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'''---555999999999:::;;;;;;===???AAABBBBBBAAA@@@;;;:::999999999<<<>>>@@@===<<<<<<;;;<<<===???@@@???===;;;::::::;;;<<<===;;;;;;<<<<<<<<<;;;999999::::::::::::<<<>>>@@@BBBCCCCCCBBBBBBBBBBBBCCCCCCCCCBBB???===;;;:::;;;<<<===<<<:::999999:::<<<===<<<<<<;;;<<<===>>>@@@AAA<<<<<<<<<;;;;;;;;;;;;;;;888777666555555666888999::::::;;;<<<============???@@@BBBDDDDDDDDDCCCCCCEEEEEEFFFFFFFFFFFFFFFFFFEEEEEEEEEDDDCCCBBBAAAAAAAAAAAAAAABBBBBBBBBBBBBBB@@@===888666777:::===???::::::::::::::::::::::::::::::;;;<<<>>>???@@@@@@BBBBBBCCCDDDEEEFFFGGGHHHFFFEEECCCAAA@@@@@@AAAAAABBBCCCDDDDDDDDDDDDCCCCCCBBBCCCDDDCCCBBBCCCDDDFFFGGGGGGGGGGGGFFFDDDBBBAAAAAAAAA??????@@@CCCFFFHHHEEEEEEGGGHHHJJJIIIHHHGGGCCCCCCDDDDDDDDDCCCBBBBBB@@@AAABBBAAA@@@@@@BBBDDDEEEDDDCCCCCCCCCCCCDDDDDDCCCAAA@@@@@@@@@<<<555000...,,,)))''''''(((***,,,******,,,000555;;;???AAAEEECCC???777)))***888BBBCCCBBB@@@>>>:::666333111'''$$$  &&&000;;;BBBDDDEEEGGGGGGGGGIIIKKKNNNMMMLLLKKKKKKJJJJJJJJJKKKKKKKKKLLLLLLMMMNNNOOOOOOOOOOOOOOOPPPPPPPPPPPPPPPNNNNNNNNNNNNOOOOOOPPPQQQPPPOOOOOOPPPQQQRRRQQQPPPPPPQQQRRRRRRSSSTTTUUUUUUSSSUUUVVVWWWVVVTTTQQQOOOSSSSSSSSSTTTTTTUUUUUUUUUWWWWWWVVVVVVTTTSSSQQQPPPSSSRRRPPPOOONNNMMMLLLLLLLLLLLLLLLJJJHHHDDD@@@===444///***''''''%%%!!!+++888@@@CCCFFFPPPTTTXXXYYYXXXXXXZZZ]]]]]]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\]]]]]]___```aaaaaa``````aaabbbdddcccaaa```___^^^^^^^^^aaaaaa`````````___^^^]]]_________aaabbbcccaaa___```___^^^]]]^^^^^^````````````aaabbbcccdddeeefffcccbbb```______aaacccdddbbbbbbcccdddeeefffggghhhjjjiiiiiiiiiiiihhhgggfffgggiiilllmmmmmmjjjgggeeebbbccceeegggiiijjjkkkkkkhhhhhhiiiiiiiiihhhfffeeeeeeddddddfffggghhhfffdddeeehhhjjjiiifffdddfffiiillllllmmmmmmmmmmmmlllllliiijjjjjjjjjkkkjjjjjjjjjiiihhhhhhiiikkklllkkkjjjjjjkkkllllllkkkkkkmmmooopppooonnnllljjjhhhgggfffiiijjjkkkkkkjjjiiihhhgggeeeeeeffffffffffffeeeeeehhhhhhgggfffdddcccbbbbbb  """***000666999999999:::<<<===>>>AAACCCDDDCCCBBBAAA???>>><<<::::::;;;===>>>======<<<<<<===???AAABBBCCCBBB???<<<::::::;;;<<<<<<<<<<<<<<<;;;::::::999999999999999:::<<<>>>???AAAAAA@@@@@@AAAAAABBBCCCAAA???