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,---,,,***))))))***,,,---++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,,,,------......---,,,,,,+++******------------------------,,,------......------,,,------------------------,,,,,,,,,,,,,,,,,,,,,,,,------------------------------++++++++++++---------------------------------,,,,,,++++++,,,,,,---+++,,,,,,------,,,,,,+++,,,,,,,,,---------......------------------------,,,,,,,,,,,,,,,,,,,,,,,,------------------------++++++++++++++++++++++++------------,,,,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,CCCBBBBBBCCCEEEGGGFFFEEEKKKJJJIIIHHHGGGHHHHHHIIIFFFFFFFFFFFFFFFEEEEEEDDDEEEHHHJJJHHHFFFIIIQQQYYYlllsssdddMMMFFFFFFEEEIIIEEEEEEDDDDDDEEEFFFHHHIIIHHHGGGEEEDDDCCCDDDEEEFFFDDDDDDEEEEEEEEEFFFFFFFFFDDDFFFFFFFFFHHHLLLKKKHHHEEEEEEEEEDDDEEEEEEFFFFFFHHHHHHIIIIIIHHHHHHGGGFFFHHHHHHHHHGGGGGGFFFFFFFFFEEEEEEFFFGGGJJJLLLMMMMMMHHHGGGFFFFFFFFFFFFCCCAAABBBBBBCCCDDDEEEGGGHHHIIIIIIHHHFFFFFFEEEFFFGGGHHHIIIIIIJJJJJJIIIIIIHHHGGGHHHGGGGGGGGGGGGHHHJJJKKKMMMLLLJJJHHHHHHIIIJJJKKKIIIIIIJJJJJJIIIHHHGGGGGGKKKLLLLLLLLLLLLLLLKKKKKKIIIHHHGGGGGGFFFFFFGGGGGGFFFFFFFFFFFFFFFFFFFFFFFFIIIHHHHHHGGGGGGHHHHHHHHHGGGFFFFFFFFFFFFFFFFFFGGGGGGGGGGGGGGGGGGGGGGGGGGGKKKLLLKKKJJJGGGFFFGGGHHHHHHFFFEEEEEEFFFGGGGGGFFFDDDDDDEEEFFFFFFFFFFFFFFFFFFFFFGGGIIIKKKLLLNNNNNNHHHGGGEEEGGGIIIJJJIIIGGGFFFEEEDDDDDDFFFFFFEEEDDDCCCEEEFFFFFFEEEDDDEEEFFFFFFGGGGGGHHHGGGFFFEEEDDDDDDEEEEEEFFFFFFEEEEEEDDDCCCCCCBBBBBBBBBBBBBBBBBBAAAAAAAAAAAABBBCCCDDDDDDFFFFFFFFFFFFEEEEEEEEEEEECCCCCCCCCCCCDDDEEEFFFGGGGGGHHHHHHFFFDDDBBBCCCDDDCCCBBBBBBBBBBBBBBBBBBCCCDDDBBB@@@???@@@BBBCCCBBBEEEFFFEEEBBB???<<<<<<<<<;;;:::999888777666555555444444333333333222222222111111111000000000//////////////////////////////------------------------------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---......---,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------......------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------------------+++,,,,,,------,,,,,,+++,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,,,,++++++,,,,,,------------,,,,,,---------,,,,,,,,,------......---------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,---------,,,,,,......---,,,,,,+++******************++++++++++++***++++++,,,,,,++++++*********+++++++++,,,,,,,,,---,,,+++******+++,,,---++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------...............------,,,++++++***------------------------,,,------......------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------------------------,,,,,,++++++,,,,,,------------------------------,,,,,,++++++,,,,,,---+++,,,,,,------,,,,,,+++,,,,,,,,,---------......------------------------,,,,,,,,,,,,,,,,,,,,,,,,------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,---------,,,,,,+++***,,,,,,,,,,,,,,,,,,,,,,,,CCCBBBBBBCCCEEEFFFFFFDDDGGGGGGGGGGGGHHHIIIJJJKKKGGGGGGGGGGGGFFFFFFEEEEEEHHHHHHHHHGGGFFFGGGJJJMMMSSS\\\TTTEEEDDDFFFEEEHHHFFFEEEEEEFFFFFFGGGHHHIIIIIIHHHEEECCCCCCEEEGGGHHHDDDDDDEEEEEEEEEEEEFFFFFFEEEGGGGGGFFFIIINNNNNNKKKFFFFFFEEEDDDDDDDDDEEEEEEHHHHHHHHHHHHHHHGGGGGGFFFHHHHHHGGGGGGGGGGGGGGGGGGCCCCCCCCCDDDFFFHHHJJJKKKHHHFFFDDDDDDDDDDDDCCCAAABBBCCCDDDEEEFFFHHHIIIIIIGGGFFFEEEEEEEEEFFFGGGHHHIIIIIIJJJJJJIIIIIIHHHHHHHHHHHHHHHGGGGGGHHHIIIIIIKKKJJJIIIHHHGGGHHHIIIJJJHHHIIIIIIIIIIIIHHHHHHGGGHHHHHHIIIJJJKKKLLLLLLMMMHHHHHHGGGGGGFFFFFFGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGHHHGGGGGGGGGHHHHHHHHHHHHEEEEEEDDDDDDDDDDDDEEEEEEIIIIIIIIIIIIIIIIIIIIIIIIKKKNNNPPPMMMIIIGGGJJJNNNKKKIIIFFFEEEFFFGGGHHHHHHEEEEEEFFFFFFFFFFFFFFFFFFIIIIIIIIIIIIJJJKKKLLLLLLIIIGGGGGGHHHJJJKKKJJJIIIGGGFFFEEEEEEFFFGGGFFFEEEDDDEEEFFFFFFEEEFFFGGGIIIJJJJJJJJJJJJIIIGGGEEEDDDEEEEEEFFFFFFFFFFFFFFFEEEDDDDDDDDDCCCCCCBBBBBBBBBAAAAAAAAAAAABBBCCCDDDEEEGGGGGGFFFFFFFFFEEEEEEEEEEEEDDDDDDDDDEEEFFFGGGHHHGGGHHHHHHFFFDDDCCCCCCDDDDDDCCCCCCCCCCCCCCCCCCDDDDDDAAA??????