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* Copyright (C) 2019 The FindStatCrew <info@findstat.org> *
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* This information is distributed in the hope that it will be useful, *
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-----------------------------------------------------------------------------
Statistic identifier: St001178
-----------------------------------------------------------------------------
Collection: Integer partitions
-----------------------------------------------------------------------------
Description: Twelve times the variance of the major index among all standard Young tableaux of a partition.
For a partition $\lambda$ of $n$, this variance is given in [1, Proposition 3.2] by
$$\frac{1}{12}\Big(\sum_{k = 1}^n i^2 - \sum_{i,j \in \lambda} h_{ij}^2\Big),$$
where the second sum ranges over all cells in $\lambda$ and $h_{ij}$ is the hook length of the cell $(i,j) \in \lambda$.
-----------------------------------------------------------------------------
References: [1] , Adin, R. M., Roichman, Y. Descent functions and random Young tableaux [[MathSciNet:1841639]] [[arXiv:math/9910165]]
-----------------------------------------------------------------------------
Code:
def statistic(L):
n = sum(L)
return sum(i^2 for i in [1 .. n] - sum(i^2 for h in L.hook_lengths() for i in h)
-----------------------------------------------------------------------------
Statistic values:
[1] => 0
[2] => 0
[1,1] => 0
[3] => 0
[2,1] => 3
[1,1,1] => 0
[4] => 0
[3,1] => 8
[2,2] => 12
[2,1,1] => 8
[1,1,1,1] => 0
[5] => 0
[4,1] => 15
[3,2] => 24
[3,1,1] => 20
[2,2,1] => 24
[2,1,1,1] => 15
[1,1,1,1,1] => 0
[6] => 0
[5,1] => 24
[4,2] => 40
[4,1,1] => 36
[3,3] => 48
[3,2,1] => 45
[3,1,1,1] => 36
[2,2,2] => 48
[2,2,1,1] => 40
[2,1,1,1,1] => 24
[1,1,1,1,1,1] => 0
[7] => 0
[6,1] => 35
[5,2] => 60
[5,1,1] => 56
[4,3] => 75
[4,2,1] => 72
[4,1,1,1] => 63
[3,3,1] => 80
[3,2,2] => 80
[3,2,1,1] => 72
[3,1,1,1,1] => 56
[2,2,2,1] => 75
[2,2,1,1,1] => 60
[2,1,1,1,1,1] => 35
[1,1,1,1,1,1,1] => 0
[8] => 0
[7,1] => 48
[6,2] => 84
[6,1,1] => 80
[5,3] => 108
[5,2,1] => 105
[5,1,1,1] => 96
[4,4] => 120
[4,3,1] => 120
[4,2,2] => 120
[4,2,1,1] => 112
[4,1,1,1,1] => 96
[3,3,2] => 128
[3,3,1,1] => 120
[3,2,2,1] => 120
[3,2,1,1,1] => 105
[3,1,1,1,1,1] => 80
[2,2,2,2] => 120
[2,2,2,1,1] => 108
[2,2,1,1,1,1] => 84
[2,1,1,1,1,1,1] => 48
[1,1,1,1,1,1,1,1] => 0
[9] => 0
[8,1] => 63
[7,2] => 112
[7,1,1] => 108
[6,3] => 147
[6,2,1] => 144
[6,1,1,1] => 135
[5,4] => 168
[5,3,1] => 168
[5,2,2] => 168
[5,2,1,1] => 160
[5,1,1,1,1] => 144
[4,4,1] => 180
[4,3,2] => 183
[4,3,1,1] => 175
[4,2,2,1] => 175
[4,2,1,1,1] => 160
[4,1,1,1,1,1] => 135
[3,3,3] => 192
[3,3,2,1] => 183
[3,3,1,1,1] => 168
[3,2,2,2] => 180
[3,2,2,1,1] => 168
[3,2,1,1,1,1] => 144
[3,1,1,1,1,1,1] => 108
[2,2,2,2,1] => 168
[2,2,2,1,1,1] => 147
[2,2,1,1,1,1,1] => 112
[2,1,1,1,1,1,1,1] => 63
[1,1,1,1,1,1,1,1,1] => 0
[10] => 0
[9,1] => 80
[8,2] => 144
[8,1,1] => 140
[7,3] => 192
[7,2,1] => 189
[7,1,1,1] => 180
[6,4] => 224
[6,3,1] => 224
[6,2,2] => 224
[6,2,1,1] => 216
[6,1,1,1,1] => 200
[5,5] => 240
[5,4,1] => 245
[5,3,2] => 248
[5,3,1,1] => 240
[5,2,2,1] => 240
[5,2,1,1,1] => 225
[5,1,1,1,1,1] => 200
[4,4,2] => 260
[4,4,1,1] => 252
[4,3,3] => 264
[4,3,2,1] => 255
[4,3,1,1,1] => 240
[4,2,2,2] => 252
[4,2,2,1,1] => 240
