Identifier
- St000484: Permutations ⟶ ℤ
Values
=>
[1]=>0
[1,2]=>0
[2,1]=>0
[1,2,3]=>1
[1,3,2]=>2
[2,1,3]=>2
[2,3,1]=>2
[3,1,2]=>2
[3,2,1]=>1
[1,2,3,4]=>5
[1,2,4,3]=>8
[1,3,2,4]=>9
[1,3,4,2]=>9
[1,4,2,3]=>10
[1,4,3,2]=>9
[2,1,3,4]=>8
[2,1,4,3]=>11
[2,3,1,4]=>10
[2,3,4,1]=>9
[2,4,1,3]=>11
[2,4,3,1]=>9
[3,1,2,4]=>9
[3,1,4,2]=>11
[3,2,1,4]=>9
[3,2,4,1]=>10
[3,4,1,2]=>11
[3,4,2,1]=>8
[4,1,2,3]=>9
[4,1,3,2]=>10
[4,2,1,3]=>9
[4,2,3,1]=>9
[4,3,1,2]=>8
[4,3,2,1]=>5
[1,2,3,4,5]=>16
[1,2,3,5,4]=>23
[1,2,4,3,5]=>26
[1,2,4,5,3]=>26
[1,2,5,3,4]=>29
[1,2,5,4,3]=>28
[1,3,2,4,5]=>26
[1,3,2,5,4]=>33
[1,3,4,2,5]=>30
[1,3,4,5,2]=>27
[1,3,5,2,4]=>33
[1,3,5,4,2]=>29
[1,4,2,3,5]=>30
[1,4,2,5,3]=>34
[1,4,3,2,5]=>32
[1,4,3,5,2]=>33
[1,4,5,2,3]=>34
[1,4,5,3,2]=>29
[1,5,2,3,4]=>31
[1,5,2,4,3]=>34
[1,5,3,2,4]=>33
[1,5,3,4,2]=>33
[1,5,4,2,3]=>32
[1,5,4,3,2]=>27
[2,1,3,4,5]=>23
[2,1,3,5,4]=>30
[2,1,4,3,5]=>33
[2,1,4,5,3]=>33
[2,1,5,3,4]=>36
[2,1,5,4,3]=>35
[2,3,1,4,5]=>29
[2,3,1,5,4]=>36
[2,3,4,1,5]=>31
[2,3,4,5,1]=>27
[2,3,5,1,4]=>34
[2,3,5,4,1]=>29
[2,4,1,3,5]=>33
[2,4,1,5,3]=>37
[2,4,3,1,5]=>33
[2,4,3,5,1]=>33
[2,4,5,1,3]=>35
[2,4,5,3,1]=>29
[2,5,1,3,4]=>34
[2,5,1,4,3]=>37
[2,5,3,1,4]=>34
[2,5,3,4,1]=>33
[2,5,4,1,3]=>33
[2,5,4,3,1]=>27
[3,1,2,4,5]=>26
[3,1,2,5,4]=>33
[3,1,4,2,5]=>34
[3,1,4,5,2]=>33
[3,1,5,2,4]=>37
[3,1,5,4,2]=>35
[3,2,1,4,5]=>28
[3,2,1,5,4]=>35
[3,2,4,1,5]=>34
[3,2,4,5,1]=>32
[3,2,5,1,4]=>37
[3,2,5,4,1]=>34
[3,4,1,2,5]=>34
[3,4,1,5,2]=>37
[3,4,2,1,5]=>32
[3,4,2,5,1]=>34
[3,4,5,1,2]=>35
[3,4,5,2,1]=>28
[3,5,1,2,4]=>35
[3,5,1,4,2]=>37
[3,5,2,1,4]=>33
[3,5,2,4,1]=>34
[3,5,4,1,2]=>33
[3,5,4,2,1]=>26
[4,1,2,3,5]=>27
[4,1,2,5,3]=>33
[4,1,3,2,5]=>33
[4,1,3,5,2]=>34
[4,1,5,2,3]=>37
[4,1,5,3,2]=>34
[4,2,1,3,5]=>29
[4,2,1,5,3]=>35
[4,2,3,1,5]=>33
[4,2,3,5,1]=>33
[4,2,5,1,3]=>37
[4,2,5,3,1]=>33
[4,3,1,2,5]=>29
[4,3,1,5,2]=>34
[4,3,2,1,5]=>27
[4,3,2,5,1]=>31
[4,3,5,1,2]=>36
[4,3,5,2,1]=>29
[4,5,1,2,3]=>35
[4,5,1,3,2]=>36
[4,5,2,1,3]=>33
[4,5,2,3,1]=>33
[4,5,3,1,2]=>30
[4,5,3,2,1]=>23
[5,1,2,3,4]=>27
[5,1,2,4,3]=>32
[5,1,3,2,4]=>33
[5,1,3,4,2]=>33
[5,1,4,2,3]=>34
[5,1,4,3,2]=>31
[5,2,1,3,4]=>29
[5,2,1,4,3]=>34
[5,2,3,1,4]=>33
[5,2,3,4,1]=>32
[5,2,4,1,3]=>34
[5,2,4,3,1]=>30
[5,3,1,2,4]=>29
[5,3,1,4,2]=>33
[5,3,2,1,4]=>27
[5,3,2,4,1]=>30
[5,3,4,1,2]=>33
[5,3,4,2,1]=>26
[5,4,1,2,3]=>28
[5,4,1,3,2]=>29
[5,4,2,1,3]=>26
[5,4,2,3,1]=>26
[5,4,3,1,2]=>23
[5,4,3,2,1]=>16
[1,2,3,4,5,6]=>42
[1,2,3,4,6,5]=>57
[1,2,3,5,4,6]=>64
[1,2,3,5,6,4]=>64
[1,2,3,6,4,5]=>71
[1,2,3,6,5,4]=>70
[1,2,4,3,5,6]=>66
[1,2,4,3,6,5]=>81
[1,2,4,5,3,6]=>74
[1,2,4,5,6,3]=>67
[1,2,4,6,3,5]=>81
[1,2,4,6,5,3]=>73
[1,2,5,3,4,6]=>76
[1,2,5,3,6,4]=>84
[1,2,5,4,3,6]=>82
[1,2,5,4,6,3]=>83
[1,2,5,6,3,4]=>84
[1,2,5,6,4,3]=>75
[1,2,6,3,4,5]=>79
[1,2,6,3,5,4]=>86
[1,2,6,4,3,5]=>85
[1,2,6,4,5,3]=>85
[1,2,6,5,3,4]=>84
[1,2,6,5,4,3]=>75
[1,3,2,4,5,6]=>64
[1,3,2,4,6,5]=>79
[1,3,2,5,4,6]=>86
[1,3,2,5,6,4]=>86
[1,3,2,6,4,5]=>93
[1,3,2,6,5,4]=>92
[1,3,4,2,5,6]=>76
[1,3,4,2,6,5]=>91
