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*                                                                           *
*       Copyright (C) 2019 The FindStatCrew <info@findstat.org>             *
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-----------------------------------------------------------------------------
Statistic identifier: St001262

-----------------------------------------------------------------------------
Collection: Integer partitions

-----------------------------------------------------------------------------
Description: The dimension of the maximal parabolic seaweed algebra corresponding to the partition.

Let $a_1,\dots,a_m$ and $b_1,\dots,b_t$ be two compositions of $n$.  The corresponding seaweed algebra is the associative subalgebra of the algebra of $n\times n$ matrices which preserves the flags
$$
\{0\} \subset V_1 \subset \cdots \subset V_{m-1} \subset V_m =V
$$
and
$$
V=W_0\supset W_1\supset \cdots \supset W_t=\{0\}, 
$$
where $V_i=\text{span}\{e_1,\dots, e_{a_1+\cdots +a_i}\}$ and $W_j=\text{span}\{e_{b_1+\cdots +b_j+1},\dots, e_n\}$.

Thus, its dimension is
$$
\frac{1}{2}\left(\sum a_i^2 + \sum b_i^2\right).
$$

It is maximal parabolic if $b_1=n$.

-----------------------------------------------------------------------------
References: [1]   Dergachev, V., Kirillov, A. Index of Lie algebras of seaweed type [[MathSciNet:1774864]]
[2]   Coll, V., Mayers, A., Mayers, N. Statistics on integer partitions arising from seaweed algebras [[arXiv:1809.09271]]

-----------------------------------------------------------------------------
Code:
def statistic(la):
    return sum(p^2/2 for p in la) + la.size()^2/2


-----------------------------------------------------------------------------
Statistic values:

[1]                               => 1
[2]                               => 4
[1,1]                             => 3
[3]                               => 9
[2,1]                             => 7
[1,1,1]                           => 6
[4]                               => 16
[3,1]                             => 13
[2,2]                             => 12
[2,1,1]                           => 11
[1,1,1,1]                         => 10
[5]                               => 25
[4,1]                             => 21
[3,2]                             => 19
[3,1,1]                           => 18
[2,2,1]                           => 17
[2,1,1,1]                         => 16
[1,1,1,1,1]                       => 15
[6]                               => 36
[5,1]                             => 31
[4,2]                             => 28
[4,1,1]                           => 27
[3,3]                             => 27
[3,2,1]                           => 25
[3,1,1,1]                         => 24
[2,2,2]                           => 24
[2,2,1,1]                         => 23
[2,1,1,1,1]                       => 22
[1,1,1,1,1,1]                     => 21
[7]                               => 49
[6,1]                             => 43
[5,2]                             => 39
[5,1,1]                           => 38
[4,3]                             => 37
[4,2,1]                           => 35
[4,1,1,1]                         => 34
[3,3,1]                           => 34
[3,2,2]                           => 33
[3,2,1,1]                         => 32
[3,1,1,1,1]                       => 31
[2,2,2,1]                         => 31
[2,2,1,1,1]                       => 30
[2,1,1,1,1,1]                     => 29
[1,1,1,1,1,1,1]                   => 28
[8]                               => 64
[7,1]                             => 57
[6,2]                             => 52
[6,1,1]                           => 51
[5,3]                             => 49
[5,2,1]                           => 47
[5,1,1,1]                         => 46
[4,4]                             => 48
[4,3,1]                           => 45
[4,2,2]                           => 44
[4,2,1,1]                         => 43
[4,1,1,1,1]                       => 42
[3,3,2]                           => 43
[3,3,1,1]                         => 42
[3,2,2,1]                         => 41
[3,2,1,1,1]                       => 40
[3,1,1,1,1,1]                     => 39
[2,2,2,2]                         => 40
[2,2,2,1,1]                       => 39
[2,2,1,1,1,1]                     => 38
[2,1,1,1,1,1,1]                   => 37
[1,1,1,1,1,1,1,1]                 => 36
[9]                               => 81
[8,1]                             => 73
[7,2]                             => 67
[7,1,1]                           => 66
[6,3]                             => 63
[6,2,1]                           => 61
[6,1,1,1]                         => 60
[5,4]                             => 61
[5,3,1]                           => 58
[5,2,2]                           => 57
[5,2,1,1]                         => 56
[5,1,1,1,1]                       => 55
[4,4,1]                           => 57
[4,3,2]                           => 55
[4,3,1,1]                         => 54
[4,2,2,1]                         => 53
[4,2,1,1,1]                       => 52
[4,1,1,1,1,1]                     => 51
[3,3,3]                           => 54
[3,3,2,1]                         => 52
[3,3,1,1,1]                       => 51
[3,2,2,2]                         => 51
[3,2,2,1,1]                       => 50
[3,2,1,1,1,1]                     => 49
[3,1,1,1,1,1,1]                   => 48
[2,2,2,2,1]                       => 49
[2,2,2,1,1,1]                     => 48
[2,2,1,1,1,1,1]                   => 47
[2,1,1,1,1,1,1,1]                 => 46
[1,1,1,1,1,1,1,1,1]               => 45
[10]                              => 100
[9,1]                             => 91
[8,2]                             => 84
[8,1,1]                           => 83
[7,3]                             => 79
[7,2,1]                           => 77
[7,1,1,1]                         => 76
[6,4]                             => 76
[6,3,1]                           => 73
[6,2,2]                           => 72
[6,2,1,1]                         => 71
[6,1,1,1,1]                       => 70
[5,5]                             => 75
[5,4,1]                           => 71
[5,3,2]                           => 69
[5,3,1,1]                         => 68
[5,2,2,1]                         => 67
[5,2,1,1,1]                       => 66
[5,1,1,1,1,1]                     => 65