@@@BBBBBBAAAFFFGGGFFFCCC>>>;;;:::;;;999999888888777666555555333333333333222222222222111111000000000000//////////////////////////////------------------------------------------------------------------------,,,,,,------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------......------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------------------------,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,,,,++++++++++++,,,,,,,,,,,,++++++,,,,,,,,,,,,,,,---------...------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------,,,++++++...------,,,,,,++++++***************+++++++++,,,***++++++,,,,,,++++++*********+++++++++,,,,,,,,,...---,,,++++++,,,---...++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,---------.........//////......------,,,+++++++++------------------------,,,------......------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------------------------,,,,,,++++++,,,,,,------------------------------,,,,,,++++++,,,,,,---+++,,,,,,------,,,,,,+++,,,,,,,,,---------......------------------------,,,,,,,,,,,,,,,,,,,,,,,,------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,DDDCCCBBBCCCEEEFFFEEEDDDFFFFFFGGGGGGHHHIIIJJJKKKHHHGGGGGGFFFFFFFFFFFFFFFKKKIIIHHHHHHIIIIIIIIIHHHHHHRRRMMMDDDFFFEEEBBBEEEFFFFFFFFFGGGGGGHHHIIIIIIIIIGGGDDDBBBBBBDDDFFFHHHDDDDDDE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,,,,,,,------,,,,,,,,,---------......,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------,,,,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++******++++++,,,---...---,,,+++++++++++++++++++++++++++++++++++++++******+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------------------++++++,,,,,,,,,,,,------,,,,,,,,,---------......------------------------------------------------------------------------,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,,,,******+++,,,++++++,,,,,,,,,,,,++++++---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,...---,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,***++++++,,,,,,++++++***+++,,,,,,------,,,,,,+++******+++++++++,,,,,,,,,++++++++++++++++++++++++++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,TTTMMMFFFCCCEEEHHHHHHGGGDDDEEEEEEDDDCCCCCCDDDFFFFFFFFFGGGHHHGGGFFFEEEDDDBBBCCCDDDEEEFFFFFFFFFFFFCCCCCCCCCCCCCCCCCCCCCCCCBBBAAAAAA@@@@@@AAAAAABBB@@@CCCFFFFFFDDDDDDEEEGGGEEEFFFGGGHHHGGGEEECCCBBB???@@@AAABBBCCCBBBAAAAAACCCCCCCCCCCCDDDEEEGGGGGGKKKIIIFFFCCCBBBCCCDDDEEEFFFFFFFFFFFFFFFEEEDDDDDDDDDFFFGGGHHHMMMQQQPPPKKKIIIJJJIIIFFFFFFIIIHHHDDDHHHIIIOOOXXXZZZUUUOOONNNLLLMMMNNNNNNMMMMMMNNNOOOFFFEEEDDDDDDDDDFFFGGGHHHEEEEEEEEEEEEEEEFFFFFFGGGGGGGGGGGGGGGFFFEEEEEEEEEIIIIIIJJJKKKKKKJJJIIIHHHFFFIIILLLLLLJJJJJJKKKNNNNNNKKKGGGEEEFFFGGGHHHHHHDDDCCCCCCDDDGGGHHHGGGFFFDDDEEEEEEFFFGGGGGGHHHHHHFFFGGGJJJLLLMMMLLLJJJHHHGGGGGGFFFFFFFFFFFFFFFGGGFFFGGGGGGHHHHHHHHHGGGGGGCCCBBBBBBAAAAAABBBBBBCCCBBBBBBBBBCCCCCCCCCDDDDDDDDDEEEGGGIIIJJJLLLLLLLLLNNNMMMJJJGGGEEECCCCCCCCCDDDEEEFFFFFFEEEEEEGGGIIINNNNNNLLLKKKJJJJJJJJJJJJKKKKKKLLLLLLLLLLLLKKKKKKEEEFFFFFFGGGFFFEEEDDDCCCCCCBBBBBBBBBCCCDDDFFFGGGEEECCCAAAAAABBBBBBAAA@@@@@@AAAAAABBBBBBCCCCCCCCCAAABBBBBBBBBCCCCCCDDDDDDAAAAAAAAA@@@>>>>>>???AAA@@@??????