQQQMMMWWW```dddiiippptttuuuuuusssqqqrrruuuxxxzzz{{{vvvbbbOOOIIIHHHCCCAAACCC@@@AAABBBEEEHHHGGGEEEBBB<<<<<<<<<======<<<<<<;;;;;;;;;;;;;;;;;;<<<===>>>;;;;;;;;;;;;::::::::::::888888888888888888888888777777777777777777777777666666777777777777888888999999888777777777777888777777777777777777666666888888888777666444333222111222333333222111222333444777???KKKWWW[[[XXXTTTSSS\\\lll}}}|||}}}}}}{{{xxxwwwwwwvvvuuuuuuvvvwwwwwwxxxxxxwwwxxxyyyzzz{{{{{{{{{{{{|||}}}}}}~~~}}}}}}~~~~~~|||nnnjjjddd^^^YYYVVVUUUUUUXXXYYYZZZ[[[ZZZYYYWWWUUUMMMMMMLLLKKKIIIIIIKKKMMMGGGJJJRRR___mmm{{{qqqcccZZZRRRNNNMMMKKKOOOUUU^^^iiivvv{{{tttmmmfff```\\\UUUTTTRRROOONNNOOOSSSVVV[[[^^^```bbbdddhhhpppuuuxxxooottt|||rrrjjjgggaaaYYYVVV\\\jjjuuu~~~{{{___VVVMMMIIIGGGIIIPPPXXX^^^iiiyyy}}}|||yyyrrrlllkkkhhhfffdddeeeeeeeeedddcccccccccbbbaaa```___^^^ZZZZZZZZZYYYXXXWWWUUUUUUPPPQQQRRRTTTUUUUUUUUUUUUTTTUUUWWWVVVUUUUUUVVVXXXVVVVVVVVVVVVVVVUUUSSSSSSPPPNNNLLLJJJHHHFFFBBB???<<<;;;:::999:::;;;===>>>|||vvvoookkkiiifffjjjttt~~~{{{oooggg]]]ZZZTTTOOONNNQQQUUUVVVTTTUUUYYY```gggkkkjjjhhh```\\\ZZZYYYVVVSSSSSSWWWaaalllwww~~~|||{{{zzzzzz___OOODDDEEEFFFAAA???BBBAAAAAAAAACCCDDDDDDAAA???:::;;;;;;<<<<<<<<<;;;;;;<<<<<<;;;;;;;;;<<<<<<===;;;;;;;;;:::::::::999999999999999999999999999999777777777777777777777777777777777888888888999999999999888777777777777777666666777777777777777777777777777777666555333222111222444333222111222333333444:::EEEPPPWWWWWWUUUTTT^^^kkk{{{{{{{{{zzzyyyyyyzzz|||}}}~~~~~~|||~~~~~~{{{xxxxxxwwwvvvuuuuuuuuuuuuuuuuuuuuuuuuvvvxxxyyy{{{|||wwwwwwxxxzzz{{{|||}}}~~~~~~}}}~~~~~~rrrooohhhaaaZZZTTTPPPNNNQQQRRRTTTUUUUUUTTTRRRQQQIIIJJJKKKJJJJJJLLLPPPTTTVVVXXXcccuuuqqqaaaWWWRRRMMMJJJKKKLLLQQQYYYdddppp~~~{{{vvvoooiiiccc___[[[XXXRRRTTTUUUUUUWWW\\\dddjjjtttwwwzzz{{{}}}}}}www}}}uuujjjccc[[[^^^___^^^^^^gggvvv}}}ZZZRRRJJJGGGEEEEEEIIIOOOSSSYYYdddooouuuvvvvvvwwwwww|||{{{yyysssllliiigggdddccccccccccccbbbaaaaaaaaaaaaaaa``````___YYYYYYZZZZZZYYYWWWUUUTTTOOOQQQRRRTTTUUUUUUUUUUUUUUUVVVXXXWWWVVVVVVWWWYYYTTTUUUUUUUUUUUUSSSRRRQQQPPPNNNKKKIIIGGGDDDAAA>>>;;;:::999999999;;;>>>???nnnjjjccc[[[YYY[[[^^^^^^cccgggoooxxxzzzwwwuuutttpppkkkkkkooo{{{xxxtttssssssyyymmmXXXTTTGGG@@@DDDFFFAAA@@@DDDBBBAAA@@@@@@AAA???===:::::::::;;;<<<<<<;;;;;;;;;===<<<<<<;;;;;;;;;<<<<<<;;;;;;;;;:::::::::999999::::::::::::::::::::::::777777777777666666666666777777888888999999999:::999999888777777666777777444555666777888888777777777777777777777555333222111222444444222111111222444444888AAALLLTTTWWWVVVNNNZZZhhhuuu{{{vvvqqqmmmooopppqqqssstttvvvxxxzzz}}}}}}~~~~~~}}}}}}yyyxxxwwwvvvuuussssssrrrrrrsssssstttuuuvvvxxxzzz{{{ttttttvvvwwwyyyzzz||||||~~~~~~wwwsssmmmddd[[[SSSMMMIIIJJJLLLNNNOOOPPPOOONNNMMMJJJLLLMMMMMMNNNQQQWWW\\\iiilllvvv|||nnnaaaUUUPPPOOOLLLKKKLLLOOOTTT^^^jjjxxx~~~{{{rrrmmmfff```]]]ZZZXXXWWWSSSVVVZZZ___eeennnyyy|||nnnccc___\\\TTTZZZ```cccgggqqq}}}YYYQQQKKKIIIHHHGGGIIINNNRRRUUU^^^hhhqqqvvvzzz~~~vvv{{{{{{zzztttnnnhhhfffcccbbbbbbbbbbbbaaa``````aaaaaaaaaaaa``````YYYYYYZZZZZZYYYWWWUUUTTTOOOPPPRRRTTTUUUVVVUUUUUUTTTUUUWWWVVVUUUUUUVVVXXXUUUUUUVVVVVVUUUTTTRRRQQQPPPNNNKKKIIIGGGDDD@@@===:::999999888999<<<>>>@@@ssslllmmmqqquuuvvv|||~~~yyyxxxyyyiiiVVVJJJFFFEEECCCAAA@@@>>>>>>===;;;;;;<<<======<<<;;;;;;:::;;;;;;<<<<<<;;;;;;:::;;;;;;:::999999:::;;;;;;888888777777777777888888777777888999::::::::::::777777777777777888888888999999::::::::::::999999:::999777666555666888999666666777777777777666666666555555444333333222222333333333222222222111111555888888;;;FFFTTTYYYVVVUUUXXXaaappp}}}pppmmmiiibbbeeennnkkkkkkmmmqqquuuxxxyyyxxx}}}|||~~~~~~}}}|||{{{xxxtttssssssuuuvvvuuusssrrrrrrsssuuuvvvtttssssssvvvzzz}}}}}}|||{{{}}}yyyyyyuuukkk___SSSLLLIIIIIIIIIJJJLLLMMMOOOQQQRRRPPPPPPQQQTTTZZZbbbjjjooo{{{{{{ppp```XXXPPPLLLJJJGGGIIIMMMOOOYYYfffsssyyyvvvjjjgggbbb^^^[[[[[[\\\^^^^^^dddmmmuuu~~~wwwwww~~~rrreee\\\TTTQQQRRRYYYaaagggnnnzzzqqqXXXQQQIIIDDDEEEIIIMMMOOOTTT\\\gggsss~~~qqqiiigggkkkrrrvvv}}}zzzyyytttooommmiiihhhfffdddbbbaaaaaaaaa``````___```aaaaaa___\\\ZZZYYYXXXWWWWWWUUURRROOORRRRRRQQQRRRSSSUUUVVVXXXVVVVVVVVVWWWWWWVVVUUUUUUXXXVVVTTTTTTTTTTTTSSSQQQOOOMMMIIIFFFDDDAAA>>>;;;===<<<;;;::::::;;;===>>>~~~{{{zzzgggXXXNNNHHHCCCBBBAAA???>>>===<<<<<<:::;;;<<<<<<<<<<<<;;;:::::::::;;;;;;;;;;;;::::::999999888777777888999999888888777777777777888888777888999:::;;;;;;;;;;;;888888888888777777777777666666777777777777666666777777888888777777666666666666777777777777666666666666555555444333333333333333333222222222222111444666666999CCCQQQWWWVVVTTTUUU\\\kkk|||yyylllbbbaaa```]]]cccnnnoooqqqtttyyy~~~|||yyyuuuttttttuuuvvvuuusssrrrrrrsssuuuvvvvvvuuuuuuxxx|||~~~}}}}}}zzzqqqeeeZZZRRRNNNJJJJJJJJJKKKLLLOOOQQQSSSSSSUUUZZZbbblllwww{{{mmmcccXXXQQQJJJIIIHHHHHHKKKQQQVVVbbbqqq~~~xxxqqqnnnfffdddaaa^^^^^^aaaeeeiiipppxxxyyyooojjjrrr~~~|||ggg^^^WWWSSSQQQUUU[[[ccciiippp|||eeePPPLLLHHHFFFIIIOOOUUUYYYaaajjjwwwzzzjjjccc[[[UUUTTTXXX]]]aaasss}}}zzzvvvtttpppkkkiiihhhhhhfffeeedddcccbbbbbbaaa`````````aaa```^^^[[[YYYXXXWWWWWWWWWUUURRRPPPQQQQQQQQQQQQRRRTTTVVVWWWVVVVVVVVVVVVVVVVVVVVVUUUWWWVVVTTTTTTTTTTTTRRRQQQOOOLLLIIIFFFDDDAAA>>>;;;===<<<:::999:::;;;===>>>xxxuuuzzzsss]]]QQQKKKGGGCCC??????===<<<<<<;;;;;;;;;999:::;;;;;;;;;;;;:::999::::::;;;;;;;;;;;;::::::999888888777777888888999888888777777777777888888888999:::;;;;;;<<<<<<;;;999999999888777777777666555666666666666666666555555666888999888777444333666666777777777777666666777777666555444444444444333333333333222222222222333444444666???LLLTTTWWWVVVUUUYYYgggxxxuuujjjaaa___^^^^^^eeeoootttvvvzzz~~~~~~{{{wwwuuuuuuvvvvvvuuutttsssssstttuuuvvvxxxwwwwwwzzz}}}~~~wwwlllaaaXXXSSSNNNMMMLLLLLLMMMPPPSSSVVVZZZ^^^gggsss{{{rrriii___WWWOOOJJJFFFFFFHHHKKKQQQYYYbbbppp{{{wwwpppkkkiiiddddddccccccfffllluuu{{{zzzkkkbbb^^^```qqqjjj\\\WWWTTTSSSSSSVVV[[[bbbgggnnnyyymmmXXXLLLLLLKKKLLLPPPXXXbbbiiirrr~~~yyyhhhVVVSSSNNNKKKKKKNNNRRRUUUaaalllxxxtttrrrmmmhhhggghhhhhhgggffffffeeeddddddbbbaaa```aaaaaa___\\\ZZZYYYWWWVVVVVVVVVUUUSSSPPPQQQQQQPPPPPPQQQSSSUUUVVVUUUUUUVVVVVVVVVVVVVVVVVVWWWVVVTTTSSSTTTSSSQQQPPPNNNKKKGGGDDDBBB@@@===;;;;;;;;;:::999:::;;;<<<===|||zzzzzzzzzsssrrrxxx{{{mmm[[[PPPLLLIIIDDD???===<<<<<<;;;;;;;;;;;;<<<888999::::::::::::999888:::::::::;;;;;;:::::::::::::::::::::::::::::::::888888777777777777888888999999:::;;;<<<<<<<<<<<<::::::999999888777666666777777777666666777777777555666777777777666444333666666777777777777666666888777666555444555555666444444333333333222222222333333333555;;;GGGQQQWWWZZZWWWZZZfffxxxzzzrrrkkkhhhggggggoooxxx}}}{{{wwwuuuuuuvvvwwwvvvuuuuuuuuuuuuvvvwwwxxxxxxyyyzzz|||~~~}}}|||{{{|||~~~zzzqqqfff\\\WWWSSSRRRPPPOOOPPPSSSVVVYYYaaagggqqq~~~}}}wwwooohhhbbb\\\UUUQQQJJJFFFDDDGGGKKKPPPZZZdddooo{{{vvvqqqkkkhhhiiidddfffiiimmmsss}}}ooo```ZZZYYY___uuutttaaaXXXVVVUUUWWWZZZ\\\```eeeiiinnnwww{{{nnn___RRROOOPPPPPPSSSYYYeeesss}}}ssscccTTTSSSRRRPPPOOORRRUUUXXX^^^hhh{{{yyyuuurrrmmmjjjiiihhhhhhhhhhhhggggggffffffcccbbbaaa``````^^^[[[XXXXXXVVVUUUUUUUUUUUUSSSQQQQQQPPPPPPPPPQQQRRRTTTUUUUUUUUUUUUUUUUUUUUUVVVVVVWWWUUUSSSSSSSSSRRRPPPOOOMMMJJJEEEBBBAAA???<<<;;;::::::999999:::;;;<<<===}}}}}}~~~}}}yyyzzzwwwbbbYYYNNNIIIHHHFFFAAA<<<<<<<<<<<<;;;;;;;;;<<<<<<888888999::::::999888888999::::::::::::::::::999::::::::::::::::::::::::888888777777777777888888999999:::;;;<<<<<<<<<<<<;;;::::::999888777777666777777666555555666777777888777555444444444555666666666777777777777666666888777555444444555666777444444444333333333222222333333333555999AAAMMMWWW\\\YYY[[[gggyyyzzzvvvtttuuu|||~~~zzzvvvtttuuuvvvwwwwwwwwwvvvvvvwwwwwwwwwwwwxxxyyyzzz{{{|||}}}~~~zzzxxxwwwwwwzzz}}}vvvmmmccc]]]YYYWWWTTTRRRRRRTTTWWWYYYeeekkkuuu~~~vvvrrrgggccc]]]XXXTTTPPPNNNLLLGGGEEEEEEJJJPPPXXXeeeppp~~~wwwpppiiidddcccfffbbbhhhqqqzzzlll^^^[[[[[[aaawwwyyylll___ZZZZZZZZZ^^^bbbhhhkkkooosssvvv{{{}}}qqqfff^^^VVVOOOPPPQQQSSSZZZgggyyysssfff[[[[[[[[[ZZZYYYZZZ^^^aaagggqqqzzzvvvrrrmmmkkklllhhhiiiiiiiiiiiihhhgggfffcccbbbaaa``````]]]ZZZWWWVVVUUUSSSSSSTTTTTTSSSRRRQQQQQQPPPPPPQQQRRRSSSTTTUUUTTTTTTTTTTTTUUUVVVWWWWWWUUUSSSRRRRRRQQQOOOMMMKKKHHHDDD@@@???===<<<:::999999::::::;;;<<<======kkk]]]WWWPPPGGGAAA??????===<<<===<<<<<<;;;;;;;;;<<<<<<888999::::::::::::999888999999::::::::::::999999777888888999999888888777888888777777777777888888888999:::;;;;;;<<<<<<;;;:::::::::999888888888777666555444333333444555666999888666444444555666888666666777777777777666666777666444333333444666777444444444444333333333333333333444666777<<>>>>>~~~jjjZZZPPPJJJHHHDDD???<<<;;;<<<======<<<;;;;;;::::::::::::888999:::;;;;;;:::999888999999::::::::::::999999777888999999999999888777888888777777777777888888777888999:::;;;;;;;;;;;;999999999999999999999999777666444333333444666777888888777777666666666666666666777777777777666666777555333222222333555777555444444444444333333333222222444666555777BBBPPPWWWXXX\\\hhh{{{~~~{{{xxxwwwxxxzzzxxxxxxyyyyyyyyyyyyxxxxxxvvvxxxzzzzzzyyyxxxzzz|||zzzyyyyyyzzz~~~|||tttnnniiigggeeebbb```^^^^^^^^^cccgggmmmsssxxxyyyxxxwwwssspppkkkeee___YYYUUURRRIIIIIIHHHFFFFFFFFFHHHJJJNNNOOOTTT]]]hhhuuuzzzqqqhhhbbb______fffnnn|||}}}hhhZZZ\\\^^^ddd}}}rrrlllhhhfffiiimmmrrryyy}}}kkk___ZZZXXXVVVUUUWWW[[[ggg~~~|||jjj\\\XXX\\\[[[aaalllvvv}}}vvvsssppplllkkknnniiijjjjjjjjjiiigggdddcccbbbaaa```______^^^ZZZXXXUUUSSSQQQQQQRRRTTTTTTSSSSSSSSSRRRQQQRRRSSSTTTUUUTTTTTTSSSRRRSSSUUUWWWXXXWWWUUURRRQQQQQQPPPMMMLLLIIIEEEAAA===<<<;;;::::::::::::<<<===>>>?????????mmm___VVVMMMGGG;;;???CCCCCC@@@>>>===>>>===<<<;;;:::999999999999999:::;;;;;;;;;;;;:::999999999999::::::999999999999:::;;;<<<<<<;;;:::999888888777777777777888888777777888999::::::::::::999999999999999999:::::::::888777666666777888:::666777999:::999888666555666666777777777777666666666555222111111333555777555555444444444333333333000111333666333333>>>MMMWWWYYY___kkk}}}|||zzzyyy{{{|||xxxyyyyyyzzzzzzyyyyyyxxxwwwyyy{{{{{{yyyxxxzzz}}}zzzyyyyyy{{{}}}vvvqqqrrrqqqooollliiifffeeedddcccfffjjjmmmmmmllliiigggeeebbb\\\VVVPPPKKKHHHGGGHHHIIIIIIIIIIIIKKKMMMOOOUUUVVV]]]hhhtttyyynnngggaaa___```fffqqq|||iii[[[]]]aaaiii|||xxxtttjjjhhhjjjqqqwww}}}{{{hhh^^^\\\]]]]]]]]]bbbgggvvvxxxeeeYYYPPPPPPVVVVVV[[[ccckkkttt|||}}}wwwtttqqqmmmnnnqqqiiijjjjjjjjjiiifffcccaaaaaa```_________^^^[[[XXXTTTRRRPPPPPPRRRTTTTTTTTTTTTTTTSSSRRRRRRSSSTTTUUUTTTSSSRRRRRRSSSUUUWWWXXXVVVUUURRRQQQQQQOOOMMMKKKIIIEEE@@@<<<;;;;;;:::999:::;;;<<<>>>???@@@@@@@@@uuugggZZZQQQKKKEEEBBBCCCBBBAAA@@@???======<<<<<<<<<;;;::::::999888888:::::::::999999999888888:::999777666666777999:::777777888888888999999999555555666777777777777777555555555555666777888999666777888999999999999999777777777777777777777777999999999888888888777777444444555555666666777777777777666555444333333333333222222222222222222222000111222222333666:::>>>UUU[[[```hhh{{{}}}|||zzzzzz{{{zzzyyyxxxwwwvvvwwwyyy{{{|||{{{{{{|||}}}{{{|||||||||}}}{{{wwwxxxvvvvvvxxxxxxrrrhhh```fffdddcccdddfffddd```[[[RRRPPPLLLIIIHHHHHHGGGFFFGGGFFFGGGHHHLLLQQQUUUXXXZZZbbbnnn{{{zzzoookkkhhhbbb___aaafffrrrmmm```aaafffpppyyypppkkkjjjkkkllljjjqqqyyy}}}rrreee``````ccceeeeeerrr{{{aaaWWWUUUTTTRRRSSS]]]aaaiiirrr{{{zzzwwwuuutttpppmmmmmmkkkiiigggfffeeebbb```bbbaaa```______]]]ZZZWWWTTTTTTTTTSSSRRRQQQQQQQQQTTTSSSRRRQQQPPPQQQQQQRRRQQQRRRRRRQQQQQQRRRUUUWWWUUUUUUVVVUUUSSSPPPLLLIIIEEEBBB>>>:::888777777888<<<<<<>>>???@@@@@@@@@@@@uuueee^^^TTTLLLGGGDDDAAA???@@@@@@???>>>===<<<;;;:::<<<;;;;;;:::999999888888::::::999999999888888888:::999777666666777999:::777777777888888888999999666777888888999999888888888777777666666666777777777777888999999999888888888888888888888888888888888888888777777666666666555555666666666666666666666555444333333222222222444444333333222111000000000111222222333666:::===SSSZZZaaahhhwww~~~}}}{{{{{{{{{zzzzzzyyyyyyxxxyyyzzz|||{{{zzzzzz{{{}}}{{{|||||||||~~~}}}}}}}}}~~~}}}vvvllldddbbb```___^^^^^^]]]YYYUUUOOOMMMJJJHHHHHHHHHHHHHHHLLLMMMNNNQQQWWW]]]bbbfffnnnvvv{{{ooofffcccbbbaaaccclllxxxqqqdddeeejjjwww{{{nnniiibbb\\\[[[]]]aaadddmmmttt}}}wwwjjjfffhhhmmmqqquuulllZZZTTTVVVYYY]]]bbbnnnssszzzzzzvvvuuussspppmmmllljjjhhhgggfffeeecccaaabbb```___^^^^^^\\\YYYVVVTTTTTTSSSRRRQQQPPPOOOOOOQQQRRRRRRSSSRRRQQQPPPPPPQQQQQQRRRRRRQQQRRRTTTVVVUUUUUUUUUSSSPPPKKKGGGDDDAAA???<<<:::888888999:::<<<<<<>>>??????@@@@@@@@@}}}hhhVVVQQQMMMHHHEEECCCBBBAAA@@@======<<<;;;::::::999999;;;;;;::::::999999888888:::999999999999888888888999888777666666777888999666777777777777777888888777888999999::::::999999:::999888777666666666666888888999999888888777666888888888888888888888888777777666666666666555555777777666666666666666666555444333222111111111222666555444333111000//////000111222333333555999<<>>???????????????tttggg]]]SSSKKKHHHFFFEEECCCBBBAAA@@@???;;;;;;;;;::::::999999888::::::::::::999999888888999999999999888888888888888777666666666666777888666666666666666666666666777777888999999999999999999999888777777777777777999999999999888777666555888888888888888888888888666666666666666666666666777777777666666555555555444444333222222222222222444444333333222111000000000111333333333555888:::CCCNNN[[[bbbffflllttt{{{}}}}}}|||{{{{{{|||~~~~~~~~~|||zzzxxxxxxzzz|||{{{|||}}}~~~~~~|||wwwoooiiikkkiiieeebbb```^^^\\\[[[SSSTTTTTTTTTUUUXXX\\\^^^dddggglllsss||||||rrrkkkeeebbbeeejjjjjjuuuzzzooogggjjjppp}}}www|||rrrccc[[[WWWUUUWWW[[[\\\^^^bbbddddddaaa]]]YYYUUUSSSPPPNNNOOOSSSYYY^^^hhhrrr{{{pppnnnrrr}}}xxxmmmdddgggnnnuuu}}}zzzvvvtttrrrooollljjjhhhfffffffffeeedddbbbaaa___\\\[[[ZZZXXXUUUSSSRRRRRRRRRQQQQQQQQQPPPPPPQQQQQQRRRRRRRRRQQQPPPOOOPPPQQQRRRRRRQQQQQQSSSTTTSSSRRRPPPMMMIIIDDD???===;;;:::999888888999;;;<<<======>>>??????@@@??????kkkYYYOOOJJJIIIIII??????@@@???>>>===<<<<<<:::::::::::::::::::::::::::999999999999999888888999999999888888888777777777666666666666666666777555555555555555555555555555666666777777777777777777777666666777888888999999999999888777666555444777777777777777777777777777777777777777777777777777777666666555555444444555444333333333333333333222222222222222222222333000222333333333444666888<<>>;;;::::::999999999:::;;;>>>???@@@@@@@@@@@@@@@@@@kkkaaaUUUMMMGGGAAA@@@BBB:::<<<>>>>>>=========>>>:::::::::::::::::::::;;;999999999999999999888888999888888888888777777777555555666666666666555555555555555444444444444333333444555555666666555555555555555555666777888999888888888888777666555444666666666666666666666666666666777777777777888888555555444444444444444444444444333333333333444444000111111222222333444444000222333444333333555666:::CCCQQQ]]]aaa```ccchhhrrr{{{yyy}}}~~~}}}}}}~~~}}}}}}}}}{{{xxxxxxyyy{{{{{{|||~~~~~~~~~}}}|||||||||||||||~~~~~~|||{{{|||}}}yyy{{{~~~~~~yyyooohhhgggdddaaa```___dddrrr||||||wwwtttrrrqqqqqqrrrrrrqqqqqqsssvvvxxx||||||{{{}}}xxxpppcccaaahhh~~~{{{___WWWQQQPPPPPPNNNMMMNNNLLLNNNPPPPPPNNNLLLKKKLLLNNNNNNNNNNNNQQQZZZfffooouuu~~~oooiiikkkmmmyyytttjjjlllrrr{{{uuusssqqqnnnkkkjjjhhhfffeeeeeedddbbb```___\\\YYYXXXXXXWWWUUUTTTPPPQQQQQQRRRSSSTTTUUUUUUUUUSSSOOOMMMLLLNNNQQQSSSOOOQQQSSSSSSQQQPPPQQQRRRNNNMMMKKKIIIFFFCCCAAA???:::::::::::::::;;;;;;<<<@@@AAAAAABBBBBBBBBAAAAAAtttgggRRRLLLHHHGGGCCC<<<:::===;;;===???>>><<<;;;<<<>>>888888999999::::::::::::888888888888888888999999888888888888777777777777555555555666666555555555444444444444333333333222333333444555555555555555666555555555555555666666777777888888777666555555555555555555555555555555555555555666666777777777222222333333333333333333333333222222222222333333222222222222222222333333000222444444333333444555777<<>>???BBBCCCCCCCCCCCCCCCBBBBBB{{{iii\\\UUUKKKFFFCCCCCC@@@999999>>><<<===>>><<<888555666888777777888888999999::::::888888888888888888999999888888888888777777777777444555555666666555555444444444444333333222222222333444444555666555555555777666555444444333444444777777777777777666666555444444444444444444444444444444444555555555666666111111111222222333333333222111111111111111222222333333333222222111111111000222444444333333333444444777AAAPPPWWWVVVVVVYYYXXXjjj{{{xxxvvvtttvvvyyy|||}}}}}}~~~~~~~~~|||{{{{{{yyy}}}}}}|||{{{zzz{{{}}}|||{{{yyyzzzzzzzzz||||||{{{}}}~~~xxxoooddd\\\ZZZ\\\```]]]aaahhhqqq{{{uuukkkgggcccaaabbbfffhhhmmmrrrwww{{{|||lllgggiiiooowwwaaaYYYQQQJJJJJJKKKJJJJJJLLLGGGJJJLLLLLLJJJJJJMMMPPPRRRTTTUUUWWW^^^kkk~~~zzzcccSSSUUUZZZ]]]iiiyyyvvvwww{{{uuurrrpppmmmkkkllliiigggeeedddccc```^^^]]][[[XXXWWWXXXXXXXXXWWWSSSSSSRRRQQQPPPOOOOOONNNQQQQQQPPPPPPPPPOOOOOOOOOOOOQQQSSSSSSQQQPPPPPPPPPMMMKKKIIIFFFBBB???<<<;;;555666888;;;===@@@AAABBBCCCDDDDDDDDDDDDDDDCCCCCCnnn```UUULLLFFFAAA@@@???===<<<<<<;;;;;;<<<;;;::::::999999999:::;;;:::999999888888999999999888777666666777888999777777777777777777777777444444555555444444333222666444333111000000111111444444333222222333333333555444444333333444444555555555666666666666555555333333333444444333222222555444333222222444666777111222222333333222222111333333222222222222111111333333333222222111111111111111222333333444555555666777;;;FFFSSS[[[ZZZWWWYYYcccwww{{{tttooooooooooooqqquuuzzz{{{}}}}}}~~~~~~}}}zzz}}}~~~~~~~~~}}}}}}}}}|||{{{{{{{{{{{{{{{||||||}}}~~~{{{vvvsssoooiiiaaa[[[YYY\\\aaadddgggooozzz}}}ssskkkiiifff```]]]___ffflllrrryyyvvvwwwyyynnn\\\SSSMMMIIIJJJLLLKKKKKKMMMIIIFFFFFFKKKMMMMMMRRRZZZ[[[]]]___```dddpppdddZZZPPPOOORRRVVV]]]cccvvv|||}}}zzzvvvtttpppnnnooollliiifffbbb```_________]]][[[XXXWWWWWWWWWUUUTTTTTTTTTSSSQQQPPPNNNMMMMMMNNNNNNOOOPPPQQQRRRSSSTTTRRRRRRRRRQQQPPPOOOMMMMMMLLLJJJGGGCCC???;;;888666777999:::===@@@BBBDDDEEEHHHCCCAAADDDEEEDDDEEEHHHtttcccVVVNNNHHHCCC@@@@@@???>>><<<;;;;;;::::::;;;::::::999888888999999999999888888777777888888888888777666666777888888777777777777777777777777444444555555444444333222555444333111000000111111444333333222222222333333444444333333333333444444444555555666666555555444222333333333333333222222444333222111111333555666111222222333333222222111111111111111222222222222444333333333222222222222111111222333333444555555555555999CCCOOOXXXYYYXXXVVV]]]lllzzzxxx{{{{{{vvvqqqmmmhhhfffiiimmmppptttzzz~~~~~~~~~~~~~~~}}}|||~~~~~~}}}}}}||||||||||||{{{{{{{{{{{{|||}}}~~~zzzsssnnniiifffdddeeeccc^^^[[[[[[aaajjjqqq{{{ppphhhaaaaaaaaa```bbbjjjuuu}}}|||eeeWWWSSSNNNKKKMMMNNNKKKJJJLLLMMMJJJJJJMMMOOORRR[[[eeelllkkkjjjkkkoooxxxttt\\\SSSKKKJJJMMMOOOTTTYYYaaajjjwww{{{vvvssspppnnnoookkkiiieeebbb___^^^^^^^^^]]][[[XXXWWWWWWWWWUUUTTTTTTTTTTTTSSSSSSRRRRRRQQQPPPPPPPPPPPPQQQQQQQQQQQQQQQQQQQQQPPPOOONNNMMMLLLKKKIIIFFFBBB>>>;;;888666888999;;;===@@@CCCEEEFFFIIIEEECCCEEEFFFFFFGGGKKKyyy___WWWLLLEEEBBBAAA@@@>>>>>>===<<<;;;:::999999999999999888777777777888888888888888777777777777666888777777666666777777888777777777777777777777777444444555555444444333222444333222111111111111111333222222222222222333333444333333222222333333444333444444555555444444333111222222333333333222222222222111000111222333444111111222222222222111111000000111111222222333333444444444444333333333333111222222333333444444555444333666>>>IIISSSXXXZZZYYY]]]eeesss~~~qqqpppnnnnnnnnnlllhhheeeeeebbbccciiiooottt{{{~~~~~~}}}}}}|||}}}}}}~~~}}}|||{{{zzz|||}}}{{{xxxwwwxxxzzz}}}|||wwwsssmmmkkkgggdddaaa``````aaaeeeggghhhgggjjjrrr{{{sssllleeeaaa^^^aaadddhhhppp|||qqq```WWWRRROOONNNPPPOOOMMMMMMOOOSSSQQQRRRSSSUUU\\\kkkxxx}}}yyyyyy}}}ooo^^^RRRKKKGGGGGGIIIIIIKKKOOORRRWWW___hhhrrr||||||wwwsssooonnnoooiiigggdddaaa___^^^]]]]]]\\\ZZZXXXWWWWWWVVVUUUTTTSSSSSSSSSSSSTTTTTTTTTTTTRRRQQQQQQQQQPPPPPPOOOOOOPPPPPPPPPPPPNNNMMMLLLKKKIIIGGGDDDAAA===:::888777999:::<<<>>>AAACCCEEEFFFKKKGGGEEEGGGHHHHHHKKKPPPkkk[[[PPPKKKDDD@@@>>>>>>>>>>>>;;;;;;:::999888777777888888777777666666666777777888888888888888777777666777777777666666777777777666666666666666666666666444444555555444444333222333222222111111111111111222111111111111222222333333333222222222222333333222333333333333333333222000111111222222222222222111000000000000111222222111111222222222222111111000000111222333444555555444444444444444444444444222222222333333444444444444333555:::DDDNNNWWW\\\\\\]]]bbbjjjtttzzz{{{yyyooorrrtttsssnnniiifffeeekkkiiikkkqqqvvv{{{~~~}}}|||}}}}}}}}}~~~~~~|||zzzzzz|||}}}xxxvvvuuutttuuutttqqqooonnnppprrrrrrssssssttttttsssqqqqqqooonnnmmmkkkiiifffcccaaaaaabbbbbbcccdddgggjjjmmmrrrvvv{{{}}}yyyoooiiifffeeeeeeiiimmmssszzziii[[[VVVQQQOOONNNPPPOOOOOOTTT[[[``````______aaakkk|||{{{nnn___SSSLLLHHHGGGIIIJJJHHHIIILLLRRRTTTVVVZZZaaalllyyy}}}wwwsssooonnnooogggfffcccaaa___]]]\\\\\\\\\YYYWWWVVVWWWVVVUUUTTTRRRRRRRRRRRRRRRRRRRRRRRRQQQQQQQQQPPPPPPPPPOOOOOOOOOOOOOOONNNMMMLLLKKKJJJFFFEEEBBB???<<<:::999888:::;;;===???BBBDDDFFFGGGKKKGGGFFFHHHIIIKKKPPPWWWqqqaaaRRRIIIFFFCCC???;;;:::::::::::::::999888777777666666777666666666555555666777777999999:::::::::999888777666666666777777666666666555555555555555555555555444444555555444444333222111111222111111111000000000000000000000111222333222222111111111111222222111111222222222222111111///000111111222222222111////////////000000111111000111111222222111111000000111222333444666777777444444444444444444444444222222333333333333444444444444555888???JJJVVV]]]ZZZYYY[[[aaakkktttyyy{{{{{{~~~vvvoookkkkkktttrrrtttzzz~~~~~~~~~}}}|||||||||}}}~~~|||yyy{{{~~~~~~zzzxxxtttooojjjgggeeeeeedddddddddcccbbbaaa```___\\\]]]^^^]]]]]]\\\\\\\\\^^^bbbggglllppptttzzz~~~{{{qqqiiigggiiillloooyyy~~~vvvaaaUUUQQQRRRPPPNNNOOOPPPTTTaaannnwwwwwwuuuqqqrrr|||xxx||||||vvvmmmdddYYYPPPIIIGGGHHHKKKLLLJJJLLLPPPTTTVVVYYY\\\bbbnnn}}}~~~xxxsssooommmnnnfffeeecccaaa___]]]\\\\\\[[[YYYWWWVVVVVVVVVUUUTTTSSSSSSRRRRRRQQQPPPPPPPPPOOOOOOOOOPPPPPPPPPPPPQQQNNNNNNMMMMMMLLLJJJIIIHHHCCCBBB???<<<:::999999999;;;<<<>>>@@@CCCEEEGGGHHHJJJGGGGGGJJJLLLOOOXXXaaaqqqbbbVVVKKKDDDCCC======;;;:::::::::::::::888888777666666666666666666666555555555666777777999999:::;;;;;;999888777555666666777777666666555555555555555555555555555444444555555444444333222000111111222111111000000////////////000111222222222111111000000111111222000000000111111000000000...///000111111111111111/////////000000000111111000000111111111111000000111111222333444555666777333333333333444444444444333333333333333333333333444555555666;;;EEESSS\\\\\\ZZZZZZ___iiivvv{{{xxxxxx}}}~~~wwwvvv~~~~~~}}}}}}~~~~~~yyy{{{}}}~~~yyytttooollljjjgggeeecccaaa```^^^^^^^^^ZZZ\\\^^^```aaacccfffhhhmmmsss|||vvvsssmmmjjjlllqqqxxx}}}qqq```WWWSSSTTTSSSRRRSSSTTT\\\ooouuukkkpppqqqnnniiicccYYYPPPHHHGGGIIIMMMNNNNNNRRRWWWXXX___gggoooxxx}}}xxxtttooolllllleeedddcccaaa```^^^]]]\\\ZZZXXXVVVUUUVVVVVVUUUTTTUUUTTTTTTSSSRRRQQQQQQPPPNNNNNNOOOOOOPPPPPPPPPQQQLLLLLLLLLLLLKKKIIIHHHGGGAAA???===:::999999::::::<<<===???AAADDDFFFHHHIIIIIIHHHIIIMMMQQQVVVbbbmmm~~~kkk```TTTNNNHHHBBB???AAA;;;<<<<<<<<<;;;;;;;;;<<<888777777666666666666777666666555555666777777888888888:::::::::999777666555555666777777666555555444444444444444444444444444444555555444444333222///000111222222111000000///......///000111222222111111000000000000111111/////////000000/////////---...///000111111111111//////000111111111111111000000111111111111000000000000111111222333444444222222222222333333333444333333333333333333333333222444555555777@@@NNNYYY___^^^]]]cccqqq~~~}}}{{{|||}}}~~~}}}{{{xxxvvvrrrooollllllllllllkkknnnqqqtttvvvyyy~~~|||wwwvvvtttsssrrrtttxxx}}}jjj___YYYXXXXXXXXXZZZ[[[]]]eeeyyyyyymmmjjjnnnpppooolllfff[[[PPPJJJIIIKKKOOORRRTTTZZZbbbkkkvvv}}}yyyuuuoookkkkkkeeeddddddbbbaaa___]]]\\\YYYXXXVVVUUUVVVVVVUUUTTTRRRRRRRRRRRRQQQQQQQQQQQQPPPPPPOOOOOOOOOOOOOOONNNKKKKKKKKKKKKJJJHHHGGGFFF???===;;;888888888:::;;;<<<===???BBBEEEGGGIIIJJJIIIIIILLLQQQVVV^^^lllzzz|||fffXXXQQQIIIEEEFFFEEE@@@>>>AAA:::;;;<<<;;;999888888888888777777666666666666777666666666666666777888888666777999:::999888666555444555666777777666555444444444444444444444444444444444555555444444333222///000111222222111000///............///000222222111111000000000000111111......////////////......---...///000111111111111//////000111111111111111000000111111111111000000/////////000111111222222111111111222222333333333333333333333333333333333111333444333555===KKKWWW]]]\\\]]]eeevvv}}}}}}}}}~~~~~~}}}}}}}}}}}}|||||||||}}}~~~}}}{{{zzz{{{|||~~~zzzuuuvvvwwwxxx{{{ppp```YYYWWWVVV[[[]]]aaacccdddlllvvvhhhooorrrtttsssqqqjjj]]]OOONNNMMMOOOSSSUUUYYYbbbkkk|||yyyvvvpppkkkjjjeeeeeedddcccaaa```^^^]]]YYYWWWUUUUUUVVVVVVUUUTTTMMMMMMNNNNNNOOOPPPPPPQQQRRRQQQQQQPPPNNNMMMMMMLLLKKKKKKKKKJJJIIIHHHFFFFFF>>><<<:::888777888:::;;;===>>>@@@BBBEEEHHHJJJKKKJJJJJJNNNTTTZZZdddsss{{{lll___SSSLLLFFFEEECCCAAA>>><<<:::999:::999999888888999999:::777777777777666666666666777777777777777777777777666666666666555555555555444444444333333222222222444444444444444444444444333333444444333333222111///000111222222222222222000111111000///......///222222111111111111111222////////////////////////222222111111000000//////000000000000111111111111------...000000111111111//////000000000000//////222111000///000111333555333333333333333333333333555444333333444999@@@EEE\\\aaaeeekkk|||}}}}}}}}}}}}~~~~~~~~~~~~}}}{{{{{{|||||||||||||||{{{|||}}}|||zzz{{{|||jjjZZZQQQRRRYYY\\\aaafffjjjoooxxxvvvvvv}}}}}}uuukkk___TTTQQQRRROOOUUU```dddmmmwwwqqqmmmlllkkkjjjhhhgggeeecccaaa___^^^]]]ZZZYYYWWWUUUTTTTTTUUUUUUUUURRRPPPQQQSSSSSSQQQOOOOOONNNNNNMMMMMMLLLLLLLLLIIIIIIIIIHHHGGGEEEBBBAAA===;;;999777666777999;;;======>>>@@@DDDFFFGGGGGGIIIHHHKKKTTTcccrrr}}}pppcccZZZRRRKKKEEEBBBAAA@@@>>><<<;;;:::999999999999888888999999999777777777777666666666555777777777777777777777777666666666666555555555555444444444333333222222222444444444444444444444444222222333333222222111000///000111222222222222111000111111000///......000111111111000111111222222////////////////////////000000000000000000000000000000000000111111111111---...///000111111111111///000000111111000000///222111000//////111222333222222222222222222222222555555444333444888???CCCVVV^^^ffflllyyy~~~~~~~~~~~~}}}|||zzz{{{|||}}}}}}}}}}}}}}}|||}}}|||yyyzzz{{{~~~}}}xxxwww|||xxxdddVVVNNNOOOVVV[[[aaaiiipppwwwzzz|||{{{sssiii```XXXXXXUUU\\\kkkrrr}}}uuuooollljjjiiihhhfffeeecccaaa___]]]\\\[[[YYYXXXVVVUUUTTTSSSTTTTTTSSSQQQOOOPPPRRRRRRPPPNNNNNNMMMMMMLLLLLLKKKKKKKKKIIIIIIHHHGGGEEECCCAAA???:::999777666777999;;;===?????????@@@BBBBBBBBBAAAEEEHHHNNNZZZhhhssszzz|||}}}ddd\\\RRRKKKGGGDDDAAA???======<<<;;;::::::999999999999888888888888999999777777777666666666555555777777777777777777777777666666666555555555555444444444333333333333222222444444444444444444444444111222222222222111000000000000111111222222111111///000111000///...///000000000000000000111222333////////////////////////000000000000111111111111000000000000111111111111//////000111222222222222000111111111111111111000333222111000///000111222111111111111111111111111666666555444444777<<<@@@LLLYYYgggmmmsss~~~~~~~~~~~~~~~~~~}}}{{{yyyzzz{{{|||}}}~~~~~~~~~|||}}}wwwrrrooonnnlllkkkjjjkkklllmmmpppxxxxxxrrrsssuuu|||qqq^^^TTTNNNOOOUUUZZZaaalllvvv}}}}}}~~~yyyrrreeedddbbbkkk~~~}}}yyyrrrmmmjjjiiigggfffccccccaaa___]]][[[ZZZYYYWWWWWWUUUTTTSSSRRRRRRRRROOONNNMMMNNNPPPPPPPPPNNNMMMMMMLLLKKKKKKJJJIIIIIIIIIHHHGGGEEECCCAAA>>>===777666666666888;;;>>>???@@@@@@AAABBBBBBBBBAAAAAAEEEKKKUUUaaakkkrrrvvvwwwwwwdddYYYQQQLLLFFFAAA???>>>===<<<<<<<<<;;;:::999999888888888888777777777777888888777777666666666555555555666666666666666666666666666666555555555444444444333333333333333333333333333333333333333333333333222222222222222111111000000000111111111111000000///000111000///...///000000//////000000111222333////////////////////////111111111000000000000000///000000000111111111111000000111222222222222222111111222222222222111111333222111000//////000000111111111111222222222222666666666555444666:::===BBBRRRdddlllmmmpppxxx~~~yyyvvvuuuxxx}}}~~~}}}}}}}}}~~~}}}{{{wwwxxxzzz{{{|||}}}~~~~~~}}}}}}~~~}}}~~~{{{uuuooohhhbbb___``````______bbbgggnnnsss~~~uuurrrrrrxxxnnn]]]VVVSSSTTTYYY^^^dddmmmxxx}}}ttttttsss}}}yyyuuupppllliiigggeeedddcccbbb```___\\\[[[YYYXXXVVVVVVTTTSSSRRRQQQPPPPPPLLLLLLLLLLLLMMMNNNNNNNNNMMMMMMLLLKKKJJJIIIIIIHHHHHHGGGEEECCC@@@>>><<<:::777666666777888;;;===???===???AAACCCDDDDDDFFFGGGJJJSSS]]]ccceeeiiisss{{{rrrdddWWWMMMGGGHHHFFFBBB???======<<<<<<======<<<;;;999888777777888777777666666777777888666666666666555555555555555555555555555555555555555555555555444444444444333333333333333333333333333333333333333333333333333333333444333222222111000000111111111000000///...000111000///...///111000000//////000111111222////////////////////////333222222111000//////...///000000000111111111111000111111222222222222111111111222222222222111111222111111000000/////////222222222222333333444444555666666555444555888:::<<>>AAABBBCCCDDDHHHKKKQQQYYY___\\\WWW^^^ppptttkkk^^^RRRJJJFFFCCCBBB>>>===<<<;;;;;;;;;<<<<<<======<<<;;;999888777777777777666666666666777777666666666555555555444444555555555555555555555555555555555444444444444333222222333333333333444444333333333333333333333333333444444444444333222222000000111111000000//////...///000000//////000111111000000//////000000000////////////////////////222222111111000/////////000000000000111111111111000000111111111111111000000111111111111111111000000000000000000000//////222222222333333444444555333555666666555555777999:::CCCRRR```dddccceeeiiiooozzz~~~xxxtttmmmlllqqq|||{{{}}}~~~|||wwwxxxyyyzzz{{{|||||||||}}}~~~~~~~~~~~~}}}vvvssspppnnnmmmkkkhhhfffdddcccaaa_________``````gggkkkpppvvv}}}}}}vvvvvvxxx|||uuuccc]]]\\\aaajjjqqqrrrvvv~~~wwwsssuuurrrpppmmmllljjjhhheeecccdddcccaaa___]]][[[ZZZYYYUUUUUUUUUTTTRRRPPPNNNMMMIIIKKKLLLKKKJJJJJJKKKLLLMMMLLLKKKJJJIIIGGGFFFFFFCCCBBB@@@===;;;999888888999999999999999999::::::===???AAAAAA@@@CCCHHHMMMVVVYYYYYYSSSPPP[[[sssxxxiii___TTTOOOHHHCCC@@@??????>>>888999999999999999:::;;;:::::::::999999999888888777666666555555666666777666666555555555444444444444444444444444444444444555555555444444444333333222222222333333444444444222222222222222222222222333333333333333222111111000000000000000//////...---///000000//////000222222111000//////...////////////////////////////////////000000111111111222000000000000111111111111///000000111111000000//////000000111111000000/////////000000000000000000000111111222333333444444222333555666555555666888:::<<>>@@@BBBBBBBBBGGGOOOWWWZZZWWWRRRPPPVVVfff{{{vvviiiaaa[[[UUUPPPEEECCCAAA@@@???>>>;;;999999:::;;;;;;:::999:::;;;777777888888999999::::::666666555555555555666666666666555555555444444444444444444444444444444444555555444444444333333333222222222333333444444444222222222222222222222222111222222222222111000000000000000000000///......---///000000//////000222333222111///............////////////////////////,,,---...000111333444555000000000000111111111111//////000000000//////...//////000000000000//////---...///000111111000000///000000111222222333333111333555666555555666777;;;999@@@RRRbbbfffeeeeee^^^dddrrrvvvpppooommmssszzz{{{vvvsssooonnnxxx}}}yyytttqqqqqqvvv~~~~~~|||}}}~~~~~~~~~~~~~~~}}}}}}~~~~~~~~~~~~|||{{{|||||||||~~~~~~~~~{{{}}}zzzsssiiihhhrrr}}}|||yyyrrrqqqwwwqqqpppnnnnnnmmmkkkhhheeebbbbbb```^^^\\\ZZZYYYXXXVVVVVVVVVUUUSSSQQQNNNMMMJJJLLLNNNLLLIIIHHHIIIKKKHHHHHHGGGEEEDDDBBBAAAAAA???>>><<<999888777777888777777888999::::::;;;;;;>>>AAACCCDDDGGGNNNZZZccc]]]VVVPPPSSSaaattttttjjj\\\RRRMMMJJJEEEAAA======<<<<<<;;;;;;;;;;;;888888888888999:::;;;<<<<<<<<<;;;::::::999888888777777777777666666666666888777555333222222222333666555444333222333444555555555444333222111111000111111111111111111111111222222222222222222222222222333333444444333333222222222000///............000000000000000000000000////////////////////////---.........//////000000///111222111000///000111////////////000000000000000000////////////000000000000000000111111111111111111000000//////......///000111222222333222222333333333444444444555555333888>>>FFFWWWhhhooommmdddccciii}}}uuuooommmlllnnnrrryyy}}}xxxtttqqqzzz~~~zzzssspppoooqqqvvv|||~~~~~~~~~~~~|||}}}}}}~~~~~~~~~~~~||||||xxxpppttt{{{zzzvvvtttsssrrrnnnnnnllljjjhhhfffeeedddeeecccaaa```___^^^\\\ZZZUUUUUUTTTRRRQQQPPPOOONNNMMMLLLLLLKKKJJJIIIIIIHHHJJJHHHEEEDDDCCCBBB???===>>>:::777666888::::::888;;;;;;;;;;;;;;;;;;;;;;;;@@@DDDFFFEEELLLYYYbbbddd___WWWOOOVVVpppvvvjjjaaaXXXPPPGGGBBBAAA@@@>>><<<;;;;;;;;;:::::::::999999888888888888999:::;;;;;;;;;;;;;;;:::999999888888777777777666666666555555666555444333333333333333555444333333333333444555444444444333333333333333111111111111111111111111222222222222222222222222111222222222222222222111222111000///............////////////////////////........................---........./////////000///000111111//////000111.../////////000000000000111111111111111111111111....../////////000000000000000000/////////////////////000111222222222222333333333333444444444444222666;;;CCCSSSfffpppqqqhhhdddfffttt{{{{{{|||vvvqqqppppppqqqtttwww||||||zzzuuu}}}zzzyyyvvvrrrrrruuuxxxyyyyyy{{{}}}|||vvvtttrrrrrrqqqnnnmmmkkkiiigggeeedddddddddbbb___^^^]]]\\\ZZZXXXUUUTTTSSSRRRQQQOOONNNNNNKKKKKKJJJJJJIIIIIIHHHHHHIIIGGGEEECCCCCCAAA???======:::777666888::::::999=========<<<;;;;;;::::::???DDDHHHJJJPPP[[[```___XXXSSSRRRaaapppddd\\\VVVOOOIIIEEE@@@<<<:::<<<===<<<;;;999999999999999888888888777777777777888999:::;;;:::::::::999999888888777777666666666666555555555333333444444444444333333333333222222333444555666333333333444444444555555111111111111111111111111111111111111111111111111000000111111111111000000222111000//////......///////////////////////////.......................................////////////000111000///...///111....../////////000000000///000111222222111000///------.........///////////////////////////000000...///000111222222222222222222333333333444444444222444777===LLL```ooouuulllfffccckkkyyy~~~uuuqqqnnnqqqwww{{{{{{yyynnnooooooooooooqqqtttwww{{{}}}xxxsssvvv|||zzzvvv{{{xxxuuussstttvvvwwwwww~~~|||xxxuuutttsssrrrqqqnnnllliiifffdddccccccdddbbb```]]]\\\[[[YYYWWWUUUTTTTTTSSSRRRPPPOOONNNMMMIIIIIIIIIIIIIIIIIIIIIIIIHHHFFFCCCBBBAAA@@@>>>;;;;;;888666666888:::::::::???>>>===<<<;;;;;;::::::===CCCIIINNNTTTYYYXXXTTTOOOQQQZZZqqquuulllcccWWWNNNJJJHHHEEECCCBBB@@@>>>===>>>===<<<:::888888888888888888888888777777777777777888999999999999999888888777777777666666666555555555444444111222333444555444444333111111222222333444555666444444444444444444444444111111111111111111111111111111111111111111111111000111111111111111111000111111000///////////////////////////////////////...................................................///000000......///000........./////////000000,,,---///000000///---,,,------........./////////---......//////000000000...///000111222222222222222222222222333333333333444444444888DDDVVVhhhrrroooiiidddgggqqqxxxxxxuuunnnnnnoooqqqssstttqqqoookkknnnqqqsssuuuxxx~~~zzztttqqquuu|||{{{wwwuuuwwwuuusssssstttwwwyyy{{{~~~~~~~~~~~~{{{xxxwwwvvvuuusssrrrmmmkkkgggcccaaaaaabbbcccaaa___\\\ZZZYYYXXXUUUSSSTTTSSSRRRQQQPPPNNNMMMMMMHHHHHHIIIIIIIIIIIIIIIIIIFFFDDDBBB@@@@@@>>><<<:::888777777777888:::;;;;;;>>>===<<<;;;;;;;;;<<<<<>>===<<<;;;:::777555888888888888888888999999777777666666666777888888777777777777777666666666555555555555444444444444000111333444555444444333000111222333444444555555666555555444333333222222000000000000000000000000000000000000000000000000111111222222222222111111111000000////////////000...............................................................------------/////////...---...///............////////////+++,,,...//////...,,,+++....../////////000000000------......//////000000......///000111111111111111111111222222222333333666444333555<<>>===:::888666777888999999;;;<<<===<<<;;;;;;;;;<<<===???AAAFFFIIINNNRRRQQQLLLHHHGGGRRRhhh|||ooojjj```UUUQQQQQQNNNHHHBBB@@@>>>======<<<;;;999;;;;;;;;;:::999888777666777777777888888888888999777777666666666666777777666666666666666666666666555555444444444333333333111111222333333333333333000111222333444444333333666555444333222111111000000000000000000000000000////////////////////////111222222222222222222111000000////////////000000........................------------------------.........------------------...///...---,,,---///------........./////////---...///000000///...---....../////////000000000..................//////---...///000111111111111000000111111111222222222555444444555888???NNN]]]llllllkkkhhhhhhllluuu}}}~~~}}}yyyzzz|||zzz}}}xxxvvvwwwvvvvvvtttrrrpppqqqtttvvvtttwww{{{~~~~~~~~~~~~sssvvv}}}zzzvvvsssqqqooollliiihhhfffccc```^^^]]]]]]^^^]]][[[YYYXXXWWWVVVTTTRRRRRRRRRQQQPPPNNNMMMLLLKKKHHHHHHHHHHHHHHHHHHHHHHHHCCCAAA???===<<<;;;999777555777999:::;;;<<<>>>@@@===<<<<<<<<<>>>@@@CCCEEELLLNNNQQQRRROOOLLLPPPWWWjjj}}}yyypppfff___[[[PPPPPPLLLFFFCCCEEEEEEBBB???>>>>>>======<<<:::999999:::::::::999888888999555555666666666777777777777666666555555666666666555555555555555555555555444444444333333333333222222222222222222222333333111222333333333333222111333333333222222111111111000000000000000000000000////////////////////////000000111111111111000000000000////////////000000........................------------------------.........------,,,,,,,,,,,,---......,,,,,,---...---------.........//////........................------........./////////..................---------...///000111111111111000000000000111111111222111111444666666888DDDRRRdddiiillliiieeekkkzzz~~~wwwwwwwwwvvvuuuqqqnnnmmmpppsssqqqtttzzz~~~}}}}}}|||}}}|||||||||~~~~~~vvvkkklllsss|||xxxtttpppnnnllliiihhheeedddbbb```^^^\\\[[[[[[YYYWWWVVVUUUUUUUUUSSSRRRRRRQQQPPPOOONNNLLLKKKKKKGGGGGGFFFFFFEEEEEEDDDDDDBBB@@@===<<<;;;:::777555444777;;;<<<<<<===@@@CCCBBBAAA@@@@@@AAACCCFFFHHHKKKLLLOOONNNKKKMMM\\\mmmdddkkkssstttpppmmmnnnqqqqqq{{{}}}wwwpppmmmkkkiiiccc^^^______\\\WWWQQQMMMKKKJJJBBBFFFFFFBBB???AAAAAA@@@<<<;;;;;;:::::::::::::::888999999888666555666777444444444555555555666666777666666555555555666666444555555555555555555555444444444333333333222222444333222111111111333333111222333444333222111000000111111111111222222222000000000000000000000000//////////////////////////////000000000000//////000000////////////000111........................------------------------.........------,,,,,,,,,,,,---......,,,,,,---...---------.........//////---,,,,,,++++++,,,,,,---,,,,,,,,,---------....../////////......------,,,---...///000111111111111000000000000111111111111---...333777555555???MMM\\\eeekkkiiifffmmm}}}tttuuutttpppmmmlllooossspppsssyyy~~~~~~~~~}}}}}}|||{{{{{{zzz}}}|||{{{{{{}}}uuuqqqkkkjjjnnntttyyy|||}}}||||||xxxsssooommmllljjjiiidddcccbbb```^^^\\\ZZZYYYVVVUUUSSSSSSTTTTTTRRRQQQRRRQQQPPPOOOMMMLLLKKKKKKFFFEEEEEEDDDCCCBBBBBBAAAAAA???===;;;;;;999777555444888<<<======>>>AAADDDGGGEEEDDDCCCCCCEEEHHHJJJFFFGGGJJJIIIGGGMMMeee}}}SSSTTTVVVXXXYYYYYYYYYXXX\\\aaaiiirrrxxx|||}}}~~~|||{{{xxxwwwyyy}}}}}}|||zzzvvvqqqkkkgggddd^^^\\\XXXUUURRRPPPPPPPPPKKKJJJHHHFFFDDDCCCBBBBBB>>>>>>===<<<<<<<<<<<<<<<::::::::::::::::::::::::888888888888888999999999555555555555555555555555555555555555555555555555444666888888666444444444333333333333333333333333111111111222222333333333555555444333333222111111444333222222111111222222222111000//////000111222000000000000000000000000......///000000000000000000000000000000000000000...---,,,+++***+++,,,,,,,,,,,,,,,,,,,,,---...///......---------......///......//////////////////......---------......///------++++++++++++------,,,---.../////////...---,,,---......------///111/////////...............///////////////////////////444999888333444<<>>>>>>>>>>>===<<<<<<;;;;;;<<<<<<::::::::::::::::::::::::999999888888777777777666555555555555555555555555555555555555555555555555444666888888666555444555333333333333333333333333111111111222222333333333555444444333222222111111222222111000000000000000111111000000000000111111000000000000000000000000......///000000000000000////////////////////////......,,,+++++++++,,,---...------,,,,,,---------///......---------..................------------......---------......///---,,,,,,++++++,,,,,,---....../////////---,,,+++111...,,,,,,...///...,,,111111111111111111111111000000000000000000000000...222555555222444:::@@@LLLYYYeeegggiiippp{{{zzzvvvwww{{{|||tttrrrooommmlllmmmnnnoooooopppsssuuuyyy{{{~~~~~~}}}|||}}}{{{zzz{{{~~~~~~~~~~~~|||{{{uuussstttwwwxxxyyywwwuuuvvv{{{~~~{{{{{{uuusssqqqnnnkkkjjjiiiiiidddbbb___]]]\\\[[[YYYWWWVVVUUUSSSQQQPPPPPPPPPPPPMMMMMMLLLLLLKKKJJJHHHHHHFFFFFFFFFDDDCCCAAA???>>><<<;;;999777777777888999::::::;;;===>>>@@@BBBCCCEEEEEEDDDCCCBBB@@@???>>>:::;;;???CCCKKK]]]{{{???@@@BBBDDDEEEEEEDDDDDDFFFGGGHHHIIIIIIIIIHHHGGGKKKJJJIIIIIIJJJKKKMMMNNNJJJJJJKKKKKKKKKJJJIIIIIIGGGFFFFFFFFFDDDCCCAAA@@@CCCBBB@@@???>>>>>>?????????>>>===<<<<<<<<<<<<<<<===<<<<<<;;;;;;;;;;;;;;;::::::::::::::::::::::::999999888777666555444444444444444444444444444444444444444444444444444444555777888888777555555555333333333333333333333333111111111222222222222222444444333333222111111111000000/////////.........000111111222222111111000000000000000000000000000......///000000000000//////////////////////////////...------,,,,,,------......---,,,,,,,,,------//////...---,,,,,,,,,---......------,,,,,,,,,+++///......---------......+++,,,,,,------,,,,,,+++////////////...,,,+++***222---)))***///111...***..................//////000000000000000000000000...///111111111333777:::BBBNNN[[[ccciiiqqquuuvvvwww|||wwwooommmqqqxxx}}}qqqnnnjjjjjjlllnnnnnnllllllmmmooorrruuuxxxzzz{{{}}}}}}}}}~~~}}}~~~{{{yyysssqqqtttzzz~~~}}}yyyyyysssrrrpppmmmkkkiiihhhgggdddbbb^^^\\\[[[YYYWWWUUUTTTSSSRRRQQQPPPOOOOOOOOOKKKKKKKKKJJJIIIHHHFFFEEEGGGGGGEEECCCAAA>>>;;;:::;;;999777666666777999;;;<<<<<<<<<===>>>???@@@AAAAAAAAA@@@???===<<<;;;;;;:::999<<>>======<<<<<<<<<=========<<<;;;:::999999888888>>><<>>???>>>>>>===999999:::;;;===???AAABBB>>>??????@@@@@@?????????>>>>>>??????@@@??????>>>>>>>>>======<<<<<<<<<<<<::::::;;;;;;<<<>>>??????;;;;;;::::::;;;;;;<<<===;;;::::::999999999999999999999999999999999999999555555555555555555666666444444444444444444444444444444444444444444444444444666888888666444444444222222222222222222222222111111111111111111111111222111111111111111000000000000111111111000///...///000111222222111000///........................------...///////////////.......................................---------******+++,,,---...000111000///...,,,,,,+++++++++////////////......------//////...---------------++++++------------++++++,,,,,,,,,,,,------............------,,,+++,,,---.........//////000000000........................000...---///222444444333777???KKKYYYiiisssrrrkkkooopppzzz}}}wwwtttwwwwwwooofffccceeeggggggeeeeeefffhhhkkknnnqqqtttuuuzzz{{{}}}~~~~~~~~~~~~~~~~~~||||||}}}~~~}}}pppnnnwwwwwwqqqoooooonnnmmmkkkhhhfffdddcccbbb___[[[YYYWWWUUUSSSQQQQQQPPPPPPOOONNNMMMLLLKKKKKKKKKJJJIIIHHHFFFDDDDDD@@@@@@@@@???===<<<:::999888777666555666999<<<>>>>>>===<<<;;;:::999999999999888777777777777888888>>>???JJJ```www:::;;;===>>>>>>>>>===<<<999999:::;;;<<<======>>>;;;;;;;;;;;;<<<<<<<<<<<<;;;<<<<<<==================<<<;;;:::999999999:::888888999:::;;;<<<<<<===999888888888888999:::;;;::::::999888888888888888999999999999999999999999555555555555666666666777333333333333333333333333333333333333333333333333333555666666555333333333222222222222222222222222111111111111111000000000000000000000000000000000000111222333222111000///...//////000000//////...........................------...////////////...........................---............---,,,,,,******+++,,,---///000111......---,,,+++++++++,,,////////////////////////000///...---------------+++,,,,,,------,,,,,,++++++***++++++,,,...///000000111000...***((()))***,,,,,,,,,------......///------------------------/////////000222333333222666;;;CCCPPPbbbpppsssnnnkkkkkkrrr}}}zzzwwwxxx~~~yyyssskkkfffeeeeeeeeeddddddeeegggjjjmmmppprrrsssvvvxxx{{{~~~}}}~~~~~~~~~~~~~~~~~~~~~{{{{{{{{{|||}}}~~~{{{yyyooorrr}}}wwwqqqooommmmmmkkkjjjgggeeebbbaaa___]]]YYYWWWVVVTTTRRRPPPOOOOOOOOONNNMMMLLLKKKJJJKKKJJJJJJIIIGGGEEECCCBBB<<<<<<===<<<<<<;;;:::999888777777888999:::<<<======<<<:::999888777666666666666555555666888:::;;;<<>>??????>>>>>>===:::;;;;;;<<<<<<<<<;;;;;;;;;:::::::::;;;<<<<<<===:::;;;;;;<<<======<<<<<<===<<<;;;:::999::::::;;;::::::;;;<<<<<<<<<<<<<<<888888888777888888999999999999888777777777777888888888888888888888888888777777666666666666666666333333333333333333333333333333333333333333333333111333555555333222111222111111111111111111111111222111111111000000000///000000000000000000000000000111222333333111000.........------------......------------------------,,,---......//////..............................,,,------...---,,,+++***------,,,,,,,,,---......------,,,,,,+++,,,,,,,,,,,,------......//////000000000///------,,,,,,------,,,,,,++++++,,,,,,---,,,++++++++++++,,,...//////...,,,+++,,,,,,++++++((())))))***++++++,,,,,,..............................000000000000111111444777;;;FFFXXXjjjrrrpppjjjhhhjjjyyy~~~}}}|||{{{}}}~~~{{{xxxuuurrrmmmjjjgggfffeeeccceeegggjjjmmmppprrrssstttvvvzzz}}}}}}~~~~~~~~~~~~}}}}}}{{{{{{{{{{{{{{{|||}}}~~~|||}}}|||xxx~~~wwwqqqoookkkkkkjjjiiifffdddaaa___]]][[[WWWVVVUUUTTTRRRPPPNNNNNNNNNNNNMMMKKKIIIHHHIIIIIIHHHGGGEEECCCAAA@@@;;;;;;;;;;;;:::999888888777888999:::;;;<<<<<<<<<;;;:::999777555555444444555555444555777:::===>>>CCCQQQkkk~~~999:::;;;<<<<<<;;;::::::777888999:::::::::999888:::999888888999:::<<<===777888999:::::::::::::::;;;:::999888999999;;;;;;::::::;;;;;;;;;;;;::::::::::::999999999999::::::999888888777777777777777888888888888888888888888999999888777666555555444333333333333333333333333333333333333333333333333111222444444333111111111111111111111111111111111222111111111000000//////////////////000000000000///000222333222111///......---,,,++++++,,,---...------------------------,,,---......//////..............................+++,,,---------,,,+++***000///...---,,,+++++++++,,,,,,+++++++++,,,------***++++++,,,---...//////111000///...---,,,,,,,,,...---++++++++++++---......---,,,+++++++++,,,---+++(((%%%(((///222111...++++++,,,---......//////////////////////////////,,,...000000///...///000333444666>>>QQQeeeppprrrmmmhhhfffnnnwwwttttttvvvvvvvvvwww{{{|||zzzxxxvvvuuuvvvwwwtttoookkkgggfffccceeegggjjjmmmppprrrssstttvvvyyy}}}~~~~~~~~~||||||}}}{{{zzzzzzzzzzzz{{{||||||wwwzzz}}}{{{tttpppnnnkkkjjjjjjhhhfffccc```^^^\\\YYYVVVUUUTTTSSSRRRPPPMMMMMMNNNMMMLLLKKKIIIHHHHHHGGGGGGEEECCCAAA???>>>;;;;;;;;;:::999888777666888999;;;<<<======<<<;;;:::999777666444333333333444444444555888;;;???AAANNN```}}}|||qqqxxxzzz|||:::::::::999999999888888999999888888888888999999;;;;;;;;;;;;;;;;;;;;;;;;::::::;;;;;;;;;:::999999<<<;;;999888888999;;;<<<999999999::::::;;;;;;;;;::::::999888777777888888555555666666777777777888999999888888777777666666555555555555555555555555444333222111111222333444222222222222222222222222111000000000111222333333222222222111111111000000222111111111000000//////......//////000000111111000000000000000000000000////////////////////////000////////////000111111///............---------///...---,,,,,,,,,,,,,,,///...---,,,,,,,,,---...************************+++***************++++++++++++,,,,,,,,,---------------------------------(((((())))))*********+++,,,,,,+++***+++,,,---...---...000///...,,,,,,---........................000///...------...///000,,,,,,------.../////////222444666:::CCCSSSggguuutttnnnfffcccooo~~~|||}}}zzzuuuqqqnnnooopppqqqwww{{{|||vvvsssssswww}}}|||~~~xxxssspppmmmhhhgggggggggiiinnntttuuutttyyywwwvvvyyy}}}}}}zzzyyy}}}|||zzz{{{}}}~~~~~~}}}|||yyytttpppnnnjjjjjjjjjhhhfffccc```___[[[ZZZYYYXXXVVVSSSQQQPPPMMMMMMLLLKKKJJJIIIIIIHHHJJJIIIGGGEEEBBB@@@>>>===;;;;;;:::999888888888999666888:::<<<<<<<<<;;;:::777555333222333444444444;;;777666:::<<<>>>GGGQQQdddwwwuuuuuuzzz;;;;;;;;;:::::::::999999999888888777777888888999888888888888888888888888888888999::::::999999999999888777666666777888999888888888888999999::::::999999888777777777777777666666666666666666666666777777666666555444444333444444444444444444444444333222222111111222222333222222222222222222222222111111000000000111222222222222222111111111000000000000000000//////............//////000000000000000000000000000000000000////////////////////////+++************+++,,,,,,...---------,,,,,,,,,,,,......---,,,,,,,,,,,,,,,,,,,,,+++*********+++,,,++++++++++++++++++++++++,,,+++***************+++++++++++++++,,,,,,,,,---------------------------++++++++++++++++++,,,,,,,,,,,,+++++++++,,,---...---...000///---,,,,,,---........................000///...------...///000,,,,,,------.../////////111333666888???MMMbbbqqqvvvqqqhhhaaaeeerrr~~~xxxttttttuuutttrrrqqqooollljjjjjjmmmrrrtttuuuooonnnqqqwww~~~yyyrrrkkkhhhhhhhhhiiinnntttxxxyyyzzzwwwttttttxxx}}}~~~|||{{{}}}{{{zzz{{{|||}}}}}}}}}zzzwwwrrrnnnlllgggggggggfffdddaaa___^^^[[[ZZZYYYWWWUUURRRPPPNNNLLLLLLKKKJJJIIIIIIHHHGGGIIIHHHFFFDDDAAA???===<<<;;;;;;999888777777777777999:::;;;<<<===<<<:::999666555444444555666666666999666777;;;???HHHYYYiii<<<;;;;;;;;;::::::::::::999888888777777888888999777777777777777777777777666777888888999999999999888777666555555666777888777777777777777888888888777777777666666666666666666666666666666555555555666666666555444444333333222222222222222222222222111222222222222222222111222222222222222222222222222111111000000000000111222111111111111000000000////////////...............////////////000000000000000000000000000000000////////////////////////------,,,,,,------...///------,,,,,,,,,+++++++++...------,,,,,,,,,,,,,,,,,,++++++******++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,---,,,+++*********************+++++++++,,,,,,,,,------------------------...------------------,,,,,,,,,+++++++++,,,---...---...///...---,,,,,,---------------------------//////...------...//////,,,,,,------...////////////333666666888DDDXXXhhhvvvuuummmbbb^^^dddmmmqqqppplllhhhiiinnnrrrqqqooohhhgggfffgggkkkrrrxxx||||||ooojjjlllqqqzzz}}}tttllljjjhhhhhhlllqqqxxx|||{{{wwwqqqpppsssxxx}}}~~~}}}|||zzz{{{|||~~~}}}}}}~~~xxxtttoookkkjjjddddddccccccaaa___^^^\\\[[[ZZZXXXVVVSSSPPPNNNLLLKKKKKKJJJIIIHHHGGGFFFFFFFFFEEECCCAAA???===;;;::::::999888777666666666666;;;<<<<<<===<<<:::888777444444555555666777777777888888:::@@@JJJ[[[uuu;;;;;;:::::::::999999999888888777777777777888888888888888888888888888888666666888999::::::::::::888888777777777777888888777777777777777777777777555555555555555555555444444444444555555666666666888888777666666555555444333333333333333333333333000111222333333222111000111111111111111111111111222111000///////////////111111111111000000000000////////////////////////////////////////////////////////////////////////////////////////////////000000000000000111111222---------,,,,,,,,,,,,+++------,,,,,,+++,,,,,,---------------------......,,,,,,,,,,,,,,,,,,,,,,,,------,,,+++*********************+++++++++,,,,,,------------------------//////......------,,,,,,+++++++++,,,,,,,,,---------...///...,,,+++,,,...------------------------........................,,,,,,------.../////////...222555333333<<>><<<;;;999888888333333444555666888:::;;;::::::999888777555444333444666777666444444555777999AAAQQQggg888888888888777777777777888777777666666777777888666666666666666666666666888999:::;;;;;;;;;;;;;;;555555666666666666555555888888888888777777777777222333444666666555444444000111222333444666777777444444444333222222111111444444444444444444444444000111111111111111111000111111111111111111111111000//////............/////////000000000000000111000000000000111111111111/////////............---........................////////////////////////,,,,,,,,,,,,,,,------...//////.........---------+++++++++++++++,,,,,,---))))))***+++,,,,,,,,,,,,************************,,,,,,++++++++++++,,,,,,++++++,,,,,,,,,---------------------------------,,,,,,,,,,,,,,,,,,++++++***+++,,,---------,,,,,,.........,,,******,,,...,,,,,,,,,,,,,,,,,,,,,,,,------............------,,,,,,------.../////////---000222111000444===DDDVVVeeerrrrrrkkkhhhiiijjjuuu}}}|||sssjjjgggfffiiiooolllmmmnnnmmmlllkkklllnnnrrruuuzzz}}}~~~}}}~~~~~~xxxmmmiiilllqqq|||uuuqqqmmmiiigggiiidddcccaaa___^^^]]]\\\\\\XXXVVVSSSOOOLLLJJJIIIIIIHHHGGGFFFEEECCCAAA@@@@@@======<<<;;;:::888888777222333444555777999;;;<<<888777777666555555444444555777888666444444777;;;>>>QQQkkk999999999888888888777777777777666666666666777777777777777777777777777777888999999:::::::::999999666666666777777666666666777777777666666666555555222333555666777666555444333333333333333444444444444444333333222111111111222222222222222222222222111111000000000000111111111111111111111111111111......---------...//////////////////000000111111/////////000000000111111//////.........---------------------------------////////////////////////...............///000000.........---------,,,,,,++++++******+++,,,,,,---((()))***,,,------,,,,,,++++++++++++++++++++++++++++++++++++,,,,,,---...,,,,,,---------.........------------------------,,,,,,,,,,,,,,,,,,------***+++,,,---------,,,,,,......---+++)))***,,,...,,,,,,,,,,,,,,,,,,,,,,,,,,,------......------,,,,,,,,,------.../////////...///000111222555888;;;HHH[[[ooovvvtttrrrqqqooo{{{}}}{{{vvvjjjiiiggggggkkkjjjllllllkkkhhhgggiiikkklllpppvvv}}}~~~~~~~~~~~~}}}||||||~~~~~~zzz}}}}}}}}}}}}llleeehhhttt|||vvvooommmjjjeeeeeehhhdddccc```^^^\\\[[[ZZZZZZVVVTTTQQQMMMKKKJJJIIIIIIGGGFFFEEECCCBBB@@@???>>><<<;;;;;;:::999888888777555555555666777888::::::666666555555555666666777555777888777555777===CCCNNNkkk:::::::::999999999888888777777666666666666777777999999999999999999999999888888999999999888888777888888999999999999888888666666555555555444444444222333555777777666555444555555444333333222111111666666555444444333333222111111111111111111111111222111000//////000111222000000000000000000000000---------------...///000.../////////000000111111---.........//////000000//////.........---------------------------------////////////////////////---------------...//////---------,,,,,,,,,+++++++++*********+++,,,,,,---***+++,,,...//////......,,,,,,,,,,,,,,,,,,,,,,,,*********+++,,,---...///---------.........//////------------------------+++,,,,,,------.........***+++,,,---...---,,,,,,......---+++)))))),,,...,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---......---,,,,,,,,,,,,------...//////000......///111444666666666@@@VVVnnn{{{~~~}}}zzz~~~zzzxxxuuuiiihhhfffeeehhhjjjkkkkkkhhheeeeeegggjjjgggkkkqqqxxx~~~~~~~~~}}}}}}~~~}}}|||zzz{{{}}}~~~~~~}}}vvvxxx{{{|||{{{|||||||||||||||}}}~~~{{{|||~~~nnn```[[[cccvvv}}}wwwqqqllljjjgggccccccfffdddccc```]]][[[YYYYYYYYYUUUSSSPPPLLLJJJIIIIIIJJJGGGFFFEEECCCAAA???>>>===;;;;;;::::::999888888777888888777777777777888888555555555555666777888999555777999777666:::BBBIII___888777666666666666666777555555666666777777888888999;;;===<<<888666666888888999:::;;;;;;999888666777777666555555666888888555555444444444444555555555555666777777666555444666555555555555444444444444444444333333222222222333333222222111000//////111111111111000000000000////////////////////////333222000...------..............................111000///......///000111///...---,,,+++,,,,,,------.........//////000000...///000000000///---,,,//////...---,,,,,,++++++,,,,,,,,,+++++++++******---,,,,,,++++++,,,,,,---,,,---///000000///---,,,***++++++,,,,,,++++++***************+++,,,------///...------,,,,,,,,,,,,...---+++******+++---...---------,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,,,,---------,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------...............///000222333444<<>>===<<<:::999888777888777666555555666777888777777777777666555555444666555555555555555666666999999;;;>>>BBBQQQooo666666888999999999888888888888888888777777777777777777888999:::;;;::::::777888888888777777666666555666666666555444222111444444333333333333444444222222222333444555666666444333333333222222222222000000000000000000000000111111111000000000000000000000000////////////...//////////////////////////////000000000...,,,+++------------------------///...---,,,,,,---...///---....................................---------///......------------------------------,,,,,,,,,,,,,,,,,,+++++++++******,,,,,,---......---,,,,,,------,,,,,,,,,,,,------***++++++,,,,,,++++++***,,,++++++***))))))))))))))))))))))))******+++,,,+++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,---------,,,,,,,,,------,,,,,,+++------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------......////////////000111222222222444888@@@NNNbbbwwwxxxssssss~~~zzzzzz||||||xxxwwwyyy}}}~~~tttllliiigggbbb]]]___^^^\\\[[[[[[]]]___```bbbbbbbbbbbbcccfffjjjnnnuuuyyy~~~}}}||||||||||||~~~|||zzzyyyzzz{{{zzzyyyyyyxxxwwwvvvvvvwwwxxxyyyvvvwwwxxxyyyzzz{{{|||}}}{{{}}}sssgggdddbbb^^^YYY]]]___dddkkkwww}}}{{{|||~~~{{{uuummmggggggeeedddccccccaaa]]][[[XXXXXXWWWVVVTTTQQQOOONNNNNNMMMKKKIIIFFFDDDBBBAAA>>>===<<<;;;:::999888888888777666555555666777888777777666555555444444444666666555555555666777777:::888:::CCCRRRhhh555666777999999999888888999888888888888777777777888888777999;;;;;;:::999777777777666666666666666555555555555444333222222444444333333333333444444222222222222222333444555333333333222222222111111000000000000111111111111000000000000000000000000000000////////////......////////////////////////000000000///...---,,,+++,,,,,,,,,,,,,,,,,,,,,,,,///...,,,++++++,,,...///------...////////////............---------------///...------,,,,,,------------------------------,,,,,,,,,+++++++++******,,,---...//////...---,,,------------------------***++++++,,,,,,++++++***++++++***)))))))))***************)))******++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,---------***++++++,,,,,,------...***+++,,,,,,---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------......000000000000000111222222---111666:::BBBTTTmmmzzzssspppxxx||||||{{{xxxtttsssvvvzzz~~~}}}~~~wwwvvvrrrnnnmmmlllggg```ZZZZZZZZZ[[[\\\^^^```aaaaaabbbbbbbbbccceeeiiilllppptttzzz~~~~~~~~~~~~}}}|||{{{{{{{{{}}}zzzyyyyyyyyyyyyxxxyyyxxxvvvuuuuuuvvvxxxyyyxxxyyyyyyxxxvvvtttuuuvvvxxx{{{~~~xxxoooccc[[[YYYXXXWWWUUUVVV\\\dddmmm{{{xxxuuuqqqkkkeeecccaaa```______]]]ZZZXXXVVVWWWVVVVVVTTTQQQOOOMMMLLLKKKIIIFFFDDDAAA@@@???<<<;;;;;;:::999888888777666666555555666666777777666555555444444444555555666555444444555777888999999:::CCCUUUnnn{{{}}}555666888:::;;;;;;:::999999999999888888888777777:::888777999;;;;;;:::777777777666666555555555666444444333333333333333444444333333222222333333444333333222111111222333444222222222222111111111111000000000111111222222222///000000000000000000000000000/////////.........////////////////////////000///......---------------------------------------,,,,,,,,,,,,,,,,,,---,,,---...///000000///............------,,,,,,,,,///...---,,,,,,,,,------------------------------,,,,,,,,,+++++++++******+++,,,...//////...,,,+++***+++,,,------,,,+++******++++++,,,,,,++++++******))))))))))))******+++,,,,,,+++*********++++++******++++++++++++************++++++,,,,,,,,,,,,******+++,,,,,,---......)))***+++,,,---.........,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------......000////////////000111111---111444444888FFF^^^ppp}}}}}}{{{wwwoooppp~~~|||uuuwwwyyywwwttttttyyy}}}yyytttqqqlllqqqssssssuuuvvvqqqiii]]]^^^^^^____________^^^]]]___aaaaaabbbcccfffhhhhhhmmmsssxxxzzz{{{{{{||||||}}}~~~}}}|||{{{zzzzzzzzz~~~{{{xxxwwwxxxyyyyyyyyyyyyxxxvvvttttttvvvxxxyyyxxxzzzzzzxxxuuussstttuuuwwwyyy|||~~~~~~kkkeee]]]WWWSSSSSSTTTTTTUUU___jjjtttyyyqqqnnnmmmlllhhhdddaaa___]]][[[[[[ZZZXXXVVVTTTUUUUUUUUUSSSPPPNNNLLLGGGGGGEEECCCAAA???===<<<999999888888777777666666444555555666777777666666555444333333333444555666555444444444555777:::;;;===GGGZZZtttzzzvvvvvvzzz}}}666777:::<<<<<<<<<;;;:::999999999999888888777777:::999777999;;;;;;999777777777666555555555555666444333222111222333444555444333333222222333333444444333222111111111222333222222222111111111111000000000111111222222222333////////////000000000000000/////////............///////////////////////////...---,,,,,,...///000........................***+++---......---+++***,,,---///000000000///............------,,,,,,,,,///...---,,,+++,,,------------------------------,,,,,,,,,+++++++++*********+++---......---+++***((()))+++,,,,,,+++)))(((+++++++++,,,,,,+++++++++))))))(((((()))***++++++------,,,+++*********+++******++++++++++++******))))))******++++++++++++******+++,,,,,,---......((()))***,,,---...//////++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------......///............//////000111333333000222===QQQ```xxxzzz|||yyypppkkksss}}}xxxsssrrrvvvyyyyyyxxxyyyvvvnnnmmmkkkiiipppvvvxxx|||{{{sssfffffffffeeebbb___\\\ZZZZZZ\\\___``````aaadddeeebbbgggnnnssswwwxxxzzz{{{zzz{{{}}}~~~}}}{{{zzzzzzyyyyyy|||yyywwwvvvxxxzzzzzzzzzyyyxxxuuuttttttuuuxxxyyywwwyyyzzzyyywwwvvvxxxzzzwwwyyy{{{||||||}}}}}}qqqjjjfff```YYYTTTSSSUUUXXX___jjjwwwzzzjjjqqqlllhhhffffffgggfffdddaaa___\\\[[[[[[ZZZYYYWWWSSSSSSTTTTTTRRROOOMMMKKKDDDDDDBBB@@@>>><<<;;;:::777777666666555555555555333444666777777777666555444333333222333444666777444444333444555888;;;===DDDUUUooo~~~{{{yyyzzz{{{666888:::;;;;;;;;;999888555666777888888777666555777777777777777777777777777666555444333222222222444333222111000111222222222111111111333555888:::666555444333222222222222222222111111111111222222222222111000//////000000111111000000/////////...////////////////////////---------.........//////000////////////.........---,,,+++,,,...///...---.........------,,,,,,,,,//////...---...///000111+++,,,---...////////////---.........---,,,,,,+++------,,,+++++++++,,,,,,---,,,+++*********+++,,,------------------------+++******+++------,,,***************************************************))))))))))))))))))))))))))))))))))))************++++++++++++++++++++++++++++++,,,,,,,,,---------)))***+++,,,---.........+++,,,,,,---------,,,,,,...---,,,,,,+++++++++,,,))))))*********+++++++++///////////////.........///000000000333:::BBBGGGcccuuussskkklllnnn|||~~~wwwuuuttt|||xxxuuutttsssqqqooonnnqqqwww}}}rrrkkkjjjjjjrrrtttxxx~~~|||tttkkkfffeeeccc^^^YYYZZZ]]]^^^]]]ZZZYYYZZZ\\\```bbbdddgggjjjpppwww{{{|||}}}~~~~~~~~~|||zzzxxxzzz}}}}}}zzzyyyyyy||||||{{{{{{{{{{{{||||||xxxxxxwwwuuussstttvvvyyy|||xxxuuuuuuwwwzzzzzzyyy~~~~~~}}}}}}}}}}}}}}}}}}~~~yyywwwtttnnneee[[[VVVWWW^^^cccooo}}}zzzqqqiiidddaaabbbcccddddddbbbaaa___^^^\\\ZZZYYYYYYYYYWWWVVVVVVUUUTTTRRRPPPNNNLLLKKKFFFDDDAAA===:::999999999888888777666555444333333444555777888888888777666111222333555666666555444444444666999777555===HHHUUUppp}}}666777888::::::999888777666666777777777666666555666666666666666666666666777777555444444333333333444444222111111111222333222111111111222555777999555444333222111111111111222111111000000111111222222111111000//////000000///.........---------------------------------------------.........//////------------,,,,,,,,,,,,---,,,+++,,,.........---------,,,,,,,,,+++++++++,,,,,,++++++,,,,,,---...,,,---------------,,,,,,------......---,,,,,,+++,,,,,,+++++++++,,,,,,------,,,+++*********++++++------------------------*********+++,,,---,,,***************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************++++++++++++++++++++++++(((((()))))))))*********)))***+++,,,,,,---------***************)))((('''...---,,,,,,++++++++++++,,,,,,,,,,,,------------////////////............000000000000111666<<>>;;;999777777777666666666555555444444444777888888888777666555444333444555555666555555444333555888<<>><<<:::888666666666555555555555555555555555999999888777666555444333555555555666666555555555999:::;;;===FFF[[[yyy333333444444555555555555555444333333333444666777555555555555555555555555333333222222111111222222222222222222222111111111111111000000000111111111000000//////......//////111000000000000000000111000///////////////000000/////////000000000000000////////////////////////.....................---///............---------,,,+++***+++---...---,,,,,,,,,,,,---------------)))***,,,---...---,,,+++,,,,,,---...............++++++,,,,,,---,,,,,,+++)))))))))***+++,,,---...,,,,,,,,,,,,++++++******++++++++++++++++++++++++***))))))***,,,,,,+++)))************************************************((((((((((((((((((((((((((()))))))))************************************(((((((((((())))))))))))(((((()))*********))))))'''((()))******+++******++++++,,,---------,,,++++++++++++,,,,,,,,,------,,,---------......//////,,,...///000000111333555777EEEXXXkkk|||xxxmmmmmmpppxxxzzziiibbb___]]][[[XXXWWWWWWWWWWWWYYYZZZZZZZZZZZZ[[[^^^```cccfffkkkqqqwww{{{}}}~~~~~~{{{wwwuuuuuuvvvxxxxxxwwwwwwwwwwwwxxxxxx}}}|||{{{vvvwwwwwwvvvuuuuuuvvvvvvttttttuuuuuuvvvwwwxxxyyyzzzzzzzzz{{{|||}}}~~~vvvlllfffmmmvvvxxxvvvsssmmmnnnrrrxxx|||uuuyyy~~~{{{wwwtttsssrrrpppooojjjiiigggffffffeeecccaaaddddddcccaaa___]]][[[ZZZZZZXXXUUUTTTSSSRRRQQQOOOKKKKKKIIIGGGEEECCCBBBAAA===<<<;;;999777666555555444555555666666777777777:::999888777666444444333666666666666666666777777:::;;;<<>>;;;;;;:::999888666666555444555555666888999:::::::::999888666555555444444666555555555666777999999666<<>><<<;;;:::::::::999888777666555444555666888999;;;<<<<<<:::999777666555555555555555555555555777888:::<<<:::EEEVVVmmm444444333333333444555666///111222444555555444444222222222222222222222222333222222111222222333333...///000000000///---,,,,,,---...///000000000000000000/////////000000111000000////////////000000...............///000111.../////////000000111111//////////////////////////////.........---------.........---------,,,,,,+++***)))***,,,---,,,+++*********++++++,,,,,,,,,...---,,,+++,,,---...///------------,,,+++******)))***+++,,,,,,,,,,,,,,,++++++******************++++++,,,---,,,+++***))))))))))))))))))))))))))))))(((((()))++++++***)))************************))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))************))))))))))))))))))))))))'''(((((((((((()))))))))******+++++++++******)))******+++++++++***)))))))))***,,,.........,,,+++))))))*********+++++++++++++++,,,,,,---...////////////...,,,+++,,,///111666777888???RRRjjjzzz{{{uuu|||qqqlllsssyyy}}}|||jjjeee^^^ZZZXXXVVVTTTRRRSSSTTTUUUUUUTTTTTTUUUVVVZZZZZZZZZ\\\aaagggnnnrrruuuxxx|||~~~~~~~~~~~~~~~yyyyyyxxxxxxxxxxxxyyyyyyxxx{{{~~~~~~{{{xxxuuutttqqqtttvvvvvvttttttuuuwwwrrrrrrqqqqqqpppqqqqqqqqqpppppppppqqqsssuuuvvvwwwwwwwwwvvvwwwyyy|||~~~}}}}}}}}}|||}}}mmmgggmmm}}}wwwpppnnnlllkkkiiigggdddaaa```^^^]]]^^^______^^^]]]]]]]]][[[YYYXXXWWWWWWWWWTTTRRROOOMMMLLLKKKIIIGGGEEEDDDBBB@@@>>><<<;;;::::::::::::999999888666666555555777888:::<<<===>>>999888777555555555666666444444444555777999<<<===BBBRRRjjj333333333333333333333333222222111111111111111111333444444444444444444444000000000000000000000000111111111111111111111111000000//////.........---///000000000111111111111---...000///---,,,,,,---////////////////////////..................------.....................---///...---,,,+++,,,------,,,,,,,,,,,,,,,,,,,,,,,,+++---...//////...,,,***,,,,,,,,,,,,,,,+++***))))))***+++,,,,,,+++***)))++++++++++++++++++++++++******++++++++++++,,,,,,&&&&&&'''((()))******+++******++++++++++++***************,,,.........---++++++************++++++))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))((((((((((((((('''''''''(((((())))))))))))((((((((()))))))))************))))))***+++++++++++++++'''(((((()))******++++++,,,,,,,,,,,,,,,,,,,,,,,,******++++++,,,,,,,,,,,,***))))))))))))+++,,,---------......///000000000111///444>>>EEEPPPhhh~~~xxxqqqmmmttt~~~qqqggg___\\\WWWQQQPPPTTTOOOQQQTTTSSSQQQPPPRRRTTTUUUTTTSSSTTTXXX^^^eeeiiiqqqrrrssswwwzzz||||||{{{{{{||||||{{{xxxuuutttuuuxxxyyyzzzzzzyyyxxxvvvuuuppppppoooooooooooooooppppppmmmkkkllloooqqqpppnnnooopppsssuuuwwwxxxxxxwwwzzzxxxwwwwwwzzz}}}~~~~~~|||zzzzzzzzz{{{{{{|||~~~xxxkkkhhhmmm{{{yyyqqqnnnkkkiiihhhgggeeeccccccaaa^^^\\\\\\[[[ZZZXXXWWWWWWWWWVVVVVVUUUUUUUUUQQQPPPNNNKKKHHHEEECCCBBBAAA@@@???===<<<:::999888888888888888888777777666888888999:::::::::999999;;;999666444444444444333999666666888888888???IIIOOOjjj333333333333333333333333111111111111111111111111222222222222222222222222222222222222222222222222111111111111111111111111000/////////.........---//////000000000111111111...///111000...------...000000000000000000000000,,,---------.../////////------------------......///...---,,,+++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,)))***+++,,,,,,,,,+++***+++,,,,,,,,,++++++***))))))***++++++++++++***)))+++++++++++++++++++++++++++++++++,,,,,,,,,------))))))******++++++,,,,,,)))******++++++******))),,,++++++,,,,,,,,,+++************))))))*********))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))((((((((((((((((((((('''))))))************))))))************+++++++++,,,((()))******++++++******)))))))))******+++++++++,,,,,,,,,,,,,,,,,,,,,,,,((((((((((((((())))))))),,,+++***))))))******+++,,,------......//////000000...111999>>>FFF\\\rrr{{{zzzssspppvvvxxxkkk^^^ZZZWWWRRRPPPPPPNNNOOOPPPPPPOOOPPPSSSWWWUUUTTTSSSSSSVVVZZZ___bbbiiikkknnnrrrwwwzzz{{{{{{}}}~~~}}}zzzxxxwwwxxxxxxxxxyyyyyyxxxwwwuuutttqqqppppppoooooopppppppppqqqooonnnnnnqqqrrrrrrppprrrssstttvvvwwwxxxyyyyyy{{{yyywwwxxxzzz}}}~~~~~~~~~|||{{{zzzzzz{{{{{{zzz{{{}}}uuulllnnnxxx}}}tttqqqpppmmmjjjhhhgggfffdddbbbaaa___\\\[[[ZZZYYYXXXVVVUUUUUUTTTTTTSSSRRRRRRQQQOOONNNLLLIIIGGGDDDBBBAAA@@@???>>>===;;;:::999888777777888888888888777777888999::::::::::::999999999888777666666666666555666666:::???@@@CCCNNNZZZsss222222222222222222222222111111111111111111111111222222111111000/////////000000000000000000000000/////////////////////////////////...............////////////000000000000///111222222000//////000000000000000000000000000+++,,,,,,---...///000000......//////000000111111......---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,*********++++++,,,,,,,,,+++++++++,,,++++++***))))))******++++++******)))++++++++++++++++++++++++*********++++++++++++,,,***+++++++++++++++++++++)))******++++++******))),,,,,,,,,,,,+++***)))(((***))))))(((((())))))***)))))))))))))))))))))))))))))))))))))))))))))))))))((((((''''''(((((()))''''''(((((((((((((((((()))******++++++******)))))))))))))))************'''((())))))******))))))*********+++++++++++++++------,,,,,,++++++******+++++++++++++++*********---,,,+++***))))))))))))++++++,,,------......///111...///444666;;;MMM___~~~|||~~~{{{uuusssyyy{{{lll\\\VVVUUURRROOOMMMPPPPPPOOOMMMLLLNNNRRRUUUSSSSSSRRRRRRTTTVVVXXXYYY^^^aaafffkkkqqqvvvzzz|||}}}~~~~~~{{{yyyyyyyyyxxxxxxxxxxxxwwwvvvuuutttrrrqqqqqqppppppqqqqqqrrrqqqpppoooppprrrrrrrrrqqqttttttttttttuuuvvvwwwxxxyyywwwuuuvvvxxxzzz{{{{{{{{{zzzzzzyyyyyyzzz{{{{{{zzz{{{|||~~~vvvttt||||||tttrrrnnnkkkhhhfffeeedddbbb```___\\\YYYXXXXXXWWWUUUTTTSSSRRRQQQPPPOOONNNMMMLLLLLLKKKIIIFFFDDDAAA???>>>>>>===<<<;;;:::999888888555666777888888888888888:::::::::;;;::::::999999777777777777888888888888666888<<>>===<<<;;;;;;::::::999888777777444555666888999:::::::::;;;;;;<<<;;;;;;:::999999666777888888777777777888===>>>BBBLLL]]]uuuzzzrrrllllllpppwww111111111111111111111111//////000000000111111111333333222111000//////...,,,,,,,,,,,,,,,,,,,,,,,,---------------------------------...............---............/////////111222333333111000000111........................//////......---------,,,&&&''''''((()))******+++,,,,,,,,,,,,,,,+++++++++++++++++++++++++++++++++,,,++++++,,,---...///000)))******++++++*********))))))))))))))))))))))))************************))))))))))))*********+++************)))))))))))))))))))))******)))))))))(((***,,,,,,***)))***+++))))))(((((((((((())))))((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''((((((&&&'''''''''(((((())))))''''''((((((((((((''''''%%%&&&&&&&&&''''''''''''''''''((()))))))))))))))+++++++++++++++,,,,,,,,,------,,,+++******)))))))))))))))))))))((((((((())))))******++++++++++++******++++++,,,---------000000000000000333<<>><<<::::::999888888888777777666666555666777999:::;;;;;;;;;=========<<<;;;:::999888666777999888666666777999???FFFTTTjjjwwwooohhhhhhkkkqqq{{{{{{rrr000000000000000000000000...//////000000111111111333333222222111111000000........................---------------------------------------.........------------.........//////111222222000//////000------------------------000000///...---,,,,,,+++******++++++,,,,,,------,,,,,,,,,,,,,,,+++******++++++++++++++++++++++++*********++++++,,,,,,,,,((()))******+++************))))))(((((())))))***************************+++++++++,,,,,,,,,------++++++,,,,,,,,,,,,,,,,,,((())))))******))))))((((((+++------***)))***---***))))))(((((())))))***(((((((((((((((((((((((())))))))))))))))))))))))(((''''''&&&&&&''''''(((&&&&&&''''''((()))))))))&&&''''''((((((''''''&&&(((((((((((())))))))))))'''((())))))******))))))))))))******+++,,,,,,---,,,,,,++++++******)))))))))))))))*********++++++(((((()))++++++,,,,,,+++******+++,,,,,,------.........///......000666<<>>===;;;:::999888666666666666666666555555777777999:::;;;<<<<<<===>>>>>>>>>===<<<:::999888666888999888666666:::>>>>>>RRRpppwwwpppkkkmmmqqqtttzzz{{{nnnhhh000000000000000000000000......//////000111111222111111111111111111111111////////////////////////........................,,,,,,,,,------.........,,,,,,---------............///111000...------.........................../////////...---------,,,//////////////////000000+++,,,,,,---,,,+++***)))************************)))***+++,,,,,,,,,+++***(((((()))******************)))(((''''''((()))************************************++++++++++++,,,+++++++++,,,,,,---------(((((())))))))))))((((((***---000...***((())),,,*********))))))*********(((((((((((((((((((((((())))))))))))))))))))))))(((''''''&&&&&&''''''(((&&&&&&''''''((())))))***''''''((((((((((((''''''(((((()))))))))*********((()))******++++++******''''''((()))+++,,,------+++++++++*********************+++,,,---......///))))))++++++++++++***)))++++++,,,,,,---............000000///...000444666>>>OOOhhh}}}|||zzz|||zzzyyy~~~~~~vvvtttxxx|||pppkkkrrryyyzzz~~~xxxpppbbb[[[SSSNNNMMMMMMMMMMMMLLLLLLNNNOOOOOOOOOOOONNNMMMQQQUUUUUUUUUWWW]]]bbbeeehhhllloooqqqsssvvvxxxxxxwwwuuutttssssssttttttppppppppppppqqqrrrssstttsssuuuxxxxxxvvvsssssstttppppppqqqrrrsssssssssrrrtttsssrrrrrrssssssqqqpppmmmoooqqqsssuuuvvvvvvvvvwwwxxxyyyyyyyyyyyyyyyyyyvvvvvvwwwwwwxxxyyyyyyyyywwwwwwwwwwwwxxxyyyzzzzzzyyyzzzzzz{{{{{{{{{zzzzzz{{{}}}~~~}}}}}}||||||}}}~~~wwwooojjjgggdddbbb^^^\\\[[[ZZZXXXVVVSSSPPPNNNLLLLLLKKKJJJHHHDDDDDDCCCBBBBBBAAA@@@@@@>>>======;;;:::999888888444444444555555555555555999:::;;;<<<============?????????>>><<<:::999888555777999888777:::@@@FFFRRRppp{{{{{{|||ooohhhhhh000000000000000000000000---......///000111111222000000000000111111111111------------------------........................,,,,,,,,,------.........,,,,,,,,,---------......---...000///---,,,,,,---////////////////////////------..................,,,,,,,,,,,,,,,,,,++++++++++++,,,---,,,+++***)))************************+++---...//////...,,,***(((((()))******************)))(((''''''((()))***))))))))))))))))))))))))''''''''''''(((((((((((((((((()))***++++++,,,,,,(((((())))))))))))((((((,,,000222///***'''(((+++++++++************++++++(((((((((((((((((((((((())))))))))))))))))))))))'''''''''&&&&&&'''''''''&&&&&&&&&'''((())))))***(((((())))))))))))((((((''''''''''''(((((((((((())))))***+++++++++++++++%%%&&&'''(((***,,,---...***************+++++++++&&&&&&'''(((***+++,,,---++++++,,,,,,+++***((('''+++,,,,,,------......///000333333111///111333444222@@@WWWooo|||vvvzzzuuurrrpppssszzz~~~xxxwww}}}|||ooolllwwwoooeeeWWWMMMIIIIIIIIIJJJLLLMMMMMMMMMMMMMMMLLLLLLNNNQQQTTTSSSPPPQQQUUUZZZ___bbbfffjjjmmmpppsssuuuvvvuuusssrrrqqqqqqrrrrrrppppppppppppqqqrrrssstttooorrruuuuuurrrpppoooppplllmmmooopppqqqqqqpppppppppooonnnooopppooommmkkkmmmnnnpppssstttuuuuuuuuuuuuvvvwwwwwwwwwwwwvvvvvvuuuuuuvvvxxxyyyzzz||||||wwwwwwwwwxxxxxxyyy{{{{{{wwwxxxyyyzzzzzzyyyxxxwwwyyy{{{~~~}}}{{{~~~~~~~~~}}}yyyxxx{{{xxxoookkkgggeeecccaaa]]][[[ZZZYYYWWWUUUPPPMMMKKKIIIIIIHHHGGGEEEAAA@@@@@@@@@??????>>>>>>======<<<;;;:::999888777333333444444444444555555:::;;;<<<===>>>>>>>>>>>>@@@@@@???>>><<<;;;999888444777999999999===FFFMMMsss~~~{{{sssjjjhhhlll000000000000000000000000000000000000000000000000111000///////////////000,,,------------------,,,------------------------###$$$&&&))),,,...000111000...,,,*********+++,,,...---,,,,,,......---,,,***++++++,,,,,,++++++******+++,,,---...---,,,,,,+++,,,------......------------,,,+++************(((((()))************)))&&&''')))+++,,,+++***(((,,,,,,++++++******))))))))))))************))))))((((((((((((((()))******,,,++++++******++++++,,,((()))))))))************,,,++++++***((('''%%%$$$+++*********))))))(((((())))))***))))))((('''&&&&&&''')))*********)))((((((((('''(((((()))***+++***)))'''&&&%%%%%%&&&'''((((((((((((((((((((((((***(((&&&'''***+++)))'''(((((((((((())))))))))))+++*********))))))((((((''')))***+++******,,,---************************))))))(((((()))***++++++---,,,,,,+++***)))((((((******+++++++++,,,,,,,,,......///000111222333333666555???WWWqqq{{{uuupppnnnqqqwwwzzzzzzyyytttqqqzzzwww[[[NNNLLLKKKHHHGGGMMMMMMNNNNNNMMMMMMLLLLLLOOOOOONNNNNNNNNOOOQQQRRRXXXYYY\\\ccciiinnnqqqqqqoooqqqrrrqqqpppnnnnnnooooooppppppooonnnmmmoooppprrrsssssstttsssrrrpppooonnnooopppppppppooommmmmmmmmllllllllllllmmmnnnnnnlllooorrrttttttsssttttttyyyvvvttttttvvvvvvtttrrrxxxxxxyyyyyyxxxxxxwwwwwwxxxxxxxxxyyyyyyyyyzzzzzzzzzyyyxxxvvvuuutttttttttvvvyyy~~~}}}zzz~~~{{{~~~}}}{{{~~~ssskkkfffeeeddd]]]\\\[[[YYYWWWUUUSSSRRRMMMLLLJJJHHHFFFDDDBBBAAA======<<<<<<<<<;;;;;;;;;777777888888888888777777666555444444555666777888===>>>???@@@@@@@@@@@@@@@BBB???===;;;;;;::::::999555111444;;;<<<>>>LLL^^^yyynnnjjjpppwww000000000000000000000000000000000000000000000000222222000///............,,,------......------,,,------------------------++++++++++++,,,,,,,,,,,,///---,,,******+++,,,---...,,,,,,,,,---...---,,,++++++,,,,,,,,,,,,++++++***+++,,,---------,,,,,,+++,,,------......------,,,,,,++++++***+++++++++)))))))))*********++++++((()))***+++++++++***)))***************)))))))))(((((())))))))))))((((((((((((((((((((()))******+++++++++******+++++++++************++++++++++++))))))***))))))((('''&&&******)))))))))(((((((((((())))))))))))(((((('''''''''((()))))))))))))))(((((((((((((((((()))***(((''''''&&&&&&&&&''''''''''''''''''''''''''''''***((('''''')))***)))''''''((((((((())))))))))))******)))))))))((((((((('''(((******)))***+++---))))))))))))))))))))))))))))))(((((()))******+++,,,++++++******)))))))))++++++++++++,,,,,,,,,,,,,,,---......000000111222666444999JJJ```vvvwwwrrrnnnooouuu|||}}}yyyxxxhhhUUUMMMIIIGGGGGGHHHIIIJJJLLLMMMMMMMMMLLLLLLKKKJJJJJJJJJKKKLLLMMMPPPQQQTTT[[[bbbiiilllnnnmmmnnnppppppnnnnnnnnnooooooppppppooommmmmmnnnoooqqqqqqrrrrrrqqqpppnnnmmmjjjkkklllllllllkkkiiihhhkkkkkkjjjkkkkkklllmmmmmmkkknnnqqqsssrrrqqqqqqrrruuutttssstttwwwxxxxxxvvvzzzyyyxxxvvvvvvwwwxxxyyyzzzzzzzzzzzzzzzyyyyyyyyyxxxwwwvvvuuuttttttttttttyyy|||}}}{{{~~~~~~xxxnnngggdddcccbbb\\\[[[XXXUUURRROOOMMMLLLJJJIIIHHHFFFDDDAAA@@@???<<<<<<;;;;;;;;;:::::::::888888888888888888777777666555555555555777888999===>>>???@@@@@@@@@@@@@@@AAA???<<<:::888777666555888777;;;@@@BBBHHH^^^vvvvvvtttzzz000000000000000000000000000000000000000000000000333222111///...---,,,,,,,,,---...//////...---,,,------------------------//////...---,,,+++******---,,,+++***+++,,,---......,,,+++,,,---...---+++,,,,,,------------,,,,,,***+++,,,---------,,,,,,+++,,,------......------+++++++++***++++++,,,,,,++++++*********+++,,,---,,,,,,++++++******++++++((())))))))))))))))))***(((((())))))))))))((((((((((((((((((((()))******++++++************++++++***++++++++++++,,,,,,,,,'''((()))))))))))))))((())))))(((((((((((((((''''''(((((())))))))))))(((((((((((((((((()))******))))))(((((('''(((((((((&&&&&&'''''''''''''''''''''''''''''''''''''''''')))(((''''''))))))((('''''''''((((((((()))))))))))))))((((((((((((((('''&&&((())))))))))))***,,,(((((((((((((((((((((((())))))((((((((()))******************************++++++++++++,,,,,,,,,,,,++++++,,,---...///000000444222333;;;JJJ```~~~zzzrrrppppppvvvyyyyyyzzz|||eeeVVVLLLHHHHHHGGGHHHJJJKKKLLLLLLLLLKKKJJJJJJIIIHHHHHHHHHIIIIIIIIIJJJLLLSSS[[[cccgggjjjiiikkkmmmmmmmmmmmmnnnooonnnooopppooommmmmmmmmoooooopppppppppooonnnlllkkkhhhhhhiiijjjiiihhhgggfffhhhhhhhhhhhhiiijjjkkkllljjjmmmooopppooonnnnnnoooqqqqqqqqqtttxxxzzz{{{zzz|||zzzwwwuuutttvvvxxxyyyyyyyyyyyyxxxxxxwwwvvvvvvuuuuuuttttttttttttuuuuuuzzz}}}~~~||||||yyytttsssyyy{{{~~~zzzuuummmgggcccaaa```___YYYXXXUUUQQQMMMJJJGGGEEEFFFEEEDDDBBB@@@???===<<<:::::::::999999999999888999999888888777777777666666666666666777888999:::>>>>>>??????@@@?????????>>>===<<<:::888777666666777888===CCCGGGSSSqqq~~~000000000000000000000000000000000000000000000000222111000///...------------...///000000///...---------------------------,,,,,,,,,,,,,,,---------++++++***++++++---...///---,,,++++++------,,,+++,,,------......------,,,++++++,,,,,,,,,---------+++,,,------......------************+++,,,---------,,,+++******,,,...//////...,,,*********,,,,,,''''''(((((())))))******)))******************)))((((((((((((((())))))*********))))))))))))***************+++++++++,,,,,,(((((())))))))))))((((((((((((((((((''''''''''''&&&'''((())))))***)))))))))((('''''''''(((***+++***)))((('''''''''''''''$$$%%%'''((()))(((''''''''''''''''''''''''''''''(((((('''((((((((((((''''''''''''((((((((())))))((((((((((((''''''''''''&&&((())))))(((((()))+++))))))))))))))))))))))))))))))((((((((())))))***((()))))))))*********+++))))))*********+++++++++++++++,,,---...///000000111111222444:::LLLjjjwwwqqqrrryyy~~~|||tttxxx}}}{{{gggUUULLLIIIIIIJJJKKKLLLKKKKKKIIIIIIKKKKKKJJJJJJIIIIIIIIIIIIHHHHHHIIINNNUUU]]]bbbdddcccfffiiijjjkkkkkkmmmooonnnoooqqqpppooonnnnnnoooooooooppppppooommmkkkjjjiiiiiijjjkkkjjjiiihhhgggeeeeeeeeefffggghhhiiijjjiiikkkmmmmmmlllkkkkkklllooooooqqqssswwwyyy{{{{{{zzzxxxwwwuuuuuuuuuvvvwwwsssssssssssssssssssssssssssssssssttttttvvvwwwxxxzzz|||~~~}}}~~~~~~rrrnnnnnnuuu}}}tttqqqqqqvvv~~~{{{vvvmmmjjjeeebbb```^^^\\\ZZZUUUTTTQQQNNNKKKGGGEEECCCCCCBBBAAA@@@>>>===<<<;;;999999888888888777777777888888777666666555555555777777888888999:::;;;<<<>>>???????????????>>>===;;;;;;;;;:::999999:::;;;777999@@@IIISSSggg}}}}}}///////////////////////////////////////////////////...............///000---...000111111000...---------------------------)))******+++,,,------...*********+++,,,---...///---,,,++++++,,,---,,,+++,,,------......------,,,+++++++++,,,,,,,,,------+++,,,------......------************+++,,,------...,,,+++******,,,...///000...,,,*********,,,---''''''(((((())))))******((())))))******))))))(((((((((((((((((())))))******))))))(((((())))))***))))))))))))*********+++*********))))))((('''&&&''''''''''''((((((((((((&&&'''((())))))***)))))))))((('''''''''(((***+++))))))(((''''''&&&''''''$$$%%%'''((()))((('''''''''''''''''''''''''''''''''((((((((('''''''''(((''''''''''''((((((((((((''''''''''''(((((((((((('''((())))))(((((()))***************************))))))((((((((((((((()))((((((((()))******++++++(((((((((((())))))))))))+++,,,------//////000111...000333555555>>>UUUjjjzzztttwww~~~tttqqqrrrttt}}}zzzbbbQQQJJJIIIIIIIIIIIIIIIIIIHHHHHHKKKKKKKKKJJJJJJIIIIIIHHHIIIHHHHHHJJJPPPUUUXXXZZZ]]]___cccfffgggiiilllnnnmmmoooqqqqqqpppppppppqqqpppqqqqqqqqqpppnnnlllkkkiiijjjjjjkkkjjjiiihhhgggcccccccccddddddeeegggggggggiiijjjjjjiiihhhiiijjjnnnoooqqqrrrtttuuuvvvxxxuuuvvvvvvwwwvvvtttrrrqqqmmmnnnooopppqqqrrrssstttrrrrrrrrrsssuuuwwwxxxyyyzzz{{{}}}~~~~~~~~~}}}}}}|||tttqqqsssxxx~~~rrrdddhhhmmmrrryyyvvvpppgggdddaaa___^^^[[[XXXUUUPPPPPPNNNLLLIIIGGGFFFEEEAAA@@@???>>>===<<<;;;;;;888777777777777666666666777666555444444444444555888888999;;;<<<=========???????????????>>>===<<<:::::::::999777777:::===<<>>>>>===<<<;;;;;;:::777777777777666666666666666555444333333444555666888999;;;===>>>????????????@@@??????>>>===<<<;;;::::::999666444555:::>>>DDDNNN```vvv|||////////////////////////////////////////////////......---------...//////---///111333333111///---------------------------------------,,,,,,,,,,,,***++++++,,,------------,,,+++***+++,,,,,,,,,***++++++,,,,,,,,,,,,++++++,,,,,,+++++++++,,,---...+++,,,------......------,,,,,,++++++***+++++++++++++++++++++,,,,,,,,,,,,,,,++++++******+++,,,---***************)))))))))))))))************))))))((((((((((((((()))******)))((((((''''''(((((()))))))))*********+++++++++(((((())))))))))))((((((((((((((()))))))))******((())))))))))))(((((('''''''''((()))))))))))))))''''''&&&&&&&&&'''(((((((((''''''&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%''')))(((&&&%%%'''(((&&&&&&&&&'''''''''((((((((((((((()))))))))******)))***+++***)))((()))+++************************))))))((('''''''''''''''((((((((())))))))))))))))))))))))************+++******+++,,,---.../////////...000333333444:::BBBYYYmmmzzzppppppuuuyyy}}}pppiiiZZZVVVQQQMMMJJJIIIJJJKKKEEEFFFGGGHHHHHHHHHGGGGGGFFFEEEDDDEEEGGGHHHGGGFFFKKKNNNSSSXXX[[[___ccceeeeeeiiimmmoooppppppqqqrrrrrrrrrrrrqqqpppnnnllljjjfffggghhhhhhhhhgggeeeddddddccccccbbbbbbbbbbbbcccccceeeffffffffffffhhhjjjjjjlllnnnnnnllllllmmmooorrrrrrssssssrrrpppnnnllljjjjjjlllmmmoooppprrrrrrnnnnnnoooppprrrsssuuuvvvwwwwwwwwwwwwxxxxxxyyyyyywwwwwwxxxyyyzzz{{{|||}}}|||}}}}}}xxxuuupppnnnrrrvvvvvvxxxzzz~~~}}}|||xxxzzzxxxfff[[[VVVUUU\\\hhhrrrvvvxxx||||||yyyzzz|||{{{zzz~~~xxxooogggaaa^^^\\\YYYWWWUUURRRNNNKKKFFFFFFEEEDDDBBBAAA@@@@@@<<<<<<<<<;;;::::::999999777777777777666666666666666555444444444666888999999:::<<<>>>@@@@@@@@@@@@@@@@@@@@@???>>><<<;;;:::888999999666555999BBBIIIWWWjjjuuuooommmwww////////////////////////////////////////////////000///...------------------///222444444222///------------------------------------.........//////++++++,,,---------,,,,,,,,,+++******,,,,,,+++******++++++,,,,,,++++++***---,,,+++***+++,,,---...+++,,,------......------------,,,+++************)))***+++,,,,,,,,,++++++************+++,,,,,,---,,,,,,++++++******)))))),,,------......------,,,((((((((((((((()))******((((((''''''''''''((((((******+++++++++,,,,,,,,,&&&'''((()))************(((((())))))******++++++))))))***))))))(((''''''&&&''')))*********)))(((&&&&&&&&&&&&&&&'''((()))***)))'''&&&%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%''')))(((&&&%%%&&&)))&&&&&&&&&'''''''''(((((((((((())))))******++++++***+++,,,+++***)))***+++))))))))))))))))))))))))***)))(((''''''''''''''')))))))))))))))(((((((((***++++++++++++,,,,,,,,,))))))***+++,,,------...111---+++...111333777<<>><<<::::::555777888888:::AAANNNWWWoooxxxooogggfffiiippp~~~000//////.........//////000000000000000///......//////000000///...------......////////////......///---***+++---///...,,,*********++++++,,,,,,,,,+++******))))))******++++++++++++***************)))************+++++++++...---+++*********++++++++++++++++++++++++++++++)))))))))))))))))))))))))))************+++++++++++++++++++++++++++++++++*********)))))))))))))))(((((())))))))))))(((((())))))(((((('''''''''&&&''''''''''''((((((((((((++++++++++++++++++++++++))))))))))))))))))))))))))))))))))))))))))))))))++++++***)))((('''&&&&&&%%%%%%%%%&&&&&&&&&&&&'''))))))((('''&&&%%%%%%%%%&&&'''''''''((()))))))))''''''&&&&&&&&&&&&''''''''''''''''''((((((((((((%%%%%%%%%&&&&&&&&&''''''&&&''')))***+++***((('''))))))))))))))))))))))))''''''((()))))))))))))))******)))(((((((((((((((******)))((((((((((((((('''(((***---...---***''',,,,,,,,,,,,,,,,,,,,,,,,---...///000222333444555===JJJaaazzzzzzwwwvvvuuuwwwzzz}}}zzzzzz{{{}}}xxxyyyzzz}}}yyyhhh\\\VVVRRROOONNNLLLGGGEEEGGGGGGEEEGGGJJJHHHHHHGGGFFFEEEEEEEEEFFFFFFGGGHHHJJJOOOSSSXXX[[[]]]aaaeeehhhiiijjjkkklllkkkjjjiiikkknnnooollliiiiiiiiiiiiiiihhhfffdddcccgggggggggfffeeebbb```^^^aaaaaaaaa```aaaaaabbbcccbbbcccdddfffhhhiiiiiijjjqqqpppnnnnnnoooooommmlllhhhhhhhhhiiijjjlllmmmnnnllllllmmmnnnooorrrtttuuuwwwvvvtttrrrrrrrrrsssssstttttttttuuuvvvvvvwwwwww{{{xxxwwwzzz|||yyyoooeee\\\ZZZ[[[```iiiqqqvvvxxx|||~~~~~~}}}~~~yyygggWWWNNNNNNSSSXXXgggkkkqqqvvvzzz|||{{{{{{yyyyyyxxxxxxyyyzzz|||}}}{{{xxxvvvnnnnnnnnnllljjjiiijjjkkkooovvv}}}wwwpppiiiccc^^^ZZZWWWTTTRRRPPPMMMJJJHHHGGGFFFBBBAAA@@@>>>===<<<<<<<<<<<<;;;:::999999888555333444444333333333333222222777888888999::::::;;;;;;<<<<<<===>>>>>>???>>>>>>:::??????======???<<<555666666888:::===HHHaaayyyvvvllleeedddeeerrrwwwrrrvvv}}}//////............/////////000000000000///......///////////////...------......////////////......///---++++++---......,,,++++++++++++,,,,,,,,,---...------------------...