[4,4,2]                           => 68
[4,4,1,1]                         => 67
[4,3,3]                           => 67
[4,3,2,1]                         => 65
[4,3,1,1,1]                       => 64
[4,2,2,2]                         => 64
[4,2,2,1,1]                       => 63
[4,2,1,1,1,1]                     => 62
[4,1,1,1,1,1,1]                   => 61
[3,3,3,1]                         => 64
[3,3,2,2]                         => 63
[3,3,2,1,1]                       => 62
[3,3,1,1,1,1]                     => 61
[3,2,2,2,1]                       => 61
[3,2,2,1,1,1]                     => 60
[3,2,1,1,1,1,1]                   => 59
[3,1,1,1,1,1,1,1]                 => 58
[2,2,2,2,2]                       => 60
[2,2,2,2,1,1]                     => 59
[2,2,2,1,1,1,1]                   => 58
[2,2,1,1,1,1,1,1]                 => 57
[2,1,1,1,1,1,1,1,1]               => 56
[1,1,1,1,1,1,1,1,1,1]             => 55
[11]                              => 121
[10,1]                            => 111
[9,2]                             => 103
[9,1,1]                           => 102
[8,3]                             => 97
[8,2,1]                           => 95
[8,1,1,1]                         => 94
[7,4]                             => 93
[7,3,1]                           => 90
[7,2,2]                           => 89
[7,2,1,1]                         => 88
[7,1,1,1,1]                       => 87
[6,5]                             => 91
[6,4,1]                           => 87
[6,3,2]                           => 85
[6,3,1,1]                         => 84
[6,2,2,1]                         => 83
[6,2,1,1,1]                       => 82
[6,1,1,1,1,1]                     => 81
[5,5,1]                           => 86
[5,4,2]                           => 83
[5,4,1,1]                         => 82
[5,3,3]                           => 82
[5,3,2,1]                         => 80
[5,3,1,1,1]                       => 79
[5,2,2,2]                         => 79
[5,2,2,1,1]                       => 78
[5,2,1,1,1,1]                     => 77
[5,1,1,1,1,1,1]                   => 76
[4,4,3]                           => 81
[4,4,2,1]                         => 79
[4,4,1,1,1]                       => 78
[4,3,3,1]                         => 78
[4,3,2,2]                         => 77
[4,3,2,1,1]                       => 76
[4,3,1,1,1,1]                     => 75
[4,2,2,2,1]                       => 75
[4,2,2,1,1,1]                     => 74
[4,2,1,1,1,1,1]                   => 73
[4,1,1,1,1,1,1,1]                 => 72
[3,3,3,2]                         => 76
[3,3,3,1,1]                       => 75
[3,3,2,2,1]                       => 74
[3,3,2,1,1,1]                     => 73
[3,3,1,1,1,1,1]                   => 72
[3,2,2,2,2]                       => 73
[3,2,2,2,1,1]                     => 72
[3,2,2,1,1,1,1]                   => 71
[3,2,1,1,1,1,1,1]                 => 70
[3,1,1,1,1,1,1,1,1]               => 69
[2,2,2,2,2,1]                     => 71
[2,2,2,2,1,1,1]                   => 70
[2,2,2,1,1,1,1,1]                 => 69
[2,2,1,1,1,1,1,1,1]               => 68
[2,1,1,1,1,1,1,1,1,1]             => 67
[1,1,1,1,1,1,1,1,1,1,1]           => 66
[12]                              => 144
[11,1]                            => 133
[10,2]                            => 124
[10,1,1]                          => 123
[9,3]                             => 117
[9,2,1]                           => 115
[9,1,1,1]                         => 114
[8,4]                             => 112
[8,3,1]                           => 109
[8,2,2]                           => 108
[8,2,1,1]                         => 107
[8,1,1,1,1]                       => 106
[7,5]                             => 109
[7,4,1]                           => 105
[7,3,2]                           => 103
[7,3,1,1]                         => 102
[7,2,2,1]                         => 101
[7,2,1,1,1]                       => 100
[7,1,1,1,1,1]                     => 99
[6,6]                             => 108
[6,5,1]                           => 103
[6,4,2]                           => 100
[6,4,1,1]                         => 99
[6,3,3]                           => 99
[6,3,2,1]                         => 97
[6,3,1,1,1]                       => 96
[6,2,2,2]                         => 96
[6,2,2,1,1]                       => 95
[6,2,1,1,1,1]                     => 94
[6,1,1,1,1,1,1]                   => 93
[5,5,2]                           => 99
[5,5,1,1]                         => 98
[5,4,3]                           => 97
[5,4,2,1]                         => 95
[5,4,1,1,1]                       => 94
[5,3,3,1]                         => 94
[5,3,2,2]                         => 93
[5,3,2,1,1]                       => 92
[5,3,1,1,1,1]                     => 91
[5,2,2,2,1]                       => 91
[5,2,2,1,1,1]                     => 90
[5,2,1,1,1,1,1]                   => 89
[5,1,1,1,1,1,1,1]                 => 88
[4,4,4]                           => 96
[4,4,3,1]                         => 93
[4,4,2,2]                         => 92
[4,4,2,1,1]                       => 91
[4,4,1,1,1,1]                     => 90
[4,3,3,2]                         => 91
[4,3,3,1,1]                       => 90
[4,3,2,2,1]                       => 89
[4,3,2,1,1,1]                     => 88
[4,3,1,1,1,1,1]                   => 87
[4,2,2,2,2]                       => 88
[4,2,2,2,1,1]                     => 87
[4,2,2,1,1,1,1]                   => 86
[4,2,1,1,1,1,1,1]                 => 85
[4,1,1,1,1,1,1,1,1]               => 84
[3,3,3,3]                         => 90
[3,3,3,2,1]                       => 88
[3,3,3,1,1,1]                     => 87
[3,3,2,2,2]                       => 87
[3,3,2,2,1,1]                     => 86
[3,3,2,1,1,1,1]                   => 85
[3,3,1,1,1,1,1,1]                 => 84
[3,2,2,2,2,1]                     => 85
[3,2,2,2,1,1,1]                   => 84
[3,2,2,1,1,1,1,1]                 => 83
[3,2,1,1,1,1,1,1,1]               => 82
[3,1,1,1,1,1,1,1,1,1]             => 81
[2,2,2,2,2,2]                     => 84
[2,2,2,2,2,1,1]                   => 83
[2,2,2,2,1,1,1,1]                 => 82
[2,2,2,1,1,1,1,1,1]               => 81
[2,2,1,1,1,1,1,1,1,1]             => 80
[2,1,1,1,1,1,1,1,1,1,1]           => 79
[1,1,1,1,1,1,1,1,1,1,1,1]         => 78
[13]                              => 169
[12,1]                            => 157
[11,2]                            => 147
