{2: [[2, 1]], 3: [[3, 1]], 4: [[4, 1]], 5: [[5, 2], [5, 4, 2, 1], [5, 4, 3, 2]], 6: [[6, 1], [6, 5, 2, 1], [6, 5, 3, 2]], 7: [[7, 1], [7, 3], [7, 3, 2, 1], [7, 4, 3, 2], [7, 5, 4, 3, 2, 1], [7, 6, 3, 1], [7, 6, 4, 2], [7, 6, 5, 2], [7, 6, 5, 4, 2, 1]], 8: [[8, 4, 3, 2], [8, 5, 3, 1], [8, 6, 4, 3, 2, 1], [8, 6, 5, 1], [8, 6, 5, 2], [8, 6, 5, 3], [8, 7, 6, 1], [8, 7, 6, 5, 2, 1]], 9: [[9, 4], [9, 5, 3, 2], [9, 6, 4, 3], [9, 6, 5, 3, 2, 1], [9, 6, 5, 4, 2, 1], [9, 7, 6, 4, 3, 1], [9, 8, 4, 1], [9, 8, 5, 4], [9, 8, 6, 5], [9, 8, 6, 5, 3, 1], [9, 8, 7, 2], [9, 8, 7, 3, 2, 1], [9, 8, 7, 6, 5, 1], [9, 8, 7, 6, 5, 3]], 10: [[10, 3], [10, 4, 3, 1], [10, 6, 5, 3, 2, 1], [10, 8, 3, 2], [10, 8, 4, 3], [10, 8, 5, 1], [10, 8, 5, 4], [10, 8, 7, 6, 5, 2], [10, 8, 7, 6, 5, 4, 3, 1], [10, 9, 4, 1], [10, 9, 6, 5, 4, 3, 2, 1], [10, 9, 8, 6, 3, 2], [10, 9, 8, 6, 5, 1], [10, 9, 8, 7, 6, 5, 4, 3]], 11: [[11, 2], [11, 5, 3, 1], [11, 5, 3, 2], [11, 6, 5, 1], [11, 7, 3, 2], [11, 8, 5, 2], [11, 8, 6, 5, 4, 1], [11, 8, 6, 5, 4, 3, 2, 1], [11, 9, 4, 1], [11, 9, 8, 7, 4, 1], [11, 10, 3, 2], [11, 10, 7, 4, 3, 1], [11, 10, 8, 7, 5, 4, 3, 1], [11, 10, 9, 8, 3, 1]], 12: [[12, 6, 4, 1], [12, 9, 3, 2], [12, 9, 8, 3, 2, 1], [12, 10, 9, 8, 6, 2], [12, 10, 9, 8, 6, 5, 4, 2], [12, 11, 6, 4, 2, 1], [12, 11, 9, 5, 3, 1], [12, 11, 9, 7, 6, 4], [12, 11, 9, 7, 6, 5], [12, 11, 9, 8, 7, 4], [12, 11, 9, 8, 7, 5, 2, 1], [12, 11, 10, 5, 2, 1], [12, 11, 10, 8, 6, 4, 3, 1], [12, 11, 10, 9, 8, 7, 5, 4, 3, 1]], 13: [[13, 4, 3, 1], [13, 9, 7, 5, 4, 3, 2, 1], [13, 9, 8, 7, 5, 1], [13, 10, 9, 7, 5, 4], [13, 10, 9, 8, 6, 3, 2, 1], [13, 11, 8, 7, 4, 1], [13, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], [13, 12, 6, 5, 4, 3], [13, 12, 8, 7, 6, 5], [13, 12, 9, 8, 4, 2], [13, 12, 10, 8, 6, 4, 3, 2], [13, 12, 11, 5, 2, 1], [13, 12, 11, 8, 7, 6, 4, 1], [13, 12, 11, 9, 5, 3]], 14: [[14, 8, 6, 1], [14, 10, 6, 1], [14, 10, 9, 7, 6, 4, 3, 1], [14, 11, 6, 1], [14, 11, 9, 6, 5, 2], [14, 12, 9, 8, 7, 6, 5, 4], [14, 12, 11, 9, 8, 7, 6, 5, 3, 1], [14, 12, 11, 10, 9, 7, 4, 3], [14, 13, 6, 5, 3, 1], [14, 13, 10, 8, 7, 5, 4, 3, 2, 1], [14, 13, 11, 6, 5, 4, 2, 1], [14, 13, 11, 