[4,2,1,1,1,1] => 216
[4,1,1,1,1,1,1] => 180
[3,3,3,1] => 264
[3,3,2,2] => 260
[3,3,2,1,1] => 248
[3,3,1,1,1,1] => 224
[3,2,2,2,1] => 245
[3,2,2,1,1,1] => 224
[3,2,1,1,1,1,1] => 189
[3,1,1,1,1,1,1,1] => 140
[2,2,2,2,2] => 240
[2,2,2,2,1,1] => 224
[2,2,2,1,1,1,1] => 192
[2,2,1,1,1,1,1,1] => 144
[2,1,1,1,1,1,1,1,1] => 80
[1,1,1,1,1,1,1,1,1,1] => 0
[11] => 0
[10,1] => 99
[9,2] => 180
[9,1,1] => 176
[8,3] => 243
[8,2,1] => 240
[8,1,1,1] => 231
[7,4] => 288
[7,3,1] => 288
[7,2,2] => 288
[7,2,1,1] => 280
[7,1,1,1,1] => 264
[6,5] => 315
[6,4,1] => 320
[6,3,2] => 323
[6,3,1,1] => 315
[6,2,2,1] => 315
[6,2,1,1,1] => 300
[6,1,1,1,1,1] => 275
[5,5,1] => 336
[5,4,2] => 344
[5,4,1,1] => 336
[5,3,3] => 348
[5,3,2,1] => 339
[5,3,1,1,1] => 324
[5,2,2,2] => 336
[5,2,2,1,1] => 324
[5,2,1,1,1,1] => 300
[5,1,1,1,1,1,1] => 264
[4,4,3] => 360
[4,4,2,1] => 351
[4,4,1,1,1] => 336
[4,3,3,1] => 355
[4,3,2,2] => 351
[4,3,2,1,1] => 339
[4,3,1,1,1,1] => 315
[4,2,2,2,1] => 336
[4,2,2,1,1,1] => 315
[4,2,1,1,1,1,1] => 280
[4,1,1,1,1,1,1,1] => 231
[3,3,3,2] => 360
[3,3,3,1,1] => 348
[3,3,2,2,1] => 344
[3,3,2,1,1,1] => 323
[3,3,1,1,1,1,1] => 288
[3,2,2,2,2] => 336
[3,2,2,2,1,1] => 320
[3,2,2,1,1,1,1] => 288
[3,2,1,1,1,1,1,1] => 240
[3,1,1,1,1,1,1,1,1] => 176
[2,2,2,2,2,1] => 315
[2,2,2,2,1,1,1] => 288
[2,2,2,1,1,1,1,1] => 243
[2,2,1,1,1,1,1,1,1] => 180
[2,1,1,1,1,1,1,1,1,1] => 99
[1,1,1,1,1,1,1,1,1,1,1] => 0
[12] => 0
[11,1] => 120
[10,2] => 220
[10,1,1] => 216
[9,3] => 300
[9,2,1] => 297
[9,1,1,1] => 288
[8,4] => 360
[8,3,1] => 360
[8,2,2] => 360
[8,2,1,1] => 352
[8,1,1,1,1] => 336
[7,5] => 400
[7,4,1] => 405
[7,3,2] => 408
[7,3,1,1] => 400
[7,2,2,1] => 400
[7,2,1,1,1] => 385
[7,1,1,1,1,1] => 360
[6,6] => 420
[6,5,1] => 432
[6,4,2] => 440
[6,4,1,1] => 432
[6,3,3] => 444
[6,3,2,1] => 435
[6,3,1,1,1] => 420
[6,2,2,2] => 432
[6,2,2,1,1] => 420
[6,2,1,1,1,1] => 396
[6,1,1,1,1,1,1] => 360
[5,5,2] => 456
[5,5,1,1] => 448
[5,4,3] => 465
[5,4,2,1] => 456
[5,4,1,1,1] => 441
[5,3,3,1] => 460
[5,3,2,2] => 456
[5,3,2,1,1] => 444
[5,3,1,1,1,1] => 420
[5,2,2,2,1] => 441
[5,2,2,1,1,1] => 420
[5,2,1,1,1,1,1] => 385
[5,1,1,1,1,1,1,1] => 336
[4,4,4] => 480
[4,4,3,1] => 472
[4,4,2,2] => 468
[4,4,2,1,1] => 456
[4,4,1,1,1,1] => 432
[4,3,3,2] => 472
[4,3,3,1,1] => 460
[4,3,2,2,1] => 456
[4,3,2,1,1,1] => 435
[4,3,1,1,1,1,1] => 400
[4,2,2,2,2] => 448
[4,2,2,2,1,1] => 432
[4,2,2,1,1,1,1] => 400
[4,2,1,1,1,1,1,1] => 352
[4,1,1,1,1,1,1,1,1] => 288
[3,3,3,3] => 480
[3,3,3,2,1] => 465
[3,3,3,1,1,1] => 444
[3,3,2,2,2] => 456
[3,3,2,2,1,1] => 440
[3,3,2,1,1,1,1] => 408
[3,3,1,1,1,1,1,1] => 360
[3,2,2,2,2,1] => 432
[3,2,2,2,1,1,1] => 405
[3,2,2,1,1,1,1,1] => 360
[3,2,1,1,1,1,1,1,1] => 297
[3,1,1,1,1,1,1,1,1,1] => 216
[2,2,2,2,2,2] => 420
[2,2,2,2,2,1,1] => 400
[2,2,2,2,1,1,1,1] => 360
[2,2,2,1,1,1,1,1,1] => 300
[2,2,1,1,1,1,1,1,1,1] => 220
[2,1,1,1,1,1,1,1,1,1,1] => 120
[1,1,1,1,1,1,1,1,1,1,1,1] => 0
[13] => 0
[12,1] => 143
[11,2] => 264
[11,1,1] => 260
[10,3] => 363
[10,2,1] => 360
[10,1,1,1] => 351
[9,4] => 440
[9,3,1] => 440
[9,2,2] => 440
[9,2,1,1] => 432
[9,1,1,1,1] => 416
[8,5] => 495
[8,4,1] => 500
[8,3,2] => 503
[8,3,1,1] => 495
[8,2,2,1] => 495
[8,2,1,1,1] => 480
[8,1,1,1,1,1] => 455
[7,6] => 528
[7,5,1] => 540
[7,4,2] => 548
[7,4,1,1] => 540
[7,3,3] => 552
[7,3,2,1] => 543
[7,3,1,1,1] => 528
[7,2,2,2] => 540
[7,2,2,1,1] => 528
[7,2,1,1,1,1] => 504
