zeta-orbits.rank This file records the full support irreducible permutations \zeta in S_n, up to conjugation by the longest element, inverse, and cyclic shift. They are listed by rank (in the new order), and k, which is the cardinality of up(\zeta), and are given in cycle notation. Maple took 352.969 seconds for S_7 (Toronto) Maple took 23268.676 seconds for S_8 (Toronto) rk k \zeta 1 1 {[1, 2]} 2 1 {[1, 2, 3]} 3 1 {[1, 2, 3, 4]} 1 3 2 {[1, 2, 4, 3]} 1 4 2 {[1, 3], [2, 4]} 1 S_5 4 1 {[1, 2, 3, 4, 5]} 1 4 2 {[1, 2, 3, 5, 4]} 2 4 2 {[1, 2, 4, 5, 3]} 5 2 {[3, 5], [1, 2, 4]} 1 6 2 {[1, 3, 5, 2, 4]} 1 S_6 5 1 {[1, 2, 3, 4, 5, 6]} 1 5 2 {[1, 2, 3, 4, 6, 5]} 3 5 2 {[1, 2, 3, 5, 6, 4]} 5 2 {[1, 2, 5, 6, 3, 4]} 5 3 {[1, 2, 5, 4, 6, 3]} 5 5 3 {[1, 2, 6, 4, 5, 3]} 5 3 {[1, 2, 4, 6, 5, 3]} 5 3 {[1, 2, 4, 3, 6, 5]} 5 3 {[1, 2, 3, 6, 5, 4]} 6 2 {[4, 6], [1, 2, 3, 5]} 3 6 2 {[3, 6], [1, 2, 4, 5]} 6 2 {[3, 5, 6], [1, 2, 4]} 6 3 {[4, 6], [1, 2, 5, 3]} 4 6 3 {[3, 6], [1, 2, 5, 4]} 6 3 {[3, 6, 5], [1, 2, 4]} 6 3 {[1, 3, 5], [2, 6, 4]} 7 2 {[1, 2, 4, 6, 3, 5]} 1 7 3 {[1, 3, 6, 4, 2, 5]} 3 7 3 {[1, 2, 5, 3, 6, 4]} 7 3 {[2, 5], [4, 6], [1, 3]} 8 2 {[2, 4, 6], [1, 3, 5]} 1 8 3 {[1, 3, 6, 4], [2, 5]} 1 9 3 {[2, 5], [1, 4], [3, 6]} 1 S_7 6 1 {[1, 2, 3, 4, 5, 6, 7]} 1 6 2 {[1, 2, 3, 4, 5, 7, 6]} 4 6 2 {[1, 2, 3, 4, 6, 7, 5]} 6 2 {[1, 2, 3, 5, 6, 7, 4]} 6 2 {[1, 2, 3, 6, 7, 4, 5]} 6 3 {[1, 2, 3, 4, 7, 6, 5]} 15 6 3 {[1, 2, 3, 5, 4, 7, 6]} 6 3 {[1, 2, 3, 5, 7, 6, 4]} 6 3 {[1, 2, 3, 6, 5, 7, 4]} 6 3 {[1, 2, 3, 6, 7, 5, 4]} 6 3 {[1, 2, 3, 7, 5, 6, 4]} 6 3 {[1, 2, 4, 3, 5, 7, 6]} 6 3 {[1, 2, 4, 3, 6, 7, 5]} 6 3 {[1, 2, 4, 5, 7, 6, 3]} 6 3 {[1, 2, 4, 6, 5, 7, 3]} 6 3 {[1, 2, 4, 6, 7, 5, 3]} 6 3 {[1, 2, 4, 7, 5, 6, 3]} 6 3 {[1, 2, 5, 4, 7, 6, 3]} 6 3 {[1, 2, 5, 6, 4, 7, 3]} 6 3 {[1, 2, 6, 7, 4, 5, 3]} 7 2 {[1, 2, 3, 4, 6], [5, 7]} 4 7 2 {[1, 2, 3, 5, 6], [4, 7]} 7 2 {[1, 2, 3, 5], [4, 6, 7]} 7 2 {[1, 2, 4, 5], [3, 6, 7]} 7 3 {[5, 7], [1, 2, 4, 6, 3]} 18 7 3 {[3, 5], [1, 2, 4, 7, 6]} 7 3 {[4, 7], [1, 2, 3, 6, 5]} 7 3 {[4, 7], [1, 2, 5, 6, 3]} 7 3 {[1, 2, 5, 7, 3], [4, 6]} 7 3 {[1, 2, 7, 5, 3], [4, 6]} 7 3 {[5, 7], [1, 2, 6, 3, 4]} 7 3 {[5, 7], [1, 2, 3, 6, 4]} 7 3 {[3, 7], [1, 2, 4, 6, 5]} 7 3 {[1, 2, 4], [3, 5, 7, 6]} 7 3 {[3, 6, 5, 7], [1, 2, 4]} 7 3 {[3, 7, 6], [1, 2, 4, 5]} 7 3 {[3, 7, 5, 6], [1, 2, 4]} 7 3 {[1, 2, 4], [3, 6, 7, 5]} 7 3 {[3, 7, 5], [1, 2, 4, 6]} 7 3 {[1, 2, 6, 4], [3, 5, 7]} 7 3 {[3, 4, 7, 6], [1, 2, 5]} 7 3 {[4, 7, 6], [1, 2, 3, 5]} 8 2 {[1, 2, 3, 5, 7, 4, 6]} 3 8 