[11,1,1]                          => 146
[10,3]                            => 139
[10,2,1]                          => 137
[10,1,1,1]                        => 136
[9,4]                             => 133
[9,3,1]                           => 130
[9,2,2]                           => 129
[9,2,1,1]                         => 128
[9,1,1,1,1]                       => 127
[8,5]                             => 129
[8,4,1]                           => 125
[8,3,2]                           => 123
[8,3,1,1]                         => 122
[8,2,2,1]                         => 121
[8,2,1,1,1]                       => 120
[8,1,1,1,1,1]                     => 119
[7,6]                             => 127
[7,5,1]                           => 122
[7,4,2]                           => 119
[7,4,1,1]                         => 118
[7,3,3]                           => 118
[7,3,2,1]                         => 116
[7,3,1,1,1]                       => 115
[7,2,2,2]                         => 115
[7,2,2,1,1]                       => 114
[7,2,1,1,1,1]                     => 113
[7,1,1,1,1,1,1]                   => 112
[6,6,1]                           => 121
[6,5,2]                           => 117
[6,5,1,1]                         => 116
[6,4,3]                           => 115
[6,4,2,1]                         => 113
[6,4,1,1,1]                       => 112
[6,3,3,1]                         => 112
[6,3,2,2]                         => 111
[6,3,2,1,1]                       => 110
[6,3,1,1,1,1]                     => 109
[6,2,2,2,1]                       => 109
[6,2,2,1,1,1]                     => 108
[6,2,1,1,1,1,1]                   => 107
[6,1,1,1,1,1,1,1]                 => 106
[5,5,3]                           => 114
[5,5,2,1]                         => 112
[5,5,1,1,1]                       => 111
[5,4,4]                           => 113
[5,4,3,1]                         => 110
[5,4,2,2]                         => 109
[5,4,2,1,1]                       => 108
[5,4,1,1,1,1]                     => 107
[5,3,3,2]                         => 108
[5,3,3,1,1]                       => 107
[5,3,2,2,1]                       => 106
[5,3,2,1,1,1]                     => 105
[5,3,1,1,1,1,1]                   => 104
[5,2,2,2,2]                       => 105
[5,2,2,2,1,1]                     => 104
[5,2,2,1,1,1,1]                   => 103
[5,2,1,1,1,1,1,1]                 => 102
[5,1,1,1,1,1,1,1,1]               => 101
[4,4,4,1]                         => 109
[4,4,3,2]                         => 107
[4,4,3,1,1]                       => 106
[4,4,2,2,1]                       => 105
[4,4,2,1,1,1]                     => 104
[4,4,1,1,1,1,1]                   => 103
[4,3,3,3]                         => 106
[4,3,3,2,1]                       => 104
[4,3,3,1,1,1]                     => 103
[4,3,2,2,2]                       => 103
[4,3,2,2,1,1]                     => 102
[4,3,2,1,1,1,1]                   => 101
[4,3,1,1,1,1,1,1]                 => 100
[4,2,2,2,2,1]                     => 101
[4,2,2,2,1,1,1]                   => 100
[4,2,2,1,1,1,1,1]                 => 99
[4,2,1,1,1,1,1,1,1]               => 98
[4,1,1,1,1,1,1,1,1,1]             => 97
[3,3,3,3,1]                       => 103
[3,3,3,2,2]                       => 102
[3,3,3,2,1,1]                     => 101
[3,3,3,1,1,1,1]                   => 100
[3,3,2,2,2,1]                     => 100
[3,3,2,2,1,1,1]                   => 99
[3,3,2,1,1,1,1,1]                 => 98
[3,3,1,1,1,1,1,1,1]               => 97
[3,2,2,2,2,2]                     => 99
[3,2,2,2,2,1,1]                   => 98
[3,2,2,2,1,1,1,1]                 => 97
[3,2,2,1,1,1,1,1,1]               => 96
[3,2,1,1,1,1,1,1,1,1]             => 95
[3,1,1,1,1,1,1,1,1,1,1]           => 94
[2,2,2,2,2,2,1]                   => 97
[2,2,2,2,2,1,1,1]                 => 96
[2,2,2,2,1,1,1,1,1]               => 95
[2,2,2,1,1,1,1,1,1,1]             => 94
[2,2,1,1,1,1,1,1,1,1,1]           => 93
[2,1,1,1,1,1,1,1,1,1,1,1]         => 92
[1,1,1,1,1,1,1,1,1,1,1,1,1]       => 91
[14]                              => 196
[13,1]                            => 183
[12,2]                            => 172
[12,1,1]                          => 171
[11,3]                            => 163
[11,2,1]                          => 161
[11,1,1,1]                        => 160
[10,4]                            => 156
[10,3,1]                          => 153
[10,2,2]                          => 152
[10,2,1,1]                        => 151
[10,1,1,1,1]                      => 150
[9,5]                             => 151
[9,4,1]                           => 147
[9,3,2]                           => 145
[9,3,1,1]                         => 144
[9,2,2,1]                         => 143
[9,2,1,1,1]                       => 142
[9,1,1,1,1,1]                     => 141
[8,6]                             => 148
[8,5,1]                           => 143
[8,4,2]                           => 140
[8,4,1,1]                         => 139
[8,3,3]                           => 139
[8,3,2,1]                         => 137
[8,3,1,1,1]                       => 136
[8,2,2,2]                         => 136
[8,2,2,1,1]                       => 135
[8,2,1,1,1,1]                     => 134
[8,1,1,1,1,1,1]                   => 133
[7,7]                             => 147
[7,6,1]                           => 141
[7,5,2]                           => 137
[7,5,1,1]                         => 136
[7,4,3]                           => 135
[7,4,2,1]                         => 133
[7,4,1,1,1]                       => 132
[7,3,3,1]                         => 132
[7,3,2,2]                         => 131
[7,3,2,1,1]                       => 130
[7,3,1,1,1,1]                     => 129
[7,2,2,2,1]                       => 129
[7,2,2,1,1,1]                     => 128
[7,2,1,1,1,1,1]                   => 127
[7,1,1,1,1,1,1,1]                 => 126
[6,6,2]                           => 136
[6,6,1,1]                         => 135
[6,5,3]                           => 133
[6,5,2,1]                         => 131
[6,5,1,1,1]                       => 130
[6,4,4]                           => 132
[6,4,3,1]                         => 129
[6,4,2,2]                         => 128
[6,4,2,1,1]                       => 127
[6,4,1,1,1,1]                     => 126
[6,3,3,2]                         => 127
[6,3,3,1,1]                       => 126
[6,3,2,2,1]                       => 125