[7,1,1,1,1,1,1] => 468
[6,6,1] => 560
[6,5,2] => 575
[6,5,1,1] => 567
[6,4,3] => 584
[6,4,2,1] => 575
[6,4,1,1,1] => 560
[6,3,3,1] => 579
[6,3,2,2] => 575
[6,3,2,1,1] => 563
[6,3,1,1,1,1] => 539
[6,2,2,2,1] => 560
[6,2,2,1,1,1] => 539
[6,2,1,1,1,1,1] => 504
[6,1,1,1,1,1,1,1] => 455
[5,5,3] => 600
[5,5,2,1] => 591
[5,5,1,1,1] => 576
[5,4,4] => 608
[5,4,3,1] => 600
[5,4,2,2] => 596
[5,4,2,1,1] => 584
[5,4,1,1,1,1] => 560
[5,3,3,2] => 600
[5,3,3,1,1] => 588
[5,3,2,2,1] => 584
[5,3,2,1,1,1] => 563
[5,3,1,1,1,1,1] => 528
[5,2,2,2,2] => 576
[5,2,2,2,1,1] => 560
[5,2,2,1,1,1,1] => 528
[5,2,1,1,1,1,1,1] => 480
[5,1,1,1,1,1,1,1,1] => 416
[4,4,4,1] => 615
[4,4,3,2] => 612
[4,4,3,1,1] => 600
[4,4,2,2,1] => 596
[4,4,2,1,1,1] => 575
[4,4,1,1,1,1,1] => 540
[4,3,3,3] => 615
[4,3,3,2,1] => 600
[4,3,3,1,1,1] => 579
[4,3,2,2,2] => 591
[4,3,2,2,1,1] => 575
[4,3,2,1,1,1,1] => 543
[4,3,1,1,1,1,1,1] => 495
[4,2,2,2,2,1] => 567
[4,2,2,2,1,1,1] => 540
[4,2,2,1,1,1,1,1] => 495
[4,2,1,1,1,1,1,1,1] => 432
[4,1,1,1,1,1,1,1,1,1] => 351
[3,3,3,3,1] => 608
[3,3,3,2,2] => 600
[3,3,3,2,1,1] => 584
[3,3,3,1,1,1,1] => 552
[3,3,2,2,2,1] => 575
[3,3,2,2,1,1,1] => 548
[3,3,2,1,1,1,1,1] => 503
[3,3,1,1,1,1,1,1,1] => 440
[3,2,2,2,2,2] => 560
[3,2,2,2,2,1,1] => 540
[3,2,2,2,1,1,1,1] => 500
[3,2,2,1,1,1,1,1,1] => 440
[3,2,1,1,1,1,1,1,1,1] => 360
[3,1,1,1,1,1,1,1,1,1,1] => 260
[2,2,2,2,2,2,1] => 528
[2,2,2,2,2,1,1,1] => 495
[2,2,2,2,1,1,1,1,1] => 440
[2,2,2,1,1,1,1,1,1,1] => 363
[2,2,1,1,1,1,1,1,1,1,1] => 264
[2,1,1,1,1,1,1,1,1,1,1,1] => 143
[1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[14] => 0
[13,1] => 168
[12,2] => 312
[12,1,1] => 308
[11,3] => 432
[11,2,1] => 429
[11,1,1,1] => 420
[10,4] => 528
[10,3,1] => 528
[10,2,2] => 528
[10,2,1,1] => 520
[10,1,1,1,1] => 504
[9,5] => 600
[9,4,1] => 605
[9,3,2] => 608
[9,3,1,1] => 600
[9,2,2,1] => 600
[9,2,1,1,1] => 585
[9,1,1,1,1,1] => 560
[8,6] => 648
[8,5,1] => 660
[8,4,2] => 668
[8,4,1,1] => 660
[8,3,3] => 672
[8,3,2,1] => 663
[8,3,1,1,1] => 648
[8,2,2,2] => 660
[8,2,2,1,1] => 648
[8,2,1,1,1,1] => 624
[8,1,1,1,1,1,1] => 588
[7,7] => 672
[7,6,1] => 693
[7,5,2] => 708
[7,5,1,1] => 700
[7,4,3] => 717
[7,4,2,1] => 708
[7,4,1,1,1] => 693
[7,3,3,1] => 712
[7,3,2,2] => 708
[7,3,2,1,1] => 696
[7,3,1,1,1,1] => 672
[7,2,2,2,1] => 693
[7,2,2,1,1,1] => 672
[7,2,1,1,1,1,1] => 637
[7,1,1,1,1,1,1,1] => 588
[6,6,2] => 728
[6,6,1,1] => 720
[6,5,3] => 744
[6,5,2,1] => 735
[6,5,1,1,1] => 720
[6,4,4] => 752
[6,4,3,1] => 744
[6,4,2,2] => 740
[6,4,2,1,1] => 728
[6,4,1,1,1,1] => 704
[6,3,3,2] => 744
[6,3,3,1,1] => 732
[6,3,2,2,1] => 728
[6,3,2,1,1,1] => 707
[6,3,1,1,1,1,1] => 672
[6,2,2,2,2] => 720
[6,2,2,2,1,1] => 704
[6,2,2,1,1,1,1] => 672
[6,2,1,1,1,1,1,1] => 624
[6,1,1,1,1,1,1,1,1] => 560
[5,5,4] => 768
[5,5,3,1] => 760
[5,5,2,2] => 756
[5,5,2,1,1] => 744
[5,5,1,1,1,1] => 720
[5,4,4,1] => 768
[5,4,3,2] => 765
[5,4,3,1,1] => 753
[5,4,2,2,1] => 749
[5,4,2,1,1,1] => 728
[5,4,1,1,1,1,1] => 693
[5,3,3,3] => 768
[5,3,3,2,1] => 753
[5,3,3,1,1,1] => 732
[5,3,2,2,2] => 744
[5,3,2,2,1,1] => 728
[5,3,2,1,1,1,1] => 696
[5,3,1,1,1,1,1,1] => 648
[5,2,2,2,2,1] => 720
[5,2,2,2,1,1,1] => 693
[5,2,2,1,1,1,1,1] => 648
[5,2,1,1,1,1,1,1,1] => 585
[5,1,1,1,1,1,1,1,1,1] => 504
[4,4,4,2] => 780
[4,4,4,1,1] => 768
[4,4,3,3] => 780
[4,4,3,2,1] => 765
[4,4,3,1,1,1] => 744
[4,4,2,2,2] => 756
[4,4,2,2,1,1] => 740
[4,4,2,1,1,1,1] => 708
