class Solver:

    def __init__(self):
        # self.move_map = [{} for _ in range(51)]
        # self.calc_one_step()
        # self.expand()
        # self.compress()
        self.move_map = [{}, {0: {(1,)}}, {0: {(2,), (1,)}}, {0: {(3,), (1,)}, 1: {(2,)}}, {0: {(2,), (1,), (4,)}, 1: {(3,)}}, {0: {(5,), (3, 2), (1,)}, 1: {(2,), (4,)}, 2: {(3,)}}, {0: {(2,), (3,), (6,), (1,)}, 1: {(5,)}, 2: {(4,)}}, {0: {(7,), (5, 2), (1,), (4, 3)}, 1: {(2,), (3,), (6,)}, 2: {(5,)}, 3: {(4,)}}, {0: {(5, 3), (2,), (8,), (1,), (4,)}, 1: {(7,), (5, 2)}, 2: {(3,), (6,)}, 3: {(5,)}}, {0: {(5, 4), (1,), (3,), (9,), (5, 2), (7, 2)}, 1: {(5, 3), (2,), (8,), (4,)}, 2: {(7,)}, 3: {(6,)}, 4: {(5,)}}, {0: {(7, 3), (6, 4), (1,), (2,), (10,), (5,)}, 1: {(3,), (9,), (7, 2)}, 2: {(8,), (4,)}, 3: {(7,)}, 4: {(6,)}}, {0: {(3, 2), (8, 3), (1,), (9, 2), (7, 4), (11,), (4, 3), (6, 5), (7, 2)}, 1: {(2,), (10,), (5,), (7, 3), (6, 4)}, 2: {(3,), (9,)}, 3: {(8,), (4,)}, 4: {(7,)}, 5: {(6,)}}, {0: {(1,), (2,), (3,), (4,), (7, 5), (6,), (12,)}, 1: {(9, 2), (7, 4), (8, 3), (11,), (7, 2)}, 2: {(10,), (5,), (7, 3)}, 3: {(9,)}, 4: {(8,)}, 5: {(7,)}}, {0: {(7, 3), (1,), (9, 2), (11, 2), (7, 6), (8, 3, 2), (9, 4), (7, 4, 2), (13,), (10, 3), (8, 5), (7, 2), (5, 3)}, 1: {(2,), (3,), (4,), (7, 5), (6,), (12,)}, 2: {(7, 4), (8, 3), (11,)}, 3: {(10,), (5,)}, 4: {(9,)}, 5: {(8,)}, 6: {(7,)}}, {0: {(5, 4), (8, 3), (10, 4), (1,), (2,), (11, 3), (7,), (8, 6), (9, 5), (14,)}, 1: {(9, 2), (11, 2), (9, 4), (13,), (10, 3), (8, 5), (5, 3)}, 2: {(12,), (3,), (6,), (4,)}, 3: {(11,)}, 4: {(10,), (5,)}, 5: {(9,)}, 6: {(8,)}}, {0: {(15,), (13, 2), (11, 4), (1,), (9, 2), (11, 2), (3,), (9, 4, 2), (5,), (8, 7), (9, 6), (10, 3, 2), (8, 5, 2)}, 1: {(8, 3), (10, 4), (2,), (11, 3), (7,), (9, 5), (8, 6), (14,)}, 2: {(13,), (10, 3), (8, 5), (9, 4)}, 3: {(4,), (6,), (12,)}, 4: {(11,)}, 5: {(10,)}, 6: {(9,)}, 7: {(8,)}}, {0: {(1,), (13, 3), (11, 5), (2,), (8,), (10, 6), (4,), (16,), (9, 4, 3), (10, 3), (9, 7)}, 1: {(15,), (13, 2), (11, 4), (9, 2), (11, 2), (3,), (9, 4, 2), (5,), (9, 6)}, 2: {(7,), (9, 5), (14,), (11, 3), (10, 4)}, 3: {(13,), (9, 4)}, 4: {(6,), (12,)}, 5: {(11,)}, 6: {(10,)}, 7: {(9,)}}, {0: {(10, 4, 3), (7, 3), (13, 4), (11, 2), (9, 8), (12, 5), (9, 4), (1,), (10, 7), (9, 6, 2), (3, 2), (13, 2), (9, 5, 3), (6, 5), (15, 2), (9, 2), (11, 3), (11, 4, 2), (17,), (14, 3), (5, 2), (11, 6)}, 1: {(13, 3), (11, 5), (2,), (8,), (10, 6), (4,), (16,), (10, 3), (9, 7)}, 2: {(15,), (5,), (3,), (11, 4), (9, 6)}, 3: {(7,), (9, 5), (14,), (10, 4)}, 4: {(13,)}, 5: {(6,), (12,)}, 6: {(11,)}, 7: {(10,)}, 8: {(9,)}}, {0: {(10, 8), (11, 7), (10, 4), (1,), (2,), (14, 4), (3,), (13, 5), (9,), (7, 4), (6,), (18,)}, 1: {(7, 3), (13, 2), (15, 2), (10, 7), (13, 4), (11, 2), (11, 