edit this statistic or download as text // json
Identifier
Values
=>
[1,2]=>0 [2,1]=>1 [1,2,3]=>0 [1,3,2]=>2 [2,1,3]=>1 [2,3,1]=>1 [3,1,2]=>1 [3,2,1]=>2 [1,2,3,4]=>0 [1,2,4,3]=>5 [1,3,2,4]=>3 [1,3,4,2]=>2 [1,4,2,3]=>2 [1,4,3,2]=>5 [2,1,3,4]=>1 [2,1,4,3]=>6 [2,3,1,4]=>4 [2,3,4,1]=>1 [2,4,1,3]=>3 [2,4,3,1]=>4 [3,1,2,4]=>4 [3,1,4,2]=>3 [3,2,1,4]=>5 [3,2,4,1]=>2 [3,4,1,2]=>2 [3,4,2,1]=>3 [4,1,2,3]=>1 [4,1,3,2]=>4 [4,2,1,3]=>2 [4,2,3,1]=>3 [4,3,1,2]=>3 [4,3,2,1]=>4 [1,2,3,4,5]=>0 [1,2,3,5,4]=>5 [1,2,4,3,5]=>5 [1,2,4,5,3]=>5 [1,2,5,3,4]=>5 [1,2,5,4,3]=>9 [1,3,2,4,5]=>3 [1,3,2,5,4]=>7 [1,3,4,2,5]=>5 [1,3,4,5,2]=>2 [1,3,5,2,4]=>7 [1,3,5,4,2]=>6 [1,4,2,3,5]=>5 [1,4,2,5,3]=>7 [1,4,3,2,5]=>7 [1,4,3,5,2]=>5 [1,4,5,2,3]=>4 [1,4,5,3,2]=>7 [1,5,2,3,4]=>2 [1,5,2,4,3]=>6 [1,5,3,2,4]=>5 [1,5,3,4,2]=>5 [1,5,4,2,3]=>7 [1,5,4,3,2]=>9 [2,1,3,4,5]=>1 [2,1,3,5,4]=>6 [2,1,4,3,5]=>6 [2,1,4,5,3]=>6 [2,1,5,3,4]=>6 [2,1,5,4,3]=>10 [2,3,1,4,5]=>4 [2,3,1,5,4]=>8 [2,3,4,1,5]=>4 [2,3,4,5,1]=>1 [2,3,5,1,4]=>6 [2,3,5,4,1]=>5 [2,4,1,3,5]=>6 [2,4,1,5,3]=>6 [2,4,3,1,5]=>6 [2,4,3,5,1]=>4 [2,4,5,1,3]=>3 [2,4,5,3,1]=>6 [2,5,1,3,4]=>3 [2,5,1,4,3]=>7 [2,5,3,1,4]=>6 [2,5,3,4,1]=>4 [2,5,4,1,3]=>6 [2,5,4,3,1]=>8 [3,1,2,4,5]=>4 [3,1,2,5,4]=>8 [3,1,4,2,5]=>6 [3,1,4,5,2]=>3 [3,1,5,2,4]=>6 [3,1,5,4,2]=>7 [3,2,1,4,5]=>5 [3,2,1,5,4]=>9 [3,2,4,1,5]=>5 [3,2,4,5,1]=>2 [3,2,5,1,4]=>7 [3,2,5,4,1]=>6 [3,4,1,2,5]=>6 [3,4,1,5,2]=>4 [3,4,2,1,5]=>7 [3,4,2,5,1]=>5 [3,4,5,1,2]=>2 [3,4,5,2,1]=>3 [3,5,1,2,4]=>4 [3,5,1,4,2]=>7 [3,5,2,1,4]=>5 [3,5,2,4,1]=>7 [3,5,4,1,2]=>4 [3,5,4,2,1]=>5 [4,1,2,3,5]=>4 [4,1,2,5,3]=>6 [4,1,3,2,5]=>6 [4,1,3,5,2]=>6 [4,1,5,2,3]=>3 [4,1,5,3,2]=>6 [4,2,1,3,5]=>5 [4,2,1,5,3]=>7 [4,2,3,1,5]=>7 [4,2,3,5,1]=>5 [4,2,5,1,3]=>4 [4,2,5,3,1]=>7 [4,3,1,2,5]=>7 [4,3,1,5,2]=>5 [4,3,2,1,5]=>8 [4,3,2,5,1]=>6 [4,3,5,1,2]=>3 [4,3,5,2,1]=>4 [4,5,1,2,3]=>2 [4,5,1,3,2]=>4 [4,5,2,1,3]=>3 [4,5,2,3,1]=>5 [4,5,3,1,2]=>6 [4,5,3,2,1]=>7 [5,1,2,3,4]=>1 [5,1,2,4,3]=>5 [5,1,3,2,4]=>4 [5,1,3,4,2]=>4 [5,1,4,2,3]=>6 [5,1,4,3,2]=>8 [5,2,1,3,4]=>2 [5,2,1,4,3]=>6 [5,2,3,1,4]=>5 [5,2,3,4,1]=>3 [5,2,4,1,3]=>7 [5,2,4,3,1]=>7 [5,3,1,2,4]=>5 [5,3,1,4,2]=>7 [5,3,2,1,4]=>6 [5,3,2,4,1]=>6 [5,3,4,1,2]=>5 [5,3,4,2,1]=>6 [5,4,1,2,3]=>3 [5,4,1,3,2]=>5 [5,4,2,1,3]=>4 [5,4,2,3,1]=>6 [5,4,3,1,2]=>7 [5,4,3,2,1]=>8 [1,2,3,4,5,6]=>0 [1,2,3,4,6,5]=>5 [1,2,3,5,4,6]=>7 [1,2,3,5,6,4]=>8 [1,2,3,6,4,5]=>8 [1,2,3,6,5,4]=>9 [1,2,4,3,5,6]=>5 [1,2,4,3,6,5]=>8 [1,2,4,5,3,6]=>8 [1,2,4,5,6,3]=>5 [1,2,4,6,3,5]=>11 [1,2,4,6,5,3]=>10 [1,2,5,3,4,6]=>8 [1,2,5,3,6,4]=>11 [1,2,5,4,3,6]=>9 [1,2,5,4,6,3]=>10 [1,2,5,6,3,4]=>10 [1,2,5,6,4,3]=>11 [1,2,6,3,4,5]=>5 [1,2,6,3,5,4]=>10 [1,2,6,4,3,5]=>10 [1,2,6,4,5,3]=>11 [1,2,6,5,3,4]=>11 [1,2,6,5,4,3]=>14 [1,3,2,4,5,6]=>3 [1,3,2,4,6,5]=>8 [1,3,2,5,4,6]=>8 [1,3,2,5,6,4]=>9 [1,3,2,6,4,5]=>9 [1,3,2,6,5,4]=>12 [1,3,4,2,5,6]=>6 [1,3,4,2,6,5]=>9 [1,3,4,5,2,6]=>5 [1,3,4,5,6,2]=>2 [1,3,4,6,2,5]=>8 [1,3,4,6,5,2]=>7 [1,3,5,2,4,6]=>9 [1,3,5,2,6,4]=>10 [1,3,5,4,2,6]=>8 [1,3,5,4,6,2]=>7 [1,3,5,6,2,4]=>7 [1,3,5,6,4,2]=>10 [1,3,6,2,4,5]=>8 [1,3,6,2,5,4]=>11 [1,3,6,4,2,5]=>11 [1,3,6,4,5,2]=>8 [1,3,6,5,2,4]=>10 [1,3,6,5,4,2]=>11 [1,4,2,3,5,6]=>6 [1,4,2,3,6,5]=>9 [1,4,2,5,3,6]=>9 [1,4,2,5,6,3]=>8 [1,4,2,6,3,5]=>10 [1,4,2,6,5,3]=>11 [1,4,3,2,5,6]=>7 [1,4,3,2,6,5]=>12 [1,4,3,5,2,6]=>8 [1,4,3,5,6,2]=>5 [1,4,3,6,2,5]=>11 [1,4,3,6,5,2]=>8 [1,4,5,2,3,6]=>10 [1,4,5,2,6,3]=>7 [1,4,5,3,2,6]=>11 [1,4,5,3,6,2]=>8 [1,4,5,6,2,3]=>4 [1,4,5,6,3,2]=>7 [1,4,6,2,3,5]=>7 [1,4,6,2,5,3]=>10 [1,4,6,3,2,5]=>10 [1,4,6,3,5,2]=>11 [1,4,6,5,2,3]=>9 [1,4,6,5,3,2]=>10 [1,5,2,3,4,6]=>5 [1,5,2,3,6,4]=>8 [1,5,2,4,3,6]=>8 [1,5,2,4,6,3]=>11 [1,5,2,6,3,4]=>7 [1,5,2,6,4,3]=>10 [1,5,3,2,4,6]=>8 [1,5,3,2,6,4]=>11 [1,5,3,4,2,6]=>9 [1,5,3,4,6,2]=>8 [1,5,3,6,2,4]=>10 [1,5,3,6,4,2]=>11 [1,5,4,2,3,6]=>11 [1,5,4,2,6,3]=>10 [1,5,4,3,2,6]=>12 [1,5,4,3,6,2]=>9 [1,5,4,6,2,3]=>7 [1,5,4,6,3,2]=>10 [1,5,6,2,3,4]=>4 [1,5,6,2,4,3]=>9 [1,5,6,3,2,4]=>7 [1,5,6,3,4,2]=>10 [1,5,6,4,2,3]=>10 [1,5,6,4,3,2]=>11 [1,6,2,3,4,5]=>2 [1,6,2,3,5,4]=>7 [1,6,2,4,3,5]=>7 [1,6,2,4,5,3]=>8 [1,6,2,5,3,4]=>10 [1,6,2,5,4,3]=>11 [1,6,3,2,4,5]=>5 [1,6,3,2,5,4]=>8 [1,6,3,4,2,5]=>8 [1,6,3,4,5,2]=>5 [1,6,3,5,2,4]=>11 [1,6,3,5,4,2]=>10 [1,6,4,2,3,5]=>8 [1,6,4,2,5,3]=>11 [1,6,4,3,2,5]=>9 [1,6,4,3,5,2]=>10 [1,6,4,5,2,3]=>10 [1,6,4,5,3,2]=>11 [1,6,5,2,3,4]=>7 [1,6,5,2,4,3]=>10 [1,6,5,3,2,4]=>10 [1,6,5,3,4,2]=>11 [1,6,5,4,2,3]=>11 [1,6,5,4,3,2]=>14 [2,1,3,4,5,6]=>1 [2,1,3,4,6,5]=>6 [2,1,3,5,4,6]=>8 [2,1,3,5,6,4]=>9 [2,1,3,6,4,5]=>9 [2,1,3,6,5,4]=>10 [2,1,4,3,5,6]=>6 [2,1,4,3,6,5]=>9 [2,1,4,5,3,6]=>9 [2,1,4,5,6,3]=>6 [2,1,4,6,3,5]=>12 [2,1,4,6,5,3]=>11 [2,1,5,3,4,6]=>9 [2,1,5,3,6,4]=>12 [2,1,5,4,3,6]=>10 [2,1,5,4,6,3]=>11 [2,1,5,6,3,4]=>11 [2,1,5,6,4,3]=>12 [2,1,6,3,4,5]=>6 [2,1,6,3,5,4]=>11 [2,1,6,4,3,5]=>11 [2,1,6,4,5,3]=>12 [2,1,6,5,3,4]=>12 [2,1,6,5,4,3]=>15 [2,3,1,4,5,6]=>4 [2,3,1,4,6,5]=>9 [2,3,1,5,4,6]=>9 [2,3,1,5,6,4]=>10 [2,3,1,6,4,5]=>10 [2,3,1,6,5,4]=>13 [2,3,4,1,5,6]=>7 [2,3,4,1,6,5]=>8 [2,3,4,5,1,6]=>4 [2,3,4,5,6,1]=>1 [2,3,4,6,1,5]=>7 [2,3,4,6,5,1]=>6 [2,3,5,1,4,6]=>10 [2,3,5,1,6,4]=>9 [2,3,5,4,1,6]=>7 [2,3,5,4,6,1]=>6 [2,3,5,6,1,4]=>6 [2,3,5,6,4,1]=>9 [2,3,6,1,4,5]=>9 [2,3,6,1,5,4]=>12 [2,3,6,4,1,5]=>10 [2,3,6,4,5,1]=>7 [2,3,6,5,1,4]=>9 [2,3,6,5,4,1]=>10 [2,4,1,3,5,6]=>7 [2,4,1,3,6,5]=>10 [2,4,1,5,3,6]=>10 [2,4,1,5,6,3]=>9 [2,4,1,6,3,5]=>11 [2,4,1,6,5,3]=>10 [2,4,3,1,5,6]=>8 [2,4,3,1,6,5]=>11 [2,4,3,5,1,6]=>7 [2,4,3,5,6,1]=>4 [2,4,3,6,1,5]=>10 [2,4,3,6,5,1]=>7 [2,4,5,1,3,6]=>9 [2,4,5,1,6,3]=>6 [2,4,5,3,1,6]=>10 [2,4,5,3,6,1]=>7 [2,4,5,6,1,3]=>3 [2,4,5,6,3,1]=>6 [2,4,6,1,3,5]=>8 [2,4,6,1,5,3]=>9 [2,4,6,3,1,5]=>11 [2,4,6,3,5,1]=>10 [2,4,6,5,1,3]=>8 [2,4,6,5,3,1]=>9 [2,5,1,3,4,6]=>6 [2,5,1,3,6,4]=>9 [2,5,1,4,3,6]=>9 [2,5,1,4,6,3]=>12 [2,5,1,6,3,4]=>8 [2,5,1,6,4,3]=>11 [2,5,3,1,4,6]=>9 [2,5,3,1,6,4]=>12 [2,5,3,4,1,6]=>8 [2,5,3,4,6,1]=>7 [2,5,3,6,1,4]=>9 [2,5,3,6,4,1]=>10 [2,5,4,1,3,6]=>12 [2,5,4,1,6,3]=>9 [2,5,4,3,1,6]=>11 [2,5,4,3,6,1]=>8 [2,5,4,6,1,3]=>6 [2,5,4,6,3,1]=>9 [2,5,6,1,3,4]=>5 [2,5,6,1,4,3]=>8 [2,5,6,3,1,4]=>8 [2,5,6,3,4,1]=>9 [2,5,6,4,1,3]=>9 [2,5,6,4,3,1]=>12 [2,6,1,3,4,5]=>3 [2,6,1,3,5,4]=>8 [2,6,1,4,3,5]=>8 [2,6,1,4,5,3]=>9 [2,6,1,5,3,4]=>11 [2,6,1,5,4,3]=>12 [2,6,3,1,4,5]=>6 [2,6,3,1,5,4]=>9 [2,6,3,4,1,5]=>7 [2,6,3,4,5,1]=>4 [2,6,3,5,1,4]=>10 [2,6,3,5,4,1]=>9 [2,6,4,1,3,5]=>9 [2,6,4,1,5,3]=>12 [2,6,4,3,1,5]=>10 [2,6,4,3,5,1]=>9 [2,6,4,5,1,3]=>9 [2,6,4,5,3,1]=>10 [2,6,5,1,3,4]=>8 [2,6,5,1,4,3]=>11 [2,6,5,3,1,4]=>11 [2,6,5,3,4,1]=>10 [2,6,5,4,1,3]=>10 [2,6,5,4,3,1]=>13 [3,1,2,4,5,6]=>4 [3,1,2,4,6,5]=>9 [3,1,2,5,4,6]=>9 [3,1,2,5,6,4]=>10 [3,1,2,6,4,5]=>10 [3,1,2,6,5,4]=>13 [3,1,4,2,5,6]=>7 [3,1,4,2,6,5]=>10 [3,1,4,5,2,6]=>6 [3,1,4,5,6,2]=>3 [3,1,4,6,2,5]=>9 [3,1,4,6,5,2]=>8 [3,1,5,2,4,6]=>10 [3,1,5,2,6,4]=>11 [3,1,5,4,2,6]=>9 [3,1,5,4,6,2]=>8 [3,1,5,6,2,4]=>8 [3,1,5,6,4,2]=>11 [3,1,6,2,4,5]=>9 [3,1,6,2,5,4]=>10 [3,1,6,4,2,5]=>12 [3,1,6,4,5,2]=>9 [3,1,6,5,2,4]=>11 [3,1,6,5,4,2]=>12 [3,2,1,4,5,6]=>5 [3,2,1,4,6,5]=>10 [3,2,1,5,4,6]=>10 [3,2,1,5,6,4]=>11 [3,2,1,6,4,5]=>11 [3,2,1,6,5,4]=>14 [3,2,4,1,5,6]=>8 [3,2,4,1,6,5]=>9 [3,2,4,5,1,6]=>5 [3,2,4,5,6,1]=>2 [3,2,4,6,1,5]=>8 [3,2,4,6,5,1]=>7 [3,2,5,1,4,6]=>11 [3,2,5,1,6,4]=>10 [3,2,5,4,1,6]=>8 [3,2,5,4,6,1]=>7 [3,2,5,6,1,4]=>7 [3,2,5,6,4,1]=>10 [3,2,6,1,4,5]=>10 [3,2,6,1,5,4]=>11 [3,2,6,4,1,5]=>11 [3,2,6,4,5,1]=>8 [3,2,6,5,1,4]=>10 [3,2,6,5,4,1]=>11 [3,4,1,2,5,6]=>10 [3,4,1,2,6,5]=>11 [3,4,1,5,2,6]=>9 [3,4,1,5,6,2]=>6 [3,4,1,6,2,5]=>8 [3,4,1,6,5,2]=>9 [3,4,2,1,5,6]=>11 [3,4,2,1,6,5]=>12 [3,4,2,5,1,6]=>8 [3,4,2,5,6,1]=>5 [3,4,2,6,1,5]=>9 [3,4,2,6,5,1]=>10 [3,4,5,1,2,6]=>6 [3,4,5,1,6,2]=>5 [3,4,5,2,1,6]=>7 [3,4,5,2,6,1]=>6 [3,4,5,6,1,2]=>2 [3,4,5,6,2,1]=>3 [3,4,6,1,2,5]=>7 [3,4,6,1,5,2]=>8 [3,4,6,2,1,5]=>8 [3,4,6,2,5,1]=>9 [3,4,6,5,1,2]=>5 [3,4,6,5,2,1]=>6 [3,5,1,2,4,6]=>9 [3,5,1,2,6,4]=>8 [3,5,1,4,2,6]=>12 [3,5,1,4,6,2]=>9 [3,5,1,6,2,4]=>7 [3,5,1,6,4,2]=>10 [3,5,2,1,4,6]=>10 [3,5,2,1,6,4]=>9 [3,5,2,4,1,6]=>11 [3,5,2,4,6,1]=>8 [3,5,2,6,1,4]=>8 [3,5,2,6,4,1]=>11 [3,5,4,1,2,6]=>9 [3,5,4,1,6,2]=>6 [3,5,4,2,1,6]=>10 [3,5,4,2,6,1]=>7 [3,5,4,6,1,2]=>5 [3,5,4,6,2,1]=>6 [3,5,6,1,2,4]=>4 [3,5,6,1,4,2]=>7 [3,5,6,2,1,4]=>5 [3,5,6,2,4,1]=>8 [3,5,6,4,1,2]=>8 [3,5,6,4,2,1]=>9 [3,6,1,2,4,5]=>6 [3,6,1,2,5,4]=>9 [3,6,1,4,2,5]=>9 [3,6,1,4,5,2]=>8 [3,6,1,5,2,4]=>10 [3,6,1,5,4,2]=>11 [3,6,2,1,4,5]=>7 [3,6,2,1,5,4]=>10 [3,6,2,4,1,5]=>10 [3,6,2,4,5,1]=>7 [3,6,2,5,1,4]=>11 [3,6,2,5,4,1]=>10 [3,6,4,1,2,5]=>10 [3,6,4,1,5,2]=>9 [3,6,4,2,1,5]=>11 [3,6,4,2,5,1]=>10 [3,6,4,5,1,2]=>6 [3,6,4,5,2,1]=>7 [3,6,5,1,2,4]=>7 [3,6,5,1,4,2]=>10 [3,6,5,2,1,4]=>8 [3,6,5,2,4,1]=>11 [3,6,5,4,1,2]=>9 [3,6,5,4,2,1]=>10 [4,1,2,3,5,6]=>7 [4,1,2,3,6,5]=>8 [4,1,2,5,3,6]=>10 [4,1,2,5,6,3]=>9 [4,1,2,6,3,5]=>9 [4,1,2,6,5,3]=>12 [4,1,3,2,5,6]=>8 [4,1,3,2,6,5]=>11 [4,1,3,5,2,6]=>9 [4,1,3,5,6,2]=>6 [4,1,3,6,2,5]=>12 [4,1,3,6,5,2]=>9 [4,1,5,2,3,6]=>9 [4,1,5,2,6,3]=>8 [4,1,5,3,2,6]=>12 [4,1,5,3,6,2]=>9 [4,1,5,6,2,3]=>5 [4,1,5,6,3,2]=>8 [4,1,6,2,3,5]=>6 [4,1,6,2,5,3]=>9 [4,1,6,3,2,5]=>9 [4,1,6,3,5,2]=>12 [4,1,6,5,2,3]=>8 [4,1,6,5,3,2]=>11 [4,2,1,3,5,6]=>8 [4,2,1,3,6,5]=>9 [4,2,1,5,3,6]=>11 [4,2,1,5,6,3]=>10 [4,2,1,6,3,5]=>10 [4,2,1,6,5,3]=>11 [4,2,3,1,5,6]=>9 [4,2,3,1,6,5]=>12 [4,2,3,5,1,6]=>8 [4,2,3,5,6,1]=>5 [4,2,3,6,1,5]=>11 [4,2,3,6,5,1]=>8 [4,2,5,1,3,6]=>10 [4,2,5,1,6,3]=>7 [4,2,5,3,1,6]=>11 [4,2,5,3,6,1]=>8 [4,2,5,6,1,3]=>4 [4,2,5,6,3,1]=>7 [4,2,6,1,3,5]=>7 [4,2,6,1,5,3]=>10 [4,2,6,3,1,5]=>10 [4,2,6,3,5,1]=>11 [4,2,6,5,1,3]=>9 [4,2,6,5,3,1]=>10 [4,3,1,2,5,6]=>11 [4,3,1,2,6,5]=>12 [4,3,1,5,2,6]=>10 [4,3,1,5,6,2]=>7 [4,3,1,6,2,5]=>9 [4,3,1,6,5,2]=>10 [4,3,2,1,5,6]=>12 [4,3,2,1,6,5]=>13 [4,3,2,5,1,6]=>9 [4,3,2,5,6,1]=>6 [4,3,2,6,1,5]=>10 [4,3,2,6,5,1]=>11 [4,3,5,1,2,6]=>7 [4,3,5,1,6,2]=>6 [4,3,5,2,1,6]=>8 [4,3,5,2,6,1]=>7 [4,3,5,6,1,2]=>3 [4,3,5,6,2,1]=>4 [4,3,6,1,2,5]=>8 [4,3,6,1,5,2]=>9 [4,3,6,2,1,5]=>9 [4,3,6,2,5,1]=>10 [4,3,6,5,1,2]=>6 [4,3,6,5,2,1]=>7 [4,5,1,2,3,6]=>6 [4,5,1,2,6,3]=>7 [4,5,1,3,2,6]=>9 [4,5,1,3,6,2]=>10 [4,5,1,6,2,3]=>4 [4,5,1,6,3,2]=>7 [4,5,2,1,3,6]=>7 [4,5,2,1,6,3]=>8 [4,5,2,3,1,6]=>10 [4,5,2,3,6,1]=>11 [4,5,2,6,1,3]=>5 [4,5,2,6,3,1]=>8 [4,5,3,1,2,6]=>10 [4,5,3,1,6,2]=>9 [4,5,3,2,1,6]=>11 [4,5,3,2,6,1]=>10 [4,5,3,6,1,2]=>6 [4,5,3,6,2,1]=>7 [4,5,6,1,2,3]=>3 [4,5,6,1,3,2]=>4 [4,5,6,2,1,3]=>4 [4,5,6,2,3,1]=>5 [4,5,6,3,1,2]=>7 [4,5,6,3,2,1]=>8 [4,6,1,2,3,5]=>5 [4,6,1,2,5,3]=>8 [4,6,1,3,2,5]=>6 [4,6,1,3,5,2]=>9 [4,6,1,5,2,3]=>7 [4,6,1,5,3,2]=>10 [4,6,2,1,3,5]=>6 [4,6,2,1,5,3]=>9 [4,6,2,3,1,5]=>7 [4,6,2,3,5,1]=>8 [4,6,2,5,1,3]=>8 [4,6,2,5,3,1]=>11 [4,6,3,1,2,5]=>9 [4,6,3,1,5,2]=>12 [4,6,3,2,1,5]=>10 [4,6,3,2,5,1]=>11 [4,6,3,5,1,2]=>9 [4,6,3,5,2,1]=>10 [4,6,5,1,2,3]=>4 [4,6,5,1,3,2]=>7 [4,6,5,2,1,3]=>5 [4,6,5,2,3,1]=>8 [4,6,5,3,1,2]=>8 [4,6,5,3,2,1]=>9 [5,1,2,3,4,6]=>4 [5,1,2,3,6,4]=>7 [5,1,2,4,3,6]=>7 [5,1,2,4,6,3]=>10 [5,1,2,6,3,4]=>6 [5,1,2,6,4,3]=>9 [5,1,3,2,4,6]=>7 [5,1,3,2,6,4]=>10 [5,1,3,4,2,6]=>8 [5,1,3,4,6,2]=>7 [5,1,3,6,2,4]=>9 [5,1,3,6,4,2]=>10 [5,1,4,2,3,6]=>10 [5,1,4,2,6,3]=>11 [5,1,4,3,2,6]=>11 [5,1,4,3,6,2]=>10 [5,1,4,6,2,3]=>8 [5,1,4,6,3,2]=>11 [5,1,6,2,3,4]=>3 [5,1,6,2,4,3]=>8 [5,1,6,3,2,4]=>6 [5,1,6,3,4,2]=>9 [5,1,6,4,2,3]=>9 [5,1,6,4,3,2]=>10 [5,2,1,3,4,6]=>5 [5,2,1,3,6,4]=>8 [5,2,1,4,3,6]=>8 [5,2,1,4,6,3]=>11 [5,2,1,6,3,4]=>7 [5,2,1,6,4,3]=>10 [5,2,3,1,4,6]=>8 [5,2,3,1,6,4]=>11 [5,2,3,4,1,6]=>7 [5,2,3,4,6,1]=>6 [5,2,3,6,1,4]=>10 [5,2,3,6,4,1]=>9 [5,2,4,1,3,6]=>11 [5,2,4,1,6,3]=>10 [5,2,4,3,1,6]=>12 [5,2,4,3,6,1]=>9 [5,2,4,6,1,3]=>7 [5,2,4,6,3,1]=>10 [5,2,6,1,3,4]=>4 [5,2,6,1,4,3]=>9 [5,2,6,3,1,4]=>7 [5,2,6,3,4,1]=>8 [5,2,6,4,1,3]=>10 [5,2,6,4,3,1]=>11 [5,3,1,2,4,6]=>8 [5,3,1,2,6,4]=>9 [5,3,1,4,2,6]=>11 [5,3,1,4,6,2]=>10 [5,3,1,6,2,4]=>8 [5,3,1,6,4,2]=>11 [5,3,2,1,4,6]=>9 [5,3,2,1,6,4]=>10 [5,3,2,4,1,6]=>10 [5,3,2,4,6,1]=>9 [5,3,2,6,1,4]=>9 [5,3,2,6,4,1]=>12 [5,3,4,1,2,6]=>10 [5,3,4,1,6,2]=>7 [5,3,4,2,1,6]=>11 [5,3,4,2,6,1]=>8 [5,3,4,6,1,2]=>6 [5,3,4,6,2,1]=>7 [5,3,6,1,2,4]=>5 [5,3,6,1,4,2]=>8 [5,3,6,2,1,4]=>6 [5,3,6,2,4,1]=>9 [5,3,6,4,1,2]=>9 [5,3,6,4,2,1]=>10 [5,4,1,2,3,6]=>7 [5,4,1,2,6,3]=>8 [5,4,1,3,2,6]=>10 [5,4,1,3,6,2]=>11 [5,4,1,6,2,3]=>5 [5,4,1,6,3,2]=>8 [5,4,2,1,3,6]=>8 [5,4,2,1,6,3]=>9 [5,4,2,3,1,6]=>11 [5,4,2,3,6,1]=>12 [5,4,2,6,1,3]=>6 [5,4,2,6,3,1]=>9 [5,4,3,1,2,6]=>11 [5,4,3,1,6,2]=>10 [5,4,3,2,1,6]=>12 [5,4,3,2,6,1]=>11 [5,4,3,6,1,2]=>7 [5,4,3,6,2,1]=>8 [5,4,6,1,2,3]=>4 [5,4,6,1,3,2]=>5 [5,4,6,2,1,3]=>5 [5,4,6,2,3,1]=>6 [5,4,6,3,1,2]=>8 [5,4,6,3,2,1]=>9 [5,6,1,2,3,4]=>2 [5,6,1,2,4,3]=>5 [5,6,1,3,2,4]=>5 [5,6,1,3,4,2]=>6 [5,6,1,4,2,3]=>8 [5,6,1,4,3,2]=>9 [5,6,2,1,3,4]=>3 [5,6,2,1,4,3]=>6 [5,6,2,3,1,4]=>6 [5,6,2,3,4,1]=>5 [5,6,2,4,1,3]=>9 [5,6,2,4,3,1]=>10 [5,6,3,1,2,4]=>6 [5,6,3,1,4,2]=>9 [5,6,3,2,1,4]=>7 [5,6,3,2,4,1]=>8 [5,6,3,4,1,2]=>10 [5,6,3,4,2,1]=>11 [5,6,4,1,2,3]=>7 [5,6,4,1,3,2]=>8 [5,6,4,2,1,3]=>8 [5,6,4,2,3,1]=>9 [5,6,4,3,1,2]=>11 [5,6,4,3,2,1]=>12 [6,1,2,3,4,5]=>1 [6,1,2,3,5,4]=>6 [6,1,2,4,3,5]=>6 [6,1,2,4,5,3]=>7 [6,1,2,5,3,4]=>9 [6,1,2,5,4,3]=>10 [6,1,3,2,4,5]=>4 [6,1,3,2,5,4]=>7 [6,1,3,4,2,5]=>7 [6,1,3,4,5,2]=>4 [6,1,3,5,2,4]=>10 [6,1,3,5,4,2]=>9 [6,1,4,2,3,5]=>7 [6,1,4,2,5,3]=>10 [6,1,4,3,2,5]=>8 [6,1,4,3,5,2]=>9 [6,1,4,5,2,3]=>9 [6,1,4,5,3,2]=>10 [6,1,5,2,3,4]=>6 [6,1,5,2,4,3]=>9 [6,1,5,3,2,4]=>9 [6,1,5,3,4,2]=>10 [6,1,5,4,2,3]=>12 [6,1,5,4,3,2]=>13 [6,2,1,3,4,5]=>2 [6,2,1,3,5,4]=>7 [6,2,1,4,3,5]=>7 [6,2,1,4,5,3]=>8 [6,2,1,5,3,4]=>10 [6,2,1,5,4,3]=>11 [6,2,3,1,4,5]=>5 [6,2,3,1,5,4]=>8 [6,2,3,4,1,5]=>6 [6,2,3,4,5,1]=>3 [6,2,3,5,1,4]=>9 [6,2,3,5,4,1]=>8 [6,2,4,1,3,5]=>8 [6,2,4,1,5,3]=>11 [6,2,4,3,1,5]=>9 [6,2,4,3,5,1]=>8 [6,2,4,5,1,3]=>8 [6,2,4,5,3,1]=>9 [6,2,5,1,3,4]=>7 [6,2,5,1,4,3]=>10 [6,2,5,3,1,4]=>10 [6,2,5,3,4,1]=>9 [6,2,5,4,1,3]=>11 [6,2,5,4,3,1]=>12 [6,3,1,2,4,5]=>5 [6,3,1,2,5,4]=>10 [6,3,1,4,2,5]=>8 [6,3,1,4,5,2]=>7 [6,3,1,5,2,4]=>11 [6,3,1,5,4,2]=>10 [6,3,2,1,4,5]=>6 [6,3,2,1,5,4]=>11 [6,3,2,4,1,5]=>9 [6,3,2,4,5,1]=>6 [6,3,2,5,1,4]=>12 [6,3,2,5,4,1]=>9 [6,3,4,1,2,5]=>11 [6,3,4,1,5,2]=>8 [6,3,4,2,1,5]=>12 [6,3,4,2,5,1]=>9 [6,3,4,5,1,2]=>5 [6,3,4,5,2,1]=>6 [6,3,5,1,2,4]=>8 [6,3,5,1,4,2]=>11 [6,3,5,2,1,4]=>9 [6,3,5,2,4,1]=>12 [6,3,5,4,1,2]=>10 [6,3,5,4,2,1]=>11 [6,4,1,2,3,5]=>6 [6,4,1,2,5,3]=>9 [6,4,1,3,2,5]=>7 [6,4,1,3,5,2]=>10 [6,4,1,5,2,3]=>8 [6,4,1,5,3,2]=>11 [6,4,2,1,3,5]=>7 [6,4,2,1,5,3]=>10 [6,4,2,3,1,5]=>8 [6,4,2,3,5,1]=>9 [6,4,2,5,1,3]=>9 [6,4,2,5,3,1]=>12 [6,4,3,1,2,5]=>10 [6,4,3,1,5,2]=>11 [6,4,3,2,1,5]=>11 [6,4,3,2,5,1]=>10 [6,4,3,5,1,2]=>8 [6,4,3,5,2,1]=>9 [6,4,5,1,2,3]=>5 [6,4,5,1,3,2]=>8 [6,4,5,2,1,3]=>6 [6,4,5,2,3,1]=>9 [6,4,5,3,1,2]=>9 [6,4,5,3,2,1]=>10 [6,5,1,2,3,4]=>3 [6,5,1,2,4,3]=>6 [6,5,1,3,2,4]=>6 [6,5,1,3,4,2]=>7 [6,5,1,4,2,3]=>9 [6,5,1,4,3,2]=>10 [6,5,2,1,3,4]=>4 [6,5,2,1,4,3]=>7 [6,5,2,3,1,4]=>7 [6,5,2,3,4,1]=>6 [6,5,2,4,1,3]=>10 [6,5,2,4,3,1]=>11 [6,5,3,1,2,4]=>7 [6,5,3,1,4,2]=>10 [6,5,3,2,1,4]=>8 [6,5,3,2,4,1]=>9 [6,5,3,4,1,2]=>11 [6,5,3,4,2,1]=>12 [6,5,4,1,2,3]=>8 [6,5,4,1,3,2]=>9 [6,5,4,2,1,3]=>9 [6,5,4,2,3,1]=>10 [6,5,4,3,1,2]=>12 [6,5,4,3,2,1]=>13 [1,2,3,4,5,6,7]=>0 [1,2,3,4,5,7,6]=>5 [1,2,3,4,6,5,7]=>7 [1,2,3,4,6,7,5]=>8 [1,2,3,4,7,5,6]=>8 [1,2,3,4,7,6,5]=>9 [1,2,3,5,4,6,7]=>7 [1,2,3,5,4,7,6]=>9 [1,2,3,5,6,4,7]=>9 [1,2,3,5,6,7,4]=>8 [1,2,3,5,7,4,6]=>11 [1,2,3,5,7,6,4]=>12 [1,2,3,6,4,5,7]=>9 [1,2,3,6,4,7,5]=>11 [1,2,3,6,5,4,7]=>11 [1,2,3,6,5,7,4]=>12 [1,2,3,6,7,4,5]=>14 [1,2,3,6,7,5,4]=>15 [1,2,3,7,4,5,6]=>8 [1,2,3,7,4,6,5]=>12 [1,2,3,7,5,4,6]=>12 [1,2,3,7,5,6,4]=>13 [1,2,3,7,6,4,5]=>15 [1,2,3,7,6,5,4]=>16 [1,2,4,3,5,6,7]=>5 [1,2,4,3,5,7,6]=>9 [1,2,4,3,6,5,7]=>9 [1,2,4,3,6,7,5]=>10 [1,2,4,3,7,5,6]=>10 [1,2,4,3,7,6,5]=>13 [1,2,4,5,3,6,7]=>8 [1,2,4,5,3,7,6]=>10 [1,2,4,5,6,3,7]=>8 [1,2,4,5,6,7,3]=>5 [1,2,4,5,7,3,6]=>11 [1,2,4,5,7,6,3]=>10 [1,2,4,6,3,5,7]=>11 [1,2,4,6,3,7,5]=>13 [1,2,4,6,5,3,7]=>12 [1,2,4,6,5,7,3]=>11 [1,2,4,6,7,3,5]=>13 [1,2,4,6,7,5,3]=>12 [1,2,4,7,3,5,6]=>11 [1,2,4,7,3,6,5]=>15 [1,2,4,7,5,3,6]=>14 [1,2,4,7,5,6,3]=>12 [1,2,4,7,6,3,5]=>15 [1,2,4,7,6,5,3]=>14 [1,2,5,3,4,6,7]=>8 [1,2,5,3,4,7,6]=>10 [1,2,5,3,6,4,7]=>11 [1,2,5,3,6,7,4]=>11 [1,2,5,3,7,4,6]=>13 [1,2,5,3,7,6,4]=>15 [1,2,5,4,3,6,7]=>9 [1,2,5,4,3,7,6]=>13 [1,2,5,4,6,3,7]=>12 [1,2,5,4,6,7,3]=>10 [1,2,5,4,7,3,6]=>15 [1,2,5,4,7,6,3]=>12 [1,2,5,6,3,4,7]=>14 [1,2,5,6,3,7,4]=>13 [1,2,5,6,4,3,7]=>15 [1,2,5,6,4,7,3]=>12 [1,2,5,6,7,3,4]=>10 [1,2,5,6,7,4,3]=>11 [1,2,5,7,3,4,6]=>13 [1,2,5,7,3,6,4]=>16 [1,2,5,7,4,3,6]=>15 [1,2,5,7,4,6,3]=>15 [1,2,5,7,6,3,4]=>14 [1,2,5,7,6,4,3]=>16 [1,2,6,3,4,5,7]=>8 [1,2,6,3,4,7,5]=>11 [1,2,6,3,5,4,7]=>12 [1,2,6,3,5,7,4]=>14 [1,2,6,3,7,4,5]=>13 [1,2,6,3,7,5,4]=>15 [1,2,6,4,3,5,7]=>12 [1,2,6,4,3,7,5]=>15 [1,2,6,4,5,3,7]=>13 [1,2,6,4,5,7,3]=>12 [1,2,6,4,7,3,5]=>16 [1,2,6,4,7,5,3]=>15 [1,2,6,5,3,4,7]=>15 [1,2,6,5,3,7,4]=>15 [1,2,6,5,4,3,7]=>16 [1,2,6,5,4,7,3]=>14 [1,2,6,5,7,3,4]=>14 [1,2,6,5,7,4,3]=>16 [1,2,6,7,3,4,5]=>10 [1,2,6,7,3,5,4]=>14 [1,2,6,7,4,3,5]=>14 [1,2,6,7,4,5,3]=>15 [1,2,6,7,5,3,4]=>15 [1,2,6,7,5,4,3]=>18 [1,2,7,3,4,5,6]=>5 [1,2,7,3,4,6,5]=>10 [1,2,7,3,5,4,6]=>11 [1,2,7,3,5,6,4]=>12 [1,2,7,3,6,4,5]=>12 [1,2,7,3,6,5,4]=>14 [1,2,7,4,3,5,6]=>10 [1,2,7,4,3,6,5]=>12 [1,2,7,4,5,3,6]=>12 [1,2,7,4,5,6,3]=>11 [1,2,7,4,6,3,5]=>15 [1,2,7,4,6,5,3]=>16 [1,2,7,5,3,4,6]=>12 [1,2,7,5,3,6,4]=>15 [1,2,7,5,4,3,6]=>14 [1,2,7,5,4,6,3]=>16 [1,2,7,5,6,3,4]=>15 [1,2,7,5,6,4,3]=>18 [1,2,7,6,3,4,5]=>11 [1,2,7,6,3,5,4]=>16 [1,2,7,6,4,3,5]=>16 [1,2,7,6,4,5,3]=>18 [1,2,7,6,5,3,4]=>18 [1,2,7,6,5,4,3]=>20 [1,3,2,4,5,6,7]=>3 [1,3,2,4,5,7,6]=>8 [1,3,2,4,6,5,7]=>9 [1,3,2,4,6,7,5]=>10 [1,3,2,4,7,5,6]=>10 [1,3,2,4,7,6,5]=>12 [1,3,2,5,4,6,7]=>8 [1,3,2,5,4,7,6]=>10 [1,3,2,5,6,4,7]=>10 [1,3,2,5,6,7,4]=>9 [1,3,2,5,7,4,6]=>13 [1,3,2,5,7,6,4]=>14 [1,3,2,6,4,5,7]=>10 [1,3,2,6,4,7,5]=>13 [1,3,2,6,5,4,7]=>12 [1,3,2,6,5,7,4]=>14 [1,3,2,6,7,4,5]=>16 [1,3,2,6,7,5,4]=>16 [1,3,2,7,4,5,6]=>9 [1,3,2,7,4,6,5]=>14 [1,3,2,7,5,4,6]=>14 [1,3,2,7,5,6,4]=>16 [1,3,2,7,6,4,5]=>16 [1,3,2,7,6,5,4]=>18 [1,3,4,2,5,6,7]=>6 [1,3,4,2,5,7,6]=>10 [1,3,4,2,6,5,7]=>10 [1,3,4,2,6,7,5]=>11 [1,3,4,2,7,5,6]=>13 [1,3,4,2,7,6,5]=>14 [1,3,4,5,2,6,7]=>8 [1,3,4,5,2,7,6]=>9 [1,3,4,5,6,2,7]=>5 [1,3,4,5,6,7,2]=>2 [1,3,4,5,7,2,6]=>8 [1,3,4,5,7,6,2]=>7 [1,3,4,6,2,5,7]=>11 [1,3,4,6,2,7,5]=>12 [1,3,4,6,5,2,7]=>9 [1,3,4,6,5,7,2]=>8 [1,3,4,6,7,2,5]=>10 [1,3,4,6,7,5,2]=>10 [1,3,4,7,2,5,6]=>14 [1,3,4,7,2,6,5]=>15 [1,3,4,7,5,2,6]=>11 [1,3,4,7,5,6,2]=>9 [1,3,4,7,6,2,5]=>12 [1,3,4,7,6,5,2]=>11 [1,3,5,2,4,6,7]=>9 [1,3,5,2,4,7,6]=>13 [1,3,5,2,6,4,7]=>12 [1,3,5,2,6,7,4]=>12 [1,3,5,2,7,4,6]=>15 [1,3,5,2,7,6,4]=>14 [1,3,5,4,2,6,7]=>10 [1,3,5,4,2,7,6]=>13 [1,3,5,4,6,2,7]=>9 [1,3,5,4,6,7,2]=>7 [1,3,5,4,7,2,6]=>12 [1,3,5,4,7,6,2]=>9 [1,3,5,6,2,4,7]=>13 [1,3,5,6,2,7,4]=>10 [1,3,5,6,4,2,7]=>12 [1,3,5,6,4,7,2]=>10 [1,3,5,6,7,2,4]=>7 [1,3,5,6,7,4,2]=>10 [1,3,5,7,2,4,6]=>15 [1,3,5,7,2,6,4]=>13 [1,3,5,7,4,2,6]=>14 [1,3,5,7,4,6,2]=>12 [1,3,5,7,6,2,4]=>11 [1,3,5,7,6,4,2]=>14 [1,3,6,2,4,5,7]=>11 [1,3,6,2,4,7,5]=>14 [1,3,6,2,5,4,7]=>13 [1,3,6,2,5,7,4]=>15 [1,3,6,2,7,4,5]=>14 [1,3,6,2,7,5,4]=>16 [1,3,6,4,2,5,7]=>13 [1,3,6,4,2,7,5]=>15 [1,3,6,4,5,2,7]=>10 [1,3,6,4,5,7,2]=>9 [1,3,6,4,7,2,5]=>13 [1,3,6,4,7,5,2]=>12 [1,3,6,5,2,4,7]=>15 [1,3,6,5,2,7,4]=>12 [1,3,6,5,4,2,7]=>13 [1,3,6,5,4,7,2]=>11 [1,3,6,5,7,2,4]=>11 [1,3,6,5,7,4,2]=>14 [1,3,6,7,2,4,5]=>12 [1,3,6,7,2,5,4]=>13 [1,3,6,7,4,2,5]=>15 [1,3,6,7,4,5,2]=>15 [1,3,6,7,5,2,4]=>14 [1,3,6,7,5,4,2]=>16 [1,3,7,2,4,5,6]=>8 [1,3,7,2,4,6,5]=>12 [1,3,7,2,5,4,6]=>12 [1,3,7,2,5,6,4]=>13 [1,3,7,2,6,4,5]=>13 [1,3,7,2,6,5,4]=>16 [1,3,7,4,2,5,6]=>11 [1,3,7,4,2,6,5]=>13 [1,3,7,4,5,2,6]=>11 [1,3,7,4,5,6,2]=>8 [1,3,7,4,6,2,5]=>14 [1,3,7,4,6,5,2]=>13 [1,3,7,5,2,4,6]=>14 [1,3,7,5,2,6,4]=>15 [1,3,7,5,4,2,6]=>15 [1,3,7,5,4,6,2]=>13 [1,3,7,5,6,2,4]=>12 [1,3,7,5,6,4,2]=>15 [1,3,7,6,2,4,5]=>14 [1,3,7,6,2,5,4]=>16 [1,3,7,6,4,2,5]=>17 [1,3,7,6,4,5,2]=>15 [1,3,7,6,5,2,4]=>15 [1,3,7,6,5,4,2]=>17 [1,4,2,3,5,6,7]=>6 [1,4,2,3,5,7,6]=>10 [1,4,2,3,6,5,7]=>10 [1,4,2,3,6,7,5]=>13 [1,4,2,3,7,5,6]=>11 [1,4,2,3,7,6,5]=>14 [1,4,2,5,3,6,7]=>9 [1,4,2,5,3,7,6]=>13 [1,4,2,5,6,3,7]=>11 [1,4,2,5,6,7,3]=>8 [1,4,2,5,7,3,6]=>14 [1,4,2,5,7,6,3]=>12 [1,4,2,6,3,5,7]=>12 [1,4,2,6,3,7,5]=>15 [1,4,2,6,5,3,7]=>13 [1,4,2,6,5,7,3]=>12 [1,4,2,6,7,3,5]=>14 [1,4,2,6,7,5,3]=>13 [1,4,2,7,3,5,6]=>12 [1,4,2,7,3,6,5]=>14 [1,4,2,7,5,3,6]=>15 [1,4,2,7,5,6,3]=>13 [1,4,2,7,6,3,5]=>16 [1,4,2,7,6,5,3]=>16 [1,4,3,2,5,6,7]=>7 [1,4,3,2,5,7,6]=>12 [1,4,3,2,6,5,7]=>12 [1,4,3,2,6,7,5]=>14 [1,4,3,2,7,5,6]=>14 [1,4,3,2,7,6,5]=>16 [1,4,3,5,2,6,7]=>10 [1,4,3,5,2,7,6]=>12 [1,4,3,5,6,2,7]=>8 [1,4,3,5,6,7,2]=>5 [1,4,3,5,7,2,6]=>11 [1,4,3,5,7,6,2]=>9 [1,4,3,6,2,5,7]=>13 [1,4,3,6,2,7,5]=>14 [1,4,3,6,5,2,7]=>10 [1,4,3,6,5,7,2]=>9 [1,4,3,6,7,2,5]=>11 [1,4,3,6,7,5,2]=>12 [1,4,3,7,2,5,6]=>15 [1,4,3,7,2,6,5]=>17 [1,4,3,7,5,2,6]=>13 [1,4,3,7,5,6,2]=>10 [1,4,3,7,6,2,5]=>15 [1,4,3,7,6,5,2]=>13 [1,4,5,2,3,6,7]=>12 [1,4,5,2,3,7,6]=>16 [1,4,5,2,6,3,7]=>13 [1,4,5,2,6,7,3]=>10 [1,4,5,2,7,3,6]=>14 [1,4,5,2,7,6,3]=>11 [1,4,5,3,2,6,7]=>13 [1,4,5,3,2,7,6]=>15 [1,4,5,3,6,2,7]=>11 [1,4,5,3,6,7,2]=>8 [1,4,5,3,7,2,6]=>13 [1,4,5,3,7,6,2]=>12 [1,4,5,6,2,3,7]=>10 [1,4,5,6,2,7,3]=>7 [1,4,5,6,3,2,7]=>11 [1,4,5,6,3,7,2]=>10 [1,4,5,6,7,2,3]=>4 [1,4,5,6,7,3,2]=>7 [1,4,5,7,2,3,6]=>12 [1,4,5,7,2,6,3]=>10 [1,4,5,7,3,2,6]=>14 [1,4,5,7,3,6,2]=>13 [1,4,5,7,6,2,3]=>9 [1,4,5,7,6,3,2]=>11 [1,4,6,2,3,5,7]=>13 [1,4,6,2,3,7,5]=>14 [1,4,6,2,5,3,7]=>16 [1,4,6,2,5,7,3]=>13 [1,4,6,2,7,3,5]=>12 [1,4,6,2,7,5,3]=>14 [1,4,6,3,2,5,7]=>15 [1,4,6,3,2,7,5]=>16 [1,4,6,3,5,2,7]=>13 [1,4,6,3,5,7,2]=>11 [1,4,6,3,7,2,5]=>14 [1,4,6,3,7,5,2]=>14 [1,4,6,5,2,3,7]=>14 [1,4,6,5,2,7,3]=>11 [1,4,6,5,3,2,7]=>15 [1,4,6,5,3,7,2]=>12
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Description
The minimal length of a factorization of a permutation using the transposition (12) and the cycle (1,...,n).
In symbols, for a permutation $\pi$ this is
$$\min\{ k \mid \pi = \tau_{i_1} \cdots \tau_{i_k} \},$$
where each factor $\tau_i$ is one of $(1,2)$, $(1,\dots,n)$ or $(1,\dots,n)^{-1}$.
Code
def statistic(pi):
    def gens(n):
        a = Permutation([2,1])
        b = Permutation([i for i in range(2,n+1)] + [1])
        return [a, b]
    G = PermutationGroup(gens(len(pi)))
    pi = G(pi)
    w = gap.Factorization(G._gap_(), pi._gap_())
    return w.Length().sage()
Created
Jan 08, 2018 at 23:24 by Martin Rubey
Updated
Feb 09, 2021 at 15:29 by Martin Rubey