[4,4,1,1,1,1,1,1] => 660
[4,3,3,3,1] => 768
[4,3,3,2,2] => 760
[4,3,3,2,1,1] => 744
[4,3,3,1,1,1,1] => 712
[4,3,2,2,2,1] => 735
[4,3,2,2,1,1,1] => 708
[4,3,2,1,1,1,1,1] => 663
[4,3,1,1,1,1,1,1,1] => 600
[4,2,2,2,2,2] => 720
[4,2,2,2,2,1,1] => 700
[4,2,2,2,1,1,1,1] => 660
[4,2,2,1,1,1,1,1,1] => 600
[4,2,1,1,1,1,1,1,1,1] => 520
[4,1,1,1,1,1,1,1,1,1,1] => 420
[3,3,3,3,2] => 768
[3,3,3,3,1,1] => 752
[3,3,3,2,2,1] => 744
[3,3,3,2,1,1,1] => 717
[3,3,3,1,1,1,1,1] => 672
[3,3,2,2,2,2] => 728
[3,3,2,2,2,1,1] => 708
[3,3,2,2,1,1,1,1] => 668
[3,3,2,1,1,1,1,1,1] => 608
[3,3,1,1,1,1,1,1,1,1] => 528
[3,2,2,2,2,2,1] => 693
[3,2,2,2,2,1,1,1] => 660
[3,2,2,2,1,1,1,1,1] => 605
[3,2,2,1,1,1,1,1,1,1] => 528
[3,2,1,1,1,1,1,1,1,1,1] => 429
[3,1,1,1,1,1,1,1,1,1,1,1] => 308
[2,2,2,2,2,2,2] => 672
[2,2,2,2,2,2,1,1] => 648
[2,2,2,2,2,1,1,1,1] => 600
[2,2,2,2,1,1,1,1,1,1] => 528
[2,2,2,1,1,1,1,1,1,1,1] => 432
[2,2,1,1,1,1,1,1,1,1,1,1] => 312
[2,1,1,1,1,1,1,1,1,1,1,1,1] => 168
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[15] => 0
[14,1] => 195
[13,2] => 364
[13,1,1] => 360
[12,3] => 507
[12,2,1] => 504
[12,1,1,1] => 495
[11,4] => 624
[11,3,1] => 624
[11,2,2] => 624
[11,2,1,1] => 616
[11,1,1,1,1] => 600
[10,5] => 715
[10,4,1] => 720
[10,3,2] => 723
[10,3,1,1] => 715
[10,2,2,1] => 715
[10,2,1,1,1] => 700
[10,1,1,1,1,1] => 675
[9,6] => 780
[9,5,1] => 792
[9,4,2] => 800
[9,4,1,1] => 792
[9,3,3] => 804
[9,3,2,1] => 795
[9,3,1,1,1] => 780
[9,2,2,2] => 792
[9,2,2,1,1] => 780
[9,2,1,1,1,1] => 756
[9,1,1,1,1,1,1] => 720
[8,7] => 819
[8,6,1] => 840
[8,5,2] => 855
[8,5,1,1] => 847
[8,4,3] => 864
[8,4,2,1] => 855
[8,4,1,1,1] => 840
[8,3,3,1] => 859
[8,3,2,2] => 855
[8,3,2,1,1] => 843
[8,3,1,1,1,1] => 819
[8,2,2,2,1] => 840
[8,2,2,1,1,1] => 819
[8,2,1,1,1,1,1] => 784
[8,1,1,1,1,1,1,1] => 735
[7,7,1] => 864
[7,6,2] => 888
[7,6,1,1] => 880
[7,5,3] => 904
[7,5,2,1] => 895
[7,5,1,1,1] => 880
[7,4,4] => 912
[7,4,3,1] => 904
[7,4,2,2] => 900
[7,4,2,1,1] => 888
[7,4,1,1,1,1] => 864
[7,3,3,2] => 904
[7,3,3,1,1] => 892
[7,3,2,2,1] => 888
[7,3,2,1,1,1] => 867
[7,3,1,1,1,1,1] => 832
[7,2,2,2,2] => 880
[7,2,2,2,1,1] => 864
[7,2,2,1,1,1,1] => 832
[7,2,1,1,1,1,1,1] => 784
[7,1,1,1,1,1,1,1,1] => 720
[6,6,3] => 924
[6,6,2,1] => 915
[6,6,1,1,1] => 900
[6,5,4] => 939
[6,5,3,1] => 931
[6,5,2,2] => 927
[6,5,2,1,1] => 915
[6,5,1,1,1,1] => 891
[6,4,4,1] => 939
[6,4,3,2] => 936
[6,4,3,1,1] => 924
[6,4,2,2,1] => 920
[6,4,2,1,1,1] => 899
[6,4,1,1,1,1,1] => 864
[6,3,3,3] => 939
[6,3,3,2,1] => 924
[6,3,3,1,1,1] => 903
[6,3,2,2,2] => 915
[6,3,2,2,1,1] => 899
[6,3,2,1,1,1,1] => 867
[6,3,1,1,1,1,1,1] => 819
[6,2,2,2,2,1] => 891
[6,2,2,2,1,1,1] => 864
[6,2,2,1,1,1,1,1] => 819
[6,2,1,1,1,1,1,1,1] => 756
[6,1,1,1,1,1,1,1,1,1] => 675
[5,5,5] => 960
[5,5,4,1] => 955
[5,5,3,2] => 952
[5,5,3,1,1] => 940
[5,5,2,2,1] => 936
[5,5,2,1,1,1] => 915
[5,5,1,1,1,1,1] => 880
[5,4,4,2] => 960
[5,4,4,1,1] => 948
[5,4,3,3] => 960
[5,4,3,2,1] => 945
[5,4,3,1,1,1] => 924
[5,4,2,2,2] => 936
[5,4,2,2,1,1] => 920
[5,4,2,1,1,1,1] => 888
[5,4,1,1,1,1,1,1] => 840
[5,3,3,3,1] => 948
[5,3,3,2,2] => 940
[5,3,3,2,1,1] => 924
[5,3,3,1,1,1,1] => 892
[5,3,2,2,2,1] => 915
[5,3,2,2,1,1,1] => 888
[5,3,2,1,1,1,1,1] => 843
[5,3,1,1,1,1,1,1,1] => 780
[5,2,2,2,2,2] => 900
[5,2,2,2,2,1,1] => 880
[5,2,2,2,1,1,1,1] => 840
[5,2,2,1,1,1,1,1,1] => 780
[5,2,1,1,1,1,1,1,1,1] => 700
[5,1,1,1,1,1,1,1,1,1,1] => 600