3), (12, 5), (11, 4, 2), (17,), (14, 3), (5, 2), (11, 6)}, 2: {(13, 3), (11, 5), (8,), (10, 6), (4,), (16,), (10, 3)}, 3: {(15,), (5,), (11, 4)}, 4: {(7,), (14,)}, 5: {(13,)}, 6: {(12,)}, 7: {(11,)}, 8: {(10,)}}, {0: {(11, 2), (13, 4, 2), (10, 6, 3), (10, 3), (1,), (13, 3), (14, 5), (11, 6, 2), (16, 3), (11, 5, 3), (17, 2), (15, 4), (10, 9), (5, 4), (13, 2), (11, 4), (12, 7), (13, 6), (14, 3, 2), (7, 5), (10, 7, 2), (8, 3), (15, 2), (11, 8), (4, 3), (7, 3, 2), (19,), (5, 2), (11, 3, 2)}, 1: {(10, 8), (11, 7), (10, 4), (2,), (14, 4), (3,), (13, 5), (9,), (7, 4), (6,), (18,)}, 2: {(7, 3), (10, 7), (13, 4), (11, 3), (12, 5), (17,), (14, 3), (11, 6)}, 3: {(11, 5), (8,), (16,), (10, 6), (4,)}, 4: {(15,), (5,)}, 5: {(7,), (14,)}, 6: {(13,)}, 7: {(12,)}, 8: {(11,)}, 9: {(10,)}}, {0: {(12, 8), (7, 3), (12, 5, 3), (1,), (2,), (7, 6), (11, 9), (11, 3), (11, 6, 3), (4,), (14, 6), (10,), (5,), (17, 3), (13, 7), (13, 4, 3), (14, 3), (20,)}, 1: {(8, 3), (13, 2), (11, 4), (14, 5), (15, 2), (13, 3), (11, 8), (16, 3), (12, 7), (11, 2), (13, 4, 2), (11, 5, 3), (11, 6, 2), (17, 2), (13, 6), (7, 5), (15, 4), (12, 5, 2), (19,)}, 2: {(11, 7), (14, 4), (3,), (13, 5), (9,), (7, 4), (6,), (18,)}, 3: {(12, 5), (13, 4), (17,), (11, 6)}, 4: {(8,), (16,), (11, 5)}, 5: {(15,)}, 6: {(7,), (14,)}, 7: {(13,)}, 8: {(12,)}, 9: {(11,)}}, {0: {(21,), (13, 4), (11, 2), (15, 4, 2), (8, 3, 2), (13, 8), (12, 5, 2), (11, 6, 4), (8, 5), (12, 9), (14, 5, 2), (11, 8, 2), (11, 10), (1,), (11, 5), (12, 5, 4), (11, 6, 2), (3,), (17, 2), (13, 3, 2), (7,), (13, 2), (12, 7, 2), (19, 2), (13, 6, 2), (17, 4), (16, 5), (15, 2), (16, 3, 2), (15, 6), (11, 4, 2)}, 1: {(20,), (12, 5, 3), (2,), (11, 9), (11, 3), (11, 6, 3), (4,), (14, 6), (10,), (5,), (17, 3), (13, 7), (14, 3), (12, 8)}, 2: {(8, 3), (11, 4), (14, 5), (13, 3), (11, 8), (16, 3), (12, 7), (13, 6), (15, 4), (19,)}, 3: {(11, 7), (14, 4), (13, 5), (9,), (6,), (18,)}, 4: {(12, 5), (17,), (11, 6)}, 5: {(8,), (16,)}, 6: {(15,)}, 7: {(14,)}, 8: {(13,)}, 9: {(12,)}, 10: {(11,)}}, {0: {(16, 6), (14, 4), (18, 4), (13, 5, 4), (12, 5), (11,), (9, 4), (15, 4, 3), (14, 5, 3), (1,), (13, 3), (16, 3), (19, 3), (8, 6), (12, 10), (6, 4), (17, 5), (22,), (12, 7, 3), (15, 7), (13, 6, 3), (8, 3), (2,), (13, 9), (14, 8)}, 1: {(21,), (13, 2), (16, 5), (15, 2), (13, 4), (12, 7, 2), (3,), (17, 2), (15, 4, 2), (19, 2), (15, 6), (13, 8), (7,), (13, 6, 2), (8, 5), (12, 9), (17, 4), (14, 5, 2)}, 2: {(12, 8), (14, 6), (4,), (10,), (5,), (17, 3), (13, 7), (14, 3), (20,)}, 3: {(15, 4), (13, 6), (12, 7), (19,), (14, 5)}, 4: {(18,), (6,), (9,), (13, 5)}, 5: {(17,)}, 6: {(8,), (16,)}, 7: {(15,)}, 8: {(14,)}, 9: {(13,)}, 10: {(12,)}}, {0: {(20, 3), (23,), (13, 4, 2), (19, 4), (21, 2), (13, 7, 3), (14, 5, 4), (17, 3), (15, 8), (14, 