BM6( ||||||yyyxxxuuutttttt~~~~~~{{{{{{|||~~~{{{vvvsssqqqpppoooppprrrsssrrrpppqqqrrrtttttttttrrrpppooonnnlllhhhdddcccdddfffggghhhhhhhhhiiikkknnnqqqsssuuutttsssuuuvvvwwwvvvuuu~~~|||yyywwwzzz|||~~~~~~~~~~~~~~~}}}{{{zzzyyy}}}~~~~~~|||yyyvvvvvvvvvwwwvvvuuuvvvxxxyyyzzzyyyvvvtttqqqooonnnoooqqqrrrvvvwwwyyyyyyyyywwwuuusssmmmkkkhhhfffeeeeeefffgggiiikkkmmmmmmjjjhhhffffff_________^^^\\\YYYVVVTTTVVVUUUTTTUUUVVVWWWWWWUUUYYYYYYXXXWWWVVVVVVUUUUUUUUUSSSPPPMMMKKKKKKMMMMMMNNNOOOOOOPPPRRRTTTUUUVVVVVVVVVVVVXXX[[[\\\[[[YYY}}}}}}yyyzzz{{{}}}~~~~~~}}}|||||||||zzzvvvsssmmmmmmlllkkkiiigggggggggeeedddcccbbbaaa```___^^^^^^^^^^^^]]]\\\ZZZVVVTTTXXXZZZ[[[\\\[[[\\\]]]___\\\\\\]]]]]]]]]\\\[[[[[[```bbbddddddbbb```______aaa___\\\\\\^^^^^^]]][[[ZZZXXXTTTQQQPPPRRRUUUWWWZZZ[[[]]]^^^]]]ZZZWWWUUUMMMLLLKKKIIIIIIIIIJJJKKKKKKMMMNNNNNNLLLJJJJJJJJJEEEEEEEEEDDDDDDCCCBBBAAABBBAAA???@@@BBBCCCCCCBBBDDDDDDCCCCCCCCCCCCDDDDDDBBBAAA@@@>>>======>>>>>>>>>???@@@AAAAAAAAAAAAAAAAAAAAAAAADDDFFFGGGGGGEEE~~~~~~~~~|||{{{uuuuuutttsssrrrsssvvvxxx~~~{{{yyyvvvtttsssrrrqqqqqqqqqnnnjjjgggaaafffiiihhhccc______aaa^^^___ccchhhooosssttttttpppmmmjjjhhhiiiiiiiiiiiiffffffdddaaa^^^]]]___``````^^^]]]]]]___```aaa```UUUVVVWWWYYY[[[]]]___```[[[[[[[[[[[[[[[XXXSSSOOOMMMNNNOOONNNLLLKKKLLLMMMIIIIIIIIIIIIIIIIIIIIIHHHFFFFFFFFFGGGHHHGGGDDDBBBAAABBBDDDDDDCCCDDDEEEGGGGGGFFFFFFFFFFFFFFFFFFFFFHHHKKKOOOQQQPPPOOONNNNNNPPPMMMIIIHHHIIIHHHFFFCCCGGGDDD???<<<;;;===@@@CCCAAACCCFFFIIIIIIHHHFFFDDD======<<<======>>>>>>???<<<===??????>>>===>>>???<<<<<<<<<<<<<<<=========:::888777888:::;;;;;;;;;999999:::;;;<<<=========;;;:::::::::::::::;;;;;;:::;;;<<<<<<<<<;;;999888:::::::::<<<>>>@@@???>>>{{{yyysssttt}}}{{{|||vvvtttqqqooopppqqqrrrqqq}}}~~~zzzyyyxxx~~~|||zzzvvvssswwwvvvvvvwwwxxxwwwuuusssrrrtttvvvvvvtttpppmmmlllmmmnnnoooqqqssstttttttttqqqqqqrrrssstttsssrrrppppppppppppooonnnoooqqqsssxxxvvvqqqmmmkkkiiiiiijjjkkkllllllllllllnnnqqqsssssssssssstttttttttttttttzzzxxxzzz~~~~~~zzzyyy{{{vvvuuurrrpppnnnnnnnnnnnnkkkkkkkkkkkkjjjiiihhhgggdddbbb___]]]]]]___aaacccbbbbbbaaabbbddddddcccaaa___ZZZVVVVVVZZZ\\\YYYVVVTTTSSSQQQPPPPPPRRRSSSUUU]]]___cccgggkkknnnppppppjjjccc[[[WWWVVVVVVSSSQQQOOONNNLLLLLLMMMMMMKKKJJJKKKKKKJJJJJJIIIHHHHHHHHHEEEFFFGGGHHHJJJLLLPPPSSSSSSRRROOOLLLIIIHHHIIIKKKIIIIIIIIIHHHGGGEEEDDDCCCGGGHHHIIIGGGFFFEEEFFFHHHEEEDDDCCCDDDFFFHHHHHHGGGEEEDDDCCCCCCEEEFFFFFFEEEBBBBBBAAABBBCCCCCCAAA@@@DDDEEEEEEBBB???>>>@@@CCC???@@@AAA@@@>>>======>>>@@@AAABBBAAA@@@@@@@@@AAA@@@>>>;;;;;;;;;===>>>>>>AAABBBBBBBBBBBBBBBAAAAAABBB???===<<<<<<<<<;;;999===;;;:::;;;<<<===<<<;;;===???BBBDDDDDDBBB???<<<>>>===;;;:::999999::::::999<<<<<<999999<<<<<<:::<<<:::999999;;;======<<<======<<<:::888777999;;;>>>>>>==================:::;;;<<<;;;:::999:::;;;::::::;;;;;;;;;999888666777888:::::::::;;;===>>>}}}sssiiiccc___]]][[[\\\dddrrr|||~~~{{{zzz}}}}}}~~~{{{~~~}}}}}}~~~~~~zzzuuurrrtttxxx|||~~~ssspppkkkgggeeefffhhhiiitttxxxxxxoooddd```fffnnn}}}{{{}}}}}}xxxvvvxxxzzzyyyvvvtttxxx|||yyyrrraaa^^^^^^bbblllvvv|||~~~|||tttsssuuunnnfff```aaabbb```^^^^^^]]]gggtttvvvlllhhhccc```______^^^\\\^^^]]]]]]___```___]]][[[[[[\\\\\\ZZZXXXWWWVVVVVVWWWXXXZZZZZZXXXWWWVVVWWWRRRRRRRRRTTTUUUUUUUUUTTTVVVVVVVVVUUUTTTUUUVVVXXXYYYXXXVVVSSSQQQPPPOOOOOOTTTUUUUUUUUUUUUVVVXXXYYYWWWVVVVVVVVVVVVVVVWWWWWWZZZYYY[[[^^^^^^YYYWWWXXXWWWWWWVVVUUUTTTTTTSSSSSSPPPPPPOOOOOONNNNNNMMMMMMKKKKKKIIIIIIHHHIIIIIIJJJLLLKKKJJJKKKLLLLLLKKKIIIKKKIIIGGGGGGIIIIIIGGGDDDCCCBBBAAA@@@AAACCCEEEFFFGGGIIIKKKNNNQQQRRRSSSTTTSSSNNNIIIFFFGGGGGGEEEBBBCCCBBBAAAAAABBBBBB@@@???AAA@@@@@@??????>>>======>>>???@@@AAACCCDDDFFFHHHJJJIIIHHHEEECCCBBBCCCCCCCCCCCCCCCCCCBBBBBBBBBBBBAAABBBCCCBBBBBBBBBEEEGGGGGGFFFEEEEEEFFFEEECCCAAACCCBBB@@@@@@BBBCCCCCCBBBEEEDDDBBBAAAAAABBBCCCCCCEEEGGGIIIHHHDDDAAA@@@AAA???@@@AAA@@@>>>>>>???AAA???@@@AAAAAAAAAAAAAAABBBDDDBBB???>>>>>>>>>>>>>>>BBBAAAAAA@@@???>>>======<<<<<<;;;::::::999999:::;;;999777777:::===>>>???:::<<>>>>>============>>>???===@@@@@@======@@@@@@===???>>>???AAAEEEIIIJJJJJJBBBBBBBBB@@@======>>>@@@DDDEEEFFFHHHIIIJJJJJJJJJEEEEEEEEECCCAAAAAABBBCCCCCCCCCBBBAAA@@@>>>===<<<<<<===>>>???@@@CCCFFFIII~~~yyytttqqqhhhddd]]]UUUOOOKKKIIIIIIKKKKKKQQQ[[[bbbbbbaaacccaaaeeeiiilllkkkhhhffffffmmmnnnooopppooonnnllljjjfffdddbbbcccfffgggdddbbb______```aaaccceeefffgggmmmnnnlllhhhhhhooovvvyyyxxxzzz}}}|||yyywwwxxxwwwvvvuuusssrrrqqqqqqvvv}}}~~~sssllliiieeeeeefffccc]]]YYY^^^ffflllooorrrrrrppprrrwww|||mmmhhhcccdddkkkttt|||{{{tttlllfffbbbaaa```aaabbbhhhnnnnnnhhhbbb```bbbbbbdddfffhhhkkkmmmooowwwuuuvvv}}}}}}tttooooooqqquuu{{{|||yyyyyytttsssrrrqqqsssuuuyyy{{{~~~yyytttqqqkkkeeeaaa___```dddfffdddeeehhhgggeeeccc```\\\\\\fffrrrxxxrrrjjjdddbbbgggmmmrrrwwwvvvrrriii```]]]```eeebbb______```___]]]]]]___fffbbb______aaacccbbb```^^^ZZZUUUTTTVVV[[[___aaaVVVTTTQQQOOOMMMMMMNNNOOOXXX[[[ZZZTTTPPPTTTbbbooo|||iiijjjuuu}}}ppplllwww{{{kkk___\\\\\\```aaa^^^[[[[[[[[[[[[YYYXXX]]]fffjjjiii```]]]___jjj}}}vvvjjjdddcccZZZSSSOOOQQQSSSQQQPPPQQQWWWbbbrrrtttfffaaa[[[WWWVVVWWWXXXXXX[[[[[[[[[]]]^^^^^^\\\ZZZVVVSSSNNNKKKIIIIIIKKKMMMOOOQQQSSSRRRNNNIIIEEECCCBBBAAA@@@AAADDDFFFFFFEEECCCCCCCCCCCCCCCDDDEEEEEEFFFFFFFFFFFFFFFEEEEEEEEEIIIIIIHHHHHHGGGGGGFFFFFFFFFEEEDDDCCCCCCDDDEEEFFFFFFEEEHHHMMMMMMHHHEEEFFFGGGGGGHHHHHHHHHGGGEEEEEECCCBBBBBBBBBBBBCCCDDDEEEEEEDDDCCCCCCBBBAAA@@@@@@AAA@@@??????@@@@@@>>><<>>>>>======<<<<<<>>>=========>>>@@@BBBCCC@@@AAABBBBBBCCCDDDDDDDDDCCCAAA@@@???@@@@@@???===AAA@@@@@@AAABBBBBB@@@>>>>>>>>>>>>>>>>>>===============>>>@@@BBBCCCEEEFFFIIIIIIIIIIIIHHHGGGGGGFFFGGGFFFEEEEEEFFFGGGIIIIIIGGGGGGGGGGGGGGGJJJNNNQQQUUUUUUTTTTTTSSSPPPKKKHHHIIIHHHGGGIIILLLOOOPPPPPPWWWUUURRRNNNMMMMMMOOOPPPOOOSSSXXXZZZXXXSSSOOOLLLJJJKKKKKKKKKJJJKKKNNNPPPRRRSSSTTTTTTUUUUUUUUUUUURRRPPPNNNKKKIIIHHHHHHIIILLLJJJHHHEEEBBB???>>>======??????===999666777999:::888666777<<>>888888;;;???===<<>>>>>AAAEEEIIIJJJJJJKKKKKKJJJHHHEEEDDDFFFGGGJJJIIIIIIHHHGGGGGGFFFFFFBBBCCCCCCBBBCCCEEEIIIMMMNNNMMMLLLLLLLLLLLLMMMNNNNNNHHHCCCBBBEEEHHHGGGFFF|||{{{}}}~~~~~~|||yyyuuutttwww|||~~~yyy}}}~~~|||vvvvvvyyy}}}wwwxxxyyyxxxvvvuuuuuuvvvppplllkkkqqq|||zzzxxx|||}}}zzz{{{~~~zzz{{{}}}~~~~~~zzz{{{|||}}}|||yyytttqqqpppuuu|||zzz|||~~~yyywwwxxx{{{~~~~~~xxxooojjjjjjmmmnnnooofffeeeeeedddcccccccccccc```dddgggfffcccdddhhhllllllllllllmmmooonnnllljjjkkkjjjgggffflllrrrqqqlll```aaacccffffffccc^^^YYYXXXTTTNNNKKKKKKPPPWWW[[[___\\\XXXUUUTTTTTTVVVWWWYYYUUUOOOMMMNNNNNNLLLJJJJJJKKKNNNSSSVVVTTTOOOJJJGGGFFFEEEDDDDDDEEEFFFGGGKKKJJJIIIGGGEEEDDDCCCCCCCCCCCCDDDDDDBBB???<<<:::>>>======???CCCFFFGGGGGGGGGFFFFFFEEEDDDCCCCCCBBB???@@@BBBCCCCCCCCCBBBBBBAAABBBCCCBBB@@@??????@@@DDDEEEFFFGGGHHHIIIIIIIIIEEEDDDCCCBBBBBBCCCDDDEEE~~~|||}}}{{{yyyzzz{{{zzzwwwqqqjjjaaa]]]___dddiiilllmmmiiigggmmmxxx}}}zzzwwwssspppppppppqqqvvv{{{{{{zzz|||}}}{{{xxxsssuuuvvvuuusssqqqqqqqqqllljjjiiiooowww|||{{{xxxsssuuuzzz|||zzzzzzzzzzzzzzz{{{xxxxxx{{{|||nnnooopppsssvvvyyy{{{|||vvvvvvvvvwwwvvvtttqqqnnnlllpppuuuwwwuuuqqqnnnlllmmmooossswwwzzz|||||||||{{{vvvssssssuuuvvvrrrmmmfffccccccfffggggggdddcccbbb```___^^^^^^^^^\\\```ddddddccccccgggkkkooonnnmmmlllllljjjfffcccaaa```]]][[[```fffeeeaaa^^^]]]]]]^^^``````___]]]___ZZZSSSLLLJJJLLLPPPSSSYYYXXXUUUSSSSSSUUUXXXYYYZZZUUUPPPMMMMMMMMMKKKIIIEEEFFFIIINNNPPPOOOJJJEEEDDDDDDCCCBBBBBBCCCDDDDDDFFFEEECCCBBBAAA@@@@@@AAABBBBBBBBBBBBBBB@@@>>>===???>>>===???BBBEEEEEEEEEDDDDDDCCCCCCBBBAAAAAA@@@>>>???@@@AAABBBAAA@@@???@@@AAABBBAAA???>>>???@@@DDDEEEFFFHHHIIIIIIIIIIIICCCCCCBBBAAAAAABBBCCCDDD~~~~~~|||{{{|||~~~|||}}}}}}zzzzzz{{{{{{}}}||||||{{{zzzvvvtttnnncccVVVOOOPPPUUUYYY[[[[[[YYYZZZaaammmxxx}}}}}}~~~yyyxxxxxxvvvpppkkkkkkjjjkkkooouuu{{{~~~zzzvvvuuuvvvvvvssspppmmmoooqqqqqqnnnkkkjjjjjjffffffhhhlllpppssstttsssoooppprrrtttvvvvvvvvvvvvrrrpppooooooqqqrrrrrrqqqssssssssstttvvvxxx{{{|||uuussssssvvvyyyzzzwwwtttkkkjjjjjjnnntttyyyzzzzzzqqqqqqpppooonnnlllkkkjjjkkkooosssssspppkkkfffcccfffiiimmmqqqtttvvvvvvvvv}}}{{{wwwssspppnnnnnnnnnllliiieeecccdddeeeeeeeee```___]]][[[YYYXXXXXXWWWWWW[[[```bbbaaabbbdddgggjjjiiihhhgggfffccc```]]]]]]\\\XXXUUUXXX^^^___[[[ZZZXXXVVVVVVZZZ^^^```bbbaaa\\\TTTMMMIIIIIIKKKMMMSSSRRRQQQQQQSSSVVVYYY\\\[[[VVVPPPMMMMMMLLLJJJHHHAAACCCFFFIIIKKKJJJFFFCCCAAAAAA@@@@@@@@@@@@AAAAAABBBAAA???>>>===>>>@@@AAABBBBBBBBBAAAAAAAAAAAAAAA???>>>===>>>AAACCCCCCCCCAAAAAA@@@@@@??????>>>>>>>>>>>>???@@@@@@???======>>>???@@@@@@>>>===>>>???DDDEEEFFFGGGHHHIIIIIIIIIBBBBBBAAA@@@@@@AAAAAABBB}}}{{{zzz~~~~~~~~~}}}{{{zzzyyyvvvzzz}}}yyyyyyzzz{{{yyywwwvvvzzz}}}zzz{{{|||}}}}}}{{{}}}}}}|||zzzzzz}}}~~~wwwtttuuuxxxzzz{{{zzzxxxvvvrrrgggZZZSSSTTTXXXYYYYYYWWWUUUVVV]]]iiiuuu|||~~~|||xxxyyy{{{yyysssllljjjiiiiiimmmssszzz}}}{{{wwwuuutttrrrooolllhhhjjjlllkkkiiifffdddcccaaacccfffhhhjjjkkkmmmooommmmmmnnnnnnnnnmmmlllkkkjjjiiiiiikkkmmmnnnnnnlllnnnooorrrtttuuuuuutttsssllljjjhhhiiillloooppppppooolllkkkooovvv{{{{{{yyyqqqpppmmmjjjgggeeeeeefffhhhlllqqqrrrpppkkkgggeeefffhhhlllpppssstttuuuuuuuuutttrrrpppmmmkkkjjjiiijjjiiihhhgggfffeeedddcccZZZYYYXXXVVVUUUTTTTTTTTTUUUXXX]]]_________```aaa^^^]]]]]]^^^______\\\ZZZ[[[[[[WWWSSSUUUZZZ[[[XXXVVVTTTRRRTTTXXX^^^bbbccc\\\XXXQQQLLLIIIIIIKKKMMMQQQPPPPPPQQQSSSVVVYYY[[[[[[VVVQQQMMMMMMLLLIIIGGG@@@BBBEEEGGGIIIGGGEEECCC@@@??????????????????@@@AAA@@@>>>>>>>>>@@@CCCDDDEEEDDDCCCBBBAAAAAABBBBBB???>>>======???AAAAAA@@@??????>>>>>>============>>>>>>?????????===<<<;;;===>>>@@@???>>>>>>???@@@BBBCCCDDDEEEFFFGGGGGGFFFAAAAAAAAA@@@@@@@@@@@@@@@{{{zzz{{{}}}|||zzzzzzzzzzzztttvvvzzz~~~{{{vvvuuuvvvvvvtttqqqvvvzzz~~~~~~}}}{{{xxxwwwyyyzzzzzz}}}~~~yyyyyy~~~{{{wwwvvvzzz~~~}}}~~~~~~~~~}}}}}}|||||||||}}}}}}|||~~~uuukkklllooossswwwxxxwwwvvvvvvpppiii```[[[\\\^^^^^^]]]\\\YYYXXX]]]gggrrr{{{|||yyywwwxxxyyywwwqqqkkkkkkiiihhhkkkpppwww|||}}}{{{xxxvvvsssooojjjgggccceeegggfffdddaaa```______bbbeeeffffffgggiiikkkkkkkkkkkkjjjjjjiiihhhhhhfffeeefffgggiiijjjhhhffflllnnnqqqttttttrrrooommmhhhfffddddddfffjjjmmmooopppllljjjmmmssswwwvvvsssrrrqqqnnnhhhccc```aaacccdddggglllmmmkkkhhheeeddddddfffiiilllooopppppppppmmmmmmmmmlllkkkiiihhhgggddddddeeecccaaa^^^[[[ZZZTTTTTTSSSSSSSSSSSSSSSTTTUUUWWWZZZ\\\\\\[[[ZZZZZZVVVVVVWWWYYY[[[\\\ZZZYYYTTTUUURRRNNNNNNRRRTTTQQQPPPPPPRRRVVV[[[^^^``````UUURRRNNNJJJHHHIIIKKKMMMQQQQQQPPPQQQRRRTTTWWWXXXZZZUUUOOOLLLLLLKKKHHHEEE>>>@@@CCCDDDEEEDDDCCCCCC???????????????????????????>>>>>>>>>???AAACCCEEEHHHGGGEEECCCBBBAAAAAAAAA>>>===<<<<<<>>>??????>>>>>>>>>===============<<<===>>>??????>>>===<<<;;;<<<===??????>>>>>>???AAAAAAAAABBBCCCCCCCCCBBBBBBAAAAAAAAA@@@@@@?????????}}}{{{|||}}}~~~|||zzzyyyyyyyyyzzzrrrsssvvv|||}}}|||{{{wwwsssrrrssssssqqqooovvvyyy~~~|||{{{~~~~~~|||{{{yyyzzz|||}}}yyyzzzxxxxxxzzzzzzyyy}}}|||zzzuuuxxx}}}zzzqqqnnnlllmmmsssyyy~~~yyywwwxxx~~~|||}}}yyywwwwwwyyy|||~~~}}}xxxzzz~~~|||}}}yyynnneeelllooosssvvvvvvuuuuuuuuummmjjjgggddddddeeeffffffgggdddccceeekkkttt{{{zzzyyyyyyxxxwwwtttooollljjjhhhfffgggkkkppptttuuuuuuuuutttrrrnnniiidddbbbaaabbbcccbbb```______```aaaccceeefffffffffggghhhffffffffffffffffffgggggghhhgggggghhhiiiiiigggeeehhhjjjmmmooopppnnnkkkiiieeedddcccccceeehhhlllnnnooommmkkkmmmqqqsssrrrqqqqqqpppmmmggg```]]]___aaaeeegggjjjjjjgggdddcccbbbccceeehhhjjjllllllkkkkkkeeeffffffffffffeeedddccc___```aaa```\\\XXXUUUTTTQQQQQQPPPPPPQQQQQQRRRSSSSSSTTTUUUWWWWWWVVVVVVUUUUUUUUUUUUWWWXXXXXXWWWUUUOOOQQQPPPLLLLLLOOOPPPNNNLLLNNNQQQVVV[[[\\\[[[YYYQQQOOOKKKHHHFFFGGGHHHJJJQQQPPPPPPPPPPPPQQQSSSTTTVVVQQQKKKHHHHHHHHHEEECCC;;;===???@@@?????????@@@>>>>>>???@@@@@@???>>>>>>;;;;;;<<<===>>>@@@AAABBBGGGFFFEEECCCAAA@@@???>>>===;;;:::;;;===>>>>>>==================<<<<<<<<<<<<======>>>>>>===<<<;;;:::;;;============???@@@AAAAAAAAAAAAAAA@@@???>>>???????????????>>>===<<<}}}|||}}}zzzxxxyyy{{{}}}}}}~~~~~~~~~}}}}}}{{{zzzyyyuuuuuuvvv|||}}}|||{{{zzzzzzxxxtttpppoooppppppooolllqqqtttxxxzzzzzzzzz{{{|||}}}~~~~~~{{{yyyuuuyyy}}}~~~|||zzzzzzzzz|||~~~|||wwwrrrqqqrrrvvvxxx{{{|||yyywwwwwwyyyxxxwww|||yyy|||~~~}}}zzzwwwuuutttsssuuuxxx{{{yyysssiiibbbdddaaabbbgggmmmttt|||vvvuuuxxx~~~}}}|||}}}||||||wwwssssssvvvzzz~~~zzzwwwyyy{{{{{{{{{}}}}}}|||{{{yyywwwrrruuuxxxyyywwwrrrlllhhhnnnqqqtttuuutttrrrssstttlllmmmllljjjhhhiiilllooopppooonnnpppsssvvvyyy{{{xxxzzzzzzwwwrrrnnnlllllliiigggddddddfffiiikkkkkkjjjlllmmmllliiidddaaa___```aaaaaa```^^^^^^```bbbeeeeeefffggghhhhhhhhhgggbbbbbbbbbccccccdddeeefffjjjiiihhhhhhiiijjjiiigggdddeeeggghhhgggeeecccbbbaaabbbbbbbbbccceeehhhkkkmmmllllllmmmnnnooopppqqqkkkllljjjddd^^^[[[]]]```eeefffgggfffdddbbbbbbcccbbbdddfffhhhhhhhhhgggfff____________^^^]]]\\\\\\YYY[[[]]]\\\XXXTTTSSSSSSPPPPPPOOONNNNNNOOOOOOOOOOOOOOOOOOPPPQQQRRRRRRRRRRRRQQQRRRSSSTTTTTTRRRPPPKKKOOOPPPMMMLLLOOOOOOMMMIIIJJJNNNSSSVVVVVVSSSPPPKKKJJJGGGFFFEEEFFFHHHIIIMMMMMMMMMMMMMMMNNNOOOPPPPPPKKKFFFCCCCCCCCCAAA???888;;;======;;;;;;===???======>>>??????>>>======888999;;;===????????????AAABBBBBBBBB@@@>>>===;;;;;;:::999:::<<<>>>>>>===;;;;;;;;;;;;;;;;;;;;;;;;999:::;;;<<<<<<<<<;;;:::666888:::::::::;;;===>>>CCCCCCBBBAAA@@@>>><<<;;;<<<<<<======<<<;;;999888|||zzz{{{|||~~~zzzzzz{{{|||zzzxxxvvvyyy~~~{{{vvvtttwww{{{}}}|||}}}|||zzz|||{{{zzz~~~}}}|||zzzxxxwwwwwwxxxyyyvvvrrrnnnmmmnnnnnnllljjjlllnnnqqqrrrrrrrrrssstttooorrrwww{{{|||zzzvvvsssppptttzzz|||{{{xxxuuusssxxxyyyxxxtttoookkklllnnnrrrsssvvvzzz~~~~~~|||zzzsssqqqqqqrrrqqqpppvvv}}}|||}}}xxxtttuuuwwwvvvtttqqqppppppsssssssssqqqlllfff```\\\\\\XXXXXX\\\```fffqqq||||||zzzuuuvvv{{{~~~~~~yyyvvvxxxtttnnnrrrxxx}}}vvvqqqppptttyyy}}}~~~zzzxxxzzz|||wwwxxxzzz{{{zzzwwwtttrrrmmmpppssssssrrrooonnnnnnllloooqqqqqqnnnlllmmmnnnjjjkkklllhhheeeffflllrrrpppqqqrrrsssttttttsssrrrsssvvvwwwrrrkkkfffeeegggjjjgggeeedddeeefffffffffcccfffhhhiiigggccc```___```aaa```^^^]]]^^^aaadddhhhgggggghhhjjjjjjhhhfffbbbbbbbbbbbbcccdddeeefffgggeeeddddddfffggggggfffddddddcccbbb```]]][[[ZZZ^^^```aaabbbbbbccceeegggfffgggiiiiiiiiijjjlllnnneeeggggggbbb\\\ZZZ\\\```___``````___^^^___aaaccc^^^___aaabbbbbbaaa___^^^\\\\\\[[[YYYXXXWWWVVVUUUQQQTTTWWWVVVSSSPPPOOOPPPPPPPPPOOOMMMLLLLLLLLLLLLKKKJJJJJJKKKNNNPPPQQQQQQKKKKKKLLLNNNPPPPPPNNNMMMEEEJJJLLLKKKJJJLLLLLLIIIGGGHHHKKKOOOQQQQQQMMMJJJEEEDDDDDDDDDEEEGGGJJJKKKJJJJJJJJJJJJKKKLLLMMMNNNKKKGGGBBB???@@@@@@>>><<<999;;;======;;;;;;===@@@;;;<<<===>>>>>>===<<<;;;888:::===???AAA@@@@@@???<<<===???@@@???>>><<<::::::999888999<<<===>>>===::::::::::::::::::::::::777777999:::;;;::::::999444666888888888999;;;===EEEDDDCCCBBB@@@>>><<<;;;::::::;;;;;;:::888777666}}}zzzxxxwwwwwwwwwuuutttrrrqqqrrrtttvvvwwwsssssstttuuuvvvwwwxxxxxxxxxyyyyyyxxxvvvuuuvvvwwwsssxxx~~~|||zzzyyyzzz{{{zzzxxxxxxwwwvvvuuutttsssssstttqqqnnnmmmnnnmmmjjjgggkkkmmmooonnnllljjjhhhhhhfffjjjnnnpppppprrrvvvyyywwwyyy|||}}}{{{wwwqqqnnnpppnnnkkkiiihhhiiijjjllluuuwwwyyyyyyxxxwwwwwwwwwuuurrrooommmmmmpppsssvvvyyyyyyyyyxxxuuurrrpppnnnqqqqqqqqqooollljjjjjjkkknnniiiffffffeee___[[[[[[SSSPPPMMMNNNSSS\\\dddhhhiiitttxxxuuuvvvzzz}}}~~~}}}zzz|||~~~~~~~~~xxxhhhfffnnntttzzz}}}~~~}}}}}}{{{vvvoookkklllpppuuuwww~~~|||yyywwwwwwzzz}}}xxxuuurrrsssuuusssnnniiihhhiiilllmmmnnnnnnpppqqqrrrrrrpppnnnkkkhhhfffdddffffffgggggghhhiiiiiiiiiooonnnnnnmmmmmmllllllkkkrrrsssqqqnnnhhhdddaaaaaajjjiiifffcccbbbbbbccccccdddeeeeeeeeecccaaa^^^\\\eeecccaaa```aaaccccccbbbdddfffjjjooorrroooiiiccc```______```ccceeefffeeedddfffgggfffdddccccccdddhhhgggddd___[[[YYYZZZ\\\`````````aaaaaaaaaaaaaaaaaacccfffeeecccccceeehhhfffdddaaa___^^^]]]ZZZXXXbbb]]]XXXYYY]]]aaaaaa___cccaaa^^^[[[ZZZZZZ[[[\\\\\\ZZZWWWUUUSSSQQQQQQQQQPPPPPPPPPQQQQQQPPPLLLJJJHHHIIIIIIIIIJJJJJJKKKKKKMMMKKKIIIIIIKKKMMMMMMMMMJJJJJJJJJKKKKKKKKKKKKKKKIIIHHHGGGGGGFFFFFFGGGGGGCCCKKKQQQQQQPPPOOOLLLHHHCCCCCCDDDDDDEEEFFFFFFFFFEEEFFFGGGHHHHHHGGGEEEEEEFFFDDDAAA>>>;;;:::::::::===<<<;;;:::;;;;;;======:::;;;<<<<<<======<<<<<<:::;;;===>>>???>>><<<;;;<<<<<<<<<;;;;;;:::::::::888777777777888999::::::888888999999999999888888666666777777777777666666666777777888999;;;<<<===>>>?????????===;;;:::888888888888888777777777777~~~~~~}}}}}}~~~~~~{{{yyywwwtttrrrqqqppppppnnnmmmmmmmmmnnnoooqqqrrrqqqqqqqqqqqqqqqqqqrrrrrrqqqrrrsssrrrpppooopppqqqrrrwww}}}}}}xxxvvvuuuttttttvvvuuusssqqqqqqrrrtttuuuwwwrrrmmmjjjjjjjjjjjjiiihhhjjjkkkjjjgggcccaaa```ZZZ^^^bbbeeegggjjjppptttwwwxxx{{{{{{yyyuuuooollljjjiiigggeeeeeefffhhhiiitttvvvwwwvvvsssqqqppppppqqqnnnkkkiiihhhiiikkkmmmooooooooonnnmmmlllkkkkkkkkklllmmmkkkiiigggggghhhccc___]]]```___[[[YYYYYYMMMJJJIIIKKKQQQZZZbbbggglllsss}}}{{{uuurrrsssvvvxxx{{{}}}}}}{{{|||~~~~~~|||~~~~~~|||}}}yyyllljjjooosssyyy~~~~~~~~~}}}|||{{{zzzzzzyyywwwrrrmmmkkkmmmrrrvvvxxx{{{zzzxxxvvvvvvxxxzzz{{{vvvsssppppppqqqqqqlllhhhggghhhjjjllllllmmmnnnooopppnnnkkkhhhfffeeeeeeeeeeeeeeeddddddddddddddddddgggggggggggggggggghhhhhhnnnnnnmmmjjjfffbbb``````hhhfffeeecccbbbbbbcccdddeeeeeeeeeeeedddaaa___]]]ddddddcccbbbaaabbbccccccfffgggjjjmmmooommmhhhccc```___^^^```bbbdddeeedddaaacccddddddcccbbbbbbcccdddcccbbb^^^[[[YYYZZZ[[[^^^^^^^^^^^^^^^^^^^^^^^^___aaabbbaaa___]]]___```bbb___[[[YYYYYYZZZZZZZZZ^^^ZZZWWWXXX\\\______]]]bbb```]]]ZZZXXXXXXYYYZZZZZZYYYWWWTTTRRRQQQPPPOOONNNMMMMMMNNNOOOMMMJJJHHHHHHHHHHHHHHHHHHHHHIIIIIILLLJJJHHHIIIJJJLLLLLLLLLJJJIIIIIIIIIHHHGGGGGGGGGGGGFFFFFFEEEEEEEEEEEEEEEDDDJJJOOONNNLLLKKKHHHDDDAAAAAAAAAAAABBBCCCCCCDDDCCCCCCDDDDDDDDDBBBAAA@@@@@@???===;;;;;;;;;<<<======<<<;;;:::::::::;;;<<<999::::::;;;<<<<<<<<<<<<;;;<<<===>>>>>>===;;;:::;;;;;;;;;::::::999999999777777777777777888999999777888888888888888888777666666666777777666666666777777777777777888999:::<<<<<<<<<<<<;;;:::888777666666666666666666666666xxxxxxyyyzzz}}}~~~}}}xxxxxxyyy{{{}}}}}}{{{xxxrrrqqqpppnnnllljjjiiihhheeeeeefffgggiiijjjkkkkkkmmmmmmlllllllllkkkkkkkkkooopppqqqpppooonnnooopppmmmqqqwww{{{}}}~~~~~~wwwqqqooonnnmmmmmmpppooommmlllmmmooosssuuuvvvpppiiicccbbbdddeeefffcccdddeeeccc^^^YYYUUUSSSJJJNNNSSSWWW[[[```hhhnnntttvvvxxxxxxuuupppjjjgggbbbaaa``````aaaccceeegggnnnpppqqqpppmmmjjjiiiiiillljjjhhhfffddddddddddddeeeeeeeeeeeeffffffggggggccceeefffeeedddccccccddd[[[WWWVVVYYYYYYUUUSSSTTTLLLLLLLLLPPPWWW```iiiooovvvyyy|||}}}|||zzzyyyyyy|||yyyuuuqqqoooppprrrsssuuuvvvxxxyyy{{{}}}zzzxxxxxxzzz}}}}}}zzzyyy{{{~~~}}}{{{xxxvvvuuuzzz|||~~~|||{{{{{{xxxxxxxxxwwwxxxzzz{{{|||~~~}}}|||ssssssuuuuuuyyy~~~|||~~~}}}|||zzzyyyxxxwwwvvvuuuuuutttqqqooollllllooosssvvvwwwvvvvvvuuuttttttuuuuuuvvvsssooolllkkklllllliiifffeeefffgggiiijjjkkkkkkkkkkkkhhheeeaaa```aaaccceeecccbbbaaa``````_________aaaaaabbbccccccdddeeeeeeggghhhgggeeebbb`````````ddddddccccccbbbbbbbbbccceeeeeeeeeeeedddbbb```___ccceeefffdddaaa```ccceeehhhhhhiiikkkllljjjfffccc```___^^^___aaaccccccbbb^^^```aaaaaa```___```aaa^^^______]]][[[YYYYYYZZZ[[[[[[[[[[[[ZZZZZZZZZZZZ\\\]]]]]]\\\YYYWWWXXXXXX\\\YYYTTTRRRTTTWWWYYYZZZXXXVVVTTTVVVZZZ]]]\\\ZZZ___]]]ZZZWWWUUUUUUUUUVVVWWWVVVUUUTTTRRROOOMMMLLLJJJJJJJJJKKKKKKKKKHHHFFFGGGGGGGGGFFFFFFFFFFFFFFFJJJIIIGGGHHHIIIJJJJJJJJJHHHGGGGGGFFFEEEDDDCCCCCCEEEDDDDDDDDDCCCCCCCCCCCCDDDIIILLLIIIFFFFFFDDD@@@???>>>>>>===>>>@@@AAABBB@@@@@@@@@@@@???===<<<;;;<<<<<<::::::999:::;;;<<<<<<;;;:::999999999999999777777888999:::;;;;;;;;;;;;<<<<<<===<<<;;;999888999999999999888888888888777777666666777777888888666777777888888777777666555555666666666666555555777666666555555666666777888888999999999888666555444444444444444444444444zzzwwwoooooosssuuuxxxyyy{{{}}}}}}|||zzzyyyuuuuuuvvvxxxyyyxxxtttqqqllllllkkkjjjiiigggeeeddd^^^```aaaccceeefffffffffiiihhhhhhhhhhhhhhhhhhhhhmmmnnnoooooonnnmmmooopppfffiiimmmrrrvvvyyy{{{|||uuuqqqkkkgggggghhhhhhiiiggggggggghhhjjjlllnnnpppmmmiiibbb]]][[[\\\]]]___^^^___^^^[[[UUUNNNIIIGGGBBBFFFJJJNNNRRRYYYcccjjjrrrssssssrrrnnniiidddaaa[[[[[[[[[\\\]]]```bbbdddfffhhhiiiiiihhhfffffffffffffffeeedddcccbbbaaaaaa```aaabbbddddddcccbbbaaa\\\^^^```aaa```___```aaa[[[VVVUUUWWWVVVRRROOOPPPOOOQQQUUUZZZaaajjjtttyyy~~~|||xxxvvvtttuuuuuurrrqqqpppnnnnnnnnnoooooooooooopppqqqssswww}}}}}}zzzwwwuuusssrrrvvvwwwxxxvvvttttttuuuwwwyyyxxxvvvtttrrrpppnnnnnnrrruuuyyy|||}}}}}}|||}}}~~~~~~|||{{{yyywwwvvvuuutttrrrpppooopppuuuzzz~~~}}}{{{{{{{{{|||}}}~~~{{{}}}~~~|||}}}~~~}}}}}}~~~~~~~~~~~~|||zzzyyyxxxuuuttttttsssrrrqqqqqqqqqooonnnlllmmmpppsssttttttqqqqqqrrrrrrrrrqqqppppppoookkkhhhfffggggggfffdddccccccdddfffhhhiiihhhgggdddccc```___^^^```bbbcccaaaaaa___^^^^^^^^^______bbbbbbccccccdddddddddeeebbbccccccbbb```___```aaaccccccbbbaaaaaa`````````eeeeeeeeeeeedddcccaaa```cccfffiiifffaaa___bbbfffiiiiiihhhhhhgggeeecccbbb___^^^]]]]]]___``````___]]]^^^```___]]]\\\\\\]]]YYY[[[\\\\\\ZZZYYYYYYZZZYYYYYYYYYYYYXXXXXXXXXXXXZZZZZZZZZYYYWWWVVVVVVVVVXXXUUUQQQPPPQQQTTTVVVWWWSSSRRRSSSVVVYYYZZZYYYWWW[[[YYYWWWTTTRRRRRRRRRRRRSSSSSSSSSRRRPPPMMMJJJIIIHHHGGGGGGHHHIIIIIIGGGEEEGGGGGGFFFFFFEEEEEEDDDDDDHHHGGGFFFFFFHHHIIIHHHGGGDDDDDDDDDCCCCCCBBBBBBBBBCCCCCCCCCCCCCCCBBBBBBBBBBBBGGGHHHEEEBBBCCCBBB??????>>>=========???AAABBB??????>>>===<<<;;;:::999===<<<;;;:::999888888999::::::999999888777777777666666666777888999:::;;;;;;;;;;;;;;;:::999888777777777777777777777777777777666666555666666777777555666666777777666666555444555555666666555555444666555555555555666666777666666777888888777666555333333333333333444444444rrrxxxyyyrrrkkklllppptttuuuvvvwwwyyyyyyyyyxxxwwwtttttttttuuutttrrrmmmjjjffffffffffffeeecccaaa```\\\]]]___aaabbbcccddddddeeeeeeeeefffggghhhhhhhhhgggiiijjjjjjiiiiiijjjlllcccdddfffjjjooorrrtttuuukkkhhhdddbbbbbbdddeeeeee^^^```dddfffhhhhhhgggfffcccaaa___[[[YYYXXXXXXYYYYYYZZZXXXTTTMMMGGGCCCAAACCCEEEHHHKKKOOOXXXccckkkqqqpppnnnjjjfffbbb^^^\\\XXXXXXXXXYYY[[[^^^```aaaaaaccceeedddcccaaaaaaaaa_________`````````______]]]___bbbcccbbb___[[[XXXVVVYYY\\\^^^]]]]]]^^^^^^[[[WWWVVVXXXYYYUUUSSSTTTSSSWWW\\\bbbiiiqqqyyyzzztttooommmmmmmmmkkkkkklllllllllllllllllllllmmmmmmlllllloootttwwwxxxxxxyyyxxxwwwtttqqqooorrrrrrrrrqqqpppppprrrsssrrrqqqpppooommmllllllkkkmmmppptttuuutttttttttuuuxxxxxxvvvtttrrrpppooonnnqqqnnnjjjhhhjjjpppvvvyyy~~~zzzxxxvvvtttrrrppppppqqqrrryyy}}}~~~}}}|||yyyzzz}}}~~~}}}~~~~~~}}}}}}|||{{{||||||}}}zzz{{{}}}~~~|||{{{zzzzzz|||~~~}}}{{{|||{{{zzzxxxwwwuuutttssspppppppppooooooooooooooopppnnnmmmnnnoooppppppooommmnnnnnnooonnnmmmlllkkkjjjhhheeedddcccccccccbbbbbbaaaaaacccfffgggfffddd^^^^^^______``````aaaaaa``````___^^^^^^```aaabbbeeeeeeeeeeeeddddddccccccaaabbbbbbaaa______aaaccccccbbbaaa___^^^^^^^^^^^^ddddddddddddcccbbbbbbaaacccfffiiigggbbb___bbbeeehhhggggggeeebbbaaa``````^^^\\\[[[[[[\\\\\\\\\[[[]]]^^^^^^]]]ZZZXXXXXXXXXUUUWWWZZZZZZYYYYYYYYYZZZYYYYYYYYYYYYXXXXXXWWWWWWXXXXXXXXXXXXYYYZZZZZZYYYUUUSSSRRRQQQRRRSSSRRRQQQPPPQQQRRRUUUWWWWWWVVVUUUVVVUUUSSSQQQPPPOOOOOOOOOPPPQQQPPPOOOMMMJJJHHHFFFGGGFFFEEEFFFHHHHHHGGGFFFGGGFFFFFFFFFEEEEEEDDDDDDFFFEEEDDDEEEFFFFFFEEEDDDAAAAAAAAABBBBBBCCCCCCDDDCCCCCCDDDDDDCCCCCCBBBAAA???DDDEEEBBB@@@BBBBBB@@@??????>>>>>>???@@@BBBCCC@@@???>>>===<<<;;;::::::<<<<<<;;;:::999999888888999999999888888777777666666555555555666777999::::::::::::999888777666666666666666666666666666666666666555444444555555555444555555666666555555444444444555555555555444444333444444444666777888999555666777888888777555555333333444444444555555555nnntttuuuppplllnnnqqqsssrrrsssuuuvvvwwwvvvvvvuuusssrrrqqqpppooolllgggdddaaaaaaaaa```___^^^^^^]]][[[\\\]]]^^^___```aaabbbaaabbbcccdddeeefffggggggdddfffggggggggggggiiijjjccccccccceeeiiilllnnnnnniiigggdddbbbbbbbbbaaa```ZZZ]]]aaaddddddbbb___\\\[[[\\\]]][[[YYYWWWWWWXXXWWWVVVTTTOOOIIIDDDBBBBBBFFFGGGIIIKKKPPPYYYfffooorrrooojjjeee```\\\ZZZZZZWWWWWWWWWXXXZZZ[[[]]]^^^```aaabbbaaa]]]ZZZYYYXXXWWWWWWXXXYYYZZZ[[[\\\\\\[[[\\\^^^___\\\XXXSSSOOOSSSVVVZZZ\\\\\\[[[[[[\\\XXXUUUUUUZZZ\\\[[[ZZZ[[[ZZZ___ffflllqqqwww~~~|||sssmmmiiigggfffdddeeeggghhhiiiiiiiiiiiikkkkkkkkkiiihhhiiilllnnnqqqssstttuuutttrrrooommmlllmmmmmmmmmnnnnnnnnnnnnjjjkkkkkklllkkkkkkjjjjjjjjjmmmoooooolllkkkmmmooorrrrrrpppnnnmmmkkkjjjiiilllhhhddddddgggnnntttwwwyyy|||~~~xxxssslllkkkgggccc``````ccceeeoootttyyy}}}~~~~~~~~~~~~~~~zzzxxxxxxzzz|||}}}{{{xxxwwwxxxzzz|||~~~}}}||||||}}}~~~}}}~~~zzzzzzxxxwwwwwwwwwxxxxxxwwwxxxzzz||||||zzzwwwvvvvvvxxx{{{}}}}}}{{{yyyxxxuuutttsssqqqpppnnnmmmlllkkkkkkkkklllmmmmmmnnnnnnooommmkkkkkkllllllkkkjjjkkkkkklllkkkkkkjjjiiihhhgggfffeeecccbbbaaaaaaaaaaaa```___aaadddfffdddaaa[[[\\\^^^___```````````````___^^^]]]^^^```bbbdddeeeeeeddddddcccbbbbbbaaabbbbbbbbb```______aaacccbbbaaa^^^\\\\\\\\\]]]^^^ccccccbbbbbbbbbbbbbbbbbbcccfffgggfffccc```aaabbbdddeeedddbbb___]]]\\\]]]\\\ZZZXXXXXXXXXXXXWWWVVVYYYZZZ[[[YYYWWWTTTTTTTTTSSSTTTVVVVVVVVVVVVXXXZZZZZZZZZZZZYYYXXXXXXWWWWWWWWWVVVVVVXXX[[[]]]]]]\\\UUUSSSRRRRRRRRRQQQPPPNNNOOOPPPQQQSSSSSSSSSSSSRRRRRRQQQPPPOOOOOONNNNNNNNNOOONNNMMMLLLJJJHHHFFFDDDEEEDDDDDDEEEGGGHHHGGGFFFEEEEEEEEEEEEDDDDDDDDDDDDDDDCCCCCCDDDEEEDDDCCCAAA??????@@@AAABBBCCCDDDDDDAAABBBCCCCCCCCCBBBAAA@@@===BBBDDDAAA???AAAAAA>>>>>>>>>>>>???@@@@@@AAAAAA???>>>===;;;;;;:::::::::888888888999999:::::::::777777888888999888888777777666555555555666888999999888888777777666666666555555555555666666666666555555444444333333444444444444444555555444444444333333444444444444333333222222333444555777999999666777777888777666555444333444444555555666666666mmmqqqrrrnnnlllnnnooonnnnnnnnnoooqqqqqqrrrrrrqqqooonnnkkkjjjiiigggdddaaa```___]]]\\\[[[\\\\\\]]]ZZZZZZYYYYYYZZZ\\\]]]^^^______``````aaaaaaaaabbb```bbbdddddddddeeefffhhhdddaaa___```ccceeefffeeefffeeeccccccbbbaaa^^^[[[[[[]]]___```___\\\XXXVVVTTTWWWXXXXXXVVVVVVWWWYYYVVVUUUQQQLLLGGGDDDEEEFFFEEEGGGHHHKKKPPP[[[iiisssvvvqqqiiibbb\\\ZZZZZZ[[[VVVVVVWWWWWWXXXYYYYYYYYY\\\]]]^^^\\\YYYUUUTTTSSSTTTTTTTTTUUUVVVWWWYYYZZZ[[[[[[ZZZXXXUUURRROOOMMMPPPSSSWWWZZZZZZYYYYYYYYYVVVSSSTTTYYY\\\[[[[[[]]]___eeelllqqqtttxxx~~~wwwoooiiifffccc```^^^___```bbbccccccdddccceeeffffffdddbbbbbbccceeeiiiiiiiiiiiihhhfffdddcccbbbcccdddfffhhhhhhgggfffeeefffhhhiiiiiihhhgggfffhhhjjjllljjjgggfffjjjnnnnnnmmmlllkkkiiihhhgggffffffccc```aaagggooouuuxxxvvvzzz|||yyyyyywwwuuuuuuvvvsssmmmggg\\\[[[XXXUUURRRTTTZZZ^^^ggglllrrrwwwzzz|||~~~}}}}}}|||zzz{{{}}}}}}zzzwwwvvvxxx{{{|||}}}~~~~~~|||xxxsssrrrsssuuuwwwyyy|||}}}}}}|||zzzzzz}}}~~~~~~|||yyyyyyyyywwwvvvuuutttssstttuuuuuurrrtttvvvxxxwwwuuurrrppprrruuuxxxzzzyyyvvvsssrrrpppooommmkkkiiigggfffeeeeeefffggghhhjjjkkklllmmmkkkiiigggfffggghhhhhhgggkkkjjjjjjiiihhhgggggggggdddeeeeeedddbbbaaa``````aaa___]]]```dddeeeccc___\\\[[[\\\\\\]]]___```aaa```^^^\\\[[[[[[]]]___```cccbbbbbbbbbbbbbbbbbbbbbccccccbbb```^^^^^^```bbb___]]][[[YYYYYY\\\```bbbaaaaaaaaaaaaaaaaaabbbbbbdddeeeeeeeeecccaaa```___```aaabbb```\\\ZZZZZZ[[[[[[XXXVVVUUUUUUUUUTTTRRRRRRTTTUUUTTTSSSRRRRRRSSSPPPQQQRRRQQQQQQRRRUUUWWWZZZZZZZZZYYYXXXWWWWWWWWWWWWVVVUUUWWW[[[]]]]]]\\\TTTRRROOONNNOOOPPPPPPOOOMMMNNNOOOPPPOOONNNNNNOOONNNNNNNNNNNNNNNNNNNNNNNNNNNMMMKKKIIIGGGEEEDDDDDDDDDBBBBBBCCCEEEFFFFFFFFFBBBBBBBBBCCCCCCCCCCCCCCCCCCBBBBBBCCCCCCCCCAAA???>>>??????@@@@@@AAAAAAAAA???@@@AAABBBBBB@@@???===<<>>>>>===:::999:::<<<>>>???>>>======;;;;;;999888888888999999666777777888888888777777555666888999:::999999999999888666555555555777888777777666666666666666666555555555555666666666777555555444333333333333333333333444444444444333333333333444444444444333333222222222333333555666666666666777777666444333111333333444444555666666777kkknnnooolllkkkmmmlllhhhhhhiiijjjkkkllllllllllllllljjjgggfffeeedddbbb```aaa___]]]\\\[[[\\\^^^___YYYXXXVVVVVVVVVXXXZZZ[[[^^^^^^^^^]]]]]]]]]]]]\\\XXXZZZ\\\]]]]]]]]]___aaabbb___[[[[[[]]]______^^^aaa``````aaabbb```\\\YYY]]]^^^]]]\\\ZZZWWWUUUSSSPPPRRRTTTSSSRRRSSSVVVYYYVVVTTTPPPKKKGGGFFFGGGJJJDDDEEEGGGIIIOOO[[[jjjuuuyyysssjjjaaa[[[ZZZ[[[\\\VVVVVVVVVVVVVVVVVVVVVVVVVVVXXXYYYYYYVVVTTTTTTTTTUUUTTTTTTTTTTTTVVVXXXYYY]]][[[WWWSSSPPPOOOOOOOOOOOORRRVVVXXXXXXWWWWWWWWWXXXTTTTTTXXXZZZXXXWWWXXX[[[bbbiiinnnooorrrwww||||||uuullleeebbb```]]][[[ZZZZZZ\\\]]]^^^_________^^^___```___]]]\\\\\\]]]```___]]]ZZZYYYXXXXXXXXXYYYZZZ\\\___aaaaaa```^^^aaaccceeeggghhhfffdddbbbgggiiijjjhhheeeeeejjjooolllkkkjjjiiihhhgggfffeeebbb___]]]```hhhqqqwwwzzzvvv{{{yyytttpppnnnllllllkkkhhhbbb\\\OOOOOOMMMKKKKKKOOOVVV\\\ccchhhnnntttxxxzzz}}}~~~~~~yyyxxx||||||~~~}}}yyywwwxxxzzzyyywwwuuuuuuxxx|||~~~}}}}}}|||}}}|||}}}~~~}}}}}}}}}|||wwwrrrpppqqqtttvvvxxx|||~~~}}}{{{yyyxxxzzz{{{zzzwwwuuussssssuuutttsssrrrrrrrrrssstttooopppsssttttttqqqnnnlllmmmqqqtttvvvtttqqqnnnlllnnnmmmkkkhhheeebbb```___bbbcccdddfffhhhjjjkkklllgggeeeccccccdddeeeeeeeeekkkjjjiiiggggggfffffffffcccdddeeeeeecccaaa``````aaa___]]]___dddeeebbb___]]]\\\ZZZYYYZZZ]]]```bbb```^^^[[[YYYXXXYYY[[[\\\aaaaaabbbbbbcccdddddddddccccccbbb___]]]\\\^^^```\\\ZZZXXXVVVXXX]]]bbbfff```````````````aaaaaabbbeeedddccccccdddbbb___]]]]]]___aaa___[[[XXXXXXZZZZZZWWWUUUTTTTTTSSSRRRPPPLLLNNNPPPQQQPPPPPPQQQRRRNNNOOOOOONNNNNNOOOSSSVVVZZZZZZYYYXXXXXXWWWVVVVVVWWWUUUTTTVVVZZZ\\\[[[YYYTTTQQQMMMKKKLLLOOOQQQRRRMMMMMMNNNMMMLLLKKKLLLMMMLLLLLLMMMMMMNNNNNNNNNOOONNNLLLJJJGGGEEEDDDCCCDDDBBBAAA@@@AAACCCEEEFFFEEE@@@@@@@@@AAAAAABBBBBBBBBBBBAAAAAABBBCCCBBB@@@===????????????>>>>>>>>>>>>===>>>@@@AAA@@@???===<<<<<>>===<<<<<<===>>>???>>>>>>============>>>>>>AAA???===:::888888888999888999:::;;;;;;:::999888888777555444444555666777999888666555444444444555222333444666777888888888888777777777666666555555666666555555555555666666333333333444444444444555444444444444444444444444333333444444555444444444333333333333333333333333222222222222222222222222555444222000000111222333333333222222111222222222ccccccddddddeeeddddddcccddddddeeeffffffggghhhhhheeedddbbbaaa_________``````^^^\\\]]]^^^^^^\\\ZZZWWWTTTQQQQQQSSSUUUUUUTTTXXXWWWWWWVVVUUUUUUTTTTTTSSSTTTUUUVVVWWWXXXYYYZZZYYYYYYXXXWWWVVVUUUUUUTTTXXXZZZ[[[[[[YYYXXXXXXYYYVVVUUUSSSQQQOOOMMMKKKKKKJJJJJJKKKKKKMMMNNNOOOPPPNNNNNNMMMKKKIIIIIIKKKMMMKKKKKKLLLSSS]]]hhhqqquuuppphhh]]]VVVTTTTTTRRRPPPNNNOOOOOOPPPQQQRRRRRRSSSVVVUUUSSSQQQPPPOOONNNNNNQQQRRRTTTUUUWWWXXXXXXXXXVVVSSSOOONNNOOOOOOMMMLLLQQQRRRTTTVVVWWWXXXWWWWWWXXXXXXWWWWWWWWWVVVUUUUUUVVV[[[aaadddcccaaa`````````\\\XXXUUUTTTTTTTTTSSSUUUTTTRRROOOMMMOOORRRVVV[[[ZZZXXXTTTPPPMMMMMMNNNPPPMMMKKKJJJLLLNNNMMMLLLMMMOOORRRUUUWWWWWWVVVUUUXXXWWWWWWWWWYYY[[[]]]___bbbeeedddbbbdddiiikkkhhhbbb___]]]\\\]]]^^^^^^^^^cccbbbbbbeeejjjmmmnnnmmmnnnnnnoooppppppmmmhhhccc[[[WWWQQQOOOOOOQQQSSSSSSYYY[[[\\\]]]^^^bbbggglllnnnpppqqqssssssrrrqqqppppppsssvvvwwwuuusssrrrrrrrrruuuxxxwwwtttrrrtttvvvsssxxx{{{yyyyyy}}}~~~{{{zzz{{{~~~{{{xxxyyy|||yyyzzzzzzyyyxxxvvvtttsssuuutttrrrrrrtttvvvvvvvvvsssrrrsssvvvxxxwwwsssoooqqqrrrqqqnnnkkkjjjlllooottt|||xxxvvvssspppmmmkkkkkkjjjlllllllllmmmnnnppprrrsssllliiieeeeeefffiiikkkkkkppppppqqqpppooommmkkkjjjiiiiiihhheeebbb``````aaaeeeeeefffggghhhhhhhhhhhhdddccccccbbbbbbbbbcccccceeeeeeeeeeeedddcccbbbbbb```aaadddeeeeeedddaaa```___aaadddfffeeebbb^^^[[[^^^]]][[[ZZZYYYZZZ[[[\\\[[[ZZZXXXVVVVVVVVVWWWXXX______^^^^^^^^^______```bbb^^^ZZZYYYYYY[[[\\\\\\YYYWWWUUUVVVYYY\\\^^^___]]]^^^_________^^^]]]\\\\\\]]]]]]]]][[[YYYVVVUUUUUUVVVWWWXXXWWWVVVTTTSSSUUUTTTRRRQQQPPPQQQSSSTTTTTTTTTTTTTTTTTTTTTTTTTTTRRROOOLLLLLLMMMOOOQQQQQQRRRSSSSSSSSSSSSRRRQQQQQQPPPPPPOOOOOOOOOQQQRRRSSSOOOMMMLLLLLLLLLLLLKKKIIIHHHHHHIIIIIIHHHGGGGGGFFFHHHIIIKKKLLLMMMNNNNNNNNNLLLKKKIIIGGGEEEEEEEEEEEECCCDDDEEEFFFFFFEEEDDDCCCBBBAAAAAAAAA@@@@@@@@@@@@????????????????????????>>>===<<<;;;;;;<<<===>>>;;;;;;::::::::::::;;;;;;???===;;;888777666777777777777777888888777777777555444444444444444555555777666555444333333333333333444555666888888888999777777777666666555555555333333333333333333333333333333444444444555555555444444444444444444444444333444444444444444333333333333333333333333333333222222222222222222222222222333333333222111111000333222222111111111222222aaabbbccceeeeeeeeeeeeddd```aaabbbddddddddddddccc]]]]]]]]]]]]]]]^^^___```___]]][[[ZZZYYYXXXVVVTTTUUURRRPPPPPPQQQSSSSSSRRRSSSSSSRRRRRRQQQQQQPPPPPPPPPQQQQQQRRRRRRSSSTTTTTTUUUTTTTTTTTTSSSRRRRRRRRRXXXZZZZZZYYYWWWUUUTTTUUURRRRRRPPPOOOMMMKKKJJJIIIIIIIIIJJJKKKLLLMMMNNNNNNNNNNNNMMMKKKIIIJJJNNNPPPQQQQQQTTTZZZcccmmmsssvvvggg```WWWRRRQQQQQQPPPOOOMMMLLLLLLKKKLLLMMMNNNOOOTTTSSSQQQOOOMMMKKKJJJJJJOOOPPPQQQRRRSSSSSSSSSSSSQQQPPPNNNMMMNNNOOONNNMMMRRRRRRSSSUUUVVVWWWXXXYYYZZZZZZYYYXXXVVVTTTRRRQQQVVVXXX[[[[[[ZZZXXXWWWVVVXXXTTTPPPNNNOOOQQQRRRSSSPPPPPPOOOMMMMMMPPPTTTXXX]]][[[XXXSSSNNNKKKJJJJJJJJJIIIHHHHHHJJJKKKJJJIIIIIIKKKNNNQQQSSSSSSSSSRRRVVVTTTRRRTTTYYY^^^````````````^^^\\\^^^cccdddaaaYYYXXXVVVWWWYYY\\\]]]]]]bbbaaa```aaadddeeeeeedddbbbaaa``````aaabbbaaa```SSSOOOJJJIIIMMMTTTZZZ^^^eeeddddddfffhhhjjjkkkjjjnnnnnnnnnnnnmmmkkkiiiggglllnnnppppppnnnlllkkkkkkjjjmmmppppppooonnnppprrrsssyyy|||zzzzzz||||||zzz||||||{{{xxxuuussssssssstttqqqnnnpppuuuzzz||||||oooqqqssstttsssqqqnnnlllnnnllljjjjjjlllooopppqqqpppqqqrrrssstttrrrnnnjjjnnnnnnllljjjiiijjjmmmpppsssyyyqqqpppnnnkkkiiihhhggggggkkklllmmmooopppqqqqqqrrrhhheeecccccceeehhhjjjkkkoooppppppooommmkkkiiihhhggggggdddaaa]]]\\\]]]___dddccccccdddeeefffgggggg```aaacccccccccaaa___]]]___``````aaaaaa``````___^^^```bbbccccccbbb```^^^```bbbcccdddbbb___[[[XXX\\\[[[YYYXXXXXXXXXYYYZZZWWWWWWVVVVVVWWWXXXZZZ[[[[[[\\\]]]_________^^^^^^\\\ZZZVVVUUUVVVWWWWWWWWWVVVTTTTTTUUUXXX[[[]]]]]]ZZZ[[[[[[\\\[[[[[[ZZZZZZWWWWWWWWWVVVUUUTTTRRRQQQQQQRRRSSSSSSSSSRRRPPPOOOPPPPPPOOOOOOOOOPPPQQQQQQSSSSSSSSSSSSSSSSSSSSSSSSQQQOOOMMMLLLNNNPPPRRRRRRNNNPPPQQQRRRRRRPPPNNNLLLMMMLLLKKKJJJKKKKKKMMMMMMMMMKKKJJJJJJJJJJJJIIIGGGFFFFFFFFFFFFFFFEEEEEEEEEHHHIIIJJJKKKLLLMMMMMMMMMIIIHHHFFFEEEEEEEEEFFFFFFDDDDDDDDDDDDCCCBBBAAA@@@?????????>>>>>>>>>>>>>>>========================<<<;;;;;;::::::;;;;;;<<<999999888888888888999999;;;:::888666555444555555555555555444444555555555111111222333444444444444444444444444333222111111444444555777777888888888666666555555555555444444111222333444444333222111444444444444555555555555333333333333333333333333444444444444333333222111222222222222222222222222111111111111111111111111000111333444333222000...222111111111111111222222___```bbbdddeeeeeeeeeddd^^^___aaabbbbbb```^^^]]]WWWWWWXXXXXXZZZ[[[\\\\\\WWWVVVTTTSSSRRRPPPOOONNNQQQPPPOOONNNOOOPPPPPPPPPOOOOOOOOOOOONNNNNNMMMMMMNNNNNNNNNNNNOOOOOOOOOOOOOOOOOOPPPPPPQQQQQQRRRRRRXXXYYYYYYWWWTTTQQQPPPQQQRRRQQQPPPOOONNNLLLKKKKKKJJJKKKLLLMMMMMMNNNNNNNNNPPPOOONNNLLLLLLNNNRRRUUUUUUUUUXXX]]]dddjjjnnnoooaaa\\\VVVQQQPPPQQQPPPPPPNNNMMMKKKJJJJJJLLLNNNOOORRRQQQOOOMMMLLLKKKJJJJJJNNNNNNOOOPPPPPPPPPOOOOOOPPPPPPOOONNNNNNNNNNNNMMMRRRRRRRRRSSSTTTVVVXXXYYYXXXXXXXXXWWWUUUSSSQQQPPPRRRSSSTTTUUUUUUUUUVVVVVVSSSPPPMMMLLLNNNQQQTTTUUURRRRRRRRRRRRRRRUUUYYY]]]bbb```]]]WWWQQQMMMKKKKKKJJJJJJKKKLLLMMMMMMLLLLLLKKKMMMPPPRRRTTTUUUUUUTTTVVVSSSPPPTTT[[[aaacccaaa]]]ZZZWWWUUUWWWXXXWWWUUURRRQQQQQQSSSVVVZZZ[[[[[[]]]]]]\\\[[[[[[[[[ZZZYYYZZZYYYWWWXXXZZZ\\\\\\[[[PPPNNNLLLNNNTTT\\\bbbfffgggeeedddhhhlllmmmjjjfffiiiiiihhhhhhfffdddbbbaaafffggghhhgggeeeccccccdddbbbeeeiiijjjiiiiiilllnnntttxxxxxxvvvvvvxxxyyyvvvwwwvvvtttqqqnnnnnnnnnooooookkkhhhiiimmmqqqrrrqqqkkklllnnnoooooommmlllkkkjjjhhhffffffiiilllnnnnnnppppppooooooooonnnmmmlllkkkjjjgggfffeeegggjjjllllllpppuuuxxxzzzyyyxxxvvvkkkjjjiiigggfffeeeddddddhhhiiikkkmmmnnnnnnmmmlllfffdddccccccgggjjjlllmmmmmmmmmmmmlllkkkhhhfffeeeeeedddaaa]]]YYYXXXZZZ\\\```_________```aaacccddd^^^___aaaaaa```^^^\\\ZZZ]]]]]]^^^^^^^^^]]]\\\\\\[[[\\\___``````___\\\[[[^^^___``````___\\\YYYWWWYYYXXXWWWVVVVVVVVVWWWWWWWWWWWWWWWXXXYYY[[[\\\]]]ZZZ\\\___aaaaaa```___^^^YYYWWWTTTTTTTTTUUUTTTTTTTTTSSSSSSUUUXXXZZZ[[[[[[XXXXXXWWWWWWVVVUUUTTTTTTOOOOOOOOOPPPPPPQQQQQQQQQNNNOOOOOOPPPOOONNNMMMMMMLLLMMMNNNNNNOOOPPPPPPPPPNNNNNNNNNNNNMMMMMMMMMMMMNNNMMMKKKKKKMMMPPPQQQQQQNNNOOOOOOOOOOOONNNLLLKKKJJJJJJHHHGGGGGGHHHIIIIIIKKKJJJHHHHHHHHHHHHFFFDDDEEEDDDDDDDDDDDDDDDDDDDDDEEEFFFGGGHHHHHHHHHHHHHHHGGGFFFDDDCCCCCCCCCDDDDDDCCCCCCBBBAAA@@@???>>>===<<<<<<<<<<<<<<<<<<<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;::::::999999999999::::::999999888888888888999999777777555444333333333333555444333222222333444555///000222444555555444333222333444444444333111000333444444555666666666666444444444444444444333333333444666777777666444333333444444444444555555555222222222222222222222222444444444444333111000000222222222222222222222222111111111111111111111111000000111222222111000///111000000000000111222222XXXZZZ]]]```aaaaaa```___^^^_________^^^[[[XXXVVVSSSSSSTTTUUUUUUUUUUUUUUUOOOOOONNNNNNLLLKKKKKKKKKMMMMMMMMMMMMLLLLLLMMMMMMMMMMMMLLLLLLLLLLLLKKKKKKLLLLLLLLLLLLLLLLLLLLLLLLKKKLLLMMMNNNPPPQQQRRRSSSUUUVVVVVVTTTQQQOOONNNNNNPPPPPPOOONNNNNNMMMLLLLLLJJJKKKLLLMMMMMMMMMMMMMMMNNNNNNNNNMMMMMMNNNRRRUUUUUUUUUWWWZZZ___bbbbbbbbb\\\XXXTTTPPPOOONNNNNNNNNNNNMMMKKKJJJJJJKKKMMMOOOOOONNNMMMMMMLLLLLLLLLLLLPPPPPPQQQQQQQQQQQQPPPPPPQQQQQQQQQPPPOOONNNMMMMMMQQQQQQQQQQQQRRRTTTUUUVVVSSSTTTUUUUUUUUUSSSRRRQQQOOOOOOOOOPPPRRRTTTUUUUUUPPPMMMJJJJJJMMMPPPRRRTTTVVVVVVVVVVVVVVVXXX\\\___cccbbb^^^YYYSSSOOONNNNNNLLLMMMOOOPPPPPPOOOOOOPPPOOOPPPRRRTTTUUUVVVVVVVVVTTTQQQQQQUUU]]]aaa```^^^TTTPPPMMMOOOQQQQQQOOOMMMNNNMMMNNNPPPTTTWWWXXXXXXWWWWWWVVVUUUSSSRRRQQQQQQUUUUUUTTTVVVXXXXXXWWWVVVNNNMMMNNNRRRWWW]]]aaabbbbbb``````dddjjjlllgggbbbaaaaaaaaaaaa```______^^^```aaaaaa___]]]\\\]]]^^^\\\```dddeeeddddddgggjjjssssssqqqmmmnnnrrruuusssrrrpppmmmkkkkkkkkklllmmmjjjfffccccccfffiiihhhggggggffffffggghhhiiijjjjjjgggeeecccdddfffiiijjjkkklllkkkiiihhhggghhhkkkmmmgggeeebbbaaaaaacccdddeeedddeeegggjjjkkkkkkiiigggdddddddddccccccbbbaaaaaabbbdddfffhhhhhhgggfffdddbbbaaa```bbbeeehhhjjjkkkiiiiiiiiiiiigggeeecccbbbcccaaa^^^ZZZVVVUUUVVVXXXZZZYYYYYYYYYZZZ\\\^^^```^^^^^^]]]\\\[[[ZZZZZZZZZ]]]]]]]]]\\\[[[ZZZXXXXXXZZZ[[[]]]______]]][[[ZZZYYYZZZ[[[[[[[[[ZZZXXXWWWVVVVVVUUUUUUTTTTTTTTTTTTWWWWWWWWWXXXXXXYYYZZZZZZ[[[]]]```bbbcccaaa___]]]XXXVVVUUUTTTUUUUUUTTTRRRRRRRRRSSSUUUWWWYYYXXXWWWUUUTTTSSSQQQPPPNNNMMMMMMKKKKKKJJJJJJKKKMMMNNNOOONNNNNNNNNNNNMMMMMMLLLLLLKKKLLLLLLMMMNNNOOOPPPPPPJJJJJJJJJIIIIIIIIIHHHHHHJJJIIIHHHIIIKKKNNNNNNNNNPPPOOOMMMLLLKKKKKKKKKLLLIIIHHHGGGFFFFFFFFFGGGHHHJJJHHHGGGFFFFFFFFFDDDBBBDDDCCCCCCBBBBBBCCCDDDDDDDDDDDDEEEFFFFFFEEEEEEEEEEEEDDDBBBAAA@@@@@@@@@@@@BBBAAA@@@>>>===<<<;;;;;;999:::::::::::::::::::::999999999999999999999999888888999999999999888888777777666666666666777777555444444333222222222222555444333222222333444555000111333444555555555444222333444555555333222111222222333333333333333222222222222222222222222333333444666777777666444333333333333333444444444444222222222222222222222222333333333333222111000///111111111111111111111111000000000000000000000000111000/////////000111222000/////////000000111222WWWYYY\\\^^^```___^^^]]]\\\\\\[[[ZZZXXXVVVTTTRRRPPPQQQQQQQQQQQQPPPOOONNNKKKLLLMMMMMMKKKJJJKKKLLLIIIJJJKKKKKKJJJIIIJJJKKKJJJJJJJJJJJJJJJJJJJJJJJJIIIIIIIIIIIIIIIJJJJJJJJJJJJJJJKKKMMMNNNPPPQQQQQQQQQRRRSSSQQQOOOMMMMMMMMMLLLLLLLLLLLLLLLKKKKKKKKKHHHIIIJJJLLLLLLLLLKKKJJJJJJKKKLLLLLLKKKMMMOOORRRQQQQQQQQQTTTVVVXXXWWWVVVSSSRRROOOMMMKKKKKKKKKKKKJJJJJJIIIIIIIIIJJJLLLLLLMMMMMMMMMLLLLLLMMMMMMMMMMMMMMMNNNNNNOOONNNNNNNNNPPPQQQRRRQQQOOOMMMMMMNNNOOOOOOOOOOOOPPPPPPPPPPPPMMMOOOQQQSSSTTTSSSRRRQQQOOOMMMLLLMMMOOOPPPQQQPPPSSSQQQOOOOOOQQQSSSTTTTTTSSSTTTTTTTTTTTTVVVYYY\\\^^^^^^[[[VVVRRROOONNNOOOOOOPPPQQQQQQPPPOOOQQQRRRQQQQQQRRRSSSTTTTTTTTTTTTUUUVVVXXX^^^bbbccc```\\\JJJFFFEEELLLRRRRRROOOMMMMMMLLLLLLNNNQQQSSSTTTSSSPPPQQQQQQPPPNNNLLLMMMNNNRRRQQQRRRTTTVVVVVVTTTRRRPPPQQQSSSWWW[[[]]]]]]\\\\\\[[[[[[```fffhhhddd___[[[[[[[[[[[[[[[\\\\\\\\\[[[[[[[[[YYYWWWWWWYYY[[[[[[^^^bbbbbbaaaaaacccffflllkkkgggccceeelllooonnnmmmkkkgggfffggghhhhhhhhhaaa^^^]]]___bbbcccaaa___^^^^^^]]]^^^___aaadddeeeaaa```___```bbbddddddcccccccccbbb___^^^___cccfff```^^^\\\\\\]]]^^^^^^^^^]]]]]]^^^___aaaaaa___]]]^^^^^^____________^^^^^^\\\]]]___``````___^^^\\\\\\[[[ZZZ\\\```cccdddeeedddeeeeeeeeedddbbb```___```___\\\XXXTTTRRRSSSTTTTTTTTTUUUVVVWWWYYYZZZ[[[]]][[[YYYWWWWWWWWWYYYZZZ\\\\\\\\\[[[YYYWWWVVVUUUYYY[[[]]]______]]][[[YYYTTTUUUUUUVVVWWWWWWWWWWWWSSSSSSSSSSSSSSSRRRRRRRRRTTTTTTTTTUUUUUUUUUVVVVVV[[[]]]___aaaaaa___]]][[[VVVUUUTTTTTTUUUTTTRRRPPPQQQQQQRRRTTTVVVVVVTTTRRRPPPOOOMMMKKKIIIHHHHHHHHHKKKJJJHHHFFFFFFGGGIIIJJJNNNMMMMMMMMMLLLLLLLLLLLLKKKKKKKKKKKKLLLMMMNNNOOOIIIIIIIIIHHHHHHGGGGGGFFFFFFEEEEEEFFFIIILLLLLLLLLPPPNNNKKKIIIHHHIIIJJJKKKGGGFFFEEEEEEEEEFFFGGGHHHIIIHHHFFFEEEEEEDDDCCCAAABBBBBBAAA@@@@@@BBBCCCDDDDDDDDDEEEEEEEEEDDDDDDCCCBBBAAA???>>>============@@@???===<<<::::::::::::888888888888999999999999888888888888888888888888777888888999999888888777444444333333333333444444333333333333333333222222555444444333333444444555111222333333444444444444333333333444444333333222111222222222222111111000000000111111111111222222111222333444444333222111222222222222333333333333111111111111111111111111222222222222222111000///000000000000000000000000////////////////////////111000...------///111222///.........///000111222UUUXXX[[[]]]^^^]]][[[ZZZVVVVVVUUUTTTSSSRRRQQQPPPMMMMMMNNNNNNMMMLLLKKKJJJKKKLLLNNNLLLJJJIIIJJJLLLFFFHHHJJJJJJHHHGGGHHHIIIGGGGGGGGGGGGGGGGGGGGGHHHEEEFFFFFFFFFGGGGGGHHHHHHKKKKKKKKKKKKLLLLLLLLLLLLLLLNNNOOOOOOMMMLLLLLLMMMJJJJJJKKKKKKKKKKKKKKKKKKIIIJJJKKKMMMMMMLLLKKKJJJHHHJJJLLLMMMLLLLLLMMMOOOKKKKKKKKKMMMPPPQQQQQQPPPLLLLLLKKKJJJJJJJJJKKKLLLGGGHHHHHHIIIJJJKKKLLLLLLNNNMMMLLLKKKKKKKKKKKKKKKHHHIIIJJJKKKKKKKKKKKKKKKLLLNNNQQQQQQOOOMMMNNNOOOLLLMMMMMMNNNMMMLLLKKKJJJIIIKKKNNNQQQRRRRRRQQQPPPNNNLLLKKKLLLOOOQQQPPPOOOVVVTTTSSSSSSSSSSSSRRRQQQMMMNNNOOOPPPPPPRRRVVVYYYXXXXXXVVVSSSPPPNNNNNNPPPRRRSSSSSSRRROOOOOORRRTTTSSSSSSSSSSSSSSSSSSSSSSSSUUUZZZaaafffgggccc]]]XXXGGGCCCDDDOOOVVVUUUQQQOOOLLLLLLKKKMMMNNNOOONNNLLLKKKMMMOOONNNLLLKKKMMMOOOQQQPPPPPPRRRTTTVVVVVVUUUUUUUUUVVVXXX[[[[[[ZZZXXXUUUUUUWWW[[[___```^^^[[[WWWWWWWWWWWWXXXYYYYYYZZZXXXXXXWWWUUUSSSTTTWWWYYY\\\___bbbbbb```___aaacccaaaaaa___]]]aaagggjjjgggiiifffcccaaabbbcccaaa```ZZZXXXXXX[[[^^^]]]ZZZVVVTTTUUUVVVXXXZZZ\\\]]]^^^\\\\\\\\\^^^``````^^^]]][[[]]]^^^\\\YYYXXXZZZ\\\WWWUUUUUUWWWZZZ\\\[[[YYYVVVVVVVVVYYY\\\\\\ZZZWWWWWWXXXZZZ[[[[[[[[[[[[ZZZWWWXXXYYYYYYYYYXXXWWWWWWWWWVVVVVVXXX[[[^^^_________```aaaaaaaaa```^^^]]]^^^]]]\\\XXXTTTQQQQQQQQQQQQRRRSSSUUUVVVWWWXXXXXXYYYXXXWWWUUUUUUVVVXXXYYYXXXYYYXXXXXXWWWVVVUUUTTTVVVXXXZZZ[[[[[[ZZZXXXVVVRRRRRRRRRRRRRRRSSSTTTTTTQQQQQQRRRRRRQQQQQQPPPOOOQQQQQQRRRSSSTTTUUUUUUUUUYYYZZZ[[[\\\[[[ZZZXXXVVVRRRQQQQQQRRRSSSRRROOOMMMNNNOOOPPPQQQSSSRRROOOLLLIIIHHHGGGEEEEEEEEEEEEFFFGGGFFFCCCBBBBBBDDDFFFHHHMMMMMMLLLKKKKKKKKKKKKKKKKKKJJJHHHHHHHHHJJJLLLMMMHHHHHHHHHGGGFFFEEEEEEEEEDDDCCCCCCEEEIIIKKKKKKKKKLLLKKKJJJHHHGGGGGGFFFFFFEEEDDDDDDCCCDDDEEEGGGHHHIIIHHHFFFEEEEEEDDDBBB@@@@@@???>>>===>>>???AAABBBBBBBBBCCCCCCBBBAAA@@@@@@===<<<;;;::::::;;;<<<======<<<;;;999999888999999777777777888888888999999888888888888888888888888777888999999999999888777444333333222222333333444333333444444444444444333333333333444444333333333222222111111111222222333222222111111111222222222222222222222222111000000/////////000000111111111000000000000000000000000000000111111111222222222111111111111111111111111000111111111111111000000000000000000000000000000////////////////////////............//////000000............///000111111PPPRRRUUUXXXYYYWWWUUUSSSQQQPPPPPPOOOOOOOOOPPPPPPJJJKKKLLLLLLLLLKKKJJJIIIJJJLLLMMMLLLHHHGGGHHHJJJEEEGGGJJJIIIGGGEEEFFFHHHEEEEEEEEEFFFFFFFFFFFFFFFCCCCCCDDDDDDEEEFFFFFFGGGMMMMMMLLLKKKIIIHHHGGGGGGJJJLLLMMMNNNMMMLLLMMMNNNKKKKKKKKKLLLLLLLLLMMMMMMKKKLLLNNNOOOPPPOOOMMMLLLIIIKKKNNNOOOOOONNNNNNOOOHHHGGGGGGIIILLLNNNOOONNNHHHIIIJJJJJJJJJLLLNNNOOOGGGHHHJJJKKKLLLMMMMMMMMMNNNNNNLLLKKKJJJIIIHHHHHHJJJKKKLLLMMMNNNNNNNNNNNNHHHKKKOOOOOONNNMMMNNNPPPJJJKKKMMMMMMLLLJJJHHHFFFHHHJJJMMMPPPQQQQQQPPPOOOLLLKKKKKKNNNRRRUUUTTTSSSRRRQQQOOOOOOOOONNNKKKIIIIIIJJJLLLMMMNNNQQQUUUXXXTTTUUUTTTRRROOONNNPPPQQQUUUVVVVVVSSSPPPPPPSSSVVVUUUUUUTTTTTTSSSSSSSSSSSSPPPWWWaaafffddd]]]UUUPPPKKKEEEHHHSSSZZZXXXQQQOOOLLLKKKKKKKKKLLLLLLJJJHHHIIIKKKNNNNNNLLLLLLNNNQQQRRRQQQPPPQQQTTTXXXZZZZZZTTTSSSSSSTTTUUUVVVUUUSSSQQQRRRTTTWWWYYYZZZYYYWWWVVVVVVUUUUUUVVVWWWWWWXXXVVVVVVTTTSSSQQQSSSVVVYYY]]]```cccbbb___^^^___bbbZZZZZZZZZZZZ___eeefffbbbfffccc```^^^___^^^[[[YYYXXXWWWWWWYYY[[[XXXSSSNNNNNNPPPTTTXXXZZZ[[[ZZZYYY[[[[[[\\\^^^```___\\\ZZZXXX[[[^^^]]]YYYVVVTTTTTTPPPPPPQQQTTTYYY[[[YYYWWWQQQQQQRRRUUUYYYZZZXXXUUUSSSUUUVVVXXXYYYYYYXXXXXXUUUUUUUUUVVVUUUUUUTTTTTTVVVUUUUUUVVVZZZ\\\]]]]]]]]]]]]^^^______^^^]]]]]]\\\]]]\\\YYYTTTQQQPPPPPPOOOQQQSSSUUUWWWWWWWWWWWWVVVVVVVVVVVVVVVVVVWWWWWWUUUUUUVVVVVVVVVVVVUUUUUUQQQSSSUUUWWWWWWUUUSSSQQQQQQQQQPPPPPPPPPPPPQQQRRRPPPPPPQQQQQQQQQPPPOOONNNPPPQQQSSSTTTVVVWWWWWWWWWWWWXXXXXXXXXVVVUUUSSSRRROOOOOOOOOPPPQQQOOOLLLIIIMMMMMMNNNOOOPPPOOOKKKHHHDDDCCCBBBBBBCCCDDDEEEFFFAAA@@@>>>>>>@@@CCCGGGJJJLLLLLLKKKJJJJJJJJJJJJKKKJJJIIIFFFEEEEEEGGGJJJLLLGGGFFFFFFEEEDDDCCCCCCBBBCCCCCCCCCEEEIIIKKKLLLKKKGGGHHHIIIIIIHHHEEECCCAAACCCCCCBBBBBBCCCEEEFFFGGGIIIHHHFFFEEEEEEDDDBBB@@@>>>===<<<;;;<<<===???AAA???????????????>>>===<<<999999888888999;;;<<<>>><<<;;;:::888888888888999666777777777888888999999888888888888888888888888777888999::::::999888777666555555444444555555666333333444555555555444444111222333444444333222111222111000//////000111111222111000//////000111222333333333333333222111000.../////////000000111111111111000000000000111111///000000000000111111111000000000000000000000000///000000111111111111000000000000000000000000000////////////////////////,,,---///000111000///...---------......000111111RRRUUUXXXXXXUUUQQQMMMLLLMMMJJJHHHIIIMMMSSSVVVXXXOOONNNLLLKKKIIIIIIJJJJJJMMMMMMLLLKKKJJJIIIHHHHHHFFFEEEDDDDDDDDDDDDEEEEEEEEEDDDDDDCCCCCCCCCDDDDDDDDDDDDCCCBBBCCCEEEGGGIIILLLLLLLLLLLLKKKJJJIIIIIIHHHHHHIIIIIIJJJIIIIIIIIIJJJJJJKKKLLLLLLKKKJJJIIIJJJIIIHHHGGGHHHHHHIIIJJJKKKLLLLLLMMMMMMMMMLLLLLLKKKJJJJJJIIIHHHGGGFFFEEEHHHHHHHHHHHHHHHHHHHHHHHHFFFEEEDDDFFFIIIKKKLLLKKKLLLKKKIIIHHHHHHJJJMMMOOOKKKJJJIIIHHHHHHIIIKKKMMMMMMKKKIIIIIIJJJKKKKKKKKKGGGHHHIIIJJJJJJHHHFFFEEEEEEKKKTTTXXXWWWQQQKKKGGGFFFIIINNNQQQRRRRRRRRRSSSQQQOOOMMMMMMOOONNNJJJGGGFFFFFFGGGHHHKKKOOORRRTTTSSSQQQOOONNNNNNOOOPPPQQQPPPPPPOOOOOOPPPQQQSSSTTTPPPSSSUUUUUUSSSQQQSSSUUUVVVYYY[[[]]][[[WWWRRRNNNKKKMMMQQQXXX]]][[[SSSKKKDDDEEEFFFFFFHHHHHHIIIJJJJJJKKKKKKJJJJJJLLLPPPSSSOOOPPPQQQRRRSSSTTTUUUVVVVVVSSSQQQQQQSSSTTTSSSQQQPPPQQQRRRTTTUUUUUUVVVVVVUUUUUUVVVZZZ]]]\\\XXXTTTPPPPPPPPPQQQSSSVVVXXXZZZ^^^]]]\\\\\\\\\ZZZWWWUUUSSSTTTUUUWWWXXXXXXWWWWWWYYYYYYXXXWWWVVVUUUTTTSSSUUUVVVWWWVVVTTTQQQPPPPPPLLLNNNQQQUUUWWWYYYYYYYYY]]]\\\[[[ZZZZZZ\\\]]]^^^]]]]]][[[YYYVVVSSSPPPOOOPPPRRRUUUXXXYYYYYYWWWVVVTTTRRRRRRTTTXXXYYYXXXUUUPPPRRRUUUXXXZZZYYYXXXWWWUUUSSSQQQOOOMMMMMMNNNOOORRRRRRSSSVVVYYYZZZYYYWWWYYYTTTSSSWWWZZZYYYWWWXXX]]][[[XXXTTTQQQPPPPPPPPPQQQRRRTTTUUUVVVWWWWWWWWWXXXVVVSSSSSSUUUTTTQQQMMMNNNNNNNNNOOOOOOPPPPPPPPPRRRQQQPPPOOOOOOOOOOOOOOOOOONNNMMMOOORRRRRROOOLLLMMMOOOQQQPPPNNNKKKKKKKKKLLLOOOSSSUUUTTTSSSRRRRRRQQQSSSUUUTTTPPPNNNMMMNNNJJJLLLMMMLLLLLLLLLNNNPPPJJJKKKLLLLLLJJJGGGEEECCCCCCBBB@@@@@@BBBCCCBBBBBBBBB@@@???@@@CCCEEEFFFFFFKKKIIIGGGEEEDDDDDDDDDEEECCCCCCDDDEEEFFFGGGGGGHHHIIIGGGEEEDDDFFFGGGGGGFFFBBBCCCDDDFFFGGGHHHIIIIIIKKKJJJHHHFFFDDDBBBAAA@@@@@@BBBDDDDDDBBBAAACCCEEEIIIHHHFFFDDDBBB@@@@@@???>>>>>>>>>===>>>??????@@@@@@???>>>===<<<;;;:::999;;;;;;:::999999999::::::999999999888888888888888777777777777777777777777777777777666555444444444777999;;;<<<;;;999555333444333222222111111222222555555555444444333333333555444333222222222333444222222222222111111111000///000000000111111111111444333111000000000111111111000//////000000///...000000111111111111000///111111000000000000111111111111222222222111111000////////////000000000000...///////////////............------------......//////............//////............////////////PPPRRRTTTSSSPPPMMMKKKJJJJJJHHHGGGIIINNNRRRUUUWWWNNNMMMLLLJJJJJJJJJJJJKKKLLLKKKJJJIIIHHHGGGFFFFFFDDDDDDCCCCCCCCCCCCDDDDDDDDDCCCCCCBBBBBBCCCCCCCCCDDDDDDBBBBBBCCCDDDFFFGGGIIIJJJJJJJJJJJJIIIIIIHHHHHHGGGFFFFFFFFFHHHIIIJJJHHHHHHIIIJJJJJJIIIHHHGGGIIIHHHHHHGGGHHHIIIJJJKKKKKKLLLLLLMMMMMMLLLLLLKKKHHHHHHGGGFFFEEEEEEEEEEEEFFFFFFFFFFFFFFFFFFFFFFFFFFFEEEDDDFFFHHHKKKKKKKKKKKKJJJHHHGGGGGGIIIKKKMMMJJJIIIGGGGGGGGGHHHJJJLLLMMMKKKIIIHHHJJJKKKKKKJJJHHHIIIKKKKKKKKKJJJHHHGGGHHHMMMTTTWWWUUUPPPJJJGGGFFFJJJNNNQQQQQQQQQQQQQQQRRROOOMMMLLLLLLLLLIIIGGGFFFGGGHHHJJJMMMPPPRRRSSSSSSRRRPPPOOONNNOOOPPPQQQPPPOOOOOOOOOPPPQQQSSSTTTSSSUUUWWWVVVSSSRRRSSSTTTUUUWWWYYYZZZXXXUUUQQQNNNJJJKKKNNNTTTXXXVVVPPPIIIDDDDDDEEEFFFGGGHHHIIIIIIKKKKKKLLLKKKJJJLLLOOORRROOOOOOPPPRRRTTTUUUWWWWWWUUUSSSRRRSSSUUUVVVUUUSSSRRRRRRRRRRRRRRRRRRSSSSSSTTTTTTTTTVVVXXXWWWSSSOOOLLLLLLMMMOOORRRUUUWWWYYYVVVUUUUUUVVVWWWWWWUUUSSSRRRRRRTTTUUUVVVVVVVVVUUUUUUTTTTTTTTTTTTTTTSSSSSSTTTUUUVVVTTTPPPMMMLLLKKKNNNOOOQQQTTTVVVXXXYYYZZZ]]]]]]]]]]]]]]]^^^______\\\[[[ZZZXXXUUURRROOONNNQQQRRRTTTVVVWWWWWWVVVUUURRRPPPPPPQQQTTTUUUSSSQQQMMMOOORRRUUUVVVUUUTTTSSSPPPOOOMMMKKKKKKKKKLLLMMMPPPPPPRRRUUUXXXZZZYYYXXXXXXSSSRRRUUUWWWUUUTTTTTTWWWVVVSSSPPPNNNMMMMMMNNNRRRSSSUUUWWWXXXWWWVVVUUUVVVTTTRRRRRRRRRRRROOOLLLLLLLLLKKKKKKKKKKKKKKKKKKOOOOOONNNMMMMMMMMMMMMMMMNNNLLLKKKMMMNNNNNNKKKIIIIIIJJJLLLKKKIIIGGGFFFGGGIIILLLOOOQQQPPPOOONNNNNNNNNPPPRRRQQQNNNKKKKKKLLLGGGHHHIIIIIIHHHIIIKKKMMMKKKKKKKKKKKKIIIGGGEEEDDDEEEDDDBBBBBBCCCDDDCCCBBBCCCBBBAAABBBEEEGGGHHHHHHHHHHHHFFFEEEDDDDDDDDDDDDCCCCCCCCCDDDEEEEEEFFFFFFGGGEEECCCCCCEEEFFFFFFFFFCCCDDDEEEFFFGGGHHHHHHHHHIIIIIIGGGFFFDDDCCCAAAAAA???AAACCCBBBAAA@@@BBBDDDGGGFFFDDDBBBAAA@@@??????===============>>>??????>>>======<<<:::999999888999999999999999:::;;;<<<999999999888888777777777777777777777777777777777666666666666666666666666777888999:::999777555333555555444333333333333444444444444333333333222222444444222111111111222333222111111111000000000000//////000000000111111111333222111000000000111111111000//////000000///---........................//////............//////...///000000000000//////....../////////000000000....../////////...............------------.........------,,,,,,------...---.........////////////LLLMMMNNNMMMJJJHHHHHHHHHGGGFFFFFFIIIMMMQQQRRRSSSLLLKKKKKKJJJJJJJJJKKKLLLJJJJJJIIIGGGFFFDDDCCCCCCBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBAAAAAAAAAAAABBBBBBDDDDDDBBBBBBBBBCCCDDDEEEFFFGGGGGGHHHHHHHHHHHHGGGGGGFFFDDDCCCDDDGGGIIIKKKIIIIIIIIIJJJIIIHHHGGGGGGGGGGGGGGGGGGHHHJJJKKKLLLKKKKKKLLLLLLLLLKKKKKKJJJFFFEEEDDDCCCCCCDDDEEEFFFEEEEEEEEEEEEEEEEEEEEEEEEFFFDDDDDDEEEHHHJJJKKKJJJIIIHHHGGGFFFFFFGGGIIIKKKHHHGGGFFFEEEEEEGGGHHHJJJKKKIIIHHHHHHIIIJJJJJJIIIJJJKKKLLLLLLLLLKKKIIIHHHJJJNNNSSSUUUSSSNNNJJJGGGHHHKKKOOOPPPPPPOOOOOOPPPRRRPPPLLLJJJJJJIIIHHHGGGGGGHHHJJJMMMOOOQQQRRRRRRSSSRRRPPPOOONNNNNNOOOOOOOOOOOONNNOOOPPPRRRSSSUUUVVVWWWWWWVVVSSSRRRRRRSSSTTTUUUUUUVVVTTTRRROOONNNIIIIIIJJJNNNQQQPPPLLLGGGDDDDDDEEEFFFGGGHHHHHHIIILLLLLLLLLKKKJJJKKKNNNPPPMMMNNNOOORRRTTTVVVXXXYYYUUUUUUUUUVVVXXXXXXVVVTTTTTTSSSQQQPPPOOOOOOOOOOOOSSSRRRQQQPPPQQQOOOMMMKKKHHHIIIJJJMMMPPPSSSVVVXXXSSSRRRQQQRRRSSSRRRPPPNNNPPPPPPQQQRRRSSSSSSSSSSSSOOOOOOPPPPPPPPPQQQQQQQQQOOOPPPQQQPPPMMMKKKJJJKKKPPPPPPQQQRRRTTTVVVXXXYYY[[[\\\]]]]]]^^^^^^]]]]]]ZZZYYYWWWUUURRRPPPNNNMMMOOOOOOOOOPPPPPPQQQQQQQQQOOONNNMMMMMMNNNNNNLLLJJJIIIKKKMMMPPPQQQPPPNNNMMMKKKJJJIIIHHHHHHIIIJJJKKKOOOOOOQQQSSSWWWXXXWWWVVVSSSPPPOOORRRTTTQQQOOOPPPQQQPPPNNNMMMLLLLLLMMMMMMRRRTTTWWWYYYYYYWWWTTTRRRRRRPPPOOOOOOOOOMMMKKKIIIMMMMMMLLLLLLKKKJJJJJJJJJMMMLLLKKKKKKJJJKKKKKKKKKLLLJJJIIIIIIJJJIIIFFFDDDEEEGGGHHHGGGEEEDDDDDDDDDEEEHHHKKKLLLLLLJJJJJJJJJKKKLLLMMMLLLJJJHHHHHHHHHEEEFFFGGGGGGFFFFFFHHHJJJLLLLLLKKKJJJHHHGGGFFFFFFHHHFFFDDDDDDDDDEEEDDDCCCCCCBBBBBBCCCFFFHHHHHHHHHEEEFFFFFFFFFEEEDDDDDDCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCBBBAAAAAACCCEEEEEEDDDDDDDDDEEEFFFFFFFFFFFFFFFGGGGGGFFFEEEDDDCCCBBBBBB>>>@@@AAAAAA@@@???AAABBBCCCBBBAAA@@@>>>>>>>>>>>><<<<<<<<<=========>>>>>>;;;;;;::::::999888777777777777777888999:::;;;<<<999999888888777666555555555555555555555555555555444444555666777777888888777777777777666555444333555444333333222222333333333222222222222111111111333222222111000111111111000000000000////////////////////////000000000000222111111000000000000111111000...///000000///---///......------...//////---------,,,,,,---------+++,,,---........................////////////000..............................------------......,,,++++++******++++++,,,---------.........//////IIIJJJJJJHHHFFFEEEFFFGGGFFFFFFFFFHHHKKKMMMMMMLLLIIIIIIIIIIIIJJJJJJKKKKKKIIIHHHGGGFFFDDDCCCAAAAAA@@@@@@@@@AAAAAAAAAAAAAAA@@@@@@@@@@@@@@@@@@AAABBBDDDCCCCCCBBBBBBBBBCCCCCCCCCDDDEEEFFFFFFGGGFFFFFFDDDEEEEEEFFFGGGHHHJJJKKKNNNMMMLLLKKKIIIHHHFFFFFFEEEEEEFFFGGGIIIJJJKKKLLLJJJKKKKKKKKKKKKJJJIIIIIIEEEDDDCCCBBBBBBDDDFFFGGGFFFFFFFFFFFFFFFFFFFFFFFFEEEDDDCCCEEEGGGIIIIIIIIIGGGFFFEEEDDDDDDEEEGGGHHHFFFEEEDDDCCCCCCEEEGGGHHHIIIHHHGGGGGGIIIJJJIIIHHHJJJJJJKKKKKKKKKJJJIIIHHHJJJMMMQQQRRRPPPMMMKKKJJJKKKMMMPPPQQQOOONNNNNNOOOSSSQQQMMMJJJIIIHHHHHHHHHHHHJJJLLLNNNPPPQQQQQQPPPQQQPPPOOOMMMLLLLLLLLLLLLNNNNNNNNNNNNOOOQQQSSSTTTVVVUUUUUUSSSQQQPPPPPPPPPRRRRRRRRRRRRQQQOOONNNMMMIIIHHHHHHIIIKKKKKKIIIFFFDDDEEEEEEFFFGGGHHHIIIIIILLLMMMMMMLLLKKKKKKMMMOOOKKKLLLNNNPPPSSSUUUWWWXXXYYYYYYZZZZZZZZZXXXUUUSSSSSSRRROOOMMMLLLLLLNNNNNNQQQOOONNNLLLLLLKKKJJJIIIHHHIIIJJJLLLOOORRRTTTUUUVVVTTTRRRQQQPPPOOOMMMKKKNNNNNNOOOOOOPPPPPPPPPPPPLLLLLLLLLMMMMMMMMMNNNNNNIIIKKKLLLMMMLLLLLLMMMOOOOOOOOOOOOOOOQQQSSSVVVWWWXXXYYYZZZ[[[[[[ZZZYYYXXXWWWVVVTTTQQQOOOMMMKKKJJJKKKJJJIIIIIIIIIJJJKKKLLLLLLLLLKKKKKKJJJIIIGGGFFFFFFHHHJJJLLLMMMLLLJJJIIIGGGGGGGGGGGGHHHIIIJJJKKKPPPOOOPPPRRRTTTUUUSSSQQQMMMKKKLLLPPPQQQNNNMMMOOONNNMMMLLLLLLLLLMMMNNNOOORRRTTTWWWYYYXXXUUUQQQOOOMMMLLLLLLKKKJJJIIIGGGEEEKKKKKKJJJJJJJJJJJJJJJJJJJJJJJJIIIIIIIIIIIIJJJJJJJJJJJJHHHGGGFFFDDDBBBAAADDDFFFGGGFFFEEEDDDDDDEEEDDDGGGIIIJJJIIIHHHHHHHHHIIIIIIIIIIIIGGGFFFFFFFFFDDDEEEFFFFFFEEEFFFHHHJJJLLLKKKJJJHHHGGGGGGGGGGGGHHHFFFDDDCCCDDDEEEDDDCCCAAA@@@@@@BBBDDDFFFGGGFFFDDDEEEFFFGGGGGGFFFDDDCCCDDDDDDDDDCCCCCCBBBBBBBBB@@@???>>>???BBBCCCCCCBBBCCCDDDDDDEEEDDDDDDCCCCCCDDDDDDCCCCCCCCCCCCBBBBBB>>>???@@@@@@@@@@@@@@@AAA???>>>===<<<<<<<<<<<<<<<:::;;;;;;<<<<<<<<<<<<<<<:::999999999888888777777777777777777888888999:::999888888777666555444444444444444444444444444444444555555666666777888888666555555444333333444444222222111000000000000000111111111111111000000000222111111000000000000000000////////////................../////////000000000000000000000000000000111///......///000...---000000/////////000111222------,,,,,,,,,,,,------******,,,---............------........./////////------------------.........------,,,,,,------...++++++************++++++,,,,,,---------.........GGGHHHHHHFFFDDDDDDEEEGGGFFFFFFFFFGGGHHHHHHGGGEEEFFFGGGGGGHHHIIIIIIIIIIIIHHHGGGFFFEEECCCBBBAAA@@@===>>>???@@@AAA@@@@@@@@@???????????????@@@AAAAAADDDCCCCCCBBBBBBBBBBBBCCCCCCCCCDDDEEEFFFFFFFFFFFFCCCEEEHHHKKKMMMLLLJJJIIIOOONNNLLLIIIGGGEEECCCBBBCCCDDDFFFGGGIIIJJJKKKLLLJJJJJJJJJJJJJJJIIIHHHGGGDDDDDDCCCCCCDDDEEEGGGHHHEEEEEEEEEEEEEEEEEEEEEEEEEEEDDDCCCDDDFFFHHHHHHHHHFFFEEEDDDDDDCCCDDDEEEEEEEEEDDDBBBBBBBBBCCCEEEGGGGGGFFFFFFGGGIIIIIIIIIGGGIIIIIIIIIIIIHHHHHHGGGGGGGGGJJJNNNPPPOOONNNNNNNNNLLLNNNPPPPPPOOOMMMMMMNNNRRRQQQNNNKKKHHHHHHIIIJJJIIIJJJLLLNNNOOOOOOOOONNNMMMMMMLLLKKKJJJJJJIIIIIINNNMMMMMMMMMMMMOOOPPPQQQSSSQQQPPPNNNNNNNNNNNNNNNPPPPPPPPPOOOOOONNNNNNNNNKKKJJJHHHHHHHHHHHHGGGFFFEEEEEEFFFGGGHHHIIIJJJJJJKKKLLLMMMMMMKKKKKKMMMNNNJJJKKKMMMOOOQQQSSSUUUVVV[[[\\\]]]\\\YYYVVVSSSQQQPPPNNNMMMKKKKKKLLLNNNOOONNNNNNMMMKKKJJJJJJJJJKKKJJJKKKLLLNNNOOOPPPQQQRRRTTTRRRPPPOOOOOONNNMMMKKKLLLLLLLLLLLLMMMMMMMMMNNNLLLLLLLLLKKKKKKKKKJJJJJJJJJKKKLLLLLLLLLLLLNNNOOOMMMMMMMMMMMMOOOQQQSSSUUUWWWXXXYYYYYYYYYXXXVVVUUUSSSQQQOOOLLLJJJHHHHHHGGGIIIHHHFFFEEEEEEGGGHHHIIIIIIJJJJJJIIIHHHFFFEEEEEEFFFGGGJJJKKKKKKJJJHHHGGGGGGGGGHHHHHHIIIKKKLLLLLLQQQPPPPPPQQQQQQQQQNNNLLLHHHGGGJJJOOOOOOMMMMMMPPPJJJJJJJJJKKKKKKLLLMMMMMMPPPRRRTTTVVVUUUQQQMMMJJJHHHIIIIIIHHHFFFDDDCCCBBBBBBBBBCCCDDDEEEEEEFFFFFFIIIHHHHHHHHHHHHHHHIIIIIIJJJIIIHHHFFFCCCAAA@@@@@@CCCDDDEEEDDDCCCCCCDDDFFFEEEGGGIIIIIIHHHGGGHHHHHHHHHHHHGGGFFFFFFFFFEEEEEEBBBCCCDDDDDDCCCDDDFFFHHHKKKJJJIIIGGGFFFFFFFFFFFFFFFDDDBBBBBBCCCCCCCCCAAAAAA@@@AAACCCEEEGGGGGGFFFEEEEEEGGGGGGGGGFFFEEEDDDDDDDDDDDDCCCBBBBBBAAAAAA>>>======>>>AAABBBAAA@@@BBBBBBBBBCCCBBBBBBAAA@@@AAAAAAAAAAAAAAAAAAAAAAAA???>>>>>>??????@@@@@@@@@<<<<<<;;;:::::::::::::::888999:::;;;;;;;;;;;;:::999888888888888888888888999888777666666666666666777777666555555444333333333333333333333333333333555555555555555555555555555444333222222222333444111111000////////////000000000000000000000000000111111111111000000//////////////////.........------............/////////////////////////////////000///......//////...---///////////////000111111...------------------...***+++,,,---.../////////------------............,,,,,,,,,+++,,,---...///------,,,,,,,,,,,,------,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,------------EEEFFFFFFEEEDDDCCCEEEGGGEEEDDDDDDDDDEEEEEECCCAAADDDEEEFFFFFFGGGGGGGGGFFFEEEEEEDDDCCCBBBAAA@@@@@@<<<===???@@@AAAAAA@@@?????????>>>??????@@@AAABBBCCCCCCCCCCCCCCCCCCCCCCCCDDDEEEEEEFFFFFFFFFFFFEEECCCFFFKKKOOOPPPNNNJJJHHHLLLJJJHHHEEECCCAAA@@@???CCCDDDFFFHHHIIIJJJJJJKKKIIIIIIIIIIIIIIIHHHGGGFFFDDDDDDEEEEEEFFFFFFGGGGGGBBBBBBBBBBBBBBBBBBBBBBBBEEEDDDCCCDDDFFFGGGGGGGGGEEEEEEDDDCCCCCCCCCDDDDDDDDDCCCBBBAAAAAACCCEEEFFFEEEEEEEEEFFFHHHIIIHHHFFFGGGGGGGGGFFFFFFFFFFFFFFFEEEHHHLLLOOOOOONNNOOOOOOKKKLLLNNNNNNLLLKKKLLLMMMNNNNNNMMMKKKHHHGGGHHHJJJIIIJJJKKKLLLLLLLLLLLLLLLJJJIIIIIIIIIIIIIIIHHHHHHNNNMMMLLLKKKKKKLLLMMMNNNOOOLLLJJJJJJLLLMMMMMMMMMOOOOOOOOOPPPOOOOOONNNNNNLLLKKKIIIHHHFFFFFFFFFFFFEEEEEEFFFGGGHHHIIIIIIJJJJJJLLLMMMMMMLLLLLLMMMNNNLLLMMMNNNOOOPPPRRRRRRSSSZZZ[[[[[[YYYUUURRRPPPOOOMMMLLLKKKKKKLLLMMMNNNOOONNNNNNNNNLLLJJJIIIJJJLLLKKKLLLMMMNNNOOOPPPPPPPPPMMMKKKJJJKKKMMMNNNOOONNNLLLKKKKKKJJJJJJKKKLLLLLLMMMLLLLLLLLLKKKKKKJJJJJJPPPPPPPPPMMMKKKJJJJJJKKKKKKKKKLLLMMMOOOQQQSSSTTTZZZZZZYYYXXXWWWVVVTTTSSSOOOMMMJJJGGGEEEDDDDDDDDDGGGFFFEEEEEEEEEFFFHHHIIIFFFGGGIIIHHHFFFEEEEEEFFFGGGHHHJJJKKKKKKJJJGGGFFFGGGGGGHHHIIIJJJKKKLLLLLLPPPOOONNNOOOOOONNNLLLIIIGGGGGGKKKPPPPPPLLLMMMPPPHHHHHHIIIIIIIIIIIIJJJJJJLLLNNNPPPPPPOOOLLLIIIGGGEEEFFFGGGEEEBBB@@@@@@@@@???@@@AAABBBDDDEEEFFFFFFFFFFFFFFFFFFFFFGGGGGGHHHHHHHHHGGGDDD@@@>>>>>>??????@@@AAA@@@@@@@@@BBBDDDEEEGGGHHHHHHGGGFFFGGGHHHHHHFFFDDDCCCDDDEEEDDDCCC???@@@AAAAAA@@@AAACCCDDDHHHHHHGGGFFFFFFEEEDDDDDDCCCBBB@@@@@@BBBCCCBBBAAACCCCCCCCCEEEHHHIIIIIIHHHFFFFFFFFFFFFEEEEEEDDDCCCCCCBBBBBBBBBAAAAAA@@@@@@===<<<<<<>>>@@@AAA???>>>??????@@@@@@@@@??????>>>>>>>>>>>>>>>>>>?????????>>><<<<<<<<<>>>???>>>===;;;:::999888888888888888777888999:::;;;:::999888777777777777777888888888999888777666555444444444555555555444444444444333333333333333333333333333555444444444444444444444444333333222222222333333333222111111000111111111/////////000000000000111000111111111111000//////////////////............------------.........///---......////////////...000///---...//////...,,,+++,,,---...............///......------......///+++,,,---...............,,,,,,,,,---------......,,,+++******+++,,,...///------,,,,,,,,,,,,---------,,,,,,++++++,,,,,,---+++++++++,,,,,,,,,------CCCDDDEEEEEECCCCCCDDDEEECCCAAAAAAAAACCCDDDCCCBBBBBBCCCDDDEEEEEEEEEDDDCCCAAAAAAAAA@@@@@@@@@??????<<<===???AAAAAAAAA@@@???????????????@@@AAABBBBBBBBBCCCCCCDDDEEEEEEEEEEEEFFFGGGGGGGGGGGGFFFFFFEEEFFFHHHLLLOOOOOOMMMJJJHHHGGGFFFDDDBBBAAAAAAAAAAAACCCDDDFFFHHHIIIIIIIIIIIIIIIIIIIIIIIIHHHGGGFFFEEECCCDDDFFFGGGGGGFFFEEEDDDAAAAAAAAAAAAAAAAAAAAAAAAEEECCCBBBCCCEEEGGGGGGFFFEEEEEEDDDDDDCCCCCCCCCCCCDDDCCCBBBAAAAAACCCDDDFFFDDDCCCDDDFFFHHHIIIGGGEEEGGGGGGFFFFFFEEEEEEEEEFFFEEEHHHLLLOOOOOONNNMMMMMMGGGIIIJJJJJJHHHHHHIIIJJJIIIJJJKKKJJJGGGEEEFFFHHHIIIIIIIIIIIIIIIIIIJJJJJJGGGHHHHHHIIIIIIIIIIIIIIINNNMMMKKKJJJIIIIIIJJJJJJKKKIIIFFFGGGKKKNNNOOONNNNNNOOOPPPQQQQQQPPPOOONNNKKKKKKJJJGGGEEEDDDDDDEEECCCCCCDDDEEEFFFGGGHHHHHHIIIJJJLLLMMMMMMMMMNNNOOOQQQQQQQQQQQQQQQQQQQQQQQQTTTUUUVVVSSSOOOMMMMMMNNNLLLLLLLLLLLLMMMMMMMMMMMMOOOPPPPPPNNNJJJHHHHHHIIIHHHJJJLLLNNNOOOPPPPPPPPPJJJIIIHHHIIILLLNNNOOOOOOLLLKKKJJJIIIIIIJJJKKKKKKLLLLLLLLLLLLMMMMMMMMMMMMSSSRRRQQQNNNJJJHHHIIIJJJIIIJJJMMMOOOQQQSSSTTTUUU[[[ZZZXXXUUUSSSRRRQQQPPPKKKIIIFFFCCCAAA@@@@@@AAABBBBBBBBBBBBCCCDDDFFFFFFBBBDDDFFFFFFEEEDDDEEEGGGGGGIIIJJJKKKKKKIIIGGGEEEEEEEEEFFFHHHIIIIIIIIIIIILLLLLLLLLMMMNNNNNNLLLJJJJJJKKKNNNRRRPPPLLLKKKOOOJJJJJJJJJJJJJJJIIIHHHHHHHHHIIIJJJJJJJJJHHHEEEDDDBBBDDDEEEDDD@@@>>>>>>???AAAAAABBBCCCDDDDDDEEEEEEDDDCCCCCCCCCCCCDDDEEEFFFFFFFFFEEEBBB>>><<<===???===>>>???>>>>>>>>>AAACCCDDDEEEFFFEEEDDDCCCDDDEEEFFFCCCAAAAAABBBDDDCCCBBB>>>???@@@@@@???@@@BBBDDDEEEEEEFFFFFFEEEDDDCCCBBBAAA@@@???@@@BBBCCCCCCCCCCCCCCCDDDFFFIIIJJJIIIHHHFFFEEEDDDCCCBBBAAAAAAAAA???????????????>>>>>>>>>=========>>>@@@@@@>>><<<<<<<<<===>>>>>>>>>======<<<<<<<<<<<<<<<<<<<<<<<<;;;999888999<<<===<<<:::;;;:::999888777666666666555666888::::::999888777444555555555666666666777777777666555444444444444333333333333444444444444444444444444444444444444111222222333333444444444333333333333333333333333222222111000000000000111//////000000000111111111111111222222222111000///000000000/////////......,,,,,,---------.........,,,---.../////////......000...------...///---,,,)))***---///000///---,,,......------------......,,,,,,------...---------+++,,,,,,,,,,,,---------++++++***)))***,,,...///---,,,,,,++++++,,,,,,------,,,,,,++++++,,,,,,---++++++++++++,,,,,,,,,,,,AAABBBDDDDDDCCCCCCCCCDDD@@@???>>>???BBBDDDDDDDDDBBBBBBCCCDDDDDDCCCBBBAAA>>>>>>>>>>>>>>>>>>>>>>>>;;;===???AAABBBAAA@@@???????????????@@@AAABBBCCCBBBBBBDDDEEEFFFFFFFFFFFFHHHHHHHHHHHHHHHGGGFFFEEEHHHJJJKKKMMMMMMLLLJJJIIIEEEDDDCCCBBBBBBCCCEEEFFFCCCEEEFFFHHHIIIIIIIIIHHHIIIIIIIIIHHHGGGFFFEEEDDDBBBDDDFFFHHHGGGFFFCCCBBBCCCCCCCCCCCCCCCCCCCCCCCCEEECCCBBBCCCEEEFFFFFFFFFEEEEEEDDDDDDDDDCCCCCCCCCDDDCCCBBBAAAAAACCCDDDFFFCCCCCCDDDFFFHHHHHHGGGEEEHHHGGGFFFFFFEEEEEEFFFFFFFFFIIIMMMOOOOOOMMMKKKKKKDDDFFFGGGGGGEEEEEEFFFHHHDDDGGGIIIHHHFFFDDDEEEFFFIIIIIIGGGFFFFFFGGGHHHIIIGGGGGGHHHIIIJJJJJJJJJJJJNNNMMMKKKIIIHHHHHHHHHHHHIIIGGGEEEFFFKKKOOOPPPPPPMMMOOOQQQRRRRRRQQQPPPOOOKKKKKKJJJGGGDDDCCCCCCCCCAAAAAABBBCCCDDDEEEFFFFFFHHHJJJLLLMMMMMMMMMNNNPPPTTTTTTTTTSSSRRRRRRQQQQQQOOOPPPQQQOOOKKKJJJLLLNNNLLLLLLMMMMMMMMMMMMLLLKKKPPPRRRRRROOOJJJFFFEEEFFFFFFGGGJJJMMMOOOPPPQQQQQQNNNLLLJJJKKKLLLNNNOOONNNLLLKKKJJJIIIIIIIIIJJJKKKKKKKKKLLLMMMNNNOOOPPPPPPQQQPPPOOOMMMJJJIIIJJJKKKIIIKKKNNNQQQTTTUUUVVVVVVZZZXXXUUUQQQOOOMMMLLLLLLIIIGGGDDDAAA???>>>??????<<<===>>>???@@@AAABBBBBB???BBBEEEEEEDDDDDDFFFHHHGGGIIIJJJKKKKKKIIIFFFDDDCCCDDDEEEFFFGGGGGGGGGGGGIIIIIIJJJLLLNNNOOOMMMLLLNNNNNNRRRTTTQQQKKKJJJMMMMMMMMMMMMMMMLLLKKKJJJIIIFFFFFFGGGGGGFFFEEECCCBBBAAACCCEEECCC???<<<===>>>??????????????????@@@@@@AAAAAAAAAAAABBBBBBCCCDDDCCCDDDDDD@@@<<<:::<<<>>>===>>>???>>>>>>???BBBDDDAAACCCCCCCCCAAAAAABBBCCCEEEBBB??????AAABBBBBB@@@@@@AAABBBBBBAAABBBDDDFFFCCCDDDEEEFFFEEEDDDAAA@@@AAA@@@???@@@BBBDDDEEEDDDAAAAAABBBDDDGGGHHHGGGEEEFFFDDDBBB@@@????????????<<<<<<==================>>>======>>>@@@???===;;;:::;;;;;;<<<======<<<<<<<<<;;;;;;;;;;;;:::::::::999777666777:::;;;999777;;;:::999777666666666555555666888999:::999777666222333333444444555555555555555444444444555555666111222222333333444444555444444444444444444444444...///000111333444555666222333333444444444333333000000///...............///000000000111111222222111222222333333111000///000000000000////////////,,,,,,,,,---------......+++,,,.../////////......000...------...///---,,,))),,,///222333111///---...------,,,,,,------...,,,,,,---------,,,++++++++++++,,,,,,,,,---------+++***))))))***,,,...///---,,,,,,++++++,,,,,,---,,,,,,++++++++++++,,,,,,******+++++++++,,,,,,,,,???@@@BBBDDDDDDCCCBBBAAA@@@AAAAAABBBBBBAAAAAA@@@CCCCCCDDDDDDCCCCCCBBBAAAAAAAAA@@@>>><<<<<<===???@@@@@@AAAAAA@@@???===<<<===>>>>>>???AAABBBBBBCCCEEEEEEEEEFFFFFFGGGGGGHHHFFFFFFGGGFFFFFFEEEDDDCCCEEEGGGIIIKKKKKKIIIGGGEEEAAAAAABBBBBBCCCDDDEEEEEEEEEFFFGGGGGGFFFGGGIIIKKKKKKJJJIIIHHHFFFEEEDDDDDDEEEEEEDDDCCCBBBBBBBBBBBB@@@AAABBBCCCDDDDDDDDDDDDEEEEEEEEEEEEEEEFFFFFFGGGDDDCCCBBBAAAAAABBBCCCDDDFFFFFFEEECCCBBBCCCEEEHHHIIIHHHGGGEEEDDDBBB@@@@@@EEEGGGIIIIIIHHHHHHHHHIIIHHHJJJMMMOOOPPPNNNKKKIIIJJJIIIGGGFFFFFFFFFGGGGGGIIIIIIIIIIIIHHHGGGFFFEEEFFFFFFEEECCCAAAAAABBBDDDHHHHHHHHHIIIIIIIIIJJJJJJMMMLLLIIIGGGFFFGGGHHHIIIIIIIIIJJJLLLMMMMMMMMMMMMNNNOOOOOOPPPOOONNNLLLKKKHHHHHHHHHHHHGGGGGGFFFFFFCCCCCCDDDEEEFFFHHHJJJKKKOOOLLLIIIGGGHHHMMMRRRVVVVVVSSSQQQRRRUUUVVVUUUTTTRRRPPPMMMLLLMMMNNNMMMMMMQQQPPPNNNMMMMMMNNNPPPQQQOOOMMMJJJGGGEEECCCBBBBBBJJJKKKLLLNNNNNNOOOOOOOOOOOOMMMLLLLLLMMMMMMLLLJJJKKKKKKKKKJJJJJJIIIHHHHHHKKKKKKKKKKKKLLLMMMOOOOOOSSSQQQOOOLLLJJJIIIIIIIIILLLNNNQQQTTTWWWXXXXXXWWWXXXUUUPPPJJJGGGEEEEEEFFFGGGDDD@@@<<<:::;;;>>>???======>>>@@@CCCEEEDDDCCCBBBBBBCCCBBBAAAAAADDDFFFKKKMMMNNNOOOMMMJJJEEECCCGGGGGGHHHIIIJJJKKKLLLMMMIIIHHHIIIKKKMMMOOONNNMMMPPPOOOOOONNNNNNMMMMMMMMMKKKKKKKKKKKKJJJIIIGGGGGGEEEEEEFFFFFFFFFFFFEEEEEEAAA@@@???>>>>>>>>>???@@@AAA???===;;;<<<>>>@@@BBB>>>>>>>>>>>>????????????@@@???>>>===;;;;;;::::::;;;:::999999;;;>>>AAADDDCCCCCCCCCCCCCCCBBBBBBBBBDDDCCCCCCBBBAAAAAA@@@@@@@@@@@@@@@@@@@@@AAABBBCCCDDDCCCAAAAAACCCDDDCCCCCCAAAAAAAAAAAAAAAAAAAAAAAABBBCCCCCCDDDEEEEEEDDDDDDAAA@@@>>><<<;;;<<<===>>>============<<<<<<<<<<<<;;;;;;<<<<<<======>>>>>><<<<<<;;;::::::::::::::::::;;;;;;;;;;;;:::999999999999999::::::999999999999888777555555777888999777888999:::999777555333444444444555555555555666777666555444555555444222444333333222222111111111444333111222333333222000111111111222222333333333222222222222222222222222000000000000////////////000000000000////////////111111111111111000//////........................---------....../////////---------.........//////---,,,,,,,,,,,,---......000///...---------------------++++++++++++------*********++++++,,,,,,,,,,,,,,,,,,------.........---,,,+++,,,...///...---///...---,,,++++++++++++))))))))))))))))))))))))++++++++++++++++++++++++>>>???@@@AAAAAAAAA@@@@@@@@@@@@AAAAAAAAAAAA@@@@@@AAAAAABBBBBBCCCBBBBBBAAA@@@@@@@@@>>>;;;;;;<<<>>>@@@@@@AAAAAA@@@???===<<<>>>>>>???@@@AAABBBCCCCCCEEEEEEFFFFFFGGGFFFFFFFFFEEEEEEFFFFFFFFFFFFFFFFFFEEEFFFHHHJJJJJJHHHFFFEEE@@@@@@@@@AAABBBCCCCCCCCCEEEFFFGGGFFFEEEEEEGGGHHHJJJJJJIIIHHHGGGFFFFFFEEEDDDDDDCCCBBBAAAAAAAAAAAA@@@AAABBBCCCCCCDDDDDDDDDEEEEEEEEEDDDEEEEEEFFFFFFFFFEEEDDDDDDCCCDDDEEEEEEEEEEEEDDDCCCBBBCCCEEEHHHKKKJJJIIIGGGFFFDDDCCCCCCGGGHHHJJJIIIHHHHHHIIIKKKJJJLLLNNNPPPPPPOOOLLLKKKJJJHHHGGGEEEDDDDDDEEEEEEJJJJJJJJJJJJIIIHHHGGGFFFEEEFFFEEEDDDBBBBBBDDDEEEHHHIIIIIIIIIJJJJJJJJJKKKLLLKKKIIIGGGGGGGGGHHHIIIJJJKKKLLLMMMNNNOOOPPPPPPPPPPPPPPPPPPOOOMMMKKKJJJIIIIIIGGGFFFEEEEEEEEEEEEFFFFFFFFFGGGHHHIIIKKKKKKKKKKKKKKKKKKMMMOOOQQQRRRWWWUUUSSSTTTWWWXXXXXXWWWTTTQQQOOONNNNNNOOONNNMMMRRRQQQPPPNNNNNNMMMNNNNNNNNNLLLIIIFFFDDDCCCCCCDDDKKKKKKLLLMMMNNNNNNNNNMMMMMMLLLJJJKKKLLLMMMLLLKKKJJJJJJIIIHHHHHHHHHHHHIIILLLKKKKKKKKKKKKKKKLLLMMMNNNMMMLLLJJJIIIHHHGGGGGGJJJLLLOOORRRTTTTTTTTTTTTQQQNNNJJJFFFDDDCCCDDDEEEGGGDDD@@@===<<<===@@@BBB???>>>???BBBEEEFFFFFFEEECCCDDDEEEEEEEEEFFFIIIKKKLLLLLLMMMMMMLLLIIIFFFDDDGGGGGGHHHIIIJJJKKKLLLMMMKKKJJJJJJLLLNNNOOONNNMMMNNNMMMMMMMMMMMMMMMLLLLLLNNNNNNLLLKKKIIIGGGFFFEEEEEEEEEFFFFFFFFFEEEDDDDDDAAAAAA????????????@@@AAABBBAAA???===<<<===>>>???>>>>>>>>>>>>???????????????>>>>>>======>>>>>>>>>;;;:::999999:::===@@@BBB@@@AAAAAABBBCCCDDDEEEEEEDDDDDDCCCCCCCCCBBBAAAAAAAAAAAA@@@@@@AAABBBBBBCCCDDDBBBAAAAAABBBCCCBBBAAA???@@@@@@@@@AAAAAABBBBBBBBBBBBCCCCCCDDDCCCCCCCCC???>>><<<::::::;;;<<<===============<<<<<<<<<<<<<<<<<<<<<<<<<<<===============<<<;;;;;;;;;;;;;;;999::::::::::::999888888888888999999999999888888888777555444444555777888888888999999888666555444444444444444555555555555777666444444555555333222333333333222222111111111333222111111222222111000///000000111222222111111222222222222222222222222000000000000///////////////////////////000000000000000111111000//////...........................,,,,,,---------.........------------.........///---,,,,,,,,,,,,---......//////...------------------,,,++++++++++++,,,---++++++++++++++++++,,,,,,,,,,,,,,,---------......---,,,+++,,,.........---------,,,+++******++++++))))))))))))))))))))))))++++++++++++++++++++++++============>>>>>>>>>>>>@@@@@@AAAAAAAAAAAA@@@@@@>>>???@@@AAAAAABBBAAAAAA??????>>><<<::::::<<<===???@@@@@@@@@@@@???===<<<>>>??????@@@AAABBBCCCCCCDDDEEEFFFGGGGGGFFFDDDCCCDDDDDDEEEEEEFFFGGGGGGHHHDDDFFFGGGIIIIIIGGGFFFDDD??????@@@@@@AAAAAABBBBBBEEEFFFFFFEEEDDDCCCDDDEEEHHHHHHHHHHHHGGGGGGGGGGGGCCCBBBAAA@@@????????????@@@@@@AAABBBCCCCCCCCCCCCFFFFFFEEEDDDDDDEEEEEEEEEGGGFFFEEEDDDDDDDDDDDDDDDCCCCCCDDDCCCBBBCCCEEEHHHLLLLLLJJJIIIHHHGGGGGGFFFJJJJJJKKKJJJIIIIIIKKKNNNMMMNNNPPPQQQQQQPPPNNNMMMJJJIIIGGGEEEDDDCCCCCCDDDJJJJJJJJJJJJIIIIIIHHHGGGDDDEEEFFFEEEDDDDDDFFFHHHJJJJJJJJJJJJKKKKKKKKKKKKKKKJJJHHHGGGGGGHHHJJJKKKKKKKKKLLLMMMNNNOOOPPPPPPNNNOOOOOONNNMMMKKKIIIHHHIIIHHHFFFDDDCCCCCCEEEEEEJJJJJJIIIIIIJJJJJJKKKLLLGGGJJJMMMPPPQQQQQQPPPNNNUUUSSSSSSSSSVVVWWWXXXWWWVVVTTTRRRQQQQQQQQQPPPNNNRRRRRRRRRPPPOOOMMMLLLKKKMMMKKKHHHEEEDDDDDDFFFGGGKKKKKKLLLLLLLLLLLLLLLKKKMMMKKKIIIIIIJJJLLLLLLLLLIIIHHHGGGGGGGGGHHHIIIJJJMMMLLLKKKJJJIIIHHHHHHHHHHHHHHHHHHHHHGGGGGGFFFEEEGGGIIILLLNNNPPPPPPOOOOOOJJJHHHEEECCCBBBCCCDDDFFFHHHEEEBBB@@@@@@BBBDDDFFF@@@@@@AAACCCFFFHHHHHHGGGCCCDDDFFFFFFGGGHHHKKKNNNLLLLLLLLLKKKJJJHHHGGGFFFGGGHHHIIIIIIJJJKKKLLLLLLLLLLLLLLLMMMOOOOOONNNMMMJJJJJJKKKKKKKKKKKKKKKKKKPPPNNNKKKHHHFFFDDDDDDCCCEEEEEEFFFFFFEEEDDDCCCCCCBBBAAA@@@@@@@@@@@@BBBBBBDDDCCCAAA???>>>===<<<<<<>>>>>>>>>>>>????????????=========>>>???@@@AAABBB<<<;;;999999:::<<<>>>???===>>>???AAACCCEEEGGGHHHDDDDDDDDDEEEDDDDDDCCCCCCBBBBBBAAAAAAAAABBBCCCCCCDDDBBB@@@@@@@@@AAA@@@???===>>>>>>???@@@AAABBBBBBAAABBBBBBBBBBBBBBBAAA@@@<<<;;;:::999999999:::;;;============<<<<<<<<<<<<<<<<<<<<<<<<;;;;;;;;;;;;<<<<<<;;;:::::::::::::::888888999999888888777666666777777888888777777666666555444333333444555666888888777777666555555555444444444444555555555555777555444444444444333111222222222222222111111111222111000000111111000///---...000111111000//////222222222222222222222222000000000000////////////.........//////000000111//////////////////...---........................,,,,,,,,,,,,------------------------............,,,,,,,,,,,,,,,---......///...---------------------,,,+++******+++,,,---,,,,,,++++++++++++++++++,,,,,,,,,,,,---------------,,,+++,,,---...---,,,++++++******************))))))))))))))))))))))))************************<<<<<<<<<;;;<<<===>>>>>>??????@@@@@@@@@@@@??????;;;<<<===???@@@AAAAAAAAA===>>>===;;;:::999;;;===>>>???@@@@@@@@@>>>===<<>>>>>>>>>>>>>>???@@@AAABBBBBBCCCCCCBBBFFFFFFEEEDDDDDDDDDDDDEEEDDDDDDCCCCCCBBBBBBAAAAAAAAACCCDDDDDDCCCDDDGGGIIIMMMLLLKKKIIIHHHHHHIIIIIILLLLLLLLLJJJIIIJJJMMMPPPPPPPPPQQQQQQQQQPPPOOONNNLLLJJJHHHFFFDDDDDDDDDDDDIIIIIIIIIIIIHHHHHHGGGFFFCCCEEEFFFFFFFFFGGGIIIJJJKKKKKKKKKKKKKKKLLLLLLLLLIIIHHHGGGGGGGGGIIIKKKLLLLLLKKKKKKKKKKKKKKKLLLLLLJJJKKKKKKLLLKKKJJJHHHGGGGGGEEECCCBBBBBBDDDGGGHHHMMMLLLKKKJJJJJJJJJJJJKKKGGGIIIMMMQQQRRRQQQOOONNNOOOOOOOOOPPPQQQRRRSSSTTTXXXVVVTTTSSSSSSRRRQQQOOOPPPQQQQQQQQQPPPNNNKKKIIIKKKIIIFFFDDDDDDEEEGGGIIIKKKKKKKKKKKKKKKKKKJJJJJJNNNLLLIIIHHHIIIJJJKKKJJJIIIHHHGGGGGGHHHIIIKKKMMMMMMLLLKKKIIIGGGFFFEEEEEEDDDEEEFFFGGGGGGGGGFFFEEEGGGHHHJJJLLLMMMMMMKKKKKKGGGFFFDDDBBBBBBCCCEEEFFFGGGFFFDDDBBBCCCEEEGGGIIIAAAAAAAAADDDFFFHHHHHHFFFAAABBBDDDEEEEEEFFFHHHJJJKKKJJJIIIHHHGGGGGGGGGGGGHHHHHHHHHIIIJJJKKKKKKKKKLLLKKKKKKLLLMMMNNNLLLKKKGGGHHHHHHHHHIIIJJJJJJJJJMMMKKKHHHEEECCCBBBCCCCCCEEEEEEEEEEEEDDDCCCBBBBBBBBBBBBAAA@@@AAABBBCCCDDDDDDCCCBBBAAA???>>><<<<<<===>>>>>>>>>????????????<<<===>>>???@@@@@@AAAAAA<<<;;;:::999999:::<<<===<<<===???AAACCCEEEGGGHHHDDDEEEFFFFFFFFFEEEEEEDDDCCCBBBBBBAAABBBBBBCCCCCCCCCAAA???>>>???@@@???>>><<<======???@@@AAABBBBBBBBBBBBBBBAAAAAA@@@>>>>>>;;;::::::999999:::;;;;;;============<<<<<<<<<<<<<<<<<<;;;;;;::::::999999:::999999888777888888888777777777888777777666555555666666777777666666555555555444444444444555555777777666555444444555555333333444444444555555555666555333333444444222111111111111111111222222222111000//////000000///...---...000111111000///...111111111111222222222222000000000000////////////------......///000111111---......///......------........................,,,,,,,,,,,,,,,,,,,,,,,,------------------------,,,,,,++++++,,,,,,---.........---,,,,,,------------,,,+++******+++,,,---,,,,,,,,,++++++*********,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***+++---...---,,,******))))))))))))******))))))))))))))))))))))))))))))))))))))))))))))))===<<<<<<<<<<<<===>>>>>>>>>??????@@@@@@??????>>>:::;;;<<<>>>???@@@@@@@@@<<<===<<<;;;999999;;;======>>>???@@@???>>>===<<<>>>??????@@@@@@AAAAAAAAABBBCCCEEEFFFFFFCCCAAA???CCCCCCBBBAAA@@@@@@AAAAAACCCCCCDDDEEEEEEDDDCCCCCCAAAAAAAAAAAABBBBBBBBBBBBCCCDDDEEEDDDBBB@@@???@@@BBBCCCCCCCCCCCCDDDDDDDDD@@@???>>>======<<<======>>>???@@@AAABBBBBBBBBBBBEEEEEEDDDDDDDDDDDDDDDEEECCCCCCCCCCCCCCCBBBBBBAAAAAACCCEEEEEEFFFGGGIIILLLMMMLLLJJJIIIHHHHHHIIIIIIMMMMMMMMMKKKJJJKKKNNNQQQQQQQQQQQQPPPPPPOOOOOOOOOMMMLLLJJJGGGFFFEEEEEEEEEFFFFFFGGGGGGGGGFFFEEEEEECCCEEEGGGHHHHHHIIIJJJLLLLLLLLLLLLLLLLLLLLLLLLLLLGGGGGGFFFFFFHHHJJJMMMNNNOOONNNMMMKKKJJJIIIIIIIIIIIIJJJKKKLLLLLLLLLKKKJJJEEECCCBBBBBBCCCFFFJJJLLLMMMLLLKKKJJJIIIIIIIIIIIIHHHJJJKKKMMMOOOOOOPPPOOOMMMMMMMMMNNNNNNOOOPPPQQQXXXVVVTTTTTTTTTTTTRRRPPPMMMNNNPPPPPPPPPNNNKKKJJJIIIHHHFFFEEEEEEFFFHHHJJJJJJJJJKKKKKKKKKJJJJJJIIIPPPNNNKKKIIIIIIIIIHHHGGGIIIIIIIIIIIIJJJKKKMMMNNNMMMLLLJJJHHHFFFDDDDDDCCCCCCDDDFFFGGGHHHHHHGGGGGGHHHIIIKKKLLLLLLKKKIIIHHHFFFEEECCCAAAAAAAAABBBCCCCCCBBBAAA@@@AAACCCEEEGGGAAAAAAAAACCCEEEFFFEEEDDDAAACCCDDDDDDDDDCCCEEEFFFIIIHHHFFFEEEEEEEEEFFFFFFGGGGGGHHHHHHIIIIIIJJJJJJIIIIIIHHHIIIKKKKKKJJJHHHFFFFFFFFFGGGGGGHHHHHHHHHFFFEEECCCAAAAAAAAACCCDDDDDDDDDDDDDDDDDDCCCBBBAAABBBBBBAAAAAAAAABBBDDDEEECCCCCCBBBAAA@@@???>>>======>>>>>>>>>????????????======>>>??????>>>>>>===<<<;;;::::::::::::;;;<<<>>>>>>???AAABBBDDDEEEFFFEEEFFFGGGHHHGGGFFFEEEDDDCCCBBBBBBAAAAAAAAABBBBBBBBB@@@>>>>>>??????>>>===<<<======???@@@AAABBBBBBBBBBBBBBBAAA@@@>>>===<<<:::::::::;;;;;;<<<==================<<<<<<<<<<<<;;;;;;::::::999999888888:::999888888777777888888666777777777777666555555555555555666666555555555555555555555555555555555666555444333333444444444333333333444444444444555555444222222333333111000000000000111111222222222111000...///000000///---//////000111111000///...000000000111111222222222000000000000////////////,,,------...///000000111------............------........................,,,,,,,,,,,,,,,,,,,,,,,,------------------,,,,,,,,,++++++++++++,,,------------,,,,,,,,,------...,,,+++************+++,,,,,,,,,,,,++++++*********,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***+++---...---,,,******))))))(((((())))))))))))))))))))))))))))))))))))))))))))))))))))))<<<<<<<<<============>>>>>>>>>????????????>>>>>>:::;;;<<<===??????@@@@@@<<<======;;;::::::<<<>>>===>>>?????????>>>===<<<>>>>>>>>>>>>??????@@@@@@AAABBBCCCDDDDDDCCCAAA@@@CCCBBB@@@???>>>>>>??????BBBBBBCCCCCCCCCCCCBBBBBBAAAAAAAAABBBBBBBBBBBBBBBAAACCCEEEDDDBBB@@@??????AAAAAAAAAAAABBBBBBBBBBBB@@@???>>>===<<<<<<<<<<<<>>>>>>???@@@AAAAAAAAAAAADDDCCCCCCCCCDDDDDDEEEFFFDDDDDDEEEEEEEEEEEEDDDDDDBBBDDDGGGHHHIIIKKKMMMOOOOOOMMMKKKHHHGGGGGGHHHIIIMMMMMMNNNMMMLLLLLLNNNQQQQQQQQQOOONNNNNNNNNNNNNNNMMMLLLJJJHHHGGGFFFGGGGGGEEEEEEEEEFFFFFFEEEEEEDDDDDDFFFIIIJJJJJJJJJLLLMMMLLLLLLLLLLLLKKKKKKKKKKKKFFFEEEEEEFFFHHHKKKNNNPPPSSSQQQOOOMMMKKKKKKKKKKKKKKKLLLNNNOOOOOONNNNNNMMMEEEDDDDDDDDDFFFIIILLLNNNMMMLLLKKKJJJIIIIIIIIIIIIJJJJJJIIIIIIKKKMMMOOOQQQNNNOOOPPPOOONNNNNNPPPRRRUUUTTTSSSTTTUUUTTTRRRPPPLLLLLLNNNNNNNNNLLLJJJIIIGGGGGGFFFFFFFFFGGGHHHIIIJJJJJJKKKKKKKKKKKKKKKJJJOOONNNLLLKKKKKKJJJHHHGGGIIIIIIJJJKKKLLLMMMMMMMMMKKKJJJIIIGGGFFFEEEDDDDDDDDDEEEFFFGGGHHHIIIIIIIIIJJJKKKLLLLLLLLLJJJHHHFFFCCCBBBAAA???????????????>>>===<<<<<<===???AAABBBBBBAAAAAABBBCCCDDDBBBAAABBBDDDFFFFFFEEEDDDDDDEEEEEEDDDDDDCCCCCCCCCDDDDDDFFFFFFFFFGGGGGGHHHHHHHHHFFFFFFFFFGGGIIIIIIHHHGGGEEEFFFFFFFFFFFFFFFGGGGGGAAAAAA@@@@@@AAABBBCCCDDDBBBBBBCCCCCCCCCCCCBBBBBBBBBAAA@@@@@@AAABBBDDDEEEEEEDDDBBBAAA@@@?????????>>>>>>>>>>>>????????????>>>>>>???@@@???>>><<<;;;;;;;;;;;;;;;;;;;;;<<<<<>>===>>>>>>???@@@AAABBBBBBDDDCCCCCCAAA???===;;;:::::::::;;;<<<===>>>>>>???============<<<<<<<<<<<<999999999999888888888888::::::999888888888888999666666777777666666555444444555555666666555555444555555555555555555555555333333333333333333333333333333333333444444444444555333222222222222111/////////000000111222333333111000//////000000///...000000000000//////////////////000000111222222222000000000000////////////---------......//////000,,,---......///.................................------------,,,,,,,,,,,,------------,,,,,,,,,,,,+++++++++++++++,,,------,,,,,,,,,,,,,,,------...,,,+++***))))))***+++,,,,,,,,,++++++++++++++++++,,,,,,,,,,,,++++++++++++,,,+++***+++,,,---,,,+++,,,+++***)))(((((((((((())))))))))))))))))))))))************************:::;;;<<<=========<<<;;;===>>>>>>>>>>>>>>>>>>===;;;;;;<<<>>>????????????<<<======<<<:::;;;===???<<<===>>>??????>>>===<<<============>>>>>>>>>>>>@@@AAAAAABBBBBBBBBBBBAAABBBAAA???>>>>>>???@@@AAAAAABBBBBBBBBBBBBBBBBBAAAAAAAAAAAA@@@@@@@@@@@@@@@@@@BBBEEEEEECCCAAA@@@@@@BBBBBBBBBAAAAAAAAAAAAAAA@@@???>>>===<<<<<<<<<<<<===>>>???@@@AAAAAAAAAAAABBBBBBBBBCCCDDDEEEFFFGGGBBBCCCDDDEEEFFFFFFEEEEEEDDDFFFIIILLLMMMNNNQQQSSSQQQOOOLLLIIIGGGGGGHHHIIIKKKMMMNNNNNNMMMMMMNNNOOOQQQPPPNNNLLLKKKLLLLLLMMMKKKJJJIIIGGGFFFFFFGGGGGGEEEEEEFFFFFFFFFFFFEEEEEEEEEGGGJJJKKKKKKKKKLLLMMMLLLLLLLLLKKKKKKJJJJJJJJJDDDDDDDDDFFFHHHLLLOOORRRQQQPPPNNNLLLKKKLLLMMMMMMNNNNNNOOOOOONNNMMMKKKJJJGGGGGGHHHHHHIIIKKKLLLMMMMMMLLLKKKJJJJJJIIIJJJJJJIIIIIIHHHGGGIIIKKKNNNPPPPPPQQQRRRPPPNNNMMMOOOQQQRRRRRRRRRSSSTTTTTTRRRPPPMMMMMMMMMLLLKKKIIIGGGFFFFFFFFFGGGGGGHHHHHHHHHGGGIIIJJJKKKLLLLLLLLLLLLLLLLLLLLLLLLMMMNNNMMMKKKHHHHHHIIIKKKLLLMMMLLLKKKJJJIIIIIIHHHGGGFFFFFFFFFFFFFFFFFFFFFFFFGGGIIIJJJKKKKKKLLLLLLLLLKKKIIIFFFEEEBBBAAAAAA@@@@@@@@@AAAAAA>>>======<<<===>>>@@@AAADDDCCCBBBBBBCCCCCCAAA???@@@BBBEEEFFFEEEEEEEEEFFFAAAAAAAAAAAABBBBBBBBBBBBEEEEEEEEEEEEFFFFFFFFFFFFDDDDDDDDDFFFHHHIIIHHHGGGFFFFFFFFFFFFFFFEEEEEEEEE@@@@@@AAAAAABBBCCCDDDDDD@@@AAABBBBBBCCCCCCCCCCCCAAA@@@@@@@@@@@@BBBCCCEEEIIIGGGDDDAAA???>>>>>>>>>>>>>>>>>>>>>????????????>>>???@@@AAA@@@???===<<<;;;;;;;;;<<<<<<======>>>>>>>>>???@@@BBBCCCDDDEEEFFFGGGHHHIIIGGGEEEBBB@@@BBBAAA@@@??????????????????>>>======???AAAAAA@@@???@@@@@@@@@AAAAAABBBBBBEEEDDDCCCBBB???===;;;:::999:::;;;<<<===>>>??????============<<<<<<<<<<<<777777777888888888888888888777666666555555666666777777777777777666555555555555666666666666555555333333444444444444333333111222333444444333222111222222333333333444444444444333111111222222000///......///000111222333333222111///000111111000...111000...---,,,---...////////////000111222222222000000000000////////////........................------...///////////////.................................---------,,,,,,---------,,,,,,,,,+++++++++++++++***++++++,,,---,,,,,,++++++,,,,,,---...,,,+++***))))))***+++,,,++++++++++++++++++,,,,,,,,,,,,,,,+++++++++******+++*********,,,---,,,+++...---,,,***)))(((''''''))))))))))))))))))))))))++++++++++++++++++++++++888999;;;======<<<;;;:::======>>>>>>>>>>>>======;;;<<<===>>>????????????=========<<<;;;;;;===???<<<===>>>??????>>>======<<<<<<<<<<<<============@@@@@@@@@AAAAAABBBBBBCCCAAA@@@>>>>>>???@@@BBBDDDAAAAAAAAAAAAAAAAAAAAAAAA@@@@@@??????????????????@@@BBBDDDEEECCCAAA@@@@@@CCCCCCCCCBBBBBBAAAAAAAAA@@@???>>>======<<<<<<======>>>???@@@@@@AAA@@@@@@AAAAAAAAABBBDDDEEEGGGHHH???@@@BBBDDDEEEEEEDDDDDDEEEGGGKKKMMMOOOQQQSSSUUUSSSQQQMMMJJJHHHHHHHHHIIIJJJLLLNNNNNNMMMMMMMMMNNNPPPOOOLLLKKKJJJJJJKKKLLLJJJIIIGGGFFFFFFFFFGGGGGGEEEFFFFFFGGGGGGGGGFFFFFFEEEHHHKKKLLLLLLLLLLLLMMMLLLLLLKKKKKKJJJJJJJJJIIICCCCCCDDDEEEHHHLLLPPPRRRMMMLLLJJJIIIJJJKKKMMMNNNNNNNNNNNNMMMKKKHHHFFFEEEJJJKKKKKKKKKKKKKKKKKKKKKMMMMMMLLLKKKKKKKKKKKKKKKHHHGGGGGGGGGIIIKKKMMMOOOPPPQQQRRRPPPMMMLLLMMMPPPPPPPPPPPPRRRTTTTTTRRRPPPOOONNNMMMKKKIIIGGGEEEDDDEEEFFFGGGIIIIIIHHHGGGFFFIIIIIIKKKLLLMMMMMMMMMMMMIIIIIIKKKNNNPPPPPPMMMKKKFFFHHHKKKLLLMMMKKKIIIHHHHHHHHHGGGGGGGGGGGGGGGHHHGGGFFFEEEEEEFFFHHHJJJKKKKKKLLLLLLLLLJJJHHHEEECCCBBBBBBBBBBBBCCCDDDDDDEEEAAAAAA@@@???@@@AAABBBCCCFFFEEEDDDCCCCCCBBB@@@>>><<>><<<======>>>>>>>>>>>>????????????>>>???AAABBBBBBAAA@@@>>>;;;;;;<<<<<<===>>>>>>???<<<===>>>@@@BBBDDDEEEFFFGGGHHHIIIIIIGGGDDDAAA>>>AAA@@@@@@???>>>>>>>>>??????===<<<>>>@@@BBBBBBBBBAAAAAAAAAAAAAAAAAAAAAAAAFFFEEEDDDBBB@@@===;;;999888999:::<<<===>>>>>>>>>>>>=========<<<<<<<<<<<<666666777777888888999999333333222111111111111222777777777777777666666555555555666666666666555555111222222333333222222111000111333444444333222000222222333333333444444444444333111111222222000///---...///000111222333444222111000000111111000///111///,,,******+++---///...//////000111222222222000000000000////////////...............---------------...///000000000///......................../////////......------------------,,,,,,+++++++++++++++******++++++,,,---++++++++++++,,,,,,---...,,,+++***))))))***+++,,,*********++++++,,,,,,---,,,,,,,,,++++++*********+++***)))***,,,---,,,+++///...---+++)))(((''''''))))))))))))))))))))))))++++++++++++++++++++++++888999:::<<<===<<<<<<;;;<<<<<<<<<<<<<<<<<<<<<<<<======<<<<<<<<<<<<======<<<<<<;;;;;;;;;<<<<<<===:::;;;===<<<;;;::::::;;;===<<<<<<<<<<<<;;;;;;;;;>>>>>>===============>>>>>>>>>??????@@@@@@AAAAAABBBBBBAAA???===>>>AAACCC<<<<<<;;;;;;;;;<<<<<<===AAABBBCCCCCCCCCBBBAAA@@@DDDEEEEEEDDDCCCAAA@@@???>>><<<;;;;;;===>>>>>>===>>>???@@@@@@>>>>>>@@@AAAAAABBBBBBCCCDDDEEEFFFFFFCCCCCCDDDEEEFFFGGGHHHHHHEEEHHHKKKMMMMMMOOOQQQRRRSSSPPPLLLHHHFFFFFFHHHIIINNNMMMKKKJJJIIIIIIJJJJJJKKKHHHEEEFFFHHHJJJIIIGGGLLLJJJFFFEEEEEEFFFFFFFFFDDDDDDEEEFFFFFFFFFEEEEEEJJJKKKLLLLLLLLLKKKJJJIIIDDDFFFHHHIIIIIIGGGDDDCCCBBBCCCDDDFFFHHHJJJLLLLLLLLLIIIGGGGGGIIIKKKLLLLLLJJJKKKKKKKKKJJJHHHFFFDDDEEEHHHKKKMMMLLLLLLLLLLLLLLLKKKJJJIIIHHHGGGGGGGGGHHHIIIKKKMMMOOOQQQSSSTTTVVVTTTRRROOONNNMMMMMMMMMPPPMMMLLLNNNRRRSSSOOOKKKLLLPPPRRRNNNFFFAAACCCGGGHHHIIIJJJIIIGGGGGGGGGHHHHHHJJJNNNPPPQQQPPPNNNLLLJJJKKKLLLLLLLLLKKKJJJIIIJJJJJJKKKKKKKKKJJJHHHGGGFFFFFFFFFFFFGGGGGGGGGGGGDDDDDDEEEFFFGGGHHHHHHIIILLLKKKKKKKKKKKKIIIEEEBBBFFFDDDBBBCCCFFFGGGEEECCCCCCAAA@@@BBBEEEGGGFFFDDDFFFEEEDDDBBBAAA@@@??????<<<>>>@@@CCCEEEEEEEEEDDDAAAAAA@@@@@@@@@AAABBBBBBEEEDDDDDDFFFHHHHHHGGGFFFGGGFFFFFFFFFGGGHHHHHHIIIKKKJJJIIIHHHFFFEEEDDDDDDBBBDDDFFFGGGGGGEEECCCAAA>>>>>>???@@@AAAAAABBBBBB??????>>>>>>???AAACCCDDDEEEDDDAAA===:::888999:::<<<===??????>>>>>>???AAACCCCCCDDDDDDCCC@@@>>><<<;;;;;;;;;<<<<<<<<<<<<<<<===>>>???@@@BBBCCCDDDEEEIIIIIIIIIIIIHHHFFFDDDCCC@@@@@@@@@???????????????<<<<<<<<<======>>>???@@@@@@@@@AAABBBBBBBBBBBBAAAAAABBBBBBAAA@@@===:::888777777777777888999;;;;;;<<<<<<<<<<<<;;;:::999999444555777888888777777666666555444333333333444555222222333444444555555666333333444444555444444444555444333333222222222333111111111111111111111111111111000000//////......////////////............---------------...///000000000//////......------000000///...---,,,,,,,,,111111222222222222111111000000000000////////////------------------------.........------,,,,,,,,,........................------............------,,,,,,,,,++++++*********************)))))))))(((,,,,,,+++***)))(((''''''))))))))))))))))))))))))++++++***************+++************))))))))))))******+++++++++,,,,,,,,,+++******)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))888999:::<<<<<<<<<<<<;;;<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>===<<<<<<<<<======<<<;;;;;;:::;;;;;;<<<<<<999;;;<<<<<<:::::::::;;;======<<<<<<;;;;;;;;;;;;>>>>>>===============>>>>>>>>>>>>????????????????????????>>>======???AAA<<<;;;;;;;;;;;;<<<======BBBBBBCCCCCCBBBAAA@@@???DDDEEEEEEEEEDDDBBB@@@>>>===<<<;;;;;;<<<======<<<===???@@@@@@?????????@@@@@@AAAAAACCCDDDEEEFFFFFFDDDDDDDDDEEEFFFFFFGGGGGGHHHJJJLLLMMMLLLLLLMMMNNNNNNLLLJJJHHHGGGHHHJJJKKKKKKJJJIIIHHHGGGHHHIIIIIIIIIFFFDDDDDDGGGJJJKKKKKKLLLJJJGGGEEEFFFGGGGGGFFFGGGGGGHHHHHHHHHGGGGGGFFFGGGHHHIIIJJJJJJJJJIIIHHHEEEEEEGGGGGGGGGFFFDDDCCCCCCCCCEEEFFFHHHIIIJJJKKKJJJHHHFFFFFFHHHJJJJJJJJJJJJKKKKKKLLLJJJHHHFFFDDDDDDGGGJJJLLLMMMMMMMMMNNNLLLKKKJJJHHHHHHHHHIIIIIIKKKKKKMMMOOOQQQRRRTTTTTTWWWUUUSSSPPPNNNMMMMMMMMMNNNLLLLLLOOOTTTUUURRRNNNNNNPPPPPPMMMGGGDDDFFFHHHGGGHHHIIIHHHGGGFFFGGGHHHIIIJJJLLLNNNNNNMMMLLLJJJKKKKKKLLLLLLKKKKKKJJJJJJJJJKKKKKKKKKJJJIIIGGGFFFEEEEEEEEEEEEEEEEEEEEEEEECCCDDDEEEFFFGGGHHHIIIJJJLLLKKKKKKKKKKKKIIIEEECCCFFFDDDBBBCCCEEEFFFEEECCCBBB@@@???AAADDDEEEDDDCCCEEEDDDBBB@@@???>>>======<<<>>>AAACCCEEEEEEDDDDDDBBBBBBBBBBBBCCCDDDEEEFFFGGGFFFFFFGGGIIIIIIHHHGGGHHHGGGGGGGGGGGGHHHIIIJJJKKKJJJIIIGGGEEECCCBBBAAACCCDDDFFFGGGFFFEEEBBBAAA>>>>>>???@@@AAABBBBBBCCC@@@?????????@@@AAACCCDDDCCCAAA>>><<<;;;;;;<<<<<<===>>>??????>>>===>>>???>>>>>>@@@@@@@@@>>><<<;;;<<<<<<=========>>>>>>>>>>>>???@@@BBBCCCEEEFFFGGGGGGHHHHHHHHHGGGFFFEEEDDD@@@@@@????????????>>>>>><<<<<<<<<<<<======>>>?????????@@@@@@@@@??????>>>???@@@@@@@@@>>><<<999777777777777777777888999:::::::::::::::999888777777777888999999888777666555555444333222222333444444444444444444444444333333333444444444444444333333444444333222222222222222111111111111111111111111111000000000/////////...////////////..................------...//////000000/////////......------/////////......------,,,000111111222222111111000000000/////////.........000000000000000000000000......---------,,,,,,,,,........................------............------,,,,,,++++++++++++++++++++++++++++++************++++++******)))(((((((((((((((((((((((((((((((((******))))))((())))))***************)))))))))))))))))))))*********++++++******)))(((((((((((()))))))))))))))))))))))))))))))))))))))))))))))))))888999:::;;;<<<<<<<<<;;;<<<<<<<<<<<<<<<<<<<<<<<>>===============<<<<<<;;;;;;:::;;;;;;<<<888:::;;;;;;:::999:::;;;======<<<;;;;;;;;;;;;;;;>>>======<<<<<<===>>>>>>???>>>>>>>>>>>>>>>>>>===<<<===>>>>>><<<<<<===>>><<<;;;;;;:::;;;<<<===>>>BBBBBBBBBBBBAAA@@@>>>>>>CCCEEEFFFGGGFFFCCC@@@???======<<<<<<<<<<<<<<<<<<;;;>>>AAABBBAAA?????????>>>???@@@BBBCCCEEEFFFFFFEEEEEEEEEEEEEEEEEEEEEEEEIIIKKKMMMLLLKKKIIIIIIIIIHHHHHHHHHHHHIIIJJJKKKLLLFFFFFFFFFEEEFFFFFFGGGHHHHHHFFFDDDEEEHHHLLLNNNOOOLLLJJJGGGFFFFFFHHHHHHHHHKKKKKKJJJJJJIIIIIIHHHHHHDDDEEEGGGHHHIIIHHHHHHGGGEEEEEEEEEEEEDDDDDDCCCCCCCCCDDDEEEGGGHHHHHHIIIIIIIIIGGGEEEEEEGGGHHHIIIIIIJJJJJJKKKLLLKKKIIIFFFEEECCCFFFJJJLLLLLLMMMNNNOOOMMMKKKIIIHHHHHHIIIKKKLLLMMMNNNOOOPPPRRRSSSTTTUUUWWWUUUSSSPPPNNNMMMLLLLLLKKKKKKMMMRRRVVVWWWTTTPPPOOONNNLLLJJJHHHHHHHHHIIIEEEGGGHHHGGGFFFFFFGGGHHHIIIJJJKKKKKKKKKKKKJJJJJJMMMLLLLLLKKKJJJJJJKKKKKKLLLLLLKKKKKKIIIHHHFFFEEECCCCCCCCCCCCCCCCCCCCCCCCCCCDDDEEEFFFHHHIIIJJJKKKLLLKKKKKKKKKKKKIIIFFFDDDEEEDDDCCCCCCDDDEEEDDDCCC@@@??????@@@BBBCCCCCCAAADDDCCCAAA???===<<<;;;;;;===>>>AAACCCDDDDDDDDDCCCCCCCCCCCCDDDFFFGGGIIIJJJKKKJJJIIIJJJKKKKKKIIIGGGHHHHHHHHHGGGHHHHHHIIIJJJJJJIIIHHHFFFDDDCCCAAAAAADDDEEEFFFFFFEEECCCAAA???>>>>>>???@@@AAABBBCCCCCC@@@@@@@@@@@@@@@AAABBBCCCAAA>>>;;;;;;>>>@@@???>>>>>>?????????===<<<===>>>??????AAAAAABBBAAA@@@???===>>>>>>>>>????????????@@@@@@BBBCCCEEEGGGHHHIIIFFFGGGGGGGGGGGGFFFEEEDDD????????????>>>>>>======<<<<<<<<<;;;<<<<<<======>>>>>>>>>>>>===<<<;;;;;;============<<<:::888777777777777666666777888888999888888777777666555555:::::::::999888666555444333333222222222222333444555555555444333222222222444444555444444333222111333222111111111111111111111111111111111111111111000000000000////////////////////////..................---------...///////////////.......................................000000111111111111000000//////.........---------,,,,,,,,,,,,,,,,,,,,,,,,------------,,,,,,,,,,,,------------------------------............------++++++++++++++++++,,,,,,,,,,,,,,,++++++++++++***))))))))))))))))))))))))'''''''''''''''''''''''')))((((((((((((((())))))************))))))))))))((((((((()))))))))******))))))(((''''''''''''((())))))))))))))))))))))))))))))))))))))))))))))))888999999:::;;;;;;<<<<<<<<<<<<<<<<<<<<<<<<<<<<<>>=====================<<<<<<;;;<<<<<<<<<777999;;;;;;:::999:::;;;>>>===<<<;;;;;;;;;;;;<<<======<<<<<<<<<===>>>>>>??????>>>>>>======<<<<<<:::<<<>>>>>>===<<<===>>><<<;;;:::::::::<<<>>>???BBBBBBBBBAAA@@@???>>>===CCCDDDFFFGGGGGGDDDAAA???>>>???@@@???>>>=========:::===AAABBBBBB@@@??????>>>>>>???AAACCCDDDEEEFFFFFFFFFFFFFFFEEEEEEDDDDDDHHHJJJLLLLLLJJJGGGGGGFFFDDDEEEFFFHHHIIIJJJJJJJJJCCCDDDDDDEEEEEEFFFGGGGGGGGGGGGHHHJJJLLLNNNOOOOOOLLLIIIGGGFFFGGGHHHIIIIIILLLLLLKKKJJJIIIHHHHHHHHHCCCDDDFFFGGGHHHHHHHHHHHHEEEDDDCCCBBBBBBBBBCCCCCCDDDEEEFFFGGGHHHHHHGGGGGGIIIGGGFFFFFFGGGIIIHHHHHHJJJJJJKKKLLLKKKIIIGGGFFFEEEHHHJJJLLLLLLLLLMMMNNNMMMKKKIIIHHHHHHJJJLLLNNNNNNNNNOOOPPPQQQRRRSSSTTTUUUTTTQQQNNNLLLKKKKKKKKKKKKLLLOOOTTTWWWWWWSSSPPPNNNJJJGGGFFFHHHJJJIIIHHHDDDEEEGGGGGGFFFFFFGGGHHHIIIIIIIIIJJJJJJLLLMMMMMMOOONNNLLLKKKJJJKKKLLLLLLMMMMMMLLLJJJIIIGGGFFFEEEDDDDDDDDDCCCCCCCCCCCCCCCCCCDDDEEEGGGHHHJJJKKKLLLLLLKKKJJJJJJJJJIIIGGGEEEDDDDDDCCCCCCCCCCCCCCCBBB@@@@@@@@@@@@AAABBBBBBAAADDDCCCAAA???===<<<;;;;;;>>>???AAACCCDDDDDDCCCBBBCCCCCCDDDEEEHHHJJJLLLMMMNNNMMMLLLLLLLLLLLLJJJHHHHHHGGGGGGFFFGGGGGGHHHHHHHHHHHHGGGFFFEEEDDDCCCCCCEEEEEEFFFEEEDDDBBB@@@>>>>>>>>>???@@@AAACCCDDDDDDAAAAAAAAAAAAAAABBBBBBBBBAAA===999;;;@@@BBB@@@===<<<>>>???>>>======>>>???AAAAAABBBBBBBBBAAA@@@???======>>>>>>??????@@@@@@@@@AAABBBCCCEEEGGGHHHIIIGGGGGGFFFFFFEEEDDDCCCCCC@@@??????>>>>>>=========<<<<<<;;;;;;;;;;;;<<<<<<>>>>>>>>>===<<<;;;:::999::::::;;;::::::999888777888777666666666666666777888888777666555555555555888888888777666666555444222222222222222222333333444444444333333333222222555555555444333222111000111111000000000000111111111111111111111111111111000000000000////////////////////////............------,,,,,,,,,------.......................................///////////////000000000000000000///......---------,,,,,,,,,)))))))))))))))))))))))),,,,,,,,,,,,,,,,,,,,,,,,------------------------,,,------......------,,,*********++++++,,,,,,,,,,,,,,,+++++++++*********(((((())))))************(((((((((((((((((((((((())))))((((((((()))******************)))))))))(((((((((((()))))))))******(((((('''&&&&&&&&&&&&'''))))))))))))))))))))))))((((((((((((((((((((((((888888999999:::;;;;;;<<<<<<<<<<<<<<<<<<<<<<<<<<<>>>>>>============>>>>>>??????>>>===<<<<<<======777999;;;;;;:::::::::<<<>>>===<<<::::::;;;<<<<<<<<<<<<<<<<<<<<<===>>>>>>??????>>>>>>======<<<<<<;;;===??????>>>>>>>>>???<<<;;;:::999:::<<<>>>@@@BBBBBBAAA@@@??????