+++++++++++++++++++++,,,)))************+++++++++---,,,+++*********++++++++++++++++++++++++++++++)))))))))))))))))))))))))))************+++++++++++++++++++++++++++++++++***)))))))))))))))))))))(((((())))))))))))((((((((('''''''''&&&&&&&&&&&&''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))''''''''''''(((((((((((())))))(((&&&&&&%%%%%%&&&''''''''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((('''''''''((((((((())))))&&&''')))*********((('''))))))))))))))))))))))))''''''((()))))))))))))))***))))))(((((((((((((((******)))((((((((((((((((((((()))***++++++***))),,,,,,,,,,,,,,,,,,,,,,,,---...///000222333444555;;;CCCSSSkkk{{{tttsssttttttwwwzzz~~~~~~vvvooolllppptttzzzrrreeeYYYPPPKKKMMMIIIFFFHHHHHHFFFFFFIIIGGGGGGFFFEEEEEEEEEEEEEEEDDDDDDDDDFFFHHHLLLOOOQQQWWWZZZ^^^aaacccdddggghhhkkkjjjjjjllloooooommmjjjhhhiiijjjjjjjjjjjjhhhhhhhhhhhhgggeeedddaaa```^^^______``````aaaaaabbbbbbbbbccceeegggiiijjjkkkkkknnnmmmlllmmmnnnooonnnmmmhhhhhhhhhhhhhhhiiijjjkkkiiijjjkkkmmmoooqqqrrrsssttttttsssrrrrrrrrrrrrsssttttttttttttttttttttttttwwwuuuuuuwwwxxxuuummmgggcccaaaaaadddkkkqqquuuvvv{{{|||}}}|||{{{|||yyypppcccWWWRRRTTTZZZ___kkkmmmqqqtttwwwwwwwwwvvvxxxwwwvvvvvvvvvwwwyyyyyyzzz{{{|||zzzuuuqqqmmmllldddeeeeeefffhhhlllqqquuuzzztttpppllleee```[[[XXXUUURRRPPPOOOMMMJJJHHHFFFDDDDDDAAA@@@???>>><<<<<<<<<<<<<<<:::999999999888666444444444555555555555555555888888999999:::;;;;;;;;;<<<<<<===>>>>>>>>>>>>>>><<>>:::999<<<;;;666888777999???III^^^}}}{{{rrrmmmnnnqqqzzzrrrrrrzzz///...............///////////////000//////...---...////////////...------......////////////......///---+++,,,---...---,,,,,,,,,,,,,,,------------........................***++++++,,,,,,---------)))************+++++++++---,,,+++*********++++++,,,,,,++++++************)))))))))))))))))))))))))))************+++++++++))))))))))))))))))))))))))))))))))))))))))******(((((())))))))))))((((((&&&&&&&&&&&&&&&%%%%%%%%%''''''''''''((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((''''''((((((((()))))))))(((((()))))))))*********)))((('''&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&%%%&&&'''(((((('''&&&%%%''''''''''''(((((((((((('''(((((((((((()))))))))&&&'''((()))***)))(((((())))))))))))))))))))))))''''''((()))))))))))))))))))))((((((''''''((((((***))))))(((((((((((((((***)))((((((((()))+++,,,,,,,,,,,,,,,,,,,,,,,,,,,---...///000111222333444777999BBBVVVppp{{{wwwrrrqqquuuxxxzzz}}}|||wwwkkkeeedddkkksss{{{}}}hhhWWWLLLKKKFFFCCCEEEEEECCCBBBDDDFFFFFFEEEDDDDDDDDDDDDEEECCCBBBBBBBBBCCCEEEGGGIIIOOOQQQTTTWWWZZZ]]]aaadddiiiiiiiiikkklllmmmkkkiiifffgggiiijjjkkklllkkkkkkjjjiiigggdddbbb```______]]]^^^```aaabbbbbbbbbaaacccdddeeegggiiijjjkkkkkkjjjiiiiiijjjmmmoooooonnniiihhhgggffffffffffffffffffgggjjjlllooopppppppppqqqqqqrrrsssssssssrrrrrrtttttttttsssrrrrrrqqqqqqssstttuuuuuutttqqqnnnlllkkkjjjiiijjjmmmqqqsssttt{{{{{{zzzyyyyyy{{{|||rrrlllccc\\\ZZZ^^^cccgggppppppqqqrrrrrrrrrqqqqqqvvvuuutttsssrrrsssssstttrrrssstttqqqmmmhhheeedddbbbeeehhhmmmttt}}}|||tttlllfffcccccc___ZZZVVVTTTRRROOOMMMLLLJJJHHHFFFDDDBBBAAA@@@@@@???>>><<<;;;;;;;;;;;;:::888777777777777555444555555666666777777888888999999999:::;;;;;;<<<<<<;;;<<<<<<==================>>><<<888888;;;<<<:::;;;<<>>>>>======<<<;;;:::999999:::777555444444555555444333444555666777888999::::::999::::::;;;<<<<<<======;;;<<<<<<=========<<<<<<;;;<<<;;;999999;;;>>>???===EEEVVVmmm}}}}}}yyyooolllqqq---------------...//////...............---,,,,,,------............------------............---------------,,,,,,,,,---...------------------------((()))************)))((('''(((((()))***++++++,,,))))))*********++++++++++++++++++++++++++++++++++++++++++******)))))))))))))))))))))))))))))))))))))))*********+++++++++(((((((((((((((((((((((((((((())))))************(((((())))))))))))((((((''''''''''''''''''((((((''''''''''''((((((((((((************************''''''''''''''''''''''''''''''''''''''''''''''''))))))((((((''''''&&&&&&''''''(((((((((((())))))(((((('''&&&&&&&&&&&&''''''''''''&&&%%%%%%%%%$$$'''(((***,,,,,,***((('''''''''''''''((((((((((((''''''''''''''''''''''''&&&''''''(((((((((((((((((((((((((((((((((((((((''''''((()))))))))))))))((((((''''''''''''(((((())))))(((((((((((())))))'''***,,,---+++***+++,,,+++++++++,,,,,,---------------...///000000111111222444666;;;FFF[[[ttt~~~|||yyyxxx}}}yyyllloooxxxzzznnnhhheeeooo}}}ttt___TTTLLLFFFGGGIIIGGGEEEFFFBBBBBBBBBAAAAAABBBCCCCCC@@@@@@AAAAAABBBCCCDDDEEEFFFGGGIIIKKKMMMRRRXXX\\\^^^```bbbdddeeeffffffggghhhiiijjjkkkkkkjjjiiiiiijjjhhheeeccc```_________^^^___bbbdddddddddcccbbbgggggggggggggggfffeeedddbbbaaabbbeeeiiilllmmmmmmhhhgggfffdddcccbbbbbbbbbbbbdddgggjjjkkklllkkkjjjmmmnnnppprrrssssssrrrrrrssssssrrrqqqpppoooooonnnooorrrtttrrrooonnnqqquuusssssssssrrrrrrsssuuuvvvzzzxxxvvvvvvxxxzzz}}}~~~}}}|||zzzwwwuuusssrrrqqqooonnnnnnnnnoooppprrrqqqpppooooooooopppqqqsssrrrpppmmmlllkkkllllllmmmnnnpppooommmlllkkkllllllrrr|||zzzpppkkkeeeeeedddbbb___\\\YYYXXXVVVTTTPPPNNNLLLKKKHHHFFFDDDCCCBBB@@@>>>=========;;;;;;:::999888888888888444222111111333444444333444555666777888999:::;;;;;;;;;;;;<<<======>>>>>><<<===============<<<<<<:::;;;;;;;;;:::999<<<@@@AAAUUUttttttnnnkkkoooyyy,,,,,,,,,,,,---...//////------......------,,,+++,,,,,,---............---------............------,,,---...---,,,+++---///------------,,,,,,,,,,,,)))***+++,,,,,,+++***)))''''''(((((()))*********)))************+++++++++******+++,,,,,,,,,++++++************************)))))))))))))))))))))))))))************+++++++++((((((((((((((((((((((((((((((((()))******++++++(((((())))))))))))(((((('''''''''(((((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%&&&'''((())))))***&&&&&&&&&'''''''''(((((((((''''''&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&((()))***++++++***)))(((''''''''''''((((((((((((*********))))))))))))(((&&&&&&'''''''''((((((((())))))))))))))))))))))))''''''((()))))))))))))))''''''&&&&&&''''''((((((((((((((((((((())))))***&&&)))------+++)))***,,,***++++++,,,,,,------...---------...///000000000000444777666999GGG^^^qqq~~~wwwyyy||||||zzzxxxxxx}}}zzzvvvxxxxxxmmmhhheeemmm{{{ooo\\\QQQHHHFFFGGGEEEBBBBBBAAA@@@@@@@@@@@@AAABBBBBB===>>>???@@@AAABBBCCCCCCCCCEEEFFFGGGIIIMMMRRRVVVYYY\\\```bbbcccdddfffhhhkkkkkklllllllllkkkiiihhhgggfffeeecccaaa```_________```bbbccccccbbbbbbaaaeeeeeeeeeeeedddcccbbbaaa`````````cccgggjjjjjjjjjgggfffeeedddddddddddddddcccdddfffhhhiiiiiiiiiiiillllllmmmnnnooopppppppppoooooooooooooooooonnnnnnlllnnnpppnnnllllllooorrrrrrssstttssssssssstttvvvwwwuuutttuuuwwwyyyzzzzzzyyy}}}|||yyyvvvsssrrrqqqkkklllmmmooopppqqqqqqrrrpppoooooonnnoooooopppqqqpppooommmjjjiiihhhhhhiiiiiikkklllmmmlllkkklllmmmooouuu~~~~~~sssiiiccc```[[[\\\\\\[[[YYYUUURRRPPPPPPNNNKKKIIIHHHFFFCCC@@@AAA@@@???>>><<<<<<;;;;;;999999888777777777777777333111000000222555555555555666777888999:::;;;;;;;;;<<<<<<===>>>>>>??????>>>>>>>>>>>>>>>======<<<<<<::::::;;;::::::???GGGUUUqqq~~~vvvjjjhhhmmmxxx,,,,,,,,,,,,---...///000,,,------------,,,+++++++++,,,------.........---,,,------......------,,,,,,......---++++++---///---,,,,,,,,,++++++++++++)))***,,,------,,,***)))))))))))))))))))))******)))************+++++++++)))***+++,,,,,,,,,,,,+++(((((())))))******++++++)))))))))))))))))))))))))))************+++++++++))))))))))))))))))))))))'''(((((()))******++++++(((((())))))))))))((((((&&&&&&&&&''''''(((((((((''''''''''''((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''$$$%%%%%%&&&'''((()))***&&&&&&'''''''''(((((((((''''''&&&&&&&&&''''''(((''''''''''''''''''((((((((((((((((((((((((((((((''''''''''''((((((((((((************)))))))))((('''&&&&&&&&&''''''(((((())))))))))))))))))))))))''''''((()))))))))))))))'''&&&&&&&&&&&&'''((()))((((((((((((((()))******&&&)))+++)))&&&&&&)))---******+++,,,,,,---......,,,------......//////000///222444333444<<>>>>>===<<<;;;::::::999999888777666666666666666666555333111222444777888999888888999:::;;;;;;<<<<<<<<<<<<===>>>>>>??????@@@???????????????>>>>>>===<<<999999<<<>>>CCCPPP]]]{{{vvvpppgggkkkvvv+++++++++,,,---...///000,,,------------,,,+++++++++,,,------.........---,,,------......------,,,,,,...///---+++***---///,,,,,,,,,++++++*********((()))+++,,,,,,+++)))(((+++++++++***************)))************+++++++++)))***+++,,,---,,,,,,+++''''''((()))***+++,,,,,,)))))))))))))))))))))))))))************+++++++++************************'''(((((()))***+++++++++(((((())))))))))))((((((%%%%%%%%%&&&&&&'''''''''''''''''''''((((((((()))(((((((((((((((((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((((((((((((''''''&&&&&&&&&''''''(((&&&'''''''''((()))))))))''''''&&&&&&&&&&&&''''''''''''''''''((((((((()))))))))(((((('''''''''&&&'''&&&&&&&&&&&&'''(((((())))))))))))))))))))))))'''(((((()))))))))))))))&&&&&&&&&&&&&&&'''((()))((((((((((((((()))******&&&((((((%%%""""""(((...******+++,,,,,,---......,,,------....../////////...000111111222999CCCJJJeeezzz~~~|||uuuiiidddiiiqqquuu{{{xxxwwwxxxuuussstttwwwwww|||zzzjjjZZZRRRNNNIIIEEEDDD??????>>>>>>???@@@AAAAAABBBBBBCCCCCCCCCBBBBBBAAA>>>???AAABBBBBBCCCFFFHHHIIINNNSSSWWWYYY[[[___bbbbbbcccdddeeeeeedddccccccccccccddddddcccbbb```___``````^^^]]]]]]\\\]]]]]]]]]]]]^^^```aaaaaaaaaaaa```______aaadddeeeeeedddeeeeeeeeefffggghhhiiijjjhhhggggggfffffffffgggggghhhgggfffffffffgggiiijjjeeefffggghhhjjjkkkmmmmmmnnnnnnnnnnnnoooooooooooorrrtttuuussspppoooppprrrooonnnnnnqqqtttuuusssppprrruuuvvvvvvvvv{{{~~~}}}|||{{{zzzxxxtttsssrrroookkkiiiiiiiiijjjkkknnnpppqqqpppooonnnllllllmmmmmmmmmlllkkkjjjiiihhhfffdddcccccccccdddfffggghhhgggeeeeeefffgggjjjlllnnnnnnmmmmmmmmmnnngggfffeee```[[[VVVTTTTTTQQQPPPNNNMMMLLLMMMMMMNNNFFFEEEDDDDDDDDDDDDAAA???<<<;;;:::999888888888888777666666555555555666666666444333333666999;;;;;;::::::;;;;;;<<<==================>>>??????@@@@@@@@@@@@@@@@@@@@@???>>>>>>;;;777888===DDDOOOcccvvv|||xxx~~~{{{qqqmmmiiippp---------,,,,,,+++++++++......................../////////...---------,,,.........------.........,,,++++++******++++++,,,------------------------************************++++++++++++++++++++++++,,,+++++++++++++++++++++---------,,,,,,++++++++++++++++++*********))))))***)))((()))***+++***)))))))))))))))))))))))))))))))))************))))))&&&'''''''''(((((())))))))))))***))))))((('''''''''''''''''''''&&&&&&&&&'''''''''''''''''''''&&&(((((((((((((((((((((((((((((('''&&&%%%%%%$$$$$$(((((('''''''''&&&&&&&&&((((((''''''&&&&&&&&&&&&$$$&&&(((((('''&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%***)))'''%%%%%%%%%''''''((('''&&&%%%%%%&&&'''(((***))))))((('''&&&&&&&&&))))))((((((''''''''''''&&&&&&&&&''''''''''''((())))))))))))))))))))))))''''''(((((((((((('''''')))))))))))))))***++++++))))))))))))************++++++++++++++++++++++++---------...............111111000111333666999;;;OOOeeeyyynnnkkkkkklllttt~~~uuulllkkkppptttyyy~~~sssdddUUUKKKDDDBBB@@@@@@???>>>>>>>>>@@@AAACCCBBBAAA@@@@@@AAABBBBBBAAAAAA@@@@@@AAAAAABBBCCCEEEEEEGGGJJJNNNSSSWWWYYY[[[]]]```aaaaaaaaabbbcccccc___[[[\\\___aaa^^^[[[aaa```^^^\\\[[[[[[[[[\\\______```````````````___cccbbbaaaaaaaaabbbcccdddccccccdddfffiiijjjjjjiiiiiiiiihhhfffeeedddcccbbbdddeeefffhhhiiiiiijjjjjjfffgggiiijjjkkkkkkjjjjjjnnnnnnnnnnnnnnnnnnmmmmmmqqqqqqqqqppppppnnnmmmmmmmmmnnnooooooooonnnmmmlllmmmmmmoooqqqtttwwwyyy{{{{{{zzzzzz|||}}}zzzxxxxxxwwwvvvuuutttsssssspppooonnnmmmjjjhhhfffeeeeeehhhlllooopppooollljjjhhhggghhhjjjmmmnnnkkkhhhgggeeeccccccddddddcccbbbeeeeeedddcccbbb```___^^^dddeeefffffffffdddbbb```]]]\\\ZZZXXXUUURRRPPPOOOJJJJJJJJJIIIHHHGGGEEEDDDCCCCCCBBBAAA@@@???>>>=========;;;:::999999888888666666666555555444444333222444555777888999888888<<<<<<;;;;;;:::::::::999888:::<<<>>>@@@AAAAAA@@@BBB@@@>>>>>>??????===:::777;;;@@@FFFQQQhhhwwwqqqrrrtttrrrooonnnsssyyy//////.........---------------------------------------------,,,,,,,,,,,,...------,,,,,,------...,,,++++++******++++++,,,++++++++++++++++++++++++************************************************++++++++++++************,,,,,,+++++++++*********+++++++++*********))))))***)))''''''(((((('''%%%))))))))))))))))))))))))&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&'''''''''((()))*********))))))((('''&&&&&&'''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((''''''&&&%%%%%%$$$$$$(((((('''''''''&&&&&&&&&))))))(((((('''''''''''''''((()))((('''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((''''''&&&(((''''''''''''''''''(((***))))))(((''''''&&&&&&((((((((('''''''''&&&&&&&&&&&&&&&''''''''''''(((((((((((((((((((((((((((''''''(((((((((((('''''''''''''''''''''(((((()))))))))))))))************((((((((((((((((((((((((------------............////////////111444777888CCCTTTkkkwwwqqqpppttt~~~{{{qqqhhhhhhkkkqqqzzzttteeeVVVLLLFFFDDDCCCBBBBBBBBBBBB@@@???CCCBBBAAAAAAAAAAAAAAABBB@@@??????>>>>>>>>>>>>???AAAAAACCCEEEIIIMMMPPPSSSVVVYYY\\\______``````bbbccc___\\\]]]```bbb```]]]___^^^]]]\\\[[[[[[[[[[[[\\\]]]^^^``````aaaaaaaaaeeedddbbbaaa``````aaaaaabbbbbbbbbeeegggiiiiiihhhgggffffffeeedddcccbbbbbbcccccceeefffggghhhhhhhhhdddeeefffhhhhhhhhhhhhgggllllllllllllllllllllllllooooooooooooooonnnmmmmmmkkkkkklllmmmlllkkkjjjiiikkkkkklllmmmoooqqqssstttsssrrrqqqsssuuuuuurrroootttssssssrrrqqqpppooooookkkkkkjjjiiihhhgggeeeddddddgggkkknnnooonnnllljjjhhhggggggiiilllllliiiffffffdddbbbbbbcccccccccbbbcccccccccbbb```___]]]\\\]]]^^^_________]]][[[ZZZWWWVVVTTTQQQOOOMMMKKKJJJHHHHHHGGGFFFEEEDDDCCCCCCBBBAAAAAA@@@>>>======<<<;;;;;;:::999888777777777666666555555444444444444444555777999;;;;;;;;;;;;======<<<<<<<<<;;;;;;;;;888999;;;===>>>>>>>>>>>>@@@???@@@BBBCCCBBB???<<<===>>>DDDQQQggg~~~zzzxxxtttooopppttt}}}............------------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,---,,,,,,++++++,,,,,,---++++++************++++++************************************************)))))))))))))))))))))))))))))))))))))))************************)))))))))+++************)))))))))'''&&&%%%%%%'''''''''%%%))))))))))))))))))))))))((())))))******))))))(((%%%%%%%%%&&&&&&&&&&&&&&&)))))))))***))))))((('''%%%&&&&&&&&&'''(((((((((&&&'''''''''(((((())))))(((((((((((((((((((((((('''''''''&&&&&&%%%%%%$$$'''''''''''''''&&&&&&&&&)))))))))((((((((((((((()))******)))&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&''''''''''''(((***+++***)))'''%%%'''(((((())))))((((((''')))))))))(((''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''((((((((((((''''''''''''&&&&&&''''''((()))))))))))))))************++++++++++++++++++++++++,,,,,,,,,------.........------------///111333555888AAARRRkkkyyyxxx~~~wwwpppiiihhhjjjqqquuueeeVVVOOOJJJFFFCCCBBBCCCBBB???<<>>==================>>>???BBBEEEHHHJJJNNNRRRWWWZZZ[[[\\\^^^___```]]][[[]]]```aaa___]]]\\\]]]]]]\\\\\\[[[ZZZZZZ[[[\\\]]]___```aaabbbbbbfffeeecccaaa```___^^^^^^aaa``````bbbeeegggffffffddddddcccccccccbbbbbbbbbaaaaaabbbcccdddeeeeeeeeeaaabbbcccdddeeeeeeeeeeeehhhhhhhhhhhhhhhhhhiiiiiikkkllllllmmmnnnmmmmmmmmmhhhiiiiiiiiiiiihhhgggfffhhhhhhiiiiiijjjkkkllllllooonnnmmmmmmnnnnnnllljjjooonnnmmmlllkkkjjjjjjjjjffffffffffffeeeeeedddcccbbbdddhhhlllmmmlllkkkiiigggffffffggghhhhhheeecccdddbbb``````aaabbbaaa`````````______]]]\\\ZZZYYYWWWWWWXXXXXXXXXVVVTTTSSSPPPOOONNNKKKIIIGGGEEEEEEEEEDDDCCCAAA@@@@@@@@@AAA??????>>>===<<<<<<;;;;;;999888777666666666666666555555555555555444444444666888:::<<<===>>>>>>>>>>>>>>>>>>>>>============;;;<<<======>>>>>>======;;;===@@@BBBBBBAAA???===CCCIIIVVVnnn}}}uuupppvvvrrrlllmmm++++++++++++++++++++++++++++++++++++++++++++++++******++++++,,,,,,------,,,++++++++++++++++++,,,++++++************++++++,,,,,,,,,,,,,,,,,,,,,,,,************************))))))))))))))))))))))))(((((((((((())))))))))))************************************))))))))))))$$$######%%%'''))))))((()))))))))))))))))))))))))))******++++++******)))&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((''''''%%%%%%%%%&&&'''((())))))&&&''''''(((((())))))***((((((((((((((((((((((((''''''&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''(((((((((((('''''''''''')))))))))(((&&&%%%%%%'''%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''((((((&&&'''((())))))((('''&&&'''((()))******)))((('''))))))((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''(((((((((((('''''')))(((((((((((()))******((()))))))))************,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,------......,,,,,,,,,---...000111222555888BBBUUUppp|||wwwrrrnnnlllnnnuuu~~~~~~vvvkkkfff]]]UUULLLFFFDDDCCCAAA???AAAAAAAAAAAA@@@@@@??????AAA@@@@@@???>>>>>>??????;;;;;;;;;<<<>>>@@@CCCDDDHHHKKKQQQUUUWWWXXXZZZ[[[ZZZYYYYYYZZZ]]]^^^]]][[[[[[\\\]]]^^^]]]\\\[[[ZZZ[[[\\\]]]^^^___`````````ccccccbbb```___^^^^^^]]]```___^^^```bbbddddddcccbbbbbbbbbbbbbbbbbbbbbbbb^^^_________```aaabbbbbb``````aaabbbbbbcccccccccddddddeeeeeeeeeeeeffffffggghhhiiikkkllllllllllllggggggggggggfffeeeeeedddeeeffffffggghhhhhhhhhhhhjjjjjjjjjjjjjjjjjjiiiiiilllkkkiiihhhgggfffggggggeeeeeeeeeeeedddcccbbbaaa```bbbeeehhhjjjiiihhhgggdddddddddddddddcccaaa```aaa___]]]^^^___```___^^^\\\\\\[[[ZZZYYYWWWVVVUUUTTTTTTUUUUUUTTTSSSRRRQQQLLLKKKJJJHHHFFFDDDCCCBBBCCCBBB???=========>>>???===<<<<<<;;;::::::999999666666555444444444555555555555555555555555555555888999;;;===???????????????????????????>>>>>>>>>@@@@@@@@@@@@@@@@@@??????>>>@@@AAABBBAAAAAACCCEEEPPP```zzzyyyooorrr~~~zzzkkkcccdddiii++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,------......+++++++++******++++++++++++******))))))******+++++++++++++++++++++++++++))))))))))))))))))))))))************************''''''((((((((()))))))))******++++++++++++++++++))))))))))))))))))))))))(((&&&&&&&&&((()))((('''((((((((((((((((((((((((&&&''''''((((((''''''&&&((((((''''''''''''''''''%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%&&&'''((())))))&&&'''''''''(((((())))))((((((((((((((((((((((((&&&&&&&&&&&&&&&%%%%%%%%%&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%''')))%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%&&&'''(((((('''&&&%%%%%%%%%&&&'''((('''((()))******)))((('''((((((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''((((((((((((''''''((((((((((((((())))))***((()))))))))************))))))))))))))))))))))))******++++++,,,------...---------...///000111111444555999EEEXXXqqq}}}{{{yyyzzz{{{{{{zzzxxxvvvtttrrrrrrsssxxxwwwuuutttrrrrrrzzzuuudddUUULLLGGGDDDBBB@@@@@@@@@@@@@@@@@@@@@@@@@@@???????????????@@@@@@<<<<<<;;;<<<===???AAABBBCCCGGGKKKNNNPPPRRRUUUWWWVVVVVVWWWYYY\\\]]]\\\[[[[[[[[[]]]^^^^^^]]]\\\[[[]]]^^^^^^^^^^^^^^^]]]\\\___________________________^^^]]]]]]```bbbbbbbbb``````aaaaaaaaaaaabbbbbb]]]\\\\\\\\\]]]^^^___```______``````aaabbbbbbcccaaabbbbbbbbbccccccdddddddddeeefffhhhiiijjjkkkkkkggggggfffeeeeeeddddddccccccdddeeefffggghhhggggggccccccddddddeeefffggghhhkkkiiigggeeeddddddeeeeeefffeeeeeedddcccaaa```___]]]___bbbdddeeeeeecccbbb`````````___^^^]]]\\\\\\]]][[[ZZZZZZ[[[\\\\\\[[[WWWWWWWWWVVVUUUSSSQQQPPPQQQQQQQQQQQQPPPOOONNNNNNGGGGGGFFFDDDCCCAAA@@@@@@AAA@@@===<<<;;;<<<===>>>;;;::::::999999888888888444444444333444444555555555555555666666777777777999:::<<<>>>??????>>>>>>>>>>>>>>>???????????????AAAAAAAAA@@@AAAAAAAAAAAACCCDDDDDDCCCBBBHHHRRRZZZmmmsssmmmhhhooo}}}zzzzzzwwwgggcccdddhhhkkk,,,,,,,,,,,,------------++++++++++++++++++++++++,,,,,,,,,,,,------------,,,++++++******++++++,,,******))))))))))))******(((((((((((((((((((((((())))))))))))))))))))))))************************''''''(((((())))))***************+++++++++++++++(((((()))))))))))))))***---+++)))(((((('''%%%$$$(((((((((((((((((((((((('''(((((())))))(((((('''((((((((((((((('''''''''$$$%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&'''(((((((((''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$###$$$''')))$$$%%%%%%&&&&&&'''''''''$$$%%%%%%&&&&&&''''''''''''&&&$$$######%%%'''((('''(((((())))))(((((('''((((((((((((((((((''''''&&&&&&&&&&&&&&&'''''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''((((((((((((''''''&&&&&&%%%%%%&&&&&&'''((())))))))))))************************************))))))***+++,,,,,,---------....../////////000000///000444;;;EEEYYYvvv}}}zzzxxxuuurrrppprrrtttwwwyyyzzzzzzzzzyyyyyyzzz||||||~~~wwwkkkjjjjjjkkkmmmrrryyynnn[[[LLLCCC@@@AAA@@@??????@@@AAACCCDDD??????>>>=========>>>>>><<<<<<;;;<<<===>>>@@@AAAAAACCCEEEFFFHHHJJJNNNQQQRRRTTTVVVYYY[[[\\\\\\\\\ZZZZZZ[[[\\\]]]]]]]]]\\\^^^^^^^^^^^^]]]\\\[[[ZZZ[[[\\\]]]^^^___`````````___]]]\\\\\\^^^```aaaaaa________________________\\\[[[ZZZZZZZZZ[[[]]]^^^____________```aaabbbbbb``````aaaaaabbbbbbccccccbbbbbbdddfffggghhhiiiiiiggggggeeedddccccccccccccaaabbbdddeeeffffffeeeddd```aaacccccccccdddgggiiiiiigggeeecccbbbbbbcccddddddccccccbbb```^^^]]]\\\[[[]]]^^^``````___^^^]]][[[\\\\\\[[[XXXWWWXXXYYYYYYWWWVVVVVVXXXYYYYYYXXXSSSSSSSSSRRRPPPOOOMMMLLLLLLKKKKKKJJJIIIIIIIIIHHHBBBAAA@@@???>>>===<<<<<<>>>===<<<;;;:::;;;<<<<<<999999999888888777777777444444444444444555666777555666666777888999999:::;;;<<<===>>>???>>>==================>>>>>>>>>>>>>>>>>>>>>??????AAABBBCCCCCCEEEFFFFFFJJJWWWjjjyyyqqqrrruuu}}}xxxuuuxxx}}}}}}wwwwww}}}lllaaacccgggiiiiii++++++,,,,,,,,,---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,++++++++++++,,,,,,******))))))))))))******(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))''''''((())))))***++++++)))))))))*********++++++(((((((((((())))))******+++***(((((((((((('''%%%((((((((((((((((((((((((******++++++++++++******(((((((((''''''&&&&&&&&&%%%&&&'''(((((((((((('''&&&&&&'''''''''''''''''''''''''''&&&%%%%%%$$$$$$((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%###!!!"""$$$&&&$$$$$$%%%%%%&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''(((''''''''''''''''''((('''(((((((((((((((((((((&&&&&&'''''''''(((((((((&&&&&&&&&''''''''''''(((((((((((((((((((((((((((''''''((((((((((((''''''&&&%%%%%%%%%%%%&&&''''''))))))))))))************,,,,,,,,,,,,,,,,,,,,,,,,(((((()))***+++,,,------------......///.........,,,---111555999DDD[[[ppp}}}yyytttoookkkjjjjjjkkkpppwww|||uuugggbbb```fffooowww}}}www^^^MMMEEEDDDBBBAAA@@@BBBEEEHHHJJJCCCBBBAAA???===<<<<<<;;;;;;:::::::::;;;===???@@@?????????>>>???BBBGGGKKKLLLOOORRRUUUWWWWWWXXXXXXXXXXXXXXXYYYYYYZZZ\\\\\\\\\]]]]]]]]]]]]\\\\\\[[[YYYZZZ\\\^^^___```_________]]][[[[[[]]]___``````\\\\\\\\\\\\\\\\\\\\\[[[[[[ZZZYYYXXXXXXZZZ\\\]]]^^^]]]]]]]]]^^^___```aaa`````````aaabbbbbbcccccc```aaacccdddeeefffgggggggggfffdddbbbaaaaaaaaaaaa```aaabbbccccccaaa___^^^___```bbbaaa```aaadddgggeeedddaaa^^^]]]^^^___```]]]]]]]]]]]]\\\[[[ZZZYYYZZZ[[[\\\\\\\\\[[[YYYXXXVVVWWWXXXVVVTTTSSSTTTVVVUUUTTTRRRSSSUUUVVVVVVUUUPPPPPPPPPOOOMMMLLLJJJIIIGGGGGGFFFEEEDDDDDDDDDDDD>>>>>>===<<<<<<;;;::::::;;;;;;::::::::::::999999888888888888777777777777444444444555666777888999666777777999:::;;;<<<<<<>>>>>>???@@@???>>>===<<<;;;;;;;;;<<<<<<<<<===============>>>@@@CCCEEEFFFFFFKKKRRRWWWaaavvvyyy~~~vvvtttuuuwwwyyysssqqqmmmttt}}}ggg```bbbeeedddddd)))))))))******+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++******))))))---,,,,,,++++++,,,,,,---******))))))))))))******************************))))))))))))))))))))))))(((((((((((((((((((((((('''(((((()))***++++++,,,'''((((((((())))))******'''((((((((())))))******%%%%%%%%%&&&)))++++++***((((((((((((((((((((((((''''''(((((((((((('''''''''''''''&&&&&&%%%%%%%%%''''''((()))******))))))'''''''''''''''&&&&&&&&&''''''&&&%%%$$$######"""((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((&&&&&&&&&'''''''''(((((('''&&&%%%""" """$$$$$$$$$%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%'''((()))((('''&&&((('''&&&%%%%%%&&&'''((('''''''''((((((((((((((('''''''''((((((((())))))&&&&&&&&&'''''''''(((((())))))))))))))))))))))))''''''((((((((((((''''''(((''''''''''''((())))))))))))))))))************))))))))))))))))))))))))'''((()))***+++,,,------,,,------......---------,,,,,,///333444888GGGWWWpppwwwwwwuuuooohhhdddccceeekkkrrr|||wwwggg]]]YYYcccrrrvvv___TTTFFFDDDBBBAAACCCGGGLLLOOOIIIHHHEEEBBB???===;;;;;;999888888999:::<<<===???======;;;999999===BBBFFFFFFIIIMMMPPPQQQRRRSSSTTTWWWVVVVVVVVVWWWXXXZZZ\\\ZZZ[[[\\\]]]]]]]]]]]]]]]ZZZ[[[\\\^^^______^^^^^^```]]][[[[[[]]]___``````ZZZZZZZZZZZZYYYYYYYYYXXX[[[ZZZYYYXXXXXXYYY[[[\\\]]]\\\\\\[[[\\\^^^___````````````aaabbbccccccddd```aaabbbcccdddeeeeeeeeefffeeecccaaa```___````````````aaaaaa___]]]ZZZYYYZZZ[[[\\\ZZZXXXXXX[[[^^^bbbaaa^^^[[[ZZZ[[[\\\]]]WWWWWWXXXXXXXXXXXXXXXWWWYYYZZZZZZZZZYYYXXXVVVUUUSSSUUUVVVTTTQQQQQQSSSUUUSSSRRRPPPQQQSSSTTTTTTSSSNNNNNNNNNMMMLLLJJJHHHHHHFFFEEEDDDCCCBBBBBBBBBBBB>>>>>>======<<<;;;;;;:::888999999999999888888777888888888888777777777777555555555666777888999:::777777888999;;;<<<======@@@@@@AAAAAA@@@???===<<<999:::::::::;;;;;;<<<<<<>>>>>>???@@@CCCFFFIIIKKKPPPYYYdddooo~~~zzzrrrrrrwww|||~~~wwwlllhhhjjjppp}}}uuufff```aaaaaa```aaa((()))++++++******+++,,,,,,++++++******++++++,,,++++++++++++++++++++++++))))))))))))))))))))))))))))))************))))))(((((())))))******++++++((((((((((((((())))))***(((((((((((((((((((((((())))))))))))************(((((('''(((((()))***+++''''''((((((((((((''''''&&&&&&'''((()))***++++++,,,+++)))((('''''''''((((((((((((((((((((((((((('''&&&%%%$$$$$$%%%&&&'''%%%%%%'''((())))))******(((((('''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%((((((((('''&&&&&&&&&%%%'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&''')))'''%%%######%%%''')))&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&&&&&&&&&&&&&'''(((***+++***)))'''&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((''''''''')))))))))))))))))))))))))))))))))))))))******+++++++++******)))*********)))***++++++,,,---............//////222666===AAAXXXsss~~~{{{uuurrrqqqqqqooolllgggbbbcccfffjjjtttwwwfff\\\\\\eeeooo|||iiiXXXMMMBBB???EEEMMMUUUZZZWWWMMMAAA;;;<<<>>>===;;;;;;;;;;;;;;;;;;<<<===>>><<<;;;::::::;;;<<<===>>>BBBBBBCCCEEEGGGKKKNNNPPPNNNPPPSSSTTTTTTUUUVVVWWWYYYXXXXXXXXXYYY[[[]]]^^^YYYYYYZZZZZZZZZ[[[[[[[[[ZZZZZZ[[[\\\]]]]]]]]]]]]^^^]]][[[YYYWWWVVVUUUTTTVVVWWWZZZ\\\]]]]]]\\\[[[ZZZZZZ[[[\\\\\\]]]^^^^^^aaa___^^^___cccffffffdddaaaaaa```aaabbbcccbbbaaagggeeeccc```^^^]]]]]]]]]\\\\\\\\\[[[YYYYYYZZZ\\\ZZZZZZZZZYYYYYYYYYYYYYYYZZZZZZYYYYYYYYYYYYZZZZZZVVVWWWWWWWWWWWWWWWWWWWWWVVVVVVVVVUUUUUUUUUTTTTTTXXXWWWUUUSSSPPPNNNLLLKKKNNNMMMLLLLLLKKKKKKLLLLLLLLLLLLJJJIIIIIIIIIIIIIIIFFFFFFEEEDDDCCCAAA???>>><<<<<<;;;::::::999888888777777777777777666666666666666666666555555555555555555555666777999:::;;;>>>===;;;:::;;;<<<>>>???BBBBBBCCCCCCBBB@@@???===>>><<<:::999;;;;;;;;;:::;;;@@@DDDFFFGGGKKKRRRYYYbbbjjjyyyzzz}}}||||||zzzrrriiicccccceeessswwwmmmiiiiiicccVVVJJJ(((***++++++******+++,,,,,,++++++******++++++,,,++++++++++++++++++++++++)))))))))))))))))))))))))))******************))))))))))))))))))*********)))(((((((((((()))******(((((((((((((((((((((((((((((()))))))))*********)))(((((((((((())))))***''''''((((((((((((''''''((((((((((((((()))))))))+++***)))''''''&&&''''''''''''''''''''''''''''''((('''&&&%%%%%%&&&'''(((&&&&&&'''(((((((((''''''(((((('''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&%%%%%%%%%%%%'''''''''''''''''''''''''''''''''&&&&&&'''''''''((('''%%%######%%%'''((('''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%'''((()))******)))'''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))))))))))))))((((((((())))))))))))))))))))))))))))))(((((())))))***+++*********)))******++++++++++++,,,,,,,,,,,,,,,,,,---...//////000333777;;;III___{{{}}}vvvwwwyyywwwsssrrrrrrrrrqqqmmmhhheeefffjjjnnnxxxqqqfff```___eeennnpppbbbQQQGGGHHHNNNVVV[[[WWWNNNCCC===>>>@@@???<<<;;;;;;;;;;;;;;;<<<======<<<;;;;;;::::::;;;<<<===<<<<<<===>>>@@@CCCFFFGGGJJJLLLNNNPPPPPPRRRTTTVVVXXXXXXXXXXXXYYYZZZ[[[\\\XXXXXXXXXXXXYYYYYYYYYYYYXXXXXXYYYZZZ[[[[[[[[[[[[ZZZYYYXXXVVVUUUUUUUUUUUUTTTVVVXXXZZZ[[[[[[ZZZZZZYYYYYYZZZZZZ[[[[[[\\\\\\___]]]\\\^^^aaaddddddccc______^^^___`````````___cccbbb```]]]\\\[[[[[[[[[ZZZZZZ[[[ZZZXXXWWWXXXZZZYYYYYYYYYXXXXXXWWWWWWWWWWWWWWWVVVVVVVVVVVVWWWWWWTTTTTTTTTTTTTTTTTTTTTTTTSSSSSSRRRRRRRRRQQQQQQQQQRRRQQQQQQOOONNNMMMLLLLLLNNNMMMLLLLLLKKKKKKLLLLLLIIIIIIHHHGGGFFFFFFFFFFFFDDDDDDCCCCCCAAA???>>>===;;;;;;:::999999888777777666666666666666666666666666666666666666666666666777777777888999:::;;;<<<>>>===<<<;;;<<<===???@@@BBBCCCCCCCCCBBB@@@???>>>;;;::::::;;;===???>>>===@@@BBBDDDGGGMMMYYYiiittt}}}{{{tttttttttqqqhhhaaa```gggooo{{{uuurrrlllaaaQQQEEE)))***++++++******+++,,,,,,++++++******++++++,,,++++++++++++++++++++++++))))))))))))))))))))))))******++++++++++++*********))))))))))))))))))((()))))))))))))))******+++(((((((((((((((((((((((((((((())))))))))))*********))))))(((((((((((()))'''(((((())))))((((((''')))))))))(((((((((''''''***)))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&''''''((('''''''''''''''&&&%%%%%%'''''''''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''''''''((((((((('''%%%$$$$$$%%%'''(((''''''''''''''''''''''''&&&&&&'''((('''&&&%%%$$$''''''))))))***)))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&''''''''''''''''''''''''))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((())))))***+++))))))))))))******+++,,,------,,,,,,++++++++++++---...//////...///111333999HHH___yyy~~~yyyxxxvvvvvvwwwmmmjjjlllrrruuutttssstttuuuwwwxxxuuupppnnnpppqqqvvv{{{ssslllhhhffffffkkkqqq{{{fffUUUOOOQQQUUUXXXQQQIII@@@<<<>>>???>>><<<;;;;;;;;;;;;;;;;;;<<<===<<<<<<;;;:::::::::;;;;;;888888888999:::<<<>>>>>>DDDFFFGGGIIIJJJMMMQQQTTTVVVVVVWWWXXXYYYYYYYYYXXXUUUUUUVVVVVVVVVWWWWWWWWWUUUVVVWWWXXXXXXYYYXXXXXXUUUTTTTTTSSSSSSSSSTTTTTTSSSTTTVVVXXXYYYYYYYYYXXXXXXYYYYYYYYYYYYYYYYYYYYY\\\[[[ZZZ\\\___aaaaaaaaa]]]]]]]]]\\\\\\\\\\\\\\\^^^]]][[[YYYXXXXXXXXXYYYWWWXXXXXXXXXVVVUUUVVVWWWXXXWWWWWWVVVUUUTTTSSSSSSSSSSSSRRRRRRRRRRRRSSSSSSQQQQQQPPPPPPPPPPPPPPPPPPNNNNNNNNNMMMMMMMMMMMMLLLKKKKKKKKKKKKKKKKKKKKKKKKJJJJJJIIIHHHHHHHHHHHHIIIEEEDDDCCCBBBBBBAAABBBBBBAAAAAAAAA@@@>>>===;;;:::999888888777777666666666555555555555555555555555555555666666777888888888:::::::::::::::;;;<<<===???>>>=========>>>@@@AAACCCCCCCCCCCCBBB@@@???>>>===<<<<<<>>>@@@BBBBBBBBBFFFHHHMMMTTT```rrr}}}sssmmmjjjnnnnnnjjjbbb^^^fffwwwxxxkkkYYYGGG<<<***+++,,,,,,******+++,,,,,,++++++******++++++,,,************************))))))))))))))))))))))))+++++++++,,,,,,+++++++++******))))))(((((((((''')))))))))))))))***++++++(((((((((((((((((((((((((((((((((((()))))))))*********)))(((((('''(((((((((((())))))))))))((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''(((((((((%%%&&&&&&&&&&&&&&&%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%######$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''%%%$$$$$$%%%''''''''''''''''''''''''''''''%%%&&&((())))))(((&&&%%%&&&'''((()))))))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))((((((((((((((((((((((((((((((((((((((()))******(((((((((((()))+++,,,,,,,,,++++++++++++++++++++++++,,,...///......///000333;;;KKKaaa{{{}}}qqqkkkiiikkkcccdddiiiqqqttttttvvvzzz|||~~~vvvpppkkkiiikkkmmmoootttzzzzzzhhh]]]YYYVVVSSSLLLFFF???===>>>@@@???>>>;;;;;;;;;::::::;;;<<<<<<<<<<<<;;;::::::999999999888888888999999:::::::::===???@@@AAACCCGGGLLLPPPQQQSSSTTTUUUVVVUUUTTTTTTSSSSSSSSSSSSTTTTTTTTTTTTRRRSSSTTTUUUVVVVVVVVVVVVRRRRRRQQQQQQQQQQQQRRRRRRRRRSSSUUUVVVWWWXXXXXXXXXXXXXXXXXXXXXWWWWWWWWWWWWYYYYYYYYYZZZ\\\^^^______[[[[[[\\\[[[ZZZYYYYYYZZZYYYXXXWWWVVVUUUUUUVVVVVVTTTUUUVVVVVVTTTSSSSSSTTTUUUTTTTTTRRRQQQPPPOOOOOOPPPOOOOOONNNNNNOOOOOOPPPNNNNNNMMMMMMMMMMMMLLLLLLJJJJJJJJJJJJIIIIIIIIIIIIGGGGGGGGGHHHHHHHHHIIIIIIDDDDDDCCCBBBBBBBBBBBBBBBBBBAAA@@@???>>>>>>>>>>>>=========<<<;;;:::999888666666666666555555444444333333444444444444444555555555666777888999:::;;;<<<<<<;;;;;;;;;<<<<<<===??????>>>>>>>>>???@@@AAADDDCCCCCCBBBBBBAAA@@@???CCCAAA???AAADDDHHHKKKLLLOOOUUU^^^jjjyyy}}}mmmffffffhhhlllllljjjeeegggwwwuuu```KKK<<<555***,,,---,,,+++***+++,,,,,,++++++******++++++,,,************************))))))))))))))))))))))))+++++++++,,,,,,+++++++++***)))))))))(((((('''''')))))))))((()))******+++))))))))))))))))))))))))'''(((((((((((()))))))))******)))(((((('''(((((((((((())))))))))))((((((%%%&&&&&&'''((()))))))))'''''''''''''''&&&&&&&&&'''''''''''''''''''''''''''(((((((((((((((((('''###$$$%%%&&&''''''''''''&&&'''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&''')))***+++)))(((&&&&&&&&&'''(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&'''''''''((((((((((((((((((((((((((((((((((((((('''((())))))***(((((((((((()))***+++,,,))))))***++++++,,,------)))+++...//////...///000111555???NNNaaawwwwwwkkkeeebbb```bbbhhhqqqvvvyyyyyyqqqnnniiihhhkkkpppuuu}}}vvvnnndddZZZQQQKKKEEEAAA@@@AAA@@@???<<<;;;;;;:::::::::;;;;;;;;;;;;;;;::::::999888888999999999999999999888888888:::;;;<<<>>>AAAFFFJJJKKKLLLNNNOOOPPPPPPOOONNNOOOOOOPPPPPPPPPQQQQQQQQQPPPPPPQQQRRRSSSSSSSSSSSSRRRQQQQQQPPPOOOOOOOOOOOORRRRRRSSSTTTUUUVVVWWWWWWWWWWWWWWWVVVVVVVVVVVVVVVVVVWWWXXXXXXYYY[[[\\\^^^ZZZ[[[\\\ZZZWWWVVVVVVXXXVVVUUUTTTSSSRRRSSSSSSTTTQQQSSSTTTTTTRRRQQQQQQRRRQQQQQQPPPOOOMMMLLLKKKKKKLLLLLLKKKKKKKKKKKKLLLLLLKKKKKKKKKJJJJJJIIIIIIIIIGGGGGGGGGGGGFFFFFFFFFFFFEEEEEEEEEEEEEEEEEEEEEEEE@@@@@@???>>>>>>>>>>>>???@@@???>>>===<<<<<<<<<<<<::::::::::::999777666555555444444444444444333333222333333333444444555555555666777888999;;;<<<<<<<<<<<<;;;;;;;;;<<<<<<===???????????????@@@@@@AAACCCCCCBBBBBBBBBBBBBBBBBBFFFDDDCCCGGGNNNWWW^^^aaaaaafffooo{{{pppccc___bbbfffiiilllmmmoooxxxhhhQQQ???666333+++,,,---,,,+++***+++,,,,,,++++++******++++++,,,************************))))))))))))))))))))))))******++++++++++++******)))(((((((((((((((((('''((((((((((((((())))))***))))))))))))))))))))))))''''''(((((((((((())))))***))))))(((((((((((()))((())))))******))))))((($$$%%%&&&'''((())))))***''''''(((((((((''''''&&&((((((((((((((((((((((((&&&''''''((((((''''''&&&###$$$%%%&&&((((((((((((&&&&&&&&&'''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&'''((()))***)))((((((&&&&&&&&&''''''(((((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&''''''((())))))))))))))))))))))))((((((''''''(((((()))***(((((((((((())))))***+++(((((()))***+++,,,------(((***---.........000111///111777???JJJ^^^zzzxxxllldddbbbcccjjjuuuyyyrrrooojjjgggkkkrrr{{{uuubbb[[[QQQHHHBBB>>><<<:::<<<;;;;;;:::::::::::::::999999:::::::::999888888777777888888777777666555666777888999:::<<<@@@CCCDDDDDDFFFGGGHHHIIIIIIIIIJJJKKKKKKKKKLLLLLLLLLLLLLLLMMMNNNOOOPPPPPPPPPPPPPPPOOONNNNNNMMMMMMMMMMMMPPPPPPQQQRRRSSSTTTUUUUUUTTTTTTTTTTTTTTTTTTTTTTTTRRRTTTUUUUUUUUUWWWYYY[[[XXXZZZ[[[YYYUUURRRTTTVVVSSSRRRQQQOOOOOOOOOPPPPPPMMMOOOQQQQQQPPPNNNMMMNNNMMMLLLLLLKKKJJJIIIIIIHHHIIIHHHHHHGGGGGGHHHHHHIIIHHHHHHHHHGGGFFFFFFEEEEEEDDDDDDDDDDDDCCCCCCCCCCCCBBBBBBBBBBBBAAAAAAAAAAAA??????>>>============>>>======<<<;;;::::::::::::888888888888777666555444333333333333333333333333222333333444444555555555777777888999:::;;;<<<===<<<<<<<<<<<<<<<===>>>>>>>>>?????????@@@@@@@@@@@@BBBAAAAAAAAABBBCCCDDDEEEFFFFFFJJJSSS___lllvvvzzzuuuwww}}}xxx~~~}}}jjj```]]]aaafffjjjnnnuuu~~~pppWWWDDD999555555,,,---...---+++***+++,,,,,,++++++******++++++,,,************************)))))))))))))))))))))))))))******************)))'''''''''((((((((((((((('''''''''''''''(((((()))))))))))))))))))))))))))'''''''''((((((((()))))))))(((((((((((())))))***))))))************))))))&&&&&&&&&''''''(((((((((''''''((()))))))))((('''''''''''''''''''''''''''%%%&&&'''(((((('''&&&%%%%%%&&&'''(((((((((((((((&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''(((%%%%%%&&&&&&'''((())))))&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((((()))))))))))))))))))))))))))(((''''''''''''((())))))))))))((((((((())))))***))))))******+++++++++,,,)))+++,,,,,,,,,,,,...000//////111666<<>>;;;<<<;;;::::::999999::::::777888999::::::999999888555666777777777666444444555666888999999999;;;=========>>>???AAACCCDDDEEEEEEEEEEEEFFFFFFFFFFFFGGGHHHHHHIIIKKKKKKKKKKKKKKKKKKKKKJJJJJJKKKKKKLLLMMMMMMMMMMMMNNNOOOPPPQQQRRROOOOOOPPPPPPQQQQQQRRRRRRNNNPPPRRRRRRQQQRRRUUUXXXUUUXXXYYYVVVQQQOOOPPPSSSPPPOOOMMMLLLKKKKKKKKKLLLIIIKKKMMMNNNLLLJJJIIIIIIIIIIIIHHHHHHHHHGGGGGGGGGEEEDDDDDDCCCCCCDDDDDDEEEEEEDDDDDDCCCBBBBBBAAAAAABBBAAAAAAAAA@@@@@@@@@@@@======>>>>>>>>>>>>>>>>>>>>>===<<<<<<;;;;;;<<<<<<;;;:::999888888777777777666666777666666555444333333333333333333333333333333333333444555555666666888999999:::;;;<<<<<<===============>>>@@@AAAAAA===>>>>>>???????????????@@@@@@@@@AAABBBDDDFFFGGGIIINNNWWWeeesssyyynnnlll{{{yyylllfffeeeiiinnnsssyyy~~~~~~rrrXXXDDD;;;777555333,,,---...---+++***+++,,,,,,++++++++++++++++++,,,))))))))))))))))))))))))))))))))))))))))))))))))))))))************))))))&&&'''''''''(((((())))))&&&&&&&&&&&&&&&'''(((((())))))))))))))))))))))))''''''''''''((((((((()))(((((('''(((((()))***+++))))))************))))))(((''''''''''''&&&&&&&&&'''((()))******)))((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&''''''&&&%%%$$$((((((((()))(((((('''&&&&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%$$$$$$$$$######""""""%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&'''%%%%%%%%%&&&&&&((()))***&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((())))))***))))))))))))))))))))))))'''''''''''''''((())))))***))))))(((((((((((()))+++++++++******************+++,,,+++******,,,...222//////222444<<>>>>>????????????>>>>>>>>>>>>999999:::;;;;;;<<<======;;;:::999999888888999999999888777666666555666666666666666666555444333333333333333333333333333333333333444444555666777777999::::::;;;;;;<<<<<<<<<>>>>>>>>>???@@@BBBCCCDDD======>>>????????????>>>?????????@@@BBBEEEHHHIIIPPPVVVcccssssssjjjeeeiiixxxpppooooootttzzz~~~wwwrrrpppwwwqqq^^^FFF777555666333...,,,,,,,,,+++++++++******++++++++++++++++++++++++)))************+++++++++))))))(((((((((((())))))******))))))(((((('''''''''((()))((('''&&&'''))))))(((((())))))***+++,,,((((((((((((((((((((((((''''''''''''''''''''''''(((((((((((((((((((((((())))))))))))))))))))))))))))))((((((''''''''''''%%%&&&'''(((((('''&&&%%%))))))))))))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%(((((('''''''''&&&&&&&&&((((((((('''&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%%%%'''''''''&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&''''''''''''(((&&&&&&&&&''''''(((((((((%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&&&&'''(((******((('''&&&$$$%%%&&&&&&''''''&&&&&&'''''''''&&&&&&%%%%%%%%%''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))(((((((((((((((((((((((())))))))))))************))))))***+++---.../////////222444333222555===CCC\\\uuu|||uuurrrrrrmmmppptttwwwyyyzzz|||~~~~~~}}}~~~|||mmmdddkkkuuuxxxyyy{{{gggTTTIIIDDD>>>;;;<<<:::666666;;;777888999999777666666777666777888999999888777666555555555444444555555555777777888999::::::;;;;;;<<<<<<===>>>???@@@AAAAAABBBBBBBBBCCCCCCCCCDDDDDDEEEFFFFFFFFFFFFGGGGGGGGGIIIHHHGGGFFFGGGHHHIIIJJJKKKKKKKKKKKKKKKKKKKKKKKKHHHHHHIIIKKKLLLNNNOOOOOORRRRRRQQQPPPNNNMMMLLLLLLHHHGGGFFFFFFFFFGGGHHHIIIGGGFFFFFFFFFEEEEEEDDDDDDCCCCCCDDDDDDCCCCCCBBBAAA@@@@@@@@@?????????>>>>>>=================================<<<<<<;;;;;;;;;999999999999888888888777:::999888666666666777888888888999999888777666666555555666666555333222000333333333444444444555555222222333555666888999999::::::;;;;;;<<<=========???@@@@@@AAABBBBBBCCCCCC???===;;;;;;===>>>??????@@@???BBBIIIKKKIIILLLSSS]]]lll~~~yyyjjjdddkkkzzzvvvrrrtttxxx~~~uuujjjiiinnn{{{uuuUUUKKK>>>666333444333222***)))))))))((((((((((((++++++++++++++++++++++++)))************+++++++++))))))(((((((((((())))))***)))))))))(((((((((''''''((()))(((''''''((())))))))))))(((((())))))***************************''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''&&&&&&&&&&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&''''''''''''%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&&&&'''((())))))((('''&&&$$$%%%&&&&&&''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''''''''''''''((((((((((((''''''''''''''''''''''''))))))))))))))))))))))))(((((((((((((((((((((((((((((()))))))))***************++++++,,,---......+++...000000///111777===LLL```zzz|||ssslllhhhhhhhhhooovvv~~~yyyiii___ccckkkqqqxxxhhhZZZNNNEEE>>>===;;;777777:::777999:::;;;:::999999:::666666777888888777777666666666555555555555666666666666666777777888888999999999:::;;;<<<===>>>>>>????????????@@@@@@@@@@@@BBBBBBCCCCCCCCCDDDDDDDDDEEEEEEDDDDDDDDDEEEFFFGGGGGGGGGGGGGGGGGGGGGGGGGGGEEEFFFGGGHHHIIIKKKLLLLLLOOONNNMMMLLLKKKJJJIIIIIIEEEEEEDDDCCCCCCDDDEEEFFFEEEDDDDDDDDDCCCCCCCCCBBB@@@AAAAAAAAAAAA@@@??????>>>>>>>>>>>>======<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;<<<<<<;;;;;;;;;:::::::::888888888888777777777777999888777666555555666777555555555555555444333333555555555444444333222111333333333333444444444444222333444555666888999999::::::;;;;;;<<<=========>>>>>>>>>??????@@@@@@@@@BBBAAA?????????@@@@@@@@@DDDBBBDDDKKKPPPUUU```kkkyyyxxxpppjjjmmm|||tttqqquuussseeedddgggnnnyyy|||nnnaaaJJJBBB777111111222111000))))))))))))((((((((((((************************)))************+++++++++))))))(((((((((((())))))))))))))))))(((((((((((('''((())))))''''''((()))))))))((((((''''''((((((************************''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%''''''''''''&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''''''''''''''&&&&&&&&&&&&'''((())))))((('''&&&$$$%%%&&&&&&''''''&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((''''''''''''''''''''''''))))))))))))))))))))))))(((((((((((((((((((((((((((((())))))))))))*********+++++++++,,,,,,------***,,,//////...///222666<<>>>>>>>>?????????@@@@@@AAAAAA@@@@@@@@@AAABBBCCCBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBCCCDDDFFFGGGHHHHHHIIIIIIHHHGGGFFFFFFEEEEEEAAAAAA@@@@@@@@@@@@AAAAAAAAAAAAAAA@@@@@@@@@@@@@@@======>>>>>>======<<<;;;<<<<<<;;;;;;;;;;;;::::::999999999999999999999999::::::999999999999888888777777666666666555555555666666555444444444555555333333333333333222222111555444333222222111222222222222222333333333444444333333444555777888999999::::::;;;;;;<<<=========??????????????????@@@@@@@@@@@@@@@@@@@@@@@@AAAAAAHHHHHHMMMUUU```mmm~~~zzzwwwxxx}}}tttkkkiiippptttfff^^^aaaeeemmmsssrrrgggUUUHHH>>>888222///000111111000,,,,,,,,,,,,++++++++++++))))))))))))))))))))))))))))))*********+++++++++))))))(((((((((((())))))))))))))))))((((((((((((''')))***)))((('''((()))(((''''''''''''(((((()))((((((((((((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&&&&'''$$$$$$%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&''''''((((((''''''&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((''''''''''''''''''''''''))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((()))))))))***++++++++++++++++++,,,,,,+++...000111000000111333555:::FFF[[[wwwxxxmmmfffeeeiiimmmooorrrxxxmmmcccaaabbbhhhxxxqqqeeeVVVNNNJJJEEE???:::===<<<;;;::::::999888666666666666666666555555555555555444444444444555555444444444444444333333333333333444555555666777777777777777888888888999999::::::;;;;;;;;;<<<<<<<<<============>>>>>>??????========================??????@@@AAABBBCCCDDDDDDDDDDDDCCCCCCBBBBBBAAAAAA>>>>>>>>>===========================<<<<<<<<<<<<;;;;;;;;;;;;;;;:::999999:::::::::::::::999999999777777777777777777777777777777777777777777777777555555555444444444444333444444333333333333333333333333333444444333333222555444222111000111222222222222222333333333333444333444555666777888999999::::::;;;;;;<<<=========AAAAAAAAAAAAAAAAAAAAAAAA???@@@AAAAAAAAABBBDDDEEEJJJRRR```nnn|||vvvlllccceeeqqqxxxiiidddcccccceeehhhfff^^^PPPAAA888777444111111222333222111......---------,,,,,,,,,))))))))))))))))))))))))))))))*********+++++++++))))))(((((((((((())))))(((((((((((())))))))))))((()))***)))((('''(((***&&&&&&&&&&&&'''(((******''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&'''''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''(((((($$$$$$%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&'''''''''''''''''''''&&&&&&''''''''''''&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((('''(((((((((((()))))))))++++++++++++++++++++++++,,,...000111000000000111111444;;;HHH^^^zzz}}}tttmmmlllnnnrrruuuwwwssskkkggggggeeefffsss~~~pppddd]]]UUUIII???BBB???<<<;;;<<<<<<;;;:::777777666555555555555555444333333333333333333444444444444444444444333333333333333444444555555666555666666666777777777777888888888888999999999999:::;;;;;;;;;<<<<<<<<<<<<::::::::::::::::::::::::<<<======>>>???@@@AAAAAA@@@@@@??????????????????<<<<<<<<<<<<<<<;;;::::::999999999999999999999999999::::::::::::999888888888888999999999999999999666666666666666666666666555666666666666666666666444444444333333333222222222222222333333333222222222222333333333333333222444333222111000111222333222222333333333444444444444555555666777888999999::::::;;;;;;<<<=========@@@AAAAAAAAAAAAAAABBBBBBBBBCCCDDDCCCCCCDDDGGGKKKRRRccczzzzzzuuuooogggcccnnniii^^^^^^cccfffddd^^^UUUKKK@@@888444333333222222222222000///,,,++++++++++++*********************************)))************+++++++++))))))(((((((((((())))))(((((((((((())))))))))))((()))******(((((()))***''''''''''''((()))***+++))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&'''''''''((('''&&&&&&&&&&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''''''''$$$%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&&&&&&&'''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&'''(((''''''&&&&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((((((((((((((((((((((((((''''''(((((((((((()))))))))*********++++++,,,,,,+++,,,---...............///000444<<>>;;;;;;<<<<<<:::888888777666555555555555444444333333333333444444444444444444444444444444333333333444444444555555555555555555666666666666555555666666666777777777888888999::::::::::::999888888888888888888888888999::::::;;;<<<<<<======<<<<<<<<<<<<<<<<<<======;;;;;;;;;;;;:::999888777666666666666777777777777888999999999999888777777777777777777777888888888555555555555555555555555444444555555555555666666444444333333333222222222111111222333333333222222000111111222222222222222333333222222222222333333333333333444444444555555555555666777777888999999::::::;;;;;;<<<============>>>>>>???@@@@@@AAAAAAAAACCCDDDCCCCCCFFFLLLRRRfff{{{wwwooolllfffcccjjjwwwfff]]]\\\___bbb[[[QQQFFF===888555444000000111111000///------*********)))))))))((((((++++++++++++++++++++++++)))************+++++++++))))))(((((((((((())))))'''((((((((()))))))))***((()))******)))((()))***+++***)))((((((((((((((())))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&'''''''''(((((((((((('''&&&&&&&&&&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''(((((('''&&&&&&&&&&&&&&&&&&'''$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((((((((((((((((((((((((((('''''''''((((((((())))))(((((()))***+++,,,,,,---+++******+++---.........//////111666<<>>@@@AAABBBBBBBBBEEEHHHJJJNNNWWWcccllltttnnnoooiiioooxxxnnneee___^^^TTTMMMDDD<<<777555444333...///000000///...------************))))))))))))++++++++++++++++++++++++)))************+++++++++))))))(((((((((((())))))'''((((((((())))))******(((***+++***)))((()))***...---,,,***((('''&&&&&&''''''''''''''''''''''''))))))))))))))))))))))))(((((((((((((((((((((((('''''''''''''''''''''''''''''''''((((((((())))))((('''&&&%%%%%%&&&'''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%%%%%%%&&&&&&&&&(((((((((''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%&&&&&&'''$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''((((((((()))'''((()))***+++,,,------,,,+++++++++---///000000222///000444555;;;JJJ[[[uuuxxxqqquuuwww|||rrrjjjfffjjjlllxxxwwwzzz|||xxxtttttt{{{{{{jjj[[[RRRMMMGGGCCC;;;:::888777666666666777777777666666666666777777000000111222333444444444222222222222333333333333222333333333333444444444111111111111222222222222333444555666666666555444444444444444444444444444333444444555555666666666555555666666777888888888777777888888777555333222333333333444444555555555555555666666555555444333222222222333333444444444444444444444444444444444444444444555555666666666444444444333333333222222000111222333444444333222444555666666777777777777222333444555666555444333555555555666666666666777666666777777888888999999::::::;;;;;;<<<======>>>===>>>???@@@BBBDDDEEEEEEIIIMMMSSSYYYbbbppp}}}rrroootttyyy{{{wwwtttjjj```[[[IIICCC;;;888777666333000...///111111000000000111+++*********))))))((((((******+++++++++,,,,,,,,,''''''((()))***++++++,,,))))))))))))(((((((((((((((((((((((())))))))))))))))))(((((('''''''''&&&(((((())))))))))))(((((())))))))))))))))))))))))((('''&&&%%%%%%&&&'''(((******))))))((((((((('''&&&'''***++++++***'''&&&)))))))))(((''''''&&&&&&((((((''''''((()))******))))))(((((('''''''''&&&&&&&&&&&&&&&'''((()))))) !!!"""###$$$%%%%%%&&&'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%)))&&&$$$###%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''%%%%%%&&&&&&'''((())))))&&&%%%%%%$$$$$$%%%%%%&&& """######""""""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''((('''%%%$$$$$$%%%'''(((&&&''''''((()))******+++'''&&&&&&&&&'''(((***+++))))))*********+++++++++,,,,,,++++++++++++++++++000111000000111555:::???QQQjjjwwwmmmhhhkkkqqqtttyyy}}}~~~yyynnnhhhiiihhhqqq~~~xxxkkkgggeeegggjjjkkklllqqqwww|||jjj[[[PPPJJJAAA<<<999::::::666555777555666666666666555444333555555444444444444444555555333222222444555555444777666555444333222222222111111222222222333333333222222222222222222222222444444444444444444444444444444444444444444444444666666666666666666666666555555555444444333333333444333333222222333333444555555555444444333333333222222222222222222222222111111222222222333333333222222333333333444444444444444444444333222111111333333555666666666555444555555555555555555555555333333333444444444555555444444444444444444444444777777777777777888999:::999::::::;;;;;;;;;<<<<<<@@@AAABBBAAAAAAEEELLLRRRSSSZZZfffqqq|||sssttt{{{~~~uuu[[[GGG;;;:::888555333111000000////////////............************)))))))))(((*********+++++++++,,,,,,))))))******++++++,,,,,,))))))))))))(((((((((((((((((((((((()))))))))))))))(((((((((''''''''''''))))))************))))))((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''))))))(((((((((''''''''''''((()))******)))(((''''''''''''(((((((((((((((''''''''''''(((((()))))))))((((((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&'''&&&&&&&&&&&&%%%%%%%%%'''''''''''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%)))&&&$$$###%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%&&&'''''''''(((&&&%%%%%%$$$$$$%%%%%%&&&"""$$$%%%%%%$$$###%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''((('''&&&%%%%%%&&&'''(((((('''&&&%%%&&&''')))***''''''&&&&&&'''((()))************+++++++++,,,,,,++++++++++++++++++++++++.../////////000222777:::@@@RRRkkkxxxllliiilllpppssszzz|||uuuqqqooopppsssqqqllllllqqqrrryyymmm^^^ZZZYYY[[[```dddhhhqqq{{{}}}iii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ooouuu}}}rrrnnnwww~~~pppWWWEEE999888666444222111000000////////////............************))))))))))))*********++++++++++++,,,++++++++++++++++++,,,,,,))))))))))))(((((((((((((((((((((((())))))))))))((((((((((((''''''''''''(((((())))))))))))((((((((((((((((((((((((((((((&&&''''''''''''''''''&&&(((''''''''''''&&&&&&&&&((((((((((((((((((((((((&&&&&&''''''((())))))***&&&&&&'''(((((((((''''''(((((((((''''''''''''''''''&&&%%%$$$############(((((('''''''''&&&&&&&&&((('''''''''&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%(((&&&$$$###%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%'''&&&%%%%%%&&&(((''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&&&&'''((()))((('''%%%$$$$$$%%%''')))((((((''''''''''''((())))))))))))*********++++++)))*********+++,,,,,,,,,+++---.........000222555222<<>>BBBEEEDDDHHHMMMRRRXXXbbbmmmvvvrrrpppzzz~~~zzzaaaLLL???555555333222111111000000/////////............---*********)))))))))))))))************++++++++++++++++++++++++++++++******))))))))))))(((((((((((((((((((((((())))))))))))((((((((((((((('''''''''%%%&&&&&&&&&&&&&&&&&&%%%((((((((((((((((((((((((%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&)))(((''''''''''''((()))''''''''''''(((((())))))&&&'''((())))))(((''''''''''''''''''''''''''''''&&&%%%$$$$$$#########$$$######$$$%%%&&&'''(((((((((''''''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$&&&''''''&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))(((''''''''''''((()))''''''&&&&&&&&&&&&&&&&&&(((((((((''''''''''''''''''''''''((((((((())))))((())))))***+++,,,,,,---***,,,...///......///111111444<<>><<<:::777444222111444333333444444555666777555444333333555666666555444444333222222222222222222222222333333333444444222222222222222222222222222222222222222222222222111111111111111111111111222222222222222222222222222222111111111111111111333333222222222222333333222222111111111111111111222222222222222222222222222222222333333333444444333333333444444444444555444444555666666666666666444444444555555555555555555555555555555555555555444444444444555555555555555555666666666666777777999888888888888999:::::::::<<<<<<<<<<<>>666222222111000000000000111//////.........---------))))))))))))))))))******))))))*********+++++++++***************)))))))))))))))))))))(((((((((((((((((((((((())))))))))))'''''''''(((((((((((((((%%%%%%&&&&&&&&&&&&%%%%%%''''''''''''''''''''''''%%%&&&'''(((((('''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&)))((('''&&&&&&'''((()))))))))((((((''''''''''''((((((((()))((((((((('''&&&&&&&&&'''''''''''''''%%%%%%%%%%%%%%%&&&''''''###$$$%%%%%%''''''((()))''''''&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%###$$$%%%&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%&&&&&&%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''(((((((((&&&'''((())))))(((&&&%%%((((((((((((((('''''''''((((((((()))))))))******(((((()))***++++++,,,,,,***,,,...///.........///222333666;;;EEEYYYssswwwrrrllljjjlllooorrruuu~~~~~~|||ooo^^^YYYUUUTTTXXXfff}}}|||qqqfff^^^[[[SSSOOOHHH@@@:::666444333444444444444444555666777666444333333555666666555555444444333333333333444222222333333333444444444222222222222222222222222333333333333333333333333111111111111111111111111222222222222222222222222111111111111111111111111333222222111111222222333111111111111111111111111222222222222222222222222222222333333333444444444333333444444444555555555666777777777666666555444444444444444555555666666555555555555555555555555444444444555555555666666444444555555555666666666888888888888999:::;;;<<<>>>???@@@@@@@@@EEENNNUUU\\\dddoooxxx~~~vvvmmmooouuu|||wwwaaaNNN@@@666000000000/////////000000000............------------))))))))))))************)))))))))************+++)))))))))))))))))))))***))))))))))))(((((((((((((((((((((((())))))))))))'''''''''(((((((((((((((''''''((((((((((((''''''''''''''''''''''''''''''&&&''''''''''''''''''&&&%%%%%%%%%&&&&&&&&&&&&''')))((('''&&&&&&'''((()))***))))))(((''''''&&&&&&)))(((''''''&&&&&&''''''&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&'''((()))***)))(((((((((((('''''''''%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$%%%&&&%%%###%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&((((((''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&###$$$&&&%%%$$$$$$%%%'''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%&&&((()))***((('''%%%''''''((((((((((((((('''*********+++++++++,,,,,,((()))))))))***+++++++++)))+++............///000...000222444666@@@VVVkkkyyyrrrlllhhhjjjnnnrrrxxx~~~|||sssbbb```^^^]]]___hhh|||uuukkk[[[KKK>>>888777888666555555444444444555555666555333444555777666666555444444333333444444555333333333333444444444444222222222222222222222222333333333333333333333333111111111111111111111111222222222222222222222222111111111111111222222222222222111111111111222222111111111111111222222222222222222222222222222222333333333333444444444444333444444444555555555555777777777777666555444333555444444444444555666666555555555555555555555555444444555555555666666666444444444555555666666777777777777888:::;;;===>>><<<@@@CCCEEEHHHQQQ___iii}}}sssnnnmmmvvvxxx^^^JJJ>>>888444000000///////////////000000.........------------,,,((()))))))))************))))))))))))************)))))))))******+++++++++))))))))))))(((((((((((((((((((((((())))))))))))''''''''''''((((((((()))(((((())))))))))))((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''%%%&&&&&&&&&'''''''''''''''''''''&&&&&&'''''''''((((((((((((((('''''''''((('''%%%###"""###%%%&&&%%%%%%%%%&&&&&&''''''''''''''''''&&&''''''((((((((((((((('''''''''&&&&&&$$$$$$$$$%%%%%%&&&&&&'''$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$%%%&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''((()))((('''&&&%%%%%%%%%&&&'''''''''(((&&&%%%%%%$$$$$$%%%%%%&&&###%%%&&&&&&%%%$$$&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&'''((((((%%%&&&'''((())))))(((((()))))))))*********++++++))))))))))))************(((***,,,,,,,,,---///000------///222111444AAAOOOiii{{{~~~xxxrrrllljjjpppxxx~~~~~~}}}xxxqqqeeehhhmmmpppqqquuukkk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lll{{{kkkooovvvkkk\\\III;;;555444333222000000////////////000000.........---------,,,,,,(((((())))))*********+++))))))))))))************))))))***+++,,,,,,------))))))))))))(((((((((((((((((((((((())))))))))))&&&'''''''''(((((())))))&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''((('''&&&%%%%%%&&&'''(((&&&&&&&&&''''''(((((((((''''''''''''''''''''''''&&&&&&''''''((()))))))))(((&&&""" !!!$$$%%%%%%%%%%%%&&&&&&'''''''''))))))((('''&&&&&&&&&&&&"""######$$$%%%&&&''''''"""###$$$%%%&&&&&&'''(((%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$&&&&&&$$$"""%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''))))))((('''&&&%%%%%%&&&&&&'''((())))))&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%'''&&&%%%%%%&&&(((''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%'''%%%"""!!!!!!%%%)))+++$$$%%%''')))))))))))))))&&&&&&&&&&&&'''''''''(((*********)))))))))))))))''')))******+++,,,...111000---///333333000555===LLLaaa{{{yyyqqqkkkkkkttt~~~zzztttqqqkkkdddiiippp{{{{{{www|||eeeRRRHHH@@@???>>>===<<<;;;;;;;;;666555444444666777777666222222222111222222333333333333333444444444555555222222222222222222222222000000000000000000000000222222222222222222222222222222222222222222222222111111222222333333333333222222111111111111222222111111222222333333333333222222222222222222222222333333333444444444555555444444444555555555666666222333444555666666666666555555444333444555666777555555555555555555555555555555555555666666666777555666666777888999999999<<<===>>>@@@CCCFFFHHHIIINNNUUU___iiiwwwzzzoooooowww~~~eeeOOOGGG<<<444111222222222111111000////////////000......---------,,,,,,,,,************))))))))))))+++******)))(((''''''&&&))))))*********+++++++++************)))(((&&&&&&((((((((((((((((((((((((%%%(((+++***&&&$$$'''***''''''''''''''''''''''''&&&&&&&&&''''''''''''(((%%%%%%&&&''''''(((((()))%%%&&&'''(((((('''&&&%%%%%%%%%'''((((((((('''&&&(((((('''''''''(((((())))))(((&&&%%%$$$%%%%%%&&&(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))'''&&&$$$$$$%%%&&&'''%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$"""$$$&&&&&&%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&$$$###%%%)))***)))(((&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$''')))***)))'''&&&&&&'''&&&%%%%%%%%%%%%&&&''''''(((((((((((())))))))))))+++*********))))))((((((&&&''')))+++,,,,,,,,,,,,******+++++++++,,,,,,,,,,,,,,,---///000222333333DDDFFFSSSooo|||||||||}}}uuuuuuvvvzzzsssllliiiiiikkktttppphhhcccgggpppyyy}}}tttcccUUUUUUPPPIIIFFFEEEBBB===;;;;;;;;;;;;999777555444666444222000000000111111444444333333444333111///333333333333333333333444555555555555555555555555222222222222222222222222222222222222222222222222222222222222222222222222111111111111111111111111000111111111111222222222444444444444444444444444333333333444444444555555666666666555555444444444666555555444444444555555888777666666555555555555555444333444666777777666333555888888666444333333555666777777666666888:::@@@CCCFFFIIIMMMRRRWWWZZZ```fffqqq~~~ttttttttt{{{kkkWWWCCC===666333444444000---000///...---,,,---............---------,,,,,,,,,************))))))))))))******))))))((((((''''''))))))*********+++++++++************)))((('''&&&''''''''''''''''''''''''$$$'''***(((%%%$$$&&&)))''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&'''''''''&&&&&&'''(((((('''&&&&&&%%%&&&'''((((((((('''&&&((('''''''''''''''((((((((('''&&&%%%%%%%%%&&&&&&((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$###%%%''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%###"""###&&&'''&&&%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%%%%%%%%%%%%%&&&'''((((((&&&%%%%%%&&&&&&%%%%%%%%%%%%&&&'''''''''((((((((()))))))))))))))))))))(((((((((''''''))))))******++++++***************+++++++++,,,,,,+++,,,---...///111222222444777CCCWWWmmm{{{zzzzzzxxxyyy{{{uuummmiiihhhnnnvvvyyyeee[[[[[[]]]cccjjjnnnuuuttttttpppiiidddbbb]]]XXXKKKGGGAAA<<<;;;:::999999666666666666666666666666444333333333444555444333111111222222222222222333222222222333333333333333222222222222222222222222222222222222222222222222222222222222222222222222111111111111111111111111111111111111222222222222444444444444444444444444333333444444444555555555666555555555444444444444777666666555555555666666888888777666666666666666666666666666666666555444555777999:::999888999999888999:::;;;;;;<<>>???@@@BBBFFFIIIPPP[[[iiirrruuutttuuuwwwxxxzzzvvvuuutttttttttssspppnnnsssvvvtttnnnpppuuuvvvgggUUUEEE<<<666222///...111222111//////......---,,,---------------------,,,,,,,,,,,,************)))))))))((())))))))))))))))))******))))))))))))************)))))))))))))))(((''''''((((((((((((((((((((((((%%%'''((((((&&&%%%'''(((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''&&&%%%$$$$$$######&&&''''''''''''''''''&&&&&&&&&&&&'''''''''''''''(((''''''&&&&&&&&&&&&'''%%%%%%%%%%%%&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''((())))))&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''((()))((('''%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&((('''&&&&&&&&&&&&%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&''''''$$$&&&''''''%%%$$$%%%&&&&&&%%%%%%%%%%%%&&&'''''''''''''''((((((((())))))''''''''''''''''''''''''+++***)))((('''((())))))************++++++++++++)))***+++,,,---.../////////333777999;;;HHHddd~~~{{{rrriiidddeeejjjooorrrzzzzzztttrrrooorrrtttuuutttsssssstttrrrwww~~~}}}jjj```TTTTTTUUUWWWZZZcccwwwuuuhhh___VVVKKKBBB???===:::888666555555555777777777555444444555666333444444444555555555555444444444444444333333333333333333333333333333333000000000000000000000000111111111111111111111111222222222222222222222222111111111222222222333333333333444444444444444444444555555555555666666666555555444444444444444444777666666666666777777888777777666666666777777888555777888999999999::::::;;;<<<======<<<===???AAABBBDDDGGGJJJMMMQQQVVVZZZgggsss{{{uuutttuuuvvvwwwxxxyyyyyy{{{vvvwww{{{~~~}}}vvvjjj\\\OOODDD;;;666222000---...000111000///......---------,,,,,,,,,---------,,,,,,,,,++++++************)))))))))((())))))))))))************))))))))))))))))))))))))((())))))))))))(((((('''))))))))))))))))))))))))((()))))))))((((((((()))''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''&&&%%%$$$######"""'''''''''&&&&&&'''''''''&&&&&&&&&&&&''''''(((((()))((('''&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&'''''''''%%%%%%&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&'''((())))))&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''((()))((('''%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&'''''''''&&&%%%$$$$$$%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&'''''''''$$$&&&((((((&&&%%%&&&'''&&&%%%%%%%%%%%%&&&''''''''''''''''''(((((((((((((((((((((((((((((((((((()))((('''&&&'''((()))***))))))*********+++++++++)))******+++,,,---......---...111222333999IIIYYYnnntttiiibbbccciiinnnqqq|||{{{yyyvvvttttttqqqsssuuuwwwxxx{{{~~~rrrkkkaaabbbdddccc```cccrrryyyhhh[[[QQQMMMGGGBBB>>>===>>>???888999:::888666555777999555555555555555555555555555555555444444333333333333333333333333333333333000000000000000000000000111111111111111111111111222222222222222222222222111222222222222333333333333333333444444444555555555555555666666666777777555555555555555555555555666666555555666777888888777777666777777888999999999;;;<<<<<<;;;;;;===???BBBDDDFFFHHHIIILLLOOORRRRRRVVV]]]dddkkkrrryyy~~~yyyuuuvvvyyy}}}~~~~~~~~~{{{mmm```PPPEEE@@@<<<777333111000///////////////...---------------,,,,,,,,,------,,,,,,,,,+++++++++************))))))))))))***************************)))))))))))))))(((((((((((())))))))))))(((((())))))))))))))))))))))))))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&&&&''''''''''''((((((''''''&&&%%%$$$$$$###((('''&&&&&&&&&&&&'''((('''&&&&&&&&&&&&'''((((((***)))((('''''''''''''''%%%%%%&&&'''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%%%%%%%&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&)))(((%%%$$$###$$$&&&'''%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%'''((((((&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%$$$###""""""###&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&'''''''''$$$&&&(((((('''&&&&&&'''&&&%%%%%%%%%%%%&&&''''''&&&&&&'''''''''(((((((((((((((((((((((()))))))))'''''''''''''''((()))))))))))))))************+++*********+++,,,---------+++***,,,111444555;;;AAAQQQddd}}}zzzjjjaaaccckkkrrruuu~~~xxxoooppptttwww{{{~~~|||}}}}}}~~~xxxqqqnnnpppsssvvvtttnnnkkkuuu|||vvvssspppqqqwwwxxxqqqfffZZZOOOGGGCCCAAA;;;===???===999666777888777777666666555444444444555444444333333222222111333333333333333333333333111111111111111111111111222222222222222222222222333333333333333333333333222222222222333333333333222333333444444555555555666666666666777777777777666666666666666777777777777666666666777888999:::888888888999:::;;;<<<===:::<<<======<<<>>>CCCGGGPPPSSSXXX\\\aaaeeejjjmmmqqqxxx}}}wwwzzz~~~zzzxxx}}}vvvmmm[[[NNN???888777777333///000000000//////.........,,,------------,,,++++++,,,,,,,,,,,,++++++++++++************)))))))))))),,,++++++******)))))))))******))))))(((((((((((((((((())))))))))))(((((('''''''''''''''''''''''')))((((((((()))))))))(((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((((('''''''''&&&&&&%%%%%%((('''&&&&&&&&&&&&'''((('''&&&&&&%%%&&&'''((()))++++++***((((((''''''(((%%%&&&'''''''''&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&###%%%''''''&&&%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&"""$$$%%%$$$"""!!!###$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$''''''''''''&&&&&&&&&&&&###$$$&&&&&&&&&%%%&&&'''&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&'''''''''((((((&&&&&&'''''''''(((((((((''''''((((((((('''&&&&&&))))))))))))******************++++++,,,------------+++,,,222444333444777>>>MMMaaatttzzzpppoootttyyyvvvqqqooovvv~~~|||sssooonnnnnnuuu{{{wwwfffaaa^^^^^^^^^^^^fffooo}}}}}}ooocccZZZUUUUUUXXXXXXSSSJJJBBB>>>>>><<<<<<;;;:::888777666555666666555444444333222222444444444444444444444444222222222222222222222222333333333333333333333333333333333333333333333333222222222333333333444444222222333333444555555666666666777777777888888888666777777777888888888999999888888999:::;;;<<<<<<;;;;;;;;;<<<===???@@@AAA@@@CCCFFFIIILLLSSS]]]fffssswww}}}yyyzzzzzz~~~vvvqqqpppuuu{{{vvveeeWWWHHHAAA888333333222000...---...//////............,,,,,,---------,,,+++***,,,,,,,,,++++++++++++***************)))))))))))),,,,,,,,,+++***)))((((((******))))))((((((((('''(((((()))))))))))))))(((&&&&&&&&&&&&&&&&&&&&&&&&((('''''''''((()))((('''''''''''''''''''''''''''&&&&&&&&&'''''''''(((((((((''''''''''''&&&&&&&&&((('''&&&%%%%%%&&&'''(((''''''&&&%%%&&&'''((())),,,,,,***)))((((((((((((&&&&&&'''((('''&&&$$$###$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''((((((&&&$$$###%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&"""$$$&&&&&&%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&###%%%'''&&&$$$###%%%'''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$((((((((('''&&&&&&&&&%%%!!!###%%%%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&'''''''''((((((%%%%%%%%%&&&&&&'''''''''((()))))))))(((&&&$$$"""))))))))))))************+++++++++,,,,,,------......++++++......,,,---000///:::HHHWWWmmm~~~~~~yyyxxx|||rrrkkkkkknnnpppttt}}}rrrcccUUURRRRRRUUUTTTTTTZZZdddrrr}}}{{{|||zzzqqqbbbTTTLLLJJJBBBBBB@@@???===;;;:::999999999888777666666555555444444444444444444444444222222222222222222222222444444444444444444444444333333333333333333333333222222333333333444444444222222333333444555666666777777777777888888888888777777888888999999999::::::::::::;;;<<<===>>>???>>>>>>>>>???@@@BBBCCCDDDKKKPPPWWW]]]eeeqqqxxx~~~{{{zzzzzz~~~kkkdddeeekkkuuu{{{hhhSSSBBB;;;999777444111000///000)))+++---............///,,,,,,---...---,,,+++***,,,,,,,,,+++++++++******'''''''''''''''((())))))'''(((***+++***)))***+++))))))((('''''''''''''''%%%&&&&&&'''((()))******''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%%%%%%%&&&'''%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''(((''''''&&&&&&''''''(((###%%%&&&&&&%%%%%%'''(((''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$#########$$$((('''%%%$$$###$$$$$$%%%'''&&&%%%%%%$$$$$$$$$$$$))))))))))))((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&%%%$$$$$$&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&%%%%%%$$$###""""""%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&'''((((((((('''&&&$$$######$$$&&&'''(((((((((((())))))))))))((((((''''''''''''((((((&&&(((***,,,---,,,++++++000///...---------------444444777@@@MMM```yyy}}}uuulllhhhggghhhooovvvjjjZZZSSSMMMHHHIIIJJJMMMTTT[[[hhhyyyzzzmmmbbb___\\\XXXUUUMMMEEEBBBEEE@@@??????@@@???;;;888888;;;555333666888555333222333333333333444444555666333444444333111111333666777333000000222444444222333333444555555333222111222444666555333333666999555666777888::::::;;;;;;===;;;999:::<<<>>>>>>>>>@@@???>>>@@@CCCFFFGGGGGGHHHJJJKKKKKKKKKOOOUUUZZZaaagggrrr~~~ssslllpppnnn```aaahhhnnnzzz{{{eeeOOOAAA:::444333222111000...------------------------------///...,,,***))))))******+++++++++*********))))))(((''''''''''''((())))))%%%'''))))))((('''((()))***)))((((((''''''((((((&&&&&&''''''(((((())))))((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&'''%%%&&&&&&''''''&&&&&&%%%((((((((((((((((((((((((&&&%%%%%%$$$$$$%%%%%%&&&$$$&&&'''&&&%%%%%%&&&'''''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''((((((((((((((((((&&&%%%$$$$$$######$$$$$$&&&&&&%%%$$$$$$$$$%%%%%%'''&&&%%%%%%$$$$$$$$$%%%(((((((((((('''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&%%%######$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$''''''&&&&&&%%%$$$$$$###%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&''''''''''''((('''&&&%%%%%%%%%&&&''''''((((((((())))))))))))))))))(((((((((((())))))))))))))))))***+++,,,,,,///......------------...333111333888???KKK^^^nnnzzzrrrlllhhhfffiiippp|||qqqbbbTTTNNNJJJJJJKKKLLLRRRYYYfffvvv{{{ssshhhaaaaaaXXXWWWWWWUUUPPPJJJDDDAAACCC===999:::<<<999777777666555555444444555666777888999888666444333444666666444333555777999777555333444555777777777777666666888:::999888777999;;;999999999;;;<<>>===>>>;;;:::888888777888999:::;;;;;;:::888777666555555444444555777999:::888777666666888999:::;;;;;;;;;;;;===????????????@@@AAABBBAAABBBDDDHHHMMMRRRUUUTTTUUUUUURRROOOPPPSSSWWW[[[cccnnnxxxyyyyyyrrrrrrpppqqqxxxrrr___LLL>>>777333222111000000000////////////------------------------++++++******++++++,,,---+++++++++***************((((((((('''((())))))***(((***,,,+++***)))***++++++******)))))))))))))))((((((((((((((('''''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%(((((((((((((((((((((((((((''''''&&&&&&''''''(((&&&'''((('''%%%$$$$$$&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$############%%%%%%$$$$$$###$$$$$$%%%"""###%%%&&&'''&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$!!! !!!###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%'''''''''&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''&&&'''''''''((((((((())))))))))))(((((((((((())))))+++***)))(((((()))******,,,+++++++++,,,---......,,,+++---111222222777===JJJZZZqqqxxxwww{{{zzzqqqkkkiiijjjlllnnnooopppppppppmmmpppvvv{{{xxxooogggaaa]]]]]]]]]]]]```fffnnnzzz|||sssjjjeeecccccciiiqqq|||ooocccXXXRRRNNNJJJHHHIIIFFFEEEEEEDDDDDDFFFGGGHHHDDDBBB@@@??????===999777999888888888:::;;;<<<======>>>???AAACCCDDDEEEEEEEEEGGGJJJLLLNNNOOOPPPQQQUUUUUUWWW\\\ccckkksssxxxyyyzzzyyytttnnnmmmqqqvvvzzzqqqpppqqqqqqzzzrrr{{{{{{dddWWWEEE999444333333333////////////////////////------------------------+++++++++++++++++++++,,,************************((((((((((((((()))******)))+++,,,,,,***)))***++++++******)))))))))))))))((((((((((((((('''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&''''''(((&&&'''((('''%%%$$$$$$&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&((('''''''''&&&&&&%%%%%%%%%$$$$$$###$$$$$$%%%%%%"""###%%%&&&'''&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$###########################$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$!!! !!!###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%''''''&&&&&&%%%%%%%%%$$$###$$$%%%&&&&&&&&&&&&&&&''''''''''''(((((((((((('''''''''&&&&&&'''''''''((()))***+++***)))((('''+++++++++++++++,,,---...++++++...333555333444888:::CCCSSShhh}}}xxxooolllpppxxxyyytttrrrnnnjjjhhhgggfffggglllrrryyy}}}}}}|||wwwrrrnnnkkkhhhiiimmmrrruuu{{{vvvoooeee[[[WWWVVVYYYaaaiiivvv~~~vvvmmmgggbbbaaabbb]]]^^^___aaacccdddfffgggddd___ZZZVVVTTTNNNFFF???AAA@@@>>>>>>@@@DDDJJJNNNPPPQQQTTTWWW[[[^^^aaaccc```bbbeeeiiimmmppprrrsssuuuwww{{{wwwkkkaaa```aaaeeerrr{{{yyyxxx~~~vvvfffKKKBBB888333444555333000.............../////////------------------------------,,,,,,+++***))))))************************))))))(((((())))))***+++((()))+++***)))(((((()))******)))(((((((((((()))'''''''''(((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&%%%$$$###%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%'''''''''%%%$$$%%%&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$###$$$$$$######$$$$$$%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$"""!!!###$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&&&&&&&&&&'''''''''((((((((('''&&&&&&%%%%%%&&&&&&'''&&&(((***++++++***((('''++++++*********+++,,,,,,---,,,...333444111111333222555>>>LLL^^^sssrrrkkkhhhgggnnnxxxvvvnnnnnnqqqrrrsssqqqnnnkkkkkkqqqzzzuuuoooooonnnllljjjjjjppp{{{zzzkkk```TTTPPPPPPSSSZZZbbbiiiuuu}}}zzzsssiiiZZZOOOGGGGGGHHHJJJOOOYYYdddllltttvvvyyy}}}uuucccZZZUUUXXX\\\aaaoooyyywwwyyy~~~wwwwwwxxxzzz~~~ooo]]]OOO>>>999444333555444000,,,---------...............---------------------------------,,,+++***((((((***************+++++++++))))))(((((())))))***+++(((***++++++)))(((((((((***)))((((((''''''((((((&&&&&&''''''(((((())))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&''''''&&&%%%$$$%%%%%%&&&''''''&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$&&&'''&&&%%%%%%&&&'''$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$######"""!!!!!! $$$$$$######$$$$$$%%%&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&'''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&%%%######$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&((()))&&&&&&&&&'''''''''((((((''''''&&&&&&&&&&&&''''''''''''((())))))*********,,,++++++************+++,,,***+++000111///...///000000555===EEESSSiii}}}zzzmmmjjjiiihhhnnnxxx{{{vvvpppmmmooouuuzzz~~~|||rrrnnnppppppmmmlllmmmvvvsssgggYYYSSSQQQRRRXXX^^^^^^jjjzzzxxxuuuvvvrrrssswww~~~pppaaaRRRVVV]]]fffqqqvvvnnnmmmmmmooo{{{kkk\\\YYY]]]iiiqqqvvv}}}~~~}}}nnnpppttt|||kkkTTTEEE@@@999666333222222222000---......------------------------------------------+++,,,,,,---,,,+++***)))))))))*********+++++++++)))))))))))))))******++++++,,,------+++*********))))))((('''''''''''''''%%%&&&&&&'''((()))******))))))))))))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&((())))))(((&&&%%%%%%%%%&&&''''''&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''(((''''''&&&&&&''''''((($$$%%%&&&&&&%%%%%%'''((($$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%''''''&&&&&&%%%$$$######$$$#########$$$%%%%%%&&&((('''%%%$$$###$$$$$$%%%$$$$$$$$$$$$%%%%%%&&&'''%%%%%%&&&''''''&&&&&&&&&''''''''''''''''''''''''$$$$$$%%%%%%%%%&&&&&&&&&###$$$$$$%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&%%%$$$$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&'''&&&%%%$$$%%%''')))+++&&&&&&&&&'''''''''((((((((((((''''''''''''((((((((('''&&&&&&''')))+++---,,,,,,+++***)))))))))******'''(((---///......000000111444777777;;;KKK]]]zzz|||pppooonnnkkkoooxxxqqqpppoooppptttzzz|||uuutttvvvtttooopppqqqzzzrrrcccZZZVVVVVVYYY]]]ZZZdddqqq{{{nnnddd[[[YYY\\\hhhllluuu~~~}}}nnnccckkkwwwoooeee\\\XXX^^^bbbeeerrrmmmiiikkkwwwooopppqqqxxxoooYYYBBB888:::777444111//////000111222......---------,,,,,,,,,------------------------)))***+++,,,---,,,++++++))))))******++++++++++++,,,,,,,,,++++++*********))))))))))))))))))))))))))))))))))))))))))))))))))))))((('''&&&%%%%%%%%%$$$%%%&&&'''''''''&&&%%%%%%%%%%%%&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&((('''%%%$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$######&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''%%%%%%%%%%%%%%%&&&(((((('''%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((((((((('''&&&&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%&&&'''(((%%%%%%%%%&&&'''((())))))(((((((((((())))))))))))))))))))))))***************++++++,,,,,,------...///111444777999;;;>>>AAAZZZfffzzz}}}tttqqqrrrvvvxxx{{{uuullloooqqqqqqssszzzzzzzzz|||zzzxxxxxxxxxtttvvvvvvjjjbbbbbbeeeffffffbbbiiittt}}}lll```YYYSSSSSSUUU\\\gggttt|||xxxmmm}}}mmm```WWWWWWVVVUUUZZZeeetttzzzrrr|||~~~}}}qqqooouuu|||~~~dddOOOCCC===888444111000000///...---------.........------,,,,,,,,,------,,,,,,,,,,,,++++++++++++++++++++++++++++++))))))))))))))))))))))))++++++***************)))))))))))))))))))))))))))***+++---......---+++***))))))(((&&&&&&%%%%%%&&&&&&''''''''''''&&&$$$###%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&''''''&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!"""###############%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%!!!###%%%'''((()))))))))&&&%%%$$$%%%'''''''''%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%%%%%%%&&&''''''''''''&&&&&&''''''((((((&&&&&&''''''((()))))))))&&&''''''''''''((((((((((((((()))))))))*********))))))******+++,,,,,,------///111333333444777999DDDMMM[[[mmm~~~zzzuuurrrtttwwwxxxzzzvvvwwwqqqooorrrvvvvvvvvvxxxyyywwwyyyxxxqqqooosssyyy||||||rrrcccYYYRRRNNNNNNQQQWWW^^^hhhrrr}}}|||wwwvvvvvv{{{}}}}}}vvvaaaVVVQQQRRRTTTXXXaaappp~~~tttllleeegggooo{{{vvvfffQQQAAA999666333111000000000///...---------......---------,,,,,,,,,------,,,,,,,,,+++++++++++++++++++++++++++++++++)))))))))))))))))))))))))))))))))))))))*********)))))))))))))))))))))))))))+++...000000...+++))))))((('''&&&&&&&&&&&&&&&((((((((('''&&&%%%###"""%%%%%%%%%&&&&&&&&&&&&'''(((''''''&&&&&&''''''(((&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%'''((()))))))))&&&%%%###$$$%%%''''''&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%%%%%%%&&&''''''((((((((((((((('''''''''(((((((((((((((((())))))%%%%%%&&&&&&&&&'''''''''(((((())))))))))))******(((((())))))***+++++++++---...////////////000222555:::AAALLLZZZmmm|||tttiiifffbbbbbbggglllnnnqqquuu}}}~~~zzzuuurrrrrrvvvwwwhhh^^^VVVPPPPPPRRRTTTVVV\\\eeessspppgggeeeddd```fffppp{{{{{{mmmkkkiiijjjjjjppp}}}rrr```WWWVVVZZZbbbkkkyyyxxxwwwvvvzzzqqqhhhdddbbbgggppp}}}qqqVVVKKK>>>555222333222000000000//////...---------------------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++))))))))))))))))))))))))((()))))))))******++++++(((((((((((((((((((((((('''(((***,,,,,,***(((''')))((('''&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''&&&&&&'''%%%######%%%''''''&&&$$$$$$$$$%%%%%%%%%&&&&&&#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%%%%%%%&&&''''''((((((((((((''''''&&&&&&((((((((((((''''''''''''%%%&&&&&&&&&&&&'''''''''(((((((((((()))))))))***(((((())))))***++++++,,,---///000///......///000222444666999AAAQQQeeettt~~~tttkkkeeeccc___^^^aaabbbdddiiiooo~~~tttllllllkkkmmmtttyyymmmbbbYYYWWWZZZZZZ\\\___dddnnnyyyfff\\\[[[]]]XXX^^^iiiuuu|||zzz{{{|||oooiii[[[[[[]]]^^^aaaiii}}}|||mmmggghhhppp|||wwwpppwwwyyy{{{zzzzzzmmmiiiiiijjjooouuuqqq^^^MMMDDD===555222333444444222/////////......---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++***************************)))))))))))))))))))))))))))******++++++,,,,,,,,,((((((((((((((((((((((((((((((''''''''''''(((((((((((('''&&&&&&&&&&&&'''%%%%%%%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%((((((''''''&&&&&&&&&&&&'''%%%$$$%%%&&&((('''&&&$$$$$$$$$%%%%%%%%%&&&&&&#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$#########$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''(((((('''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%%%%%%%&&&'''''''''''''''''''''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''''''''((((((((('''(((((((((((()))))))))))))))******+++,,,,,,,,,+++---...///......000111...000222111333;;;GGGQQQkkkwwwtttlllhhhhhhppplllhhhfffcccbbbhhhpppwwwlllgggjjjjjjlllrrr|||vvvjjjbbbbbbfffmmmqqquuuxxx}}}iiiZZZTTTUUUXXXZZZbbbmmmxxxxxxllljjjnnnwww}}}tttnnnjjjrrryyy}}}kkk```[[[OOOQQQVVV[[[```nnnyyysssqqqxxxwwwpppkkkooozzzwwwqqqmmmooorrrtttuuuwww~~~uuuggg[[[QQQDDD::::::777333111222333222000............------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++*********************************))))))))))))))))))))))))+++++++++++++++,,,,,,,,,))))))))))))))))))))))))+++)))'''&&&&&&''')))+++(((''''''&&&&&&&&&''''''$$$$$$$$$%%%&&&'''((()))'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%'''(((((('''&&&&&&'''))))))(((&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$###$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%%%%%%%&&&''''''%%%&&&'''''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''(((((((((''''''(((((((((((())))))))))))******+++,,,,,,---)))***,,,,,,,,,---...000+++...111111111444999===LLLYYYnnn}}}xxxxxxyyy}}}rrrkkkjjjmmm~~~|||{{{xxxssspppvvv~~~rrrkkkjjjiiikkknnnssszzzwwwqqqnnnttt{{{zzzbbbVVVSSSTTTUUUZZZccckkksss~~~pppaaaXXXXXX]]]fffkkkooovvv~~~lllggghhhkkkqqqyyy~~~uuuggg```^^^]]]dddlllyyyuuudddZZZWWWQQQUUU\\\eeennn}}}xxxrrrssswww~~~pppaaa```aaahhhuuuyyyssssssuuuyyy}}}{{{wwwrrrmmmhhhZZZKKKAAA>>>;;;666333222000//////...,,,+++------------------------++++++++++++,,,,,,,,,,,,++++++++++++************************************))))))))))))))))))))))))++++++++++++************))))))))))))))))))))))))***)))(((((((((((()))***''''''&&&&&&&&&''''''(((&&&%%%%%%$$$%%%&&&((((((''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''(((((((((((((((######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$%%%''''''&&&'''(((***,,,+++)))&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%%%%%%%&&&''''''$$$%%%'''(((((((((&&&%%%$$$%%%%%%%%%&&&'''''''''%%%%%%&&&&&&&&&''''''''''''''''''((((((((())))))(((((())))))***+++++++++)))+++,,,,,,++++++---...---...///111333444555555999BBBPPP```pppwwwpppooooooqqqwwwrrrrrrwww{{{tttjjjhhhkkklllpppvvv||||||uuuqqqqqquuusssddd```\\\___eeekkkmmmqqq}}}tttcccWWWRRRQQQSSSWWWYYY]]]fffooo{{{lll\\\YYYYYYYYY___hhhmmmyyypppaaaZZZZZZ[[[bbbjjjwww}}}ooojjjiiikkkoooxxx|||zzzzzzwwwvvv~~~xxxjjj\\\aaaiiiuuu}}}xxxkkkaaaRRRNNNEEE;;;666777555222//////.........---,,,+++------------------------******+++++++++,,,,,,,,,++++++++++++************************************))))))))))))))))))))))))++++++******))))))(((((())))))))))))))))))))))))&&&'''((())))))((('''&&&''''''&&&&&&&&&''''''(((((('''&&&%%%$$$%%%&&&''''''''''''&&&&&&%%%%%%%%%'''''''''&&&&&&'''''''''"""###%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$######&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%###""""""######&&&'''))),,,...---)))&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&'''((((((&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&'''((()))%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%%%%%%%&&&''''''$$$&&&((()))***)))((('''%%%%%%&&&&&&'''((())))))$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''((((((((()))''''''(((((()))*********,,,...///...---,,,---...---++++++,,,///000000000111666<<>>>>>;;;555333444000+++//////000000111000000///------------------------*********++++++,,,,,,,,,+++++++++************)))))))))))))))))))))))))))))))))))))))))))))))))))+++***((('''''''''((()))---,,,***(((((()))+++,,,******))))))((((((''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''&&&$$$###''''''''''''&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&'''''''''&&&%%%%%%$$$$$$%%%%%%###$$$$$$%%%%%%$$$$$$###*********((('''%%%###"""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&""""""###$$$%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$''''''''''''&&&%%%$$$$$$%%%%%%%%%$$$$$$$$$######'''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%&&&'''(((((()))((('''%%%$$$$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%$$$######$$$%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''''''''''''''''''''''')))(((&&&%%%%%%&&&((())))))((('''&&&&&&'''((()))'''''''''''''''&&&&&&&&&))))))))))))************************************+++,,,---...////////////000111444888@@@LLLYYYaaa~~~|||qqqhhhdddccceeefffssswwwrrrkkkiiieee___\\\]]]dddiiiuuu}}}|||uuuqqqmmmjjjfffcccfffqqqxxxxxx}}}nnngggaaabbbbbb``````fffqqqzzz}}}oooaaa[[[aaaooozzzuuuqqquuu|||{{{uuuzzzyyy{{{vvv|||kkkVVVGGGAAA666666555444222111111000////////////.....................------,,,,,,,,,+++,,,,,,,,,,,,,,,,,,,,,***************************+++++++++***)))'''&&&(((((()))***++++++,,,,,,******((('''''''''((()))++++++***))))))***+++,,,))))))))))))((((((''''''))))))((((((((('''''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$&&&&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%&&&&&&%%%$$$$$$%%%%%%$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$$$$%%%&&&'''((((((''''''&&&'''''''''&&&&&&''''''''''''''''''(((((()))))))))***************************************+++,,,---------,,,......///000444:::CCCIIIZZZlll~~~wwwoooiiifffdddbbbppp~~~zzztttnnnjjjiiiiiihhhggggggkkkrrrxxx|||yyyxxxtttpppnnnmmmkkkiiigggjjjsss{{{xxx{{{|||uuullloooqqqrrrvvv~~~tttpppxxx~~~tttnnnpppxxxzzz~~~yyyyyyvvv~~~tttbbbQQQCCC===<<<444444333222111000///...////////////.........------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++************************+++++++++***)))((('''''')))))))))******+++++++++***)))((((((''''''((((((&&&&&&&&&''''''(((((())))))))))))(((((((((((('''((((((((((((((('''''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&%%%%%%&&&&&&'''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&'''''''''&&&%%%%%%$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$!!!"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$!!!"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%&&&""""""""""""###$$$%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&########################&&&%%%$$$######$$$%%%&&&'''''''''''''''&&&%%%%%%%%%&&&&&&&&&'''((((((((((((((())))))))))))*********************************++++++,,,,,,,,,++++++/////////......000555888<<>>HHHNNN```kkk|||~~~tttlllhhhhhhjjjlllrrrvvvsssooommmsss~~~wwwiiiaaa^^^aaalllwwwzzz}}}|||oooaaaZZZVVVYYY]]]aaagggooowww}}}yyydddYYYVVVTTTTTTUUU]]]eeeoooxxxqqqfffbbbbbbjjjttttttgggbbbbbbdddmmmzzzsssjjjgggiiipppwww~~~pppVVVJJJ>>>888555111000111/////////////////////////////////...