9), (10, 3), (7, 2), (16, 7), (14, 5, 2), (14, 6, 3), (17, 6), (1,), (18, 5), (17, 2), (12, 8, 3), (15, 4), (3, 2), (15, 6, 2), (13, 2), (17, 4, 2), (19, 2), (16, 5, 2), (12, 11), (8, 7), (13, 6, 2), (13, 10), (6, 5), (5, 3), (15, 2), (13, 6, 4), (13, 5), (13, 8, 2), (12, 7, 4), (4, 3), (14, 3), (9, 5), (12, 9, 2), (8, 5, 2)}, 1: {(16, 6), (14, 4), (18, 4), (12, 5), (11,), (9, 4), (14, 5, 3), (13, 3), (16, 3), (19, 3), (8, 6), (12, 10), (6, 4), (17, 5), (22,), (12, 7, 3), (15, 7), (13, 6, 3), (8, 3), (2,), (13, 9), (14, 8)}, 2: {(21,), (16, 5), (13, 4), (3,), (15, 6), (13, 8), (7,), (8, 5), (12, 9), (17, 4)}, 3: {(12, 8), (14, 6), (4,), (10,), (5,), (13, 7), (20,)}, 4: {(13, 6), (12, 7), (19,), (14, 5)}, 5: {(18,), (6,), (9,)}, 6: {(17,)}, 7: {(8,), (16,)}, 8: {(15,)}, 9: {(14,)}, 10: {(13,)}, 11: {(12,)}}, {0: {(14, 10), (1,), (17, 7), (14, 5), (2,), (8,), (3,), (13, 6, 5), (4,), (19, 5), (6,), (12,), (15, 9), (24,), (13, 11)}, 1: {(20, 3), (23,), (13, 4, 2), (21, 2), (19, 4), (13, 7, 3), (17, 3), (15, 8), (14, 9), (10, 3), (16, 7), (7, 2), (14, 6, 3), (17, 6), (18, 5), (17, 2), (15, 4), (15, 6, 2), (13, 2), (17, 4, 2), (19, 2), (16, 5, 2), (13, 6, 2), (13, 10), (5, 3), (15, 2), (13, 6, 4), (13, 5), (13, 8, 2), (14, 3), (9, 5)}, 2: {(17, 5), (16, 6), (22,), (13, 3), (14, 4), (16, 3), (18, 4), (11,), (19, 3), (9, 4), (15, 7), (13, 9), (14, 8), (13, 6, 3)}, 3: {(21,), (16, 5), (13, 4), (15, 6), (13, 8), (7,), (17, 4)}, 4: {(14, 6), (10,), (5,), (13, 7), (20,)}, 5: {(13, 6), (19,)}, 6: {(18,), (9,)}, 7: {(17,)}, 8: {(16,)}, 9: {(15,)}, 10: {(14,)}, 11: {(13,)}}, {0: {(17, 8), (16, 9), (13, 4), (21, 2), (14, 4, 3), (15, 4, 2), (17, 6, 2), (7, 2), (13, 12), (1,), (13, 3), (14, 8, 3), (16, 3), (16, 5, 4), (23, 2), (17, 2), (15, 7, 3), (5,), (17, 5, 3), (19, 3), (17, 3, 2), (14, 9, 2), (13, 10, 2), (20, 3, 2), (9, 7), (22, 3), (15, 6, 2), (13, 2), (19, 6), (13, 7, 3, 2), (14, 6, 3, 2), (19, 4, 2), (15, 10), (13, 6), (14, 3, 2), (19, 2), (21, 4), (16, 5, 2), (18, 4, 3), (13, 9, 3), (25,), (17, 4), (14, 11), (13, 8, 4), (9, 5, 2), (15, 8, 2), (15, 2), (18, 5, 2), (15, 6, 4), (11, 3), (13, 8, 2), (7, 4), (18, 7), (16, 6, 3), (9, 4, 3), (10, 3, 2), (13, 5, 2)}, 1: {(14, 10), (14, 5), (17, 7), (2,), (8,), (3,), (4,), (19, 5), (6,), (12,), (15, 9), (24,), (13, 11)}, 2: {(14, 6, 3), (17, 6), (20, 3), (23,), (18, 5), (19, 4), (13, 5), (13, 7, 3), (17, 3), (15, 8), (15, 4), (9, 5), (14, 3), (14, 9), (10, 3), (13, 10), (16, 7)}, 3: {(17, 5), (16, 6), (22,), (14, 4), (18, 4), (11,), (15, 7), (9, 4), (13, 9), (14, 8)}, 4: {(7,), (21,), (15, 6), (16, 5), (13, 8)}, 5: {(14, 6), (10,), (13, 7), (20,)}, 6: {(19,)}, 7: {(18,), (9,)}, 8: {(17,)}, 9: {(16,)}, 10: {(15,)}, 11: {(14,)}, 12: {(13,)}}, {0: {(20, 3), (14, 