[4,4,4,3] => 975
[4,4,4,2,1] => 960
[4,4,4,1,1,1] => 939
[4,4,3,3,1] => 960
[4,4,3,2,2] => 952
[4,4,3,2,1,1] => 936
[4,4,3,1,1,1,1] => 904
[4,4,2,2,2,1] => 927
[4,4,2,2,1,1,1] => 900
[4,4,2,1,1,1,1,1] => 855
[4,4,1,1,1,1,1,1,1] => 792
[4,3,3,3,2] => 955
[4,3,3,3,1,1] => 939
[4,3,3,2,2,1] => 931
[4,3,3,2,1,1,1] => 904
[4,3,3,1,1,1,1,1] => 859
[4,3,2,2,2,2] => 915
[4,3,2,2,2,1,1] => 895
[4,3,2,2,1,1,1,1] => 855
[4,3,2,1,1,1,1,1,1] => 795
[4,3,1,1,1,1,1,1,1,1] => 715
[4,2,2,2,2,2,1] => 880
[4,2,2,2,2,1,1,1] => 847
[4,2,2,2,1,1,1,1,1] => 792
[4,2,2,1,1,1,1,1,1,1] => 715
[4,2,1,1,1,1,1,1,1,1,1] => 616
[4,1,1,1,1,1,1,1,1,1,1,1] => 495
[3,3,3,3,3] => 960
[3,3,3,3,2,1] => 939
[3,3,3,3,1,1,1] => 912
[3,3,3,2,2,2] => 924
[3,3,3,2,2,1,1] => 904
[3,3,3,2,1,1,1,1] => 864
[3,3,3,1,1,1,1,1,1] => 804
[3,3,2,2,2,2,1] => 888
[3,3,2,2,2,1,1,1] => 855
[3,3,2,2,1,1,1,1,1] => 800
[3,3,2,1,1,1,1,1,1,1] => 723
[3,3,1,1,1,1,1,1,1,1,1] => 624
[3,2,2,2,2,2,2] => 864
[3,2,2,2,2,2,1,1] => 840
[3,2,2,2,2,1,1,1,1] => 792
[3,2,2,2,1,1,1,1,1,1] => 720
[3,2,2,1,1,1,1,1,1,1,1] => 624
[3,2,1,1,1,1,1,1,1,1,1,1] => 504
[3,1,1,1,1,1,1,1,1,1,1,1,1] => 360
[2,2,2,2,2,2,2,1] => 819
[2,2,2,2,2,2,1,1,1] => 780
[2,2,2,2,2,1,1,1,1,1] => 715
[2,2,2,2,1,1,1,1,1,1,1] => 624
[2,2,2,1,1,1,1,1,1,1,1,1] => 507
[2,2,1,1,1,1,1,1,1,1,1,1,1] => 364
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] => 195
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[16] => 0
[15,1] => 224
[14,2] => 420
[14,1,1] => 416
[13,3] => 588
[13,2,1] => 585
[13,1,1,1] => 576
[12,4] => 728
[12,3,1] => 728
[12,2,2] => 728
[12,2,1,1] => 720
[12,1,1,1,1] => 704
[11,5] => 840
[11,4,1] => 845
[11,3,2] => 848
[11,3,1,1] => 840
[11,2,2,1] => 840
[11,2,1,1,1] => 825
[11,1,1,1,1,1] => 800
[10,6] => 924
[10,5,1] => 936
[10,4,2] => 944
[10,4,1,1] => 936
[10,3,3] => 948
[10,3,2,1] => 939
[10,3,1,1,1] => 924
[10,2,2,2] => 936
[10,2,2,1,1] => 924
[10,2,1,1,1,1] => 900
[10,1,1,1,1,1,1] => 864
[9,7] => 980
[9,6,1] => 1001
[9,5,2] => 1016
[9,5,1,1] => 1008
[9,4,3] => 1025
[9,4,2,1] => 1016
[9,4,1,1,1] => 1001
[9,3,3,1] => 1020
[9,3,2,2] => 1016
[9,3,2,1,1] => 1004
[9,3,1,1,1,1] => 980
[9,2,2,2,1] => 1001
[9,2,2,1,1,1] => 980
[9,2,1,1,1,1,1] => 945
[9,1,1,1,1,1,1,1] => 896
[8,8] => 1008
[8,7,1] => 1040
[8,6,2] => 1064
[8,6,1,1] => 1056
[8,5,3] => 1080
[8,5,2,1] => 1071
[8,5,1,1,1] => 1056
[8,4,4] => 1088
[8,4,3,1] => 1080
[8,4,2,2] => 1076
[8,4,2,1,1] => 1064
[8,4,1,1,1,1] => 1040
[8,3,3,2] => 1080
[8,3,3,1,1] => 1068
[8,3,2,2,1] => 1064
[8,3,2,1,1,1] => 1043
[8,3,1,1,1,1,1] => 1008
[8,2,2,2,2] => 1056
[8,2,2,2,1,1] => 1040
[8,2,2,1,1,1,1] => 1008
[8,2,1,1,1,1,1,1] => 960
[8,1,1,1,1,1,1,1,1] => 896
[7,7,2] => 1088
[7,7,1,1] => 1080
[7,6,3] => 1113
[7,6,2,1] => 1104
[7,6,1,1,1] => 1089
[7,5,4] => 1128
[7,5,3,1] => 1120
[7,5,2,2] => 1116
[7,5,2,1,1] => 1104
[7,5,1,1,1,1] => 1080
[7,4,4,1] => 1128
[7,4,3,2] => 1125
[7,4,3,1,1] => 1113
[7,4,2,2,1] => 1109
[7,4,2,1,1,1] => 1088
[7,4,1,1,1,1,1] => 1053
[7,3,3,3] => 1128
[7,3,3,2,1] => 1113
[7,3,3,1,1,1] => 1092
[7,3,2,2,2] => 1104
[7,3,2,2,1,1] => 1088
[7,3,2,1,1,1,1] => 1056
[7,3,1,1,1,1,1,1] => 1008
[7,2,2,2,2,1] => 1080
[7,2,2,2,1,1,1] => 1053
[7,2,2,1,1,1,1,1] => 1008
[7,2,1,1,1,1,1,1,1] => 945
[7,1,1,1,1,1,1,1,1,1] => 864
[6,6,4] => 1148
[6,6,3,1] => 1140
[6,6,2,2] => 1136
[6,6,2,1,1] => 1124
[6,6,1,1,1,1] => 1100
[6,5,5] => 1160
[6,5,4,1] => 1155