>>>>>>CCCDDDEEEFFFFFFDDDAAA@@@@@@BBBDDDCCC@@@>>>>>>???999===@@@BBBBBB@@@@@@???>>>???@@@AAACCCDDDEEEEEEGGGGGGFFFFFFEEEDDDDDDDDDFFFHHHKKKKKKJJJHHHGGGFFFEEEEEEFFFGGGHHHGGGGGGFFFCCCCCCDDDEEEFFFGGGGGGHHHGGGJJJMMMOOOPPPNNNMMMLLLJJJHHHFFFEEEGGGIIIIIIIIIKKKKKKIIIHHHGGGGGGGGGGGGDDDEEEGGGHHHIIIIIIIIIHHHEEEDDDBBBAAA@@@AAABBBCCCEEEFFFGGGIIIIIIIIIHHHGGGJJJIIIGGGGGGIIIIIIIIIHHHIIIJJJLLLLLLLLLJJJHHHFFFIIIKKKLLLLLLJJJJJJJJJKKKLLLKKKJJJIIIIIIJJJLLLMMMLLLMMMNNNOOOPPPQQQRRRRRRRRRPPPNNNLLLJJJIIIIIIIIIMMMNNNQQQTTTUUUSSSPPPLLLJJJGGGCCCDDDGGGIIIHHHFFFCCCEEEFFFFFFFFFFFFHHHIIIIIIIIIIIIJJJLLLNNNPPPQQQQQQPPPNNNMMMLLLLLLMMMNNNNNNMMMLLLJJJIIIHHHGGGFFFFFFFFFFFFFFFEEEEEEDDDDDDEEEEEEFFFHHHIIIJJJKKKLLLLLLJJJIIIIIIIIIIIIGGGEEECCCCCCCCCCCCBBBAAAAAABBB@@@AAAAAAAAAAAAAAABBBBBBDDDCCCAAA@@@>>>=========???@@@BBBDDDDDDCCCBBBAAABBBBBBDDDEEEHHHKKKMMMNNNOOONNNLLLLLLMMMLLLJJJHHHFFFFFFEEEEEEEEEEEEEEEFFFGGGGGGGGGGGGGGGGGGGGGGGGDDDEEEEEEDDDCCCAAA???>>>===>>>???@@@BBBCCCDDDEEEBBBBBBCCCCCCBBBBBBBBBAAABBB>>>;;;<<<@@@BBB???<<<;;;===??????>>>???@@@BBB@@@@@@???>>>===<<<;;;:::<<<<<<===>>>??????@@@@@@@@@@@@AAABBBDDDEEEFFFGGGHHHGGGFFFDDDCCCBBBAAA@@@@@@@@@@@@???>>>======<<<<<<;;;;;;;;;;;;<<<<<<===?????????>>>===;;;:::999888999999999999999888888888777666666666666666777999888777666555555666666555555444444444555555555111111111222333333333333222222222333333333444444444444444444333222111000000000000//////000111111000000000000000000000000////////////000000000000////////////............,,,,,,++++++***++++++,,,,,,,,,------......//////......//////////////////...//////000000//////...------------,,,,,,,,,,,,------------------------,,,,,,,,,,,,,,,,,,,,,,,,------------------------,,,,,,------------,,,,,,*********++++++,,,,,,,,,+++*********))))))))))))((((((((()))******++++++))))))))))))))))))))))))))))))))))))******+++,,,************)))))))))((()))))))))*********++++++(((''''''&&&&&&&&&&&&&&&((((((((((((((((((((((((((((((((((((((((((((((((999888888888999:::;;;<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<;;;;;;<<<<<<===>>>?????????>>>===<<<<<<<<<<<<888:::<<<<<<;;;;;;<<<===???===;;;:::::::::<<<===;;;;;;;;;;;;<<<===>>>>>>???>>>>>>>>>>>>>>>>>>===<<<>>>????????????@@@BBB<<<;;;999999:::<<>>???AAABBBDDDEEEFFFCCCDDDDDDDDDCCCBBBAAAAAABBB???===>>>@@@AAA???<<<===???@@@@@@@@@@@@AAACCCBBBBBB@@@???>>><<<;;;;;;<<<<<<===>>>???@@@@@@AAA@@@AAAAAABBBBBBCCCDDDDDDGGGFFFEEECCCBBBAAA@@@@@@BBBAAAAAA@@@???>>>======;;;;;;;;;;;;<<<===>>>????????????>>>===<<<::::::888888888999999:::::::::777777777666666777888888:::999777666555555666777333333333333333444555555000111222333444444444333111111111222333444444444333333444333333222111000000000000000000000111222000000000000000000000000////////////000000000000////////////............,,,,,,+++*********++++++++++++,,,---.../////////////////////////////////......////////////............---------,,,,,,,,,////////////////////////++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------,,,,,,++++++++++++++++++,,,,,,*********)))))))))(((((((((((())))))*********+++***************************)))))))))***+++,,,---************)))))))))))))))))))))*********++++++(((((('''&&&&&&&&&&&&'''(((((((((((((((((((((((())))))))))))))))))))))))999888888888888:::;;;<<<<<<<<<<<<<<<<<<<<<<<<<<<999999999:::<<<===???@@@>>>===<<<;;;;;;:::::::::888:::<<<===<<<<<<===>>>???>>>;;;999999:::<<<===;;;;;;;;;;;;<<<===>>>>>>>>>>>>>>>???????????????===>>>???>>>===>>>AAACCC<<<;;;999888999<<>>>>>???;;;===???@@@@@@@@@AAABBBBBBBBBCCCCCCCCCDDDDDDDDDFFFFFFFFFEEEEEEEEEEEEEEEFFFIIILLLMMMKKKHHHFFFFFFGGGFFFEEEEEEDDDCCCBBBBBBBBBCCCDDDFFFFFFFFFEEEEEEHHHJJJLLLLLLJJJHHHIIIJJJGGGEEECCCCCCEEEHHHIIIIIIGGGFFFEEEDDDCCCDDDFFFGGGFFFGGGHHHIIIIIIIIIHHHGGGDDDDDDCCCBBBBBBBBBBBBBBBEEEGGGJJJLLLMMMLLLKKKJJJIIIHHHGGGGGGHHHHHHGGGEEEIIIJJJLLLMMMLLLKKKIIIHHHKKKLLLLLLKKKIIIIIIJJJKKKJJJJJJKKKKKKJJJIIIHHHGGGIIIIIIKKKMMMOOOPPPRRRSSSLLLKKKJJJIIIIIIIIIJJJKKKLLLNNNOOOOOONNNLLLJJJIIIDDDDDDEEEGGGHHHHHHFFFDDDCCCEEEGGGGGGHHHHHHJJJLLLLLLLLLMMMMMMNNNOOOOOOOOOTTTTTTTTTSSSRRRQQQPPPOOOPPPOOOMMMLLLKKKKKKKKKLLLKKKKKKKKKJJJIIIHHHHHHHHHHHHIIIIIIIIIJJJJJJJJJJJJIIIGGGFFFEEEFFFFFFEEEDDDBBBCCCDDDCCC@@@>>>???AAA>>>@@@BBBAAA???>>>???AAAAAAAAA@@@@@@@@@@@@AAAAAA@@@AAACCCDDDDDDCCCAAA@@@CCCDDDEEEGGGIIILLLNNNOOOLLLKKKJJJKKKKKKKKKIIIGGGFFFFFFEEEDDDDDDDDDDDDDDDHHHHHHGGGGGGFFFEEEEEEEEEBBBBBBBBBBBBAAAAAA@@@@@@===>>>???AAACCCDDDFFFFFFDDDEEEEEEEEEDDDCCCAAA@@@????????????@@@@@@??????AAABBBCCCBBB@@@???@@@AAACCCBBBAAA@@@@@@?????????======>>>???@@@AAABBBBBBBBBBBBBBBBBBBBBBBBBBBBBBDDDCCCBBBAAAAAABBBBBBCCCCCCCCCBBBAAA@@@???>>>>>>::::::;;;<<<===???@@@AAA>>>>>>>>>>>>===<<<;;;:::999999999999:::;;;<<<===777777777777777888999::::::999777555444555666777666555444333333333444555000111333444555555555444222222222222222222333333222222333333333222222111111000000000000111222333000000000000000000000000.../////////000000000111////////////...............------,,,++++++,,,,,,***++++++,,,...//////000111111000000//////......---......//////......---............------------------------------------******+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,------,,,,,,+++,,,,,,+++++++++++++++++++++++++++*********)))))))))))))))))))))*********))))))))))))))))))))))))((((((((())))))***+++,,,************))))))))))))((((((((()))))))))******)))(((((('''&&&'''''''''(((((((((((((((((((((((())))))))))))))))))))))))999888888777888:::;;;<<<<<<<<<<<<<<<<<<<<<<<<<<<777777888999;;;===???@@@===<<<;;;:::999888888999999;;;===>>>======>>>??????>>>;;;999999:::<<<>>>:::::::::;;;<<<===>>>???>>>>>>??????@@@@@@AAAAAA>>>>>>>>>===<<<>>>AAADDD<<<;;;999888999<<<@@@BBBBBBAAA@@@@@@AAABBBDDDEEECCCBBBAAA??????@@@AAABBBAAAEEEHHHGGGAAA======???;;;===?????????@@@BBBCCCDDDDDDDDDDDDDDDDDDDDDDDDEEEEEEEEEEEEEEEEEEFFFFFFGGGJJJMMMNNNKKKHHHEEEDDDFFFFFFDDDCCCCCCBBBBBBCCCBBBCCCDDDEEEEEEEEEDDDCCCGGGHHHIIIGGGEEEEEEIIILLLFFFDDDBBBBBBEEEGGGHHHIIIGGGFFFDDDCCCCCCEEEFFFHHHFFFGGGHHHIIIHHHHHHFFFEEEDDDDDDCCCCCCCCCBBBBBBBBBEEEGGGJJJMMMNNNMMMLLLKKKHHHGGGFFFGGGGGGGGGEEECCCIIIJJJLLLMMMMMMKKKIIIHHHIIIJJJKKKJJJIIIJJJLLLMMMIIIJJJKKKKKKKKKHHHFFFDDDHHHIIIKKKMMMOOOQQQSSSTTTLLLKKKJJJIIIIIIJJJKKKLLLKKKLLLMMMMMMLLLJJJJJJJJJCCCEEEHHHIIIIIIGGGFFFDDDCCCEEEGGGHHHHHHIIIKKKMMMNNNNNNNNNNNNNNNMMMLLLKKKUUUUUUVVVVVVTTTRRRPPPOOOPPPOOONNNLLLLLLLLLMMMMMMLLLLLLKKKJJJJJJIIIHHHHHHJJJJJJJJJJJJJJJJJJJJJJJJHHHGGGEEEDDDEEEEEEEEEDDDAAACCCDDDCCC???>>>???AAA===???AAA@@@===<<<>>>@@@@@@@@@??????@@@AAABBBBBBAAABBBCCCDDDDDDBBBAAA???EEEEEEFFFHHHJJJLLLNNNPPPKKKJJJIIIJJJKKKKKKIIIGGGGGGGGGFFFEEEEEEDDDEEEEEEJJJIIIHHHFFFEEECCCBBBAAAAAAAAAAAAAAAAAAAAAAAAAAA===>>>???AAACCCEEEFFFGGGEEEEEEFFFEEEEEECCCAAA@@@<<<>>>@@@@@@@@@???@@@AAAEEEFFFFFFDDD@@@>>>>>>???>>>>>>============>>>>>>>>>??????@@@BBBCCCDDDDDDDDDDDDCCCCCCBBBBBBBBBBBBAAA@@@@@@@@@AAACCCEEEFFFDDDDDDCCCBBBAAA??????>>>::::::;;;<<<>>>@@@BBBCCC============<<<;;;::::::999999999:::;;;<<<>>>???777777777777888999;;;;;;:::888666444333444555666999777666444333333333444111222333555666666555555444444333222222111111111111111222333333333222222111111000000111222333333000000000000000000000000.../////////000000111111000/////////............000///...---------------******+++,,,...///000000222111111000///......------..................---//////.........---------------------------------*********++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,------,,,,,,+++---,,,,,,++++++*********,,,,,,,,,+++++++++************))))))))))))))))))((((((((((((((((((((((((''''''''''''((()))++++++************))))))))))))''''''''''''((((((((()))))))))(((''''''''''''((((((((((((((((((((((((((())))))))))))))))))))))))::::::999999999:::;;;;;;===<<<;;;:::999999999999888999999:::;;;;;;;;;;;;;;;::::::999888777666666999999999999999999999999:::999888888888:::===>>>::::::;;;;;;<<<=========@@@AAAAAAAAA@@@???===<<<>>>>>>============>>>???;;;;;;;;;;;;;;;<<<===>>>@@@AAAAAA@@@??????@@@BBBAAA@@@??????>>>>>>??????BBBBBBAAA@@@???>>>===<<<;;;<<<===>>>@@@@@@AAAAAACCCDDDDDDDDDBBBBBBDDDEEECCCCCCCCCCCCDDDFFFGGGHHHGGGFFFFFFFFFEEEEEEDDDDDDCCCCCCBBBAAA@@@@@@@@@@@@BBBBBBCCCBBBBBBCCCGGGJJJJJJIIIHHHGGGFFFFFFFFFFFFCCCBBBAAAAAABBBCCCEEEFFFCCCBBBAAAAAABBBCCCEEEFFFHHHHHHHHHFFFDDDBBB@@@???BBBCCCCCCDDDCCCCCCBBBAAAKKKMMMNNNNNNLLLKKKLLLMMMGGGGGGGGGGGGGGGFFFDDDDDDFFFGGGHHHHHHIIIIIIHHHHHHKKKKKKKKKKKKKKKJJJIIIIIIOOOLLLHHHEEEDDDFFFHHHJJJSSSSSSRRRRRRRRRRRRSSSTTTSSSOOONNNRRRSSSNNNIIIGGGFFFIIILLLLLLJJJHHHIIIKKKFFFFFFFFFEEEDDDBBBAAA@@@BBBCCCDDDEEEHHHJJJLLLMMMJJJNNNQQQOOOKKKHHHJJJMMMRRRWWW\\\[[[VVVQQQPPPQQQPPPOOOMMMLLLLLLMMMOOOPPPPPPNNNKKKIIIGGGFFFGGGGGGGGGHHHHHHIIIJJJIIIIIIIIIGGGHHHIIIJJJIIIGGGEEECCCDDDDDDBBBAAA@@@?????????>>>???@@@@@@AAAAAAAAAAAA???BBBCCCBBB???===???AAAEEEEEEEEECCCAAAAAADDDFFFGGGHHHIIIKKKLLLMMMMMMMMMJJJJJJKKKKKKLLLLLLMMMMMMHHHIIIIIIGGGEEEDDDEEEFFFJJJHHHFFFCCCAAA@@@@@@@@@@@@???>>>???AAABBBAAA@@@??????@@@AAABBBCCCDDDEEEIIIHHHGGGEEEDDDDDDCCCCCCAAA@@@@@@@@@AAABBBBBBCCCDDDCCCAAA??????@@@AAABBBAAA@@@>>>======???@@@AAA???@@@BBBCCCDDDCCCBBBBBBEEEDDDCCCBBBBBBBBBBBBBBBEEEDDDCCCBBBBBBAAAAAABBBBBBBBBBBBCCCBBBBBBAAAAAA???????????????@@@@@@@@@======<<<;;;:::999999888;;;;;;:::999999999::::::777666555888<<<===<<<:::777777666666666666777777555555444444444333333333333333333222222333444444222222222111111000000000222111111000000111111222111111111111111000//////......////////////......////////////////////////111111000...---,,,+++***......---,,,,,,+++******)))***+++,,,...///000000------,,,,,,,,,+++++++++---------///111333222111---+++******,,,,,,+++)))++++++------------++++++))))))***++++++,,,------.........------,,,,,,,,,---------,,,,,,+++++++++************))))))))))))+++*********))))))((((((***)))((((((((()))+++,,,++++++******))))))(((((())))))))))))))))))))))))))))))************))))))******)))((((((((((((((()))((('''&&&&&&&&&&&&&&&&&&'''(((*********)))))))))))))))(((''''''&&&&&&999999999999999:::;;;<<<===<<<;;;:::999888888888999999::::::;;;::::::::::::999999888888777777777<<<<<<<<<<<<<<<<<<<<<<<<:::999888888888:::<<<===:::::::::;;;<<<<<<======??????@@@@@@???===<<<;;;<<<<<<<<<<<<<<<<<<<<<<<<:::::::::::::::;;;<<<<<<<<<===>>>>>>>>>>>>@@@BBBDDDCCCBBB@@@???>>>======????????????>>>>>>>>>>>><<<<<<>>>???@@@AAAAAAAAADDDEEEEEEDDDCCCCCCDDDFFFDDDCCCBBBAAAAAAAAAAAABBBEEEDDDDDDDDDCCCCCCCCCCCCBBBBBB@@@???????????????@@@@@@AAA@@@@@@AAADDDGGGIIIHHHGGGFFFEEEEEEEEEEEEBBBAAAAAA@@@AAABBBCCCDDDCCCBBBBBBBBBCCCDDDEEEFFFFFFFFFEEEDDDCCCBBBAAA@@@CCCCCCCCCDDDDDDDDDDDDDDDJJJLLLMMMMMMKKKJJJJJJKKKHHHHHHHHHGGGGGGFFFFFFFFFGGGHHHHHHIIIIIIIIIIIIIIILLLLLLLLLKKKKKKKKKJJJJJJOOOMMMIIIGGGFFFGGGJJJLLLPPPPPPPPPOOOOOOPPPPPPQQQPPPMMMNNNSSSUUUPPPIIIGGGIIILLLNNNNNNKKKIIIIIIJJJGGGFFFFFFDDDCCCBBBAAAAAACCCCCCCCCDDDGGGIIILLLMMMIIIMMMPPPPPPMMMLLLNNNQQQUUUYYY]]]\\\WWWRRRQQQRRRQQQPPPNNNMMMMMMNNNPPPQQQPPPOOOLLLJJJIIIHHHIIIJJJHHHIIIIIIJJJKKKKKKJJJJJJKKKKKKJJJIIIGGGDDDBBB@@@DDDDDDCCCBBBAAA@@@@@@@@@AAAAAABBBBBBBBBBBBAAAAAA===???AAAAAA@@@@@@BBBEEEDDDDDDCCCAAA@@@@@@CCCEEEFFFHHHIIIKKKLLLLLLLLLLLLLLLMMMMMMMMMLLLKKKJJJJJJFFFFFFGGGFFFDDDDDDEEEGGGIIIGGGEEECCCBBBAAAAAABBB@@@??????@@@BBBCCCCCCBBBAAABBBCCCDDDFFFGGGHHHIIIHHHGGGFFFEEEDDDCCCCCCCCC@@@@@@@@@@@@@@@AAABBBBBBDDDBBBAAA??????@@@AAABBBAAA@@@>>>>>>>>>???AAABBB@@@@@@AAABBBBBBBBBBBBBBBCCCDDDEEEFFFFFFEEECCCBBBFFFFFFEEEDDDCCCCCCCCCCCCAAABBBBBBBBBBBBBBBAAAAAA????????????????????????>>>>>>======<<<;;;;;;;;;<<<;;;::::::::::::::::::777666666888;;;<<<;;;999777777666666666666777777555555444444444333333333333333222222222333333444444444333333222222222222444333333333333333333444000111111111111000//////......////////////......000000000000000000000000111111000///...------,,,//////......---,,,,,,+++***++++++,,,---...///////////////.........------...------...000000///---,,,+++***+++,,,---,,,++++++,,,,,,,,,,,,,,,,,,+++*********+++,,,---------......---------,,,,,,,,,------,,,,,,,,,+++++++++************))))))))))))++++++++++++******))))))***)))((((((((()))++++++))))))(((((((((((((((((())))))))))))))))))))))))))))))************))))))***))))))((((((((((((((()))((('''&&&&&&&&&&&&'''(((((()))***))))))(((''''''''''''(((((((((((((((888888888999999;;;<<<<<<======;;;:::999888888888::::::::::::::::::999888888888888888888888888888<<<<<<<<<<<<<<<<<<<<<<<<::::::888888888999:::;;;999::::::;;;;;;<<<<<<===============<<<;;;::::::999:::;;;<<<<<<;;;:::999999999888888888999::::::===>>>@@@AAAAAABBBDDDFFFGGGFFFDDDAAA???===<<<;;;<<<<<<<<<======>>>>>>>>>======>>>???@@@AAAAAAAAACCCEEEFFFEEEDDDCCCDDDFFFFFFEEEEEEDDDDDDDDDDDDDDDBBBBBBBBBBBBAAAAAAAAAAAAAAA@@@???>>>>>>===>>>>>>===>>>>>>>>>>>>???BBBDDDGGGFFFEEEDDDCCCCCCCCCCCCAAAAAA@@@@@@@@@AAABBBBBBBBBBBBBBBBBBCCCDDDEEEFFFDDDCCCBBBAAAAAABBBCCCCCCEEEDDDDDDDDDDDDFFFGGGHHHJJJKKKMMMLLLJJJIIIIIIJJJJJJIIIHHHGGGGGGGGGHHHIIIIIIIIIIIIJJJJJJJJJJJJJJJNNNMMMLLLKKKKKKKKKKKKLLLNNNMMMJJJIIIIIIJJJMMMNNNSSSSSSSSSRRRRRRRRRRRRRRRMMMJJJKKKQQQTTTOOOJJJGGGJJJLLLNNNNNNKKKHHHGGGGGGHHHGGGEEEDDDCCCCCCCCCCCCDDDCCCCCCDDDFFFIIILLLNNNIIILLLPPPQQQPPPPPPSSSVVVXXX[[[^^^\\\XXXTTTRRRSSSQQQPPPNNNMMMMMMNNNPPPQQQQQQOOONNNLLLLLLLLLLLLMMMLLLLLLLLLLLLKKKKKKKKKKKKLLLKKKIIIHHHFFFDDDBBBBBBDDDDDDDDDCCCCCCBBBBBBBBBDDDEEEEEEDDDDDDCCCBBBAAA>>>???@@@@@@@@@AAACCCEEEBBBBBBAAA???>>>???BBBEEEFFFGGGJJJLLLMMMLLLKKKJJJNNNOOOOOOOOOMMMJJJGGGFFFDDDEEEEEEDDDCCCCCCFFFHHHGGGFFFDDDCCCBBBCCCCCCDDDAAA@@@@@@BBBDDDFFFFFFEEEFFFFFFFFFGGGIIIJJJLLLMMMGGGFFFEEEDDDCCCBBBBBBBBB@@@@@@??????@@@@@@AAAAAACCCBBBAAA@@@???@@@AAABBB@@@@@@???>>>???@@@BBBCCCAAAAAA@@@@@@@@@AAABBBCCCBBBDDDGGGIIIIIIGGGEEECCCHHHGGGFFFEEEDDDDDDDDDDDDAAAAAABBBBBBBBBBBBAAAAAA@@@@@@@@@??????>>>>>>===>>>>>>>>>>>>>>>>>>=========<<<;;;:::::::::::::::888777777999:::;;;:::888777777666666666666777777555555444444444333333333333333222222222222222333555555444444444444333333333333333333333333333333000000111111000000///.........////////////......111111111111111111111111111111000000////////////000000//////...---------,,,,,,,,,---------......///////////////.........///...------......,,,***,,,+++***+++---...---,,,,,,,,,++++++++++++,,,,,,***++++++,,,,,,------...------------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++************)))))))))))),,,,,,++++++++++++******)))))))))((()))******+++''''''''''''''''''((((((((((((((((((((((((((((((((())))))******))))))((())))))((((((''''''((((((((((((''''''&&&&&&''''''))))))***))))))'''&&&%%%&&&&&&''''''((())))))***777777888888999:::<<<<<<======;;;:::999888888888:::::::::::::::999888777666777777777888888888999999999999999999999999999:::999888888888888999999999999999:::;;;;;;<<<<<<;;;;;;;;;::::::999999999888:::;;;<<<<<<:::888777777777777666666777888888<<>>???@@@@@@BBBCCCDDDDDDCCCBBBCCCDDDCCCCCCDDDDDDFFFGGGIIIJJJAAAAAAAAAAAAAAAAAA@@@@@@AAAAAA@@@???>>>>>>>>>>>><<<===>>>>>>===>>>@@@BBBDDDDDDCCCBBBBBBBBBBBBBBBBBBBBBAAAAAAAAAAAAAAAAAA@@@@@@AAABBBCCCDDDDDDEEEDDDCCCAAAAAAAAACCCEEEGGGEEEEEEDDDDDDEEEHHHJJJLLLKKKMMMNNNMMMJJJIIIIIIIIIKKKIIIHHHGGGGGGHHHJJJKKKJJJJJJJJJJJJJJJKKKKKKLLLNNNNNNMMMLLLKKKLLLLLLMMMMMMLLLKKKKKKKKKLLLNNNPPPTTTTTTTTTTTTTTTSSSSSSSSSIIIEEEFFFKKKNNNLLLIIIHHHIIIJJJLLLMMMKKKIIIGGGFFFIIIGGGEEECCCCCCCCCEEEFFFEEEEEEDDDEEEGGGJJJNNNPPPLLLNNNRRRSSSSSSTTTVVVXXXYYYZZZ[[[ZZZVVVSSSRRRSSSPPPOOONNNLLLLLLNNNOOOPPPQQQQQQPPPOOOOOOOOOPPPPPPQQQPPPOOOMMMKKKJJJJJJIIIIIIHHHGGGFFFFFFFFFFFFFFFDDDDDDEEEEEEEEEEEEDDDDDDHHHHHHHHHGGGEEEDDDBBBAAABBBBBBBBBAAA@@@AAABBBCCC@@@@@@>>>===<<<===AAADDDFFFGGGJJJLLLMMMLLLKKKJJJNNNOOOPPPPPPNNNKKKGGGEEEEEEEEEDDDCCCAAABBBDDDFFFFFFEEEDDDCCCCCCDDDEEEFFFAAAAAAAAACCCFFFIIIIIIHHHIIIIIIHHHHHHHHHIIIKKKKKKEEEEEEDDDCCCBBBAAAAAAAAA@@@@@@?????????@@@@@@AAACCCBBBAAA@@@@@@@@@AAAAAA????????????@@@AAACCCDDDCCCBBB@@@>>>>>>@@@BBBCCCBBBDDDEEEGGGGGGGGGFFFEEEGGGFFFEEEDDDDDDCCCCCCDDD@@@@@@AAABBBBBBBBBAAAAAAAAA@@@@@@???>>>======<<<=========>>>>>>>>>??????======<<<;;;::::::::::::888888888999999999888777777777666666666666777777555555444444444333333333333222222111111111111222444444444444444444444444111111111111111111111111000000000000000//////.........////////////......111111111111111111111111/////////////////////////////////.........------------------------------------------------------///...------......---++++++******+++---///...------,,,+++******+++,,,---++++++,,,,,,,,,---------,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++++++++************)))))))))(((************************)))))))))))))))******+++&&&&&&&&&''''''(((((()))''''''''''''''''''''''''(((((())))))))))))(((((()))(((((('''''''''((((((((((((''''''''''''(((((()))))))))((((((''''''&&&''''''''''''(((((())))))888888888888999:::;;;<<<<<<<<<;;;:::999999999999::::::::::::999888888777666666666777888888999999777777777777777777777777999888888888777777888888888888999999:::;;;;;;;;;999999888888888888888888999:::<<<<<<<<<:::888777777666666555555555666666888:::<<<===<<<<<<<<<===??????===<<<;;;:::::::::;;;;;;;;;::::::::::::999;;;;;;::::::;;;<<<===>>>???AAABBBBBBAAA@@@@@@AAA?????????@@@BBBDDDEEEFFFAAAAAAAAAAAAAAAAAAAAAAAABBBAAA@@@??????>>>>>>???===???@@@@@@??????AAACCCBBBBBBAAAAAA@@@@@@AAAAAADDDCCCCCCCCCBBBBBBAAAAAA>>>???@@@AAABBBCCCCCCDDDDDDCCCBBBBBBBBBDDDGGGHHHEEEDDDDDDEEEGGGJJJMMMOOOMMMOOOOOONNNKKKIIIIIIIIIJJJIIIGGGGGGGGGIIIKKKMMMKKKKKKJJJJJJJJJKKKLLLMMMNNNMMMMMMLLLLLLLLLLLLLLLLLLLLLKKKKKKLLLMMMNNNOOOPPPPPPQQQQQQPPPOOONNNNNNHHHBBB@@@DDDHHHHHHHHHIIIIIIJJJLLLNNNOOOMMMJJJHHHHHHGGGEEEDDDCCCEEEFFFGGGFFFFFFFFFGGGIIILLLOOOQQQPPPRRRTTTUUUUUUVVVWWWXXXWWWWWWWWWUUUSSSQQQQQQQQQPPPNNNMMMLLLLLLMMMNNNPPPRRRRRRRRRRRRQQQRRRRRRRRRTTTSSSPPPMMMJJJHHHGGGGGGIIIHHHGGGGGGFFFGGGGGGHHHDDDDDDFFFGGGGGGGGGGGGGGGKKKKKKJJJIIIGGGEEECCCBBBDDDCCCAAA@@@AAABBBCCCDDD??????===<<<;;;===BBBFFFGGGIIIKKKLLLMMMLLLKKKJJJMMMNNNOOOPPPOOOLLLIIIGGGHHHGGGEEEBBB@@@???AAADDDEEEDDDDDDCCCDDDEEEFFFGGGBBBBBBBBBDDDHHHJJJKKKJJJKKKJJJHHHFFFEEEEEEFFFGGGEEEDDDCCCBBBBBBAAAAAABBBAAAAAA@@@@@@???@@@@@@AAABBBBBBAAAAAA@@@@@@@@@@@@?????????@@@BBBCCCDDDEEEDDDCCC@@@>>>>>>@@@BBBDDDDDDCCCBBBBBBCCCDDDFFFGGGEEEEEECCCBBBBBBBBBBBBBBB???@@@@@@AAABBBBBBAAAAAA@@@@@@??????>>>===<<<<<<<<<<<<<<<===>>>>>>??????======<<<;;;:::999999999888888999999888777777777777777666666666666777777555555444444444333333333333222111000000000000000222222222222222222333333000111111222222111111000000000000000000///............////////////......111111111111111111111111------............//////.........---------------...------------,,,,,,,,,,,,,,,------------------...------...000000///---+++***)))+++---......---,,,,,,***))))))***,,,,,,++++++,,,,,,,,,,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++************)))))))))(((((((((((()))))))))))))))((()))))))))************'''''''''(((((()))))))))&&&&&&&&&&&&&&&&&&&&&&&&(((((())))))))))))((((((((((((''''''''''''(((((((((((('''''''''(((((()))'''''''''''''''(((((()))))))))((((((''''''''''''999888888888888999::::::;;;::::::999999::::::;;;999999999999999999888777666666666777777888888888888888888888888888888888777777777777777888777777777888888999999::::::;;;888888777666666777777888::::::;;;;;;;;;999888777666666555444444444555555777999<<<<<<<<<;;;;;;;;;;;;::::::999999999999:::;;;;;;;;;::::::999999999::::::999888999:::<<<======???AAAAAA@@@?????????BBBAAAAAAAAAAAABBBCCCCCCAAAAAAAAAAAABBBBBBBBBBBBBBBBBBAAA??????????????????AAABBBBBBAAAAAABBBCCCAAAAAA@@@@@@@@@@@@AAAAAADDDDDDEEEDDDCCCBBBAAA@@@===>>>@@@AAACCCCCCDDDDDDEEEDDDDDDCCCDDDEEEFFFGGGBBBCCCDDDEEEHHHLLLOOOPPPOOOPPPPPPOOOLLLIIIIIIIIIHHHHHHGGGGGGHHHJJJKKKLLLKKKKKKJJJIIIIIIKKKLLLMMMLLLLLLMMMMMMMMMLLLKKKJJJJJJJJJKKKKKKLLLLLLLLLLLLPPPQQQQQQRRRQQQPPPNNNMMMHHHBBB???CCCHHHHHHIIIJJJKKKLLLNNNQQQSSSRRRNNNKKKGGGFFFFFFEEEEEEFFFGGGHHHEEEFFFGGGHHHJJJMMMOOOPPPSSSTTTUUUVVVWWWWWWWWWWWWSSSSSSQQQPPPOOOOOOPPPPPPPPPOOOMMMLLLLLLMMMOOOPPPTTTTTTTTTSSSSSSSSSSSSSSSTTTRRROOOKKKIIIGGGFFFFFFLLLLLLKKKIIIHHHGGGEEEEEECCCEEEGGGIIIJJJJJJJJJIIILLLLLLKKKJJJHHHFFFDDDCCCBBB@@@>>>???BBBFFFGGGHHH@@@???===<<<<<>>???@@@AAACCCDDDEEEFFFEEEDDDAAA??????@@@CCCDDDEEECCCAAA???@@@BBBDDDFFFDDDCCCBBBAAA@@@@@@@@@@@@>>>???@@@AAAAAABBBBBBAAA?????????>>>>>>======<<<<<<<<<======>>>>>>??????===<<<;;;:::999888888888666888999999888777777888777777666666666666777777555555444444444333333333222222111000////////////000000111111111111222222222333444555555444333222//////000000//////...---......////////////......111111111111111111111111---------...............---------------------------------------------------------...............---------...000000///...+++***)))***,,,---,,,+++++++++************++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,*********+++++++++++++++************))))))))))))'''''''''(((((((((((()))(((((()))************)))((((((((((((((()))))))))'''''''''''''''''''''''''''(((((())))))(((((('''''''''&&&&&&''''''((((((((((((''''''(((((())))))&&&&&&&&&&&&'''((()))******))))))(((''''''&&&&&&:::999999888888888888888999999999999:::;;;<<<<<<777888888999999999999888666666666777777777777777888888888888888888888888555555666777888888888888777777888888999:::::::::888777666666666666777888::::::999888888777666666777666555444444444444444666999<<<>>>>>>===>>>>>>:::999888888888888888888999999:::::::::::::::;;;;;;:::999888999:::<<<======???AAABBBAAA???>>>???BBBBBBBBBBBBBBBCCCDDDDDD@@@@@@@@@AAAAAABBBBBBBBBAAA@@@???>>>>>>===>>>>>>@@@AAACCCCCCBBBAAABBBCCCAAA@@@@@@@@@@@@@@@AAAAAADDDDDDDDDDDDCCCAAA???>>>>>>???AAACCCEEEEEEFFFEEEEEEEEEDDDDDDDDDCCCCCCCCC@@@AAACCCFFFJJJMMMOOOPPPOOOPPPPPPNNNKKKHHHGGGGGGEEEFFFGGGHHHIIIJJJKKKKKKKKKJJJIIIHHHHHHJJJLLLMMMJJJKKKMMMNNNMMMLLLIIIHHHHHHIIIJJJKKKKKKJJJJJJIIIQQQRRRSSSSSSRRRPPPNNNMMMHHHDDDDDDJJJNNNMMMKKKKKKLLLMMMNNNQQQSSSQQQMMMHHHFFFFFFFFFGGGGGGGGGHHHHHHBBBDDDFFFIIIKKKLLLLLLMMMTTTTTTUUUVVVXXXYYYYYYXXXQQQOOOMMMMMMMMMOOOOOOPPPRRRQQQOOONNNNNNOOOQQQRRRUUUUUUUUUUUUTTTSSSSSSRRRPPPNNNKKKIIIGGGGGGGGGHHHLLLLLLLLLLLLJJJIIIGGGEEECCCEEEHHHJJJLLLLLLLLLKKKLLLLLLKKKJJJHHHGGGEEEDDDCCC@@@>>>???CCCGGGIIIIIIAAA@@@>>>======@@@FFFJJJNNNMMMLLLLLLLLLMMMNNNOOOOOOOOOOOONNNMMMLLLKKKJJJIIIHHHFFFBBB@@@@@@CCCEEEFFFEEEDDDDDDDDDEEEFFFGGGDDDCCCDDDFFFIIIJJJKKKJJJIIIHHHEEEDDDCCCDDDFFFGGGEEEDDDCCCCCCCCCCCCCCCCCCDDDCCCBBBBBBAAAAAABBBBBBAAABBBBBBBBBAAAAAA@@@@@@===>>>@@@BBBDDDEEEFFFGGGFFFEEECCCAAAAAABBBCCCDDDDDDCCCBBBAAAAAAAAABBBCCCCCCBBBAAA@@@@@@??????@@@>>>>>>???AAAAAABBBBBBAAA>>>>>>>>>>>>>>>=========>>>>>>>>>???????????????<<<;;;:::999888777777777555777999999777666777999777777666666666666777777555555444444444333333333222222111000///......///000000000111111111222222111222444555555444222111//////000000//////...---......////////////......000000000000000000000000////////////....................................,,,---------------------,,,,,,,,,---------.........---------......---++++++)))))))))++++++***)))******++++++++++++************************************+++++++++,,,,,,,,,)))*********++++++++++++************))))))))))))'''((((((((())))))))))))'''((()))***+++******)))((((((''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((('''''''''&&&&&&&&&&&&'''((()))((((((((((((((()))******((('''&&&&&&&&&'''(((((((((((((((((((((''''''''';;;:::999888777777777777888888888999:::;;;===>>>666777888999999999999999777777777777777666666666777777777777777777777777444444666777888888888888777777777888999999::::::888777666555555666888888999999777666555555555555777666555444444444444444000444888:::;;;<<<<<<===;;;:::999888777777777777777888999:::;;;<<<======<<<;;;:::999999:::<<<======@@@BBBCCCBBB@@@??????;;;;;;<<<===???AAACCCDDD??????@@@@@@AAAAAAAAAAAA@@@???>>>======<<<<<<<<<@@@BBBCCCCCCBBBAAABBBCCCAAA@@@@@@@@@@@@@@@AAAAAACCCCCCCCCCCCBBB@@@>>><<>>@@@CCCGGGKKKMMMOOOPPPNNNOOOOOOMMMJJJGGGFFFFFFDDDEEEFFFHHHIIIJJJJJJJJJKKKJJJHHHGGGHHHIIIKKKMMMHHHJJJLLLNNNNNNKKKHHHFFFGGGHHHIIIJJJJJJIIIHHHGGGMMMNNNOOOOOOOOOMMMJJJIIIIIIGGGIIIPPPTTTQQQMMMKKKLLLKKKLLLOOOPPPNNNHHHCCCEEEEEEGGGHHHHHHHHHHHHHHH@@@BBBEEEHHHJJJKKKKKKJJJSSSSSSTTTVVVYYYZZZZZZYYYPPPNNNLLLKKKMMMOOOPPPPPPTTTSSSQQQPPPPPPQQQSSSTTTUUUUUUUUUUUUTTTSSSRRRRRRKKKJJJHHHGGGGGGGGGIIIJJJHHHJJJKKKMMMMMMLLLJJJIIICCCEEEHHHKKKMMMMMMMMMLLLLLLLLLKKKJJJIIIGGGEEEDDDGGGCCC@@@@@@BBBEEEFFFFFFBBBAAA???===>>>AAAGGGLLLPPPOOOMMMLLLLLLNNNPPPQQQRRRQQQOOONNNLLLKKKJJJIIIHHHGGGEEEBBB@@@AAAEEEHHHGGGFFFEEEDDDDDDEEEFFFGGGEEEDDDDDDFFFHHHJJJJJJIIIHHHGGGEEEDDDEEEGGGIIIKKKEEEDDDDDDCCCCCCCCCDDDDDDEEEDDDCCCBBBBBBBBBBBBBBBAAAAAABBBBBBBBBAAA@@@???===>>>@@@BBBDDDFFFGGGGGGFFFEEEDDDCCCBBBCCCCCCDDDCCCDDDDDDDDDCCCBBBAAAAAACCCCCCBBBAAA@@@@@@@@@@@@===>>>???@@@AAABBBBBBBBB============>>>>>>>>>>>>@@@@@@@@@@@@@@@@@@@@@@@@<<<;;;:::888777666666666444777999999777666888:::777777666666666666777777555555444444444333333333222222000///............000000111111111222222222///000222333333222000//////////////////......---......////////////......////////////////////////111000000000////////////////////////000000000000,,,,,,,,,---------......)))))))))******+++++++++///...---------,,,***(((+++)))((()))******)))((()))***+++,,,,,,+++***)))******))))))))))))))))))*********++++++,,,,,,,,,))))))******++++++++++++************))))))))))))(((((())))))*********+++'''((()))++++++******)))'''''''''&&&&&&%%%%%%%%%((((((((((((((((((((((((''''''((((((((((((''''''&&&&&&&&&&&&&&&'''((()))((((((((((((((()))*********)))'''&&&%%%%%%&&&'''&&&&&&''''''((()))))))))999888777666555555555555888888888888888888888888777777888888888999999999888777666666666777999:::888777777666666666666666888666444222111222333444777888999999888777888::::::666444555999;;;888555999999999888888888777777888888666555444444444444555777:::>>>??????>>>===;;;:::999999999999888777777888999999::::::999999:::999777666666777999:::<<<<<<<<<<<<============;;;<<<<<<===>>>??????@@@???>>>===>>>???@@@???>>>===<<<<<<;;;;;;===>>>???@@@@@@@@@@@@??????>>>======>>>???@@@AAABBBBBBBBB>>>???AAAAAAAAA???===<<>>>>>>>>???AAACCCDDDDDDCCCBBB@@@@@@@@@???????????????===>>>@@@AAA@@@???===<<<888999999999999888777777888999999999999888777777333333444444555444444444111333555666777666555444555444333222111111111111111111222222222333333333000000111111111222222222000000000000//////////////////.........---------000///---,,,,,,---///000////////////////////////111000///...............------,,,,,,,,,,,,+++++++++)))&&&'''***------,,,---------...------,,,,,,,,,,,,++++++***)))))))))************************+++******)))))))))))))))+++***)))(((((()))***+++************************+++***((('''((()))((('''((((((''''''((()))***+++%%%%%%%%%&&&''')))+++---((((((((((((((((((((((((((((((''''''''''''((((((&&&''''''(((''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''((('''&&&%%%%%%&&&'''(((888888777666555555555666888888888888888888888888666666666777777777888888777777666666666777888999888777666666555555666666777555444222222333444555666888999888777777888999888555333555:::<<<:::777999999999888888777777777:::999888777666666666666444666999<<<>>>>>>===<<<;;;:::888999::::::999888777777888999999999999888:::999888777777888999:::<<<<<<<<<<<<============;;;<<<<<<===>>>>>>??????>>>===<<<===?????????===>>>===<<<<<<<<<===???@@@===>>>???@@@@@@@@@???>>>===>>>???@@@AAAAAAAAAAAA???@@@AAABBBAAA???>>><<>>>>>>>>>>>???AAACCCDDDCCCAAA???@@@CCCIIIMMMNNNSSSPPPLLLLLLNNNPPPQQQPPPQQQPPPNNNMMMKKKJJJJJJJJJJJJGGGDDDCCCDDDFFFGGGGGGFFFDDDCCCBBBCCCEEEGGGIIIFFFFFFFFFHHHIIIIIIGGGEEEEEEEEEEEEFFFGGGHHHIIIJJJIIIGGGEEECCCBBBBBBCCCCCCEEEEEEDDDDDDCCCCCCCCCCCC???@@@AAAAAABBBBBBAAAAAA@@@@@@@@@@@@AAACCCDDDFFFEEEEEECCCCCCCCCDDDFFFGGGEEEDDDCCCCCCBBBBBBCCCCCCCCCBBBBBBAAA@@@???>>>>>>===???AAACCCCCCCCCBBBAAA>>>>>>>>>>>>>>>>>>>>>>>>;;;<<<===>>>>>><<<;;;:::999999999999999888777777777888888888888777666666333444444555555444444444222333555666666666444333444333222111000000000000111111111111222222222333000000111111111222222222000000000/////////......//////.........---------000...---,,,,,,---...000........................000000///...............------,,,,,,,,,,,,++++++,,,)))'''(((+++------,,,,,,---------------,,,,,,******************++++++************************+++******)))))))))))))))******))))))))))))******************************+++)))((('''((()))((('''***))))))(((((((((((((((''''''&&&&&&'''((()))***((((((((((((((((((((((((((((((''''''''''''(((((('''''''''''''''''''''&&&''''''''''''&&&&&&%%%%%%''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''((('''&&&&&&&&&&&&'''(((777666666555555555666666888888888888888888888888555555555555666666666666666666555555666666777888777666666555555555555555555444333333333444666777777888999888777666777888666444333666:::<<<;;;999888888888888777777777777:::999888777777666666777444666999;;;<<<<<<;;;::::::999888999:::;;;:::999666777777888999888888888:::999888777777888999:::;;;;;;<<<===============;;;;;;<<<<<<===>>>>>>>>>===<<<;;;<<<>>>???>>>===>>>>>>===<<<===>>>???@@@;;;<<<>>>@@@AAA@@@???>>>>>>>>>???@@@AAAAAAAAAAAAAAAAAABBBBBBAAA@@@>>>===@@@BBBCCCEEEFFFFFFFFFEEEHHHGGGEEECCCCCCCCCEEEFFFHHHHHHIIIKKKNNNOOONNNMMMLLLMMMLLLJJJGGGFFFGGGHHHCCCDDDFFFHHHKKKMMMNNNNNNJJJHHHGGGIIILLLMMMJJJGGGDDDEEEFFFEEECCCCCCCCCEEEFFFFFFGGGHHHHHHHHHHHHHHHHHHGGGFFFFFFFFFHHHKKKLLLLLLMMMMMMJJJGGGEEEDDDEEEGGGHHHKKKLLLMMMKKKIIIGGGHHHGGGFFFFFFFFFGGGHHHIIIJJJIIIJJJLLLPPPSSSSSSSSSQQQRRRTTTUUUVVVVVVVVVUUUQQQQQQQQQSSSUUUTTTRRRPPPKKKJJJJJJIIIHHHHHHIIIIIIOOONNNMMMLLLKKKJJJIIIHHHEEEEEEEEEDDDDDDDDDDDDDDDBBBEEEHHHJJJHHHFFFEEEEEEHHHIIIIIIJJJJJJIIIIIIHHHCCCBBBBBBBBBCCCCCCAAA@@@<<<<<<<<<===???AAACCCDDDDDDBBBBBBDDDHHHLLLOOOPPPPPPNNNMMMMMMOOOQQQQQQQQQQQQPPPNNNLLLJJJIIIHHHGGGHHHFFFEEEEEEFFFGGGGGGFFFCCCCCCCCCDDDEEEGGGIIIJJJFFFFFFFFFGGGIIIHHHEEECCCEEEEEEFFFGGGHHHJJJKKKLLLIIIHHHFFFDDDCCCCCCDDDDDDFFFFFFEEEDDDCCCBBBBBBAAA???@@@@@@AAAAAAAAAAAAAAA??????@@@AAABBBCCCDDDDDDDDDCCCBBBBBBBBBCCCDDDEEEDDDCCCBBBBBBBBBBBBBBBBBBCCCCCCBBBAAA@@@???>>>>>>===>>>@@@AAABBBAAA@@@@@@<<<<<<<<<<<<<<<<<<<<<<<<999:::;;;;;;;;;:::888777999999999999888888777777777777777777777666555555444444555555555444444333333444555666555444333222333222111000/////////000000000000111111111222222000000000111111111111222/////////.........------...............---------///...---,,,,,,---...///......................../////////...............------,,,,,,,,,,,,++++++,,,***)))***,,,---------,,,,,,------------,,,,,,((())))))***++++++,,,,,,************************+++******)))))))))))))))))))))************))))))************************+++)))''''''((()))(((''')))((((((((((((((((((((()))(((((('''''''''(((((())))))))))))))))))))))))((((((''''''''''''((((((''''''&&&&&&&&&''''''((((((((((((''''''''''''&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''((('''&&&&&&&&&&&&'''(((555444444444555555666777666666666666666666666666555555555555555666666666555555555555555666666666666555555444444444444444333333333333444666777888888999:::999888777888999777666555666999;;;:::999777777777777777777777777777777666555555555555555666777999;;;<<<;;;;;;:::999888888999;;;<<<;;;:::777777888999999999999888:::999888888888888999:::999:::;;;============<<<;;;;;;;;;<<<<<<=========;;;::::::;;;===>>>===<<<===<<<<<<;;;<<<===>>>???;;;<<>>>>>???@@@@@@@@@@@@@@@AAABBBBBBBBBAAA@@@>>>>>>AAABBBCCCDDDEEEDDDCCCCCCDDDCCCAAAAAABBBDDDGGGIIIJJJJJJKKKMMMOOOPPPNNNMMMKKKKKKKKKIIIGGGEEEFFFGGGCCCEEEHHHJJJKKKLLLKKKKKKGGGFFFFFFGGGJJJKKKIIIGGGFFFGGGHHHGGGFFFEEEFFFGGGEEEGGGHHHHHHHHHHHHHHHIIIFFFEEEDDDDDDEEEHHHJJJLLLNNNNNNMMMJJJFFFDDDEEEFFFGGGHHHJJJLLLLLLKKKIIIHHHIIIHHHFFFEEEEEEFFFHHHIIIHHHHHHIIIKKKMMMOOOPPPQQQQQQRRRTTTUUUVVVUUUTTTSSSPPPQQQRRRUUUVVVTTTQQQMMMHHHHHHHHHGGGGGGHHHHHHIIIOOOOOOMMMLLLJJJHHHGGGFFFCCCCCCDDDDDDDDDDDDDDDDDDCCCFFFJJJLLLKKKHHHGGGFFFIIIIIIJJJIIIIIIHHHGGGGGGEEECCCBBBCCCFFFGGGDDDAAA;;;<<<===???@@@BBBDDDEEEDDDCCCDDDGGGKKKOOOQQQQQQMMMMMMNNNOOOQQQRRRRRRRRRQQQPPPNNNKKKIIIGGGFFFFFFFFFEEEEEEFFFHHHHHHGGGFFF@@@AAACCCEEEGGGIIIIIIJJJIIIGGGEEEEEEFFFGGGFFFEEEGGGGGGGGGGGGHHHJJJKKKKKKIIIHHHGGGFFFEEEEEEEEEEEEFFFFFFEEEDDDCCCBBBAAA@@@??????@@@AAAAAAAAAAAA@@@>>>???@@@AAACCCCCCCCCCCCCCCBBBBBBAAAAAABBBCCCCCCCCCBBBBBBAAAAAAAAABBBBBBCCCCCCBBBAAA@@@??????>>>===>>>??????@@@??????>>>::::::::::::::::::;;;;;;888999999:::999888777777999999999888888888888888777777888888777777666555555555555555555444444333444444555555444333222111111111000//////////////////000000000000111111111000000000000111111111111///.........------------........................///...------------...///.............................................---------,,,,,,,,,+++++++++,,,+++++++++,,,---------++++++,,,---------,,,,,,))))))*********+++++++++************************+++******)))))))))))))))((()))***++++++***)))(((***************************)))''''''((())))))(((&&&&&&'''(((((()))))))))(((((('''''''''((((((((())))))))))))))))))))))))(((''''''&&&&&&''''''(((''''''&&&&&&&&&'''(((((((((((((((((((((((((((''''''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&'''''''''333333333333444666777777444444444444444444444444666666666666666666666666333333444444555555555555555444444333333333333333222222333444555777888999:::;;;<<<;;;999888999:::888777777777777888777666666666666666666666666666777666666555555555555666888999:::;;;<<<<<<;;;;;;999777777888:::;;;:::999777888888999999999999999888888888888888888888888888999;;;===>>>======<<<;;;;;;;;;;;;<<<<<<<<<<<<;;;:::999:::===>>>===<<<;;;;;;:::999:::;;;<<<======>>>?????????===;;;999>>>>>>???@@@@@@@@@??????AAAAAAAAAAAA@@@@@@??????AAABBBCCCDDDDDDCCCBBBAAA>>>>>>===>>>@@@DDDHHHKKKJJJJJJKKKMMMOOOOOONNNLLLIIIJJJJJJHHHFFFEEEEEEGGGEEEFFFHHHJJJJJJHHHFFFEEEEEEDDDEEEFFFGGGHHHGGGFFFGGGHHHIIIHHHGGGGGGHHHIIIFFFHHHJJJJJJHHHGGGHHHIIIEEEDDDDDDDDDFFFHHHKKKMMMOOOOOONNNKKKHHHFFFGGGHHHGGGHHHJJJKKKLLLKKKJJJIIIIIIHHHFFFEEEEEEFFFHHHIIIGGGHHHJJJKKKMMMNNNPPPQQQTTTUUUUUUUUUTTTRRRPPPOOOQQQQQQSSSUUUUUUSSSNNNJJJIIIIIIHHHHHHIIIIIIJJJKKKPPPOOOMMMLLLJJJHHHFFFEEECCCCCCDDDFFFFFFFFFFFFEEEEEEIIIMMMNNNMMMKKKIIIHHHIIIIIIIIIIIIHHHGGGFFFEEEEEECCCCCCEEEHHHIIIFFFBBB===>>>???AAACCCEEEFFFGGGCCCCCCDDDGGGKKKNNNOOOOOOJJJLLLOOORRRSSSRRRRRRRRRQQQOOOMMMKKKIIIGGGFFFEEEFFFEEEEEEGGGHHHHHHFFFDDD@@@AAACCCFFFGGGHHHHHHHHHKKKHHHDDDBBBCCCFFFHHHIIIIIIIIIHHHGGGGGGGGGHHHHHHHHHHHHGGGFFFFFFFFFEEEEEEEEEEEEDDDCCCBBBAAA@@@???>>>???@@@@@@AAAAAA@@@@@@===>>>@@@AAABBBCCCCCCCCCBBBBBBAAAAAAAAAAAAAAABBBBBBBBBAAAAAAAAABBBBBBCCCDDDCCCCCCBBBAAA@@@??????>>>>>>>>>>>>>>>>>>======888888999999:::::::::;;;:::::::::::::::999888888:::999888777777777888888888888999999888888777666555666666666555555444333444444444333333222111111000000//////...////////////000000000000111111111000000000000000000000000///.........---------------..............................------.................................,,,---......///...------------,,,,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,---***++++++,,,------,,,,,,+++++++++*********))))))************************+++******)))))))))))))))((()))***++++++***)))((())))))))))))))))))))))))***((('''''')))***)))((('''(((((()))((('''&&&&&&&&&&&&'''(((((()))))))))((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&'''(((((('''(((((((((((((((((((((''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&111111111222444666777888333333333333333333333333666666666666666555555555222222333444444444444333444333333222222222222222111222333555666777888999:::;;;<<<;;;999888888999888777777666666555444444555555555555666666666666888888777777777777888888::::::;;;;;;;;;;;;;;;:::888777666777888999888777666777888888999999888888777777777777777777777777777888;;;===>>>===<<<<<<;;;;;;;;;;;;;;;;;;;;;;;;:::999999;;;===>>>>>>===::::::999888999:::;;;<<<@@@??????>>><<<;;;999999>>>>>>???????????????>>>???????????????@@@@@@@@@@@@AAABBBCCCCCCBBBAAA@@@;;;;;;;;;<<>>??????@@@@@@@@@@@@@@@>>>>>>???@@@AAABBBCCCCCCBBBBBBBBBBBBAAAAAAAAAAAABBBBBBBBBBBBBBBBBBCCCDDDDDDDDDCCCBBBAAA@@@???????????????>>>============888999999::::::;;;;;;<<<<<<;;;;;;;;;::::::::::::;;;:::888777777777888999999999999999999888777777666666666666666555444333333333222222222222222222000000////////////000000000000000111111111222222111000000000000000///////////////.........---------------.......................................------------------------+++,,,---//////...------------,,,,,,,,,,,,++++++***+++------,,,++++++,,,)))***+++,,,,,,------,,,,,,,,,++++++***))))))(((************************+++******)))))))))))))))))))))************))))))))))))))))))))))))))))))***((('''''')))******)))*********)))(((%%%###!!!%%%&&&'''((())))))))))))((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''$$$%%%&&&'''((((((((((((&&&''''''''''''(((((((((''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&'''(((((('''&&&&&&//////000222444666888999444444444444444444444444555555555555444444444333111111333444444444333222333333222111111111111111222333444555777888888888999::::::999777666666777555555666555444444444555444444444555555666666666888888777777777777888888:::::::::::::::999999999888777555666777777666555444555555666777666666666555555666666666666555555666888:::===>>>>>><<<;;;::::::::::::::::::::::::;;;::::::;;;>>>??????>>>;;;:::999999999:::;;;<<>>===;;;::::::;;;;;;>>>>>>????????????>>>>>><<<<<<<<<===>>>???AAAAAA???@@@AAABBBBBBAAA@@@@@@<<<<<<<<<>>>???AAACCCDDDGGGFFFGGGJJJLLLMMMLLLJJJGGGHHHHHHFFFDDDCCCDDDFFFFFFGGGGGGGGGGGGEEEDDDCCCFFFGGGHHHHHHGGGFFFFFFFFFCCCEEEFFFFFFEEEEEEFFFGGGKKKNNNPPPNNNIIIFFFGGGIIICCCEEEGGGJJJLLLMMMNNNNNNLLLMMMOOONNNLLLJJJJJJJJJGGGHHHIIIJJJKKKKKKKKKKKKKKKKKKKKKKKKJJJJJJJJJIIIIIILLLPPPQQQRRRSSSWWWZZZWWWUUUSSSQQQOOOOOOPPPPPPLLLMMMNNNPPPRRRRRROOOMMMNNNNNNMMMLLLLLLLLLMMMMMMLLLKKKJJJIIIGGGFFFEEEDDDCCCDDDFFFHHHJJJJJJIIIHHHHHHJJJKKKKKKHHHFFFEEEEEEDDDEEEEEEEEEEEEEEEDDDCCCAAADDDFFFGGGFFFDDDCCCBBBAAABBBDDDEEEFFFGGGGGGFFF@@@???>>>???BBBEEEGGGGGGHHHMMMSSSVVVUUURRRPPPPPPPPPOOOMMMKKKJJJIIIHHHHHHHHHFFFDDDDDDDDDDDDBBBAAADDDDDDDDDCCCCCCCCCCCCCCCCCCAAA@@@@@@CCCEEEFFFFFFEEEEEEDDDCCCCCCCCCDDDDDDFFFFFFFFFFFFFFFFFFEEEDDD@@@@@@@@@?????????>>>>>>>>>>>>???@@@@@@@@@@@@@@@??????>>>>>>@@@AAACCCDDDBBBBBBBBBBBBBBBAAAAAA@@@CCCCCCBBBBBBCCCCCCDDDEEEDDDDDDCCCBBBAAA@@@@@@???AAA@@@???>>>============999999:::;;;;;;<<<=========<<<;;;;;;::::::;;;;;;;;;:::888777666777888999888888888888888777777666777777777777666555444333111111111111111222222333111000000//////000000111111111111111222222222333111111000000////////////000000000/////////......---------.........//////---..................---------------------------***+++---//////...---,,,------,,,,,,,,,,,,++++++(((+++------+++)))***+++))))))***,,,,,,------,,,++++++******************************************+++******)))))))))))))))******))))))))))))******)))))))))))))))))))))))))))(((&&&''')))******)))''''''))))))((('''%%%$$$&&&'''((())))))(((''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''"""$$$''')))***)))'''&&&%%%%%%&&&&&&''''''''''''''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&'''(((((('''&&&&&&...///000111333666888999555555555555555555555555444444444333333222222222000111222333444333222222333222222111000111111111222333444666777888888888777888999888555444444555222333444444444444555666444444444555555555666666666666555555555555666777999999999888888888888888888666555555666666555333222333444444555555444444444444555555555555444444555777:::===>>>>>><<<;;;::::::::::::::::::::::::;;;::::::;;;>>>@@@??????;;;;;;:::999:::;;;<<<===>>>===;;;::::::;;;<<<>>>>>>>>>?????????>>>>>>===:::;;;;;;<<<===???AAABBB>>>???@@@AAABBBAAA@@@@@@>>>>>>??????@@@@@@@@@@@@EEEEEEFFFIIIKKKLLLKKKJJJFFFGGGGGGFFFDDDCCCDDDFFFFFFFFFGGGGGGGGGFFFFFFEEEHHHIIIJJJJJJHHHGGGGGGGGGDDDFFFGGGGGGFFFFFFGGGIIIMMMPPPRRROOOIIIFFFGGGIIICCCEEEHHHLLLNNNOOOOOOOOOIIILLLNNNOOOMMMKKKJJJJJJGGGHHHIIIJJJKKKKKKKKKKKKMMMMMMNNNNNNMMMLLLKKKJJJHHHLLLPPPQQQRRRTTTWWW[[[VVVTTTQQQOOONNNPPPQQQSSSIIIJJJKKKNNNQQQRRRQQQOOOOOOOOONNNMMMMMMMMMMMMMMMJJJIIIHHHGGGFFFDDDCCCCCCBBBDDDFFFIIIJJJJJJIIIIIIGGGHHHIIIGGGDDDBBBBBBBBBCCCCCCDDDDDDDDDDDDCCCCCCBBBFFFJJJJJJGGGDDDCCCDDDAAABBBDDDFFFFFFFFFFFFEEE???===<<<<<>>AAADDDEEEDDDBBBBBBBBBBBBBBBBBBCCCDDDEEEEEEEEEFFFFFFFFFEEEEEEDDD?????????>>>>>>>>>>>>>>>>>>>>>???@@@@@@@@@@@@???@@@???>>>===???AAACCCEEECCCCCCCCCCCCBBBBBBAAA@@@CCCCCCCCCCCCCCCDDDEEEFFFDDDDDDCCCBBBAAA@@@@@@???BBBAAA@@@>>>============::::::;;;<<<<<<===>>>>>>===<<<;;;;;;::::::;;;;;;;;;:::888666666777888999777777777777777666666555777777777777666555444333111000000000111222333333111000000000000000111111111222222222222333333333111111000000/////////...000000000000////////////---------.........//////------............------------------------------***+++---//////...---,,,---------,,,,,,,,,++++++'''***------***((()))***((()))***+++,,,---------)))))))))***++++++,,,,,,************************+++******)))))))))))))))+++***)))(((((()))***+++)))))))))))))))))))))))))))(((&&&''')))******))) """%%%(((************((())))))))))))'''%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''!!!$$$'''***+++)))'''%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&'''(((((('''&&&%%%111222222333333444444555444333333333333444555555777777666444333222111000333333222111111222333333333222111/////////000111000111222444555666666666666777777666444222333444444333333333333444555555555555444333444555666777666666666666666666666666666888999999777666777777777555333333444444333222444444555555555555555555333444444444555666666666555666777999::::::::::::888888888777666777999;;;???>>><<<;;;<<<===???@@@;;;<<<<<<<<<<<<<<<<<<<<<;;;<<<<<<;;;999888999:::???===<<<:::999999::::::;;;;;;;;;<<<===>>>??????===>>>@@@AAABBBBBBAAAAAAAAAAAA@@@???>>>???CCCFFFFFFFFFHHHJJJMMMNNNLLLJJJFFFDDDAAA??????AAADDDFFFEEEDDDBBBCCCEEEGGGHHHHHHGGGGGGFFFFFFEEEFFFFFFGGGLLLEEEAAAEEEGGGDDDCCCFFFJJJIIIIIIIIIJJJIIIFFFCCCFFFHHHKKKNNNNNNNNNLLLKKKIIILLLQQQRRRPPPMMMKKKJJJIIIHHHGGGHHHJJJKKKJJJIIINNNOOOOOOOOONNNLLLKKKJJJOOOQQQSSSVVVWWWWWWVVVVVVXXXSSSOOOOOORRRSSSQQQNNNKKKLLLLLLMMMOOOPPPQQQQQQLLLNNNPPPQQQPPPOOOOOOPPPJJJJJJIIIHHHFFFEEEDDDDDD???CCCHHHJJJJJJHHHFFFFFFFFFDDDBBB@@@???@@@AAABBB???BBBEEEGGGFFFDDDCCCCCCEEEFFFGGGHHHHHHGGGFFFEEEAAACCCEEEFFFEEECCC@@@???=========>>>???@@@AAABBBCCCKKKUUUZZZWWWQQQNNNMMMNNNMMMJJJHHHGGGHHHIIIJJJLLLIIIGGGEEEEEEDDDBBBAAAAAA@@@@@@???>>>?????????>>>===<<<===@@@AAA???============>>>@@@BBBEEEFFFFFFEEEEEEDDDBBBAAA@@@@@@>>>>>>???@@@AAABBBBBBCCC??????@@@@@@@@@??????>>><<<===???AAABBBDDDDDDEEEHHHHHHEEEBBB???@@@BBBEEEDDDDDDEEEFFFFFFFFFFFFFFFDDDDDDCCCBBBAAA@@@@@@???BBBAAA@@@>>>===<<<<<<<<<999;;;<<<===<<<===>>>@@@>>>>>>>>>===<<<<<<;;;;;;:::::::::999999999888888666666666666666555555444333222111111000000111111111111000000000000111111000000000000////////////...///111222333333222222222222333333222111///...////////////............+++,,,---...////////////++++++,,,,,,---...//////---------...............///......---------.........---,,,+++***+++,,,,,,***++++++,,,,,,++++++***,,,,,,,,,++++++*********+++******)))))))))))))))))))))************))))))+++*********))))))((((((******++++++++++++******************))))))))))))''''''''''''((((((((()))((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&%%%$$$"""!!!111111222222333444444444333333333333333444555555777666555555444333222222333222222111111222222333333222000/////////000111000111222444555666666666555666777666333222333444444333333333333444555555555444444333444555666777555555555555555555555555555777888888777666666777777555333333444444444222555555444444333333222222444444444444555555555555444555555777888999::::::999::::::999888999;;;===>>>>>>>>>>>>======<<<;;;;;;;;;;;;;;;;;;;;;;;;;;;:::<<<<<<;;;999888999:::===<<<;;;999999999::::::;;;;;;<<<<<<=========>>>>>>>>>???@@@AAAAAAAAA@@@BBBBBBAAA@@@???@@@CCCEEEDDDDDDFFFHHHKKKKKKJJJHHHDDDCCCAAA???@@@AAADDDEEEGGGEEEDDDDDDGGGHHHIIIIIIGGGGGGFFFFFFGGGHHHHHHIIIKKKEEEBBBEEEGGGEEEDDDFFFFFFFFFEEEFFFGGGFFFDDDBBBFFFHHHKKKMMMNNNMMMKKKJJJGGGKKKOOOPPPOOOLLLJJJIIIIIIHHHHHHIIIJJJKKKKKKIIIOOOOOOQQQQQQQQQQQQPPPOOOPPPRRRTTTVVVWWWWWWWWWVVVVVVRRRNNNOOORRRSSSQQQNNNMMMNNNNNNOOOPPPPPPPPPPPPMMMOOOQQQQQQOOONNNNNNNNNJJJJJJIIIHHHGGGFFFEEEEEECCCEEEHHHHHHHHHGGGHHHIIIHHHGGGDDDBBB@@@@@@AAABBBBBBEEEHHHIIIHHHGGGFFFFFFGGGGGGHHHHHHGGGEEEDDDCCCAAABBBDDDDDDDDDBBB???>>>::::::999:::;;;<<<>>>???DDDLLLUUUXXXVVVQQQOOONNNLLLKKKJJJHHHHHHHHHIIIIIIJJJHHHEEEDDDDDDCCCBBB@@@@@@???>>>>>>===>>>>>>>>>???======>>>AAABBB@@@>>>>>>>>>>>>???AAACCCEEEFFFFFFEEEDDDCCCAAA@@@@@@???>>>>>>??????@@@AAAAAAAAA?????????@@@@@@??????>>>:::;;;>>>AAADDDFFFHHHHHHGGGGGGFFFCCCAAA@@@BBBDDDDDDDDDEEEFFFFFFFFFFFFFFFEEEDDDCCCCCCBBBAAA@@@@@@AAAAAA???>>>===<<<<<<<<<<<<===>>>>>>>>>>>>???AAA>>>>>>======<<<;;;;;;;;;999999888888888777777777666666666666666555444444333222222111111111111111111111000000000000111111000000000000////////////...///111222333333222222222222333333222111///...////////////............,,,,,,---...////////////++++++,,,------.../////////............---------,,,,,,,,,,,,,,,---...///...---,,,+++++++++,,,,,,+++,,,,,,------,,,,,,+++,,,++++++++++++++++++***,,,+++******))))))************++++++++++++******************)))))))))((()))******++++++******)))*********)))))))))((((((''''''''''''((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''((('''&&&%%%$$$111111111222333333444444333333222222333333444555555555555555444444444333333222111111111111222333222111000000///000000000000111222444555555555555444666666555333222222333333333333333333444555555444444444333444555555666555555555555555555555555333555777777555444555666666444333333444444444333555555444333222111111000555555555555444444444444333333333333555777999::::::;;;<<<;;;::::::<<<>>>===>>>???@@@>>><<<:::888::::::::::::::::::::::::999:::;;;;;;999888999:::;;;:::999888888999:::;;;;;;;;;<<<<<<<<<<<<<<<;;;??????>>>>>>>>>??????@@@CCCDDDCCCAAA@@@@@@BBBDDDBBBBBBCCCFFFHHHHHHFFFDDDBBBAAAAAA@@@AAABBBDDDEEEIIIGGGFFFGGGIIIJJJKKKJJJGGGGGGGGGGGGHHHIIIIIIIIIIIIEEECCCEEEFFFDDDDDDEEEBBBAAAAAACCCEEEEEEDDDBBBFFFHHHKKKMMMMMMLLLKKKIIIGGGKKKOOOPPPOOOMMMKKKJJJKKKJJJIIIJJJKKKLLLKKKJJJMMMNNNPPPRRRRRRRRRRRRRRRQQQRRRUUUWWWWWWWWWVVVUUUTTTQQQOOOOOOQQQRRROOOMMMNNNOOOPPPQQQQQQPPPOOONNNNNNOOOQQQQQQOOOMMMLLLLLLJJJJJJIIIHHHGGGGGGFFFFFFIIIIIIHHHGGGFFFGGGKKKMMMLLLIIIFFFBBB@@@@@@@@@AAAEEEHHHKKKLLLKKKIIIHHHHHHHHHHHHHHHGGGFFFDDDBBB@@@AAABBBCCCCCCCCCAAA>>>===<<<<<<;;;:::;;;>>>@@@BBBDDDJJJQQQSSSRRROOONNNNNNIIIIIIIIIIIIIIIIIIIIIIIIHHHFFFCCCBBBCCCBBBAAA@@@@@@???>>>===<<<======>>>@@@??????@@@BBBBBBAAA???@@@@@@???@@@AAACCCEEEFFFFFFEEECCCBBB@@@??????>>>????????????????????????>>>>>>???????????????>>>;;;===@@@CCCEEEGGGHHHHHHFFFFFFGGGEEECCCAAABBBCCCDDDEEEEEEFFFFFFFFFFFFEEEEEEEEEDDDCCCBBBAAA@@@@@@@@@@@@???>>>===<<<<<<;;;<<<===>>>>>>===<<<===???>>>======<<<<<<;;;::::::777777777777666666666666555666666666666555444444222222222111111111111000111111000000000000111111000000000000///////////////000111333333333333222222222222222222111000///////////////............------...............---,,,,,,,,,---......///////////////...------,,,,,,*********+++,,,---...///...---,,,+++++++++,,,,,,,,,,,,------------,,,,,,*********+++++++++++++++,,,+++******))))))*********++++++,,,,,,++++++***************)))))))))))))))******++++++******)))******))))))))))))((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%'''(((((('''&&&&&&000000111111222333333333222222222222222333333444444444444444444444555555222222111111111111222222111111000000000000000000111111222333444555555444333555555444222111222333333333222222333333444555333333333444444444555555444444444444444444444444222444555555444444444555666444333333444555444333555444444444333333222222555555555444444333333333222111111111333555888::::::;;;<<<<<<;;;;;;<<<>>><<<======>>>===<<<:::999999999999999888888888888777888999999888777999::::::999888888888999:::;;;;;;;;;<<<===<<<<<<;;;:::@@@???>>>=========>>>???DDDEEEEEEDDDBBBAAABBBCCCAAAAAABBBEEEGGGFFFDDDBBBAAAAAAAAABBBCCCDDDFFFFFFKKKIIIIIIIIIKKKLLLLLLKKKGGGGGGGGGGGGGGGGGGGGGFFFEEEDDDCCCDDDDDDDDDCCCDDDAAA@@@@@@BBBEEEFFFFFFEEEHHHJJJLLLNNNNNNMMMJJJIIIIIIMMMPPPRRRQQQOOONNNNNNLLLKKKJJJKKKLLLMMMLLLKKKJJJKKKMMMOOOPPPPPPOOOOOOPPPRRRTTTUUUVVVUUUTTTSSSSSSQQQOOOOOOPPPOOOLLLJJJLLLMMMOOOPPPPPPOOONNNMMMNNNPPPQQQPPPNNNKKKJJJJJJJJJJJJIIIIIIHHHHHHGGGGGGKKKKKKJJJIIIGGGHHHKKKNNNLLLJJJEEEAAA???>>>???@@@EEEHHHLLLMMMKKKIIIHHHHHHGGGGGGGGGGGGFFFDDDBBBAAABBBCCCCCCCCCBBBAAA???===>>>===;;;;;;<<<>>>AAACCCBBBFFFJJJLLLLLLKKKJJJKKKGGGHHHIIIIIIJJJIIIIIIHHHFFFDDDBBBAAABBBBBBBBB@@@AAA@@@>>>=========>>>???@@@@@@AAAAAABBBBBBAAA@@@@@@@@@??????@@@BBBCCCEEEFFFEEECCCAAA???>>>>>>>>>?????????>>>>>>>>>======>>>>>>??????@@@?????????AAABBBDDDFFFGGGFFFFFFEEEDDDFFFGGGGGGDDDBBBBBBBBBDDDEEEFFFFFFFFFFFFEEEEEEFFFEEEDDDCCCBBB@@@@@@??????>>>>>>>>>===<<<;;;;;;:::;;;<<<;;;:::999:::;;;======<<<<<<;;;::::::999777777777666666666555555555555666666555555444333222222222222111111000000111111000000000000111111000000000000///////////////000111333444333333222222222222222111111000000////////////..............................------,,,---------......//////..................------,,,+++++++++,,,---......------,,,,,,,,,++++++++++++,,,,,,------,,,,,,+++))))))******++++++,,,,,,+++***))))))(((((()))))))))******++++++******)))*********)))))))))))))))))))))************))))))***)))))))))((((((((((((((((((''''''''''''&&&&&&''''''''''''''''''''''''(((((((((((((((((((((((('''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$&&&&&&&&&%%%%%%//////000111111222222333222111111111111222333333333333333333444444444444111111111111111111111111000000000111111111000000111111222333444444444444222333444333222111222333333222222222222333444444333333333444444444444444444444444444444444444444111222444555444333444555555444222222444555555444333333444444555555666666555555444444333333333222222111000111222555888999888:::;;;;;;::::::;;;<<<;;;;;;:::::::::<<<===>>>999999888888888777777777555777888888777777999::::::999888888888999:::;;;;;;<<<=========<<<;;;:::@@@???>>>=========>>>???DDDEEEFFFFFFDDDBBBCCCCCCBBBBBBCCCEEEFFFFFFCCCAAAAAAAAABBBCCCEEEFFFHHHIIIKKKJJJJJJKKKLLLMMMLLLJJJGGGGGGGGGGGGFFFDDDCCCBBBBBBCCCDDDCCCCCCCCCCCCCCCBBBAAABBBDDDGGGIIIJJJIIIJJJKKKMMMOOOOOOMMMKKKIIIIIILLLOOOQQQPPPOOOOOOOOOMMMLLLKKKKKKLLLMMMLLLJJJJJJKKKLLLMMMNNNNNNMMMLLLOOOPPPRRRSSSSSSRRRQQQPPPRRRQQQOOONNNMMMLLLJJJIIIJJJKKKLLLMMMNNNMMMMMMLLLNNNOOOQQQPPPMMMJJJIIIIIIJJJJJJIIIIIIIIIIIIIIIIIIJJJLLLMMMLLLKKKJJJJJJKKKJJJGGGCCC???<<<<<<===>>>EEEHHHKKKLLLJJJHHHGGGGGGEEEEEEFFFGGGGGGFFFDDDCCCDDDDDDDDDDDDCCCAAA@@@???::::::999999:::<<<>>>@@@BBBDDDGGGIIIJJJJJJJJJJJJHHHHHHIIIJJJJJJJJJIIIIIIEEECCCAAAAAACCCDDDCCCBBBCCCBBB@@@>>>>>>???@@@AAA@@@AAABBBBBBBBBAAAAAAAAA@@@?????????@@@AAACCCDDDGGGEEECCC@@@>>>>>>>>>>>>@@@@@@??????>>>=========>>>>>>???@@@@@@@@@@@@@@@CCCDDDFFFHHHIIIHHHFFFEEECCCEEEGGGGGGEEECCCBBBBBBEEEEEEFFFFFFFFFEEEEEEDDDEEEEEEDDDBBBAAA@@@>>>>>>===============<<<;;;:::999:::;;;:::999888999:::<<<<<<;;;;;;::::::999999888777777777777666666666555555555555555444444333111222222222222111000///111111000000000000111111000000000000///////////////000222333444444333333222222111111111111111111////////////..............................------------...............///,,,---------...///////////////...------,,,---------------,,,,,,,,,++++++******++++++++++++******)))))))))******+++++++++))))))(((''''''''''''((((((((())))))))))))(((((())))))))))))))))))******)))))))))******))))))))))))))))))((((((((((((''''''''''''''''''&&&&&&&&&''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&"""###%%%&&&'''&&&&&&%%%/////////000111111222222111111000000111111222333222222222222222333333333000000111222222111000000//////000111111111111000111111222333333333333333111222333333111111222333222222222222222333444444222222333444444444444333333333333333333333333333000222444444444333444555555333222222444555555444222333333444555666777888444444444444333333333333333333222333444555777888777999:::;;;:::999::::::::::::888888999;;;>>>@@@999999999888777777666666555777999999888999:::<<<;;;:::999888888999:::;;;:::<<<===??????>>><<<;;;??????>>>>>>>>>??????@@@CCCEEEGGGGGGFFFDDDDDDDDDCCCCCCCCCEEEFFFEEEBBB@@@@@@@@@AAABBBDDDGGGIIIKKKKKKJJJJJJKKKLLLLLLKKKIIIFFFFFFGGGGGGFFFDDDBBBAAA@@@EEEFFFDDDCCCEEEEEEDDDDDDCCCCCCEEEHHHKKKLLLLLLJJJLLLMMMNNNNNNLLLIIIHHHEEEHHHLLLMMMMMMMMMMMMNNNMMMLLLKKKKKKLLLLLLKKKJJJKKKLLLMMMOOOOOOOOONNNMMMOOOPPPQQQRRRRRRQQQOOONNNPPPOOOMMMKKKJJJJJJKKKKKKLLLLLLKKKKKKKKKKKKKKKKKKMMMNNNPPPOOOLLLJJJIIIIIIIIIIIIJJJJJJJJJJJJJJJJJJJJJLLLOOOOOOMMMKKKIIIIIIGGGDDD???<<<:::;;;===???FFFIIIKKKLLLKKKHHHGGGFFFEEEFFFGGGHHHHHHGGGFFFEEEFFFEEEEEEDDDCCCAAA@@@???;;;;;;<<<<<<===>>>@@@@@@DDDEEEHHHKKKLLLMMMMMMLLLJJJJJJJJJJJJJJJJJJJJJJJJEEECCCBBBCCCDDDFFFFFFEEEDDDCCC@@@>>>>>>???AAACCC@@@BBBCCCCCCAAA@@@@@@AAA@@@??????@@@AAACCCDDDFFFIIIGGGCCC@@@>>>>>>>>>???@@@@@@@@@??????>>>>>>>>>??????@@@AAABBBBBBBBBBBBAAACCCGGGJJJKKKKKKJJJIIIDDDFFFGGGGGGEEEDDDCCCDDDEEEFFFFFFFFFFFFEEEEEEDDDEEEDDDCCCAAA@@@>>>===<<<;;;<<<=========<<<:::999999:::;;;;;;:::999:::<<<<<<;;;;;;::::::999888888777777777777666666666666444555555555555444333333111111222333333111000///111111000000000000111111000000000000////////////000111222444444444444333222222111111000111111222////////////............------...............---........................---------.........//////111000///...---,,,,,,,,,,,,,,,---------,,,+++***))))))************)))))))))))))))***************))))))(((''''''''''''((('''(((((((((((((((((('''))))))))))))************((())))))******))))))((())))))((((((((((((''''''%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&((())))))(((''''''......//////000111111222000000000000000111222222222111111111111111111111///000111222222111000///...///000111222111111000111111222333333333333222000222333222111000111333222222222111222222333444111222333444444444333333222222222222222222222222000222444555444444555666555333222222444555555555333333333444444555555555333333333333333333444444555555555555666666777777666888;;;;;;:::999999:::999999999::::::;;;<<<<<<::::::999888888777666666777999;;;;;;;;;<<<>>>???===<<<;;;999999999:::::::::<<<>>>@@@@@@@@@>>>===>>>>>>???@@@AAAAAAAAA@@@BBBEEEHHHIIIHHHFFFEEEEEEBBBBBBBBBDDDEEEDDDAAA>>>???>>>>>>???AAAEEEIIILLLJJJIIIIIIJJJKKKKKKIIIGGGCCCDDDFFFGGGGGGFFFEEEDDDAAAHHHJJJGGGEEEHHHHHHFFFCCCBBBBBBCCCGGGJJJKKKKKKIIIJJJLLLMMMLLLJJJGGGEEEDDDGGGJJJLLLLLLLLLMMMNNNMMMLLLJJJJJJKKKLLLJJJIIIIIIKKKMMMOOOPPPQQQQQQPPPOOOPPPRRRRRRRRRPPPNNNMMMLLLKKKIIIHHHHHHJJJNNNQQQQQQPPPMMMKKKIIIHHHIIIIIILLLMMMOOONNNLLLJJJIIIIIIIIIIIIJJJJJJKKKKKKKKKLLLKKKMMMOOONNNLLLJJJIIIIIIDDDAAA===:::999<<>>===>>>@@@AAABBBBBBBBBBBBDDDFFFHHHKKKNNNNNNMMMLLLNNNMMMKKKJJJIIIJJJJJJKKKFFFDDDCCCDDDGGGHHHHHHHHHDDDBBB???======>>>AAABBB???AAACCCBBB@@@>>>???@@@AAAAAAAAAAAACCCEEEGGGIIIJJJHHHDDDAAA???>>>??????@@@@@@@@@@@@@@@????????????@@@AAABBBCCCCCCCCCCCCCCCEEEIIILLLMMMLLLJJJIIIDDDFFFGGGGGGEEEDDDDDDEEEFFFFFFFFFFFFFFFEEEDDDDDDDDDCCCBBB@@@>>>===;;;;;;:::;;;<<<======<<<:::999777999::::::999999;;;<<<;;;;;;::::::999888888888666666666555555555444444444444555555444444333222000111222333333222000///111111000000000000111111000000000000////////////000111222444555444444333222222111000000111222333////////////............,,,,,,---...////////////////////////............000//////...------,,,,,,//////...---,,,,,,,,,,,,,,,,,,---------,,,+++************++++++*********************))))))))))))++++++***)))))))))))))))(((((())))))))))))((((((((()))))))))************(((((())))))))))))(((((())))))((((((((('''''''''$$$$$$%%%&&&''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''(((((())))))((('''&&&......//////000111111111000000000000000111111222111111111111000000/////////000111222222111000///...///000222222222111000111111222333333333222222000111222222111000111333222222111111222222333444111222333444555444333333222222222222222222222222000222444555444444555666444333222222444666555555333333333333333333333333222222222333333444444444666666777888888777666666777999;;;<<<;;;:::::::::999:::;;;<<<<<<;;;999888:::::::::999888777777666999;;;===>>>>>>>>>@@@BBB???===<<<:::999999:::::::::<<<>>>AAABBBAAA???>>>===>>>@@@AAABBBBBBBBBAAAAAADDDHHHIIIIIIGGGFFFFFFBBBAAABBBCCCCCCBBB???======<<<;;;<<>>===999;;;>>>@@@AAAAAA@@@???BBBDDDGGGJJJMMMNNNLLLJJJPPPNNNLLLJJJIIIIIIKKKLLLFFFEEEDDDEEEHHHJJJJJJJJJCCCAAA>>><<<<<<===@@@BBB???AAACCCBBB???===>>>@@@BBBBBBBBBCCCEEEHHHJJJLLLKKKIIIEEEAAA?????????@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@AAABBBCCCDDDDDDDDDDDDGGGIIILLLMMMMMMKKKHHHFFFEEEFFFGGGFFFDDDDDDEEEFFFFFFFFFFFFFFFFFFEEEDDDDDDCCCBBBAAA???===<<<::::::999;;;<<<======;;;:::888444666777888777777999;;;;;;;;;::::::999888888777555555444444444333333333444444555555444444333222000111333333333222000...111111000000000000111111000000000000////////////000111333444555555444333222222111000000111222333000/////////............+++,,,---...///////////////////////////.........333222111///---+++)))))),,,,,,,,,++++++,,,------,,,,,,---...---,,,+++***+++++++++,,,,,,+++++++++++++++******))))))((((((---,,,++++++***+++++++++))))))************))))))(((((())))))*********+++(((((())))))))))))(((((()))(((((((((''''''''''''"""###$$$%%%'''((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&$$$###............////////////////////////000111222333222222111000///...------000000////////////000000000000111000000///...---...///111222222111000///222111///...---...000111...///111222333444555555333333333222222222111111222111111111000/////////333333333444444555555555666555444333333444555666666666555444333333222222222222222222444555777777::::::999999888777777666444555555666777999;;;<<<999:::;;;;;;<<<<<<<<<;;;777777888888888999999999===<<<;;;;;;;;;===???@@@===<<<;;;:::::::::::::::888;;;@@@BBBBBB@@@>>>>>>AAAAAABBBBBBAAAAAA@@@???@@@AAABBBBBBBBB@@@>>>===AAA@@@???>>>============999:::;;;===@@@CCCFFFHHHHHHIIIIIIJJJIIIHHHGGGFFFFFFGGGGGGHHHHHHHHHGGGGGGGGGHHHJJJIIIHHHGGGGGGHHH@@@BBBDDDDDDDDDDDDEEEGGGGGGIIIKKKKKKJJJJJJKKKLLLFFFJJJNNNOOONNNNNNOOOQQQJJJIIIFFFEEEFFFHHHLLLNNNKKKJJJIIIJJJNNNQQQRRRRRRRRRRRRRRROOOMMMLLLMMMNNNDDDEEEGGGJJJMMMPPPRRRSSSQQQPPPMMMJJJIIIIIIIIIJJJIIIHHHHHHGGGGGGGGGHHHHHHIIIIIIJJJKKKJJJIIIHHHFFFJJJJJJJJJJJJJJJKKKKKKKKKEEEDDD@@@;;;888:::AAAGGGSSSTTTUUUUUURRRPPPOOONNNJJJJJJJJJIIIHHHFFFEEEDDDGGGEEEAAA>>><<<===>>>@@@;;;<<<>>>??????>>>======BBBEEEFFFFFFIIIMMMMMMJJJJJJJJJJJJJJJIIIIIIHHHGGGCCCCCCCCCEEEGGGIIIHHHGGGAAAAAA@@@@@@AAAAAABBBBBB???@@@BBBCCCCCCCCCBBBAAACCCEEECCCAAADDDLLLRRRSSSWWWKKKAAA???AAAAAA??????AAAAAA@@@>>><<<;;;===??????@@@BBBCCCEEEFFFFFFFFFKKKLLLLLLLLLLLLJJJHHHGGGBBBDDDEEEDDDCCCBBBCCCDDDJJJIIIGGGEEECCCBBBAAA@@@?????????>>>===;;;:::999::::::;;;;;;;;;:::888777888999::::::;;;;;;;;;;;;;;;;;;:::999888666555555666555444222333444666777555444222111000000111111444333222222333333111000////////////////////////000000000000//////////////////000111222222222222444333333222111000/////////............---------//////............//////......////////////.....................---------...------,,,,,,------...,,,,,,,,,+++++++++******************************+++++++++++++++***)))(((***)))((()))***)))'''&&&(((((())))))))))))(((((())))))))))))))))))))))))))))))))))))))))))))))))***))))))(((''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$#########$$$$$$%%%&&&'''''''''''''''&&&&&&%%%%%%%%%'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%######$$$&&&'''$$$!!!........./////////000000////////////000111222222222222111111000000//////000000000000000000000000///000000000000//////......///000000111000000000111000///......///000111//////111222333444444444333333333222222111111111333333333222222222222222333333333333444444444555333222222333444666888:::666555555444333333222222111111111222333555666777999999999888777777666666444444444444555555666777999999:::;;;;;;;;;::::::777777888888888999999999;;;;;;;;;;;;;;;<<<===>>><<<<<<;;;:::::::::::::::999<<>>???BBBBBBBBBBBBAAA@@@@@@??????@@@AAABBBAAA@@@>>>===AAA@@@???>>>============::::::;;;===???BBBEEEGGGFFFGGGHHHHHHHHHGGGEEEDDDEEEFFFGGGGGGGGGGGGGGGGGGHHHIIIJJJIIIGGGEEEEEEEEEAAABBBCCCCCCBBBBBBCCCEEEGGGIIIJJJKKKIIIHHHIIIJJJHHHKKKNNNOOONNNMMMNNNOOOKKKJJJHHHGGGGGGJJJMMMOOOLLLKKKJJJKKKMMMPPPQQQQQQMMMOOOOOONNNLLLKKKLLLMMMFFFGGGJJJLLLOOOQQQRRRRRRPPPNNNLLLJJJIIIIIIJJJKKKJJJJJJIIIHHHGGGGGGHHHHHHIIIIIIIIIIIIIIIIIIHHHHHHLLLLLLLLLLLLLLLLLLLLLLLLGGGEEEAAA===;;;???FFFLLLXXXYYYYYYWWWTTTQQQOOONNNLLLLLLJJJIIIGGGFFFEEEDDDGGGDDDAAA===<<<<<<>>>?????????@@@???>>><<<;;;:::BBBEEEFFFFFFHHHMMMMMMIIIIIIJJJJJJJJJJJJIIIGGGFFFCCCBBBCCCEEEGGGHHHGGGFFFBBBAAAAAA@@@@@@AAACCCDDDCCCCCCDDDEEEEEEDDDCCCCCCBBBBBBAAABBBJJJVVV]]]^^^ZZZNNNCCCAAABBBAAA??????AAAAAA@@@???<<<<<<===???@@@AAACCCDDDFFFGGGGGGGGGJJJJJJKKKKKKJJJHHHGGGFFFBBBCCCEEEEEEDDDDDDFFFGGGIIIHHHFFFDDDBBBAAA@@@@@@??????>>>>>>===;;;:::999<<<<<<===>>>===<<<;;;:::888999999:::;;;;;;::::::;;;:::999888777666555555666555444444444555666777777666555333333333333333444222111111222222111///000000000000000000000000000000000000///////////////000111222222333333333333222222111111000000000///............---------......------------............////////////......------......//////000000------,,,,,,,,,,,,------,,,,,,+++++++++******************************************++++++******)))***)))((()))***)))(((&&&(((((())))))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((())))))(((''''''&&&%%%%%%'''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%###$$$$$$%%%&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$&&&((((((%%%###////////////000000000000...//////000000111111222111111111111111111111111000000111222222111000000...///////////////000000111000000/////////000000111000///......///000111///000111222333444444444444444333222111111000000222222222222222333333333222333333333333333444444333333333444555777999999555555444444333333222222111111222333444555555666888888888777666666555555888888888777777777777777999999999:::999999888888777777777888888888888999888888999:::;;;<<<<<<<<<;;;;;;::::::999999:::::::::<<<>>>???>>>>>>>>>???BBBBBBBBBBBBAAA@@@???>>>>>>???@@@AAAAAA@@@>>>===@@@@@@???>>>============;;;;;;;;;===???BBBDDDFFFEEEFFFFFFGGGGGGFFFDDDDDDDDDEEEFFFFFFGGGGGGFFFFFFHHHJJJKKKJJJGGGDDDCCCCCCAAABBBBBBAAA???>>>???AAAEEEGGGIIIJJJIIIHHHHHHIIIKKKMMMOOOPPPOOONNNNNNOOOMMMLLLJJJIIIJJJLLLOOOQQQNNNLLLKKKKKKMMMOOOOOOOOOIIIKKKMMMNNNLLLKKKKKKKKKHHHJJJMMMOOOQQQQQQQQQPPPNNNMMMKKKJJJJJJJJJKKKLLLLLLKKKJJJIIIHHHGGGGGGGGGHHHHHHHHHHHHHHHHHHIIIJJJNNNNNNNNNNNNNNNNNNNNNNNNIIIGGGCCC@@@@@@EEEMMMTTT]]]]]][[[YYYVVVSSSPPPOOONNNMMMKKKHHHFFFEEEEEEEEEEEECCC@@@===<<<<<<>>>???????????????>>>===;;;:::@@@DDDGGGFFFHHHKKKKKKIIIIIIIIIJJJJJJIIIHHHFFFEEECCCBBBBBBDDDGGGHHHGGGEEEDDDBBBAAA???@@@BBBDDDFFFGGGGGGGGGGGGFFFEEEDDDCCC@@@@@@???DDDRRRccckkklll___RRRGGGCCCBBB@@@???@@@@@@AAAAAA???======>>>???AAABBBDDDFFFHHHHHHHHHHHHHHHHHHHHHHHHHHHGGGFFFEEEBBBDDDFFFFFFFFFFFFHHHIIIHHHGGGEEECCCAAA@@@@@@???>>>>>>>>>===<<<;;;:::999<<<<<<===>>>>>>===;;;:::888888999::::::::::::999999999888888777666555555666666666666666666666666777666555444333333444444222111000000111111000///111111111111111111111111000000000000///////////////000111222333333333333111111111111111111111111///............---------------,,,,,,,,,,,,------......////////////......,,,------...///000111222---,,,,,,++++++,,,,,,---,,,++++++++++++*********************************))))))******++++++*********)))((()))******(((&&&'''(((((())))))(((((('''((((((((((((((((((((((((''''''''''''''''''''''''(((''''''&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&$$$%%%%%%&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((())))))'''%%%/////////000000000111111......///000000111111111//////000000000111111111///000222333333222000///............//////000111555444222000///...//////000//////...//////000111000111222222333333333333444444333222111000///////////////000111111111222222222222222333333333333555555555555555555555555444444444333333333222222222222333444555666666666777777666666555444444444888888999999999999888888888888888888888777777666777777777777888888888888555666888:::;;;;;;::::::::::::999999999999::::::;;;=========<<<<<<>>>@@@BBBBBBBBBAAA@@@???>>>======>>>???@@@@@@??????>>>??????>>>===============<<<<<<<<<===???BBBDDDFFFEEEFFFGGGGGGGGGFFFEEEEEEDDDDDDEEEFFFFFFFFFFFFFFFGGGIIIKKKJJJHHHFFFEEEEEEBBBBBBAAA???<<<;;;<<<===@@@CCCGGGIIIIIIIIIJJJKKKMMMOOOQQQRRRRRRQQQQQQQQQNNNMMMLLLKKKLLLNNNPPPRRRPPPNNNLLLKKKMMMNNNNNNNNNIIIKKKNNNNNNLLLJJJIIIHHHIIIKKKNNNQQQQQQPPPOOOMMMLLLKKKKKKJJJKKKLLLMMMMMMMMMLLLKKKIIIHHHGGGGGGGGGHHHGGGGGGGGGGGGIIIKKKLLLPPPPPPPPPPPPPPPOOOOOOOOOKKKIIIEEECCCEEEKKKTTTYYY]]][[[YYYWWWVVVTTTRRRPPPPPPNNNJJJGGGEEEEEEEEEFFFDDDBBB???===<<<<<<===>>>;;;<<<======>>>>>>>>>>>>???EEEHHHGGGGGGJJJKKKHHHGGGHHHHHHHHHHHHFFFEEECCCDDDCCCCCCEEEGGGGGGFFFEEEEEECCCAAA???@@@BBBFFFHHHJJJIIIHHHGGGFFFDDDCCCCCCAAA??????FFFXXXjjjssssss```UUUJJJEEECCC@@@???@@@@@@AAABBB@@@???>>>???@@@BBBCCCFFFHHHIIIJJJIIIIIIGGGGGGGGGGGGFFFFFFEEEEEEEEEFFFGGGGGGFFFFFFGGGHHHFFFEEEDDDBBB@@@?????????============<<<;;;:::999999:::;;;<<<<<<;;;:::999888888999999999999999888777777777666666555555555666666777777777666555444444333333222222222222222111000...///000111000...111111111111111111111111000000000000///////////////000111222333333333333///000000000111111111222///............---------------,,,,,,,,,,,,---------......//////......---,,,,,,------...//////000,,,,,,++++++++++++,,,,,,++++++++++++************************************)))***************)))((()))(((((((((******(((''''''(((((((((((((((((('''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((((((((('''&&&////////////000000000000------///000111111000000------......///000000000///000222333333222000///......------...///000111999777555222///.........///////////////000111111111222222333333333222222333333222111111000///////////////000111111111222222222222222222222222222444444555555555555444444333333333333333222222222333444555666777777666666666666555444444333333222222333444555666666666555777777777888888777666666777777777777777777777777333555777999::::::999999999999888888888999999:::<<<<<<===<<<;;;;;;===???@@@@@@@@@@@@???>>>===<<<<<<======>>>???????????????>>>===========================>>>@@@CCCEEEGGGFFFGGGHHHIIIIIIIIIHHHGGGEEEEEEFFFFFFFFFFFFEEEEEEEEEGGGJJJKKKJJJHHHHHHHHHBBBAAA@@@===999888999:::;;;???EEEIIILLLMMMOOOPPPOOOPPPRRRSSSUUUVVVUUUTTTOOONNNMMMMMMMMMOOOQQQRRRQQQNNNLLLKKKLLLMMMMMMMMMKKKMMMOOONNNKKKHHHFFFEEEIIIKKKMMMOOOOOONNNLLLJJJJJJJJJJJJKKKKKKLLLMMMNNNMMMLLLJJJIIIHHHGGGFFFFFFGGGGGGGGGGGGHHHJJJMMMNNNRRRQQQQQQQQQPPPPPPOOOOOOLLLIIIFFFEEEHHHOOOVVVZZZWWWTTTRRRRRRSSSSSSQQQPPPNNNMMMIIIGGGEEEDDDEEEEEEBBBAAA???===<<<<<<======;;;;;;;;;<<<<<<===>>>>>>???EEEIIIHHHHHHJJJJJJHHHFFFFFFFFFFFFFFFEEEEEEDDDHHHGGGFFFGGGHHHHHHFFFEEEDDDCCC@@@???@@@CCCFFFHHHJJJIIIGGGEEEDDDBBBAAAAAABBBAAAAAAGGGWWWhhhnnnmmm\\\RRRIIIFFFCCC@@@???@@@@@@AAABBBBBB@@@???@@@AAABBBDDDGGGIIIJJJJJJJJJIIIGGGGGGFFFFFFFFFFFFFFFFFFHHHIIIIIIGGGEEEDDDDDDEEEDDDCCCBBB@@@???>>>>>>>>><<<=========<<<;;;:::999888999:::;;;;;;:::999999777888888999888888777777555555555555555555555555666666777777666555444444222222222222222222111111000///......000111000...111111111111111111111111000000000000//////////////////000111222222222222/////////000111111222222///............---------......------------......------............------,,,,,,,,,,,,,,,,,,,,,,,,++++++************+++++++++++++++*********))))))))))))))))))))))))))))))+++++++++***)))((('''&&&)))((('''(((******)))'''''''''((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""$$$&&&'''&&&&&&&&&%%%............////////////,,,---///000111111000///---------....../////////000000111222222111000000///...---------...///000888777555222000...------......//////000000111111222222333333333222111111222111111111111000000000222222222222222333333333222222222111111111111000///000222333555666666666333333333333222222222222333444555777777777666555555444444333222222111111111222444666777666666555555666777777888888777777888777777777777777666666333444666777999999::::::888888777777888888999999;;;<<<<<<<<<::::::<<<>>>======>>>>>>======<<<;;;;;;<<<<<<===>>>??????@@@>>>======<<<<<<=========>>>>>>>>>@@@BBBEEEGGGIIIHHHIIIJJJKKKKKKKKKJJJIIIGGGGGGGGGGGGFFFEEEDDDDDDCCCFFFIIIKKKJJJIIIHHHHHHBBBAAA???;;;888777888999999>>>EEEKKKOOOQQQTTTUUURRRRRRRRRTTTWWWWWWVVVTTTNNNMMMMMMMMMMMMOOOPPPQQQQQQNNNLLLKKKLLLMMMMMMLLLMMMNNNNNNMMMIIIFFFEEEDDDIIIJJJLLLMMMMMMLLLJJJIIIIIIJJJJJJKKKLLLMMMMMMMMMKKKJJJIIIHHHGGGFFFFFFFFFFFFGGGGGGIIIKKKMMMOOOPPPQQQQQQQQQPPPPPPOOOOOONNNKKKHHHEEEFFFJJJOOOTTTVVVPPPMMMKKKLLLOOOPPPOOOMMMKKKJJJHHHFFFEEEDDDDDDDDDAAA@@@>>>===<<<<<<<<<======<<<;;;:::::::::::::::???FFFKKKJJJIIIJJJJJJIIIGGGFFFEEEDDDEEEFFFGGGIIIMMMLLLJJJJJJJJJIIIGGGEEEBBBAAA@@@???@@@CCCEEEGGGHHHGGGEEECCCAAA@@@??????BBBBBBBBBFFFQQQ]]]```^^^SSSLLLGGGEEECCC??????AAA@@@AAACCCCCCAAA@@@@@@AAAAAADDDGGGJJJKKKKKKIIIHHHFFFFFFEEEEEEEEEEEEEEEFFFHHHIIIHHHFFFCCCAAAAAABBBBBBBBB@@@???>>>=========<<<<<<<<<<<<<<<;;;::::::888999;;;<<<<<<;;;::::::777888888888888777666666444444444444444444555555666666666555444444333333222222333333333333222222000///...///000111000///111111111111111111111111000000000000////////////---...///000111111111111/////////000000111111111///............---------......------------......------............------,,,,,,+++++++++*********+++******))))))******++++++************)))))))))))))))))))))))))))))))))************)))((('''&&&(((''''''(((******)))(((&&&''''''((((((''''''&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% """%%%&&&%%%$$$$$$%%%------------............+++---///000111000//////............////////////000000000000000000000000000///---,,,,,,---...///222222222111000///......---...///000000111111111333333333333333222111000000000000000111111111111333333333222222222222222222222111111000000000000---///111222444444444444222222222222222222222222111222444555666555444333444333333222111111000000444555666777888777555444444555666777888999999999888888777777666666666666444555555666777999;;;<<<777777777777777888999999:::;;;===<<<;;;:::;;;<<<::::::;;;<<<<<<<<<;;;;;;:::;;;;;;<<<===>>>@@@@@@======<<<<<<<<<======>>>>>>??????AAADDDGGGJJJLLLHHHIIIJJJKKKLLLKKKJJJJJJIIIIIIIIIHHHGGGEEECCCCCCBBBEEEHHHJJJIIIGGGEEEEEEBBBAAA>>>:::777666888::::::@@@GGGMMMQQQTTTVVVWWWUUUTTTSSSTTTVVVUUURRROOOLLLLLLLLLLLLMMMNNNOOOPPPPPPNNNLLLKKKMMMNNNNNNMMMKKKLLLKKKIIIFFFDDDDDDEEEJJJKKKKKKLLLLLLKKKKKKJJJJJJJJJKKKLLLLLLMMMMMMLLLIIIHHHGGGFFFFFFFFFFFFFFFEEEGGGIIIKKKMMMOOOPPPQQQQQQPPPPPPOOONNNNNNMMMMMMIIIFFFDDDFFFJJJNNNPPPPPPLLLHHHEEEGGGKKKMMMLLLJJJGGGGGGFFFFFFEEEDDDDDDCCC??????===<<<<<<<<<<<<<<<;;;:::999888888888999:::@@@HHHMMMLLLJJJJJJKKKJJJJJJHHHFFFEEEFFFIIILLLOOORRRQQQOOONNNMMMKKKHHHEEE@@@@@@???@@@AAABBBDDDFFFGGGFFFDDDBBB@@@????????????BBBCCCDDDIIIOOOQQQNNNIIIEEECCCDDDCCC??????AAA???AAACCCCCCBBBAAAAAABBBAAACCCGGGJJJKKKKKKIIIHHHEEEDDDCCCBBBBBBCCCDDDEEEEEEFFFFFFDDDBBB@@@@@@AAAAAA@@@???>>>===<<<<<<<<<;;;;;;<<<<<<<<<;;;::::::777888999:::;;;:::999999777777888888777666666555222222333333444444444555777666444333222222333333000111222222222222111000000///...///111222111000000000000000000000000000000000000000////////////,,,---...//////000000000/////////000000000000000///............---------------,,,,,,,,,,,,------,,,------......------,,,++++++++++++++++++,,,,,,******))))))))))))******************))))))))))))))))))))))))))))))))))))''''''((()))******))))))(((''''''(((***+++)))(((&&&''''''((((((''''''&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""%%%&&&$$$###$$$&&&,,,,,,,,,---------......+++,,,///000111000///...000000000000000/////////000000////////////000000111000...,,,+++,,,---...,,,---...000000000///...------///000111111111111333333333333222222111000/////////000111111222222222111111111000000//////222111111111000000//////000111222333333222111000222222222222222222222222000111333444444333222111333333222222111000000000222333444444333222///...333444666777999:::::::::888888777777666666666555555555555555777999;;;===777777666777777888999999999;;;===<<<;;;::::::;;;888888999:::;;;;;;;;;;;;::::::;;;;;;===>>>@@@AAA======<<<<<<<<<======>>>>>>???@@@BBBEEEHHHKKKMMMGGGHHHJJJKKKKKKKKKJJJJJJKKKKKKJJJIIIGGGEEECCCBBBAAADDDHHHIIIGGGDDDBBBAAABBBAAA>>>:::777666888:::===BBBIIIOOOSSSUUUVVVXXXWWWUUUSSSSSSTTTSSSNNNKKKKKKKKKKKKKKKLLLMMMNNNOOOPPPNNNLLLKKKMMMNNNNNNMMMHHHIIIHHHGGGDDDDDDEEEFFFKKKKKKKKKKKKKKKLLLLLLLLLJJJJJJKKKLLLLLLLLLLLLLLLGGGGGGFFFFFFEEEFFFFFFFFFEEEGGGJJJMMMOOOQQQQQQQQQPPPPPPOOONNNNNNMMMLLLLLLGGGEEEDDDEEEIIILLLMMMLLLKKKGGGCCCDDDHHHKKKJJJGGGDDDEEEEEEEEEEEEDDDCCCCCC???>>>===<<<<<<<<<<<<<<<777666666666777999;;;<<<@@@IIIOOOMMMJJJKKKKKKJJJLLLJJJGGGEEEGGGKKKPPPTTTVVVTTTQQQPPPNNNLLLHHHFFF>>>??????@@@AAABBBDDDDDDGGGEEECCCAAA@@@?????????===AAACCCBBBCCCGGGGGGDDDCCC@@@@@@BBBBBB???>>>AAA???AAACCCDDDCCCAAAAAABBB@@@CCCFFFJJJKKKJJJIIIGGGCCCBBBAAAAAAAAABBBCCCDDDBBBCCCDDDCCCAAA@@@@@@AAA@@@@@@???===<<<<<<<<<<<<;;;;;;;;;<<<;;;;;;::::::444555666777888888777666777777888777777666555555222222222333333444444555777666333111000111222333---...///000000///...---000//////000111222222111////////////////////////000000000000////////////+++,,,---...////////////000000000000000///////////////.........---------,,,++++++++++++++++++,,,,,,------......------,,,******+++,,,------...///******))))))))))))******************))))))))))))))))))))))))))))))))))))$$$%%%&&&(((***+++,,,,,,(((''''''(((***+++***(((&&&''''''''''''''''''&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''((((((((((((''''''$$$##############################$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""&&&&&&%%%$$$%%%''',,,,,,,,,---------......000000000000////////////---///111222333222000//////............//////000000///...---------------............////////////---...000111222222111111333333222222111000000000///000111222333222111111111111111222222111111111444333222111000000000000......///000111222222333222222222222222111000///222222222111111111000000222222111111111111222222444444444444333222111000444444555666777888999999555555555555555555444444555555555555666777999999888888888888888777666555888888888999:::;;;<<<===;;;::::::::::::;;;<<<<<<@@@>>><<<:::;;;<<>><<<;;;<<<>>>??????>>>>>>>>>@@@DDDIIIKKKKKKJJJLLLJJJHHHHHHJJJJJJJJJIIIPPPMMMIIIGGGFFFDDD@@@<<>>=========<<<<<<<<<<<<888777777777999;;;>>>@@@CCCDDDFFFIIIJJJKKKKKKKKKJJJJJJKKKLLLMMMMMMNNNNNNLLLLLLKKKIIIGGGEEEDDDBBB?????????@@@AAABBBCCCCCCCCCCCCCCCBBBAAA@@@>>>>>>;;;===???BBBBBBAAA@@@>>>AAA???===>>>@@@AAA@@@===??????@@@AAAAAAAAA@@@@@@EEEEEEEEEGGGHHHGGGDDDBBB<<<<<<===>>>???AAACCCDDDCCCCCCCCCBBBAAA@@@>>>======>>>???>>><<<;;;;;;<<<999999999999999999999999444555666777888888888888666666555444444444444555222222111000111222444555777555333222333333222111////////////............---...///000000111111111000000000000000000000000------............---------------.........//////111111000000/////////.........---------,,,,,,,,,...------,,,,,,------............------,,,,,,,,,,,,,,,++++++***)))))))))---,,,+++***)))))))))))),,,+++++++++******))))))******))))))((((((''''''(((((('''(((((()))***+++'''''''''(((((((((((((((&&&((()))(((%%%$$$%%%'''$$$%%%&&&''''''&&&%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######""""""!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$#########$$$"""$$$$$$$$$###"""###$$$&&&%%%%%%$$$$$$%%%%%%&&&,,,,,,,,,---------......000/////////////////////...///000222222111000/////////...............//////......------------...............////////////---...000111222222111111333333222111111000000//////000111222333222111111111111000000000000111111333222111000000//////////////////000111111111222111111222222111000000///222222222111111111000000222111111000000111111222444444555555555555555444444555555666666777888888555555555444444444444444555555555555666777888999888888888888888777666666888888888888999;;;<<<===:::::::::::::::;;;<<<<<>>===<<<<<<===???@@@???===<<<<<<>>>??????>>>??????AAAEEEIIIKKKKKKJJJKKKIIIHHHHHHIIIJJJJJJIIIKKKIIIFFFEEEEEEDDDAAA???@@@BBBCCCEEEEEEDDDCCCBBBFFFEEECCC@@@===<<<>>>AAAEEEKKKTTTZZZ[[[YYYVVVTTTRRRQQQOOOOOOOOONNNKKKIIIMMMLLLLLLNNNOOONNNKKKIIIJJJJJJJJJKKKMMMMMMKKKIIIDDDEEEGGGIIIIIIIIIIIIHHHFFFIIIKKKLLLKKKKKKLLLLLLMMMMMMMMMLLLKKKIIIHHHGGGGGGHHHHHHGGGFFFFFFHHHKKKIIIJJJJJJHHHFFFFFFGGGHHHMMMOOOQQQQQQOOOMMMMMMMMMKKKKKKJJJIIIJJJKKKLLLMMMEEEDDDEEEFFFGGGGGGEEECCCEEEFFFEEEDDDBBBAAA@@@@@@======<<<<<<<<<;;;;;;;;;:::999999999;;;===@@@AAABBBCCCFFFHHHJJJKKKKKKKKKLLLLLLMMMMMMMMMNNNNNNNNNKKKKKKKKKJJJHHHEEECCCBBB???@@@AAABBBCCCCCCCCCCCCFFFEEEDDDBBB@@@>>><<<;;;<<<===@@@AAABBBAAA???===???>>>===>>>AAACCCBBB@@@@@@@@@AAABBBBBBBBBBBBAAADDDDDDDDDFFFGGGFFFCCCAAA>>>>>>>>>>>>???@@@AAABBBBBBBBBAAAAAA@@@>>>===<<<===>>>???===;;;:::;;;<<<::::::::::::999999888888333444555666777777777777666555444444333333444444333222222111222333444555666444222222333333222111////////////...............///000111222222222222000000000000000000000000---......//////......------------.........//////000000000000000///.........------------,,,,,,,,,------,,,,,,,,,,,,---------------,,,,,,,,,++++++,,,,,,,,,+++++++++++++++''''''((()))***,,,...///)))))))))(((((((((''''''***)))))))))((((((((('''(((((((((((((((((()))***''''''''''''''''''''''''''')))***)))'''%%%'''(((%%%&&&&&&&&&&&&&&&&&&%%%'''''''''&&&&&&&&&%%%%%%'''&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$"""$$$%%%$$$###"""###$$$&&&%%%%%%$$$$$$%%%%%%&&&,,,,,,,,,---------......////////////////////////...///000111222111000///000000///...------------------------------...///---............/////////---...///000111111111111333222222111111000/////////000111222222222111000111000...------...000111333222111000////////////000000000000000000000000000000111111000000//////222111111111111000000000222111111000000111111222222222444555666666666666555555555555555555555555444444444444444444444444555555555555666777888888888888999999888888777777777777777888999:::;;;<<<::::::999999::::::;;;<<<=========>>>>>>?????????AAA???======>>>???>>>===@@@@@@BBBEEEIIIKKKJJJIIIJJJHHHGGGGGGHHHIIIIIIHHHFFFEEECCCCCCDDDDDDCCCAAA@@@AAABBBCCCDDDCCCBBBBBBDDDDDDCCCAAA??????AAACCCFFFLLLTTTZZZ[[[YYYVVVTTTNNNNNNMMMLLLJJJKKKMMMPPPQQQPPPOOOOOOOOOMMMJJJGGGGGGGGGHHHIIIKKKLLLJJJHHHFFFGGGHHHIIIJJJJJJIIIIIIHHHJJJMMMOOONNNLLLLLLLLLMMMMMMLLLKKKJJJHHHFFFEEEFFFGGGGGGFFFEEEFFFHHHIIIEEEFFFGGGFFFDDDDDDEEEGGGLLLNNNPPPPPPNNNMMMLLLMMMMMMLLLKKKKKKJJJJJJKKKKKKDDDCCCCCCDDDFFFGGGGGGFFFHHHGGGFFFDDDBBBAAAAAAAAA<<<<<<<<<<<<;;;;;;;;;;;;<<<;;;;;;<<<===???AAABBB@@@BBBEEEGGGJJJKKKLLLLLLNNNNNNNNNMMMMMMMMMLLLLLLIIIIIIJJJJJJHHHEEECCCAAA@@@BBBDDDEEEFFFEEEDDDCCCEEEDDDCCCAAA???>>><<<;;;>>>???@@@AAAAAA???===<<<=========???AAACCCCCCCCCAAAAAABBBCCCCCCCCCCCCCCCCCCCCCCCCCCCDDDDDDAAA????????????>>>??????@@@AAAAAA@@@@@@???>>>===<<<<<<===>>>???===;;;::::::;;;<<<<<<;;;:::999888888777333333444555666666666666555444333333222222333333333333333333333333444555666444222222222333222111////////////............///000111222222333333333000000000000000000000000---......//////......------------..................///111222111000...---------------,,,,,,,,,,,,,,,++++++++++++++++++,,,,,,,,,,,,++++++++++++++++++,,,,,,,,,,,,---------++++++***))))))))))))***))))))((((((((((((''''''))))))))))))(((((((((((())))))(((((('''(((((((((((((((''''''&&&&&&%%%%%%'''((()))(((&&&&&&&&&((('''&&&&&&%%%%%%&&&&&&'''((((((''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''((())))))$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$######$$$$$$###$$$%%%$$$###"""###%%%%%%%%%%%%%%%%%%%%%%%%%%%,,,,,,,,,---------...............///////////////...///000000111111000000111000///...---,,,,,,,,,,,,,,,,,,,,,---......///---------.........//////......///000000111111111222222222111000000//////...///111222222222111000111///---++++++---///111333333222111000000000000000000000000000///////////////000000000000//////111111111111000000000000111111000000000000111111000000111222333333333333666666555555444333333333333333333333333444444444555555555555555666777888777888888999888888777777666666666777888999:::;;;999999999999999::::::;;;;;;<<<>>>????????????>>>BBB@@@>>>>>>>>>???>>>===??????AAADDDGGGHHHHHHFFFHHHFFFEEEEEEGGGHHHHHHGGGDDDDDDCCCCCCCCCCCCCCCBBBBBBCCCDDDEEEEEEEEEEEEDDDCCCCCCCCCBBBAAAAAADDDFFFFFFLLLTTTYYYYYYWWWUUUSSSJJJKKKKKKIIIGGGIIIOOOTTTVVVTTTRRRQQQOOOMMMIIIFFFEEEEEEFFFHHHJJJKKKIIIGGGGGGGGGIIIJJJJJJJJJIIIIIIIIIKKKNNNPPPNNNMMMLLLLLLLLLLLLKKKJJJHHHGGGEEEDDDEEEFFFGGGFFFEEEEEEGGGHHHDDDEEEFFFFFFEEEEEEGGGIIIKKKMMMOOOOOOMMMLLLLLLLLLNNNMMMLLLKKKJJJIIIIIIIIICCCBBBAAABBBEEEHHHHHHHHHJJJHHHEEECCCBBBBBBAAA@@@============<<<<<<<<<<<<<<<<<<<<<===>>>???AAABBB???@@@CCCGGGIIIKKKLLLLLLNNNNNNMMMLLLKKKJJJIIIIIIGGGGGGIIIIIIHHHEEEBBB@@@AAACCCFFFGGGHHHFFFDDDBBB@@@@@@?????????@@@@@@@@@???@@@@@@AAA@@@>>><<<;;;<<<<<<===>>>???AAAAAAAAA@@@AAABBBCCCCCCCCCCCCCCCBBBAAAAAAAAABBBAAA???===>>>>>>>>>>>>???@@@AAAAAA@@@@@@???>>>===============>>>>>>===;;;999:::;;;===<<<;;;:::999888777666222333444444555555555444444333222222111111222222444444444444444444444444555333111111222333222111////////////............//////000111222222222222000000000000000000000000......////////////..............................---///111222222111...,,,---------,,,,,,,,,++++++++++++************++++++++++++************************++++++,,,------...------+++***((('''''''''******************))))))))))))))))))((((((((((((***)))((('''''''''''''''(((((('''&&&%%%$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%&&&'''&&&%%%$$$$$$%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$$$$%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%$$$$$$###$$$$$$%%%###$$$%%%%%%######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%,,,,,,,,,---------......------....../////////000......///000000000000000000000///---,,,,,,,,,,,,,,,,,,,,,,,,,,,---...///------------.....................//////000111111222222111111000//////......///000111222111000000000...,,,******,,,...000444444222111111111111111000000000///////////////...///000000000000//////000000000000000000000000111000000000000000000111111222222222222222222111666666555444333222111111222222222222333333444444555555555555555666666777666777777888888888777777555555555666777888999:::999888888888888999:::::::::;;;===?????????>>>===AAA???>>>===>>>>>>>>>===<<<===>>>AAADDDFFFEEEDDDFFFEEECCCDDDFFFGGGGGGFFFEEEFFFEEEDDDCCCBBBBBBBBBDDDDDDEEEEEEFFFFFFFFFFFFBBBCCCDDDDDDCCCDDDFFFHHHKKKOOOTTTVVVUUUQQQNNNMMMHHHIIIJJJHHHGGGIIIPPPUUUWWWUUURRRQQQOOOMMMJJJGGGDDDDDDEEEGGGIIIIIIHHHFFFGGGHHHIIIJJJJJJJJJIIIHHHIIIKKKMMMNNNLLLJJJJJJJJJJJJJJJJJJIIIGGGEEEDDDCCCDDDFFFGGGGGGFFFFFFGGGHHHFFFGGGHHHHHHGGGHHHJJJKKKIIIKKKMMMNNNMMMKKKKKKLLLNNNMMMLLLKKKJJJHHHGGGGGGBBBAAA@@@BBBEEEHHHIIIIIIIIIGGGDDDCCCCCCCCCAAA???????????????>>>>>>>>>>>>;;;;;;<<<<<<===>>>???@@@>>>@@@CCCFFFIIIJJJKKKKKKLLLKKKJJJIIIGGGFFFEEEEEEEEEFFFGGGGGGFFFDDDBBBAAABBBDDDFFFHHHGGGFFFCCCAAA>>>>>>>>>>>>>>>???AAAAAA@@@@@@@@@@@@???===<<<;;;;;;<<<<<<<<<<<<<<<======??????AAABBBBBBCCCCCCCCCBBBAAA??????@@@@@@>>><<<<<<<<<===>>>???AAACCCDDDAAA@@@???>>>======>>>>>>===>>>>>>===:::999999:::<<<<<<;;;999888777666666222333333444444444444444333333222111111111111222444444444444444444444333444222111111222333222111////////////............---...///000111111111111////////////////////////...//////////////////........................---,,,...111222222111///---------,,,,,,,,,++++++++++++******))))))******+++************************(((((()))***+++,,,------'''''''''((()))+++,,,---))))))))))))))))))******(((((((((((())))))))))))))))))(((''''''&&&''''''(((((('''&&&%%%$$$$$$$$$&&&&&&&&&&&&&&&'''&&&&&&'''&&&%%%$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$######""""""$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$$$$###$$$$$$%%%%%%###%%%%%%%%%$$$###$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$,,,,,,,,,---------......---------......//////000........./////////000000//////...---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---...,,,------------.....................///000111222222111111000000///.........///000111111111000//////...,,,++++++,,,...///444333222111000000000000//////////////////////////////000000111111000000//////000000000000000111111000000//////000000111333444444444444444333222555555444333222111000000000111111222222333333444666555555444555555666666555555666666777777666666444444444555666777888999888888777777888888999:::888999;;;===>>>>>>>>>===@@@>>><<<<<<===>>>===<<<::::::<<>>>>>>>>>>>@@@CCCEEEHHHIIIJJJJJJIIIHHHGGGFFFEEECCCBBBBBBEEEEEEEEEEEEDDDCCCCCCBBBCCCDDDEEEFFFEEEDDDBBB@@@@@@???>>>=========>>>???????????????>>>===<<<;;;:::;;;<<<<<<::::::;;;<<<>>>???@@@AAABBBCCCCCCCCCBBB@@@???>>>???>>>===;;;;;;<<<<<<>>>???BBBCCCDDDAAA@@@>>>=========>>>???>>>>>>>>>===:::888888999::::::999888777666666555333333444444555444444333444333222222111111222222333444444444444333333222444222000000222222222111////////////............---...///000000111111000////////////////////////...//////000000//////..................------------...000111222111///...,,,,,,,,,,,,+++++++++++++++******************+++***************+++++++++(((((()))***++++++,,,,,,))))))((((((((()))******&&&&&&''''''''''''(((((((((((((((((())))))))))))((((((''''''&&&'''''''''((((((''''''&&&&&&%%%%%%((('''&&&'''((()))(((''''''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%$$$%%%&&&%%%$$$###$$$&&&$$$$$$&&&&&&&&&&&&$$$$$$,,,,,,,,,---------......,,,,,,---......///000000...............///000000......---,,,,,,---------------,,,,,,+++,,,,,,,,,,,,,,,---------...............------...///111222111111111000//////......---...000111111111000///......------------......222111000///............---.........///000000000///000000111222222111111////////////000000111111000000////////////000000111222333444444444444444444444333222111000000///000000000111222333333333666555555444444555555555333333444555555555555555333333333444555666888888777777777777777888999999777888999;;;<<<============<<<;;;;;;===>>>======999999;;;???CCCEEEEEEDDDCCCBBBAAABBBDDDEEEEEEEEEBBBDDDEEEDDDAAA@@@AAABBBBBBBBBAAAAAABBBBBBCCCCCCCCCEEEFFFGGGFFFGGGIIIJJJRRRRRRQQQMMMHHHEEECCCCCCIIIHHHIIIKKKMMMNNNNNNMMMLLLKKKIIIIIIJJJJJJJJJHHHFFFEEEEEEGGGHHHHHHFFFDDDFFFGGGHHHIIIIIIHHHGGGFFFGGGGGGGGGEEEBBBBBBCCCEEEEEEFFFFFFFFFFFFEEEDDDCCCDDDGGGIIIIIIHHHGGGHHHHHHHHHIIIIIIIIIHHHHHHIIIKKKGGGIIIKKKLLLKKKJJJJJJKKKJJJJJJJJJJJJHHHGGGEEEDDD???@@@AAADDDGGGHHHGGGFFFCCCAAA@@@BBBFFFEEE@@@<<<@@@@@@@@@?????????>>>>>>;;;;;;<<<===>>>>>>>>>>>>???@@@CCCEEEGGGHHHHHHHHHGGGGGGFFFEEECCCBBBAAAAAAEEEDDDCCCBBBBBBBBBCCCDDDCCCCCCCCCCCCBBBAAA@@@??????>>>===<<<<<<===???@@@??????>>>>>>>>>===<<<<<<888:::<<<<<<::::::<<<>>>???@@@AAACCCDDDDDDDDDDDDCCCAAA???>>>>>>>>>===;;;=========>>>???AAABBBCCC@@@>>>===;;;;;;<<<===>>>>>>>>>>>><<<:::888888888888777777777666666555555444444555555555555444444444444333222222222222222222333444444444222111000333111000000111222222111////////////..................///000111111111111//////////////////////////////000000000000////////////.........---------......///000000000000000,,,,,,,,,++++++++++++***+++++++++******+++++++++*********+++++++++,,,,,,*********++++++,,,,,,,,,---,,,+++)))'''&&&&&&%%%&&&&&&&&&'''''''''(((((('''((((((((()))))))))***''''''&&&&&&&&&'''((((((''''''''''''''''''''''''&&&$$$###$$$&&&(((&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&''''''%%%%%%%%%$$$$$$$$$$$$###%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$%%%&&&&&&$$$$$$%%%&&&###$$$&&&''''''&&&$$$###,,,,,,,,,---------......,,,,,,------...///000000...............///000000------,,,,,,,,,---.........------,,,++++++++++++,,,,,,,,,---------............------...///111222111111111000//////......---...000111111111000///........................000///...------,,,,,,---,,,------...///000111111000000111222222222222222.../////////000000111111000000////////////000000---...///111333444444444333333222222111000000//////000000111222222333333666555555444444444555555222333333444555555555444333333333444555666777888777777777777777888888999777777888999:::<<<<<<===<<<;;;999:::<<<=========888999;;;???DDDFFFFFFEEEBBBAAA@@@AAACCCEEEEEEEEE???AAACCCBBB@@@???AAACCCCCCBBBBBBBBBBBBCCCDDDDDDDDDEEEGGGGGGGGGGGGIIIJJJNNNMMMLLLIIIFFFDDDFFFGGGJJJIIIIIILLLPPPPPPMMMIIIGGGFFFEEEEEEGGGIIIIIIHHHGGGFFFFFFGGGHHHHHHFFFDDDFFFGGGHHHHHHHHHGGGFFFEEEFFFFFFDDDAAA??????AAACCCDDDDDDEEEEEEEEEEEEDDDDDDEEEGGGIIIJJJIIIHHHHHHIIIGGGHHHHHHGGGFFFFFFGGGIIIFFFHHHKKKLLLKKKJJJJJJKKKHHHIIIIIIIIIHHHFFFDDDCCC??????AAADDDGGGHHHFFFDDD@@@??????CCCFFFFFF@@@;;;????????????>>>>>>>>>>>>;;;<<<===>>>>>>???>>>>>>???AAACCCEEEGGGGGGGGGGGGFFFFFFEEEDDDCCCBBBAAAAAAEEEDDDBBBAAAAAABBBDDDEEECCCCCCBBBAAA@@@?????????;;;;;;:::;;;<<>>>>>>>>>>>============777999<<<<<<;;;<<<>>>AAA@@@AAABBBDDDEEEFFFFFFFFFCCCAAA???>>>>>>>>>===;;;??????>>>>>>???@@@@@@AAA>>>===;;;::::::;;;<<<===>>>>>>>>><<<999888777888666666666666555555555555555555555666555555444444555444333333222222333333222333333444333222000///333111000000111222222111000/////////............///000111222222333222222//////////////////////////////000000000000////////////.........---------////////////000000111111,,,,,,,,,+++++++++******,,,,,,++++++++++++,,,,,,******++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,------''''''''''''((()))++++++'''((((((((())))))******'''((((((((())))))******&&&&&&&&&&&&&&&'''((()))'''''''''((((((((((((((("""  ###$$$###!!!