BM6P6(@ &&&''''''''''''''''''&&&%%%'''(((((('''&&&'''((('''''''''(((((((((((()))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''%%%&&&((())))))(((&&&%%%###!!!"""(((+++)))&&&((((((((((((((((((((((((((((((((((((((()))******&&&''''''((()))***++++++'''&&&&&&''')))***)))((('''''''''''''''((()))))))))((((((((((((***,,,---++++++******************)))***+++,,,------------+++,,,...000000///...---............////////////000000111222222222222111444444444444444444444444444444444444444444444444555555666666777777888888::::::999999888999999999888888999:::;;;;;;;;;;;;:::::::::;;;;;;;;;<<<<<<>>>>>>============>>>>>>??????>>>===<<<;;;::::::999;;;>>>AAABBBBBBBBBAAAEEEEEEDDDCCCCCCCCCCCCCCCHHHJJJKKKKKKJJJIIIIIIJJJLLLLLLMMMNNNOOOOOOOOOOOOPPPPPPPPPOOOOOONNNNNNNNNQQQPPPNNNMMMLLLMMMMMMNNNOOOQQQTTTVVVVVVVVVTTTSSSSSSTTTTTTUUUVVVWWWWWWWWWUUUUUUUUUTTTRRRQQQOOONNNNNNOOOOOOMMMJJJJJJNNNQQQQQQQQQRRRSSSSSSRRRQQQPPPOOOOOONNNNNNOOOQQQRRRTTTRRRQQQQQQQQQQQQRRRRRRSSSMMMLLLLLLLLLMMMOOORRRTTTVVVVVVVVVVVVTTTRRRPPPOOOIIIIIIHHHHHHIIIJJJLLLMMMMMMMMMNNNOOOOOOOOONNNNNNOOONNNNNNOOOPPPRRRTTTUUUTTTPPPMMMLLLMMMNNNMMMKKKGGGGGGGGGHHHHHHIIIIIIIIIGGGHHHHHHIIIHHHGGGEEEDDDEEEEEEDDDCCCCCCCCCCCCCCC????????????>>>>>>>>>>>><<<<<<============<<<<<<;;;:::::::::;;;===>>>@@@<<<;;;;;;::::::999999999555666666777777777777777777888888888999999999999333333444444555555555666444555666888999999999999666666444444333444555666666555555555555444444444444444444555555555555666444444333333333222222222444444444555555555555666666666666666666555555444555666666777888999999:::;;;:::999888888888999:::===<<<<<<<<<<<<===>>>>>>BBBDDDGGGLLLRRR[[[dddjjjtttyyyyyyvvvppphhhaaa[[[WWWVVVOOOLLLHHHCCC???===<<<;;;<<<;;;:::999::::::<<<===<<<<<<======<<<:::999777777888999:::::::::::::::::::::999999999999999999;;;::::::999999::::::;;;======<<<<<<===>>>@@@AAA@@@@@@??????????????????>>>>>>>>>>>>>>>>>>>>>>>>???>>>===<<<<<<===>>>???>>>===<<<;;;<<<>>>@@@AAA&&&&&&''''''''''''&&&&&&###%%%&&&&&&%%%$$$$$$%%%&&&&&&'''''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''%%%&&&'''(((((('''&&&%%%&&&$$$"""%%%))),,,***(((((((((((((((((((((((((((((((((((((((((())))))***%%%%%%&&&&&&''''''((((((((('''&&&''')))))))))((())))))(((((())))))******)))((((((((((((***+++,,,************************)))***+++,,,------------------,,,---------..................////////////000000111222222222222111444444444444444444333333444444444444444444444444666666666666666666555555999999888888888999999:::777888999:::;;;;;;;;;;;;:::::::::;;;;;;;;;<<<<<<=========<<<<<<=====================<<<<<<<<<<<<;;;===???AAABBBCCCCCCCCCDDDDDDDDDCCCCCCDDDDDDEEEGGGHHHJJJJJJHHHGGGHHHIIILLLMMMNNNOOOOOOPPPPPPPPPOOOOOOOOOOOOOOONNNNNNNNNPPPPPPOOONNNNNNNNNNNNNNNOOOQQQSSSUUUVVVUUUTTTRRRRRRSSSSSSTTTUUUUUUVVVVVVVVVVVVVVVUUUTTTSSSQQQQQQNNNOOOOOOMMMKKKKKKNNNQQQPPPQQQRRRSSSSSSRRRQQQPPPNNNNNNNNNNNNOOOQQQRRRSSSRRRRRRQQQQQQRRRRRRSSSSSSNNNMMMLLLLLLLLLNNNPPPQQQNNNOOOPPPQQQRRRQQQQQQPPPJJJIIIHHHHHHHHHIIIKKKLLLLLLMMMNNNNNNOOOOOONNNNNNOOOOOONNNOOOPPPQQQSSSTTTSSSPPPMMMMMMNNNNNNLLLJJJGGGGGGHHHHHHHHHHHHHHHHHHHHHHHHIIIIIIIIIHHHFFFEEEFFFEEEDDDCCCBBBBBBBBBBBB>>>>>>>>>>>>============<<<<<<============<<<<<<<<<;;;:::::::::;;;<<<===::::::999999888777666666444555555666777666666666666666666777777777888888888888888999999:::::::::333444555666666666666666666555444333333444555555555555555555444444444444444444444444555555555555444444444444333333333333444444444444555555555555666666666666666555444444555555666666777888888999999888777777777777888999::::::999999::::::;;;<<<>>>@@@AAABBBEEEIIINNNSSSVVVZZZcccmmmyyy}}}~~~yyywwwsssqqqpppooommmkkk```]]]YYYSSSNNNJJJGGGFFFDDDBBB@@@===<<<;;;;;;<<<<<<;;;:::999999:::;;;<<<;;;;;;;;;;;;:::999888888777888999999:::::::::999999999999999999999999999;;;::::::999999::::::;;;<<<<<<;;;;;;<<<===???@@@>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>???>>>===<<<<<<===>>>???>>>===<<<;;;<<<>>>@@@AAA%%%%%%&&&&&&&&&&&&%%%%%%###%%%&&&&&&$$$###$$$%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&'''''''''''''''''''''''''''''''''%%%$$$&&&)))+++)))'''((((((((((((((((((((((((((((((''''''(((((()))***&&&&&&&&&'''''''''''''''((('''&&&'''((()))((('''***************+++++++++)))))))))(((((()))******************************)))***+++,,,---------------,,,+++******,,,...///---............////////////000111111222222111111333333333333333333333333444444444444444444444444777666666555444444333333777777777777888999999:::777888999:::;;;;;;;;;;;;:::::::::;;;;;;;;;<<<<<<======<<<<<<<<<<<<======;;;;;;<<<<<<<<<======>>>===>>>???@@@AAACCCDDDDDDCCCCCCDDDDDDEEEEEEFFFFFFEEEGGGHHHHHHGGGFFFGGGHHHLLLLLLMMMNNNOOOOOOOOOOOONNNNNNNNNNNNNNNOOOOOOOOOOOOPPPPPPPPPPPPOOOOOONNNOOOPPPRRRTTTUUUTTTSSSRRRQQQRRRRRRSSSSSSTTTTTTTTTXXXXXXXXXWWWVVVUUUTTTSSSNNNOOOOOOMMMLLLLLLNNNPPPPPPQQQRRRSSSSSSRRRQQQPPPMMMMMMMMMNNNOOOQQQRRRSSSRRRRRRRRRRRRSSSSSSTTTTTTPPPOOOMMMLLLKKKLLLLLLMMMKKKLLLMMMOOOPPPPPPPPPPPPKKKJJJIIIHHHGGGHHHIIIIIILLLLLLMMMNNNNNNNNNNNNNNNPPPOOONNNNNNNNNPPPQQQRRRPPPOOONNNNNNNNNMMMKKKIIIHHHHHHHHHHHHHHHGGGGGGGGGHHHIIIJJJKKKJJJIIIHHHGGGFFFEEEDDDBBBAAA@@@@@@@@@======<<<<<<<<<;;;;;;;;;<<<<<<============<<<<<<<<<;;;:::999888999999:::;;;;;;:::999888777666666444444555666666666666666555555555555666666666666888888888888999999999999444444555555555555555444444333222222222333444555555555555555444444444444333333333444444444555555555555555444444444444333444444444444555555555555555555666666555555444333444444444555666666777777777777666666666666777777999999888888999999:::;;;===?????????>>>???AAACCCAAADDDIIIQQQZZZcccjjjnnnyyy|||}}}|||~~~yyysssfffaaa[[[VVVTTTTTTTTTSSSLLLJJJGGGDDDBBB@@@>>>>>>===<<<:::999999999:::;;;;;;;;;:::999999::::::;;;;;;:::999999888888888888777888999999:::999999999888888888999999::::::;;;::::::999999999999::::::;;;;;;;;;;;;;;;<<<>>>>>>========================>>>>>>>>>>>>>>>>>>>>>>>>???>>>===<<<<<<===>>>???======<<<<<<<<<>>>@@@AAA$$$%%%%%%&&&&&&%%%%%%$$$%%%'''((((((&&&%%%%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''((('''&&&&&&&&&&&&'''(((&&&%%%$$$%%%'''(((&&&%%%(((((((((((((((((((((((((((''''''''''''((()))))))))))))))))))))(((((((((((('''&&&'''((()))((('''))))))******++++++++++++)))))))))((((((((((((((())))))))))))******************+++,,,,,,,,,,,,,,,,,,+++*********+++,,,------------........./////////000000111111111111111222222222222333333333333444444444444444444444444444444444444444444444333555555555666777888999:::777888999::::::;;;:::::::::::::::;;;;;;;;;<<<<<<=========>>>>>>=========;;;;;;;;;<<<<<<<<<======>>>>>>>>>???@@@AAACCCDDDBBBBBBCCCEEEFFFGGGGGGGGGEEEFFFHHHHHHGGGFFFGGGHHHJJJKKKLLLMMMMMMNNNNNNMMMLLLLLLMMMMMMNNNNNNOOOOOONNNOOOPPPQQQRRRQQQPPPOOOOOOPPPRRRSSSTTTTTTSSSRRRQQQQQQQQQRRRRRRSSSSSSSSSWWWWWWXXXWWWWWWVVVUUUUUUOOOOOOOOONNNNNNNNNOOOPPPPPPQQQRRRSSSSSSSSSRRRQQQLLLMMMMMMOOOPPPQQQRRRSSSRRRRRRSSSTTTTTTUUUUUUUUURRRQQQOOOMMMLLLKKKJJJJJJOOOOOOOOOOOOOOOOOOOOOOOOMMMKKKJJJHHHGGGGGGGGGGGGKKKKKKLLLMMMNNNNNNNNNNNNPPPOOONNNMMMMMMNNNOOOPPPNNNNNNNNNNNNNNNLLLJJJHHHIIIHHHHHHHHHGGGGGGFFFFFFIIIJJJKKKLLLLLLKKKJJJIIIGGGFFFDDDBBB@@@???>>>>>><<<<<<<<<;;;::::::999999;;;<<<<<<======<<<<<<;;;:::999888777777888999:::>>>>>>===;;;:::999888777555555666777777777777777555555555555666666666666777777777777777777888888777777777777777666555444333222111111111222333444555555555444444444333333222333333333444444444444666666555555555444444444333333444444444555555555444555555555555444333333333333333444444555555555666666666666666666777777:::999999999999:::;;;;;;999;;;>>>>>>>>>>>>???AAA@@@@@@AAACCCGGGLLLQQQSSSZZZ]]]aaagggqqq~~~|||xxxtttooohhh```ZZZQQQMMMHHHFFFEEEGGGGGGHHHCCCCCCAAA@@@???>>>=========<<<;;;:::999999999::::::::::::999999999999999:::999888666666666777888888888999999999999888888777777888999::::::;;;;;;::::::999999999999::::::999:::::::::;;;<<<======<<<===============>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>???>>>===<<<<<<===>>>???===<<<<<<<<<===>>>???@@@$$$%%%%%%&&&&&&%%%%%%$$$%%%'''((('''&&&$$$$$$%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''((('''&&&&&&&&&&&&'''(((&&&&&&%%%%%%&&&'''&&&%%%(((((((((((((((((((((((('''''''''''''''(((((())))))))))))))))))((((((((()))(((''''''((()))(((&&&'''((())))))******))))))))))))))))))(((((((((((((((((()))))))))***************++++++,,,,,,++++++)))***+++,,,,,,,,,+++***------------............//////000111111111111000111111111222222222333333444444444444444444444444111222222333444555555666444444444555666777888999777777888999:::::::::::::::::::::;;;;;;;;;<<<<<<===>>>>>>??????>>>>>>===<<<<<<<<<<<<;;;;;;;;;;;;============>>>???AAABBB@@@AAACCCEEEFFFGGGGGGGGGEEEFFFHHHHHHHHHGGGHHHIIIHHHIIIJJJKKKKKKLLLLLLLLLLLLLLLLLLMMMMMMNNNNNNNNNMMMNNNPPPQQQRRRQQQQQQPPPPPPQQQRRRSSSTTTTTTTTTSSSRRRRRRRRRRRRSSSSSSSSSSSSUUUVVVVVVVVVVVVVVVUUUUUUQQQQQQPPPPPPPPPQQQQQQQQQOOOPPPRRRSSSSSSSSSRRRQQQLLLMMMNNNPPPQQQRRRSSSTTTRRRSSSTTTUUUVVVVVVVVVVVVTTTSSSQQQOOOMMMLLLKKKJJJNNNNNNNNNNNNOOOOOOOOOPPPNNNLLLJJJHHHGGGFFFFFFGGGIIIJJJKKKLLLMMMMMMMMMMMMPPPOOOMMMLLLLLLMMMNNNNNNMMMNNNOOONNNMMMKKKIIIHHHHHHHHHHHHGGGGGGFFFFFFFFFHHHIIIKKKLLLMMMLLLLLLKKKGGGFFFDDDBBB@@@???>>>======<<<<<<;;;::::::999999;;;;;;<<<<<<<<<<<<;;;;;;777777666666777888:::;;;>>>>>>===<<<;;;:::999888777777888999999999999999666666777777777888888888::::::999999999999999999666666777666666555444333222111111000111222333444555444444444444333333333222222222222333333333444666666555555555444444444333333333444444444444555444444444444444333333222333333333333444444444444555666666777777777888888888888888888888999::::::333666999:::;;;;;;<<<===???>>>===<<<===???AAABBBKKKMMMOOOSSSZZZdddpppwww}}}}}}vvvqqqoooiiifffbbb]]]XXXQQQJJJFFFDDDBBB@@@@@@AAABBBAAA@@@=========<<<;;;;;;:::999::::::999999999999:::::::::::::::999999888888777999888777666555666777888888888888999999888888777777777888999::::::;;;;;;:::999999888888999999:::999999:::;;;;;;<<<<<<<<<=========>>>>>>?????????>>>>>>>>>>>>>>>>>>>>>>>>???>>>===<<<<<<===>>>???<<<<<<<<<======>>>???@@@%%%%%%&&&&&&&&&&&&%%%%%%###%%%&&&%%%###"""""""""$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''((((((((((((((()))))))))((((((((((((((((((((((((''''''&&&&&&''''''((()))&&&&&&&&&''''''''''''''')))(((''''''(((((('''&&&%%%&&&'''))))))(((((('''''''''((()))))))))(((((('''(((((())))))***************+++++++++++++++***((())),,,---...---+++***,,,------------............///000000111111000000000000000111111222222333222222222222222222222222000111222333555666777777444444444444555666777777666777888999:::::::::::::::::::::;;;;;;;;;<<<<<<<<<===>>>??????>>>===<<<===<<<<<<<<<;;;;;;::::::<<<<<<======>>>??????@@@???@@@BBBDDDFFFFFFEEEEEEDDDFFFHHHHHHGGGGGGHHHIIIHHHHHHIIIJJJKKKKKKKKKKKKLLLLLLLLLLLLLLLMMMMMMMMMMMMMMMNNNPPPPPPQQQQQQQQQQQQRRRSSSTTTTTTUUUUUUUUUTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTUUUVVVVVVVVVUUUUUUTTTSSSRRRRRRTTTTTTSSSRRROOOPPPQQQSSSSSSSSSRRRRRRLLLMMMOOOQQQSSSTTTUUUUUURRRSSSUUUWWWXXXXXXWWWWWWUUUUUUSSSRRRPPPOOOMMMMMMJJJKKKKKKLLLNNNOOOQQQRRROOOMMMKKKIIIHHHGGGGGGGGGHHHIIIJJJLLLMMMMMMMMMMMMNNNNNNLLLKKKKKKLLLMMMNNNLLLNNNNNNMMMKKKIIIIIIIIIGGGGGGGGGGGGGGGFFFFFFFFFHHHIIIJJJLLLMMMMMMLLLLLLHHHGGGEEECCCAAA??????>>>>>>>>>===<<<;;;::::::999;;;;;;<<<<<<<<<<<<;;;;;;666666666666777999;;;<<<;;;;;;::::::999999888888888888999:::::::::::::::888888888888999999999999888888888777777777777666333444444444333222111111222111111000111222444555444444444444333333333333111111222222222333333333555555555444444444444333333333333333444444444444333333444444333333222111333333333333333333444444444555666777888888888777555555555444555666666777555777999999888888999:::::::::999999:::<<<>>>???BBBCCCDDDEEEHHHMMMUUUZZZ\\\```ffflllppptttxxx{{{|||~~~xxxuuuwwwwwwtttlllbbbZZZUUUOOONNNLLLIIIFFFCCC@@@>>>>>>===<<<=========:::888:::;;;;;;;;;:::999888888444555666777888999:::;;;999999999999999888777666888777777666666777777777888888888999888888777666888888888999999::::::;;;999999888888888888999999888999:::;;;<<<<<<<<<<<<=========>>>>>>??????@@@>>>>>>>>>>>>>>>>>>>>>>>>???>>>===<<<<<<===>>>???<<<<<<======>>>?????????&&&&&&''''''''''''&&&&&&###%%%&&&%%%###!!!!!!"""%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''%%%&&&'''(((((('''&&&%%%'''(((((()))((())))))***(((((((((((((((((((((((('''&&&&&&&&&&&&'''((((((%%%%%%&&&&&&''''''((((((***(((''''''(((((('''&&&$$$&&&'''))))))((('''&&&%%%&&&''')))))))))((((((''''''(((((()))******+++******++++++++++++*********++++++,,,,,,,,,,,,,,,,,,,,,---------............//////000000000000000//////000000111222222333111111111111111111111111222222333444555666666777555444444444444444555555666777888999999::::::999:::::::::;;;;;;;;;<<<<<<:::;;;<<<======<<<;;;:::::::::;;;;;;;;;;;;<<<<<<;;;<<<>>>???@@@@@@??????>>>@@@BBBDDDEEEDDDDDDCCCBBBDDDFFFGGGFFFFFFGGGHHHIIIIIIJJJKKKLLLLLLLLLLLLLLLLLLLLLLLLLLLKKKKKKKKKLLLLLLMMMMMMOOOPPPQQQRRRSSSSSSTTTTTTUUUVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVVSSSTTTUUUVVVVVVVVVVVVVVVVVVTTTSSSTTTVVVWWWUUUSSSNNNOOOQQQSSSSSSSSSSSSRRRMMMNNNQQQSSSUUUVVVVVVVVVRRRSSSVVVXXXYYYYYYXXXWWWVVVVVVUUUUUUTTTRRRQQQPPPMMMMMMMMMMMMNNNPPPRRRSSSOOONNNLLLJJJIIIIIIIIIIIIGGGHHHJJJKKKLLLMMMMMMMMMMMMLLLKKKKKKKKKLLLMMMNNNMMMNNNNNNLLLIIIGGGIIIJJJFFFFFFFFFFFFGGGGGGGGGGGGGGGHHHJJJLLLMMMMMMMMMLLLHHHGGGEEECCCBBBAAA@@@@@@@@@@@@???>>>===<<<;;;;;;:::;;;;;;<<<<<<;;;;;;:::888888777777777888:::;;;::::::::::::::::::::::::888888999::::::::::::999888888888999999999999:::666666555555555444444444222222333333333222222111222222111111222333555666444444444333333333222222111111111111222222222222444444444444333333333333222222333333333444444444333333333333333222111111444444444444444444444444222333555666777777666666444444444333444555555666999::::::999777666666888555666777999;;;<<<===>>>:::;;;<<<======???CCCFFFGGGJJJNNNPPPRRRUUUYYY]]][[[___cccgggiiilllppptttuuuvvvzzz~~~zzzwwwvvvvvvwwwoooqqqpppkkkgggfffccc^^^]]]^^^^^^ZZZTTTLLLGGGDDD???@@@???>>>===<<<<<<===;;;999888999999999888666999:::;;;;;;<<<;;;::::::555555666777888999999999888999999999888777666555666777777888888888777777888888888888888777666666999999999999999999999999999999888888888888999999999999;;;<<<======<<<<<<;;;;;;<<<======>>>??????>>>>>>>>>>>>>>>>>>>>>>>>???>>>===<<<<<<===>>>???;;;<<<===>>>>>>?????????&&&''''''((((((''''''&&&&&&'''((('''%%%#########%%%%%%&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&''''''%%%&&&((())))))(((&&&%%%$$$%%%''''''&&&'''((()))(((((((((((((((((((((((('''&&&&&&&&&&&&'''((((((&&&''''''((()))***++++++***(((''''''(((((('''%%%%%%&&&((()))***)))'''&&&$$$%%%''')))))))))))))))&&&''''''((()))******+++******+++++++++******)))---,,,+++******,,,...///,,,,,,,,,---------.........//////000000000000000...//////000111222222222000000000000000000000000444555555555555555555555555555444333333333444444666777888999999:::999999:::::::::;;;;;;;;;<<<<<<888999;;;<<<<<<;;;999888888999999:::;;;======>>><<<===???AAABBBAAA@@@???>>>@@@BBBCCCDDDDDDBBBAAAAAACCCEEEEEEEEEEEEFFFGGGJJJKKKLLLMMMNNNNNNNNNNNNMMMMMMLLLLLLKKKKKKJJJJJJLLLLLLLLLLLLMMMOOOQQQSSSTTTTTTTTTUUUVVVVVVWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWTTTTTTUUUVVVWWWWWWWWWWWWWWWUUUTTTVVVXXXYYYVVVTTTNNNOOOQQQSSSSSSSSSSSSRRRMMMOOOQQQTTTVVVWWWWWWWWWRRRTTTVVVXXXYYYYYYYYYXXXVVVVVVVVVVVVVVVUUUTTTSSSTTTSSSRRRQQQPPPQQQRRRRRRPPPOOOMMMKKKJJJJJJJJJJJJGGGHHHIIIKKKLLLMMMMMMMMMLLLKKKJJJJJJJJJLLLMMMNNNMMMNNNNNNKKKGGGFFFIIIKKKEEEEEEFFFFFFGGGGGGGGGHHHFFFGGGIIIKKKLLLMMMMMMLLLHHHGGGEEEDDDBBBBBBAAAAAABBBAAA@@@???>>>===<<<<<<:::;;;;;;<<<<<<;;;;;;:::::::::888777777777888999;;;;;;;;;<<<<<<<<<======777777888999999999999888777888888888999999999999:::999999999888888777777333444444555555444444444222222111111222444555777444444444333333333222222000111111111111222222222444444333333333222222222222222333333333444444444222333333333333222111111444444444444444444444444000222333555666666555555666555555555555666777777666666666555222222333444111222444666888999999999777999;;;<<<======???@@@@@@AAACCCBBB@@@AAAEEEIIIFFFJJJNNNOOOPPPQQQUUUYYYXXXZZZ]]]bbbeeefffdddaaafffhhhkkklllkkkkkkllllllgggfffccc```]]][[[YYYYYYUUUWWWUUUPPPMMMNNNLLLIIIHHHIIIIIIGGGCCCAAA@@@@@@;;;<<<<<<:::999999:::<<<888777555555777999999999555666888999:::::::::999;;;;;;::::::999777666555888999999999888777555444666777888999999888777666888888888888888777666666::::::999999999999999999999999888888888888999999999:::;;;===>>>======<<<::::::;;;;;;<<<===>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>???>>>===<<<<<<===>>>???;;;<<<===>>>????????????''''''&&&%%%$$$$$$#########$$$%%%&&&&&&&&&%%%$$$((((((((('''&&&&&&&&&%%%$$$$$$$$$%%%&&&'''((()))&&&&&&&&&'''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$%%%&&&'''******))))))(((((('''''''''''''''''''''''''''''')))))))))((('''''''''&&&'''''''''''''''((())))))'''''''''''''''&&&&&&%%%((((((((((((((('''''''''++++++************++++++++++++******************,,,+++*********+++,,,---***,,,///111111111222444---...............------111111111111111111111111111000000///000222333444444444333333333444555555444444444333333222222222555555555555555555555555888888888999:::;;;<<<===::::::;;;;;;<<<;;;;;;;;;888999:::<<<<<<<<<<<<;;;??????@@@AAAAAAAAAAAA@@@CCCCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDEEEFFFHHHHHHIIIKKKMMMNNNNNNNNNOOOQQQMMMLLLKKKKKKKKKLLLNNNOOONNNNNNNNNMMMNNNNNNOOOOOOQQQTTTXXXYYYXXXWWWVVVVVVVVVVVVWWWWWWVVVTTTSSSRRRRRRUUUXXXYYYXXXVVVUUUUUUWWWWWWVVVVVVWWWWWWXXXXXXUUUTTTRRRQQQOOONNNNNNMMMNNNPPPQQQQQQPPPPPPQQQSSSTTTUUUUUUUUUUUUTTTSSSSSSTTTUUUUUUUUUUUUTTTSSSSSSVVVVVVUUUSSSRRRRRRTTTVVVUUUUUUSSSQQQNNNJJJFFFDDDFFFFFFFFFIIILLLNNNMMMLLLKKKIIIGGGFFFFFFHHHKKKLLLMMMLLLJJJIIIGGGGGGFFFFFFDDDFFFGGGGGGEEEDDDDDDEEEGGGGGGHHHIIIIIIJJJKKKKKKIIIGGGEEECCCAAAAAAAAAAAAAAA@@@???===<<<;;;;;;;;;:::;;;;;;<<<<<<;;;::::::777888:::;;;;;;:::888777777888999::::::::::::999777777777777888888888888777666555444444555666777999999999888888666555444222222111111111111222222222222222333333333444444333333333222222222111111//////000111222333333444777444111111444666555333111111222333333444555555666444222111222222000///333333222111111222333333333333333333333333333333222333333222111111222444555444444333333333444444333333333444444666777888999999888888888888999999;;;::::::999999::::::;;;===???@@@@@@??????@@@BBBGGGHHHIIIJJJKKKLLLMMMMMMQQQPPPOOOOOONNNNNNNNNNNNJJJJJJIIIHHHGGGFFFEEEEEECCCCCCBBBBBBAAA@@@@@@???===>>>>>>>>>===<<<<<<;;;888999999999999888777777666666666666666777777888888999999999999888777777999888777777777888::::::999999999888888888777777666777777777777888888888777888::::::888777888999888888888888888999999999888888888888888888888888999;;;<<<<<<;;;::::::;;;:::;;;<<<===>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>???>>>===<<<<<<<<<<<<<<<>>>===<<<<<<<<<===???@@@&&&&&&&&&&&&'''''''''''''''''''''''''''&&&%%%$$$&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&'''(((%%%&&&&&&'''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%&&&'''((())))))))))))((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%((((((((('''(((((())))))'''(((((((((((('''&&&&&&(((((())))))))))))))))))+++******))))))******+++************************++++++*********+++,,,---***+++---,,,++++++---........./////////......---111111111111111111111111222222111111000111111111333333333333333444444555222222222111111111000000444444555555666777888888999999999999999999::::::999999:::;;;<<<<<<;;;;;;::::::<<<===>>>>>>======>>>???@@@@@@AAAAAA@@@@@@BBBBBBBBBBBBCCCCCCCCCDDDCCCCCCCCCCCCDDDEEEFFFFFFGGGIIIKKKLLLLLLLLLMMMOOOMMMMMMLLLLLLMMMMMMNNNOOONNNNNNMMMMMMMMMNNNNNNOOOQQQTTTWWWXXXWWWVVVVVVVVVUUUVVVVVVWWWVVVTTTSSSRRRRRRTTTVVVVVVUUUTTTUUUUUUVVVUUUUUUUUUUUUVVVXXXXXXVVVUUUTTTRRRPPPOOOOOOOOONNNOOOOOOOOONNNNNNPPPRRRRRRRRRSSSSSSSSSRRRRRRQQQTTTTTTTTTTTTTTTTTTSSSSSSUUUUUUUUUTTTRRRRRRSSSSSSUUUTTTSSSQQQNNNKKKHHHFFFFFFFFFFFFIIILLLMMMMMMLLLLLLJJJIIIGGGHHHJJJLLLMMMLLLKKKJJJHHHGGGFFFFFFEEEDDDFFFGGGFFFDDDCCCCCCDDDEEEFFFFFFGGGHHHHHHIIIIIIHHHGGGFFFDDDBBBAAAAAAAAA@@@@@@???>>>===<<<<<<<<<===<<<<<<;;;:::999888888888999:::;;;;;;:::999888888888999999:::999999999888888888777777777666666666666555444444555666777777777777777666555444333222111111000000111111222222222222333333333333444333333222222222111111111000000000111111222222333666333111111333555444333111111222222333444444444555333222111222222111000333222222111111222222333333333333333333333333333222222333222111111222444555444444333333333444444444444444444555555666777777777666666666666777777888888888777777888888888999;;;<<<<<<;;;;;;<<<===<<<<<<===>>>???@@@AAAAAABBBAAAAAA@@@??????@@@@@@@@@@@@@@@@@@@@@?????????>>>>>>===<<<<<<;;;::::::999999:::999999888888777888888888999888777777666666666555555666666777888555666777888999:::::::::888888777777777888999:::999999888888888777777777777777777777888888888888666888999999888777777888666777777777777888888888999999999999999999999999999;;;<<<<<<;;;::::::;;;888999:::;;;<<<<<<<<<<<<>>>>>>>>>>>>>>>>>>>>>>>>>>>======<<<<<<<<<<<<===>>>>>>=========>>>???@@@$$$%%%&&&''')))***++++++((('''&&&%%%$$$#########$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''%%%%%%&&&&&&'''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&''''''((())))))))))))(((((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&)))(((((('''''''''(((((((((((()))))))))(((''''''(((((())))))******+++++++++******))))))******+++************************++++++******++++++,,,---/////////---+++***,,,......//////000000/////////000000000000000000000000222222222222111000///...222222222222333333444444222222222222111111111111333444555666777999:::::::::999888888777777777888888888999;;;<<<<<<<<<<<<<<<<<<===>>>????????????>>>???@@@@@@AAAAAA@@@@@@@@@@@@AAABBBCCCDDDDDDEEECCCCCCCCCBBBBBBCCCDDDDDDEEEGGGIIIJJJJJJJJJKKKLLLLLLMMMMMMNNNNNNNNNNNNNNNNNNNNNMMMMMMMMMMMMMMMNNNQQQSSSUUUUUUUUUUUUVVVWWWUUUUUUVVVVVVUUUTTTSSSQQQQQQRRRSSSRRRQQQRRRSSSUUUTTTSSSRRRRRRSSSUUUWWWYYYWWWVVVUUUTTTSSSQQQQQQPPPNNNNNNMMMLLLKKKLLLNNNQQQQQQRRRRRRSSSSSSSSSRRRRRRSSSSSSSSSSSSSSSSSSSSSSSSUUUUUUUUUUUUTTTSSSRRRQQQTTTSSSSSSQQQOOOMMMKKKJJJGGGFFFFFFHHHKKKLLLLLLKKKLLLKKKJJJIIIIIIKKKMMMNNNLLLKKKJJJHHHGGGFFFFFFEEEEEEFFFGGGFFFDDDBBBBBBBBBCCCCCCDDDDDDEEEFFFFFFFFFGGGGGGFFFEEEDDDCCCAAA@@@??????>>>>>>============>>>===;;;999777777777777888999:::;;;;;;:::999888888888999999999888888777:::999999888666555555444666555555444444444555555555555555555555444333222222111111000000111111222111111222222222333333333333222222222222111111111111111111111111111111111444222000000222333222222222222222222222222333333444222111111222333333222333222111111111111222333222222222222222222222222111222333222000000222333444444333333333333444444666555555555555555666666666555555555555555555666555555555555555555555555444666777777666555666888666666777888999::::::;;;::::::999999888888999999777777777888888999999999999999888888777777666666666666777777777666555555777777777888777666666555555555555555555666666777555666777999::::::::::::777777777777777888999999888888777777777777777666777777777888888888999999666777999999777777777888555555666666777777777777::::::::::::::::::::::::999:::<<<<<<:::::::::;;;888999:::;;;;;;<<<<<<;;;>>>>>>>>>>>>>>>>>>>>>>>><<<<<<<<<;;;<<<<<<======???>>>>>>>>>>>>???@@@@@@$$$%%%&&&'''((()))***+++)))(((&&&%%%$$$%%%&&&&&&$$$$$$%%%%%%&&&&&&&&&'''''''''&&&%%%%%%%%%&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''(((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((()))))))))(((''''''&&&&&&&&&&&&&&&)))))))))))))))(((((('''''''''((()))******++++++******))))))))))))******))))))))))))************+++***++++++++++++,,,,,,000///...,,,******,,,///...///000000000000000000////////////////////////000111222222222111///...000111111222333333333333444444444444444444444444333444555666777888999999888777777666666666777777666777999:::;;;<<<======<<<======>>>??????@@@@@@>>>>>>???@@@@@@@@@@@@@@@>>>???@@@AAACCCDDDEEEFFFDDDDDDCCCCCCBBBCCCCCCCCCEEEGGGIIIIIIIIIIIIJJJKKKJJJKKKMMMNNNNNNNNNMMMLLLNNNNNNMMMLLLLLLLLLLLLMMMPPPQQQSSSSSSSSSSSSUUUWWWTTTTTTUUUUUUUUUTTTRRRQQQOOOPPPPPPNNNNNNOOORRRTTTSSSRRRQQQPPPQQQSSSVVVXXXWWWWWWVVVUUUTTTSSSRRRQQQNNNNNNLLLJJJIIIJJJNNNQQQRRRRRRSSSTTTTTTTTTTTTTTTQQQQQQQQQRRRRRRSSSSSSTTTVVVVVVVVVVVVVVVUUURRRPPPSSSRRRRRRQQQPPPNNNMMMMMMHHHGGGFFFHHHJJJKKKKKKKKKLLLKKKJJJIIIJJJKKKLLLMMMMMMLLLKKKIIIHHHGGGGGGFFFFFFHHHHHHGGGDDDBBBBBBBBBAAAAAABBBBBBCCCCCCCCCCCCEEEFFFFFFFFFEEECCCAAA@@@======>>>>>>>>>======<<<<<<;;;888666555666777888999999::::::::::::999999888888888999888888777666999888888777666666555555555555444444444444444444444444444555444444333333111111000000000000111111111111111111222222222222222222222222111111111111222111111111000000000///111111000000111111111111222222222222111111111111333111000111222444444333222222111111111111222222222222222222222222222222111222222111000000111333333333333222333333444444666666555555444555555555555555444444444444555555333444444444444444444333222444555444333333444555555555666777777888999999::::::999888888999999999555555555555555555555555777777777777666666555555666777777777777777666666666666666666666555444444444444444444444555555666888888999999888888777666666666666666777777888888666666666666666666666666777777777888888888999999555777888888777666666777555555666666777888888888::::::::::::::::::::::::888:::<<<;;;:::999:::;;;::::::;;;<<<====================================;;;;;;;;;;;;<<<<<<===>>>???????????????@@@@@@@@@%%%%%%%%%&&&&&&'''''''''***)))(((((((((***+++,,,%%%%%%&&&&&&''''''((((((''''''&&&%%%%%%%%%&&&&&&$$$%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((()))))))))&&&%%%%%%$$$$$$%%%%%%%%%)))))))))))))))(((((('''&&&&&&''''''((()))*********))))))))))))))))))***(((((()))))))))***************++++++,,,,,,,,,,,,******)))'''&&&'''***---......///000000000000000...........................///000111222111111000///000111333333444333333444444444444444444444444444444555555555555666666555555555555666777888999666777888:::;;;<<<<<<<<<<<<<<<<<<<<<===>>>??????>>>>>>???@@@@@@@@@@@@???===>>>???AAACCCDDDEEEFFFEEEEEEDDDCCCCCCCCCDDDDDDFFFHHHJJJJJJIIIIIIJJJKKKHHHIIIKKKLLLLLLLLLKKKJJJNNNMMMLLLLLLKKKKKKKKKLLLNNNPPPQQQRRRQQQRRRTTTVVVRRRSSSTTTTTTTTTSSSRRRQQQMMMMMMMMMLLLKKKMMMPPPSSSRRRQQQPPPPPPPPPRRRTTTVVVVVVVVVVVVVVVUUUTTTRRRQQQNNNNNNLLLJJJIIIJJJMMMPPPOOOPPPQQQRRRSSSTTTTTTTTTPPPPPPOOOPPPQQQRRRSSSTTTXXXWWWVVVWWWXXXWWWTTTQQQRRRQQQQQQPPPOOOOOOOOOOOOIIIHHHFFFGGGIIIJJJJJJJJJJJJJJJIIIIIIIIIJJJKKKLLLOOONNNLLLJJJIIIHHHHHHHHHGGGHHHIIIHHHEEECCCCCCCCC@@@@@@AAAAAAAAAAAABBBBBBDDDEEEEEEEEEDDDCCCAAA@@@<<<<<<=========<<<;;;;;;888777666444555666888999888999999999999999999888777777777888888777777666666666666666666666666777444444444444444333222222333333444444555444444444111000000000000000000111000000000111111111222222222222222111111111000000222222111111000////////////000000000000000000000111111111111111111000000222111000000222444444333111111111111111111111111111111111111111111111111111222222111000000111333222222222222222333444555666555555444444444444555555555555444444555555555333333444555555444333333333444555444333222333444222222333333444444555555666555555444555555666666666555555444333333222222555555555555555444444444666666777777777777666666444555555555555444333333333333333333333444444555777777888888777777666555555555666666777777777777555555555555555555555555666666777777777888888888444666888777666555666777666666777888888999::::::::::::::::::::::::::::::888:::;;;;;;:::999999:::999:::;;;<<<============<<<<<<<<<<<<<<<<<<<<<<<<;;;;;;;;;;;;;;;<<<===>>>>>>>>>??????@@@@@@@@@@@@%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&'''((()))&&&&&&''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&'''$$$$$$%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&&&&''''''''''''(((((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%&&&&&&(((((()))))))))(((''''''&&&&&&''''''(((((())))))***))))))(((((())))))***'''(((((())))))*********)))***+++,,,,,,,,,,,,+++((()))***))))))***,,,///------...///000000000000////////////////////////---...///000111111111111///000222444444555444444222222222222333333333333555555555555555444444444444444444555666777999999777777888:::;;;;;;;;;;;;;;;;;;;;;;;;<<<===>>>>>>===>>>??????@@@@@@??????>>>>>>???AAABBBDDDEEEEEEEEEDDDDDDCCCDDDDDDEEEEEEGGGHHHJJJKKKJJJIIIJJJKKKHHHHHHIIIJJJJJJJJJJJJJJJNNNMMMLLLKKKJJJJJJJJJKKKLLLNNNPPPQQQQQQQQQSSSTTTQQQRRRSSSTTTTTTSSSRRRQQQKKKLLLLLLKKKJJJLLLOOORRRQQQQQQQQQQQQQQQRRRRRRSSSTTTTTTUUUUUUTTTSSSQQQPPPMMMMMMLLLJJJIIIIIIKKKNNNJJJKKKMMMNNNOOOPPPQQQQQQNNNNNNNNNNNNOOOQQQSSSUUUXXXVVVTTTUUUXXXXXXUUURRRQQQPPPPPPOOONNNOOOOOOOOOJJJHHHFFFFFFHHHIIIJJJIIIJJJJJJIIIIIIJJJJJJKKKKKKNNNNNNLLLJJJIIIHHHHHHHHHFFFGGGHHHGGGEEECCCCCCDDDAAAAAAAAAAAAAAAAAAAAAAAACCCDDDDDDCCCBBBAAA@@@@@@:::;;;<<<<<<<<<;;;999888555444444444444666777888888888888888888888888888555555666777777777777777555555555666666777777777444444444444333222111111111222333444444444444444111000000//////000000111///000000000000111111111222111111111111000000000111111111000000/////////...000111111000//////000000000000000000000111111333111000111222444444333000000111222222111000000000000000000000000000000000111222111//////111222222111111222222333444555444333333333333333444444555555444444444444555555222333444555555444333222333444555444333222333444222222222333333444444444333333222222222333444444444444333222111000//////222222222222222222222222333333444555555555444444333333444444333333222111222222222222222333333444222333444666777777777777444444555666666666666666333444444444444555555555555555555666666666777777444555777777555555555666666666777888999::::::;;;::::::::::::::::::::::::888999;;;;;;999999999:::777888999::::::;;;;;;:::<<<<<<<<<<<<<<<<<<<<<<<<;;;;;;;;;:::;;;;;;<<<<<<===>>>??????@@@@@@??????%%%%%%%%%%%%%%%$$$$$$$$$!!!!!!"""######$$$$$$###''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''(((###$$$%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%&&&'''((()))(((((('''&&&&&&&&&'''''''''((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&'''))))))'''(((((((((((('''&&&&&&(((((((((((((((((())))))))))))(((((((((((())))))''''''(((((()))******+++)))***+++,,,,,,,,,++++++***,,,------,,,---...000,,,,,,---...///000000///////////////////////////000000/////////000000111///000333555666666555444222222222333333333444444444444555555666666777777666666555555666777888888777888999:::::::::::::::;;;;;;;;;;;;;;;===>>>???===>>>>>>???????????????>>>??????AAABBBCCCDDDDDDBBBBBBBBBBBBCCCDDDEEEEEEFFFHHHJJJJJJIIIHHHIIIJJJJJJIIIIIIIIIIIIJJJKKKKKKMMMMMMLLLKKKJJJJJJJJJJJJIIILLLPPPQQQRRRQQQRRRRRRPPPQQQRRRSSSSSSSSSQQQQQQIIIJJJKKKKKKKKKLLLNNNQQQQQQRRRRRRSSSSSSRRRQQQPPPQQQRRRSSSTTTSSSRRRPPPNNNJJJKKKKKKJJJHHHHHHIIIJJJHHHIIIKKKLLLNNNOOOOOOPPPMMMMMMMMMMMMNNNQQQSSSUUUWWWSSSPPPRRRUUUWWWVVVSSSQQQPPPOOONNNMMMNNNNNNOOOKKKIIIFFFFFFGGGHHHIIIIIIJJJJJJKKKKKKKKKLLLLLLLLLMMMLLLJJJIIIGGGFFFFFFFFFCCCEEEFFFEEECCCBBBBBBCCCBBBBBBBBBBBBAAAAAAAAAAAACCCBBBBBBAAA@@@@@@@@@@@@::::::;;;;;;:::999666555444444444444444555555555777777666666666666777777333444555666777888888888666666666666666555555555333444444444333222000//////000111222333333333333000000////////////000000/////////000000000111111111111111111000000000000000000000000000/////////---000333222000//////111.../////////000111111111333222000111222333333222///000111222222111000///000000000000000000000000000111111111//////111222111111111111222333444555111111111111222333333444333333222222222222333333111222333444444333222111222333333333111000111222333333333333333444444444333333333333333444555555222111111111000000//////000111111111111111111111111222333444444444444444222222333333222222111000111111111111111222333333111111333444555666666666333444555666666666555555222333333333444444444444444444444444555555555555333555777666555444555555555555666777888999::::::999999999999999999999999888999;;;;;;999888999:::777777888999::::::::::::;;;;;;;;;;;;;;;;;;;;;;;;<<<<<<;;;:::::::::;;;;;;<<<===>>>?????????>>>>>>$$$$$$$$$%%%%%%&&&&&&&&&&&&'''((()))((('''&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&'''((()))###$$$%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&''')))*********)))(((&&&&&&&&&'''''''''(((((()))))))))))))))))))))))))))))))))((((((''''''&&&%%%%%%&&&&&&((()))+++,,,'''''''''''''''&&&&&&%%%************))))))))))))))))))(((((((((((())))))&&&''''''((()))******+++)))***+++,,,---,,,++++++(((***+++,,,*********++++++,,,---...////////////000000000000000000000000333222000........./////////111333555777777666555444444444555555666666666333444555666777888999:::888888777666666666666777888999999:::::::::999999<<<<<<;;;;;;<<<===???@@@======>>>?????????????????????@@@AAABBBBBBCCCCCC@@@@@@@@@AAABBBCCCDDDEEEFFFHHHIIIIIIHHHGGGHHHIIIKKKKKKJJJIIIIIIKKKLLLMMMMMMMMMLLLJJJJJJIIIIIIIIIGGGKKKOOORRRRRRQQQQQQQQQPPPQQQRRRSSSSSSRRRQQQQQQHHHJJJKKKKKKKKKLLLNNNPPPQQQRRRTTTTTTTTTRRROOONNNPPPQQQRRRSSSRRRQQQOOOMMMHHHIIIJJJIIIGGGFFFGGGHHHIIIJJJKKKMMMOOOPPPQQQQQQMMMLLLLLLLLLNNNQQQSSSUUUUUUQQQMMMOOOSSSVVVUUUSSSQQQPPPNNNMMMLLLMMMNNNNNNLLLIIIFFFEEEGGGHHHIIIHHHKKKLLLLLLLLLMMMMMMMMMMMMKKKJJJIIIGGGFFFEEEDDDDDD@@@BBBCCCCCCBBBAAAAAABBBBBBBBBBBBBBBBBBBBBBBBBBBCCCBBB@@@???>>>??????@@@999:::;;;;;;:::777555333444555555555555444222222666666555555555555666666222222444666777888888888888888777666555444444333333333444444333222000///---...///111222222222222000000////////////000000////////////000000000000111111111111000000000000/////////000000000000000---000333333111///000111---......///000111111222444222111111222333333222///000111222222111000///000000000000000000000000000111111000//////000222111111111111222333444555000000000000111222333444222222111111111111222222///111222333333222111///000111222111///...///000//////000000000000000000222222222222222333444555000000111111111111222222111111111222222222222222222333444555555555555555222222222222222111000000111111111000111222222333333333444444333333222111333333555666666666555444222222222333333444444444333333333444444444555555333555666666555444444555444444555666777888999999888888888888888888888888777999;;;:::999888999:::999999:::;;;<<<<<<<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;===<<<;;;;;;::::::::::::;;;<<<===??????>>>>>>===$$$$$$&&&&&&&&&&&&$$$$$$%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&%%%$$$$$$''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''))))))(((((('''''''''&&&''''''''''''''''''''''''###$$$%%%&&&''''''''''''***))))))((('''&&&&&&&&&(((((())))))))))))((((((((((((((((((((('''''''''))))))))))))************+++,,,,,,+++***)))+++---,,,++++++++++++++++++++++++***))))))***---000111......////////////......//////...//////000111222111222333333444444333333222222333444444555555666777777777666666666666666777777666555444222000///999999999:::::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;<<<<<<<<<<<<============@@@@@@@@@@@@@@@@@@AAAAAA???@@@AAACCCDDDEEEEEEEEEEEEFFFFFFFFFFFFGGGGGGGGGIIIJJJLLLLLLKKKKKKMMMNNNMMMMMMMMMKKKHHHFFFFFFGGGHHHJJJMMMPPPRRRRRRRRRRRRVVVUUUTTTSSSQQQPPPOOONNNKKKKKKKKKKKKKKKJJJJJJJJJNNNOOOQQQSSSTTTSSSRRRQQQQQQPPPPPPPPPQQQPPPMMMKKKJJJJJJJJJIIIIIIHHHHHHGGGHHHGGGGGGHHHIIIKKKMMMOOONNNNNNNNNNNNOOOPPPQQQRRRPPPQQQQQQRRRRRRQQQPPPOOOLLLLLLMMMMMMMMMMMMMMMMMMMMMKKKIIIGGGFFFGGGHHHIIIKKKLLLNNNOOOOOONNNMMMLLLMMMKKKHHHGGGGGGFFFCCCAAA?????????????????????@@@CCCCCCCCCCCCCCCCCCCCCCCC@@@???>>>>>>>>>>>>>>>>>>===<<<;;;999777666555444444555666555444444555666888888888888888777666666666666666666555444333222333333333333333333333333111111111111111000//////111111111111111111111111111111000000//////......000000////////////000000///////////////............///000111111000///...333222111000////////////////////////000111222333111111111111111111111111000000111111111222222222............///000222222000///.........///111222000000000000000000000000111111222222222333333333111111000000111111222333444444333333333333222222111111111111111111111111222333333222111111222444111222333444555444333222444444222111111111222333111111222222222222111111111111222222222222111111222222222222222222222222222111000000000111333333444444444333333222222222333444555666666666555444555555666666555555444333555444444333333444444555444444444444444444444444111333555666888888888777999999888888777777666666888888999:::;;;<<<<<<======<<<<<<;;;;;;;;;<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;===<<<;;;:::999999999999999;;;===>>>======>>>???$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&&&&'''''')))((((((((('''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&''''''''''''&&&&&&&&&&&&''''''''''''(((((())))))))))))(((((())))))))))))))))))))))))(((((()))))))))***************))))))))))))******%%%&&&''')))+++---...///,,,+++++++++,,,...///000......////////////......++++++,,,,,,------...///111222333333444444333333222222333333444555555555777777777777777777777777888888777777666666555555888888888888999999999:::;;;;;;;;;;;;;;;:::::::::;;;<<<<<<<<<============????????????@@@@@@@@@@@@@@@AAABBBCCCDDDDDDDDDDDDFFFFFFFFFFFFGGGGGGGGGGGGHHHIIIKKKKKKKKKKKKMMMNNNMMMNNNMMMKKKHHHFFFFFFGGGJJJLLLOOORRRSSSTTTTTTSSSTTTTTTRRRQQQOOONNNLLLLLLIIIIIIIIIIIIIIIIIIIIIJJJNNNOOOQQQSSSTTTSSSRRRQQQRRRPPPOOOOOOPPPOOOMMMKKKKKKKKKKKKJJJJJJIIIIIIIIIHHHHHHHHHHHHJJJLLLMMMOOONNNNNNMMMMMMNNNNNNOOOOOOQQQQQQQQQPPPPPPPPPQQQQQQLLLKKKKKKJJJJJJKKKLLLLLLNNNLLLJJJIIIHHHHHHIIIJJJLLLLLLMMMMMMMMMMMMMMMLLLMMMKKKIIIGGGGGGFFFDDDBBB@@@@@@@@@@@@@@@@@@@@@@@@BBBBBBBBBBBBBBBBBBBBBBBB@@@???>>>>>>============;;;:::999888777666555444444555666555444333444666777777888888777777666555666666666666555444333222333333333333333333333333111111111111111000//////000000000000000000000000000000000000//////......000//////////////////000////////////...............///000000000000///.../////////......///000000.........//////000111222111111111111111111111111000000000111111111222222............///000111222000///.........///111111000000000000000000000000111111111111222222222222111111000000000111222222333333333222222111111000111111111111111111111111111222333222111111222444000111222333444444444444222111000/////////000111000111111222222111111000000111111222222111111000222222222222222222222222111111000000000111222333333333222222222111111111222333444555555555444444333333444444444333333222444444333333333333444444444444444444444444444444111333444666777777777777888888888777777777777777888888888999999::::::;;;;;;::::::::::::;;;<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;<<<<<<;;;999999888888888:::<<<>>>>>>======>>>???&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&&&&'''((()))'''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&&&&''''''((((((((('''''''''''''''((((((((((((((((((((((((###$$$%%%&&&''''''''''''"""###$$$%%%&&&((())))))'''(((((())))))(((((('''))))))))))))************(((((())))))))))))*********'''%%%&&&(((***(((&&&###$$$&&&(((***---...///,,,,,,---.....................////////////......---......//////000111111111222222333333333333333222222333333444444555555777777777777777777888888777777666555555666777888666777777777777888888888;;;;;;;;;::::::999999999;;;;;;;;;<<<<<<<<<===============>>>>>>?????????AAAAAABBBCCCDDDDDDCCCCCCEEEEEEEEEFFFFFFFFFFFFGGGFFFHHHIIIJJJJJJJJJLLLNNNNNNNNNLLLJJJFFFEEEFFFGGGKKKLLLOOOQQQRRRSSSSSSSSSQQQQQQOOONNNLLLKKKIIIIIIFFFGGGGGGHHHHHHIIIIIIIIINNNOOOQQQSSSTTTSSSRRRQQQSSSQQQOOONNNNNNNNNMMMKKKLLLLLLLLLKKKKKKKKKKKKKKKHHHHHHHHHIIIJJJLLLNNNOOOMMMMMMMMMLLLLLLLLLLLLLLLQQQPPPPPPPPPPPPPPPQQQQQQKKKJJJHHHGGGGGGHHHJJJKKKMMMLLLJJJHHHHHHHHHIIIIIIMMMMMMLLLLLLKKKLLLLLLMMMLLLKKKHHHGGGGGGFFFDDDBBBAAAAAA@@@@@@@@@@@@@@@@@@AAAAAAAAABBBBBBAAAAAAAAA@@@???>>>===<<<<<<<<<<<<888888777777666555555444333555666555444333444555666666666777666555555444555666666555555444333222222222222222222222222222111111111000000000//////////////////////////////000000000////////////...//////............//////..............................///000000///......,,,,,,,,,------///000000---------...//////000000000000000000000000000000000000000000111111111111............///000111111//////......//////000111000000000000000000000000//////000000000111111111000000000000000111111222333333222111000000//////111111111111111111111111111222333222111000222333///000000111222444555666222111000000//////000000000111111222222111111000000111111222222111111000111111111111111111111111111000000000000111222222111111111111111000000000111222333444444444444333111111111222222222222222444444333333333333444444444444444444444444444444222222444555666777777666666777777777777777777888777777888888888888888888777777777888999:::;;;<<<;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;:::999888888888888;;;<<<>>>>>>===<<<<<<===&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%$$$%%%''')))***(((''''''&&&&&&''''''(((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''(((((()))))))))))))))***###$$$%%%&&&''''''''''''######$$$%%%'''((())))))'''(((((((((((((((((('''((()))))))))))))))******(((((((((((()))))))))******&&&###$$$)))+++)))%%%((()))))))))******+++++++++,,,---//////...,,,+++---......//////......---...//////000111111222222111111222333333333333222111222222333444444555555777777777888888888888888666444222111111222444555666666777777777888888888;;;;;;::::::999999888888::::::;;;;;;;;;<<<<<<<<<;;;<<<<<<======>>>>>>>>>BBBBBBCCCCCCCCCCCCCCCBBBCCCCCCCCCDDDDDDDDDEEEEEEDDDFFFHHHIIIIIIIIIKKKMMMNNNMMMLLLIIIFFFEEEFFFHHHIIIJJJLLLNNNOOOOOOOOOOOONNNNNNMMMKKKJJJHHHGGGGGGFFFFFFGGGHHHHHHIIIJJJJJJNNNOOOQQQSSSTTTSSSRRRQQQTTTQQQNNNMMMMMMNNNMMMLLLLLLLLLKKKKKKKKKKKKJJJJJJHHHHHHIIIJJJLLLMMMNNNOOOMMMMMMMMMLLLKKKJJJIIIIIINNNOOOPPPRRRRRRQQQPPPOOOKKKIIIGGGEEEEEEFFFHHHJJJKKKJJJIIIHHHHHHHHHHHHHHHMMMLLLKKKJJJJJJJJJKKKLLLLLLJJJHHHGGGGGGFFFDDDBBB@@@@@@@@@??????????????????@@@@@@AAAAAA@@@@@@?????????===<<<;;;;;;::::::666666555555555555444444333444555555333333444555555555666666555555444333555555555555444333222222222222222222222222222222111111000//////////////////////////////////////////////////////////////////......------......///------...............///........................---------------...//////,,,,,,------............/////////////////////////////////000000000111111...............///000111............//////000000000000000000000000000000........./////////000000000////////////000111111333333222111000//////...111111111111111111111111000222333222111000111222111000000000111222444555333333333222222222222222000000111111111111000000000000111111111111000000111111111111111111111111000000000000000111111222111111111111111111111111111111222222333333333333111111111111111222222333444333333333333333333444333333333333333333333333222222333444555555666666555666666666777777888888777777777666666555555555333444444666777999;;;<<<;;;;;;;;;;;;;;;;;;;;;;;;::::::999888888888888888:::;;;===<<<;;;::::::;;;&&&&&&$$$$$$$$$$$$&&&&&&$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%#########%%%''')))))))))(((((((((((())))))''''''&&&&&&&&&&&&''''''&&&&&&&&&'''''''''''''''###$$$$$$$$$%%%%%%%%%&&&###$$$%%%&&&''''''''''''&&&&&&''''''((((((((((((''''''(((((((((((('''''''''''''''(((((()))))))))'''(((((((((((()))))))))+++'''###%%%***,,,***''',,,,,,,,,++++++******)))(((***,,,......,,,+++)))------............------***+++,,,...............000111222222333333222222111111222222333444444555666666777777888888888888666555222000000000222333777777777777888888888888::::::999999999888888888::::::::::::;;;;;;;;;;;;::::::;;;<<<======>>>>>>BBBBBBCCCCCCCCCCCCCCCBBBAAAAAAAAAAAABBBBBBBBBBBBCCCEEEGGGGGGGGGHHHIIIKKKKKKKKKKKKIIIFFFFFFGGGIIIIIIJJJJJJKKKLLLMMMMMMMMMLLLLLLKKKJJJIIIIIIHHHHHHGGGHHHHHHIIIJJJKKKKKKLLLNNNOOOQQQSSSTTTSSSRRRQQQSSSQQQNNNMMMNNNOOOOOONNNLLLLLLKKKKKKJJJIIIIIIHHHHHHIIIJJJKKKMMMNNNOOOOOOMMMMMMMMMMMMLLLJJJIIIHHHJJJMMMQQQTTTUUURRROOOLLLLLLJJJGGGEEEEEEFFFHHHJJJLLLKKKKKKJJJJJJJJJJJJJJJMMMLLLJJJIIIHHHIIIJJJJJJJJJHHHFFFFFFFFFEEECCCBBB???>>>>>>>>>======<<<<<<===>>>???@@@@@@???>>>===>>>===<<<;;;::::::::::::444444444444444444444444333444555444333222333555555555555555555444333333555555555555444333222111111111111111111111111111111000//////......//////000000000000000000000000.............../////////......------------......,,,---------......//////......------------......000///......---------...++++++,,,------------,,,............................../////////000000000...............//////000---......///////////////////////////////////////------.........///////////////......//////000111444333333222111111000000000000000000000000000000///111333333111000000111333222111//////000111222333333333333222222111111000000000111111000000000000000000111111000000000000000000000000000000000//////000000111111111111111111222222222222222222111111111111222222333333333333222222222222333444333333333222222333333333333333333333333333333333222222333333444444555555555555666666777777777888777666666555555444444333111111222444666888:::<<<;;;;;;;;;;;;;;;;;;;;;;;;999999888777777777888888888999;;;:::999888888999&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$%%%&&&)))(((((((((((((((((()))''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&'''''''''$$$$$$$$$%%%&&&&&&''''''###$$$%%%&&&''''''''''''((((((((((((((((((''''''&&&''''''((((((''''''&&&&&&&&&''''''(((((())))))''''''(((((((((((())))))***'''%%%&&&***++++++)))***++++++++++++,,,,,,,,,''')))+++,,,---,,,+++***------............------+++,,,...///000000//////000111111222222222222222111111222222333333444444555555666666777777888888888777555333333333333333777777777777888888888888888888888888888888888888999999999:::::::::;;;;;;::::::;;;<<<======>>>???AAAAAABBBCCCDDDDDDCCCCCC@@@@@@@@@AAAAAAAAAAAABBBCCCEEEFFFFFFFFFFFFGGGIIIGGGIIIJJJIIIHHHGGGHHHIIIJJJJJJKKKKKKKKKLLLLLLMMMKKKKKKKKKKKKKKKKKKKKKKKKIIIJJJJJJKKKKKKLLLLLLLLLNNNOOOQQQSSSTTTSSSRRRQQQRRRQQQOOOOOOQQQQQQQQQPPPMMMMMMLLLKKKIIIHHHGGGGGGHHHIIIKKKMMMNNNOOOOOOOOOMMMNNNNNNNNNMMMLLLJJJIIIHHHLLLQQQUUUUUUSSSNNNKKKMMMLLLJJJHHHHHHHHHIIIJJJNNNNNNNNNNNNNNNNNNMMMMMMKKKKKKJJJIIIHHHHHHHHHHHHHHHFFFEEEDDDDDDDDDBBB@@@>>>>>>======<<<;;;;;;;;;;;;<<<>>>??????>>><<<;;;<<<;;;::::::999:::::::::555555555444444444444444222444555444333222333444555555555666555444444333444555555444444333222111000000000000000000000000111000///...---...///000000000000000000000000000---............/////////------,,,,,,,,,,,,------,,,,,,,,,---......//////...---,,,,,,,,,,,,---...000000///...---,,,,,,---+++,,,---......---,,,+++------------------------............///////////////......---......//////------...////////////...////////////////////////------........./////////...............///000000333222222222222111111111000000000000000000000000...000333333111000000000333222111000////////////000111111111111000/////////000000111111000000//////000000111111000000///////////////////////////...///000000111111000000111111111222222222222222222222111111222222333444666555444222222222333444333333222222222222333333333333333333333333333333333222222222222333444555555666666666666666666777666666555555444444444333000111222333555888:::;;;999999999999999999999999888888777777777777777888666888::::::888888888999$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%$$$$$$''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&''''''''''''''''''((()))*********###$$$%%%&&&''''''''''''''''''''''''''''''''''''&&&''''''((((((''''''&&&&&&''''''((())))))******'''''''''((((((((())))))''''''''''''((()))***+++((())))))***+++,,,,,,---((()))***,,,------,,,,,,,,,------......------,,,---...000222333222111000000000111222222222222222111111111222333333444444333444444555666666777777666666666666666666666666555555666666666777777777666666777777888999999999999999999999::::::::::::::::::;;;<<<===>>>??????@@@AAABBBCCCDDDDDDDDDDDDAAAAAAAAAAAABBBBBBBBBBBBDDDEEEFFFFFFDDDDDDEEEFFFCCCFFFIIIJJJJJJIIIIIIIIIIIIIIIIIIIIIIIIIIIJJJJJJKKKKKKLLLMMMMMMNNNOOOOOOKKKKKKKKKKKKKKKKKKKKKKKKNNNOOOQQQSSSTTTSSSRRRQQQPPPPPPPPPQQQSSSTTTSSSRRRPPPPPPNNNLLLJJJHHHGGGFFFHHHJJJKKKMMMOOOOOOOOOOOONNNNNNPPPPPPPPPNNNLLLKKKJJJLLLOOORRRRRRQQQPPPNNNOOONNNMMMLLLLLLKKKKKKKKKMMMMMMMMMNNNNNNNNNMMMMMMJJJJJJJJJIIIIIIHHHGGGFFFFFFEEECCCCCCCCCCCCAAA??????>>>>>>===<<<<<<;;;;;;:::;;;===??????===;;;:::999999999999999::::::;;;666666555555444444333333222333444444222222333444666666666666666555444444444444444444333222111111000000000000000000000000111000///------...///000////////////////////////---------.........//////------,,,,,,,,,,,,------++++++,,,------...//////------,,,++++++,,,------...---,,,,,,,,,,,,,,,---+++,,,...///...---,,,+++,,,,,,,,,,,,,,,,,,,,,,,,------.........////////////......------.........,,,---.../////////......////////////////////////............////////////......------......///000000000000111111111111111000000000000000000000000...000222333222000000000000000000000000000//////000111111222111000///...//////000000000000////////////000000000000//////////////////////////////......000111111111000///000000000111111111222222333222222111222333444555888666444222111111222333333333222222222222333333222222222222222222222222333222222111111222333444666666666666666555555555555555555555555444444444111111222333555777999:::888888888888888888888888777777666666666777777888666888:::;;;:::999:::;;;$$$$$$&&&''''''&&&$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&'''''''''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&'''(((((()))$$$$$$%%%&&&''''''''''''%%%%%%%%%&&&&&&'''''''''&&&''''''''''''''''''&&&'''(((((()))***+++++++++''''''''''''((((((((()))%%%'''((('''''''''***,,,))))))))))))************((()))+++,,,---......///,,,------......------,,,***+++---///000///...---000000111222222222222111000111111222333333444444333333444444555666666777333444555666777777777777444444444555555555666666555555666777888999::::::888888999999999:::::::::::::::;;;<<<===>>>???@@@???@@@AAACCCDDDEEEEEEEEEBBBBBBBBBCCCCCCCCCDDDDDDDDDEEEFFFEEEDDDCCCDDDEEEAAADDDIIIKKKKKKJJJIIIIIIGGGFFFFFFEEEEEEFFFGGGGGGKKKLLLMMMNNNOOOPPPQQQRRRKKKKKKKKKKKKKKKJJJJJJJJJNNNOOOQQQSSSTTTSSSRRRQQQOOOOOOPPPSSSUUUVVVUUUSSSSSSRRRPPPNNNKKKIIIGGGFFFHHHJJJLLLNNNOOOPPPPPPOOONNNOOOPPPQQQQQQPPPNNNMMMMMMMMMNNNOOOOOOPPPQQQQQQPPPPPPPPPOOONNNMMMMMMLLLIIIJJJKKKKKKKKKKKKKKKJJJIIIIIIJJJJJJIIIGGGFFFDDDEEECCCBBBBBBBBBBBB@@@???@@@??????>>>===<<<<<<;;;999;;;===>>>>>>===;;;999888888888888999:::;;;<<<777777666555555444333333222333444444222222333444666666777777666666555444444444444444333222111111000000000000000000000000222000...---,,,---///000........................---------.........//////---,,,,,,++++++,,,,,,---++++++,,,,,,---...//////------++++++++++++------************+++,,,------+++,,,...//////...,,,+++,,,,,,,,,,,,,,,,,,,,,,,,---------........./////////......---------......,,,,,,.../////////...---////////////////////////........./////////000000...------------...//////......//////000000111111000000000000000000000000---000222333222000//////---...///111111111000///222222333444333222111000//////000000000000////////////000000000000//////////////////////////////---...000111111111000///.../////////000000111111444333222222222333444555999777444222000000111222333222222222222222222333222222222222222222222222333222111111111222333444777777666666555555555444555555555555555555555555111111222333555777999:::777777777777777777777777777777666666666666777888777999;;;<<<;;;;;;<<<>>>%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&'''(((((('''&&&%%%%%%''''''&&&%%%$$$$$$%%%%%%%%%$$$######%%%$$$$$$######$$$$$$%%%&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&)))(((&&&$$$$$$$$$&&&'''(((((())))))((('''&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$$$$$$$&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&&&&''''''%%%%%%%%%&&&'''((())))))''''''''''''((((((((((((++++++******)))(((((('''************************++++++******++++++,,,---++++++++++++++++++++++++)))***+++,,,...///000111---...///000111222333333111111222222222333333333444333333333333444555666555555555555555555444444555555555555666666666666555555555666777888888888555777999:::;;;;;;::::::::::::;;;<<<<<<=========AAABBBCCCDDDDDDCCCCCCCCCCCCCCCCCCCCCDDDDDDDDDDDDFFFEEEEEEEEEEEEEEEFFFFFFCCCEEEHHHJJJJJJHHHEEECCCFFFGGGHHHHHHGGGGGGIIIKKKLLLLLLMMMMMMMMMMMMLLLLLLJJJKKKLLLLLLLLLLLLLLLKKKOOOOOOPPPQQQPPPOOONNNMMMOOOPPPRRRTTTUUUTTTSSSRRRSSSQQQOOOLLLJJJIIIIIIHHHIIIHHHHHHJJJLLLNNNMMMMMMNNNMMMMMMLLLLLLMMMMMMNNNKKKLLLMMMNNNOOONNNNNNMMMKKKLLLMMMKKKJJJJJJLLLMMMIIIIIIHHHHHHIIIKKKLLLMMMLLLIIIGGGGGGIIIIIIGGGDDDBBBBBBBBBBBBAAA@@@???>>>AAA@@@>>>===;;;:::::::::777999:::<<<<<<;;;:::999777777888999999999999888888777444222222333555777444333222222222222333444999888666555444444444555333333111///,,,,,,...000......------------..............................//////.........---------++++++------------++++++++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,***++++++,,,,,,++++++***++++++------------++++++++++++,,,---.........---.........------,,,,,,,,,,,,------......------,,,////////////////////////000...,,,,,,------,,,+++---------............///---------......000111111......////////////...............///////////////000000000000////////////---.........//////000000111111111111111000//////---------............///000000//////.........---////////////////////////.........////////////000...............---------000000000000111111111111333222222222111000000000000000000000000000000000////////////000000000000111111111111222333444555666666555333333333333333777666555444444444444444555444333333444555777888888888777777777777777777666666666666666666666666888888999:::;;;;;;;;;;;;%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&''''''''''''&&&%%%%%%''''''&&&%%%$$$%%%%%%&&&&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&)))(((&&&%%%$$$%%%&&&''''''''''''''''''&&&%%%%%%''''''&&&&&&&&&&&&''''''((('''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&&&&''''''%%%&&&&&&&&&'''(((((((((''''''''''''(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))++++++******++++++,,,---++++++++++++++++++++++++,,,,,,,,,---------......---...///000111222333333111111111222222222333333333333333444444444444555444444444444444444555555555555555555666666666666555666666666777777888888888999999:::::::::999999;;;;;;;;;;;;<<<===>>>>>>AAABBBBBBBBBBBBCCCCCCCCCCCCCCCDDDDDDDDDEEEEEEEEEHHHGGGFFFEEEDDDDDDDDDDDDEEEFFFHHHJJJJJJHHHFFFEEEGGGHHHIIIHHHGGGGGGHHHJJJKKKKKKLLLLLLLLLLLLKKKKKKJJJJJJKKKLLLLLLLLLLLLLLLOOOOOOPPPPPPPPPOOONNNMMMOOOPPPRRRTTTUUUTTTSSSRRRRRRPPPNNNKKKIIIHHHHHHHHHIIIHHHGGGIIIKKKMMMMMMMMMNNNNNNMMMMMMMMMMMMNNNNNNLLLMMMNNNOOOOOOOOONNNMMMLLLMMMMMMLLLJJJHHHIIIJJJHHHGGGGGGGGGGGGIIIKKKLLLKKKIIIGGGGGGIIIIIIGGGDDDBBBBBBBBBBBBAAA@@@??????@@@???>>><<<;;;:::::::::;;;<<<======<<<:::888666777777888999999999999888888666444222222333555666555444333222222333444555888777666555444444444444555555333111......000222......------------..............................///.........------------+++,,,,,,------,,,,,,+++++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,+++++++++,,,,,,,,,,,,,,,,,,+++,,,,,,------......------,,,,,,,,,++++++*********,,,,,,------------,,,,,,........................///...,,,,,,------,,,+++------------............,,,,,,,,,,,,---...///000......////////////......------....../////////000000000000/////////......//////////////////000000//////000000///......---------------............000/////////.........---........................,,,,,,---------.........111111111111111000000000//////000000000111111111222222111111111111111111000000000000000000000000////////////000000000000111111111111222333444444555555444444333333333444555555444333333333333333444444333333444666777888888888888888888888888888777777777777777777777777888888999:::;;;;;;;;;;;;%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%''''''&&&%%%$$$%%%&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&'''$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&%%%$$$)))(((((((((((((((((()))(((((('''&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''''''''''''''''''''((((((((((((''''''((())))))***++++++((((((((((((((((((((((((++++++******++++++,,,---++++++++++++++++++++++++......------,,,,,,++++++......//////000111222222111111111222222222222333111222444555555555444333222222333333444444555555444555555555555666666666666666777777777777777777;;;;;;:::999999999999:::<<<;;;::::::;;;<<<>>>@@@AAAAAA@@@@@@@@@AAACCCCCCDDDEEEEEEEEEEEEFFFFFFFFFGGGGGGFFFEEEEEEDDDEEEEEEGGGHHHIIIIIIIIIIIIHHHGGGHHHIIIIIIIIIGGGFFFGGGIIIJJJJJJKKKKKKKKKKKKJJJJJJIIIIIIJJJLLLMMMMMMMMMMMMOOOOOOOOOPPPOOONNNNNNMMMOOOPPPRRRSSSTTTTTTSSSRRRQQQPPPMMMKKKIIIGGGGGGGGGJJJHHHGGGGGGJJJLLLMMMMMMOOONNNNNNMMMMMMNNNNNNOOOMMMNNNOOOPPPPPPOOONNNMMMKKKLLLMMMLLLIIIGGGFFFFFFFFFEEEEEEDDDEEEFFFHHHIIIIIIHHHGGGGGGHHHHHHFFFDDDCCCCCCCCCCCCBBBAAA@@@??????>>>===<<<;;;:::::::::;;;<<<<<<<<<;;;999777666777777888999999999999888888666444333222333555666555555444444444444555555666666666666555444333333444444333111///...000111......------------..........................................------------+++,,,,,,------,,,,,,+++++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,------,,,,,,+++,,,,,,++++++++++++,,,,,,............------------//////............------,,,,,,------------,,,,,,------------------------///---++++++,,,---,,,+++------------............++++++++++++,,,---...///......////////////......,,,,,,---...///000000111000////////////.........//////////////////......---------...------,,,+++------------............/////////.......................................++++++++++++,,,,,,,,,,,,111111111111111111111111//////000000000000111111000000111111111111111111000000000000000000000000////////////000000000000111111000111111222333444333333333444444444555555444444333222222222333333333333444444555777888999999999999999999999999999888888888888888888888888888888999:::;;;;;;;;;;;;%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%%%%%%%%%%%%%&&&%%%$$$%%%'''''''''%%%######%%%&&&''''''''''''&&&&&&&&&''''''&&&&&&&&&######$$$$$$$$$%%%%%%%%%'''''''''''''''''''''''')))(((''''''''''''((((((&&&&&&'''''''''&&&&&&%%%))))))(((((((((((())))))''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&&&&'''''''''''''''''''''&&&&&&&&&''''''''''''((((((((((((''''''(((((()))*********))))))))))))))))))))))))++++++******++++++,,,---++++++++++++++++++++++++...------,,,,,,+++++++++......//////000111111222111111111111222222222222000222444555555555333222111111222222333444555555444444444555555555666666777777777777777777777777<<<;;;:::999999:::;;;<<<>>><<<:::999:::<<>>>>>>>>@@@BBBDDDEEEEEEFFFFFFFFFGGGGGGGGGEEEEEEDDDDDDEEEFFFGGGGGGHHHHHHGGGGGGGGGGGGHHHHHHHHHIIIJJJIIIGGGFFFFFFGGGHHHIIIIIIJJJJJJIIIIIIHHHHHHIIIJJJLLLMMMNNNNNNNNNOOOOOOOOOOOONNNNNNMMMMMMOOOPPPQQQRRRSSSSSSSSSSSSRRRQQQNNNKKKIIIHHHHHHHHHJJJHHHFFFGGGIIIKKKLLLLLLNNNNNNMMMMMMMMMMMMNNNNNNMMMMMMNNNOOONNNMMMLLLKKKHHHJJJLLLLLLIIIFFFEEEDDDDDDDDDCCCBBBCCCDDDEEEFFFHHHHHHHHHHHHHHHFFFEEECCCCCCCCCCCCBBBBBBAAA@@@???======<<<;;;:::::::::;;;777888999:::::::::999999777777888999999999999888777666555333333444555555555555555555555555555555444555555666555444333222222222222000---,,,---///......------------..............................------------------------,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,,,,------++++++++++++++++++++++++++++++,,,,,,,,,,,,------,,,,,,------------,,,,,,---,,,+++******+++,,,---//////...------,,,,,,,,,/////////...............,,,,,,,,,------,,,,,,,,,++++++++++++++++++++++++...,,,++++++,,,---,,,,,,,,,,,,---------.........,,,,,,,,,,,,,,,---......---......//////......---++++++,,,---///000111111/////////.........------//////......------,,,,,,,,,,,,---------,,,,,,+++,,,,,,---------.........................................................***++++++++++++,,,,,,,,,............////////////////////////000000000111//////000000111111222222000000000000000000000000////////////000000000000000000000000111222333444111222333444555555555555444444333333333333333444333333444555777888999:::999999:::::::::::::::;;;999999999999999999999999888888999:::;;;;;;;;;;;;%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%$$$$$$&&&%%%$$$%%%'''((('''&&&""""""###%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%#########$$$$$$$$$%%%%%%''''''''''''''''''''''''(((((('''''''''(((((((((&&&''''''(((((((((''''''(((''''''&&&&&&''''''(((&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&&&&'''''''''''''''''''''&&&&&&&&&''''''''''''((((((((((((((((((((((((((((((((((((************************++++++******++++++,,,---+++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,.........///000000111111000000111111111222222222000111333555555444333222111111222222333444555555444444444444555555555555777777777777888888888888:::999999999:::<<<>>>@@@>>><<<;;;::::::===???AAA@@@???>>>===>>>@@@BBBDDDFFFFFFFFFFFFGGGGGGGGGGGGFFFFFFEEEEEEEEEEEEEEEFFFHHHGGGFFFEEEEEEFFFGGGHHHGGGIIIJJJJJJHHHFFFFFFGGGHHHHHHIIIIIIIIIIIIHHHHHHHHHIIIJJJLLLMMMNNNNNNNNNOOOOOONNNNNNMMMMMMMMMMMMOOOPPPQQQQQQRRRSSSSSSSSSTTTRRRPPPMMMKKKJJJIIIIIIKKKIIIGGGHHHJJJKKKLLLKKKLLLLLLKKKKKKKKKKKKLLLLLLJJJKKKLLLMMMMMMLLLKKKJJJEEEGGGJJJJJJIIIGGGFFFFFFDDDCCCBBBAAABBBCCCDDDEEEFFFGGGHHHHHHGGGEEEDDDCCCBBBBBBBBBBBBAAA@@@???>>><<<;;;:::::::::::::::;;;666666777888888888888888777777888999999999999888777666555444444444444555555555555555555555555555333333444555555444222111111222222000...------.........------------..............................,,,,,,------------------,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,,,,------+++++++++++++++++++++++++++++++++,,,,,,---------+++,,,,,,------,,,,,,+++,,,,,,***))))))***,,,,,,///...---,,,++++++,,,,,,)))))))))***************+++,,,,,,,,,,,,,,,,,,+++++++++++++++++++++++++++---,,,******,,,------,,,,,,,,,,,,------------...------------------...///------............------***+++,,,---...///000111............---------------------,,,,,,+++++++++,,,------.........------,,,,,,,,,------------...---------.......................................,,,,,,,,,,,,------------,,,,,,,,,---------.........////////////000000000/////////000000111111222////////////////////////////////////000000000000000000000000111222333333000111333444555666666555555555444444444444555555444444555777888999999999999999:::::::::;;;;;;;;;999999999999999999999999888888999:::;;;;;;;;;;;;%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%'''((('''&&&""""""###$$$%%%%%%%%%%%%$$$%%%&&&''''''&&&%%%$$$######$$$$$$$$$%%%%%%%%%''''''''''''''''''''''''&&&''''''''''''(((((((((&&&'''(((((()))((((((((('''&&&&&&%%%%%%&&&&&&'''%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((************************++++++******++++++,,,---++++++++++++++++++++++++)))******+++,,,------............//////000000000000000000111111111111222000111333444444444333222222222333333444444555555333444444444444555555555666666777888888999999:::888888999:::<<<>>>@@@AAA===<<<;;;;;;<<<===???AAA??????>>>>>>???AAACCCDDDEEEFFFFFFFFFFFFGGGGGGGGGJJJIIIGGGEEEDDDCCCCCCBBBGGGFFFFFFEEEEEEFFFFFFGGGFFFHHHJJJJJJIIIGGGGGGGGGHHHHHHIIIIIIIIIIIIHHHHHHIIIIIIJJJLLLMMMMMMMMMMMMOOOOOONNNMMMMMMMMMMMMNNNPPPPPPPPPQQQQQQRRRSSSSSSTTTSSSPPPNNNLLLJJJJJJJJJKKKJJJIIIJJJLLLMMMLLLKKKJJJIIIIIIHHHHHHIIIIIIJJJHHHIIIJJJKKKLLLKKKKKKJJJEEEGGGIIIIIIHHHGGGGGGGGGDDDCCCBBBBBBBBBCCCDDDEEEDDDFFFHHHHHHFFFDDDCCCBBBAAAAAAAAAAAA@@@???>>>===::::::999999999:::;;;;;;:::999999888777666555555777777888999999999999888666666555444444444444444444444555555555555444444222333333444333333222222333444444333000//////000......------------..............................,,,,,,,,,,,,---------------,,,,,,++++++,,,,,,---++++++,,,,,,,,,,,,------++++++++++++++++++++++++***++++++,,,,,,------...***++++++,,,,,,++++++***++++++************++++++------+++******+++,,,,,,)))***************++++++++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++---+++******,,,------,,,,,,,,,,,,,,,------------......------------......------............------++++++,,,---...//////000......---------,,,,,,,,,,,,,,,,,,,,,,,,+++++++++------......//////......,,,,,,,,,,,,---------------------------.........------------------------------------............---------......//////000......////////////000000//////000000000000000000////////////////////////////////////000000000000000000///000000111222333000222333555666666555555555555444444444555666666555666777888999999999888888999999::::::;;;;;;<<<999999999999999999999999888888999:::;;;;;;;;;;;;%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$#########$$$%%%%%%%%%&&&%%%$$$$$$%%%'''(((((('''$$$$$$%%%%%%%%%%%%%%%$$$%%%&&&'''(((((('''&&&%%%$$$$$$$$$$$$%%%%%%%%%&&&''''''''''''''''''''''''%%%%%%&&&'''''''''''''''%%%&&&''''''(((((((((''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%&&&''''''&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&&&&''''''%%%&&&&&&&&&'''(((((((((''''''''''''((((((((((((&&&&&&''''''((()))))))))************************++++++******++++++,,,---++++++++++++++++++++++++)))******+++,,,,,,------.........///////////////000000000000111111111111111222222222222333333333444444444444444444555555333333444444444555555555555555666777999:::;;;;;;999999;;;<<<>>>>>>??????<<<<<<<<<<<<===>>>???@@@>>>>>>???@@@AAABBBCCCCCCEEEEEEEEEFFFFFFFFFFFFGGGGGGFFFEEEEEEEEEEEEEEEEEEGGGGGGGGGGGGGGGGGGGGGGGGEEEGGGJJJJJJIIIHHHGGGHHHHHHHHHIIIIIIIIIIIIHHHHHHJJJJJJKKKLLLLLLLLLLLLLLLOOOOOOMMMLLLLLLLLLMMMNNNPPPPPPPPPPPPQQQRRRSSSSSSTTTRRRPPPMMMKKKJJJIIIIIIJJJJJJKKKMMMNNNNNNLLLJJJGGGFFFFFFEEEEEEFFFFFFGGGGGGHHHJJJLLLLLLMMMLLLLLLHHHIIIJJJIIIGGGFFFFFFGGGEEEEEEDDDCCCCCCCCCDDDEEECCCFFFIIIIIIFFFCCCBBBBBB??????@@@??????>>>===<<<999999888999999:::;;;;;;<<<;;;:::999888777777666777777888999999999999888666666555555444444444444222333444555555444333222333333222222222222333333222444444333111/////////......------------..............................++++++,,,,,,,,,------------,,,,,,++++++,,,,,,---++++++,,,,,,,,,,,,------******************************+++,,,,,,---......)))******++++++******)))******++++++++++++******+++***)))((((((***+++,,,,,,,,,,,,------.........++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++,,,***)))***,,,------,,,++++++,,,,,,,,,---------------,,,,,,,,,,,,,,,---,,,------......------,,,,,,,,,,,,------.........---------,,,,,,,,,,,,+++---------------.........,,,,,,---...............++++++,,,,,,,,,---------,,,,,,,,,------.........------------------------------------............------......///000000111........./////////000000000000000000000/////////////////////////////////////////////000000000000/////////000000111222333111222444555666555444333444333333333444444555666777777888999999999888777888888888999:::;;;;;;;;;999999999999999999999999888888999:::;;;;;;;;;;;;%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$""""""###$$$%%%%%%&&&&&&%%%$$$$$$%%%'''(((((('''&&&&&&&&&'''&&&&&&%%%%%%&&&'''(((******((('''&&&$$$$$$%%%%%%%%%&&&&&&&&&(((((((((((((((((((((((($$$$$$%%%&&&'''''''''&&&$$$%%%%%%&&&'''''''''&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&'''((()))&&&''''''''''''''''''&&&'''''''''&&&&&&'''''''''%%%%%%&&&&&&'''((())))))''''''''''''((((((((()))$$$%%%&&&'''(((***++++++))))))))))))))))))))))))++++++******++++++,,,---++++++++++++++++++++++++++++++++++++++++++,,,,,,.........///////////////000000000000111111111111222222111111111222333444555555555555555555444444333333333444444444555555444555666777999;;;<<<===:::;;;===>>>>>>>>>===<<<<<<<<<======>>>?????????===>>>@@@AAACCCCCCCCCCCCDDDEEEEEEEEEEEEFFFFFFFFF@@@AAABBBDDDFFFHHHKKKLLLGGGHHHHHHIIIIIIHHHHHHGGGDDDFFFIIIJJJJJJHHHHHHHHHHHHIIIIIIJJJJJJIIIIIIHHHKKKKKKLLLLLLLLLLLLLLLKKKPPPOOOMMMLLLLLLLLLMMMNNNPPPPPPPPPPPPPPPQQQSSSSSSSSSQQQOOOLLLJJJIIIIIIHHHJJJKKKLLLOOOPPPOOOLLLIIIEEEEEEDDDDDDDDDDDDEEEEEEGGGHHHJJJLLLNNNNNNNNNNNNKKKLLLKKKIIIFFFEEEEEEGGGFFFFFFDDDDDDCCCDDDEEEFFFBBBEEEIIIIIIFFFBBBBBBBBB?????????>>>>>>===<<<;;;888888888888999:::;;;;;;::::::999999::::::;;;<<<777777888999999999999888666555555555555444444444222222333444444333222222333333111111111222333444000222222111///---------.........------.................................+++++++++,,,,,,---------------++++++++++++------++++++,,,,,,,,,---------******************************+++,,,,,,---......))))))************)))))))))***+++,,,,,,+++***)))***)))((('''((()))+++---*********++++++,,,,,,,,,+++++++++,,,,,,+++++++++++++++++++++++++++++++++,,,***)))***+++------,,,++++++,,,,,,,,,---------,,,,,,++++++***+++++++++,,,------......------,,,---------------------------------,,,,,,,,,++++++---......//////000000000+++,,,------............++++++,,,,,,,,,---------,,,,,,,,,------.........------------------------,,,,,,------------......,,,,,,------...//////000............/////////000111111000000//////......////////////////////////////////////000000000000////////////000111222333111222444666666555444333222222222222333333444555888888999:::999888777666777777888999999:::;;;;;;888888888888888888888888888888999:::;;;;;;;;;;;;&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$###&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''(((&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$&&&&&&'''(((((('''&&&&&&%%%%%%%%%%%%%%%&&&'''(((((('''%%%$$$###$$$%%%%%%%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''&&&%%%$$$###$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((''''''&&&(((((((((((())))))))))))&&&''''''((()))******+++***++++++,,,,,,++++++*********+++++++++,,,,,,,,,............////////////000000000000////////////---...///111111222222222333333222222222222222333666444333222222333555666444555555555555555444444555666777888999:::::::::999999888888999:::<<<===;;;;;;;;;<<<===>>>??????>>>???AAABBBCCCBBBAAAAAAAAAAAABBBBBBCCCDDDDDDEEEBBBAAA@@@???@@@BBBDDDFFFJJJJJJJJJJJJIIIHHHGGGFFFGGGGGGGGGHHHIIIJJJKKKLLLLLLKKKIIIHHHGGGFFFFFFFFFKKKLLLMMMNNNNNNMMMLLLKKKPPPOOONNNLLLKKKKKKKKKKKKJJJKKKMMMNNNOOOPPPPPPQQQQQQNNNKKKIIIHHHIIIKKKMMMMMMLLLLLLLLLLLLKKKHHHEEEGGGEEEDDDDDDEEEEEEDDDCCCFFFFFFGGGJJJMMMOOOOOONNNNNNLLLJJJHHHGGGFFFGGGGGGFFFEEEDDDCCCCCCDDDEEEFFFFFFEEEDDDCCCAAA@@@???>>><<<<<<;;;::::::999999888999999999:::;;;<<<===>>><<<<<<<<<<<<;;;:::999999555666888999:::;;;;;;;;;888888777666555444333333333222222111111222222333555555444333222222222222222222000///..................------------..............................++++++++++++++++++++++++++++++,,,,,,,,,,,,------,,,,,,+++******+++,,,,,,******+++,,,,,,,,,,,,+++++++++******************++++++************++++++***++++++,,,,,,++++++***,,,+++++++++***)))))))))++++++++++++++++++++++++******+++++++++,,,,,,,,,,,,++++++******++++++,,,,,,***''''''(((******************++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,.........------,,,,,,,,,,,,,,,,,,---------.........---,,,+++,,,---...//////...---,,,,,,,,,,,,,,,,,,,,,,,,++++++*********++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,++++++------------++++++,,,,,,,,,++++++*********+++,,,------......------000000//////......---------......///////////////////////////000000000000////////////////////////000111111111111222222222333333333444444444555555555555555555666777999999555999<<<;;;666333444777888888888777777777666666;;;;;;:::999999:::;;;<<<888888888999999:::::::::&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&%%%$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&%%%&&&&&&''''''((('''&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''')))((('''%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))(((((((((((((((((())))))))))))((((((((())))))******+++***++++++,,,,,,++++++*********+++++++++,,,,,,,,,------------..................//////000000000111...///000111111111111111222111111111111111222333555444222222222444666777666666777777666666555555555666777888::::::;;;;;;:::999999999999;;;<<<===:::::::::;;;;;;<<<<<<<<<>>>>>>@@@AAAAAAAAA@@@@@@BBBBBBCCCCCCDDDEEEEEEFFFBBBAAAAAAAAACCCEEEHHHJJJJJJIIIIIIIIIIIIHHHHHHHHHHHHGGGGGGHHHHHHJJJKKKKKKKKKJJJIIIHHHGGGFFFFFFFFFJJJKKKLLLMMMMMMMMMLLLLLLOOONNNMMMKKKJJJJJJJJJJJJJJJKKKLLLNNNOOOPPPPPPPPPOOOMMMJJJHHHGGGHHHJJJLLLMMMLLLKKKKKKKKKKKKIIIGGGHHHFFFDDDCCCDDDEEEDDDDDDFFFFFFGGGIIILLLNNNNNNMMMMMMLLLJJJHHHFFFFFFFFFFFFEEEDDDCCCCCCCCCCCCDDDEEEDDDCCCBBBAAA???>>>======<<<;;;;;;:::999999888888;;;;;;:::999999999999:::;;;;;;;;;;;;;;;;;;::::::999999999999999:::::::::999888777666555444333333333333333333333333333333333333222222222333333444222111000///..................------------..............................+++++++++++++++++++++++++++++++++,,,,,,,,,------,,,++++++******++++++,,,***+++++++++***))))))(((************************++++++************++++++***++++++,,,,,,++++++***++++++******************++++++++++++++++++++++++*********+++++++++,,,,,,,,,++++++******++++++,,,---***(((''')))***++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,++++++++++++,,,,,,,,,,,,------------...---,,,+++++++++,,,,,,......---,,,,,,,,,,,,,,,,,,,,,,,,+++++++++******+++++++++,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,------,,,++++++,,,,,,,,,+++++++++******+++,,,------......------////////////............------...///////////////.../////////000000000000////////////////////////000000111111111222222222333333333444444444444555444444444444555666777888888<<>>;;;;;;;;;;;;<<<<<<<<<<<<===>>>??????@@@?????????CCCCCCCCCDDDEEEEEEFFFFFF@@@@@@@@@AAACCCFFFIIIKKKIIIHHHGGGGGGGGGHHHJJJKKKHHHGGGGGGHHHHHHIIIJJJKKKKKKJJJIIIGGGFFFFFFFFFFFFHHHIIIJJJKKKLLLMMMMMMMMMNNNMMMLLLJJJIIIIIIHHHHHHIIIJJJKKKMMMNNNOOOPPPPPPNNNLLLIIIGGGGGGGGGIIIKKKMMMKKKIIIIIIJJJKKKKKKKKKKKKHHHDDDBBBCCCDDDEEEEEEFFFEEEFFFIIIKKKMMMMMMLLLKKKJJJIIIGGGFFFEEEEEEEEEDDDCCCCCCBBBBBBCCCCCCDDDBBBAAA@@@???>>><<<<<<;;;;;;;;;::::::999999888888::::::999888888888888999999::::::;;;;;;;;;;;;:::<<<;;;:::999888888999:::999888777777666555444444222333444555555444333222111111111222222333555555111111000///..................------------......------------------------++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,+++************+++,,,+++++++++***)))(((&&&%%%************************++++++************++++++******++++++++++++******))))))******************++++++++++++++++++++++++*********++++++++++++,,,++++++************++++++---+++))))))***+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++************++++++,,,,,,,,,---------------,,,+++************------,,,,,,++++++,,,,,,,,,,,,,,,++++++++++++***++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,++++++,,,,,,,,,++++++++++++***+++,,,------......------.............../////////------...////////////........./////////000000000////////////////////////000000000111111111222222333333333333444444444444333333333333444555666666999;;;>>><<<999777888:::999999999888888888777777222222222333555666888999999999999:::::::::::::::&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''(((((((((((()))(((&&&%%%%%%&&&((())))))(((((('''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''''''''((((((%%%%%%&&&&&&&&&&&&&&&&&&%%%&&&'''((())))))))))))(((((((((((())))))))))))))))))((((((((((((((((((******++++++++++++************+++++++++,,,,,,,,,,,,,,,,,,,,,------------------......///000000111000111111111111000000//////......//////000111222222222222222444555777888777777888888777777666555444555777999:::<<<<<<<<<;;;::::::999:::<<<===>>>??????>>>>>>>>>>>>>>>>>>>>>?????????????????????BBBCCCCCCCCCDDDDDDDDDEEE@@@?????????AAACCCFFFHHHHHHGGGFFFEEEGGGIIIKKKMMMHHHGGGGGGGGGHHHIIIIIIJJJJJJIIIHHHGGGFFFFFFFFFFFFFFFGGGHHHJJJKKKLLLMMMNNNLLLLLLJJJIIIHHHGGGGGGGGGGGGHHHJJJLLLMMMOOOOOOOOONNNLLLJJJHHHGGGHHHIIIKKKLLLJJJGGGGGGIIILLLMMMNNNMMMIIIEEEBBBCCCEEEFFFFFFFFFFFFFFFHHHKKKLLLKKKJJJJJJIIIHHHGGGEEEDDDCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBAAA@@@???>>>===<<<;;;;;;;;;;;;;;;:::999999888888777777888888999;;;<<<===888999:::;;;;;;;;;;;;;;;===;;;999888777888:::;;;888888777666666555444444222333555666666555333222222222111111222333333444111000///..................------,,,,,,------...------------------------++++++++++++++++++++++++***++++++++++++,,,,,,,,,++++++************++++++************)))((('''&&&***************+++++++++++++++************++++++******++++++++++++******(((((())))))******++++++************************************++++++++++++++++++************++++++---+++******+++,,,,,,+++---------,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++******++++++++++++,,,,,,,,,,,,,,,,,,++++++++++++++++++,,,,,,++++++++++++,,,,,,++++++++++++++++++++++++***++++++++++++,,,,,,,,,+++++++++++++++++++++++++++++++++,,,,,,++++++++++++++++++++++++++++++++++++,,,------......---------------....../////////,,,---......//////.............../////////000000////////////////////////000000000000111111111111222222333333333444444444444444333333444555666666666888999888666444555777666666666555555555444444444444444555666888999999999999999:::::::::::::::&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''(((((((((((()))(((&&&%%%%%%&&&((())))))((('''&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''(((((((((((((((''''''(((((((((((())))))))))))'''''''''''''''''''''&&&)))******++++++******)))******+++++++++,,,,,,,,,,,,------------........./////////...............000111111111111000000/////////......///000000111111111222333444555777777555666666777777666666555555666777999;;;<<<<<<<<<::::::999999:::;;;===>>>??????????????????>>>>>>@@@@@@@@@?????????@@@@@@AAAAAABBBBBBBBBBBBCCCCCCBBBAAA@@@@@@@@@BBBDDDEEEFFFFFFEEEEEEFFFIIILLLNNNHHHHHHGGGGGGGGGHHHIIIIIIIIIHHHHHHGGGFFFFFFFFFFFFEEEFFFGGGHHHJJJKKKMMMNNNLLLKKKJJJHHHGGGGGGFFFFFFFFFGGGIIIKKKMMMNNNOOOOOOOOOMMMKKKJJJIIIJJJJJJKKKLLLIIIGGGFFFIIILLLNNNOOONNNKKKFFFDDDEEEGGGHHHHHHGGGFFFGGGHHHKKKKKKKKKIIIIIIIIIHHHGGGFFFDDDCCCBBBAAAAAABBBBBBBBBBBBAAAAAAAAAAAA@@@???>>>======<<<<<<<<<;;;;;;:::999999999999999999999:::<<<===>>>888888999:::;;;;;;;;;;;;:::999888777777888:::<<<777777666666555555444444222333555666666555333222444333222222111111111111000//////...............------,,,,,,,,,,,,------------------------------++++++++++++++++++++++++*********+++++++++,,,,,,************************))))))***************)))))))))*********+++++++++++++++************++++++)))******++++++******)))((((((((())))))******+++************************))))))*********++++++++++++******))))))******+++---+++******,,,,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,*********+++++++++,,,,,,******++++++,,,,,,,,,,,,++++++*********++++++,,,++++++++++++++++++++++++*********+++++++++,,,,,,+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,------......------,,,,,,------......//////,,,------...........................//////////////////////////////////////////000000000111111111222222222333333333444444555555555444555555666666555555555555444333444555555555555444444444333333666666777777777777777777999999999999999999999999&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&'''''''''%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%&&&'''''''''''''''((('''&&&%%%%%%&&&'''(((''''''&&&%%%%%%%%%&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&%%%%%%%%%$$$%%%%%%&&&&&&'''''''''((((((((((((((('''&&&&&&(((((((((((())))))))))))''''''''''''''''''''''''))))))************))))))******+++++++++,,,,,,,,,------------............/////////.........------///000000111111111000000000000////////////000000111222333444444555666666444444555666777777777777666777999:::;;;;;;;;;;;;999999888888999:::<<<===============>>>>>>>>>>>>AAAAAA@@@?????????@@@@@@AAAAAAAAAAAAAAAAAAAAAAAAFFFEEECCCBBBBBBCCCEEEFFFEEEEEEEEEFFFGGGIIIKKKLLLHHHHHHGGGGGGGGGGGGHHHHHHHHHHHHGGGFFFFFFFFFFFFFFFEEEEEEFFFGGGHHHJJJLLLMMMLLLKKKJJJHHHGGGGGGFFFFFFDDDFFFGGGJJJLLLMMMNNNNNNOOONNNLLLKKKJJJJJJKKKKKKLLLIIIGGGGGGIIILLLNNNOOONNNLLLHHHGGGHHHJJJKKKKKKHHHHHHHHHIIIKKKLLLJJJIIIIIIIIIIIIHHHFFFEEECCCBBBAAABBBBBBCCCCCCBBBBBBAAAAAAAAA@@@@@@???>>>>>>=========<<<<<<;;;:::::::::===<<<;;;;;;::::::;;;;;;888999999::::::::::::999888777666666777888999:::555555555444444444333333222333444555555444333222444444222111111000000000//////......---......///------,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++************++++++++++++))))))***++++++***))))))((()))******+++++++++***)))))))))***++++++,,,,,,++++++************++++++))))))************))))))(((((())))))))))))))))))************************)))))))))************+++******))))))))))))******,,,*********+++,,,+++************++++++,,,,,,,,,+++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,))))))*********+++++++++))))))***++++++++++++*********))))))******++++++***++++++++++++,,,,,,,,,************++++++++++++++++++++++++++++++++++++++++++************++++++***++++++++++++,,,,,,,,,+++,,,------......---------------------.........,,,,,,---............---------.........//////////////////////////////////////////000000000111111222222222222333333333333666555555555555555666666666555555444444555555666666666666555555555444444555555666666666666555555888888888888888777777777&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%&&&''''''(((&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%''''''''''''''''''''''''%%%%%%$$$$$$$$$%%%%%%&&&###$$$&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&&&&%%%$$$$$$$$$%%%%%%&&&''''''(((&&&'''((((((((((((((('''(((((((((((())))))))))))''''''(((((()))*********))))))************))))))******+++++++++,,,,,,,,,+++,,,,,,,,,------------------.....................///000111111111111111222222111000////////////222333333444555555555555333444555777888999::::::888999::::::;;;;;;::::::888888777777888999;;;<<<=========>>>>>>?????????AAA@@@???>>>===>>>>>>???BBBBBBBBBBBBBBBBBBBBBBBBDDDDDDBBBBBBBBBDDDFFFGGGDDDEEEEEEGGGHHHIIIJJJJJJHHHHHHGGGGGGGGGGGGGGGHHHHHHGGGGGGFFFFFFFFFFFFFFFFFFEEEEEEFFFGGGIIIKKKLLLLLLKKKJJJIIIHHHGGGGGGGGGCCCDDDGGGIIIKKKMMMNNNNNNMMMMMMKKKJJJJJJJJJJJJJJJKKKIIIGGGHHHJJJLLLNNNNNNNNNLLLJJJJJJLLLMMMMMMMMMJJJIIIIIIJJJLLLLLLKKKIIIIIIIIIIIIIIIGGGEEECCCBBBAAABBBCCCDDDDDDCCCBBBAAAAAA@@@@@@??????>>>>>>>>>>>>>>>>>>===<<<<<<;;;;;;<<<;;;::::::999999::::::999999:::::::::999999888777777777666666666666666444333333333333222222222333333333333333333333333222222111111111111111222.........------......///---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++************++++++++++++((()))***++++++***)))((()))))))))***))))))((((((((())))))***++++++,,,,,,++++++************++++++))))))************)))))))))))))))))))))(((((((((************************))))))))))))******************))))))))))))*********))))))***++++++***((((((((())))))***+++,,,,,,************************************+++++++++,,,))))))))))))*********+++)))))))))))))))'''&&&%%%)))))))))))))))***++++++******+++++++++,,,,,,,,,************++++++++++++************************,,,+++***))))))***+++,,,******+++++++++,,,,,,,,,+++,,,------......------...------------------,,,+++,,,------......---------------.........//////////////////////////////////////////000000000111111222222222222333333333555555444444444444444555777555444444444555666666555555555555444444444444333444555666777777666666777777777777666666666555&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$###$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%&&&'''(((((('''''''''&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$&&&&&&'''(((((('''&&&&&&############$$$%%%%%%&&&$$$%%%'''(((((((((''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%"""###%%%&&&'''&&&%%%%%%$$$$$$%%%%%%&&&'''((((((%%%%%%'''((())))))******(((((((((((())))))))))))((())))))***+++,,,,,,---))))))************))))))******+++++++++,,,,,,,,,******+++++++++,,,,,,,,,+++,,,,,,---...///000000......///111111222222222444333222000////////////333333444555555444444444333444666888:::;;;<<<<<<999::::::;;;;;;::::::999888777777777777999:::;;;>>>>>>???@@@AAABBBBBBBBB@@@???>>><<<<<<<<<===>>>CCCCCCCCCCCCCCCCCCCCCBBBAAA@@@??????@@@CCCEEEGGGDDDDDDFFFGGGIIIIIIIIIIIIHHHHHHGGGGGGFFFGGGGGGGGGGGGGGGFFFFFFFFFFFFFFFFFFFFFFFFEEEEEEFFFHHHJJJKKKLLLKKKJJJIIIHHHGGGGGGGGGCCCDDDFFFHHHKKKLLLMMMNNNLLLLLLKKKJJJIIIIIIIIIIIIKKKIIIHHHHHHKKKLLLMMMMMMMMMLLLKKKLLLNNNOOOOOONNNKKKJJJJJJKKKLLLLLLKKKIIIIIIJJJJJJIIIHHHFFFDDDBBBBBBBBBCCCDDDDDDCCCBBBBBB@@@@@@??????>>>>>>======?????????>>>======<<<<<<777777777888999:::<<<<<<:::::::::::::::999888777888888888777666444333222333333222222222222222222333222222111111222222333000000000000111222333444......---------......///---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++)))************+++++++++((()))***++++++***)))((())))))))))))((('''%%%%%%((())))))***++++++,,,,,,++++++************++++++))))))************))))))******))))))((((((''''''))))))))))))))))))))))))))))))))))))******************))))))))))))*********)))((()))++++++)))(((&&&&&&''')))***+++,,,---************************(((((())))))*********+++))))))))))))******************)))(((&&&$$$!!!))))))((())))))***++++++*********++++++,,,,,,,,,)))************+++++++++************************,,,+++***))))))***+++,,,*********++++++,,,,,,,,,+++,,,------......------.........------,,,,,,,,,+++,,,------......---------------.........//////////////////////////////////////////000000000000111111222222222333333333444444333222222333333333666444222222333444555555333333333222222222111111222333555777999999999999777777666666555555555444&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&'''&&&$$$"""""""""$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&%%%$$$$$$'''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""""""""###$$$%%%%%%%%%%%%&&&&&&&&&''''''###$$$&&&''''''&&&$$$###''''''''''''''''''&&&&&&((((((((((((((((((((((((((('''%%%$$$$$$%%%'''(((%%%$$$$$$###$$$%%%'''(((%%%%%%%%%%%%&&&((()))***'''''''''&&&&&&%%%%%%%%%$$$%%%'''((((((((('''&&&***)))'''''')))***)))(((******************************))))))(((((('''''',,,+++***))))))***+++,,,+++++++++++++++++++++++++++***))))))***+++---...222222222222222111000000000000000000000111111222333333333333333333333333111222444777999:::::::::<<<<<<=========<<<:::999:::999888888888999:::;;;;;;<<>>>>>>>>>>>BBBBBBCCCCCCBBBBBBAAA@@@DDDCCCAAA@@@??????@@@AAACCCDDDFFFGGGHHHHHHGGGFFFFFFEEEDDDCCCDDDEEEGGGIIIGGGGGGGGGGGGGGGFFFDDDDDDCCCCCCDDDEEEEEEEEEEEEEEEIIIIIIHHHHHHIIIJJJLLLMMMOOOMMMKKKIIIGGGFFFFFFFFFFFFEEEEEEEEEFFFHHHJJJKKKNNNMMMLLLKKKKKKLLLMMMNNNLLLMMMNNNOOONNNMMMLLLKKKJJJJJJJJJKKKKKKKKKKKKKKKHHHHHHGGGFFFEEEEEEEEEEEEBBBBBBCCCDDDDDDCCCBBBAAA??????>>>>>>===<<<<<<<<>><<<::::::;;;<<<===777777888888888999999999:::999999999888777777777666666555444444444444555222222222222222222222222111111111000000000000///............///000111222///............---------++++++******++++++,,,---,,,+++******,,,,,,+++***++++++++++++++++++++++++((((((((((((((()))))))))******))))))))))))******))))))))))))************((((((((((((((((((((((((((()))+++,,,,,,+++)))((()))))))))))))))))))))***(((((()))***************)))))))))))))))(((''''''))))))***++++++++++++***,,,,,,***)))((((((''''''************************))))))))))))))))))))))))((((((((((((((((((((((((************************+++***)))(((((()))***+++******))))))((((((''''''))))))))))))))))))))))))************************))))))))))))))))))))))))******+++++++++,,,,,,,,,************************,,,***)))***+++---,,,,,,,,,,,,,,,---------......---------,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------...///000000---------...............////////////////////////333333222222222222222222000111111222222333444444222222333333333333444444333333333444444333222222444555555555666666777777888888777777666666555555&&&&&&&&&%%%%%%$$$$$$$$$$$$&&&'''&&&$$$""""""###$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&%%%%%%$$$''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%'''(((((('''%%%$$$''''''''''''''''''&&&&&&'''''''''''''''''''''''''''&&&$$$######$$$&&&'''&&&%%%$$$$$$$$$%%%&&&'''&&&&&&%%%%%%%%%&&&&&&&&&'''&&&&&&&&&%%%%%%%%%%%%%%%&&&''''''((('''''''''((((((((('''''''''((()))))))))))))))))))))))))))***)))))))))((((((((('''++++++***))))))***++++++++++++++++++++++++++++++++++++******+++,,,......//////000000///......---000000//////000000111222333333333333333333333333111222444777999:::::::::;;;;;;<<<<<<<<<;;;:::999888888777777777888999:::===>>>???