[1,3,4,5,2,6]=>78
[1,3,4,5,6,2]=>68
[1,3,4,6,2,5]=>85
[1,3,4,6,5,2]=>74
[1,3,5,2,4,6]=>86
[1,3,5,2,6,4]=>94
[1,3,5,4,2,6]=>86
[1,3,5,4,6,2]=>84
[1,3,5,6,2,4]=>88
[1,3,5,6,4,2]=>76
[1,3,6,2,4,5]=>89
[1,3,6,2,5,4]=>96
[1,3,6,4,2,5]=>89
[1,3,6,4,5,2]=>86
[1,3,6,5,2,4]=>88
[1,3,6,5,4,2]=>76
[1,4,2,3,5,6]=>74
[1,4,2,3,6,5]=>89
[1,4,2,5,3,6]=>90
[1,4,2,5,6,3]=>87
[1,4,2,6,3,5]=>97
[1,4,2,6,5,3]=>93
[1,4,3,2,5,6]=>82
[1,4,3,2,6,5]=>97
[1,4,3,5,2,6]=>92
[1,4,3,5,6,2]=>86
[1,4,3,6,2,5]=>99
[1,4,3,6,5,2]=>92
[1,4,5,2,3,6]=>90
[1,4,5,2,6,3]=>95
[1,4,5,3,2,6]=>88
[1,4,5,3,6,2]=>90
[1,4,5,6,2,3]=>89
[1,4,5,6,3,2]=>76
[1,4,6,2,3,5]=>93
[1,4,6,2,5,3]=>97
[1,4,6,3,2,5]=>91
[1,4,6,3,5,2]=>92
[1,4,6,5,2,3]=>89
[1,4,6,5,3,2]=>76
[1,5,2,3,4,6]=>78
[1,5,2,3,6,4]=>90
[1,5,2,4,3,6]=>92
[1,5,2,4,6,3]=>93
[1,5,2,6,3,4]=>98
[1,5,2,6,4,3]=>93
[1,5,3,2,4,6]=>86
[1,5,3,2,6,4]=>98
[1,5,3,4,2,6]=>94
[1,5,3,4,6,2]=>92
[1,5,3,6,2,4]=>100
[1,5,3,6,4,2]=>92
[1,5,4,2,3,6]=>88
[1,5,4,2,6,3]=>97
[1,5,4,3,2,6]=>86
[1,5,4,3,6,2]=>92
[1,5,4,6,2,3]=>99
[1,5,4,6,3,2]=>86
[1,5,6,2,3,4]=>94
[1,5,6,2,4,3]=>97
[1,5,6,3,2,4]=>92
[1,5,6,3,4,2]=>92
[1,5,6,4,2,3]=>87
[1,5,6,4,3,2]=>74
[1,6,2,3,4,5]=>79
[1,6,2,3,5,4]=>90
[1,6,2,4,3,5]=>93
[1,6,2,4,5,3]=>93
[1,6,2,5,3,4]=>96
[1,6,2,5,4,3]=>91
[1,6,3,2,4,5]=>87
[1,6,3,2,5,4]=>98
[1,6,3,4,2,5]=>95
[1,6,3,4,5,2]=>92
[1,6,3,5,2,4]=>98
[1,6,3,5,4,2]=>90
[1,6,4,2,3,5]=>89
[1,6,4,2,5,3]=>97
[1,6,4,3,2,5]=>87
[1,6,4,3,5,2]=>92
[1,6,4,5,2,3]=>97
[1,6,4,5,3,2]=>84
[1,6,5,2,3,4]=>88
[1,6,5,2,4,3]=>91
[1,6,5,3,2,4]=>86
[1,6,5,3,4,2]=>86
[1,6,5,4,2,3]=>81
[1,6,5,4,3,2]=>68
[2,1,3,4,5,6]=>57
[2,1,3,4,6,5]=>72
[2,1,3,5,4,6]=>79
[2,1,3,5,6,4]=>79
[2,1,3,6,4,5]=>86
[2,1,3,6,5,4]=>85
[2,1,4,3,5,6]=>81
[2,1,4,3,6,5]=>96
[2,1,4,5,3,6]=>89
[2,1,4,5,6,3]=>82
[2,1,4,6,3,5]=>96
[2,1,4,6,5,3]=>88
[2,1,5,3,4,6]=>91
[2,1,5,3,6,4]=>99
[2,1,5,4,3,6]=>97
[2,1,5,4,6,3]=>98
[2,1,5,6,3,4]=>99
[2,1,5,6,4,3]=>90
[2,1,6,3,4,5]=>94
[2,1,6,3,5,4]=>101
[2,1,6,4,3,5]=>100
[2,1,6,4,5,3]=>100
[2,1,6,5,3,4]=>99
[2,1,6,5,4,3]=>90
[2,3,1,4,5,6]=>71
[2,3,1,4,6,5]=>86
[2,3,1,5,4,6]=>93
[2,3,1,5,6,4]=>93
[2,3,1,6,4,5]=>100
[2,3,1,6,5,4]=>99
[2,3,4,1,5,6]=>79
[2,3,4,1,6,5]=>94
[2,3,4,5,1,6]=>79
[2,3,4,5,6,1]=>68
[2,3,4,6,1,5]=>86
[2,3,4,6,5,1]=>74
[2,3,5,1,4,6]=>89
[2,3,5,1,6,4]=>97
[2,3,5,4,1,6]=>87
[2,3,5,4,6,1]=>84
[2,3,5,6,1,4]=>89
[2,3,5,6,4,1]=>76
[2,3,6,1,4,5]=>92
[2,3,6,1,5,4]=>99
[2,3,6,4,1,5]=>90
[2,3,6,4,5,1]=>86
[2,3,6,5,1,4]=>89
[2,3,6,5,4,1]=>76
[2,4,1,3,5,6]=>81
[2,4,1,3,6,5]=>96
[2,4,1,5,3,6]=>97
[2,4,1,5,6,3]=>94
[2,4,1,6,3,5]=>104
[2,4,1,6,5,3]=>100
[2,4,3,1,5,6]=>85
[2,4,3,1,6,5]=>100
[2,4,3,5,1,6]=>93
[2,4,3,5,6,1]=>86
[2,4,3,6,1,5]=>100
[2,4,3,6,5,1]=>92
[2,4,5,1,3,6]=>93
[2,4,5,1,6,3]=>98
[2,4,5,3,1,6]=>89
[2,4,5,3,6,1]=>90
[2,4,5,6,1,3]=>90
[2,4,5,6,3,1]=>76
[2,4,6,1,3,5]=>96
[2,4,6,1,5,3]=>100
[2,4,6,3,1,5]=>92
[2,4,6,3,5,1]=>92
[2,4,6,5,1,3]=>90
[2,4,6,5,3,1]=>76
[2,5,1,3,4,6]=>85
[2,5,1,3,6,4]=>97
[2,5,1,4,3,6]=>99