$$$%%%''''''''''''%%%$$$&&&&&&&&&'''''''''((((((%%%%%%%%%$$$$$$$$$######%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""$$$#########$$$%%%%%%&&&$$$%%%&&&&&&$$$$$$%%%&&&###$$$&&&''''''&&&$$$###++++++,,,,,,,,,,,,------------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---,,,,,,++++++************************.........------,,,,,,,,,---......///////////////...///////////////......///...,,,++++++,,,---...,,,,,,,,,------.........///////////////...............////////////......////////////000000000000000000//////.........---111111000000000000000111222222222333333444444444000000000000////////////111111111111222333444444222222333333333444444444222333333444333222000///333333333333444666888999555666777888888888888888777888:::;;;;;;:::999777999999888888999999:::;;;:::<<<>>>@@@BBBBBBAAAAAA???????????????@@@@@@@@@>>>===<<<<<<<<<>>>???@@@DDDBBB@@@>>>>>>???@@@AAACCCCCCDDDGGGIIIJJJHHHGGGEEEEEEDDDBBBBBBCCCGGGKKKKKKIIIHHHIIIJJJJJJIIIGGGDDDCCCBBBDDDHHHIIIHHHEEEFFFGGGGGGHHHHHHHHHGGGGGGGGGGGGHHHIIIHHHGGGFFFEEEFFFEEEDDDCCCBBBAAAAAABBBGGGFFFFFFFFFGGGHHHIIIIIIHHHHHHHHHHHHHHHHHHHHHHHHIIIJJJKKKKKKKKKKKKKKKJJJJJJKKKLLLLLLLLLKKKIIIHHHHHHFFFEEEHHHKKKKKKFFFAAA===???BBBCCCAAA@@@??????AAA@@@@@@CCCEEEDDD???;;;;;;===???AAAAAA@@@===<<<<<<======>>>???@@@@@@AAA??????@@@AAABBBDDDEEEFFFEEECCC@@@>>>>>>@@@CCCEEEIIIFFFDDDDDDFFFHHHIIIIIIIIIFFFCCCBBBBBBAAA>>>:::999:::;;;===>>>@@@AAABBBAAA@@@>>><<<;;;::::::;;;;;;;;;<<<<<<===???@@@AAACCCDDDDDDEEEEEEEEEEEEDDD>>>===<<<;;;::::::;;;<<>>>>>===>>>>>>;;;666666999999666666666666666666555555555444444222222222222444444222222222222222222222222222222333333333222111111000000000000000000000000000000//////.........---000000000000000000000000......---------,,,,,,,,,..........................................------........................111///---+++***+++,,,---************)))))))))(((++++++******************++++++++++++++++++++++++((((((((((((''''''''''''$$$%%%&&&(((***+++------***)))(((''''''((()))***((((((''''''''''''(((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&%%%$$$$$$###''''''&&&&&&&&&%%%%%%%%%'''&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&%%%$$$!!!"""$$$%%%%%%$$$"""!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%!!!"""""""""###############$$$%%%%%%%%%%%%$$$###$$$))),,,***### """&&&###$$$%%%%%%&&&&&&%%%%%%++++++,,,,,,,,,,,,------------------------------,,,,,,,,,,,,,,,,,,,,,,,,+++,,,,,,---------,,,,,,++++++++++++++++++++++++------,,,,,,,,,+++++++++,,,,,,---...............,,,,,,------------,,,,,,...---,,,++++++,,,---...,,,,,,,,,---------......////////////..................////////////.............../////////000000000/////////............000000//////...//////000111111111111222222333333000000000000////////////111111000000000111222222222222222222333333333333222222333333333222111000222111111222333444666777555555666777777777666666555666888999:::999888777999999888888888999:::::::::<<<>>>@@@AAAAAA@@@???>>>>>>>>>>>>????????????;;;;;;::::::;;;<<<<<<===BBBAAA???>>>>>>>>>??????BBBBBBCCCDDDEEEEEEDDDBBBCCCBBB@@@@@@BBBGGGKKKNNNMMMKKKHHHGGGGGGFFFEEECCCAAA@@@@@@CCCGGGIIIIIIGGGFFFFFFGGGGGGGGGGGGFFFFFFEEEFFFFFFGGGFFFEEECCCBBBCCCBBBBBBBBBBBBBBBCCCCCCFFFFFFFFFFFFGGGHHHIIIJJJHHHHHHGGGGGGGGGGGGGGGHHHJJJJJJKKKKKKKKKJJJJJJIIIIIIIIIJJJJJJJJJIIIHHHGGGFFFDDDDDDFFFJJJIIIEEE@@@???AAACCCDDDCCCAAAAAAAAA@@@??????AAABBBBBB???<<<===>>>???@@@@@@???===<<>>>>>>>>>>>?????????@@@AAACCCEEEFFFDDDBBB@@@??????AAADDDFFFIIIGGGEEEEEEGGGJJJKKKKKKHHHFFFCCCAAAAAA@@@===;;;999:::;;;<<<>>>???@@@AAA@@@>>>===;;;:::::::::;;;;;;;;;<<<<<<>>>???@@@AAABBBBBBCCCCCCDDDDDDCCCCCC>>>===;;;:::::::::;;;<<<>>>???@@@AAABBBBBBBBBBBBAAA???======>>>??????>>>>>>>>>;;;666555888999666666666666666555555555555444333333222222333333444222222222222222222222222333333333333222111111000000000000000000000000000000/////////.........---////////////////////////............---------,,,........................//////......---,,,++++++------------------------///...,,,***)))***+++,,,++++++++++++*********)))************************************************))))))((((((((('''''''''###$$$$$$%%%&&&'''(((((()))((((((''''''(((((()))((((((''''''''''''(((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%######$$$%%%%%%$$$""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###"""%%%((('''$$$"""###&&&###$$$%%%%%%&&&&&&%%%%%%++++++,,,,,,,,,,,,------------------------------,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,---............,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++******++++++,,,---------------,,,,,,------------,,,,,,((((((((())))))******+++,,,,,,,,,------------.................................////////////......---------.........//////////////////............///......------...//////000000000000000111111111////////////000000000000111111000/////////000000111111111222222222222333111111222333333333222222000000000000111333444555555555555555555555444333333444666777888888888777:::999999888888888999999;;;<<<>>>@@@@@@???>>>===<<<<<<<<<=========>>>>>>888888999::::::::::::999>>>>>>>>>>>>>>>=========@@@AAAAAAAAA@@@???>>>>>>@@@>>>===@@@GGGMMMQQQQQQOOOKKKGGGDDDCCCBBB@@@???>>>>>>???BBBEEEHHHIIIHHHEEEEEEEEEEEEEEEEEEEEEEEEEEEFFFFFFFFFEEEDDDBBBAAA???@@@@@@AAABBBCCCCCCDDDDDDDDDEEEEEEGGGHHHJJJJJJGGGFFFEEEDDDDDDEEEGGGGGGJJJJJJKKKJJJJJJIIIHHHGGGGGGGGGHHHIIIHHHGGGFFFEEEDDDCCCCCCEEEHHHHHHEEEAAA???BBBDDDDDDBBBAAAAAAAAA@@@???>>>>>>??????>>>===????????????>>>>>>======BBBBBBAAA???>>>===<<<;;;>>>>>>>>>???AAABBBDDDEEEDDDBBBAAA@@@AAADDDGGGHHHJJJHHHGGGGGGIIIKKKLLLLLLGGGEEEBBBAAA@@@???===;;;999999:::;;;<<<>>>>>>???===<<<;;;999999999:::;;;;;;;;;<<<===>>>???@@@@@@???@@@AAAAAABBBBBBBBBAAA>>>===<<<;;;:::;;;<<<===>>>>>>@@@AAAAAAAAAAAAAAA@@@>>><<<<<<>>>@@@@@@@@@>>>>>>;;;555444777888666666666666555555555444444444333333222222333333444333333333333333333333333333333333333222111000///000000000000000000000000/////////.............../////////////////////////////////.........------////////////////////////000///...---+++***))))))------------------------...,,,+++)))))))))******,,,,,,+++++++++*********************************))))))))))))))))))))))))))))))))))))(((((((((((('''''''''((((((((((((((('''''''''(((((('''''''''((((((''''''''''''(((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$%%%%%%%%%%%%$$$$$$#########"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%######$$$%%%%%%$$$######""""""###$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%+++++++++,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++***+++,,,---.../////////,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++++++++,,,---------------------.../////////......'''((()))***+++,,,,,,+++------------------------------...............///---......//////......---,,,,,,,,,---------......///////////////..................---......//////000000000000000000000000////////////000000000000222111000000////////////000000111111111222222222000111111222333333333333000000000111222222333444555555666555555444333222222333555777888888888888:::999999888888888888888;;;===>>>??????>>><<<;;;:::::::::;;;<<<<<<======888999:::;;;;;;;;;999999<<<<<<=========<<<<<<;;;===>>>???>>>===<<<======@@@>>>@@@FFFOOOTTTSSSQQQMMMIIIEEEBBBAAA@@@>>>===>>>>>>???AAACCCEEEGGGGGGEEEDDDDDDCCCCCCCCCCCCCCCGGGGGGHHHHHHGGGEEECCCBBB??????@@@AAABBBBBBBBBBBBAAABBBBBBCCCEEEGGGHHHIIIFFFEEEDDDCCCCCCEEEFFFGGGJJJJJJJJJJJJIIIHHHFFFFFFFFFGGGGGGHHHGGGFFFEEEDDDDDDDDDDDDFFFIIIIIIGGGDDD@@@AAACCCCCCAAA@@@@@@AAAAAA@@@>>>>>>>>>>>>??????AAA@@@???=========>>>>>>BBBBBBAAA@@@>>>===<<<<<<======>>>???@@@BBBCCCDDDDDDCCCBBBCCCDDDGGGJJJKKKMMMLLLJJJIIIJJJKKKKKKJJJEEEDDDBBB@@@???>>><<<;;;999999::::::;;;<<<======::::::999888888999:::;;;;;;<<<======>>>?????????>>>???@@@AAAAAAAAAAAAAAA???>>>===<<<<<<===>>>???===>>>???@@@AAAAAAAAAAAA>>>===;;;<<<>>>@@@AAA@@@===???<<<666333666888777666666666555555444444333333333333333333333333333333333333333333333333333333333333333222000///...000000000000000000000000........................////////////////////////000////////////.........////////////////////////------,,,,,,+++***)))))),,,,,,,,,,,,,,,,,,,,,,,,---,,,+++************++++++++++++*********))))))))))))))))))************))))))))))))))))))))))))******)))))))))((((((((((((((((((((())))))))))))%%%&&&'''(((((('''&&&%%%(((''''''&&&&&&''''''((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$######"""######$$$########################$$$###""""""###$$$&&&'''&&&&&&%%%###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%######$$$$$$$$$$$$######$$$"""!!!###&&&'''%%%"""###$$$%%%%%%&&&&&&%%%%%%+++++++++,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++***+++,,,---............,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------------,,,,,,---............---,,,,,,---...//////......+++,,,---//////000000000------------------------,,,---------......//////------............------,,,,,,,,,,,,------------.........//////////////////.........//////000111111111111111111000000000.../////////000000000111333222111000000000000000000000111111111222222222111111111222222333333444111111222333333444444444666666666666555444444333333444555666888999999999999999888777777888888888;;;<<<===>>>>>><<<;;;999888999999:::;;;;;;<<<<<<;;;;;;=========<<<;;;::::::;;;;;;<<<<<<<<<;;;;;;;;;===>>>===<<<<<<>>>@@@AAABBBFFFNNNVVVXXXRRRLLLHHHEEEBBBAAAAAAAAA@@@>>>AAAAAAAAA@@@AAAAAACCCDDDDDDCCCBBBAAAAAAAAAAAABBBFFFFFFGGGGGGFFFEEECCCBBB@@@@@@AAABBBBBBAAAAAA@@@??????@@@AAACCCDDDFFFGGGEEEEEEDDDDDDDDDEEEGGGHHHIIIIIIIIIIIIHHHFFFEEEEEEFFFFFFGGGHHHGGGFFFEEEDDDEEEEEEFFFGGGIIIJJJIIIHHHBBBDDDEEEDDDBBBAAAAAABBBBBBAAA@@@>>>===>>>@@@AAAAAA@@@>>>===<<<===>>>???AAA@@@@@@@@@??????>>>>>>======>>>???@@@BBBCCCDDDEEEEEEDDDEEEGGGIIILLLMMMPPPNNNLLLKKKJJJJJJHHHFFFBBBBBBAAA@@@>>><<<;;;;;;999:::::::::;;;;;;<<<<<<999999888777888999:::;;;;;;<<<===>>>??????>>>>>>===>>>???@@@AAAAAAAAAAAA@@@@@@???>>>>>>???@@@AAA======>>>???@@@@@@@@@@@@===;;;:::;;;===???@@@@@@===@@@>>>888555666777666777666666555444333333333333333333333333333333333333333333333333333333333222222222222111000///...////////////////////////---------.......................................000////////////.........////////////////////////******++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,---,,,,,,+++++++++++++++))))))))))))(((((((((((((((((()))))))))*********************************))))))))))))(((((((((((("""######$$$%%%&&&'''(((%%%&&&'''(((((('''&&&%%%''''''&&&&&&&&&&&&''''''(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%$$$$$$######&&&&&&%%%%%%%%%$$$$$$$$$$$$######"""######$$$$$$########################%%%$$$#########%%%&&&'''&&&&&&%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""#########$$$########################'''$$$"""$$$''''''$$$!!!###$$$%%%%%%&&&&&&%%%%%%++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++******+++,,,------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------......,,,,,,---...............)))***+++,,,,,,---,,,,,,*********++++++,,,,,,---...------------,,,,,,,,,,,,,,,,,,---......//////------............------,,,,,,,,,---------...............///////////////............///000111111111111111111000000000000......//////000000111111222222111000000000111111111111111222222222222333222222222111111222333333222222333444555555444444555555555666555555444444444555555666777888999999777777777777777888999999:::;;;<<<======<<<:::999777888999999:::;;;<<<<<<===============<<<<<<;;;:::::::::;;;;;;;;;;;;;;;:::===>>>===;;;;;;>>>AAAAAADDDJJJRRRWWWUUUNNNHHHDDDBBBAAABBBCCCCCCBBBAAACCCDDDCCCAAA??????@@@BBBCCCBBBAAA?????????@@@@@@BBBCCCDDDDDDDDDCCCAAA@@@@@@AAABBBCCCCCCBBBAAA@@@??????@@@@@@BBBCCCEEEEEEEEEEEEFFFGGGGGGHHHHHHHHHGGGGGGHHHGGGGGGFFFEEEDDDEEEFFFFFFGGGFFFEEEDDDCCCBBBCCCDDDFFFGGGHHHHHHIIIEEEFFFGGGFFFDDDCCCCCCDDDAAAAAAAAA???>>>>>>???AAA@@@???>>>======>>>???@@@?????????@@@@@@@@@@@@@@@>>>>>>>>>???AAABBBDDDEEEEEEEEEEEEEEEGGGIIIKKKLLLOOOMMMKKKJJJJJJHHHFFFDDD@@@AAAAAA???<<<::::::;;;:::;;;;;;;;;;;;;;;;;;;;;:::999888777777888999:::;;;<<<===?????????>>>===<<<===>>>???@@@AAAAAAAAAAAA@@@???>>>???@@@AAABBB<<<===>>>??????@@@??????<<<:::999999;;;===>>>>>><<>>@@@===:::999<<<@@@???CCCIIINNNPPPMMMIIIEEEAAAAAABBBDDDFFFFFFCCCAAADDDEEEDDDAAA>>>>>>@@@CCCCCCAAA???>>>======>>>???@@@AAABBBCCCCCCCCCBBBAAA???@@@BBBDDDDDDDDDCCCBBBAAAAAAAAAAAABBBCCCDDDEEEEEEFFFHHHJJJKKKJJJJJJIIIEEEFFFFFFFFFFFFFFFEEEEEECCCDDDEEEEEEEEEDDDBBBAAA===???@@@BBBBBBCCCEEEFFFEEEEEEEEEDDDBBBAAABBBCCC???@@@AAA???===<<<>>>@@@=========>>>>>>???@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@?????????@@@AAACCCEEEFFFCCCCCCCCCDDDEEEGGGHHHIIIKKKJJJIIIHHHIIIHHHFFFDDD???@@@AAA???;;;999:::;;;<<<<<<<<<;;;;;;;;;;;;;;;;;;:::999888888888999:::;;;<<<>>>?????????===<<<:::;;;<<<===???????????????>>>>>>===>>>???@@@AAA;;;<<<===>>>????????????;;;999888888:::;;;<<<<<<;;;AAADDD@@@:::888777555777666666555333222222111222333333444444333333222111111111111111111111111///000000111111111111111////////////////////////,,,,,,,,,------.............................................---------,,,------------------------+++++++++,,,,,,,,,,,,,,,++++++++++++++++++++++++******+++++++++++++++***))))))))))))((((((((((((''''''(((((()))******+++))))))))))))))))))))))))''''''''''''&&&&&&&&&&&&'''''''''(((((())))))))))))((((((''''''(((((()))'''&&&&&&%%%%%%&&&&&&'''(((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$######%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""!!!"""###$$$&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&########################""""""#########$$$$$$$$$$$$###"""!!!!!!"""###$$$#########$$$%%%%%%$$$######$$$%%%%%%&&&&&&%%%%%%++++++,,,,,,,,,---------++++++++++++++++++++++++******************************+++++++++***))))))*********************************++++++,,,,,,,,,******+++,,,,,,,,,,,,+++***+++,,,---......///......---+++))))))***,,,---.........------,,,,,,,,,++++++,,,,,,---...//////,,,------......------,,,---------.........//////---.........//////000000+++++++++,,,---...///000//////.........------------......///000111111222...............///000111222222333333333444444444555444222111111111222222111222333444555444333222000111222333333333333333444444333333333444555555555555555666777999;;;;;;777888:::<<<<<<;;;:::999777888888:::;;;<<<======;;;:::888777777777888999<<<;;;999999999;;;===>>>===@@@@@@===888666:::===>>>BBBGGGIIIIIIGGGEEEEEEAAABBBCCCFFFHHHGGGDDDAAADDDEEEDDDBBB>>>>>>AAADDDCCCAAA???===<<<<<<>>>>>>AAABBBCCCEEEEEEEEEEEEDDD===???BBBDDDFFFFFFEEEEEECCCCCCCCCCCCCCCDDDEEEFFFEEEGGGJJJLLLMMMLLLKKKIIIDDDEEEEEEFFFFFFFFFFFFEEEAAABBBCCCCCCCCCBBBAAA@@@999;;;===>>>>>>@@@BBBCCCBBBBBBBBB@@@>>>===>>>@@@<<>><<<<<<===>>>???@@@AAAAAAAAAAAAAAA@@@@@@???????????????@@@AAABBBDDDEEEFFFBBBBBBBBBBBBCCCEEEFFFFFFHHHGGGFFFGGGHHHHHHGGGEEE>>>@@@AAA???;;;999:::;;;===<<<<<<<<<<<<;;;;;;;;;<<<;;;999888888888999:::;;;<<<>>>???@@@???===<<<888999:::<<<===>>>>>>>>>>>>===<<<<<<<<<>>>???@@@;;;<<<===>>>????????????;;;999777777999::::::::::::BBBFFFBBB<<<999777555777666666555333222111111222222444444444444222222000000000000000000000000...///000111111222222111////////////////////////,,,,,,,,,------.......................................---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------,,,,,,+++++++++************************((()))************))))))************))))))))))))&&&''''''((()))******+++((((((((((((((((((((((((''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$***)))(((''''''((()))***'''&&&&&&%%%%%%&&&&&&'''(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%$$$$$$$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$###"""  """$$$'''((('''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&##############################$$$$$$$$$%%%%%%%%%$$$###"""!!!!!!"""###$$$ !!!######$$$$$$%%%$$$$$$%%%&&&&&&&&&%%%%%%,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++***)))(((++++++************+++++++++++++++++++++++++++++++++,,,------------,,,+++******++++++++++++******,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++******+++++++++,,,,,,,,,++++++++++++++++++++++++,,,,,,,,,---------......---------,,,,,,+++++++++***++++++,,,,,,++++++***---......///000/////////------------......//////......---,,,---...///000,,,---///000111111111000111111111111111111111111111111111000///000222444111111111000000000000000///111333444444333222000222222111111222222333444555666666666666666555555666666666666777777777777888777777777777777888999:::999888888888999:::;;;<<<:::888999:::;;;::::::999999999999:::;;;===>>>BBBDDDCCC>>>888666999===AAACCCEEEFFFEEEDDDDDDEEECCCBBBCCCGGGKKKKKKHHHDDDDDDCCCAAA@@@???>>>??????AAA@@@??????>>>?????????DDDCCCBBBCCCFFFIIIKKKKKKJJJGGGDDDCCCEEEHHHIIIJJJHHHFFFDDDCCCBBBCCCDDDEEEFFFFFFGGGHHHJJJKKKIIIGGGGGGHHHIIIGGGEEEDDDDDDEEEIIIHHHFFFCCCAAA???>>>>>>;;;<<<>>>???AAACCCDDDEEEDDDCCCBBBAAAAAAAAAAAAAAAAAAAAAAAA@@@>>>;;;999777999:::;;;===???@@@BBBBBB>>>>>>???@@@@@@@@@@@@???======>>>???????????????DDDBBB@@@AAAEEEHHHHHHGGGEEEFFFGGGHHHGGGEEECCCBBB@@@???>>><<<<<<<<<============<<<<<<<<<<<<======:::;;;;;;<<<<<<;;;;;;:::;;;;;;<<<======<<<;;;:::888:::<<<>>>???>>><<<:::???>>>>>>>>>>>>>>>>>>?????????@@@@@@@@@@@@??????888777666666777999;;;===<<<======;;;888666555555444444444444444444444444333333222222222222222222000////////////000000111///000222222222111///...------------------------///---+++))))))+++---///........................000///...---,,,+++++++++.........------,,,,,,,,,------,,,,,,,,,,,,++++++,,,,,,,,,++++++*********))))))))))))))))))))))))))))))(((((('''''''''&&&(((((((((((())))))))))))''''''&&&&&&&&&&&&''''''((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%))))))(((((('''''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$$$$"""############$$$$$$$$$######$$$$$$$$$%%%%%%%%%'''&&&%%%%%%$$$$$$$$$$$$%%%&&&'''((((((&&&$$$###!!!!!!"""###$$$$$$%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######""""""""""""""""""""""""$$$$$$###"""!!!!!!!!!"""########################$$$$$$$$$$$$$$$$$$$$$$$$+++++++++++++++++++++++++++++++++++++++***))))))++++++************++++++++++++++++++++++++++++++***+++,,,------,,,+++*********++++++++++++******,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++*********+++++++++,,,,,,++++++++++++++++++++++++,,,,,,,,,,,,---------------------,,,,,,,,,+++++++++,,,,,,------,,,,,,+++,,,---......//////................../////////000///...---,,,,,,---...///......///000111111111111111111111111111111111111111111222111000000222444111111000//////...------///000111222333222111111222111111111111222333333444444555555555444444333555666666666777777777777777777777777777777888888999999888777888999:::;;;:::999777888:::;;;;;;:::;;;;;;<<<<<<===>>>>>>???AAABBBBBB>>>999777:::===@@@BBBDDDDDDCCCBBBBBBCCCBBBCCCFFFIIIJJJJJJGGGDDDCCCAAA???===;;;:::::::::@@@@@@???????????????@@@AAA@@@AAADDDIIINNNQQQQQQHHHGGGFFFEEEEEEFFFGGGHHHGGGFFFDDDBBBBBBCCCDDDEEEEEEEEEEEEGGGIIIIIIHHHFFFGGGHHHHHHGGGEEEDDDEEEFFFHHHGGGEEEBBB@@@>>>===<<<======>>>???AAACCCEEEFFFDDDCCCBBBAAA@@@@@@@@@@@@AAAAAA@@@???===;;;999888999999:::;;;<<<<<<======>>>>>>???@@@@@@@@@@@@@@@>>>>>>>>>???????????????DDDBBB@@@BBBFFFIIIIIIHHHFFFGGGGGGGGGFFFEEECCCBBB@@@@@@>>>===<<<<<<============<<<<<<;;;<<<<<<<<<:::;;;;;;<<<<<<;;;;;;:::::::::;;;<<<<<<;;;:::999888999;;;<<<===<<<;;;:::>>>>>>>>>>>>>>>>>>>>>>>>===>>>>>>??????>>>>>>===999888666555555666888999888888888888888777666666555555555444444333333333333222222222222111111111///////////////000000111///000111222222111///...........................------------------------........................//////...,,,,,,++++++,,,......---------,,,,,,,,,------,,,,,,,,,+++++++++,,,,,,,,,++++++*********))))))))))))))))))))))))))))))((((((((('''''''''(((((((((((())))))))))))''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$##################$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%'''&&&%%%$$$$$$$$$$$$$$$$$$%%%'''''''''%%%$$$"""!!!""""""###$$$$$$%%%%%%#########$$$$$$%%%%%%%%%#########"""""""""!!!!!!""""""""""""""""""""""""$$$###""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$***************************++++++++++++***))))))++++++************++++++++++++++++++++++++++++++******++++++++++++************++++++++++++******,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++*********++++++++++++,,,,,,,,,++++++************++++++,,,,,,,,,---------------------,,,,,,,,,,,,,,,,,,------------,,,,,,+++,,,,,,---------------......///////////////000///...---,,,,,,---......111000000000000000111111000000000000000000000000111222222111000111333444333333222000///...---,,,000000000111111111222222111111111111111222222333222333333444444333333222555555666666666777777777666666666777777888888888888888777666777888999:::999777666888:::<<<<<<;;;<<<===???@@@AAA@@@@@@???>>>@@@@@@===999888:::===@@@AAACCCBBBAAA@@@@@@AAAAAAEEEIIIKKKJJJGGGEEECCCBBB@@@>>>;;;999888888888@@@@@@@@@@@@@@@@@@@@@AAA??????@@@DDDJJJNNNQQQRRRFFFIIIJJJIIIFFFDDDEEEGGGEEEDDDCCCBBBAAABBBCCCDDDCCCCCCDDDFFFHHHHHHGGGEEEEEEFFFGGGGGGEEEDDDEEEGGGHHHFFFDDDAAA???===<<<;;;????????????AAACCCFFFGGGDDDCCCBBBAAA@@@@@@@@@@@@BBBAAA@@@>>><<<;;;::::::999:::::::::::::::::::::>>>>>>???@@@@@@@@@@@@@@@@@@???>>>======>>>>>>???BBBBBBBBBDDDGGGJJJJJJJJJHHHHHHGGGFFFEEEDDDCCCCCCAAA@@@???>>>==================<<<;;;;;;:::;;;;;;:::;;;;;;<<<<<<;;;;;;:::888999:::;;;;;;:::999999999999::::::::::::::::::<<<<<<============<<<<<<;;;<<<<<<======<<<<<<;;;:::999777555444444555555555444333555888999888555666666555444333333222222222222222222111111000000///////////////000111111000000111222111000///...////////////////////////,,,---///000000///---,,,........................///...---,,,,,,++++++,,,------------,,,,,,,,,,,,,,,,,,,,,,,,+++++++++++++++++++++++++++*********))))))))))))))))))))))))))))))((((((((((((''''''))))))))))))((((((((((((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$###$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""############$$$$$$$$$%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$$$$$$$%%%###$$$%%%&&&%%%$$$###""""""""""""###$$$$$$%%%%%%#########$$$$$$$$$$$$$$$#########"""""""""""""""""""""""""""""""""""""""""""""""""""""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$))))))))))))))))))))))))******+++++++++******)))++++++************++++++************************))))))************))))))******++++++++++++******++++++++++++++++++++++++************************************++++++++++++,,,,,,++++++******))))))++++++++++++,,,,,,,,,,,,---------,,,,,,,,,,,,,,,+++,,,,,,------,,,,,,+++******+++,,,,,,,,,,,,,,,........................---,,,++++++,,,...///000333222000//////000111222000000000000000000000000000111222222111111222444555444444333222111000000000000000000111222333333000000000000000111222222111222333333444333333333555555555666666666777777555555666777777888888888777777666666666777888999888777777888;;;===>>>>>><<<>>>@@@AAABBBAAA???>>><<<======<<<999999;;;===???AAABBBBBB@@@??????@@@AAAFFFKKKLLLIIIEEECCCCCCAAA@@@>>><<<;;;::::::;;;??????@@@AAAAAABBBBBBBBBBBBAAAAAACCCGGGIIIJJJJJJFFFJJJNNNMMMHHHDDDDDDFFFCCCCCCBBBAAAAAAAAABBBCCCBBBBBBCCCEEEHHHHHHGGGEEEDDDEEEFFFFFFEEEEEEFFFGGGGGGFFFDDDBBB@@@>>>===<<>>??????@@@@@@?????????>>><<<;;;:::;;;===>>>AAABBBCCCFFFHHHJJJJJJJJJIIIHHHGGGEEEDDDCCCCCCCCCAAA@@@???>>>===<<<<<<<<<===<<<;;;::::::999999::::::;;;;;;<<<<<<;;;;;;:::888999:::;;;<<<;;;::::::;;;;;;:::999999:::;;;<<<;;;;;;<<<======<<<;;;;;;999::::::;;;;;;::::::999:::999777666555555666666666333111444999;;;888444777666666444333222111111222222222111000000/////////......//////000111222000111111111000///...---........................------............------...........................------,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++***+++++++++***************))))))))))))))))))))))))))))))(((((((((((((((((())))))))))))((((((((((((''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###""""""#########$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%######$$$$$$$$$$$$###"""""""""#########$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""""""""""""""""""""!!!!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$(((((((((((((((((((((((()))******+++++++++******++++++************++++++************************))))))))))))))))))))))))******++++++++++++******++++++++++++++++++++++++************************))))))*********++++++++++++++++++******)))))))))*********+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,******++++++++++++******)))******+++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,***)))***+++,,,///111222222111000/////////111111///////////////////////////000222222111000111333222222222222222333333333000000000000111222444444000000//////000000111222111222333444444444444444555555555555666666666666333444666777888888888777666666555444555666777888999888888999<<>>@@@@@@???===<<<:::;;;;;;::::::999:::;;;???AAACCCDDDBBBAAA@@@@@@AAAEEEJJJKKKGGGCCCBBBBBB>>>===<<<;;;;;;<<<===>>>>>>???@@@BBBCCCCCCCCCCCCDDDCCCCCCDDDFFFGGGGGGFFFGGGLLLQQQPPPJJJFFFEEEFFFBBBBBBAAAAAAAAABBBBBBBBBBBBBBBCCCFFFHHHIIIHHHFFFDDDEEEFFFFFFEEEDDDEEEGGGGGGFFFEEECCCAAA@@@??????BBBBBBBBBBBBDDDFFFHHHIIIGGGFFFEEECCCBBBBBBAAAAAABBBAAA???===;;;;;;;;;<<<888999999:::;;;<<<======<<<===>>>>>>??????>>>>>>===<<<:::999999:::;;;===@@@BBBEEEHHHIIIIIIIIIIIIHHHGGGEEEDDDCCCBBBBBBBBB@@@@@@???>>>===<<<;;;:::;;;;;;:::999999999999999:::;;;;;;<<<<<<;;;;;;:::999:::;;;=========<<<;;;===<<<;;;::::::;;;<<<===:::;;;<<<======<<<;;;:::888888888999999888888888777777777777888888999999999666333555:::;;;888444777666666444333222111111222222111000000///..................///000111222111111111000///...------------------------------...---+++******+++---...........................------,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++*********************************))))))))))))))))))))))))(((((())))))))))))))))))***)))))))))((((((((('''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""###$$$$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$%%%"""####################################$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$"""""""""""""""""""""""""""!!!!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$(((((((((((((((((((((((())))))***++++++++++++***++++++************++++++******************************))))))))))))************++++++++++++******++++++++++++++++++++++++************************)))))))))************+++************************))))))*********+++++++++************++++++++++++))))))************)))))))))******+++++++++++++++,,,++++++++++++*********)))))))))***,,,///111333000///////////////000000////////////////////////---///111111000///000111......//////000111111222...//////000111222333333///////////////000000111111111222333444444444444444444555555555666666666222333555777888888777777555555444444444555666777999888888999<<>>BBBFFFHHHGGGEEECCCBBBAAADDDFFFGGGEEECCCAAAAAA;;;;;;::::::;;;<<<>>>???===???AAACCCDDDDDDDDDDDDCCCCCCDDDFFFIIIJJJJJJIIIHHHKKKOOOOOOLLLGGGFFFEEEAAAAAABBBBBBBBBBBBBBBBBBBBBBBBCCCEEEHHHIIIHHHFFFDDDEEEFFFFFFDDDCCCDDDFFFFFFEEEDDDCCCBBBBBBBBBBBBCCCCCCDDDEEEFFFGGGHHHHHHGGGFFFEEECCCBBBAAAAAAAAAAAA@@@???===<<<<<<;;;;;;666666777888:::;;;<<<<<<;;;;;;<<<===============::::::999999999:::<<<<<>>===<<<;;;999888999999888888888888999999:::;;;;;;<<<<<<;;;;;;:::999:::<<<===>>>======<<<>>>===<<<;;;:::;;;<<<===:::;;;===>>>>>>===;;;:::666777777888888777777666555666777888999:::;;;;;;:::888666888::::::888555666666555444333333222222222111111000///...------............///111222333222111000///......------------------------------///---+++))))))+++---///........................,,,,,,++++++++++++,,,,,,++++++++++++,,,,,,,,,,,,++++++++++++************)))))))))***************))))))))))))))))))))))))(((((())))))))))))************))))))((((((''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$############$$$$$$%%%###############$$$$$$$$$#######################################""""""""""""""""""""""""#########""""""""""""""""""""""""""""""""""""""""""###$$$########################$$$$$$$$$$$$$$$$$$$$$$$$(((((((((((((((((((((((())))))***+++++++++++++++++++++************++++++************************+++***))))))))))))***+++******++++++++++++******************************************************))))))))))))************(((((())))))******++++++))))))))))))*********+++(((((()))))))))******************++++++*********)))***++++++,,,,,,++++++,,,,,,,,,+++++++++******+++*********+++---///000,,,---...///////////////........................+++...000000///...//////.../////////////////////+++,,,...///111111000000///............///000000///000111222333333333333444444444555555555666666111333555777888888777777555444333333333444666666888777777888:::<<<===<<<;;;;;;;;;;;;;;;;;;;;;;;;999999888999999999888777>>>CCCIIIMMMLLLJJJGGGEEEBBBBBBAAABBBCCCCCCAAA@@@>>>===<<<<<<<<<===>>>???===???AAADDDEEEEEEEEEDDDBBBBBBCCCFFFIIIKKKJJJIIIHHHIIIKKKLLLKKKHHHEEECCCAAAAAABBBCCCCCCCCCCCCCCC@@@@@@AAADDDGGGHHHGGGEEEEEEFFFGGGFFFDDDCCCCCCDDDCCCBBBBBBAAAAAABBBBBBCCCBBBDDDFFFHHHIIIIIIHHHGGGFFFEEECCCBBB@@@?????????????????????>>><<<;;;:::888999999999:::::::::;;;999:::;;;;;;<<<<<<;;;;;;999999:::;;;<<<======>>>>>>BBBGGGIIIHHHFFFEEEEEE@@@AAABBBBBBBBBAAA@@@@@@============;;;999777666777777777777777888999::::::;;;;;;<<<<<<;;;;;;:::888999;;;<<<======<<<<<<===<<<;;;;;;:::::::::;;;:::;;;===??????===;;;:::666666777777777777666666444555666888999999::::::777888888999999888888777555555555444444333333333222111000///...------,,,------......///111222333222111000///...---------...........................---,,,,,,,,,,,,---...........................,,,+++++++++++++++,,,,,,******+++++++++,,,,,,,,,++++++++++++************((()))))))))*********+++))))))))))))))))))))))))(((((()))))))))******************)))((('''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%###############$$$%%%%%%###############$$$%%%%%%########################$$$#########"""""""""!!!!!!!!!"""""""""#########""""""""""""""""""""""""$$$###""""""""""""""""""""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$))))))))))))))))))))))))((()))***+++++++++++++++++++++************++++++)))))))))))))))))))))))),,,+++***))))))***+++,,,******++++++++++++******************************))))))))))))))))))))))))))))))))))))************''''''((()))***+++,,,,,,))))))))))))************''''''(((((()))))))))***+++++++++,,,,,,+++++++++******+++,,,,,,,,,,,,+++---------,,,,,,+++++++++------,,,+++++++++------***+++---///000000///...........................***---///000///.........222222111111000000//////((())),,,...000///.....................///000000......000111111222222222444444444555555555666666111222555777888888777777444444333222333444555666777666555666999;;;;;;:::<<<;;;;;;:::::::::;;;;;;999888888999999999888666>>>DDDKKKPPPPPPMMMIIIGGGCCC@@@>>>???BBBCCCBBB???CCCBBB@@@?????????@@@AAA===>>>AAADDDFFFFFFEEEEEEAAAAAABBBEEEGGGHHHFFFEEEGGGGGGHHHIIIJJJHHHEEEBBBAAABBBBBBCCCDDDDDDDDDCCC??????@@@CCCFFFGGGFFFDDDFFFGGGGGGFFFCCCBBBBBBCCC@@@@@@@@@@@@AAABBBCCCCCCBBBDDDGGGJJJJJJJJJHHHGGGEEEDDDBBB@@@???>>>======>>>????????????===;;;:::=========<<<<<<;;;;;;;;;888999::::::;;;;;;::::::999:::;;;===>>>?????????>>>BBBHHHIIIGGGDDDCCCCCC===>>>@@@BBBBBBAAA@@@???<<<======<<<;;;888666555666666666666777999:::;;;:::;;;;;;<<<<<<;;;;;;:::777888999;;;<<<<<<;;;;;;;;;;;;;;;::::::999999999:::<<<>>>??????>>><<<:::666666777777777777666666444555666777888888888888444666888999888777888999444444444444444444444444222111000///...---,,,,,,------......///111222333222111000///------,,,,,,////////////////////////------...//////...------........................+++++++++***++++++,,,,,,*********++++++,,,,,,,,,+++++++++************)))(((((())))))*********+++))))))))))))))))))))))))(((((())))))*********++++++******)))(((''''''&&&'''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$#########""""""&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!"""###$$$%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%######""""""###$$$%%%%%%$$$$$$######$$$%%%&&&&&&$$$$$$##################$$$#########""""""!!!!!!######$$$$$$%%%%%%%%%%%%""""""""""""""""""""""""$$$$$$###"""!!!!!!""""""!!!!!!!!!!!!!!!!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$+++(((&&&'''***,,,+++)))************************))))))))))))))))))))))))...***&&&'''+++---+++)))******************************)))(((((('''(((((()))************+++++++++,,,,,,,,,+++++++++************)))))))))))))))***,,,+++***((((((((())))))---,,,,,,,,,+++*********+++***)))(((((()))***+++...---,,,,,,++++++++++++***++++++,,,,,,++++++***------,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,---.........---,,,,,,+++)))***,,,,,,,,,,,,...//////......------///000111000000000000000111111111///.........///000222333///......---------......//////000111222333333333666333000000333555444333222444666777888777666555111111111222333444666666777777888888888888777777<<<;;;:::999999999:::;;;999::::::;;;;;;::::::999<<<@@@FFFMMMQQQQQQLLLHHH@@@???>>>@@@CCCDDDCCC@@@?????????@@@@@@AAAAAAAAABBB@@@@@@BBBGGGIIIIIIHHHFFFDDDBBBAAACCCFFFGGGGGGFFFEEECCCBBBAAAAAABBBCCCDDDDDDCCCBBBBBBBBBBBBBBBCCCBBBAAAAAABBBCCCDDDEEEGGGGGGFFFEEEDDDCCCCCCBBB@@@AAABBBBBBCCCCCCCCCCCCCCCDDDFFFFFFFFFEEECCCBBBBBBBBBAAA@@@?????????@@@CCCBBB@@@>>>===<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<888:::;;;;;;:::999:::<<<===<<<<<>>???>>>===;;;777444222666777777888999:::::::::>>>===<<<<<<<<<;;;888666777777888999:::<<<===>>><<<;;;:::::::::<<<>>>???>>>===<<<<<<===<<<:::888555555555666666666666666333333444777999:::888777666555555444333333222222222111111111222333444444111000000///...---------............////////////111111000000//////......------......///......---------------------------......---,,,+++++++++,,,------,,,,,,+++***))))))******+++++++++,,,,,,,,,,,,,,,,,,+++++++++******)))((('''%%%%%%&&&&&&'''******))))))((((((''''''***++++++++++++***))))))(((((())))))))))))(((((((((((((((((((((((((((((($$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$######$$$%%%%%%&&&''''''###$$$$$$%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$############$$$$$$$$$$$$$$$######"""""" !!!!!!""""""##############################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$$$$%%%%%%""""""""""""""""""""""""&&&%%%$$$###""" """######""" !!!"""######$$$$$$$$$%%%%%%%%%###""""""###$$$''')))***+++(((''''''***++++++)))************************))))))))))))))))))))))))...***''''''+++---+++)))************************+++******))))))))))))***))))))*********+++++++++,,,,,,+++++++++***************)))))))))))))))***+++***)))((((((((()))***+++++++++++++++*********+++***))))))))))))***+++,,,,,,+++******************++++++,,,,,,++++++***---,,,,,,+++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,------......---,,,,,,+++)))+++,,,,,,,,,,,,---//////......---...///000111000000000000000000000000......------...///111222///......---------......//////000111222222222222666333111111333444444222222333555666777666555444111111111222333555666777777777666666666666777777666666555666777888:::;;;999999::::::::::::999999;;;>>>DDDKKKOOONNNJJJFFFBBB???======@@@BBBCCCBBBAAABBBBBBBBBBBBBBBCCCCCC@@@??????BBBFFFHHHHHHFFFDDDCCCAAABBBDDDFFFGGGFFFDDDCCCAAA@@@@@@@@@AAAAAADDDDDDDDDCCCCCCCCCCCCDDDBBBBBBAAAAAAAAABBBDDDDDDDDDCCCBBBAAA@@@???>>>===??????@@@AAAAAAAAAAAAAAA???AAACCCEEEFFFEEECCCBBB@@@??????>>>>>>>>>??????AAAAAA@@@@@@>>>===<<<;;;;;;;;;;;;;;;;;;<<<<<<<<<999:::;;;;;;999999:::<<<<<<<<<===???AAABBBAAA@@@DDDDDDDDDCCCBBBBBBAAAAAAAAAAAA@@@@@@???>>>======@@@??????===:::777333111666666777888999999::::::>>>===;;;;;;;;;:::888666666666777888999;;;<<<==================>>>??????===<<<;;;;;;;;;;;;999777555555555666666777777777666555555666888999888777777777777666555444444444222111111111111222222333111000000///......------//////000000111111111222000000000000//////......---------.........------------------------------+++******)))(((((())))))------,,,,,,+++******)))******+++++++++,,,,,,,,,+++++++++*********)))))),,,+++***)))((())))))***))))))))))))((((((''''''))))))*********)))(((((((((((())))))))))))((((((''''''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%&&&&&&''''''(((%%%&&&''''''((((((''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$#########"""$$$$$$$$$$$$#########""""""""""""#######################################$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$##################""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$######$$$$$$###!!!!!!"""$$$######$$$$$$$$$%%%%%%%%%$$$######"""###$$$&&&'''***((('''''')))******)))))))))))))))))))))))))))))))))))))))))))))))))))---***'''(((***,,,+++)))))))))))))))))))))))))))+++***************+++,,,)))))))))*********++++++++++++++++++*********))))))))))))(((((())))))***)))))))))((())))))***+++))))))******************++++++************++++++++++++***))))))))))))******++++++,,,,,,++++++***,,,,,,+++++++++*********,,,,,,,,,,,,,,,,,,,,,,,,---------------,,,,,,+++)))+++,,,,,,,,,,,,---//////............///000000000000000000000/////////---------------...///000......---------....../////////000111222222222222444333111111333444333222111222444555555555444333222222222333444555666777666555444444444444555666666666666666666777888999999999::::::::::::999999999<<>>;;;;;;===@@@BBBBBBBBBBBBAAAAAAAAAAAAAAAAAA===>>>???CCCEEEFFFEEECCCAAAAAABBBDDDFFFGGGFFFEEEBBBAAA@@@?????????@@@AAAEEEEEEEEEEEEEEEEEEEEEEEECCCBBBBBBBBBBBBCCCCCCDDDFFFEEEDDDBBBAAA@@@>>>>>>======>>>????????????>>>;;;>>>AAADDDEEEDDDBBBAAA???>>>>>>>>>>>>??????@@@????????????>>>===;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;:::;;;;;;;;;999999:::<<<<<<>>>???@@@???>>>???@@@CCCCCCCCCBBBAAAAAA@@@@@@BBBAAA@@@???>>>===<<<;;;@@@??????===:::777333222666666777888999999999999===<<<::::::::::::888777555555666888999:::;;;<<<======>>>>>>>>>>>>>>>>>>;;;:::999:::::::::888666444555555666777888999999999777666666777888888777777666666555555444444333222222111000000000111111000000000///......------......///000111111222222000000000////////////...---------------,,,,,,,,,---------------------------,,,,,,+++++++++++++++---,,,,,,++++++***************+++++++++,,,,,,,,,*********)))))))))((((((,,,,,,+++***************)))))))))(((((((((((('''(((((())))))(((((('''&&&'''(((((())))))(((((('''''''''''''''''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''''''''&&&&&&''''''((((((''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$""""""$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""%%%%%%$$$$$$###""""""!!!"""""""""""""""""""""""" !!!!!!"""$$$$$$%%%&&&$$$%%%%%%$$$""""""###%%%######$$$$$$$$$%%%%%%%%%$$$$$$###""""""#########)))((('''(((((()))******(((((((((((((((((((((((())))))))))))))))))))))))+++)))((((((***+++***((())))))))))))))))))))))))))))))))))))******+++,,,))))))))))))************+++************))))))))))))(((((((((((())))))***((((((((()))******+++,,,((((((((()))*********+++,,,++++++++++++++++++,,,+++******)))))))))*********++++++,,,,,,++++++***,,,,,,,,,,,,,,,++++++***++++++++++++++++++++++++,,,,,,---------,,,,,,+++***+++---,,,,,,+++---.............../////////000000///////////////......,,,,,,,,,,,,------.........------------...////////////000111111111111111333222222222222333222222111222333333333333222222333333333333444555666777666444333111111333444666<<<<<<;;;999888777777666888888999999999999888888999<<<@@@FFFIIIHHHCCC???===<<<;;;;;;<<<>>>???@@@>>>>>>>>>======<<<<<<;;;;;;===@@@BBBDDDDDDBBB@@@???@@@BBBFFFHHHHHHFFFCCCAAA@@@?????????@@@AAABBBEEEEEEFFFFFFGGGGGGFFFFFFDDDDDDDDDDDDDDDDDDDDDDDDGGGGGGEEEDDDBBBAAA@@@???======>>>>>>???>>>>>>===;;;>>>AAADDDEEEDDDAAA???>>>>>>>>>>>>???@@@AAAAAA>>>>>>===<<<;;;;;;;;;<<<;;;;;;;;;;;;::::::::::::;;;;;;<<<:::999999;;;======@@@BBBAAA>>>===???AAA@@@AAAAAABBBBBBCCCDDDDDDCCCCCCBBB@@@???===<<<;;;>>>======<<<:::888666555666666888999999999888888<<<;;;999999::::::999777666666888999;;;<<<<<<===;;;;;;<<<======<<<;;;:::;;;:::999:::;;;:::999777555555666777888999:::;;;<<<999777666666777777666333333333333222222111111222222111000/////////000000000//////............++++++,,,---...000000111////////////////////////------,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,...------,,,,,,,,,------,,,,,,,,,++++++***************+++++++++,,,,,,,,,+++*********))))))))))))))))))((((((((('''''''''((((((((((((((((((((((((((())))))))))))((('''''''''(((((((((((((((((('''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&$$$$$$%%%%%%&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$&&&''''''%%%###"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$#########"""########################$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$#########"""""""""""""""""""""""""""""" !!!"""######$$$%%%%%%$$$""""""###$$$######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$(((((((((((((((((()))***((((((((((((((((((((((((((((((((((((((((((((((((***)))))))))******)))(((((((((((((((((((((((((((((((((((((((((()))***+++(((((()))))))))******************)))))))))((((((((((((''''''((()))******''''''((()))***++++++,,,((((((((()))*********+++++++++++++++++++++++++++++++++*********++++++,,,***++++++,,,,,,++++++***,,,------...---,,,++++++++++++++++++++++++++++++++++++,,,,,,---,,,,,,+++***,,,------++++++,,,...---......////////////////////////.........------,,,,,,,,,------------------------------...////////////000111111111000000111222222222222222222222222222222222222222111111333333333333333444555666444333111000000111333444<<<<<<;;;:::999888777666777888888999999888888777:::<<>>===>>>???????????????>>>>>>>>>@@@BBBDDDDDDBBB@@@>>>===============>>>???@@@???===:::888777999<<<>>><<<<<<<<<;;;;;;:::::::::;;;;;;;;;:::999:::<<<>>>@@@BBBDDDBBB???>>>@@@CCCBBBBBBBBBCCCDDDDDDEEEEEEEEEDDDCCCBBB@@@???>>>===;;;;;;;;;;;;:::999999888666777999::::::999888888;;;999777777888999999888888999:::<<<>>>>>>??????;;;<<<=========;;;:::999;;;:::::::::<<<<<<:::888666666777888999;;;;;;<<<===:::777666666666666555222222222222222111111111222222111000/////////000////////////............***+++,,,---...///000111.............../////////...---,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,******))))))))))))******,,,,,,+++++++++++++++*********+++++++++,,,,,,,,,,,,,,,+++++++++*********'''(((''''''''''''&&&&&&'''''''''''''''((((((((())))))******))))))((('''''''''((((((((((((''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$%%%%%%&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###%%%&&&(((((('''%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$######""""""!!!########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$"""""""""""""""""""""""" !!!!!!""""""###$$$$$$###!!!!!!"""$$$######$$$$$$$$$%%%%%%%%%######$$$%%%%%%&&&&&&&&&'''((((((((('''''')))+++))))))))))))))))))))))))((((((((((((((((((((((((((())))))******))))))((((((((((((((((((((((((((((((((((((((((((((()))***((((((((()))))))))******))))))))))))((((((((((((''''''''''''((()))******'''''')))***++++++++++++))))))************************++++++++++++******+++************+++,,,,,,***++++++,,,,,,++++++***,,,,,,---...---,,,+++***++++++++++++++++++++++++***++++++,,,,,,,,,,,,,,,+++,,,------++++++,,,------......///000//////////////////...------,,,,,,,,,,,,---......------,,,---------------...///000//////000111111000000///000222333333222111111222222222222222111111111111333222222222222333444555333333111111111111333333555666666777888888888777777777888888888888777777999;;;>>>BBBDDDBBB>>>:::333666:::<<<<<<:::999999<<<<<<;;;;;;;;;;;;;;;;;;;;;>>>@@@BBBAAA?????????AAACCCFFFIIIKKKJJJFFFBBBBBBBBBAAAAAABBBDDDEEEGGGFFFGGGHHHHHHHHHGGGEEEDDDEEEFFFFFFFFFFFFFFFEEEDDDEEEDDDCCCCCCBBBAAA@@@@@@???@@@@@@@@@@@@??????>>>@@@AAABBBCCCBBBAAA???>>><<<;;;;;;;;;;;;;;;<<<===???===:::888888:::>>>@@@=========<<<<<<;;;;;;:::::::::::::::999;;;>>>AAABBBCCCCCCBBB@@@@@@AAACCCFFFEEEEEEDDDCCCCCCBBBBBBEEEDDDCCCBBBAAA@@@???>>>;;;:::::::::::::::::::::777999:::<<<<<<;;;999888:::888666666888999999999999;;;===???@@@AAAAAA@@@????????????>>>===;;;;;;;;;::::::;;;<<<<<<:::999777888888999:::;;;<<<<<<;;;999777666666666555333333333333333333333333333222222111000000000111111//////////////////......------...///000000111111---............////////////...---+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++************+++,,,,,,++++++++++++++++++++++++******+++++++++,,,,,,,,,,,,,,,,,,++++++++++++***)))))))))))))))(((''''''&&&''''''''''''((((((((()))************)))((((((&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''((((((''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&'''''''''&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%###############"""""""""########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!""""""###$$$$$$%%%%%%""""""""""""""""""""""""###########################$$$$$$###!!!!!!"""$$$######$$$$$$$$$%%%%%%%%%"""###$$$&&&&&&''''''&&&&&&((()))(((&&&&&&(((+++************************(((((((((((((((((((((((('''(((******)))(((((((((''''''''''''''''''''''''******))))))((()))))))))(((((((((((()))))))))***))))))(((((((((''''''''''''&&&&&&'''''')))******'''((()))***++++++******+++++++++++++++*********))))))***++++++***)))))))))))))))))))))***++++++***++++++,,,,,,++++++***)))***+++,,,,,,***)))'''******************************+++,,,,,,,,,,,,,,,+++,,,------++++++,,,---------///000000000///...//////......---,,,,,,+++,,,---...//////...---,,,---,,,,,,------///000000///000000000000000/////////111444444222000111222333333222222111111111111222222111111111222333333222222222222222222222222111222444555666666666666666777777777777777777666888999<<>>:::777222666999:::888777888999;;;;;;;;;<<<<<<<<<<<<<<<<<>>???AAADDDEEEGGGJJJLLLJJJFFFCCCBBBAAAAAAAAABBBDDDFFFGGGGGGHHHIIIIIIHHHFFFDDDBBBDDDEEEEEEFFFEEEDDDCCCBBBDDDDDDDDDCCCCCCCCCBBBBBB???@@@@@@@@@@@@???>>>===>>>?????????????????????>>>>>>===<<<<<<<<<==================>>>??????@@@??????>>>======<<<;;;;;;999999999999999<<<@@@CCCCCCAAA??????AAABBBBBBBBBEEEDDDDDDCCCCCCBBBAAAAAACCCCCCBBBAAAAAA@@@??????===<<<;;;:::999888888888999:::<<<======<<<:::888999777555555777999:::::::::<<<>>>@@@BBBBBBAAAAAAAAA@@@???>>><<<<<<;;;;;;:::999888999;;;;;;:::888999999::::::;;;;;;;;;<<<888777666666666666333111222222222333333333333333222111111111111222222333.../////////////////////.........//////000000000---------.........//////111000...,,,++++++,,,---++++++++++++++++++++++++---,,,,,,,,,------...///++++++++++++++++++++++++******+++++++++,,,,,,,,,++++++++++++************)))******+++***)))((('''&&&&&&&&&'''''''''(((((((((((())))))(((((('''&&&&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&''''''''''''((((((''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&#########$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$##########################################$$$$$$""""""""""""""""""""""""#########$$$$$$$$$%%%%%%$$$%%%%%%$$$""""""###%%%######$$$$$$$$$%%%%%%%%%###$$$%%%%%%&&&%%%$$$###&&&((()))(((&&&&&&(((+++************************((((((((((((((((((((((((&&&(((******)))((((((((('''''''''''''''''''''''',,,,,,+++***)))))))))***(((((((((((()))))))))))))))(((((((((''''''''''''&&&&&&&&&'''''')))******'''(((***++++++***))))))---,,,,,,,,,+++*********((()))***++++++***)))(((((((((((((((((()))******+++++++++,,,,,,+++++++++'''(((***+++***)))'''&&&************************)))***+++,,,,,,,,,,,,,,,+++---------++++++,,,---,,,---///000000000///...//////...------,,,++++++---.../////////...---,,,,,,,,,,,,---...///000111///000000000000000//////...111444444111000000222444444333222111111222222111111111000111111222222111222333333333333222111444555666666666555444333666666777777777777666666777777:::<<<>>><<<888444444666888777555555888;;;:::::::::;;;;;;<<<<<<<<<>>>@@@AAA@@@>>>===???BBBGGGGGGIIIKKKLLLJJJFFFCCCAAAAAA@@@AAABBBDDDFFFGGGHHHHHHIIIIIIGGGEEEBBBAAACCCCCCDDDDDDDDDCCCAAA@@@???????????????????????????????????????>>>======<<<<<<<<<<<<===???@@@AAABBBBBBAAA@@@??????@@@@@@<<<>>>AAACCCCCCBBBAAA???@@@??????>>>===<<<<<<<<<888888999999:::===AAAEEECCC???======@@@CCCBBB@@@@@@@@@AAABBBBBBCCCCCCDDDAAAAAAAAA@@@@@@?????????@@@>>>===:::888777666666:::;;;===???>>>===:::999999777555444666999:::::::::<<<>>>AAABBBBBBAAAAAA@@@???===;;;999999999:::888777777888::::::999777;;;;;;;;;;;;;;;;;;;;;;;;666555555666666555333000000000000000000000111111222111111111222333444444.........///////////////,,,,,,---------------------------.........//////222000...,,,+++,,,---...++++++++++++++++++++++++***)))))))))******+++,,,++++++++++++++++++++++++******+++++++++,,,,,,,,,************))))))))))))((())))))******((('''&&&&&&&&&&&&'''''''''((((((''''''((((((''''''&&&%%%&&&''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&'''((())))))%%%&&&&&&&&&%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""!!!!!!"""###$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""%%%%%%$$$$$$###""""""""""""""""""""""""""""""""" !!!"""###$$$$$$%%%&&&&&&&&&%%%$$$###$$$&&&######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%$$$###!!! ''''''''''''(((((((((((('''%%%$$$%%%''''''$$$!!!(((''''''''''''((())))))((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''(((***+++,,,((((((''''''''''''((((((+++++++++***)))(((((('''&&&&&&&&&'''((())))))***))))))))))))(((((((((((())))))))))))(((((((((((())))))))))))))))))))))))((((((''''''''''''(((((()))))))))***+++++++++,,,*********))))))))))))((("""###%%%''')))+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,---......------,,,,,,,,,------000///...---------------111000///...---...//////---------...............------............------111000000////////////000111222222222222111000000111111000000000000111111333333333222222222222222555444333222222444555666555555444444444444555555777777777777777888888888888777666666666777999:::???===;;;;;;===>>>???>>>???@@@@@@???===<<<>>>???BBBCCCEEEFFFFFFDDDBBB@@@EEECCC@@@???@@@BBBCCCCCCDDDFFFGGGFFFDDDAAA@@@@@@CCCCCCCCCCCCCCCBBBBBBBBBBBBAAA@@@@@@??????????????????>>><<<<<<;;;;;;;;;999::::::;;;===>>>@@@AAACCCGGGJJJHHHCCC@@@@@@CCCAAABBBBBBBBBBBBBBBAAAAAABBBBBBAAA???===<<<;;;:::;;;777555777===AAAAAA???@@@@@@@@@@@@???===<<<;;;===>>>???BBBCCCEEEEEEFFFCCCBBBAAAAAA@@@@@@@@@@@@>>>===<<<:::999888777777;;;===>>>>>>;;;888666555777777777777888999:::::::::<<>><<<;;;;;;===?????????>>>??????>>><<<;;;===>>>@@@BBBDDDEEEFFFDDDBBBAAADDDBBB@@@???@@@BBBBBBBBBBBBCCCEEEDDDBBBAAA@@@@@@CCCBBBAAAAAA@@@@@@AAAAAACCCBBBAAA@@@????????????>>>>>>===<<<<<<<<<<<<===;;;;;;;;;<<<>>>???AAABBBDDDGGGIIIHHHCCCAAABBBDDDDDDDDDDDDDDDCCCCCCBBBBBBBBBBBBAAA???>>><<<;;;;;;;;;888666888>>>BBBAAA@@@>>>>>>======<<<;;;::::::===>>>@@@AAACCCDDDDDDDDDAAA@@@@@@@@@@@@AAAAAABBB<<<;;;:::888777666666666:::;;;<<<;;;888666555555666666666777888999:::;;;;;;<<<>>>??????>>><<<:::<<<999666777:::;;;888555999777555555777999:::::::::999999888888777666666555555555444444444333333444333222222222222333444000000000111111000000000------........./////////...///000000000...,,,++++++,,,---.........------///.........------------///...---,,,++++++,,,------,,,,,,++++++,,,,,,---))))))))))))))))))))))))************)))))))))(((************************((()))))))))((('''&&&%%%((((((''''''''''''((((((((('''''''''&&&&&&&&&&&&((((((((((((((('''&&&&&&&&&&&&'''''''''''''''''')))(((((('''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$######$$$%%%%%%$$$$$$######$$$$$$%%%&&&###############$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$############$$$$$$"""""""""###$$$$$$$$$%%%$$$$$$$$$###############$$$######""""""######$$$#########$$$$$$%%%%%%%%%&&&%%%$$$$$$######$$$$$$%%%$$$###"""""""""######%%%$$$$$$$$$############$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%(((((((((((())))))))))))***)))((()))******(((&&&$$$$$$######$$$$$$%%%&&&))))))))))))))))))))))))''''''''''''''''''''''''***)))((((((''''''((((((((((((''''''''''''((((((+++******))))))(((((('''&&&&&&''''''((()))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))***))))))(((((())))))*********************))))))+++++++++************)))++++++,,,,,,++++++***)))+++++++++++++++++++++++++++,,,---......---,,,+++,,,,,,,,,,,,,,,---......+++******))))))))))))***---,,,+++*********++++++,,,,,,------............------------------------............///000111111---...000111222333333333111000000//////000000111//////000000111111222222222222333444444444444444555444444333333444444555666666666666777777888888777777666666666777888999<<<;;;:::;;;===?????????<<<======<<<::::::;;;<<<>>>@@@BBBDDDDDDDDDCCCBBBCCCAAA??????@@@AAABBBAAA???AAABBBBBBAAA@@@@@@AAACCCBBBAAA??????@@@@@@AAAEEEDDDCCCAAA@@@?????????===<<<<<<<<<======>>>???=========>>>???AAABBBCCCEEEGGGHHHFFFCCCBBBDDDGGGGGGFFFFFFEEEDDDCCCBBBBBBBBBBBBAAA@@@>>>===<<<<<<<<<:::888:::>>>AAAAAA@@@>>>===<<<;;;:::;;;;;;<<<>>>???@@@AAABBBBBBBBBBBB>>>>>>??????@@@AAAAAABBB999999888777666555555555999:::999777555333444555555555555666777999:::;;;;;;<<<===>>>===;;;999777<<<999777888:::;;;999666:::777555555777888888888999999888888777777666666555555555555444444444444333333222111111222333333//////000000000000//////,,,---------............,,,---...//////...---,,,+++,,,---.........------............------------///...------,,,---------,,,,,,++++++++++++,,,,,,))))))))))))))))))))))))************))))))))))))************************((()))))))))((('''&&&%%%((((((''''''''''''((((((''''''''''''&&&&&&&&&&&&'''(((((((((((('''&&&&&&%%%&&&&&&&&&'''((((((((()))((('''%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%'''&&&$$$######$$$&&&'''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$######$$$$$$%%%&&&$$$$$$$$$##################$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$############$$$$$$##################$$$$$$$$$$$$$$$$$$######""""""$$$######""""""######$$$######$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$$$$$$$$$$%%%$$$###""""""!!!!!!""""""%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&((((((((()))))))))******))))))))))))******)))(((''''''&&&&&&&&&'''(((((())))))))))))))))))))))))'''''''''''''''''''''''')))(((((('''''''''((((((((((((''''''''''''((((((******))))))((((((((((((''''''''''''(((((())))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))******))))))))))))******++++++******))))))((((((++++++++++++************,,,,,,,,,,,,+++******)))++++++++++++++++++++++++))))))***+++---///000111000///...,,,+++*********---,,,,,,+++++++++,,,,,,,,,+++++++++************,,,,,,,,,------......///---------------------------------...///000111222...///000111222222222222000000////////////000000---......///000111111222000111333444555555444333444444333333333333444444444555555666666777777777777666666555666777888999:::999999;;;===??????>>>:::;;;;;;:::888888999;;;<<<>>>@@@BBBCCCCCCCCCBBBAAA???>>>>>>@@@AAAAAA@@@>>>???AAAAAAAAAAAABBBCCCEEEDDDBBBAAA@@@AAABBBCCCFFFEEECCCAAA@@@???>>>>>>;;;;;;<<<<<<===???@@@AAA?????????@@@AAACCCDDDEEEEEEFFFFFFDDDBBBBBBEEEGGGGGGFFFEEEDDDCCCBBBAAAAAAAAAAAA@@@???>>>>>>=========;;;:::<<>><<<;;;;;;<<<>>>?????????@@@@@@@@@@@@??????>>>>>>??????????????????888888777666666666666777:::999888555333222444666333444444555666888999::::::;;;<<<===<<<;;;999888<<<:::888999;;;;;;:::888;;;999777777777888888777999888888777666666555555555555555444444444444333222222111111111111222222//////000000000000//////,,,,,,,,,---------......++++++------......------,,,---------------------------------------------........................,,,,,,++++++++++++,,,,,,))))))))))))))))))))))))*********)))))))))))))))(((((((((((((((((((((((((((((((((((((((''''''&&&(((''''''&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%%%%&&&'''((()))))))))(((&&&$$$$$$%%%&&&'''&&&&&&&&&%%%%%%%%%%%%$$$'''&&&%%%$$$$$$%%%&&&'''%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&%%%$$$$$$$$$###"""""""""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$############$$$$$$$$$$$$$$$###############%%%%%%$$$$$$###"""""""""######""""""""""""######$$$$$$$$$$$$############%%%$$$$$$######$$$$$$$$$$$$#########""""""""""""%%%%%%%%%$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%(((((((((((())))))))))))'''((()))))))))(((((((((((((((((((((((()))******((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&'''((()))***((((((''''''''''''(((((()))))))))(((((((((((((((''''''''''''(((((((((((())))))))))))(((((((((((('''((((((((()))))))))***))))))))))))))))))))))))******))))))))))))******+++******))))))(((((((((+++++++++*********))))))))))))***************)))************************+++***((((((***---000333000///---,,,+++***))))))------,,,,,,,,,,,,------,,,,,,,,,,,,,,,++++++***++++++,,,,,,---......///...---,,,,,,,,,,,,---...------------...///111111000000111111111000000///000000////////////000000------...///000000111111///111222444555555444333333333222222222222333333333444444555666666777777777666555555555666888888999888999:::===>>>>>>===999::::::999777666888999;;;<<<>>>@@@AAABBBBBBBBB???>>>======???@@@@@@???>>>???AAAAAAAAAAAACCCEEEGGGFFFEEEDDDDDDDDDEEEEEEFFFEEECCCAAA???>>>>>>>>>;;;;;;;;;<<<>>>???AAABBBAAAAAAAAABBBBBBDDDEEEFFFEEEEEEEEECCCBBBCCCDDDFFFEEEDDDBBB@@@???>>>>>>>>>?????????>>>>>>============<<<<<<===??????>>>>>>===<<<;;;:::;;;<<>>>>>===????????????>>>===<<<;;;888888777777777888999999;;;:::888666333333666888333333333444555666888999999:::;;;<<<<<<<<<;;;;;;;;;:::::::::;;;;;;;;;:::<<<:::888888999999888777888888777666666555555444444444444444333333333333111111111111111111111111000111111222222111111000,,,,,,,,,---------......++++++,,,------.........------------------------,,,,,,---------------------.....................,,,++++++******++++++,,,))))))))))))))))))))))))))))))))))))))))))******(((((((((((((((((((((((()))(((((('''''''''''''''''''''&&&&&&&&&&&&''''''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&'''((())))))((('''%%%$$$###$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((('''&&&%%%######$$$$$$$$$$$$######$$$$$$######$$$$$$%%%&&&%%%$$$$$$$$$###"""""""""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$############$$$$$$$$$$$$$$$###############$$$$$$$$$#########""""""###""""""""""""""""""###$$$###########################""""""""""""######$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%$$$$$$############$$$$$$''''''''''''((((((((((((%%%'''))))))((('''((()))'''''''''&&&'''(((((()))((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&'''(((***+++((((((''''''''''''((((((((((((((((((((((((((((((''''''(((((((((((((((((())))))))))))((((((((((((''''''(((((())))))******))))))))))))))))))))))))***))))))(((((())))))***))))))))))))))))))((((((*********))))))))))))(((''''''((()))************))))))))))))))))))))))))...,,,***(((((())),,,---+++++++++++++++,,,------+++************+++,,,,,,,,,------------,,,++++++******+++,,,---......///...---,,,++++++,,,---...------------...///000000000000111111000000///...000//////......//////000......//////000000111111///000111333444444444444333222222111111222222333222333333444555666777777666666555555555666777888999888999:::===>>>===;;;888999999888666666777888;;;;;;===>>>???@@@@@@AAA===<<<<<<===???@@@???>>>>>>???@@@@@@@@@AAADDDFFFFFFFFFFFFFFFFFFEEEEEEEEEDDDCCCBBB@@@???>>>>>>>>>;;;;;;<<<===>>>@@@AAABBBBBBBBBBBBBBBCCCDDDEEEFFFEEEDDDCCCCCCBBBBBBBBBCCCAAA@@@>>><<<<<<<<<<<<=================================>>>>>>>>>===<<<<<<888888888888999;;;===>>>>>>>>>??????>>>======<<>><<<999888777777777888999:::;;;<<<::::::999777444444777999333333333333444555666666888999:::;;;;;;<<<<<<<<<888999999999999999:::::::::999888888999999777666777777666666555555444444333333333333222222222222000000111111111111000000111111222222222222111111,,,---------............,,,,,,---------......///......---,,,,,,,,,------,,,,,,,,,,,,------------,,,,,,---............---++++++************++++++))))))))))))))))))))))))))))))))))))************************************)))(((''''''''''''((((((''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&%%%&&&&&&&&&'''((((((((('''&&&%%%$$$$$$%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%$$$%%%'''(((((('''%%%$$$"""######$$$$$$######"""$$$$$$######$$$$$$%%%&&&$$$$$$$$$##################$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$##################$$$$$$###########################""""""!!!!!!""""""###""""""##################"""!!!!!!!!!!!!"""######$$$%%%%%%%%%%%%$$$######"""############$$$$$$$$$############$$$$$$$$$$$$$$$######""""""######$$$&&&&&&&&&&&&''''''''''''%%%'''))))))((('''(((***&&&&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))((((((''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((('''))))))))))))(((((((((((('''''''''((()))*********)))))))))))))))))))))))))))((((((''''''(((((()))((((((((())))))))))))))))))))))))((((((((('''''''''((())))))***)))))))))))))))))))))))))))))))))************))))))((((((************+++,,,---...)))))))))))))))***++++++,,,,,,---------,,,+++***)))***+++,,,---......///...---+++******+++---.........---------......///...///000000000000000/////////............//////000000000000000000000000000000000111222444555666222222111111111111222222111222333444555666666777666666555444555666777888999999999;;;<<<===;;;999888999999888666555777888;;;;;;<<<===>>>>>>??????<<<;;;;;;<<>>>>>??????>>>???BBBDDDCCCCCCEEEEEEEEEDDDBBBAAABBBAAA@@@???>>>>>>>>>>>><<<<<<<<<===>>>@@@AAABBBCCCBBBBBBCCCCCCDDDEEEFFFDDDCCCCCCBBBBBBAAA@@@>>>>>>===;;;:::999:::;;;<<<;;;;;;;;;<<<<<<<<<<<<<<<<<<===>>>>>>===;;;::::::555666777888:::;;;============>>>>>>>>>===<<<<<<======>>>>>>>>><<<999888666777777888999:::<<<===999999999777555555666888444444333333333333444444888888999999999999999999555555666666666666777888777666666666888888666444777777666555555444444333222222222111111111000000//////000111111000//////000000111111111111000000------........./////////................../////////...---,,,,,,,,,,,,---++++++,,,,,,,,,---------***+++,,,---......---,,,++++++************++++++))))))))))))))))))))))))((()))))))))************************************)))((('''&&&&&&'''((()))'''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%&&&&&&'''''''''&&&&&&&&&''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%&&&&&&'''$$$$$$$$$%%%%%%$$$$$$$$$######$$$%%%%%%$$$######$$$$$$######$$$$$$%%%&&&###############$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$"""""""""###$$$$$$$$$%%%"""""""""###$$$$$$%%%%%%""""""!!!!!!!!!!!!""""""!!!!!!""""""######$$$$$$""""""!!!!!!"""######$$$###$$$$$$%%%$$$###"""!!!!!!!!!"""""""""#####################$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%&&&&&&&&&''''''%%%(((******(((''')))+++(((''''''''''''((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&&&&&&&'''((((((''''''''''''(((((('''''''''(((((((((((((((((((((((((((((('''''''''))))))))))))((((((((((((&&&''''''((()))******+++))))))))))))))))))))))))((((((''''''''''''((((((''''''(((((())))))******(((((((((((('''''''''''')))************))))))((())))))))))))))))))))))))$$$&&&))),,,,,,+++(((&&&,,,,,,++++++***+++++++++******)))******+++,,,,,,++++++,,,---,,,+++***))))))******+++---...//////...---+++******+++---...///......---------......,,,---...000111111111111//////............//////111111111111000000000000111000000000111333555777222222111111111111222222111111222333555666666777666555555444555666777888999999999;;;<<<<<<:::888888999999888666666777888;;;;;;<<<<<<===>>>>>>>>>;;;:::;;;<<<>>>???>>>======>>>>>>======>>>@@@CCC???@@@CCCDDDDDDBBB???===@@@@@@???>>>======>>>>>><<<<<<======>>>@@@AAABBBCCCCCCBBBCCCCCCDDDEEEFFFCCCCCCBBBCCCBBBAAA>>><<<===<<<:::999999:::;;;<<<:::::::::;;;;;;;;;;;;;;;;;;===>>>>>><<<:::999999666777999;;;===>>>>>>???<<<===============<<<<<<:::;;;===>>>>>><<<;;;999555666666777888:::<<<===888888888777555444555777555444333333222222333333999999888888777666666666222333444444333333555666555444444555666666555333777666666555444444333333111111111000000000000///...///000111111000///...//////000000000000//////.........////////////000000//////........./////////...---,,,+++,,,,,,---+++++++++,,,,,,---------)))***,,,---...---,,,,,,++++++************++++++))))))))))))))))))))))))(((((())))))*********+++(((((((((((((((((((((((()))((('''&&&&&&'''((()))'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%&&&&&&'''''''''&&&'''''''''''''''&&&&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%!!!!!!"""###%%%&&&'''((($$$###""" """###$$$$$$$$$&&&&&&&&&&&&$$$$$$$$$$$$######$$$$$$%%%&&&""""""######$$$$$$$$$%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$!!!!!!"""###$$$%%%%%%&&&!!!!!!"""###$$$%%%%%%&&&""""""!!!!!!!!!!!!"""""" !!!!!!"""###$$$$$$%%%######""""""###$$$%%%%%%"""######$$$$$$"""!!! !!!!!!"""""""""###"""############$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&((('''&&&''')))++++++***&&&&&&''')))************%%%&&&''''''(((((('''''''''((()))((('''&&&''')))(((((('''''''''&&&&&&&&&''''''&&&%%%&&&'''((()))***)))((('''''''''''''''***(((&&&%%%$$$%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&(((((((((((())))))))))))((((((''''''&&&&&&%%%%%%%%%'''((('''&&&%%%&&&(((***)))(((&&&&&&&&&'''((('''((((((((((((((('''&&&''''''&&&&&&&&&&&&''''''++++++)))(((''''''''''''))))))))))))))))))))))))***)))((()))*********((()))*********++++++++++++)))))))))))))))))))))))))))***+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***))))))+++---...,,,,,,,,,++++++*********............////////////000,,,)))***...000///,,,////////////000111222333333111000000111222222111222222111111111111111111000111222333444444444444666555333222333444666777777888888999888777666555<<<999555444666777666444777888999:::;;;;;;;;;;;;:::;;;<<<======<<<<<<;;;999::::::;;;===???@@@AAA@@@@@@AAA@@@@@@???>>>======<<<;;;::::::;;;<<<===@@@>>>===<<<<<<===>>>@@@BBBAAAAAA@@@AAACCCFFFGGGFFFAAA======???AAA???;;;:::;;;;;;:::999888:::;;;<<<<<<;;;;;;;;;::::::::::::;;;<<<<<<<<<:::888666444777:::;;;;;;:::::::::===>>>@@@???===<<<<<<<<>>===<<<<<<:::::::::;;;===???@@@AAA???@@@@@@??????>>>===<<<<<<<<<;;;;;;;;;;;;<<<<<<>>>===<<<;;;;;;===>>>@@@@@@???>>>>>>@@@BBBDDDFFFFFFAAA======???@@@===::::::;;;;;;:::888888999;;;<<<<<<<<<;;;;;;::::::999;;;<<<=========;;;999888555777:::<<<;;;:::::::::???@@@AAA@@@>>>>>>???@@@@@@@@@???>>><<<:::999888555666777999999999999999888888888888888888888888777777666444444333333444777666777888999999777555222222333333333222222222555666777888888777666555555444333222111111111111333333222222111000000000---...///////////////...///000000111111000000///------...///////////////------------------------++++++++++++++++++++++++,,,---......---,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,---,,,,,,++++++,,,,,,---*********)))))))))))))))))))))))))))))))))))))))***)))))))))((((((((('''((((((((((((''''''''''''''''''''''''''''''''''''((('''''''''&&&&&&&&&&&&%%%&&&'''((('''&&&$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%$$$$$$#########$$$%%%%%%%%%$$$###"""$$$%%%&&&''''''&&&%%%$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$########################$$$$$$$$$$$$$$$$$$$$$$$$  !!!"""$$$$$$$$$$$$$$$###############""""""######$$$%%%"""######$$$$$$$$$$$$###%%%%%%###"""""""""####################################$$$$$$$$$%%%%%%%%%((('''&&&&&&(((******)))'''(((((()))))))))((((((%%%&&&''''''((((((''''''&&&'''(((((('''&&&'''((('''''''''''''''&&&&&&&&&'''&&&&&&&&&&&&'''(((((('''''''''&&&''''''((((((***)))((('''&&&'''((()))((((((((((((((((((((((((''''''((((((((()))))))))((((((((()))))))))))))))((())))))'''&&&&&&(((***(((((('''&&&&&&&&&''''''''''''((()))***************)))((((((''''''''''''((()))******)))(((&&&%%%(((((((((((((((((((((((()))((('''((()))***)))'''************++++++++++++))))))))))))))))))))))))/////////......---,,,+++,,,,,,,,,,,,,,,,,,,,,,,,,,,+++*********+++,,,---------,,,,,,,,,,,,++++++---............/////////000---+++,,,///111000...111000000///////////////000///------/////////...000000000000000000000000111222333333333333333222333333222222333555777888777888888888888777777666333444444444444555777999999999:::;;;<<<<<<<<<<<<;;;<<<===>>>???>>>======::::::;;;<<<===???@@@AAA????????????>>>===<<<;;;;;;;;;<<<<<<<<<<<<;;;;;;;;;:::::::::;;;===???@@@??????>>>>>>@@@BBBEEEGGGEEEAAA======>>>>>><<<999:::;;;;;;:::888888999:::======<<<;;;::::::999999;;;;;;<<<;;;;;;:::888888666888;;;<<<;;;:::;;;;;;?????????>>>===>>>@@@BBBAAA@@@>>>===;;;:::999999555666777888999999999888888888888888888888888888777666555444444444444444777666666888999999777555222333333333333333333333666666777777777777666666333333222222222222333333333333222222111000000000...///////////////......//////000000000000//////------...////////////...------------------------++++++++++++++++++++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++,,,,,,++++++++++++,,,,,,(((((())))))************))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&'''((((((((('''%%%###"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$&&&&&&&&&%%%%%%%%%%%%$$$""""""###$$$%%%%%%$$$$$$%%%&&&'''(((((('''&&&%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%$$$$$$$$$$$$$$$%%%%%%%%%######""""""######$$$%%%$$$$$$$$$###############%%%$$$######"""#######################################$$$$$$$$$%%%%%%%%%((('''&&&&&&((()))))))))((((((((()))((((((''''''%%%&&&''''''((('''''''''&&&'''((((((&&&&&&'''(((''''''''''''''''''''''''&&&&&&&&&&&&''''''((((((&&&&&&&&&&&&''''''((()))******)))(((((((((((()))'''''''''''''''''''''''''''''''''((((((((())))))%%%%%%&&&&&&''''''(((((()))***)))(((&&&''')))+++)))(((((((((((((((((((((%%%&&&'''((())))))))))))+++***)))(((((('''(((((('''((()))******(((&&&%%%((((((((((((((((((((((((***)))((((((******)))((((((((()))))))))*********))))))))))))))))))))))))///////////////...------++++++++++++++++++++++++++++++*********+++,,,------,,,,,,,,,,,,,,,,,,,,,---------........./////////---+++,,,...//////...000000000//////000111111111///------...///...---//////////////////000000222222222333333333222222444333333444555666888999777777777777777777777777333666888888666666999<<<999:::;;;<<<<<<<<<<<<<<<;;;<<<===?????????>>>>>>;;;;;;;;;<<<===???@@@AAA@@@@@@@@@??????>>>===<<<::::::<<<======<<<::::::888888888999;;;===>>>@@@@@@@@@???@@@AAADDDGGGIIICCCAAA>>>=========:::888:::;;;;;;:::888777888999===<<<<<<;;;;;;:::999999999999888888777666666666777999;;;<<<;;;;;;;;;<<<<<<===<<<;;;:::;;;>>>AAABBB@@@>>>;;;:::999999999555555666777777888888888888888888888888888888888777666555444444444444444666666666777999888666444333333333333333444555555777777777777777666666666222222222222222333444555333333222222111000000000....../////////...------...//////000000//////...------...//////.........------------------------++++++++++++++++++++++++,,,,,,+++******++++++,,,++++++++++++++++++++++++,,,,,,++++++++++++,,,,,,))))))))))))))))))******))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$"""######$$$$$$$$$$$$$$$######$$$%%%%%%$$$#########$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########"""######$$$%%%################################################%%%%%%$$$$$$$$$%%%&&&&&&!!!!!!"""""""""""""""#########""""""######$$$%%%%%%%%%$$$######"""""""""$$$$$$################################################$$$$$$$$$%%%%%%%%%((('''&&&&&&((()))(((((('''((((((((((((''''''&&&%%%&&&''''''((('''''''''&&&'''((('''&&&%%%&&&(((&&&'''''''''''''''''''''&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&'''((()))***))))))(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((((((%%%%%%&&&&&&''''''(((((()))))))))((('''''')))+++))))))))))))***)))))))))###$$$%%%&&&''''''''''''******)))(((((((((((((((&&&''')))***)))(((&&&%%%''''''''''''''''''''''''+++***))))))++++++***)))''''''''''''(((((((((((())))))))))))))))))))))))((())))))***++++++******++++++++++++++++++++++++++++++***+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------............---+++++++++,,,---------...//////000111222444555222000......//////...------------....../////////111111222222333333222222555555555666666777888999666666666666666666666777444777:::999777666888;;;::::::;;;;;;<<<;;;;;;;;;:::;;;===????????????>>><<<<<<<<<======???@@@AAAAAAAAAAAAAAA@@@???>>>>>>999:::;;;<<<<<<;;;:::999777777888999;;;===>>>???@@@?????????@@@CCCFFFGGGBBB@@@???>>>===<<<:::999;;;;;;;;;999777666777999<<<<<<;;;;;;;;;::::::::::::999777666555555666666888:::<<<<<<;;;;;;<<<>>><<<<<<<<<;;;:::;;;>>>AAAAAA@@@===;;;999888999999555555555666666777888888888888888888888888888888666666555444444444444555666666666777888888666444333333333333444555666777888888777666666666666666222222222222333444555555333333222222111000000000------.........------,,,......////////////......------............------------------------------++++++++++++++++++++++++,,,++++++******+++,,,,,,------------------------,,,++++++******++++++,,,++++++******)))(((((('''(((((((((((((((((((((((((((((((((((())))))))))))((((((((((((''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###############$$$$$$$$$$$$$$$$$$#########"""""""""""""""############""""""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""###$$$$$$%%%################################################"""!!!!!!!!!!!!"""###### !!!!!!!!!""""""######""""""######$$$%%%&&&%%%$$$###"""""""""###############$$$#######################################$$$$$$$$$%%%%%%%%%)))'''&&&&&&'''(((((('''&&&''''''(((((((((''''''%%%&&&''''''((((((''''''%%%&&&''''''&&&%%%&&&'''&&&&&&&&&'''''''''''''''%%%&&&''''''((((((''''''&&&&&&&&&%%%&&&&&&'''''')))))))))(((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((((((((((((((()))))))))))))))'''((())))))((('''((()))(((((()))*********))))))######$$$%%%&&&&&&&&&%%%)))((((((''''''(((((()))&&&'''((((((((((((&&&&&&''''''''''''''''''''''''***)))((()))***+++***(((''''''''''''(((((((((((())))))))))))))))))))))))'''((()))***++++++++++++++++++++++++++++++++++++******+++++++++,,,,,,,,,******++++++++++++,,,,,,,,,------------.........+++++++++++++++,,,,,,---------...///111333444555222000.........///...---,,,,,,,,,------......//////000111222333333333333555666666666666777777777555444444444444555555666333555777777666666666777999999:::;;;;;;::::::999999:::<<<>>>?????????>>>============>>>???@@@AAABBBBBBBBBBBBAAA@@@???>>>::::::;;;;;;;;;;;;::::::777888999:::<<<===>>>???>>>===<<<<<<===???AAACCC@@@@@@@@@???>>>===<<<;;;;;;;;;;;;999777666777888:::::::::;;;;;;;;;<<<<<<===<<<999777777777999:::999;;;<<<<<<;;;<<<===???>>>>>>>>>===<<<===???AAA@@@???===<<<:::999888888555444444444555666777888888888888888888888888888666555555444444444555555666555555777888888666444333333333333444666888999999888777666555555666666333333333333333444555555333333222222111000000000,,,------...//////......------............---------............---,,,,,,------------------------+++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,------------------------++++++************++++++,,,,,,+++***)))(((''''''(((((((((((((((((((((((((((((((((((())))))))))))((((((((((((''''''''''''''''''''''''''''''''''''%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$######"""###############$$$$$$%%%$$$###"""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""###$$$%%%%%%################################################"""""""""""""""######$$$!!!!!!!!!"""######$$$$$$######""""""######$$$%%%%%%$$$###"""""""""###$$$""""""###$$$$$$$$$$$$#################################$$$$$$$$$%%%%%%%%%)))'''%%%&&&'''((('''&&&%%%%%%&&&'''((((((((((((%%%&&&''''''((((((''''''%%%&&&''''''%%%%%%&&&'''&&&&&&&&&'''''''''((((((%%%&&&'''((((((((('''&&&''''''&&&%%%%%%%%%&&&&&&((((((((((((((('''&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''(((((()))))))))))))))((((((((($$$''')))***((('''&&&&&&%%%&&&'''((()))(((((('''$$$%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&'''((())))))'''''''''''''''''''''''''''''''''''''''''''''''')))'''&&&'''((()))((('''((((((((()))))))))******))))))))))))))))))))))))++++++,,,,,,,,,,,,,,,+++******************************++++++,,,,,,,,,+++)))))))))******+++++++++,,,,,,---------.........+++,,,,,,++++++,,,---...,,,,,,------///000222222111///---,,,------,,,++++++++++++,,,------......---...000111333444444444555555555555555444444333333333222222222333444555333333444666999:::999888888999999:::999999888888888999;;;===>>>>>>>>>>>>============>>>???@@@@@@AAAAAAAAAAAA@@@???>>>>>>;;;::::::::::::::::::;;;888999:::;;;======>>>>>>===<<<;;;:::;;;<<<>>>???>>>???@@@@@@???>>>======;;;;;;;;;999777555666777888999999:::;;;<<<======>>><<<:::777666888:::;;;:::;;;<<<<<<;;;<<<>>>@@@===>>>??????===<<<===>>>???>>>>>><<<;;;999777666444444444444444666777888888888888888888888888888555555444444444555555666555555555666888888555333333333222333444777999;;;:::999777666555555555666444444333333333444444555333333222222111000000000,,,---...000111111111111---------......------------.........------,,,+++------------------------++++++++++++++++++++++++***+++,,,---......---,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++************+++++++++*********))))))(((((((((((((((((((((((((((((('''((((((((()))))))))***((((((((((((''''''''''''''''''''''''''''''''''''$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$###############$$$$$$%%%%%%%%%###""""""!!!!!!"""$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""###$$$%%%&&&################################################$$$############$$$%%%%%%!!!""""""###$$$$$$%%%%%%######""""""######$$$%%%$$$$$$"""!!!"""###$$$&&&!!!"""###$$$%%%$$$$$$#################################$$$$$$$$$%%%%%%%%%)))'''%%%&&&'''((('''&&&$$$%%%&&&'''((((((((((((%%%&&&''''''((((((''''''%%%&&&''''''%%%%%%&&&'''&&&&&&&&&'''''''''((((((%%%%%%'''((((((((('''&&&((('''&&&&&&%%%%%%%%%%%%'''''''''((('''&&&&&&%%%((((((((((((((((((((((((&&&&&&&&&'''''''''((((((((((((''''''&&&&&&&&&%%%###&&&)))***)))'''%%%%%%###$$$&&&'''''''''&&&&&&&&&&&&&&&'''&&&&&&%%%%%%%%%%%%%%%&&&'''((()))***''''''&&&&&&&&&''''''((('''''''''''''''''''''''''''&&&%%%%%%&&&'''&&&%%%************++++++++++++))))))))))))))))))))))))************)))(((''''''******************************+++,,,,,,,,,,,,+++(((((())))))*********+++,,,,,,,,,---------......,,,---------,,,,,,...///,,,,,,,,,,,,,,,---...///000...,,,+++,,,,,,+++*********+++,,,,,,---......,,,---///111333444555555444444444444333222111111222222111000111222444555333222333777<<>>>>>>>>===>>>=========>>>???@@@@@@@@@@@@AAA@@@@@@???>>>===<<<;;;999999999999;;;<<<999:::;;;<<<===>>>>>>>>>???>>>===<<<<<<===>>>@@@===???AAAAAA@@@?????????;;;;;;;;;999666555666777777888999:::<<<===>>>???===;;;888555555666888:::;;;<<<===<<<<<<<<<>>>@@@;;;===>>>===<<<:::::::::>>>>>>>>>===<<<999777555444444333333444555777888888888888888888888888888555555444444444555555666555555555666888777555333444333222333444777:::<<<:::999777666555555555666555444444333333444444444333333222222111000000000---...000111333444444444,,,------......------,,,---.........------,,,+++------------------------++++++++++++++++++++++++***+++---/////////---,,,++++++++++++++++++++++++++++++************++++++))))))))))))************(((((((((((((((((((((((('''((((((((())))))******)))(((((((((''''''''''''''''''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&)))((('''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$######$$$$$$$$$%%%%%%&&&&&&&&&!!!!!! !!!"""###%%%'''%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""###$$$%%%&&&########################"""""""""""""""""""""""" !!!!!!""" !!!!!!"""######$$$$$$#########"""###$$$$$$%%%$$$###"""!!!"""###%%%'''!!!"""###$$$%%%%%%$$$#################################$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%%%%''''''''''''''''''''''''(((''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&)))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&'''&&&&&&%%%%%%&&&((()))******)))(((&&&%%%%%%$$$$$$%%%'''((()))''''''''''''''''''''''''%%%&&&&&&&&&'''(((((((((''''''((((((((((((''''''''''''''''''''''''&&&&&&&&&'''((())))))((('''&&&&&&'''''''''(((((())))))))))))(((((((((((())))))---,,,***(((((('''((((((************************))))))))))))))))))))))))---,,,***(((((()))***++++++***(((''''''(((***+++------------------------,,,,,,,,,---------............---------,,,,,,,,,------,,,------...///000...///111444555555555555666666555444333333222222111222222333333444444555444444444555777888:::;;;888666555444444666999;;;;;;<<<=========<<<;;;:::======<<<<<<<<<>>>???AAA???@@@AAABBBAAA???===<<<===<<<;;;:::::::::;;;<<<999;;;======<<<;;;<<<======<<<;;;::::::;;;===>>>>>>======<<<===>>>???@@@???<<<:::999999999999888======<<<<<<<<<===???@@@;;;:::999888888999;;;<<<======<<<<<<===>>>??????===???@@@???<<<999777777<<<;;;:::999777666555444666666555555555555666666888777777777999999777555555444333444555555333111444555777888999888777666666444222444777999888666555444222111111222444555333333333333333333333333333222111000000111222333222222222111111111000000000///...---,,,,,,---...------..................,,,++++++******++++++,,,''')))+++---.........---...---,,,+++************+++***)))((()))***,,,---*********************************)))))))))))))))))))))))))))))))))))))))))))))(((((((((***,,,---'''''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&''''''''''''''''''&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%(((''''''&&&$$$######"""###########################$$$%%%&&&&&&%%%$$$######$$$%%%&&&&&&%%%$$$###&&&&&&$$$###""""""!!!!!!""""""!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$#########$$$$$$%%%%%%$$$$$$###""""""###$$$%%%&&&&&&'''###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$###"""!!!""""""############""""""$$$#########""""""!!!!!!""""""!!!!!! """############$$$$$$$$$""""""!!!!!!"""###$$$$$$$$$$$$$$$#########""""""$$$#########""""""!!!!!!$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&'''&&&&&&%%%%%%%%%&&&((())))))(((&&&%%%&&&%%%%%%$$$%%%&&&((((((''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''''''''((((((((((((''''''%%%%%%&&&&&&''''''(((((('''((()))******)))((('''((((((((((((''''''''''''))))))(((((((((((()))))),,,+++***(((((((((((((((************************))))))))))))))))))))))))---,,,***)))((()))***+++...---,,,++++++,,,---...------------------------,,,,,,,,,---------......//////.........---------------,,,------...///000000111222444555555555444555555555444333222222222111111222222333444444444444444444444555777888999888777555555555777:::;;;======>>>>>>===<<<;;;:::<<<<<<<<<<<<===>>>???@@@???@@@AAAAAA@@@>>><<<;;;;;;;;;:::999999:::;;;<<<999;;;======<<<;;;<<<======<<<;;;::::::<<<===?????????>>>>>>???@@@BBBCCC>>><<<999888:::;;;;;;;;;@@@AAABBBBBBBBB@@@>>>======<<<;;;::::::<<<===???======<<<<<<===>>>>>>???>>>??????>>>;;;999888888<<<<<<;;;:::999888777777666666666555666666777777777666555666777777666444777666444555666666555333444555777888888777666555444222222333666888777666555444333222222333555666444444444333333333222222111111000000000000111111222222111111111000000000111000///...------.../////////......------,,,,,,,,,,,,++++++++++++,,,,,,***+++...222555555333000///...---,,,++++++++++++))))))***+++++++++++++++************************)))))))))))))))*********))))))))))))))))))))))))''''''&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&'''((((((''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%$$$###"""""""""""""""""""""""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$#########$$$$$$%%%%%%$$$$$$############$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$###""""""""""""############""""""############"""""""""!!!"""""""""!!!!!!!!! """############$$$$$$$$$###############$$$%%%%%%$$$$$$$$$#########""""""$$$$$$$$$$$$#########"""$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&'''((((((''''''''''''''''''''''''''''''''''''''''''''''''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&'''&&&&&&%%%$$$%%%&&&''''''&&&%%%$$$&&&&&&%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''((((((((((((''''''$$$$$$%%%&&&'''((())))))((()))************)))((())))))(((((('''&&&&&&&&&))))))(((((((((((())))))+++***)))(((((((((((((((************************)))))))))))))))))))))))),,,+++***)))))))))***+++........................------------------------,,,,,,,,,---------......000000/////////.........------,,,------...///000222333444555555555444444444444444333222222111111111111111222333333444444333333333333333444555555888777666555666888:::<<<>>>>>>>>>>>>===<<<::::::999:::;;;===>>>????????????@@@@@@@@@???===;;;999999999999999999:::<<<<<<999;;;======<<<;;;<<<======<<<;;;:::;;;<<<>>>@@@BBBCCCCCCDDDEEEFFFFFFGGG???<<<:::999;;;===??????BBBDDDGGGHHHGGGBBB===:::===<<<;;;;;;;;;<<<>>>???============>>>>>>>>>>>>>>>>>>>>><<<999888999:::;;;;;;;;;;;;::::::::::::777777666666777888999999888666666666888888777666999777555444555666666666444555666777777666444333333222222333666777777666666555444444444666777888666555555444333222222111000111111222222111111000111111111111000000000000000000///.........//////000000///...---,,,++++++,,,,,,++++++++++++,,,,,,---///333;;;AAAAAA:::444///...---,,,,,,,,,,,,,,,''')))+++,,,---,,,***)))************************(((((())))))******++++++))))))))))))))))))))))))))))))))))))((('''&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''((((((((('''&&&%%%%%%$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$###############$$$""""""""""""""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$#########$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%###$$$$$$$$$$$$###""""""""""""############""""""############""""""""""""#########""""""""""""""""""############$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&$$$$$$$$$###############%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&))))))((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&'''&&&&&&&&&%%%%%%&&&''''''&&&%%%%%%'''&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&''''''((((((''''''&&&%%%%%%%%%&&&&&&''''''''''''((()))******)))(((''''''''''''''''''''''''&&&))))))(((((((((((()))))))))))))))(((((((((((((((************************))))))))))))))))))))))))++++++***))))))******++++++,,,,,,------,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------......////////////.........---------,,,------...///000333444555555555555333333333333222222222111111111000000111111222333333333333222222111111111222222666555555555555777999:::=========<<<;;;:::999888777999;;;===>>>???>>>>>>?????????>>>===;;;999888888888888999:::;;;<<<<<<:::<<<======<<<;;;;;;<<<>>>===;;;;;;;;;===???AAAGGGIIILLLOOOOOOLLLIIIGGGBBB???;;;:::<<<>>>@@@@@@AAADDDFFFHHHFFFBBB===999::::::999999:::;;;<<<===?????????@@@@@@@@@??????>>>>>>===;;;888888:::;;;::::::::::::;;;;;;;;;;;;777777777777888999:::::::::999888888:::;;;:::999:::777444333444666666666444555555666555555444333333333444555666888888888666666666666666777999999777666555444333222111000111222333444444333222111111111000000000/////////............---..................------,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,///222999EEEMMMKKK@@@555...---,,,+++++++++++++++((()))***+++,,,+++******************************''''''((()))***++++++,,,((((((((((((((((((((((((((()))*********)))'''&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&)))(((''''''&&&%%%$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######$$$%%%&&&&&&%%%$$$######$$$%%%&&&######""""""###$$$$$$%%%###"""""""""""""""####################################$$$$$$$$$$$$#########$$$$$$%%%%%%$$$$$$###%%%%%%%%%$$$$$$#########$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$######""""""######$$$$$$######"""#########"""""""""""""""########################""""""#########$$$$$$$$$$$$$$$#########$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&((('''''''''&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%%%%$$$&&&&&&''''''''''''&&&&&&''''''&&&&&&%%%%%%%%%$$$&&&&&&'''(((((('''&&&&&&$$$%%%%%%&&&'''(((((()))))))))(((((((((((())))))(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))******************++++++)))***++++++++++++***))),,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------...............---------,,,,,,------,,,------...///000333444555555555444333222111111111111111000000000//////000111111222222333222111111000000000000000333333333333444666777999;;;;;;:::999888888777777777888:::<<<===>>>======>>>======<<<;;;:::888888888888999:::;;;;;;<<<<<<:::<<<======<<<;;;;;;<<<>>>===<<<;;;<<<>>>@@@BBBJJJNNNTTTWWWVVVQQQJJJEEEDDDAAA>>><<<===>>>??????