edit this statistic or download as text // json
Identifier
Values
=>
[1]=>0 [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]=>3 [3,2,1]=>4 [1,2,3,4]=>0 [1,2,4,3]=>1 [1,3,2,4]=>1 [1,3,4,2]=>3 [1,4,2,3]=>3 [1,4,3,2]=>4 [2,1,3,4]=>1 [2,1,4,3]=>2 [2,3,1,4]=>3 [2,3,4,1]=>6 [2,4,1,3]=>5 [2,4,3,1]=>7 [3,1,2,4]=>3 [3,1,4,2]=>5 [3,2,1,4]=>4 [3,2,4,1]=>7 [3,4,1,2]=>6 [3,4,2,1]=>7 [4,1,2,3]=>6 [4,1,3,2]=>7 [4,2,1,3]=>7 [4,2,3,1]=>9 [4,3,1,2]=>7 [4,3,2,1]=>8 [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]=>3 [1,2,5,4,3]=>4 [1,3,2,4,5]=>1 [1,3,2,5,4]=>2 [1,3,4,2,5]=>3 [1,3,4,5,2]=>6 [1,3,5,2,4]=>5 [1,3,5,4,2]=>7 [1,4,2,3,5]=>3 [1,4,2,5,3]=>5 [1,4,3,2,5]=>4 [1,4,3,5,2]=>7 [1,4,5,2,3]=>6 [1,4,5,3,2]=>7 [1,5,2,3,4]=>6 [1,5,2,4,3]=>7 [1,5,3,2,4]=>7 [1,5,3,4,2]=>9 [1,5,4,2,3]=>7 [1,5,4,3,2]=>8 [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]=>4 [2,1,5,4,3]=>5 [2,3,1,4,5]=>3 [2,3,1,5,4]=>4 [2,3,4,1,5]=>6 [2,3,4,5,1]=>10 [2,3,5,1,4]=>8 [2,3,5,4,1]=>11 [2,4,1,3,5]=>5 [2,4,1,5,3]=>7 [2,4,3,1,5]=>7 [2,4,3,5,1]=>11 [2,4,5,1,3]=>9 [2,4,5,3,1]=>11 [2,5,1,3,4]=>8 [2,5,1,4,3]=>9 [2,5,3,1,4]=>10 [2,5,3,4,1]=>13 [2,5,4,1,3]=>10 [2,5,4,3,1]=>12 [3,1,2,4,5]=>3 [3,1,2,5,4]=>4 [3,1,4,2,5]=>5 [3,1,4,5,2]=>8 [3,1,5,2,4]=>7 [3,1,5,4,2]=>9 [3,2,1,4,5]=>4 [3,2,1,5,4]=>5 [3,2,4,1,5]=>7 [3,2,4,5,1]=>11 [3,2,5,1,4]=>9 [3,2,5,4,1]=>12 [3,4,1,2,5]=>6 [3,4,1,5,2]=>9 [3,4,2,1,5]=>7 [3,4,2,5,1]=>11 [3,4,5,1,2]=>9 [3,4,5,2,1]=>10 [3,5,1,2,4]=>9 [3,5,1,4,2]=>11 [3,5,2,1,4]=>10 [3,5,2,4,1]=>13 [3,5,4,1,2]=>10 [3,5,4,2,1]=>11 [4,1,2,3,5]=>6 [4,1,2,5,3]=>8 [4,1,3,2,5]=>7 [4,1,3,5,2]=>10 [4,1,5,2,3]=>9 [4,1,5,3,2]=>10 [4,2,1,3,5]=>7 [4,2,1,5,3]=>9 [4,2,3,1,5]=>9 [4,2,3,5,1]=>13 [4,2,5,1,3]=>11 [4,2,5,3,1]=>13 [4,3,1,2,5]=>7 [4,3,1,5,2]=>10 [4,3,2,1,5]=>8 [4,3,2,5,1]=>12 [4,3,5,1,2]=>10 [4,3,5,2,1]=>11 [4,5,1,2,3]=>9 [4,5,1,3,2]=>10 [4,5,2,1,3]=>10 [4,5,2,3,1]=>12 [4,5,3,1,2]=>10 [4,5,3,2,1]=>11 [5,1,2,3,4]=>10 [5,1,2,4,3]=>11 [5,1,3,2,4]=>11 [5,1,3,4,2]=>13 [5,1,4,2,3]=>11 [5,1,4,3,2]=>12 [5,2,1,3,4]=>11 [5,2,1,4,3]=>12 [5,2,3,1,4]=>13 [5,2,3,4,1]=>16 [5,2,4,1,3]=>13 [5,2,4,3,1]=>15 [5,3,1,2,4]=>11 [5,3,1,4,2]=>13 [5,3,2,1,4]=>12 [5,3,2,4,1]=>15 [5,3,4,1,2]=>12 [5,3,4,2,1]=>13 [5,4,1,2,3]=>10 [5,4,1,3,2]=>11 [5,4,2,1,3]=>11 [5,4,2,3,1]=>13 [5,4,3,1,2]=>11 [5,4,3,2,1]=>12 [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]=>3 [1,2,3,6,5,4]=>4 [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]=>6 [1,2,4,6,3,5]=>5 [1,2,4,6,5,3]=>7 [1,2,5,3,4,6]=>3 [1,2,5,3,6,4]=>5 [1,2,5,4,3,6]=>4 [1,2,5,4,6,3]=>7 [1,2,5,6,3,4]=>6 [1,2,5,6,4,3]=>7 [1,2,6,3,4,5]=>6 [1,2,6,3,5,4]=>7 [1,2,6,4,3,5]=>7 [1,2,6,4,5,3]=>9 [1,2,6,5,3,4]=>7 [1,2,6,5,4,3]=>8 [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]=>4 [1,3,2,6,5,4]=>5 [1,3,4,2,5,6]=>3 [1,3,4,2,6,5]=>4 [1,3,4,5,2,6]=>6 [1,3,4,5,6,2]=>10 [1,3,4,6,2,5]=>8 [1,3,4,6,5,2]=>11 [1,3,5,2,4,6]=>5 [1,3,5,2,6,4]=>7 [1,3,5,4,2,6]=>7 [1,3,5,4,6,2]=>11 [1,3,5,6,2,4]=>9 [1,3,5,6,4,2]=>11 [1,3,6,2,4,5]=>8 [1,3,6,2,5,4]=>9 [1,3,6,4,2,5]=>10 [1,3,6,4,5,2]=>13 [1,3,6,5,2,4]=>10 [1,3,6,5,4,2]=>12 [1,4,2,3,5,6]=>3 [1,4,2,3,6,5]=>4 [1,4,2,5,3,6]=>5 [1,4,2,5,6,3]=>8 [1,4,2,6,3,5]=>7 [1,4,2,6,5,3]=>9 [1,4,3,2,5,6]=>4 [1,4,3,2,6,5]=>5 [1,4,3,5,2,6]=>7 [1,4,3,5,6,2]=>11 [1,4,3,6,2,5]=>9 [1,4,3,6,5,2]=>12 [1,4,5,2,3,6]=>6 [1,4,5,2,6,3]=>9 [1,4,5,3,2,6]=>7 [1,4,5,3,6,2]=>11 [1,4,5,6,2,3]=>9 [1,4,5,6,3,2]=>10 [1,4,6,2,3,5]=>9 [1,4,6,2,5,3]=>11 [1,4,6,3,2,5]=>10 [1,4,6,3,5,2]=>13 [1,4,6,5,2,3]=>10 [1,4,6,5,3,2]=>11 [1,5,2,3,4,6]=>6 [1,5,2,3,6,4]=>8 [1,5,2,4,3,6]=>7 [1,5,2,4,6,3]=>10 [1,5,2,6,3,4]=>9 [1,5,2,6,4,3]=>10 [1,5,3,2,4,6]=>7 [1,5,3,2,6,4]=>9 [1,5,3,4,2,6]=>9 [1,5,3,4,6,2]=>13 [1,5,3,6,2,4]=>11 [1,5,3,6,4,2]=>13 [1,5,4,2,3,6]=>7 [1,5,4,2,6,3]=>10 [1,5,4,3,2,6]=>8 [1,5,4,3,6,2]=>12 [1,5,4,6,2,3]=>10 [1,5,4,6,3,2]=>11 [1,5,6,2,3,4]=>9 [1,5,6,2,4,3]=>10 [1,5,6,3,2,4]=>10 [1,5,6,3,4,2]=>12 [1,5,6,4,2,3]=>10 [1,5,6,4,3,2]=>11 [1,6,2,3,4,5]=>10 [1,6,2,3,5,4]=>11 [1,6,2,4,3,5]=>11 [1,6,2,4,5,3]=>13 [1,6,2,5,3,4]=>11 [1,6,2,5,4,3]=>12 [1,6,3,2,4,5]=>11 [1,6,3,2,5,4]=>12 [1,6,3,4,2,5]=>13 [1,6,3,4,5,2]=>16 [1,6,3,5,2,4]=>13 [1,6,3,5,4,2]=>15 [1,6,4,2,3,5]=>11 [1,6,4,2,5,3]=>13 [1,6,4,3,2,5]=>12 [1,6,4,3,5,2]=>15 [1,6,4,5,2,3]=>12 [1,6,4,5,3,2]=>13 [1,6,5,2,3,4]=>10 [1,6,5,2,4,3]=>11 [1,6,5,3,2,4]=>11 [1,6,5,3,4,2]=>13 [1,6,5,4,2,3]=>11 [1,6,5,4,3,2]=>12 [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]=>4 [2,1,3,6,5,4]=>5 [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]=>7 [2,1,4,6,3,5]=>6 [2,1,4,6,5,3]=>8 [2,1,5,3,4,6]=>4 [2,1,5,3,6,4]=>6 [2,1,5,4,3,6]=>5 [2,1,5,4,6,3]=>8 [2,1,5,6,3,4]=>7 [2,1,5,6,4,3]=>8 [2,1,6,3,4,5]=>7 [2,1,6,3,5,4]=>8 [2,1,6,4,3,5]=>8 [2,1,6,4,5,3]=>10 [2,1,6,5,3,4]=>8 [2,1,6,5,4,3]=>9 [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]=>6 [2,3,1,6,5,4]=>7 [2,3,4,1,5,6]=>6 [2,3,4,1,6,5]=>7 [2,3,4,5,1,6]=>10 [2,3,4,5,6,1]=>15 [2,3,4,6,1,5]=>12 [2,3,4,6,5,1]=>16 [2,3,5,1,4,6]=>8 [2,3,5,1,6,4]=>10 [2,3,5,4,1,6]=>11 [2,3,5,4,6,1]=>16 [2,3,5,6,1,4]=>13 [2,3,5,6,4,1]=>16 [2,3,6,1,4,5]=>11 [2,3,6,1,5,4]=>12 [2,3,6,4,1,5]=>14 [2,3,6,4,5,1]=>18 [2,3,6,5,1,4]=>14 [2,3,6,5,4,1]=>17 [2,4,1,3,5,6]=>5 [2,4,1,3,6,5]=>6 [2,4,1,5,3,6]=>7 [2,4,1,5,6,3]=>10 [2,4,1,6,3,5]=>9 [2,4,1,6,5,3]=>11 [2,4,3,1,5,6]=>7 [2,4,3,1,6,5]=>8 [2,4,3,5,1,6]=>11 [2,4,3,5,6,1]=>16 [2,4,3,6,1,5]=>13 [2,4,3,6,5,1]=>17 [2,4,5,1,3,6]=>9 [2,4,5,1,6,3]=>12 [2,4,5,3,1,6]=>11 [2,4,5,3,6,1]=>16 [2,4,5,6,1,3]=>13 [2,4,5,6,3,1]=>15 [2,4,6,1,3,5]=>12 [2,4,6,1,5,3]=>14 [2,4,6,3,1,5]=>14 [2,4,6,3,5,1]=>18 [2,4,6,5,1,3]=>14 [2,4,6,5,3,1]=>16 [2,5,1,3,4,6]=>8 [2,5,1,3,6,4]=>10 [2,5,1,4,3,6]=>9 [2,5,1,4,6,3]=>12 [2,5,1,6,3,4]=>11 [2,5,1,6,4,3]=>12 [2,5,3,1,4,6]=>10 [2,5,3,1,6,4]=>12 [2,5,3,4,1,6]=>13 [2,5,3,4,6,1]=>18 [2,5,3,6,1,4]=>15 [2,5,3,6,4,1]=>18 [2,5,4,1,3,6]=>10 [2,5,4,1,6,3]=>13 [2,5,4,3,1,6]=>12 [2,5,4,3,6,1]=>17 [2,5,4,6,1,3]=>14 [2,5,4,6,3,1]=>16 [2,5,6,1,3,4]=>12 [2,5,6,1,4,3]=>13 [2,5,6,3,1,4]=>14 [2,5,6,3,4,1]=>17 [2,5,6,4,1,3]=>14 [2,5,6,4,3,1]=>16 [2,6,1,3,4,5]=>12 [2,6,1,3,5,4]=>13 [2,6,1,4,3,5]=>13 [2,6,1,4,5,3]=>15 [2,6,1,5,3,4]=>13 [2,6,1,5,4,3]=>14 [2,6,3,1,4,5]=>14 [2,6,3,1,5,4]=>15 [2,6,3,4,1,5]=>17 [2,6,3,4,5,1]=>21 [2,6,3,5,1,4]=>17 [2,6,3,5,4,1]=>20 [2,6,4,1,3,5]=>14 [2,6,4,1,5,3]=>16 [2,6,4,3,1,5]=>16 [2,6,4,3,5,1]=>20 [2,6,4,5,1,3]=>16 [2,6,4,5,3,1]=>18 [2,6,5,1,3,4]=>13 [2,6,5,1,4,3]=>14 [2,6,5,3,1,4]=>15 [2,6,5,3,4,1]=>18 [2,6,5,4,1,3]=>15 [2,6,5,4,3,1]=>17 [3,1,2,4,5,6]=>3 [3,1,2,4,6,5]=>4 [3,1,2,5,4,6]=>4 [3,1,2,5,6,4]=>6 [3,1,2,6,4,5]=>6 [3,1,2,6,5,4]=>7 [3,1,4,2,5,6]=>5 [3,1,4,2,6,5]=>6 [3,1,4,5,2,6]=>8 [3,1,4,5,6,2]=>12 [3,1,4,6,2,5]=>10 [3,1,4,6,5,2]=>13 [3,1,5,2,4,6]=>7 [3,1,5,2,6,4]=>9 [3,1,5,4,2,6]=>9 [3,1,5,4,6,2]=>13 [3,1,5,6,2,4]=>11 [3,1,5,6,4,2]=>13 [3,1,6,2,4,5]=>10 [3,1,6,2,5,4]=>11 [3,1,6,4,2,5]=>12 [3,1,6,4,5,2]=>15 [3,1,6,5,2,4]=>12 [3,1,6,5,4,2]=>14 [3,2,1,4,5,6]=>4 [3,2,1,4,6,5]=>5 [3,2,1,5,4,6]=>5 [3,2,1,5,6,4]=>7 [3,2,1,6,4,5]=>7 [3,2,1,6,5,4]=>8 [3,2,4,1,5,6]=>7 [3,2,4,1,6,5]=>8 [3,2,4,5,1,6]=>11 [3,2,4,5,6,1]=>16 [3,2,4,6,1,5]=>13 [3,2,4,6,5,1]=>17 [3,2,5,1,4,6]=>9 [3,2,5,1,6,4]=>11 [3,2,5,4,1,6]=>12 [3,2,5,4,6,1]=>17 [3,2,5,6,1,4]=>14 [3,2,5,6,4,1]=>17 [3,2,6,1,4,5]=>12 [3,2,6,1,5,4]=>13 [3,2,6,4,1,5]=>15 [3,2,6,4,5,1]=>19 [3,2,6,5,1,4]=>15 [3,2,6,5,4,1]=>18 [3,4,1,2,5,6]=>6 [3,4,1,2,6,5]=>7 [3,4,1,5,2,6]=>9 [3,4,1,5,6,2]=>13 [3,4,1,6,2,5]=>11 [3,4,1,6,5,2]=>14 [3,4,2,1,5,6]=>7 [3,4,2,1,6,5]=>8 [3,4,2,5,1,6]=>11 [3,4,2,5,6,1]=>16 [3,4,2,6,1,5]=>13 [3,4,2,6,5,1]=>17 [3,4,5,1,2,6]=>9 [3,4,5,1,6,2]=>13 [3,4,5,2,1,6]=>10 [3,4,5,2,6,1]=>15 [3,4,5,6,1,2]=>12 [3,4,5,6,2,1]=>13 [3,4,6,1,2,5]=>12 [3,4,6,1,5,2]=>15 [3,4,6,2,1,5]=>13 [3,4,6,2,5,1]=>17 [3,4,6,5,1,2]=>13 [3,4,6,5,2,1]=>14 [3,5,1,2,4,6]=>9 [3,5,1,2,6,4]=>11 [3,5,1,4,2,6]=>11 [3,5,1,4,6,2]=>15 [3,5,1,6,2,4]=>13 [3,5,1,6,4,2]=>15 [3,5,2,1,4,6]=>10 [3,5,2,1,6,4]=>12 [3,5,2,4,1,6]=>13 [3,5,2,4,6,1]=>18 [3,5,2,6,1,4]=>15 [3,5,2,6,4,1]=>18 [3,5,4,1,2,6]=>10 [3,5,4,1,6,2]=>14 [3,5,4,2,1,6]=>11 [3,5,4,2,6,1]=>16 [3,5,4,6,1,2]=>13 [3,5,4,6,2,1]=>14 [3,5,6,1,2,4]=>12 [3,5,6,1,4,2]=>14 [3,5,6,2,1,4]=>13 [3,5,6,2,4,1]=>16 [3,5,6,4,1,2]=>13 [3,5,6,4,2,1]=>14 [3,6,1,2,4,5]=>13 [3,6,1,2,5,4]=>14 [3,6,1,4,2,5]=>15 [3,6,1,4,5,2]=>18 [3,6,1,5,2,4]=>15 [3,6,1,5,4,2]=>17 [3,6,2,1,4,5]=>14 [3,6,2,1,5,4]=>15 [3,6,2,4,1,5]=>17 [3,6,2,4,5,1]=>21 [3,6,2,5,1,4]=>17 [3,6,2,5,4,1]=>20 [3,6,4,1,2,5]=>14 [3,6,4,1,5,2]=>17 [3,6,4,2,1,5]=>15 [3,6,4,2,5,1]=>19 [3,6,4,5,1,2]=>15 [3,6,4,5,2,1]=>16 [3,6,5,1,2,4]=>13 [3,6,5,1,4,2]=>15 [3,6,5,2,1,4]=>14 [3,6,5,2,4,1]=>17 [3,6,5,4,1,2]=>14 [3,6,5,4,2,1]=>15 [4,1,2,3,5,6]=>6 [4,1,2,3,6,5]=>7 [4,1,2,5,3,6]=>8 [4,1,2,5,6,3]=>11 [4,1,2,6,3,5]=>10 [4,1,2,6,5,3]=>12 [4,1,3,2,5,6]=>7 [4,1,3,2,6,5]=>8 [4,1,3,5,2,6]=>10 [4,1,3,5,6,2]=>14 [4,1,3,6,2,5]=>12 [4,1,3,6,5,2]=>15 [4,1,5,2,3,6]=>9 [4,1,5,2,6,3]=>12 [4,1,5,3,2,6]=>10 [4,1,5,3,6,2]=>14 [4,1,5,6,2,3]=>12 [4,1,5,6,3,2]=>13 [4,1,6,2,3,5]=>12 [4,1,6,2,5,3]=>14 [4,1,6,3,2,5]=>13 [4,1,6,3,5,2]=>16 [4,1,6,5,2,3]=>13 [4,1,6,5,3,2]=>14 [4,2,1,3,5,6]=>7 [4,2,1,3,6,5]=>8 [4,2,1,5,3,6]=>9 [4,2,1,5,6,3]=>12 [4,2,1,6,3,5]=>11 [4,2,1,6,5,3]=>13 [4,2,3,1,5,6]=>9 [4,2,3,1,6,5]=>10 [4,2,3,5,1,6]=>13 [4,2,3,5,6,1]=>18 [4,2,3,6,1,5]=>15 [4,2,3,6,5,1]=>19 [4,2,5,1,3,6]=>11 [4,2,5,1,6,3]=>14 [4,2,5,3,1,6]=>13 [4,2,5,3,6,1]=>18 [4,2,5,6,1,3]=>15 [4,2,5,6,3,1]=>17 [4,2,6,1,3,5]=>14 [4,2,6,1,5,3]=>16 [4,2,6,3,1,5]=>16 [4,2,6,3,5,1]=>20 [4,2,6,5,1,3]=>16 [4,2,6,5,3,1]=>18 [4,3,1,2,5,6]=>7 [4,3,1,2,6,5]=>8 [4,3,1,5,2,6]=>10 [4,3,1,5,6,2]=>14 [4,3,1,6,2,5]=>12 [4,3,1,6,5,2]=>15 [4,3,2,1,5,6]=>8 [4,3,2,1,6,5]=>9 [4,3,2,5,1,6]=>12 [4,3,2,5,6,1]=>17 [4,3,2,6,1,5]=>14 [4,3,2,6,5,1]=>18 [4,3,5,1,2,6]=>10 [4,3,5,1,6,2]=>14 [4,3,5,2,1,6]=>11 [4,3,5,2,6,1]=>16 [4,3,5,6,1,2]=>13 [4,3,5,6,2,1]=>14 [4,3,6,1,2,5]=>13 [4,3,6,1,5,2]=>16 [4,3,6,2,1,5]=>14 [4,3,6,2,5,1]=>18 [4,3,6,5,1,2]=>14 [4,3,6,5,2,1]=>15 [4,5,1,2,3,6]=>9 [4,5,1,2,6,3]=>12 [4,5,1,3,2,6]=>10 [4,5,1,3,6,2]=>14 [4,5,1,6,2,3]=>12 [4,5,1,6,3,2]=>13 [4,5,2,1,3,6]=>10 [4,5,2,1,6,3]=>13 [4,5,2,3,1,6]=>12 [4,5,2,3,6,1]=>17 [4,5,2,6,1,3]=>14 [4,5,2,6,3,1]=>16 [4,5,3,1,2,6]=>10 [4,5,3,1,6,2]=>14 [4,5,3,2,1,6]=>11 [4,5,3,2,6,1]=>16 [4,5,3,6,1,2]=>13 [4,5,3,6,2,1]=>14 [4,5,6,1,2,3]=>12 [4,5,6,1,3,2]=>13 [4,5,6,2,1,3]=>13 [4,5,6,2,3,1]=>15 [4,5,6,3,1,2]=>13 [4,5,6,3,2,1]=>14 [4,6,1,2,3,5]=>13 [4,6,1,2,5,3]=>15 [4,6,1,3,2,5]=>14 [4,6,1,3,5,2]=>17 [4,6,1,5,2,3]=>14 [4,6,1,5,3,2]=>15 [4,6,2,1,3,5]=>14 [4,6,2,1,5,3]=>16 [4,6,2,3,1,5]=>16 [4,6,2,3,5,1]=>20 [4,6,2,5,1,3]=>16 [4,6,2,5,3,1]=>18 [4,6,3,1,2,5]=>14 [4,6,3,1,5,2]=>17 [4,6,3,2,1,5]=>15 [4,6,3,2,5,1]=>19 [4,6,3,5,1,2]=>15 [4,6,3,5,2,1]=>16 [4,6,5,1,2,3]=>13 [4,6,5,1,3,2]=>14 [4,6,5,2,1,3]=>14 [4,6,5,2,3,1]=>16 [4,6,5,3,1,2]=>14 [4,6,5,3,2,1]=>15 [5,1,2,3,4,6]=>10 [5,1,2,3,6,4]=>12 [5,1,2,4,3,6]=>11 [5,1,2,4,6,3]=>14 [5,1,2,6,3,4]=>13 [5,1,2,6,4,3]=>14 [5,1,3,2,4,6]=>11 [5,1,3,2,6,4]=>13 [5,1,3,4,2,6]=>13 [5,1,3,4,6,2]=>17 [5,1,3,6,2,4]=>15 [5,1,3,6,4,2]=>17 [5,1,4,2,3,6]=>11 [5,1,4,2,6,3]=>14 [5,1,4,3,2,6]=>12 [5,1,4,3,6,2]=>16 [5,1,4,6,2,3]=>14 [5,1,4,6,3,2]=>15 [5,1,6,2,3,4]=>13 [5,1,6,2,4,3]=>14 [5,1,6,3,2,4]=>14 [5,1,6,3,4,2]=>16 [5,1,6,4,2,3]=>14 [5,1,6,4,3,2]=>15 [5,2,1,3,4,6]=>11 [5,2,1,3,6,4]=>13 [5,2,1,4,3,6]=>12 [5,2,1,4,6,3]=>15 [5,2,1,6,3,4]=>14 [5,2,1,6,4,3]=>15 [5,2,3,1,4,6]=>13 [5,2,3,1,6,4]=>15 [5,2,3,4,1,6]=>16 [5,2,3,4,6,1]=>21 [5,2,3,6,1,4]=>18 [5,2,3,6,4,1]=>21 [5,2,4,1,3,6]=>13 [5,2,4,1,6,3]=>16 [5,2,4,3,1,6]=>15 [5,2,4,3,6,1]=>20 [5,2,4,6,1,3]=>17 [5,2,4,6,3,1]=>19 [5,2,6,1,3,4]=>15 [5,2,6,1,4,3]=>16 [5,2,6,3,1,4]=>17 [5,2,6,3,4,1]=>20 [5,2,6,4,1,3]=>17 [5,2,6,4,3,1]=>19 [5,3,1,2,4,6]=>11 [5,3,1,2,6,4]=>13 [5,3,1,4,2,6]=>13 [5,3,1,4,6,2]=>17 [5,3,1,6,2,4]=>15 [5,3,1,6,4,2]=>17 [5,3,2,1,4,6]=>12 [5,3,2,1,6,4]=>14 [5,3,2,4,1,6]=>15 [5,3,2,4,6,1]=>20 [5,3,2,6,1,4]=>17 [5,3,2,6,4,1]=>20 [5,3,4,1,2,6]=>12 [5,3,4,1,6,2]=>16 [5,3,4,2,1,6]=>13 [5,3,4,2,6,1]=>18 [5,3,4,6,1,2]=>15 [5,3,4,6,2,1]=>16 [5,3,6,1,2,4]=>14 [5,3,6,1,4,2]=>16 [5,3,6,2,1,4]=>15 [5,3,6,2,4,1]=>18 [5,3,6,4,1,2]=>15 [5,3,6,4,2,1]=>16 [5,4,1,2,3,6]=>10 [5,4,1,2,6,3]=>13 [5,4,1,3,2,6]=>11 [5,4,1,3,6,2]=>15 [5,4,1,6,2,3]=>13 [5,4,1,6,3,2]=>14 [5,4,2,1,3,6]=>11 [5,4,2,1,6,3]=>14 [5,4,2,3,1,6]=>13 [5,4,2,3,6,1]=>18 [5,4,2,6,1,3]=>15 [5,4,2,6,3,1]=>17 [5,4,3,1,2,6]=>11 [5,4,3,1,6,2]=>15 [5,4,3,2,1,6]=>12 [5,4,3,2,6,1]=>17 [5,4,3,6,1,2]=>14 [5,4,3,6,2,1]=>15 [5,4,6,1,2,3]=>13 [5,4,6,1,3,2]=>14 [5,4,6,2,1,3]=>14 [5,4,6,2,3,1]=>16 [5,4,6,3,1,2]=>14 [5,4,6,3,2,1]=>15 [5,6,1,2,3,4]=>12 [5,6,1,2,4,3]=>13 [5,6,1,3,2,4]=>13 [5,6,1,3,4,2]=>15 [5,6,1,4,2,3]=>13 [5,6,1,4,3,2]=>14 [5,6,2,1,3,4]=>13 [5,6,2,1,4,3]=>14 [5,6,2,3,1,4]=>15 [5,6,2,3,4,1]=>18 [5,6,2,4,1,3]=>15 [5,6,2,4,3,1]=>17 [5,6,3,1,2,4]=>13 [5,6,3,1,4,2]=>15 [5,6,3,2,1,4]=>14 [5,6,3,2,4,1]=>17 [5,6,3,4,1,2]=>14 [5,6,3,4,2,1]=>15 [5,6,4,1,2,3]=>13 [5,6,4,1,3,2]=>14 [5,6,4,2,1,3]=>14 [5,6,4,2,3,1]=>16 [5,6,4,3,1,2]=>14 [5,6,4,3,2,1]=>15 [6,1,2,3,4,5]=>15 [6,1,2,3,5,4]=>16 [6,1,2,4,3,5]=>16 [6,1,2,4,5,3]=>18 [6,1,2,5,3,4]=>16 [6,1,2,5,4,3]=>17 [6,1,3,2,4,5]=>16 [6,1,3,2,5,4]=>17 [6,1,3,4,2,5]=>18 [6,1,3,4,5,2]=>21 [6,1,3,5,2,4]=>18 [6,1,3,5,4,2]=>20 [6,1,4,2,3,5]=>16 [6,1,4,2,5,3]=>18 [6,1,4,3,2,5]=>17 [6,1,4,3,5,2]=>20 [6,1,4,5,2,3]=>17 [6,1,4,5,3,2]=>18 [6,1,5,2,3,4]=>15 [6,1,5,2,4,3]=>16 [6,1,5,3,2,4]=>16 [6,1,5,3,4,2]=>18 [6,1,5,4,2,3]=>16 [6,1,5,4,3,2]=>17 [6,2,1,3,4,5]=>16 [6,2,1,3,5,4]=>17 [6,2,1,4,3,5]=>17 [6,2,1,4,5,3]=>19 [6,2,1,5,3,4]=>17 [6,2,1,5,4,3]=>18 [6,2,3,1,4,5]=>18 [6,2,3,1,5,4]=>19 [6,2,3,4,1,5]=>21 [6,2,3,4,5,1]=>25 [6,2,3,5,1,4]=>21 [6,2,3,5,4,1]=>24 [6,2,4,1,3,5]=>18 [6,2,4,1,5,3]=>20 [6,2,4,3,1,5]=>20 [6,2,4,3,5,1]=>24 [6,2,4,5,1,3]=>20 [6,2,4,5,3,1]=>22 [6,2,5,1,3,4]=>17 [6,2,5,1,4,3]=>18 [6,2,5,3,1,4]=>19 [6,2,5,3,4,1]=>22 [6,2,5,4,1,3]=>19 [6,2,5,4,3,1]=>21 [6,3,1,2,4,5]=>16 [6,3,1,2,5,4]=>17 [6,3,1,4,2,5]=>18 [6,3,1,4,5,2]=>21 [6,3,1,5,2,4]=>18 [6,3,1,5,4,2]=>20 [6,3,2,1,4,5]=>17 [6,3,2,1,5,4]=>18 [6,3,2,4,1,5]=>20 [6,3,2,4,5,1]=>24 [6,3,2,5,1,4]=>20 [6,3,2,5,4,1]=>23 [6,3,4,1,2,5]=>17 [6,3,4,1,5,2]=>20 [6,3,4,2,1,5]=>18 [6,3,4,2,5,1]=>22 [6,3,4,5,1,2]=>18 [6,3,4,5,2,1]=>19 [6,3,5,1,2,4]=>16 [6,3,5,1,4,2]=>18 [6,3,5,2,1,4]=>17 [6,3,5,2,4,1]=>20 [6,3,5,4,1,2]=>17 [6,3,5,4,2,1]=>18 [6,4,1,2,3,5]=>15 [6,4,1,2,5,3]=>17 [6,4,1,3,2,5]=>16 [6,4,1,3,5,2]=>19 [6,4,1,5,2,3]=>16 [6,4,1,5,3,2]=>17 [6,4,2,1,3,5]=>16 [6,4,2,1,5,3]=>18 [6,4,2,3,1,5]=>18 [6,4,2,3,5,1]=>22 [6,4,2,5,1,3]=>18 [6,4,2,5,3,1]=>20 [6,4,3,1,2,5]=>16 [6,4,3,1,5,2]=>19 [6,4,3,2,1,5]=>17 [6,4,3,2,5,1]=>21 [6,4,3,5,1,2]=>17 [6,4,3,5,2,1]=>18 [6,4,5,1,2,3]=>15 [6,4,5,1,3,2]=>16 [6,4,5,2,1,3]=>16 [6,4,5,2,3,1]=>18 [6,4,5,3,1,2]=>16 [6,4,5,3,2,1]=>17 [6,5,1,2,3,4]=>13 [6,5,1,2,4,3]=>14 [6,5,1,3,2,4]=>14 [6,5,1,3,4,2]=>16 [6,5,1,4,2,3]=>14 [6,5,1,4,3,2]=>15 [6,5,2,1,3,4]=>14 [6,5,2,1,4,3]=>15 [6,5,2,3,1,4]=>16 [6,5,2,3,4,1]=>19 [6,5,2,4,1,3]=>16 [6,5,2,4,3,1]=>18 [6,5,3,1,2,4]=>14 [6,5,3,1,4,2]=>16 [6,5,3,2,1,4]=>15 [6,5,3,2,4,1]=>18 [6,5,3,4,1,2]=>15 [6,5,3,4,2,1]=>16 [6,5,4,1,2,3]=>14 [6,5,4,1,3,2]=>15 [6,5,4,2,1,3]=>15 [6,5,4,2,3,1]=>17 [6,5,4,3,1,2]=>15 [6,5,4,3,2,1]=>16 [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]=>3 [1,2,3,4,7,6,5]=>4 [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]=>6 [1,2,3,5,7,4,6]=>5 [1,2,3,5,7,6,4]=>7 [1,2,3,6,4,5,7]=>3 [1,2,3,6,4,7,5]=>5 [1,2,3,6,5,4,7]=>4 [1,2,3,6,5,7,4]=>7 [1,2,3,6,7,4,5]=>6 [1,2,3,6,7,5,4]=>7 [1,2,3,7,4,5,6]=>6 [1,2,3,7,4,6,5]=>7 [1,2,3,7,5,4,6]=>7 [1,2,3,7,5,6,4]=>9 [1,2,3,7,6,4,5]=>7 [1,2,3,7,6,5,4]=>8 [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]=>4 [1,2,4,3,7,6,5]=>5 [1,2,4,5,3,6,7]=>3 [1,2,4,5,3,7,6]=>4 [1,2,4,5,6,3,7]=>6 [1,2,4,5,6,7,3]=>10 [1,2,4,5,7,3,6]=>8 [1,2,4,5,7,6,3]=>11 [1,2,4,6,3,5,7]=>5 [1,2,4,6,3,7,5]=>7 [1,2,4,6,5,3,7]=>7 [1,2,4,6,5,7,3]=>11 [1,2,4,6,7,3,5]=>9 [1,2,4,6,7,5,3]=>11 [1,2,4,7,3,5,6]=>8 [1,2,4,7,3,6,5]=>9 [1,2,4,7,5,3,6]=>10 [1,2,4,7,5,6,3]=>13 [1,2,4,7,6,3,5]=>10 [1,2,4,7,6,5,3]=>12 [1,2,5,3,4,6,7]=>3 [1,2,5,3,4,7,6]=>4 [1,2,5,3,6,4,7]=>5 [1,2,5,3,6,7,4]=>8 [1,2,5,3,7,4,6]=>7 [1,2,5,3,7,6,4]=>9 [1,2,5,4,3,6,7]=>4 [1,2,5,4,3,7,6]=>5 [1,2,5,4,6,3,7]=>7 [1,2,5,4,6,7,3]=>11 [1,2,5,4,7,3,6]=>9 [1,2,5,4,7,6,3]=>12 [1,2,5,6,3,4,7]=>6 [1,2,5,6,3,7,4]=>9 [1,2,5,6,4,3,7]=>7 [1,2,5,6,4,7,3]=>11 [1,2,5,6,7,3,4]=>9 [1,2,5,6,7,4,3]=>10 [1,2,5,7,3,4,6]=>9 [1,2,5,7,3,6,4]=>11 [1,2,5,7,4,3,6]=>10 [1,2,5,7,4,6,3]=>13 [1,2,5,7,6,3,4]=>10 [1,2,5,7,6,4,3]=>11 [1,2,6,3,4,5,7]=>6 [1,2,6,3,4,7,5]=>8 [1,2,6,3,5,4,7]=>7 [1,2,6,3,5,7,4]=>10 [1,2,6,3,7,4,5]=>9 [1,2,6,3,7,5,4]=>10 [1,2,6,4,3,5,7]=>7 [1,2,6,4,3,7,5]=>9 [1,2,6,4,5,3,7]=>9 [1,2,6,4,5,7,3]=>13 [1,2,6,4,7,3,5]=>11 [1,2,6,4,7,5,3]=>13 [1,2,6,5,3,4,7]=>7 [1,2,6,5,3,7,4]=>10 [1,2,6,5,4,3,7]=>8 [1,2,6,5,4,7,3]=>12 [1,2,6,5,7,3,4]=>10 [1,2,6,5,7,4,3]=>11 [1,2,6,7,3,4,5]=>9 [1,2,6,7,3,5,4]=>10 [1,2,6,7,4,3,5]=>10 [1,2,6,7,4,5,3]=>12 [1,2,6,7,5,3,4]=>10 [1,2,6,7,5,4,3]=>11 [1,2,7,3,4,5,6]=>10 [1,2,7,3,4,6,5]=>11 [1,2,7,3,5,4,6]=>11 [1,2,7,3,5,6,4]=>13 [1,2,7,3,6,4,5]=>11 [1,2,7,3,6,5,4]=>12 [1,2,7,4,3,5,6]=>11 [1,2,7,4,3,6,5]=>12 [1,2,7,4,5,3,6]=>13 [1,2,7,4,5,6,3]=>16 [1,2,7,4,6,3,5]=>13 [1,2,7,4,6,5,3]=>15 [1,2,7,5,3,4,6]=>11 [1,2,7,5,3,6,4]=>13 [1,2,7,5,4,3,6]=>12 [1,2,7,5,4,6,3]=>15 [1,2,7,5,6,3,4]=>12 [1,2,7,5,6,4,3]=>13 [1,2,7,6,3,4,5]=>10 [1,2,7,6,3,5,4]=>11 [1,2,7,6,4,3,5]=>11 [1,2,7,6,4,5,3]=>13 [1,2,7,6,5,3,4]=>11 [1,2,7,6,5,4,3]=>12 [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]=>4 [1,3,2,4,7,6,5]=>5 [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]=>7 [1,3,2,5,7,4,6]=>6 [1,3,2,5,7,6,4]=>8 [1,3,2,6,4,5,7]=>4 [1,3,2,6,4,7,5]=>6 [1,3,2,6,5,4,7]=>5 [1,3,2,6,5,7,4]=>8 [1,3,2,6,7,4,5]=>7 [1,3,2,6,7,5,4]=>8 [1,3,2,7,4,5,6]=>7 [1,3,2,7,4,6,5]=>8 [1,3,2,7,5,4,6]=>8 [1,3,2,7,5,6,4]=>10 [1,3,2,7,6,4,5]=>8 [1,3,2,7,6,5,4]=>9 [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]=>6 [1,3,4,2,7,6,5]=>7 [1,3,4,5,2,6,7]=>6 [1,3,4,5,2,7,6]=>7 [1,3,4,5,6,2,7]=>10 [1,3,4,5,6,7,2]=>15 [1,3,4,5,7,2,6]=>12 [1,3,4,5,7,6,2]=>16 [1,3,4,6,2,5,7]=>8 [1,3,4,6,2,7,5]=>10 [1,3,4,6,5,2,7]=>11 [1,3,4,6,5,7,2]=>16 [1,3,4,6,7,2,5]=>13 [1,3,4,6,7,5,2]=>16 [1,3,4,7,2,5,6]=>11 [1,3,4,7,2,6,5]=>12 [1,3,4,7,5,2,6]=>14 [1,3,4,7,5,6,2]=>18 [1,3,4,7,6,2,5]=>14 [1,3,4,7,6,5,2]=>17 [1,3,5,2,4,6,7]=>5 [1,3,5,2,4,7,6]=>6 [1,3,5,2,6,4,7]=>7 [1,3,5,2,6,7,4]=>10 [1,3,5,2,7,4,6]=>9 [1,3,5,2,7,6,4]=>11 [1,3,5,4,2,6,7]=>7 [1,3,5,4,2,7,6]=>8 [1,3,5,4,6,2,7]=>11 [1,3,5,4,6,7,2]=>16 [1,3,5,4,7,2,6]=>13 [1,3,5,4,7,6,2]=>17 [1,3,5,6,2,4,7]=>9 [1,3,5,6,2,7,4]=>12 [1,3,5,6,4,2,7]=>11 [1,3,5,6,4,7,2]=>16 [1,3,5,6,7,2,4]=>13 [1,3,5,6,7,4,2]=>15 [1,3,5,7,2,4,6]=>12 [1,3,5,7,2,6,4]=>14 [1,3,5,7,4,2,6]=>14 [1,3,5,7,4,6,2]=>18 [1,3,5,7,6,2,4]=>14 [1,3,5,7,6,4,2]=>16 [1,3,6,2,4,5,7]=>8 [1,3,6,2,4,7,5]=>10 [1,3,6,2,5,4,7]=>9 [1,3,6,2,5,7,4]=>12 [1,3,6,2,7,4,5]=>11 [1,3,6,2,7,5,4]=>12 [1,3,6,4,2,5,7]=>10 [1,3,6,4,2,7,5]=>12 [1,3,6,4,5,2,7]=>13 [1,3,6,4,5,7,2]=>18 [1,3,6,4,7,2,5]=>15 [1,3,6,4,7,5,2]=>18 [1,3,6,5,2,4,7]=>10 [1,3,6,5,2,7,4]=>13 [1,3,6,5,4,2,7]=>12 [1,3,6,5,4,7,2]=>17 [1,3,6,5,7,2,4]=>14 [1,3,6,5,7,4,2]=>16 [1,3,6,7,2,4,5]=>12 [1,3,6,7,2,5,4]=>13 [1,3,6,7,4,2,5]=>14 [1,3,6,7,4,5,2]=>17 [1,3,6,7,5,2,4]=>14 [1,3,6,7,5,4,2]=>16 [1,3,7,2,4,5,6]=>12 [1,3,7,2,4,6,5]=>13 [1,3,7,2,5,4,6]=>13 [1,3,7,2,5,6,4]=>15 [1,3,7,2,6,4,5]=>13 [1,3,7,2,6,5,4]=>14 [1,3,7,4,2,5,6]=>14 [1,3,7,4,2,6,5]=>15 [1,3,7,4,5,2,6]=>17 [1,3,7,4,5,6,2]=>21 [1,3,7,4,6,2,5]=>17 [1,3,7,4,6,5,2]=>20 [1,3,7,5,2,4,6]=>14 [1,3,7,5,2,6,4]=>16 [1,3,7,5,4,2,6]=>16 [1,3,7,5,4,6,2]=>20 [1,3,7,5,6,2,4]=>16 [1,3,7,5,6,4,2]=>18 [1,3,7,6,2,4,5]=>13 [1,3,7,6,2,5,4]=>14 [1,3,7,6,4,2,5]=>15 [1,3,7,6,4,5,2]=>18 [1,3,7,6,5,2,4]=>15 [1,3,7,6,5,4,2]=>17 [1,4,2,3,5,6,7]=>3 [1,4,2,3,5,7,6]=>4 [1,4,2,3,6,5,7]=>4 [1,4,2,3,6,7,5]=>6 [1,4,2,3,7,5,6]=>6 [1,4,2,3,7,6,5]=>7 [1,4,2,5,3,6,7]=>5 [1,4,2,5,3,7,6]=>6 [1,4,2,5,6,3,7]=>8 [1,4,2,5,6,7,3]=>12 [1,4,2,5,7,3,6]=>10 [1,4,2,5,7,6,3]=>13 [1,4,2,6,3,5,7]=>7 [1,4,2,6,3,7,5]=>9 [1,4,2,6,5,3,7]=>9 [1,4,2,6,5,7,3]=>13 [1,4,2,6,7,3,5]=>11 [1,4,2,6,7,5,3]=>13 [1,4,2,7,3,5,6]=>10 [1,4,2,7,3,6,5]=>11 [1,4,2,7,5,3,6]=>12 [1,4,2,7,5,6,3]=>15 [1,4,2,7,6,3,5]=>12 [1,4,2,7,6,5,3]=>14 [1,4,3,2,5,6,7]=>4 [1,4,3,2,5,7,6]=>5 [1,4,3,2,6,5,7]=>5 [1,4,3,2,6,7,5]=>7 [1,4,3,2,7,5,6]=>7 [1,4,3,2,7,6,5]=>8 [1,4,3,5,2,6,7]=>7 [1,4,3,5,2,7,6]=>8 [1,4,3,5,6,2,7]=>11 [1,4,3,5,6,7,2]=>16 [1,4,3,5,7,2,6]=>13 [1,4,3,5,7,6,2]=>17 [1,4,3,6,2,5,7]=>9 [1,4,3,6,2,7,5]=>11 [1,4,3,6,5,2,7]=>12 [1,4,3,6,5,7,2]=>17 [1,4,3,6,7,2,5]=>14 [1,4,3,6,7,5,2]=>17 [1,4,3,7,2,5,6]=>12 [1,4,3,7,2,6,5]=>13 [1,4,3,7,5,2,6]=>15 [1,4,3,7,5,6,2]=>19 [1,4,3,7,6,2,5]=>15 [1,4,3,7,6,5,2]=>18 [1,4,5,2,3,6,7]=>6 [1,4,5,2,3,7,6]=>7 [1,4,5,2,6,3,7]=>9 [1,4,5,2,6,7,3]=>13 [1,4,5,2,7,3,6]=>11 [1,4,5,2,7,6,3]=>14 [1,4,5,3,2,6,7]=>7 [1,4,5,3,2,7,6]=>8 [1,4,5,3,6,2,7]=>11 [1,4,5,3,6,7,2]=>16 [1,4,5,3,7,2,6]=>13 [1,4,5,3,7,6,2]=>17 [1,4,5,6,2,3,7]=>9 [1,4,5,6,2,7,3]=>13 [1,4,5,6,3,2,7]=>10 [1,4,5,6,3,7,2]=>15 [1,4,5,6,7,2,3]=>12 [1,4,5,6,7,3,2]=>13 [1,4,5,7,2,3,6]=>12 [1,4,5,7,2,6,3]=>15 [1,4,5,7,3,2,6]=>13 [1,4,5,7,3,6,2]=>17 [1,4,5,7,6,2,3]=>13 [1,4,5,7,6,3,2]=>14 [1,4,6,2,3,5,7]=>9 [1,4,6,2,3,7,5]=>11 [1,4,6,2,5,3,7]=>11 [1,4,6,2,5,7,3]=>15 [1,4,6,2,7,3,5]=>13 [1,4,6,2,7,5,3]=>15 [1,4,6,3,2,5,7]=>10 [1,4,6,3,2,7,5]=>12 [1,4,6,3,5,2,7]=>13 [1,4,6,3,5,7,2]=>18 [1,4,6,3,7,2,5]=>15 [1,4,6,3,7,5,2]=>18 [1,4,6,5,2,3,7]=>10 [1,4,6,5,2,7,3]=>14 [1,4,6,5,3,2,7]=>11
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Description
Number of minimal entries in the Bruhat order matrix of a permutation.
Associate to a permutation $\sigma$ of length $n$ the $n \times n$ matrix with entries
$$r_{ij}(\sigma) = \left| \big\{ u \in \{1,\dots,i\} \mid \sigma(u) \leq j \big\}\right|.$$
For the identity permutation, one has $r_{ij} = \min\{i,j\}$, and $\sigma \leq \tau$ in the (strong) Bruhat order if and only if $r_{ij}(\tau) \leq r_{ij}(\sigma)$ for all $i,j$.
This statistic records the number of indices $i,j$ with $r_{ij} = \min\{i,j\}$.
Code
def B(sigma):        
    n = len(sigma)                                                                 
    return Matrix([[sum(1 for u in [1 .. i] if sigma(u) <= j) for i in [1 .. n]] for j in [1 .. n]])

def statistic(sigma):
    n = len(sigma)
    M = B(sigma)
    return sum(1 for i in range(n) for j in range(n) if M[i,j] == min(i,j))
Created
Jun 06, 2019 at 13:50 by Christian Stump
Updated
Jun 06, 2019 at 13:50 by Christian Stump