2 {[1, 2, 4, 6, 7, 3, 5]} 8 2 {[1, 2, 4, 7, 3, 5, 6]} 8 3 {[1, 2, 3, 6, 4, 7, 5]} 15 8 3 {[1, 2, 4, 6, 3, 7, 5]} 8 3 {[1, 2, 4, 7, 6, 3, 5]} 8 3 {[1, 2, 5, 7, 4, 6, 3]} 8 3 {[1, 2, 5, 6, 3, 7, 4]} 8 3 {[1, 2, 5, 7, 3, 6, 4]} 8 3 {[1, 2, 5, 3, 6, 7, 4]} 8 3 {[1, 2, 6, 3, 5, 7, 4]} 8 3 {[1, 2, 6, 4, 7, 5, 3]} 8 3 {[1, 3, 7, 5, 2, 4, 6]} 8 3 {[1, 2, 4, 7, 5, 3, 6]} 8 3 {[1, 2, 4, 7, 3, 6, 5]} 8 3 {[5, 7], [1, 3], [2, 4, 6]} 8 3 {[3, 7], [1, 2, 5], [4, 6]} 8 3 {[5, 7], [1, 2, 4], [3, 6]} 9 2 {[1, 2, 4, 6], [3, 5, 7]} 1 9 3 {[1, 2, 4, 7, 5], [3, 6]} 8 9 3 {[1, 3, 7, 4, 6], [2, 5]} 9 3 {[5, 7], [1, 3, 6, 2, 4]} 9 3 {[1, 2, 5, 7, 4], [3, 6]} 9 3 {[3, 7, 5], [1, 2, 6, 4]} 9 3 {[1, 3, 6], [2, 4, 7, 5]} 9 3 {[3, 7, 4, 6], [1, 2, 5]} 9 3 {[3, 6, 4, 7], [1, 2, 5]} 10 2 {[1, 3, 5, 7, 2, 4, 6]} 1 10 3 {[4, 7], [1, 3, 6], [2, 5]} 4 10 3 {[4, 7], [1, 2, 5], [3, 6]} 10 3 {[1, 3, 6, 2, 4, 7, 5]} 10 3 {[1, 3, 6, 2, 5, 7, 4]} 11 3 {[4, 7], [1, 3, 6, 2, 5]} 1 12 3 {[1, 4, 7, 3, 6, 2, 5]} 1 S_8 7 1 {[1, 2, 3, 4, 5, 6, 7, 8]} 1 7 2 {[1, 2, 3, 4, 5, 6, 8, 7]} 5 7 2 {[1, 2, 3, 4, 5, 7, 8, 6]} 7 2 {[1, 2, 3, 4, 6, 7, 8, 5]} 7 2 {[1, 2, 3, 4, 7, 8, 5, 6]} 7 2 {[1, 2, 3, 6, 7, 8, 4, 5]} 7 3 {[1, 2, 3, 4, 5, 8, 7, 6]} 35 7 3 {[1, 2, 3, 4, 6, 5, 8, 7]} 7 3 {[1, 2, 3, 4, 6, 8, 7, 5]} 7 3 {[1, 2, 3, 4, 7, 8, 6, 5]} 7 3 {[1, 2, 3, 4, 7, 6, 8, 5]} 7 3 {[1, 2, 3, 4, 8, 6, 7, 5]} 7 3 {[1, 2, 3, 5, 4, 6, 8, 7]} 7 3 {[1, 2, 3, 5, 4, 7, 8, 6]} 7 3 {[1, 2, 3, 5, 4, 8, 6, 7]} 7 3 {[1, 2, 3, 5, 6, 8, 7, 4]} 7 3 {[1, 2, 3, 5, 7, 6, 8, 4]} 7 3 {[1, 2, 3, 5, 7, 8, 6, 4]} 7 3 {[1, 2, 3, 5, 8, 6, 7, 4]} 7 3 {[1, 2, 3, 6, 5, 7, 8, 4]} 7 3 {[1, 2, 3, 6, 7, 5, 8, 4]} 7 3 {[1, 2, 3, 6, 7, 8, 5, 4]} 7 3 {[1, 2, 3, 6, 8, 7, 4, 5]} 7 3 {[1, 2, 3, 7, 5, 6, 8, 4]} 7 3 {[1, 2, 3, 7, 6, 8, 4, 5]} 7 3 {[1, 2, 3, 7, 8, 5, 6, 4]} 7 3 {[1, 2, 3, 7, 8, 6, 4, 5]} 7 3 {[1, 2, 3, 8, 5, 6, 7, 4]} 7 3 {[1, 2, 4, 3, 5, 6, 8, 7]} 7 3 {[1, 2, 4, 3, 7, 8, 5, 6]} 7 3 {[1, 2, 4, 5, 7, 6, 8, 3]} 7 3 {[1, 2, 4, 5, 7, 8, 6, 3]} 7 3 {[1, 2, 4, 5, 8, 6, 7, 3]} 7 3 {[1, 2, 4, 6, 5, 7, 8, 3]} 7 3 {[1, 2, 4, 6, 7, 5, 8, 3]} 7 3 {[1, 2, 4, 7, 5, 6, 8, 3]} 7 3 {[1, 2, 4, 7, 8, 5, 6, 3]} 7 3 {[1, 2, 5, 6, 4, 7, 8, 3]} 7 3 {[1, 2, 5, 7, 6, 8, 3, 4]} 7 3 {[1, 2, 5, 8, 6, 7, 3, 4]} 7 3 {[1, 2, 7, 8, 5, 6, 3, 4]} 7 4 {[1, 2, 3, 4, 8, 7, 6, 5]} 34 7 4 {[1, 2, 3, 5, 4, 8, 7, 6]} 7 4 {[1, 2, 3, 5, 8, 7, 6, 4]} 7 4 {[1, 2, 3, 6, 5, 8, 7, 4]} 7 4 {[1, 2, 3, 6, 8, 7, 5, 4]} 7 4 {[1, 2, 3, 7, 6, 8, 5, 4]} 7 4 {[1, 2, 3, 7, 6, 5, 8, 4]} 7 4 {[1, 