>>>???AAAAAA@@@>>><<<:::999999::::::;;;<<<======@@@AAABBBBBBBBBAAAAAA@@@<<<===<<<:::888888:::<<<888888999999:::;;;;;;;;;888888888888888999:::::::::999777888999;;;;;;:::999777444333444555666555555555555555555555444444555666777777888888999:::777777777777888888999999666555444333222111000000///000111222222111000///000000000/////////......+++,,,,,,,,,,,,,,,,,,,,,+++,,,,,,,,,------......---,,,,,,,,,,,,,,,,,,---...333===JJJRRRNNN@@@333,,,+++******************+++***)))))))))***,,,,,,************************''''''((()))***++++++,,,(((((((((((((((((((((((("""###%%%&&&&&&&&&%%%$$$''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&&&&%%%$$$######$$$%%%&&&""""""""""""###$$$%%%%%%######"""""""""""""""###""""""""""""""""""""""""######$$$$$$$$$$$$#########$$$$$$%%%%%%$$$$$$###&&&%%%%%%$$$$$$###############$$$$$$$$$$$$######"""######$$$$$$$$$############$$$$$$$$$$$$######""""""""""""""""""##################$$$$$$$$$$$$""""""#########$$$$$$$$$$$$###""""""""""""##############################""""""#####################$$$$$$%%%%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((((('''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&(((((('''&&&%%%$$$######%%%&&&''''''''''''&&&%%%######$$$&&&'''((()))***))))))(((((((((((())))))&&&'''((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))*********++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------.........------------,,,,,,,,,------,,,------...///000222333444444444333222111000000000000000000000000/////////000111111222222111000000/////////000000111111222222444555777777999888888777777777777888999999:::;;;<<<<<<<<<<<<<<<;;;;;;:::999999888888999999:::;;;<<<<<<<<<<<<;;;<<<>>>===<<<:::;;;;;;>>>===<<<<<<===???AAACCCJJJNNNTTTWWWVVVPPPIIIDDDDDDBBB???>>>>>>???>>>===<<<<<<<<<<<<<<<<<<;;;;;;;;;;;;<<<===>>>??????@@@AAABBBCCCCCCCCCBBBAAA@@@:::;;;<<<;;;999999:::<<<888888888999:::;;;;;;;;;999999888888888888888999888666444444666888999999888666444333444555555444444444555555555666666666777999:::999888777888:::888888999999888888888888444444333222111000000///---..................---////////////............)))***++++++,,,,,,++++++******+++,,,---...//////------,,,,,,,,,,,,---------111:::EEEKKKGGG;;;000******))))))))))))******,,,***)))((((((***,,,---************************(((((())))))******++++++))))))))))))))))))))))))###$$$%%%&&&&&&'''''''''''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$########################%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%###"""""""""###$$$%%%%%%$$$######"""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!######$$$$$$$$$$$$#########$$$$$$%%%%%%$$$$$$###%%%%%%%%%$$$$$$#########""""""############""""""""""""###$$$$$$$$$$$$#########$$$$$$$$$$$$######""""""""""""###########################$$$$$$$$$"""############$$$$$$$$$$$$###""""""!!!"""""""""###############$$$$$$$$$"""""""""""""""###############$$$$$$$$$$$$######&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&''''''(((&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%&&&''''''''''''%%%%%%$$$$$$$$$$$$%%%%%%###$$$&&&''''''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%'''&&&&&&%%%%%%$$$$$$$$$%%%&&&'''(((((('''&&&%%%$$$$$$%%%&&&&&&'''(((((())))))(((((((((((())))))%%%&&&''')))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))***+++++++++++++++,,,+++***))))))***+++,,,++++++++++++++++++++++++,,,,,,,,,---------..................------------------,,,------...///000000111222333333333222111////////////////////////......//////000111111222000000/////////000000111000111222333555666777888888777777666777888999999;;;:::::::::::::::;;;;;;999999999888888999999999;;;;;;<<<=========<<<;;;;;;===>>>===<<<::::::;;;>>>======<<<>>>@@@BBBDDDFFFHHHLLLNNNMMMKKKGGGEEEAAA@@@??????@@@@@@>>>===;;;;;;<<<<<<<<<;;;:::999:::;;;<<<===??????@@@@@@@@@AAABBBCCCBBBAAA???>>>888:::;;;;;;:::999:::;;;999999::::::;;;;;;<<<<<<:::999888777777777777777777555333333555777999999888777555666777777666444444444444555666777888999888:::;;;:::777555666888999999999999888888777666111111111000000000////////////............///////////////.........------)))***+++,,,---,,,,,,++++++++++++,,,,,,------...------,,,,,,,,,,,,------,,,///444999;;;999333...+++***************++++++***************++++++,,,************************)))))))))))))))*********))))))))))))))))))))))))''''''''''''''''''((((((''''''''''''''''''''''''%%%%%%&&&''''''&&&%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$##################$$$$$$$$$$$$###"""""""""""""""##############################$$$$$$$$$$$$#########$$$$$$%%%%%%$$$$$$###%%%%%%$$$$$$$$$$$$$$$$$$#########$$$$$$#########""""""###$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###!!!"""""""""############"""""""""#########$$$$$$"""############$$$$$$$$$%%%$$$######"""""""""###""""""#########$$$$$$$$$"""""""""######$$$$$$$$$######$$$$$$$$$$$$######&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&'''((((((&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%&&&''''''''''''$$$$$$############$$$$$$"""###%%%'''((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((())))))((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&))))))(((((((((((())))))$$$%%%''')))******))))))))))))))))))))))))))))))))))))))))))))))))))))))((()))***++++++++++++++++++***(((''''''(((***+++++++++++++++++++++++++++,,,,,,,,,---------......000/////////............---------------...000000///000111222333222222111.........///////////////......//////000111111111///////////////000111111111222333444666777888999888777777777777999:::;;;<<<;;;:::999888999:::;;;888888888777888888999:::<<<===>>>>>>>>>===<<<;;;;;;===>>>===<<<::::::;;;>>>>>>======>>>@@@CCCDDDCCCCCCDDDEEEEEEFFFFFFFFF>>>>>>>>>@@@BBBAAA???===;;;<<<>>>>>>>>>;;;999777888999:::<<<===>>>>>>>>>>>>???AAAAAAAAA???===<<<777999;;;<<<;;;:::::::::;;;;;;;;;<<<<<<<<<======::::::888777666666555555888666444444777999::::::888888777888999888777555444444444555777888:::;;;888:::;;;999666444555666:::::::::999888777666555000000000000////////////333222111000000111222333//////.........---------******,,,---...------,,,,,,,,,,,,,,,,,,,,,,,,,,,...------,,,,,,------...------..................+++++++++***++++++,,,,,,''')))+++,,,,,,,,,***)))*********************************)))))))))))))))))))))))))))))))))))))))'''&&&$$$###""""""###$$$''''''''''''''''''''''''%%%%%%&&&''''''&&&%%%%%%###$$$$$$%%%%%%&&&&&&'''$$$$$$$$$%%%%%%$$$$$$$$$"""######$$$&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&%%%$$$######$$$%%%&&&&&&%%%$$$###$$$$$$###############$$$$$$$$$###""""""!!!""""""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$!!!"""###$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###!!!!!!""""""#########$$$!!!!!!""""""############"""############$$$$$$$$$&&&%%%%%%$$$#########$$$""""""######$$$$$$$$$$$$#########$$$$$$%%%%%%%%%######$$$$$$$$$$$$######%%%$$$###$$$&&&'''&&&%%%&&&&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''((()))((('''%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''(((((())))))((('''&&&&&&###$$$&&&((())))))((('''((((((''''''''''''(((((())))))))))))))))))))))))))))))))))))))))))))))))&&&'''((()))***))))))((((((((())))))*********+++*********)))))))))))))))++++++++++++++++++++++++---+++)))+++---///---+++------,,,,,,,,,---......,,,---...000000000000///111222222333333222222111......////////////......,,,------...///000111111...000111111///......///222111111111222333333444666666555555555777888999999999888888777666666666777777777777777777888888<<<===>>>===<<<;;;<<<===???>>>===<<<<<<<<<<<<<<<>>>>>><<<<<<===???AAACCC???AAACCCEEEFFFFFFEEEDDDAAA???===???AAABBB???===;;;<<<<<<============<<<<<>>;;;<<>>===<<<;;;;;;:::777777777666555555444444444444555666777888999999;;;888666777;;;;;;888444666555555666777888:::;;;::::::::::::999777666555555666777777777666444333000000000000////////////.........///////////////000///...------...///000000///...---,,,+++++++++---,,,+++******+++,,,---,,,++++++******++++++,,,++++++******++++++,,,---//////...---+++***))))))***++++++,,,,,,++++++******++++++)))&&&$$$$$$%%%''''''(((((())))))******(((((((((((((((''''''&&&&&&&&&&&&''''''''''''(((((('''&&&%%%%%%&&&'''(((%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########'''&&&%%%$$$$$$%%%''')))$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''%%%$$$###"""""""""%%%%%%%%%$$$$$$#########'''&&&%%%$$$###$$$%%%&&&$$$$$$$$$############"""$$$$$$$$$#########""""""$$$$$$$$$#########""""""!!!!!!"""############"""$$$###$$$'''******&&&###$$$###############$$$$$$#################################"""""""""""""""""""""#########$$$$$$$$$###$$$%%%%%%$$$###"""!!!#########$$$$$$%%%%%%%%%%%%$$$###""""""###$$$%%%%%%$$$###$$$&&&'''&&&%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""$$$&&&(((******))))))&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&((((((((((((((('''&&&&&&###$$$&&&((()))(((''''''((((((''''''''''''(((((())))))))))))))))))))))))(((((((((((((((((((((((()))))))))))))))******+++(((((()))))))))*********))))))))))))))))))))))))************************---+++***+++---...---+++...---,,,++++++++++++++++++,,,---////////////...000000111111111111000000......////////////......------......//////000000000222333333222111222333333222222222333333444555777666555555555666777888888888888777777666666666666666666777777888888888<<<===>>>===;;;:::;;;<<<>>>===<<<;;;;;;;;;;;;<<<===============???@@@AAA???@@@BBBDDDDDDDDDCCCBBB@@@>>>===???AAAAAA@@@=========>>>>>>>>>======<<<<<>>======;;;;;;:::999777777666666555444444333555555666777888999999999:::777555666::::::777333444444666777999:::;;;<<<::::::999888777666666555555666777777777666444333000000000000/////////...............////////////000///...------...///000//////...---,,,,,,,,,,,,,,,,,,+++******+++,,,,,,,,,++++++++++++++++++,,,******))))))******+++,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++***+++,,,+++)))(((((()))(((((((((((())))))))))))((((((((((((((('''&&&&&&&&&&&&&&&''''''''''''(((((('''&&&&&&&&&&&&'''(((%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$######$$$%%%'''((($$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$############%%%%%%%%%$$$$$$#########&&&%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$############"""$$$$$$$$$#########""""""$$$$$$$$$#########""""""!!!"""######$$$$$$######$$$###$$$&&&((((((%%%"""$$$$$$#############################################"""""""""""""""""""""#########$$$$$$$$$$$$%%%###$$$$$$%%%$$$###"""!!!"""""""""######$$$$$$$$$$$$$$$###""""""###$$$$$$%%%$$$###$$$&&&'''&&&%%%%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''))))))))))))(((&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%'''(((((((((((('''&&&&&&###$$$&&&'''(((((('''&&&((((((''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((***)))((('''((()))***+++(((((())))))))))))******)))))))))))))))))))))))))))))))))))))))))))))))),,,+++***+++,,,------+++...---,,,***))))))((((((***+++,,,---............//////000000000000//////......////////////........................//////000222333333222222333555444333333333333444555555777666555555444555555666777777777777777666666666555555666777888888999999;;;======<<<;;;:::;;;<<<<<<;;;;;;::::::::::::;;;<<<<<<===>>>????????????>>>???@@@AAAAAA@@@???>>>>>>======???@@@AAA@@@>>>@@@@@@??????>>>>>>=========AAADDDDDDBBBBBBDDDGGGQQQSSSTTTPPPFFF===999777:::999777888:::<<<<<<;;;>>>===<<<;;;:::999999888666666555555444333333333666777777777888888999999999777555666999999666333333444777999;;;<<<======;;;:::888666555555555666555555666777666555444333000000000/////////......------........./////////000///............/////////...------,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,++++++++++++++++++++++++))))))(((((())))))***+++)))******+++,,,---......,,,+++***))))))***+++,,,(((***++++++))))))***+++))))))))))))(((((((((((('''(((((((((((('''&&&&&&&&&&&&&&&''''''''''''(((((('''&&&&&&&&&&&&'''(((%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###!!!""""""###$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$$$$%%%$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$############"""$$$$$$$$$###############$$$$$$$$$###############"""######$$$$$$$$$$$$$$$%%%$$$###$$$%%%%%%###"""%%%%%%$$$###"""""""""###""""""""""""""""""""""""""""""""""""""""""######$$$$$$$$$$$$%%%%%%%%%%%%###$$$$$$$$$$$$###"""""""""""""""""""""#########$$$$$$###""""""###$$$$$$%%%$$$###$$$&&&'''&&&%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&*********)))((('''%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&'''''''''(((((('''&&&&&&$$$%%%&&&''''''''''''&&&(((''''''&&&&&&''''''(((''''''''''''''''''''''''(((((((((((((((((((((((('''''''''''''''((((((((((((((())))))))))))))))))((((((((()))))))))))))))(((((()))))))))))))))***+++******+++,,,,,,,,,,,,------,,,******))))))))))))***++++++,,,,,,------//////000000000000//////---......//////......---.....................------...////////////111333333333222222222333333444666666555444444444333333666666666666666666666666555666777888999:::;;;<<<<<<===>>>===;;;;;;;;;<<<::::::999999999999999:::;;;<<<>>>???@@@???>>>======>>>>>>>>>>>>===<<<;;;=========???@@@@@@@@@???BBBAAA@@@???>>>>>>======???BBBEEEEEECCCBBBAAABBBBBBFFFHHHKKKMMMDDD;;;<<<:::999888888999;;;<<<<<<===<<<<<<;;;:::999888777555555555444333333222222666666666666777777777888999888777777999999777555444666999;;;======<<<;;;;;;999777555333444555666444555666666666555444333000000/////////.........,,,------....../////////000//////...............///...---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++)))))))))))))))***++++++))))))***+++,,,------...---+++***((((((***+++---'''((())))))''''''((()))******))))))((((((''''''''''''((((((''''''&&&%%%&&&&&&&&&''''''''''''((('''''''''&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%################################################$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%&&&$$$$$$$$$###############"""###%%%&&&&&&%%%$$$###$$$$$$$$$#########""""""######################################################$$$%%%%%%%%%%%%$$$%%%$$$###""""""""""""!!!%%%%%%$$$###""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!"""""""""""""""#########$$$$$$%%%%%%%%%&&&&&&&&&#########$$$############""""""##################$$$##################$$$%%%$$$###$$$&&&'''&&&%%%$$$%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&*********)))'''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%&&&(((******)))((('''))))))((((((((((((((((((''''''(((((()))))))))))))))))))))*********++++++******++++++++++++,,,,,,,,,,,,++++++++++++,,,,,,))))))******+++,,,,,,---//////000000000000//////------............------............------------+++,,,------,,,---000222222222111111111111111222444444444444333333222222444444444555666666666777777777888999;;;<<<=========>>>???>>><<<;;;<<<===999999888888888999999::::::<<<>>>@@@@@@???===<<<=========<<<<<<;;;::::::<<<===>>>???????????????AAAAAA???>>>============@@@BBBDDDDDDAAA???<<<;;;===@@@>>>EEERRRHHH777888888999999999::::::<<<===<<<<<<;;;:::999888888777555555555444333333222222333333444444555666666666:::999999999::::::888777888999;;;<<<<<<;;;:::888:::888666333222333444555444555666666666555333222////////////............,,,,,,,,,---...//////000///////////////......---......---,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,***++++++,,,,,,++++++***+++************+++,,,,,,++++++++++++++++++++++++,,,+++)))(((((()))+++,,,)))***+++***'''&&&'''(((******))))))(((((('''''''''''''''''''''&&&&&&%%%&&&&&&&&&''''''''''''(((&&&''''''''''''''''''&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%################################################$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&&&&########################!!!"""$$$%%%&&&%%%$$$$$$$$$$$$$$$#########""""""######################################################$$$%%%%%%%%%%%%$$$#########"""!!!!!!!!!!!!%%%$$$$$$###""""""######!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""############$$$$$$%%%%%%%%%&&&&&&&&&##################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$#########%%%$$$###$$$&&&'''&&&%%%$$$$$$%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&&&&''''''(((%%%%%%&&&''''''''''''&&&%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''((()))***+++***))))))))))))((((((((((((''''''&&&''''''(((((())))))***((())))))******+++++++++)))***++++++******+++---+++++++++++++++,,,------***)))))))))***+++,,,---//////000000000000//////------............------------------------......---......---------000222222111111000000000000111222333333333333222222111222333333444555666777777888888999:::;;;;;;<<<<<<===>>>>>>>>><<<;;;<<<===999888888888888999999:::;;;<<<>>>??????>>><<<;;;======<<<<<<;;;;;;;;;:::<<<>>>??????>>>======>>>???>>>===;;;;;;;;;<<<<<>>>>>===<<<;;;======<<<<<<<<<<<<<<<<<<===???AAA@@@===;;;<<<===<<<;;;:::999888999;;;<<<===============<<<:::888444;;;555@@@YYYLLL555===444888<<<===<<<::::::;;;======<<<;;;:::999888888777777666666555444444333000000222333555666777888999:::;;;:::999888888888::::::::::::999999999999666666555444333222111111444444555555555444333222//////.........---------***++++++,,,...//////000///000000000///...---,,,---------,,,,,,------...,,,,,,---......---,,,,,,)))***,,,------,,,***)))***************++++++,,,++++++++++++*********)))******))))))))))))*********,,,,,,,,,******+++,,,(((((((((((())))))))))))&&&&&&''''''&&&&&&%%%$$$&&&&&&&&&''''''''''''(((&&&&&&'''(((((('''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$###""""""###$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$###$$$$$$%%%%%%!!!"""""""""#########$$$""""""""""""###$$$%%%&&&$$$$$$$$$############"""""""""#########$$$$$$$$$""""""#########$$$$$$$$$!!!"""######$$$$$$######!!!$$$%%%###!!!!!!"""""""""""""""###$$$%%%%%%######################## !!!!!!"""######$$$$$$#########$$$$$$$$$$$$%%%######"""""""""###%%%%%%$$$$$$$$$$$$#########""""""###$$$$$$$$$$$$###"""%%%$$$###$$$&&&'''&&&%%%###$$$%%%&&&''''''''''''''''''''''''''''''''''''''''''&&&%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%&&&&&&'''''''''&&&&&&&&&%%%$$$$$$%%%%%%%%%'''&&&&&&%%%%%%&&&&&&'''((((((((((((((((((((((((''''''''''''''''''''''''(((%%% !!!&&&)))))))))(((((('''''''''&&&&&&&&&&&&'''((())))))***&&&&&&&&&'''((())))))***(((***,,,+++))))))+++------,,,+++)))((((((((((((+++************,,,---...,,,------......------,,,,,,------......------,,,++++++,,,,,,---...////////////...,,,++++++...000444333333222111111111222///000111222333333222111111111222333555666777777777777777777777777888888999:::;;;:::888777888999999999888888999:::;;;;;;<<<===============<<<<<<=========<<<<<<======>>>>>>@@@AAA@@@<<<:::;;;<<<:::999888777777888:::;;;;;;;;;;;;;;;======<<<;;;888BBB:::AAAVVVCCC,,,777333888===>>>===:::::::::>>>===<<<<<<::::::999888777777777666555555444444000000222444666888999:::888999::::::888777777888999999888888888999:::;;;555555555444333222000000333444555555555444333222//////.........---------******+++,,,...//////000///000000000000...,,,+++------,,,,,,,,,------...,,,,,,---......---,,,,,,)))***,,,------,,,***))))))))))))))))))******+++******************++++++))))))************))))))&&&((()))***))))))+++,,,''''''(((((())))))******&&&&&&''''''&&&&&&%%%$$$&&&&&&&&&'''''''''((((((%%%&&&'''(((((('''&&&%%%%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%!!! !!!$$$'''((($$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%$$$$$$###$$$$$$%%%!!!!!!""""""#########$$$###"""!!!!!!"""$$$&&&'''$$$$$$$$$############"""""""""######$$$$$$$$$$$$""""""######$$$$$$$$$$$$!!!!!!"""###############!!!%%%&&&$$$""""""###!!!!!!""""""###$$$&&&&&&######################## !!!!!!"""###$$$$$$$$$""""""#########$$$$$$$$$######"""""""""###%%%&&&$$$#########""""""!!!!!!"""###$$$%%%%%%$$$###"""''''''''''''&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$)))'''&&&$$$$$$%%%&&&'''(((((('''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&'''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$&&&&&&&&&&&&$$$###'''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''''''''((((((((((((''''''(((((())))))******(((''''''&&&&&&((()))***)))******++++++******)))+++++++++*********))))))(((,,,///...+++)))+++///,,,***(((***---...,,,***+++++++++,,,,,,,,,------++++++,,,---.........---------------------------222///,,,---///222111000000111111222222222111111000111333555666777888888999999888888999999:::;;;::::::999999999:::;;;;;;888888888888999:::;;;;;;???>>><<<;;;:::999999999:::999777888:::<<<======>>>===;;;::::::;;;<<<>>><<<;;;999888888888888999888999:::;;;<<<;;;:::999<<<777<<>>>>>???>>><<<:::888666777777777777666444222000///000333555777888888888999999888888888888999999666666666666666777777777555444444333222111000000444444444444333222111111000000////////////000000......------------......------.........---+++***,,,,,,++++++,,,,,,---...,,,------......------,,,+++++++++*********))))))************************+++***)))'''''')))***+++++++++******))))))(((((()))******++++++)))(((''''''''''''''''''((()))***###$$$%%%&&&&&&&&&%%%$$$((((((''''''''''''(((((())))))((('''&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###""""""""""""""""""""""""$$$$$$##################%%%%%%%%%$$$$$$#########&&&%%%$$$######$$$%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$"""""""""""""""""""""""""""$$$$$$$$$###"""###$$$######""""""""""""#################################$$$$$$%%%%%%$$$$$$###"""############$$$$$$$$$%%%$$$""" !!!###$$$$$$###""""""!!!"""""""""######""""""""""""###### !!!!!!!!!!!!""""""###$$$$$$$$$$$$###"""""""""###$$$$$$%%%%%%$$$$$$$$$#########""""""%%%$$$###""""""######$$$''''''''''''&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###$$$&&&)))***(((''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&'''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''(((''''''''''''''''''''''''''''''''''''(((((((((((()))))))))((((((((((((((((((''''''&&&'''((()))*********++++++++++++******+++++++++*********)))))),,,000222111---+++,,,///,,,***)))***,,,---,,,***+++,,,,,,,,,------------,,,,,,---.........------------------------------111///---...000111111//////000111222222222222222000111333444666777777777888888888888888999:::::::::999999999999::::::;;;::::::::::::;;;<<<======>>>===;;;:::999888888888888777777777999:::::::::<<<<<<;;;::::::;;;<<<======<<<:::888777777888888888999:::;;;;;;;;;:::999777;;;CCCHHHFFF===666555888999:::<<<===>>>>>>>>>??????>>>===;;;999888777777777777777666555333222111222555777999:::::::::999999888888888888999999777777777777777777777777555444444333333222222111...//////000//////......000000////////////000000......------------......---......///...---,,,+++,,,,,,++++++,,,,,,---...,,,,,,------------,,,,,,+++++++++*********))))))************************+++***)))(((((()))***+++*********))))))))))))))))))******+++***)))((('''(((''''''''''''(((((()))&&&'''''''''''''''&&&&&&)))((('''''''''''''''((()))))))))(((''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$###"""!!! !!!"""###%%%%%%%%%%%%$$$$$$$$$$$$########################"""$$$%%%$$$###"""###$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###"""############$$$$$$$$$%%%$$$###""""""###$$$&&&$$$$$$###""""""""""""#########""""""""""""######!!!!!!"""""""""#########""""""###$$$$$$$$$$$$###$$$$$$##################$$$$$$$$$#########"""""""""###$$$$$$$$$$$$###"""&&&''''''&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&(((***''''''&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&%%%''''''''''''''''''''''''(((''''''&&&&&&''''''((('''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&''''''''''''(((((((((******))))))(((''''''&&&(((''''''''''''((())))))******++++++++++++******+++************)))))))))...000222000,,,***+++---+++***)))***,,,---,,,+++,,,,,,,,,---------...............///......------,,,,,,,,,,,,------------///......///111111000......///000111222222333333000111222444555666666777777777777777777888999999888888888888888999:::;;;:::999999::::::;;;<<<===<<<;;;:::999888777777777555555666777888888888888999999::::::;;;;;;<<<<<<===<<<:::888777777777777777888999::::::::::::999888EEENNNJJJ???999:::;;;;;;;;;;;;;;;<<<===??????@@@???>>><<<:::999888888666666777777666555444444333555777999;;;<<<<<<<<<999999888888888888999999888888777777777777777777333333333333333333333333...///000000111111000000000//////......//////000......------------...............///......---,,,,,,,,,++++++,,,,,,---...,,,,,,------------,,,,,,+++++++++***************))))))))))))))))))))))))+++***)))(((((()))***+++))))))))))))************))))))*********)))(((''')))((((((''''''''''''(((******)))(((''''''''''''))))))((('''&&&&&&&&&'''((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%$$$###"""###%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######"""############$$$$$$$$$$$$$$$#########%%%&&&'''%%%%%%$$$##################""""""!!!!!!""""""############$$$$$$$$$%%%%%%""""""###$$$$$$$$$$$$###%%%%%%$$$$$$###""""""!!!$$$$$$$$$############### """$$$&&&&&&%%%""" &&&&&&&&&&&&&&&%%%$$$###$$$$$$%%%%%%%%%%%%&&&&&&&&&''''''((((((''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&''''''''''''''''''''''''((('''&&&%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&&&&&&&'''''''''(((((())))))((((((((('''''''''''''''''''''((((((((()))******++++++++++++******************)))))))))))))))+++---,,,***(((((()))+++******+++,,,,,,,,,,,,,,,,,,---------.........////////////......---,,,,,,,,,,,,,,,,,,---------------...000111000///...---...///111222333333333000111222333555555555666666666666555666777777888777777777777888888999:::777777777777888999:::;;;::::::888777777666666666333555777888888777777777777888999:::;;;<<<;;;;;;>>><<<:::888777777777777777777888999999::::::::::::IIIPPPEEE:::999===>>><<<;;;:::::::::<<<===>>>@@@???===:::999888888999555555555555555555555444444666888:::<<<<<<<<<<<<:::999999888888999999:::888888888888888777777777111111222222222333333333000000111222222111111000/////////....../////////......------------..............................,,,,,,++++++,,,,,,---...,,,,,,,,,------,,,,,,,,,************************((((((((((((((((((((((((******)))(((((()))******(((((())))))******++++++)))))))))))))))(((((((((***)))(((''''''''''''''',,,+++)))'''&&&&&&'''((())))))((('''&&&&&&&&&&&&&&&'''''''''((((((((()))%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###########################$$$$$$$$$%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&!!!!!!""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%######$$$%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######""""""#########$$$$$$$$$###"""""""""###%%%&&&'''&&&%%%$$$$$$######$$$$$$""""""!!!!!!!!!!!!""""""#########$$$$$$$$$%%%%%%""""""###$$$$$$$$$$$$###$$$$$$$$$#########""""""########################!!!"""$$$%%%%%%$$$###"""%%%%%%%%%&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''&&&'''''''''((((((((()))&&&''''''((((((((((((((()))******++++++******)))))))))))))))))))))))))))&&&'''((())))))((()))*********++++++++++++,,,,,,,,,,,,,,,---------........./////////...---,,,,,,+++++++++,,,,,,,,,------,,,---///000000///......,,,---///000111222333333000000222333444444444444555444444444444555666666666555555666777888999999777777777777888999::::::999888777777666666666666444777::::::999777777888777888999:::;;;<<<;;;;;;===<<<:::888777777777888777888888999999:::;;;;;;999CCCDDD;;;555999<<<:::;;;:::999999999:::;;;<<>><<<::::::999999999999999999;;;;;;:::::::::::::::;;;777666555444444444444444555666888999:::;;;::::::::::::999999999999::::::888888777777666666555555....../////////000000000//////000000000//////...///......------......///......------------......------,,,,,,,,,---......,,,,,,++++++,,,,,,---...++++++,,,,,,,,,,,,++++++***************+++++++++)))))))))))))))))))))))))))))))))******)))))))))))))))))))))***************)))((('''''''''(((((()))((((((''''''''''''((((((((('''&&&%%%%%%%%%%%%'''&&&&&&&&&&&&&&&''''''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$"""""""""######$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%%%%###$$$%%%%%%%%%%%%$$$###"""""""""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&%%%$$$###$$$&&&###""""""""""""""""""###########################""""""############"""""""""############$$$$$$$$$!!!!!!!!!"""#########$$$%%%%%%$$$###############"""!!!!!! !!!!!!"""!!!!!!!!!""""""""""""###""""""###$$$$$$$$$$$$###!!!""""""###$$$$$$%%%%%%###############$$$$$$$$$######"""!!!"""###%%%&&&###$$$$$$%%%%%%%%%$$$$$$######$$$%%%%%%&&&''''''$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$################################################$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&###$$$&&&''''''&&&$$$######$$$%%%&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''(((''''''''''''''''''''''''%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&((()))))))))((('''''''''((((((((((((''''''(((((((((((())))))******))))))***+++,,,---,,,+++)))+++,,,,,,******+++...*********+++++++++,,,,,,++++++,,,,,,,,,,,,,,,,,,)))******+++,,,,,,------,,,...///...,,,,,,///111......///000111111000000///000111222222333333222222222222222222333444444333333333444555666888999888888888888999:::;;;<<<999888777777666777777777777:::<<<:::666555888<<<<<<<<<;;;::::::;;;<<<===;;;:::999888888888:::::::::999999999;;;<<<>>>???HHH@@@:::<<>>:::999888888888999:::;;;::::::::::::;;;===???@@@III===777<<<>>>::::::>>>;;;<<<<<<===<<<;;;999888555777999;;;<<<<<<<<<<<<===<<<:::888666666666777666777999;;;<<<<<<;;;;;;;;;::::::999999::::::;;;777666666555444444333333111111111000000000000000%%%&&&)))+++...000111111.........------..................------.........++++++***)))***+++---...,,,,,,++++++,,,,,,---...+++++++++,,,,,,+++++++++))))))******++++++++++++************************))))))************))))))++++++******))))))((((((***)))(((&&&&&&''''''((('''''''''''''''((()))***%%%&&&'''(((((((((&&&&&&$$$$$$$$$%%%&&&'''((()))''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''&&&%%%%%%$$$$$$###############$$$%%%%%%$$$######%%%%%%$$$$$$######""""""""""""""""""""""""""""""$$$%%%&&&&&&$$$$$$%%%&&&%%%$$$$$$$$$$$$$$$$$$%%%!!!!!!!!!!!!!!!!!!!!!!!!""""""############"""""""""############$$$$$$$$$$$$$$$%%%%%%%%%$$$######$$$######"""!!!"""""""""!!!!!! !!!!!!!!!""""""""""""#########""""""###$$$$$$$$$$$$###%%%%%%$$$$$$###"""""""""""""""######$$$$$$$$$$$$ ###%%%&&&&&&$$$###&&&&&&&&&&&&%%%$$$######$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%'''$$$$$$'''&&&######&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###"""!!!!!!###%%%$$$$$$######$$$$$$%%%&&&&&&%%%######$$$%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%###"""""""""######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%(((((('''''''''&&&&&&&&&######$$$%%%&&&(((((()))&&&&&&&&&''''''''''''(((((((((((((((((((((((((((''''''''''''((((((((((((''''''''''''((((((((((((((()))***++++++***)))(((''''''((())))))))))))))),,,,,,+++***))))))******+++++++++,,,,,,---------((()))+++,,,,,,+++)))(((***+++,,,,,,------,,,,,,,,,,,,,,,------.........000//////.........//////000000111111111222222222111111111111222333444555111222333555666666777777666666666666777777777777999888777666555555555555999888777666777888:::<<<;;;;;;:::999999999::::::888888888:::<<<<<<:::888999::::::::::::<<>>>>>?????????>>>======<<<<<<;;;;;;;;;;;;<<<<<<999999::::::;;;<<<=========;;;999666555666888999;;;<<<===>>>>>><<<:::999777777888999999999999888444555666777777555333222000000111111111222222222////////////////////////------------------------//////...------------...111000...---,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++*********************************(((((((((((((((((((((((())))))))))))************+++*********))))))((((((******)))(((((((((((((((***((('''&&&&&&'''(((***''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&)))(((&&&%%%$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###""""""######"""###$$$%%%%%%%%%%%%%%%"""############$$$$$$$$$#################################$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%######$$$%%%$$$$$$$$$###"""!!! ########################################################################""""""""""""""""""""""""""""""""""""############!!!"""#########!!!  !!!!!!!!!!!!!!!!!!""""""""""""$$$$$$$$$######"""""""""##############################""""""!!!!!! $$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%'''$$$$$$%%%%%%!!! ###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%$$$###"""###$$$$$$$$$######$$$$$$%%%&&&&&&$$$""""""$$$%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""""""""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((''''''''''''((((((((((((((()))************)))(((''''''((())))))))))))))),,,++++++***))))))***************++++++,,,,,,,,,++++++------------+++++++++,,,------......---------------------..................------...//////111111111111111111111111111111111111222333444444333333444555666666666666555555666666666666777777::::::999888777777777777666666888999:::;;;<<<<<<;;;;;;:::999999:::::::::888888888999;;;;;;999777888999999:::;;;>>>CCCFFF===>>>>>>>>>?????????@@@???>>>===<<<;;;:::::::::888888999::::::;;;;;;<<<;;;:::777555444555777888;;;<<<=========<<<:::999888888999999999888888777333444666666666555333222000000111111111222222222000000000000000000000000------------------------//////...---------------------,,,,,,---...000111,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++************************(((((()))))))))******************)))))))))((((((***))))))((((((((((((((()))((('''&&&&&&'''((()))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###""""""#########$$$%%%&&&&&&&&&&&&%%%"""############$$$$$$$$$########################$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%######$$$%%%&&&%%%%%%%%%%%%%%%&&&'''########################################################################!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""##############################"""!!! !!!!!!!!!!!!!!!!!!!!!"""""""""###&&&&&&&&&%%%%%%$$$$$$$$$##############################""""""!!!!!!!!!!!!"""###$$$%%%&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%'''$$$###$$$### %%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""$$$&&&&&&%%%######$$$$$$############$$$%%%%%%$$$###!!!!!!###$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########"""######$$$%%%######$$$$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&&&&&&&&&&(((((('''&&&%%%$$$######&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((''''''''''''((((((((((((((())))))******))))))(((''''''((())))))))))))))),,,+++******)))*********)))***************++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,------..................---------------------,,,,,,,,,,,,---......///111111111111000000000000111111000111111222333444444555555666666666555555444444555555555666666666999999888777666666666666444666999<<<=========<<<:::::::::999999:::;;;;;;999888888999::::::888666777888888999;;;???EEEJJJBBBAAA@@@???>>>??????@@@AAA@@@>>><<<:::999888777777888999:::::::::::::::;;;:::777666555666777888:::;;;<<<===<<<;;;:::999999999999999999888777666333444555555555444222111111111111111111222222222111111111111111111111111------------------------///......---------------,,,,,,,,,,,,---...///000,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++,,,,,,++++++++++++++++++++++++************************(((((())))))))))))************))))))))))))((((((***)))((((((''''''(((((()))((('''&&&&&&'''((()))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######"""#########$$$%%%&&&&&&&&&&&&&&&&&&"""############$$$$$$$$$########################%%%$$$$$$###""""""!!!!!!###########################$$$%%%%%%######$$$%%%$$$###!!! !!!"""###########################################################################!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""##############################$$$%%% !!!!!!!!!!!!!!!!!!!!!"""""""""######%%%%%%%%%%%%%%%$$$$$$$$$""""""""""""""""""""""""###""""""""""""!!!!!!!!!######$$$%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&###"""$$$### """$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ """%%%&&&&&&$$$$$$$$$###############$$$$$$%%%###""" !!!"""$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""######$$$%%%%%%""""""###$$$%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&%%%$$$######%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''((((((((((((''''''''''''((((((((((((((())))))))))))))))))(((''''''((()))))))))))))))++++++***************+++************++++++++++++******))))))))))))******+++,,,------......---------,,,,,,,,,,,,+++++++++******++++++,,,---...///111000000000000/////////000000000000111222333444666666666666666555444333333333444444555555666666666666555444444444444444666777999:::;;;<<<;;;;;;999999999999::::::;;;<<<:::999888888999:::888777888888888888:::>>>DDDIIIJJJHHHEEEAAA???>>>>>>>>>AAA@@@>>><<<:::999888888888999:::;;;;;;;;;;;;:::;;;:::999777777777888999::::::;;;;;;;;;;;;:::999:::::::::999888777666555333333444444444333222111111111111111111111111111111111111111111111111111........................///...------,,,,,,------//////...---,,,,,,,,,,,,++++++++++++++++++++++++*********++++++,,,,,,,,,++++++++++++++++++++++++************************(((((((((((()))))))))***))))))))))))))))))(((((())))))(((''''''''''''((((((''''''&&&&&&''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&"""###%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$%%%%%%&&&%%%%%%$$$""""""#########$$$$$$$$$#################################"""""""""!!!!!!""""""""""""""""""""""""###$$$%%%%%%######$$$%%%%%%###########################################################################""""""""""""""""""""""""!!!"""""""""###############""""""!!!"""###%%%&&& !!!!!!!!!"""""""""!!!!!!"""""""""##################"""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""""""""""""""$$$%%%%%%%%%$$$$$$###"""#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%""""""%%%%%%######&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###%%%%%%$$$$$$%%%######""""""######$$$%%%###!!! !!!###$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$$$$$$$$$$""""""######$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''((((((((((((''''''''''''(((((((((((()))(((((((((((((((((()))''''''((()))))))))))))))+++***************++++++,,,,,,,,,,,,,,,,,,,,,+++***))))))(((((())))))*********+++,,,,,,,,,,,,+++*********************************+++,,,---...///////////////////////////000000000000111222333333555666666555555444333222333333444444555666666777666555555444444444444555;;;:::888777777888888999888888888999:::;;;<<<===;;;999888888::::::999888999999999888888;;;@@@CCCLLLJJJGGGCCCAAA???@@@@@@>>>>>><<<;;;;;;:::;;;;;;999:::<<<=========<<<;;;:::999888777777777888888999999:::::::::::::::999;;;;;;::::::888777555444333333444333333333222222111111111111111111111111111111111111111111111111..............................---,,,,,,,,,,,,,,,.........------,,,++++++++++++++++++++++++++++++*********++++++,,,,,,,,,++++++++++++++++++++++++))))))))))))))))))))))))'''(((((((((((()))))))))(((((((((((((((((()))))))))(((((('''''''''''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&"""###%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$######$$$$$$$$$######"""""""""#########$$$$$$$$$########################!!!!!!"""""""""#########""""""""""""""""""""""""###$$$%%%%%%######$$$%%%)))'''$$$!!!!!!"""################################################################################################!!!"""""""""############"""!!! !!!"""$$$%%%!!!!!!!!!"""""""""######""""""""""""############""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""############%%%%%%%%%%%%$$$###"""!!!############$$$$$$$$$$$$#########$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%"""###&&&'''%%%%%%((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""#########$$$%%%###""""""""""""###$$$$$$###""" !!!###%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$$$$$$$######""""""######$$$$$$%%%%%%###$$$$$$$$$$$$%%%%%%%%%#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&######$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((((((''''''''''''(((((((((((()))((((((''''''(((((()))''''''((()))))))))))))))*********)))******+++,,,---------,,,,,,,,,,,,,,,++++++++++++++++++++++++))))))***+++++++++++++++))))))*********+++++++++++++++++++++,,,------.............../////////000000000///000000111222333444444444444444333222111333333444555666777777888888888777666666777777888===;;;999666555666777888888888888999:::;;;===>>>;;;:::888999;;;<<<<<<;;;999::::::999888999<<>>???===<<<;;;777777666666666666666777888888999999999999::::::;;;;;;::::::888777555555444444444444333333333333222222222111111111111111111111111111111111111111...........................------,,,,,,,,,,,,,,,***+++,,,---.........---++++++++++++++++++++++++++++++++++++++++++,,,,,,************************((((((((((((((((((((((((''''''(((((((((((())))))''''''(((((((((((()))))))))(((''''''&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########"""######$$$%%%###############""""""!!!"""############$$$$$$$$$########################!!!!!!""""""###$$$$$$%%%""""""""""""""""""""""""###$$$%%%%%%######$$$%%%%%%$$$###"""###$$$&&&'''########################################################################$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""############!!!!!!!!!!!!!!!!!!"""###""""""""""""############"""""""""#########$$$$$$#########$$$$$$$$$$$$$$$"""""""""""""""""""""""""""""""""############$$$######$$$$$$$$$######"""############$$$$$$$$$$$$"""#########$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&$$$$$$''''''$$$%%%'''########################$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$$$$###"""###%%%"""""""""""""""###$$$$$$###"""!!!"""$$$&&&&&&%%%########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%$$$###""""""###############$$$$$$$$$######$$$$$$$$$%%%%%%%%%"""#########$$$$$$$$$$$$########################%%%%%%%%%$$$$$$$$$#########$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((((((''''''''''''(((((((((((()))(((''''''''''''((()))''''''((()))))))))))))))******))))))***++++++,,,,,,,,,,,,,,,++++++******)))***+++,,,,,,+++***)))******+++,,,,,,,,,,,,+++))))))***+++,,,---......------,,,,,,,,,,,,---...,,,,,,---...//////000000/////////000000111222333222222333333333222111111333444444555777888888999888888888777777888888999;;;::::::999888888888888777777888999:::<<<===>>><<<:::999:::<<<>>>???>>>999:::;;;;;;::::::<<<===AAAAAAAAABBBBBBBBBCCCCCC<<<<<<;;;;;;;;;<<<<<<===999;;;===>>>>>>===;;;999888888888888888888888888888888888888888999:::::::::::::::999888777666555666555555444444444444444222222222111111111000000000000000000000000000000...........................---,,,,,,++++++,,,,,,)))***,,,---......------************************,,,,,,++++++++++++++++++))))))))))))))))))))))))))))))))))))))))))))))))'''''''''((((((((())))))'''''''''((((((((())))))(((((('''&&&&&&&&&&&&'''&&&&&&&&&''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""###$$$$$$%%%$$$$$$$$$$$$$$$###"""""""""############$$$$$$$$$#################################$$$$$$$$$$$$$$$###########################$$$%%%%%%######$$$%%% !!!"""###$$$%%%################################################################################################""""""""""""############""""""#########"""!!!!!!"""""""""#########$$$$$$""""""#########$$$$$$$$$"""#########$$$$$$$$$%%%########################""""""#########$$$$$$$$$!!!"""###$$$$$$$$$$$$$$$"""############$$$$$$$$$""""""######$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%(((%%%$$$'''&&&######%%%########################$$$$$$$$$$$$$$$$$$$$$$$$&&&'''&&&$$$"""!!!"""$$$"""""""""""""""######$$$$$$###"""###%%%&&&'''&&&########################""""""""""""""""""""""""###$$$%%%%%%$$$###"""!!!$$$$$$$$$########################$$$$$$%%%%%%%%%""""""######$$$$$$$$$$$$########################%%%%%%%%%$$$$$$###############$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((()))''''''''''''((((((((())))))((('''&&&&&&'''((()))'''(((((()))))))))))))))******))))))***+++,,,,,,++++++++++++******))))))&&&((()))++++++)))(((&&&++++++,,,------------,,,******+++,,,...///000000......---,,,,,,,,,------***+++,,,---...000111111////////////000111222333000111111222222222111111444444555666777888999:::777666666666666666777777888999;;;<<<<<<;;;999888777777777999:::<<<>>>???<<<:::999:::===???@@@@@@888:::<<<===<<<<<<===>>>@@@@@@AAAAAAAAA@@@???>>>======<<<;;;;;;;;;;;;<<<999:::<<<>>>===<<<:::888<<<<<<<<<<<<<<<<<<<<<<<<888888777777888999::::::999999999999999888777666666666555444444444444555222222222222111111000000////////////////////////////////////////////////...---,,,,,,++++++,,,,,,,,,---......---,,,***)))************************---,,,,,,++++++*********((((((((((((((((((((((((************************''''''''''''((((((((()))&&&'''''''''(((((())))))(((((('''&&&&&&&&&&&&'''%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&$$$###"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""###$$$%%%%%%%%%%%%%%%%%%%%%$$$###""""""############$$$$$$$$$########################&&&&&&%%%%%%$$$####################################$$$%%%%%%######$$$%%%"""###############""""""########################################################################""""""""""""""""""""""""""""""""""""###############$$$%%%%%%%%%###""" """############$$$$$$$$$"""############$$$$$$$$$ !!!!!!"""""""""###########################""""""######$$$$$$$$$$$$######$$$$$$$$$$$$######"""############$$$$$$$$$ !!!"""###$$$%%%&&&&&&%%%$$$###""""""###$$$%%%%%%%%%$$$$$$###""""""!!!######""""""###$$$%%%%%%"""############$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$###########################"""""""""""""""########################"""""""""###$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%"""""""""###$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###%%%%%%$$$"""!!!"""###&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$#########'''&&&$$$######$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&''''''''''''&&&%%%$$$$$$''''''''''''''''''''''''+++***((('''&&&&&&''''''))))))))))))((((((((((((&&&'''((()))******)))(((+++++++++++++++***)))((())))))))))))))))))))))))(((((((((((((((((((((((('''+++***(((///;;;<<<333&&&(((***,,,------------...///000111111000///...111111111000000000000000111111222222222333333333333333444555666777888999666666666666777888999:::<<<;;;:::999999;;;===>>>999999888888999;;;<<<>>><<<===>>>??????>>>======:::;;;<<<>>>??????@@@@@@DDDBBB@@@???>>>???@@@AAA???>>>===;;;999888888888::::::999888777777777888::::::<<<===>>>>>>>>>>>>;;;:::888777666666777888888777777888888888777555222111111111333444333222222222222111111111000000111000//////000000///...////////////000000000000........................------,,,,,,,,,+++++++++,,,+++)))(((((()))+++,,,)))***,,,,,,,,,***((('''(((((((((((())))))))))))))))))))))))(((((((((((())))))))))))))))))))))))((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&%%%%%%$$$$$$&&&'''((())))))((('''&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$###############$$$$$$$$$$$$######$$$$$$######"""!!!!!!!!!########################$$$$$$%%%%%%%%%$$$######%%%$$$"""""""""$$$&&&((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""!!!"""###$$$$$$###"""!!!$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$$$$$$$#########"""""" """###%%%%%%&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$######""""""!!!!!! """""""""###$$$$$$$$$%%%$$$$$$############$$$$$$######"""""""""""""""###!!!###$$$###"""!!!"""###%%%$$$"""!!!!!!"""$$$%%%$$$$$$%%%%%%%%%%%%$$$$$$"""############$$$$$$$$$###############$$$$$$$$$$$$$$$###""""""###$$$$$$##############################""""""###$$$$$$%%%"""############$$$$$$$$$%%%%%%%%%$$$$$$#################################$$$$$$$$$######################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%$$$"""!!!"""###%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$######&&&%%%$$$$$$$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&''''''''''''''''''&&&&&&''''''''''''''''''''''''&&&&&&%%%%%%&&&'''((()))(((((((((((())))))))))))'''((()))*********)))(((***************)))((((((************************++++++++++++++++++++++++'''+++***'''---777777///)))***+++,,,------,,,,,,//////000000000000//////000000000000000000000000111111111222222222333333333333444555666777888888666666666777777888999:::999888777666777888:::;;;::::::999888888999:::;;;999:::;;;===>>>>>>>>>===:::;;;<<<===????????????BBBAAA???>>>===>>>???@@@>>>===<<<:::999888777777888777777888888999:::;;;;;;;;;<<<>>>>>>??????>>>======;;;:::999999::::::888777777777777777666444555444444444555666666555333222222222222111111111000///......//////...---.../////////000000000000........................------------,,,,,,,,,,,,---+++***))))))***+++---)))***,,,,,,,,,***)))'''''''''((((((((()))))))))******)))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''%%%&&&'''(((((('''&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$%%%%%%##############################$$$%%%%%%$$$$$$$$$$$$###"""""""""###$$$%%%########################$$$$$$$$$#########""""""#########$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$!!!!!! !!!!!!"""###$$$$$$$$$$$$#########"""""" !!!"""###$$$$$$$$$######################################################""""""!!!!!!!!!!!!""""""""""""""""""######$$$######""""""######$$$""""""!!!!!!!!!!!!""""""!!!###$$$###"""!!!"""###$$$###!!! !!!###$$$%%%%%%%%%&&&&&&%%%%%%%%%"""############$$$$$$$$$%%%$$$$$$$$$######""""""$$$$$$###""""""###$$$$$$!!!!!!"""###$$$$$$%%%%%%#########"""######$$$%%%"""############$$$$$$$$$&&&&&&%%%$$$######""""""########################$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$##########################################$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%$$$"""""""""$$$$$$######""""""######$$$%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&''''''''''''((((((((((((''''''''''''''''''''''''%%%%%%$$$%%%%%%&&&((((((''''''(((((())))))***************+++******)))(((((())))))))))))(((''''''++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,(((+++)))&&&***222222+++,,,,,,------------,,,+++000//////////////////000/////////000000000000000111111111222222222222333222333333444555666777777777777777777888888999:::888777666555666777888999;;;:::888777777777888999777888:::;;;======>>>>>>:::;;;<<<===>>>?????????@@@???>>>=========>>>???===<<<;;;999888777777777555666666888999;;;===>>><<<===>>>???????????????>>>===<<<;;;::::::::::::999888888777666555444444666666666666666666777777333333333333222222222222000...------...///---,,,....../////////000000000.................................------------,,,---,,,+++******+++,,,---******+++,,,,,,***)))((('''(((((((((((()))))))))++++++*********)))))))))''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''(((((())))))%%%%%%&&&&&&&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%######$$$$$$$$$$$$######"""######$$$%%%%%%&&&&&&########################""""""###$$$%%%%%%%%%%%%#########"""""""""""""""""""""""""""""""""""""""$$$$$$$$$###############$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$############### !!!!!!"""######""""""########################""""""""""""""""""""""""###""""""""""""!!!!!!!!!"""""""""!!!!!!!!!!!!!!!######""""""""""""######"""!!!!!!!!!!!!!!!""""""!!!###$$$###"""!!!"""######"""!!! !!!"""###$$$$$$%%%%%%%%%%%%$$$$$$""""""#########$$$$$$$$$$$$$$$$$$############"""$$$##################$$$"""""""""###$$$$$$%%%%%%$$$###############$$$$$$""""""#########$$$$$$$$$&&&&&&%%%$$$###"""!!!!!!###############$$$$$$$$$#########$$$$$$$$$$$$$$$########################%%%$$$$$$$$$###"""""""""""""""""""""""""""""""""######$$$%%%%%%%%%%%%$$$###"""""""""!!! $$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%$$$###"""###$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&''''''((((((''''''''''''''''''''''''(((((('''&&&&&&%%%%%%%%%&&&''''''((()))******+++++++++++++++******))))))((()))))))))))))))((((((***************************************************,,,***''')))......))),,,,,,------------------000///...------...///000......///////////////000111111111111222222222222222333333444555555666666777777777777777888999:::888777777777777888999:::888888777666666777888999999999:::;;;<<<=========:::;;;<<<===>>>>>>>>>>>>======<<<<<<<<<===>>>>>>>>>===;;;:::999888888888666666777888:::<<<===>>>===>>>???@@@@@@@@@@@@@@@<<<<<<;;;:::999999999999::::::999888666444444555666777888777666666666777444444444333333333222222111///......//////...---........./////////000000........................//////.........------------,,,,,,++++++,,,,,,---******+++++++++******)))))))))))))))************++++++++++++*********)))''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&''''''((()))))))))%%%%%%&&&&&&&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%######$$$$$$$$$$$$######!!!!!!"""""""""#################################!!!!!!"""$$$%%%%%%%%%%%%######$$$$$$###"""!!! ################################################$$$###"""!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$#########$$$$$$########################""""""############""""""################################################""""""""""""""""""""""""#########""""""!!!!!! ###""""""!!!!!!""""""###""""""!!!!!!""""""######!!!###$$$###"""!!!"""######"""!!!!!!!!!!!!"""#########$$$$$$$$$$$$######""""""#########$$$$$$$$$"""############$$$$$$$$$#########$$$$$$#################################$$$$$$###############$$$""""""#########$$$$$$$$$%%%%%%$$$######"""!!!!!!""""""#########$$$$$$$$$""""""""""""######$$$$$$########################%%%$$$$$$$$$###""""""""""""""""""""""""""""""""""""###$$$$$$%%%%%%$$$$$$###"""""""""!!! $$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$###"""###$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$%%%''''''''''''''''''''''''''''''))))))(((((('''&&&&&&%%%&&&''''''((()))******+++,,,,,,+++******)))))))))))))))***++++++*********)))))))))))))))))))))))))))))))))))))))))))))))),,,---,,,)))***,,,,,,)))***++++++,,,---...///000000///...------...///000------........./////////000000111111111222222222222222333333444444555555777777666666777777888888777666666666777777888888555555555555666888:::;;;======<<<<<<<<<<<<<<<<<<:::;;;<<<======>>>======;;;;;;;;;<<<<<<======>>>???>>>===;;;;;;:::::::::999999999999:::;;;<<<===>>>??????@@@@@@@@@@@@???;;;;;;;;;;;;:::999888888;;;;;;;;;999555444555777888;;;======:::777777777444444444333333333222222222111000000111111000...............////////////........................//////.........---------,,,,,,,,,,,,,,,,,,,,,,,,*********+++++++++************+++++++++,,,,,,,,,++++++++++++*********)))''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''(((((((((((((((((((((((('''&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%######$$$$$$$$$$$$###############"""""""""!!!!!!######################## !!!"""###$$$%%%%%%%%%$$$%%%%%%%%%$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$###########################"""!!! !!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""""""""##############################$$$$$$%%%%%%%%%$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""############$$$$$$$$$######"""""""""######""""""""""""######"""""""""""""""###$$$%%%!!!###$$$###"""!!!"""###########################"""######$$$$$$######""""""############$$$$$$$$$""""""######$$$$$$$$$%%%"""###$$$$$$$$$$$$###"""$$$$$$##################%%%$$$######"""#########"""############$$$$$$$$$$$$############""""""""""""""""""###$$$$$$%%%%%%!!!!!!!!!"""######$$$$$$########################$$$$$$$$$#######################################"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$###"""$$$%%%&&&%%%%%%%%%%%%%%%%%%&&&###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%$$$#########$$$%%%&&&''''''''''''''''''''''''%%%&&&'''((())))))))))))''''''(((((())))))******++++++***)))))))))******)))******++++++++++++***((((((((((((((((((((((((************************------,,,+++++++++,,,,,,*********+++,,,...000111///..................///,,,,,,------.../////////000000000111111111111222222222222333333333444444666666666555555666666777444444555555555666666666444444444555777999<<<===???>>>===<<<;;;;;;;;;;;;:::;;;<<<===============::::::;;;<<<======>>>>>>???>>>===<<<;;;;;;;;;;;;;;;;;;;;;::::::;;;<<<<<<>>>??????@@@@@@@@@??????<<<=========<<<;;;:::999999:::;;;888444333666999===BBBFFFFFFAAA<<<999888333333333333222222222222333222000111222222111///------........./////////.................................------------,,,++++++,,,,,,,,,,,,++++++***************+++++++++***++++++++++++,,,,,,,,,++++++*********)))))))))''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''((('''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&""""""""""""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%######$$$$$$$$$$$$######&&&&&&%%%%%%$$$######"""########################!!!!!!"""###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$######""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$###"""""""""""""""#####################$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$"""""""""############$$$$$$$$$$$$$$$############$$$$$$############$$$$$$"""!!!!!!!!!"""###$$$%%%!!!###$$$###"""!!!"""############$$$$$$############$$$$$$%%%%%%$$$$$$###"""############$$$$$$$$$$$$$$$$$$###############"""###$$$$$$$$$$$$###""""""""""""###$$$$$$%%%%%%%%%$$$$$$###""""""######"""############$$$$$$$$$""""""""""""############!!!""""""###$$$$$$%%%%%%!!!!!!"""######$$$%%%%%%#######################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$$$$######$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%%%%$$$###""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&'''&&&$$$######$$$%%%&&&''''''''''''''''''''''''$$$%%%&&&((((((((((((((((((((((((((())))))))))))***)))((((((((()))***+++(((((()))***************((((((((((((((((((((((((+++++++++++++++++++++++++++++++++++++++***+++---+++*********+++,,,...///---......//////......---+++,,,,,,---......//////000000000000111111111111222222222222333333333333555555444444444444555555444444555666666666666666666666666666777999;;;<<<===<<<;;;:::::::::;;;<<<;;;;;;<<<<<<======<<<<<<999:::;;;<<<>>>>>>??????>>>===<<<;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;<<<<<<===>>>???????????????>>>>>>;;;<<<<<<<<<;;;:::999888666888999666222111555999@@@FFFLLLLLLFFF>>>999777333222222222222111111111222111000000111111000///---------.........//////........................------------,,,,,,,,,,,,***++++++++++++++++++*********)))******++++++,,,)))))))))*********++++++******)))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%%%%&&&''''''((((((&&&&&&%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######%%%%%%$$$$$$$$$$$$$$$$$$########################""""""############""""""$$$######""""""###$$$%%%########################""""""#########$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""!!!""""""###$$$%%%""""""#########$$$$$$$$$###$$$$$$%%%%%%%%%$$$$$$################################################""""""#########$$$$$$$$$""""""""""""############%%%%%%$$$$$$$$$$$$%%%%%% !!!"""###!!!###$$$###"""!!!"""###""""""############""""""$$$%%%%%%&&&&&&%%%%%%$$$"""############$$$$$$$$$&&&&&&%%%$$$###"""!!! """###$$$%%%%%%$$$###""" !!!###$$$%%%&&&'''%%%%%%$$$###""""""######"""############$$$$$$$$$!!!!!!!!!"""######$$$$$$!!!""""""###$$$$$$%%%%%%""""""###$$$%%%%%%&&&&&&########################""""""######$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###"""""""""###$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$$$$######$$$&&&$$$$$$############$$$$$$#########$$$$$$%%%%%%%%%%%%$$$"""!!!!!!"""$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&)))(((&&&$$$$$$$$$&&&'''''''''''''''''''''''''''&&&''''''((('''%%%$$$###))))))))))))((((((((((((((((((''''''''')))***+++''''''((()))))))))))))))))))))))))))))))))))))))************************)))))))))+++***)))+++...,,,,,,*********+++,,,---,,,---...//////...---,,,++++++,,,------...//////000000000000111111111111222222222222222222333333555444444333333333444444666777777888999888888888888888777777777999:::;;;:::999999888999:::<<<===;;;;;;<<<<<<===<<<<<<<<<999:::;;;===>>>?????????===<<<;;;;;;:::::::::::::::::::::;;;<<<===>>>>>>>>>>>>?????????>>>>>>===888999::::::999888666555333666777444000///444888@@@GGGNNNNNNFFF===666444222222222111111111000000111000//////000000///...---------.........//////........................------,,,,,,,,,+++++++++)))******++++++******)))******))))))***+++,,,,,,(((((((((((())))))))))))))))))))))))(((((((((((())))))))))))))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((("""###$$$%%%'''((()))***&&&%%%$$$######$$$%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$###############$$$$$$$$$$$$######!!!!!!!!!"""######$$$$$$########################"""############""""""!!!###"""!!! !!!"""$$$&&&""""""""""""""""""""""""""""""######$$$$$$$$$$$$%%%%%%'''(((((('''%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""###$$$%%%&&&""""""######$$$$$$$$$$$$""""""###$$$$$$$$$$$$$$$########################""""""""""""""""""""""""""""""######$$$$$$$$$$$$ !!!!!!""""""######&&&%%%%%%$$$$$$%%%%%%&&& !!!"""!!!###$$$###"""!!!"""###!!!!!!""""""""""""!!!!!!""""""""""""############$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$#####################$$$%%%&&&&&&%%%$$$###$$$############"""!!!!!!########################"""############$$$$$$$$$$$$$$$$$$#########"""""""""############$$$$$$$$$  !!!""""""""""""#########$$$$$$$$$########################&&&&&&%%%$$$#########$$$###$$$$$$%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$######""""""###$$$$$$$$$$$$$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$((('''&&&%%%%%%%%%%%%%%%%%%######$$$''''''$$$ $$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''&&&&&&(((((((((((())))))))))))++++++***)))(((((())))))...---,,,***))))))(((((()))))))))))))))((('''''',,,,,,,,,++++++++++++***)))************+++++++++++++++++++++++++++++++++000000000000////////////,,,,,,,,,---------.....................///000000111000/////////000222333222333333333333333333444222555999;;;:::888777666555444444444555888:::<<<:::999888888999<<<>>>@@@<<<>>>@@@@@@>>>===<<<===>>>===<<<;;;;;;<<<===>>>===<<<;;;:::::::::::::::<<<<<<<<<<<<<<<<<<<<<<<<===<<<<<<<<<<<<===>>>>>>===;;;::::::<<<<<<:::777;;;:::777333000111555888DDDFFFHHHFFFAAA:::444222666666555555555444444444111111000......---------,,,,,,------------,,,,,,------,,,,,,,,,,,,++++++,,,,,,,,,++++++*********++++++++++++++++++++++++************))))))))))))&&&(((***+++,,,+++)))((())))))(((''''''''''''''''''''''''((()))******+++''''''''''''''''''''''''&&&&&&''''''(((((()))))))))((('''&&&&&&'''((()))%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$######""""""""""""######%%%$$$$$$$$$###""""""""""""""""""""""""######$$$"""""""""!!!!!!!!!!!!!!!""""""###$$$$$$$$$$$$###$$$###"""!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&&&&%%%$$$###""""""""""""""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%$$$###""""""#########$$$$$$%%%%%%$$$$$$###############""""""!!!!!!#########"""""""""""""""$$$#########""""""!!!!!!""""""!!!!!!"""###$$$$$$"""############$$$$$$$$$"""!!!!!!!!!"""###$$$$$$"""""""""###$$$$$$$$$%%%""""""""""""##########################################$$$$$$$$$$$$####################################$$$$$$$$$$$$######$$$###""""""!!!!!!!!!"""########################!!!""""""""""""#########%%%%%%%%%$$$$$$$$$######"""############$$$$$$$$$$$$$$$#########$$$%%%%%%""""""#########$$$$$$$$$########################&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&%%%%%%%%%%%%%%%%%%###"""###%%%&&&###!!!$$$%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''''''''''''''((((((((())))))))))))+++******)))(((((()))))),,,+++***))))))((()))))))))))))))))))))(((''''''(((((())))))******++++++))))))*********+++++++++++++++++++++++++++++++++////////////............,,,,,,,,,------------..................//////000111000/////////000222222222222333333333333444444666888::::::999888888999888777666555666777999;;;::::::999888999;;;===???===???@@@@@@>>><<<<<<<<<>>>===<<<;;;;;;<<<===>>>======<<<::::::999999999;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;<<<<<<<<<============;;;:::;;;======;;;888999888666222000222555888BBBDDDEEECCC???999666444444444333333333222222222111000///...---------------------......---------------,,,,,,,,,+++++++++,,,,,,,,,+++++++++******++++++++++++++++++++++++*********)))))))))(((((('''(((***+++++++++)))((())))))((('''''''''''''''&&&&&&'''(((((()))******&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((((((((((('''&&&%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$#########""""""#########$$$$$$$$$##############################$$$$$$%%%$$$$$$$$$$$$############""""""###$$$$$$$$$$$$###$$$###"""!!!!!!"""###$$$########################$$$$$$######$$$$$$%%%&&&&&&%%%$$$#######################################################################################%%%$$$$$$###""""""#########$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$###"""""""""""""""""""""$$$#########"""""""""""""""""""""""""""###$$$$$$"""############$$$$$$$$$######"""""""""###$$$$$$""""""""""""""""""######"""""""""#########$$$$$$""""""""""""""""""""""""######$$$$$$$$$$$$#######################################""""""#########'''&&&$$$###"""###%%%&&&########################!!!!!!!!!""""""""""""###&&&&&&%%%%%%%%%$$$$$$$$$"""############$$$$$$$$$$$$$$$###"""""""""#####################$$$$$$$$$########################$$$$$$$$$%%%%%%%%%%%%%%%&&&%%%%%%$$$######""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%'''&&&%%%$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%%%%%%%%%%%%%###""""""$$$%%%$$$###$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''((((((((()))))))))******)))((((((((())))))))))))(((((((((((()))))))))))))))))))))(((((('''%%%%%%&&&'''((()))******)))))))))*********++++++++++++++++++++++++++++++.........---------,,,,,,,,,,,,,,,,,,------------......------......///000000000/////////000111222222222222333333444444444555666555444222222444666:::999888777777777888999;;;:::999999999;;;<<<======???@@@???===;;;;;;;;;======<<<;;;;;;<<<======>>>===<<<:::999888888888::::::::::::::::::::::::999:::;;;<<<===<<<;;;;;;;;;::::::;;;======<<<:::888777555333111333666:::CCCDDDDDDAAA<<<777444333222222111111111000000000000000///...---------------..................---,,,,,,,,,,,,++++++++++++,,,,,,,,,++++++++++++***++++++++++++++++++++++++******))))))))))))(((((('''((()))++++++******)))))))))((('''''''''''''''&&&&&&&&&'''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''%%%%%%$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$#########$$$$$$############$$$$$$###############$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###$$$###""""""""""""###$$$""""""""""""""""""""""""$$$############$$$%%%%%%%%%%%%$$$$$$###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""########################%%%$$$######"""#########$$$$$$$$$$$$$$$$$$$$$$$$"""#####################""""""""""""""""""#####################"""""""""""""""""""""#########$$$"""############$$$$$$$$$$$$$$$$$$$$$############"""""""""!!!!!!!!!!!!!!!""""""#########$$$$$$$$$##############################$$$$$$$$$$$$#####################$$$$$$$$$$$$###"""!!!!!!"""###$$$&&&$$$""" !!!$$$%%%########################""""""""""""############%%%%%%$$$$$$$$$$$$######""""""#########$$$$$$$$$$$$$$$###""""""!!!""""""################################################""""""###$$$$$$%%%%%%%%%$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%$$$###"""!!!!!!!!!!!!%%%$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%#########%%%&&&&&&$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''((((((((())))))***))))))((((((((())))))'''''''''''''''((())))))(((((())))))))))))((((((%%%%%%&&&''''''((())))))))))))))))))************************************,,,,,,,,,,,,++++++++++++++++++,,,,,,,,,---------...------------...//////000//////...///000111222222222222333333444444444444444444333111000222333888777666666666777888999;;;::::::999999:::;;;;;;<<<===>>><<<:::888999999<<<<<<<<<<<<<<<<<<<<<<<>><<<:::999888777777999999999999999999999999777888:::<<<<<<;;;:::999:::::::::;;;<<<===<<<<<<777777666444333555999<<>>===<<<:::888777777777888888888888888888888888555777999:::;;;:::888777888999;;;;;;;;;;;;;;;<<<888888888666666777:::===GGGFFFCCC>>>888444222222111111111111000000000000///......------------...------............------,,,,,,+++++++++*********++++++++++++++++++++++++************************)))))))))(((((((((((('''(((((()))***************))))))((('''''''''''''''&&&&&&&&&'''''''''''''''((((((((((((((((((((((((((((((''''''&&&&&&%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$$$$$$$$$$$$$$$$%%%"""""""""###$$$$$$$$$%%%"""""""""""""""###$$$$$$!!!!!!""""""#########$$$""""""###$$$$$$$$$$$$#########$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%$$$$$$$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$###############$$$$$$$$$######""""""######$$$$$$###"""!!! !!!!!!""""""###########################$$$$$$$$$######$$$$$$$$$$$$###"""""""""#########$$$$$$$$$%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$######"""""""""#########$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######"""""""""###$$$$$$%%%%%%#########""""""############""" !!!###$$$########################$$$$$$$$$%%%%%%%%%&&&&&&###""""""""""""!!!!!!!!!"""############$$$$$$$$$&&&%%%%%%$$$$$$$$$$$$%%%$$$$$$$$$#######################################!!!"""###$$$$$$$$$###"""""""""######$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&$$$%%%&&&%%%%%%%%%''')))######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''(((((((((&&&&&&'''''''''(((((((((((((((''''''(((((())))))'''''''''''''''((())))))'''(((((()))))))))))))))******))))))((((((((((((((((((((()))))))))******************************+++++++++*********))))))++++++++++++,,,,,,,,,,,,------,,,,,,------.../////////.........///000111111111222333333444555555444666888888777555555555111222333444666777888999888888999999:::::::::;;;888999999888666666777999;;;;;;<<<<<<<<<<<<;;;;;;===<<<;;;999888777777777666666666666666666666666555666777888999888777777777999;;;;;;999999999:::888888888777666777:::===>>>???>>><<<888666555666222222111111111000000000......---------------...,,,------------------,,,++++++++++++***************++++++++++++,,,,,,,,,************************))))))(((((((((((('''''')))))))))))))))*********))))))((('''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$############$$$$$$###############$$$$$$$$$""""""!!!!!!""""""###$$$######$$$$$$%%%&&&&&&&&&""""""###$$$$$$$$$$$$#########$$$%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$###""""""""""""###$$$$$$$$$$$$######"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#################################"""######$$$%%%$$$###"""!!!!!!"""###$$$&&&&&&%%%$$$"""!!! !!!!!!!!!"""######$$$$$$#########$$$$$$$$$$$$$$$###$$$%%%%%%%%%$$$###""""""############$$$$$$$$$###$$$%%%%%%%%%$$$###"""$$$$$$$$$$$$#####################$$$$$$$$$%%%%%%##############################$$$$$$$$$$$$######!!!""""""###$$$$$$%%%%%%######$$$$$$$$$$$$######%%%%%%%%%%%%%%%&&&''''''##############################$$$$$$$$$%%%%%%%%%#########""""""""""""!!!"""############$$$$$$$$$"""!!!!!!!!!!!!""""""###$$$$$$$$$#########""""""###########################$$$%%%&&&&&&%%%###"""$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###""""""######$$$%%%&&&%%%%%%$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&& """%%%%%%$$$###%%%'''######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''(((((()))&&&&&&&&&'''''''''(((((('''''''''''''''((())))))((((((((('''(((((())))))''''''((()))))))))))))))((((((((((((((()))))))))(((((((((((()))))))))***************************+++++++++*********))))))***++++++++++++,,,,,,,,,------,,,,,,------.../////////...---...///000111000111111222444555555666333444444333222222444666333444555666666777777777666777888999:::;;;;;;;;;888999999888777888:::<<<:::;;;;;;<<<<<<;;;;;;:::<<<;;;:::999888888888888555555555555555555555555555555666666666777777777666999;;;:::888666777888777777777666555555888:::777999:::999777555555555111111111111000000000000...------,,,,,,------...++++++,,,,,,,,,,,,++++++++++++++++++******************+++++++++,,,,,,,,,************************))))))(((((((((''''''''')))))))))))))))******+++))))))((('''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''%%%&&&&&&&&&&&&&&&&&&'''$$$%%%&&&&&&&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$%%%%%%%%%&&&#########""""""#########$$$$$$$$$#####################""""""######$$$%%%######$$$%%%%%%&&&''''''""""""###$$$$$$$$$$$$######$$$$$$%%%%%%$$$$$$###########################"""""""""""""""###$$$$$$$$$$$$###"""!!!!!!!!!!!!##############################################################################""""""###$$$$$$%%%$$$###"""!!!!!!"""###$$$$$$$$$$$$$$$$$$######### !!!!!!"""######$$$$$$#########$$$$$$%%%%%%%%%###$$$%%%&&&&&&$$$"""!!!"""############$$$$$$$$$ """###%%%%%%$$$###"""""""""""""""##################$$$$$$$$$%%%%%%%%%""""""""""""""""""""""""######$$$$$$$$$$$$######!!!""""""###$$$$$$%%%%%%###$$$%%%&&&&&&%%%$$$###!!!!!!""""""####################################"""############$$$$$$$$$$$$$$$$$$############""""""############$$$$$$$$$$$$#########$$$%%%&&&&&&$$$$$$$$$$$$######""""""########################%%%&&&(((((((((&&&$$$###''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$##############################$$$$$$$$$%%%%%%%%% !!!###$$$%%%%%%%%%$$$###""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%%%%&&& $$$%%%###"""###%%%######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((())))))&&&&&&&&&'''''''''(((((('''''''''''''''((()))***))))))(((((((((((())))))''''''((()))))))))))))))%%%&&&&&&'''((()))******(((((((((((())))))))))))))))))))))))))))))))))))++++++++++++******************+++++++++,,,,,,,,,---,,,,,,,,,,,,---......///......---...///000111000111111222444555666666777666555333222444888<<<666666777777777777666666555666888999:::;;;;;;<<<999::::::999888999<<<>>>::::::;;;<<<<<<;;;::::::;;;::::::999888888888999555555555555555555555555666555555555555666777777666999;;;999666555555777666666666555444444666888555777888777555222111111111000000000////////////------,,,,,,,,,------...***++++++,,,,,,++++++***+++++++++************)))*********++++++,,,,,,,,,)))))))))))))))))))))))))))((((((((('''''''''''')))))))))))))))******+++))))))(((''''''''''''''')))))))))))))))(((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''###$$$%%%&&&&&&%%%$$$###''''''''''''''''''''''''#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$%%%%%%&&&&&&&&&######""""""""""""######%%%$$$$$$$$$######""""""$$$$$$######$$$$$$%%%&&&!!!!!!"""###$$$$$$%%%%%%""""""###$$$$$$$$$$$$######$$$%%%&&&&&&%%%$$$###"""""""""""""""""""""""""""""""""""""""######$$$$$$$$$"""!!! """"""""""""""""""""""""""""""""""""""""""""""""##############################""""""###$$$%%%%%%$$$###""" """###$$$ !!!!!!"""###$$$$$$%%% !!!!!!"""###$$$$$$$$$#########$$$$$$%%%%%%%%%###$$$&&&&&&&&&$$$"""!!!"""############$$$$$$$$$ """$$$%%%$$$###""" !!!!!!""""""######&&&%%%###"""""""""######""""""""""""###$$$%%%&&&###########################################################################$$$$$$&&&'''((()))))) !!!######""""""###$$$%%%%%%$$$###"""""""""""""""############%%%%%%$$$###"""!!! &&&&&&&&&&&&&&&&&&&&&&&&$$$$$$############$$$$$$$$$$$$$$$######"""""""""$$$$$$$$$$$$$$$$$$$$$$$$###$$$&&&&&&&&&%%%###!!! !!!###$$$$$$###!!! $$$#########""""""!!!!!!$$$$$$$$$#######################################$$$$$$%%%###"""!!!###$$$$$$#########""""""!!!!!!###%%%%%%$$$"""!!!"""#########$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''''''''(((((((((((()))))))))))))))))))))))))))((('''&&&%%%&&&&&&'''''''''((()))***+++++++++*********)))))))))))))))******))))))))))))******++++++++++++,,,---......---.........---,,,,,,+++---------............//////000222333333222111000222222444555666666666666777888888777555444555777555666777888:::;;;<<<===;;;;;;;;;;;;;;;;;;;;;;;;;;;:::999888777777777777777666555444444555666777777666444333333444666777333444666888888666555333999888666555555555666777999888666555444444555555333333444444333333222111000000000000////////////222///+++***,,,...///000000000000///......------)))************+++++++++)))************+++++++++,,,,,,++++++***)))((((((***++++++,,,+++***((('''(((((())))))))))))((((((***)))(((''''''((()))***''''''((((((((((((''''''''''''&&&&&&&&&%%%%%%%%%(((((('''&&&%%%$$$$$$###%%%%%%%%%&&&'''((()))))))))((('''%%%$$$$$$%%%%%%'''''''''&&&&&&%%%%%%%%%$$$$$$############$$$$$$%%%%%%%%%$$$$$$$$$##############################!!!!!!!!!!!!!!!!!!!!!!!!$$$#########""""""!!!!!!!!!!!!"""############"""###$$$$$$%%%%%%$$$$$$### """%%%&&&&&&%%%$$$#########$$$$$$%%%%%%&&&########################"""############$$$$$$$$$"""###$$$%%%&&&%%%$$$###$$$#########""""""!!!!!!##############################$$$$$$$$$$$$######%%%###!!!"""$$$%%%$$$!!!$$$$$$$$$#########""""""!!!!!!!!!!!!!!!!!!!!!!!!"""&&&'''&&&###""""""######""""""###%%%&&&(((000222111,,,&&&######%%%########################&&&&&&%%%$$$###"""!!! !!!!!!###$$$$$$###"""!!!%%%$$$###""""""######$$$"""!!!!!!!!!"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%################################################!!!!!!"""""""""""""""######"""!!!!!!###%%%%%%$$$######$$$%%%%%%$$$######""""""""""""############$$$$$$$$$###############%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&%%%$$$###"""$$$%%%%%%%%%%%%###"""!!!$$$#########""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$%%%###"""!!!###$$$$$$#########""""""""""""###$$$%%%$$$"""!!!"""#########$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&'''((((((((((((((('''''''''(((''''''&&&&&&''''''(((''''''''''''(((((((((((((((((((((((((((((((((((()))((('''&&&%%%&&&&&&'''''''''(((((())))))*********)))))))))))))))))))))))))))(((((((((((())))))++++++++++++,,,---......------......---,,,,,,+++,,,,,,,,,,,,---------......///000111222111000000222333444555555666666666888999999777666555666888666777777888999:::;;;;;;::::::::::::::::::::::::999999888777777777777888777777666555555666777777888777555444444555777888777777888888888777666666:::999888777666777888888888777555444333333444444222222333333222222111000000000000000/////////...111...,,,+++---...///...//////...------,,,,,,+++************++++++++++++************++++++++++++,,,,,,++++++***))))))(((***+++,,,,,,,,,+++***)))(((((())))))))))))((((((***)))(((''''''((()))***''''''((((((((((((''''''''''''''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''((((((((('''&&&%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$############$$$$$$%%%%%%$$$$$$####################################""""""""""""""""""""""""$$$#########""""""""""""""""""""""""###############$$$$$$%%%%%%$$$$$$#########$$$%%%%%%$$$###""" !!!!!!"""###$$$%%%&&&########################"""############$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$#########""""""""""""##############################$$$$$$$$$$$$######%%%###!!!"""$$$%%%$$$"""$$$$$$$$$#########"""""""""""""""""""""""""""""" """%%%%%%$$$"""""""""###############%%%&&&'''333000+++'''$$$#################################$$$$$$###############"""$$$$$$%%%$$$$$$""" $$$############$$$$$$%%%""""""!!!!!!!!!""""""###%%%%%%%%%%%%%%%%%%%%%%%%################################################$$$$$$$$$######"""""""""&&&$$$######$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%$$$$$$"""""""""#########$$$$$$!!!"""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%$$$$$$$$$###########################"""""""""$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$%%%###"""!!!###$$$###############"""""""""###$$$%%%$$$"""""""""$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""#########$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&***)))))))))((((((''''''((((((''''''''''''((((((&&&''''''''''''((((((((((((((((((((((((((((((((((((((('''&&&&&&&&&&&&'''((((((((((((((()))))))))))))))))))))))))))******((((((''''''''''''((((((+++******++++++,,,---...---------------,,,,,,++++++++++++,,,,,,,,,------......//////000000000000333333444555666666666666999999:::888777666888999888888888888999999999999888888888888888999999999666666666777777777888888888777777666666777777888777666555444444555666777888888777666666666666666888888777666666666666777666555444333222222333333111222222222222111000000000000000/////////......///...,,,---...///...---------,,,,,,+++*********************+++++++++,,,************+++++++++,,,,,,,,,++++++***)))))))))))))))******+++*********(((((())))))))))))(((((()))((((((''''''(((((()))''''''((((((((((((''''''(((((((((''''''''''''&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&''''''''''''&&&%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$######$$$$$$############$$$$$$$$$############"""""""""###############################################################"""""""""###"""!!!!!!!!!"""$$$%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$ !!!"""$$$$$$%%%########################"""############$$$$$$$$$$$$$$$######$$$$$$%%%&&&###############"""""""""""""""""""""""""""""""""######$$$$$$$$$$$$######$$$###"""###$$$$$$###"""$$$$$$$$$#######################################!!!###$$$###"""!!!"""###############$$$%%%&&&&&&555...'''######$$$### ########################"""""""""######$$$$$$$$$$$$$$$%%%%%%$$$###""""""############$$$%%%%%%&&&$$$###"""""""""""""""###########################################################################%%%%%%%%%%%%$$$$$$$$$$$$%%%###""""""###$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%""""""#########$$$$$$$$$!!!!!!!!!!!!""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$$$$$$$$$$%%%"""""""""""""""###$$$%%%########################""""""##########################################$$$$$$%%%###"""!!!###$$$########################"""$$$%%%$$$###"""###$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&))))))((((((''''''&&&&&&)))((((((''''''(((((()))&&&&&&&&&'''''''''((((((((((((((((((((((((((((((''''''''''''&&&&&&''''''***))))))))))))))))))))))))))))))))))))*********)))((((((''''''(((((()))************+++,,,---...,,,,,,---------,,,,,,++++++,,,,,,,,,,,,---------///////////////000111222555555666777777777777777999::::::999777777999:::999888888888888777777777666666777777777777777888444555555666777888888888888888777777777777888888444333222222222222333444888666444333222222444444555555444444333333333333444333333222222222222222222222222222222111111000000000/////////............------...000///---,,,------,,,,,,+++******************+++++++++,,,,,,*********+++++++++,,,,,,+++++++++*********))))))&&&''''''((())))))))))))(((((())))))))))))((((((((((((((((((((((((((((((&&&''''''((((((''''''&&&((((((((((((((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$############$$$$$$###"""""""""""""""""""""########################################################################$$$###!!! """$$$%%%###$$$$$$%%%%%%$$$$$$###"""""""""###$$$&&&((())) !!!!!!""""""#################################""""""#########$$$$$$$$$%%%$$$###"""###$$$%%%&&&########################""""""""""""""""""""""""######$$$$$$$$$$$$######$$$############$$$##############################$$$$$$$$$$$$$$$$$$$$$$$$"""######""" """$$$#########$$$$$$%%%%%%%%%222...)))&&&&&&%%%###!!!########################""""""""""""############!!!!!!###$$$%%%&&&''''''######$$$$$$%%%%%%%%%%%%%%%%%%$$$#########$$$$$$########################################################################!!!!!!"""""""""#########&&&$$$""""""###$$$######%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$$$$$$$$$$############""""""%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$$$$$$$%%%%%%%%%%%%$$$#########$$$$$$###############$$$$$$$$$!!!!!!!!!!!!""""""##############################$$$$$$%%%###"""!!!###$$$###############$$$$$$$$$"""###$$$$$$###"""###$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&$$$$$$$$$%%%%%%%%%&&&&&&'''''''''&&&&&&%%%%%%%%%((((((''''''''''''((((((&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''&&&&&&''''''''''''''''''******************))))))(((((())))))***************))))))(((((())))))***************+++,,,------++++++,,,,,,---,,,,,,+++------------............000000///000111222333444666666777888888888777777777888999888777777888:::999999888777777666555555555555555666666666777777333444555777888888888888777777888888888888777777333333333222222333333333777555333111111222333555444444444444444333333222222222222222222111111111333333333444333222222111////////////............---------///000000---+++......------,,,,,,++++++***++++++++++++,,,,,,,,,***++++++++++++,,,,,,,,,+++++++++***************(((((((((((())))))******(((((())))))))))))((((((''''''((((((((((((''''''&&&&&&''''''''''''&&&&&&'''((((((((((((((((((((((((((('''&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&$$$$$$############$$$$$$"""""""""""""""""""""##################################################################$$$$$$$$$$$$###!!! """$$$%%%###$$$$$$%%%%%%$$$$$$###"""""""""###$$$%%%'''(((###############"""""""""########################""""""#########$$$$$$$$$%%%$$$###"""###$$$%%%&&&###############$$$$$$$$$""""""""""""""""""""""""######$$$$$$$$$$$$############$$$############$$$########################$$$$$$$$$$$$$$$$$$$$$$$$#########!!! ###%%%######$$$$$$%%%%%%%%%$$$+++---///---)))&&&$$$$$$#################################"""""""""!!!!!!!!!""""""###%%%&&&'''(((###$$$%%%%%%&&&%%%%%%$$$%%%%%%$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%################################################""""""######$$$$$$$$$%%%'''%%%###$$$%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%#########$$$$$$$$$$$$%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%))))))(((&&&%%%$$$###"""#########$$$$$$$$$$$$$$$ !!!!!!"""#################################$$$$$$%%%###"""!!!###$$$#########$$$$$$$$$$$$$$$"""###$$$$$$###"""$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''%%%&&&&&&&&&&&&'''''''''''''''''''''''''''''''''%%%&&&''''''((('''''''''))))))))))))************((((((((()))******++++++******))))))))))))*********))))))******+++,,,---***++++++,,,,,,,,,,,,,,,---------.........////////////000111222333333444555666666777777666666666555666777666555555777999888888888777666555555444444444555555666666777777333555666888999999888888666777777888888777777666555555555555555555555555777666444333333444666777666666777777666666555444111111222222222222111111333444444444444333222222/////////.........---------------...000000---+++//////......------,,,,,,++++++++++++,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,************************++++++*********+++,,,,,,(((((())))))))))))((((((&&&''''''((((((''''''&&&&&&&&&''''''''''''&&&&&&&&&''''''''''''((((((((()))((('''&&&%%%$$$$$$###%%%%%%%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%$$$###%%%%%%&&&&&&&&&&&&''''''$$$$$$############$$$$$$"""""""""############$$$#########################################################$$$$$$$$$$$$$$$###"""!!!!!!!!!"""$$$%%%###$$$$$$%%%%%%$$$$$$###&&&%%%%%%$$$###"""!!!!!!$$$$$$#########"""""""""########################"""############$$$$$$$$$$$$$$$######$$$$$$%%%&&&#########$$$$$$$$$$$$$$$##############################$$$$$$$$$$$$######"""$$$$$$$$$###"""###$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###!!!"""$$$&&&###$$$$$$%%%%%%%%%$$$$$$%%%***//////+++&&&%%%&&&#################################""""""!!!!!!!!!&&&%%%$$$###############$$$%%%&&&&&&&&&%%%$$$###############$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%################################################%%%%%%%%%%%%%%%$$$$$$$$$%%%###"""###%%%&&&&&&&&&%%%$$$############$$$%%%#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''''''''&&&$$$$$$###$$$%%%%%%%%%$$$###"""#########$$$$$$%%%%%%%%%"""""""""###$$$%%%%%%%%%########################$$$$$$%%%###"""!!!###$$$#########$$$$$$%%%%%%%%%!!!