edit this statistic or download as text // json
Identifier
Values
=>
[1,2]=>1 [2,1]=>1 [1,2,3]=>1 [1,3,2]=>2 [2,1,3]=>1 [2,3,1]=>1 [3,1,2]=>2 [3,2,1]=>1 [1,2,3,4]=>1 [1,2,4,3]=>2 [1,3,2,4]=>2 [1,3,4,2]=>3 [1,4,2,3]=>1 [1,4,3,2]=>2 [2,1,3,4]=>1 [2,1,4,3]=>3 [2,3,1,4]=>1 [2,3,4,1]=>1 [2,4,1,3]=>3 [2,4,3,1]=>2 [3,1,2,4]=>2 [3,1,4,2]=>3 [3,2,1,4]=>1 [3,2,4,1]=>1 [3,4,1,2]=>3 [3,4,2,1]=>1 [4,1,2,3]=>2 [4,1,3,2]=>1 [4,2,1,3]=>3 [4,2,3,1]=>2 [4,3,1,2]=>2 [4,3,2,1]=>1 [1,2,3,4,5]=>1 [1,2,3,5,4]=>2 [1,2,4,3,5]=>2 [1,2,4,5,3]=>6 [1,2,5,3,4]=>2 [1,2,5,4,3]=>2 [1,3,2,4,5]=>2 [1,3,2,5,4]=>7 [1,3,4,2,5]=>3 [1,3,4,5,2]=>4 [1,3,5,2,4]=>7 [1,3,5,4,2]=>7 [1,4,2,3,5]=>1 [1,4,2,5,3]=>6 [1,4,3,2,5]=>2 [1,4,3,5,2]=>3 [1,4,5,2,3]=>6 [1,4,5,3,2]=>4 [1,5,2,3,4]=>2 [1,5,2,4,3]=>2 [1,5,3,2,4]=>7 [1,5,3,4,2]=>7 [1,5,4,2,3]=>1 [1,5,4,3,2]=>2 [2,1,3,4,5]=>1 [2,1,3,5,4]=>4 [2,1,4,3,5]=>3 [2,1,4,5,3]=>4 [2,1,5,3,4]=>4 [2,1,5,4,3]=>6 [2,3,1,4,5]=>1 [2,3,1,5,4]=>3 [2,3,4,1,5]=>1 [2,3,4,5,1]=>1 [2,3,5,1,4]=>3 [2,3,5,4,1]=>2 [2,4,1,3,5]=>3 [2,4,1,5,3]=>2 [2,4,3,1,5]=>2 [2,4,3,5,1]=>2 [2,4,5,1,3]=>4 [2,4,5,3,1]=>3 [2,5,1,3,4]=>4 [2,5,1,4,3]=>6 [2,5,3,1,4]=>1 [2,5,3,4,1]=>1 [2,5,4,1,3]=>6 [2,5,4,3,1]=>2 [3,1,2,4,5]=>2 [3,1,2,5,4]=>7 [3,1,4,2,5]=>3 [3,1,4,5,2]=>4 [3,1,5,2,4]=>1 [3,1,5,4,2]=>7 [3,2,1,4,5]=>1 [3,2,1,5,4]=>4 [3,2,4,1,5]=>1 [3,2,4,5,1]=>1 [3,2,5,1,4]=>4 [3,2,5,4,1]=>3 [3,4,1,2,5]=>3 [3,4,1,5,2]=>4 [3,4,2,1,5]=>1 [3,4,2,5,1]=>1 [3,4,5,1,2]=>4 [3,4,5,2,1]=>1 [3,5,1,2,4]=>7 [3,5,1,4,2]=>1 [3,5,2,1,4]=>4 [3,5,2,4,1]=>3 [3,5,4,1,2]=>7 [3,5,4,2,1]=>2 [4,1,2,3,5]=>2 [4,1,2,5,3]=>6 [4,1,3,2,5]=>1 [4,1,3,5,2]=>1 [4,1,5,2,3]=>6 [4,1,5,3,2]=>4 [4,2,1,3,5]=>3 [4,2,1,5,3]=>4 [4,2,3,1,5]=>2 [4,2,3,5,1]=>2 [4,2,5,1,3]=>2 [4,2,5,3,1]=>3 [4,3,1,2,5]=>2 [4,3,1,5,2]=>3 [4,3,2,1,5]=>1 [4,3,2,5,1]=>1 [4,3,5,1,2]=>3 [4,3,5,2,1]=>1 [4,5,1,2,3]=>6 [4,5,1,3,2]=>4 [4,5,2,1,3]=>4 [4,5,2,3,1]=>3 [4,5,3,1,2]=>4 [4,5,3,2,1]=>1 [5,1,2,3,4]=>2 [5,1,2,4,3]=>1 [5,1,3,2,4]=>7 [5,1,3,4,2]=>7 [5,1,4,2,3]=>2 [5,1,4,3,2]=>2 [5,2,1,3,4]=>4 [5,2,1,4,3]=>6 [5,2,3,1,4]=>3 [5,2,3,4,1]=>2 [5,2,4,1,3]=>6 [5,2,4,3,1]=>1 [5,3,1,2,4]=>7 [5,3,1,4,2]=>7 [5,3,2,1,4]=>4 [5,3,2,4,1]=>3 [5,3,4,1,2]=>7 [5,3,4,2,1]=>2 [5,4,1,2,3]=>2 [5,4,1,3,2]=>2 [5,4,2,1,3]=>6 [5,4,2,3,1]=>2 [5,4,3,1,2]=>2 [5,4,3,2,1]=>1 [1,2,3,4,5,6]=>1 [1,2,3,4,6,5]=>2 [1,2,3,5,4,6]=>2 [1,2,3,5,6,4]=>7 [1,2,3,6,4,5]=>2 [1,2,3,6,5,4]=>2 [1,2,4,3,5,6]=>2 [1,2,4,3,6,5]=>12 [1,2,4,5,3,6]=>6 [1,2,4,5,6,3]=>4 [1,2,4,6,3,5]=>12 [1,2,4,6,5,3]=>16 [1,2,5,3,4,6]=>2 [1,2,5,3,6,4]=>7 [1,2,5,4,3,6]=>2 [1,2,5,4,6,3]=>9 [1,2,5,6,3,4]=>3 [1,2,5,6,4,3]=>6 [1,2,6,3,4,5]=>1 [1,2,6,3,5,4]=>2 [1,2,6,4,3,5]=>12 [1,2,6,4,5,3]=>16 [1,2,6,5,3,4]=>2 [1,2,6,5,4,3]=>2 [1,3,2,4,5,6]=>2 [1,3,2,4,6,5]=>4 [1,3,2,5,4,6]=>7 [1,3,2,5,6,4]=>4 [1,3,2,6,4,5]=>4 [1,3,2,6,5,4]=>16 [1,3,4,2,5,6]=>3 [1,3,4,2,6,5]=>3 [1,3,4,5,2,6]=>4 [1,3,4,5,6,2]=>5 [1,3,4,6,2,5]=>3 [1,3,4,6,5,2]=>5 [1,3,5,2,4,6]=>7 [1,3,5,2,6,4]=>6 [1,3,5,4,2,6]=>7 [1,3,5,4,6,2]=>4 [1,3,5,6,2,4]=>9 [1,3,5,6,4,2]=>3 [1,3,6,2,4,5]=>3 [1,3,6,2,5,4]=>16 [1,3,6,4,2,5]=>4 [1,3,6,4,5,2]=>9 [1,3,6,5,2,4]=>16 [1,3,6,5,4,2]=>12 [1,4,2,3,5,6]=>1 [1,4,2,3,6,5]=>12 [1,4,2,5,3,6]=>6 [1,4,2,5,6,3]=>6 [1,4,2,6,3,5]=>2 [1,4,2,6,5,3]=>16 [1,4,3,2,5,6]=>2 [1,4,3,2,6,5]=>5 [1,4,3,5,2,6]=>3 [1,4,3,5,6,2]=>4 [1,4,3,6,2,5]=>9 [1,4,3,6,5,2]=>3 [1,4,5,2,3,6]=>6 [1,4,5,2,6,3]=>6 [1,4,5,3,2,6]=>4 [1,4,5,3,6,2]=>5 [1,4,5,6,2,3]=>6 [1,4,5,6,3,2]=>3 [1,4,6,2,3,5]=>12 [1,4,6,2,5,3]=>4 [1,4,6,3,2,5]=>5 [1,4,6,3,5,2]=>3 [1,4,6,5,2,3]=>16 [1,4,6,5,3,2]=>4 [1,5,2,3,4,6]=>2 [1,5,2,3,6,4]=>3 [1,5,2,4,3,6]=>2 [1,5,2,4,6,3]=>9 [1,5,2,6,3,4]=>7 [1,5,2,6,4,3]=>6 [1,5,3,2,4,6]=>7 [1,5,3,2,6,4]=>9 [1,5,3,4,2,6]=>7 [1,5,3,4,6,2]=>5 [1,5,3,6,2,4]=>9 [1,5,3,6,4,2]=>3 [1,5,4,2,3,6]=>1 [1,5,4,2,6,3]=>9 [1,5,4,3,2,6]=>2 [1,5,4,3,6,2]=>3 [1,5,4,6,2,3]=>9 [1,5,4,6,3,2]=>5 [1,5,6,2,3,4]=>7 [1,5,6,2,4,3]=>4 [1,5,6,3,2,4]=>1 [1,5,6,3,4,2]=>8 [1,5,6,4,2,3]=>4 [1,5,6,4,3,2]=>4 [1,6,2,3,4,5]=>2 [1,6,2,3,5,4]=>2 [1,6,2,4,3,5]=>12 [1,6,2,4,5,3]=>16 [1,6,2,5,3,4]=>1 [1,6,2,5,4,3]=>2 [1,6,3,2,4,5]=>3 [1,6,3,2,5,4]=>16 [1,6,3,4,2,5]=>1 [1,6,3,4,5,2]=>9 [1,6,3,5,2,4]=>16 [1,6,3,5,4,2]=>12 [1,6,4,2,3,5]=>12 [1,6,4,2,5,3]=>16 [1,6,4,3,2,5]=>9 [1,6,4,3,5,2]=>3 [1,6,4,5,2,3]=>16 [1,6,4,5,3,2]=>3 [1,6,5,2,3,4]=>2 [1,6,5,2,4,3]=>2 [1,6,5,3,2,4]=>16 [1,6,5,3,4,2]=>12 [1,6,5,4,2,3]=>1 [1,6,5,4,3,2]=>2 [2,1,3,4,5,6]=>1 [2,1,3,4,6,5]=>4 [2,1,3,5,4,6]=>4 [2,1,3,5,6,4]=>9 [2,1,3,6,4,5]=>4 [2,1,3,6,5,4]=>6 [2,1,4,3,5,6]=>3 [2,1,4,3,6,5]=>3 [2,1,4,5,3,6]=>4 [2,1,4,5,6,3]=>5 [2,1,4,6,3,5]=>3 [2,1,4,6,5,3]=>9 [2,1,5,3,4,6]=>4 [2,1,5,3,6,4]=>9 [2,1,5,4,3,6]=>6 [2,1,5,4,6,3]=>8 [2,1,5,6,3,4]=>9 [2,1,5,6,4,3]=>9 [2,1,6,3,4,5]=>1 [2,1,6,3,5,4]=>6 [2,1,6,4,3,5]=>8 [2,1,6,4,5,3]=>9 [2,1,6,5,3,4]=>6 [2,1,6,5,4,3]=>7 [2,3,1,4,5,6]=>1 [2,3,1,4,6,5]=>5 [2,3,1,5,4,6]=>3 [2,3,1,5,6,4]=>8 [2,3,1,6,4,5]=>5 [2,3,1,6,5,4]=>9 [2,3,4,1,5,6]=>1 [2,3,4,1,6,5]=>3 [2,3,4,5,1,6]=>1 [2,3,4,5,6,1]=>1 [2,3,4,6,1,5]=>3 [2,3,4,6,5,1]=>2 [2,3,5,1,4,6]=>3 [2,3,5,1,6,4]=>2 [2,3,5,4,1,6]=>2 [2,3,5,4,6,1]=>2 [2,3,5,6,1,4]=>8 [2,3,5,6,4,1]=>6 [2,3,6,1,4,5]=>5 [2,3,6,1,5,4]=>9 [2,3,6,4,1,5]=>2 [2,3,6,4,5,1]=>2 [2,3,6,5,1,4]=>9 [2,3,6,5,4,1]=>2 [2,4,1,3,5,6]=>3 [2,4,1,3,6,5]=>8 [2,4,1,5,3,6]=>2 [2,4,1,5,6,3]=>5 [2,4,1,6,3,5]=>8 [2,4,1,6,5,3]=>6 [2,4,3,1,5,6]=>2 [2,4,3,1,6,5]=>4 [2,4,3,5,1,6]=>2 [2,4,3,5,6,1]=>2 [2,4,3,6,1,5]=>5 [2,4,3,6,5,1]=>7 [2,4,5,1,3,6]=>4 [2,4,5,1,6,3]=>5 [2,4,5,3,1,6]=>3 [2,4,5,3,6,1]=>3 [2,4,5,6,1,3]=>5 [2,4,5,6,3,1]=>4 [2,4,6,1,3,5]=>3 [2,4,6,1,5,3]=>6 [2,4,6,3,1,5]=>4 [2,4,6,3,5,1]=>7 [2,4,6,5,1,3]=>4 [2,4,6,5,3,1]=>7 [2,5,1,3,4,6]=>4 [2,5,1,3,6,4]=>9 [2,5,1,4,3,6]=>6 [2,5,1,4,6,3]=>8 [2,5,1,6,3,4]=>1 [2,5,1,6,4,3]=>9 [2,5,3,1,4,6]=>1 [2,5,3,1,6,4]=>8 [2,5,3,4,1,6]=>1 [2,5,3,4,6,1]=>1 [2,5,3,6,1,4]=>8 [2,5,3,6,4,1]=>6 [2,5,4,1,3,6]=>6 [2,5,4,1,6,3]=>2 [2,5,4,3,1,6]=>2 [2,5,4,3,6,1]=>2 [2,5,4,6,1,3]=>8 [2,5,4,6,3,1]=>3 [2,5,6,1,3,4]=>9 [2,5,6,1,4,3]=>9 [2,5,6,3,1,4]=>8 [2,5,6,3,4,1]=>6 [2,5,6,4,1,3]=>9 [2,5,6,4,3,1]=>4 [2,6,1,3,4,5]=>4 [2,6,1,3,5,4]=>4 [2,6,1,4,3,5]=>1 [2,6,1,4,5,3]=>4 [2,6,1,5,3,4]=>4 [2,6,1,5,4,3]=>3 [2,6,3,1,4,5]=>5 [2,6,3,1,5,4]=>9 [2,6,3,4,1,5]=>2 [2,6,3,4,5,1]=>2 [2,6,3,5,1,4]=>9 [2,6,3,5,4,1]=>2 [2,6,4,1,3,5]=>8 [2,6,4,1,5,3]=>9 [2,6,4,3,1,5]=>5 [2,6,4,3,5,1]=>7 [2,6,4,5,1,3]=>9 [2,6,4,5,3,1]=>7 [2,6,5,1,3,4]=>6 [2,6,5,1,4,3]=>7 [2,6,5,3,1,4]=>1 [2,6,5,3,4,1]=>1 [2,6,5,4,1,3]=>7 [2,6,5,4,3,1]=>2 [3,1,2,4,5,6]=>2 [3,1,2,4,6,5]=>3 [3,1,2,5,4,6]=>7 [3,1,2,5,6,4]=>9 [3,1,2,6,4,5]=>3 [3,1,2,6,5,4]=>16 [3,1,4,2,5,6]=>3 [3,1,4,2,6,5]=>3 [3,1,4,5,2,6]=>4 [3,1,4,5,6,2]=>5 [3,1,4,6,2,5]=>3 [3,1,4,6,5,2]=>9 [3,1,5,2,4,6]=>1 [3,1,5,2,6,4]=>6 [3,1,5,4,2,6]=>7 [3,1,5,4,6,2]=>5 [3,1,5,6,2,4]=>6 [3,1,5,6,4,2]=>8 [3,1,6,2,4,5]=>3 [3,1,6,2,5,4]=>4 [3,1,6,4,2,5]=>4 [3,1,6,4,5,2]=>9 [3,1,6,5,2,4]=>4 [3,1,6,5,4,2]=>12 [3,2,1,4,5,6]=>1 [3,2,1,4,6,5]=>3 [3,2,1,5,4,6]=>4 [3,2,1,5,6,4]=>5 [3,2,1,6,4,5]=>2 [3,2,1,6,5,4]=>4 [3,2,4,1,5,6]=>1 [3,2,4,1,6,5]=>5 [3,2,4,5,1,6]=>1 [3,2,4,5,6,1]=>1 [3,2,4,6,1,5]=>5 [3,2,4,6,5,1]=>4 [3,2,5,1,4,6]=>4 [3,2,5,1,6,4]=>5 [3,2,5,4,1,6]=>3 [3,2,5,4,6,1]=>3 [3,2,5,6,1,4]=>5 [3,2,5,6,4,1]=>4 [3,2,6,1,4,5]=>3 [3,2,6,1,5,4]=>6 [3,2,6,4,1,5]=>5 [3,2,6,4,5,1]=>4 [3,2,6,5,1,4]=>6 [3,2,6,5,4,1]=>6 [3,4,1,2,5,6]=>3 [3,4,1,2,6,5]=>3 [3,4,1,5,2,6]=>4 [3,4,1,5,6,2]=>5 [3,4,1,6,2,5]=>1 [3,4,1,6,5,2]=>5 [3,4,2,1,5,6]=>1 [3,4,2,1,6,5]=>4 [3,4,2,5,1,6]=>1 [3,4,2,5,6,1]=>1 [3,4,2,6,1,5]=>4 [3,4,2,6,5,1]=>3 [3,4,5,1,2,6]=>4 [3,4,5,1,6,2]=>5 [3,4,5,2,1,6]=>1 [3,4,5,2,6,1]=>1 [3,4,5,6,1,2]=>5 [3,4,5,6,2,1]=>1 [3,4,6,1,2,5]=>3 [3,4,6,1,5,2]=>1 [3,4,6,2,1,5]=>4 [3,4,6,2,5,1]=>3 [3,4,6,5,1,2]=>9 [3,4,6,5,2,1]=>2 [3,5,1,2,4,6]=>7 [3,5,1,2,6,4]=>9 [3,5,1,4,2,6]=>1 [3,5,1,4,6,2]=>1 [3,5,1,6,2,4]=>6 [3,5,1,6,4,2]=>8 [3,5,2,1,4,6]=>4 [3,5,2,1,6,4]=>5 [3,5,2,4,1,6]=>3 [3,5,2,4,6,1]=>3 [3,5,2,6,1,4]=>5 [3,5,2,6,4,1]=>2 [3,5,4,1,2,6]=>7 [3,5,4,1,6,2]=>4 [3,5,4,2,1,6]=>2 [3,5,4,2,6,1]=>2 [3,5,4,6,1,2]=>5 [3,5,4,6,2,1]=>2 [3,5,6,1,2,4]=>4 [3,5,6,1,4,2]=>8 [3,5,6,2,1,4]=>5 [3,5,6,2,4,1]=>4 [3,5,6,4,1,2]=>3 [3,5,6,4,2,1]=>3 [3,6,1,2,4,5]=>4 [3,6,1,2,5,4]=>16 [3,6,1,4,2,5]=>4 [3,6,1,4,5,2]=>5 [3,6,1,5,2,4]=>4 [3,6,1,5,4,2]=>2 [3,6,2,1,4,5]=>2 [3,6,2,1,5,4]=>6 [3,6,2,4,1,5]=>5 [3,6,2,4,5,1]=>4 [3,6,2,5,1,4]=>4 [3,6,2,5,4,1]=>6 [3,6,4,1,2,5]=>4 [3,6,4,1,5,2]=>9 [3,6,4,2,1,5]=>1 [3,6,4,2,5,1]=>1 [3,6,4,5,1,2]=>9 [3,6,4,5,2,1]=>1 [3,6,5,1,2,4]=>16 [3,6,5,1,4,2]=>1 [3,6,5,2,1,4]=>4 [3,6,5,2,4,1]=>6 [3,6,5,4,1,2]=>12 [3,6,5,4,2,1]=>2 [4,1,2,3,5,6]=>2 [4,1,2,3,6,5]=>12 [4,1,2,5,3,6]=>6 [4,1,2,5,6,3]=>4 [4,1,2,6,3,5]=>1 [4,1,2,6,5,3]=>16 [4,1,3,2,5,6]=>1 [4,1,3,2,6,5]=>9 [4,1,3,5,2,6]=>1 [4,1,3,5,6,2]=>1 [4,1,3,6,2,5]=>9 [4,1,3,6,5,2]=>4 [4,1,5,2,3,6]=>6 [4,1,5,2,6,3]=>4 [4,1,5,3,2,6]=>4 [4,1,5,3,6,2]=>5 [4,1,5,6,2,3]=>6 [4,1,5,6,3,2]=>2 [4,1,6,2,3,5]=>2 [4,1,6,2,5,3]=>4 [4,1,6,3,2,5]=>5 [4,1,6,3,5,2]=>4 [4,1,6,5,2,3]=>16 [4,1,6,5,3,2]=>4 [4,2,1,3,5,6]=>3 [4,2,1,3,6,5]=>3 [4,2,1,5,3,6]=>4 [4,2,1,5,6,3]=>5 [4,2,1,6,3,5]=>8 [4,2,1,6,5,3]=>4 [4,2,3,1,5,6]=>2 [4,2,3,1,6,5]=>5 [4,2,3,5,1,6]=>2 [4,2,3,5,6,1]=>2 [4,2,3,6,1,5]=>4 [4,2,3,6,5,1]=>7 [4,2,5,1,3,6]=>2 [4,2,5,1,6,3]=>5 [4,2,5,3,1,6]=>3 [4,2,5,3,6,1]=>3 [4,2,5,6,1,3]=>5 [4,2,5,6,3,1]=>4 [4,2,6,1,3,5]=>8 [4,2,6,1,5,3]=>6 [4,2,6,3,1,5]=>1 [4,2,6,3,5,1]=>1 [4,2,6,5,1,3]=>9 [4,2,6,5,3,1]=>7 [4,3,1,2,5,6]=>2 [4,3,1,2,6,5]=>9 [4,3,1,5,2,6]=>3 [4,3,1,5,6,2]=>4 [4,3,1,6,2,5]=>1 [4,3,1,6,5,2]=>3 [4,3,2,1,5,6]=>1 [4,3,2,1,6,5]=>5 [4,3,2,5,1,6]=>1 [4,3,2,5,6,1]=>1 [4,3,2,6,1,5]=>5 [4,3,2,6,5,1]=>4 [4,3,5,1,2,6]=>3 [4,3,5,1,6,2]=>4 [4,3,5,2,1,6]=>1 [4,3,5,2,6,1]=>1 [4,3,5,6,1,2]=>4 [4,3,5,6,2,1]=>1 [4,3,6,1,2,5]=>5 [4,3,6,1,5,2]=>1 [4,3,6,2,1,5]=>5 [4,3,6,2,5,1]=>4 [4,3,6,5,1,2]=>3 [4,3,6,5,2,1]=>3 [4,5,1,2,3,6]=>6 [4,5,1,2,6,3]=>6 [4,5,1,3,2,6]=>4 [4,5,1,3,6,2]=>5 [4,5,1,6,2,3]=>6 [4,5,1,6,3,2]=>3 [4,5,2,1,3,6]=>4 [4,5,2,1,6,3]=>5 [4,5,2,3,1,6]=>3 [4,5,2,3,6,1]=>3 [4,5,2,6,1,3]=>5 [4,5,2,6,3,1]=>4 [4,5,3,1,2,6]=>4 [4,5,3,1,6,2]=>5 [4,5,3,2,1,6]=>1 [4,5,3,2,6,1]=>1 [4,5,3,6,1,2]=>5 [4,5,3,6,2,1]=>1 [4,5,6,1,2,3]=>4 [4,5,6,1,3,2]=>2 [4,5,6,2,1,3]=>5 [4,5,6,2,3,1]=>4 [4,5,6,3,1,2]=>3 [4,5,6,3,2,1]=>1 [4,6,1,2,3,5]=>12 [4,6,1,2,5,3]=>4 [4,6,1,3,2,5]=>9 [4,6,1,3,5,2]=>4 [4,6,1,5,2,3]=>4 [4,6,1,5,3,2]=>3 [4,6,2,1,3,5]=>8 [4,6,2,1,5,3]=>6 [4,6,2,3,1,5]=>5 [4,6,2,3,5,1]=>7 [4,6,2,5,1,3]=>6 [4,6,2,5,3,1]=>1 [4,6,3,1,2,5]=>9 [4,6,3,1,5,2]=>3 [4,6,3,2,1,5]=>5 [4,6,3,2,5,1]=>4 [4,6,3,5,1,2]=>3 [4,6,3,5,2,1]=>3 [4,6,5,1,2,3]=>16 [4,6,5,1,3,2]=>3 [4,6,5,2,1,3]=>9 [4,6,5,2,3,1]=>7 [4,6,5,3,1,2]=>3 [4,6,5,3,2,1]=>2 [5,1,2,3,4,6]=>2 [5,1,2,3,6,4]=>7 [5,1,2,4,3,6]=>1 [5,1,2,4,6,3]=>1 [5,1,2,6,3,4]=>7 [5,1,2,6,4,3]=>6 [5,1,3,2,4,6]=>7 [5,1,3,2,6,4]=>9 [5,1,3,4,2,6]=>7 [5,1,3,4,6,2]=>5 [5,1,3,6,2,4]=>9 [5,1,3,6,4,2]=>8 [5,1,4,2,3,6]=>2 [5,1,4,2,6,3]=>9 [5,1,4,3,2,6]=>2 [5,1,4,3,6,2]=>2 [5,1,4,6,2,3]=>9 [5,1,4,6,3,2]=>5 [5,1,6,2,3,4]=>3 [5,1,6,2,4,3]=>4 [5,1,6,3,2,4]=>4 [5,1,6,3,4,2]=>1 [5,1,6,4,2,3]=>4 [5,1,6,4,3,2]=>4 [5,2,1,3,4,6]=>4 [5,2,1,3,6,4]=>9 [5,2,1,4,3,6]=>6 [5,2,1,4,6,3]=>8 [5,2,1,6,3,4]=>9 [5,2,1,6,4,3]=>9 [5,2,3,1,4,6]=>3 [5,2,3,1,6,4]=>8 [5,2,3,4,1,6]=>2 [5,2,3,4,6,1]=>2 [5,2,3,6,1,4]=>2 [5,2,3,6,4,1]=>6 [5,2,4,1,3,6]=>6 [5,2,4,1,6,3]=>8 [5,2,4,3,1,6]=>1 [5,2,4,3,6,1]=>1 [5,2,4,6,1,3]=>8 [5,2,4,6,3,1]=>1 [5,2,6,1,3,4]=>9 [5,2,6,1,4,3]=>1 [5,2,6,3,1,4]=>8 [5,2,6,3,4,1]=>6 [5,2,6,4,1,3]=>9 [5,2,6,4,3,1]=>4 [5,3,1,2,4,6]=>7 [5,3,1,2,6,4]=>4 [5,3,1,4,2,6]=>7 [5,3,1,4,6,2]=>4 [5,3,1,6,2,4]=>6 [5,3,1,6,4,2]=>3 [5,3,2,1,4,6]=>4 [5,3,2,1,6,4]=>5 [5,3,2,4,1,6]=>3 [5,3,2,4,6,1]=>3 [5,3,2,6,1,4]=>5 [5,3,2,6,4,1]=>4 [5,3,4,1,2,6]=>7 [5,3,4,1,6,2]=>5 [5,3,4,2,1,6]=>2 [5,3,4,2,6,1]=>2 [5,3,4,6,1,2]=>4 [5,3,4,6,2,1]=>2 [5,3,6,1,2,4]=>6 [5,3,6,1,4,2]=>8 [5,3,6,2,1,4]=>5 [5,3,6,2,4,1]=>2 [5,3,6,4,1,2]=>8 [5,3,6,4,2,1]=>3 [5,4,1,2,3,6]=>2 [5,4,1,2,6,3]=>9 [5,4,1,3,2,6]=>2 [5,4,1,3,6,2]=>2 [5,4,1,6,2,3]=>9 [5,4,1,6,3,2]=>5 [5,4,2,1,3,6]=>6 [5,4,2,1,6,3]=>8 [5,4,2,3,1,6]=>2 [5,4,2,3,6,1]=>2 [5,4,2,6,1,3]=>2 [5,4,2,6,3,1]=>3 [5,4,3,1,2,6]=>2 [5,4,3,1,6,2]=>3 [5,4,3,2,1,6]=>1 [5,4,3,2,6,1]=>1 [5,4,3,6,1,2]=>3 [5,4,3,6,2,1]=>1 [5,4,6,1,2,3]=>9 [5,4,6,1,3,2]=>5 [5,4,6,2,1,3]=>8 [5,4,6,2,3,1]=>3 [5,4,6,3,1,2]=>5 [5,4,6,3,2,1]=>1 [5,6,1,2,3,4]=>7 [5,6,1,2,4,3]=>6 [5,6,1,3,2,4]=>9 [5,6,1,3,4,2]=>8 [5,6,1,4,2,3]=>6 [5,6,1,4,3,2]=>1 [5,6,2,1,3,4]=>9 [5,6,2,1,4,3]=>9 [5,6,2,3,1,4]=>8 [5,6,2,3,4,1]=>6 [5,6,2,4,1,3]=>9 [5,6,2,4,3,1]=>4 [5,6,3,1,2,4]=>9 [5,6,3,1,4,2]=>3 [5,6,3,2,1,4]=>5 [5,6,3,2,4,1]=>4 [5,6,3,4,1,2]=>3 [5,6,3,4,2,1]=>3 [5,6,4,1,2,3]=>6 [5,6,4,1,3,2]=>4 [5,6,4,2,1,3]=>9 [5,6,4,2,3,1]=>4 [5,6,4,3,1,2]=>4 [5,6,4,3,2,1]=>1 [6,1,2,3,4,5]=>2 [6,1,2,3,5,4]=>1 [6,1,2,4,3,5]=>12 [6,1,2,4,5,3]=>16 [6,1,2,5,3,4]=>2 [6,1,2,5,4,3]=>2 [6,1,3,2,4,5]=>3 [6,1,3,2,5,4]=>16 [6,1,3,4,2,5]=>3 [6,1,3,4,5,2]=>9 [6,1,3,5,2,4]=>16 [6,1,3,5,4,2]=>12 [6,1,4,2,3,5]=>12 [6,1,4,2,5,3]=>16 [6,1,4,3,2,5]=>9 [6,1,4,3,5,2]=>1 [6,1,4,5,2,3]=>16 [6,1,4,5,3,2]=>3 [6,1,5,2,3,4]=>2 [6,1,5,2,4,3]=>1 [6,1,5,3,2,4]=>16 [6,1,5,3,4,2]=>12 [6,1,5,4,2,3]=>2 [6,1,5,4,3,2]=>2 [6,2,1,3,4,5]=>4 [6,2,1,3,5,4]=>4 [6,2,1,4,3,5]=>8 [6,2,1,4,5,3]=>1 [6,2,1,5,3,4]=>4 [6,2,1,5,4,3]=>7 [6,2,3,1,4,5]=>5 [6,2,3,1,5,4]=>9 [6,2,3,4,1,5]=>3 [6,2,3,4,5,1]=>2 [6,2,3,5,1,4]=>9 [6,2,3,5,4,1]=>1 [6,2,4,1,3,5]=>3 [6,2,4,1,5,3]=>9 [6,2,4,3,1,5]=>5 [6,2,4,3,5,1]=>7 [6,2,4,5,1,3]=>9 [6,2,4,5,3,1]=>7 [6,2,5,1,3,4]=>6 [6,2,5,1,4,3]=>7 [6,2,5,3,1,4]=>9 [6,2,5,3,4,1]=>2 [6,2,5,4,1,3]=>3 [6,2,5,4,3,1]=>2 [6,3,1,2,4,5]=>4 [6,3,1,2,5,4]=>16 [6,3,1,4,2,5]=>3 [6,3,1,4,5,2]=>5 [6,3,1,5,2,4]=>4 [6,3,1,5,4,2]=>12 [6,3,2,1,4,5]=>3 [6,3,2,1,5,4]=>6 [6,3,2,4,1,5]=>5 [6,3,2,4,5,1]=>4 [6,3,2,5,1,4]=>6 [6,3,2,5,4,1]=>6 [6,3,4,1,2,5]=>3 [6,3,4,1,5,2]=>9 [6,3,4,2,1,5]=>4 [6,3,4,2,5,1]=>3 [6,3,4,5,1,2]=>5 [6,3,4,5,2,1]=>2 [6,3,5,1,2,4]=>16 [6,3,5,1,4,2]=>2 [6,3,5,2,1,4]=>6 [6,3,5,2,4,1]=>6 [6,3,5,4,1,2]=>12 [6,3,5,4,2,1]=>1 [6,4,1,2,3,5]=>12 [6,4,1,2,5,3]=>16 [6,4,1,3,2,5]=>9 [6,4,1,3,5,2]=>4 [6,4,1,5,2,3]=>16 [6,4,1,5,3,2]=>3 [6,4,2,1,3,5]=>3 [6,4,2,1,5,3]=>9 [6,4,2,3,1,5]=>4 [6,4,2,3,5,1]=>7 [6,4,2,5,1,3]=>6 [6,4,2,5,3,1]=>7 [6,4,3,1,2,5]=>5 [6,4,3,1,5,2]=>3 [6,4,3,2,1,5]=>5 [6,4,3,2,5,1]=>4 [6,4,3,5,1,2]=>3 [6,4,3,5,2,1]=>3 [6,4,5,1,2,3]=>16 [6,4,5,1,3,2]=>4 [6,4,5,2,1,3]=>4 [6,4,5,2,3,1]=>7 [6,4,5,3,1,2]=>4 [6,4,5,3,2,1]=>2 [6,5,1,2,3,4]=>2 [6,5,1,2,4,3]=>2 [6,5,1,3,2,4]=>16 [6,5,1,3,4,2]=>12 [6,5,1,4,2,3]=>2 [6,5,1,4,3,2]=>1 [6,5,2,1,3,4]=>6 [6,5,2,1,4,3]=>3 [6,5,2,3,1,4]=>9 [6,5,2,3,4,1]=>2 [6,5,2,4,1,3]=>7 [6,5,2,4,3,1]=>2 [6,5,3,1,2,4]=>16 [6,5,3,1,4,2]=>12 [6,5,3,2,1,4]=>4 [6,5,3,2,4,1]=>6 [6,5,3,4,1,2]=>12 [6,5,3,4,2,1]=>2 [6,5,4,1,2,3]=>2 [6,5,4,1,3,2]=>2 [6,5,4,2,1,3]=>7 [6,5,4,2,3,1]=>2 [6,5,4,3,1,2]=>2 [6,5,4,3,2,1]=>1 [1,2,3,4,5,6,7]=>1 [1,2,3,4,5,7,6]=>2 [1,2,3,4,6,5,7]=>2 [1,2,3,4,6,7,5]=>15 [1,2,3,4,7,5,6]=>2 [1,2,3,4,7,6,5]=>2 [1,2,3,5,4,6,7]=>2 [1,2,3,5,4,7,6]=>13 [1,2,3,5,6,4,7]=>7 [1,2,3,5,6,7,4]=>19 [1,2,3,5,7,4,6]=>13 [1,2,3,5,7,6,4]=>20 [1,2,3,6,4,5,7]=>2 [1,2,3,6,4,7,5]=>15 [1,2,3,6,5,4,7]=>2 [1,2,3,6,5,7,4]=>19 [1,2,3,6,7,4,5]=>15 [1,2,3,6,7,5,4]=>8 [1,2,3,7,4,5,6]=>2 [1,2,3,7,4,6,5]=>2 [1,2,3,7,5,4,6]=>13 [1,2,3,7,5,6,4]=>20 [1,2,3,7,6,4,5]=>2 [1,2,3,7,6,5,4]=>2 [1,2,4,3,5,6,7]=>2 [1,2,4,3,5,7,6]=>4 [1,2,4,3,6,5,7]=>12 [1,2,4,3,6,7,5]=>8 [1,2,4,3,7,5,6]=>4 [1,2,4,3,7,6,5]=>16 [1,2,4,5,3,6,7]=>6 [1,2,4,5,3,7,6]=>9 [1,2,4,5,6,3,7]=>4 [1,2,4,5,6,7,3]=>8 [1,2,4,5,7,3,6]=>6 [1,2,4,5,7,6,3]=>6 [1,2,4,6,3,5,7]=>12 [1,2,4,6,3,7,5]=>32 [1,2,4,6,5,3,7]=>16 [1,2,4,6,5,7,3]=>4 [1,2,4,6,7,3,5]=>32 [1,2,4,6,7,5,3]=>27 [1,2,4,7,3,5,6]=>14 [1,2,4,7,3,6,5]=>10 [1,2,4,7,5,3,6]=>6 [1,2,4,7,5,6,3]=>4 [1,2,4,7,6,3,5]=>16 [1,2,4,7,6,5,3]=>16 [1,2,5,3,4,6,7]=>2 [1,2,5,3,4,7,6]=>13 [1,2,5,3,6,4,7]=>7 [1,2,5,3,6,7,4]=>19 [1,2,5,3,7,4,6]=>2 [1,2,5,3,7,6,4]=>20 [1,2,5,4,3,6,7]=>2 [1,2,5,4,3,7,6]=>26 [1,2,5,4,6,3,7]=>9 [1,2,5,4,6,7,3]=>14 [1,2,5,4,7,3,6]=>26 [1,2,5,4,7,6,3]=>27 [1,2,5,6,3,4,7]=>3 [1,2,5,6,3,7,4]=>19 [1,2,5,6,4,3,7]=>6 [1,2,5,6,4,7,3]=>15 [1,2,5,6,7,3,4]=>19 [1,2,5,6,7,4,3]=>14 [1,2,5,7,3,4,6]=>5 [1,2,5,7,3,6,4]=>6 [1,2,5,7,4,3,6]=>26 [1,2,5,7,4,6,3]=>27 [1,2,5,7,6,3,4]=>20 [1,2,5,7,6,4,3]=>6 [1,2,6,3,4,5,7]=>1 [1,2,6,3,4,7,5]=>15 [1,2,6,3,5,4,7]=>2 [1,2,6,3,5,7,4]=>19 [1,2,6,3,7,4,5]=>15 [1,2,6,3,7,5,4]=>8 [1,2,6,4,3,5,7]=>12 [1,2,6,4,3,7,5]=>32 [1,2,6,4,5,3,7]=>16 [1,2,6,4,5,7,3]=>15 [1,2,6,4,7,3,5]=>5 [1,2,6,4,7,5,3]=>27 [1,2,6,5,3,4,7]=>2 [1,2,6,5,3,7,4]=>19 [1,2,6,5,4,3,7]=>2 [1,2,6,5,4,7,3]=>9 [1,2,6,5,7,3,4]=>19 [1,2,6,5,7,4,3]=>15 [1,2,6,7,3,4,5]=>15 [1,2,6,7,3,5,4]=>12 [1,2,6,7,4,3,5]=>8 [1,2,6,7,4,5,3]=>27 [1,2,6,7,5,3,4]=>12 [1,2,6,7,5,4,3]=>6 [1,2,7,3,4,5,6]=>2 [1,2,7,3,4,6,5]=>2 [1,2,7,3,5,4,6]=>5 [1,2,7,3,5,6,4]=>10 [1,2,7,3,6,4,5]=>2 [1,2,7,3,6,5,4]=>2 [1,2,7,4,3,5,6]=>14 [1,2,7,4,3,6,5]=>16 [1,2,7,4,5,3,6]=>9 [1,2,7,4,5,6,3]=>5 [1,2,7,4,6,3,5]=>5 [1,2,7,4,6,5,3]=>5 [1,2,7,5,3,4,6]=>13 [1,2,7,5,3,6,4]=>20 [1,2,7,5,4,3,6]=>26 [1,2,7,5,4,6,3]=>6 [1,2,7,5,6,3,4]=>20 [1,2,7,5,6,4,3]=>6 [1,2,7,6,3,4,5]=>1 [1,2,7,6,3,5,4]=>2 [1,2,7,6,4,3,5]=>10 [1,2,7,6,4,5,3]=>10 [1,2,7,6,5,3,4]=>2 [1,2,7,6,5,4,3]=>2 [1,3,2,4,5,6,7]=>2 [1,3,2,4,5,7,6]=>4 [1,3,2,4,6,5,7]=>4 [1,3,2,4,6,7,5]=>30 [1,3,2,4,7,5,6]=>4 [1,3,2,4,7,6,5]=>6 [1,3,2,5,4,6,7]=>7 [1,3,2,5,4,7,6]=>38 [1,3,2,5,6,4,7]=>4 [1,3,2,5,6,7,4]=>10 [1,3,2,5,7,4,6]=>38 [1,3,2,5,7,6,4]=>27 [1,3,2,6,4,5,7]=>4 [1,3,2,6,4,7,5]=>30 [1,3,2,6,5,4,7]=>16 [1,3,2,6,5,7,4]=>34 [1,3,2,6,7,4,5]=>30 [1,3,2,6,7,5,4]=>14 [1,3,2,7,4,5,6]=>8 [1,3,2,7,4,6,5]=>6 [1,3,2,7,5,4,6]=>38 [1,3,2,7,5,6,4]=>27 [1,3,2,7,6,4,5]=>6 [1,3,2,7,6,5,4]=>20 [1,3,4,2,5,6,7]=>3 [1,3,4,2,5,7,6]=>8 [1,3,4,2,6,5,7]=>3 [1,3,4,2,6,7,5]=>29 [1,3,4,2,7,5,6]=>10 [1,3,4,2,7,6,5]=>27 [1,3,4,5,2,6,7]=>4 [1,3,4,5,2,7,6]=>18 [1,3,4,5,6,2,7]=>5 [1,3,4,5,6,7,2]=>6 [1,3,4,5,7,2,6]=>18 [1,3,4,5,7,6,2]=>23 [1,3,4,6,2,5,7]=>3 [1,3,4,6,2,7,5]=>10 [1,3,4,6,5,2,7]=>5 [1,3,4,6,5,7,2]=>17 [1,3,4,6,7,2,5]=>29 [1,3,4,6,7,5,2]=>18 [1,3,4,7,2,5,6]=>10 [1,3,4,7,2,6,5]=>27 [1,3,4,7,5,2,6]=>18 [1,3,4,7,5,6,2]=>23 [1,3,4,7,6,2,5]=>27 [1,3,4,7,6,5,2]=>26 [1,3,5,2,4,6,7]=>7 [1,3,5,2,4,7,6]=>38 [1,3,5,2,6,4,7]=>6 [1,3,5,2,6,7,4]=>7 [1,3,5,2,7,4,6]=>38 [1,3,5,2,7,6,4]=>7 [1,3,5,4,2,6,7]=>7 [1,3,5,4,2,7,6]=>43 [1,3,5,4,6,2,7]=>4 [1,3,5,4,6,7,2]=>11 [1,3,5,4,7,2,6]=>43 [1,3,5,4,7,6,2]=>43 [1,3,5,6,2,4,7]=>9 [1,3,5,6,2,7,4]=>7 [1,3,5,6,4,2,7]=>3 [1,3,5,6,4,7,2]=>17 [1,3,5,6,7,2,4]=>10 [1,3,5,6,7,4,2]=>24 [1,3,5,7,2,4,6]=>38 [1,3,5,7,2,6,4]=>7 [1,3,5,7,4,2,6]=>43 [1,3,5,7,4,6,2]=>43 [1,3,5,7,6,2,4]=>27 [1,3,5,7,6,4,2]=>38 [1,3,6,2,4,5,7]=>3 [1,3,6,2,4,7,5]=>30 [1,3,6,2,5,4,7]=>16 [1,3,6,2,5,7,4]=>34 [1,3,6,2,7,4,5]=>30 [1,3,6,2,7,5,4]=>14 [1,3,6,4,2,5,7]=>4 [1,3,6,4,2,7,5]=>29 [1,3,6,4,5,2,7]=>9 [1,3,6,4,5,7,2]=>17 [1,3,6,4,7,2,5]=>29 [1,3,6,4,7,5,2]=>18 [1,3,6,5,2,4,7]=>16 [1,3,6,5,2,7,4]=>34 [1,3,6,5,4,2,7]=>12 [1,3,6,5,4,7,2]=>4 [1,3,6,5,7,2,4]=>34 [1,3,6,5,7,4,2]=>3 [1,3,6,7,2,4,5]=>30 [1,3,6,7,2,5,4]=>17 [1,3,6,7,4,2,5]=>29 [1,3,6,7,4,5,2]=>14 [1,3,6,7,5,2,4]=>17 [1,3,6,7,5,4,2]=>19 [1,3,7,2,4,5,6]=>8 [1,3,7,2,4,6,5]=>4 [1,3,7,2,5,4,6]=>38 [1,3,7,2,5,6,4]=>4 [1,3,7,2,6,4,5]=>6 [1,3,7,2,6,5,4]=>20 [1,3,7,4,2,5,6]=>8 [1,3,7,4,2,6,5]=>27 [1,3,7,4,5,2,6]=>5 [1,3,7,4,5,6,2]=>23 [1,3,7,4,6,2,5]=>27 [1,3,7,4,6,5,2]=>26 [1,3,7,5,2,4,6]=>38 [1,3,7,5,2,6,4]=>27 [1,3,7,5,4,2,6]=>43 [1,3,7,5,4,6,2]=>43 [1,3,7,5,6,2,4]=>27 [1,3,7,5,6,4,2]=>38 [1,3,7,6,2,4,5]=>7 [1,3,7,6,2,5,4]=>10 [1,3,7,6,4,2,5]=>4 [1,3,7,6,4,5,2]=>26 [1,3,7,6,5,2,4]=>20 [1,3,7,6,5,4,2]=>13 [1,4,2,3,5,6,7]=>1 [1,4,2,3,5,7,6]=>14 [1,4,2,3,6,5,7]=>12 [1,4,2,3,6,7,5]=>32 [1,4,2,3,7,5,6]=>14 [1,4,2,3,7,6,5]=>5 [1,4,2,5,3,6,7]=>6 [1,4,2,5,3,7,6]=>6 [1,4,2,5,6,3,7]=>6 [1,4,2,5,6,7,3]=>5 [1,4,2,5,7,3,6]=>6 [1,4,2,5,7,6,3]=>5 [1,4,2,6,3,5,7]=>2 [1,4,2,6,3,7,5]=>32 [1,4,2,6,5,3,7]=>16 [1,4,2,6,5,7,3]=>11 [1,4,2,6,7,3,5]=>32 [1,4,2,6,7,5,3]=>27 [1,4,2,7,3,5,6]=>14 [1,4,2,7,3,6,5]=>4 [1,4,2,7,5,3,6]=>6 [1,4,2,7,5,6,3]=>11 [1,4,2,7,6,3,5]=>4 [1,4,2,7,6,5,3]=>16 [1,4,3,2,5,6,7]=>2 [1,4,3,2,5,7,6]=>10 [1,4,3,2,6,5,7]=>5 [1,4,3,2,6,7,5]=>11 [1,4,3,2,7,5,6]=>2 [1,4,3,2,7,6,5]=>6 [1,4,3,5,2,6,7]=>3 [1,4,3,5,2,7,6]=>17 [1,4,3,5,6,2,7]=>4 [1,4,3,5,6,7,2]=>5 [1,4,3,5,7,2,6]=>17 [1,4,3,5,7,6,2]=>4 [1,4,3,6,2,5,7]=>9 [1,4,3,6,2,7,5]=>24 [1,4,3,6,5,2,7]=>3 [1,4,3,6,5,7,2]=>12 [1,4,3,6,7,2,5]=>11 [1,4,3,6,7,5,2]=>17 [1,4,3,7,2,5,6]=>10 [1,4,3,7,2,6,5]=>6 [1,4,3,7,5,2,6]=>17 [1,4,3,7,5,6,2]=>5 [1,4,3,7,6,2,5]=>5 [1,4,3,7,6,5,2]=>6 [1,4,5,2,3,6,7]=>6 [1,4,5,2,3,7,6]=>9 [1,4,5,2,6,3,7]=>6 [1,4,5,2,6,7,3]=>8 [1,4,5,2,7,3,6]=>4 [1,4,5,2,7,6,3]=>6 [1,4,5,3,2,6,7]=>4 [1,4,5,3,2,7,6]=>5 [1,4,5,3,6,2,7]=>5 [1,4,5,3,6,7,2]=>6 [1,4,5,3,7,2,6]=>4 [1,4,5,3,7,6,2]=>17 [1,4,5,6,2,3,7]=>6 [1,4,5,6,2,7,3]=>2 [1,4,5,6,3,2,7]=>3 [1,4,5,6,3,7,2]=>4 [1,4,5,6,7,2,3]=>5 [1,4,5,6,7,3,2]=>6 [1,4,5,7,2,3,6]=>6 [1,4,5,7,2,6,3]=>3 [1,4,5,7,3,2,6]=>4 [1,4,5,7,3,6,2]=>17 [1,4,5,7,6,2,3]=>6 [1,4,5,7,6,3,2]=>10 [1,4,6,2,3,5,7]=>12 [1,4,6,2,3,7,5]=>32 [1,4,6,2,5,3,7]=>4 [1,4,6,2,5,7,3]=>15 [1,4,6,2,7,3,5]=>32 [1,4,6,2,7,5,3]=>15 [1,4,6,3,2,5,7]=>5 [1,4,6,3,2,7,5]=>24 [1,4,6,3,5,2,7]=>3 [1,4,6,3,5,7,2]=>12 [1,4,6,3,7,2,5]=>3 [1,4,6,3,7,5,2]=>8 [1,4,6,5,2,3,7]=>16 [1,4,6,5,2,7,3]=>11 [1,4,6,5,3,2,7]=>4 [1,4,6,5,3,7,2]=>9
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Description
The orbit size of a permutation under Foata's bijection.
References
[1] Foata bijection Mp00067
Code
def foata_bijection(elt):
    L = list(elt)
    M = []
    for e in L:
        M.append(e)
        k = len(M)
        if k <= 1:
            continue

        a = M[-2]
        M_prime = [0]*k
        if a > e:
            index_list = [-1] + [i for i in range(k - 1) if M[i] > e]
        else:
            index_list = [-1] + [i for i in range(k - 1) if M[i] < e]

        for j in range(1, len(index_list)):
            start = index_list[j-1] + 1
            end = index_list[j]
            M_prime[start] = M[end]
            for x in range(start + 1, end + 1):
                M_prime[x] = M[x-1]
        M_prime[k-1] = e
        M = M_prime
    return Permutations()(M)

def statistic(pi):
    l = 1
    pi_new = pi
    while True:
        pi_new = foata_bijection(pi_new)
        if pi_new == pi:
            return l
        l += 1

Created
Sep 24, 2017 at 11:48 by Martin Rubey
Updated
Sep 24, 2017 at 11:48 by Martin Rubey