[2,5,1,4,6,3]=>100
[2,5,1,6,3,4]=>105
[2,5,1,6,4,3]=>100
[2,5,3,1,4,6]=>89
[2,5,3,1,6,4]=>101
[2,5,3,4,1,6]=>95
[2,5,3,4,6,1]=>92
[2,5,3,6,1,4]=>101
[2,5,3,6,4,1]=>92
[2,5,4,1,3,6]=>91
[2,5,4,1,6,3]=>100
[2,5,4,3,1,6]=>87
[2,5,4,3,6,1]=>92
[2,5,4,6,1,3]=>100
[2,5,4,6,3,1]=>86
[2,5,6,1,3,4]=>97
[2,5,6,1,4,3]=>100
[2,5,6,3,1,4]=>93
[2,5,6,3,4,1]=>92
[2,5,6,4,1,3]=>88
[2,5,6,4,3,1]=>74
[2,6,1,3,4,5]=>86
[2,6,1,3,5,4]=>97
[2,6,1,4,3,5]=>100
[2,6,1,4,5,3]=>100
[2,6,1,5,3,4]=>103
[2,6,1,5,4,3]=>98
[2,6,3,1,4,5]=>90
[2,6,3,1,5,4]=>101
[2,6,3,4,1,5]=>96
[2,6,3,4,5,1]=>92
[2,6,3,5,1,4]=>99
[2,6,3,5,4,1]=>90
[2,6,4,1,3,5]=>92
[2,6,4,1,5,3]=>100
[2,6,4,3,1,5]=>88
[2,6,4,3,5,1]=>92
[2,6,4,5,1,3]=>98
[2,6,4,5,3,1]=>84
[2,6,5,1,3,4]=>91
[2,6,5,1,4,3]=>94
[2,6,5,3,1,4]=>87
[2,6,5,3,4,1]=>86
[2,6,5,4,1,3]=>82
[2,6,5,4,3,1]=>68
[3,1,2,4,5,6]=>64
[3,1,2,4,6,5]=>79
[3,1,2,5,4,6]=>86
[3,1,2,5,6,4]=>86
[3,1,2,6,4,5]=>93
[3,1,2,6,5,4]=>92
[3,1,4,2,5,6]=>84
[3,1,4,2,6,5]=>99
[3,1,4,5,2,6]=>90
[3,1,4,5,6,2]=>82
[3,1,4,6,2,5]=>97
[3,1,4,6,5,2]=>88
[3,1,5,2,4,6]=>94
[3,1,5,2,6,4]=>102
[3,1,5,4,2,6]=>98
[3,1,5,4,6,2]=>98
[3,1,5,6,2,4]=>100
[3,1,5,6,4,2]=>90
[3,1,6,2,4,5]=>97
[3,1,6,2,5,4]=>104
[3,1,6,4,2,5]=>101
[3,1,6,4,5,2]=>100
[3,1,6,5,2,4]=>100
[3,1,6,5,4,2]=>90
[3,2,1,4,5,6]=>70
[3,2,1,4,6,5]=>85
[3,2,1,5,4,6]=>92
[3,2,1,5,6,4]=>92
[3,2,1,6,4,5]=>99
[3,2,1,6,5,4]=>98
[3,2,4,1,5,6]=>86
[3,2,4,1,6,5]=>101
[3,2,4,5,1,6]=>90
[3,2,4,5,6,1]=>81
[3,2,4,6,1,5]=>97
[3,2,4,6,5,1]=>87
[3,2,5,1,4,6]=>96
[3,2,5,1,6,4]=>104
[3,2,5,4,1,6]=>98
[3,2,5,4,6,1]=>97
[3,2,5,6,1,4]=>100
[3,2,5,6,4,1]=>89
[3,2,6,1,4,5]=>99
[3,2,6,1,5,4]=>106
[3,2,6,4,1,5]=>101
[3,2,6,4,5,1]=>99
[3,2,6,5,1,4]=>100
[3,2,6,5,4,1]=>89
[3,4,1,2,5,6]=>84
[3,4,1,2,6,5]=>99
[3,4,1,5,2,6]=>98
[3,4,1,5,6,2]=>94
[3,4,1,6,2,5]=>105
[3,4,1,6,5,2]=>100
[3,4,2,1,5,6]=>84
[3,4,2,1,6,5]=>99
[3,4,2,5,1,6]=>96
[3,4,2,5,6,1]=>91
[3,4,2,6,1,5]=>103
[3,4,2,6,5,1]=>97
[3,4,5,1,2,6]=>94
[3,4,5,1,6,2]=>98
[3,4,5,2,1,6]=>88
[3,4,5,2,6,1]=>91
[3,4,5,6,1,2]=>90
[3,4,5,6,2,1]=>75
[3,4,6,1,2,5]=>97
[3,4,6,1,5,2]=>100
[3,4,6,2,1,5]=>91
[3,4,6,2,5,1]=>93
[3,4,6,5,1,2]=>90
[3,4,6,5,2,1]=>75
[3,5,1,2,4,6]=>88
[3,5,1,2,6,4]=>100
[3,5,1,4,2,6]=>100
[3,5,1,4,6,2]=>100
[3,5,1,6,2,4]=>106
[3,5,1,6,4,2]=>100
[3,5,2,1,4,6]=>88
[3,5,2,1,6,4]=>100
[3,5,2,4,1,6]=>98
[3,5,2,4,6,1]=>97
[3,5,2,6,1,4]=>104
[3,5,2,6,4,1]=>97
[3,5,4,1,2,6]=>92
[3,5,4,1,6,2]=>100
[3,5,4,2,1,6]=>86
[3,5,4,2,6,1]=>93
[3,5,4,6,1,2]=>100
[3,5,4,6,2,1]=>85
[3,5,6,1,2,4]=>98
[3,5,6,1,4,2]=>100
[3,5,6,2,1,4]=>92
[3,5,6,2,4,1]=>93
[3,5,6,4,1,2]=>88
[3,5,6,4,2,1]=>73
[3,6,1,2,4,5]=>89
[3,6,1,2,5,4]=>100
[3,6,1,4,2,5]=>101
[3,6,1,4,5,2]=>100
[3,6,1,5,2,4]=>104
[3,6,1,5,4,2]=>98
[3,6,2,1,4,5]=>89
[3,6,2,1,5,4]=>100
[3,6,2,4,1,5]=>99
[3,6,2,4,5,1]=>97
[3,6,2,5,1,4]=>102
[3,6,2,5,4,1]=>95
[3,6,4,1,2,5]=>93
[3,6,4,1,5,2]=>100
[3,6,4,2,1,5]=>87
[3,6,4,2,5,1]=>93
[3,6,4,5,1,2]=>98
[3,6,4,5,2,1]=>83
[3,6,5,1,2,4]=>92
[3,6,5,1,4,2]=>94