------,,,,,,++++++++++++++++++++++++)))******++++++******)))++++++)))((((((((())))))))))))))))))))))))))))))******))))))(((''''''&&&''''''''''''''''''''''''(((((('''&&&&&&&&&&&&'''((((((((((((((((((((((((&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$######&&&(((&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%'''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############"""$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%&&&''''''&&&%%%$$$######$$$%%%%%%&&&''''''$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%$$$#########$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%'''''''''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$##################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$'''$$$"""###'''(((&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&'''$$$%%%%%%&&&&&&%%%%%%$$$$$$&&&''''''&&&%%%&&&&&&*********))))))))))))((((((((((((((('''''''''''')))))))))))))))******+++)))(((((((((((()))******+++,,,------.........---///000000//////222777;;;AAAKKKZZZiiiuuu}}}}}}wwwpppmmmlllnnnppptttwwwppptttzzzxxxooolllsssccc^^^]]]eeerrr}}}ggg\\\[[[___fffkkksss|||xxxssszzz}}}rrrjjjeeegggkkkuuuzzzzzznnnbbb^^^___dddnnnwwwzzzmmm]]]PPPEEE;;;333222111......///////////////////////////000000///......------,,,++++++++++++++++++++++++)))******++++++******)))******)))((((((((())))))))))))))))))))))))))))))***))))))((((((''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&'''(((((((((((((((((((((((('''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%$$$###$$$&&&((('''&&&&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&###$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%'''(((((('''%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&######$$$%%%%%%%%%%%%$$$&&&%%%%%%$$$$$$#########$$$#########$$$$$$%%%&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######%%%''''''%%%######$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%''''''&&&%%%&&&''')))))))))((((((((((((((((((((((((((((((''''''''')))))))))))))))***++++++)))(((((((((((()))******,,,,,,---------,,,,,,+++///000111111111222555777888;;;@@@GGGPPP[[[gggoootttuuuvvvvvvwwwxxx{{{}}}}}}~~~|||qqqlllllluuuqqqqqqvvvzzzpppqqq{{{|||{{{uuuppppppuuu~~~uuukkkbbb```dddjjjsss||||||iiiZZZNNNCCC;;;:::444000111111///...000........................///......------,,,++++++************************))))))************)))))))))))))))((((((((())))))))))))))))))))))))))))))))))))((((((((('''''''''''''''''''''''''''''''''&&&'''''''''''''''''''''(((((((((((((((((((((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''&&&$$$###$$$&&&'''''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%'''(((((('''%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$"""###$$$$$$%%%%%%%%%$$$%%%%%%%%%%%%$$$######"""############$$$%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###%%%&&&&&&$$$"""#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$##################$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###%%%''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''((((((((((((((()))))))))((()))******+++***))))))))))))***++++++,,,,,,,,,,,,,,,++++++******+++---......///111333666555555555999AAAKKKRRRZZZaaakkkttt}}}}}}|||tttiiiiiimmmxxxxxxooonnnttt|||}}}|||ooohhhcccfffmmmttt~~~vvvkkk\\\NNNEEE>>>999888555111///111222///...///------------------------------,,,++++++******)))************************)))))))))******)))))))))((((((((()))))))))((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''&&&'''(((((()))(((((((((((((((((((((((((((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''%%%$$$$$$%%%''''''''''''&&&&&&&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$$$$$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&'''''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&#########$$$$$$%%%%%%&&&"""############$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%&&&''''''&&&%%%$$$''''''&&&%%%%%%$$$######!!!"""###$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############""""""""""""######$$$$$$$$$%%%%%%%%%#########$$$$$$$$$$$$$$$!!!"""###$$$%%%$$$###############$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$######"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$############$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###%%%&&&'''&&&&&&'''(((%%%&&&&&&&&&&&&&&&'''''''''''''''(((((((((((((((((((((((((((((())))))******))))))))))))***++++++++++++,,,,,,,,,+++******)))+++,,,,,,,,,+++---......000222444444666999;;;???HHHVVVeeerrr{{{sssrrrsssuuuxxxrrrmmmkkknnnttt~~~pppgggeeehhhqqqyyyssslllhhhiiiqqqzzztttcccVVVMMMCCC===888333333555111......000000,,,+++...------------------------,,,++++++******)))((((((************************((())))))******))))))(((''''''((()))))))))((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''')))*********))))))((((((((((((((((((((((((''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%''''''&&&%%%&&&'''''''''''''''&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''$$$#########$$$$$$%%%&&&'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&"""######$$$%%%%%%&&&&&&""""""#########$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!"""###$$$$$$%%%%%%%%%"""###$$$%%%%%%%%%$$$$$$&&&%%%%%%%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$####################################""""""""""""######$$$$$$$$$%%%%%%%%%"""#########$$$$$$$$$$$$"""###$$$%%%$$$$$$$$$%%%"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$"""$$$&&&'''&&&&&&'''(((&&&&&&&&&&&&''''''((((((''''''''''''((((((((()))'''''''''''''''(((((())))))(((((((((((()))******)))***+++++++++++++++***,,,---...---,,,+++---...***---000222222111111222333999CCCLLLWWWfffvvvzzznnniiijjjmmmooossszzzrrrlllmmmssswww~~~zzz|||}}}tttllllllpppuuu}}}wwwxxxvvvwwwvvviii\\\OOOGGGBBB;;;555555222......111///------000///++++++...,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++***)))))))))************************(((((())))))))))))((((((&&&&&&((()))))))))((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''((()))+++++++++***)))(((((((((((((((((((((((((((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%!!!###&&&'''&&&'''((()))(((((('''''''''&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''""""""!!!!!!"""###$$$$$$'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&""""""###$$$%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$$$$######$$$$$$%%%###$$$$$$%%%%%%&&&&&&'''!!!!!!"""$$$$$$%%%%%%%%%!!!"""$$$%%%&&&%%%%%%$$$'''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%""""""######$$$$$$$$$$$$###%%%%%%%%%%%%%%%&&&'''""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%''''''&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''(((((($$$%%%%%%&&&&&&%%%%%%$$$"""$$$&&&'''&&&&&&'''(((&&&'''''''''(((((())))))&&&'''''''''(((((())))))&&&&&&&&&&&&&&&'''(((((('''''''''''''''((())))))))))))***+++++++++++++++***+++,,,,,,++++++---///---------,,,,,,---000333333555888:::@@@MMM^^^jjjqqqzzztttjjjggghhhjjjlllrrrwww{{{qqqqqqvvvyyy~~~xxxxxxzzzuuurrrxxx{{{wwwwww~~~xxxqqqooorrrxxx|||~~~}}}ooo___TTTKKKCCC@@@AAA;;;666444666555000000333///---...000///,,,---111,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,+++******)))))))))))))))))))))))))))(((((())))))))))))((((((%%%&&&((()))))))))((((((((((((((((((((((((((((((&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((())))))))))))((((((+++***)))(((((('''((((((&&&&&&&&&&&&&&&&&&&&&&&&+++(((%%%$$$$$$%%%%%%%%%'''''''''&&&&&&%%%%%%%%%((('''&&&%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''###$$$$$$%%%%%%$$$$$$#########$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%######$$$%%%%%%%%%%%%$$$&&&&&&$$$$$$$$$$$$&&&&&&$$$######""""""######$$$&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%%%%%%%$$$###!!!"""###$$$%%%&&&&&&&&&######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###%%%'''&&&###""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&(((((((((&&&$$$"""&&&&&&&&&&&&&&&&&&&&&&&&(((((())))))))))))((((((***)))(((''''''((()))***''''''(((((())))))******,,,***)))***---...,,,***---------,,,,,,+++++++++,,,,,,,,,---------......000000000333777===DDDGGGQQQYYYccclllrrrzzz}}}tttooommmnnnpppnnnttt}}}~~~~~~~~~|||zzzsssppptttyyy~~~{{{xxxqqqnnnsss|||~~~pppppppppoooooorrrxxx}}}|||wwwnnngggWWWQQQHHHAAA<<<999777666333333333222111000000///---------............///.........------,,,,,,,,,,,,,,,,,,+++++++++************++++++++++++******+++*********))))))((((((((((((''''''''''''(((((())))))))))))))))))))))))(((((((((((((((((((((((((((''''''''''''&&&&&&&&&(((((())))))))))))((((((***))))))(((((((((((()))&&&&&&&&&&&&&&&&&&&&&&&&,,,)))&&&%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&######$$$%%%%%%%%%%%%$$$&&&%%%$$$$$$$$$$$$%%%&&&$$$$$$############$$$$$$&&&&&&''''''''''''&&&&&&######$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%%%%%%%$$$###"""###$$$$$$%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$"""$$$&&&%%%###!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&(((((('''%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&(((((())))))))))))((((((***)))(((''''''((()))***((((((((((((((()))))))))***((('''(((+++,,,+++)))++++++++++++++++++******,,,,,,,,,,,,------------/////////000333777;;;>>>:::@@@GGGNNNTTT^^^iiiqqq~~~|||yyywwwuuuvvvwwwxxxtttxxx~~~sssppprrryyy~~~}}}uuuuuuyyypppnnnqqq{{{uuupppqqqqqqppppppwwwzzzpppfff___XXXOOOHHHFFFBBB<<<888777666666555111111111000///.........000000///...---,,,++++++---------,,,,,,,,,++++++++++++*********))))))))))))******++++++******)))*********)))))))))((((((((((((''''''''''''((((((((((((((((((((((((((((((''''''''''''''''''''''''(((''''''''''''&&&&&&&&&(((((())))))))))))(((((()))(((((((((((())))))***''''''''''''''''''''''''+++)))&&&&&&&&&''''''&&&'''&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&''''''''''''&&&%%%%%%$$$######%%%%%%&&&&&&&&&&&&%%%%%%''''''''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&'''&&&%%%$$$###%%%$$$$$$######$$$$$$%%%$$$######""""""######$$$$$$$$$$$$%%%%%%%%%%%%&&&######$$$%%%%%%%%%%%%$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&((())))))(((&&&%%%######$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$"""!!!!!!"""$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((())))))((((((''')))((((((''''''(((((()))))))))((((((((((((((((((((('''&&&''')))***)))(((((()))***+++++++++***)))++++++,,,,,,,,,---------............///111222333000222555888<<>>;;;888666333222222333333222//////......---,,,,,,,,,000///......,,,,,,+++***,,,,,,,,,+++++++++++++++******)))))))))((((((((()))******++++++******)))******))))))))))))((((((((((((''''''''''''((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&(((''''''''''''&&&&&&&&&(((((())))))))))))(((((((((((('''(((((()))******((((((((((((((((((((((((***(((&&&%%%&&&'''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%''''''''''''&&&%%%######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""$$$&&&&&&%%%$$$###%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$############$$$$$$!!!!!!"""""""""###############$$$%%%%%%%%%%%%$$$%%%$$$$$$$$$$$$$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%''')))++++++)))'''%%%######$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$############$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$"""!!!!!!"""$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%&&&'''''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&'''(((((((((((((((((('''(((((((((((((((((((((((()))))))))((((((''''''&&&''''''''''''((())))))((('''(((***+++,,,+++***)))++++++++++++,,,,,,,,,,,,,,,------.........------444444444333444999???EEEHHHMMMVVVaaalllvvv}}}vvvnnnjjjiiigggiiiqqq||||||}}}|||vvvqqqooosssyyysssqqqrrrvvvpppnnnvvv|||yyy|||{{{xxxwwwyyyuuuggg___MMMHHHAAA<<<;;;;;;::::::555333222111111111///......---------,,,,,,,,,++++++,,,,,,,,,,,,---------++++++************************)))))))))((((((((())))))************))))))))))))))))))))))))((((((((((((''''''''''''((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&(((''''''''''''&&&&&&&&&(((((())))))))))))(((((((((((('''(((((()))******(((((((((((((((((((((((('''&&&$$$$$$%%%&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''((($$$$$$$$$%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&%%%%%%###""""""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!$$$%%%%%%%%%$$$&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%!!!!!!"""""""""###############$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%''')))++++++)))'''%%%######$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$############$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''''''''((((((((((((''''''''''''((((((((((((''''''))))))((((((''''''&&&&&&(((((())))))))))))******((()))***,,,,,,,,,++++++*********+++++++++,,,,,,+++,,,---/////////......000000111000000111333555777;;;AAAJJJTTT^^^fffjjjwww~~~~~~sssjjjeeeccccccbbbeeemmmvvv~~~{{{zzzyyyyyyvvvtttsssuuuyyyxxxrrrpppqqq{{{zzzssspppmmmmmmpppvvv{{{~~~rrrdddXXXMMMEEE>>>;;;777555333222111000444222111111111111///---......------------,,,,,,++++++++++++,,,,,,,,,---************************++++++*********))))))))))))))))))******)))))))))(((((((((((((((((())))))((((((''''''''''''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((''''''''''''&&&&&&&&&(((((())))))))))))(((((()))(((((((((((())))))***''''''''''''''''''''''''%%%$$$###$$$%%%%%%$$$###%%%%%%%%%&&&&&&&&&&&&'''&&&&&&%%%%%%%%%&&&''''''######$$$%%%%%%&&&''''''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$###""""""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&#########$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$ ###$$$%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$%%%%%%%%%%%%&&&######$$$%%%%%%%%%%%%$$$######$$$$$$$$$$$$######%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&((())))))(((&&&%%%######$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%###$$$$$$%%%%%%%%%$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$%%%'''(((&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&&&&'''(((((('''&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&'''''''''&&&''''''((((((''''''&&&&&&''''''((((((''''''&&&((((((''''''''''''''''''(((***++++++))))))+++,,,*********++++++++++++,,,))))))*********++++++++++++,,,---...////////////)))***,,,...////////////333444666999>>>DDDIIILLL^^^gggsss}}}vvvooojjjgggeeedddgggnnnwww~~~zzzyyy|||xxxuuuvvv~~~vvvnnnkkkkkklllnnnsssyyy~~~yyynnn```SSSJJJCCC===999555555555444333222111000///...---...000111000///.........---------------...---,,,,,,******)))(((***************+++++++++++++++*********)))))))))((())))))******))))))(((''''''(((((((((((())))))((((((''''''''''''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((''''''''''''&&&&&&&&&(((((())))))))))))((((((***))))))(((((((((((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$%%%&&&&&&%%%$$$%%%%%%%%%&&&&&&&&&''''''''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&"""#########$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&######$$$%%%%%%%%%%%%$$$"""###$$$%%%%%%$$$###"""$$$$$$############$$$$$$&&&&&&''''''''''''&&&&&&######$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%"""###$$$$$$%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###$$$'''(((&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&%%%%%%%%%%%%$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&'''''''''&&&&&&%%%%%%%%%&&&&&&$$$$$$%%%%%%&&&''''''(((&&&''''''((((((''''''&&&&&&&&&'''(((((('''&&&&&&&&&&&&''''''''''''''''''(((***++++++))))))***,,,,,,+++)))(((((()))***+++))))))))))))*********+++***++++++,,,------......++++++,,,...000000000///222222222222444666888999EEELLLVVV```gggooowww|||}}}}}}}}}|||zzzwwwuuusssqqqtttzzz{{{yyyzzz{{{ssspppnnnooorrrwww~~~xxxiii```SSSLLLCCC<<<999888666444222333333333333333444555...---,,,,,,///000000000------------------------------,,,+++***)))((((((*********+++++++++,,,,,,******)))))))))((((((((((((((())))))))))))(((((('''''''''((((((((())))))((((((''''''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''(((''''''''''''&&&&&&&&&(((((())))))))))))((((((+++***)))(((((('''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''(((&&&%%%%%%%%%%%%&&&&&&'''''''''((('''&&&&&&%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$###%%%%%%&&&&&&'''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&""""""######$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$############$$$$$$######$$$$$$$$$%%%%%%%%%######$$$%%%%%%%%%%%%$$$"""###$$$%%%%%%$$$###"""$$$##################$$$&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######$$$%%%&&&!!!"""###$$$%%%&&&&&&&&&######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###&&&'''%%%###$$$$$$$$$$$$$$$$$$$$$$$$"""$$$&&&((((((&&&$$$"""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''%%%%%%%%%%%%&&&'''(((((($$$$$$%%%%%%&&&'''((((((&&&''''''''''''''''''&&&%%%&&&'''(((((('''&&&%%%%%%&&&&&&''''''(((((((((''')))++++++((((((***,,,---+++(((&&&%%%''')))***))))))))))))***************************+++,,,,,,///...------.........---000000111222333444444444222666===BBBHHHPPPZZZaaahhhlllssszzz~~~~~~xxxpppmmmkkknnnuuu|||wwwuuuuuusssuuuyyyuuuiii[[[MMMDDDBBB===888555666777666555666555333000---,,,---...222000...---...000000///,,,,,,,,,,,,,,,,,,,,,,,,)))************+++++++++******++++++,,,,,,,,,,,,)))(((((((((''''''''''''(((((())))))))))))((((((&&&'''''''''(((((())))))((((((''''''''''''((((((''''''''''''''''''''''''(((((((((((((((((((((((((((((('''''''''&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''((((((((()))((('''&&&%%%$$$############$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&''''''((($$$$$$$$$$$$%%%&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$#################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$###""""""$$$&&&'''&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$***)))((('''&&&%%%%%%%%%%%%$$$###"""###$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((((((((''''''((()))******(((((((((((()))***,,,,,,)))************+++++++++)))******++++++,,,------'''%%%%%%'''+++...---+++---......///000111111222111222444777;;;>>>AAACCCMMMQQQXXX```hhhrrrzzzwwwlllfffeeehhhjjjkkkrrrwwwvvvxxxyyysssqqquuuyyy{{{rrrpppjjj```UUUKKKCCC>>>;;;777555444222111111222222222111111000///......---...///000000000...---,,,,,,,,,,,,,,,,,,,,,,,,,,,************************))))))))))))))))))))))))************))))))))))))&&&&&&'''((())))))((((((&&&&&&''''''''''''&&&&&&((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''&&&&&&&&&%%%&&&''''''((((((''''''&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&'''&&&&&&&&&&&&''''''''''''&&&&&&%%%$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%$$$$$$$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######"""$$$&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$############$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%%%%$$$%%%%%%%%%$$$$$$###$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((())))))(((((())))))***+++(((((((((((()))***++++++(((((()))))))))*********)))******++++++,,,,,,---+++***)))***---...---,,,---------......//////000000000111333555888:::;;;<<>>CCCJJJNNNUUU\\\bbbhhhmmmppprrrvvvzzz~~~}}}|||pppooooooppppppsss~~~wwwrrrooorrr}}}|||nnnhhhggghhhgggnnnzzz|||~~~{{{vvvqqqkkkeee```XXXSSSKKKCCC<<<888666666777666444333222222333333000//////.........------/////////......---------,,,+++******+++,,,...///...------,,,+++***))))))************************))))))))))))))))))))))))(((((('''''''''&&&&&&&&&(((((((((((('''&&&%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''((((((''''''((((((((((((''''''&&&'''''''''((((((((()))''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''''''''$$$$$$%%%''')))***+++,,,%%%$$$$$$$$$%%%%%%&&&'''$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$""""""######$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$""""""$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''((()))%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((((((((('''&&&&&&'''''''''((((((''''''''''''''''''((((((((()))))))))******((())))))******+++,,,,,,)))******************+++......------------------,,,,,,,,,,,,,,,---...////////////......000444888777:::???CCCFFFKKKOOORRRYYY]]]ccchhhmmmrrrxxx{{{{{{~~~}}}nnnkkkffffffkkkqqquuu{{{wwwooooooyyy}}}{{{}}}ssskkkfffdddffflllwww}}}uuussstttuuuxxxtttqqqqqqpppooogggccc\\\VVVQQQLLLHHHEEEAAA???<<<888666666666666555444222111000//////000//////////////////..................------------,,,,,,+++***+++,,,...///------,,,+++******))))))))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''&&&&&&&&&&&&''''''(((''''''&&&%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''((())))))&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''(((((()))'''''''''&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&###$$$%%%&&&(((***++++++$$$$$$$$$$$$%%%&&&'''((($$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$""""""######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###############$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###!!!"""$$$&&&'''&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''((()))$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((+++***))))))((()))))))))''''''&&&&&&&&&''''''((((((((()))))))))*********(((((())))))***+++++++++***+++,,,,,,+++***+++---------------------------,,,,,,,,,,,,---...///000------...------...000222222444666888999:::===???@@@CCCHHHMMMRRRXXX___ccckkkpppwww{{{ssslllgggfffnnnwww}}}rrrfffcccfffqqq{{{ooohhhiiimmmttt{{{zzznnnhhhccceeekkksss}}}mmm```ZZZWWWTTTQQQLLLIIIDDD@@@???>>>===<<<555555444444333333222222111111000000///000000000//////000000000//////...------------------------,,,,,,,,,+++,,,,,,------,,,,,,++++++******))))))))))))))))))))))))))))))))))))))))))))))))))))))(((''''''''''''&&&&&&&&&&&&&&&'''''''''&&&&&&%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''(((((((((%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&'''$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&''''''((((((%%%%%%%%%$$$$$$%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$##################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$""" !!!$$$&&&(((((($$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$$$$######$$$############$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%&&&&&&''''''######%%%&&&&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((***)))(((((('''''''''(((%%%%%%%%%%%%&&&'''(((((('''''''''((((((((())))))(((((())))))******++++++***,,,---+++)))'''(((*********++++++,,,,,,------------,,,,,,,,,------...+++---///000//////000222000222444444444444555666444666888:::===BBBHHHLLLTTTYYYaaajjjrrryyy{{{xxxqqqnnnpppxxxxxxiiibbbbbbfffooowwwzzz{{{|||rrrpppqqqvvvuuuwww~~~yyynnnmmmpppvvv{{{xxxnnnddd```bbbhhhsss}}}~~~wwwrrrnnnsss|||~~~eee]]]SSSJJJEEECCCAAA???===;;;999999999999888777222222222222111111000//////000000000000111111111---...///000000///......,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++******+++++++++***************))))))))))))))))))))))))))))))))))))))))))))))))(((((((((''''''''''''&&&%%%%%%&&&'''''''''&&&&&&&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$'''&&&&&&%%%%%%$$$$$$######$$$$$$%%%&&&(((((()))%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%''''''&&&%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&'''((())))))$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############"""#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$''''''%%%%%%%%%%%%''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#################################$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###!!! !!!$$$'''))))))$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$$$$############""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&"""###$$$%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''(((((('''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%&&&'''((()))&&&&&&&&&'''''''''((((((((((((((()))******++++++***+++,,,)))%%%###$$$%%%(((((()))***+++,,,,,,---------,,,++++++***++++++(((+++...//////...///000---///111222111111111222444555555555555888===AAA???CCCIIIPPPWWW]]]aaacccnnnqqqvvvzzzzzzuuusssssstttuuuzzzvvvjjjeeegggjjjqqqwww~~~|||yyykkkdddeeegggnnnlllmmmqqqwwwuuueeebbbccciiipppuuuxxxlllhhhdddeeegggooo}}}zzz|||uuurrrqqqlllbbbZZZJJJFFF@@@<<<::::::::::::777777777777777555222///333333222222222222222222..................------,,,---.../////////...---,,,,,,,,,,,,,,,,,,,,,,,,)))***+++++++++)))((('''***************+++++++++)))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((('''''''''$$$$$$%%%&&&''''''''''''&&&''''''''''''''''''&&&((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%&&&&&&&&&''''''''''''''''''''''''$$$$$$%%%%%%&&&'''(((((((((((('''''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%'''''''''&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$###!!! """&&&'''%%%"""!!!"""###%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&%%%$$$###"""%%%$$$$$$######$$$$$$%%%''''''%%%$$$###"""""""""$$$$$$$$$#########""""""$$$"""!!!###&&&'''&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%$$$$$$#################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########%%%$$$$$$######$$$$$$%%%$$$######""""""######$$$######$$$%%%%%%%%%%%%$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$######"""%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$&&&''''''&&&%%%%%%&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$)))((('''&&&%%%$$$######"""######$$$%%%&&&''''''%%%&&&'''&&&$$$######%%%)))))))))))))))******+++)))))))))))))))))))))***************************++++++******++++++,,,---,,,,,,,,,---------.........------------...//////222222333444444555555666999:::<<>>@@@CCCFFFHHHJJJLLLPPPRRRWWW[[[bbbjjjsss}}}|||yyy}}}}}}sssooooooqqqzzzzzz|||{{{uuusssqqqsssuuuzzz~~~}}}{{{{{{~~~jjj^^^]]]\\\WWWQQQNNNIIICCCAAAAAA@@@<<<999888777666444333333333333333333333222222111111111333333222111111000//////////////////////////////------------------------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++))))))))))))))))))))))))************************))))))))))))))))))))))))(((((((((((('''&&&%%%$$$%%%&&&&&&'''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&(((%%%"""$$$''')))&&&###%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&'''''''''''''''''''''&&&&&&&&&&&&''''''(((((((((((('''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$&&&&&&&&&%%%######%%%'''###############$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$######%%%$$$$$$######$$$$$$%%%%%%%%%$$$######$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%$$$'''&&&$$$$$$$$$$$$###!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%######$$$%%%%%%%%%%%%$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$###############"""%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$&&&''''''&&&%%%%%%&&&'''&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''***+++,,,+++)))((()))***))))))(((((())))))***+++*********))))))(((((((((************************+++************+++,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,---------............//////000000111111222222222333444555666777777888888888999<<>>>>>:::777666888888666333444333222222111111222222222222222222222111111111222222111111000000//////////////////////////////------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,))))))))))))))))))))))))++++++++++++++++++++++++))))))))))))))))))))))))(((((((((((('''&&&%%%%%%%%%%%%&&&'''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%(((&&&$$$%%%((()))'''$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$&&&''''''$$$!!!!!!$$$(((%%%$$$###"""###$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$#########$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%$$$&&&%%%$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$############%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''))))))(((((('''''''''&&&''')))***)))''''''((()))((((((((((((((()))***************)))((((((''''''***************************************++++++,,,******+++++++++,,,,,,,,,+++,,,,,,------------------------...//////000000444333333333333444555555555555555444444777;;;???;;;===???BBBEEEJJJOOOSSSWWWXXXZZZ^^^ccchhhllloooqqqpppmmmkkkmmmsss|||}}}tttmmmkkkiiiccc```bbbaaaaaa```^^^[[[XXXUUUSSSKKKGGGAAA===;;;;;;;;;;;;888666555555777777666444111111111000000111222222222222222111111111111111111111000000000/////////////////////////////////,,,,,,------------------++++++++++++++++++++++++++++++++++++++++++++++++))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))''''''(((((('''&&&&&&%%%%%%%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%((('''%%%&&&(((((('''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$&&&&&&&&&&&&$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&### ###&&&%%%$$$#########$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%############$$$%%%&&&&&&############$$$$$$$$$$$$######$$$$$$$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%)))))))))((((((''''''&&&&&&'''((((((&&&&&&'''(((((((((((('''((())))))***))))))))))))((((((''''''))))))))))))))))))))))))******))))))******+++,,,******+++++++++,,,,,,,,,+++,,,---.........------------......///000000000////////////000111222222000111333333222333555666888999::::::;;;<<>>???AAABBBCCCDDDDDDDDDDDDDDDGGGLLLOOOYYY[[[]]]^^^^^^___aaacccbbbcccdddddddddgggjjjmmmqqqqqqsssvvvyyy||||||{{{xxxzzz{{{{{{yyywwwwwwwwwyyyzzz{{{{{{zzz{{{}}}{{{}}}~~~}}}zzzwwwuuutttkkkkkkjjjjjjiiifffbbb___\\\[[[ZZZUUUPPPLLLJJJJJJFFFEEEDDDCCCAAA@@@?????????>>>===<<<;;;:::999888666777777555333111222222111222222222111000///...222111111111111111222222000000000111111111111111////////////............,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,------.........++++++++++++++++++++++++))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((&&&'''''''''''''''&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((((((''''''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""#########$$$$$$$$$$$$$$$#########%%%%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$%%%&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$###$$$$$$%%%%%%#########$$$$$$%%%%%%%%%"""$$$&&&%%%######$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%!!!"""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$############$$$$$$######$$$%%%%%%%%%%%%$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$&&&''''''&&&%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&'''((('''''''''''''''''''''&&&''')))((((((''')))***(((''''''''''''((())))))&&&&&&''''''((())))))))))))))))))))))))))))))))))))))))))))))))***++++++,,,,,,,,,,,,------------,,,---///111111000///...,,,,,,---......//////000111000000000000111111222...000222333222222333333000222444444444555777999666777888::::::;;;;;;;;;:::;;;<<<;;;;;;<<>><<<======<<<;;;;;;<<<<<<::::::999888777666555555666666666555444222222222111222333333222111000000222111000000000000000111///000000000111111111222........................------------------------++++++,,,,,,---......///************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((&&&&&&'''''''''''''''&&&$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&###$$$$$$%%%%%%$$$$$$###%%%%%%%%%&&&&&&'''''''''''''''&&&&&&&&&&&&'''''''''&&&$$$$$$$$$$$$&&&'''######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$$$$$$$%%%###"""$$$((()))&&&######$$$%%%&&&'''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$&&&'''%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$###$$$$$$%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$&&&'''&&&###!!!"""$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!""""""#########$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$##################$$$######$$$%%%%%%%%%%%%$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&&&&'''&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$""""""######$$$$$$$$$$$$&&&'''&&&&&&%%%$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$&&&''''''&&&%%%%%%&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$%%%%%%&&&&&&&&&###$$$$$$%%%&&&(((((()))''''''''''''''''''''''''$$$&&&''''''&&&&&&''')))'''''''''''''''((())))))%%%%%%&&&'''((()))******)))))))))))))))))))))))))))))))))))))))******+++,,,,,,------------......---...000111222111000...+++,,,,,,------......///000//////...---------------...000000///000111333///111222333222222333555111333555777888999888888222444666666666888:::<<<999:::===???@@@BBBCCCDDDCCCCCCBBB@@@@@@AAAEEEHHHEEEEEEFFFHHHJJJJJJHHHFFFIIIIIIIIIIIIIIIIIIHHHHHHCCCFFFJJJLLLKKKJJJIIIIIIHHHGGGFFFFFFHHHHHHFFFDDDCCCAAA@@@AAACCCBBB???<<<<<<>>>???===:::999:::<<<666888888666555777888888222333333444444333222222222111111111222222222111...000222222111000000000111111000/////////////////////000000111111111222---.............................................++++++,,,,,,---...//////************************************************))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&'''''''''''''''&&&$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$%%%&&&%%%$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$%%%&&&'''))))))((('''&&&&&&%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%""""""#########$$$$$$$$$$$$$$$###"""!!!!!!!!!""""""######$$$$$$%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""###$$$$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&'''(((((($$$$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$########################"""###$$$%%%%%%$$$###"""######$$$%%%%%%&&&''''''###$$$%%%%%%$$$###"""!!!"""%%%&&&%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((&&&$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%'''&&&%%%%%%''''''&&&%%%$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&$$$%%%'''((((((((('''&&&''''''(((((())))))******)))************+++++++++)))************+++++++++******))))))))))))******(((---333888:::777222...++++++,,,,,,,,,,,,------///////////////.........000///.........///111222222222222222222222222222666666666666666666555555666555555555555666666777666999<<<<<<:::999;;;===<<<;;;::::::<<<=========???@@@@@@@@@???>>><<<;;;;;;<<<>>>???AAABBBBBBCCC>>>???????????????>>>===>>>>>>>>>AAADDDCCC???;;;:::::::::;;;;;;;;;<<<<<<;;;;;;:::999888777666666888777666444333222111111333333333222222222111111222111000//////000111222000000000000000000000000---------......000111111111111000000//////......000000///...---,,,,,,+++,,,,,,,,,+++++++++*********+++,,,---...---,,,+++*********))))))))))))((())))))))))))))))))))))))((((((((((((''''''''''''(((((((((((((((((((((((((((''''''''''''&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&'''((()))(((((('''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$%%%%%%%%%%%%&&&%%%$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$$$$######"""$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$##################$$$$$$$$$%%%%%%((('''&&&%%%$$$$$$$$$$$$%%%$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########"""$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$%%%%%%$$$############$$$$$$%%%&&&&&&'''###$$$$$$%%%$$$###"""!!! ###&&&'''&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''((('''&&&$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%'''%%%$$$%%%&&&'''&&&$$$%%%&&&'''&&&%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%&&&''''''((('''''''''((((((((((((((()))))))))(((((()))))))))*********))))))*********+++++++++******))))))))))))******))),,,222666777555111...++++++,,,,,,,,,,,,------////////////............000//////...///000111222222222222222222222222222555555555555555555555555666555555555555666777777777999;;;:::777666777888:::999999999:::;;;<<<<<<===>>>>>>>>>>>><<<;;;:::999999:::;;;<<<<<<<<<<<<>>>>>>======<<<;;;:::999888777888;;;>>>>>><<<999888888999999999:::::::::999888888777666555444333777666555333222222222222333333222222222111111111111111000//////000111111000000000000000000000000---------......///000111000000000000//////......000//////......------------------,,,,,,,,,++++++++++++,,,,,,------,,,,,,++++++*********)))))))))))))))))))))))))))))))))++++++*********)))))))))''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&'''((()))((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$######"""$$$%%%%%%&&&&&&%%%%%%$$$''''''&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%$$$###""""""""""""#########$$$$$$$$$'''&&&%%%$$$############%%%%%%$$$$$$###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%&&&&&&$$$$$$$$$%%%$$$$$$###""""""$$$''''''&&&%%%%%%%%%''''''''''''''''''''''''%%%%%%&&&''''''&&&$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%%%%$$$###$$$%%%&&&%%%$$$%%%&&&''''''%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&'''&&&&&&&&&&&&'''(((((())))))(((((((((((((((((('''''''''((((((((()))))))))))))))*********++++++***))))))(((((())))))***))),,,///222333222000...++++++,,,,,,,,,,,,------........................///////////////000111111222222222222222222222222444444444444444444444444555555555555555666777777888999999777555333333444777777777888999::::::;;;;;;<<<<<<===<<<;;;999888777888888888888888777777<<<;;;;;;:::999777666555333333444666999:::999888666666666777777777888888888888777666555444333333555444333333222222333333333222222222222111111111111000000//////000000111000000000000000000000000------......//////000000000000000////////////...///////////////..................---------,,,,,,,,,,,,++++++,,,,,,------,,,+++++++++************))))))))))))))))))))))))(((((('''''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''((('''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$%%%%%%%%%%%%&&&""""""""""""######$$$%%%"""######$$$$$$%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$)))((('''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#####################$$$$$$$$$$$$""""""""""""###$$$%%%&&&%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$######$$$&&&&&&%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$###"""###%%%&&&%%%$$$$$$&&&'''&&&%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&''''''&&&%%%%%%'''((())))))))))))((((((''''''&&&''''''((((((((()))))))))))))))))))))************))))))(((((((((((())))))***+++---///000///......+++++++++,,,,,,,,,------------...............//////////////////000000111111111111111222222222222222333333333333333444444555555444555555666777888888888777666444333333333666777888999999999:::;;;::::::;;;<<<;;;:::999888777888888999999888888777999999999888777666555444555444444555777888888888555555666666666777777777:::999888777666555555444333333222222222222333333222222222222111111111111000000000//////000000000000000000000000000000000---......///////////////////////////////////////......//////////////////------------,,,,,,,,,,,,---,,,+++***+++,,,---...,,,,,,,,,+++++++++******((((((((((((((((((((((((&&&&&&&&&%%%%%%%%%$$$$$$'''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$####################################$$$$$$$$$$$$###"""""""""###$$$%%%%%%"""######$$$$$$%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$)))((('''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%$$$###"""###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&""""""""""""###$$$%%%%%%&&&%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$######$$$$$$%%%###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%%%%"""$$$%%%%%%###"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$###"""###%%%&&&%%%$$$###%%%&&&%%%$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&''''''&&&%%%%%%'''((()))))))))((((((''''''&&&&&&((((((((()))))))))******(((((()))))))))*********))))))(((((((((((())))))***++++++,,,------------+++++++++,,,,,,,,,------,,,---------......//////...//////000000000000000000000000111111222222222222222222222333333444444444444444555555666888888777666555555555666666666666999;;;;;;:::999:::;;;999:::;;;;;;;;;:::999888666777888999999999999999666777777888888888777777777777777777666666666666666666666666777777777888999888888777666555444444222111111111111222333333222222222111111111000000/////////000000/////////////////////////////////---...//////000//////................../////////............////////////,,,,,,,,,,,,++++++++++++---,,,+++***+++,,,---...,,,,,,,,,+++++++++******(((((((((((((((((((((((()))))))))((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$&&&%%%%%%%%%%%%&&&&&&'''&&&&&&%%%$$$$$$######"""$$$%%%%%%&&&&&&%%%%%%$$$''''''&&&%%%$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$!!!$$$&&&$$$"""!!!###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%&&&&&&'''$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%$$$###""""""""""""&&&&&&%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$######$$$$$$%%%######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%######$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$%%%&&&&&&###$$$%%%$$$"""!!!"""$$$########################$$$$$$$$$$$$%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$###"""$$$&&&'''&&&%%%$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&'''&&&&&&&&&&&&'''((((((((((((''''''''''''''''''(((((()))))))))*********((((((((()))))))))******)))((((((''''''(((((()))******+++,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,------,,,,,,,,,---......//////......///000000000000000//////000000111222222222111222222333333444444555444444444555555777888999777555333444666888999999888;;;>>>>>>;;;888999:::888999::::::::::::888888444555666777888888888888555666777888999999999999666777888777555444444444666666777777777888888888666666555444333222111111111111111000111111222222222111111111111000000000...//////000000//////...////////////////////////---...///000000///...------............/////////...............---------,,,,,,+++++++++*********,,,,,,++++++,,,,,,------,,,+++++++++************))))))))))))))))))))))))((((((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$%%%%%%''''''&&&%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$######"""$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$$$$%%%%%%########################$$$$$$%%%%%%&&&''''''((($$$$$$$$$$$$$$$$$$$$$$$$!!!%%%'''&&&"""!!!###&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&###$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%###############'''&&&%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$######$$$$$$%%%"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$############$$$%%%$$$$$$##################%%%$$$$$$$$$$$$%%%&&&'''$$$%%%%%%$$$###"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%$$$###$$$&&&((('''&&&&&&'''((('''&&&&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%&&&''''''((('''''''''&&&&&&'''''''''''''''''''''''''''((((((((())))))(((((((((((()))))))))***((((((''''''''''''((((((******+++,,,,,,,,,++++++++++++,,,,,,,,,,,,------++++++,,,------...//////---...///000111000000////////////000111222222222222222222333444555555555444444444444666777888999777444222222555888888888999===@@@???:::777777999666777888999999888777666666666777888888777777777777777888888999888888888444666999:::777555555666666666666666777777777777666555555444333222111111222111111000000000111111111111111111000000000000......///000000///......////////////////////////---...///000000///...------------.........//////......------,,,,,,++++++------,,,,,,,,,+++++++++++++++,,,,,,------,,,,,,++++++*********)))))))))))))))))))))))))))))))))'''''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''((((((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$############"""######$$$%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$######$$$%%%%%%########################$$$$$$%%%%%%&&&'''(((((($$$$$$$$$$$$$$$$$$$$$$$$"""&&&((('''###"""$$$(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$############$$$%%%&&&''''''&&&%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$$$$$$$$$$$$$%%%"""###$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###""""""###$$$%%%$$$$$$##################%%%%%%$$$###$$$%%%'''(((&&&''''''%%%######$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%'''(((((('''((()))***)))((('''(((***%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&''''''''''''''''''&&&$$$%%%'''((((((((('''&&&%%%&&&&&&''''''(((((((((&&&&&&&&&'''''''''(((((((((((((((((())))))))))))((((((''''''''''''(((((()))***,,,------,,,+++***++++++,,,,,,,,,---------++++++,,,,,,---...//////---...000111111111000///...//////000111222222222222222333444444555666666333333444444666777888999888555111111444777777666999===@@@???999555555777444555666777777666555555::::::::::::999888777666888888999999888777666666333777;;;<<<;;;888888999555555555666666666777777888777666555444333333222222222111000000000000000111111111111000000000000---...///000000///...---////////////////////////---...000111111///...,,,---------.........//////......---,,,++++++******......---------,,,,,,,,,***+++,,,---...---,,,+++*********))))))))))))((())))))))))))))))))))))))+++************)))))))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%''''''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&&&&&&&&&&&&&%%%%%%(((((('''''''''&&&&&&&&&"""###&&&'''(((((('''&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&''''''&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$ !!!"""""""""""""""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%########################$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######"""###$$$%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$&&&&&&%%%$$$$$$%%%&&&&&&$$$$$$######$$$$$$%%%&&&%%%%%%%%%$$$$$$#########"""###$$$%%%&&&'''''''''%%%$$$######%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$######""""""$$$$$$$$$$$$$$$$$$$$$$$$((('''%%%###"""""""""###$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$%%%%%%&&&'''%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%%%%&&&&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''((((((((((((((((((((('''&&&&&&%%%%%%'''((()))((('''&&&''')))(((((()))(((((('''&&&&&&(((((((((((()))))))))))),,,+++***+++,,,,,,+++))),,,,,,,,,,,,,,,,,,,,,,,,...------------...//////////////////000111222333222222222333333333444444222333333444555666777777777777666666666666666777:::999888888777777888888777666555444444444444444777777777777777777666666;;;<<<;;;999666333333444999999999999999999999999444444666666666555444333666555555444444333222222222222111111111111222222111111000///...---,,,,,,000///...---------------////////////////////////......//////...---,,,,,,............////////////......---------,,,,,,,,,,,,++++++******++++++,,,---------,,,,,,+++++++++,,,+++)))(((((()))+++,,,+++*********))))))((((((''''''''''''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$''''''((()))((('''%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%'''(((((('''%%%$$$'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&(((((('''''''''&&&&&&&&&"""$$$&&&'''(((((('''&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&''''''&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$############""""""###$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%########################%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$#########$$$%%%%%%%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###&&&%%%$$$######$$$%%%&&&###############$$$$$$%%%%%%%%%%%%$$$$$$$$$#########$$$$$$%%%&&&&&&&&&&&&%%%$$$######%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$#########"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''''''''((((((((())))))&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$&&&%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((('''''''''(((((((((((((((&&&((()))((('''&&&'''))))))))))))))))))(((''''''(((((((((((()))))))))))),,,+++***+++,,,,,,+++))),,,,,,,,,,,,,,,,,,,,,,,,---------------...//////............///000111222222222222333333333333444222222333444555666777777777777777666666777777777999999888888777777777888888777666555555555555555555555666666666666666666999::::::888666444444555777777777777777777777777444444555555555555444444555555555444333333222222111000000000000000000111///////////////.........//////...---------------////////////////////////...............---,,,,,,............////////////...------------,,,,,,,,,,,,++++++******++++++,,,......---------,,,,,,,,,,,,+++)))(((((()))+++,,,*********)))))))))((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&%%%$$$$$$''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((((('''''''''''''''''''''&&&&&&&&&###$$$&&&'''(((''''''&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%''''''%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&############$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$$$$$$$############$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%$$$$$$$$$$$$###$$$$$$%%%&&&&&&%%%%%%%%%%%%$$$######%%%%%%$$$####################################$$$$$$$$$$$$%%%$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$"""""""""""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%(((((((((((())))))))))))&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$%%%%%%''''''''''''''''''''''''&&&''''''''''''(((((((((&&&''''''((())))))******&&&'''(((((('''&&&'''((())))))*********)))(((((((((((((((((())))))))))))+++******+++,,,,,,+++)))++++++++++++++++++++++++---------------......///,,,,,,,,,---...///111222111111222222222333333333111222333333555555666777777777777777777777888888888888888888777777777777777777666666666666666666444444444555555666666666777888888777555444555666555555555555555555555555444444444333333444444555555555444444333333222222000000////////////000000............//////000000//////...------------...////////////////////////......------------,,,,,,---............/////////------------,,,,,,,,,,,,++++++************++++++.........------------,,,+++***)))(((((()))***+++******))))))))))))(((((('''''''''''''''''''''''''''&&&%%%$$$$$$%%%&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((((((((((((((''''''''''''''''''''''''$$$%%%&&&'''''''''&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%###%%%'''&&&%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&'''&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%########################%%%%%%%%%%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$%%%$$$######%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################"""""""""""""""#################################%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&%%%$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((&&&'''''''''((((((((()))&&&'''((((((&&&&&&'''((((((((())))))))))))((('''(((((((((((())))))))))))***))))))***,,,,,,+++)))************++++++++++++------,,,,,,------...///,,,,,,,,,---...000111222111111111111222222222222111111222333444555666666777777777888888888888888777777777777777666666666666555555555555555666777222333333444444555555666444555666666555444555666444444444444444444444444444333222222222333444555555555444444333222222111000000////////////000000.........//////////////////......---------......////////////////////////------,,,,,,,,,,,,,,,,,,---------.........//////---------,,,,,,,,,++++++++++++************++++++,,,,,,,,,,,,,,,,,,,,,,,,******))))))))))))******))))))))))))))))))((((((''''''''''''''''''''''''%%%$$$"""!!!!!!"""$$$%%%'''&&&$$$######$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&''''''((())))))((((((&&&'''''''''''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''%%%&&&&&&&&&%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&########################$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$%%%$$$######%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%####################################""""""!!!!!!########################%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%&&&&&&&&&&&&%%%############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''&&&&&&%%%%%%%%%&&&'''((('''&&&%%%&&&(((&&&&&&''''''(((''''''&&&(((((((((((())))))))))))))))))(((***,,,,,,+++))))))))))))******+++++++++,,,,,,,,,,,,,,,---......---------...///000222333000000000111111111222222000000111222333444555555555666777888888888888777666666777777777666555444333333333333444444555666222333333333444444555555222444555555444444555666444444444444444444444444333222111111111333444555555444444333222222111111222111111000000111111222111000000///......------......---------......///........................,,,,,,++++++++++++,,,---------------............------,,,,,,,,,++++++++++++******))))))******+++***************************))))))))))))))))))***(((((((((((((((((())))))''''''''''''''''''''''''%%%$$$"""!!!!!!"""$$$%%%&&&%%%$$$######$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&'''(((((((((((((((&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&&&&$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''$$$$$$%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%######%%%%%%%%%%%%######%%%%%%%%%%%%%%%%%%%%%%%%$$$######""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%&&&######$$$%%%%%%$$$######""""""!!!!!!""""""###$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%$$$######%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$$$$%%%$$$$$$$$$$$$%%%%%%%%%%%%###########################$$$$$$$$$###"""!!!!!!########################%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''%%%$$$$$$######$$$$$$%%%$$$%%%&&&'''&&&%%%$$$###$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''''''''&&&&&&%%%$$$$$$###%%%&&&''''''&&&%%%&&&'''%%%%%%&&&'''''''''&&&&&&(((((((((((()))))))))))))))(((((()))+++,,,+++***((((((((()))******++++++,,,,,,,,,,,,,,,------...............///000111111///000000000000111111111///000111111333333444555333555666888888888777777555666777777777666444333222222222222333444555666444444444444444444444444111333444444333333444555444444444444444444444444111111111111222333444444444444333333222222111111222222111111111111222222111111000///...---,,,,,,...------------...//////------------------------,,,+++***)))***+++,,,---,,,------------.........,,,,,,,,,,,,++++++++++++******))))))))))))******((())))))))))))*********))))))))))))))))))))))))''''''(((((((((((())))))'''''''''''''''''''''''''''&&&%%%$$$$$$%%%&&&'''%%%%%%%%%%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%$$$$$$###$$$$$$&&&''''''(((((((((&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&&&&$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$%%%&&&&&&######$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''(((((('''%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######%%%$$$############$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$###$$$%%%&&&&&&%%%$$$######""""""""""""###$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%&&&&&&&&&&&&%%%$$$######%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&########################"""###$$$%%%%%%%%%$$$###########################%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&''''''(((%%%$$$$$$######$$$$$$%%%###$$$%%%''''''&&&%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%&&&'''((()))***&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''%%%%%%&&&'''%%%&&&&&&'''((((((''''''(((((((((((())))))))))))((('''((()))+++,,,+++***''''''(((((()))******+++,,,,,,++++++,,,,,,---...///......------......////////////000000000111111//////000111222333444444222333555777888777666555444555666777777555444222222222222333444555777777666666555555444444333333111222333333222222333444333333333333333333333333///000111222333333333333444444333333222111111111111111000000000000111111000000//////.........------------------...//////,,,,,,,,,,,,,,,,,,,,,,,,+++***)))))))))***,,,---,,,,,,---------.........,,,,,,,,,++++++++++++*********))))))))))))******((()))))))))************(((((())))))))))))(((((('''''''''((((((((())))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&&&&&&&%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''&&&%%%%%%$$$#########$$$%%%&&&''''''''''''&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%"""$$$&&&%%%$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$ !!!!!!"""######$$$$$$######$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&''')))******)))'''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%$$$###"""$$$%%%&&&&&&&&&&&&%%%$$$&&&&&&%%%%%%&&&&&&'''(((#########$$$$$$%%%%%%%%%"""###$$$%%%&&&'''''''''%%%$$$######%%%%%%$$$###########################$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&"""""""""""""""""""""""" !!!###%%%&&&&&&&&&&&&""""""""""""""""""""""""%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''((((((%%%$$$$$$$$$$$$$$$$$$%%%"""###%%%'''''''''%%%$$$%%%%%%&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&((()))+++,,,''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&'''(((((((((%%%&&&''''''%%%%%%&&&'''&&&&&&'''((())))))(((((((((((((((((())))))))))))((('''''')))+++,,,+++***&&&''''''((()))******+++,,,,,,++++++,,,,,,---.........---,,,,,,,,,,,,---////////////000000000000//////000111222333444444111222444666777777666555444555666777777555333222222222333444555666888999777777666555444333333222111222333333222111222333222222222222222222222222...///111222333333222222444444333333222111111000000000////////////000000.........///////////////---------------...///000+++++++++++++++++++++++++++***)))((()))***,,,...,,,,,,,,,---------......,,,,,,,,,+++++++++************))))))))))))******))))))******+++++++++,,,(((((())))))))))))((((((&&&'''''''''(((((())))))''''''''''''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%'''((()))(((''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&"""###%%%&&&&&&%%%###"""#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''&&&%%%%%%$$$######''''''''''''''''''''''''$$$###!!! !!!###$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######"""""""""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''' !!!###&&&'''(((((('''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%""""""""""""###$$$%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########&&&''''''&&&$$$######$$$%%%$$$###"""###$$$%%%&&&"""###%%%'''((((((''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""############$$$$$$$$$######""""""######$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$########################%%%$$$"""!!!!!!###%%%&&&%%%%%%$$$######$$$%%%%%%&&&%%%$$$######$$$%%%&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%$$$$$$#########%%%%%%&&&'''&&&%%%###"""######$$$$$$$$$%%%%%%%%%'''&&&$$$""" """&&&)))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''((('''''''''&&&&&&%%%%%%%%%((('''&&&&&&&&&&&&'''(((''''''&&&&&&&&&&&&'''''')))))))))(((''''''&&&&&&((((((''''''((()))***+++))))))))))))))))))))))))))))))*********+++++++++---,,,,,,,,,,,,---......---...///000000111111111000000//////111444777888444444444444555666777777999888777555555444444444000000000111222333555555333333333222222111111111444333222222111111222222222222222111111111000000111111000000000222333444444333222222111111222222111111111111000000000000////////////............,,,,,,,,,---------.........------,,,,,,------...++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,+++*********))))))(((((())))))))))))))))))))))))&&&&&&''''''(((((())))))))))))((((((''''''&&&&&&''''''((((((((((((''''''''''''&&&&&&&&&&&&''''''&&&&&&''''''&&&$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%$$$######$$$%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%##############################""""""######$$$$$$$$$$$$%%%&&&''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$#########$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$%%%&&&&&&$$$$$$%%%&&&$$$$$$$$$###$$$$$$%%%&&&###$$$%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""############$$$$$$$$$######""""""######$$$%%%&&&&&&%%%%%%%%%$$$$$$$$$########################(((&&&$$$"""!!!!!!""""""%%%%%%$$$######$$$%%%%%%$$$###""""""""""""###$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%$$$$$$$$$######$$$%%%%%%%%%$$$$$$###"""######$$$$$$$$$%%%%%%%%%######""" """%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''((('''''''''&&&&&&&&&%%%''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''((((((((((((''''''''''''((((((((()))))))))))))))))))))))))))))))))))))))******+++++++++,,,,,,,,,---------------...//////---...///000000111111111//////...///000333555777333333333333444555666777666666555444333333222222222222222222222333444555333333333222222222111111444333222222111111222222222222222111111111000000222222111111111222333444222222111000000000000111000000000000000000000000////////////............,,,,,,,,,---------......,,,,,,,,,++++++,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,+++++++++*********))))))))))))))))))))))))'''''''''(((((((((((((((((((((((((((((('''''''''''''''((((((((((((''''''''''''&&&&&&&&&&&&''''''"""###%%%&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$######$$$$$$$$$%%%%%%%%%########################""""""#########$$$$$$$$$((('''&&&&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$########################%%%%%%%%%$$$$$$$$$$$$###"""$$$%%%%%%%%%%%%&&&(((###$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""############$$$$$$$$$######""""""######$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$########################'''&&&$$$"""!!!!!!""""""%%%$$$$$$######$$$$$$%%%$$$$$$############$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%$$$$$$$$$$$$###$$$$$$######""""""############$$$$$$$$$%%%%%%%%%$$$%%%%%%$$$###"""$$$&&&$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&%%%&&&'''(((((('''&&&%%%''''''&&&&&&&&&&&&''''''''''''''''''((((((((((((((())))))******)))''''''))))))))))))))))))))))))+++++++++,,,,,,,,,------......------......///000---...///000000111111111............///111333555222222222222333444555555333333333333222111000000333333222222222333333444333333333222222222222111333333222111111111111222222111111111111000000000333333222111111111222222111111000////////////000////////////////////////////////////............,,,,,,,,,---------......,,,++++++******++++++,,,++++++++++++++++++++++++************************++++++************))))))))))))))))))))))))))))))(((((((((((((((''''''''''''''''''(((((((((((((((''''''((((((((((((''''''''''''&&&&&&&&&&&&''''''"""###$$$&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%''''''&&&%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$#########""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$###$$$&&&%%%%%%$$$&&&'''"""###%%%&&&&&&&&&%%%$$$&&&%%%$$$###"""###$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$######""""""######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$###########################"""""""""###$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%######$$$$$$$$$%%%%%%%%%$$$&&&''''''%%%%%%%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&((())))))(((&&&%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&'''((())))))***&&&''')))++++++***((('''))))))))))))))))))))))))******++++++++++++,,,,,,---,,,,,,,,,,,,---......---...///000000111111111...------......000111222111111111111222333444555222222333333222111000///444333222111111111111111222222222222222222222222333222222111111111111111111111111111000000000000333222222111000000000000111111000////////////000............////////////////////////............,,,,,,,,,---------......,,,,,,++++++++++++,,,,,,++++++++++++++++++++++++************************((((((((('''''''''''''''(((((((((((((((((((((((())))))((((((''''''&&&&&&&&&&&&''''''(((((())))))&&&''''''((((((''''''&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%&&&'''&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&###############$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&%%%%%%$$$######"""###%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%''''''&&&%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$#########""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''&&&$$$###$$$%%%###$$$%%%&&&'''&&&%%%%%%&&&%%%$$$###"""###$$$%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################""""""""""""###$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$&&&&&&######$$$$$$$$$%%%%%%%%%!!!"""$$$$$$###""""""###%%%&&&&&&&&&''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&'''$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&((())))))(((&&&%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%&&&&&&'''((()))******$$$&&&(((***++++++))))))(((((((((((((((((((((((())))))))))))************++++++******++++++,,,------...///000000111111111---------......//////000111111111111222333444444222333333333333222222111333222111000000//////000222222222222222222222222333222111111000000111111000000000000000000000000111111111000000///......222222111000000000000111---........./////////000////////////............,,,,,,,,,---------......------,,,,,,,,,,,,------++++++++++++++++++++++++++++++++++++++++++++++++'''''''''''''''((((((((((((((((((((((((((((((((())))))((((((''''''&&&&&&&&&&&&''''''(((((())))))&&&&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$%%%&&&&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&"""""""""######$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%########################!!!"""###$$$%%%$$$######""""""""""""###$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""###$$$$$$$$$$$$%%%%%%%%%&&&''''''&&&$$$######$$$$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$######""""""######$$$%%%#########$$$$$$$$$$$$$$$########################$$$$$$$$$$$$######""""""###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$$$$############$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%"""$$$&&&&&&$$$###$$$%%%%%%%%%&&&&&&''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&'''(((((('''&&&%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&'''((())))))***%%%&&&((()))*********)))((((((((((((((((((((((((((((((((())))))))))))*********)))))))))***++++++---...///000000111111111........................111111111111222333444444444444333222222333333444333222111000000000000000111222222222222333333333222222111000000000000111//////000000000000000111000000000111000000///...222222111000000000000111.........//////000000111////////////............,,,,,,,,,---------.........------,,,,,,------...++++++++++++++++++++++++++++++++++++++++++++++++))))))************++++++))))))))))))))))))))))))(((((((((((((((''''''''''''''''''(((((((((((((((&&&&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&& """$$$&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%"""""""""###$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%######################## """###%%%%%%$$$###"""###$$$$$$%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$#########$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%%%%##############################$$$$$$$$$%%%%%%%%%$$$&&&&&&&&&$$$$$$$$$&&&%%%%%%%%%%%%%%%&&&''''''###$$$%%%&&&&&&&&&&&&&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$################################################"""############$$$$$$$$$######""""""######$$$%%%"""#########$$$$$$$$$$$$###########################$$$$$$$$$$$$###""""""###$$$%%%%%%%%%%%%$$$###""""""###$$$$$$###""""""######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%######$$$%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&'''((('''&&&&&&'''(((######$$$$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&''''''(((((())))))***)))))))))((((((''''''((((((((((((((((((((((((((())))))))))))************************++++++,,,---...///000000111111111....../////////.........222111111222222333444555555444222000000222444555333333222222222222222333111111222222222333333333222222111000000000000000////////////000000111111000000222222333222111111111111000////////////000......///000000111222222////////////............,,,,,,,,,---------......---,,,,,,,,,,,,,,,,,,---++++++++++++++++++++++++*********************************+++++++++,,,,,,))))))))))))))))))))))))'''''''''(((((((((((((((((((((((((((((('''''''''%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&& !!!###&&&'''(((((('''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$%%%%%%%%%""""""######$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((('''%%%$$$$$$%%%'''((($$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""""""""######$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""$$$%%%''''''&&&%%%$$$&&&&&&''''''&&&%%%###"""&&&&&&&&&&&&&&&&&&&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%""""""""""""###$$$%%%%%%#########$$$$$$%%%%%%&&&#################################$$$$$$%%%%%%%%%"""$$$%%%%%%%%%%%%&&&((('''&&&%%%$$$%%%&&&'''((("""###%%%'''((((((''''''$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$################################################"""############$$$$$$$$$#########"""###$$$$$$%%%""""""######$$$$$$$$$$$$######################## !!!"""###%%%%%%%%%&&&###$$$%%%&&&&&&%%%$$$######$$$%%%&&&&&&%%%$$$#########$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%!!!"""###%%%%%%%%%$$$#########$$$$$$$$$%%%%%%%%%$$$$$$%%%$$$""""""$$$&&&!!!!!!"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&'''''''''((((((((())))))((('''&&&&&&&&&&&&'''(((&&&%%%%%%$$$$$$%%%%%%&&&'''''''''(((((((((((((((...,,,+++)))'''&&&%%%%%%(((((((((((((((((((((((()))************+++++++++++++++******++++++,,,------...///000111111111111/////////000//////...---222222222222333444555666555333111//////111444666555444444333333444444555111111111222222333333333222111111000000000000000.../////////000000111111000111333444555444444333000000///..................//////000111222222333000/////////............,,,,,,,,,---------......,,,++++++++++++++++++,,,++++++++++++++++++++++++))))))))))))))))))))))))(((((())))))*********+++))))))))))))))))))))))))&&&'''''''''(((((())))))))))))(((((('''''''''&&&%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%&&&&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&)))((('''&&&%%%&&&&&&'''###$$$$$$%%%%%%$$$$$$###'''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$(((&&&$$$$$$%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%$$$###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&&&&%%%%%%$$$#########$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$#########$$$ !!!!!!!!! $$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%!!! !!!###%%%$$$###%%%$$$###""""""###$$$%%%########################""""""""""""""""""""""""%%%$$$###""""""###$$$%%%######""""""""""""""""""!!!"""""""""############%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%$$$###"""!!!!!!$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""###%%%&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''))))))************))))))((((((((((((((((((((((((''''''(((((())))))******)))))))))+++,,,...000111---...//////////////////......------------............000111333555666666222111///...///111444666555444222000///000000111444333333222222333333444333222111000/////////000000000000000//////////////////000333666777333000111111000///...------,,,........................///...---,,,,,,,,,,,,,,,------------------------++++++************++++++***++++++++++++***))))))+++*********))))))((((((************))))))))))))))))))))))))))))))))))))&&&&&&'''((()))***++++++'''&&&&&&%%%%%%&&&&&&'''%%%&&&'''(((((('''&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%"""############$$$$$$$$$%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&((('''&&&%%%$$$$$$%%%&&&###$$$$$$%%%%%%$$$$$$###'''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%###""""""$$$%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&&&&&&&%%%$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$######$$$$$$$$$$$$%%%%%%$$$###"""!!!$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$"""!!! !!!$$$%%%$$$###$$$$$$###""""""###$$$$$$########################""""""""""""""""""""""""$$$$$$###""""""###$$$$$$####################################$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$"""!!!!!!$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$###$$$%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''((())))))******))))))(((''''''''''''''''''''''''((((((((((((((()))))))))************+++,,,......---......///////////////......------------......//////000111333444555555111000000///000111333555444333222000000000000111333333222222222222333333222222111000000000000000222222222222111111111111//////000333666666333000111000000000///.................................///......---,,,,,,------------------------------++++++************+++++++++++++++++++++***))))))*********)))))))))((((((*********)))))))))(((((((((((((((((((((((((((((('''''''''((())))))******'''&&&&&&%%%%%%&&&&&&'''%%%&&&'''(((((('''&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&(((((())))))))))))((((((%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$$$$$$$$$$$$$#########""""""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%(((((('''&&&%%%$$$######$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%###$$$$$$%%%%%%$$$$$$###&&&%%%%%%$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$"""!!! !!!###%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$$$$$$$###"""!!!!!!"""$$$%%%$$$###$$$$$$###""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""$$$$$$###""""""###$$$$$$###########################$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%'''%%%$$$$$$$$$$$$###!!!%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''(((((())))))))))))((((((''''''''''''''''''''''''))))))((((((((((((((((((******************+++,,,------...///////////////......------------......000000000111222222333333000000000111111222333333444333222111000000000000222222111111111111222222222111111000000000111111222222222222111111111111//////000222444444222000000000////////////////////////////////////////////////...------------...------------------------++++++************++++++++++++,,,,,,++++++***)))******))))))))))))((((((******))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''&&&&&&''''''''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&''''''((((((''''''&&&$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$%%%############""""""""""""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%###$$$$$$%%%%%%$$$$$$###%%%%%%$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!!!!###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$############"""!!!"""$$$%%%$$$###$$$##################$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""$$$##################$$$############$$$$$$$$$$$$#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$###$$$%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&'''''''''(((((())))))((((((''''''''''''''''''''''''''')))))))))((((((''''''&&&)))((((((((()))***+++,,,,,,,,,---...////////////......------------......000000000111111111111111...///111222333333222222333222222111111000000000111111000000000000111111111111111000000111222222000000000000/////////......///000222333222111000...............////////////////////////////////////......------.........,,,,,,,,,,,,,,,,,,,,,,,,++++++************+++++++++++++++,,,+++******)))))))))))))))))))))((((((***)))))))))(((((((((((((((((((((((((((((((((((())))))(((((((((''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$#################################$$$$$$$$$%%%%%%$$$$$$##################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%#########$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$############$$$$$$#########$$$$$$$$$%%%%%%%%%$$$#########$$$%%%%%%######$$$$$$$$$%%%%%%%%%#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$%%%%%%&&&&&&$$$$$$######$$$$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$###"""###$$$%%%$$$############$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""#########$$$$$$#########""""""#########$$$$$$$$$""""""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$###""""""$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""###%%%'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''''''''((((((((((((''''''''''''''''''''''''''''''))))))((((((''''''&&&&&&&&&&&&'''((()))+++,,,---+++,,,---...////////////......------------......000000000000000000000000...///111333333333222111222222222222111111111000111000000//////000000111111111000000111222333333000000000000/////////......///111111111000000000---------------------...////////////////////////......---------......///,,,,,,,,,,,,,,,,,,,,,,,,++++++************++++++******++++++******)))((((((((((((((((((((()))))))))))))))(((((((((((('''''''''''''''''''''''''''))))))((((((''''''&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&''''''''''''&&&&&&###########################$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&&&&&&&%%%###$$$$$$%%%%%%$$$$$$###$$$############$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$'''%%%#########$$$###!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&######""""""""""""##################$$$$$$$$$$$$$$$$$$###""""""###%%%&&&######$$$$$$$$$%%%%%%%%%############$$$$$$$$$$$$######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&%%%%%%%%%%%%&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%###"""###$$$%%%$$$###"""###$$$$$$$$$$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%"""""""""""""""""""""""""""###$$$$$$$$$$$$###"""!!!!!!!!!"""######$$$$$$!!!!!!"""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$######$$$$$$$$$######"""$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###"""###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""!!!!!!###&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''''''''''''''%%%&&&'''(((***,,,---///***+++,,,---.../////////......------------......////////////000000000000...///111222333333222222111111222222222111111000111111000000000000111111000000000111222333444555222222222222111111111111...///111111/////////000------------------------........................---,,,,,,,,,,,,---......,,,,,,,,,,,,,,,,,,,,,,,,++++++************++++++))))))******))))))((('''''''''(((((((((((())))))))))))((((((((((((''''''''''''''''''''''''''''''(((((((((''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$%%%%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&"""###$$$%%%&&&&&&%%%$$$###$$$$$$%%%%%%$$$$$$##################$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%###!!!!!!#########"""###########################$$$$$$%%%$$$###"""!!!$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%$$$$$$##################$$$############$$$$$$$$$$$$$$$###"""!!!"""###%%%&&&######$$$$$$$$$%%%%%%%%%############$$$$$$$$$$$$"""""""""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''')))(((&&&%%%%%%%%%%%%&&&################################################$$$$$$############$$$$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$$$$%%%%%%%%%$$$######%%%%%%$$$###"""###$$$$$$$$$$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%"""""""""""""""""""""""""""###$$$$$$$$$$$$###""" !!!""""""######""""""#########$$$$$$$$$########################"""#########$$$$$$$$$$$$"""######$$$$$$$$$######$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$############$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###########################""""""###%%%'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''((((((((()))***+++---...******,,,---.../////////......------------...............//////000000000///000000111222222333222000111222222222222111000222111111000000111111222000000000111222333555666222222222222111111111111---///111000...---...000000000000//////......---------------------------+++++++++++++++,,,------++++++++++++++++++++++++++++++************++++++((((((((((((((('''&&&&&&'''''''''((((((((())))))))))))(((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&"""######$$$$$$######"""%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&!!!"""###$$$%%%%%%$$$###$$$$$$$$$%%%%%%$$$$$$$$$######""""""###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""  """#######################################$$$%%%$$$###"""!!!$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""###%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%"""############$$$$$$$$$$$$###"""!!!"""###%%%&&&######$$$$$$$$$%%%%%%%%%"""############$$$$$$$$$!!!!!!""""""#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((('''%%%$$$#########$$$""""""""""""""""""""""""########################$$$$$$############$$$$$$########################""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""###$$$%%%%%%&&&&&&$$$###$$$%%%%%%$$$###"""###$$$%%%%%%$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%"""""""""""""""""""""""""""###$$$%%%%%%$$$###""" !!!""""""#########$$$$$$$$$%%%%%%%%%########################""""""######$$$$$$$$$$$$"""######$$$$$$$$$######$$$$$$############$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%########################%%%$$$######%%%&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''(((((((((***************++++++,,,)))***,,,---.../////////.........------.........------......///000000111000000000111111222333333000000222333333222111000222222111111111111222222000000000111222444555666000000000000////////////---///111000---,,,...000333222222111000//////...,,,,,,,,,,,,,,,,,,,,,,,,************++++++,,,---++++++++++++++++++++++++++++++************++++++'''''''''((('''&&&&&&%%%&&&'''''''''(((((()))))))))((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$%%%'''((($$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%$$$###"""%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$#########$$$$$$&&&&&&&&&&&&$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$"""###$$$$$$%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%""""""###$$$%%%'''((()))%%%###"""###$$$&&&%%%%%%$$$%%%&&&&&&&&&&&&%%%$$$###############"""!!!!!!########################!!!"""###$$$%%%%%%$$$###%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######################################################$$$$$$$$$#########""""""%%%%%%%%%$$$###"""!!!!!!""""""###$$$$$$$$$$$$###'''&&&$$$######$$$&&&'''$$$###"""!!!!!!"""###$$$$$$$$$##########################################&&&%%%$$$###""""""""""""######""""""""""""##############################$$$$$$############$$$$$$######$$$$$$$$$$$$######""""""###""""""!!!  !!!"""$$$$$$$$$###"""######$$$$$$$$$$$$######""""""#########$$$$$$$$$%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%############$$$%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&######$$$%%%%%%&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((((((((((((''''''(((((()))*********,,,---...///000000000000........................111///,,,---///111///...////////////000000000000000111111111111222222222000000000000111111222333222111000111333444333222333333333222222222111111000000////////////000000111000000///...---------......---,,,,,,,,,,,,---+++,,,,,,------,,,,,,+++------,,,,,,,,,,,,++++++))))))))))))))))))))))))''''''(((((())))))******(((((())))))))))))(((((())))))))))))((((((((((((%%%&&&&&&''''''&&&&&&%%%'''$$$""""""%%%''''''%%%%%%%%%&&&&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%$$$###"""%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$######$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%%%%%%%%%%$$$######$$$$$$$$$%%%%%%%%%#########$$$%%%&&&'''(((%%%$$$######%%%&&&&&&%%%""""""""""""""""""""""""###############"""!!!!!!########################!!!"""###$$$%%%$$$$$$###%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######################################################$$$$$$$$$#########""""""%%%$$$$$$$$$###"""""""""""""""###$$$$$$$$$$$$###&&&%%%$$$$$$$$$$$$%%%&&&%%%$$$###""""""###$$$%%%################################################$$$###############$$$$$$$$$$$$############$$$$$$########################$$$$$$############$$$$$$"""######$$$$$$######"""$$$%%%%%%&&&&&&&&&%%%%%% """#########"""!!!######$$$$$$$$$$$$######""""""#########$$$$$$$$$%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%&&&&&&'''((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((((((&&&''''''(((((()))******+++,,,---...////////////...............---------000...,,,---///000///---.../////////000000000000000111111111111222222222111111000111111333555666555333111111222222111000333222222222111111111111......------------......111000000///......------......---,,,,,,,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++*********))))))))))))))))))))))))'''((((((((()))))))))***))))))************))))))))))))))))))((((((((('''&&&''''''((((((''''''&&&(((%%%###$$$&&&((((((''''''&&&&&&&&&%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$%%%%%%%%%$$$######%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&######$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&%%%$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&%%%$$$"""###%%%&&&&&&%%%$$$$$$###""""""###$$$$$$#########$$$######"""!!!########################""""""###$$$$$$$$$$$$###%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######################################################$$$$$$$$$###############$$$$$$##################""""""###$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%################################################""""""""""""###$$$%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%########################$$$$$$############$$$$$$"""######$$$$$$######"""!!!""""""###$$$%%%%%%%%% !!!###$$$$$$###""""""######$$$$$$$$$$$$#####################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((('''%%%&&&&&&'''(((((())))))***+++,,,---------------///.........------,,,,,,///---,,,---...///...,,,....../////////000000000000111111111111222222222111111000111333555888:::999666222000000000///...111111111111000000000000......------------......000000000///......------......---,,,,,,,,,,,,,,,,,,++++++******++++++,,,+++************)))))))))))))))))))))))))))))))))(((((((((((()))))))))))))))******++++++******))))))))))))((((((((('''''''''(((((((((((((((((('''(((&&&%%%%%%'''(((((((((''''''&&&%%%$$$###""""""&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$###%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!"""""""""#########"""#########$$$%%%&&&'''&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&%%%$$$#########$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%$$$"""!!!"""