8, 5, 3, 2, 1], [14, 13, 12, 11, 10, 7, 6, 1], [14, 13, 12, 11, 10, 9, 6, 5]], 15: [[15, 1], [15, 4], [15, 7], [15, 7, 6, 3, 2, 1], [15, 10, 5, 1], [15, 10, 5, 4], [15, 10, 5, 4, 2, 1], [15, 10, 9, 7, 5, 3], [15, 10, 9, 8, 5, 3], [15, 11, 7, 6, 2, 1], [15, 12, 3, 1], [15, 12, 5, 4, 3, 2], [15, 12, 11, 8, 7, 6, 4, 2], [15, 14, 13, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2]], 16: [[16, 9, 8, 7, 6, 4, 3, 2], [16, 12, 3, 1], [16, 12, 7, 2], [16, 13, 12, 10, 9, 7, 6, 1], [16, 13, 12, 11, 7, 6, 3, 1], [16, 13, 12, 11, 10, 6, 2, 1], [16, 14, 10, 8, 3, 1], [16, 14, 13, 12, 6, 5, 3, 2], [16, 14, 13, 12, 10, 7], [16, 15, 10, 6, 5, 3, 2, 1], [16, 15, 11, 9, 8, 7, 5, 4, 2, 1], [16, 15, 11, 10, 7, 6, 5, 3, 2, 1], [16, 15, 11, 10, 9, 6, 2, 1], [16, 15, 11, 10, 9, 8, 6, 4, 2, 1]], 17: [[17, 3], [17, 3, 2, 1], [17, 5], [17, 6], [17, 8, 4, 3], [17, 8, 7, 6, 4, 3], [17, 10, 9, 8, 6, 5, 3, 2], [17, 12, 6, 3, 2, 1], [17, 12, 9, 5, 4, 3, 2, 1], [17, 12, 9, 7, 6, 4, 3, 2], [17, 14, 11, 7, 5, 3, 2, 1], [17, 15, 13, 11, 9, 7, 5, 3], [17, 15, 13, 11, 9, 7, 6, 4, 2, 1], [17, 16, 3, 1]], 18: [[18, 5, 4, 3, 2, 1], [18, 7], [18, 7, 5, 2, 1], [18, 8, 2, 1], [18, 9, 7, 6, 5, 4], [18, 9, 8, 6, 5, 4, 2, 1], [18, 9, 8, 7, 6, 4, 2, 1], [18, 10, 7, 5], [18, 10, 8, 5], [18, 10, 8, 7, 6, 5, 4, 3, 2, 1], [18, 10, 9, 3], [18, 13, 6, 4], [18, 15, 5, 2], [18, 15, 9, 2]], 19: [[19, 5, 2, 1], [19, 5, 4, 3, 2, 1], [19, 6, 2, 1], [19, 6, 5, 3, 2, 1], [19, 6, 5, 4, 3, 2], [19, 7, 5, 3, 2, 1], [19, 8, 7, 5], [19, 8, 7, 5, 4, 3, 2, 1], [19, 8, 7, 6, 4, 3, 2, 1], [19, 9, 8, 5], [19, 9, 8, 6, 5, 3, 2, 1], [19, 9, 8, 7, 4, 3, 2, 1], [19, 11, 9, 8, 7, 6, 5, 4, 3, 2], [19, 11, 10, 8, 7, 5, 4, 3, 2, 1], [19, 16, 13, 10, 7, 4, 1]], 20: [[20, 3], [20, 9, 5, 3], [20, 11, 8, 6, 3, 2], [20, 14, 10, 9, 8, 6, 5, 4], [20, 17, 14, 10, 7, 4, 3, 2], [20, 19, 4, 3]], 21: [[21, 2], [21, 8, 7, 4, 3, 2], [21, 10, 6, 4, 3, 2], [21, 13, 5, 2], [21, 14, 7, 2], [21, 14, 7, 6, 3, 2], [21, 14, 12, 7, 6, 4, 3, 2], [21, 15, 10, 9, 5, 4, 3, 2], [21, 20, 19, 18, 5, 4, 3, 2]], 22: [[22, 1], [22, 9, 5, 1], [22, 14, 13, 12, 7, 3, 2, 1], [22, 17, 9, 7, 2, 1], [22, 17, 13, 12, 8, 