[6,3,2,1,1,1]                     => 124
[6,3,1,1,1,1,1]                   => 123
[6,2,2,2,2]                       => 124
[6,2,2,2,1,1]                     => 123
[6,2,2,1,1,1,1]                   => 122
[6,2,1,1,1,1,1,1]                 => 121
[6,1,1,1,1,1,1,1,1]               => 120
[5,5,4]                           => 131
[5,5,3,1]                         => 128
[5,5,2,2]                         => 127
[5,5,2,1,1]                       => 126
[5,5,1,1,1,1]                     => 125
[5,4,4,1]                         => 127
[5,4,3,2]                         => 125
[5,4,3,1,1]                       => 124
[5,4,2,2,1]                       => 123
[5,4,2,1,1,1]                     => 122
[5,4,1,1,1,1,1]                   => 121
[5,3,3,3]                         => 124
[5,3,3,2,1]                       => 122
[5,3,3,1,1,1]                     => 121
[5,3,2,2,2]                       => 121
[5,3,2,2,1,1]                     => 120
[5,3,2,1,1,1,1]                   => 119
[5,3,1,1,1,1,1,1]                 => 118
[5,2,2,2,2,1]                     => 119
[5,2,2,2,1,1,1]                   => 118
[5,2,2,1,1,1,1,1]                 => 117
[5,2,1,1,1,1,1,1,1]               => 116
[5,1,1,1,1,1,1,1,1,1]             => 115
[4,4,4,2]                         => 124
[4,4,4,1,1]                       => 123
[4,4,3,3]                         => 123
[4,4,3,2,1]                       => 121
[4,4,3,1,1,1]                     => 120
[4,4,2,2,2]                       => 120
[4,4,2,2,1,1]                     => 119
[4,4,2,1,1,1,1]                   => 118
[4,4,1,1,1,1,1,1]                 => 117
[4,3,3,3,1]                       => 120
[4,3,3,2,2]                       => 119
[4,3,3,2,1,1]                     => 118
[4,3,3,1,1,1,1]                   => 117
[4,3,2,2,2,1]                     => 117
[4,3,2,2,1,1,1]                   => 116
[4,3,2,1,1,1,1,1]                 => 115
[4,3,1,1,1,1,1,1,1]               => 114
[4,2,2,2,2,2]                     => 116
[4,2,2,2,2,1,1]                   => 115
[4,2,2,2,1,1,1,1]                 => 114
[4,2,2,1,1,1,1,1,1]               => 113
[4,2,1,1,1,1,1,1,1,1]             => 112
[4,1,1,1,1,1,1,1,1,1,1]           => 111
[3,3,3,3,2]                       => 118
[3,3,3,3,1,1]                     => 117
[3,3,3,2,2,1]                     => 116
[3,3,3,2,1,1,1]                   => 115
[3,3,3,1,1,1,1,1]                 => 114
[3,3,2,2,2,2]                     => 115
[3,3,2,2,2,1,1]                   => 114
[3,3,2,2,1,1,1,1]                 => 113
[3,3,2,1,1,1,1,1,1]               => 112
[3,3,1,1,1,1,1,1,1,1]             => 111
[3,2,2,2,2,2,1]                   => 113
[3,2,2,2,2,1,1,1]                 => 112
[3,2,2,2,1,1,1,1,1]               => 111
[3,2,2,1,1,1,1,1,1,1]             => 110
[3,2,1,1,1,1,1,1,1,1,1]           => 109
[3,1,1,1,1,1,1,1,1,1,1,1]         => 108
[2,2,2,2,2,2,2]                   => 112
[2,2,2,2,2,2,1,1]                 => 111
[2,2,2,2,2,1,1,1,1]               => 110
[2,2,2,2,1,1,1,1,1,1]             => 109
[2,2,2,1,1,1,1,1,1,1,1]           => 108
[2,2,1,1,1,1,1,1,1,1,1,1]         => 107
[2,1,1,1,1,1,1,1,1,1,1,1,1]       => 106
[1,1,1,1,1,1,1,1,1,1,1,1,1,1]     => 105
[15]                              => 225
[14,1]                            => 211
[13,2]                            => 199
[13,1,1]                          => 198
[12,3]                            => 189
[12,2,1]                          => 187
[12,1,1,1]                        => 186
[11,4]                            => 181
[11,3,1]                          => 178
[11,2,2]                          => 177
[11,2,1,1]                        => 176
[11,1,1,1,1]                      => 175
[10,5]                            => 175
[10,4,1]                          => 171
[10,3,2]                          => 169
[10,3,1,1]                        => 168
[10,2,2,1]                        => 167
[10,2,1,1,1]                      => 166
[10,1,1,1,1,1]                    => 165
[9,6]                             => 171
[9,5,1]                           => 166
[9,4,2]                           => 163
[9,4,1,1]                         => 162
[9,3,3]                           => 162
[9,3,2,1]                         => 160
[9,3,1,1,1]                       => 159
[9,2,2,2]                         => 159
[9,2,2,1,1]                       => 158
[9,2,1,1,1,1]                     => 157
[9,1,1,1,1,1,1]                   => 156
[8,7]                             => 169
[8,6,1]                           => 163
[8,5,2]                           => 159
[8,5,1,1]                         => 158
[8,4,3]                           => 157
[8,4,2,1]                         => 155
[8,4,1,1,1]                       => 154
[8,3,3,1]                         => 154
[8,3,2,2]                         => 153
[8,3,2,1,1]                       => 152
[8,3,1,1,1,1]                     => 151
[8,2,2,2,1]                       => 151
[8,2,2,1,1,1]                     => 150
[8,2,1,1,1,1,1]                   => 149
[8,1,1,1,1,1,1,1]                 => 148
[7,7,1]                           => 162
[7,6,2]                           => 157
[7,6,1,1]                         => 156
[7,5,3]                           => 154
[7,5,2,1]                         => 152
[7,5,1,1,1]                       => 151
[7,4,4]                           => 153
[7,4,3,1]                         => 150
[7,4,2,2]                         => 149
[7,4,2,1,1]                       => 148
[7,4,1,1,1,1]                     => 147
[7,3,3,2]                         => 148
[7,3,3,1,1]                       => 147
[7,3,2,2,1]                       => 146
[7,3,2,1,1,1]                     => 145
[7,3,1,1,1,1,1]                   => 144
[7,2,2,2,2]                       => 145
[7,2,2,2,1,1]                     => 144
[7,2,2,1,1,1,1]                   => 143
[7,2,1,1,1,1,1,1]                 => 142
[7,1,1,1,1,1,1,1,1]               => 141
[6,6,3]                           => 153
[6,6,2,1]                         => 151
[6,6,1,1,1]                       => 150
[6,5,4]                           => 151
[6,5,3,1]                         => 148
[6,5,2,2]                         => 147
[6,5,2,1,1]                       => 146
[6,5,1,1,1,1]                     => 145
[6,4,4,1]                         => 147
[6,4,3,2]                         => 145
[6,4,3,1,1]                       => 144
[6,4,2,2,1]                       => 143