4), (9, 8), (10, 6), (18, 4), (16, 7, 3), (23, 3), (17, 5, 4), (17, 3), (9, 4), (15, 4, 3), (18, 8), (13,), (17, 6, 3), (10, 3), (26,), (16, 10), (1,), (19, 7), (15, 11), (21, 5), (14, 8, 4), (14, 9, 3), (11, 4), (15, 7, 4), (14, 6), (22, 4), (16, 6, 4), (7, 5), (19, 4, 3), (9, 5, 3), (16, 5), (17, 9), (2,), (15, 8, 3), (14, 12), (18, 5, 3), (15, 6, 5), (20, 6), (14, 3)}, 1: {(17, 8), (16, 9), (21, 2), (15, 4, 2), (17, 6, 2), (7, 2), (14, 8, 3), (16, 3), (23, 2), (17, 2), (15, 7, 3), (5,), (17, 5, 3), (19, 3), (14, 9, 2), (9, 7), (22, 3), (15, 6, 2), (19, 6), (19, 4, 2), (15, 10), (21, 4), (19, 2), (17, 4), (25,), (14, 11), (9, 5, 2), (15, 8, 2), (15, 2), (18, 5, 2), (15, 6, 4), (11, 3), (7, 4), (18, 7), (16, 6, 3)}, 2: {(14, 10), (14, 5), (17, 7), (8,), (3,), (4,), (19, 5), (6,), (12,), (15, 9), (24,)}, 3: {(17, 6), (23,), (18, 5), (19, 4), (15, 8), (15, 4), (9, 5), (14, 9), (16, 7)}, 4: {(17, 5), (16, 6), (22,), (11,), (15, 7), (14, 8)}, 5: {(7,), (21,), (15, 6)}, 6: {(10,), (20,)}, 7: {(19,)}, 8: {(18,), (9,)}, 9: {(17,)}, 10: {(16,)}, 11: {(15,)}, 12: {(14,)}}, {0: {(19, 8), (23, 4), (16, 9, 2), (14, 11, 2), (19, 4), (21, 2), (9,), (14, 13), (20, 7), (18, 5, 4), (17, 6, 2), (15, 10, 2), (21, 6), (7, 2), (15, 12), (1,), (11, 5), (10, 7), (22, 3, 2), (7, 6), (3,), (23, 2), (17, 2), (14, 8, 5), (15, 4), (7, 4, 2), (14, 9, 2), (15, 8, 4), (16, 6, 3, 2), (15, 7, 5), (17, 5), (16, 11), (15, 7, 3, 2), (17, 4, 2), (17, 10), (16, 6, 5), (19, 2), (19, 3, 2), (14, 8, 3, 2), (21, 4, 2), (27,), (14, 9, 4), (15, 2), (15, 8, 2), (16, 3, 2), (17, 6, 4), (22, 5), (15, 6), (17, 8, 2), (25, 2), (16, 7, 4), (5, 2), (19, 6, 2), (11, 3, 2)}, 1: {(20, 3), (14, 4), (10, 6), (18, 4), (16, 7, 3), (23, 3), (17, 3), (18, 8), (13,), (17, 6, 3), (10, 3), (26,), (16, 10), (19, 7), (15, 11), (21, 5), (14, 8, 4), (14, 9, 3), (11, 4), (15, 7, 4), (14, 6), (22, 4), (16, 6, 4), (7, 5), (16, 5), (17, 9), (2,), (15, 8, 3), (14, 12), (18, 5, 3), (20, 6), (14, 3)}, 2: {(22, 3), (14, 11), (17, 8), (19, 6), (16, 9), (14, 8, 3), (16, 3), (11, 3), (15, 10), (7, 4), (18, 7), (5,), (21, 4), (15, 7, 3), (19, 3), (16, 6, 3), (25,), (17, 4)}, 3: {(14, 10), (14, 5), (17, 7), (8,), (4,), (19, 5), (6,), (12,), (15, 9), (24,)}, 4: {(17, 6), (23,), (18, 5), (15, 8), (14, 9), (16, 7)}, 5: {(16, 6), (11,), (22,), (15, 7), (14, 8)}, 6: {(7,), (21,)}, 7: {(10,), (20,)}, 8: {(19,)}, 9: {(18,)}, 10: {(17,)}, 11: {(16,)}, 12: {(15,)}, 13: {(14,)}}, {0: {(16, 6), (15, 13), (19, 6, 3), (16, 9, 3), (22, 6), (20, 8), (15, 10, 3), (10, 8), (1,), (28,), (16, 3), (18, 5), (17, 11), (15, 7, 3), (19, 3), (7,), (18, 7, 3), (22, 3), (15, 8, 5), (17, 4, 3), (15, 7, 6), (25, 3), (14,), (5, 3), (16, 12), (18, 10), (23, 5), (19, 9), (2,), (21, 4, 3), (11, 3), (4,), (17, 