@@@???>>><<<;;;>>>>>>>>>=========<<<<<>>>>>>>>;;;;;;;;;::::::999888888777777777888888888999999888888888888888888777777666555555444444444444444222222222222222222222222111111111111000000000000//////......//////000000------------,,,,,,,,,,,,++++++******++++++,,,---,,,+++******,,,,,,+++***++++++++++++++++++++++++*********++++++,,,,,,,,,******))))))))))))******(((((()))))))))*********((((((((((((((((((((((((((()))+++,,,,,,+++)))(((******))))))))))))))))))(((((((((((()))))))))))))))))))))))))))(((''''''(((((()))************))),,,+++***)))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))************************+++***)))(((((()))***++++++*********))))))))))))))))))))))))))))))))))))************************))))))))))))))))))))))))************+++++++++,,,************************+++)))((()))***+++++++++,,,,,,,,,------------...------,,,,,,,,,+++++++++,,,,,,++++++++++++++++++,,,,,,------...//////000........................////////////////////////000000111111111111111111000111111222222333333444222222222333333333444444222333333333333333222222333333444444444555555555666666666555555555555444&&&&&&%%%%%%%%%%%%$$$$$$$$$&&&'''&&&$$$#########%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&'''$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&((((((((((((&&&%%%&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%############%%%%%%'''&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%###"""!!!&&&&&&%%%%%%%%%%%%$$$$$$'''&&&&&&&&&&&&'''((((((&&&((()))'''%%%$$$''')))(((((((((((((((((((((((())))))))))))((((((((((((++++++***))))))***++++++++++++++++++++++++++++++++++++++++++,,,---...///..................---,,,000000//////000000111222333333333333333333333333111222555777999999999999999::::::::::::999888888777666666666666777888888;;;<<<=========<<<;;;:::=========<<<<<<<<<;;;;;;>>>???@@@AAABBBBBBBBBBBBBBBBBBAAA@@@AAABBBCCCDDDFFFGGGHHHIIIJJJJJJJJJJJJCCCCCCBBBAAAAAABBBDDDEEEGGGGGGGGGFFFFFFEEEDDDCCCCCCCCCCCCDDDDDDDDDDDDDDDGGGHHHIIIJJJJJJJJJIIIHHHJJJIIIHHHFFFEEEDDDDDDDDDCCCCCCCCCDDDEEEFFFGGGHHHHHHGGGGGGGGGHHHJJJLLLMMMPPPPPPPPPPPPNNNLLLJJJIIIIIIIIIIIIHHHHHHGGGGGGGGGHHHGGGEEEDDDCCCBBBBBBBBBAAAAAAAAAAAA@@@>>>===<<>>>>>>>>777888999:::999777555333777777777777888888888888777777777777777777888888555555444333333333333333111111111111111111111111222222111111111000000000000//////...............,,,,,,,,,+++++++++******+++************+++,,,,,,,,,+++******+++,,,+++***))))))))))))))))))))))))&&&''''''((()))******+++***))))))(((((())))))***(((((())))))))))))******((((((((((((((((((((((((((()))***++++++***)))(((*********))))))((((((((()))((('''''''''''''''((()))))))))))))))(((((('''''''''((()))))))))))))))++++++***************+++(((((((((((((((((((((((())))))))))))))))))))))))******************************************************))))))))))))******++++++++++++************))))))))))))))))))))))))************************))))))))))))))))))))))))))))))))))))***************************************((('''((()))+++******,,,,,,,,,,,,------------,,,,,,,,,,,,++++++++++++++++++++++++++++++,,,,,,,,,,,,------...///////////////////////////......000000000000000000000000......//////000000111111000000111111222333333333222222222222333333333333222222222222222222222222222222333333333333444444333333333444444444444555%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&'''&&&%%%######$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$###"""%%%%%%%%%%%%%%%%%%%%%$$$''''''&&&%%%%%%'''((()))###''')))'''###"""%%%***(((((((((((((((((((((((())))))))))))((((((((((((+++******************+++++++++++++++++++++++++++,,,,,,,,,,,,---...//////...//////000//////......///////////////000111111222222333333333333444444111333555777999999999999888888888888888888777777666666666666777777888888777888:::;;;=====================<<<<<<<<<;;;;;;<<<===>>>@@@AAABBBBBBBBBAAAAAA@@@@@@AAACCCDDDEEEFFFGGGGGGHHHIIIIIIJJJJJJCCCCCCBBBBBBBBBCCCCCCDDDFFFFFFFFFFFFEEEDDDCCCBBBCCCCCCBBBCCCCCCCCCDDDDDDDDDFFFHHHJJJKKKKKKIIIHHHKKKJJJIIIHHHGGGGGGFFFFFFCCCCCCCCCDDDEEEFFFGGGHHHFFFEEEEEEFFFHHHJJJLLLMMMOOOOOOOOOOOOOOOMMMKKKJJJJJJJJJIIIHHHGGGFFFFFFFFFFFFFFFEEEDDDCCCCCCCCCCCCAAAAAA@@@???>>>===<<<;;;<<<<<<<<<<<<<<<<<<<<<<<<888999999888777555333222666666666777777777888888555555555666666777777888444444333222222222222222111111111111111111111111222222111111111000000000000///...---,,,,,,,,,,,,,,,,,,+++++++++************************++++++,,,+++***)))***+++,,,+++)))))))))))))))))))))))))))%%%%%%&&&'''(((((()))***))))))(((((((((((())))))(((((((((((()))))))))***(((((((((((((((((((((((((((((()))******)))((((((*********)))((((((''''''***)))((('''''''''(((((((((((())))))))))))(((((('''((())))))******))))))***************+++,,,,,,************************))))))))))))))))))))))))***************************************************))))))))))))))))))***************************))))))))))))))))))))))))************************))))))))))))))))))))))))((((((((()))))))))))))))***************************)))((((((***++++++***++++++,,,,,,,,,---------,,,+++++++++++++++++++++,,,,,,,,,,,,---------------------.........//////000///////////////......////////////////////////------...///000111111111000000000111222222333333111222222222222333333333111111111111111222222333333333333333333333333333222222222333444555555666%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&''''''%%%$$$$$$%%%%%%&&&&&&''''''&&&&&&%%%$$$%%%&&&&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&''''''''''''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''&&&%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%'''((()))###''')))'''###"""%%%)))))))))))))))))))))))))))(((((((((((())))))))))))*********++++++*********++++++++++++++++++++++++++++++,,,---..................////////////....../////////...///000000111222222222333333444444444222333555777888999999888777777777666777777777777777777777888888888888888777777999:::<<<===>>>>>>>>>>>>>>>=========<<<<<<;;;<<<===???@@@AAAAAAAAAAAA@@@@@@@@@AAACCCDDDFFFEEEEEEEEEFFFFFFGGGHHHHHHEEEEEEDDDDDDDDDDDDDDDDDDEEEEEEEEEEEEDDDCCCBBBBBBBBBBBBBBBAAABBBBBBDDDDDD@@@CCCGGGJJJLLLKKKJJJIIIGGGGGGGGGGGGFFFEEEEEEEEECCCCCCDDDFFFGGGGGGHHHHHHEEEEEEEEEFFFGGGJJJLLLMMMKKKLLLMMMNNNNNNNNNMMMLLLJJJJJJJJJIIIHHHGGGFFFFFFEEEEEEDDDDDDDDDEEEFFFFFFBBBAAA@@@???===<<<<<<;;;:::::::::;;;<<<<<<<<<======<<<999777666555555555555555666666666777777777444444444555555666666666333333222111111111111111000000000000000000000000111111111000000000////////////---,,,++++++++++++,,,,,,,,,,,,+++++++++*********))))))******+++,,,+++***))))))++++++***)))(((((((((((((((((((((((((((((()))******+++,,,,,,))))))(((((((((((())))))'''(((((((((((()))))))))((((((((((((((((((((((((((((((((())))))((((((((())))))))))))((((((''''''******))))))((()))))))))(((((())))))))))))((((((((()))******++++++******))))))))))))***+++,,,,,,************************))))))))))))))))))))))))************************)))))))))))))))))))))))))))))))))******)))))))))))))))))))))))))))))))))))))))))))))))))))))))))************************))))))))))))))))))))))))(((((((((((((((((((((((()))))))))))))))))))))))),,,***))))))+++,,,,,,++++++++++++,,,,,,,,,------++++++++++++++++++++++++,,,---------......//////---------...............000/////////.........---------------------------.........///000111222222///000000111111222333333111111111222222222333333111000000000000111222333333333333333333333333333222222333444555666666777$$$$$$%%%%%%%%%%%%&&&&&&$$$&&&''''''%%%$$$%%%&&&&&&&&&''''''''''''&&&&&&$$$%%%&&&''''''(((''''''$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%######$$$$$$%%%'''((()))%%%%%%&&&&&&&&&&&&'''''''''&&&&&&&&&&&&'''((((((%%%'''(((&&&$$$###&&&((())))))))))))))))))))))))(((((((((((()))))))))))))))***++++++++++++***)))++++++++++++++++++++++++***+++,,,---.........---+++,,,------...---------//////......//////000111111222222333333444444555222444555777888999888888666666666555666666777888666777888999999999888888999999::::::::::::;;;;;;>>>>>>>>>=========<<<<<<:::;;;<<<>>>???@@@@@@@@@@@@@@@??????@@@BBBCCCDDDDDDCCCCCCDDDDDDEEEFFFGGGFFFFFFFFFFFFFFFEEEEEEEEEEEEEEEEEEEEEDDDCCCBBBAAABBBBBBAAA@@@AAABBBCCCDDD@@@BBBFFFIIIKKKKKKIIIIIIGGGHHHHHHIIIHHHHHHGGGGGGCCCCCCEEEFFFGGGHHHHHHHHHEEEDDDDDDEEEGGGIIIKKKLLLIIIJJJKKKMMMMMMMMMMMMLLLIIIIIIIIIHHHHHHGGGGGGGGGEEEEEEDDDDDDEEEEEEFFFFFFAAA@@@>>>===<<<<<<<<<<<<:::;;;;;;<<<===>>>??????@@@>>>;;;888666666666777555555555555666666666666444444444444444444555555222222111000000000000000////////////////////////000000/////////............---,,,+++************,,,,,,,,,+++++++++*********))))))))))))***+++++++++***))))))***+++***)))(((((((((((((((((((((((((((((((((((()))))))))))))))((((((''''''(((((()))''''''(((((((((((())))))((((((((((((((((((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((()))***+++*********'''(((((()))))))))))))))))))))***+++++++++++++++))))))(((((()))***++++++(((((((((((((((((((((((())))))))))))))))))))))))************************))))))))))))))))))))))))))))))************))))))((((((((((((((()))))))))))))))))))))))))))))))))************************))))))))))))))))))))))))))))))))))))(((((((((((()))))))))))))))))))))))),,,+++)))***,,,------,,,++++++++++++,,,,,,,,,,,,*********+++++++++++++++,,,,,,------......//////......................../////////...------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,......//////000000111111//////000000111222222222111111111111222222222222000000/////////111222333444444333333333333222222222222333444444555666666$$$$$$$$$%%%%%%&&&&&&&&&$$$&&&''''''&&&%%%%%%&&&&&&&&&''''''''''''&&&&&&$$$%%%&&&'''((((((((((((######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&&&&%%%&&&&&&'''''''''(((((((((&&&&&&%%%%%%%%%%%%&&&&&&###$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&'''((((((''''''&&&$$$###"""!!!###%%%(((***&&&&&&&&&''''''(((((((((%%%&&&''''''((('''''''''''''''&&&&&&&&&&&&''''''(((((((((((((((((((((((('''((((((((()))))))))***)))***++++++++++++***)))++++++++++++++++++++++++)))***+++,,,---------,,,,,,,,,---...............///............///000000111111222333333444555555333444666777888888888888777666555555666777888999555666777888888888777777888777777777888999999:::=========<<<<<<<<<;;;;;;:::;;;<<<===>>>?????????@@@??????>>>???@@@BBBBBBDDDCCCCCCCCCCCCEEEFFFGGGFFFGGGGGGGGGFFFEEEEEEDDDDDDDDDDDDDDDCCCBBBAAAAAABBBAAA@@@???@@@AAACCCDDDCCCDDDFFFHHHIIIHHHGGGFFFHHHIIIJJJJJJJJJJJJIIIHHHAAABBBDDDEEEGGGGGGGGGFFFDDDCCCCCCCCCEEEFFFHHHJJJIIIJJJKKKLLLLLLKKKJJJJJJGGGGGGGGGGGGGGGGGGFFFFFFGGGFFFEEEDDDCCCCCCCCCCCC>>>===<<<;;;::::::;;;<<<999:::;;;<<<===>>>??????@@@???===;;;999777666555444444555555555666666666444444444444333333333333111111000////////////000////////////////////////............---------------,,,+++***************++++++*********))))))))))))))))))))))))***+++++++++)))((()))***+++***((())))))))))))))))))))))))'''&&&&&&&&&&&&%%%%%%%%%((((((''''''''''''(((((('''''''''((((((((())))))(((((((((((((((((((((((((((''''''''''''''''''(((&&&&&&''''''((()))))))))$$$&&&(((+++,,,+++***)))''''''((()))))))))))))))((())))))***************((((((((('''(((((())))))(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((()))***++++++***)))((((((((()))))))))*********))))))))))))))))))))))))************************))))))))))))))))))))))))*********))))))((((((((())))))))))))))))))))))))+++***((()))+++,,,,,,+++***++++++++++++,,,,,,,,,)))*********++++++++++++******++++++,,,------....................................---,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,...................../////////000000111111222222111111111111222222222222000///.........000222333333333222222222111111111111111222222333333444444$$$$$$$$$%%%%%%&&&&&&&&&$$$&&&''''''&&&%%%&&&'''&&&&&&''''''''''''&&&&&&$$$%%%&&&'''((((((((((((#########$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&&&&&&&%%%$$$'''''''''(((((((((((()))(((''''''&&&&&&''''''(((######$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%$$$$$$###$$$%%%'''(((((((((''''''%%%###!!! ###&&&)))'''''''''((((((((())))))$$$%%%'''((((((((('''&&&)))'''%%%&&&'''((('''&&&'''''''''''''''''''''''''''((((((((())))))******)))***+++,,,,,,+++***)))++++++++++++++++++++++++((()))+++,,,------,,,+++......///000111111111000...............///000000111111222333333444555555333444666777888888888777777666555555666777888999333444666777777777666555333333444555777999;;;<<<<<<<<<;;;;;;;;;::::::::::::;;;<<<===>>>>>>>>>>>>@@@???>>>>>>>>>???@@@AAADDDDDDCCCCCCCCCEEEFFFHHHFFFFFFFFFFFFFFFEEEDDDDDDDDDDDDDDDDDDCCCBBBAAA@@@BBBAAA@@@??????AAACCCDDDFFFGGGGGGHHHGGGFFFEEEDDDCCCDDDEEEFFFGGGFFFEEEEEE@@@AAACCCDDDFFFFFFEEEEEECCCBBBBBBBBBCCCEEEFFFGGGJJJJJJKKKKKKKKKJJJHHHGGGEEEEEEEEEEEEFFFFFFFFFFFFHHHGGGEEECCCAAA@@@??????<<<;;;:::999999999:::;;;777777888999;;;<<<======>>>>>>>>>===;;;888444222444444444555555555666666444444444333333222222222111111000///////////////////////////////////////......---------,,,,,,,,,,,,+++******************))))))))))))(((((((((((()))))))))))))))******+++***)))((()))***+++***(((*********************************)))((((((''''''((((((''''''''''''((((((''''''''''''((((((((()))(((((((((((((((((((((((((((''''''&&&&&&''''''(((%%%%%%&&&'''((()))******!!!###'''***,,,+++)))(((''''''((()))))))))))))))'''(((((()))))))))))))))((((((''''''''''''((((((************************))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))((()))***++++++***)))((())))))******+++++++++,,,))))))))))))))))))))))))************************))))))))))))))))))))))))++++++******))))))(((((())))))))))))))))))))))))***)))'''(((***++++++*********+++++++++,,,,,,,,,))))))******++++++++++++(((((()))***++++++,,,,,,.....................---......---,,,,,,+++******---------------------------------------------,,,/////////000111111222222000111111111111222222222//////...---...000222444222111111111000000//////111111111111111222222222((('''&&&&&&$$$$$$###"""$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((())))))&&&&&&&&&''''''''''''(((&&&'''((('''%%%%%%'''((( !!!"""$$$&&&''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$###$$$%%%&&&'''%%%&&&&&&''''''&&&&&&%%%))))))(((((('''&&&$$$$$$''''''''''''''''''''''''%%%&&&((()))))))))(((''''''''''''''''''((())))))((()))***++++++***)))(((++++++,,,,,,,,,,,,------+++,,,---.........------......//////000000111111000000//////......------111111222333333333333222333444666777777777666555555555555666777888888999888888777666666666666666444555777999;;;;;;;;;::::::::::::999999999999888999999999999:::;;;<<<<<>>>>>???@@@AAAFFFFFFEEEEEEDDDDDDCCCCCCDDDDDDDDDDDDDDDDDDCCCBBBAAAAAACCCFFFHHHHHHEEECCCFFFBBB>>>>>>@@@BBBAAA@@@CCCDDDFFFGGGGGGFFFFFFEEEIIIIIIIIIIIIIIIIIIIIIIIIHHHEEEBBBBBBDDDDDDCCC@@@CCCBBBBBBBBBCCCDDDFFFGGGLLLKKKJJJIIIIIIIIIIIIIIIIIIHHHGGGEEEDDDEEEEEEFFFDDDBBB???>>>>>>>>>>>>===>>><<<:::999:::999888777<<<;;;:::999888999::::::<<<;;;::::::;;;:::888666222111111000000111111222444333222111111111222333111111000000//////......,,,,,,,,,------.........//////...---,,,,,,++++++...---,,,,,,++++++,,,,,,((((((((((((((((((((((((***)))(((''''''((()))***************************************************$$$$$$######$$$%%%&&&'''((((((((((((((()))******'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''((())))))((('''''''''''''''(((((())))))******++++++(((((((((''''''((((((((((((''''''&&&&&&&&&''''''((()))*********)))'''&&&&&&&&&''''''''''''&&&&&&(((((())))))((('''&&&&&&******))))))((((((''''''&&&&&&''''''((()))))))))+++++++++************)))((((((((((((''''''''''''))))))(((((((((((())))))))))))(((((((((((())))))++++++***************+++***************************+++---......---+++************)))))))))))))))***************************+++,,,------,,,+++******************+++++++++)))************+++++++++******+++,,,,,,,,,,,,+++***+++,,,,,,------,,,,,,------,,,,,,,,,---......---------............///111111000000//////......222222111111222222333333000000000000000111111222000111333444444333222111222333333444444555555555'''&&&&&&%%%%%%$$$$$$###$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&'''(((((()))&&&&&&&&&&&&''''''''''''&&&'''((('''%%%%%%'''(((&&&&&&&&&%%%%%%$$$###"""&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&'''%%%&&&&&&''''''&&&&&&%%%(((((((((((('''&&&%%%%%%'''''''''''''''''''''''''''((()))*********))))))'''''''''''''''((())))))((()))***++++++***)))(((+++++++++,,,,,,,,,------,,,,,,,,,------------............///000000111111///////////////.........111111222333333333333222333444555666777666666555333333333444555666666666777666666555555555555555333444555666777777888888::::::999999999999999999999999999999:::;;;<<<===BBBAAA@@@??????@@@AAABBBFFFFFFEEEEEEDDDCCCCCCBBBCCCDDDDDDDDDDDDDDDCCCCCCAAAAAACCCFFFIIIIIIGGGEEEGGGDDD@@@???@@@BBBAAA@@@BBBCCCDDDEEEFFFEEEEEEDDDFFFGGGGGGHHHIIIJJJJJJJJJHHHEEECCCCCCDDDDDDCCCAAABBBBBBAAAAAABBBCCCEEEFFFHHHHHHGGGGGGGGGHHHIIIIIIIIIHHHGGGFFFEEEEEEEEEFFFDDDBBB???============<<<===;;;999999::::::999888<<<;;;::::::999999::::::<<<:::999:::::::::888666333333333222222333333333444333222111111111111222000000000///////////////,,,,,,,,,---------......///......---,,,,,,++++++---,,,,,,+++++++++++++++))))))))))))))))))))))))***)))(((''''''((())))))************************************************+++***)))(((((()))+++,,,((((((((((((((())))))***'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''((())))))((('''''''''''''''&&&&&&&&&&&&''''''''''''''''''((((((((((((''''''''''''&&&&&&&&&''''''(((((())))))***)))((('''&&&'''''''''(((((('''''''''((((((((((((((('''&&&&&&))))))))))))((((((''''''((((((((((((((('''''''''*********)))))))))(((((((((((((((((((((((((((((())))))(((((((((((())))))))))))(((((((((((())))))******))))))))))))******************************)))***+++,,,,,,+++***)))))))))))))))))))))))))))************************)))******++++++******)))************************)))************+++++++++******+++,,,,,,,,,,,,+++***+++,,,,,,------,,,,,,,,,,,,,,,+++,,,,,,---...------------............000000000///////////////000000000000000111222333000000//////000000111222111111222333333222111111111111111222333555555666%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%&&&''''''((((((&&&&&&&&&&&&''''''''''''&&&''''''&&&%%%%%%&&&((()))((('''&&&$$$###"""!!!%%%%%%$$$$$$$$$$$$######%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&'''%%%&&&&&&''''''&&&&&&%%%&&&'''''''''''''''&&&&&&''''''''''''''''''''''''&&&'''(((((())))))(((((('''''''''''''''((())))))((()))************))))))++++++++++++,,,,,,,,,,,,---,,,+++++++++,,,...///---......//////000111111...///////////////000000111111222333333333333222333444555666666666555444333333333444555555666666555555555444444444444333777777777777888888999:::999999999999:::::::::::::::::::::::::::;;;======@@@@@@@@@AAABBBBBBCCCCCCEEEEEEEEEDDDCCCCCCBBBBBBCCCCCCDDDEEEEEEDDDDDDDDDAAABBBDDDGGGJJJKKKIIIGGGHHHFFFCCCAAAAAAAAAAAA@@@AAAAAABBBCCCCCCCCCCCCCCCDDDDDDFFFGGGHHHJJJKKKLLLHHHFFFDDDCCCDDDDDDDDDBBBBBBBBBAAAAAAAAACCCDDDEEEDDDDDDDDDDDDEEEFFFGGGHHHIIIIIIGGGFFFFFFEEEFFFFFFDDDAAA>>><<<<<<<<<;;;:::<<<:::999999:::;;;:::999;;;;;;;;;;;;;;;::::::999:::999888888999999777555555555444444444444555555555444333111111000000000//////////////////000000,,,,,,,,,------------.........------,,,,,,++++++,,,++++++***************))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))************************+++)))'''%%%%%%&&&((()))((((((''''''(((((())))))'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''((()))((((((''''''''''''(((&&&&&&&&&&&&%%%%%%%%%%%%&&&'''((())))))((('''&&&&&&&&&&&&&&&&&&'''((())))))))))))))))))((('''''''''(((((())))))(((((('''(((((((((((((((''''''&&&)))))))))(((((((((((('''***))))))(((''''''&&&&&&))))))((((((((('''''''''''''''(((((())))))******))))))(((((((((((())))))))))))(((((((((((())))))))))))(((((((((((())))))************************'''((()))******)))((('''))))))))))))))))))))))))***************************))))))))))))))))))***+++++++++******))))))((()))************+++++++++******+++,,,,,,,,,,,,+++***++++++,,,,,,,,,,,,,,,++++++******++++++,,,---------------................../////////000000000............///000222222000000//////000000111222111111111111111111111111000000111222333444555666$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&'''''''''%%%%%%&&&&&&&&&'''''''''&&&''''''&&&%%%%%%&&&(((&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''((((((''''''''''''''''''''''''''''''$$$$$$%%%%%%%%%&&&&&&&&&'''''''''''''''((())))))((())))))******************++++++++++++,,,,,,,,,---,,,+++******,,,...///------......///000000111......//////000000000111111111222333333333333222222333444555666555444444555555555666666777777777555555555555555444333333999888777666666777999:::999999999::::::;;;;;;;;;::::::::::::;;;<<<===>>>>>>???AAABBBCCCDDDDDDDDDEEEEEEDDDCCCCCCBBBBBBAAABBBCCCDDDEEEEEEEEEEEEEEEBBBBBBDDDGGGJJJLLLKKKIIIIIIHHHEEECCCBBBAAA@@@@@@@@@@@@@@@AAAAAAAAAAAAAAACCCDDDEEEFFFGGGIIIJJJJJJGGGFFFEEEDDDDDDEEEDDDDDDDDDCCCBBBBBBBBBDDDEEEFFFEEEDDDDDDDDDDDDDDDEEEEEEIIIHHHHHHGGGFFFFFFEEEEEECCC@@@===;;;;;;;;;:::999;;;999888888:::<<<;;;;;;:::;;;<<<<<<<<<;;;999888888777666777888777666444555555444444444444555555555444333222111000//////---......//////000000000---------------------------------,,,,,,,,,+++++++++******)))))))))))))))************************((((((((((((((()))))))))))))))))))))))))))))))))************************)))'''$$$!!!!!!"""$$$&&&(((((('''''''''(((((()))'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''((()))(((''''''''''''(((((()))))))))(((((('''''''''%%%&&&((())))))(((&&&%%%%%%%%%%%%&&&'''((()))***)))))))))))))))(((((('''(((((())))))))))))(((((('''(((((((((((((((''''''(((((((((((((((((((((((())))))(((((('''''''''''')))))))))(((((((((''''''''''''(((((()))***++++++))))))(((((((((((())))))))))))(((((((((((())))))(((''''''''''''(((((()))************************'''(((((())))))(((((('''((((((((()))))))))))))))************************+++***)))(((((()))***+++,,,++++++***)))(((((('''))))))*********+++++++++******+++,,,,,,,,,,,,+++******+++,,,,,,,,,,,,+++*********)))***++++++,,,,,,,,,---------.........------......///000000111------......///000222222///////////////000111111111111000000000111222222555444333333333444444555###$$$$$$%%%%%%&&&&&&'''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%&&&'''&&&$$$$$$&&&'''%%%%%%%%%%%%&&&'''((()))%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$%%%&&&'''((((((((((((''''''''''''''''''''''''$$$$$$$$$$$$$$$%%%%%%&&&'''''''''''''''((()))))))))))))))))))))******+++*********+++++++++,,,,,,---,,,*********+++---///---------...//////000000.../////////000000111111111111222333333333333222111222444555555555444333555555555555666666666666555555666666666555444333444333222222222333444555888888999:::;;;;;;<<<<<<;;;;;;;;;;;;<<<===>>>>>>>>>???@@@BBBCCCDDDDDDDDDDDDDDDCCCCCCBBBAAAAAAAAABBBCCCDDDEEEFFFFFFFFFFFFCCCCCCDDDGGGJJJLLLKKKJJJIIIHHHGGGEEEBBB@@@@@@@@@???????????????@@@@@@@@@DDDDDDEEEEEEFFFGGGGGGGGGGGGGGGFFFEEEEEEEEEEEEFFFFFFEEEEEEDDDDDDEEEFFFGGGGGGGGGEEEDDDCCCCCCCCCCCCGGGGGGGGGGGGFFFEEEDDDDDDAAA???<<<;;;;;;<<<;;;::::::999888888:::<<<<<<;;;999:::;;;;;;;;;:::888777666555444555666666444222444444333333333333444444444444333222111///......------......//////000000------------------------,,,,,,,,,,,,,,,++++++++++++***))))))(((((())))))))))))))))))))))))))))))''''''((()))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))+++***'''%%%%%%&&&''')))((((((''''''''''''(((((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''(((((((((''''''''''''((((((+++******))))))(((((((((%%%&&&'''(((((('''&&&%%%%%%%%%%%%&&&'''((()))******))))))((((((((((((((((((((())))))))))))((((((''''''(((((((((((((((''''''''''''''''''(((((((((''''''''''''(((((())))))******)))))))))(((((((((&&&''''''((()))******+++))))))(((((((((((())))))))))))(((((((((((())))))''''''&&&&&&'''((())))))))))))))))))))))))))))))((())))))))))))))))))(((''''''(((((()))))))))))))))))))))))))))))))))))),,,+++***))))))***+++,,,++++++******)))(((''''''))))))*********+++++++++******+++,,,,,,,,,,,,+++)))***++++++,,,,,,++++++******)))))))))***++++++,,,,,,,,,------------...,,,,,,---...///000111111.........//////111222222/////////...///000000111111000//////000222444555;;;:::777555333333333333$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&%%%$$$$$$%%%'''***)))'''&&&%%%&&&&&&'''%%%%%%&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&'''(((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&'''(((((('''''''''''''''((()))))))))((((((((()))***+++,,,************++++++++++++,,,+++*********+++---...,,,------......///000000///000000000000000000111111111222333333333333222111222333444444444333222333333333333333333333333555555666777777555444333444333333333444555555666777888999:::;;;<<<===>>><<<<<<;;;<<<<<<===>>>???>>>???@@@AAABBBCCCDDDDDDCCCCCCCCCBBBAAAAAA@@@@@@AAABBBDDDEEEFFFGGGGGGGGGDDDCCCDDDFFFIIIKKKKKKJJJGGGHHHHHHEEEBBB@@@???@@@???>>>>>>>>>>>>???@@@@@@CCCDDDDDDEEEEEEFFFFFFFFFFFFGGGGGGFFFEEEEEEFFFHHHHHHGGGFFFEEEEEEFFFGGGHHHIIIHHHFFFEEECCCBBBBBBBBBFFFFFFFFFFFFEEEDDDCCCBBB@@@>>>;;;;;;<<<======<<<:::999888888:::<<<<<<;;;999999999999999888888777444333222333444555333111333333222222222222333333222222222222111000///.....................//////...------------,,,,,,,,,,,,,,,,,,,,,+++++++++++++++******)))))))))))))))((((((((((((((((((((((((&&&'''((()))*********)))(((((((((((((((((((((((())))))))))))))))))))))))***)))((('''''''''((()))((((((''''''&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''((((((''''''''''''(((((()))((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))******)))((((((((((((((('''(((((())))))(((((('''&&&'''((((((((((((((((((&&&''''''''''''(((((((((&&&&&&''''''((())))))************)))))))))((((((&&&&&&''''''(((((())))))))))))(((((((((((())))))))))))(((((((((((())))))''''''&&&''''''((()))***))))))))))))))))))))))))******))))))))))))******&&&''''''(((((())))))***)))))))))))))))))))))))),,,,,,++++++++++++,,,,,,*********))))))((((((''')))************+++++++++******+++,,,,,,,,,,,,+++)))******+++++++++++++++******))))))******+++,,,,,,,,,,,,,,,------------,,,,,,---...//////000000///////////////000000111//////......//////000111111000//////000333777999???===:::666333222222222%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&&&&%%%$$$$$$%%%''',,,+++(((&&&%%%%%%%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''''''''''''''''''''''''''''''''''''''((('''&&&&&&&&&'''))))))'''''''''''''''((()))))))))((((((((()))***+++,,,************++++++++++++***++++++++++++,,,,,,,,,,,,,,,---......//////000111111111000000000000000111111222333333333333222000111222444444333333222333333333333333333333333333444555666666444333222555666777888999999::::::777888999:::;;;===>>>>>><<<<<<<<<<<<===>>>???@@@@@@?????????@@@AAACCCDDDCCCCCCBBBBBBAAA@@@@@@@@@AAABBBCCCEEEGGGHHHHHHHHHEEEDDDDDDEEEHHHJJJIIIHHHEEEGGGGGGEEEBBB??????@@@???>>>=========>>>@@@@@@AAAAAABBBCCCEEEFFFGGGGGGFFFGGGHHHGGGEEEEEEGGGIIIHHHGGGFFFEEEEEEFFFGGGGGGGGGFFFEEEDDDCCCBBBBBBBBBDDDDDDEEEEEEDDDCCCBBBAAA???===;;;;;;===>>>???>>>;;;:::888999:::;;;;;;:::999888777777666666777777222111111222333444222000333333222222222222333333111111222222111000///.....................------......---------,,,,,,,,,++++++++++++++++++++++++++++++***))))))))))))***''''''''''''''''''''''''%%%&&&((()))*********)))''''''''''''''''''''''''))))))))))))))))))))))))%%%%%%&&&&&&&&&&&&&&&&&&)))((('''&&&&&&&&&&&&''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''((('''''''''''''''((())))))&&&&&&''''''''''''''''''((('''%%%$$$$$$%%%'''(((''''''&&&&&&&&&''''''(((+++***)))((('''(((((()))'''''''''(((((('''''''''&&&&&&'''(((((((((((((((&&&&&&&&&'''''''''(((((('''''''''((((((((((((((())))))((((((((('''''''''&&&&&&&&&&&&''''''''''''))))))(((((((((((())))))))))))(((((((((((())))))''''''''''''((()))***+++))))))))))))))))))))))))***))))))))))))))))))***&&&&&&''''''((())))))***))))))))))))))))))))))))******++++++++++++******)))))))))))))))((((((((()))************+++++++++******+++,,,,,,,,,,,,+++))))))***++++++++++++++++++************+++,,,,,,++++++,,,,,,,,,------------------....../////////000///......---.........///............///000000111///......111555:::===???===999555333222222333%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&&&&%%%$$$$$$%%%''',,,***(((&&&%%%&&&'''(((#########$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&'''&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&'''''''''''''''&&&&&&''''''''''''''''''''''''&&&&&&%%%$$$%%%&&&'''((('''''''''''''''((()))))))))((((((((((((***,,,---)))************+++++++++)))***+++,,,,,,,,,,,,+++,,,,,,------...//////000222222111111000000//////111111222333333333333222000111222333444333222222555555555555555555555555222333444555555333111000222333555777999999888888777777999:::<<<===>>>???<<<<<<<<<======>>>???@@@AAA@@@>>>>>>>>>@@@BBBDDDCCCCCCBBBAAAAAA@@@@@@???AAABBBCCCEEEGGGHHHIIIIIIEEEDDDDDDEEEGGGIIIHHHGGGCCCFFFGGGEEEAAA??????@@@???>>>=========>>>@@@AAA>>>???AAACCCEEEGGGHHHIIIFFFHHHIIIHHHEEEEEEGGGJJJGGGFFFEEEDDDDDDEEEFFFFFFDDDDDDCCCBBBBBBBBBCCCCCCCCCDDDDDDDDDDDDBBBAAA@@@>>><<<;;;;;;===???@@@@@@<<<:::999999:::;;;:::999999888666555555555666777111111000111333333222000444333333222222333333444///000111222222111000////////////......------,,,.........------,,,,,,,,,++++++++++++++++++++++++,,,++++++***************''''''''''''''''''''''''%%%&&&((()))*********)))''''''''''''''''''''''''))))))))))))))))))))))))$$$%%%'''((()))((('''''')))((('''&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&'''''''''(((((('''''''''''''''((()))***&&&''''''(((((())))))))))))'''%%%######%%%''')))(((''''''&&&&&&&&&''''''+++***((('''''''''((()))&&&&&&''''''''''''&&&&&&&&&&&&'''((())))))((((((&&&&&&&&&'''''''''(((((()))))))))(((''''''&&&&&&(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%))))))(((((((((((())))))))))))(((((((((((())))))'''''''''((((((***++++++))))))))))))))))))))))))))))))(((((((((((())))))&&&&&&&&&'''((())))))***))))))))))))))))))))))))((()))***++++++***)))((((((((((((((()))))))))))))))************+++++++++******+++,,,,,,,,,,,,+++))))))***++++++++++++***++++++******++++++,,,---++++++,,,,,,,,,------------------...............//////...---,,,,,,,,,,,,...............///000000000///......111777<<<@@@===;;;777444222222333333%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''((((((((('''&&&%%%%%%%%%%%%%%%&&&'''((('''((((((((('''&&&%%%%%%$$$$$$%%%%%%&&&'''((((((&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&%%%%%%&&&''')))***&&&&&&&&&%%%%%%$$$$$$$$$))))))((('''&&&%%%%%%$$$###!!! ###%%%&&&&&&)))(((&&&%%%$$$$$$%%%&&&+++)))%%%######%%%)))+++)))((('''&&&&&&'''((())))))(((&&&%%%%%%&&&'''(((+++***)))'''''''''((()))&&&''''''((()))******+++(((((())))))******++++++++++++++++++,,,---......---------............///,,,---///000111111111000222111000000000111333333333333333333333333444444444333222111222333444555555555555555555555444444555555666666666666555555777777888999;;;<<<======<<<<<<===>>>???@@@@@@AAA>>>>>>===>>>>>>@@@BBBCCCCCCCCCBBBAAA@@@??????>>>AAACCCFFFGGGGGGGGGIIIJJJJJJIIIHHHGGGFFFFFFEEEFFFDDDDDDCCCBBBAAAAAAAAAAAA@@@@@@??????????????????BBBCCCDDDDDDDDDFFFIIILLLIIIJJJKKKLLLMMMLLLKKKKKKJJJGGGCCC@@@???BBBEEEHHHFFFFFFFFFFFFEEEDDDBBBBBBDDDDDDCCCBBBAAAAAAAAAAAA<<<<<<======>>>@@@AAABBBBBB@@@>>><<<;;;:::::::::999888888888777777666666555333222000000111333444000111222333333222111000111111111111111000//////......---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++***)))(((''''''(((((()))))))))***&&&&&&&&&''''''''''''(((''''''''''''((((((((((((******))))))((((((''''''))))))))))))))))))))))))&&&&&&''''''''''''&&&&&&(((((('''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&&&&''''''$$$%%%&&&&&&''''''&&&&&&))))))))))))))))))))))))''''''''''''''''''''''''&&&%%%%%%%%%&&&''')))***'''''''''&&&&&&%%%%%%%%%((((((((((((((((((''''''%%%%%%%%%&&&&&&&&&''''''&&&''''''((()))((((((((('''''''''''''''((()))***(((((((((((((((((((((((('''(((((()))))))))))))))(((((((((((())))))))))))''''''''''''''''''''''''&&&&&&&&&''''''''''''(((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((('''''''''(((((((((((((((((((((((()))((('''&&&&&&'''((()))******))))))(((((('''''',,,+++***)))))))))++++++***++++++,,,,,,++++++***************************((())))))***,,,---..................---,,,+++***............////////////000000000000111111111111//////.........---------......///111222333444555777555333111111111222333%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''''''''&&&&&&%%%%%%%%%&&&''''''&&&''''''''''''&&&&&&%%%$$$%%%%%%%%%&&&'''''''''############""""""!!!!!!&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''')))***'''&&&&&&&&&%%%%%%%%%$$$((((((((('''&&&&&&%%%%%%&&&$$$###$$$&&&(((((('''&&&%%%$$$$$$$$$%%%&&&&&&&&&$$$!!! """%%%''''''&&&%%%%%%%%%%%%&&&'''((('''&&&&&&&&&'''((((((+++***)))(((''''''((()))'''''''''((()))************************+++++++++*********++++++,,,---...------------............,,,---///000111111000000111111000000000111222333000000111111111111222222555444333222222333444444555555555555555555444444444555666777888888888888999999999::::::;;;;;;;;;======>>>>>>??????@@@@@@===<<<<<<===???AAACCCEEEEEEDDDCCCBBBAAA@@@???>>>BBBDDDEEEFFFEEEEEEEEEFFFHHHGGGGGGFFFFFFFFFFFFFFFCCCCCCBBBAAAAAAAAABBBBBBAAAAAAAAAAAA@@@@@@@@@@@@BBBCCCEEEEEEEEEFFFIIIKKKJJJKKKLLLMMMNNNMMMMMMLLLLLLIIIEEEAAAAAABBBEEEGGGFFFFFFFFFFFFEEEDDDCCCBBBDDDCCCBBBAAAAAA@@@@@@@@@============>>>???@@@@@@???>>>===;;;;;;;;;;;;<<<888888888777777777666666444333111000///000111222000111222222222222111000111111111111111000//////...------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++***))))))((((((((())))))*********(((((('''''''''&&&&&&&&&''''''''''''(((((((((((())))))))))))((((((''''''((((((((((((((((((((((((&&&&&&''''''''''''&&&&&&(((((('''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&&&&''''''$$$%%%&&&&&&''''''&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&%%%%%%&&&'''((()))''''''&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&'''(((((((((((('''%%%%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''%%%%%%&&&'''''''''''''''&&&''''''''''''(((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((('''(((((((((((((((((((((((((((((())))))))))))(((((())))))))))))((((((''''''++++++***))))))******+++***++++++,,,,,,++++++***************************))))))***+++,,,---..................---,,,+++***............////////////....../////////000000000//////.........------------......///111222333333555444222111000111333333%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''(((''''''&&&%%%%%%%%%&&&&&&%%%%%%&&&'''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&'''((()))'''''''''&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&'''(((((('''%%%############$$$%%%&&&'''%%%$$$######$$$%%%&&&''''''&&&%%%%%%%%%%%%&&&'''&&&&&&&&&&&&'''((())))))***))))))(((((((((((()))''''''(((((())))))******++++++++++++++++++************)))******+++,,,---------------............------///000000000000000111000000000000111222222000000000111111111222222666555444333333333333333444444444444444444555555444555666888999:::;;;;;;::::::::::::::::::::::::>>>?????????????????????;;;;;;<<<===???BBBDDDFFFFFFFFFDDDCCCBBB@@@???>>>BBBCCCEEEDDDCCCBBBBBBCCCFFFFFFFFFFFFFFFFFFFFFFFFBBBBBBAAAAAABBBBBBCCCDDDCCCCCCCCCCCCBBBBBBBBBAAABBBDDDFFFGGGGGGHHHIIIJJJJJJKKKLLLNNNNNNOOOOOOOOOMMMKKKGGGDDDBBBCCCEEEGGGEEEFFFFFFEEEEEEDDDCCCBBBCCCBBBBBBAAAAAA@@@@@@??????>>>>>>======>>>>>>???<<<<<<;;;;;;;;;;;;<<<<<<777777777777666666666666444333111000/////////000000000111222222111000000000000111111000000//////------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,***++++++++++++***)))))))))))))))******************)))((('''&&&%%%$$$$$$''''''''''''(((((((((((()))))))))(((((((((((('''''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&'''''''''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&&&&''''''%%%%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&''''''((('''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&'''''''''''''''&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''%%%%%%&&&''''''''''''&&&%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((((((((((()))***++++++***)))((()))))))))(((((((((((('''******)))))))))******+++******++++++++++++******))))))))))))))))))))))))******+++,,,---......///............---,,,++++++---............/////////------........./////////...............---------------......///000111111222111000000000111333444%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%$$$%%%&&&'''(((((('''&&&%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''((((((&&&&&&&&&&&&''''''((((((''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&&&&'''((('''$$$"""$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%&&&&&&'''((((((((((((((((((''''''(((((((((%%%&&&&&&'''((())))))***)))))))))(((((((((((()))'''((((((((()))))))))***+++++++++******)))))))))))))))))))))***+++,,,---,,,,,,---------.........---......//////000000000000000000000000111111222111111222222333333444444777666555444333333222222333333444444444444555555444555666888999:::::::::999:::::::::;;;;;;<<<<<<@@@?????????????????????===<<<<<<===???AAACCCDDDGGGFFFEEEDDDBBB@@@??????AAABBBDDDDDDCCCBBBCCCDDDHHHHHHHHHHHHGGGFFFFFFEEEAAAAAAAAABBBCCCDDDEEEEEEFFFFFFEEEEEEDDDDDDCCCCCCBBBDDDGGGIIIIIIHHHIIIJJJKKKLLLMMMNNNOOOOOOPPPPPPNNNLLLIIIFFFDDDDDDEEEFFFEEEEEEEEEEEEEEEDDDCCCCCCBBBBBBBBBAAAAAA@@@????????????>>>===============<<<<<<;;;;;;::::::::::::666666666666666666666666555444333111000////////////000111222222111000//////000000000000000//////---------,,,,,,,,,++++++++++++++++++++++++++++++******+++++++++******)))******************++++++)))(((((('''&&&&&&%%%%%%''''''''''''((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''%%%&&&&&&'''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''''''''&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&&&&''''''&&&&&&(((((('''''''''(((((()))''''''''''''''''''''''''&&&'''(((((())))))((((((%%%&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))(((((((((((((((((((((((()))))))))))))))***************++++++++++++******((((((((((((((((((((((((++++++,,,------...//////---.........------,,,+++---------.........//////------........./////////.................................//////000000000////////////000111222333%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$&&&'''(((((('''&&&%%%%%%%%%%%%%%%######$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''((((((&&&&&&&&&'''''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&'''(((((((((''''''&&&'''((('''$$$"""'''''''''''''''&&&&&&%%%###$$$%%%%%%&&&&&&&&&&&&'''(((((((((((((((((('''%%%&&&'''((())))))******((((((((())))))))))))((((((((((((((())))))))))))******))))))((((((''''''))))))))))))***+++,,,---,,,,,,,,,------------..................///////////////000000111111111111000000111222222333444444666666555555444333222111333333333333444444555555666666777777888888777777777888999:::<<<===>>>???@@@@@@@@@@@@??????????????????>>>>>>>>>???AAABBBGGGFFFEEEDDDBBBAAA@@@???@@@BBBDDDEEEEEEEEEFFFGGGKKKKKKKKKJJJIIIHHHFFFEEEBBBBBBCCCCCCDDDEEEGGGGGGHHHHHHGGGGGGFFFEEEEEEDDDBBBEEEHHHIIIIIIHHHHHHIIIKKKLLLLLLLLLMMMNNNOOOOOONNNLLLJJJHHHFFFFFFFFFFFFDDDEEEEEEEEEEEEDDDDDDCCCBBBBBBBBBBBBBBB@@@???>>>@@@???>>>===<<<<<<<<<<<>><<<:::888777666555555555555555555555666666666444333222111000000///000111111111111000///...//////000000000//////------,,,,,,,,,+++++++++++++++++++++++++++++++++)))******+++++++++******++++++******************''''''''''''''''''''''''''''''''''''(((((((((((('''''''''''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%&&&&&&%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&&&&''''''&&&&&&)))(((((('''''''''((((((''''''''''''''''''''''''&&&''''''(((((((((((((((&&&&&&'''''''''(((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''((((((((((((((((((((((((&&&'''''''''(((((())))))((((((((((((((((((((((((***)))'''&&&&&&''')))***'''''''''''''''((((((((((((((())))))************)))******++++++******)))((((((((((((((((((((((((+++,,,,,,------.........---------...------,,,,,,------------................../////////000000000---.....................000000000000000000000000......//////000111222333%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&%%%%%%%%%&&&&&&######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&'''''''''&&&&&&''''''(((''''''&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&'''''''''(((((()))((((((((())))))'''%%%))))))))))))((('''%%%%%%''''''''''''''''''''''''%%%%%%&&&''''''&&&%%%%%%&&&'''((()))))))))))))))'''(((((())))))))))))((((((((((((((())))))))))))((((((((((((((((((''''''******)))******+++,,,---,,,,,,,,,,,,------------///......------...//////...///000000111111000000---......///000111222222444444444444333222111111222222333333444444555555666777777888777777666666666777888:::<<<>>>@@@AAA??????@@@@@@@@@@@@@@@@@@AAA@@@???>>>>>>???@@@AAAEEEDDDDDDCCCBBBAAA@@@@@@@@@BBBEEEFFFFFFFFFHHHIIIKKKLLLLLLLLLKKKIIIGGGFFFEEEEEEEEEEEEFFFGGGHHHIIIJJJIIIIIIHHHGGGFFFEEEEEECCCEEEGGGHHHGGGGGGHHHIIIKKKKKKKKKJJJKKKKKKLLLMMMLLLKKKJJJIIIGGGGGGFFFFFFDDDDDDEEEEEEEEEEEEDDDDDDBBBCCCDDDDDDCCCBBB@@@??????>>>======<<<<<<<<<<<>>;;;777444333444444444555555555555555666666555444333222222111//////000111111000//////......///000000000//////,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++))))))***++++++++++++******************)))))))))&&&&&&&&&'''''''''((((((''''''''''''((((((((((((&&&''''''''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''(((((((((((('''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''(((''''''&&&%%%%%%%%%&&&&&&&&&&&&'''###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&'''''''''''''''''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&&&&%%%&&&''''''''''''(((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&''''''((()))))))))(((((((((((((((((((((((()))((('''&&&&&&'''((()))&&&''''''''''''(((((((((''''''((()))************))))))************))))))))))))))))))))))))))))))+++,,,,,,,,,------------,,,------...------,,,,,,,,,------------.............../////////000000000---------...............111000000000000000000000...//////000111222222222%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%&&&&&&%%%%%%%%%&&&''''''###$$$$$$$$$$$$######"""#########$$$%%%%%%%%%&&&''''''''''''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((('''&&&%%%$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&''''''''''''''')))(((&&&&&&'''((('''&&&&&&'''((((((((('''&&&%%%+++***)))(((((((((((((((%%%%%%&&&''''''&&&%%%%%%'''((())))))***)))((((((&&&'''((()))******)))((())))))))))))(((((((((((((((((((((((())))))))))))*********++++++,,,---...++++++,,,,,,,,,---------///...------------...///......000111111111000///------...///000111222222111222333333333222111000111222222333444444555555666666777888999999999999888888999;;;<<<>>>???@@@?????????@@@@@@AAAAAAAAA??????>>>>>>>>>???AAABBBBBBBBBBBBBBBAAAAAAAAA@@@AAACCCEEEFFFEEEEEEFFFHHHHHHIIIJJJKKKLLLKKKIIIHHHGGGGGGGGGGGGGGGHHHIIIJJJKKKJJJIIIHHHGGGFFFEEEEEEDDDEEEFFFFFFEEEEEEGGGIIIKKKJJJIIIHHHHHHHHHIIIJJJJJJJJJIIIIIIHHHGGGFFFFFFDDDDDDEEEEEEEEEEEEDDDDDDCCCDDDEEEEEEDDDCCCAAA???>>>======<<<<<<<<<======CCCCCCAAA???<<<888555333333333444444444555555555444444444444333333222111...///000111111000///...---......///000000//////,,,,,,,,,++++++++++++***************************))))))***+++++++++++++++*********))))))((((((((('''''''''''''''&&&&&&&&&''''''''''''((((((((((((&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&'''(((((((((((((((''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&(((((((((''''''%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%&&&'''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&'''(((((((((((('''''''''&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((())))))***((((((((((((((((((((((((&&&''')))******)))'''&&&&&&&&&&&&'''''''''((((((&&&'''((()))*********)))))))))************))))))************************++++++++++++,,,,,,,,,,,,,,,,,,------...------,,,,,,,,,---------.........------........./////////---------.........//////000000000//////.........///000000111222222222222%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&%%%$$$%%%%%%%%%%%%&&&&&&'''((($$$$$$$$$$$$$$$###"""!!!""""""###$$$%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&((((((((('''&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&'''''''''''''''''''''''''''%%%######$$$%%%&&&%%%###$$$&&&'''(((''''''&&&)))(((&&&$$$#########$$$&&&'''((())))))((('''&&&(((((()))******)))((('''&&&'''(((*********)))((())))))))))))(((((((((((((((((())))))******++++++++++++++++++,,,---...///++++++,,,,,,,,,---------//////---,,,,,,---...///---...000111111111000///...///000111222333444444///000111222333222111000111111222333333444555555555666888999:::;;;<<<<<<::::::;;;;;;<<<===>>>>>>>>>>>>???@@@AAAAAABBBBBB>>>=========???@@@BBBDDDAAAAAAAAAAAAAAAAAAAAAAAACCCEEEFFFFFFEEEDDDDDDEEEDDDEEEHHHJJJLLLLLLKKKJJJIIIIIIHHHHHHHHHIIIJJJJJJKKKJJJJJJHHHGGGFFFEEEEEEDDDEEEEEEDDDCCCDDDGGGIIIKKKJJJHHHGGGFFFFFFGGGGGGHHHIIIIIIIIIHHHHHHGGGFFFDDDDDDEEEEEEEEEEEEEEEDDDCCCDDDFFFFFFEEEDDDAAA@@@======<<<<<<<<<<<<======CCCCCCBBB@@@===999666444333333333444444555555555222222333333333222222111...///000111111000///...------...///000000//////,,,,,,,,,+++++++++******************************((()))***+++++++++++++++***)))))))))((((((''''''))))))((('''&&&%%%%%%$$$''''''''''''((((((((()))&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&''''''''''''''''''&&&&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&&&&''''''(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&((())))))((((((%%%%%%%%%&&&&&&'''''''''$$$$$$%%%&&&&&&'''((((((%%%%%%%%%&&&&&&&&&''''''&&&'''(((((())))))((((((***)))((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))***(((((((((((((((((((((((($$$''',,,//////,,,'''$$$&&&&&&&&&'''''''''((((((%%%&&&((()))*********)))))))))************))))))************************++++++++++++++++++,,,,,,,,,,,,------...---------,,,,,,,,,---------......,,,,,,,,,---------......---------.........///////////////...------,,,,,,000000111222222222222111&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%((((((''''''''''''((((((''''''(((((('''&&&%%%%%%(((((((((((('''&&&%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&''''''(((((((((((((((&&&&&&&&&'''''''''(((((((((((())))))*********+++))))))*********+++++++++)))******++++++,,,---------------............///000000111///---++++++,,,000000000000000///.........//////111222333444444555555444333333222222222222222222111222222333333333444555777888:::;;;<<<:::999888888888:::===>>>AAAAAAAAAAAA@@@@@@???>>>===>>>>>>?????????>>>>>>AAABBBDDDDDDCCCBBBCCCDDDEEECCCBBBCCCEEEHHHIIIIIIJJJKKKLLLLLLLLLKKKJJJIIIFFFFFFFFFFFFFFFFFFGGGGGGHHHHHHIIIIIIHHHFFFEEEDDDEEECCCAAAAAABBBEEEIIIKKKIIIIIIHHHGGGGGGGGGHHHHHHJJJHHHEEEBBBBBBCCCEEEGGGHHHGGGFFFFFFFFFFFFDDDBBBCCCCCCCCCBBBAAA@@@>>>>>>;;;;;;;;;;;;;;;;;;::::::<<<;;;:::888777555444333333333333333333333333333111111111111111111111111111111000///////////////000///...------...///000......---------,,,,,,,,,******)))(((((('''((((((+++++++++************)))&&&&&&''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((()))(((&&&&&&'''''''''&&&''''''''''''(((((((((((($$$%%%'''(((((('''%%%$$$'''''''''&&&&&&%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%'''&&&&&&&&&&&&'''((((((%%%%%%%%%&&&&&&&&&''''''))))))((('''&&&&&&%%%%%%&&&&&&&&&''''''''''''(((%%%$$$###$$$&&&(((((((((%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((('''&&&%%%$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''(((((())))))((('''&&&&&&((((((((((((((((((((((((''''''''''''(((((((((((())))))(((((((((((())))))))))))))))))))))))******''')))***++++++***)))'''(((((((((((())))))))))))******+++++++++,,,,,,,,,,,,---...---+++***+++,,,000---,,,---///000...,,,...---,,,,,,++++++,,,,,,///////////////.........////////////000000000000---...///111222222222222&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$###%%%&&&&&&''''''&&&&&&%%%(((''''''&&&&&&''''''(((&&&&&&''''''&&&%%%%%%$$$'''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&'''(((((((((((((((&&&&&&&&&'''''''''(((((((((((()))))))))*********************++++++++++++)))******++++++,,,------------------............---/////////---,,,---...000000111111000000///...//////000111222333333444000000000000000000111111333333333222333333444555555555666777888888999999999999888777888:::<<<===??????@@@@@@@@@@@@??????===>>>???????????????>>>@@@BBBDDDDDDCCCBBBCCCDDDCCCBBBAAACCCFFFIIIJJJIIIIIIJJJKKKKKKKKKJJJHHHGGGFFFEEEEEEDDDEEEFFFGGGHHHIIIIIIJJJJJJIIIGGGFFFEEEFFFEEEBBBAAAAAACCCFFFHHHIIIHHHHHHGGGGGGGGGGGGGGGEEEEEEEEEDDDDDDEEEFFFFFFDDDCCCCCCDDDEEEFFFDDDCCCCCCCCCBBBAAA@@@>>>===<<<;;;;;;;;;;;;::::::::::::999888777666555444333222444444444444444444444444111111111111111111111111111000000///......//////000///...------...///000...------------,,,,,,,,,+++***))))))((((((((()))+++++++++*********))))))''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((()))(((&&&&&&'''''''''&&&&&&&&&&&&&&&''''''''''''$$$%%%'''(((((('''%%%$$$''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''))))))((('''%%%$$$######&&&&&&&&&&&&&&&'''((((((%%%%%%%%%&&&&&&&&&'''''')))(((((('''&&&&&&%%%%%%&&&&&&&&&''''''''''''((('''%%%$$$%%%'''(((((('''&&&&&&&&&''''''(((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((((('''&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((((((((((((((('''&&&&&&''''''''''''''''''''''''''''''''''''((((((((((((((((((''''''''''''((((((,,,+++***)))))))))))))))((()))***++++++***)))((())))))))))))*********************+++++++++,,,,,,,,,---...---+++***+++,,,///---,,,---//////...,,,...---,,,,,,++++++,,,,,,........................///000000000000111111111///000000111111111111000&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&$$$###"""!!!%%%&&&&&&''''''&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&%%%%%%$$$###%%%%%%&&&''''''''''''&&&&&&&&&''''''''''''&&&&&&&&&&&&'''(((((((((((('''&&&&&&'''''''''((((((((((((((())))))))))))************+++++++++,,,,,,,,,)))******++++++,,,------------------............+++---......------///000000111111111111000000///000000111111111222222222......//////000111111222444333333333444444555666666666666666777777777777999888777777888999;;;<<<======>>>>>>???>>>>>>>>>===>>>>>>???@@@@@@@@@???@@@AAACCCCCCCCCBBBCCCDDDAAAAAABBBDDDHHHJJJIIIIIIGGGHHHIIIIIIIIIHHHFFFFFFFFFDDDCCCBBBCCCEEEHHHJJJJJJJJJKKKKKKJJJIIIGGGFFFGGGEEEBBB@@@@@@AAACCCDDDHHHGGGGGGFFFFFFFFFFFFFFFAAABBBDDDFFFFFFFFFFFFEEECCCBBBBBBBBBDDDCCCBBB@@@BBBBBBAAA???>>>===;;;;;;;;;;;;::::::999999999999555555444444333222222222444444444444444444444444000000000000000000000000000000///............/////////...------...//////------------,,,,,,,,,,,,++++++***))))))))))))***++++++*********)))))))))''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((()))(((&&&&&&'''''''''&&&$$$%%%%%%%%%&&&&&&&&&&&&$$$%%%&&&''''''&&&%%%$$$'''&&&&&&&&&&&&%%%%%%%%%''''''&&&&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''(((''''''&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&''''''(((%%%%%%%%%&&&&&&&&&''''''((((((''''''&&&%%%%%%%%%&&&&&&&&&''''''''''''((()))'''%%%&&&'''((((((''''''''''''(((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''''''''''''''(((((((((((('''&&&&&&''''''''''''''''''''''''''''''''''''((((((((((((''''''&&&&&&&&&&&&''''''...---+++***))))))((((((((()))***++++++***)))(((************++++++++++++*********++++++++++++,,,,,,---...---+++***+++,,,...---,,,---...///...,,,...---,,,,,,++++++,,,,,,,,,,,,,,,------.........000000000000111111111222111111111111111000//////%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''')))((('''&&&$$$###"""!!!%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&%%%%%%$$$###$$$%%%&&&''''''''''''&&&''''''''''''''''''&&&%%%&&&''''''((((((''''''''''''''''''(((((((((((((((((())))))))))))))))))++++++++++++,,,,,,,,,,,,)))******++++++,,,------,,,,,,---------.........,,,---......------...000000111111111111111000000111111111111111111222222111111222222333333333333333333222333333444555666555555666666666777777777888888777777777888999:::<<<=========<<<<<<;;;:::<<<===>>>???@@@@@@@@@@@@???AAACCCCCCBBBBBBCCCDDDBBBBBBCCCFFFHHHIIIHHHFFFFFFFFFGGGHHHGGGFFFEEEDDDEEECCCAAA@@@AAADDDHHHJJJJJJKKKKKKLLLKKKJJJIIIHHHFFFDDDBBB@@@???@@@BBBCCCGGGFFFEEEEEEDDDDDDEEEEEEBBBCCCDDDEEEEEEEEEDDDDDDGGGEEEDDDCCCBBBAAA>>>;;;AAA@@@???===<<<;;;:::::::::::::::999888888777777333333333333333222222222444444333333333333333222000000000000000000000000//////...------.................................---------,,,,,,,,,++++++++++++***************+++************))))))))))))((((((((((((''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((()))'''&&&&&&'''''''''%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''######$$$%%%&&&(((((()))&&&&&&%%%%%%&&&&&&'''(((%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''(((***((('''&&&((((((((('''''''''''''''''''''((((((''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''''''''''''''''''''(((((('''&&&&&&''''''''''''''''''''''''''''''''''''(((((((((((((((''''''&&&&&&''''''(((---,,,+++******)))******((()))************)))((()))))))))*********++++++************+++++++++++++++,,,------++++++,,,---------------------------...---,,,,,,++++++,,,,,,******+++,,,------......////////////000000000000000000111111111000000///%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&'''''''''&&&''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&''''''''''''&&&&&&######%%%&&&''''''((('''&&&''''''''''''''''''&&&%%%&&&&&&''''''''''''''''''''''''((((((((())))))))))))((((((((((((((((((******+++++++++,,,,,,,,,)))******++++++,,,------,,,,,,,,,------------....../////////---,,,---...///000000111111111000000111111111111111111222222555555444444444333333333111111111111222333444555444444555666777888999999888888888888888888999999<<<<<<<<<;;;:::888777666:::;;;===>>>???@@@@@@AAA>>>@@@BBBCCCBBBBBBCCCDDDDDDDDDDDDFFFHHHHHHFFFDDDEEEFFFGGGGGGGGGFFFEEEDDDEEECCCAAA???@@@CCCFFFIIIIIIJJJKKKKKKKKKJJJIIIHHHDDDBBBAAA@@@@@@AAABBBCCCEEEEEEDDDCCCCCCCCCCCCDDDEEEEEECCCBBBBBBBBBCCCCCCGGGFFFDDDCCCBBBAAA>>>;;;@@@???===<<<;;;::::::::::::999999888777777666666333333333333333333333333222222222111111111000000////////////////////////...---------------......------............------------,,,,,,,,,++++++++++++***************++++++*********)))))))))(((((())))))((((((((('''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((()))'''&&&&&&'''''''''%%%%%%&&&&&&&&&&&&'''''''''%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''######$$$%%%'''((())))))%%%%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''(((***((('''&&&((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''''''''''''''(((((((((((()))(((((((((((((((((()))))))))))))))***+++,,,,,,))))))************))))))((((((((()))))))))******))))))*********++++++++++++,,,------++++++,,,---,,,---------,,,,,,------...---,,,,,,++++++,,,,,,)))******+++,,,---......------------.........///......000111111222222222$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&''''''(((''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&''''''((((((''''''######$$$&&&&&&'''''''''&&&&&&''''''''''''&&&&&&%%%%%%&&&''''''''''''&&&''''''((((((((()))))))))))))))((((((((((((''''''))))))*********+++++++++)))******++++++,,,------,,,,,,,,,,,,------------...///000///---,,,,,,......//////000000000000///000000111111111222222222555444444333222222111111000000000111222333444555444555666777888999::::::888999999999999999999999;;;;;;:::999888666555444888999;;;===>>>???@@@@@@===???BBBBBBBBBBBBCCCDDDEEEDDDDDDEEEGGGGGGFFFEEEFFFGGGHHHHHHHHHGGGEEEEEEDDDCCCAAA???@@@BBBDDDEEEGGGHHHIIIJJJJJJIIIHHHGGGCCCCCCBBBAAAAAAAAABBBCCCDDDDDDCCCBBBBBBBBBBBBBBBFFFEEECCCBBBAAAAAABBBBBBBBBAAAAAABBBCCCCCCAAA???>>>===<<<::::::;;;;;;<<<999999888777666555555444444444444444333333333333222111111000000/////////////////////////////////---,,,,,,,,,,,,---......------............------,,,,,,,,,,,,++++++++++++***))))))))))))***++++++******)))))))))(((((((((***))))))(((((('''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((()))(((&&&&&&'''''''''&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''((()))'''%%%&&&'''(((((('''&&&&&&&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''$$$%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((())))))(((((((((((())))))''''''(((((()))+++,,,---***))))))))))))))))))***'''((((((((()))))))))))))))))))))************+++***,,,------++++++,,,...+++---...---,,,+++,,,---...---,,,,,,++++++,,,,,,+++++++++,,,,,,---------,,,,,,,,,,,,---------------...///000222222222333$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&%%%%%%%%%%%%&&&&&&$$$%%%&&&''''''''''''&&&###$$$%%%&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&'''((((((((())))))))))))))))))((((((((('''''''''(((((()))))))))*********)))******++++++,,,------++++++,,,,,,,,,---------,,,---///...------...///------.../////////////////////000111222333333444222222222222222222222222111111111222333444555666777888888888999999999:::999999::::::::::::999999666777777777777666666555666777999;;;===??????@@@===???AAABBBBBBBBBCCCDDDCCCBBBBBBCCCFFFHHHIIIIIIHHHHHHIIIJJJIIIHHHGGGFFFCCCCCCAAA@@@@@@@@@AAABBBEEEFFFGGGHHHHHHGGGFFFEEEFFFEEEDDDBBBAAAAAAAAAAAACCCCCCBBBAAAAAAAAAAAAAAABBBBBBCCCCCCCCCBBBBBBAAA@@@??????@@@AAABBB@@@???===<<<:::::::::;;;===>>>999888888777555444444333444444444333333222222222222222222111000/////////........................,,,,,,++++++,,,------...,,,------......------,,,,,,,,,,,,++++++++++++***)))((((((((())))))***+++***)))))))))((((((((((((******))))))(((''''''&&&''''''''''''''''''''''''&&&&&&&&&''''''''''''((()))(((&&&&&&'''''''''&&&$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''((('''%%%$$$%%%'''(((((('''((('''''''''&&&&&&&&&&&&''''''''''''''''''''''''$$$$$$%%%%%%&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((((((((((((''''''(((((((((''''''''''''((()))************))))))))))))******(((((()))))))))*********))))))))))))***************+++---,,,,,,+++---...+++---...---+++***,,,......---,,,,,,++++++,,,,,,,,,,,,,,,,,,------------,,,,,,,,,---------.........///000111111111111111$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''###$$$%%%%%%&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&(((((((((((())))))))))))))))))(((((('''''''''&&&(((((((((((()))))))))))))))******+++,,,,,,------++++++,,,,,,,,,---------***,,,---.........000222,,,,,,---...//////.........///000111222333444444222222222333333444555555222222222333444555777888:::::::::999999999888888::::::;;;;;;;;;::::::999333444555666777777777777555666888:::<<<>>>??????<<>>@@@999888777666555444333333444444333333222111111000333333222222111000000///........................++++++++++++,,,,,,---...,,,,,,---......---,,,,,,,,,,,,,,,+++++++++******(((((('''(((((()))******))))))))))))((((((((((((+++******)))(((''''''&&&''''''''''''''''''''''''&&&&&&&&&'''''''''(((((()))(((&&&&&&'''''''''&&&######$$$$$$$$$%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&'''''''''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&'''''''''%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((%%%$$$###$$$&&&((((((((())))))(((((('''''''''&&&''''''''''''''''''''''''$$$$$$%%%%%%&&&'''((((((''''''''''''''''''''''''###$$$&&&'''((('''&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''$$$%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((()))'''''''''&&&&&&''''''''')))((((((''''''''''''(((******))))))))))))******)))************+++++++++))))))))))))***************+++---,,,,,,,,,---...***,,,...---+++***,,,......---,,,,,,++++++,,,,,,---------------------------------.........//////111111111111111000//////%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''''''''((('''&&&%%%%%%&&&'''((($$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&$$$"""!!!!!!"""$$$&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&((()))))))))((('''%%%&&&&&&&&&'''((((((((((((((((((((((((((((((((()))))))))))))))))))))))))))))))))***++++++,,,,,,*********++++++,,,,,,,,,............///000111111000000000000///////////////000111222222222222222444444444333333222222222///000111222444555666777777888;;;===>>>===;;;999;;;;;;;;;;;;:::999999888999888666444333444666777777888999;;;===>>>@@@AAA?????????@@@AAABBBCCCDDDCCCCCCCCCDDDEEEGGGHHHIIIMMMLLLJJJHHHGGGGGGGGGHHHFFFEEEDDDCCCAAAAAA@@@@@@CCCDDDDDDEEEFFFGGGHHHHHHGGGGGGEEEDDDBBB@@@???>>>AAAAAA@@@@@@AAACCCDDDEEEBBBAAAAAACCCFFFFFFBBB???===>>>>>>????????????>>><<<;;;::::::999999999999999999888666444444555777666666555444333333222222......///000000000000000------......------,,,+++,,,,,,,,,,,,,,,,,,,,,,,,***++++++,,,------------,,,,,,------,,,,,,+++*********))))))))))))******$$$&&&(((******(((&&&$$$***))))))((('''&&&&&&&&&(((''''''''''''&&&&&&&&&&&&&&&&&&''''''''''''(((***)))'''%%%$$$%%%'''(((&&&&&&&&&&&&&&&'''((()))''''''''''''''''''''''''$$$$$$%%%%%%&&&'''((((((((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''&&&$$$###&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''''''''&&&&&&%%%%%%&&&&&&'''(((''''''''''''&&&&&&&&&***(((''''''))))))'''$$$&&&'''((())))))((('''&&&((('''&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&)))((((((''''''''''''(((&&&&&&&&&%%%%%%$$$$$$$$$###$$$$$$%%%&&&'''(((((('''''''''&&&&&&%%%%%%%%%&&&&&&''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''((((((((((((((((((((((((((((((((((((((((((((((((''''''((()))***+++,,,,,,((()))))))))))))))((((((************))))))))))))************************---------,,,,,,+++++++++)))************+++++++++++++++,,,,,,,,,,,,------...------,,,,,,,,,------000000000000000000000000%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''((('''&&&%%%%%%&&&'''((($$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((((((((''''''&&&&&&''''''''''''''''''(((((((((((((((((((((((()))))))))))))))))))))))))))))))))***++++++,,,,,,++++++++++++++++++,,,,,,************+++,,,---...000000000000///////////////000111222222222222111222222222222222111111111000000111222333555666666777999;;;===>>>===;;;:::::::::;;;;;;;;;:::999999888777555444444444555666777888999;;;<<<>>>???@@@AAAAAAAAAAAABBBCCCDDDEEECCCCCCCCCDDDFFFGGGIIIJJJLLLKKKIIIGGGFFFFFFFFFGGGFFFFFFEEECCCBBBAAAAAAAAA@@@@@@AAAAAABBBBBBCCCCCCDDDDDDCCCCCCBBBAAAAAA@@@??????>>>???@@@BBBDDDEEEDDDCCCCCCDDDFFFFFFCCC@@@???>>>>>>>>>>>>=========<<<;;;:::999999999999999888999888666444444555777666555555444333333222222333222000.........//////------......------,,,+++++++++++++++++++++++++++++++++,,,,,,---,,,,,,,,,,,,,,,------,,,,,,+++***++++++************++++++&&&''')))******)))'''&&&***))))))(((''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''')))(((&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&''''''(((''''''''''''''''''''''''$$$%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%&&&&&&'''(((''''''''''''&&&&&&&&&)))'''&&&'''))))))'''$$$&&&'''(((((((((((('''&&&((('''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''''''''''''''(((((((((((((((''''''&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%((((((''''''&&&&&&%%%%%%&&&&&&&&&'''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''(((((((((((((((((((((((())))))))))))(((((((((((())))))*********+++************************------,,,,,,,,,+++++++++)))************++++++++++++++++++,,,,,,,,,------000//////....../////////////////////////////////%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&'''''''''&&&&&&&&&&&&''''''$$$%%%&&&&&&''''''&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''###$$$&&&''''''&&&$$$###$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$'''&&&&&&&&&&&&%%%%%%%%%((((((''''''&&&%%%%%%%%%%%%%%%&&&''''''''''''&&&((((((''''''''''''''''''(((((((((((((((((((((((()))))))))))))))))))))))))))))))))***++++++,,,,,,,,,,,,++++++++++++++++++,,,,,,,,,,,,---...//////////////////000000000000000000111111222222111111000000000111111111111111111111111222333444444555777999;;;=========<<<;;;999999:::;;;;;;;;;::::::888777555444444555666666777777888:::<<<===>>>???BBBBBBBBBBBBCCCDDDEEEEEEBBBBBBCCCCCCEEEGGGHHHIIIJJJIIIHHHGGGFFFEEEEEEEEEGGGFFFEEEDDDCCCCCCBBBBBB>>>>>>>>>???????????????AAAAAAAAAAAABBBBBBBBBBBB<<<<<<<<<===???AAACCCEEEEEEEEEDDDEEEFFFFFFCCCAAAAAA@@@>>><<<;;;;;;;;;;;;;;;::::::999999999999:::888999888777555444555777555555444444333333222222777444111---,,,,,,---...------......------,,,+++************************,,,,,,,,,,,,,,,,,,+++***,,,,,,,,,,,,,,,++++++***,,,++++++******++++++,,,)))))))))))))))))))))))))))))))))(((''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((&&&%%%%%%%%%&&&'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''((()))(((''''''''''''&&&&&&&&&&&&''''''(((''''''''''''&&&&&&&&&&&&%%%%%%&&&(((((('''%%%&&&&&&''''''''''''&&&&&&((('''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))((((((((('''''''''''''''''''''&&&&&&&&&%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%))))))((('''&&&%%%$$$$$$'''''''''((((((((())))))(((((((((((((((((((((((((((((((((((((((((((((((('''''''''&&&&&&&&&%%%%%%(((((())))))))))))((((((''''''((()))***+++,,,,,,************************,,,,,,,,,,,,++++++++++++)))************+++++++++++++++++++++,,,,,,,,,,,,000///////////////000000........................%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&'''''''''&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&&&&&&&&&&%%%###$$$&&&''''''&&&$$$######$$$&&&''''''&&&$$$###&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&))))))((((((''''''&&&&&&(((((((((((((((((((((((()))))))))))))))))))))))))))))))))***++++++,,,,,,,,,,,,,,,++++++*********,,,,,,,,,------...///000////////////000000000000000000111111111111000000///000000111111222222222111111222222333333333444777888:::<<<======<<<;;;888999999:::;;;;;;;;;;;;777666666555555555666777777777999:::;;;===>>>>>>BBBBBBAAAAAABBBCCCCCCDDD???@@@@@@AAACCCEEEGGGHHHHHHHHHGGGFFFEEEDDDDDDCCCFFFFFFFFFEEEEEEDDDCCCBBB@@@@@@@@@@@@@@@?????????@@@@@@@@@AAAAAAAAAAAAAAA;;;;;;<<<===???AAADDDEEEFFFFFFFFFFFFFFFEEEDDDBBBCCCAAA>>>;;;999888888999::::::999999999999999:::777888999777555444555666444444444333333333222222555333111///------------------......------,,,+++)))))))))))))))))))))))),,,,,,,,,,,,,,,+++***)))+++,,,,,,,,,,,,+++******+++******))))))******+++))))))(((''''''((())))))))))))(((((('''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&'''''''''''''''&&&%%%%%%&&&&&&'''(((''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%###$$$$$$%%%&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&(((******)))(((&&&''''''&&&&&&&&&&&&''''''(((''''''''''''&&&&&&&&&$$$$$$%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&'''((()))***&&&&&&&&&&&&&&&%%%%%%%%%###$$$$$$%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&'''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''(((((())))))))))))((('''(((((()))******++++++************************,,,+++++++++++++++++++++))))))*********+++++++++***++++++++++++,,,,,,,,,---------,,,------..............................%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&''''''''''''&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%$$$%%%&&&&&&''''''&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''((('''%%%$$$$$$%%%'''(((###$$$&&&''''''&&&$$$######$$$&&&''''''&&&$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((())))))%%%%%%%%%%%%&&&&&&'''''')))))))))((((((''''''&&&(((((((((((((((((((((((((((((((((((((((((((((((()))))))))***++++++,,,,,,,,,,,,,,,++++++*********))))))))))))***+++,,,---.../////////000000000111000000111111111000000///000111111111222222333333111111111222222333333333666777888:::;;;<<<<<<;;;888999999:::;;;;;;;;;;;;777777777666777777777888888888999:::<<<===>>>>>>@@@@@@?????????@@@AAAAAA======>>>???AAACCCEEEFFFGGGGGGGGGFFFEEEDDDCCCBBBEEEEEEFFFFFFEEEDDDCCCBBBAAAAAAAAAAAA@@@@@@@@@@@@AAAAAA@@@@@@??????>>>>>><<<<<<<<<===???BBBDDDFFFFFFGGGGGGFFFFFFEEEDDDEEEDDDBBB>>>;;;888777777777999999999888888999999:::777888999888666444555555333333333333333222222222///000111111111000...---------......------,,,+++)))))))))))))))))))))))),,,,,,,,,,,,+++******)))++++++,,,,,,++++++***)))))))))(((((((((((()))))))))(((&&&%%%%%%&&&((()))(((((((((((('''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&&&&((('''&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%&&&'''(((((()))&&&&&&&&&&&&&&&&&&&&&&&&***(((&&&%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&(((******)))(((&&&(((''''''&&&&&&''''''((((((''''''''''''&&&&&&&&&###$$$&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&((())))))&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%&&&&&&''''''%%%%%%&&&&&&&&&'''''''''((((((((((((((((((((((((((((((((((((((((((((((((%%%&&&&&&'''(((((())))))''''''((()))))))))))))))******))))))))))))))))))************************++++++++++++++++++++++++))))))*********+++++++++*********+++++++++,,,,,,,,,,,,,,,,,,,,,---..............................%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''')))'''%%%######%%%''')))$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&'''######$$$&&&'''((()))***&&&&&&&&&%%%&&&''''''((())))))(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((()))))))))***++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++,,,---............//////000000111111000000111111000000//////111111111222222222222222000000000111222333333444444555666888999:::;;;;;;999999:::;;;;;;;;;::::::888888888888999999999999999999:::;;;<<<===>>>???>>>>>>>>>======>>>>>>???;;;<<<===>>>@@@BBBDDDEEEGGGGGGGGGFFFEEEDDDBBBAAADDDDDDEEEFFFEEEDDDCCCBBB??????@@@@@@@@@@@@@@@@@@BBBAAA@@@???>>>===<<<<<<===<<<<<<===???AAACCCEEEDDDFFFGGGFFFEEEDDDEEEGGGDDDBBB???<<<999777666666999888888888888999999:::666888999888666555444555333333333333222222222222+++---000222333111///...------......------,,,+++))))))))))))))))))))))))++++++++++++++++++***)))+++++++++++++++******)))(((((((((''''''(((((((((((('''&&&%%%%%%&&&'''(((((((((((((((((((((''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&***)))(((&&&%%%$$$######&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''((()))(((''''''((((((''''''''''''(((((((((''''''''''''&&&&&&&&&$$$&&&((((((&&&&&&&&&'''''''''&&&&&&&&&&&&'''''''''''''''&&&''''''((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''((((((((((((((((((((()))))))))''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''######$$$%%%&&&'''((((((%%%%%%%%%&&&&&&&&&&&&'''((((((((((((((((((((((((((((((((((((((((((((((((%%%&&&'''((()))***++++++&&&'''((())))))******)))************))))))((((((*********************************+++++++++++++++)))************+++++++++************++++++++++++,,,,,,,,,,,,---...///000........................%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$%%%&&&&&&&&&&&&%%%$$$$$$%%%&&&&&&''''''&&&&&&$$$%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''###$$$$$$%%%&&&''''''(((''''''&&&&&&&&&'''((()))((((((((((((((()))))))))(((((((((((((((((((((((((((((((((((((((((((((((()))))))))***++++++,,,,,,++++++++++++++++++,,,,,,............///000111222.........///000111111111000000000000000//////...111111111111111000000000...///000111222333444555333333555666777999::::::::::::;;;;;;;;;:::999999888999::::::;;;;;;;;;::::::;;;<<<<<<===>>>??????>>>>>>===============>>><<<<<<===???AAACCCFFFGGGGGGGGGGGGGGGFFFDDDBBBAAABBBCCCDDDEEEEEEDDDBBBAAA?????????@@@AAAAAAAAABBBAAA@@@???>>>===<<<<<<;;;<<<<<<<<<<<<===???AAABBBBBBDDDFFFEEEDDDDDDFFFHHHCCCBBB@@@>>>;;;888777666888888888888888999::::::666888999999777555444555222222222222222222222222---...000111111111000///------......------,,,+++************************)))******++++++++++++***+++++++++++++++***))))))))))))(((((((((((())))))((((((''''''''''''(((((('''(((((((((((((((((((((&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$$$$###$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&''''''''''''((((((''''''''''''(((((((((''''''''''''&&&&&&&&&&&&(((***)))'''%%%&&&'''(((((('''&&&&&&'''(((((('''''''''''''''((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''''''''((((((((()))))))))***''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&'''&&&&&&&&&&&&''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((''''''((((((((()))))))))&&&'''((()))************)))))))))))))))*********************************)))*********++++++++++++)))************+++++++++************++++++++++++++++++++++++,,,---...///////////////////////////%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$""""""############""""""$$$$$$%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$$$$%%%&&&&&&''''''&&&&&&###$$$$$$%%%&&&'''((((((%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%&&&&&&%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&'''''''''$$$%%%%%%%%%%%%%%%%%%%%%(((((('''&&&'''((()))***''''''(((((())))))******(((((((((((((((((((((((((((((((((((((((((((((((()))))))))***++++++,,,,,,*********++++++,,,,,,---,,,,,,,,,,,,,,,---//////---......///000111111222000000000000000///......111111000000//////......---...///000222444555555222222333555666888999999;;;;;;;;;;;;::::::999888999:::;;;;;;<<<<<<<<<;;;;;;<<<<<<===>>>???@@@@@@>>>>>>===============>>>===>>>???@@@BBBEEEGGGHHHGGGGGGHHHGGGFFFEEECCCBBBAAABBBDDDEEEEEECCCAAA@@@@@@@@@AAABBBCCCCCCDDDDDD??????>>>>>>======<<<<<<<<<;;;;;;;;;<<<===???@@@AAACCCEEEDDDCCCCCCFFFJJJCCCBBBAAA???<<<999777555888888777777888999::::::666888999999777555444444222222222222222222222222000000////////////000000------......------,,,+++************************((()))***+++++++++++++++***++++++++++++***))))))******))))))))))))******(((((())))))))))))(((((('''''''''(((((((((((((((&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&###$$$%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''((((((%%%%%%$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''''''''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''############$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''((((((''''''''''''(((((((((((('''''''''&&&&&&&&&''')))+++***'''%%%&&&((()))((('''&&&&&&'''((()))'''''''''''''''((())))))&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&%%%&&&&&&&&&''''''((((((###$$$$$$%%%&&&'''((()))%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''((((((((()))(((((((((((((((((((((((((((((((((((((((((((((((()))(((((((((((('''''''''&&&'''((()))************''''''((()))***+++,,,,,,************************))))))******++++++++++++)))************+++++++++)))************+++++++++(((((((((((()))***+++,,,000000000000000000000000&&&%%%############%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$######%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''(((&&&%%%%%%$$$$$$%%%%%%&&&(((((('''&&&%%%$$$$$$###&&&'''''''''&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%)))))))))((('''''''''&&&&&&&&&&&&''''''''''''((())))))))))))))))))))))))&&&&&&(((***------+++)))''''''&&&&&&&&&'''((((((+++***((('''&&&&&&''''''++++++)))(((((()))******))))))***+++,,,,,,,,,,,,,,,,,,,,,---------......///////////////.........000000000///......------111111000///////////////222222333333333222222111555555444444444555666666999:::;;;<<<<<<<<<;;;;;;999999:::;;;;;;:::999999>>>===<<<<<<======<<<;;;======<<<<<<===>>>@@@AAA===???AAACCCCCCCCCBBBAAABBBBBBBBBBBBCCCEEEGGGHHHFFFEEECCCBBBBBBBBBCCCDDDDDDCCCBBBDDDFFFGGGDDDAAABBBAAA???===<<<<<<======;;;;;;<<<===>>>@@@BBBCCCDDDCCCBBBAAAAAABBBCCCDDDEEEDDDCCC@@@>>>;;;888666555666777888999999888777777888888888666555333111111111111111111111111111222111000//////000111222000///---,,,+++*********,,,,,,,,,++++++*********))))))))))))))))))))))))))))))))))))(((((((((((('''((()))******)))(((''')))***++++++***)))((('''(((((((((((((((((((((((($$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&'''(((((((((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''(((''''''&&&&&&%%%$$$$$$&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''(((((())))))((('''&&&&&&'''((((((((((((((('''''''''(((***+++++++++***))))))************++++++++++++++++++************)))******++++++++++++******))))))))))))************))))))*********+++++++++******+++++++++,,,,,,,,,------..................%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&))))))((('''''''''''''''&&&&&&%%%%%%$$$$$$######%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%$$$$$$######&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''')))++++++)))'''&&&%%%%%%&&&&&&((()))))))))((('''''''''((())))))))))))((((((((())))))***))))))***+++,,,,,,,,,,,,,,,,,,,,,------------...////////////............////////////............111111000///////////////222222333333333222222111444333333333444555666666777888888999999999999999999:::;;;<<<<<<;;;:::999;;;;;;;;;;;;==================<<<<<<===>>>@@@AAA???@@@BBBCCCCCCBBBAAA@@@AAAAAAAAAAAABBBDDDEEEFFFFFFFFFEEEEEEEEEEEEEEEFFFDDDBBBAAACCCEEEFFFDDDBBBBBBAAA???>>>>>>>>>>>>???>>>>>>>>>>>>???AAABBBCCCDDDCCCBBBAAABBBBBBCCCDDDCCCCCCBBB@@@===;;;999777444555666777777777666555555666666666555333111000111111111111111111111111111111000//////000111111///...---,,,+++*********,,,,,,,,,++++++*********))))))))))))))))))))))))))))))))))))(((((((((((('''((()))******)))((('''(((((()))))))))((('''&&&''''''''''''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$###""""""'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''((((((((((((((('''&&&&&&''''''((((((((((((''''''&&&&&&'''((((((((((((((((((((()))))))))*********+++++++++*********)))))))))******++++++******)))))))))))))))************))))))*********+++++++++******+++++++++,,,,,,,,,,,,---------......//////%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%(((''''''&&&%%%$$$$$$###%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&########################$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&((())))))'''%%%%%%%%%%%%&&&'''((()))***''''''''''''((()))***+++&&&'''(((((())))))))))))))))))***+++,,,,,,,,,,,,,,,,,,,,,,,,------------....................................////////////111000000///////////////222222333333333333222222222222222222333444666666777777777888888888999999:::;;;<<<======<<<;;;:::999::::::;;;===>>>>>>???>>>============???@@@AAAAAABBBCCCDDDDDDBBB@@@???????????????@@@BBBCCCDDDFFFGGGGGGHHHHHHHHHGGGGGGCCCBBBAAAAAACCCDDDDDDCCCBBBAAA@@@??????@@@AAABBBAAAAAAAAAAAAAAAAAABBBCCCCCCCCCBBBBBBBBBBBBCCCCCCAAAAAA@@@???===;;;999888444444555555555444444333333444444444333111///...111111111111111111111111000000////////////000000///...---+++************+++++++++++++++*********))))))))))))))))))))))))))))))))))))(((((((((((('''(((((())))))((((((''''''''''''(((''''''&&&%%%''''''''''''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&%%%$$$$$$(((''''''&&&&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%&&&&&&'''((((((&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&'''''''''''''''''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%(((((((((((((((((((((((($$$%%%%%%&&&'''((()))***''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((''''''&&&''''''((((((((((((((('''''''''&&&&&&''''''((()))'''''''''((((((((())))))++++++*********))))))))))))******++++++******)))))))))))))))***************************+++++++++******+++++++++,,,,,,,,,++++++,,,---...//////000$$$%%%''''''''''''%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$$$$######(((((('''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$%%%%%%%%%&&&%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((((((((&&&&&&&&&''''''''''''((((((((((((((((((((((((((((((''''''((())))))'''%%%''''''&&&&&&&&&'''((((((((((((((((((((())))))***$$$%%%'''))))))))))))((())))))***+++,,,,,,,,,,,,++++++,,,,,,,,,---------------...............///---------...///000000111000000////////////000000222222333333444333333333111111111222333444555666888888888888999999::::::;;;;;;<<<======<<<;;;;;;:::<<<============???@@@>>>>>>======>>>???AAABBBBBBCCCDDDEEEDDDBBB@@@>>>>>>>>>>>>??????@@@AAAAAAEEEFFFGGGIIIIIIIIIHHHGGGCCCBBBAAAAAAAAACCCDDDEEEBBBAAA@@@@@@AAABBBCCCDDDDDDDDDCCCBBBBBBBBBBBBCCCCCCBBBBBBBBBAAAAAAAAAAAA>>>>>>>>>===<<<;;;:::999555555555444444333333222222333333333333111///...111111111111111111111111////////////////////////...---,,,+++************+++++++++***************))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((&&&''''''''''''&&&&&&&&&''''''''''''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%'''(((((())))))''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%'''&&&&&&%%%$$$######"""%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%%%%&&&'''(((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((((((''''''&&&'''(((((((((((((((((())))))((('''''')))***+++''''''((((((((()))))))))************))))))))))))))))))************))))))((()))))))))******************************************+++++++++,,,,,,,,,******+++,,,...///000000$$$%%%''''''''''''%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''&&&&&&(((((('''&&&&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&&&&%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%&&&&&&''''''%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''((((((&&&&&&&&&''''''''''''((()))))))))))))))))))))))))))((('''((())))))(((&&&)))((('''&&&&&&&&&&&&&&&)))))))))))))))(((((('''$$$%%%'''))))))))))))((())))))***+++,,,,,,,,,,,,+++++++++,,,,,,,,,------,,,---------......//////,,,------...///000111111000000////////////000000111222333444444444444444222111111222333444555666888777777777777888999:::;;;;;;<<<======<<<;;;;;;===???@@@???===<<<>>>?????????>>>>>>???@@@BBBCCCDDDDDDEEEFFFEEEBBB@@@???======>>>??????@@@@@@@@@BBBCCCEEEGGGGGGGGGGGGFFFDDDDDDCCCBBBAAABBBCCCEEEBBBAAAAAAAAAAAACCCDDDEEEFFFEEEDDDCCCBBBBBBBBBBBBAAAAAAAAAAAA@@@@@@??????<<<<<<<<<<<<<<<;;;:::999666555555444333333333333333333444444333222111000000000000000000000000000.........//////.........---,,,,,,+++************************************))))))))))))))))))))))))))))))))))))((((((((((((((((((''''''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& !!!"""###%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%(((''''''&&&%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((((('''&&&&&&'''((((((((((((((()))((('''''''''(((***+++((((((((()))))))))***************)))))))))(((((()))))))))******)))))))))((()))))))))******************************************+++++++++,,,,,,,,,******+++,,,---...///000%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&%%%$$$&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((('''&&&%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&'''''''''%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&''''''''''''((((((((((((((((((((((((((()))((('''''')))***)))((()))((('''&&&&&&&&&&&&&&&************)))((('''&&&&&&'''(((((())))))))))))))))))***+++,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,---......//////---------...///000000111///////////////000000111111222333444444555555444333333333333333444444555555555444333444555666777:::;;;<<<======<<<;;;:::===???AAA@@@<<<;;;===???@@@????????????AAABBBCCCDDDEEEFFFFFFEEECCCAAA@@@>>>>>>???@@@AAAAAA@@@@@@@@@@@@BBBCCCEEEEEEFFFFFFEEEFFFFFFDDDBBBAAABBBDDDBBBBBBAAAAAAAAACCCDDDEEEEEEDDDCCCBBBAAAAAAAAAAAA???@@@@@@@@@???>>>===<<<;;;;;;;;;;;;;;;:::999888555444333333333333333444333333444555444333222111000000000000000000000000------............------,,,,,,+++***************)))))))))***************))))))))))))))))))))))))))))))))))))(((((((((((((((''''''&&&&&&''''''(((''''''&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$###%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''(((((('''&&&%%%%%%$$$$$$&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''#########$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((((((((((((((%%%&&&'''((())))))))))))&&&&&&%%%%%%&&&&&&'''((((((((()))))))))***************)))))))))(((((((((((())))))******))))))((())))))))))))************+++++++++*********************+++++++++,,,,,,,,,******+++,,,---......///%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$ !!!###$$$$$$$$$""""""$$$$$$$$$$$$%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&'''((())))))'''%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$&&&&&&&&&''''''''''''((((((((((((((((((((((((((('''&&&%%%&&&((())))))(((&&&&&&&&&&&&&&&'''((((((((()))*********)))(((((())))))((((((((())))))***))))))***+++,,,,,,,,,,,,***++++++++++++,,,,,,,,,++++++,,,------...//////------......//////000000///////////////000111111111222333444555555555555666555444444333444444444555444333222333444666777999:::;;;<<<<<<;;;:::999999===???>>>;;;:::<<>>>>>>>>>>>>>><<<;;;:::;;;;;;;;;;;;:::999888777222222111111111222333444222333444444444333222111000000000000000000000000,,,---............---,,,,,,++++++***************((()))))))))*********+++))))))))))))))))))))))))))))))))))))((((((((((((((('''&&&&&&&&&&&&'''(((&&&%%%$$$$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$'''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%''''''((((((''''''&&&%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&%%%&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''######$$$%%%%%%&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''(((((((((((((((%%%&&&'''((())))))))))))$$$%%%&&&&&&''''''&&&&&&'''''''''((((((((())))))***)))))))))(((((((((((((((((())))))))))))(((((())))))))))))************+++++++++*********))))))******+++++++++,,,,,,,,,+++++++++,,,,,,---------&&&%%%############%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###%%%'''''''''%%%$$$"""######$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%'''''''''&&&&&&%%%%%%%%%########################'''((()))******(((&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%'''''''''&&&&&&%%%%%%%%%&&&&&&&&&'''''''''(((((())))))))))))))))))))))))%%%$$$###$$$&&&((((((((($$$$$$$$$%%%''')))***+++&&&''')))***++++++******++++++)))(((((()))***+++))))))***+++,,,,,,,,,,,,******+++++++++,,,,,,,,,++++++,,,,,,---...//////.........//////////////////////////////000111111111222333444555555555555777777666555444444444444777666444444444555777999999999:::;;;;;;:::999999555999===<<<999999<<<@@@AAA@@@??????@@@AAACCCDDDCCCDDDFFFGGGFFFEEECCCBBB@@@AAABBBCCCDDDCCCBBBAAA????????????AAACCCFFFGGGGGGIIIKKKIIIEEEAAAAAAAAACCCBBBAAAAAA@@@AAABBBCCCBBBAAA@@@????????????@@@<<<============;;;999888;;;;;;;;;:::999888777666000000/////////111222333111222333444333222111000000000000000000000000000,,,,,,---......---,,,,,,++++++******************(((((())))))*********+++))))))))))))))))))))))))))))))))))))((((((((((((((('''&&&%%%%%%&&&'''((($$$$$$#########$$$&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$'''&&&%%%%%%%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!###$$$%%%&&&&&&&&&'''''''''&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&''''''(((&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%&&&&&&'''((((((''''''''''''''''''''''''(((((((((((((((((((((((($$$%%%%%%&&&'''((())))))''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((())))))((((((%%%&&&'''((())))))))))))%%%&&&((()))))))))((('''&&&&&&&&&'''''''''(((((())))))))))))(((((((((((((((((())))))))))))(((((())))))))))))************++++++++++++******))))))******+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''%%%$$$###"""""""""$$$$$$""""""#########$$$$$$$$$%%%%%%%%%%%%$$$$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&"""###%%%''''''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))***$$$%%%'''(((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((&&&&&&&&&''''''''''''(((***)))(((''''''((()))***&&&&&&&&&&&&&&&'''(((((((((((((((((())))))))))))******)))))))))))))))***,,,,,,++++++***+++++++++,,,+++***)))***+++,,,---...