[6,4,2,1,1,1]                     => 142
[6,4,1,1,1,1,1]                   => 141
[6,3,3,3]                         => 144
[6,3,3,2,1]                       => 142
[6,3,3,1,1,1]                     => 141
[6,3,2,2,2]                       => 141
[6,3,2,2,1,1]                     => 140
[6,3,2,1,1,1,1]                   => 139
[6,3,1,1,1,1,1,1]                 => 138
[6,2,2,2,2,1]                     => 139
[6,2,2,2,1,1,1]                   => 138
[6,2,2,1,1,1,1,1]                 => 137
[6,2,1,1,1,1,1,1,1]               => 136
[6,1,1,1,1,1,1,1,1,1]             => 135
[5,5,5]                           => 150
[5,5,4,1]                         => 146
[5,5,3,2]                         => 144
[5,5,3,1,1]                       => 143
[5,5,2,2,1]                       => 142
[5,5,2,1,1,1]                     => 141
[5,5,1,1,1,1,1]                   => 140
[5,4,4,2]                         => 143
[5,4,4,1,1]                       => 142
[5,4,3,3]                         => 142
[5,4,3,2,1]                       => 140
[5,4,3,1,1,1]                     => 139
[5,4,2,2,2]                       => 139
[5,4,2,2,1,1]                     => 138
[5,4,2,1,1,1,1]                   => 137
[5,4,1,1,1,1,1,1]                 => 136
[5,3,3,3,1]                       => 139
[5,3,3,2,2]                       => 138
[5,3,3,2,1,1]                     => 137
[5,3,3,1,1,1,1]                   => 136
[5,3,2,2,2,1]                     => 136
[5,3,2,2,1,1,1]                   => 135
[5,3,2,1,1,1,1,1]                 => 134
[5,3,1,1,1,1,1,1,1]               => 133
[5,2,2,2,2,2]                     => 135
[5,2,2,2,2,1,1]                   => 134
[5,2,2,2,1,1,1,1]                 => 133
[5,2,2,1,1,1,1,1,1]               => 132
[5,2,1,1,1,1,1,1,1,1]             => 131
[5,1,1,1,1,1,1,1,1,1,1]           => 130
[4,4,4,3]                         => 141
[4,4,4,2,1]                       => 139
[4,4,4,1,1,1]                     => 138
[4,4,3,3,1]                       => 138
[4,4,3,2,2]                       => 137
[4,4,3,2,1,1]                     => 136
[4,4,3,1,1,1,1]                   => 135
[4,4,2,2,2,1]                     => 135
[4,4,2,2,1,1,1]                   => 134
[4,4,2,1,1,1,1,1]                 => 133
[4,4,1,1,1,1,1,1,1]               => 132
[4,3,3,3,2]                       => 136
[4,3,3,3,1,1]                     => 135
[4,3,3,2,2,1]                     => 134
[4,3,3,2,1,1,1]                   => 133
[4,3,3,1,1,1,1,1]                 => 132
[4,3,2,2,2,2]                     => 133
[4,3,2,2,2,1,1]                   => 132
[4,3,2,2,1,1,1,1]                 => 131
[4,3,2,1,1,1,1,1,1]               => 130
[4,3,1,1,1,1,1,1,1,1]             => 129
[4,2,2,2,2,2,1]                   => 131
[4,2,2,2,2,1,1,1]                 => 130
[4,2,2,2,1,1,1,1,1]               => 129
[4,2,2,1,1,1,1,1,1,1]             => 128
[4,2,1,1,1,1,1,1,1,1,1]           => 127
[4,1,1,1,1,1,1,1,1,1,1,1]         => 126
[3,3,3,3,3]                       => 135
[3,3,3,3,2,1]                     => 133
[3,3,3,3,1,1,1]                   => 132
[3,3,3,2,2,2]                     => 132
[3,3,3,2,2,1,1]                   => 131
[3,3,3,2,1,1,1,1]                 => 130
[3,3,3,1,1,1,1,1,1]               => 129
[3,3,2,2,2,2,1]                   => 130
[3,3,2,2,2,1,1,1]                 => 129
[3,3,2,2,1,1,1,1,1]               => 128
[3,3,2,1,1,1,1,1,1,1]             => 127
[3,3,1,1,1,1,1,1,1,1,1]           => 126
[3,2,2,2,2,2,2]                   => 129
[3,2,2,2,2,2,1,1]                 => 128
[3,2,2,2,2,1,1,1,1]               => 127
[3,2,2,2,1,1,1,1,1,1]             => 126
[3,2,2,1,1,1,1,1,1,1,1]           => 125
[3,2,1,1,1,1,1,1,1,1,1,1]         => 124
[3,1,1,1,1,1,1,1,1,1,1,1,1]       => 123
[2,2,2,2,2,2,2,1]                 => 127
[2,2,2,2,2,2,1,1,1]               => 126
[2,2,2,2,2,1,1,1,1,1]             => 125
[2,2,2,2,1,1,1,1,1,1,1]           => 124
[2,2,2,1,1,1,1,1,1,1,1,1]         => 123
[2,2,1,1,1,1,1,1,1,1,1,1,1]       => 122
[2,1,1,1,1,1,1,1,1,1,1,1,1,1]     => 121
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]   => 120
[16]                              => 256
[15,1]                            => 241
[14,2]                            => 228
[14,1,1]                          => 227
[13,3]                            => 217
[13,2,1]                          => 215
[13,1,1,1]                        => 214
[12,4]                            => 208
[12,3,1]                          => 205
[12,2,2]                          => 204
[12,2,1,1]                        => 203
[12,1,1,1,1]                      => 202
[11,5]                            => 201
[11,4,1]                          => 197
[11,3,2]                          => 195
[11,3,1,1]                        => 194
[11,2,2,1]                        => 193
[11,2,1,1,1]                      => 192
[11,1,1,1,1,1]                    => 191
[10,6]                            => 196
[10,5,1]                          => 191
[10,4,2]                          => 188
[10,4,1,1]                        => 187
[10,3,3]                          => 187
[10,3,2,1]                        => 185
[10,3,1,1,1]                      => 184
[10,2,2,2]                        => 184
[10,2,2,1,1]                      => 183
[10,2,1,1,1,1]                    => 182
[10,1,1,1,1,1,1]                  => 181
[9,7]                             => 193
[9,6,1]                           => 187
[9,5,2]                           => 183
[9,5,1,1]                         => 182
[9,4,3]                           => 181
[9,4,2,1]                         => 179
[9,4,1,1,1]                       => 178
[9,3,3,1]                         => 178
[9,3,2,2]                         => 177
[9,3,2,1,1]                       => 176
[9,3,1,1,1,1]                     => 175
[9,2,2,2,1]                       => 175
[9,2,2,1,1,1]                     => 174
[9,2,1,1,1,1,1]                   => 173
[9,1,1,1,1,1,1,1]                 => 172
[8,8]                             => 192
[8,7,1]                           => 185
[8,6,2]                           => 180
[8,6,1,1]                         => 179
[8,5,3]                           => 177
[8,5,2,1]                         => 175
[8,5,1,1,1]                       => 174
[8,4,4]                           => 176
[8,4,3,1]                         => 173
[8,4,2,2]                         => 172
[8,4,2,1,1]                       => 171
[8,4,1,1,1,1]                     => 170