###$$$$$$######$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$&&&''''''&&&$$$##############################$$$$$$$$$%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''%%%%%%'''(((((((((''''''&&&&&&''''''(((((())))))'''(((((()))******++++++))))))(((((((((((())))))))))))))))))***+++,,,---******+++,,,,,,,,,,,,,,,,,,,,,---------.........---...000111222333222222333333444444444444333333333444555444333333555777777777777666666555555444444444555555666777777777555666888999:::999888777555666777777777777666555666666666777777666666666444333333333333555666777666777777888777666555444111111222333333333222111333333333333333222111111//////.........---------...------...//////...,,,//////......------,,,,,,+++++++++,,,,,,,,,------+++++++++,,,,,,,,,------************************,,,+++***)))))))))******(((((())))))))))))((((((&&&&&&'''(((((('''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&'''''''''''''''''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&'''%%%%%%&&&&&&%%%$$$###"""$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$############$$$$$$############$$$$$$%%%%%%########################""""""""""""""""""""""""#########$$$$$$%%%%%%%%%""""""""""""###############$$$$$$%%%%%%$$$$$$###%%%%%%%%%$$$###  !!!!!!"""######$$$########################"""############$$$$$$$$$######$$$%%%%%%%%%%%%$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######"""$$$%%%$$$"""!!!###%%%""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%######$$$&&&###$$$%%%%%%%%%%%%$$$######%%%((())))))'''%%%$$$########################!!!!!!!!!"""""""""""""""&&&%%%$$$"""!!!!!!!!!"""%%%&&&&&&'''&&&%%%###"""""""""""""""###$$$%%%&&&##############################################################################"""!!! """  ###$$$%%%$$$%%%$$$###""""""###$$$%%%######$$$$$$$$$%%%%%%%%% !!!"""###$$$%%%%%%""""""""""""""""""""""""$$$$$$############$$$$$$"""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''((((((&&&$$$###!!!$$$%%%%%%$$$#########$$$$$$%%%%%%%%%######$$$%%%&&&&&&''''''########################$$$%%%%%%###"""!!!###$$$#########$$$$$$%%%%%%%%%!!!###$$$$$$######$$$&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$&&&''''''&&&$$$###"""""""""""""""""""""""""""############$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&'''((())))))&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''$$$%%%'''(((((((((''''''$$$$$$%%%%%%&&&'''(((((('''(((((()))***+++++++++((((((''''''''''''(((((())))))))))))***+++,,,---)))***+++,,,,,,,,,,,,,,,++++++,,,,,,,,,---------***,,,///111222222111000111111222222222111111000111222333333222222444666777777666666555555555555444444555555666777888888666777999:::;;;:::888777444555666777777666555444444444555555555555444444000000000111222333444555444555666666666555333333111111333444444333222111111222222222222111000000//////.........---------///...------...///...---///......------,,,,,,+++++++++,,,,,,,,,---------++++++,,,,,,,,,---------******************++++++)))((('''&&&%%%%%%&&&'''(((((())))))))))))((((((%%%&&&'''(((((('''&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&''''''######$$$%%%%%%&&&''''''%%%%%%&&&&&&%%%###"""!!!#########$$$$$$%%%%%%%%%$$$$$$############$$$$$$######$$$$$$$$$%%%%%%%%%########################!!!!!!!!!!!!!!!!!!!!!!!!#########$$$$$$%%%%%%%%%!!!!!!"""############"""$$$$$$$$$%%%%%%$$$$$$$$$!!!"""###$$$###!!! """###%%%%%%########################"""############$$$$$$$$$"""###$$$%%%&&&%%%$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$######!!!$$$%%%%%%"""!!!###%%%""""""######$$$$$$$$$$$$########################$$$%%%&&&&&&%%%$$$%%%&&&###$$$%%%&&&%%%%%%###"""###!!! """&&&'''%%%"""######################## !!!"""###$$$$$$######"""!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""###$$$$$$%%%%%%######""""""######$$$%%%%%%%%%$$$###""""""######$$$$$$$$$#########""""""$$$$$$$$$$$$$$$###"""!!!$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$###"""!!!!!! '''''''''&&&%%%$$$###"""$$$$$$##########################################$$$$$$%%%%%%%%%&&&&&&&&&###$$$$$$%%%%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$############""""""""""""######""""""""""""""""""""""""################################################$$$$$$$$$#########""""""$$$$$$############$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&%%%$$$###""""""%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''''''''&&&%%%$$$"""!!!&&&'''''''''''''''&&&&&&$$$%%%&&&''''''&&&%%%$$$%%%&&&&&&%%%$$$%%%'''))))))))))))(((''''''&&&&&&$$$$$$%%%'''(((***++++++(((((((((((((((((((((((('''((()))******+++*********++++++,,,,,,++++++***++++++******************+++---///000//////000111------...///000111222222222222222333444555666777666777777777888888888888444444555555666666777777444666888888888777888999888666555666777888777555666777888888888777555444444444444444444444444444333444555555444333111000222333333333222222444666555555555444333000...---........................////////////..................//////......---,,,++++++,,,,,,,,,,,,------+++,,,,,,------,,,,,,+++,,,+++******,,,---,,,++++++******)))(((''''''&&&''''''&&&&&&&&&%%%%%%%%%((((((((((((((((((((((((%%%'''(((((('''&&&&&&''')))'''&&&'''***---//////'''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########&&&&&&%%%$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$$$$$$$%%%""""""""""""""""""""""""!!!!!!!!!!!!!!!!!!!!!!!!"""""""""###$$$$$$$$$%%%"""""""""""""""######$$$&&&%%%%%%$$$$$$%%%%%%&&&###!!!!!!"""###$$$###"""""""""""""""""""""""""""!!!!!!!!!!!!"""""""""""""""############$$$$$$$$$"""############$$$$$$$$$""""""""""""""""""""""""&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$"""!!!!!!!!!"""#########$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$!!! !!!!!!"""###$$$########################$$$$$$%%%%%%%%%%%%$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%&&&&&&######""""""######$$$%%%"""!!! !!!$$$$$$$$$#########""""""$$$$$$$$$$$$$$$###""""""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$###"""!!!!!!!!!&&&&&&&&&%%%%%%$$$###"""########################"""""""""""""""""""""""""""""""""#########$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$##################""""""""""""##############################################################################$$$$$$$$$#########""""""$$$$$$############$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$##################$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&''''''''''''&&&&&&%%%&&&&&&''''''''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&%%%$$$%%%''')))''''''''''''((((((((((((&&&''''''(((((()))))))))(((((((((((((((((((((((('''((()))***++++++++++++***++++++,,,,,,++++++***************************+++---///000///...///000------...///000111222222333222222333333555666666666666777777777888888888666666666666777777777777555666888888777777888999777777888888777777777888888888888888888777666666444444444444444444444444333333444444333222000000111222222222111111333444444555444444222000...---........................////////////...........................------,,,+++++++++,,,,,,,,,------+++,,,,,,------,,,,,,+++,,,***)))***+++,,,+++************)))((('''''''''''''''''''''&&&&&&%%%%%%''''''''''''''''''''''''$$$&&&(((((('''&&&'''((('''&&&%%%&&&))),,,------((((((''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$########################""""""""""""""""""""""""###############$$$$$$$$$"""""""""""""""######$$$%%%%%%$$$$$$$$$$$$%%%%%%###"""!!!"""###$$$###"""########################""""""""""""############"""############$$$$$$$$$"""############$$$$$$$$$########################&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$###"""######$$$""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###""""""!!!!!!!!!""""""########################!!!!!!!!!!!! ########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######""""""######$$$%%%  !!!!!!$$$$$$$$$##################$$$$$$$$$$$$###""""""######$$$$$$$$$$$$$$$###$$$$$$$$$###""""""!!!!!!$$$$$$$$$$$$$$$###"""!!!################################################"""""""""############$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$############"""""""""######""""""""""""##############################################################################$$$$$$$$$###############$$$$$$############$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%#########$$$$$$$$$%%%%%%########################$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%&&&&&&'''&&&&&&&&&&&&''''''''''''&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%&&&&&&&&&%%%%%%''')))%%%&&&&&&'''(((((())))))))))))))))))((((((((((((((((((((((((((((((((((((((()))***+++,,,,,,,,,,,,***++++++,,,,,,++++++***************************,,,...000000...---...///------...///000111222222333222222333333444555666666666666666777777777777888888888777777777777777555666888888777666777888666888:::999777666888:::999999888777777777777777444444444444444444444444222222333222222111000//////111222111000000222333444444333333111000...---/////////////////////////////////............---...............---,,,,,,++++++++++++,,,,,,,,,,,,+++,,,,,,------,,,,,,++++++***))))))***+++***)))******))))))((((((''''''(((((((((''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&'''(((''''''''')))&&&%%%%%%&&&)))+++******((((((((('''&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############################################################$$$$$$$$$###############"""""""""""""""######$$$$$$$$$############$$$$$$###"""!!!"""$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$"""############$$$$$$$$$"""############$$$$$$$$$########################&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$%%%!!!!!!"""############"""$$$$$$$$$$$$$$$$$$$$$$$$#########""""""#########$$$$$$############$$$$$$########################$$$$$$###"""!!!!!!!!!!!!########################%%%$$$###""""""###$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$######""""""######$$$%%%"""""""""""""""###$$$%%%##############################$$$$$$$$$######""""""######$$$$$$$$$$$$###$$$$$$$$$######"""""""""###############"""!!!!!!###############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$##############################"""""""""""""""""""""$$$######""""""######$$$################################################################################################%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$$$$######%%%%%%&&&'''''''''&&&&&&'''&&&%%%$$$$$$%%%&&&'''$$$%%%&&&&&&%%%%%%&&&(((&&&&&&&&&''''''((((((((())))))))))))))))))))))))(((((((((((((((((((((((())))))+++,,,,,,,,,,,,,,,***++++++,,,,,,++++++******************+++++++++---...000///...------...------...///000111222222333222222222333444444555555555555666666666777777888888777777666666555555555666888888777666666777444888;;;999555444777:::999888666555555555666777333333333333333333333333222222222111000000///...///111222222111111222333333222222111111000///...000000000000000000000000//////.........---------------.........---,,,,,,***++++++++++++,,,,,,,,,+++,,,,,,------,,,,,,++++++***((()))******)))(((***)))))))))((((((((('''((((((((((((((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%'''(((((('''&&&&&&'''%%%%%%%%%''')))***)))((()))(((''''''&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$###"""""""""########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$###""""""""""""""""""""""""######$$$######""""""""""""#########"""!!!"""$$$%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$"""""""""#########$$$$$$""""""#########$$$$$$$$$""""""#########$$$$$$$$$########################&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$%%%!!!""""""#############################################""""""""""""######$$$$$$############$$$$$$""""""""""""""""""""""""$$$######"""!!!!!!""""""########################((('''%%%$$$$$$&&&((()))########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################""""""######$$$%%%############$$$%%%&&&&&&########################"""######$$$$$$$$$######!!!"""######$$$$$$$$$$$$$$$$$$$$$$$$############""""""#########"""!!!!!!""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###########################"""""""""""""""""""""###$$$$$$############$$$$$$################################################################################################%%%%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$###"""""""""%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$######""""""$$$$$$%%%&&&''''''&&&&&&'''&&&%%%$$$$$$%%%&&&'''$$$%%%''''''&&&%%%&&&'''((('''''''''&&&&&&&&&%%%'''''''''((())))))******(((((((((((((((((((((((())))))+++,,,,,,,,,,,,,,,***++++++,,,,,,++++++***))))))*********+++++++++,,,...//////---,,,------------...///000111222222333333222222222333444444444555555555555666666666666666666555555444444333555666888888666555666666333666999888444222555999777666555333333444555555333333333333333333333333222222111000////////////000222444444333222333444222111111000////////////000000000000000000000000............---------------------...---,,,,,,+++*********+++++++++,,,,,,+++,,,,,,------,,,,,,++++++***))))))******)))'''))))))))))))(((((((((((('''(((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&((()))***)))&&&$$$$$$%%%'''&&&&&&(((******)))'''(((''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$###"""""""""########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$###""""""""""""""""""""""""######$$$###""""""!!!!!!""""""###$$$""""""###$$$%%%$$$###########################!!!!!!!!!"""""""""######""""""#########$$$$$$$$$""""""#########$$$$$$$$$########################&&&%%%%%%$$$$$$%%%%%%&&&######$$$$$$$$$$$$$$$$$$"""###$$$$$$%%%%%%$$$$$$##############################""""""""""""######$$$######""""""######$$$"""""""""""""""""""""""""""""""""""""""###$$$$$$###########################"""!!! """$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################""""""######$$$%%%######"""""""""###$$$$$$###############$$$$$$$$$""""""###$$$$$$$$$$$$###!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""############"""""""""""""""###$$$$$$%%%%%%!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""######$$$$$$%%%%%%$$$$$$###########################"""""""""############$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############################################################$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$############$$$$$$$$$###"""!!! %%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$&&&&&&'''&&&&&&%%%$$$$$$###$$$%%%&&&&&&'''&&&&&&'''&&&&&&%%%%%%&&&&&&'''###%%%''''''&&&%%%&&&'''((((((''''''&&&%%%%%%$$$%%%&&&&&&'''((())))))***((((((((((((((((((((((((((()))***+++,,,,,,,,,,,,***++++++,,,,,,++++++***)))))))))***++++++,,,,,,+++---//////---,,,---...------...///000111222222333333222222222222333333444444444444555555555666555555444444444444444444555777888777666555555666333555777666444333555777555555444333333333333333333333333333333333333333333222111000////////////000222444555444333333444111000///////////////000////////////////////////.........------------,,,---------------,,,++++++************+++++++++++++++,,,,,,------,,,,,,+++,,,+++***)))******)))'''))))))))))))((((((((((((&&&''''''''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&((()))***)))&&&$$$$$$%%%((('''&&&'''((()))((('''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############"""""""""""""""######$$$######""""""""""""######$$$###"""###%%%%%%%%%$$$"""""""""""""""""""""""" !!!!!!!!!"""""""""""""""############$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&"""###$$$$$$$$$$$$$$$#########$$$%%%%%%%%%%%%%%%#################################""""""###############""""""""""""##############################""""""""""""###$$$%%%%%%########################!!!  !!!###$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$$$$%%%%%%%%%######""""""######$$$%%%$$$###""""""""""""""""""""""""#########$$$$$$$$$""""""###$$$$$$$$$$$$$$$ !!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$$$$######"""!!!""""""###$$$$$$%%%%%%""""""""""""""""""""""""!!!!!!!!!!!!""""""""""""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$################################################""""""#########$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$############$$$$$$###"""""""""!!!!!! $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######%%%&&&&&&''''''''''''&&&######$$$%%%&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&%%%###%%%'''((('''&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((((((((((((((('''((()))***++++++++++++***++++++,,,,,,++++++***((())))))***++++++,,,,,,***,,,......------...///------...///000111222222333333222222222222222333333333444444444555555555444444444555555555555555555777888777666444444555555666666666555555666666444444555555444444333222222222222222222222222222444333111000//////000000///111444555444222222222000///.........///000000.................................---------,,,,,,,,,------------,,,++++++************+++++++++++++++,,,,,,------,,,,,,+++...,,,+++***++++++)))((((((((((((((())))))))))))%%%%%%&&&&&&''''''''''''''''''''''''''''''''''''%%%'''(((((('''&&&&&&''')))'''%%%$$$&&&''''''&&&$$$%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$"""""""""""""""######$$$$$$######""""""######$$$$$$###"""###%%%&&&%%%$$$########################!!!!!!"""""""""#########"""############$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&"""###%%%&&&&&&&&&%%%%%%""""""###$$$$$$$$$$$$$$$########################$$$$$$############$$$$$$######""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$#########"""######$$$$$$########################""""""###$$$$$$%%%&&&&&&########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''#########"""###$$$$$$%%%%%%%%%$$$###""""""######""""""######$$$$$$$$$$$$!!!"""###$$$$$$$$$$$$$$$ """######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$$$$$$$######!!!""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$################################################""""""######$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$############$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%########################$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$#########""""""$$$%%%&&&'''''''''"""###$$$%%%&&&&&&'''&&&$$$%%%''''''''''''%%%$$$###%%%'''((('''&&&&&&&&&$$$%%%%%%&&&&&&''''''((((((''''''&&&%%%%%%$$$$$$(((((((((((((((((((((((('''((()))******+++******+++++++++,,,,,,+++++++++((())))))***++++++,,,,,,)))+++---...------...000------...///000111222222333333222222111222222222333333333444444444555555444555555555666666777777555777888777555444444555888666555666777888777555444555666666666555333222222222222222222222222222444333222000000000000111---000333444333111111111//////...------...000111..............................---------,,,,,,,,,,,,,,,---------,,,++++++)))************++++++++++++,,,,,,------,,,,,,+++...---++++++,,,+++***((((((((((((((())))))))))))%%%%%%%%%&&&&&&&&&''''''(((((((((((((((((((((((("""$$$'''((('''((()))***)))&&&###"""###%%%&&&%%%###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%#########$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################""""""######$$$$$$$$$%%%"""""""""""""""######$$$$$$$$$############$$$$$$$$$###"""###%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$"""############$$$$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&###$$$&&&'''((('''&&&&&&!!!!!!"""###############""""""""""""""""""""""""%%%%%%$$$$$$$$$$$$%%%%%%######""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$###""""""""""""########################!!!"""###%%%%%%&&&%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%###!!! !!!""""""###$$$%%%%%%$$$###"""############$$$$$$$$$$$$ !!!!!!""""""""""""!!!######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%&&&&&&&&&$$$$$$##################"""###%%%&&&&&&%%%###"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%##############################$$$$$$$$$$$$######$$$###"""###$$$$$$###"""###$$$%%%%%%%%%###"""!!!##############################$$$$$$$$$%%%%%%%%%"""###$$$$$$###"""###$$$&&&'''((('''%%%$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&'''''''''$$$%%%%%%&&&&&&%%%%%%$$$&&&'''((('''%%%$$$%%%&&&"""$$$%%%%%%$$$###$$$&&&&&&&&&&&&''''''''''''(((((((((&&&%%%%%%&&&'''((((((''''''&&&&&&((()))***++++++++++++************************************++++++++++++++++++++++++)))+++------------///111......////////////......000000000000000111111222555444222111222444666777777555333111000111222333999888666555444444444555444444444444444444444444111111111222222333333444111222222333444444444444444333111///......///000333333333333333222111000000///.........///111222222111000//////...............---------,,,,,,,,,.........------,,,,,,+++)))***---///000///---+++,,,,,,,,,++++++*********------,,,,,,+++***))))))((((((((((((((((((((((((&&&'''((())))))((('''&&&%%%%%%%%%$$$$$$#########''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%$$$"""!!!!!!"""$$$%%%'''%%%$$$######$$$&&&((($$$$$$############$$$$$$%%%$$$###!!!!!!!!!"""###$$$$$$$$$############"""""""""###$$$$$$$$$$$$###&&&%%%$$$###"""""""""""""""############""""""!!!""""""""""""############$$$$$$$$$$$$$$$$$$$$$$$$"""""""""""""""""""""""" !!!"""###$$$$$$############$$$%%%&&&'''$$$$$$######""""""!!!!!!$$$$$$%%%%%%%%%%%%&&&&&&$$$###!!!###%%%&&&###!!!###################################################$$$$$$###!!! !!!"""$$$$$$%%%%%%%%%&&&&&&&&&"""############$$$$$$$$$########################""""""""""""############!!!!!!"""###$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""$$$###""""""###$$$######$$$$$$$$$$$$###### !!!!!!!!!""""""""" !!!"""###$$$$$$$$$$$$"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$##############################$$$%%%%%%%%%%%%$$$###""""""""""""""""""""""""$$$$$$$$$######"""""""""%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$############$$$##############################$$$$$$$$$$$$######$$$###"""###$$$$$$###"""###############"""!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%"""###$$$$$$###"""###$$$%%%&&&'''&&&$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$&&&'''((('''%%%$$$%%%&&&$$$%%%&&&%%%#########%%%&&&&&&&&&&&&''''''''''''((('''&&&&&&&&&&&&'''((((((''''''&&&'''((()))******)))******************************************++++++++++++++++++++++++***))))))+++---///............////////////......000000/////////000111111333333222222333444555666555555333222222333333444999888666555444444444555444444444444444444444444111111222333333333333333222222333333444333333333333222000...------...///222222222222222111000000000///.........///111222222111000///............------------,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,+++---///111111///...,,,,,,,,,,,,++++++*********,,,,,,+++******)))((((((((((((((((((((((((((((((&&&'''((())))))((('''&&&&&&&&&%%%%%%%%%$$$$$$$$$''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&'''&&&$$$######$$$%%%&&&$$$$$$############$$$$$$%%%$$$###"""!!!!!!"""###$$$$$$$$$#########""""""""""""###$$$$$$$$$$$$###$$$###############$$$$$$""""""############""""""""""""""""""#################################################################################$$$$$$#########$$$%%%%%%&&&$$$$$$$$$$$$############$$$$$$$$$%%%%%%%%%&&&&&&$$$###"""###%%%%%%###!!!###################################################$$$$$$###"""!!!!!!###!!!!!!"""""""""#########"""############$$$$$$$$$##############################"""!!!!!!!!!!!!""""""""""""###$$$$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!######"""###$$$&&&$$$$$$############$$$$$$############$$$$$$$$$$$$!!!"""###$$$%%%%%%%%%%%%!!!"""######$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$######"""!!!########################$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""#########"""""""""""""""$$$############"""""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$###""""""##############################$$$$$$$$$$$$######$$$###"""###$$$$$$###"""&&&%%%%%%$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$%%%"""###$$$$$$###"""###$$$$$$%%%&&&%%%#########$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&'''&&&%%%$$$%%%&&&%%%&&&'''&&&$$$"""###$$$&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&''''''(((''''''&&&&&&''''''((()))''''''(((((())))))******))))))))))))))))))))))))++++++++++++++++++++++++,,,)))(((***...111///,,,---......//////......---//////......//////000111111111222333444444555555333333444555555555555555888777666555444444444444444444444444444444444444000111333444555444222111333333333333333333222111111000///---------......000111111111111000000///000///.........///000111222111000///............,,,,,,,,,,,,++++++++++++++++++,,,,,,,,,,,,,,,,,,...///000111111000...---+++++++++++++++******************))))))(((((('''((((((((((((((((((((((((''''''((((((((((((''''''&&&&&&&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%'''&&&%%%$$$$$$%%%&&&''''''&&&%%%#########$$$%%%$$$$$$############$$$$$$$$$$$$###"""""""""######$$$$$$#########"""""""""""""""###$$$$$$$$$$$$###"""""""""######%%%&&&&&&!!!!!!"""###$$$$$$$$$$$$"""""""""#########$$$$$$""""""""""""""""""""""""########################&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$###"""###%%%%%%###"""################################################"""$$$$$$$$$"""!!!"""### !!!!!!!!!""""""""""""############$$$$$$$$$########################%%%$$$"""!!! !!!"""##################$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""$$$$$$###"""$$$%%%%%%$$$###""""""###$$$%%%############$$$$$$$$$$$$"""###$$$$$$$$$$$$$$$$$$!!!!!!"""############"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""#########""""""!!!###############$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$##################""""""###"""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$$$$$$$""""""##############################$$$$$$$$$$$$######$$$###"""###$$$$$$###"""&&&%%%###""""""###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$"""###$$$$$$###"""###$$$###$$$%%%$$$"""""""""###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$&&&'''&&&$$$$$$%%%&&&$$$%%%&&&&&&$$$###$$$%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&'''''''''(((&&&&&&&&&&&&''''''((((((%%%%%%&&&'''((()))***+++))))))))))))))))))))))))************++++++++++++,,,++++++,,,...//////...---------......---------.........---......///000...000222444555555444333111222444666777777666555666666555555444444444444444444444444444444444444000111444666666444222000333333333333333222111000111000///............/////////000000000000////////////...---...///000111111111///...............,,,,,,,,,+++++++++******++++++,,,,,,------......//////000111000///---,,,+++++++++************************))))))((((((((((((((((((((((((((((((((('''(((((((((((((((((('''''''''''''''''''''&&&&&&''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%&&&%%%$$$$$$$$$$$$%%%&&&''''''%%%$$$############$$$$$$############$$$$$$$$$#################################""""""""""""""""""###$$$$$$$$$$$$###############$$$%%%&&&&&& !!!"""###$$$%%%%%%%%%""""""#########$$$$$$$$$################################################%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$%%%%%%######$$$$$$%%%%%%&&&&&&###$$$$$$$$$$$$%%%%%%%%%#########$$$$$$$$$###"""################################################"""$$$$$$$$$""""""###$$$############$$$$$$$$$%%%""""""#########$$$$$$$$$########################%%%$$$"""!!!!!!"""###$$$$$$$$$$$$#######################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###%%%%%%$$$###""""""###%%%$$$###""""""###$$$%%% $$$$$$$$$$$$###"""!!!!!!!!!!!!"""############"""$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!######$$$$$$$$$""""""#########$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""""""""""""""###$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$$$$####################################$$$$$$$$$$$$######$$$###"""###$$$$$$###""""""!!!  !!!"""$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$"""###$$$$$$###"""###$$$###$$$%%%$$$"""!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&%%%$$$$$$%%%&&&###$$$&&&&&&%%%%%%&&&(((%%%%%%%%%&&&&&&&&&&&&'''%%%&&&&&&'''''''''((((((%%%&&&&&&'''''''''''''''$$$%%%%%%'''((()))***+++(((((((((((((((((((((((()))))))))******+++++++++'''+++...---***))),,,000,,,,,,------------,,,,,,------,,,,,,------...///---...111444555444333222000222444777888777666555555555555555555444444444444444444444444444444444111222444666666444222000333333333333222111111000111111000000000000000000...//////000000000/////////...---------...000111111000///...------------,,,,,,,,,+++++++++******,,,,,,------......//////---............---++++++***************************************)))))))))(((((((((((((((((((((((((((((((((''''''(((((((((''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$############$$$$$$'''&&&%%%$$$######""""""$$$$$$############$$$$$$#########$$$$$$$$$$$$############"""""""""!!!!!!""""""###$$$$$$$$$$$$###%%%%%%$$$$$$$$$$$$%%%%%%!!!!!!"""$$$%%%%%%%%%%%%############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################""""""######$$$%%%%%%&&&$$$$$$######$$$$$$%%%%%%"""#########$$$$$$%%%%%%#########$$$$$$$$$%%%%%%"""###$$$$$$$$$#########################################################"""###$$$$$$###"""###%%%$$$$$$$$$%%%%%%%%%&&&&&&""""""#########$$$$$$$$$########################$$$######"""###$$$&&&&&&$$$$$$$$$#######################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&%%%###!!!"""###$$$$$$############$$$$$$ !!!!!!!!!!!!$$$$$$$$$$$$###"""!!! !!!"""######$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ """###$$$%%%%%%%%%"""""""""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""$$$$$$$$$$$$$$$%%%%%%%%%"""""""""############$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""######$$$$$$##############################$$$$$$$$$$$$######$$$###"""###$$$$$$###"""$$$$$$#########$$$%%%%%%########################"""""""""############$$$"""###$$$$$$###"""###$$$###$$$%%%$$$"""""""""###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$%%%%%%$$$$$$%%%&&&$$$%%%&&&&&&%%%%%%&&&'''%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%&&&'''((((((((((((%%%%%%&&&''''''''''''&&&%%%%%%&&&'''((()))***+++(((((((((((((((((((((((((((((())))))***+++++++++"""(((---+++%%%###(((...+++,,,,,,------,,,,,,+++,,,,,,,,,+++,,,------...,,,...000333444444333222000222444666777666555444444444555555555444444333444444444444444444444444222333555666555444222111222222222222222222111000111111111111111000000000...//////000000000000000///...---------...///000111000///...------------,,,,,,,,,,,,++++++++++++,,,,,,---------------...+++,,,,,,,,,,,,++++++***)))))))))***************************************((((((((((((((((((((((((((((((''''''''''''((((((&&&&&&&&&'''''''''''''''''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%########################%%%%%%%%%$$$######""""""$$$$$$############$$$$$$"""###$$$$$$%%%$$$$$$$$$######"""""""""!!!!!!!!!""""""###$$$$$$$$$$$$###&&&%%%%%%$$$$$$$$$%%%%%%""""""###$$$%%%%%%%%%%%%#########$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!"""###$$$%%%%%%############$$$%%%&&&'''############$$$$$$$$$$$$############$$$$$$$$$$$$"""###%%%%%%###"""###$$$################################################"""###%%%$$$######$$$%%%"""############$$$$$$$$$"""############$$$$$$$$$#################################$$$$$$$$$%%%%%%##################$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###%%%%%%%%%#########%%%######$$$$$$$$$$$$######$$$$$$$$$$$$%%%%%%%%%%%%"""######$$$%%%%%%$$$$$$"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""""""""##############################$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%$$$$$$!!!""""""###$$$$$$%%%%%%###$$$%%%%%%%%%%%%$$$###"""""""""""""""""""""""""""#########$$$$$$$$$$$$############$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$##############################$$$$$$$$$$$$######$$$###"""###$$$$$$###"""%%%%%%&&&'''''''''''''''""""""""""""""""""""""""""""""""""""############"""###$$$$$$###"""###$$$$$$%%%&&&%%%###"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$%%%%%%&&&&&&%%%%%%$$$"""$$$%%%%%%$$$$$$%%%&&&'''(((((('''%%%###$$$%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%&&&(((((((((((('''$$$%%%&&&'''''''''&&&&&&&&&&&&'''((())))))******''''''''''''''''''''''''((((((((()))***+++++++++%%%))),,,***'''%%%(((,,,++++++,,,,,,,,,,,,+++++++++++++++++++++,,,------,,,---///111333333333333111222333444555555444444333333444555555555444333444444444444444444444444444444555555444333333222000111111222222222222111//////000000000000000///...///000000111111111000......---,,,---...///000000000///...------------------------,,,,,,,,,,,,,,,,,,++++++++++++++++++******++++++++++++++++++((()))))))))*********+++))))))))))))))))))))))))(((((((((((((((((((((((()))((('''&&&&&&'''((()))%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$#########$$$$$$$$$#########$$$$$$############$$$$$$"""###$$$%%%%%%%%%$$$$$$###"""""""""!!!!!!!!!!!!""""""###$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%&&&'''######$$$%%%%%%$$$$$$$$$#########$$$$$$$$$%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$!!!"""""""""######$$$$$$!!!""""""###$$$&&&'''(((%%%%%%%%%%%%%%%$$$$$$$$$############$$$$$$$$$$$$!!!###%%%%%%###"""###$$$################################################"""###%%%$$$$$$###%%%&&&""""""""""""############"""############$$$$$$$$$########################"""###$$$$$$$$$""" """""""""###$$$$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$%%%$$$$$$%%%'''"""###$$$%%%%%%$$$###"""""""""#########$$$$$$$$$!!!!!!###%%%&&&'''((((((######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""""""""##############################$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$######!!!""""""###$$$$$$%%%%%%"""###%%%&&&&&&%%%###"""$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!""""""#########$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$***(((&&&$$$#########$$$##############################$$$$$$$$$$$$######$$$###"""###$$$$$$$$$""" !!!"""###""""""!!!!!!!!!!!!!!!!!!!!!!!!!!!""""""""""""############"""$$$$$$$$$###"""###$$$$$$%%%&&&%%%#########$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$%%%%%%&&&&&&%%%%%%$$$"""###%%%%%%$$$$$$%%%&&&*********((($$$"""!!!"""$$$$$$%%%%%%%%%&&&&&&&&&###$$$&&&((())))))((('''$$$%%%&&&'''''''''&&&%%%''''''(((((()))*********'''''''''''''''''''''''''''(((((()))***+++++++++***+++,,,,,,++++++,,,,,,+++++++++,,,,,,+++++++++++++++******++++++,,,---,,,---...000222333333444222222333333444444333333222333444555555555444333444444444444444444444444555555444444333333333333///000111222222222222222......///////////////...//////000111111111111111......---,,,---...///000000000...---------------......------------,,,,,,+++*********))))))((((((*********++++++,,,,,,,,,(((((())))))*********+++'''''''''((((((((((((((((((((((((((((((((((((((()))((('''&&&&&&'''((()))%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$#########$$$%%%%%%&&&&&&%%%%%%$$$"""######$$$$$$$$$######$$$$$$############$$$$$$"""###$$$%%%&&&%%%%%%$$$""""""""""""!!!!!!!!!!!!""""""###$$$$$$$$$$$$###""""""###$$$%%%'''((()))$$$$$$%%%%%%%%%$$$############$$$$$$$$$%%%%%%%%%""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############"""!!!!!!!!!###$$$&&&((()))'''''''''&&&&&&%%%%%%%%%"""############$$$$$$$$$!!!###&&&%%%###!!!###$$$################################################"""###%%%%%%$$$$$$%%%&&&############$$$$$$$$$$$$"""############$$$$$$$$$###########################$$$%%%$$$"""!!!!!!"""###$$$%%%%%%&&&########################&&&%%%%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########""""""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$###%%%%%%%%%$$$###"""!!!!!!%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$##########################################""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""%%%$$$$$$$$$%%%''')))***&&&&&&%%%$$$$$$######"""########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$###"""!!!$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""''''''%%%###$$$'''''''''&&&%%%%%%%%%%%%&&&***((('''%%%$$$%%%&&&'''******))))))(((((('''''''''((()))++++++******)))&&&&&&&&&&&&''')))***+++,,,---.../////////...---,,,,,,++++++,,,,,,---............//////000111222222222222222222222222222222222111111111111222222333333333333333333333333666555333333222333444555111000///......///000111///............---------////////////000000000000/////////...------,,,,,,.........///////////////,,,,,,,,,,,,,,,,,,,,,,,,++++++************+++++++++++++++******(((''''''&&&'''((())))))***))))))'''((()))******)))((('''(((((((((((())))))))))))+++***)))'''''''''((()))''''''&&&&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$#########"""############$$$$$$$$$!!!""""""""""""#########%%%###!!!  !!!"""""""""!!!!!!!!!!!!""""""$$$$$$$$$#########""""""######$$$%%%&&&&&&''''''%%%$$$#########$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$"""!!!"""$$$$$$"""%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$############"""""""""############""""""$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###""""""""" """###%%%&&&&&&########################%%%%%%$$$$$$###"""!!!!!!########################""""""""""""""""""""""""""""""""""""############&&&%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%$$$######%%%%%%$$$$$$######""""""%%%%%%%%%%%%%%%%%%%%%%%%########################################################################$$$$$$$$$$$$$$$$$$$$$$$$########################&&&%%%%%%%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%% $$$))))))&&&$$$&&&((((((((('''&&&%%%$$$$$$%%%((((((((((((''''''&&&&&&''''''''''''(((((((((((('''((()))***+++******)))'''''''''((()))***+++,,,------...//////...---,,,,,,++++++++++++,,,------......---......///000111222222222222222222222222222222111111111111222222333333333333333333333333555444333222111111222333111000///......///000111///............---------....../////////000000000/////////...------,,,,,,.........------,,,,,,,,,,,,,,,+++++++++*********++++++************+++++++++++++++******)))(((''''''(((((())))))))))))((('''((()))******)))((('''(((((((((((())))))))))))***)))((('''''''''((((((''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""######"""############$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$###!!! """"""""""""!!!!!!!!!!!!""""""$$$$$$$$$#########""""""######$$$$$$%%%%%%&&&&&&$$$$$$#########$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################%%%###"""###%%%%%%### #########""""""#################################$$$$$$$$$############"""""""""############""""""$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$##################$$$$$$""""""""""""""""""##############################$$$$$$######"""!!!!!! ########################""""""""""""""""""""""""""""""""""""############%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###$$$$$$%%%%%%"""""""""######$$$$$$%%%$$$$$$$$$##################$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$$$$######"""$$$$$$$$$$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%################################################$$$$$$$$$$$$$$$$$$$$$$$$################################################&&&&&&&&&&&&&&&%%%$$$###""""""######$$$%%%%%%&&&########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$'''******'''&&&'''((()))((('''&&&%%%$$$$$$$$$&&&''')))******(((&&&%%%%%%%%%&&&&&&'''(((((()))'''((()))*********))))))(((((((((((()))+++,,,---............---,,,+++++++++++++++++++++,,,------,,,,,,,,,,,,---...///000111111111111111111222222222222111111111111222222333333333333333333333333444333222111000000000000000//////......//////000///............---------------.........//////////////////...------,,,,,,------,,,+++***)))(((((((((((())))))***+++++++++++++++++++++++++++++++++******+++******)))((('''((())))))))))))((((((''''''(((((())))))(((((('''(((((((((((())))))))))))(((((('''&&&&&&&&&''''''''''''&&&&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!!!!"""######$$$$$$"""############$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$###"""!!! !!!"""######""""""!!!!!!""""""###$$$$$$$$$##############################$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###########################!!! !!!"""""" """"""""""""""""""""""""########################$$$$$$$$$############"""""""""############""""""$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%########################!!!""""""###$$$$$$%%%%%%######""""""""""""""""""#################################"""!!!!!! ########################"""""""""""""""""""""""""""""""""#########$$$$$$%%%%%%$$$$$$###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%!!!""""""###$$$%%%%%%&&&###########################$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""""""""######"""""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""###########################$$$%%%&&&&&&%%%$$$###""""""######$$$$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&(((***)))'''&&&&&&'''&&&&&&&&&%%%%%%&&&&&&''''''((()))))))))((('''&&&&&&&&&&&&''''''(((((((((((((((((()))))))))))))))'''''''''((()))***,,,,,,.........---,,,+++******+++++++++***+++,,,,,,---++++++++++++,,,---...///000000000111111111111111222222111111111111222222333333333333333333333333444444333111000///......///////////////////////////............---------------------.........////////////...------,,,,,,,,,,,,+++***))))))((((((%%%&&&''')))+++---...///++++++++++++++++++++++++***************)))(((((())))))***))))))((('''&&&(((((((((((((((((((((((((((((((((((())))))))))))&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$'''&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%""""""#########$$$$$$$$$!!!!!!"""""""""###############"""!!!!!!""""""######""""""""""""""""""#######################################""""""""""""$$$###$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################"""!!!!!!"""!!!!!!""""""""""""""""""""""""%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########"""""""""######$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%""""""""""""""""""""""""""""""#########$$$$$$$$$ !!!"""###$$$%%%%%%########################$$$#########"""""""""!!!########################""""""""""""""""""""""""""""""#########$$$$$$$$$%%%$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%&&&"""######$$$%%%&&&''''''###########################$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###""""""""""""""""""###$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""######################## !!!###%%%&&&&&&%%%$$$$$$$$$$$$######"""""""""########################$$$$$$$$$$$$$$$$$$$$$$$$######""""""""""""#########$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&%%%&&&&&&$$$$$$$$$%%%&&&'''((())))))((('''&&&&&&'''((())))))))))))(((((((((''''''((((((((((((((()))))))))&&&&&&&&&'''((()))***+++......---,,,+++*********+++************+++,,,,,,*********++++++,,,---.../////////000000111111111222222111111111111222222333333333333333333333333444444333222111000///.........////////////......///............---------------------.........////////////...------,,,,,,***************+++++++++(((((()))***+++,,,---...***+++,,,,,,,,,,,,+++***)))************))))))((())))))***))))))((('''&&&((((((''''''''''''(((((((((((((((((())))))))))))%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######""""""#########$$$$$$$$$!!!!!!"""""""""############""""""""""""###############""""""""""""#################################"""""""""""""""""""""######$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################&&&&&&&&&$$$$$$$$$%%%%%%""""""###$$$$$$###""""""%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########""""""######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%""""""""""""""""""""""""$$$$$$$$$#########"""""" !!!"""###$$$$$$%%%########################%%%%%%$$$$$$$$$$$$##############################""""""""""""""""""""""""############$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&'''###############$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$$$$%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$ !!!"""###$$$%%%%%%%%%%%%$$$$$$###""""""!!!!!!########################$$$$$$$$$$$$$$$$$$$$$$$$""""""!!!!!!!!!!!!""""""""""""###$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&######$$$%%%&&&''')))***((('''%%%$$$%%%&&&(((***+++******)))((((((''''''(((((('''''''''((()))***&&&&&&&&&&&&''')))***+++------,,,+++***************************+++,,,,,,************+++,,,---.........//////000000111111222222111111111111222222333333333333333333333333333333333333222000///...---......//////......---///............---------------.........//////////////////...------,,,,,,*********+++++++++,,,,,,------,,,+++******))))))***+++,,,------,,,+++***))))))************))))))((())))))))))))(((((('''(((''''''&&&&&&''''''((((((((((((((())))))))))))$$$%%%&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""!!!!!! """############$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%""""""##################$$$######""""""######$$$###############$$$$$$$$$"""""""""""""""#########"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$#################################!!!!!!###""""""$$$$$$$$$$$$""""""########################$$$$$$$$$############"""######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%########################%%%%%%$$$$$$###""""""!!!$$$$$$######"""!!!!!!!!!########################%%%%%%%%%%%%%%%%%%%%%%%%########################""""""""""""""""""""""""#########$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&'''$$$$$$$$$$$$$$$$$$%%%%%%""""""#########$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$############$$$%%%&&&&&&&&&%%%%%%$$$$$$###########################!!!""""""###$$$$$$%%%%%%################################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""""""""###$$$%%%############""""""""""""########################$$$$$$$$$$$$$$$$$$$$$$$$######""""""""""""###### !!!"""############"""$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&''''''&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%&&&''''''((((((((((((((((((((('''(((''''''&&&'''((()))***&&&&&&''''''((()))+++,,,,,,+++***))))))***++++++***************++++++,,,++++++++++++,,,---......------...//////000111111222222111111111111222222333333333333333333333333000000111111111000......------...//////...------///............---------....../////////000000000/////////...------,,,,,,+++++++++***************,,,++++++***))))))((((((***+++---......---+++***))))))************))))))'''(((((())))))))))))(((((('''&&&&&&&&&&&&'''((((((((((((((())))))))))))$$$%%%&&&'''(((''''''&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&'''''''''((($$$%%%%%%&&&&&&%%%%%%$$$"""##################$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""""""""""""""""""""############$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%""""""######$$$$$$$$$$$$$$$######""""""######$$$""""""#########$$$$$$$$$!!!""""""######$$$$$$$$$"""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################!!!!!!!!!""" !!!###$$$$$$###!!! ########################$$$$$$$$$############"""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################$$$$$$######"""!!!!!! ########################$$$$$$$$$$$$$$$$$$$$$$$$########################""""""""""""""""""""""""#########$$$$$$$$$%%%%%%$$$#########$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&'''$$$$$$$$$###############""""""######$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&''''''&&&%%%%%%$$$##############################!!!""""""###$$$$$$%%%%%%########################""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$"""!!!!!!!!!"""###!!!!!!!!!"""######$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$ !!!"""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$&&&((((((((((((((('''&&&%%%%%%%%%%%%"""###%%%''''''&&&%%%$$$%%%%%%&&&&&&'''((((((((((((''''''&&&&&&((()))***''''''(((((()))+++,,,---+++***)))))))))***+++,,,*********)))***++++++,,,++++++++++++,,,---...///---------...///000000111222222111111111111222222333333333333333333333333......///000000///...---,,,---...//////...---,,,//////.........---------////////////000000000000000//////...------,,,,,,,,,,,,+++***)))(((''''''&&&&&&'''((()))***++++++***+++---......---+++***((())))))*********))))))''''''((())))))***))))))((('''&&&%%%%%%&&&'''((((((((((((((())))))))))))$$$%%%'''(((((((((''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&'''''''''(((((($$$%%%%%%&&&&&&%%%%%%$$$!!!!!!""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%%%%&&&&&&"""############$$$$$$$$$!!!""""""""""""#########!!!"""###$$$$$$$$$$$$$$$$$$$$$############$$$$$$""""""######$$$$$$$$$$$$!!!!!!"""###$$$%%%%%%&&&"""###$$$%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################&&&&&&&&&$$$!!!!!!$$$''' !!!######!!! %%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$############"""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$#########"""###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$$$$%%%%%%!!!!!!""""""######$$$$$$##########################################$$$$$$########################""""""""""""""""""""""""######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%$$$$$$#########&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$""""""$$$%%%&&&###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$#########$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%###  ###%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$$$$######$$$$$$%%%"""###$$$%%%%%%$$$###""" !!!"""###$$$%%%%%%%%%"""""""""###$$$$$$%%%%%%$$$$$$$$$############"""######$$$$$$$$$%%%%%%%%%######$$$$$$$$$$$$######%%%%%%%%%###!!!!!!"""$$$$$$$$$#########$$$%%%&&&"""$$$&&&&&&%%%$$$###$$$$$$$$$$$$$$$$$$###"""!!!$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$###""""""###%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&&&&'''(((((((((((((((''''''''''''((((((&&&&&&''''''''''''&&&&&&)))(((&&&%%%&&&''')))+++*********))))))))))))))))))************+++++++++)))******++++++,,,------------...000111111111111,,,---///111222333222222444444333333222111000000111111000///////////////......//////......---,,,---...............---------...///000000111000000000//////---,,,+++******))))))))))))))))))))))))************************---.../////////...,,,++++++*********))))))(((((())))))))))))))))))))))))))))))(((((((((((())))))))))))(((((((((((())))))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((()))******+++''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$%%%%%%&&&&&&###############"""!!!!!!""""""""""""""""""""""""###$$$$$$%%%%%%$$$$$$###""""""############"""""" !!!"""###$$$%%%%%%%%%&&&%%%###!!!!!!"""###$$$'''$$$""""""###$$$""" $$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$$$$######$$$$$$%%%$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!! ########################""""""""""""""""""""""""########################%%%$$$$$$######$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$########################"""######$$$$$$######"""""""""""""""""""""""""""%%%$$$$$$$$$###""""""""" !!!"""###############%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%$$$$$$$$$######%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!  !!!###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%###""""""###%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$$$$######$$$$$$%%%"""##################"""$$$%%%%%%%%%%%%$$$######$$$$$$##################$$$$$$$$$############"""######$$$$$$$$$%%%%%%%%%######$$$$$$$$$$$$######!!!"""###""""""###%%%'''%%%%%%%%%&&&&&&&&&''''''"""$$$%%%%%%$$$######$$$$$$$$$$$$$$$$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$###""""""###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&)))(((&&&&&&&&&''')))***))))))))))))))))))))))))))))))*********+++++++++)))******++++++,,,---------...///000000000000000---...///111111222222222444444333222222111000000000//////.....................//////......---,,,....../////////......---...//////000000000000///000///...---,,,++++++***************************************************---......///...---,,,+++************)))))))))((())))))))))))))))))))))))))))))(((((((((((())))))))))))(((((((((((())))))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''((((((((('''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%&&&&&&''' !!!###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###""""""############""""""!!!"""###$$$$$$$$$$$$$$$&&&%%%###"""!!!"""###$$$(((%%%###$$$%%%&&&%%%###$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$##################################################################$$$$$$$$$$$$######""""""######$$$$$$%%%%%%&&&&&&%%%%%%$$$##############################$$$$$$$$$$$$##############################%%%%%%%%%$$$$$$$$$$$$$$$######$$$######"""!!!  !!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%$$$$$$$$$$$$###$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!!!!"""###$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$############$$$$$$###""""""!!!!!!""""""###%%%%%%&&&&&&%%%%%%$$$###%%%%%%$$$$$$###""""""!!!$$$$$$$$$############"""######$$$$$$$$$%%%%%%%%%######$$$$$$$$$$$$######!!!"""######"""###%%%'''###$$$&&&'''''''''&&&%%%"""###$$$###"""!!!###$$$###$$$$$$$$$$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$###""""""###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&''''''&&&%%%$$$&&&&&&''''''''''''&&&&&&(((''''''&&&&&&((()))***)))))))))))))))))))))))))))))))))*********++++++)))******++++++,,,------...//////000000000//////000000///000000111222222333333333222111111000000//////...---------------......//////......---,,,...//////000000////////////000000000000//////...//////...---,,,++++++*********************************************************+++++++++***)))(((************)))))))))))))))))))))))))))))))))))))))((((((''''''(((((())))))((((((''''''(((((()))&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%&&&&&&&&& """###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###""""""############"""""""""######$$$$$$$$$######%%%$$$###"""""""""###$$$%%%$$$###$$$%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$###"""########################$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$$$$$$$###""""""""""""""""""###$$$$$$%%%%%%%%%%%%$$$$$$########################$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%"""###############""""""!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%%%%%%%&&&'''###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$######""""""$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$############$$$$$$###"""!!! !!!"""###!!!"""###$$$%%%&&&&&&&&&$$$$$$$$$#########""""""$$$$$$$$$#########""""""######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%&&&&&&$$$"""!!!!!!""" """$$$%%%&&&%%%###"""#########!!! ###%%%######$$$$$$$$$######"""$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""###$$$$$$###""""""###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%'''(((((('''%%%$$$&&&&&&''''''''''''&&&&&&(((''''''''''''((())))))((((((((()))))))))))))))))))))))))))************)))******++++++,,,------/////////000//////......111111000//////000111222333222222222111111000000000///......------...............///......---,,,...///000000000000000000000000111000000///...---//////...---,,,,,,++++++************************************************,,,,,,,,,+++++++++***************)))))))))))))))(((((((((((((((((((((((((((((((((''''''((((((((((((((((((''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%###$$$$$$$$$$$$###""""""""""""""""""""""""""""""###$$$$$$%%%%%%$$$$$$###"""######$$$$$$######"""######$$$$$$$$$######"""$$$$$$###""""""######$$$ !!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%$$$###"""########################$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$""" ########################$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$$$$%%%%%%######""""""""""""######$$$$$$%%%%%%%%%%%%$$$$$$########################$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%!!!###%%%&&&&&&&&&######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""############$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""""""""$$$$$$$$$$$$$$$$$$$$$$$$########################$$$######""""""######$$$###"""!!! !!!"""### !!!###$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$#########""""""######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%&&&&&&%%%"""!!! !!! !!!###%%%%%%$$$###"""#########!!! ###%%%"""######$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""###$$$$$$###""""""###%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''((((((''''''&&&&&&%%%%%%%%%&&&((())))))(((&&&%%%&&&&&&''''''''''''&&&&&&'''''''''''''''((())))))''''''(((((())))))))))))(((((()))))))))*********)))******++++++,,,------...////////////......---111111000//////000111222222222111111111111111000111000//////......//////.........///......---,,,......///000000000000000000000111000000///...---.........------,,,,,,+++************************************************000000/////////.........))))))))))))))))))******((((((((((((((((((((((((((((((''''''''''''((((((((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""############$$$$$$$$$$$$$$$###""""""""""""""""""""""""""""""###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$$$$############$$$$$$$$$######"""##################$$$$$$ !!!#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$$$$######"""########################$$$$$$$$$$$$$$$$$$$$$$$$###############"""!!! ################################################""""""#########$$$$$$$$$$$$$$$$$$######$$$$$$$$$###$$$$$$%%%%%%$$$$$$###########################$$$%%%%%%&&&&&&%%%%%%$$$########################!!!!!!""""""######$$$$$$ !!!###%%%&&&&&&'''"""######$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$##############################""""""""""""#########""""""!!!!!!""""""###"""""""""###"""!!!!!! !!!""""""###$$$$$$%%%%%%$$$$$$$$$############"""######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$!!!###%%%%%%###"""###$$$"""###%%%&&&&&&&&&%%%$$$"""###$$$###"""!!!###$$$""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$###""""""###%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''&&&&&&''''''((())))))(((''''''&&&&&&''''''''''''&&&&&&'''''''''(((((((((((((((&&&''''''(((((())))))***((((((((()))))))))******)))******++++++,,,---------....../////////......000000///000000111222222111111111111111111111111111111000///////////////......//////......---,,,------...///000000000000///000000000000//////.........---------,,,,,,,,,++++++++++++++++++++++++************************...---,,,+++++++++,,,,,,))))))))))))************))))))))))))))))))))))))(((''''''&&&&&&''''''((((((''''''&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""##################### !!!###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$$$$######"""######$$$$$$$$$######"""#########$$$$$$$$$$$$"""$$$%%%%%%$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$###""""""""""""###$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!###$$$&&&'''''''''########################""""""""""""""""""""""""########################%%%%%%$$$$$$$$$$$$%%%%%%######$$$$$$$$$$$$##############################$$$$$$%%%%%%%%%%%%$$$$$$""""""""""""""""""""""""!!!!!!!!!"""""""""""""""###$$$$$$$$$$$$$$$######!!!"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%''''''''''''&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################""""""""""""######"""##################"""###############"""!!!!!!##################$$$$$$$$$$$$$$$############"""######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$!!!###%%%%%%$$$""""""######$$$$$$$$$%%%%%%%%%%%%"""$$$%%%%%%$$$######$$$""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$###""""""###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&&&&''''''(((((((((((((((&&&&&&''''''((())))))***(((((((((((()))))))))***)))******++++++,,,------,,,,,,---...////////////---...///111111222222222000000000000111111111111000000///............///......//////......---,,,,,,,,,---...///000000///...//////000000000000///...------------,,,,,,,,,++++++++++++++++++++++++************************+++***)))((('''(((((()))((()))))))))************))))))))))))))))))))))))(((''''''&&&&&&''''''((((((''''''&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''$$$%%%%%%%%%&&&'''''''''%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$###!!!"""###$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$$$$"""%%%&&&%%%###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$!!! !!!$$$%%%""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""###$$$%%%&&&&&&&&&################################################%%%%%%$$$$$$###"""""""""$$$$$$############$$$$$$######$$$$$$$$$$$$####################################$$$$$$$$$$$$#######################################"""""""""""""""%%%%%%%%%%%%$$$###"""""" """###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!""""""###$$$&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$#################################$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%'''((((((''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!"""###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################""""""""""""######"""###$$$%%%%%%$$$###""" !!!"""###$$$%%%%%%%%%%%%%%%$$$$$$###"""""""""$$$$$$$$$############"""######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&'''&&&### """"""!!!!!!""""""###$$$"""$$$&&&&&&%%%$$$###$$$!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$###""""""###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&''''''''''''''''''&&&&&&''''''((()))(((((((((&&&&&&&&&'''((())))))***(((((((((((()))))))))))))))******+++,,,,,,------+++,,,---...////////////,,,---///111333333222222000000000000000111111111//////...------------.........//////......---,,,+++,,,---...////////////......///000000111000000------------------,,,,,,++++++++++++++++++++++++************************///...,,,+++++++++,,,---(((((())))))*********+++))))))))))))))))))))))))'''''''''&&&&&&''''''''''''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''######$$$%%%&&&&&&''''''%%%%%%%%%$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%$$$######""""""""""""""""""""""""$$$$$$$$$%%%%%%$$$$$$$$$###$$$$$$%%%%%%$$$$$$### !!!"""###$$$%%%%%%%%%!!!"""###$$$$$$$$$$$$$$$ $$$%%%""" !!!"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$!!!!!!$$$&&&""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$"""!!!########################$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$###"""!!!!!!######""""""""""""############$$$$$$$$$$$$#######################################$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$######"""""""""###$$$%%%%%%%%%%%%%%%!!!!!!"""###############&&&&&&%%%$$$$$$######"""$$$###"""""""""###%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$""" !!!%%%''''''&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%%%%%%%$$$######$$$%%%%%%###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$###"""!!! $$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################'''&&&%%%%%%$$$$$$$$$$$$&&&%%%$$$###""""""""""""##############################$$$$$$$$$######"""############""""""!!!!!!""""""###$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&$$$"""$$$'''%%%$$$###""""""###$$$%%%'''$$$!!!!!!###$$$$$$"""""""""""""""""""""""""""######$$$%%%%%%%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!""""""""""""""""""""""""%%%%%%$$$###""""""############$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((())))))((($$$ !!!%%%'''%%%"""&&&&&&''''''''''''&&&&&&&&&''')))*********)))(((******))))))))))))******&&&'''''')))***---...///111000///...---...//////000///...///000111000///444444333222111000///...111111000000//////............///000000000000000////////////////////////////////////...............------,,,,,,------...************************+++++++++************)))************************))))))))))))))))))))))))((()))*********((('''&&&((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''"""$$$&&&((((((&&&$$$"""%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$############""""""""""""$$$$$$##################$$$###"""!!!!!!"""###$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$#########""""""""""""""""""""""""$$$$$$############$$$$$$'''&&&$$$###""""""!!!!!!%%%%%%%%%%%%%%%%%%%%%%%%&&&'''))))))'''$$$!!!"""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$######################## """###"""!!! !!!#########""""""######$$$%%%%%%$$$###""""""###$$$%%%######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""""""""#########$$$$$$$$$"""###$$$%%%&&&%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###"""""""""###%%%%%%###$$$$$$$$$######""""""###!!! !!!$$$&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%%%%%%%$$$######$$$%%%%%%$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$########################'''&&&%%%$$$$$$$$$$$$$$$$$$###############$$$$$$#############################################"""$$$$$$#########"""""""""""""""###$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$### """$$$%%%%%%$$$######$$$$$$###""""""###$$$$$$###!!!!!!$$$&&&&&&%%%########################"""###$$$$$$%%%%%%$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###""""""########################%%%$$$$$$###""""""############$$$$$$$$$%%%%%%%%%&&&%%%$$$$$$$$$$$$%%%&&&#########$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''(((((()))+++'''$$$$$$(((***(((&&&&&&&&&''''''''''''&&&&&&''''''((()))))))))))))))******))))))))))))******(((((())))))***+++,,,---000///...---,,,------...111000///000111222111000222222111111111111000000111000000000/////////......///000000111111000000....................................------------,,,,,,,,,++++++,,,,,,,,,+++++++++++++++++++++++++++++++++*********))))))************************)))))))))))))))))))))))))))))))))))))))(((''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$############""""""""""""########################$$$###"""!!!!!!"""###$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$####################################""""""""""""######%%%%%%$$$######"""""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&%%%###!!!############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$##############################################################################!!!"""###"""!!! !!!###$$$############$$$$$$%%%$$$$$$###""""""###$$$$$$######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""""""""#########$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%&&&&&&$$$############$$$%%%%%%###############"""""""""$$$###""""""$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&%%%%%%$$$$$$$$$#########$$$$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##########################################&&&%%%%%%$$$$$$$$$$$$%%%""""""""""""###$$$%%%&&&########################""""""""""""######""""""$$$$$$$$$$$$$$$#########""""""###$$$$$$$$$$$$###""""""############""""""%%%###"""###&&&'''%%%###$$$$$$###""""""###$$$$$$"""!!! !!!$$$&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######"""###############$$$$$$$$$%%%%%%%%%'''&&&$$$######$$$&&&'''""""""#########$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''((((((+++(((%%%&&&)))***)))'''&&&&&&''''''''''''&&&&&&((((((''''''(((((()))******))))))(((((())))))*********)))))))))***++++++...---,,,,,,++++++,,,,,,,,,+++***+++---...---,,,//////000000111111222222000000000000//////////////////000111111111111111...........................------------,,,,,,,,,,,,++++++******++++++,,,++++++++++++++++++++++++++++++*********)))))))))************************))))))))))))))))))))))))***))))))(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%'''&&&%%%$$$$$$%%%&&&'''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$#########"""""""""########################$$$###""""""""""""###$$$$$$$$$############$$$$$$%%%%%%%%%$$$$$$$$$$$$###########################""""""!!!!!!!!!!!!""""""$$$$$$$$$$$$###$$$$$$$$$########################$$$$$$$$$$$$#########"""###$$$$$$$$$$$$%%%%%%%%%""""""""""""""""""#########$$$$$$$$$$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$################################################!!!"""######!!!!!!"""###%%%%%%$$$$$$###$$$$$$$$$$$$$$$###""""""###$$$$$$######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%############$$$$$$%%%%%%&&&%%%%%%$$$$$$$$$$$$$$$%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&&&&%%%%%%$$$#########$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############""""""########################%%%%%%$$$$$$$$$$$$$$$%%%######""""""###$$$$$$%%%########################""""""""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###"""##################""""""!!!!!!"""$$$&&&(((((($$$##################$$$%%%$$$###############"""$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$######$$$$$$$$$%%%%%%%%%'''&&&$$$######$$$&&&'''############$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''%%%$$$$$$&&&'''&&&$$$%%%&&&&&&''''''&&&&&&%%%(((((('''&&&&&&((()))***))))))(((((((((((()))))))))))))))))))))***++++++,,,,,,++++++***************)))((()))+++,,,,,,+++/////////000000000111111000000000000///////////////000000111111111111111.................................---------,,,,,,,,,,,,++++++++++++,,,,,,++++++++++++++++++++++++************))))))))))))************************((((((((((((((((((((((((***)))(((''''''((()))***&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$#########""""""###############$$$$$$$$$########################$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################""""""""""""######"""######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%&&&$$$$$$$$$$$$$$$%%%%%%%%%"""""""""###############""""""############""""""$$$$$$$$$$$$$$$$$$$$$$$$################################################!!!"""######"""!!!"""###&&&%%%%%%$$$$$$$$$$$$$$$$$$##################$$$######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$################################################%%%$$$###"""###$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$############$$$$$$%%%%%%%%%%%%&&&%%%$$$#########$$$$$$%%%%%%%%%$$$######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$#########&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##########################################$$$$$$$$$######$$$$$$%%%%%%$$$$$$###""""""##############################""""""!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$#########$$$$$$$$$$$$######!!!###""" !!!&&&***#########$$$$$$############$$$$$$$$$###"""""""""$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%$$$$$$########################$$$###############$$$$$$######$$$$$$$$$%%%%%%%%%'''&&&$$$######$$$&&&'''$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%$$$###%%%%%%&&&&&&&&&&&&%%%%%%((('''&&&&&&&&&''')))***))))))(((((((((((())))))'''''''''((()))***,,,,,,***************))))))(((---,,,+++---///000000///000000000/////////......////////////000000000000//////000111111111111111........................////////////.........---------,,,,,,,,,,,,------++++++++++++++++++++++++*********)))))))))(((((())))))))))))))))))))))))((((((((((((((((((((((((***)))(((''''''((()))***&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%$$$%%%'''(((((('''%%%$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$############""""""#########$$$$$$$$$######$$$$$$$$$$$$######$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$$$$######$$$$$$%%%"""###$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""!!! !!!###%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&''''''!!!""""""######"""""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%########################"""###$$$###"""!!!"""$$$%%%%%%$$$######$$$$$$$$$#########$$$$$$###############""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$################################################%%%$$$###"""###$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$######"""###$$$$$$%%%&&&%%%%%%%%%$$$###"""!!! !!!""""""%%%%%%&&&%%%######$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$##############################""""""######$$$%%%###$$$$$$%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################$$$############$$$$$$%%%&&&%%%$$$###""""""""""""##############################"""""""""$$$%%%&&&#########$$$$$$$$$$$$$$$""""""###$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$###!!!$$$&&&###!!!'''"""###$$$$$$$$$$$$###"""!!!###$$$$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$!!!"""######$$$$$$###############$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%%%%%%%""""""""""""""""""""""""#########"""######$$$%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&%%%%%%''''''&&&&&&''''''((())))))((((((''''''(((((()))'''''''''((()))***,,,---)))************)))((((((,,,+++***,,,...000///...000000//////......------////////////000000000000......///000000000000000------------------------000000/////////............------,,,,,,------...******************************)))))))))((((((((())))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((())))))***&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%###%%%((())))))(((%%%###$$$$$$%%%%%%%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%$$$$$$$$$$$$#########"""""""""###$$$$$$%%%%%%######$$$%%%%%%$$$############""""""""""""#########$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%"""###%%%&&&&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%% !!!###$$$$$$$$$$$$############"""!!!!!!!!!""""""######$$$!!!""""""############"""%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&########################"""###$$$$$$""""""###$$$######""""""######$$$%%%"""###$$$$$$$$$$$$###"""######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$###############$$$$$$######$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&&&&%%%%%%$$$###!!! """"""$$$%%%&&&%%%######%%%'''$$$$$$$$$$$$$$$$$$$$$$$$##############################""""""######$$$%%%###$$$%%%%%%%%%%%%$$$###"""######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&'''%%%$$$$$$######$$$$$$%%%"""""""""###$$$$$$%%%%%%#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%&&&''''''(((#######################################$$$%%%%%%$$$$$$###############$$$########################$$$$$$###"""###%%%'''((("""""""""#########$$$$$$""""""###$$$$$$$$$$$$###""""""############""""""###$$$%%%$$$!!! """$$$"""###$$$$$$$$$$$$###"""!!!$$$%%%$$$###%%%&&&########################!!!""""""###############"""#########$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%##############################""""""###$$$$$$%%%######$$$$$$$$$%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&((((((''''''&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&''''''((((((''''''((((((''''''''''''((((((((((((((((((((()))******)))******+++***)))((('''((((((''')))+++------,,,---...............//////.../////////000000000111------...///////////////------------------------//////.........------------,,,,,,,,,,,,,,,,,,---))))))))))))))))))))))))***)))))))))(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))''''''((()))))))))))))))''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''(((((('''&&&&&&$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%$$$$$$$$$#########!!!""""""###$$$$$$%%%%%%###$$$$$$%%%%%%$$$$$$#########""""""""""""############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%###$$$%%%''''''&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!!!!!!!!!!"""###$$$#########"""""""""!!!!!! !!!!!!"""!!!"""######$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################"""###$$$$$$""""""###$$$ !!!"""###$$$%%%"""###$$$$$$$$$$$$###"""######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$#########""""""######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%&&&&&&###$$$%%%&&&'''&&&%%%%%%&&&%%%###"""!!!"""$$$%%%###%%%&&&%%%######&&&)))$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""#########"""###$$$$$$%%%###$$$%%%&&&&&&%%%$$$###!!!"""###$$$%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%&&&'''%%%$$$$$$$$$$$$$$$$$$%%%!!!!!!"""###$$$%%%%%%&&& !!!"""###$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%'''((())))))##############################""""""###$$$%%%%%%""""""""""""###$$$%%%&&&########################%%%$$$######$$$%%%((()))!!!!!!""""""#########$$$""""""###$$$$$$$$$$$$###!!!!!!""""""""""""!!!!!!###"""!!!###&&&'''&&&%%%"""###$$$%%%%%%$$$###"""!!!$$$&&&&&&###!!!"""###""""""""""""""""""""""""!!!!!!"""###############""""""######$$$$$$$$$$$$###$$$%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######""""""###$$$%%%%%%######$$$$$$$$$%%%%%%%%%###$$$&&&''''''&&&$$$###"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''((('''%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%'''((((((((('''&&&((((((''''''''''''((((((******)))((((((((((((((()))***+++++++++***((('''******)))+++...//////...++++++,,,---...///000111.../////////000000111111,,,------...............------------------------......---------,,,,,,,,,,,,++++++++++++++++++,,,(((((((((((((((((((((((())))))))))))(((((((((((())))))))))))))))))))))))))))))))))))))))))))))))&&&'''(((*********)))(((((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''((('''&&&%%%%%%&&&'''((($$$$$$$$$%%%%%%$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$%%%%%%%%%$$$$$$$$$######!!!""""""###$$$$$$%%%%%%###$$$%%%&&&&&&%%%$$$#########""""""""""""###############$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$###$$$&&&''''''&&&$$$###########################$$$$$$%%%%%%&&&&&&&&&&&&###"""""""""!!!!!! """######$$$%%%&&&&&&'''""""""###$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################"""$$$$$$$$$###"""###$$$ !!!###%%%&&&"""###$$$%%%%%%$$$###"""#########"""###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$$$$$$$$$$$$$$$$$$$######"""""""""###$$$%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$######"""#########'''&&&$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$############""""""###&&&(((((((((%%%$$$###!!!!!!!!!"""###""""""""""""""""""""""""""""""""""""############!!!"""$$$$$$"""!!!"""###$$$##################$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%% !!!"""###$$$%%%%%%%%%%%%%%%%%%$$$$$$#########$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$""""""###$$$%%%&&&&&&'''######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''&&&'''''''''&&&%%%%%%$$$&&&%%%#########%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&((())))))((('''''')))***,,,***((('''((()))(((((((((((((((((())))))))))))******))))))******+++,,,,,,+++*********+++,,,------------............///111111000000000000111111............///////////////...,,,++++++,,,...///...------,,,+++++++++,,,++++++,,,,,,,,,,,,++++++...---,,,+++***(((''''''''''''((((((((((((''''''))))))************))))))***)))))))))++++++)))'''))))))(((((((((((())))))''''''''''''&&&%%%$$$######$$$&&&((())))))((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%""""""""""""""""""""""""""""""""""""""""""""""""$$$%%%%%%&&&%%%$$$"""!!!$$$$$$$$$$$$$$$###"""!!!"""######$$$$$$$$$######!!!"""###$$$$$$$$$$$$$$$$$$$$$##########################################&&&%%%$$$"""""""""######&&&&&&&&&%%%%%%%%%$$$$$$########################%%%%%%$$$######$$$$$$$$$&&&%%%%%%$$$###"""!!!!!!###$$$%%%&&&&&&%%%$$$###$$$$$$############$$$$$$%%%$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$############$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%$$$#########""""""!!!!!!""""""""""""""""""""""""######$$$######"""!!! $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$###############&&&%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$#########"""!!!"""%%%&&&&&&&&&%%%$$$###"""!!!!!!"""###########################""""""""""""############!!!"""$$$$$$"""""""""###&&&%%%$$$######$$$%%%&&&########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%"""######$$$$$$$$$$$$###%%%%%%%%%$$$$$$$$$######$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%&&&&&&&&&&&& !!!!!!""""""############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''&&&&&&''''''&&&&&&%%%$$$'''&&&%%%$$$$$$&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&((()))((('''&&&'''(((+++)))'''&&&'''((((((''''''((((((((())))))))))))))))))(((((())))))******++++++*********+++,,,---------------............111000000////////////000---.........////////////...---,,,******+++---...------,,,+++++++++++++++++++++++++++++++++++++++,,,,,,++++++***)))))))))))))))************))))))))))))************))))))***)))((()))***+++)))((((((((())))))))))))((((((((((((((((((''''''&&&%%%%%%%%%&&&'''((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%###################################################$$$%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$###""""""######$$$$$$$$$$$$############$$$$$$$$$######"""################################################&&&%%%###"""""""""###############"""""""""!!!!!!########################%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###"""""""""######$$$$$$$$$$$$######$$$$$$############$$$$$$%%%$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$############$$$$$$$$$$$$############$$$$$$############"""""""""!!!########################"""###$$$$$$$$$$$$$$$###!!!!!!!!!!!!!!!!!!!!!!!!$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&''''''%%%$$$$$$######$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###############&&&%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$###$$$%%%%%%%%%%%%$$$###%%%%%%%%%$$$$$$$$$$$$######"""!!!"""$$$%%%$$$###$$$$$$###"""""""""##############################"""""""""#########$$$$$$!!!###$$$$$$###""""""###&&&%%%###""""""###%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%$$$###""""""%%%%%%%%%$$$$$$$$$$$$###$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''&&&&&&''''''&&&&&&%%%%%%)))((('''&&&%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&((()))'''&&&&&&&&&***(((&&&%%%&&&'''''''''''''''((((((((()))))))))'''''''''((((((((())))))+++************+++,,,,,,,,,,,,,,,---------......000//////.........---------------.........//////,,,,,,+++******+++,,,---,,,,,,+++************++++++******))))))******+++******************+++++++++++++++,,,,,,+++++++++))))))************))))))***)))((((((******)))((('''((()))******)))((('''(((((()))))))))(((((('''''''''&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################"""###$$$$$$%%%$$$$$$$$$$$$$$$$$$############"""###$$$$$$$$$$$$$$$######%%%%%%%%%$$$$$$"""!!!!!!################################################%%%$$$######"""######$$$"""""""""!!!!!!!!! """"""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$#################################""""""#########$$$$$$############$$$$$$$$$$$$$$$############"""########################"""##################"""$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$$$$$$$############$$$$$$#########""""""#####################""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$""""""###%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&'''((((((%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$############$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$"""###%%%&&&&&&%%%###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$#########%%%%%%###"""$$$#############################################""""""#########$$$$$$$$$!!!###%%%$$$###"""######$$$"""  """$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''%%%&&&&&&'''&&&&&&%%%%%%)))((('''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&)))***((('''&&&&&&)))'''%%%%%%&&&''''''''''''''''''((((((((())))))''''''(((((())))))))))))***************++++++,,,+++,,,,,,,,,------------............---,,,,,,+++,,,,,,---------.........+++******)))******+++,,,++++++******)))******+++++++++***))))))***++++++************************++++++,,,,,,,,,,,,++++++))))))************)))))))))((('''''')))******)))&&&((()))++++++)))(((&&&''''''((()))))))))(((((()))((('''%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$########################""""""######$$$$$$$$$%%%$$$$$$##################$$$$$$%%%%%%$$$$$$######$$$$$$$$$$$$$$$###"""!!!###############$$$$$$$$$##########################################$$$$$$%%%$$$$$$$$$############""""""""""""""""""""""""######$$$$$$%%%%%%$$$$$$""""""#########$$$$$$$$$$$$###"""!!!!!!"""###$$$$$$$$$############$$$$$$$$$$$$$$$$$$######""""""""""""""""""""""""""""""""""""############""""""########################""""""#########$$$$$$$$$$$$$$$############$$$$$$######""""""""""""###############"""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&'''((((((%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$"""###%%%&&&&&&%%%###"""$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$%%%&&&&&&$$$"""#########$$$$$$$$$$$$#######################################$$$$$$$$$$$$"""###%%%%%%###"""###$$$###"""  """###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""######$$$$$$$$$%%%%%%%%%######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%$$$##################"""""""""######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''%%%%%%&&&&&&'''&&&&&&%%%''''''&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%(((***+++***((('''''')))'''%%%%%%&&&'''((('''''''''''''''(((((((((((('''((()))*********))))))))))))******++++++++++++++++++++++++,,,,,,,,,------------...---,,,+++***,,,,,,,,,,,,------------))))))))))))******+++++++++******)))******++++++,,,,,,++++++++++++,,,,,,,,,,,,++++++***)))))))))***++++++++++++++++++***))))))************)))))))))(((&&&&&&(((******)))&&&((()))++++++)))(((&&&&&&''''''(((((((((''''''***)))'''&&&%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########%%%$$$$$$######$$$$$$%%%################################################"""""""""######$$$$$$%%%$$$######""""""###$$$$$$%%%%%%%%%%%%%%%$$$######!!!"""###$$$$$$$$$$$$$$$""""""#########$$$$$$$$$########################""""""######$$$$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$"""""""""""""""""""""""""""###$$$%%%%%%%%%%%%$$$"""""""""###$$$$$$%%%%%%$$$###"""!!!!!!"""###$$$$$$$$$############$$$$$$###$$$$$$$$$$$$###"""!!!""""""""""""""""""""""""""""""############""""""########################""""""#########$$$$$$$$$$$$$$$############$$$$$$######""""""""""""######""""""""""""""""""####################################$$$$$$###"""!!!!!!""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&'''%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&''''''%%%$$$$$$######$$$$$$%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$$$$$$$$$$$$$######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$###$$$%%%%%%%%%%%%$$$######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&''''''%%%""""""###$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$%%%"""$$$%%%%%%$$$######$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%######$$$%%%&&&&&&%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$###$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$'''''''''&&&%%%$$$###"""$$$$$$$$$$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&(((***+++)))((((((((()))'''%%%%%%'''((()))(((&&&&&&'''''''''((((((((('''((()))***+++***)))(((((()))******++++++************+++++++++,,,,,,,,,+++,,,---......---,,,++++++++++++,,,,,,,,,------)))))))))***+++++++++,,,+++************+++,,,,,,---......//////......---,,,,,,++++++***)))(((((()))******++++++******)))))))))************)))))))))'''%%%&&&(((*********'''((()))******)))((('''''''''(((((((((''''''&&&)))((('''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$######"""""""""###$$$$$$$$$###"""""""""###$$$%%%&&&&&&&&&&&&%%%$$$###"""!!!!!!"""