[3,6,5,2,1,4]=>86
[3,6,5,2,4,1]=>87
[3,6,5,4,1,2]=>82
[3,6,5,4,2,1]=>67
[4,1,2,3,5,6]=>67
[4,1,2,3,6,5]=>82
[4,1,2,5,3,6]=>87
[4,1,2,5,6,3]=>86
[4,1,2,6,3,5]=>94
[4,1,2,6,5,3]=>92
[4,1,3,2,5,6]=>83
[4,1,3,2,6,5]=>98
[4,1,3,5,2,6]=>93
[4,1,3,5,6,2]=>87
[4,1,3,6,2,5]=>100
[4,1,3,6,5,2]=>93
[4,1,5,2,3,6]=>95
[4,1,5,2,6,3]=>102
[4,1,5,3,2,6]=>97
[4,1,5,3,6,2]=>99
[4,1,5,6,2,3]=>100
[4,1,5,6,3,2]=>89
[4,1,6,2,3,5]=>98
[4,1,6,2,5,3]=>104
[4,1,6,3,2,5]=>100
[4,1,6,3,5,2]=>101
[4,1,6,5,2,3]=>100
[4,1,6,5,3,2]=>89
[4,2,1,3,5,6]=>73
[4,2,1,3,6,5]=>88
[4,2,1,5,3,6]=>93
[4,2,1,5,6,3]=>92
[4,2,1,6,3,5]=>100
[4,2,1,6,5,3]=>98
[4,2,3,1,5,6]=>85
[4,2,3,1,6,5]=>100
[4,2,3,5,1,6]=>93
[4,2,3,5,6,1]=>86
[4,2,3,6,1,5]=>100
[4,2,3,6,5,1]=>92
[4,2,5,1,3,6]=>97
[4,2,5,1,6,3]=>104
[4,2,5,3,1,6]=>97
[4,2,5,3,6,1]=>98
[4,2,5,6,1,3]=>100
[4,2,5,6,3,1]=>88
[4,2,6,1,3,5]=>100
[4,2,6,1,5,3]=>106
[4,2,6,3,1,5]=>100
[4,2,6,3,5,1]=>100
[4,2,6,5,1,3]=>100
[4,2,6,5,3,1]=>88
[4,3,1,2,5,6]=>75
[4,3,1,2,6,5]=>90
[4,3,1,5,2,6]=>93
[4,3,1,5,6,2]=>91
[4,3,1,6,2,5]=>100
[4,3,1,6,5,2]=>97
[4,3,2,1,5,6]=>75
[4,3,2,1,6,5]=>90
[4,3,2,5,1,6]=>91
[4,3,2,5,6,1]=>88
[4,3,2,6,1,5]=>98
[4,3,2,6,5,1]=>94
[4,3,5,1,2,6]=>97
[4,3,5,1,6,2]=>103
[4,3,5,2,1,6]=>91
[4,3,5,2,6,1]=>96
[4,3,5,6,1,2]=>99
[4,3,5,6,2,1]=>84
[4,3,6,1,2,5]=>100
[4,3,6,1,5,2]=>105
[4,3,6,2,1,5]=>94
[4,3,6,2,5,1]=>98
[4,3,6,5,1,2]=>99
[4,3,6,5,2,1]=>84
[4,5,1,2,3,6]=>89
[4,5,1,2,6,3]=>100
[4,5,1,3,2,6]=>99
[4,5,1,3,6,2]=>101
[4,5,1,6,2,3]=>106
[4,5,1,6,3,2]=>99
[4,5,2,1,3,6]=>89
[4,5,2,1,6,3]=>100
[4,5,2,3,1,6]=>97
[4,5,2,3,6,1]=>98
[4,5,2,6,1,3]=>104
[4,5,2,6,3,1]=>96
[4,5,3,1,2,6]=>87
[4,5,3,1,6,2]=>97
[4,5,3,2,1,6]=>81
[4,5,3,2,6,1]=>90
[4,5,3,6,1,2]=>101
[4,5,3,6,2,1]=>86
[4,5,6,1,2,3]=>98
[4,5,6,1,3,2]=>99
[4,5,6,2,1,3]=>92
[4,5,6,2,3,1]=>92
[4,5,6,3,1,2]=>85
[4,5,6,3,2,1]=>70
[4,6,1,2,3,5]=>90
[4,6,1,2,5,3]=>100
[4,6,1,3,2,5]=>100
[4,6,1,3,5,2]=>101
[4,6,1,5,2,3]=>104
[4,6,1,5,3,2]=>97
[4,6,2,1,3,5]=>90
[4,6,2,1,5,3]=>100
[4,6,2,3,1,5]=>98
[4,6,2,3,5,1]=>98
[4,6,2,5,1,3]=>102
[4,6,2,5,3,1]=>94
[4,6,3,1,2,5]=>88
[4,6,3,1,5,2]=>97
[4,6,3,2,1,5]=>82
[4,6,3,2,5,1]=>90
[4,6,3,5,1,2]=>99
[4,6,3,5,2,1]=>84
[4,6,5,1,2,3]=>92
[4,6,5,1,3,2]=>93
[4,6,5,2,1,3]=>86
[4,6,5,2,3,1]=>86
[4,6,5,3,1,2]=>79
[4,6,5,3,2,1]=>64
[5,1,2,3,4,6]=>68
[5,1,2,3,6,4]=>82
[5,1,2,4,3,6]=>86
[5,1,2,4,6,3]=>87
[5,1,2,6,3,4]=>94
[5,1,2,6,4,3]=>91
[5,1,3,2,4,6]=>84
[5,1,3,2,6,4]=>98
[5,1,3,4,2,6]=>92
[5,1,3,4,6,2]=>88
[5,1,3,6,2,4]=>100
[5,1,3,6,4,2]=>92
[5,1,4,2,3,6]=>90
[5,1,4,2,6,3]=>99
[5,1,4,3,2,6]=>92
[5,1,4,3,6,2]=>96
[5,1,4,6,2,3]=>101
[5,1,4,6,3,2]=>90
[5,1,6,2,3,4]=>98
[5,1,6,2,4,3]=>103
[5,1,6,3,2,4]=>100
[5,1,6,3,4,2]=>100
[5,1,6,4,2,3]=>97
[5,1,6,4,3,2]=>86
[5,2,1,3,4,6]=>74
[5,2,1,3,6,4]=>88
[5,2,1,4,3,6]=>92
[5,2,1,4,6,3]=>93
[5,2,1,6,3,4]=>100
[5,2,1,6,4,3]=>97
[5,2,3,1,4,6]=>86
[5,2,3,1,6,4]=>100
[5,2,3,4,1,6]=>92
[5,2,3,4,6,1]=>87
[5,2,3,6,1,4]=>100
[5,2,3,6,4,1]=>91
[5,2,4,1,3,6]=>92
[5,2,4,1,6,3]=>101