---,,,...000111...+++,,,,,,,,,---...///000000000000000000111222333444222333333444444555555555444444333333444444555666444555666555555555777999888777666777999:::999888777777777777888999:::;;;???@@@@@@AAAAAABBBCCCCCCEEEEEEEEEEEEDDDDDDDDDDDD???@@@AAAAAABBBBBBAAAAAABBBAAA@@@@@@AAADDDFFFHHHIIIIIIHHHHHHFFFEEECCCBBBBBBAAA@@@?????????AAAAAAAAAAAA@@@@@@???>>>>>>>>><<<<<<;;;:::999777777666555666777888888777666555444333222111111111222333000111111222222222111111.........///////////////...---,,,,,,++++++++++++,,,,,,,,,+++++++++******))))))))))))************(((((()))(((((('''&&&%%%))))))))))))((((((((((((''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%$$$###$$$&&&(((***%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%"""###%%%&&&'''&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&%%%$$$$$$%%%&&&'''%%%%%%%%%&&&&&&''''''''''''''''''&&&&&&%%%%%%%%%'''''''''&&&&&&%%%%%%%%%((('''&&&%%%%%%%%%%%%%%%$$$###"""""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&###%%%))),,,------+++)))***))))))((('''&&&&&&&&&))))))))))))************))))))((('''''''''''''''((((((''''''''''''((((((***************)))((((((((()))))))))******************+++++++++,,,,,,,,,---------,,,,,,+++++++++%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%$$$######$$$%%%%%%#########$$$$$$$$$%%%%%%'''(((((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))))))))&&&'''((()))))))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&'''''''''''')))((('''&&&&&&'''((()))((((((((((((((())))))***(((((((((((())))))))))))******))))))))))))******,,,,,,++++++***++++++,,,+++++++++***++++++,,,------,,,+++---//////---***------------...///000000000000000111111222333444333333333444444555555555333333333333333444555555222333555555555666999;;;:::999888999;;;;;;:::999888888888888999::::::;;;>>>??????@@@@@@AAABBBBBBDDDDDDDDDDDDDDDDDDDDDDDDAAAAAABBBCCCCCCCCCCCCCCCBBBBBBAAA@@@AAACCCEEEGGGHHHHHHHHHGGGFFFDDDCCCBBBCCCBBBAAA@@@@@@AAAAAABBB???>>>>>>======<<<;;;;;;<<<;;;:::999888777777666444555666777777666555444444444222111111111222222000111111222222111111111////////////...............---,,,+++++++++++++++,,,,,,,,,+++++++++******))))))))))))************))))))*********)))(((((())))))))))))((((((((('''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%'''((()))%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######%%%&&&(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%&&&&&&&&&$$$%%%%%%%%%&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%((('''&&&%%%%%%%%%%%%&&&%%%$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&$$$&&&))),,,---,,,***(((***))))))(((''''''&&&&&&(((((()))))))))***************)))(((((((((((((((((((((''''''''''''((((((***************)))(((((()))*********++++++++++++******+++++++++,,,,,,,,,.........------,,,,,,,,,%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&'''$$$$$$$$$%%%%%%%%%&&&&&&(((((((((((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((())))))(((((()))))))))(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&''''''((((((''''''(((((()))***(((((((((((())))))))))))***)))))))))))))))******,,,++++++***++++++,,,,,,***++++++,,,,,,,,,,,,,,,...---------//////---,,,------------...///000000111111111111222333444555444444444444444555555555333333333333333444444555000222444555666888;;;======<<<:::;;;<<<<<<;;;:::::::::::::::::::::;;;;;;======>>>>>>???@@@@@@@@@BBBBBBBBBCCCCCCDDDDDDDDDBBBCCCDDDDDDEEEEEEDDDDDDCCCBBBAAAAAABBBCCCDDDEEEGGGGGGFFFFFFEEEDDDCCCBBBDDDDDDCCCBBBAAAAAABBBBBB>>>>>>===<<<<<<;;;;;;:::;;;::::::999888777666666333444444555555444444333555444333222111111000111000111111222111111000000000/////////...------------,,,,,,++++++++++++,,,,,,,,,,,,+++++++++******))))))))))))******************++++++,,,+++++++++)))))))))(((((((((''''''%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%&&&'''(((((((((((($$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$###$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%''''''&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%''')))++++++***)))((()))))))))(((''''''&&&&&&(((((())))))))))))******(((''''''&&&&&&&&&&&&''')))((((((''''''(((((()))***************)))((((((*********+++++++++,,,,,,******+++++++++,,,,,,,,,............------------%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$######%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((())))))((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&''''''(((((((((((())))))))))))))))))))))))))))))***+++++++++******++++++,,,,,,)))***,,,---------,,,+++///......////////////..................///000000111111111111222333444555444444444444555555555555333333333333333444444555222333555666666777:::<<<===<<<;;;;;;<<<<<<;;;:::<<<<<<<<<<<<<<<;;;;;;;;;;;;<<<<<<======>>>?????????@@@@@@AAABBBCCCDDDDDDBBBCCCCCCDDDDDDDDDDDDDDDCCCCCCBBBBBBBBBCCCCCCDDDEEEEEEEEEEEEEEEDDDCCCBBBEEEDDDCCCBBBBBBAAAAAA@@@??????>>>>>>======<<<<<<:::999999888777777666666222222333333333333222222555555444222111000000///111111111111111000000///000000///...------,,,,,,,,,,,,+++++++++++++++,,,,,,,,,,,,+++++++++******((()))))))))************)))******+++,,,,,,,,,,,,))))))((((((((('''''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%'''))))))((('''&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&***)))'''&&&%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&'''((()))))))))((('''))))))((((((''''''''''''(((((((((((()))))))))***)))(((((('''''''''(((((())))))(((((((((((())))))***************)))(((((())))))*********+++++++++******+++++++++,,,,,,,,,------------------------%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%###$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''"""######$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&'''%%%$$$"""###$$$'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''((((((((((((((((((((((((%%%%%%%%%%%%%%%&&&''''''(((((((((((())))))))))))))))))(((((()))***+++++++++*********++++++,,,---***+++,,,---...---,,,,,,---------------------...//////.........///000000111111111111222333444444333333444555555666666777444444333333444444555666666777777777555555777999<<<:::999:::;;;;;;:::999<<<<<<=========<<<;;;;;;:::;;;;;;<<<<<<======>>>>>>>>>???@@@AAABBBBBBCCCAAAAAABBBCCCCCCCCCCCCBBBCCCCCCBBBBBBBBBCCCCCCCCCDDDDDDEEEEEEEEEDDDDDDCCCDDDDDDCCCBBBAAA@@@???>>>??????>>>>>>======<<<<<<888888888777777666666666222222111111111111222222555555444333222000//////111111111111111000///...000//////...---,,,,,,++++++++++++******++++++,,,,,,,,,,,,+++++++++******((()))))))))************(((((()))***+++++++++***((((((((((((''''''''''''''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%'''))))))(((&&&%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&***)))'''&&&%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''%%%%%%&&&&&&&&&'''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''((((((((((((''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&'''''''''''''''((((((((((((((((((((('''''''''''''''(((((((((((())))))))),,,+++++++++++++++,,,,,,))))))(((((((((((())))))***************)))(((((((((((((((((())))))))))))******+++++++++,,,,,,,,,++++++++++++++++++++++++%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%"""###$$$%%%&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''###$$$$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$######%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&(((((())))))))))))((((((''''''&&&&&&''''''((()))(((((((((((())))))))))))(((((((((((()))***+++,,,************+++,,,------++++++,,,---------------***++++++***))))))***,,,000//////...//////000000000000000000111222333444222222333555666777888999555555555555555666666777999:::999888555444555666999888888888:::;;;:::999;;;;;;===>>>>>>===<<<;;;::::::;;;;;;<<<=========>>>>>>>>>??????@@@@@@@@@???@@@AAAAAABBBAAAAAAAAAAAABBBBBBCCCCCCCCCDDDDDDDDDDDDEEEFFFFFFFFFEEEEEEEEEDDDDDDCCCAAA???>>>===>>>>>>===<<<<<<;;;;;;:::777777777777666666555555222111111000000111111222444444444333222111000///111111111111000///......///.........---,,,,,,,,,+++************++++++,,,,,,,,,,,,+++++++++******))))))))))))************(((((())))))))))))))))))((((((((('''''''''&&&&&&(((''''''&&&&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&$$$%%%'''(((((('''%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&'''''''''''''''(((%%%&&&&&&&&&''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%&&&&&&&&&&&&'''&&&&&&%%%%%%%%%&&&''''''((((((((((((((('''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&'''((()))((((((((((((((((((''''''''''''(((((((((((())))))((((((((((((((())))))******))))))(((((())))))******************)))(((((('''''''''((((((((())))))******+++++++++,,,,,,,,,************++++++++++++%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%"""###%%%&&&'''''''''&&&$$$%%%%%%%%%&&&&&&&&&&&&###$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!""""""###$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%$$$$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$$$$%%%%%%%%%&&&&&&&&&''''''((())))))(((''''''''''''&&&&&&''''''((()))(((((((((((())))))))))))(((((((((((()))***+++,,,************+++,,,---...,,,,,,,,,,,,,,,---......+++,,,,,,+++))))))+++...000000////////////000000////////////000111222222000111333444777888:::;;;666666666666666777888888:::::::::888555444555666888777777888;;;<<<<<<;;;999:::<<<===>>>===<<<<<<::::::;;;;;;<<<=========>>>>>>>>>>>>>>>>>>>>>>>>???@@@@@@AAAAAAAAAAAAAAA@@@AAABBBCCCDDDDDDDDDEEEDDDEEEEEEFFFGGGGGGGGGFFFFFFFFFFFFDDDCCC@@@>>>===???>>>>>>======<<<;;;;;;777777666666666666555555222222111000000111222222222333333444333222111000111111111111000///...---------------------------***************+++,,,,,,,,,,,,,,,+++++++++******))))))))))))************)))))))))***))))))(((((((((((('''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&%%%$$$###%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''######$$$%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%&&&'''((((((((((((((((((&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&%%%$$$$$$%%%''')))***'''((((((((((((((((((((('''''''''((((((((())))))&&&&&&%%%%%%&&&''''''(((******))))))))))))*********************)))(((((((((((((((((())))))))))))******+++++++++,,,,,,,,,*********++++++,,,,,,,,,%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%###$$$&&&((())))))((('''$$$$$$$$$%%%%%%%%%&&&&&&"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!""""""###$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%&&&''')))***&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((($$$$$$%%%%%%%%%&&&&&&&&&%%%&&&'''(((((('''&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&(((((((((((())))))))))))(((((((((((()))***+++,,,************+++,,,---......---,,,+++,,,---...///---///000...++++++...111111000////////////000000............///000111222///000222444777999;;;<<<777777777777777888888999999::::::888666555555777888777777999;;;======<<<777999;;;===>>>>>>===<<<::::::;;;<<<<<<======>>>>>>>>>>>>>>>============???@@@AAAAAABBBBBBAAAAAA???@@@AAACCCDDDEEEEEEEEEDDDEEEFFFGGGGGGHHHGGGGGGGGGGGGGGGFFFDDDAAA???===AAAAAA@@@@@@??????>>>>>>666666666666666555555555333222111000000111222333111222333444333333111000111111111111000///...---,,,,,,------------------******))))))***+++,,,,,,,,,,,,,,,+++++++++******))))))))))))***************************)))((('''(((((('''''''''&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$###%%%%%%&&&&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''######$$$%%%%%%&&&''''''%%%%%%%%%&&&&&&'''''''''"""###%%%&&&'''&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&'''''''''((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''%%%$$$$$$%%%'''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%&&&'''((('''((((((((((((&&&$$$###&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&%%%$$$######$$$''')))+++'''''''''(((((((((((((((''''''''''''((((((((()))+++++++++++++++,,,------******))))))))))))*********************)))(((((())))))))))))******************+++++++++,,,,,,,,,+++++++++,,,,,,---------%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%$$$$$$%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&"""""""""###$$$%%%'''((('''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&"""$$$&&&%%%$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''((()))((('''&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&######%%%&&&''''''(((((($$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%''''''''''''''''''&&&&&&%%%&&&&&&%%%$$$%%%''')))(((((((((((()))))))))))))))************+++++++++------------------------........................---...///000000///...------...//////......///111111222444666888999::::::<<<;;;999888777888999999999888777666666777888999888888999999:::;;;<<<<<<<<<<<<<<<<<<<<<===>>>???===???@@@@@@??????@@@AAA???@@@@@@AAAAAA@@@@@@???@@@@@@@@@AAAAAA@@@????????????@@@@@@BBBCCCEEEFFFDDDEEEGGGHHHGGGFFFDDDCCCFFFGGGHHHHHHGGGDDDBBB@@@EEEBBB???======>>>>>>>>>999888777555555555666666555444333222111111111111//////000000111111111222444333111///......///000------------------------,,,,,,,,,+++++++++******((((((((((((((((((((((((((()))***++++++***)))(((&&&&&&'''((()))***++++++(((((((((((('''&&&%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$(((((('''''''''&&&&&&&&&(((((((((((((((''''''&&&'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&"""######$$$$$$######"""''''''''''''''''''''''''((((((''''''''''''(((((((((((('''''''''&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&((('''&&&%%%%%%%%%%%%%%%((((((((('''&&&&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))***'''&&&%%%%%%'''((((((((('''''''''''''''((())))))******)))((('''&&&%%%%%%&&&&&&&&&&&&''''''''''''***,,,---+++(((&&&''')))(((((((((((()))))))))))),,,------......------,,,,,,,,,,,,,,,,,,,,,,,,,,,%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%$$$######"""$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$#########&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''(((((('''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&&&&&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&''''''''''''''''''''''''"""%%%)))+++***(((&&&&&&(((((((((((()))))))))***)))************+++++++++,,,,,,,,,,,,,,,,,,,,,,,,........................---...///000000///...------...000///......///111222333555777888::::::;;;<<<;;;:::999888999999:::999888888777777888888999888888888999::::::;;;;;;999999999:::;;;<<<>>>>>>===???@@@@@@??????@@@AAA@@@@@@AAAAAAAAAAAA@@@@@@@@@@@@AAAAAAAAAAAA@@@@@@BBBBBBBBBBBBBBBBBBBBBBBBBBBCCCEEEFFFFFFEEEDDDCCCEEEFFFGGGGGGGGGEEECCCBBBDDDAAA>>><<<============<<<;;;999666555444444444444333222111111000000111//////000000000111111111333222///...------...///------------------------+++++++++*********))))))************************((()))************)))((((((((((((((((((((((((((((((((((((((('''&&&%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&(((((('''''''''&&&&&&&&&((((((((((((((('''&&&&&&'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''((((((''''''''''''((((((((('''''''''&&&&&&&&&&&&))))))((('''''''''''''''&&&&&&&&&''''''''''''(((((('''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))))))))'''%%%%%%'''''''''&&&'''''''''''''''(((((())))))))))))(((''''''&&&&&&(((((((((((()))))))))))))))***+++***(((''''''((((((((((((((())))))))))))++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++%%%$$$############$$$%%%$$$$$$%%%%%%%%%$$$"""!!!$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%$$$""""""&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&''''''&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''$$$'''***+++***(((((((((((((((((()))))))))******)))************+++++++++++++++++++++++++++++++++..............................////////////......---///000000//////000111333444555777999:::;;;;;;<<<;;;:::::::::::::::::::::999999888888999999:::888888888999::::::;;;;;;777777777888999;;;<<<======???@@@@@@??????@@@AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBBBBBBBAAAAAADDDDDDDDDDDDCCCAAA@@@>>>@@@AAABBBDDDDDDDDDCCCCCCDDDDDDFFFGGGGGGFFFEEEDDDCCC@@@===<<<<<<===<<<<<<<<<;;;999777666666666666333333222111000000000000//////000000000000111111111000...---,,,------...------------------------*********)))))))))((((((************************((())))))******))))))(((******))))))((('''&&&&&&(((((((((((('''&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$######$$$%%%&&&'''(((((('''''''''''''''&&&&&&&&&)))))))))((('''&&&%%%$$$'''&&&%%%%%%$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((((())))))))))))((((((&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''''''''((((((''''''''''''&&&&&&&&&&&&)))(((((('''''''''''''''&&&&&&&&&&&&''''''''''''''''''&&&%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((())))))***(((&&&%%%&&&&&&%%%$$$''''''&&&&&&''''''((()))(((((((((((((((((((((((((((((((((((()))))))))))))))((('''((())))))((('''(((((((((((())))))))))))******++++++++++++******************************'''%%%$$$""""""$$$%%%''' """%%%&&&&&&%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%&&&&&&!!!###%%%'''((('''&&&%%%&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%'''(((((('''&&&&&&'''%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&''''''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&'''''''''(((&&&&&&&&&'''''''''''''''***)))'''$$$###&&&***...(((((()))))))))*********))))))*********+++++++++++++++++++++,,,,,,,,,,,,...........................//////////////////......000111111000///111222333444666888999:::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;::::::::::::::::::::::::999999::::::;;;;;;;;;;;;888888888888999:::;;;;;;===???@@@@@@??????@@@AAAAAAAAA@@@@@@@@@@@@AAAAAAAAAAAABBBBBBCCCCCCBBBBBBCCCDDDEEEEEEDDDAAA???===>>>>>>@@@AAABBBBBBBBBBBBBBBCCCDDDEEEFFFFFFFFFEEECCCAAA>>>===>>>>>>===<<<888888777777777999:::;;;333222111000//////////////////000000000000000000000000...---------......------------------,,,,,,+++*********))))))))))))((((((((((((((((((((((((((())))))))))))))))))(((***))))))(((''''''&&&&&&''''''(((((('''&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''''''((('''''''''''''''''''''''')))))))))((('''&&&%%%$$$'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%'''&&&&&&%%%%%%%%%&&&&&&$$$$$$%%%%%%&&&&&&&&&'''%%%&&&&&&''''''&&&&&&%%%########################%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((&&&%%%%%%&&&'''&&&%%%'''&&&&&&&&&&&&'''((((((''''''''''''(((((())))))&&&&&&&&&&&&'''''''''''')))'''%%%&&&)))***(((&&&(((((((((((())))))))))))******++++++++++++******++++++++++++++++++++++++(((&&&%%%######%%%&&&((( """%%%&&&&&&%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%&&&&&&###%%%'''))))))((('''&&&%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%'''(((((('''&&&''''''%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&''''''((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))************%%%&&&&&&''''''&&&&&&%%%&&&&&&'''''''''(((((((((&&&&&&&&&'''''''''((((((***(((&&&###"""%%%)))---))))))))))))************))))))*********++++++++++++,,,,,,,,,------............................../////////......////////////000111111000000111333333444666777999999:::::::::;;;;;;;;;;;;;;;;;;;;;:::::::::;;;;;;:::::::::;;;;;;;;;;;;<<<<<<<<<<<<<<<;;;;;;:::::::::::::::===???@@@@@@??????@@@AAAAAA@@@????????????@@@AAA@@@AAABBBBBBCCCCCCCCCBBBAAABBBCCCDDDCCCBBB@@@>>>======>>>???@@@AAAAAAAAA@@@AAABBBCCCDDDEEEEEEEEEDDDBBB@@@???@@@@@@>>>===888888777777777999:::;;;333222111000////////////000000//////////////////000000//////////////////......---------,,,,,,,,,,,,,,,+++++++++*********(((((((((((((((((((((((()))(((((((((((((((((()))''''''''''''(((((((((((('''''''''(((''''''&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''(((((((((((('''&&&%%%$$$'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&'''%%%%%%&&&&&&''''''((((((%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''%%%$$$###$$$&&&(((((((((&&&&&&&&&&&&&&&'''((((((&&&&&&''''''((()))))))))&&&&&&&&&&&&'''''''''''')))'''%%%&&&)))***(((&&&(((((((((((())))))))))))++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,''''''&&&%%%%%%&&&''''''$$$$$$%%%%%%%%%$$$"""!!!$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&(((((())))))(((&&&$$$###%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%'''(((((('''&&&&&&'''%%%%%%%%%&&&''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&'''((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''')))***+++++++++&&&&&&''''''''''''&&&&&&&&&&&&&&&'''''''''((((((%%%%%%&&&&&&'''(((((((((###&&&)))***)))''''''''')))))))))*********++++++)))************+++++++++,,,,,,,,,------......///........................//////............/////////111222222111111222333333444555777888888999999999::::::;;;;;;;;;;;;:::999::::::;;;;;;::::::999;;;;;;;;;;;;;;;<<<<<<<<<===<<<<<<;;;;;;;;;;;;;;;===???@@@@@@??????@@@AAA@@@???>>>======>>>???@@@???@@@AAABBBBBBCCCBBBBBB???@@@AAABBBBBBAAA@@@???======>>>>>>??????@@@@@@??????@@@AAABBBCCCDDDDDDDDDCCCAAAAAAAAAAAA???===<<<;;;999777666666666666333333222111000000000000000000////////////......////////////////////////.........------,,,,,,+++,,,,,,,,,++++++++++++***************************)))((((((''''''(((((()))$$$%%%&&&'''((()))******&&&'''''''''''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&&&&'''''''''''''''&&&''''''''''''&&&%%%%%%'''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%&&&&&&&&&&&&(((''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''&&&&&&''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$""""""###&&&((()))(((&&&&&&%%%%%%&&&&&&'''(((&&&'''''''''(((((())))))(((((((((((()))))))))))))))((('''((())))))((('''(((((((((((())))))))))))++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%$$$######"""$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&(((((('''&&&%%%$$$######%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&((((((&&&%%%&&&'''%%%%%%&&&&&&'''(((((((((''''''''''''''''''''''''$$$$$$%%%%%%%%%&&&&&&&&&((('''%%%%%%%%%(((***,,,''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''(((((((((((((((&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&&&&'''''''''%%%%%%&&&&&&'''(((((()))###&&&***,,,+++)))''''''))))))*********+++++++++)))************+++++++++***++++++,,,------..............................000///...------...///000000111333222111111222444222333444666666777777777777888999;;;;;;;;;:::999888999:::;;;;;;:::999888::::::::::::::::::::::::::::::::::::;;;<<<===>>>===???@@@@@@??????@@@AAA???>>>===<<<<<<===>>>???>>>???@@@AAABBBBBBBBBBBB@@@@@@@@@?????????>>>>>>???>>>>>>>>>>>>>>>??????>>>>>>>>>>>>???AAABBBBBBCCCBBBAAAAAAAAA@@@>>><<<<<<;;;999666555444444444444333222111111000000111000000/////////.........---......//////.........///......---,,,,,,++++++++++++++++++************************************)))(((''''''''''''((()))$$$$$$%%%&&&'''((()))***&&&&&&'''''''''''''''&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''''''(((&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&'''''''''((((((%%%%%%&&&'''''''''&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%%%%%%%&&&&&&&&&((('''&&&&&&%%%%%%&&&&&&$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((''''''&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%###"""###&&&'''((('''&&&&&&%%%%%%&&&&&&'''((('''''''''((((((((((((((((((((((((((()))))))))))))))***+++***(((''''''((((((((((((((())))))))))))******++++++++++++******++++++++++++++++++++++++###$$$$$$%%%%%%$$$$$$###&&&%%%%%%$$$$$$%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$#########$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&''''''&&&%%%%%%&&&%%%%%%&&&&&&'''((())))))''''''''''''''''''''''''$$$$$$%%%%%%%%%&&&&&&&&&)))'''%%%$$$%%%(((+++...''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%$$$&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&'''((())))))))))))***)))((((((***---)))************+++++++++)))************+++++++++))))))***+++,,,,,,------........................000///...------...///000000222333333222111333444222222444555666666666666666777999:::;;;::::::999888888::::::::::::888888999888888888888888888888777777888999;;;===???@@@===???@@@@@@??????@@@AAA???===<<<;;;;;;<<<===???===>>>???@@@AAAAAABBBAAAAAAAAA???>>>============@@@??????>>>>>>>>>>>>???============>>>???@@@AAABBBAAA@@@@@@@@@???===;;;999888777555555555666666555444333222111111111111000000//////.........---,,,,,,---......---------//////...---,,,,,,++++++************))))))))))))(((((((((((((((((((((((()))((('''&&&&&&'''((()))%%%%%%&&&&&&'''(((((()))&&&&&&'''''''''''''''&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''((((((&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&'''((())))))&&&&&&&&&'''''''''(((((($$$$$$%%%&&&'''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%$$$$$$######$$$$$$""""""#########$$$$$$$$$%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%###$$$%%%&&&&&&%%%&&&%%%%%%%%%%%%&&&''''''((((((((((((((((((((((((&&&&&&&&&&&&'''''''''(((***,,,---+++(((&&&''')))(((((((((((())))))))))))))))))************))))))************************&&&&&&&&&%%%%%%$$$$$$$$$###%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%###""""""###%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%&&&''''''''''''&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&''''''''''''(((***)))'''''''''((('''&&&))))))((((((''''''''''''))))))(((''''''''''''(((***)))'''&&&&&&''')))***$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%((('''%%%$$$$$$%%%'''(((******))))))((((((''''''))))))))))))(((((((((((())))))))))))************%%%&&&))),,,......///...,,,,,,,,,---------......///......------///000111222222222111111111111111111222333333444444333333===;;;999777666666888999:::::::::999999999888888<<<;;;:::999888888888888555666777888999:::;;;;;;<<<======>>>???@@@AAAAAA@@@>>>;;;999888888:::;;;:::;;;===???@@@AAAAAA@@@??????>>>>>>======<<<<<<;;;<<<===>>>>>>===<<<;;;;;;;;;<<<<<<<<<<<<;;;;;;>>>>>>>>>???>>>>>>===<<<:::999888777666555444444777555333111000000000111000///...------,,,------,,,,,,,,,---------.........---,,,+++************,,,,,,,,,+++++++++******++++++++++++++++++++++++))))))((('''''''''''''''''''''((((((((((((''''''%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$'''%%%###""""""###%%%'''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&((('''%%%$$$###$$$''''''&&&&&&&&&&&&''''''&&&&&&$$$$$$$$$$$$&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&''''''&&&%%%$$$"""###$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((''''''(((((())))))******'''((()))******)))((('''))))))))))))))))))))))))+++***)))))))))***,,,,,,&&&&&&&&&%%%%%%$$$$$$$$$###$$$&&&&&&$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%&&&'''&&&&&&%%%%%%%%%$$$$$$$$$&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&''''''''''''(((***(((&&&&&&'''((('''&&&(((((((((''''''&&&&&&&&&'''''''''''''''((())))))'''&&&%%%$$$$$$%%%&&&'''%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&$$$$$$%%%&&&''''''''''''''''''&&&&&&&&&))))))))))))(((((((((((())))))))))))************))))))***+++,,,,,,,,,,,,,,,,,,,,,---------......///......---...///000111111111111111111111111111111222333333444444333333555555444333444555666777:::999999999888888888888999888888888888999::::::888888999999:::::::::;;;:::::::::;;;;;;<<<<<<===@@@>>>;;;999888999:::;;;:::;;;===???@@@@@@@@@@@@@@@@@@@@@???>>>======<<<;;;;;;<<<======<<<;;;;;;;;;;;;<<<<<<<<<<<<;;;;;;============<<<;;;;;;:::888777666555444333222222555444333111000///000000000///...------,,,,,,---,,,,,,,,,------------......---,,,+++*********************))))))(((((((((++++++++++++++++++++++++))))))((('''''''''''''''&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###"""$$$)))//////)))"""%%%%%%%%%&&&&&&&&&&&&'''$$$%%%%%%%%%&&&&&&&&&&&&'''&&&%%%###############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###"""!!!###%%%''''''&&&&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((''''''(((((())))))))))))(((((())))))))))))(((((())))))))))))))))))))))))+++***)))))))))***+++,,,&&&&&&%%%%%%%%%%%%$$$$$$###$$$&&&&&&$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%'''(((((('''%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%$$$$$$$$$$$$######&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((()))'''&&&&&&'''''''''&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&''')))***+++&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((())))))((((((%%%%%%%%%&&&'''''''''((()))(((&&&%%%%%%%%%&&&&&&&&&'''''''''''''''(((((((((((((((((())))))))))))))))))))))))************---,,,++++++******++++++,,,,,,,,,---------............------......///000000000000000000000000000111222333333444444333333000000111222333555666666888888888888777777777777555666666777888999;;;<<<::::::::::::::::::::::::<<<<<<<<<===============???===;;;999999:::;;;<<<;;;<<<===>>>???@@@@@@???BBBBBBAAA@@@>>>===<<<<<<::::::;;;;;;;;;;;;::::::;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;:::999888888777555555444333222222111111444333111000////////////000///...---,,,,,,,,,,,,,,,,,,,,,,,,---------------,,,+++***************))))))))))))(((((((((((())))))))))))))))))))))))))))))((('''''''''''''''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%"""###%%%&&&&&&%%%###"""%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&$$$&&&111<<<===222&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&%%%$$$#########$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$### ###%%%''''''&&&&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''))))))))))))))))))))))))'''(((((((((((()))))))))))))))(((((((((((())))))))))))))))))))))))))))))******))))))******+++,,,%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%''''''%%%$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%&&&''''''&&&%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((&&&%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''((()))***''''''((())))))(((''''''&&&&&&'''((((((((((((((($$$%%%%%%&&&'''(((((())))))((('''&&&%%%%%%&&&&&&(((((())))))*********+++(((((((((((())))))))))))((()))))))))************---,,,+++***)))***+++,,,,,,,,,,,,---------......------------......//////////////////000000000000111222333333444444333333000111333555666777777777777777777777777666666666555555555666777888::::::888999999999::::::;;;;;;>>>>>>>>>===============>>>===;;;::::::;;;<<<===<<<<<<===>>>>>>?????????BBBBBBAAA???===<<<;;;:::999999999::::::999999999;;;::::::::::::::::::;;;:::999888777666555555555444444444333222111111111222111111000///.........//////...---,,,,,,,,,,,,++++++,,,,,,,,,---------,,,,,,+++***************************************))))))))))))))))))))))))))))))((('''''''''''''''%%%&&&&&&''''''&&&&&&%%%'''&&&%%%$$$$$$%%%&&&''''''''''''&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%(((222======333((($$$$$$%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&'''''''''######$$$$$$%%%&&&&&&'''%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$###!!! ###%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&'''$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''))))))))))))))))))))))))(((((((((((((((((((((((())))))(((''''''(((***+++((((((((((((((((((((((((***************+++++++++%%%%%%%%%%%%%%%%%%%%%%%%%%%'''(((((('''&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$######$$$%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((('''%%%$$$$$$&&&'''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''''''''((())))))(((''''''%%%%%%&&&''''''''''''&&&%%%%%%&&&&&&'''((())))))((((((''''''&&&&&&&&&&&&((()))))))))******++++++'''((((((((()))))))))***((()))))))))************+++******)))***+++---...,,,,,,,,,---------......,,,------.....................//////000000000000111222333333444444333333333444555666666666666555666666666666666666666666777666666555555666666777555555666888999;;;<<<<<<;;;:::::::::::::::::::::<<<<<<;;;;;;;;;<<<========================>>>>>>AAA@@@???>>><<<:::999999999999999888888999999999;;;:::999999999999:::;;;999888666555444444444555555555444444333222222222000000000000///......---///...---,,,,,,++++++,,,+++++++++,,,,,,,,,------++++++******))))))******))))))))))))))))))))))))(((((((((((((((((((((((())))))((('''''''''''''''''''''((((((((((((''''''((('''&&&%%%%%%&&&'''((('''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%###""""""###%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$""""""%%%***...///***%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&&&&######$$$$$$%%%%%%%%%%%%"""$$$%%%%%%$$$###$$$%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&'''''''''&&&%%%$$$######$$$%%%&&&$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((((((''''''''''''''')))((('''''''''(((***+++''''''''''''''''''''''''))))))******++++++++++++$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&((((((&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%###""""""###%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''(((&&&$$$######%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&(((''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&'''((((((((()))'''''''''''''''''''''''''''(((((((((((((((((()))''''''(((((())))))******))))))))))))************)))))))))***+++---...///,,,,,,,,,---------......,,,,,,---............---...//////000000111111222111222333333444444333333444444444444444444333333666666666666777777777777888777666555444444444444333444555777999;;;======<<<<<<<<<<<<<<<<<<<<<<<<;;;;;;;;;;;;<<<===>>>>>>>>>>>>===<<<<<<<<<======??????>>>===;;;:::999999999999888888888888999999::::::888888888888::::::888777555444444444555666555555555444444333333333000000000000000///......///...---,,,++++++++++++++++++++++++,,,,,,,,,,,,+++******)))))))))******&&&&&&&&&&&&''''''''''''(((((((((((((((((((((((())))))(((''''''''''''''''''(((((((((((((((((('''(((''''''&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!""""""######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%'''%%%###!!!!!!###%%%'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$&&&&&&&&&%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''&&&%%%$$$###""""""######$$$$$$%%%%%%&&&"""$$$''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&''''''((((((%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((((((''''''''''''&&&(((''''''(((((()))***+++''''''''''''''''''''''''))))))***++++++++++++***$$$$$$$$$%%%%%%&&&&&&&&&###%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''&&&%%%%%%$$$$$$$$$%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''(((%%%$$$"""###%%%&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%%%%&&&'''''''''&&&%%%$$$$$$%%%&&&'''%%%&&&&&&'''''''''''''''''''''''''''((((((((((((%%%&&&'''(((((())))))))))))))))))((((((((((((((('''''''''((()))*********))))))))))))************((()))***+++,,,---------,,,,,,,,,---------......+++,,,---.........------//////000000111222222333111222333333444444333333555444333222222333444555666666666777777888888888777666555444333333333333555666777888:::;;;<<<===>>>>>>>>>??????@@@@@@@@@;;;;;;;;;<<<===>>>>>>??????>>>===<<<;;;<<<<<<===???>>>>>>===<<<;;;;;;;;;:::999888888888888999::::::999888777777888999:::777666555444444666777999444444444444444333333333000000111111111000///...///...---,,,++++++++++++***++++++++++++,,,,,,,,,******))))))))))))******%%%%%%%%%&&&&&&'''''''''))))))))))))))))))))))))))))))((('''''''''''''''&&&''''''((((((''''''&&&%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$'''(((((('''&&&&&&''')))###$$$$$$$$$$$$%%%%%%%%%#########$$$$$$$$$%%%%%%!!!"""###$$$%%%$$$$$$#########$$$$$$%%%&&&&&&'''$$$%%%&&&&&&%%%%%%&&&(((&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&'''((((((((($$$$$$%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&&&&'''((())))))*********))))))))))))))))))))))))((()))***+++,,,++++++***$$$$$$$$$%%%%%%&&&&&&&&&!!!###%%%%%%###"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%'''(((((('''%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&'''&&&%%%%%%$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((%%%###"""###$$$&&&&&&%%%%%%%%%%%%&&&&&&'''''''''$$$$$$$$$%%%&&&'''((()))***)))'''&&&&&&''')))***&&&''''''(((((((((((((((((((((((((((((('''''''''$$$%%%&&&((())))))***))),,,,,,++++++******))))))&&&''''''((()))******+++))))))))))))************((()))+++,,,------,,,+++,,,,,,,,,---------......+++,,,---.........---,,,///000000111222333333333222222333444444444333333666555333333333555777888666666777777888888999999666555444333333333333444888888999::::::;;;<<<<<<:::;;;;;;<<<===>>>>>>???:::;;;;;;<<<===>>>??????@@@???===<<<;;;;;;<<<<<>>>>>======<<<<<<;;;:::999888888999:::;;;:::999777666666777999:::777666555444555777999:::444444333333333333333333000000111222222111//////......---,,,++++++++++++******+++++++++,,,,,,,,,***)))))))))))))))******'''''''''((((((((())))))************************))))))((('''''''''''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$&&&''''''&&&$$$$$$###$$$$$$%%%&&&'''(((((($$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%""""""#########$$$$$$$$$!!!$$$'''(((((($$$$$$%%%&&&&&&'''((((((%%%%%%%%%###"""$$$'''***&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&'''((())))))###$$$%%%&&&&&&%%%$$$#########$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&%%%&&&(((************)))************************((()))***+++,,,+++******#########$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###%%%&&&&&&%%%$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$###$$$$$$%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''######$$$$$$$$$%%%%%%%%%'''''''''&&&&&&%%%%%%%%%(((((('''''''''&&&&&&&&&((('''&&&%%%%%%&&&'''(((%%%%%%&&&'''((((((((('''$$$%%%&&&''''''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&(((((('''&&&%%%))))))(((((('''''''''&&&))))))))))))))))))))))))))))))))))))************)))))))))))))))*********))))))))))))************///............------------------.........///////////////000111111222222333444444555555444444444000111111222444555666666555666777888888888888888666555444333333333333333777888999:::;;;<<<<<<<<<>>>>>>>>>>>>============<<<<<<<<<<<<<<<<<<<<<<<<<<<===>>>===<<<<<<>>>@@@AAA@@@???===<<<<<<<<<<<<888888999::::::::::::999777888888999999999888888888888999999999999::::::888777555333222222222222222111111000///......------------,,,,,,+++++++++,,,,,,,,,++++++*********))))))))))))(((((((((((()))))))))(((''''''&&&&&&(((((((((((((((((((((((())))))((((((''''''&&&&&&******)))(((''''''&&&&&&'''''''''''''''''''''''''''%%%###$$$&&&'''%%%###)))'''&&&$$$######$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&'''&&&$$$######$$$&&&'''########################%%%%%%%%%%%%%%%%%%%%%%%%)))((('''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$######$$$%%%%%%%%%$$$$$$&&&'''''''''&&&&&&%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$######"""&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&&&&$$$"""&&&&&&&&&%%%%%%$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&''''''''''''((((((((())))))******&&&&&&&&&''''''''''''((((((((('''''''''&&&&&&&&&))))))))))))************)))************+++++++++$$$$$$$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&''''''&&&%%%$$$&&&%%%%%%%%%%%%%%%%%%$$$''''''''''''''''''''''''###%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$#########((('''''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%&&&''''''''''''''''''%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''''''''&&&%%%((('''''''''&&&&&&&&&&&&(((((((((((((((((((((((((((((()))))))))*********+++*********)))(((((((((((((((((()))))))))******,,,,,,,,,------.........+++,,,,,,,,,------------......//////000111111111111111222222222111111000000000111222333444555555888888888999888888777777666555444444333333333444666777999:::;;;<<<<<<<<<=====================<<<<<<<<<<<<;;;;;;;;;;;;;;;===>>>???>>>======???AAAAAA@@@???===<<<;;;;;;;;;::::::;;;;;;;;;;;;::::::777888888999999999888888888888999999999:::::::::888777555444222222222333111111000000///......------------,,,,,,+++++++++,,,,,,,,,++++++*********))))))))))))((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((((((((('''''''''''''''&&&&&&%%%$$$$$$######'''''''''''''''''''''''''''%%%###$$$&&&'''%%%###)))(((&&&%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$###!!! !!!###$$$########################%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%$$$$$$###$$$%%%%%%&&&&&&&&&&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''''''''(((''''''%%%###"""&&&&&&&&&%%%%%%%%%$$$$$$'''&&&&&&%%%%%%&&&&&&'''%%%%%%&&&&&&&&&&&&&&&&&&'''''''''((((((((())))))&&&&&&&&&''''''''''''((((((((('''''''''&&&&&&&&&))))))))))))************))))))*********+++++++++%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###%%%&&&&&&%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$''''''&&&%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%$$$$$$$$$$$$######''''''''''''&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%$$$&&&''''''''''''&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''(((((())))))))))))******,,,+++******(((((('''&&&''''''((((((((())))))))))))***+++,,,---......///*********+++++++++,,,,,,------......///000000000111111111111111000///...//////000111222333333444888888888888777666555444666555444444333444444444555666888:::;;;<<<======:::;;;<<<=========;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;>>>???@@@???>>>>>>@@@BBBBBBAAA???===<<<;;;::::::===============<<<;;;:::888888999999999888888777888999999999999:::::::::888777666444444333333333111000000//////.........------,,,,,,,,,,,,+++++++++++++++++++++*********))))))))))))(((((((((((($$$%%%%%%&&&''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''((((((((()))((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$&&&&&&%%%$$$((('''&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$############$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&###"""!!! !!!"""###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%&&&%%%%%%$$$###"""!!!"""###%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&(((((('''''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&''''''''''''(((&&&&&&&&&''''''''''''((('''''''''''''''&&&&&&&&&))))))))))))************)))))))))*********++++++&&&&&&&&&%%%%%%$$$$$$###$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&###########################%%%&&&&&&%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$!!!!!!"""""""""#########&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&''''''&&&%%%$$$''''''''''''&&&&&&%%%$$$'''&&&%%%$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((((((((()))))))))*********))))))((((((((('''''''''''''''(((((((((((()))******+++,,,,,,------******+++++++++,,,,,,,,,,,,,,,------...//////000222333333222222111000///...//////000111222222222444444555555555444444333555555444444444444555555555666888:::;;;======>>>999:::;;;======<<<;;;:::::::::::::::;;;;;;;;;;;;>>>???@@@@@@??????AAACCCCCCBBB@@@>>><<<;;;::::::?????????>>>===;;;:::999888888999999999888777777888888888999999999::::::777777666555444444333333000000/////////.........,,,,,,,,,,,,,,,,,,,,,,,,+++++++++***************))))))))))))(((((((((((('''((((((((()))))))))***&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((())))))))))))((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%&&&&&&%%%%%%%%%&&&%%%###""""""###%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%$$$###""" """$$$&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''&&&&&&&&&&&&&&&&&&%%%%%%'''&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''''''''''''''''''''((()))))))))************))))))))))))************'''&&&&&&%%%%%%$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###%%%&&&&&&%%%$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%!!!!!!"""""""""#########&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%&&&'''(((((('''&&&%%%&&&'''''''''&&&%%%$$$$$$'''&&&%%%$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''(((''''''''''''''''''(((((('''''''''''''''''''''''''''(((((((((((()))))))))''''''(((((()))))))))***''''''''''''((((((((((((++++++++++++++++++++++++,,,,,,,,,,,,---------...,,,,,,,,,---......//////222222222222222111000////////////000000111111222222333444555666666666666555555444444444555555666666777888:::;;;<<<======888999:::<<<<<<<<<;;;::::::::::::;;;;;;<<<<<<<<<>>>???@@@@@@???@@@BBBDDDCCCBBBAAA???===<<<<<<<<>>===;;;999999999999999999999888777666777777777888888888999999666666666555555444333333////////////............,,,,,,,,,,,,,,,,,,,,,,,,************************))))))))))))((((((((((((******)))))))))(((((((((''''''''''''''''''''''''%%%%%%&&&&&&''''''((((((&&&&&&%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''$$$%%%%%%%%%%%%%%%%%%$$$&&&%%%###""""""###%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&'''''''''&&&%%%$$$###""" """$$$&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''(((&&&'''''''''''''''''''''((()))))))))************(((((()))))))))*********&&&&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%%%%&&&&&&'''%%%%%%$$$$$$$$$$$$%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###%%%&&&&&&%%%$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&######$$$%%%%%%&&&''''''%%%%%%''''''''''''%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''((((((''''''&&&%%%&&&&&&&&&&&&%%%%%%$$$'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''(((((((((((((((''''''''''''''''''''''''''''''(((((((((((())))))%%%&&&'''''')))******+++''''''((((((((())))))))),,,,,,,,,+++++++++******------............//////,,,,,,------...///////////////000000000000////////////000000111111111111333333555777888999999999555555555444555555666777777888999:::;;;<<<<<<<<<999:::::::::;;;<<<<<<===:::;;;;;;<<<<<<============???@@@@@@???@@@BBBDDDCCCCCCAAA@@@?????????>>>?????????>>>===<<<:::999999999999999999888777666555666666666666777777777444444555555444444333222........................++++++,,,,,,,,,,,,------)))))))))***************))))))))))))(((((((((((())))))(((''''''&&&%%%%%%((((((((((((((((((((((((&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&######$$$$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&((('''&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&'''&&&&&&%%%$$$###!!!"""###%%%&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###""""""!!!"""###%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%''''''((((((((((((((((((&&&&&&&&&&&&'''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&%%%%%%'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''''''''))))))))))))************((((((((()))))))))******%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&######$$$%%%%%%&&&'''''''''&&&%%%$$$$$$%%%&&&'''&&&%%%%%%%%%%%%%%%%%%$$$""""""""""""""""""""""""###%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&''''''&&&$$$###%%%%%%%%%%%%&&&&&&&&&&&&#########$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''''''''&&&%%%&&&&&&&&&''''''((((((((((((((((((((((((((((((((('''''''''((((((((())))))&&&'''''''''((()))))))))((((((((()))))))))******+++++++++,,,,,,,,,,,,,,,------........./////////---------...//////000000......///000111111111111000000111111111111222222222333444666666777777777555555555555555666777777888999::::::;;;;;;;;;:::;;;;;;:::999:::<<<>>>???;;;;;;<<<======>>>??????<<<>>>?????????@@@BBBDDDDDDCCCBBBAAAAAAAAAAAAAAA@@@@@@@@@@@@???>>><<<<<<999::::::999999777666666444444444555555555555666222333444444444333222111........................+++++++++,,,,,,---------((()))))))))*********+++))))))))))))(((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&%%%))))))))))))))))))))))))%%%%%%%%%%%%%%%%%%%%%%%%###%%%'''&&&$$$###%%%'''$$$%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%&&&&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&&&&&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!!!!!!!###%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%&&&'''((()))((('''&&&&&&&&&&&&&&&&&&'''''''''((('''&&&&&&%%%%%%&&&&&&'''%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&%%%&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''(((((())))))))))))************(((((((((((()))))))))***%%%%%%%%%&&&&&&''''''''''''&&&$$$$$$$$$$$$&&&'''######$$$%%%%%%&&&''''''''''''%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###%%%'''&&&%%%$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&'''&&&&&&%%%%%%$$$$$$###"""###%%%&&&&&&%%%###"""######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&'''''''''$$$$$$$$$%%%%%%&&&&&&&&&'''&&&$$$$$$$$$$$$&&&'''###$$$%%%%%%&&&&&&&&&&&&$$$%%%''''''''''''%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&(((((('''&&&%%%%%%%%%%%%&&&&&&'''''''''))))))))))))))))))))))))''''''''''''((((((((()))((((((((((((((('''''''''))))))))))))******************+++,,,---......///---------.........//////------......///000000000///000111333444444444444111111111111111222222222111111222333333333222222555555555555555666777777999::::::;;;;;;::::::999===;;;:::999999<<>>??????@@@<<<===>>>???>>>???BBBDDDDDDCCCCCCBBBBBBCCCCCCCCCAAAAAAAAAAAA@@@@@@???>>>:::::::::999999777666666333333333444444444555555111222333444333222111000---.....................+++++++++,,,,,,---------(((((())))))*********+++))))))))))))(((((((((((((((((())))))******++++++&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###%%%'''&&&$$$###%%%'''%%%&&&'''((((((((('''&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%$$$###"""&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''########################$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&'''&&&&&&&&&&&&'''''''''&&&&&&%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!!!!"""$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$%%%&&&''''''%%%###"""&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&'''''''''(((((((((''''''&&&&&&&&&&&&&&&&&&'''''''''((((((&&&&&&&&&'''''''''(((((())))))))))))************(((((((((((())))))))))))%%%&&&&&&''''''&&&&&&%%%)))((('''&&&%%%$$$######&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%&&&''''''&&&$$$%%%(((******'''&&&''')))$$$$$$$$$$$$$$$$$$$$$$$$))))))((('''%%%$$$######%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&)))(((&&&%%%%%%&&&((()))((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&%%%%%%((((((((((((((((((((((((''''''&&&'''((()))+++,,,(((((((((((())))))))))))(((((((((((()))))))))))),,,,,,++++++++++++++++++////////////////////////...............///000000111///...000333444333111...000222222111111111222777666555444555888;;;===666666666777888888999999;;;<<<<<<;;;888666666777999:::;;;<<<============:::;;;===>>>>>>>>>===<<<===>>>>>><<<:::999:::;;;???@@@AAACCCDDDDDDCCCCCCBBBAAA???>>>>>>>>>???@@@===<<<;;;999666444222222000000///......///000111111111111111000000000///...............---------,,,,,,,,,,,,,,,+++***))))))******++++++)))((('''(((((((((((((((((((((((())))))(((((('''''''''&&&''''''&&&&&&&&&&&&'''''''''))))))((('''&&&'''(((&&&''''''''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&%%%###"""'''&&&&&&%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$###"""""""""###'''&&&$$$###"""###$$$$$$%%%$$$$$$######$$$$$$%%%"""###%%%'''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&""""""###$$$%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&******)))''''''&&&&&&&&&###$$$&&&(((((('''&&&%%%''''''(((((('''&&&%%%%%%'''''''''&&&&&&%%%%%%%%%$$$%%%&&&'''(((((((((((('''(((((()))))))))))))))))))))))))))))))))))))))%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%&&&''''''&&&$$$###&&&((('''%%%$$$%%%'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''''''''&&&&&&&&&&&&((((((((((((((((((((((((((('''''''''((()))***+++'''((((((((())))))))))))))))))))))))************,,,,,,,,,,,,,,,,,,,,,---.......................................///000000111///...000333444333111000222333444333222333444777777555444555666888999444555555666666777888888888999:::888777666888999:::;;;<<<===>>>>>>>>>>>>;;;<<<<<<===============???@@@@@@>>><<<;;;;;;===>>>???AAABBBCCCCCCBBBBBBAAA@@@???>>>===>>>>>>???===<<<:::888666444333222111000000//////000111111111111111000000000////////////......------,,,,,,,,,,,,,,,,,,,,,+++***))))))******+++***)))((('''(((((((((((((((((((((((()))(((((((((''''''''''''''''''&&&&&&&&&&&&'''''''''((()))((('''&&&'''(((&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&%%%$$$$$$$$$$$$$$$&&&%%%%%%$$$######$$$$$$&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#########$$$%%%%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&***)))((('''&&&&&&&&&&&&&&&'''((()))***))))))(((''''''(((((('''&&&&&&%%%'''''''''&&&&&&%%%%%%%%%$$$%%%&&&'''((((((((((((%%%&&&&&&'''''''''''''''((((((((((((((((((((((((%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%''''''&&&%%%$$$%%%''''''%%%$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%&&&'''((()))%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%###$$$%%%&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&###%%%&&&((((((&&&%%%###$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''''''''(((((((((((((((((((((((((((((((((((()))((((((''''''((())))))''''''((((((((()))))))))************++++++++++++,,,,,,,,,------................................................///000000111000///000222333333222222444666666555444555666777777666666555555444444333333333444444555666777777777888777666777999;;;;;;<<<<<<===>>>>>>??????===<<<<<<<<<<<<======>>>AAABBBBBB@@@>>><<<===>>>===>>>@@@AAABBBBBBAAA@@@??????>>>=========>>>>>><<<;;;:::888666555333333222222111000000111111222000000000000//////////////////...------,,,++++++++++++,,,,,,,,,+++******)))************)))((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''&&&&&&&&&&&&'''''''''((()))(((&&&&&&&&&'''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#####################$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%$$$$$$###'''&&&&&&%%%%%%&&&&&&'''((('''&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''(((''''''&&&%%%'''''''''&&&&&&&&&&&&&&&%%%%%%&&&'''((((((((((((%%%&&&&&&'''''''''''''''((((((((((((((((((((((((%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''&&&$$$%%%&&&'''&&&%%%&&&'''((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%&&&(((((()))%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%###$$$%%%&&&''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''((((((((((((((())))))))))))(((((((((((((((((((((((())))))(((((('''''''''''''''''''''((((((((()))))))))))))))*********++++++***++++++,,,---......///------------------------...............///000000000000000111222333333333444666777888666666777888666666777777777666555444444333333333444555666777888999888777666777:::<<<;;;;;;;;;<<<<<<===>>>???>>>===<<<;;;;;;<<<===>>>AAABBBCCCAAA???======>>>===>>>???@@@AAA@@@@@@???>>>>>>==================;;;;;;:::888777555444333333333222222222222222222000000/////////.........///......---,,,+++******++++++,,,,,,,,,++++++***************)))))))))(((((((((((((((((((((((((((((((((((((((((('''''''''''''''&&&&&&&&&&&&'''''''''((()))(((&&&%%%&&&'''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''########################&&&%%%%%%$$$$$$##################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%&&&$$$$$$&&&&&&&&&%%%$$$###&&&&&&%%%%%%%%%%%%&&&&&&((('''%%%$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$$$$%%%$$$$$$#########$$$%%%&&&&&&'''''''''''''''&&&&&&'''''''''''''''&&&&&&&&&%%%&&&&&&'''(((((('''''''''(((((()))))))))))))))((((((((((((((((((((((((%%%&&&&&&''''''&&&&&&%%%&&&&&&%%%%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&(((&&&$$$$$$&&&'''&&&&&&&&&&&&''''''((('''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&'''''''''%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&$$$%%%&&&&&&'''''''''&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&''''''''''''''''''''''''$$$$$$%%%%%%&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''(((((((((((()))))))))******(((((((((((((((((((((((())))))((((((''''''&&&&&&''''''''''''((((((((((((((((((((()))))))))******)))******+++,,,------...------------------------...............///000000///000111111111222333333444666888888777777777888444666777999999888777666555444333333444555777888;;;;;;;;;:::888888999;;;:::::::::::::::<<<===>>>>>>===<<<;;;;;;<<<===>>>???@@@AAAAAA???============>>>???@@@@@@@@@???>>>=========>>>>>>>>>======::::::999888777666555444333333333333222222111111/////////............---...------,,,++++++*********++++++,,,,,,,,,++++++*********)))))))))))))))(((((((((((((((((((((((('''''''''(((((((((((((((''''''&&&&&&&&&&&&''''''&&&(((((('''&&&%%%&&&'''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''########################%%%%%%%%%$$$$$$############$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&'''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$''''''''''''''''''''''''%%%%%%$$$$$$$$$$$$%%%%%%###$$$&&&''''''&&&%%%$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%&&&((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%(((''''''''''''((())))))&&&&&&'''''''''''''''&&&''''''''''''''''''''''''%%%&&&''''''(((''''''''''''(((((()))))))))))))))''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&%%%%%%$$$$$$######&&&%%%%%%$$$$$$%%%%%%&&&(((&&&$$$$$$%%%''''''&&&%%%$$$###$$$&&&&&&$$$###$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&(((&&&%%%######%%%&&&(((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&''''''''''''(((''''''(((((())))))******((((((((((((((((((((((((((((((((((((((('''&&&%%%&&&&&&'''''''''((((((((('''((((((((())))))))))))*********++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,...............///000000...000222222111111222444444666888888777666777888555666777999999999888777555444333222333555777999;;;<<<===<<<:::999999::::::999999888999;;;<<<===>>>======<<<<<<<<<<<<===<<<>>>@@@@@@???>>>===>>>>>>???@@@AAAAAA@@@???>>>======>>>?????????>>>>>>999999999888777666666555333333333333333222111000///.........------------,,,,,,++++++++++++************+++,,,,,,,,,+++++++++******)))((()))))))))(((((((((((((((((((((((('''''''''(((((((((((((((''''''&&&&&&&&&&&&''''''&&&'''((('''%%%%%%%%%&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&%%%%%%$$$#########$$$$$$%%%%%%&&&&&&'''&&&&&&%%%%%%%%%&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$'''''''''&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%&&&'''))))))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&'''''''''(((((((((%%%&&&''''''(((''''''''''''''''''''''''(((((((((&&&&&&'''''''''''''''&&&%%%&&&&&&'''''''''''''''''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&)))&&&$$$###%%%&&&''''''%%%######$$$&&&&&&$$$"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&(((((((((((('''&&&%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''(((&&&&&&'''(((((()))******((((((((((((((((((((((((&&&'''((((((((('''&&&%%%&&&&&&&&&'''''''''(((((((((((()))))))))*********+++,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++...............///000000...000222222111000222555333555666777666555666777777777777777777777666666444333111111111333666888777999<<<<<<;;;:::::::::;;;:::999999999;;;===>>>===============<<<<<<;;;:::===???AAA@@@???????????????@@@AAAAAA@@@???>>>======???@@@@@@@@@??????999999888888777777666666222333333333222111//////.........---------,,,,,,************++++++++++++)))***+++,,,,,,,,,,,,+++++++++)))((((((((()))***((((((((((((((((((((((((''''''''''''((((((((()))''''''&&&&&&&&&&&&''''''&&&'''((('''%%%$$$%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%$$$$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''&&&%%%%%%%%%%%%&&&'''((($$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%&&&''''''%%%%%%%%%$$$$$$%%%%%%%%%$$$%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%&&&'''''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$%%%&&&'''''''''&&&&&&%%%&&&&&&'''((((((''''''&&&'''''''''((((((((()))&&&'''''''''''''''&&&&&&%%%&&&&&&'''''''''''''''''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%!!!"""###$$$%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&)))&&&$$$###%%%&&&'''''''''%%%$$$%%%((((((&&&$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''((((((%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''))))))(((((('''&&&$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&((())))))(((&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((%%%&&&&&&'''((())))))***((((((((((((((((((((((((%%%&&&'''(((((('''&&&&&&&&&&&&&&&'''''''''(((((()))************+++++++++---------------------,,,++++++++++++++++++++++++...............///000000...000222222000000222555222444666666555444555666999888777666555444333333333222000///000222555777222666:::<<<<<<;;;::::::<<<;;;:::999:::<<<>>>@@@<<<===>>>>>>>>>===;;;:::999<<<@@@AAAAAA@@@AAAAAA???@@@AAABBBAAAAAA??????===>>>???AAAAAAAAA@@@???888888888888777777666666222222333333222111///.........---------,,,,,,,,,)))))))))***++++++,,,,,,)))***+++,,,,,,,,,,,,,,,,,,+++)))((((((((()))***((((((((((((((((((((((((&&&'''''''''(((((())))))'''''''''&&&&&&'''''''''&&&'''((('''%%%$$$%%%&&&&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%&&&&&&'''$$$$$$%%%%%%%%%&&&&&&&&&#########$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((('''%%%$$$###$$$$$$%%%###$$$$$$%%%%%%&&&&&&'''######$$$%%%%%%&&&''''''&&&%%%%%%$$$%%%&&&'''((($$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&'''((()))&&&%%%%%%$$$%%%&&&((()))'''&&&&&&%%%%%%&&&&&&'''%%%&&&'''((('''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''(((((($$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''''''''(((***,,,,,,+++***(((%%%%%%&&&'''((((((((('''&&&'''''''''(((((())))))&&&'''''''''''''''&&&&&&'''(((((()))))))))))))))''''''''''''''''''''''''######$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''&&&&&&%%%$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%''''''&&&$$$%%%%%%$$$###$$$%%%&&&'''$$$%%%&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$#########"""###%%%''''''&&&%%%$$$''''''''''''''''''''''''%%%&&&((()))************&&&'''''''''&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&'''&&&$$$$$$$$$&&&((()))))))))((((((((((((((())))))(((''''''((()))(((&&&&&&&&&&&&'''''')))******))))))((((((''''''&&&&&&,,,,,,,,,++++++++++++***...------,,,,,,++++++******+++,,,,,,+++***((('''222000---***((()))***+++/////////000111111222222333444555666666666555444444666888888666333222111000111111222444555555666444444444444666888:::;;;:::888666888;;;======;;;:::;;;<<<=========<<<;;;<<<===>>>??????@@@@@@@@@=========;;;:::999;;;===???>>>===<<<<<<===>>>???:::999888777666555444333555555444333111///---,,,......---,,,,,,+++******,,,,,,+++******+++,,,,,,,,,,,,+++***)))))))))***+++******)))))))))))))))'''''''''''''''''''''&&&%%%&&&'''(((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$%%%&&&'''(((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$""" !!!$$$&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######$$$%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&%%%%%%%%%$$$#########""""""!!!!!! !!!"""######$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$######&&&&&&&&&&&&&&&&&&&&&&&&########################$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$$$$######&&&'''''''''&&&%%%%%%$$$%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%$$$$$$$$$%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$#########''''''''''''&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%&&&'''(((((('''&&&%%%%%%%%%%%%&&&&&&'''''''''&&&''''''((()))(((((((((''''''((((((((((((''''''%%%%%%&&&&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###%%%''''''&&&%%%'''&&&&&&&&&&&&'''(((((($$$%%%&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%###%%%&&&(((((('''&&&%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%$$$$$$&&&''')))))))))((((((((((((((())))))'''''''''((()))(((&&&&&&&&&&&&&&&'''((()))***)))))))))(((((('''''''''))))))******++++++,,,,,,,,,,,,,,,,,,,,,---------++++++++++++++++++***)))222111...,,,++++++,,,,,,/////////000111111222222444555555666666666666666666777888777555222111111000111111222444555555666555555444555666777999:::999777666888;;;======;;;;;;;;;<<<=========<<<;;;;;;;;;<<<======>>>===============;;;:::999;;;======<<<;;;:::::::::;;;<<<:::999999888777666555555333333333222111000///...//////...------,,,++++++,,,++++++******++++++,,,,,,+++******))))))******+++***))))))(((((())))))''''''''''''''''''((((((&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&'''(((&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$"""###%%%((($$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$############""""""###$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%'''''''''&&&&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%$$$$$$$$$$$$%%%%%%((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$######&&&&&&&&&'''&&&&&&%%%%%%&&&&&&&&&&&&&&&'''''''''&&&&&&'''(((((('''&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&'''(((((((((((('''''''''((((((((((((''''''%%%%%%&&&&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$'''((('''&&&%%%&&&''''''((((((''''''$$$%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&###$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&((((((((('''''''''''''''%%%&&&'''((()))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&$$$#########$$$%%%&&&&&&''''''&&&&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%$$$%%%&&&'''((()))((((((''''''((())))))((('''''''''))))))(((&&&&&&&&&&&&&&&'''((())))))))))))))))))((((((((((((''''''((()))***+++,,,,,,******++++++,,,------...+++++++++++++++,,,,,,---222111000000///...------...//////000000111111222555555555555666666777888888888888666333111111222111111222333333444555555666555555555555666777777888777666777:::<<<<<<;;;;;;;;;<<<<<<<<<;;;;;;:::999::::::;;;;;;;;;;;;:::<<<======;;;:::999;;;<<<<<<<<<;;;:::999999::::::999999888888777777777666111111111111111000000000//////......------,,,,,,,,,+++************+++,,,++++++***)))))))))******+++***))))))(((((())))))'''''''''(((((()))))))))'''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''(((&&&&&&%%%%%%%%%$$$$$$$$$'''''''''''''''''''''''''''''''''&&&$$$%%%''')))$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&''''''(((&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&%%%''''''''''''&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$###&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&'''&&&&&&&&&((('''''''''''''''''''''&&&&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&'''''''''%%%%%%&&&'''''''''''''''''''''((((((((((((''''''#########$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$'''(((((((((###$$$%%%&&&'''&&&%%%$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&((((((((('''''''''''''''%%%%%%&&&'''(((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&)))(((&&&$$$$$$%%%'''(((%%%&&&&&&'''&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%&&&&&&'''(((((('''''''''((())))))'''&&&&&&((()))***(((&&&&&&&&&&&&&&&&&&'''((()))))))))))))))))))))))))))'''''''''((()))******+++))))))*********+++++++++,,,+++******+++---...000///000111111000///...---......//////000111111111555444333333444555777888999999888555222111111222111111222333333444555555666555555555555555555555777777666777999:::;;;;;;::::::::::::999999999888999999::::::::::::999999;;;<<<===<<<:::999:::;;;======<<<<<<;;;;;;::::::777777777777666666666666111111000000////////////......---------,,,,,,,,,++++++************++++++******))))))))))))************)))(((((((((((((((''''''(((((()))*********((('''&&&%%%%%%&&&'''(((''''''''''''''''''''''''%%%%%%%%%%%%&&&&&&''''''&&&%%%%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%''')))$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&'''''''''(((&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%$$$$$$###'''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&''''''''''''((((((((((((((('''''''''&&&''''''''''''''''''&&&&&&&&&&&&'''''''''''''''$$$%%%&&&&&&''''''&&&&&&''''''((((((((((((''''''#########$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$###$$$&&&(((((((((###$$$%%%&&&'''&&&%%%$$$$$$%%%&&&&&&''''''&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''%%%%%%&&&(((***+++%%%%%%&&&&&&'''&&&&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&&&&'''''''''''''''((())))))&&&&&&&&&(((******(((&&&'''&&&&&&&&&&&&''''''(((((((((((((((((()))))))))(((((((((((((((((((((((())))))))))))((((((''''''++++++******+++---///000---...///000000///---,,,.........///000000111111222222111111222333555666888888888555222111222333111222222333333444444444555555555555555444444333666666777777888999:::<<<888888888777777666666666999999:::;;;;;;;;;:::::::::<<<===<<<:::999:::;;;;;;;;;;;;;;;;;;:::999999555555555555555444444444333222000///...---------,,,,,,,,,+++++++++++++++***************************))))))((())))))*********))))))((('''((((((((('''((((((((())))))******((('''&&&%%%%%%&&&'''(((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&$$$$$$%%%'''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&&&&'''&&&&&&%%%&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%$$$$$$$$$''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&''''''''''''(((((((((((((((((((((''''''''''''&&&&&&'''''''''''''''''''''''''''''''''$$$%%%&&&&&&''''''&&&&&&''''''((((((((((((''''''%%%%%%&&&&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((&&&$$$$$$&&&'''((((((%%%&&&''''''((((((''''''$$$%%%&&&&&&''''''&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''((((((((((((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$%%%&&&((()))%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&'''((())))))%%%%%%&&&)))++++++(((&&&'''&&&&&&&&&&&&&&&''''''''''''''''''((((((((((((***)))))))))((((((((('''***))))))(((''''''&&&&&&************+++,,,......+++,,,---...///...---,,,---......//////000000111000000000111222333444555666777777666444222222333222222222333333444444444333444444555444444333333444666777777666777:::<<<999888777666555555555555888999:::;;;<<<<<<<<<<<<999;;;<<<<<<:::999999:::777777888888888888777777555555444444333333333222333222000...---,,,------++++++++++++************))))))***++++++***))))))))))))((((((((()))*********)))((((((''''''(((((((((((((((((((((((((((((('''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&%%%$$$###$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$%%%%%%%%%%%%############$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%(((((((((((('''''''''&&&%%%%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%%%%%%%%%%''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&'''''''''(((((((((((('''&&&&&&&&&&&&'''(((((((((((('''''''''''''''%%%%%%&&&'''''''''''''''''''''((((((((((((''''''%%%%%%&&&&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%***(((%%%$$$%%%''''''''''''&&&&&&&&&&&&'''(((((($$$%%%&&&&&&''''''&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&'''''''''((((((&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%%%%&&&$$$%%%&&&&&&''''''&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&'''''''''&&&%%%%%%$$$&&&&&&&&&&&&'''((())))))$$$%%%&&&)))++++++(((&&&'''&&&&&&%%%%%%&&&&&&'''%%%&&&&&&&&&'''''''''((()))))))))))))))))))))***))))))))))))))))))))))))))))))***+++,,,,,,,,,++++++,,,------............------......///000000000///000111222333444444444333555777777555333333333222222333333333333444444222222444444555444333333333555777777666666999<<<:::999888666666666666666666777888:::;;;<<<======999;;;<<<<<<:::999999999444555666888888888888777666666555444333333222222111000...,,,,,,---...///++++++++++++++++++++++++((()))***++++++***)))(((((((((((((((((()))******))))))(((''''''''''''((())))))(((((('''&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&&&&$$$###$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%########################$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%((((((((((((''''''''''''$$$%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''&&&&&&%%%%%%$$$$$$%%%&&&'''(((((()))((('''&&&&&&&&&&&&'''((()))((((((((('''''''''&&&&&&&&&'''(((((((((((('''''''''((((((((((((''''''######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%,,,)))&&&$$$%%%&&&&&&&&&&&&%%%$$$###$$$%%%&&&'''$$$%%%&&&&&&''''''&&&&&&''''''&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&'''''''''&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$&&&'''''''''&&&&&&%%%$$$%%%%%%%%%&&&'''((()))***$$$%%%&&&)))++++++)))&&&'''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''((()))***+++,,,,,,)))))))))***++++++,,,,,,((()))***,,,,,,+++***))),,,,,,------......//////------......///000000000///000222444555555555444222444777888666444444444333333333333333333333444111222333444555444333333333555777777555666999<<<<<<;;;999777777777777888444555777999;;;<<<======999:::<<<<<<;;;999888999555666888999::::::::::::888777777555444333222222///...,,,,,,,,,...000111,,,,,,,,,,,,,,,,,,,,,,,,((()))***++++++***)))(((((((((((((((((()))******))))))((('''''''''''''''))))))((('''&&&%%%%%%$$$%%%&&&'''(((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&%%%)))(((((((((((('''''''''''''''''''''''''''''''''###%%%&&&&&&%%%$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$#########$$$$$$%%%%%%%%%########################$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&#########$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&'''''''''&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''''''''&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&'''''''''''''''''''''&&&%%%$$$$$$"""###$$$%%%&&&((())))))((('''&&&%%%%%%&&&'''((())))))(((((('''''''''&&&&&&'''(((((())))))((((((''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&&&&&&&'''&&&&&&&&&%%%%%%$$$$$$$$$(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&'''((())))))&&&%%%%%%$$$$$$#########!!!"""###$$$&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&''''''''''''''''''''''''%%%%%%%%%$$$$$$$$$######$$$$$$$$$&&&((()))(((&&&&&&'''''''''&&&&&&%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&'''''''''''''''''''''''''''&&&%%%$$$$$$&&&((()))''''''((())))))((('''&&&(((((()))***************)))(((((((((***+++---///,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,---------////////////000000000000000000000000111222333444444333222333555666555444555555555555555555555555444444333333333333222222555666777888888777666555;;;:::888666555666777888888777777777888:::===>>><<<<<<;;;:::999999888888;;;;;;;;;;;;::::::::::::666555555444222111000000...///000///...---...///,,,,,,+++******))))))(((************************,,,+++***)))((((((((((((((((((((((((''''''''''''&&&'''''''''((()))))))))((((((((((((((((((((((((&&&&&&%%%$$$$$$&&&'''((()))((((((&&&%%%$$$######'''%%%###$$$%%%'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&((())))))(((&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&&&&&&&%%%$$$######"""#########%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""$$$''')))***)))'''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$$$$%%%&&&''''''***)))(((&&&&&&&&&'''(((%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&''''''((()))))))))%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''((((((''''''''''''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''''''''((((((((((((''''''''''''(((((('''''''''''''''((()))***&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''))))))))))))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&((((((&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$"""""""""$$$&&&'''&&&$$$'''''''''&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&'''''''''''''''---+++(((%%%###"""######&&&'''((())))))(((''''''(((((()))***************))))))((()))***+++---...,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,---------....../////////000000000000000000000111222333444444333222333555555555444666666666666666555555555333333333333333333333333666666777777777777666666888777666555555666888999999888888999999;;;<<<<<<<<<<<<;;;;;;::::::999999555555555555444444444444555444333222111000/////////000000000/////////000...------,,,++++++******************************,,,+++***)))((((((((((((((((((((((((''''''''''''))))))(((((('''&&&&&&%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%%%%&&&(((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$######%%%$$$$$$###############%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""$$$''')))))))))'''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$$$$%%%%%%))))))(((((('''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&''''''((((((''''''&&&&&&''''''(((((('''''''''(((((()))***&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%&&&'''&&&'''((()))))))))((('''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%###""""""$$$&&&&&&%%%$$$''''''&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&'''''''''((((((((('''&&&%%%%%%&&&'''(((%%%&&&'''((()))))))))(((((())))))************)))******))))))***+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------------........./////////000000000000111111222333444333222333444555444333888777777777666666555555222222333333444555555555777666666666666666666777666555444444555777888999888999999:::;;;;;;::::::;;;;;;;;;;;;;;;;;;;;;;;;666666666555555555444444333333222111000//////...000///////////////000000//////......---,,,,,,,,,))))))))))))))))))))))))++++++***)))((((((((((((((((((((((((''''''''''''((((((''''''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&###$$$$$$%%%&&&'''((((((***(((&&&&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%$$$######$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$###"""%%%%%%$$$###############%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&((()))((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$######$$$$$$%%%)))((((((''''''&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&''''''''''''''''''(((((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%&&&&&&'''%%%&&&(((*********)))((("""######$$$&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%$$$&&&(((((('''%%%''''''&&&%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''((((((((($$$$$$$$$%%%&&&(((***+++%%%&&&&&&'''((())))))***((()))************))))))******************++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------...------------.........///000000000000000111222222333222111222444555444333777777666666555555444444222222333444555666777777777666555444444555666777555555555444555666777888555666888:::;;;;;;:::999;;;;;;;;;;;;;;;;;;<<<<<<888888777777777666666666333222222111000000/////////...,,,,,,...//////////////////...------,,,,,,******************************)))(((((((((((((((((((((((((((''''''''''''###$$$$$$%%%&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$&&&&&&%%%$$$$$$###$$$$$$%%%&&&'''(((((()))(((&&&&&&''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###!!! !!!###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&'''&&&&&&%%%%%%%%%%%%$$$############$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&'''((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((()))((((((&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$%%%&&&$$$%%%%%%&&&''''''((((((%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&''''''(((%%%&&&'''((())))))((('''######$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%&&&'''(((&&&%%%&&&&&&%%%%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&'''''''''((((((******((('''&&&%%%%%%$$$&&&&&&&&&'''((()))******))))))*********))))))(((************++++++******,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------.........------------.........///000000000///000000111111333222111222444555444333555555555444444333333333222222333444666777888888777666555444444555666777777777666555555555555555222444666888::::::::::::::::::;;;;;;;;;;;;;;;;;;333333333333222222222222333333222222111111000000...+++))))))+++---...---......------,,,+++++++++++++++++++++++++++++++++***)))((((((((((((((((((((((((((((((''''''''''''######$$$%%%&&&'''((()))%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&'''''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%&&&&&&$$$"""&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###!!! !!!###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###%%%%%%&&&&&&&&&&&&%%%%%%$$$###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''######$$$%%%%%%&&&''''''%%%&&&'''(((((('''&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%&&&''''''$$$$$$%%%%%%&&&'''''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''%%%$$$###&&&&&&&&&&&&&&&'''''''''&&&&&&'''''''''''''''((($$$%%%%%%&&&&&&''''''''''''''''''&&&&&&''''''(((&&&&&&&&&&&&'''''''''''''''&&&&&&%%%%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%$$$######$$$%%%&&&$$$###$$$%%%&&&'''''''''&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((()))***)))************))))))(((((()))***+++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,---------............------........./////////000000000//////000000111333222111222333444333222333333333333333333333333333333444555666777888999666555555555555555555666888888777777666555444444444444666888999::::::;;;::::::::::::::::::::::::222222222222111111111111333333222222222111111111---)))&&&'''***------,,,------,,,,,,+++*********************************)))((((((''''''((((((((((((((((((((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((())))))(((((('''''''''&&&&&&%%%%%%%%%%%%$$$$$$%%%&&&&&&$$$"""&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$######$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$ """###$$$$$$$$$&&&&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&"""######$$$&&&''''''(((###$$$$$$%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%&&&'''(((((('''&&&&&&%%%%%%$$$######%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$$$$###############&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&''''''%%%$$$"""''''''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$%%%%%%&&&''''''((('''&&&&&&%%%%%%&&&&&&''')))(((&&&%%%%%%&&&'''(((''''''&&&%%%%%%$$$######&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%$$$###$$$%%%%%%$$$""""""$$$&&&(((((('''&&&$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&((((((((('''&&&&&&%%%%%%"""###%%%''')))***+++,,,(((((('''&&&''''''((()))***************)))(((((('''((()))+++,,,,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,------------................../////////000000000000000////////////000000222111111111333444333222222222333333444555555555444444555666777777888888444555555666666555555444777777777777777777666666999999999999999999:::::::::::::::999999888888777555555444444444333333333111111111111111000000000...)))%%%&&&***......,,,------,,,,,,+++*********(((((((((((((((((((((((((((((('''''''''(((((()))((((((((((((''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&''''''((()))''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%''''''%%%###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&''''''&&&%%%$$$######################## !!!"""###$$$$$$$$$&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$######$$$$$$%%%&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$%%%&&&'''(((&&&&&&%%%%%%$$$#########%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''%%%###""""""###%%%'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&''''''%%%###"""((((((((('''&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%&&&'''((((((&&&&&&%%%$$$$$$%%%%%%%%%,,,***'''%%%$$$&&&((()))$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$########################%%%%%%%%%$$$$$$$$$######'''&&&%%%&&&''''''&&&$$$!!!###''')))***(((%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&))))))((('''&&&%%%%%%$$$((((((((()))(((''''''&&&***)))'''&&&&&&'''((()))***************)))((((((&&&''')))+++,,,---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------.........//////////////////000000000000111000////////////000000222111000111333444333222222333333444555666777777555555666666777777888888333444555666666555444333555666777888999999999888???>>><<<:::999999::::::::::::999999888777666666444444444333333333222222000000000000///////////////***&&&&&&+++//////---...------,,,,,,+++******''''''''''''''''''''''''(((((('''''''''(((((())))))(((((((((''''''''''''$$$%%%&&&''')))***+++,,,&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$###"""###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$&&&(((((('''%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$&&&''''''&&&$$$###########################$$$%%%%%%&&&&&&&&&%%%%%%'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$########################&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&%%%$$$%%%&&&((()))%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''############$$$%%%&&&'''"""######$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''(((&&&###!!!!!!###&&&(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''((('''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%(((((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((())))))%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''&&&###$$$$$$%%%&&&'''((((((&&&'''''''''&&&$$$"""!!!%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&'''''')))((('''&&&&&&&&&&&&&&&''''''&&&%%%$$$###"""!!!###%%%%%%###!!!"""###%%%&&&'''&&&&&&%%%'''&&&&&&%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&''''''''''''''''''''''''&&&''''''((((((((((((((()))((('''''''''(((***+++*********)))))))))))))))(((((()))***+++,,,,,,,,,***+++,,,---..................//////000000111111////////////000000000000000000111222222222222111000000000000111222333444555444333333444666999:::777888999999999888666555555555444333333444666777777999:::;;;;;;:::888777555555555777999999777555888888777777666666666555888777555444333333444444222222222222222111000000...---+++******+++---.........---,,,,,,+++******))))))))))))))))))))))))''''''(((((())))))******)))(((''''''''')))***+++((('''&&&%%%$$$#########'''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$%%%%%%%%%$$$$$$#########$$$###"""!!!!!!"""###$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&&&&%%%$$$$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&'''''''''&&&###$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$#########$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$((((((''''''''''''((((((&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$$$$$$$'''''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&((('''&&&&&&&&&&&&'''(((&&&&&&&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((((()))%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&$$$%%%%%%&&&&&&'''''''''%%%%%%&&&&&&%%%$$$"""!!!''''''''''''''''''''''''