2, 3, 8, 5, 7, 6, 4]} 7 4 {[1, 2, 3, 8, 6, 7, 5, 4]} 7 4 {[1, 2, 4, 3, 6, 5, 8, 7]} 7 4 {[1, 2, 4, 3, 7, 6, 8, 5]} 7 4 {[1, 2, 4, 3, 7, 8, 6, 5]} 7 4 {[1, 2, 4, 3, 8, 5, 7, 6]} 7 4 {[1, 2, 4, 3, 8, 6, 7, 5]} 7 4 {[1, 2, 4, 3, 8, 7, 5, 6]} 7 4 {[1, 2, 4, 6, 5, 8, 7, 3]} 7 4 {[1, 2, 4, 6, 8, 7, 5, 3]} 7 4 {[1, 2, 4, 7, 6, 8, 5, 3]} 7 4 {[1, 2, 4, 7, 8, 6, 5, 3]} 7 4 {[1, 2, 4, 8, 5, 7, 6, 3]} 7 4 {[1, 2, 4, 8, 6, 5, 7, 3]} 7 4 {[1, 2, 4, 8, 6, 7, 5, 3]} 7 4 {[1, 2, 4, 8, 7, 5, 6, 3]} 7 4 {[1, 2, 5, 4, 6, 8, 7, 3]} 7 4 {[1, 2, 5, 4, 7, 6, 8, 3]} 7 4 {[1, 2, 5, 4, 7, 8, 6, 3]} 7 4 {[1, 2, 5, 4, 8, 6, 7, 3]} 7 4 {[1, 2, 5, 6, 4, 8, 7, 3]} 7 4 {[1, 2, 6, 5, 7, 4, 8, 3]} 7 4 {[1, 2, 6, 5, 8, 7, 3, 4]} 7 4 {[1, 2, 7, 4, 6, 5, 8, 3]} 7 4 {[1, 2, 7, 5, 6, 4, 8, 3]} 7 4 {[1, 2, 7, 8, 6, 4, 5, 3]} 7 4 {[1, 2, 8, 4, 6, 5, 7, 3]} 8 2 {[4, 6, 7, 8], [1, 2, 3, 5]} 8 8 2 {[4, 5, 7, 8], [1, 2, 3, 6]} 8 2 {[3, 4, 7, 8], [1, 2, 5, 6]} 8 2 {[5, 7, 8], [1, 2, 3, 4, 6]} 8 2 {[4, 7, 8], [1, 2, 3, 5, 6]} 8 2 {[6, 8], [1, 2, 3, 4, 5, 7]} 8 2 {[5, 8], [1, 2, 3, 4, 6, 7]} 8 2 {[4, 8], [1, 2, 3, 5, 6, 7]} 8 3 {[1, 2, 3, 5], [4, 6, 8, 7]} 50 8 3 {[1, 2, 3, 5], [4, 7, 6, 8]} 8 3 {[1, 2, 3, 5], [4, 7, 8, 6]} 8 3 {[1, 2, 3, 5], [4, 8, 6, 7]} 8 3 {[1, 2, 3, 6], [4, 5, 8, 7]} 8 3 {[1, 2, 4, 5], [3, 6, 8, 7]} 8 3 {[1, 2, 4, 5], [3, 7, 8, 6]} 8 3 {[1, 2, 4, 6], [3, 7, 8, 5]} 8 3 {[1, 2, 4, 7], [3, 8, 5, 6]} 8 3 {[1, 2, 5, 6], [3, 4, 8, 7]} 8 3 {[1, 2, 3, 4, 6], [5, 8, 7]} 8 3 {[1, 2, 3, 5, 6], [4, 8, 7]} 8 3 {[1, 2, 3, 5, 7], [4, 8, 6]} 8 3 {[1, 2, 3, 6, 4], [5, 7, 8]} 8 3 {[1, 2, 3, 6, 5], [4, 7, 8]} 8 3 {[1, 2, 3, 7, 4], [5, 6, 8]} 8 3 {[1, 2, 3, 7, 5], [4, 6, 8]} 8 3 {[1, 2, 4, 5, 7], [3, 8, 6]} 8 3 {[1, 2, 4, 6, 3], [5, 7, 8]} 8 3 {[1, 2, 4, 6, 5], [3, 7, 8]} 8 3 {[1, 2, 4, 7, 3], [5, 6, 8]} 8 3 {[1, 2, 5, 6, 3], [4, 7, 8]} 8 3 {[1, 2, 6, 7, 4], [3, 5, 8]} 8 3 {[1, 2, 4], [3, 5, 6, 8, 7]} 8 3 {[1, 2, 4], [3, 5, 7, 6, 8]} 8 3 {[1, 2, 4], [3, 5, 8, 6, 7]} 8 3 {[1, 2, 4], [3, 6, 5, 7, 8]} 8 3 {[1, 2, 4], [3, 7, 8, 5, 6]} 8 3 {[1, 2, 5], [3, 4, 7, 6, 8]} 8 3 {[1, 2, 5], [3, 4, 8, 6, 7]} 8 3 {[1, 2, 4], [3, 6, 7, 5, 8]} 8 3 {[1, 2, 3, 4, 7, 5], [6, 8]} 8 3 {[1, 2, 3, 5, 7, 4], [6, 8]} 8 3 {[1, 2, 3, 5, 7, 6], [4, 8]} 8 3 {[1, 2, 3, 5, 8, 7], [4, 6]} 8 3 {[1, 2, 3, 6, 7, 4], [5, 8]} 8 3 {[1, 2, 3, 6, 7, 5], [4, 8]} 8 3 {[1, 2, 3, 6, 8, 4], [5, 7]} 8 3 {[1, 2, 3, 7, 4, 5], [6, 8]} 8 3 {[1, 2, 4, 3, 5, 7], [6, 8]} 8 3 {[1, 2, 4, 3, 6, 7], [5, 8]} 8 3 {[1, 2, 4, 5, 7, 3], [6, 8]} 8 3 {[1, 2, 4, 