[5,2,4,3,1,6]=>92
[5,2,4,3,6,1]=>95
[5,2,4,6,1,3]=>101
[5,2,4,6,3,1]=>89
[5,2,6,1,3,4]=>100
[5,2,6,1,4,3]=>105
[5,2,6,3,1,4]=>100
[5,2,6,3,4,1]=>99
[5,2,6,4,1,3]=>97
[5,2,6,4,3,1]=>85
[5,3,1,2,4,6]=>76
[5,3,1,2,6,4]=>90
[5,3,1,4,2,6]=>92
[5,3,1,4,6,2]=>92
[5,3,1,6,2,4]=>100
[5,3,1,6,4,2]=>96
[5,3,2,1,4,6]=>76
[5,3,2,1,6,4]=>90
[5,3,2,4,1,6]=>90
[5,3,2,4,6,1]=>89
[5,3,2,6,1,4]=>98
[5,3,2,6,4,1]=>93
[5,3,4,1,2,6]=>92
[5,3,4,1,6,2]=>100
[5,3,4,2,1,6]=>86
[5,3,4,2,6,1]=>93
[5,3,4,6,1,2]=>100
[5,3,4,6,2,1]=>85
[5,3,6,1,2,4]=>100
[5,3,6,1,4,2]=>104
[5,3,6,2,1,4]=>94
[5,3,6,2,4,1]=>97
[5,3,6,4,1,2]=>96
[5,3,6,4,2,1]=>81
[5,4,1,2,3,6]=>76
[5,4,1,2,6,3]=>89
[5,4,1,3,2,6]=>86
[5,4,1,3,6,2]=>90
[5,4,1,6,2,3]=>99
[5,4,1,6,3,2]=>92
[5,4,2,1,3,6]=>76
[5,4,2,1,6,3]=>89
[5,4,2,3,1,6]=>84
[5,4,2,3,6,1]=>87
[5,4,2,6,1,3]=>97
[5,4,2,6,3,1]=>89
[5,4,3,1,2,6]=>74
[5,4,3,1,6,2]=>86
[5,4,3,2,1,6]=>68
[5,4,3,2,6,1]=>79
[5,4,3,6,1,2]=>94
[5,4,3,6,2,1]=>79
[5,4,6,1,2,3]=>99
[5,4,6,1,3,2]=>100
[5,4,6,2,1,3]=>93
[5,4,6,2,3,1]=>93
[5,4,6,3,1,2]=>86
[5,4,6,3,2,1]=>71
[5,6,1,2,3,4]=>90
[5,6,1,2,4,3]=>99
[5,6,1,3,2,4]=>100
[5,6,1,3,4,2]=>100
[5,6,1,4,2,3]=>101
[5,6,1,4,3,2]=>94
[5,6,2,1,3,4]=>90
[5,6,2,1,4,3]=>99
[5,6,2,3,1,4]=>98
[5,6,2,3,4,1]=>97
[5,6,2,4,1,3]=>99
[5,6,2,4,3,1]=>91
[5,6,3,1,2,4]=>88
[5,6,3,1,4,2]=>96
[5,6,3,2,1,4]=>82
[5,6,3,2,4,1]=>89
[5,6,3,4,1,2]=>96
[5,6,3,4,2,1]=>81
[5,6,4,1,2,3]=>85
[5,6,4,1,3,2]=>86
[5,6,4,2,1,3]=>79
[5,6,4,2,3,1]=>79
[5,6,4,3,1,2]=>72
[5,6,4,3,2,1]=>57
[6,1,2,3,4,5]=>68
[6,1,2,3,5,4]=>81
[6,1,2,4,3,5]=>86
[6,1,2,4,5,3]=>86
[6,1,2,5,3,4]=>91
[6,1,2,5,4,3]=>88
[6,1,3,2,4,5]=>84
[6,1,3,2,5,4]=>97
[6,1,3,4,2,5]=>92
[6,1,3,4,5,2]=>87
[6,1,3,5,2,4]=>97
[6,1,3,5,4,2]=>89
[6,1,4,2,3,5]=>90
[6,1,4,2,5,3]=>98
[6,1,4,3,2,5]=>92
[6,1,4,3,5,2]=>95
[6,1,4,5,2,3]=>98
[6,1,4,5,3,2]=>87
[6,1,5,2,3,4]=>91
[6,1,5,2,4,3]=>96
[6,1,5,3,2,4]=>93
[6,1,5,3,4,2]=>93
[6,1,5,4,2,3]=>90
[6,1,5,4,3,2]=>79
[6,2,1,3,4,5]=>74
[6,2,1,3,5,4]=>87
[6,2,1,4,3,5]=>92
[6,2,1,4,5,3]=>92
[6,2,1,5,3,4]=>97
[6,2,1,5,4,3]=>94
[6,2,3,1,4,5]=>86
[6,2,3,1,5,4]=>99
[6,2,3,4,1,5]=>92
[6,2,3,4,5,1]=>86
[6,2,3,5,1,4]=>97
[6,2,3,5,4,1]=>88
[6,2,4,1,3,5]=>92
[6,2,4,1,5,3]=>100
[6,2,4,3,1,5]=>92
[6,2,4,3,5,1]=>94
[6,2,4,5,1,3]=>98
[6,2,4,5,3,1]=>86
[6,2,5,1,3,4]=>93
[6,2,5,1,4,3]=>98
[6,2,5,3,1,4]=>93
[6,2,5,3,4,1]=>92
[6,2,5,4,1,3]=>90
[6,2,5,4,3,1]=>78
[6,3,1,2,4,5]=>76
[6,3,1,2,5,4]=>89
[6,3,1,4,2,5]=>92
[6,3,1,4,5,2]=>91
[6,3,1,5,2,4]=>97
[6,3,1,5,4,2]=>93
[6,3,2,1,4,5]=>76
[6,3,2,1,5,4]=>89
[6,3,2,4,1,5]=>90
[6,3,2,4,5,1]=>88
[6,3,2,5,1,4]=>95
[6,3,2,5,4,1]=>90
[6,3,4,1,2,5]=>92
[6,3,4,1,5,2]=>99
[6,3,4,2,1,5]=>86
[6,3,4,2,5,1]=>92
[6,3,4,5,1,2]=>97
[6,3,4,5,2,1]=>82
[6,3,5,1,2,4]=>93
[6,3,5,1,4,2]=>97
[6,3,5,2,1,4]=>87
[6,3,5,2,4,1]=>90
[6,3,5,4,1,2]=>89
[6,3,5,4,2,1]=>74
[6,4,1,2,3,5]=>76
[6,4,1,2,5,3]=>88
[6,4,1,3,2,5]=>86
[6,4,1,3,5,2]=>89
[6,4,1,5,2,3]=>96
[6,4,1,5,3,2]=>89
[6,4,2,1,3,5]=>76
[6,4,2,1,5,3]=>88
[6,4,2,3,1,5]=>84