[6,5,3,2] => 1152
[6,5,3,1,1] => 1140
[6,5,2,2,1] => 1136
[6,5,2,1,1,1] => 1115
[6,5,1,1,1,1,1] => 1080
[6,4,4,2] => 1160
[6,4,4,1,1] => 1148
[6,4,3,3] => 1160
[6,4,3,2,1] => 1145
[6,4,3,1,1,1] => 1124
[6,4,2,2,2] => 1136
[6,4,2,2,1,1] => 1120
[6,4,2,1,1,1,1] => 1088
[6,4,1,1,1,1,1,1] => 1040
[6,3,3,3,1] => 1148
[6,3,3,2,2] => 1140
[6,3,3,2,1,1] => 1124
[6,3,3,1,1,1,1] => 1092
[6,3,2,2,2,1] => 1115
[6,3,2,2,1,1,1] => 1088
[6,3,2,1,1,1,1,1] => 1043
[6,3,1,1,1,1,1,1,1] => 980
[6,2,2,2,2,2] => 1100
[6,2,2,2,2,1,1] => 1080
[6,2,2,2,1,1,1,1] => 1040
[6,2,2,1,1,1,1,1,1] => 980
[6,2,1,1,1,1,1,1,1,1] => 900
[6,1,1,1,1,1,1,1,1,1,1] => 800
[5,5,5,1] => 1176
[5,5,4,2] => 1176
[5,5,4,1,1] => 1164
[5,5,3,3] => 1176
[5,5,3,2,1] => 1161
[5,5,3,1,1,1] => 1140
[5,5,2,2,2] => 1152
[5,5,2,2,1,1] => 1136
[5,5,2,1,1,1,1] => 1104
[5,5,1,1,1,1,1,1] => 1056
[5,4,4,3] => 1184
[5,4,4,2,1] => 1169
[5,4,4,1,1,1] => 1148
[5,4,3,3,1] => 1169
[5,4,3,2,2] => 1161
[5,4,3,2,1,1] => 1145
[5,4,3,1,1,1,1] => 1113
[5,4,2,2,2,1] => 1136
[5,4,2,2,1,1,1] => 1109
[5,4,2,1,1,1,1,1] => 1064
[5,4,1,1,1,1,1,1,1] => 1001
[5,3,3,3,2] => 1164
[5,3,3,3,1,1] => 1148
[5,3,3,2,2,1] => 1140
[5,3,3,2,1,1,1] => 1113
[5,3,3,1,1,1,1,1] => 1068
[5,3,2,2,2,2] => 1124
[5,3,2,2,2,1,1] => 1104
[5,3,2,2,1,1,1,1] => 1064
[5,3,2,1,1,1,1,1,1] => 1004
[5,3,1,1,1,1,1,1,1,1] => 924
[5,2,2,2,2,2,1] => 1089
[5,2,2,2,2,1,1,1] => 1056
[5,2,2,2,1,1,1,1,1] => 1001
[5,2,2,1,1,1,1,1,1,1] => 924
[5,2,1,1,1,1,1,1,1,1,1] => 825
[5,1,1,1,1,1,1,1,1,1,1,1] => 704
[4,4,4,4] => 1200
[4,4,4,3,1] => 1184
[4,4,4,2,2] => 1176
[4,4,4,2,1,1] => 1160
[4,4,4,1,1,1,1] => 1128
[4,4,3,3,2] => 1176
[4,4,3,3,1,1] => 1160
[4,4,3,2,2,1] => 1152
[4,4,3,2,1,1,1] => 1125
[4,4,3,1,1,1,1,1] => 1080
[4,4,2,2,2,2] => 1136
[4,4,2,2,2,1,1] => 1116
[4,4,2,2,1,1,1,1] => 1076
[4,4,2,1,1,1,1,1,1] => 1016
[4,4,1,1,1,1,1,1,1,1] => 936
[4,3,3,3,3] => 1176
[4,3,3,3,2,1] => 1155
[4,3,3,3,1,1,1] => 1128
[4,3,3,2,2,2] => 1140
[4,3,3,2,2,1,1] => 1120
[4,3,3,2,1,1,1,1] => 1080
[4,3,3,1,1,1,1,1,1] => 1020
[4,3,2,2,2,2,1] => 1104
[4,3,2,2,2,1,1,1] => 1071
[4,3,2,2,1,1,1,1,1] => 1016
[4,3,2,1,1,1,1,1,1,1] => 939
[4,3,1,1,1,1,1,1,1,1,1] => 840
[4,2,2,2,2,2,2] => 1080
[4,2,2,2,2,2,1,1] => 1056
[4,2,2,2,2,1,1,1,1] => 1008
[4,2,2,2,1,1,1,1,1,1] => 936
[4,2,2,1,1,1,1,1,1,1,1] => 840
[4,2,1,1,1,1,1,1,1,1,1,1] => 720
[4,1,1,1,1,1,1,1,1,1,1,1,1] => 576
[3,3,3,3,3,1] => 1160
[3,3,3,3,2,2] => 1148
[3,3,3,3,2,1,1] => 1128
[3,3,3,3,1,1,1,1] => 1088
[3,3,3,2,2,2,1] => 1113
[3,3,3,2,2,1,1,1] => 1080
[3,3,3,2,1,1,1,1,1] => 1025
[3,3,3,1,1,1,1,1,1,1] => 948
[3,3,2,2,2,2,2] => 1088
[3,3,2,2,2,2,1,1] => 1064
[3,3,2,2,2,1,1,1,1] => 1016
[3,3,2,2,1,1,1,1,1,1] => 944
[3,3,2,1,1,1,1,1,1,1,1] => 848
[3,3,1,1,1,1,1,1,1,1,1,1] => 728
[3,2,2,2,2,2,2,1] => 1040
[3,2,2,2,2,2,1,1,1] => 1001
[3,2,2,2,2,1,1,1,1,1] => 936
[3,2,2,2,1,1,1,1,1,1,1] => 845
[3,2,2,1,1,1,1,1,1,1,1,1] => 728
[3,2,1,1,1,1,1,1,1,1,1,1,1] => 585
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] => 416
[2,2,2,2,2,2,2,2] => 1008
[2,2,2,2,2,2,2,1,1] => 980
[2,2,2,2,2,2,1,1,1,1] => 924
[2,2,2,2,2,1,1,1,1,1,1] => 840
[2,2,2,2,1,1,1,1,1,1,1,1] => 728
[2,2,2,1,1,1,1,1,1,1,1,1,1] => 588
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] => 420
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 224
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] => 0
[17] => 0
[16,1] => 255