###$$$$$$$$$&&&%%%###""""""###%%%&&&#########$$$$$$######"""####################################$$$#########$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$%%%%%%######$$$$$$$$$$$$#############################################################################################$$$$$$$$$""""""###$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$##############################""""""###$$$$$$%%%$$$$$$$$$######$$$$$$$$$########################$$$$$$############$$$$$$""""""############""""""!!!!!!!!!!!!!!!"""######"""###$$$%%%%%%%%%$$$#########$$$$$$$$$$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$###"""$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$(((''''''&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''%%%%%%&&&&&&'''((((((((())))))***+++,,,,,,++++++///......------,,,,,,+++---------------------,,,........./////////000000000000111111111222222222222111111111444777;;;===999666111///.../////////000000000000000/////////000000////////////000000000000//////...............---,,,,,,++++++,,,,,,,,,+++************+++,,,++++++*********)))))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))************))))))))))))((((((((('''''''''''''''((((((((((((''''''&&&&&&%%%&&&''''''''''''&&&&&&%%%$$$$$$###""""""&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!"""""""""############""""""######%%%&&&'''&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&%%%$$$############$$$$$$$$$%%%%%%%%%%%%%%%$$$#########$$$$$$"""!!! """######"""###"""  """#########$$$$$$$$$$$$##############################$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%######$$$$$$$$$$$$#############################################################################################$$$$$$$$$""""""###$$$$$$$$$$$$######$$$$$$%%%%%%$$$$$$###"""##################"""""""""#########$$$$$$$$$########################%%%$$$$$$###""""""############""""""""""""##############################$$$$$$############$$$$$$"""""""""######"""""""""%%%%%%###"""""""""######""""""###$$$$$$###"""!!!######$$$$$$$$$$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''''''''''''''%%%%%%&&&&&&'''(((((((((((()))******************......------,,,,,,,,,,,,+++,,,......------,,,,,,............////////////000000111111111222222222222111111222444777:::<<<777444000...///000111111////////////////////////000000////////////000000////////////............------,,,++++++++++++,,,,,,++++++++++++++++++,,,,,,+++++++++************))))))))))))))))))))))))))))))))))))((((((((((((''''''((((((((((((''''''((((((((((((''''''''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%&&&%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%######$$$%%%%%%%%%$$$$$$%%%$$$$$$######$$$$$$%%%###$$$$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%%%%&&&$$$###""""""###$$$%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%$$$############$$$$$$$$$%%%%%%%%%%%%$$$$$$#########$$$$$$"""!!! """######"""$$$###"""!!!!!!"""###$$$"""###$$$$$$%%%$$$$$$$$$########################%%%$$$######"""############$$$$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%&&&######$$$$$$$$$$$$#####################################################################$$$$$$$$$$$$$$$##################""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$!!!"""############"""!!!"""""""""###$$$$$$%%%%%%########################&&&%%%$$$###""""""""""""###""""""""""""""""""###########################$$$$$$############$$$$$$!!!""""""######""""""!!!%%%###"""  !!! !!!"""""" ######$$$$$$$$$$$$######$$$$$$$$$##################$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%'''&&&&&&%%%%%%$$$$$$######$$$%%%&&&%%%$$$###"""$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%% !!!###$$$&&&'''(((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&%%%&&&&&&'''(((((())))))((())))))*********)))))),,,,,,,,,,,,,,,,,,------+++---//////...---------------........./////////000111111111111222222222111111222333444555777777444222///...///111111111////////////000000000000......------------......//////////////////......------,,,++++++++++++++++++,,,,,,------,,,,,,+++,,,,,,+++++++++*********))))))))))))))))))))))))))))))))))))((((((((((((&&&''''''((((((''''''&&&((((((((('''''''''&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%"""$$$&&&&&&%%%$$$%%%&&&$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%"""###$$$%%%%%%%%%%%%$$$%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$"""""""""###$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$""""""###$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$###############$$$$$$$$$"""!!!!!!###$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$$$$%%%%%%%%%$$$########################%%%%%%###"""""""""############$$$$$$$$$%%%%%%%%%"""######$$$%%%%%%&&&&&&######$$$$$$$$$$$$######################################################""""""#########$$$$$$$$$%%%$$$$$$$$$###"""""""""""""""###$$$$$$$$$$$$###%%%$$$###""""""###$$$%%%"""###$$$$$$$$$$$$###"""!!!""""""###$$$$$$%%%%%%########################$$$$$$###############$$$$$$######""""""######$$$########################$$$$$$############$$$$$$!!!!!!""""""""""""!!!!!!"""!!! !!!!!!!!!"""###"""!!! ######$$$$$$$$$$$$######$$$$$$$$$#########""""""######$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%''''''&&&%%%%%%$$$######"""###%%%&&&&&&%%%$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&!!!""""""###%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&''''''(((((()))******))))))************))))))+++++++++,,,,,,------...+++...111111///------...---------.........//////000111111111111222222222111111222333333333222222333111//////000111000////////////000000111111111......------------........./////////////////////---,,,++++++***++++++++++++,,,...000000...,,,++++++************)))))))))))))))))))))))))))))))))***)))))))))((((((((('''''''''((((((((((((''''''(((((('''''''''&&&&&&&&&&&&&&&''''''''''''&&&&&&"""%%%'''(((&&&%%%&&&'''&&&&&&&&&&&&%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!""""""###$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%"""######$$$%%%%%%&&&&&&$$$$$$%%%&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%((('''%%%$$$###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$#########$$$$$$%%%%%%%%%"""###$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%#########$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&######$$$$$$$$$%%%%%%%%%&&&%%%###!!!!!!"""$$$%%%$$$$$$&&&''''''&&&$$$$$$ !!!"""#####################$$$$$$$$$%%%%%%%%%######""""""###$$$$$$%%%%%%$$$"""###$$$&&&&&&%%%"""###$$$$$$$$$$$$###""""""###$$$%%%%%%%%%%%%%%%########################&&&%%%###"""""""""###############$$$$$$%%%%%%%%%""""""###$$$%%%%%%&&&&&&######$$$$$$$$$$$$######################################################""""""######$$$$$$$$$$$$&&&%%%%%%$$$###"""!!!!!!""""""###$$$$$$$$$$$$###%%%$$$"""!!!!!!"""$$$%%%###$$$%%%&&&&&&%%%$$$###!!!""""""###$$$$$$%%%%%%########################""""""""""""###$$$%%%&&&%%%$$$$$$$$$$$$$$$$$$%%%########################$$$$$$############$$$$$$!!!!!!""""""""""""!!!!!!$$$###"""!!!"""$$$&&&'''$$$%%%&&&&&&%%%$$$###"""######$$$$$$$$$$$$######$$$$$$$$$$$$######""""""#########$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%''''''&&&%%%%%%$$$######!!!"""$$$&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&######$$$%%%%%%&&&''''''((('''&&&&&&%%%$$$######%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&''''''(((((()))*********)))***************)))))))))***+++,,,------...///+++...222222000------///---------.........//////000111111111111222222222000111333444333111///...333222000000111111///---//////000000111111222222000000////////////000000.........///////////////---,,,++++++******++++++***,,,///111111///,,,***))))))))))))(((((((((((())))))))))))))))))))))))******))))))((((((((('''(((((())))))))))))(((((((((((('''''''''&&&&&&&&&''''''((((((((((((''''''###&&&))))))'''&&&'''((()))(((''''''&&&%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!""""""###$$$$$$%%%%%%#########$$$$$$%%%%%%%%%""""""###$$$%%%%%%&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$&&&''''''&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%'''***++++++(((%%%###&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$######""""""######$$$%%%"""""""""""""""""""""#################################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###"""###$$$%%%%%%%%%$$$$$$'''&&&%%%%%%&&&%%%###""" !!!###$$$$$$###!!! ######$$$$$$$$$%%%%%%%%%########################%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$########################""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""""""""###%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&###!!!!!!###$$$"""%%%%%%$$$###""""""######$$$$$$$$$#########"""""""""############$$$$$$$$$'''&&&$$$""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########""""""""""""""""""""""""########################"""  ###$$$###!!!###""""""%%%((((((%%%!!!((('''%%%$$$###$$$%%%%%%%%%$$$###""""""###$$$%%%$$$#########""""""!!!!!!########################%%%%%%$$$###""""""######################################################!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""############'''&&&&&&%%%$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######%%%%%%%%%$$$$$$"""!!!!!!######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''&&&%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&'''''''''(((((()))(((((('''''''''(((((())))))))))))************+++++++++,,,,,,---------////////////////////////,,,,,,,,,---...///000111111111111111111111222222000000000000////////////...000111000///...///000////////////////////////111000000///...------------------..................------,,,,,,------...++++++,,,---,,,+++***)))************************))))))***++++++++++++***+++***)))(((((('''((((((((((((''''''''''''(((((((((((('''''''''&&&&&&&&&(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$##################$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&((('''&&&&&&''')))$$$$$$############$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$#########%%%&&&((()))(((&&&$$$###%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$###############$$$$$$%%%$$$$$$$$$#############################################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%***'''$$$%%%(((***+++***#########""""""###############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$################################################$$$###"""""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%###!!!"""###$$$""" %%%$$$$$$###""""""######$$$$$$$$$#########"""""""""############$$$$$$$$$&&&%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$############################################################!!! ###$$$"""!!!$$$###"""$$$&&&'''$$$"""'''&&&%%%$$$$$$$$$$$$%%%%%%$$$###""""""###$$$%%%############"""""""""!!!########################%%%$$$$$$###""""""######################################################$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""############&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$##################"""!!! ######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''''''''((((((''''''''''''(((((((((((()))))))))***************+++,,,,,,---..............................------,,,------...///000111000000//////000222222111111000000/////////...///000111000///...///111////////////////////////000000//////...------,,,++++++,,,,,,---............------,,,,,,------...***+++,,,,,,,,,+++))))))************************))))))***++++++++++++******))))))(((((((((((()))((((((''''''''''''(((((((((((('''''''''&&&&&&&&&(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&''''''&&&%%%'''((($$$$$$############$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$######$$$$$$%%%%%%%%%$$$######$$$$$$%%%%%%$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$"""############$$$$$$$$$%%%%%%%%%$$$$$$#######################################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###&&&%%%$$$$$$$$$%%%'''(((...)))######(((,,,---,,,&&&%%%###!!!!!!###%%%&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################""""""""""""""""""""""""######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!"""$$$$$$###"""%%%$$$######"""#########$$$$$$$$$###############"""############$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############################################################"""!!!!!!"""###""" %%%$$$######$$$%%%$$$"""&&&&&&%%%$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%############""""""""""""########################%%%$$$######"""#########################################################%%%%%%%%%%%%%%%%%%%%%%%%"""""""""#########$$$$$$%%%%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$###"""!!! ######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''((('''&&&&&&%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&((('''''''''''''''(((((((((((())))))))))))******))))))***+++---...//////..............................------------......000///...------///111222222222111000000///......///000111111//////000111/////////////////////////////////......------,,,******++++++,,,---............------------......******++++++******)))(((************************))))))***++++++++++++***)))(((((((((((())))))***((((((''''''''''''(((((('''''''''''''''&&&&&&&&&(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$######$$$$$$$$$$$$%%%%%%%%%############$$$$$$%%%%%%###%%%&&&&&&%%%$$$&&&'''$$$$$$############$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$############$$$$$$%%%%%%%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$""""""######$$$$$$$$$$$$%%%$$$$$$######"""""""""##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###'''&&&%%%$$$$$$&&&((()))///)))###"""&&&)))'''$$$&&&%%%$$$######$$$%%%&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###############################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$$$$$$$$$$$$$$$$###############$$$########################""""""#########$$$$$$$$$######$$$$$$$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############################################################$$$######"""""""""!!! %%%$$$###"""############%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%#########"""""""""""""""########################$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$################################################""""""#########$$$$$$$$$$$$$$$######"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######&&&&&&&&&&&&&&&%%%$$$#########$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''''''''&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$%%%%%%%%%&&&&&&''''''&&&&&&&&&'''(((((((((((((((((()))))))))***((()))***+++---...///000........................///...------,,,,,,,,,---///...,,,+++,,,...000222222222111000//////...---///000111111//////000111.................................---------,,,,,,,,,,,,,,,,,,,,,---------......------------......************))))))((((((************************))))))***++++++++++++***(((((('''(((((()))******((((((''''''''''''((((((''''''''''''''''''''''''(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$%%%%%%"""$$$%%%%%%$$$###%%%&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$!!!"""###$$$$$$$$$$$$#########""""""!!!!!!!!! ##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###'''&&&%%%$$$$$$&&&((())))))&&&######&&&'''$$$ ###$$$%%%&&&&&&%%%$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$%%%$$$###############$$$$$$########################""""""#########$$$$$$$$$"""######$$$$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$########################################################################$$$$$$$$$###"""!!!!!!"""$$$$$$######""""""###$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""######""""""""""""""""""""""""$$$###############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%############################################################$$$$$$$$$$$$$$$######"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######%%%%%%&&&&&&&&&%%%$$$$$$######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&'''(((((('''(((((((((((()))))))))((()))***+++---...///000........................///...---,,,,,,,,,,,,,,,---,,,++++++,,,...000111111111000000///......---...///000000///...///000------------------------------------,,,,,,,,,,,,//////......------,,,,,,///......------......///*********)))))))))))))))))))))))))))))))))))))))))))))***++++++++++++***(((((('''(((((()))******((((((''''''''''''((((((&&&'''''''''''''''''''''(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""######$$$$$$$$$"""###%%%$$$######$$$&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''&&&''''''''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$!!!"""###%%%%%%$$$######!!!!!!!!!!!!!!!!!!!!!!!!##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###&&&%%%$$$$$$$$$%%%'''(((######$$$%%%'''((('''%%%!!!###%%%&&&&&&%%%###!!!######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%$$$######$$$%%%#########"""######$$$%%%###############$$$$$$$$$"""############$$$$$$$$$"""""""""###############$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###############$$$$$$$$$$$$$$$$$$$$$$$$########################"""$$$$$$$$$"""!!!"""###!!!"""######""""""###%%%"""###$$$$$$%%%$$$$$$$$$"""######$$$$$$######"""""""""""""""############""""""""""""""""""""""""#########"""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$$$$%%%$$$############$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######"""###############""""""######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''%%%%%%$$$############$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&'''((((((''''''(((((((((((())))))))))))***+++---...//////------------------------......---,,,++++++,,,,,,++++++,,,,,,---...000000//////............---------...//////------...///------------------------,,,,,,,,,,,,,,,,,,,,,,,,000//////......------,,,//////............//////++++++***))))))))))))***))))))))))))))))))))))))))))))***++++++++++++***)))(((((((((((())))))***((((((''''''''''''((((((&&&&&&&&&'''''''''''''''(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###########################"""$$$%%%%%%$$$###%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$!!!"""$$$%%%%%%$$$###""" !!!!!!""""""####################################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%###$$$%%%%%%###$$$&&&)))"""##################"""######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################!!!"""###$$$%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$###%%%&&&%%%###"""###%%%######""""""###$$$$$$%%%""""""#########$$$$$$$$$"""############$$$$$$$$$###"""!!!!!!!!!###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$########################!!!###%%%$$$""""""###%%% ###$$$######$$$%%%!!!"""###$$$%%%$$$$$$###!!!"""############"""!!!!!!"""""""""############""""""""""""""""""""""""######""""""###$$$$$$%%%################################################$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######!!!!!!""""""###""""""!!!######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''&&&&&&%%%$$$$$$$$$$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''''''''%%%%%%%%%%%%&&&'''((()))'''''''''((((((((())))))******+++,,,,,,---......------------------------------,,,,,,+++,,,,,,,,,***+++,,,...///000//////,,,,,,,,,---------------,,,---...---,,,,,,---...,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++,,,,,,,,,,,,,,,------.........//////............//////---,,,+++***)))******+++))))))))))))))))))))))))))))))***++++++++++++******))))))(((((((((((()))((((((''''''''''''((((((&&&&&&&&&'''''''''(((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$######""""""!!!!!!###$$$%%%%%%$$$$$$%%%'''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%"""###$$$%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$ """$$$%%%%%%%%%###""" !!!"""###$$$%%%%%%##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$"""###$$$%%%%%%%%%$$$$$$%%%'''&&&""""""'''$$$###""" """###$$$######$$$$$$$$$%%%%%%%%%#################################$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""!!!"""###$$$%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&'''&&&###!!!###%%%######""""""###$$$%%%%%%""""""######$$$$$$$$$$$$"""############$$$$$$$$$###"""!!! !!!"""$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$######################## ###%%%$$$""""""$$$&&&$$$%%%$$$###$$$&&&!!!"""###$$$%%%%%%$$$### !!!"""######"""!!! !!!!!!""""""#########$$$""""""""""""""""""""""""######""""""###$$$%%%%%%!!!!!!!!!!!!!!!!!!!!!!!!########################!!!!!!!!!!!!!!!!!!!!!!!!######$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######"""######$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''''''''&&&%%%%%%%%%%%%&&&#########$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&'''''''''(((((($$$$$$$$$%%%&&&'''((()))''''''''''''((((((((()))+++++++++,,,,,,------------------------------------,,,,,,++++++,,,,,,---)))+++---000111000//////***++++++,,,,,,------...+++,,,------++++++,,,---,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++++++++,,,((()))***+++---...///000//////............//////------+++*********+++,,,))))))))))))))))))))))))))))))***++++++++++++***+++***)))(((((('''((((((((((((''''''''''''((((((&&&&&&&&&'''''''''(((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%$$$###"""!!! ###%%%&&&&&&%%%$$$&&&'''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$#########$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$%%%%%%$$$$$$#################################$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###""""""############""""""!!!!!!!!!!!!!!!!!!!!!!!!$$$$$$%%%%%%%%%%%%&&&&&&((('''%%%$$$###$$$%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%((('''&&&$$$######$$$$$$&&&&&&%%%$$$$$$######"""######$$$$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$((('''%%%$$$###$$$%%%%%%######$$$$$$$$$$$$######################################################$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#################################$$$$$$$$$%%%%%%%%%""""""""""""####################################$$$$$$############$$$$$$!!!"""""""""############$$$###"""""""""###%%%%%%########################$$$$$$############$$$$$$ !!!!!!"""###$$$$$$$$$%%%%%%$$$###"""""""""#########""""""!!!!!! """"""""""""""""""""""""########################!!!###$$$&&&''''''&&&&&&!!!!!!!!!!!!!!!"""""""""&&&%%%$$$!!! !!!$$$'''########################"""############$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%$$$$$$######""""""############$$$$$$$$$!!!!!!"""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###""""""$$$&&&'''###$$$%%%&&&&&&%%%$$$###%%%%%%$$$$$$###$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$###$$$$$$%%%&&&'''(((((($$$%%%&&&&&&''''''&&&&&&((((((((((((((('''''''''(((((()))***++++++,,,,,,,,,+++*********+++,,,---,,,++++++++++++++++++,,,+++,,,...000000///...---)))************+++++++++******+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++************************))))))***+++,,,,,,------++++++,,,---............---,,,***((('''(((((())))))((('''&&&&&&'''((()))))))))((('''''''''''''''(((((((((((((((((((((((())))))))))))))))))))))))(((((((((((((((((((((((((((((((((((('''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######'''&&&$$$###"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&)))***)))&&&### &&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$%%%%%%$$$$$$#######################################$$$$$$$$$%%%###$$$$$$%%%%%%$$$$$$###""""""############""""""""""""""""""""""""""""""$$$$$$%%%%%%%%%%%%&&&&&&'''&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%&&&&&&((('''%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$'''&&&%%%$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###########################""""""""""""############""""""""""""####################################$$$$$$############$$$$$$############$$$$$$$$$$$$$$$###"""""""""###$$$%%%########################$$$######""""""######$$$!!!!!!!!!"""###$$$$$$$$$$$$$$$###"""""""""############""""""!!!!!!!!!!!!""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!"""###%%%%%%%%%%%%$$$""""""""""""""""""""""""!!!###$$$$$$###"""###$$$########################"""############$$$$$$$$$"""######$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$%%%"""############$$$$$$$$$""""""######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""###$$$&&&'''$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$###$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&'''''''''$$$%%%&&&&&&''''''&&&&&&((((((((((((''''''''''''(((((()))******+++,,,,,,++++++*********+++,,,---++++++************++++++***,,,---//////...---,,,)))************+++++++++,,,,,,,,,++++++*********++++++,,,,,,,,,,,,,,,,,,************************))))))******++++++,,,,,,,,,---------------,,,,,,...---,,,************+++))))))(((''''''((())))))))))))((('''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''&&&%%%$$$%%%%%%$$$$$$######""""""$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######%%%$$$#########$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%######%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$%%%%%%$$$$$$###########################"""""""""#########$$$$$$######$$$$$$$$$$$$######""""""############""""""########################$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&%%%$$$$$$###$$$$$$""""""######$$$%%%%%%&&&######$$$$$$$$$$$$####################################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###########################################################################$$$$$$%%%%%%$$$$$$########################### !!!!!!!!!"""""""""""""""#########$$$$$$########################$$$$$$############$$$$$$###$$$$$$$$$$$$%%%%%%%%%######""""""######$$$%%%########################$$$######""""""######$$$!!!!!!""""""###$$$$$$$$$""""""!!!!!!!!!"""#########""""""""""""!!!!!!!!!""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!""""""######$$$######"""$$$$$$$$$###"""""""""!!! $$$&&&%%%###!!!!!!########################"""############$$$$$$$$$""""""############"""""""""######$$$%%%%%%&&&&&&"""############$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$&&&'''%%%%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$###$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&''''''''''''''''''''''''((())))))******+++++++++++++++******++++++,,,---*********))))))*********)))***,,,---------,,,+++)))************+++++++++...---,,,+++***)))((((((*********+++,,,,,,,,,---************************************************............---,,,+++***...---,,,+++***************))))))(((((())))))***)))((((((''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''(((''''''&&&%%%$$$%%%$$$$$$###"""!!! $$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$##################$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%######""""""$$$&&&((()))%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$%%%%%%$$$$$$###########################!!!""""""""""""###############$$$$$$$$$$$$######""""""############""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%&&&'''&&&%%%$$$############$$$%%%&&&'''(((&&&%%%%%%$$$$$$$$$######""""""######$$$$$$$$$%%%######$$$$$$$$$$$$######""""""""""""""""""""""""######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%################################################""""""""""""""""""""""""###$$$$$$%%%%%%$$$$$$########################### !!!!!!!!!""""""""""""#########$$$$$$$$$########################$$$$$$############$$$$$$#########$$$$$$$$$%%%%%%###############$$$$$$$$$##############################""""""""""""######"""""""""######$$$$$$$$$!!!!!! !!!"""######""""""""""""""""""""""""""""""""""""""""""""""""##########################################""""""&&&%%%%%%$$$###"""!!!!!!###%%%%%%###"""!!!########################""""""#########$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%""""""#########$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$%%%&&&'''&&&%%%$$$######$$$%%%&&&$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&'''''''''''''''(((((()))))))))*********++++++***++++++++++++,,,,,,******))))))))))))******))))))***+++,,,++++++***))))))*********+++++++++,,,,,,,,,+++***))))))(((((())))))***+++,,,,,,---*********************************)))))))))))))))---------------,,,+++***+++******))))))(((((((((******))))))))))))******)))(((''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&'''''''''&&&&&&%%%$$$$$$$$$######""""""!!!!!!$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$###############$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$%%%%%%$$$$$$###########################!!!""""""""""""#########"""######$$$$$$######"""""""""############""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&###$$$%%%&&&'''&&&%%%$$$#########$$$%%%&&&'''((($$$$$$$$$$$$$$$$$$######$$$$$$$$$######"""""""""######$$$$$$$$$$$$######""""""""""""""""""""""""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$################################################""""""""""""""""""""""""###$$$$$$%%%%%%$$$$$$###########################!!!!!!!!!"""""""""##################$$$$$$$$$$$$########################$$$$$$############$$$$$$""""""""""""#########$$$""""""######$$$$$$$$$$$$###########################""""""""""""""""""###############$$$$$$$$$$$$!!!!!! !!!"""######""""""""""""############""""""""""""""""""""""""########################$$$$$$$$$###############&&&%%%%%%$$$###"""!!!!!!""""""""""""###$$$########################""""""#########$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%$$$$$$$$$######""""""#########$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&'''&&&%%%$$$$$$%%%&&&'''$$$#########$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$######$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&''''''(((((()))))))))))))))***************++++++,,,,,,,,,,,,******))))))))))))******)))))))))***************))))))*********+++++++++************************(((((())))))***+++,,,,,,))))))))))))))))))))))))*********)))))))))))))))***++++++,,,------,,,,,,************)))))))))((())))))************))))))((((((''''''''''''((((((((((((((((((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&%%%$$$#########$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$%%%%%%$$$$$$###########################"""""""""#########$$$$$$""""""############""""""""""""############""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&'''######$$$$$$$$$$$$######%%%$$$$$$###""""""!!!!!!######$$$$$$$$$$$$######""""""""""""""""""""""""######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%$$$""""""""""""$$$%%%###########################################################################$$$$$$%%%%%%$$$$$$###########################""""""#########$$$$$$$$$#########$$$$$$$$$$$$%%%########################$$$$$$############$$$$$$!!!!!!"""""""""#########""""""###$$$$$$$$$$$$##############################""""""!!!!!!""""""###$$$$$$$$$$$$$$$$$$$$$$$$""""""!!!!!!!!!"""######"""""""""############$$$""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!$$$$$$#########$$$$$$%%%$$$$$$$$$###"""""""""!!!!!!!!!"""!!!!!!!!!###%%%########################"""############$$$$$$$$$!!!!!!""""""""""""!!!!!!&&&&&&%%%%%%$$$######""""""############$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&############$$$%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$######$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&''''''(((((()))))))))))))))))))))))))))***+++,,,,,,,,,,,,+++*********))))))*********))))))))))))******++++++)))************+++++++++)))))))))*********++++++((((((((()))*********+++))))))))))))))))))))))))************************)))***+++,,,------------++++++,,,,,,,,,++++++***((())))))******))))))((((((''''''''''''(((((()))((((((((((((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((%%%%%%&&&&&&&&&&&&%%%%%%######$$$%%%&&&''''''(((%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$######%%%%%%&&&%%%%%%###"""!!!$$$$$$$$$$$$$$$$$$$$$$$$!!!"""""""""""""""######%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%% !!!###%%%'''''''''&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$%%%%%%$$$$$$#######################################$$$$$$$$$%%%""""""############""""""""""""############""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%&&&'''%%%%%%%%%$$$$$$%%%&&&&&&"""###$$$%%%%%%$$$###"""############""""""""""""######$$$$$$$$$$$$####################################$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$###"""!!!!!!###$$$%%%&&&&&&&&&%%%%%%&&&%%%###""""""###%%%&&&################################################$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###########################"""""""""#########$$$$$$#########$$$$$$$$$%%%%%%########################$$$$$$############$$$$$$""""""#########$$$$$$$$$!!!"""###$$$%%%$$$$$$###########################""""""!!!!!!!!!!!!""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""""""""######""""""#########$$$$$$$$$""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!""""""!!!!!!"""###$$$%%%"""""""""""""""""""""""""""###$$$###""""""###%%%########################"""############$$$$$$$$$!!!!!!""""""""""""!!!!!!%%%$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$""""""######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$######$$$%%%%%%&&&''''''$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%############$$$%%%&&&'''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&$$$$$$%%%&&&&&&'''(((((()))))))))))))))))))))((()))***+++,,,,,,,,,++++++++++++************++++++******))))))******++++++)))************+++++++++************))))))))))))((()))))))))))))))))))))))))))))))))))))))))))))))))))******++++++,,,,,,***++++++,,,,,,,,,++++++***+++,,,,,,,,,,,,+++***'''((())))))))))))(((''''''''''''''''''((())))))((((((((((((((((((((((((''''''''''''''''''''''''(((((((((((((((((((((((($$$%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$#########$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$"""""""""######$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%$$$$$$$$$###########################$$$$$$$$$$$$%%%%%%%%%""""""############""""""""""""############""""""########################$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$###$$$%%%'''(((&&&&&&%%%$$$$$$$$$%%%%%%""""""$$$%%%%%%$$$###"""!!!!!!!!!"""######$$$$$$######$$$$$$$$$$$$####################################$$$$$$$$$%%%%%%%%%%%%$$$###"""!!!"""###%%%&&&'''&&&%%%%%%'''&&&$$$######$$$&&&'''################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$########################""""""""""""##################$$$$$$$$$%%%%%%%%%########################$$$$$$############$$$$$$######$$$$$$$$$%%%%%%%%%!!!"""###$$$%%%$$$##############################""""""!!!!!!!!!!!!""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###""""""######""""""######$$$$$$$$$$$$""""""""""""""""""""""""########################!!! !!!"""$$$%%%!!!!!!!!!!!!"""""""""""""""$$$%%%%%%$$$""""""###########################"""############$$$$$$$$$######$$$$$$$$$$$$###############$$$$$$%%%&&&&&&"""############$$$$$$$$$!!!!!!"""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$######$$$%%%%%%&&&''''''$$$%%%&&&&&&''''''&&&&&&$$$%%%''''''''''''%%%$$$############$$$%%%&&&'''$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&$$$$$$%%%%%%&&&'''(((((())))))))))))(((((((((((()))***+++,,,---,,,++++++,,,,,,++++++++++++,,,,,,***************++++++,,,)))************+++++++++,,,,,,+++***)))(((''''''))))))))))))(((((((((((())))))))))))))))))))))))))))))***+++,,,---------,,,,,,,,,,,,++++++***)))((((((***++++++***)))(((&&&'''((())))))((('''&&&'''''''''''''''((()))***((((((((((((((((((((((((''''''''''''''''''''''''(((((((((((((((((((((((($$$$$$%%%&&&&&&%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$######!!!"""$$$%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&'''''''''%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%,,,)))&&&###"""###%%%'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%""""""""""""""""""""""""########################$$$$$$$$$#########""""""########################!!!""""""!!! !!!###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$######"""#########""""""""""""!!!######$$$%%%%%%%%%%%%%%%$$$$$$######"""##################$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%%%%%%%%%%########################!!!!!!"""###$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$##################"""############$$$$$$$$$######################## !!!######!!! !!!"""%%%%%%%%%$$$$$$#########""""""""""""""""""""""""#########"""""""""""""""################################################""""""""""""""""""""""""########################$$$###"""""""""###%%%%%%""""""""""""####################################&&&$$$!!!!!!###$$$$$$$$$&&&$$$!!! """%%%((($$$###""" !!!"""%%%$$$###""""""###$$$%%%""""""""""""""""""""""""""""""############""""""!!!!!!!!!"""######$$$$$$$$$###!!! !!!###$$$$$$$$$$$$$$$$$$$$$$$$$$$########################&&&%%%$$$#########$$$%%%###################################################"""!!!!!!"""$$$&&&'''!!! %%%(((&&&###$$$$$$%%%%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%############%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&((('''%%%#########%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%)))(((((((((((()))******'''***,,,---+++***))))))++++++++++++*********)))************************,,,,,,++++++***)))((((((,,,+++***)))(((((((((((())))))))))))))))))))))))&&&'''''''''''''''&&&&&&))))))))))))*********************++++++,,,,,,,,,***************)))((((((((((((((((((((((((((((((''''''''''''((((((((((((,,,,,,++++++***)))((((((''''''((((((((((((''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###"""!!! """###%%%''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%################################################$$$$$$$$$#########""""""########################!!!"""######!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%###$$$$$$%%%%%%$$$$$$###"""######$$$$$$$$$######$$$$$$#########"""""""""######$$$$$$$$$$$$$$$###$$$###############$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%$$$$$$########################!!!""""""###$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%########################"""############$$$$$$$$$########################!!!###%%%$$$###"""######%%%%%%%%%$$$$$$$$$##############################$$$$$$$$$###############################################################################################################""""""!!!!!!!!!"""###$$$""""""""""""####################################%%%###"""!!!###$$$$$$###$$$"""!!! """$$$%%%!!! !!!###%%%&&&$$$$$$###""""""###$$$$$$########################"""##################"""!!!!!!""""""######$$$$$$%%%$$$"""!!!!!!"""$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%$$$#########$$$%%%$$$$$$$$$##########################################"""!!!!!!"""$$$&&&''''''$$$!!!###&&&'''%%%!!!$$$$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%%%%%%%%%%&&&&&&'''&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''(((((()))(((***,,,---,,,***)))******))))))))))))(((((((((************************------,,,,,,+++******)))---,,,+++***))))))))))))))))))))))))))))))))))))(((((())))))))))))(((((((((((())))))******++++++***++++++++++++++++++,,,***************)))((((((((((((((((((((((((((((((''''''''''''((((((((((((,,,,,,+++******)))((((((''''''((((((((((((''''''&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%##################""""""###$$$%%%&&&&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%################################################$$$$$$$$$#######################################!!!###$$$$$$###""""""###$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$%%%###$$$$$$%%%%%%$$$$$$###!!!"""###$$$$$$$$$$$$$$$%%%$$$$$$$$$#####################$$$######""""""""""""""""""###$$$%%%%%%#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$###########################"""""""""###$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%########################"""############$$$$$$$$$###########################%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################################################################""""""""""""###$$$$$$"""""""""#########$$$$$$########################%%%###""""""###$$$$$$###!!!!!!!!! !!!""""""###!!!!!!!!!!!!###$$$%%%&&&$$$$$$###""""""###$$$$$$##############################$$$$$$$$$$$$######!!!!!!""""""###$$$$$$$$$%%%$$$###""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$#########$$$$$$%%%$$$$$$$$$$$$######""""""##############################"""""""""$$$%%%&&&(((%%%######%%%&&&$$$!!!###$$$$$$%%%%%%$$$$$$$$$########################%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''((((((((((((***,,,---,,,******+++((((((((('''''''''&&&&&&************************---------,,,++++++******------,,,+++************)))))))))))))))))))))))))))******+++++++++******(((((())))))***+++,,,,,,+++++++++++++++*********)))************))))))(((((((((((((((((((((((((((''''''''''''((((((((((((++++++******))))))((((((''''''(((((((((((('''''''''(((((((((((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&############$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$################################################################################################!!!###%%%%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$### !!!"""###$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######"""############"""!!!!!!""""""""""""###$$$%%%&&&###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$####################################""""""#########$$$$$$$$$######$$$$$$$$$%%%%%%%%%###############$$$$$$$$$""""""#########$$$$$$$$$###########################%%%&&&&&&%%%$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################################################################%%%%%%%%%%%%%%%&&&&&&&&&""""""#########$$$$$$$$$########################%%%###""""""$$$$$$$$$""" !!!""""""######""""""$$$$$$##################$$$##################$$$########################$$$$$$$$$%%%%%%$$$$$$$$$!!!""""""######$$$%%%%%%%%%%%%$$$######$$$%%%%%%###############################################################$$$$$$$$$%%%%%%$$$$$$###"""""""""##############################""""""######%%%%%%"""!!! !!!###%%%$$$"""######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''(((((())))))))))))(((***,,,,,,+++***++++++(((((('''''''''&&&&&&&&&************************,,,,,,,,,++++++*********,,,+++******)))))))))***(((((((((((((((((((((((()))***++++++,,,+++++++++(((((()))***++++++,,,---,,,,,,++++++******))))))))))))************)))(((((((((((((((((((((((((((''''''''''''((((((((((((******)))))))))(((((((((''''''((((((((((((''''''''''''((((((((((((''''''''''''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$################################################################################################"""###%%%%%%###"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$###$$$$$$%%%%%%$$$$$$### !!!"""###$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######""""""#########""""""!!!""""""""""""###$$$%%%&&&########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%############$$$#######################################$$$$$$$$$######$$$$$$$$$%%%%%%%%%""""""#########$$$$$$$$$""""""#########$$$$$$$$$########################"""$$$%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################################################################$$$$$$%%%%%%&&&&&&&&&&&&############$$$$$$$$$$$$########################$$$###"""###$$$%%%###"""!!!"""###$$$$$$$$$###############$$$$$$$$$###############$$$$$$#################################$$$$$$$$$%%%%%%$$$$$$$$$"""""""""###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%################################################""""""######$$$$$$$$$$$$$$$$$$$$$#########""""""##########################################$$$$$$"""!!!!!!"""###$$$######"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((((((''''''''')))++++++******+++,,,)))))))))(((((((((''''''))))))))))))))))))))))))************))))))))))))***))))))(((((((((((()))((((((((((((((((((((((((((()))******+++++++++***((())))))***+++,,,,,,,,,+++++++++******)))))))))((())))))*********))))))((((((((((((((((((((((((''''''''''''(((((((((((())))))((((((((((((((((((''''''((((((((((((''''''%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################&&&&&&%%%%%%$$$######"""$$$$$$#########$$$%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$#######################################$$$$$$$$$##############################$$$###!!!!!!###%%%$$$$$$$$$$$$$$$$$$$$$$$$"""""""""############$$$###$$$$$$%%%%%%$$$$$$###!!!"""###$$$$$$$$$$$$$$$%%%$$$$$$$$$############!!!"""######$$$$$$######""""""""""""###$$$%%%%%%###############"""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$#########$$$%%%######################################################$$$$$$$$$%%%%%%%%%"""""""""###$$$$$$%%%%%%"""############$$$$$$$$$########################!!!###$$$$$$###""""""######$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!!!!"""######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$########################!!!""""""###$$$##################$$$$$$$$$$$$%%%########################$$$###"""###%%%%%%###!!!""""""###$$$$$$$$$$$$$$$!!!###$$$%%%&&&&&&"""###$$$$$$$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######""""""######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$################################################ !!!"""###$$$$$$$$$$$$########################################################################&&&%%%%%%%%%$$$#########"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%%%%&&&((())))))((((((***,,,*********)))))))))(((((()))))))))))))))))))))))))))))))))))))))))))))))))))(((((('''''''''(((((())))))))))))))))))))))))'''((()))************************+++++++++++++++***************)))))))))((())))))************)))((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((''''''''''''''''''((((((((((((''''''%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################&&&&&&%%%$$$###"""!!!!!!############$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%$$$$$$''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$########################""""""#########$$$$$$$$$##############################"""  ###%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""###############$$$$$$%%%%%%$$$$$$###"""######$$$$$$$$$######$$$$$$#########"""""""""!!!!!!###$$$%%%%%%%%%%%%$$$###############$$$$$$$$$#########"""""""""!!!$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$###""""""$$$%%%&&&######################################################$$$$$$$$$%%%%%%%%%!!!""""""###$$$$$$%%%%%%"""############$$$$$$$$$########################!!!###$$$$$$###""""""#########$$$$$$$$$%%%%%%%%%########################!!!!!!"""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$######################## !!!"""#########""""""#########$$$$$$$$$%%%%%%#################################$$$%%%%%%###!!!""""""""""""#########$$$ """$$$%%%%%%%%%"""###$$$$$$$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$"""##################""""""######$$$$$$%%%%%%&&&"""##################"""################################################ """###$$$$$$$$$###"""""""""###$$$$$$%%%%%%##############################$$$$$$$$$#########$$$%%%%%%%%%$$$###$$$$$$""""""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''((()))((('''&&&%%%&&&'''''''''''')))+++*********)))))))))(((((())))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))'''((()))***++++++++++++,,,,,,++++++++++++******))))))))))))************(((((()))***************((((((((((((((((((((((((''''''''''''((((((((((((''''''''''''''''''''''''''''''((((((((((((''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$######"""""""""!!!"""###$$$%%%$$$$$$#########$$$%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$########################""""""######$$$$$$$$$$$$########################$$$###!!!###&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""############$$$$$$$$$%%%%%%$$$$$$$$$######$$$$$$$$$######"""#########""""""""""""!!! !!!###$$$&&&&&&''''''$$$$$$##################$$$#########""""""!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$###""""""$$$&&&(((########################$$$$$$########################$$$$$$$$$%%%%%%%%%!!!""""""###$$$$$$%%%%%%"""############$$$$$$$$$########################"""###%%%%%%###"""###$$$#########$$$$$$%%%%%%%%%""""""""""""""""""""""""""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$########################!!!"""###$$$%%%$$$############$$$$$$$$$%%%%%%%%%###########################"""###$$$%%%%%%###!!!!!!!!!!!!!!!!!!"""###### !!!#########"""!!!"""###$$$%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$""""""############"""""""""######$$$$$$%%%&&&&&&""""""############""""""""""""""""""""""""""""""######################## """###$$$$$$$$$###!!!!!!"""###$$$%%%%%%&&&##############################$$$$$$$$$######"""!!!"""###$$$%%%'''!!!"""###$$$%%%&&&&&&&&&########################&&&%%%############%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%#########%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((()))+++,,,---,,,***)))$$$%%%&&&&&&&&&&&&(((***))))))))))))(((((((((((())))))))))))))))))))))))******************++++++***)))))))))))))))******))))))))))))))))))))))))'''((()))***+++,,,,,,,,,------,,,++++++******)))(((((())))))******++++++(((((()))***************((((((((((((((((((((((((''''''''''''((((((((()))&&&'''''''''''''''''''''''''''((((((((((((''''''''''''((((((((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""""""""######### """$$$%%%&&&%%%###"""######$$$%%%%%%&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###""""""#########$$$$$$$$$$$$$$$##################""""""""""""""""""""""""(((&&&$$$""""""###$$$%%%%%%$$$"""!!!!!!!!!"""###$$$#########""""""!!!!!!"""#########$$$$$$$$$$$$!!!!!!!!!!!!!!!!!!!!!!!!######$$$$$$$$$%%%%%%%%%!!!!!!!!!!!!!!!!!!!!!!!! !!!"""######"""!!! """"""""""""""""""""""""$$$$$$##################%%%&&&''''''%%%%%%&&&'''***)))'''%%%$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$#########"""############$$$$$$$$$%%%%%%$$$###""""""#########"""""""""###$$$$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$##################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########""""""################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""######$$$$$$$$$######"""############""""""!!!!!!###"""!!! """$$$%%%######$$$%%%$$$###"""!!! !!!"""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""""""""""""""""""""""""""############$$$$$$$$$######""""""""""""######%%%%%%$$$$$$$$$$$$%%%%%%&&&%%%$$$###""""""""""""######""""""###$$$%%%%%%""""""""""""""""""""""""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$###############$$$%%%%%%%%%%%%%%%%%%%%%%%%"""############$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%((('''%%%$$$###$$$%%%%%%''''''''''''''''''&&&&&&'''''''''''''''((())))))))))))))))))))))))))))))(((((((((((((((((((((((()))*********++++++++++++,,,+++***)))((((((((((((((((((((((((''''''''''''(((((())))))******++++++,,,,,,,,,++++++*********(((((())))))******++++++)))***,,,------+++((('''''''''&&&%%%%%%%%%%%%&&&$$$$$$%%%%%%&&&'''(((((((((((((((((((((((((((((()))((('''&&&%%%&&&&&&'''%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$'''&&&&&&%%%$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$################################################$$$$$$##################'''&&&&&&%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###############$$$$$$$$$$$$################################################&&&%%%$$$###"""######$$$$$$$$$###""""""#########$$$#########"""""""""""""""""""""#########$$$$$$##############################$$$$$$$$$%%%%%%%%%"""""""""""""""""""""""""""""""""!!!!!!"""""""""################################################%%%'''((('''&&&%%%&&&'''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$#########""""""############$$$$$$$$$%%%$$$$$$###""""""######$$$#########$$$$$$%%%&&&""""""#########$$$$$$$$$$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########""""""################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""######$$$$$$$$$######"""$$$$$$#########"""""""""%%%$$$###""""""###%%%&&&######$$$%%%$$$###"""!!!"""######$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$########################!!!!!!"""""""""###############""""""""""""############""""""""""""######"""!!!!!!!!!!!!!!!"""#########""""""###$$$$$$%%%###########################$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$###############$$$%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$%%%''''''''''''''''''&&&&&&'''''''''''''''(((((()))((((((((((((((((((((((((''''''''''''''''''''''''((((((((())))))))))))******)))))))))))))))******((((((((((((((((((((())))))))))))))))))***************************)))))))))))))))))))))******************)))))))))((((((''''''&&&%%%%%%%%%%%%&&&$$$$$$%%%%%%&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&%%%&&&&&&'''%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$############$$$$$$$$$%%%%%%%%%################################################$$$############"""""""""############$$$$$$$$$$$$###############"""""""""!!!!!!!!!"""""""""######%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%########################%%%###!!! !!!###%%%$$$$$$$$$$$$$$$$$$$$$$$$########################%%%&&&''''''%%%%%%&&&'''###############$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$###############""""""############$$$$$$$$$%%%$$$######"""##################"""######$$$%%%!!!!!!"""""""""#########$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############"""######$$$$$$$$$######$$$$$$$$$$$$$$$#########!!!  !!!"""######$$$%%%$$$###"""!!!$$$$$$$$$$$$$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!!!!!!!""""""""""""######""""""""""""############""""""""""""###### !!!!!!###$$$$$$#########"""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$###############$$$$$$######$$$$$$%%%%%%&&&&&&############$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&''''''((()))((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((((((((((((((()))***+++,,,((((((((()))******++++++************))))))))))))(((((())))))))))))))))))************))))))))))))***)))((('''&&&'''((()))''''''&&&%%%%%%%%%%%%&&&$$$%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&&&&%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$#########%%%%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&###$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$%%%%%%%%%%%%###############$$$$$$$$$########################""""""#########""""""!!!"""""""""#######################################!!!!!!!!!!!!""""""""""""%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$%%%&&&%%%$$$$$$%%%&&&""""""""""""###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$###############$$$""""""!!!!!!!!!""""""###""""""""""""#########$$$$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""###$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$ !!!######$$$%%%$$$###"""!!!######$$$$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!!!!"""""""""######$$$######""""""######$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$#########$$$$$$%%%&&&$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%#########"""######$$$%%%""""""###$$$%%%&&&&&&'''#########$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''&&&%%%$$$###%%%%%%&&&&&&&&&&&&'''''''''&&&&&&&&&&&&'''((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((((((((((()))***+++,,,(((((()))***++++++,,,,,,++++++******))))))((((((((((((((())))))*********++++++******))))))((((((***)))((((((''''''((((((''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''(((((((((((((((((((((((('''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$######"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$$$$######"""######$$$$$$$$$%%%%%%%%%""""""#########$$$$$$$$$########################!!!""""""#########""""""""""""""""""""""""""""""###############$$$$$$$$$!!!!!!!!!!!!""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%$$$###"""########################""""""#########$$$$$$$$$"""###$$$$$$###"""###$$$$$$$$$######"""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$%%%%%%%%%%%%%%%%%%""""""#########$$$$$$$$$$$$###############$$$$$$$$$######"""""""""###############$$$$$$$$$%%%%%%$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%######$$$%%%$$$###"""!!!!!!!!!"""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################"""""""""#########$$$$$$$$$$$$############$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######""""""###$$$$$$%%%""""""######$$$%%%&&&&&&###$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&'''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((()))))))))******))))))))))))******((())))))***+++,,,,,,---++++++******))))))((((((((())))))******+++++++++++++++******))))))((((((((()))***++++++)))'''&&&''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%&&&&&&&&&&&&&&&((((((((((((((((((((((((%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$######"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$%%%%%%&&&&&&'''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""############""""""""""""#########$$$$$$$$$"""""""""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""""""""############$$$%%%$$$"""!!!!!!!!!"""############$$$$$$$$$$$$$$$!!!!!!!!!"""""""""####################################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###%%%''''''%%%###""""""""""""""""""""""""""""""""""""###$$$$$$%%%%%%"""###$$$$$$""""""###$$$'''&&&%%%$$$###"""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############"""""""""$$$$$$$$$$$$$$$%%%%%%%%%"""############$$$$$$$$$#########"""######$$$%%%'''&&&%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###"""""""""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$!!!"""###$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%######$$$%%%$$$###"""!!! !!!"""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""############$$$$$$$$$$$$$$$$$$############$$$$$$######""""""""""""######%%%%%%$$$""""""!!!!!!!!!%%%$$$######"""#########$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%""""""""""""###$$$%%%%%%""""""######$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((()))))))))***************)))))))))))))))***)))))))))***+++++++++,,,************))))))))))))))))))******************************))))))))))))''')))+++,,,,,,***'''%%%''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$############$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%&&&&&&((((((''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""############""""""!!!!!!"""""""""#########!!!""""""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""###$$$%%%&&&***((($$$"""!!!"""###%%%#########$$$$$$%%%%%%%%%"""""""""#########$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$########################!!!""""""###$$$$$$%%%%%%###%%%&&&%%%$$$###$$$%%%'''&&&%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########"""""""""!!!!!!!!!""""""############"""############$$$$$$$$$######""""""###$$$$$$%%%&&&&&&%%%$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###!!!""""""###$$$$$$%%%%%%########################""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$!!!!!!"""$$$$$$%%%%%%$$$"""""""""#########$$$$$$ !!!"""""""""###""""""######$$$%%%$$$###"""!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""""""""############%%%$$$$$$######$$$$$$%%%######""""""""""""######$$$$$$###"""""""""######%%%$$$$$$###""""""#################################$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%""""""""""""###$$$%%%&&&###############$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&'''###$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''(((''''''''''''''''''''''''''''''''''''''''''''''''(((((()))))))))*********)))((((((((()))***+++,,,))))))******************)))))))))))))))*********))))))))))))))))))(((((()))))))))))))))*********(((((()))))))))((('''&&&''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&'''&&&&&&%%%%%%%%%$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$%%%%%%%%%&&&$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$""""""############""""""!!!!!!!!!!!!""""""""""""!!!""""""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""$$$&&&(((...+++&&&###!!!"""%%%'''#########$$$$$$%%%%%%%%%############$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%########################'''&&&$$$######$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$!!!""""""###$$$$$$%%%%%%%%%&&&''''''%%%%%%&&&'''&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""!!!!!! !!!!!!"""""""""############$$$$$$$$$######""""""###$$$%%%%%%######"""!!!!!! !!!!!!""""""""""""############$$$$$$############$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$!!!""""""###$$$$$$%%%%%%########################""""""######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$$$$$$$!!!!!!"""$$$$$$%%%%%%%%%!!!!!!""""""#########$$$######$$$%%%%%%%%%%%%%%%######$$$%%%$$$###"""!!!###$$$$$$$$$$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!!!!!!!""""""""""""%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%&&&''''''%%%%%%$$$###""""""######""""""""""""""""""""""""$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%""""""""""""###$$$%%%&&&$$$$$$$$$###############$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$%%%'''(((######$$$%%%%%%&&&''''''&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))&&&''''''((()))+++---...*********)))))))))))))))(((((())))))******++++++))))))(((((('''''''''&&&(((((())))))******++++++)))((('''&&&%%%&&&''''''''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((("""###%%%&&&'''&&&&&&%%%&&&%%%$$$######$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%&&&&&&'''((())))))%%%%%%&&&&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%###############$$$$$$%%%%%%%%%$$$###"""%%%$$$###$$$%%%%%%$$$###"""!!! !!!###$$$$$$$$$""""""!!!!!!"""###$$$$$$################################################!!!""""""""""""#########%%%$$$$$$######$$$$$$%%%########################$$$$$$%%%%%%%%%$$$$$$###""""""""""""""""""""""""&&&%%%###""""""###%%%&&&%%%$$$$$$######$$$$$$%%%############$$$%%%&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$###""""""###$$$%%%""""""""""""""""""""""""#######################################"""!!! ######"""###%%%%%%###"""%%%%%%%%%$$$$$$$$$##############################$$$$$$$$$#########""""""""""""""""""""""""""""""&&&&&&&&&&&&&&&&&&&&&&&& !!!######$$$$$$$$$%%%&&&'''&&&$$$###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""!!!!!!!!!!!!%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""""""""############""""""""""""""""""""""""$$$$$$$$$######"""""""""########################***)))&&&$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""""""""###$$$$$$$$$%%%######$$$$$$$$$$$$######"""############$$$$$$$$$################################################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&"""############$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$$$$$$$######%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&''''''((()))******+++''''''(((((())))))******&&&'''(((*********)))((((((((((((((()))))))))))),,,+++)))((((((((()))***((((((((()))))))))******&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""!!!"""%%%''')))"""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$%%%&&&'''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###############$$$$$$$$$$$$######&&&&&&%%%%%%%%%$$$$$$$$$%%%###"""###$$$%%%$$$###%%%###"""###%%%&&&&&&%%%"""""""""""""""###$$$$$$################################################"""""""""#########$$$$$$$$$######""""""######$$$########################$$$$$$$$$%%%%%%$$$$$$###########################%%%$$$###!!!!!!"""$$$%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$###$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$%%%%%%%%%$$$######%%%###"""###$$$$$$###"""%%%%%%$$$$$$####################################$$$$$$$$$#########""""""########################%%%%%%%%%%%%%%%%%%%%%%%% !!!"""######$$$######%%%&&&'''&&&$$$###$$$%%%########################$$$$$$###"""!!! $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$########################&&&&&&&&&%%%%%%$$$$$$$$$########################((('''%%%#########$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$######$$$$$$$$$$$$######"""############$$$$$$$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$"""############$$$$$$$$$########################""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""!!! %%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&''''''''''''''''''&&&&&&&&&%%%%%%''''''(((((())))))******'''((((((((()))))))))***'''(((((())))))))))))((((((((((((((())))))))))))+++***)))((((((((())))))&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$%%%&&&###$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######!!!"""$$$%%%%%%%%%$$$###&&&%%%$$$#########$$$$$$$$$###""""""$$$$$$###"""%%%$$$######$$$%%%%%%$$$""""""""""""""""""###$$$############################################################$$$$$$$$$%%%###""""""""""""""""""##############################$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!!!!"""###$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%""""""############""""""%%%%%%%%%%%%%%%%%%%%%%%%###########################$$$$$$%%%%%%%%%$$$$$$'''%%%"""""""""######"""$$$############"""""""""########################$$$$$$$$$#######################################$$$$$$$$$$$$$$$$$$$$$$$$""""""###############"""$$$%%%&&&%%%$$$###$$$%%%""""""""""""""""""""""""%%%%%%$$$###!!! """#########$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$########################%%%$$$###""""""###$$$%%%########################$$$$$$$$$#####################$$$$$$$$$$$$######"""############$$$$$$$$$########################""""""""""""""""""""""""########################$$$$$$$$$$$$$$$$$$$$$$$$"""""""""!!!!!!""""""""""""############$$$$$$$$$########################!!!!!!"""""""""#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""!!! %%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&%%%(((((((((((())))))))))))(((((((((((())))))))))))***))))))(((((((((((()))(((((((((((())))))))))))***)))((('''''''''((((((&&&&&&&&&&&&&&&&&&%%%%%%'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&$$$###&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$%%%%%%%%%%%%%%%$$$&&&$$$"""!!! !!!###$$$###"""!!!"""#########!!!$$$"""!!!!!!"""######"""###"""""""""""""""############################################################$$$$$$$$$%%%%%%%%%######""""""""""""####################################$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""######$$$%%%%%%$$$$$$######$$$$$$%%%&&&&&&%%%$$$##################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%!!!!!!###$$$$$$###!!!!!!%%%%%%%%%%%%%%%%%%%%%%%%######################## !!!"""###############(((%%%"""!!!!!!############"""""""""""""""""""""########################################################################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$###""""""$$$%%%&&&%%%$$$###$$$%%%########################$$$$$$######"""!!! !!!""""""###$$$%%%%%%&&&#################################$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########"""""""""""""""#######################################$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$###"""""""""######$$$$$$$$$$$$######""""""#########$$$$$$$$$########################!!!!!!!!!!!!!!!!!!!!!!!!########################$$$$$$$$$$$$$$$$$$$$$$$$""""""!!!!!!!!!!!!""""""""""""#########$$$$$$$$$########################""""""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&))))))))))))(((((((((((((((((((((((())))))))))))+++***)))'''''''''((()))(((((((((((()))))))))))))))(((((('''''''''''''''(((((((((((('''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&'''(((((((((%%%###!!!&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%&&&&&&%%%###"""$$$%%%&&&&&&''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$#########$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$)))'''&&&$$$$$$$$$&&&&&&'''%%%###"""!!!"""$$$%%%###"""!!!"""#########!!!###""" !!!"""$$$###"""######"""""""""""""""#########################################################$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$########################"""###$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%&&&&&&%%%$$$##################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%!!!"""###$$$$$$###"""!!!$$$$$$$$$$$$$$$$$$$$$$$$######################## !!!"""###############(((%%%"""!!!"""#########"""""""""""""""""""""###########################################################################%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$######"""###$$$%%%%%%######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""############!!!!!!"""###$$$$$$%%%%%%########################""""""""""""#########$$$########################""""""""""""""""""""""""#################################$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###"""""""""######$$$$$$$$$$$$######""""""#########$$$$$$$$$########################!!!!!!!!!!!!!!!!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$""""""#########$$$$$$$$$#################################$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''(((((((((((('''''''''&&&&&&&&&))))))))))))(((((((((((())))))))))))((((((((((((+++***)))'''''''''((()))(((((((((((())))))))))))(((((((((((((((''''''&&&(((((((((((((((((((((((((((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&'''(((((((((%%%###!!!&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!$$$&&&'''&&&%%%$$$$$$%%%&&&&&&''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$###"""###$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$$$$%%%&&&'''((('''&&&%%%%%%%%%&&&'''$$$###""""""$$$$$$###"""$$$###"""###%%%&&&&&&&&&$$$######"""""""""""""""############################################################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%########################"""###$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&'''''''''%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%%%%$$$$$$%%%###!!!!!!###$$$$$$$$$"""""""""############$$$#######################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$$$$###"""###$$$$$$######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""######$$$$$$%%%!!!"""""""""###$$$$$$$$$########################!!!!!!"""""""""#########""""""""""""""""""""""""#########$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#####################$$$$$$$$$$$$######"""############$$$$$$$$$########################""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%"""############$$$$$$$$$###########################$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''(((((((((((((((((('''''''''&&&&&&(((((((((((())))))))))))))))))))))))((((((((((((***))))))(((((((((((()))(((((((((((())))))))))))((())))))))))))((('''&&&&&&&&&&&&'''''''''(((((())))))))))))))))))))))))'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&''''''''''''&&&$$$###&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$!!!###&&&''''''&&&%%%$$$$$$%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###############$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%% ###%%%'''&&&&&&%%%&&&&&&&&&%%%%%%%%%%%%$$$%%%###"""###$$$%%%$$$######!!!!!!"""%%%'''((('''$$$$$$###"""""""""""""""################################################"""""""""#########$$$$$$$$$$$$############$$$$$$########################""""""###$$$%%%%%%%%%%%%##############################$$$%%%&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$###$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$%%%%%%%%%$$$#########"""!!!"""$$$%%%%%%$$$############$$$$$$%%%%%%########################""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%%%%%%%!!!###$$$$$$######$$$%%%##########################################$$$$$$""""""""""""####################################""""""#########$$$$$$$$$########################"""#########$$$$$$$$$%%%##############################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$######$$$$$$$$$$$$######"""############$$$$$$$$$########################################################################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%"""############$$$$$$$$$####################################$$$$$$$$$$$$###########################$$$$$$$$$$$$###""""""######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''((((((((((((((((((((((((''''''''''''''''''(((((())))))*********)))))))))(((((((((''''''(((((())))))))))))((((((((((((((())))))))))))))))))*********)))((('''%%%&&&&&&'''((()))******))))))))))))))))))))))))'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&########################"""###$$$%%%&&&%%%%%%$$$###$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%!!!&&&)))(((%%%###"""############"""!!!!!!%%%$$$###$$$%%%%%%$$$###  ###&&&&&&&&&$$$$$$###""""""!!!""""""################################################!!!""""""""""""###############""""""""""""##############################!!!"""###$$$%%%&&&&&&&&&""""""""""""""""""""""""!!!"""###$$$%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%############$$$%%%&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%'''&&&%%%$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&#######################################"""!!! !!!!!!!!!###%%%&&&%%%$$$######$$$$$$$$$%%%%%%%%%########################""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""!!!"""###$$$%%%&&&&&&&&&!!!###$$$$$$######$$$&&&""""""""""""""""""""""""%%%$$$$$$$$$######""""""#########"""""""""""""""""""""""""""""""""""""""######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$ !!!!!!"""""""""###########################""""""############""""""########################""""""######$$$$$$$$$%%%######$$$$$$$$$$$$######"""############$$$$$$$$$################################################""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$"""############$$$$$$$$$########################""""""""""""#################################### !!!"""###%%%%%%%%%&&&#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''((((((((())))))(((((((((''''''''''''&&&''''''((()))******+++******))))))((((((((('''&&&'''(((*********)))((((((((((((((()))))))))))))))***+++++++++***(((''''''((()))***+++,,,---...))))))))))))))))))))))))'''&&&&&&%%%%%%&&&&&&'''((((((((((((((((((((((((&&&&&&%%%%%%%%%&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$%%%%%%%%%%%%$$$############$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$########################!!!"""###%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%'''&&&&&&%%%%%%$$$$$$###$$$$$$##################%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%!!!!!!"""###$$$%%%%%%&&&!!!!!!""""""#########$$$"""###$$$%%%%%%$$$###"""""""""#########$$$$$$$$$$$$#########$$$$$$&&&&&&###%%%'''&&&%%%$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$%%%%%%&&&&&&%%%%%%$$$'''&&&%%%###"""!!!!!!!!!######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$#########&&&&&&&&&%%%%%%$$$$$$$$$######$$$%%%%%%%%%%%%$$$%%%%%%%%%$$$###""""""!!!########################%%%%%%$$$$$$%%%%%%&&&'''################################################!!!!!!!!!!!!!!!"""######""""""#########$$$$$$$$$$$$$$$$$$#########""""""%%%%%%$$$######$$$%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%$$$$$$#########%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$###"""!!! !!!###$$$$$$###"""!!!!!!###$$$$$$#########$$$#########$$$$$$%%%%%%%%%$$$######"""###$$$&&&'''%%%%%%%%%$$$$$$#########!!!"""$$$%%%%%%%%%$$$""""""""""""""""""""""""$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$#########""""""#########$$$$$$%%%%%%%%%&&&&&&%%%$$$#########$$$###$$$$$$%%%%%%$$$$$$######"""!!!!!!!!!"""$$$%%%%%%%%%###"""""""""###$$$$$$###""" """###$$$$$$$$$############$$$$$$#########$$$$$$%%%%%%%%%$$$$$$###############$$$######""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$#########""""""&&&%%%%%%$$$#########$$$""""""""""""""""""""""""$$$&&&''''''&&&%%%%%%&&&######$$$$$$$$$%%%%%%%%%######$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%$$$$$$%%%%%%&&&'''&&&&&&''''''(((((())))))%%%&&&((())))))(((&&&%%%'''''')))***++++++++++++))))))((((((''''''&&&&&&(((((((((((())))))))))))&&&'''((())))))******)))))))))))))))((((((((((((''''''''''''(((***---...((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$%%%%%%$$$############$$$$$$$$$%%%%%%%%%################################################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%&&&%%%%%%$$$######$$$%%%%%%%%%%%%$$$###""""""######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%###############$$$$$$$$$"""#########$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%&&&%%%###!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$######$$$%%%%%%%%%%%%$$$#########"""!!! ########################%%%$$$$$$$$$$$$%%%&&&&&&################################################!!!!!!!!!!!!!!!"""######""""""#########$$$$$$$$$$$$$$$$$$#########""""""%%%%%%$$$######$$$%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%$$$$$$$$$######%%%%%%%%%$$$$$$$$$######"""######$$$$$$$$$###############""""""""""""### """$$$$$$######$$$%%%"""###############$$$$$$%%%$$$###"""""""""###$$$%%%%%%%%%$$$$$$#########!!!""""""#########""""""########################$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$#########""""""######$$$$$$$$$%%%%%%%%%######"""""""""""""""""""""######$$$$$$######"""###""""""!!!"""###$$$%%%%%%$$$###"""""""""###$$$$$$###"""!!!!!!"""###$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###############$$$######""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$%%%%%%%%%%%%#########$$$$$$$$$%%%%%%$$$$$$$$$#########""""""&&&%%%$$$$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&&&&%%%$$$$$$%%%######$$$$$$$$$%%%%%%%%%######$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&''''''''''''%%%&&&'''))))))'''&&&%%%&&&'''((()))************(((((((((((('''''''''''''''((((((((())))))))))))&&&'''((()))************))))))))))))((((((((((((************+++---...///***))))))((('''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$%%%$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%################################################$$$$$$$$$$$$$$$$$$$$$$$$)))((('''&&&&&&&&&&&&&&&%%%%%%$$$######$$$%%%%%%%%%%%%$$$###############$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$#########""""""$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%&&&&&&%%%$$$"""!!!!!!###$$$###""" !!!$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$$$$######!!!!!!""""""###$$$&&&&&&%%%%%%%%%%%%&&&&&&&&&'''$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$#########"""!!!!!! ########################$$$$$$$$$$$$$$$%%%&&&&&&################################################"""!!!!!!!!!!!!"""#####################$$$$$$$$$$$$$$$$$$###############%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%$$$$$$$$$$$$###!!!!!!"""$$$$$$%%%%%%%%%&&&%%%###!!! !!!###$$$!!!$$$$$$$$$$$$%%%&&&#########"""""""""""""""%%%$$$###"""!!!!!!!!!!!!$$$$$$$$$$$$$$$###############"""!!!!!!!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$##################$$$$$$$$$$$$%%%%%%%%%"""""""""""""""#########"""""""""######"""""""""###""""""""""""###$$$$$$%%%$$$######""""""######$$$###"""!!!!!!"""###$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$###############$$$$$$######""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&#########$$$$$$$$$$$$%%%$$$$$$$$$###############%%%%%%$$$############$$$########################"""$$$%%%%%%$$$######$$$######$$$$$$$$$%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&'''(((((('''&&&%%%%%%&&&'''((((((((((((((('''''''''''''''(((((((((''''''((((((((()))))))))'''((()))******++++++***))))))))))))((((((((((((++++++,,,---------------++++++***((('''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$###$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%######$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%***)))(((&&&%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%%%%%%%%%%###""""""!!!!!!""""""#########$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%############%%%&&&######$$$$$$$$$$$$%%%%%%"""$$$%%%&&&&&&%%%###"""!!!""""""###$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$########################"""######$$$$$$######"""!!!!!!""""""###$$$&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&#########$$$$$$%%%%%%%%%######$$$$$$%%%%%%%%%&&&######$$$%%%%%%%%%%%%$$$%%%%%%%%%$$$$$$#################################$$$$$$$$$###$$$%%%%%%&&&################################################""""""!!!!!!""""""###$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$$$$$$$$$$$$$&&&%%%###"""!!!""""""###!!!###$$$$$$$$$%%%&&&$$$$$$######"""""""""!!!$$$$$$######""""""""""""$$$$$$$$$###############$$$###"""!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%$$$$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%""""""############"""""""""""""""#########$$$$$$$$$$$$$$$###############$$$######""""""######$$$$$$######""""""######$$$%%%%%%%%%$$$$$$##################"""######$$$%%%$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&############$$$$$$$$$$$$########################$$$$$$###############$$$""""""""""""""""""""""""###$$$&&&&&&$$$###$$$%%%######$$$$$$$$$%%%%%%%%%######$$$%%%&&&''''''(((%%%$$$$$$$$$######""""""$$$$$$$$$###$$$%%%%%%&&&''''''&&&&&&%%%%%%$$$$$$&&&&&&'''(((((('''&&&&&&$$$%%%&&&'''''''''''''''&&&&&&&&&''''''((((((((('''''''''((((((((())))))'''((()))***++++++++++++))))))))))))(((((((((((()))***+++,,,,,,+++***)))******)))((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$###$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%######$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$"""#########$$$$$$$$$%%%###""""""!!!!!!""""""#########$$$$$$$$$%%%%%%%%%!!!""""""###$$$$$$%%%%%%##################""""""$$$###"""!!!!!!"""###$$$""""""""""""############ !!!$$$&&&'''&&&%%%$$$"""###$$$$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$########################"""######$$$$$$######"""$$$###############$$$$$$"""#########$$$$$$$$$$$$#########$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%######$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%$$$$$$$$$$$$########################$$$############$$$%%%%%%################################################"""""""""""""""###$$$$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!###$$$%%%%%%$$$###"""!!! """$$$$$$$$$###$$$&&&%%%%%%%%%$$$$$$######""""""######$$$$$$%%%%%%%%%########################$$$###""""""###$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#################################$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%%%%###$$$$$$$$$$$$$$$$$$###"""#########$$$$$$$$$$$$$$$$$$$$$$$$######""""""$$$$$$############$$$$$$""""""!!!!!!!!!!!!""""""%%%%%%%%%$$$$$$###############""""""###$$$$$$%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$""""""#########$$$$$$$$$#################################""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&''''''&&&%%%%%%&&&######$$$$$$$$$%%%%%%%%%######$$$%%%%%%&&&''''''$$$$$$$$$######"""""""""$$$############$$$%%%%%%((('''''''''&&&&&&%%%%%%&&&''''''''''''''''''&&&$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''((((((''''''''''''(((((((((((('''((()))******+++******))))))))))))(((((((((((()))***+++,,,+++***)))(((((((((((((((''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$"""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$############$$$###$$$%%%%%%&&&&&&&&&%%%######$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&###############$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%''''''&&&%%%%%%$$$######"""""""""######$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%% !!!"""###$$$%%%&&&&&&#########"""""""""""""""""""""!!!!!!!!!!!!""""""!!!!!!!!!""""""""""""###!!!###%%%&&&''''''&&&"""$$$%%%%%%$$$###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$$$$######%%%%%%$$$###"""""""""###""""""""""""############$$$$$$$$$$$$$$$$$$%%%%%%#########$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$###############################################################$$$%%%%%%###################################################""""""""""""###$$$$$$$$$$$$$$$##############################$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%$$$$$$$$$#########$$$$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$"""!!!!!!!!!###%%%&&&&&&%%%###"""!!!###$$$$$$#########$$$%%%%%%%%%$$$$$$$$$$$$$$$""""""$$$%%%%%%&&&&&&%%%"""""""""########################$$$%%%&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$### !!!###$$$$$$###"""!!!$$$$$$%%%%%%%%%%%%$$$$$$"""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$"""""""""!!!!!!"""""""""%%%%%%$$$$$$$$$$$$$$$$$$""""""""""""###$$$%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$"""""""""############$$$###############$$$$$$$$$###""""""""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&((('''&&&%%%&&&&&&######$$$$$$$$$%%%%%%%%%######$$$$$$$$$$$$%%%%%%$$$$$$$$$##############################$$$%%%%%%''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&'''''''''&&&&&&'''''''''(((((((((&&&'''((())))))******)))))))))))))))((((((((((((++++++,,,,,,,,,++++++***''''''((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$###############""""""###$$$%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''$$$$$$$$$$$$%%%'''((()))###$$$$$$%%%%%%$$$$$$###%%%$$$$$$$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%""""""#########$$$$$$$$$$$$$$$$$$######"""""""""""""""############""""""!!!""""""""""""