[6,4,2,3,5,1]=>86
[6,4,2,5,1,3]=>94
[6,4,2,5,3,1]=>86
[6,4,3,1,2,5]=>74
[6,4,3,1,5,2]=>85
[6,4,3,2,1,5]=>68
[6,4,3,2,5,1]=>78
[6,4,3,5,1,2]=>91
[6,4,3,5,2,1]=>76
[6,4,5,1,2,3]=>92
[6,4,5,1,3,2]=>93
[6,4,5,2,1,3]=>86
[6,4,5,2,3,1]=>86
[6,4,5,3,1,2]=>79
[6,4,5,3,2,1]=>64
[6,5,1,2,3,4]=>75
[6,5,1,2,4,3]=>84
[6,5,1,3,2,4]=>85
[6,5,1,3,4,2]=>85
[6,5,1,4,2,3]=>86
[6,5,1,4,3,2]=>79
[6,5,2,1,3,4]=>75
[6,5,2,1,4,3]=>84
[6,5,2,3,1,4]=>83
[6,5,2,3,4,1]=>82
[6,5,2,4,1,3]=>84
[6,5,2,4,3,1]=>76
[6,5,3,1,2,4]=>73
[6,5,3,1,4,2]=>81
[6,5,3,2,1,4]=>67
[6,5,3,2,4,1]=>74
[6,5,3,4,1,2]=>81
[6,5,3,4,2,1]=>66
[6,5,4,1,2,3]=>70
[6,5,4,1,3,2]=>71
[6,5,4,2,1,3]=>64
[6,5,4,2,3,1]=>64
[6,5,4,3,1,2]=>57
[6,5,4,3,2,1]=>42
[1,2,3,4,5,6,7]=>99
[1,2,3,4,5,7,6]=>130
[1,2,3,4,6,5,7]=>145
[1,2,3,4,6,7,5]=>145
[1,2,3,4,7,5,6]=>160
[1,2,3,4,7,6,5]=>159
[1,2,3,5,4,6,7]=>151
[1,2,3,5,4,7,6]=>182
[1,2,3,5,6,4,7]=>167
[1,2,3,5,6,7,4]=>152
[1,2,3,5,7,4,6]=>182
[1,2,3,5,7,6,4]=>166
[1,2,3,6,4,5,7]=>173
[1,2,3,6,4,7,5]=>189
[1,2,3,6,5,4,7]=>187
[1,2,3,6,5,7,4]=>188
[1,2,3,6,7,4,5]=>189
[1,2,3,6,7,5,4]=>172
[1,2,3,7,4,5,6]=>180
[1,2,3,7,4,6,5]=>195
[1,2,3,7,5,4,6]=>194
[1,2,3,7,5,6,4]=>194
[1,2,3,7,6,4,5]=>193
[1,2,3,7,6,5,4]=>176
[1,2,4,3,5,6,7]=>151
[1,2,4,3,5,7,6]=>182
[1,2,4,3,6,5,7]=>197
[1,2,4,3,6,7,5]=>197
[1,2,4,3,7,5,6]=>212
[1,2,4,3,7,6,5]=>211
[1,2,4,5,3,6,7]=>175
[1,2,4,5,3,7,6]=>206
[1,2,4,5,6,3,7]=>177
[1,2,4,5,6,7,3]=>155
[1,2,4,5,7,3,6]=>192
[1,2,4,5,7,6,3]=>169
[1,2,4,6,3,5,7]=>197
[1,2,4,6,3,7,5]=>213
[1,2,4,6,5,3,7]=>197
[1,2,4,6,5,7,3]=>191
[1,2,4,6,7,3,5]=>199
[1,2,4,6,7,5,3]=>175
[1,2,4,7,3,5,6]=>204
[1,2,4,7,3,6,5]=>219
[1,2,4,7,5,3,6]=>204
[1,2,4,7,5,6,3]=>197
[1,2,4,7,6,3,5]=>203
[1,2,4,7,6,5,3]=>179
[1,2,5,3,4,6,7]=>175
[1,2,5,3,4,7,6]=>206
[1,2,5,3,6,4,7]=>207
[1,2,5,3,6,7,4]=>200
[1,2,5,3,7,4,6]=>222
[1,2,5,3,7,6,4]=>214
[1,2,5,4,3,6,7]=>195
[1,2,5,4,3,7,6]=>226
[1,2,5,4,6,3,7]=>213
[1,2,5,4,6,7,3]=>199
[1,2,5,4,7,3,6]=>228
[1,2,5,4,7,6,3]=>213
[1,2,5,6,3,4,7]=>207
[1,2,5,6,3,7,4]=>216
[1,2,5,6,4,3,7]=>205
[1,2,5,6,4,7,3]=>207
[1,2,5,6,7,3,4]=>202
[1,2,5,6,7,4,3]=>177
[1,2,5,7,3,4,6]=>214
[1,2,5,7,3,6,4]=>222
[1,2,5,7,4,3,6]=>212
[1,2,5,7,4,6,3]=>213
[1,2,5,7,6,3,4]=>206
[1,2,5,7,6,4,3]=>181
[1,2,6,3,4,5,7]=>185
[1,2,6,3,4,7,5]=>209
[1,2,6,3,5,4,7]=>215
[1,2,6,3,5,7,4]=>216
[1,2,6,3,7,4,5]=>225
[1,2,6,3,7,5,4]=>216
[1,2,6,4,3,5,7]=>205
[1,2,6,4,3,7,5]=>229
[1,2,6,4,5,3,7]=>221
[1,2,6,4,5,7,3]=>215
[1,2,6,4,7,3,5]=>231
[1,2,6,4,7,5,3]=>215
[1,2,6,5,3,4,7]=>211
[1,2,6,5,3,7,4]=>228
[1,2,6,5,4,3,7]=>209
[1,2,6,5,4,7,3]=>219
[1,2,6,5,7,3,4]=>230
[1,2,6,5,7,4,3]=>205
[1,2,6,7,3,4,5]=>217
[1,2,6,7,3,5,4]=>224
[1,2,6,7,4,3,5]=>215
[1,2,6,7,4,5,3]=>215
[1,2,6,7,5,3,4]=>206
[1,2,6,7,5,4,3]=>181
[1,2,7,3,4,5,6]=>188
[1,2,7,3,4,6,5]=>211
[1,2,7,3,5,4,6]=>218
[1,2,7,3,5,6,4]=>218
[1,2,7,3,6,4,5]=>225
[1,2,7,3,6,5,4]=>216
[1,2,7,4,3,5,6]=>208
[1,2,7,4,3,6,5]=>231
[1,2,7,4,5,3,6]=>224
[1,2,7,4,5,6,3]=>217
[1,2,7,4,6,3,5]=>231
