edit this statistic or download as text // json
Identifier
Values
=>
[1,2]=>0 [2,1]=>1 [1,2,3]=>0 [1,3,2]=>1 [2,1,3]=>1 [2,3,1]=>3 [3,1,2]=>2 [3,2,1]=>2 [1,2,3,4]=>0 [1,2,4,3]=>1 [1,3,2,4]=>1 [1,3,4,2]=>3 [1,4,2,3]=>2 [1,4,3,2]=>2 [2,1,3,4]=>1 [2,1,4,3]=>2 [2,3,1,4]=>3 [2,3,4,1]=>5 [2,4,1,3]=>4 [2,4,3,1]=>4 [3,1,2,4]=>2 [3,1,4,2]=>5 [3,2,1,4]=>2 [3,2,4,1]=>6 [3,4,1,2]=>4 [3,4,2,1]=>4 [4,1,2,3]=>3 [4,1,3,2]=>4 [4,2,1,3]=>3 [4,2,3,1]=>5 [4,3,1,2]=>3 [4,3,2,1]=>3 [1,2,3,4,5]=>0 [1,2,3,5,4]=>1 [1,2,4,3,5]=>1 [1,2,4,5,3]=>3 [1,2,5,3,4]=>2 [1,2,5,4,3]=>2 [1,3,2,4,5]=>1 [1,3,2,5,4]=>2 [1,3,4,2,5]=>3 [1,3,4,5,2]=>5 [1,3,5,2,4]=>4 [1,3,5,4,2]=>4 [1,4,2,3,5]=>2 [1,4,2,5,3]=>5 [1,4,3,2,5]=>2 [1,4,3,5,2]=>6 [1,4,5,2,3]=>4 [1,4,5,3,2]=>4 [1,5,2,3,4]=>3 [1,5,2,4,3]=>4 [1,5,3,2,4]=>3 [1,5,3,4,2]=>5 [1,5,4,2,3]=>3 [1,5,4,3,2]=>3 [2,1,3,4,5]=>1 [2,1,3,5,4]=>2 [2,1,4,3,5]=>2 [2,1,4,5,3]=>4 [2,1,5,3,4]=>3 [2,1,5,4,3]=>3 [2,3,1,4,5]=>3 [2,3,1,5,4]=>4 [2,3,4,1,5]=>5 [2,3,4,5,1]=>7 [2,3,5,1,4]=>6 [2,3,5,4,1]=>6 [2,4,1,3,5]=>4 [2,4,1,5,3]=>7 [2,4,3,1,5]=>4 [2,4,3,5,1]=>8 [2,4,5,1,3]=>6 [2,4,5,3,1]=>6 [2,5,1,3,4]=>5 [2,5,1,4,3]=>6 [2,5,3,1,4]=>5 [2,5,3,4,1]=>7 [2,5,4,1,3]=>5 [2,5,4,3,1]=>5 [3,1,2,4,5]=>2 [3,1,2,5,4]=>3 [3,1,4,2,5]=>5 [3,1,4,5,2]=>7 [3,1,5,2,4]=>6 [3,1,5,4,2]=>6 [3,2,1,4,5]=>2 [3,2,1,5,4]=>3 [3,2,4,1,5]=>6 [3,2,4,5,1]=>8 [3,2,5,1,4]=>7 [3,2,5,4,1]=>7 [3,4,1,2,5]=>4 [3,4,1,5,2]=>9 [3,4,2,1,5]=>4 [3,4,2,5,1]=>10 [3,4,5,1,2]=>6 [3,4,5,2,1]=>6 [3,5,1,2,4]=>5 [3,5,1,4,2]=>8 [3,5,2,1,4]=>5 [3,5,2,4,1]=>9 [3,5,4,1,2]=>5 [3,5,4,2,1]=>5 [4,1,2,3,5]=>3 [4,1,2,5,3]=>6 [4,1,3,2,5]=>4 [4,1,3,5,2]=>8 [4,1,5,2,3]=>7 [4,1,5,3,2]=>7 [4,2,1,3,5]=>3 [4,2,1,5,3]=>6 [4,2,3,1,5]=>5 [4,2,3,5,1]=>9 [4,2,5,1,3]=>8 [4,2,5,3,1]=>8 [4,3,1,2,5]=>3 [4,3,1,5,2]=>8 [4,3,2,1,5]=>3 [4,3,2,5,1]=>9 [4,3,5,1,2]=>7 [4,3,5,2,1]=>7 [4,5,1,2,3]=>5 [4,5,1,3,2]=>6 [4,5,2,1,3]=>5 [4,5,2,3,1]=>7 [4,5,3,1,2]=>5 [4,5,3,2,1]=>5 [5,1,2,3,4]=>4 [5,1,2,4,3]=>5 [5,1,3,2,4]=>5 [5,1,3,4,2]=>7 [5,1,4,2,3]=>6 [5,1,4,3,2]=>6 [5,2,1,3,4]=>4 [5,2,1,4,3]=>5 [5,2,3,1,4]=>6 [5,2,3,4,1]=>8 [5,2,4,1,3]=>7 [5,2,4,3,1]=>7 [5,3,1,2,4]=>4 [5,3,1,4,2]=>7 [5,3,2,1,4]=>4 [5,3,2,4,1]=>8 [5,3,4,1,2]=>6 [5,3,4,2,1]=>6 [5,4,1,2,3]=>4 [5,4,1,3,2]=>5 [5,4,2,1,3]=>4 [5,4,2,3,1]=>6 [5,4,3,1,2]=>4 [5,4,3,2,1]=>4 [1,2,3,4,5,6]=>0 [1,2,3,4,6,5]=>1 [1,2,3,5,4,6]=>1 [1,2,3,5,6,4]=>3 [1,2,3,6,4,5]=>2 [1,2,3,6,5,4]=>2 [1,2,4,3,5,6]=>1 [1,2,4,3,6,5]=>2 [1,2,4,5,3,6]=>3 [1,2,4,5,6,3]=>5 [1,2,4,6,3,5]=>4 [1,2,4,6,5,3]=>4 [1,2,5,3,4,6]=>2 [1,2,5,3,6,4]=>5 [1,2,5,4,3,6]=>2 [1,2,5,4,6,3]=>6 [1,2,5,6,3,4]=>4 [1,2,5,6,4,3]=>4 [1,2,6,3,4,5]=>3 [1,2,6,3,5,4]=>4 [1,2,6,4,3,5]=>3 [1,2,6,4,5,3]=>5 [1,2,6,5,3,4]=>3 [1,2,6,5,4,3]=>3 [1,3,2,4,5,6]=>1 [1,3,2,4,6,5]=>2 [1,3,2,5,4,6]=>2 [1,3,2,5,6,4]=>4 [1,3,2,6,4,5]=>3 [1,3,2,6,5,4]=>3 [1,3,4,2,5,6]=>3 [1,3,4,2,6,5]=>4 [1,3,4,5,2,6]=>5 [1,3,4,5,6,2]=>7 [1,3,4,6,2,5]=>6 [1,3,4,6,5,2]=>6 [1,3,5,2,4,6]=>4 [1,3,5,2,6,4]=>7 [1,3,5,4,2,6]=>4 [1,3,5,4,6,2]=>8 [1,3,5,6,2,4]=>6 [1,3,5,6,4,2]=>6 [1,3,6,2,4,5]=>5 [1,3,6,2,5,4]=>6 [1,3,6,4,2,5]=>5 [1,3,6,4,5,2]=>7 [1,3,6,5,2,4]=>5 [1,3,6,5,4,2]=>5 [1,4,2,3,5,6]=>2 [1,4,2,3,6,5]=>3 [1,4,2,5,3,6]=>5 [1,4,2,5,6,3]=>7 [1,4,2,6,3,5]=>6 [1,4,2,6,5,3]=>6 [1,4,3,2,5,6]=>2 [1,4,3,2,6,5]=>3 [1,4,3,5,2,6]=>6 [1,4,3,5,6,2]=>8 [1,4,3,6,2,5]=>7 [1,4,3,6,5,2]=>7 [1,4,5,2,3,6]=>4 [1,4,5,2,6,3]=>9 [1,4,5,3,2,6]=>4 [1,4,5,3,6,2]=>10 [1,4,5,6,2,3]=>6 [1,4,5,6,3,2]=>6 [1,4,6,2,3,5]=>5 [1,4,6,2,5,3]=>8 [1,4,6,3,2,5]=>5 [1,4,6,3,5,2]=>9 [1,4,6,5,2,3]=>5 [1,4,6,5,3,2]=>5 [1,5,2,3,4,6]=>3 [1,5,2,3,6,4]=>6 [1,5,2,4,3,6]=>4 [1,5,2,4,6,3]=>8 [1,5,2,6,3,4]=>7 [1,5,2,6,4,3]=>7 [1,5,3,2,4,6]=>3 [1,5,3,2,6,4]=>6 [1,5,3,4,2,6]=>5 [1,5,3,4,6,2]=>9 [1,5,3,6,2,4]=>8 [1,5,3,6,4,2]=>8 [1,5,4,2,3,6]=>3 [1,5,4,2,6,3]=>8 [1,5,4,3,2,6]=>3 [1,5,4,3,6,2]=>9 [1,5,4,6,2,3]=>7 [1,5,4,6,3,2]=>7 [1,5,6,2,3,4]=>5 [1,5,6,2,4,3]=>6 [1,5,6,3,2,4]=>5 [1,5,6,3,4,2]=>7 [1,5,6,4,2,3]=>5 [1,5,6,4,3,2]=>5 [1,6,2,3,4,5]=>4 [1,6,2,3,5,4]=>5 [1,6,2,4,3,5]=>5 [1,6,2,4,5,3]=>7 [1,6,2,5,3,4]=>6 [1,6,2,5,4,3]=>6 [1,6,3,2,4,5]=>4 [1,6,3,2,5,4]=>5 [1,6,3,4,2,5]=>6 [1,6,3,4,5,2]=>8 [1,6,3,5,2,4]=>7 [1,6,3,5,4,2]=>7 [1,6,4,2,3,5]=>4 [1,6,4,2,5,3]=>7 [1,6,4,3,2,5]=>4 [1,6,4,3,5,2]=>8 [1,6,4,5,2,3]=>6 [1,6,4,5,3,2]=>6 [1,6,5,2,3,4]=>4 [1,6,5,2,4,3]=>5 [1,6,5,3,2,4]=>4 [1,6,5,3,4,2]=>6 [1,6,5,4,2,3]=>4 [1,6,5,4,3,2]=>4 [2,1,3,4,5,6]=>1 [2,1,3,4,6,5]=>2 [2,1,3,5,4,6]=>2 [2,1,3,5,6,4]=>4 [2,1,3,6,4,5]=>3 [2,1,3,6,5,4]=>3 [2,1,4,3,5,6]=>2 [2,1,4,3,6,5]=>3 [2,1,4,5,3,6]=>4 [2,1,4,5,6,3]=>6 [2,1,4,6,3,5]=>5 [2,1,4,6,5,3]=>5 [2,1,5,3,4,6]=>3 [2,1,5,3,6,4]=>6 [2,1,5,4,3,6]=>3 [2,1,5,4,6,3]=>7 [2,1,5,6,3,4]=>5 [2,1,5,6,4,3]=>5 [2,1,6,3,4,5]=>4 [2,1,6,3,5,4]=>5 [2,1,6,4,3,5]=>4 [2,1,6,4,5,3]=>6 [2,1,6,5,3,4]=>4 [2,1,6,5,4,3]=>4 [2,3,1,4,5,6]=>3 [2,3,1,4,6,5]=>4 [2,3,1,5,4,6]=>4 [2,3,1,5,6,4]=>6 [2,3,1,6,4,5]=>5 [2,3,1,6,5,4]=>5 [2,3,4,1,5,6]=>5 [2,3,4,1,6,5]=>6 [2,3,4,5,1,6]=>7 [2,3,4,5,6,1]=>9 [2,3,4,6,1,5]=>8 [2,3,4,6,5,1]=>8 [2,3,5,1,4,6]=>6 [2,3,5,1,6,4]=>9 [2,3,5,4,1,6]=>6 [2,3,5,4,6,1]=>10 [2,3,5,6,1,4]=>8 [2,3,5,6,4,1]=>8 [2,3,6,1,4,5]=>7 [2,3,6,1,5,4]=>8 [2,3,6,4,1,5]=>7 [2,3,6,4,5,1]=>9 [2,3,6,5,1,4]=>7 [2,3,6,5,4,1]=>7 [2,4,1,3,5,6]=>4 [2,4,1,3,6,5]=>5 [2,4,1,5,3,6]=>7 [2,4,1,5,6,3]=>9 [2,4,1,6,3,5]=>8 [2,4,1,6,5,3]=>8 [2,4,3,1,5,6]=>4 [2,4,3,1,6,5]=>5 [2,4,3,5,1,6]=>8 [2,4,3,5,6,1]=>10 [2,4,3,6,1,5]=>9 [2,4,3,6,5,1]=>9 [2,4,5,1,3,6]=>6 [2,4,5,1,6,3]=>11 [2,4,5,3,1,6]=>6 [2,4,5,3,6,1]=>12 [2,4,5,6,1,3]=>8 [2,4,5,6,3,1]=>8 [2,4,6,1,3,5]=>7 [2,4,6,1,5,3]=>10 [2,4,6,3,1,5]=>7 [2,4,6,3,5,1]=>11 [2,4,6,5,1,3]=>7 [2,4,6,5,3,1]=>7 [2,5,1,3,4,6]=>5 [2,5,1,3,6,4]=>8 [2,5,1,4,3,6]=>6 [2,5,1,4,6,3]=>10 [2,5,1,6,3,4]=>9 [2,5,1,6,4,3]=>9 [2,5,3,1,4,6]=>5 [2,5,3,1,6,4]=>8 [2,5,3,4,1,6]=>7 [2,5,3,4,6,1]=>11 [2,5,3,6,1,4]=>10 [2,5,3,6,4,1]=>10 [2,5,4,1,3,6]=>5 [2,5,4,1,6,3]=>10 [2,5,4,3,1,6]=>5 [2,5,4,3,6,1]=>11 [2,5,4,6,1,3]=>9 [2,5,4,6,3,1]=>9 [2,5,6,1,3,4]=>7 [2,5,6,1,4,3]=>8 [2,5,6,3,1,4]=>7 [2,5,6,3,4,1]=>9 [2,5,6,4,1,3]=>7 [2,5,6,4,3,1]=>7 [2,6,1,3,4,5]=>6 [2,6,1,3,5,4]=>7 [2,6,1,4,3,5]=>7 [2,6,1,4,5,3]=>9 [2,6,1,5,3,4]=>8 [2,6,1,5,4,3]=>8 [2,6,3,1,4,5]=>6 [2,6,3,1,5,4]=>7 [2,6,3,4,1,5]=>8 [2,6,3,4,5,1]=>10 [2,6,3,5,1,4]=>9 [2,6,3,5,4,1]=>9 [2,6,4,1,3,5]=>6 [2,6,4,1,5,3]=>9 [2,6,4,3,1,5]=>6 [2,6,4,3,5,1]=>10 [2,6,4,5,1,3]=>8 [2,6,4,5,3,1]=>8 [2,6,5,1,3,4]=>6 [2,6,5,1,4,3]=>7 [2,6,5,3,1,4]=>6 [2,6,5,3,4,1]=>8 [2,6,5,4,1,3]=>6 [2,6,5,4,3,1]=>6 [3,1,2,4,5,6]=>2 [3,1,2,4,6,5]=>3 [3,1,2,5,4,6]=>3 [3,1,2,5,6,4]=>5 [3,1,2,6,4,5]=>4 [3,1,2,6,5,4]=>4 [3,1,4,2,5,6]=>5 [3,1,4,2,6,5]=>6 [3,1,4,5,2,6]=>7 [3,1,4,5,6,2]=>9 [3,1,4,6,2,5]=>8 [3,1,4,6,5,2]=>8 [3,1,5,2,4,6]=>6 [3,1,5,2,6,4]=>9 [3,1,5,4,2,6]=>6 [3,1,5,4,6,2]=>10 [3,1,5,6,2,4]=>8 [3,1,5,6,4,2]=>8 [3,1,6,2,4,5]=>7 [3,1,6,2,5,4]=>8 [3,1,6,4,2,5]=>7 [3,1,6,4,5,2]=>9 [3,1,6,5,2,4]=>7 [3,1,6,5,4,2]=>7 [3,2,1,4,5,6]=>2 [3,2,1,4,6,5]=>3 [3,2,1,5,4,6]=>3 [3,2,1,5,6,4]=>5 [3,2,1,6,4,5]=>4 [3,2,1,6,5,4]=>4 [3,2,4,1,5,6]=>6 [3,2,4,1,6,5]=>7 [3,2,4,5,1,6]=>8 [3,2,4,5,6,1]=>10 [3,2,4,6,1,5]=>9 [3,2,4,6,5,1]=>9 [3,2,5,1,4,6]=>7 [3,2,5,1,6,4]=>10 [3,2,5,4,1,6]=>7 [3,2,5,4,6,1]=>11 [3,2,5,6,1,4]=>9 [3,2,5,6,4,1]=>9 [3,2,6,1,4,5]=>8 [3,2,6,1,5,4]=>9 [3,2,6,4,1,5]=>8 [3,2,6,4,5,1]=>10 [3,2,6,5,1,4]=>8 [3,2,6,5,4,1]=>8 [3,4,1,2,5,6]=>4 [3,4,1,2,6,5]=>5 [3,4,1,5,2,6]=>9 [3,4,1,5,6,2]=>11 [3,4,1,6,2,5]=>10 [3,4,1,6,5,2]=>10 [3,4,2,1,5,6]=>4 [3,4,2,1,6,5]=>5 [3,4,2,5,1,6]=>10 [3,4,2,5,6,1]=>12 [3,4,2,6,1,5]=>11 [3,4,2,6,5,1]=>11 [3,4,5,1,2,6]=>6 [3,4,5,1,6,2]=>13 [3,4,5,2,1,6]=>6 [3,4,5,2,6,1]=>14 [3,4,5,6,1,2]=>8 [3,4,5,6,2,1]=>8 [3,4,6,1,2,5]=>7 [3,4,6,1,5,2]=>12 [3,4,6,2,1,5]=>7 [3,4,6,2,5,1]=>13 [3,4,6,5,1,2]=>7 [3,4,6,5,2,1]=>7 [3,5,1,2,4,6]=>5 [3,5,1,2,6,4]=>8 [3,5,1,4,2,6]=>8 [3,5,1,4,6,2]=>12 [3,5,1,6,2,4]=>11 [3,5,1,6,4,2]=>11 [3,5,2,1,4,6]=>5 [3,5,2,1,6,4]=>8 [3,5,2,4,1,6]=>9 [3,5,2,4,6,1]=>13 [3,5,2,6,1,4]=>12 [3,5,2,6,4,1]=>12 [3,5,4,1,2,6]=>5 [3,5,4,1,6,2]=>12 [3,5,4,2,1,6]=>5 [3,5,4,2,6,1]=>13 [3,5,4,6,1,2]=>9 [3,5,4,6,2,1]=>9 [3,5,6,1,2,4]=>7 [3,5,6,1,4,2]=>10 [3,5,6,2,1,4]=>7 [3,5,6,2,4,1]=>11 [3,5,6,4,1,2]=>7 [3,5,6,4,2,1]=>7 [3,6,1,2,4,5]=>6 [3,6,1,2,5,4]=>7 [3,6,1,4,2,5]=>9 [3,6,1,4,5,2]=>11 [3,6,1,5,2,4]=>10 [3,6,1,5,4,2]=>10 [3,6,2,1,4,5]=>6 [3,6,2,1,5,4]=>7 [3,6,2,4,1,5]=>10 [3,6,2,4,5,1]=>12 [3,6,2,5,1,4]=>11 [3,6,2,5,4,1]=>11 [3,6,4,1,2,5]=>6 [3,6,4,1,5,2]=>11 [3,6,4,2,1,5]=>6 [3,6,4,2,5,1]=>12 [3,6,4,5,1,2]=>8 [3,6,4,5,2,1]=>8 [3,6,5,1,2,4]=>6 [3,6,5,1,4,2]=>9 [3,6,5,2,1,4]=>6 [3,6,5,2,4,1]=>10 [3,6,5,4,1,2]=>6 [3,6,5,4,2,1]=>6 [4,1,2,3,5,6]=>3 [4,1,2,3,6,5]=>4 [4,1,2,5,3,6]=>6 [4,1,2,5,6,3]=>8 [4,1,2,6,3,5]=>7 [4,1,2,6,5,3]=>7 [4,1,3,2,5,6]=>4 [4,1,3,2,6,5]=>5 [4,1,3,5,2,6]=>8 [4,1,3,5,6,2]=>10 [4,1,3,6,2,5]=>9 [4,1,3,6,5,2]=>9 [4,1,5,2,3,6]=>7 [4,1,5,2,6,3]=>12 [4,1,5,3,2,6]=>7 [4,1,5,3,6,2]=>13 [4,1,5,6,2,3]=>9 [4,1,5,6,3,2]=>9 [4,1,6,2,3,5]=>8 [4,1,6,2,5,3]=>11 [4,1,6,3,2,5]=>8 [4,1,6,3,5,2]=>12 [4,1,6,5,2,3]=>8 [4,1,6,5,3,2]=>8 [4,2,1,3,5,6]=>3 [4,2,1,3,6,5]=>4 [4,2,1,5,3,6]=>6 [4,2,1,5,6,3]=>8 [4,2,1,6,3,5]=>7 [4,2,1,6,5,3]=>7 [4,2,3,1,5,6]=>5 [4,2,3,1,6,5]=>6 [4,2,3,5,1,6]=>9 [4,2,3,5,6,1]=>11 [4,2,3,6,1,5]=>10 [4,2,3,6,5,1]=>10 [4,2,5,1,3,6]=>8 [4,2,5,1,6,3]=>13 [4,2,5,3,1,6]=>8 [4,2,5,3,6,1]=>14 [4,2,5,6,1,3]=>10 [4,2,5,6,3,1]=>10 [4,2,6,1,3,5]=>9 [4,2,6,1,5,3]=>12 [4,2,6,3,1,5]=>9 [4,2,6,3,5,1]=>13 [4,2,6,5,1,3]=>9 [4,2,6,5,3,1]=>9 [4,3,1,2,5,6]=>3 [4,3,1,2,6,5]=>4 [4,3,1,5,2,6]=>8 [4,3,1,5,6,2]=>10 [4,3,1,6,2,5]=>9 [4,3,1,6,5,2]=>9 [4,3,2,1,5,6]=>3 [4,3,2,1,6,5]=>4 [4,3,2,5,1,6]=>9 [4,3,2,5,6,1]=>11 [4,3,2,6,1,5]=>10 [4,3,2,6,5,1]=>10 [4,3,5,1,2,6]=>7 [4,3,5,1,6,2]=>14 [4,3,5,2,1,6]=>7 [4,3,5,2,6,1]=>15 [4,3,5,6,1,2]=>9 [4,3,5,6,2,1]=>9 [4,3,6,1,2,5]=>8 [4,3,6,1,5,2]=>13 [4,3,6,2,1,5]=>8 [4,3,6,2,5,1]=>14 [4,3,6,5,1,2]=>8 [4,3,6,5,2,1]=>8 [4,5,1,2,3,6]=>5 [4,5,1,2,6,3]=>10 [4,5,1,3,2,6]=>6 [4,5,1,3,6,2]=>12 [4,5,1,6,2,3]=>11 [4,5,1,6,3,2]=>11 [4,5,2,1,3,6]=>5 [4,5,2,1,6,3]=>10 [4,5,2,3,1,6]=>7 [4,5,2,3,6,1]=>13 [4,5,2,6,1,3]=>12 [4,5,2,6,3,1]=>12 [4,5,3,1,2,6]=>5 [4,5,3,1,6,2]=>12 [4,5,3,2,1,6]=>5 [4,5,3,2,6,1]=>13 [4,5,3,6,1,2]=>11 [4,5,3,6,2,1]=>11 [4,5,6,1,2,3]=>7 [4,5,6,1,3,2]=>8 [4,5,6,2,1,3]=>7 [4,5,6,2,3,1]=>9 [4,5,6,3,1,2]=>7 [4,5,6,3,2,1]=>7 [4,6,1,2,3,5]=>6 [4,6,1,2,5,3]=>9 [4,6,1,3,2,5]=>7 [4,6,1,3,5,2]=>11 [4,6,1,5,2,3]=>10 [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]=>8 [4,6,2,3,5,1]=>12 [4,6,2,5,1,3]=>11 [4,6,2,5,3,1]=>11 [4,6,3,1,2,5]=>6 [4,6,3,1,5,2]=>11 [4,6,3,2,1,5]=>6 [4,6,3,2,5,1]=>12 [4,6,3,5,1,2]=>10 [4,6,3,5,2,1]=>10 [4,6,5,1,2,3]=>6 [4,6,5,1,3,2]=>7 [4,6,5,2,1,3]=>6 [4,6,5,2,3,1]=>8 [4,6,5,3,1,2]=>6 [4,6,5,3,2,1]=>6 [5,1,2,3,4,6]=>4 [5,1,2,3,6,4]=>7 [5,1,2,4,3,6]=>5 [5,1,2,4,6,3]=>9 [5,1,2,6,3,4]=>8 [5,1,2,6,4,3]=>8 [5,1,3,2,4,6]=>5 [5,1,3,2,6,4]=>8 [5,1,3,4,2,6]=>7 [5,1,3,4,6,2]=>11 [5,1,3,6,2,4]=>10 [5,1,3,6,4,2]=>10 [5,1,4,2,3,6]=>6 [5,1,4,2,6,3]=>11 [5,1,4,3,2,6]=>6 [5,1,4,3,6,2]=>12 [5,1,4,6,2,3]=>10 [5,1,4,6,3,2]=>10 [5,1,6,2,3,4]=>9 [5,1,6,2,4,3]=>10 [5,1,6,3,2,4]=>9 [5,1,6,3,4,2]=>11 [5,1,6,4,2,3]=>9 [5,1,6,4,3,2]=>9 [5,2,1,3,4,6]=>4 [5,2,1,3,6,4]=>7 [5,2,1,4,3,6]=>5 [5,2,1,4,6,3]=>9 [5,2,1,6,3,4]=>8 [5,2,1,6,4,3]=>8 [5,2,3,1,4,6]=>6 [5,2,3,1,6,4]=>9 [5,2,3,4,1,6]=>8 [5,2,3,4,6,1]=>12 [5,2,3,6,1,4]=>11 [5,2,3,6,4,1]=>11 [5,2,4,1,3,6]=>7 [5,2,4,1,6,3]=>12 [5,2,4,3,1,6]=>7 [5,2,4,3,6,1]=>13 [5,2,4,6,1,3]=>11 [5,2,4,6,3,1]=>11 [5,2,6,1,3,4]=>10 [5,2,6,1,4,3]=>11 [5,2,6,3,1,4]=>10 [5,2,6,3,4,1]=>12 [5,2,6,4,1,3]=>10 [5,2,6,4,3,1]=>10 [5,3,1,2,4,6]=>4 [5,3,1,2,6,4]=>7 [5,3,1,4,2,6]=>7 [5,3,1,4,6,2]=>11 [5,3,1,6,2,4]=>10 [5,3,1,6,4,2]=>10 [5,3,2,1,4,6]=>4 [5,3,2,1,6,4]=>7 [5,3,2,4,1,6]=>8 [5,3,2,4,6,1]=>12 [5,3,2,6,1,4]=>11 [5,3,2,6,4,1]=>11 [5,3,4,1,2,6]=>6 [5,3,4,1,6,2]=>13 [5,3,4,2,1,6]=>6 [5,3,4,2,6,1]=>14 [5,3,4,6,1,2]=>10 [5,3,4,6,2,1]=>10 [5,3,6,1,2,4]=>9 [5,3,6,1,4,2]=>12 [5,3,6,2,1,4]=>9 [5,3,6,2,4,1]=>13 [5,3,6,4,1,2]=>9 [5,3,6,4,2,1]=>9 [5,4,1,2,3,6]=>4 [5,4,1,2,6,3]=>9 [5,4,1,3,2,6]=>5 [5,4,1,3,6,2]=>11 [5,4,1,6,2,3]=>10 [5,4,1,6,3,2]=>10 [5,4,2,1,3,6]=>4 [5,4,2,1,6,3]=>9 [5,4,2,3,1,6]=>6 [5,4,2,3,6,1]=>12 [5,4,2,6,1,3]=>11 [5,4,2,6,3,1]=>11 [5,4,3,1,2,6]=>4 [5,4,3,1,6,2]=>11 [5,4,3,2,1,6]=>4 [5,4,3,2,6,1]=>12 [5,4,3,6,1,2]=>10 [5,4,3,6,2,1]=>10 [5,4,6,1,2,3]=>8 [5,4,6,1,3,2]=>9 [5,4,6,2,1,3]=>8 [5,4,6,2,3,1]=>10 [5,4,6,3,1,2]=>8 [5,4,6,3,2,1]=>8 [5,6,1,2,3,4]=>6 [5,6,1,2,4,3]=>7 [5,6,1,3,2,4]=>7 [5,6,1,3,4,2]=>9 [5,6,1,4,2,3]=>8 [5,6,1,4,3,2]=>8 [5,6,2,1,3,4]=>6 [5,6,2,1,4,3]=>7 [5,6,2,3,1,4]=>8 [5,6,2,3,4,1]=>10 [5,6,2,4,1,3]=>9 [5,6,2,4,3,1]=>9 [5,6,3,1,2,4]=>6 [5,6,3,1,4,2]=>9 [5,6,3,2,1,4]=>6 [5,6,3,2,4,1]=>10 [5,6,3,4,1,2]=>8 [5,6,3,4,2,1]=>8 [5,6,4,1,2,3]=>6 [5,6,4,1,3,2]=>7 [5,6,4,2,1,3]=>6 [5,6,4,2,3,1]=>8 [5,6,4,3,1,2]=>6 [5,6,4,3,2,1]=>6 [6,1,2,3,4,5]=>5 [6,1,2,3,5,4]=>6 [6,1,2,4,3,5]=>6 [6,1,2,4,5,3]=>8 [6,1,2,5,3,4]=>7 [6,1,2,5,4,3]=>7 [6,1,3,2,4,5]=>6 [6,1,3,2,5,4]=>7 [6,1,3,4,2,5]=>8 [6,1,3,4,5,2]=>10 [6,1,3,5,2,4]=>9 [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]=>7 [6,1,4,3,5,2]=>11 [6,1,4,5,2,3]=>9 [6,1,4,5,3,2]=>9 [6,1,5,2,3,4]=>8 [6,1,5,2,4,3]=>9 [6,1,5,3,2,4]=>8 [6,1,5,3,4,2]=>10 [6,1,5,4,2,3]=>8 [6,1,5,4,3,2]=>8 [6,2,1,3,4,5]=>5 [6,2,1,3,5,4]=>6 [6,2,1,4,3,5]=>6 [6,2,1,4,5,3]=>8 [6,2,1,5,3,4]=>7 [6,2,1,5,4,3]=>7 [6,2,3,1,4,5]=>7 [6,2,3,1,5,4]=>8 [6,2,3,4,1,5]=>9 [6,2,3,4,5,1]=>11 [6,2,3,5,1,4]=>10 [6,2,3,5,4,1]=>10 [6,2,4,1,3,5]=>8 [6,2,4,1,5,3]=>11 [6,2,4,3,1,5]=>8 [6,2,4,3,5,1]=>12 [6,2,4,5,1,3]=>10 [6,2,4,5,3,1]=>10 [6,2,5,1,3,4]=>9 [6,2,5,1,4,3]=>10 [6,2,5,3,1,4]=>9 [6,2,5,3,4,1]=>11 [6,2,5,4,1,3]=>9 [6,2,5,4,3,1]=>9 [6,3,1,2,4,5]=>5 [6,3,1,2,5,4]=>6 [6,3,1,4,2,5]=>8 [6,3,1,4,5,2]=>10 [6,3,1,5,2,4]=>9 [6,3,1,5,4,2]=>9 [6,3,2,1,4,5]=>5 [6,3,2,1,5,4]=>6 [6,3,2,4,1,5]=>9 [6,3,2,4,5,1]=>11 [6,3,2,5,1,4]=>10 [6,3,2,5,4,1]=>10 [6,3,4,1,2,5]=>7 [6,3,4,1,5,2]=>12 [6,3,4,2,1,5]=>7 [6,3,4,2,5,1]=>13 [6,3,4,5,1,2]=>9 [6,3,4,5,2,1]=>9 [6,3,5,1,2,4]=>8 [6,3,5,1,4,2]=>11 [6,3,5,2,1,4]=>8 [6,3,5,2,4,1]=>12 [6,3,5,4,1,2]=>8 [6,3,5,4,2,1]=>8 [6,4,1,2,3,5]=>5 [6,4,1,2,5,3]=>8 [6,4,1,3,2,5]=>6 [6,4,1,3,5,2]=>10 [6,4,1,5,2,3]=>9 [6,4,1,5,3,2]=>9 [6,4,2,1,3,5]=>5 [6,4,2,1,5,3]=>8 [6,4,2,3,1,5]=>7 [6,4,2,3,5,1]=>11 [6,4,2,5,1,3]=>10 [6,4,2,5,3,1]=>10 [6,4,3,1,2,5]=>5 [6,4,3,1,5,2]=>10 [6,4,3,2,1,5]=>5 [6,4,3,2,5,1]=>11 [6,4,3,5,1,2]=>9 [6,4,3,5,2,1]=>9 [6,4,5,1,2,3]=>7 [6,4,5,1,3,2]=>8 [6,4,5,2,1,3]=>7 [6,4,5,2,3,1]=>9 [6,4,5,3,1,2]=>7 [6,4,5,3,2,1]=>7 [6,5,1,2,3,4]=>5 [6,5,1,2,4,3]=>6 [6,5,1,3,2,4]=>6 [6,5,1,3,4,2]=>8 [6,5,1,4,2,3]=>7 [6,5,1,4,3,2]=>7 [6,5,2,1,3,4]=>5 [6,5,2,1,4,3]=>6 [6,5,2,3,1,4]=>7 [6,5,2,3,4,1]=>9 [6,5,2,4,1,3]=>8 [6,5,2,4,3,1]=>8 [6,5,3,1,2,4]=>5 [6,5,3,1,4,2]=>8 [6,5,3,2,1,4]=>5 [6,5,3,2,4,1]=>9 [6,5,3,4,1,2]=>7 [6,5,3,4,2,1]=>7 [6,5,4,1,2,3]=>5 [6,5,4,1,3,2]=>6 [6,5,4,2,1,3]=>5 [6,5,4,2,3,1]=>7 [6,5,4,3,1,2]=>5 [6,5,4,3,2,1]=>5 [1,2,3,4,5,6,7]=>0 [1,2,3,4,5,7,6]=>1 [1,2,3,4,6,5,7]=>1 [1,2,3,4,6,7,5]=>3 [1,2,3,4,7,5,6]=>2 [1,2,3,4,7,6,5]=>2 [1,2,3,5,4,6,7]=>1 [1,2,3,5,4,7,6]=>2 [1,2,3,5,6,4,7]=>3 [1,2,3,5,6,7,4]=>5 [1,2,3,5,7,4,6]=>4 [1,2,3,5,7,6,4]=>4 [1,2,3,6,4,5,7]=>2 [1,2,3,6,4,7,5]=>5 [1,2,3,6,5,4,7]=>2 [1,2,3,6,5,7,4]=>6 [1,2,3,6,7,4,5]=>4 [1,2,3,6,7,5,4]=>4 [1,2,3,7,4,5,6]=>3 [1,2,3,7,4,6,5]=>4 [1,2,3,7,5,4,6]=>3 [1,2,3,7,5,6,4]=>5 [1,2,3,7,6,4,5]=>3 [1,2,3,7,6,5,4]=>3 [1,2,4,3,5,6,7]=>1 [1,2,4,3,5,7,6]=>2 [1,2,4,3,6,5,7]=>2 [1,2,4,3,6,7,5]=>4 [1,2,4,3,7,5,6]=>3 [1,2,4,3,7,6,5]=>3 [1,2,4,5,3,6,7]=>3 [1,2,4,5,3,7,6]=>4 [1,2,4,5,6,3,7]=>5 [1,2,4,5,6,7,3]=>7 [1,2,4,5,7,3,6]=>6 [1,2,4,5,7,6,3]=>6 [1,2,4,6,3,5,7]=>4 [1,2,4,6,3,7,5]=>7 [1,2,4,6,5,3,7]=>4 [1,2,4,6,5,7,3]=>8 [1,2,4,6,7,3,5]=>6 [1,2,4,6,7,5,3]=>6 [1,2,4,7,3,5,6]=>5 [1,2,4,7,3,6,5]=>6 [1,2,4,7,5,3,6]=>5 [1,2,4,7,5,6,3]=>7 [1,2,4,7,6,3,5]=>5 [1,2,4,7,6,5,3]=>5 [1,2,5,3,4,6,7]=>2 [1,2,5,3,4,7,6]=>3 [1,2,5,3,6,4,7]=>5 [1,2,5,3,6,7,4]=>7 [1,2,5,3,7,4,6]=>6 [1,2,5,3,7,6,4]=>6 [1,2,5,4,3,6,7]=>2 [1,2,5,4,3,7,6]=>3 [1,2,5,4,6,3,7]=>6 [1,2,5,4,6,7,3]=>8 [1,2,5,4,7,3,6]=>7 [1,2,5,4,7,6,3]=>7 [1,2,5,6,3,4,7]=>4 [1,2,5,6,3,7,4]=>9 [1,2,5,6,4,3,7]=>4 [1,2,5,6,4,7,3]=>10 [1,2,5,6,7,3,4]=>6 [1,2,5,6,7,4,3]=>6 [1,2,5,7,3,4,6]=>5 [1,2,5,7,3,6,4]=>8 [1,2,5,7,4,3,6]=>5 [1,2,5,7,4,6,3]=>9 [1,2,5,7,6,3,4]=>5 [1,2,5,7,6,4,3]=>5 [1,2,6,3,4,5,7]=>3 [1,2,6,3,4,7,5]=>6 [1,2,6,3,5,4,7]=>4 [1,2,6,3,5,7,4]=>8 [1,2,6,3,7,4,5]=>7 [1,2,6,3,7,5,4]=>7 [1,2,6,4,3,5,7]=>3 [1,2,6,4,3,7,5]=>6 [1,2,6,4,5,3,7]=>5 [1,2,6,4,5,7,3]=>9 [1,2,6,4,7,3,5]=>8 [1,2,6,4,7,5,3]=>8 [1,2,6,5,3,4,7]=>3 [1,2,6,5,3,7,4]=>8 [1,2,6,5,4,3,7]=>3 [1,2,6,5,4,7,3]=>9 [1,2,6,5,7,3,4]=>7 [1,2,6,5,7,4,3]=>7 [1,2,6,7,3,4,5]=>5 [1,2,6,7,3,5,4]=>6 [1,2,6,7,4,3,5]=>5 [1,2,6,7,4,5,3]=>7 [1,2,6,7,5,3,4]=>5 [1,2,6,7,5,4,3]=>5 [1,2,7,3,4,5,6]=>4 [1,2,7,3,4,6,5]=>5 [1,2,7,3,5,4,6]=>5 [1,2,7,3,5,6,4]=>7 [1,2,7,3,6,4,5]=>6 [1,2,7,3,6,5,4]=>6 [1,2,7,4,3,5,6]=>4 [1,2,7,4,3,6,5]=>5 [1,2,7,4,5,3,6]=>6 [1,2,7,4,5,6,3]=>8 [1,2,7,4,6,3,5]=>7 [1,2,7,4,6,5,3]=>7 [1,2,7,5,3,4,6]=>4 [1,2,7,5,3,6,4]=>7 [1,2,7,5,4,3,6]=>4 [1,2,7,5,4,6,3]=>8 [1,2,7,5,6,3,4]=>6 [1,2,7,5,6,4,3]=>6 [1,2,7,6,3,4,5]=>4 [1,2,7,6,3,5,4]=>5 [1,2,7,6,4,3,5]=>4 [1,2,7,6,4,5,3]=>6 [1,2,7,6,5,3,4]=>4 [1,2,7,6,5,4,3]=>4 [1,3,2,4,5,6,7]=>1 [1,3,2,4,5,7,6]=>2 [1,3,2,4,6,5,7]=>2 [1,3,2,4,6,7,5]=>4 [1,3,2,4,7,5,6]=>3 [1,3,2,4,7,6,5]=>3 [1,3,2,5,4,6,7]=>2 [1,3,2,5,4,7,6]=>3 [1,3,2,5,6,4,7]=>4 [1,3,2,5,6,7,4]=>6 [1,3,2,5,7,4,6]=>5 [1,3,2,5,7,6,4]=>5 [1,3,2,6,4,5,7]=>3 [1,3,2,6,4,7,5]=>6 [1,3,2,6,5,4,7]=>3 [1,3,2,6,5,7,4]=>7 [1,3,2,6,7,4,5]=>5 [1,3,2,6,7,5,4]=>5 [1,3,2,7,4,5,6]=>4 [1,3,2,7,4,6,5]=>5 [1,3,2,7,5,4,6]=>4 [1,3,2,7,5,6,4]=>6 [1,3,2,7,6,4,5]=>4 [1,3,2,7,6,5,4]=>4 [1,3,4,2,5,6,7]=>3 [1,3,4,2,5,7,6]=>4 [1,3,4,2,6,5,7]=>4 [1,3,4,2,6,7,5]=>6 [1,3,4,2,7,5,6]=>5 [1,3,4,2,7,6,5]=>5 [1,3,4,5,2,6,7]=>5 [1,3,4,5,2,7,6]=>6 [1,3,4,5,6,2,7]=>7 [1,3,4,5,6,7,2]=>9 [1,3,4,5,7,2,6]=>8 [1,3,4,5,7,6,2]=>8 [1,3,4,6,2,5,7]=>6 [1,3,4,6,2,7,5]=>9 [1,3,4,6,5,2,7]=>6 [1,3,4,6,5,7,2]=>10 [1,3,4,6,7,2,5]=>8 [1,3,4,6,7,5,2]=>8 [1,3,4,7,2,5,6]=>7 [1,3,4,7,2,6,5]=>8 [1,3,4,7,5,2,6]=>7 [1,3,4,7,5,6,2]=>9 [1,3,4,7,6,2,5]=>7 [1,3,4,7,6,5,2]=>7 [1,3,5,2,4,6,7]=>4 [1,3,5,2,4,7,6]=>5 [1,3,5,2,6,4,7]=>7 [1,3,5,2,6,7,4]=>9 [1,3,5,2,7,4,6]=>8 [1,3,5,2,7,6,4]=>8 [1,3,5,4,2,6,7]=>4 [1,3,5,4,2,7,6]=>5 [1,3,5,4,6,2,7]=>8 [1,3,5,4,6,7,2]=>10 [1,3,5,4,7,2,6]=>9 [1,3,5,4,7,6,2]=>9 [1,3,5,6,2,4,7]=>6 [1,3,5,6,2,7,4]=>11 [1,3,5,6,4,2,7]=>6 [1,3,5,6,4,7,2]=>12 [1,3,5,6,7,2,4]=>8 [1,3,5,6,7,4,2]=>8 [1,3,5,7,2,4,6]=>7 [1,3,5,7,2,6,4]=>10 [1,3,5,7,4,2,6]=>7 [1,3,5,7,4,6,2]=>11 [1,3,5,7,6,2,4]=>7 [1,3,5,7,6,4,2]=>7 [1,3,6,2,4,5,7]=>5 [1,3,6,2,4,7,5]=>8 [1,3,6,2,5,4,7]=>6 [1,3,6,2,5,7,4]=>10 [1,3,6,2,7,4,5]=>9 [1,3,6,2,7,5,4]=>9 [1,3,6,4,2,5,7]=>5 [1,3,6,4,2,7,5]=>8 [1,3,6,4,5,2,7]=>7 [1,3,6,4,5,7,2]=>11 [1,3,6,4,7,2,5]=>10 [1,3,6,4,7,5,2]=>10 [1,3,6,5,2,4,7]=>5 [1,3,6,5,2,7,4]=>10 [1,3,6,5,4,2,7]=>5 [1,3,6,5,4,7,2]=>11 [1,3,6,5,7,2,4]=>9 [1,3,6,5,7,4,2]=>9 [1,3,6,7,2,4,5]=>7 [1,3,6,7,2,5,4]=>8 [1,3,6,7,4,2,5]=>7 [1,3,6,7,4,5,2]=>9 [1,3,6,7,5,2,4]=>7 [1,3,6,7,5,4,2]=>7 [1,3,7,2,4,5,6]=>6 [1,3,7,2,4,6,5]=>7 [1,3,7,2,5,4,6]=>7 [1,3,7,2,5,6,4]=>9 [1,3,7,2,6,4,5]=>8 [1,3,7,2,6,5,4]=>8 [1,3,7,4,2,5,6]=>6 [1,3,7,4,2,6,5]=>7 [1,3,7,4,5,2,6]=>8 [1,3,7,4,5,6,2]=>10 [1,3,7,4,6,2,5]=>9 [1,3,7,4,6,5,2]=>9 [1,3,7,5,2,4,6]=>6 [1,3,7,5,2,6,4]=>9 [1,3,7,5,4,2,6]=>6 [1,3,7,5,4,6,2]=>10 [1,3,7,5,6,2,4]=>8 [1,3,7,5,6,4,2]=>8 [1,3,7,6,2,4,5]=>6 [1,3,7,6,2,5,4]=>7 [1,3,7,6,4,2,5]=>6 [1,3,7,6,4,5,2]=>8 [1,3,7,6,5,2,4]=>6 [1,3,7,6,5,4,2]=>6 [1,4,2,3,5,6,7]=>2 [1,4,2,3,5,7,6]=>3 [1,4,2,3,6,5,7]=>3 [1,4,2,3,6,7,5]=>5 [1,4,2,3,7,5,6]=>4 [1,4,2,3,7,6,5]=>4 [1,4,2,5,3,6,7]=>5 [1,4,2,5,3,7,6]=>6 [1,4,2,5,6,3,7]=>7 [1,4,2,5,6,7,3]=>9 [1,4,2,5,7,3,6]=>8 [1,4,2,5,7,6,3]=>8 [1,4,2,6,3,5,7]=>6 [1,4,2,6,3,7,5]=>9 [1,4,2,6,5,3,7]=>6 [1,4,2,6,5,7,3]=>10 [1,4,2,6,7,3,5]=>8 [1,4,2,6,7,5,3]=>8 [1,4,2,7,3,5,6]=>7 [1,4,2,7,3,6,5]=>8 [1,4,2,7,5,3,6]=>7 [1,4,2,7,5,6,3]=>9 [1,4,2,7,6,3,5]=>7 [1,4,2,7,6,5,3]=>7 [1,4,3,2,5,6,7]=>2 [1,4,3,2,5,7,6]=>3 [1,4,3,2,6,5,7]=>3 [1,4,3,2,6,7,5]=>5 [1,4,3,2,7,5,6]=>4 [1,4,3,2,7,6,5]=>4 [1,4,3,5,2,6,7]=>6 [1,4,3,5,2,7,6]=>7 [1,4,3,5,6,2,7]=>8 [1,4,3,5,6,7,2]=>10 [1,4,3,5,7,2,6]=>9 [1,4,3,5,7,6,2]=>9 [1,4,3,6,2,5,7]=>7 [1,4,3,6,2,7,5]=>10 [1,4,3,6,5,2,7]=>7 [1,4,3,6,5,7,2]=>11 [1,4,3,6,7,2,5]=>9 [1,4,3,6,7,5,2]=>9 [1,4,3,7,2,5,6]=>8 [1,4,3,7,2,6,5]=>9 [1,4,3,7,5,2,6]=>8 [1,4,3,7,5,6,2]=>10 [1,4,3,7,6,2,5]=>8 [1,4,3,7,6,5,2]=>8 [1,4,5,2,3,6,7]=>4 [1,4,5,2,3,7,6]=>5 [1,4,5,2,6,3,7]=>9 [1,4,5,2,6,7,3]=>11 [1,4,5,2,7,3,6]=>10 [1,4,5,2,7,6,3]=>10 [1,4,5,3,2,6,7]=>4 [1,4,5,3,2,7,6]=>5 [1,4,5,3,6,2,7]=>10 [1,4,5,3,6,7,2]=>12 [1,4,5,3,7,2,6]=>11 [1,4,5,3,7,6,2]=>11 [1,4,5,6,2,3,7]=>6 [1,4,5,6,2,7,3]=>13 [1,4,5,6,3,2,7]=>6 [1,4,5,6,3,7,2]=>14 [1,4,5,6,7,2,3]=>8 [1,4,5,6,7,3,2]=>8 [1,4,5,7,2,3,6]=>7 [1,4,5,7,2,6,3]=>12 [1,4,5,7,3,2,6]=>7 [1,4,5,7,3,6,2]=>13 [1,4,5,7,6,2,3]=>7 [1,4,5,7,6,3,2]=>7 [1,4,6,2,3,5,7]=>5 [1,4,6,2,3,7,5]=>8 [1,4,6,2,5,3,7]=>8 [1,4,6,2,5,7,3]=>12 [1,4,6,2,7,3,5]=>11 [1,4,6,2,7,5,3]=>11 [1,4,6,3,2,5,7]=>5 [1,4,6,3,2,7,5]=>8 [1,4,6,3,5,2,7]=>9 [1,4,6,3,5,7,2]=>13 [1,4,6,3,7,2,5]=>12 [1,4,6,3,7,5,2]=>12 [1,4,6,5,2,3,7]=>5 [1,4,6,5,2,7,3]=>12 [1,4,6,5,3,2,7]=>5 [1,4,6,5,3,7,2]=>13
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Description
The mad of a permutation.
According to [1], this is the sum of twice the number of occurrences of the vincular pattern of $(2\underline{31})$ plus the number of occurrences of the vincular patterns $(\underline{31}2)$ and $(\underline{21})$, where matches of the underlined letters must be adjacent.
References
[1] Babson, E., Steingr'─▒msson, E. Generalized permutation patterns and a classification of the Mahonian statistics MathSciNet:1758852
Code
def statistic(pi):
    patterns = [([2,3,1],[2]), ([2,3,1],[2]), ([3,1,2],[1]), ([2,1],[1])]
    return sum(vincular_occurrences(pi, p, c) for p, c in patterns)

def vincular_occurrences(perm, pat, columns):
    n = len(pat)
    R = [(c, i) for c in columns for i in range(n+1)]
    return mesh_pattern_occurrences(perm, pat, R=R)

def G(w):
    return [ (x+1,y) for (x,y) in enumerate(w) ]

def mesh_pattern_occurrences(perm, pat, R=[]):
    occs = 0
    k = len(pat)
    n = len(perm)
    pat = G(pat)
    perm = G(perm)
    for H in Subsets(perm, k):
        H = sorted(H)
        X = dict(G(sorted(i for (i,_) in H)))
        Y = dict(G(sorted(j for (_,j) in H)))
        if H == [ (X[i], Y[j]) for (i,j) in pat ]:
            X[0], X[k+1] = 0, n+1
            Y[0], Y[k+1] = 0, n+1
            shady = ( X[i] < x < X[i+1] and Y[j] < y < Y[j+1]
                      for (i,j) in R
                      for (x,y) in perm
                      )
            if not any(shady):
                occs = occs + 1
    return occs

Created
May 16, 2017 at 16:42 by Martin Rubey
Updated
Jan 11, 2018 at 08:01 by Martin Rubey