===;;;;;;<<<===>>><<<;;;999888999:::<<<===<<<<<<<<<===>>>??????@@@;;;;;;<<<<<<<<<<<<<<<<<<:::999777666666777999:::;;;;;;<<<>>>>>>?????????>>>@@@BBBEEEFFFEEEDDDCCCCCCCCCCCCDDDEEEGGGHHHHHHGGGFFFDDDCCCAAA@@@???>>>@@@@@@@@@@@@@@@AAAAAAAAABBB===888666777:::;;;;;;999999999999999999999999999:::;;;<<<===>>>??????AAAAAABBBDDDEEEGGGHHHIIIFFFFFFDDDCCCBBBBBBBBBBBBDDDDDDDDDDDDDDDDDDDDDCCCBBBCCCDDDCCCBBBCCCDDDFFFEEEFFFGGGFFFEEECCCAAA???BBBAAAAAAAAABBBDDDGGGHHHEEEFFFGGGHHHHHHHHHGGGGGGBBBCCCCCCCCCCCCBBBBBBAAACCCDDDDDDBBBAAA@@@AAACCCDDDDDDCCCCCCCCCDDDDDDDDDCCCAAA@@@???===777...&&&$$$""" !!!&&&,,,333:::>>>BBBAAA???777)))***888CCCCCCCCCCCCBBB@@@===:::888...+++'''$$$!!!"""(((111;;;BBBDDDEEEGGGGGGGGGIIIKKKNNNLLLKKKJJJJJJIIIJJJJJJJJJJJJKKKLLLMMMNNNOOOPPPQQQRRRQQQQQQPPPPPPOOOOOOOOONNNNNNNNNNNNOOOOOOPPPQQQPPPOOONNNNNNPPPQQQQQQPPPPPPQQQQQQRRRSSSSSSTTTTTTRRRSSSUUUUUUUUUTTTRRRQQQTTTTTTTTTTTTTTTUUUUUUUUUWWWWWWVVVUUUTTTSSSRRRQQQTTTSSSRRROOOMMMLLLKKKLLLMMMMMMLLLHHHCCC>>>999666---)))$$$!!!!!! 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%%%---222777999999:::<<>>>>>@@@AAABBBBBBAAA@@@@@@???===<<<;;;;;;<<<<<<<<<<<<======???@@@AAABBBEEEEEECCC@@@<<<::::::<<<<<<<<<<<<;;;;;;:::::::::999888888888999;;;===>>>@@@?????????@@@BBBDDDEEE@@@>>><<<;;;<<<=========::::::999999:::;;;===>>>>>>>>>>>>>>>????????????999:::;;;<<<<<<<<<<<<<<<<<<:::888777777888999:::<<<<<<>>>???@@@@@@@@@@@@???AAADDDGGGGGGGGGEEEDDDAAAAAABBBBBBDDDFFFGGGHHHFFFEEECCCAAA@@@???>>>>>>??????>>>>>>>>>???@@@AAABBB===999777999;;;;;;999999999999999999999999999999::::::;;;<<<===>>>>>>??????AAACCCEEEFFFHHHHHHFFFFFFEEEDDDDDDDDDDDDEEEEEEEEEEEEEEEDDDDDDDDDDDDBBBCCCDDDCCCBBBCCCDDDFFFEEEEEEFFFFFFEEECCCAAA@@@CCCCCCCCCDDDEEEFFFGGGGGGEEEFFFHHHGGGFFFEEEFFFGGGBBBBBBBBBBBBBBBBBBCCCCCCDDDEEEEEECCCAAA@@@AAACCCCCCCCCCCCDDDDDDDDDDDDDDDBBBAAA???<<<666...