[1,2,7,4,6,5,3]=>215
[1,2,7,5,3,4,6]=>214
[1,2,7,5,3,6,4]=>230
[1,2,7,5,4,3,6]=>212
[1,2,7,5,4,6,3]=>221
[1,2,7,5,6,3,4]=>230
[1,2,7,5,6,4,3]=>205
[1,2,7,6,3,4,5]=>213
[1,2,7,6,3,5,4]=>220
[1,2,7,6,4,3,5]=>211
[1,2,7,6,4,5,3]=>211
[1,2,7,6,5,3,4]=>202
[1,2,7,6,5,4,3]=>177
[1,3,2,4,5,6,7]=>145
[1,3,2,4,5,7,6]=>176
[1,3,2,4,6,5,7]=>191
[1,3,2,4,6,7,5]=>191
[1,3,2,4,7,5,6]=>206
[1,3,2,4,7,6,5]=>205
[1,3,2,5,4,6,7]=>197
[1,3,2,5,4,7,6]=>228
[1,3,2,5,6,4,7]=>213
[1,3,2,5,6,7,4]=>198
[1,3,2,5,7,4,6]=>228
[1,3,2,5,7,6,4]=>212
[1,3,2,6,4,5,7]=>219
[1,3,2,6,4,7,5]=>235
[1,3,2,6,5,4,7]=>233
[1,3,2,6,5,7,4]=>234
[1,3,2,6,7,4,5]=>235
[1,3,2,6,7,5,4]=>218
[1,3,2,7,4,5,6]=>226
[1,3,2,7,4,6,5]=>241
[1,3,2,7,5,4,6]=>240
[1,3,2,7,5,6,4]=>240
[1,3,2,7,6,4,5]=>239
[1,3,2,7,6,5,4]=>222
[1,3,4,2,5,6,7]=>173
[1,3,4,2,5,7,6]=>204
[1,3,4,2,6,5,7]=>219
[1,3,4,2,6,7,5]=>219
[1,3,4,2,7,5,6]=>234
[1,3,4,2,7,6,5]=>233
[1,3,4,5,2,6,7]=>185
[1,3,4,5,2,7,6]=>216
[1,3,4,5,6,2,7]=>181
[1,3,4,5,6,7,2]=>156
[1,3,4,5,7,2,6]=>196
[1,3,4,5,7,6,2]=>170
[1,3,4,6,2,5,7]=>207
[1,3,4,6,2,7,5]=>223
[1,3,4,6,5,2,7]=>201
[1,3,4,6,5,7,2]=>192
[1,3,4,6,7,2,5]=>203
[1,3,4,6,7,5,2]=>176
[1,3,4,7,2,5,6]=>214
[1,3,4,7,2,6,5]=>229
[1,3,4,7,5,2,6]=>208
[1,3,4,7,5,6,2]=>198
[1,3,4,7,6,2,5]=>207
[1,3,4,7,6,5,2]=>180
[1,3,5,2,4,6,7]=>197
[1,3,5,2,4,7,6]=>228
[1,3,5,2,6,4,7]=>229
[1,3,5,2,6,7,4]=>222
[1,3,5,2,7,4,6]=>244
[1,3,5,2,7,6,4]=>236
[1,3,5,4,2,6,7]=>205
[1,3,5,4,2,7,6]=>236
[1,3,5,4,6,2,7]=>217
[1,3,5,4,6,7,2]=>200
[1,3,5,4,7,2,6]=>232
[1,3,5,4,7,6,2]=>214
[1,3,5,6,2,4,7]=>217
[1,3,5,6,2,7,4]=>226
[1,3,5,6,4,2,7]=>209
[1,3,5,6,4,7,2]=>208
[1,3,5,6,7,2,4]=>206
[1,3,5,6,7,4,2]=>178
[1,3,5,7,2,4,6]=>224
[1,3,5,7,2,6,4]=>232
[1,3,5,7,4,2,6]=>216
[1,3,5,7,4,6,2]=>214
[1,3,5,7,6,2,4]=>210
[1,3,5,7,6,4,2]=>182
[1,3,6,2,4,5,7]=>207
[1,3,6,2,4,7,5]=>231
[1,3,6,2,5,4,7]=>237
[1,3,6,2,5,7,4]=>238
[1,3,6,2,7,4,5]=>247
[1,3,6,2,7,5,4]=>238
[1,3,6,4,2,5,7]=>215
[1,3,6,4,2,7,5]=>239
[1,3,6,4,5,2,7]=>225
[1,3,6,4,5,7,2]=>216
[1,3,6,4,7,2,5]=>235
[1,3,6,4,7,5,2]=>216
[1,3,6,5,2,4,7]=>221
[1,3,6,5,2,7,4]=>238
[1,3,6,5,4,2,7]=>213
[1,3,6,5,4,7,2]=>220
[1,3,6,5,7,2,4]=>234
[1,3,6,5,7,4,2]=>206
[1,3,6,7,2,4,5]=>227
[1,3,6,7,2,5,4]=>234
[1,3,6,7,4,2,5]=>219
[1,3,6,7,4,5,2]=>216
[1,3,6,7,5,2,4]=>210
[1,3,6,7,5,4,2]=>182
[1,3,7,2,4,5,6]=>210
[1,3,7,2,4,6,5]=>233
[1,3,7,2,5,4,6]=>240
[1,3,7,2,5,6,4]=>240
[1,3,7,2,6,4,5]=>247
[1,3,7,2,6,5,4]=>238
[1,3,7,4,2,5,6]=>218
[1,3,7,4,2,6,5]=>241
[1,3,7,4,5,2,6]=>228
[1,3,7,4,5,6,2]=>218
[1,3,7,4,6,2,5]=>235
[1,3,7,4,6,5,2]=>216
[1,3,7,5,2,4,6]=>224
[1,3,7,5,2,6,4]=>240
[1,3,7,5,4,2,6]=>216
[1,3,7,5,4,6,2]=>222
[1,3,7,5,6,2,4]=>234
[1,3,7,5,6,4,2]=>206
[1,3,7,6,2,4,5]=>223
[1,3,7,6,2,5,4]=>230
[1,3,7,6,4,2,5]=>215
[1,3,7,6,4,5,2]=>212
[1,3,7,6,5,2,4]=>206
[1,3,7,6,5,4,2]=>178
[1,4,2,3,5,6,7]=>167
[1,4,2,3,5,7,6]=>198
[1,4,2,3,6,5,7]=>213
[1,4,2,3,6,7,5]=>213
[1,4,2,3,7,5,6]=>228
[1,4,2,3,7,6,5]=>227
[1,4,2,5,3,6,7]=>207