[15,2] => 480
[15,1,1] => 476
[14,3] => 675
[14,2,1] => 672
[14,1,1,1] => 663
[13,4] => 840
[13,3,1] => 840
[13,2,2] => 840
[13,2,1,1] => 832
[13,1,1,1,1] => 816
[12,5] => 975
[12,4,1] => 980
[12,3,2] => 983
[12,3,1,1] => 975
[12,2,2,1] => 975
[12,2,1,1,1] => 960
[12,1,1,1,1,1] => 935
[11,6] => 1080
[11,5,1] => 1092
[11,4,2] => 1100
[11,4,1,1] => 1092
[11,3,3] => 1104
[11,3,2,1] => 1095
[11,3,1,1,1] => 1080
[11,2,2,2] => 1092
[11,2,2,1,1] => 1080
[11,2,1,1,1,1] => 1056
[11,1,1,1,1,1,1] => 1020
[10,7] => 1155
[10,6,1] => 1176
[10,5,2] => 1191
[10,5,1,1] => 1183
[10,4,3] => 1200
[10,4,2,1] => 1191
[10,4,1,1,1] => 1176
[10,3,3,1] => 1195
[10,3,2,2] => 1191
[10,3,2,1,1] => 1179
[10,3,1,1,1,1] => 1155
[10,2,2,2,1] => 1176
[10,2,2,1,1,1] => 1155
[10,2,1,1,1,1,1] => 1120
[10,1,1,1,1,1,1,1] => 1071
[9,8] => 1200
[9,7,1] => 1232
[9,6,2] => 1256
[9,6,1,1] => 1248
[9,5,3] => 1272
[9,5,2,1] => 1263
[9,5,1,1,1] => 1248
[9,4,4] => 1280
[9,4,3,1] => 1272
[9,4,2,2] => 1268
[9,4,2,1,1] => 1256
[9,4,1,1,1,1] => 1232
[9,3,3,2] => 1272
[9,3,3,1,1] => 1260
[9,3,2,2,1] => 1256
[9,3,2,1,1,1] => 1235
[9,3,1,1,1,1,1] => 1200
[9,2,2,2,2] => 1248
[9,2,2,2,1,1] => 1232
[9,2,2,1,1,1,1] => 1200
[9,2,1,1,1,1,1,1] => 1152
[9,1,1,1,1,1,1,1,1] => 1088
[8,8,1] => 1260
[8,7,2] => 1295
[8,7,1,1] => 1287
[8,6,3] => 1320
[8,6,2,1] => 1311
[8,6,1,1,1] => 1296
[8,5,4] => 1335
[8,5,3,1] => 1327
[8,5,2,2] => 1323
[8,5,2,1,1] => 1311
[8,5,1,1,1,1] => 1287
[8,4,4,1] => 1335
[8,4,3,2] => 1332
[8,4,3,1,1] => 1320
[8,4,2,2,1] => 1316
[8,4,2,1,1,1] => 1295
[8,4,1,1,1,1,1] => 1260
[8,3,3,3] => 1335
[8,3,3,2,1] => 1320
[8,3,3,1,1,1] => 1299
[8,3,2,2,2] => 1311
[8,3,2,2,1,1] => 1295
[8,3,2,1,1,1,1] => 1263
[8,3,1,1,1,1,1,1] => 1215
[8,2,2,2,2,1] => 1287
[8,2,2,2,1,1,1] => 1260
[8,2,2,1,1,1,1,1] => 1215
[8,2,1,1,1,1,1,1,1] => 1152
[8,1,1,1,1,1,1,1,1,1] => 1071
[7,7,3] => 1344
[7,7,2,1] => 1335
[7,7,1,1,1] => 1320
[7,6,4] => 1368
[7,6,3,1] => 1360
[7,6,2,2] => 1356
[7,6,2,1,1] => 1344
[7,6,1,1,1,1] => 1320
[7,5,5] => 1380
[7,5,4,1] => 1375
[7,5,3,2] => 1372
[7,5,3,1,1] => 1360
[7,5,2,2,1] => 1356
[7,5,2,1,1,1] => 1335
[7,5,1,1,1,1,1] => 1300
[7,4,4,2] => 1380
[7,4,4,1,1] => 1368
[7,4,3,3] => 1380
[7,4,3,2,1] => 1365
[7,4,3,1,1,1] => 1344
[7,4,2,2,2] => 1356
[7,4,2,2,1,1] => 1340
[7,4,2,1,1,1,1] => 1308
[7,4,1,1,1,1,1,1] => 1260
[7,3,3,3,1] => 1368
[7,3,3,2,2] => 1360
[7,3,3,2,1,1] => 1344
[7,3,3,1,1,1,1] => 1312
[7,3,2,2,2,1] => 1335
[7,3,2,2,1,1,1] => 1308
[7,3,2,1,1,1,1,1] => 1263
[7,3,1,1,1,1,1,1,1] => 1200
[7,2,2,2,2,2] => 1320
[7,2,2,2,2,1,1] => 1300
[7,2,2,2,1,1,1,1] => 1260
[7,2,2,1,1,1,1,1,1] => 1200
[7,2,1,1,1,1,1,1,1,1] => 1120
[7,1,1,1,1,1,1,1,1,1,1] => 1020
[6,6,5] => 1400
[6,6,4,1] => 1395
[6,6,3,2] => 1392
[6,6,3,1,1] => 1380
[6,6,2,2,1] => 1376
[6,6,2,1,1,1] => 1355
[6,6,1,1,1,1,1] => 1320
[6,5,5,1] => 1407
[6,5,4,2] => 1407
[6,5,4,1,1] => 1395
[6,5,3,3] => 1407
[6,5,3,2,1] => 1392
[6,5,3,1,1,1] => 1371
[6,5,2,2,2] => 1383
[6,5,2,2,1,1] => 1367
[6,5,2,1,1,1,1] => 1335
[6,5,1,1,1,1,1,1] => 1287
[6,4,4,3] => 1415
[6,4,4,2,1] => 1400
[6,4,4,1,1,1] => 1379
[6,4,3,3,1] => 1400
[6,4,3,2,2] => 1392
[6,4,3,2,1,1] => 1376
[6,4,3,1,1,1,1] => 1344
[6,4,2,2,2,1] => 1367
[6,4,2,2,1,1,1] => 1340
[6,4,2,1,1,1,1,1] => 1295
[6,4,1,1,1,1,1,1,1] => 1232
[6,3,3,3,2] => 1395
[6,3,3,3,1,1] => 1379
[6,3,3,2,2,1] => 1371
[6,3,3,2,1,1,1] => 1344
[6,3,3,1,1,1,1,1] => 1299
