edit this statistic or download as text // json
Identifier
Values
=>
[+]=>0 [-]=>0 [+,+]=>0 [-,+]=>1 [+,-]=>1 [-,-]=>0 [2,1]=>0 [+,+,+]=>0 [-,+,+]=>2 [+,-,+]=>2 [+,+,-]=>2 [-,-,+]=>2 [-,+,-]=>2 [+,-,-]=>2 [-,-,-]=>0 [+,3,2]=>1 [-,3,2]=>1 [2,1,+]=>1 [2,1,-]=>1 [2,3,1]=>0 [3,1,2]=>0 [3,+,1]=>1 [3,-,1]=>1 [+,+,+,+]=>0 [-,+,+,+]=>3 [+,-,+,+]=>3 [+,+,-,+]=>3 [+,+,+,-]=>3 [-,-,+,+]=>4 [-,+,-,+]=>4 [-,+,+,-]=>4 [+,-,-,+]=>4 [+,-,+,-]=>4 [+,+,-,-]=>4 [-,-,-,+]=>3 [-,-,+,-]=>3 [-,+,-,-]=>3 [+,-,-,-]=>3 [-,-,-,-]=>0 [+,+,4,3]=>2 [-,+,4,3]=>3 [+,-,4,3]=>3 [-,-,4,3]=>2 [+,3,2,+]=>2 [-,3,2,+]=>3 [+,3,2,-]=>3 [-,3,2,-]=>2 [+,3,4,2]=>2 [-,3,4,2]=>1 [+,4,2,3]=>1 [-,4,2,3]=>2 [+,4,+,2]=>2 [-,4,+,2]=>3 [+,4,-,2]=>3 [-,4,-,2]=>2 [2,1,+,+]=>2 [2,1,-,+]=>3 [2,1,+,-]=>3 [2,1,-,-]=>2 [2,1,4,3]=>2 [2,3,1,+]=>2 [2,3,1,-]=>1 [2,3,4,1]=>0 [2,4,1,3]=>1 [2,4,+,1]=>2 [2,4,-,1]=>1 [3,1,2,+]=>1 [3,1,2,-]=>2 [3,1,4,2]=>1 [3,+,1,+]=>2 [3,-,1,+]=>3 [3,+,1,-]=>3 [3,-,1,-]=>2 [3,+,4,1]=>2 [3,-,4,1]=>1 [3,4,1,2]=>0 [3,4,2,1]=>1 [4,1,2,3]=>0 [4,1,+,2]=>1 [4,1,-,2]=>2 [4,+,1,3]=>1 [4,-,1,3]=>2 [4,+,+,1]=>2 [4,-,+,1]=>3 [4,+,-,1]=>3 [4,-,-,1]=>2 [4,3,1,2]=>1 [4,3,2,1]=>2 [+,+,+,+,+]=>0 [-,+,+,+,+]=>4 [+,-,+,+,+]=>4 [+,+,-,+,+]=>4 [+,+,+,-,+]=>4 [+,+,+,+,-]=>4 [-,-,+,+,+]=>6 [-,+,-,+,+]=>6 [-,+,+,-,+]=>6 [-,+,+,+,-]=>6 [+,-,-,+,+]=>6 [+,-,+,-,+]=>6 [+,-,+,+,-]=>6 [+,+,-,-,+]=>6 [+,+,-,+,-]=>6 [+,+,+,-,-]=>6 [-,-,-,+,+]=>6 [-,-,+,-,+]=>6 [-,-,+,+,-]=>6 [-,+,-,-,+]=>6 [-,+,-,+,-]=>6 [-,+,+,-,-]=>6 [+,-,-,-,+]=>6 [+,-,-,+,-]=>6 [+,-,+,-,-]=>6 [+,+,-,-,-]=>6 [-,-,-,-,+]=>4 [-,-,-,+,-]=>4 [-,-,+,-,-]=>4 [-,+,-,-,-]=>4 [+,-,-,-,-]=>4 [-,-,-,-,-]=>0 [+,+,+,5,4]=>3 [-,+,+,5,4]=>5 [+,-,+,5,4]=>5 [+,+,-,5,4]=>5 [-,-,+,5,4]=>5 [-,+,-,5,4]=>5 [+,-,-,5,4]=>5 [-,-,-,5,4]=>3 [+,+,4,3,+]=>3 [-,+,4,3,+]=>5 [+,-,4,3,+]=>5 [+,+,4,3,-]=>5 [-,-,4,3,+]=>5 [-,+,4,3,-]=>5 [+,-,4,3,-]=>5 [-,-,4,3,-]=>3 [+,+,4,5,3]=>4 [-,+,4,5,3]=>4 [+,-,4,5,3]=>4 [-,-,4,5,3]=>2 [+,+,5,3,4]=>2 [-,+,5,3,4]=>4 [+,-,5,3,4]=>4 [-,-,5,3,4]=>4 [+,+,5,+,3]=>3 [-,+,5,+,3]=>5 [+,-,5,+,3]=>5 [+,+,5,-,3]=>5 [-,-,5,+,3]=>5 [-,+,5,-,3]=>5 [+,-,5,-,3]=>5 [-,-,5,-,3]=>3 [+,3,2,+,+]=>3 [-,3,2,+,+]=>5 [+,3,2,-,+]=>5 [+,3,2,+,-]=>5 [-,3,2,-,+]=>5 [-,3,2,+,-]=>5 [+,3,2,-,-]=>5 [-,3,2,-,-]=>3 [+,3,2,5,4]=>4 [-,3,2,5,4]=>4 [+,3,4,2,+]=>4 [-,3,4,2,+]=>4 [+,3,4,2,-]=>4 [-,3,4,2,-]=>2 [+,3,4,5,2]=>3 [-,3,4,5,2]=>1 [+,3,5,2,4]=>3 [-,3,5,2,4]=>3 [+,3,5,+,2]=>4 [-,3,5,+,2]=>4 [+,3,5,-,2]=>4 [-,3,5,-,2]=>2 [+,4,2,3,+]=>2 [-,4,2,3,+]=>4 [+,4,2,3,-]=>4 [-,4,2,3,-]=>4 [+,4,2,5,3]=>3 [-,4,2,5,3]=>3 [+,4,+,2,+]=>3 [-,4,+,2,+]=>5 [+,4,-,2,+]=>5 [+,4,+,2,-]=>5 [-,4,-,2,+]=>5 [-,4,+,2,-]=>5 [+,4,-,2,-]=>5 [-,4,-,2,-]=>3 [+,4,+,5,2]=>4 [-,4,+,5,2]=>4 [+,4,-,5,2]=>4 [-,4,-,5,2]=>2 [+,4,5,2,3]=>2 [-,4,5,2,3]=>2 [+,4,5,3,2]=>3 [-,4,5,3,2]=>3 [+,5,2,3,4]=>1 [-,5,2,3,4]=>3 [+,5,2,+,3]=>2 [-,5,2,+,3]=>4 [+,5,2,-,3]=>4 [-,5,2,-,3]=>4 [+,5,+,2,4]=>2 [-,5,+,2,4]=>4 [+,5,-,2,4]=>4 [-,5,-,2,4]=>4 [+,5,+,+,2]=>3 [-,5,+,+,2]=>5 [+,5,-,+,2]=>5 [+,5,+,-,2]=>5 [-,5,-,+,2]=>5 [-,5,+,-,2]=>5 [+,5,-,-,2]=>5 [-,5,-,-,2]=>3 [+,5,4,2,3]=>3 [-,5,4,2,3]=>3 [+,5,4,3,2]=>4 [-,5,4,3,2]=>4 [2,1,+,+,+]=>3 [2,1,-,+,+]=>5 [2,1,+,-,+]=>5 [2,1,+,+,-]=>5 [2,1,-,-,+]=>5 [2,1,-,+,-]=>5 [2,1,+,-,-]=>5 [2,1,-,-,-]=>3 [2,1,+,5,4]=>4 [2,1,-,5,4]=>4 [2,1,4,3,+]=>4 [2,1,4,3,-]=>4 [2,1,4,5,3]=>3 [2,1,5,3,4]=>3 [2,1,5,+,3]=>4 [2,1,5,-,3]=>4 [2,3,1,+,+]=>4 [2,3,1,-,+]=>4 [2,3,1,+,-]=>4 [2,3,1,-,-]=>2 [2,3,1,5,4]=>3 [2,3,4,1,+]=>3 [2,3,4,1,-]=>1 [2,3,4,5,1]=>0 [2,3,5,1,4]=>2 [2,3,5,+,1]=>3 [2,3,5,-,1]=>1 [2,4,1,3,+]=>3 [2,4,1,3,-]=>3 [2,4,1,5,3]=>2 [2,4,+,1,+]=>4 [2,4,-,1,+]=>4 [2,4,+,1,-]=>4 [2,4,-,1,-]=>2 [2,4,+,5,1]=>3 [2,4,-,5,1]=>1 [2,4,5,1,3]=>1 [2,4,5,3,1]=>2 [2,5,1,3,4]=>2 [2,5,1,+,3]=>3 [2,5,1,-,3]=>3 [2,5,+,1,4]=>3 [2,5,-,1,4]=>3 [2,5,+,+,1]=>4 [2,5,-,+,1]=>4 [2,5,+,-,1]=>4 [2,5,-,-,1]=>2 [2,5,4,1,3]=>2 [2,5,4,3,1]=>3 [3,1,2,+,+]=>2 [3,1,2,-,+]=>4 [3,1,2,+,-]=>4 [3,1,2,-,-]=>4 [3,1,2,5,4]=>3 [3,1,4,2,+]=>3 [3,1,4,2,-]=>3 [3,1,4,5,2]=>2 [3,1,5,2,4]=>2 [3,1,5,+,2]=>3 [3,1,5,-,2]=>3 [3,+,1,+,+]=>3 [3,-,1,+,+]=>5 [3,+,1,-,+]=>5 [3,+,1,+,-]=>5 [3,-,1,-,+]=>5 [3,-,1,+,-]=>5 [3,+,1,-,-]=>5 [3,-,1,-,-]=>3 [3,+,1,5,4]=>4 [3,-,1,5,4]=>4 [3,+,4,1,+]=>4 [3,-,4,1,+]=>4 [3,+,4,1,-]=>4 [3,-,4,1,-]=>2 [3,+,4,5,1]=>3 [3,-,4,5,1]=>1 [3,+,5,1,4]=>3 [3,-,5,1,4]=>3 [3,+,5,+,1]=>4 [3,-,5,+,1]=>4 [3,+,5,-,1]=>4 [3,-,5,-,1]=>2 [3,4,1,2,+]=>2 [3,4,1,2,-]=>2 [3,4,1,5,2]=>1 [3,4,2,1,+]=>3 [3,4,2,1,-]=>3 [3,4,2,5,1]=>2 [3,4,5,1,2]=>0 [3,4,5,2,1]=>1 [3,5,1,2,4]=>1 [3,5,1,+,2]=>2 [3,5,1,-,2]=>2 [3,5,2,1,4]=>2 [3,5,2,+,1]=>3 [3,5,2,-,1]=>3 [3,5,4,1,2]=>1 [3,5,4,2,1]=>2 [4,1,2,3,+]=>1 [4,1,2,3,-]=>3 [4,1,2,5,3]=>2 [4,1,+,2,+]=>2 [4,1,-,2,+]=>4 [4,1,+,2,-]=>4 [4,1,-,2,-]=>4 [4,1,+,5,2]=>3 [4,1,-,5,2]=>3 [4,1,5,2,3]=>1 [4,1,5,3,2]=>2 [4,+,1,3,+]=>2 [4,-,1,3,+]=>4 [4,+,1,3,-]=>4 [4,-,1,3,-]=>4 [4,+,1,5,3]=>3 [4,-,1,5,3]=>3 [4,+,+,1,+]=>3 [4,-,+,1,+]=>5 [4,+,-,1,+]=>5 [4,+,+,1,-]=>5 [4,-,-,1,+]=>5 [4,-,+,1,-]=>5 [4,+,-,1,-]=>5 [4,-,-,1,-]=>3 [4,+,+,5,1]=>4 [4,-,+,5,1]=>4 [4,+,-,5,1]=>4 [4,-,-,5,1]=>2 [4,+,5,1,3]=>2 [4,-,5,1,3]=>2 [4,+,5,3,1]=>3 [4,-,5,3,1]=>3 [4,3,1,2,+]=>3 [4,3,1,2,-]=>3 [4,3,1,5,2]=>2 [4,3,2,1,+]=>4 [4,3,2,1,-]=>4 [4,3,2,5,1]=>3 [4,3,5,1,2]=>1 [4,3,5,2,1]=>2 [4,5,1,2,3]=>0 [4,5,1,3,2]=>1 [4,5,2,1,3]=>1 [4,5,2,3,1]=>2 [4,5,+,1,2]=>2 [4,5,-,1,2]=>2 [4,5,+,2,1]=>3 [4,5,-,2,1]=>3 [5,1,2,3,4]=>0 [5,1,2,+,3]=>1 [5,1,2,-,3]=>3 [5,1,+,2,4]=>1 [5,1,-,2,4]=>3 [5,1,+,+,2]=>2 [5,1,-,+,2]=>4 [5,1,+,-,2]=>4 [5,1,-,-,2]=>4 [5,1,4,2,3]=>2 [5,1,4,3,2]=>3 [5,+,1,3,4]=>1 [5,-,1,3,4]=>3 [5,+,1,+,3]=>2 [5,-,1,+,3]=>4 [5,+,1,-,3]=>4 [5,-,1,-,3]=>4 [5,+,+,1,4]=>2 [5,-,+,1,4]=>4 [5,+,-,1,4]=>4 [5,-,-,1,4]=>4 [5,+,+,+,1]=>3 [5,-,+,+,1]=>5 [5,+,-,+,1]=>5 [5,+,+,-,1]=>5 [5,-,-,+,1]=>5 [5,-,+,-,1]=>5 [5,+,-,-,1]=>5 [5,-,-,-,1]=>3 [5,+,4,1,3]=>3 [5,-,4,1,3]=>3 [5,+,4,3,1]=>4 [5,-,4,3,1]=>4 [5,3,1,2,4]=>2 [5,3,1,+,2]=>3 [5,3,1,-,2]=>3 [5,3,2,1,4]=>3 [5,3,2,+,1]=>4 [5,3,2,-,1]=>4 [5,3,4,1,2]=>2 [5,3,4,2,1]=>3 [5,4,1,2,3]=>1 [5,4,1,3,2]=>2 [5,4,2,1,3]=>2 [5,4,2,3,1]=>3 [5,4,+,1,2]=>3 [5,4,-,1,2]=>3 [5,4,+,2,1]=>4 [5,4,-,2,1]=>4 [+,+,+,+,+,+]=>0 [-,+,+,+,+,+]=>5 [+,-,+,+,+,+]=>5 [+,+,-,+,+,+]=>5 [+,+,+,-,+,+]=>5 [+,+,+,+,-,+]=>5 [+,+,+,+,+,-]=>5 [-,-,+,+,+,+]=>8 [-,+,-,+,+,+]=>8 [-,+,+,-,+,+]=>8 [-,+,+,+,-,+]=>8 [-,+,+,+,+,-]=>8 [+,-,-,+,+,+]=>8 [+,-,+,-,+,+]=>8 [+,-,+,+,-,+]=>8 [+,-,+,+,+,-]=>8 [+,+,-,-,+,+]=>8 [+,+,-,+,-,+]=>8 [+,+,-,+,+,-]=>8 [+,+,+,-,-,+]=>8 [+,+,+,-,+,-]=>8 [+,+,+,+,-,-]=>8 [-,-,-,+,+,+]=>9 [-,-,+,-,+,+]=>9 [-,-,+,+,-,+]=>9 [-,-,+,+,+,-]=>9 [-,+,-,-,+,+]=>9 [-,+,-,+,-,+]=>9 [-,+,-,+,+,-]=>9 [-,+,+,-,-,+]=>9 [-,+,+,-,+,-]=>9 [-,+,+,+,-,-]=>9 [+,-,-,-,+,+]=>9 [+,-,-,+,-,+]=>9 [+,-,-,+,+,-]=>9 [+,-,+,-,-,+]=>9 [+,-,+,-,+,-]=>9 [+,-,+,+,-,-]=>9 [+,+,-,-,-,+]=>9 [+,+,-,-,+,-]=>9 [+,+,-,+,-,-]=>9 [+,+,+,-,-,-]=>9 [-,-,-,-,+,+]=>8 [-,-,-,+,-,+]=>8 [-,-,-,+,+,-]=>8 [-,-,+,-,-,+]=>8 [-,-,+,-,+,-]=>8 [-,-,+,+,-,-]=>8 [-,+,-,-,-,+]=>8 [-,+,-,-,+,-]=>8 [-,+,-,+,-,-]=>8 [-,+,+,-,-,-]=>8 [+,-,-,-,-,+]=>8 [+,-,-,-,+,-]=>8 [+,-,-,+,-,-]=>8 [+,-,+,-,-,-]=>8 [+,+,-,-,-,-]=>8 [-,-,-,-,-,+]=>5 [-,-,-,-,+,-]=>5 [-,-,-,+,-,-]=>5 [-,-,+,-,-,-]=>5 [-,+,-,-,-,-]=>5 [+,-,-,-,-,-]=>5 [-,-,-,-,-,-]=>0 [+,+,+,+,6,5]=>4 [-,+,+,+,6,5]=>7 [+,-,+,+,6,5]=>7 [+,+,-,+,6,5]=>7 [+,+,+,-,6,5]=>7 [-,-,+,+,6,5]=>8 [-,+,-,+,6,5]=>8 [-,+,+,-,6,5]=>8 [+,-,-,+,6,5]=>8 [+,-,+,-,6,5]=>8 [+,+,-,-,6,5]=>8 [-,-,-,+,6,5]=>7 [-,-,+,-,6,5]=>7 [-,+,-,-,6,5]=>7 [+,-,-,-,6,5]=>7 [-,-,-,-,6,5]=>4 [+,+,+,5,4,+]=>4 [-,+,+,5,4,+]=>7 [+,-,+,5,4,+]=>7 [+,+,-,5,4,+]=>7 [+,+,+,5,4,-]=>7 [-,-,+,5,4,+]=>8 [-,+,-,5,4,+]=>8 [-,+,+,5,4,-]=>8 [+,-,-,5,4,+]=>8 [+,-,+,5,4,-]=>8 [+,+,-,5,4,-]=>8 [-,-,-,5,4,+]=>7 [-,-,+,5,4,-]=>7 [-,+,-,5,4,-]=>7 [+,-,-,5,4,-]=>7 [-,-,-,5,4,-]=>4 [+,+,+,5,6,4]=>6 [-,+,+,5,6,4]=>7 [+,-,+,5,6,4]=>7 [+,+,-,5,6,4]=>7 [-,-,+,5,6,4]=>6 [-,+,-,5,6,4]=>6 [+,-,-,5,6,4]=>6 [-,-,-,5,6,4]=>3 [+,+,+,6,4,5]=>3 [-,+,+,6,4,5]=>6 [+,-,+,6,4,5]=>6 [+,+,-,6,4,5]=>6 [-,-,+,6,4,5]=>7 [-,+,-,6,4,5]=>7 [+,-,-,6,4,5]=>7 [-,-,-,6,4,5]=>6 [+,+,+,6,+,4]=>4 [-,+,+,6,+,4]=>7 [+,-,+,6,+,4]=>7 [+,+,-,6,+,4]=>7 [+,+,+,6,-,4]=>7 [-,-,+,6,+,4]=>8 [-,+,-,6,+,4]=>8 [-,+,+,6,-,4]=>8 [+,-,-,6,+,4]=>8 [+,-,+,6,-,4]=>8 [+,+,-,6,-,4]=>8 [-,-,-,6,+,4]=>7 [-,-,+,6,-,4]=>7 [-,+,-,6,-,4]=>7 [+,-,-,6,-,4]=>7 [-,-,-,6,-,4]=>4 [+,+,4,3,+,+]=>4 [-,+,4,3,+,+]=>7 [+,-,4,3,+,+]=>7 [+,+,4,3,-,+]=>7 [+,+,4,3,+,-]=>7 [-,-,4,3,+,+]=>8 [-,+,4,3,-,+]=>8 [-,+,4,3,+,-]=>8 [+,-,4,3,-,+]=>8 [+,-,4,3,+,-]=>8 [+,+,4,3,-,-]=>8 [-,-,4,3,-,+]=>7 [-,-,4,3,+,-]=>7 [-,+,4,3,-,-]=>7 [+,-,4,3,-,-]=>7 [-,-,4,3,-,-]=>4 [+,+,4,3,6,5]=>6 [-,+,4,3,6,5]=>7 [+,-,4,3,6,5]=>7 [-,-,4,3,6,5]=>6 [+,+,4,5,3,+]=>6 [-,+,4,5,3,+]=>7 [+,-,4,5,3,+]=>7 [+,+,4,5,3,-]=>7 [-,-,4,5,3,+]=>6 [-,+,4,5,3,-]=>6 [+,-,4,5,3,-]=>6 [-,-,4,5,3,-]=>3 [+,+,4,5,6,3]=>6 [-,+,4,5,6,3]=>5 [+,-,4,5,6,3]=>5 [-,-,4,5,6,3]=>2 [+,+,4,6,3,5]=>5 [-,+,4,6,3,5]=>6 [+,-,4,6,3,5]=>6 [-,-,4,6,3,5]=>5 [+,+,4,6,+,3]=>6 [-,+,4,6,+,3]=>7 [+,-,4,6,+,3]=>7 [+,+,4,6,-,3]=>7 [-,-,4,6,+,3]=>6 [-,+,4,6,-,3]=>6 [+,-,4,6,-,3]=>6 [-,-,4,6,-,3]=>3 [+,+,5,3,4,+]=>3 [-,+,5,3,4,+]=>6 [+,-,5,3,4,+]=>6 [+,+,5,3,4,-]=>6 [-,-,5,3,4,+]=>7 [-,+,5,3,4,-]=>7 [+,-,5,3,4,-]=>7 [-,-,5,3,4,-]=>6 [+,+,5,3,6,4]=>5 [-,+,5,3,6,4]=>6 [+,-,5,3,6,4]=>6 [-,-,5,3,6,4]=>5 [+,+,5,+,3,+]=>4 [-,+,5,+,3,+]=>7 [+,-,5,+,3,+]=>7 [+,+,5,-,3,+]=>7 [+,+,5,+,3,-]=>7 [-,-,5,+,3,+]=>8 [-,+,5,-,3,+]=>8 [-,+,5,+,3,-]=>8 [+,-,5,-,3,+]=>8 [+,-,5,+,3,-]=>8 [+,+,5,-,3,-]=>8 [-,-,5,-,3,+]=>7 [-,-,5,+,3,-]=>7 [-,+,5,-,3,-]=>7 [+,-,5,-,3,-]=>7 [-,-,5,-,3,-]=>4 [+,+,5,+,6,3]=>6 [-,+,5,+,6,3]=>7 [+,-,5,+,6,3]=>7 [+,+,5,-,6,3]=>7 [-,-,5,+,6,3]=>6 [-,+,5,-,6,3]=>6 [+,-,5,-,6,3]=>6 [-,-,5,-,6,3]=>3 [+,+,5,6,3,4]=>4 [-,+,5,6,3,4]=>5 [+,-,5,6,3,4]=>5 [-,-,5,6,3,4]=>4 [+,+,5,6,4,3]=>5 [-,+,5,6,4,3]=>6 [+,-,5,6,4,3]=>6 [-,-,5,6,4,3]=>5 [+,+,6,3,4,5]=>2 [-,+,6,3,4,5]=>5 [+,-,6,3,4,5]=>5 [-,-,6,3,4,5]=>6 [+,+,6,3,+,4]=>3 [-,+,6,3,+,4]=>6 [+,-,6,3,+,4]=>6 [+,+,6,3,-,4]=>6 [-,-,6,3,+,4]=>7 [-,+,6,3,-,4]=>7 [+,-,6,3,-,4]=>7 [-,-,6,3,-,4]=>6 [+,+,6,+,3,5]=>3 [-,+,6,+,3,5]=>6 [+,-,6,+,3,5]=>6 [+,+,6,-,3,5]=>6 [-,-,6,+,3,5]=>7 [-,+,6,-,3,5]=>7 [+,-,6,-,3,5]=>7 [-,-,6,-,3,5]=>6 [+,+,6,+,+,3]=>4 [-,+,6,+,+,3]=>7 [+,-,6,+,+,3]=>7 [+,+,6,-,+,3]=>7 [+,+,6,+,-,3]=>7 [-,-,6,+,+,3]=>8 [-,+,6,-,+,3]=>8 [-,+,6,+,-,3]=>8 [+,-,6,-,+,3]=>8 [+,-,6,+,-,3]=>8 [+,+,6,-,-,3]=>8 [-,-,6,-,+,3]=>7 [-,-,6,+,-,3]=>7 [-,+,6,-,-,3]=>7 [+,-,6,-,-,3]=>7 [-,-,6,-,-,3]=>4 [+,+,6,5,3,4]=>5 [-,+,6,5,3,4]=>6 [+,-,6,5,3,4]=>6 [-,-,6,5,3,4]=>5 [+,+,6,5,4,3]=>6 [-,+,6,5,4,3]=>7 [+,-,6,5,4,3]=>7 [-,-,6,5,4,3]=>6 [+,3,2,+,+,+]=>4 [-,3,2,+,+,+]=>7 [+,3,2,-,+,+]=>7 [+,3,2,+,-,+]=>7 [+,3,2,+,+,-]=>7 [-,3,2,-,+,+]=>8 [-,3,2,+,-,+]=>8 [-,3,2,+,+,-]=>8 [+,3,2,-,-,+]=>8 [+,3,2,-,+,-]=>8 [+,3,2,+,-,-]=>8 [-,3,2,-,-,+]=>7 [-,3,2,-,+,-]=>7 [-,3,2,+,-,-]=>7 [+,3,2,-,-,-]=>7 [-,3,2,-,-,-]=>4 [+,3,2,+,6,5]=>6 [-,3,2,+,6,5]=>7 [+,3,2,-,6,5]=>7 [-,3,2,-,6,5]=>6 [+,3,2,5,4,+]=>6 [-,3,2,5,4,+]=>7 [+,3,2,5,4,-]=>7 [-,3,2,5,4,-]=>6 [+,3,2,5,6,4]=>6 [-,3,2,5,6,4]=>5 [+,3,2,6,4,5]=>5 [-,3,2,6,4,5]=>6 [+,3,2,6,+,4]=>6 [-,3,2,6,+,4]=>7 [+,3,2,6,-,4]=>7 [-,3,2,6,-,4]=>6 [+,3,4,2,+,+]=>6 [-,3,4,2,+,+]=>7 [+,3,4,2,-,+]=>7 [+,3,4,2,+,-]=>7 [-,3,4,2,-,+]=>6 [-,3,4,2,+,-]=>6 [+,3,4,2,-,-]=>6 [-,3,4,2,-,-]=>3 [+,3,4,2,6,5]=>6 [-,3,4,2,6,5]=>5 [+,3,4,5,2,+]=>6 [-,3,4,5,2,+]=>5 [+,3,4,5,2,-]=>5 [-,3,4,5,2,-]=>2 [+,3,4,5,6,2]=>4 [-,3,4,5,6,2]=>1 [+,3,4,6,2,5]=>5 [-,3,4,6,2,5]=>4 [+,3,4,6,+,2]=>6 [-,3,4,6,+,2]=>5 [+,3,4,6,-,2]=>5 [-,3,4,6,-,2]=>2 [+,3,5,2,4,+]=>5 [-,3,5,2,4,+]=>6 [+,3,5,2,4,-]=>6 [-,3,5,2,4,-]=>5 [+,3,5,2,6,4]=>5 [-,3,5,2,6,4]=>4 [+,3,5,+,2,+]=>6 [-,3,5,+,2,+]=>7 [+,3,5,-,2,+]=>7 [+,3,5,+,2,-]=>7 [-,3,5,-,2,+]=>6 [-,3,5,+,2,-]=>6 [+,3,5,-,2,-]=>6 [-,3,5,-,2,-]=>3 [+,3,5,+,6,2]=>6 [-,3,5,+,6,2]=>5 [+,3,5,-,6,2]=>5 [-,3,5,-,6,2]=>2 [+,3,5,6,2,4]=>4 [-,3,5,6,2,4]=>3 [+,3,5,6,4,2]=>5 [-,3,5,6,4,2]=>4 [+,3,6,2,4,5]=>4 [-,3,6,2,4,5]=>5 [+,3,6,2,+,4]=>5 [-,3,6,2,+,4]=>6 [+,3,6,2,-,4]=>6 [-,3,6,2,-,4]=>5 [+,3,6,+,2,5]=>5 [-,3,6,+,2,5]=>6 [+,3,6,-,2,5]=>6 [-,3,6,-,2,5]=>5 [+,3,6,+,+,2]=>6 [-,3,6,+,+,2]=>7 [+,3,6,-,+,2]=>7 [+,3,6,+,-,2]=>7 [-,3,6,-,+,2]=>6 [-,3,6,+,-,2]=>6 [+,3,6,-,-,2]=>6 [-,3,6,-,-,2]=>3 [+,3,6,5,2,4]=>5 [-,3,6,5,2,4]=>4 [+,3,6,5,4,2]=>6 [-,3,6,5,4,2]=>5 [+,4,2,3,+,+]=>3 [-,4,2,3,+,+]=>6 [+,4,2,3,-,+]=>6 [+,4,2,3,+,-]=>6 [-,4,2,3,-,+]=>7 [-,4,2,3,+,-]=>7 [+,4,2,3,-,-]=>7 [-,4,2,3,-,-]=>6 [+,4,2,3,6,5]=>5 [-,4,2,3,6,5]=>6 [+,4,2,5,3,+]=>5 [-,4,2,5,3,+]=>6 [+,4,2,5,3,-]=>6 [-,4,2,5,3,-]=>5 [+,4,2,5,6,3]=>5 [-,4,2,5,6,3]=>4 [+,4,2,6,3,5]=>4 [-,4,2,6,3,5]=>5 [+,4,2,6,+,3]=>5 [-,4,2,6,+,3]=>6 [+,4,2,6,-,3]=>6 [-,4,2,6,-,3]=>5 [+,4,+,2,+,+]=>4 [-,4,+,2,+,+]=>7 [+,4,-,2,+,+]=>7 [+,4,+,2,-,+]=>7 [+,4,+,2,+,-]=>7 [-,4,-,2,+,+]=>8 [-,4,+,2,-,+]=>8 [-,4,+,2,+,-]=>8 [+,4,-,2,-,+]=>8 [+,4,-,2,+,-]=>8 [+,4,+,2,-,-]=>8 [-,4,-,2,-,+]=>7 [-,4,-,2,+,-]=>7 [-,4,+,2,-,-]=>7 [+,4,-,2,-,-]=>7 [-,4,-,2,-,-]=>4 [+,4,+,2,6,5]=>6 [-,4,+,2,6,5]=>7 [+,4,-,2,6,5]=>7 [-,4,-,2,6,5]=>6 [+,4,+,5,2,+]=>6 [-,4,+,5,2,+]=>7 [+,4,-,5,2,+]=>7 [+,4,+,5,2,-]=>7 [-,4,-,5,2,+]=>6 [-,4,+,5,2,-]=>6 [+,4,-,5,2,-]=>6 [-,4,-,5,2,-]=>3 [+,4,+,5,6,2]=>6 [-,4,+,5,6,2]=>5 [+,4,-,5,6,2]=>5 [-,4,-,5,6,2]=>2 [+,4,+,6,2,5]=>5 [-,4,+,6,2,5]=>6 [+,4,-,6,2,5]=>6 [-,4,-,6,2,5]=>5 [+,4,+,6,+,2]=>6 [-,4,+,6,+,2]=>7 [+,4,-,6,+,2]=>7 [+,4,+,6,-,2]=>7 [-,4,-,6,+,2]=>6 [-,4,+,6,-,2]=>6 [+,4,-,6,-,2]=>6 [-,4,-,6,-,2]=>3 [+,4,5,2,3,+]=>4 [-,4,5,2,3,+]=>5 [+,4,5,2,3,-]=>5 [-,4,5,2,3,-]=>4 [+,4,5,2,6,3]=>4 [-,4,5,2,6,3]=>3 [+,4,5,3,2,+]=>5 [-,4,5,3,2,+]=>6 [+,4,5,3,2,-]=>6 [-,4,5,3,2,-]=>5 [+,4,5,3,6,2]=>5 [-,4,5,3,6,2]=>4 [+,4,5,6,2,3]=>3 [-,4,5,6,2,3]=>2 [+,4,5,6,3,2]=>4 [-,4,5,6,3,2]=>3 [+,4,6,2,3,5]=>3 [-,4,6,2,3,5]=>4 [+,4,6,2,+,3]=>4 [-,4,6,2,+,3]=>5 [+,4,6,2,-,3]=>5 [-,4,6,2,-,3]=>4 [+,4,6,3,2,5]=>4 [-,4,6,3,2,5]=>5 [+,4,6,3,+,2]=>5 [-,4,6,3,+,2]=>6 [+,4,6,3,-,2]=>6 [-,4,6,3,-,2]=>5 [+,4,6,5,2,3]=>4 [-,4,6,5,2,3]=>3 [+,4,6,5,3,2]=>5 [-,4,6,5,3,2]=>4 [+,5,2,3,4,+]=>2 [-,5,2,3,4,+]=>5 [+,5,2,3,4,-]=>5 [-,5,2,3,4,-]=>6 [+,5,2,3,6,4]=>4 [-,5,2,3,6,4]=>5 [+,5,2,+,3,+]=>3 [-,5,2,+,3,+]=>6 [+,5,2,-,3,+]=>6 [+,5,2,+,3,-]=>6 [-,5,2,-,3,+]=>7 [-,5,2,+,3,-]=>7 [+,5,2,-,3,-]=>7 [-,5,2,-,3,-]=>6 [+,5,2,+,6,3]=>5 [-,5,2,+,6,3]=>6 [+,5,2,-,6,3]=>6 [-,5,2,-,6,3]=>5 [+,5,2,6,3,4]=>3 [-,5,2,6,3,4]=>4 [+,5,2,6,4,3]=>4 [-,5,2,6,4,3]=>5 [+,5,+,2,4,+]=>3 [-,5,+,2,4,+]=>6 [+,5,-,2,4,+]=>6 [+,5,+,2,4,-]=>6 [-,5,-,2,4,+]=>7 [-,5,+,2,4,-]=>7 [+,5,-,2,4,-]=>7 [-,5,-,2,4,-]=>6 [+,5,+,2,6,4]=>5 [-,5,+,2,6,4]=>6 [+,5,-,2,6,4]=>6 [-,5,-,2,6,4]=>5 [+,5,+,+,2,+]=>4 [-,5,+,+,2,+]=>7 [+,5,-,+,2,+]=>7 [+,5,+,-,2,+]=>7 [+,5,+,+,2,-]=>7 [-,5,-,+,2,+]=>8 [-,5,+,-,2,+]=>8 [-,5,+,+,2,-]=>8 [+,5,-,-,2,+]=>8 [+,5,-,+,2,-]=>8 [+,5,+,-,2,-]=>8 [-,5,-,-,2,+]=>7 [-,5,-,+,2,-]=>7 [-,5,+,-,2,-]=>7 [+,5,-,-,2,-]=>7 [-,5,-,-,2,-]=>4 [+,5,+,+,6,2]=>6 [-,5,+,+,6,2]=>7 [+,5,-,+,6,2]=>7 [+,5,+,-,6,2]=>7 [-,5,-,+,6,2]=>6 [-,5,+,-,6,2]=>6 [+,5,-,-,6,2]=>6 [-,5,-,-,6,2]=>3 [+,5,+,6,2,4]=>4 [-,5,+,6,2,4]=>5 [+,5,-,6,2,4]=>5 [-,5,-,6,2,4]=>4 [+,5,+,6,4,2]=>5 [-,5,+,6,4,2]=>6 [+,5,-,6,4,2]=>6 [-,5,-,6,4,2]=>5 [+,5,4,2,3,+]=>5 [-,5,4,2,3,+]=>6 [+,5,4,2,3,-]=>6 [-,5,4,2,3,-]=>5 [+,5,4,2,6,3]=>5 [-,5,4,2,6,3]=>4 [+,5,4,3,2,+]=>6 [-,5,4,3,2,+]=>7 [+,5,4,3,2,-]=>7 [-,5,4,3,2,-]=>6 [+,5,4,3,6,2]=>6 [-,5,4,3,6,2]=>5 [+,5,4,6,2,3]=>4 [-,5,4,6,2,3]=>3 [+,5,4,6,3,2]=>5 [-,5,4,6,3,2]=>4 [+,5,6,2,3,4]=>2 [-,5,6,2,3,4]=>3 [+,5,6,2,4,3]=>3 [-,5,6,2,4,3]=>4 [+,5,6,3,2,4]=>3 [-,5,6,3,2,4]=>4 [+,5,6,3,4,2]=>4 [-,5,6,3,4,2]=>5 [+,5,6,+,2,3]=>4 [-,5,6,+,2,3]=>5 [+,5,6,-,2,3]=>5 [-,5,6,-,2,3]=>4 [+,5,6,+,3,2]=>5 [-,5,6,+,3,2]=>6 [+,5,6,-,3,2]=>6 [-,5,6,-,3,2]=>5 [+,6,2,3,4,5]=>1 [-,6,2,3,4,5]=>4 [+,6,2,3,+,4]=>2 [-,6,2,3,+,4]=>5 [+,6,2,3,-,4]=>5 [-,6,2,3,-,4]=>6 [+,6,2,+,3,5]=>2 [-,6,2,+,3,5]=>5 [+,6,2,-,3,5]=>5 [-,6,2,-,3,5]=>6 [+,6,2,+,+,3]=>3 [-,6,2,+,+,3]=>6 [+,6,2,-,+,3]=>6 [+,6,2,+,-,3]=>6 [-,6,2,-,+,3]=>7 [-,6,2,+,-,3]=>7 [+,6,2,-,-,3]=>7 [-,6,2,-,-,3]=>6 [+,6,2,5,3,4]=>4 [-,6,2,5,3,4]=>5 [+,6,2,5,4,3]=>5 [-,6,2,5,4,3]=>6 [+,6,+,2,4,5]=>2 [-,6,+,2,4,5]=>5 [+,6,-,2,4,5]=>5 [-,6,-,2,4,5]=>6 [+,6,+,2,+,4]=>3 [-,6,+,2,+,4]=>6 [+,6,-,2,+,4]=>6 [+,6,+,2,-,4]=>6 [-,6,-,2,+,4]=>7 [-,6,+,2,-,4]=>7 [+,6,-,2,-,4]=>7 [-,6,-,2,-,4]=>6 [+,6,+,+,2,5]=>3 [-,6,+,+,2,5]=>6 [+,6,-,+,2,5]=>6 [+,6,+,-,2,5]=>6 [-,6,-,+,2,5]=>7 [-,6,+,-,2,5]=>7 [+,6,-,-,2,5]=>7 [-,6,-,-,2,5]=>6 [+,6,+,+,+,2]=>4 [-,6,+,+,+,2]=>7 [+,6,-,+,+,2]=>7 [+,6,+,-,+,2]=>7 [+,6,+,+,-,2]=>7 [-,6,-,+,+,2]=>8 [-,6,+,-,+,2]=>8 [-,6,+,+,-,2]=>8 [+,6,-,-,+,2]=>8 [+,6,-,+,-,2]=>8 [+,6,+,-,-,2]=>8 [-,6,-,-,+,2]=>7 [-,6,-,+,-,2]=>7 [-,6,+,-,-,2]=>7 [+,6,-,-,-,2]=>7 [-,6,-,-,-,2]=>4 [+,6,+,5,2,4]=>5 [-,6,+,5,2,4]=>6 [+,6,-,5,2,4]=>6 [-,6,-,5,2,4]=>5 [+,6,+,5,4,2]=>6 [-,6,+,5,4,2]=>7 [+,6,-,5,4,2]=>7 [-,6,-,5,4,2]=>6 [+,6,4,2,3,5]=>4 [-,6,4,2,3,5]=>5 [+,6,4,2,+,3]=>5 [-,6,4,2,+,3]=>6 [+,6,4,2,-,3]=>6 [-,6,4,2,-,3]=>5 [+,6,4,3,2,5]=>5 [-,6,4,3,2,5]=>6 [+,6,4,3,+,2]=>6 [-,6,4,3,+,2]=>7 [+,6,4,3,-,2]=>7 [-,6,4,3,-,2]=>6 [+,6,4,5,2,3]=>5 [-,6,4,5,2,3]=>4 [+,6,4,5,3,2]=>6 [-,6,4,5,3,2]=>5 [+,6,5,2,3,4]=>3 [-,6,5,2,3,4]=>4 [+,6,5,2,4,3]=>4 [-,6,5,2,4,3]=>5 [+,6,5,3,2,4]=>4 [-,6,5,3,2,4]=>5 [+,6,5,3,4,2]=>5 [-,6,5,3,4,2]=>6 [+,6,5,+,2,3]=>5 [-,6,5,+,2,3]=>6 [+,6,5,-,2,3]=>6 [-,6,5,-,2,3]=>5 [+,6,5,+,3,2]=>6 [-,6,5,+,3,2]=>7 [+,6,5,-,3,2]=>7 [-,6,5,-,3,2]=>6 [2,1,+,+,+,+]=>4 [2,1,-,+,+,+]=>7 [2,1,+,-,+,+]=>7 [2,1,+,+,-,+]=>7 [2,1,+,+,+,-]=>7 [2,1,-,-,+,+]=>8 [2,1,-,+,-,+]=>8 [2,1,-,+,+,-]=>8 [2,1,+,-,-,+]=>8 [2,1,+,-,+,-]=>8 [2,1,+,+,-,-]=>8 [2,1,-,-,-,+]=>7 [2,1,-,-,+,-]=>7 [2,1,-,+,-,-]=>7 [2,1,+,-,-,-]=>7 [2,1,-,-,-,-]=>4 [2,1,+,+,6,5]=>6 [2,1,-,+,6,5]=>7 [2,1,+,-,6,5]=>7 [2,1,-,-,6,5]=>6 [2,1,+,5,4,+]=>6 [2,1,-,5,4,+]=>7 [2,1,+,5,4,-]=>7 [2,1,-,5,4,-]=>6 [2,1,+,5,6,4]=>6 [2,1,-,5,6,4]=>5 [2,1,+,6,4,5]=>5 [2,1,-,6,4,5]=>6 [2,1,+,6,+,4]=>6 [2,1,-,6,+,4]=>7 [2,1,+,6,-,4]=>7 [2,1,-,6,-,4]=>6 [2,1,4,3,+,+]=>6 [2,1,4,3,-,+]=>7 [2,1,4,3,+,-]=>7 [2,1,4,3,-,-]=>6 [2,1,4,3,6,5]=>6 [2,1,4,5,3,+]=>6 [2,1,4,5,3,-]=>5 [2,1,4,5,6,3]=>4 [2,1,4,6,3,5]=>5 [2,1,4,6,+,3]=>6 [2,1,4,6,-,3]=>5 [2,1,5,3,4,+]=>5 [2,1,5,3,4,-]=>6 [2,1,5,3,6,4]=>5 [2,1,5,+,3,+]=>6 [2,1,5,-,3,+]=>7 [2,1,5,+,3,-]=>7 [2,1,5,-,3,-]=>6 [2,1,5,+,6,3]=>6 [2,1,5,-,6,3]=>5 [2,1,5,6,3,4]=>4 [2,1,5,6,4,3]=>5 [2,1,6,3,4,5]=>4 [2,1,6,3,+,4]=>5 [2,1,6,3,-,4]=>6 [2,1,6,+,3,5]=>5 [2,1,6,-,3,5]=>6 [2,1,6,+,+,3]=>6 [2,1,6,-,+,3]=>7 [2,1,6,+,-,3]=>7 [2,1,6,-,-,3]=>6 [2,1,6,5,3,4]=>5 [2,1,6,5,4,3]=>6 [2,3,1,+,+,+]=>6 [2,3,1,-,+,+]=>7 [2,3,1,+,-,+]=>7 [2,3,1,+,+,-]=>7 [2,3,1,-,-,+]=>6 [2,3,1,-,+,-]=>6 [2,3,1,+,-,-]=>6 [2,3,1,-,-,-]=>3 [2,3,1,+,6,5]=>6 [2,3,1,-,6,5]=>5 [2,3,1,5,4,+]=>6 [2,3,1,5,4,-]=>5 [2,3,1,5,6,4]=>4 [2,3,1,6,4,5]=>5 [2,3,1,6,+,4]=>6 [2,3,1,6,-,4]=>5 [2,3,4,1,+,+]=>6 [2,3,4,1,-,+]=>5 [2,3,4,1,+,-]=>5 [2,3,4,1,-,-]=>2 [2,3,4,1,6,5]=>4 [2,3,4,5,1,+]=>4 [2,3,4,5,1,-]=>1 [2,3,4,5,6,1]=>0 [2,3,4,6,1,5]=>3 [2,3,4,6,+,1]=>4 [2,3,4,6,-,1]=>1 [2,3,5,1,4,+]=>5 [2,3,5,1,4,-]=>4 [2,3,5,1,6,4]=>3 [2,3,5,+,1,+]=>6 [2,3,5,-,1,+]=>5 [2,3,5,+,1,-]=>5 [2,3,5,-,1,-]=>2 [2,3,5,+,6,1]=>4 [2,3,5,-,6,1]=>1 [2,3,5,6,1,4]=>2 [2,3,5,6,4,1]=>3 [2,3,6,1,4,5]=>4 [2,3,6,1,+,4]=>5 [2,3,6,1,-,4]=>4 [2,3,6,+,1,5]=>5 [2,3,6,-,1,5]=>4 [2,3,6,+,+,1]=>6 [2,3,6,-,+,1]=>5 [2,3,6,+,-,1]=>5 [2,3,6,-,-,1]=>2 [2,3,6,5,1,4]=>3 [2,3,6,5,4,1]=>4 [2,4,1,3,+,+]=>5 [2,4,1,3,-,+]=>6 [2,4,1,3,+,-]=>6 [2,4,1,3,-,-]=>5 [2,4,1,3,6,5]=>5 [2,4,1,5,3,+]=>5 [2,4,1,5,3,-]=>4 [2,4,1,5,6,3]=>3 [2,4,1,6,3,5]=>4 [2,4,1,6,+,3]=>5 [2,4,1,6,-,3]=>4 [2,4,+,1,+,+]=>6 [2,4,-,1,+,+]=>7 [2,4,+,1,-,+]=>7 [2,4,+,1,+,-]=>7 [2,4,-,1,-,+]=>6 [2,4,-,1,+,-]=>6 [2,4,+,1,-,-]=>6 [2,4,-,1,-,-]=>3 [2,4,+,1,6,5]=>6
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Description
The number of alignments of a decorated permutation.
An alignment in a decorated permutation $w$ is a pair of directed edges $(i\mapsto w(i), j\mapsto w(j))$ which can be drawn as distinct noncrossing arcs oriented in the same direction in the circular chord diagram.
According to [1], the number of alignments of a decorated permutation on $n$ letters with $k$ anit-exceedances equals and associated Grassmann interval $[u, v]$ equals $k(n - k) - [\ell(v) − \ell(u)]$.
References
[1] A. Postnikov, Total positivity, Grassmannians, and networks. 27 Sep 2006. Postnikov, A. Total positivity, Grassmannians, and networks arXiv:math/0609764
[2] Billey, S. C., Weaver, J. E. Criteria for smoothness of Positroid varieties via pattern avoidance, Johnson graphs, and spirographs arXiv:2207.06508
Code
# please simplify
def cyclic_interval(a, b, n):
    if a <= b:
        return list(range(a, b+1))
    return list(range(a, n+1)) + list(range(1, b+1))

def alignments(x):
    pi = x.to_signed_permutation().permutation()
    n = len(pi)
    al = []
    for i, e in enumerate(pi, 1):
        for j, f in enumerate(pi, 1):
            if i == j:
                continue
            a, b = sorted([i, e])
            c, d = sorted([j, f])
            if a <= c <= b <= d or c <= a <= d <= b:
                continue
            if (e not in cyclic_interval(i, f-1, n)
                or f not in cyclic_interval(e+1, j, n)):
                continue
            if j == f and x[j-1] < 0:
                continue
            if i == e and x[i-1] > 0:
                continue
            al.append((i, e, j, f))

    return al

def statistic(x):
    return len(alignments(x))
Created
Jul 15, 2022 at 18:19 by Martin Rubey
Updated
Jul 15, 2022 at 18:19 by Martin Rubey