[1,4,2,5,3,7,6]=>238
[1,4,2,5,6,3,7]=>217
[1,4,2,5,6,7,3]=>199
[1,4,2,5,7,3,6]=>232
[1,4,2,5,7,6,3]=>213
[1,4,2,6,3,5,7]=>229
[1,4,2,6,3,7,5]=>245
[1,4,2,6,5,3,7]=>237
[1,4,2,6,5,7,3]=>235
[1,4,2,6,7,3,5]=>239
[1,4,2,6,7,5,3]=>219
[1,4,2,7,3,5,6]=>236
[1,4,2,7,3,6,5]=>251
[1,4,2,7,5,3,6]=>244
[1,4,2,7,5,6,3]=>241
[1,4,2,7,6,3,5]=>243
[1,4,2,7,6,5,3]=>223
[1,4,3,2,5,6,7]=>187
[1,4,3,2,5,7,6]=>218
[1,4,3,2,6,5,7]=>233
[1,4,3,2,6,7,5]=>233
[1,4,3,2,7,5,6]=>248
[1,4,3,2,7,6,5]=>247
[1,4,3,5,2,6,7]=>215
[1,4,3,5,2,7,6]=>246
[1,4,3,5,6,2,7]=>219
[1,4,3,5,6,7,2]=>198
[1,4,3,5,7,2,6]=>234
[1,4,3,5,7,6,2]=>212
[1,4,3,6,2,5,7]=>237
[1,4,3,6,2,7,5]=>253
[1,4,3,6,5,2,7]=>239
[1,4,3,6,5,7,2]=>234
[1,4,3,6,7,2,5]=>241
[1,4,3,6,7,5,2]=>218
[1,4,3,7,2,5,6]=>244
[1,4,3,7,2,6,5]=>259
[1,4,3,7,5,2,6]=>246
[1,4,3,7,5,6,2]=>240
[1,4,3,7,6,2,5]=>245
[1,4,3,7,6,5,2]=>222
[1,4,5,2,3,6,7]=>207
[1,4,5,2,3,7,6]=>238
[1,4,5,2,6,3,7]=>233
[1,4,5,2,6,7,3]=>223
[1,4,5,2,7,3,6]=>248
[1,4,5,2,7,6,3]=>237
[1,4,5,3,2,6,7]=>211
[1,4,5,3,2,7,6]=>242
[1,4,5,3,6,2,7]=>231
[1,4,5,3,6,7,2]=>218
[1,4,5,3,7,2,6]=>246
[1,4,5,3,7,6,2]=>232
[1,4,5,6,2,3,7]=>221
[1,4,5,6,2,7,3]=>227
[1,4,5,6,3,2,7]=>211
[1,4,5,6,3,7,2]=>214
[1,4,5,6,7,2,3]=>207
[1,4,5,6,7,3,2]=>178
[1,4,5,7,2,3,6]=>228
[1,4,5,7,2,6,3]=>233
[1,4,5,7,3,2,6]=>218
[1,4,5,7,3,6,2]=>220
[1,4,5,7,6,2,3]=>211
[1,4,5,7,6,3,2]=>182
[1,4,6,2,3,5,7]=>217
[1,4,6,2,3,7,5]=>241
[1,4,6,2,5,3,7]=>241
[1,4,6,2,5,7,3]=>239
[1,4,6,2,7,3,5]=>251
[1,4,6,2,7,5,3]=>239
[1,4,6,3,2,5,7]=>221
[1,4,6,3,2,7,5]=>245
[1,4,6,3,5,2,7]=>239
[1,4,6,3,5,7,2]=>234
[1,4,6,3,7,2,5]=>249
[1,4,6,3,7,5,2]=>234
[1,4,6,5,2,3,7]=>225
[1,4,6,5,2,7,3]=>239
[1,4,6,5,3,2,7]=>215
[1,4,6,5,3,7,2]=>226
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Description
The sum of St000483 over all subsequences of length at least three.
References
[1] Ahmed, T., Snevily, H. Some properties of roller coaster permutations MathSciNet:3136863
Code
# code could be simplified...
def inc_runs(w):
"""
runs in w of length at least 2
sage: sage: pi = Permutation([2,1,4,3])
sage: inc_runs(pi)
"""
runs = []
current_value = w[0]
current_run = [w[0]]
for i in w[1:]:
if i < current_value:
if len(current_run) > 1:
runs.append(current_run)
current_run = [i]
else:
current_run.append(i)
current_value = i
if len(current_run) > 1:
runs.append(current_run)
return len(runs)
def dec_runs(w):
"""
sage: pi = Permutation([2,1,4,3])
sage: dec_runs(pi)
"""
return inc_runs(w[::-1])
def total_runs(w):
"""
sage: all(total_runs(pi)==1+pi.number_of_peaks()+pi.complement().number_of_peaks() for pi in Permutations(6))
True
"""
return inc_runs(w) + dec_runs(w)
def statistic(pi):
"""
sage: statistic([2,1,4,3])
11
sage: statistic([1,2,3,4])
5
"""
return sum([total_runs(tau) for k in range(3, len(pi)+1) for tau in Subwords(pi, k)])
Created
May 10, 2016 at 15:02 by Martin Rubey
Updated
May 10, 2019 at 17:38 by Henning Ulfarsson
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