edit this statistic or download as text // json
Identifier
Values
=>
[1]=>1 [1,2]=>1 [2,1]=>2 [1,2,3]=>1 [1,3,2]=>2 [2,1,3]=>2 [2,3,1]=>3 [3,1,2]=>3 [3,2,1]=>2 [1,2,3,4]=>1 [1,2,4,3]=>2 [1,3,2,4]=>2 [1,3,4,2]=>3 [1,4,2,3]=>3 [1,4,3,2]=>2 [2,1,3,4]=>2 [2,1,4,3]=>4 [2,3,1,4]=>3 [2,3,4,1]=>4 [2,4,1,3]=>5 [2,4,3,1]=>3 [3,1,2,4]=>3 [3,1,4,2]=>5 [3,2,1,4]=>2 [3,2,4,1]=>3 [3,4,1,2]=>6 [3,4,2,1]=>5 [4,1,2,3]=>4 [4,1,3,2]=>3 [4,2,1,3]=>3 [4,2,3,1]=>2 [4,3,1,2]=>5 [4,3,2,1]=>4 [1,2,3,4,5]=>1 [1,2,3,5,4]=>2 [1,2,4,3,5]=>2 [1,2,4,5,3]=>3 [1,2,5,3,4]=>3 [1,2,5,4,3]=>2 [1,3,2,4,5]=>2 [1,3,2,5,4]=>4 [1,3,4,2,5]=>3 [1,3,4,5,2]=>4 [1,3,5,2,4]=>5 [1,3,5,4,2]=>3 [1,4,2,3,5]=>3 [1,4,2,5,3]=>5 [1,4,3,2,5]=>2 [1,4,3,5,2]=>3 [1,4,5,2,3]=>6 [1,4,5,3,2]=>5 [1,5,2,3,4]=>4 [1,5,2,4,3]=>3 [1,5,3,2,4]=>3 [1,5,3,4,2]=>2 [1,5,4,2,3]=>5 [1,5,4,3,2]=>4 [2,1,3,4,5]=>2 [2,1,3,5,4]=>4 [2,1,4,3,5]=>4 [2,1,4,5,3]=>6 [2,1,5,3,4]=>6 [2,1,5,4,3]=>4 [2,3,1,4,5]=>3 [2,3,1,5,4]=>6 [2,3,4,1,5]=>4 [2,3,4,5,1]=>5 [2,3,5,1,4]=>7 [2,3,5,4,1]=>4 [2,4,1,3,5]=>5 [2,4,1,5,3]=>8 [2,4,3,1,5]=>3 [2,4,3,5,1]=>4 [2,4,5,1,3]=>9 [2,4,5,3,1]=>7 [2,5,1,3,4]=>7 [2,5,1,4,3]=>5 [2,5,3,1,4]=>5 [2,5,3,4,1]=>3 [2,5,4,1,3]=>8 [2,5,4,3,1]=>6 [3,1,2,4,5]=>3 [3,1,2,5,4]=>6 [3,1,4,2,5]=>5 [3,1,4,5,2]=>7 [3,1,5,2,4]=>8 [3,1,5,4,2]=>5 [3,2,1,4,5]=>2 [3,2,1,5,4]=>4 [3,2,4,1,5]=>3 [3,2,4,5,1]=>4 [3,2,5,1,4]=>5 [3,2,5,4,1]=>3 [3,4,1,2,5]=>6 [3,4,1,5,2]=>9 [3,4,2,1,5]=>5 [3,4,2,5,1]=>7 [3,4,5,1,2]=>10 [3,4,5,2,1]=>9 [3,5,1,2,4]=>9 [3,5,1,4,2]=>6 [3,5,2,1,4]=>8 [3,5,2,4,1]=>5 [3,5,4,1,2]=>9 [3,5,4,2,1]=>8 [4,1,2,3,5]=>4 [4,1,2,5,3]=>7 [4,1,3,2,5]=>3 [4,1,3,5,2]=>5 [4,1,5,2,3]=>9 [4,1,5,3,2]=>8 [4,2,1,3,5]=>3 [4,2,1,5,3]=>5 [4,2,3,1,5]=>2 [4,2,3,5,1]=>3 [4,2,5,1,3]=>6 [4,2,5,3,1]=>5 [4,3,1,2,5]=>5 [4,3,1,5,2]=>8 [4,3,2,1,5]=>4 [4,3,2,5,1]=>6 [4,3,5,1,2]=>9 [4,3,5,2,1]=>8 [4,5,1,2,3]=>10 [4,5,1,3,2]=>9 [4,5,2,1,3]=>9 [4,5,2,3,1]=>7 [4,5,3,1,2]=>6 [4,5,3,2,1]=>5 [5,1,2,3,4]=>5 [5,1,2,4,3]=>4 [5,1,3,2,4]=>4 [5,1,3,4,2]=>3 [5,1,4,2,3]=>7 [5,1,4,3,2]=>6 [5,2,1,3,4]=>4 [5,2,1,4,3]=>3 [5,2,3,1,4]=>3 [5,2,3,4,1]=>2 [5,2,4,1,3]=>5 [5,2,4,3,1]=>4 [5,3,1,2,4]=>7 [5,3,1,4,2]=>5 [5,3,2,1,4]=>6 [5,3,2,4,1]=>4 [5,3,4,1,2]=>7 [5,3,4,2,1]=>6 [5,4,1,2,3]=>9 [5,4,1,3,2]=>8 [5,4,2,1,3]=>8 [5,4,2,3,1]=>6 [5,4,3,1,2]=>5 [5,4,3,2,1]=>4 [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]=>3 [1,2,3,6,4,5]=>3 [1,2,3,6,5,4]=>2 [1,2,4,3,5,6]=>2 [1,2,4,3,6,5]=>4 [1,2,4,5,3,6]=>3 [1,2,4,5,6,3]=>4 [1,2,4,6,3,5]=>5 [1,2,4,6,5,3]=>3 [1,2,5,3,4,6]=>3 [1,2,5,3,6,4]=>5 [1,2,5,4,3,6]=>2 [1,2,5,4,6,3]=>3 [1,2,5,6,3,4]=>6 [1,2,5,6,4,3]=>5 [1,2,6,3,4,5]=>4 [1,2,6,3,5,4]=>3 [1,2,6,4,3,5]=>3 [1,2,6,4,5,3]=>2 [1,2,6,5,3,4]=>5 [1,2,6,5,4,3]=>4 [1,3,2,4,5,6]=>2 [1,3,2,4,6,5]=>4 [1,3,2,5,4,6]=>4 [1,3,2,5,6,4]=>6 [1,3,2,6,4,5]=>6 [1,3,2,6,5,4]=>4 [1,3,4,2,5,6]=>3 [1,3,4,2,6,5]=>6 [1,3,4,5,2,6]=>4 [1,3,4,5,6,2]=>5 [1,3,4,6,2,5]=>7 [1,3,4,6,5,2]=>4 [1,3,5,2,4,6]=>5 [1,3,5,2,6,4]=>8 [1,3,5,4,2,6]=>3 [1,3,5,4,6,2]=>4 [1,3,5,6,2,4]=>9 [1,3,5,6,4,2]=>7 [1,3,6,2,4,5]=>7 [1,3,6,2,5,4]=>5 [1,3,6,4,2,5]=>5 [1,3,6,4,5,2]=>3 [1,3,6,5,2,4]=>8 [1,3,6,5,4,2]=>6 [1,4,2,3,5,6]=>3 [1,4,2,3,6,5]=>6 [1,4,2,5,3,6]=>5 [1,4,2,5,6,3]=>7 [1,4,2,6,3,5]=>8 [1,4,2,6,5,3]=>5 [1,4,3,2,5,6]=>2 [1,4,3,2,6,5]=>4 [1,4,3,5,2,6]=>3 [1,4,3,5,6,2]=>4 [1,4,3,6,2,5]=>5 [1,4,3,6,5,2]=>3 [1,4,5,2,3,6]=>6 [1,4,5,2,6,3]=>9 [1,4,5,3,2,6]=>5 [1,4,5,3,6,2]=>7 [1,4,5,6,2,3]=>10 [1,4,5,6,3,2]=>9 [1,4,6,2,3,5]=>9 [1,4,6,2,5,3]=>6 [1,4,6,3,2,5]=>8 [1,4,6,3,5,2]=>5 [1,4,6,5,2,3]=>9 [1,4,6,5,3,2]=>8 [1,5,2,3,4,6]=>4 [1,5,2,3,6,4]=>7 [1,5,2,4,3,6]=>3 [1,5,2,4,6,3]=>5 [1,5,2,6,3,4]=>9 [1,5,2,6,4,3]=>8 [1,5,3,2,4,6]=>3 [1,5,3,2,6,4]=>5 [1,5,3,4,2,6]=>2 [1,5,3,4,6,2]=>3 [1,5,3,6,2,4]=>6 [1,5,3,6,4,2]=>5 [1,5,4,2,3,6]=>5 [1,5,4,2,6,3]=>8 [1,5,4,3,2,6]=>4 [1,5,4,3,6,2]=>6 [1,5,4,6,2,3]=>9 [1,5,4,6,3,2]=>8 [1,5,6,2,3,4]=>10 [1,5,6,2,4,3]=>9 [1,5,6,3,2,4]=>9 [1,5,6,3,4,2]=>7 [1,5,6,4,2,3]=>6 [1,5,6,4,3,2]=>5 [1,6,2,3,4,5]=>5 [1,6,2,3,5,4]=>4 [1,6,2,4,3,5]=>4 [1,6,2,4,5,3]=>3 [1,6,2,5,3,4]=>7 [1,6,2,5,4,3]=>6 [1,6,3,2,4,5]=>4 [1,6,3,2,5,4]=>3 [1,6,3,4,2,5]=>3 [1,6,3,4,5,2]=>2 [1,6,3,5,2,4]=>5 [1,6,3,5,4,2]=>4 [1,6,4,2,3,5]=>7 [1,6,4,2,5,3]=>5 [1,6,4,3,2,5]=>6 [1,6,4,3,5,2]=>4 [1,6,4,5,2,3]=>7 [1,6,4,5,3,2]=>6 [1,6,5,2,3,4]=>9 [1,6,5,2,4,3]=>8 [1,6,5,3,2,4]=>8 [1,6,5,3,4,2]=>6 [1,6,5,4,2,3]=>5 [1,6,5,4,3,2]=>4 [2,1,3,4,5,6]=>2 [2,1,3,4,6,5]=>4 [2,1,3,5,4,6]=>4 [2,1,3,5,6,4]=>6 [2,1,3,6,4,5]=>6 [2,1,3,6,5,4]=>4 [2,1,4,3,5,6]=>4 [2,1,4,3,6,5]=>8 [2,1,4,5,3,6]=>6 [2,1,4,5,6,3]=>8 [2,1,4,6,3,5]=>10 [2,1,4,6,5,3]=>6 [2,1,5,3,4,6]=>6 [2,1,5,3,6,4]=>10 [2,1,5,4,3,6]=>4 [2,1,5,4,6,3]=>6 [2,1,5,6,3,4]=>12 [2,1,5,6,4,3]=>10 [2,1,6,3,4,5]=>8 [2,1,6,3,5,4]=>6 [2,1,6,4,3,5]=>6 [2,1,6,4,5,3]=>4 [2,1,6,5,3,4]=>10 [2,1,6,5,4,3]=>8 [2,3,1,4,5,6]=>3 [2,3,1,4,6,5]=>6 [2,3,1,5,4,6]=>6 [2,3,1,5,6,4]=>9 [2,3,1,6,4,5]=>9 [2,3,1,6,5,4]=>6 [2,3,4,1,5,6]=>4 [2,3,4,1,6,5]=>8 [2,3,4,5,1,6]=>5 [2,3,4,5,6,1]=>6 [2,3,4,6,1,5]=>9 [2,3,4,6,5,1]=>5 [2,3,5,1,4,6]=>7 [2,3,5,1,6,4]=>11 [2,3,5,4,1,6]=>4 [2,3,5,4,6,1]=>5 [2,3,5,6,1,4]=>12 [2,3,5,6,4,1]=>9 [2,3,6,1,4,5]=>10 [2,3,6,1,5,4]=>7 [2,3,6,4,1,5]=>7 [2,3,6,4,5,1]=>4 [2,3,6,5,1,4]=>11 [2,3,6,5,4,1]=>8 [2,4,1,3,5,6]=>5 [2,4,1,3,6,5]=>10 [2,4,1,5,3,6]=>8 [2,4,1,5,6,3]=>11 [2,4,1,6,3,5]=>13 [2,4,1,6,5,3]=>8 [2,4,3,1,5,6]=>3 [2,4,3,1,6,5]=>6 [2,4,3,5,1,6]=>4 [2,4,3,5,6,1]=>5 [2,4,3,6,1,5]=>7 [2,4,3,6,5,1]=>4 [2,4,5,1,3,6]=>9 [2,4,5,1,6,3]=>13 [2,4,5,3,1,6]=>7 [2,4,5,3,6,1]=>9 [2,4,5,6,1,3]=>14 [2,4,5,6,3,1]=>12 [2,4,6,1,3,5]=>14 [2,4,6,1,5,3]=>9 [2,4,6,3,1,5]=>12 [2,4,6,3,5,1]=>7 [2,4,6,5,1,3]=>13 [2,4,6,5,3,1]=>11 [2,5,1,3,4,6]=>7 [2,5,1,3,6,4]=>12 [2,5,1,4,3,6]=>5 [2,5,1,4,6,3]=>8 [2,5,1,6,3,4]=>15 [2,5,1,6,4,3]=>13 [2,5,3,1,4,6]=>5 [2,5,3,1,6,4]=>8 [2,5,3,4,1,6]=>3 [2,5,3,4,6,1]=>4 [2,5,3,6,1,4]=>9 [2,5,3,6,4,1]=>7 [2,5,4,1,3,6]=>8 [2,5,4,1,6,3]=>12 [2,5,4,3,1,6]=>6 [2,5,4,3,6,1]=>8 [2,5,4,6,1,3]=>13 [2,5,4,6,3,1]=>11 [2,5,6,1,3,4]=>16 [2,5,6,1,4,3]=>14 [2,5,6,3,1,4]=>14 [2,5,6,3,4,1]=>10 [2,5,6,4,1,3]=>9 [2,5,6,4,3,1]=>7 [2,6,1,3,4,5]=>9 [2,6,1,3,5,4]=>7 [2,6,1,4,3,5]=>7 [2,6,1,4,5,3]=>5 [2,6,1,5,3,4]=>12 [2,6,1,5,4,3]=>10 [2,6,3,1,4,5]=>7 [2,6,3,1,5,4]=>5 [2,6,3,4,1,5]=>5 [2,6,3,4,5,1]=>3 [2,6,3,5,1,4]=>8 [2,6,3,5,4,1]=>6 [2,6,4,1,3,5]=>12 [2,6,4,1,5,3]=>8 [2,6,4,3,1,5]=>10 [2,6,4,3,5,1]=>6 [2,6,4,5,1,3]=>11 [2,6,4,5,3,1]=>9 [2,6,5,1,3,4]=>15 [2,6,5,1,4,3]=>13 [2,6,5,3,1,4]=>13 [2,6,5,3,4,1]=>9 [2,6,5,4,1,3]=>8 [2,6,5,4,3,1]=>6 [3,1,2,4,5,6]=>3 [3,1,2,4,6,5]=>6 [3,1,2,5,4,6]=>6 [3,1,2,5,6,4]=>9 [3,1,2,6,4,5]=>9 [3,1,2,6,5,4]=>6 [3,1,4,2,5,6]=>5 [3,1,4,2,6,5]=>10 [3,1,4,5,2,6]=>7 [3,1,4,5,6,2]=>9 [3,1,4,6,2,5]=>12 [3,1,4,6,5,2]=>7 [3,1,5,2,4,6]=>8 [3,1,5,2,6,4]=>13 [3,1,5,4,2,6]=>5 [3,1,5,4,6,2]=>7 [3,1,5,6,2,4]=>15 [3,1,5,6,4,2]=>12 [3,1,6,2,4,5]=>11 [3,1,6,2,5,4]=>8 [3,1,6,4,2,5]=>8 [3,1,6,4,5,2]=>5 [3,1,6,5,2,4]=>13 [3,1,6,5,4,2]=>10 [3,2,1,4,5,6]=>2 [3,2,1,4,6,5]=>4 [3,2,1,5,4,6]=>4 [3,2,1,5,6,4]=>6 [3,2,1,6,4,5]=>6 [3,2,1,6,5,4]=>4 [3,2,4,1,5,6]=>3 [3,2,4,1,6,5]=>6 [3,2,4,5,1,6]=>4 [3,2,4,5,6,1]=>5 [3,2,4,6,1,5]=>7 [3,2,4,6,5,1]=>4 [3,2,5,1,4,6]=>5 [3,2,5,1,6,4]=>8 [3,2,5,4,1,6]=>3 [3,2,5,4,6,1]=>4 [3,2,5,6,1,4]=>9 [3,2,5,6,4,1]=>7 [3,2,6,1,4,5]=>7 [3,2,6,1,5,4]=>5 [3,2,6,4,1,5]=>5 [3,2,6,4,5,1]=>3 [3,2,6,5,1,4]=>8 [3,2,6,5,4,1]=>6 [3,4,1,2,5,6]=>6 [3,4,1,2,6,5]=>12 [3,4,1,5,2,6]=>9 [3,4,1,5,6,2]=>12 [3,4,1,6,2,5]=>15 [3,4,1,6,5,2]=>9 [3,4,2,1,5,6]=>5 [3,4,2,1,6,5]=>10 [3,4,2,5,1,6]=>7 [3,4,2,5,6,1]=>9 [3,4,2,6,1,5]=>12 [3,4,2,6,5,1]=>7 [3,4,5,1,2,6]=>10 [3,4,5,1,6,2]=>14 [3,4,5,2,1,6]=>9 [3,4,5,2,6,1]=>12 [3,4,5,6,1,2]=>15 [3,4,5,6,2,1]=>14 [3,4,6,1,2,5]=>16 [3,4,6,1,5,2]=>10 [3,4,6,2,1,5]=>15 [3,4,6,2,5,1]=>9 [3,4,6,5,1,2]=>14 [3,4,6,5,2,1]=>13 [3,5,1,2,4,6]=>9 [3,5,1,2,6,4]=>15 [3,5,1,4,2,6]=>6 [3,5,1,4,6,2]=>9 [3,5,1,6,2,4]=>18 [3,5,1,6,4,2]=>15 [3,5,2,1,4,6]=>8 [3,5,2,1,6,4]=>13 [3,5,2,4,1,6]=>5 [3,5,2,4,6,1]=>7 [3,5,2,6,1,4]=>15 [3,5,2,6,4,1]=>12 [3,5,4,1,2,6]=>9 [3,5,4,1,6,2]=>13 [3,5,4,2,1,6]=>8 [3,5,4,2,6,1]=>11 [3,5,4,6,1,2]=>14 [3,5,4,6,2,1]=>13 [3,5,6,1,2,4]=>19 [3,5,6,1,4,2]=>16 [3,5,6,2,1,4]=>18 [3,5,6,2,4,1]=>14 [3,5,6,4,1,2]=>10 [3,5,6,4,2,1]=>9 [3,6,1,2,4,5]=>12 [3,6,1,2,5,4]=>9 [3,6,1,4,2,5]=>9 [3,6,1,4,5,2]=>6 [3,6,1,5,2,4]=>15 [3,6,1,5,4,2]=>12 [3,6,2,1,4,5]=>11 [3,6,2,1,5,4]=>8 [3,6,2,4,1,5]=>8 [3,6,2,4,5,1]=>5 [3,6,2,5,1,4]=>13 [3,6,2,5,4,1]=>10 [3,6,4,1,2,5]=>14 [3,6,4,1,5,2]=>9 [3,6,4,2,1,5]=>13 [3,6,4,2,5,1]=>8 [3,6,4,5,1,2]=>12 [3,6,4,5,2,1]=>11 [3,6,5,1,2,4]=>18 [3,6,5,1,4,2]=>15 [3,6,5,2,1,4]=>17 [3,6,5,2,4,1]=>13 [3,6,5,4,1,2]=>9 [3,6,5,4,2,1]=>8 [4,1,2,3,5,6]=>4 [4,1,2,3,6,5]=>8 [4,1,2,5,3,6]=>7 [4,1,2,5,6,3]=>10 [4,1,2,6,3,5]=>11 [4,1,2,6,5,3]=>7 [4,1,3,2,5,6]=>3 [4,1,3,2,6,5]=>6 [4,1,3,5,2,6]=>5 [4,1,3,5,6,2]=>7 [4,1,3,6,2,5]=>8 [4,1,3,6,5,2]=>5 [4,1,5,2,3,6]=>9 [4,1,5,2,6,3]=>14 [4,1,5,3,2,6]=>8 [4,1,5,3,6,2]=>12 [4,1,5,6,2,3]=>16 [4,1,5,6,3,2]=>15 [4,1,6,2,3,5]=>13 [4,1,6,2,5,3]=>9 [4,1,6,3,2,5]=>12 [4,1,6,3,5,2]=>8 [4,1,6,5,2,3]=>14 [4,1,6,5,3,2]=>13 [4,2,1,3,5,6]=>3 [4,2,1,3,6,5]=>6 [4,2,1,5,3,6]=>5 [4,2,1,5,6,3]=>7 [4,2,1,6,3,5]=>8 [4,2,1,6,5,3]=>5 [4,2,3,1,5,6]=>2 [4,2,3,1,6,5]=>4 [4,2,3,5,1,6]=>3 [4,2,3,5,6,1]=>4 [4,2,3,6,1,5]=>5 [4,2,3,6,5,1]=>3 [4,2,5,1,3,6]=>6 [4,2,5,1,6,3]=>9 [4,2,5,3,1,6]=>5 [4,2,5,3,6,1]=>7 [4,2,5,6,1,3]=>10 [4,2,5,6,3,1]=>9 [4,2,6,1,3,5]=>9 [4,2,6,1,5,3]=>6 [4,2,6,3,1,5]=>8 [4,2,6,3,5,1]=>5 [4,2,6,5,1,3]=>9 [4,2,6,5,3,1]=>8 [4,3,1,2,5,6]=>5 [4,3,1,2,6,5]=>10 [4,3,1,5,2,6]=>8 [4,3,1,5,6,2]=>11 [4,3,1,6,2,5]=>13 [4,3,1,6,5,2]=>8 [4,3,2,1,5,6]=>4 [4,3,2,1,6,5]=>8 [4,3,2,5,1,6]=>6 [4,3,2,5,6,1]=>8 [4,3,2,6,1,5]=>10 [4,3,2,6,5,1]=>6 [4,3,5,1,2,6]=>9 [4,3,5,1,6,2]=>13 [4,3,5,2,1,6]=>8 [4,3,5,2,6,1]=>11 [4,3,5,6,1,2]=>14 [4,3,5,6,2,1]=>13 [4,3,6,1,2,5]=>14 [4,3,6,1,5,2]=>9 [4,3,6,2,1,5]=>13 [4,3,6,2,5,1]=>8 [4,3,6,5,1,2]=>13 [4,3,6,5,2,1]=>12 [4,5,1,2,3,6]=>10 [4,5,1,2,6,3]=>16 [4,5,1,3,2,6]=>9 [4,5,1,3,6,2]=>14 [4,5,1,6,2,3]=>19 [4,5,1,6,3,2]=>18 [4,5,2,1,3,6]=>9 [4,5,2,1,6,3]=>14 [4,5,2,3,1,6]=>7 [4,5,2,3,6,1]=>10 [4,5,2,6,1,3]=>16 [4,5,2,6,3,1]=>14 [4,5,3,1,2,6]=>6 [4,5,3,1,6,2]=>9 [4,5,3,2,1,6]=>5 [4,5,3,2,6,1]=>7 [4,5,3,6,1,2]=>10 [4,5,3,6,2,1]=>9 [4,5,6,1,2,3]=>20 [4,5,6,1,3,2]=>19 [4,5,6,2,1,3]=>19 [4,5,6,2,3,1]=>16 [4,5,6,3,1,2]=>16 [4,5,6,3,2,1]=>14 [4,6,1,2,3,5]=>14 [4,6,1,2,5,3]=>10 [4,6,1,3,2,5]=>13 [4,6,1,3,5,2]=>9 [4,6,1,5,2,3]=>16 [4,6,1,5,3,2]=>15 [4,6,2,1,3,5]=>13 [4,6,2,1,5,3]=>9 [4,6,2,3,1,5]=>11 [4,6,2,3,5,1]=>7 [4,6,2,5,1,3]=>14 [4,6,2,5,3,1]=>12 [4,6,3,1,2,5]=>9 [4,6,3,1,5,2]=>6 [4,6,3,2,1,5]=>8 [4,6,3,2,5,1]=>5 [4,6,3,5,1,2]=>9 [4,6,3,5,2,1]=>8 [4,6,5,1,2,3]=>19 [4,6,5,1,3,2]=>18 [4,6,5,2,1,3]=>18 [4,6,5,2,3,1]=>15 [4,6,5,3,1,2]=>15 [4,6,5,3,2,1]=>13 [5,1,2,3,4,6]=>5 [5,1,2,3,6,4]=>9 [5,1,2,4,3,6]=>4 [5,1,2,4,6,3]=>7 [5,1,2,6,3,4]=>12 [5,1,2,6,4,3]=>11 [5,1,3,2,4,6]=>4 [5,1,3,2,6,4]=>7 [5,1,3,4,2,6]=>3 [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]=>7 [5,1,4,2,6,3]=>12 [5,1,4,3,2,6]=>6 [5,1,4,3,6,2]=>10 [5,1,4,6,2,3]=>14 [5,1,4,6,3,2]=>13 [5,1,6,2,3,4]=>14 [5,1,6,2,4,3]=>13 [5,1,6,3,2,4]=>13 [5,1,6,3,4,2]=>11 [5,1,6,4,2,3]=>9 [5,1,6,4,3,2]=>8 [5,2,1,3,4,6]=>4 [5,2,1,3,6,4]=>7 [5,2,1,4,3,6]=>3 [5,2,1,4,6,3]=>5 [5,2,1,6,3,4]=>9 [5,2,1,6,4,3]=>8 [5,2,3,1,4,6]=>3 [5,2,3,1,6,4]=>5 [5,2,3,4,1,6]=>2 [5,2,3,4,6,1]=>3 [5,2,3,6,1,4]=>6 [5,2,3,6,4,1]=>5 [5,2,4,1,3,6]=>5 [5,2,4,1,6,3]=>8 [5,2,4,3,1,6]=>4 [5,2,4,3,6,1]=>6 [5,2,4,6,1,3]=>9 [5,2,4,6,3,1]=>8 [5,2,6,1,3,4]=>10 [5,2,6,1,4,3]=>9 [5,2,6,3,1,4]=>9 [5,2,6,3,4,1]=>7 [5,2,6,4,1,3]=>6 [5,2,6,4,3,1]=>5 [5,3,1,2,4,6]=>7 [5,3,1,2,6,4]=>12 [5,3,1,4,2,6]=>5 [5,3,1,4,6,2]=>8 [5,3,1,6,2,4]=>15 [5,3,1,6,4,2]=>13 [5,3,2,1,4,6]=>6 [5,3,2,1,6,4]=>10 [5,3,2,4,1,6]=>4 [5,3,2,4,6,1]=>6 [5,3,2,6,1,4]=>12 [5,3,2,6,4,1]=>10 [5,3,4,1,2,6]=>7 [5,3,4,1,6,2]=>11 [5,3,4,2,1,6]=>6 [5,3,4,2,6,1]=>9 [5,3,4,6,1,2]=>12 [5,3,4,6,2,1]=>11 [5,3,6,1,2,4]=>16 [5,3,6,1,4,2]=>14 [5,3,6,2,1,4]=>15 [5,3,6,2,4,1]=>12 [5,3,6,4,1,2]=>9 [5,3,6,4,2,1]=>8 [5,4,1,2,3,6]=>9 [5,4,1,2,6,3]=>15 [5,4,1,3,2,6]=>8 [5,4,1,3,6,2]=>13 [5,4,1,6,2,3]=>18 [5,4,1,6,3,2]=>17 [5,4,2,1,3,6]=>8 [5,4,2,1,6,3]=>13 [5,4,2,3,1,6]=>6 [5,4,2,3,6,1]=>9 [5,4,2,6,1,3]=>15 [5,4,2,6,3,1]=>13 [5,4,3,1,2,6]=>5 [5,4,3,1,6,2]=>8 [5,4,3,2,1,6]=>4 [5,4,3,2,6,1]=>6 [5,4,3,6,1,2]=>9 [5,4,3,6,2,1]=>8 [5,4,6,1,2,3]=>19 [5,4,6,1,3,2]=>18 [5,4,6,2,1,3]=>18 [5,4,6,2,3,1]=>15 [5,4,6,3,1,2]=>15 [5,4,6,3,2,1]=>13 [5,6,1,2,3,4]=>15 [5,6,1,2,4,3]=>14 [5,6,1,3,2,4]=>14 [5,6,1,3,4,2]=>12 [5,6,1,4,2,3]=>10 [5,6,1,4,3,2]=>9 [5,6,2,1,3,4]=>14 [5,6,2,1,4,3]=>13 [5,6,2,3,1,4]=>12 [5,6,2,3,4,1]=>9 [5,6,2,4,1,3]=>9 [5,6,2,4,3,1]=>7 [5,6,3,1,2,4]=>10 [5,6,3,1,4,2]=>9 [5,6,3,2,1,4]=>9 [5,6,3,2,4,1]=>7 [5,6,3,4,1,2]=>6 [5,6,3,4,2,1]=>5 [5,6,4,1,2,3]=>16 [5,6,4,1,3,2]=>15 [5,6,4,2,1,3]=>15 [5,6,4,2,3,1]=>12 [5,6,4,3,1,2]=>12 [5,6,4,3,2,1]=>10 [6,1,2,3,4,5]=>6 [6,1,2,3,5,4]=>5 [6,1,2,4,3,5]=>5 [6,1,2,4,5,3]=>4 [6,1,2,5,3,4]=>9 [6,1,2,5,4,3]=>8 [6,1,3,2,4,5]=>5 [6,1,3,2,5,4]=>4 [6,1,3,4,2,5]=>4 [6,1,3,4,5,2]=>3 [6,1,3,5,2,4]=>7 [6,1,3,5,4,2]=>6 [6,1,4,2,3,5]=>9 [6,1,4,2,5,3]=>7 [6,1,4,3,2,5]=>8 [6,1,4,3,5,2]=>6 [6,1,4,5,2,3]=>10 [6,1,4,5,3,2]=>9 [6,1,5,2,3,4]=>12 [6,1,5,2,4,3]=>11 [6,1,5,3,2,4]=>11 [6,1,5,3,4,2]=>9 [6,1,5,4,2,3]=>7 [6,1,5,4,3,2]=>6 [6,2,1,3,4,5]=>5 [6,2,1,3,5,4]=>4 [6,2,1,4,3,5]=>4 [6,2,1,4,5,3]=>3 [6,2,1,5,3,4]=>7 [6,2,1,5,4,3]=>6 [6,2,3,1,4,5]=>4 [6,2,3,1,5,4]=>3 [6,2,3,4,1,5]=>3 [6,2,3,4,5,1]=>2 [6,2,3,5,1,4]=>5 [6,2,3,5,4,1]=>4 [6,2,4,1,3,5]=>7 [6,2,4,1,5,3]=>5 [6,2,4,3,1,5]=>6 [6,2,4,3,5,1]=>4 [6,2,4,5,1,3]=>7 [6,2,4,5,3,1]=>6 [6,2,5,1,3,4]=>9 [6,2,5,1,4,3]=>8 [6,2,5,3,1,4]=>8 [6,2,5,3,4,1]=>6 [6,2,5,4,1,3]=>5 [6,2,5,4,3,1]=>4 [6,3,1,2,4,5]=>9 [6,3,1,2,5,4]=>7 [6,3,1,4,2,5]=>7 [6,3,1,4,5,2]=>5 [6,3,1,5,2,4]=>12 [6,3,1,5,4,2]=>10 [6,3,2,1,4,5]=>8 [6,3,2,1,5,4]=>6 [6,3,2,4,1,5]=>6 [6,3,2,4,5,1]=>4 [6,3,2,5,1,4]=>10 [6,3,2,5,4,1]=>8 [6,3,4,1,2,5]=>10 [6,3,4,1,5,2]=>7 [6,3,4,2,1,5]=>9 [6,3,4,2,5,1]=>6 [6,3,4,5,1,2]=>9 [6,3,4,5,2,1]=>8 [6,3,5,1,2,4]=>14 [6,3,5,1,4,2]=>12 [6,3,5,2,1,4]=>13 [6,3,5,2,4,1]=>10 [6,3,5,4,1,2]=>7 [6,3,5,4,2,1]=>6 [6,4,1,2,3,5]=>12 [6,4,1,2,5,3]=>9 [6,4,1,3,2,5]=>11 [6,4,1,3,5,2]=>8 [6,4,1,5,2,3]=>14 [6,4,1,5,3,2]=>13 [6,4,2,1,3,5]=>11 [6,4,2,1,5,3]=>8 [6,4,2,3,1,5]=>9 [6,4,2,3,5,1]=>6 [6,4,2,5,1,3]=>12 [6,4,2,5,3,1]=>10 [6,4,3,1,2,5]=>7 [6,4,3,1,5,2]=>5 [6,4,3,2,1,5]=>6 [6,4,3,2,5,1]=>4 [6,4,3,5,1,2]=>7 [6,4,3,5,2,1]=>6 [6,4,5,1,2,3]=>16 [6,4,5,1,3,2]=>15 [6,4,5,2,1,3]=>15 [6,4,5,2,3,1]=>12 [6,4,5,3,1,2]=>12 [6,4,5,3,2,1]=>10 [6,5,1,2,3,4]=>14 [6,5,1,2,4,3]=>13 [6,5,1,3,2,4]=>13 [6,5,1,3,4,2]=>11 [6,5,1,4,2,3]=>9 [6,5,1,4,3,2]=>8 [6,5,2,1,3,4]=>13 [6,5,2,1,4,3]=>12 [6,5,2,3,1,4]=>11 [6,5,2,3,4,1]=>8 [6,5,2,4,1,3]=>8 [6,5,2,4,3,1]=>6 [6,5,3,1,2,4]=>9 [6,5,3,1,4,2]=>8 [6,5,3,2,1,4]=>8 [6,5,3,2,4,1]=>6 [6,5,3,4,1,2]=>5 [6,5,3,4,2,1]=>4 [6,5,4,1,2,3]=>14 [6,5,4,1,3,2]=>13 [6,5,4,2,1,3]=>13 [6,5,4,2,3,1]=>10 [6,5,4,3,1,2]=>10 [6,5,4,3,2,1]=>8 [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]=>3 [1,2,3,4,7,5,6]=>3 [1,2,3,4,7,6,5]=>2 [1,2,3,5,4,6,7]=>2 [1,2,3,5,4,7,6]=>4 [1,2,3,5,6,4,7]=>3 [1,2,3,5,6,7,4]=>4 [1,2,3,5,7,4,6]=>5 [1,2,3,5,7,6,4]=>3 [1,2,3,6,4,5,7]=>3 [1,2,3,6,4,7,5]=>5 [1,2,3,6,5,4,7]=>2 [1,2,3,6,5,7,4]=>3 [1,2,3,6,7,4,5]=>6 [1,2,3,6,7,5,4]=>5 [1,2,3,7,4,5,6]=>4 [1,2,3,7,4,6,5]=>3 [1,2,3,7,5,4,6]=>3 [1,2,3,7,5,6,4]=>2 [1,2,3,7,6,4,5]=>5 [1,2,3,7,6,5,4]=>4 [1,2,4,3,5,6,7]=>2 [1,2,4,3,5,7,6]=>4 [1,2,4,3,6,5,7]=>4 [1,2,4,3,6,7,5]=>6 [1,2,4,3,7,5,6]=>6 [1,2,4,3,7,6,5]=>4 [1,2,4,5,3,6,7]=>3 [1,2,4,5,3,7,6]=>6 [1,2,4,5,6,3,7]=>4 [1,2,4,5,6,7,3]=>5 [1,2,4,5,7,3,6]=>7 [1,2,4,5,7,6,3]=>4 [1,2,4,6,3,5,7]=>5 [1,2,4,6,3,7,5]=>8 [1,2,4,6,5,3,7]=>3 [1,2,4,6,5,7,3]=>4 [1,2,4,6,7,3,5]=>9 [1,2,4,6,7,5,3]=>7 [1,2,4,7,3,5,6]=>7 [1,2,4,7,3,6,5]=>5 [1,2,4,7,5,3,6]=>5 [1,2,4,7,5,6,3]=>3 [1,2,4,7,6,3,5]=>8 [1,2,4,7,6,5,3]=>6 [1,2,5,3,4,6,7]=>3 [1,2,5,3,4,7,6]=>6 [1,2,5,3,6,4,7]=>5 [1,2,5,3,6,7,4]=>7 [1,2,5,3,7,4,6]=>8 [1,2,5,3,7,6,4]=>5 [1,2,5,4,3,6,7]=>2 [1,2,5,4,3,7,6]=>4 [1,2,5,4,6,3,7]=>3 [1,2,5,4,6,7,3]=>4 [1,2,5,4,7,3,6]=>5 [1,2,5,4,7,6,3]=>3 [1,2,5,6,3,4,7]=>6 [1,2,5,6,3,7,4]=>9 [1,2,5,6,4,3,7]=>5 [1,2,5,6,4,7,3]=>7 [1,2,5,6,7,3,4]=>10 [1,2,5,6,7,4,3]=>9 [1,2,5,7,3,4,6]=>9 [1,2,5,7,3,6,4]=>6 [1,2,5,7,4,3,6]=>8 [1,2,5,7,4,6,3]=>5 [1,2,5,7,6,3,4]=>9 [1,2,5,7,6,4,3]=>8 [1,2,6,3,4,5,7]=>4 [1,2,6,3,4,7,5]=>7 [1,2,6,3,5,4,7]=>3 [1,2,6,3,5,7,4]=>5 [1,2,6,3,7,4,5]=>9 [1,2,6,3,7,5,4]=>8 [1,2,6,4,3,5,7]=>3 [1,2,6,4,3,7,5]=>5 [1,2,6,4,5,3,7]=>2 [1,2,6,4,5,7,3]=>3 [1,2,6,4,7,3,5]=>6 [1,2,6,4,7,5,3]=>5 [1,2,6,5,3,4,7]=>5 [1,2,6,5,3,7,4]=>8 [1,2,6,5,4,3,7]=>4 [1,2,6,5,4,7,3]=>6 [1,2,6,5,7,3,4]=>9 [1,2,6,5,7,4,3]=>8 [1,2,6,7,3,4,5]=>10 [1,2,6,7,3,5,4]=>9 [1,2,6,7,4,3,5]=>9 [1,2,6,7,4,5,3]=>7 [1,2,6,7,5,3,4]=>6 [1,2,6,7,5,4,3]=>5 [1,2,7,3,4,5,6]=>5 [1,2,7,3,4,6,5]=>4 [1,2,7,3,5,4,6]=>4 [1,2,7,3,5,6,4]=>3 [1,2,7,3,6,4,5]=>7 [1,2,7,3,6,5,4]=>6 [1,2,7,4,3,5,6]=>4 [1,2,7,4,3,6,5]=>3 [1,2,7,4,5,3,6]=>3 [1,2,7,4,5,6,3]=>2 [1,2,7,4,6,3,5]=>5 [1,2,7,4,6,5,3]=>4 [1,2,7,5,3,4,6]=>7 [1,2,7,5,3,6,4]=>5 [1,2,7,5,4,3,6]=>6 [1,2,7,5,4,6,3]=>4 [1,2,7,5,6,3,4]=>7 [1,2,7,5,6,4,3]=>6 [1,2,7,6,3,4,5]=>9 [1,2,7,6,3,5,4]=>8 [1,2,7,6,4,3,5]=>8 [1,2,7,6,4,5,3]=>6 [1,2,7,6,5,3,4]=>5 [1,2,7,6,5,4,3]=>4 [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]=>6 [1,3,2,4,7,5,6]=>6 [1,3,2,4,7,6,5]=>4 [1,3,2,5,4,6,7]=>4 [1,3,2,5,4,7,6]=>8 [1,3,2,5,6,4,7]=>6 [1,3,2,5,6,7,4]=>8 [1,3,2,5,7,4,6]=>10 [1,3,2,5,7,6,4]=>6 [1,3,2,6,4,5,7]=>6 [1,3,2,6,4,7,5]=>10 [1,3,2,6,5,4,7]=>4 [1,3,2,6,5,7,4]=>6 [1,3,2,6,7,4,5]=>12 [1,3,2,6,7,5,4]=>10 [1,3,2,7,4,5,6]=>8 [1,3,2,7,4,6,5]=>6 [1,3,2,7,5,4,6]=>6 [1,3,2,7,5,6,4]=>4 [1,3,2,7,6,4,5]=>10 [1,3,2,7,6,5,4]=>8 [1,3,4,2,5,6,7]=>3 [1,3,4,2,5,7,6]=>6 [1,3,4,2,6,5,7]=>6 [1,3,4,2,6,7,5]=>9 [1,3,4,2,7,5,6]=>9 [1,3,4,2,7,6,5]=>6 [1,3,4,5,2,6,7]=>4 [1,3,4,5,2,7,6]=>8 [1,3,4,5,6,2,7]=>5 [1,3,4,5,6,7,2]=>6 [1,3,4,5,7,2,6]=>9 [1,3,4,5,7,6,2]=>5 [1,3,4,6,2,5,7]=>7 [1,3,4,6,2,7,5]=>11 [1,3,4,6,5,2,7]=>4 [1,3,4,6,5,7,2]=>5 [1,3,4,6,7,2,5]=>12 [1,3,4,6,7,5,2]=>9 [1,3,4,7,2,5,6]=>10 [1,3,4,7,2,6,5]=>7 [1,3,4,7,5,2,6]=>7 [1,3,4,7,5,6,2]=>4 [1,3,4,7,6,2,5]=>11 [1,3,4,7,6,5,2]=>8 [1,3,5,2,4,6,7]=>5 [1,3,5,2,4,7,6]=>10 [1,3,5,2,6,4,7]=>8 [1,3,5,2,6,7,4]=>11 [1,3,5,2,7,4,6]=>13 [1,3,5,2,7,6,4]=>8 [1,3,5,4,2,6,7]=>3 [1,3,5,4,2,7,6]=>6 [1,3,5,4,6,2,7]=>4 [1,3,5,4,6,7,2]=>5 [1,3,5,4,7,2,6]=>7 [1,3,5,4,7,6,2]=>4 [1,3,5,6,2,4,7]=>9 [1,3,5,6,2,7,4]=>13 [1,3,5,6,4,2,7]=>7 [1,3,5,6,4,7,2]=>9 [1,3,5,6,7,2,4]=>14 [1,3,5,6,7,4,2]=>12 [1,3,5,7,2,4,6]=>14 [1,3,5,7,2,6,4]=>9 [1,3,5,7,4,2,6]=>12 [1,3,5,7,4,6,2]=>7 [1,3,5,7,6,2,4]=>13 [1,3,5,7,6,4,2]=>11 [1,3,6,2,4,5,7]=>7 [1,3,6,2,4,7,5]=>12 [1,3,6,2,5,4,7]=>5 [1,3,6,2,5,7,4]=>8 [1,3,6,2,7,4,5]=>15 [1,3,6,2,7,5,4]=>13 [1,3,6,4,2,5,7]=>5 [1,3,6,4,2,7,5]=>8 [1,3,6,4,5,2,7]=>3 [1,3,6,4,5,7,2]=>4 [1,3,6,4,7,2,5]=>9 [1,3,6,4,7,5,2]=>7 [1,3,6,5,2,4,7]=>8 [1,3,6,5,2,7,4]=>12 [1,3,6,5,4,2,7]=>6 [1,3,6,5,4,7,2]=>8 [1,3,6,5,7,2,4]=>13 [1,3,6,5,7,4,2]=>11 [1,3,6,7,2,4,5]=>16 [1,3,6,7,2,5,4]=>14 [1,3,6,7,4,2,5]=>14 [1,3,6,7,4,5,2]=>10 [1,3,6,7,5,2,4]=>9 [1,3,6,7,5,4,2]=>7 [1,3,7,2,4,5,6]=>9 [1,3,7,2,4,6,5]=>7 [1,3,7,2,5,4,6]=>7 [1,3,7,2,5,6,4]=>5 [1,3,7,2,6,4,5]=>12 [1,3,7,2,6,5,4]=>10 [1,3,7,4,2,5,6]=>7 [1,3,7,4,2,6,5]=>5 [1,3,7,4,5,2,6]=>5 [1,3,7,4,5,6,2]=>3 [1,3,7,4,6,2,5]=>8 [1,3,7,4,6,5,2]=>6 [1,3,7,5,2,4,6]=>12 [1,3,7,5,2,6,4]=>8 [1,3,7,5,4,2,6]=>10 [1,3,7,5,4,6,2]=>6 [1,3,7,5,6,2,4]=>11 [1,3,7,5,6,4,2]=>9 [1,3,7,6,2,4,5]=>15 [1,3,7,6,2,5,4]=>13 [1,3,7,6,4,2,5]=>13 [1,3,7,6,4,5,2]=>9 [1,3,7,6,5,2,4]=>8 [1,3,7,6,5,4,2]=>6 [1,4,2,3,5,6,7]=>3 [1,4,2,3,5,7,6]=>6 [1,4,2,3,6,5,7]=>6 [1,4,2,3,6,7,5]=>9 [1,4,2,3,7,5,6]=>9 [1,4,2,3,7,6,5]=>6 [1,4,2,5,3,6,7]=>5 [1,4,2,5,3,7,6]=>10 [1,4,2,5,6,3,7]=>7 [1,4,2,5,6,7,3]=>9 [1,4,2,5,7,3,6]=>12 [1,4,2,5,7,6,3]=>7 [1,4,2,6,3,5,7]=>8 [1,4,2,6,3,7,5]=>13 [1,4,2,6,5,3,7]=>5 [1,4,2,6,5,7,3]=>7 [1,4,2,6,7,3,5]=>15 [1,4,2,6,7,5,3]=>12 [1,4,2,7,3,5,6]=>11 [1,4,2,7,3,6,5]=>8 [1,4,2,7,5,3,6]=>8 [1,4,2,7,5,6,3]=>5 [1,4,2,7,6,3,5]=>13 [1,4,2,7,6,5,3]=>10 [1,4,3,2,5,6,7]=>2 [1,4,3,2,5,7,6]=>4 [1,4,3,2,6,5,7]=>4 [1,4,3,2,6,7,5]=>6 [1,4,3,2,7,5,6]=>6 [1,4,3,2,7,6,5]=>4 [1,4,3,5,2,6,7]=>3 [1,4,3,5,2,7,6]=>6 [1,4,3,5,6,2,7]=>4 [1,4,3,5,6,7,2]=>5 [1,4,3,5,7,2,6]=>7 [1,4,3,5,7,6,2]=>4 [1,4,3,6,2,5,7]=>5 [1,4,3,6,2,7,5]=>8 [1,4,3,6,5,2,7]=>3 [1,4,3,6,5,7,2]=>4 [1,4,3,6,7,2,5]=>9 [1,4,3,6,7,5,2]=>7 [1,4,3,7,2,5,6]=>7 [1,4,3,7,2,6,5]=>5 [1,4,3,7,5,2,6]=>5 [1,4,3,7,5,6,2]=>3 [1,4,3,7,6,2,5]=>8 [1,4,3,7,6,5,2]=>6 [1,4,5,2,3,6,7]=>6 [1,4,5,2,3,7,6]=>12 [1,4,5,2,6,3,7]=>9 [1,4,5,2,6,7,3]=>12 [1,4,5,2,7,3,6]=>15 [1,4,5,2,7,6,3]=>9 [1,4,5,3,2,6,7]=>5 [1,4,5,3,2,7,6]=>10 [1,4,5,3,6,2,7]=>7 [1,4,5,3,6,7,2]=>9 [1,4,5,3,7,2,6]=>12 [1,4,5,3,7,6,2]=>7 [1,4,5,6,2,3,7]=>10 [1,4,5,6,2,7,3]=>14 [1,4,5,6,3,2,7]=>9 [1,4,5,6,3,7,2]=>12 [1,4,5,6,7,2,3]=>15 [1,4,5,6,7,3,2]=>14 [1,4,5,7,2,3,6]=>16 [1,4,5,7,2,6,3]=>10 [1,4,5,7,3,2,6]=>15 [1,4,5,7,3,6,2]=>9 [1,4,5,7,6,2,3]=>14 [1,4,5,7,6,3,2]=>13 [1,4,6,2,3,5,7]=>9 [1,4,6,2,3,7,5]=>15 [1,4,6,2,5,3,7]=>6 [1,4,6,2,5,7,3]=>9 [1,4,6,2,7,3,5]=>18 [1,4,6,2,7,5,3]=>15 [1,4,6,3,2,5,7]=>8 [1,4,6,3,2,7,5]=>13 [1,4,6,3,5,2,7]=>5 [1,4,6,3,5,7,2]=>7 [1,4,6,3,7,2,5]=>15 [1,4,6,3,7,5,2]=>12 [1,4,6,5,2,3,7]=>9 [1,4,6,5,2,7,3]=>13 [1,4,6,5,3,2,7]=>8
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Description
The number of bases of the positroid corresponding to the permutation, with all fixed points counterclockwise.
References
[1] Ardila, F., Rincón, F., Williams, L. Positroids and non-crossing partitions arXiv:1308.2698
Code
def i_less(a, b, i):
    """
    Return whether a < b for i < i+1 < ... < n < 1 < ... < i-1.
    """
    if min(a, b) >= i or max(a, b) < i:
        return a < b
    return a >= i > b

def Grassmann_necklace(pi):
    """
    Return the Grassmann necklace corresponding to pi.

    sage: pi = Permutation([3,4,2,1])
    sage: Grassmann_necklace(pi)
    [{1, 2}, {2, 4}, {3, 4}, {1, 4}]
    """
    pi = Permutation(pi)
    N = []
    n = len(pi)
    for i in range(1,n+1):
        iWEX = [j for j in range(1,n+1) if j == pi(j) or i_less(j, pi(j), i)]
        N.append(set(iWEX))
    return N

def Gale_less(S, T, i):
    from functools import cmp_to_key
    key = cmp_to_key(lambda a,b: 0 if a == b else int(-1) if i_less(a,b,i) else int(1))
    S_sorted = sorted(S, key=key)
    T_sorted = sorted(T, key=key)
    return all(s == t or i_less(s, t, i) for s,t in zip(S_sorted, T_sorted))

def positroid(N):
    """
    Return the positroid corresponding to the Grassmann necklace.

    sage: pi = Permutation([3,4,2,1])
    sage: N = Grassmann_necklace(pi)
    sage: positroid(N)
    [{1, 2}, {1, 3}, {1, 4}, {2, 4}, {3, 4}]

    sage: [set([len(positroid(Grassmann_necklace(p))) for p in orbit(pi)]) for pi in Permutations(4)]


    """
    n = len(N)
    d = len(N[0])
    result = []
    for B in Subsets(range(1,n+1), d):
        if all(B == N[j] or Gale_less(N[j], B, j+1) for j in range(n)):
            result.append(B)

    return result

def statistic(pi):
    return len(positroid(Grassmann_necklace(pi)))

Created
Aug 12, 2019 at 16:34 by Martin Rubey
Updated
Mar 09, 2023 at 15:54 by Tilman Möller