>>>===>>>>>>>>>???<<<:::;;;>>>>>>;;;777555555555555555555444444111111111111111111222222000/////////............------------------------+++,,,,,,------,,,,,,++++++++++++++++++++++++++++++,,,,,,------,,,,,,++++++++++++,,,,,,---------+++++++++,,,,,,---------+++++++++,,,,,,------------.........---,,,,,,+++***+++,,,,,,---------------,,,,,,++++++,,,,,,---++++++------------++++++++++++,,,,,,,,,---------------------------------++++++------------++++++,,,,,,,,,------.........,,,,,,,,,---------......,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------,,,,,,,,,++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++******++++++,,,---...---,,,,,,++++++++++++++++++++++++++++++++++++*********++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------------------++++++,,,,,,,,,---------,,,,,,,,,---------......------------------------------------------------------------------------,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,,,,******+++,,,+++++++++,,,,,,+++++++++---,,,,,,++++++,,,,,,---,,,,,,,,,,,,,,,,,,,,,,,,...---,,,,,,++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,+++++++++,,,,,,++++++++++++,,,,,,------,,,,,,+++******+++++++++,,,,,,,,,++++++++++++++++++++++++++++++,,,,,,,,,---------++++++++++++++++++++++++IIIIIIGGGGGGGGGGGGIIIIIIHHHGGGEEECCCCCCCCCCCCDDDGGGGGGHHHHHHGGGFFFDDDCCCDDDDDDEEEEEEEEEDDDDDDCCCEEEEEEEEEEEEEEEEEEEEEEEEEEEBBB??????BBBCCCCCCAAAEEEDDDDDDEEEDDDCCCCCCEEEGGGFFFFFFFFFEEEDDDDDDDDDCCCCCCBBBBBBBBBAAAAAAAAACCCCCCCCCCCCDDDDDDDDDDDDJJJIIIGGGEEECCCCCCFFFHHHEEEDDDCCCBBBBBBCCCDDDEEECCCDDDEEEGGGIIIKKKLLLMMMMMMKKKHHHEEECCCDDDEEEGGGHHHJJJMMMNNNNNNKKKGGGDDDFFFFFFEEEGGGNNNWWWWWWSSSMMMHHHDDDDDDGGGHHHDDD@@@CCCCCCDDDEEEGGGHHHHHHGGGDDDEEEFFFFFFFFFFFFEEEEEEGGGEEEDDDHHHLLLMMMIIIEEEEEEFFFHHHIIIHHHGGGEEECCCGGGGGGGGGFFFEEEDDDDDDCCCDDDEEEFFFGGGGGGGGGGGGGGGEEEFFFFFFGGGGGGGGGFFFFFFIIIIIIHHHHHHHHHGGGGGGGGGGGGHHHGGGFFFDDDCCCDDDEEEDDDDDDDDDEEEFFFFFFGGGGGGEEEDDDAAA?????????@@@AAABBBCCCEEEFFFEEEDDDEEEFFFEEEEEEFFFGGGGGGGGGGGGFFFIIIHHHFFFDDDCCCCCCDDDEEEEEEDDDDDDCCCCCCDDDEEEFFFIIIJJJKKKLLLLLLLLLKKKKKKIIIKKKMMMNNNNNNLLLJJJHHHBBBBBBBBBBBBBBBCCCDDDEEEBBBBBBBBBCCCEEEFFFHHHIIIFFFEEEDDDBBBBBBCCCCCCDDDBBBAAA@@@@@@BBBBBBAAA@@@AAAAAAAAAAAAAAAAAAAAAAAA???@@@AAABBBAAA???===;;;>>>>>>>>>>>>>>>?????????>>>>>>===<<<;;;::::::999777777555444333222222222111111111111000000000000////////////............------------------------,,,,,,,,,,,,,,,,,,,,,,,,++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++------------++++++++++++++++++++++++++++++,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,,,,,,,,,,---------,,,+++,,,...///...---,,,,,,---,,,+++***,,,.........------------.................................------,,,,,,------...++++++,,,,,,,,,,,,------...---,,,+++++++++,,,---+++,,,,,,------,,,,,,+++******+++++++++,,,,,,,,,---------------------------,,,,,,++++++,,,,,,---------------------------++++++------------++++++,,,,,,,,,,,,,,,,,,,,,,,,---------,,,,,,+++++++++,,,,,,++++++,,,,,,---...,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------......------------------------,,,,,,,,,,,,,,,,,,,,,,,,------------------------------,,,++++++***)))))))))************+++++++++++++++++++++++++++++++++***,,,......---++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,------------------------++++++,,,,,,,,,,,,------+++,,,,,,------,,,,,,+++++++++,,,,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,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