6, 5), (17, 8, 3), (11, 6), (16, 7, 5)}, 1: {(23, 4), (19, 8), (16, 9, 2), (16, 7, 2), (21, 2), (19, 4), (9,), (20, 7), (17, 6, 2), (15, 10, 2), (21, 6), (15, 12), (11, 5), (10, 7), (3,), (23, 2), (17, 2), (15, 4), (18, 7, 2), (15, 8, 4), (15, 7, 5), (17, 5), (16, 11), (17, 4, 2), (17, 10), (19, 2), (21, 4, 2), (27,), (15, 8, 2), (15, 2), (17, 6, 4), (22, 5), (15, 6), (17, 8, 2), (25, 2), (16, 7, 4), (5, 2), (19, 6, 2)}, 2: {(20, 3), (10, 6), (18, 4), (16, 7, 3), (23, 3), (17, 3), (18, 8), (13,), (17, 6, 3), (10, 3), (26,), (16, 10), (19, 7), (15, 11), (21, 5), (11, 4), (15, 7, 4), (22, 4), (16, 5), (17, 9), (15, 8, 3), (20, 6)}, 3: {(17, 8), (19, 6), (16, 9), (15, 10), (18, 7), (5,), (21, 4), (25,), (17, 4)}, 4: {(17, 7), (8,), (19, 5), (6,), (12,), (15, 9), (24,)}, 5: {(23,), (17, 6), (15, 8), (16, 7)}, 6: {(11,), (22,), (15, 7)}, 7: {(21,)}, 8: {(10,), (20,)}, 9: {(19,)}, 10: {(18,)}, 11: {(17,)}, 12: {(16,)}, 13: {(15,)}}, {0: {(15, 11, 3), (20, 3), (16, 7, 2), (15, 10, 4), (21, 2), (16, 7, 3), (16, 9, 4), (12, 5), (23, 3), (20, 6, 3), (17, 3), (15, 4, 2), (10, 6, 3), (15, 10, 2), (27, 2), (8, 5), (10, 3), (17, 8, 4), (20, 7, 2), (17, 6), (1,), (13, 3), (25, 4), (24, 5), (26, 3), (21, 8), (23, 2), (17, 2), (21, 6, 2), (16, 11, 2), (20, 9), (22, 7), (18, 7, 2), (23, 6), (19, 10), (18, 8, 3), (15, 8, 4, 2), (10, 9), (17, 10, 2), (3, 2), (5, 4), (15, 6, 2), (15, 9, 5), (18, 7, 4), (16, 7, 4, 2), (15, 12, 2), (15, 8, 6), (19, 4, 2), (21, 5, 3), (19, 2), (21, 4), (15, 7), (18, 4, 3), (15, 14), (16, 5, 3), (6, 5), (17, 4), (10, 7, 2), (11, 7), (17, 9, 3), (22, 4, 3), (15, 8, 2), (15, 2), (9, 2), (19, 8, 2), (29,), (15, 8, 3), (16, 7, 6), (23, 4, 2), (19, 7, 3), (19, 5), (19, 6, 4), (17, 8, 2), (17, 7, 5), (17, 12), (25, 2), (11, 4, 3), (16, 13), (18, 11), (5, 2), (19, 6, 2)}, 1: {(16, 6), (15, 13), (19, 6, 3), (16, 9, 3), (22, 6), (20, 8), (15, 10, 3), (10, 8), (28,), (18, 5), (17, 11), (16, 3), (19, 3), (7,), (18, 7, 3), (22, 3), (15, 8, 5), (25, 3), (14,), (18, 10), (16, 12), (5, 3), (23, 5), (19, 9), (2,), (11, 3), (4,), (17, 8, 3), (11, 6), (16, 7, 5)}, 2: {(23, 4), (19, 8), (15, 12), (17, 5), (27,), (16, 11), (11, 5), (10, 7), (17, 10), (3,), (19, 4), (9,), (22, 5), (20, 7), (15, 6), (21, 6), (15, 4), (15, 8, 4), (16, 7, 4)}, 3: {(26,), (11, 4), (17, 9), (16, 10), (16, 5), (19, 7), (10, 6), (18, 4), (22, 4), (15, 11), (21, 5), (20, 6), (18, 8), (13,)}, 4: {(17, 8), (19, 6), (16, 9), (15, 10), (18, 7), (5,), (25,)}, 5: {(17, 7), (8,), (6,), (15, 9), (12,), (24,)}, 6: {(23,), (15, 8), (16, 7)}, 7: {(11,), (22,)}, 8: {(21,)}, 9: {(10,), (20,)}, 10: {(19,)}, 11: {(18,)}, 12: {(17,)}, 13: {(16,)}, 14: {(15,)}}, {0: {(13, 4), (18, 4), (21, 9), (16, 14), (18, 8, 4), (23, 7), (16, 7), (19, 11), (15,), (18, 