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.....+++,,,---......---,,,+++,,,,,,,,,,,,,,,---...///***++++++,,,---...//////***+++---...///...---,,,------............------***+++,,,---------,,,,,,++++++,,,,,,---......///........................,,,,,,+++++++++,,,,,,---++++++++++++,,,---...///------......------,,,++++++,,,------......------,,,,,,,,,,,,,,,,,,,,,,,,)))+++,,,......---,,,+++------,,,,,,,,,,,,------+++,,,,,,------,,,,,,+++++++++++++++,,,---...///+++++++++,,,,,,---------...------,,,,,,------...------------------,,,,,,,,,,,,------------,,,,,,,,,,,,------......//////,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---...////////////+++++++++++++++,,,------+++++++++,,,,,,,,,------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---......---,,,,,,,,,++++++******++++++,,,,,,---......,,,,,,---...++++++++++++++++++++++++------------,,,+++******........................---...............---------...///000000///...---........................+++,,,------......------........................---------------------------,,,+++*********+++,,,***,,,...---+++***,,,...---------------------------,,,,,,++++++,,,,,,---,,,,,,---------.........+++,,,---.........---,,,++++++,,,,,,,,,,,,------++++++++++++,,,,,,,,,---++++++************++++++,,,++++++******++++++,,,***++++++,,,,,,------...,,,,,,,,,,,,,,,,,,,,,,,,******,,,---------,,,+++------........./////////------------------------++++++++++++++++++++++++***+++---------,,,+++)))+++++++++,,,,,,---------+++++++++,,,,,,---------.........------,,,,,,,,,...............///000111+++---///...,,,+++,,,///------------------------***+++---...///...------++++++,,,,,,,,,---------------------------------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------......,,,,,,,,,,,,,,,,,,,,,,,,------------------,,,,,,,,,,,,,,,------.........------------------------------------------------------------------------------------------------+++,,,,,,------......///,,,,,,,,,------,,,,,,+++......---,,,,,,+++******,,,,,,,,,------.........,,,------......------,,,------------------------+++++++++,,,---...///000+++,,,...000000///...---/////////......---------+++,,,,,,---.........---......---,,,,,,,,,------,,,------......------,,,++++++---...//////000000---......///////////////++++++,,,------,,,++++++,,,,,,,,,,,,,,,---...///......---------,,,,,,,,,***+++---//////...---,,,------............------***+++,,,---...---,,,,,,++++++,,,,,,---...//////........................------------......///000++++++++++++,,,---......------......------,,,++++++,,,------......------...------,,,,,,++++++***(((***---//////...,,,***...------,,,,,,------...++++++------------++++++++++++++++++,,,---...///+++++++++,,,,,,---------...------,,,,,,------............------,,,,,,,,,,,,------......------,,,---------...............,,,,,,,,,,,,,,,,,,,,,,,,((()))***,,,---...////////////...------///000111,,,,,,,,,---------..............................,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---......---,,,,,,...------,,,,,,------...,,,---......,,,,,,---...........................++++++,,,---............////////////////////////------......///.........---...///111111///...---........................,,,---......//////......////////////////////////........................---,,,+++*********+++,,,***,,,...---+++***,,,...---------------------------,,,,,,++++++,,,,,,------------....../////////+++,,,---.........---,,,++++++,,,,,,,,,---------*********++++++,,,,,,,,,+++******************+++,,,++++++++++++++++++,,,)))***+++,,,------...///,,,,,,,,,,,,,,,,,,,,,,,,***+++,,,---...---,,,,,,.........////////////000------------------------------------------------''')))+++---------,,,++++++++++++,,,,,,---------+++++++++,,,,,,---------......---------,,,,,,,,,//////.........---------.........------,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,//////.........---------+++)))(((***...000///---------------------------.........------,,,,,,,,,***+++---......---+++***---------,,,,,,+++++++++++++++++++++++++++++++++.........------,,,,,,,,,+++---///111111///---+++.........------,,,,,,,,,........................------------------------------------------------........................---------------------------------,,,,,,+++++++++------,,,,,,,,,+++++++++***+++---------+++)))(((,,,,,,,,,------.........------------------------,,,,,,,,,,,,,,,---...///...------,,,,,,------...++++++,,,,,,---...//////---,,,,,,,,,,,,---......---------.........//////...---+++++++++,,,...000222222111///...---,,,++++++++++++++++++++++++++++++,,,------......------,,,------......------,,,,,,------......------,,,/////////......---------,,,,,,,,,---------......,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,---------......)))***,,,...//////...---,,,,,,------...///000000111111000000///...,,,,,,***+++,,,------,,,+++***+++++++++++++++++++++++++++,,,,,,------,,,,,,+++---------,,,,,,+++++++++,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,...------,,,,,,------...,,,,,,,,,,,,,,,,,,,,,,,,++++++,,,---............------------------------,,,,,,,,,,,,,,,,,,,,,,,,++++++------------++++++,,,,,,,,,------..................------,,,,,,,,,******+++,,,,,,---.........------,,,,,,------...++++++++++++++++++++++++---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