#########""""""###$$$%%%%%%&&&&&&###$$$&&&%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$%%%%%%%%%%%%$$$$$$%%%$$$$$$###""""""######""""""#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################$$$%%%%%%%%%%%%$$$###############################################################$$$$$$%%%######################################################""""""######$$$%%%$$$$$$$$$#########""""""""""""#########$$$$$$$$$###$$$%%%%%%%%%%%%$$$###%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%######$$$$$$$$$######"""""""""###$$$%%%%%%%%%%%%"""$$$%%%%%%###""""""###############$$$$$$$$$$$$"""###$$$%%%%%%$$$######!!!"""""""""#########$$$"""###$$$%%%%%%%%%%%%%%%####################################$$$$$$$$$$$$""""""#########$$$$$$$$$%%%%%%%%%$$$$$$$$$######!!!"""###$$$$$$###!!! ######$$$$$$$$$$$$######"""###$$$%%%%%%%%%$$$$$$###$$$$$$%%%$$$###"""!!!###$$$$$$$$$$$$$$$$$$###$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%""""""""""""###$$$%%%&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%""""""""""""############""""""#########$$$$$$$$$"""""""""""""""###$$$$$$!!!!!!!!!!!!!!!!!!!!!!!!$$$%%%''''''%%%$$$%%%&&&######$$$$$$$$$%%%%%%%%%$$$$$$############""""""#########$$$$$$$$$$$$$$$###############$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&'''''''''%%%&&&&&&&&&&&&&&&%%%%%%'''&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&'''''''''((((((%%%&&&'''(((((())))))((())))))))))))((((((((((((*********)))******++++++))))))((((((''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$############### !!!"""###$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''''''((($$$$$$$$$$$$%%%&&&''''''###$$$%%%%%%%%%%%%$$$###$$$$$$$$$$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''######$$$%%%%%%&&&''''''%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$###############%%%%%%%%%$$$$$$#########"""###$$$%%%%%%$$$###""""""############$$$$$$$$$%%%$$$$$$######$$$%%%%%%!!!###$$$$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$%%%%%%&&&&&&%%%%%%$$$$$$###############$$$$$$######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$#########%%%$$$$$$$$$######""""""######$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%#################################"""###$$$$$$%%%#########################################################"""######$$$%%%$$$$$$$$$$$$######""""""""""""######$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$###%%%%%%%%%$$$$$$$$$###############$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%!!!"""###$$$$$$$$$$$$$$$$$$###""""""###%%%''')))###%%%&&&%%%###!!!!!!"""!!!!!!""""""######$$$$$$######$$$$$$###""" !!!!!!""""""#########$$$######$$$%%%%%%###"""!!!""""""""""""""""""""""""""""""######$$$$$$$$$%%%""""""######$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$%%%&&&'''&&&$$$"""!!!""""""############"""""""""###$$$%%%&&&%%%$$$$$$######$$$%%%$$$###"""!!!###$$$$$$%%%%%%$$$$$$###&&&%%%%%%$$$$$$%%%%%%&&&#########$$$$$$%%%%%%&&&""""""""""""###$$$%%%&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&""""""""""""############""""""######$$$$$$$$$$$$""""""!!!""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""$$$&&&%%%$$$###$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$######"""!!!!!!!!!#########$$$%%%%%%%%%&&&#########"""###$$$$$$%%%#########$$$$$$%%%%%%&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&''''''&&&%%%%%%'''''''''&&&&&&%%%%%%%%%&&&&&&&&&'''''''''(((((($$$%%%&&&'''(((((((((((())))))))))))((((((((((((((('''&&&&&&&&&''')))***++++++***((('''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$###"""######### !!!######$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''(((((($$$$$$######"""############$$$%%%&&&&&&%%%$$$###$$$$$$$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%"""###%%%'''((()))******#########$$$$$$%%%%%%%%%######""""""######$$$%%%######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$"""!!! !!!###%%%'''$$$$$$$$$$$$$$$###"""!!!########################%%%%%%%%%$$$$$$#########""""""############""""""$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################!!!"""###$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$######""""""######$$$%%%######$$$$$$$$$$$$######'''&&&&&&%%%$$$###""""""######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$########################%%%%%%%%%$$$$$$#########!!!!!!!!!"""#########$$$'''&&&$$$"""!!!!!!""""""######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!!!!!!!!!!!!!""""""$$$######"""""""""""""""""""""############""""""!!!!!!"""############"""$$$$$$##################"""############$$$$$$$$$$$$$$$############$$$$$$########################$$$$$$$$$$$$$$$$$$%%%%%%"""############$$$$$$$$$$$$############$$$&&&&&&$$$$$$$$$############"""##############################$$$%%%%%%%%%%%%$$$###$$$$$$%%%%%%$$$$$$###$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$###"""!!!########################""""""""""""""""""""""""!!!!!!"""###$$$$$$%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$######"""$$$$$$$$$#########""""""'''&&&$$$#########$$$$$$%%%&&&&&&''''''&&&&&&%%%'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$######%%%''''''&&&%%%&&&''''''&&&&&&%%%%%%&&&&&&'''''''''''''''((((((((((((,,,,,,+++***))))))******''''''''''''''''''''''''(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''''''''&&&%%%%%%$$$######""""""###$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%$$$$$$$$$######%%%$$$###"""!!!!!!""""""%%%%%%&&&&&&'''((())))))########################"""###$$$%%%%%%$$$###"""&&&%%%%%%$$$$$$%%%%%%&&&$$$######""""""######$$$"""###%%%&&&'''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%###$$$%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$%%%%%%######""""""######$$$%%%######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%"""  $$$$$$$$$$$$$$$###""""""########################$$$$$$$$$######"""""""""######$$$$$$$$$$$$######$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#######################################$$$$$$$$$%%%$$$###""""""###$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$######""""""######$$$%%%######$$$$$$$$$$$$######&&&%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$########################%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$%%%%%%%%%&&&%%%$$$""""""""""""###"""######$$$$$$$$$$$$$$$########################"""""""""###$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################"""!!!!!! !!!!!!"""##################"""!!!"""######$$$$$$##############################"""############$$$$$$$$$$$$$$$############$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!""""""######$$$$$$$$$%%%##############################$$$%%%%%%%%%%%%$$$###$$$$$$$$$$$$$$$$$$###$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###########################$$$$$$$$$$$$######"""################################################!!!""""""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$######&&&%%%$$$#########$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$###$$$%%%&&&&&&%%%%%%&&&((('''&&&&&&%%%%%%&&&&&&'''''''''''''''((((((((((((***)))((((((''''''(((((((((((((((((((((((((((((((((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''''''''''''''&&&&&&%%%$$$$$$############$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$#########%%%%%%%%%&&&&&&''''''(((##############################$$$$$$$$$$$$######%%%$$$$$$######$$$$$$%%%$$$$$$############$$$$$$###$$$%%%&&&&&&&&&%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%$$$###"""!!!%%%%%%$$$$$$$$$$$$$$$$$$######""""""######$$$%%%######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$'''%%%### ###$$$$$$$$$$$$###""""""#################################"""""""""""""""$$$$$$%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$######"""#########$$$$$$############$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$######""""""######$$$%%%######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$########################%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$######"""######$$$!!!"""######$$$$$$######!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!"""###$$$%%%%%%&&&########################%%%$$$$$$$$$######""""""$$$###""""""!!!!!!""""""######$$$$$$$$$$$$######"""######$$$$$$$$$$$$$$$########################"""############$$$$$$$$$$$$$$$############$$$$$$########################&&&%%%%%%$$$$$$#########"""############$$$$$$$$$###$$$%%%%%%$$$###!!! !!!"""###$$$%%%&&&&&&##############################$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%########################"""###$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%"""######$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$&&&%%%$$$#########$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$%%%&&&&&&%%%$$$$$$''')))'''&&&&&&%%%%%%&&&&&&'''&&&''''''''''''((((((((()))((((((''''''''''''(((************************'''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''''''''''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$#########$$$%%%&&&&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$######""""""######$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$%%%%%%&&&%%%%%%$$$###$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%$$$$$$%%%$$$$$$###"""!!!%%%%%%%%%$$$$$$###############""""""######$$$%%%######$$$$$$$$$$$$##############################""""""!!!!!!!!!!!!"""#########$$$$$$$$$######"""##########################################""""""$$$$$$%%%%%%%%%%%%$$$$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################&&&%%%$$$"""""""""######$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$##############################""""""######$$$%%%###$$$$$$%%%%%%$$$$$$############$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$#########"""!!!!!!!!!""""""#########$$$$$$%%%!!!!!!"""############"""!!!!!!!!!!!!!!!!!!!!!!!!"""""""""###$$$$$$$$$%%%""""""""""""""""""""""""######""""""!!! '''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$######$$$%%%%%%%%%%%%$$$###############$$$$$$$$$""""""#########$$$$$$$$$$$$$$$############$$$$$$########################&&&&&&%%%%%%$$$###""""""""""""#########$$$$$$$$$######$$$$$$$$$$$$$$$$$$!!!""""""###$$$$$$%%%%%%##############################$$$%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$%%%&&&%%%$$$###$$$''')))'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&'''''''''((((((***))))))(((((()))))))))))))))))))))))))))))))))''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######!!!"""%%%&&&'''&&&%%%$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%###""""""###%%%%%%$$$$$$############$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###############""""""######$$$%%%######$$$$$$$$$$$$############################## !!!!!!"""###%%%&&&'''"""######$$$$$$$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%$$$###""""""""""""$$$$$$$$$%%%%%%$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$##############################""""""######$$$%%%$$$$$$%%%%%%%%%%%%$$$$$$#########$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$#########"""!!!!!!!!!!!!""""""###$$$$$$$$$%%%!!!!!!"""############"""""""""""""""""""""""""""%%%$$$$$$$$$###"""""""""""""""""""""""""""""""""""""""""""""!!!!!! '''&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$######$$$%%%%%%%%%%%%$$$""""""#########$$$$$$$$$""""""#########$$$$$$$$$$$$$$$############$$$$$$########################&&&&&&%%%%%%$$$###""""""""""""#########$$$$$$$$$'''&&&$$$#########%%%&&&######################################################$$$%%%%%%%%%%%%$$$$$$######""""""######$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%###"""###&&&)))'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&'''''''''''')))((((((((((((((())))))((((((((((((((((((((((((&&&'''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''&&&&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###### """$$$&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$############"""######$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%######%%%&&&''''''''''''%%%%%%$$$$$$$$$$$$$$$$$$######""""""######$$$%%%######$$$$$$$$$$$$#######################################$$$$$$$$$%%%%%%""""""###$$$$$$$$$$$$###########################$$$$$$$$$$$$$$$%%%%%%%%%######$$$$$$$$$$$$###############$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$###""""""$$$$$$%%%%%%%%%%%%$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#####################""""""######$$$%%%$$$$$$%%%%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$###########################$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$!!!"""###$$$$$$$$$$$$$$$!!!"""######$$$$$$##############################&&&%%%%%%$$$###"""!!!!!!#############################################$$$%%%$$$######""""""############$$$$$$$$$$$$######"""######$$$$$$$$$$$$$$$"""""""""###$$$$$$%%%%%%"""############$$$$$$$$$$$$$$$############$$$$$$########################&&&%%%%%%$$$$$$#########"""############$$$$$$$$$((('''%%%###""""""######$$$$$$$$$#########""""""##############################$$$%%%%%%%%%%%%$$$$$$###"""!!!!!!"""###$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###&&&&&&%%%%%%$$$######""""""###############$$$$$$######$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$%%%%%%$$$######&&&((('''&&&&&&%%%%%%&&&&&&'''%%%&&&&&&&&&&&&'''''''''&&&%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$######"""###$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$############$$$#########$$$$$$############$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%###$$$%%%&&&''''''''''''$$$$$$$$$$$$$$$$$$%%%%%%######""""""######$$$%%%######$$$$$$$$$$$$####################################$$$$$$$$$######"""""""""###$$$$$$$$$$$$$$$########################"""#########$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######################## """$$$&&&&&&%%%###!!!$$$$$$%%%&&&&&&%%%$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""######""""""######$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%""""""###$$$$$$$$$######"""######$$$$$$$$$$$$$$$########################%%%$$$$$$$$$###"""""""""$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$$$$%%%%%%$$$$$$###""""""""""""""""""##################"""!!!"""######$$$$$$######!!!""""""###$$$$$$%%%%%%"""############$$$$$$$$$$$$$$$############$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$ """$$$%%%$$$###"""###############$$$$$$$$$##############################$$$%%%%%%%%%%%%$$$$$$###"""!!!!!!"""###$$$$$$$$$######$$$$$$%%%&&&################################################%%%%%%%%%&&&%%%%%%$$$$$$########################################################################""""""######$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%$$$$$$$$$######%%%$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%"""###$$$%%%%%%%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%######$$$$$$$$$%%%%%%%%%###$$$%%%%%%&&&&&&&&&%%%"""$$$%%%%%%$$$$$$%%%&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%&&&&&&&&&'''''''''%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%&&&&&&''''''''''''''''''#########$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$############$$$$$$$$$######""""""###$$$%%%###$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%#########$$$$$$%%%%%%&&&#########"""###$$$$$$%%%######$$$$$$$$$$$$######"""""""""""""""""""""""" !!!"""###############!!!"""###$$$$$$$$$$$$$$$########################!!!!!!""""""#########$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################!!!$$$''''''%%%###!!!$$$$$$&&&&&&&&&&&&$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""#########"""###$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$#################################$$$$$$%%%%%%%%%!!!!!!""""""#########$$$"""###$$$%%%%%%$$$###"""######$$$%%%%%%%%%%%%$$$#######################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!"""###$$$$$$&&&%%%$$$$$$######$$$$$$""""""############""""""!!!!!!"""###############!!!""""""###$$$$$$%%%%%%"""############$$$$$$$$$$$$$$$############$$$$$$########################$$$$$$$$$$$$$$$$$$%%%%%%"""############$$$$$$$$$$$$((((((&&&$$$!!!!!!"""###$$$%%%%%%&&&##############################$$$%%%%%%%%%%%%$$$$$$###""" """###$$$$$$$$$######$$$$$$%%%&&&########################%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$###########################""""""""""""""""""""""""$$$$$$##################!!!!!!"""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%$$$$$$##################$$$$$$%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&"""###$$$%%%&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%#########$$$$$$%%%%%%%%%###$$$%%%%%%&&&&&&&&&&&&!!!###%%%&&&$$$$$$$$$%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''''''((()))''''''''''''''''''''''''&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%&&&&&&''''''''''''''''''""""""###$$$%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$######((('''&&&%%%%%%%%%%%%%%%######$$$%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&''''''&&&$$$$$$$$$$$$############$$$$$$$$$##################$$$######"""""""""###%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$######""""""$$$$$$$$$$$$$$$$$$$$$$$$#########""""""""""""""" !!!!!!""""""##################""""""!!!!!!$$$%%%%%%%%%%%%$$$######$$$###"""""""""###%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$################################################&&&&&&&&&%%%%%%$$$$$$$$$((('''%%%###""""""######$$$%%%%%%###""""""$$$'''$$$$$$$$$$$$$$$$$$$$$$$$###!!! """%%%&&&%%%###$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######"""#########&&&%%%$$$######%%%&&&((($$$$$$############$$$$$$###$$$%%%&&&&&&&&&&&&&&&########################""""""""""""""""""""""""""""""######$$$$$$$$$%%%$$$$$$$$$###############$$$$$$$$$#########""""""$$$$$$$$$$$$$$$###"""!!!######$$$$$$$$$######"""$$$$$$############$$$$$$######"""!!!!!!"""###$$$######"""""""""###%%%&&&######""""""""""""######$$$###"""!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$#########""""""######$$$$$$$$$$$$######$$$$$$######$$$$$$%%%&&&""""""############""""""$$$$$$########################"""""""""""""""###$$$$$$#####################$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&&&&&&&&&&&&&%%%%%%$$$###$$$$$$############$$$$$$########################$$$$$$$$$$$$$$$###"""!!!"""""""""###$$$$$$$$$%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((((('''&&&%%%%%%$$$$$$''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$#########'''&&&&&&%%%$$$$$$$$$%%%'''&&&$$$###"""######$$$######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%""""""""""""""""""""""""%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&''''''%%%%%%$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$##################""""""!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############!!!!!!!!!"""""""""""""""$$$$$$#########"""""""""""""""###$$$%%%%%%$$$$$$$$$###"""""""""###$$$%%%$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$############"""!!!"""###$$$%%%###$$$$$$###!!!"""###%%%$$$$$$$$$$$$$$$$$$$$$$$$###!!! !!!###%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&''' !!!"""###$$$$$$$$$$$$$$$############$$$$$$######$$$%%%%%%%%%%%%%%%########################""""""""""""""""""""""""#########"""""""""""""""########################$$$$$$$$$#########""""""$$$$$$$$$$$$$$$###""""""######$$$$$$$$$######"""""""""!!!!!!!!!!!!""""""######"""!!!!!!"""###$$$###"""!!!!!!!!!"""###$$$######""""""""""""######$$$###"""!!!!!!"""###$$$########################""""""#########$$$$$$$$$$$$$$$$$$#########""""""######$$$$$$$$$$$$######$$$$$$######$$$$$$%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$##############################""""""""""""#################################$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$###$$$$$$############$$$$$$########################$$$$$$$$$$$$$$$###""""""###############$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$######&&&&&&%%%$$$$$$$$$$$$$$$%%%$$$#########$$$%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%$$$$$$######"""""""""!!!"""""""""""""""!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""!!!!!!$$$$$$$$$############### """###$$$%%%%%%%%%######""""""######$$$%%%$$$$$$$$$############"""%%%%%%%%%%%%%%%%%%%%%%%%##########################################$$$$$$ !!!###$$$%%%"""#########!!!!!!###$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%###!!! """$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&''''''"""###$$$$$$###!!!$$$$$$############$$$$$$"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""%%%$$$$$$######"""!!!!!!""""""""""""""""""""""""$$$$$$$$$##################$$$$$$$$$$$$###"""""""""######$$$$$$$$$######""""""!!!!!!!!!!!!""""""######""""""""""""#########"""!!!!!! !!!!!!"""######""""""""""""############""""""""""""######""""""""""""""""""""""""###############$$$$$$$$$$$$$$$$$$#####################$$$$$$$$$$$$######$$$$$$######$$$$$$%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$##############################"""""""""######$$$###########################$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$###$$$$$$############$$$$$$###########################$$$$$$$$$$$$###""""""$$$$$$$$$###############$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$######""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%&&&'''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%&&&"""###############$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$$$$###%%%%%%$$$############$$$############$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%$$$$$$$$$######"""!!!!!!############""""""""""""#################################$$$$$$$$$$$$$$$$$$######""""""!!!!!!!!!$$$$$$$$$$$$############ !!!######$$$$$$$$$###############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################""""""######$$$$$$%%%%%% !!!"""###$$$%%%###$$$$$$$$$""""""###%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$"""""""""###%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$((('''&&&%%%$$$#########%%%%%%%%%%%%$$$###!!! $$$$$$############$$$$$$"""######$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""%%%$$$$$$$$$$$$$$$$$$$$$!!!!!!!!!!!!""""""""""""##############################$$$$$$$$$######"""""""""###$$$$$$$$$######%%%$$$$$$######$$$$$$%%%#########"""""""""""""""######""""""!!!!!!!!!!!!######""""""""""""#########""""""""""""""""""###"""""""""#####################################################################$$$$$$$$$$$$######$$$$$$######$$$$$$%%%&&&""""""############""""""###############$$$$$$$$$######""""""######$$$$$$###############$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$###$$$$$$%%%%%%%%%$$$$$$###$$$$$$############$$$$$$##############################$$$$$$$$$######"""%%%$$$$$$$$$###"""""""""$$$$$$$$$#######################################%%%$$$$$$$$$######""""""########################%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%&&&&&&''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&############$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""######$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""""""""""""""""""""%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$########################""""""""""""######$$$$$$$$$$$$######""""""!!!!!!########################""""""#########""""""!!!""""""######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###########################$$$$$$$$$%%%%%%&&&&&&"""""""""###$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$###""""""""""""!!!!!!"""###$$$''')))+++$$$$$$############$$$$$$######$$$$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$"""""""""""""""""""""""" !!!!!!"""###$$$$$$%%% !!!!!!""""""""""""########################"""######$$$$$$$$$######!!!"""###$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%############""""""!!!!!!$$$$$$$$$$$$###""""""!!!######""""""""""""######"""""""""######"""""""""#########$$$$$$$$$%%%%%%######################################################$$$$$$$$$$$$######$$$$$$######$$$$$$%%%&&&""""""############""""""""""""#########$$$$$$$$$###############$$$%%%%%%""""""#########$$$$$$$$$###$$$$$$%%%%%%$$$$$$############$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$#########$$$%%%%%%$$$$$$$$$$$$$$$############$$$$$$########################"""######$$$$$$$$$######%%%$$$$$$$$$###"""""""""################################################"""""""""######$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""######$$$$$$%%%%%%%%%%%%$$$$$$######%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%########################!!!!!!!!!"""######$$$$$$##################"""""""""""""""""""""###############$$$$$$######"""!!!""""""###$$$$$$$$$$$$###"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%$$$$$$###$$$&&&''''''&&&%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###%%%%%%%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!!!!"""###$$$&&&&&&&&&$$$"""!!!!!!"""$$$&&&$$$$$$############$$$$$$$$$$$$$$$%%%$$$$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%""""""""""""""""""""""""!!!"""###### !!!!!!""""""######$$$###############$$$$$$$$$""""""###$$$$$$$$$$$$###!!!"""###$$$$$$$$$$$$$$$######""""""""""""############$$$######"""!!! ###$$$$$$$$$$$$######"""######""""""""""""######""""""############""""""#########$$$%%%%%%&&&&&&$$$$$$$$$##############################$$$$$$$$$######$$$$$$$$$$$$######$$$$$$######$$$$$$%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$"""""""""###$$$$$$%%%%%%###############$$$%%%&&&"""""""""###$$$$$$%%%%%%###$$$$$$%%%%%%$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$"""###$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$########################""""""###$$$$$$$$$$$$###$$$$$$$$$###############"""""""""#######################################!!!!!!""""""###$$$$$$%%%####################################$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%######$$$$$$$$$$$$#########$$$$$$$$$$$$%%%%%%%%%$$$############$$$%%%%%%%%%%%%&&&%%%%%%###"""!!!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$%%%&&&&&&#########$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%!!!!!!""""""###$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################!!!!!!"""######$$$%%%%%%##################$$$$$$ !!!!!!!!!"""""""""######$$$$$$$$$$$$$$$###!!!"""###$$$%%%$$$$$$###""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&%%%$$$######%%%''''''&&&$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$ $$$%%%$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$ !!!!!!"""$$$&&&((()))&&&%%%$$$###!!! $$$$$$############$$$$$$%%%%%%%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%"""""""""""""""""""""""" !!!""""""###!!!!!!""""""###$$$$$$%%%""""""#########$$$$$$$$$""""""###$$$$$$$$$$$$$$$!!!!!!"""$$$$$$%%%%%%$$$$$$######""""""######$$$######$$$$$$###""" !!!"""###$$$$$$######"""######""""""""""""######!!!"""###$$$$$$###"""!!!"""""""""###$$$%%%%%%%%%$$$$$$$$$#########""""""""""""#########$$$$$$$$$######$$$$$$$$$$$$######$$$$$$######$$$$$$%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$!!!""""""###$$$$$$%%%%%%############$$$%%%&&&'''!!!""""""###$$$$$$%%%%%%###$$$$$$%%%%%%$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%""""""###$$$$$$$$$$$$$$$$$$$$$############$$$$$$########################""""""###$$$$$$$$$$$$$$$###############$$$$$$$$$!!!"""""""""#########$$$########################""""""""""""####################################!!!!!!"""###$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&'''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&###$$$%%%%%%%%%$$$######$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%########################%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$###$$$$$$%%%&&&""""""###$$$%%%&&&&&&'''######$$$$$$$$$%%%%%%%%% !!!"""###$$$$$$""""""######$$$$$$$$$$$$""""""""""""""""""""""""""""""###$$$%%%%%%&&&&&&"""""""""###$$$$$$$$$%%% !!!!!!""""""!!!"""###$$$%%%&&&&&&&&&!!!"""###$$$%%%$$$######$$$$$$$$$%%%%%%&&&&&&&&&################################################%%%$$$$$$$$$######"""""""""###$$$%%%&&&%%%%%%$$$"""$$$&&&&&&%%%######$$$$$$$$$$$$$$$$$$$$$$$$$$$"""%%%$$$######%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''''' $$$'''((())))))$$$$$$############$$$$$$&&&&&&&&&&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%""""""""""""""""""""""""############$$$$$$$$$$$$!!!""""""###$$$%%%%%%%%%""""""######$$$$$$$$$$$$!!!"""###$$$$$$$$$$$$$$$!!!!!!"""$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$$$$###"""  !!!#########""""""######""""""""""""######!!!"""###$$$$$$###"""!!! !!!!!!"""###$$$$$$$$$$$$$$$$$$$$$######""""""""""""######$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$######$$$$$$%%%&&&""""""############""""""!!!""""""###$$$$$$%%%%%%############$$$%%%&&&'''!!!""""""###$$$$$$%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&!!!"""###$$$$$$$$$$$$$$$$$$$$$############$$$$$$########################!!!"""###$$$$$$$$$$$$$$$""""""######$$$$$$$$$%%%!!!!!!""""""#########$$$""""""""""""""""""""""""$$$$$$######"""!!!!!!!!!"""""""""""""""""""""""" !!!###$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%"""###$$$%%%'''((()))***''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&########################%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$$$$$$$$$$###############$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&'''!!!"""$$$%%%&&&&&&%%%$$$######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%"""""""""""""""""""""""" !!!""""""""""""""""""""""""""""""######$$$##############################""""""""""""######"""###$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$$$$$$$###""""""############$$$$$$$$$"""$$$&&&&&&&&&%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&%%%%%%$$$###""""""$$$######$$$&&&&&&%%%$$$######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######!!! $$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$###"""!!!!!!######$$$$$$$$$$$$######!!!"""###$$$$$$###"""!!!$$$######"""$$$&&&)))***%%%%%%$$$###"""""""""###!!!"""###$$$$$$###"""!!!#########"""""""""""""""###!!! ###%%%""""""""""""""""""""""""######$$$$$$$$$%%%%%%%%%########################""""""######$$$$$$$$$$$$########################$$$$$$############$$$$$$$$$#########"""!!!!!!!!!$$$$$$$$$############"""""""""""""""""""""""""""%%%%%%$$$$$$###"""""""""######""""""!!!!!! !!!!!!"""###############$$$$$$$$$$$$$$$###"""!!!!!!!!!"""###$$$%%%%%%%%%%%%%%%$$$$$$###"""""""""#########$$$$$$%%%%%%%%%!!!!!!"""###$$$$$$%%%%%%$$$$$$$$$#########""""""###%%%''')))))))))'''&&&$$$$$$$$$#########""""""########################!!!"""""""""############$$$%%%%%%%%%%%%$$$######""""""###$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$#########""""""!!!!!!##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%''''''&&&%%%%%%'''((()))&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&''''''&&&&&&%%%######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""%%%%%%%%%$$$$$$$$$######$$$$$$##################%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%((((((((((((((((((((((((''''''&&&%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''((()))%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%########################""""""###$$$$$$$$$######"""""""""""""""###$$$$$$########################$$$$$$############$$$$$$"""###$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$#########"""############$$$$$$$$$###$$$%%%%%%$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&%%%%%%$$$######"""""""""!!!###$$$%%%$$$"""######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!! $$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###"""""""""!!!!!!""""""""""""!!!!!!######$$$$$$$$$$$$######&&&%%%$$$######$$$%%%&&&$$$$$$######"""#########""""""############""""""###"""""""""""""""""""""!!!!!! !!!!!!"""###""""""""""""""""""""""""############$$$$$$$$$%%%##############################""""""######$$$%%%########################$$$##################$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############"""""""""""""""""""""""""""$$$$$$$$$###############$$$$$$#########"""""""""!!!""""""###############$$$$$$$$$$$$$$$###""""""""""""######$$$$$$%%%%%%##################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%!!!""""""###$$$$$$%%%%%%$$$$$$$$$#########""""""###$$$%%%&&&&&&&&&%%%$$$$$$$$$$$$#########""""""########################""""""""""""############$$$$$$$$$$$$$$$######"""%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""""""""##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&''''''&&&&&&%%%###$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""%%%$$$$$$$$$###############################################################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%''''''''''''''''''''''''''''''&&&%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$%%%%%%'''((((((%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$######""""""""""""###$$$$$$########################%%%%%%$$$$$$$$$$$$%%%%%%######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$"""############$$$$$$$$$%%%%%%%%%###""""""$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$#########""""""!!!###$$$%%%$$$"""######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$######""""""$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$########################!!!!!!""""""""""""!!!!!!%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%$$$###""""""!!!#########"""######$$$$$$#########""""""#########""""""""""""""""""###### !!!"""$$$$$$###"""""""""""""""""""""""""""""""""""""""#########$$$$$$##############################"""!!!"""###$$$%%%################################################$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$############""""""""""""""""""""""""""""""############$$$$$$$$$$$$$$$$$$$$$$$$#########!!!"""######$$$$$$#########$$$$$$$$$$$$###""""""#########$$$$$$$$$$$$$$$!!!""""""###$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$"""""""""###$$$$$$%%%%%%$$$$$$$$$###############$$$$$$$$$###############$$$$$$$$$#########################################################""""""$$$$$$#########"""""""""%%%%%%%%%$$$$$$$$$#############################################"""""""""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$"""""""""###$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$#########"""""""""########################""""""""""""""""""""""""###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%$$$############""""""######$$$%%%########################$$$$$$$$$######$$$$$$$$$###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$############$$$%%%""""""#########$$$$$$$$$&&&%%%$$$""" ###%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$###############"""$$$%%%&&&%%%#########$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$######$$$###########################$$$$$$$$$$$$$$$%%%%%%""""""#########$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%$$$###""""""###$$$%%%%%%%%%%%%$$$###"""!!! ###"""""""""###$$$%%%%%%%%%$$$""""""""""""$$$%%%"""""""""""""""#########!!!"""###$$$$$$$$$######""""""""""""""""""""""""!!!""""""""""""#######################################!!!!!!!!!"""$$$%%%#################################$$$$$$#########!!!!!!!!!"""#########$$$$$$$$$$$$#########""""""""""""""""""""""""""""""!!!""""""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$######""""""###$$$$$$$$$$$$#########$$$$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$###""""""#########$$$$$$$$$%%%%%%%%%$$$$$$#########""""""#########$$$$$$$$$########################%%%$$$###"""""""""""""""################################################$$$$$$############""""""$$$######"""""""""""""""""""""###$$$%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$%%%''''''&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$!!!!!!"""###$$$%%%%%%%%%#########################################################""""""""""""!!!###############$$$$$$$$$""""""""""""""""""""""""###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$###""""""###############$$$$$$%%%##############################""""""""""""######$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%""""""#########$$$$$$$$$&&&%%%$$$""" ###%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###############$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$###"""!!!!!!"""$$$%%%###"""######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$#########$$$%%%#################################$$$$$$%%%%%%%%%"""""""""###$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$###"""!!!!!!"""###$$$######$$$$$$$$$######"""###"""""""""###$$$%%%%%%%%%$$$###""""""###$$$%%%!!!!!!""""""############$$$######"""###$$$%%%%%%""""""""""""""""""""""""!!!""""""""""""####################################"""!!!!!!!!!"""###$$$########################"""###$$$$$$$$$$$$###"""!!!!!!!!!"""#########$$$$$$$$$$$$#########""""""""""""""""""""""""""""""!!!!!!"""###$$$%%%%%%&&&########################""""""###$$$$$$$$$$$$$$$"""######$$$$$$$$$######%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########""""""%%%%%%%%%$$$$$$########################$$$$$$$$$########################&&&%%%$$$###""""""##############################""""""""""""""""""""""""$$$$$$$$$###############$$$###""""""!!!!!!""""""""""""###$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$%%%'''((((((((('''&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$!!!!!!"""###$$$%%%%%%%%%#########################################################""""""""""""!!!""""""#########$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$##################"""!!!$$$############$$$%%%%%%###########################""""""""""""""""""###$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$"""############$$$$$$$$$%%%%%%%%%###""""""$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""###$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$ !!!"""###""" ######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%###############$$$$$$$$$#########$$$$$$%%%%%%&&&""""""######$$$$$$$$$%%%""""""############""""""###""""""""""""""""""###"""#########$$$$$$%%%%%%#########"""######$$$$$$$$$$$$############$$$$$$!!!!!!!!!"""######$$$$$$$$$###"""""""""###%%%&&&"""""""""""""""""""""""""""""""""#########$$$$$$########################!!!!!!!!!"""""""""##############################"""###$$$%%%%%%$$$###"""$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$############"""""""""""""""""""""""""""!!!!!!"""###$$$$$$%%%%%%"""""""""###############"""###$$$$$$%%%$$$$$$$$$""""""###$$$$$$$$$$$$###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$###""""""!!!%%%%%%$$$$$$$$$$$$$$$$$$#######################################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$###############$$$$$$$$$""""""""""""""""""""""""#########$$$$$$$$$%%%%%%%%%$$$###"""!!!"""######%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%&&&''''''((((((''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$"""""""""###$$$$$$$$$%%%#######################################$$$$$$$$$$$$$$$#########""""""""""""""""""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%########################!!!"""##################$$$$$$######$$$$$$%%%&&&########################$$$######""""""######$$$$$$%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$"""$$$&&&''''''&&&$$$""""""############$$$$$$$$$###$$$%%%%%%$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$"""!!!!!!"""$$$$$$###"""######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%###"""!!!!!!"""$$$%%%""""""#########$$$$$$$$$"""######$$$%%%%%%&&&&&&###############$$$$$$$$$"""######$$$$$$######""""""######$$$$$$######"""%%%$$$#########%%%&&&'''$$$$$$######"""############$$$$$$%%%%%%$$$$$$### !!!!!!"""######$$$$$$!!!""""""###$$$#########""""""""""""""""""""""""############$$$$$$$$$%%%######################## """###$$$###"""!!!########################!!!###$$$%%%%%%$$$###!!!%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############""""""""""""""""""""""""""""""""""""###$$$$$$$$$%%%#########$$$$$$$$$%%%%%%"""###$$$$$$%%%%%%$$$$$$""""""###$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&&&&$$$$$$##################$$$$$$$$$$$$$$$$$$%%%%%%########################""""""#########$$$$$$$$$"""###$$$%%%%%%%%%$$$###""""""#########$$$$$$$$$""""""""""""""""""""""""""""""######$$$%%%&&&&&&&&&%%%###"""""""""$$$%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%&&&&&&'''(((&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$##################$$$$$$########################""""""#########$$$$$$$$$%%%$$$$$$$$$############!!!""""""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%$$$$$$$$$$$$$$$$$$%%%""""""""""""""""""""""""!!!"""###$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&########################%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$"""$$$&&&))))))&&&$$$""""""############$$$$$$$$$"""$$$&&&&&&&&&%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''((($$$$$$%%%%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%&&&(((((('''%%%######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###!!! """###%%%""""""######$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&########################$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%&&&&&&%%%$$$###(((&&&$$$######$$$&&&'''%%%%%%$$$###"""""""""######$$$%%%&&&&&&%%%$$$### !!!!!!"""###$$$$$$$$$ ###%%%&&&$$$""" """"""""""""""""""""""""###$$$$$$$$$$$$%%%%%%%%%######################## """$$$%%%###!!! ########################!!!"""$$$%%%%%%$$$"""!!!$$$#########""""""!!!!!!$$$$$$$$$############"""""""""""""""""""""""""""###############$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&######$$$%%%%%%%%%%%%$$$!!!"""###$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''"""""""""###$$$$$$%%%%%%#########$$$$$$%%%%%%&&&$$$$$$##################""""""######$$$$$$$$$$$$ !!!$$$%%%&&&%%%$$$###""""""######$$$$$$$$$$$$""""""""""""""""""""""""!!!!!!"""###%%%&&&'''((('''&&&$$$""""""###$$$%%%""""""###$$$%%%&&&&&&'''#################################$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&%%%$$$###$$$%%%&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$###############""""""""""""""""""""""""""""""######$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###!!!""""""###$$$$$$%%%%%%########################$$$$$$$$$%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$############'''&&&&&&%%%$$$###""""""""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&%%%$$$###!!!"""###$$$%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$######$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#######################################"""!!!!!!"""###$$$######$$$$$$$$$%%%%%%%%%"""############$$$$$$$$$$$$#########$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$######""""""######$$$########################$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$#########$$$&&&&&&&&&&&&%%%$$$$$$###$$$%%%&&&&&&$$$!!!##############################$$$$$$$$$$$$######################################################$$$$$$############$$$$$$######""""""!!!!!! %%%$$$"""!!!!!!!!!"""#########$$$######"""!!! !!!!!!!!!!!!!!!!!!!!!!!!&&&&&&&&&&&&%%%###!!! """############$$$$$$$$$##############################""""""######$$$%%%""""""""""""############""""""#########""""""!!!"""""""""######$$$$$$$$$########################"""############$$$$$$$$$###$$$$$$%%%%%%$$$$$$#####################$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$########################################################################$$$""" """%%%&&&%%%###&&&%%%$$$#########$$$%%%%%%$$$$$$###"""""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$###"""!!! !!!"""###$$$%%%$$$######&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############"""############$$$$$$$$$$$$#########""""""!!!!!! !!!"""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###$$$&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''%%%%%%%%%$$$$$$#########''''''&&&%%%%%%$$$############$$$$$$$$$%%%%%%%%%"""###$$$%%%%%%%%%%%%%%%########################&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########&&&%%%%%%$$$$$$#################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%$$$$$$###""""""###$$$%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$##############################$$$###"""!!!!!!"""###$$$######$$$$$$$$$%%%%%%%%%############$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$############$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$$$$######$$$$$$$$$$$$%%%%%%$$$$$$######"""###$$$%%%%%%$$$"""!!!##############################$$$$$$$$$$$$######################################################$$$$$$############$$$$$$###"""""""""""""""!!!!!!$$$######""""""""""""""""""###$$$$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%%%%$$$###""""""############$$$$$$$$$##############################""""""######$$$%%%""""""""""""############"""######$$$$$$######"""#########$$$$$$$$$%%%%%%####################################$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#################################$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$########################################################################$$$"""!!!"""%%%&&&$$$###$$$$$$$$$###$$$$$$%%%%%%'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%$$$###""""""###$$$%%%%%%%%%$$$$$$'''&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((((('''&&&%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$##################$$$$$$"""############$$$$$$$$$$$$#########""""""""""""!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###%%%&&&'''&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''%%%%%%%%%$$$$$$$$$######''''''&&&%%%%%%$$$############$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########%%%%%%$$$$$$############!!!"""###$$$$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$######"""######$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""""""""############$$$$$$$$$%%%%%%%%%############$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$""""""###$$$$$$$$$######$$$$$$$$$$$$%%%%%%%%%%%%##############################$$$$$$$$$$$$######################################################$$$$$$############$$$$$$"""""""""###############"""############""""""!!!""""""###%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%$$$$$$"""############$$$$$$$$$##############################""""""######$$$%%%"""""""""#########$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%####################################$$$$$$$$$%%%###$$$$$$%%%%%%$$$$$$#################################$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$########################################################################$$$"""""""""$$$%%%$$$###"""###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%''''''(((''''''&&&%%%$$$###$$$%%%%%%&&&&&&%%%%%%'''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$$$$$$$%%%"""############$$$$$$$$$###############""""""""""""######$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$#########%%%''''''%%%###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$'''&&&&&&%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$###""""""%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%$$$$$$######"""""" """$$$%%%$$$###"""#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######################## """$$$$$$###!!! $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%$$$$$$######"""###$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$%%%%%%%%%#########$$$$$$$$$%%%%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&################################################%%%%%%$$$$$$###$$$$$$%%%""""""###$$$$$$%%%$$$$$$'''&&&%%%###"""""""""#################################$$$$$$$$$$$$######################################################$$$$$$############$$$$$$""""""######$$$$$$%%%%%%!!!"""###$$$$$$###"""!!!"""######$$$%%%%%%$$$$$$"""""""""""""""""""""""""""######$$$$$$$$$$$$$$$""""""#########$$$$$$$$$##############################""""""######$$$%%%""""""#########$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#################################$$$$$$$$$%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$#####################$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$####################################################################################$$$$$$$$$### """###%%%&&&&&&%%%%%%$$$$$$######"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%'''''''''''''''&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""###$$$%%%%%%%%%""""""#########$$$$$$$$$##############################$$$$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$#########%%%''''''%%%"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$######""""""""""""$$$%%%%%%###############$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$&&&''''''%%%$$$"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%$$$$$$######$$$%%%%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&################################################%%%$$$$$$###$$$$$$%%%%%%######$$$%%%&&&&&&&&&%%%&&&$$$###!!!!!!!!!"""#################################$$$$$$$$$$$$######################################################$$$$$$############$$$$$$""""""######$$$$$$%%%%%%!!!"""###$$$$$$###"""!!!######$$$$$$###"""!!!!!!########################$$$$$$#########"""""""""""""""#########$$$$$$$$$##############################""""""######$$$%%%############$$$$$$$$$$$$###$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###########################$$$$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$#########""""""######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################################################################$$$$$$$$$############ """###%%%&&&&&&%%%%%%$$$######"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&&&&&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""###$$$%%%%%%%%%""""""#########$$$$$$$$$###############$$$$$$$$$######$$$$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$###"""###$$$&&&&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%""""""$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$$$$$$$########################!!!"""$$$%%%%%%$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$%%%&&&%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%###$$$$$$%%%%%%$$$$$$$$$######$$$$$$$$$$$$############$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$######""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""!!!######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$#########%%%%%%$$$$$$$$$$$$%%%%%%################################################$$$$$$######$$$$$$%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%!!! !!!###%%%'''##############################$$$$$$$$$$$$######################################################$$$$$$############$$$$$$"""""""""###############!!!""""""############"""###$$$$$$###"""!!! !!!!!!!!!!!!!!!!!!!!!!!!%%%$$$###""""""""""""""""""############$$$$$$$$$##############################""""""######$$$%%%#########$$$$$$$$$$$$%%%######$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$########################$$$$$$$$$$$$%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%$$$$$$###"""""""""######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################################################################$$$%%%$$$"""""""""$$$"""###$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&''''''$$$$$$%%%%%%%%%%%%$$$$$$&&&%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$$$$$$$%%%"""############$$$$$$$$$#########$$$$$$$$$$$$$$$"""######$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""###$$$%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%% """###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&!!!!!!""""""######$$$$$$"""#########$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$########################$$$#########""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''''''''''''''$$$$$$$$$%%%%%%$$$$$$#########$$$$$$$$$$$$############$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%###"""!!!######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$######$$$$$$$$$$$$$$$$$$#########"""$$$$$$############$$$$$$################################################$$$$$$######$$$$$$%%%&&&$$$%%%%%%%%%%%%$$$$$$### !!!"""###%%%&&&'''##############################$$$$$$$$$$$$######################################################$$$$$$############$$$$$$###"""""""""""""""!!!!!!"""""""""""""""######$$$######$$$$$$$$$###"""""" ###""""""!!!!!!"""$$$$$$"""############$$$$$$$$$##############################""""""######$$$%%%#########$$$$$$$$$%%%%%%"""###$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$#################################$$$$$$$$$%%%%%%%%%&&&&&&###$$$$$$%%%%%%$$$$$$###%%%%%%$$$$$$###""""""!!!######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################################################################$$$&&&$$$"""!!!"""$$$$$$$$$$$$###$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&''''''((($$$$$$%%%%%%%%%%%%$$$$$$&&&%%%$$$$$$$$$%%%''''''$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##################$$$$$$"""############$$$$$$$$$#########$$$$$$%%%%%%%%%!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%###!!!!!!"""$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%% !!!"""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&& !!!"""###$$$%%%%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""(((((('''&&&%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&'''((((((((('''$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$############$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$"""!!!######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$#########$$$$$$$$$$$$$$$######""""""$$$##################$$$########################""""""""""""""""""""""""$$$#########$$$%%%%%%&&&$$$$$$$$$$$$$$$###"""!!!###$$$$$$$$$$$$%%%%%%%%%##############################$$$$$$$$$$$$######################################################$$$$$$############$$$$$$######""""""!!!!!! ###"""!!!!!!!!!"""$$$%%%"""###$$$$$$%%%%%%%%%%%%########################!!!!!! !!!"""###%%%'''"""############$$$$$$$$$#################################"""###$$$$$$%%%######$$$$$$$$$%%%%%%%%%!!!"""###$$$%%%%%%&&&%%%$$$$$$$$$######"""""""""########################$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%$$$$$$###""""""!!!######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################################################################%%%&&&%%%""" """$$$&&&%%%$$$#########$$$%%%###"""""""""###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&'''(((((($$$$$$%%%&&&&&&%%%%%%%%%%%%%%%$$$###$$$%%%&&&'''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%'''(((((()))$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############"""############$$$$$$$$$#########$$$$$$%%%%%%%%% !!!"""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&### !!!$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%&&&'''''''''&&&&&&########################%%%%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""###$$$$$$$$$"""########################!!!!!!""""""######$$$$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######"""""""""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$%%%&&&'''$$$$$$$$$######"""""""""'''&&&$$$#########$$$$$$######""""""###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%$$$######%%%'''((('''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###$$$%%%&&&'''%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$############"""""""""!!!!!! ######$$$$$$$$$%%%%%%%%%########################!!!###&&&%%%###!!!"""$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%######$$$%%%######""""""###%%%'''((("""######"""!!!!!!###$$$""""""!!!!!!"""###$$$$$$########################""""""""""""""""""""""""$$$"""!!!!!!"""$$$$$$%%%&&&'''&&&%%%$$$###$$$###!!!###%%%&&&###!!!$$$#########""""""!!!!!!$$$#########""""""!!!!!!"""###$$$%%%%%%$$$###""""""############$$$$$$$$$$$$$$$############$$$$$$""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###""""""######$$$$$$##################""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########!!!"""""""""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''%%%######$$$%%%$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''###$$$&&&&&&&&&&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""$$$&&&&&&%%%%%%%%%&&&##############################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((('''%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""###$$$%%%$$$"""####################################$$$$$$$$$$$$###$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''%%%%%%$$$$$$$$$#########&&&%%%$$$#########$$$$$$###############$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&'''&&&%%%$$$$$$&&&''')))'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&'''%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$######%%%$$$$$$$$$##################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%$$$"""!!!###%%%###############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%######$$$%%%$$$############$$$&&&'''"""###$$$###"""!!!"""###"""""""""""""""###$$$$$$################################################%%%###"""!!!!!!"""###%%%######$$$%%%&&&&&&&&&&&&$$$###"""###%%%%%%###!!!$$$#########""""""""""""$$$#########"""""""""""""""###$$$$$$$$$$$$###""""""############$$$$$$$$$!!!!!! !!!!!!########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###############$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$######$$$$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!###%%%%%%$$$###$$$%%%########################$$$$$$%%%%%%%%%&&&&&&&&&""""""""""""""""""""""""%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""$$$%%%$$$###"""###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%###"""###$$$%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''&&&%%%%%%%%%%%%%%%$$$$$$&&&%%%$$$#########$$$$$$$$$############$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&'''&&&%%%%%%%%%&&&((()))'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%&&&########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&'''%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$###!!!!!!$$$&&&$$$$$$$$$$$$$$$#########&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%$$$######$$$%%%$$$$$$############$$$%%%"""$$$%%%%%%###!!!!!!!!!###""""""""""""###$$$$$$################################################%%%$$$###""""""###$$$%%%############%%%&&&'''((($$$###"""###%%%%%%###"""###############"""""""""###############""""""""""""###$$$$$$$$$$$$###""""""############$$$$$$$$$$$$######""""""######$$$########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$############$$$######$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$######$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$$$$%%%###""""""###$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""$$$$$$#########$$$########################%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%"""$$$%%%$$$######$$$%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######""""""###$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&'''((('''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###!!!!!!"""$$$&&&%%%%%%$$$$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%"""$$$%%%$$$###"""###$$$%%%$$$$$$###############"""$$$&&&&&&$$$"""!!! #########""""""###$$$$$$################################################%%%$$$############$$$%%%$$$$$$#########$$$&&&'''#########$$$$$$$$$###"""#########################################################$$$$$$#########""""""#########$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$##############################$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$$$$######$$$$$$$$$$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$%%%$$$"""!!!!!!###$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$""""""""""""$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$########################!!!###%%%%%%$$$###$$$%%%########################%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''((()))(((&&&%%%&&&'''######$$$%%%%%%&&&''''''%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###$$$%%%%%%%%%###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$#########"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$#########""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$######$$$$$$%%%#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""""""""""""""###############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$"""!!!!!!###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$########################"""###$$$$$$""""""###$$$$$$$$$$$$$$$###""""""!!!!!!$$$&&&&&&%%%"""!!!!!!$$$$$$###############$$$#########################################################""""""#########'''&&&$$$###"""######$$$"""###$$$$$$$$$########################$$$$$$$$$###############$$$$$$$$$$$$##################$$$""""""#########$$$$$$$$$"""""""""!!!!!!"""""""""########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$####################################$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%######$$$$$$%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%###""""""###$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$""""""""""""$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""######$$$$$$$$$########################"""$$$&&&&&&%%%$$$%%%&&&########################$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%+++,,,,,,***'''&&&&&&&&&######$$$%%%%%%&&&''''''$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$###$$$%%%&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$############""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&'''######$$$%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$"""#########$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&&&&%%%%%%%%%$$$$$$######$$$$$$%%%############$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%########################&&&$$$"""!!!###$$$$$$###$$$$$$$$$$$$%%%%%%%%%&&&########################"""###$$$###""""""###$$$###$$$$$$$$$###"""!!!!!!!!!###%%%&&&$$$######$$$%%%%%%$$$############$$$########################$$$$$$$$$$$$$$$$$$$$$$$$########################'''&&&%%%$$$###""""""""""""###%%%%%%###"""###$$$#########$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$###""""""###$$$$$$"""############$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$####################################$$$$$$%%%%%%&&&%%%$$$$$$$$$$$$%%%%%%&&&######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%!!!!!!"""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&'''%%%######$$$%%%$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!""""""###$$$$$$$$$###########################$$$&&&&&&%%%%%%%%%&&&#################################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%)))******(((%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%############$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&"""###$$$%%%%%%%%%%%%$$$'''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$######$$$$$$%%%%%%%%%$$$'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&&&&%%%%%%%%%$$$$$$######$$$$$$%%%############$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%###!!!"""$$$%%%$$$""""""######$$$%%%&&&''''''########################!!!###$$$###"""!!!"""$$$""""""###$$$$$$###"""!!!!!!###$$$$$$$$$$$$%%%'''&&&%%%$$$$$$#########$$$########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$###"""!!!!!!###%%%%%%###"""###$$$#########$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$###""""""###$$$$$$"""############$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$###########################"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$%%%&&&'''######$$$$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$####################################$$$$$$$$$$$$)))'''%%%$$$%%%%%%$$$"""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$########################!!!!!!!!!"""###$$$$$$$$$########################"""$$$%%%%%%$$$$$$%%%&&&########################$$$$$$$$$%%%%%%%%%&&&&&&((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''&&&%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!""""""###$$$&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######"""""""""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&"""###$$$%%%&&&%%%%%%$$$'''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$###$$$%%%&&&&&&&&&%%%%%%'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$&&&(((***+++,,,&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&'''&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%"""############$$$$$$$$$#########$$$$$$%%%%%%%%%"""""""""######$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$"""!!!###%%%&&&###!!!""""""###$$$&&&'''(((((($$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$###"""!!!"""###!!!"""###$$$$$$###"""!!!!!!###$$$######$$$&&&)))&&&%%%%%%$$$#########$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$!!!"""$$$%%%%%%$$$###"""!!!###&&&%%%###!!!###$$$#########$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%%%%$$$###""""""###$$$%%%"""############$$$$$$$$$$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$########################""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%&&&'''######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""""""""############+++)))&&&%%%%%%%%%$$$"""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$&&&''''''&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$######################## !!!!!!"""###$$$$$$$$$""""""""""""""""""""""""!!!###$$$$$$######$$$%%%########################%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&(((((())))))))))))((((((%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&&&&&&&&&&''')))&&&%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$######"""###$$$###!!!"""%%%'''&&&$$$"""$$$######""""""######$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""""""""###$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&)))(((&&&$$$$$$$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%###$$$%%%%%%&&&'''((()))$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!"""###$$$%%%%%%%%%&&&%%%$$$###""""""""""""#########$$$%%%(((***,,,'''&&&%%%%%%$$$$$$$$$%%%"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$%%%%%%$$$###"""""""""###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$##############################&&&'''''''''%%%### $$$%%%&&&&&&%%%$$$"""!!!$$$###"""""""""###%%%%%%######$$$$$$$$$%%%%%%%%%######$$$%%%%%%%%%$$$$$$ """###$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$)))(((&&&%%%%%%&&&((()))$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%"""###$$$###"""!!!!!!###$$$$$$$$$$$$$$$###"""!!!######$$$$$$$$$%%%%%%%%%########################"""###$$$%%%&&&'''''''''&&&&&&$$$$$$$$$$$$&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%&&&'''''''''&&&&&&%%%%%%&&&&&&'''(((((('''&&&%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""!!!!!!!!!!!!"""###$$$%%%%%%%%%"""######$$$$$$%%%&&&&&&########################,,,+++)))'''&&&'''((()))'''&&&&&&%%%%%%$$$$$$###&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$&&&&&&%%%'''***,,,,,,***'''%%%$$$#########$$$%%%%%%&&&%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%###!!!"""$$$%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$$$$$$$%%%&&&%%%%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%$$$###$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$$$$%%%%%%&&&%%%$$$###""""""""""""'''&&&%%%$$$$$$%%%&&&'''&&&&&&%%%%%%$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%%%%$$$$$$&&&%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$##############################$$$%%%&&&''''''%%%###"""$$$$$$$$$$$$$$$$$$###"""$$$###"""""""""###$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$### !!!###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$%%%"""###$$$###"""!!!!!!###$$$$$$$$$$$$$$$###""""""######$$$$$$$$$%%%%%%%%%########################$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%(((((('''&&&%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%&&&'''''''''&&&&&&%%%%%%&&&&&&''''''''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$#########"""""""""""""""""""""###$$$$$$$$$%%%&&&&&&%%%$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$...,,,***'''%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$&&&((())))))(((&&&$$$$$$$$$######$$$$$$%%%&&&&&&''''''''''''''''''&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$&&&&&&%%%###!!!"""######$$$$$$#########$$$%%%&&&&&&%%%$$$######$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%&&&&&&''''''%%%%%%%%%%%%$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$$$$$$$&&&%%%$$$######"""######''''''&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$############$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$&&&&&&%%%%%%$$$%%%%%%%%%##############################$$$$$$$$$$$$##############################"""$$$%%%''''''''''''&&&######"""""""""###$$$$$$######""""""######$$$%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$###"""######$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%''''''%%%$$$"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########"""###$$$###"""!!!!!!######$$$$$$$$$$$$###""""""######$$$$$$$$$%%%%%%%%%########################%%%%%%%%%%%%%%%$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&&&&%%%###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&'''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###############"""""""""##################$$$$$$&&&&&&%%%$$$$$$######"""%%%%%%%%%%%%%%%%%%%%%%%%,,,***(((&&&$$$$$$$$$$$$######$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$######$$$$$$%%%%%%''''''((((((((((((''''''$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###""""""###%%%&&&%%%$$$$$$$$$######"""############$$$&&&''''''&&&$$$######$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$######""""""""""""""""""""""""""""""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###&&&%%%$$$$$$############$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$&&&%%%%%%$$$$$$$$$%%%%%%""""""""""""""""""""""""######$$$$$$$$$$$$##############################"""###$$$%%%&&&'''&&&&&&""""""!!!!!!!!!"""$$$%%%###############$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$###"""!!!$$$%%%%%%%%%$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&''''''''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$######"""""""""###$$$###!!!!!!!!!#########$$$$$$$$$######"""######$$$$$$$$$%%%%%%%%%########################$$$$$$%%%%%%%%%$$$$$$######$$$%%%&&&&&&%%%$$$###!!!$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$###############"""######$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%&&&'''$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$###$$$$$$%%%%%%&&&&&&''''''''''''&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###!!!!!!!!!###%%%$$$###%%%$$$###""""""######$$$###$$$&&&''''''&&&$$$######$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""#########$$$$$$$$$%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%$$$###"""!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%$$$$$$######""""""!!!""""""""""""""""""""""""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$&&&%%%$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%$$$$$$######$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$%%%%%%%%%$$$$$$$$$############$$$$$$""""""""""""""""""""""""######$$$$$$$$$$$$##############################"""######$$$$$$$$$$$$###""""""!!!!!!!!!"""$$$%%%""""""######$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$###"""!!!%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""""""""###$$$###!!!!!!!!!###"""######$$$$$$$$$############$$$$$$$$$%%%%%%%%%########################!!!"""###$$$%%%%%%%%%%%%"""###%%%%%%%%%%%%###"""!!!###%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$%%%&&&&&&'''&&&&&&%%%%%%&&&&&&'''######$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$###############"""######$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$%%%&&&&&&%%%%%%$$$$$$###$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###""" !!!"""#########%%%$$$$$$#########$$$$$$###$$$%%%&&&&&&%%%$$$######$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""######$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%'''''''''''''''&&&&&&%%%$$$###"""!!!!!!#########$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$#########""""""########################"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%###""" """"""$$$%%%%%%%%%$$$###$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%%%%%%%%%%######""""""######$$$$$$##############################$$$$$$$$$$$$##########################################""""""""""""######"""""""""###$$$$$$""""""###$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$###"""$$$$$$#########$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$###!!!!!!###$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############""""""""""""###$$$###"""!!!!!!###""""""###$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%######################## !!!"""$$$%%%%%%&&&&&&######$$$$$$$$$$$$#########$$$%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&'''&&&&&&%%%%%%&&&&&&'''######$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$##################$$$$$$&&&&&&%%%$$$$$$######"""########################&&&%%%%%%%%%$$$$$$######''''''&&&%%%%%%$$$######&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$'''&&&&&&%%%%%%&&&&&&'''%%%%%%$$$$$$######$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$"""!!!"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""###%%%&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""#########$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$###########################$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$###""" !!!"""$$$%%%%%%%%%$$$###$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$$$$%%%%%%%%%$$$############$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$##############################$$$##################$$$$$$$$$$$$$$$$$$$$$###"""!!!"""###$$$%%%$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$######""""""!!!"""###%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""############"""###$$$###"""!!!!!!###""""""###$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################!!!"""###$$$$$$$$$$$$$$$$$$$$$############$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%"""""""""###$$$$$$$$$%%%&&&&&&%%%$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&########################$$$$$$$$$$$$$$$$$$$$$$$$(((&&&###"""###$$$$$$###"""###$$$%%%%%%%%%%%%$$$$$$$$$###""""""###$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################'''&&&&&&%%%%%%$$$$$$###$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%!!!"""$$$%%%&&&&&&%%%%%%$$$$$$%%%&&&((())))))***""""""######$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&'''''''''&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$##############################$$$%%%%%%&&&''''''%%%%%%%%%$$$$$$%%%&&&&&& """###$$$$$$###### !!!###%%%&&&%%%###"""$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$##########################################$$$%%%&&&&&&$$$%%%&&&&&&%%%$$$"""!!!!!!"""###$$$%%%$$$############$$$$$$$$$%%%%%%%%%######$$$%%%%%%%%%$$$$$$!!!!!! !!!###%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$&&&''''''&&&$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!""""""######$$$$$$"""###$$$###"""!!!!!!###!!!"""###$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###########################$$$$$$$$$$$$###""""""%%%$$$###""""""###$$$%%%###""""""###$$$%%%''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%!!!!!!"""###$$$%%%%%%&&&"""######$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%!!!"""$$$%%%''''''((((((###$$$$$$%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$#########$$$%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$%%%%%%&&&%%%$$$"""!!!$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%%%%$$$######$$$%%%%%%&&&%%%%%%$$$#########$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''(((((()))(((&&&$$$$$$$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$######"""'''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$$$$$$$$$$$$$#########""""""%%%$$$$$$$$$######"""""""""############$$$$$$$$$'''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################!!! """&&&'''$$$"""########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$$$$### ###&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%$$$###"""###$$$%%%'''&&&&&&$$$$$$$$$$$$&&&&&&"""""""""###$$$$$$$$$%%%######$$$$$$$$$%%%%%%%%%&&&%%%$$$###""" ######$$$$$$$$$%%%%%%%%%######%%%%%%&&&%%%$$$######$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################&&&%%%%%%$$$###"""!!!!!!!!!!!!"""###$$$$$$%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$###""""""###$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$$$$######%%%%%%%%%$$$$$$#########"""###$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''(((((('''%%%$$$%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%$$$###"""$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$###""""""###$$$%%%%%%$$$###"""""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((((('''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''""" %%%((('''%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''(((((('''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$######%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%$$$###"""&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%%%%$$$######$$$%%%%%%&&&%%%$$$$$$######$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&''''''(((&&&%%%$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$###$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$#########""""""###"""""""""!!!!!!!!!!!!"""############$$$$$$$$$&&&%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$#########%%%%%%%%%$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$#########!!! """$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$######"""""""""######$$$$$$%%%$$$############$$$%%%$$$$$$$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$"""!!!!!! ######$$$$$$$$$%%%%%%%%%###$$$%%%%%%%%%$$$#########$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$############$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%$$$$$$###"""""""""!!!""""""###$$$$$$%%%%%%!!!!!!"""""""""#########%%%$$$###""""""###$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######%%%%%%%%%$$$$$$$$$############$$$%%%&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&((((((&&&%%%$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######"""###$$$%%%%%%$$$###""""""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''&&&###!!!###(((++++++(((&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&''''''(((''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$######"""%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$######$$$$$$########################%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""######$$$$$$%%%$$$######"""###$$$&&&'''%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&''''''"""""""""###############%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&'''((((((&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%$$$$$$$$$$$$$$$$$$###$$$%%%&&&''''''&&&&&&$$$$$$$$$###############"""""""""""""""!!!!!!!!!"""############$$$$$$$$$$$$$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###!!!!!!###%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$###"""############!!!!!!###%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$### !!!"""###$$$###""""""$$$######""""""######$$$&&&&&&&&&%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$###""""""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$################################################"""""""""###$$$$$$%%%%%% !!!!!!!!!"""""""""$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$######%%%%%%%%%$$$$$$$$$$$$######$$$%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$#########$$$$$$$$$$$$###############$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''(((%%%###%%%))),,,+++***&&&&&&%%%%%%%%%%%%$$$$$$###$$$$$$%%%&&&''''''((('''''''''&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!%%%$$$$$$######$$$$$$%%%&&&%%%$$$#########%%%%%%""""""""""""""""""""""""%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!""""""###$$$%%%%%%&&&&&&%%%$$$######$$$&&&'''%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%&&&&&&&&& !!!"""###$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%"""###&&&((()))((('''&&&########################$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$!!!!!!%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$###"""""""""%%%&&&$$$!!! """$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###!!!###%%%%%%$$$"""!!!$$$$$$############$$$$$$&&&&&&%%%%%%$$$$$$$$$#########$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$######"""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""#########$$$$$$$$$""""""#########$$$$$$$$$############$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&&&&&&&%%%$$$#########$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$######$$$$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''&&&$$$###$$$&&&(((((('''%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&''''''(((''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!%%%$$$$$$######$$$$$$%%%%%%%%%#########$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%&&&''''''((('''&&&%%%$$$$$$%%%%%%%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%""""""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$((((((''''''&&&&&&&&&%%%"""###&&&((()))((('''&&&########################$$$$$$$$$$$$$$$%%%%%%%%%""""""#########$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%""""""&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$###"""###%%%'''%%%""" !!!$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$### """%%%''''''&&&###"""$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%$$$$$$######""""""######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$############$$$$$$%%%%%%$$$$$$############$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################"""""""""###$$$$$$%%%%%%###############$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%$$$$$$########################$$$%%%%%%%%%%%%%%%%%%$$$#########$$$$$$%%%%%%%%%###$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%###$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''$$$###"""###$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%&&&''''''&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$######"""%%%$$$$$$######$$$$$$%%%$$$$$$######$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%###$$$$$$%%%%%%$$$$$$###$$$$$$######$$$$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&'''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$(((((('''&&&&&&%%%$$$$$$%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%((((((''''''&&&&&&%%%%%%###$$$%%%&&&''''''&&&&&&###############$$$$$$$$$"""""""""###############"""############$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&'''&&&%%%######%%%'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$$$$###%%%&&&%%%$$$""""""###$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###!!!"""%%%''''''&&&$$$"""$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$########################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$%%%%%%###$$$$$$%%%%%%$$$$$$###""""""######$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################""""""######$$$$$$$$$%%%########################"""############$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$#########$$$$$$$$$$$$%%%%%%%%%!!!"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%######$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$#########$$$%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%$$$$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$######%%%$$$$$$######$$$$$$%%%"""###$$$%%%%%%%%%%%%%%%########################%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%###$$$%%%%%%%%%%%%$$$###$$$$$$######$$$$$$%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$########################$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%!!!###%%%%%%%%%$$$###$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$###$$$%%%%%%########################&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%%%%'''&&&&&&%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%""""""#########$$$$$$$$$"""""""""######$$$$$$$$$"""############$$$$$$$$$$$$$$$######$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$%%%&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%%%%%%%$$$$$$$$$%%%&&&%%%###"""$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###!!!"""$$$%%%%%%%%%###"""###$$$%%%%%%%%%%%%$$$#########$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$%%%%%%%%%&&&######$$$$$$$$$%%%%%%%%%$$$############%%%&&&'''###$$$$$$%%%%%%$$$$$$###!!!""""""