$$$$$$%%%%%%%%%"""""""""###$$$$$$%%%%%%######################## !!!"""$$$$$$%%%%%%%%%$$$$$$$$$############"""########################!!!"""$$$%%%&&&&&&%%%$$$""""""######$$$$$$$$$%%%#########""""""#########$$$$$$############$$$$$$######$$$%%%%%%###"""!!!########################"""##################"""########################"""############$$$$$$$$$$$$$$$############$$$$$$#########""""""#########""""""""""""############""""""""""""""""""""""""###$$$$$$###"""!!! ########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$$$$$$$$$$%%%"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$%%%''''''$$$""""""###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%"""$$$%%%%%%$$$######$$$$$$$$$%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%$$$$$$###%%%&&&&&&&&&'''(((((((((######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''$$$%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))''''''((())))))'''&&&&&&((()))***)))&&&&&&&&&'''''''''((((((%%%&&&(((******)))(((''''''((()))***+++******)))************++++++++++++)))+++---...///...---,,,++++++++++++,,,,,,,,,,,,((()))***+++,,,,,,,,,,,,+++++++++++++++,,,------...000222333333222000...******************************++++++++++++******))))))************)))))))))'''%%%%%%''')))******(((((())))))))))))(((((())))))))))))(((((('''&&&''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!!!!"""######$$$###"""!!!"""###%%%&&&&&&&&&&&&&&&%%%$$$###""""""######$$$$$$$$$######!!!""""""###$$$$$$%%%%%%######################## """$$$%%%%%%%%%%%%############""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$ """$$$&&&&&&&&&%%%$$$###############$$$$$$$$$######$$$$$$$$$$$$######$$$$$$############$$$$$$"""###$$$%%%%%%$$$"""!!!$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$##############################"""############$$$$$$$$$$$$$$$############$$$$$$$$$$$$############$$$$$$!!!"""""""""##########################################$$$$$$$$$###""""""%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%"""###$$$%%%&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%$$$$$$######$$$$$$%%%#########$$$$$$%%%%%%%%%!!!!!!"""$$$&&&&&&$$$!!!"""###$$$%%%&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%"""$$$&&&%%%$$$###$$$%%%!!!"""$$$%%%%%%$$$"""!!!%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%'''''''''&&&%%%$$$""""""#########$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%""""""######$$$%%%&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''$$$%%%%%%&&&'''''''''&&&%%%%%%&&&'''((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&''''''((('''%%%%%%''')))***(((&&&&&&(((*********&&&&&&&&&'''''''''(((((($$$%%%'''))))))((('''&&&'''((()))++++++******))))))************+++++++++(((***,,,///000///......******+++++++++,,,,,,,,,((()))***,,,,,,---------,,,+++++++++,,,------...///111444666666444111///((())))))***++++++,,,,,,***++++++,,,,,,++++++***))))))************)))))))))&&&$$$%%%''')))***+++))))))(((((((((((())))))+++++++++******(((''''''%%%&&&'''(((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###!!!!!!!!!""""""$$$###"""!!!"""###%%%&&&&&&'''&&&&&&%%%$$$###"""$$$$$$$$$$$$$$$###"""!!!!!!""""""###$$$$$$%%%%%%######################## """$$$%%%&&&%%%%%%$$$$$$$$$$$$############%%%%%%%%%%%%%%%%%%%%%%%% """$$$&&&'''&&&%%%$$$###########################$$$%%%&&&&&&%%%$$$###$$$$$$############$$$$$$"""###%%%%%%%%%$$$""" $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$"""""""""""""""""""""""""""############$$$$$$$$$$$$$$$############$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%!!!!!!""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$%%%%%%%%%%%%""""""""""""""""""""""""$$$$$$$$$######"""""""""$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######"""######$$$&&&%%%$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$##############################$$$%%%%%%&&&&&&%%%%%%$$$""""""""""""""""""""""""%%%$$$###$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$###"""!!!&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$%%%%%%%%%%%%&&&&&&(((((('''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&########################$$$$$$$$$$$$######""""""$$$$$$$$$$$$$$$$$$$$$$$$###"""""""""###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''&&&&&&(((''''''&&&&&&&&&''''''))))))((((((''''''''''''&&&''')))***++++++++++++(((((((((((()))))))))))))))************+++++++++)))***+++,,,---.........,,,++++++******++++++,,,/////////......---------------,,,,,,+++***))))))...///000222222000///...*********+++,,,,,,,,,---+++++++++***++++++,,,,,,))))))(((((((((((())))))(((((('''(((((()))***+++&&&'''''''''(((((())))))))))))))))))))))))))))))'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&(((((((((''''''&&&&&&&&&""""""###$$$%%%%%%%%%%%%!!!"""$$$&&&&&&&&&$$$###%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$########################"""###$$$%%%%%%$$$###""""""############$$$$$$$$$$$$$$$$$$#####################$$$$$$$$$%%%%%%%%%########################$$$$$$###"""!!!!!!""""""""""""""""""""""""""""""%%%%%%%%%%%%%%%$$$###"""##############################""""""######$$$%%%$$$$$$$$$#########""""""%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######"""""""""""""""######$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$%%%%%%""""""""""""###$$$%%%&&&$$$#########""""""!!!!!! !!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########''''''''''''&&&&&&%%%$$$%%%%%%$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$##############################$$$%%%%%%&&&&&&%%%%%%$$$########################$$$#########$$$$$$$$$###$$$$$$$$$$$$$$$$$$######&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&'''''''''&&&%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&########################$$$$$$$$$$$$#########"""%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''(((''''''&&&&&&&&&''''''((((((((('''''''''&&&&&&'''(((((())))))*********'''((((((((())))))))))))))))))*********+++++++++******+++,,,------------,,,++++++******++++++,,,------,,,,,,,,,+++++++++------,,,,,,+++******))),,,---...//////...---,,,************++++++++++++,,,+++***)))))))))))))))))))))(((((((((((()))))))))(((((((((((())))))***'''''''''((((((((())))))''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%$$$$$$###!!!###$$$&&&&&&%%%$$$###%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$########################""""""###$$$$$$###"""""""""############$$$$$$$$$&&&%%%%%%$$$###"""!!!!!!######$$$$$$$$$%%%%%%%%%########################$$$######""""""""""""###########################%%%%%%%%%%%%%%%$$$###"""##############################""""""######$$$%%%$$$$$$$$$#########""""""%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$#########"""""""""""""""###$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$ !!!!!!"""$$$$$$$$$$$$#########"""!!!!!!!!!"""###$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######!!!"""$$$%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$"""###$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%%%%%%%$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%%%%%%%'''&&&&&&%%%$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&%%%'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''&&&&&&&&&''''''((('''''''''&&&&&&&&&&&&&&&(((((('''''''''(((((()))''''''((((((((())))))))))))))))))*********++++++++++++,,,,,,,,,,,,,,,+++,,,++++++******++++++,,,,,,,,,,,,,,,++++++++++++---,,,,,,++++++************+++,,,------,,,+++***************))))))))))))+++***)))((('''&&&&&&&&&))))))(((((((((((())))))***))))))(((((((((((()))''''''(((((((((((())))))'''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""""""""###$$$%%%&&&%%%$$$###$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$########################""""""############"""""""""############$$$$$$$$$'''&&&%%%$$$###!!! ######$$$$$$$$$%%%%%%%%%##############################"""""""""###$$$$$$########################$$$$$$%%%%%%%%%$$$####################################""""""######$$$%%%$$$$$$$$$###############$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$############""""""""""""###$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&%%%%%%$$$$$$#########$$$$$$$$$############"""%%%%%%%%%$$$$$$$$$$$$$$$!!!!!!""""""###$$$$$$$$$""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###!!!###$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$!!!###%%%&&&&&&%%%$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$"""#########"""!!!""""""###$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$%%%%%%'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&&&&'''''''''''''''((((((((())))))))))))))))))************++++++,,,,,,,,,++++++***,,,++++++******++++++,,,------------------------,,,,,,,,,++++++*********)))******++++++******)))******))))))((((((''''''***)))((('''''''''''''''))))))(((((((((((())))))******)))(((((('''(((((((((((((((((((((((())))))))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""###$$$$$$%%%%%%%%%$$$###$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$###########################$$$$$$$$$$$$$$$$$$###""""""#########$$$$$$$$$%%%%%%$$$$$$###"""!!!!!!######$$$$$$$$$%%%%%%%%%########################""""""""""""###$$$$$$%%%########################$$$$$$%%%%%%%%%$$$$$$#################################""""""######$$$%%%########################$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$##################""""""######$$$%%%###$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$###""""""&&&&&&&&&%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$"""""""""######$$$$$$$$$###########################$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%$$$ """$$$%%%%%%$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$########################"""$$$%%%###!!! !!!######$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######"""###############$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&&&&&&&&&&&&&'''''''''''''''(((((((((((((((((()))))))))*********+++++++++,,,++++++******,,,++++++******++++++,,,------------------------,,,,,,+++++++++++++++************++++++************))))))(((((('''''''''(((((((((((())))))***+++))))))(((((((((((())))))******)))(((((('''(((((())))))))))))))))))(((((())))))))))))))))))))))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%%%%%%%%%%$$$$$$$$$%%%$$$$$$$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%""""""#########$$$$$$$$$##################$$$$$$######$$$$$$$$$%%%%%%%%%##############################""""""###$$$%%%%%%###########################$$$$$$%%%%%%%%%$$$$$$##############################""""""######$$$%%%###########################$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""###############$$$$$$%%%#########$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###""""""######$$$###"""!!!""""""##############################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%$$$###"""$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$############$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$&&&&&&&&&%%%%%% !!!"""$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$"""""""""""""""""""""""""""%%%&&&%%%!!! !!!######$$$$$$%%%%%%%%%%%%$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######""""""######""""""###$$$%%%&&&&&&'''#########$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&''''''''''''%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''(((((((((&&&&&&&&&&&&&&&'''((()))&&&&&&&&&&&&&&&'''''''''&&&&&&''''''(((''''''&&&&&&&&&'''''''''(((((((((((((((((()))))))))************+++++++++++++++***,,,++++++******++++++,,,************++++++++++++++++++++++++++++++++++++************************))))))))))))((((((((((((((((((((()))***+++,,,---))))))(((((((((((())))))***))))))(((((((((((()))******))))))))))))((((((''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&""""""###$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$"""""""""###############$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%$$$$$$$$$$$$%%%%%%"""############$$$$$$$$$"""""""""###$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%########################$$$$$$#########$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%$$$$$$##############################""""""######$$$%%%###############$$$$$$$$$######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############"""""""""$$$############$$$%%%%%%############$$$$$$$$$$$$&&&%%%%%%$$$$$$#########$$$%%%%%%%%%$$$###!!! """""""""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&###$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!###%%%&&&''''''&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$###########################&&&(((&&&""" !!!$$$$$$$$$$$$$$$$$$$$$######&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&###$$$$$$%%%&&&'''''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$%%%%%%#########$$$$$$%%%%%%&&&"""######$$$%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%########################"""######$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&''''''''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''(((((()))&&&%%%%%%&&&&&&((())))))&&&&&&'''''''''(((((((((###%%%''')))***)))'''&&&&&&&&&&&&'''''''''(((((((((((((((((()))))))))***((()))***+++++++++++++++,,,++++++******++++++,,,))))))*********+++++++++++++++++++++++++++++++++******))))))))))))******((()))))))))))))))******))))))))))))***++++++,,,))))))(((((((((((()))))))))(((((((((((())))))************)))))))))((((((''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&'''''''''###$$$$$$%%%%%%%%%$$$$$$&&&%%%$$$$$$#########$$$!!!"""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$###""""""###$$$$$$"""############$$$$$$$$$###############$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################%%%%%%$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%$$$##############################""""""######$$$%%%""""""#########$$$$$$$$$"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$############""""""""""""$$$$$$######$$$$$$%%%&&&############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''((('''&&&$$$###"""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################"""######$$$%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%######$$$%%%%%%%%%%%%%%%"""""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!"""%%%'''''''''&&&%%%''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$###''')))'''""" """%%%$$$$$$$$$$$$$$$###"""!!!&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%&&&&&&'''(((((($$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%&&&&&&'''%%%%%%$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%!!!!!!!!!!!!!!!!!!!!!!!!""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&''''''''''''%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''((())))))%%%%%%%%%&&&'''((()))***'''''''''((((((((())))))"""$$$(((+++,,,***(((&&&&&&&&&&&&'''''''''(((((((((((((((((())))))))))))'''((()))***+++,,,,,,,,,,,,++++++++++++++++++,,,+++++++++,,,,,,---------++++++++++++++++++++++++))))))(((((((((((())))))(((((())))))******+++++++++***)))))))))))))))***))))))(((((((((((())))))(((((('''(((((()))***++++++*********))))))(((((())))))))))))))))))))))))''''''''''''''''''''''''%%%%%%%%%&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&''''''(((((((((%%%%%%%%%%%%$$$$$$###"""&&&%%%%%%$$$#########$$$!!!!!!""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$###########################"""!!! !!!"""###"""############$$$$$$$$$%%%$$$$$$$$$######""""""######$$$$$$$$$%%%%%%%%%########################&&&&&&%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%%%%#################################"""###$$$$$$%%%""""""######$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############""""""""""""$$$$$$######$$$$$$%%%&&&"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%"""###$$$%%%%%%###""" #########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""""""""###$$$%%%%%%&&&&&&#########$$$$$$%%%%%%%%%&&&&&&'''''''''&&&%%%%%%#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########***'''$$$"""!!!###%%%'''$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%$$$$$$$$$%%%########################%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%$$$######%%%$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%!!!!!!"""""""""#########%%%%%%%%%$$$$$$#########!!!"""$$$%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$######!!!###%%%&&&%%%$$$###!!!###$$$&&&&&&%%%$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$#########&&&###$$$((((((&&&$$$$$$&&&&&&$$$"""########################%%%%%%%%%%%%%%%%%%%%%%%%!!!"""$$$%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&$$$###"""###$$$$$$"""############$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''&&&%%%$$$$$$%%%&&&((()))""""""!!!!!!"""$$$&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&(((((('''&&&'''((())))))))))))(((((((((((((((((((((((())))))))))))------++++++++++++------************************************************))))))))))))))))))))))))''''''((()))***++++++,,,***)))((((((((()))+++,,,))))))))))))))))))))))))''''''''''''((((((((((((&&&&&&''''''''''''&&&&&&''''''&&&&&&&&&%%%%%%%%%((((((''''''''''''((((((((('''%%%$$$$$$%%%'''((('''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%########################%%%%%%%%%$$$$$$#########!!!"""$$$%%%&&&&&&%%%$$$"""""""""###$$$$$$$$$%%%######""""""""""""""""""######""""""""""""######%%%$$$$$$$$$$$$$$$$$$%%%!!!!!!!!!!!!!!!!!!!!!!!!$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$############%%%&&&%%%###!!!!!!"""$$$%%%%%%&&&%%%$$$"""!!!$$$$$$$$$$$$$$$$$$$$$$$$###"""!!! !!!"""%%%&&&!!!!!!!!!!!!""""""""""""##############################""""""######$$$%%%##############################################################################$$$$$$$$$$$$######&&&&&&%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%$$$###""""""###$$$%%%########################'''&&&&&&%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$((('''%%%###"""###%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$############$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$###### !!!###%%%&&&%%%$$$###!!!###$$$&&&&&&%%%$$$#########$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$######&&&%%%$$$######%%%&&&((((((&&&$$$$$$&&&&&&%%%"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$#########$$$%%%"""############$$$$$$$$$%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%&&&&&&'''######""""""###$$$%%%&&&''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&(((((('''&&&'''(((((((((((((((((())))))))))))))))))*********++++++,,,,,,,,,++++++,,,,,,,,,************************************************))))))))))))))))))))))))((((((((()))*********+++***)))((((((((()))++++++))))))))))))))))))))))))((((((((())))))))))))***'''(((((())))))(((((('''(((((('''''''''&&&&&&&&&((((((''''''''''''((((((((('''%%%$$$$$$%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$############$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$#########$$$$$$%%%$$$$$$############$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%########################$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######!!!###%%%%%%#########$$$###$$$$$$$$$######"""!!!$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$"""!!!!!!"""###$$$############$$$$$$$$$$$$#######################################$$$%%%%%%##############################################################################$$$$$$$$$$$$######%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$############$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%################################################$$$%%%%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&'''''''''%%%%%%%%%$$$$$$$$$$$$###%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$######!!!"""###%%%%%%%%%$$$$$$"""###$$$%%%&&&%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$%%%'''((((((((('''&&&'''%%%$$$$$$&&&&&&%%%###%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%%%%"""############$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&%%%&&&&&&&&&&&&%%%%%%$$$%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&'''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&(((((('''&&&'''((('''''''''(((((())))))******+++++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,++++++************************************************)))))))))))))))))))))))))))))))))))))))))))))))))))))))))((()))******+++))))))))))))))))))))))))))))))))))))************((())))))******))))))((())))))(((((((((''''''''''''''''''''''''''''''''''''&&&%%%$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$#########%%%%%%%%%%%%%%%&&&'''(((%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$### """$$$%%%$$$$$$%%%&&&$$$###""""""!!!"""""""""$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%###"""!!!!!!""""""#########$$$$$$$$$%%%%%%########################$$$$$$######$$$$$$%%%&&&##############################################################################$$$$$$$$$$$$######$$$$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$###$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''%%%%%%%%%$$$$$$#########$$$$$$%%%%%%%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""###$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$$$$%%%%%%$$$$$$######"""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$###############$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$##################$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$"""""""""###$$$###$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###"""###$$$%%%%%%%%%$$$$$$"""###$$$%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###%%%&&&'''&&&%%%$$$&&&%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&$$$###"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&""""""#########$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&%%%&&&''''''&&&%%%###"""&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""$$$%%%'''((()))))))))%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''%%%'''(((((('''&&&&&&'''&&&&&&''''''((()))************+++++++++,,,,,,,,,***+++,,,------,,,+++***************************************************)))))))))))))))))))))))))))))))))))))))((((((((()))))))))))))))******+++))))))))))))))))))))))))(((((()))))))))*********((())))))******))))))((((((((((((((('''''''''&&&'''''''''''''''''''''''''''&&&%%%%%%%%%%%%&&&'''########################$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$'''&&&$$$###"""###$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%'''((()))$$$$$$$$$######$$$$$$$$$$$$$$$############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!###%%%%%%$$$$$$$$$%%%$$$###"""!!!!!!"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###"""""""""######!!!!!!"""""""""#################################$$$$$$$$$$$$$$$%%%%%%&&&###########################################################################$$$$$$%%%%%%$$$$$$###############$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$#########$$$$$$$$$%%%%%%&&&&&&&&&'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ !!!!!!"""###$$$$$$%%%##################$$$$$$$$$$$$%%%&&&&&&&&&%%%$$$#########$$$$$$%%%%%%%%%$$$######"""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%$$$######!!!"""""""""#########$$$%%%%%%%%%$$$$$$#########""""""""""""############$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%###"""!!!"""###############$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%%%%######$$$$$$%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$%%%$$$%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$###"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%%%%%%%""""""#########$$$$$$$$$$$$############$$$%%%%%%%%%%%%&&&'''&&&%%%###"""%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""$$$&&&((()))))))))(((%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''%%%'''(((((('''&&&&&&'''%%%&&&&&&'''((())))))***))))))))))))************)))***,,,,,,,,,,,,***)))************************)))))))))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((()))))))))************))))))))))))))))))))))))'''''''''((((((((())))))'''(((((())))))((((((''''''''''''&&&&&&&&&%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$'''&&&$$$###"""###$$$$$$&&&%%%%%%%%%$$$$$$##################$$$%%%''''''######""""""""""""############""""""""""""######$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&$$$######$$$%%%$$$###""""""###%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$%%%""""""""""""####################################$$$$$$######$$$$$$%%%&&&########################################################################$$$$$$%%%%%%%%%%%%$$$$$$############$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$%%%&&&&&&%%%###"""$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&''''''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!""""""######$$$$$$""""""""""""############$$$$$$%%%&&&&&&&&&%%%%%%#########$$$$$$%%%%%%&&&$$$############$$$%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%$$$######!!!!!!""""""###$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$######"""""""""###############$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%$$$#########$$$&&&'''###%%%&&&&&&$$$$$$%%%'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%$$$$$$"""############$$$$$$$$$###############$$$%%%%%%$$$%%%%%%%%%%%%$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$''')))***)))((('''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''')))((('''%%%&&&&&&&&&&&&&&&''''''(((((()))''''''((((((((()))))))))******++++++++++++******************************))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((((((((()))************)))))))))))))))))))))))))))''''''''''''(((((((((((('''(((((())))))((((((''''''&&&&&&&&&&&&%%%%%%%%%%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$######"""######$$$%%%&&&###""""""""""""""""""#########""""""""""""##########################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%&&&'''&&&$$$###"""###$$$$$$$$$$$$$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""######$$$%%%%%%&&&$$$$$$$$$%%%%%%%%%%%%&&&##############################""""""######$$$%%%########################################################################$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%!!!"""$$$&&&&&&&&&$$$###$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%$$$######$$$$$$$$$$$$$$$$$$%%%%%%######$$$%%%%%%&&&'''''''''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%""""""#########$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$######"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%!!!""""""############""""""######$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&"""%%%&&&&&&$$$$$$&&&((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$###""""""############$$$$$$$$$###############$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%%%%!!!"""###%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%(((******)))'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&((()))((('''%%%%%%&&&''''''''''''''''''''''''''''''((((((((()))))))))++++++************++++++************************))))))))))))))))))))))))))))))))))))))))))))))))&&&'''''''''((()))))))))'''((()))***+++******)))))))))))))))))))))))))))'''(((((((((((()))))))))((())))))******))))))(((''''''''''''&&&&&&&&&&&&$$$%%%'''(((((('''%%%$$$%%%&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%######$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$######""""""######$$$%%%%%%$$$$$$$$$$$$%%%%%%####################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$%%%'''&&&%%%$$$$$$%%%""""""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&########################""""""!!!!!!""""""###$$$########################################################################$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%!!!$$$&&&''''''%%%$$$$$$$$$%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%&&&######$$$%%%%%%&&&'''''''''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&'''""""""###$$$%%%%%%&&&&&&%%%$$$$$$$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$%%%%%%%%%%%%$$$######$$$$$$%%%&&&&&&'''((((((#########$$$$$$%%%%%%&&&######$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%% !!!"""$$$$$$$$$###"""""""""###$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%&&&######$$$$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%!!!"""###$$$$$$$$$######"""$$$'''&&&$$$$$$&&&(((################################################!!!"""$$$%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%$$$"""!!!"""############$$$$$$$$$#########"""###$$$$$$%%%$$$$$$###"""###$$$&&&''' !!!"""$$$%%%%%%%%%$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&)))******)))'''%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&((()))((('''%%%%%%&&&'''''''''''''''&&&&&&&&&(((((((((((()))))))))))),,,+++***))))))***+++,,,************************))))))))))))))))))))))))))))))))))))))))))))))))%%%&&&&&&'''((()))******'''((()))++++++******)))))))))))))))))))))))))))))))))))))))******************++++++++++++******)))(((((((((''''''''''''$$$%%%'''(((((('''%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%!!!"""$$$%%%&&&&&&%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$###$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%'''&&&&&&%%%%%%&&&&&&'''########################"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%"""$$$&&&&&&%%%%%%&&&''' !!!"""$$$$$$$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$""""""""""""#########$$$$$$$$$########################!!!!!!!!!!!!!!!""""""###########################################################################$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&%%%$$$############$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%% ###&&&''''''&&&%%%$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''""""""""""""###$$$%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%$$$$$$'''&&&&&&%%%$$$###"""""""""""""""!!!"""######$$$((('''%%%$$$$$$%%%'''(((%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$(((%%%"""###%%%''''''&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$"""###$$$$$$%%%%%%$$$$$$############$$$$$$%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%###"""""""""!!!!!! $$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%'''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$######$$$%%%%%%########################&&&%%%###"""""""""######%%%%%%$$$######$$$%%%%%%%%%###""""""###$$$$$$######$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%""""""###$$$%%%%%%&&&&&&""""""""""""""""""""""""$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&+++***)))((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((((((((((((((((((((((()))((((((((()))***,,,---,,,,,,+++***)))(((''''''+++***)))(((((()))******))))))))))))))))))))))))((()))))))))))))))((('''((()))***+++++++++++++++))))))************)))))))))))))))))))))))))))***************))))))))))))******))))))((((((''''''((((((((((((((((((((((((''''''(((((((((((((((((($$$$$$%%%%%%%%%%%%%%%%%%((('''&&&%%%$$$#########&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&&&&'''&&&&&&%%%%%%$$$%%%%%%$$$######$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##################$$$$$$%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%$$$######$$$%%%%%%$$$$$$##########################################$$$$$$$$$$$$$$$$$$$$$$$$"""""""""######$$$$$$%%%#########$$$$$$%%%%%%%%%###"""""""""###$$$%%%%%%%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$############$$$%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$###############$$$%%%%%%(((&&&%%%$$$$$$%%%&&&(((%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""" !!!""""""!!!$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&%%%$$$######$$$$$$%%%%%%$$$$$$#########$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$#########""""""$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!###$$$%%%&&&######$$$$$$$$$%%%%%%%%%%%%%%%$$$######$$$%%%%%%########################&&&%%%$$$###"""######$$$%%%%%%$$$######$$$%%%%%%'''%%%$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%%%%$$$######%%%%%%%%%%%%%%%$$$$$$$$$#########$$$$$$%%%%%%%%%#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''((((((''''''((()))+++,,,++++++******)))(((((((((+++***)))(((((()))******))))))))))))))))))))))))(((((((((((())))))))))))******************++++++))))))************))))))******))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))((((((((((((((((((((((((''''''(((((((((''''''&&&''''''''''''(((((((((((((((((('''&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&$$$%%%%%%$$$######$$$&&&########################"""###$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%$$$######$$$%%%%%%################################################$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$%%%##################$$$%%%%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$#########$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&%%%%%%$$$######&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&'''&&&%%%$$$$$$%%%&&&'''$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$"""!!!!!!###$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$%%%%%%%%%$$$$$$###$$$$$$%%%%%%$$$$$$###"""###$$$%%%&&&%%%$$$###!!!"""###%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$!!!###%%%&&&######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%########################&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$######$$$$$$%%%&&&%%%######%%%&&&%%%$$$%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''((()))***))))))))))))))))))))))))******))))))))))))******))))))))))))))))))))))))((((((''''''((()))***+++,,,+++***)))((()))***+++((())))))******))))))(((*********))))))((((((((((((((((((((((((((((((((('''''''''((()))*********(((((((((((((((((((((((('''''''''''''''&&&%%%$$$&&&'''''''''((((((((()))(((''''''&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$###############$$$$$$$$$$$$$$$#########$$$$$$%%%&&&&&&&&&&&&&&&$$$%%%%%%$$$######$$$&&&##############################$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$#########%%%$$$$$$############$$$$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!! ###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$%%%&&&&&&#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&''''''((('''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%############""""""!!!!!!###$$$$$$%%%%%%$$$$$$###"""###%%%&&&&&&%%%$$$### ###%%%&&&%%%$$$#########$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""##################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################&&&%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$"""!!!!!!"""######"""%%%%%%%%%%%%$$$###""""""###############$$$$$$$$$###############$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$###''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((((((((((((((())))))******)))))))))))))))*********((((((((((((((((((((((((((('''&&&&&&''')))+++------,,,)))((('''((()))***(((((())))))))))))((((((*********)))((((((''''''''''''''''''(((((((((((('''((((((((()))))))))***((((((((((((((((((((((((''''''''''''&&&%%%$$$#########$$$$$$%%%%%%&&&&&&'''&&&&&&&&&&&&&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&########################%%%$$$$$$######"""""""""###$$$%%%%%%&&&&&&&&&&&&$$$%%%%%%$$$######$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$######""""""&&&%%%$$$$$$############$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#####################"""!!!#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&%%%%%%$$$###"""""""""###$$$$$$%%%%%%$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$$$$$$$$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$%%%%%%########################$$$$$$$$$$$$$$$$$$$$$%%%###$$$$$$%%%%%%$$$$$$######$$$%%%%%%%%%$$$###### ###%%%&&&%%%$$$#########$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%$$$$$$###""""""######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$"""!!!!!!"""######"""%%%%%%%%%%%%%%%$$$###"""""""""#########$$$$$$$$$########################%%%%%%$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%&&&&&&%%%$$$###(((((('''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((())))))******(((((())))))************((((((((((((((((((((((((((('''&&&&&&''')))+++------+++)))''''''((()))***(((((())))))))))))(((((())))))))))))((((((''''''&&&'''''''''((((((((()))***)))))))))((((((((('''((((((((((((((((((((((((''''''''''''&&&%%%$$$###!!!""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##################$$$$$$%%%$$$$$$######"""""""""###$$$$$$%%%&&&&&&%%%%%%$$$%%%%%%$$$######$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########""""""###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$######"""""""""&&&&&&%%%$$$#########$$$###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########"""###$$$$$$###!!!############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%$$$$$$'''&&&&&&%%%$$$###"""!!!!!!"""$$$%%%%%%%%%$$$###$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!"""$$$%%%$$$######$$$$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%######################## !!!###$$$&&&'''###$$$$$$%%%%%%$$$$$$###%%%%%%$$$$$$$$$$$$$$$$$$!!!"""###%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%######$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$##############################$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$##############################$$$$$$%%%%%%%%%%%%$$$###$$$$$$%%%%%%$$$$$$###%%%$$$""""""$$$%%%$$$######$$$$$$%%%%%%$$$$$$$$$""""""######$$$%%%%%%%%%###############"""""""""$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$&&&%%%%%%%%%$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((''''''&&&'''''''''(((((()))))))))'''((()))******+++******))))))))))))))))))))))))((((((''''''((()))***++++++***)))((('''((()))***'''(((((())))))(((((('''(((((((((((((((((((((((('''''''''(((((())))))************)))((('''''''''(((((((((((((((((((((((('''''''''''''''&&&%%%$$$######$$$%%%&&&''''''(((&&&%%%%%%$$$$$$$$$%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$######$$$&&&########################$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###"""""""""######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%###$$$$$$%%%%%%$$$$$$###"""""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$###############"""""""""&&&%%%%%%$$$$$$$$$$$$%%%######$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$###$$$%%%&&&%%%###""" ############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$#########"""###%%%&&&'''&&&%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""%%%((((((&&&%%%&&&'''$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%%%%########################!!!"""$$$&&&###$$$$$$%%%%%%$$$$$$###'''&&&$$$###"""###$$$%%%$$$$$$$$$$$$%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%$$$%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""#########$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%###$$$%%%%%%%%%%%%$$$###########################""""""$$$%%%%%%%%%$$$$$$###$$$%%%%%%%%%%%%$$$###%%%$$$""""""$$$$$$$$$###"""######$$$%%%%%%%%%%%%#########$$$%%%&&&&&&&&&$$$#########"""""""""!!!#########$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%######$$$%%%&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&'''(((((((((((('''&&&''''''((((((((((((((((((&&&''')))***++++++******))))))))))))))))))))))))(((((((((((())))))))))))(((((((((((())))))))))))''''''((((((((((((''''''&&&&&&''''''((()))))))))''''''((())))))***++++++))))))))))))((((((((((((((((((((((((((((((((((((''''''(((((((((''''''&&&$$$%%%&&&'''((())))))***((('''&&&%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""$$$%%%%%%$$$######$$$&&&########################$$$%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###""""""!!!"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%###$$$%%%%%%%%%%%%$$$###!!!""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$""""""""""""############%%%%%%$$$$$$$$$%%%&&&&&&"""###$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$%%%&&&''''''&&&$$$""""""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%$$$$$$###&&&&&&&&&%%%%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%###$$$&&&(((((('''&&&%%%###$$$$$$%%%%%%$$$$$$###&&&%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$!!!$$$''''''%%%$$$%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$$$$$$$%%%&&&$$$$$$$$$%%%%%%$$$$$$$$$(((&&&$$$"""!!!"""$$$&&&&&&&&&%%%$$$$$$$$$%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%###$$$%%%&&&&&&%%%$$$###########################!!!"""###$$$%%%$$$$$$######$$$%%%&&&&&&%%%$$$######!!! !!!""""""!!!!!!"""###$$$%%%&&&&&&&&&######$$$%%%&&&&&&''''''$$$#########""""""!!!!!!""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$######$$$%%%&&&"""###%%%''')))+++,,,---%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''(((((((((((((((((((((((('''''')))))))))((('''&&&((((((((((((((((((((((((&&&''')))***+++++++++***))))))))))))))))))))))))((()))))))))))))))((('''&&&'''((()))******))))))''''''((((((((((((''''''%%%%%%&&&'''((()))******'''(((((()))***++++++,,,''''''(((((())))))******((((((((((((((((((((((((''''''(((((()))((((((((($$$$$$%%%&&&'''((()))******)))((('''&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%$$$###"""!!!$$$%%%%%%$$$######$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$###""""""!!!"""###$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%###$$$%%%&&&&&&%%%$$$###!!!""""""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""""""""######$$$$$$%%%!!!!!!""""""######$$$$$$$$$$$$$$$$$$%%%&&&&&&'''"""###$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###############$$$###$$$%%%&&&%%%###!!!$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%"""###$$$%%%&&&'''''''''########################$$$$$$##################$$$$$$&&&&&&&&&&&&$$$$$$""""""#########$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&&&&'''((()))((('''&&&%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$######$$$%%%%%%%%%$$$""" $$$''''''''''''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%######""""""######$$$%%%######$$$$$$$$$%%%%%%%%%&&&%%%$$$$$$$$$%%%&&&'''############""""""!!!!!!######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''(((((((((((()))))))))(((''''''''''''(((''''''''''''((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((%%%&&&&&&&&&'''(((((((((''''''((((((((((((''''''''''''''''''(((((((((((((((((((((((((((((((((((()))(((''''''''''''(((((())))))))))))))))))))))))''''''((()))))))))))))))******))))))((((((''''''(((&&&%%%%%%&&&&&&&&&%%%$$$%%%'''))))))((('''&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&######$$$%%%&&&&&&&&&&&&%%%$$$######%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%########################%%%$$$$$$$$$###"""""""""$$$$$$$$$$$$$$$$$$$$$$$$'''&&&$$$#########$$$$$$&&&%%%%%%$$$$$$######"""%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%$$$$$$############$$$$$$%%%%%%$$$$$$###&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''((('''%%%$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$%%%%%%%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&$$$$$$$$$$$$&&&&&&&&&%%%###!!! !!!!!!%%%&&&&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$"""###$$$%%%%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###"""""""""###$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$""""""###$$$%%%%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$#########$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&(((((('''%%%%%%$$$$$$%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$######$$$%%%%%%$$$$$$$$$###!!!"""$$$&&&%%%%%%%%%%%%$$$$$$####################################""""""######$$$%%%######$$$$$$$$$%%%%%%%%%%%%$$$$$$###$$$%%%&&&'''$$$$$$#########"""""""""######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&)))(((''''''&&&&&&''''''&&&&&&&&&&&&''''''''''''&&&&&&''''''(((((())))))))))))))))))))))))))))))&&&&&&&&&'''''''''''''''''''''((((((((((((''''''''''''''''''(((((((((((((((((((((((((((((((((((())))))((((((''''''((((((((((((((((((((((((((((((''''''((()))))))))))))))***)))))))))(((((((((''')))'''&&&%%%&&&'''&&&%%%$$$%%%'''((()))((('''&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&%%%$$$$$$%%%$$$######%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$#########$$$$$$%%%%%%$$$$$$###%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&$$$###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$%%%%%%%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%$$$######$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$######$$$%%%%%%&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###""""""""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$$$$$$$$$$$$$"""######$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&%%%%%%%%%%%%((('''&&&%%%%%%$$$$$$%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%"""$$$&&&&&&$$$###$$$$$$###############"""""""""""""""""""""""""""""""""######""""""######$$$%%%######$$$$$$$$$%%%%%%%%%$$$############$$$%%%%%%$$$$$$$$$$$$$$$###############$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&''''''%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&'''$$$%%%&&&'''((()))******))))))))))))))))))))))))'''''''''''''''&&&&&&&&&''''''((((((((((((''''''''''''''''''((((((((((((((((((((((((((((((((((((******))))))((((((((((((((((((((((((((((((((((((''''''((()))))))))))))))))))))))))))((((((((((((+++)))'''&&&''''''&&&%%%$$$%%%'''(((((('''&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%$$$###"""%%%$$$######%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%#######################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$#########$$$$$$""""""###$$$$$$%%%&&&&&&$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$######$$$$$$%%%%%%$$$$$$###$$$$$$###############"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%$$$###"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$%%%%%%%%%%%%$$$&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%%%%%%%%%%$$$%%%%%%&&&(((((($$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""""""""######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$'''&&&&&&%%%$$$$$$$$$%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%%%%$$$######$$$###############"""""""""######$$$$$$$$$$$$%%%%%%######""""""######$$$%%%######$$$$$$$$$%%%%%%%%%###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''((((((((('''&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&'''''''''%%%%%%&&&''''''((())))))((((((((((((((((((((((((((((((((('''&&&&&&&&&%%%''''''((((((((((((''''''''''''''''''((((((((((((((((((((((((((((((((((((***************))))))(((((((((((((((((((((((((((''''''((()))))))))))))))))))))))))))((((((((((((,,,***((('''''''''&&&%%%%%%%%%&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&&&&%%%%%%$$$###%%%$$$######%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################"""""""""###$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$!!!"""""""""#########$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$############%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%$$$###"""###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""""""""######$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&'''&&&&&&%%%%%%&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$"""#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!""""""###$$$%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$###""" !!!###%%%###$$$$$$$$$$$$$$$$$$$$$######$$$$$$%%%%%%%%%%%%######""""""######$$$%%%######$$$$$$$$$%%%%%%%%%""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$###"""!!!!!!%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''(((&&&&&&%%%$$$$$$$$$$$$%%%&&&'''''''''(((((((((((('''''''''''''''&&&&&&&&&''''''''''''''''''''''''((((((((('''&&&&&&&&&%%%''''''((((((((((((''''''''''''''''''((((((((((((((((((((((((((((((((((((******+++,,,,,,+++******))))))))))))))))))))))))''''''((()))))))))))))))(((((((((((())))))))))))+++)))'''''''''((('''%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&###$$$%%%%%%&&&&&&&&&%%%%%%$$$######%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################"""""""""###$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$##################$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###%%%&&&%%%$$$###$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%!!!""""""###$$$$$$%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%&&&'''&&&&&&&&&&&&&&&&&&&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''''''''&&&&&&&&&&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%"""""""""######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!!!!"""###$$$%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%############$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$############!!! ###%%%$$$$$$$$$%%%%%%%%%%%%%%%"""""""""###$$$$$$%%%%%%######""""""######$$$%%%######$$$$$$$$$%%%%%%%%%"""###$$$$$$%%%%%%$$$$$$#########$$$$$$$$$$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$###"""!!!!!! %%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%'''''''''((((((((())))))'''''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&''''''((((((((((((''''''''''''''''''(((((((((((((((((((((((((((((((((((()))***+++------------,,,************************''''''((()))))))))))))))(((((((((((())))))))))))***(((&&&&&&'''((('''&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&"""###$$$%%%&&&&&&&&&&&&%%%$$$######%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$##########################################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%$$$$$$((((((''''''&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$&&&%%%$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%&&&''''''&&&&&&###$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&''''''###$$$%%%&&&''''''&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&$$$$$$%%%%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$%%%%%%############$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$###"""###$$$$$$""""""###$$$$$$$$$$$$%%%%%%%%%&&&&&&"""######$$$%%%%%%&&&&&&######""""""######$$$%%%######$$$$$$$$$%%%%%%%%%######%%%&&&&&&&&&%%%$$$"""""""""#########$$$$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%''''''&&&%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''''''''''''''((((((((((((''''''''''''''''''((((((((((((((((((((((((((((((((((((''')))+++.../////////...++++++++++++++++++++++++''''''((()))))))))))))))'''((((((((()))))))))***'''&&&$$$%%%'''((('''''''''&&&&&&%%%$$$$$$$$$%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%&&&&&&%%%%%%%%%%%%$$$######%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$##############################$$$$$$$$$###############$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%$$$&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%###$$$$$$%%%%%%$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################"""###$$$$$$######$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$#########$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&'''''''''&&&%%%###$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&'''(((!!!$$$&&&(((((('''&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%$$$"""!!!%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%"""######$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%(((((('''''''''&&&&&&&&&$$$$$$$$$###$$$$$$%%%%%%"""############$$$$$$$$$###$$$%%%&&&&&&%%%$$$###!!!###&&&'''&&&$$$############$$$$$$$$$%%%%%%%%%%%%%%%&&&''''''((())))))#########"""###$$$$$$%%%######$$$$$$$$$%%%%%%%%%###$$$%%%&&&'''&&&%%%%%%!!!!!!""""""#########$$$######$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$!!!""""""$$$%%%&&&''''''%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((('''&&&&&&%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''###$$$$$$%%%&&&'''((((((((((((((((((((((((((((((%%%&&&&&&''''''(((((((((''''''((((((((((((''''''''''''''''''((((((((()))((((((((((((((((((((((((&&&(((+++...000000000///,,,,,,,,,,,,,,,,,,,,,,,,'''(((((()))))))))))))))'''((((((((())))))******&&&$$$###$$$&&&((((((''''''&&&%%%%%%$$$$$$$$$%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$$$$$$$$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%$$$######%%%$$$######%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#################################%%%$$$$$$$$$######""""""$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&%%%%%%$$$!!!!!!!!!"""######$$$$$$%%%%%%&&&&&&&&&&&&''''''#########$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%$$$$$$$$$""""""######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######################## """######""""""###%%%$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$######$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$###$$$%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%#########$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''&&&&&&&&&%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%###$$$&&&''''''&&&$$$###$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$######""""""######$$$%%%"""$$$%%%%%%$$$###$$$%%%''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$"""!!!!!!"""$$$%%%$$$$$$$$$#########""""""######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''((('''&&&%%%%%%$$$$$$$$$$$$''''''''''''''''''''''''%%%%%%&&&&&&&&&'''''''''((((((((((((((((((''''''%%%%%%&&&&&&'''(((((((((''''''((((((((((((''''''(((&&&%%%&&&((())))))(((''''''''''''''''''''''''(((+++---......---...///000000//////.........---******))))))))))))************))))))((((((''''''+++******)))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$###$$$''''''%%%###)))(((&&&%%%$$$%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$###"""$$$$$$$$$$$$$$$$$$$$$$$$##################$$$$$$###$$$%%%###!!! !!!&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$###"""###%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$#########$$$%%%########################$$$$$$$$$############"""!!!###$$$$$$$$$%%%&&&$$$$$$$$$############"""###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%&&&((())))))'''&&&$$$###$$$$$$%%%%%%%%%$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$############$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$%%%%%%"""$$$%%%%%%$$$$$$%%%'''''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$$$$%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###""""""###$$$%%%%%%$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&''''''((((((((((((''''''***)))((((((***+++******'''''''''''''''''''''''')))+++.........---......000000000000//////.........---,,,***))))))((((((***)))))))))((((((((('''))))))))))))((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&'''%%%%%%&&&((((((&&&$$$((('''&&&$$$$$$$$$%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$######$$$$$$$$$$$$$$$$$$$$$$$$##################$$$$$$###$$$%%%$$$!!! !!!"""$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$######%%%$$$###$$$&&&'''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########$$$&&&'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############ """$$$$$$$$$###$$$%%%""""""######$$$$$$$$$%%%###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%&&&'''(((((('''&&&%%%$$$$$$%%%%%%&&&%%%%%%$$$&&&&&&&&&%%%%%%$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$#####################$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&###$$$%%%$$$$$$%%%(((***''''''&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%"""###############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$########################%%%$$$###""""""###$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&&&&%%%$$$$$$&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&)))(((((('''&&&&&&%%%%%%''''''((((((((((((''''''+++***(((((()))***)))((('''''''''''''''''''''''')))+++...///...------...000000000000////////////000///...,,,***((('''&&&))))))))))))((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&'''(((((('''%%%&&&%%%%%%$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$%%%$$$"""!!!!!!"""!!!!!!""""""######$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###&&&%%%$$$%%%'''''''''&&&$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""""""""###$$$%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$############"""###%%%%%%$$$######$$$ !!!"""###$$$%%%&&&&&&###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%&&&'''(((((('''&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########""""""#########$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&%%%$$$"""!!!%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''$$$$$$%%%$$$$$$&&&))),,,''''''&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%%%%############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&&&&&&&%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''((('''''''''((((((((((((((((((((('''''''''&&&&&&&&&''''''((((((((((((''''''***(((&&&&&&''''''&&&%%%''''''''''''''''''''''''))),,,...///...------...........................///......,,,***((('''&&&))))))))))))(((((((((((()))))))))((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$#########$$$%%%$$$"""!!!"""### !!!!!!"""###$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$###$$$&&&'''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""#########$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$############$$$&&&%%%$$$######$$$!!!""""""###$$$$$$%%%%%%###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$%%%&&&'''''''''&&&&&&$$$%%%%%%%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%%%%&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$#########""""""###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&%%%$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&'''((($$$$$$%%%$$$$$$&&&))),,,''''''&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%&&&&&&&&&%%%%%%%%%$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((('''''''''((((((((())))))&&&&&&&&&'''''''''((((((''''''(((((((((((('''''')))(((&&&%%%&&&'''&&&%%%((((((((((((((((((((((((***,,,...///...---------,,,,,,,,,,,,,,,,,,,,,,,,***+++++++++***)))((('''(((((((((((())))))))))))+++***)))((('''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$#########$$$%%%$$$###"""###$$$"""""""""###$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""""""""$$$%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$######%%%&&&&&&$$$######$$$###########################$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$%%%%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$###""""""%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$#########$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''###$$$%%%$$$$$$%%%(((***''''''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%$$$$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&'''((((((%%%%%%$$$$$$$$$%%%&&&&&&''''''''''''''''''''''''$$$%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%&&&'''''''''%%%%%%&&&&&&'''(((((()))''''''((((((((((((''''''***)))''''''((()))((('''((((((((((((((((((((((((***,,,//////...,,,,,,---***************+++++++++'''(((***++++++***)))((((((((((((((())))))))))))***))))))((('''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&###%%%&&&&&&%%%$$$$$$%%%###$$$%%%%%%&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%$$$$$$#########$$$%%%$$$###"""###%%%###$$$$$$$$$%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%###"""!!!"""###$$$$$$"""$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###$$$&&&&&&%%%$$$$$$%%%$$$$$$$$$#########""""""###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$%%%&&&&&&''''''%%%%%%%%%%%%$$$###""""""$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&######$$$$$$%%%&&&&&&&&&(((((((((((((((((((((((($$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%############$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&'''"""$$$%%%%%%$$$$$$%%%'''''''''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&''''''&&&$$$###%%%$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$ !!!"""###$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%$$$%%%$$$$$$$$$$$$###############$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%&&&''''''(((&&&&&&''''''''''''''''''''''''(((((((((((('''''')))'''&&&&&&((())))))(((((((((((((((((((((((((((+++---//////---,,,,,,,,,)))*********++++++++++++((()))+++,,,,,,+++)))((('''((((((((()))))))))***''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&###&&&((('''%%%$$$%%%'''###$$$%%%&&&'''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&''''''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%$$$$$$#########$$$%%%%%%######$$$%%%$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###"""!!!"""$$$%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%%%%$$$###$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&%%%%%%%%%$$$$$$$$$"""$$$&&&&&&%%%%%%&&&'''###############$$$$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$%%%&&&'''(((''''''''''''&&&%%%$$$###$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''$$$%%%%%%&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#########$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&""""""###$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%###$$$&&&''''''&&&$$$###$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%######""""""###%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&&&&"""$$$%%%&&&$$$###$$$%%%''''''&&&%%%%%%%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&''''''&&&$$$###$$$$$$$$$$$$%%%%%%&&&'''$$$$$$$$$$$$######""""""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$ !!!######$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""############$$$$$$$$$$$$$$$$$$$$$$$$########################$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$#########""""""######$$$$$$$$$%%%%%%%%%########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%'''''''''((((((((())))))&&&&&&''''''((()))******((((((((('''&&&&&&%%%%%%''''''((((((((((((''''''&&&%%%$$$$$$&&&'''''''''))))))))))))))))))))))))+++---//////---,,,,,,,,,******+++++++++,,,,,,,,,***+++,,,------,,,***((('''((((((((())))))******###$$$%%%&&&''')))******&&&&&&&&&&&&&&&&&&&&&&&&$$$'''))))))&&&%%%&&&(((###$$$&&&'''((('''&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&'''''''''&&&$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&%%%%%%$$$#########$$$%%%%%%$$$###$$$&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%$$$###"""###%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% !!!###%%%&&&&&&&&&%%%########################&&&&&&&&&%%%%%%%%%$$$$$$!!!###%%%&&&%%%%%%&&&(((!!!!!!"""###$$$%%%%%%&&&$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$%%%&&&'''((())))))))))))((('''&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&'''''''''&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%%%%%%%&&&'''"""######$$$$$$$$$######&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########"""###$$$%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%$$$$$$(((((((((''''''&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%$$$######&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&''''''&&&&&&%%%&&&%%%$$$######$$$%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$"""############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&$$$#########$$$$$$%%%%%%%%%$$$$$$#######################################$$$$$$$$$%%%%%%%%%!!!###%%%%%%$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&'''&&&%%%$$$###%%%&&&&&&''''''&&&&&&%%%'''''''''''''''''''''''')))(((&&&%%%$$$%%%%%%&&&&&&&&&%%%$$$%%%&&&'''(((---,,,)))(((((())),,,---***+++---///000000///...+++)))((((((+++---......---------,,,+++***)))(((&&&&&&'''((()))***++++++...---,,,+++***(((''''''%%%&&&&&&''''''&&&&&&%%%&&&'''''''''&&&%%%%%%$$$%%%%%%%%%&&&&&&&&&''''''!!!"""###%%%%%%$$$######"""###%%%&&&'''&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$---(((###!!!"""%%%%%%%%%%%%&&&'''&&&$$$###$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%########################%%%%%%$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!"""###%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$#########$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%"""######$$$$$$%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$%%%%%%&&&&&&%%%%%%,,,,,,***)))'''%%%$$$#########$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%!!!"""""""""############%%%%%%%%%&&&&&&&&&'''''''''&&&%%%%%%%%%%%%&&&'''###$$$$$$%%%&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######"""###$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&'''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%$$$### """############%%%$$$$$$######$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$############$$$%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$#########$$$$$$%%%%%%%%%$$$$$$$$$####################################$$$$$$$$$%%%%%%%%%"""$$$%%%%%%$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&'''''''''&&&%%%$$$%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''((('''&&&&&&&&&'''((()))&&&&&&%%%%%%%%%&&&'''((()))((('''&&&&&&'''((()))***+++---///000///...---...,,,******,,,---...---,,,,,,,,,++++++*********((((((((((((((()))))))))******))))))((((((''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%&&&&&&&&&''''''""""""###$$$$$$$$$$$$$$$###$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$***'''###!!!###$$$$$$$$$%%%&&&'''&&&$$$###$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$######$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%&&&%%%$$$###$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&'''''''''''''''******)))(((&&&%%%$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%$$$###"""&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$#########$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$&&&''''''(((&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%$$$$$$!!!"""###$$$%%%&&&&&&&&&$$$######""""""######$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$###""""""###$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%$$$#########$$$$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%###%%%&&&&&&$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$%%%%%%&&&&&&&&&'''&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$''''''((((((((('''&&&%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''''''''&&&''''''(((******&&&&&&%%%%%%&&&&&&'''(((''''''&&&&&&&&&&&&''''''***+++,,,.........------000///---,,,---...---,,,,,,++++++*********++++++)))))))))(((((((((''''''&&&&&&&&&'''''''''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''###############$$$%%%%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''%%%#########$$$###"""###%%%&&&&&&$$$$$$%%%'''%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%########################$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$######"""$$$$$$$$$$$$%%%%%%%%%%%%###$$$%%%$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&(((''''''&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$##############################$$$$$$$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$%%%&&&&&&$$$""""""###%%%%%%%%%%%%%%%%%%%%%%%%$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''######$$$%%%%%%&&&''''''(((''''''&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''''''''''''''''''''((((((&&&&&&&&&&&&&&&''''''((((((((()))******)))((((((******+++,,,------,,,,,,///---,,,,,,---...---,,,---,,,+++***))))))******((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%$$$###"""###$$$%%%&&&$$$%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$###"""!!!###$$$%%%%%%%%%%%%&&&'''%%%%%%&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$############$$$$$$$$$$$$%%%%%%%%%"""###$$$$$$""""""###$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%!!!"""######$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$"""!!! %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$###$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%%%%###############""""""!!!%%%%%%$$$$$$$$$$$$%%%%%%###$$$$$$%%%%%%$$$$$$############$$$$$$#########$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%$$$%%%&&&&&&$$$""""""###%%%%%%%%%%%%%%%%%%%%%%%%$$$######""""""######$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$%%%%%%&&&'''######$$$%%%%%%&&&'''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''((((((((('''&&&%%%$$$$$$&&&&&&'''''''''(((((('''((()))+++,,,,,,+++)))(((*********+++++++++++++++***))))))***---...---,,,...---,,,***)))(((((((((%%%&&&&&&'''((()))))))))))))))(((''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''%%%$$$#########$$$&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%$$$###""""""###$$$%%%%%%%%%%%%&&&'''%%%%%%%%%&&&&&&'''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%#########$$$$$$$$$%%%%%%"""###$$$$$$""""""###$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%!!!"""######$$$$$$######$$$$$$$$$%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%%%%%%%%%%$$$$$$"""###$$$%%%&&&'''''''''$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%$$$######$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%!!!"""###$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$###$$$%%%%%%%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$######$$$%%%%%%%%%$$$$$$###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%###%%%&&&&&&$$$######$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''((((((((('''&&&$$$"""!!!&&&&&&'''((((((((((((''''''((()))******)))((('''******)))***************'''''''''))),,,---,,,+++,,,,,,,,,+++***)))'''&&&$$$%%%&&&'''((())))))*********)))(((''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%%%%$$$######$$$###%%%&&&&&&$$$$$$%%%'''$$$$$$%%%%%%&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$###########################$$$$$$%%%%%%$$$$$$###$$$$$$$$$%%%%%%&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$###"""######$$$%%%%%%&&&&&&############$$$$$$$$$$$$###$$$%%%$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$%%%%%%&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&'''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''((((((((()))%%%%%%%%%&&&&&&&&&''''''###$$$%%%%%%%%%%%%$$$###$$$$$$%%%''''''(((((('''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%##############################$$$$$$$$$%%%%%%%%%$$$%%%%%%%%%%%%$$$###"""$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''###$$$%%%%%%&&&&&&&&&%%%$$$$$$&&&'''((()))))))))%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$%%%&&&&&&&&&&&&%%%$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%"""$$$%%%%%%$$$###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&((('''&&&%%%$$$%%%%%%&&&%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''(((((((((((('''&&&$$$###%%%&&&'''((()))(((((('''''''''((((((((((((''''''***))))))(((((()))))))))((('''((()))++++++***((('''(((***,,,,,,+++)))'''&&&&&&&&&''''''(((((((((((((((((((((''''''''''''%%%&&&&&&''''''&&&&&&%%%$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''###$$$%%%%%%&&&&&&%%%%%%'''&&&%%%$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###%%%&&&%%%######$$$&&&%%%&&&'''&&&$$$###$$$%%%######$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%%%%%%%$$$###"""######$$$%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$%%%############$$$$$$$$$$$$$$$%%%&&&%%%$$$###$$$&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%&&&'''''''''''''''%%%%%%%%%%%%&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&&&&'''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''###$$$%%%&&&&&&%%%$$$###'''''''''&&&%%%$$$"""!!!$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%#################################$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$###"""%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&&&&'''(((&&&&&&&&&''''''(((((((((###$$$%%%%%%&&&&&&&&&&&&$$$$$$%%%%%%$$$$$$###"""$$$$$$############$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%''''''''''''%%%%%%&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%&&&%%%%%%$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%!!!###%%%%%%$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%%%%%%%%%%%%%%%%!!!"""###$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&)))((('''&&&%%%&&&''''''%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''''''''((())))))((('''&&&%%%&&&((()))))))))((('''))))))))))))))))))))))))***)))(((((((((((())))))***))))))***++++++(((&&&###%%%))),,,...---+++)))(((''''''''''''&&&&&&&&&%%%%%%&&&&&&'''((())))))%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%&&&'''''''''&&&%%%%%%%%%&&&&&&&&&''''''###$$$%%%&&&'''&&&%%%$$$((('''%%%$$$###$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&'''&&&######%%%(((%%%&&&'''&&&$$$###$$$%%%""""""###$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%&&&&&&%%%$$$###!!!""""""###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########&&&&&&%%%$$$$$$#########"""############$$$$$$$$$$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$############$$$%%%%%%&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%&&&''''''((((((''''''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$%%%&&&%%%###&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&%%%$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$###""""""$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&''''''''''''&&&&&&$$$$$$$$$$$$&&&&&&$$$$$$%%%%%%&&&'''(((((("""""""""###$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%%%%$$$$$$###$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$########################'''&&&%%%$$$$$$&&&((()))((((((''''''&&&&&&&&&%%%''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''))))))))))))((((((((((((((())))))(((((('''&&&%%%++++++***)))((('''&&&&&&))))))(((((('''''''''&&&(((((((((((((((((((((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$'''&&&$$$""""""###$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&$$$$$$$$$$$$&&&&&&***)))((('''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''%%%""""""###%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$#########$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%###""""""###$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$###""""""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$######$$$$$$###"""&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$!!!!!!###$$$%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$$$$%%%&&&&&&&&&############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''(((((((((((($$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###"""!!! !!!###$$$((((((((('''''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&)))(((((((((((('''''''''''''''((()))))))))(((((())))))))))))(((((((((((()))(((((((((''''''''''''(((((((((((((((((((((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%###!!!!!!!!!!!!&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$######$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%###""""""###$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$######$$$$$$"""!!!%%%%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%%%%&&&&&&)))((('''%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%""""""$$$%%%&&&'''''''''&&&%%%$$$######$$$%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%$$$$$$$$$%%%&&&((((((((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&((((((((((((''''''''''''&&&'''((()))************'''''''''(((((()))))))))((((((((((((''''''''''''(((((((((((((((((((((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$######""""""""""""###""""""""""""""""""""""""%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$"""!!!###$$$$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%$$$""""""$$$%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$"""""""""$$$$$$###"""%%%%%%$$$$$$%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$######$$$%%%&&&+++***'''%%%$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%$$$'''&&&$$$######$$$&&&'''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&############$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''$$$$$$%%%&&&&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&''''''&&&$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%+++***))))))((()))))))))((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&)))))))))(((((((((''''''(((((()))***************'''''''''((((((((())))))((((((((((((((('''''''''(((((((((((((((((((((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%***(((&&&&&&'''(((((('''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$"""###$$$%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((('''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""!!!!!!"""$$$&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$$$$%%%'''(((+++***'''%%%$$$%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''''''''&&&%%%%%%&&&&&&%%%$$$$$$%%%&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''&&&%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&%%%%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&&&&''''''''''''$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$%%%&&&&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&''''''&&&$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&&&&''''''''''''(((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''*********)))))))))((((((***************)))(((((((((((((((((('''''''''''''''''''''((((((((((((((((((((((((((((((((((((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%###$$$%%%&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&$$$######$$$%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###""""""###%%%''''''&&&$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''((()))***+++)))((('''%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######%%%&&&'''(((((((((%%%%%%&&&&&&&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$#########$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&"""""""""#########$$$$$$$$$$$$%%%%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&'''''''''((((((((())))))))))))((((((((((((************)))((('''&&&(((((((((''''''&&&&&&&&&'''''''''((((((((((((((((((((((((((((((((((((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%$$$$$$$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%###"""###$$$%%%$$$"""$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%######%%%&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%""""""###$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$%%%&&&&&&%%%$$$$$$$$$$$$###$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%"""###%%%''')))******+++&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$%%%&&&'''''''''$$$%%%&&&''''''&&&%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&'''$$$$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$"""######$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%""""""""""""############$$$$$$%%%%%%%%%%%%&&&&&&#########$$$$$$$$$%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''((()))))))))%%%%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%&&&'''((()))******(((''''''''''''&&&&&&&&&(((((()))))))))(((''''''&&&&&&'''''''''''''''(((''''''''''''((((((((()))(((((((((((((((((((((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$%%%&&&&&&########################%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$%%%''''''%%%$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&'''%%%###$$$%%%&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%***(((&&&&&&&&&&&&$$$"""$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%"""$$$'''((((((((($$$$$$%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&%%%%%%$$$######%%%'''))))))'''%%%###&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&''''''''''''$$$$$$&&&&&&&&&&&&$$$$$$""""""###$$$%%%%%%&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$""""""###$$$%%%%%%&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&&&&'''$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&'''''''''((((((%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''""""""$$$&&&'''((((((((($$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''$$$%%%&&&'''(((***++++++&&&&&&%%%%%%%%%$$$$$$$$$%%%&&&'''((())))))))))))$$$$$$%%%&&&'''((()))***&&&'''''''''(((((())))))(((((((((((((((((((((((((((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&$$$$$$$$$&&&((()))%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&$$$$$$$$$$$$&&&'''&&&%%%%%%%%%&&&''''''((($$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%$$$"""$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&'''''''''$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&'''%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''######$$$$$$$$$%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$&&&'''(((***++++++)))((('''&&&%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&'''&&&%%%$$$$$$$$$%%%%%%###$$$%%%%%%######$$$%%%&&&&&&&&&'''''''''(((((($$$$$$$$$######$$$%%%%%%'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&############$$$%%%%%%&&&***)))&&&$$$$$$%%%''')))%%%%%%&&&&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$######$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$)))&&&$$$$$$%%%%%%""" $$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&#########$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$######$$$%%%&&&%%%%%%$$$###""""""######"""############$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%'''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&%%%%%%%%%%%%&&&'''(((((((((((((((((((((((((((((('''''''''&&&&&&&&&'''''''''''''''''''''''''''((()))******)))((('''(((((((((((())))))))))))((((((((((((''''''''''''&&&''''''((('''&&&$$$###((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%'''((()))))))))'''&&&%%%%%%''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%&&&&&&'''''''''%%%$$$$$$###$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$############$$$%%%&&&'''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########%%%$$$$$$######$$$$$$%%%$$$$$$############$$$$$$%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%$$$$$$############$$$%%%%%%&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&***(((&&&$$$###$$$&&&'''######$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!###$$$$$$$$$$$$%%%'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''(((((('''''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&######%%%&&&&&&&&&&&&%%%$$$%%%&&&%%%$$$###$$$&&&###$$$$$$$$$$$$%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$#########$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%$$$$$$$$$&&&''')))#########$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$&&&$$$###$$$&&&'''&&&$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%########################$$$$$$$$$$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%$$$######$$$%%%%%%%%%%%%$$$###########################$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$########################%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%'''&&&%%%%%%%%%%%%&&&'''''''''''''''''''''''''''(((((('''''''''&&&&&&&&&''''''''''''''''''''''''(((((())))))))))))(((((('''((((((((())))))))))))((((((((((((''''''''''''&&&&&&''''''&&&&&&%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$###%%%$$$###$$$&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$#########$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%$$$$$$############$$$$$$$$$$$$%%%&&&&&&%%%$$$$$$%%%%%%%%%$$$$$$$$$#########$$$%%%%%%&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$$$$$$$$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&'''''''''%%%$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$######"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&!!!%%%'''((((((&&&%%%$$$&&&'''&&&%%%$$$%%%&&&######$$$$$$$$$%%%%%%%%%'''&&&&&&%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$######$$$$$$$$$$$$$$$$$$$$$$$$'''''''''&&&&&&%%%%%%$$$'''&&&%%%%%%%%%%%%%%%%%%"""######$$$%%%&&&'''(((""""""###$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$$$$######%%%$$$###$$$&&&'''&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%$$$$$$############$$$############$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$###'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''(((((((((''''''''''''&&&'''''''''''''''''''''''')))(((((((((((((((((()))''''''((((((((()))))))))((((((((((((''''''''''''&&&&&&&&&%%%&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%%%%$$$###"""$$$###"""###%%%&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%############$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$$$$%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%$$$$$$$$$$$$###$$$$$$%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$############$$$$$$###$$$$$$%%%%%%$$$$$$###%%%%%%%%%%%%$$$$$$$$$$$$###$$$%%%%%%&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$)))******)))&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$###"""!!!%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&!!!###%%%'''''''''&&&%%%%%%&&&''''''%%%%%%&&&'''&&&''''''''''''((((((((((((''''''&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&%%%%%%$$$$$$((('''&&&&&&%%%%%%%%%%%%"""###%%%&&&''''''&&&&&&$$$$$$%%%%%%&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%$$$######''''''%%%%%%$$$###"""!!!$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%************************&&&&&&&&&%%%%%%$$$$$$###&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$######$$$$$$$$$#########$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$######"""&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((((((''''''''''''''''''''''''''''''''''''''')))((('''&&&&&&'''((()))'''''''''((((((((())))))((((((((((((''''''''''''&&&%%%%%%%%%%%%''')))***&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&'''''''''((($$$###"""###%%%'''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$%%%%%%&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%$$$$$$######$$$$$$%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&%%%%%%$$$%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&'''''''''''''''''''''''')))******)))&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''(((((((((''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&''''''%%%%%%&&&'''(((((((((((()))))))))))))))(((''''''&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((((('''&&&%%%%%%$$$$$$((('''&&&&&&%%%%%%%%%%%%%%%&&&'''(((((('''&&&$$$$$$$$$%%%&&&&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&%%%$$$###"""!!!!!!$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%###$$$$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$#########&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''(((((((((((((((((((((((((((((((((((((((((((((((()))((('''&&&&&&'''((()))''''''''''''((((((((((((((((((((((((''''''''''''&&&%%%%%%%%%&&&(((***+++''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&'''((((((%%%$$$$$$%%%&&&''''''&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&%%%$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&'''&&&###!!!!!!