directions = [ [0, 1], [1, 1, 3], [1, 1, 3, 1], [2, 1, 1, 1], [1, 1, 1, 3, 3], [4, 1, 3, 5, 13], [2, 1, 1, 5, 5, 17], [4, 1, 1, 5, 5, 5], [7, 1, 1, 7, 11, 19], [11, 1, 1, 5, 1, 1], [13, 1, 1, 1, 3, 11], [14, 1, 3, 5, 5, 31], [1, 1, 3, 3, 9, 7, 49], [13, 1, 1, 1, 15, 21, 21], [16, 1, 3, 1, 13, 27, 49], [19, 1, 1, 1, 15, 7, 5], [22, 1, 3, 1, 15, 13, 25], [25, 1, 1, 5, 5, 19, 61], [1, 1, 3, 7, 11, 23, 15, 103], [4, 1, 3, 7, 13, 13, 15, 69], [7, 1, 1, 3, 13, 7, 35, 63], [8, 1, 3, 5, 9, 1, 25, 53], [14, 1, 3, 1, 13, 9, 35, 107], [19, 1, 3, 1, 5, 27, 61, 31], [21, 1, 1, 5, 11, 19, 41, 61], [28, 1, 3, 5, 3, 3, 13, 69], [31, 1, 1, 7, 13, 1, 19, 1], [32, 1, 3, 7, 5, 13, 19, 59], [37, 1, 1, 3, 9, 25, 29, 41], [41, 1, 3, 5, 13, 23, 1, 55], [42, 1, 3, 7, 3, 13, 59, 17], [50, 1, 3, 1, 3, 5, 53, 69], [55, 1, 1, 5, 5, 23, 33, 13], [56, 1, 1, 7, 7, 1, 61, 123], [59, 1, 1, 7, 9, 13, 61, 49], [62, 1, 3, 3, 5, 3, 55, 33], [14, 1, 3, 1, 15, 31, 13, 49, 245], [21, 1, 3, 5, 15, 31, 59, 63, 97], [22, 1, 3, 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