###$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#######################################$$$$$$$$$########################""""""""""""############$$$$$$%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$############$$$$$$$$$%%%%%%%%% """###%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%$$$############$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###"""###$$$&&&'''&&&%%%$$$$$$$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$#########$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%$$$$$$$$$%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%!!!###$$$%%%&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%###$$$%%%&&&&&&%%%$$$###$$$#########$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$########################$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############### ###%%%%%%%%%$$$#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$(((&&&$$$""""""###$$$%%%########################"""######$$$$$$%%%%%%&&&$$$$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&%%%%%%$$$$$$###"""!!!!!!%%%%%%$$$#########$$$$$$""""""######$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&"""############$$$$$$$$$######""""""###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!$$$%%%### %%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%&&&&&&&&&%%%###"""$$$''''''$$$!!!$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$ !!!"""###$$$######""""""###$$$%%%%%%$$$###"""$$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%"""######$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%######""""""###%%%'''((($$$$$$$$$%%%%%%$$$$$$$$$!!!""""""###$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$################################################$$$$$$##############################$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$$$$###############$$$$$$%%%%%%%%%!!!###%%%&&&''''''''''''''''''''''''''''''%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$#########"""###$$$%%%%%%%%%%%%%%%"""############$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""$$$&&&'''&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$#########$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$###"""!!!###$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$######"""&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###""""""############################## !!!###$$$%%%%%%%%%%%%((($$$!!! ###$$$###!!!$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$###"""  !!!###%%%&&&&&&&&&&&&"""%%%%%%$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&&&&$$$$$$$$$$$$%%%%%%&&&'''"""###%%%&&&&&&%%%###"""$$$%%%%%%&&&&&&%%%%%%$$$#########"""######$$$%%%''''''%%%$$$###"""""""""$$$$$$$$$###"""!!! $$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%$$$$$$#########$$$%%%%%%&&&''''''((('''&&&%%%%%%&&&'''(((+++&&&!!!!!!$$$&&&$$$"""&&&&&&''''''&&&$$$###!!!$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!$$$$$$$$$#########""""""&&&&&&%%%$$$###"""!!! %%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$$$$######$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$###""""""""""""###$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$###"""!!!"""""""""###$$$$$$$$$%%%########################&&&&&&&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$############""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&%%%$$$$$$"""###$$$%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$#########$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&'''&&&%%%###"""%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&%%%%%%%%%%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&)))$$$ %%%((('''$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""######$$$%%%%%%%%%###"""###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!  """############ ###'''(((&&&$$$$$$$$$%%%%%%$$$$$$###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%&&&'''%%%%%%$$$$$$$$$%%%&&&&&&###$$$&&&''''''&&&$$$###$$$%%%%%%&&&&&&%%%%%%$$$###############$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&"""""""""""""""""""""###$$$$$$$$$%%%%%%$$$$$$#########$$$$$$%%%&&&&&&'''''''''&&&%%%%%%&&&''''''((($$$ !!!$$$'''&&&$$$&&&&&&&&&&&&%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$###""""""$$$$$$$$$#########""""""$$$$$$$$$###############%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%%%%&&&%%%$$$$$$######$$$$$$%%%###############$$$$$$$$$######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$###""""""###############$$$$$$$$$########################%%%&&&&&&&&&%%%%%%$$$###########################%%%%%%%%%$$$$$$$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%$$$$$$"""###$$$%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&'''(((!!!!!!"""""""""#########(((&&&###$$$'''******(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$#########&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############%%%%%%%%%%%%%%%%%%%%%%%%""""""!!!!!!!!!###$$$%%%"""###%%%&&&%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$ !!!"""#########%%%&&&((('''&&&$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$"""""""""###$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%''''''''''''%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###############$$$%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$$$$######$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&### !!!$$$''''''%%%''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$###$$$$$$$$$$$$###""""""$$$$$$$$$###############""""""######$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######################################################$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$%%%'''(((%%%$$$$$$######$$$$$$%%%""""""######$$$%%%%%%&&&$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%###$$$$$$$$$$$$###""""""$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%'''((()))$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&'''((())))))***%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''########################%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%###"""!!! """$$$%%%"""%%%))))))&&&$$$%%%'''$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""###$$$%%%&&&""""""###$$$%%%%%%&&&&&&"""############$$$%%%&&&$$$$$$######$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$"""""""""###%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%############$$$%%%&&&&&&'''&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&''''''&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$############$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&""""""######$$$#########$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''&&&&&&&&&&&&######$$$%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%###!!!"""$$$&&&&&&%%%((('''%%%$$$###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$######"""########################"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###########################""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&'''%%%$$$$$$######$$$$$$%%%#########$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%######$$$$$$$$$######"""%%%$$$$$$$$$###"""""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&###%%%''''''&&&%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''####################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###!!! """$$$%%%%%%(((***)))&&&######%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########%%%&&&(((%%%%%%%%%%%%&&&''''''(((###"""!!!!!!"""###$$$$$$$$$#########$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$###$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$$$$%%%&&&'''&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$###$$$%%%%%%&&&((('''&&&%%%$$$$$$$$$$$$"""######$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$$$$$$$#########""""""###$$$%%%%%%%%%%%%%%%######$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$$$$$$$$$$######'''&&&%%%$$$###$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################"""######$$$$$$$$$##############################$$$$$$$$$############"""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$########################""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%$$$$$$######%%%%%%%%%%%%$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%"""######$$$$$$$$$######%%%$$$$$$$$$###"""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$$$$%%%%%%############""""""""""""$$$&&&''''''$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''#########$$$$$$$$$$$$$$$"""###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######%%%&&&&&&&&&%%%$$$########################$$$$$$###""""""###$$$%%%((())))))(((%%%###"""###$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$%%%&&&&&&'''%%%%%%$$$$$$%%%%%%&&&'''(((&&&$$$$$$$$$$$$###"""############$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%&&&&&&&&&'''%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&&&&)))((('''%%%$$$$$$######%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&%%%%%%$$$$$$$$$"""###$$$$$$%%%%%%%%%%%%######$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###&&&&&&%%%%%%$$$###""""""&&&%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############""""""###$$$$$$$$$$$$##################$$$$$$$$$%%%$$$$$$$$$######""""""###$$$$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%###$$$%%%&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$################################################$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$$$$######$$$$$$%%%$$$$$$######$$$$$$%%%'''&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%""""""###$$$$$$$$$$$$###$$$$$$$$$###############%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######""""""######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########''''''&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$%%%%%%%%%&&&#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###%%%&&&'''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$)))'''%%%%%%%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%$$$###$$$%%%&&&'''(((&&&%%%%%%''''''%%%###############$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$!!!"""$$$&&&&&&&&&%%%$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$$$$$$$%%%&&&&&&((('''&&&%%%%%%%%%%%%%%%''''''''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&***))))))(((''''''&&&&&&""""""###$$$%%%%%%%%%%%%$$$$$$##################$$$$$$%%%&&&&&&%%%$$$$$$###$$$%%%%%%$$$######$$$$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""""""""###$$$$$$$$$$$$$$$""""""#########$$$$$$$$$###############$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%"""###%%%&&&&&&%%%###"""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%""""""###$$$$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######!!!!!!""""""###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%&&&&&&%%%$$$$$$$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$%%%%%%'''''''''&&&&&&%%%%%%%%%&&&###!!!!!!$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###%%%'''''''''%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$)))%%%""""""%%%'''&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%'''''''''&&&%%%$$$'''&&&%%%%%%%%%&&&'''(((###"""!!!$$$''')))'''%%%############$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$ ###&&&'''&&&$$$"""%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%)))((('''&&&%%%$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&%%%$$$###"""!!!$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%$$$$$$######!!!"""###$$$%%%&&&&&&&&&$$$$$$##################$$$%%%&&&&&&&&&&&&%%%$$$!!!###$$$%%%%%%$$$%%%&&&###$$$%%%&&&'''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""!!!"""###$$$$$$$$$$$$$$$""""""######$$$$$$$$$$$$ !!!"""###$$$%%%&&&&&&#########$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%"""###%%%&&&&&&%%%###"""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$%%%''''''%%%$$$$$$$$$$$$$$$$$$%%%###$$$$$$%%%%%%&&&&&&'''"""###$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%!!!"""###$$$$$$$$$$$$$$$""""""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%$$$$$$$$$###### !!!!!!"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$#########$$$%%%&&&&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###$$$%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&"""""""""###$$$%%%''''''$$$$$$$$$######"""""""""###"""&&&&&&$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&###%%%(((++++++***'''%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%+++)))'''$$$###$$$%%%%%%###$$$&&&''''''&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&""""""""""""""""""""""""###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$%%%%%%$$$$$$###&&&&&&%%%$$$$$$######"""###############$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$###""""""###$$$$$$%%%&&&&&&&&&%%%###"""""""""##############################$$$#########""""""!!!!!!""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%%%%&&&%%%$$$#########$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$#########"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###&&&%%%$$$#########$$$$$$""""""###$$$$$$$$$$$$###"""######""" !!!###%%%"""############$$$$$$$$$&&&&&&&&&%%%$$$###"""!!!&&&&&&&&&&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&######$$$%%%&&&&&&&&&&&&'''&&&$$$%%%%%%&&&$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%########################%%%%%%$$$###$$$%%%&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$&&&'''&&&%%%$$$$$$%%%&&&'''))))))***((('''%%%$$$###$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''(((((('''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&###$$$&&&((()))(((&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&)))'''&&&$$$###$$$%%%&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$#########&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&&&&%%%%%%$$$#########$$$$$$%%%&&&&&&&&&&&&%%%$$$###"""######$$$########################$$$#########""""""""""""!!!!!!!!!"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$%%%&&&''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$#########$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%%%%$$$$$$$$$######""""""###$$$$$$$$$$$$######$$$$$$"""!!!!!!###%%%"""############$$$$$$$$$%%%%%%%%%%%%$$$######"""###############"""!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&&&&&&&%%%'''&&&$$$%%%%%%&&&$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''%%%$$$$$$&&&&&&%%%###$$$$$$%%%&&&''''''(((((('''&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''((('''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&%%%$$$######$$$%%%&&&&&&&&&%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&''')))((('''%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$########################&&&%%%%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$###$$$$$$%%%%%%$$$$$$###"""######$$$%%%%%%&&&&&&''''''&&&%%%$$$###"""!!!&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%&&&&&&'''''''''&&&$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###############"""""""""!!!!!!""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###%%%$$$#########$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$%%%&&&%%%$$$###"""""""""###$$$$$$$$$$$$###%%%%%%%%%$$$"""!!!###$$$"""############$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###"""""""""""""""!!!!!! $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&'''''''''&&&&&&%%%'''%%%$$$$$$&&&&&&%%%###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((&&&%%%%%%%%%%%%$$$"""$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$#########$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&''''''''''''&&&$$$############$$$%%%&&&%%%###!!! !!!###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((()))+++***'''%%%$$$%%%&&&'''%%%%%%%%%&&&&&&'''(((((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&''''''&&&$$$######$$$$$$%%%%%%$$$$$$############$$$$$$%%%%%%%%%&&&%%%%%%$$$###"""""""""&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&''''''''''''&&&%%%$$$$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$######### """###$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$%%%&&&&&&%%%"""!!!""""""###$$$$$$$$$$$$###&&&&&&'''%%%###""""""###""""""#########$$$$$$$$$"""###$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&(((((((((((('''&&&%%%%%%&&&%%%$$$$$$&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$&&&&&&%%%###$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&&&&%%%$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$%%%%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&############$$$%%%&&&&&&%%%###!!!!!!###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''')))***++++++***'''%%%$$$%%%&&&'''%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&''''''&&&$$$######$$$$$$%%%%%%$$$$$$###%%%%%%%%%$$$$$$$$$##############################&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&%%%$$$$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######### """###$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$%%%&&&&&&%%%"""!!!""""""###$$$$$$$$$$$$###%%%&&&'''&&&###""""""###""""""#########$$$$$$$$$""""""###$$$%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&(((((((((((('''&&&%%%%%%&&&%%%$$$$$$&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$###$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$&&&''''''&&&###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&'''(((((('''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$%%%%%%&&&&&&'''###$$$%%%%%%&&&&&&%%%%%%###$$$$$$$$$%%%%%%&&&&&&'''%%%###""""""###%%%'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''((()))***)))((('''%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$''''''''''''''''''''''''###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$###$$$$$$%%%%%%$$$$$$###&&&&&&%%%%%%$$$######"""""""""#########$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$######$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%$$$#########$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$%%%&&&%%%$$$###"""""""""###$$$$$$$$$$$$######%%%&&&%%%###""""""""""""############$$$$$$$$$"""###$$$%%%%%%%%%%%%%%%###$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&'''''''''&&&&&&%%%%%%$$$###$$$&&&'''&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&&&&%%%$$$###%%%%%%%%%%%%&&&&&&&&&&&&###########################$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%###""""""$$$&&&(((((('''#########$$$$$$%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))***'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$%%%%%%&&&&&&#################################$$$$$$%%%%%%&&&###$$$$$$%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&######$$$%%%%%%&&&''''''"""###$$$$$$%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%'''&&&$$$######$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######"""###$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%'''&&&%%%$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$#########$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%&&&&&&###########################$$$$$$%%%%%%$$$$$$###%%%%%%%%%$$$$$$$$$######""""""###$$$$$$$$$$$$###!!!###%%%%%%###""""""""""""############$$$$$$$$$######$$$%%%%%%%%%$$$$$$"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$#########$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$###$$$&&&'''&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&%%%$$$###%%%%%%%%%&&&&&&&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""$$$&&&''''''&&&"""######$$$%%%&&&''''''###$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''')))++++++'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&########################""""""###$$$%%%&&&&&&'''""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&######$$$%%%%%%&&&''''''""""""###$$$$$$$$$$$$###%%%&&&&&&''''''&&&&&&%%%$$$$$$###""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%&&&%%%%%%$$$###"""!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%$$$$$$$$$#########$$$$$$%%%&&&&&&))))))((('''&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######"""""""""###%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%''''''%%%%%%%%%%%%''''''""""""""""""""""""""""""#########$$$$$$%%%%%%&&&&&&%%%$$$#########$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&########################$$$$$$$$$%%%%%%$$$$$$$$$&&&%%%$$$#########$$$$$$""""""###$$$$$$$$$$$$###"""$$$$$$###""""""""""""############$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$######$$$%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$#########$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&######$$$%%%&&&&&&&&&&&&%%%$$$###$$$&&&'''&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&%%%$$$###%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$&&&'''&&&$$$"""######%%%&&&'''(((((("""###%%%&&&'''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&(((***,,,---'''&&&&&&%%%%%%&&&&&&'''%%%$$$###!!!!!!!!!!!!"""'''&&&$$$#########$$$$$$$$$$$$$$$######"""""""""$$$%%%&&&$$$"""!!!"""$$$!!!"""######"""!!!"""###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$$$$$$$$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''%%%%%%%%%$$$$$$#########&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$'''&&&%%%%%%$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''$$$$$$%%%&&&''''''''''''######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$#########""""""""""""!!!""""""$$$%%%&&&''''''''''''&&&$$$######$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$###""""""$$$######$$$&&&&&&%%%###$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$###$$$%%%&&&'''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######### !!!"""###$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$#########$$$$$$%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%)))(((&&&$$$$$$$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""!!!!!!!!!!!!!!!"""###"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""############$$$$$$$$$&&&'''(((((('''%%%###!!!###$$$&&&(((((('''&&&%%%$$$$$$######"""#########''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&(((((('''''''''&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%$$$&&&'''((('''''''''(((((('''&&&%%%$$$%%%%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$&&&%%%$$$%%%&&&&&&$$$######$$$&&&''''''&&&$$$###'''''''''(((''''''&&&&&&)))((('''&&&&&&&&&&&&&&&%%%$$$#########$$$%%%%%%&&&%%%$$$#########$$$$$$%%%%%%$$$$$$$$$#########%%%%%%$$$###"""###$$$&&&###$$$%%%%%%$$$%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&#########""""""!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''&&&%%%%%%%%%$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$###'''&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''%%%&&&&&&&&&&&&&&&%%%%%%###$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$############$$$%%%&&&&&&&&&&&&&&&&&&%%%$$$######$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&&&&%%%$$$$$$###$$$######$$$&&&&&&%%%###$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$%%%%%%%%%%%%###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$########################%%%%%%%%%$$$$$$$$$#####################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&)))'''&&&$$$$$$$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################"""""""""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$$$$$$$%%%&&&'''&&&%%%###!!!###$$$&&&'''((('''&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&((('''''''''&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%$$$&&&(((((('''&&&'''(((((('''&&&%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$&&&(((((('''&&&$$$%%%&&&&&&&&&&&&%%%$$$&&&&&&'''''''''&&&&&&%%%(((''''''&&&%%%%%%&&&&&&$$$$$$$$$$$$%%%&&&((((((&&&%%%$$$#########$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$&&&$$$""""""###%%%&&&&&&$$$$$$$$$###""""""%%%'''&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%&&&###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$############%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$######"""######$$$$$$######"""&&&%%%%%%$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%$$$###$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$(((''''''&&&&&&%%%%%%$$$$$$######$$$&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&###############$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$############$$$########################%%%%%%%%%$$$$$$$$$$$$###&&&&&&%%%$$$###""""""!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$%%%%%%$$$$$$$$$$$$$$$$$$!!!"""###$$$$$$###"""!!!%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((('''%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$%%%%%%%%%%%%$$$"""!!!"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$%%%"""###$$$%%%%%%$$$###"""###$$$&&&''''''&&&%%%%%%$$$$$$$$$$$$%%%&&&''''''###$$$$$$%%%&&&'''((()))&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%'''((((((&&&%%%%%%&&&''''''&&&%%%%%%%%%&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$&&&)))***)))(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""###%%%&&&%%%###%%%%%%$$$""" """$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$$$$######"""######$$$$$$$$$$$$######%%%%%%$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$###$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%'''''''''''''''&&&%%%$$$$$$$$$%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&&&&%%%%%%%%%$$$$$$$$$###%%%&&&'''&&&$$$########################$$$$$$$$$%%%%%%%%%%%%&&&$$$###"""!!!"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######"""######$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$######"""!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$%%%%%%%%%$$$$$$######### """###%%%%%%###""" %%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&%%%###!!!""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$%%%%%%""""""###$$$%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$#########$$$%%%&&&'''((($$$$$$%%%%%%&&&'''((((((&&&''''''''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&&&&'''&&&&&&&&&&&&'''((((((&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%%%%$$$$$$&&&((()))(((''''''&&&%%%%%%%%%%%%&&&'''$$$$$$%%%%%%&&&&&&%%%%%%&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""###%%%&&&&&&$$$"""%%%%%%%%%$$$######%%%'''%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&###$$$$$$%%%%%%$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$$$$######"""$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$''''''''''''&&&%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%$$$$$$%%%''''''&&&$$$####################################$$$$$$$$$$$$$$$###"""!!!"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######"""######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$%%%%%%%%%$$$$$$#########"""###%%%&&&&&&%%%###"""%%%%%%%%%%%%%%%%%%%%%%%%$$$############$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%%%%""" """"""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%######$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$""""""""""""###%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&'''''''''&&&%%%'''((('''%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&###$$$%%%%%%&&&&&&&&&%%%&&&%%%$$$%%%''''''%%%###'''&&&&&&%%%%%%&&&&&&'''###$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%$$$###"""!!!######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%!!!###%%%&&&&&&''')))+++&&&'''((('''%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%&&&###$$$$$$%%%%%%$$$$$$###""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$$$$$$$######%%%%%%%%%&&&&&&%%%%%%%%%$$$############$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$############&&&&&&&&&&&&%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$%%%''''''&&&%%%########################""""""#########$$$$$$$$$###############$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$############$$$%%%%%%###########################$$$$$$$$$$$$%%%%%%%%%######$$$$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###############$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$"""!!! """############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$""""""""""""###$$$%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&''''''''''''$$$&&&''''''%%%$$$$$$%%%$$$%%%&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&'''###$$$$$$%%%%%%&&&&&&'''######$$$%%%&&&&&&&&&&&&&&&%%%$$$%%%&&&&&&$$$"""&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&&&&''''''&&&%%%%%%%%%%%%%%%&&&&&&'''######$$$%%%%%%$$$###""""""###$$$%%%%%%%%%%%%$$$#########$$$$$$$$$%%%%%%"""$$$&&&%%%$$$)))333;;;777888777333---((($$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$############$$$$$$$$$%%%%%%########################%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&''''''&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$###############$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&'''$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$############$$$$$$$$$%%%$$$$$$######$$$$$$###""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&'''(((&&&%%%#################################$$$$$$$$$%%%%%%###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&##############################$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$############$$$$$$%%%&&&%%%%%%$$$$$$###$$$$$$$$$$$$#########$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$######$$$%%%&&&''''''''''''###%%%&&&&&&%%%%%%%%%&&&$$$%%%&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''######$$$%%%%%%&&&''''''"""###$$$%%%&&&&&&&&&&&&&&&%%%$$$&&&''''''&&&$$$%%%&&&'''(((((('''&&&%%%$$$$$$%%%''''''(((((((((&&&&&&%%%%%%&&&''''''(((!!!"""$$$%%%&&&&&&%%%$$$"""###$$$%%%&&&%%%%%%$$$"""""""""######$$$$$$$$$###&&&&&&###"""***;;;IIIPPPOOOLLLEEE:::000((($$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&########################'''&&&%%%$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&!!!!!!"""""""""#########&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&''''''&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$$$$############""""""###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###"""%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$######"""######$$$$$$$$$######$$$"""!!!!!!"""$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$&&&'''((('''%%%""""""""""""""""""""""""$$$$$$%%%%%%%%%&&&&&&&&&###$$$%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$#########$$$$$$%%%%%%&&&%%%%%%$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########"""###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%$$$$$$$$$%%%&&&&&&"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&######""""""""""""######&&&%%%%%%$$$#########$$$&&&&&&%%%$$$$$$$$$%%%%%%###$$$$$$%%%&&&'''(((((($$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$#########$$$%%%&&&''''''''''''"""$$$&&&&&&%%%%%%&&&'''###$$$&&&'''((('''&&&&&&%%%%%%%%%&&&&&&'''''''''######$$$%%%%%%&&&''''''"""###$$$%%%&&&&&&'''&&&%%%$$$$$$&&&)))***)))(((%%%&&&((())))))(((&&&%%%$$$%%%&&&'''((((((((((((&&&&&&&&&&&&&&&'''((()))$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$""""""###'''***---///777...777>>>000,,,((('''&&&%%%%%%$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&%%%$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$((('''&&&&&&$$$$$$###"""'''&&&&&&%%%%%%$$$$$$###$$$$$$###"""###$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&#########$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&''')))***++++++%%%%%%$$$$$$%%%%%%&&&'''###$$$$$$%%%%%%$$$$$$###%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%&&&'''(((((($$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%###"""!!!$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$###""""""#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###'''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%!!!"""###$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&((('''%%%###"""""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""""""""""""""""""""##############################$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$######"""&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%$$$&&&'''((('''%%%%%%%%%%%%%%%&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%''''''(((((('''%%%###"""$$$$$$%%%%%%%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&'''((())))))%%%%%%%%%%%%%%%&&&'''((('''&&&&&&&&&&&&'''(((((('''***,,,+++(((&&&'''((($$$$$$$$$%%%%%%%%%&&&&&&'''&&&%%%%%%%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''%%%$$$###$$$&&&(((***'''...%%%...444***)))###&&&&&&%%%$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%$$$######&&&''''''''''''''''''&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$""""""###$$$%%%&&&&&&'''%%%%%%$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%%%%$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%&&&''''''((($$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$#########$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################################################################$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$$$$$$$%%%%%%%%%&&&%%%%%%&&&(((((('''%%%((('''&&&%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&''''''''''''&&&$$$###$$$$$$%%%%%%%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&''''''''')))+++***(((&&&'''(((&&&&&&&&&&&&'''''''''''''''&&&%%%%%%%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%%%%%%%&&&&&&###)))!!!(((,,,(((+++"""%%%%%%$$$$$$$$$%%%&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!###$$$$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%%%%""""""""""""#########$$$%%%%%%$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%%%%$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%&&&'''((($$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""###%%%&&&''''''###$$$$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""############"""###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$#########$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$!!!""""""$$$%%%&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%&&&(((((('''%%%***)))&&&%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''&&&%%%&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$(((((('''&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&''')))******(((''''''(((''''''((((((((()))))))))'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%***$$$)))***---666((($$$$$$$$$$$$%%%%%%&&&'''%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%$$$$$$############""""""#########$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$%%%%%%'''&&&&&&%%%%%%$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''$$$%%%%%%%%%%%%%%%%%%$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$%%%&&&&&&'''&&&&&&%%%$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""###%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!""""""###"""""""""$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%&&&((()))'''&&&***)))&&&$$$$$$%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%$$$%%%%%%&&&''''''((())))))(((''''''''''''(((((((((((()))))))))&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$&&&&&&&&&&&&%%%&&&)))&&&***'''111???+++$$$$$$$$$$$$%%%%%%&&&'''%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&&&&%%%$$$&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&$$$&&&(((((('''$$$ %%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&'''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%'''((()))(((&&&((('''&&&%%%%%%''')))***&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''&&&&&&%%%%%%&&&&&&&&&'''$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&'''((((((((($$$$$$$$$%%%&&&'''((()))&&&&&&&&&&&&&&&''''''((('''''''''(((((((((''''''&&&&&&'''''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""$$$%%%&&&&&&&&&&&&###%%%$$$'''!!!000BBB(((%%%%%%$$$$$$$$$%%%&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$&&&'''''''''&&&%%%%%%%%%############%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""#########$$$$$$%%%%%%''''''&&&%%%%%%$$$######$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%#########$$$$$$$$$%%%%%%&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''''''''%%%&&&(((((('''###%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&''''''''''''&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&'''))))))(((&&&&&&&&&&&&&&&'''((()))***&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''&&&'''&&&&&&%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&'''((()))***######$$$%%%&&&((()))***'''&&&&&&&&&&&&'''(((((('''&&&&&&'''))))))(((&&&%%%%%%&&&&&&&&&'''''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%"""$$$%%%'''111FFF&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&'''&&&%%%%%%###"""!!! !!!"""###$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$###"""!!!%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$%%%&&&&&&'''###$$$$$$%%%%%%&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&'''''''''((($$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&'''''''''&&&%%%###"""!!!&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###%%%%%%&&&''''''((())))))%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$"""###$$$%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&''''''&&&&&&'''))))))((('''&&&'''((())))))(((''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&((((((&&&%%%$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$%%%&&&'''((()))&&&&&&%%%%%%&&&&&&'''((('''%%%%%%&&&)))***(((&&&%%%%%%&&&&&&&&&'''''''''%%%%%%&&&''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$############$$$&&&)))*** 444JJJ''''''&&&&&&%%%$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&%%%$$$$$$&&&%%%$$$""""""$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%&&&&&&'''"""###$$$$$$###"""!!! &&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&#########$$$%%%&&&'''((("""###$$$%%%&&&&&&'''((('''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((%%%%%%&&&&&&&&&'''''''''%%%%%%$$$$$$%%%%%%&&&'''%%%&&&&&&''''''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%***(((&&&######$$$&&&'''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%######%%%''')))+++,,,---%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''%%%&&&&&&&&&%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$ !!!###%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$(((((('''%%%###"""!!! $$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$%%%%%%&&&'''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&''')))***(((''''''((()))******(((%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%)))((('''%%%$$$$$$%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&%%%%%%%%%&&&''''''%%%%%%$$$$$$%%%%%%&&&''''''%%%$$$&&&)))***(((&&&&&&&&&&&&''''''''''''(((%%%%%%&&&''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$###$$$$$$%%%&&&***###+++---%%%000999+++%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%$$$######"""""""""$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$#########################################################&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$&&&((())))))(((((($$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$###$$$$$$$$$$$$######""""""$$$%%%&&&&&&&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&!!!!!!"""###$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% !!!###%%%%%%######$$$%%%%%%&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&''''''&&&$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$###$$$%%%&&&'''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&&&&&&&'''((())))))((('''&&&''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$%%%&&&'''''''''&&&'''&&&&&&%%%%%%&&&&&&''')))((('''&&&%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######!!!!!!!!!!!!""""""""""""%%%&&&((("""+++333'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$%%%&&&'''((((((''''''$$$$$$$$$$$$$$$$$$$$$$$$'''''''''&&&&&&%%%%%%$$$%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$###$$$$$$$$$$$$#########"""###$$$%%%&&&&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!""""""###$$$&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&'''((())))))((('''&&&''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''((('''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###"""###$$$%%%%%%%%%$$$$$$&&&!!!&&&'''$$$+++000'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$ !!!"""###$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%(((((('''&&&%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$###############$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$'''&&&$$$######$$$&&&'''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''((('''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''''''''''''''''''''((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''((('''&&&%%%%%%%%%&&&''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$&&&(((((('''%%%$$$%%%$$$%%%''''''***+++'''%%%%%%%%%%%%%%%%%%%%%%%%##############################$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%&&&&&&''''''(((&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$###&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''$$$%%%%%%&&&&&&''''''''')))((('''&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$###$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&''''''''''''''''''(((((((((((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''***)))&&&%%%$$$%%%&&&''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!###%%%%%%$$$###!!!!!!######%%%)))'''""""""%%%%%%%%%%%%%%%%%%%%%%%%##############################$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&'''(((((('''&&&&&&$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&'''''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''''''''''''''''''''''''''%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''%%%%%%%%%&&&&&&''''''''')))((('''&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$###$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&'''''''''(((((((((((((((''''''(((((((((''''''''''''''''''''''''''''''''''''''''''''''''***)))'''%%%$$$%%%'''((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%"""###$$$%%%&&&%%%$$$$$$"""((('''+++222*** $$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&(((((('''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&'''((((((&&&'''((())))))((('''&&&$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&''''''''''''''''''''''''''''''%%%&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&''''''&&&$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&######$$$$$$$$$%%%%%%%%%######$$$$$$%%%%%%&&&&&&%%%&&&&&&&&&''''''''''''%%%%%%&&&&&&'''(((((((((((((((''''''''''''(((((('''''''''''''''''''''''''''''''''''''''''''''''')))((('''&&&&&&&&&'''((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''(((%%%------222<<<000!!!&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%$$$$$$$$$$$$%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&'''''''''&&&'''((())))))((('''&&&###$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&((('''%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''&&&&&&%%%%%%$$$'''&&&&&&%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''''''''&&&&&&######$$$$$$$$$%%%%%%%%%"""######$$$%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''%%%%%%&&&&&&'''(((((())))))((('''&&&&&&'''((()))''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((('''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''''''(((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$#########$$$%%%&&&"""---,,,222===///$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&###$$$$$$%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""###$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''$$$$$$######$$$&&&''')))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&((())))))(((&&&%%%###$$$%%%%%%&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&)))(((&&&$$$#########$$$&&&&&&&&&&&&&&&&&&&&&&&&(((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%########################%%%$$$$$$$$$$$$%%%&&&'''######$$$%%%%%%&&&''''''%%%$$$$$$######"""""""""$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&&&&'''((('''&&&$$$######$$$&&&'''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((((('''&&&%%%$$$$$$###&&&&&&%%%%%%%%%&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&###$$$%%%&&&'''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$&&&'''((('''&&&&&&######$$$$$$$$$%%%%%%%%%""""""###$$$%%%%%%&&&&&&&&&&&&&&&'''''''''((((((%%%%%%&&&&&&'''((()))))))))((('''&&&&&&'''((()))''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&'''((())))))(((((('''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&+++BBB,,,---&&&$$$###$$$$$$$$$$$$$$$$$$$$$$$$)))(((%%%#########$$$%%%%%%&&&&&&'''&&&%%%###"""$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&$$$"""""""""$$$%%%%%%%%%%%%&&&&&&&&&''''''((('''%%%$$$###$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%&&&'''''''''&&&%%%$$$%%%&&&'''(((((('''&&&%%%%%%%%%%%%&&&&&&'''''''''$$$%%%&&&&&&$$$$$$%%%&&&(((((('''&&&%%%%%%$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$######$$$$$$%%%&&&"""###%%%&&&'''&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$"""%%%&&&%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###""""""###$$$%%%$$$&&&''''''&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$%%%&&&'''(((***(((%%%######$$$&&&(((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''(((((('''''')))((('''&&&$$$###!!!!!!&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%&&&'''(((((('''&&&%%%&&&&&&''''''''''''&&&&&&#########$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''''''''&&&&&&%%%%%%%%%)))((('''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$&&&''''''&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''(((((((((((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&%%%%%%$$$((((((((((((((((((((((((''''''''''''''''''''''''###%%%&&&&&&&&&&&&''')))%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$###"""###%%%&&&%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%###$$$%%%&&&''''''''''''&&&&&&&&&''''''''''''(((******))))))((((((''''''$$$$$$%%%%%%%%%%%%%%%%%%&&&'''''''''&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&***...CCC,,,,,,%%%$$$###&&&&&&&&&%%%%%%%%%$$$$$$((('''%%%###"""###$$$$$$%%%%%%&&&''''''&&&%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$#########$$$%%%%%%%%%%%%&&&&&&&&&'''''''''&&&%%%$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''''''''&&&%%%$$$%%%&&&'''(((((('''&&&%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&&&&$$$$$$%%%&&&))))))(((''''''&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%&&&'''###$$$%%%&&&'''&&&&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$!!!###%%%%%%$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$%%%''''''%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&'''((()))'''&&&$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$''''''''''''''''''''''''%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''''''''&&&&&&%%%%%%%%%((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&''''''%%%$$$%%%'''&&&&&&%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%$$$###$$$%%%&&&&&&$$$%%%%%%&&&&&&&&&&&&%%%%%%###$$$%%%%%%&&&&&&%%%%%%###$$$%%%&&&''''''''''''&&&&&&&&&&&&''''''''''''))))))))))))((((((''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''((((((***---AAA))))))$$$$$$$$$'''''''''&&&&&&%%%%%%%%%'''&&&$$$###""""""###$$$$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''%%%$$$$$$$$$%%%&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&&&&%%%$$$&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&'''$$$%%%&&&&&&$$$$$$%%%&&&)))))))))(((''''''&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&$$$$$$%%%&&&&&&&&&&&&%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$###$$$%%%$$$######$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&$$$%%%''''''%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&'''(((''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''''''''''''''$$$%%%%%%&&&''''''((((((&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&%%%'''''''''&&&&&&'''''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%''''''''''''''''''''''''%%%&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''''''''&&&&&&&&&&&&&&&((((((''''''''''''''''''''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%%%%%%%''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%'''''''''''''''''''''''''''''''''''''''''''''''''''(((((('''%%%$$$$$$%%%''''''&&&&&&&&&&&&''''''(((''''''&&&&&&''''''(((&&&$$$$$$%%%&&&'''&&&%%%&&&&&&''''''''''''&&&&&&###$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&''''''''''''&&&&&&&&&&&&'''''''''''')))))))))(((((((((((('''((((((''''''&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''(((((())))))'''***===%%%&&&###%%%&&&%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$###"""""""""######"""######$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&'''%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&((((((((((((''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%######""""""######$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###""""""$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((('''&&&%%%%%%&&&((((((&&&%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''%%%&&&'''''''''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''''''''&&&&&&%%%%%%&&&&&&'''((())))))&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''(((((('''''''''&&&&&&&&&((('''&&&%%%%%%&&&'''(((&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''''''''''''''&&&&&&&&&''''''((((((((('''''''''''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%'''&&&%%%$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&'''''''''&&&%%%$$$$$$%%%''')))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&&&&'''&&&&&&%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''&&&'''((('''%%%$$$%%%&&&''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&%%%$$$%%%'''((('''&&&&&&''''''''''''''''''&&&###$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&'''''''''&&&%%%%%%&&&&&&&&&'''''''''(((((((((((((((((((((((())))))((('''&&&&&&%%%%%%%%%&&&&&&'''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''((()))*********,,,???&&&&&&###$$$%%%""""""###$$$%%%&&&&&&'''$$$$$$##################!!!!!!!!!""""""###$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&'''%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$$$$$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###""""""$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&''''''&&&%%%$$$&&&'''))))))'''&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&$$$%%%&&&(((((('''%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&'''&&&&&&&&&&&&&&&'''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''((((((((('''''''''&&&&&&&&&((('''&&&%%%%%%&&&'''(((&&&&&&''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''((())))))(((((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%((('''%%%%%%%%%%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&'''''''''&&&$$$$$$$$$&&&((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((((((%%%%%%%%%&&&&&&&&&''''''((((((''''''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&'''&&&&&&%%%''''''''''''''''''''''''''''''''''''''''''''''''$$$%%%&&&&&&%%%%%%'''(((&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%$$$%%%'''((('''&&&&&&''''''''''''''''''&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&'''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&''''''''''''''''''((((((((())))))((('''&&&&&&%%%%%%%%%%%%&&&&&&'''&&&&&&%%%###$$$$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((()))******///111CCC)))(((###$$$$$$!!!"""######$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$###"""""""""!!!""""""###$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$$$$%%%%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%((('''&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''''''''''''''((())))))((('''&&&&&&%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%$$$######$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$&&&'''))))))'''&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&$$$%%%&&&'''''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''((('''''''''&&&&&&&&&&&&%%%'''''''''&&&&&&'''''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''&&&&&&'''''''''(((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''''''''''''''(((((((((&&&'''((()))***)))((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''&&&%%%$$$$$$%%%&&&((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((())))))((((((%%%%%%%%%&&&&&&&&&''''''((((((''''''''''''(((((($$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''###$$$&&&&&&&&&&&&''')))&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&$$$$$$%%%&&&'''&&&%%%&&&&&&''''''''''''&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''(((((((((((((((''''''&&&%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''((())))))******---@@@((()))$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%######"""###$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%&&&&&&'''###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''###$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%((('''&&&%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&&&&'''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&'''(((((()))((('''&&&%%%&&&&&&'''$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&!!!###%%%%%%$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$&&&''''''&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&$$$%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%%%%&&&'''((((((&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&''''''''''''&&&&&&&&&%%%&&&&&&&&&&&&'''''''''(((''''''''''''''''''''''''''''''''''''((((((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&'''''''''((((((((()))&&&''')))*********((((((''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%&&&''''''(((''''''''''''''''''''''''%%%&&&''''''((((((''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$&&&'''&&&%%%%%%&&&'''''''''&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%$$$###$$$%%%&&&&&&$$$%%%%%%&&&&&&&&&&&&%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&'''&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&'''''''''((((((&&&&&&&&&&&&%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&#########$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&'''((()))*** $$$:::$$$'''%%%'''((()))(((((('''%%%$$$######$$$%%%%%%&&&&&&&&&%%%%%%((('''%%%$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!""""""#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&'''(((((("""###$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''"""###%%%&&&'''&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%((('''&&&%%%$$$%%%&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&'''''''''&&&&&&%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&'''''''''((((((((((((((($$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$######$$$$$$%%%&&&)))((('''&&&%%%&&&&&&'''$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&"""%%%&&&%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$######$$$&&&&&&"""$$$&&&%%%$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%###$$$$$$%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''$$$$$$$$$%%%&&&'''((()))&&&&&&%%%%%%%%%$$$$$$$$$%%%&&&'''(((((('''&&&%%%&&&''''''''''''''''''&&&))))))(((((('''''''''&&&&&&&&&&&&'''''''''((((((''''''''''''''''''''''''''''''''''''((((((((()))''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&'''''''''(((((())))))%%%''')))***+++***)))((())))))))))))))))))))))))%%%&&&&&&''''''&&&&&&%%%%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''###$$$%%%&&&''''''''''''''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''(((((((((((((((((((((((($$$%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''(((((('''%%%$$$$$$%%%((((((''''''''''''(((((('''''''''&&&&&&'''''''''$$$###"""###%%%&&&%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&'''&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&'''''''''(((((($$$%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''''''''&&&###$$$$$$%%%%%%$$$$$$###'''&&&%%%$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''((((((,,,000222...'''###%%%(((((('''%%%$$$$$$%%%'''((('''''''''&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$%%%######$$$$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&'''''''''%%%$$$$$$&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$%%%%%%###!!!%%%&&&&&&%%%$$$%%%''')))&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''((($$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&&&&'''''''''&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%############%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%&&&'''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$$$$######$$$$$$%%%'''&&&&&&%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$''''''''''''''''''''''''%%%%%%$$$$$$%%%%%%&&&'''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&'''''''''''''''''''''''''''''''''&&&&&&%%%%%%'''((()))(((((((((((((((((((((((("""$$$&&&'''))))))((((((''''''&&&%%%&&&'''((()))******)))'''&&&%%%$$$###''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''(((((((((((((((((((((((())))))(((((('''''''''&&&&&&&&&&&&'''''''''(((((((((((('''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((('''&&&%%%%%%$$$$$$&&&%%%%%%%%%%%%&&&'''(((((('''&&&&&&'''((('''%%%&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''''''''((()))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((())))))&&&&&&''''''''''''&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''***)))((('''%%%$$$###"""$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&%%%%%%$$$$$$'''&&&$$$######$$$%%%&&&%%%%%%$$$###$$$%%%&&&'''''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%&&&'''''''''&&&,,,222111,,,'''%%%&&&'''&&&%%%$$$$$$%%%&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''+++)))&&&%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$%%%%%%###"""$$$$$$%%%$$$######%%%(((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######$$$%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''(((''''''''''''''''''''''''))))))((('''((()))***+++((((((((((((((((((((((((&&&'''((()))))))))((('''''''''&&&&&&&&&'''((()))'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((())))))((((((((((((((((((((((((''''''''''''''''''''''''(((((((((((((((((((((((())))))((((((((('''''''''&&&&&&&&&'''''''''(((((((((((('''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&))))))((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''(((''''''&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%&&&'''&&&%%%&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''''''''((()))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%&&&&&&'''(((((()))&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%''''''''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$(((---...+++'''%%%&&&%%%%%%%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&''''''''''''&&&%%%$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&///,,,'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$%%%&&&&&&$$$""""""#########""""""$$$&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''&&&&&&'''''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######$$$%%%&&&&&&&&&''''''''''''&&&&&&###$$$&&&'''(((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&%%%%%%&&&&&&'''&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&%%%&&&&&&'''(((''''''''''''''''''''''''))))))((((((((()))***+++((((((((((((((((((((((((((((((((((((((('''&&&%%%''''''&&&&&&''''''((()))$$$%%%&&&'''((())))))***((((((((((((((((((((((((''''''''''''''''''''''''%%%&&&&&&''')))******+++(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))((((((((((((''''''&&&&&&'''''''''(((((((((((((((((('''''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%)))))))))))))))(((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&''''''''''''''''''&&&&&&%%%%%%$$$$$$%%%&&&'''''''''&&&%%%&&&%%%$$$$$$&&&'''&&&$$$&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''''''''((())))))))))))(((&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((%%%%%%&&&&&&'''(((((((((&&&&&&''''''''''''&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&&&&''''''$$$$$$%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%&&&&&&'''(((''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$%%%&&&''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%&&&'''((('''&&&%%%&&&&&&$$$$$$%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&((((((&&&%%%######$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&...+++&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&%%%###"""###$$$###""""""$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''&&&%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%###""""""###%%%&&&%%%%%%&&&'''''''''&&&&&&"""###%%%'''''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&%%%%%%%%%&&&''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&'''(((((('''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&%%%%%%%%%'''''''''''''''(((((()))$$$%%%&&&'''((()))***+++((((((((((((((((((((((((''''''''''''''''''''''''&&&''''''((())))))******(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))((((((((((((((((((''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&'''''''''(((((((((''''''&&&&&&&&&%%%%%%%%%###$$$&&&(((((('''&&&%%%&&&%%%$$$%%%'''((('''&&&&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''&&&'''(((((())))))((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''###############$$$$$$%%%&&&&&&&&&&&&''''''((((((''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$######$$$%%%&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$'''''')))***+++***'''$$$$$$%%%%%%%%%%%%$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%"""$$$%%%''''''%%%$$$"""""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&***'''###"""###%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%''''''%%%$$$###$$$&&&&&&%%%$$$%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%###""""""###%%%&&&$$$$$$%%%&&&''''''&&&&&&"""###$$$%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''%%%###!!!!!!###%%%'''%%%%%%%%%%%%%%%&&&'''(((%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''&&&&&&''''''''''''&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&'''(((((((((((((((((((((((((((((('''''''''((((((((((((((((((((((((((((((((((((((('''''''''''''''((((((((('''''''''(((((((((((((((&&&''''''(((((()))))))))))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))(((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((())))))))))))))))))'''''''''((((((((())))))))))))((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((()))))))))&&&&&&&&&&&&&&&%%%%%%%%%###$$$&&&(((((('''&&&%%%'''&&&&&&'''((())))))(((&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''&&&&&&'''(((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((''''''&&&&&&%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%)))((((((((('''''''''&&&&&&%%%###""""""$$$'''(((&&&&&&&&&'''''''''''''''''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%''',,,333666333+++$$$&&&&&&%%%%%%$$$$$$######$$$$$$$$$$$$%%%%%%%%%%%%######$$$%%%%%%$$$######!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$""""""$$$&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%''''''&&&$$$###%%%''''''&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&%%%%%%$$$$$$###%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&&&&%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######$$$%%%&&&###$$$%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&'''&&&&&&&&&&&&''''''''''''***'''%%%""""""%%%'''***%%%%%%%%%%%%&&&''''''((($$$%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''''''''&&&&&&''''''((()))((((((((((((((((((((((((((()))***+++++++++******((((((((((((((((((((((((***)))))))))***+++,,,,,,&&&'''((())))))))))))((((((((((((((((((((((((((())))))))))))))))))))))))((((((((((((((((((((((((*********))))))((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((())))))))))))******''''''((((((((())))))))))))))))))(((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''((((((((()))))))))&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''''''''&&&%%%((('''&&&''')))******)))&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''&&&&&&'''(((((((((((('''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%&&&&&&&&&''''''(((((('''&&&%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%))))))(((((('''&&&&&&%%%((('''%%%%%%%%%''')))+++%%%%%%&&&''''''''''''&&&''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%%%%%%%&&&%%%&&&)))000666777111,,,)))(((&&&%%%$$$$$$$$$%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$###$$$&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%'''((('''%%%###%%%(((((('''&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%$$$######$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&%%%%%%%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&%%%$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&&&&&&&&&&***)))'''%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''&&&&&&&&&&&&'''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''((((((%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&''''''''''''&&&&&&'''''''''''''''''''''''''''''''''''''''(((((()))((((((((((((((((((((((((((()))***+++,,,+++******((((((((((((((((((((((((++++++))))))((()))******&&&'''((()))***))))))((('''((((((((())))))))))))************************(((((((((((((((((((((((()))))))))))))))*********))))))))))))))))))))))))************************))))))))))))))))))))))))(((((()))))))))*********'''((((((((())))))))))))))))))))))))((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%&&&'''((((((&&&'''''''''((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&%%%''')))******)))&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''%%%&&&''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%###$$$&&&'''((((((''''''###$$$%%%&&&'''&&&&&&%%%''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$&&&%%%$$$######$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&)))$$$!!!$$$---555777666***)))&&&$$$###$$$%%%&&&#########$$$$$$%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''"""###$$$%%%&&&&&&'''&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%'''((((((&&&###%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&'''((('''%%%###%%%'''((('''&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&%%%%%%$$$######$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%######%%%%%%%%%%%%######$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%"""###$$$%%%&&&&&&'''&&&...,,,)))&&&%%%&&&((()))&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%&&&''''''&&&&&&&&&'''''''''((((((!!!###%%%''''''%%%###!!!$$$$$$$$$%%%&&&'''((()))&&&''''''''''''''''''&&&''''''''''''''''''''''''%%%%%%$$$$$$%%%%%%&&&'''&&&''''''''''''''''''&&&'''''''''''''''''''''''''''''''''''''''((())))))))))))))))))))))))))))))&&&'''(((******))))))(((((((((((((((((((((((((((+++***(((&&&%%%$$$%%%%%%&&&''')))*********)))(((&&&''''''((()))***++++++************************))))))))))))))))))))))))''''''((()))***+++,,,,,,))))))))))))))))))))))))************************))))))))))))))))))))))))(((((())))))*********+++(((((((((((())))))))))))))))))))))))((((((((((((''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((('''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$%%%'''((())))))'''((((((((())))))******(((((((((((((((((((((((($$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&'''(((&&&%%%$$$&&&((())))))(((&&&''''''''''''''''''&&&''''''''''''''''''''''''%%%&&&''''''((((((''''''(((((((((((((((((((((((((((((((((((((((((((((((('''''''''''''''''''''&&&&&&''''''''''''''''''&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%&&&&&&'''(((((($$$%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$$$$%%%%%%&&&$$$((((((&&&### ###$$$%%%&&&&&&&&&%%%$$$''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%$$$$$$#########""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""%%%)))...111:::666...'''""" !!!"""######$$$%%%&&&'''(((((($$$%%%&&&''''''&&&%%%$$$'''%%%###"""$$$&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$#########%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$'''''''''(((''''''&&&%%%''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&(((((((((''''''&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''''''''&&&&&&%%%%%%%%%((('''%%%%%%'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&((('''&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&'''(((''''''''''''''''''&&&&&&&&&'''(((*********)))((()))(((((((((''''''''''''''''''''''''((((((((()))******))))))((((((''''''''''''(((((())))))************))))))((((((((('''******))))))(((((('''''',,,,,,++++++++++++++++++******************************))))))((((((((('''******************************+++++++++******))))))))))))))))))))))))))),,,,,,,,,+++***)))((('''+++++++++++++++++++++++++++++++++++++++++++++++++++***((('''''''''((()))******++++++++++++******))))))))))))))))))))))))******))))))((((((((('''&&&&&&%%%%%%$$$$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''###$$$%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&(((''''''''''''&&&&&&&&&(((''''''&&&&&&&&&''''''(((&&&%%%%%%'''(((((('''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%((((((((((((((((((((((((&&&&&&&&&''''''''''''((('''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''***)))'''&&&%%%$$$$$$$$$((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######%%%%%%%%%$$$$$$$$$######"""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%######$$$'''***,,,000///,,,***((('''''''''((((((''''''(((((('''&&&---...////////////...------***&&&$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$######&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&'''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''&&&&&&%%%%%%%%%((('''%%%%%%'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&((('''&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''((()))******)))(((((())))))(((((((((''''''''''''''''''((((((((())))))******))))))((((((((((((((((((((()))))))))))))))******)))))))))((((((((()))))))))))))))(((((((((++++++++++++++++++++++++++++++++++++++++++++++++++++++******))))))))))))))))))))))))))))))))))))******++++++++++++******************************+++,,,,,,++++++***)))(((+++++++++++++++++++++++++++++++++++++++++++++++++++***)))((('''((())))))*********+++******)))))))))))))))))))))))))))))))))))))))(((((((((''''''))))))))))))((((((((('''(((''''''&&&&&&''''''(((%%%&&&''''''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&&&&'''''''''(((((((((''''''&&&&&&''''''''')))'''&&&&&&((())))))(((''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&''''''''''''((('''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######%%%%%%%%%$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$$$$%%%%%%&&&)))+++...111333333222222(((''''''***...111111///111222222333333222222111333...)))%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$$$$###&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$###$$$%%%&&&((((((((()))%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''((((((((((((''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&%%%$$$######$$$&&&&&&((('''''''''&&&&&&%%%%%%%%%%%%$$$######$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''&&&&&&&&&&&&&&&((('''%%%%%%'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&((('''&&&&&&%%%&&&&&&&&&***)))((('''&&&&&&&&&&&&''''''''''''''''''''''''(((((())))))))))))(((''')))))))))(((((((((''''''''''''((((((((()))))))))***))))))))))))((((((((())))))))))))))))))((((((*********))))))))))))))))))))))))))))))*********************************,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++***************************************++++++++++++++++++++++++++++++++++++++++++***++++++,,,,,,++++++***,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***))))))(((((())))))***************)))((('''))))))))))))))))))))))))((((((((((((''''''''''''(((((((((''''''''''''&&&)))(((((((((((((((((()))'''(((((()))))))))((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''(((((())))))&&&&&&''''''''''''&&&&&&(((((((((((((((((((((((('''''''''''''''&&&&&&&&&$$$$$$%%%&&&'''((()))***(((''''''&&&''''''(((((()))((('''''')))******)))''''''''''''''''''''''''(((((((((((((((((())))))((((((((((((((((((((((((&&&&&&&&&''''''''''''((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%#########$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$######&&&)))---111333444444444...,,,+++---333666444222+++,,,,,,,,,,,,,,,,,,+++333///)))%%%###$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$###$$$%%%'''(((((((((''''''&&&&&&%%%%%%&&&%%%###""""""###%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&((('''%%%%%%'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''''''''&&&&&&&&&&&&''''''***)))((('''&&&&&&&&&&&&''''''''''''(((((((((((()))))))))))))))((((((''')))))))))((((((((((((''''''(((((((((((()))))))))))))))))))))))))))))))))+++******))))))(((((((((************************)))))))))******+++++++++))))))************++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++******++++++,,,,,,++++++++++++++++++++++++******+++,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++******))))))))))))************)))(((''''''))))))))))))))))))))))))(((((('''''''''''''''''''''''''''''''''''''''''')))((((((''''''(((((()))(((((()))))))))(((''''''&&&&&&&&&&&&''''''''''''&&&'''''''''((((((((()))&&&&&&''''''''''''&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%&&&&&&'''(((((()))'''''''''''''''(((((())))))'''&&&'''(((***))))))''''''''''''''''''''''''((('''''''''&&&&&&%%%%%%((((((((((((((((((((((((&&&&&&&&&''''''''''''((('''''''''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%$$$#########$$$%%%''')))******+++888444111///...,,,)))%%%&&&%%%%%%%%%%%%%%%%%%&&&...+++&&&######$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%'''((()))(((((((((''''''&&&&&&&&&%%%%%%$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''''''''((('''%%%%%%'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''''''''&&&&&&&&&''''''(((''''''&&&&&&&&&&&&'''''''''''''''((((((((()))))))))))))))(((((((((((((((***)))))))))(((((((((((((((((((((((()))))))))***))))))))))))************++++++******))))))((((((*********+++++++++++++++))))))******++++++,,,,,,))))))******++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++........................++++++******+++,,,------++++++++++++++++++++++++***+++,,,------...------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++******)))***************)))((((((************************''''''((((((((((((((((((***************+++++++++(((''''''''''''''''''(((''''''(((((((((''''''&&&&&&&&&&&&''''''((((((((())))))((((((((('''''''''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((()))***(((&&&%%%&&&'''(((((((((''''''''''''''''''''''''******)))'''&&&%%%$$$###((((((((((((((((((((((((&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%$$$$$$$$$#########$$$$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%%%%$$$%%%%%%$$$$$$$$$%%%%%%&&&///...---***'''%%%######%%%%%%$$$$$$$$$$$$%%%%%%)))&&&###"""###%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$''''''''''''''''''''''''###$$$$$$$$$%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&''''''(((((((((''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''''''''(((((((((((('''%%%%%%'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&'''''''''''''''''''''&&&''''''((()))&&&&&&&&&%%%&&&&&&'''''''''''''''(((((())))))***((((((((((((((()))************)))))))))(((((((((((((((((()))))))))******)))))))))************+++******************))))))+++++++++++++++,,,,,,,,,+++++++++++++++,,,,,,,,,*********+++,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------,,,,,,,,,,,,,,,,,,,,,,,,++++++******+++,,,...///+++++++++++++++++++++++++++,,,------............,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,,,,,,,+++************++++++++++++******************************(((((((((((())))))))))))(((((())))))))))))******(((''''''&&&&&&''''''(((&&&''''''(((((((((''''''&&&&&&&&&'''(((((())))))******)))(((((('''&&&&&&&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''''''''(((((('''''''''&&&&&&&&&''''''''''''((()))******'''&&&%%%%%%'''((((((''''''''''''''''''''''''''',,,,,,+++***((('''&&&&&&((((((((((((((((((((((((&&&&&&&&&''''''''''''((('''''''''''''''(((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$%%%&&&'''((()))%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&'''''''''%%%%%%%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%"""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%''''''''''''''''''''''''!!!%%%''''''$$$###&&&)))&&&&&&%%%$$$$$$%%%&&&&&&&&&$$$###$$$%%%&&&%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&'''''''''"""$$$&&&'''(((((('''&&&&&&&&&''''''(((((())))))$$$%%%'''(((((('''%%%$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&'''''''''((((((((()))((('''%%%%%%'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''((())))))))))))((('''&&&&&&&&&&&&&&&''''''((())))))******''''''''''''((()))+++,,,*********)))))))))(((((((((((()))))))))*********))))))*********+++++++++******************+++++++++++++++,,,,,,,,,------,,,,,,,,,,,,,,,+++++++++***++++++,,,------..................................../////////000000000------------------------,,,+++*********,,,...000,,,,,,,,,,,,,,,,,,,,,,,,,,,------............---------------------------------------------------+++,,,---------,,,+++***)))***+++,,,,,,---,,,,,,************************))))))))))))******++++++%%%%%%%%%&&&&&&''''''''')))((((((''''''(((((()))&&&'''(((((())))))))))))&&&&&&&&&'''((())))))))))))))))))(((((((((((((((&&&&&&''''''''''''&&&&&&((((((((((((((((((((((((&&&&&&&&&'''''''''((((((&&&&&&&&&'''''''''''''''''''''''''''((()))***+++((('''%%%&&&((())))))(((''''''''''''''''''''''''*********)))))))))))))))((((((((((((((((((((((((&&&&&&&&&''''''''''''(((&&&'''''''''((((((((()))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%&&&'''(((((((((((((((((((((((((((&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&''''''(((%%%%%%%%%$$$$$$$$$###############$$$$$$%%%%%%%%%""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$((('''&&&%%%$$$$$$$$$$$$"""$$$%%%'''((('''&&&%%%"""&&&***(((###!!!%%%***%%%$$$###""""""###$$$%%%%%%%%%$$$%%%&&&&&&%%%###$$$%%%%%%&&&&&&%%%%%%$$$#########$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&"""###$$$%%%&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&''''''((((((((( """%%%'''((('''&&&$$$%%%%%%&&&'''((()))******$$$&&&(((******(((&&&$$$#########$$$$$$%%%%%%%%%''''''''''''''''''''''''$$$$$$%%%%%%%%%&&&&&&&&&&&&'''''''''(((((())))))((('''%%%%%%'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((('''''''''''''''((())))))---,,,***)))'''&&&&&&%%%&&&''''''((()))******+++&&&&&&&&&&&&(((***,,,---************))))))))))))))))))))))))************))))))******++++++++++++)))))))))***+++++++++,,,+++++++++,,,,,,------------------,,,,,,+++++++++++++++,,,------...//////000000000000000000000000000000111111222222222333000000000000000000000000,,,+++*********,,,///000........................---...............------------------------------------------------------,,,,,,---...---,,,+++***)))***+++,,,---.........************************))))))******+++++++++,,,'''((((((((())))))************))))))))))))******''''''(((******+++++++++&&&&&&&&&'''((())))))***''''''(((((())))))******&&&''''''''''''''''''&&&))))))))))))))))))))))))&&&&&&&&&'''''''''(((((($$$%%%%%%&&&'''((())))))''''''''''''((()))++++++)))((('''''')))******)))''''''''''''''''''''''''%%%&&&&&&'''((())))))***((((((((((((((((((((((((&&&&&&&&&'''''''''((((((&&&'''''''''(((((())))))((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((())))))++++++)))(((&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%&&&'''(((************************&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&'''(((((($$$$$$$$$$$$$$$$$$$$$$$$''''''&&&$$$!!!!!!###$$$%%%%%%%%%$$$$$$#########(((%%%"""###&&&(((((('''&&&&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###%%%&&&'''&&&&&&%%%########################%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&)))(((%%%$$$######$$$%%%&&&%%%%%%%%%%%%&&&''''''((('''&&&%%%%%%&&&'''(((%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&&&&%%%$$$$$$###%%%%%%%%%$$$$$$$$$$$$$$$''''''''''''''''''&&&&&&$$$$$$######$$$&&&'''((('''&&&%%%%%%$$$$$$$$$$$$&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''(((((($$$%%%&&&&&&''''''&&&&&&***)))(((''''''((()))***$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&''''''''''''&&&&&&)))((('''&&&&&&'''((()))***************)))((((((###%%%%%%%%%#########%%%))))))))))))))))))))))))+++(((&&&'''))))))'''%%%"""###$$$%%%&&&((())))))))))))(((((((((((())))))))))))))))))))))))))))))))))))***+++++++++++++++&&&''')))++++++++++++***************************,,,+++***************+++,,,,,,---------------,,,...------------......///000///---------...000222333555777888999888666555444555666777888999999999:::999888666555444444444333222111000////////////------......///000000111......------......///000......///000000///////////////.........---------,,,,,,,,,,,,++++++******,,,,,,,,,,,,++++++++++++++++++***))))))))))))))),,,,,,,,,,,,,,,,,,,,,,,,))))))))))))))))))))))))))))))))))))))))))))))))+++)))(((((())))))(((&&&(((((((((((())))))))))))(((((('''(((((()))***+++(((((())))))))))))((((((&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&''''''''''''''''''''''''(((((())))))))))))((((((&&&'''''''''(((((())))))******))))))((((((''''''((((((((((((((((((((((((******))))))(((((('''''''''''''''''''''''''''''')))((('''&&&&&&&&&&&&&&&&&&&&&''''''(((((())))))''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&''')))*********)))((('''''''''''''''''''''''')))))))))))))))((('''''')))))))))((('''&&&$$$###((('''&&&%%%$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&'''(((((((((&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&''''''%%%###"""###$$$%%%%%%%%%$$$$$$$$$######(((%%%######&&&''''''&&&$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$######&&&%%%%%%%%%%%%&&&''''''''''''&&&&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&(((((())))))(((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$&&&'''((('''&&&%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''(((%%%&&&''''''(((((('''''')))(((((((((((((((((()))%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%'''''''''&&&&&&''''''''''''''''''''''''&&&%%%%%%%%%&&&''''''%%%%%%%%%'''))))))))))))))))))))))))+++)))'''(((******(((&&&&&&&&&'''((()))******+++))))))(((((((((((())))))************************)))***+++++++++++++++***((()))***+++,,,,,,+++***))))))))))))************------,,,,,,,,,------...------...///000000000000000000000000111222333444444333222111222333555666999:::<<<>>>??????>>>=========???@@@BBBBBBCCCCCCAAA@@@???===<<<;;;;;;:::999888777555333222111000000000111111222222222222000000////////////000000......////////////......////////////............------------------------,,,,,,++++++++++++******++++++***************+++++++++++++++++++++++++++))))))))))))))))))))))))************************+++)))(((((())))))((('''(((((((((((()))))))))***++++++)))(((((('''''''''(((((())))))))))))(((((((((((((((((((((((((((((((((((('''''''''&&&&&&&&&(((((((((((((((((((((((((((((())))))))))))((((((''''''''''''((((((((()))***)))))))))((((((((('''((((((((((((((((((((((((***)))))))))((((((((('''''''''''''''''''''''''''(((''''''&&&&&&&&&&&&'''''''''''''''((((((((((((''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&'''(((((())))))((((((''''''''''''''''''''''''((((((((((((((('''&&&&&&&&&''''''''''''&&&%%%%%%((('''&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''&&&%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%'''((('''%%%$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###(((&&&$$$$$$%%%&&&&&&%%%###$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''((('''%%%###"""&&&%%%%%%%%%%%%&&&''''''&&&''''''''''''''''''&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&((())))))))))))(((((('''$$$$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''(((&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&'''(((((())))))((((((''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$&&&((()))(((''''''((()))))))))))))))))))))))))))+++***))))))******)))(((((()))))))))************))))))))))))))))))))))))************************++++++,,,,,,,,,+++************+++,,,,,,,,,++++++*********++++++,,,,,,,,,.........//////000000111000000111222333333444444333333444555555666777888888777666666666777999:::>>>???AAACCCEEEEEEEEEDDDEEEFFFHHHIIIKKKLLLMMMMMMKKKJJJHHHGGGEEEDDDDDDDDDBBBAAA@@@>>>;;;888666444666777777888888888777777666555444333222222222222111111111111111000000000111111111000000000//////------..................