###&&&((($$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''%%%'''''''''&&&%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''(((((()))'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&((('''%%%$$$###$$$%%%&&&$$$&&&'''&&&%%%$$$%%%&&&%%%&&&&&&&&&'''''''''''')))((('''&&&&&&&&&&&&&&&######$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''''''''&&&&&&%%%%%%$$$'''&&&%%%%%%%%%%%%%%%%%%''''''((()))((('''%%%$$$######$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$#########$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&"""$$$%%%%%%$$$###%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&$$$$$$$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((()))))))))(((((((((((((((((((((((((((''''''''''''''''''(((&&&&&&'''''''''(((((((((((((((((((((''''''''''''&&&&&&&&&&&&'''((()))***((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%)))'''&&&$$$######$$$$$$'''&&&%%%%%%''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%$$$$$$$$$$$$&&&&&&%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$$$$$$$%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%%%%%%%$$$$$$$$$$$$%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%&&&&&&&&&&&&###$$$%%%%%%&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%###!!! """$$$&&&%%%%%%%%%%%%&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%&&&%%%%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&!!!"""###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&$$$%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&%%%$$$###$$$&&&$$$$$$$$$$$$%%%%%%%%%&&&)))((('''&&&%%%%%%%%%%%%#########$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%%%%&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%$$$$$$$$$$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''''''''$$$&&&''''''%%%%%%&&&((($$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&''''''&&&%%%%%%$$$$$$$$$$$$$$$%%%&&&'''$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&''''''%%%%%%&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''((((((((())))))))))))((((((((((((((((((((((((&&&''''''((((((''''''&&&&&&&&&&&&'''''''''((((((((((((((((((''''''''''''&&&&&&'''(((((((((((((((''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%((('''%%%#########%%%&&&(((&&&%%%%%%&&&%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%&&&'''((($$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$######$$$$$$$$$%%%%%%%%%###$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$######$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%$$$$$$%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''###$$$%%%%%%&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&"""###$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''$$$$$$$$$$$$$$$$$$$$$$$$"""$$$%%%&&&%%%%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&"""######$$$%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$###""""""!!!""""""$$$%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&& """%%%'''((((((&&&%%%###$$$%%%%%%######$$$%%%$$$$$$%%%%%%%%%&&&&&&&&&)))((('''&&&%%%$$$$$$$$$%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&############$$$%%%%%%&&&######$$$$$$%%%&&&'''((((((''''''&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&'''(((((()))***+++***&&&$$$%%%'''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&''''''&&&%%%%%%$$$$$$$$$$$$%%%%%%&&&'''$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%$$$$$$%%%%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&''''''((()))%%%%%%&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''((((((((())))))******))))))))))))))))))))))))%%%&&&'''(((((('''&&&%%%&&&&&&&&&'''''''''(((((()))(((((((((''''''''''''%%%&&&((()))))))))((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$$$$&&&(((***,,,(((&&&$$$$$$$$$$$$"""!!!''''''''''''''''''''''''$$$%%%%%%&&&&&&%%%%%%$$$'''''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%&&&'''((()))$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$#########$$$%%%%%%&&&&&&%%%%%%$$$#########$$$$$$%%%%%%%%%###$$$%%%&&&'''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$#########%%%$$$$$$$$$$$$$$$$$$%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%$$$######$$$%%%&&&%%%%%%%%%&&&&&&'''''''''$$$$$$%%%&&&&&&&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&###%%%))),,,,,,***'''%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&%%%%%%&&&(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&%%%%%%''''''''''''''''''''''''$$$$$$&&&''''''&&&$$$$$$&&&'''''''''&&&%%%%%%$$$(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&%%%$$$"""!!!'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$&&&''''''((((((''''''&&&'''&&&&&&&&&&&&%%%%%%%%%&&&&&&'''(((((('''&&&&&&&&&&&&''''''''''''&&&&&&***))))))))))))(((((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&%%%$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&%%%$$$$$$######$$$$$$%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&'''''''''&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$%%%&&&((()))$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$"""###$$$%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&''''''''''''''''''''''''(((&&&$$$""""""$$$&&&(((&&&'''''''''&&&%%%%%%$$$$$$$$$$$$%%%$$$$$$######&&&%%%%%%$$$$$$%%%%%%&&&###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&'''''''''&&&%%%$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&'''((((((''''''%%%&&&''''''((((((''''''''''''''''''(((((((((((((((((((((((((((((((((((())))))((('''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&''''''(((((())))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&"""###%%%&&&&&&%%%###"""%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%&&&(((((()))$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%$$$%%%'''(((((('''%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&'''((()))))))))(((&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&#########$$$%%%&&&'''(((&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%$$$###$$$&&&(((''''''''''''&&&%%%$$$###&&&%%%$$$$$$&&&&&&%%%$$$'''&&&$$$###"""######$$$$$$$$$$$$############"""$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&'''((()))))))))(((&&&%%%$$$%%%%%%&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%$$$'''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%$$$###"""'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''')))((('''&&&&&&&&&&&&'''$$$%%%&&&&&&''''''&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&'''((($$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$######$$$&&&'''&&&&&&''''''&&&&&&%%%$$$&&&&&&''''''((('''''''''&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&%%%%%%$$$&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&''''''(((''''''&&&&&&&&&''''''''''''(((''''''''''''(((((((((((((((((((((((((((((((((((())))))((('''''''''''''''&&&&&&&&&''''''''''''(((''''''''''''((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&'''((()))$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&%%%$$$$$$$$$$$$$$$$$$%%%&&&((((((&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%&&&&&&'''&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%$$$######%%%(((&&&&&&&&&&&&%%%$$$###"""&&&%%%$$$$$$&&&&&&%%%$$$%%%%%%$$$$$$######$$$$$$$$$$$$$$$$$$############$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$""""""""""""""""""""""""%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&'''(((((((((((('''&&&%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%$$$$$$'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&'''''')))((('''&&&&&&'''((()))&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&(((((('''&&&&&&&&&''''''$$$%%%%%%&&&&&&'''''''''$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%$$$$$$$$$$$$%%%%%%'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&'''&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%######$$$%%%&&&&&&&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''''''''''''''&&&%%%&&&'''((()))&&&''''''''''''((((((((((((((((((((((((((((((((()))((((((''''''''''''(((&&&&&&&&&''''''''''''(((((((((((('''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%&&&'''((((((%%%%%%%%%%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$######%%%%%%$$$############$$$$$$%%%&&&''''''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$###$$$$$$###"""###%%%&&&%%%%%%%%%%%%$$$###""""""&&&%%%$$$$$$&&&&&&%%%$$$######$$$%%%%%%%%%%%%$$$%%%$$$$$$$$$############%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$######$$$%%%&&&%%%&&&&&&'''&&&&&&%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%"""######$$$%%%%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$&&&''''''((((((''''''&&&%%%%%%&&&&&&''''''((((((((('''%%%$$$$$$%%%'''(((&&&&&&''''''''''''&&&&&&(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%'''&&&&&&&&&%%%&&&&&&&&&$$$%%%&&&&&&$$$$$$%%%&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&'''&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((''''''&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$######%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&&&&&&&&&&$$$$$$%%%&&&&&&'''&&&&&&%%%%%% !!!"""$$$$$$%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&$$$%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&'''''''''((('''%%%$$$%%%&&&(((***&&&&&&&&&'''''''''(((((((((((((((((((((((((((((()))(((''''''''''''((((((&&&&&&&&&''''''''''''((((((((((((''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&'''((((((&&&&&&%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%$$$######""""""######$$$%%%&&&&&&&&&&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%###"""""""""###$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""###$$$###""""""$$$%%%%%%%%%%%%%%%%%%$$$######&&&%%%$$$$$$&&&&&&%%%$$$!!!"""$$$%%%&&&&&&%%%%%%%%%%%%$$$$$$$$$#########%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%%%%%%%'''''''''&&&%%%$$$''''''''''''''''''''''''''''''''''''''''''''''''%%%$$$###""""""###$$$%%%%%%%%%&&&&&&'''&&&&&&%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%&&&'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$&&&''''''((((((''''''&&&%%%%%%&&&&&&'''((())))))'''&&&$$$######$$$&&&'''&&&&&&''''''''''''&&&&&&(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&)))((('''%%%$$$$$$$$$$$$$$$%%%&&&&&&$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%###$$$&&&''''''&&&$$$###%%%%%%&&&&&&'''&&&&&&%%%$$$$$$&&&'''((((((((((((&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$%%%%%%%%%&&&&&&%%%&&&'''(((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''((('''&&&&&&&&&&&&''''''((('''%%%$$$%%%&&&(((***&&&&&&&&&&&&''''''''''''((((((((((((((((((((((((((((((''''''''''''((((((&&&&&&&&&''''''''''''(((((((((''''''&&&&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&'''''''''&&&&&&%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$######""""""######$$$%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$#########$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!###$$$$$$######$$$%%%&&&&&&&&&&&&&&&%%%%%%$$$&&&%%%$$$$$$&&&&&&%%%$$$ !!!###%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&'''''''''''''''&&&%%%%%%$$$$$$$$$%%%&&&'''''''''%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$############$$$$$$%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$######$$$%%%%%%'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&'''((()))******'''&&&%%%$$$$$$%%%&&&'''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%''''''&&&&&&&&&'''((((((***)))'''%%%$$$$$$$$$%%%$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%&&&''''''(((((('''&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&%%%$$$%%%&&&'''(((########################$$$$$$&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&''''''&&&&&&###$$$%%%&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&''''''(((((((((((('''&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''')))((('''%%%%%%&&&''''''''''''&&&%%%&&&'''((()))%%%&&&&&&&&&&&&'''''''''(((((((((((((((((((((((((((''''''''''''(((((()))&&&&&&&&&''''''''''''((('''''''''&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''%%%%%%$$$############$$$%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%$$$$$$%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&!!!###%%%%%%$$$###$$$%%%&&&&&&&&&''''''&&&&&&%%%&&&%%%$$$$$$&&&&&&%%%$$$!!!"""###$$$%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$#########$$$%%%'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$$$$%%%'''(((***++++++''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&'''((()))'''&&&%%%$$$$$$%%%'''((($$$%%%&&&&&&$$$$$$%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&'''(((((((((''''''&&&&&&&&&%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&''''''''''''''''''''''''$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''''''''&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&'''&&&%%%$$$$$$&&&''')))%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&"""######$$$$$$$$$######&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$&&&&&&&&&&&&'''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''***((('''%%%%%%%%%'''(((&&&&&&&&&''''''''''''(((%%%%%%&&&&&&&&&'''''''''(((((((((((((((((((((((('''''''''''''''((())))))&&&&&&&&&''''''''''''(((%%%&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''$$$$$$$$$$$$$$$%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$$$$$$$%%%&&&&&&'''$$$$$$$$$%%%%%%&&&&&&&&&!!!$$$&&&&&&%%%$$$%%%%%%$$$%%%%%%&&&&&&&&&%%%%%%&&&%%%$$$$$$&&&&&&%%%$$$############$$$%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&((((((((((((&&&%%%$$$%%%%%%&&&'''''''''&&&(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''&&&$$$#########$$$$$$'''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&&&&%%%%%%$$$&&&''''''((((((''''''&&&$$$$$$%%%'''(((***+++,,,(((((())))))))))))((((((&&&''''''''''''''''''&&&***))))))))))))(((((((((%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$%%%%%%%%%$$$$$$$$$$$$$$$%%%&&&'''%%%$$$######$$$''')))+++$$$%%%&&&&&&$$$$$$%%%&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%&&&&&&'''''''''%%%%%%&&&&&&'''((())))))'''''''''&&&&&&%%%%%%%%%$$$%%%%%%&&&'''''''''&&&''''''''''''''''''''''''$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&'''((('''&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&'''&&&%%%$$$$$$&&&''')))))))))))))))))))))))))))%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''''''''&&&&&&&&&'''''''''&&&%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$###"""&&&&&&&&&'''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''***)))'''%%%%%%%%%'''(((%%%&&&''''''((((((''''''%%%%%%%%%&&&&&&&&&''''''(((((((((((((((((((((((('''''''''''''''((()))***&&&&&&&&&'''''''''((((((%%%%%%%%%&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%'''(((((('''%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$######$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%#########$$$$$$%%%%%%%%%'''&&&%%%%%%$$$$$$%%%%%%%%%$$$$$$######$$$$$$%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&$$$###"""%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&#########$$$%%%&&&'''((($$$$$$$$$%%%%%%&&&&&&&&&"""$$$&&&'''&&&%%%%%%&&&###$$$$$$%%%%%%%%%$$$$$$&&&%%%$$$$$$&&&&&&%%%$$$%%%$$$#########$$$%%%&&&&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%$$$%%%&&&((()))''''''''''''''''''''''''((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%!!!###%%%&&&&&&''')))***)))((('''&&&%%%&&&&&&'''&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%((((((((('''%%%%%%&&&'''&&&%%%$$$#########$$$$$$&&&&&&&&&''''''''''''(((&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&'''''''''$$$%%%&&&'''(((((((((((())))))((('''&&&%%%%%%$$$%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$$$$######%%%(((***+++***&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&%%%%%%$$$$$$%%%$$$######""""""######&&&&&&((((((((('''&&&%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&)))&&&$$$###$$$%%%%%%$$$%%%%%%%%%&&&&&&'''''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''%%%%%%%%%%%%'''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%&&&&&&&&&'''(((((((((((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%$$$######$$$&&&$$$$$$%%%%%%%%%&&&&&&&&&((('''&&&%%%$$$%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&'''((())))))'''&&&&&&%%%%%%&&&&&&'''$$$$$$%%%&&&&&&'''((((((&&&&&&&&&&&&&&&'''((()))(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((%%%&&&&&&&&&&&&&&&&&&%%%$$$%%%'''(((((((((''''''&&&&&&%%%$$$%%%&&&'''(((''''''''''''((((((((((((((((((''''''&&&&&&%%%%%%'''(((((((((&&&&&&((()))%%%%%%&&&&&&&&&&&&&&&&&&$$$&&&'''&&&%%%%%%&&&'''$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%$$$$$$###%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$&&&&&&&&&%%%############%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%((('''%%%$$$###$$$%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$#########&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&'''((())))))))))))%%%&&&&&&''''''&&&&&&%%%&&&'''''''''&&&%%%%%%$$$$$$%%%'''(((((((((''''''&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%!!!###$$$%%%$$$%%%&&&((()))((('''&&&%%%&&&&&&'''&&&&&&&&&%%%%%%$$$$$$$$$&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''%%%$$$###$$$&&&%%%%%%%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&$$$$$$%%%''''''(((((((((((((((((('''&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''&&&)))'''&&&&&&''''''%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&%%%&&&%%%$$$$$$######$$$$$$&&&&&&'''(((((('''&&&%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&***(((&&&&&&'''(((((('''%%%%%%%%%&&&&&&'''''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$######$$$%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%$$$######$$$&&&$$$$$$%%%%%%%%%&&&&&&&&&((('''&&&%%%%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&'''((((((((('''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$%%%&&&'''''''''%%%$$$$$$$$$%%%%%%&&&'''(((((('''''''''&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&''''''''''''(((&&&&&&''''''''''''&&&&&&%%%&&&'''((((((((('''&&&'''&&&&&&&&&''''''((((((''''''''''''(((((((((((())))))))))))(((((((((((((((((()))(((&&&&&&''')))&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((('''%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$###$$$$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$#########$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%&&&&&&'''((((((((((((%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%'''(((((((((''''''&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%###%%%&&&&&&%%%%%%&&&'''((('''&&&&&&%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%$$$""""""###%%%%%%%%%&&&'''((('''&&&%%%&&&&&&&&&&&&''''''''''''%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%###$$$%%%&&&&&&''''''&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&&&&''''''&&&&&&&&&%%%%%%$$$$$$&&&''''''((((((''''''&&&)))(((&&&%%%&&&%%%###"""&&&&&&&&&&&&&&&&&&&&&&&&"""###$$$%%%'''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''(((((((((''''''&&&&&&%%%$$$%%%%%%%%%&&&&&&''''''(((''''''&&&''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&)))'''%%%%%%'''))))))(((&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$%%%%%%%%%######%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&((('''&&&&&&%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&'''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''###$$$$$$%%%%%%&&&&&&'''%%%%%%%%%$$$%%%%%%&&&''''''''''''''''''&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&&&&''''''''''''(((''''''(((((((((((('''''''''''''''(((''''''&&&%%%&&&'''(((((())))))((((((''''''''''''((((((((((((((((((((((((((()))))))))((())))))(((&&&%%%&&&((('''''''''&&&&&&%%%%%%$$$'''((()))'''%%%######$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$############$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&''''''&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&''''''((('''''''''&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%'''((())))))'''&&&''')))'''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%$$$""""""###%%%%%%&&&((()))***)))'''&&&%%%%%%&&&&&&&&&'''''''''$$$%%%%%%%%%&&&&&&'''''''''''''''&&&&&&%%%%%%%%%###$$$%%%%%%&&&&&&&&&%%%&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&%%%%%%$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$######$$$&&&'''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%'''((())))))))))))(((((('''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&'''''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$""""""$$$&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&'''''''''%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&''''''''''''''''''&&&&&&%%%%%%$$$$$$###$$$%%%&&&%%%######%%%&&&%%%%%%%%%&&&&&&&&&&&&'''(((''''''&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%'''''''''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$$$$$$$$$$%%%%%%&&&&&&((((((''''''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((((((((())))))))))))(((((((((((((((''''''&&&%%%%%%%%%&&&'''))))))(((''''''''''''''''''((((((((((((%%%%%%%%%&&&&&&'''''''''((())))))'''%%%%%%&&&'''(((((('''&&&%%%%%%$$$$$$&&&'''((('''%%%$$$$$$&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$&&&&&&&&&&&&$$$$$$$$$%%%&&&''''''&&&%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%&&&&&&&&&%%%$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%&&&&&&''''''''''''''''''&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%((()))))))))'''&&&'''(((%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%######%%%'''&&&''')))******)))'''&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%&&&&&&''''''''''''''''''&&&&&&%%%%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&'''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$"""""""""###&&&(((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''((())))))***))))))(((''''''&&&&&&''''''&&&&&&&&&&&&''''''(((((('''''''''&&&&&&'''''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$"""!!!!!!###%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&''''''''''''''''''&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%''''''&&&&&&%%%%%%%%%$$$%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&'''''''''((((((&&&&&&&&&%%%%%%$$$$$$$$$%%%&&&&&&%%%$$$$$$%%%'''%%%%%%&&&&&&&&&''''''''''''(((((('''''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%'''''''''''''''&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$%%%%%%%%%%%%%%%&&&&&&)))(((((('''''''''((((((&&&'''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((((((((())))))))))))((((((((((((''''''&&&&&&&&&&&&$$$%%%&&&'''((('''&&&&&&''''''''''''(((((((((((($$$$$$%%%%%%&&&&&&'''''''''(((((('''%%%$$$&&&'''(((((('''&&&%%%%%%$$$$$$###%%%&&&&&&%%%%%%'''((($$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&(((((('''&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$&&&&&&&&&&&&$$$$$$###$$$%%%&&&&&&%%%$$$###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&'''&&&&&&%%%''''''''''''&&&&&&''''''&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''&&&%%%$$$%%%&&&$$$%%%%%%&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&$$$%%%&&&((((((((()))***)))((('''&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&'''''''''(((((('''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((''''''&&&%%%$$$$$$%%%&&&''''''%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((()))))))))((()))(((''''''&&&'''''''''&&&&&&&&&&&&&&&'''((()))''''''&&&&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''%%%######%%%&&&'''&&&((((((((('''''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%%%%&&&''''''%%%%%%%%%&&&''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&$$$$$$&&&'''%%%&&&&&&&&&'''''''''''''''(((((((((((('''&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&'''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&&&&%%%&&&&&&&&&&&&&&&&&&'''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''((((((((())))))))))))(((((((((((('''&&&&&&&&&''''''$$$%%%%%%&&&'''&&&&&&&&&''''''''''''(((((((((((('''''''''''''''(((((((((&&&''''''&&&%%%%%%&&&((('''''''''&&&&&&%%%%%%$$$"""$$$&&&&&&&&&&&&(((***&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%!!!""""""######$$$$$$%%%%%%%%%%%%&&&''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&$$$%%%%%%&&&&&&%%%%%%$$$###$$$$$$%%%%%%$$$$$$###$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&$$$$$$%%%&&&&&&%%%%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&(((((('''&&&&&&&&&''''''&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%$$$###%%%&&&###$$$%%%&&&'''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&%%%$$$%%%&&&(((******)))((('''&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%&&&&&&&&&'''''''''''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&'''(((((((((&&&''''''((((((''''''&&&(((&&&%%%&&&''''''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((((((''''''(((((('''&&&&&&&&&&&&'''&&&&&&%%%%%%&&&''')))***&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&***(((&&&%%%&&&''''''''')))((((((((('''''''''&&&&&&&&&&&&&&&'''''''''(((''''''''''''''''''''''''$$$%%%&&&''''''&&&%%%$$$&&&&&&&&&&&&&&&&&&%%%%%%''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&''''''&&&%%%%%%%%%&&&&&&$$$$$$$$$%%%&&&'''''''''###$$$$$$%%%%%%&&&&&&'''%%%&&&'''&&&$$$$$$&&&'''&&&&&&&&&&&&'''''''''''''''(((((()))((('''&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&'''((((((((('''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''(((((('''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((('''(((((())))))(((((('''''''''&&&%%%&&&'''((((((&&&&&&&&&&&&&&&'''((((((''''''''''''(((((((((((((((''''''''''''''''''&&&$$$%%%&&&&&&%%%%%%''')))&&&&&&&&&&&&&&&&&&&&&&&&###%%%&&&&&&%%%%%%'''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%""""""######$$$%%%%%%&&&%%%%%%&&&&&&'''(((((((((%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%$$$$$$%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&'''''''''&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&###$$$%%%&&&&&&'''&&&&&&%%%&&&&&&''''''&&&&&&%%%$$$%%%&&&&&&''''''&&&&&&)))((('''&&&%%%&&&&&&'''&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%'''&&&%%%%%%'''((("""###%%%&&&'''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%$$$$$$&&&(((,,,+++)))'''&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&((((((((('''&&&&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''''''''(((''''''&&&&&&'''''''''''''''''''''''''''''''''&&&&&&%%%%%%%%%$$$%%%%%%&&&'''((())))))$$$%%%%%%&&&&&&%%%%%%$$$'''&&&%%%&&&((()))((('''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$&&&'''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&(((((('''&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''')))***&&&%%%%%%$$$$$$%%%%%%&&&&&&''''''''''''''''''&&&''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&***(((&&&%%%&&&'''&&&&&&))))))(((((('''''''''&&&&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&'''((())))))((('''&&&'''''''''&&&&&&%%%%%%%%%(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''$$$$$$$$$%%%%%%&&&&&&&&&((('''&&&&&&%%%%%%%%%%%%######$$$%%%%%%&&&''''''"""###$$$%%%&&&&&&'''(((&&&&&&'''&&&%%%$$$&&&(((&&&&&&&&&'''''''''(((((('''((()))))))))(((&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&'''((())))))'''&&&&&&%%%%%%&&&&&&'''((((((((((((((((((''''''******)))(((((((((((((((&&&&&&&&&'''''''''((((((((((((((((((((((((((((((&&&&&&&&&'''''''''((((((''''''(((((((((((('''''''''&&&%%%%%%&&&'''(((***(((((('''&&&&&&((()))***''''''''''''((((((((()))&&&&&&&&&%%%%%%$$$$$$$$$###$$$%%%%%%%%%&&&(((***%%%%%%&&&&&&&&&&&&&&&&&&%%%'''''''''%%%$$$%%%'''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((()))))))))(((((('''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&'''&&&$$$$$$$$$$$$&&&'''''''''%%%$$$$$$%%%''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%"""###%%%&&&'''&&&%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&###$$$%%%&&&'''(((((((((%%%&&&&&&''''''&&&&&&%%%$$$%%%%%%&&&'''''''''&&&)))((('''&&&%%%&&&&&&'''&&&&&&&&&'''''''''((((((%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%&&&''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%(((((('''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''+++)))'''''''''((('''&&&(((((('''''''''&&&&&&&&&'''''''''''''''''''''''''''&&&%%%%%%&&&''')))***,,,+++)))'''$$$#########((($$$!!!###(((+++(((%%%%%%'''(((((('''&&&&&&'''&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&((((((((('''&&&&&&%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&''''''''''''&&&&&&&&&%%%%%%&&&&&&&&&(((''''''''''''&&&&&&&&&''''''(((((('''&&&%%%%%%###$$$%%%&&&''')))******&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&%%%%%%%%%&&&''''''''''''&&&&&&&&&&&&''''''%%%%%%%%%%%%&&&'''((((((&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&***))))))((((((((())))))'''&&&%%%%%%$$$$$$%%%%%%'''((())))))(((((()))***)))((('''&&&&&&&&&&&&&&&((('''&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&))))))(((((('''''''''&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''(((&&&&&&)))---...)))$$$'''%%%###$$$&&&'''&&&###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$'''&&&&&&%%%%%%&&&&&&'''%%%$$$$$$######$$$$$$%%%'''&&&%%%%%%%%%%%%&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%############%%%%%%&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%###%%%''''''%%%$$$&&&(((&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((''''''$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&''''''&&&&&&&&&&&&'''((((((((((((((((((((((((((((((%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&'''&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$###$$$%%%%%%&&&&&&%%%%%%$$$''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%(((''''''&&&%%%%%%$$$$$$((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''+++)))''''''((())))))((((((((('''''''''&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&''''''(((''''''&&&((()))***)))(((,,,+++***)))((('''&&&%%%%%%'''((((((&&&%%%&&&'''&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&''''''((((((''''''&&&(((''''''''''''&&&&&&&&&((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((('''&&&&&&))))))(((((((((((())))))(((''''''''''''&&&&&&&&&''''''(((((('''&&&&&&%%%$$$%%%%%%&&&'''((())))))''''''''''''''''''''''''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&'''(((((((((((((((''''''(((((((((''''''&&&%%%%%%&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&''')))(((''''''(((***(((((('''&&&&&&&&&&&&&&&)))(((((('''''''''((((((''''''''''''''''''''''''((('''''''''&&&&&&&&&&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&(((&&&&&&)))------)))%%%&&&$$$###$$$&&&'''%%%###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$'''&&&&&&%%%%%%&&&&&&'''&&&&&&%%%%%%%%%%%%&&&&&&'''&&&%%%%%%%%%%%%&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%&&&''''''&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$&&&((('''%%%%%%''')))&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((('''''''''$$$$$$%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%&&&&&&''''''&&&&&&&&&&&&'''((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&%%%%%%$$$###%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%'''''''''&&&&&&%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&&&&''''''***)))'''((()))******)))'''''''''''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''&&&&&&'''&&&%%%&&&&&&&&&%%%###'''((()))(((%%%%%%'''***&&&''')))(((&&&%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&''''''((((((''''''&&&&&&&&&'''''''''(((((((((((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&))))))))))))((('''&&&%%%))))))(((((((((((())))))(((''''''''''''&&&&&&&&&'''''''''(((''''''&&&%%%&&&&&&&&&'''''''''((((((((((((((((((((((((((((((&&&&&&'''''''''(((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''&&&&&&&&&&&&'''(((((())))))(((((((((((()))))))))((('''&&&%%%%%%%%%%%%''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&'''&&&&&&%%%%%%%%%%%%%%%%%%&&&((('''&&&&&&''')))(((((('''&&&&&&&&&&&&'''(((((('''''''''((())))))((((((((((((((((((((((((&&&&&&&&&&&&&&&%%%%%%%%%'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((((((((((((((('''%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&))),,,,,,)))%%%%%%$$$######%%%%%%$$$###&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%$$$$$$%%%%%%&&&'''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&&&&''')))&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&&&&&&&&&&'''''''''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&%%%$$$$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%&&&&&&%%%%%%$$$###%%%%%%&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%''''''&&&&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&&&&&&&&&&'''''')))'''&&&''')))******)))''''''''''''''''''''''''''''''''''''''''''''''''''''''((()))((('''%%%$$$###%%%'''%%%###$$$)))---444111,,,(((%%%%%%''')))&&&'''((((((&&&$$$$$$%%%&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((''''''%%%&&&&&&'''((()))))))))&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''''''''(((((((((''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&(((''''''''''''&&&&&&&&&&&&'''''''''''''''&&&&&&'''''''''''''''''''''&&&'''''''''''''''(((((((((''''''''''''((((((((((((''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&&&&%%%%%%&&&&&&'''((()))(((((((((((((((((()))(((((('''&&&&&&&&&&&&&&&'''''''''(((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''''''''''''''''''''''''''''''''&&&''''''((((((''''''&&&%%%%%%%%%%%%%%%$$$%%%'''&&&%%%%%%&&&((((((''''''&&&&&&&&&''''''%%%%%%%%%%%%%%%&&&'''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%'''))))))'''%%%$$$$$$###$$$$$$$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$'''&&&&&&%%%%%%&&&&&&'''#########""""""#########&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&''''''''''''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&'''''''''&&&&&&&&&&&&'''''''''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&%%%$$$$$$%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%&&&&&&%%%%%%$$$###%%%&&&&&&''''''&&&&&&%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''''''''&&&&&&&&&&&&'''''''''&&&%%%%%%'''))))))(((&&&'''''''''''''''''''''''''''''''''''''''''''''''''''((()))((('''%%%$$$###))))))''',,,:::GGGPPPEEE777---((('''$$$"""%%%'''((('''%%%$$$$$$%%%&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&'''''''''''''''''''''''''''''''''''''''''''''&&&'''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((('''%%%&&&&&&'''((()))******&&&&&&%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''###$$$%%%&&&'''(((((((((%%%$$$$$$$$$$$$$$$$$$%%%(((''''''''''''&&&&&&&&&&&&&&&'''''''''''''''&&&'''''''''''''''&&&&&&&&&%%%%%%&&&&&&&&&''''''''''''''''''((((((((())))))''''''''''''''''''''''''&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%&&&&&&'''(((''''''&&&&&&''''''(((&&&&&&&&&&&&&&&'''((()))''''''''''''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((&&&&&&&&&''''''''''''(((''''''''''''''''''''''''((((((''''''((()))******((('''&&&&&&%%%%%%&&&&&&$$$%%%&&&&&&%%%%%%&&&'''''''''&&&&&&&&&''''''(((%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$###$$$%%%&&&'''%%%$$$$$$$$$%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&######$$$%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$'''&&&&&&%%%%%%&&&&&&'''$$$##################$$$&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&'''(((''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&'''''''''(((''''''&&&&&&''''''((('''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%###$$$$$$%%%%%%&&&&&&'''%%%%%%&&&&&&%%%%%%$$$###&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&'''''''''&&&$$$%%%&&&''''''&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&+++)))%%%)))888EEELLLAAA333+++((((((%%%"""$$$%%%''''''%%%%%%%%%&&&&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&'''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''''''''(((((())))))(((((('''&&&&&&'''((())))))******((((((''''''''''''((((((''''''''''''''''''''''''"""###$$$&&&'''(((((()))''''''&&&&&&&&&&&&''''''(((''''''''''''&&&&&&&&&%%%&&&''''''((('''''''''''''''''''''''''''&&&&&&$$$$$$%%%%%%&&&'''''''''''''''((((((((()))))))))''''''''''''''''''''''''&&&&&&&&&''''''''''''(((&&&%%%%%%%%%%%%&&&''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&'''((()))***&&&&&&&&&''''''(((((()))&&&&&&&&&&&&&&&&&&&&&&&&((((((((((((((((((((((((&&&&&&&&&''''''''''''(((''''''''''''''''''''''''&&&&&&&&&&&&&&&'''((()))(((''''''&&&&&&&&&&&&&&&$$$%%%'''&&&%%%%%%&&&((('''&&&&&&&&&&&&'''(((((((((((('''''''''((())))))&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((((((((((('''''''''''''''(((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%%%%%%%%%%$$$%%%&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$'''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%&&&&&&'''&&&%%%$$$%%%'''((('''&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&%%%&&&&&&&&&''''''''''''((((((''''''''''''(((((('''&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&'''&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%######$$$%%%%%%&&&''''''%%%%%%&&&&&&%%%%%%$$$###&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$''''''&&&&&&&&&&&&'''''')))'''&&&%%%'''''''''&&&&&&&&&&&&'''''''''((((((''''''''''''''''''''''''''''''&&&&&&&&&''''''(((''')))***'''###$$$***///111---(((&&&&&&'''''''''"""$$$&&&&&&%%%%%%&&&'''&&&&&&''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&''''''''''''''''''''''''(((((('''''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''(((((())))))))))))((((((''''''(((((()))))))))***((((((''''''''''''((((((''''''''''''''''''''''''$$$$$$&&&'''(((((((((((()))((((((''''''(((((()))(((''''''''''''&&&&&&&&&%%%&&&&&&'''((((((''''''&&&&&&''''''''''''''''''%%%%%%%%%&&&'''((((((((('''((((((((())))))))))))''''''''''''''''''''''''&&&&&&&&&''''''''''''((('''''''''''''''((())))))((((((''''''''''''((((((((('''''''''''''''((()))$$$%%%%%%&&&''''''((((((''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&''''''''''''(((''''''''''''''''''''''''%%%%%%%%%%%%&&&'''(((((((((((('''&&&&&&&&&&&&&&&%%%&&&''''''&&&&&&'''(((&&&&&&&&&&&&&&&'''(((((()))(((((('''''''''((((((''''''''''''''''''''''''&&&&&&&&&''''''(((((((((&&&'''''''''((((((((()))''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&%%%%%%&&&'''%%%'''((('''%%%$$$&&&(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$'''&&&&&&%%%%%%&&&&&&'''(((''''''&&&&&&''''''(((%%%%%%&&&''''''&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))((('''&&&&&&&&&&&&&&&'''''''''(((''''''''''''''''''''''''######$$$%%%%%%&&&''''''%%%$$$"""$$$&&&'''&&&$$$$$$$$$$$$$$$$$$$$$$$$$$$'''''''''(((((('''''''''&&&&&&&&&&&&''''''''''''((((((''''''''''''(((((('''&&&&&&&&&&&&'''((((((''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%&&&''''''''''''%%%&&&&&&''''''&&&&&&%%%######$$$%%%%%%&&&''''''%%%%%%&&&&&&&&&%%%$$$$$$&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&'''''''''+++)))'''''''''((('''&&&&&&&&&&&&'''''''''(((((('''''''''''''''''''''''''''&&&%%%%%%&&&''')))***(((((((((((())))))))))))%%%'''(((((('''%%%&&&'''!!!###%%%&&&&&&&&&'''(((&&&''''''''''''''''''&&&&&&''''''''''''''''''&&&''''''''''''''''''''''''(((((('''''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''(((((())))))))))))(((((((((((((((((())))))))))))&&&&&&&&&%%%%%%&&&&&&&&&((((((((((((((((((((((((''''''((((((((((((((('''((((((''''''''''''(((((((((((('''''''''&&&&&&&&&%%%%%%&&&'''((((((((('''&&&&&&&&&'''''''''((((((&&&&&&&&&'''((())))))***(((((((((((())))))))))))''''''''''''''''''''''''&&&&&&&&&'''''''''(((((()))))))))))))))***++++++))))))(((((((((((())))))***)))(((''''''&&&''''''$$$$$$%%%%%%&&&'''(((((())))))))))))))))))))))))))))))))))))))))))))))))&&&&&&&&&'''''''''((((((((((((((((((((((((((((((%%%%%%%%%&&&'''((()))***(((((('''&&&&&&&&&&&&'''%%%&&&((('''&&&&&&''')))&&&&&&&&&&&&&&&'''((()))((('''&&&%%%%%%%%%%%%%%%((((((((((((((((((((((((%%%%%%%%%&&&&&&'''''''''&&&'''''''''(((((())))))((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''((((((((((((''''''''''''''''''''''''''''''%%%&&&''''''&&&&&&''')))%%%''')))(((&&&%%%&&&)))&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$%%%%%%&&&''''''$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&%%%%%%$$$'''&&&&&&%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&'''%%%%%%&&&''''''&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&''''''&&&%%%$$$&&&&&&&&&'''''''''((((((''''''''''''''''''''''''######$$$%%%%%%&&&''''''%%%###!!!###%%%'''%%%###$$$$$$$$$$$$$$$$$$$$$$$$''''''((((((((((((''''''&&&&&&&&&'''''''''((((((((((((''''''''''''(((((('''&&&&&&&&&&&&'''((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&%%%$$$''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''((('''&&&%%%$$$%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%%%%&&&&&&%%%%%%$$$%%%&&&((())))))(((&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''')))*********)))(((''''''''''''((((((((((((''''''&&&&&&&&&&&&'''''''''''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((&&&%%%'''***+++(((&&&&&&(((***)))&&&%%%'''******)))'''%%%$$$%%%'''(((''''''&&&&&&&&&&&&''''''''''''((((((((((((''''''&&&'''&&&%%%$$$%%%(((+++******)))(((((((((((((((((((((((((((((((((((((((&&&''''''(((((((((((((((''''''''''''((((((((()))(((((((((((())))))))))))''''''''''''''''''''''''))))))(((((('''''''''&&&''''''((((((((((((''''''(((((()))***************''''''''''''((((((((((((''''''''''''((((((((()))(((((((((((((((((((((((())))))))))))))))))))))))((((((((('''&&&&&&&&&%%%((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''))))))))))))))))))))))))''''''((((((((((((''''''&&&'''((())))))((('''&&&'''''''''''''''((())))))))))))((('''&&&%%%%%%%%%***((('''((()))***)))(((''''''''''''''''''''''''''''''''''''''''''''''''*********)))(((&&&%%%$$$&&&''''''((()))))))))(((&&&'''((())))))((('''&&&((((((((((((((('''''''''''''''((((((((((((''''''&&&%%%$$$$$$&&&&&&%%%$$$))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))))))))******))))))((((((((('''(((((('''''''''&&&&&&&&&''''''&&&%%%%%%$$$######%%%%%%&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%$$$$$$$$$$$$'''''''''&&&&&&%%%%%%%%%$$$$$$%%%&&&''''''''''''%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&%%%$$$###"""!!!$$$$$$&&&''')))((('''%%%'''&&&&&&%%%%%%%%%&&&&&&''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%&&&&&&''''''&&&&&&%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%"""""""""######$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%'''(((((('''%%%$$$)))---///...***'''''')))&&&&&&&&&''''''''''''(((((('''&&&&&&(((((('''&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''%%%$$$$$$%%%&&&%%%$$$(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''((('''&&&%%%%%%%%%&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&'''(((((('''&&&%%%''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''((()))(((((('''''''''''''''((((((((((((''''''&&&&&&&&&&&&''''''(((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&)))((('''(((++++++***(((&&&'''(((((('''&&&'''((()))((('''&&&%%%&&&'''''')))((((((''''''(((((()))&&&''''''((((((''''''&&&'''''''''&&&%%%%%%(((*********)))(((((((((((((((((((((((((((((((((((((((&&&'''(((((())))))(((((('''''''''((((((((())))))(((((((((((())))))))))))''''''''''''''''''''''''))))))((((((((('''''''''''''''(((((((((((('''''''''((())))))******))))))((((((((())))))))))))***'''''''''((((((((())))))((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''&&&&&&(((((((((((((((((((((((((((''''''&&&&&&''''''((())))))))))))))))))))))))''''''((((((((((((''''''''''''(((((((((((('''''''''''''''''''''((())))))))))))((('''&&&&&&&&&&&&)))(((''''''))))))((('''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((('''&&&&&&&&&''''''''''''&&&&&&'''((((((((((((''''''&&&'''''''''(((((((((((((((''''''(((((((((((('''''''''&&&%%%%%%''''''&&&%%%(((((((((((((((((((((((('''((((((((())))))))))))(((((((((((((((((((((((())))))((((((''''''''''''(((((('''''''''&&&&&&&&&(((''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&%%%&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%######$$$%%%%%%%%%%%%$$$&&&%%%'''///777888222***'''&&&&&&%%%%%%&&&&&&&&&''''''''''''''''''''''''$$$$$$$$$$$$$$$$$$$$$$$$%%%%%%&&&&&&&&&&&&%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%######$$$$$$$$$$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&((())))))(((&&&%%%((()))******(((&&&&&&'''&&&&&&&&&&&&''''''''''''(((&&&%%%%%%&&&''''''&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''&&&%%%%%%&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((&&&%%%%%%&&&'''&&&&&&(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&((()))*********))))))))))))))))))))))))''''''&&&&&&&&&&&&''''''((('''&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%&&&'''(((((('''&&&%%%''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&''''''''''''((((((((((((''''''&&&&&&&&&&&&''''''((((((((((((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&((()))***)))''''''&&&%%%&&&'''''''''&&&(((((((((''''''''''''&&&***))))))(((((())))))***&&&''''''((((((''''''&&&((((((((('''%%%%%%''')))******)))(((((((((((((((((((((((((((((((((((((((&&&'''(((((())))))((((((''''''((((((((()))))))))))))))))))))((((((((((((''''''''''''''''''''''''))))))(((((((((((('''''''''(((((())))))(((((('''''''''((())))))))))))((())))))))))))************''''''((((((((()))))))))((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''(((((((((((((((((((((((((((((((((''''''&&&&&&''''''((())))))))))))))))))))))))''''''((((((((((((''''''''''''&&&&&&&&&&&&'''''''''''''''''''''((())))))))))))((('''&&&&&&&&&&&&)))'''&&&'''((()))((('''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&'''((())))))((((((&&&''''''''''''&&&&&&%%%))))))((('''&&&&&&&&&'''&&&&&&''''''(((((())))))''''''((((((((((((''''''((('''&&&&&&(((((('''&&&''''''''''''''''''''''''''''''((((((((()))))))))'''''''''''''''''''''''')))((('''&&&%%%&&&'''((('''''''''''''''&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''((())))))'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%!!!!!!###%%%&&&'''''''''&&&$$$'''444BBBEEE999,,,&&&&&&&&&%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''((())))))((('''&&&'''&&&$$$$$$%%%&&&&&&%%%&&&&&&&&&&&&''''''''''''(((&&&$$$###%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%%%%%%%&&&'''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''%%%&&&'''((((((''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&(((((()))))))))((((((((((((((((((((((((''''''&&&&&&&&&&&&''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&'''&&&''''''''''''''''''&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''''''''''''''''''''((((((((((((''''''&&&&&&&&&&&&''''''((((((''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%&&&&&&%%%%%%'''%%%###$$$''')))'''$$$''''''(((((((((((('''&&&***))))))(((((())))))***'''(((((())))))((((((''')))))))))'''&&&%%%&&&(((***))))))(((((((((((((((((((((((((((((((((((((((''''''((()))))))))))))))'''(((((((((((()))))))))))))))))))))((((((((((((''''''''''''''''''''''''))))))(((((((((((((((((((((((())))))))))))((((((&&&''''''((((((((((((((((((((()))))))))*********'''(((((((((((()))))))))((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&''''''(((((())))))((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((''''''((((((((((((''''''((('''&&&%%%%%%&&&'''((('''''''''''''''((())))))))))))((('''''''''''''''((('''&&&'''((()))(((&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&''''''(((((((((((((((&&&&&&'''(((((((((((((((***)))'''&&&%%%%%%&&&'''%%%&&&&&&'''((()))******''''''(((((((((((('''''''''&&&%%%&&&'''((('''&&&'''''''''''''''''''''''''''''''''((((((((())))))''''''''''''''''''''''''((('''%%%$$$$$$%%%&&&'''''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''$$$%%%%%%&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%$$$$$$%%%&&&&&&''''''&&&&&&%%%!!!"""###%%%&&&'''''''''$$$"""%%%111>>>@@@444(((&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''(((((('''&&&&&&'''$$$!!!!!!%%%'''&&&%%%%%%%%%&&&&&&&&&'''''''''(((%%%###"""$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''(((&&&%%%%%%'''(((''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&%%%''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&'''''''''&&&''''''''''''''''''&&&%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''(((((((((''''''''''''((((((((((((''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%%%%%%%%%%%%%'''$$$###$$$''')))'''%%%''''''((())))))((((((''')))((((((''''''(((((())))))))))))******)))))))))((()))***(((&&&&&&'''(((***))))))((((((((((((((((((((((((((((((((((((((('''(((((()))))))))))))))(((((((((((()))))))))******)))))))))((((((((('''(((((((((((((((((((((((((((((())))))))))))))))))(((((())))))))))))((((((&&&''''''((((((((((((((('''''''''((((((((())))))(((((((((((()))))))))***((((((((((((((((((((((((((((((((((((((((((((((((&&&''''''(((((()))))))))))))))))))))))))))))))))(((((((((''''''(((((((((((((((((((((((((((((((((''''''((((((((((((''''''((('''&&&%%%%%%&&&'''((('''''''''''''''((())))))))))))((('''''''''(((((()))'''&&&'''((()))((('''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&"""###%%%&&&'''((()))))))))((('''%%%%%%%%%&&&'''%%%&&&&&&'''((()))******''''''((((((((((((''''''%%%$$$###$$$&&&'''&&&%%%''''''''''''''''''''''''''''''''''''(((((((((((('''''''''''''''''''''''''''&&&%%%$$$$$$%%%&&&'''&&&'''''''''''''''''''''%%%%%%%%%%%%%%%&&&&&&&&&$$$$$$%%%%%%&&&'''(((((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%$$$$$$%%%&&&&&&''''''&&&&&&%%%###$$$%%%&&&&&&&&&&&&&&&###"""$$$***000000***###%%%%%%%%%%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%###$$$$$$%%%%%%$$$$$$###&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&&&&%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''$$$!!!"""%%%((((((&&&%%%%%%%%%&&&&&&&&&&&&''''''%%%######$$$&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''''''''''''''''''''''''''''''''''''''&&&$$$###$$$&&&''''''&&&&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&%%%%%%$$$''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&''''''&&&&&&%%%$$$%%%&&&&&&&&&''''''''''''&&&&&&''''''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''&&&&&&''''''((()))''''''''''''((((((((((((''''''&&&&&&&&&&&&''''''%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$&&&(((((('''&&&'''(((&&&%%%$$$%%%'''((((((''''''(((((((((((())))))))))))((((((''''''(((((()))((())))))******))))))(((((()))***)))'''''''''(((******)))((((((((((((((((((((((((((((((((((((((('''((())))))******))))))((((((((()))))))))************))))))((((((''''''(((((((((((((((((((((((((((((())))))))))))******((())))))******))))))(((''''''((())))))))))))(((''''''''''''((((((((((((((((((((()))))))))******(((((((((((((((((((((((())))))))))))))))))))))))(((((((((((((((((()))))))))))))))))))))))))))))))))((((((''''''(((((()))))))))))))))))))))))))))''''''((((((((((((''''''((((((''''''''''''(((((('''''''''''''''((())))))))))))(((((('''(((((()))***((('''((()))***)))((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))((('''&&&&&& !!!###$$$&&&&&&'''''''''&&&&&&&&&&&&&&&''''''&&&&&&''''''(((((())))))''''''((((((((((((''''''$$$######$$$&&&'''&&&%%%''''''''''''''''''''''''&&&&&&'''''''''(((((((((''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%###$$$%%%%%%&&&'''(((((('''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&%%%$$$######$$$%%%%%%%%%&&&&&&&&&&&&'''&&&&&&&&&'''&&&&&&%%%%%%%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%$$$%%%%%%&&&&&&&&&%%%###"""%%%%%%%%%%%%&&&''''''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%%%%%%%%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%###$$$$$$%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$$$$$$$$$$'''%%%%%%%%%'''(((((('''%%%%%%%%%%%%&&&&&&&&&&&&&&&%%%$$$%%%&&&'''&&&$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''&&&%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''''''''''''''''''''''''''''''''%%%$$$"""###%%%''''''&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&'''''''''''''''&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&'''''''''&&&%%%$$$&&&&&&&&&&&&''''''''''''%%%%%%&&&&&&&&&&&&%%%%%%&&&%%%%%%%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&'''(((''''''''''''((((((((((((''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&'''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$'''))))))'''&&&((()))$$$&&&'''''''''''')))***)))((('''''''''(((***+++***))))))(((((())))))***''''''((((((((((((''''''&&&((())))))((((((((()))******)))((((((((((((((((((((((((((((((((((((((((((((()))************)))(((((()))))))))******************)))((('''''''''(((((((((((((((((((((((((((((()))))))))*********))))))************))))))'''((())))))******))))))'''(((((((((((()))))))))(((((()))))))))*********((((((((((((((((((((((((************************)))))))))((((((((((((((())))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))''''''((((((((((((''''''((())))))))))))))))))((('''''''''''''''((())))))))))))(((((((((((())))))+++)))((()))***+++***)))((((((((((((((((((((((((((((((((((((((((((((((((&&&'''((((((((((((((((((%%%%%%&&&&&&''''''&&&&&&$$$$$$%%%&&&'''''''''''''''''''''(((((((((((((((''''''((((((((((((''''''%%%$$$###%%%'''(((((('''((((((((((((((((((((((((&&&&&&&&&'''''''''(((((((((((((((((((((((((((((($$$%%%'''((((((((('''&&&&&&&&&&&&'''''''''((((((''''''&&&&&&%%%%%%$$$$$$###$$$$$$%%%&&&'''((()))'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&'''&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&&&&&&&%%%%%%&&&&&&%%%%%%$$$$$$######%%%%%%%%%%%%&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&######$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$%%%%%%%%%%%%'''(((((('''''''''((($$$$$$%%%%%%%%%&&&&&&&&&&&&%%%&&&''')))(((&&&###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%%%%&&&'''&&&%%%%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((''''''''''''''''''''''''%%%$$$###$$$&&&(((((('''&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%'''((())))))******))))))))))))))))))))))))'''''''''&&&&&&'''''''''%%%&&&'''''''''&&&%%%$$$&&&&&&&&&'''''''''(((((($$$%%%%%%&&&&&&%%%%%%$$$&&&%%%%%%$$$$$$%%%%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&&&&''''''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$###$$$%%%&&&'''''''''''''''((((((((()))'''''''''&&&&&&'''''''''&&&'''''''''(((((())))))&&&&&&&&&&&&&&&&&&&&&&&&###%%%((((((%%%$$$&&&((($$$&&&))))))'''&&&))),,,)))((('''&&&'''(((***,,,++++++************++++++%%%&&&&&&&&&&&&&&&&&&%%%%%%''')))***)))((()))*********)))((((((((((((((((((((((((((((((((((((((((((((()))***************))))))))))))************+++******)))(((''''''&&&))))))))))))))))))))))))(((((())))))*********+++))))))************))))))(((((()))***************))))))))))))************))))))))))))************((((((((((((((((((((((((******************************))))))((((((''''''))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))''''''((((((((((((''''''((()))***++++++***)))((('''''''''''''''((())))))))))))(((((((((((()))***+++***)))***+++,,,+++)))))))))))))))))))))))))))))))))))))))))))))))))))$$$%%%&&&((()))*********++++++++++++***)))((('''"""###%%%'''((((((''''''((((((((((((((('''''''''''''''((((((((((((''''''&&&%%%$$$&&&((())))))((())))))))))))))))))))))))&&&&&&&&&'''''''''(((((())))))))))))))))))))))))###%%%'''******)))'''%%%&&&&&&&&&'''''''''(((((())))))((('''&&&&&&%%%%%%######$$$%%%&&&(((((()))'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&'''((()))%%%%%%%%%&&&&&&'''''''''$$$$$$%%%&&&''''''''''''%%%&&&&&&''''''&&&&&&%%%$$$%%%&&&&&&'''''''''&&&%%%$$$###$$$&&&'''%%%$$$$$$$$$$$$%%%&&&'''((()))%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$%%%%%%&&&&&&&&&######$$$%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&'''$$$'''******'''%%%&&&'''$$$$$$%%%%%%%%%&&&&&&&&&%%%%%%''')))***)))&&&###%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%'''&&&%%%%%%%%%%%%&&&'''&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''&&&&&&&&&'''''''''((((((((((((((((((((((((((((((&&&%%%$$$%%%'''))))))(((&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&'''(((((((((%%%&&&''''''((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&)))((('''&&&%%%&&&''''''***)))((('''&&&%%%%%%%%%&&&&&&&&&''''''''''''((('''''''''&&&&&&%%%%%%%%%&&&&&&'''''''''''''''''''''&&&%%%%%%&&&'''&&&$$$&&&&&&&&&''''''''''''(((%%%&&&&&&''''''&&&&&&%%%%%%&&&&&&&&&%%%$$$######'''''''''(((((((((((()))''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&&&&''''''''''''((())))))))))))))))))))))))***)))'''&&&'''(((***,,,''''''''''''((((((((()))++++++******))))))((((((++++++***)))((('''&&&&&&&&&'''((())))))((('''&&&(((((()))***************'''(((((()))***++++++,,,))))))))))))))))))))))))))))))))))))))))))))))))''''''''''''((((((((((((+++***)))(((((()))***+++))))))))))))))))))))))))))))))))))))))))))))))))***+++,,,------,,,+++***))))))))))))))))))))))))+++*********))))))((((((+++*********))))))(((((())))))))))))))))))))))))(((((())))))))))))((((((((((((((((((((()))************))))))))))))******************************'''''''''''''''((()))***!!!$$$&&&'''(((((((((((((((((())))))))))))+++******)))(((''''''&&&)))((('''&&&&&&'''((()))((((((((((((((('''''''''$$$%%%&&&'''((((((((((((&&&&&&&&&''''''''''''((()))((('''&&&&&&'''((()))******))))))((((((''''''((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''))))))(((((('''''''''&&&''''''''''''''''''''''''''''''''''''''''''''''''(((''''''&&&&&&%%%$$$$$$&&&%%%%%%$$$$$$%%%%%%&&&(((%%%######&&&'''&&&$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&%%%$$$$$$###%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%&&&'''(((((('''&&&%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((('''&&&%%%%%%&&&'''(((%%%%%%&&&''''''&&&%%%%%%((('''&&&&&&%%%%%%%%%%%%)))'''%%%######%%%''')))&&&&&&&&&''''''''''''(((((((((&&&%%%%%%&&&'''((('''&&&%%%$$$$$$%%%&&&''')))((('''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''%%%&&&''''''((((((''''''''''''''''''''''''''''''&&&&&&'''''''''''''''&&&)))((('''&&&%%%&&&&&&''')))((('''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((('''''''''&&&&&&%%%%%%%%%&&&'''''''''''''''&&&&&&((('''&&&&&&'''((('''&&&&&&&&&&&&''''''''''''(((&&&&&&&&&''''''&&&&&&&&&((((((((((((((('''&&&&&&%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''''''''(((((((((((((((((((((((('''''''''((((((((()))))))))))))))))))))))))))))))))((('''''''''(((***+++'''''''''((((((((())))))******)))))))))))))))(((*********)))(((((('''''''''(((((())))))(((((('''((())))))***************''''''((())))))***++++++))))))))))))))))))))))))((())))))))))))))))))(((((((((((()))))))))******+++***)))(((((()))***+++))))))))))))))))))))))))))))))))))))))))))))))))******+++,,,,,,+++******))))))))))))))))))))))))************)))))))))(((************)))))))))((())))))))))))))))))))))))(((((())))))))))))((((((((((((((((((((()))************))))))))))))******************************(((((('''''''''((())))))%%%&&&'''((())))))))))))))))))))))))************+++******)))(((((('''''')))(((''''''''''''((()))(((((((((((((((((((((((($$$%%%&&&'''(((((((((((('''''''''((((((((())))))'''&&&%%%%%%%%%%%%&&&'''))))))))))))((((((''''''(((((((((((((((((((((((((((((((((((((((((((((((()))))))))))))))))))))))))))(((((((((''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''''''''''''''&&&%%%%%%$$$$$$%%%%%%&&&'''%%%###$$$&&&'''&&&$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&%%%%%%&&&''''''&&&%%%%%%''''''&&&%%%%%%%%%%%%%%%((('''%%%$$$$$$%%%'''(((&&&&&&&&&&&&''''''''''''((('''&&&&&&&&&&&&'''((((((((('''&&&&&&'''(((((((((((('''&&&&&&&&&&&&'''&&&&&&&&&''''''''''''(((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&%%%&&&''''''((((((''''''''''''''''''''''''''''''%%%%%%&&&'''(((((((((((((((((('''&&&&&&&&&&&&'''(((''''''&&&&&&&&&''''''&&&&&&&&&''''''''''''((('''''''''&&&&&&&&&&&&&&&(((((((((((('''&&&%%%%%%((('''&&&'''((()))((('''&&&&&&&&&''''''''''''(((&&&&&&&&&&&&&&&&&&&&&&&&)))))))))))))))(((((('''%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''''''''(((((((((((((((((((((((((((((()))))))))*********))))))))))))))))))))))))(((((((((((())))))))))))''''''((((((((()))))))))(((((((((((())))))))))))))))))))))))))))))))))))))))))(((((((((((())))))((()))******++++++******''''''(((((())))))******))))))))))))))))))))))))'''((()))******)))(((''')))))))))*********+++++++++***))))))))))))***+++)))))))))))))))))))))))))))))))))))))))))))))))))))******++++++******)))))))))))))))))))))))))))************))))))))))))************))))))))))))))))))))))))))))))))))))((())))))******))))))((()))(((((((((((()))************))))))))))))******))))))))))))))))))))))))))))))((('''''''''((((((******++++++******)))(((************++++++++++++*********))))))((((((''')))((((((''''''(((((()))((((((((((((((((((((((((%%%&&&''''''(((((((((((((((((((((((()))))))))***'''&&&&&&%%%%%%&&&&&&''')))))))))(((((((((((('''((((((((((((((((((((((((((((((((((((((((((((((((************************((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&''''''((())))))***&&&&&&%%%%%%%%%%%%&&&&&&'''%%%$$$%%%&&&'''&&&$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&'''''''''''''''''''''(((((((((%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&$$$%%%%%%%%%%%%%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%%%%%%%%%%%%%$$$%%%&&&&&&''''''&&&&&&%%%&&&%%%%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&''''''(((''''''&&&&&&&&&&&&'''''''''&&&&&&&&&&&&'''((((((&&&&&&&&&''''''''''''(((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''&&&&&&&&&%%%%%%&&&''''''((('''''''''''''''''''''''''''''''''$$$%%%&&&'''((((((((((((((((((''''''&&&&&&&&&&&&''''''&&&&&&&&&''''''(((&&&&&&&&&''''''''''''((('''''''''''''''&&&&&&&&&(((((((((((('''&&&%%%$$$'''&&&%%%&&&'''((('''&&&&&&&&&&&&''''''''''''(((''''''&&&&&&&&&&&&''''''''''''(((((((((((('''''''''''''''(((((((((((()))''''''''''''''''''''''''((((((((((((((((((((((((((((((((()))))))))******((((((((((((((((((((((((''''''((()))***)))))))))'''(((((((((((()))))))))'''''''''(((((())))))***(((((()))))))))*********+++***((((((((((((***+++))))))***++++++++++++***''''''((((((((()))))))))))))))))))))))))))))))))((()))***,,,,,,***)))((()))))))))*********++++++************************)))))))))))))))))))))))))))))))))))))))))))))))))))))))))******)))))))))))))))))))))))))))))))))*********)))))))))))))))*********))))))))))))))))))))))))))))))))))))))))))))))))******)))))))))))))))(((((())))))***+++******))))))))))))******((((((((((((((((((((((((******)))((('''''''''((()))*********)))((('''''')))))))))*********++++++*********)))))))))(((((()))(((((((((((((((((()))((((((((((((((()))))))))&&&&&&'''(((((((((((((((''''''((((((((()))))))))))))))(((((((((((())))))((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''((((((((((((&&&&&&%%%%%%%%%%%%&&&&&&&&&%%%%%%&&&&&&&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&&&&''''''''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&$$$######$$$&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%&&&''''''&&&%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$######$$$$$$$$$%%%%%%&&&''''''&&&%%%%%%%%%%%%&&&&&&&&&'''''''''&&&&&&&&&&&&'''''''''((($$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&&&&((())))))&&&&&&&&&''''''''''''(((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''&&&&&&&&&%%%%%%&&&''''''((('''''''''''''''''''''''''''''''''$$$%%%&&&'''(((((((((((('''''''''''''''&&&&&&&&&''''''&&&&&&&&&''''''(((&&&&&&&&&''''''''''''(((''''''''''''''''''''''''(((((((((((('''&&&%%%$$$%%%$$$###$$$&&&'''&&&%%%&&&&&&&&&''''''''''''((((((''''''&&&&&&''''''(((''''''(((((((((((((((''''''''''''(((((((((((()))''''''''''''''''''''''''((((((((((((((((((((((((''''''((((((((()))))))))((((((((((((((((((((((((''''''((()))***)))))))))(((((((((((()))))))))***''''''(((((())))))******(((((())))))******+++++++++***)))(((((()))***+++))))))***+++++++++++++++(((((((((((())))))))))))))))))))))))))))))))))))******+++,,,,,,+++******((((((((()))))))))************++++++++++++*********************************************************))))))))))))))))))***************************))))))))))))))))))******))))))))))))))))))******************************))))))************)))))))))))))))))))))***++++++******))))))))))))******((((((((((((((((((((((((+++***)))((((((((((((((('''(((((()))))))))((((((((((((((()))))))))******************))))))))))))((())))))))))))))))))((((((((((((((())))))******&&&'''(((((()))(((((((((&&&&&&'''''''''((((((((())))))))))))))))))))))))'''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''''''''''''''''''''''''''''''''(((((((((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&%%%%%%'''&&&&&&%%%%%%&&&&&&'''%%%&&&'''''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((''''''&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$%%%%%%&&&&&&&&&''''''&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$$$$%%%%%%&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&$$$######$$$&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&'''(((((('''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$$$$######$$$$$$%%%$$$%%%'''(((((('''%%%$$$%%%%%%%%%&&&&&&&&&&&&'''%%%&&&&&&'''''''''(((((($$$$$$$$$$$$$$$$$$$$$$$$%%%%%%%%%&&&'''((()))***&&&&&&&&&''''''''''''(((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&%%%&&&''''''((((((''''''''''''''''''''''''''''''%%%%%%&&&'''((((((((((((''''''((((((''''''&&&%%%(((''''''&&&&&&&&&''''''&&&&&&&&&''''''''''''((('''''''''''''''((((((((((((((((((((('''&&&%%%%%%$$$###"""###%%%&&&&&&%%%&&&&&&&&&''''''''''''((()))((('''&&&&&&'''((()))((())))))***************%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''''''''(((((((((((((((((((((((('''''''''((((((((())))))))))))))))))))))))))))))(((((((((((())))))))))))((((((((()))))))))******))))))))))))************)))))))))******+++++++++++++++************++++++)))***++++++,,,+++++++++))))))))))))************))))))))))))))))))))))))++++++++++++++++++++++++((((((((()))))))))************+++,,,,,,+++******************************************************+++******))))))******+++************************))))))))))))************))))))))))))************************************)))******++++++******)))***))))))))))))***++++++******))))))))))))******))))))))))))))))))))))))******)))((((((((())))))(((((()))***++++++++++++'''((((((((())))))))))))************************((())))))******))))))((('''(((((())))))******+++'''(((((())))))(((((((((&&&&&&&&&&&&''''''''''''&&&''''''((((((''''''&&&&&&''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))))))))'''''''''(((((((((((((((''''''''''''''''''''''''))))))))))))))))))))))))(((''''''&&&%%%%%%$$$$$$''''''&&&&&&&&&&&&''''''$$$&&&(((((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&''''''''''''&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&&&&'''''''''''''''&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''#########$$$%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&''''''((((((''''''&&&'''&&&&&&%%%%%%&&&&&&'''%%%$$$$$$$$$$$$%%%%%%&&&%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&$$$%%%&&&'''((((((((((((&&&&&&''''''''''''&&&&&&%%%%%%%%%&&&'''((()))***&&&&&&&&&''''''''''''(((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''%%%&&&''''''((((((''''''''''''''''''''''''''''''&&&&&&'''''''''''''''&&&&&&'''((((((((('''&&&%%%)))((('''&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((&&&'''''''''((((((((()))&&&'''''''''''''''&&&&&&$$$######$$$&&&''''''&&&&&&&&&&&&''''''''''''((()))((('''&&&&&&'''((()))'''((())))))*********)))%%%%%%%%%&&&&&&&&&&&&'''''''''''''''''''''''''''(((((((((((((((((((((((((((((()))))))))*********)))))))))))))))))))))))))))((('''''''''(((***+++(((((()))))))))*********++++++++++++******************************++++++***++++++++++++++++++***)))***++++++,,,,,,++++++++++++++++++************))))))))))))))))))))))))+++***(((''''''(((***+++)))))))))*********++++++***++++++,,,,,,++++++***************************************************,,,+++************+++,,,************************((()))))))))************((()))))))))************************************)))******++++++******)))******))))))******+++,,,******))))))))))))******************************)))))))))((())))))******))))))***++++++++++++***(((((()))))))))*********************************((()))************)))((('''(((((()))******++++++(((((())))))))))))((((((''''''''''''((((((((((((&&&'''((())))))((('''&&&&&&&&&&&&'''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''((((((((()))''''''''''''''''''''''''((((((((((((((((((((((((''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''###&&&))))))'''&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%%%%&&&''''''(((((((((''''''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''######$$$%%%%%%&&&''''''%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''''''''&&&&&&%%%&&&&&&''''''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&%%%%%%&&&&&&''''''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%%%%%%%&&&''''''%%%&&&&&&&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&$$$%%%&&&(((((((((((('''&&&'''(((((((((((('''&&&&&&&&&&&&&&&&&&'''((()))&&&&&&&&&''''''''''''(((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''(((((((((%%%&&&''''''(((((('''''''''''''''''''''''''''''''''''''''(((''''''&&&&&&&&&'''((((((((('''%%%%%%***)))((('''&&&%%%%%%%%%&&&&&&&&&'''''''''((((((&&&'''''''''(((((())))))&&&&&&''''''((('''''''''%%%$$$$$$%%%'''(((((('''&&&&&&&&&'''''''''((((((***((('''&&&&&&'''(((***%%%%%%&&&''''''''''''''''''''''''((((((((())))))''''''''''''''''''''''''(((((((((((((((((((((((()))************+++++++++))))))))))))))))))))))))***)))'''&&&'''(((***,,,))))))))))))************---,,,,,,,,,+++************************************+++,,,------,,,+++*********+++,,,,,,,,,,,,+++,,,,,,++++++++++++++++++))))))))))))))))))))))))***)))&&&%%%%%%&&&)))*********+++++++++,,,,,,,,,***+++,,,------,,,+++***************************************************---,,,+++******+++,,,---************************(((((())))))*********+++(((((())))))*********+++******************************++++++++++++***************)))******+++,,,******))))))))))))******************************))))))(((((()))***++++++))))))*********)))(((((()))************+++++++++******************++++++((()))***++++++***)))((('''(((((()))***+++++++++((()))))))))))))))(((((((((((((((((())))))))))))((()))***++++++***)))(((&&&&&&&&&'''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((%%%%%%%%%%%%%%%%%%%%%%%%&&&'''''''''(((((())))))''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''((()))))))))''''''&&&&&&&&&&&&''''''###&&&******(((%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%%%%&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&'''((())))))(((((('''&&&%%%%%%$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''$$$$$$%%%&&&&&&'''((((((%%%%%%%%%&&&&&&&&&''''''%%%&&&((((((((((((&&&%%%$$$%%%%%%&&&&&&%%%%%%$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&$$$$$$$$$$$$&&&''''''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%%%%&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%&&&&&&&&&###$$$&&&((())))))((('''%%%%%%&&&''''''&&&%%%%%%'''&&&&&&&&&&&&'''((((((&&&&&&&&&'''''''''((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&%%%%%%&&&&&&&&&&&&%%%%%%%%%&&&((()))))))))((('''(((((((((((((((((((((((((((((((((((((((((((((((()))((('''&&&&&&&&&&&&&&&)))((('''&&&$$$###!!!!!!(((((((((((('''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''(((((((((((((((((((((((((((''''''''''''''''''''''''(((((())))))))))))((((((''''''''''''((((((((()))******))))))((((((''''''))))))'''%%%###$$$'''***))))))))))))))))))))))))******))))))((((((''''''******))))))******+++,,,))))))))))))))))))))))))(((((()))************)))******))))))))))))))))))///---+++***++++++***)))******+++++++++,,,,,,,,,......---,,,,,,+++******,,,+++++++++***))))))))))))*********++++++++++++******))))))))))))******---,,,+++******+++,,,---,,,,,,,,,++++++*********************************************************,,,,,,,,,,,,,,,,,,,,,,,,******++++++++++++******++++++***))))))***++++++++++++***)))(((((())))))))))))))))))))))))))))))*********************************++++++,,,------)))))))))))))))*********************************))))))))))))))))))))))))+++++++++******(((''''''''''''((()))))))))))))))************************)))************+++++++++(((((())))))((('''&&&&&&))))))))))))))))))))))))((((((((((((((((((((((((''''''(((((())))))******&&&&&&&&&&&&&&&&&&&&&&&&))))))(((((('''''''''&&&''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((((('''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%))))))((((((((('''''''''&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%))))))'''&&&%%%$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&&&&'''(((((((((&&&&&&%%%%%%%%%%%%$$$$$$%%%%%%$$$$$$%%%%%%&&&'''((('''&&&%%%%%%%%%%%%%%%''''''''''''''''''''''''((('''&&&%%%$$$%%%&&&&&&%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$%%%&&&''''''$$$"""((('''&&&%%%%%%%%%%%%%%%######$$$$$$$$$$$$%%%%%%&&&&&&$$$$$$$$$$$$&&&&&&((('''&&&%%%%%%%%%%%%%%%$$$###"""""""""###$$$%%%'''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''''''''&&&&&&%%%%%%%%%$$$$$$$$$$$$$$$$$$$$$$$$&&&&&&''''''''''''&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$''''''''''''''''''''''''$$$%%%''')))((('''$$$###'''(((((()))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))'''''''''''''''&&&&&&&&&))))))))))))))))))))))))''''''''''''''''''''''''(((((((((((((((((((((((('''(((((())))))(((((('''&&&&&&((()))))))))((('''(((((((((((((((((((((((((((((((((((((((((((((((((((((('''&&&&&&&&&&&&&&&((((((''''''&&&&&&&&&&&&(((((((((((('''''''''''''''&&&&&&%%%%%%&&&&&&'''&&&&&&&&&''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))(((((('''''''''((((((((())))))******))))))((((((((((((((()))((('''&&&&&&)))+++))))))))))))))))))))))))******))))))(((((((((((())))))(((((())))))***+++******************************+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++***((((((***++++++******++++++++++++,,,,,,,,,......---,,,,,,+++******++++++++++++*********************)))((((((''''''++++++************++++++---,,,++++++++++++,,,---,,,,,,,,,+++++++++******++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,******++++++++++++*********++++++++++++++++++***---,,,++++++*********+++++++++++++++++++++++++++************************,,,,,,++++++++++++++++++))))))))))))************************************************************++++++++++++***)))((('''******+++,,,,,,,,,,,,,,,************************)))************+++++++++))))))******))))))((('''))))))))))))))))))))))))((((((((((((((((((((((((((((((((()))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&)))(((((((((''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((('''''''''(((((((((((((((''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%(((''''''&&&&&&&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''%%%%%%%%%&&&&&&'''''''''&&&&&&%%%%%%&&&&&&'''(((((('''&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''((('''&&&%%%%%%%%%&&&&&&%%%%%%&&&''''''&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%'''%%%$$$$$$&&&&&&&&&%%%''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%%%%&&&&&&&&&'''&&&&&&%%%$$$$$$%%%&&&&&&))))))((('''''''''''''''%%%%%%$$$$$$$$$%%%&&&'''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$''''''''''''''''''''''''&&&'''''''''''''''''''''&&&'''(((((())))))((((((((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''))))))))))))))))))))))))((((((((((((((((((((((((((()))))))))))))))))))))'''(((((())))))(((((('''&&&''''''((()))((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((('''&&&&&&&&&&&&'''''''''(((((()))*********((((((((((((''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&''''''''''''((((((((((((((((((((((((((())))))))))))))))))))))))(((((())))))))))))((((((''''''((((((((()))))))))***))))))))))))((((((((('''((())))))))))))***,,,))))))))))))))))))))))))***))))))))))))(((((((((((((((((((((((())))))******************************++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,((('''&&&''')))++++++***++++++++++++,,,,,,,,,,,,...------,,,,,,++++++************+++++++++++++++------+++***((('''&&&%%%,,,,,,++++++++++++,,,,,,---,,,,,,++++++,,,,,,---,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++------------------------++++++++++++++++++++++++***++++++,,,,,,++++++*********,,,,,,,,,,,,******......---,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++---------,,,+++*********************************++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++***)))((((((++++++,,,---------------************************)))************+++++++++******++++++******))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))((((((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&''''''(((((())))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&'''((((((&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&$$$%%%%%%&&&'''((()))***'''&&&&&&&&&&&&'''((((((''''''&&&%%%%%%%%%&&&&&&''''''''''''''''''''''''((('''&&&&&&%%%%%%&&&&&&%%%&&&&&&''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%)))&&&$$$###$$$&&&''''''%%%%%%&&&&&&&&&&&&&&&'''&&&'''''''''((((((((((((&&&&&&%%%%%%%%%%%%&&&&&&)))((('''''''''''''''''''''&&&&&&&&&&&&'''(((((('''&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&%%%%%%%%%''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%''''''''''''''''''''''''((('''&&&&&&&&&(((***+++%%%&&&''''''((((((''''''((((((((((((((((((((((((''''''''''''''''''''''''(((((((((((((((((((((((())))))))))))))))))))))))''''''''''''''''''''''''((((((((((((((()))))))))&&&&&&''''''''''''&&&&&&&&&''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&''''''''''''((())))))***++++++((((((((((((''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))(((((('''(((((((((((()))))))))))))))))))))))))))))))))$$$''')))******)))***+++)))))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((()))******************************((()))******++++++***************+++++++++++++++***((('''((()))++++++***+++++++++,,,,,,,,,---------------,,,,,,+++++++++*********++++++,,,,,,,,,//////...,,,+++***)))(((,,,,,,++++++++++++,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++,,,,,,,,,,,,++++++***+++---......---+++***......---------------...,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++------,,,,,,,,,+++++++++++++++***************)))++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++******)))(((((()))******++++++******************************))))))*********+++++++++)))***************))))))))))))))))))))))))))))))************************+++******))))))(((((((((((((((((((((((((((((((((((((((((((((((('''''''''''''''''''''''''''''''''((((((((((((((((((((((((%%%&&&&&&'''((()))******''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((($$$%%%%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''&&&&&&&&&%%%$$$%%%%%%&&&'''(((((((((&&&&&&&&&&&&&&&''''''((('''&&&&&&%%%%%%%%%&&&&&&''''''''''''''''''''''''(((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%(((&&&$$$$$$&&&'''''''''$$$%%%%%%&&&''''''''''''''''''''''''((((((((((((&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&%%%$$$$$$%%%%%%%%%'''''''''''''''(((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%''''''''''''''''''''''''&&&&&&&&&&&&'''((()))***$$$%%%&&&&&&''''''&&&&&&((((((((((((((((((((((((''''''''''''''''''''''''(((((((((((())))))))))))((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((((((((&&&''''''''''''''''''&&&''''''''''''((((((((()))((((((((((((((((((((((((((((((((((((((((((((((((''''''&&&&&&&&&''''''((((((((((((((((((((())))))((((((((((((''''''''''''(((''''''&&&&&&''''''(((&&&&&&&&&''''''''''''(((((((((((((((((((((((((((''''''''''''''''''''''''(((((())))))))))))(((((((((((((((((()))))))))***))))))))))))************###&&&)))******))))))***))))))))))))))))))))))))))))))))))))***************))))))))))))***++++++************************))))))***++++++++++++*********++++++,,,,,,,,,,,,...,,,******+++++++++***++++++,,,,,,,,,---------------,,,,,,,,,,,,++++++******++++++,,,,,,,,,---------------,,,,,,,,,,,,++++++************++++++******++++++++++++******,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++,,,,,,------------,,,,,,***+++---......---+++***------,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++,,,,,,,,,---------,,,+++++++++******))))))++++++++++++++++++++++++***************************++++++++++++******)))'''(((((()))))))))))))))************************))))))*********+++++++++(((((()))******)))))))))))))))))))))))))))))))))++++++++++++++++++++++++++++++******))))))(((((())))))))))))))))))))))))'''''''''(((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((%%%&&&&&&'''((()))******'''''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$###$$$$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&((((((((('''&&&&&&&&&%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&'''&&&&&&%%%%%%%%%&&&&&&''''''''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$&&&((((((&&&%%%$$$$$$%%%''''''''''''&&&%%%&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$%%%%%%&&&%%%&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''"""###&&&((()))((('''&&&$$$%%%%%%&&&&&&&&&&&&&&&(((((((((((((((((((((((((((((((((((((((((((((((('''((((((((())))))******((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&''''''((((((((())))))******))))))((((((''''''''''''((())))))(((((((((((((((((((((((((((((((((((((((((((((((('''&&&&&&&&&&&&'''((((((((((((((((((''''''''''''((((((((((((''''''''''''((((((''''''''''''((((((&&&&&&&&&''''''''''''(((((((((((((((((((((((((((''''''''''''''''''''''''(((((())))))))))))((((((((((((((()))))))))******)))))))))************+++$$$&&&)))***)))(((((())))))))))))))))))))))))))))))))))))************+++***************++++++,,,+++++++++++++++++++++++++++,,,,,,---------------,,,------......//////000000...,,,,,,,,,---,,,***,,,,,,,,,,,,------------,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,,,,,,,,,,*********++++++,,,,,,,,,++++++************++++++***++++++,,,,,,++++++***,,,,,,,,,,,,------------------------------------++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,------......------,,,,,,,,,............,,,,,,,,,,,,+++++++++,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,---.........,,,,,,,,,+++******)))))),,,,,,,,,,,,,,,,,,,,,,,,***************************+++++++++++++++******))))))***++++++++++++***************************)))************+++++++++'''((())))))***)))))))))))))))))))))))))))))))))******************************************))))))))))))))))))))))))))))))'''''''''(((((((((((((((''''''''''''''''''''''''((((((((((((((((((((((((&&&&&&''''''(((((())))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$###$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&%%%%%%%%%$$$$$$$$$%%%$$$$$$$$$$$$%%%&&&&&&&&&&&&%%%%%%%%%&&&'''''''''''''''''''''''''''''''''(((((((((((('''&&&&&&'''&&&&&&%%%%%%&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%""""""$$$&&&((((((&&&###$$$%%%&&&'''''''''&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&''''''((($$$%%%&&&&&&''''''&&&&&&%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%&&&''''''((((((%%%%%%%%%&&&&&&&&&&&&'''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''!!!###&&&((()))(((&&&$$$$$$%%%&&&&&&''''''&&&&&&(((((((((((((((((((((((())))))))))))))))))))))))&&&''''''(((((())))))***))))))))))))))))))))))))''''''''''''''''''''''''&&&&&&&&&'''(((((())))))))))))************))))))(((''''''&&&'''((()))***((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&'''((((((((((((((((((((((((((((((((((((((((((''''''''''''((((((''''''''''''((((((&&&&&&&&&''''''''''''(((((((((((((((((((((((((((''''''''''''''''''''''''(((((())))))))))))(((((((((((()))))))))*********))))))*********+++++++++''')))******)))((()))***))))))))))))))))))))))))))))))*********+++++++++)))))))))))))))***+++++++++++++++++++++++++++++++++,,,------......---------------...///000000000///...,,,,,,---...---,,,,,,,,,,,,------------...,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++***+++++++++,,,,,,------,,,,,,++++++++++++,,,,,,,,,,,,---......---,,,,,,,,,,,,,,,---------......------------------------------------------------------------------------------............------------------------------,,,,,,++++++,,,,,,---...------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------------------,,,++++++***)))))),,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++***++++++,,,,,,++++++*********+++,,,,,,,,,,,,+++************************)))************+++++++++((()))******++++++******))))))))))))))))))))))))******************************************++++++((((((((((((((((((((((((''''''''''''((((((((()))''''''''''''''''''''''''(((((((((((((((((((((((('''''''''(((((((((((((((''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''%%%%%%%%%&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%&&&'''((('''''''''''''''''''''''''''(((((()))((('''&&&%%%'''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%###""""""###%%%&&&&&&$$$%%%&&&'''((((((&&&%%%$$$$$$%%%%%%%%%%%%&&&&&&&&&%%%&&&'''(((((('''&&&%%%&&&&&&%%%%%%&&&&&&'''((($$$%%%&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&'''(((((((((%%%%%%%%%&&&&&&&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&'''''''''(((''''''''''''''''''''''''%%%&&&'''(((((('''&&&&&&%%%%%%&&&'''''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((%%%&&&&&&'''(((((())))))))))))))))))))))))))))))((((((((((((((((((((((((&&&''''''((()))******+++''''''((((((((((((''''''(((''''''&&&&&&((()))***((((((((((((((((((((((((((((((((((((((((((((((((&&&&&&&&&&&&&&&'''((()))''''''(((((())))))******)))(((((((((''''''''''''((((((''''''''''''((((((&&&&&&&&&'''''''''(((((((((((((((((((((((((((((())))))))))))))))))))))))(((((())))))))))))(((((())))))))))))************))))))******++++++++++++***+++,,,+++))))))***+++))))))))))))))))))))))))))))))******++++++++++++((((((((((((((()))******++++++++++++++++++++++++)))***++++++,,,,,,++++++++++++,,,,,,---...//////---,,,++++++---//////...,,,,,,,,,---------......,,,,,,,,,,,,,,,,,,,,,,,,---------,,,,,,+++++++++...........................------,,,,,,------...---...///000000///...---,,,,,,,,,------.................................................................................------............------///...------------...///,,,,,,,,,,,,,,,---...///////////////////////////,,,,,,,,,,,,,,,,,,,,,,,,///......