%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%"""###$$$&&&''''''''''''$$$$$$%%%&&&&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&''''''(((''''''&&&%%%%%%&&&'''''''''''''''''''''''''''''''''(((((())))))))))))))))))(((((('''((()))***+++***))))))))))))))))))))))))))))))***+++++++++,,,***+++,,,---............000000000////////////////////////000000000111111000000111222222222222111000000000000111222333444444333222222333444666777444555666777888888888777555444333333333444555666777888:::;;;;;;:::888777666555555666888999777666777777666666666555555555666555444222222222222333111111111111111000000///...---,,,++++++,,,---......------,,,++++++******))))))))))))))))))))))))''''''(((((())))))))))))(((((('''''''''((()))***(((((('''&&&%%%%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$######%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%$$$$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&###$$$%%%%%%&&&&&&%%%%%%+++***((('''%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&%%%%%%%%%$$$(((''''''&&&&&&''''''(((&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$$$$%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$''''''''''''''''''''''''$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&'''%%%%%%&&&&&&'''''''''(((+++***(((&&&&&&'''((()))&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&######$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&'''(((((((((''''''&&&&&&''''''(((''''''''''''''''''''''''(((((()))************)))((((((((((((((()))******))))))))))))))))))************************++++++***+++,,,------......---000000000///......------000000000000111111111111000000111222222222222111111000000111111222333444444333222111111222333444111222333555777888888999444444444444444555666666777888999::::::999888777888666555555777888888777666555555555555444444444444333222111000000000111000000000000000//////...------------------------------,,,,,,++++++******))))))))))))))))))))))))'''(((((((((((()))))))))''''''&&&&&&&&&'''(((((((((''''''&&&&&&''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&'''(((((()))%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!"""###$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''&&&&&&###$$$%%%%%%&&&&&&%%%%%%+++***)))'''&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$%%%%%%'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((((('''&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&&&&&&&''''''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$'''''''''&&&&&&%%%%%%%%%%%%&&&&&&'''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$%%%%%%&&&'''%%%&&&&&&&&&&&&''''''''')))(((&&&$$$$$$$$$&&&'''((('''%%%$$$###$$$$$$%%%''''''&&&&&&&&&'''((((((######$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''((()))))))))))))))((((((((((((((())))))***)))))))))))))))*********+++++++++******************+++,,,---------------///.....................000000000000111111111222000000111222222222222111111111111111222333444444444444333222111111222222000111222444555666777777555555555555666777777888777777888999999999999888999777555555666888888888444444444444444444444444333333222222111000000000/////////000///......---,,,------......------,,,,,,,,,,,,,,,++++++******((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((('''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((('''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&%%%###$$$%%%%%%&&&&&&%%%%%%&&&&&&%%%%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%$$$%%%&&&((())))))(((&&&%%%%%%&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$'''''''''&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$%%%%%%&&&'''&&&&&&&&&&&&%%%%%%%%%%%%######$$$$$$$$$$$$$$$$$$((('''%%%$$$###$$$$$$%%%((((((((((((((()))******$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&%%%%%%%%%''''''''''''''''''''''''%%%&&&''''''(((((('''''''''(((((()))))))))))))))(((((())))))************+++++++++***************++++++,,,,,,---,,,,,,,,,+++,,,,,,---...//////000///000000000000111111111000000111222222222222111111111111111222333444555555555444333333222222222333333333333333444444555555666666777888999999999777777888888999999999999:::888666555777888888888333333333444444444444444444444444333333222111111///////////////...------,,,,,,---......---,,,,,,,,,+++++++++++++++******((((((((((((((((((((((((((((((((('''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&'''(((&&&&&&&&&%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$###""""""!!!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&''''''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&'''(((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%$$$$$$$$$$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%&&&((())))))(((&&&%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%"""""""""""""""######$$$$$$%%%%%%&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%'''''''''&&&&&&%%%%%%%%%"""""""""""""""###$$$%%%''''''''''''''''''''''''$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$!!!###%%%'''''''''%%%$$$&&&&&&%%%%%%$$$$$$%%%%%%((((((((((((((()))***+++&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''''''''&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$''''''''''''''''''''''''%%%%%%&&&''''''''''''&&&''''''((()))))))))))))))((((((((()))******++++++******************++++++++++++,,,,,,,,,,,,++++++)))***+++,,,---///000000////////////000000000000000000111222222222222111222111111222222333444555666666555555444444333333555555444333222222333333444555777888999999999999666666777777888999999999:::888777777888888888777333333333444444444444555555555555555444333222111///////////////......---,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++******))))))))))))))))))))))))(((((((((''''''''''''&&&&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&******)))(((&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&'''''''''$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&&&&%%%%%%###$$$%%%%%%&&&&&&%%%%%%***)))((('''&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&%%%&&&'''(((((('''&&&%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###"""""""""######$$$%%%$$$$$$%%%%%%&&&''''''(((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$#########$$$%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''###%%%&&&'''((('''&&&%%%$$$$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&'''((()))***'''''''''&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&''''''&&&%%%%%%''''''''''''''''''''''''%%%&&&&&&'''''''''''''''&&&'''((()))***))))))((('''(((((()))******++++++)))))))))***+++++++++,,,++++++,,,,,,,,,++++++*********+++,,,---......///---.........////////////000000111222222222222111222222222222333444555555444555555555555444444444666555444333222333333444222333555777888888888888666666666777777888999::::::888888888999999777555333444444444555555555555444555555555444333222111///000000000000///......,,,+++************+++,,,******************++++++))))))))))))))))))))))))(((((('''''''''&&&&&&&&&&&&''''''((('''&&&%%%$$$&&&&&&%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&,,,++++++***)))(((((('''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$"""###%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''$$$$$$%%%%%%&&&''''''((($$$$$$$$$%%%%%%&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$###$$$%%%%%%&&&&&&%%%%%%)))((('''&&&&&&%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$$$$$$$%%%%%%&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''%%%%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((($$$$$$%%%%%%&&&'''(((((('''''''''''''''''''''&&&''''''''''''''''''''''''&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((&&&&&&&&&&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&'''((()))(((''''''&&&&&&&&&&&&%%%%%%&&&'''((()))******&&&&&&&&&&&&&&&%%%%%%%%%"""###%%%&&&'''&&&&&&%%%$$$$$$$$$%%%&&&'''((()))(((((('''&&&%%%$$$$$$###$$$$$$$$$%%%%%%&&&&&&&&&"""###$$$%%%'''((()))***%%%&&&'''(((((('''&&&%%%''''''''''''''''''''''''&&&''''''(((((((((((((((&&&''')))*********)))((('''(((((()))***+++++++++(((((()))***+++,,,,,,---++++++,,,,,,,,,++++++***,,,,,,,,,,,,,,,,,,,,,,,,------------.........///000000111222222222222111222222222222333444555555333444444555555444444333555555444333333333555555000222444555777777777666666666666666777888999:::999888888999:::999777555444444444555555666666666333444555555444333111000000000000000000//////...,,,+++)))(((((()))+++,,,******************++++++))))))))))))))))))))))))(((((('''''''''&&&&&&&&&''''''((((((((('''%%%$$$(((''''''&&&&&&&&&''''''&&&&&&&&&&&&&&&'''((()))%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&&&&'''&&&%%%%%%%%%&&&&&&''''''''''''&&&%%%$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######%%%&&&((()))***+++%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$!!!"""$$$&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''((())))))$$$$$$%%%%%%&&&'''(((((($$$$$$$$$%%%%%%&&&&&&&&&&&&'''''''''&&&%%%%%%$$$$$$$$$%%%&&&&&&&&&%%%%%%###""""""###$$$%%%&&&'''&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$%%%%%%&&&'''%%%%%%%%%&&&&&&'''''''''%%%&&&&&&&&&'''(((((((((((('''&&&&&&&&&&&&'''(((%%%%%%&&&'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''(((%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&'''&&&%%%%%%%%%%%%&&&''''''&&&%%%$$$%%%&&&'''((('''&&&&&&&&&&&&'''((((((%%%&&&((())))))(((&&&%%%(((&&&$$$###$$$&&&***,,,...,,,***(((''''''((()))'''&&&%%%%%%$$$$$$%%%%%%"""###%%%&&&&&&%%%###"""###$$$$$$%%%&&&'''((((((''''''''''''''''''&&&&&&(((''''''&&&&&&&&&''''''%%%%%%&&&&&&'''((())))))%%%%%%%%%&&&&&&''''''''')))((('''&&&%%%&&&'''(((%%%&&&&&&&&&%%%$$$$$$###&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&'''''''''''''''************************&&&((()))***))))))+++---))))))***+++,,,,,,------+++++++++,,,,,,---------...//////000111222222333---...///000000111111111000000111222444777999:::555555555555555555555555222333333444444333333222111222444555555555777999666777777888999888888888666777888999888777666555555555555555555555555555444444444444333222111000333222222111000//////...------,,,+++*********+++************************)))(((&&&&&&&&&''')))***'''''''''((((((((((((((('''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''&&&$$$"""""""""&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$###$$$''''''%%%###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%$$$######$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''((('''&&&%%%%%%&&&'''(((&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$'''''''''&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%(((''''''&&&&&&&&&''''''&&&'''''''''&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&'''''''''((()))(((&&&%%%%%%'''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&((('''&&&&&&&&&&&&'''((()))(((&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&'''''''''&&&%%%$$$%%%''')))+++---,,,***(((''''''((()))'''&&&%%%%%%$$$$$$%%%%%%'''((())))))))))))((('''$$$%%%%%%&&&&&&''''''''''''''''''''''''''''''''')))((('''&&&&&&&&&&&&&&&$$$%%%%%%&&&''''''((((((%%%%%%%%%&&&&&&&&&''''''&&&%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&%%%$$$$$$''''''&&&&&&&&&&&&''''''((((((((('''''''''&&&&&&************************'''(((******))))))***,,,(((((()))******+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---......//////000000000...///000111222222222222222222222222333444555666444444444444444444444444333444444444444444444333000111333444333444666777444444444444555555555555888999:::::::::999888777444444444444444444444444444444444444333222111000000000000000////////////++++++***)))))))))))))))************************&&&''''''((((((((((((((('''((((((((((((((((((((((((((((((''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""$$$%%%%%%$$$$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$###%%%''''''%%%###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''&&&&&&%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&%%%%%%&&&''''''&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%%%%$$$$$$''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%'''''''''&&&&&&&&&''''''&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%&&&&&&&&&'''''''''((()))(((&&&%%%&&&'''&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&&&&&&&%%%%%%%%%&&&''''''''''''&&&)))(((''''''''''''((()))***)))'''&&&%%%$$$$$$$$$%%%&&&'''((((((((('''&&&)))'''%%%$$$$$$%%%''')))&&&%%%%%%%%%&&&'''((()))+++***)))'''''''''((()))'''&&&&&&%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''***)))((('''&&&%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&'''%%%%%%$$$$$$$$$%%%%%%&&&''''''''''''''''''&&&%%%((((((''''''''''''(((((()))))))))(((((('''''''''))))))))))))))))))))))))((()))******)))((()))+++((((((((()))******++++++,,,,,,,,,,,,,,,,,,,,,,,,------------------------///000111222222333333333444333222222111111222222444444444444444444444444444444444555555444444444///111222333222333444666777666555555555666888999888999:::::::::888777666333333333333333333333333333333333333333222111000---------.........//////))))))((('''''''''((((((************************$$$&&&(((******)))'''&&&((((((((((((((((((''''''((((((((((((((('''''''''%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""$$$%%%%%%%%%'''(((&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&%%%###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%#########$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$###############%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&&&&&&&'''(((((((((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''%%%$$$############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&(((((((((&&&%%%&&&'''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&%%%&&&&&&'''''''''''''''(((''''''''''''''''''(((((((((''''''&&&&&&&&&&&&&&&''')))++++++***((('''((('''&&&%%%%%%&&&'''((($$$%%%&&&&&&''''''''''''))))))((('''''''''((((((''''''&&&%%%%%%%%%%%%%%%###"""!!! !!!"""###'''''''''&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''******((('''%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&''''''((((((''''''((((((((((((''''''))))))(((((((((((())))))((((((((()))))))))))))))************************)))***+++***)))((()))***))))))))))))******++++++------,,,,,,,,,,,,++++++...---------------------//////000111222222222222333333222111000000000111333333333333333333333333222333333444444333333222000111333333222222444666999888666555555777999:::666777777777777666444333111111111111111111111111222222222222222111000000---------,,,,,,,,,,,,,,,)))(((((('''''''''((((((************************%%%&&&((()))))))))((('''((((((((((((''''''''''''((((((''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%% """$$$%%%%%%&&&''')))&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%&&&''''''((())))))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''''''''''''''%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&'''((('''&&&%%%&&&(((&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''(((((((((''')))+++,,,---,,,***)))&&&&&&((((((((((((&&&&&&$$$%%%&&&'''''''''&&&%%%''''''''''''''''''((((((((('''&&&&&&%%%%%%&&&&&&'''&&&$$$""""""$$$&&&''''''''''''&&&&&&%%%%%%$$$&&&&&&&&&'''''''''((((((******((('''%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''(((((((((''''''(((((()))(((((('''))))))(((((((((((())))))&&&''''''((()))***++++++++++++++++++++++++++++++)))***+++***)))((()))************+++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,/////////...............---...///000111111111111111111000000000111222222333333333333333333333333111111111222222111111111111222444444333333444666555444222222222333555777666666777777666555333222111111111111111111111111111111222222111111000000......---,,,+++***)))((()))))))))(((((())))))***))))))))))))))))))))))))(((''''''&&&'''((()))***))))))(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""$$$&&&&&&%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''$$$%%%%%%&&&'''((())))))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&'''((((((''''''%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''%%%'''((('''&&&&&&'''(((''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''((((((((('''''''''&&&&&&&&&&&&'''(((((((((((('''%%%%%%&&&&&&&&&&&&%%%%%%$$$%%%&&&((()))))))))))))))***+++,,,,,,,,,++++++&&&''')))******)))'''&&&$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''(((((((((''''''&&&&&&&&&&&&&&&((('''%%%$$$$$$%%%'''((('''''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&'''(((((((((***)))((('''&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%######$$$%%%&&&&&&&&&&&&&&&'''(((((((((((((((((())))))(((((((((((())))))&&&&&&'''((())))))***+++************************((()))******)))((()))++++++++++++++++++++++++++++++++++++,,,,,,---------//////////////////000000---...///000000111111000000000000000111222333333222222222222222222222222///000000111111000000///111333444444333333444666555555444333444555666777888888888888777666444333111111111111111111111111000000111111111000000/////////---,,,***)))''''''******)))))))))***++++++)))))))))))))))))))))))))))(((&&&%%%&&&''')))+++)))))))))(((''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&'''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&''''''%%%$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&###$$$$$$%%%%%%&&&&&&'''###%%%'''&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&###$$$$$$%%%%%%$$$$$$#########$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''(((((($$$%%%%%%%%%&&&'''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''%%%%%%%%%&&&&&&&&&&&&'''%%%&&&&&&''''''&&&&&&%%%$$$%%%&&&(((((((((''''''%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&((('''&&&&&&'''(((''''''(((((((((((('''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''((((((((((((''''''''''''&&&&&&'''(((((((((((((((%%%&&&'''(((((('''&&&%%%%%%&&&'''((())))))(((((()))))))))************+++))))))************))))))%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&'''((((((((((((((('''&&&&&&&&&&&&&&&&&&%%%$$$######$$$%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''(((((())))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%"""###$$$&&&&&&&&&&&&&&&%%%&&&'''((((((((((((''')))((((((''''''(((((()))''''''''''''''''''''''''(((((((((((((((((((((((('''(((******))))))***,,,+++++++++*********************++++++,,,---...............///000000000111......///000111111111111222111111111111222333333222222222222222222222222000000111111111111000000111222333333222222333444666666666777777777888888777888888888777555333222111111111111111111111111//////000000000000000///......---,,,***)))((((((***)))))))))******+++,,,))))))))))))))))))))))))'''''''''''''''((())))))***))))))(((''''''&&&&&&&&&&&&&&&&&&'''''''''(((%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&''''''&&&%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%&&&''''''###%%%''''''%%%###$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&'''###$$$%%%%%%%%%%%%$$$###""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''$$$$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&''''''''''''&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&'''''''''(((%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%###$$$&&&((())))))((('''$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&''''''&&&&&&''')))''''''(((((((((((('''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&'''''')))(((((((((''''''''''''&&&''''''(((((((((((((((&&&'''((())))))((('''&&&''''''((())))))((('''&&&((((((((('''((())))))***,,,+++***((((((***+++,,,&&&&&&%%%$$$$$$%%%%%%%%%###$$$%%%&&&'''((((((((((((((('''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((())))))(((''''''&&&&&&&&&'''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%###%%%&&&((())))))((((((%%%%%%&&&'''((((((''''''((((((''''''''''''((((((***)))((('''&&&%%%$$$$$$''''''''''''''''''''''''&&&((()))***))))))+++---*********)))))))))))))))))))))***+++---...//////---------...///000111111///000111222222333222222444333222222222222222222111111111111111111111111111111222222222222111111000111222222111000111333222333444444555555444444555666666666555333111000111111111111111111111111//////000000000000000///---,,,,,,,,,++++++******)))))))))))))))***++++++))))))))))))))))))))))))%%%&&&((()))***)))((('''***))))))((('''&&&&&&&&&&&&'''''''''(((((())))))%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&'''''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###%%%''''''&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$######$$$%%%%%%&&&''''''###%%%''''''$$$###$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''###$$$%%%&&&&&&%%%$$$### !!!!!!"""###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&'''(((((('''&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&'''''''''((((((%%%%%%%%%&&&&&&'''''''''%%%&&&&&&''''''&&&&&&%%%###$$$&&&((())))))((('''$$$%%%%%%&&&'''''''''&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&''''''&&&&&&((()))$$$&&&(((******)))((('''''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%'''))))))(((&&&'''&&&&&&&&&&&&'''((((((,,,***(((&&&%%%&&&'''(((&&&''')))***++++++******((((((((((((((((((((((((%%%&&&(((((('''''')))+++///+++&&&$$$%%%'''***+++''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%&&&'''((()))***))))))((('''&&&%%%$$$$$$$$$$$$$$$$$$$$$%%%&&&'''%%%'''))))))((()))***,,,***))))))((('''&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''&&&&&&)))(((&&&%%%$$$$$$%%%%%%))))))(((((((((((()))))))))************+++++++++------------,,,+++******------,,,+++,,,---.../////////.........000222333222222333333333444444444222111000000000111333444222222111111111111222222111000000000//////......222222222222222222222222555555555666666777777777444444444444444444444444000000111111111000000///111000000///......------,,,,,,++++++***)))(((((((((((())))))*********+++***)))((()))***+++***((()))(((&&&%%%%%%&&&((()))&&&&&&%%%%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%)))(((&&&%%%$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$###""""""''''''(((&&&$$$"""###$$$%%%&&&&&&''''''&&&&&&%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%$$$######$$$$$$%%%%%%%%%%%%&&&&&&#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((''''''&&&$$$######"""&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$(((((('''&&&%%%%%%$$$$$$%%%&&&''''''&&&%%%###"""&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''&&&### &&&&&&%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&%%%%%%###"""%%%%%%%%%%%%%%%$$$###"""'''&&&&&&%%%%%%$$$$$$###)))((('''&&&%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''$$$%%%&&&'''''''''&&&%%%''''''((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&'''))))))'''%%%'''&&&&&&&&&&&&'''((((((+++***(((&&&%%%&&&''''''&&&''')))***++++++******((((((((((((((((((((((((%%%'''(((((('''''')))***---***&&&%%%&&&(((******''''''''''''&&&&&&&&&%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&'''(((''''''&&&&&&%%%%%%%%%''''''&&&&&&&&&'''((((((%%%'''(((((((((((()))+++)))))))))((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&%%%%%%%%%&&&''''''))))))(((((((((((())))))))))))*********+++++++++,,,,,,------,,,,,,+++***,,,,,,,,,,,,,,,---.........---------...///000111222222222222333333333333111111000000111222222333222111111000000111111222111111111000000000//////111111111222222333333333111111222222222333333333333333333333333333333333111111111111111111000///000000///......---,,,,,,,,,,,,++++++***))))))((((((((()))))))))************)))((((((******)))((()))'''&&&%%%%%%&&&''')))''''''&&&&&&%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$######%%%&&&'''&&&%%%$$$%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$(((''''''&&&%%%%%%$$$$$$###$$$&&&'''((((((''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&%%%$$$$$$$$$''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%%%%%%%$$$###&&&&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&%%%%%%%%%''''''((((((((((((''''''((((((((((((((((((((((((((('''&&&'''((((((&&&$$$'''&&&&&&&&&&&&'''((((((***)))(((&&&&&&&&&''''''&&&'''((()))************((((((((((((((((((((((((&&&((())))))''''''(((***+++)))&&&&&&((()))***)))((((((((('''''''''&&&&&&''''''&&&&&&&&&&&&'''((('''&&&%%%$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&&&&''''''$$$&&&''''''&&&&&&((()))))))))(((((('''&&&&&&&&&%%%&&&&&&&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&!!!""""""$$$%%%&&&'''(((''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%%%%&&&'''((())))))((((((''''''(((((())))))))))))*********++++++***++++++,,,,,,,,,,,,,,,+++,,,,,,------------------,,,,,,,,,---...///000222222222222222111111111000000111222222222222111222111111000000111111222222222222111111111111000000000111222333333444444333333333333444444444444222222222222222222222222222222222222222111000000///......------,,,,,,+++,,,,,,++++++***)))))))))(((((())))))))))))*********((('''((()))***)))(((((('''&&&%%%%%%&&&'''((()))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%%%%'''((()))%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%&&&(((%%%&&&&&&''''''&&&&&&%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!"""###%%%&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$'''''''''&&&&&&%%%%%%$$$$$$%%%&&&'''((((((((((((%%%&&&((())))))(((&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$%%%&&&'''(((''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$&&&&&&'''''''''&&&%%%%%%######$$$%%%%%%&&&''''''!!!"""###%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''***)))((('''''''''''''''&&&''''''((((((''''''&&&'''''''''''''''((((((((()))(((&&&'''''''''&&&$$$'''&&&&&&&&&&&&'''(((((()))((('''&&&&&&&&&&&&'''&&&&&&'''((())))))))))))(((((((((((((((((((((((('''((())))))((('''((())))))((('''((()))***)))((()))(((((((((((('''''''''(((''''''''''''(((((()))'''&&&%%%%%%$$$%%%%%%%%%&&&&&&'''''''''((((((((('''&&&%%%$$$$$$$$$$$$$$$$$$%%%'''&&&%%%%%%'''((((((((((((''''''&&&&&&&&&%%%&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&''')))******&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''%%%%%%%%%&&&''''''((()))(((((((((''''''((((((((())))))))))))************))))))***,,,,,,---------***+++,,,---...---,,,,,,------------...///000000222222222111111111111000000000222333333222111000111111000000000000111111222222222222222222222222//////000111333444555555444444444444444444444444222222222222222222222222222333333222222111000///---------,,,,,,++++++++++++++++++*********))))))(((((()))))))))))))))))))))(((''''''))))))((('''((('''&&&&&&&&&&&&'''(((***)))((('''&&&%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&'''''''''&&&&&&%%%%%%%%%###%%%&&&%%%$$$$$$%%%&&&''''''((((((((((((''''''$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%((((((((('''&&&&&&%%%$$$%%%''')))++++++)))'''%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&###$$$&&&'''((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''***)))((('''''''''''''''&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&&&&''''''''')))(((&&&&&&''''''&&&%%%'''&&&&&&&&&&&&'''(((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''((())))))(((((((((((((((((((((((('''(((***)))(((((()))***)))((('''(((******)))''')))((((((((((((''''''''''''''''''''''''((()))***&&&&&&&&&&&&&&&''''''((('''''''''((())))))******'''&&&%%%$$$$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%&&&'''''''''''''''&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((''''''''''''''''''''''''((((((''''''''''''(((((((((((()))))))))*********((()))***+++,,,---------)))***,,,---------,,,+++---......///000000111111111111111111111111111111000111222333333222000000111000000000000000000111222222222222222333333333//////000111333444555555000000000000000000000000333333333333333333333333222333333222111000//////,,,,,,,,,,,,,,,++++++++++++++++++***************))))))((((((((((((((((((((('''&&&'''(((((((((&&&'''''''''&&&&&&'''''''''***)))(((&&&&&&%%%%%%%%%'''''''''''''''''''''''''''''''''&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&%%%%%%$$$%%%&&&%%%"""!!!"""###&&&&&&''''''''''''&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%''''''&&&%%%%%%$$$$$$$$$%%%''')))++++++)))'''%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''&&&$$$"""!!!%%%%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&'''###$$$%%%%%%%%%%%%$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%'''''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&$$$$$$%%%%%%&&&''''''''')))'''&&&%%%'''''''''&&&'''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((()))((((((((((((((((((((((((&&&((())))))))))))***,,,***)))(((((())))))(((&&&((((((((('''''''''&&&&&&'''''''''''''''((()))***&&&&&&&&&&&&''''''((()))''''''((((((((()))))))))(((((('''&&&&&&&&&''''''%%%&&&''''''%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''(((((((((''''''(((((((((''''''&&&(((''''''&&&&&&''''''(((((((((((()))))))))******((()))***+++,,,,,,,,,,,,***++++++,,,,,,,,,,,,,,,---...///000111111111111111111111222222222333333111222222222222111000000111000000//////000000111111222222222222333333333000000111222333333444444222222222222222111111111333333333333333333333333222222222111000///...---,,,,,,,,,,,,,,,,,,,,,,,,************************))))))((((((((((((''''''(((&&&%%%&&&'''((('''&&&''''''''''''''''''''''''((('''&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%$$$######$$$$$$%%%%%%&&&&&&'''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&%%%"""!!!!!!"""###$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$&&&''''''%%%&&&((())))))(((&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&###%%%&&&'''&&&$$$!!!$$$$$$$$$$$$##################$$$$$$%%%%%%&&&&&&%%%$$$$$$$$$%%%&&&'''(((######$$$$$$%%%%%%$$$$$$''''''&&&%%%%%%$$$######$$$$$$$$$$$$$$$###""""""%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''$$$%%%&&&'''''''''&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&'''(((((((((((('''%%%%%%&&&((((((''''''&&&&&&&&&&&&'''((((((%%%&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%'''((()))((((((((((((((((((((((((%%%''')))))))))***,,,...---+++(((((((((((('''&&&''''''''''''&&&&&&&&&%%%&&&&&&&&&&&&'''((()))***''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&'''((((((&&&'''((('''&&&%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((((()))%%%&&&'''((())))))(((((((((''''''&&&&&&''''''((((((((((((((()))))))))***((()))***++++++++++++++++++++++++***++++++,,,---,,,---...000000000000///000000111222333444555555333222222111000000111111000000////////////000000111111111111222222222333111111111222222333333333666555555555444444444444222222222222222222222222111111111000///...---,,,,,,,,,,,,---------------************************))))))(((((((((''''''''''''&&&%%%%%%''''''&&&%%%&&&''''''''''''''''''&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&%%%$$$######$$$%%%%%%&&&''''''$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&'''&&&$$$###$$$%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%&&&((()))&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%$$$###%%%%%%%%%$$$$$$$$$######"""######$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&((()))###$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%&&&''''''$$$&&&(((******)))((('''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&'''((())))))***(((&&&$$$$$$&&&((()))((('''&&&&&&&&&&&&'''((((((%%%%%%&&&''''''&&&&&&&&&&&&%%%$$$$$$%%%&&&((()))(((((((((((((((((((((((($$$&&&((()))***+++---///...,,,)))'''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&((()))))))))(((&&&%%%$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&'''&&&'''((((((&&&%%%&&&(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((())))))''''''''''''''''''''''''%%%%%%&&&&&&'''((())))))###$$$&&&(((************'''''''''&&&&&&'''''''''(((((((((((())))))))))))))))))***++++++++++++***,,,+++***)))***+++---...+++,,,---////////////...000000111222444555666777444333111000000000111222000000////////////000000000000000111111222222222222222222222222222222333333333333222222111111111000000000000000000000000111111000000///---,,,+++------------------------******************++++++))))))(((((('''''''''&&&'''&&&%%%%%%''''''&&&%%%&&&&&&''''''''''''&&&&&&$$$$$$$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&'''(((''''''&&&######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&((('''&&&&&&''')))'''(((((((((((((((((('''$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''((((((((($$$$$$%%%%%%%%%&&&&&&&&&#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$&&&''''''&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$&&&''''''((($$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&***)))'''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%'''((()))&&&&&&&&&%%%%%%%%%$$$$$$""""""###$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%'''((()))$$$%%%&&&&&&'''''''''&&&###$$$$$$%%%%%%&&&&&&'''$$$$$$######$$$&&&((()))$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&%%%### %%%%%%%%%&&&&&&&&&''''''''''''''''''(((***+++,,,''''''''''''''''''&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%&&&'''(((((((((((()))))))))))))))))))))))))))((('''&&&%%%$$$$$$$$$&&&&&&%%%$$$%%%&&&'''((('''((((((((('''&&&%%%%%%&&&%%%%%%%%%%%%&&&'''''''''&&&%%%%%%%%%%%%&&&'''###%%%''''''%%%$$$$$$$$$'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%''''''((((((((((((''''''(((''''''&&&&&&&&&''''''$$$%%%''''''&&&'''(((***(((((('''''''''&&&&&&&&&((('''&&&&&&'''((()))***''')))***+++***)))***+++******))))))))))))******((()))+++,,,------,,,,,,---------............///000000000111222222333333000000000000000111111111111111000000000000000111222222222111111111111000111222222333333444444555333333333222222111111111222222222111111111111111///////////////......---,,,,,,,,,,,,,,,+++***)))+++++++++***************&&&&&&'''((())))))((((((''''''((()))******))))))&&&&&&''''''''''''&&&&&&&&&%%%$$$###"""!!!!!!!!!&&&&&&%%%$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&''''''((((((''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&%%%$$$###&&&&&&%%%$$$%%%&&&'''((('''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$$$$%%%&&&&&&''''''&&&&&&######""""""######$$$%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''%%%%%%%%%'''((('''&&&'''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$"""###$$$$$$###"""###%%%&&&&&&''')))'''%%%$$$&&&%%%%%%%%%%%%&&&'''((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%&&&(((((()))%%%%%%%%%%%%%%%%%%%%%%%%'''%%%$$$$$$$$$$$$###!!!"""###$$$%%%&&&'''''''''&&&&&&&&&&&&%%%$$$###"""'''''''''((((((((())))))''''''''''''((())))))***''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%&&&'''(((((((((((()))))))))))))))))))))))))))((('''&&&&&&&&&&&&&&&'''&&&%%%%%%%%%&&&(((((('''''''''(((''''''&&&&&&&&&%%%%%%%%%%%%&&&'''''''''&&&%%%%%%%%%%%%&&&'''"""%%%&&&%%%%%%&&&''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%%%%$$$%%%''''''&&&'''(((***(((((('''''''''&&&&&&&&&))))))((('''((()))******''')))++++++***)))***+++++++++++++++++++++++++++((()))+++,,,------,,,,,,---------............/////////000000111222222333111111111000000000000000111000000//////000000111222222222111111111111000111111222333333444444555333333333222222222111111333333333222222222222222///////////////...------++++++++++++++++++++++++,,,,,,+++******))))))(((&&&'''(((((((((((((((((())))))((('''%%%$$$"""!!!(((((())))))))))))((((((((('''&&&%%%$$$$$$###$$$&&&&&&%%%%%%&&&&&&'''((('''&&&&&&%%%%%%&&&&&&'''%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&''''''((((((''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&&&&&&&######%%%&&&&&&&&&&&&%%%&&&%%%%%%$$$%%%&&&'''(((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%'''&&&%%%%%%%%%&&&$$$###'''&&&&&&&&&&&&&&&'''(((&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&'''&&&$$$###$$$%%%%%%$$$$$$%%%$$$$$$%%%'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######%%%&&&%%%###%%%%%%&&&&&&%%%%%%$$$###''''''&&&&&&'''(((((()))'''''''''(((((((((((((((''''''&&&&&&&&&''''''(((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&''''''(((((((((''''''))))))))))))))))))))))))'''&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&''''''((()))&&&&&&''''''((('''''''''&&&%%%%%%%%%%%%&&&'''''''''&&&&&&%%%%%%&&&&&&''' """%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%######$$$$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&''''''&&&&&&((()))'''''''''''''''&&&&&&&&&+++******))))))))))))***''')))++++++***)))***+++***+++,,,------,,,+++***)))***+++,,,---------,,,---------............///......///000000111111222222222111111000000//////000000////////////000000222222222111111111111000111111222222333444444444333333333333222222222222444444444333333333222222...////////////...------++++++******++++++,,,---,,,,,,+++***))))))(((((((((((((((((((((((('''&&&))))))(((&&&$$$""" (((((())))))))))))(((((()))((('''&&&&&&&&&&&&&&&'''&&&&&&&&&'''((())))))(((''''''&&&&&&''''''(((%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&''''''((((((''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''!!!"""$$$%%%&&&'''''''''%%%%%%$$$$$$$$$%%%&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######$$$%%%&&&'''%%%$$$%%%''''''&&&%%%&&&&&&&&&&&&&&&'''((((((&&&&&&%%%%%%%%%%%%$$$$$$((()))***(((&&&$$$$$$%%%%%%%%%$$$###$$$&&&((((((&&&&&&&&&&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%###""""""###%%%&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$###(((((('''&&&'''(((***+++&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&&&&%%%%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''''''''$$$%%%%%%&&&'''((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((''''''&&&(((((((((((((((((((((((($$$$$$$$$$$$$$$$$$%%%%%%''''''''''''(((((())))))%%%%%%&&&'''((((((((('''&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''%%%###$$$%%%'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&''''''''''''''''''%%%&&&''''''&&&&&&''')))''''''''''''''''''''''''+++******))))))(((((((((((()))++++++*********+++)))+++,,,......,,,+++)))***++++++,,,,,,------------------............///.........///000000111111333222222111000///....../////////...//////000111222222222111111111000000111111111222333333444444333333333333333333333333444444444333222222111111......//////......---,,,---,,,+++*********+++,,,************))))))))))))(((((())))))((('''&&&&&&''''''((((((((('''&&&&&&&&&&&&''''''''''''&&&&&&((((((''''''''''''''''''((((((''''''&&&''''''(((''''''&&&&&&&&&&&&''''''%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&''''''((('''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''((((((######$$$%%%&&&&&&''''''$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$######$$$&&&'''%%%%%%%%%&&&)))++++++***%%%$$$$$$%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%((())))))(((&&&%%%&&&'''&&&''''''%%%'''******'''$$$%%%&&&''''''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""###%%%&&&%%%$$$"""###$$$%%%&&&''''''''')))((('''&&&&&&'''((()))&&&&&&&&&&&&&&&&&&&&&%%%((('''&&&%%%%%%$$$%%%%%%&&&&&&&&&'''''''''((((((''''''''''''''''''''''''######$$$%%%&&&''''''(((''''''''''''''''''''''''''''''''''''''''''''''''((((((((()))((((((''''''''''''''''''''''''''''''&&&%%%%%%%%%%%%%%%&&&''''''''''''(((((((((((((((%%%%%%&&&'''((((((((('''&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&((())))))'''%%%$$$%%%&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%&&&'''(((((((((''''''%%%&&&((('''&&&&&&'''(((&&&''''''''''''''''''''')))))))))((((((''''''&&&(((***+++,,,+++***+++,,,)))***,,,------,,,***))),,,,,,,,,,,,,,,,,,---------------............///.........///000000111111333222222111000///......///////////////000111111222222222111111111000000000000111222222333333444333333333333333333333333333333333222111000000000...............------,,,...---,,,+++******))))))((((((((()))******++++++(((((())))))((('''&&&&&&%%%&&&'''))))))*********&&&&&&''''''''''''&&&&&&'''&&&&&&&&&&&&&&&'''((())))))'''&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&''''''((('''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&$$$%%%&&&&&&''''''&&&&&&$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$%%%&&&&&&&&&%%%%%%&&&)))******)))$$$$$$######$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&''''''&&&&&&''')))$$$'''(((''')))---+++$$$$$$%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$%%%%%%###""""""###$$$%%%&&&'''''''''(((((('''&&&%%%%%%%%%%%%((((((((((((((('''''''''((('''&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&'''(((((((((''''''''''''''''''''''''######$$$$$$%%%&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((()))))))))(((((('''''''''''''''''''''''')))(((((('''''''''((((((&&&&&&'''(((((((((((('''&&&&&&''''''((('''''''''&&&%%%%%%%%%%%%&&&''''''%%%&&&&&&''''''&&&&&&%%%%%%&&&'''&&&%%%&&&''')))'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&&&&'''$$$$$$%%%%%%%%%%%%$$$$$$"""###%%%&&&'''&&&&&&%%%&&&'''((('''&&&&&&'''(((&&&&&&&&&''''''''''''''''''((((((((((((''''''&&&(((***,,,,,,+++***+++,,,)))***+++,,,,,,+++***)))------,,,,,,,,,,,,---------------............///......///000000111111222222222111111000000//////000//////000000111222333222222222111111111111000000000111111222333333333333333333333444444444444333333222222111000//////---............---,,,,,,,,,,,,,,,,,,,,,***))))))'''(((((())))))*********(((((((((((((((((('''&&&&&&''''''''''''''''''&&&(((((())))))))))))((((((%%%%%%%%%%%%%%%&&&'''((())))))'''&&&%%%%%%$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&''''''((((((''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%'''&&&%%%$$$$$$$$$$$$%%%$$$%%%&&&'''''''''&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%&&&&&&''''''&&&&&&$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%'''&&&%%%&&&'''((('''&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&"""$$$%%%&&&&&&&&&((()))!!!&&&&&&%%%)))000///'''(((''''''&&&''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$$$$$$$$$$###!!!%%%%%%&&&&&&%%%%%%$$$###&&&&&&&&&&&&&&&%%%%%%$$$))))))((((((((('''''''''((('''&&&&&&&&&&&&&&&'''%%%%%%&&&&&&'''(((((()))''''''''''''''''''''''''$$$%%%%%%%%%&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&'''((()))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&))))))((('''&&&&&&&&&&&&$$$%%%&&&'''(((''''''&&&'''''''''(((''''''&&&&&&&&&%%%%%%%%%%%%&&&''''''%%%%%%&&&''''''&&&%%%%%%$$$%%%%%%$$$###$$$&&&((('''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''######$$$$$$$$$$$$######!!!###%%%&&&''''''&&&%%%&&&'''((('''&&&%%%&&&(((&&&&&&&&&'''''''''((((((''''''((()))***)))(((((((((***,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,...---,,,,,,,,,,,,---...---------............/////////000000111222222333111111111000000000000000000000000000111222333444222222222111111111111000000000000111222222333333333333333444444444555555555444333222111000000///------......------,,,+++''')))+++---...---+++*********))))))((((((((((((&&&'''((((((((((((((((((&&&'''''''''&&&&&&%%%$$$(((((())))))))))))((((((%%%%%%%%%%%%&&&'''((()))((('''''''''''''''((((((&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&''''''((((((''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&%%%$$$$$$$$$%%%&&&'''%%%&&&'''(((((((((''''''######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&''''''&&&%%%$$$&&&%%%%%%(((+++------,,,(((((('''&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%&&&&&&&&&&&&'''(((###&&&%%%###***777999222...,,,)))'''&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$###$$$%%%%%%$$$###%%%%%%&&&&&&%%%%%%$$$###$$$%%%&&&'''''''''&&&%%%''''''&&&&&&&&&%%%%%%%%%'''''''''&&&&&&''''''(((%%%%%%&&&&&&'''((())))))''''''''''''''''''''''''&&&&&&&&&''''''''''''(((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&((()))************&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$###"""""""""$$$$$$&&&'''''''''&&&%%%'''((((((((('''&&&%%%%%%&&&%%%%%%%%%%%%&&&''''''%%%%%%&&&''''''&&&%%%%%%&&&&&&%%%###!!! !!!###'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&'''''''''$$$$$$%%%%%%%%%%%%$$$$$$###$$$''')))))))))((('''&&&'''((((((&&&%%%&&&'''&&&&&&&&&'''''''''(((((('''((()))+++++++++***))))))***,,,,,,+++++++++,,,...------,,,,,,------...///...---,,,+++,,,---...---------.........//////000000000111222222333333000000000000000111111111111111111111222333444555222222222111111111111000000000000111222222333333333333333444444555555555666666555444222111111000------......------,,,+++###&&&***...//////---,,,,,,,,,+++)))(((&&&%%%%%%&&&&&&'''((()))))))))(((&&&&&&''''''((('''''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&'''((()))***&&&&&&''''''(((***+++,,,'''''''''&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&''''''((((((''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((((((((((((''''''&&&&&&%%%$$$#########$$$&&&((()))&&&&&&((()))))))))((('''#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&''''''&&&$$$$$$$$$%%%&&&&&&''''''&&&&&&'''&&&&&&&&&&&&'''((((((&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###%%%'''))))))'''%%%######$$$&&&***000555777777+++***)))((('''&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&'''((('''&&&%%%&&&'''''')))&&&###--->>>DDD???333000,,,'''%%%$$$&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""###%%%&&&&&&%%%"""###$$$%%%&&&''''''''''''''''''&&&&&&%%%%%%%%%(((''''''&&&&&&%%%%%%$$$%%%&&&''''''((((((''''''''''''''''''((((((((((((&&&''''''((((((''''''&&&''''''&&&%%%&&&'''((()))***)))((('''&&&%%%%%%%%%$$$%%%'''(((((('''%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((((((&&&&&&&&&''''''''''''''' !!!%%%(((***+++'''''''''&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%'''''''''&&&&&&%%%%%%%%%$$$%%%&&&'''&&&%%%$$$###'''&&&&&&%%%%%%$$$$$$###''''''((((((((((((''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&''')))***++++++***)))))))))***,,,,,,++++++,,,,,,,,,---------......---,,,,,,+++******////////////////////////////////////000111222333111222444444222111111222111111111111111111111111555444111///------,,,---111222222333333444444555444444555555555555444444444444333222111000///...---++++++,,,...///...------,,,,,,++++++,,,,,,---'''((()))((('''&&&'''((())))))))))))))))))))))))))))))))))))))))))))))))&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$$$$$$$&&&&&&&&&'''''''''((((((''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%&&&'''''''''&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''(((((()))(((&&&$$$$$$$$$&&&'''"""###$$$$$$&&&&&&'''(((((('''&&&%%%$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%$$$$$$###&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$(((***%%%"""%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''(((((('''''''''''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&'''((('''%%%$$$###$$$%%%%%%&&&%%%%%%$$$$$$#########%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$''')))'''$$$111GGGTTTTTT999555...((($$$$$$'''(((%%%&&&((((((&&&$$$$$$%%%$$$######$$$&&&'''&&&%%%(((***)))(((///<<>>AAAAAA@@@>>>;;;777444222++++++***'''%%%###$$$&&&((('''''''''&&&'''''''''&&&'''%%%###%%%---222333:::777666777888666...(((&&&%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''***)))'''%%%$$$$$$$$$%%%$$$&&&'''&&&%%%$$$%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%$$$%%%&&&''''''''''''''''''&&&&&&&&&%%%&&&&&&&&&'''''''''(((&&&&&&'''(((((((((((((((''''''''''''((((((((((((((())))))******))))))(((&&&&&&&&&&&&''''''(((((('''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&((((((((((((((((((((((((******))))))(((''''''&&&***))))))((('''&&&&&&%%%)))'''&&&&&&''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''')))(((((((((((('''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$###$$$%%%&&&'''%%%&&&&&&&&&'''''''''(((&&&''''''((((((''''''&&&&&&&&&&&&''''''''''''(((((((((''''''''''''(((((()))))))))))))))******+++))))))*********+++++++++++++++,,,,,,---.................................+++---///111111111000///...000222222111000111222222222222222222222222222111111///......///000000//////000000111222222333333333444444444444333333222222111000//////......///---,,,,,,------+++*********))))))))))))******'''((()))((('''&&&'''((((((((((((((((((((((((((())))))))))))))))))))))))&&&&&&''''''''''''&&&&&&(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''))))))((('''&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&'''''''''''''''''''''''')))(((&&&$$$###$$$&&&'''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%'''((('''$$$"""%%%)))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$''')))'''""""""'''(((%%%(((+++000555:::===???@@@::::::999666111---******'''''''''&&&%%%%%%&&&((($$$)))++++++---222333111222000000555;;;;;;333+++(((&&&&&&((('''%%%%%%(((%%%%%%&&&&&&&&&&&&%%%%%%&&&%%%%%%%%%%%%&&&''''''((((((((((((((((((((((((&&&&&&%%%%%%%%%&&&'''(((%%%&&&'''&&&%%%$$$%%%'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((('''&&&%%%%%%%%%%%%%%%''''''''''''''''''''''''(((((((((''''''&&&&&&&&&&&&'''(((((())))))((((((''''''''''''((((((((((((((((((((())))))(((((((((&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%&&&''''''''''''''''''''''''''''''(((((((((((((((((((((((((((((())))))))))))))))))******)))(((''''''&&&&&&((('''&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''')))(((((((((((('''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%$$$###$$$$$$%%%&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&''''''''''''&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&''''''(((******(((((())))))************))))))*********+++++++++------------------------........................***,,,...000111000///...---///111111000000000111222222222222222222222222111000///......///000111000000111111222333333333222222333333333333222222111000000//////............---++++++,,,,,,+++)))***))))))(((((())))))***'''((()))((('''&&&'''((())))))))))))))))))))))))))))))))))))))))))))))))&&&&&&''''''''''''&&&&&&&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((('''&&&%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&'''''''''''''''''''''&&&&&&'''''''''((((((((()))%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&'''''''''''''''''''''''')))(((&&&$$$###$$$&&&''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%'''&&&&&&%%%%%%$$$$$$###%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''###$$$#########%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&'''#########$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&%%%'''((('''###$$$'''***---000333444???BBBEEEEEEBBB???<<<;;;222222111---***(((***,,,(((...444555777888555///000------444<<>>??????>>>999222444111111555<<<@@@???<<<444)))"""$$$&&&######(((&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''((((((''''''%%%$$$$$$###%%%'''((('''&&&%%%&&&'''&&&%%%$$$###$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&'''''''''((((((((()))((((((((((((''''''''''''''''''((()))))))))))))))''''''''''''((((((((((((&&&''''''((((((''''''&&&%%%&&&'''((((((((('''&&&&&&&&&&&&'''((()))***+++((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&*********))))))))))))))))))))))))(((((((((((((((&&&&&&&&&'''((((((&&&$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''"""###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&''''''''''''((('''''''''''''''((()))***'''''')))*********)))(((++++++++++++,,,,,,,,,,,,,,,,,,------......//////------------------------+++,,,,,,---......//////+++---///000//////000111000000000000000000000000222111000.........///000//////000000111222222222111111222222222222111111//////............------,,,+++******,,,---,,,++++++******))))))******+++)))***+++***)))((()))***))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&'''((())))))%%%$$$$$$$$$%%%%%%&&&'''(((((('''''''''&&&&&&&&&&&&&&&''''''((())))))***''''''''''''''''''''''''%%%&&&&&&&&&&&&'''''''''$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''###$$$$$$%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&''''''''''''''')))'''###$$$''''''"""%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%###$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###%%%''''''$$$!!!!!!###&&&%%%%%%%%%%%%%%%&&&&&&$$$&&&***---///111444777===??????===999:::>>>CCCCCCHHHKKKKKKKKKLLLIIIDDDBBBAAAAAACCCFFFHHHHHHGGGBBB111$$$%%%((($$$###&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''&&&%%%######&&&'''((('''&&&%%%&&&(((&&&%%%$$$######%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&'''''''''(((((())))))&&&&&&''''''((()))))))))'''(((((()))))))))))))))''''''''''''((((((((()))******++++++++++++******%%%%%%'''((((((((('''&&&''''''''''''(((***+++,,,((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&,,,,,,+++***)))(((''''''(((((((((((())))))))))))''''''&&&'''''''''$$$"""%%%%%%%%%&&&&&&'''''''''&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&''''''''' ###&&&((()))))))))%%%%%%&&&&&&'''(((((((((%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&'''''''''(((((())))))(((''''''''''''(((&&&''')))*********)))(((++++++,,,,,,,,,---------***+++,,,---///000111111------------------------,,,,,,,,,,,,,,,...//////+++---///000//////000111////////////////////////333222000///.........///......//////000111111111111111222222222222111111..................------+++***)))***,,,------+++++++++************++++++'''))))))((('''&&&'''((((((((((((((((((((((((((())))))))))))))))))))))))&&&''''''''''''''''''&&&((((((((('''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((''''''''''''(((***+++,,,$$$$$$$$$$$$%%%%%%&&&'''(((((('''''''''&&&&&&&&&%%%%%%&&&&&&'''((())))))((((((((((((((((((((((((&&&&&&&&&'''''''''(((((($$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%&&&'''''''''&&&''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''!!!"""###$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&'''''''''((((((###(((((($$$"""'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%"""###%%%&&&'''&&&%%%%%%'''''''''&&&&&&%%%%%%%%%)))(((&&&%%%$$$#########$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ """%%%'''&&&$$$%%%)))###$$$&&&'''((((((''''''((((((&&&$$$"""###''')))$$$(((+++,,,,,,000888>>>PPPTTTUUUUUUVVV[[[[[[YYYUUUVVVWWWWWWWWWVVVUUUUUUNNN999))))))+++'''%%%'''&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&'''((('''&&&&&&'''(((&&&%%%$$$######%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&''''''''''''"""###$$$&&&''''''&&&&&&$$$%%%&&&&&&''''''&&&&&&)))((((((''''''(((((())))))((('''''''''(((***+++)))(((&&&%%%%%%&&&((()))---+++(((%%%$$$$$$$$$%%%'''((((((((())))))******(((((('''''''''&&&&&&&&&((((((((((((((('''''''''''''''''''''((((((((((((((((((''''''''''''((((((***(((&&&&&&&&&&&&%%%$$$''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%'''&&&%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''((()))))))))(((&&&%%%(((((((((((('''''''''''''''''''''((())))))************+++++++++,,,,,,,,,+++,,,---///000//////...//////.........---------------...///000000000///111000///......///000111111111000000//////............////////////......000///...---...000222333222111///.........///000//////...---,,,,,,++++++)))***+++,,,,,,+++***)))))))))))))))(((((((((((('''&&&&&&%%%%%%'''((())))))******(((&&&&&&(((+++***)))&&&$$$###$$$%%%%%%'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%(((((((((''''''&&&&&&&&&$$$$$$%%%&&&'''''''''&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&''''''((()))******(((&&&$$$)))+++,,,***&&&%%%&&&(((&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&'''''''''%%%&&&&&&''''''&&&&&&%%%'''''''''((((((((())))))((('''&&&&&&$$$$$$###"""&&&&&&&&&''''''''''''(((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%&&&&&&'''###$$$$$$%%%&&&'''((((((***)))'''&&&%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&$$$######""""""###$$$%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((((((((('''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$%%%%%%%%%&&&''')))***,,,---...777;;;DDDJJJIIICCCAAACCCNNNIIIEEEGGGMMMRRRTTTTTTPPP999&&&&&&***'''$$$&&&''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$)))((('''&&&&&&&&&&&&&&&'''&&&&&&%%%%%%$$$$$$###%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###%%%''''''''''''&&&$$$%%%&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&((((((((((((((())))))***)))'''&&&%%%%%%&&&''')))***)))'''&&&%%%%%%&&&'''''''''''''''''''''''''''))))))((((((((('''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((''''''''''''((((((---+++)))((())))))((('''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((((((''''''***))))))))))))(((((((((''''''((())))))******+++******+++++++++,,,,,,,,,+++,,,---......////////////.........------------000000000000///...---,,,111000///......///000111000000000///////////////......////////////......000///...---...000222333111111///.........///000///......---,,,,,,++++++)))***++++++++++++***)))''''''(((((())))))******((('''&&&&&&&&&'''((()))***)))((('''&&&'''((())))))(((&&&%%%$$$$$$%%%&&&''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%'''''''''&&&&&&&&&%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&''''''((()))))))))'''&&&%%%'''***,,,+++(((&&&''')))'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&'''&&&&&&%%%%%%$$$$$$###&&&&&&&&&&&&''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&'''''''''(((''''''&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$###$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''$$$$$$%%%'''(((***++++++---///555;;;;;;777555666===;;;:::???EEEJJJJJJHHH<<<...&&&(((***&&&&&&+++''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&''''''&&&&&&&&&'''''''''((((((%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&(((((((((''''''%%%%%%&&&''''''''''''&&&((((((''''''''''''((((((''''''((())))))))))))(((((('''&&&%%%%%%&&&'''(((&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&)))))))))))))))(((((((((''''''(((((())))))******''''''''''''((((((((((((((((((''''''''''''((((((---+++)))((()))***)))(((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((('''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''((())))))************))))))))))))(((((())))))***++++++,,,******+++++++++,,,,,,,,,,,,,,,,,,,,,---...//////............------------000000000000///...---,,,000000////////////000000//////////////////000000......////////////......//////.........000222333111000//////......//////......------,,,,,,++++++)))***++++++++++++***)))&&&&&&'''((()))***++++++(((((('''''''''((()))******(((&&&&&&'''''''''&&&((('''&&&%%%%%%&&&'''((('''''''''''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''((((((((('''''''''''''''&&&)))------***(((((()))((((((''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&'''''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%$$$$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''(((((((((((("""###$$$%%%&&&'''(((((()))'''***000222000---...------///444999:::888444(((%%%&&&+++)))$$$&&&---&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&$$$$$$$$$%%%&&&&&&''''''''''''''''''((((((((((((%%%%%%$$$#########$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''')))))))))((('''%%%&&&&&&'''''''''''''''***))))))(((((())))))***%%%&&&((()))))))))((('''((('''&&&&&&&&&&&&'''(((&&&&&&'''(((((('''&&&&&&'''((((((((())))))******(((((((((((((((((((((((((((((()))***+++,,,,,,---''''''''''''((((((((((((((((((''''''''''''((((((+++)))''''''(((((('''&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&''''''(((((())))))''''''''''''''''''''''''&&&&&&&&&&&&&&&'''''''''%%%&&&((())))))(((&&&$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&)))((('''''''''(((***+++*********)))))))))(((((()))))))))***++++++,,,,,,******+++++++++,,,,,,,,,,,,++++++***+++---...000------------------------,,,,,,...///000000000000000000////////////000000---......//////000000000......////////////......///.........///000111222000000//////............---------,,,,,,,,,++++++*********++++++*********''''''(((((())))))******(((((((((((()))))))))******(((&&&&&&''''''&&&$$$&&&&&&&&&%%%&&&'''((()))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''(((''''''&&&&&&&&&'''(((&&&***......+++((('''(((''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%'''((((((((())))))))))))$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%###$$$&&&'''(((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''(((((((((((("""######$$$%%%&&&''''''((($$$$$$)))---,,,******(((((()))+++---,,,)))%%%######'''+++(((######)))&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%&&&&&&&&&&&&'''''''''&&&%%%%%%$$$$$$&&&&&&&&&&&&''''''''''''&&&&&&%%%$$$######$$$$$$'''&&&&&&%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((()))))))))((('''%%%&&&''''''(((((('''''''''&&&&&&&&&&&&&&&&&&'''%%%&&&((()))))))))(((''''''''''''&&&&&&'''''''''(((((((((((('''&&&%%%$$$%%%&&&'''((()))++++++,,,''''''''''''''''''''''''''''''(((((()))***++++++''''''''''''((((((((((((((((((''''''''''''((((((***(((&&&&&&'''((('''&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((()))))))))''''''''''''''''''''''''&&&&&&''''''((((((((()))$$$&&&((())))))(((&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&((('''''''''((()))+++,,,))))))(((((((((''''''''')))))))))***++++++,,,,,,******+++++++++,,,,,,,,,++++++******+++,,,...///,,,,,,------------------+++,,,---///000000111111//////000000000000//////------......//////000000......////////////...............//////000111222///////////////......---,,,,,,,,,,,,,,,++++++++++++******************+++******))))))(((((('''''''''(((((())))))))))))))))))((('''''''''&&&%%%$$$&&&&&&&&&&&&'''(((((()))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''(((((((((((('''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&&&&&&&'''((((((+++///...***&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&&&&'''''''''''''''&&&&&&%%%%%%$$$###$$$&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''$$$$$$$$$%%%%%%&&&&&&&&&%%% ###'''&&&%%%%%%((('''&&&&&&&&&&&&%%%$$$&&&$$$$$$''''''%%%%%%'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$&&&&&&&&&&&&%%%(((((('''&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&((('''&&&%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((())))))(((''''''&&&&&&'''(((((((((((('''((((((''''''''''''((((((&&&&&&'''(((((((((((('''''''''''''''''''''''''''))))))((('''&&&&&&%%%%%%###$$$%%%&&&'''))))))***&&&&&&&&&&&&''''''''''''$$$$$$%%%%%%&&&&&&''''''''''''''''''((((((((((((((((((''''''''''''((((((***)))'''''')))))))))((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((''''''''''''''''''''''''&&&&&&&&&'''(((((())))))$$$%%%&&&'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((()))+++,,,---((((((((((((''''''''''''(((((())))))***++++++,,,******+++++++++,,,,,,,,,************+++,,,------,,,,,,,,,,,,------------...///////////////......//////000000000000//////..................//////......////////////............//////000111111111...////////////...------,,,,,,,,,,,,++++++++++++++++++***))))))***++++++++++++***)))((('''&&&&&&&&&'''((()))))))))((((((((()))***)))'''%%%%%%%%%&&&&&&''''''((((((((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%&&&&&&&&&&&&'''(((((((((((('''&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&''''''''''''***---,,,(((%%%%%%&&&$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&'''(((((('''''''''&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%&&&&&&''''''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$###############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$ $$$&&&$$$$$$&&&&&&%%%$$$$$$%%%&&&((()))'''$$$"""###&&&))))))(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&''''''&&&%%%%%%%%%%%%%%%&&&''''''((((((###$$$$$$$$$%%%%%%%%%%%%''''''&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((((((((&&&&&&&&&&&&'''(((((((((((((((++++++************++++++'''&&&&&&&&&&&&'''((((((&&&''''''''''''''''''&&&((('''&&&&&&%%%&&&'''(((&&&&&&&&&&&&''''''''''''&&&'''''''''((((((((((((%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''((((((((((((((((((''''''''''''(((((()))'''&&&&&&((()))((('''''''''''''''''''''''''''''''''''''''''''''''''''((((((''''''''''''''''''''''''''''''''''''''''''$$$$$$%%%%%%&&&''''''((($$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''')))+++,,,,,,,,,)))))))))(((((((((((('''''''''((())))))******+++******+++++++++,,,,,,,,,((()))***++++++,,,,,,,,,++++++,,,,,,,,,---------......////////////.........///000111111000///.....................------......////////////......---...///000000111111111....../////////...---,,,++++++++++++++++++++++++++++++***))))))***++++++******))))))((((((''''''%%%&&&'''((()))(((''''''&&&+++...,,,&&&###$$$((('''''''''(((((((((((('''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&'''''''''&&&&&&''''''&&&%%%%%%$$$'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''$$$%%%&&&'''''''''&&&&&&$$$'''***)))'''%%%''')))%%%%%%%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%(((((((((((()))))))))***%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%)))(((%%%&&&***%%%%%%%%%%%%%%%&&&((()))&&&%%%######%%%((()))(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''(((((('''%%%$$$%%%%%%&&&&&&'''((((((((($$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''(((((('''&&&%%%&&&''''''(((((((((((((((((((((''''''''''''((((((''''''&&&%%%%%%'''((()))&&&&&&''''''''''''&&&&&&'''&&&%%%$$$%%%''')))++++++******)))(((''''''''''''((((((((())))))******((((((((((((((('''''''''''''''''''''((((((((()))((((((''''''''''''((((((&&&%%%######%%%&&&&&&%%%''''''''''''''''''''''''''''''''''''''''''''''''((((((''''''&&&&&&&&&%%%''''''''''''''''''''''''""""""###$$$$$$%%%&&&&&&%%%$$$$$$$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''###$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%(((***,,,,,,,,,,,,************))))))))))))'''''''''((())))))************+++++++++,,,,,,,,,'''(((***+++,,,,,,+++++++++++++++,,,,,,---------***+++---///000111222222...///000111111000///.../////////......------,,,......////////////......---...///000111111111111---.../////////...,,,,,,++++++++++++++++++++++++,,,+++***))))))***+++,,,(((((((((((())))))))))))$$$%%%'''((((((((('''&&&%%%,,,111...&&&"""$$$)))''''''((((((((((((''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''&&&&&&&&&''''''(((((((((%%%%%%%%%%%%$$$$$$###"""'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''###$$$&&&(((((('''&&&%%%!!!$$$''''''&&&&&&))),,,&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&&&&&&&''''''''''''&&&&&&'''''''''&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%$$$###$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&"""######$$$&&&''''''((("""###$$$%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%$$$$$$###'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%$$$$$$$$$$$$$$$######&&&)))'''###%%%***%%%&&&'''&&&%%%$$$$$$$$$%%%'''(((%%%###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&'''((())))))'''%%%$$$)))(((((('''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''############$$$%%%&&&&&&"""###$$$%%%&&&&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''((()))***((((((((('''&&&&&&&&&%%%(((((((((((((((((((((((()))***+++,,,,,,+++***)))''''''''''''((((((((((((%%%&&&&&&&&&'''((((((((((((((()))******)))((('''$$$######%%%(((*********''''''&&&&&&&&&&&&''''''%%%&&&''''''((((((''''''))))))(((((((((((())))))'''''''''''''''&&&&&&&&&&&&'''''''''(((((())))))((('''&&&%%%%%%%%%%%%%%%)))'''&&&%%%$$$%%%%%%&&&''''''''''''&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&***)))((('''''''''''''''))))))(((((((((((())))))))))))(((((((((((())))))(((((())))))))))))(((((()))***+++***)))((()))*********+++++++++,,,,,,,,,+++++++++,,,,,,---------...,,,,,,---///000///...333222111000///...---,,,...------------...//////000000////////////000000000000000000////////////......---------,,,,,,,,,///...------++++++***)))+++***************++++++***((('''((()))***)))'''''''''&&&&&&&&&%%%%%%%%%'''((()))******)))((((((((((((((((((''''''''''''+++***(((&&&%%%%%%%%%%%%&&&&&&'''(((((((((''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%%%%%%%&&&&&&&&&''''''"""%%%''''''&&&$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&&&&$$$######%%%'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&& !!!###%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$######%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%############%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&''''''%%%%%%&&&'''%%%%%%$$$###$$$%%%&&&'''%%%&&&''''''((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''((('''&&&%%%$$$%%%&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$(((''''''''''''(((((()))&&&&&&&&&&&&&&&%%%%%%%%%(((((((((((((((((((((((('''(((((((((((((((((('''&&&&&&&&&&&&''''''''''''&&&&&&&&&'''''''''''''''''''''((()))))))))(((''')))(((''''''((()))(((&&&''''''&&&&&&&&&&&&''''''%%%&&&''''''((((((''''''))))))(((((((((((())))))&&&&&&''''''''''''''''''&&&'''''''''((((((((()))((('''&&&%%%%%%%%%%%%&&&)))(((''''''&&&&&&&&&'''&&&&&&&&&'''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%%%%))))))(((((((((((())))))))))))(((((((((((())))))))))))************)))))))))***+++***)))((()))*********+++++++++,,,,,,,,,------........./////////---///000///---,,,---///222222111000///...------...------------...//////000000////////////000000444333222111000...------......---------,,,,,,,,,---------,,,,,,++++++***+++******))))))***++++++***((('''((()))***)))'''(((((((((((('''''''''&&&))))))))))))((('''&&&&&&''''''''''''&&&&&&&&&&&&(((((('''&&&%%%&&&''''''!!!"""###$$$%%%%%%'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&&&&'''''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''###%%%&&&&&&%%%$$$$$$%%%((((((((((((((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%&&&&&&'''(((&&&%%%###$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%%%%%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$######%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&''''''%%%%%%&&&'''&&&%%%$$$$$$$$$%%%''''''###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''((('''&&&%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$)))((((((''''''''''''(((%%%%%%%%%%%%%%%&&&&&&&&&((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&%%%&&&'''(((((((((((((((+++***(((((())))))(((&&&''''''&&&&&&&&&&&&''''''&&&&&&'''((((((((((((''')))((((((''''''(((((()))%%%&&&&&&&&&'''((((((((('''''''''''''''(((((((((''''''&&&%%%%%%%%%&&&&&&((((((((()))((((((''''''%%%%%%&&&&&&'''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%&&&&&&'''''''''((('''&&&&&&&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%%%%&&&)))((((((''''''(((((()))))))))(((((((((((())))))******++++++++++++******((()))******)))((()))+++******+++++++++,,,,,,,,,+++++++++++++++,,,,,,,,,,,,000333111+++(((+++000000000000000////////////......------......///000000000////////////000000444333333111000///...---......---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++******)))))))))*********((('''((()))***)))'''******)))))))))))))))(((***)))((('''&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$&&&&&&%%%%%%&&&'''(((((("""###$$$%%%&&&&&&&&&&&&((((((''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''(((((($$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&%%%$$$$$$%%%'''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''((('''%%%$$$$$$%%%&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%###"""!!!&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$######%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&''''''%%%%%%&&&'''&&&&&&%%%%%%&&&&&&'''(((###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''((('''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$***)))((('''''''''''''''%%%%%%%%%&&&&&&'''''''''(((((((((((((((((((((((()))((('''&&&&&&'''((()))%%%%%%&&&&&&&&&'''''''''((((((((('''&&&&&&&&&%%%$$$%%%%%%&&&'''(((((()))((('''&&&''')))******(((''''''&&&&&&&&&&&&''''''&&&&&&'''((((((((((((((((((((((((''''''(((((((((%%%%%%%%%&&&'''((())))))'''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&'''((())))))((('''&&&$$$$$$%%%&&&''''''''''''%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&'''(((((())))))''''''''''''))))))&&&&&&&&&&&&&&&&&&&&&&&&)))(((((('''''''''(((((((((((((((''''''((((((((())))))(((((((((((()))))))))******++++++******)))((()))******))))))***+++******+++++++++,,,,,,,,,)))))))))))))))*********,,,///111000,,,***---000////////////000000000000...............//////000000000////////////000000////////////000000000000......---------,,,,,,,,,******++++++,,,,,,,,,,,,+++******))))))))))))******((('''((()))***)))''')))))))))))))))))))))))))))(((&&&%%%$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''*********))))))'''&&&%%%''''''''''''&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&&&&$$$######%%%(((#########$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&'''&&&$$$$$$%%%&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$###"""&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$######%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%''''''''''''%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&''''''%%%%%%&&&'''&&&&&&&&&&&&''''''((((((%%%&&&''''''((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%***)))((('''''''''''''''&&&&&&''''''(((((())))))(((((((((((((((((((((((()))((('''&&&&&&'''((()))&&&'''''''''((((((((((((((((((((('''&&&&&&&&&%%%%%%%%%%%%&&&'''((())))))'''&&&%%%&&&((()))((('''''''''&&&&&&&&&&&&''''''&&&'''(((((())))))((((((((((((''''''''''''((((((%%%%%%%%%&&&'''((())))))'''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''$$$%%%'''(((((('''&&&%%%$$$$$$%%%&&&''''''''''''%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''(((((('''&&&%%%$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''(((((()))((((((''''''''''''(((((())))))(((((((((((())))))(((((())))))))))))((((((''')))******))))))***+++******+++++++++,,,,,,,,,---------------,,,,,,,,,,,,,,,,,,---///000000///////////////000000000000///............///000000000000////////////000000------------......//////......---------,,,,,,,,,)))******++++++,,,,,,---+++******)))(((((())))))***((('''((()))***)))'''((((((((((((((((((((((((&&&%%%$$$$$$$$$&&&'''((('''''''''&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&%%%%%%%%%''''''''''''&&&$$$######%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&&&&$$$######%%%(((%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''''''%%%$$$$$$%%%&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&$$$######%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%''''''''''''%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&''''''%%%%%%&&&'''&&&&&&&&&'''''''''''''''%%%&&&''''''((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%)))((((((''''''''''''(((((((((((((((((()))))))))((((((((((((((((((((((((&&&&&&%%%%%%%%%%%%&&&&&&'''''''''((((((((())))))'''''''''''''''&&&&&&&&&'''&&&&&&&&&'''((()))))))))(((&&&&&&''''''&&&$$$''''''&&&&&&&&&&&&''''''''''''((())))))))))))((((((''''''&&&&&&''''''(((%%%&&&&&&&&&'''((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''$$$%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&&&&&&&%%%$$$%%%%%%&&&&&&'''''''''$$$###"""!!!!!!"""###$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''(((''''''&&&&&&''''''((())))))(((((((((((())))))(((((())))))))))))(((((('''(((******))))))***,,,******+++++++++,,,,,,,,,------,,,,,,,,,,,,++++++,,,******,,,000222111000////////////000000000000//////......//////000111000000////////////000000///......---,,,,,,++++++......---------,,,,,,,,,)))*********++++++,,,,,,+++******)))((((((((((((***((('''((()))***)))'''&&&&&&''''''''''''(((((($$$$$$$$$%%%&&&'''((()))''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$###"""###$$$%%%&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%%%%&&&'''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&''''''(((&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$%%%'''$$$$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''(((((()))&&&$$$######%%%'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$&&&$$$######%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&''''''%%%%%%&&&'''%%%%%%&&&''''''''''''&&&###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&(((''''''''''''(((((()))((((((((((((((('''''''''((((((((((((((((((((((((&&&&&&''''''''''''&&&&&&&&&&&&&&&'''''''''((((((&&&&&&&&&''''''''''''''')))((('''''''''((()))))))))'''&&&'''(((((('''&&&''''''&&&&&&&&&&&&''''''''''''((()))))))))))))))(((''''''&&&&&&''''''(((&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&'''((((((&&&&&&&&&'''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$######$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&''''''(((''''''&&&&&&''''''((())))))(((((((((((()))))))))))))))******)))))))))&&&(((******))))))+++,,,******+++++++++,,,,,,,,,,,,+++++++++************+++,,,---.........000111000000000000///////////////////////////000000111000000////////////000000///......------,,,,,,+++......---------,,,,,,,,,***************+++++++++++++++)))(((((('''''''''***((('''((()))***)))'''&&&&&&&&&''''''((((((((($$$%%%&&&'''''''''''''''&&&&&&&&&&&&%%%%%%%%%$$$###$$$%%%&&&&&&&&&%%%%%%$$$%%%&&&((()))*********%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''((())))))&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&###$$$$$$$$$$$$%%%%%%%%%###%%%&&&&&&%%%$$$$$$%%%######$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''((())))))$$$###"""###&&&'''((('''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$######%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&''''''%%%%%%&&&'''###$$$%%%&&&'''&&&&&&%%%###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&'''''''''&&&%%%$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&'''''''''''''''((()))***((((((((('''&&&&&&&&&%%%(((((((((((((((((((((((('''((()))******)))((('''%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''(((((((((******(((''''''((())))))&&&%%%%%%'''***,,,,,,+++'''''''''&&&&&&''''''''''''(((((()))))))))))))))'''''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((('''&&&&&&&&&((()))***''''''''''''&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%***)))(((''''''((()))***&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''((()))***'''''''''&&&&&&'''''''''))))))(((((((((((())))))******++++++++++++******&&&((()))***))))))+++---******+++++++++,,,,,,,,,/////////......---------***...111000,,,***---222111000000000///////////////////////////000111111000000////////////000000,,,,,,------...///000000......---------,,,,,,,,,************************++++++)))(((''''''''''''***((('''((()))***)))(((&&&'''''''''(((((())))))&&&'''((((((((('''&&&%%%%%%%%%%%%$$$$$$$$$######!!!"""$$$&&&''''''''''''&&&&&&''''''''''''''''''&&&&&&&&&'''''''''((((((%%%&&&&&&&&&'''(((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((()))******&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%###%%%''''''&&&$$$$$$%%%(((((())))))***++++++,,,&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''###""""""###&&&(((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&((('''%%%%%%$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%############%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&''''''%%%%%%&&&'''###$$$%%%&&&&&&&&&%%%$$$%%%&&&''''''((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&'''''''''&&&%%%$$$#########$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&((((((((((((''''''''''''%%%'''))))))((('''((()))%%%&&&&&&'''''''''''''''((((((''''''&&&&&&&&&%%%''''''''''''''''''''''''******)))((('''&&&%%%%%%)))))))))(((''''''&&&&&&)))))))))))))))(((''''''%%%&&&&&&&&&'''((((((((('''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&'''''')))***+++(((((('''&&&&&&&&&&&&'''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%((((((((((((((((((((((((''''''''''''''''''''''''(((''''''&&&&&&''''''(((&&&%%%$$$$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%(((&&&""" !!!$$$&&&$$$$$$&&&&&&&&&&&&$$$$$$(((((())))))))))))((((((&&&&&&&&&'''''''''(((((()))((('''((()))***)))(((,,,,,,,,,,,,,,,+++***)))++++++++++++++++++++++++------------------------............////////////000000000000000000000000//////////////////////////////000000000000//////111000...---,,,,,,------.........------,,,,,,,,,************)))))))))))))))******))))))((('''&&&)))+++,,,,,,***)))******&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&((())))))((((((%%%%%%%%%%%%%%%&&&'''(((+++)))%%%$$$%%%&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''######$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''(((''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$%%%&&&'''((((((((((((''''''&&&%%%%%%((('''%%%$$$###$$$$$$%%%(((((('''&&&%%%###"""!!!$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&'''''''''&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&(((%%%######&&&((((((&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&''''''%%%%%%&&&'''%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%(((''''''&&&&&&%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&%%%%%%%%%$$$%%%''''''''''''%%%$$$%%%&&&'''''''''&&&%%%$$$%%%%%%&&&'''((((((''''''%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%&&&&&&%%%%%%%%%###$$$$$$%%%%%%$$$$$$###&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&'''((('''&&&%%%((((((((((((''''''''''''&&&'''))))))(((''''''((('''(((((()))))))))))))))((((((((('''''''''&&&&&&'''''''''''''''''''''''')))))))))(((''''''&&&&&&''''''''''''(((((((((((()))))))))))))))(((''''''&&&&&&&&&'''''''''''''''(((''''''&&&&&&''''''''''''''''''''''''((()))***(((((('''&&&&&&&&&&&&'''%%%&&&&&&&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%$$$$$$$$$$$$%%%%%%&&&%%%$$$$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%'''&&&%%%#########$$$%%%%%%&&&''''''''''''&&&%%%'''(((((())))))(((((('''&&&&&&&&&'''''''''((((((***)))((()))***+++***)))+++,,,,,,,,,++++++***)))++++++++++++++++++++++++------------------------............//////////////////////////////////////////////////////////////////000000000000//////000///...,,,,,,,,,,,,,,,//////......------------************))))))))))))'''(((((()))))))))((((((,,,------,,,)))'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((''''''''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((((((((('''&&&%%%''''''&&&%%%%%%%%%&&&&&&((('''%%%&&&'''((('''&&&''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&''''''''''''&&&%%%$$$$$$$$$%%%&&&''''''''''''&&&$$$###"""$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''))))))((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((&&&###$$$&&&''''''&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%&&&$$$%%%&&&%%%$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''$$$$$$%%%&&&&&&''''''(((###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%&&&&&&''''''&&&%%%%%%$$$%%%%%%&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%&&&''''''''''''((((((((((((''''''''''''&&&((())))))(((&&&'''((('''(((((()))))))))))))))))))))((((((((((((''''''((((((((((((((((((((((((((((((((((((((((((((((((%%%&&&&&&'''(((((())))))(((((()))))))))((('''''''''''''''''''''&&&&&&&&&(((((('''''''''(((((()))(((((('''''''''(((((()))(((((('''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''%%%$$$$$$######$$$$$$%%%&&&%%%$$$%%%&&&'''&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&'''''''''&&&%%%$$$''''''(((((((((((('''''''''''''''(((((('''''''''&&&&&&&&&'''''''''''''''***)))((()))+++,,,+++***+++++++++,,,++++++***)))++++++++++++++++++++++++,,,,,,,,,,,,---------------............/////////////////////////////////////////////////////////...//////000000//////.........---,,,++++++++++++//////............------************))))))))))))&&&&&&'''((())))))))))))***+++,,,+++(((&&&%%%&&&((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&******))))))((((((((('''''''''''''''''''''''''''''''''(((((()))(((((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''''''''''''''''''''&&&&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((''''''&&&%%%)))((('''&&&%%%%%%%%%%%%&&&%%%&&&((())))))'''%%%''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''((()))(((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&'''((($$$$$$$$$%%%&&&'''''''''&&&%%%%%%%%%%%%%%%&&&''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((&&&%%%$$$&&&'''&&&%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%###$$$%%%%%%######$$$%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''$$$$$$%%%&&&&&&''''''((($$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&%%%%%%%%%''''''&&&&&&&&&&&&''''''%%%%%%&&&''''''&&&&&&%%%###$$$%%%%%%&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&'''((()))(((((((((((('''''''''''''''(((***)))'''&&&&&&'''%%%&&&&&&''''''''''''''')))))))))))))))((((((((())))))))))))))))))))))))''''''''''''(((((())))))&&&&&&&&&''''''((((((((('''(((((((((((((((''''''((((((((('''&&&&&&&&&%%%''''''''''''''''''((())))))((((((''''''''''''((((((((('''&&&&&&&&&&&&'''((((((''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&'''%%%$$$%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&&&&%%%''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&'''''''''''''''''''''''')))((('''(((***++++++*********++++++++++++******++++++++++++++++++++++++,,,,,,,,,,,,,,,------------------.........//////////////////////////////////////////////////////...//////////////////...---,,,,,,++++++*********------------------------************)))))))))(((&&&''''''((())))))((((((%%%'''))))))((('''((()))((((((((((((((((((((((((''''''''''''''''''''''''******))))))((('''''''''''''''''''''''''''''''''&&&'''((((((((((((((((((''''''''''''''''''''''''&&&''''''(((((((((((((((((((((''''''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&(((((())))))(((''''''&&&&&&&&&&&&'''((('''&&&'''((((((&&&$$$''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&'''''''''(((&&&&&&&&&''''''''''''((()))))))))))))))(((((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&''''''(((''''''&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&%%%%%%%%%###%%%&&&%%%$$$###$$$%%%%%%%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%%%%&&&(((''''''&&&&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&'''%%%%%%&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&%%%$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%''')))***((((((((((((''''''''''''&&&((())))))(((''''''(((%%%&&&&&&'''''''''''''''((((((((()))))))))))))))))))))))))))))))))))))))&&&&&&''''''((()))))))))((('''''''''&&&&&&&&&%%%''''''((((((((((((''''''((((((((('''&&&&&&&&&%%%&&&%%%%%%%%%&&&&&&'''((()))((((((''''''''''''((((((((('''&&&&&&&&&&&&'''(((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&''''''&&&%%%%%%''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&'''&&&%%%$$$$$$%%%'''((('''&&&&&&&&&&&&&&&&&&'''&&&&&&''''''''''''&&&&&&'''''''''''''''''''''&&&'''&&&%%%''')))******))))))******++++++*********+++++++++++++++++++++++++++++++++,,,,,,,,,------------------....................................////////////////////////......////////////......