---------,,,,,,++++++++++++++++++***++++++,,,,,,))))))))))))))))))))))))))))))))))))))))))))))))************************+++)))(((((()))***)))'''((((((((()))))))))******+++***))))))((((((((((((((())))))******))))))((())))))))))))))))))))))))(((((((((''''''''''''&&&))))))))))))))))))))))))(((((())))))))))))((((((''''''''''''(((((((((((())))))))))))(((((((((((())))))))))))))))))))))))))))))))))))((((((((((((''''''''''''''''''''''''&&&&&&&&&'''''''''''''''(((((((((''''''''''''''''''''''''''''''''''''''''''''''''((((((((())))))''''''&&&&&&&&&'''((((((''''''''''''''''''''''''&&&''''''''''''&&&%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&((('''&&&&&&%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&(((''''''&&&&&&''''''(((''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%'''(((((('''%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%%%%%%%$$$$$$%%%&&&'''((())))))))))))$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&((((((''''''&&&&&&%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&$$$###&&&%%%%%%%%%%%%&&&''''''%%%&&&'''(((((('''&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&&&&&&&&&&%%%%%%"""######$$$%%%&&&&&&'''%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((((((&&&&&&((())))))(((&&&&&&''''''''''''''''''''''''&&&''''''((((((''''''&&&&&&'''((())))))((('''&&&((((((((())))))(((((('''&&&((())))))((('''(((***((((((((((((((((((((((((***))))))))))))))))))((())))))(((((((((((((((((()))))))))******)))))))))************************,,,,,,,,,,,,,,,,,,+++***+++++++++,,,,,,,,,+++++++++,,,,,,---...//////000///000111222333333444444666666555555555555666666666666777777777777777777777666666666666777888999<<<>>>@@@BBBDDDEEEEEEEEEFFFGGGHHHJJJLLLMMMNNNNNNNNNNNNLLLKKKJJJIIIIIIHHHFFFEEEDDDCCC@@@>>>;;;999<<<===>>>>>>>>>>>>===<<<<<<;;;999888777666666666555555444444333333444444333333222222222111111111//////......---------,,,//////......------,,,,,,++++++******++++++,,,,,,))))))))))))))))))))))))***************************************************)))((()))******)))((((((((()))))))))*********''''''(((((()))***+++,,,)))))))))******)))))))))************************((((((((('''''''''''''''))))))))))))))))))))))))(((((())))))))))))(((((('''''''''((((((((((((((())))))))))))(((((((((((((((((((((((((((((((((((())))))))))))((((((((((((''''''''''''''''''''''''%%%%%%&&&''''''((((((((((((((((((''''''&&&&&&&&&''''''''''''''''''''''''&&&'''''''''(((((((((((('''&&&%%%$$$$$$%%%'''(((''''''''''''''''''''''''&&&&&&'''''''''&&&&&&%%%###$$$%%%%%%&&&&&&%%%%%%'''''''''&&&&&&&&&&&&'''%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%''''''&&&&&&&&&&&&''''''(((((((((((((((((((((((($$$$$$$$$$$$$$$$$$$$$$$$$$$&&&(((((('''%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%$$$###$$$%%%&&&'''((())))))))))))$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''((('''&&&%%%%%%%%%&&&'''&&&%%%%%%%%%%%%&&&''''''%%%&&&'''(((((('''&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$%%%%%%$$$$$$$$$!!!""""""###$$$%%%%%%&&&%%%&&&&&&&&&'''''''''(((%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''''''''&&&%%%&&&'''(((((('''&&&%%%''''''''''''''''''''''''(((((())))))))))))(((((('''((()))******)))((('''((())))))*********))))))%%%'''((((((''''''((()))(((((((((((((((((((((((('''((((((((((((((((((((()))))))))))))))((((((((())))))************))))))************************,,,,,,---------,,,,,,+++,,,,,,,,,,,,,,,,,,------,,,------///000111222222666666888999::::::::::::<<<;;;:::888666666555555777777888888777666555444444444444444444555555555777888:::<<<>>>@@@AAABBB@@@AAACCCEEEFFFGGGHHHHHHIIIHHHGGGFFFFFFEEEFFFFFFBBBBBBAAA@@@???===<<<;;;>>>???@@@AAABBBAAA@@@???>>>===<<<:::999888888888888777666555444555555555555555555444444444333333444444333111000///...---000//////...---,,,,,,,,,+++++++++******++++++,,,++++++++++++++++++++++++++++++++++++++++++++++++***************************)))((()))***+++***)))))))))))))))************''''''(((((()))+++,,,---))))))************))))))))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))((((((((((((((((((((('''''''''(((((((((((())))))))))))''''''''''''''''''''''''(((((((((((())))))))))))''''''''''''''''''''''''$$$%%%&&&'''((((((((('''((((((''''''&&&&&&%%%%%%''''''''''''''''''''''''%%%%%%&&&&&&&&&''''''''''''&&&%%%$$$$$$%%%&&&'''''''''''''''''''''''''''&&&''''''(((((((((''''''%%%%%%&&&&&&%%%%%%$$$###&&&'''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%$$$%%%%%%%%%&&&&&&%%%%%%%%%(((((((((((((((((((((((($$$$$$$$$$$$$$$$$$$$$$$$$$$&&&''''''%%%$$$%%%&&&###$$$$$$$$$$$$%%%%%%%%%###%%%&&&&&&$$$######$$$###$$$%%%&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&&&&'''###$$$$$$%%%%%%&&&&&&'''&&&&&&%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&''''''''')))'''&&&$$$$$$%%%'''(((&&&%%%%%%%%%%%%&&&''''''&&&''''''''''''''''''&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&&&&''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%&&&&&&&&&&&&%%%#########$$$$$$%%%%%%%%%%%%&&&&&&''''''(((((((((%%%&&&''''''''''''&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%&&&'''&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%''''''''''''''''''''''''((((((((())))))(((((((((''''''((((((((((((''''''&&&'''(((((((((((((((((($$$&&&''''''&&&&&&((()))))))))))))))))))))))))))&&&'''((((((''''''((()))+++++++++***************((()))***++++++***)))(((+++++++++++++++++++++++++++,,,------.........---......---......000111111...///000222333555666666>>>???AAABBBCCCBBBBBBAAA@@@>>><<<999666555555555777888888999888777555444444444444555555555666666666777888:::<<<>>>???@@@>>>???@@@AAABBBCCCCCCCCCAAAAAA@@@@@@AAAAAABBBBBB>>>===<<<;;;:::::::::;;;===>>>AAACCCCCCCCCBBBAAA@@@???===<<<;;;:::::::::999888777555444555666666777777666666666555555555::::::999777666555444333111111000///...------,,,...---,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++***)))((()))+++++++++***)))))))))*********+++++++++******))))))*********)))******++++++******)))(((((((((((((((((((((((('''(((((((((((()))))))))(((((((((((((((((((((((((((((())))))))))))((((((((((((((((((((('''''''''(((((((((((())))))))))))(((((((((((((((((((((((((((((((((((())))))))))))''''''''''''''''''''''''%%%&&&'''((((((((('''&&&'''''''''&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&&&&'''''''''&&&%%%%%%%%%&&&&&&''''''''''''''''''''''''&&&&&&'''(((((((((((('''&&&&&&&&&&&&&&&%%%$$$$$$&&&&&&'''(((((((((((('''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%######%%%&&&######$$$$$$$$$%%%%%%%%%!!!$$$&&&&&&$$$###$$$%%%$$$$$$%%%%%%%%%%%%$$$$$$######$$$%%%%%%&&&''''''######$$$%%%%%%&&&''''''&&&&&&%%%$$$%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&''''''(((''''''&&&&&&&&&'''''''''&&&%%%%%%%%%%%%&&&''''''''''''&&&&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&'''((((((&&&&&&'''(((((('''&&&%%%%%%$$$$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$%%%&&&&&&'''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%&&&''''''((((((''''''$$$&&&''''''''''''(((***))))))))))))))))))))))))&&&(((***)))'''''')))+++))))))******************((()))+++,,,,,,+++)))(((++++++++++++++++++++++++***+++,,,...////////////111000000111222444666777666666888999;;;===>>>???CCCDDDEEEFFFGGGFFFDDDCCC@@@>>>;;;888666555555666666888999;;;;;;;;;999888999::::::;;;;;;;;;;;;;;;<<<<<<===>>>???AAACCCDDDBBBCCCCCCDDDEEEEEEDDDDDD@@@@@@AAAAAABBBDDDEEEFFF@@@>>><<<:::999:::<<<===???AAADDDGGGHHHHHHGGGFFFDDDDDDCCCAAAAAA@@@@@@@@@>>><<<:::888888888999:::888888888888777777777777;;;;;;;;;;;;::::::::::::777777666555444333222222222111000...------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++***)))((()))+++,,,+++***))))))*********++++++++++++******))))))***++++++)))******++++++******)))))))))))))))))))))))))))'''((((((((())))))))))))))))))))))))))))))))))))(((((())))))))))))(((((()))((((((((('''''''''''''''((((((((()))))))))***))))))))))))))))))))))))'''((((((((()))))))))***''''''''''''''''''''''''&&&&&&((()))((('''&&&$$$%%%&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&'''''''''''''''''''''''''''&&&%%%%%%''''''''''''''''''''''''%%%%%%&&&'''''''''''''''%%%%%%&&&''''''''''''&&&%%%&&&'''((())))))((('''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""%%%'''#########$$$$$$%%%%%%%%% ###&&&&&&%%%###$$$&&&&&&&&&&&&'''&&&&&&%%%%%%######$$$%%%%%%&&&''''''######$$$%%%%%%&&&'''''''''&&&%%%%%%&&&''')))***%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''((((((%%%&&&'''))))))(((&&&%%%&&&%%%%%%%%%%%%&&&''''''((('''&&&%%%%%%&&&'''(((%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&'''''''''((((((&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%%%%&&&&&&&&&%%%((((((((((((((('''''''''######$$$%%%%%%&&&''''''&&&&&&((((((((('''&&&%%%$$$$$$$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&''''''((((((((((((((('''&&&$$$$$$$$$$$$&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%############%%%&&&&&&&&&'''((()))))))))((($$$&&&(((((('''((()))+++))))))))))))))))))))))))&&&)))+++***((((((***,,,&&&'''''''''((((((((((((((()))+++,,,,,,+++)))(((++++++++++++++++++++++++***+++,,,...///000000111333333333444555888:::;;;===>>>@@@AAACCCEEEGGGGGGCCCDDDEEEFFFFFFEEECCCBBB???===:::888666666777777666888:::===>>>???>>>===??????@@@AAAAAAAAAAAA@@@BBBBBBBBBCCCDDDFFFHHHHHHHHHHHHIIIIIIIIIIIIHHHHHHDDDDDDEEEFFFHHHJJJKKKLLLFFFCCC@@@===<<<===???AAADDDFFFIIILLLNNNNNNMMMLLLJJJJJJIIIHHHGGGGGGGGGGGGCCCAAA???===<<<===>>>???999999999888888888777777999999:::;;;;;;<<<======>>>>>>===<<<;;;:::999888555444222111///.........,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++***)))((()))+++,,,,,,***)))************+++++++++''''''((()))***,,,...///******++++++++++++******))))))))))))))))))))))))'''((((((((())))))******************************(((((())))))))))))(((((())))))(((((('''''''''&&&'''((((((((())))))******++++++++++++++++++++++++'''((((((((())))))******''''''''''''''''''''''''&&&'''((())))))'''%%%###%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''''''''''''''((((((((()))''''''((()))((('''%%%$$$''''''''''''''''''''''''###$$$%%%%%%&&&&&&&&&&&&###$$$&&&'''((()))))))))%%%&&&((()))))))))((('''%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%!!!"""###$$$%%%&&&&&&&&&"""###%%%&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&$$$$$$%%%''''''''''''&&&&&&%%%%%%%%%,,,((($$$$$$&&&))))))(((&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%&&&'''((((((&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&'''&&&%%%%%%%%%%%%&&&'''&&&'''''''''&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%######""""""###%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&%%%$$$$$$###&&&%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''''''''&&&&&&'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%''''''&&&%%%%%%%%%%%%&&&(((((((((((((((((((((((('''&&&&&&&&&'''(((***+++''''''&&&&&&&&&%%%%%%%%%))))))(((((('''''''''&&&***)))((((((((((((((())))))((('''''''''(((***+++++++++++++++,,,,,,,,,,,,+++,,,---------+++***)))111000//////111444777999999:::<<<>>>@@@BBBDDDDDDHHHGGGFFFDDDCCCCCCDDDDDDBBBBBB@@@???>>>>>>>>>>>>======<<<<<<<<<<<<======>>>@@@BBBCCCEEEEEEDDDDDDGGGEEECCCDDDEEEGGGHHHHHHIIIGGGEEEEEEGGGHHHIIIIIIMMMLLLLLLMMMMMMMMMLLLJJJJJJIIIFFFEEEJJJSSSWWWVVVSSSOOOIIIDDDAAABBBDDDEEEKKKLLLNNNPPPQQQRRRRRRRRRPPPPPPOOOOOOPPPPPPOOOOOOLLLIIIFFFDDDDDDDDDCCCBBBAAA???<<<<<<<<<===<<<<<<<<<<<<;;;::::::999999888<<<===>>>??????>>>>>>===<<<:::999777666333000---------...///000000000000///.........---------,,,******))))))***++++++,,,+++++++++************))),,,***((('''&&&'''((()))+++***)))***,,,---,,,+++************************,,,+++***((((((((())))))((((((((((((((((((((((((***)))((((((((((((((())),,,,,,++++++***)))))))))***)))(((''''''((()))***(((((((((((())))))))))))'''(((***++++++)))'''%%%))))))))))))))))))))))))((((((''''''&&&&&&&&&%%%((((((((('''&&&&&&%%%%%%''''''((((((((((((''''''%%%%%%&&&&&&'''(((((((((((('''&&&%%%%%%&&&'''(((%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%%%%%%%&&&''''''&&&&&&%%%%%%$$$$$$###$$$%%%&&&&&&''''''&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%""""""###$$$%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&$$$$$$%%%'''%%%%%%%%%$$$$$$#########)))&&&######%%%(((((('''$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%&&&&&&'''''''''&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&((('''''''''&&&&&&&&&&&&'''&&&%%%%%%%%%%%%&&&'''&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%&&&''''''''''''&&&%%%((('''&&&&&&%%%%%%&&&&&&''''''''''''''''''''''''(((''''''''''''(((***+++((('''''''''&&&&&&&&&%%%))))))((((((((('''''''''******))))))))))))***+++)))(((((('''((()))***+++************************)))***+++,,,---.........000000111333666999<<<======???BBBDDDFFFFFFEEEEEEGGGEEECCCBBB@@@@@@@@@@@@@@@??????>>>>>>>>>??????>>>>>>>>>>>>???@@@AAAAAACCCEEEFFFHHHJJJJJJJJJJJJJJJIIIIIIIIIJJJKKKLLLKKKKKKIIIHHHGGGHHHIIIIIIIIIPPPPPPPPPPPPQQQQQQPPPOOOOOOOOOLLLJJJOOOVVVYYYWWWVVVSSSNNNJJJHHHIIILLLNNNMMMMMMNNNPPPQQQSSSUUUVVVWWWVVVVVVVVVVVVVVVUUUTTTQQQOOOMMMLLLMMMMMMLLLKKKIIIFFFCCCBBBBBBBBBAAAAAA;;;;;;;;;<<<<<<<<<=========>>>???@@@AAA@@@??????@@@???>>>======:::777444222222222111111///......------..................000//////...------......++++++++++++************---+++***(((((()))***+++,,,+++***+++---...---,,,************************++++++))))))((()))******))))))))))))))))))))))))))))))(((((((((((())))))******************++++++***)))(((((((((((()))***(((((((((((()))))))))))))))***+++++++++***(((((())))))))))))))))))))))))((((((((('''''''''&&&&&&))))))))))))((((((((((((''''''(((((((((((('''''''''''''''''''''&&&&&&&&&((('''&&&&&&&&&&&&'''(((%%%%%%&&&&&&&&&''''''''''''&&&%%%%%%%%%%%%&&&'''&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&'''(((%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%"""######$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&$$$$$$%%%&&&%%%%%%$$$$$$$$$$$$######%%%$$$######%%%''''''&&&"""######$$$&&&''''''((($$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&%%%&&&''''''''''''&&&%%%((('''&&&&&&%%%&&&&&&&&&''''''''''''''''''''''''))))))((((((((())))))***((((((((((((''''''''''''))))))((((((((((((''''''***)))))))))***+++,,,---)))(((((((((((()))***+++***************************++++++,,,...000222333222333666:::>>>AAACCCDDDCCCFFFIIIKKKKKKIIIFFFCCCBBBAAA@@@>>><<<;;;;;;;;;=========>>>???@@@AAAAAABBBBBBCCCCCCDDDEEEGGGGGGGGGGGGIIIJJJKKKLLLLLLLLLLLLLLLLLLMMMMMMMMMMMMNNNMMMLLLKKKJJJJJJKKKLLLLLLRRRRRRRRRSSSSSSSSSSSSSSSTTTUUUSSSQQQSSSXXXYYYWWWYYYWWWSSSPPPOOOQQQSSSUUUSSSSSSSSSSSSTTTUUUVVVWWWWWWVVVUUUUUUWWWWWWVVVUUUQQQOOOOOOPPPRRRSSSSSSRRRQQQNNNIIIGGGFFFGGGFFFFFFDDDCCCCCCBBBBBBBBBBBBBBB???@@@AAABBBCCCBBBAAAAAADDDCCCCCCCCCCCCAAA>>>;;;999999888666444222///...------..................111000...---,,,+++++++++,,,,,,,,,+++++++++******---,,,+++*********+++,,,---,,,+++,,,...///...---*********************************))))))***++++++************************)))))))))(((((())))))***((())))))***++++++,,,,,,+++***))))))))))))***+++(((((((((((()))))))))))),,,++++++***************))))))))))))))))))))))))))))))((((((((((((''''''%%%%%%%%%&&&&&&&&&&&&&&&''''''((((((((((((''''''((((((''''''&&&%%%%%%$$$((('''&&&&&&&&&&&&'''(((%%%&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&%%%&&&&&&'''(((%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%"""###$$$%%%%%%%%%%%%%%%((('''%%%$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''%%%$$$###$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&#########$$$%%%&&&&&&&&&######$$$%%%%%%&&&''''''$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&''''''''''''&&&&&&(((((('''&&&&&&&&&&&&&&&''''''''''''''''''''''''*********))))))))))))))))))))))))((((((((((((((())))))((((((((((((((((((((((((((()))***+++,,,---)))))))))))))))*********++++++,,,,,,,,,,,,,,,,,,.........///111333666777:::<<<@@@DDDGGGIIIJJJJJJKKKKKKKKKKKKIIIEEEBBB@@@===<<<;;;;;;:::999999999<<<===???@@@BBBCCCDDDEEEHHHHHHHHHHHHIIIIIIJJJKKKJJJJJJJJJKKKLLLLLLLLLLLLLLLNNNOOOPPPPPPPPPPPPQQQNNNNNNNNNNNNMMMOOOQQQSSSUUUUUUVVVVVVVVVVVVWWWYYY[[[]]]]]][[[\\\```___\\\^^^\\\YYYWWWVVVWWWXXXZZZ^^^___aaaaaaaaa___]]][[[ZZZWWWTTTSSSUUUVVVUUUSSSOOOOOOOOOQQQTTTWWWXXXXXXYYYUUUPPPMMMMMMMMMNNNNNNRRRQQQOOOLLLJJJHHHHHHGGGDDDDDDFFFFFFGGGFFFEEEDDDEEEDDDEEEGGGHHHFFFCCC@@@@@@@@@???===;;;888666555111111000///......------///...---,,,+++*********---,,,,,,,,,++++++++++++---,,,+++******+++,,,,,,---,,,+++,,,---......,,,************************************++++++,,,,,,++++++++++++++++++++++++)))))))))((())))))******))))))*********++++++++++++******************+++(((((((((((())))))))))))---+++***(((((()))***+++(((((((((((((((((((((((()))))))))))))))(((((((((###$$$$$$%%%&&&&&&''''''''''''(((((((((((('''''''''''''''&&&&&&%%%%%%%%%'''''''''&&&&&&'''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%######$$$%%%%%%%%%$$$$$$((('''%%%$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%######$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&$$$"""!!!%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''(((((('''&&&&&&&&&&&&'''''''''''''''''''''''''''***************)))))))))))))))))))))))))))))))))(((((())))))))))))))))))'''''''''((()))***+++,,,((())))))*********************+++,,,,,,---......000000111333666:::===@@@DDDFFFIIILLLMMMMMMMMMLLLNNNLLLIIIEEEAAA???===<<<888999999:::;;;;;;<<<<<>>???@@@@@@CCCDDDFFFHHHJJJJJJJJJJJJIIIHHHHHHGGGGGGHHHHHHHHHGGGHHHHHHIIIKKKMMMOOOPPPSSSVVVZZZ[[[\\\___eeejjjllloooqqqqqqpppqqqvvvzzzqqqgggbbb```\\\YYY\\\ZZZXXXYYY]]]cccgggiiihhhccc[[[UUURRRSSSTTTUUUZZZYYYVVVTTTTTTTTTUUUVVVYYYYYYYYYYYYXXXVVVTTTSSSMMMMMMPPPRRRTTTSSSOOOLLLJJJJJJKKKKKKKKKJJJJJJIIIBBBAAA???;;;888444222000111000000////////////000......---------,,,,,,,,,******++++++++++++,,,,,,+++***)))***,,,---,,,+++************************++++++,,,---------,,,,,,++++++++++++++++++++++++))))))))))))******+++,,,,,,,,,++++++***))))))((())))))***++++++***))))))(((((((((((())))))))))))+++***(((&&&&&&'''(((***))))))))))))))))))))))))''''''(((((((((((())))))'''(((((()))***++++++,,,''''''((((((((((((''''''###$$$$$$%%%&&&&&&''''''&&&&&&'''(((((('''&&&&&&&&&&&&'''''''''(((((((((%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%&&&'''(((((()))$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''')))(((''''''&&&'''''''''%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%%%%$$$$$$###$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$###"""$$$%%%#########$$$$$$%%%%%%%%%&&&&&&&&&### ###&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%&&&&&&'''''''''&&&&&&&&&&&&'''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''$$$%%%&&&'''((((((((((((((((((((((((((((((((((((&&&'''''''''((((((((())))))((('''&&&&&&'''((())))))(((((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((()))***))))))((('''''''''(((((()))))))))(((((()))))))))************))))))((())))))******((()))***+++++++++******)))***,,,...111333555666777999<<<@@@CCCFFFHHHIIIIIIIIIIIIIIIIIIGGGEEEDDDAAA@@@???===<<<<<<<<<<<<<<<===???AAABBBCCCCCCCCCFFFGGGIIIKKKLLLKKKJJJIIIHHHHHHHHHIIIJJJKKKMMMMMMNNNOOOQQQTTTXXX]]]aaacccnnnrrruuuwwwyyy~~~yyyuuutttqqqoooppplllhhhhhhlllrrrxxx{{{zzzrrrhhh```[[[ZZZZZZZZZ]]][[[YYYWWWWWWWWWYYYZZZ______^^^]]][[[XXXUUUTTTPPPRRRTTTWWWYYYWWWSSSPPPMMMMMMNNNOOOOOOOOOOOONNNKKKIIIGGGCCC@@@===:::999333222111000///.....................------------++++++,,,---------------,,,+++***+++---...---,,,************************,,,------......---,,,+++++++++++++++++++++++++++))))))))))))***+++,,,---++++++******************((())))))******))))))((((((((((((((())))))))))))+++***)))((((((((())))))))))))))))))))))))))))))&&&&&&'''''''''(((((((((%%%&&&&&&&&&''''''((((((''''''((((((((((((''''''%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''(((((('''&&&&&&''''''''''''((((((((((((%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%&&&'''((()))***$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((())))))((('''''''''''''''%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$%%%%%%%%%$$$$$$###"""###%%%&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$###"""###%%%%%%%%%%%%&&&&&&'''''''''&&&&&&%%%!!!!!!$$$######$$$%%%&&&&&&'''((($$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%&&&'''((((((&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%$$$%%%%%%&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%$$$$$$%%%'''((($$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''$$$%%%&&&'''(((((((((((())))))))))))))))))))))))&&&'''''''''(((((()))))))))((('''&&&&&&'''((()))))))))((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%'''((()))))))))(((&&&'''''''''(((((())))))(((((())))))*********+++++++++******************((()))***+++,,,+++******---...000333666999;;;<<<@@@AAACCCEEEFFFFFFEEEEEEFFFFFFEEEEEEDDDCCCBBBAAA:::;;;===>>>??????>>>>>>@@@AAACCCDDDEEEEEEDDDDDDHHHIIIKKKLLLLLLKKKIIIHHHIIIIIIJJJLLLOOOQQQSSSUUU]]]^^^bbbgggmmmsssyyy|||}}}||||||rrrkkkiiihhhgggdddaaa^^^[[[YYYYYYZZZ[[[___^^^^^^\\\YYYVVVSSSQQQQQQRRRUUUXXXZZZXXXTTTPPPOOOOOOPPPPPPPPPPPPPPPPPPOOONNNLLLIIIFFFCCCAAA@@@:::999777555333222111111//////.........---------,,,,,,---.../////////...---,,,+++,,,...///...---************************------...///...---+++***************************))))))))))))***+++,,,---)))))))))***++++++,,,,,,'''((()))******)))((('''(((((((((((()))))))))))),,,++++++***************))))))))))))))))))))))))%%%&&&&&&&&&''''''((((((((((((((()))))))))))))))''''''(((((((((((('''''''''&&&&&&%%%%%%$$$$$$###%%%&&&'''(((((('''&&&%%%''''''''''''((((((((()))%%%%%%&&&''''''&&&%%%%%%###$$$%%%&&&''')))******$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((())))))((('''''''''''''''%%%%%%%%%$$$$$$#########%%%%%%$$$###$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%)))(((''''''((()))(((&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''&&&%%%$$$$$$$$$&&&(((***'''(((((((((((((((''''''%%%&&&'''''''''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&''''''&&&%%%%%%&&&''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&)))))))))'''%%%$$$%%%&&&''')))++++++)))'''''''''&&&%%%%%%%%%%%%&&&''''''((('''&&&$$$######$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&(((***+++,,,)))((('''&&&%%%%%%&&&'''(((((((((((((((((((((((('''((()))((('''&&&''')))))))))))))))((((((((((((''''''''''''((((((((())))))******)))(((''''''(((((()))***++++++***)))(((%%%%%%%%%%%%''')))+++---+++++++++++++++*********,,,,,,---...///......---000222666;;;???BBBDDDEEECCCCCCCCCCCCCCCCCCCCCCCC===<<<<<<;;;<<<===???@@@BBB??????BBBDDDCCCBBBDDDGGGFFFEEEFFFIIIKKKLLLLLLIIIHHHKKKOOOPPPNNNPPPTTTWWWVVVWWWZZZ___gggooosssxxx{{{zzzzzz}}}xxxooofff___^^^bbbeeeeeegggfffcccaaa___YYYRRRPPPPPPQQQSSSVVVXXXWWWVVVQQQQQQRRRRRRQQQQQQPPPOOONNNOOOPPPPPPOOOMMMJJJIIIDDDCCC???<<<888666444333000000111000000...,,,+++........................------------------------.../////////...---,,,,,,---,,,,,,++++++,,,,,,---------,,,,,,+++***))))))++++++******)))(((((((((************))))))))))))(((((())))))))))))((((((&&&''')))***++++++******))))))*********+++++++++))))))************))))))))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&&&&'''''''''(((((())))))((((((''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&'''(((((((((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%$$$$$$$$$######%%%%%%$$$$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%&&&&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$'''%%%%%%%%%''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''''''''((('''%%%$$$$$$%%%&&&'''''''''(((((((((((('''''' !!!###%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$&&&)))'''&&&&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%&&&&&&%%%&&&((()))&&&((())))))'''&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''((('''&&&$$$######$$$$$$$$$%%%&&&&&&''''''&&&&&&'''''''''&&&&&&%%%%%%%%%'''''''''''''''((()))))),,,+++***)))))))))******(((((((((((((((((((((((('''((()))((('''&&&''')))))))))))))))((((((((((((&&&&&&&&&''''''''''''''')))******)))((('''''')))))))))***++++++***)))(((*********+++,,,---......++++++++++++++++++,,,,,,+++,,,---...000222333444777888;;;???BBBDDDEEEEEEGGGEEEBBB???======>>>???======<<<===>>>@@@BBBCCCEEEBBBBBBFFFGGGEEEEEEGGGFFFGGGHHHJJJMMMOOOOOOOOOOOOMMMPPPUUUXXXZZZ___eeekkknnnrrrzzzyyyqqqnnnpppssszzz|||zzzuuuppplllcccZZZTTTSSSRRRSSSUUUVVVUUUTTTVVVVVVVVVVVVVVVTTTSSSRRRMMMMMMMMMMMMMMMKKKIIIGGGEEEEEEDDDBBBAAA???>>>>>>666555333111000/////////.../////////////////////------------------------......//////......---,,,---,,,,,,++++++,,,,,,---------,,,,,,+++******))))))))))))***************************))))))))))))(((((())))))))))))(((((('''((())))))******))))))))))))*********+++++++++'''((()))***************))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&&&&'''''''''(((((())))))))))))((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&'''(((((((((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%$$$$$$$$$$$$###%%%%%%$$$$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&############$$$$$$$$$$$$$$$###"""###%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&''''''''''''''')))(((&&&%%%$$$$$$%%%%%%&&&''''''(((((((((''''''!!!"""###%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&$$$"""###'''***&&&&&&&&&&&&%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&'''(((%%%&&&((('''&&&%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''''''''&&&%%%$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&''''''''''''''''''''''''***)))((('''&&&&&&&&&&&&)))((((((''''''''''''((((((((((((((((((((((((((('''((()))((('''&&&''')))))))))))))))((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&((()))***)))((('''((()))))))))******+++******)))***+++++++++++++++******+++++++++,,,,,,---......,,,---///111444888;;;===>>>???@@@BBBCCCDDDDDDDDDIIIEEE@@@:::888777999:::;;;;;;<<<===???AAACCCDDDFFFDDDEEEIIIIIIFFFFFFHHHGGGJJJNNNSSSVVVWWWWWWVVVYYYXXX[[[dddnnnuuuwwwmmm___\\\XXXWWWWWWWWWWWWVVVUUUVVVWWWWWWWWWTTTRRRPPPOOONNNLLLLLLLLLKKKIIIGGGHHHIIIJJJJJJIIIHHHGGGFFF>>><<<888444222222333444////////////////////////............................../////////...------------,,,,,,,,,,,,------------,,,,,,++++++******((())))))***++++++,,,,,,++++++*********)))))))))((())))))******))))))((()))))))))((())))))*********************+++++++++))))))************))))))))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&'''''''''(((((((((''''''''''''((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&'''(((((('''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((())))))(((((($$$$$$%%%%%%&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%"""!!!!!!"""%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&'''''''''&&&&&&((('''&&&%%%%%%%%%%%%&&&&&&&&&''''''((((((''''''(((((((((''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$&&&(((&&&&&&&&&%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$'''%%%$$$###$$$$$$$$$###%%%&&&''''''%%%$$$%%%&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&%%%$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&$$$$$$%%%&&&'''((())))))))))))((('''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%(((((((((((((((((((((((('''((()))((('''&&&''')))))))))))))))(((((((((((((((''''''''''''&&&&&&&&&((()))***)))((('''((()))))))))*********+++*********++++++,,,+++)))(((&&&******+++,,,...///000111000222555888;;;>>>???@@@@@@@@@@@@@@@@@@@@@??????BBB@@@<<<888666777888999===>>>AAACCCFFFGGGGGGHHHJJJHHHIIILLLKKKGGGGGGJJJKKKQQQZZZbbbggghhhhhhhhhmmmmmmsssoookkkeeeaaa`````````___WWWYYY\\\]]]]]]ZZZWWWUUUVVVRRRNNNMMMMMMMMMKKKIIIKKKLLLMMMNNNMMMKKKHHHGGGEEECCC???;;;999777777777000000000000//////....................................////////////......------,,,,,,,,,,,,------------,,,,,,,,,+++++++++*********+++++++++,,,,,,+++++++++*********)))))))))))))))******)))))))))***))))))))))))+++---...************************,,,+++++++++)))((('''&&&((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''(((((((((((($$$$$$%%%&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&'''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((((((###$$$$$$%%%&&&'''((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''###""""""###&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&'''&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''%%%%%%&&&'''''''''''''''))))))((('''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###%%%(((((('''%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$'''$$$""""""$$$%%%$$$"""%%%&&&'''&&&%%%%%%&&&(((&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&'''&&&&&&&&&&&&''''''(((&&&&&&''''''''''''''''''(((((((((((((((((((((((('''((()))((('''&&&''')))))))))))))))(((((((((((()))))))))(((((((((((((((''')))***)))((('''(((******************++++++,,,------.........,,,***)))***+++,,,...000222444555666999===@@@BBBAAA???>>>>>>===<<<;;;;;;::::::999999999999999:::;;;<<<===AAADDDIIINNNPPPPPPOOONNNMMMLLLMMMOOOMMMJJJLLLPPPUUU___mmmzzz|||vvvqqqoooooonnnnnnfffiiinnnqqqpppmmmiiieee]]]WWWPPPLLLLLLKKKIIIFFFIIIJJJKKKMMMMMMKKKIIIHHHJJJIIIGGGEEEBBB>>><<<:::444333333111000///......////////////////////////......///////////////......------,,,,,,------...---------,,,,,,,,,,,,,,,---,,,,,,,,,+++++++++***++++++++++++************))))))************)))))))))))))))***+++...000222************************)))************))))))((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''((((((((())))))%%%%%%&&&'''((())))))***&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&'''((((((&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&$$$$$$%%%&&&&&&'''((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''###$$$$$$$$$$$$%%%%%%%%%###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&''''''((((((%%%$$$###$$$&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&''''''((($$$%%%&&&'''''''''''''''%%%%%%$$$$$$%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&"""%%%(((***(((&&&$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%%%%%%%%%%%%%$$$$$$!!! !!!%%%((((((&&&%%%&&&&&&&&&%%%%%%'''(((&&&%%%%%%%%%%%%&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&)))((('''&&&$$$###"""!!!%%%%%%%%%%%%&&&'''((()))$$$$$$%%%&&&&&&&&&%%%%%%(((((((((((((((((((((((('''((()))((('''&&&''')))))))))))))))(((((((((((((((((()))))))))*********'''((())))))(((((()))******************+++,,,---++++++,,,,,,,,,,,,++++++---...000222555888:::;;;===???BBBCCCCCC@@@===;;;::::::999888777777888888666777999;;;>>>@@@AAABBB@@@FFFOOOWWW[[[[[[XXXUUUPPPPPPQQQTTTSSSRRRWWW___lllxxx~~~}}}yyyggg___UUUOOOMMMLLLIIIFFFFFFHHHJJJLLLNNNOOOOOOOOOOOOOOONNNLLLIIIEEEAAA???:::999888666444111000///000000000000000000000000......///000000000//////......------------......------------,,,,,,,,,,,,......---,,,,,,+++******,,,++++++++++++*********)))******++++++******)))))))))***+++,,,...000111+++++++++***************%%%&&&((()))+++,,,,,,,,,))))))))))))))))))))))))((((((((((((((((((((((((''''''((((((((()))))))))((((((((()))***++++++,,,&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&'''((((((&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&'''&&&&&&&&&%%%%%%&&&&&&''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''######$$$$$$$$$%%%%%%%%%###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''((())))))'''''''''&&&&&&&&&%%%%%%$$$$$$%%%&&&&&&'''((((((&&&$$$###$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&###$$$%%%&&&''''''''''''&&&%%%%%%$$$%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&###%%%(((((('''%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%&&&$$$!!!"""&&&***)))&&&$$$$$$%%%$$$######&&&(((&&&%%%%%%%%%%%%&&&''''''$$$$$$%%%&&&&&&&&&%%%$$$$$$%%%&&&&&&''''''&&&&&&(((''''''&&&%%%$$$$$$$$$%%%%%%%%%%%%&&&'''(((((("""###$$$%%%&&&%%%%%%$$$(((((((((((((((((((((((('''((()))((('''&&&''')))))))))))))))((((((((((((&&&&&&'''((()))***++++++&&&((())))))(((((()))+++******))))))***,,,---...))))))))))))***+++,,,---111222555888;;;>>>AAABBBCCCBBBAAA@@@>>><<<;;;:::999999888888888:::;;;<<<;;;;;;<<<===???BBBDDDFFFFFFOOO\\\hhhnnnoookkkgggbbbbbbeeeiiijjjnnnwww|||qqqddd\\\YYYWWWSSSOOOMMMNNNOOOPPPRRRTTTUUUVVVUUUTTTQQQNNNKKKIIIGGGFFFBBBAAA>>><<<888555333222000000000000000000000000......///000000000000000......------------......---------------------------------------,,,,,,,,,,,,,,,+++++++++*********)))******++++++******)))))))))***+++,,,,,,,,,,,,+++++++++*********))))))''''''(((******+++++++++))))))))))))))))))))))))(((((((((((((((((((((((('''((((((((())))))))))))'''(((((())))))*********'''''''''''''''''''''''''''&&&&&&&&&&&&'''((((((&&&&&&&&&'''''''''((((((''''''''''''''''''''''''%%%&&&&&&'''''''''''''''&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''#########$$$$$$%%%%%%%%%###$$$%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$###$$$%%%&&&''')))******(((((((((''''''&&&&&&&&&######$$$%%%%%%&&&''''''&&&$$$###$$$%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%''''''''''''&&&%%%$$$$$$###$$$%%%&&&'''''''''''',,,+++)))'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''&&&%%%$$$&&&'''%%%%%%%%%$$$$$$$$$######&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&((($$$!!!###&&&(((&&&###"""######"""!!!"""%%%'''&&&%%%%%%%%%%%%&&&''''''###$$$%%%&&&&&&&&&%%%$$$$$$%%%&&&&&&''''''&&&&&&###$$$%%%&&&''')))******&&&&&&%%%%%%%%%&&&''''''&&&''')))*********))))))(((((((((((((((((((((((('''((()))((('''&&&''')))))))))))))))(((((((((((($$$%%%&&&'''(((***++++++&&&((())))))(((((()))+++******))))))***,,,---///---,,,,,,---...000333444555666999<<<@@@CCCFFFGGGEEECCC???;;;999999::::::::::::999:::;;;===???@@@BBBAAA>>>===>>>BBBFFFHHHSSS^^^nnn}}}~~~|||}}}{{{xxx{{{|||tttrrrqqqttt|||tttjjjgggddd```[[[WWWVVVVVVVVVVVVWWWXXXXXXYYYWWWSSSOOOLLLKKKKKKKKKGGGFFFCCC@@@<<<888666444000000000000000000000000......///000000000000000......------------......------------------------+++,,,,,,------......///,,,,,,,,,+++++++++************++++++++++++******)))***+++++++++)))((('''++++++++++++******)))))),,,,,,,,,+++)))(((&&&%%%))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))%%%%%%%%%&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&'''((((((&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&''''''((((((((((((((('''''''''''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&%%%%%%%%%&&&&&&'''''''''))))))((('''&&&%%%%%%$$$&&&%%%$$$$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%&&&&&&&&&%%%$$$$$$###$$$%%%&&&''''''&&&%%%$$$((('''&&&$$$######$$$$$$%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%&&&&&&&&&%%%$$$$$$%%%%%%&&&&&&%%%%%%''''''''''''''''''&&&&&&''''''''''''''''''''''''))))))))))))))))))))))))$$$%%%'''((((((((('''&&&'''&&&&&&&&&&&&'''(((((())))))))))))************++++++***************+++++++++++++++,,,,,,,,,,,,000//////000111333555777999;;;===AAACCCDDDEEEEEECCC>>>999777888;;;;;;:::<<<===>>>===<<<<<<>>>@@@BBB>>>===@@@CCCEEEIIINNN```qqq}}}wwwssstttwww{{{~~~zzzwwwtttsssrrrtttyyy}}}uuuvvvyyy{{{yyytttpppnnnnnniiibbb____________^^^aaa\\\UUUQQQPPPOOOLLLJJJKKKLLLLLLIIIDDD???;;;:::888666333111111000///---111000///000111111///...000000000000000//////...........................,,,,,,,,,++++++*********+++++++++,,,,,,---------+++*********))))))(((((((((***++++++******+++,,,+++,,,,,,,,,,,,+++******,,,,,,+++***)))(((''''''))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))******))))))((((((''''''''''''''''''''''''''''''''''''((()))))))))))))))&&&&&&''''''(((((())))))''''''''''''&&&&&&&&&&&&%%%''')))******)))'''%%%'''%%%%%%&&&((()))((('''******)))'''&&&%%%$$$###%%%%%%&&&'''&&&%%%###"""((('''&&&%%%%%%&&&'''(((''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$######&&&&&&&&&&&&%%%$$$######%%%%%%%%%&&&&&&&&&''''''((((((((('''&&&&&&%%%%%%&&&%%%$$$$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&'''(((&&&&&&&&&&&&&&&%%%$$$$$$&&&&&&''''''''''''&&&&&&)))(((&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((()))*********)))((('''((((((''''''(((((()))***))))))))))))************,,,,,,+++++++++++++++,,,++++++,,,,,,---------......///000333666:::<<<>>><<<===>>>???@@@AAAAAAAAA>>>;;;888777999<<<===<<<===>>>>>>??????AAABBBCCCDDDBBBBBBCCCCCCFFFPPPZZZnnnzzzrrrlllmmmpppuuu~~~{{{wwwssspppppppppnnnmmmkkkeee\\\WWWTTTSSSQQQPPPPPPQQQQQQOOOKKKGGGEEEDDDBBB???:::777555555444333222111000000000000...,,,000000000000000///..............................------,,,,,,,,,+++++++++++++++,,,,,,,,,---------,,,,,,+++++++++*********(((***++++++******+++,,,+++,,,,,,,,,,,,+++******++++++******)))((((((((())))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))((((((((((((''''''''''''''''''''''''''''''((()))))))))))))))'''''''''((((((((((((((())))))))))))((((((((((((%%%''')))******)))'''%%%'''&&&%%%&&&((()))((('''((((((((('''&&&&&&%%%%%%'''''''''''''''&&&%%%%%%((('''&&&&&&&&&&&&'''(((''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%$$$###""""""&&&&&&&&&%%%$$$###!!!!!!%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&(((''''''&&&&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&'''((((((''''''''''''''''''&&&%%%(((''''''''''''''''''((()))((('''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&''''''''''''&&&'''''''''''''''&&&%%%$$$'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((()))************)))))))))(((((())))))***+++)))))))))*********++++++,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,---...///000000111333666999<<>>===<<<<<<<<<<<<<<<;;;:::999:::===???AAAAAACCCCCCBBBCCCEEEGGGFFFFFFGGGGGGJJJKKKKKKQQQaaappp~~~|||zzzzzz|||zzzvvvwwwxxx{{{wwwlllbbb\\\YYYXXXXXXVVVVVVVVVSSSOOOMMMLLLLLLIIIEEE@@@;;;999777666444444333111111111111///...//////000000//////...---.................................------------,,,,,,,,,,,,---------------------,,,,,,,,,,,,++++++)))***++++++******+++---+++,,,,,,,,,,,,+++******))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''''''''''''''))))))))))))))))))))))))(((((((((((())))))))))))''''''''''''''''''''''''''''''((()))))))))))))))((((((((((((((('''''''''))))))))))))((((((((((((&&&'''(((******((('''&&&'''&&&&&&&&&((()))((('''&&&&&&''''''''''''''''''***)))(((((('''(((((((((((('''&&&&&&&&&&&&'''(((''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%$$$###"""&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&%%%$$$$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''(((''''''(((((((((((('''''')))((('''&&&&&&'''((()))((((((''''''&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&''''''''''''''''''&&&''''''''''''''''''''''''$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&''''''(((''''''&&&'''''''''(((''''''&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''###$$$%%%'''(((******+++)))(((((((((((()))******))))))*********+++++++++++++++,,,,,,,,,,,,,,,,,,++++++,,,...///111222222:::;;;<<<>>>>>>>>>======???===<<<:::999999::::::<<<<<<===???AAACCCEEEEEEJJJHHHHHHIIILLLMMMKKKIIIIIILLLSSS\\\cccmmm}}}}}}xxx{{{}}}|||{{{~~~|||||||||sssgggaaa______```___]]]YYYTTTPPPOOOPPPLLLJJJFFFCCC@@@===999666666555333333333333222111///000000000000///............................../////////...............---------------.........,,,,,,,,,,,,,,,,,,,,,,,,)))***,,,+++******+++---+++,,,,,,,,,,,,+++******(((((())))))************((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''(((((())))))******''''''''''''''''''''''''''''''((()))))))))))))))))))))((((((''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&'''((())))))((('''&&&((('''&&&'''((()))((('''''''''''''''''''''''''''***)))(((''''''((()))***'''''''''&&&&&&'''''''''''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''(((((($$$$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''''''''&&&%%%$$$$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''''''''(((((()))((((((''')))((('''&&&&&&'''((()))''''''''''''''''''&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&''''''''''''''''''&&&''''''''''''''''''''''''$$$$$$%%%%%%%%%&&&&&&&&&&&&''''''(((''''''&&&&&&%%%%%%&&&'''((((((((((((&&&&&&&&&'''''''''((((((''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&''''''(((((())))))((((((''''''(((((()))***************++++++++++++******,,,---------,,,,,,+++,,,---///111333444555??????@@@???>>><<<:::999<<<;;;:::999999:::;;;<<<===>>>???AAABBBDDDFFFHHHJJJJJJLLLPPPSSSUUUVVVUUUSSSWWWdddvvvxxxpppllllllmmm|||wwwlllhhhgggkkkjjjfff```XXXSSSQQQPPPPPPOOONNNMMMKKKFFF@@@<<<777555333333444444333222000000000111000000///...////////////////////////////////////////////////........................+++,,,,,,,,,,,,,,,,,,,,,)))+++,,,,,,++++++,,,---+++,,,,,,,,,,,,+++******((((((((()))******++++++(((((((((((((((((((((((())))))))))))))))))))))))((((((((((((((((((((((((''''''(((((())))))******((((((((((((((((((((((((''''''((()))))))))))))))))))))((((((''''''&&&&&&''''''''''''&&&&&&&&&&&&''''''((())))))((('''''')))(((''''''((()))((('''((((((((('''&&&&&&%%%%%%((((((&&&&&&&&&'''((()))&&&''''''''''''''''''&&&''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&'''((())))))###$$$%%%&&&'''((((((((('''&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&'''&&&%%%$$$$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&'''(((((((((((((((((((((''''''''''''''''''(((&&&&&&'''''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&''''''&&&''''''''''''&&&%%%%%%%%%%%%&&&'''''''''''''''%%%%%%&&&&&&'''(((((((((''''''''''''''''''''''''))))))))))))))))))))))))...---+++***)))((((((((((((''''''''''''((())))))*********++++++++++++,,,***+++---...///......------...000222555777999:::??????>>>>>>===;;;:::999999999999:::;;;<<<===>>><<<>>>???AAABBBDDDHHHLLLMMMQQQWWW]]]aaaeeeiiikkkhhhnnnwwwqqqnnnmmmttt|||{{{uuutttrrrqqqmmmggg___XXXUUUTTTUUUUUUTTTSSSQQQLLLEEE@@@<<<:::666444444444333222111111222222111111000///////////////////////////...////////////000000000///////////////.........++++++,,,,,,,,,,,,------***+++,,,,,,++++++,,,...+++,,,,,,,,,,,,+++******(((((())))))*********+++))))))))))))))))))))))))************************))))))))))))))))))))))))(((((((((((())))))))))))((((((((((((((((((((((((''''''((()))))))))))))))((((((((((((((('''''''''))))))))))))((((((((((((''''''((((((((((((''''''***((('''((())))))(((&&&))))))((('''&&&&&&%%%%%%&&&&&&%%%%%%&&&&&&''''''&&&&&&'''(((((('''&&&&&&''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&"""######$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&&&&###$$$%%%&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''%%%&&&'''(((((((((((('''&&&&&&''''''''''''&&&&&&$$$%%%&&&''''''&&&%%%$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''''''(((&&&&&&&&&&&&&&&%%%$$$$$$''''''''''''&&&%%%######%%%%%%&&&&&&'''(((((()))''''''''''''''''''''''''((((((((((((((((((((((((---,,,***)))))))))******))))))(((((())))))***+++*********+++++++++,,,,,,,,,---///111111111000///000111444666999<<<>>>???@@@???>>><<<;;;:::::::::888999:::<<<===>>>>>>???===???AAACCCDDDIIIOOOTTT]]]eeennnsssuuuxxx~~~}}}{{{zzz~~~}}}~~~~~~}}}xxxrrrlllhhhgggeeeccc___\\\XXXTTTNNNKKKHHHDDD???;;;999777555444222333333333333222111111////////////////////////........./////////000000000000000/////////......,,,,,,---------.........***+++---,,,++++++,,,...+++,,,,,,,,,,,,+++******)))))))))))))))*********))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((''''''((()))))))))))))))'''''''''((((((((((((((())))))))))))(((((((((((('''(((((((((((((((((('''***)))(((((())))))(((&&&''''''''''''''''''''''''$$$%%%&&&'''''''''''''''&&&&&&'''(((((('''&&&&&&''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################$$$$$$%%%%%%%%%$$$$$$###'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&'''''''''&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&'''((((((%%%%%%&&&'''((((((''''''$$$%%%&&&''''''&&&%%%$$$###$$$%%%&&&&&&&&&%%%$$$%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''((((((%%%&&&&&&&&&%%%%%%$$$###))))))((('''%%%""" %%%%%%&&&&&&'''((())))))''''''''''''''''''''''''''''''''''''''''''''''''&&&%%%%%%&&&(((***---...*********)))***++++++,,,******+++++++++,,,,,,,,,---///111333444333222111333444777999===@@@BBBCCCCCCAAA???<<<:::999888999999:::<<<>>>?????????>>>@@@BBBDDDFFFIIIOOOWWW]]]qqqzzz}}}sss{{{{{{zzzuuunnnhhhddd```]]]ZZZTTTOOOIIICCC???<<<999777333444444444444333222222000000000000000000000000---.........//////000000111111000000/////////...---.........//////000000***,,,------,,,+++---...+++,,,,,,,,,,,,+++************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))******))))))((((((''''''))))))))))))))))))))))))'''(((((()))))))))))))))&&&'''''''''(((((())))))((('''''''''&&&&&&&&&&&&((((((((((((((((((((((((+++)))(((((())))))(((&&&%%%%%%&&&&&&'''(((((()))$$$%%%'''((((((((('''&&&%%%&&&'''(((((('''&&&%%%''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$###$$$%%%'''((())))))***&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$&&&''''''&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$'''&&&$$$######$$$&&&'''''''''''''''''''''''''''&&&''''''((((((''''''&&&$$$$$$$$$$$$%%%&&&'''(((&&&'''((())))))((('''&&&###%%%''')))******(((((('''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&'''''''''&&&''''''''''''''''''&&&%%%%%%%%%&&&&&&'''''''''''''''&&&&&&&&&&&&''''''((('''&&&%%%%%%%%%%%%%%%((('''&&&%%%%%%%%%%%%%%%((('''&&&%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((())))))((((((((((((((('''''''''''''''''''''((((((((()))******))))))))))))******((('''''''''(((***---...'''((()))******+++******...333:::???AAA@@@@@@???@@@>>><<<;;;===@@@CCCFFFBBB???<<<:::999::::::999:::;;;<<>>???@@@AAAAAABBB<<<;;;999888888999999999AAAAAAAAACCCEEEFFFGGGGGGEEEJJJRRRYYYbbbooo~~~yyyvvvyyy~~~|||sssnnnjjjfffddd```[[[UUUOOOKKKHHHFFFDDDAAA???===:::888777333222111111222222111///000000////////////000000000000/////////.........------------------------++++++,,,------------,,,+++,,,,,,---------,,,,,,---,,,,,,,,,++++++++++++************************************************)))))))))))))))*********+++***((('''''''''((()))((((((''''''&&&&&&&&&&&&'''(((((()))))))))((((((&&&&&&&&&&&&&&&'''((((((''''''''''''''''''''''''))))))))))))((((((((((((*********))))))'''&&&%%%&&&'''''''''%%%%%%&&&(((&&&&&&((())))))*********'''''''''(((((((((((()))''''''&&&&&&&&&''''''(((&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%###$$$%%%&&&&&&&&&&&&%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''))))))'''%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&$$$$$$$$$$$$%%%&&&'''(((''''''&&&&&&&&&&&&''''''&&&&&&&&&'''(((((())))))))))))((('''&&&&&&%%%%%%&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''&&&&&&&&&&&&''''''''''''&&&%%%%%%%%%&&&&&&''''''&&&%%%%%%%%%&&&&&&''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((('''''''''&&&&&&''''''(((((())))))''''''((((((((()))))))))))))))))))))))))))))))))******+++,,,,,,,,,,,,,,,)))***+++,,,------------000000111000///000333666:::<<>>===888888888888999:::;;;<<>>???BBBFFFLLLRRRXXX\\\___aaa```iiiwww}}}wwwxxxwwwvvvsssqqqnnnlllkkkccc___ZZZVVVRRRKKKCCC===;;;999666555555555555444222111000000000000000000000000000////////////...........................+++,,,,,,---...---------++++++,,,---......------,,,,,,+++++++++*********************************************************++++++******))))))(((((('''(((***++++++)))'''%%%''''''''''''''''''''''''''''''(((***++++++++++++%%%&&&'''(((((((((&&&&&&''''''''''''''''''''''''))))))))))))(((((((((((())))))))))))((('''&&&%%%)))******)))'''&&&&&&&&&&&&''''''((())))))((((((''''''''''''(((((((((((()))((('''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$######$$$$$$%%%%%%$$$$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$"""$$$%%%%%%$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$&&&&&&%%%%%%&&&&&&'''''''''&&&%%%$$$$$$%%%&&&''''''&&&&&&&&&&&&''''''((()))(((((('''&&&&&&%%%%%%&&&%%%%%%%%%%%%&&&'''''''''''''''&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&'''&&&&&&%%%%%%%%%&&&&&&'''&&&&&&%%%%%%%%%&&&&&&'''%%%%%%&&&&&&&&&'''''''''&&&&&&&&&''''''((((((((())))))((((((''''''&&&&&&%%%&&&&&&'''((()))******(((((((((((()))))))))***((()))************)))(((((()))***++++++***))))))******,,,---.../////////,,,///333666888:::<<<>>>999999999:::::::::::::::888:::<<<===<<<>>>AAADDDHHHQQQ___kkksssxxx{{{}}}yyyzzzvvv{{{{{{~~~}}}zzzyyyxxxyyyyyyvvvrrrmmmiiiccc[[[OOOGGGAAA>>>999666555555444333222111111000//////000000111000000000////////////........................,,,,,,---.........---------.........------,,,+++,,,,,,,,,+++++++++******************************************************++++++******))))))(((((()))))))))))))))(((((('''((((((((((((((()))))))))''''''(((***++++++++++++'''((()))******)))((('''''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&''''''(((((((((((('''***+++,,,+++)))'''''''''&&&''''''(((((((((((('''%%%%%%%%%&&&&&&&&&'''''')))((('''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$)))'''%%%$$$$$$%%%''')))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%'''&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&(((''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%'''&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&''''''&&&&&&%%%%%%%%%&&&''''''&&&&&&%%%%%%%%%&&&''''''%%%&&&&&&&&&''''''''''''&&&&&&&&&'''(((((())))))((((((((((((((('''''''''&&&&&&''''''(((((())))))((((((((()))))))))******((()))***++++++***)))((('''((()))***************+++,,,---///000111111111000444888;;;;;;;;;;;;;;;999888777666777888:::;;;999;;;===>>>>>>AAAGGGLLLTTT```rrr~~~uuupppqqqqqquuu}}}zzzuuupppggg\\\SSSKKKFFF???:::777666555444333333222111000000000000111111000000000/////////........................,,,,,,---.............../////////......---++++++---------,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++++++++************))))))))))))******)))((('''(((((()))((())))))))))))*********''''''((()))************))))))*********)))(((((('''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&'''(((((((((((()))***,,,,,,***(((((((((&&&''''''(((((((((''''''$$$$$$%%%%%%%%%&&&&&&&&&(((((('''&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%''''''%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%$$$$$$######&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''(((((((((((((((((('''''''''&&&&&&&&&&&&'''''''''''''''(((((('''''''''%%%&&&'''''''''&&&%%%%%%&&&&&&&&&'''''''''''''''&&&%%%%%%%%%%%%&&&''''''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%&&&'''(((%%%%%%%%%%%%%%%&&&'''(((%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&''''''''''''&&&&&&&&&'''((()))))))))'''''''''((((((((((((((('''''''''((((((((((((((((((((()))))))))*********((()))***++++++***)))(((((((((((()))***+++,,,------...000222333444444555666999<<<======;;;;;;;;;888888777777888:::;;;<<<;;;>>>AAABBBCCCIIIRRRYYYfffssszzzxxxzzz{{{vvvmmmfff[[[UUULLLDDD@@@===;;;:::666666444333333222222222111111111000000000//////........................,,,------...............---...............------.........---------,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++)))))))))))))))*********))))))))))))(((((((((((((((((((((((()))))))))***'''(((((()))))))))((((((******)))(((((((((((((((''''''''''''''''''''''''((('''''''''&&&&&&&&&&&&&&&&&&''''''((('''''''''&&&(((***+++)))(((''''''&&&''''''(((((('''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&''''''(((&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''((((((((((((''''''###$$$%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$&&&''''''&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%(((((('''&&&$$$###""""""###$$$&&&''''''&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%$$$(((''''''&&&&&&&&&''''''&&&'''((())))))((('''&&&$$$%%%'''(((((('''%%%###%%%%%%&&&&&&'''(((((((((&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&'''''''''&&&''''''((((((''''''&&&'''''''''&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%&&&'''(((%%%%%%%%%%%%%%%&&&'''(((%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&'''''''''((((((&&&&&&&&&'''((())))))***&&&'''''''''(((((())))))((((((((((((((('''''''''))))))))))))************''')))***++++++***)))'''***)))))))))***,,,...000000000222444555666777777999;;;>>>>>>>>>===>>>???777777999:::;;;<<<======>>>AAAEEEGGGIIIQQQ\\\eeezzz|||hhhaaaXXXOOOIIIFFFCCCBBB888888777666555444444444111111111111000000000000////////////////////////,,,---......//////......+++,,,---...//////////////////.........---------++++++++++++++++++++++++++++++++++++++++++++++++(((((())))))******++++++((()))*********)))'''&&&&&&'''''''''(((((())))))'''((((((((((((((('''&&&***)))(((&&&&&&&&&'''((('''''''''''''''''''''''')))((((((((('''''''''''''''((((((((('''&&&%%%%%%###&&&((()))((('''&&&&&&&&&''''''(((''''''&&&&&&&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&'''((()))$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$###"""!!! $$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&#########$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((&&&'''((()))***************)))((('''&&&%%%%%%%%%(((((((((((('''&&&%%%$$$######$$$%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$'''''''''''''''''''''''''''&&&&&&&&&&&&'''((((((''''''''''''((((((((((((''''''((()))))))))))))))))))))))))))))))))))))))************************++++++++++++***)))((('''+++---......------///000666777888999;;;<<<===>>>>>>>>>;;;999:::<<<<<<::::::888;;;AAAAAA===>>>DDDCCCKKKTTTVVVWWW___ooo|||}}}rrrfff]]]VVVOOOGGGCCC<<<:::777666666666555444555444333333222333333333111111111111000000000000////////////////////////...............///000000///......------,,,++++++******))))))***,,,---///,,,+++******)))***************))))))))))))******+++*********))))))(((((())))))(((((((((((())))))(((((()))***************''''''''''''((((((((((((((((((((((((((((((((((((,,,***)))((()))((('''%%%((((((((((((((((((((((((%%%&&&&&&'''((()))******''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%$$$$$$###$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&'''(((%%%&&&&&&&&&&&&&&&%%%%%%(((((('''&&&&&&&&&&&&'''''''''((((((((((((((((((""""""######$$$%%%%%%&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&'''((((((''''''''''''((((((((((((''''''((()))))))))))))))))))))))))))))))))))))))***************++++++++++++++++++++++++***)))))),,,---/////////000222444:::<<<>>>@@@@@@@@@>>>===<<<<<<;;;:::;;;===>>>>>>>>>===@@@EEEEEECCCFFFMMMLLLWWWbbbhhhllluuuxxxpppjjjddd[[[PPPJJJCCC@@@;;;888777666555444555555444333222222222333111111111111000000000000////////////////////////...............///000000///......------,,,++++++,,,+++++++++,,,---...///,,,++++++***************))))))(((((((((((())))))************)))))))))((())))))(((((((((((())))))'''((())))))******))))))''''''''''''((((((((((((((((((((((((((((((((((((***))))))((((((((('''&&&((((((((((((((((((((((((&&&&&&''''''(((((())))))))))))))))))))))))))))))''''''''''''''''''''''''((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''&&&&&&''''''&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&%%%$$$###"""&&&&&&&&&&&&&&&'''((()))&&&''''''((())))))******######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&'''((((((''''''''''''((((((((((((''''''((()))))))))))))))))))))))))))))))))))))))))))))******+++++++++++++++++++++++++++++++++++++++---///000222444888;;;???AAADDDEEEEEEBBB???<<<999999:::;;;===???AAACCCFFFGGGLLLQQQRRRRRRWWW^^^dddooo}}}~~~yyyvvvwww~~~|||wwwmmm```VVVRRRMMMEEE@@@<<<:::888777666666555333222222222222222222111111111000000000////////////////////////...............///000000///......------,,,++++++---,,,,,,,,,---...///000,,,,,,+++***************(((((((((''''''(((((((((************))))))))))))))))))(((((((((((())))))''''''((())))))))))))(((''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''((((((((((((((())))))))))))))))))))))))''''''''''''''''''''''''((((((((((((((((((((((((""""""""""""""""""""""""%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))(((((('''''''''((((((&&&&&&%%%%%%%%%&&&&&&'''((((((((((((((('''&&&%%%'''&&&&&&&&&&&&'''(((((('''''''''''''''((())))))''''''''''''(((((())))))'''&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&'''((((((''''''''''''((((((((((((''''''((())))))))))))))))))))))))))))))))))))))))))))))))***++++++,,,,,,*********++++++,,,,,,,,,***---000333666:::???BBBBBBCCCDDDDDDBBB@@@===;;;:::999:::===???@@@DDDIIIPPPVVV```gggjjjlllpppuuu~~~yyyxxx}}}ssshhhddd^^^TTTKKKEEEBBB???===999888777555444333222222222222222111111111000000////////////////////////...............///000000///......------,,,++++++,,,,,,---------......///,,,,,,+++************+++))))))(((((((((((())))))*********)))))))))))))))(((((())))))))))))((((((&&&''''''(((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((('''(((((((((''''''((()))((((((((((((((((((((((((((((((((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((""""""""""""""""""""""""&&&&&&&&&&&&%%%$$$###"""&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''(((((()))'''&&&&&&%%%%%%%%%&&&&&&''''''((()))))))))))))))(((((('''&&&&&&&&&&&&'''((('''&&&%%%%%%%%%%%%&&&''''''(((((((((((())))))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&'''((((((''''''''''''((((((((((((''''''((()))))))))))))))************************))))))*********+++++++++)))))))))***+++,,,---...+++...333888;;;???DDDGGGBBBAAA???===<<<<<<<<<<<<===:::<<<@@@BBBCCCIIIRRR^^^kkk{{{zzzsssggg[[[QQQKKKEEEBBB===<<<:::888666555444333222222222222111111111111000000000000000000000000...............///000000///......------,,,++++++,,,,,,,,,------------------,,,,,,+++***++++++++++++******))))))******+++))))))))))))))))))******(((((())))))))))))((((((&&&''''''(((((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((&&&''')))((('''&&&((()))((((((((((((((((((((((((((((((((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&%%%###"""!!!&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&''''''((((((''''''&&&%%%%%%%%%&&&&&&$$$%%%&&&'''(((((((((((()))((('''&&&&&&&&&&&&&&&)))'''&&&$$$###$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&'''((((((''''''''''''((((((((((((''''''((()))))))))))))))***************************************************))))))***+++...000111000444:::>>>@@@BBBCCCEEE???===;;;::::::;;;===>>>BBB>>>???DDDGGGIIISSS```rrr|||yyy}}}~~~|||wwwwwwyyy}}}pppbbbVVVMMMHHHBBBAAA???<<<999777666666333222222222222111111111000000000000000000000000...............///000000///......------,,,+++++++++,,,------------,,,,,,------,,,+++++++++++++++,,,++++++******++++++,,,))))))))))))************'''((()))******)))((('''''''''((())))))))))))(((''''''''''''((((((((((((((((((((((((((((((((((((%%%(((***)))&&&%%%&&&)))(((((((((((((((((((((((('''''''''((((((((((((((())))))))))))))))))))))))''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&''''''&&&&&&&&&%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''(((((('''&&&%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&&&&&&&'''&&&&&&&&&&&&'''((((((((('''%%%$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&'''((((((''''''''''''((((((((((((''''''((()))))))))))))))************************,,,,,,++++++***)))))))))+++++++++,,,...000333555888<<>>;;;;;;<<<<<<>>>@@@AAACCCFFFAAABBBIIIMMMQQQ```qqq~~~ssslllhhheeehhhllltttuuuhhhaaa``````dddjjjppp{{{yyyvvvtttqqqttt|||wwwfffXXXPPPGGGEEECCC@@@===:::999888333333222222222111111111000000000000000000000000...............///000000///......------,,,++++++,,,---...//////...---,,,------,,,++++++++++++,,,++++++************++++++((()))))))))************'''((()))******)))(((''''''((())))))******))))))''''''''''''((((((((((((((((((((((((((((((((((((&&&)))+++)))%%%###%%%(((((((((((((((((((((((((((&&&&&&''''''(((((())))))))))))))))))))))))))))))''''''''''''''''''''''''(((((((((((((((((((((((($$$$$$$$$$$$$$$$$$$$$$$$%%%&&&''''''((('''''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((((('''&&&%%%%%%%%%%%%%%%(((((((((((('''&&&%%%%%%%%%%%%%%%&&&'''((()))***'''&&&%%%$$$%%%''')))***'''''''''''''''''''''&&&"""###$$$%%%'''((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((&&&&&&''''''''''''&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&'''((((((''''''''''''((((((((()))'''(((((()))))))))))))))************************---,,,,,,+++***)))((((((------------000333666888???CCCGGGHHHEEE@@@;;;888:::;;;>>>AAACCCEEEFFFFFFHHHCCCDDDMMMRRRXXXiii}}}wwwgggaaa___^^^\\\[[[```jjjxxxxxxkkk```YYYUUUVVVVVVYYY^^^ccclllnnnaaaaaacccccckkkvvvrrrbbbXXXJJJHHHEEEBBB???<<<;;;:::333333333222222222111111000000000000000000000000...............///000000///......------,,,++++++......///000000///...---...---,,,,,,++++++,,,,,,******))))))))))))******(((((())))))*********+++'''((()))++++++)))((('''(((((()))***************''''''''''''((((((((()))((((((((((((((((((((((((&&&)))+++)))$$$"""$$$'''((((((((((((((((((((((((%%%&&&&&&'''((()))******''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((###$$$%%%&&&''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$'''((()))(((''''''''')))'''&&&%%%%%%%%%%%%&&&'''$$$$$$&&&&&&&&&&&&$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%###"""###'''((('''%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''))))))((('''&&&%%%%%%%%%&&&'''((((((((('''%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%$$$$$$%%%'''(((''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''#########$$$$$$%%%%%%%%%'''&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((('''%%%$$$$$$%%%&&&'''''''''''''''((((((((((((+++***)))))))))***+++,,,...+++***+++...000000...////////////222777>>>CCCFFFHHHHHHEEE@@@<<<<<<======???BBBFFFHHHIIIGGGEEELLLLLLMMMOOOVVVeeevvv}}}sssqqqqqqrrruuuzzzuuucccYYYTTTQQQPPPRRRSSSYYY___eeerrrnnnaaaZZZVVVRRRNNNTTTSSSSSSTTTVVV]]]nnn~~~xxxccc[[[UUUVVVYYYZZZ]]]aaarrrqqqcccTTTPPPJJJEEECCCBBB@@@???999777555444333444555666222222111000000000000000000000000000000000000000......---,,,,,,,,,,,,---......------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++******)))))))))))))))++++++++++++******))))))+++******)))))))))))))))******))))))((((((''''''''''''''''''''''''''''''&&&$$$###$$$&&&(((((('''%%%&&&&&&'''((()))******+++***)))'''&&&&&&&&&&&&))))))(((((('''''''''&&&''''''''''''''''''''''''###$$$%%%%%%&&&&&&%%%%%%))))))))))))((((((((((((###$$$%%%&&&''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&''''''%%%%%%&&&''''''&&&%%%%%%%%%%%%&&&'''$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%###"""$$$&&&((('''%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''))))))(((&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%$$$$$$%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((()))'''&&&%%%%%%&&&'''(((''''''((((((((()))))))))+++***)))))))))***,,,,,,,,,***((())),,,------+++///000222444777<<>>???AAAFFFFFFHHHIIIKKKLLLMMMMMMOOORRRVVV\\\ffftttwwwnnneeecccdddeeeiiinnnyyyqqqdddWWWQQQOOOLLLLLLNNNPPPTTTXXX]]]ggguuuwwwiii]]]WWWTTTRRRPPPPPPPPPQQQSSSTTTYYYgggtttsssddd^^^WWWQQQRRRTTTTTTVVVZZZcccwww{{{yyyxxx|||nnn]]]XXXRRRMMMIIIGGGDDDBBB???>>>;;;888666666666777333222111111000000111111111111111111111111111111///...------,,,,,,------,,,,,,++++++++++++******,,,,,,,,,,,,,,,,,,,,,,,,++++++***)))))))))))))))************))))))((((((+++******)))))))))))))))))))))))))))(((((((((((('''''''''''''''''''''''')))'''%%%%%%&&&''''''&&&%%%%%%&&&&&&''''''((((((***)))(((''''''&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%&&&''''''''''''&&&''''''''''''&&&&&&&&&&&&$$$$$$%%%&&&''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$###%%%&&&%%%$$$###$$$%%%'''&&&&&&%%%%%%&&&&&&'''$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$&&&''''''&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&''''''''')))((('''&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''$$$%%%&&&''''''&&&&&&%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((()))((('''&&&'''''')))***((())))))))))))*********+++***))))))***+++,,,---,,,***))))))+++,,,,,,+++000333777:::>>>CCCIIILLLJJJKKKJJJFFFBBB@@@BBBEEEJJJKKKLLLLLLMMMOOORRRUUUXXX___iiisssxxxhhh```YYYXXXYYYZZZ^^^ccchhhtttsssbbbYYYPPPNNNMMMLLLLLLNNNNNNSSSWWW[[[eeesss}}}}}}pppddd[[[WWWWWWWWWTTTTTTWWWZZZ\\\___jjjuuu}}}lll___[[[UUUQQQRRRRRRQQQQQQTTT[[[lllrrriiieeeeeeeeepppxxxzzzjjjeee___YYYTTTPPPLLLJJJGGGDDD@@@;;;888555444444333333222111111111111111111111111111111111111111///...------,,,---------,,,,,,++++++++++++******,,,,,,,,,,,,,,,,,,,,,,,,++++++***))))))))))))***)))))))))))))))(((((((((+++******)))))))))))))))(((((((((((())))))))))))''''''''''''''''''''''''+++)))''''''''''''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&((((((''''''''''''(((((('''''''''''''''(((((((((''''''''''''''''''''''''&&&&&&'''(((((((((((((((''''''''''''&&&&&&&&&&&&$$$%%%&&&&&&'''''''''&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&%%%$$$###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''((((((((((((((((((((((((&&&%%%%%%%%%%%%&&&'''(((&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&'''''''''''')))((('''&&&&&&&&&&&&&&&((('''%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''###$$$&&&(((((('''&&&$$$''''''&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&''''''''''''((())))))((((((((()))***+++))))))*********++++++++++++******)))***+++---...------,,,,,,---...//////444888===AAAEEEHHHKKKNNNKKKLLLKKKGGGCCCCCCFFFJJJKKKPPPVVVXXXYYY[[[___cccjjjtttpppaaaZZZUUUUUUUUUVVVZZZ```]]]gggrrr{{{|||ooofff]]]VVVUUUUUUTTTVVVYYYWWW]]]dddkkkxxxvvvhhhbbbcccfffffffffjjjooorrrwww{{{nnn```[[[YYY[[[ZZZXXXXXX[[[iiixxxvvvgggaaa```aaacccgggppp{{{vvvrrrmmmhhhccc___[[[XXXTTTQQQKKKDDD>>>999777666444333222111111111111111111111111111111111111111//////...---------------......---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++******))))))******************))))))))))))+++******)))))))))))))))''''''(((((())))))******''''''''''''''''''''''''+++)))((('''((()))((('''''''''&&&&&&&&&&&&&&&&&&'''''''''''''''((())))))******))))))((((((((((((''''''''''''''''''''''''&&&&&&'''(((((((((((('''))))))))))))((((((((((((%%%%%%&&&&&&'''&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&'''&&&%%%$$$%%%'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''(((((((((((((((((((((((('''&&&&&&%%%&&&(((***+++&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''&&&&&&&&&'''''''''(((((((((((('''&&&&&&&&&&&&''')))(((&&&%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%###$$$&&&(((((('''&&&%%%''''''&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&''''''''''''((())))))))))))******++++++************+++++++++++++++************,,,---///,,,---......///111333444:::>>>CCCGGGIIIJJJKKKMMMMMMMMMMMMJJJGGGGGGKKKOOOQQQ\\\jjjrrrttttttwww{{{}}}}}}}}}tttfff[[[WWWSSSTTTTTTTTTYYY___cccjjjttt}}}}}}uuullleee___```bbbdddjjjpppooowwwvvvrrruuuzzz}}}mmmjjjjjjmmmmmmkkkmmmqqqwwwggg```^^^______ccckkkrrrwww~~~{{{zzzxxxvvvsssppplllggg___UUUKKKDDD>>><<<666555444222111000000000111111111111111111111111//////...------------.........---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++***************+++++++++++++++++++++++++++******)))))))))))))))''''''(((((())))))******(((((((((((((((((((((((()))((('''''')))******)))((((((((('''''''''''''''''''''&&&''''''((()))***...---,,,+++***(((''''''''''''''''''''''''''''''%%%%%%&&&'''''''''''''''))))))))))))((((((((((((%%%%%%&&&&&&'''&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%'''((('''&&&%%%&&&(((%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%&&&&&&&&&''''''((((((((((((((((((((((((''''''&&&&&&'''))),,,---&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''&&&&&&'''''''''((((((((((((''''''&&&&&&&&&''''''(((((('''&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%###$$$&&&''''''''''''&&&''''''&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&''''''''''''(((((())))))******+++++++++)))************++++++++++++*********+++,,,...///)))+++---///111333777:::AAADDDHHHKKKLLLLLLLLLMMMNNNPPPQQQOOOLLLMMMQQQUUUXXXiii~~~|||uuuiiijjjjjjkkkqqqzzz}}}wwwmmmbbbZZZWWWTTTSSSVVVWWWXXX]]]dddvvv{{{{{{vvvlllhhhggglllrrryyy|||{{{}}}sssiiidddaaa___]]]eeejjjlllxxxsssmmmllllllrrrxxxvvvhhhYYYMMMDDD???:::999777555333111111000222222222222222222222222000///......------......,,,,,,++++++++++++******,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++************++++++++++++,,,,,,,,,,,,,,,+++******)))))))))))))))(((((((((((())))))))))))((((((((((((((((((((((((((('''&&&''')))++++++***'''((((((((((((((((((((('''''''''''''''((()))***...---,,,+++***)))((('''''''''''''''''''''''''''%%%%%%&&&''''''''''''&&&''''''''''''&&&&&&&&&&&&%%%&&&&&&'''&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%'''((('''&&&%%%&&&(((%%%%%%&&&''''''&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''&&&$$$###%%%&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&%%%$$$&&&))),,,...&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''''''''''''''((((((((((((''''''&&&&&&&&&''''''(((&&&''''''''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((''''''''''''&&&&&&&&&%%%$$$$$$%%%&&&&&&''''''(((''''''&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''((()))******+++++++++)))))))))************+++************+++---///000'''+++///222444888===AAAEEEHHHLLLNNNNNNOOOOOOPPPQQQTTTVVVUUUSSSTTTWWWZZZcccxxxtttkkkeeeYYY[[[[[[[[[aaajjjnnnkkkllliiifffdddbbb^^^ZZZWWW[[[ZZZ]]]bbbeeegggooowwwxxxssssssnnnnnnsss}}}zzztttoookkkeeeooouuuyyyqqqfffbbb```___dddlllxxx~~~jjjYYYLLLFFF@@@>>><<<999666444222222222222222222222222222222000//////...............,,,,,,++++++++++++******,,,,,,,,,,,,,,,,,,,,,,,,---,,,++++++******++++++******+++++++++,,,,,,,,,+++******)))))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((()))(((&&&'''((())))))(((&&&&&&&&&''''''((((((((((((((('''''''''(((((()))******))))))))))))((((((''''''''''''''''''''''''&&&&&&'''(((((((((((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&''''''%%%%%%&&&'''%%%%%%&&&''''''&&&%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&'''&&&$$$###$$$'''%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%$$$######%%%(((+++...&&&%%%%%%%%%%%%&&&''''''((((((((((((((((((((((((''''''''''''((((((((()))''''''&&&&&&&&&''''''((($$$%%%&&&'''&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%'''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((()))))))))(((((('''''''''&&&%%%$$$$$$%%%%%%'''((()))''''''&&&&&&&&&%%%%%%%%%((((((((((((((((((((((((&&&&&&&&&'''''''''((((((''''''(((******+++++++++((())))))))))))*********************+++---///000)))---222555999===CCCHHHGGGJJJNNNPPPPPPQQQSSSTTTSSSWWWZZZZZZXXXXXX[[[^^^rrr~~~rrriii```YYYUUUQQQSSSSSSRRRXXXaaaddd``````[[[XXXYYYZZZ[[[\\\^^^eeeeeejjjqqquuuyyy~~~rrrnnnppptttwww{{{wwwyyysssgggbbb___\\\aaaiiirrr{{{}}}hhhYYYQQQDDDCCC@@@<<<999666444333222222222222222222222222000000///........................---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---,,,++++++******++++++))))))******+++++++++++++++******)))))))))))))))******))))))((((((''''''))))))))))))))))))))))))+++)))'''''''''((('''&&&$$$$$$%%%%%%&&&'''((((((((((((''''''''''''((((((%%%&&&&&&'''((())))))***'''''''''''''''''''''''''''(((((()))))))))))))))***)))))))))((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%###!!!###%%%'''%%%###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%$$$$$$%%%&&&(((***,,,%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$###%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$######"""""""""%%%%%%$$$$$$%%%%%%&&&'''''''''''''''''''''''''''%%%%%%&&&'''((()))******)))(((&&&%%%%%%&&&((())))))&&&%%%&&&)))***)))'''''''''''''''''''''''''''(((((('''''''''&&&&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''((((((((((((&&&&&&&&&''''''''''''((((((%%%$$$%%%'''(((&&&$$$&&&%%%%%%'''((()))'''&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&%%%%%%&&&))),,,'''((()))******(((&&&$$$&&&&&&&&&'''''''''((((((%%%&&&(((*********))))))++++++++++++++++++++++++)))************+++++++++((()))+++++++++,,,...000---000555;;;AAAFFFJJJLLLQQQPPPNNNMMMNNNQQQTTTWWWXXXTTTTTTWWWYYYZZZcccmmm|||zzz}}}zzztttjjjaaa[[[WWWUUUTTTUUURRRPPPUUU^^^gggkkkkkkbbb^^^YYYWWWYYY]]]aaacccllluuu~~~oooeeebbbbbbccceeekkkttt{{{yyyeeeYYYTTTIII@@@>>><<<666444555333444444333222222111///222111///.........///000//////...---,,,,,,++++++---------,,,,,,,,,++++++...---+++******+++---...)))***+++,,,,,,,,,++++++(((+++---+++'''%%%%%%'''))))))))))))))))))))))))+++******)))(((''''''&&&((((((''''''''''''((((((((((((((((((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((((((((('''''''''&&&&&&&&&&&&''''''(((((((((((((((''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%###"""###&&&'''&&&$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$%%%'''((()))%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$###%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&%%%%%%&&&&&&'''(((''''''''''''''''''''''''%%%%%%&&&'''((()))******)))'''&&&%%%%%%&&&''')))(((&&&%%%&&&)))***)))'''&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&''''''''''''((((((&&&$$$%%%'''(((&&&$$$&&&%%%%%%&&&((()))'''&&&%%%%%%&&&&&&&&&'''''''''$$$%%%&&&&&&%%%%%%''')))'''((()))))))))(((&&&%%%&&&&&&&&&'''''''''((((((&&&'''((()))******))))))))))))))))))))))))))))))************++++++++++++)))***+++,,,+++,,,///111111444:::AAAGGGKKKNNNOOOSSSSSSSSSSSSSSSTTTUUUWWWUUUUUUXXX^^^aaafffrrr~~~wwwnnnkkklllqqquuuzzz~~~|||vvvrrriiieee```\\\ZZZZZZZZZ[[[[[[ZZZ\\\cccmmmvvvyyyxxxllljjjfffdddfffkkkqqquuu~~~xxxsssrrrnnnmmmnnnpppsss}}}lll```^^^UUUMMMKKKGGG???:::999333444333333333444222111111111000////////////000000000///......---,,,,,,---------,,,,,,,,,++++++...---+++******+++---...++++++++++++,,,,,,,,,,,,)))*********(((((()))***))))))))))))))))))))))))*********)))((('''''''''((((((''''''''''''((((((((((((((((((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((())))))((((((((('''''''''&&&''''''(((((((((((((((''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$$$$%%%&&&'''&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%$$$$$$$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((''''''''''''&&&&&&&&&'''&&&&&&&&&&&&'''((((((''''''''''''''''''''''''%%%%%%&&&'''((()))******((('''&&&%%%%%%&&&'''((('''&&&&&&&&&((()))((('''%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''&&&&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&''''''''''''((('''&&&%%%&&&'''''''''%%%&&&%%%%%%&&&'''((('''&&&%%%&&&&&&&&&&&&'''''''''###%%%'''&&&%%%$$$%%%&&&((((((((((((((('''''''''&&&&&&'''''''''(((((((((&&&'''((()))*********)))))))))))))))))))))))))))************+++++++++,,,+++,,,,,,,,,,,,---///222777;;;BBBIIINNNRRRSSSSSSSSSTTTVVVVVVTTTSSSSSSSSSVVVZZZaaaiiinnnwwwwwwooohhh```]]]]]]^^^aaaeeeggggggeeeaaa^^^ZZZZZZ[[[]]]aaafffjjjmmmooopppttt}}}|||{{{}}}~~~|||mmmmmmlllqqq{{{|||yyywwwzzz~~~wwwlllddd]]]XXXWWWSSSJJJAAA===999777555555555444333222111111111111111000//////111111000//////.........------------,,,,,,,,,,,,------++++++++++++------,,,,,,+++++++++,,,---...+++***((((((***+++,,,,,,((((((((((((((((((((((((******))))))((((((''''''((((((''''''''''''((((((((((((((((((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((()))))))))))))))(((((((((&&&''''''(((((((((((((((''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''''''''''''''''''''&&&&&&&&&&&&&&&''''''(((''''''''''''''''''''''''%%%%%%&&&'''((()))******((('''&&&&&&&&&&&&'''(((&&&&&&&&&&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%&&&&&&&&&'''''''''&&&&&&&&&''''''''''''((('''&&&&&&&&&'''''''''&&&'''%%%$$$%%%'''((('''&&&&&&&&&&&&&&&''''''''''''%%%'''(((((('''%%%$$$$$$)))(((''''''''''''((((((''''''''''''((((((((((((&&&'''(((((()))*********++++++++++++++++++++++++*********+++++++++,,,,,,+++,,,,,,,,,,,,...222444===BBBHHHOOOTTTVVVVVVVVVUUUWWWXXXVVVSSSQQQRRRTTT\\\dddooowwwxxxnnnccc___]]]ZZZXXXXXXVVVYYY[[[]]]\\\[[[[[[ZZZZZZ]]]cccjjjrrrzzzmmm```cccbbbfffpppwww|||yyy{{{uuugggeeeddddddaaaYYYOOOHHHBBB<<<777777666444222111000111222333222111000///000000000//////............------------,,,,,,,,,---,,,,,,++++++,,,,,,---...,,,+++******,,,...//////+++((('''***------+++((((((((((((((((((((((((***)))))))))((((((((('''((((((''''''''''''((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&''''''(((((((((((((((''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''%%%%%%%%%$$$%%%%%%&&&'''''''''''''''''''''''''''%%%%%%&&&'''((()))******'''''''''&&&&&&'''''''''%%%&&&&&&'''&&&''''''(((((((((((((((((((((((((((&&&'''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''&&&'''''''''((((((((((((&&&&&&&&&''''''''''''((('''''''''''''''&&&'''''''''%%%$$$$$$&&&''''''&&&&&&&&&&&&'''''''''(((((('''(((******(((&&&%%%%%%((((((''''''''''''((()))'''''''''((((((((())))))'''''''''((())))))******++++++++++++++++++++++++***++++++++++++,,,,,,,,,+++,,,------///222777:::CCCGGGMMMSSSWWWXXXWWWVVVWWWXXXXXXUUURRRRRRWWW[[[eeeppp~~~|||ggg^^^WWWVVVVVVVVVWWWYYYZZZ[[[]]]]]]\\\]]]```cccffflllttt}}}rrrdddaaa^^^___gggmmmxxx{{{rrrsssttttttsssmmmbbbYYYLLLBBB999777777333222333111222333333333222000////////////........................---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---,,,+++******,,,...///222---)))(((***,,,+++)))))))))))))))))))))))))))))))))))))))((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&''''''(((((((((((((((''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&%%%%%%&&&'''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''(((((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&''''''''''''''''''''''''%%%%%%&&&'''((()))******''''''''''''''''''''''''$$$&&&''''''&&&&&&'''(((((((((((((((((((((((((((&&&&&&&&&'''''''''''''''(((((((((((((((((((((((('''''''''''''''''''''''''''''''''((((((((())))))&&&&&&&&&''''''''''''(((&&&((((((((('''&&&'''((('''%%%######%%%'''''''''&&&&&&'''''''''(((((((((((()))******(((''''''''''''''''''(((((((((((((((''''''((((((((()))))))))((('''''''''((()))***+++))))))))))))))))))))))))++++++++++++,,,,,,,,,,,,,,,---///111444999???CCCJJJMMMQQQUUUWWWXXXWWWVVVQQQTTTVVVUUUTTTWWW___fffuuu{{{mmm___YYYUUUVVVWWWYYY___fffkkklllllljjjhhhjjjpppttt|||rrrddd]]][[[```fffmmm}}}zzzppp___OOOAAA===;;;666444888222333333333333222111111....................................---------,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++*********+++,,,---000...+++************)))))))))))))))))))))))))))))))))))))))((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&''''''''''''&&&''''''(((((((((((((((''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%"""$$$&&&%%%$$$###%%%'''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$%%%%%%'''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''%%%%%%&&&'''((()))******&&&''''''''''''''''''&&&$$$&&&''''''%%%%%%&&&(((((((((((((((((((((((((((&&&&&&&&&'''''''''((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&&&&''''''''''''(((&&&((())))))&&&&&&''')))'''%%%###"""$$$&&&''''''''''''''''''((((((((((((((())))))(((&&&&&&''')))%%%&&&((()))))))))(((''''''((((((((())))))))))))((((((''''''((()))***+++))))))))))))))))))))))))+++++++++,,,,,,,,,------...///222555:::@@@HHHNNNPPPQQQTTTVVVWWWWWWVVVUUUPPPVVV^^^bbbeeekkkuuu~~~xxx{{{}}}{{{{{{~~~vvvlllddd___]]]^^^aaadddjjjwwwuuujjjccceeegggiiirrr}}}lllVVVLLLDDD;;;777;;;444444333222222222222222////////////////////////............------------+++,,,,,,------,,,,,,+++)))))))))*********+++++++++,,,,,,+++***))))))***++++++++++++++++++++++++(((((((((((())))))))))))((((((''''''''''''((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((&&&'''''''''((((((((((((&&&''''''(((((((((((((((''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%!!!$$$&&&%%%###"""$$$'''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''###$$$%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&&&&&&&$$$$$$$$$%%%&&&'''((()))%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&''''''(((((('''&&&&&&&&&&&&'''((((((''''''''''''''''''''''''%%%%%%&&&'''((()))******&&&&&&''''''''''''&&&&&&###&&&((('''%%%$$$&&&)))''''''''''''''''''''''''&&&&&&&&&'''''''''((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((&&&(((***)))&&&%%%''')))'''%%%""""""$$$&&&''''''''''''''''''((((((((()))'''''''''&&&%%%%%%''')))$$$&&&(((******)))((('''(((((((((((())))))))))))((((((''''''((()))+++,,,++++++++++++++++++++++++++++++,,,,,,,,,---------///111444888>>>FFFOOOUUUTTTTTTVVVWWWWWWWWWVVVUUUYYYcccooowww}}}pppfffiiilllhhhhhhmmmiiimmmoookkkgggddd___ZZZaaaccchhhnnnttt|||qqqpppooolllooovvv}}}kkk[[[NNN???999;;;555444333222111222333444000000000000000111111111//////.........---------+++,,,,,,------,,,,,,+++(((((()))************)))&&&***---,,,***(((***,,,++++++++++++++++++++++++(((((((((((())))))))))))((((((''''''''''''((((((((((((((((((((((((((((((''''''''''''((((((((()))(((((((((((((((((((((((('''((((((((())))))******&&&''''''((((((((((((((('''''''''&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$'''''''''&&&&&&%%%%%%%%%%%%%%%$$$######$$$$$$%%%''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%&&&&&&&&&''''''))))))(((((('''''''''&&&'''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((''''''((('''&&&%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&%%%%%%$$$$$$'''''''''(((((((((((()))))))))(((''''''''''''(((''''''''''''((((((((((((+++)))'''''''''((('''&&&(((((((((((('''''''''''''''''''''''''''''''''''')))((((((''''''''''''((())))))))))))))))))))))))((((((((((((((()))******((())))))************)))***,,,...///...---...///111666===DDDIIIMMMQQQTTTVVVSSSRRRVVVWWWSSSQQQQQQZZZnnnllleee^^^[[[\\\______^^^bbbeeefffbbb[[[YYY]]]cccgggoooxxx~~~{{{|||mmm\\\OOODDD<<<>>>:::555222111111111111000000111111111///...---////////////////////////------------------------,,,++++++******++++++,,,++++++++++++++++++++++++))))))************))))))++++++***)))(((((())))))'''((()))((('''((()))+++''''''((((((((((((''''''%%%&&&''''''((((((''''''))))))))))))))))))))))))((((((''''''&&&&&&%%%%%%)))))))))))))))(((''''''&&&&&&&&&&&&'''''''''((($$$$$$$$$$$$$$$$$$$$$$$$''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&'''(((######$$$%%%'''((()))))))))((((((((('''''''''&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((''''''((('''&&&&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&))))))(((''''''&&&%%%%%%&&&&&&'''''''''(((((((((&&&&&&&&&&&&&&&'''((((((''''''''''''((((((((((((***)))'''&&&'''((('''&&&((((((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''((((((((())))))))))))))))))))))))((((((((((((((()))******)))***++++++,,,++++++++++++,,,------,,,,,,...000777<<>>CCCIIINNNQQQRRRSSSTTTUUUQQQOOONNNMMMNNNWWWaaa}}}|||ggg[[[WWWSSSSSSYYYaaahhhllluuuxxx|||{{{yyyzzzuuujjjcccaaagggmmmuuulllZZZMMMCCC@@@;;;888666444333111222222222333222222111000////////////////////////------------------------......------------......++++++++++++++++++++++++))))))************))))))+++*********)))))))))))))))******+++++++++++++++''''''((((((((((((''''''&&&&&&&&&'''''''''''''''(((((((((((((((((((((((('''((((((((((((((())))))(((((()))))))))(((''''''''''''((((((((()))))))))%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''((()))''''''&&&&&&&&&%%%%%%%%%''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''((())))))((('''&&&%%%$$$$$$''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&''''''(((((('''''''''&&&&&&'''''''''&&&&&&&&&&&&''''''''''''((((((((((((''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%&&&'''((()))''''''''''''((((((((((((***(((&&&&&&((((((((('''((((((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''(((((()))))))))(((((((((((((((((((((((((((((())))))***************+++,,,---------------///000000000222666===BBBDDDHHHNNNRRRSSSRRRQQQQQQSSSOOOLLLKKKKKKPPP___nnn|||nnn```[[[\\\___dddlllvvvuuukkkddddddeeeiiiwww|||jjj]]]OOOJJJBBB<<<888666444333222222222222222222111111////////////////////////..............................------------......++++++++++++++++++++++++)))******++++++******)))*********************)))'''((((((***++++++)))(((''''''((((((((((((''''''&&&&&&&&&&&&''''''((((((((((((((((((((((((((((((''''''(((((())))))******'''(((((((((((((((''''''(((((((((((())))))))))))%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''******)))(((&&&%%%$$$$$$&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&%%%&&&'''((()))&&&''''''''''''''''''&&&&&&&&&&&&''''''(((((((((''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((((('''''''''''''''(((''''''''''''(((((((((((()))'''&&&&&&((()))((('''((((((((((((''''''''''''(((((((((((((((((((((((($$$%%%'''((())))))))))))(((((((((((((((((((((((((((((()))***+++******))))))***+++,,,---------------...000333777===EEEJJJKKKOOOSSSUUUTTTSSSRRRQQQNNNKKKIIIJJJMMMWWWjjjzzzxxxqqqmmmhhhccc```gggrrr|||sssjjjhhhfffeeemmmyyyvvvlllaaaZZZPPPFFF@@@===:::999444444333222111111111111000000000000000000000000........................------,,,,,,,,,,,,------++++++++++++++++++++++++******++++++++++++******)))***++++++++++++******''''''(((+++------)))&&&''''''(((((((((((('''''''''&&&&&&&&&&&&'''((()))''''''''''''''''''''''''''''''(((((())))))******''''''((((((((((((''''''(((((((((((())))))))))))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&%%%%%%%%%%%%%%%&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&'''''''''''''''(((((((((&&&&&&&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&%%%%%%%%%'''((()))&&&&&&'''(((((('''&&&&&&&&&&&&&&&'''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&''''''''''''))))))((('''''''''''''''''''''''''''(((((((((((()))'''&&&&&&((())))))(((((((((((((((''''''''''''((((((((((((((((((((((((%%%&&&''')))))))))((((((((((((((((((((((((((((((((()))***+++++++++***))))))***+++,,,---.........+++...333888===CCCJJJNNNSSSUUUXXXXXXVVVTTTTTTTTTKKKIIIIIIOOOXXXeeexxx{{{xxxuuuqqqkkkeeebbbccceeegggkkkvvv{{{wwwppphhhiiiooosss~~~wwwnnnhhh^^^TTTLLLFFFBBB???888777555333222111111111000000000000000000000000........................------,,,,,,,,,,,,------++++++++++++++++++++++++******++++++++++++******)))***+++,,,,,,,,,+++***))))))***...111000,,,'''''''''((((((((((((''''''''''''&&&%%%&&&'''((()))'''''''''''''''''''''''''''((((((((((((((())))))&&&&&&'''(((((((((''''''''''''((((((((()))))))))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''')))((('''&&&%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&&&&''''''(((((())))))%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&%%%$$$$$$%%%&&&(((***&&&&&&'''(((((('''&&&&&&&&&&&&&&&'''((()))))))))&&&&&&&&&'''''''''''''''&&&&&&'''''''''(((((((((''''''&&&&&&&&&'''((((((''''''''''''((((((((((((((('''&&&&&&((())))))(((((((((((((((''''''''''''((((((((((((((((((((((((&&&'''((()))))))))'''&&&))))))))))))))))))))))))''')))***,,,,,,+++***)))***+++,,,---.../////////...333:::@@@FFFJJJNNNQQQWWWXXXXXXWWWUUUSSSSSSTTTOOOMMMQQQ\\\jjjzzzyyyqqqmmmjjjffffffhhhbbbaaa```aaadddiiipppuuu~~~{{{vvvxxxtttyyyuuuoooiiiaaaXXXOOOIII<<<;;;999666444333222222000000000000000000000000..............................------------......++++++++++++++++++++++++***++++++,,,,,,++++++***((()))+++------,,,+++***))))))***...222111,,,&&&''''''((((((((((((''''''((('''&&&%%%%%%'''((()))''''''''''''''''''''''''((((((((('''''''''''''''%%%&&&''''''((((((''''''&&&&&&'''''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''+++***)))(((&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%'''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%'''&&&&&&&&&&&&'''(((((()))))))))(((''''''&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&%%%$$$###$$$&&&)))***%%%&&&'''(((((('''&&&%%%&&&&&&&&&'''((())))))***'''''''''((((((((((((((('''''''''(((((((((((()))$$$$$$$$$%%%&&&'''((()))''''''''''''((((((((()))((('''%%%&&&((())))))((()))(((((((((''''''''''''''''''''''''''''''''''''&&&''')))******(((&&&%%%************************''')))+++,,,,,,,,,***)))+++,,,---///000111111111444999BBBIIIMMMPPPRRRTTTWWWWWWVVVTTTRRRQQQQQQSSSVVVTTTYYYhhhzzzooofff]]]YYYVVVVVV\\\ccc\\\^^^ccckkkrrrzzzxxxmmm```XXX@@@>>>;;;888666444444333000000000000000000000000//////////////////////////////............