7, 2, 1], [22, 20, 18, 16, 6, 4, 2, 1]], 23: [[23, 5], [23, 5, 4, 1], [23, 11, 10, 7, 6, 5], [23, 12, 5, 4], [23, 15, 10, 9, 7, 5, 4, 3], [23, 16, 13, 6, 5, 3], [23, 17, 11, 5], [23, 17, 11, 9, 8, 5, 4, 1], [23, 18, 16, 13, 11, 8, 5, 2], [23, 21, 7, 5]], 24: [[24, 7, 2, 1], [24, 21, 19, 18, 17, 16, 15, 14, 13, 10, 9, 5, 4, 1], [24, 22, 20, 18, 16, 14, 11, 9, 8, 7, 5, 4]], 25: [[25, 3], [25, 3, 2, 1], [25, 11, 9, 8, 6, 4, 3, 2], [25, 12, 4, 3], [25, 12, 11, 8, 7, 6, 4, 3], [25, 17, 10, 3, 2, 1], [25, 18, 12, 11, 6, 5, 4, 3], [25, 20, 5, 3], [25, 20, 16, 11, 5, 3, 2, 1], [25, 23, 21, 19, 9, 7, 5, 3]], 26: [[26, 6, 2, 1], [26, 19, 16, 15, 14, 13, 11, 9, 8, 7, 6, 5, 3, 2], [26, 21, 18, 16, 15, 13, 12, 11, 9, 8, 6, 5, 4, 3], [26, 22, 20, 19, 16, 13, 11, 9, 8, 7, 5, 4, 2, 1], [26, 22, 21, 16, 12, 11, 10, 8, 5, 4, 3, 1], [26, 23, 22, 21, 19, 18, 15, 14, 13, 11, 10, 9, 8, 6, 5, 2], [26, 24, 21, 17, 16, 14, 13, 11, 7, 6, 4, 1]], 27: [[27, 5, 2, 1], [27, 18, 11, 10, 9, 5, 4, 3], [27, 22, 13, 11, 6, 5, 4, 3], [27, 22, 17, 15, 14, 13, 6, 1], [27, 22, 21, 20, 18, 17, 15, 13, 12, 7, 5], [27, 24, 19, 16, 12, 8, 7, 3, 2, 1], [27, 24, 21, 19, 16, 13, 11, 9, 6, 5, 4, 3], [27, 25, 23, 21, 13, 11, 9, 8, 7, 6, 5, 3, 2, 1], [27, 25, 23, 21, 20, 19, 18, 16, 14, 10, 8, 7, 4, 3]], 28: [[28, 3], [28, 13, 11, 9, 5, 3], [28, 18, 17, 16, 9, 5, 4, 3], [28, 19, 17, 15, 10, 6, 3, 2], [28, 22, 11, 10, 4, 3], [28, 24, 20, 16, 12, 8, 4, 3]], 29: [[29, 2], [29, 12, 7, 2], [29, 18, 14, 6, 3, 2], [29, 19, 16, 6, 3, 2], [29, 20, 11, 2], [29, 20, 16, 11, 8, 4, 3, 2], [29, 21, 5, 2], [29, 23, 10, 9, 5, 4, 3, 2], [29, 24, 14, 13, 8, 4, 3, 2], [29, 26, 5, 2]], 30: [[30, 23, 2, 1], [30, 24, 20, 16, 14, 13, 11, 7, 2, 1], [30, 24, 21, 20, 18, 15, 13, 12, 9, 7, 6, 4, 3, 1], [30, 25, 24, 23, 19, 18, 16, 14, 11, 8, 6, 4, 3, 1], [30, 27, 25, 24, 23, 22, 19, 16, 12, 10, 8, 7, 6, 1]], 31: [[31, 3], [31, 3, 2, 1], [31, 13, 8, 3], [31, 16, 8, 4, 3, 2], [31, 20, 15, 5, 4, 3], [31, 20, 18, 7, 5, 3], [31, 21, 12, 3, 2, 1], [31, 23, 22, 15, 14, 7, 4, 3], [31, 25, 19, 14, 7, 3, 2, 1], [31, 27, 23, 19, 15, 11, 7, 3], [31, 27, 23, 19, 15, 11, 10, 9, 7, 6, 5, 3, 2, 1]]}