$$$###***222888<<<======888))) 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###&&&***///666===BBBFFFGGGHHHHHHGGGHHHJJJLLLJJJIIIIIIHHHIIIIIIJJJJJJJJJKKKLLLNNNPPPQQQSSSSSSNNNNNNNNNNNNOOOOOOPPPPPPPPPPPPOOONNNNNNNNNOOOOOOQQQOOOMMMNNNOOOQQQQQQQQQPPPPPPPPPPPPPPPOOOOOOOOONNNMMMNNNNNNPPPRRRTTTUUUWWWWWWVVVVVVUUUUUUUUUTTTTTTTTTTTTSSSSSSSSSTTTTTTRRRSSSSSSPPPMMMKKKKKKMMMNNNNNNKKKEEE===666444333///+++&&&""" 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""")))111777::::::;;;???AAA@@@>>>===<<<;;;:::;;;;;;<<<888888888999:::;;;===>>>999999:::;;;<<<===>>>???CCCBBBBBBAAA???>>><<<;;;===<<<:::888777777888888::::::;;;;;;<<<===============<<<<<<<<>>======<<<<<<:::999888777888:::<<<>>>??????@@@@@@@@@AAAAAAAAA===>>>???@@@AAABBBBBBBBB???;;;666555666888888777888999<<<>>>@@@@@@@@@@@@AAABBBDDDFFFGGGFFFEEEDDDBBBCCCDDDDDDCCC@@@>>><<<>>>@@@BBBBBB@@@>>>>>>>>>>>>>>>=========???@@@AAA;;;<<<===<<<<<<<<<>>>@@@<<<===>>>>>>>>>===;;;;;;999999:::::::::;;;;;;;;;<<<<<<===???@@@AAABBBCCCEEEEEEEEEDDDCCCCCCEEEGGGFFFGGGHHHGGGEEECCCCCCCCCCCCDDDEEEFFFFFFEEEDDDCCCDDDEEEFFFGGGHHHIIIIIIHHHFFFGGGHHHJJJJJJHHHGGGFFFJJJHHHFFFEEEEEEFFFEEEDDDAAA@@@@@@AAABBBCCCAAA???@@@AAAAAA@@@???AAADDDGGGFFFEEEDDDEEEGGGGGGEEEDDD@@@;;;333)))  $$$...444666000$$$!!!***999DDDIIIHHHFFFEEEEEEEEEFFFGGGDDDBBBAAAAAAAAAAAA???>>>;;;666000------...,,,+++---///222666;;;@@@CCCEEEIIIHHHFFFEEEFFFHHHKKKLLLHHHGGGFFFGGGIIIJJJIIIHHHMMMNNNOOOOOOOOOOOOPPPQQQOOOOOOOOOOOOPPPRRRTTTUUUWWWUUURRRPPPNNNNNNNNNOOOQQQQQQQQQQQQQQQQQQQQQQQQRRRPPPOOOOOOOOOOOONNNLLLLLLMMMMMMMMMNNNQQQUUUXXXXXXVVVTTTQQQPPPPPPQQQQQQOOOPPPRRRTTTUUUVVVUUUUUUWWWUUURRROOOMMMNNNOOOPPPMMMLLLIIIDDD???:::666444...***)))***&&&"""$$$+++555999===@@@BBBFFFKKKPPPUUUWWWZZZ[[[[[[\\\]]]^^^]]]]]]]]]^^^^^^^^^______^^^\\\YYYWWWWWWYYY[[[]]]^^^______]]]\\\\\\^^^```aaa```^^^]]]^^^___aaaccc___^^^\\\\\\\\\^^^```aaa```___]]][[[ZZZZZZ[[[[[[```___]]][[[ZZZZZZ[[[[[[aaaaaa``````___^^^]]]]]]```````````````_________bbbbbbcccddddddddddddcccbbbcccdddeeeffffffffffffdddeeeggghhhhhhhhhgggfffllljjjgggeeedddfffhhhiiijjjiiifffeeeeeegggiiijjjkkkkkkjjjjjjjjjjjjjjjkkkjjjjjjjjjiiiiiiiiihhhhhhiiikkkmmmoooppppppooonnnkkkkkklllllllllkkkjjjjjjffffffgggiiijjjkkklllmmmhhhiiijjjkkklllkkkjjjjjjhhhjjjkkkjjjggggggiiillliiiiiiiiiiiiiiijjjkkkkkkhhhhhhhhhggggggggggggggg``````aaaccceeeeeebbb``` 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