6, 5, 7], [3, 8]} 8 3 {[1, 2, 4, 6, 7, 3], [5, 8]} 8 3 {[1, 2, 4, 6, 8, 3], [5, 7]} 8 3 {[1, 2, 4, 7, 5, 6], [3, 8]} 8 3 {[1, 2, 3, 4, 7, 6], [5, 8]} 8 3 {[1, 2, 4, 7, 8, 6], [3, 5]} 8 3 {[1, 2, 5, 7, 3, 4], [6, 8]} 8 3 {[1, 2, 6, 7, 3, 4], [5, 8]} 8 4 {[5, 8, 7], [1, 2, 4, 3, 6]} 59 8 4 {[1, 2, 7, 4], [3, 6, 5, 8]} 8 4 {[1, 2, 5, 3], [4, 6, 8, 7]} 8 4 {[1, 2, 7, 5, 6, 4], [3, 8]} 8 4 {[5, 8, 7], [1, 2, 4, 6, 3]} 8 4 {[3, 8, 7], [1, 2, 4, 6, 5]} 8 4 {[1, 2, 5, 3], [4, 7, 6, 8]} 8 4 {[1, 2, 5, 3], [4, 7, 8, 6]} 8 4 {[4, 8, 7, 6], [1, 2, 3, 5]} 8 4 {[5, 8, 6], [1, 2, 4, 7, 3]} 8 4 {[5, 8], [1, 2, 4, 7, 6, 3]} 8 4 {[5, 8, 7], [1, 2, 3, 6, 4]} 8 4 {[3, 8, 7, 5], [1, 2, 4, 6]} 8 4 {[6, 8], [1, 2, 4, 7, 5, 3]} 8 4 {[6, 8], [1, 2, 7, 4, 5, 3]} 8 4 {[1, 2, 5, 3], [4, 8, 6, 7]} 8 4 {[1, 2, 5, 4, 7, 6], [3, 8]} 8 4 {[1, 2, 5, 6, 3], [4, 8, 7]} 8 4 {[1, 2, 4, 8, 7], [3, 6, 5]} 8 4 {[4, 7], [1, 2, 6, 5, 8, 3]} 8 4 {[1, 2, 4, 8, 6, 3], [5, 7]} 8 4 {[4, 6], [1, 2, 7, 8, 5, 3]} 8 4 {[4, 8, 7, 5], [1, 2, 3, 6]} 8 4 {[4, 8, 7], [1, 2, 3, 6, 5]} 8 4 {[1, 2, 4], [3, 7, 6, 8, 5]} 8 4 {[4, 8], [1, 2, 6, 7, 5, 3]} 8 4 {[4, 6, 8], [1, 2, 7, 5, 3]} 8 4 {[4, 8], [1, 2, 5, 7, 6, 3]} 8 4 {[6, 8], [1, 2, 3, 7, 5, 4]} 8 4 {[6, 8], [1, 2, 4, 3, 7, 5]} 8 4 {[5, 8, 6], [1, 2, 3, 7, 4]} 8 4 {[5, 7], [1, 2, 8, 4, 6, 3]} 8 4 {[5, 8], [1, 2, 4, 3, 7, 6]} 8 4 {[1, 2, 6, 5], [3, 4, 8, 7]} 8 4 {[3, 7, 8, 6], [1, 2, 5, 4]} 8 4 {[5, 7], [1, 2, 6, 4, 8, 3]} 8 4 {[4, 8], [1, 2, 6, 5, 7, 3]} 8 4 {[5, 7], [1, 2, 3, 8, 6, 4]} 8 4 {[1, 2, 4, 7, 6], [3, 8, 5]} 8 4 {[4, 6], [1, 2, 7, 5, 8, 3]} 8 4 {[1, 2, 4, 7], [3, 8, 6, 5]} 8 4 {[1, 2, 7, 3], [4, 6, 5, 8]} 8 4 {[3, 6, 8, 7], [1, 2, 5, 4]} 8 4 {[1, 3, 5, 7], [2, 8, 6, 4]} 8 4 {[1, 2, 5, 7, 3], [4, 8, 6]} 8 4 {[1, 2, 6, 4], [3, 5, 8, 7]} 8 4 {[5, 7], [1, 2, 4, 3, 8, 6]} 8 4 {[3, 8, 6, 7, 4], [1, 2, 5]} 8 4 {[1, 2, 5, 4, 7, 3], [6, 8]} 8 4 {[1, 2, 5, 8, 7, 3], [4, 6]} 8 4 {[4, 8], [1, 2, 7, 5, 6, 3]} 8 4 {[1, 2, 5], [3, 7, 6, 8, 4]} 8 4 {[1, 2, 7, 3], [4, 8, 5, 6]} 8 4 {[3, 8, 7, 4], [1, 2, 5, 6]} 8 4 {[1, 2, 4], [3, 6, 5, 8, 7]} 8 4 {[1, 2, 4], [3, 8, 6, 7, 5]} 8 4 {[4, 8], [1, 2, 3, 7, 6, 5]} 8 4 {[1, 2, 4], [3, 8, 5, 7, 6]} 8 4 {[5, 8], [1, 2, 3, 7, 6, 4]} 9 2 {[1, 2, 3, 4, 6, 8, 5, 7]} 5 9 2 {[1, 2, 3, 5, 7, 8, 4, 6]} 9 2 {[1, 2, 3, 5, 8, 4, 6, 7]} 9 2 {[1, 2, 4, 5, 7, 8, 3, 6]} 9 2 {[1, 2, 4, 7, 8, 3, 5, 6]} 9 3 {[1, 2, 3, 4, 7, 5, 8, 6]} 55 9 3 {[1, 2, 3, 5, 7, 4, 8, 6]} 9 3 {[1, 2, 3, 5, 8, 4, 7, 6]} 9 3 {[1, 2, 3, 5, 8, 6, 4, 7]} 9 3 {[1, 2, 