++++++++++++++++++******++++++++++++++++++++++++************)))))))))(((((((((((((((((('''&&&&&&%%%&&&((((((((('''((()))))))))))))))))))))))))))''''''''''''''''''''''''(((((((((''''''&&&&&&&&&''''''''''''''''''''''''$$$%%%&&&'''''''''''''''''''''''''''''''''''''''&&&'''(((((())))))(((((()))((((((''''''(((((()))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&'''((()))***%%%%%%%%%&&&'''((()))***---***'''%%%%%%%%%%%%$$$''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&'''''''''(((((((((&&&&&&&&&''''''''''''((())))))*********)))((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&''''''''''''%%%&&&''''''((((((''''''$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''&&&&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''&&&%%%$$$%%%'''&&&&&&%%%%%%&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&(((''''''&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$######$$$%%%&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&''''''''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$###%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&((()))((((((((((((''''''''''''%%%'''))))))((('''((()))'''(((((()))))))))))))))''''''(((((((((((())))))((((((((((((((((((((((((&&&'''''''''(((((())))))((((((''''''&&&%%%%%%$$$&&&&&&'''((((((((('''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&'''((((((((('''''''''(((((()))(((((('''&&&&&&&&&&&&'''((((((((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%&&&'''((('''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&'''&&&%%%$$$$$$%%%''')))''''''&&&%%%%%%&&&'''''''''''''''((((((''''''''''''''''''''''''&&&&&&&&&&&&%%%$$$&&&(((***)))(((((()))******+++*********++++++++++++++++++++++++******++++++,,,,,,------,,,------------.................................////////////////////////---......//////......---++++++,,,,,,,,,++++++***))))))************++++++************))))))))))))(((((((((((('''&&&%%%%%%((()))***)))'''&&&%%%&&&))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''######$$$%%%&&&&&&&&&&&&''''''''''''''''''''''''&&&''''''(((((((((((((((((((((''''''''''''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&&&&&&&'''$$$%%%%%%&&&''')))***+++...+++&&&$$$$$$%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&&&&''''''''''''(((((()))*********)))'''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&'''''''''&&&%%%$$$$$$$$$%%%&&&&&&''''''''''''&&&%%%&&&&&&'''''''''&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&###%%%''''''&&&&&&&&&'''$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%&&&&&&%%%&&&&&&&&&''''''''''''%%%&&&''''''%%%%%%&&&'''&&&&&&&&&&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((((($$$$$$%%%&&&&&&''''''(((%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&((((((''''''((((((''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&%%%$$$######%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&''''''((((((((((((''''''''''''###&&&(((((((((((()))***'''(((((()))))))))))))))&&&&&&'''''''''((((((((('''''''''''''''''''''''''''''''''(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''&&&&&&&&&'''''''''''''''%%%%%%%%%&&&&&&'''((()))'''''''''''''''((()))***(((((('''&&&&&&&&&&&&'''''''''''''''((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''(((&&&%%%&&&'''((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''''''''((((((((((((((('''&&&&&&'''(((((('''(((((())))))(((((('''(((((('''''''''&&&&&&&&&&&&%%%%%%&&&)))******)))(((((()))***************++++++++++++++++++++++++)))******+++,,,,,,------,,,,,,---------.................................////////////////////////---......//////......---***+++,,,------,,,++++++))))))******++++++++++++************))))))))))))'''''''''(((''''''&&&&&&((()))+++***(((&&&&&&'''((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&''''''(((((())))))''''''''''''''''''''''''"""###$$$%%%&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&'''(((((((((((('''(((''''''&&&&&&''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&%%%&&&''''''&&&&&&&&&&&&'''(((*********(((%%%%%%&&&''''''&&&''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&&&&'''''''''&&&&&&&&&''''''''''''((('''((()))******(((&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&''''''(((((('''&&&%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''#########$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&!!!$$$'''(((&&&&&&''')))$$$$$$$$$%%%%%%&&&&&&&&&######$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&'''((())))))$$$%%%&&&&&&%%%$$$%%%&&&&&&&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((($$$$$$%%%&&&&&&''''''(((%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%$$$$$$%%%&&&((()))&&&''''''''''''&&&%%%$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&%%%$$$###"""$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%)))(((((((((''''''''''''###%%%'''(((((()))***+++%%%&&&&&&'''''''''''''''%%%&&&&&&&&&''''''((((((''''''''''''''''''''''''(((((((((((((((((((((((($$$%%%%%%&&&&&&''''''(((%%%%%%&&&'''((((((((('''%%%&&&&&&''''''(((((((((&&&&&&&&&'''''')))******&&&&&&&&&'''''')))***+++(((((('''&&&&&&&&&&&&'''&&&&&&''''''(((((())))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''))))))(((((((((((())))))((('''&&&&&&'''((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%&&&)))++++++***((('''***)))(((''''''((()))***(((((())))))))))))(((((((((((('''''''''&&&&&&&&&'''&&&&&&'''***++++++***(((((()))***************++++++++++++++++++++++++))))))***+++,,,,,,------,,,,,,,,,---------..............................////////////////////////---..................---***+++------...---,,,+++******+++++++++,,,,,,,,,************))))))))))))%%%%%%&&&'''((((((((((((%%%''')))***))))))***+++((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&'''((()))***++++++''''''''''''''''''''''''"""###$$$%%%&&&&&&&&&&&&((((((((((((((((((((((((%%%&&&&&&'''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&(((***+++(((((('''''''''(((((()))$$$$$$%%%''')))***((('''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((&&&''')))***)))(((&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''''''''&&&%%%%%%&&&&&&''''''(((((()))''''''((((((((('''%%%$$$%%%&&&&&&&&&%%%%%%$$$###$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&&&&''''''(((&&&&&&&&&''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&###'''((('''&&&(((***$$$$$$$$$%%%%%%&&&&&&&&&######$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%&&&''')))******###$$$%%%%%%######$$$%%%'''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((''''''&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&'''''''''&&&'''((())))))((('''&&&%%%%%%$$$$$$%%%'''((()))&&&&&&&&&&&&%%%%%%$$$###%%%&&&&&&''''''&&&&&&%%%&&&'''&&&&&&%%%$$$###"""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%&&&&&&&&&&&&''''''((('''&&&$$$###+++)))(((''''''((()))+++((()))*********)))'''&&&***)))(((&&&&&&&&&'''(((((((((((((((((()))******((((((((((((((((((((((((******))))))))))))******&&&&&&&&&&&&''''''''''''(((((((((((((((((((((((()))((('''&&&&&&&&&&&&&&&(((''''''&&&&&&%%%%%%$$$)))((('''&&&''')))+++,,,((('''&&&%%%%%%&&&(((((()))(((((((((((('''''''''''''''''''''''''''''''''''''''(((((('''&&&%%%%%%((()))***++++++***)))(((((((((((((((((((((((((((''''''''''''((((((((((((((('''&&&%%%$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%'''((((((((('''&&&&&&&&&&&&''''''''''''(((((()))*********((('''&&&'''''''''(((((((((((((((******))))))((((((''''''))))))*********+++++++++******************************+++++++++,,,,,,,,,.........------,,,,,,,,,------...///000000//////000...---...///000///.........////////////......//////.........---------++++++************++++++++++++++++++++++++++++++***))))))((((((((((((((()))))))))))))))(((''''''&&&&&&&&&''''''''''''(((((((((((('''&&&&&&&&&%%%''''''((((((((((((''''''###$$$%%%&&&&&&&&&%%%$$$%%%$$$###$$$&&&((((((((())))))))))))************)))))))))(((''''''&&&&&&(((((('''''''''&&&&&&&&&''''''''''''''''''''''''(((((('''''''''&&&&&&&&&)))(((((('''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))((('''&&&'''&&&###!!!!!!###&&&'''((((((''''''''''''((((((''''''''''''''''''''''''&&&'''''''''(((((()))))))))((((((((()))+++...000'''&&&&&&%%%%%%&&&&&&'''%%%&&&&&&&&&'''(((((((((((((((((((((((('''''''''%%%%%%%%%$$$$$$#########&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&(((***+++&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%&&&'''***)))'''%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((((((&&&&&&'''((('''&&&%%%%%%&&&'''&&&%%%&&&$$$###$$$''')))(((&&&)))(((&&&$$$$$$$$$&&&'''''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$)))((('''&&&&&&'''((()))''''''((()))))))))))))))))))))((('''''''''''''''((((((''''''(((((()))***((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''(((((((((((())))))))))))((((((((((((((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&&&&''')))***((('''&&&&&&&&&&&&'''(((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((('''&&&&&&%%%((((((((())))))(((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((((((''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((())))))((((((&&&&&&&&&''''''''''''((((((((()))))))))(((''''''))))))((((((''''''&&&&&&))))))))))))(((((((((((())))))*********+++++++++******************************+++++++++,,,,,,,,,......---------,,,,,,,,,------...//////////////////...---...///000///------......//////......---...---------,,,,,,,,,,,,++++++************+++++++++++++++++++++++++++++++++******))))))))))))))))))))))))))))))(((''''''&&&&&&&&&''''''''''''(((''''''''''''''''''&&&&&&''''''((((((((((((''''''$$$$$$&&&'''''''''&&&%%%'''&&&%%%&&&)))+++++++++((((((((()))))))))******((((((((('''''''''''''''(((((('''''''''&&&&&&&&&''''''''''''''''''''''''(((((('''''''''&&&&&&&&&'''''''''''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((''''''((('''$$$######$$$'''((()))((((((''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((((((((('''&&&&&&''')))+++---'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&''''''''''''&&&&&&&&&''''''(((((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%%%%''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&(((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%'''''''''&&&%%%&&&''''''&&&%%%&&&''''''&&&%%%(((&&&$$$%%%'''(((&&&$$$)))'''&&&$$$$$$%%%&&&'''''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$((((((&&&&&&&&&&&&((((((&&&&&&''''''(((***+++,,,(((((())))))((((((''''''''''''&&&&&&''''''((()))(((((((((((((((((((((((())))))(((((((((((())))))(((((((((((())))))))))))(((((((((((((((((((((((('''&&&&&&&&&&&&''''''((($$$%%%%%%&&&''''''(((((()))((('''&&&%%%&&&'''((((((''''''&&&&&&&&&''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''(((''''''&&&%%%(((''''''&&&&&&''''''((($$$$$$$$$$$$$$$$$$$$$$$$&&&''''''''''''(((((((((''''''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((()))***&&&&&&&&&''''''''''''(((&&&'''(((((()))(((((((((******)))((('''&&&%%%%%%(((((((((((())))))))))))***************+++++++++******************************+++++++++,,,,,,,,,...------------,,,,,,,,,------...////////////...///...------//////...---,,,------......------,,,,,,,,,,,,,,,++++++++++++++++++************++++++++++++++++++++++++++++++,,,+++******))))))******)))))))))))))))(((''''''&&&&&&&&&''''''''''''(((''''''''''''''''''(((((('''(((((())))))(((((('''%%%&&&&&&'''((('''''''''+++***((((((***+++***)))'''''''''(((((((((((()))&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%&&&&&&'''((()))))))))&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''''''''(((((()))(((&&&%%%%%%&&&((()))))))))(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((('''&&&%%%%%%%%%&&&((()))'''&&&&&&%%%%%%&&&&&&'''''''''''''''&&&&&&&&&&&&###$$$$$$%%%&&&'''((()))))))))((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$######$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&'''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&'''&&&%%%$$$%%%&&&((('''&&&&&&'''((('''&&&)))'''&&&&&&&&&&&&$$$###((('''&&&%%%$$$%%%&&&'''''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%)))(((''''''''''''((()))((('''''''''''')))+++,,,'''((()))******)))((('''&&&&&&&&&&&&&&&'''((((((((((((((((((((((((((((((******))))))))))))******&&&&&&&&&&&&''''''''''''(((((((((((((((((((((((('''''''''''''''((()))***%%%&&&&&&&&&'''''''''(((((('''&&&%%%%%%%%%%%%&&&((('''''''''&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''''''''&&&&&&)))((('''&&&&&&'''((()))$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&'''''''''((((((&&&'''((())))))((('''&&&'''''''''''''''''''''''')))((('''&&&&&&'''((()))&&&&&&&&&''''''''''''(((%%%&&&&&&'''(((((((((((())))))((((((''''''&&&&&&''''''(((((())))))************************************************************+++++++++,,,,,,,,,------------------------------...//////............---,,,---......---,,,+++,,,,,,------,,,,,,+++,,,,,,,,,,,,,,,+++++++++++++++************++++++************************+++***))))))(((((()))))))))))))))))))))(((''''''&&&&&&&&&''''''''''''(((&&&&&&''''''(((((())))))(((((())))))))))))((((((&&&''''''(((((((((((((((...,,,***(((((((((&&&$$$&&&&&&&&&'''''''''(((((($$$%%%%%%&&&'''(((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&''''''((((((''''''''''''''''''''''''(((((('''&&&&&&''')))***((('''&&&&&&&&&&&&'''((()))))))))(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((((((((((((((('''&&&%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$$$$$$$###$$$&&&'''((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&((('''&&&&&&(((((('''&&&''''''&&&&&&&&&&&&%%%$$$'''&&&&&&%%%%%%%%%&&&'''''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%***))))))))))))))))))******)))(((''''''((()))***'''((()))******)))((('''&&&&&&&&&&&&&&&'''((((((((((((((((((((((((((((((&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((((((((((((((()))((((((((()))***++++++(((((((((''''''&&&&&&&&&''''''&&&%%%%%%%%%%%%%%%(((((('''''''''&&&&&&%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&***)))'''''''''''')))***%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&'''((())))))((('''&&&''''''''''''''''''''''''((('''%%%%%%$$$%%%&&&'''&&&&&&&&&''''''''''''(((%%%%%%&&&&&&&&&'''((((((&&&&&&''''''(((((())))))''''''(((((())))))************************************************************+++++++++,,,,,,,,,------------------------------............------...,,,+++,,,---...---+++++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,,,,---------++++++************++++++************************))))))(((''''''''''''((()))))))))))))))(((''''''&&&&&&&&&''''''''''''(((&&&''''''(((((()))))))))(((((())))))))))))((((((''''''''''''(((((())))))***(((&&&&&&&&&&&&%%%$$$&&&&&&&&&&&&''''''''''''$$$%%%%%%&&&'''((())))))&&&'''''''''''''''''''''''''''''''''''''''''''''&&&'''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''((('''&&&&&&&&&((()))***''''''&&&&&&&&&&&&''''''(((((())))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))''''''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&%%%%%%%%%$$$&&&&&&%%%%%%$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%$$$$$$$$$$$$###$$$&&&'''(((''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&(((&&&%%%&&&'''((('''&&&$$$%%%&&&&&&&&&&&&''''''&&&&&&&&&%%%&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%******************************)))((((((((((((((((((((())))))******))))))''''''&&&&&&''''''((()))((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''(((((((((((())))))))))))((((((((((((((((((((((((***))))))))))))******+++))))))(((((('''&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%%%%(((((((((((('''&&&%%%$$$''''''''''''&&&&&&&&&%%%''''''''''''''''''''''''%%%&&&''''''(((''''''''')))(((((((((((((((((()))''''''''''''''''''''''''%%%&&&&&&&&&&&&'''''''''&&&&&&'''((((((((('''''''''''''''''''''''''''''''''&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''''''''(((&&&&&&%%%%%%%%%&&&''''''%%%%%%&&&'''((()))******(((((((((((())))))))))))+++++++++*********************************************+++++++++,,,,,,,,,,,,,,,,,,------------...---............---,,,,,,---,,,++++++------,,,++++++,,,,,,------,,,,,,+++,,,,,,,,,,,,------------++++++************++++++************************(((((('''&&&&&&&&&&&&''')))))))))))))))(((''''''&&&&&&&&&''''''''''''((((((((((((((((((((())))))((())))))******))))))((((((''''''''''''((())))))%%%$$$###$$$&&&(((((((((&&&&&&&&&''''''''''''(((&&&&&&''''''((()))******&&&&&&&&&'''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''&&&''''''((()))***&&&&&&'''(((((('''&&&&&&&&&'''((())))))((('''&&&''''''''''''''''''''''''******)))))))))))))))(((''''''''''''&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%((('''&&&&&&$$$$$$###"""%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&'''''''''&&&&&&%%%$$$$$$$$$%%%%%%$$$%%%%%%&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&'''&&&%%%$$$%%%&&&'''&&&%%%%%%&&&'''&&&%%%###$$$&&&&&&&&&&&&''')))%%%%%%&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%))))))************))))))'''(((((())))))))))))((())))))(((((()))******+++((((((''''''(((((()))***(((((((((((((((((((((((()))))))))(((((()))))))))(((((((((((())))))))))))(((((((((((((((((((((((())))))(((((('''(((((((((((((((((((((''''''''''''%%%&&&&&&''''''''''''&&&'''((((((((((((&&&%%%$$$((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''((((((''''''&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%$$$&&&&&&&&&''''''''''''((('''&&&%%%$$$$$$$$$%%%&&&&&&&&&''''''(((((())))))))))))))))))((((((((((((+++++++++*********))))))******************************+++++++++,,,,,,,,,,,,,,,,,,---------......---.........------,,,+++,,,+++***+++,,,---,,,***,,,,,,------------,,,,,,***+++++++++,,,,,,,,,,,,++++++************++++++************************))))))(((''''''''''''''')))))))))))))))(((''''''&&&&&&&&&''''''''''''((()))))))))((((((((((((((())))))************))))))''''''&&&&&&&&&'''((()))'''&&&%%%&&&((())))))(((&&&''''''''''''((((((((('''((((((((()))*********&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&&&&&&&'''''''''((((((%%%&&&&&&''''''(((((((((''''''''''''''''''''''''%%%&&&'''((())))))))))))&&&''')))******)))'''&&&$$$&&&''')))***)))((('''(((((((((((((((((((((((((((((((((((('''''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%$$$$$$&&&&&&&&&&&&''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&%%%%%%######&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&''''''(((%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''((('''''''''&&&&&&&&&&&&''''''''''''''''''''''''%%%'''''''''&&&%%%&&&'''&&&$$$$$$$$$%%%&&&%%%$$$$$$&&&''''''%%%$$$&&&((($$$%%%%%%&&&'''''''''&&&''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((((())))))))))))((((((%%%&&&(((***++++++*********)))((((((((()))+++,,,((((((((((((((()))******((((((((((((((((((((((((&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&'''''''''((((((((((((((((((((((((((()))((('''&&&&&&&&&&&&&&&&&&&&&''''''((()))))))))%%%%%%&&&'''(((((((((((('''((())))))(((&&&$$$###)))(((((((((((('''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((((('''$$$%%%''''''''''''%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&%%%$$$$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''((()))((('''%%%$$$&&&&&&&&&'''''''''((((((((('''%%%$$$###$$$$$$%%%((((((((((((((('''''''''******))))))((((((''''''++++++++++++******))))))******************************+++++++++,,,,,,,,,,,,,,,,,,------.........---.........------,,,+++,,,+++******,,,,,,+++***,,,------......------,,,))))))******++++++++++++++++++************++++++))))))))))))))))))))))))******)))((((((((((((((()))))))))))))))(((((('''&&&&&&&&&'''''''''((((((******))))))((((((''''''))))))************))))))'''&&&&&&%%%%%%'''((()))...,,,***)))))))))'''&&&'''''''''(((((((((((()))))))))))))))************&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&&&&&&&'''''''''((((((%%%%%%'''((()))+++,,,,,,(((((((((((((((((((((((($$$%%%''')))***))))))(((''')))***++++++***)))'''###%%%''')))******)))((())))))))))))))))))))))))''''''&&&&&&&&&%%%%%%%%%###$$$%%%&&&&&&&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$""" &&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''(((((($$$$$$$$$$$$%%%&&&&&&'''((('''%%%$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''(((((('''''''''&&&&&&&&&((((((((((((((((((((((((&&&'''((((((&&&&&&'''(((%%%$$$######%%%%%%$$$###&&&((()))'''$$$###$$$&&&$$$%%%&&&&&&'''''''''&&&''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((()))))))))))))))))))))))),,,+++***((((((((()))***''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''&&&%%%((((((((((((((('''''''''&&&&&&&&&''''''''''''(((%%%&&&&&&&&&'''((((((((($$$$$$%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''(((((('''&&&'''((()))***((('''&&&%%%$$$%%%%%%&&&)))))))))))))))(((''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$###$$$%%%&&&'''&&&%%%((('''&&&%%%%%%&&&'''((()))&&&%%%&&&((()))'''%%%%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%&&&'''(((''''''''''''''''''''''''(((((((((((())))))))))))(((((()))*********************++++++++++++************+++++++++,,,,,,,,,)))***+++,,,---,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,*********++++++,,,------,,,,,,,,,++++++*********,,,,,,,,,,,,,,,,,,,,,,,,---,,,+++******+++,,,---************************************************))))))(((((('''''''''&&&))))))))))))))))))))))))&&&&&&&&&'''((())))))***,,,,,,+++***)))((('''''')))))))))))))))))))))))))))'''&&&'''((()))((('''((((((((((((((((((((((((&&&&&&&&&''''''''''''((())))))))))))))))))))))))((((((((((((((((((((((((************))))))))))))''''''''''''((((((((((((((((((((((((''''''''''''))))))))))))(((((((((((()))(((((('''''''''((((((%%%%%%%%%&&&&&&&&&&&&''''''''''''''''''((())))))***************+++++++++''''''''''''''''''''''''(((((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$&&&'''((($$$%%%%%%&&&&&&''''''''''''''''''(((((((((((()))%%%&&&&&&''''''&&&&&&%%%'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&'''''''''(((((($$$$$$$$$%%%%%%&&&&&&&&&((('''&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&%%%$$$#########$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######### !!!"""###$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&((((((((((((((((((((((((%%%%%%%%%&&&&&&&&&''''''(((((((((((('''&&&%%%%%%&&&'''((('''%%%$$$%%%&&&'''&&&%%%%%%%%%%%%&&&'''(((&&&###$$$&&&((('''%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&%%%$$$))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((()))))))))))))))))))))))))))((('''&&&&&&''''''(((''''''''''''''''''''''''((((((((((((((((((((((((***************)))(((''''''''''''(((((((((((((((&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''''''''%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''###############$$$%%%%%%((('''&&&%%%%%%%%%&&&&&&((((((((((((((('''&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%&&&''''''&&&%%%((('''&&&&&&&&&&&&'''((((((&&&%%%&&&(((((('''%%%%%%%%%&&&''''''&&&%%%%%%&&&%%%%%%%%%%%%&&&'''(((''''''''''''''''''''''''''''''((((((((()))))))))(((((()))*********************++++++++++++************+++++++++,,,,,,,,,)))***+++,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++,,,,,,,,,+++++++++******,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***))))))***+++,,,++++++++++++++++++++++++************************))))))((((((((('''''''''((((((((((((((((((((((((&&&&&&''''''((())))))************)))((((((''''''((((((((((((((((((((((((***)))((((((******)))(((((((((((((((((((((((((((&&&&&&&&&''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''&&&&&&''''''''''''((((((((((((&&&&&&'''((())))))******))))))))))))(((((((((((('''''''''''''''((()))***''''''''''''(((((((((((())))))(((((())))))***+++''''''(((((((((((((((((('''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$%%%'''(((&&&&&&&&&&&&&&&'''''''''$$$$$$$$$$$$%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%&&&&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%&&&&&&((('''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&%%%$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$#########$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&'''''''''&&&&&&%%%&&&'''((('''%%%$$$%%%&&&'''&&&%%%%%%%%%%%%&&&'''(((&&&$$$$$$&&&(((&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$###))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))(((''''''''''''(((((()))((((((((((((((((((((((((((((((((((((((((((((((((+++++++++***)))((('''&&&&&&&&&''''''(((((())))))&&&&&&&&&''''''''''''((('''''''''''''''&&&&&&&&&&&&''''''''''''(((((((((''''''''''''''''''''''''$$$$$$%%%&&&&&&&&&&&&%%%((('''&&&&&&%%%&&&&&&&&&&&&''''''''''''&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&''''''''''''''''''((('''&&&&&&&&&&&&'''((('''&&&%%%&&&'''((('''%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((((((((()))*********************++++++++++++************+++++++++,,,,,,,,,)))***+++,,,,,,,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,---------,,,+++*********,,,,,,,,,++++++++++++***,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***))))))***+++,,,,,,,,,,,,,,,,,,,,,,,,,,,************************))))))((((((((((((''''''((((((((((((((((((((((((&&&&&&''''''((()))))))))(((((((((((((((((((((((('''''''''''''''''''''''')))((('''((())))))((('''((((((((((((((((((((((((&&&&&&&&&''''''''''''(((''''''''''''''''''''''''(((((((((((((((((((((((('''''''''&&&&&&&&&%%%%%%&&&''''''''''''(((((((((((((((((())))))*********))))))))))))((((((((((((%%%%%%&&&'''((()))******(((((()))))))))************************++++++,,,%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&''''''''''''''''''&&&&&&&&&#########$$$$$$$$$%%%%%%&&&%%%$$$######$$$%%%&&&''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%''''''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''$$$$$$%%%&&&&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&&&&&&&%%%&&&'''''''''%%%$$$%%%&&&'''&&&&&&%%%%%%&&&&&&''''''&&&%%%%%%&&&'''&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%$$$###"""))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((())))))))))))(((((((((((((((((((((((((((((())))))******++++++))))))))))))))))))))))))((((((((((((((((((((((((((((((((('''&&&%%%$$$###%%%&&&&&&'''((()))******&&&&&&&&&''''''''''''(((((((((((('''&&&&&&&&&%%%&&&&&&'''''''''(((((((((''''''''''''''''''''''''%%%&&&'''((()))((('''&&&'''''''''&&&&&&&&&&&&'''&&&&&&'''''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&'''((()))(((''''''((('''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((()))*********************++++++++++++************+++++++++,,,,,,,,,******++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,+++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++))))))))))))++++++,,,,,,,,,,,,,,,,,,,,,,,,************************))))))((((((((((((((((((''''''''''''''''''''''''''''''''''''(((((())))))&&&&&&&&&'''''''''(((((('''''''''''''''''''''''''''%%%$$$%%%&&&'''&&&%%%((((((((((((((((((((((((&&&&&&&&&''''''''''''(((''''''''''''''''''''''''(((((((((((((((((((((((()))(((((((((''''''''''''&&&&&&&&&'''''''''((((((---,,,+++***)))((('''&&&))))))))))))((((((((((((&&&&&&'''(((((()))))))))(((((()))))))))***************))))))******+++,,,&&&&&&&&&&&&%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''(((((((((''''''&&&&&&&&&%%%&&&&&&&&&&&&''''''''''''&&&$$$######$$$&&&'''''''''''''''''''''''''''%%%%%%$$$$$$$$$$$$%%%%%%'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%$$$'''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''######$$$%%%&&&&&&&&&&&&%%%&&&''''''%%%%%%%%%'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$###))))))))))))))))))))))))(((((((((((((((((((((((('''((((((((()))))))))***(((((((((((((((((((((((((((((())))))******++++++))))))))))))))))))))))))((((((((((((((((((((((((&&&&&&&&&&&&%%%$$$###"""%%%&&&&&&'''((()))******&&&&&&&&&''''''''''''(((((((((((('''&&&&&&&&&%%%%%%&&&&&&&&&&&&'''''''''''''''''''''''''''''''''"""###%%%&&&'''&&&%%%$$$&&&'''''''''''''''''''''&&&''''''(((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&(((******(((&&&'''(((&&&''''''''''''''''''&&&%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((()))*********************++++++++++++************+++++++++,,,,,,,,,+++***++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,---------++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***))))))***+++,,,++++++++++++++++++++++++))))))))))))))))))))))))(((((())))))))))))))))))((((((((((((((((((((((((''''''''''''((((((((((((%%%%%%&&&&&&''''''(((((('''''''''''''''''''''''''''%%%$$$%%%&&&'''&&&%%%((((((((((((((((((((((((&&&&&&&&&''''''''''''(((''''''''''''''''''''''''(((((((((((((((((((((((()))(((((((((''''''''''''&&&&&&&&&&&&''''''''''''---,,,+++***)))((('''&&&))))))))))))(((((((((((((((((())))))((('''&&&%%%''''''(((((((((((())))))((((((((((((((()))******))))))((((((((('''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((((((((((((((''''''&&&&&&&&&%%%''''''''''''(((((((((((()))(((&&&$$$$$$&&&((()))''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$%%%%%%%%%&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&)))(((((('''&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''######$$$%%%&&&&&&&&&&&&%%%&&&'''&&&%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''''''''&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%))))))))))))))))))))))))))))))))))))))))))))))))''''''(((((())))))******))))))))))))))))))))))))&&&'''((((((((((((((('''(((((((((((((((((((((((((((((((((((((((((((((((('''(((((((((((('''&&&&&&&&&&&&''''''(((((())))))&&&&&&&&&''''''''''''((('''''''''''''''&&&&&&&&&%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''%%%&&&&&&'''''''''''''''&&&&&&'''(((((((((((('''&&&&&&'''(((((((((((('''&&&&&&&&&&&&''''''''''''&&&(((+++***'''%%%&&&(((&&&&&&'''(((((('''&&&&&&$$$&&&'''&&&%%%$$$%%%&&&'''&&&&&&%%%%%%&&&&&&'''''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''((((((((((((((()))*********************++++++++++++************+++++++++,,,,,,,,,++++++******++++++,,,---,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,---.........***++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---,,,+++******+++,,,---************************))))))))))))))))))))))))(((((())))))))))))******))))))))))))))))))))))))''''''((((((((((((((((((%%%&&&&&&&&&''''''(((((('''''''''''''''''''''''')))((('''((())))))((('''((((((((((((((((((((((((&&&&&&&&&''''''''''''(((''''''''''''''''''''''''(((((((((((((((((((((((('''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''''''''((((((((())))))*********))))))))))))(((((((((((())))))******)))'''%%%$$$&&&&&&&&&'''''''''(((((('''''''''''''''(((((()))++++++******)))(((((((((''''''''''''''''''''''''%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((())))))(((((('''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''')))((('''&&&&&&'''((()))'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''###$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%(((((('''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&&&&&&&%%%$$$&&&'''&&&%%%%%%&&&(((%%%&&&&&&''''''&&&&&&%%%###&&&(((((('''%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&''''''((((((((('''&&&%%%%%%%%%&&&&&&))))))))))))))))))))))))))))))))))))))))))))))))'''''''''((()))*********))))))))))))))))))))))))'''(((((())))))((('''&&&''''''''''''''''''''''''(((((((((((((((((((((((('''((())))))***)))))))))'''''''''(((((((((((((((&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''''''''&&&''''''''''''(((((((((''''''''''''''''''''''''((((((''''''(((((())))))%%%&&&'''((())))))((('''%%%%%%&&&'''''''''''''''&&&&&&&&&&&&'''''''''(((%%%(((+++***&&&$$$%%%(((&&&&&&'''(((((('''&&&&&&$$$&&&'''&&&$$$###%%%''''''&&&%%%%%%%%%%%%&&&'''((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''((((((((()))))))))(((((()))*********************++++++++++++************+++++++++,,,,,,,,,++++++*********+++,,,---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------------******+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,...---,,,++++++,,,---...++++++++++++++++++++++++))))))))))))))))))))))))(((((()))))))))*********************************(((((((((((((((((((((''''''''''''''''''(((((((((((((((((((((((((((((((((***)))((((((******)))(((((((((((((((((((((((((((&&&&&&&&&''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&'''((())))))******))))))))))))(((((((((((('''((()))***)))(((&&&$$$&&&&&&'''''''''(((((((((''''''&&&&&&''''''((()))*********)))((('''''''''''''''''''''''''''''''''%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''%%%&&&'''(((((('''&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''(((''''''&&&&&&''''''((('''&&&&&&%%%%%%&&&&&&'''%%%&&&&&&&&&&&&'''''''''&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''###$$$&&&'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&'''''''''&&&&&&%%%$$$%%%'''&&&%%%%%%&&&(((%%%%%%&&&''''''&&&%%%%%%###%%%((()))'''%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''((((((((('''&&&%%%$$$$$$$$$%%%%%%))))))))))))))))))))))))))))))))))))))))))))))))&&&''''''((()))******+++))))))))))))))))))))))))******+++++++++)))((('''''''''''''''''''''''''''((((((((((((((((((((((((&&&'''((()))************((((((((((((((('''''''''&&&&&&&&&'''''''''((((((%%%&&&&&&''''''((((((((((((((((((((())))))))))))''''''''''''''''''''''''%%%$$$###"""###$$$%%%&&&%%%&&&((()))))))))((('''###$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&'''''''''(((((($$$(((+++)))%%%###%%%(((%%%&&&'''(((((('''&&&%%%###%%%'''&&&$$$###%%%''''''&&&%%%%%%%%%%%%&&&'''((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((((((((((())))))))))))(((((()))*********************++++++++++++************+++++++++,,,,,,,,,,,,+++*********+++,,,---,,,,,,,,,,,,,,,,,,,,,,,,///......------,,,,,,+++*********++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,......,,,,,,,,,,,,......,,,,,,,,,,,,,,,,,,,,,,,,))))))))))))))))))))))))(((((())))))*********+++************************((((((((((((((('''''''''(((((((((((((((((((((((()))))))))))))))))))))))))))'''&&&'''((()))((('''((((((((((((((((((((((((&&&&&&&&&'''''''''(((((())))))))))))))))))))))))((((((((((((((((((((((((************))))))))))))%%%%%%%%%&&&&&&&&&''''''((((((((((((''''''''''''))))))))))))((((((((((((%%%&&&(((******)))'''&&&''''''''''''(((((((((((('''''''''''''''((())))))))))))((('''&&&&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&''''''(((((((((''''''''''''''''''''''''$$$%%%&&&&&&&&&%%%$$$############$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&'''''''''%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''((((((''''''''''''(((((('''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&'''''''''((((((%%%&&&&&&&&&'''(((((((((%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%'''))))))))))))(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%''''''''''''''''''''''''$$$%%%%%%&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%"""######$$$%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''(((((((((((('''&&&%%%%%%$$$%%%&&&&&&%%%%%%'''(((%%%%%%&&&''''''&&&%%%%%%"""%%%))))))'''%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''((())))))&&&%%%$$$#########$$$%%%+++++++++*********))))))(((((((((((((((((((((((((((((())))))))))))(((((((((((())))))))))))(((((())))))((()))***+++---...))))))(((((('''''''''&&&((((((((((((((((((((((((''''''''''''((()))++++++''''''''''''''''''''''''************************((((((((((((''''''''''''))))))((((((''''''&&&&&&(((((((((((((((((((((((())))))))))))))))))))))))'''''''''''''''''''''''')))((('''&&&&&&'''((()))&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''((()))))))))((((((((((((((()))******$$$$$$%%%'''(((***++++++))))))))))))***************+++,,,---...---,,,,,,......---,,,++++++++++++++++++++++++++++++++++++*********++++++,,,,,,,,,************************...------------...//////,,,,,,,,,,,,,,,,,,,,,,,,+++++++++************)))...---,,,***((('''&&&%%%******))))))((((((''''''******)))(((''''''((((((((((((((((((((('''''''''+++***)))'''''''''((()))******))))))))))))******))))))(((((('''&&&$$$$$$((((((''''''''''''(((((())))))))))))((((((((((((''''''''''''''''''''''''))))))(((((('''''''''&&&(((((())))))))))))(((((()))(((((((((((())))))***)))))))))))))))))))))))))))(((%%%$$$$$$&&&(((***(((((((((((((((((((((((((((((('''''''''&&&&&&&&&''''''''''''''''''''''''''''''(((((('''%%%###""" !!!$$$&&&(((((('''&&&$$$$$$$$$%%%&&&'''(((((())))))))))))))))))))))))'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''((((((&&&&&&&&&''''''''''''((('''''''''(((((((((((()))&&&&&&&&&''''''''''''(((&&&&&&%%%%%%%%%$$$$$$$$$'''''''''''''''''''''''''''''''''&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((###$$$$$$%%%&&&'''((((((''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$#########$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''&&&&&&'''''''''&&&&&&%%%%%%%%%"""###%%%&&&'''(((((((((''''''&&&%%%$$$$$$$$$$$$''''''&&&%%%%%%%%%&&&&&&''''''''''''''''''''''''(((''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%+++++++++*********))))))))))))))))))))))))))))))(((((())))))))))))(((((((((((())))))))))))(((((((((''''''&&&&&&'''((()))))))))((((((((('''''''''(((((((((((((((((((((((('''''''''((()))*********''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((''''''''''''((((((((((((''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''((('''&&&&&&&&&&&&'''(((''''''&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&""""""######$$$$$$%%%%%%((((((''''''(((((()))***''''''((((((((()))))))))))))))))))))***************+++,,,---------,,,,,,*********)))******++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------++++++++++++++++++++++++------,,,,,,------...///+++++++++++++++++++++++++++++++++************)))(((((())))))************(((((((((((())))))))))))***)))(((((('''''''''(((((((((((((((((((((((('''+++***)))(((''''''((()))))))))))))))))))))))))))(((((((((((('''&&&%%%%%%((((((''''''''''''(((((())))))))))))(((((((((((('''''''''''''''''''''''')))))))))(((((((((''''''(((((())))))))))))((((((&&&&&&&&&&&&&&&''''''((())))))))))))))))))))))))***)))((('''&&&''')))***(((((((((((((((((((((((((((((('''''''''&&&&&&&&&'''''''''''''''&&&&&&&&&((())))))))))))(((&&&%%%!!!"""%%%'''((((((''''''&&&&&&&&&&&&'''((()))***&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''''''''(((&&&&&&&&&'''''''''(((((((((((('''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&%%%%%%%%%%%%''''''''''''''''''''''''''''''(((&&&%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%%%%&&&&&&'''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$######$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%+++++++++***************************************((())))))******))))))((((((((())))))))))))(((((((((((('''&&&%%%&&&&&&&&&))))))((((((((((((''''''((((((((((((((((((((((((&&&'''((()))******))))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''''''''&&&'''''''''''''''((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&''')))(((((((((((((((((()))&&&&&&&&&%%%&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&'''''''''&&&&&&''''''((()))+++******))))))(((((('''))))))))))))***************++++++,,,---,,,,,,,,,))))))))))))***+++,,,---------------------------............------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---...************************+++++++++************)))&&&'''((()))***+++,,,,,,'''''''''((()))*********)))))))))(((((((((((((((''''''((((((((((((((((((***))))))(((((((((((()))((((((************(((((('''''''''((((((''''''&&&)))((((((''''''(((((()))))))))))))))((((((((((((((((((((((((((((((((((((***)))))))))))))))(((((((((((())))))))))))((((((&&&&&&&&&&&&''''''(((((())))))))))))))))))))))))))))))(((((('''''''''&&&(((((((((((((((((((((((((((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((()))))))))(((((('''###$$$&&&((())))))((('''((((((((((((((()))***+++&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''((()))******&&&&&&&&&'''''''''''''''***)))((('''&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&''''''''''''(((((('''''''''&&&&&&&&&&&&''''''''''''''''''''''''&&&'''((('''&&&&&&((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%&&&'''''''''&&&%%%%%%$$$$$$$$$$$$$$$%%%&&&'''(((%%%%%%%%%%%%&&&&&&'''(((''''''''''''''''''''''''$$$$$$%%%&&&&&&'''((((((((((((''''''&&&&&&%%%%%%%%%&&&'''(((((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%************************************************)))))))))******)))))))))(((((())))))))))))(((((())))))))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((%%%''')))***+++***)))'''''''''''''''''''''''''''(((((((((((((((((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&''''''(((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''))))))(((((((((((())))))''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&***(((&&&$$$$$$%%%&&&'''&&&&&&&&&&&&&&&'''((((((++++++******))))))((((((((()))))))))******************++++++,,,,,,,,,,,,,,,+++++++++,,,,,,---...------------------------///.........------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++******++++++,,,---+++++++++++++++++++++++++++++++++*********))))))************)))))))))((('''((((((((()))))))))***)))***************))))))''''''''''''(((((((((((()))))))))(((((((((((()))'''(((***++++++***((('''&&&&&&'''((((((((((((((())))))(((((((((((())))))))))))))))))(((((((((((())))))))))))))))))))))))************))))))))))))(((((())))))))))))((((((''''''((())))))*********((((((((((((((((((((((((&&&'''''''''&&&%%%###"""((((((((((((((((((((((((((((((((('''''''''''''''&&&&&&&&&&&&&&&'''''''''&&&&&&&&&'''''''''''''''%%%&&&'''((())))))((((((((((((((((((((()))******((((((((((((((((((((((((&&&&&&''''''((())))))***'''''''''''''''''''''''')))(((((('''&&&&&&%%%%%%'''''''''(((((((((((()))&&&&&&&&&''''''''''''(((((((((((((((''''''''''''''''''''''''''''''''''''&&&'''(((''''''''')))+++&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&''''''''''''''''''''''''&&&''''''''''''''''''&&&%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%&&&''''''$$$$$$$$$%%%&&&'''((()))''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''((((((''''''&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%************************************************))))))************))))))(((((())))))))))))(((((((((((()))***++++++,,,,,,(((((())))))))))))))))))((((((((((((((((((((((((&&&''')))++++++***((('''(((((((((((((((((((((((())))))))))))))))))))))))''''''''''''&&&&&&&&&&&&%%%%%%&&&&&&''''''((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((((((((())))))((((((((((((''''''&&&&&&''''''((((((''''''&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''&&&###"""!!!"""###$$$&&&&&&&&&&&&&&&'''(((((())))))))))))************((()))))))))************************++++++,,,,,,...---,,,,,,+++++++++,,,++++++++++++++++++++++++......------,,,,,,+++++++++++++++++++++++++++++++++************+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++*********)))))),,,,,,+++***)))(((''''''***)))))))))((((((((('''***++++++,,,,,,,,,+++***&&&'''''''''(((((())))))((((((((())))))))))))(((&&&''')))******)))'''&&&&&&&&&'''((())))))))))))))))))(((((((((((())))))))))))))))))((((((((((((************************))))))))))))************(((((())))))))))))((((((&&&'''((()))************((((((((((((((((((((((((&&&'''(((((('''%%%###"""((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&''''''((((((((('''&&&&&&&&&'''''''''(((''''''((((((((((((((((((''''''&&&&&&&&&'''(((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&'''''''''''''''''''''''''''''''''(((((((((((()))&&&&&&&&&''''''''''''((())))))((((((((('''''''''''''''''''''''''''''''''&&&'''(((''''''''')))+++&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&''''''''''''''''''&&&%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&((('''&&&&&&%%%%%%%%%&&&$$$$$$$$$%%%&&&'''((()))''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%'''&&&&&&&&&%%%%%%%%%$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%***************+++++++++************************)))******++++++******)))(((((())))))))))))((((((%%%&&&''')))******++++++(((((())))))))))))******(((((((((((((((((((((((('''((()))******)))((('''(((((((((((((((((((((((((((((((((((((((((((((((('''''''''&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((())))))******))))))((('''&&&&&&%%%%%%&&&&&&''')))(((''''''&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%$$$$$$%%%&&&''''''&&&&&&''''''((()))''''''(((((()))***++++++))))))))))))************+++************+++,,,,,,---,,,+++***))))))))))))++++++++++++++++++++++++---------,,,,,,,,,,,,,,,************************++++++******++++++,,,---,,,,,,,,,,,,,,,,,,,,,,,,+++++++++************))))))))))))))))))******************)))(((''''''''')))***,,,------,,,++++++&&&&&&''''''((()))))))))'''(((((())))))))))))(((''''''))))))))))))''''''&&&'''((()))))))))))))))***))))))(((((())))))***))))))))))))(((((((((((())))))))))))))))))))))))(((((()))))))))))))))***(((((())))))))))))((((((###$$$&&&((())))))(((((())))))))))))))))))))))))))))))*********((('''&&&(((((((((((((((((((((((('''(((((((((((()))))))))'''''''''((())))))************)))(((((())))))***((((((((((((''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((((((((('''''''''&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&'''''''''((((((%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&''''''''''''((()))(((((((((''''''''''''''''''''''''''''''''''''&&&'''((('''&&&&&&((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&'''$$$%%%%%%&&&'''''''''&&&)))((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''(((''''''''''''''''''''''''(((((('''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%))))))*********+++++++++)))))))))))))))))))))))))))******++++++******)))(((((())))))))))))((((((%%%&&&''')))))))))(((((((((((()))))))))*********(((((((((((((((((((((((())))))))))))(((((((((((((((((((((((((((((((((((('''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%'''&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''((()))******)))(((''''''&&&&&&%%%%%%&&&&&&'''))))))((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&)))))))))))))))))))))(((((((((''''''(((((()))***&&&''''''(((((()))******))))))))))))************+++***)))))))))***,,,,,,++++++******)))*********,,,,,,,,,,,,,,,,,,,,,,,,------------............+++++++++++++++++++++++++++++++++++++++,,,------+++++++++++++++++++++++++++++++++************)))''''''((()))***++++++,,,))))))))))))(((((((((((('''(((***+++,,,+++***)))&&&&&&''''''((())))))***&&&'''((()))******)))((((((((((((((((((((((((((('''(((((()))))))))((((((******))))))))))))******))))))))))))(((((((((((())))))))))))))))))))))))''''''((((((((()))))))))(((((())))))))))))(((((("""$$$&&&((())))))(((((())))))))))))))))))))))))******************))))))(((((((((((((((((((((((('''((((((((())))))))))))((((((((()))***+++++++++,,,+++***((((((((()))))))))(((((('''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&'''''''''(((((('''''''''&&&&&&&&&'''''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&''''''''''''(((((((((((('''''''''&&&&&&''''''''''''''''''''''''''''''(((&&&%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%&&&''''''&&&&&&'''''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''&&&&&&%%%%%%(((''''''&&&&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''((((((((('''&&&%%%$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%))))))******++++++++++++((((((((((((((((((((((((******++++++++++++******(((((())))))))))))((((((((()))*********)))''''''(((((())))))*********+++((((((((((((((((((((((((***)))(((((((((((())))))))))))))))))))))))))))))((((((((((((((((((((((((''''''&&&&&&&&&%%%%%%%%%'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&'''((())))))((('''&&&''''''&&&&&&&&&&&&''''''))))))((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((('''&&&&&&((((((((((((((()))******''''''''''''(((((((((((())))))))))))************+++***)))))))))***,,,---++++++++++++,,,---......---------------------------.........//////000000,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---...************************+++++++++************)))(((((())))))*********+++''''''(((((())))))******%%%''')))***+++***)))(((&&&&&&&&&'''((())))))***&&&'''(((*********)))(((((((((''''''''''''(((((((((((())))))))))))((((((******))))))))))))******))))))))))))((((((((((((((((((((((((((((((((((((&&&'''''''''(((((())))))(((((())))))))))))(((((($$$%%%(((***++++++******))))))))))))))))))))))))((((((((((((((()))))))))(((((((((((((((((((((((('''((((((((())))))******((())))))***+++,,,,,,,,,+++***((('''&&&&&&&&&''')))((('''&&&&&&%%%&&&&&&'''&&&&&&%%%%%%%%%&&&&&&''''''''''''''''''''''''###$$$$$$%%%&&&'''(((((((((((('''''''''&&&&&&&&&))))))((('''&&&%%%%%%$$$'''''''''((((((((())))))&&&&&&&&&'''''''''((((((((('''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''(((&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%&&&'''((('''''''''(((((((((((()))%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%&&&&&&'''''''''((((((((('''&&&%%%###"""&&&&&&&&&&&&&&&'''((()))''''''&&&%%%%%%%%%&&&&&&''''''''''''''''''''''''$$$%%%%%%&&&&&&''''''(((%%%%%%&&&'''((()))******)))((('''&&&%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%************************************))))))))))))*********************************)))(((&&&%%%$$$(((((())))))))))))(((((()))((((((''''''''''''(((&&&&&&&&&'''''''''(((((()))((('''''''''(((***+++))))))(((((((((((())))))'''&&&%%%%%%&&&'''((()))&&&&&&''''''(((((())))))''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''(((((())))))***)))((('''&&&&&&&&&&&&$$$&&&((()))))))))+++---&&&&&&&&&&&&&&&&&&&&&&&&)))(((((('''&&&&&&%%%%%%$$$%%%&&&''''''&&&%%%$$$&&&%%%%%%$$$#########$$$&&&&&&&&&''''''''''''(((%%%%%%%%%&&&&&&&&&''''''(((((((((((((((((((((((())))))))))))))))))))))))(((((()))***+++,,,,,,,,,)))))))))***+++,,,......,,,+++*********+++,,,---++++++,,,,,,,,,,,,------........................,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++///...---,,,++++++++++++)))***+++,,,,,,+++***)))(((((((((((((((((((((((())))))))))))))))))))))))***)))(((&&&'''((()))+++(((((())))))*********+++))))))))))))))))))))))))))))))************))))))************************************************))))))))))))************))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))(((((((((((())))))))))))(((((((((((()))))))))))))))))))))))))))))))))))))))))))))))))))(((((('''******))))))((((((''''''%%%&&&'''(((((('''&&&%%%((((((((((((((((((''''''))))))))))))))))))))))))---,,,+++)))(((&&&%%%$$$((((((((((((''''''''''''(((((('''''''''&&&&&&&&&&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%&&&'''((($$$$$$%%%%%%&&&'''((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&''''''''''''&&&&&&))))))(((((('''&&&$$$$$$$$$$$$%%%%%%&&&'''(((((('''''''''''''''&&&&&&&&&%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((((()))(((''''''&&&%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%'''(((((((((''''''''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&&&&&&&%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%###!!! &&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((&&&%%%%%%%%%%%%&&&''''''%%%&&&&&&&&&'''(((((((((%%%%%%&&&'''((((((''''''''''''''''''''''''''''''&&&&&&&&&'''''''''((((((((((((((('''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&************************************))))))))))))************************'''(((((((((((((((''''''(((((())))))))))))(((((()))(((((('''''''''((((((&&&&&&&&&'''''''''(((((()))(((((('''((()))***+++))))))(((((((((((())))))((('''&&&%%%&&&'''((()))(((((())))))************''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%&&&''''''((((((''''''&&&''''''''''''((((((((((((&&&&&&%%%$$$###############%%%'''''''''''')))***((((((((((((((((((((((((******))))))(((''''''&&&%%%&&&&&&&&&&&&&&&&&&%%%'''&&&&&&%%%$$$$$$%%%%%%&&&&&&&&&''''''''''''(((&&&&&&&&&&&&''''''''''''(((((((((((((((((((((((()))))))))))))))))))))))))))))))))***+++++++++,,,+++++++++***++++++,,,,,,++++++*********+++,,,---++++++,,,,,,,,,,,,------........................,,,,,,,,,,,,,,,,,,,,,,,,************************......---,,,++++++++++++******++++++++++++******))))))))))))))))))))))))))))))))))))))))))))))))+++***(((''''''''')))************)))))))))))))))))))))))))))))))))))))))))))))************))))))************************(((((((((((((((((((((((())))))))))))************))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))(((((((((((()))))))))***(((((((((((()))))))))***))))))))))))))))))))))))((())))))))))))(((''''''***)))))))))((((((((('''&&&''''''((((((''''''&&&'''''''''((((((((((((((((((((((((((((((((((((((('''''''''''''''(((((((((''''''''''''&&&&&&&&&&&&(((((('''''''''&&&&&&&&&&&&&&&&&&'''''''''(((((((((((('''&&&&&&&&&''''''%%%%%%&&&''''''((())))))''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&''''''''''''&&&&&&(((((((((((('''&&&%%%%%%$$$$$$%%%&&&&&&'''((((((&&&&&&''''''''''''''''''&&&&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((('''&&&&&&%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$&&&'''''''''&&&&&&((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((&&&&&&&&&'''''''''''''''%%%&&&&&&'''((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&'''''''''(((''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&&&&&&&'''************************++++++*********)))))))))))))))))))))))))))))))))%%%&&&'''((()))*********(((((())))))))))))(((((((((((((((''''''((())))))&&&&&&'''''''''(((((((((((((((((((((((()))******))))))(((((((((((()))))))))((('''&&&&&&&&&'''(((((())))))))))))*********''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%$$$$$$&&&''''''((((((''''''&&&((((((((('''''''''''''''((((((''''''&&&&&&%%%%%%###%%%&&&&&&%%%%%%&&&'''(((((((((((((((((((((((())))))(((((('''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&''''''''''''(((''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))******************++++++---,,,++++++******++++++++++++******++++++,,,---++++++,,,,,,,,,,,,------------------------------++++++++++++++++++++++++))))))))))))))))))))))))...---,,,++++++***++++++++++++************++++++++++++++++++++++++++++++))))))))))))))))))))))))+++***)))'''''''''((()))++++++******)))((((((((())))))))))))))))))))))))))))))************))))))))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))************))))))))))))))))))))))))***))))))(((((())))))***))))))))))))))))))))))))((((((((()))))))))******((((((((()))))))))******))))))))))))))))))))))))(((((((((((((((''''''&&&))))))))))))(((((((((((((((''''''''''''''''''(((&&&'''''''''(((((())))))((((((((((((((((((((((((%%%%%%&&&&&&'''((((((((('''&&&&&&&&&&&&%%%%%%%%%'''''''''''''''&&&&&&&&&&&&&&&'''''''''(((((((((******)))''''''''''''''''''''''''(((((()))******''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&''''''''''''&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%&&&''''''((((((%%%&&&&&&&&&'''(((((((((&&&&&&'''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$$$$%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&'''((('''''''''''''''&&&&&&&&&%%%&&&''''''((('''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&'''''''''************************+++++++++*********))))))((((((((((((((((((((((((%%%&&&'''((()))*********(((((())))))))))))((((((((((((''''''((()))******''''''''''''((((((((((((((((((((((((((())))))***))))))(((((((((((())))))***)))(((&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%''''''((((((((((((''''''(((((((((''''''&&&&&&&&&))))))))))))((((((''''''$$$&&&'''&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$'''&&&%%%$$$$$$%%%&&&'''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''((((((((((((((())))))))))))(((((((((((((((((((((((())))))))))))))))))))))))+++++++++***************,,,,,,++++++***++++++,,,+++***++++++++++++,,,,,,+++++++++,,,,,,,,,------------------------------************************************************---,,,,,,+++******++++++,,,+++***))))))***+++,,,++++++++++++++++++++++++((((((((((((((((((((((((+++***)))(((''''''((((((*********))))))))))))))))))))))))))))))))))))))))))******++++++******)))((((((((((((((((((((((((************************((()))))))))************))))))))))))))))))))))))***))))))))))))))))))***))))))))))))))))))))))))(((((()))))))))*********(((((()))))))))*********))))))))))))))))))))))))((((((((((((((('''&&&&&&))))))))))))(((((((((((()))((('''&&&&&&'''((()))&&&&&&''''''((()))))))))(((((((((((((((((((((((((((((('''''''''''''''&&&'''''''''&&&&&&&&&%%%%%%''''''''''''''''''''''''''''''''''''(((((((((((((((((('''''''''''''''((('''''''''(((((()))))))))''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&''''''''''''&&&&&&%%%&&&&&&'''((((((''''''%%%&&&&&&&&&''''''((((((%%%%%%%%%&&&'''((())))))&&&''''''''''''''''''&&&''''''''''''''''''''''''&&&&&&''''''&&&&&&%%%$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%''''''''''''((((((((((((&&&&&&&&&&&&&&&'''((((((((((((((('''&&&&&&&&&%%%&&&&&&'''''''''''''''&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''(((''''''&&&&&&''''''(((************************++++++++++++************(((((((((((((((((((((((((((((()))))))))))))))((((((((())))))))))))(((((('''''''''((((((***+++,,,'''''''''((((((((())))))'''(((((()))))))))))))))))))))(((((((((((())))))***)))((('''&&&&&&'''((('''''''''&&&&&&&&&&&&&&&(((((((((((((((((((((((((((((((((((('''''''''''''''(((((((((((((((((('''((((((''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$&&&'''((('''&&&%%%%%%'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$'''&&&%%%$$$$$$%%%&&&'''%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''(((((((((((()))))))))******(((((((((((((((((((((((())))))))))))))))))))))))+++++++++***************************+++,,,---...******++++++,,,,,,,,,,,,+++++++++,,,,,,,,,------------------------------************************++++++++++++++++++++++++,,,,,,+++*********++++++,,,+++***))))))***+++,,,************************((((((((((((((((((((((((******)))(((((((((((((((''''''((()))***++++++,,,))))))))))))))))))))))))******++++++++++++******((((((((((((((((((((((((************************((()))))))))******************************************))))))))))))******************************))))))))))))************))))))))))))************************************((((((((()))(((''''''&&&(((((((((((()))))))))))))))((('''&&&&&&'''((()))&&&'''''''''(((((())))))''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((('''''''''&&&&&&''''''''''''''''''''''''''''''((((((((())))))%%%%%%%%%%%%&&&'''((()))'''''''''''''''(((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&''''''''''''&&&&&&$$$%%%&&&'''((((((((((((&&&&&&'''''''''''''''(((%%%%%%%%%&&&'''((())))))'''''''''&&&&&&'''''''''''''''''''''''''''''''''&&&&&&''''''&&&&&&%%%$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$#########%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''''''''((((((((())))))'''&&&&&&&&&&&&'''((((((((((((((('''&&&&&&&&&%%%&&&'''''''''''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''************************,,,++++++++++++*********))))))))))))))))))))))))************))))))((('''(((((())))))))))))(((((('''''''''((()))***,,,---''''''((((((((()))))))))''''''((()))))))))))))))))))))(((((((((((())))))***)))((('''''''''((())))))))))))(((((((((((('''(((((((((((((((((((((((()))))))))((((((((((((''''''(((((())))))((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&((((((((('''&&&%%%'''((()))((('''&&&'''((((((((((((((((((((((((((((((((('''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''$$$$$$#########$$$%%%%%%&&&&&&&&&''''''''''''((((((((((((((())))))))))))(((((((((((((((((((((((())))))))))))))))))))))))******************++++++)))))))))***+++,,,...///)))***+++,,,,,,,,,,,,+++++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++++++++************++++++++++++************++++++))))))))))))))))))))))))))))))))))))))))))))))))((((((((()))))))))))))))&&&&&&''')))***+++,,,---))))))))))))))))))))))))******++++++++++++******))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))************************************+++******))))))******+++************************)))))))))*********++++++)))))))))*********++++++************************)))))))))))))))(((((('''(((((((((((()))))))))))))))(((((((((((((((((()))((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&'''((()))***+++,,,))))))((((((((('''''''''&&&&&&&&&'''''''''''''''''''''((((((((()))))))))#########$$$&&&''')))***''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&''''''''''''&&&&&&%%%%%%&&&'''((((((((('''''''''''''''''''''''''''%%%&&&&&&&&&'''(((((((((((('''&&&&&&&&&&&&'''((('''''''''''''''''''''''''''''''''''''''&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''(((((('''&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''############$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''%%%%%%&&&&&&&&&'''''''''''''''&&&&&&''''''((()))'''''''''''''''&&&&&&&&&'''''''''(((''''''&&&%%%''''''''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&************************,,,,,,+++++++++************************************************)))(((((((((((())))))))))))((((((&&&&&&'''((()))+++---...'''((((((((())))))))))))&&&'''((()))***))))))((())))))(((((((((((()))))))))((('''''''''((()))***))))))((((((((('''''''''(((((((((((((((((((((((()))(((((((((((('''''''''(((((())))))))))))((((((%%%&&&&&&&&&&&&&&&&&&'''''')))***++++++***)))(((&&&'''(((((('''&&&''')))((((((((((((((((((((((((((((((((((((((((((((((((%%%&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&''''''''''''((('''''''''((((((((())))))(((((((((((((((((((((((()))))))))))))))))))))))))))))))))***+++++++++,,,+++*********+++,,,,,,---)))***+++,,,,,,,,,++++++++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,************************++++++************++++++******++++++++++++******))))))))))))))))))))))))))))))))))))))))))))))))&&&'''((())))))*********''''''((()))***++++++,,,))))))))))))))))))))))))***++++++,,,,,,++++++***************************(((((((((((((((((((((((())))))))))))************************************+++******))))))******+++************************))))))*********+++++++++))))))*********+++++++++***************************************))))))((('''((((((((()))))))))***(((((())))))))))))(((((()))))))))(((''''''&&&&&&''''''''''''''''''''''''&&&&&&''''''((()))******(((((('''''''''&&&&&&&&&&&&&&&&&&'''''''''(((((('''((((((((())))))))))))%%%%%%%%%%%%&&&((())))))((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''''''''((((((((((((''''''''''''&&&&&&''''''''''''''''''((('''&&&&&&&&&&&&'''((('''''''''''''''''''''''''''(((((((((((('''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''(((((('''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''(((((()))&&&&&&&&&'''''''''''''''''''''(((((('''&&&&&&%%%''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%************************,,,,,,,,,+++++++++******************************((()))************))))))(((((())))))))))))((((((&&&&&&'''(((***+++---...(((((((((((())))))))))))&&&''')))*********)))((())))))(((((((((((())))))((((((''''''''')))***+++''''''&&&&&&&&&%%%%%%%%%))))))))))))))))))))))))(((((('''''''''&&&&&&&&&(((((())))))))))))((((((%%%%%%%%%&&&&&&'''''''''$$$%%%'''((()))(((&&&%%%%%%&&&((('''&&&&&&((()))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''$$$%%%''''''''''''%%%$$$%%%%%%%%%%%%&&&&&&'''(((&&&&&&&&&'''''''''((((((''''''''''''(((((((((((((((((((((((((((((((((((())))))))))))))))))))))))(((((()))***+++,,,,,,------,,,++++++******++++++)))***+++,,,---,,,++++++++++++,,,,,,,,,---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,))))))))))))))))))))))))+++***************++++++)))***+++,,,,,,+++***)))))))))))))))))))))))))))))))))))))))))))))))))))%%%&&&''')))************))))))))))))************))))))))))))))))))))))))***++++++,,,,,,++++++***************************************************))))))))))))************************************++++++************++++++************************)))************+++++++++)))************+++++++++************************+++++++++++++++***))))))'''((((((((())))))******'''((()))******)))((('''******)))((('''&&&%%%%%%'''''''''''''''''''''''')))(((((('''&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''(((((((((((((((((())))))))))))(((((('''''''''(((((()))*********)))))))))))))))))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&''''''''''''''''''&&&&&&'''''''''''''''&&&&&&(((((((((((((((''''''''''''''''''''''''&&&&&&&&&((('''&&&%%%%%%&&&'''((((((((((((((((((((((((((((((((())))))(((((('''&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((((('''%%%$$$###$$$%%%%%%''''''''''''''''''''''''((((((((((((((((((((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%'''''''''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%(((((((((((()))))))))***'''''''''''''''((())))))%%%&&&&&&''''''((((((((('''((((((((('''&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%************************+++++++++++++++***)))(((++++++++++++++++++++++++(((((((((((((((((((((((((((((())))))******++++++(((((((((((()))***+++,,,))))))***+++++++++++++++''''''''''''(((((((((((()))+++,,,***'''&&&)))+++######$$$$$$%%%&&&''''''&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&''''''''''''(((''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''(((((('''''''''&&&&&&&&&******))))))((((((''''''(((((('''&&&%%%%%%$$$$$$((('''%%%%%%$$$%%%&&&''''''''''''''''''((())))))((((((((((((((('''''''''******)))(((((((((((((((&&&&&&&&&&&&''''''''''''************************+++,,,---...---,,,+++***************************+++++++++,,,,,,---------------------------------))))))************)))))),,,,,,,,,,,,,,,+++***)))*********++++++,,,,,,,,,))))))************))))))))))))))))))))))))******'''''''''''''''((())))))++++++***)))(((((())))))******))))))((((((''''''++++++******)))))))))(((+++++++++***((()))+++---)))************+++++++++)))******)))(((((()))+++++++++************++++++,,,,,,,,,++++++*********((()))))))))************''''''((()))***)))))))))+++***)))(((((()))******))))))))))))))))))))))))))))))))))))))))))))))))***+++,,,------,,,+++***,,,+++***))))))***+++,,,++++++******)))'''&&&%%%((('''%%%%%%'''((('''&&&(((((())))))))))))(((((('''''''''''''''((()))))))))(((((((((''''''''''''((((((''''''''''''((((((((((((((((((((('''''''''******))))))))))))******((((((''''''''''''((((((''''''''''''''''''''''''))))))((((((''''''&&&&&&(((((('''''''''&&&&&&&&&&&&&&&&&&''''''''''''((())))))((('''&&&&&&&&&&&&'''''''''''''''((()))))))))((('''&&&&&&&&&&&&'''&&&'''(((*********)))(((((('''%%%$$$$$$''')))+++)))'''&&&%%%$$$%%%%%%&&&((((((((((((((((((((((((&&&'''((('''%%%$$$%%%&&&'''&&&%%%%%%$$$$$$$$$$$$'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&''''''''')))((('''&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((((()))%%%&&&''''''%%%###!!!))))))))))))))))))((((((((('''&&&%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&'''((('''&&&%%%&&&((($$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%************************+++++++++++++++***)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))*********(((((((((((()))***+++,,,'''''''''((((((((())))))((((((((())))))))))))************)))''''''(((***$$$$$$%%%%%%&&&''''''(((&&&%%%%%%%%%&&&&&&''''''&&&&&&&&&''''''''''''(((''''''''''''((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''(((((('''''''''&&&&&&&&&((((((((('''''''''&&&&&&'''''''''&&&&&&%%%%%%$$$((('''&&&&&&&&&&&&'''((('''''''''''''''((())))))(((((((((((((((((((((((((((((('''&&&&&&&&&&&&''''''(((((((((((()))))))))((((((((((((((((((((((((++++++,,,,,,---,,,,,,,,,------------------------++++++++++++++++++++++++++++++++++++++++++++++++******++++++++++++******))))))*********)))((((((*********++++++,,,,,,,,,))))))************))))))*********)))))))))))))))((((((((((((((()))******++++++***)))))))))))))))+++*********))))))))))))(((((('''''''''&&&&&&&&&((())))))(((''''''(((***)))************+++++++++,,,------,,,++++++,,,...++++++************+++++++++++++++*********))))))************++++++++++++(((((((((((()))))))))***,,,+++***))))))***+++,,,************************************************))))))************))))))))))))(((''''''((())))))******************)))(((***(((''''''((()))(((((((((((())))))))))))(((((((((''''''''''''((())))))))))))((((((((('''''''''((((((''''''''''''((((((((((((((((((((((((((('''(((''''''&&&&&&''''''(((((((((''''''''''''((((((((((((((((((((((((((((((((((((((((((((('''''''''))))))((((((((('''''''''&&&&&&&&&''''''''''''(((%%%%%%%%%$$$$$$%%%&&&&&&'''''''''''''''((())))))''''''&&&&&&'''''''''(((&&&'''((()))))))))((((((((('''%%%$$$$$$&&&((())))))(((''''''&&&&&&&&&'''''''''''''''''''''''''''&&&'''((('''%%%$$$%%%&&&'''&&&%%%%%%$$$$$$%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&&&&'''''''''((((((''''''&&&%%%%%%&&&&&&&&&''''''''''''''''''&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%'''((('''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''((()))******)))((()))***$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%***************************++++++++++++***))))))))))))))))))))))))))))))************************************))))))))))))(((((((((((()))***+++,,,''''''&&&&&&''''''((()))))))))))))))***************)))''''''((((((((('''%%%%%%&&&&&&'''(((((((((%%%&&&&&&&&&&&&'''''''''&&&&&&&&&''''''''''''(((''''''''''''((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((''''''''''''(((((('''''''''''''''((())))))(((((((((((((((((((((((()))(((''''''&&&&&&'''''')))))))))*********++++++((((((((((((((((((((((((+++******++++++,,,---...........................++++++++++++************++++++++++++++++++++++++++++++,,,,,,,,,,,,++++++((())))))*********))))))*********+++++++++++++++))))))************))))))+++*********))))))(((((()))))))))))))))***+++++++++***))))))))))))))))))++++++++++++*********************)))))))))))))))'''(((******((('''((())))))************+++++++++)))***+++***)))(((***,,,++++++************++++++************))))))))))))***++++++++++++,,,,,,,,,))))))((('''((()))***+++,,,,,,++++++++++++,,,---++++++++++++++++++++++++******************************))))))))))))******((((((''''''''''''(((((())))))***++++++++++++++++++)))(((((()))******)))(((((())))))))))))((((((((((((''''''(((((()))***)))))))))(((((((((''''''((((((''''''''''''((((((''''''(((((((((((((((((('''&&&&&&&&&&&&&&&&&&'''((((((''''''''''''(((((())))))))))))))))))))))))'''''''''((((((((((((((()))))))))))))))(((((((((&&&&&&&&&''''''''''''((($$$$$$$$$$$$%%%&&&'''((('''''''''''''''((())))))((((((((('''''''''&&&&&&&&&&&&'''(((((((((''''''((('''%%%$$$$$$%%%&&&'''((((((((()))((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''%%%$$$%%%&&&'''&&&%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%%%%%%%''''''((((((((((((''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&###%%%'''((()))))))))(((%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%'''((('''&&&%%%&&&'''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%******************************+++++++++******)))++++++++++++++++++++++++************************++++++******))))))(((((((((((((((((()))***+++,,,)))(((((('''((()))******(((((()))))))))*********+++(((%%%&&&((()))(((%%%&&&'''''''''((((((((()))%%%&&&&&&'''''''''''''''&&&&&&&&&''''''''''''(((''''''''''''((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((('''''''''''''''((())))))((((((((((((((()))))))))+++******)))((()))))))))))))))*********+++++++++************************,,,+++*********+++---...++++++++++++++++++++++++,,,,,,,,,++++++++++++***------------------------***++++++++++++++++++***)))***+++,,,,,,,,,,,,,,,***************+++++++++))))))************))))))++++++******)))((((((((())))))(((((())))))***+++******)))))))))))))))***************************++++++++++++++++++++++++(((***,,,---+++*********))))))*********+++++++++((()))***)))'''''')))***++++++************++++++++++++***************************+++++++++,,,,,,***)))((('''''')))+++,,,+++++++++++++++,,,,,,,,,++++++++++++++++++++++++************************---,,,+++******+++,,,---***))))))))))))))))))***((()))******++++++******+++)))'''((()))***))))))(((((())))))))))))((((((((((((((('''((())))))***)))))))))(((((((((((('''((((((''''''''''''((((((''''''''''''((((((((((((((((((''''''''''''((((((((((((''''''''''''((((((((((((((((((((((((((((((&&&&&&''''''(((((())))))((((((((((((((((((((((((&&&&&&&&&''''''''''''((('''''''''''''''((())))))'''''''''''''''((())))))******)))((('''&&&&&&%%%&&&&&&'''''''''''''''''')))'''&&&$$$$$$$$$%%%&&&&&&'''((())))))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''%%%$$$%%%&&&'''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((($$$%%%&&&((())))))))))))%%%&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$%%%&&&%%%$$$###$$$&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&************************)))******+++++++++******++++++++++++++++++++++++))))))))))))))))))))))))++++++******))))))(((((((((((((((((()))***+++,,,((((((((((((((())))))***'''''''''((((((((())))))+++(((%%%&&&((()))(((%%%''''''((((((((((((((()))%%%&&&'''(((((((((''''''&&&&&&&&&''''''''''''(((''''''''''''((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&'''''''''''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&&&&&&&'''''''''''''''((())))))(((((((((((())))))******++++++***)))))))))))))))((((((((()))))))))******************************---,,,***))))))***+++,,,))))))))))))))))))))))))---------------------,,,------------------------))))))************)))))))))***+++,,,,,,,,,,,,,,,************************))))))************))))))************))))))(((((((((''''''''''''((())))))***)))))))))))))))******))))))))))))))))))))))))(((((((((((((((((((((((((((***,,,---+++*********))))))*********++++++++++++,,,---,,,+++***,,,...++++++************++++++,,,,,,,,,,,,,,,,,,,,,,,,))))))))))))*********++++++***((('''((()))+++---)))******+++++++++,,,,,,************************************************---,,,+++******+++,,,---))))))************))))))))))))******))))))((('''***(((''''''((())))))((((((((())))))))))))((((((((((((((((((((()))*********)))))))))((((((((((((((((((''''''''''''((((((&&&'''''''''(((((())))))((((((''''''''''''((((((((((((''''''''''''((((((''''''''''''''''''''''''&&&&&&''''''(((((())))))''''''''''''''''''''''''&&&&&&&&&''''''''''''(((***)))(((''''''''''''''''''''''''''''''((()))))))))((((((((((((***+++,,,'''''''''&&&&&&&&&''''''((('''&&&%%%%%%%%%%%%&&&$$$%%%'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''%%%$$$%%%&&&&&&&&&&&&%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&&&&&&&'''''''''&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&'''((((((&&&&&&'''(((%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&************************))))))***++++++++++++***))))))))))))))))))))))))))))))))))))))))))))))))************))))))))))))(((((((((((()))***+++,,,%%%&&&'''(((((((((((('''''''''''''''((((((((((((***)))''''''((((((((('''''''''((((((((((((((((((%%%&&&'''((()))(((''''''&&&&&&&&&''''''''''''(((''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''''''''''''''''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$%%%%%%&&&%%%%%%'''''''''''''''((())))))'''(((((())))))******+++***)))((((((''''''(((((('''''''''((((((((())))))((((((((((((((((((((((((+++************++++++,,,++++++++++++++++++++++++------------.........///++++++++++++++++++++++++)))))))))******)))))))))((())))))*********))))))***************)))))))))))))))************)))))))))))))))))))))))))))***'''''''''''''''(((((())))))))))))))))))******+++((((((((((((((()))))))))))))))))))))************'''(((******((('''((())))))************+++++++++***+++,,,+++))))))+++,,,++++++************++++++,,,,,,,,,---------------(((((()))))))))***************)))((()))***+++,,,((()))***+++,,,,,,,,,+++************************++++++++++++++++++++++++******))))))))))))******(((((())))))))))))(((((()))))))))))))))((('''&&&***(((&&&'''((()))(((((((((((())))))))))))(((((())))))(((((())))))***+++******)))))))))(((((((((((((((''''''''''''((((((&&&&&&''''''((()))))))))'''&&&&&&&&&&&&&&&&&&'''((((((''''''''''''(((((('''''''''''''''''''''''''''''''''(((((((((((((((&&&&&&&&&&&&''''''''''''&&&&&&&&&''''''''''''((()))((('''&&&%%%%%%%%%%%%'''''''''''''''((())))))%%%%%%%%%&&&***///333666)))(((''''''&&&'''''''''(((((('''&&&&&&&&&''''''$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''%%%$$$%%%&&&&&&&&&&&&&&&&&&&&&'''(((%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&'''$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$$$$"""######$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$&&&&&&&&&%%%$$$%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&************************))))))***+++++++++++++++))))))))))))))))))))))))************************)))))))))))))))*********(((((((((((()))***+++,,,%%%&&&(((******)))(((&&&'''(((((((((((()))))))))*********)))''''''(((***''''''''''''''''''''''''%%%&&&((()))))))))''''''&&&&&&&&&''''''''''''(((''''''''''''((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&'''''''''((((((%%%%%%&&&&&&&&&''''''''''''''''''&&&&&&%%%%%%$$$"""###$$$&&&&&&&&&&&&&&&'''''''''''''''((())))))'''(((((()))******++++++***)))((((((''''''(((((('''''''''((((((((())))))((((((((((((((((((((((((&&&'''(((***,,,------...++++++++++++++++++++++++***+++,,,,,,---...//////++++++++++++++++++++++++)))******++++++******)))))))))*********)))((((((+++*********)))))))))((())))))************))))))((((((((()))******++++++((((((((('''((())))))***)))))))))))))))***++++++(((((()))))))))*********+++++++++,,,,,,---------((())))))(((''''''(((***)))************+++++++++((())))))(((''''''(((***++++++************+++++++++++++++,,,,,,---------))))))*********+++++++++))))))*********+++++++++)))***+++,,,---------,,,++++++++++++++++++++++++++++++++++++++++++++++++))))))************))))))((()))***++++++***)))((((((((()))*********))))))+++)))(((((()))******)))(((((())))))))))))(((((())))))(((((())))))***+++*********)))))))))((((((((((((''''''''''''((((((&&&&&&''''''((())))))***(((''''''&&&&&&''''''(((((((((''''''''''''((((((''''''''''''''''''''''''((((((((((((((('''''''''&&&'''''''''((((((((((((&&&&&&&&&''''''''''''(((((('''&&&&&&&&&&&&&&&''''''''''''''''''((())))))((('''%%%&&&***000777;;;***)))((('''''''''(((((('''''''''(((((((((((()))&&&&&&&&&&&&&&&'''((((((''''''''''''''''''''''''&&&'''((('''%%%$$$%%%&&&&&&&&&&&&&&&&&&'''((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%&&&''''''((($$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%'''&&&&&&%%%%%%%%%%%%%%%#########$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''!!!###$$$###"""!!!"""$$$&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''************************((()))***+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++(((((())))))******++++++(((((((((((()))***+++,,,&&&(((+++......,,,***((())))))))))))************)))+++,,,***'''&&&)))+++'''''''''''''''&&&&&&&&&%%%&&&((()))***)))(((&&&&&&&&&&&&'''''''''((((((''''''''''''((((((((()))((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&&&&'''''''''(((((($$$$$$$$$%%%%%%&&&&&&&&&(((((('''&&&%%%%%%$$$$$$"""$$$%%%'''(((((('''''''''''''''''''''((())))))'''(((((()))***+++++++++,,,++++++***************(((((((((((())))))))))))************************"""$$$'''***---///000000************************))))))***+++---...//////------------------------+++++++++,,,,,,+++++++++,,,,,,,,,,,,,,,+++***)))+++*********))))))(((((())))))************))))))''''''((()))***+++,,,,,,)))))))))))))))******+++))))))((())))))***++++++))))))******+++++++++,,,(((((()))))))))*********+++++++++***((()))+++---)))************++++++++++++,,,,,,+++******+++---++++++************++++++*********++++++,,,,,,,,,******+++++++++,,,,,,,,,))))))***++++++++++++***)))+++,,,...//////......,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++***+++,,,------,,,+++***+++,,,---......---,,,+++'''((()))***,,,,,,,,,,,,,,,***))))))***++++++***(((((())))))))))))(((((()))))))))))))))******+++************))))))))))))((((((''''''''''''((((((&&&&&&&&&'''((())))))*********))))))))))))******((((((''''''''''''(((((())))))))))))))))))))))))))))))(((((('''''''''&&&'''((((((((())))))******&&&&&&&&&'''''''''(((((((((((('''(((((()))***+++'''''''''''''''((())))))///,,,(((''')))...555999+++***)))(((''''''((()))''''''(((((())))))******((('''&&&&&&&&&((()))***((((((((((((((((((((((((&&&'''((('''%%%$$$%%%&&&&&&&&&&&&&&&&&&'''((()))%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&))))))((((((((('''''''''&&&&&&&&&&&&&&&'''((()))%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&'''%%%%%%&&&''''''((())))))%%%%%%%%%%%%%%%&&&'''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$%%%&&&&&&%%%$$$%%%&&&&&&&&&''''''''''''&&&&&&'''''''''''''''''''''''',,,,,,,,,,,,,,,,,,,,,,,,)))))))))))))))))))))))),,,,,,++++++***)))))))))))))))))))))))))))))))))))))))))))))))))))))))))***)))((((((((()))+++,,,((()))))))))))))))((((((******))))))((((((''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''((((((((((((''''''&&&''')))*********)))((((((((())))))))))))((((((((((((((((((((('''''''''&&&&&&''''''(((((()))))),,,+++***((('''%%%$$$$$$&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''((())))))''''''''''''''''''''''''''''''''''''''''''''''''+++***'''&&&%%%&&&'''))))))((('''&&&%%%%%%&&&'''''''''''''''((((((((((((((((((&&&&&&''')))+++---,,,,,,,,,+++***))))))((()))************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,000...---+++******++++++*********)))))))))))))))************+++,,,---...+++***)))(((((()))***+++(((((((((((())))))))))))))))))(((((((((((())))))((()))***++++++,,,++++++)))))))))***+++++++++,,,******+++,,,,,,,,,,,,+++++++++++++++++++++++++++)))************++++++++++++++++++*********))))))((((((((((((((((((((((((,,,***))))))******((('''************************************************,,,+++++++++***))))))))))))***+++,,,,,,+++***)))******+++,,,,,,,,,,,,+++,,,++++++******++++++,,,---,,,***)))))))))******++++++++++++++++++++++++************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))'''''''''''''''((())))))((((((''''''''''''((((((((((((((((((''''''''''''%%%&&&&&&'''((())))))***%%%&&&&&&&&&'''((((((((((((((())))))((('''&&&&&&)))))))))))))))(((((((((%%%''')))***)))((()))***+++******)))((('''''''''&&&'''''''''(((((())))))+++)))(((((())))))(((&&&((('''&&&%%%%%%%%%%%%%%%((((((''''''''''''(((((((((''''''%%%"""$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%$$$#########$$$%%%***)))'''%%%%%%%%%'''(((''''''''''''&&&%%%$$$$$$###$$$&&&&&&&&&&&&$$$###$$$$$$$$$$$$$$$$$$$$$$$$)))((((((&&&%%%$$$######'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$#########''''''''''''''''''''''''$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&******************************************************************++++++))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((()))++++++(((((())))))))))))((((((***)))))))))((((((((('''(((''''''&&&&&&''''''(((''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&&&&'''((()))***))))))(((%%%%%%&&&&&&&&&&&&%%%%%%((((((((((((((((((((('''(((((())))))************''''''''''''((((((((((((&&&''''''''''''''''''&&&%%%%%%&&&&&&'''(((((()))''''''''''''''''''''''''''''''''''''''''''''''''***)))(((&&&&&&&&&'''((((((((('''&&&%%%&&&''''''''''''''''''(((((((((((((((((('''&&&''')))+++,,,,,,++++++***))))))(((((()))************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,---,,,+++)))))))))))))))***)))))))))))))))))))))************+++,,,---...+++***)))(((((()))***+++(((((((((((()))))))))***))))))(((((((((((())))))*********+++******))))))))))))))))))))))))******)))***++++++,,,,,,++++++++++++++++++++++++++++++)))************++++++++++++++++++*********))))))))))))))))))))))))))))))+++***))))))******)))(((************************************************++++++++++++******************++++++++++++************+++,,,,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,---,,,***)))))))))***+++++++++++++++++++++++++++************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((''''''''''''((())))))((((((''''''''''''((((((((((((((((((((((((((((((''''''(((((()))*********&&&&&&''''''''''''''''''((((((((((((((('''&&&&&&&&&&&&&&&'''''''''''''''&&&(((******)))(((((()))******)))(((((('''&&&&&&''''''''''''((((((((()))***)))(((((())))))(((&&&((('''&&&&&&%%%%%%%%%&&&((((((''''''''''''((((((%%%&&&'''''''''&&&%%%$$$%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''')))******)))'''&&&%%%&&&'''(((%%%%%%&&&&&&'''&&&&&&&&&&&&&&&''''''''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$'''''''''''''''&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&************************************************((())))))***++++++,,,,,,))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((()))******(((((())))))))))))(((((())))))))))))(((((((((((((((''''''&&&&&&''''''(((''''''&&&&&&&&&&&&''''''%%%&&&&&&''''''&&&&&&%%%&&&'''((())))))))))))((('''(((((())))))(((((('''''''''((((((((((((((((((((())))))))))))*********&&&&&&&&&'''((((((((()))''''''''''''''''''''''''%%%%%%&&&&&&'''(((((((((''''''''''''''''''''''''''''''''''''''''''''''''((((((((('''''''''''''''''''''&&&&&&&&&'''((((((''''''''''''((((((((((((((((((''''''''')))***++++++******))))))((((((''')))************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***))))))))))))))))))))))))))))))******************+++,,,------+++***)))(((((()))***+++((((((((()))))))))*********))))))(((((())))))***************)))((('''&&&)))))))))((((((((((((((()))***++++++,,,,,,++++++++++++++++++++++++++++++)))************++++++++++++++++++******************************************)))((()))++++++***)))++++++++++++++++++++++++++++++++++++++++++++++++*********+++++++++++++++++++++************++++++***+++,,,,,,------,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,+++************+++++++++++++++++++++++++++++++++*********)))))))))))))))))))))))))))))))))))))))))))))))))))))))))************************************************))))))))))))))))))))))))((((((''''''(((((()))***(((''''''&&&&&&''''''((())))))))))))))))))))))))))))))))))))************((((((''''''''''''''''''(((((((((((((((''''''&&&%%%%%%&&&&&&''''''((((((''')))******((('''(((((())))))(((((('''&&&&&&&&&''''''''''''((((((((((((***((('''((())))))(((&&&((('''&&&&&&%%%&&&&&&&&&((((((''''''''''''(((((($$$%%%'''((()))*********&&&&&&&&&'''''''''''''''&&&&&&&&&'''((()))***+++)))((('''&&&%%%&&&'''(((###$$$%%%&&&''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&'''(((((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&(((((('''''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&,,,,,,,,,,,,,,,,,,,,,,,,************************))))))*********+++++++++))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((()))))))))'''(((((())))))))))))((())))))))))))((((((((((((((((((''''''''''''((((((''''''&&&&&&&&&&&&''''''&&&''''''''''''''''''&&&'''''''''((((((((((((((())))))************))))))''''''''''''((((((((((((''''''''''''''''''''''''(((((((((''''''&&&&&&&&&'''''''''&&&&&&'''''''''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&''''''(((((('''&&&&&&&&&&&&&&&&&&''''''((((((''''''''''''((((((((((((((((((''''''((()))***+++***)))))))))((((((''''''))))))*********+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++---------,,,,,,+++++++++)))))))))))))))*********+++*********++++++,,,---+++***)))(((((()))***+++(((((()))))))))************))))))))))))))))))***)))))))))))))))(((''''''*********))))))(((((('''))))))***+++++++++++++++************************))))))*********+++++++++************************++++++++++++++++++++++++***)))((()))+++,,,+++***++++++++++++++++++++++++++++++++++++++++++++++++*********++++++,,,,,,,,,,,,,,,***))))))***,,,,,,+++,,,,,,---------------,,,,,,,,,++++++,,,,,,,,,+++++++++++++++++++++++++++++++++++++++++++++++++++++++++*********))))))))))))))))))))))))))))))))))))))))))))))))))))))************************))))))))))))))))))))))))((((((((((((((((((((((((((((((((('''((())))))***(((''''''''''''''''''((())))))))))))***************)))))))))))))))))))))))))))((((((''''''&&&&&&'''(((((((((((((((''''''&&&''''''((()))***++++++(((***+++***(((''''''(((((((((''''''&&&&&&&&&&&&'''''''''((((((((((((((()))(((''''''((()))((('''''''''&&&&&&&&&&&&''''''((((((''''''''''''((((((&&&&&&''''''&&&&&&&&&&&&'''''''''((((((((((((((($$$$$$%%%%%%%%%&&&'''''''''&&&%%%%%%%%%%%%&&&&&&$$$%%%&&&&&&'''''''''&&&%%%$$$""""""""""""$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&'''(((((('''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&((((((((('''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&,,,,,,,,,,,,,,,,,,,,,,,,************************+++++++++*********))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((()))))))))(((((((((''''''((()))))))))))))))(((((((((((())))))))))))(((((((((''''''(((((((((''''''&&&&&&&&&&&&''''''(((((())))))))))))(((((('''''''''''''''(((((()))%%%&&&&&&''''''&&&&&&%%%&&&'''''''''(((((())))))'''''''''&&&&&&&&&&&&&&&((((((''''''&&&&&&&&&%%%((('''&&&&&&&&&&&&'''(((&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&''''''''''''&&&&&&%%%%%%&&&''''''(((((((((''''''''''''((((((((((((((((((((((((((()))))))))))))))))))))(((((((((((())))))*********+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,---------,,,,,,++++++(((((())))))************++++++******++++++,,,,,,+++***)))(((((()))***+++))))))))))))******************))))))))))))******''''''((()))))))))))))))+++++++++******)))))))))))))))***++++++++++++***************************))))))*********+++++++++************************++++++++++++++++++++++++***)))((()))+++,,,,,,+++++++++++++++++++++++++++++++++++++++++++++++++++******++++++,,,,,,,,,------,,,+++******+++,,,---,,,,,,---............