[8,3,3,2]                         => 171
[8,3,3,1,1]                       => 170
[8,3,2,2,1]                       => 169
[8,3,2,1,1,1]                     => 168
[8,3,1,1,1,1,1]                   => 167
[8,2,2,2,2]                       => 168
[8,2,2,2,1,1]                     => 167
[8,2,2,1,1,1,1]                   => 166
[8,2,1,1,1,1,1,1]                 => 165
[8,1,1,1,1,1,1,1,1]               => 164
[7,7,2]                           => 179
[7,7,1,1]                         => 178
[7,6,3]                           => 175
[7,6,2,1]                         => 173
[7,6,1,1,1]                       => 172
[7,5,4]                           => 173
[7,5,3,1]                         => 170
[7,5,2,2]                         => 169
[7,5,2,1,1]                       => 168
[7,5,1,1,1,1]                     => 167
[7,4,4,1]                         => 169
[7,4,3,2]                         => 167
[7,4,3,1,1]                       => 166
[7,4,2,2,1]                       => 165
[7,4,2,1,1,1]                     => 164
[7,4,1,1,1,1,1]                   => 163
[7,3,3,3]                         => 166
[7,3,3,2,1]                       => 164
[7,3,3,1,1,1]                     => 163
[7,3,2,2,2]                       => 163
[7,3,2,2,1,1]                     => 162
[7,3,2,1,1,1,1]                   => 161
[7,3,1,1,1,1,1,1]                 => 160
[7,2,2,2,2,1]                     => 161
[7,2,2,2,1,1,1]                   => 160
[7,2,2,1,1,1,1,1]                 => 159
[7,2,1,1,1,1,1,1,1]               => 158
[7,1,1,1,1,1,1,1,1,1]             => 157
[6,6,4]                           => 172
[6,6,3,1]                         => 169
[6,6,2,2]                         => 168
[6,6,2,1,1]                       => 167
[6,6,1,1,1,1]                     => 166
[6,5,5]                           => 171
[6,5,4,1]                         => 167
[6,5,3,2]                         => 165
[6,5,3,1,1]                       => 164
[6,5,2,2,1]                       => 163
[6,5,2,1,1,1]                     => 162
[6,5,1,1,1,1,1]                   => 161
[6,4,4,2]                         => 164
[6,4,4,1,1]                       => 163
[6,4,3,3]                         => 163
[6,4,3,2,1]                       => 161
[6,4,3,1,1,1]                     => 160
[6,4,2,2,2]                       => 160
[6,4,2,2,1,1]                     => 159
[6,4,2,1,1,1,1]                   => 158
[6,4,1,1,1,1,1,1]                 => 157
[6,3,3,3,1]                       => 160
[6,3,3,2,2]                       => 159
[6,3,3,2,1,1]                     => 158
[6,3,3,1,1,1,1]                   => 157
[6,3,2,2,2,1]                     => 157
[6,3,2,2,1,1,1]                   => 156
[6,3,2,1,1,1,1,1]                 => 155
[6,3,1,1,1,1,1,1,1]               => 154
[6,2,2,2,2,2]                     => 156
[6,2,2,2,2,1,1]                   => 155
[6,2,2,2,1,1,1,1]                 => 154
[6,2,2,1,1,1,1,1,1]               => 153
[6,2,1,1,1,1,1,1,1,1]             => 152
[6,1,1,1,1,1,1,1,1,1,1]           => 151
[5,5,5,1]                         => 166
[5,5,4,2]                         => 163
[5,5,4,1,1]                       => 162
[5,5,3,3]                         => 162
[5,5,3,2,1]                       => 160
[5,5,3,1,1,1]                     => 159
[5,5,2,2,2]                       => 159
[5,5,2,2,1,1]                     => 158
[5,5,2,1,1,1,1]                   => 157
[5,5,1,1,1,1,1,1]                 => 156
[5,4,4,3]                         => 161
[5,4,4,2,1]                       => 159
[5,4,4,1,1,1]                     => 158
[5,4,3,3,1]                       => 158
[5,4,3,2,2]                       => 157
[5,4,3,2,1,1]                     => 156
[5,4,3,1,1,1,1]                   => 155
[5,4,2,2,2,1]                     => 155
[5,4,2,2,1,1,1]                   => 154
[5,4,2,1,1,1,1,1]                 => 153
[5,4,1,1,1,1,1,1,1]               => 152
[5,3,3,3,2]                       => 156
[5,3,3,3,1,1]                     => 155
[5,3,3,2,2,1]                     => 154
[5,3,3,2,1,1,1]                   => 153
[5,3,3,1,1,1,1,1]                 => 152
[5,3,2,2,2,2]                     => 153
[5,3,2,2,2,1,1]                   => 152
[5,3,2,2,1,1,1,1]                 => 151
[5,3,2,1,1,1,1,1,1]               => 150
[5,3,1,1,1,1,1,1,1,1]             => 149
[5,2,2,2,2,2,1]                   => 151
[5,2,2,2,2,1,1,1]                 => 150
[5,2,2,2,1,1,1,1,1]               => 149
[5,2,2,1,1,1,1,1,1,1]             => 148
[5,2,1,1,1,1,1,1,1,1,1]           => 147
[5,1,1,1,1,1,1,1,1,1,1,1]         => 146
[4,4,4,4]                         => 160
[4,4,4,3,1]                       => 157
[4,4,4,2,2]                       => 156
[4,4,4,2,1,1]                     => 155
[4,4,4,1,1,1,1]                   => 154
[4,4,3,3,2]                       => 155
[4,4,3,3,1,1]                     => 154
[4,4,3,2,2,1]                     => 153
[4,4,3,2,1,1,1]                   => 152
[4,4,3,1,1,1,1,1]                 => 151
[4,4,2,2,2,2]                     => 152
[4,4,2,2,2,1,1]                   => 151
[4,4,2,2,1,1,1,1]                 => 150
[4,4,2,1,1,1,1,1,1]               => 149
[4,4,1,1,1,1,1,1,1,1]             => 148
[4,3,3,3,3]                       => 154
[4,3,3,3,2,1]                     => 152
[4,3,3,3,1,1,1]                   => 151
[4,3,3,2,2,2]                     => 151
[4,3,3,2,2,1,1]                   => 150
[4,3,3,2,1,1,1,1]                 => 149
[4,3,3,1,1,1,1,1,1]               => 148
[4,3,2,2,2,2,1]                   => 149
[4,3,2,2,2,1,1,1]                 => 148
[4,3,2,2,1,1,1,1,1]               => 147
[4,3,2,1,1,1,1,1,1,1]             => 146
[4,3,1,1,1,1,1,1,1,1,1]           => 145
[4,2,2,2,2,2,2]                   => 148
[4,2,2,2,2,2,1,1]                 => 147
[4,2,2,2,2,1,1,1,1]               => 146
[4,2,2,2,1,1,1,1,1,1]             => 145
[4,2,2,1,1,1,1,1,1,1,1]           => 144
[4,2,1,1,1,1,1,1,1,1,1,1]         => 143
[4,1,1,1,1,1,1,1,1,1,1,1,1]       => 142
[3,3,3,3,3,1]                     => 151
[3,3,3,3,2,2]                     => 150
[3,3,3,3,2,1,1]                   => 149
[3,3,3,3,1,1,1,1]                 => 148
[3,3,3,2,2,2,1]                   => 148
[3,3,3,2,2,1,1,1]                 => 147
[3,3,3,2,1,1,1,1,1]               => 146
[3,3,3,1,1,1,1,1,1,1]             => 145
[3,3,2,2,2,2,2]                   => 147
[3,3,2,2,2,2,1,1]                 => 146
[3,3,2,2,2,1,1,1,1]               => 145
[3,3,2,2,1,1,1,1,1,1]             => 144