//////++++++++++++++++++++++++***++++++,,,,,,++++++***((()))+++---------+++***''''''(((---111000***###''''''((((((((((((''''''((('''%%%%%%%%%&&&(((***''''''''''''''''''''''''((((((''''''&&&&&&&&&%%%%%%%%%&&&'''((((((((('''&&&&&&&&&&&&'''''''''(((***)))((('''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%$$$######!!!"""$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&)))))))))))))))))))))((($$$%%%&&&'''''''''&&&%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''(((%%%$$$%%%)))***)))&&&''''''''''''''''''''''''(((''''''''''''((())))))))))))(((''''''''''''''')))((('''&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%'''((('''&&&'''((('''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((***)))((((((((()))+++,,,'''((((((((()))))))))*********+++,,,------------.........------000444777999???HHHPPPTTTVVVWWWWWWXXXWWWUUUTTTUUUVVVXXXYYY^^^bbblll}}}{{{rrraaa\\\VVVUUUXXX^^^aaabbbeeehhhoooyyyuuu```QQQ@@@999666444222333000000111111111111111000...............///000111......---------,,,,,,,,,+++,,,,,,------,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,))))))))))))))))))******))))))))))))((((((((((((&&&&&&''''''(((((())))))(((((())))))))))))((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''))))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$$$$###$$$%%%&&&'''''''''&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&%%%$$$%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&%%%%%%%%%'''''''''&&&''''''''''''''''''''''''''''''&&&&&&''''''((()))))))))((('''''''''''''''(((''''''&&&%%%%%%&&&&&&''''''''''''''''''''''''&&&(((******)))((()))***((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((***)))((((((((()))++++++))))))))))))))))))))))))******+++,,,,,,------,,,/////////......111666:::>>>CCCKKKRRRUUUVVVWWWXXXUUUTTTSSSRRRTTT\\\fffnnnwww|||zzzkkkbbb\\\[[[\\\^^^dddkkkqqquuuyyy~~~vvvyyy}}}|||fffMMM@@@<<<999555333333333444444333222111000------,,,,,,------...............---------,,,,,,+++,,,,,,------,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,************))))))))))))***)))))))))(((((((((((('''''''''((((((((((((((((((((())))))))))))((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''(((''''''&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$$$$$$$&&&&&&'''''''''&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''((((((''''''''''''''''''''''''''''''''''''&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&'''((((((&&&%%%&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&''''''((()))((((((''''''''''''((((((''''''&&&&&&&&&&&&&&&''''''''''''''''''''''''((()))******((('''(((((()))))))))(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((()))))))))((()))******+++))))))))))))))))))((((((***+++++++++++++++++++++////////////111555;;;???EEEIIIPPPTTTVVVWWWWWWXXXTTTSSSRRRTTT]]]mmmwwwjjj```ZZZ]]]cccmmmvvv}}}xxxvvvwwwxxx|||^^^KKKDDD???999555555666666666555333111000///......---------------.........------------,,,+++,,,,,,------,,,,,,+++++++++++++++++++++++++++++++++*********)))))))))******)))))))))((((((((())))))((((((((((((((('''(((((())))))))))))((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((%%%%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$######"""$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''((((((((((((((())))))((((((''''''&&&%%%$$$###%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''(((***,,,***'''%%%''')))''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&'''''')))(((''''''''''''(((((()))(((((('''''''''((((((''''''''''''''''''''''''&&&((()))(((&&&%%%%%%&&&((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''(((((((((((()))))))))))))))******+++(((((()))))))))*********+++++++++******+++++++++,,,---///111444:::BBBGGGLLLOOOTTTVVVWWWWWWWWWWWWVVVTTTVVV___rrrsssjjjfffdddcccjjjwww~~~}}}}}}}}}}}}~~~|||zzzxxxyyyzzz||||||||||||||||||||||||{{{{{{{{{{{{{{{||||||}}}||||||}}}}}}~~~{{{wwwuuu|||~~~}}}sss\\\OOODDD<<<999555555666666555333111000333222111000////////////............------------+++,,,,,,------,,,,,,+++************************,,,++++++******))))))(((*********)))))))))((((((***)))))))))((((((''''''(((((())))))))))))((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))############$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&%%%%%%&&&%%%%%%$$$############$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&(((((('''&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&)))***)))%%%$$$&&&(((''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&''''''((((((''''''''''''((((((***)))))))))))))))******''''''''''''''''''''''''&&&((()))(((&&&%%%%%%&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((())))))((()))))))))************&&&'''((()))***+++,,,---++++++*********+++,,,---***,,,000555:::BBBIIIOOOQQQSSSVVVWWWVVVUUUUUUVVVWWWWWW^^^qqqpppeeeccchhhooosss~~~|||{{{{{{zzzyyyxxxvvvuuuuuutttuuuvvvuuutttrrrqqqrrrsssqqqqqqqqqrrrrrrqqqqqqqqqqqqqqqqqqqqqqqqrrrssssssuuuvvvvvvwwwyyyzzzzzz{{{yyyzzz{{{|||}}}~~~~~~wwwqqqrrrxxxsss]]]KKK@@@===555555555444333333222111444333222111000///////////////.........---------+++,,,,,,------,,,,,,+++************************,,,+++++++++******))))))************))))))))))))******))))))((((((((('''(((((())))))))))))((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))############$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$&&&&&&&&&'''(((((())))))((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''$$$%%%&&&%%%$$$###$$$%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&''''''((((((''''''''''''(((((()))***))))))))))))******+++''''''''''''''''''''''''((()))******((('''((((((&&&&&&''''''''''''((((((''''''''''''''''''''''''''''''((((((((()))))))))(((((()))************)))''''''((()))+++,,,------,,,+++******+++---...///,,,000666<<>>FFFLLLQQQTTTWWWYYYSSSSSSSSSQQQNNNMMMNNNOOOZZZooowwwoookkkiiihhhhhhooowww~~~|||zzzyyyyyyxxxwwwuuusssrrrpppmmmiiieeeaaa___aaa```^^^\\\ZZZWWWVVVUUUXXXXXXXXXXXXWWWVVVUUUUUUPPPQQQRRRQQQPPPQQQRRRTTTNNNOOOPPPQQQQQQPPPOOONNNRRRRRRRRRSSSTTTUUUVVVWWW[[[[[[\\\^^^___aaabbbbbb```aaabbbccceeefffggghhhhhhlllppprrrrrrrrrssstttvvvxxx{{{vvveee\\\NNNIIIBBB<<<888777888999444333222222111222222222000/////////............+++,,,,,,------,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,))))))***+++,,,------...+++++++++************)))(((((())))))******++++++(((((())))))))))))((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''((($$$ """%%%''''''&&&$$$###$$$''''''%%%"""''''''''''''''''''''''''%%%%%%%%%&&&&&&''''''''''''''''''&&&&&&'''''''''((('''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&'''((()))******+++*********))))))((((((''''''''''''''''''''''''&&&&&&&&&'''''''''((((((((((((''''''&&&&&&&&&%%%(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%)))((('''&&&&&&''')))***))))))(((''''''''''''(((&&&((()))'''$$$%%%)))---))))))))))))))))))))))))((((((((()))******++++++---............000333666999EEEPPPSSSUUUWWWUUUOOOWWWQQQOOOPPPNNNLLLPPPXXXbbbvvvtttooohhhccccccffflllpppuuu~~~|||||||||uuussspppmmmjjjhhhhhhgggeeedddbbb___\\\YYYVVVUUUSSSRRRQQQPPPOOOMMMLLLLLLHHHHHHHHHHHHHHHHHHGGGGGGGGGGGGHHHHHHHHHHHHGGGGGGEEEEEEGGGHHHIIIJJJJJJJJJLLLKKKJJJIIIIIIJJJKKKLLLNNNPPPTTTVVVXXXWWWVVVUUUVVVVVVVVVWWWXXXYYY[[[\\\```aaabbbeeegggiiikkklllnnnqqquuuxxxzzz|||vvvnnnlllcccUUUGGGAAABBBAAA===:::999666666888777333111222000///......///000...---.........------,,,,,,,,,,,,------------------------,,,+++***))))))))))))---------,,,,,,+++++++++))))))))))))))))))))))))))))))))))))))))))))))))''''''(((((((((((('''''')))))))))(((''''''&&&&&&(((((((((((((((((((((((((((((((((((((((((((((((((((%%%!!!!!!$$$&&&''''''&&&%%%$$$%%%'''(((&&&###''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$''''''''''''''''''''''''$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''(((((())))))******)))))))))(((((((((''''''''''''''''''''''''&&&&&&&&&'''''''''((((((((((((((('''''''''&&&&&&(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&+++***(((&&&&&&&&&'''((('''''''''''''''((()))***))))))((('''&&&''')))+++************************))))))******+++,,,,,,,,,---...//////000333888;;;GGGOOOUUUWWWYYY[[[XXXSSSTTTOOOLLLMMMNNNOOOVVV___qqqtttmmmfffeeecccdddhhhrrr~~~zzzvvvsssrrrqqqjjjhhheeeaaa^^^\\\ZZZZZZWWWVVVSSSQQQNNNLLLKKKJJJJJJJJJIIIHHHGGGFFFFFFEEEFFFFFFFFFEEEEEEEEEDDDDDDDDDDDDEEEEEEEEEEEEDDDDDDBBBCCCDDDEEEFFFFFFFFFFFFGGGFFFEEEDDDDDDEEEFFFGGGHHHJJJMMMPPPQQQQQQPPPOOONNNMMMMMMMMMNNNNNNOOOPPPSSSTTTUUUWWWYYY[[[\\\]]]bbbeeeiiilllooossswwwzzzzzz||||||}}}~~~uuuppppppnnncccUUUMMMKKKIIIFFFCCCAAA??????@@@<<<555222444111///......///000///---.........------,,,,,,,,,---------,,,,,,,,,,,,,,,,,,,,,+++***)))))))))))),,,,,,+++++++++*********))))))))))))))))))))))))))))))))))))))))))))))))(((((())))))))))))(((((((((((())))))))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((('''%%%$$$$$$&&&''''''&&&'''&&&%%%&&&((((((&&&%%%''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&&&&'''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$%%%%%%$$$$$$%%%&&&'''(((((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''((((((((((((((((((((('''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''(((((((((((((((''''''''''''''''''''''''&&&&&&&&&'''''''''''''''''''''''',,,***((('''&&&&&&&&&&&&%%%&&&&&&&&&((()))***+++,,,***((('''((()))))))))***************************++++++,,,,,,---......---...000111444888>>>CCCNNNQQQTTTUUUXXXZZZXXXSSSTTTPPPMMMNNNQQQXXXcccnnnmmmbbb___```dddjjjoooxxx}}}ooonnnuuu|||~~~~~~|||{{{wwwuuurrrnnniiieeebbb```[[[YYYVVVSSSPPPMMMLLLKKKLLLJJJHHHFFFDDDDDDDDDDDDAAAAAAAAA@@@@@@?????????BBBBBBCCCCCCDDDEEEEEEEEEEEEEEEFFFFFFFFFFFFEEEEEECCCDDDDDDEEEEEEEEEDDDDDDDDDDDDCCCCCCCCCCCCDDDDDDDDDFFFHHHJJJKKKJJJIIIHHHEEEEEEDDDDDDDDDDDDEEEEEEJJJJJJKKKMMMNNNPPPQQQQQQSSSVVVZZZ]]]aaaeeejjjnnnnnnqqquuuwwwyyyzzz}}}~~~}}}uuuppprrryyyzzztttsssuuuxxxrrrjjjccc___]]][[[ZZZWWWUUUTTTQQQFFF:::444444111000//////000000///---.........---------------------,,,,,,++++++******++++++***************+++***************)))))))))))))))))))))))))))))))))))))))))))))))))))))))))'''(((((())))))(((((('''((((((((()))***+++++++++((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&'''(((''''''&&&'''&&&''''''(((((('''&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$########################$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''''''&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''***)))((('''&&&&&&''''''&&&&&&&&&''''''(((******---***''''''***+++***(((************************+++++++++,,,------......,,,...111444888>>>EEEJJJMMMNNNPPPSSSWWWYYYWWWSSSTTTRRRRRRTTT\\\hhhwww~~~ooodddbbbfffmmmuuuzzzqqqkkkvvv|||xxxuuusssrrrooommmiiigggeeeaaa\\\WWWSSSQQQOOONNNLLLJJJHHHFFFDDDDDDEEECCCBBB@@@@@@@@@AAABBB??????????????????@@@@@@@@@AAABBBDDDFFFHHHIIIJJJJJJJJJJJJKKKKKKJJJJJJJJJHHHHHHHHHHHHHHHGGGFFFEEEFFFFFFFFFFFFFFFFFFFFFFFFFFFGGGHHHHHHHHHFFFEEEDDDAAAAAAAAAAAABBBCCCDDDEEEEEEFFFFFFGGGHHHIIIJJJJJJKKKMMMPPPRRRTTTXXX\\\______bbbfffjjjmmmqqquuuxxxzzz~~~}}}pppmmmppp}}}|||xxxxxx{{{}}}~~~}}}{{{yyyuuurrrlllbbbQQQ???555444333111000000000000///..................---------------,,,++++++***))))))*********)))******++++++************************))))))))))))))))))))))))))))))))))))))))))))))))&&&&&&''''''''''''&&&&&&((((((((())))))*********((((((((((((((((((((((((((((((((((((((((((((((((&&&'''((((((((('''&&&&&&&&&'''((((((''''''&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$''''''''''''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%(((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&'''''''''(((((((((((((((&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''((())))))((((((''''''''''''((((((,,,)))'''(((***,,,***'''******************************++++++,,,---------,,,///333777<<>>>>>>>>???@@@AAACCCCCCCCCDDDDDDDDDDDDEEEEEEEEEFFFGGGHHHIIIJJJKKKLLLLLLMMMMMMMMMMMMLLLLLLIIIIIIIIIIIIHHHGGGFFFFFFGGGGGGGGGHHHHHHGGGGGGGGGHHHHHHGGGFFFEEEBBB@@@???>>>???@@@AAACCCEEEGGGHHHCCCCCCDDDDDDEEEFFFFFFGGGHHHJJJLLLLLLLLLMMMPPPRRRRRRTTTXXX\\\```eeekkkooorrrwww~~~tttnnnnnnyyyyyykkkWWWCCC777555444222111000111111///...........................------,,,++++++***))))))*********)))******++++++******++++++++++++++++++))))))))))))))))))))))))))))))))))))))))))))))))(((((())))))))))))(((((()))))))))(((((('''''''''((((((((((((((((((((((((((((((((((((((((((((((((&&&''')))((('''%%%&&&&&&%%%&&&((((((&&&%%%&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&%%%%%%)))(((((('''&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''((()))******))))))(((''''''''''''''')))((('''(((***+++***)))++++++++++++++++++++++++******+++,,,,,,------......222888===CCCHHHNNNQQQRRRRRRTTTWWWWWWUUUXXX]]]\\\dddnnnxxxzzztttooommmnnnqqqzzzyyyzzzuuurrrooollljjjhhheeebbb___]]]ZZZVVVTTTSSSRRROOOLLLIIIFFFCCCBBB??????@@@AAABBBBBBAAAAAA@@@AAAAAABBBCCCCCCCCCDDDFFFFFFFFFFFFGGGGGGGGGGGGIIIIIIHHHGGGGGGFFFEEEEEEGGGGGGHHHHHHHHHHHHGGGGGGDDDDDDDDDDDDDDDCCCBBBBBBCCCCCCDDDDDDDDDDDDCCCCCCDDDCCCBBBAAA???===<<<;;;;;;<<<===???BBBEEEGGGHHHFFFFFFGGGHHHIIIJJJJJJKKKHHHJJJLLLMMMMMMLLLMMMNNNMMMOOOQQQTTTWWW[[[aaafffnnnttt|||wwwrrruuu}}}xxxiiiWWWEEE;;;999555333222111222111000................../////////------,,,,,,++++++******++++++***************+++*********+++++++++++++++))))))))))))))))))))))))))))))))))))))))))))))))***++++++,,,,,,++++++***)))))))))((('''&&&&&&&&&((((((((((((((((((((((((((((((((((((((((((((((((&&&''')))'''%%%$$$%%%'''###&&&((('''%%%$$$%%%&&&''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%''''''&&&&&&&&&&&&'''''''''&&&&&&&&&''''''((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$''''''&&&&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&'''''''''&&&&&&''''''((((((((((((''''''''''''''''''''''''(((((('''''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&'''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&&&&'''(((((()))))))))(((''''''''''''(((((()))$$$&&&((()))((()))***+++++++++++++++++++++++++++,,,,,,,,,---......//////111666>>>DDDIIIMMMQQQSSSRRRQQQSSSVVVVVVXXXbbbooowww}}}wwwoooooorrrzzzuuurrrmmmjjjgggccc___\\\XXXVVVTTTSSSRRRPPPMMMKKKLLLJJJGGGEEEBBBAAAAAAAAA???@@@AAABBBBBBBBBAAAAAA@@@BBBDDDEEEFFFFFFEEEDDDDDDDDDDDDDDDDDDDDDCCCCCCDDDDDDCCCBBBBBBAAAAAA@@@???@@@@@@AAAAAA@@@@@@???>>>>>>?????????>>>=========>>>????????????>>>=========<<<<<<<<<;;;::::::999999:::<<>>;;;666444222222222111000...---........./////////000---------,,,,,,,,,,,,,,,,,,,,,+++***)))))))))))))))))))))*********++++++))))))))))))))))))))))))))))))))))))))))))))))))******++++++++++++******)))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&((((((&&&$$$###%%%'''"""%%%''''''$$$###$$$&&&'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%(((''''''&&&&&&''''''((('''''''''''''''((()))***&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$))))))))))))))))))))))))%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%&&&'''(((((('''''''''((((((((())))))''''''''''''''''''''''''(((((('''''''''&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&'''''''''(((((())))))))))))))))))))))))'''(((((((((((((((''''''&&&&&&&&&'''((()))***+++!!!%%%((()))((('''***,,,++++++++++++++++++++++++------......///000000000444:::BBBIIINNNQQQSSSUUUTTTTTTVVVZZZ[[[aaattttttkkkiiimmmqqq{{{xxxsssqqqfffccc```]]]YYYUUUQQQMMMLLLKKKJJJJJJKKKKKKHHHGGGHHHFFFCCC@@@??????@@@@@@BBBCCCDDDEEEDDDDDDBBBAAA:::<<>>AAA@@@@@@@@@????????????:::;;;<<<===>>>???@@@@@@;;;;;;<<<<<<<<<<<<;;;;;;;;;;;;<<<<<<<<<<<<;;;;;;999:::;;;<<<<<<;;;:::999888999999:::;;;;;;<<<<<<999999:::;;;===???@@@AAABBBCCCDDDEEEGGGHHHIIIJJJMMMQQQXXX]]]```aaabbbcccaaaaaa___\\\[[[\\\```ccciiimmmqqqsssqqqmmmiiihhhjjjkkklllnnnqqqtttwwwxxx}}}~~~vvvcccUUUHHH>>>:::666444333222222222000...---.........//////000000---------------------------,,,+++***))))))))))))'''((((((((())))))******))))))))))))))))))))))))))))))))))))))))))))))))''''''((((((((((((''''''(((((())))))******++++++((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%$$$$$$%%%'''((((((((('''''''''&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&((('''&&&%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&%%%###""""""###%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''')))((('''&&&&&&&&&&&&&&&***)))(((''''''((()))***((((((((((((((((((((((((((((((((((((((((((((((((&&&''''''(((((((((((((((******))))))((((((''''''))))))))))))(((((((((((())))))(((((()))***++++++---,,,+++***+++---///111---...//////000111444666>>>CCCJJJOOORRRSSSSSSTTTTTTUUUWWW[[[cccuuutttkkkjjjkkkvvvzzztttoooiii```YYYYYYVVVRRROOOMMMJJJGGGEEEDDDDDDDDDDDDCCCCCCCCCCCCCCCBBB@@@>>>>>>???@@@AAAEEEEEEEEEDDDDDDCCCCCCCCC@@@???>>>===<<<;;;::::::<<<<<<<<<<<<<<<;;;:::999;;;:::::::::999999888888888888888888999999999999888888888888888888888888::::::::::::::::::::::::888888888777666666555555;;;:::999777777999:::;;;<<<===>>>???@@@BBBCCCCCCGGGMMMVVV^^^eeejjjnnnqqqrrrrrrpppmmmjjjiiikkknnnrrrnnniiiddd```\\\WWWTTT^^^]]]]]]___dddkkkrrrvvvtttwww{{{~~~jjjZZZNNNFFFAAA888666444333333222000///.........///////////////////////////............+++++++++************)))++++++++++++++++++++++++))))))))))))))))))))))))******++++++++++++******)))***++++++)))(((((()))))))))))))))))))))))))))***)))((('''&&&&&&'''(((++++++***)))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%###$$$$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$"""!!!!!!"""$$$%%%(((((('''''''''&&&&&&&&&&&&&&&%%%$$$$$$%%%&&&&&&((('''&&&%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&)))((('''&&&&&&'''((()))%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''(((((('''&&&&&&&&&&&&&&&((((((''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&'''(((((())))))(((((((((((((((((('''''''''&&&''''''(((((())))))************))))))))))))******,,,++++++***+++,,,............//////111444888<<>>===>>>???@@@AAAAAA@@@@@@@@@?????????<<<<<<<<<<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;:::999999;;;;;;:::::::::999999999777777777888888888999999::::::::::::::::::::::::999999999999999999999999888888888888888888888888:::999888777777888999:::::::::;;;;;;<<<===>>>>>>AAAEEELLLSSS[[[ccckkkpppuuuwwwzzz{{{zzzxxxwwwuuuqqqjjj```XXXRRRNNNLLLJJJMMMNNNOOOQQQVVV[[[```ccciiilllppptttwww{{{vvvfff[[[RRRMMMCCC>>>888444333222000...////////////////////////////////////............,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++******************************++++++++++++******)))***++++++)))(((((()))))))))))))))))))))))))))***)))((('''&&&''''''(((******))))))((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&!!!"""###%%%&&&((())))))&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&''''''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&&&&'''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&%%%$$$$$$###$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''(((((('''&&&&&&&&&&&&'''&&&&&&''''''''''''&&&&&&((((((((((((((((((((((((((((((((((((((((((((((((&&&'''(((((())))))((((((''''''''''''&&&&&&&&&&&&&&&&&&'''((()))***+++++++++***)))))))))))))))***+++++++++++++++,,,,,,,,,...//////000222777???DDDLLLPPPVVVZZZ[[[[[[[[[[[[WWW[[[cccqqqzzzpppmmmmmmkkkjjjlllvvvzzzrrrnnnooommmmmmrrr~~~}}}zzzxxxuuutttjjjddd\\\WWWSSSPPPKKKGGGGGGEEECCCBBBCCCCCCBBB@@@BBBCCCCCCCCCCCCCCCCCCCCC@@@???>>><<<<<<===>>>>>>============<<<<<<<<<<<<999999::::::;;;;;;<<<<<<::::::;;;;;;::::::999999;;;;;;::::::::::::999999888999999999999:::::::::;;;;;;;;;;;;;;;;;;;;;;;;888888888888888888888888888888888999:::;;;;;;;;;;;;:::999888888999:::;;;999999999999:::::::::;;;<<<>>>AAAEEELLLUUU^^^eeeiiimmmrrrxxx{{{zzzuuuqqqmmmdddVVVIIIBBB@@@@@@AAABBBDDDGGGKKKOOORRRUUUVVV\\\___cccgggkkkqqqwww{{{|||~~~qqqggg___ZZZPPPFFF;;;333111000...+++000000//////////////////////////////............------------,,,,,,,,,,,,++++++++++++++++++++++++******************************++++++++++++******)))***++++++)))(((((()))))))))))))))))))))))))))))))))((('''''''''(((((())))))))))))(((((((((((((((((((((((((((((((((((()))(((((((((((((((((()))"""###$$$%%%&&&((())))))&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&'''((((((''''''''''''''''''''''''&&&&&&&&&%%%%%%&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&$$$%%%&&&&&&&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''(((''''''&&&&&&&&&''''''&&&&&&((())))))(((&&&&&&((((((((((((((((((((((((((((((((((((((((((((((((''''''((()))))))))))))))'''''''''''''''''''''''''''''''''((()))*********))))))(((((()))***+++++++++,,,,,,---------,,,+++......///000444;;;DDDJJJNNNRRRWWWZZZ[[[ZZZZZZ[[[VVV[[[eeexxxwwwkkkfffgggjjjnnnrrrzzz~~~ooohhhhhhiiimmmppprrrqqqttt{{{uuupppllljjjgggeee]]]XXXQQQLLLJJJHHHFFFDDDDDDCCCAAABBBCCCDDDDDDCCCFFFFFFFFFEEEDDDDDDCCCCCC>>>===<<<;;;;;;;;;<<<<<<<<<<<<<<<;;;;;;;;;;;;;;;999999999999:::::::::::::::::::::;;;;;;:::999999::::::::::::::::::999999;;;;;;<<<<<<<<<=========<<<<<<<<<<<<<<<<<<<<<<<<999999999999999999999999999999::::::;;;;;;;;;;;;===<<<;;;;;;;;;;;;<<<===::::::::::::::::::::::::<<<<<<<<<===???EEEMMMRRRXXXZZZ```gggmmmooollliiiddd[[[MMMAAA<<<;;;===???AAADDDIIINNNRRRSSSTTTTTTUUUWWWZZZ]]]aaafffmmmqqquuuxxx}}}zzzyyyyyyrrrllliii^^^QQQBBB777444333111...111111000000000000//////////////////............------------,,,,,,,,,,,,++++++++++++++++++++++++******************************++++++++++++******)))***++++++)))(((((()))(((((((((((((((((((((((())))))(((((((((((((((((('''((((((((()))))))))***(((((((((((((((((((((((((((((('''&&&&&&'''((((((%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&'''(((%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$%%%&&&&&&''''''&&&&&&(((((())))))))))))((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''((('''((()))******)))((('''(((((((((((((((((((((((((((((((((((((((((((((((('''(((((()))))))))))))))(((((((((((((((((((((((())))))))))))(((((((((((('''''''''((()))+++,,,---,,,---......///......------...000333888???GGGMMMOOOSSSWWWYYYYYYYYYYYYZZZWWW^^^lll|||iiidddfffmmmsss|||vvviii___^^^ccciiiooottt|||zzz}}}|||tttpppiiiccc___\\\YYYWWWSSSOOOKKKGGGFFFEEEEEEEEEHHHFFFEEEFFFGGGIIIHHHHHHHHHGGGFFFDDDBBBAAA@@@???<<<<<<;;;;;;;;;:::;;;;;;::::::::::::::::::::::::;;;;;;:::::::::999999999:::;;;;;;<<<<<<<<<;;;;;;::::::::::::::::::::::::<<<<<<=========>>>>>>>>>========================;;;;;;;;;;;;;;;;;;;;;;;;<<<<<<<<<;;;;;;;;;::::::<<<<<<<<<;;;;;;<<<<<<<<<;;;::::::::::::999999999;;;;;;<<<;;;;;;===AAAEEENNNOOOSSSXXX]]]```bbbbbbVVVOOOEEE>>>;;;<<<>>>???@@@DDDIIIOOOTTTVVVVVVVVVTTTUUUWWWXXXYYY]]]aaaeeejjjmmmrrryyyyyyzzz|||yyywwwlll___NNN@@@:::888666444222222111111000000000000////////////............,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++******************************++++++++++++******)))***++++++)))(((((()))(((((((((((((((((((((((((((((())))))))))))))))))''''''(((((())))))******&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&'''((('''''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&''''''(((%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%&&&'''(((((($$$%%%&&&&&&''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&'''(((((((((((())))))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((('''((())))))******))))))((((((((()))))))))))))))***)))))))))(((((((((''''''''''''((()))+++,,,------------...//////000000---000555999>>>DDDJJJNNNPPPSSSVVVYYYYYYYYYYYYZZZTTT___qqqmmmbbbeeeooozzzvvvbbb\\\[[[bbblllssszzz|||uuupppfffaaa[[[VVVSSSPPPMMMKKKJJJIIIGGGEEEDDDEEEFFFGGGLLLJJJIIIHHHIIIJJJIIIHHHDDDCCCBBB@@@>>><<<;;;:::<<<;;;;;;;;;;;;:::::::::888888888888999999999999===<<<<<<<<<;;;;;;::::::<<<===>>>>>>???>>>>>>>>>;;;;;;;;;<<<<<<<<<<<<===<<<<<<=========>>>>>>>>>????????????????????????>>>>>>>>>>>>>>>>>>>>>>>>??????>>>>>>===<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;;;;::::::::::::999999999999999;;;<<<======???BBBDDDFFFIIIMMMOOOOOOPPPQQQRRRHHHDDD>>>;;;;;;<<<>>>>>>BBBEEEJJJQQQVVVZZZ\\\]]]XXXYYYYYYXXXWWWXXXZZZ\\\^^^aaafffmmmuuu|||yyyxxxzzzooo]]]KKK???777444333333333222222111000000000////////////............,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++******++++++++++++******)))***++++++)))(((((()))))))))))))))))))))))))))(((((()))*********))))))''''''(((((())))))******&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&$$$$$$&&&'''(((((((((''''''&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&(((((())))))))))))((((((&&&&&&&&&'''''''''((((((%%%&&&'''(((((('''&&&%%%%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&'''((((((%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&'''''''''$$$%%%&&&&&&''''''&&&&&&%%%$$$###""""""###$$$%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&'''(((((((((((((((''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((()))************)))'''''''''((((((((())))))(((((((((((())))))))))))))))))))))))))))))***+++,,,,,,+++,,,---///111222///444;;;AAAEEEHHHLLLNNNNNNQQQTTTVVVWWWWWWXXXYYYVVVdddxxxuuugggfffsssvvvkkk___aaajjjxxxxxxqqqiiidddXXXTTTPPPLLLKKKJJJHHHGGGFFFFFFFFFFFFFFFGGGHHHJJJMMMKKKHHHGGGFFFFFFDDDCCC???>>>>>>===<<<;;;::::::;;;;;;<<<;;;;;;;;;:::999999999999:::::::::;;;;;;===============>>>>>>>>>??????@@@AAAAAAAAAAAAAAA>>>>>>??????@@@@@@@@@@@@??????@@@@@@@@@AAAAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBAAAAAAAAA@@@@@@@@@@@@@@@===>>>>>>>>>>>>>>>>>>===<<<<<<<<<<<<<<<<<<<<<<<<===>>>??????@@@CCCGGGJJJMMMUUU]]]^^^WWWOOOJJJIIICCC@@@;;;999999;;;<<<===AAACCCHHHNNNUUU\\\aaaccc```aaaaaa___\\\[[[[[[\\\YYYZZZ]]]bbbhhhnnntttwwwtttuuuwww{{{~~~wwwwww```KKK===666555444333333222111111000000////////////............------------,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++******++++++++++++******)))***++++++)))(((((()))))))))))))))))))))))))))'''((()))***+++******)))(((((((((((())))))))))))((((((((((((((((((((((((,,,***)))(((((()))***,,,''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''((((((%%%&&&'''(((((('''&&&%%%%%%%%%%%%%%%%%%&&&'''((('''&&&&&&&&&&&&'''((((((%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$%%%&&&&&&''''''&&&&&&((('''%%%$$$$$$%%%'''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&'''((()))((('''&&&%%%%%%&&&'''((((((((((((((((((((((((((((((((((((((((((((((((((((((((()))***************&&&&&&&&&'''''''''((((((&&&&&&'''((()))***++++++,,,+++***)))((((((((((((+++*********,,,...111333111777???FFFJJJLLLMMMNNNKKKMMMQQQSSSTTTTTTUUUWWW___nnn|||nnnhhhnnn{{{tttmmmhhhooouuu{{{tttlllddd[[[VVVPPPMMMJJJHHHHHHHHHHHHGGGEEEGGGHHHIIIJJJJJJLLLMMMLLLIIIFFFDDDCCCAAA???===========================;;;;;;<<<<<<<<<;;;:::999<<<<<<<<<======>>>>>>>>><<<<<<===>>>???@@@AAAAAA@@@AAABBBBBBCCCCCCCCCCCCAAAAAAAAABBBBBBCCCCCCCCCDDDDDDDDDEEEEEEEEEEEEFFFEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEEAAAAAABBBCCCCCCDDDDDDDDDAAABBBBBBCCCCCCBBBBBBAAA????????????@@@@@@AAAAAACCCCCCBBBAAAAAADDDJJJNNNcccooo||||||ppp```UUUQQQEEEAAA<<<888888:::<<<<<<;;;===AAAGGGOOOWWW^^^bbbggghhhiiigggdddaaa``````[[[ZZZ[[[\\\___cccfffhhhfffiiinnntttzzz{{{xxx]]]JJJAAA???444444333333222111000000000/////////............//////.........---------++++++++++++++++++++++++++++++++++++++++++++++++******++++++++++++******)))***++++++)))(((((()))))))))))))))))))))))))))'''((()))+++++++++***)))))))))))))))((((((((((((%%%%%%&&&'''((()))*********))))))((('''&&&&&&%%%((('''''''''&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&'''(((&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''((((((((((((((((((((((((((((((((((((((((((((((((%%%%%%&&&'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&''''''(((((())))))''''''((((((((((((''''''&&&'''''''''(((((())))))***((('''&&&&&&'''(((***&&&''''''((((((((((((((())))))(((((('''''''''&&&%%%&&&&&&'''((()))************)))))))))))))))*********)))))))))))))))***,,,***))),,,000222111///444:::CCCIIIMMMNNNNNNOOOMMMKKKLLLNNNNNNOOOUUU]]]lllrrrooosss~~~zzzvvvtttsssooollltttyyyuuummmeee\\\TTTNNNKKKKKKJJJHHHIIIKKKLLLLLLKKKOOOMMMKKKIIIGGGGGGHHHIIIEEEDDDAAA>>>=========>>><<<<<<;;;;;;::::::999999:::::::::;;;;;;;;;<<<<<<======>>>??????@@@AAAAAA@@@@@@AAABBBBBBAAAAAAAAAFFFFFFHHHHHHHHHHHHGGGFFFEEEFFFGGGFFFEEEFFFHHHJJJLLLKKKJJJIIIIIIIIIJJJJJJGGGHHHIIIJJJKKKKKKKKKKKKOOOOOONNNNNNMMMLLLKKKKKKIIIIIIJJJJJJIIIIIIHHHGGGGGGHHHHHHGGGEEEDDDEEEFFFCCCBBBAAAAAACCCCCCBBBAAAEEE???>>>DDDEEEFFFTTTeeejjjTTTMMMEEE<<<888999::::::999<<<===>>>BBBFFFLLLQQQSSS]]]aaafffjjjkkkkkklllmmmiiifffaaa^^^]]]\\\\\\\\\\\\ZZZ___lllwwwzzz|||}}}bbbKKK;;;<<<777444555333000000333222111111111000000//////111///.........,,,)))''')))***,,,------,,,***))),,,,,,,,,,,,++++++***)))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((((()))***++++++***)))((())))))))))))))))))))))))&&&&&&''''''((()))))))))''''''''''''((((((((((((((((((((('''''''''&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&'''''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''(((((((((((((((''''''((((((((((((''''''''''''''''''((((((((())))))((('''&&&&&&'''((()))&&&''''''((((((((((((((()))(((((((((''''''''''''&&&'''''''''((()))))))))))))))((((((((((((((()))******))))))))))))******+++++++++,,,000222333333===AAAFFFIIIJJJIIIIIIIIINNNNNNOOOOOOMMMOOO[[[hhhwwwrrruuu}}}ooofffcccbbbdddiiimmmtttyyytttiiiddd]]]UUUPPPLLLIIIHHHMMMKKKJJJKKKOOOSSSVVVXXXUUURRRMMMHHHEEECCCBBBBBBAAA@@@>>>;;;::::::;;;;;;;;;<<<<<<<<<============>>>>>>???@@@AAABBBBBBCCCAAAAAABBBCCCDDDEEEEEEFFFGGGGGGHHHIIIIIIIIIIIIIIIIIIJJJKKKLLLLLLLLLKKKJJJMMMNNNOOOOOOOOOOOOQQQSSSTTTSSSSSSSSSSSSSSSTTTTTTVVVWWWWWWWWWWWWWWWVVVVVVWWWWWWWWWVVVUUUUUUTTTTTTVVVVVVUUUUUUTTTSSSSSSRRRPPPPPPPPPOOOMMMLLLLLLMMMKKKIIIHHHHHHIIIIIIGGGFFFIIIDDDDDDIIIKKKOOO___rrr{{{cccPPPIII@@@;;;:::;;;:::888::::::;;;===@@@DDDHHHJJJQQQVVV\\\cccggglllooorrrpppnnnkkkhhhfffccc```^^^[[[WWWWWW___fffjjjnnnrrrxxx|||}}}{{{zzzzzzwwwZZZEEE<<<888666777666222000222000000000000000000//////...,,,,,,---...//////---***+++,,,------,,,+++***.../////////......---,,,************************************************(((((((((((((((((((((((())))))************))))))))))))))))))))))))))))))(((((((((((((((((((((((($$$%%%&&&'''(((******+++)))))))))((((((((('''''''''''''''&&&&&&&&&&&&&&&'''''''''((((((((())))))'''''''''&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((('''&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((((((((((((((('''''''''''''''((((((((((((''''''''''''''''''(((((((((((()))((('''&&&&&&'''((()))&&&''''''(((((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((''''''''''''((((((+++******)))******++++++***+++,,,...///333777;;;CCCEEEHHHHHHGGGGGGGGGHHHPPPPPPRRRRRRQQQXXXjjj}}}sssssswww|||dddXXXUUUTTTWWW___kkkxxxyyyrrrkkkfff]]]WWWPPPJJJIIIJJJLLLMMMOOOPPPRRRVVVZZZ]]]^^^]]]VVVRRRLLLEEEAAA>>>>>>>>>???===<<<:::999999::::::;;;<<<<<<>>>???@@@AAAAAA??????@@@AAACCCDDDEEEFFFDDDDDDEEEFFFHHHIIIJJJJJJKKKLLLMMMNNNOOOPPPPPPPPPQQQRRRTTTUUUVVVVVVVVVVVVWWWYYY[[[[[[[[[\\\^^^```bbbbbbbbbccccccdddeeeeeegggggggggffffffeeecccccceeeeeeeeeeeeeeeeeeeeeeeeeeedddbbb```___^^^^^^^^^^^^]]]\\\[[[ZZZYYYXXXWWWSSSQQQOOONNNNNNMMMKKKIIIIIIGGGHHHLLLMMMSSSfff{{{gggQQQJJJBBB===<<<<<<:::888999999999999;;;===???@@@CCCHHHOOOUUU\\\ccciiinnnqqqrrrsssrrroookkkfffccc```ZZZUUUWWWZZZ^^^ccchhhmmmrrryyy~~~}}}||||||lllRRR???:::888999888333111111000000000000000000111111///...,,,,,,...000000000+++,,,,,,,,,,,,,,,,,,+++///////////////......---++++++++++++++++++++++++++++++++++++++++++++++++))))))))))))))))))))))))******))))))))))))******))))))))))))))))))))))))))))))((((((''''''''''''$$$%%%&&&'''((()))***+++))))))))))))(((((((((((('''''''''''''''&&&&&&&&&&&&'''''''''(((((((((((((((((((((((('''&&&&&&%%%&&&&&&''''''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''')))((('''&&&%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''))))))((((((''''''&&&&&&''''''(((((((((((('''''''''''''''((((((((((((((()))(((''''''''''''((()))&&&''''''((((((((((((((((((((((((((((((''''''''')))))))))((((((((((((((((((((('''''''''((())))))++++++*********+++,,,,,,))),,,...///000555<<>>???>>>>>>===<<<<<<<<<<<<===<<<<<<===>>>@@@AAABBBBBBAAAAAABBBCCCEEEFFFGGGGGGIIIJJJKKKMMMNNNPPPQQQRRRRRRSSSUUUVVVXXXYYYZZZZZZ\\\^^^aaadddfffhhhiiiiiiiiikkknnnooooooppprrrssstttuuuvvvwwwxxxyyyyyyzzzyyyyyyzzzzzzyyyxxxxxxwwwxxxxxxxxxyyyyyyyyyyyyyyyxxxvvvssspppnnnnnnnnnooonnnllljjjiiihhhgggeeeccc___]]]ZZZYYYXXXVVVSSSQQQNNNMMMOOOOOOOOOUUUiii|||sss\\\LLLGGGAAA===;;;;;;:::999::::::999999:::;;;<<<======???DDDHHHLLLRRRXXX\\\eeejjjooosssssspppmmmkkkfffaaa\\\YYYXXXZZZ^^^aaadddiiipppvvvzzz|||~~~{{{```HHH@@@:::888777333111222000000111111222222333333666333///------...---------,,,++++++++++++,,,---+++,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++++++++************************+++***)))(((((()))***+++(((((((((((((((((((((((()))))))))(((''''''&&&&&&&&&'''''''''(((((())))))))))))))))))((((((((((((''''''''''''''''''''''''%%%%%%&&&&&&&&&''''''''')))))))))))))))((('''&&&'''''''''(((((()))))))))&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''(((((('''''''''''''''''''''''''''''''''''''''''''''''')))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((())))))((((((''''''&&&&&&''''''((((((((((((''''''((((((((((((((('''''''''((((((''''''''''''((((((&&&''''''((((((((((((((('''''''''((((((((((((((()))))))))))))))((((((((()))((((((((())))))***++++++++++++++++++,,,------***---000111333888@@@FFFCCCDDDDDDDDDEEEHHHNNNQQQSSSSSSYYYhhhzzzxxxqqqqqqzzzkkk]]]TTTUUUYYY^^^kkk~~~zzzrrrjjjccc\\\VVVSSSJJJHHHHHHNNNXXXaaafffhhhgggfffccc```[[[UUUNNNIIIEEECCC@@@<<<;;;<<<>>>???>>>>>>======>>>>>>???????????????@@@AAABBBBBBCCCFFFFFFGGGHHHJJJKKKLLLMMMQQQRRRTTTVVVYYY[[[]]]^^^___aaacccfffhhhjjjkkklllkkkmmmqqqvvv{{{~~~}}}zzzyyyxxxwwwtttqqqpppnnnkkkhhhgggeeebbb___YYYYYYYYYVVVTTTYYYhhhwwwuuu^^^NNNBBB@@@<<<::::::::::::::::::::::::::::::;;;<<<<<<;;;===>>>???AAADDDIIILLLSSSZZZccckkknnnpppqqqrrrkkkiiifff```\\\ZZZZZZYYY^^^aaaeeeiiimmmrrrwwwzzz~~~~~~sssVVVJJJ===777555222222444222222222333333444444444999555111...------,,,+++------,,,++++++,,,------)))******+++++++++******+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++***)))(((((()))***+++(((((((((((((((((((((((())))))(((((('''''''''&&&(((((((((((((((''''''''')))))))))((((((((('''''''''''''''''''''(((((((((%%%%%%%%%&&&&&&&&&&&&''''''((()))******)))(((''''''''''''(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&'''''''''(((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((((((((((((((((((((((('''''''''''''''((((((((((((''''''((((((((((((((('''''''''((((((((((((((((((((((((&&&''''''((((((((((((((('''''''''((((((((((((((())))))))))))))))))))))))))))))((())))))***+++,,,++++++++++++,,,---......,,,---000333777===CCCGGGEEEEEEDDDDDDDDDHHHMMMQQQXXX[[[hhhzzznnnggglllwwwjjj\\\WWWUUU[[[bbbttt|||xxxsssmmmeee]]]VVVQQQLLLIIIHHHJJJQQQ___mmmwwwxxxwwwqqqiii\\\QQQJJJGGGEEEEEEBBB@@@>>><<<;;;;;;<<<=========>>>???@@@@@@AAAAAACCCCCCDDDDDDEEEFFFGGGGGGIIIJJJKKKNNNPPPSSSTTTUUUYYYZZZ]]]aaaeeehhhkkklllqqqsssuuuyyy|||~~~|||yyywwwuuusssooommmeeeeeeccc^^^ZZZ[[[ccckkkrrrrrroookkkcccWWWJJJ@@@;;;;;;:::999999:::;;;<<<::::::::::::;;;;;;;;;;;;:::;;;<<<======???BBBEEEEEELLLUUU\\\aaaffflllqqqooorrrrrrlllgggccc```\\\]]]^^^^^^___aaaffflllppptttwwwzzz}}}}}}fffVVVDDD;;;666444333555333333333333333444444444444222///......///...---,,,,,,------------,,,,,,***++++++,,,,,,,,,,,,+++++++++++++++++++++++++++++++++++++++++++++++++++******************************))))))))))))******))))))))))))))))))))))))((((((((((((((('''''''''((((((((((((((((((((((((((((((((('''''''''&&&&&&&&&'''''''''((((((((()))&&&&&&&&&&&&''''''''''''###$$$&&&((()))((('''&&&((((((''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%'''))))))(((&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((((()))'''''''''(((((((((((((((''''''(((((((((((('''''')))(((((((((''''''''''''''''''((((((((((((''''''&&&''''''(((((((((((((((''''''''''''((((((((()))((((((((()))*********+++'''''''''((((((***+++++++++++++++,,,,,,---...///......000555<<>>>>>>>>>>>>>>>>>???@@@AAABBBDDDDDDEEEEEEGGGHHHIIIKKKLLLNNNOOOPPPPPPRRRUUUZZZ___cccfffhhhkkkmmmqqquuuzzz~~~vvvuuuqqqlllgggfffggggggfff___XXXQQQLLLEEE???<<<::::::;;;;;;;;;<<<===>>>============<<<;;;;;;:::999:::;;;;;;;;;;;;===???===BBBGGGJJJMMMSSS\\\ccchhhppptttqqqoooooonnnjjjbbbbbb```^^^]]]^^^bbbfffhhhlllqqqvvvyyy}}}rrraaaMMMBBB<<<777555555222222222222222111111111000///......000000///...+++,,,---......---,,,+++***+++,,,------------,,,************************************************************************))))))************))))))))))))))))))))))))))))))((((((((((((((((((((((((''''''''''''(((((())))))((('''''''''&&&&&&&&&&&&&&&'''''''''(((((())))))''''''''''''((((((((())) """$$$&&&''''''&&&%%%((((((''''''&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''((((((((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&"""$$$'''***+++)))&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((())))))&&&'''''''''(((((())))))''''''((((((((((((''''''))))))(((((('''''''''&&&''''''((((((((((((''''''&&&''''''(((((((((((((((&&&'''''''''(((((())))))''''''((()))***++++++,,,&&&&&&&&&'''''')))******+++++++++,,,---...///000///...000666>>>DDDEEEEEEAAABBBCCCDDDFFFKKKQQQUUUbbbrrroooeee^^^```bbbgggyyyttteee[[[]]]dddoooyyyrrrkkkddd```UUUQQQMMMKKKLLLNNNOOOOOOQQQXXXeeevvvuuujjjSSSOOOIIIDDDBBB@@@>>><<<;;;<<<>>>@@@AAABBBBBBBBBBBBCCCEEEGGGHHHIIIIIIJJJJJJKKKMMMPPPRRRUUUWWWXXX]]]```dddjjjqqqwww|||~~~}}}yyywwwrrrnnneee\\\RRRKKKGGGCCCAAA@@@;;;===>>>>>>======???@@@BBBBBBAAA@@@???===<<<;;;999:::;;;:::888777888999:::<<<=========CCCMMMUUUXXXbbbjjjkkknnntttvvvtttiiihhhfffaaa^^^\\\^^^______dddkkkqqquuuyyy|||~~~}}}yyyhhhTTTIIIBBB;;;666444222111111111000000/////////......///000000...,,,+++,,,...//////...,,,+++)))***++++++,,,,,,,,,,,,))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((()))***++++++***)))((())))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))(((((((((((()))))))))))))))))))))))))))((((((((()))))))))(((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((((((((''''''''''''((((((((('''&&&&&&'''((('''&&&###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((''''''''''''''''''''''''(((((((((((((((((((((((((((&&&$$$&&&((()))(((%%%&&&&&&''''''&&&%%%$$$$$$''''''&&&&&&&&&&&&''''''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''))))))))))))))))))))))))(((((((((((((((''''''&&&'''((()))++++++***))))))))))))))))))************)))*********))))))+++---)))000777===???AAADDDFFFDDD???AAAJJJLLLJJJQQQ^^^ooorrrccc]]]\\\ccclllwww}}}ccc```^^^bbbnnn{{{tttlllddd]]]VVVRRRNNNNNNMMMMMMNNNQQQUUUWWWZZZ[[[```fffjjjfff[[[RRRKKKGGGBBB@@@AAACCCBBBAAADDDCCCBBBBBBCCCDDDDDDDDDIIIIIIIIIJJJKKKLLLMMMNNNQQQSSSWWWYYY\\\```dddgggjjjoooxxx}}}ttthhhXXXKKKFFFCCC@@@>>>????????????@@@@@@AAABBBGGGEEECCCBBBBBBAAA???===>>><<<;;;:::;;;:::999777>>>===<<<<<<===@@@CCCEEELLLQQQWWW^^^dddkkkrrrwwwxxxwwwtttnnnfff```\\\ZZZ[[[]]]```eeekkkqqquuuxxxzzz{{{|||~~~yyy~~~yyypppbbbSSSHHHAAA===<<<===777111///111222222000000000000000000//////...//////.........---------+++,,,,,,------,,,,,,+++++++++++++++++++++++++++))))))(((&&&&&&%%%%%%%%%((()))***++++++++++++++++++******)))(((''''''&&&))))))))))))))))))))))))))))))))))))))))))))))))((((((''''''&&&'''''''''(((((((((((())))))))))))&&&&&&&&&'''''''''''''''&&&'''''''''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&((('''&&&&&&'''((('''&&&$$$$$$%%%&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&***(((&&&&&&''''''%%%###'''''''''''''''&&&%%%%%%''''''&&&&&&&&&&&&''''''''''''''''''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((&&&&&&'''((()))))))))((((((((()))***************))))))))))))***************+++,,,,,,++++++---...000444999===???AAADDDGGGJJJFFFIIIOOOOOOMMMUUUbbb}}}ssseee^^^```gggsss|||yyyiii]]]]]]___hhhyyysssnnnfff___YYYTTTNNNKKKLLLOOOTTTYYY\\\^^^^^^^^^YYYXXXWWWXXXYYYUUUMMMFFFFFFCCC@@@???AAACCCCCCBBBFFFEEEDDDEEEGGGHHHIIIIIILLLMMMNNNPPPRRRUUUYYY[[[[[[^^^ccchhhmmmrrrxxx|||tttdddWWWOOOJJJEEEBBBBBBBBBAAAAAAAAABBBDDDEEEIIIGGGFFFFFFFFFFFFEEECCC@@@>>><<<<<<<<<;;;999888;;;:::999999999<<>>BBBAAA@@@AAADDDFFFFFFFFFFFFFFFFFFGGGHHHKKKMMMNNNPPPRRRUUUWWWZZZ___eeeiiinnnrrrzzzxxxlllbbbZZZRRRMMMLLLKKKHHHFFFFFFGGGIIIKKKKKKIIIHHHHHHIIIIIIHHHFFFEEECCCAAA@@@@@@???===;;;;;;:::888777888999;;;===:::<<<@@@DDDIIIPPPXXX^^^gggnnnvvv{{{|||yyyuuussslllhhhbbb]]]\\\^^^bbbeeekkkmmmqqquuuyyy|||~~~|||vvvqqqkkkbbbVVVMMM???===:::777555444333222000000111111000000///.../////////.........------,,,,,,------------,,,,,,++++++++++++++++++++++++---,,,+++***))))))))))))******************+++,,,,,,,,,++++++******))))))((((((((((((((((((((((((((((((((((((((((((((((((---,,,+++******))))))***(((((((((((())))))))))))&&&''''''((()))***+++++++++******((('''&&&%%%$$$''''''''''''''''''''''''((((((((((((((((((((((((((((((''''''''''''(((((((((&&&&&&&&&'''((('''&&&$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((#########%%%&&&(((((((((((((((((('''''''''((((((''''''&&&&&&&&&&&&''''''''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&'''))))))************)))((((((((()))+++,,,))))))*********+++++++++,,,---......------///111888:::===@@@BBBDDDFFFGGGIIIHHHIIIKKKLLLRRRccctttmmmcccbbbooo~~~{{{jjj]]]WWW[[[aaalllyyyxxxooogggbbb]]]XXXQQQMMMNNNSSSXXXZZZeeejjjpppsssqqqjjj```ZZZKKKHHHCCCAAAAAABBBAAA@@@CCCCCCDDDFFFHHHJJJJJJJJJKKKKKKLLLMMMNNNPPPTTTVVV\\\___cccfffiiiooowww}}}zzzpppgggbbb^^^[[[WWWSSSQQQQQQSSSTTTUUUSSSQQQPPPPPPOOOMMMKKKLLLJJJGGGFFFEEEDDDAAA???>>>===;;;:::999:::;;;;;;<<<<<<======???CCCIIINNNVVV]]]iiisssyyy{{{|||}}}wwwrrrllleeeaaa``````aaabbbeeeiiinnntttyyy}}}~~~zzzqqq\\\QQQCCC:::666555333111000111111111111000//////////////////............------............------***+++++++++++++++,,,,,,---,,,+++*********************)))(((((()))***++++++++++++******)))))))))((((((((((((((((((((((((((((((((((((((((((((((((,,,,,,+++***************(((((((((((())))))))))))&&&''''''((()))***++++++******)))((('''&&&%%%%%%''''''''''''''''''''''''((((((((((((((((((((((((((((((''''''''''''(((((((((&&&&&&&&&'''((('''&&&%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((())))))''''''''''''''''''''''''(((((((((((((((((((((((("""###%%%&&&&&&'''((()))((((((''''''''''''((()))''''''&&&&&&&&&&&&''''''''''''''''''(((((((((((())))))))))))))))))))))))((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''((()))))))))))))))((((((***)))((((((((()))+++,,,************++++++++++++***,,,---------...000222555888>>>DDDHHHIIIHHHFFFKKKJJJKKKNNNUUUddd|||xxxiiijjjqqqyyylllccc\\\ZZZ[[[___jjjwww|||tttkkkccc[[[VVVOOOKKKGGGIIIQQQ]]]gggnnnyyyxxxvvvqqqhhh]]]RRRLLLCCCBBBAAAAAABBBCCCCCCCCCEEEGGGHHHJJJKKKMMMNNNOOOQQQSSSUUUUUUVVVZZZ___ccclllqqqxxx}}}|||vvvsssmmmhhhdddccccccdddhhheeebbb___]]]ZZZWWWTTTRRRPPPMMMKKKIIIGGGEEEBBBBBBAAA???===<<<;;;;;;;;;===<<<;;;::::::<<>><<<;;;:::999:::999888888:::>>>AAA???CCCJJJRRR[[[eeeooovvv}}}uuummmggg```______```ccciiinnnqqqwwwzzz~~~|||yyywwwzzzmmmNNN???999555222111111222222111111000///000000000/////////............////////////......*********++++++,,,,,,---******)))))))))))))))*********+++++++++***)))))))))((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))&&&&&&&&&&&&'''((())))))(((((((((((())))))))))))&&&&&&&&&'''''''''''''''$$$%%%&&&'''(((******+++''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&((('''&&&&&&'''((('''&&&%%%&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''((((((((())))))))))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&)))***+++)))&&&%%%&&&''''''&&&%%%$$$%%%&&&((()))''''''&&&&&&&&&&&&''''''''''''''''''((((((((((((''''''''''''''''''''''''(((((((((((((((((((((((())))))))))))))))))))))))((((((((((((((((((((((((((())))))*********))))))(((((()))************************+++++++++,,,,,,(((***---...000222666999;;;===BBBIIIOOOQQQOOOMMMHHHJJJQQQ^^^uuuwwwssstttuuu```VVVMMMIIIIIILLLSSS[[[hhh~~~|||yyymmmggg___XXXSSSPPPNNNLLLQQQTTT[[[ccclllrrruuuuuulllfff\\\QQQHHHCCCBBBAAAAAACCCEEEGGGGGGHHHIIIJJJNNNPPPRRRTTTUUUYYY^^^ccc___ccciiinnnttt|||zzzuuupppkkkhhhbbb```\\\YYYWWWTTTQQQNNNLLLKKKIIIFFFCCC@@@>>>===:::;;;;;;:::999:::<<<>>><<<>>>AAAEEEKKKTTT^^^dddqqqwww{{{vvvnnnjjjeeeaaaaaadddiiilllppptttyyy}}}~~~~~~~~~~~~|||~~~|||zzz{{{dddKKK===888666111222222222222111000000000000000000/////////.../////////000000/////////)))******+++,,,,,,------******))))))))))))******,,,---///000///...+++***))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''(((***+++,,,(((((((((((()))))))))))))))))))))))))))(((((((((''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''(((((((((((('''&&&&&&'''((('''&&&%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((())))))))))))''''''''''''''''''''''''((((((((((((((((((((((((&&&)))+++***'''''')))+++'''&&&$$$$$$$$$&&&((()))'''''''''&&&&&&'''''''''''''''''''''((((((((()))************************))))))))))))))))))))))))''''''''''''''''''''''''))))))))))))))))))))))))&&&'''(((***++++++++++++'''(((***+++++++++***)))******+++++++++,,,,,,,,,(((+++---000222555888;;;AAABBBDDDJJJPPPSSSRRRPPPLLLPPPZZZlll}}}|||ooopppuuu|||ttt```OOOIIIEEEFFFIIINNNUUU]]]lll|||wwwqqqmmmbbb\\\UUUNNNLLLKKKLLLLLLWWW\\\dddlllooommmfffaaa[[[UUULLLEEE@@@@@@CCCEEEBBBDDDFFFIIIKKKMMMQQQSSSRRRUUUXXXZZZ\\\aaahhhnnnooouuu}}}|||xxxllliiieeebbb```]]]YYYVVVRRRQQQNNNKKKHHHEEEBBBAAA@@@@@@@@@>>>;;;999:::;;;:::;;;<<<>>>AAAHHHOOOUUU```hhhuuu|||vvvmmmfffbbbdddhhhkkkkkkpppvvvzzz|||}}}~~~~~~{{{}}}uuuTTT@@@::::::111222222222222111000000000000000000//////////////////000000000000//////))))))***+++,,,,,,------*********)))******++++++---///222333333111---+++******************++++++************************))))))(((''''''''''''(((''''''(((((())))))******&&&&&&'''(((((()))((((((+++*********))))))(((((())))))((('''''''''''''''''''''''''''((((((((()))))))))(((((('''''''''&&&)))'''%%%&&&)))***(((&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((&&&'''((())))))((('''&&&''''''&&&&&&&&&''''''((('''''''''''''''''''''''',,,+++)))(((''''''((((((''''''''''''''''''''''''((((((((((((((((((((((((******))))))((((((''''''))))))(((((((((((())))))(((((((((((((((((((((((())))))(((((('''''''''&&&'''(((((()))***+++++++++*********))))))))))))))))))+++,,,,,,+++++++++,,,111000///111555999<<<===???GGGLLLJJJIIILLLNNNMMMPPPZZZkkkyyyyyypppfffdddnnn}}}uuu```TTTJJJIIIGGGFFFGGGNNNXXX```xxx|||vvvpppjjjccc]]]XXXSSSKKKFFFGGGNNNXXX^^^dddfffiiijjjfff^^^VVVPPPJJJGGGDDDCCCEEEFFFEEECCCGGGHHHIIILLLOOOSSSXXXZZZZZZ]]]aaabbbeeemmmzzz{{{wwwsssnnnjjjfffaaa^^^[[[WWWQQQMMMKKKIIIFFFBBBCCCAAA???======<<<999777999:::;;;===???BBBDDDFFFRRRYYYeeepppzzz}}}vvvoooiiieeecccggghhhlllssszzz~~~|||zzzzzz|||~~~eeeHHH;;;;;;333222222333444444333111111111000000//////......000000000000///...---,,,,,,,,,,,,,,,,,,,,,,,,,,,))))))))))))))))))))))))''',,,222666666222,,,'''+++++++++*********))))))******+++++++++,,,,,,,,,***)))(((''''''''''''''''''((((((((()))))))))***%%%&&&'''((()))(((((('''))))))))))))((((((''''''))))))((('''''''''''''''&&&&&&&&&''''''''''''((()))((((((((('''''''''''')))'''&&&'''))))))(((&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&''''''''''''(((&&&'''((())))))((('''&&&---,,,***'''%%%###"""!!!''''''''''''''''''''''''***)))((('''''''''((((((''''''''''''''''''''''''((((((((((((((((((((((((***)))))))))((((((((('''))))))(((((((((((())))))(((((((((((((((((((((((())))))(((((((((''''''''''''(((((()))******++++++************))))))))))))+++,,,,,,+++******,,,...000000111444888<<>>???FFFLLLTTT___jjjuuu}}}vvvpppmmmeeeeeegggmmmtttyyy{{{{{{zzz{{{~~~rrrTTTCCC???666444333333444333222000111111111000//////......000000000000///...---,,,,,,,,,,,,,,,,,,,,,,,,,,,************************)))+++...111111...+++)))+++++++++*********))))))))))))*********++++++++++++***)))(((''''''&&&'''(((((((((((())))))))))))&&&((()))++++++***)))(((((((((((((((''''''''''''))))))((('''''''''''''''%%%%%%&&&&&&&&&'''''''''(((((((((((('''''''''''')))'''&&&'''((()))((('''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&'''''''''&&&&&&&&&''''''''''''(((&&&'''(((((((((((('''&&&((('''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&''''''((()))(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))(((((((((((())))))(((((((((((())))))(((((((((((((((((((((((())))))((((((((((((''''''((((((((()))******++++++************************------,,,***)))***,,,///...000444888<<<@@@BBBDDDCCCEEEKKKQQQPPPMMMWWWfffssskkkiiidddfffhhhiiimmmzzzdddMMMEEEFFFCCCDDDFFFJJJQQQ\\\iiiqqqzzz~~~uuuooofff^^^WWWRRRNNNLLLKKKKKKMMMQQQXXX```hhhlllkkkfff^^^UUUMMMFFFCCCAAAEEECCCBBBDDDGGGJJJLLLLLLNNNQQQUUUYYY[[[^^^bbbeeeooowww{{{vvvmmmhhhaaa]]]ZZZVVVQQQMMMJJJHHHFFFEEEEEEDDDBBB@@@======<<<;;;:::::::::;;;>>>AAAEEELLLUUUbbbpppyyy}}}xxxiiigggeeefffkkkqqquuuxxxxxxzzz}}}~~~{{{{{{}}}dddNNNCCC:::888555333333222111000222111111000000///......///////////////...---,,,,,,,,,,,,,,,,,,,,,,,,,,,************************+++++++++++++++++++++++++++++++++***************(((((()))))))))*********++++++)))(((''''''''''''(((((((((((())))))))))))(((***,,,---...,,,***)))(((((((((((((((((((((((())))))((('''''''''''''''&&&&&&&&&'''''''''((((((((((((((((((((('''''''''((((((''''''((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''$$$%%%&&&'''((((((((()))''''''''''''''''''''''''%%%%%%%%%&&&'''(((((()))))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))(((((((((((())))))(((((((((((())))))(((((((((((((((((((((((())))))(((((((((((((((((((((((())))))************)))***************++++++,,,------,,,++++++---...---111777<<<@@@CCCFFFGGGIIIFFFKKKTTTSSSTTTfffnnncccbbbeeehhhlllrrrvvv|||www[[[IIIEEEJJJFFFGGGJJJPPPYYYeeepppwwwzzz~~~xxxkkkeee\\\TTTNNNKKKJJJJJJJJJNNNTTT[[[aaaeeegggggg^^^YYYRRRJJJDDDBBBBBBBBBFFFFFFFFFHHHKKKOOOQQQRRRTTTXXX]]]aaaffflllsssyyysssoooiiieeebbb^^^YYYTTTOOOMMMKKKJJJIIIHHHFFFDDDBBBAAA???>>>===<<<;;;;;;>>>???@@@BBBHHHRRR]]]eeeqqqxxxvvvqqqjjjfffeeehhhllloootttvvvzzz}}}vvvtttuuuwwwnnnXXXIII>>>;;;666333222222111111222222111111000//////....../////////......---,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++++++++++++++******))))))******+++************************))))))))))))*********+++++++++***(((((('''''''''))))))))))))((((((((((((((()))+++,,,,,,+++)))((())))))))))))))))))))))))))))))((('''''''''''''''(((((((((((())))))))))))'''''''''((((((((((((((('''(((((((((''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&&&&''''''''''''(((''''''&&&&&&&&&&&&''''''******)))((('''%%%###"""''''''''''''''''''''''''$$$$$$%%%&&&'''((())))))))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((())))))))))))))))))(((((((((((())))))(((((((((((((((((((((((((((((()))))))))))))))))))))))))))))))))*********))))))******+++++++++,,,***,,,...///...------...///444:::@@@CCCEEEHHHJJJRRRLLLOOOXXX\\\ddd~~~lllccc___bbbgggsssvvv|||hhhTTTGGGDDDGGGGGGJJJOOOYYYdddoooyyy}}}{{{~~~}}}zzzxxxrrrkkk```[[[TTTMMMIIIIIILLLOOOTTTYYY```fffhhheee```\\\NNNLLLHHHEEECCCCCCDDDEEEHHHIIIKKKLLLOOORRRUUUXXX]]]bbbhhhnnnuuu~~~xxxrrrnnniiibbb]]]VVVTTTQQQOOONNNLLLJJJGGGDDDCCCBBB@@@???>>>>>>>>>>>>>>>???@@@BBBGGGNNNSSS\\\dddrrrwwwnnngggeeeeeegggnnnqqqvvv{{{|||uuurrrrrrttttttaaaSSSDDD???999444222222333222222222222111000000//////...............------,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++******++++++++++++***************************************+++++++++,,,,,,******))))))(((((())))))))))))))))))(((((((((((('''''''''(((''''''&&&&&&))))))))))))************))))))((('''''''''''''''(((((()))))))))*********'''''''''((((((((((((((('''((()))((('''&&&''')))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((&&&&&&&&&''''''''''''(((''''''&&&&&&&&&&&&''''''&&&'''((((((((('''%%%$$$''''''''''''''''''''''''$$$%%%&&&(((((()))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))(((((((((((())))))(((((((((((((((((((((((((((((())))))))))))******))))))))))))))))))******))))))******+++,,,,,,,,,***,,,...//////...///111444999@@@DDDEEEGGGJJJMMMQQQNNNPPPXXXbbbtttkkk___^^^aaahhhpppttt\\\OOOGGGDDDEEEGGGLLLUUUbbbppp{{{~~~xxxrrrnnnfff]]]SSSQQQMMMIIIHHHLLLRRRWWWcccfffiiijjjfff___WWWQQQGGGFFFEEEDDDEEEEEEFFFGGGLLLNNNPPPRRRTTTXXX\\\```dddkkkuuu~~~~~~xxxppphhhaaa```]]]ZZZWWWVVVSSSPPPMMMFFFEEEDDDBBBAAA@@@@@@@@@:::<<<>>>???@@@CCCFFFIIINNNVVVbbbppp|||zzzqqqjjjfffeeejjjlllpppvvv{{{zzzvvvvvvwwwwwwkkk___OOOIII???888444444444444333222222111111000//////------.........------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,)))***+++,,,,,,+++***)))***************+++++++++***++++++++++++,,,,,,,,,)))))))))((())))))***+++***)))))))))(((((((((''')))((('''&&&&&&&&&&&&'''((((((((()))))))))******))))))((('''''''''''''''(((((((((((())))))))))))''''''''''''((((((((()))&&&((())))))'''&&&''')))''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''((((((((((((&&&&&&&&&''''''''''''((('''&&&&&&%%%%%%&&&&&&'''!!!###%%%((()))***))))))''''''''''''''''''''''''&&&&&&((())))))))))))(((''''''''''''''''''''''''(((((((((((((((((((((((('''((((((((()))))))))***))))))(((((((((((())))))(((((((((((((((((((((((((((((()))))))))************)))))))))))))))))))))))))))***++++++,,,------,,,,,,,,,,,,,,,...333666:::@@@EEEHHHHHHIIIMMMPPPNNNPPPUUU]]]nnnrrr]]]YYY___hhhuuucccQQQJJJHHHHHHIIILLLQQQ\\\jjjyyyzzzrrrkkkfff]]]TTTJJJJJJJJJJJJLLLRRR[[[bbbmmmkkkhhhbbb[[[SSSMMMIIIDDDDDDDDDEEEGGGIIIKKKLLLRRRUUUYYY\\\___ccciiinnnttt~~~{{{rrrlllllliiieeeaaa___[[[WWWTTTLLLKKKIIIGGGEEECCCBBBBBB;;;===??????@@@AAACCCEEEFFFJJJRRR]]]iiittt|||}}}tttnnnjjjggghhhkkkoootttzzz~~~}}}zzzwwwpppggg]]]UUUHHH>>>888555444444333333222111111000000///,,,------......---------,,,,,,,,,,,,,,,,,,,,,,,,------------------------************************))))))*********+++++++++************++++++++++++(((((((((((()))***+++,,,******))))))((((((((('''---+++)))''''''((()))***&&&'''''''''(((((())))))))))))((('''''''''''''''''''''''''''((((((((()))&&&'''''''''(((((())))))&&&(((***)))&&&%%%''')))''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''((((((((()))&&&&&&&&&'''''''''(((((('''&&&%%%%%%%%%%%%&&&''''''((())))))((('''$$$###'''''''''''''''''''''''''''''')))*********)))(((''''''''''''''''''''''''(((((((((((((((((((((((('''((((((((())))))******))))))(((((((((((())))))(((((((((((((((((((((((((((((())))))*********+++*********)))))))))))))))))))))***+++,,,,,,------...---***((()))...666;;;@@@DDDJJJKKKJJJKKKOOOSSSQQQXXX___hhh}}}tttcccVVVZZZcccooo|||iiiRRRFFFCCCEEEIIIMMMRRRWWWbbbppp}}}yyywwwqqqhhhccc^^^VVVMMMFFFHHHJJJLLLQQQYYYccckkkooojjjaaaWWWOOOIIIEEECCCCCCCCCCCCEEEHHHLLLPPPSSSXXX\\\aaaeeeiiinnnvvv{{{|||tttqqqlllhhheeeaaa]]]ZZZSSSQQQOOOLLLIIIGGGFFFEEEAAABBBBBBAAA@@@@@@AAACCC@@@BBBFFFMMMWWWcccnnnttt}}}}}}uuuqqqffffffhhhkkkooouuuzzz}}}{{{}}}zzzuuuuuuqqqjjjggg]]]OOOCCC:::666444333333333222222111000000000,,,,,,------...---------,,,,,,,,,,,,,,,,,,,,,,,,------------------------+++***)))(((((()))***+++))))))******++++++++++++))))))))))))************+++,,,,,,,,,,,,+++***************)))))))))))))))(((((((((((((((((((((((())))))(((((('''''''''&&&''''''((((((((((((''''''&&&&&&''''''''''''&&&&&&((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((((('''&&&%%%%%%&&&'''(((&&&&&&''''''''''''&&&&&&###$$$%%%&&&''''''''''''))))))(((((('''''''''&&&(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))((('''&&&%%%%%%%%%%%%%%%&&&&&&&&&'''''''''(((((((((((((((((((((((((((((((((((((((((()))))))))))))))((('''((()))***)))((((((((((((((()))))))))))),,,,,,+++***))))))******)))******++++++,,,------...---,,,---///333888;;;DDDFFFIIIIIIIIIKKKQQQVVVZZZ[[[dddvvveee^^^WWWZZZjjjzzz___PPPEEEEEEIIIIIIIIILLLZZZaaakkkuuu|||}}}|||zzzwwwqqqhhh___XXXQQQKKKGGGCCCDDDHHHPPPZZZcccggghhhddd\\\PPPHHHEEEDDDDDDDDDCCCEEEGGGJJJNNNRRRUUUWWW[[[]]]fffqqqxxx~~~~~~{{{wwwtttqqqooommmkkkiiigggffffffiiiiiihhhfffddddddfffhhhpppppprrruuuzzz}}}yyyuuupppjjjccc___^^^ZZZUUUPPPNNNLLLIIIHHHFFFCCC@@@>>>>>>>>><<<;;;BBBCCCDDDGGGLLLTTTZZZ^^^lllyyyzzzssspppkkkgggfffkkksssyyyvvvzzz~~~}}}zzzyyy{{{}}}~~~~~~{{{rrrdddWWWJJJ???999777111///000444444000...///000/////////.....................------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++******)))*********)))))))))******+++++++++,,,+++***((((((***+++,,,++++++,,,,,,++++++***)))************))))))))))))************************))))))((((((((('''''''''''''''((((((((((((''''''&&&''''''((((((''''''&&&((((((((((((((((((((((((((((((''''''''''''((((((''''''''''''''''''''''''((('''&&&&&&&&&&&&'''(((&&&&&&''''''''''''&&&&&&$$$%%%&&&'''(((((((((((()))(((((((((''''''''''''))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))))))))((('''''''''''''''&&&&&&&&&'''''''''(((((((((((((((((((((((((((((((((((((((((())))))))))))***)))((()))***++++++)))))))))))))))************,,,++++++***))))))***************+++,,,,,,------.........///222777<<>>AAAEEEGGGNNN\\\iiipppssswwwzzzyyyuuuooolll```[[[SSSMMMIIIFFFDDDCCCLLLKKKKKKLLLOOOPPPPPPOOOHHHEEEAAA@@@AAADDDFFFGGGNNNOOOQQQSSSWWW^^^fffkkkvvv|||wwwlllfff\\\WWWPPPMMMNNNOOONNNMMMKKKKKKKKKKKKKKKLLLMMMMMMIIIKKKMMMNNNOOORRRVVVYYYZZZ\\\^^^aaaeeehhhkkklllmmmooosssyyy}}}wwwsssppplllfffaaa]]]YYYVVVSSSNNNLLLHHHFFFFFFFFFDDDCCCCCCAAA@@@???@@@BBBEEEGGGMMMZZZiiittt||||||tttlllgggeeeeeemmmqqquuuyyyzzz{{{}}}~~~|||wwwsssqqquuu}}}~~~fffPPPDDD>>>888444444333111000333000000000/////////...............---------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***************+++,,,,,,,,,,,,---------+++***)))(((((()))***+++******++++++******)))((()))***************++++++************************))))))(((((((((((((((((((((((())))))))))))((((((''''''((((((((((((''''''((((((((((((((((((((((((((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&'''''''''&&&&&&''''''''''''&&&&&&&&&&&&'''(((((((((((((((((((((((((((((('''''''''))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))******))))))((())))))***''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))***)))((()))+++,,,+++***)))))))))*********++++++++++++***************+++******++++++,,,------...---...000333888>>>DDDGGGHHHKKKMMMNNNMMMOOOTTTXXX\\\fffvvv{{{ooonnnvvvttt___NNNEEECCC<<<@@@FFFKKKPPPXXXfffrrrvvvwwwwwwvvvqqqkkkddd```XXXSSSMMMHHHFFFFFFFFFEEELLLKKKJJJIIIHHHGGGEEEDDDAAAAAAAAABBBEEEIIIKKKMMMRRRTTTVVVXXX\\\eeepppxxxwwwkkkbbbZZZVVVPPPLLLIIIHHHIIIKKKKKKKKKLLLKKKKKKJJJKKKKKKLLLLLLOOOPPPRRRTTTUUUWWWZZZ]]]bbbdddhhhlllooorrrssstttooopppssswww{{{}}}yyyuuupppjjjfffaaa]]]ZZZQQQOOOKKKIIIHHHGGGFFFDDDFFFDDDBBB@@@???@@@AAABBBDDDLLLWWWaaajjjuuu~~~vvvnnniiifffhhhkkkooosssvvvyyy|||~~~~~~{{{wwwtttsssxxxbbbKKKAAA:::444444444111000222000000000////////////..................---------------------------------,,,,,,+++************+++***************************))))))(((((())))))***+++++++++++++++***))))))))))))******+++++++++,,,))))))))))))))))))))))))(((((())))))))))))))))))(((((())))))))))))(((((('''(((((((((((((((((('''((((((((((((((((((((((((((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&''''''''''''&&&&&&%%%%%%&&&'''''''''&&&&&&'''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''(((((()))'''''''''((((((((())))))(((((((((((((((((((((((((((((((((((()))))))))))))))((('''(((*********)))((((((((()))))))))******+++***************++++++***++++++,,,------......---...000444:::???EEEHHHGGGIIIKKKKKKKKKMMMSSSXXXaaasss{{{zzz}}}vvvttt|||ppp]]]NNNCCC@@@CCC@@@DDDJJJQQQ[[[fffooouuuxxxwwwtttpppjjjccc\\\YYYQQQMMMHHHEEEEEEFFFFFFFFFGGGGGGFFFEEECCCAAA@@@@@@@@@AAACCCFFFIIILLLPPPRRRXXX[[[^^^aaagggrrrxxxlll```WWWQQQMMMKKKIIIGGGFFFFFFGGGIIIJJJJJJGGGGGGHHHHHHJJJKKKMMMMMMSSSUUUXXX[[[]]]___cccffflllooosssxxx|||~~~xxxxxxyyyzzz{{{}}}~~~xxxsssnnniiiddd```ZZZWWWSSSPPPNNNMMMKKKIIIHHHGGGDDDBBBAAA@@@AAAAAABBBEEEJJJQQQYYYdddrrr|||wwwpppmmmgggiiilllnnnqqqvvv{{{}}}}}}{{{zzz~~~xxxYYYCCC;;;555555555222//////111000000000////////////........................---------------------------,,,,,,+++***+++++++++******************************))))))))))))******+++,,,,,,,,,,,,+++******))))))******+++,,,,,,,,,(((((((((((((((((((((((((((((())))))))))))******((())))))******))))))((('''(((((())))))(((((('''((((((((((((((((((((((((((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((('''&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&%%%'''''''''(((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&'''((((((''''''((((((((()))))))))(((((((((((((((((((((((((((((((((((())))))))))))(((''''''''')))***)))((('''((((((((())))))))))))*********)))******+++,,,++++++,,,,,,------.........///222666:::@@@DDDGGGJJJKKKKKKJJJJJJNNNUUU[[[jjjvvvrrrwwwzzzpppooosss|||rrrZZZMMMEEE===;;;???@@@EEEMMMVVVdddqqqvvvuuuwwwtttpppjjjccc\\\WWWSSSKKKHHHEEECCCCCCCCCBBBAAA@@@AAABBBBBB@@@???@@@AAA@@@CCCFFFIIILLLOOOTTTWWWZZZ___eeekkkttt|||mmmfff[[[RRRLLLIIIFFFEEEFFFFFFFFFGGGHHHIIIKKKKKKEEEFFFHHHKKKNNNRRRUUUWWWXXX\\\aaaeeeiiinnnrrruuuxxxzzz~~~|||wwwrrrlllhhhaaa^^^YYYUUURRRPPPMMMKKKJJJIIIFFFDDDBBBAAAAAAAAABBBAAACCCHHHNNNWWWeeerrr~~~yyyuuummmmmmllllllmmmrrryyy~~~|||zzzmmmMMMBBB888666555222//////111111000000000/////////.............../////////------------------------------,,,+++++++++++++++---------,,,,,,,,,,,,+++************************,,,------------,,,++++++))))))***++++++,,,------))))))))))))))))))))))))(((((()))))))))*********))))))************))))))(((((())))))))))))((((((((((((((((((((((((((((((((((((''''''''''''((((((''''''''''''''''''''''''&&&&&&'''(((((('''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&''''''''''''((((((((()))(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''&&&&&&&&&''''''((()))'''((((((((())))))))))))(((((((((((((((((((((((((((((((((((()))))))))))))))((('''(((***+++***)))(((((()))))))))***************))))))***++++++,,,++++++,,,,,,---.........111222444888<<<@@@DDDFFFKKKKKKLLLLLLOOOVVVaaaiiitttwwwuuujjjfffjjjqqqtttttt]]]HHHCCCBBB>>>>>>AAACCCKKKUUU^^^kkkvvvxxxuuussspppjjjccc[[[TTTOOOLLLHHHFFFCCCBBBAAA@@@>>><<<;;;===???@@@??????AAADDDCCCFFFJJJMMMPPPTTTYYY^^^```gggrrr|||yyyoooggg\\\WWWOOOIIIGGGFFFEEEEEEFFFHHHJJJLLLMMMNNNPPPQQQNNNOOORRRVVVZZZ___ccceeedddhhhmmmrrrvvv{{{{{{uuurrriiieee___ZZZWWWTTTPPPNNNOOOMMMKKKHHHEEECCCBBBBBBCCC@@@AAAEEEGGGJJJTTT```mmmttt~~~wwwuuupppkkkjjjnnnuuuzzz}}}}}}^^^OOO???888555222111222111111111000000000//////---........./////////000........................------,,,++++++++++++,,,---------,,,,,,,,,++++++++++++,,,,,,,,,,,,++++++------......------,,,+++))))))***+++,,,,,,------************************(((((())))))*********+++))))))************))))))(((((())))))))))))((((((((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((%%%&&&'''(((((('''&&&%%%&&&''''''''''''''''''&&&'''(((((((((((((((''''''&&&'''''''''(((((())))))))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((('''''''''''''''((())))))(((((((((((())))))))))))(((((((((((((((((((((((((((((((((((())))))))))))***)))))))))+++,,,+++***)))************+++++++++******))))))***+++,,,,,,++++++,,,------......///333444666999===@@@CCCEEEHHHJJJLLLNNNTTT```nnnyyy{{{rrrgggbbbbbbhhhppprrr}}}aaaJJJ999:::AAAAAABBBEEEGGGSSS^^^fffooowwwxxxtttoookkkeee\\\TTTMMMHHHEEEHHHFFFDDDCCCBBB@@@<<<:::888;;;>>>???>>>???BBBEEEGGGJJJNNNQQQTTTYYY___dddkkkuuu~~~uuujjj```XXXLLLHHHCCCAAAAAACCCDDDDDDEEEGGGKKKMMMOOOQQQSSSUUUYYYZZZ\\\___bbbfffiiikkkmmmpppuuuyyy{{{~~~|||xxxsssoooiiiccc___[[[WWWUUUTTTSSSPPPLLLIIIFFFDDDCCCCCC@@@AAADDDCCC@@@EEENNN]]]ggguuu{{{ssskkkhhhjjjqqqwwwzzz{{{}}}lllYYYDDD999555333333555111111111111000000000000---.........//////000000...........................---,,,,,,++++++,,,,,,+++++++++******)))))))))+++,,,,,,------,,,,,,+++------,,,,,,,,,------...------------,,,+++******)))(((((((((''''''&&&&&&%%%'''(((***++++++++++++******))))))(((((('''''')))(((((((((''''''''''''(((((((((((((((((((((((((((''''''&&&&&&%%%%%%$$$))))))((((((((('''''''''''''''''''''''''''''''''((((((((((((((((((((((((''''''((((((((((((''''''((('''&&&'''((())))))'''&&&&&&''''''((()))))))))))))))))))))))))))))))))''''''((((((((((((((((((''''''''''''((((((((()))''''''''''''(((((((((((())))))(((((((((((())))))))))))))))))))))))))))))(((((())))))******++++++((()))))))))************++++++******************))))))))))))***,,,...///444888;;;:::888:::@@@FFFHHHKKKSSS\\\bbbooo|||ooodddccceeefffjjjnnnvvvmmmUUUFFF<<>>@@@FFFNNN[[[hhhnnnooopppooommmfff```WWWNNNJJJGGGFFFEEEFFFEEEBBB???===<<<;;;;;;===>>>???@@@@@@BBBFFFIIIMMMPPPSSSUUUXXX^^^gggmmmwwwyyypppfff[[[RRRLLLFFFFFFEEECCCAAABBBFFFIIIJJJLLLNNNNNNOOOTTT[[[aaaeeefffhhhlllqqqtttvvvvvvxxxxxxzzz}}}}}}xxxqqqjjjeee```\\\YYYXXXUUUQQQOOOMMMKKKIIIFFFFFFCCC???<<<<<>><<<<<<;;;<<<;;;===@@@AAACCCEEEIIILLLPPPSSSXXX\\\aaaiiissszzzyyytttlllccc[[[SSSKKKGGGDDDDDDDDDCCCBBBDDDGGGJJJMMMPPPTTTVVVYYY^^^eeekkkssstttvvvyyy|||}}}wwwrrrmmmgggbbb___[[[XXXTTTQQQOOOMMMJJJHHHIIIFFFBBB???>>>@@@BBBDDDEEELLLXXXeeeqqq|||}}}wwwrrrooommmnnnrrrvvvzzz}}}}}}iiiTTTGGG@@@999555555222111///000000111///...//////000000000000//////......---,,,,,,---......---------------,,,+++***,,,,,,,,,+++++++++******------------------------......---------------...)))***+++,,,------------++++++++++++************((()))************))))))***))))))))))))((((((((()))))))))(((((((((''''''(((((((((((((((((((((((($$$%%%%%%&&&''''''(((((('''''''''&&&&&&&&&&&&%%%''''''''''''''''''''''''((((((((((((((((((((((((''''''((((((((((((''''''((('''&&&'''((())))))''')))))))))(((''''''&&&&&&))))))))))))))))))))))))))))))(((((('''''''''&&&''''''((((((((()))))))))))))))))))))************))))))(((((((((((())))))))))))))))))))))))))))))************))))))))))))***++++++++++++,,,,,,,,,******++++++++++++++++++...---++++++---000333555888888777888;;;???EEEHHHRRRRRR\\\tttyyyjjj]]]\\\^^^dddjjjqqqzzzeeeNNNDDD===;;;@@@DDDEEEKKKTTTYYYcccjjjjjjgggccc^^^YYYQQQNNNJJJHHHHHHHHHGGGGGGAAA@@@>>>===<<<<<<<<<<<<===@@@CCCFFFIIIKKKOOOQQQSSSXXX]]]dddkkkuuu~~~xxxiiiddd\\\UUUOOOJJJEEEBBB@@@AAACCCCCCDDDFFFJJJLLLPPPUUU\\\aaaeeejjjqqqvvv|||}}}|||wwwrrrlllgggbbb___[[[WWWUUUSSSPPPMMMKKKIIIFFFCCCAAA@@@AAAAAAAAADDDJJJSSS___mmm|||~~~xxxrrroookkkmmmpppuuuzzz~~~|||lllYYYNNNFFF>>>777333444222111111222222222111//////000000000000//////......---,,,,,,---......,,,------------,,,,,,+++++++++++++++************++++++++++++++++++++++++///......------------...***+++,,,,,,---------,,,))))))))))))))))))))))))************))))))(((((()))))))))))))))))))))))))))))))))(((((((((((('''((((((((((((((((((((((((%%%&&&&&&&&&'''''''''((()))))))))(((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((''''''((((((((((((''''''((('''&&&'''((())))))'''&&&&&&''''''((()))))))))(((((((((((((((((((((((()))))))))(((''''''&&&&&&'''(((((((((((()))))))))(((((()))))))))*********))))))(((((((((((())))))))))))))))))))))))))))))++++++******))))))((((((*********+++++++++,,,,,,******+++++++++++++++,,,,,,+++******,,,///333666:::888666888>>>DDDHHHKKKTTTZZZlll}}}ggg\\\XXX\\\ccciiioooxxxiiiSSSFFF@@@>>>???CCCEEEGGGMMMVVV___eeeiiieee___ZZZSSSMMMHHHFFFDDDDDDEEEFFFEEEDDD>>>===<<<<<<<<<===>>>???BBBEEEIIILLLOOORRRUUUWWW[[[```fffnnnyyy|||rrrlll___YYYRRRKKKGGGEEEBBBAAA>>>@@@BBBEEEGGGJJJNNNQQQVVV\\\dddkkkoootttyyy}}}{{{tttooojjjgggccc___\\\YYYVVVSSSLLLKKKIIIFFFDDDBBBAAAAAADDDDDDEEEIIIQQQ^^^lllvvvzzzvvvpppnnnmmmqqqwww}}}vvvkkk]]]TTTNNNFFF<<<444555333111111222333222111///000000000000//////.........------------......,,,---------------,,,,,,,,,,,,,,,+++++++++******))))))))))))************000///...---------------,,,---------,,,,,,+++***+++++++++++++++,,,,,,,,,++++++***))))))((((((((())))))))))))***************)))))))))(((((((((((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((''''''((((((((((((''''''((('''&&&'''((())))))'''&&&&&&''''''((()))))))))(((((((((((((((((((((((())))))(((((('''''''''&&&(((((((((((()))))))))***'''''''''((((((((())))))))))))(((((((((((())))))))))))))))))))))))))))))++++++******))))))(((((())))))))))))*********+++******++++++,,,,,,,,,,,,...---------000333777999:::999888;;;AAAHHHMMMOOOUUUggglll\\\WWWYYY```iiiooowwwfffTTTIIIDDD>>>???BBBGGGJJJMMMSSSZZZaaaeeeddd]]]VVVQQQJJJDDDDDDBBBAAAAAABBBBBBAAA???<<<;;;;;;<<<===???AAABBBFFFIIILLLOOORRRUUUYYY\\\dddiiissswwwmmmddd]]]WWWRRRKKKEEECCCAAAAAA@@@>>>@@@CCCFFFIIINNNSSSWWW```fffooouuuxxx{{{{{{vvvqqqmmmhhhdddaaa]]]YYYWWWMMMLLLKKKIIIGGGEEEDDDCCCDDDDDDDDDEEEIIIRRR\\\cccuuuzzzwwwrrrmmmmmmrrrxxx|||}}}{{{tttoooiii```ZZZWWWQQQFFF<<<666444111000111222111111000000000000000///..............................,,,------......---------...------------,,,,,,,,,,,,,,,,,,,,,------......000000///...------------------------,,,+++***))))))***************++++++++++++***)))(((((()))))))))))))))************+++******)))))))))((((((((((((((((((((((((((((((((())))))(((((('''&&&&&&%%%&&&''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''((((((((((((''''''((('''&&&'''((())))))''')))))))))(((''''''&&&&&&))))))))))))))))))))))))((((((((((((((((((((((((((((((((()))))))))******''''''''''''(((((((((((())))))(((((((((((())))))))))))))))))))))))))))))************))))))))))))(((((()))))))))***************++++++,,,---------++++++,,,...000444666888999:::===@@@EEEKKKPPPTTT\\\wwwttt```XXXWWW___iiittt|||{{{tttvvvpppaaaQQQIIIFFFFFF@@@AAAFFFLLLRRRXXX]]]`````````\\\SSSMMMJJJFFF@@@CCCAAA???>>>??????===<<<;;;;;;<<<===???BBBEEEGGGIIIKKKOOORRRUUUZZZ```ccciiirrrvvvmmmcccZZZTTTNNNIIIDDD@@@@@@@@@@@@@@@AAACCCEEEHHHLLLRRRYYY^^^jjjpppxxx}}}~~~vvvsssmmmiiieeeaaa]]]ZZZRRRQQQOOOLLLJJJIIIHHHGGGAAABBBBBBCCCEEEJJJPPPUUUdddkkkuuuyyyrrrnnnnnnqqquuuwww}}}~~~}}}tttooohhheee```]]]\\\YYYNNNAAA999666222000111111111000000111111000000///...------...////////////...---,,,------............---............------------******++++++,,,,,,------111000///...------------,,,,,,,,,------,,,++++++((((((((()))))))))******+++***)))(((((())))))***))))))*********+++++++++*********)))))))))((((((((((((((((((((((((((((((((((((((((((''''''''''''&&&'''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''((((((((((((''''''((('''&&&'''((())))))''')))))))))(((''''''&&&&&&))))))))))))))))))))))))&&&&&&''''''((()))))))))(((((()))))))))*********'''(((((((((((()))))))))))))))(((((((((((()))))))))))))))))))))))))))))))))))))))))))))*********))))))*********+++++++++******++++++,,,------...((())),,,///111444666666777<<>>=========<<<;;;;;;;;;===???BBBEEEIIIKKKNNNPPPSSSWWW\\\ccclllqqqwww~~~vvvmmmddd[[[SSSNNNEEEBBB???>>>@@@AAABBBCCCFFFFFFHHHJJJNNNUUU^^^dddnnnttt{{{{{{vvvppplllhhhccc```ZZZXXXUUUQQQNNNLLLKKKJJJDDDDDDDDDCCCCCCEEEIIILLLUUU\\\hhhuuu}}}vvvpppnnnppprrryyy|||~~~~~~xxxtttrrriiiiiigggeeefffdddYYYKKK===999555222111111111000111111111111000///...------...///000000///...---,,,,,,---.....................---------,,,,,,,,,'''(((((()))******++++++111111000......---------******+++,,,------------,,,,,,,,,------.........+++***)))(((((()))***+++))))))******++++++++++++************))))))))))))((((((((((((((((((((((((&&&&&&''''''((()))))))))((()))))))))******++++++))))))))))))))))))))))))((((((((((((((((((((((((''''''((((((((((((''''''((('''&&&''')))))))))'''&&&&&&''''''((()))))))))))))))))))))))))))))))))%%%%%%&&&'''((()))******))))))))))))************))))))))))))************))))))(((((((((((())))))))))))))))))))))))))))))(((((())))))******++++++******+++++++++,,,,,,,,,******+++,,,,,,---......+++---000444777999::::::666<<>>???BBBEEEFFFGGGIIIIIIIIIKKKOOOWWWaaahhhmmmrrryyy~~~}}}xxxtttooojjjgggaaa^^^YYYTTTPPPNNNLLLLLLKKKJJJHHHEEEBBBBBBEEEHHHLLLTTT```mmmyyyvvvooonnnoooxxxzzz}}}yyyvvvvvvvvvtttvvvtttrrrtttssshhhYYY@@@<<<777444222222222111111111111111000///...------...///000000///...---,,,,,,---.../////////...---------,,,,,,,,,++++++******+++,,,------......555444222000///...------..................------+++++++++++++++***)))(((************************************************************************(((((((((((((((((((((((())))))(((((('''''''''&&&(((((('''&&&%%%$$$$$$###******))))))((((((''''''))))))))))))))))))))))))((((((''''''&&&&&&&&&%%%(((((())))))((('''&&&&&&''''''((((((((((((''''''(((((('''&&&%%%%%%$$$$$$***)))(((''''''((()))*********)))(((((((((((((((+++***)))(((((()))***+++&&&'''((()))+++,,,......))))))))))))))))))))))))++++++************++++++))))))*********+++++++++------..................,,,///444777999:::;;;<<<@@@CCCIIILLLKKKNNNZZZggg~~~nnnhhhhhhsssrrr```QQQKKKNNNEEEIIIIIIGGGIIIPPPVVVXXXYYYWWWXXX]]]cccdddaaa\\\SSSMMMFFFDDDFFFHHHGGGFFFPPPGGG===777888;;;<<<;;;<<<===@@@DDDHHHMMMQQQSSSXXXXXX\\\dddjjjssszzzuuuhhh[[[TTTOOOIIIEEEDDD@@@???===>>>@@@CCCDDDDDDGGGJJJOOOSSSWWW^^^hhhoootttvvvzzz|||ssslllhhhddd^^^YYYWWWUUUSSSRRRMMMJJJEEECCCCCCCCCCCCCCCHHHHHHOOOZZZfffqqq~~~}}}xxxqqqiiiqqqsssvvvzzz}}}yyytttvvv|||zzznnnWWWFFF999999999222000444222111111000000000000000///000111111111///...---------------------------...---,,,+++***+++,,,---+++,,,------------,,,+++555444333111000///.....................---------)))******++++++++++++***************************************************************************(((((((((((((((((((((((()))(((((((((''''''''''''((((((''''''&&&&&&%%%%%%***)))))))))((((((((('''))))))))))))))))))))))))((((((((('''''''''&&&&&&(((((())))))(((''''''&&&(((((())))))))))))(((((())))))(((''''''&&&%%%%%%))))))(((''''''((())))))******)))(((((((((((((((******))))))))))))******))))))))))))))))))))))))))))))))))))))))))))))))++++++************++++++***+++++++++,,,,,,,,,,,,------------............---000444777999:::===>>>CCCFFFKKKNNNNNNRRR___mmmvvvmmmooovvvyyygggYYYLLLHHHKKKIIINNNQQQQQQUUU\\\bbbcccgggdddbbbcccdddbbb[[[VVVJJJEEEAAACCCIIIOOOQQQQQQNNNGGG===999:::<<<======@@@BBBDDDGGGIIILLLPPPRRR\\\]]]cccnnnzzzvvvooohhh]]]RRRLLLIIIDDDAAAAAA>>>>>>===>>>AAACCCEEEFFFKKKOOOTTTYYY]]]dddmmmsss{{{}}}yyyrrrmmmiiiccc^^^[[[YYYVVVUUURRRNNNJJJGGGFFFEEEDDDCCCDDDDDDIIIRRR\\\fffsss~~~}}}uuunnnoooppprrruuuyyy}}}~~~|||||||||yyy}}}dddOOO===999888444222666222222111000000000000000000000000000000///......------------------------...---,,,,,,++++++++++++***+++,,,------,,,+++***777666555444333222111000//////......------------((()))***+++,,,,,,,,,,,,************************************************))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((''''''''''''((((((((((((((('''''''''))))))))))))(((((((((((())))))))))))))))))))))))))))))((((((((((((''''''(((((()))))))))(((''''''))))))************))))))******)))(((((('''''''''(((((('''&&&&&&'''((((((***))))))((((((((((((((())))))************)))))))))))))))(((((('''''''''))))))))))))))))))))))))++++++************++++++++++++,,,,,,,,,---------,,,,,,,,,---------......///222444777999;;;???BBBGGGGGGJJJMMMOOOVVVfffuuuooonnnxxxjjjYYYPPPIIIHHHKKKNNNUUU[[[^^^ccckkkoooppprrrnnnjjjfffbbb\\\SSSMMMBBB@@@@@@EEEMMMTTTXXXYYYLLLEEE>>>:::;;;>>>@@@@@@DDDFFFIIIKKKMMMPPPSSSVVV]]]aaakkkzzzzzzrrrhhhaaaZZZPPPHHHEEECCC@@@>>>?????????@@@AAADDDGGGJJJLLLQQQVVV]]]cccgggmmmtttyyy{{{uuuqqqkkkfffbbb___[[[YYYVVVSSSOOOMMMKKKIIIFFFDDDDDDBBBDDDJJJQQQXXXdddoooyyy{{{tttooonnnmmmnnnrrrxxx}}}uuuvvvwwwzzz{{{aaaGGG;;;888555444777222222111000000000000111111000000///////////////---------------------------...------,,,+++***)))******++++++++++++******::::::999888777666555444/////////......---------******++++++,,,+++++++++************************************************((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''''''''(((((()))))))))***))))))))))))(((((((((((((((((((((((((((((((((((()))))))))))))))((((((((((((((()))))))))(((((('''((())))))******))))))((()))))))))((((((''''''''''''''''''&&&&&&'''''''''))))))(((((((((((())))))((()))***++++++***)))((('''''''''(((((()))))))))))))))))))))))))))))))))++++++************+++++++++++++++,,,,,,,,,,,,---++++++,,,,,,------......111222444666888<<>>===???@@@BBBDDDFFFIIIMMMRRRUUUXXX^^^ffflllqqquuu{{{}}}yyytttnnnjjjeeeaaa]]]YYYVVVSSSQQQOOOMMMJJJGGGGGGDDDCCCFFFIIINNNXXXbbblllttt|||{{{tttqqqnnnlllnnnsssxxx|||~~~|||xxxsssvvvzzzvvvTTTAAA:::666555666333222111111000000111111111000///......///000111........................------......---+++)))(((************************999999:::999888777555555111111000//////...---------------,,,+++***)))(((************************************************(((((((((((((((((((((((())))))))))))))))))))))))'''''''''(((((((((((((((''''''(((((()))*********(((((((((((())))))))))))((((((((((((((((((((((((((((((((()))))))))))))))(((((()))))))))))))))((('''(((((())))))(((((('''((((((((('''''''''''''''&&&''''''''''''''''''&&&))))))(((((((((((())))))((()))***++++++***)))(((((((((((())))))*********))))))))))))))))))))))))++++++************++++++************++++++++++++++++++,,,------...//////222333555777999>>>DDDHHHRRROOONNNRRR[[[lllyyypppttt{{{wwwtttuuu||||||ZZZKKKIIILLLUUU^^^gggooouuuwwwyyyzzzyyyvvvrrrmmmddd[[[SSSKKKDDD@@@BBBFFFKKKQQQSSSQQQLLLHHHAAA???<<<<<<>>>AAADDDEEEGGGKKKNNNPPPRRRWWW___eeennn}}}~~~|||wwwpppjjjddd]]]TTTMMMIIICCC@@@@@@???<<<<<>>======>>>@@@CCCGGGIIIKKKOOORRRSSSUUU\\\gggppp~~~~~~xxxtttoooiiiaaaZZZVVVPPPJJJEEEBBB>>>===???>>>;;;<<>>???CCCDDDIIIPPPTTTXXX___gggnnntttyyy{{{tttoooeeebbb]]]ZZZXXXWWWVVVTTTNNNJJJHHHHHHEEECCCEEEJJJPPPWWW___gggrrr~~~{{{vvvrrrooonnnrrrwww}}}tttlllfff^^^bbbkkkjjjzzzwww]]]JJJ@@@:::666444333222222111111222222......///000000000000000........................,,,,,,++++++,,,,,,---------,,,+++******+++,,,---:::;;;=========;;;999777666666555444333111111000,,,,,,---------,,,++++++************************************************************************))))))))))))))))))))))))&&&'''''''''(((((())))))(((((((((((((((''''''''''''((((((((())))))******))))))))))))))))))))))))%%%&&&&&&&&&''''''(((((((((((()))***************))))))************)))))))))))))))))))))*********'''((()))******)))((('''((((((((((((((()))******+++***)))(((((()))***+++######%%%&&&((()))***+++))))))))))))))))))))))))++++++************++++++++++++,,,,,,,,,---------------...///000111222333999<<<@@@CCCGGGKKKPPPSSSXXX___ooovvvoookkknnnooorrrxxxrrr___SSSMMMTTT^^^hhhvvv|||uuunnngggWWWRRRJJJBBB>>>@@@FFFJJJOOOOOONNNJJJEEEAAA>>>>>>===>>>AAACCCFFFIIINNNQQQPPPUUU[[[```iiixxx{{{xxxtttoookkkfff```\\\^^^VVVLLLFFFCCCBBBAAA???<<<;;;===BBBCCCBBBDDDHHHIIIOOOVVV[[[___eeeooovvvzzz~~~xxxssskkkgggaaa\\\ZZZXXXWWWVVVQQQNNNLLLLLLIIIEEEFFFKKKGGGMMMTTT[[[gggvvv~~~yyytttooommmooottt{{{zzzqqqjjj___aaahhhfffuuu{{{zzzbbbNNNCCC===999444333222222111111222222---...///111111111000///////////////////////////,,,+++******+++,,,...///------,,,++++++,,,------???<<<;;;<<<<<<:::888777888888666444111//////000///...,,,+++***++++++,,,,,,,,,,,,+++++++++******++++++++++++++++++++++++++++++******)))((((((((((((((((((((((((((((((((())))))(((((((((((())))))(((((())))))))))))(((((((((((((((((((((((((((((()))((('''&&&&&&&&&&&&&&&((((((((((((((()))******''''''''''''''''''''''''(((((((((((((((''''''''''''&&&&&&''''''((()))***((()))*********((('''&&&'''((()))((('''&&&''')))))))))))))))***+++,,,---+++++++++*********))))))******************************+++++++++,,,,,,,,,++++++++++++,,,---......---...------...111666:::>>>BBBEEEFFFIIIOOOVVVYYY^^^vvvyyyhhhcccfffjjjmmmllloooxxxxxxhhh]]]VVVUUUVVV^^^kkkxxx{{{pppddd[[[SSSMMMEEEBBBDDDGGGJJJKKKPPPKKKDDD@@@??????>>><<>><<<;;;<<<>>>???AAADDDGGGJJJOOOUUU]]]cccggglllttt{{{~~~}}}xxxsssoooiiiddd```\\\YYYVVVUUUQQQNNNKKKJJJIIIGGGFFFGGGEEEIIISSS^^^iiivvv|||tttpppnnnppptttzzztttlllgggfffffflllrrrwwwiii[[[JJJ???===:::555111222111///000444111000000///////////////111000...,,,+++,,,---...,,,,,,,,,+++++++++******------,,,,,,,,,,,,++++++FFFCCC@@@???===<<<;;;;;;::::::999666444222111111111000...---,,,,,,------,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++)))))))))***************))))))))))))))))))))))))))))))(((((((((((())))))((())))))******))))))(((((((((((((((((((((((((((***)))((('''''''''''''''((((((((((((((()))******''''''''''''''''''''''''))))))))))))))))))))))))))))))(((((('''(((((((((((((((((()))((((((''''''((()))***)))((('''(((***))))))))))))***+++,,,,,,+++++++++*********))))))******************************+++++++++,,,,,,,,,++++++++++++,,,---..................///333999>>>CCCFFFJJJJJJLLLPPPVVVZZZlll~~~jjj```bbbiiinnntttrrrsss|||tttjjjccc]]]YYYVVVZZZaaakkkvvv|||sssgggYYYQQQMMMIIIDDDBBBEEEIIILLLNNNMMMHHHBBB????????????>>>DDDEEEGGGJJJLLLPPPSSSVVV[[[```lll|||yyyrrrnnniiibbbZZZUUUSSSPPPLLLHHHFFFCCC>>><<<======<<<:::<<<>>>???AAACCCFFFKKKOOOUUU[[[ccchhhmmmrrrzzz{{{wwwsssnnnhhhddd```[[[XXXVVVSSSPPPNNNMMMKKKIIIHHHFFFCCCDDDLLLVVV___kkkuuuyyyuuuqqqrrrtttyyy}}}xxxsssooommmpppsss}}}tttkkkaaaTTTJJJGGG;;;555222333222000111444111111000/////////000000333222///---,,,---......------------,,,,,,,,,+++------,,,,,,,,,,,,++++++TTTRRROOOJJJFFFBBB???===<<<;;;:::888777555444333333222111//////...//////------,,,,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,((())))))***++++++,,,,,,***************************))))))(((((())))))***)))******************)))))))))))))))))))))))))))******)))(((((((((((()))((((((((((((((()))******(((((((((((((((((((((((())))))))))))************++++++***)))(((((((((((((((((('''''''''(((((())))))***+++***)))((()))++++++***************+++++++++++++++*********************************************+++++++++,,,,,,,,,++++++++++++,,,---......////////////111777>>>CCCEEEIIINNNOOOOOORRRYYY```|||~~~iii\\\\\\fffqqqwww{{{{{{xxxgggZZZUUUUUUWWWXXX___gggsss~~~|||ssshhh[[[OOOGGGFFFEEEDDDFFFIIIMMMOOOOOOGGGDDD@@@>>>>>>???@@@@@@DDDFFFIIIKKKNNNRRRVVVYYY```hhhyyy~~~yyytttpppkkkeeebbb[[[UUUNNNJJJHHHFFFBBB???===;;;::::::;;;<<<<<<;;;>>>???AAACCCFFFKKKQQQVVV\\\bbbjjjpppuuuzzz}}}zzzuuupppjjjddd^^^ZZZXXXVVVSSSRRRQQQOOOLLLJJJGGGCCCBBBFFFMMMTTT^^^gggttt{{{}}}vvvuuuuuuvvvyyy}}}~~~xxxuuuvvvvvv{{{zzznnnhhheee]]]UUUQQQAAA;;;666666555222111333222222111000000000000111111000...---,,,---///000............------------------,,,,,,,,,,,,++++++fffjjjjjjeee\\\RRRGGG???;;;:::999888888777555444444333222111000000//////------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,*********+++++++++,,,,,,++++++++++++++++++++++++***))))))))))))))))))*********++++++++++++******))))))))))))))))))))))))))))))((((((((((((((()))((((((((((((((())))))***))))))))))))))))))))))))((()))))))))))))))******++++++***)))))))))))))))***)))((('''((()))***+++((()))******(((((()))***++++++******)))***************************************************************+++++++++,,,,,,,,,++++++++++++,,,---............//////333999BBBHHHEEEIIINNNQQQQQQTTT___kkkqqq```[[[cccqqq~~~llleee[[[UUUUUUYYY]]]```oooxxx}}}tttiii]]]RRRJJJEEEBBBEEEIIINNNPPPOOOMMMKKKAAA???>>>===>>>@@@BBBCCCEEEHHHLLLNNNQQQUUU[[[```jjjvvv|||yyyuuuqqqkkkeee```\\\XXXUUUPPPLLLGGGDDDBBB@@@>>><<<:::::::::;;;===>>>>>>===@@@BBBDDDFFFJJJQQQXXX]]]ccchhhooovvv{{{{{{vvvqqqjjjccc^^^[[[YYYWWWUUUTTTRRROOOLLLMMMGGGDDDEEEHHHLLLSSS[[[iiirrr~~~{{{zzzwwwuuuvvvyyy~~~{{{|||{{{||||||sssjjjhhhhhheee]]]WWWHHH@@@:::888666333111222333222222111111111111111------,,,+++,,,...000222.........------------,,,------,,,,,,,,,+++++++++zzzyyyiiiVVVHHH===;;;888777888888777555444444333222111000///............---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---,,,,,,,,,+++++++++***++++++++++++++++++++++++******))))))))))))************++++++++++++******))))))))))))))))))))))))'''''''''&&&&&&''''''(((((((((((((((((())))))***************************'''''''''(((((())))))))))))))))))))))))***+++++++++***)))))))))***+++,,,'''((())))))''''''((()))++++++******)))***************************************************************+++++++++,,,,,,,,,++++++++++++,,,---......---...///000444<<>>???BBBEEEGGGJJJMMMQQQTTTWWW]]]fffnnn~~~}}}yyyvvvsssooommmgggccc]]]WWWTTTPPPMMMKKKGGGEEEBBB@@@???>>><<<;;;:::;;;<<<======>>>???@@@CCCEEEHHHLLLPPPWWW^^^ccciiimmmssszzz|||vvvooohhhdddaaa^^^[[[XXXWWWTTTQQQOOOQQQKKKFFFFFFFFFGGGLLLRRR^^^gggttt{{{wwwuuuvvv|||uuuqqqkkkiiijjjiiibbb[[[KKKAAA999666666333222333333222222111111111111111222111///...---...///000------------,,,,,,,,,,,,------,,,,,,,,,+++++++++}}}iiiXXXFFFAAA;;;888888999888666555555555444333111000/////////.........---------,,,,,,,,,,,,,,,,,,,,,,,,......---,,,,,,+++******+++++++++++++++++++++++++++******))))))******+++)))******************)))))))))))))))))))))))))))'''&&&&&&&&&&&&''''''(((((((((((((((((()))******))))))))))))))))))))))))&&&&&&''''''(((((())))))(((((((((((()))***++++++,,,+++******)))))))))***&&&((()))((('''&&&'''(((+++***************++++++***************+++++++++******************************+++++++++,,,,,,,,,++++++++++++,,,---......,,,...000333888>>>FFFKKKNNNMMMPPPRRRQQQWWWooo~~~gggfffiiisssmmm___VVVSSSRRRTTT]]]kkkyyyxxxqqqeeeWWWLLLEEEEEEFFFKKKPPPWWWXXXTTTKKKBBB===;;;<<<>>>@@@AAADDDHHHKKKHHHMMMRRRUUU[[[eeesss~~~xxxtttoookkkhhheeeaaa^^^YYYUUUPPPMMMJJJHHHEEECCC??????===<<<;;;;;;;;;;;;:::;;;<<<===<<<===@@@BBBGGGJJJNNNSSSXXX^^^eeeiiiooorrrxxx~~~{{{vvvppplllhhheee```\\\YYYWWWTTTRRRRRRLLLHHHGGGFFFDDDFFFKKKTTT\\\hhhsss|||{{{vvvuuuyyy}}}~~~zzzxxxyyyyyymmmmmmlllkkkkkklllggg```RRRFFF:::666555444333444222222111000000000000111<<<999666222///...---------------,,,,,,,,,,,,+++------,,,,,,,,,,,,++++++vvviiiTTTLLLBBB<<<;;;:::888666777777777777555333111000////////////.........------------------------------------------,,,,,,,,,+++++++++++++++++++++++++++******))))))******+++((())))))******))))))((((((((((((((((((((((((((('''''''''''''''((())))))((((((((((((((()))******))))))))))))))))))))))))&&&''''''((())))))******((((((((('''(((((())))))*********)))((('''&&&%%%''')))***)))((('''((()))))))))))))))***+++,,,,,,))))))*********+++++++++******************************+++++++++,,,,,,,,,++++++++++++,,,---......,,,///333777;;;AAAHHHLLLPPPNNNPPPSSSTTT```yyykkkqqq~~~ppp___WWWRRRUUUZZZbbbnnn{{{nnnhhh]]]PPPFFFCCCGGGKKKRRRUUUWWWUUUMMMEEE>>>;;;:::===@@@BBBCCCFFFJJJNNNIIINNNUUU[[[dddsss{{{xxxvvvkkkgggbbb]]]ZZZVVVSSSPPPLLLJJJFFFDDDCCCBBB@@@>>>:::;;;;;;;;;;;;:::;;;<<<:::<<<=========???CCCGGGLLLPPPVVV\\\aaafffkkkooovvvxxx}}}|||xxxuuuqqqllleee___\\\ZZZXXXVVVRRRNNNKKKKKKIIIFFFFFFIIILLLRRR[[[fffpppyyyxxxuuuwwwzzz|||~~~{{{ttttttxxx|||uuummmtttxxxwwwxxxzzzxxxtttfffVVVEEE<<<999555444444111111000/////////000000;;;999666222///---------............------------------,,,,,,,,,,,,++++++xxx|||rrr___UUUIII@@@===<<<999777999999999999777555333111000/////////............------------------------+++,,,,,,------......///************************++++++************++++++(((((())))))))))))((((((((((((((((((((((((((((((((((((((((((((()))******((((((((((((((()))******(((((((((((((((((((((((('''(((((()))***+++++++++***)))(((''''''&&&&&&'''))))))))))))'''%%%###"""(((***+++***)))((()))***))))))))))))***+++,,,---))))))******++++++++++++******************************+++++++++,,,,,,,,,++++++++++++,,,---......---111555:::>>>DDDIIIMMMMMMKKKNNNTTTYYYiiiwwwvvvzzzcccWWWTTTPPPZZZhhhwww|||wwwddd___UUUJJJDDDEEELLLRRRWWWXXXVVVPPPGGG@@@<<<<<<;;;>>>BBBDDDEEEGGGLLLPPPQQQWWW^^^fffrrryyytttqqqnnnjjjhhhccc___YYYTTTPPPMMMIIIGGGEEECCCAAA@@@@@@???===;;;999;;;<<<<<<<<<<<<===>>>;;;===>>>>>>???BBBHHHMMMOOOTTT[[[aaafffkkkooorrr{{{}}}~~~|||wwwqqqiiibbb^^^\\\ZZZZZZTTTPPPNNNOOOMMMIIIHHHJJJGGGLLLSSS]]]gggrrr}}}zzzuuuuuuxxxzzz}}}|||yyy|||}}}{{{xxx{{{xxxxxx|||iiiSSSFFF>>>777333222111000000///////////////444333000...------......000/////////............---------,,,,,,,,,++++++