12), (1,), (20, 6, 4), (16, 5, 4), (3,), (30,), (5,), (16, 10, 4), (11, 4), (19, 7, 4), (10,), (22, 4), (26, 4), (17, 13), (21, 5, 4), (11, 8), (2,), (6,), (22, 8), (17, 9, 4)}, 1: {(20, 3), (21, 2), (16, 9, 4), (12, 5), (23, 3), (20, 6, 3), (17, 3), (27, 2), (8, 5), (17, 8, 4), (16, 10, 3), (20, 7, 2), (17, 6), (25, 4), (13, 3), (26, 3), (24, 5), (23, 2), (21, 8), (17, 2), (21, 6, 2), (11, 5, 2), (16, 11, 2), (22, 7), 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2), (19, 7, 2), (35, 10, 4), (31, 7, 4), (26, 17, 4, 2), (35, 4, 2), (17, 11, 2), (34, 9, 3), (47, 2), (29, 13, 5, 2), (33, 14, 2), (13, 7, 3), (26, 9, 5), (20, 6, 3), (26, 7, 2), (33, 8), (27, 20, 2), (34, 15), (31, 15, 3), (26, 10, 3), (37, 2), (19, 11), (43, 6), (17, 15), (31, 10, 8), (27, 15, 5, 2), (32, 13, 4), (29, 11, 3), (36, 11, 2), (36, 5, 3), (27, 12, 7, 3), (45, 4), (28, 15, 4, 2), (34, 10, 5), (28, 13, 5, 3), (33, 10, 4, 2), (26, 17, 6), (28, 16, 5), (30, 11, 5, 3), (35, 11, 3), (31, 10, 4), (34, 5), (35, 8, 4, 2), (29, 11, 6, 3), (38, 8, 3), (17, 5), (30, 17, 2), (13, 2), (31, 10, 2), (26, 5, 3), (38, 7, 4), (26, 17, 2), (32, 17), (29, 12, 6, 2), (43, 4, 2), (37, 9, 3), (29, 14, 3), (30, 8, 3), (27, 13, 7, 2), (17, 9, 3), (35, 2), (27, 14, 6, 2), (29, 11, 9), (28, 6, 3), (30, 13, 6), (27, 12, 8, 2), (27, 12, 2), (13, 5), (13, 8, 2), (30, 11, 8), (39, 5), (38, 7, 2), (30, 11, 6, 2), (33, 10, 3), (31, 12, 2), (27, 16, 3), (33, 7, 2), (29, 12, 2), (31, 9), (29, 6, 2), (28, 8, 5), (29, 14, 4, 2), (27, 12, 6, 4), (18, 8, 5), (17, 3), (36, 10, 3), (31, 12, 6), (35, 8, 2), (31, 12, 4, 2), (14, 5, 2), (34, 6, 3), (27, 13, 3), (27, 12, 10), (27, 12, 4, 2), (27, 18, 2), (32, 12, 5), (29, 12, 4), (40, 9), (30, 16, 3), (37, 10, 2), (35, 8, 6), (41, 4), (30, 19), (30, 11, 2), (29, 16, 4), (27, 13, 6, 3), (39, 2), (35, 9, 5), (18, 13), (30, 11, 4), (29, 16, 2), (29, 12, 8), (27, 6, 4), (33, 16), (39, 6, 2), (28, 3), (34, 12, 3), (29, 2), (27, 18, 4), (27, 6, 2), (21, 5, 2), (27, 8, 3), (31, 3), (28, 15, 6), (34, 9, 4, 2), (27, 5, 2), (37, 4), (34, 9, 6), (32, 11, 2), (26, 14, 7, 2), (15, 2), (31, 10, 5, 3), (38, 11), (27, 13, 9), (30, 12, 5, 2), (32, 10, 5, 2), (22, 5), (19, 8, 3), (28, 21), (26, 19, 4), (39, 6, 4), (30, 7, 5), (39, 8, 2), (29, 5), (32, 11, 6)}, 2: {(34, 7), (30, 13, 5), (33, 10, 5), (17, 7), (27, 21), (29, 19), (27, 14, 7), (31, 12, 5), (27, 16, 5), (32, 11, 5), (26, 11), (24,), (30, 18), (27, 12, 9), (28, 5), (29, 12, 7), (30, 9), (3,), (35, 8, 5), (33, 15), (31, 10, 7), (16,), (28, 13, 7), (19, 10), (17, 14), (43, 5), (26, 17, 5), (28, 10), (8,), (38, 10), (31, 17), (33, 5), (48,), (28, 20), (12,), (30, 11, 7), (41, 7), (29, 14, 5), (27, 8, 5), (35, 13), (37, 11), (26, 22), (26, 15, 7), (17, 9, 5), (4,), (19, 