[3,3,2,1,1,1,1,1,1,1,1]           => 143
[3,3,1,1,1,1,1,1,1,1,1,1]         => 142
[3,2,2,2,2,2,2,1]                 => 145
[3,2,2,2,2,2,1,1,1]               => 144
[3,2,2,2,2,1,1,1,1,1]             => 143
[3,2,2,2,1,1,1,1,1,1,1]           => 142
[3,2,2,1,1,1,1,1,1,1,1,1]         => 141
[3,2,1,1,1,1,1,1,1,1,1,1,1]       => 140
[3,1,1,1,1,1,1,1,1,1,1,1,1,1]     => 139
[2,2,2,2,2,2,2,2]                 => 144
[2,2,2,2,2,2,2,1,1]               => 143
[2,2,2,2,2,2,1,1,1,1]             => 142
[2,2,2,2,2,1,1,1,1,1,1]           => 141
[2,2,2,2,1,1,1,1,1,1,1,1]         => 140
[2,2,2,1,1,1,1,1,1,1,1,1,1]       => 139
[2,2,1,1,1,1,1,1,1,1,1,1,1,1]     => 138
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1]   => 137
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 136
[17]                              => 289
[16,1]                            => 273
[15,2]                            => 259
[15,1,1]                          => 258
[14,3]                            => 247
[14,2,1]                          => 245
[14,1,1,1]                        => 244
[13,4]                            => 237
[13,3,1]                          => 234
[13,2,2]                          => 233
[13,2,1,1]                        => 232
[13,1,1,1,1]                      => 231
[12,5]                            => 229
[12,4,1]                          => 225
[12,3,2]                          => 223
[12,3,1,1]                        => 222
[12,2,2,1]                        => 221
[12,2,1,1,1]                      => 220
[12,1,1,1,1,1]                    => 219
[11,6]                            => 223
[11,5,1]                          => 218
[11,4,2]                          => 215
[11,4,1,1]                        => 214
[11,3,3]                          => 214
[11,3,2,1]                        => 212
[11,3,1,1,1]                      => 211
[11,2,2,2]                        => 211
[11,2,2,1,1]                      => 210
[11,2,1,1,1,1]                    => 209
[11,1,1,1,1,1,1]                  => 208
[10,7]                            => 219
[10,6,1]                          => 213
[10,5,2]                          => 209
[10,5,1,1]                        => 208
[10,4,3]                          => 207
[10,4,2,1]                        => 205
[10,4,1,1,1]                      => 204
[10,3,3,1]                        => 204
[10,3,2,2]                        => 203
[10,3,2,1,1]                      => 202
[10,3,1,1,1,1]                    => 201
[10,2,2,2,1]                      => 201
[10,2,2,1,1,1]                    => 200
[10,2,1,1,1,1,1]                  => 199
[10,1,1,1,1,1,1,1]                => 198
[9,8]                             => 217
[9,7,1]                           => 210
[9,6,2]                           => 205
[9,6,1,1]                         => 204
[9,5,3]                           => 202
[9,5,2,1]                         => 200
[9,5,1,1,1]                       => 199
[9,4,4]                           => 201
[9,4,3,1]                         => 198
[9,4,2,2]                         => 197
[9,4,2,1,1]                       => 196
[9,4,1,1,1,1]                     => 195
[9,3,3,2]                         => 196
[9,3,3,1,1]                       => 195
[9,3,2,2,1]                       => 194
[9,3,2,1,1,1]                     => 193
[9,3,1,1,1,1,1]                   => 192
[9,2,2,2,2]                       => 193
[9,2,2,2,1,1]                     => 192
[9,2,2,1,1,1,1]                   => 191
[9,2,1,1,1,1,1,1]                 => 190
[9,1,1,1,1,1,1,1,1]               => 189
[8,8,1]                           => 209
[8,7,2]                           => 203
[8,7,1,1]                         => 202
[8,6,3]                           => 199
[8,6,2,1]                         => 197
[8,6,1,1,1]                       => 196
[8,5,4]                           => 197
[8,5,3,1]                         => 194
[8,5,2,2]                         => 193
[8,5,2,1,1]                       => 192
[8,5,1,1,1,1]                     => 191
[8,4,4,1]                         => 193
[8,4,3,2]                         => 191
[8,4,3,1,1]                       => 190
[8,4,2,2,1]                       => 189
[8,4,2,1,1,1]                     => 188
[8,4,1,1,1,1,1]                   => 187
[8,3,3,3]                         => 190
[8,3,3,2,1]                       => 188
[8,3,3,1,1,1]                     => 187
[8,3,2,2,2]                       => 187
[8,3,2,2,1,1]                     => 186
[8,3,2,1,1,1,1]                   => 185
[8,3,1,1,1,1,1,1]                 => 184
[8,2,2,2,2,1]                     => 185
[8,2,2,2,1,1,1]                   => 184
[8,2,2,1,1,1,1,1]                 => 183
[8,2,1,1,1,1,1,1,1]               => 182
[8,1,1,1,1,1,1,1,1,1]             => 181
[7,7,3]                           => 198
[7,7,2,1]                         => 196
[7,7,1,1,1]                       => 195
[7,6,4]                           => 195
[7,6,3,1]                         => 192
[7,6,2,2]                         => 191
[7,6,2,1,1]                       => 190
[7,6,1,1,1,1]                     => 189
[7,5,5]                           => 194
[7,5,4,1]                         => 190
[7,5,3,2]                         => 188
[7,5,3,1,1]                       => 187
[7,5,2,2,1]                       => 186
[7,5,2,1,1,1]                     => 185
[7,5,1,1,1,1,1]                   => 184
[7,4,4,2]                         => 187
[7,4,4,1,1]                       => 186
[7,4,3,3]                         => 186
[7,4,3,2,1]                       => 184
[7,4,3,1,1,1]                     => 183
[7,4,2,2,2]                       => 183
[7,4,2,2,1,1]                     => 182
[7,4,2,1,1,1,1]                   => 181
[7,4,1,1,1,1,1,1]                 => 180
[7,3,3,3,1]                       => 183
[7,3,3,2,2]                       => 182
[7,3,3,2,1,1]                     => 181
[7,3,3,1,1,1,1]                   => 180
[7,3,2,2,2,1]                     => 180
[7,3,2,2,1,1,1]                   => 179
[7,3,2,1,1,1,1,1]                 => 178
[7,3,1,1,1,1,1,1,1]               => 177
[7,2,2,2,2,2]                     => 179
[7,2,2,2,2,1,1]                   => 178
[7,2,2,2,1,1,1,1]                 => 177
[7,2,2,1,1,1,1,1,1]               => 176
[7,2,1,1,1,1,1,1,1,1]             => 175
[7,1,1,1,1,1,1,1,1,1,1]           => 174
[6,6,5]                           => 193
[6,6,4,1]                         => 189
[6,6,3,2]                         => 187