------,,,,,,,,,,,,,,,,,,---+++++++++,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((()))******)))((((((''''''(((((()))((()))))))))*********+++(((((((((((((((((('''''')))))))))((((((''''''&&&''''''((((((((((((((('''&&&''''''((()))***++++++(((***+++***(((''''''((('''''''''''''''&&&&&&&&&((((((((((((((('''''''''((('''&&&'''((()))((('''''''''&&&&&&&&&''''''(((((((((''''''''''''(((((((((''''''&&&%%%$$$$$$$$$((((((((((((((((((((((((%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$%%%&&&'''''''''&&&&&&%%%$$$%%%$$$""""""""""""$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&(((((('''''''''&&&&&&&&&%%%%%%&&&&&&&&&'''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&************************++++++++++++++++++++++++,,,,,,++++++***))))))((())))))))))))))))))))))))))))))))))))))))))))))))(((((()))))))))(((''''''&&&'''((())))))******)))(((((((((((()))))))))))))))((((((''''''(((((()))''''''&&&&&&&&&&&&'''''')))))))))******)))))))))''''''&&&&&&''''''((()))''''''((((((((((((''''''&&&&&&''''''((())))))))))))))))))(((((((((((('''%%%%%%%%%&&&'''''''''(((((('''&&&%%%%%%&&&'''(((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&'''''''''%%%&&&''''''((('''''''''''''''''''''((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++******+++++++++******)))((((((((()))******++++++,,,++++++***++++++,,,,,,+++***)))(((((()))***+++)))))))))*********+++++++++******))))))******+++&&&'''((()))************++++++++++++************((()))******++++++******************************)))************+++++++++***************++++++++++++++++++++++++++++++++++++***)))***,,,,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,,,,---......//////......------,,,,,,,,,,,,------***+++,,,,,,---,,,,,,,,,++++++++++++++++++++++++,,,++++++++++++*********))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''''''''''''''))))))))))))))))))))))))))))))(((((())))))***+++***))))))(((((())))))***'''(((((())))))*********''''''''''''(((((((((((())))))((((((((((((((((((&&&'''((((((((((((((((((%%%%%%&&&&&&''''''((((((''')))******((('''((((((''''''''''''''''''''''''(((((((((((((((''''''''''''&&&&&&&&&((()))(((''''''''''''&&&''''''((()))((((((''''''''''''((((((''''''&&&&&&&&&''''''(((((((((((((((((('''''''''((((((((('''&&&%%%###"""######$$$$$$$$$$$$$$$$$$''''''''''''&&&%%%$$$###&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''%%%&&&&&&&&&''''''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&************************++++++++++++++++++++++++++++++******************))))))))))))))))))))))))))))))))))))))))))))))))(((((()))))))))(((&&&&&&&&&'''((()))************'''((((((((()))))))))***))))))(((((((((((())))))''''''&&&&&&&&&&&&''''''(((((())))))))))))((((((''''''&&&&&&&&&'''((()))))))))************))))))&&&&&&''''''((())))))***))))))((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&)))(((&&&%%%%%%&&&((()))''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&'''(((&&&'''((((((((('''&&&%%%''''''''''''(((((((((((((((((())))))))))))((((((************************)))************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++************************)))***++++++++++++***)))'''(((((()))******++++++,,,,,,++++++***++++++,,,+++***)))(((((()))***+++))))))*********++++++++++++******))))))******+++))))))******************))))))))))))************((())))))***************************************)))************+++++++++))))))*********+++++++++++++++++++++++++++++++++---+++******,,,,,,+++))),,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,,,,,,,,,,,,,+++------...///////////////------,,,,,,,,,,,,------***+++,,,---------,,,,,,++++++++++++++++++++++++,,,,,,+++++++++*********))))))))))))))))))))))))))))))))))))))))))))))))************************(((((((((((((((((((((((())))))))))))))))))))))))))))))(((((())))))***+++++++++************++++++&&&&&&'''(((((()))******'''''''''((())))))******((((((((((((((()))))))))&&&&&&'''(((((((((((((((&&&&&&&&&'''''''''''''''&&&(((******)))(((((()))(((((((((((((((((((((((()))((((((((('''''''''''''''&&&%%%&&&((()))(((''''''''''''''''''((())))))((((((''''''''''''((((((''''''&&&&&&&&&'''((()))((((((((('''''''''&&&&&&''''''(((((((((&&&%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&''''''''''''%%%%%%&&&&&&'''(((((((((&&&&&&&&&&&&''''''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++)))))))))***++++++,,,,,,))))))))))))))))))))))))))))))))))))))))))))))))(((((()))))))))(((&&&%%%&&&'''((()))************'''((((((((())))))******))))))(((((((((((())))))'''''''''&&&&&&'''''''''''''''((((((((((((''''''''''''&&&%%%&&&'''((()))&&&&&&''''''''''''&&&&&&&&&&&&&&&'''((())))))***''''''&&&&&&&&&%%%%%%%%%***)))((('''%%%$$$###""")))(((&&&%%%%%%&&&((()))'''''''''''''''''''''&&&'''''''''''''''''''''''''''''''''''''''''''''''''''&&&$$$$$$$$$&&&((()))''''''((((((((('''%%%$$$''''''''''''((((((((()))((()))))))))))))))((('''***************+++++++++)))************+++++++++++++++++++++++++++++++++++++++++++++++++++++++++***************************+++------...---,,,+++'''(((((()))***+++++++++,,,,,,++++++***++++++++++++***)))(((((()))***+++)))************+++++++++++++++************++++++++++++,,,++++++***)))(((''''''(((((())))))******(((((()))***************)))))))))))))))))))))))))))************+++++++++))))))******++++++++++++************************...,,,++++++,,,,,,***))),,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------,,,,,,+++++++++++++++---......---++++++---......///////////////...------,,,,,,------...)))***,,,---...---,,,,,,++++++++++++++++++++++++,,,,,,,,,+++++++++******))))))))))))))))))))))))))))))))))))))))))))))))++++++++++++++++++++++++)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))******+++,,,,,,++++++++++++,,,,,,%%%&&&&&&'''((())))))***'''(((((()))***++++++,,,''''''(((((())))))******&&&&&&'''((())))))(((((()))))))))))))))(((((((((%%%''')))***)))((()))***((((((((()))))))))))))))))))))(((((('''''''''&&&'''&&&%%%&&&((()))(((''''''''''''''''''((())))))((((((''''''''''''((((((((('''&&&%%%$$$$$$%%%&&&((((((''''''&&&&&&&&&%%%$$$%%%&&&'''''''''&&&%%%%%%&&&''''''((((((((('''$$$$$$%%%&&&''''''''''''$$$$$$&&&''''''&&&$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$%%%'''((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((())))))$$$%%%%%%&&&'''((())))))&&&&&&&&&'''''''''((((((%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&---------,,,,,,,,,++++++))))))***+++++++++++++++((()))***+++,,,+++******))))))************))))))******))))))((((((''''''++++++******))))))((((((((()))***++++++***)))(((******))))))((((((''''''&&&&&&''''''(((((())))))((((((((((((((((((((((((((((((((((((((((((((((((************))))))))))))'''&&&%%%'''***+++)))'''((((((((((((((('''''''''+++******)))((('''''''''(((''''''''''''&&&&&&&&&)))((('''&&&%%%&&&&&&'''%%%%%%&&&'''(((((((((''''''((((((((('''&&&%%%%%%&&&&&&''''''((('''''''''''''''''''''(((((((((((($$$%%%&&&&&&''''''&&&&&&((((((((((((''''''''''''******)))(((((('''(((((())))))))))))************************************,,,------------------------,,,,,,++++++*********++++++++++++++++++++++++***+++,,,------,,,+++***************************)))***++++++++++++***))))))************+++++++++************************))))))))))))))))))))))))(((((()))))))))*********---,,,,,,+++***)))(((((())))))))))))************)))(((''')))---//////---,,,,,,,,,++++++***************+++++++++,,,,,,,,,******+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------,,,,,,+++***---------,,,,,,+++++++++//////......---,,,,,,++++++,,,,,,,,,---------...,,,---...............---000000//////......------//////...---,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,------------------------************************...,,,))))))***++++++******+++,,,------,,,+++***))))))(((((((((((()))))))))))))))))))))******+++))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))''''''(((((()))+++,,,---(((((((((((((((((((((((())))))(((((('''''''''&&&&&&(((++++++***))))))***((((((''''''''''''((((((%%%""" ###(((+++)))&&&''''''(((((())))))************)))((((((((((((((('''''''''''''''((())))))(((((('''''''''&&&&&&&&&''''''''''''''''''''''''(((((('''''''''&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%###$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''(((%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&'''''''''(((((($$$%%%'''((()))(((''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&'''((('''&&&%%%&&&((((((((('''''''''(((((()))---------,,,,,,,,,++++++)))***++++++,,,,,,++++++)))***+++,,,---,,,,,,+++))))))************))))))******))))))((((((((((((*********)))))))))))))))&&&'''((())))))(((''''''***)))))))))(((((((((''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))'''%%%%%%&&&))))))'''%%%((((((((((((((((((((('''******))))))(((''''''&&&(((''''''''''''&&&&&&&&&)))((('''&&&%%%&&&&&&''''''''''''(((''''''&&&&&&'''''''''(((''''''&&&&&&)))))))))((('''&&&$$$###''''''''''''((((((((((((%%%%%%&&&'''''''''''''''&&&'''''''''(((((())))))+++***))))))((((((((()))))))))))))))************,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------,,,,,,,,,+++++++++++++++++++++++++++++++++++++++***++++++++++++++++++***************************************************)))************+++++++++************************))))))))))))))))))))))))(((((()))))))))))))))))),,,,,,++++++***)))))))))))))))))))))************---+++***+++...///...,,,,,,,,,,,,+++++++++*********++++++++++++,,,,,,,,,***++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------------,,,+++***---------,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,+++,,,,,,,,,,,,,,,,,,,,,++++++,,,------------,,,/////////......---------,,,,,,------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++,,,***))))))***+++***)))******+++,,,,,,+++******)))))))))(((((())))))))))))))))))))))))***++++++************************(((((((((((((((((((((((())))))))))))))))))))))))(((((((((((()))***+++,,,((((((((((((((((((((((((******)))))))))(((((((((&&&(((******)))((()))***))))))(((((('''((((((((()))'''&&&'''+++---,,,***(((((((((((())))))))))))******)))((((((((((((((('''''''''''''''((())))))(((((('''''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&'''''''''((((((&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&''''''%%%%%%&&&'''))))))(((&&&%%%%%%%%%%%%------------,,,,,,,,,,,,******+++,,,,,,,,,,,,+++++++++,,,------------,,,))))))************))))))***))))))))))))((((((((())))))))))))************%%%&&&'''((())))))(((((())))))))))))(((((((((((())))))((((((((((((((('''))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''(((((('''%%%''''''(((((((((((((((((())))))((((((''''''&&&&&&(((''''''''''''&&&&&&&&&(((((('''&&&&&&&&&&&&'''(((((((((((('''&&&%%%%%%&&&&&&''''''(((''''''''')))))))))((('''&&&%%%$$$''''''''''''((((((((((((&&&''''''(((((((((((((((%%%%%%&&&'''((()))******++++++***))))))))))))***))))))))))))************,,,,,,,,,,,,,,,,,,,,,,,,******+++++++++,,,,,,,,,++++++++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++************++++++************************,,,+++***))))))***+++,,,)))************+++++++++************************))))))))))))))))))))))))))))))))))))))))))((((((************************)))))))))*********++++++---,,,++++++,,,---,,,***,,,,,,,,,,,,++++++++++++++++++++++++,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------,,,,,,+++---,,,,,,,,,,,,+++++++++******++++++,,,---......------------------,,,,,,++++++,,,---------------/////////////////////...,,,,,,---......///000000------------------------,,,,,,,,,,,,,,,,,,,,,,,,------------------------+++******+++,,,---+++*********++++++++++++************))))))))))))*********))))))))))))***++++++************************(((((((((((((((((((((((())))))))))))))))))))))))******))))))))))))******((((((((((((((((((((((((************))))))))))))'''((()))((('''''')))++++++***)))((((((((((((((('''''''''(((((()))))))))))))))))))))((((((((((((******)))((((((((((((((('''''''''''''''((())))))((((((((('''''''''&&&&&&''''''''''''''''''''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$###$$$&&&'''((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&'''''''''''''''(((''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&''''''%%%%%%&&&'''((('''&&&%%%%%%%%%%%%%%%...------------,,,,,,,,,)))******++++++++++++++++++++++++,,,,,,,,,,,,,,,)))******++++++******)))))))))))))))))))))))))))(((((())))))******++++++(((((())))))***+++++++++))))))))))))((((((((((((***)))))))))((((((''''''))))))))))))))))))))))))((((((((((((((((((((((((&&&&&&&&&'''''''''''''''******)))))))))((('''%%%''''''''''''((((((((((((((((((((((((''''''&&&&&&(((''''''''''''&&&&&&&&&''''''''''''&&&&&&'''''''''((((((((((((''''''&&&%%%%%%&&&'''((((((((('''%%%&&&'''(((((()))((((((''''''''''''((((((((((((''''''((()))))))))))))))&&&&&&&&&'''((())))))***++++++***************+++((()))))))))************)))))))))))))))))))))))))))))))))***++++++,,,,,,***++++++,,,,,,---------++++++++++++++++++++++++++++++)))(((((()))++++++++++++++++++++++++++++++,,,+++)))(((((()))+++,,,))))))*********+++++++++************************))))))))))))))))))))))))***************)))))))))))))))*********+++++++++))))))*********+++++++++)))))))))))))))***)))))),,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,,,,------+++++++++,,,,,,,,,------------------------------,,,---------------,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,,,,------.../////////////////////............,,,,,,---...////////////000000000000000000111111......///000000111111222000000///////////////..........................................---------++++++,,,---//////---+++***++++++++++++++++++***+++******))))))******+++******))))))******+++,,,************************))))))))))))))))))))))))))))))))))))))))))))))))++++++***)))(((((())))))(((((((((((((((((((((((())))))))))))))))))))))))'''(((((('''&&&&&&)))+++,,,+++***))))))(((((()))'''((()))((('''&&&''')))******))))))((((((''''''***))))))((((((((((((((('''''''''''''''((())))))((((((((((((''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&''''''(((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&((()))((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''***)))'''&&&%%%%%%&&&'''''''''''''''''''''''''''''''''''''''''''''''''''&&&'''((((((&&&&&&'''((($$$$$$$$$%%%&&&((()))***.........---------,,,,,,((())))))***+++************************++++++,,,******++++++++++++******))))))))))))************(((((())))))******++++++)))))))))))))))***++++++(((((((((((())))))))))))******))))))((((((((('''))))))))))))))))))))))))((((((((((((((((((((((((%%%&&&&&&&&&'''''''''(((((())))))((('''%%%%%%$$$&&&'''''''''(((((())))))((((((((((((((('''''''''(((''''''''''''&&&&&&&&&&&&&&&''''''''''''''''''%%%&&&'''((())))))))))))%%%%%%&&&'''((((((((('''%%%&&&'''((())))))))))))''''''''''''(((((((((((('''((())))))******))))))((((((((((((((('''''''''+++***************++++++((()))))))))************))))))))))))))))))))))))(((((()))******+++,,,,,,+++++++++,,,,,,------...++++++++++++++++++++++++,,,+++***))))))***+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++)))(((((()))+++,,,))))))*********+++++++++************************))))))))))))))))))))))))++++++++++++++++++++++++)))))))))***++++++,,,,,,************++++++++++++'''((()))))))))***++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,---------++++++,,,,,,,,,---------------------------------,,,------......------------------------------...........................////////////............,,,---...///000000000000000000000111111222222333222222222222222222222222222222111111000000000000000000000000000000000000.........------,,,,,,,,,,,,,,,,,,---//////---***,,,++++++++++++++++++,,,++++++************++++++***************++++++,,,************************************************************************,,,+++***)))(((((((((((())))))))))))))))))))))))(((((((((((((((((((((((('''(((((('''&&&&&&)))+++++++++***)))))))))))))))+++,,,---,,,*********,,,******))))))((((((''''''***))))))((((((((((((((('''''''''''''''((())))))))))))((((((((('''''''''''''''''''''''''''''''''&&&'''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%&&&''''''(((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''###%%%''')))))))))''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&'''''''''''''''''''''''''''&&&***)))'''&&&%%%%%%&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''')))***)))((('''((()))%%%%%%%%%&&&''')))***+++............---------,,,))))))***++++++++++++*********)))))))))***+++,,,******++++++++++++******)))))))))************+++))))))))))))************((((((''''''''''''(((((((((((((((((())))))))))))***))))))))))))))))))((())))))))))))))))))))))))((((((((((((((((((((((((%%%%%%&&&&&&'''(((((((((%%%&&&'''&&&$$$"""""""""&&&&&&''''''((())))))))))))))))))))))))((((((((((((''''''''''''&&&&&&&&&%%%&&&''''''((('''''''''$$$%%%&&&((()))***++++++&&&&&&''''''(((''''''''')))))))))))))))((('''&&&''''''''''''(((((((((((('''(((((()))))))))))))))))))))((((((''''''''''''***))))))))))))***++++++))))))))))))************++++++++++++++++++++++++(((((()))***+++,,,,,,---,,,,,,,,,,,,------------++++++++++++++++++++++++,,,++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***))))))***+++,,,)))************+++++++++************************))))))))))))))))))))))))*********+++++++++,,,,,,))))))******+++++++++,,,*********++++++++++++,,,)))***,,,,,,+++,,,---///,,,,,,,,,,,,------------,,,,,,,,,,,,------------,,,,,,,,,,,,------------------------------------,,,------............---.........////////////000..................------////////////000000000111///000111222333444444444333444444555666777777888777777777777666666666666777777666666555555444444444444444444444444444444111111000000//////......///...---...//////---+++------,,,,,,,,,,,,------,,,,,,++++++++++++,,,,,,+++************+++,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++************************++++++***)))(((((())))))))))))))))))))))))))))))''''''''''''(((((((((((('''((()))((('''''')))+++)))))))))(((((())))))************************)))))))))))))))((((((((((((******)))((((((((((((((('''''''''''''''((()))))))))))))))(((((((((''''''''''''''''''''''''''''''(((((('''''''''&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&''''''''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((($$$%%%'''((())))))((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&'''''''''''''''''''''&&&&&&&&&(((''''''&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''((())))))((('''((()))***)))((('''''''''''''''............------------++++++,,,------------,,,++++++*********+++,,,---***++++++,,,,,,++++++***))))))*********+++++++++*********)))))))))))))))***)))((('''&&&&&&'''''''''((((((((()))))))))***)))))))))))))))*********((((((((((((((((((((((((((((((((((((((((((((((((%%%&&&&&&'''(((((())))))$$$&&&((('''$$$"""###$$$&&&&&&''''''((())))))***)))*********************(((''''''''''''&&&&&&&&&%%%%%%'''(((((((((''''''%%%&&&'''))))))*********'''''''''(((''''''&&&&&&((())))))))))))(((''''''''''''''''''((((((((((((&&&'''(((((())))))(((((('''''''''((((((((((((((()))((((((((())))))***+++))))))))))))************++++++++++++++++++++++++(((((()))***+++,,,---...---------------,,,,,,,,,++++++++++++++++++++++++,,,,,,------------,,,,,,************************************************)))************+++++++++************************))))))))))))))))))))))))''''''((()))***++++++,,,***************+++++++++*********+++++++++,,,,,,+++---......,,,+++,,,...,,,,,,,,,---------......,,,,,,,,,------------...,,,,,,,,,------------...........................,,,,,,---...............///000000000111111111111000000000111111222222333333333444555666777777888777777999:::;;;<<<<<<<<<===>>>>>>???AAABBBBBBCCC@@@@@@AAAAAABBBBBBCCCCCCBBBBBBBBBAAA@@@@@@??????<<<<<<<<<<<<<<<<<<<<<<<<;;;;;;;;;:::999888888888888666333333333333222111///...------------...///,,,,,,++++++++++++,,,,,,++++++******++++++,,,---++++++++++++++++++++++++******************************************************)))))))))))))))***))))))))))))))))))))))))''''''(((((())))))))))))&&&(((******)))((()))***''''''''''''((()))******(((&&&$$$&&&((()))(((%%%(((((((((((())))))))))))******)))((((((((((((((('''''''''''''''((())))))))))))))))))((((((((('''''''''''''''''''''''''''))))))((('''&&&%%%%%%$$$''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&''''''(((((())))))''''''''''''''''''''''''''''''''''''''''''''''''$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''(((((('''''''''&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&'''((('''&&&%%%&&&(((***)))((('''&&&%%%%%%%%%//////.........---------,,,---......//////......---,,,+++++++++,,,---...***++++++,,,,,,++++++***))))))******++++++++++++++++++******))))))((((((---,,,***)))(((((((((((('''((((((((())))))******(((((())))))******++++++((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&''''''((()))******&&&)))+++***'''%%%&&&(((&&&&&&&&&'''((())))))******************+++++++++(((((('''''''''&&&&&&&&&$$$%%%'''((((((((('''''''''((()))))))))))))))((('''((((((((('''&&&%%%%%%%%%&&&''')))******++++++''''''''''''((((((((()))&&&''''''(((((((((((((((%%%&&&&&&'''((()))******(((((('''(((((()))******))))))))))))************((((((((((((((((((((((((((()))***+++,,,---...............------,,,,,,,,,++++++++++++++++++++++++,,,,,,............,,,,,,(((((((((((((((((((((((()))***++++++++++++***))))))************+++++++++************************))))))))))))))))))))))))$$$%%%&&&'''((()))***+++******************************+++++++++,,,,,,,,,+++---...---***((()))+++,,,,,,,,,------.........,,,,,,,,,---------......,,,,,,,,,---------..............................,,,,,,---.../////////...000000111111222222222333222333444555777888999:::999999:::;;;===>>>???@@@???@@@AAACCCDDDDDDEEEEEEGGGHHHIIIJJJKKKLLLMMMNNNHHHIIIJJJKKKMMMNNNOOOPPPMMMMMMLLLLLLKKKJJJJJJIIIEEEEEEEEEEEEEEEEEEEEEEEEFFFFFFEEEEEEDDDCCCBBBBBB@@@>>>;;;999999999888777000///...------...///000---,,,,,,++++++,,,,,,---++++++******++++++,,,---++++++++++++++++++++++++))))))))))))))))))))))))******************************))))))))))))******))))))))))))))))))))))))(((((())))))*********+++&&&(((+++,,,***))))))***&&&&&&&&&&&&''')))***+++,,,(((%%%''',,,...+++'''''''''(((((())))))************)))((((((((((((((('''''''''''''''((())))))))))))))))))((((((((((((''''''''''''''''''''''''******)))'''&&&%%%$$$###''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$###''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''''''''&&&&&&'''((()))***((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&'''''''''(((((('''''''''&&&&&&&&&$$$%%%'''((()))(((''''''''''''''''''''''''''''''''''''''''''''''''''''''$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%%%%&&&&&&'''...///000///---,,,------////////////...---,,,+++------++++++++++++------************************+++++++++)))'''''')))+++***)))(((''''''((()))***((()))*********((('''&&&))))))))))))))))))))))))&&&&&&&&&'''((())))))*********))))))))))))*********)))'''%%%%%%%%%'''((('''((((((((((((((('''''')))'''%%%$$$$$$%%%&&&(((((((((((((((((('''''''''((((((((((((''''''''''''((((((((((((((((((((((((###$$$%%%&&&''')))******))))))))))))((((((((((((&&&&&&&&&'''''''''''''''(((((((((''''''&&&&&&&&&&&&&&&((())))))(((&&&&&&'''((()))++++++)))((('''(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))************************************((((((''''''(((***---...000,,,))))))+++------,,,++++++++++++++++++++++++...---,,,+++++++++,,,---,,,+++++++++***)))))))))---,,,***))))))***,,,---************))))))((((((******++++++++++++******++++++++++++++++++++++++******+++++++++,,,,,,,,,---------,,,,,,+++++++++++++++,,,,,,,,,,,,------))))))***+++,,,,,,------***++++++,,,,,,++++++***)))***,,,---......---,,,000000//////...---,,,,,,000000///......///000111------------...///000111333222222222333555777888888888999;;;===???AAABBBEEEEEEEEEEEEEEEFFFFFFFFFGGGHHHHHHHHHHHHGGGGGGFFFJJJLLLNNNPPPQQQQQQQQQQQQSSSSSSRRRRRRRRRQQQQQQQQQTTTTTTTTTTTTSSSRRRPPPPPPKKKMMMNNNMMMKKKIIIIIIIIIMMMNNNOOOOOOOOOMMMKKKIIIHHHGGGGGGHHHHHHFFFBBB???999888777777777666444222000000//////...---,,,,,,,,,***))))))+++,,,,,,+++,,,,,,,,,---,,,,,,++++++++++++++++++*********)))***)))))))))***+++,,,,,,,,,,,,++++++***)))))))))''')))+++,,,,,,,,,---...++++++++++++*********)))))))))))))))))))))))))))************************))))))))))))))))))))))))((((((((((((((((((((((((++++++***)))((('''&&&&&&''''''(((((())))))******))))))))))))))))))))))))&&&&&&''''''(((((())))))******)))((('''&&&%%%%%%))))))))))))))))))))))))''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''((((((((((((((('''''''''%%%$$$$$$%%%&&&(((***,,,))))))((('''&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((((())))))(((&&&%%%###'''''''''''''''''''''&&&((('''&&&%%%%%%&&&'''(((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((+++***(((&&&%%%%%%%%%%%%''''''''''''((((((((((((***)))((('''&&&%%%%%%%%%%%%%%%&&&&&&'''(((((((((''''''''''''''''''''''''222222111000...---......111111111000///...---,,,---,,,,,,++++++,,,,,,---+++++++++++++++++++++++++++++++++)))(((''')))+++***)))(((((((((((()))***((()))******)))((('''&&&))))))))))))))))))))))))&&&&&&''''''((())))))******))))))(((((())))))******)))'''%%%%%%&&&'''(((''''''((())))))))))))))))))(((''''''''''''((())))))))))))))))))(((((((((((((((((((((''''''''''''(((((((((((((((((((((((($$$%%%%%%&&&'''((()))))))))))))))(((((((((''''''$$$%%%%%%&&&'''((())))))&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&''')))******)))'''&&&(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))************************************++++++******+++---///111///,,,))))))+++------,,,++++++++++++++++++++++++---,,,++++++++++++,,,---,,,,,,,,,,,,,,,+++++++++---,,,***))))))***,,,---++++++*********)))))))))******++++++++++++******++++++++++++++++++++++++***++++++++++++,,,,,,,,,+++++++++*********))))))++++++,,,,,,,,,,,,------*********+++,,,,,,,,,---++++++,,,,,,,,,,,,++++++)))***,,,---......------............------------111111//////...///000000000000111222333444666777666777777999:::<<<>>>???????????????@@@BBBDDDFFFKKKKKKJJJJJJIIIIIIHHHHHHIIIIIIHHHHHHGGGEEEDDDCCCFFFGGGIIIKKKMMMNNNOOOOOOQQQQQQQQQQQQQQQQQQPPPPPPMMMNNNOOOOOOPPPOOOOOOOOOOOOPPPQQQOOOMMMLLLLLLMMMPPPQQQRRRSSSSSSQQQPPPNNNMMMMMMLLLLLLMMMLLLIIIFFFEEECCCBBBAAAAAA???<<<:::666555444222111///......,,,+++)))***,,,------,,,+++,,,,,,,,,,,,,,,++++++++++++++++++++++++******++++++******+++,,,,,,---***************************+++---,,,***))))))***++++++*********)))))))))))))))))))))))))))))))))************************))))))))))))))))))))))))((((((((((((((((((((((((******))))))((((((''''''))))))))))))(((((((((((())))))))))))))))))))))))'''''''''(((((((((((((((,,,++++++******))))))(((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''(((((((((((((((((((((''''''''''''%%%%%%%%%%%%&&&((()))***((((((''''''&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((%%%%%%%%%%%%$$$###"""!!!&&&&&&&&&'''''''''(((((((((((('''&&&&&&'''((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''((()))((('''&&&%%%&&&''''''''''''''''''(((((((((((((((((('''&&&&&&&&&&&&'''''''''''''''''''''&&&&&&''''''''''''''''''''''''777555222000......000000333333333222111///...------,,,,,,++++++,,,,,,---++++++++++++++++++++++++***++++++***(((((()))+++***))))))(((((())))))***((())))))))))))(((((('''((((((((((((((((((((((((&&&''''''(((((())))))***)))((((((''''''(((((())))))((('''&&&&&&&&&'''((('''((()))***************''''''((()))************))))))))))))))))))))))))((((((((((((''''''''''''((((((((((((((((((((((((&&&&&&&&&'''''''''((((((((((((((('''''''''&&&&&&###$$$%%%&&&''')))******&&&&&&&&&%%%%%%%%%%%%%%%((((((((((((((((((((((((&&&'''((())))))((('''&&&(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))************************************))))))(((((()))+++---......,,,******+++,,,,,,,,,++++++++++++++++++++++++,,,,,,++++++++++++,,,---******++++++++++++++++++---,,,+++******+++,,,---+++++++++++++++***************++++++++++++******++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,++++++++++++************++++++,,,,,,,,,,,,------++++++++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,++++++***+++,,,------......---------........./////////111111000///000000111111222333555666888:::<<<===>>>???AAACCCEEEGGGGGGHHHHHHGGGEEECCCCCCEEEGGGIIIMMMMMMLLLKKKJJJIIIHHHGGGHHHHHHGGGFFFDDDBBB@@@???@@@@@@AAABBBDDDFFFHHHIIIIIIJJJLLLLLLMMMLLLKKKJJJEEEFFFGGGIIIJJJKKKKKKLLLLLLMMMLLLJJJHHHHHHIIIKKKRRRSSSTTTUUUVVVUUUTTTSSSTTTRRRQQQQQQRRRRRRQQQPPPPPPOOOMMMLLLKKKJJJGGGEEE???>>><<<:::888555444333///...------......---,,,,,,------------------,,,******++++++++++++++++++,,,,,,,,,+++,,,,,,------*********+++++++++++++++)))+++,,,+++***((())))))************)))))))))((())))))))))))))))))))))))************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((*********)))((('''''''''))))))))))))))))))))))))((((((((((((((('''''''''************************'''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((('''''''''''''''''''''''''''&&&&&&&&&&&&'''((((((''''''&&&&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''(((((('''&&&%%%%%%%%%%%%%%%&&&&&&''''''(((((((((((((((''''''''''''((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&'''((()))&&&''''''''''''(((((((((&&&&&&&&&&&&&&&'''((())))))(((((('''&&&&&&%%%%%%'''''''''''''''''''''''';;;777222//////000222333333333333222000///---,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++***+++,,,+++)))((()))+++))))))))))))))))))))))))((())))))))))))(((((((((((((((((((((((((((((((((''''''(((((())))))))))))((((((''''''''''''(((((()))(((''''''&&&'''(((((((((((()))))))))(((((('''$$$%%%''')))******)))((((((((((((((())))))))))))((((((((((((''''''''''''(((((((((((((((((((((((('''''''''''''''''''''&&&((('''''''''&&&&&&&&&&&&%%%%%%%%%&&&'''((())))))((((((((((((((('''''''''))))))(((((((((((())))))&&&&&&'''(((((('''&&&&&&(((((((((((((((((((((((())))))))))))))))))))))))((()))))))))************************************(((((((((((()))***+++,,,---,,,******++++++,,,,,,+++++++++++++++++++++++++++++++++++++++,,,,,,,,,'''''''''((()))))))))***,,,++++++******++++++,,,++++++++++++++++++++++++***++++++,,,,,,++++++***+++++++++++++++++++++++++++++++++,,,,,,,,,------------------------------+++++++++,,,,,,,,,------,,,,,,,,,,,,,,,,,,+++++++++,,,,,,,,,,,,,,,,,,+++++++++,,,------.........////////////000000000000///000000111222444555555666777999<<>>;;;;;;::::::;;;<<<>>>???@@@AAACCCDDDEEEDDDCCCBBB@@@@@@BBBDDDEEEFFFFFFFFFGGGGGGFFFDDDBBBBBBEEEGGGPPPPPPRRRSSSTTTTTTTTTTTTVVVTTTSSSSSSTTTUUUUUUTTTTTTSSSQQQQQQRRRQQQOOOMMMJJJIIIGGGDDDBBB???===<<<777555333333333222///---....../////////...------))))))*********+++++++++,,,,,,+++++++++,,,,,,---+++++++++++++++++++++***%%%''')))*********+++,,,*********)))))))))(((((())))))))))))))))))))))))************************))))))))))))))))))))))))************************'''((((((((()))))))))******)))))))))((((((((('''(((((((((((((((((((((((())))))((((((''''''&&&&&&%%%%%%&&&&&&'''''''''((())))))))))))))))))))))))''''''''''''''''''''''''''''''''''''''''''((((((&&&&&&'''''''''''''''(((''''''''''''&&&&&&''''''%%%%%%%%%%%%%%%%%%$$$$$$''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''***)))(((&&&&&&&&&'''((('''''''''''''''''''''&&&((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&''''''((((((&&&&&&&&&'''''''''(((((('''&&&&&&&&&&&&'''(((((((((((('''''''''&&&&&&&&&''''''''''''''''''''''''>>>999333000000222444444111111111000///---,,,+++,,,,,,,,,,,,,,,,,,,,,,,,***************************+++,,,,,,***))))))***))))))************)))))))))(((((((((((()))))))))((((((((((((((((((((((((((((((((()))))))))))))))((((((''''''''''''(((((((((((('''''''''((((((((()))))))))((('''&&&%%%$$$!!!###%%%((((((((('''%%%&&&&&&&&&'''''''''((((((((((((((((((''''''''''''(((((((((((((((((((((((('''''''''''''''&&&&&&&&&((('''''''''&&&&&&&&&&&&'''''''''''''''&&&&&&&&&((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&))))))))))))))))))))))))))))))))))))))))))))))))((()))))))))************************************,,,,,,,,,,,,---......///++++++++++++******+++,,,++++++++++++++++++++++++*********++++++,,,,,,,,,'''''''''((()))))))))***++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++,,,,,,,,,---------------------------------+++++++++,,,,,,,,,------------,,,,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,---.../////////////////////////////////111333555888:::<<<===>>>@@@BBBEEEGGGIIIJJJJJJPPPPPPQQQRRRQQQPPPOOONNNJJJGGGDDD@@@???@@@BBBDDD@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@AAABBBBBBBBBAAAAAA???>>><<<:::999999:::;;;;;;<<<===???@@@@@@??????@@@AAABBBBBBCCCCCCCCCCCCFFFFFFEEECCCBBBBBBEEEGGGKKKKKKLLLNNNNNNOOOPPPPPPSSSQQQPPPPPPRRRSSSSSSRRRRRRQQQQQQRRRTTTTTTSSSRRRRRRQQQPPPMMMKKKIIIGGGFFFAAA???===;;;:::888444111000000000//////...,,,,,,************************++++++************++++++---------,,,+++***))))))%%%''')))*********+++,,,************))))))))))))************************************************************************++++++++++++++++++++++++''''''(((((())))))******'''((((((((()))))))))***(((((((((((((((((((((((())))))((((((''''''&&&&&&###$$$$$$%%%%%%&&&&&&&&&))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&''''''(((((('''''''''''''''&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%(((((((((''''''&&&&&&&&&'''''''''''''''''''''&&&&&&%%%$$$#########$$$%%%))))))((('''&&&%%%%%%$$$''''''((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((('''&&&&&&&&&&&&'''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''DDD>>>777333333444444333...//////......---,,,++++++,,,,,,------,,,,,,+++***************************+++---,,,+++))))))***)))******++++++******))))))(((((((((((())))))***(((((((((((((((((((((((()))))))))))))))))))))))))))((((((''''''(((((()))''''''((((((((()))))))))((((((((('''&&&%%%$$$###"""$$$&&&'''((('''&&&%%%%%%%%%%%%&&&&&&''''''(((((((((((((((''''''''''''((((((((((((((((((((((((''''''''''''''''''&&&&&&((((((((('''''''''&&&&&&((((((((('''&&&&&&%%%%%%&&&&&&&&&&&&&&&'''''''''%%%&&&'''(((((('''&&&%%%''''''''''''''''''''''''))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************************************+++++++++,,,,,,---------)))+++,,,+++***)))***,,,++++++++++++++++++++++++((()))***+++,,,,,,,,,+++******++++++++++++++++++++++++++++++++++++++++++*********+++++++++++++++++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++,,,,,,,,,,,,------------++++++++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,------,,,,,,,,,,,,------------,,,,,,------------,,,,,,,,,,,,,,,,,,---...///000/////////000000111111111555777:::===@@@CCCDDDEEEHHHIIILLLNNNOOOPPPPPPPPPRRRRRRQQQQQQOOONNNMMMLLLGGGEEEBBB???>>>???@@@BBB?????????@@@@@@AAAAAAAAA???@@@BBBCCCEEEEEEFFFFFFGGGFFFDDDBBB@@@???>>>>>><<<======???@@@AAABBBCCCFFFFFFFFFGGGFFFFFFEEEEEEEEEFFFFFFDDDCCCCCCEEEGGGHHHHHHIIIIIIJJJKKKLLLLLLNNNMMMLLLMMMNNNOOONNNMMMNNNNNNNNNPPPSSSTTTSSSRRRSSSSSSRRRQQQPPPOOOOOONNNJJJHHHGGGEEEDDDAAA===:::555555444333111///...------,,,,,,,,,++++++++++++++++++******))))))******---------,,,++++++******)))+++,,,+++***((())))))++++++++++++*********)))************************************************************************************************''''''(((((())))))******'''''''''((()))*********))))))))))))))))))))))))((((((((((((((('''''''''%%%&&&&&&&&&''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&''''''((((((&&&''''''(((''''''&&&&&&$$$$$$%%%%%%&&&&&&''''''))))))(((((('''&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&))))))((('''&&&%%%%%%$$$&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''(((((('''&&&%%%%%%%%%&&&&&&&&&&&&''''''''')))((('''&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((((()))''''''''''''''''''''''''LLLFFF===888777666333///------.........------,,,+++,,,,,,------,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,***+++------+++*********)))***++++++++++++***))))))(((''''''((()))***+++))))))))))))))))))))))))))))))))))))))))))))))))***))))))(((((())))))***''''''((()))))))))))))))&&&&&&'''''''''''''''&&&'''((())))))***)))((('''%%%%%%&&&&&&'''(((((()))((((((((((((''''''''''''((((((((((((((((((((((((&&&&&&'''''''''''''''''')))))))))((((((((('''''''''''''''''''''&&&&&&&&&%%%&&&&&&&&&'''''''''((((((***,,,......,,,***((()))(((((((((((((((((()))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************************************))))))******++++++******(((+++,,,,,,***)))***+++++++++++++++++++++++++++'''(((***+++,,,,,,,,,+++,,,,,,,,,,,,,,,++++++++++++++++++,,,,,,+++++++++)))))))))*********+++++++++,,,,,,------,,,,,,+++++++++++++++++++++++++++,,,,,,,,,------------...+++++++++,,,,,,,,,------++++++,,,,,,,,,,,,------+++,,,,,,,,,---.........,,,,,,------------,,,,,,------,,,,,,---...000000000111333444666888::::::???AAADDDGGGIIIKKKLLLLLLMMMOOOPPPRRRSSSRRRQQQPPPOOONNNMMMLLLKKKJJJJJJJJJEEEDDDCCCBBBAAABBBCCCCCCCCCCCCCCCBBBBBBBBBBBBBBBCCCDDDFFFGGGIIIJJJKKKKKKLLLLLLKKKJJJHHHFFFEEECCC@@@?????????AAACCCFFFGGGLLLMMMMMMNNNNNNMMMMMMLLLHHHIIIJJJJJJIIIHHHIIIJJJIIIIIIIIIIIIIIIJJJKKKLLLKKKJJJJJJKKKLLLLLLJJJHHHIIIIIIIIIKKKMMMNNNNNNLLLNNNNNNOOOOOOPPPQQQRRRRRROOONNNNNNNNNNNNLLLHHHEEE@@@@@@>>><<<:::777555444111111000///...------,,,---,,,+++************++++++++++++,,,,,,---------***+++---,,,***))))))***,,,,,,,,,,,,++++++++++++************************************************************************************************(((((((((((())))))))))))(((((((((((())))))))))))))))))))))))))))))))))))'''''''''(((((((((((((((((((((((((((((((((((()))''''''''''''''''''''''''''''''''''''''''''''''''((('''''''''&&&&&&&&&&&&$$$$$$%%%&&&&&&'''((((((%%%&&&'''((((((''''''&&&$$$%%%%%%&&&''''''(((((()))))))))((('''&&&&&&&&&(((((('''''''''&&&&&&&&&''''''((((((((((((((('''''''''''''''''''''''''''$$$%%%&&&''''''&&&%%%$$$''''''''''''''''''''''''&&&&&&&&&''''''''''''(((%%%&&&'''((((((((('''&&&%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&'''((((((&&&&&&''''''''''''''''''''''''''''''''''''''''''SSSLLLBBB<<<:::777111---,,,---......///.........++++++------------++++++........................***,,,------,,,*********)))***+++,,,,,,+++***))))))(((''''''''')))***+++*********************************)))))))))))))))******))))))))))))******''''''((()))))))))))))))$$$%%%&&&((()))*********++++++,,,,,,,,,++++++***&&&&&&''''''((())))))***)))(((((((((''''''''''''((((((((((((((((((((((((&&&&&&&&&'''''''''(((((())))))))))))((((((((((((%%%&&&&&&''''''((((((((('''((((((((())))))******&&&(((,,,......,,,(((&&&))))))(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************************************,,,,,,---.........------(((***---,,,***(((***+++++++++++++++++++++++++++'''(((***+++,,,,,,++++++,,,+++++++++***)))))))))***++++++,,,,,,++++++***(((((())))))*********++++++,,,,,,------,,,,,,+++++++++++++++++++++++++++,,,,,,,,,---------......---------....../////////++++++,,,,,,,,,---------++++++,,,,,,---...//////,,,------......------,,,------,,,,,,---...000111444555777;;;>>>AAACCCEEEGGGIIIKKKMMMOOOPPPPPPPPPNNNOOOQQQRRRQQQPPPNNNMMMKKKJJJIIIHHHGGGHHHIIIIIIEEEEEEEEEEEEEEEEEEFFFFFFFFFFFFEEEDDDCCCBBBBBBAAAGGGHHHIIIKKKLLLMMMNNNNNNMMMNNNNNNNNNLLLJJJHHHGGGAAA@@@??????@@@DDDGGGIIIQQQQQQRRRSSSSSSSSSSSSSSSPPPRRRTTTTTTSSSRRRRRRSSSKKKKKKKKKKKKKKKKKKLLLMMMIIIIIIIIIKKKLLLKKKHHHEEEEEEDDDDDDFFFGGGHHHGGGEEEHHHIIIKKKLLLNNNPPPRRRSSSQQQQQQQQQRRRTTTSSSPPPMMMKKKJJJIIIFFFCCC@@@>>><<<555444333222111000///......---,,,,,,++++++++++++((((((***+++---...000000''')))+++,,,,,,,,,---...---------,,,,,,,,,++++++************************************************************************))))))))))))))))))))))))))))))))))))((((((((((((******))))))((((((''''''))))))))))))))))))))))))&&&'''''''''(((((())))))((((((((((((((((((((('''))))))))))))))))))))))))''''''''''''''''''''''''))))))(((((('''''''''&&&$$$$$$%%%%%%&&&'''(((((($$$%%%'''((((((((('''&&&$$$%%%&&&&&&'''((())))))***))))))((('''&&&&&&&&&(((((('''''''''&&&&&&&&&###$$$%%%&&&&&&&&&$$$$$$$$$$$$%%%&&&'''((()))***$$$$$$%%%&&&&&&%%%$$$$$$''''''''''''''''''''''''&&&&&&&&&'''''''''((((((###$$$&&&((()))))))))(((%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&'''((()))***((((((((('''&&&&&&%%%%%%''''''''''''''''''''''''YYYVVVNNNEEE;;;444000///111000///...---...//////......---------,,,,,,,,,------,,,,,,+++***))))))++++++++++++++++++++++++))))))))))))))))))))))))))))))))))))))))))))))))))))))***++++++++++++***,,,+++******))))))******)))))))))))))))(((''''''***)))(((''''''&&&''''''))))))(((''''''''''''''')))))))))))))))(((''''''((((((((((((((((((((((((,,,+++)))((('''&&&''''''((((((&&&%%%%%%&&&'''((())))))(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%)))(((((('''''''''((((((''''''''''''((((((((((((+++*********))))))((((((((((((((((((((()))************))))))******+++,,,************************)))************+++++++++++++++++++++++++++++++++************************)))***+++,,,,,,,,,,,,,,,***+++,,,------,,,+++***++++++++++++++++++++++++,,,,,,,,,++++++*********,,,,,,,,,++++++***************+++++++++,,,,,,,,,///---+++))))))+++---///,,,,,,,,,++++++*********,,,,,,,,,---------......,,,,,,++++++,,,,,,---...///...------,,,,,,------...---,,,,,,,,,---//////...//////...///222777;;;<<<<<<>>>BBBGGGJJJKKKKKKRRRSSSSSSSSSRRRPPPNNNMMMPPPNNNLLLIIIHHHGGGGGGHHHGGGEEEBBBAAAAAADDDHHHKKKIIIIIIIIIJJJKKKMMMOOOPPPPPPNNNJJJGGGEEEDDDEEEFFFFFFJJJNNNRRRSSSTTTVVVWWWSSSQQQOOONNNNNNMMMKKKJJJKKKJJJHHHGGGHHHJJJMMMOOOUUUWWWZZZ\\\\\\[[[YYYXXXZZZZZZYYYXXXYYYZZZ\\\]]]TTTRRROOONNNMMMMMMKKKJJJJJJKKKKKKLLLLLLLLLLLLKKKHHHHHHHHHHHHGGGEEECCCBBBCCCCCCEEEFFFHHHIIIJJJKKKKKKLLLNNNOOOQQQRRRRRRRRRRRRSSSTTTTTTRRROOOKKKHHHDDDBBB>>>:::555222///...111///---,,,---//////...---+++******+++++++++*********))))))((('''''''''***)))))))))((((((''''''************************+++++++++++++++***)))(((************************************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))******))))))(((((('''''')))))))))))))))(((''''''((()))***)))'''&&&&&&'''))))))))))))))))))))))))%%%&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&'''((((((&&&&&&&&&%%%%%%$$$$$$$$$''''''''''''((((((((((((%%%&&&&&&&&&'''(((((((((((((((''''''''''''((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''((("""###$$$%%%&&&'''''''''''''''''''''''''''&&&&&&((((((((((((((((((((((((&&&&&&&&&''''''''''''(((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''&&&'''((()))))))))((('''%%%%%%%%%%%%&&&'''(((((([[[XXXQQQHHH???777222000000///...---------...///------,,,,,,,,,+++++++++,,,++++++******)))))))))************************))))))))))))))))))))))))))))))))))))))))))))))))))))))***++++++++++++***,,,+++******))))))******)))))))))))))))(((''''''''''''&&&&&&&&&''''''((())))))((('''''''''''''''((((((((((((((('''&&&&&&((((((((((((((((((((((((+++***)))((('''''''''(((((('''&&&&&&&&&&&&'''((()))(((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%''''''&&&&&&&&&&&&''''''''''''''''''((((((((((((*********)))))))))((((((((((((((((((((()))************))))))******+++,,,************************************++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++)))***+++,,,,,,,,,,,,,,,+++++++++,,,,,,+++++++++++++++++++++++++++++++++,,,,,,,,,++++++*********,,,,,,,,,,,,++++++************+++++++++,,,,,,,,,,,,+++***))))))***+++,,,,,,,,,,,,,,,+++++++++***+++++++++,,,,,,,,,------,,,,,,,,,+++,,,------...//////...------------...---,,,,,,---...000222333...000111222444777<<>>@@@DDDHHHKKKNNNNNNNNNNNNPPPRRRTTTUUUQQQOOOLLLIIIHHHHHHIIIJJJIIILLLPPPRRRTTTUUUWWWXXXYYYXXXVVVUUUVVVUUUSSSQQQLLLKKKIIIHHHHHHJJJLLLNNNSSSUUUYYY[[[\\\\\\\\\\\\XXXXXXWWWWWWXXXYYY[[[\\\YYYWWWTTTRRRPPPOOOMMMLLLMMMNNNPPPRRRSSSSSSSSSSSSNNNNNNMMMLLLJJJGGGDDDCCCAAAAAAAAAAAABBBCCCDDDEEECCCEEEGGGJJJNNNQQQTTTUUUTTTUUUVVVVVVUUUSSSQQQOOOJJJHHHEEEAAA<<<888555333222000...---...///......///---++++++,,,,,,+++***++++++++++++,,,,,,,,,,,,+++++++++*********))))))************************+++++++++++++++***))))))************************************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((()))))))))))))))(((''''''((()))))))))'''&&&'''(((((((((((((((((((((((((((''''''''''''&&&&&&&&&%%%'''&&&&&&&&&&&&'''(((((('''&&&&&&&&&%%%%%%%%%$$$&&&&&&&&&'''((()))))))))&&&&&&&&&'''''''''''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((($$$%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((&&&&&&&&&''''''''''''(((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''&&&''''''&&&%%%$$$"""!!!'''&&&&&&%%%%%%%%%&&&&&&]]]ZZZUUUNNNEEE===666222...---,,,+++,,,,,,......,,,,,,,,,,,,+++++++++******************)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))***++++++++++++***++++++***))))))))))))***)))))))))))))))(((''''''%%%%%%%%%%%%&&&'''((())))))((((((''''''''''''((('''''''''''''''&&&&&&%%%(((((((((((((((((((((((())))))(((''''''(((((()))(((''''''&&&&&&'''((((((((((((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''''''''((((((((((((******))))))))))))((((((((((((((((((((()))************))))))******+++,,,************************************+++++++++,,,************************,,,,,,,,,,,,,,,,,,,,,,,,******+++,,,,,,,,,++++++,,,++++++++++++++++++,,,+++++++++++++++++++++++++++++++++++++++************+++,,,---,,,+++***)))******+++++++++,,,,,,,,,++++++************++++++---,,,,,,,,,,,,,,,++++++***+++++++++,,,,,,,,,,,,---,,,,,,,,,,,,---......000//////............///......//////111222444555111444777:::<<<>>>BBBEEEHHHIIILLLPPPTTTUUUTTTSSSOOONNNLLLJJJHHHFFFFFFEEEBBBBBBBBBBBBAAA@@@???>>>???>>>>>>>>>AAAEEEIIILLLSSSSSSSSSSSSTTTWWWYYYZZZUUUSSSPPPMMMLLLMMMNNNOOOMMMOOOQQQSSSTTTUUUWWWYYYZZZYYYXXXXXXXXXXXXVVVTTTKKKJJJHHHFFFGGGHHHKKKLLLQQQSSSVVVXXXXXXYYYZZZ\\\YYYXXXXXXXXXYYYZZZ[[[\\\YYYXXXVVVTTTSSSQQQQQQPPPOOOQQQSSSUUUUUUUUUTTTSSSTTTTTTSSSQQQNNNKKKHHHFFFDDDBBB@@@>>>>>>>>>???@@@>>>???AAADDDHHHMMMQQQSSSUUUUUUVVVVVVWWWWWWWWWWWWRRRQQQOOOLLLGGGCCC???<<<666555222111111111///---111///---,,,,,,,,,+++***(((((())))))***++++++,,,------,,,,,,,,,,,,,,,+++***************************++++++++++++***))))))************************************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))((())))))))))))((('''''''''((()))((('''&&&'''((('''''''''''''''''''''''')))((((((''''''&&&&&&&&&'''&&&&&&&&&&&&'''(((((('''''''''&&&&&&&&&&&&&&&%%%%%%&&&'''((()))))))))'''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''((((((((((((''''''%%%%%%%%%&&&&&&&&&&&&&&&((((((((((((((((((((((((&&&&&&&&&''''''''''''(((&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&%%%$$$###!!!!!!(((((('''&&&%%%%%%%%%%%%]]][[[WWWRRRKKKCCC:::444...---,,,++++++,,,---...---------,,,,,,,,,++++++***************+++++++++************************))))))))))))))))))))))))))))))))))))))))))))))))))))))***++++++++++++***++++++***))))))))))))))))))))))))))))))(((''''''&&&&&&&&&&&&&&&'''((())))))(((''''''''''''(((((('''''''''((((((''''''&&&((((((((((((((((((((((((''''''''''''(((((())))))'''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''''''''''''''(((((((((((())))))))))))))))))((((((((((((((((((((())))))*********))))))******+++,,,*********************************+++++++++,,,,,,************************,,,,,,,,,,,,,,,,,,,,,,,,***++++++,,,,,,,,,++++++---,,,+++******+++,,,---************************+++++++++******************+++,,,------,,,***)))******+++++++++,,,,,,,,,,,,,,,---......---,,,,,,------------,,,,,,,,,,,,++++++,,,,,,,,,------------------------....../////////.........//////000222222222333333444555555999<<>>???@@@@@@@@@@@@@@@BBBEEEIIIKKKRRRRRRRRRSSSTTTWWWYYYZZZXXXXXXWWWUUUQQQMMMIIIFFF@@@>>><<<:::888555222///000...,,,,,,,,,---,,,+++(((((()))))))))*********------------,,,,,,,,,,,,******************************+++++++++******)))************************************************))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((''''''(((((())))))******(((((())))))(((((('''&&&'''((()))((('''&&&'''(((''''''''''''''''''''''''''''''(((((((((((((((((('''&&&&&&&&&&&&'''((((((''''''''''''''''''''''''&&&&&&'''''''''''''''(((((((((((('''&&&&&&&&&%%%'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((((((((((((((((('''&&&%%%&&&&&&&&&'''''''''''''''((((((((((((((((((((((((&&&&&&&&&''''''''''''(((&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&'''''''''(((((('''&&&%%%%%%%%%%%%%%%^^^\\\YYYUUUPPPHHH???888///...---,,,,,,,,,------............------------++++++,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++))))))))))))))))))))))))))))))))))))))))))))))))))))))***++++++++++++***+++***))))))(((((()))))))))))))))))))))(((''''''******)))(((((('''((((((((((((''''''''''''(((((('''(((((()))))))))((((((((((((((((((((((((((((((&&&&&&''''''(((((())))))&&&''''''(((((()))))))))'''''''''(((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&'''((())))))''''''''''''(((((((((((((((((((((((((((((())))))((((((((((((((())))))*********))))))******+++,,,***************************++++++++++++,,,,,,,,,************************++++++++++++++++++++++++++++++,,,,,,,,,++++++***---,,,+++******+++,,,---******************************************************+++,,,,,,,,,+++*********+++++++++,,,,,,,,,+++,,,...//////...,,,+++------------------------------------..................------......///000.........///000111222333333333555777888:::;;;;;;AAADDDGGGIIIHHHHHHHHHIIIDDDEEEGGGJJJMMMNNNMMMKKKLLLKKKJJJJJJJJJKKKMMMNNNLLLLLLLLLKKKIIIFFFDDDBBBCCCCCCDDDDDDFFFHHHIIIJJJKKKKKKKKKKKKMMMOOOQQQRRRWWWUUUQQQMMMKKKJJJKKKLLLLLLMMMMMMMMMLLLMMMOOOQQQSSSRRRSSSUUUVVVVVVTTTRRREEEDDDCCCCCCDDDHHHKKKMMMPPPRRRSSSRRROOOQQQUUUZZZ^^^]]]]]]\\\ZZZYYYXXXWWWXXXYYYYYYXXXUUUTTTVVVWWW\\\]]]^^^^^^]]]\\\ZZZXXXUUUUUUUUUUUUUUUSSSQQQPPPPPPMMMIIIEEEBBBAAAAAABBBBBBAAA@@@??????AAACCCDDDKKKKKKKKKLLLOOORRRUUUWWWYYYYYYYYYYYYWWWTTTPPPNNNLLLJJJHHHEEEBBB>>>888444111///------......---,,,.........------,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,************************)))******+++++++++******************************************************))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((((((((''''''(((((())))))******((((((((((((((('''&&&&&&&&&((()))(((''''''((()))''''''''''''''''''''''''%%%&&&&&&'''((()))******'''&&&&&&&&&&&&'''((((((''''''''''''''''''''''''((((((''''''&&&&&&%%%%%%((((((((('''&&&&&&&&&%%%((((((''''''''''''((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''''''''''''''&&&%%%$$$'''((((((((()))))))))***((((((((((((((((((((((((&&&&&&&&&''''''''''''((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''(((((()))***%%%%%%%%%%%%%%%&&&'''(((___\\\ZZZXXXUUUNNNEEE===333111000...---------...////////////............---------------,,,,,,,,,++++++++++++++++++++++++))))))))))))))))))))))))))))))))))))))))))))))))))))))***++++++++++++*********)))(((((((((((())))))))))))))))))((('''''',,,+++***)))(((((((((((((((''''''''''''(((((()))'''((())))))))))))))))))((((((((((((((((((((((((%%%&&&'''(((((((((((((((&&&&&&((()))))))))))))))'''''''''((((((((((((((('''''''''''''''''''''''''''''''''''''''((((((((('''''''''''''''((()))***''''''''''''((((((((((((''''''(((((((((((())))))((((((((((((((()))************))))))******+++,,,************************++++++++++++,,,,,,,,,,,,++++++++++++++++++++++++************************++++++,,,,,,,,,+++******,,,++++++++++++++++++,,,************************)))))))))***************++++++++++++++++++,,,,,,******+++++++++,,,,,,,,,***+++,,,------,,,+++***---------............///............///////////////............///000000...//////111333555777888444666999<<<@@@BBBDDDEEEFFFHHHJJJJJJHHHGGGFFFGGGDDDDDDEEEGGGKKKMMMLLLLLLNNNNNNOOOOOOQQQRRRTTTTTTNNNMMMMMMKKKJJJHHHFFFEEEGGGGGGHHHHHHIIIIIIIIIIIIFFFFFFFFFGGGHHHJJJLLLMMMVVVSSSPPPLLLJJJJJJJJJKKKMMMNNNOOONNNMMMLLLMMMNNNNNNNNNOOORRRTTTTTTRRRPPPHHHGGGFFFFFFHHHKKKOOOQQQPPPSSSUUUUUUTTTXXX```gggooonnnllljjjgggccc```___```bbbbbb___[[[YYYZZZ\\\_______________^^^]]]]]]SSSTTTUUUVVVVVVVVVUUUTTTRRRPPPLLLIIIFFFDDDDDDDDDBBBAAAAAA@@@AAABBBCCCDDDDDDDDDEEEGGGIIILLLOOOQQQTTTUUUVVVVVVVVVVVVUUUTTTUUUSSSRRRPPPNNNIIICCC>>>888666333222222111000............---,,,+++++++++******++++++++++++,,,,,,************************))))))***++++++++++++***************************************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))'''(((((((((((('''&&&&&&&&&'''((((((''''''((()))''''''''''''''''''''''''%%%%%%&&&'''((())))))***'''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&'''''''''((((((''''''&&&%%%%%%%%%'''''''''''''''&&&&&&&&&(((((((((''''''(((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''''''''''''''&&&%%%$$$(((((())))))***+++++++++((((((((((((((((((((((((&&&&&&&&&''''''''''''(((''''''&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''((('''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&'''((((((```^^^[[[ZZZYYYTTTKKKDDD777555333000///.........//////.........------------------,,,,,,+++++++++************************))))))))))))))))))))))))))))))))))))))))))))))))))))))***++++++++++++*********)))((((((((((((((()))))))))))))))(((''''''***))))))((((((((())))))'''''''''''''''((())))))&&&'''(((((())))))((((((((((((((((((((((((((((((%%%&&&'''((((((((('''&&&%%%&&&((()))******))))))''''''''''''((((((((()))''''''''''''''''''''''''&&&'''''''''((((((((()))&&&&&&&&&&&&'''((())))))''''''''''''(((((((((((('''''''''((((((((())))))((((((((((((((()))************))))))******+++,,,************************+++++++++,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++++++++++++++,,,,,,,,,,,,+++***)))+++++++++,,,,,,+++++++++************************((()))))))))*********+++,,,+++***)))***+++---...******+++++++++,,,,,,,,,+++,,,,,,,,,,,,,,,,,,+++------......////////////---------.........////////////......//////000111000000222444777:::===>>>===???AAADDDGGGHHHIIIIIIFFFGGGHHHGGGEEEDDDDDDDDDEEEDDDCCCEEEIIILLLNNNNNNNNNNNNPPPQQQRRRSSSSSSSSSLLLKKKJJJIIIIIIIIIIIIIIILLLMMMNNNOOOPPPPPPOOOOOOKKKKKKKKKLLLMMMOOOQQQRRRXXXWWWTTTQQQQQQQQQSSSTTTVVVXXXZZZYYYWWWVVVUUUUUURRRRRRTTTXXXZZZZZZXXXVVVRRRQQQOOONNNNNNQQQSSSUUUTTTXXXZZZYYYYYY]]]hhhqqq|||zzzxxxtttooojjjeeebbbaaadddfffdddaaa```cccfffhhhfffccc```^^^\\\[[[ZZZTTTUUUVVVWWWXXXXXXWWWVVVTTTSSSPPPNNNKKKIIIHHHGGGCCCCCCCCCCCCCCCDDDDDDDDD@@@AAABBBDDDFFFHHHJJJLLLMMMNNNOOOQQQSSSUUUVVVWWWWWWWWWXXXXXXWWWSSSNNNIIIEEEBBB===:::888666333000+++++++++++++++***************+++++++++,,,,,,,,,************************))))))***+++++++++++++++************************************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((''''''((((((''''''&&&%%%&&&'''((((((''''''(((***(((((((((((((((((((((((('''&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&'''(((((($$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&'''''''''''''''(((''''''&&&&&&''''''(((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((''''''(((((((((''''''&&&'''(((((()))******++++++((((((((((((((((((((((((&&&&&&&&&''''''''''''(((''''''&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&'''''''''&&&%%%$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%&&&&&&'''bbb___\\\\\\\\\XXXOOOIII999888555222000///............---------,,,,,,,,,------,,,,,,+++***))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))***++++++++++++*********)))((((((((((((((()))))))))))))))(((((('''''''''&&&''''''((()))***'''''''''''''''((()))***%%%%%%&&&'''((((((((('''((((((((((((((((((((((((&&&&&&'''(((((('''&&&%%%%%%&&&((()))*********)))&&&'''''''''(((((())))))((((((((((((((((((((((((&&&'''''''''(((((())))))$$$$$$$$$%%%&&&'''((()))''''''''''''((((((((()))&&&'''''''''(((((())))))((((((((((((((()))***************)))***++++++,,,************************++++++,,,,,,,,,---------------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***)))***+++,,,------,,,+++***))))))))))))))))))))))))(((((())))))*********+++---+++)))((()))+++---///******+++++++++,,,,,,,,,........................---.........//////000000,,,,,,,,,---------......///////////////000111111111222444777:::>>>AAACCCHHHIIIJJJJJJJJJJJJHHHHHHCCCDDDEEEDDDBBBAAABBBCCCEEECCCBBBDDDGGGKKKNNNOOOKKKLLLMMMOOOOOOOOONNNMMMJJJIIIIIIHHHIIIJJJLLLMMMQQQRRRTTTVVVWWWWWWVVVVVVTTTTTTTTTTTTVVVXXXZZZ[[[]]]\\\ZZZYYYYYY[[[]]]___aaaccceeeeeeccc```______^^^___bbbeeehhhhhhfffdddZZZYYYVVVTTTTTTUUUWWWXXXYYY\\\^^^\\\ZZZ^^^iiirrr{{{yyyvvvqqqkkkeee___\\\\\\```dddeeedddeeejjjooowwwsssmmmgggaaa]]]ZZZYYYUUUVVVXXXYYYYYYXXXXXXWWWWWWVVVUUUSSSPPPNNNLLLLLLGGGGGGGGGFFFEEEDDDBBBAAA???@@@BBBCCCEEEGGGHHHIIIHHHIIIJJJMMMPPPSSSVVVXXXWWWXXXYYY\\\\\\ZZZUUUQQQOOOKKKFFFAAA===999555222,,,------......//////000+++++++++,,,,,,---------************************((()))***+++++++++++++++************************************************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))******))))))((((((''''''''''''((((((''''''&&&%%%%%%'''((((((''''''(((***)))))))))))))))))))))))))))((('''&&&%%%$$$######'''&&&&&&&&&&&&'''(((((($$$$$$$$$%%%%%%&&&&&&&&&"""###$$$%%%'''((()))***%%%&&&&&&''''''((((((((('''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&'''''''''(((((((((((())))))))))))((((((&&&''''''((()))******+++((((((((((((((((((((((((&&&&&&&&&'''''''''((((((''''''&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$%%%''')))***(((((('''&&&%%%%%%%%%%%%bbbccccccbbb^^^XXXRRRNNNEEE===333......///...,,,,,,---...//////...---,,,333111...,,,+++,,,---...************************)))((((((''''''''''''(((************************************************************))))))))))))******))))))(((((('''''''''((()))******)))((('''$$$%%%'''((((((((('''&&&(((((()))))))))'''&&&%%%))))))))))))))))))))))))''''''''''''''''''''''''(((((((((((((((((((((((())))))(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))***++++++''''''''''''''''''''''''((()))***)))'''&&&&&&(((+++***)))))))))***,,,---))))))))))))************,,,+++*********+++,,,---++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,+++***))))))***+++,,,,,,,,,,,,+++++++++*********************)))((('''++++++++++++******))))))***+++,,,------,,,+++***++++++******++++++,,,---******+++,,,,,,---......------------------------//////////////////////////////..................000//////000111222444555888:::===AAADDDEEEFFFGGGMMMLLLIIIGGGEEECCCBBBAAACCCBBBBBBBBBBBBCCCDDDDDDCCCEEEGGGJJJLLLLLLLLLLLLHHHIIILLLNNNNNNMMMKKKIIIFFFHHHKKKKKKIIIJJJMMMQQQZZZ[[[]]]___aaadddiiimmmccc___]]]```hhhpppssssssrrrpppooorrrvvvxxxtttpppssspppmmmpppuuuyyyxxxvvvtttssssssuuuxxx{{{||||||sssnnngggcccaaabbbccccccgggaaa^^^^^^```bbbhhhnnnrrrooojjjeeeaaa\\\WWWTTTVVVZZZ___dddgggjjjmmmppp}}}{{{yyyuuulll```VVVRRRUUURRRSSSXXX[[[XXXVVVWWWYYYYYYXXXWWWUUUTTTSSSRRRUUUPPPKKKJJJLLLLLLHHHDDDFFFHHHKKKNNNOOOMMMKKKIIIFFFFFFFFFHHHJJJMMMPPPRRRUUUWWWYYYZZZXXXWWWWWWWWWTTTSSSPPPKKKFFFAAA===;;;;;;666111000222222...***+++++++++,,,,,,---------******************++++++++++++++++++++++++++++++************************++++++************++++++******++++++++++++******))))))))))))************************))))))))))))))))))))))))))))))))))))(((((((((((((((''''''''''''((()))******)))((('''&&&'''((('''%%%$$$%%%&&&((((((''''''''''''((((((---)))%%%%%%'''((((((&&&&&&&&&&&&'''''''''(((((((((''''''''''''&&&&&&&&&''''''(((((('''&&&%%%%%%#########$$$%%%&&&'''(((''''''&&&%%%%%%&&&((()))((('''&&&&&&'''((()))***''''''&&&&&&&&&&&&''''''''''''''''''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''((('''&&&%%%%%%&&&'''((('''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&'''''''''```aaabbbaaa^^^XXXSSSPPPIIIAAA777111000000///...------...//////...------...---,,,++++++,,,,,,---************************+++***)))(((((((((((((((************************************************************))))))))))))***)))))))))(((((((((''''''((())))))))))))((('''%%%&&&'''((()))((('''''''''(((((())))))((('''&&&))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((()))))))))(((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''((()))(((&&&&&&&&&'''%%%%%%%%%%%%%%%&&&''''''))))))))))))************++++++*********+++,,,---++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,+++***))))))***+++,,,------,,,,,,,,,+++++++++***+++++++++******)))(((++++++++++++*********)))++++++,,,,,,,,,,,,++++++,,,,,,,,,+++,,,,,,------***++++++,,,------......,,,,,,,,,,,,,,,,,,++++++............------------........................111111000111333666999;;;>>>@@@CCCGGGJJJLLLMMMNNNLLLKKKHHHFFFCCCAAA@@@???@@@AAAAAABBBCCCDDDFFFFFFIIIIIIJJJKKKLLLLLLLLLLLLHHHJJJKKKMMMMMMLLLKKKJJJIIIKKKMMMNNNOOOTTT[[[bbbjjjjjjjjjlllqqqvvv|||{{{xxxwww{{{~~~~~~yyyuuusssuuu{{{}}}}}}~~~xxxtttqqqpppnnnmmmpppnnnnnnqqqooojjjhhhiiiiiieeeaaa]]]ZZZWWWSSSPPPTTTWWWZZZ]]]aaaeeejjjnnnxxxyyyzzzxxxqqqfff]]]YYYXXXTTTSSSVVVXXXVVVUUUVVVWWWWWWWWWWWWWWWWWWXXXXXXYYYVVVSSSRRRSSSSSSQQQNNNMMMOOORRRTTTTTTTTTRRRQQQNNNNNNMMMLLLLLLLLLLLLLLLPPPRRRTTTVVVVVVVVVXXXYYY[[[ZZZWWWTTTPPPLLLIIIGGGAAA===888666666555111---)))***,,,------,,,+++************+++++++++++++++++++++++++++++++++++++++************************+++******************+++******++++++++++++******))))))))))))************************))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((())))))(((((((((((())))))'''((()))(((&&&%%%&&&'''((((((''''''''''''((((((,,,(((%%%%%%'''(((((('''%%%%%%%%%&&&&&&&&&''''''(((''''''''''''&&&&&&&&&''''''(((((('''&&&&&&%%%$$$$$$$$$%%%%%%&&&'''((()))((('''&&&&&&&&&'''((('''&&&%%%%%%%%%&&&'''((('''''''''&&&&&&'''''''''''''''''''''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((''''''((('''&&&&&&&&&&&&'''((('''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''']]]^^^``````]]]YYYUUURRRNNNFFF<<<555222222111///------...//////...------*********++++++,,,,,,,,,++++++++++++++++++++++++---,,,+++***)))(((((((((************************))))))))))))))))))))))))************))))))))))))))))))))))))((((((((((((&&&'''(((((((((((('''&&&&&&'''((()))))))))((((((&&&'''(((((()))(((((('''))))))))))))))))))))))))************************((((((((((((((((((((((((***)))))))))))))))((((((''''''''''''''''''''''''((((((''''''&&&&&&&&&&&&''''''''''''''''''''''''&&&(((((((((&&&%%%&&&'''&&&'''(((((())))))(((((())))))))))))************++++++******++++++,,,---++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++************++++++,,,,,,,,,,,,,,,+++++++++++++++,,,,,,,,,+++******++++++++++++************,,,,,,++++++++++++,,,,,,......---,,,,,,---------+++++++++,,,------......,,,,,,------------------//////.........---------///////////////000000000444333333555888<<<@@@BBBFFFHHHJJJLLLNNNNNNNNNNNNJJJIIIGGGDDDBBB@@@???>>>AAAAAACCCDDDFFFHHHIIIJJJMMMMMMLLLLLLLLLLLLLLLMMMJJJKKKLLLMMMMMMMMMLLLLLLOOOQQQRRRTTTYYYbbbnnnwwwzzzvvvsssuuu|||uuurrrnnnpppvvv|||}}}|||{{{xxxuuuqqqnnnqqqrrrxxx~~~|||rrrjjjggggggccc]]]XXXUUUSSSPPPNNNTTTTTTVVVWWW[[[bbbjjjpppsssvvvxxxwwwqqqiiibbb^^^[[[VVVRRRTTTTTTRRRRRRTTTTTTTTTVVVWWWYYYZZZ[[[\\\ZZZYYYYYYXXXWWWVVVTTTTTTUUUVVVWWWXXXYYYYYYYYYYYYVVVUUUUUUSSSQQQOOOMMMLLLLLLNNNPPPQQQRRRTTTWWWZZZZZZYYYXXXWWWUUUTTTRRRRRRJJJFFFAAA???>>>;;;777333+++,,,.........---+++***++++++++++++++++++++++++++++++++++++++++++++++++******************************************************++++++++++++******))))))))))))************************))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((+++)))(((&&&&&&((()))+++((()))***)))'''&&&'''(((((((((''''''''''''((((((***(((%%%%%%''')))))))))$$$$$$%%%%%%%%%&&&&&&&&&(((''''''''''''&&&&&&&&&'''''''''(((''''''&&&%%%&&&&&&&&&&&&&&&'''((())),,,+++)))'''&&&&&&&&&''''''&&&%%%$$$###$$$%%%&&&''''''''''''''''''''''''''''''''''''((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((('''((('''&&&&&&&&&&&&'''((('''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&\\\]]]______^^^[[[XXXVVVSSSKKKBBB:::555333111000---..................---***++++++,,,,,,,,,++++++++++++++++++++++++++++++---,,,+++***)))(((((((((************************))))))))))))))))))))))))************)))))))))((())))))))))))((((((((((((&&&''''''''''''''''''&&&'''(((((()))))))))))))))&&&&&&'''(((((()))))))))(((((((((((((((((((((((())))))))))))))))))))))))((((((((((((((((((((((((************))))))))))))'''''''''''''''''''''''')))))))))))))))(((((((((''''''''''''''''''''''''&&&'''((('''&&&%%%&&&''')))***+++,,,---,,,+++***((()))))))))************+++***++++++++++++,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++***+++++++++++++++,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,------,,,++++++++++++++++++++++++++++++---,,,+++******+++,,,---...------,,,,,,,,,,,,---,,,,,,,,,,,,------......////////////000000000000111000000//////......---000000111111222333333333666777999<<<@@@CCCFFFGGGKKKLLLLLLLLLKKKIIIGGGFFFGGGFFFEEEDDDBBBBBBAAAAAADDDEEEFFFHHHIIIKKKKKKLLLMMMLLLKKKKKKKKKMMMNNNOOONNNNNNOOOOOOOOOPPPPPPPPPVVVXXX[[[^^^dddnnnzzz~~~xxxxxx~~~~~~|||yyyxxxyyyzzzzzzyyymmmjjjfffgggkkkqqqvvvxxxzzzxxxttttttwww{{{}}}{{{yyywwwtttpppjjjfffjjjmmmuuu~~~zzztttrrrrrrmmmfff```\\\YYYVVVUUUXXXWWWWWWYYY^^^hhhttt||||||zzzsssnnnjjjfffccc\\\WWWVVVUUUSSSSSSVVVUUUVVVXXXZZZ[[[[[[[[[[[[[[[\\\\\\ZZZXXXVVVVVVWWWYYYYYYYYYYYYZZZ[[[\\\]]]XXXYYYYYYZZZYYYWWWUUUTTTNNNOOOOOOOOOOOOPPPSSSVVVTTTTTTUUUVVVWWWXXXYYYZZZSSSPPPLLLIIIFFFCCC>>>;;;333222111///...---------,,,,,,,,,,,,,,,+++++++++++++++++++++++++++++++++*********************************++++++***************++++++++++++******((()))))))))************************)))))))))(((((((((((((((((((((((((((((((((((((((((()))))))))***)))(((''''''((()))***((()))***)))'''&&&'''(((((((((''''''''''''((((((((('''&&&&&&'''((()))***%%%%%%%%%&&&&&&&&&''''''(((''''''''''''&&&&&&&&&&&&'''''''''''''''&&&&&&'''''''''''''''((())))))...,,,***((('''&&&&&&&&&((('''%%%$$$###$$$$$$%%%&&&''''''''''''''''''&&&''''''''''''((((((((((((''''''''''''''''''''''''&&&&&&'''((((((((((((((('''''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&((((((''''''&&&&&&%%%%%%[[[]]]^^^______]]][[[YYYUUUOOOGGG???888444111///.........------.....................---,,,+++***++++++++++++++++++++++++,,,+++***)))((((((((((((************************))))))))))))))))))))))))************)))))))))((((((((((((((())))))))))))'''''''''&&&&&&'''''''''((((((((((((((())))))***''''''''''''(((((())))))(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))************((((((((((((((((((((((((''''''(((((()))******+++''''''''''''''''''''''''&&&'''((('''&&&&&&'''(((&&&'''((()))***)))((('''((()))))))))******************++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++*********++++++,,,,,,,,,+++++++++,,,,,,+++++++++)))))))))***************+++,,,,,,---------,,,,,,+++++++++++++++++++++,,,...---,,,++++++,,,---...,,,,,,+++++++++++++++,,,,,,,,,------------....../////////000000111111111/////////.........------...///000111333555666666999<<>>>>>@@@DDDHHHKKKLLLLLLLLLOOONNNMMMLLLKKKKKKKKKKKKLLLMMMNNNNNNNNNMMMKKKJJJEEEDDDCCCBBBDDDGGGKKKNNNOOOPPPOOOLLLNNNTTTVVVTTTWWWYYY\\\```bbbdddeeeeeekkkllllllkkkhhhgggggghhhffffffdddbbb``````bbbddddddmmmttttttvvvyyyxxxsssyyy}}}zzzqqqggg___ZZZVVVVVVZZZ\\\[[[XXXQQQUUUZZZ\\\ZZZYYYZZZ\\\___^^^]]][[[ZZZZZZZZZZZZ]]]\\\ZZZWWWTTTQQQOOONNNLLLOOOSSSVVVYYYYYYXXXXXX[[[YYYWWWUUURRRMMMHHHDDD;;;999555111...---------............---,,,******++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,(((((()))*********************))))))))))))************)))*********)))'''))))))))))))))))))))))))+++*********))))))(((((())))))(((((('''''''''&&&((((((((((((((((((((((((************))))))))))))(((''''''&&&&&&&&&''''''(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''*********)))((((((''''''''''''((((((((((((''''''%%%%%%%%%&&&'''((()))***((((((''''''''''''(((((((((((((((((((((((((((((())))))(((((('''''''''&&&(((((('''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''(((((('''''''''&&&&&&&&&```\\\XXXVVVYYY\\\]]]]]]^^^^^^]]]ZZZRRRHHH>>>888333111///...///000///...---------------...//////000//////......---,,,,,,++++++++++++************)))))))))))))))))))))))))))))))))))))))***++++++---------,,,,,,+++++++++))))))))))))))))))))))))((())))))******))))))(((''')))******((('''((()))))))))***+++******(((((())))))(((((((((((()))))))))((('''((()))***)))((()))((()))***++++++)))'''''''''''''''''''''''''''((((((((((((((((((((((((***++++++******(((''''''))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************))))))))))))))))))))))))+++,,,---,,,***)))***+++******+++,,,,,,,,,,,,,,,***************+++++++++************++++++++++++---+++)))***,,,---,,,******++++++,,,,,,+++++++++---+++((()))+++------,,,,,,,,,++++++,,,,,,---...++++++,,,,,,,,,---------,,,,,,---------............,,,,,,...000111000...---...///...------///111///111222333555888<<<@@@@@@BBBEEEHHHKKKMMMNNNOOOJJJKKKKKKKKKKKKLLLLLLLLLNNNNNNNNNNNNLLLKKKIIIHHHCCCCCCCCCDDDFFFKKKPPPSSSYYY[[[ZZZWWWYYY^^^```^^^[[[]]]```ccceeeggghhhhhhmmmoooooonnnlllkkkkkklllmmmnnnnnnmmmlllmmmpppsss|||qqqlllggggggjjjkkkfffaaaZZZYYYWWWWWWXXXZZZ[[[\\\]]]]]]]]]]]]]]]^^^^^^^^^```___]]][[[YYYWWWUUUTTTNNNOOOOOOPPPQQQRRRTTTTTT___^^^]]]\\\[[[WWWRRRNNNCCCAAA===888444111///.........------------,,,,,,++++++++++++++++++++++++************************)))******+++++++++++++++++++++************++++++******************)))'''))))))))))))))))))))))))************)))))))))((())))))((((((((('''''''''(((((((((((((((((((((((())))))))))))))))))))))))(((((('''''''''(((((()))(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((((((((((((((((((((((((''''''((((((((((((''''''&&&&&&&&&&&&''''''((()))((((((''''''''''''(((((((((((((((((((((((((((((()))(((((((((''''''''''''(((((('''&&&&&&%%%$$$$$$''''''''''''''''''''''''''''''''''''''''''''''''(((((('''''''''&&&&&&&&&aaa^^^ZZZYYYZZZ\\\^^^^^^```___^^^]]]YYYQQQEEE===555222///......//////......------------...//////------,,,,,,++++++******---,,,+++***)))******+++))))))))))))))))))))))))***))))))))))))***++++++************))))))))))))************************)))((((((''''''(((((())))))*********(((''''''(((((())))))************)))******))))))))))))******)))((('''((()))***)))(((***)))((((((******)))(((((((((((((((((((((((((((''''''''''''''''''''''''************)))(((''''''))))))))))))))))))))))))************************))))))))))))************))))))))))))))))))))))))+++,,,---,,,***)))***+++++++++,,,------------,,,+++++++++++++++*********+++++++++++++++*********,,,+++******,,,,,,+++***+++++++++,,,,,,++++++***,,,+++)))***,,,------,,,,,,,,,++++++,,,,,,---...,,,,,,,,,,,,------------,,,------------............------...//////...,,,...///000///......000222111333666999;;;===AAADDDFFFGGGHHHIIIKKKMMMNNNNNNIIIJJJLLLMMMNNNNNNNNNMMMNNNMMMMMMLLLJJJHHHFFFEEEBBBDDDFFFIIILLLQQQWWW\\\aaacccbbb___```dddeeedddaaabbbdddfffgggiiiiiiiiioooqqqssstttuuuuuuwwwxxx}}}~~~~~~{{{ssslllddd[[[VVVWWWYYYZZZYYYYYYYYYZZZZZZ[[[\\\\\\\\\_________^^^]]]\\\[[[ZZZTTTRRROOOLLLLLLMMMPPPRRRZZZ[[[\\\]]]]]]YYYTTTPPPKKKIIIEEEAAA;;;777333111//////---,,,,,,---......,,,,,,,,,,,,,,,,,,,,,,,,***************************++++++,,,---,,,,,,,,,,,,,,,++++++++++++,,,,,,*********+++******)))((())))))))))))))))))))))))************))))))))))))))))))((((((((((((''''''(((((((((((((((((((((((('''''''''(((((())))))***((((((((((((((()))***+++((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%&&&&&&'''(((((())))))''''''(((((((((((('''''''''''''''&&&''''''((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((((((((''''''''''''((((((''''''&&&%%%%%%%%%'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&aaa___]]]\\\\\\]]]]]]^^^bbb___^^^^^^^^^WWWLLLCCC999555111.........///.........---------......///++++++++++++******))))))...---+++))))))***+++,,,))))))))))))))))))))))))*********))))))***++++++(((((((((((((((((((((((()))))))))))))))))))))))))))((('''&&&&&&'''((())))))******)))'''&&&'''((((((((())))))***************))))))(((((())))))***)))((('''((()))***)))(((+++)))'''''')))***)))((())))))))))))))))))))))))(((((((((((((((((((((((())))))******)))(((''''''(((((((((((((((((((((((())))))))))))))))))))))))((()))))))))************))))))))))))))))))))))))+++,,,---,,,***)))***+++***++++++,,,---,,,,,,,,,,,,,,,++++++++++++******,,,,,,,,,++++++*********+++++++++++++++,,,++++++++++++,,,,,,,,,+++******,,,+++++++++,,,---------,,,,,,++++++,,,,,,---...,,,,,,,,,------------...------------..............................---,,,...///000000///000222444555888===@@@BBBDDDFFFHHHKKKKKKJJJJJJJJJKKKKKKLLLNNNOOOPPPQQQQQQOOOMMMKKKJJJJJJIIIHHHGGGFFFEEEEEEFFFIIIMMMQQQTTTXXX^^^cccfffiiiiiieeedddggghhhgggfffggghhhiiikkklllmmmmmmtttwww}}}xxxlllaaa[[[YYYWWWVVVVVVVVVWWWWWWXXXYYYYYYYYY\\\]]]^^^_________^^^^^^ZZZWWWSSSPPPNNNNNNPPPQQQUUUVVVXXX[[[[[[WWWQQQMMMKKKJJJHHHEEEAAA===:::888444222///---+++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,***++++++,,,,,,,,,,,,,,,+++++++++******+++++++++***+++,,,+++***)))))))))))))))))))))))))))))))))*********)))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((%%%&&&&&&'''((())))))***''''''''''''((()))***+++((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&''''''((((((''''''(((((((((((('''''')))((('''''''''''''''(((((((((''''''''''''((((((((((((((((((((((((((((((((((((((((((((('''''''''((((((''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''aaaaaa```^^^]]]\\\]]]]]]```^^^]]]^^^___[[[QQQIII???:::444000///////////////......---------..................------------...---+++))))))***+++---++++++++++++++++++++++++++++++***************+++++++++++++++++++++++++++(((((((((((((((((((((((()))((('''&&&&&&'''((())))))******((('''&&&((()))((((((((())))))***++++++)))((((((''''''(((((())))))((('''((()))***)))(((***(((''''''((())))))(((************************))))))))))))))))))))))))((())))))))))))(((((('''''''''''''''''''''''''''((((((((((((((((((((((((((()))))))))************************************+++,,,---,,,***)))***+++)))******+++++++++++++++,,,+++++++++++++++++++++---,,,,,,,,,++++++******++++++,,,+++++++++++++++,,,,,,,,,,,,,,,+++***)))++++++,,,,,,,,,,,,------,,,,,,++++++,,,,,,---...,,,,,,---------.........---------.........//////---...//////...---------...///111111111333555777;;;>>>CCCFFFGGGHHHJJJKKKIIIIIIIIIIIIJJJKKKMMMMMMSSSSSSSSSRRROOOKKKHHHEEEEEEEEEEEEEEEFFFGGGGGGHHHMMMRRRWWWZZZ[[[^^^dddiiikkkooopppmmmkkkmmmooonnnlllmmmpppsssvvvzzz|||~~~uuufff]]]YYYXXXVVVVVVUUUVVVWWWXXXZZZ[[[YYY[[[]]]___aaaaaaaaa```\\\[[[YYYVVVTTTRRRRRRQQQXXXYYY[[[]]]\\\XXXRRRMMMGGGGGGFFFEEEDDDBBB@@@???:::777333///---+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,)))******+++,,,+++++++++******))))))))))))******)))+++---,,,***))))))***))))))))))))))))))))))))))))))))))))))))))******(((((())))))))))))))))))))))))))))))))))))))))))%%%&&&&&&'''((())))))***%%%%%%%%%&&&'''((()))***))))))((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((''''''&&&&&&&&&&&&''''''(((((((((((('''''')))(((((('''''''''((((((((((((''''''''''''(((((((((((((((((((((((((((((('''''''''(((((((((((((((((('''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&'''''''''''''''''''''```aaaaaa```]]]\\\[[[\\\^^^]]]\\\]]]^^^[[[VVVQQQGGGAAA999333000000000000//////...------------...------,,,,,,,,,,,,,,,,,,...---,,,+++***++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++************+++)))))))))))))))*********'''''''''''''''''''''''')))((((((''''''(((((())))))))))))(((&&&''')))+++***)))))))))))))))***+++((((((''''''''''''(((((()))((('''((()))***)))((()))(((''''''))))))((('''))))))))))))))))))))))))************************((((((((())))))(((((('''''''''''''''''''''''''''''''''''''''''''''''''''))))))))))))************************************+++,,,---,,,***)))***+++))))))***++++++++++++***++++++++++++,,,,,,,,,---,,,,,,,,,,,,,,,+++++++++***+++,,,,,,******+++,,,,,,,,,,,,,,,++++++***)))***,,,......---,,,---...,,,,,,++++++,,,,,,---...,,,---------............------........./////////---...000000///......///...000222444555777;;;===@@@CCCFFFHHHHHHIIIJJJKKKDDDEEEGGGJJJLLLOOOQQQRRRQQQQQQPPPMMMJJJFFFCCCAAACCCCCCDDDEEEGGGIIILLLMMMSSSYYY___aaaaaabbbgggllljjjpppsssqqqppptttwwwwwwxxxzzz}}}vvvjjjeeedddXXXVVVTTTRRRRRRTTTVVVXXXWWWYYY\\\___bbbbbbbbbbbb[[[[[[[[[ZZZXXXVVVUUUSSS[[[[[[\\\]]]\\\XXXSSSNNNFFFFFFEEEEEEDDDDDDDDDDDD???===999555111...,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,************************)))******+++++++++++++++***))))))))))))))))))***))),,,...---***((()))+++))))))))))))))))))))))))))))))))))))************(((((())))))))))))******))))))))))))))))))))))))'''''''''(((((())))))***&&&&&&&&&&&&&&&'''((())))))))))))(((((((((''''''''''''''''''''''''''''''&&&&&&'''''''''(((((((((''''''''''''''''''''''''))))))(((((('''&&&&&&%%%''''''((((((((((((''''''((((((((('''(((((())))))((((((''''''''''''(((((((((((((((((((((((((((((('''''''''(((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''___aaabbbaaa]]]ZZZZZZ[[[]]]]]]]]]]]]\\\[[[YYYXXXNNNGGG>>>666222111111111//////...---------------************************------,,,,,,,,,+++++++++++++++++++++++++++++++++---,,,++++++*********+++&&&&&&&&&'''''''''((((((((((((((((((((((((((((((((())))))******))))))(((((((((((('''&&&'''***---+++***)))(((((())))))***))))))(((((((((((()))))))))((('''((()))***)))((((((''''''(((***)))'''%%%))))))))))))))))))))))))))))))))))))))))))))))))''''''((((((((((((((('''))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))************************************+++,,,---,,,***)))***+++)))***++++++,,,,,,++++++)))******+++,,,---......++++++,,,,,,,,,,,,,,,,,,***+++---,,,***)))+++---,,,,,,,,,,,,+++***))))))))),,,//////---,,,---...,,,,,,++++++,,,,,,---...------------........................////////////,,,///111111000///000222000222555888:::===AAADDDDDDEEEGGGGGGFFFFFFGGGHHHEEEGGGJJJMMMOOOQQQQQQQQQMMMLLLKKKIIIGGGEEEDDDCCCEEEEEEFFFHHHJJJMMMOOOQQQUUU\\\ccceeedddeeeiiinnnhhhqqqwwwwwwyyy~~~~~~yyywwwjjjeee]]]VVVQQQOOOPPPQQQRRRUUUYYY]]]___``````___\\\\\\\\\\\\\\\[[[ZZZZZZ[[[[[[[[[[[[[[[YYYTTTQQQKKKJJJHHHFFFEEEDDDDDDEEECCCBBB???<<<888444222000------------------------***************************++++++,,,,,,,,,,,,,,,+++******))))))******+++))),,,///...***((())),,,))))))))))))))))))))))))((()))))))))************(((((()))))))))*********))))))))))))))))))))))))))))))))))))))))))))))))((('''''''''''''''(((((())))))))))))((((((((('''''''''''''''''''''''''''%%%%%%&&&'''((()))******''''''''''''''''''''''''((((((((((((((((((((((((''''''((((((((((((''''''((('''''''''((()))******((((((''''''''''''((((((((((((((((((((((((((((((''''''''''''((((((((()))''''''''''''((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''((((((___aaacccaaa]]]ZZZYYYZZZ]]]^^^^^^]]]\\\[[[\\\]]]RRRKKKAAA888444222111111000///...---------------------------------------,,,,,,---------,,,+++***************************---,,,,,,+++*********+++((()))))))))******++++++))))))))))))))))))))))))((()))***++++++***)))(((''''''''''''&&&(((+++...,,,+++***((((((((())))))******))))))))))))******)))((('''((()))******(((''''''''')))******'''$$$((((((((((((((((((((((((((((((((((((((((((((((((''''''((((((((((((((('''************************))))))))))))))))))))))))))))))))))))************************************+++,,,---,,,***)))***+++++++++,,,------------,,,))))))***+++---...//////+++++++++,,,,,,---------))),,,---,,,***)))+++------------,,,+++***)))((())),,,//////---,,,---...,,,,,,++++++,,,,,,---...---------.........//////............/////////000,,,///222222000000222444222444888;;;>>>AAAFFFIIIEEEFFFGGGFFFDDDCCCDDDEEEKKKLLLNNNPPPQQQPPPNNNMMMJJJIIIIIIHHHHHHHHHIIIIIIIIIIIIIIIJJJLLLOOORRRSSSTTT\\\dddgggeeefffjjjooolllvvv~~~|||ooobbbXXXRRRPPPOOONNNPPPUUUYYY[[[\\\\\\[[[______^^^^^^^^^___```aaa^^^]]]]]]^^^^^^]]]ZZZWWWQQQOOOKKKHHHEEEDDDDDDDDDEEEEEECCC@@@===999666555------------------------,,,,,,,,,,,,,,,,,,,,,,,,+++,,,------......------,,,++++++++++++++++++,,,(((,,,///...***((())),,,))))))))))))))))))))))))(((((())))))*********+++(((((())))))*********+++))))))))))))))))))))))))************))))))))))))***))))))(((((((((((()))))))))))))))(((((((((((((((((((((((((((((((((((($$$%%%&&&'''(((***++++++''''''''''''''''''''''''''''''(((((()))*********''''''((((((((((((''''''''''''''''''(((***++++++((((((''''''''''''((((((((((((((((((((((((((((((&&&'''''''''(((((())))))'''''''''(((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&'''''''''((((((^^^______^^^\\\ZZZZZZ[[[\\\]]]]]]^^^]]]\\\ZZZZZZXXXRRRHHH>>>777222111000000000///...............------------------------------,,,++++++++++++,,,************************************************************))))))))))))((((((((((((((())))))***++++++******))))))(((((())))))))))))))))))))))))***)))(((''''''((()))***)))%%%!!!"""&&&)))(((&&&'''((()))******)))((('''+++*********))))))((((((''''''''''''''''''''''''$$$%%%'''((((((((('''&&&))))))(((((('''''''''&&&(((((((((((())))))))))))******+++******)))((('''))))))))))))************222///,,,)))(((((()))+++///...------++++++***)))---,,,***)))((()))******------------,,,+++******,,,,,,,,,,,,,,,,,,,,,,,,+++******))))))******+++------,,,++++++******))),,,,,,,,,---------......------------------------......///---++++++,,,------...///000111111111111---......------///333666555999???DDDGGGGGGEEEDDDFFFCCC???<<<<<>>???@@@CCCEEE@@@@@@??????@@@AAACCCDDDKKKJJJJJJJJJMMMQQQUUUWWW```ccceeefffggglllvvv~~~}}}~~~{{{ooocccZZZWWWWWWYYYWWWXXXZZZZZZZZZYYYZZZ[[[\\\\\\ZZZXXXTTTPPPLLLIIIBBBAAAAAACCCFFFHHHGGGGGGIIIJJJJJJIIIFFFAAA;;;888222111000///............,,,,,,,,,,,,,,,,,,,,,,,,------,,,+++***)))((((((++++++***))))))))))))***)))))))))))))))))))))))))))))))))))))))))))))))))))******++++++******)))************))))))))))))''''''(((((((((((())))))(((((((((((((((((((((((('''(((((())))))((((((''''''''''''((((((((())))))(((''''''''''''(((((()))''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&)))((((((''''''''''''((()))++++++***(((&&&&&&&&&((((((((((((((((((((((((&&&&&&&&&''''''(((******'''''''''''''''&&&&&&&&&%%%&&&&&&'''((()))******&&&&&&'''(((((('''&&&&&&zzzpppccc\\\[[[^^^aaabbb]]]^^^```aaaaaaaaa``````]]]^^^]]]ZZZTTTJJJAAA<<<333222111000///.................................------,,,++++++++++++,,,************************************************************))))))))))))))))))((((((((()))******((((((((((((((('''''''''))))))))))))))))))))))))))))))(((((((((((())))))%%%&&&((()))))))))***+++***)))(((''''''((()))***((()))))))))************''''''''''''''''''''''''&&&&&&'''((((((((((((((((((((()))))))))*********(((((((((((())))))))))))))))))*********))))))((())))))))))))************+++,,,,,,,,,,,,,,,+++++++++++++++++++++,,,,,,,,,+++++++++++++++,,,------,,,,,,,,,------,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,+++++++++******+++++++++++++++,,,,,,---.........,,,,,,,,,---------......++++++,,,,,,---......///---...///...---...///111///......///111444777999===???AAAAAA@@@@@@AAABBBAAAAAAAAABBBCCCEEEGGGHHHIIIJJJMMMSSSZZZbbbiiimmmwwwwwwuuurrrqqqssswwwzzzwwwyyy|||yyyooogggbbb```\\\]]]]]][[[XXXWWWXXX[[[[[[[[[\\\[[[YYYVVVSSSQQQHHHEEECCCBBBDDDGGGIIIIIIGGGHHHJJJJJJIIIFFFBBB@@@999777555222///...------,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,+++***************)))))))))))))))))))))))))))))))))))))))))))))))))))***++++++++++++***)))***))))))))))))(((((((((((((((((())))))*********(((((((((((((((((((((((((((((())))))))))))((((((&&&&&&&&&'''''''''(((((('''''''''''''''((())))))((((((((('''&&&&&&&&&%%%$$$%%%&&&&&&'''&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''((((((''''''''''''(((((('''(((******((((((((()))((((((((((((((((((((((((''''''((((((((((((((('''&&&&&&&&&''''''''''''''')))((('''&&&&&&'''((()))&&&&&&'''(((((('''&&&&&&~~~lll```\\\\\\]]]]]]]]]^^^___aaaaaaaaa```___]]]^^^___]]]WWWNNNEEE???555444222111///.........////////////////////////,,,+++******))))))******************************************************************))))))))))))((((((((((((((())))))***))))))(((((('''''''''&&&))))))))))))))))))))))))***)))(((''''''((()))***!!!###%%%&&&''''''((()))***)))(((''''''((()))***(((((())))))*********+++************************&&&''')))*********)))((((((((())))))*********+++(((((((((((())))))))))))'''((()))******++++++***))))))))))))************,,,,,,,,,+++++++++************************************)))((()))***,,,---******+++,,,------------,,,,,,,,,,,,,,,,,,,,,,,,///......------......//////......------,,,++++++,,,,,,,,,---------......++++++,,,,,,---...//////---...///.........000222111000111222444888;;;===@@@BBBCCCBBBAAA??????@@@CCCCCCDDDEEEGGGIIIJJJKKKLLLPPPWWWaaalllwww|||xxxvvvwwwyyyzzz}}}xxxoooiiiccccccaaa\\\XXXVVVXXXZZZYYYZZZ\\\]]]]]][[[XXXWWWMMMIIICCCAAACCCFFFJJJLLLGGGHHHHHHIIIIIIHHHGGGGGG???<<<999444111...---,,,,,,,,,,,,,,,,,,,,,,,,,,,******+++,,,...//////000---,,,++++++******++++++)))))))))))))))))))))))))))))))))))))))))))))))))))***+++,,,,,,+++***))))))(((((((((''''''''''''))))))******++++++++++++(((((((((((((((((((((((((((((())))))))))))((((((%%%%%%%%%&&&&&&&&&'''''''''''''''''''''((()))***))))))((('''&&&&&&%%%%%%%%%&&&((()))))))))((('''&&&%%%%%%$$$$$$%%%%%%&&&(((((((((((((((((((((((('''''''''''''''((())))))$$$&&&((()))))))))+++,,,))))))))))))))))))))))))(((((()))))))))'''&&&%%%%%%&&&&&&''''''(((((((((---+++(((&&&%%%%%%&&&'''%%%&&&'''(((((('''&&&%%%{{{jjjdddbbb___\\\______```aaabbbcccccccccaaa___]]]]]][[[UUUJJJAAA:::777222000111111000...........................