3, 5, 8, 7, 4, 6]} 9 3 {[1, 2, 3, 6, 4, 7, 8, 5]} 9 3 {[1, 2, 3, 6, 7, 4, 8, 5]} 9 3 {[1, 2, 3, 6, 8, 5, 7, 4]} 9 3 {[1, 2, 3, 6, 8, 4, 7, 5]} 9 3 {[1, 2, 3, 7, 4, 6, 8, 5]} 9 3 {[1, 2, 4, 5, 8, 7, 3, 6]} 9 3 {[1, 2, 4, 6, 3, 5, 8, 7]} 9 3 {[1, 2, 4, 6, 3, 7, 8, 5]} 9 3 {[1, 2, 4, 6, 3, 8, 5, 7]} 9 3 {[1, 2, 4, 6, 7, 3, 8, 5]} 9 3 {[1, 2, 4, 6, 8, 3, 7, 5]} 9 3 {[1, 2, 4, 6, 8, 5, 7, 3]} 9 3 {[1, 2, 4, 6, 8, 7, 3, 5]} 9 3 {[1, 2, 4, 7, 3, 8, 5, 6]} 9 3 {[1, 2, 4, 7, 6, 8, 3, 5]} 9 3 {[1, 2, 4, 7, 8, 3, 6, 5]} 9 3 {[1, 2, 4, 7, 8, 5, 3, 6]} 9 3 {[1, 2, 4, 7, 8, 6, 3, 5]} 9 3 {[1, 2, 4, 8, 3, 5, 7, 6]} 9 3 {[1, 2, 4, 8, 3, 6, 5, 7]} 9 3 {[1, 2, 4, 8, 3, 6, 7, 5]} 9 3 {[1, 2, 4, 8, 3, 7, 5, 6]} 9 3 {[1, 2, 4, 8, 5, 3, 6, 7]} 9 3 {[1, 2, 4, 8, 5, 6, 3, 7]} 9 3 {[1, 2, 4, 8, 6, 3, 5, 7]} 9 3 {[1, 2, 4, 8, 6, 7, 3, 5]} 9 3 {[1, 2, 4, 8, 7, 3, 5, 6]} 9 3 {[1, 2, 5, 6, 3, 7, 8, 4]} 9 3 {[1, 2, 5, 7, 3, 4, 8, 6]} 9 3 {[1, 2, 5, 7, 4, 6, 8, 3]} 9 3 {[1, 2, 5, 8, 3, 4, 7, 6]} 9 3 {[1, 2, 5, 8, 3, 6, 7, 4]} 9 3 {[1, 2, 6, 7, 3, 4, 8, 5]} 9 3 {[1, 2, 6, 7, 3, 5, 8, 4]} 9 3 {[1, 2, 6, 8, 3, 5, 7, 4]} 9 3 {[1, 2, 6, 8, 5, 7, 3, 4]} 9 3 {[1, 2, 8, 6, 4, 7, 5, 3]} 9 3 {[1, 2, 3, 5], [4, 7], [6, 8]} 9 3 {[1, 2, 4, 7], [3, 5], [6, 8]} 9 3 {[1, 2, 4, 5], [6, 8], [3, 7]} 9 3 {[2, 4, 6, 8], [5, 7], [1, 3]} 9 3 {[6, 8], [3, 5, 7], [1, 2, 4]} 9 3 {[6, 8], [3, 4, 7], [1, 2, 5]} 9 3 {[5, 7], [3, 8], [1, 2, 4, 6]} 9 3 {[4, 7], [3, 8], [1, 2, 5, 6]} 9 3 {[5, 7], [4, 8], [1, 2, 3, 6]} 9 3 {[5, 6, 8], [1, 2, 4], [3, 7]} 9 3 {[5, 7, 8], [1, 2, 4], [3, 6]} 9 3 {[5, 8], [1, 2, 4], [3, 6, 7]} 9 3 {[5, 7], [1, 2, 4], [3, 6, 8]} 9 4 {[1, 2, 3, 6, 4, 8, 7, 5]} 59 9 4 {[1, 2, 3, 7, 5, 8, 6, 4]} 9 4 {[1, 2, 3, 7, 6, 4, 8, 5]} 9 4 {[1, 2, 4, 3, 7, 5, 8, 6]} 9 4 {[1, 2, 4, 7, 3, 8, 6, 5]} 9 4 {[1, 2, 4, 7, 5, 3, 8, 6]} 9 4 {[1, 2, 4, 7, 5, 8, 6, 3]} 9 4 {[1, 2, 4, 7, 6, 3, 8, 5]} 9 4 {[1, 2, 4, 8, 5, 3, 7, 6]} 9 4 {[1, 2, 4, 8, 6, 5, 3, 7]} 9 4 {[1, 2, 4, 8, 7, 5, 3, 6]} 9 4 {[1, 2, 4, 8, 7, 3, 6, 5]} 9 4 {[1, 2, 5, 3, 7, 6, 8, 4]} 9 4 {[1, 2, 5, 3, 7, 8, 6, 4]} 9 4 {[1, 2, 5, 3, 8, 4, 7, 6]} 9 4 {[1, 2, 5, 3, 8, 6, 7, 4]} 9 4 {[1, 2, 5, 4, 8, 3, 7, 6]} 9 4 {[1, 2, 5, 4, 8, 7, 3, 6]} 9 4 {[1, 2, 5, 7, 3, 8, 6, 4]} 9 4 {[1, 2, 5, 7, 4, 3, 8, 6]} 9 4 {[1, 2, 5, 7, 4, 8, 6, 3]} 9 4 {[1, 2, 5, 8, 4, 7, 6, 3]} 9 4 {[1, 2, 5, 8, 6, 4, 7, 3]} 9 4 {[1, 2, 5, 8, 7, 3, 6, 4]} 9 4 {[1, 2, 5, 8, 7, 4, 3, 6]} 9 4 {[1, 2, 5, 8, 7, 4, 6, 3]} 9 4 {[1, 2, 6, 4, 7, 5, 8, 3]} 9 4 {[1, 2, 6, 4, 8, 5, 7, 3]} 9 4 {[1, 2, 6, 4, 8, 7, 3, 5]} 9 4 {[1, 2, 6, 5, 8, 3, 7, 4]} 9 4 {[1, 2, 6, 5, 8, 4, 7, 3]} 9 4 {[1, 2, 6, 7, 4, 8, 5, 3]} 9 4 {[1, 2, 6, 8, 4, 7, 5, 3]} 9 4 {[1, 2, 7, 4, 6, 8, 5, 3]} 9 4 {[1, 2, 7, 4, 8, 5, 6, 3]} 9 4 {[1, 2, 7, 5, 8, 3, 6, 4]} 9 4 {[1, 2, 7, 5, 8, 4, 6, 3]} 9 4 {[1, 2, 7, 5, 8, 6, 3, 4]} 9 4 {[1, 2, 7, 3, 5, 8, 6, 4]} 9 4 {[1, 2, 7, 3, 6, 5, 8, 4]} 9 4 {[1, 2, 8, 5, 7, 4, 6, 3]} 9 4 {[1, 3, 6, 8, 4, 2, 7, 5]} 9 4 {[1, 3, 8, 6, 4, 2, 5, 7]} 9 4 {[1, 2, 5, 3], [6, 8], [4, 7]} 9 4 {[2, 4, 7, 5], [6, 8], [1, 3]} 9 4 {[1, 2, 6, 5], [4, 7], [3, 8]} 9 4 {[5, 7], [2, 4, 8, 6], [1, 3]} 9 4 {[5, 7], [4, 8], [1, 2, 6, 3]} 9 4 {[1, 2, 7, 4], [6, 8], [3, 5]} 9 4 {[5, 8], [1, 2, 7, 3], [4, 6]} 9 4 {[6, 8], [3, 7], [1, 2, 5, 4]} 9 4 {[1, 2, 6, 4], [5, 7], [3, 8]} 9 4 {[4, 8, 6], [1, 3], [2, 5, 7]} 9 4 {[6, 8], [1, 2, 4], [3, 7, 5]} 9 4 {[5, 8, 6], [1, 2, 4], [3, 7]} 9 4 {[5, 8], [1, 2, 4], [3, 7, 6]} 9 4 {[6, 8], [3, 7, 4], [1, 2, 5]} 9 4 {[5, 7], [1, 2, 4], [3, 8, 6]} 9 4 {[5, 8, 7], [1, 2, 4], [3, 6]} 10 2 {[3, 5, 7, 8], [1, 2, 4, 6]} 4 10 2 {[1, 2, 4, 7], [3, 5, 6, 8]} 10 2 {[3, 5, 8], [1, 2, 4, 6, 7]} 10 2 {[4, 6, 8], [1, 2, 3, 5, 7]} 10 3 {[3, 7, 8, 4, 6], [1, 2, 5]} 36 10 3 {[3, 7, 4, 6, 8], [1, 2, 5]} 10 3 {[2, 4, 6, 8, 5, 7], [1, 3]} 10 3 {[3, 5, 8, 7], [1, 2, 4, 6]} 10 3 {[1, 2, 5, 7, 3], [4, 6, 8]} 10 3 {[1, 2, 4, 7, 3, 5], [6, 8]} 10 3 {[1, 2, 4, 7], [3, 5, 8, 6]} 10 3 {[1, 2, 4, 7, 5], [3, 6, 8]} 10 3 {[1, 2, 4, 7, 6], [3, 5, 8]} 10 3 {[1, 2, 4, 7, 8, 5], [3, 6]} 10 3 {[1, 2, 5, 7, 4, 6], [3, 8]} 10 3 {[1, 2, 4, 7], [3, 6, 5, 8]} 10 3 {[1, 2, 3, 6, 8, 5], [4, 7]} 10 3 {[4, 7], [1, 2, 6, 8, 3, 5]} 10 3 {[3, 8, 5, 7], [1, 2, 4, 6]} 10 3 {[1, 2, 4, 8, 5], [3, 6, 7]} 10 3 {[3, 7, 4, 8], [1, 2, 5, 6]} 10 3 {[4, 7, 5, 8], [1, 2, 3, 6]} 10 3 {[1, 2, 4, 8, 5, 7], [3, 6]} 10 3 {[5, 7], [1, 2, 4, 8, 3, 6]} 10 3 {[1, 2, 5, 8, 6], [3, 4, 7]} 10 3 {[3, 5, 7], [1, 2, 4, 8, 6]} 10 3 {[4, 8, 5, 7], [1, 2, 3, 6]} 10 3 {[1, 3, 7], [2, 4, 6, 8, 5]} 10 3 {[4, 8, 6], [1, 2, 7, 5, 3]} 10 3 {[3, 7], [1, 2, 4, 5, 8, 6]} 10 3 {[3, 6, 8], [1, 2, 5, 7, 4]} 10 3 {[3, 7], [1, 2, 4, 6, 8, 5]} 10 3 {[1, 2, 5, 8, 4], [3, 6, 7]} 10 3 {[3, 7, 5, 8], [1, 2, 4, 6]} 10 3 {[1, 2, 4], [3, 6, 8, 5, 7]} 10 3 {[3, 7], [1, 2, 4, 8, 5, 6]} 10 3 {[4, 7], [1, 2, 3, 5, 8, 6]} 10 3 {[1, 2, 6, 8, 4], [3, 5, 7]} 10 3 {[4, 8], [1, 2, 6, 7, 3, 5]} 10 3 {[2, 4, 8, 6], [1, 3, 5, 7]} 10 4 {[2, 5], [1, 3, 8, 6, 4, 7]} 48 10 4 {[1, 3], [2, 5, 8, 6, 4, 7]} 10 4 {[2, 5, 7, 4, 8, 6], [1, 3]} 10 4 {[1, 2, 6, 4, 7, 5], [3, 8]} 10 4 {[2, 4, 7, 5, 8, 6], [1, 3]} 10 4 {[1, 2, 7, 5, 8, 4], [3, 6]} 10 4 {[1, 2, 6, 8, 5, 3], [4, 7]} 10 4 {[4, 8], [1, 2, 5, 3, 7, 6]} 10 4 {[1, 2, 5, 8, 6, 3], [4, 7]} 10 4 {[4, 7], [1, 2, 5, 3, 8, 6]} 10 4 {[5, 8], [1, 2, 6, 4, 7, 3]} 10 4 {[5, 7], [1, 2, 6, 3, 8, 4]} 10 4 {[1, 2, 4, 8, 7, 5], [3, 6]} 10 4 {[3, 7], [1, 2, 6, 5, 8, 4]} 10 4 {[5, 8], [1, 2, 7, 4, 6, 3]} 10 4 {[6, 8], [1, 2, 5, 3, 7, 4]} 10 4 {[3, 7], [1, 2, 5, 8, 6, 4]} 10 4 {[1, 2, 5, 8, 7, 4], [3, 6]} 10 4 {[1, 2, 4, 8, 6, 5], [3, 7]} 10 4 {[3, 6, 4, 8, 7], [1, 2, 5]} 10 4 {[1, 2, 6, 8, 4], [3, 7, 5]} 10 4 {[4, 8, 7], [1, 2, 5, 3, 6]} 10 4 {[1, 2, 6, 7, 4], [3, 8, 5]} 10 4 {[3, 8, 6, 4, 7], [1, 2, 5]} 10 4 {[1, 2, 4], [3, 7, 5, 8, 6]} 10 4 {[1, 3, 7], [2, 5, 8, 6, 4]} 10 4 {[3, 8, 6], [1, 2, 5, 7, 4]} 10 4 {[1, 2, 5, 8, 4], [3, 7, 6]} 10 4 {[1, 2, 4, 8, 5], [3, 7, 6]} 10 4 {[1, 2, 4, 8, 6], [3, 7, 5]} 10 4 {[1, 2, 4, 7, 5], [3, 8, 6]} 10 4 {[1, 3, 8, 6, 4], [2, 5, 7]} 10 4 {[4, 8, 6], [1, 2, 3, 7, 5]} 10 4 {[1, 2, 7, 4], [3, 5, 8, 6]} 10 4 {[2, 7, 5], [1, 3, 6, 8, 4]} 10 4 {[1, 2, 7, 4], [3, 8, 5, 6]} 10 4 {[1, 2, 6, 5], [3, 7, 4, 8]} 10 4 {[1, 2, 6, 5], [3, 8, 4, 7]} 10 4 {[1, 2, 6, 4], [3, 7, 8, 5]} 10 4 {[1, 2, 6, 4], [3, 8, 5, 7]} 10 4 {[4, 7, 5, 8], [1, 2, 6, 3]} 10 4 {[2, 5, 7, 4], [1, 3, 8, 6]} 10 4 {[1, 2, 6, 4], [3, 7, 5, 8]} 10 4 {[4, 8, 5, 7], [1, 2, 6, 3]} 10 4 {[2, 4, 7, 5], [1, 3, 8, 6]} 10 4 {[1, 3, 7, 5], [2, 6, 8, 4]} 10 4 {[6, 8], [2, 5], [4, 7], [1, 3]} 10 4 {[5, 7], [4, 8], [1, 3], [2, 6]} 11 2 {[1, 2, 4, 6, 8, 3, 5, 7]} 1 11 3 {[1, 2, 7, 5, 3, 8, 6, 4]} 24 11 3 {[1, 2, 4, 7, 3, 6, 8, 5]} 11 3 {[1, 2, 4, 7, 3, 5, 8, 6]} 11 3 {[1, 2, 4, 7, 5, 8, 3, 6]} 11 3 {[1, 2, 6, 8, 4, 7, 3, 5]} 11 3 {[1, 3, 6, 8, 5, 2, 4, 7]} 11 3 {[1, 2, 5, 7, 3, 8, 4, 6]} 11 3 {[1, 3, 6, 8, 5, 7, 2, 4]} 11 3 {[1, 2, 5, 7, 3, 6, 8, 4]} 11 3 {[1, 2, 5, 7, 4, 8, 3, 6]} 11 3 {[1, 3, 5, 8, 6, 2, 4, 7]} 11 3 {[1, 2, 4, 8, 5, 7, 3, 6]} 11 3 {[1, 3, 6, 2, 4, 8, 5, 7]} 11 3 {[6, 8], [1, 3, 5], [2, 4, 7]} 11 3 {[4, 7, 8], [3, 6], [1, 2, 5]} 11 3 {[5, 8], [2, 4, 6], [1, 3, 7]} 11 3 {[4, 7], [3, 6, 8], [1, 2, 5]} 11 3 {[4, 8], [3, 6, 7], [1, 2, 5]} 11 3 {[4, 6, 8], [3, 7], [1, 2, 5]} 11 3 {[5, 8], [3, 7], [1, 2, 4, 6]} 11 3 {[5, 8], [4, 7], [1, 2, 3, 6]} 11 3 {[1, 2, 4, 7], [5, 8], [3, 6]} 11 3 {[4, 8], [3, 7], [1, 2, 5, 6]} 11 3 {[4, 8], [2, 6], [1, 3, 5, 7]} 11 4 {[1, 3, 7, 5, 2, 4, 8, 6]} 29 11 4 {[1, 2, 6, 4, 8, 3, 7, 5]} 11 4 {[1, 2, 6, 3, 8, 4, 7, 5]} 11 4 {[1, 3, 7, 