edit this statistic or download as text // json
Identifier
Values
=>
[1]=>0 [1,2]=>1 [2,1]=>0 [1,2,3]=>4 [1,3,2]=>3 [2,1,3]=>3 [2,3,1]=>1 [3,1,2]=>1 [3,2,1]=>0 [1,2,3,4]=>10 [1,2,4,3]=>9 [1,3,2,4]=>9 [1,3,4,2]=>7 [1,4,2,3]=>7 [1,4,3,2]=>6 [2,1,3,4]=>9 [2,1,4,3]=>8 [2,3,1,4]=>7 [2,3,4,1]=>4 [2,4,1,3]=>5 [2,4,3,1]=>3 [3,1,2,4]=>7 [3,1,4,2]=>5 [3,2,1,4]=>6 [3,2,4,1]=>3 [3,4,1,2]=>2 [3,4,2,1]=>1 [4,1,2,3]=>4 [4,1,3,2]=>3 [4,2,1,3]=>3 [4,2,3,1]=>1 [4,3,1,2]=>1 [4,3,2,1]=>0 [1,2,3,4,5]=>20 [1,2,3,5,4]=>19 [1,2,4,3,5]=>19 [1,2,4,5,3]=>17 [1,2,5,3,4]=>17 [1,2,5,4,3]=>16 [1,3,2,4,5]=>19 [1,3,2,5,4]=>18 [1,3,4,2,5]=>17 [1,3,4,5,2]=>14 [1,3,5,2,4]=>15 [1,3,5,4,2]=>13 [1,4,2,3,5]=>17 [1,4,2,5,3]=>15 [1,4,3,2,5]=>16 [1,4,3,5,2]=>13 [1,4,5,2,3]=>12 [1,4,5,3,2]=>11 [1,5,2,3,4]=>14 [1,5,2,4,3]=>13 [1,5,3,2,4]=>13 [1,5,3,4,2]=>11 [1,5,4,2,3]=>11 [1,5,4,3,2]=>10 [2,1,3,4,5]=>19 [2,1,3,5,4]=>18 [2,1,4,3,5]=>18 [2,1,4,5,3]=>16 [2,1,5,3,4]=>16 [2,1,5,4,3]=>15 [2,3,1,4,5]=>17 [2,3,1,5,4]=>16 [2,3,4,1,5]=>14 [2,3,4,5,1]=>10 [2,3,5,1,4]=>12 [2,3,5,4,1]=>9 [2,4,1,3,5]=>15 [2,4,1,5,3]=>13 [2,4,3,1,5]=>13 [2,4,3,5,1]=>9 [2,4,5,1,3]=>9 [2,4,5,3,1]=>7 [2,5,1,3,4]=>12 [2,5,1,4,3]=>11 [2,5,3,1,4]=>10 [2,5,3,4,1]=>7 [2,5,4,1,3]=>8 [2,5,4,3,1]=>6 [3,1,2,4,5]=>17 [3,1,2,5,4]=>16 [3,1,4,2,5]=>15 [3,1,4,5,2]=>12 [3,1,5,2,4]=>13 [3,1,5,4,2]=>11 [3,2,1,4,5]=>16 [3,2,1,5,4]=>15 [3,2,4,1,5]=>13 [3,2,4,5,1]=>9 [3,2,5,1,4]=>11 [3,2,5,4,1]=>8 [3,4,1,2,5]=>12 [3,4,1,5,2]=>9 [3,4,2,1,5]=>11 [3,4,2,5,1]=>7 [3,4,5,1,2]=>5 [3,4,5,2,1]=>4 [3,5,1,2,4]=>9 [3,5,1,4,2]=>7 [3,5,2,1,4]=>8 [3,5,2,4,1]=>5 [3,5,4,1,2]=>4 [3,5,4,2,1]=>3 [4,1,2,3,5]=>14 [4,1,2,5,3]=>12 [4,1,3,2,5]=>13 [4,1,3,5,2]=>10 [4,1,5,2,3]=>9 [4,1,5,3,2]=>8 [4,2,1,3,5]=>13 [4,2,1,5,3]=>11 [4,2,3,1,5]=>11 [4,2,3,5,1]=>7 [4,2,5,1,3]=>7 [4,2,5,3,1]=>5 [4,3,1,2,5]=>11 [4,3,1,5,2]=>8 [4,3,2,1,5]=>10 [4,3,2,5,1]=>6 [4,3,5,1,2]=>4 [4,3,5,2,1]=>3 [4,5,1,2,3]=>5 [4,5,1,3,2]=>4 [4,5,2,1,3]=>4 [4,5,2,3,1]=>2 [4,5,3,1,2]=>2 [4,5,3,2,1]=>1 [5,1,2,3,4]=>10 [5,1,2,4,3]=>9 [5,1,3,2,4]=>9 [5,1,3,4,2]=>7 [5,1,4,2,3]=>7 [5,1,4,3,2]=>6 [5,2,1,3,4]=>9 [5,2,1,4,3]=>8 [5,2,3,1,4]=>7 [5,2,3,4,1]=>4 [5,2,4,1,3]=>5 [5,2,4,3,1]=>3 [5,3,1,2,4]=>7 [5,3,1,4,2]=>5 [5,3,2,1,4]=>6 [5,3,2,4,1]=>3 [5,3,4,1,2]=>2 [5,3,4,2,1]=>1 [5,4,1,2,3]=>4 [5,4,1,3,2]=>3 [5,4,2,1,3]=>3 [5,4,2,3,1]=>1 [5,4,3,1,2]=>1 [5,4,3,2,1]=>0 [1,2,3,4,5,6]=>35 [1,2,3,4,6,5]=>34 [1,2,3,5,4,6]=>34 [1,2,3,5,6,4]=>32 [1,2,3,6,4,5]=>32 [1,2,3,6,5,4]=>31 [1,2,4,3,5,6]=>34 [1,2,4,3,6,5]=>33 [1,2,4,5,3,6]=>32 [1,2,4,5,6,3]=>29 [1,2,4,6,3,5]=>30 [1,2,4,6,5,3]=>28 [1,2,5,3,4,6]=>32 [1,2,5,3,6,4]=>30 [1,2,5,4,3,6]=>31 [1,2,5,4,6,3]=>28 [1,2,5,6,3,4]=>27 [1,2,5,6,4,3]=>26 [1,2,6,3,4,5]=>29 [1,2,6,3,5,4]=>28 [1,2,6,4,3,5]=>28 [1,2,6,4,5,3]=>26 [1,2,6,5,3,4]=>26 [1,2,6,5,4,3]=>25 [1,3,2,4,5,6]=>34 [1,3,2,4,6,5]=>33 [1,3,2,5,4,6]=>33 [1,3,2,5,6,4]=>31 [1,3,2,6,4,5]=>31 [1,3,2,6,5,4]=>30 [1,3,4,2,5,6]=>32 [1,3,4,2,6,5]=>31 [1,3,4,5,2,6]=>29 [1,3,4,5,6,2]=>25 [1,3,4,6,2,5]=>27 [1,3,4,6,5,2]=>24 [1,3,5,2,4,6]=>30 [1,3,5,2,6,4]=>28 [1,3,5,4,2,6]=>28 [1,3,5,4,6,2]=>24 [1,3,5,6,2,4]=>24 [1,3,5,6,4,2]=>22 [1,3,6,2,4,5]=>27 [1,3,6,2,5,4]=>26 [1,3,6,4,2,5]=>25 [1,3,6,4,5,2]=>22 [1,3,6,5,2,4]=>23 [1,3,6,5,4,2]=>21 [1,4,2,3,5,6]=>32 [1,4,2,3,6,5]=>31 [1,4,2,5,3,6]=>30 [1,4,2,5,6,3]=>27 [1,4,2,6,3,5]=>28 [1,4,2,6,5,3]=>26 [1,4,3,2,5,6]=>31 [1,4,3,2,6,5]=>30 [1,4,3,5,2,6]=>28 [1,4,3,5,6,2]=>24 [1,4,3,6,2,5]=>26 [1,4,3,6,5,2]=>23 [1,4,5,2,3,6]=>27 [1,4,5,2,6,3]=>24 [1,4,5,3,2,6]=>26 [1,4,5,3,6,2]=>22 [1,4,5,6,2,3]=>20 [1,4,5,6,3,2]=>19 [1,4,6,2,3,5]=>24 [1,4,6,2,5,3]=>22 [1,4,6,3,2,5]=>23 [1,4,6,3,5,2]=>20 [1,4,6,5,2,3]=>19 [1,4,6,5,3,2]=>18 [1,5,2,3,4,6]=>29 [1,5,2,3,6,4]=>27 [1,5,2,4,3,6]=>28 [1,5,2,4,6,3]=>25 [1,5,2,6,3,4]=>24 [1,5,2,6,4,3]=>23 [1,5,3,2,4,6]=>28 [1,5,3,2,6,4]=>26 [1,5,3,4,2,6]=>26 [1,5,3,4,6,2]=>22 [1,5,3,6,2,4]=>22 [1,5,3,6,4,2]=>20 [1,5,4,2,3,6]=>26 [1,5,4,2,6,3]=>23 [1,5,4,3,2,6]=>25 [1,5,4,3,6,2]=>21 [1,5,4,6,2,3]=>19 [1,5,4,6,3,2]=>18 [1,5,6,2,3,4]=>20 [1,5,6,2,4,3]=>19 [1,5,6,3,2,4]=>19 [1,5,6,3,4,2]=>17 [1,5,6,4,2,3]=>17 [1,5,6,4,3,2]=>16 [1,6,2,3,4,5]=>25 [1,6,2,3,5,4]=>24 [1,6,2,4,3,5]=>24 [1,6,2,4,5,3]=>22 [1,6,2,5,3,4]=>22 [1,6,2,5,4,3]=>21 [1,6,3,2,4,5]=>24 [1,6,3,2,5,4]=>23 [1,6,3,4,2,5]=>22 [1,6,3,4,5,2]=>19 [1,6,3,5,2,4]=>20 [1,6,3,5,4,2]=>18 [1,6,4,2,3,5]=>22 [1,6,4,2,5,3]=>20 [1,6,4,3,2,5]=>21 [1,6,4,3,5,2]=>18 [1,6,4,5,2,3]=>17 [1,6,4,5,3,2]=>16 [1,6,5,2,3,4]=>19 [1,6,5,2,4,3]=>18 [1,6,5,3,2,4]=>18 [1,6,5,3,4,2]=>16 [1,6,5,4,2,3]=>16 [1,6,5,4,3,2]=>15 [2,1,3,4,5,6]=>34 [2,1,3,4,6,5]=>33 [2,1,3,5,4,6]=>33 [2,1,3,5,6,4]=>31 [2,1,3,6,4,5]=>31 [2,1,3,6,5,4]=>30 [2,1,4,3,5,6]=>33 [2,1,4,3,6,5]=>32 [2,1,4,5,3,6]=>31 [2,1,4,5,6,3]=>28 [2,1,4,6,3,5]=>29 [2,1,4,6,5,3]=>27 [2,1,5,3,4,6]=>31 [2,1,5,3,6,4]=>29 [2,1,5,4,3,6]=>30 [2,1,5,4,6,3]=>27 [2,1,5,6,3,4]=>26 [2,1,5,6,4,3]=>25 [2,1,6,3,4,5]=>28 [2,1,6,3,5,4]=>27 [2,1,6,4,3,5]=>27 [2,1,6,4,5,3]=>25 [2,1,6,5,3,4]=>25 [2,1,6,5,4,3]=>24 [2,3,1,4,5,6]=>32 [2,3,1,4,6,5]=>31 [2,3,1,5,4,6]=>31 [2,3,1,5,6,4]=>29 [2,3,1,6,4,5]=>29 [2,3,1,6,5,4]=>28 [2,3,4,1,5,6]=>29 [2,3,4,1,6,5]=>28 [2,3,4,5,1,6]=>25 [2,3,4,5,6,1]=>20 [2,3,4,6,1,5]=>23 [2,3,4,6,5,1]=>19 [2,3,5,1,4,6]=>27 [2,3,5,1,6,4]=>25 [2,3,5,4,1,6]=>24 [2,3,5,4,6,1]=>19 [2,3,5,6,1,4]=>20 [2,3,5,6,4,1]=>17 [2,3,6,1,4,5]=>24 [2,3,6,1,5,4]=>23 [2,3,6,4,1,5]=>21 [2,3,6,4,5,1]=>17 [2,3,6,5,1,4]=>19 [2,3,6,5,4,1]=>16 [2,4,1,3,5,6]=>30 [2,4,1,3,6,5]=>29 [2,4,1,5,3,6]=>28 [2,4,1,5,6,3]=>25 [2,4,1,6,3,5]=>26 [2,4,1,6,5,3]=>24 [2,4,3,1,5,6]=>28 [2,4,3,1,6,5]=>27 [2,4,3,5,1,6]=>24 [2,4,3,5,6,1]=>19 [2,4,3,6,1,5]=>22 [2,4,3,6,5,1]=>18 [2,4,5,1,3,6]=>24 [2,4,5,1,6,3]=>21 [2,4,5,3,1,6]=>22 [2,4,5,3,6,1]=>17 [2,4,5,6,1,3]=>16 [2,4,5,6,3,1]=>14 [2,4,6,1,3,5]=>21 [2,4,6,1,5,3]=>19 [2,4,6,3,1,5]=>19 [2,4,6,3,5,1]=>15 [2,4,6,5,1,3]=>15 [2,4,6,5,3,1]=>13 [2,5,1,3,4,6]=>27 [2,5,1,3,6,4]=>25 [2,5,1,4,3,6]=>26 [2,5,1,4,6,3]=>23 [2,5,1,6,3,4]=>22 [2,5,1,6,4,3]=>21 [2,5,3,1,4,6]=>25 [2,5,3,1,6,4]=>23 [2,5,3,4,1,6]=>22 [2,5,3,4,6,1]=>17 [2,5,3,6,1,4]=>18 [2,5,3,6,4,1]=>15 [2,5,4,1,3,6]=>23 [2,5,4,1,6,3]=>20 [2,5,4,3,1,6]=>21 [2,5,4,3,6,1]=>16 [2,5,4,6,1,3]=>15 [2,5,4,6,3,1]=>13 [2,5,6,1,3,4]=>17 [2,5,6,1,4,3]=>16 [2,5,6,3,1,4]=>15 [2,5,6,3,4,1]=>12 [2,5,6,4,1,3]=>13 [2,5,6,4,3,1]=>11 [2,6,1,3,4,5]=>23 [2,6,1,3,5,4]=>22 [2,6,1,4,3,5]=>22 [2,6,1,4,5,3]=>20 [2,6,1,5,3,4]=>20 [2,6,1,5,4,3]=>19 [2,6,3,1,4,5]=>21 [2,6,3,1,5,4]=>20 [2,6,3,4,1,5]=>18 [2,6,3,4,5,1]=>14 [2,6,3,5,1,4]=>16 [2,6,3,5,4,1]=>13 [2,6,4,1,3,5]=>19 [2,6,4,1,5,3]=>17 [2,6,4,3,1,5]=>17 [2,6,4,3,5,1]=>13 [2,6,4,5,1,3]=>13 [2,6,4,5,3,1]=>11 [2,6,5,1,3,4]=>16 [2,6,5,1,4,3]=>15 [2,6,5,3,1,4]=>14 [2,6,5,3,4,1]=>11 [2,6,5,4,1,3]=>12 [2,6,5,4,3,1]=>10 [3,1,2,4,5,6]=>32 [3,1,2,4,6,5]=>31 [3,1,2,5,4,6]=>31 [3,1,2,5,6,4]=>29 [3,1,2,6,4,5]=>29 [3,1,2,6,5,4]=>28 [3,1,4,2,5,6]=>30 [3,1,4,2,6,5]=>29 [3,1,4,5,2,6]=>27 [3,1,4,5,6,2]=>23 [3,1,4,6,2,5]=>25 [3,1,4,6,5,2]=>22 [3,1,5,2,4,6]=>28 [3,1,5,2,6,4]=>26 [3,1,5,4,2,6]=>26 [3,1,5,4,6,2]=>22 [3,1,5,6,2,4]=>22 [3,1,5,6,4,2]=>20 [3,1,6,2,4,5]=>25 [3,1,6,2,5,4]=>24 [3,1,6,4,2,5]=>23 [3,1,6,4,5,2]=>20 [3,1,6,5,2,4]=>21 [3,1,6,5,4,2]=>19 [3,2,1,4,5,6]=>31 [3,2,1,4,6,5]=>30 [3,2,1,5,4,6]=>30 [3,2,1,5,6,4]=>28 [3,2,1,6,4,5]=>28 [3,2,1,6,5,4]=>27 [3,2,4,1,5,6]=>28 [3,2,4,1,6,5]=>27 [3,2,4,5,1,6]=>24 [3,2,4,5,6,1]=>19 [3,2,4,6,1,5]=>22 [3,2,4,6,5,1]=>18 [3,2,5,1,4,6]=>26 [3,2,5,1,6,4]=>24 [3,2,5,4,1,6]=>23 [3,2,5,4,6,1]=>18 [3,2,5,6,1,4]=>19 [3,2,5,6,4,1]=>16 [3,2,6,1,4,5]=>23 [3,2,6,1,5,4]=>22 [3,2,6,4,1,5]=>20 [3,2,6,4,5,1]=>16 [3,2,6,5,1,4]=>18 [3,2,6,5,4,1]=>15 [3,4,1,2,5,6]=>27 [3,4,1,2,6,5]=>26 [3,4,1,5,2,6]=>24 [3,4,1,5,6,2]=>20 [3,4,1,6,2,5]=>22 [3,4,1,6,5,2]=>19 [3,4,2,1,5,6]=>26 [3,4,2,1,6,5]=>25 [3,4,2,5,1,6]=>22 [3,4,2,5,6,1]=>17 [3,4,2,6,1,5]=>20 [3,4,2,6,5,1]=>16 [3,4,5,1,2,6]=>20 [3,4,5,1,6,2]=>16 [3,4,5,2,1,6]=>19 [3,4,5,2,6,1]=>14 [3,4,5,6,1,2]=>11 [3,4,5,6,2,1]=>10 [3,4,6,1,2,5]=>17 [3,4,6,1,5,2]=>14 [3,4,6,2,1,5]=>16 [3,4,6,2,5,1]=>12 [3,4,6,5,1,2]=>10 [3,4,6,5,2,1]=>9 [3,5,1,2,4,6]=>24 [3,5,1,2,6,4]=>22 [3,5,1,4,2,6]=>22 [3,5,1,4,6,2]=>18 [3,5,1,6,2,4]=>18 [3,5,1,6,4,2]=>16 [3,5,2,1,4,6]=>23 [3,5,2,1,6,4]=>21 [3,5,2,4,1,6]=>20 [3,5,2,4,6,1]=>15 [3,5,2,6,1,4]=>16 [3,5,2,6,4,1]=>13 [3,5,4,1,2,6]=>19 [3,5,4,1,6,2]=>15 [3,5,4,2,1,6]=>18 [3,5,4,2,6,1]=>13 [3,5,4,6,1,2]=>10 [3,5,4,6,2,1]=>9 [3,5,6,1,2,4]=>13 [3,5,6,1,4,2]=>11 [3,5,6,2,1,4]=>12 [3,5,6,2,4,1]=>9 [3,5,6,4,1,2]=>8 [3,5,6,4,2,1]=>7 [3,6,1,2,4,5]=>20 [3,6,1,2,5,4]=>19 [3,6,1,4,2,5]=>18 [3,6,1,4,5,2]=>15 [3,6,1,5,2,4]=>16 [3,6,1,5,4,2]=>14 [3,6,2,1,4,5]=>19 [3,6,2,1,5,4]=>18 [3,6,2,4,1,5]=>16 [3,6,2,4,5,1]=>12 [3,6,2,5,1,4]=>14 [3,6,2,5,4,1]=>11 [3,6,4,1,2,5]=>15 [3,6,4,1,5,2]=>12 [3,6,4,2,1,5]=>14 [3,6,4,2,5,1]=>10 [3,6,4,5,1,2]=>8 [3,6,4,5,2,1]=>7 [3,6,5,1,2,4]=>12 [3,6,5,1,4,2]=>10 [3,6,5,2,1,4]=>11 [3,6,5,2,4,1]=>8 [3,6,5,4,1,2]=>7 [3,6,5,4,2,1]=>6 [4,1,2,3,5,6]=>29 [4,1,2,3,6,5]=>28 [4,1,2,5,3,6]=>27 [4,1,2,5,6,3]=>24 [4,1,2,6,3,5]=>25 [4,1,2,6,5,3]=>23 [4,1,3,2,5,6]=>28 [4,1,3,2,6,5]=>27 [4,1,3,5,2,6]=>25 [4,1,3,5,6,2]=>21 [4,1,3,6,2,5]=>23 [4,1,3,6,5,2]=>20 [4,1,5,2,3,6]=>24 [4,1,5,2,6,3]=>21 [4,1,5,3,2,6]=>23 [4,1,5,3,6,2]=>19 [4,1,5,6,2,3]=>17 [4,1,5,6,3,2]=>16 [4,1,6,2,3,5]=>21 [4,1,6,2,5,3]=>19 [4,1,6,3,2,5]=>20 [4,1,6,3,5,2]=>17 [4,1,6,5,2,3]=>16 [4,1,6,5,3,2]=>15 [4,2,1,3,5,6]=>28 [4,2,1,3,6,5]=>27 [4,2,1,5,3,6]=>26 [4,2,1,5,6,3]=>23 [4,2,1,6,3,5]=>24 [4,2,1,6,5,3]=>22 [4,2,3,1,5,6]=>26 [4,2,3,1,6,5]=>25 [4,2,3,5,1,6]=>22 [4,2,3,5,6,1]=>17 [4,2,3,6,1,5]=>20 [4,2,3,6,5,1]=>16 [4,2,5,1,3,6]=>22 [4,2,5,1,6,3]=>19 [4,2,5,3,1,6]=>20 [4,2,5,3,6,1]=>15 [4,2,5,6,1,3]=>14 [4,2,5,6,3,1]=>12 [4,2,6,1,3,5]=>19 [4,2,6,1,5,3]=>17 [4,2,6,3,1,5]=>17 [4,2,6,3,5,1]=>13 [4,2,6,5,1,3]=>13 [4,2,6,5,3,1]=>11 [4,3,1,2,5,6]=>26 [4,3,1,2,6,5]=>25 [4,3,1,5,2,6]=>23 [4,3,1,5,6,2]=>19 [4,3,1,6,2,5]=>21 [4,3,1,6,5,2]=>18 [4,3,2,1,5,6]=>25 [4,3,2,1,6,5]=>24 [4,3,2,5,1,6]=>21 [4,3,2,5,6,1]=>16 [4,3,2,6,1,5]=>19 [4,3,2,6,5,1]=>15 [4,3,5,1,2,6]=>19 [4,3,5,1,6,2]=>15 [4,3,5,2,1,6]=>18 [4,3,5,2,6,1]=>13 [4,3,5,6,1,2]=>10 [4,3,5,6,2,1]=>9 [4,3,6,1,2,5]=>16 [4,3,6,1,5,2]=>13 [4,3,6,2,1,5]=>15 [4,3,6,2,5,1]=>11 [4,3,6,5,1,2]=>9 [4,3,6,5,2,1]=>8 [4,5,1,2,3,6]=>20 [4,5,1,2,6,3]=>17 [4,5,1,3,2,6]=>19 [4,5,1,3,6,2]=>15 [4,5,1,6,2,3]=>13 [4,5,1,6,3,2]=>12 [4,5,2,1,3,6]=>19 [4,5,2,1,6,3]=>16 [4,5,2,3,1,6]=>17 [4,5,2,3,6,1]=>12 [4,5,2,6,1,3]=>11 [4,5,2,6,3,1]=>9 [4,5,3,1,2,6]=>17 [4,5,3,1,6,2]=>13 [4,5,3,2,1,6]=>16 [4,5,3,2,6,1]=>11 [4,5,3,6,1,2]=>8 [4,5,3,6,2,1]=>7 [4,5,6,1,2,3]=>8 [4,5,6,1,3,2]=>7 [4,5,6,2,1,3]=>7 [4,5,6,2,3,1]=>5 [4,5,6,3,1,2]=>5 [4,5,6,3,2,1]=>4 [4,6,1,2,3,5]=>16 [4,6,1,2,5,3]=>14 [4,6,1,3,2,5]=>15 [4,6,1,3,5,2]=>12 [4,6,1,5,2,3]=>11 [4,6,1,5,3,2]=>10 [4,6,2,1,3,5]=>15 [4,6,2,1,5,3]=>13 [4,6,2,3,1,5]=>13 [4,6,2,3,5,1]=>9 [4,6,2,5,1,3]=>9 [4,6,2,5,3,1]=>7 [4,6,3,1,2,5]=>13 [4,6,3,1,5,2]=>10 [4,6,3,2,1,5]=>12 [4,6,3,2,5,1]=>8 [4,6,3,5,1,2]=>6 [4,6,3,5,2,1]=>5 [4,6,5,1,2,3]=>7 [4,6,5,1,3,2]=>6 [4,6,5,2,1,3]=>6 [4,6,5,2,3,1]=>4 [4,6,5,3,1,2]=>4 [4,6,5,3,2,1]=>3 [5,1,2,3,4,6]=>25 [5,1,2,3,6,4]=>23 [5,1,2,4,3,6]=>24 [5,1,2,4,6,3]=>21 [5,1,2,6,3,4]=>20 [5,1,2,6,4,3]=>19 [5,1,3,2,4,6]=>24 [5,1,3,2,6,4]=>22 [5,1,3,4,2,6]=>22 [5,1,3,4,6,2]=>18 [5,1,3,6,2,4]=>18 [5,1,3,6,4,2]=>16 [5,1,4,2,3,6]=>22 [5,1,4,2,6,3]=>19 [5,1,4,3,2,6]=>21 [5,1,4,3,6,2]=>17 [5,1,4,6,2,3]=>15 [5,1,4,6,3,2]=>14 [5,1,6,2,3,4]=>16 [5,1,6,2,4,3]=>15 [5,1,6,3,2,4]=>15 [5,1,6,3,4,2]=>13 [5,1,6,4,2,3]=>13 [5,1,6,4,3,2]=>12 [5,2,1,3,4,6]=>24 [5,2,1,3,6,4]=>22 [5,2,1,4,3,6]=>23 [5,2,1,4,6,3]=>20 [5,2,1,6,3,4]=>19 [5,2,1,6,4,3]=>18 [5,2,3,1,4,6]=>22 [5,2,3,1,6,4]=>20 [5,2,3,4,1,6]=>19 [5,2,3,4,6,1]=>14 [5,2,3,6,1,4]=>15 [5,2,3,6,4,1]=>12 [5,2,4,1,3,6]=>20 [5,2,4,1,6,3]=>17 [5,2,4,3,1,6]=>18 [5,2,4,3,6,1]=>13 [5,2,4,6,1,3]=>12 [5,2,4,6,3,1]=>10 [5,2,6,1,3,4]=>14 [5,2,6,1,4,3]=>13 [5,2,6,3,1,4]=>12 [5,2,6,3,4,1]=>9 [5,2,6,4,1,3]=>10 [5,2,6,4,3,1]=>8 [5,3,1,2,4,6]=>22 [5,3,1,2,6,4]=>20 [5,3,1,4,2,6]=>20 [5,3,1,4,6,2]=>16 [5,3,1,6,2,4]=>16 [5,3,1,6,4,2]=>14 [5,3,2,1,4,6]=>21 [5,3,2,1,6,4]=>19 [5,3,2,4,1,6]=>18 [5,3,2,4,6,1]=>13 [5,3,2,6,1,4]=>14 [5,3,2,6,4,1]=>11 [5,3,4,1,2,6]=>17 [5,3,4,1,6,2]=>13 [5,3,4,2,1,6]=>16 [5,3,4,2,6,1]=>11 [5,3,4,6,1,2]=>8 [5,3,4,6,2,1]=>7 [5,3,6,1,2,4]=>11 [5,3,6,1,4,2]=>9 [5,3,6,2,1,4]=>10 [5,3,6,2,4,1]=>7 [5,3,6,4,1,2]=>6 [5,3,6,4,2,1]=>5 [5,4,1,2,3,6]=>19 [5,4,1,2,6,3]=>16 [5,4,1,3,2,6]=>18 [5,4,1,3,6,2]=>14 [5,4,1,6,2,3]=>12 [5,4,1,6,3,2]=>11 [5,4,2,1,3,6]=>18 [5,4,2,1,6,3]=>15 [5,4,2,3,1,6]=>16 [5,4,2,3,6,1]=>11 [5,4,2,6,1,3]=>10 [5,4,2,6,3,1]=>8 [5,4,3,1,2,6]=>16 [5,4,3,1,6,2]=>12 [5,4,3,2,1,6]=>15 [5,4,3,2,6,1]=>10 [5,4,3,6,1,2]=>7 [5,4,3,6,2,1]=>6 [5,4,6,1,2,3]=>7 [5,4,6,1,3,2]=>6 [5,4,6,2,1,3]=>6 [5,4,6,2,3,1]=>4 [5,4,6,3,1,2]=>4 [5,4,6,3,2,1]=>3 [5,6,1,2,3,4]=>11 [5,6,1,2,4,3]=>10 [5,6,1,3,2,4]=>10 [5,6,1,3,4,2]=>8 [5,6,1,4,2,3]=>8 [5,6,1,4,3,2]=>7 [5,6,2,1,3,4]=>10 [5,6,2,1,4,3]=>9 [5,6,2,3,1,4]=>8 [5,6,2,3,4,1]=>5 [5,6,2,4,1,3]=>6 [5,6,2,4,3,1]=>4 [5,6,3,1,2,4]=>8 [5,6,3,1,4,2]=>6 [5,6,3,2,1,4]=>7 [5,6,3,2,4,1]=>4 [5,6,3,4,1,2]=>3 [5,6,3,4,2,1]=>2 [5,6,4,1,2,3]=>5 [5,6,4,1,3,2]=>4 [5,6,4,2,1,3]=>4 [5,6,4,2,3,1]=>2 [5,6,4,3,1,2]=>2 [5,6,4,3,2,1]=>1 [6,1,2,3,4,5]=>20 [6,1,2,3,5,4]=>19 [6,1,2,4,3,5]=>19 [6,1,2,4,5,3]=>17 [6,1,2,5,3,4]=>17 [6,1,2,5,4,3]=>16 [6,1,3,2,4,5]=>19 [6,1,3,2,5,4]=>18 [6,1,3,4,2,5]=>17 [6,1,3,4,5,2]=>14 [6,1,3,5,2,4]=>15 [6,1,3,5,4,2]=>13 [6,1,4,2,3,5]=>17 [6,1,4,2,5,3]=>15 [6,1,4,3,2,5]=>16 [6,1,4,3,5,2]=>13 [6,1,4,5,2,3]=>12 [6,1,4,5,3,2]=>11 [6,1,5,2,3,4]=>14 [6,1,5,2,4,3]=>13 [6,1,5,3,2,4]=>13 [6,1,5,3,4,2]=>11 [6,1,5,4,2,3]=>11 [6,1,5,4,3,2]=>10 [6,2,1,3,4,5]=>19 [6,2,1,3,5,4]=>18 [6,2,1,4,3,5]=>18 [6,2,1,4,5,3]=>16 [6,2,1,5,3,4]=>16 [6,2,1,5,4,3]=>15 [6,2,3,1,4,5]=>17 [6,2,3,1,5,4]=>16 [6,2,3,4,1,5]=>14 [6,2,3,4,5,1]=>10 [6,2,3,5,1,4]=>12 [6,2,3,5,4,1]=>9 [6,2,4,1,3,5]=>15 [6,2,4,1,5,3]=>13 [6,2,4,3,1,5]=>13 [6,2,4,3,5,1]=>9 [6,2,4,5,1,3]=>9 [6,2,4,5,3,1]=>7 [6,2,5,1,3,4]=>12 [6,2,5,1,4,3]=>11 [6,2,5,3,1,4]=>10 [6,2,5,3,4,1]=>7 [6,2,5,4,1,3]=>8 [6,2,5,4,3,1]=>6 [6,3,1,2,4,5]=>17 [6,3,1,2,5,4]=>16 [6,3,1,4,2,5]=>15 [6,3,1,4,5,2]=>12 [6,3,1,5,2,4]=>13 [6,3,1,5,4,2]=>11 [6,3,2,1,4,5]=>16 [6,3,2,1,5,4]=>15 [6,3,2,4,1,5]=>13 [6,3,2,4,5,1]=>9 [6,3,2,5,1,4]=>11 [6,3,2,5,4,1]=>8 [6,3,4,1,2,5]=>12 [6,3,4,1,5,2]=>9 [6,3,4,2,1,5]=>11 [6,3,4,2,5,1]=>7 [6,3,4,5,1,2]=>5 [6,3,4,5,2,1]=>4 [6,3,5,1,2,4]=>9 [6,3,5,1,4,2]=>7 [6,3,5,2,1,4]=>8 [6,3,5,2,4,1]=>5 [6,3,5,4,1,2]=>4 [6,3,5,4,2,1]=>3 [6,4,1,2,3,5]=>14 [6,4,1,2,5,3]=>12 [6,4,1,3,2,5]=>13 [6,4,1,3,5,2]=>10 [6,4,1,5,2,3]=>9 [6,4,1,5,3,2]=>8 [6,4,2,1,3,5]=>13 [6,4,2,1,5,3]=>11 [6,4,2,3,1,5]=>11 [6,4,2,3,5,1]=>7 [6,4,2,5,1,3]=>7 [6,4,2,5,3,1]=>5 [6,4,3,1,2,5]=>11 [6,4,3,1,5,2]=>8 [6,4,3,2,1,5]=>10 [6,4,3,2,5,1]=>6 [6,4,3,5,1,2]=>4 [6,4,3,5,2,1]=>3 [6,4,5,1,2,3]=>5 [6,4,5,1,3,2]=>4 [6,4,5,2,1,3]=>4 [6,4,5,2,3,1]=>2 [6,4,5,3,1,2]=>2 [6,4,5,3,2,1]=>1 [6,5,1,2,3,4]=>10 [6,5,1,2,4,3]=>9 [6,5,1,3,2,4]=>9 [6,5,1,3,4,2]=>7 [6,5,1,4,2,3]=>7 [6,5,1,4,3,2]=>6 [6,5,2,1,3,4]=>9 [6,5,2,1,4,3]=>8 [6,5,2,3,1,4]=>7 [6,5,2,3,4,1]=>4 [6,5,2,4,1,3]=>5 [6,5,2,4,3,1]=>3 [6,5,3,1,2,4]=>7 [6,5,3,1,4,2]=>5 [6,5,3,2,1,4]=>6 [6,5,3,2,4,1]=>3 [6,5,3,4,1,2]=>2 [6,5,3,4,2,1]=>1 [6,5,4,1,2,3]=>4 [6,5,4,1,3,2]=>3 [6,5,4,2,1,3]=>3 [6,5,4,2,3,1]=>1 [6,5,4,3,1,2]=>1 [6,5,4,3,2,1]=>0 [1,2,3,4,5,6,7]=>56 [1,2,3,4,5,7,6]=>55 [1,2,3,4,6,5,7]=>55 [1,2,3,4,6,7,5]=>53 [1,2,3,4,7,5,6]=>53 [1,2,3,4,7,6,5]=>52 [1,2,3,5,4,6,7]=>55 [1,2,3,5,4,7,6]=>54 [1,2,3,5,6,4,7]=>53 [1,2,3,5,6,7,4]=>50 [1,2,3,5,7,4,6]=>51 [1,2,3,5,7,6,4]=>49 [1,2,3,6,4,5,7]=>53 [1,2,3,6,4,7,5]=>51 [1,2,3,6,5,4,7]=>52 [1,2,3,6,5,7,4]=>49 [1,2,3,6,7,4,5]=>48 [1,2,3,6,7,5,4]=>47 [1,2,3,7,4,5,6]=>50 [1,2,3,7,4,6,5]=>49 [1,2,3,7,5,4,6]=>49 [1,2,3,7,5,6,4]=>47 [1,2,3,7,6,4,5]=>47 [1,2,3,7,6,5,4]=>46 [1,2,4,3,5,6,7]=>55 [1,2,4,3,5,7,6]=>54 [1,2,4,3,6,5,7]=>54 [1,2,4,3,6,7,5]=>52 [1,2,4,3,7,5,6]=>52 [1,2,4,3,7,6,5]=>51 [1,2,4,5,3,6,7]=>53 [1,2,4,5,3,7,6]=>52 [1,2,4,5,6,3,7]=>50 [1,2,4,5,6,7,3]=>46 [1,2,4,5,7,3,6]=>48 [1,2,4,5,7,6,3]=>45 [1,2,4,6,3,5,7]=>51 [1,2,4,6,3,7,5]=>49 [1,2,4,6,5,3,7]=>49 [1,2,4,6,5,7,3]=>45 [1,2,4,6,7,3,5]=>45 [1,2,4,6,7,5,3]=>43 [1,2,4,7,3,5,6]=>48 [1,2,4,7,3,6,5]=>47 [1,2,4,7,5,3,6]=>46 [1,2,4,7,5,6,3]=>43 [1,2,4,7,6,3,5]=>44 [1,2,4,7,6,5,3]=>42 [1,2,5,3,4,6,7]=>53 [1,2,5,3,4,7,6]=>52 [1,2,5,3,6,4,7]=>51 [1,2,5,3,6,7,4]=>48 [1,2,5,3,7,4,6]=>49 [1,2,5,3,7,6,4]=>47 [1,2,5,4,3,6,7]=>52 [1,2,5,4,3,7,6]=>51 [1,2,5,4,6,3,7]=>49 [1,2,5,4,6,7,3]=>45 [1,2,5,4,7,3,6]=>47 [1,2,5,4,7,6,3]=>44 [1,2,5,6,3,4,7]=>48 [1,2,5,6,3,7,4]=>45 [1,2,5,6,4,3,7]=>47 [1,2,5,6,4,7,3]=>43 [1,2,5,6,7,3,4]=>41 [1,2,5,6,7,4,3]=>40 [1,2,5,7,3,4,6]=>45 [1,2,5,7,3,6,4]=>43 [1,2,5,7,4,3,6]=>44 [1,2,5,7,4,6,3]=>41 [1,2,5,7,6,3,4]=>40 [1,2,5,7,6,4,3]=>39 [1,2,6,3,4,5,7]=>50 [1,2,6,3,4,7,5]=>48 [1,2,6,3,5,4,7]=>49 [1,2,6,3,5,7,4]=>46 [1,2,6,3,7,4,5]=>45 [1,2,6,3,7,5,4]=>44 [1,2,6,4,3,5,7]=>49 [1,2,6,4,3,7,5]=>47 [1,2,6,4,5,3,7]=>47 [1,2,6,4,5,7,3]=>43 [1,2,6,4,7,3,5]=>43 [1,2,6,4,7,5,3]=>41 [1,2,6,5,3,4,7]=>47 [1,2,6,5,3,7,4]=>44 [1,2,6,5,4,3,7]=>46 [1,2,6,5,4,7,3]=>42 [1,2,6,5,7,3,4]=>40 [1,2,6,5,7,4,3]=>39 [1,2,6,7,3,4,5]=>41 [1,2,6,7,3,5,4]=>40 [1,2,6,7,4,3,5]=>40 [1,2,6,7,4,5,3]=>38 [1,2,6,7,5,3,4]=>38 [1,2,6,7,5,4,3]=>37 [1,2,7,3,4,5,6]=>46 [1,2,7,3,4,6,5]=>45 [1,2,7,3,5,4,6]=>45 [1,2,7,3,5,6,4]=>43 [1,2,7,3,6,4,5]=>43 [1,2,7,3,6,5,4]=>42 [1,2,7,4,3,5,6]=>45 [1,2,7,4,3,6,5]=>44 [1,2,7,4,5,3,6]=>43 [1,2,7,4,5,6,3]=>40 [1,2,7,4,6,3,5]=>41 [1,2,7,4,6,5,3]=>39 [1,2,7,5,3,4,6]=>43 [1,2,7,5,3,6,4]=>41 [1,2,7,5,4,3,6]=>42 [1,2,7,5,4,6,3]=>39 [1,2,7,5,6,3,4]=>38 [1,2,7,5,6,4,3]=>37 [1,2,7,6,3,4,5]=>40 [1,2,7,6,3,5,4]=>39 [1,2,7,6,4,3,5]=>39 [1,2,7,6,4,5,3]=>37 [1,2,7,6,5,3,4]=>37 [1,2,7,6,5,4,3]=>36 [1,3,2,4,5,6,7]=>55 [1,3,2,4,5,7,6]=>54 [1,3,2,4,6,5,7]=>54 [1,3,2,4,6,7,5]=>52 [1,3,2,4,7,5,6]=>52 [1,3,2,4,7,6,5]=>51 [1,3,2,5,4,6,7]=>54 [1,3,2,5,4,7,6]=>53 [1,3,2,5,6,4,7]=>52 [1,3,2,5,6,7,4]=>49 [1,3,2,5,7,4,6]=>50 [1,3,2,5,7,6,4]=>48 [1,3,2,6,4,5,7]=>52 [1,3,2,6,4,7,5]=>50 [1,3,2,6,5,4,7]=>51 [1,3,2,6,5,7,4]=>48 [1,3,2,6,7,4,5]=>47 [1,3,2,6,7,5,4]=>46 [1,3,2,7,4,5,6]=>49 [1,3,2,7,4,6,5]=>48 [1,3,2,7,5,4,6]=>48 [1,3,2,7,5,6,4]=>46 [1,3,2,7,6,4,5]=>46 [1,3,2,7,6,5,4]=>45 [1,3,4,2,5,6,7]=>53 [1,3,4,2,5,7,6]=>52 [1,3,4,2,6,5,7]=>52 [1,3,4,2,6,7,5]=>50 [1,3,4,2,7,5,6]=>50 [1,3,4,2,7,6,5]=>49 [1,3,4,5,2,6,7]=>50 [1,3,4,5,2,7,6]=>49 [1,3,4,5,6,2,7]=>46 [1,3,4,5,6,7,2]=>41 [1,3,4,5,7,2,6]=>44 [1,3,4,5,7,6,2]=>40 [1,3,4,6,2,5,7]=>48 [1,3,4,6,2,7,5]=>46 [1,3,4,6,5,2,7]=>45 [1,3,4,6,5,7,2]=>40 [1,3,4,6,7,2,5]=>41 [1,3,4,6,7,5,2]=>38 [1,3,4,7,2,5,6]=>45 [1,3,4,7,2,6,5]=>44 [1,3,4,7,5,2,6]=>42 [1,3,4,7,5,6,2]=>38 [1,3,4,7,6,2,5]=>40 [1,3,4,7,6,5,2]=>37 [1,3,5,2,4,6,7]=>51 [1,3,5,2,4,7,6]=>50 [1,3,5,2,6,4,7]=>49 [1,3,5,2,6,7,4]=>46 [1,3,5,2,7,4,6]=>47 [1,3,5,2,7,6,4]=>45 [1,3,5,4,2,6,7]=>49 [1,3,5,4,2,7,6]=>48 [1,3,5,4,6,2,7]=>45 [1,3,5,4,6,7,2]=>40 [1,3,5,4,7,2,6]=>43 [1,3,5,4,7,6,2]=>39 [1,3,5,6,2,4,7]=>45 [1,3,5,6,2,7,4]=>42 [1,3,5,6,4,2,7]=>43 [1,3,5,6,4,7,2]=>38 [1,3,5,6,7,2,4]=>37 [1,3,5,6,7,4,2]=>35 [1,3,5,7,2,4,6]=>42 [1,3,5,7,2,6,4]=>40 [1,3,5,7,4,2,6]=>40 [1,3,5,7,4,6,2]=>36 [1,3,5,7,6,2,4]=>36 [1,3,5,7,6,4,2]=>34 [1,3,6,2,4,5,7]=>48 [1,3,6,2,4,7,5]=>46 [1,3,6,2,5,4,7]=>47 [1,3,6,2,5,7,4]=>44 [1,3,6,2,7,4,5]=>43 [1,3,6,2,7,5,4]=>42 [1,3,6,4,2,5,7]=>46 [1,3,6,4,2,7,5]=>44 [1,3,6,4,5,2,7]=>43 [1,3,6,4,5,7,2]=>38 [1,3,6,4,7,2,5]=>39 [1,3,6,4,7,5,2]=>36 [1,3,6,5,2,4,7]=>44 [1,3,6,5,2,7,4]=>41 [1,3,6,5,4,2,7]=>42 [1,3,6,5,4,7,2]=>37 [1,3,6,5,7,2,4]=>36 [1,3,6,5,7,4,2]=>34 [1,3,6,7,2,4,5]=>38 [1,3,6,7,2,5,4]=>37 [1,3,6,7,4,2,5]=>36 [1,3,6,7,4,5,2]=>33 [1,3,6,7,5,2,4]=>34 [1,3,6,7,5,4,2]=>32 [1,3,7,2,4,5,6]=>44 [1,3,7,2,4,6,5]=>43 [1,3,7,2,5,4,6]=>43 [1,3,7,2,5,6,4]=>41 [1,3,7,2,6,4,5]=>41 [1,3,7,2,6,5,4]=>40 [1,3,7,4,2,5,6]=>42 [1,3,7,4,2,6,5]=>41 [1,3,7,4,5,2,6]=>39 [1,3,7,4,5,6,2]=>35 [1,3,7,4,6,2,5]=>37 [1,3,7,4,6,5,2]=>34 [1,3,7,5,2,4,6]=>40 [1,3,7,5,2,6,4]=>38 [1,3,7,5,4,2,6]=>38 [1,3,7,5,4,6,2]=>34 [1,3,7,5,6,2,4]=>34 [1,3,7,5,6,4,2]=>32 [1,3,7,6,2,4,5]=>37 [1,3,7,6,2,5,4]=>36 [1,3,7,6,4,2,5]=>35 [1,3,7,6,4,5,2]=>32 [1,3,7,6,5,2,4]=>33 [1,3,7,6,5,4,2]=>31 [1,4,2,3,5,6,7]=>53 [1,4,2,3,5,7,6]=>52 [1,4,2,3,6,5,7]=>52 [1,4,2,3,6,7,5]=>50 [1,4,2,3,7,5,6]=>50 [1,4,2,3,7,6,5]=>49 [1,4,2,5,3,6,7]=>51 [1,4,2,5,3,7,6]=>50 [1,4,2,5,6,3,7]=>48 [1,4,2,5,6,7,3]=>44 [1,4,2,5,7,3,6]=>46 [1,4,2,5,7,6,3]=>43 [1,4,2,6,3,5,7]=>49 [1,4,2,6,3,7,5]=>47 [1,4,2,6,5,3,7]=>47 [1,4,2,6,5,7,3]=>43 [1,4,2,6,7,3,5]=>43 [1,4,2,6,7,5,3]=>41 [1,4,2,7,3,5,6]=>46 [1,4,2,7,3,6,5]=>45 [1,4,2,7,5,3,6]=>44 [1,4,2,7,5,6,3]=>41 [1,4,2,7,6,3,5]=>42 [1,4,2,7,6,5,3]=>40 [1,4,3,2,5,6,7]=>52 [1,4,3,2,5,7,6]=>51 [1,4,3,2,6,5,7]=>51 [1,4,3,2,6,7,5]=>49 [1,4,3,2,7,5,6]=>49 [1,4,3,2,7,6,5]=>48 [1,4,3,5,2,6,7]=>49 [1,4,3,5,2,7,6]=>48 [1,4,3,5,6,2,7]=>45 [1,4,3,5,6,7,2]=>40 [1,4,3,5,7,2,6]=>43 [1,4,3,5,7,6,2]=>39 [1,4,3,6,2,5,7]=>47 [1,4,3,6,2,7,5]=>45 [1,4,3,6,5,2,7]=>44 [1,4,3,6,5,7,2]=>39 [1,4,3,6,7,2,5]=>40 [1,4,3,6,7,5,2]=>37 [1,4,3,7,2,5,6]=>44 [1,4,3,7,2,6,5]=>43 [1,4,3,7,5,2,6]=>41 [1,4,3,7,5,6,2]=>37 [1,4,3,7,6,2,5]=>39 [1,4,3,7,6,5,2]=>36 [1,4,5,2,3,6,7]=>48 [1,4,5,2,3,7,6]=>47 [1,4,5,2,6,3,7]=>45 [1,4,5,2,6,7,3]=>41 [1,4,5,2,7,3,6]=>43 [1,4,5,2,7,6,3]=>40 [1,4,5,3,2,6,7]=>47 [1,4,5,3,2,7,6]=>46 [1,4,5,3,6,2,7]=>43 [1,4,5,3,6,7,2]=>38 [1,4,5,3,7,2,6]=>41 [1,4,5,3,7,6,2]=>37 [1,4,5,6,2,3,7]=>41 [1,4,5,6,2,7,3]=>37 [1,4,5,6,3,2,7]=>40 [1,4,5,6,3,7,2]=>35 [1,4,5,6,7,2,3]=>32 [1,4,5,6,7,3,2]=>31 [1,4,5,7,2,3,6]=>38 [1,4,5,7,2,6,3]=>35 [1,4,5,7,3,2,6]=>37 [1,4,5,7,3,6,2]=>33 [1,4,5,7,6,2,3]=>31 [1,4,5,7,6,3,2]=>30 [1,4,6,2,3,5,7]=>45 [1,4,6,2,3,7,5]=>43 [1,4,6,2,5,3,7]=>43 [1,4,6,2,5,7,3]=>39 [1,4,6,2,7,3,5]=>39 [1,4,6,2,7,5,3]=>37 [1,4,6,3,2,5,7]=>44 [1,4,6,3,2,7,5]=>42 [1,4,6,3,5,2,7]=>41 [1,4,6,3,5,7,2]=>36 [1,4,6,3,7,2,5]=>37 [1,4,6,3,7,5,2]=>34 [1,4,6,5,2,3,7]=>40 [1,4,6,5,2,7,3]=>36 [1,4,6,5,3,2,7]=>39 [1,4,6,5,3,7,2]=>34
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Description
The non-inversion sum of a permutation.
A pair $a < b$ is an noninversion of a permutation $\pi$ if $\pi(a) < \pi(b)$. The non-inversion sum is given by $\sum(b-a)$ over all non-inversions of $\pi$.
References
[1] Sack, J., Ăšlfarsson, H. Refined inversion statistics on permutations MathSciNet:2880660 arXiv:1106.1995
[2] The inversion sum of a permutation. St000055
Code
def statistic(pi):
        return sum( inv[1]-inv[0] for inv in pi.noninversions(2) )

Created
Dec 23, 2015 at 08:49 by Christian Stump
Updated
Sep 29, 2022 at 19:06 by Will Dowling