************************++++++++++++******)))))))))************+++++++++***)))))))))))))))******)))))))))))))))))))))))),,,++++++***)))(((''''''((((((((((((((((((((((((&&&&&&''''''((()))))))))''''''((()))))))))))))))))))))))))))))))))))))))++++++************++++++)))((('''&&&&&&'''((()))&&&''')))+++++++++******))))))))))))(((((((((((()))((('''&&&&&&'''((()))******))))))))))))******)))************+++++++++++++++***************+++---,,,+++***+++,,,---...++++++++++++++++++++++++,,,,,,,,,---------......,,,,,,,,,,,,,,,,,,,,,,,,,,,---......//////......,,,---------,,,++++++***++++++++++++++++++++++++------------------------+++,,,---...////////////222222333555888<<<@@@BBBAAA@@@===<<<<<<>>>@@@BBBGGGEEEEEEIIIKKKJJJKKKNNNPPPZZZlllyyywwwzzz|||sssiii___[[[[[[\\\WWWVVVYYY]]]]]]ZZZ[[[___XXXRRRJJJEEEFFFHHHJJJJJJHHHHHHIIIIIIHHHGGGEEEDDDIIIEEE???888333111000000///---+++)))))),,,...000,,,,,,------...------,,,,,,,,,------,,,,,,+++***++++++++++++++++++++++++***)))((()))+++,,,,,,+++,,,,,,++++++***)))(((((())))))((((((''''''&&&&&&+++*********))))))(((((())))))))))))))))))))))))&&&'''((())))))((('''&&&&&&'''((())))))((('''&&&'''&&&%%%$$$$$$%%%'''((('''''''''&&&&&&%%%%%%%%%))))))(((((('''''''''&&&'''''''''(((((((((((((((###$$$%%%'''((())))))***))))))(((((('''''''''&&&'''***,,,,,,+++)))(((((((((((((((((((((((((((((((((((('''''''''&&&&&&&&&(((((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''&&&&&&&&&oooccc^^^]]]``````aaaaaabbbbbbccccccbbb```_________ZZZQQQIII???999333000222222000...........................++++++++++++++++++++++++++++++++++++*********))))))************+++++++++,,,+++++++++++++++,,,,,,))))))))))))))))))))))))+++*********)))(((((((((((((((((((((((((((((((((***))))))(((''''''&&&&&&''''''((())))))))))))))))))))))))))))))))))))))))))((((((''''''(((((()))***)))(((((((((((()))***))))))*********))))))((())))))))))))(((((((((((((((((()))******)))((((((,,,+++***))))))(((((()))************++++++++++++,,,,,,+++++++++++++++,,,,,,++++++++++++,,,------+++++++++++++++++++++++++++,,,,,,,,,,,,---------,,,,,,,,,,,,,,,,,,,,,,,,,,,------.....................//////......---,,,------------------------........................------...///000000111222222333666:::===???AAAAAABBBAAA@@@???@@@AAACCCDDDGGGFFFFFFGGGGGGHHHQQQZZZgggooo{{{yyymmmbbbYYYTTTTTTTTTWWW\\\]]]ZZZZZZ]]]]]]XXXQQQLLLKKKJJJIIIHHHJJJKKKKKKKKKJJJHHHGGGFFFFFFEEEAAA>>>:::666444333111000///---,,,,,,,,,,,,,,,,,,------...---------,,,,,,------,,,,,,+++***++++++++++++++++++++++++,,,*********,,,---,,,+++,,,,,,++++++***))))))((())))))((((((((((((((((((************)))))))))((())))))))))))))))))))))))''''''((((((((((((''''''''''''((((((((((((''''''((('''&&&%%%$$$%%%'''(((((((((''''''&&&&&&&&&&&&)))(((((((((''''''''''''******)))((('''&&&&&&%%%$$$$$$&&&'''(((((()))))))))((((((((('''''''''''''''))),,,,,,***((((((((((((((((((((((((((((((((())))))((((((((('''''''''((((((((((((((((((((((((''''''''''''''''''''''''(((((('''''''''&&&&&&&&&kkkbbbbbbbbbaaaaaaaaaaaaaaabbbbbbaaa``````aaabbb^^^WWWRRRFFF===333000222444111...........................------------------------++++++++++++************)))************+++++++++,,,,,,+++++++++++++++,,,))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))***))))))((((((''''''&&&''''''((()))))))))))))))))))))))))))))))))))))))(((''''''&&&&&&''''''(((******))))))))))))******,,,+++***)))(((((((((((((((((((((((())))))))))))''')))+++------+++)))'''---,,,+++***)))(((((((((************+++++++++,,,---,,,,,,+++,,,,,,------***++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---.....................//////......------//////////////////////////////////////////////////////...///000222444555333666;;;???BBBBBBAAA@@@<<<===>>>???AAABBBCCCDDDGGGGGGGGGFFFEEEKKK[[[lllooo]]]RRRQQQPPPSSSZZZ\\\[[[\\\___bbb___ZZZVVVSSSPPPLLLIIINNNNNNNNNMMMLLLJJJIIIHHHDDDDDDDDDDDDAAA>>>:::888333333222000///---,,,++++++,,,------.........---,,,,,,------,,,,,,+++***++++++++++++++++++++++++---,,,++++++,,,---,,,***,,,,,,++++++***)))))))))(((((())))))))))))))))))************))))))))))))))))))))))))))))))))))))((((((''''''''''''((((((((((((''''''''''''((((((***)))'''&&&%%%&&&''''''((('''''''''''''''&&&&&&((((((((((((''''''''''''))))))(((((('''''''''&&&%%%&&&&&&'''((((((''''''((((((((((((''''''''''''''')))++++++***((('''((((((((((((((((((((((((((()))))))))))))))(((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''''''''&&&{{{lllgggcccbbbaaa`````````aaabbb```___```aaaaaa___ZZZVVVMMMBBB666000222333111---........................,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++))))))*********++++++++++++***))))))((()))))))))))))))))))))))))))))))))((((((((()))))))))))))))))))))))))))))))))))))))'''''''''((())))))******''''''((()))))))))))))))(((((((((((((((((((((((())))))(((((((((((())))))))))))))))))))))))))))))+++***)))'''''''''((()))(((((((((((())))))))))))((()))+++,,,,,,+++)))(((++++++******))))))***************+++++++++,,,,,,,,,++++++++++++,,,------)))***+++------,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,------------.........------------------------,,,,,,---.........------+++,,,,,,---,,,,,,++++++////////////////////////......////////////000000000///...///000333666888888:::>>>AAABBBAAA@@@???:::;;;>>>AAACCCEEEFFFFFFFFFDDDDDDFFFIIISSSfffwwwkkk]]]SSSPPPPPPUUUZZZ\\\___dddaaaaaa```___]]]XXXTTTQQQQQQQQQPPPOOOMMMLLLJJJJJJDDDEEEFFFFFFEEECCCAAA???777666444222000///......+++,,,------......------,,,,,,------,,,,,,+++***++++++++++++++++++++++++---,,,++++++++++++***)))+++++++++*********))))))(((((())))))******++++++*********)))))))))))))))(((((((((((((((((((((((()))((('''&&&&&&'''((())))))((('''&&&&&&'''((()))+++***)))'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((('''''''''%%%%%%&&&'''((()))***+++&&&'''''''''''''''&&&&&&((((((((((((((('''''''''((()))+++***)))''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''''''''''''''tttgggbbbaaa```___^^^___```aaabbbbbbbbbbbbaaa___\\\YYYRRRGGG:::333222333000---........................,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++++++++,,,))))))*********++++++++++++******)))(((((())))))))))))))))))))))))))))))((((((((((((((()))))))))))))))))))))))))))))))))''''''(((((()))*********''''''((()))))))))))))))(((((((((((((((((((((((())))))(((((((((((())))))(((((((((((((((((((((((()))((('''''''''(((***+++'''((((((((()))))))))******))))))(((((())))))***))))))))))))***,,,------***++++++++++++,,,,,,,,,***************+++,,,,,,)))***+++,,,---,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,............////////////------------------------+++,,,,,,---...---------++++++,,,,,,---,,,,,,+++........................------........./////////000/////////111444777999?????????>>>????????????AAABBBEEEGGGHHHHHHHHHGGGDDDAAABBBIIIRRR]]]kkkwww{{{|||~~~}}}qqq```XXXRRRRRRTTTVVV[[[___\\\^^^bbbcccccc```^^^\\\UUUTTTSSSQQQOOOMMMLLLKKKIIIHHHFFFEEEDDDDDDEEEFFFBBB???:::555111///......,,,------......------,,,,,,,,,------,,,,,,+++***++++++++++++++++++++++++,,,***))))))******)))'''+++++++++***************(((((())))))******++++++))))))))))))))))))******(((((((((((((((((((((((()))((('''&&&&&&'''((())))))((('''&&&&&&'''((()))******)))((('''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&'''''''''(((((((((((((((%%%%%%&&&'''((()))***+++'''''''''(((''''''&&&%%%'''''''''(((((((((((((((((()))******(((''''''(((((((((((((((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((yyyfff```___^^^\\\]]]^^^```aaaeeeeeeeeedddbbb```^^^]]]WWWNNNBBB999555333111///........................++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,)))************+++++++++------,,,+++************))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))+++******))))))(((((('''''''''((()))))))))))))))))))))))))))))))))))))))(((''''''&&&&&&''''''(((''''''((((((((((((''''''''''''''''''((()))***+++''''''(((((())))))*********)))(((''''''((()))***''''''((()))+++---///000++++++++++++,,,,,,,,,,,,))))))))))))***+++,,,,,,)))******+++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,---.........////////////------------------------++++++,,,---------------------......//////..............................---------......//////000000000111222444777:::;;;AAA@@@>>><<<<<<>>>@@@AAAFFFGGGHHHIIIIIIHHHGGGFFFJJJGGGJJJSSS]]]eeennnvvvwww|||sssggg[[[VVVTTTSSSTTTWWWXXX\\\aaadddddddddddddddZZZXXXVVVTTTQQQPPPOOONNNOOOLLLHHHEEEDDDEEEGGGIIIMMMIIIDDD===777111...,,,............---,,,++++++,,,,,,------,,,,,,+++***++++++++++++++++++++++++***)))(((((()))***((('''************************(((((())))))))))))))))))))))))))))))************))))))))))))))))))))))))((((((''''''''''''((((((((((((''''''''''''(((((((((((((((((('''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&'''''''''((((((((((((((())))))(((((('''''''''&&&&&&'''''''''''''''&&&&&&'''''''''(((((((((((((((((()))***)))'''&&&'''(((((((((((((((((((((((((((&&&&&&&&&&&&''''''''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((()))))))))jjj^^^]]][[[ZZZ[[[]]]___aaaccccccdddcccaaa`````````[[[UUULLLAAA999444333333........................------------------------+++++++++,,,,,,,,,------)))************+++++++++...---,,,+++************)))))))))))))))))))))))))))))))))((('''''''''&&&((((((((((((((((((((((((++++++******)))(((((((((''''''((())))))))))))))))))))))))))))))))))))))))))((((((''''''(((((()))'''((())))))))))))((('''''''''(((((((((((((((((('''''''''((()))*********************************(((((()))***+++---...///+++++++++,,,,,,,,,------************+++,,,------***************++++++,,,------------------------,,,,,,,,,,,,---------...........................++++++,,,------------,,,,,,---......//////..............................---......///000000111111111222444666999;;;===>>>???>>>======>>>AAACCCEEEGGGHHHJJJLLLNNNPPPQQQRRRZZZZZZ___eeejjjmmmttt|||~~~xxxkkkddd```[[[WWWXXXYYY]]]```bbbbbbbbbdddfff___]]][[[XXXUUUSSSRRRRRRTTTQQQLLLHHHFFFFFFGGGHHHOOONNNLLLGGGAAA:::444000000000///...---+++***))),,,,,,------,,,,,,+++***++++++++++++++++++++++++***)))((((((***+++***)))************************))))))((((((((((((((((((((()))))))))************))))))))))))))))))))))))''''''((((((((((((''''''''''''((((((((((((''''''&&&&&&'''''''''&&&&&&&&&''''''''''''(((((())))))''''''''''''((((((((()))******)))((('''&&&&&&%%%&&&&&&'''''''''''''''&&&''''''''''''((((((((()))((())))))(((&&&&&&'''(((((((((((((((((((((((((((&&&'''''''''(((((((((((((((((((((((((((((((((((('''''''''''''''''''''''''''((((((((())))))))))))rrr]]][[[ZZZYYYZZZ\\\___aaa___`````````___^^^___```^^^ZZZRRRGGG<<<555555666................................................+++++++++,,,,,,---------)))************+++++++++,,,+++***)))(((((((((((())))))))))))))))))))))))******)))((('''&&&&&&%%%((((((((((((((((((((((((((((((((()))******++++++'''(((((()))))))))))))))))))))))))))))))))))))))++++++************++++++((()))***++++++***)))((((((((()))))))))'''&&&%%%&&&''''''((()))******+++)))***,,,......,,,***)))************+++,,,------++++++,,,,,,,,,---------++++++++++++,,,---...///+++***)))))))))***,,,---------------------------******+++++++++,,,,,,,,,........................++++++,,,---------,,,,,,***++++++,,,---------,,,////////////////////////...//////000111222222222333444777:::<<<>>>???@@@<<<<<<===???AAADDDGGGHHHIIIKKKOOOUUUZZZ```dddfffiiilllrrruuutttsss{{{~~~vvvqqqmmmfffaaa___\\\^^^aaa```______bbbeeecccaaa^^^ZZZXXXVVVUUUUUUVVVTTTPPPLLLHHHGGGGGGGGGKKKMMMOOOOOOKKKCCC;;;666111111000...---+++)))(((,,,,,,---------,,,++++++++++++++++++++++++++++++***)))((()))+++,,,,,,+++******************++++++))))))((((((''''''&&&&&&(((((())))))*********+++))))))))))))))))))))))))&&&'''((())))))((('''&&&&&&'''((())))))((('''&&&%%%%%%&&&&&&'''&&&&&&&&&(((((())))))******++++++&&&'''''''''(((((())))))'''''''''(((((((((((((((%%%&&&&&&'''((((((''''''&&&'''''''''(((((())))))((())))))(((&&&&&&''')))(((((((((((((((((((((((('''((((((((())))))******(((((((((((((((((((((((((((((((((((((((((((((((('''((((((((())))))******nnn```\\\YYY[[[[[[YYYZZZ]]]\\\^^^aaaccccccaaa^^^\\\\\\[[[VVVMMMAAA777111000...///////////////......------------------------''')))***,,,,,,+++***)))************************,,,,,,,,,,,,,,,,,,,,,,,,************************''''''''''''((((((((((((+++(((%%%&&&(((******)))++++++******))))))((((((+++***)))(((((()))***+++))))))(((((((((((())))))''''''((((((((((((''''''++++++******))))))((((((''''''(((((())))))***************)))))))))))))))+++***)))(((((()))***+++(((((((((((())))))))))))+++++++++***************++++++++++++++++++++++++---,,,,,,++++++,,,,,,---------++++++++++++---------...//////000000//////.................................------,,,,,,,,,......////////////......000000...------...///000000///---,,,---///111222555888<<<>>>?????????@@@===>>>@@@CCCEEEFFFGGGFFFOOOWWWcccnnntttwwwxxxyyyyyy~~~|||xxxuuusssnnnggg```]]]]]]^^^```ccccccbbbaaa___]]][[[ZZZYYYWWWVVVUUURRROOOKKKHHHGGGMMMOOOQQQQQQNNNHHHBBB>>>444222000.........,,,++++++,,,,,,,,,,,,+++******++++++++++++++++++++++++,,,,,,,,,++++++*********+++*********))))))(((((((((((())))))******++++++))))))(((((((((((())))))******))))))((((((''''''************************(((((((((((((((''''''''')))))))))(((''''''&&&&&&******))))))((((((''''''(((((((((((((((((((((((())))))(((((((((((()))))))))((('''&&&&&&'''((()))))))))((((((''''''&&&&&&)))))))))(((''''''&&&&&&))))))))))))))))))))))))''''''''''''''''''''''''$$$%%%%%%&&&&&&''''''(((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((lll[[[WWWVVVXXXYYYXXXZZZ]]]]]]___bbbdddeeedddaaa```]]]\\\XXXPPPEEE:::444111...////////////......---------------------------***************+++,,,,,,************************************************************************((((((((()))))))))******)))'''%%%&&&)))++++++************)))))))))))))))((((((''''''''''''(((((())))))(((((((((((())))))(((((())))))))))))(((((())))))))))))))))))((((((((((((((()))))))))))))))***)))))))))))))))))))))+++***)))(((((()))***+++(((((((((((()))))))))******************+++++++++++++++++++++++++++++++++...---,,,+++++++++++++++---,,,,,,++++++,,,,,,---++++++,,,------------,,,..............................---------,,,,,,,,,......////////////......000//////.........//////000///......///000222444888;;;???@@@@@@@@@@@@AAA@@@CCCFFFFFFFFFIIIOOOTTT```iiiwww||||||~~~vvvkkkccc^^^\\\\\\\\\_________^^^^^^]]]\\\\\\YYYXXXWWWTTTQQQNNNKKKJJJKKKMMMPPPRRRQQQMMMIIIEEE===999333///.........---,,,,,,---------,,,,,,,,,++++++++++++++++++++++++,,,,,,,,,+++++++++******)))))))))***************************++++++++++++))))))(((((((((((())))))******))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))***)))))))))(((((((((''''''''''''''''''''''''''')))((((((''''''(((((()))(((((('''&&&&&&'''((((((((((((((((((((('''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&''''''''''''(((kkk\\\VVVTTTVVVXXXXXXYYY\\\\\\^^^aaacccddddddbbbaaa]]]]]][[[UUUKKK@@@888444/////////......------------------------------------,,,***))))))+++---///++++++++++++++++++++++++************************************************)))))))))*********++++++((('''&&&''')))++++++***))))))))))))************''''''((((((((((((''''''))))))(((((((((((())))))))))))************))))))(((((((((((((((((())))))))))))))))))))))))(((((())))))))))))))))))************))))))))))))******((((((((()))))))))******))))))******++++++,,,,,,++++++++++++,,,,,,,,,,,,,,,++++++******+++,,,,,,---,,,,,,++++++,,,,,,---******+++,,,,,,,,,,,,,,,...........................------------,,,,,,,,,......////////////.........//////000000///////////////000111222555777888===???BBBCCCBBBAAABBBBBBAAAEEEGGGFFFEEEKKKXXXdddrrrzzz~~~}}}}}}}}}zzzmmmeeeaaa]]]YYY[[[\\\]]]___```aaaaaaaaa\\\\\\[[[YYYVVVRRROOOMMMHHHKKKOOORRRTTTSSSQQQOOOHHHBBB999333000000000000------------------------,,,,,,,,,,,,++++++++++++,,,,,,,,,++++++++++++***((())))))******+++,,,,,,,,,,,,,,,+++++++++++++++))))))))))))))))))))))))***))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((()))***+++++++++))))))))))))(((((((((((((((((((((((((((((((((((((((''''''''''''''''''(((''''''&&&&&&&&&&&&'''''''''''''''(((((((((((((((&&&&&&'''(((((()))******(((((((((((((((((((((((())))))))))))))))))))))))((((((''''''&&&%%%%%%$$$''''''''''''''''''''''''&&&&&&&&&''''''''''''(((ooobbb[[[UUUVVVWWWVVVWWWYYY[[[]]]___aaaaaa```___^^^\\\]]]\\\XXXPPPFFF<<<666111000///...---------,,,---------------------------,,,+++++++++,,,---...++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,************************)))))))))*********++++++)))((((((((())))))))))))(((((())))))******++++++((()))***++++++***)))((())))))(((((((((((())))))((())))))******))))))(((&&&&&&''''''(((((())))))+++******))))))((((((((()))))))))))))))************))))))))))))))))))***(((((()))))))))*********))))))******+++,,,------+++++++++,,,,,,,,,,,,,,,)))))))))***+++,,,......,,,,,,,,,,,,,,,,,,,,,,,,+++,,,------......------........................------------------------......////////////......---...000111111000///...---...111444777;;;===>>>???AAACCCDDDBBBBBBBBBCCCCCCEEEFFFFFFIIITTTeeerrr}}}~~~}}}|||||||||tttooofff^^^XXXYYY\\\^^^aaacccddddddaaaaaa```]]]ZZZUUURRROOOHHHKKKNNNRRRTTTUUUUUUUUUNNNIIIAAA:::666333111000......------------......,,,,,,,,,,,,,,,+++++++++++++++++++++++++++++++++******++++++++++++++++++,,,,,,,,,++++++******))))))))))))******)))))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((()))))))))((((((((())))))*********))))))))))))(((((((((((())))))))))))))))))))))))''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&''''''(((((())))))''''''(((((())))))))))))''''''''''''''''''''''''((((((((((((((((((((((((((('''''''''&&&&&&&&&%%%''''''''''''''''''''''''&&&&&&&&&''''''''''''((({{{hhh^^^VVVUUUVVVVVVVVVXXX]]]^^^___``````___]]]\\\\\\]]]]]][[[TTTKKK@@@999333222000///------------------------------------***+++,,,---...---,,,,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,************************((((((((()))))))))******)))******)))((('''''''''(((((())))))******++++++((()))***++++++***)))((())))))(((((((((((())))))'''(((((())))))(((((('''&&&&&&''''''(((((())))))++++++******))))))(((((((((((())))))************)))))))))******)))))))))))))))))))))************))))))***+++,,,------...++++++,,,,,,,,,---------+++++++++***++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++,,,------......------........................------------------------......////////////......---...000111111111000///,,,///333888===@@@CCCDDD@@@BBBCCCCCCBBBAAABBBCCCGGGFFFFFFJJJSSSbbbqqq{{{}}}~~~qqqcccUUUVVVXXXZZZ\\\___aaabbbeeeeeedddaaa]]]XXXSSSPPPKKKLLLNNNPPPSSSTTTUUUVVVPPPMMMHHHDDD???:::444000000///...------------...---------,,,,,,,,,++++++++++++++++++++++++++++++...------,,,+++******)))++++++******)))))))))((())))))************))))))))))))))))))************))))))))))))))))))))))))(((((((((((())))))******)))))))))(((((('''''''''(((((((((((())))))))))))((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&''''''(((((())))))******))))))((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&''''''(((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((rrrfffYYYUUUVVVWWWXXX[[[___```aaaaaaaaaaaa```___]]]]]]^^^]]]XXXOOOEEE===555444222///...------...------------------------(((***,,,......---+++***,,,,,,,,,,,,,,,,,,,,,,,,************************************************((((((((()))))))))******(((***+++***((('''''''''))))))))))))************''''''((((((((((((''''''))))))(((((((((((())))))''''''((((((((((((''''''(((((((((((((((((())))))******************))))))((((((((()))******++++++))))))************)))))))))))))))*********++++++******++++++,,,,,,------++++++,,,,,,------......000///...,,,+++***))))))+++,,,,,,------,,,,,,+++******+++,,,,,,,,,,,,,,,........................,,,,,,,,,------------.........////////////............///000111111111111///222777<<>>>>>@@@BBBBBBBBBAAABBBDDDFFFEEEEEEGGGMMMQQQXXXbbbjjjmmmooowwwvvvppphhhbbb]]]ZZZXXXVVV[[[ZZZ[[[]]]___aaa```^^^^^^[[[VVVRRRQQQSSSVVVYYYYYYZZZYYYUUUPPPLLLLLLMMMFFFAAA999333000000111111...---,,,,,,...///...,,,,,,,,,------,,,,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++***)))((((((************************++++++++++++++++++++++++))))))))))))************---+++)))((('''((()))***)))))))))(((''''''&&&&&&***((('''&&&&&&'''(((***((((((((((((((((((((((((''''''((((((((((((''''''******))))))((((((''''''((((((((((((((('''''''''''''''''''''((((((((()))))))))))))))))))))))))))(((((((((((((((((((((((())))))(((((((((((())))))(((((((((((((((((((((((())))))))))))))))))))))))vvveee\\\ZZZXXXYYYZZZ[[[\\\^^^aaaccc_________^^^\\\YYYWWWVVVHHH@@@777222222222111///,,,------......------,,,---,,,,,,,,,,,,,,,,,,---++++++++++++++++++,,,---------,,,++++++++++++++++++++++++************)))+++++++++*********))))))+++***))))))((((((((()))+++***)))************)))(((((((((((())))))))))))(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))((()))***,,,,,,+++***)))*********+++++++++++++++)))************+++++++++)))***,,,+++******+++---.........---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------............///......------------......---...//////------.../////////...------...///000...///000222555888:::<<<@@@???>>>>>>@@@AAACCCCCCDDDFFFHHHHHHIIIMMMUUUZZZfffmmmssswww~~~}}}uuunnniiifffcccaaa^^^]]]\\\[[[\\\^^^aaacccbbb___\\\XXXVVVVVVWWWXXXZZZ[[[[[[WWWQQQMMMKKKKKKHHHDDD>>>999666333111000000///------......---,,,,,,,,,------,,,,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,++++++******)))(((((('''************************************************))))))))))))************,,,+++)))((('''((()))***''''''(((((((((((((((((()))((('''&&&&&&'''((()))))))))))))))))))))))))))(((((())))))))))))(((((())))))))))))(((((((((((((((((((((((((((((((((((('''''''''((((((((())))))))))))))))))))))))))))))(((((((((((((((((((((((()))((('''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((uuufff___YYYYYYZZZ[[[\\\^^^___```]]]]]]^^^^^^]]]\\\[[[ZZZMMMEEE;;;555222222111///......------------......,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++***,,,,,,------,,,,,,+++***+++++++++************)))+++************)))))))))++++++***))))))))))))******)))))))))))))))***+++(((((((((((())))))))))))''''''''''''''''''''''''))))))))))))))))))))))))))))))))))))))))))))))))((()))***+++,,,+++************************)))))))))************+++++++++)))***++++++******+++---//////............------,,,,,,,,,,,,,,,,,,,,,,,,------------------------,,,,,,,,,,,,,,,,,,,,,,,,---------............///......------------......---...//////------...//////.....................,,,...111555888;;;===>>>???>>>======>>>AAACCCEEEEEEHHHKKKMMMOOOTTT\\\bbblllrrrxxx}}}yyyvvvsssqqqllljjjfff```\\\]]]bbbgggeeedddbbb```]]][[[ZZZYYY[[[]]]]]]ZZZUUUOOOKKKIIIIIIGGGDDDAAA>>>999333///222000...---......,,,+++,,,,,,------,,,,,,+++***++++++++++++++++++++++++*********)))((((((''''''************************))))))))))))))))))))))))))))))))))))************++++++)))((((((((()))***&&&&&&'''(((((()))******)))((('''&&&&&&'''((()))************************))))))************))))))(((((((((((())))))))))))((((((((((((((((((((((((''''''((((((((()))))))))))))))))))))))))))))))))(((((((((((((((((((((((((((((('''&&&&&&&&&&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''wwwggg[[[ZZZZZZZZZ\\\]]]^^^^^^]]]]]]^^^______^^^\\\[[[RRRJJJ@@@777333111000//////...---,,,,,,---...///,,,------------------,,,,,,---......---+++***((('''(((***,,,------,,,,,,+++++++++*********))))))************))))))))))))++++++***************+++((()))(((((('''((()))+++(((((((((((())))))))))))(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))((()))***++++++++++++***+++*********)))((((((((())))))*********+++++++++)))***++++++******+++,,,............------------------------------------........................---------------------------------............///......------------......---///000///...---...///....../////////...------,,,...222666999<<<=========>>>??????@@@AAADDDFFFFFFJJJOOORRRTTTXXX^^^bbbiiisssyyyoooddd___bbbfffcccdddddddddbbb```]]][[[]]]^^^___]]]XXXRRRLLLIIIGGGGGGHHHHHHEEE???888222333000...------...---,,,,,,,,,------,,,,,,+++***************************+++*********)))))))))(((************************************************((()))))))))************+++***)))(((((()))******''''''(((((()))))))))))))))(((''''''''''''((()))))))))))))))))))))))))))((())))))******))))))(((''''''(((((())))))******((((((((((((((()))))))))'''(((((((((((()))))))))(((((((((((((((((((((((((((((((((((((((((((((((())))))((('''&&&&&&&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''ppp___]]]ZZZZZZ[[[]]]]]]\\\______``````___^^^\\\[[[UUUNNNDDD;;;444111////////////---,,,,,,---//////,,,------......------,,,---.........---+++)))(((%%%''')))+++,,,,,,+++++++++++++++*********))))))))))))))))))))))))))))))+++***************++++++'''((()))((('''&&&(((***(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))******+++++++++++++++*********)))((((((((())))))*********+++++++++(((***++++++***)))+++,,,,,,,,,,,,,,,,,,,,,,,,---------------------------........................---------------------------------............///......------------.........///000///......///000...//////000000///......111333666999;;;=========:::===AAACCCCCCCCCEEEFFFIIINNNTTTWWWXXXZZZ]]]```jjj{{{oooccc______^^^```bbbccccccbbb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|||eee```ZZZYYY[[[]]]]]]]]]aaaaaaaaaaaa```^^^]]][[[WWWRRRIII@@@888333111000//////............//////,,,---...//////...---,,,............---,,,*********************))))))(((+++++++++************)))(((((()))))))))))))))******))))))))))))***++++++'''***---,,,)))'''(((***(((((((((((())))))))))))************************))))))))))))))))))))))))))))))))))))))))))))))))***************+++++++++******************)))))))))************+++++++++((()))******))))))***,,,+++++++++,,,,,,,,,,,,------------------------------------------------------------------------------------............///......------------.........///000000......///000//////000000000111111111888999;;;===>>>???@@@@@@:::>>>CCCDDDDDDDDDGGGJJJOOOSSSXXX[[[\\\___dddhhhsssyyyjjj```\\\ZZZ[[[]]]___aaaaaaaaa```^^^^^^______^^^ZZZTTTPPPHHHHHHIIIJJJJJJGGGBBB???777444111//////000000///,,,,,,------,,,,,,+++***++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,************************++++++++++++++++++++++++))))))))))))************))))))))))))************++++++***))))))(((''''''((((((((((((((((((((((((''''''''''''''''''''''''''''''((((((((((((''''''(((((((((((())))))))))))'''(((((())))))******+++((((((((()))))))))******))))))))))))))))))))))))(((((((((((((((((((((((())))))(((((((((((())))))((((((((((((((((((((((((''''''''''''''''''''''''iiiccc[[[XXXZZZ]]]^^^^^^```aaaaaabbbaaa```^^^]]]YYYVVVOOOFFF===777333222......////////////......,,,---...//////...---,,,///...---,,,,,,,,,,,,,,,---,,,,,,++++++++++++++++++++++++************)))(((((((((((())))))******)))((((((((())))))***+++***...222111---))))))***(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))***************++++++,,,*********+++++++++++++++)))************+++++++++((()))******))))))***+++,,,,,,,,,,,,------..............................,,,,,,,,,,,,,,,,,,,,,,,,........................---------............///......------------.........000111000///...///000000000///000111222444555;;;;;;<<<===???@@@BBBCCC>>>AAACCCBBBAAADDDJJJPPPVVVXXX[[[]]]aaahhhssszzzuuujjjdddYYYYYYZZZ[[[]]]___```bbb]]]]]]]]]___```^^^YYYUUUOOOMMMKKKIIIIIIHHHFFFDDD???;;;666333222111000///,,,,,,------,,,,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++************************************************))))))))))))************(((((()))*********************))))))))))))))))))''''''((((((((((((''''''(((((((((((((((((((((((((((((())))))))))))(((((())))))))))))(((((((((((('''(((((()))******++++++(((((()))))))))*********))))))))))))))))))))))))(((((((((((((((((((((((('''''''''''''''((()))***((((((((((((((((((((((((((((((((((((((((((((((((mmmddd[[[WWWYYY]]]_________```aaabbbbbbaaa```___[[[XXXRRRJJJAAA999555444---...///000000///...---,,,---///000000///---,,,///...---,,,+++,,,---...,,,+++++++++,,,...000111+++++++++************)))'''((((((((())))))******(((((('''(((((()))******,,,111666555000+++***+++(((((((((((())))))))))))(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))******))))))******+++,,,*********+++,,,,,,,,,---)))************+++++++++((()))******))))))***+++---------.........//////........................,,,,,,,,,,,,,,,,,,,,,,,,........................---------.........//////.........------............000111000///...///111111000//////111333666888:::::::::;;;===@@@BBBDDDBBBCCCCCC@@@???CCCMMMUUU[[[\\\]]]^^^dddpppvvvoooZZZZZZYYYYYYZZZ]]]```bbb]]]\\\\\\^^^aaa```\\\XXXUUUQQQLLLIIIHHHHHHHHHGGGEEEAAA;;;666444222000///,,,,,,---------,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,******************++++++************************))))))))))))))))))))))))))))))))))))************'''((()))***************((((((((()))******++++++''''''((((((((((((''''''))))))))))))))))))))))))))))))************))))))******))))))(((((('''''''''(((((()))***+++++++++))))))))))))************))))))))))))))))))))))))((((((((((((((((((((((((%%%%%%%%%&&&'''((()))***(((((((((((((((((((((((())))))))))))))))))))))))yyyggg[[[[[[]]]YYYYYY___]]]\\\\\\___bbbccc```]]]\\\\\\[[[SSSHHH===666333333111...---------,,,***......---------,,,,,,,,,******+++++++++,,,,,,,,,......---------,,,,,,,,,,,,,,,++++++***)))(((((())))))***++++++++++++***++++++*********+++---...777IIIQQQDDD444...,,,)))+++*********))))))((((((,,,,,,,,,++++++***************+++++++++,,,,,,,,,************************))))))))))))))))))))))))************************************************************************222000......000000...++++++++++++,,,,,,,,,------...---,,,++++++,,,---...//////.........---------------..............................////////////...------......///111111111111222222222444888<<<::::::;;;===@@@CCCCCCCCCAAA@@@??????AAAHHHPPPVVV[[[^^^ccckkkwwwooofff]]]ZZZ\\\^^^[[[WWW[[[\\\^^^___```aaabbbccc\\\XXXQQQJJJEEEDDDEEEFFFGGGFFFBBB<<<666222111111000...---,,,------,,,+++,,,,,,,,,++++++,,,------******,,,------,,,******************************))))))))))))***+++,,,,,,************))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((())))))))))))(((((())))))))))))))))))))))))))))))))))))))))))))))))''''''''''''''''''''''''%%%%%%&&&'''((()))******(((((())))))*********+++************))))))))))))******))))))((((((''''''&&&&&&'''((()))***++++++))))))))))))))))))))))))$$$&&&(((******)))((('''ssscccWWWXXX[[[YYYZZZ```aaa```___```aaa```]]]YYY[[[\\\[[[UUUKKK@@@888444333111///.........---,,,......---------,,,,,,,,,***++++++++++++,,,,,,,,,......---------,,,,,,,,,,,,,,,++++++***))))))((())))))***++++++++++++***++++++*********+++,,,---:::GGGJJJ===///+++***(((************)))))))))(((+++++++++******)))))))))*********+++++++++,,,,,,************************))))))))))))))))))))))))************************************************************************...,,,***+++,,,---+++))),,,,,,---------...............------------............---------,,,,,,,,,....................................////////////111111000000/////////...111222444444444666999<<<>>>>>>>>>@@@BBBCCCDDDDDDDDDCCCBBBAAACCCIIIRRRXXX___eeennnzzz{{{mmmaaaZZZXXXYYY[[[ZZZZZZ\\\^^^aaabbbbbbaaa]]]YYYSSSMMMHHHFFFFFFGGGHHHGGGEEEAAA===888333000111///------.........------,,,,,,++++++,,,,,,---++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++*********++++++,,,************))))))))))))************************))))))))))))))))))))))))))))))************))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((('''''''''(((((((((((((((''''''(((((())))))))))))************))))))))))))***)))))))))((((((((('''(((((((((((())))))))))))))))))))))))))))))))))))&&&'''((()))))))))((('''qqqbbbWWWWWWYYYXXXZZZ___aaaaaa```aaaaaa___\\\YYYZZZ\\\\\\WWWNNNDDD;;;777444222///...//////...---......---------,,,,,,,,,++++++++++++,,,,,,,,,,,,......---------,,,,,,,,,,,,,,,++++++***)))))))))))))))***++++++++++++***+++************+++,,,,,,777>>>>>>333******+++)))************))))))))))))*********)))))))))))))))*********++++++++++++,,,))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************************************************+++***)))***+++,,,+++***---------.........//////.........//////.........---------,,,,,,,,,,,,,,,....................................////////////000000111111111000//////222444777888888999;;;===>>>>>>>>>>>>???@@@AAAAAABBBBBBAAAAAADDDJJJRRRXXXfffpppsssbbbZZZ[[[___\\\ZZZZZZ]]]aaacccaaa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zzztttggg\\\YYYYYYXXXYYY]]]^^^^^^```aaabbbaaa___]]]ZZZ\\\\\\ZZZSSSIII@@@:::555222///......///............---------,,,,,,,,,+++++++++,,,,,,,,,------......---------,,,,,,,,,+++++++++*********))))))))))))***++++++++++++*********************++++++...222111+++))),,,---+++*********)))))))))))))))******************))))))************++++++++++++(((((((((((((((((((((((())))))))))))))))))))))))((((((((((((((((((((((((************************************************+++++++++,,,---.........------------............---...///000000///...---------------------------////////////........................////////////+++,,,...000222222222222444777:::=========>>>>>>@@@@@@@@@???>>>>>>@@@AAACCCCCCDDDFFFKKKSSS\\\bbbssswwwkkkggggggeeeaaa\\\\\\___bbbbbb``````^^^[[[XXXSSSOOOLLLJJJKKKIIIGGGIIILLLIIIBBB;;;444222///......//////...------,,,+++++++++,,,,,,......,,,++++++,,,......,,,,,,,,,,,,,,,,,,,,,,,,......---,,,++++++++++++************)))))))))(((************************)))))))))))))))))))))))))))******++++++******)))(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))((((((((((((((('''''''''((((((((((((((((((((((((************)))))))))((())))))))))))(((((((((((())))))))))))((((((((((((((((((((((((((((((((((((+++***)))(((''''''((((((}}}zzzxxxmmmbbb[[[YYYXXXYYY\\\]]]___aaabbbbbbaaa______[[[\\\]]][[[WWWNNNEEE???666333///------......---......---------,,,,,,,,,++++++,,,,,,,,,---------......---------,,,,,,,,,+++++++++***************))))))***++++++++++++***************************(((******)))+++---,,,((())))))))))))))))))******++++++++++++++++++++++++))))))*********+++++++++(((((((((((((((((((((((())))))))))))))))))))))))((((((((((((((((((((((((************************************************++++++,,,---......///000+++,,,,,,,,,,,,------------...///000000///...---............////////////000000/////////.....................////////////***+++---///111222333333777:::>>>AAAAAAAAAAAAAAADDDEEEEEECCCAAAAAADDDFFFHHHJJJNNNSSSZZZdddooovvv|||wwwoooeee___^^^___aaabbbaaa```___\\\XXXTTTPPPNNNMMMIIIGGGHHHMMMNNNJJJFFF999555111///.........---...---,,,,,,+++++++++,,,......,,,++++++,,,......++++++++++++++++++++++++......---,,,++++++++++++************)))))))))(((************************))))))))))))))))))))))))(((((())))))))))))((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&''''''((())))))***))))))))))))))))))))))))************)))))))))((((((((((((((())))))))))))'''''''''((()))*********((((((((((((((((((((((((+++***)))(((((((((((((((yyyyyywwwkkkaaa\\\[[[[[[]]]___aaaccccccaaa___^^^^^^\\\\\\]]]\\\YYYSSSKKKEEE999666111...---...------......---------,,,,,,,,,,,,,,,,,,,,,------------......---------,,,,,,,,,************************))))))***++++++++++++************+++******)))((())))))***+++++++++(((%%%))))))))))))************+++++++++++++++,,,,,,,,,)))))))))************+++))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************************************************(((***,,,,,,+++,,,---///+++++++++,,,,,,,,,------.........//////.........///////////////000000000111000000//////.....................////////////.........///000111222333:::===AAACCCDDDDDDDDDEEECCCEEEEEEDDDAAABBBFFFJJJNNNQQQWWW___iiiuuuuuuiii```]]]___aaaaaaaaa```^^^[[[XXXUUUSSSMMMJJJGGGHHHKKKMMMMMMLLL@@@<<<666222000///---,,,......---,,,++++++++++++------,,,,,,,,,,,,------************************---,,,,,,++++++++++++,,,************))))))))))))++++++++++++++++++++++++))))))))))))))))))))))))(((((())))))))))))(((((())))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((%%%%%%&&&'''((()))******************))))))))))))************))))))))))))(((((((((((())))))))))))&&&&&&'''((()))***++++++))))))))))))))))))))))))***)))))))))))))))((((((xxxzzz}}}nnnccc___]]]\\\]]]```ccccccaaa______```^^^]]]\\\\\\[[[VVVOOOIII>>>:::444000//////............---------,,,,,,,,,,,,,,,,,,------------.........---------,,,,,,,,,************************))))))***++++++++++++***)))***++++++***)))((('''))))))***++++++)))((('''((()))))))))************)))*********++++++++++++))))))))))))************************************))))))))))))))))))))))))************************************************************************(((***,,,+++***)))+++---,,,,,,,,,,,,---------.........------------..................//////000000111111000000///......---............////////////222111//////000333666777===@@@CCCEEEEEEFFFGGGHHHFFFHHHIIIHHHFFFGGGMMMRRRZZZ___fffooozzzvvvfff]]][[[]]]aaaaaa```___]]][[[XXXWWWMMMLLLJJJIIIIIIJJJKKKKKKIIIDDD===777333000...---///...---,,,++++++++++++++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++*********++++++,,,************))))))))))))++++++++++++++++++++++++)))))))))))))))))))))))))))))))))******)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))&&&'''''''''(((((())))))******)))))))))(((((((((************))))))))))))'''((((((((()))))))))***''''''(((((())))))******))))))))))))))))))))))))'''((()))***+++***))))))~~~zzzkkkbbb^^^[[[XXX]]]aaacccbbbbbbccceee___]]]\\\\\\[[[XXXQQQLLLAAA===777222111000000///......---------,,,,,,,,,,,,,,,,,,---------............---------,,,,,,,,,******************++++++))))))***++++++++++++***)))***+++++++++)))((('''(((((((((*********+++...(((((())))))*********+++(((((())))))*********+++))))))))))))************************************))))))))))))))))))))))))************************************************************************)))+++---,,,******+++...---------.........//////...---,,,++++++,,,---...---------.........//////222111111000///......---............/////////000111000//////222666;;;>>>???BBBDDDFFFFFFGGGIIIJJJOOOQQQSSSRRRQQQSSSYYY___kkkpppwwwkkk]]]XXXZZZaaaaaa```___^^^\\\ZZZYYYMMMNNNMMMKKKIIIGGGGGGHHHOOOJJJBBB:::555222///---///...---,,,++++++++++++******,,,------,,,******,,,,,,,,,,,,,,,,,,,,,,,,))))))))))))***+++,,,,,,************))))))))))))++++++++++++++++++++++++))))))))))))))))))))))))******++++++++++++******))))))))))))))))))))))))))))))))))))))))))))))))************************((((((((((((((('''''''''))))))(((((('''''''''&&&************))))))))))))'''((((((((())))))******))))))))))))(((((((((((())))))))))))))))))))))))&&&'''***+++,,,+++***)))pppeeebbb]]]^^^^^^]]]^^^```aaa``````^^^]]]^^^^^^[[[VVVQQQEEE???777222///000000111//////...------------......---,,,+++***+++,,,---............---,,,+++***++++++************++++++************************,,,,,,+++***))))))******...---,,,***)))'''&&&%%%)))))))))))))))))))))))),,,)))'''(((***+++***(((************************))))))))))))))))))))))))************************+++)))((()))******)))((())))))))))))************))))))***+++,,,,,,---------------,,,,,,+++++++++---------,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,------------------------000000000000000000000000000111111222222222222111111111333666:::===>>>>>>AAAAAADDDGGGFFFEEEIIIPPP```ccceeebbb^^^^^^eeekkkyyy|||qqqaaaXXXVVV]]]]]]]]][[[YYYXXXXXXYYYVVVSSSNNNLLLJJJIIIGGGFFFIIIHHHFFFBBB;;;555222111///000000111000///---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++*********+++,,,------,,,+++***)))***+++,,,,,,,,,,,,,,,******+++++++++,,,,,,,,,))))))))))))))))))))))))))))))))))))))))))))))))+++***)))(((((('''(((((())))))))))))((((((((((((******))))))((((((''''''+++)))(((&&&&&&((()))++++++*********))))))(((((())))))))))))))))))))))))***************)))(((((('''(((((((((((((((''''''))))))))))))))))))))))))***************)))((((((oooeee``````___^^^___aaaaaa___```___^^^______\\\WWWRRRKKKDDD;;;444000000000000//////...------------......---,,,++++++,,,------............---,,,+++*********))))))))))))******************************,,,++++++***))))))******((((((((())))))*********)))))))))))))))))))))))),,,***((((((***,,,+++)))************************))))))))))))))))))))))))************************+++)))((()))***+++***((())))))))))))*********************+++,,,,,,,,,---------,,,,,,,,,,,,,,,,,,.........---------,,,,,,------------------------........................000000000000000000000000000111111222222111111111222222333666:::???BBBCCCFFFDDDDDDFFFFFFHHHPPPYYYhhhjjjkkkiiigggjjjsss|||wwwggg\\\WWWXXXYYYZZZ[[[[[[ZZZ[[[[[[ZZZWWWRRROOOLLLIIIFFFCCCGGGGGGGGGEEEBBB===777444......///......------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++******+++++++++,,,,,,+++++++++******++++++,,,+++++++++************+++++++++,,,************************))))))))))))))))))))))))***))))))(((((((((((()))))))))))))))((((((((((((***)))))))))((((((((('''***)))(((''''''((()))***************)))))))))((((((((((((((((((((((((((()))************)))(((((('''(((((((((((((((''''''))))))))))))))))))))))))))))))******))))))((('''}}}hhhcccaaa___```aaaaaa```___aaa````````````]]]XXXUUUQQQJJJ@@@777222000//////000///......------.........------,,,------..................---,,,++++++++++++************++++++************************,,,+++******)))*********&&&&&&'''((()))***++++++)))))))))))))))))))))))),,,***))))))***++++++***************************))))))))))))))))))))))))************************+++)))((()))***+++***))))))))))))*********++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,------------/////////.......................................////////////////////////000000000000000000000000111111111111111111111000333333555888<<>>BBBBBBBBBCCCDDDDDDEEEJJJQQQVVV[[[eeeooowww}}}~~~kkkdddZZZUUUTTTWWWZZZ\\\^^^^^^]]]\\\ZZZUUUOOOKKKDDDDDDHHHOOOUUUTTTLLLEEE===:::666222000///000111.........------,,,,,,,,,,,,,,,,,,+++++++++******---,,,+++******+++,,,---+++++++++++++++***)))(((((())))))))))))*********************************))))))))))))))))))))))))))))))((())))))***+++,,,))))))))))))(((((((((((((((((((((((())))))))))))))))))(((((((((((())))))))))))))))))))))))******************************)))))))))))))))(((''''''''''''((()))******))))))((((((((((((((((((((((((''''''((((((((((((''''''hhh\\\UUUYYY]]]\\\^^^bbb___bbbdddccc```]]][[[ZZZSSSNNNFFF???999666333111111000//////......//////+++,,,---...............,,,------...------,,,,,,)))(((((((((((((((((()))*********************************)))******+++,,,+++*********)))))))))(((************************(((((()))((('''&&&(((***************************))))))))))))))))))))))))***************************))))))***,,,---,,,+++*********++++++++++++,,,,,,,,,,,,,,,---------------------------.........---------------.........------------------------........................000000000000000000000000222111111111222444555777888===CCCEEEEEEDDDEEEGGGGGGKKKTTT___eeeiiipppxxx~~~ssseee[[[XXXXXXYYYZZZ]]]]]]]]]]]]\\\YYYUUUQQQIIIIIIJJJNNNSSSSSSPPPMMMDDD@@@;;;666222///////////////......---,,,,,,,,,,,,,,,,,,+++++++++******,,,++++++++++++++++++,,,++++++,,,,,,,,,+++******)))))))))*********++++++))))))))))))))))))))))))))))))))))))))))))))))))******)))))))))***++++++))))))))))))(((((((((((((((((((((((())))))))))))(((((())))))))))))(((((())))))))))))************++++++++++++++++++++++++(((((())))))(((((('''&&&''''''((()))************))))))))))))))))))))))))''''''((()))))))))((((((ooo___UUUXXX[[[ZZZ\\\bbb^^^aaadddccc```\\\[[[[[[UUUQQQJJJCCC>>>888333000111000000///////////////)))***,,,---.........---,,,,,,------...------,,,***))))))(((((())))))*********************************))))))***++++++,,,************++++++++++++************************)))***+++***((('''))),,,************************))))))))))))))))))))))))***************************))))))***,,,------,,,*********+++++++++,,,,,,+++,,,,,,,,,---.....................------------------........./////////........................////////////////////////000000000000000000000000111111111111333666888:::===AAAEEEFFFEEEGGGKKKOOOQQQVVVbbbnnnuuuxxx~~~yyymmmgggdddaaa^^^^^^]]]]]]]]]]]][[[XXXUUUOOOOOONNNNNNOOOQQQSSSTTTMMMJJJDDD===777333000////////////...------,,,,,,,,,,,,,,,+++++++++******+++++++++,,,,,,++++++++++++,,,,,,---------,,,,,,************+++++++++,,,************************))))))))))))))))))))))))++++++******)))*********))))))))))))(((((((((((('''((((((((()))))))))***(((((())))))))))))((((((((()))))))))************************************(((((())))))(((((('''&&&''''''(((******++++++***))))))))))))))))))))))))'''((())))))******))))))uuucccWWWXXX[[[YYY[[[aaa]]]aaadddccc___\\\ZZZ[[[XXXTTTNNNGGGAAA:::333///111111000///////////////(((***+++---......------,,,,,,------...------------,,,,,,,,,,,,,,,,,,---******************************))))))***+++,,,,,,,,,,,,,,,+++++++++*********************************,,,---,,,))))))+++...************************))))))))))))))))))))))))***************************))))))***,,,...---,,,******+++++++++,,,,,,,,,++++++,,,,,,---...///////////////...---------,,,.../////////000000111111000000000000000000000000000000000000000000000000000000000000000000000000111111111222444777:::<<>>888333111000000///...------,,,,,,,,,,,,,,,+++++++++*********+++,,,------,,,+++***+++,,,,,,---............***++++++++++++,,,,,,,,,++++++++++++++++++++++++)))))))))))))))))))))))),,,,,,+++***)))))))))***))))))))))))(((((((((((('''((((((((())))))******(((((())))))))))))(((((((((((())))))*********+++))))))))))))))))))))))))(((((((((((((((''''''&&&''''''(((******+++++++++))))))))))))))))))))))))(((((()))***************zzzeeeUUUTTTWWWVVVYYY___[[[]]]```bbbbbb___\\\YYY[[[WWWRRRLLLFFF???888333222222111111000000//////000000///...---,,,,,,+++***+++,,,---...---,,,+++*********++++++,,,,,,,,,,,,,,,,,,++++++*********+++++++++*********))))))))))))*********+++++++++******))))))((((((''''''++++++******************************************+++++++++***************)))***+++,,,---,,,++++++)))************+++++++++,,,,,,,,,++++++*********------------------------,,,---///000111000///---+++,,,.../////////...---///000000000......000111000000//////......------111111111000111111222333555444333555999<<<>>>???>>>EEEIIIGGGHHHPPPXXX]]]eeennn{{{ssseee\\\VVVVVVYYYZZZ]]]```\\\YYYTTTNNNJJJJJJMMMQQQUUUUUUTTTPPPIII@@@777111444000,,,+++---...---,,,---------,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,,,,++++++---///************************++++++++++++++++++++++++++++++******+++,,,------************************)))***+++++++++)))((('''*********))))))))))))))))))************+++++++++***************++++++,,,+++++++++************)))******))))))))))))******))))))))))))******************))))))(((((('''''')))))))))))))))))))))))){{{gggXXXWWWYYYXXXYYY___]]]^^^aaabbbaaa^^^ZZZXXX[[[XXXSSSNNNIIIAAA:::555222111111000000//////////////////...------,,,,,,)))***+++,,,,,,+++***)))++++++++++++++++++,,,,,,,,,,,,,,,+++++++++******+++++++++*********))))))))))))*********+++++++++******))))))((((((((((((++++++******************++++++++++++++++++++++++---,,,,,,,,,++++++******)))***+++,,,,,,,,,++++++************++++++++++++,,,,,,++++++++++++++++++------------------------+++,,,...///000///...---,,,---......//////......///000000000......000111111111111000000000//////222222222222222222222333333333555888<<<@@@BBBCCCGGGIIIIIIKKKRRR^^^eeefffoooxxxlllbbbZZZYYY[[[[[[[[[]]]```^^^ZZZUUUQQQPPPRRRTTTVVVVVVVVVSSSMMMEEE>>>999222000......//////...,,,---------,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,***+++---,,,+++***+++,,,++++++++++++++++++++++++++++++++++++++++++++++++))))))(((((()))******+++***************************************)))((((((************)))))))))))))))************+++++++++***))))))))))))***+++++++++++++++************)))******))))))))))))******))))))))))))***************)))))))))((((((((('''))))))))))))))))))))))))vvvzzzzzziiiZZZXXXYYYXXXYYY]]]^^^___aaabbbaaa]]]ZZZWWWZZZXXXUUUQQQLLLDDD<<<666222111000//////.................................)))***+++,,,,,,+++***))),,,,,,++++++++++++++++++,,,,,,,,,++++++++++++***+++++++++******************************+++++++++***))))))))))))(((((((((******++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,......------,,,+++******)))***++++++,,,,,,++++++************+++++++++,,,++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,***+++---.........---,,,......------......///000///000000000......000111333222222222222111111111222333333333333333222222111333777;;;@@@CCCFFFGGGKKKLLLNNNUUUcccrrrwwwuuuyyyuuuiii^^^\\\]]]]]]\\\\\\bbbaaa___[[[WWWUUUUUUVVVWWWWWWWWWVVVRRRLLLGGGCCC444222111111111000...,,,------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,)))+++------,,,*********,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++)))))))))((())))))***+++************************+++******)))))))))))))))************************)))************+++++++++))))))((((((((()))******+++++++++************)))******))))))))))))******))))))))))))************))))))))))))((((((((((((((((((((((((((((((((((((qqqqqqyyyiii[[[WWWWWWWWWXXX[[[]]]^^^```aaa```^^^[[[YYYXXXWWWUUUSSSNNNGGG>>>999333222000///...---......---------.........//////,,,---.........---,,,+++,,,,,,,,,++++++*********++++++++++++++++++++++++************************************************))))))))))))))))))))))))******+++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,......---,,,+++******))))))******+++++++++++++++*********+++++++++,,,,,,*********++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++,,,---.........------///...---------...000111///000000000......000111222222222222222222222222111222333333333333222111222555:::>>>BBBDDDGGGHHHHHHPPPZZZgggvvv|||lll^^^ZZZ\\\]]]]]]^^^`````````]]]YYYVVVUUUUUUUUUVVVVVVUUUSSSPPPLLLJJJ<<<999666333000///...---...------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(((+++---...---+++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++,,,+++++++++++++++,,,,,,************************+++***)))(((((()))***+++)))***************++++++))))))*********+++++++++((((((((((((((())))))***+++++++++*********))))))******))))))))))))******((()))))))))************))))))))))))((((((((((((((((((((((((((((((((((((sssnnnvvv{{{nnn___WWWUUUUUUWWWYYYZZZ\\\^^^```aaa```^^^]]]XXXWWWVVVTTTPPPIIIAAA<<<444333111///------......,,,,,,------.../////////---......///...---,,,+++,,,,,,,,,++++++*********++++++++++++++++++++++++************************************************))))))))))))******************++++++,,,,,,,,,,,,++++++++++++++++++++++++,,,,,,,,,+++***))))))))))))))))))*********++++++***++++++++++++,,,,,,,,,*********++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------.../////////////////////...------///000111///000000000......000111111111111111111111111111000111222222333222222222555999>>>AAABBBCCCFFFHHHHHHYYYmmm{{{|||lll[[[UUUVVVXXX\\\```]]]^^^___^^^ZZZWWWUUUUUURRRSSSSSSRRRQQQOOOMMMKKKFFFBBB<<<555000......///.........---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,(((***---...------...///++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,+++++++++++++++,,,************************+++***)))(((((()))***+++))))))******+++++++++,,,))))))*********+++++++++((((((((((((((())))))***+++++++++*********))))))******))))))))))))******((()))))))))************(((((((((((())))))))))))))))))))))))))))))))))))|||qqqpppvvv{{{jjj]]]WWWWWWXXXYYYYYYZZZ]]]___```aaa```___YYYXXXWWWUUURRRLLLFFFAAA666444111///......//////---------.........//////,,,,,,------,,,+++***))),,,,,,++++++++++++++++++***++++++++++++,,,,,,,,,***************++++++++++++++++++***************)))))))))************+++******++++++,,,---------************************+++++++++*********))))))***))))))))))))***++++++++++++++++++,,,,,,,,,,,,++++++++++++++++++,,,,,,------------------------........./////////000000//////......//////000111///000000000......000111/////////000000000000000111111111111222444555666999===AAACCCBBBCCCFFFIIIOOOeee|||~~~ppp```WWWSSSSSSWWW\\\\\\]]]___^^^\\\YYYXXXXXXRRRRRRQQQPPPNNNLLLJJJJJJKKKHHHAAA999333///000222............---------,,,,,,,,,,,,,,,,,,,,,,,,,,,)))+++,,,,,,,,,,,,---///************************+++++++++++++++++++++++++++***))))))((()))))))))************************)))))))))))))))******+++))))))******+++,,,,,,,,,)))************+++++++++))))))((((((((()))******+++++++++************)))******))))))))))))******))))))))))))************(((((((((((())))))))))))))))))))))))))))))))))))}}}vvvwwwzzzggg]]][[[[[[[[[ZZZ[[[]]]___``````______\\\[[[YYYWWWTTTPPPKKKGGG888666333000......///000---------...............,,,------------+++***)))++++++++++++++++++,,,,,,******+++++++++,,,,,,,,,))))))*********++++++++++++++++++*********))))))))))))*********+++++++++******++++++,,,------...++++++++++++++++++++++++*********+++++++++,,,,,,***))))))((()))***+++,,,+++++++++,,,,,,,,,------,,,,,,++++++++++++++++++...........................---------......//////......///000000000000000///000000000......000111/////////000000000111111333222111111333666999;;;<<<@@@DDDDDDCCCDDDIIIMMMXXXkkk|||oooddd[[[TTTTTTYYYYYY[[[\\\\\\[[[YYYYYYZZZUUUSSSQQQOOOLLLJJJIIIHHHJJJIIIFFF@@@999444333333............------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++)))'''(((***,,,+++++++++++++++++++++++++++++++++++++++++++++++++++******)))(((((())))))************************(((((()))***************))))))***++++++,,,------)))************+++++++++***))))))))))))***+++++++++++++++************)))******))))))))))))******))))))))))))************'''((((((((()))))))))***++++++++++++++++++++++++~~~pppbbb^^^^^^]]]\\\]]]^^^_________^^^]]]___]]]ZZZXXXVVVSSSNNNKKK999777333000//////000111........................//////000000///---,,,+++*********++++++,,,,,,---*********++++++,,,,,,,,,))))))******++++++++++++++++++++++++******))))))))))))******++++++++++++******+++,,,,,,---......,,,,,,,,,,,,,,,,,,,,,,,,***++++++,,,,,,------...***)))((((((((()))+++,,,++++++,,,,,,,,,------------,,,,,,++++++*********////////////////////////---,,,,,,,,,,,,---......---...000111111111000//////000000000......000111//////000000111111111222555333222222444888===@@@>>>BBBEEEEEEDDDFFFLLLQQQ]]]lllzzzsssdddXXXUUUWWWVVVXXXYYYYYYXXXXXXXXXYYYWWWVVVSSSPPPLLLJJJHHHHHHFFFHHHHHHEEE>>>888555444//////.........---------,,,,,,,,,,,,,,,,,,,,,,,,...---+++'''$$$$$$&&&(((,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++------,,,+++******++++++************************'''((()))+++++++++***)))))))))***+++,,,,,,------)))************+++++++++***************++++++,,,+++++++++************)))******))))))))))))******))))))))))))************'''((((((((())))))******++++++++++++++++++++++++vvvhhhcccccc^^^```___\\\ZZZZZZZZZZZZ\\\\\\[[[ZZZWWWTTTQQQOOO>>>999222111222333111...000000//////.........---........................,,,,,,,,,+++++++++******+++++++++++++++++++++++++++++++++++++++++++++++++++++++++*********))))))************************))))))************))))))((()))***++++++***)))((((((((()))***************---,,,***)))))))))******++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,------,,,+++,,,---...///,,,,,,---...///000111222//////............//////000000000000///////////////000000111222222333333666555333444777:::<<<===EEEEEEEEEFFFHHHLLLSSSWWWeeennnxxx~~~zzziii]]]XXXXXXTTTSSSWWWXXXWWWWWWZZZ]]]YYYUUUQQQOOOLLLIIIGGGFFFIIIMMMLLLGGG???999555000000///...---------------------,,,,,,++++++++++++***++++++,,,---...///,,,,,,,,,,,,,,,,,,,,,,,,)))***+++,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++******++++++,,,---***+++,,,,,,,,,,,,+++***************************)))***,,,.........,,,+++,,,,,,+++***))))))******************************))))))))))))************++++++***)))(((((())))))+++***)))'''&&&$$$###"""))))))))))))))))))))))))}}}nnnfff``````___]]][[[ZZZ[[[[[[\\\\\\[[[ZZZWWWTTTQQQOOODDD>>>666333222333000...000/////////....................................,,,,,,,,,+++++++++******++++++++++++++++++++++++************************+++++++++*********))))))))))))))))))))))))))))))******++++++++++++******((()))***++++++***)))((((((((()))***************---,,,+++************+++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,...---------......//////,,,,,,---...///000111111//////............//////000000000000000000000////////////000111111222222444444444666:::===@@@AAADDDDDDEEEFFFIIIOOOWWW]]]hhhssszzziii___[[[VVVSSSVVVWWWVVVUUUVVVZZZWWWTTTRRRPPPNNNJJJGGGGGGIIIKKKKKKHHHBBB<<<888222111///...---,,,---------------,,,,,,,,,++++++************+++,,,------------------------------)))***+++,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++******++++++,,,---***++++++,,,,,,++++++******************************+++,,,......---,,,+++,,,++++++***))))))******************************))))))))))))************++++++***)))))))))))))))*********)))))))))(((((())))))))))))))))))))))))nnncccaaa___^^^\\\[[[[[[[[[\\\\\\[[[ZZZXXXUUURRRQQQKKKDDD;;;555222111000...////////////....................................,,,,,,,,,+++++++++******++++++++++++++++++++++++))))))))))))))))))))))))+++++++++***************************************++++++++++++++++++++++++((()))***++++++***)))((((((((()))***************,,,,,,+++*********++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,---...//////000000//////,,,------...///000111111......------------......000000000000000000000000////////////000111222222222333666:::===AAACCCEEEDDDEEEFFFIIIOOOXXXcccjjjqqq~~~yyykkkbbbZZZTTTVVVXXXXXXWWWWWWWWWVVVTTTTTTRRROOOKKKHHHIIIGGGFFFHHHIIIGGGCCC>>>777444111...,,,,,,---...------------,,,,,,,,,,,,,,,,,,,,,++++++,,,------........................******+++,,,,,,,,,++++++++++++++++++++++++++++++++++++******++++++,,,---******+++,,,,,,+++******************************+++,,,---------,,,+++***,,,+++******)))*********************************))))))))))))************++++++***))))))))))))***((())))))***++++++,,,,,,))))))))))))))))))))))))wwwgggbbb___^^^]]][[[[[[\\\\\\\\\\\\[[[YYYVVVTTTRRROOOHHH>>>666222111000//////////////////.................................,,,,,,,,,+++++++++******++++++++++++++++++++++++************************************************,,,,,,,,,,,,,,,,,,,,,,,,+++++++++******+++++++++)))***++++++++++++***)))(((((()))***************************************++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,---...000000///......------......///000000111......------------......000000000000000111111111000000000000000222333444222555999===@@@BBBEEEGGGFFFHHHKKKQQQZZZfffsss{{{pppdddZZZXXX[[[[[[\\\]]]VVVVVVVVVUUUTTTPPPJJJFFFGGGDDDAAADDDIIILLLJJJFFF<<<999444///---,,,---...------------------,,,,,,///......------------...------------------------***++++++,,,,,,,,,++++++++++++++++++++++++++++++++++++******++++++,,,---******++++++++++++******************************,,,,,,,,,,,,,,,+++***)))++++++***************+++************************((()))))))))************++++++***))))))*********''''''((()))******++++++((((((((((((((((((((((((~~~jjjccc^^^___^^^[[[ZZZ\\\[[[\\\\\\[[[YYYWWWUUUTTTOOOIII???777333111111111.........///////////////........................,,,,,,,,,+++++++++******++++++++++++++++++++++++++++++++++++++++++++++++************************+++++++++++++++++++++++++++***))))))))))))***+++)))***+++,,,,,,+++***)))(((((()))***************(((((())))))))))))))))))++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,+++,,,---...///...------------......//////000000.........------.........///000000000111111111222333222111111222333555666444777<<>>AAAHHHMMMMMMKKKAAA===888333///......///------------------------...---,,,,,,,,,,,,,,,---++++++++++++++++++++++++++++++,,,,,,,,,++++++***++++++++++++++++++++++++++++++******++++++,,,---************************************************,,,,,,,,,,,,+++******)))+++***************++++++************************((()))))))))************+++***************++++++))))))))))))************((((((((((((((((((((((((mmmbbb\\\______ZZZXXX[[[[[[\\\\\\[[[ZZZXXXWWWUUUOOOJJJBBB:::444222222222.........///////////////........................,,,,,,,,,+++++++++******++++++++++++++++++++++++++++++++++++++++++++++++***************+++++++++((((((((((((((((((((((((+++***)))(((((()))***+++)))***+++,,,,,,+++***)))(((((()))***************'''((())))))******))))))++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,---...---------............//////000000//////............/////////000000111111222222222444444222222222444666888777;;;???BBBCCCEEEJJJNNNPPPTTT[[[dddooo|||zzzmmmaaaWWWTTTUUUVVVVVVVVVVVVUUUQQQKKKGGGCCC@@@>>>@@@EEEJJJKKKKKKEEEBBB===777333000//////------------............*********))))))******+++************************++++++,,,,,,,,,+++******++++++++++++++++++++++++++++++******++++++,,,---+++***))))))))))))***+++************************++++++++++++*********************)))******+++,,,************************))))))))))))************+++************+++,,,,,,,,,,,,,,,+++++++++++++++))))))))))))))))))))))))nnnbbb[[[^^^___YYYWWW[[[[[[[[[\\\\\\[[[YYYXXXVVVQQQMMMGGG>>>777333222222............/////////000........................,,,,,,,,,+++++++++******++++++++++++++++++++++++************************))))))*********+++++++++)))))))))))))))))))))))),,,+++)))(((((()))+++,,,******,,,,,,,,,,,,******(((((()))***************((()))***+++,,,,,,+++***++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,---------------...//////............////////////000000////////////000000///000000111111222333333555333222111222444666888999===BBBDDDEEEIIIPPPVVV^^^bbbiiiqqqzzznnn]]]TTTTTTTTTSSSTTTUUUUUUSSSOOOLLLDDDCCCAAA@@@AAACCCEEEFFFHHHFFFAAA;;;666222000///------------.........///***************+++,,,---+++++++++++++++++++++++++++,,,,,,,,,,,,+++***)))++++++++++++++++++++++++++++++******++++++,,,---+++***)))(((((()))***+++******************************************++++++******))))))***++++++,,,************************))))))))))))************+++*********++++++,,,---++++++++++++++++++++++++))))))))))))))))))))))))oooaaaZZZ^^^^^^XXXVVVZZZ[[[[[[\\\\\\[[[ZZZXXXWWWTTTQQQJJJBBB:::444222111---.........//////000000........................,,,,,,,,,+++++++++******++++++++++++++++++++++++))))))))))))))))))))))))))))))******++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,---,,,***))))))***,,,---***+++,,,,,,,,,,,,+++***(((((()))******************+++,,,---...------,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,//////...------///000111.........///////////////111111000000000000111111///000000111222222333333444333111000111333666777999>>>CCCFFFHHHMMMVVV]]]kkkooouuu|||{{{fffZZZYYYQQQQQQRRRTTTUUUUUURRRPPPFFFEEEDDDAAA>>>>>>@@@BBBJJJHHHCCC>>>999444000...---------.........//////,,,,,,,,,---...///000111,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***)))++++++++++++++++++++++++++++++******++++++,,,---+++***)))(((((()))***+++***************************)))))))))***+++,,,,,,******))))))***+++,,,,,,************************))))))))))))************+++*********+++,,,,,,---'''''''''((())))))******))))))))))))))))))))))))xxxdddUUUWWW[[[XXXVVVYYY\\\\\\]]]]]]\\\[[[YYYXXXRRRQQQLLLDDD:::333111111000/////////....................................,,,,,,,,,+++++++++******++++++++++++++++++++++++...,,,******,,,---...---++++++******++++++,,,---++++++************++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++************++++++***+++,,,,,,******+++,,,,,,+++***+++---/////////,,,,,,,,,---------......------------------------//////.........---------,,,,,,---...///000111222111111000000000000000111222222222111111444888<<>>>>>@@@AAA@@@CCCCCCCCC@@@===888444111...---++++++,,,---,,,+++------------------------,,,++++++******++++++,,,------------------------,,,,,,,,,,,,++++++***)))************************---+++******++++++)))(((***++++++,,,,,,++++++***++++++************++++++((()))))))))***************)))))))))***++++++,,,************************************************))))))))))))))))))))))))+++***)))(((((()))***+++xxxeeeVVVWWWZZZXXXVVVYYY\\\]]]]]]]]]\\\[[[YYYXXXSSSSSSOOOHHH>>>666222111000000/////////.................................---------,,,,,,,,,++++++++++++++++++++++++++++++,,,***))))))+++,,,,,,,,,++++++******++++++,,,---++++++************++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++************++++++***+++,,,,,,******+++,,,,,,***)))***,,,------,,,,,,,,,,,,---------......------------------------//////.........---------,,,------...///000111111111111000000000000111111111222222222333666:::>>>DDDDDDDDDIIIQQQ]]]iiippptttwww}}}zzzjjjaaaVVVVVVUUUUUUUUUUUUUUUUUUSSSNNNGGGBBB????????????BBBDDDDDDDDD@@@;;;555111000...,,,,,,---...------------------------------,,,,,,++++++++++++,,,,,,++++++++++++++++++++++++++++++,,,,,,,,,+++******++++++++++++++++++++++++---,,,***+++,,,,,,+++******++++++,,,,,,++++++***++++++************++++++************++++++++++++***************+++,,,,,,++++++++++++++++++++++++************************))))))))))))))))))))))))+++***)))(((((()))***+++wwweeeVVVUUUXXXWWWWWWYYY]]]^^^^^^^^^\\\ZZZYYYWWWUUUUUUSSSLLLCCC:::444111000000000/////////.......................................---------,,,,,,+++++++++++++++++++++++++++)))((((((***+++++++++++++++******++++++,,,---++++++************++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++************++++++***+++,,,,,,******+++,,,+++***))))))+++++++++))),,,,,,,,,---------......------------------------/////////............---.........//////000000000111111000000000111111222111222333444666999>>>AAAEEEDDDEEELLLXXXeeennnsssuuuzzz~~~{{{{{{}}}}}}}}}zzz~~~vvvoooaaa]]]XXXVVVVVVWWWUUUSSSUUUSSSNNNGGGAAA>>>===>>>AAACCCFFFGGGDDD???999555222000...---...//////...------------------------,,,,,,++++++++++++,,,,,,++++++++++++++++++++++++******+++,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,---+++++++++---...---,,,***++++++,,,,,,++++++***++++++************++++++***++++++++++++,,,,,,,,,+++++++++++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,))))))))))))))))))))))))))))))))))))))))))))))))******))))))))))))******uuueeeVVVSSSVVVWWWXXX[[[^^^^^^^^^^^^]]][[[YYYWWWWWWWWWUUUPPPHHH>>>666111000000000////////////...........................------------,,,,,,,,,,,,+++++++++++++++++++++++++++***))))))+++,,,,,,+++++++++******++++++,,,---++++++************++++++************************++++++++++++++++++++++++++++++************++++++***+++,,,,,,******+++,,,+++***)))***++++++***(((,,,,,,,,,---------......------------------------/////////...............///////////////000000000111111000000111111222222111333555777999===AAAEEEEEEGGGLLLRRR[[[eeennntttwww~~~~~~{{{zzz{{{||||||uuuvvvvvvxxx}}}}}}pppggg[[[UUUTTTUUUTTTRRRTTTTTTQQQKKKCCC>>>>>>???@@@BBBDDDFFFEEECCCAAA???555333///......//////...------------------------,,,,,,,,,++++++,,,,,,,,,------------------------)))***++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++******+++---...---,,,***++++++,,,,,,++++++***++++++************++++++*********+++++++++,,,,,,---,,,,,,++++++,,,------,,,,,,,,,,,,,,,,,,,,,,,,(((((((((((((((((((((((())))))))))))))))))))))))***))))))))))))))))))***vvvgggXXXRRRTTTWWWZZZ\\\^^^^^^^^^^^^]]][[[YYYXXXWWWWWWVVVRRRLLLBBB888222111000000000////////////........................,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++,,,+++***+++---...---+++++++++******++++++,,,---++++++************++++++************************++++++++++++++++++++++++++++++************++++++***+++,,,,,,******+++,,,,,,,,,+++,,,------+++))),,,,,,,,,---------......------------------------/////////////////////////////////000000000000000111111111111111222333333333555888:::<<<@@@EEEHHHIIIPPPYYY]]]```fffpppxxx||||||||||||||||||vvvssspppnnnpppwwwsssbbbVVVRRRSSSSSSRRRQQQRRRRRRMMMFFFAAA@@@AAA@@@@@@AAABBBDDDFFFGGGHHH999666111///.........------------------------------,,,,,,,,,,,,,,,,,,---------------------------)))***++++++,,,,,,,,,,,,++++++++++++++++++++++++***))))))***+++---,,,+++***++++++,,,,,,++++++***++++++************++++++))))))))))))*********+++------,,,++++++,,,,,,,,,++++++++++++++++++++++++(((((((((((((((((((((((()))))))))))))))))))))))))))))))))******)))))))))|||ooo^^^UUUTTTWWWZZZ\\\]]]]]]^^^^^^^^^\\\[[[ZZZXXXXXXWWWTTTOOOFFF<<<555111111000000000/////////........................,,,,,,+++++++++*********++++++++++++++++++++++++,,,++++++,,,......---+++++++++******++++++,,,---++++++************++++++************************++++++++++++++++++++++++++++++************++++++***+++,,,,,,******+++,,,,,,,,,,,,...//////---+++,,,,,,,,,---------......------------------------...////////////000000000/////////000000111111111111111111111111222333444555777:::===@@@CCCGGGJJJOOOZZZfffkkkkkknnnxxx~~~~~~~~~}}}wwwsssmmmiiihhhlllqqquuuooo___VVVSSSSSSRRROOOPPPQQQNNNJJJFFFDDDCCC@@@??????@@@BBBFFFJJJLLL???:::555111///...---,,,------------------------------,,,,,,,,,,,,------++++++++++++++++++++++++******+++,,,,,,,,,++++++************************+++)))))))))+++,,,+++******++++++,,,,,,++++++***++++++************++++++(((((()))))))))*********---,,,,,,++++++++++++,,,************************))))))))))))))))))))))))))))))))))))))))))))))))))))))************))))))zzzgggYYYUUUWWWZZZ[[[\\\\\\]]]^^^^^^]]]\\\[[[[[[YYYXXXVVVRRRKKKAAA:::111111111000000000//////........................------,,,,,,,,,+++++++++++++++++++++++++++++++++*********,,,---...,,,***++++++******++++++,,,---++++++************++++++************************++++++++++++++++++++++++++++++************++++++***+++,,,,,,******+++,,,++++++,,,...000000...,,,,,,,,,,,,---------......------------------------.../////////000000000000......///000111222222333111111111111222333444555777999===???BBBEEEHHHKKKSSS]]]jjjrrrwww|||xxxsssmmmhhhfffgggiiijjjrrr{{{nnn```XXXTTTSSSQQQQQQQQQQQQOOOLLLGGGCCC?????????@@@BBBDDDGGGHHHEEE@@@999444111000...---------------------------------,,,,,,,,,,,,------++++++++++++++++++++++++++++++,,,,,,,,,+++******++++++++++++++++++++++++---+++******+++,,,+++)))***++++++,,,,,,++++++***++++++************++++++))))))*********+++++++++,,,,,,+++***************++++++++++++++++++++++++************************))))))))))))))))))))))))((()))***++++++***)))(((nnn]]]WWWXXXZZZYYY[[[\\\]]]^^^^^^^^^]]]]]]]]][[[YYYXXXUUUNNNEEE>>>111111111111000000000000..............................---------,,,,,,,,,++++++++++++++++++++++++)))))))))+++------+++)))++++++******++++++,,,---++++++************++++++))))))))))))))))))))))))++++++++++++++++++++++++++++++************++++++***+++,,,,,,******+++,,,******+++...000000...,,,,,,,,,,,,---------......------------------------.../////////000000111111---...///000111222333333111111111111222333444555888;;;>>>AAACCCFFFIIILLLSSS[[[hhhttt~~~yyyuuuooojjjhhhgggggggggjjjoooyyyzzziii]]]VVVTTTTTTRRRRRRRRRSSSOOOIIICCC???@@@AAABBBCCCCCCCCCCCCIIIDDD===777333111///...------------------------...------,,,,,,------...------------------------,,,,,,,,,,,,,,,+++***))),,,,,,,,,,,,,,,,,,,,,,,,...---,,,,,,,,,,,,+++***+++++++++,,,,,,+++++++++++++++************++++++******+++++++++,,,,,,,,,,,,++++++***)))))))))***,,,,,,,,,,,,,,,,,,,,,,,,************************))))))))))))))))))))))))((()))***++++++***)))(((|||fffZZZYYY[[[ZZZ______^^^]]]]]]\\\[[[[[[[[[ZZZZZZYYYUUUOOOGGGAAA777444000...---...---,,,,,,,,,,,,------.........///...---,,,+++***************+++++++++******)))***++++++,,,,,,++++++***+++++++++***************************************))))))*********++++++++++++******+++,,,---+++***++++++++++++++++++++++++++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,------------------------000000000000000000000000000000000000////////////333333333222222222222222111111111000111333777:::???>>>???BBBFFFIIIKKKJJJWWWcccqqq|||yyyooolllllliiidddbbbeeekkkuuuwwwkkkaaaXXXVVVVVVTTTRRRQQQPPPLLLGGGEEECCCAAA??????AAACCCEEEHHHHHHFFFAAA:::444111///000///......//////---+++...---,,,+++***+++,,,---.........------,,,,,,,,,+++,,,,,,------,,,,,,+++)))***+++,,,,,,,,,,,,+++++++++++++++******))))))((()))***+++,,,+++******++++++************++++++,,,+++++++++***)))))))))//////...---,,,,,,+++***++++++++++++++++++++++++)))************+++++++++************************+++*********))))))((((((pppaaa\\\\\\ZZZ^^^^^^]]]\\\\\\[[[ZZZZZZ\\\[[[[[[ZZZXXXRRRJJJEEE999666222/////////......,,,,,,,,,------...............---,,,++++++++++++)))******+++++++++++++++***++++++,,,,,,++++++******************+++++++++*********************************++++++++++++,,,,,,+++++++++---,,,+++))),,,,,,,,,+++++++++******++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,................................................000000000000////////////222222222222222222222111222222222222222444999<<<>>>AAACCCDDDEEEIIIOOOUUUcccnnn{{{~~~xxxtttmmmddd```bbbfffnnn|||{{{pppfff[[[XXXTTTSSSTTTSSSOOOIIIFFFEEEBBB@@@???@@@AAABBBFFFGGGFFFCCC>>>888333000///...---...///...---+++...---,,,+++++++++,,,,,,......---------,,,,,,,,,+++,,,,,,------,,,,,,+++******+++++++++,,,,,,,,,++++++++++++*********)))((()))***+++,,,++++++***++++++************++++++++++++++++++************,,,,,,,,,+++++++++++++++++++++++++++++++++++++++)))************+++++++++************************************)))))))))(((oooddd^^^YYY]]]]]]\\\\\\[[[[[[ZZZZZZ]]]\\\\\\\\\ZZZUUUOOOJJJ===999444111000000000///---------------.........------,,,,,,,,,,,,------*********++++++,,,,,,,,,***++++++,,,,,,++++++***))))))******++++++,,,,,,++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,---,,,+++,,,---,,,***)))---,,,,,,++++++*********++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,////////////////////////........................////////////000000000000111111111111111111222222333333333333444666;;;>>>>>>CCCGGGGGGGGGMMMZZZeeettt}}}xxxmmmcccaaaaaafffrrrxxxeee\\\TTTSSSVVVWWWQQQKKKIIIGGGEEEBBB@@@?????????CCCEEEGGGGGGCCC===666222///...------...///---,,,...------,,,+++,,,,,,,,,...------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++*********+++,,,---++++++++++++************)))******+++,,,+++++++++++++++************++++++*********+++++++++++++++))))))))))))******++++++++++++++++++++++++++++++)))************+++++++++************************************))))))))))))ttteeeZZZ]]]]]]]]]\\\\\\\\\\\\\\\\\\\\\\\\]]]\\\XXXRRRNNN@@@;;;666222111000000///---------...............,,,,,,,,,,,,,,,---......,,,,,,,,,+++++++++,,,,,,***++++++,,,,,,++++++***))))))******+++,,,------++++++++++++++++++++++++++++++,,,,,,,,,---------...---,,,,,,---,,,***)))+++++++++++++++++++++++++++++++++,,,,,,,,,------++++++,,,,,,,,,,,,------................................................////////////000000000000000000000111111222222222333333444444555888<<<@@@@@@DDDIIIKKKNNNYYYiiivvv~~~kkkfffaaadddlllyyypppaaaTTTRRRWWWWWWRRRLLLLLLJJJHHHDDDBBB???======AAACCCGGGIIIHHHCCC;;;666000///------...///...---......------,,,,,,,,,,,,------------------------,,,,,,,,,,,,,,,,,,,,,,,,---,,,***))))))***,,,...++++++++++++++++++++++++******+++++++++,,,,,,,,,,,,++++++******++++++,,,*********++++++,,,,,,,,,)))))))))***************++++++++++++++++++++++++))))))*********+++++++++*********************************)))))))))))))))tttaaa]]]]]]]]]^^^^^^^^^^^^^^^\\\[[[\\\\\\\\\YYYTTTPPPBBB===777222000000//////........................,,,,,,,,,,,,---...//////000///---,,,++++++++++++***++++++,,,,,,++++++***))))))***+++,,,------...++++++++++++++++++++++++++++++,,,,,,,,,---------...---,,,,,,------+++)))))))))***+++,,,------...+++++++++,,,,,,,,,------+++++++++,,,,,,---------------------------------////////////////////////.../////////000000000111//////000111222333333444333333444444666999>>>BBBDDDGGGMMMTTT]]]kkkzzzuuulllddddddiiiqqq|||hhhVVVRRRVVVUUUPPPLLLMMMLLLJJJGGGDDDAAA>>><<>>>>>???BBBHHHLLLKKKFFFAAA666444111////////////...---............---,,,,,,,,,,,,,,,------------...------++++++++++++---------,,,+++*********+++,,,++++++++++++,,,,,,,,,,,,,,,++++++++++++,,,------,,,,,,++++++++++++,,,,,,+++++++++,,,,,,,,,,,,,,,///...---,,,+++***))))))++++++++++++++++++++++++)))************+++++++++))))))))))))))))))))))))))))))))))))************qqq\\\\\\]]]^^^^^^___``````]]]]]]\\\\\\\\\ZZZVVVRRRIIICCC;;;555222111111111000/////////.........---...------------......//////...---,,,,,,---...///***++++++,,,,,,++++++***,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,*********++++++++++++,,,,,,++++++,,,...///...---++++++++++++++++++++++++++++++,,,,,,,,,,,,------******+++,,,,,,---..............................////////////////////////.........///000111111111///000111333444555666777666777888999;;;???EEEIIIRRR]]]lllwwwwwwllljjjjjjjjjuuuyyyaaaWWWTTTNNNKKKNNNMMMNNNNNNMMMKKKGGGCCCAAA>>>>>>???EEEKKKMMMJJJFFF:::777333111000000///...---.../////////...,,,,,,,,,,,,,,,---------.........---+++******+++---...,,,,,,,,,+++++++++******+++++++++,,,,,,,,,------,,,,,,+++++++++,,,---...---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,++++++------,,,,,,+++++++++***++++++++++++++++++++++++)))************+++++++++))))))))))))))))))))))))((()))))))))************qqq[[[[[[\\\]]]^^^^^^_________^^^]]]]]]]]][[[WWWTTTKKKEEE===777444333222222000000//////.........---///......---------......---,,,++++++,,,///111333+++++++++,,,,,,+++++++++---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,))))))*********++++++++++++******,,,///000///.........---,,,+++))))))(((++++++,,,,,,,,,---------******+++,,,,,,---......////////////////////////........................---......///000111111222000000222333555666888888888999;;;<<<>>>BBBGGGKKKWWWggg{{{|||qqqooonnnllluuueeeZZZTTTLLLJJJOOOMMMNNNOOONNNLLLIIIEEECCC???===>>>CCCJJJNNNMMMJJJ===999555222111000///...---.../////////...,,,,,,,,,,,,,,,------............---+++******+++---...,,,,,,,,,,,,,,,+++***)))+++++++++,,,,,,------------,,,+++***+++,,,---...---,,,,,,++++++,,,,,,------------,,,,,,+++++++++***++++++++++++,,,,,,,,,++++++++++++++++++++++++)))************+++++++++))))))))))))))))))))))))(((((())))))*********+++yyy^^^YYYVVVWWWYYYYYY]]]bbb^^^^^^^^^]]][[[YYYXXXWWWLLLHHHAAA:::444000///...,,,---.../////////------000///...---,,,+++++++++,,,,,,,,,+++++++++******++++++++++++++++++++++++++++++++++++++++++++++++///......---+++******)))++++++******++++++,,,---++++++,,,------......///,,,++++++******++++++,,,---------------------------,,,,,,,,,---...000111...//////000000000000000...///000///...---...000333333222222111000000000/////////111333777:::<<<===<<>>888555333111///000//////......---,,,,,,---------.........//////++++++,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,------)))))))))***+++,,,---------,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***************---,,,,,,+++******++++++------,,,,,,+++,,,,,,,,,))))))))))))))))))))))))))))))******+++++++++,,,******))))))))))))******+++++++++************)))qqq\\\WWWTTTVVVXXXXXXYYY\\\______^^^]]]\\\[[[YYYXXXTTTOOOGGG>>>777333222222//////......---......//////...------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,---------++++++******++++++,,,---++++++,,,------......///......------------......------------------------......---------......///------...////////////......///000000......///000000111111111111222222222444333333333555888;;;===@@@???AAADDDFFFIIIRRR\\\nnnzzz|||}}}~~~vvvkkkaaaXXXQQQMMMNNNOOOPPPPPPPPPOOOOOOKKKJJJHHHEEEDDDGGGKKKOOORRRMMMEEE>>>999444111...000000///......------,,,........./////////000000++++++,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,------))))))***+++,,,---...///***+++,,,,,,---...//////,,,++++++************+++---,,,,,,+++++++++++++++------,,,,,,------......))))))))))))))))))))))))***************+++++++++******)))))))))******++++++++++++************)))~~~mmmZZZUUURRRUUUXXXXXXYYY\\\______^^^^^^\\\[[[ZZZYYYVVVQQQIII@@@999555333333111000...---------/////////...---,,,,,,,,,,,,,,,------,,,,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,------------------------++++++,,,,,,,,,,,,------++++++******++++++,,,---++++++,,,------......///......------------......------------------------///.........---------...,,,------..................000111000///...///000///000000111222222333333444444333333555777:::<<>>???CCCEEEJJJTTT^^^ppp{{{}}}yyynnnaaaWWWSSSSSSRRRRRRQQQPPPOOONNNOOOOOOMMMIIIFFFFFFJJJOOOSSSOOOIIICCC<<<777222000000000//////...------------.........////////////+++,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,---...//////000,,,++++++******+++++++++---,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,---...///++++++++++++++++++++++++...---,,,+++***(((''''''******))))))******+++++++++++++++*********))))))zzzkkk[[[TTTQQQTTTYYYZZZ[[[\\\^^^^^^^^^]]]\\\[[[ZZZYYYVVVRRRJJJBBB;;;666444333111000///...---......///......---,,,,,,,,,---------------,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,------------------------------,,,,,,,,,,,,++++++++++++******++++++,,,---++++++,,,------......///------,,,,,,,,,,,,------------------------------..................------,,,------...............///000111000///...///111//////000111222333333444333333222222444777999;;;BBBAAACCCHHHLLLQQQ\\\gggrrr|||nnnbbbVVVTTTRRRPPPNNNMMMMMMNNNQQQRRRQQQNNNIIIHHHKKKNNNOOONNNKKKFFF@@@:::555333111000000///......------,,,,,,---------.........,,,,,,,,,------,,,,,,,,,+++++++++,,,,,,,,,------------,,,,,,,,,,,,,,,+++------------------------,,,+++++++++++++++,,,,,,---,,,,,,+++,,,,,,------++++++******+++,,,------++++++++++++++++++++++++------,,,+++***)))((('''***************+++,,,,,,+++++++++*********))))))}}}{{{oooaaaXXXRRRTTTYYYZZZ[[[]]]\\\]]]]]]\\\[[[ZZZYYYYYYUUURRRMMMFFF???999555333111111000///...............------,,,,,,---------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------,,,,,,+++++++++++++++******++++++,,,---++++++,,,------......///------,,,,,,,,,,,,------------------------------------......///......---------...////////////...///000111111//////000111//////000111222222333333222222222222444777:::<<>>AAADDDLLLWWWaaakkkxxx~~~uuuuuunnnhhh___VVVPPPNNNNNNPPPRRRRRRSSSTTTTTTSSSOOOLLLKKKMMMOOOLLLFFF???;;;999111111000000///.........------------............,,,,,,------------,,,,,,++++++,,,,,,,,,,,,------++++++++++++++++++++++++,,,,,,+++++++++*********+++++++++++++++,,,---...,,,,,,,,,,,,,,,---......------,,,+++++++++,,,,,,))))))))))))))))))))))))''''''(((***+++,,,---...************+++,,,---...+++++++++************)))pppdddXXXVVVXXXXXXXXXYYYZZZZZZZZZZZZZZZYYYXXXWWWUUUTTTQQQMMMGGG@@@:::777000111111111111///---,,,------,,,,,,,,,------.........---------,,,,,,,,,------------------------++++++++++++++++++++++++)))******+++---......///++++++******++++++,,,---++++++,,,------....../////////............//////------------------------***+++---///000000//////...//////000000000000000///111222111000///000111111111111111111222222222333333333444777:::>>>@@@FFFJJJUUUcccooo{{{zzzpppzzzlll^^^TTTOOOOOOOOOQQQQQQRRRUUUXXXVVVPPPKKKLLLOOOQQQNNNHHH@@@<<<:::111111000000//////................../////////000,,,------......------,,,++++++,,,,,,,,,---------......---+++)))((('''&&&************************++++++++++++,,,,,,---...,,,,,,,,,,,,,,,---...//////...------,,,,,,,,,,,,++++++++++++++++++++++++)))************+++++++++************+++,,,---...+++++++++************)))tttaaaXXXXXX[[[YYYVVVZZZZZZZZZZZZZZZYYYXXXXXXYYYWWWTTTPPPKKKDDD;;;666333111000000111111000...---.../////////...,,,+++------,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,------,,,,,,,,,,,,+++***)))))),,,,,,++++++,,,,,,---...,,,,,,+++++++++,,,---............------,,,,,,,,,222000...,,,+++***++++++((()))+++---......------,,,,,,,,,---------................../////////000000000000000111111111111000111222222111222444666333666888888777:::???CCCFFFSSSbbbnnn{{{vvv{{{zzz}}}ooo^^^TTTQQQQQQPPPPPPQQQSSSUUUUUUTTTRRRWWWTTTQQQNNNKKKGGGAAA>>>999555111///000000///---......//////000000111111......------------......------------------------++++++++++++++++++++++++......---,,,+++***)))(((...------,,,,,,------...------------------------///---+++***++++++***)))---------,,,,,,+++++++++((()))***++++++***)))(((((())))))+++,,,---......---------,,,,,,+++++++++}}}iii]]]ZZZ\\\[[[YYYZZZZZZ[[[[[[ZZZZZZYYYXXXWWWVVVTTTQQQMMMEEE===777333111000000000000///.........//////...------,,,------,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,------++++++,,,,,,,,,,,,,,,+++,,,,,,++++++,,,,,,---...,,,,,,++++++,,,,,,---.........---------,,,,,,,,,000///...,,,+++++++++,,,,,,,,,---...////////////,,,,,,---------................../////////000000//////000000000111111111111222222222111111333555333555888999:::===DDDIIIJJJXXXhhhvvv~~~wwwyyy{{{hhhZZZSSSQQQPPPPPPQQQSSSUUUVVVTTTSSSUUUSSSQQQOOOMMMJJJEEEBBB;;;777222///000000///...---.........////////////......------------......------------------------++++++++++++++++++++++++---------,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,///---+++***++++++***))),,,,,,,,,++++++*********)))***+++,,,,,,+++***))),,,,,,,,,++++++++++++***------,,,,,,,,,+++++++++yyyggg___^^^]]]]]]ZZZ[[[[[[[[[[[[ZZZZZZYYYVVVUUUUUUSSSOOOHHH???888333111////////////...---//////...------------...------,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,------***+++,,,------.........,,,,,,++++++,,,,,,---...,,,,,,,,,,,,,,,---------...------------,,,,,,,,,///...---,,,,,,,,,,,,---......---------......///,,,------------.............../////////000000000////////////000000000000222333333222111111333555333666999:::===BBBJJJPPPWWWeeevvv|||zzzzzztttcccWWWQQQPPPPPPQQQSSSUUUVVVUUUTTTSSSRRRQQQQQQPPPNNNJJJGGG>>>:::444111000000000000------------..................------------......------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------.........,,,++++++******++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,///---+++***+++,,,+++***++++++***************)))++++++,,,,,,,,,,,,++++++,,,,,,,,,+++++++++******,,,,,,,,,,,,++++++++++++xxxhhh```^^^^^^ZZZ[[[[[[[[[[[[[[[ZZZZZZVVVWWWWWWVVVQQQIII???888444111///......///...---//////---,,,,,,---...///------,,,,,,,,,++++++++++++++++++,,,,,,,,,------+++,,,------.........---,,,,,,++++++,,,,,,---...+++,,,,,,---------------------------------------------------------------...---,,,******+++,,,---------------...............////////////000000000....../////////000000000222333444333222111333555555777:::<<<@@@GGGPPPXXXjjjwww~~~zzz|||}}}~~~kkk[[[SSSQQQPPPPPPRRRTTTVVVUUUTTTSSSSSSSSSSSSSSSPPPLLLIIIAAA===777333111000111222..............................------------......------------------------------------------------,,,,,,,,,,,,------------,,,,,,++++++++++++,,,,,,++++++++++++++++++++++++///---++++++,,,,,,+++***++++++++++++************++++++,,,,,,,,,,,,++++++))))))***+++,,,,,,------,,,+++++++++++++++++++++sssddd___^^^YYYZZZZZZ[[[[[[[[[ZZZZZZYYYYYYXXXWWWSSSJJJ@@@999555222///......///...---///...---,,,,,,---//////------,,,,,,,,,++++++++++++++++++,,,,,,,,,---------.........------,,,+++,,,,,,++++++,,,,,,---...+++,,,---.........------------------------------,,,,,,------------------...---,,,******+++,,,------------.........//////////////////000000000111////////////000000000000222333444333222222444555777:::<<>>BBBGGGPPP^^^mmmxxx{{{tttlllgggiiipppzzzlll^^^TTTQQQOOONNNOOOPPPOOONNNRRRRRRSSSTTTSSSPPPJJJFFFDDDEEECCC>>>888333111222000000/////////...............------------......------------------------........................+++++++++,,,,,,,,,,,,,,,---,,,,,,,,,,,,,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,...---++++++---...------******++++++,,,,,,,,,,,,---,,,+++******+++,,,---...------,,,+++***)))((()))*********++++++++++++ooo^^^YYYVVVVVVWWWXXXYYYYYYXXXXXXVVVVVVUUUUUUTTTPPPKKKGGG:::666222000000000000000+++,,,...///000///...------------,,,,,,,,,++++++++++++,,,,,,,,,---------))))))***+++,,,,,,,,,,,,,,,,,,++++++,,,,,,---...+++,,,...000000///...---,,,,,,,,,------.........------.........---++++++((()))+++---......------............