5, 8, 6, 2, 4]} 11 4 {[1, 3, 6, 8, 5, 2, 7, 4]} 11 4 {[1, 2, 6, 3, 8, 5, 7, 4]} 11 4 {[1, 2, 5, 3, 7, 4, 8, 6]} 11 4 {[1, 2, 6, 8, 5, 3, 7, 4]} 11 4 {[1, 3, 7, 2, 5, 8, 6, 4]} 11 4 {[1, 3, 7, 5, 2, 6, 8, 4]} 11 4 {[1, 2, 6, 3, 7, 5, 8, 4]} 11 4 {[1, 2, 4, 8, 6, 3, 7, 5]} 11 4 {[1, 3, 8, 4, 7, 5, 2, 6]} 11 4 {[1, 3, 7, 4, 2, 5, 8, 6]} 11 4 {[1, 2, 5, 8, 6, 3, 7, 4]} 11 4 {[1, 2, 6, 4], [5, 8], [3, 7]} 11 4 {[4, 7, 5, 8], [1, 3], [2, 6]} 11 4 {[2, 7, 5], [1, 3, 6], [4, 8]} 11 4 {[2, 5], [4, 8, 6], [1, 3, 7]} 11 4 {[2, 5, 8, 6], [4, 7], [1, 3]} 11 4 {[4, 8, 7], [3, 6], [1, 2, 5]} 11 4 {[5, 8], [4, 7], [1, 2, 6, 3]} 11 4 {[1, 3, 6], [5, 8], [2, 7, 4]} 11 4 {[4, 8, 6], [3, 7], [1, 2, 5]} 11 4 {[2, 5], [1, 3, 8, 6], [4, 7]} 11 4 {[4, 8], [1, 2, 5], [3, 7, 6]} 11 4 {[4, 7], [3, 8, 6], [1, 2, 5]} 11 4 {[1, 2, 6, 5], [4, 8], [3, 7]} 11 4 {[1, 2, 7, 4], [5, 8], [3, 6]} 12 2 {[2, 4, 6, 8], [1, 3, 5, 7]} 1 12 3 {[1, 3, 6, 2, 5, 7], [4, 8]} 9 12 3 {[1, 2, 5, 8, 3, 6], [4, 7]} 12 3 {[1, 3, 6, 8, 5], [2, 4, 7]} 12 3 {[1, 3, 6, 2, 4, 7], [5, 8]} 12 3 {[1, 3, 5, 8, 6], [2, 4, 7]} 12 3 {[1, 3, 7, 2, 5], [4, 6, 8]} 12 3 {[5, 8], [1, 2, 4, 7, 3, 6]} 12 3 {[4, 8], [1, 2, 5, 7, 3, 6]} 12 3 {[1, 2, 5], [3, 6, 8, 4, 7]} 12 4 {[4, 8], [1, 2, 6, 3, 7, 5]} 17 12 4 {[1, 3, 7, 5, 2, 6], [4, 8]} 12 4 {[1, 2, 6, 3, 8, 5], [4, 7]} 12 4 {[2, 5, 8, 6], [1, 3, 7, 4]} 12 4 {[3, 7, 4, 8, 6], [1, 2, 5]} 12 4 {[5, 8], [1, 2, 6, 3, 7, 4]} 12 4 {[2, 6, 8, 5], [1, 3, 7, 4]} 12 4 {[1, 3, 8, 5, 7, 4], [2, 6]} 12 4 {[1, 3, 7, 2, 5], [4, 8, 6]} 12 4 {[1, 3, 7, 5, 8, 4], [2, 6]} 12 4 {[2, 4, 8, 6], [1, 3, 7, 5]} 12 4 {[2, 5], [1, 3, 7, 4, 8, 6]} 12 4 {[1, 3, 6], [2, 7, 4, 8, 5]} 12 4 {[1, 3, 8, 5, 2, 6], [4, 7]} 12 4 {[5, 8], [1, 3, 7, 4, 2, 6]} 12 4 {[1, 4], [2, 7], [5, 8], [3, 6]} 12 4 {[5, 8], [4, 7], [1, 3], [2, 6]} 13 3 {[1, 3, 6, 2, 5, 8, 4, 7]} 5 13 3 {[1, 3, 6, 8, 4, 7, 2, 5]} 13 3 {[1, 2, 5, 8, 4, 7, 3, 6]} 13 3 {[1, 3, 6], [5, 8], [2, 4, 7]} 13 3 {[1, 3, 6], [4, 8], [2, 5, 7]} 13 4 {[1, 2, 6, 3, 7, 4, 8, 5]} 7 13 4 {[1, 3, 7, 4, 8, 5, 2, 6]} 13 4 {[1, 3, 7, 4, 8, 6, 2, 5]} 13 4 {[1, 4, 7, 2, 6, 3, 8, 5]} 13 4 {[5, 8], [1, 3, 7, 4], [2, 6]} 13 4 {[1, 4], [5, 8], [2, 6, 3, 7]} 13 4 {[4, 8], [1, 3, 7, 5], [2, 6]} 14 3 {[1, 3, 6], [2, 5, 8, 4, 7]} 1 14 4 {[1, 4, 8, 5, 2, 6], [3, 7]} 14 4 {[2, 6], [1, 3, 7, 4, 8, 5]} 4 14 4 {[1, 4, 8, 5], [2, 6, 3, 7]} 14 4 {[1, 4], [5, 8], [3, 7], [2, 6]} 15 3 {[1, 4, 7, 2, 5, 8, 3, 6]} 15 4 {[1, 4, 8, 5], [3, 7], [2, 6]} 16 4 {[4, 8], [3, 7], [2, 6], [1, 5]}