5), (27, 7), (28, 15, 5), (6,), (34, 9, 5), (13, 9), (34, 14), (38, 5), (39, 9)}, 3: {(33, 10, 4), (42, 5), (27, 14, 6), (37, 10), (35, 12), (31, 12, 4), (27, 16, 4), (29, 9), (13, 4), (31, 11, 5), (32, 11, 4), (39, 4), (20, 7), (26, 16, 5), (13, 8), (33, 7), (27, 12, 8), (35, 4), (39, 8), (28, 19), (33, 9, 5), (29, 12, 6), (38, 9), (31, 8), (29, 18), (14, 5), (27, 20), (35, 8, 4), (31, 10, 6), (28, 12, 7), (28, 13, 6), (27, 10), (21, 5), (27, 5), (26, 7), (29, 11, 7), (27, 13, 7), (47,), (26, 17, 4), (26, 21), (27, 12, 4), (37, 5), (32, 15), (31, 4), (30, 12, 5), (33, 14), (34, 13), (27, 4), (30, 11, 6), (35, 6), (17, 13), (32, 10, 5), (29, 14, 4), (29, 6), (27, 8, 4), (27, 15, 5), (19, 9), (43, 4), (26, 14, 7), (26, 15, 6), (31, 16), (28, 15, 4), (34, 9, 4), (30, 17), (32, 5), (17, 9, 4), (40, 7), (41, 6), (18, 11), (36, 11), (29, 13, 5)}, 4: {(19, 8), (28, 18), (38, 8), (23,), (30, 8), (27, 14, 5), (41, 5), (37, 9), (17, 6), (26, 20), (28, 13, 5), (32, 14), (18, 5), (31, 5), (28, 9), (39, 7), (35, 11), (32, 7), (28, 12, 6), (13, 7), (29, 12, 5), (34, 12), (28, 6), (31, 10, 5), (29, 17), (29, 11, 6), (27, 13, 6), (31, 15), (27, 19), (30, 11, 5), (30, 16), (27, 12, 7), (40, 6), (26, 15, 5), (18, 10), (36, 10), (34, 6), (36, 5), (33, 13), (26, 14, 6), (26, 5), (20, 6), (17, 12), (26, 10), (46,)}, 5: {(33, 12), (34, 11), (32, 13), (9,), (27, 6), (15,), (29, 8), (19, 7), (17, 11), (33, 6), (45,), (37, 8), (38, 7), (39, 6), (35, 10), (13, 6), (27, 12, 6), (29, 16), (28, 17), (31, 7), (31, 14), (27, 18), (26, 19)}, 6: {(22,), (36, 8), (17, 10), (30, 14), (28, 16), (37, 7), (26, 9), (34, 10), (32, 12), (28, 8), (35, 9), (11,), (31, 13), (27, 17), (44,), (18, 8), (29, 15), (30, 7), (26, 18)}, 7: {(17, 9), (34, 9), (35, 8), (31, 12), (32, 11), (28, 15), (43,), (27, 16), (26, 17), (33, 10), (29, 14), (27, 8), (30, 13)}, 8: {(31, 11), (21,), (30, 12), (27, 15), (42,), (33, 9), (32, 10), (29, 13), (26, 16), (14,)}, 9: {(26, 15), (27, 14), (41,), (30, 11), (29, 12), (28, 13), (31, 10)}, 10: {(26, 14), (40,), (29, 11), (27, 13), (28, 12), (20,)}, 11: {(39,), (13,), (27, 12)}, 12: {(19,), (38,)}, 13: {(37,)}, 14: {(18,), (36,)}, 15: {(35,)}, 16: {(34,), (17,)}, 17: {(33,)}, 18: {(32,)}, 19: {(31,)}, 20: {(30,)}, 21: {(29,)}, 22: {(28,)}, 23: {(27,)}, 24: {(26,)}}]
        self.best_cost = float('inf')

    @staticmethod
    def cost(a):
        return sum(2 ** i for i in a)

    @staticmethod
    def prod(now, aa, bb):
        for a in aa:
            for b in bb:
                now.add(a + b)
        return now

    def calc_one_step(self):
        for i in range(51):
            for j in range(1, i + 1):
                m = i % j
                if m not in self.move_map[i]:
                    self.move_map[i][m] = {(j,)}
                else:
                    self.move_map[i][m].add((j,))

    def expand(self):
        for i in range(51):
            self.move_map[i] = self._expand(i)

    def _expand(self, n):
        new = self.move_map[n].copy()
        for m, a in self.move_map[n].items():
            for mm, aa in self.move_map[m].items():
                if mm not in new:
                    new[mm] = aa
                else:
                    self.prod(new[mm], a, aa)
        return new

    def compress(self):
        for i in range(51):
            for j in self.move_map[i]:
                self.move_map[i][j] = self._compress(self.move_map[i][j])

    @staticmethod
    def _compress(path_set):
        new = set()
        for path in sorted(path_set, key=len):
            for short_path in new:
                if path[-len(short_path):] == short_path:
                    break
            else:
                new.add(path)
        return new

    def solve(self, start, goal):
        path_list = []
        for s, g in zip(start, goal):
            if s == g:
                continue
            path = self.move_map[s].get(g)
            if path is None:
                self.best_cost = -1
                return
            path_list.append(path)
        self._solve(0, path_list, [])

    def _solve(self, cost, path_list, divs):
        if not path_list:
            if cost < self.best_cost:
                self.best_cost = cost
            return
        for one, new_list in self.iter_one(path_list):
            d = divs + [one]
            c = cost + 2 ** one
            if c >= self.best_cost:
                break
            elif not new_list and c < self.best_cost:
                self.best_cost = c
            else:
                self._solve(c, new_list, d)

    def iter_one(self, path_list):
        ones = set()
        for path_set in path_list:
            for path in path_set:
                ones.add(path[0])
        for one in sorted(ones):
            new_list = []
            for path_set in path_list:
                new_set = set()
                for path in path_set:
                    if path[0] == one:
                        path = path[1:]
                        if not path:
                            break
                    new_set.add(path)
                else:
                    new_list.append(new_set)
            yield one, new_list


def main():
    solver = Solver()
    # print(solver.move_map)
    int(input())
    start = list(map(int, input().split()))
    goal = list(map(int, input().split()))
    solver.solve(start, goal)
    print(solver.best_cost)


if __name__ == '__main__':
    main()


# Example run
# Input:
945
0
1
# Output:
-1