/////////000000000000000111111111111111111222222222333333333///111222333333555888:::;;;>>>DDDJJJUUUdddvvv{{{ssslllhhheeehhhjjjooo{{{sssfffTTTRRROOOMMMNNNNNNMMMLLLOOOPPPQQQSSSSSSPPPKKKFFFDDDEEEEEE@@@999333111111//////.........---------.........------.........------------------------////////////////////////***++++++,,,---//////000,,,++++++++++++++++++,,,------------------------...---++++++---......---))))))******++++++++++++...---,,,,,,,,,,,,---...++++++++++++++++++,,,,,,))))))******++++++++++++sss___[[[WWWVVVUUUUUUVVVWWWYYYZZZ\\\XXXTTTSSSTTTRRRKKKFFF<<<888444111111222222111////////////............------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++***)))))))))++++++++++++++++++++++++---------,,,,,,+++++++++------------------------...------,,,,,,------...////////////////////////............/////////000///////////////000111111111111111000111111222333555333111000222555777888>>>@@@EEEQQQ```nnnxxx|||xxxnnnfffdddcccbbbdddjjjuuuxxxkkk\\\UUUPPPNNNLLLJJJMMMRRRMMMMMMNNNOOOOOOLLLGGGCCCCCCEEEFFFEEEBBB<<<666222///......///000000...---///...---,,,---///111222................................................,,,---///000000///---,,,---------,,,,,,+++++++++........................++++++,,,,,,,,,---------,,,,,,+++,,,------,,,***,,,,,,++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,qqq]]]XXXVVVVVVVVVVVVVVVWWWXXXYYY\\\XXXUUUTTTUUUSSSMMMHHH>>>:::555222111111111000////////////............------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++,,,,,,,,,------......---------,,,,,,+++++++++------------------------...------,,,,,,------..................................../////////000000///////////////000111111111111111111111222222333666555444444777:::===>>>DDDFFFLLLWWWfffttt~~~{{{qqqhhhbbb```______ccckkkuuu|||}}}rrraaaYYYRRROOOMMMKKKKKKMMMMMMMMMNNNOOOOOOMMMIIIEEECCCCCCDDDEEEDDD@@@999444000///...///000000///---///...,,,,,,,,,---///000................................................+++,,,---......---,,,+++---------,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,------------,,,+++,,,---...,,,***,,,,,,,,,,,,,,,,,,,,,---++++++++++++++++++++++++++++++++++++++++++++++++ooo\\\WWWTTTUUUVVVWWWWWWXXXXXXXXXZZZXXXUUUUUUVVVUUUPPPLLLBBB===888333111111000///////////////............------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------,,,,,,---...///000111111------,,,,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,...------,,,,,,------................................./////////000000000000////////////000111111111111111111111222333333111111222333666:::===???IIINNNWWWcccqqq~~~uuulllccc```]]][[[]]]bbbgggkkkyyy~~~kkk___TTTQQQOOOLLLJJJJJJNNNNNNOOOPPPQQQOOOKKKHHHDDDBBBBBBDDDGGGDDD===666111/////////111111000//////...,,,++++++,,,---...................................................,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------------,,,+++,,,......,,,+++,,,,,,,,,------.........++++++++++++++++++++++++************************jjj[[[WWWRRRTTTUUUWWWXXXXXXXXXWWWYYYWWWVVVWWWWWWVVVSSSPPPFFFAAA:::444222000///...////////////............------------------------,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,------......------......//////000000,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,...------,,,,,,------...------------------------...////////////000000000000000//////000000111222222111111111111222333333///000111333555999===@@@KKKTTTbbbqqq~~~zzzppphhheee```]]]]]]___aaabbbkkkuuuwwwgggWWWPPPOOOMMMKKKKKKNNNNNNOOOPPPRRRPPPMMMKKKEEEAAA@@@CCCHHHHHHAAA:::333111000000111111111000//////...---,,,,,,,,,---................................................------,,,++++++,,,------,,,,,,,,,,,,,,,,,,,,,,,,........................,,,,,,,,,------------...---,,,,,,---......---+++***++++++,,,---......///++++++++++++++++++++++++++++++++++++++++++++++++vvvcccWWWTTTQQQSSSUUUWWWXXXXXXXXXWWWWWWWWWWWWXXXXXXWWWUUUSSSJJJDDD<<<666222000///...////////////............------------------------,,,,,,,,,,,,,,,,,,,,,,,,******++++++,,,,,,------///.........------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,...------,,,,,,------...........................////////////000000000111000000000000000111222222222222222111222333333444333555666777888<<>>666444111111111111111000000000///......---------......................................................------------......,,,,,,,,,,,,,,,,,,,,,,,,........................,,,,,,---------.........------,,,---...///---+++)))******+++,,,------...++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,zzzmmm^^^TTTPPPRRRRRRTTTUUUWWWXXXXXXXXXVVVWWWXXXXXXXXXWWWUUUTTTMMMGGG>>>777333111000///////////////............------------------------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,///......---,,,+++******++++++,,,,,,,,,,,,------------------------------...------,,,,,,------.../////////////////////////////////000000000111111111000000000000111222222222222222222222333444444444555666666888>>>GGGNNNZZZiii}}}}}}tttmmmeeeaaa______^^^\\\ZZZaaalllwww~~~|||{{{{{{|||xxxdddXXXQQQLLLKKKMMMMMMMMMNNNPPPRRRRRRQQQOOOIIIDDD@@@@@@CCCEEEDDDAAA999777333111111111000/////////////////////..............................................................................++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,---------...............---,,,---//////---,,,*********++++++,,,,,,,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,{{{|||~~~nnn```UUUOOORRRRRRSSSTTTUUUWWWYYYYYYUUUWWWXXXXXXWWWVVVUUUTTTNNNHHH???777333222111000////////////............------------------------,,,,,,,,,,,,,,,,,,,,,,,,------------,,,,,,,,,,,,...---------,,,++++++++++++++++++,,,,,,---------...........................------,,,,,,------...000000000000000000000000//////000000000111111111111111000000111111222333333222222222222333444444222444555666888AAAMMMWWWmmmzzzzzzrrrhhhbbb```___]]]ZZZXXX]]]eeennnyyy~~~{{{{{{||||||zzzxxxvvvuuuuuuxxx~~~wwwiii]]]SSSNNNOOOLLLLLLMMMOOOQQQRRRRRRPPPKKKGGGAAA>>>???AAACCCDDD===999555222111000///...------......///.........................................................,,,---............---,,,+++++++++,,,,,,---------,,,,,,,,,,,,,,,,,,,,,,,,------------...............------...//////...,,,+++,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++~~~ssseeeYYYRRRSSSSSSRRRSSSTTTWWWYYYZZZUUUWWWXXXXXXVVVUUUTTTTTTOOOIII???888444222222111000/////////............------------------------,,,,,,,,,,,,,,,,,,,,,,,,/////////......------,,,,,,,,,------------------+++++++++,,,,,,---------////////////////////////...------,,,,,,------...000000000000000000000000000000000000111111111111111111111000111111222333333333222222333333444555666777999:::>>>HHHWWWccc}}}xxxllldddaaa```]]]ZZZVVVZZZaaaiiisss~~~}}}|||}}}zzzxxxyyy{{{|||{{{yyyuuusssrrruuuzzz~~~yyyiiiZZZRRRQQQLLLKKKLLLNNNQQQRRRRRRQQQMMMHHHBBB===<<<>>>BBBEEE>>>;;;666333111000///---++++++,,,---............................................................***+++---......---+++***+++++++++,,,,,,---------........................---------.........//////...------...//////...,,,---------------------,,,++++++++++++++++++++++++************************qqq]]]QQQTTTTTTTTTRRRSSSVVVWWWVVVSSSTTTUUUVVVVVVVVVVVVVVVQQQMMMEEE===777333111000//////............//////.........------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,......////////////......++++++++++++++++++++++++,,,,,,++++++,,,,,,---...................................................000000000000000111222222555555444333222222222222222222222111111111111000333444444333222333555777999999===CCCIIITTTeeeuuu|||ssslllhhhfffdddaaa]]]\\\]]]dddmmmvvv}}}yyy}}}{{{wwwssspppqqquuuxxxzzzzzzzzz{{{}}}|||yyyvvvwwwuuurrrpppqqqsssvvvxxx|||lllXXXNNNNNNNNNMMMMMMOOORRRRRROOOMMMIIICCC>>><<<===@@@BBB@@@>>>999555222111222222111///---...111222000...//////.........---------...............---------------,,,,,,,,,---....../////////......---,,,,,,------............------111111000000///---,,,++++++,,,---......---,,,++++++,,,,,,------,,,,,,+++........................++++++******++++++,,,---{{{fffYYYUUUUUUSSSRRRSSSUUUVVVVVVSSSTTTTTTUUUVVVVVVUUUUUUQQQMMMFFF>>>888444111111//////............//////......---------,,,,,,,,,,,,,,,,,,---------------......////////////......,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---...........................,,,,,,,,,,,,,,,,,,,,,,,,...............//////000555444333222222222222222222222222222111111111111333333444333222333555777::::::>>>GGGRRR```rrrzzztttqqqnnnjjjggg___]]]]]]bbbiiirrr|||yyysssqqqnnnjjjhhhjjjnnnrrrsssuuuxxxzzz{{{{{{{{{{{{vvvuuusssqqqqqqsssuuuvvvxxx{{{}}}zzzaaaSSSPPPOOOMMMLLLOOOQQQQQQOOOLLLHHHBBB===;;;;;;===???FFFCCC>>>888444000///...111///---...000111000...//////.........---------------.....................------,,,,,,,,,------------------............------............------///000000//////...---,,,,,,------------------,,,******++++++++++++******,,,,,,,,,,,,,,,,,,,,,,,,++++++******++++++,,,---qqqaaaXXXUUURRRQQQRRRTTTUUUUUUSSSSSSTTTUUUUUUUUUUUUTTTRRRNNNGGG@@@:::555222111//////............//////...------------,,,,,,,,,,,,---------......//////......////////////......,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---...////////////////////////,,,,,,,,,,,,,,,,,,,,,,,,......------......///000444333333222222222222333333222222222111111111111222222333222222333555888;;;<<>>>>>AAA@@@???===:::777555333///.........//////....../////////...............,,,,,,,,,---...///000000000///...---,,,+++++++++,,,,,,,,,,,,------......------............------,,,---....../////////......---,,,++++++,,,---.........////////////..............................++++++******++++++,,,---qqqcccYYYRRRRRRTTTRRRRRRUUUTTTTTTUUUUUUUUUTTTTTTSSSRRRPPPKKKEEE>>>888444111//////............//////------------------------.........//////000000000------............------------------------------,,,,,,++++++,,,,,,---...///////////////////////////////////////////////////////////////000000111111111111111222222333444333333333222222222222111000222333333333555888:::@@@GGGZZZttt}}}xxxuuunnngggddddddgggqqq|||~~~uuuqqqooommmllliiiiiijjjjjjkkkkkklllllliiigggddd```^^^```eeehhhmmmrrrvvvvvvsssrrrvvvzzz|||{{{xxxvvvsssqqqpppooonnnnnnkkkgggcccaaabbbcccaaacccfffkkkpppuuuyyy{{{|||yyywwwwwwyyyyyy{{{~~~```UUUKKKKKKNNNMMMMMMNNNPPPNNNKKKHHHDDDAAA>>>===<<<===>>>>>><<<:::777555.../////////......//////////////////////////////,,,,,,,,,---...///000000000///...---,,,+++++++++.........------,,,,,,,,,------............------+++,,,---...////////////...---,,,++++++,,,---......//////000000//////...........................++++++******++++++,,,---hhh[[[RRRSSSUUURRRRRRVVVUUUVVVVVVVVVVVVUUUTTTTTTSSSQQQMMMGGGAAA:::555222//////............//////,,,,,,,,,------------...////////////////////////------............------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---...........................------------------------------,,,,,,------...///000000000111111333444555333333333333222222222222111222333444444666:::===CCCOOOeeeyyyrrrkkkgggdddeeemmmvvv|||oooeee```^^^]]]\\\ZZZZZZ\\\```fffmmmsssxxxvvvtttoooiiieeeeeegggjjjkkknnnrrrsssssstttxxx|||zzzxxxuuuqqqmmmkkkjjjiiieeedddbbb___\\\[[[\\\^^^]]]___bbbhhhooovvv|||~~~gggXXXLLLLLLOOOMMMMMMOOONNNMMMKKKHHHEEEAAA===;;;===>>>@@@@@@>>>;;;666333///000111000///...///111...////////////000000000,,,---------...////////////...------,,,,,,,,,,,,000//////...------,,,,,,------............------+++,,,---..................------,,,,,,------...,,,,,,------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++******++++++,,,---mmm^^^SSSUUUVVVSSSRRRWWWWWWWWWWWWWWWWWWVVVUUUUUUSSSQQQNNNIIIBBB;;;555222//////............//////,,,,,,,,,---------......000//////......------,,,,,,------......------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---...---------------------------------------------------,,,,,,,,,,,,---....../////////000111333444555444444333333333222222222111333444555666888<<<>>>GGGTTTlllxxxqqqmmmiiihhhnnnvvvxxxiii^^^ZZZXXXVVVUUUXXXWWWYYY]]]fffqqq|||wwwpppmmmnnnpppnnnnnnpppqqqsssvvvxxxyyyvvvsssnnnhhhdddbbbaaaaaa]]]]]]]]]\\\[[[]]]aaadddfffhhhlllsss|||mmmZZZMMMMMMPPPMMMMMMPPPMMMMMMLLLJJJGGGCCC???<<<>>>@@@CCCCCCAAA===777444///111222222000///000222.../////////000000000000------.....................------,,,,,,,,,------////////////////////////------............------,,,,,,---.........------,,,------------------,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++******++++++,,,---ppp___SSSUUUWWWSSSSSSXXXXXXXXXXXXXXXWWWWWWVVVUUUSSSRRROOOJJJCCC<<<666222//////............//////,,,,,,,,,------.........000000///...---,,,++++++,,,------......------,,,++++++++++++++++++++++++,,,,,,++++++,,,,,,---...,,,,,,,,,,,,,,,,,,,,,,,,000000000000000000000000///............///000000/////////000111333444555444444444333333333222222222333555666777999===@@@IIIWWWnnnxxxsssooommmrrryyy}}}|||lll```[[[ZZZXXXVVV]]]\\\\\\___hhhtttzzzuuuuuuvvvsssrrrqqqqqqsssuuuuuutttqqqnnnhhhaaa]]][[[[[[[[[ZZZ[[[\\\]]]___bbbhhhllltttuuuzzzppp\\\MMMNNNPPPMMMMMMQQQNNNNNNNNNMMMJJJFFFAAA???===@@@CCCEEEDDD@@@:::777000222444333000///111333.../////////000000111111...............---------------,,,,,,,,,---............//////000111111111---..................---,,,------......------,,,+++,,,............,,,+++---..................---........................++++++******++++++,,,---www```QQQTTTVVVQQQPPPWWWYYYYYYXXXWWWVVVUUUSSSRRRTTTRRROOOLLLGGG@@@888222111111111111000///...---------..................////////////////////////,,,,,,,,,,,,,,,,,,,,,,,,******,,,---.../////////,,,+++++++++,,,,,,---...////////////////////////...............///000000000000//////......------000000000000000111111222555444444444444555666666555333444666666666<<>>FFFPPP]]]pppzzztttrrrrrrsssxxxxxx}}}vvvllldddffflllqqqpppllliiijjjqqq}}}}}}uuuqqqkkklllllljjjgggeeedddeeeaaabbbaaa___]]]^^^```bbblllqqqwwwzzz}}}~~~qqqbbbZZZWWWVVVTTTQQQOOOOOOPPPNNNJJJFFFCCCAAA??????AAACCCDDDBBB===999555222000///000111000000////////////////////////,,,,,,---------.................................///////////////000111111........................000000000000//////............---------......///---...............------...---,,,+++++++++,,,---------------------------lllYYYUUUUUUQQQQQQWWWVVVVVVVVVVVVUUUTTTSSSRRRRRRQQQOOOLLLHHHAAA999444111111111000000///......000000//////......------------------------------------------------------------......------,,,+++------,,,,,,,,,,,,,,,---////////////////////////...............///000000/////////000000000111111111000000000000111222222555444444444444555666666555333444666777:::BBBLLLXXXeeewwwyyytttrrrqqqsssqqqssszzzvvvqqquuu{{{zzzsssooosss}}}wwwooojjjeeeffffffeeecccbbbcccdddbbbdddfffgggiiimmmqqqtttqqqeee___\\\YYYUUUNNNOOOPPPOOOMMMHHHCCC@@@??????AAACCCDDDCCC???===999666111//////000000///////////////////////////+++++++++,,,,,,,,,------........................---------------......///........................000000000////////////...+++,,,---....../////////......////////////............---,,,++++++,,,,,,------------------------ttt]]]VVVTTTQQQRRRWWWUUUUUUUUUUUUUUUTTTSSSRRRRRRQQQOOOLLLIIIBBB;;;666222222111000////////////000//////...---,,,++++++++++++++++++++++++++++++........................******,,,---.../////////......---,,,,,,,,,,,,---////////////////////////...............///000000...//////000111222222222111111000000111111222333555444444444444555666666555444555888;;;AAALLLXXXhhhsss}}}xxxuuusssmmmlllnnnuuu|||~~~xxxxxx}}}~~~vvvmmmgggddddddeeeeeeeeeeeegggjjjmmmnnnppptttxxx|||pppgggbbb[[[UUUMMMNNNOOOPPPOOOKKKFFFBBB??????@@@BBBDDDDDDBBB???===999333///////////////////////////////////////++++++,,,,,,,,,,,,------........................,,,,,,++++++,,,,,,---...........................////////////////////////***,,,---...///...------,,,---..................///......---,,,,,,++++++------------------------xxx```VVVSSSQQQRRRVVVTTTTTTUUUUUUUUUTTTTTTSSSRRRQQQOOOMMMJJJEEE>>>999333222111000/////////000......------,,,+++******,,,,,,,,,,,,,,,,,,,,,,,,........................******,,,---.../////////......---,,,,,,---------////////////////////////...............///000000......///000111222333333111111111111111222222333555444444444444555666666666444666<<>>>>>???AAAAAA@@@???<<<888555333222///...000000000000000000000000....../////////000000000////////////////////////,,,++++++++++++,,,------........................---------.........//////------,,,,,,+++,,,,,,,,,)))***+++,,,------------+++,,,---...//////......------------------------xxxaaaTTTQQQSSSSSSSSSTTTUUUVVVVVVWWWWWWWWWWWWTTTSSSRRRRRRPPPKKKEEEAAA555444111000//////111222/////////000000000000000------------------------,,,,,,,,,,,,,,,,,,,,,,,,******,,,---.../////////++++++,,,,,,...///111222////////////////////////...............///000000............////////////222222111111222222333444555444444444444555666666666777===JJJ[[[ppp{{{wwwtttsssvvvxxx|||~~~vvvrrrsssuuuyyy|||iii___SSSLLLKKKLLLLLLJJJBBB@@@======>>>@@@@@@??????<<<888666444222000...000000000000000000000000.........////////////000000000000000000000000000///............///000000........................---------.........//////,,,+++******+++,,,...///***+++,,,---............***+++---///000000//////------------------------|||eeeUUUPPPRRRTTTTTTUUUUUUUUUUUUUUUUUUVVVVVVTTTSSSQQQOOONNNKKKGGGDDD:::777333000000000///...------......//////000000...---+++******+++---...------------------------,,,++++++***+++,,,...///,,,++++++++++++,,,---...---,,,,,,,,,,,,---......---------.........//////////////////000000000000111111222222222333333333000222333444444666888;;;;;;???HHHVVViii~~~~~~||||||{{{yyywwwxxx|||~~~|||}}}xxxcccPPPLLLNNNNNNKKKJJJEEEBBB???>>>>>>>>>>>>======???>>>999222///111555//////////////////////////////000000000000////////////000000000000//////......////////////........................------........................,,,,,,,,,---------......+++++++++,,,,,,,,,---------,,,,,,++++++,,,,,,---...---,,,,,,,,,,,,---...kkk[[[SSSQQQRRRQQQRRRSSSSSSSSSTTTTTTUUUUUUTTTSSSQQQPPPNNNKKKGGGDDD:::777333111000000//////////////////000000000000...---+++******+++---...---------------------------,,,,,,++++++,,,---...---,,,,,,,,,,,,,,,---...------,,,,,,------...///---------.........//////////////////000000000111111111222222222333333333111333444444444666888;;;===BBBOOObbbxxx}}}{{{yyyzzz|||}}}|||zzz|||mmmWWWNNNNNNMMMKKKKKKFFFCCC@@@>>>>>>>>>===<<<===??????;;;444000111333//////////////////////////////000000000000////////////000000000000//////------............------................................................,,,,,,,,,---------......,,,,,,---------.........---,,,,,,++++++,,,,,,---...---,,,,,,,,,,,,---...yyyhhhZZZSSSQQQQQQPPPPPPQQQQQQRRRSSSTTTTTTTTTSSSQQQPPPOOOLLLHHHEEE<<<888444111000000//////111111111000000000000000...---,,,++++++,,,---...------------------------///...------,,,---------......---------------...---------,,,------...///------.........//////////////////000000000111111111111222222222333333333333444555555555666999;;;AAAIII[[[sss|||uuuqqqooopppssswww|||{{{aaaRRRNNNLLLKKKLLLHHHEEEAAA??????>>>===<<<===???AAA>>>888333111111000000000000000000000000//////000000000000//////...//////000000//////...------------------------................................................,,,,,,,,,---------......---------.........//////------,,,,,,,,,,,,------...------,,,,,,------...wwweeeYYYTTTTTTOOOOOOPPPQQQRRRTTTTTTUUUUUUSSSRRRQQQOOOMMMIIIFFF>>>:::555111000000000///111111000000//////.........---,,,,,,,,,,,,---...------------------------/////////...------------//////...------------...---------------...//////............//////////////////000000000111111111111111222222222333333333444555555555555777:::===FFFTTTjjj~~~uuunnniiifffdddhhhnnnvvv}}}kkkVVVMMMKKKKKKKKKIIIFFFCCC@@@@@@???===<<<===@@@BBB@@@;;;666222000//////////////////////////////000000000000//////...//////////////////......------------------...---------.......................................,,,,,,,,,---------......------------............------,,,,,,,,,,,,------------------------------qqqaaaXXXVVVPPPPPPQQQRRRTTTUUUVVVVVVUUUSSSRRRQQQPPPNNNJJJGGG@@@<<<666111000000000////////////......------,,,------------------------------------------------/////////......------,,,///......---------.........------------...//////........./////////000000000000000000111111111111111111222222222333333333555555666555666888<<>>======@@@BBBBBB>>>999444111........................//////000000000000//////......////////////......//////...------...//////---------.........//////........................,,,,,,,,,---------......+++,,,,,,,,,,,,---------...------,,,,,,------...------------------------nnn___WWWRRRRRRSSSTTTTTTUUUVVVVVVUUUTTTRRRRRRQQQOOOKKKHHHBBB===777222000000000000......------------------------------------------------------------------------.........------,,,------,,,,,,---......///......------......///000....../////////000000000000000000111111111222222111111222222222333333333555555666666777:::???CCCSSSeee|||sssmmmfff```]]][[[ZZZZZZ\\\bbblllvvv}}}~~~xxx```RRRNNNLLLJJJKKKHHHDDDBBBBBBAAA@@@???===???BBBCCCAAA<<<666333//////////////////////////////000000000000//////---......//////......---000///...------...///000,,,,,,------.../////////........................,,,,,,,,,---------......+++++++++,,,,,,,,,------......------------......,,,------......------,,,iiiZZZSSSSSSSSSTTTTTTUUUUUUUUUUUUTTTSSSRRRQQQOOOLLLIIIDDD???777222000000000000---------...............------............------------------------------+++,,,---......---,,,,,,++++++++++++,,,...///000...............//////000.../////////000000000000000000111111111222222222111111222222222333333333444444555666777;;;AAAFFFWWWggg{{{zzzrrrkkkfffbbb]]]YYYXXXYYYYYYYYYXXX___jjjttt|||{{{fffXXXSSSOOOKKKJJJHHHDDDCCCCCCCCCBBBAAA===???AAABBBBBB>>>999666000000000000000000000000//////000000000000//////---......//////......---000///---,,,,,,---///000,,,,,,------...//////000........................,,,,,,,,,---------......,,,,,,,,,,,,---------.........------------......,,,,,,---......---,,,,,,rrr^^^SSSSSSSSSSSSTTTTTTTTTTTTUUUTTTSSSRRRRRRPPPLLLJJJEEE???888222000000000000---.........//////000000------............------------------------------)))***,,,---...------,,,))))))***+++,,,...///000...............///000000////////////000000000000000111111111111222222222111111222222222333333333333444555666888<<>>???@@@BBBBBB@@@;;;777222222222222222222222222//////000000000000//////---..................---///...,,,++++++,,,...///,,,,,,------...///000000........................,,,,,,,,,---------......---------.........//////......------------......,,,,,,---......---,,,,,,}}}aaaYYYUUUQQQQQQTTTWWWWWWVVVWWWVVVTTTRRRPPPOOONNNNNNFFFBBB<<<666222111222333////////////////////////........................////////////////////////..................------,,,,,,,,,---------......,,,+++***)))***,,,///000...//////000111222222222222222222111111111111000333333333333444555666666777888888777888>>>GGGOOO^^^gggwww|||tttmmmkkkiiiccc```______bbbaaa\\\[[[^^^```___```ccchhhqqq{{{xxxkkk```XXXUUUPPPKKKGGGGGGFFFCCCDDDGGGFFFCCCAAABBBDDDCCC===888666444222111111111///...////////////////////////...------,,,,,,...///000000///---,,,++++++,,,,,,------............------111111000000//////......111000///...............------------------,,,,,,++++++++++++++++++++++++,,,------....../////////gggZZZVVVRRRRRRTTTWWWWWWVVVXXXWWWUUUSSSQQQPPPOOOOOOGGGCCC===777333111111222////////////////////////................................................,,,,,,,,,,,,,,,,,,,,,,,,,,,---------............---......///000000000000...//////000111111222222000000111111222222222333222222222333333444555666444666888888:::@@@IIIPPPaaakkk{{{yyyqqqjjjhhhfffcccaaabbbfffiiijjjfffdddeeeeeeccccccfffkkksss}}}xxxjjj^^^XXXSSSMMMIIIHHHGGGCCCCCCFFFGGGEEECCCDDDFFFEEE???:::666444111000111111///...........................///...---------...///000000///...,,,++++++,,,,,,------............------////////////.........---------,,,+++++++++++++++------------------------,,,,,,,,,,,,,,,,,,,,,,,,...------------......///lll[[[WWWSSSRRRUUUXXXXXXWWWXXXWWWVVVUUUSSSRRRPPPPPPIIIEEE???888444111111111////////////////////////........................------------------------+++++++++,,,---------...------........./////////...///111222333111000.../////////000111111222222...///000111222333444444222222222222333444555555333666999<<>>666444111000000000000///------------------------//////.........///000111000///...---,,,,,,,,,,,,------............------............------------,,,,,,+++*********++++++,,,,,,,,,---.........///------------------------000///---,,,,,,---...///ppp\\\XXXTTTSSSVVVXXXXXXWWWWWWWWWVVVUUUSSSRRRPPPPPPJJJGGGAAA:::555222000000////////////////////////........................------------------------,,,------...///000000111.........////////////000---.../////////...---,,,//////000000111111111111///000000111222222333333222222111222222333444555777999<<>>999555333222////////////////////////................................................------------............,,,---------............////////////000111222222111000000000000000000000111111111111111222222222444444444444555666777777888===EEEPPP___sss}}}gggYYYQQQLLLIIIIIIGGGIIIKKKLLLKKKJJJIIIIIICCC>>>888444111111000///000000000000000000000000,,,---...///000///......---...///000000///...---------............------........./////////000000,,,+++++++++,,,,,,---...............////////////------------------------+++---...///000///...---xxx\\\WWWSSSQQQSSSUUUUUUTTTUUUVVVWWWXXXWWWUUURRRQQQKKKHHHDDD???:::666444333////////////////////////........................------------------------000000000000000/////////,,,,,,,,,---------......+++---///111222111000000111111111000000000000000//////000111222333333444555555444555555666777888999@@@LLLZZZkkk~~~ppp^^^TTTMMMJJJIIIHHHJJJMMMNNNMMMLLLKKKKKKEEE@@@:::555222111000///////////////////////////+++,,,.../////////...------...///000000///......---..................------------.........//////,,,,,,,,,,,,------...//////////////////.........------------------------***+++...000111000...,,,sss\\\VVVRRRTTTTTTSSSRRRTTTUUUTTTTTTTTTUUUTTTQQQOOOKKKIIIEEE@@@;;;666222000111111111111000000000000.../////////...---,,,,,,//////.........---------........................////////////////////////000000000000000000000000////////////////////////111111111000111111222333444000000444666555444666???CCCQQQgggyyy|||aaaRRRPPPNNNIIIGGGHHHJJJMMMOOONNNJJJGGGEEEAAA;;;555111000111222222222111111000000//////......------------......//////............/////////...---,,,,,,---...////////////......---,,,,,,------++++++++++++------000//////.........//////......------------......////////////////////////{{{lllWWWRRROOORRRUUUUUUUUUXXXVVVUUUTTTUUUUUUTTTQQQNNNIIIGGGDDD@@@;;;777444222000000000////////////.../////////000//////......//////.........---------------------------------////////////////////////000000000000000000000000111111111111111111111111111111111111111222222333555222222666888666777:::AAAKKK```wwwgggVVVQQQNNNKKKIIIJJJKKKNNNPPPOOOKKKIIIGGGDDD>>>888333222222222111111000000000000000//////................../////////............/////////...------------...///.............../////////------,,,++++++,,,------............////////////......------------......////////////////////////xxxkkkXXXRRROOORRRUUUUUUVVVWWWXXXVVVUUUUUUUUUSSSPPPMMMGGGFFFDDD@@@<<<888555333////////////...............///000000000000000000/////////............---------------------------////////////////////////000000000000000000000000111111111111111111111111111111111111111222333333666333333777888888:::>>>DDDUUUppprrr]]]SSSPPPNNNKKKKKKLLLNNNPPPOOOMMMJJJJJJGGGAAA;;;666333222222////////////000000000000000//////......//////000//////............/////////...------------...///,,,------...//////000000------,,,,,,,,,,,,------,,,---...///000000///.........------------......000000000000000000000000~~~rrraaaXXXRRRSSSUUUTTTSSSTTTYYYWWWVVVVVVUUUSSSPPPMMMHHHGGGEEEBBB===999555222000000/////////.........---...///000000000000000/////////...............------------------------////////////////////////////////////////////////111111111111111111111111222111111111111222333333555333333777888999===BBBHHH]]]{{{gggVVVQQQPPPKKKKKKKKKLLLNNNNNNMMMKKKKKKHHHCCC===888444222111.........//////000000111000000////////////000000//////............//////.........------.........,,,,,,------............---------,,,,,,---------***+++...000000000///.........------------......000000000000000000000000}}}lllaaaVVVTTTVVVUUUSSSTTTYYYXXXVVVVVVUUUSSSPPPMMMKKKJJJHHHDDD???999444111111111111000000000//////,,,---......////////////////////////////////////------------------------////////////////////////////////////////////////000000000000000000000000222222222111222333333444444222333666777888???FFFQQQeeeqqq[[[RRRQQQKKKJJJIIIJJJLLLMMMLLLKKKKKKIIIDDD???999555222000......//////000000111111000000////////////000000//////............//////---..................------------,,,,,,,,,++++++------------------------)))+++---///000000///.........------------......////////////////////////xxxiii[[[WWWWWWWWWWWWXXXXXXWWWVVVVVVVVVTTTQQQNNNNNNMMMKKKGGGAAA;;;555222111111111111000000000000,,,---...............---...////////////000000000........................////////////////////////000000000000000000000000////////////////////////222222222222222333444444333222333666777999AAAJJJ[[[mmmzzzaaaTTTRRRLLLJJJHHHIIIJJJLLLLLLKKKKKKIIIFFFAAA<<<777333000000000000000111111111111000//////......//////000//////............//////------...//////...------......------,,,++++++***------............------+++,,,---...//////...---......------------......////////////////////////uuubbbZZZYYYXXXWWWXXXXXXWWWVVVVVVVVVUUURRRPPPNNNMMMLLLHHHCCC===888444111000000000000/////////...////////////......---.../////////000000000000////////////////////////////////////////////////000000000000000000000000000000000000000000000000333222222222222333444444444333444777888;;;DDDOOOaaapppfffWWWSSSMMMKKKIIIIIIJJJLLLMMMMMMLLLJJJHHHDDD???999555222222222222222111111111111///................../////////............//////------...//////...------........................,,,---...//////...---,,,------------------------......------------......------------------------iii]]]YYYVVVUUUUUUWWWVVVVVVVVVWWWVVVSSSQQQLLLLLLLLLIIIEEE@@@;;;777000/////////............000000111000000///........./////////000000111111000000000000000000000000////////////////////////000000000000000000000000111111111111111111111111333333222222333333444555555444666888999<<>>:::777666444222111222222111000////////////////////////...............///000111000000///...............000000///...------,,,,,,222222111000///...---------...///...------...///---------............///........................ppp___WWWUUUTTTYYYYYYWWWVVVTTTRRRQQQPPPNNNMMMKKKGGGCCC???;;;999111111111000000000000000000000/////////.........////////////000000000000------------------------////////////000000000000000000000000000000000000111111111111111111111111222222222222222222333333555666777777;;;CCCOOOXXXkkkzzzwwweeeXXXTTTOOOLLLLLLLLLJJJKKKNNNNNNKKKHHHFFFCCC???;;;888555333111111111222111000000000000000000000000000///............//////000000000///...............000//////...------,,,,,,........./////////000000---...///...------...///---------............///////////////////////////|||eeeWWWTTTUUUWWWWWWVVVUUUTTTRRRPPPOOOMMMLLLJJJGGGCCC???;;;999222222111000000000000000000000////////////......000000000000////////////////////////////////////////////////000000000000000000000000000000000000000000000000000000000000333333333333222222222222333555777999>>>IIIVVV```tttwwwfffXXXRRRNNNOOOOOOLLLLLLNNNNNNLLLIIIGGGEEEAAA===999555333111000111111000///111111111111111111111111000//////............///000//////............////////////...------,,,,,,---------.........//////---...///...------...///---------............///000000000000000000000000gggWWWTTTVVVUUUUUUUUUUUUTTTRRRPPPOOOMMMLLLJJJGGGCCC???<<<:::444333111000000000000111000000//////////////////111111000000//////......////////////////////////////////////000000000000000000000000000000000000000000000111111111111111444333333333333222222222333555888;;;BBBNNN]]]hhh{{{ttt]]]UUUPPPPPPPPPMMMMMMNNNNNNLLLJJJIIIGGGCCC???;;;444222000000111111000///000000000000000000000000111000///...............000///............////////////.........---------000///...---,,,++++++***---...///...---------///---------............///////////////////////////hhhVVVSSSWWWTTTTTTUUUUUUTTTSSSQQQPPPLLLKKKJJJGGGDDD@@@>>><<<555444222000///000000111//////000000000000000000111111000000//////......000000000000000000000000////////////000000000000000000000000000000000000111111111222222222333333333333333333333333333333555777:::???GGGUUUfffrrr~~~fff\\\RRROOOOOOMMMMMMNNNNNNMMMLLLKKKIIIFFFAAA===555333111000111111000///////////////////////////111000///...............//////............//////...............---------//////...---,,,+++******---...///...---------///---------............///........................jjjWWWSSSUUUSSSTTTUUUVVVVVVTTTRRRQQQMMMLLLJJJHHHEEEBBB???>>>666555222000///000111111//////000000000000111111000000000000////////////000000000000000000000000////////////000000000000000000000000000000000000111111111222333333444444333333333333444444444444777999>>>DDDOOO___rrrxxxiiiYYYQQQNNNLLLMMMOOONNNNNNMMMMMMLLLHHHCCC???666444222111222222111000........................000//////............//////............//////000........................,,,,,,,,,---------......---...///...------...///---------............///........................lllZZZUUUVVVSSSTTTVVVWWWWWWUUUSSSRRRMMMMMMKKKIIIGGGDDDAAA@@@777555333000//////111222//////000000000111111111////////////000000000000////////////////////////////////////000000000000000000000000000000000000000000000111222333333333111222222333444555666666777;;;AAAJJJXXXkkk{{{dddVVVOOOMMMMMMOOONNNNNNNNNNNNMMMJJJEEEAAA777555333222333333222111///////////////////////////............//////000...............///000000........................------------............---...///...------...///---------............///........................lll\\\WWWWWWSSSTTTVVVXXXXXXVVVTTTRRRNNNMMMLLLJJJHHHEEECCCAAA888666333000//////111222//////000000111111111222......//////000000111111////////////////////////////////////000000000000000000000000000000000000...//////000111222222222000111222333555666777777888<<>><<<;;;888444111111111000///000000000000000000000000333333333222222222111111////////////////////////////////////////////////000000000000111111111111000111111111111222222222222333444444333444666888;;;===HHH[[[mmm}}}xxx___RRROOOPPPQQQPPPOOONNNNNNMMMJJJFFFCCC@@@:::444000000111111000000000000000////////////---.........//////000000000000000000000000000000222111111000///......---/////////...---------,,,////////////////////////...------------...//////......///000000000000000vvvdddWWWRRRRRRRRRRRRSSSSSSSSSSSSSSSSSSNNNMMMKKKIIIFFFDDDBBBAAA;;;888444222111111000///000000000000000000000000222111111111000000000000////////////////////////////////////////////////000000000000111111111111111111111111222222222222111333444444333444666888:::>>>LLL```rrr|||cccTTTOOOOOOPPPNNNNNNMMMNNNNNNLLLHHHEEECCC>>>888444333444444333111000000000////////////............/////////000////////////////////////000000000///...---------..................------........................---------------...///000......///000000000000000nnn^^^SSSPPPPPPQQQRRRSSSTTTTTTTTTTTTTTTOOONNNLLLJJJHHHFFFDDDCCC<<<999555222111111000///000000000000000000000000000000////////////......////////////////////////////////////////////////000000000000111111111111111111111111222222222333111333444444444555777999:::BBBRRRgggzzziiiXXXPPPNNNOOOMMMLLLMMMNNNOOONNNKKKHHHEEE@@@:::666555555444444111111000000000/////////............////////////........................//////......------,,,,,,..................//////------------------------,,,,,,,,,---...///000111......///000000000000000}}}mmm]]]TTTQQQQQQQQQRRRSSSUUUUUUUUUUUUTTTRRRQQQNNNKKKGGGDDDBBB@@@===:::666333222111111000///////////////////////////////////////////////////////////////////////////////////////////////////000000000111111111111111111111222222222333333111333444555555666999;;;<<>>;;;777444333222111000////////////////////////000000000000000000000000////////////////////////000000000000000000000000///000000000111111111111111222222222222333333333111222444555666777:::<<>>EEEUUUkkkzzzcccRRRLLLLLLMMMLLLLLLMMMNNNLLLIIIFFFEEECCC@@@;;;555222222333222222111111111000000000///////////////.................................000000000000000000////////////////////////000000------------------------...------------...//////......///000000000000000}}}iii[[[TTTUUUVVVXXXXXXXXXVVVSSSRRRNNNNNNLLLKKKIIIHHHGGGFFF@@@===888555444333111000000000000000000000000000000000000111111222222222////////////////////////000000000000000000000000000000000000111111111111222222222333333333444444000222444666777999===???JJJ[[[qqq}}}dddSSSLLLLLLJJJIIIJJJLLLMMMLLLJJJGGGFFFEEECCC===777333222444222222222111111111000000000/////////............////////////////////////////////////////////////000000000///////////////........................//////...------------.........///000000000000000rrraaaWWWVVVWWWYYYYYYXXXVVVSSSQQQSSSRRRPPPMMMJJJGGGEEEDDDAAA===999555444333111000000000000000000000000000//////000000111111222222////////////////////////000000000000000000000000000000000000111111111111222222333333333444444444000222555666777:::===@@@MMM___ttt~~~zzzwwwxxx~~~eeeSSSLLLLLLFFFGGGHHHKKKMMMMMMKKKIIIEEEEEECCC===666222111333222222222111111111111000000000//////.........---000000000000000000000000---.....................111111000000//////......////////////////////////000///...---------------...//////000000000000000ooo\\\XXXXXXWWWVVVXXXYYYWWWSSSRRRRRRPPPMMMJJJFFFCCCAAA@@@>>>:::666333111111111000000////////////000000...------...000111///...111111000000//////......//////000000111111222222444333333222222111111111111111222222222333333333333222444777777888???GGGYYYgggxxxxxxqqqooorrr}}}mmmZZZMMMHHHMMMJJJJJJMMMMMMKKKKKKNNNHHHEEEAAA===888555333333////////////000000000000000...,,,---000111///---////////////////////////111111000///...---,,,,,,---------.........//////.........////////////000.........////////////000////////////000000000000iii[[[ZZZXXXWWWXXXXXXVVVRRRQQQPPPOOOMMMJJJGGGEEEDDD@@@>>>:::666333222111111000000////////////000000......---///000111000...000000000000////////////000000000000000111111111333333333333333222222222222222222222333333333333333333555888888:::BBBLLL___mmm~~~tttnnnkkknnnyyytttdddVVVNNNLLLIIIHHHKKKKKKHHHHHHIIIHHHFFFBBB===999666333222000000000000000000000000000...---...000000///---////////////////////////000000000///......------,,,,,,,,,---------......---............/////////---............/////////////////////000000000000ttt```\\\XXXWWWXXXXXXUUUSSSPPPOOONNNLLLJJJHHHGGGFFFAAA???;;;777444222111111111000000//////000000111///......///111111000///////////////000000000000111111111111000000000000222222222333333333333333333333333333444444444444444444666999999<<>>MMM]]]lllzzz{{{sssvvv{{{yyyqqqhhhccc```aaaiiirrrlllVVVOOOJJJLLLOOONNNMMMMMMJJJIIIFFFBBB>>>:::777555333333222222111111111000.../////////......//////////////////////////////------......///000000000............////////////---------.........//////---------.........//////////////////000000000000ooo```VVVXXX[[[YYYXXXZZZVVVTTTPPPLLLIIIFFFEEEEEEBBBAAA???;;;777444111000222111111000000111111222111000000111333333222111////////////000000000000111111111111000000000000000000000111111111111111333333333333444444444444666777999;;;;;;BBBTTTfffxxxzzzoooqqqvvvvvvnnnfffbbb^^^^^^eeennn~~~yyy]]]SSSKKKKKKMMMMMMLLLMMMIIIHHHFFFDDD@@@===999888444444333333222111111111...///000///...---...000////////////////////////---.........//////000000...////////////000000000.........////////////000.........////////////000////////////000000000000vvveeeXXXYYY[[[WWWUUUXXXUUUSSSPPPLLLIIIGGGGGGGGGCCCBBB???<<<888444111000222111111000000111111222111111000222333444333111000000000000////////////000000000000000111111111333333333222222222222222222222222222333333333333444666999<<>>BBBNNNfff{{{|||ooopppuuuqqqjjjccc___[[[[[[```hhh{{{rrrdddUUUPPPOOONNNMMMMMMGGGGGGGGGEEECCC@@@===<<<555555444333333222111111---///111000---,,,...000////////////////////////////////////////////////---------.........//////000000000000111111111111000000000000111111111111////////////000000000000mmm\\\WWWYYYYYYXXXVVVUUURRROOOLLLKKKJJJGGGFFFBBB@@@>>>;;;777444222000222222222111000//////......///000222444666777888111000000/////////000000444333222111111111222333333333333444444444555555555555444444444555666666666666999@@@KKK\\\ttt|||rrrttt{{{{{{uuujjjddd^^^\\\ZZZZZZ```hhh{{{oooWWWMMMJJJGGGFFFHHHHHHGGGFFFFFFEEEAAA<<<999666333000////////////...////////////////////////////////////..................//////000000111111//////............//////////////////000000000000............/////////000000000000000000000000000|||kkk[[[WWWYYYYYYWWWUUUSSSQQQNNNLLLKKKJJJHHHFFFBBBAAA>>>;;;888444222111222222222111000////////////000000111222333333444111111000//////000000111333333222111111111222333333333333333444444444444444444444444444555555666888777:::DDDQQQbbbyyywww}}}wwwpppiiiccc^^^[[[ZZZZZZaaaiii{{{vvv]]]QQQNNNLLLKKKKKKIIIHHHGGGGGGFFFCCC>>>:::666444111////////////...////////////////////////111000000000000/////////.../////////000000000111//////............//////....../////////000000000........./////////000000000000000000000000000000tttfffYYYWWWYYYYYYVVVTTTRRROOOMMMKKKKKKJJJHHHFFFCCCAAA???<<<888555333111222222222111000000//////111111000000000/////////111000000///000000111111222222111111111222222333222222222222333333333333333333333333333444555666:::888===IIIZZZlll|||ssskkkgggbbb\\\ZZZYYY[[[bbbkkk|||~~~cccUUUQQQOOOMMMLLLJJJIIIHHHHHHGGGDDD@@@<<<777555111000000000///...////////////////////////111111111111000000000000////////////000000000000//////............//////------........./////////....../////////000000000000000000000000000000000iii]]]TTTTTTXXXXXXVVVTTTQQQOOOLLLKKKJJJJJJHHHGGGCCCBBB???<<<999666333222222222222111111000000000111111000000/////////...//////......//////000000111111111111111222222222111111222222222333333333333333222333333444555666:::999@@@PPPdddvvv|||rrrkkkfff```[[[YYYYYY[[[ccclll|||hhhVVVOOOMMMKKKIIIKKKIIIHHHHHHGGGDDDAAA>>>888666222111000000///...////////////////////////111111111000000000//////////////////000000000000//////............//////------------.........///...////////////000000000000000000000000000000000ppp___VVVOOORRRVVVWWWVVVVVVQQQOOOLLLKKKKKKJJJIIIGGGDDDCCC@@@===999666444333222222222222111111111111000111111111111111111111---------------...///000000000111111222222222222111111222222222333333333333333333333444555666777:::;;;EEEXXXlll~~~vvvooofff```ZZZXXXXXX[[[dddmmm|||qqq[[[OOOLLLJJJHHHJJJIIIGGGFFFFFFDDDAAA>>>999777333111111111///...////////////////////////000000/////////.........000000000000//////////////////............//////------------.........///////////////000000000111111111111111111111111111wwwhhh[[[SSSNNNQQQUUUVVVVVVWWWSSSPPPNNNLLLLLLKKKIIIGGGEEECCCAAA>>>:::777555333222222222222222222222222000111111222222333333333------------...///000000...///000111222222222222222222222222333333333333333333333444555666777888999>>>LLLaaatttzzzrrrggg```ZZZXXXWWWZZZcccmmm{{{dddSSSMMMLLLKKKJJJIIIGGGFFFFFFDDDAAA???:::888444222222111000...////////////////////////////////////............000000000000//////////////////............//////------.........//////////////////000000000111111111111111111111111111111}}}ooo^^^VVVPPPRRRUUUUUUVVVWWWUUURRROOOMMMLLLKKKIIIGGGEEEDDDAAA>>>;;;777555444222222222222222222222222111111111222222222333333.........//////111222222---...000111222222222111333333333333444444444444444444444555666777999999:::BBBTTTjjj{{{zzzssshhhaaaZZZWWWVVVYYYbbblllzzznnnWWWNNNNNNNNNLLLJJJHHHGGGGGGFFFCCCAAA;;;888555333222111000///////////////////////////000000000////////////...111000000000/////////...//////............//////....../////////000000000//////000000000111111111111111111111111111111111|||bbbZZZSSSTTTUUUUUUUUUWWWVVVTTTPPPNNNMMMKKKIIIGGGEEEDDDBBB>>>;;;888555444222222222222222222222222222222222111111111111111000000000000111222333444---...000111222222222111333333444444444444555555444444555555777888999:::;;;FFFZZZoooyyyrrrhhhaaaZZZWWWVVVYYYbbblllzzzsssXXXNNNNNNPPPMMMKKKIIIHHHHHHGGGEEECCC<<<999555333222111000///////////////////////////111111111111000000000000111111000000/////////...//////............//////////////////000000000000000000000000111111111111111111111111111111111111lll^^^SSSTTTXXXWWWVVVWWWWWWVVVSSSPPPMMMJJJIIIHHHJJJGGGDDDAAA???;;;777444555333111///...000222333222222333333333333222222000000000000000000000000000111111111111222222222333333333444444333222222666555444444555777:::<<<===OOOdddttt{{{tttnnndddYYYSSSRRRVVV___iiiyyy{{{dddTTTNNNNNNIIIJJJKKKKKKJJJHHHFFFDDDAAA===666222000000000000000000000000000000000000000000000000000000000000//////000000000000////////////...------------...////////////////////////000000111222222222222222000111222222111222444666|||kkk[[[XXXYYYXXXWWWVVVWWWUUURRROOOMMMKKKJJJJJJIIIGGGCCCAAA>>>;;;777444444333111000///000111222000000111111111111000000000000000000000000000000000111111111111222222222333333333444444333333222555555555555666888:::<<<@@@RRRgggwww}}}~~~~~~wwwpppeeeZZZTTTSSSVVV```jjjyyyyyydddTTTMMMKKKIIIIIIJJJJJJIIIGGGEEEDDDBBB===777222111000000000000000000000000000000000000000000000000000000000//////000000000000////////////...------------...////////////////////////......///000000000000000000111222222111222444666zzzdddZZZZZZZZZXXXVVVWWWUUURRRNNNLLLLLLLLLLLLHHHFFFCCC@@@>>>;;;666333333222222222111111111111000000111111111111000000000000000000000000000000000111111111111222222222222333333444444333333333333555666777777888;;;===EEEWWWlll|||~~~tttqqqttt|||rrrggg\\\UUUTTTWWWaaakkkyyy}}}{{{}}}~~~}}}xxxxxxxxxwwwwwwwwwwwwwwwwwwyyy{{{}}}yyyhhhXXXOOOKKKIIIIIIIIIIIIHHHFFFEEECCCBBB>>>888333222111111000000000000000000000000000000000000000000000000000//////000000000000//////000///......------......////////////////////////......///000000000000000000111222222111222444666kkk\\\YYYZZZYYYWWWVVVTTTQQQNNNLLLLLLMMMNNNGGGEEEBBB@@@>>>;;;777444222222333333333222111000222222333333333333222222000000000000000000000000000000111111111222222222222222333444444444333333222555888999888999<<>>;;;777444111222444444444333111000222222333333333333222222000000000000000000000000000000111111111222222222111222333333444444444333222666999999888:::>>>BBBPPPbbbxxxvvvpppkkkgggcccbbbiiirrruuuiii]]]WWWVVVZZZeeeppp}}}}}}zzzooommmkkkjjjjjjlllnnnooouuuqqqlllhhhffffffffffff`````````______^^^^^^]]]]]]___bbbdddffffffeeedddbbbccceeehhhkkkooorrrssswwwyyy|||~~~xxxiiiZZZOOOLLLLLLKKKKKKIIIHHHGGGGGGDDD@@@;;;777444333222000000000000000000000000000//////////////////////////////000000000000//////000000///............///////////////////////////000000111222222222222222000111222222111222444666{{{uuutttsssppp___ZZZXXXVVVUUUTTTRRRQQQOOONNNMMMMMMHHHFFFCCCAAA???<<<999666222333444444444333111000000000111111111111000000000000000000000000000000000111111111111222222222111111222333444444444444333777:::999888:::@@@FFFWWWiiivvvooogggbbb______gggppptttiii\\\VVVVVV[[[gggrrr~~~{{{vvvqqqmmmdddcccaaa______```aaabbbgggeeebbb___\\\[[[[[[[[[XXXXXXWWWWWWWWWWWWWWWWWWVVVWWWYYYZZZ[[[\\\[[[[[[\\\\\\]]]___bbbeeegggiiijjjllloooppprrruuuxxx{{{ppp^^^QQQMMMMMMLLLKKKJJJIIIHHHHHHEEEAAA<<<888666444222000000000000000000000000000000000000000000000000000//////000000000000//////111000//////......//////////////////////////////......///000000000000000000111222222111222444666yyypppnnnkkkzzz{{{ddd\\\ZZZYYYTTTTTTTTTSSSQQQNNNLLLKKKHHHFFFDDDBBB@@@>>>:::777333333444444333333222111000000111111111111000000000000000000000000000000000111111111111222222222000111222333444444444444444888:::999777:::BBBJJJ]]]pppyyyppphhhdddbbbdddkkktttsssggg[[[VVVVVV\\\iiittt}}}|||wwwrrrnnniiidddaaa\\\[[[ZZZXXXWWWWWWXXXXXXXXXXXXXXXWWWVVVUUUUUUVVVSSSSSSSSSTTTTTTTTTTTTTTTRRRSSSSSSTTTUUUVVVWWWWWWXXXXXXXXXYYY[[[]]]^^^___```bbbdddeeegggiiillloooqqquuuzzzxxxcccTTTMMMLLLKKKJJJIIIHHHHHHHHHFFFBBB===999777555222000000000000000000000000000000000000000000000000000//////000000000000//////111000000///////////////////////////////////////......///000000000000000000111222222111222444666yyyooolllffftttggg^^^]]]\\\TTTTTTUUUTTTRRROOOKKKIIIIIIGGGDDDCCCAAA>>>;;;888444444333333333222222222222222333333333333222222000000000000000000000000000111111111111222222222000111222333444444555444555888:::888666999CCCLLLaaatttyyyrrrkkkhhhiiilllttt|||qqqfffZZZUUUVVV]]]jjjvvv||||||zzztttqqqlllhhhddd```\\\XXXTTTSSSRRRPPPOOONNNNNNNNNOOOQQQSSSSSSSSSSSSTTTTTTSSSSSSSSSTTTTTTUUUUUUUUURRRRRRRRRSSSSSSUUUVVVWWWVVVVVVVVVVVVWWWXXXYYYZZZZZZ\\\^^^___```bbbeeeggggggkkkpppvvv|||~~~hhhXXXLLLKKKJJJIIIHHHGGGGGGGGGFFFCCC>>>:::777555222000000000000000000000000000000000000000000000000000//////000000000000//////111111000///////////////////////////////////////000000111222222222222222000111222222111222444666rrriiieeeppp|||eee[[[YYYXXXWWWVVVTTTRRRPPPOOOMMMMMMIIIFFFCCCAAA???===:::888555333111///...000111333111222333333333333222111000000000000000000000000222222222222222222222222444444444555555555666666666666:::>>>:::777FFF[[[mmm~~~tttkkkmmmlllsss}}}rrrdddWWWVVVYYY___kkkyyyyyynnneeehhheee```]]]\\\YYYTTTPPPQQQPPPOOOOOONNNNNNNNNNNNOOOOOOPPPQQQRRRRRRRRRRRRTTTTTTTTTTTTSSSSSSSSSSSSTTTTTTSSSSSSSSSSSSSSSTTTTTTUUUVVVWWWXXXYYYXXXXXXXXXXXXYYYYYY[[[\\\]]]^^^bbbcccfffjjjpppuuuzzz}}}rrr]]]QQQNNNIIIFFFGGGJJJIIIFFFHHHFFFBBB===999555222111000000000000000000000000////////////////////////000000000000000000000000////////////000000000000000000//////.........---////////////////////////111///000333444222333666vvvnnngggmmm{{{ddd[[[YYYXXXVVVVVVUUUSSSQQQOOOMMMLLLHHHEEECCCAAA???>>>;;;888333333222222111111111111111222333333333333222111111111111111111111111111333333222222222222222222111111111222222222333333666666:::>>>;;;;;;LLLaaasssyyymmmooorrr{{{ttteeeYYYWWWZZZ```mmm{{{~~~|||vvvlllddd___\\\YYYXXXXXXWWWTTTQQQPPPPPPOOONNNNNNNNNNNNNNNOOOOOOPPPQQQRRRRRRRRRRRRSSSSSSSSSSSSSSSSSSSSSSSSUUUUUUTTTTTTTTTTTTTTTUUUUUUUUUUUUVVVWWWXXXXXXXXXWWWWWWXXXXXXYYY[[[\\\]]]___```aaadddgggkkkoooqqqyyyiiiVVVQQQKKKGGGIIIKKKJJJGGGHHHFFFBBB>>>999555333111000000000000000000000000////////////////////////000000000000000000000000////////////000000000000000000/////////.........////////////////////////222000111444555333444888zzzuuulllmmmzzzyyyddd[[[YYYXXXUUUUUUUUUUUUSSSOOOLLLKKKGGGEEEBBBAAA@@@>>><<<:::222333444444444333111000111222222333333222222111111111111111111111111111333333333222222111111111000111111111222222222222777777:::======AAATTTiiiyyyooorrryyyvvvfffZZZXXX[[[aaannn|||}}}xxxuuutttoooggg```XXXVVVTTTTTTTTTSSSQQQOOOPPPOOOOOONNNNNNNNNNNNOOOOOOPPPQQQRRRRRRSSSSSSRRRQQQRRRRRRSSSSSSTTTTTTTTTUUUUUUTTTTTTTTTUUUUUUVVVVVVUUUUUUTTTUUUVVVXXXYYYVVVVVVVVVWWWXXXYYYZZZ[[[\\\\\\\\\]]]___aaacccdddkkkqqqyyy{{{]]]UUUMMMIIIKKKKKKJJJHHHHHHFFFCCC???:::666333222000000000000000000000000000000000000000000000000000000000000000000000000////////////000000000000000000////////////......////////////////////////333111222555444333666;;;~~~yyytttrrrzzzwwwcccZZZXXXVVVTTTUUUVVVUUUSSSPPPLLLJJJFFFDDDBBB@@@@@@???<<<:::333444444444444333222222222222222222222222222222111111111111111111111111444333333222222111111111333333444444444555555555777777999;;;<<>><<<:::666444222000///111333555333222222111111222222333222222222222222222222222222222222222222222222222444444444444555555555555555777999;;;AAAQQQhhhzzzwwwgggYYYWWWZZZ```ooo~~~~~~yyytttnnnjjjcccaaa^^^\\\[[[YYYVVVTTTTTTUUUWWWVVVUUUUUUVVVXXXUUUTTTTTTTTTTTTUUUUUUVVVTTTUUUVVVWWWWWWXXXWWWWWWSSSTTTTTTUUUUUUVVVVVVVVVTTTTTTTTTTTTTTTUUUVVVWWWXXXWWWVVVVVVVVVWWWXXXXXXWWWWWWWWWWWWWWWXXXYYYZZZXXXXXXWWWXXXXXXZZZ\\\]]]___```aaabbbeeeiiippptttuuuaaaPPPLLLKKKGGGDDDFFFGGGFFFEEEBBB>>>:::666333000000000000000000000000000000000000000000000000111111111111111111111111////////////000000000000//////000000000000111111000000000000000000000000000000222444333444===GGGjjj\\\WWWWWWVVVVVVVVVUUUSSSQQQOOOMMMLLLHHHEEECCCAAA???>>>;;;888444333222111000111111222333333222111111222333333222222222222222222222222111111111222222333333444333333333444444444555555444888;;;???III\\\tttyyyhhhZZZXXX[[[bbbppp}}}zzzvvvqqqnnniiieeeaaa\\\ZZZYYYXXXWWWWWWVVVUUUTTTVVVXXXWWWUUUUUUVVVXXXTTTTTTTTTTTTTTTUUUVVVVVVVVVWWWXXXYYYYYYZZZZZZYYYVVVVVVVVVVVVVVVVVVVVVVVVVVVUUUUUUVVVWWWXXXYYYYYYXXXXXXXXXXXXXXXXXXXXXXXXYYYYYYYYYYYYYYYZZZZZZ[[[[[[ZZZZZZZZZZZZ\\\]]]^^^^^^^^^___```bbbfffkkknnnvvv|||fffRRRNNNMMMHHHDDDFFFGGGFFFEEECCC???:::666444000000000000000000000000////////////////////////111111111111111111111111////////////000000000000//////000000000111111111000000000000000000000000111111444666555777BBBMMMyyyfffYYYWWWWWWWWWWWWVVVUUURRRPPPOOOMMMMMMIIIFFFCCCAAA???===:::888111111222333222111000///444333222111111222333444222222222222222222222222000000111222333444444555444444444555555555666666444999>>>CCCOOOeee}}}zzzjjj\\\YYY\\\cccrrr}}}xxxssspppllliiifffccc___\\\WWWVVVVVVVVVVVVWWWXXXXXXWWWXXXYYYWWWTTTRRRSSSTTTTTTTTTSSSSSSTTTUUUVVVVVVWWWXXXYYYZZZ[[[[[[[[[[[[WWWWWWWWWWWWWWWWWWWWWVVVWWWWWWWWWXXXYYYZZZ[[[[[[XXXYYYYYYZZZZZZYYYXXXXXX[[[ZZZZZZZZZZZZ[[[[[[\\\______^^^]]]^^^___```aaa^^^^^^___```cccgggkkkmmmoooyyyiiiTTTOOONNNHHHEEEGGGFFFFFFEEECCC???;;;777444000000000000000000000000////////////////////////111111111111111111111111////////////000000000000//////000000111111111222000000000000000000000000222222555777777:::EEERRRvvvbbbXXXXXXVVVRRRWWWVVVTTTRRRPPPNNNNNNMMMKKKGGGCCC@@@>>>===<<<;;;888666444333333333222111333333333222222111111111111111111111111111111111000000111222333555666777555555444444444555555666777<<>>888444222111000000000000000000111111000000000000111111222111111111000000//////111111111111111111111111---......///////////////000111111111111222222222666000111888;;;===JJJ\\\lll]]]YYYXXXVVVXXXWWWUUURRRPPPOOONNNMMMKKKHHHDDDAAA???>>>===;;;888666333333333333222000333333333222222222111111111111111111111111111111111111111222333444555666555555444444444555666666777;;;>>>EEEWWWqqqvvvfffYYYXXX^^^dddqqq~~~uuupppiiiccc___\\\ZZZXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXWWWVVVUUUTTTTTTSSSSSSSSSUUUVVVWWWWWWXXXXXXYYYYYYZZZZZZZZZYYYYYYZZZZZZ[[[[[[ZZZZZZYYY[[[ZZZZZZZZZ\\\]]]^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^aaaaaabbbcccddddddeeeeeedddbbb```^^^]]]^^^______\\\\\\\\\\\\___bbbeeegggkkkpppxxxnnnWWWOOOLLLGGGEEEHHHGGGFFFEEEDDDBBB>>>999555222111111000000000000000111111000000000000111111111111111111000000000///////////////////////////---...//////000000//////000111111111111222222222444000222999<<<@@@QQQddd{{{fff\\\ZZZZZZXXXWWWUUUSSSQQQOOONNNNNNLLLIIIEEEBBBAAA???>>><<<777555333222222222111000333333333222222222222111111111111111111111111111333222222222333333444555555555444444555555666777999;;;???III___yyyqqqbbbWWWYYY^^^eeeqqq}}}xxxrrriiibbb]]][[[ZZZYYY[[[ZZZZZZYYYYYYXXXXXXWWWYYYYYYYYYYYYYYYXXXWWWVVVUUUUUUUUUUUUVVVWWWWWWXXXYYYYYYYYYZZZZZZZZZ[[[[[[[[[[[[\\\\\\\\\\\\[[[[[[\\\\\\\\\]]]^^^```aaabbbbbbbbbccccccccccccbbbbbbcccdddfffhhhiiiiiiiiiiiigggeeecccaaa````````````^^^^^^^^^^^^```aaabbbccchhhmmmttt}}}pppYYYPPPLLLGGGFFFHHHGGGFFFEEEDDDCCC???:::666222222111000000000000000000000000000000000000000111111111111000000000000////////////////////////---...//////000000//////000111111111111222222222222111444:::>>>FFFZZZppprrr```ZZZ[[[YYYXXXVVVSSSQQQPPPOOONNNLLLJJJFFFCCCBBB@@@>>>===666444222111222111000///222222222222222222222222111111111111111111111111444333333222222333333333555444444444555666777888:::;;;AAAPPPhhhmmm___VVVYYY```fffrrr}}}vvvpppggg___\\\[[[[[[\\\]]]\\\[[[ZZZYYYXXXWWWWWWYYYZZZZZZ[[[[[[[[[ZZZZZZWWWXXXXXXXXXWWWXXXYYY[[[]]]]]]]]]]]]]]]^^^^^^___\\\\\\]]]]]]]]]]]]\\\\\\\\\]]]___```aaabbbeeegggffffffggghhhggggggfffeeeeeegggjjjlllmmmmmmmmmlllkkkjjjhhhfffdddccccccbbb]]]]]]^^^___```aaaaaaaaahhhlllsssyyyrrr\\\QQQLLLHHHFFFGGGFFFFFFEEEEEEDDD@@@;;;777333222111000/////////000000000111111111111000000111111111000000000000000000000000000000000000000......///000000000000000000000111111111222222222111222666;;;@@@LLLcccyyyjjj]]]ZZZZZZXXXVVVTTTRRRPPPPPPOOOLLLJJJFFFDDDCCCAAA>>><<<666444222111222111000///222222222222222222222222111111111111111111111111444444333222222222333333444444444555666777888888;;;<<>><<<777555333222222222111000111222222222222333333333111111111111111111111111444444333222222333333333444444444555666777888999;;;>>>JJJaaayyy|||uuuqqqrrruuuxxxyyy~~~kkk^^^VVV[[[ccckkkxxxyyyvvvuuutttqqqnnnhhheee```]]]]]]^^^^^^^^^___^^^^^^\\\[[[ZZZYYYYYY[[[[[[]]]^^^___`````````___aaacccaaa___^^^aaadddaaaaaa```___```aaabbbcccbbbbbbbbbccccccbbbbbbbbbaaadddggggggfffgggkkkooonnnppprrrtttuuuuuutttsssqqqrrrssstttuuuuuuttttttsssrrrpppmmmkkkhhhfffddd````````````aaacccdddeeeiiinnntttxxx|||wwwcccTTTLLLIIIGGGFFFFFFFFFEEEFFFEEEBBB>>>;;;333333111000///////////////000111222222111000///000000000000111111111111////////////////////////...///000000111111000000000111111111111222222222333555999???KKK^^^uuurrraaa[[[ZZZXXXUUUSSSRRRQQQPPPKKKIIIFFFDDDCCCAAA===;;;888666333333333333222000111111222222222333333333111111111111111111111111333333222222222333444444444444555555666888999:::;;;@@@PPPhhh~~~~~~tttmmmlllooosssuuu~~~lll___WWW\\\eeennn|||xxxtttooommmmmmnnnllljjjdddcccaaa```aaa```___]]]___^^^^^^]]]\\\[[[[[[ZZZ[[[\\\^^^```aaabbbcccccccccfffhhhfffcccbbbeeehhhdddcccbbbaaabbbccceeeffffffggggggggggggggggggffffffiiilllllljjjjjjnnnsssuuuwww{{{~~~~~~yyyyyyyyyyyyyyyyyyyyyyyy{{{zzzxxxuuurrrooolllkkkgggfffdddccccccdddfffgggffflllsssvvvzzzyyyfffUUULLLJJJHHHFFFFFFEEEEEEFFFFFFCCC???<<<444333222000//////......///000111222222111000//////000000000111111111111//////////////////////////////000111111111111000000111111111111222222222444666:::BBBSSSjjj|||fff[[[ZZZXXXVVVSSSRRRQQQQQQJJJHHHFFFDDDCCC@@@===:::888666444333444333222111111111111222222333333333111111111111111111111111333222222222333333444555444444555555666888999:::;;;BBBSSSlllxxxpppmmmnnnrrrttt}}}mmm```WWW\\\fffppp~~~{{{wwwnnnjjjgggfffiiikkkkkkiiidddccccccccccccbbb^^^\\\___^^^^^^]]]]]]\\\\\\[[[[[[\\\^^^```bbbcccddddddfffiiikkkiiieeedddgggkkkhhhgggeeeeeeeeefffhhhjjjjjjjjjkkkkkkkkkkkkjjjjjjiiimmmpppooommmmmmqqquuu{{{}}}~~~~~~}}}||||||||||||}}}~~~zzzvvvsssrrrmmmkkkhhheeedddeeeggghhhdddjjjqqquuuxxxzzzgggUUUMMMJJJHHHEEEFFFEEEFFFFFFFFFDDD@@@<<<444333222000///............000111222222111000...//////000000111111111222111111111111111111111111//////000111111111111111000111111111111222222222444555:::DDDYYYrrrhhh^^^[[[XXXVVVUUUSSSQQQOOOMMMJJJGGGDDDBBB@@@>>>;;;;;;888555333333333333222222222222222222222222222444333333222222333333444111111222333333444555555555444444555777999999999===GGGZZZrrr}}}ssskkkiiinnnttt{{{mmm```WWWZZZgggwwwyyyqqqllljjjiiihhhiiijjjiiigggeeeeeeeeefffffffffeeecccbbbbbbdddfffeeecccaaa``````cccccccccccceeefffhhhiiikkklllmmmmmmmmmlllkkkjjjkkkkkkkkkkkklllmmmnnnooommmmmmlllkkklllmmmnnnoooppppppppprrrvvvxxxxxxwww~~~zzz{{{uuummmhhhfffggghhhiiikkkiiikkkqqqvvv~~~~~~lll]]]SSSMMMJJJHHHFFFFFFDDDCCCAAA???>>>>>>;;;777222///...///000000//////000000111111111222000000111222222222222111////////////////////////000000000000111111111111000111222333555666777888<<<666;;;OOOcccqqqnnn___\\\YYYWWWUUUTTTQQQOOOMMMJJJGGGDDDBBB@@@>>><<<;;;888555333333333333222222222222222222222222222333333222222222222333333111111222333333444555555555555444555777999::::::AAAMMMaaaxxxtttiiigggmmmttt|||lllaaaXXX[[[ggguuu}}}xxxsssnnnllljjjiiiiiiiiigggfffcccdddeeefffggggggfffeeeeeefffgggfffdddcccccccccdddeeefffggghhhjjjkkkkkkmmmnnnoooppppppooonnnnnnnnnnnnnnnnnnooopppqqqqqqppppppooooooooopppqqqrrruuuttttttuuuyyy{{{||||||yyyrrrmmmkkkjjjjjjjjjjjjhhhiiinnnsssyyyxxxfffVVVLLLGGGEEEFFFFFFEEECCCAAA@@@>>>>>>;;;777333000000111111000///000000000111111111111000000111222222222222111////////////////////////000000000000111111111111111111222333444555666777:::666<<>><<<;;;888555333333333333222222222222222222222222222222222111111111111222222111222222333333444444555666666555666777888:::;;;FFFUUUkkkxxxjjjjjjqqqxxx~~~~~~kkkaaaYYY^^^iiiuuu}}}uuuqqqlllhhhhhhhhhhhhhhhcccdddeeeggghhhhhhiiiiiihhhiiiiiigggeeeeeefffgggggghhhjjjlllnnnnnnnnnnnnpppqqqssstttttttttssssssssssssrrrrrrrrrrrrssssssttttttssssssttttttuuuvvvzzzyyyxxxyyy|||{{{uuurrrpppnnnlllkkkhhhiiimmmqqqwww~~~ttt^^^OOOHHHFFFGGGFFFEEEDDDBBB@@@???>>>999777444333333333333222000000000000111111111111000000111222222222222111////////////////////////000000000000111111111111111111111222333444555666999888BBBSSSbbbkkkwwwiii```]]][[[YYYXXXUUURRROOONNNKKKGGGEEECCCAAA>>><<<;;;888555333333333333222222222222222222222222222222111111000000111111222222222222333333444444444666666666666666888;;;===JJJ]]]uuuqqqqqqxxx}}}|||{{{iii```[[[aaalllxxx{{{uuunnniiiggghhhiiiiiieeeeeefffggghhhiiijjjjjjiiiiiiiiigggffffffhhhjjjiiikkknnnqqqrrrsssrrrqqqssstttvvvwwwxxxxxxxxxwwwvvvvvvuuutttttttttuuuuuuxxxxxxxxxyyyyyyyyyzzzzzz~~~|||{{{|||{{{vvvrrrooonnnkkkjjjnnnsssxxx{{{iiiVVVMMMKKKHHHGGGFFFDDDBBBAAA@@@???999777555555555555444333000000000000000111111111000000111222222222222111///////////////////////////000000000111111111111222222111111222333555666:::???KKK\\\gggnnnvvv{{{eee^^^\\\ZZZYYYXXXVVVSSSPPPNNNKKKHHHEEECCCAAA???<<<;;;888555333333333333222222222222222222222222222222111111000000111111222222222333333333333444444555666777666666999===AAAOOOeee~~~yyywwwzzz|||}}}yyyggg___\\\dddppp{{{}}}wwwpppjjjiiiiiijjjjjjhhhhhhhhhiiiiiiiiijjjjjjiiiiiiiiihhhfffgggiiillllllnnnqqqtttvvvvvvvvvuuuvvvwwwyyy{{{||||||{{{{{{yyyxxxwwwwwwwwwwwwwwwxxx}}}}}}~~~~~~~~~~~~}}}~~~}}}xxxtttppplllkkkpppuuuzzzzzzttt]]]QQQNNNHHHHHHFFFEEECCCAAA@@@@@@:::888666555666666555333111111000000000000000000000000111222222222222111000000000000000000000000///000000000111111111111222222111111222444666777;;;EEEUUUeeennnsssyyyyyyeee[[[ZZZYYYYYYYYYWWWSSSPPPNNNLLLHHHEEECCCBBB???===;;;888555333333333333222222222222222222222222222222222111111111111222222333333333333333333333333333555777777666999@@@EEEWWWppp}}}yyyzzzxxxzzzggg```]]]fffrrr}}}~~~}}}|||{{{yyyzzzvvvqqqmmmkkkkkkkkkjjjkkkjjjjjjiiijjjjjjkkkllljjjkkklllkkkkkkkkkmmmoooppprrrtttwwwyyyzzzzzzzzz{{{|||}}}~~~~~~~~~|||||||||{{{||||||}}}}}}{{{tttooommmqqqvvvzzz{{{}}}cccSSSLLLIIIHHHGGGEEEDDDBBBAAA@@@;;;999666555555555444444111111111111000000000000000000111222222222222111000000000000000000000000000000000000111111111111222222111111333555888:::>>>LLL```ooovvv{{{tttcccXXXXXXWWWXXXXXXWWWTTTQQQOOOLLLHHHEEEDDDBBB???===;;;888555333333333333222222222222222222222222222333333222222222222333333333333333333333333333333111444666777777:::BBBHHHbbb{{{zzzyyy|||zzz~~~|||hhhaaa^^^eeerrr||||||yyywwwwwwvvvuuusssvvvtttqqqooonnnmmmllljjjjjjjjjiiijjjkkklllnnnooommmoooqqqrrrqqqqqqrrrtttuuuvvvwwwyyy|||~~~}}}vvvsssuuuyyy{{{~~~~~~jjjWWWNNNIIIIIIHHHFFFDDDCCCAAAAAA===:::666333333444444333111111111111000000000///000000111222222222222111000000000000000000000000000000000000111111111111222222111222444777:::===DDDVVVlllzzzmmm^^^VVVVVVVVVXXXXXXWWWTTTQQQOOOLLLHHHFFFDDDBBB???===;;;888555333333333333222222222222222222222222222444333333222222333333444333333333333333333333333000333666777777;;;CCCJJJjjjwwwzzz|||~~~}}}jjjbbb^^^eeepppzzz{{{xxxuuussssssrrrqqqpppsssrrrqqqppppppooollljjjiiiiiiiiijjjkkknnnppprrrqqqsssvvvwwwwwwvvvwwwxxxyyyyyyzzz{{{~~~~~~yyyzzz}}}}}}~~~ppp]]]SSSJJJIIIHHHFFFEEECCCBBBAAA???;;;666222222333333333222111111111000000//////000000111222222222222111000000000000000000000000000000000000111111111111222222111222444888<<<>>>JJJ^^^uuusssaaaVVVTTTUUUUUUVVVUUUTTTSSSRRRQQQMMMHHHDDDBBBAAA???>>>555555555555555444444444+++---000222444444333333333333222222111222222222222222222333444555666777444999666777===<<>><<<888555222111111222//////000000111111111222222222222222222222222222111111111111111111111111/////////000111111222222...777666333888999;;;CCCTTTjjj{{{kkk[[[QQQTTTUUUWWWXXXWWWVVVTTTSSSQQQMMMHHHEEECCCAAA???>>>777777666555444444444444222333444555666555555444222222222111222222333333333333333333444555666666333888666777======AAAPPPppptttooottt|||~~~}}}~~~~~~~~~rrrbbb```___bbbkkkuuu~~~}}}zzzvvvssspppppppppqqquuurrrooonnnooopppooommmnnnmmmmmmnnnooorrruuuwwwwwwyyy|||~~~}}}www```TTTLLLKKKHHHEEECCCAAA@@@@@@>>><<<888555333222111222000000000000111111111222////////////////////////111111111111111111111111000000111222222333333444///777666333888999<<>><<<999555333222222222000000000111111111111111222222222222222222222222111111111111111111111111222222333333444555555555000777555333888999>>>KKKjjjrrrbbbVVVSSSUUUXXXZZZZZZYYYVVVUUUQQQNNNIIIFFFDDDBBB???======:::777444222222333444444333222111000000000000111111111111222333444555333333333333333444555666444999888777<<<===DDDUUUlllkkkcccfffnnntttxxx~~~|||{{{||||||{{{lll______aaafffooowww}}}zzzuuussstttvvvxxx|||{{{zzzyyyxxxwwwwwwvvvwwwvvvuuuuuuvvvxxx{{{|||{{{}}}nnn[[[NNNJJJIIIGGGEEECCCAAA@@@???>>><<<999666333222222222111111111111111111111111333333333333333333333333111111111111111111111111222222333333444555555555111777555333999:::BBBSSSqqqiiiZZZTTTUUUXXXYYYYYYXXXVVVTTTPPPNNNJJJGGGEEECCC???===>>>;;;777444222222333444555555444444444555666666111111111111222333444555444444333333333444555555666<<<:::888<<<<<>>KKKaaaxxxzzzggg[[[WWW___gggkkkrrr|||{{{|||vvvgggeeeiiipppyyy}}}|||}}}|||~~~tttcccSSSJJJJJJIIIIIIGGGEEEBBBAAA???===:::666444333333333333333333222222111111111333333333333333333333333111111111111111111111111000000111111222222333333444666444777???CCCUUUrrrrrr^^^]]][[[YYYWWWWWWWWWXXXPPPNNNKKKIIIGGGDDD@@@===:::999888777666555444333222444555777777666555333333333222222111222222222555444444333333333444444000888888777<<<@@@NNNfff{{{{{{ssslll```WWWUUU^^^eeegggnnnyyyzzz{{{~~~uuueeehhhlllsss|||}}}~~~{{{iiiXXXJJJJJJJJJIIIHHHFFFCCCBBB???===:::777444333333333333333333222222111111111000000000000000000000000111111111111111111111111000111111222222333444444444666555888@@@EEEXXXwww~~~nnn___[[[\\\WWWVVVWWWQQQRRROOOKKKIIIFFFCCC???<<<===<<<999777555444444444222222333333333444444444555444444333333444444555333333444444555444444444999666777;;;;;;@@@SSShhhxxxrrrjjjbbbYYYVVVTTTWWW^^^hhhpppuuuzzzzzz|||~~~sssjjjgggppp|||ppp]]]LLLGGGEEEIIIKKKHHHDDDBBB@@@>>>:::777444333222222000000000000000000000000111222222333333222222111111111111111111111111111111222333333222111222444333555777888===MMMdddvvvtttbbb\\\\\\XXXXXXXXXQQQRRROOOKKKHHHEEECCC@@@>>>===<<<999777555444444444111111222222222333333333444444333333333333444444222222333444444444444333777555777;;;<<>>;;;777444333333333111111111111111111111111111222222333333222222111111111111111111111111111111222333333222111333444222555777999@@@QQQiiizzz|||ggg]]]\\\ZZZ[[[ZZZRRRSSSOOOJJJGGGEEECCCBBB@@@===<<<999777555444444444111111111111222222222222444444333333333333444444222222333333444444444444666555777<<<>>>CCCUUUjjjnnn^^^VVVVVVWWW\\\dddmmmsssvvvwwwwwwxxx{{{|||~~~ooohhhfffppp}}}wwwcccSSSMMMIIIKKKMMMIIICCC@@@@@@???;;;888555444333333111111111111111111111111111222222333333222222111111111111111111111111111000222333333222222333555333555777:::DDDWWWnnnjjj]]]]]][[[]]]\\\SSSTTTOOOJJJFFFDDDCCCBBBBBB===<<<999777555444444444111111222222222333333333444333333333333333333444333333333444444555666666888666999===???DDDWWWkkkvvv___ZZZZZZ\\\aaahhhnnnrrrssswwwvvvxxxzzz||||||nnniiigggppp~~~zzzfffVVVNNNHHHJJJMMMJJJDDDAAAAAA???<<<999666444333333111111111111111111111111111222222333333222222111111111111111111111111111000222333333222222444555555555777===III\\\qqqjjj]]]\\\[[[]]]]]]TTTTTTPPPKKKFFFDDDCCCBBBBBB===<<<999777555444444444333333333444444444444555333333333222222333333333444444444444555666777888;;;888:::>>>@@@FFFYYYooofff[[[\\\___dddkkkqqqtttuuuwwwvvvxxx{{{~~~{{{nnniiigggqqq~~~~~~kkkYYYOOOGGGHHHLLLJJJFFFDDDAAA???===:::888555444333111111111111111111111111111222222333333222222111111111111111111111111111000222333333333333555666777777999AAANNNaaasss~~~}}}~~~}}}ggg\\\\\\YYY\\\]]]VVVUUUQQQLLLHHHEEECCCAAA@@@===<<<999777555444444444444444444444555555555555333333222222222222333333444444333333444666888999<<<999:::>>>AAAIII___vvvrrr\\\]]]```gggnnntttwwwxxxvvvvvvxxx{{{{{{nnniiigggppp}}}vvv```SSSHHHGGGKKKKKKHHHFFFAAA@@@>>><<<999666444333222222222222222222222222111222222333333222222111111111111111111111111111000222333444333444555777888888<<>>BBBNNNgggcccccceeeiiinnnrrruuuuuuuuutttvvv{{{zzzmmmhhheeennnyyyjjjZZZKKKHHHJJJKKKHHHGGGAAA@@@???<<<:::777555333222222222222222222222222111222222333333222222111111111111111111111111111000222333444444444666888888999???LLL^^^ppp|||ppp```ZZZ[[[VVVXXX[[[XXXVVVSSSOOOKKKGGGCCC???<<<===<<<999777555444444444222222333333333444444444333222222222222222222333111000000///111333555777999666777===CCCQQQmmmlllkkkjjjkkkmmmooooooooossssssuuuzzzyyykkkfffccckkkwwwrrr```NNNIIIJJJKKKHHHGGGAAA@@@???===:::777555333222222222222222222222222222222222333333222222222111111111111111111111111000222333444444444666888777999@@@PPPdddvvvfff^^^XXXYYYZZZYYYYYY[[[YYYTTTMMMHHHFFFCCC@@@===;;;:::999666333333444777444333333222222333333444666555333111111111333444333222111111111222333444888777888===FFFWWWrrrnnnmmmlllmmmoooqqqpppooopppppprrrwwwzzzlllgggccclllxxx~~~gggPPPHHHLLLMMMKKKHHHFFFCCCAAA>>><<<999555222222222222222222222222222222222222222222222222222111111222222222333333333222333444444333333555777555888DDDYYYmmm{{{yyybbb[[[VVVXXXZZZYYYYYY[[[YYYTTTMMMIIIFFFCCC@@@===::::::999777444333444666444333333222222333333444666555444222222222333444666555444444444555666777999888999???III[[[uuummmmmmmmmnnnqqqsssrrrrrrttttttuuuzzzxxxlllgggccclllwww~~~hhhQQQIIILLLNNNKKKIIIFFFDDDAAA>>><<<999555333222222222222222222222222222222222222222222222222111111222222222333333333222333444444333333555777777:::FFF[[[qqqmmm^^^XXXTTTWWWZZZYYYYYYZZZXXXTTTNNNJJJFFFCCC@@@>>>:::::::::888555444444444444333333222222333333444555555555444444444444444777666555555555666888999:::999;;;BBBMMM^^^xxxvvvlllkkklllooorrruuuuuuuuuxxxxxxyyy~~~uuujjjfffeeemmmxxx~~~~~~~~~jjjSSSKKKMMMNNNLLLJJJGGGDDDAAA>>><<<999666333222222222222222222222222222222222222222222222222111111222222222333333333222333444444333444666888;;;===III___vvvzzzggg[[[UUURRRVVVYYYYYYXXXZZZVVVTTTOOOKKKGGGCCC@@@???999;;;;;;:::777444333333444333333222222333333444444555555666666555444444444333333333333444666777;;;999;;;CCCOOO```xxxllliiiiiijjjnnnrrrvvvwwwwww{{{{{{|||rrriiiggghhhrrr~~~zzz{{{kkkUUUMMMNNNNNNMMMLLLGGGEEEAAA>>><<<999666444222222222222222222222222222222222222222222222222111111222222222333333333222333444444444444777999>>>@@@MMMddd|||}}}lll\\\VVVRRRUUUXXXXXXXXXZZZUUUSSSPPPLLLGGGCCCAAA@@@:::;;;<<<:::777444333333444333333222222333333444444444555666666555555444333222222222222444666777;;;999;;;DDDQQQcccyyy|||gggffffffhhhlllqqqvvvxxxxxx{{{{{{~~~|||oooiiigggnnnxxxzzzrrrmmmnnnssswww~~~mmmWWWNNNNNNNNNMMMMMMHHHEEEAAA>>><<<:::777555222222222222222222222222222222222222222222222222111111222222222333333333222333444444444555777999>>>BBBRRRmmmxxxaaaYYYTTTVVVXXXXXXXXXZZZTTTSSSRRRMMMHHHCCCAAAAAA<<<<<<<<<:::666444333444444333333222222333333444444444444444444555555555444444333333444666888999;;;999<<>><<<:::777666222222222222222222222222222222222222222222222222111111222222222333333333222333444555555666888:::===DDDYYYyyyggg^^^WWWVVVWWWWWWXXX[[[SSSSSSRRRNNNHHHCCCAAAAAA>>>===<<<999555333444555444333333222222333333444444333222222222444555666555444444444666777999::::::999???LLL^^^rrrsssfffeeeeeehhhlllrrrwwwyyyyyyxxx{{{uuullliiijjjwww~~~{{{wwwpppggg___\\\\\\^^^iiirrrzzz|||}}}~~~yyytttqqqrrrxxx|||mmmYYYOOOMMMLLLLLLMMMJJJFFFAAA===;;;:::888666222222222222222222222222222222222222222222222222111111222222222333333333111333444555555666999;;;???IIIaaakkkaaaXXXVVVWWWWWWXXX[[[RRRSSSSSSOOOHHHCCCAAABBB???>>><<<888444333444666444333333222222333333444444333111111111333555666444444333444555777999:::::::::@@@PPPdddzzz}}}mmmbbbfffgggiiimmmsssxxxzzz{{{xxx{{{tttllliiikkkxxx~~~~~~{{{zzzyyy|||yyyrrriii```ZZZXXXXXXccckkkqqqqqqrrrwwwwwwsssjjjeeeccchhhlllqqq}}}mmmYYYOOOLLLKKKKKKMMMJJJFFFAAA===;;;:::888777222222222222222222222222222222222222222222222222111111222222222333333333111333444555555666999;;;CCCNNNgggwwweeeWWWVVVZZZZZZXXXWWWWWWUUUQQQMMMIIIEEEBBBAAA>>>===;;;999777555444444333333222111111222333333555555555444444333333333333333333444555666777888<<<===DDDUUUmmm}}}zzzqqqggg```___dddkkkqqqtttvvvxxxyyyyyy{{{{{{nnnffffffjjjuuu~~~}}}||||||{{{xxxxxxuuuoooggg^^^XXXVVV\\\bbbjjjpppqqqooommmllleeeaaaaaafffjjjllluuuvvv```OOOIIIKKKNNNOOOIIIHHHDDD@@@===:::777666444333222222111111222222333222111000////////////222222333333333333444444555222111555888777777:::???SSSqqqnnn]]]YYY[[[[[[ZZZZZZYYYVVVRRRMMMIIIEEECCCBBB>>>===;;;999777555444444555444333222222333444555333333333222222222111111444444444555666777888999<<<>>>EEEUUUnnnxxxyyyxxxuuuooofff^^^YYY```dddkkkqqqtttvvvxxxyyyzzz{{{zzzmmmddddddhhhvvv}}}}}}|||{{{zzzzzz{{{{{{}}}}}}|||wwwmmmcccZZZVVVXXX^^^ffflllmmmkkkiiigggbbb```ccciiinnnqqqzzz|||eeeTTTKKKKKKLLLMMMKKKIIIFFFBBB>>>;;;999888333222222111111111111111444444333222111111111111222222333333333333444444666333333666888888999<<>>===;;;999777555444444555555444444444444555555333333333333222222222222555555555666777888999:::<<<>>>EEEVVVpppxxxuuupppjjjccc]]]YYYVVV```eeekkkpppsssuuuwwwxxxzzz|||{{{mmmddddddhhhuuu}}}{{{yyywwwvvvuuuvvvxxxzzz|||~~~uuuiii___YYYVVV[[[bbbggghhhhhhgggfffeeeeeejjjrrrxxx|||lllYYYNNNKKKKKKLLLLLLJJJGGGCCC???<<<:::999444444333222222222222222666555444333333222333333222222333333333333444444777444444777999888:::>>>DDDXXXssspppaaa]]]___aaabbb^^^ZZZUUUNNNIIIEEEDDDCCC>>>===;;;999777555444444555444444444444444444555555555555555555555444444444444444555666777999999;;;===EEEXXXsssyyyoooeee^^^[[[ZZZ[[[aaaeeekkkppprrrtttvvvwwwyyy|||}}}oooffffffjjjssszzzyyyvvvsssppppppqqqtttvvvvvv{{{|||pppeee^^^[[[]]]aaadddfffhhhkkkmmmooorrrxxxooo[[[PPPLLLLLLLLLLLLJJJGGGCCC@@@<<<:::999666555555444444444444444555555444333333333333333222222222333333333444444666444444777888777:::@@@FFF[[[tttjjj``````aaaaaa^^^[[[UUUOOOJJJFFFDDDCCC>>>===;;;999777555444444333333444444444444333333555555555555555555555555333333333444555666777888:::<<>>===;;;999777555444444333333444444444444333333333333333333444444444444333333333333444666777888:::===III^^^zzzvvvcccWWWTTTXXX\\\dddgggkkknnnppprrrtttvvvxxx~~~}}}ppphhhhhhlllrrrxxxyyyuuupppkkkhhhggghhhjjjttt{{{~~~uuupppmmmnnnoooppptttzzzuuubbbTTTNNNMMMNNNLLLJJJGGGCCC???<<<:::999333222222111111111111111222222111111111111222222222222333333333333444444444333444666555555:::BBBOOOdddxxxrrraaa______]]]XXXWWWUUUQQQLLLGGGCCCAAA>>>===;;;999777555444444333444555666666555444333333333333333444444444555333333444444555777888999;;;@@@MMMdddkkk[[[VVVYYY\\\dddgggkkknnnoooqqqtttuuuyyytttlllmmmqqqwww{{{zzzvvvpppjjjfffccccccccclllttt~~~}}}zzz|||iiiXXXNNNKKKLLLMMMKKKHHHDDDAAA===;;;:::444444333222222222222222222222111111111111222222222222333333333333444444444444555777555555<<>>===;;;999777555444444444555666777777666555444555555555666666666777777555555555555666888999:::<<>>DDDTTTmmmiiiaaaaaabbbfffhhhiiijjjkkknnnqqqtttwww{{{sssppprrr|||yyysssqqqjjj```\\\^^^]]]```iiiwwwvvv]]]NNNKKKMMMPPPLLLGGGCCCAAA???<<<:::555555444333222222222222222222333333333333444444222222222222222222222222555666444666<<<999>>>PPPfffyyy}}}ggg^^^]]]]]]\\\[[[YYYUUUQQQLLLHHHDDDBBB???===;;;888666555555444444444444444444444444444333333333444444444555555333444555666777999::::::===EEEXXXrrrmmmaaa```aaafffgggiiijjjkkkmmmqqqtttxxxzzztttsssuuu}}}|||vvvrrrkkk```YYYYYYXXX\\\eeerrr|||cccPPPKKKLLLPPPLLLHHHDDDBBB???===:::555444333222222111111111222222333333333333444444222222222222222222222222444666444777<<<:::AAATTTlllwwwddd^^^^^^^^^^^^\\\ZZZWWWRRRNNNIIIFFFDDD???>>>;;;888666555555555222222333444444555666666333333333444444444555555444444555666777999:::;;;===GGG]]]yyynnn```___aaaeeegggiiijjjkkkmmmpppsssyyy~~~yyywwwwwwyyy~~~yyytttlllaaaWWWTTTRRRVVV___jjjsss}}}iiiSSSLLLNNNPPPMMMHHHEEEBBB@@@===;;;555444333222222111222222222222333333333333444444333333333333333333333333444777555777===<<>>;;;999777555555555333333333444444444555555333333333444444444555555555555555555777999;;;<<<>>>JJJ```|||jjj^^^___bbbdddfffhhhjjjkkkmmmooorrrxxxyyyxxxzzz{{{}}}~~~|||zzzzzz|||}}}|||vvvooodddZZZSSSNNNRRRZZZbbbjjjuuukkkTTTMMMOOOPPPMMMIIIFFFDDDAAA===;;;666666555444333333333333222222222333333333444444333333333333333333333333333777666888===>>>LLLeee{{{hhh\\\YYY[[[[[[ZZZ\\\ZZZVVVRRRMMMIIIEEECCC@@@>>><<<999777666555555555555444444444333333333333333333444444444555555666555555555777999;;;===AAAMMMccc~~~eee[[[^^^aaabbbeeehhhjjjkkkllloooqqqvvvwwwxxx{{{~~~~~~{{{xxxwwwxxxzzz~~~yyyssskkk```WWWPPPRRRWWW]]]cccmmmjjjSSSLLLNNNPPPMMMJJJGGGEEEBBB>>>;;;888777666555555444444555222222222333333333444444333333333333333333333333222777777999>>>AAASSSppp{{{ooo___XXXYYY]]]^^^]]]\\\ZZZWWWRRRMMMIIIFFFDDD@@@???<<<999777666666666666666555444333333222222333333333444444444555555666666555555666999<<<===CCCPPPgggvvv```ZZZ\\\^^^aaadddgggiiijjjlllnnnooosss|||vvvwww{{{~~~{{{zzzzzz{{{~~~~~~{{{xxxssshhh]]]UUUTTTVVVYYY]]]eeesssgggSSSLLLMMMPPPNNNKKKHHHFFFBBB>>>;;;888888777666555555555555222222333333333333444444333333333333333333333333111888888999>>>CCCYYYzzztttiii\\\WWWZZZ^^^___^^^]]][[[XXXTTTOOOJJJGGGEEE@@@???<<<:::888666666666444444444444444444444333333333333444444444555555777666555555666999<<<>>>BBBRRRllllll\\\ZZZ\\\\\\```cccgggiiijjjkkkmmmooosss{{{wwwwwwzzz}}}{{{xxxnnnbbb[[[WWWUUUWWWYYY\\\fffoooyyy~~~}}}~~~{{{dddSSSMMMNNNPPPNNNLLLIIIGGGCCC???;;;777666555444333333333333222222333333333333444444444444444444444444444444111888999:::>>>EEE^^^uuujjj^^^XXXZZZ^^^^^^\\\___]]]YYYUUUPPPLLLHHHFFFAAA???<<<:::888777666666222333333444444555555666333333333444444444555555777666555555666999<<<>>>BBBSSSppp|||dddYYY[[[]]]]]]```cccgggiiijjjkkkmmmnnnsss{{{xxxxxxyyy~~~~~~|||{{{qqqddd^^^YYYUUUUUUVVVWWW]]]cccfffrrr{{{uuusssqqqppprrrzzzttt```TTTPPPQQQPPPNNNLLLJJJGGGDDD???;;;555555444333222222222222222222333333333444444444444444444444444444444444000888999:::???FFFaaatttbbb\\\ZZZZZZ\\\aaa^^^\\\XXXSSSNNNJJJFFFDDDAAA???<<<888666555555555666666666666666666666666666555555444444555555666333444666666666888;;;>>>EEEYYYvvvooo___YYYXXX[[[```bbbccceeeffffffhhhkkkmmmqqqtttsssyyy~~~|||rrrjjjaaaZZZTTTRRRRRRQQQRRRVVV^^^cccjjjssszzz|||uuuoookkkfffgggggghhhjjjqqq{{{nnn\\\PPPMMMNNNNNNPPPNNNIIIEEEDDD@@@;;;999888666444333333333333333444444555555444444333333333333444444444555555444555999<<>>EEEZZZwwwwwwcccYYYWWWXXX\\\aaaaaaccceeeeeefffgggjjjlllrrruuussszzz|||uuuooobbb[[[TTTRRRQQQOOOPPPSSSSSSWWW]]]dddlllrrrvvvxxxvvvvvvuuutttpppkkkfffcccbbbccceeefffjjjrrr|||nnn[[[OOOLLLMMMNNNPPPOOOIIIFFFDDD@@@;;;999888666444333333333444333444444555555444444333333333333444444444555555444666999<<>>FFF\\\xxxuuugggYYYTTTVVVXXX\\\aaaaaabbbdddeeeeeefffiiikkkrrr~~~wwwuuu{{{}}}xxxsssddd\\\UUUSSSQQQMMMMMMPPPKKKMMMQQQVVV\\\bbbfffiiiggghhhiiiiiigggeeecccaaacccdddfffiiinnnvvvmmm[[[OOOLLLMMMNNNQQQOOOJJJFFFEEE@@@;;;999888666444333333333444333444444555555444444333333333333444444444555555444666:::<<<@@@PPPooozzzhhh```^^^\\\[[[ZZZYYYVVVRRRMMMIIIFFFEEEAAA???===:::888666555555444444444444444444444444444444333333333333444444444555666777777999<<>><<<999777555444444444444444444444444444555555555444444555555555555666777777888999===???JJJbbb~~~pppaaaWWWPPPQQQUUUXXX[[[^^^___aaabbbbbbbbbccceeegggmmmvvv}}}|||~~~vvvpppiiibbb\\\ZZZWWWRRRPPPRRROOONNNNNNNNNPPPRRRUUUWWW\\\bbblllwwwsss___QQQLLLLLLOOORRRRRRNNNJJJGGGBBB<<<:::999777555444444444555333444444555555444444333333333333444444444555555222888<<<===GGGaaajjjbbb```___ZZZYYYWWWTTTPPPMMMKKKJJJ@@@@@@>>><<<:::777555444555555555555555555555555777666666555555666666777555666777888888:::===@@@KKKcccyyycccXXXOOOPPPTTTXXX\\\______```aaaaaaaaabbbdddfffoooxxx~~~~~~yyyuuuiiiccc^^^]]]ZZZVVVUUUVVVQQQQQQRRRTTTWWW[[[^^^```eeelllxxxwwwaaaRRRMMMLLLOOORRRSSSOOOKKKHHHBBB<<<:::999777666555444555555333444444555555444444333333333333444444444555555222888<<<>>>JJJfff~~~}}}ooocccaaa```[[[YYYWWWTTTQQQNNNLLLKKK@@@@@@???===:::888555444666666666666666666666666777777666666666666777777555666777888888:::===@@@LLLdddiii]]]RRRQQQUUUXXX\\\______```aaaaaaaaaaaaccceeessszzz|||{{{jjjccc___^^^]]]YYYXXXYYYUUUVVVYYY]]]aaafffiiikkkpppwwwyyycccSSSMMMMMMOOORRRSSSOOOKKKHHHBBB<<<:::999777666555555555555333444444555555444444333333333333444444444555555111999===???LLLiii~~~|||wwwggg```\\\\\\[[[XXXUUUQQQMMMJJJHHHBBBAAA???<<<:::777555444666666666555444444444333555666777666555444555777444333555888777777<<>>EEETTTmmm~~~bbbTTTWWWTTTUUU\\\^^^___``````______```dddgggqqq}}}}}}zzzyyypppjjjdddbbbdddffffffdddcccdddgggkkkpppwww|||nnnYYYOOOOOOQQQRRRRRROOOJJJEEEAAA@@@;;;999777555444333333444555555666666666555444444444555555555444444666777777999;;;AAASSSooovvvrrrwwwsssgggdddccc^^^]]]ZZZVVVQQQLLLIIIFFFDDDBBB>>>:::888666666666444444444555555555555555444555666666555444555666666666777:::::::::???GGGXXXppphhhWWWXXXWWWWWW[[[[[[^^^______^^^^^^___cccfffmmmyyy|||zzzyyyppplllgggfffiiilllllllllmmmmmmooorrrwww~~~vvv]]]QQQPPPQQQRRRSSSPPPKKKFFFBBB@@@;;;999777555444444444444444444333333333444555555444555555555444444666777777999<<>>999777666666777333444444444555666666666444555666666444444555666777666777:::999:::@@@HHHYYYqqqmmmYYYZZZXXXXXX[[[YYY^^^______^^^^^^```cccffflllxxx~~~zzzyyypppmmmiiiiiikkkooopppqqqsssssstttwww|||}}}bbbTTTRRRPPPRRRSSSQQQLLLFFFBBB@@@;;;:::888666444444444444333333222111222333555666333555555555444444555777777999===GGG\\\vvvuuuoooqqqyyyiiiaaa```bbb```^^^[[[WWWRRRMMMIIIFFFEEEBBB>>>999777666666777333444444444555666666666444555666555444333444666666555666888888999@@@IIIZZZrrrmmmZZZZZZYYYYYY[[[YYY___``````______```dddfffnnnzzz}}}zzzrrrpppmmmlllmmmppprrrssswwwwwwyyy}}}dddVVVSSSPPPRRRSSSRRRMMMGGGCCCAAA;;;:::888666555444444444333222111111111333444666333555555555444444555777888999===JJJbbb|||tttnnnppppppfff``````ccc___^^^[[[WWWRRRMMMJJJGGGDDDBBB>>>:::888666666666444444444555555555555555333444555555444333444555777555666888888:::AAAJJJ___vvviiiXXX[[[YYYXXX\\\[[[___``````______```dddgggqqq|||~~~zzzzzzyyyxxx|||~~~xxxvvvsssppppppqqqsssuuuzzz|||}}}aaaTTTRRROOOQQQSSSRRRNNNHHHCCCAAA<<<:::888666555444555555333333222222222333444444444555555555444444666777999999>>>MMMiiiwwwqqqsssqqqfffaaa^^^___ccc^^^]]]ZZZWWWSSSNNNKKKIIIBBBAAA???<<<999777555555555555555555555444444444333444555555333333444555888666777999999;;;CCCLLLggg}}}}}}bbbVVVZZZXXXWWW\\\]]]^^^______^^^^^^___cccfffqqq}}}}}}zzzvvvvvvzzz}}}~~~|||~~~{{{wwwttttttvvvwwwzzz}}}}}}zzzwwwwww|||xxx\\\OOONNNNNNQQQTTTSSSNNNIIIDDDAAA<<<;;;999777555555555555333444444444444333333222444555555555444444666777::::::>>>OOOnnn{{{uuuwwwvvvddd]]][[[ZZZ]]]aaa^^^\\\ZZZWWWSSSOOOLLLJJJBBBAAA???<<<:::777555444666666666555555444444333333444555555333333444555999888888:::;;;<<>>QQQqqqxxxxxxmmm]]]YYY[[[[[[\\\^^^```]]]ZZZWWWTTTQQQLLLIIICCCBBB???<<<999666555444222333555666666666555444555555555555555666777777666888666999@@@>>>CCCUUUrrrlll\\\SSSXXX[[[XXXXXX\\\ZZZZZZ\\\^^^\\\\\\cccmmmyyy}}}zzz|||xxxyyyyyyxxxwww{{{~~~{{{www{{{zzzsssnnnllllllmmmnnnxxxkkkUUULLLLLLNNNTTTVVVSSSNNNKKKFFF@@@:::999777555444333333333444444444444444444444444666555444333444555666777777<<>><<>>GGGZZZyyy~~~|||hhh^^^[[[[[[\\\^^^```^^^ZZZXXXUUUQQQMMMIIIDDDBBB???<<<999777555444444444333333444444555666555555555555555666777777444666444777>>>===DDDXXXsss{{{bbbWWWPPPSSSWWWUUUUUUXXXYYYYYY[[[]]]]]]^^^fffppp{{{}}}vvvoookkknnnwww}}}{{{|||yyyrrrnnnjjjqqq}}}yyybbbOOOIIIKKKOOOTTTVVVRRRMMMJJJDDD???;;;999777555444444444444444444444444444444444444555555444444444555777777;;;???III^^^~~~qqqbbb\\\\\\]]]^^^aaa^^^[[[XXXUUUQQQMMMJJJDDDBBB@@@<<<999777555444666555444333444555666777555555555555555666777777666999777:::@@@???HHH^^^vvvrrr]]]TTTOOORRRUUUUUUUUUXXXZZZYYY[[[\\\[[[\\\dddnnn{{{{{{}}}yyyqqqkkkkkkqqqwww}}}~~~~~~zzzvvvwww{{{|||xxxqqqsss{{{xxxbbbQQQKKKNNNPPPUUUWWWSSSMMMIIIDDD>>>;;;:::888666444444444444444444444444444444444444555555444444444666777888<<>>;;;:::888666555444444444444444444444444444444444555555444444555666888999;;;>>>LLLffflllbbbbbbcccbbbaaa___[[[YYYVVVRRRNNNJJJEEECCC@@@===:::888666555666666555555666666777888555555555555555666777777444888666888===>>>KKKddd~~~|||xxxpppeee]]]SSSRRRQQQRRRUUUWWWXXXYYY[[[ZZZZZZZZZXXXYYYcccmmm~~~|||tttwww{{{}}}vvvqqqpppppptttyyy}}}xxxrrrmmmhhhfffcccaaadddjjjpppuuuyyy}}}}}}hhhUUUMMMNNNTTTXXXZZZUUUOOOJJJDDD>>><<<:::888666555444555555444444444444444444444444555555444444555777999:::;;;>>>MMMjjjqqqeeeffffffdddbbb___\\\YYYVVVRRRNNNKKKEEECCCAAA===:::888666555333444444555555555555555555555555555555666777777444888777888===???MMMggg}}}vvvkkk^^^WWWOOOPPPQQQRRRTTTWWWXXXXXXZZZYYYZZZ[[[ZZZ]]]gggrrr}}}vvvqqqtttxxx{{{}}}xxxtttrrrsssqqqtttzzz{{{tttpppllleee```[[[ZZZXXXXXX[[[```fffjjjrrrvvv}}}oooZZZPPPOOOUUUZZZ\\\VVVPPPKKKEEE???<<<;;;999777555555555555444444444444444444444444555555444555666777999:::<<>>:::888666555111222333444555444333222555555555555555666777777666:::999:::???AAAPPPkkkyyykkk]]]VVVLLLNNNPPPQQQSSSWWWXXXWWWYYYXXXZZZ\\\\\\```kkkwwwxxxrrrpppsssvvvxxxzzz~~~yyyuuuuuuvvvnnnpppttt{{{wwwnnnjjjeee^^^YYYSSSRRRQQQRRRUUUZZZ___cccgggmmmttt|||vvv___SSSRRRWWW[[[]]]WWWQQQLLLEEE???<<<;;;999777555555555555444444444444444444444444555555444555666888:::;;;===@@@RRRqqqvvviiiggggggfffdddaaa\\\XXXVVVSSSOOOMMMIIIFFF@@@===;;;999777666444444555555555555444444555555555555666888999:::777:::888:::??????KKKdddrrr```SSSPPPPPPPPPRRRUUUWWWWWWVVV\\\XXXWWWYYY\\\aaalllvvv~~~vvvrrrrrrmmmpppsssvvvxxx{{{~~~~~~|||zzzyyyxxxrrrnnnmmmsss{{{~~~}}}xxxmmmddd]]]YYYWWWQQQOOOMMMNNNQQQVVVYYYZZZaaafffmmmqqqsssxxxzzzcccWWWUUUZZZ^^^^^^WWWPPPKKKEEE@@@>>>===:::777555444333333555555555555555555555555555555555666666666666666>>>AAATTTvvvlllfffeeeddddddaaa]]]YYYVVVSSSPPPMMMIIIEEE@@@<<<:::999777555444444555555555555444444444444444555666777999999666:::888:::??????JJJbbb}}}}}}gggWWWQQQPPPPPPRRRUUUWWWWWWVVV[[[XXXWWWYYY\\\aaalllvvvzzzrrrmmmnnnllloootttwwwzzz}}}~~~{{{zzzyyyyyytttpppnnnqqqxxx~~~~~~|||~~~|||ssskkkbbbZZZTTTSSSPPPLLLKKKNNNQQQSSSTTTZZZ^^^cccfffgggjjjqqqvvv~~~wwwaaaWWWWWWXXX\\\\\\UUUNNNJJJDDD>>>===<<<999666444333222222555555555555555555555555666666666666777777777888;;;???TTTvvvssshhheeeeeedddbbb^^^ZZZWWWTTTPPPNNNHHHDDD???;;;999888666444444444555555555555444444333333333444555666888888555999888:::???>>>III```{{{qqq[[[RRRQQQQQQRRRUUUVVVWWWVVVZZZWWWWWWYYY[[[```kkkwww}}}vvvmmmhhhhhhiiimmmtttyyy}}}}}}{{{zzzzzzyyywwwrrrnnnoootttyyy}}}~~~||||||wwwooocccZZZXXXSSSNNNKKKKKKMMMOOOPPPUUUWWWZZZ[[[[[[]]]bbbfffqqqwwwwww```WWWXXXVVVZZZZZZTTTMMMHHHCCC===<<<;;;888666444222222222555555555555555555555555777777777777777888999999999@@@VVVuuu}}}mmmhhhgggeeebbb___\\\YYYUUUQQQNNNGGGDDD???;;;999777555444444444555555555555444444333333333333555666777888555999888:::???>>>III```~~~}}}```TTTRRRQQQRRRTTTVVVWWWVVVXXXWWWWWWYYYZZZ___kkkwww{{{sssiiicccccceeekkkssszzz~~~}}}|||{{{zzzzzzyyyuuupppmmmpppuuuzzz}}}~~~sssjjj___ZZZSSSNNNMMMOOOPPPQQQSSSUUUVVVVVVVVVWWW[[[___fffjjjpppxxx}}}cccWWWWWWVVVZZZZZZTTTMMMHHHCCC===<<<;;;999666444333333333444444444444444444444444777666666666666888999:::;;;BBBVVVppprrrjjjgggeeeccc```]]]ZZZWWWRRROOOGGGDDD???;;;999777555444444444555555555555444444333333333333555666777888444999888:::??????JJJbbbhhhVVVTTTRRRRRRTTTVVVVVVVVVXXXWWWXXXZZZZZZ___lllyyy|||ssshhhaaa```bbbiiirrrzzz~~~~~~}}}}}}||||||{{{zzzyyyvvvrrrnnnnnnrrrxxx|||wwwgggaaaYYYRRRQQQRRRTTTUUUSSSSSSRRRRRRSSSUUUXXX[[[]]]```eeekkkrrr{{{gggWWWUUUWWW[[[[[[UUUNNNJJJDDD???>>><<<:::888666555555555333333333333333333333333555555444444555666888999===BBBSSSjjjyyytttjjjffffffdddaaa___\\\XXXSSSOOOHHHDDD???;;;999888666444444444555555555555444444333333333444555666888888555999777999???@@@MMMfffnnnWWWUUURRRRRRSSSUUUVVVVVVWWWXXXYYY[[[[[[___mmm{{{}}}tttggg```^^^```fffooowww|||~~~~~~~~~~~~}}}|||{{{{{{wwwwwwuuuqqqooopppvvv{{{ssslllaaaYYYVVVWWWYYYZZZUUUSSSRRRQQQRRRUUUXXXZZZ[[[^^^cccjjjqqqyyyhhhWWWTTTWWW[[[[[[VVVOOOKKKFFFAAA>>>===:::888777666666777333333333333333333333333555444333333444666888:::<<