[6,6,3,1,1]                       => 186
[6,6,2,2,1]                       => 185
[6,6,2,1,1,1]                     => 184
[6,6,1,1,1,1,1]                   => 183
[6,5,5,1]                         => 188
[6,5,4,2]                         => 185
[6,5,4,1,1]                       => 184
[6,5,3,3]                         => 184
[6,5,3,2,1]                       => 182
[6,5,3,1,1,1]                     => 181
[6,5,2,2,2]                       => 181
[6,5,2,2,1,1]                     => 180
[6,5,2,1,1,1,1]                   => 179
[6,5,1,1,1,1,1,1]                 => 178
[6,4,4,3]                         => 183
[6,4,4,2,1]                       => 181
[6,4,4,1,1,1]                     => 180
[6,4,3,3,1]                       => 180
[6,4,3,2,2]                       => 179
[6,4,3,2,1,1]                     => 178
[6,4,3,1,1,1,1]                   => 177
[6,4,2,2,2,1]                     => 177
[6,4,2,2,1,1,1]                   => 176
[6,4,2,1,1,1,1,1]                 => 175
[6,4,1,1,1,1,1,1,1]               => 174
[6,3,3,3,2]                       => 178
[6,3,3,3,1,1]                     => 177
[6,3,3,2,2,1]                     => 176
[6,3,3,2,1,1,1]                   => 175
[6,3,3,1,1,1,1,1]                 => 174
[6,3,2,2,2,2]                     => 175
[6,3,2,2,2,1,1]                   => 174
[6,3,2,2,1,1,1,1]                 => 173
[6,3,2,1,1,1,1,1,1]               => 172
[6,3,1,1,1,1,1,1,1,1]             => 171
[6,2,2,2,2,2,1]                   => 173
[6,2,2,2,2,1,1,1]                 => 172
[6,2,2,2,1,1,1,1,1]               => 171
[6,2,2,1,1,1,1,1,1,1]             => 170
[6,2,1,1,1,1,1,1,1,1,1]           => 169
[6,1,1,1,1,1,1,1,1,1,1,1]         => 168
[5,5,5,2]                         => 184
[5,5,5,1,1]                       => 183
[5,5,4,3]                         => 182
[5,5,4,2,1]                       => 180
[5,5,4,1,1,1]                     => 179
[5,5,3,3,1]                       => 179
[5,5,3,2,2]                       => 178
[5,5,3,2,1,1]                     => 177
[5,5,3,1,1,1,1]                   => 176
[5,5,2,2,2,1]                     => 176
[5,5,2,2,1,1,1]                   => 175
[5,5,2,1,1,1,1,1]                 => 174
[5,5,1,1,1,1,1,1,1]               => 173
[5,4,4,4]                         => 181
[5,4,4,3,1]                       => 178
[5,4,4,2,2]                       => 177
[5,4,4,2,1,1]                     => 176
[5,4,4,1,1,1,1]                   => 175
[5,4,3,3,2]                       => 176
[5,4,3,3,1,1]                     => 175
[5,4,3,2,2,1]                     => 174
[5,4,3,2,1,1,1]                   => 173
[5,4,3,1,1,1,1,1]                 => 172
[5,4,2,2,2,2]                     => 173
[5,4,2,2,2,1,1]                   => 172
[5,4,2,2,1,1,1,1]                 => 171
[5,4,2,1,1,1,1,1,1]               => 170
[5,4,1,1,1,1,1,1,1,1]             => 169
[5,3,3,3,3]                       => 175
[5,3,3,3,2,1]                     => 173
[5,3,3,3,1,1,1]                   => 172
[5,3,3,2,2,2]                     => 172
[5,3,3,2,2,1,1]                   => 171
[5,3,3,2,1,1,1,1]                 => 170
[5,3,3,1,1,1,1,1,1]               => 169
[5,3,2,2,2,2,1]                   => 170
[5,3,2,2,2,1,1,1]                 => 169
[5,3,2,2,1,1,1,1,1]               => 168
[5,3,2,1,1,1,1,1,1,1]             => 167
[5,3,1,1,1,1,1,1,1,1,1]           => 166
[5,2,2,2,2,2,2]                   => 169
[5,2,2,2,2,2,1,1]                 => 168
[5,2,2,2,2,1,1,1,1]               => 167
[5,2,2,2,1,1,1,1,1,1]             => 166
[5,2,2,1,1,1,1,1,1,1,1]           => 165
[5,2,1,1,1,1,1,1,1,1,1,1]         => 164
[5,1,1,1,1,1,1,1,1,1,1,1,1]       => 163
[4,4,4,4,1]                       => 177
[4,4,4,3,2]                       => 175
[4,4,4,3,1,1]                     => 174
[4,4,4,2,2,1]                     => 173
[4,4,4,2,1,1,1]                   => 172
[4,4,4,1,1,1,1,1]                 => 171
[4,4,3,3,3]                       => 174
[4,4,3,3,2,1]                     => 172
[4,4,3,3,1,1,1]                   => 171
[4,4,3,2,2,2]                     => 171
[4,4,3,2,2,1,1]                   => 170
[4,4,3,2,1,1,1,1]                 => 169
[4,4,3,1,1,1,1,1,1]               => 168
[4,4,2,2,2,2,1]                   => 169
[4,4,2,2,2,1,1,1]                 => 168
[4,4,2,2,1,1,1,1,1]               => 167
[4,4,2,1,1,1,1,1,1,1]             => 166
[4,4,1,1,1,1,1,1,1,1,1]           => 165
[4,3,3,3,3,1]                     => 171
[4,3,3,3,2,2]                     => 170
[4,3,3,3,2,1,1]                   => 169
[4,3,3,3,1,1,1,1]                 => 168
[4,3,3,2,2,2,1]                   => 168
[4,3,3,2,2,1,1,1]                 => 167
[4,3,3,2,1,1,1,1,1]               => 166
[4,3,3,1,1,1,1,1,1,1]             => 165
[4,3,2,2,2,2,2]                   => 167
[4,3,2,2,2,2,1,1]                 => 166
[4,3,2,2,2,1,1,1,1]               => 165
[4,3,2,2,1,1,1,1,1,1]             => 164
[4,3,2,1,1,1,1,1,1,1,1]           => 163
[4,3,1,1,1,1,1,1,1,1,1,1]         => 162
[4,2,2,2,2,2,2,1]                 => 165
[4,2,2,2,2,2,1,1,1]               => 164
[4,2,2,2,2,1,1,1,1,1]             => 163
[4,2,2,2,1,1,1,1,1,1,1]           => 162
[4,2,2,1,1,1,1,1,1,1,1,1]         => 161
[4,2,1,1,1,1,1,1,1,1,1,1,1]       => 160
[4,1,1,1,1,1,1,1,1,1,1,1,1,1]     => 159
[3,3,3,3,3,2]                     => 169
[3,3,3,3,3,1,1]                   => 168
[3,3,3,3,2,2,1]                   => 167
[3,3,3,3,2,1,1,1]                 => 166
[3,3,3,3,1,1,1,1,1]               => 165
[3,3,3,2,2,2,2]                   => 166
[3,3,3,2,2,2,1,1]                 => 165
[3,3,3,2,2,1,1,1,1]               => 164
[3,3,3,2,1,1,1,1,1,1]             => 163
[3,3,3,1,1,1,1,1,1,1,1]           => 162
[3,3,2,2,2,2,2,1]                 => 164
[3,3,2,2,2,2,1,1,1]               => 163
[3,3,2,2,2,1,1,1,1,1]             => 162
[3,3,2,2,1,1,1,1,1,1,1]           => 161
[3,3,2,1,1,1,1,1,1,1,1,1]         => 160
[3,3,1,1,1,1,1,1,1,1,1,1,1]       => 159
[3,2,2,2,2,2,2,2]                 => 163
[3,2,2,2,2,2,2,1,1]               => 162
[3,2,2,2,2,2,1,1,1,1]             => 161
[3,2,2,2,2,1,1,1,1,1,1]           => 160
[3,2,2,2,1,1,1,1,1,1,1,1]         => 159
[3,2,2,1,1,1,1,1,1,1,1,1,1]       => 158

-----------------------------------------------------------------------------
Created: Sep 26, 2018 at 05:12 by Martin Rubey

-----------------------------------------------------------------------------
Last Updated: May 12, 2020 at 15:38 by Martin Rubey