------,,,,,,+++------,,,,,,+++***)))))),,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,***++++++,,,,,,,,,++++++))))))***++++++++++++***************************)))************+++++++++)))***+++,,,,,,,,,,,,,,,)))))))))))))))))))))))))))))))))))))))))))))))))))))))))***+++++++++,,,((((((((((((((((((((((((&&&'''''''''(((((())))))''''''''''''''''''''''''((((((((((((((((((((((((((((((((((((((('''''''''''''''''''''''''''''''''%%%%%%%%%%%%%%%%%%%%%%%%'''''''''((((((((())))))((((((((('''&&&&&&&&&%%%''''''''''''''''''''''''&&&&&&&&&'''((()))***+++&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&&&&''''''((((((((($$$%%%%%%&&&'''((())))))'''&&&&&&&&&&&&'''((((((%%%%%%%%%%%%%%%&&&'''((('''''''''''''''''''''''''''((()))))))))(((&&&%%%'''&&&%%%%%%%%%%%%&&&'''%%%%%%%%%%%%%%%%%%%%%%%%$$$""" """%%%&&&&&&%%%&&&(((((((((&&&$$$###%%%%%%%%%&&&&&&&&&''''''%%%&&&'''(((((('''&&&%%%############$$$$$$%%%&&&$$$%%%'''((((((((('''&&&%%%%%%%%%&&&&&&'''''''''%%%%%%&&&&&&'''((())))))%%%%%%%%%&&&&&&'''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''&&&&&&&&&&&&'''''''''((((((''''''''''''''''''''''''))))))'''&&&&&&'''((((((%%%&&&''''''((((((''''''((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%%%%&&&'''(((((()))))))))))))))))))))))))))&&&&&&'''((())))))(((((((((&&&%%%(((---...+++'''%%%''')))++++++***(((''''''((()))******)))((('''&&&'''''''''(((((())))))&&&&&&''''''(((((())))))((('''&&&%%%%%%&&&'''(((((((((((((((((((((((((((''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''((((((''''''''''''(((((())))))))))))(((((((((((()))))))))))))))((((((((((((((((((((())))))))))))))))))))))))))))))))))))*********))))))))))))(((++++++++++++++++++++++++)))************+++++++++,,,,,,++++++***))))))))),,,,,,++++++++++++,,,,,,******+++,,,,,,,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,,,,------......//////000+++,,,---,,,******,,,...222111111111333333111///------------------------------------------------------------------------..................///000////////////////////////...---,,,+++,,,---///111///...,,,,,,---/////////,,,------,,,***+++---///...///000111111000///...000///...------...///000111000///......///000111------....../////////000......---...000000...,,,////////////............++++++,,,---------,,,,,,.........///......---,,,......------,,,,,,++++++++++++,,,---///000111111++++++,,,,,,,,,---------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++,,,,,,,,,+++++++++******,,,+++++++++***))))))))))))))))))))))))******+++************************************))))))))))))))))))(((((('''''''''&&&)))))))))))))))))))))))))))((('''&&&&&&'''((()))''''''''''''(((((((((((())))))))))))((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&+++***)))(((''''''(((((((((((('''''''''&&&&&&&&&)))(((((('''&&&&&&%%%%%%%%%%%%&&&''''''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&(((((('''''''''&&&&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((******)))''''''&&&&&&&&&(((&&&$$$%%%((()))(((&&&''''''((((((''''''&&&%%%%%%###"""###'''((('''%%%''''''''''''''''''''''''###%%%((('''$$$###$$$'''%%%%%%%%%&&&&&&&&&''''''&&&'''''''''&&&%%%%%%$$$''''''((())))))(((''''''&&&&&&&&&&&&&&&&&&&&&&&&))))))(((((((((''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''((()))*********)))''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((('''''''''))))))))))))((((((((((((***)))(((''''''((()))***(((((((((((((((((((((((('''((()))******)))((('''&&&'''((((((((((((((((((%%%###!!!$$$(((***'''$$$'''(((((()))))))))))))))'''((()))******)))(((''''''''''''((((((((())))))'''''''''(((((((((((((((((('''&&&&&&&&&&&&'''(((((((((((((((((((((((((((''''''''''''''''''''''''(((''''''&&&&&&''''''(((((((((''''''''''''(((((())))))))))))(((((((((((((((((((((((((((((((((((((((((((((((()))))))))***************************)))))))))******+++++++++************************************++++++++++++***************++++++++++++++++++******+++++++++******+++,,,,,,,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,........................//////////////////000111000///...///111111000..............................................................................---------------......////////////////////////111111111111111111111111111///......///000000000111222222111//////111333000111111111111111111000111111000//////000111111000//////......///000111---........./////////000000///...///000111000...000000/////////................../////////........................---------,,,,,,,,,,,,,,,,,,+++,,,,,,,,,------------............------,,,,,,,,,************************++++++++++++++++++++++++,,,,,,,,,++++++++++++***++++++++++++************)))))))))))))))***++++++************************************))))))))))))******)))))))))((((((((()))))))))))))))))))))))))))(((''''''''''''((()))''''''''''''(((((((((((())))))))))))(((((((((((()))))))))))))))))))))))))))(((((((((((((((((('''(((((('''''''''&&&&&&&&&'''''''''''''''''''''''''''&&&&&&%%%%%%&&&&&&'''''''''''''''''''''''''''''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((()))((('''&&&&&&%%%%%%%%%'''&&&$$$%%%((()))(((&&&''''''((((((''''''&&&%%%&&&$$$###%%%((()))(((&&&''''''''''''''''''''''''%%%%%%&&&%%%$$$$$$%%%&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''&&&&&&%%%$$$''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%$$$$$$$$$$$$&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((''''''''''''''''''((((((((('''&&&%%%%%%%%%%%%&&&'''))))))))))))))))))))))))(((((())))))))))))(((((((((((((((((((((((('''&&&(((%%%###$$$(((***)))''')))((('''''''''(((***+++'''(((((())))))(((((('''''''''(((((((((((())))))((((((((((((((('''''''''(((''''''&&&&&&''''''(((((((((((((((((((((((((((''''''''''''''''''''''''(((''''''&&&&&&''''''(((((((((''''''''''''(((((())))))))))))(((((((((((('''''''''(((((((((((((((((((((((()))))))))******************************(((((()))***+++,,,------))))))))))))))))))))))))************+++++++++,,,))))))******+++,,,,,,---++++++************++++++***++++++,,,,,,,,,,,,,,,---------------------------------............//////...------///000000000111///......///000000...////////////////////////......................................................------------......------------------------+++,,,.../////////...---000000////////////000000///000000///......///111222111111111111111111222111111111111111111111111000000//////000000111222////////////000000000000111000//////000111000///000000//////......------///////////////.........,,,,,,++++++++++++,,,,,,---------------.........///......------,,,,,,,,,000000///...---,,,++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++*********+++++++++++++++***))))))))))))***++++++************************++++++*********)))))))))************)))))))))))))))))))))))))))))))))))))))((((((''''''(((((()))''''''''''''(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))%%%&&&'''((()))((('''''''''''''''''''''&&&&&&&&&%%%%%%&&&&&&'''((()))))))))'''%%%$$$$$$%%%''')))(((((((((((((((((((((((((((((('''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((((('''&&&%%%%%%%%%%%%%%%'''%%%%%%%%%'''((('''&&&''''''((((((''''''&&&%%%&&&%%%%%%&&&((()))((('''&&&&&&&&&&&&&&&&&&&&&&&&'''%%%######$$$%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&''''''&&&&&&%%%%%%((('''&&&%%%%%%&&&'''(((%%%%%%%%%%%%%%%%%%%%%%%%%%%$$$$$$$$$$$$#########%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&%%%$$$$$$''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((((((((%%%%%%&&&&&&''''''(((((())))))(((((((((((())))))************************))))))(((((((((((())))))(((((())))))((('''&&&&&&)))'''$$$%%%''')))))))))((((((((((((((())))))***(((((((((((((((((((((((((((((((((((((((((())))))))))))((((((''''''&&&&&&((((((''''''''''''((((((((((((((((((((((((((((((''''''''''''''''''''''''((((((''''''''''''((((((((((((''''''''''''(((((())))))))))))(((((((((((('''''''''''''''((((((((((((((()))))))))*********************************)))******+++,,,,,,------)))))))))************************+++++++++,,,,,,*********++++++,,,,,,,,,+++******))))))******+++***+++,,,,,,------,,,,,,------------............******+++,,,...///000111///---,,,---000222222111555222000///000000000///////////////////////////------------------------..................//////000//////......//////000////////////////////////***+++,,,...000111222222111222222222111111222333000111222111000000111333666555444333333444555666444444444555555444444444555555555555666666777777555555555555555555555555555333222333444555444333333333333333333333222222222222111000000000000000...---,,,,,,,,,------............//////000000000111000000//////.........//////...------,,,++++++------------------------,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,+++++++++*********++++++,,,,,,,,,******))))))******+++,,,************************+++++++++*********))))))))))))))))))))))))))))))(((((((((((((((((((((((()))(((((((((((((((((()))''''''''''''(((((((((((((((((((((((())))))))))))&&&&&&&&&&&&&&&&&&&&&&&&###%%%'''))))))((('''&&&''''''''''''''''''''''''%%%%%%&&&&&&'''(((((((((''''''&&&&&&&&&&&&''''''(((((((((((((((((((((((())))))))))))((((((((('''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((((((''''''&&&%%%%%%%%%&&&&&&%%%%%%&&&&&&''''''''''''''''''(((''''''&&&%%%&&&%%%%%%&&&'''(((''''''&&&&&&&&&&&&&&&&&&&&&&&&)))%%%""""""%%%'''&&&%%%%%%%%%%%%&&&&&&&&&''''''%%%&&&&&&'''&&&&&&%%%%%%((('''%%%$$$$$$%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%'''&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''&&&&&&%%%$$$''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((((((%%%%%%&&&''''''((())))))************************))))))))))))))))))))))))***)))(((''''''((()))***(((((())))))((('''&&&&&&&&&$$$""""""###%%%%%%&&&&&&''')))***+++***((('''((((((''''''''''''(((((())))))))))))))))))(((((())))))((((((''''''&&&&&&(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((''''''(((((((((((((((''''''''''''(((((())))))))))))((((((((((((''''''''''''(((((())))))))))))))))))************************************++++++++++++++++++++++++*********+++++++++,,,,,,***++++++++++++,,,,,,,,,,,,,,,,,,,,,++++++******++++++************++++++++++++,,,------------,,,---------....../////////+++,,,,,,---...///000000000000000222555777888999;;;888333000000000000///............................................................//////000000///////////////000000111333333333333333333333333222222222333444666777999333555777777555444666777777999;;;;;;;;;;;;<<<===>>>===;;;;;;;;;;;;===>>>;;;;;;;;;;;;;;;;;;;;;;;;========================;;;;;;;;;;;;;;;;;;;;;;;;::::::999;;;<<<<<<:::888888888888888999999999999777777555444333333333333333222111111000000111111......//////000000111111000000000000000000//////,,,,,,,,,,,,------------------------------------,,,,,,,,,,,,,,,,,,,,,,,,---------,,,,,,,,,++++++******++++++,,,,,,,,,---***************++++++,,,************************++++++++++++************((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))))))))(((''''''''''''(((((((((((('''((((((((()))))))))***%%%%%%%%%%%%%%%%%%%%%%%%###%%%'''))))))((('''&&&&&&'''''''''''''''''''''''''''''''''''''''''''''%%%&&&((())))))(((&&&%%%''''''''''''''''''''''''((((((((('''''''''&&&&&&%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&''''''''''''((()))(((''''''''''''''''''$$$%%%&&&&&&&&&&&&&&&''''''''''''(((''''''&&&%%%$$$%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&(((%%%""""""%%%'''&&&$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&'''&&&&&&%%%((('''%%%$$$$$$%%%'''(((%%%%%%%%%%%%%%%%%%%%%%%%''''''''''''((((((((((((%%%%%%%%%&&&&&&'''''''''%%%%%%%%%&&&&&&&&&''''''&&&'''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''&&&%%%$$$$$$''''''''''''''''''''''''''''''''''''''''''''''''&&&'''''''''(((((())))))&&&&&&'''((())))))******''''''''''''''''''''''''((((((((((((((((((((((((***)))(((''''''((()))***(((((((((((((((((('''&&&&&&&&&&&&%%%%%%&&&&&&'''%%%''')))+++,,,***(((&&&(((''''''&&&&&&''''''(((******))))))))))))(((((((((((((((((((((''''''''''''(((((())))))(((((('''(((((((((((((((((((((((((((((((((((((((((((((((()))((((((''''''(((((()))((((((''''''''''''(((((())))))))))))((((((((((((''''''(((((())))))******)))))))))*********++++++++++++++++++++++++++++++,,,,,,++++++*********************+++,,,,,,------++++++++++++,,,,,,,,,,,,...------,,,++++++******,,,++++++++++++++++++,,,++++++,,,---------------------......///000000000111111111111111000000000000222555777888;;;???BBBEEE@@@:::555222111000000000000000000000000000000000000000000000000000000///000000111111222222333//////000000111333444555333333333333333333333333555555666666777777888888777:::===>>><<<;;;===@@@???BBBDDDFFFFFFGGGHHHJJJJJJJJJIIIIIIIIIIIIJJJJJJIIIHHHGGGFFFFFFGGGHHHIIIHHHIIIIIIIIIHHHGGGFFFEEEDDDDDDDDDDDDDDDCCCCCCCCCCCCCCCDDDGGGHHHGGGCCC@@@@@@@@@??????>>>=========<<<;;;999777555555555666444444444444333222000///000000111111111111111111000000000000000000000000,,,,,,---------.........++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,------------,,,,,,,,,,,,+++++++++,,,,,,,,,,,,,,,+++************+++,,,,,,************************,,,++++++++++++*********''''''''''''(((((((((((())))))))))))))))))))))))((())))))******))))))(((''''''''''''((((((((((((''''''(((((())))))******((((((((((((((((((((((((%%%&&&'''((()))(((''''''&&&&&&&&&'''''''''''''''''''''''''''''''''&&&&&&$$$&&&)))++++++)))&&&$$$''''''''''''''''''''''''&&&%%%%%%%%%%%%$$$$$$$$$%%%%%%%%%%%%%%%%%%%%%%%%$$$%%%%%%&&&&&&'''''''''&&&&&&&&&''''''''''''((()))(((((('''''''''((((((###%%%&&&&&&%%%%%%&&&'''''''''((((((''''''&&&%%%$$$%%%&&&%%%$$$$$$%%%&&&%%%%%%%%%%%%%%%%%%%%%%%%&&&%%%$$$%%%&&&&&&%%%$$$%%%%%%%%%&&&&&&&&&''''''%%%%%%&&&&&&''''''&&&&&&((('''&&&%%%%%%&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&&&&&&&&&&&&&'''%%%%%%&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%%%%$$$######''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&''''''((()))))))))''''''(((((())))))******(((((())))))))))))((((((''''''''''''''''''''''''))))))(((((((((((())))))&&&'''((((((((((((((((((((()))******))))))))))))''''''((()))***))))))(((((('''&&&&&&&&&&&&'''(((*********)))))))))(((((('''''''''((((((((((((((('''((()))******)))((('''(((((((((((((((((((((((((((((((((((((((((((((((())))))(((((((((((())))))((((((''''''''''''(((((())))))))))))(((((((((((((((((())))))***++++++,,,))))))*********+++++++++++++++++++++++++++++++++))))))******************)))))))))***+++,,,,,,,,,+++++++++,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,+++------,,,,,,,,,,,,------+++,,,------...------------......///000000111111222222333444666777888888555;;;AAABBBBBBEEELLLRRRTTTNNNEEE>>>:::888666555222222222222222222222222333333333333333333333333333333444444555666666777555555555777888:::<<<===;;;;;;;;;;;;;;;;;;;;;;;;>>>AAAFFFJJJLLLKKKIIIHHHKKKOOOTTTUUUSSSSSSUUUYYYXXX[[[___aaabbbccceeeggghhhhhhiiiiiiiiiiiihhhhhhhhhfffdddbbbbbbdddfffhhhhhhhhhhhhgggfffdddbbbaaaaaaaaaaaaaaa``````______[[[]]]```cccdddbbb]]]YYYXXXWWWUUUSSSPPPNNNLLLKKKJJJHHHFFFCCCBBBBBBBBBCCC>>>>>>??????===:::777555888777777777777777666666666666555444333222222111000000000000////////////,,,,,,,,,,,,,,,,,,,,,,,,------------------------...------------,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++******++++++,,,---************************,,,,,,+++++++++*********''''''(((((())))))))))))))))))))))))))))))))))))((()))************)))(((''''''''''''(((((((((((('''''''''((()))*********************************)))(((((((((((((((((('''&&&&&&&&&'''''''''((((((%%%%%%&&&&&&'''(((((((((%%%'''(((******((('''%%%((((((((((((((((((((((((&&&&&&&&&&&&%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&$$$$$$%%%%%%&&&''''''(((&&&&&&&&&''''''''''''((('''''''''&&&&&&''''''(((###%%%&&&&&&$$$$$$&&&(((''''''((((((''''''&&&%%%$$$&&&((('''%%%$$$%%%'''%%%%%%%%%%%%%%%%%%%%%%%%"""$$$''''''&&&%%%$$$$$$%%%%%%%%%&&&&&&&&&''''''$$$%%%&&&&&&''''''&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''$$$$$$$$$%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$$$$%%%%%%%%%%%%$$$''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&''''''((())))))***((((((((((((((((((((((((***+++,,,,,,,,,,,,+++***(((((((((((((((((((((((((((((())))))))))))((((((&&&&&&'''((()))))))))(((%%%'''((()))(((&&&&&&&&&)))((((((''''''(((***+++((('''&&&%%%%%%&&&'''(((+++*********))))))((((((&&&'''''''''(((((())))))'''((()))******)))((('''(((((((((((((((((((((((())))))))))))))))))))))))))))))(((((((((((())))))((((((''''''''''''(((((())))))))))))((((((((((((((())))))***+++,,,,,,,,,)))************+++++++++++++++++++++++++++++++++''''''((()))***++++++,,,'''(((((()))***+++++++++++++++,,,,,,,,,---------***++++++,,,,,,------......------,,,,,,------...+++,,,------......---------......///000111111222///000333777;;;>>>AAABBBBBBIIIQQQSSSQQQTTT\\\eee```ZZZPPPHHHBBB???===<<<444444444444444444444444666666666666666666666666666666666777888999999:::;;;;;;<<<>>>@@@CCCEEEFFFKKKKKKKKKKKKKKKKKKKKKKKKQQQWWWaaaiiinnnnnnkkkiiiggglllqqqsssqqqqqqtttwww|||yyy||||||wwwvvvuuurrrnnnjjjfffcccaaa^^^\\\ZZZWWWUUUUUUUUUVVVNNNOOOPPPPPPNNNJJJFFFCCC?????????>>>>>>===============;;;:::888666444444444333333222111000//////........................------------------------......---------,,,,,,,,,---------,,,,,,+++++++++++++++******++++++,,,---************************,,,,,,,,,+++++++++******(((((())))))*********+++))))))))))))))))))))))))((()))***++++++***)))(((''''''''''''((((((((()))&&&''''''((()))******+++))))))))))))))))))))))))+++***)))(((((((((((((((&&&&&&&&&'''''''''((((((###$$$%%%&&&((()))******(((((((((((((((((((((((())))))))))))))))))))))))***)))))))))((((((((((((''''''''''''''''''''''''$$$$$$%%%%%%&&&'''((((((&&&&&&&&&'''''''''((((((&&&&&&%%%%%%%%%&&&&&&'''"""%%%'''&&&$$$###%%%(((''''''((((((''''''&&&%%%%%%((()))(((&&&$$$&&&(((%%%%%%%%%%%%%%%%%%%%%%%% $$$))))))&&&$$$###$$$%%%%%%%%%&&&&&&&&&''''''$$$%%%%%%&&&'''''''''&&&''''''((())))))(((''''''((((((((((((((((((((((((%%%%%%%%%&&&&&&''''''''''''''''''&&&&&&%%%%%%%%%%%%%%%%%%&&&&&&&&&''''''&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''((((((((((((''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''((())))))***'''''''''''''''&&&&&&&&&'''((()))******)))((('''))))))))))))))))))))))))'''((()))******)))((('''((((((((((((((((((((((((***************)))(((((()))))))))))))))))))))))))))((('''''''''(((***++++++***)))'''''''''((()))''''''((())))))((('''&&&((((((''''''''''''((((((***)))((('''''''''''''''''''''((((((((((((''''''(((((((((((((((((((((((()))***+++++++++)))((('''***)))(((''''''((()))***)))*********++++++++++++))))))))))))))))))))))))------,,,,,,+++***)))))))))************+++++++++++++++++++++++++++++++++******+++++++++,,,,,,,,,---------.........//////------------------------/////////......---------,,,---......//////000111111222444:::CCCLLLSSSVVVVVVcccqqqsssmmmiiimmmtttvvvlllbbb\\\VVVOOOKKKKKK>>>;;;888999<<<===;;;888===;;;::::::===???@@@@@@BBBCCCEEEEEEEEEFFFIIILLLHHHPPPVVVVVVWWW\\\aaaccchhhhhhhhhjjjkkkjjjhhhfffoooyyy~~~|||}}}{{{xxxyyy}}}~~~yyytttnnnmmmllljjjhhhddd___[[[VVVUUUSSSPPPNNNKKKJJJIIIGGGFFFDDDBBB???===<<<;;;:::777444222222333333222...111333222///...///111000...------.........---///.........///000000111++++++++++++,,,,,,,,,,,,---,,,+++***+++,,,---......---,,,+++++++++,,,------------,,,,,,,,,++++++************************''')))***)))((('''(((***))))))))))))))))))))))))++++++***)))((('''&&&&&&))))))))))))))))))))))))************************++++++******))))))(((((())))))))))))))))))))))))(((((((((((((((((((((((('''''''''&&&%%%%%%$$$$$$(((((('''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&%%%$$$$$$&&&(((''''''((((((((((((((((((((((((***))))))((('''&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''(((((((((&&&%%%&&&''''''''''''&&&&&&%%%%%%%%%)))(((&&&%%%$$$$$$%%%&&&'''''''''&&&&&&%%%%%%%%%&&&&&&&&&'''''''''(((((((((((())))))((('''&&&&&&(((((('''''''''&&&&&&&&&''''''''''''''''''''''''%%%&&&'''&&&$$$###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((( ###%%%&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&))))))(((((('''''''''&&&'''''''''&&&&&&%%%%%%%%%''''''&&&&&&&&&&&&''''''&&&&&&%%%'''(((((('''%%%))))))))))))))))))))))))&&&&&&''''''(((((())))))))))))))))))))))))))))))))))))))))))))))))))))))'''''''''''''''''''''''')))************)))((('''))))))))))))))))))))))))((('''&&&&&&&&&'''))))))((('''&&&%%%%%%%%%&&&&&&''''''((())))))((('''&&&((((((''''''''''''(((((())))))((('''''''''''''''''''''((((((((((((''''''))))))))))))))))))))))))***************)))((((((***)))(((((((((((()))***)))))))))*********++++++************************------,,,,,,+++******)))************++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,------------............------------------------,,,---------.........///111111222222111000000000333555888@@@JJJTTT]]]bbbrrr}}}}}}tttggg\\\XXXRRROOOKKKIIIJJJJJJJJJHHHKKKIIIHHHJJJNNNTTTWWWYYYYYY[[[^^^______```aaabbbbbbkkkrrrssstttxxx|||}}}{{{xxxtttsssoookkkfffbbb^^^\\\XXXXXXWWWTTTQQQMMMIIIGGGCCC@@@<<<:::999999888777444555666555333222111222444222111111222333222111333222000///...---....../////////...............---,,,+++***++++++,,,------,,,+++******+++,,,,,,---------,,,,,,,,,++++++************************((()))***)))(((((()))***)))))))))))))))))))))))))))))))))))))))((((((((())))))))))))))))))))))))************************)))((((((((('''''''''&&&))))))))))))))))))))))))((((((((((((((((((((((((&&&&&&&&&&&&''''''''''''(((((('''''''''&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''%%%$$$$$$&&&(((''''''((((((((((((((((((((((((((((((((('''&&&%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&&&&'''(((((((((&&&%%%&&&'''''''''&&&&&&&&&%%%%%%%%%''''''&&&%%%%%%%%%&&&&&&''''''&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''(((((('''(((((((((''''''&&&%%%(((((('''''''''&&&&&&&&&''''''''''''''''''''''''%%%&&&'''&&&$$$###$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((($$$%%%''')))***)))((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&)))((((((((('''''''''&&&'''''''''&&&&&&%%%%%%%%%''''''&&&&&&&&&&&&''''''+++***((()))***+++***((())))))))))))))))))))))))'''''''''((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))'''''''''''''''''''''''')))))))))))))))(((((('''))))))))))))))))))))))))&&&&&&&&&&&&&&&'''((((((''''''&&&%%%%%%%%%&&&&&&''''''((((((((((((''''''((((((''''''''''''(((((())))))(((((((((((('''''''''(((((())))))(((((('''************************+++******)))))))))))))))***))))))(((((())))))***((()))))))))************************************---,,,,,,++++++*********************+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,,,,------,,,,,,,,,---------......------..................,,,---...///000111222222000111333333222000111111888888:::BBBOOO___oooyyytttpppqqqnnniiieeeccccccdddeeefffeeeeeeiiiooowww|||~~~}}}zzzxxxtttuuutttrrrmmmggg```\\\VVVSSSOOOMMMKKKIIIGGGEEECCCAAA???>>><<<:::777555888666555555666666555444555333111///.........///000000000///...---------...------,,,,,,,,,---------,,,,,,,,,,,,,,,------------------,,,,,,,,,,,,++++++++++++++++++++++++(((*********)))((()))***))))))))))))))))))))))))((((((((())))))*********))))))))))))))))))))))))************************((((((((((((''''''''''''))))))))))))))))))))))))((((((((((((((((((((((((&&&&&&&&&'''((()))))))))(((((((((''''''''''''&&&'''''''''''''''''''''''''''''''''''''''''''''''''''&&&$$$%%%&&&(((''''''(((((((((((((((((((((((('''''''''&&&%%%%%%$$$$$$&&&&&&&&&&&&&&&&&&%%%%%%'''(((((((((&&&%%%&&&''''''&&&&&&&&&&&&%%%%%%%%%%%%%%%&&&&&&'''&&&&&&&&&'''&&&&&&&&&&&&%%%%%%%%%&&&&&&&&&'''''''''''''''&&&&&&''''''&&&&&&%%%%%%'''''''''''''''&&&&&&&&&''''''''''''''''''''''''%%%&&&'''&&&%%%$$$$$$&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((('''((((((((('''&&&$$$###''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''''''''''''''''''''&&&&&&&&&&&&&&&''''''&&&&&&&&&&&&''''''+++)))&&&&&&&&&''''''&&&))))))))))))))))))))))))((((((((((((((('''''''''(((((((((((((((((((((((())))))))))))))))))))))))''''''''''''''''''''''''((((((((())))))(((''''''((((((((((((((((((((((((&&&&&&&&&'''''''''((((((***)))))))))))))))))))))'''''''''(((((((((((((((((((((''''''''''''(((((((((((()))))))))((((((((((((((())))))))))))(((((())))))))))))))))))))))))+++***)))(((((()))***+++))))))))))))))))))))))))(((((()))))))))*********************************,,,,,,,,,++++++******************+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------,,,,,,,,,,,,------------.............../////////000000111222333444444555///222555666555555777999;;;;;;>>>GGGWWWnnnyyytttooommmjjjiiigggfffccc```[[[WWWRRRPPPNNNKKKEEE@@@???>>><<<;;;;;;;;;888666666555333222222222333444222222111111000///......000//////......---------//////............//////...------------,,,,,,,,,++++++++++++++++++++++++)))***++++++))))))***+++************************(((((()))))))))*********))))))))))))))))))))))))************************************))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((('''((((((((()))))))))***((((((((('''''''''''''''''''''''''''''''''''''''(((((((((((((((((((((((((((&&&%%%%%%'''((('''&&&(((((((((((((((((((((((('''''''''&&&&&&&&&%%%%%%'''''''''&&&&&&%%%%%%%%%'''(((((((((&&&%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''%%%%%%%%%&&&&&&%%%%%%$$$''''''''''''''''''''''''''''''''''''''''''''''''&&&'''''''''%%%$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((''''''&&&&&&$$$"""!!! ''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''&&&&&&&&&&&&''''''+++)))%%%$$$$$$%%%%%%%%%))))))))))))))))))))))))))))))((((((''''''&&&&&&(((((((((((((((((((((((())))))))))))))))))))))))''''''''''''''''''''''''&&&''''''(((((((((''''''((((((((((((((((((((((((''''''(((((())))))))))))************+++*********''''''''''''(((((())))))((((((''''''''''''(((((('''((()))******)))(((((((((((())))))))))))((((((((((((((((((((((((((((((+++***)))(((((()))***+++))))))************))))))))))))))))))************************************,,,,,,+++++++++++++++******++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------.........,,,,,,,,,---------...............//////000000000111222222222333333333333111555999999999:::>>>BBB???EEEPPP^^^ooo~~~xxxtttnnnjjjgggbbb[[[VVVPPPOOOMMMLLLKKKIIIFFFCCC???>>>===<<<:::999999888777777666555444333222111000000000///...---,,,,,,///////////////..................---------,,,,,,++++++++++++++++++++++++***+++,,,+++***)))***,,,++++++++++++++++++++++++************))))))))))))))))))))))))))))))))))))************************))))))))))))************((((((((((((((((((((((((((((((((((((((((((((((((******)))))))))(((((((((((((((((((((((((((((((((''''''''''''''''''''''''(((((((((((((((((((((((()))'''&&&&&&'''((('''&&&(((((((((((((((((((((((((((((((((''''''''''''''''''''''''&&&&&&%%%%%%%%%'''(((((((((&&&%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&###$$$&&&'''((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''&&&$$$$$$%%%%%%%%%%%%%%%$$$&&&'''''''''''''''''''''''''''''''''''''''''''''&&&'''((('''%%%$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''((()))))))))(((((('''&&&%%%''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''///,,,(((''''''((((((((((((((((((((((((((((((((())))))((((((''''''&&&&&&(((((((((((((((((((((((())))))))))))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&%%%&&&''''''''''''''''''))))))))))))))))))))))))'''(((((()))***)))))))))''''''((()))))))))((((((''''''&&&''''''((()))***((((((''''''''''''(((((('''((()))***+++***)))(((((())))))******))))))((('''''''''''''''''''''''')))))))))))))))******+++)))******++++++******))))))*********++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------.........//////---------.........//////......//////000000111111111111111111111111222222111555999999999<<>>@@@CCCKKKWWWaaannnyyy}}}|||yyytttpppuuuzzz{{{{{{|||qqqbbbUUURRRTTT```rrrzzzxxxvvvtttssstttuuuvvvfffeeecccfffrrrzzzvvvyyyyyysssmmmlllllluuu}}}zzzppplllsss{{{||||||zzz}}}~~~vvvwwwvvvsssnnnhhhaaa]]]VVVTTTQQQLLLGGGCCC@@@>>>============;;;999777666444444444333111///---+++............------------,,,,,,,,,,,,,,,,,,,,,,,,+++,,,---,,,+++++++++---,,,,,,,,,,,,,,,,,,,,,,,,)))***************++++++))))))))))))))))))))))))************************&&&'''''''''((((((((()))))))))))))))))))))))))))(((((((((((((((((((((((((((((((((((((((((((((((('''((((((((())))))))))))''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&***((('''&&&'''((('''&&&((((((((((((((((((((((((''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&'''(((((((((&&&%%%&&&'''%%%%%%%%%&&&&&&&&&''''''''''''&&&%%%%%%%%%&&&&&&%%%%%%%%%&&&&&&&&&''''''(((((('''''''''&&&&&&&&&$$$$$$%%%&&&&&&&&&&&&&&&&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&(((((('''&&&%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''(((%%%%%%%%%%%%%%%%%%&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&'''''''''((((((((()))''''''&&&&&&&&&&&&'''''''''&&&%%%%%%&&&'''&&&$$$(((((((((((((((((((((((('''''''''((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&&&&'''''''''&&&))))))))))))))))))))))))%%%%%%'''((((((((('''&&&$$$%%%'''((((((((('''''''''&&&&&&&&&'''(((***+++((((((''''''''''''((((((&&&(((***+++,,,+++***)))))))))************))))))))))))))))))))))))))))))'''((()))+++++++++***))))))***+++,,,,,,+++***)))++++++,,,,,,,,,---------++++++++++++++++++++++++++++++++++++++++++++++++++++++,,,,,,,,,---------------------------------............/////////000////////////000000000000...//////000111222222222222333444666888999;;;;;;;;;AAAIIINNNUUUaaaqqq~~~{{{rrrhhhcccddddddaaahhhmmmrrrrrrpppooorrruuutttvvvxxxwwwtttrrrsssuuu|||}}}~~~~~~}}}~~~}}}xxxnnn^^^RRRRRROOOSSScccwww|||jjjhhhfffeeeddddddeeefff^^^```aaafffsssssskkkgggkkkllleee___]]]XXXaaahhheee^^^^^^jjjvvvzzzzzzwwwsssmmmiiihhhhhhbbbgggkkkiiidddbbbeeeiiisssyyy~~~{{{vvvqqqnnnjjjccc]]]WWWRRROOOGGGGGGGGGFFFEEEBBB@@@???999999999777555222000...//////.........---------,,,,,,,,,,,,,,,,,,,,,,,,+++,,,------++++++,,,---,,,,,,,,,,,,,,,,,,,,,,,,'''((()))***+++,,,------))))))))))))))))))))))))************************((()))))))))******++++++))))))))))))))))))))))))((((((((((((((((((((((((&&&&&&''''''(((((())))))'''((((((((())))))******''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&+++)))'''''''''((('''&&&((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&''''''''''''(((((((((&&&%%%&&&'''%%%%%%%%%&&&&&&''''''''')))(((&&&%%%$$$%%%%%%&&&%%%%%%%%%&&&&&&'''''''''(((((('''''''''&&&&&&&&&$$$%%%&&&&&&''''''''''''&&&&&&&&&'''''''''(((((('''''''''''''''''''''''''''(((((((((&&&%%%&&&'''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''(((((('''&&&&&&%%%%%%%%%&&&&&&''''''''''''''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%%%%&&&&&&'''''''''&&&'''''''''(((((())))))'''''''''&&&&&&'''''''''((((((((()))***+++)))'''((((((((((((((((((((((((&&&'''''''''(((((())))))************************))))))))))))))))))))))))+++(((%%%%%%((())))))'''''''''''''''''''''&&&&&&&&&&&&&&&'''''''''((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((***+++,,,***((('''((()))++++++************++++++,,,+++***((((((((()))******)))(((''''''((()))***)))***+++++++++)))((('''************************((()))***++++++***)))(((,,,,,,,,,,,,,,,,,,,,,,,,******+++++++++,,,,,,,,,---------,,,,,,+++++++++.........////////////000///---...111222///000333111111111222333444555666777222000222111///333:::777888<<<@@@@@@>>>AAAGGGHHHPPPZZZbbblllzzz|||sssoooqqqsssqqquuutttsssrrrqqqooonnnnnniiieee```^^^___```aaabbbnnnuuuwwwqqqlllkkkhhhcccfffccc___\\\[[[]]]```bbbsssuuuuuurrrnnnkkklllnnnsssmmmgggdddbbb^^^VVVPPPMMMPPPYYYiiiwww~~~{{{uuueeedddaaa^^^]]]___cccgggaaa^^^^^^fffqqqxxxxxxuuuhhhhhhhhheee```\\\ZZZYYYZZZYYYXXXXXXZZZ^^^bbbeeellljjjgggaaa\\\YYYYYYYYYWWWZZZ]]]]]]ZZZYYY[[[^^^jjjpppvvvwwwrrrnnnmmmmmmssssssuuuwwwxxxuuunnnhhhooommmkkknnntttyyy{{{|||~~~yyyuuurrrqqqffffffdddcccdddcccZZZNNNKKKJJJHHHEEEAAA===999666222111000000111111///---222///,,,***+++...///000,,,------------,,,++++++...---,,,,,,,,,,,,,,,,,,)))+++,,,+++((((((***---,,,,,,+++******++++++,,,++++++************++++++************************''''''''''''''''''''''''))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((('''''''''''''''''''''''''''((()))***)))))))))))))))))))))))))))((('''&&&&&&'''((()))))))))))))))))))))))))))***************)))((((((&&&&&&&&&&&&&&&&&&&&&&&&...+++'''%%%%%%%%%%%%$$$((((((''''''''''''((((((%%%&&&&&&''''''&&&&&&%%%''''''''''''''''''''''''((('''&&&%%%%%%%%%%%%%%%((('''&&&&&&%%%%%%%%%%%%&&&%%%%%%%%%%%%&&&''''''''''''''''''''''''''''''))))))(((((('''''''''&&&''''''''''''''''''&&&&&&''''''''''''''''''''''''(((((('''''''''&&&&&&&&&%%%%%%%%%%%%&&&&&&'''((('''''''''''''''''''''''''''''''''(((''''''&&&%%%((((((((((((((((((((((((''''''''''''((((((((((((((((((''''''''''''((((((((((((((((((((((((''''''))))))))))))(((((((((((((((((((((((())))))))))))(((((()))))))))(((((('''***(((%%%%%%((()))((('''''''''''''''''''''''''''&&&&&&&&&'''''''''((((((((((((((((((((((((((((((''''''''''''(((((((((((((((((((((((((((((((((((()))***+++***(((((((((************))))))***************))))))(((((())))))***)))(((((('''((()))***)))***++++++***)))((('''******************************++++++++++++******,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,,,,------............---------,,,............////////////000......111222000222666444444444555666777888888:::666555777777666888>>>???@@@EEEKKKMMMMMMPPPVVVPPPYYYfffssszzzrrrrrrnnnhhhggglllooonnnooommmkkkhhheeecccbbbaaa^^^___`````````cccgggkkkvvvyyyvvvmmmeeecccbbb^^^\\\ZZZWWWUUUUUUWWWYYY[[[iiiiiiiiieeebbbaaadddhhhlllhhhccc```___]]]YYYVVVVVVZZZbbbnnnxxx}}}{{{wwwqqqpppmmmjjjhhhhhhjjjlllllliiigggiiiooorrrqqqoooqqqsssvvvuuupppjjjeeecccbbbaaa______```cccfffhhhfffeeedddaaa]]]ZZZYYYXXXZZZ\\\^^^]]]\\\]]]```dddlllppptttuuuqqqkkkgggeeeaaaaaaccceeefffccc\\\WWW]]]\\\]]]```fffkkkllllllmmmppprrrsssssstttwwwzzz}}}xxxnnnmmmjjjeee^^^UUUMMMFFFBBB>>>;;;888666555555333222444222///.../////////.../////////......---------------,,,++++++,,,,,,,,,***+++,,,+++))))))+++---,,,,,,+++++++++++++++,,,++++++************++++++************************(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))(((((((((((((((((((((((((((((('''''''''((()))))))))))))))))))))))))))))))))((('''&&&&&&'''((())))))))))))))))))))))))))))))))))))))))))(((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$"""###%%%((())))))((((((''''''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''((('''&&&&&&%%%%%%%%%&&&''''''&&&%%%%%%%%%&&&&&&'''&&&&&&&&&&&&'''(((((('''''''''''''''''''''''')))((((((((('''''''''&&&''''''''''''''''''''''''''''''''''''''''''''''''(((((('''''''''&&&&&&&&&&&&&&&%%%%%%%%%&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&%%%%%%&&&'''((((((((('''((((((((((((((((((((((((''''''''''''((((((((((((((((((''''''''''''(((((('''''''''((((((((((((((())))))))))))(((((((((((())))))))))))******************++++++++++++******)))(((&&&&&&((()))((('''''''''''''''''''''''''''&&&''''''''''''(((((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((''')))******(((((()))+++***))))))(((((())))))***'''(((((())))))))))))((())))))((((((((())))))************+++******)))(((++++++++++++++++++++++++---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------.........///////////////.........------........./////////111...///111111111555<<<999:::===@@@AAABBBBBBAAABBB@@@AAADDDFFFEEEFFFIIIPPPPPPRRRWWWXXXXXX[[[```dddlllyyy{{{uuunnnjjjjjjkkkhhhdddeeejjjmmmmmmgggddd```\\\YYYWWWVVVVVVVVV\\\cccffffffhhhooouuu|||{{{vvvkkkeeeccccccbbb```___^^^]]]]]]^^^```aaaiiiiiigggdddaaabbbggglllnnnllliiigggfffggghhhiiijjjnnnuuu{{{}}}{{{zzzyyyuuutttrrrtttxxx{{{}}}~~~xxxtttsssrrrpppooonnnooopppppplllmmmlllllljjjhhhfffdddeeeggghhhhhhggghhhmmmqqquuuuuuvvvvvvtttnnnfff```[[[\\\]]]______\\\WWWRRRUUUVVVXXX\\\aaacccbbbaaa]]]^^^^^^___aaaffflllqqqjjjmmmppprrrtttvvvyyy||||||}}}{{{pppfff^^^ZZZPPPKKKDDD???<<<;;;:::999888666444333333333000///000///---,,,+++,,,,,,---...---------------......,,,,,,---,,,+++***,,,...+++++++++++++++,,,,,,,,,++++++************++++++************************************************))))))))))))))))))))))))))))))))))))))))))))))))'''(((((())))))*********))))))((('''''''''(((((())))))))))))))))))))))))((((((''''''''''''(((((())))))))))))))))))))))))((((((((((((((('''&&&&&&''''''''''''''''''''''''###!!!!!!"""&&&)))***+++((((((''''''''''''((((((((('''&&&%%%%%%&&&'''(((''''''''''''''''''''''''((('''&&&&&&%%%&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''(((''''''''''''((())))))&&&&&&&&&&&&&&&&&&&&&&&&(((((((((''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&###$$$%%%'''((()))))))))((((((((((((((((((((((((''''''''''''((((((((((((((((((''''''''''''((((((&&&'''''''''(((((())))))(((((((((((())))))))))))************++++++++++++******++++++++++++******((((((''''''((((((((((((''''''''''''(((((((((((('''''''''''''''(((((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((&&&'''))))))((()))***,,,))))))(((((((((((())))))%%%&&&((()))******)))((())))))))))))))))))******************************++++++++++++++++++++++++...---,,,++++++,,,---...------------------------............////////////////////////////////////------........./////////111//////111111222999AAADDDIIIRRRYYY]]]\\\ZZZWWWWWWWWWYYY]]]````````````___\\\\\\```bbbeeejjjqqq|||~~~}}}}}}zzzxxxtttpppmmmlllkkkkkkqqqrrrooojjjiiilllmmmlll```]]]ZZZWWWUUUUUUVVVWWW\\\ccckkkqqqsssuuuyyy}}}{{{uuusssssstttuuuvvvwwwwwwxxxyyyzzzzzzzzz~~~~~~}}}zzzwwwwww|||~~~|||{{{}}}~~~}}}|||zzzxxxwwwwwwwwwvvvuuuwwwzzz~~~~~~}}}||||||rrrjjjggghhhiiijjjjjjgggcccaaa___```ccceeeeeeccc___]]]XXXWWWVVVVVVWWW[[[___cccYYYZZZ\\\^^^aaaeeehhhkkkrrrtttzzz~~~yyyvvvfff```WWWPPPLLLJJJHHHHHHBBB@@@<<<:::999888666444333111///---------///000/////////......//////000---------,,,,,,,,,---...++++++,,,,,,,,,,,,,,,,,,,,,++++++******++++++,,,************************++++++++++++++++++++++++))))))))))))))))))))))))(((((((((((((((((((((((('''(((((()))***++++++,,,******)))((('''''''''((((((((((((((((((((((((((((((((((((''''''((((((((((((((((((((((((((((((((((((((())))))(((((('''&&&((((((((((((((((((((((((&&&%%%###$$$&&&(((((('''((((((''''''''''''(((((()))'''&&&$$$$$$&&&''')))''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''&&&&&&&&&&&&&&&'''((()))'''''''''''''''(((((()))&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''')))((('''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&$$$%%%&&&'''((((((((((((((((((((((((((((((((((((''''''''''''((((((((((((((((((''''''''''''((((((&&&&&&''''''((()))))))))(((((((((((()))))))))))))))))))))*********++++++'''(((((())))))))))))((('''((((((((((((''''''((('''''''''((((((((())))))((((((((((((((((((((((((((((((((((((((((((((((((''''''''''''(((((((((((())))))))))))))))))))))))%%%&&&((()))((((((***,,,))))))(((((((((((())))))&&&'''(((*********)))((((((((()))*********************************++++++++++++++++++++++++++++++---,,,+++******+++,,,---------------------------....../////////000000000..................//////........./////////000000000///000222333555===GGGVVV___mmmzzz{{{wwwuuuwwwyyy}}}nnniiihhhlllrrryyy~~~yyywwwxxx{{{|||yyyvvvrrrllleeebbbaaabbbcccsssuuurrrllljjjlllllliii```___]]]]]]^^^```ccceeelllpppxxx}}}zzz{{{~~~yyyzzz{{{|||zzzxxxvvvuuurrrssssssqqqlllfff```]]]^^^\\\ZZZXXXWWWVVVVVVUUUXXXWWWWWWXXX[[[^^^```bbbbbbdddiiimmmmmmmmmsss|||~~~}}}{{{rrrlllhhhfffdddcccZZZVVVOOOIIIEEEBBB@@@>>>;;;999666444222222333444000///......------.........---,,,,,,------------***+++,,,------------,,,,,,,,,++++++++++++,,,,,,************************************************************************(((((((((((((((((((((((('''(((((()))***++++++,,,+++***)))((((((((((((((((((((((((((((((((((((((('''(((((((((((((((((('''(((((((((((((((((((((((()))************)))(((((((((((((((((((((((((((((()))(((&&&'''(((((('''&&&((((((''''''''''''(((((()))(((&&&%%%%%%&&&((()))''''''''''''''''''''''''''''''&&&&&&&&&''''''(((&&&&&&&&&&&&''''''((()))&&&&&&%%%%%%&&&&&&'''(((&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''&&&''''''''''''''''''''')))(((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&'''''''''''''''&&&&&&((((((((((((((((((((((((''''''''''''((((((((((((((((((''''''''''''((((((&&&'''''''''(((((())))))'''((((((((()))))))))***((((((((()))))))))******''''''((()))))))))))))))&&&((())))))(((''''''((('''''''''(((((())))))***)))))))))(((((((((((('''((((((((((((((((((((((((''''''''''''(((((((((((())))))))))))))))))))))))%%%&&&((((((((((((***+++***))))))(((((())))))***((())))))************)))(((((()))***+++++++++++++++************+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---,,,,,,++++++,,,,,,---------------------------....../////////000000000............//////////////////000000000111111111000111333666777999BBBMMMbbblll}}}~~~zzz|||{{{uuurrrsssvvvyyy{{{~~~uuukkkjjjgggbbb^^^]]]^^^aaacccppprrrrrrnnnnnnqqqqqqnnnoooooooooqqqssswwwzzz|||yyyqqqllliiiooommmjjjhhhfffbbb^^^ZZZ^^^]]][[[[[[]]]^^^___^^^TTTTTTVVVYYYYYYXXX]]]dddcccgggjjjjjjjjjnnnwww~~~xxxssskkkddd^^^XXXRRROOOGGGEEEAAA===999666444333111000///...---,,,,,,,,,///---+++,,,---...------***+++,,,.........------,,,,,,++++++++++++,,,,,,************************))))))))))))))))))))))))************************))))))))))))))))))))))))'''(((((())))))***************)))((((((((())))))))))))))))))))))))))))))''''''((((((((((((''''''))))))))))))))))))))))))***************))))))(((''''''''''''''''''''''''((('''&&&''')))******(((((((((''''''''''''(((((()))((('''&&&&&&'''((()))'''''''''''''''''''''''''''''''''&&&''''''((()))'''''''''&&&''''''((((((%%%%%%%%%%%%%%%&&&''''''%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&&&&&&&&&&'''''''''%%%%%%&&&&&&'''(((((((((''''''''''''''''''''''''&&&&&&&&&'''''''''''''''((((((''''''&&&'''''''''''''''''''''''''''''''''''''''(((((('''&&&&&&%%%((((((((((((((((((((((((''''''''''''((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((''''''(((((())))))******'''((((((((())))))))))))((()))***++++++,,,++++++%%%(((******(((&&&'''(((&&&''''''((())))))******))))))))))))((((((((('''((((((((((((((((((((((((''''''''''''(((((((((((())))))))))))))))))))))))%%%'''(((((('''''')))************))))))*********,,,++++++************+++'''(((***+++,,,,,,++++++++++++*********+++,,,---,,,,,,,,,,,,,,,,,,,,,,,,------............------................................./////////000000/////////000000000111111111111111111222222222222222444888<<<<<<>>>HHHSSS[[[eeesss}}}}}}wwwmmmiiilllppptttuuurrrvvv|||yyyooohhheeeeeeeeefffhhhlllpppsssyyy|||~~~}}}}}}zzzzzz|||yyywwwvvvtttpppmmmgggdddbbbbbbcccdddbbbaaaWWWSSSRRRTTTUUUSSSUUUYYYWWWZZZ]]]\\\ZZZ^^^fffnnnssssssrrrrrrssstttvvvwww~~~wwwooojjj```]]]WWWPPPIIIBBB===:::888777555333111000/////////,,,***+++---...---+++)))***,,,...//////...------,,,,,,++++++,,,,,,---************************))))))))))))))))))))))))************************))))))))))))))))))))))))(((((((((((((((((((((((()))))))))((())))))******))))))))))))))))))))))))&&&'''((())))))((('''&&&)))))))))))))))))))))))))))))))))***)))(((((('''&&&&&&&&&&&&&&&&&&&&&&&&'''&&&&&&''')))***)))(((((((((''''''''''''(((((((((''''''''''''''''''((('''''''''''''''''''''''''''''''''''''''((()))))))))((((((''''''''''''(((&&&&&&&&&&&&&&&'''((((((%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%&&&&&&'''(((((()))''''''''''''''''''''''''&&&&&&&&&'''''''''(((((((((''''''''''''(((((()))((((((((((((((((((((((((&&&&&&''''''''''''''''''((((((((((((((((((((((((''''''''''''((((((((((((((((((''''''''''''(((((()))))))))(((''''''&&&&&&'''''''''((()))*********(((((()))))))))*********((()))***++++++,,,,,,,,,$$$(((******(((&&&'''(((&&&''''''((()))******+++******))))))((((((((('''((((((((((((((((((((((((''''''''''''((((((((()))))))))))))))))))))))))))&&&'''((((((''''''((()))++++++************++++++...---+++***)))***++++++'''(((***+++,,,,,,++++++++++++*********+++---...,,,,,,,,,,,,,,,,,,,,,,,,---...///000000///...---....................................////////////000000111111222222222222111111222222222333333333333666<<<@@@@@@BBBLLLWWWNNNUUUaaannnwww|||}}}}}}|||rrrnnnooovvv{{{zzzyyyyyy~~~~~~{{{yyy{{{zzzqqqgggdddhhhlllllljjjgggmmmuuu{{{}}}{{{vvvsssrrrrrrsssvvvxxx||||||{{{||||||{{{yyypppmmmkkkkkkmmmmmmjjjhhhccc]]]ZZZ[[[\\\ZZZZZZ\\\[[[^^^```\\\WWWWWW^^^eeeiiiiiiiiijjjlllnnnpppqqqvvv}}}|||xxxrrriii___UUUMMMHHH???>>>;;;999777555444444...,,,)))***,,,...---+++)))***---...//////...------,,,,,,++++++,,,,,,---************************************************************************))))))))))))))))))))))))((((((((((((''''''''''''))))))(((((()))***++++++))))))))))))))))))))))))&&&'''((())))))((('''&&&))))))))))))))))))))))))(((((((((((((((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&((('''&&&'''((((((&&&$$$((((((''''''''''''((((((''''''(((((((((((('''''''''''''''''''''''''''''''''''''''''''''((())))))***)))(((''''''''''''''''''''''''''''''((())))))%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%&&&&&&'''''''''%%%%%%&&&&&&'''((())))))''''''''''''''''''''''''&&&&&&&&&'''''''''(((((('''''''''''''''((()))***))))))))))))))))))))))))$$$$$$&&&'''(((((())))))((((((((((((((((((((((((''''''''''''((((((((()))((((((''''''''''''((((((******)))((('''&&&%%%%%%&&&''''''((()))******+++)))************+++++++++&&&&&&'''))))))*********''''''''''''(((((((((((((((((()))******)))((('''******))))))((((((''''''%%%&&&&&&&&&&&&&&&&&&%%%((((((((((((((((((((((((((('''&&&%%%%%%&&&'''((())))))))))))************'''(((***+++,,,,,,+++************)))))))))))))))++++++******************+++,,,------......------///...---,,,+++,,,---...---------.........////////////000000///---+++***,,,,,,---///111222111000222000//////000000000///222333444333111///222666AAAAAACCCHHHMMMQQQRRRRRRLLLOOOVVV```jjjpppqqqpppvvvvvvuuuuuuuuuvvvvvvwwwnnnnnnpppvvv|||}}}}}}wwwvvvyyyxxxxxxyyy}}}oooiiicccaaadddhhhjjjjjjlllnnnrrr{{{~~~yyywwwxxxwwwssspppppplllhhhkkktttuuuooommmsssmmmjjjfffbbb______```aaagggfffdddaaa```aaaeeehhhnnnzzz{{{uuuzzzuuuggg^^^WWWTTTOOOJJJFFFBBB>>>::::::888555444444333111///000000...+++******,,,...))),,,...---+++***,,,...************************++++++++++++++++++++++++++++++++++++++++++++++++++++++************++++++))))))))))))))))))))))))))))))))))))))))))))))))***************)))(((((())))))((('''''''''''''''''''''(((((())))))******''''''&&&&&&&&&&&&''''''***)))'''&&&%%%%%%%%%&&&))))))(((((('''''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&)))'''%%%%%%&&&'''''''''&&&%%%$$$######%%%'''((('''''''''''''''''''''''')))((('''&&&&&&'''((()))&&&%%%%%%$$$$$$%%%%%%&&&''''''''''''''''''''''''((('''&&&%%%$$$%%%%%%&&&******)))((('''&&&%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((''''''''''''''''''((((((((((((+++)))'''(((+++,,,***((()))(((((('''''''''(((((())))))))))))***************)))((((((((()))+++,,,,,,,,,+++***))))))******''''''''''''(((((((((((('''((()))******)))((('''***)))))))))((((((((('''&&&&&&''''''''''''&&&&&&(((((((((((((((((((((((('''((()))))))))((('''&&&))))))))))))******************+++++++++******)))+++++++++***************++++++******************+++,,,------......------......---,,,,,,,,,---...------........./////////......///000000///......111111000111111111000///111111222444555666555444777999<<<======<<<>>>BBBIIIIIILLLPPPTTTWWWXXXWWWPPPRRRWWW___hhhoooqqqpppsssrrrrrrrrrssstttuuuvvvqqqqqqsssxxx{{{vvvuuutttrrrtttxxxzzzyyyxxxyyy{{{{{{xxxuuugggdddbbbeeellltttxxxzzz{{{}}}yyyuuutttrrrrrrwww}}}~~~}}}xxxvvvrrrpppoooooommmllleeeeeeddd```\\\[[[^^^aaaiiiqqqsssllleeeiiipppuuu{{{|||}}}{{{wwwsssllleee^^^VVVNNNIIIAAA>>>:::777666555333222333333222000///...//////---///000///---,,,---///++++++,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++++++++************++++++))))))))))))))))))))))))))))))))))))))))))))))))***************)))((((((++++++***)))))))))))))))'''((((((((()))))))))***(((''''''&&&&&&''''''((())))))'''&&&%%%&&&&&&''')))((((((((('''''''''''''''''''''''''''''''''''',,,***(((((()))*********%%%%%%#########$$$&&&''''''''''''''''''''''''''')))((('''&&&&&&'''((()))''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''***)))((('''&&&''''''((()))))))))(((''''''&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((''''''''''''''''''((((((((((((***(((&&&''')))***)))'''***))))))((((((((())))))))))))))))))***************)))((((((((()))++++++,,,++++++***))))))******''''''''''''((((((((((((''''''))))))))))))((('''))))))))))))((((((((((((''''''((((((((((((''''''((((((((((((((((((((((((''')))+++,,,,,,***'''%%%))))))))))))************---,,,+++***))))))))))))++++++++++++++++++++++++******+++++++++++++++++++++,,,------......------...------,,,------..................////////////,,,---///000111111111111000000000000000000/////////111444777888999888777???BBBFFFHHHKKKMMMPPPRRRWWWWWWYYY]]]aaabbbaaa___YYYYYY[[[```gggmmmppprrrsssssssssssstttuuuwwwxxxwwwwwwyyy|||uuullljjjlllooossswwwxxxvvvuuuuuutttrrrooolllgggfffiiiqqq}}}~~~|||yyy~~~zzzvvvwwwzzzzzzwwwssskkknnnpppmmmhhhfffhhhkkkoooqqqmmmccc\\\\\\___```hhhiiikkknnnsssxxx}}}}}}uuulllfffXXXSSSLLLFFFAAA===999777222222222111000000///............---+++***+++,,,,,,,,,------.........///,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++************++++++)))))))))))))))))))))))))))))))))))))))))))))))))))************))))))(((++++++***)))))))))))))))(((((((((((())))))))))))(((''''''&&&&&&''''''((((((((('''&&&&&&''''''(((((((((((((((''''''''''''((((((((((((((((((((((((,,,***))))))***++++++***&&&&&&%%%$$$%%%&&&'''(((''''''''''''''''''''''''((((((''''''''''''((((((((((((''''''''''''((((((''''''''''''''''''''''''))))))(((''''''''''''(((((((((((((((((((((((((((&&&&&&&&&&&&&&&&&&&&&&&&''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''''''''''''''''''''''''''''''''((((((((((((''''''''''''''''''(((((((((((()))'''&&&'''((()))(((&&&******))))))))))))******))))))))))))************)))))))))((()))******+++,,,+++******)))*********''''''''''''((((((((((((&&&'''((()))))))))((('''))))))))))))(((((((((((((((((())))))))))))(((((((((((((((((((((((((((((())))))+++++++++)))'''%%%((()))))))))************---,,,***)))))))))***+++*********+++++++++++++++******+++++++++++++++,,,+++,,,------......---------------------.............../////////000000000------...///000111111222...///000111111222444555333555999;;;<<<>>>@@@AAAJJJNNNQQQTTT[[[dddjjjmmmpppppppppqqqrrrpppmmmjjjeeedddcccdddhhhmmmqqqtttzzzyyyxxxxxxxxxzzz{{{}}}~~~zzzoooffffffjjjmmmqqqtttppppppqqqsssssssssrrrqqqvvvvvvzzz}}}}}}xxxsssuuu{{{~~~{{{vvvvvv{{{|||zzz}}}}}}uuulllfffdddcccbbbbbbaaa___```bbbggglllpppuuuvvvyyy~~~yyytttlllcccZZZPPPGGGBBB:::888555333333222111000......---,,,+++++++++,,,,,,,,,---....../////////,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++************++++++************************))))))))))))))))))))))))))))))************)))((()))(((((('''''''''''''''(((((((((((())))))))))))((((((''''''''''''(((((('''''''''''''''(((((((((((((((((((((((('''''''''(((((((((((((((((((((((()))'''&&&&&&((((((((('''(((((('''''''''((()))***''''''''''''''''''''''''(((((((((''''''((((((((((((''''''''''''''''''(((''''''''''''''''''''''''&&&&&&&&&&&&%%%%%%&&&&&&''''''''''''(((((())))))''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%%%%&&&&&&&&&&&&((((((((((((((((((((((((''''''((((((((((((''''''''''''''''''(((((((((((((((((('''((((((((((((((())))))(((((())))))******((()))))))))************)))))))))))))))******+++++++++***************+++''''''''''''((((((((((((%%%&&&''')))))))))((('''(((((((((((())))))))))))(((((())))))))))))(((((())))))))))))))))))))))))***)))(((((('''''''''(((((()))))))))************+++***)))))))))***,,,---))))))))))))******++++++******++++++,,,,,,,,,,,,+++,,,------......---------------......//////////////////000000000111111....../////////000000111///111333444444666:::===999<<<@@@CCCFFFKKKQQQUUUZZZ___bbbgggssszzzuuupppnnnlllkkkkkknnnrrruuu~~~}}}{{{yyyyyyzzz|||}}}|||vvvooolllnnnfffbbbfffkkklllmmmnnnjjjmmmrrrwww|||{{{uuuvvv|||~~~zzz|||~~~zzzxxxwwwvvvuuuooojjjddd^^^[[[]]]```bbbaaacccgggmmmttt{{{yyymmmaaaZZZSSSMMMEEE???;;;999666444444222000///...//////000------------......//////,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++************++++++++++++++++++++++++++++++************************((())))))*********)))))))))(((((('''''''''''''''))))))))))))(((((((((((((((((((((''''''(((((((((''''''(((((((((((((((((('''''''''((((((((((((((('''''''''''''''''''''''''''%%%%%%%%%''''''&&&%%%'''''''''''''''(((((()))(((((((((((((((((((((((('''(((((((((((((((((('''''''''&&&&&&&&&&&&''''''''''''''''''''''''''''''%%%%%%&&&&&&&&&&&&&&&&&&&&&&&&''''''((()))))))))''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''%%%%%%%%%&&&&&&&&&''''''((((((((((((((((((((((((''''''((((((((((((''''''''''''''''''(((((((((((())))))***)))))))))))))))'''''''''''''''((()))***((()))))))))************((()))))))))************+++***************++++++''''''''''''(((((((((((($$$%%%'''((())))))((('''(((((((((((())))))))))))(((((())))))))))))(((((())))))))))))))))))))))))))))))'''&&&&&&''')))***))))))))))))************))))))))))))***+++,,,---((((((((()))******++++++******++++++,,,---------+++,,,------......------,,,---...///////////////000000000000111111111111000000//////000111222222000333666777888:::@@@DDDDDDHHHNNNSSSWWW]]]dddjjjooouuuyyy|||xxxwwwuuurrroooooorrrtttyyywwwuuussssssuuuwwwyyy~~~{{{tttkkkddd```cccaaaccclllrrrqqqooooooqqqvvv}}}}}}{{{rrrjjjccc`````````ZZZ\\\```dddgggiiijjjjjjkkkmmmqqqvvv{{{yyyoooggg\\\RRRKKKEEE>>>999;;;777333111000000000///........................,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++++++++************++++++++++++++++++++++++++++++************************((())))))************)))++++++***)))))))))))))))))))))))))))(((((((((((()))((((((''''''(((((()))(((((()))))))))((((((''''''''''''(((((((((((((((''''''''''''''''''''''''''''''&&&'''))))))'''%%%%%%%%%%%%&&&&&&&&&&&&&&&((((((((((((((((((((((((''''''(((((((((((('''''''''&&&&&&&&&&&&&&&&&&'''''''''''''''''''''''''''&&&'''(((((()))(((((((((&&&'''''''''(((((())))))''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''&&&&&&&&&'''''''''((((((''''''''''''''''''''''''''''''((((((((((((''''''''''''''''''(((((((((((()))***+++***)))((()))+++'''&&&&&&''''''((()))***))))))))))))************(((((()))************)))*********)))******+++,,,''''''''''''(((((((((((($$$%%%&&&((())))))(((''''''((((((((()))))))))***'''(((((())))))(((((('''))))))))))))))))))))))))'''(((((()))************))))))))))))************)))******+++++++++******(((((()))******+++,,,,,,******++++++,,,------...+++,,,------......------+++,,,...///000000000///000000000111111111222222111000000111222444666777555:::???CCCGGGMMMUUU\\\aaagggoootttuuuwwwzzz~~~||||||{{{wwwsssppppppqqqmmmllljjjjjjkkknnnqqqsssuuuvvvuuupppjjjdddaaaaaacccfffooo{{{{{{wwwrrrooommmhhhjjjmmmnnnkkkfff```\\\\\\]]]___bbbfffjjjnnnppppppwwwvvvnnnggg^^^TTTLLLIIIDDD>>>999777666333111111111111000//////......------------------------++++++++++++++++++++++++++++++************++++++,,,,,,,,,,,,,,,,,,,,,,,,************************(((((()))***************++++++***)))))))))))))))***)))))))))((((((((('''))))))(((((((((((())))))))))))******)))((('''&&&''''''''''''((((((((()))(((((((((((((((((((((((((((''''''(((***)))'''%%%&&&&&&''''''((((((((('''((((((((((((((((((((((((&&&'''((())))))((('''&&&((((((''''''''''''((((((''''''''''''''''''''''''&&&&&&((()))))))))(((((('''''''''((((((((((((((('''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''((((((((())))))&&&&&&&&&&&&&&&&&&&&&&&&''''''((((((((((((''''''''''''''''''((((((((((((''')))+++***((('''(((***''''''''''''((()))***+++))))))))))))************'''((()))***+++******)))******))))))***++++++,,,''''''''''''((((((((()))###$$$&&&((())))))(((((('''((((((((())))))******''''''((((((((((((''''''))))))))))))))))))))))))%%%'''***,,,------+++***))))))))))))***************+++,,,,,,+++***((('''))))))***+++,,,,,,------******+++,,,,,,---......+++,,,------......------+++,,,...000000000000///000111111111111222222222000111111222555888:::<<>>???<<<888666444333000.........------------------///...---...000000...,,,******+++++++++,,,,,,,,,***++++++,,,,,,++++++***++++++++++++++++++++++++))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))))))))))))))))))))************))))))---,,,+++)))((('''''''''******))))))((((((''''''(((((())))))))))))(((((())))))(((((((((((())))))(((((((((((((((((((((((())))))))))))((('''&&&%%%''''''(((((((((((((((((())))))))))))))))))))))))))))))(((((('''''''''&&&'''''''''''''''''''''''')))'''%%%%%%&&&%%%"""(((+++,,,+++)))'''((()))(((((())))))))))))(((((((((''''''&&&&&&&&&''''''---***'''''')))++++++))),,,+++)))'''&&&%%%&&&&&&((((((((((((((((((((((((''''''''''''''''''&&&&&&))))))))))))))))))))))))))))))))))))))))))))))))&&&&&&&&&&&&'''''''''((())))))))))))************+++,,,,,,,,,,,,,,,,,,---(((((((((((((((''''''&&&&&&''''''((((((((((((((())))))))))))))))))))))))(((((((((((((((((((((((('''''''''((((((((())))))))))))))))))*********+++******+++++++++,,,,,,,,,***************+++++++++++++++++++++++++++++++++,,,++++++++++++,,,------,,,---............---,,,111333444333111000000111///000111222333555777999888;;;>>>AAAEEEMMMXXX```rrr|||tttuuuuuuuuutttsssrrrqqqtttsssrrrqqqoookkkgggeeeaaabbbccc```___bbbiiioootttwww|||xxx}}}yyywwwsssqqqooommmjjjeee```]]]TTTUUUWWWYYY\\\^^^______```bbbfffkkkssszzz|||uuupppiii___XXXNNNIIIBBB===:::777555444444333222111111000...------,,,+++,,,---...,,,+++++++++++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++***************************)))))))))(((((((((((())))))))))))))))))))))))((())))))******))))))((())))))((((((((((((((((((***)))))))))((((((((('''(((((())))))))))))(((((())))))(((((((((((())))))(((((((((((((((((((((((())))))))))))((('''&&&%%%(((((((((((((((''''''''')))))))))))))))))))))))))))(((((((((''''''''''''''''''''''''''''''''''''***(((&&&'''((('''%%%"""(((***,,,+++)))'''((()))'''(((((())))))(((((('''(((''''''&&&&&&&&&''''''***'''%%%%%%'''(((((('''))))))((('''&&&'''((((((((((((((((((((((((((((((''''''''''''''''''''''''))))))))))))))))))))))))))))))))))))))))))))))))(((((((((((())))))))))))************++++++++++++++++++,,,,,,,,,,,,------(((((((((((((((''''''&&&&&&''''''((((((((((((((())))))))))))))))))))))))((((((((((((((((((((((((''''''((((((((())))))))))))))))))*********************+++++++++,,,,,,,,,))))))******++++++,,,,,,++++++++++++,,,,,,,,,,,,---,,,,,,,,,,,,---......------............------///000111111000///000111---///222444555666888:::BBBGGGNNNUUU]]]gggttt}}}~~~sssiiimmmqqqrrrpppnnnnnnoooiiijjjkkkkkkjjjhhhgggeeeeeeiiijjjhhheeeiiittt~~~xxxpppiiifffdddcccdddffffffccc```UUUUUUWWW[[[```gggmmmqqquuuxxx|||}}}wwwhhhaaaWWWMMMFFFAAA===;;;555444222111111000...,,,---,,,++++++------,,,++++++++++++,,,,,,,,,------++++++,,,,,,,,,,,,++++++++++++++++++++++++++++++******************************)))))))))((((((((())))))))))))))))))))))))'''(((((())))))(((((('''&&&&&&''''''(((((())))))))))))))))))(((((((((((((((((())))))))))))(((((())))))(((((((((((())))))(((((((((((((((((((((((())))))))))))((('''&&&&&&))))))(((((('''''''''&&&))))))))))))))))))))))))((((((((((((''''''''''''''''''''''''''''''''''''***)))(((((())))))(((&&&(((***+++***)))(((((()))'''''''''(((((('''''''''''''''&&&&&&&&&''''''((((((&&&%%%%%%&&&''''''&&&'''''''''''''''((()))***(((((((((((((((((((((((('''''''''''''''''''''''')))))))))))))))))))))))))))))))))))))))))))))))))))*********+++++++++++++++++++++,,,,,,,,,,,,---+++++++++,,,,,,---------(((((((((((((((''''''&&&&&&''''''((((((((((((((())))))))))))))))))))))))(((((((((((((((((((((((('''(((((((((((()))))))))******************************+++++++++,,,,,,,,,))))))******+++,,,------+++++++++,,,,,,,,,,,,,,,---------------...//////---.........////////////***+++---......///222444333555666777777;;;AAAFFFVVV]]]fffoooxxxtttllliiiooottttttoookkkjjjkkkdddfffhhhjjjkkkkkklllmmmpppssstttsssttt{{{yyy~~~zzzwwwxxxzzzxxxqqqkkk```^^^[[[YYYYYY[[[]]]___gggiiilllpppuuu||||||rrrfff\\\RRRJJJFFF===999444222222333222000///...,,,,,,......---,,,,,,,,,,,,,,,------------+++,,,,,,,,,,,,,,,,,,+++++++++++++++++++++++++++*********************************)))))))))(((((())))))))))))))))))))))))''''''((((((((((((''''''''''''((((((((()))(((((())))))))))))(((((((((((((((((())))))))))))(((((())))))(((((((((((())))))(((((((((((((((((((((((()))))))))))))))((('''''')))))))))(((''''''&&&&&&(((((((((((((((((((((((((((((((((((((((''''''''''''''''''''''''''''''''')))(((((((((((()))))))))((()))******)))(((((((((&&&&&&''''''''''''&&&&&&'''&&&&&&&&&&&&'''((((((((((((''''''((((((((((((''''''''''''((((((((()))((((((((((((((((((((((((''''''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((*********+++++++++,,,,,,++++++++++++,,,,,,,,,,,,+++++++++,,,,,,---------(((((((((((((((''''''&&&&&&''''''((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))(((((((((((()))))))))***+++++++++*********************+++++++++,,,,,,,,,))))))***+++,,,------...++++++,,,,,,,,,---------......------......///000............//////000000...///000111111222555777888;;;===@@@FFFQQQ___jjj{{{{{{rrrkkkhhhhhhnnnttttttnnniiiggghhhkkknnnrrrtttvvvxxx{{{}}}~~~}}}~~~yyyrrrqqqnnniiiccc^^^\\\ZZZZZZ___]]]\\\]]]aaaffflllpppzzzvvvlllbbb[[[QQQJJJAAA<<<::::::888555222000---------...---,,,,,,,,,---------.........,,,,,,,,,------,,,,,,,,,++++++++++++++++++++++++************************************))))))))))))************************''''''((((((((((((''''''))))))*********)))((('''(((((((((((())))))))))))(((((())))))))))))(((((())))))(((((((((((())))))(((((((((((((((((((((((())))))))))))))))))((('''))))))(((((('''''''''&&&(((((((((((((((((((((((('''''''''((((((((((((((((((((((((((((((((((((((('''''''''&&&&&&'''((()))((((((((()))))))))((((((&&&&&&''''''''''''&&&&&&&&&&&&&&&&&&&&&'''(((((('''((((((((((((''''''((((((((((((((((((''''''&&&(((((((((((((((((((((((('''''''''((((((((())))))(((((((((((((((((((((((((((((((((((((((((((((((()))))))))*********++++++*********++++++++++++,,,******+++,,,,,,---......(((((((((((((((''''''&&&&&&''''''((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))((((((((()))))))))******+++++++++++++++***************+++++++++,,,,,,,,,******++++++,,,,,,------++++++,,,,,,------.........------------...////////////...//////000111222222333333222222333666888999???IIISSS```rrr}}}vvvoooiiigggjjjnnnsssyyyzzzxxxuuutttttt}}}{{{uuuzzzxxxsssooojjjgggeeeddd```\\\WWWUUUVVVZZZ]]]^^^fffmmmvvv|||~~~~~~~~~xxxhhh___TTTLLLHHHCCC<<<777555333///---------,,,+++---------.........//////,,,,,,------------,,,,,,++++++++++++++++++++++++++++++++++++++++++++++++++++++*********)))))))))************************'''(((((())))))((((((''')))***+++++++++)))((('''(((((((((((())))))))))))(((((())))))))))))(((((())))))(((((((((((())))))(((((((((((((((((((((((()))))))))******))))))((((((((((((((((((((((((((())))))))))))))))))))))))'''''''''(((((((((((((((((((((((((((((((((((((((&&&''''''%%%$$$%%%''')))(((''''''((()))***)))''''''''''''(((((('''''''''&&&&&&&&&&&&&&&'''((()))$$$&&&((((((&&&%%%&&&&&&(((((())))))((('''&&&&&&(((((((((((((((((((((((('''''''''(((((())))))***))))))))))))))))))))))))))))))))))))))))))))))))(((((()))))))))*********************++++++++++++******+++,,,,,,---......(((((((((((((((''''''&&&&&&''''''((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))(((((()))))))))*********,,,,,,,,,++++++***************+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---......///------,,,,,,------...//////////////////111222333222333444555666888===@@@HHHTTTfffvvv}}}}}}yyytttsssqqqooottt{{{zzz{{{{{{zzzyyywwwuuussssssmmmhhhccc______^^^]]][[[[[[```gggkkkmmmooouuuyyyzzzsssjjjddd```WWWLLLBBB<<<999555222111000///...---.........////////////,,,,,,------------,,,,,,+++++++++++++++++++++++++++++++++++++++++++++++++++++++++*********))))))************************((())))))******))))))(((&&&''')))***+++***(((((('''((((((((()))))))))***(((((())))))))))))(((((())))))(((((((((((())))))((((((((((((((((((((((((((())))))*********))))))&&&&&&''''''((()))))))))))))))))))))))))))))))))''''''''''''((((((((()))(((((((((((((((((((((((('''((('''%%%######&&&)))(((&&&&&&'''******)))''''''(((((())))))(((((('''&&&%%%%%%&&&&&&((())))))$$$'''))))))'''&&&&&&'''&&&'''((())))))(((((('''((((((((((((((((((((((((&&&''''''((())))))******))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************++++++++++++,,,,,,,,,---)))******+++---......///(((((((((((((((''''''&&&&&&''''''((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************,,,,,,,,,++++++***************+++++++++,,,,,,,,,---,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,---...//////---,,,,,,,,,,,,---......000////////////111333444333555888;;;???DDDJJJOOObbbqqq}}}yyyyyyzzz}}}vvvrrrrrrwwwzzz}}}|||{{{|||~~~~~~}}}|||zzzvvvqqqnnnllliiieeeaaa]]]```cccccccccgggooovvv}}}}}}zzzpppaaaVVVCCC@@@;;;777666555333222............/////////000,,,------......------,,,+++++++++++++++++++++++++++++++++++++++++++++++++++++++++************)))************************))))))************))))))###$$$''')))******)))((('''((((((((())))))******(((((())))))))))))(((((())))))(((((((((((())))))((((((((((((((((((((((((((())))))*********))))))%%%%%%&&&'''((()))******))))))))))))))))))))))))&&&'''''''''(((((())))))))))))))))))))))))))))))((())))))&&&######&&&***(((&&&%%%'''***+++)))&&&(((((())))))))))))((((((%%%%%%%%%&&&'''((()))***&&&))),,,,,,***((()))***###%%%'''(((*********)))((((((((((((((((((((((((&&&''''''((()))******+++))))))))))))))))))))))))))))))))))))))))))))))))))))))*********+++++++++,,,,,,,,,---------......)))******+++---...//////(((((())))))))))))(((((('''(((((()))))))))))))))&&&''''''((()))******+++++++++++++++++++++++++++************************,,,+++***)))***+++,,,---++++++,,,,,,,,,,,,------,,,,,,,,,---------......---------.........//////111///......///000000///000111111222444666777888888===AAACCCIIITTT___ddd}}}uuuxxxyyy{{{}}}~~~}}}|||}}}}}}}}}~~~}}}}}}~~~~~~zzztttoooppphhhdddeeefffdddfffkkkpppxxx{{{tttjjj]]]MMMBBB>>><<<888444333111...---...///000///...------,,,,,,,,,,,,---111///,,,***)))+++...000,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++***))))))******(((((()))***++++++,,,,,,+++******)))))))))))))))***)))(((((((((***+++,,,+++++++++*********)))))))))))))))))))))))))))))))))))))))))))))))))))))))))***,,,,,,***)))***+++))))))))))))))))))))))))''''''(((((())))))******))))))(((((('''''''''&&&''''''''''''''''''''''''*********)))((((((''''''************))))))))))))******))))))((((((((('''))))))))))))(((((((((((()))(((''''''(((***---...))))))((((((''''''&&&&&&((((((((((((((((((((((((((((((((((((((((((((((((''''''(((((())))))******))))))))))))(((((((((((((((((((((((()))))))))))))))************+++++++++++++++++++++,,,---......///......---------......(((((())))))))))))(((((('''(((((()))))))))))))))((()))))))))***+++++++++*********+++++++++++++++))))))))))))))))))))))))+++++++++++++++,,,------++++++,,,,,,,,,,,,------,,,,,,---------.........---.....................///.........///////////////222444444333555<<>>;;;777333111000111111...////////////...------------------------------------,,,,,,,,,---......************************+++******))))))))))))))))))************)))(((((((((((()))))))))))))))***))))))))))))))))))))))))))))))))))))))))))))))))''')))+++***)))((())))))))))))))))))))))))))))))))))))))))))(((((((((((('''''''''(((((((((((((((((((((((((((((((((((((((%%%%%%&&&&&&'''(((((((((%%%%%%%%%&&&&&&''''''((('''''''''''''''((((((((()))))))))))))))((((((((('''''''''&&&&&&&&&&&&%%%'''''''''((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))((((((((((((''''''(((((())))))******)))))))))*********++++++)))************+++++++++++++++++++++,,,---..................///000111111(((((())))))))))))(((((())))))***++++++++++++***)))*********+++,,,,,,,,,,,,,,,,,,+++******))))))************************+++++++++++++++,,,------++++++,,,,,,,,,,,,------............////////////------...///000111111222000333666777777;;;BBBHHHRRReeevvvllliiijjjllloooqqqqqqrrrtttvvvwww|||}}}yyyvvvtttrrrqqqpppoooppppppnnnmmmnnnrrrvvv{{{zzz|||{{{oooddd^^^OOOKKKDDD>>>888555333333111000000000////////////........................---------------...//////************************+++******))))))))))))))))))******+++***)))((('''(((((((((((())))))******))))))))))))))))))))))))))))))))))))))))))))))))&&&((())))))(((''''''((())))))))))))))))))))))))***)))))))))((((((((('''''''''''''''((((((((()))''''''''''''''''''''''''%%%%%%&&&&&&'''((((((((($$$$$$%%%&&&&&&'''(((((('''''''''(((((()))))))))******))))))((((((''''''&&&&&&''''''((((((''''''((((((((((((((('''''''''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))'''''''''((()))*********))))))*********+++++++++)))************+++++++++++++++++++++,,,---..................///000111222(((((())))))))))))(((((())))))***++++++++++++*********+++,,,,,,---.........------,,,+++***)))))),,,,,,,,,,,,,,,,,,,,,,,,,,,+++***)))***+++,,,---++++++,,,,,,,,,---------............/////////000,,,---...///000111222333222666:::<<<>>>DDDNNNVVVaaaxxxxxxiiicccbbbaaadddgggjjjmmmrrrzzz|||xxxvvvuuuwwwxxxxxxxxxyyyxxxuuupppnnnoooqqqssspppnnnrrr{{{{{{sssgggaaaXXXNNNDDD>>>:::999222222111000000000000000........................---------------...///000++++++******************+++******))))))))))))))))))***+++++++++)))(((''''''((((((((())))))******))))))))))))))))))))))))))))))))))))))))))))))))%%%'''(((((('''&&&&&&'''))))))))))))))))))))))))******))))))((((((((('''&&&'''''''''(((((())))))''''''''''''''''''''''''*********)))((((((''''''&&&&&&''''''((()))******'''((((((((())))))******++++++***)))((('''&&&&&&$$$%%%''')))+++---......))))))(((((('''''''''&&&((((((((((((((((((((((((((((((((((((((((((((((((''''''(((((())))))******&&&''''''((()))******+++)))************+++++++++)))************+++++++++++++++++++++,,,---..................///000222222(((((())))))******++++++)))************)))((((((++++++++++++++++++++++++777222,,,))))))+++++++++++++++,,,,,,,,,---------)))************+++++++++,,,,,,------...////////////000111111///------...222...,,,000444444666999:::===BBBGGGOOOXXXbbbhhh{{{zzzmmmddd```^^^aaa___cccnnnyyyxxxvvvuuuwww{{{~~~~~~|||xxx{{{{{{vvvtttvvvwwwvvvwwwrrrllljjjooowww|||pppcccWWWLLLDDD???;;;555111444444///...222000...,,,,,,---.........//////.........------------------,,,,,,,,,++++++))))))******++++++++++++))))))))))))))))))))))))''''''((((((((((((''''''))))))))))))))))))))))))************))))))))))))))))))))))))))))))))))))******))))))((((((''''''(((((())))))((('''&&&&&&******))))))((((((''''''))))))))))))))))))))))))(((((()))***************))))))(((((((((((())))))))))))(((''''''''''''((()))(((''''''''')))***+++))))))))))))))))))))))))***'''$$$%%%(((***)))((((((''''''&&&&&&((()))***'''''''''''''''((()))))))))))))))))))))(((((((((((())))))((('''''')))+++)))))))))))))))))))))))),,,,,,++++++***+++++++++++++++,,,------......///000111222111000000111222)))))))))))))))*********------,,,+++***(((&&&%%%++++++++++++++++++++++++///,,,******,,,...---,,,++++++++++++,,,,,,,,,---++++++++++++,,,,,,,,,,,,,,,,,,---......//////000...///111111/////////000000111444999888666777<<>>444444444333333333333222//////.........------------------,,,,,,++++++++++++++++++++++++++++++++++++++++++,,,,,,+++++++++))))))))))))))))))))))))((((((((((((''''''''''''))))))))))))))))))))))))'''((((((((())))))******'''((()))***************'''((((((((())))))******))))))))))))))))))))))))***************)))(((((())))))(((((((((((())))))&&&&&&&&&'''((()))***+++)))(((''''''''')))***+++))))))))))))))))))))))))$$$'''******((('''''')))'''((()))++++++******)))'''''''''((()))+++---...((())))))***+++,,,,,,,,,$$$'''+++,,,,,,,,,,,,,,,++++++++++++++++++++++++************+++,,,---...------......///000000000000222444777:::@@@GGGLLL************************))))))***++++++++++++***,,,,,,------,,,,,,+++***,,,,,,,,,++++++*********///......------,,,,,,+++,,,---...000000000//////...---000333333111333888888999;;;<<<<<>>;;;666444333222111000111...+++***+++---------//////...---,,,,,,++++++,,,++++++******++++++,,,))))))))))))))))))))))))************************))))))))))))************************))))))))))))******))))))((((((''''''&&&'''((()))***+++,,,,,,((((((''''''''''''(((((())))))))))))((((((((((((******))))))((((((''''''''''''''''''((((((((()))))))))(((((((((((())))))(((((((((((((((((((((((((((((((((((((((((((((((())))))))))))(((((((((((('''((((((((((((''''''&&&(((((((((((())))))))))))******+++++++++******)))((((((((((((((((((((((((******+++++++++,,,,,,,,,***++++++,,,,,,------...,,,,,,,,,---///111222333000000...555@@@BBBIII\\\************************))))))***+++++++++++++++******,,,---.../////////,,,,,,,,,,,,+++++++++***---------------------------...///111111111000000111000222555555444888>>>======???DDDGGGMMMYYYdddttt~~~vvvtttttttttuuuxxx~~~~~~{{{xxxvvvqqqnnnqqqwwwttt|||wwwlllbbb[[[OOOIIIAAA:::666555444333333000...------......---///......------,,,,,,,,,,,,,,,++++++++++++,,,,,,++++++++++++++++++++++++************************))))))))))))************************)))))))))))))))))))))))))))((((((((())))))))))))))))))******+++******)))))))))******))))))))))))((((((((((((***)))))))))(((((((((''''''''''''((((((((())))))(((((())))))))))))(((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))(((((((((((())))))************))))))(((((((((((())))))))))))*********++++++******)))((((((((((((((((((((((((******++++++++++++++++++***++++++,,,,,,---......------......///111222333333666555:::EEEHHHRRRggg************************)))******+++++++++++++++))))))+++,,,---.........---,,,,,,,,,,,,,,,+++++++++,,,,,,---....../////////000000111111111111000111000111444555888@@@JJJOOOLLLMMMRRRXXX^^^fffnnnzzz|||sssrrrtttyyy|||}}}|||uuussstttmmmrrrwww|||~~~~~~yyyjjjbbbUUUIIIAAA<<<999777333000...---------,,,+++...............---------,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,************************))))))))))))************************))))))))))))(((((()))))))))))))))))),,,++++++***)))((('''''',,,+++***)))))))))))))))))))))))))))(((((((((((())))))))))))((((((((((((''''''((((((((()))))))))'''((()))******)))((('''(((((((((((((((((((((((((((((((((((((((((((((((((((((((((((())))))))))))'''((()))******+++******(((((((((((())))))))))))))))))******+++******)))))))))))))))))))))))))))++++++******************+++++++++,,,------............//////000111222333222666777<<>>FFFLLL```}}}******************************+++,,,,,,,,,,,,+++,,,,,,,,,,,,,,,++++++***------------------------/////////......---------/////////000000111222222666888===FFFOOO]]]rrrzzzyyyyyywwwtttttt}}}|||{{{{{{{{{{{{yyywwwtttrrrpppyyy~~~{{{uuurrrsssyyy{{{xxxxxx{{{}}}wwwiii[[[OOOGGG???;;;666333222111000///.../////////////////////---,,,,,,,,,,,,,,,,,,---++++++++++++++++++++++++************************((()))))))))************************)))))))))((((((((())))))******++++++*********)))))))))))))))******)))((((((((((((((())))))))))))(((((((((((((((((((((((())))))))))))(((((((((((()))))))))***&&&((()))++++++)))(((&&&(((((((((((((((((((((((())))))))))))))))))))))))'''((((((((()))))))))***%%%%%%&&&((())))))))))))(((((((((((())))))))))))'''((()))***************++++++++++++++++++++++++++++++******************+++,,,,,,------...//////------......///000111222666===@@@DDDLLLSSSiii***************************++++++,,,,,,,,,,,,,,,+++,,,---...///000000000---------............///000000//////...------,,,/////////000111333444555777>>>JJJYYYdddrrrxxxsssssssssrrrpppppppppsssuuuwww|||pppjjjmmmxxx}}}yyyyyyqqqddd[[[JJJDDD<<<555111///------000000000000000/////////------,,,,,,,,,,,,------++++++++++++++++++++++++************************))))))))))))************************))))))))))))))))))******************(((((())))))******+++++++++++++++******++++++,,,))))))))))))(((((((((((((((((((((((())))))))))))((((((((()))))))))******'''((()))******)))((('''(((((((((((((((((((((((())))))))))))))))))))))))''''''(((((())))))******'''((()))******+++******(((((((((((())))))))))))''''''((()))******************************************+++++++++,,,,,,,,,,,,,,,,,,---......//////------...///000222333444999???AAAEEENNNVVVlll***************************+++,,,,,,------,,,,,,***+++,,,---.../////////------......////////////////////////............000000000111444666999:::<<>>DDDGGGIIINNNYYYiii~~~++++++++++++***************++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,------...///---///000000///...///000/////////000111222444444222666<<>>DDDJJJIIIMMMUUUaaarrr++++++++++++++++++++++++***+++,,,,,,------,,,,,,******++++++---...///000---///000111/////////000111111111222333555777888:::>>>EEELLLTTTbbbttt}}}wwwrrrooonnnrrryyy}}}{{{zzzzzzzzzzzzlllbbbTTTHHH@@@;;;666222000000111111000///////////////......---......///,,,,,,+++++++++,,,,,,---+++,,,,,,,,,,,,+++******************************------+++***)))((((((((())))))))))))))))))))))))'''(((******((((((((()))******************************))))))((((((''''''(((((((((((())))))))))))))))))))))))))))))))))))***))))))(((((())))))***)))))))))))))))*********))))))))))))))))))))))))((((((''''''((()))***,,,((((((''''''''''''(((((())))))))))))))))))))))))))))))*********+++++++++,,,,,,,,,,,,------..................///000111222222222666<<>>888555333111///......------...//////000///...---,,,,,,,,,,,,,,,+++,,,,,,,,,,,,+++******,,,++++++******++++++,,,************+++,,,---...))))))))))))))))))))))))'''(((******((((((((()))))))))))))))))))))))))))(((((((((((())))))))))))(((((((((((())))))))))))++++++++++++++++++++++++***))))))(((((())))))***'''(((((()))******++++++)))))))))))))))))))))))),,,+++)))(((''''''((((((***))))))(((((())))))***************************)))************+++++++++..................------////////////000111222333555777<<>>FFFPPP[[[dddjjjmmmzzzsssgggaaaccclllvvvyyy}}}xxxooooooyyy}}}tttnnn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ooo,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---.../////////...000000000//////.........222000000444555333555999:::CCCNNNWWWbbbqqq{{{yyykkkfffgggggg{{{~~~yyyzzztttuuu{{{zzzmmm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ggg}}},,,,,,,,,,,,,,,,,,,,,,,,------......///.........///////////////000000000111///000555777777:::???DDDRRRcccnnnxxxpppiiikkkppp|||}}}{{{yyyyyy~~~rrrbbb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lll,,,,,,,,,,,,,,,,,,------....../////////...------.........///000111111111222111333777999:::???FFFMMMaaaxxxtttmmmpppzzz~~~|||iiiVVVFFF===999888444000000444444111......---------------------///000///---++++++,,,,,,,,,---.........------,,,,,,++++++******++++++,,,+++++++++************))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************)))******)))''''''(((***))))))))))))))))))))))))************************))))))))))))))))))))))))************************++++++++++++++++++++++++((())))))***+++,,,------------------------------///000000111222666<<<@@@GGGEEEEEELLL\\\rrr,,,,,,,,,---------------///////////////...---,,,.........///000000111111555444666;;;===???FFFNNNXXXooo|||xxxvvvzzziii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ppp,,,,,,,,,------.........///000000000///...------////////////000000000000444555999???DDDIIISSS^^^mmm|||pppuuu}}}~~~~~~kkk___PPPGGG>>>888666444222111---.....................000111111///,,,++++++,,,,,,,,,++++++++++++++++++,,,++++++***++++++,,,,,,,,,,,,,,,++++++++++++***))))))))))))))))))))))))************************(((((((((((((((((((((((())))))))))))))))))))))))((()))))))))************((()))))))))'''''')))***))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************************++++++++++++++++++++++++*********+++,,,,,,---------------....../////////000///...000555<<>>FFFMMMVVVdddrrr{{{rrrrrr}}}~~~yyyzzzooobbbUUUGGG@@@<<<666222000000/////////////////////111111111///,,,+++,,,---,,,,,,+++*********++++++++++++******++++++,,,,,,,,,,,,,,,,,,++++++++++++))))))))))))))))))))))))++++++++++++++++++++++++))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************&&&(((******)))((())))))))))))))))))))))))))))))(((((((((((((((((((((((())))))))))))))))))))))))************************++++++++++++++++++++++++++++++++++++,,,,,,---------------...//////000000111000000333999AAAFFFHHHFFFHHHOOOVVVZZZggg,,,,,,------.../////////...//////000000000000//////000111444666888:::;;;<<>>777555222222111111000000//////111111000...,,,,,,---......---,,,+++***++++++,,,++++++******++++++,,,---------,,,,,,,,,+++++++++))))))))))))))))))))))))************************************************))))))))))))))))))))))))))))))))))))************$$$'''***+++***)))(((((())))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))************************+++++++++++++++++++++++++++++++++,,,,,,,,,,,,------------...///000000000333222333777>>>EEEIIIJJJKKKLLLSSS___fffrrr,,,,,,------...///000000......///000000111000000...000222666999===???AAAFFFIIIOOOVVV[[[dddttt}}}xxx~~~wwwdddZZZQQQFFF>>><<<444333333222111000//////111111000...,,,,,,.../////////---,,,+++,,,,,,---+++*********+++,,,,,,------------,,,,,,,,,++++++))))))))))))))))))))))))))))))))))))))))))))))))************************))))))))))))))))))))))))))))))))))))************###&&&***,,,,,,)))((('''))))))))))))))))))))))))************************))))))))))))))))))))))))************************+++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,------------...///000000111555444555:::BBBHHHKKKLLLSSSQQQXXXgggsss,,,,,,,,,---------......111///...000333555444222111444888;;;<<>>EEEKKKQQQVVVYYYbbbrrr{{{------------.........///000//////000444666777666999===BBBGGGPPP```sss~~~~~~wwwssssssqqq```OOOHHH???999777666333111------............---,,,.........---------------///......------......///,,,,,,,,,,,,++++++++++++************************************))))))))))))))))))))))))))))))))))))************))))))))))))((('''%%%&&&(((******))))))))))))))))))))))))))))))******++++++******)))))))))))))))************+++&&&"""###(((,,,---,,,************************************+++++++++,,,,,,,,,,,,,,,,,,,,,------...///000///......000222888<<>>EEEIIINNNPPP]]]uuu///111333444555777;;;===DDDIIIPPPWWW___lll{{{|||xxxssssssxxxtttwww~~~|||zzz}}}zzzwwwfffWWWKKKBBB<<<555333111000000///...,,,.........---------,,,,,,------,,,,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,+++++++++******+++++++++))))))))))))))))))))))))))))))))))))))))))))))))************************)))))))))))))))))))))))))))((((((((((((***,,,---)))************+++++++++************************++++++++++++++++++++++++++++++++++++,,,,,,,,,,,,------...//////000111111222333444777<<>>666333111111000000000000/////////............---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++******+++++++++))))))))))))))))))))))))))))))))))))))))))))))))************************))))))))))))))))))))))))...---+++)))'''''''''((()))************+++++++++************************)))))))))))))))))))))))),,,,,,,,,,,,------------------...///111222333333222555;;;AAAGGGKKKNNNOOOTTT\\\ppp555:::AAAHHHQQQaaauuu{{{|||~~~zzzqqq{{{}}}qqq^^^UUUHHH<<<444111//////000000/////////.........------------,,,,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++,,,,,,))))))))))))))))))))))))))))))))))))))))))))))))************************)))))))))))))))))))))))),,,+++)))((((((((()))***)))************+++++++++************************************************,,,,,,,,,------------...------...000111222333444555888>>>EEEJJJNNNOOOPPPVVVaaayyy666>>>HHHRRR]]]lll|||~~~~~~wwwrrrgggVVVGGG<<<777555555////////////............------,,,,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++************++++++))))))))))))))))))))))))))))))))))))))))))))))))************************)))))))))))))))))))))))))))((((((((((((***+++---)))************+++++++++************************++++++++++++++++++++++++,,,,,,,,,---------......------...000111333444444777;;;AAAHHHMMMPPPQQQQQQZZZggg???AAAMMMaaarrr|||}}}{{{}}}~~~ooo[[[HHH;;;555333...000222222111000000111//////.........---------,,,,,,,,,+++++++++******+++***)))(((((()))***+++++++++++++++++++++++++++++++++++++++++++++++++++))))))))))))))))))))))))+++++++++************))))))************++++++++++++++++++*********))))))******************************+++++++++,,,,,,,,,******+++,,,,,,---......///000111000000111444666888>>>EEEKKKNNNPPPRRRTTTccczzzGGGLLLYYYkkkxxx~~~||||||~~~rrr___MMM>>>666222222111000000000000000//////.........---------,,,,,,,,,++++++++++++***,,,+++***))))))***+++,,,++++++++++++++++++++++++++++++++++++++++++++++++************************+++++++++************))))))************++++++++++++++++++*********))))))******************************+++++++++,,,,,,,,,)))*********+++,,,,,,,,,...///000000000222555888<<>>HHHKKKOOORRRXXXdddsss~~~eeessszzzqqqooossszzzyyyjjjSSSIII<<<555333444222111000000/////////.........---------,,,,,,,,,++++++***++++++++++++++++++***++++++++++++++++++++++++++++++++++++++++++++++++************************+++++++++*********))))))))))))*********+++++++++******************************************************+++++++++,,,,,,,,,000/////////////////////---...///000333888>>>BBBIIILLLRRR[[[iii{{{uuuzzzqqqnnnrrr~~~ggg\\\MMM@@@888444222000000000000/////////......------------,,,,,,,,,,,,******++++++++++++******++++++++++++++++++++++++++++++++++++++++++++++++))))))))))))))))))))))))+++++++++************))))))************+++++++++***************+++++++++******************************+++++++++,,,,,,,,,,,,------------------------...000222555;;;BBBGGGIIILLLVVVggg~~~zzzwww|||wwweeeSSSCCC999444333000000000000/////////......------------,,,,,,,,,***+++,,,------,,,+++***++++++++++++++++++++++++++++++++++++++++++++++++************************+++++++++************))))))************+++++++++))))))*********+++++++++******************************+++++++++,,,,,,,,,+++++++++,,,,,,------......///111333777>>>FFFKKKLLLOOOZZZqqqyyycccNNN@@@999777000000000000////////////......---------,,,,,,,,,,,,,,,---......---,,,,,,+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++************))))))************+++++++++))))))******++++++++++++******************************+++++++++,,,,,,,,,,,,,,,------...///000000...000111444888@@@HHHNNNQQQSSS^^^vvv|||~~~{{{~~~mmm\\\MMM???666555444111//////000///---......---------,,,,,,,,,------------,,,,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++************************,,,+++***+++,,,,,,,,,+++************************)))************+++++++++---,,,,,,+++*********+++,,,,,,,,,,,,,,,,,,,,,,,,---------------...///000000111444888===DDDJJJNNNPPPPPP\\\vvvxxxtttyyyvvvrrrtttzzzxxxhhhWWWGGG<<<666555333111000000///,,,.........---------,,,,,,++++++,,,,,,,,,+++******,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++************************+++***)))***++++++******************************)))************+++++++++---,,,++++++******++++++,,,,,,++++++++++++++++++------------...//////000111222444:::AAAGGGLLLNNNOOOQQQ]]]sss|||uuuxxxssspppvvv~~~sssiiijjjrrrzzzgggTTTHHH===:::666444333111///...///.........------------)))******++++++++++++***,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++***************************************)))))))))************************)))************+++++++++,,,,,,++++++******++++++++++++++++++++++++,,,,,,------------...///000111222222555<<>>GGGOOOVVVUUURRRVVVdddpppqqqeeeqqq~~~~~~~~~yyy}}}ttteeeRRRGGG;;;444555555333000000000000000//////......+++---......---,,,,,,---,,,++++++***************++++++++++++++++++++++++************************++++++++++++++++++++++++))))))*********+++++++++------,,,+++************,,,,,,,,,------------.../////////000222777===BBBJJJPPPWWWZZZ\\\fffvvvrrrkkk~~~~~~~~~|||~~~{{{vvvtttdddUUUBBB666333444333111//////..................,,,---......---,,,---...------,,,++++++++++++,,,++++++++++++++++++++++++************************))))))******************))))))*********+++++++++------,,,+++************,,,,,,---------...............//////222888???EEEOOORRRWWWbbbqqqvvvppp}}}}}}{{{|||tttxxxuuueeeOOO===555333333222//////...------......///,,,...///...---,,,---///......---,,,,,,,,,,,,,,,++++++++++++++++++++++++************************)))))))))))))))*********)))************+++++++++,,,,,,++++++***+++++++++,,,---------.....................000333:::BBBHHHTTTTTT\\\nnnxxx|||xxxyyyvvvaaaLLL???888666555000000///......///000000---...///...,,,,,,...///...---,,,,,,++++++,,,,,,++++++++++++++++++++++++************************)))))))))******+++++++++)))************++++++++++++++++++***++++++,,,,,,------------............//////000111555===FFFLLLTTTVVVaaawww~~~zzz~~~pppZZZIII???:::999111111000//////000111222---...///...,,,,,,...000---,,,++++++******++++++++++++++++++++++++++++++*********************************++++++,,,,,,,,,)))************+++++++++************+++,,,---------------.........//////000000111333777???HHHOOORRRVVVccc{{{