[6,3,2,2,2,2] => 1355
[6,3,2,2,2,1,1] => 1335
[6,3,2,2,1,1,1,1] => 1295
[6,3,2,1,1,1,1,1,1] => 1235
[6,3,1,1,1,1,1,1,1,1] => 1155
[6,2,2,2,2,2,1] => 1320
[6,2,2,2,2,1,1,1] => 1287
[6,2,2,2,1,1,1,1,1] => 1232
[6,2,2,1,1,1,1,1,1,1] => 1155
[6,2,1,1,1,1,1,1,1,1,1] => 1056
[6,1,1,1,1,1,1,1,1,1,1,1] => 935
[5,5,5,2] => 1428
[5,5,5,1,1] => 1416
[5,5,4,3] => 1431
[5,5,4,2,1] => 1416
[5,5,4,1,1,1] => 1395
[5,5,3,3,1] => 1416
[5,5,3,2,2] => 1408
[5,5,3,2,1,1] => 1392
[5,5,3,1,1,1,1] => 1360
[5,5,2,2,2,1] => 1383
[5,5,2,2,1,1,1] => 1356
[5,5,2,1,1,1,1,1] => 1311
[5,5,1,1,1,1,1,1,1] => 1248
[5,4,4,4] => 1440
[5,4,4,3,1] => 1424
[5,4,4,2,2] => 1416
[5,4,4,2,1,1] => 1400
[5,4,4,1,1,1,1] => 1368
[5,4,3,3,2] => 1416
[5,4,3,3,1,1] => 1400
[5,4,3,2,2,1] => 1392
[5,4,3,2,1,1,1] => 1365
[5,4,3,1,1,1,1,1] => 1320
[5,4,2,2,2,2] => 1376
[5,4,2,2,2,1,1] => 1356
[5,4,2,2,1,1,1,1] => 1316
[5,4,2,1,1,1,1,1,1] => 1256
[5,4,1,1,1,1,1,1,1,1] => 1176
[5,3,3,3,3] => 1416
[5,3,3,3,2,1] => 1395
[5,3,3,3,1,1,1] => 1368
[5,3,3,2,2,2] => 1380
[5,3,3,2,2,1,1] => 1360
[5,3,3,2,1,1,1,1] => 1320
[5,3,3,1,1,1,1,1,1] => 1260
[5,3,2,2,2,2,1] => 1344
[5,3,2,2,2,1,1,1] => 1311
[5,3,2,2,1,1,1,1,1] => 1256
[5,3,2,1,1,1,1,1,1,1] => 1179
[5,3,1,1,1,1,1,1,1,1,1] => 1080
[5,2,2,2,2,2,2] => 1320
[5,2,2,2,2,2,1,1] => 1296
[5,2,2,2,2,1,1,1,1] => 1248
[5,2,2,2,1,1,1,1,1,1] => 1176
[5,2,2,1,1,1,1,1,1,1,1] => 1080
[5,2,1,1,1,1,1,1,1,1,1,1] => 960
[5,1,1,1,1,1,1,1,1,1,1,1,1] => 816
[4,4,4,4,1] => 1440
[4,4,4,3,2] => 1431
[4,4,4,3,1,1] => 1415
[4,4,4,2,2,1] => 1407
[4,4,4,2,1,1,1] => 1380
[4,4,4,1,1,1,1,1] => 1335
[4,4,3,3,3] => 1428
[4,4,3,3,2,1] => 1407
[4,4,3,3,1,1,1] => 1380
[4,4,3,2,2,2] => 1392
[4,4,3,2,2,1,1] => 1372
[4,4,3,2,1,1,1,1] => 1332
[4,4,3,1,1,1,1,1,1] => 1272
[4,4,2,2,2,2,1] => 1356
[4,4,2,2,2,1,1,1] => 1323
[4,4,2,2,1,1,1,1,1] => 1268
[4,4,2,1,1,1,1,1,1,1] => 1191
[4,4,1,1,1,1,1,1,1,1,1] => 1092
[4,3,3,3,3,1] => 1407
[4,3,3,3,2,2] => 1395
[4,3,3,3,2,1,1] => 1375
[4,3,3,3,1,1,1,1] => 1335
[4,3,3,2,2,2,1] => 1360
[4,3,3,2,2,1,1,1] => 1327
[4,3,3,2,1,1,1,1,1] => 1272
[4,3,3,1,1,1,1,1,1,1] => 1195
[4,3,2,2,2,2,2] => 1335
[4,3,2,2,2,2,1,1] => 1311
[4,3,2,2,2,1,1,1,1] => 1263
[4,3,2,2,1,1,1,1,1,1] => 1191
[4,3,2,1,1,1,1,1,1,1,1] => 1095
[4,3,1,1,1,1,1,1,1,1,1,1] => 975
[4,2,2,2,2,2,2,1] => 1287
[4,2,2,2,2,2,1,1,1] => 1248
[4,2,2,2,2,1,1,1,1,1] => 1183
[4,2,2,2,1,1,1,1,1,1,1] => 1092
[4,2,2,1,1,1,1,1,1,1,1,1] => 975
[4,2,1,1,1,1,1,1,1,1,1,1,1] => 832
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] => 663
[3,3,3,3,3,2] => 1400
[3,3,3,3,3,1,1] => 1380
[3,3,3,3,2,2,1] => 1368
[3,3,3,3,2,1,1,1] => 1335
[3,3,3,3,1,1,1,1,1] => 1280
[3,3,3,2,2,2,2] => 1344
[3,3,3,2,2,2,1,1] => 1320
[3,3,3,2,2,1,1,1,1] => 1272
[3,3,3,2,1,1,1,1,1,1] => 1200
[3,3,3,1,1,1,1,1,1,1,1] => 1104
[3,3,2,2,2,2,2,1] => 1295
[3,3,2,2,2,2,1,1,1] => 1256
[3,3,2,2,2,1,1,1,1,1] => 1191
[3,3,2,2,1,1,1,1,1,1,1] => 1100
[3,3,2,1,1,1,1,1,1,1,1,1] => 983
[3,3,1,1,1,1,1,1,1,1,1,1,1] => 840
[3,2,2,2,2,2,2,2] => 1260
[3,2,2,2,2,2,2,1,1] => 1232
[3,2,2,2,2,2,1,1,1,1] => 1176
[3,2,2,2,2,1,1,1,1,1,1] => 1092
[3,2,2,2,1,1,1,1,1,1,1,1] => 980
[3,2,2,1,1,1,1,1,1,1,1,1,1] => 840
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Created: May 07, 2018 at 20:47 by Christian Stump
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Last Updated: May 07, 2018 at 20:47 by Christian Stump