Identifier
Identifier
Values
[1] generating graphics... => 0
[2] generating graphics... => 0
[1,1] generating graphics... => 0
[3] generating graphics... => 0
[2,1] generating graphics... => 3
[1,1,1] generating graphics... => 0
[4] generating graphics... => 0
[3,1] generating graphics... => 8
[2,2] generating graphics... => 12
[2,1,1] generating graphics... => 8
[1,1,1,1] generating graphics... => 0
[5] generating graphics... => 0
[4,1] generating graphics... => 15
[3,2] generating graphics... => 24
[3,1,1] generating graphics... => 20
[2,2,1] generating graphics... => 24
[2,1,1,1] generating graphics... => 15
[1,1,1,1,1] generating graphics... => 0
[6] generating graphics... => 0
[5,1] generating graphics... => 24
[4,2] generating graphics... => 40
[4,1,1] generating graphics... => 36
[3,3] generating graphics... => 48
[3,2,1] generating graphics... => 45
[3,1,1,1] generating graphics... => 36
[2,2,2] generating graphics... => 48
[2,2,1,1] generating graphics... => 40
[2,1,1,1,1] generating graphics... => 24
[1,1,1,1,1,1] generating graphics... => 0
[7] generating graphics... => 0
[6,1] generating graphics... => 35
[5,2] generating graphics... => 60
[5,1,1] generating graphics... => 56
[4,3] generating graphics... => 75
[4,2,1] generating graphics... => 72
[4,1,1,1] generating graphics... => 63
[3,3,1] generating graphics... => 80
[3,2,2] generating graphics... => 80
[3,2,1,1] generating graphics... => 72
[3,1,1,1,1] generating graphics... => 56
[2,2,2,1] generating graphics... => 75
[2,2,1,1,1] generating graphics... => 60
[2,1,1,1,1,1] generating graphics... => 35
[1,1,1,1,1,1,1] generating graphics... => 0
[8] generating graphics... => 0
[7,1] generating graphics... => 48
[6,2] generating graphics... => 84
[6,1,1] generating graphics... => 80
[5,3] generating graphics... => 108
[5,2,1] generating graphics... => 105
[5,1,1,1] generating graphics... => 96
[4,4] generating graphics... => 120
[4,3,1] generating graphics... => 120
[4,2,2] generating graphics... => 120
[4,2,1,1] generating graphics... => 112
[4,1,1,1,1] generating graphics... => 96
[3,3,2] generating graphics... => 128
[3,3,1,1] generating graphics... => 120
[3,2,2,1] generating graphics... => 120
[3,2,1,1,1] generating graphics... => 105
[3,1,1,1,1,1] generating graphics... => 80
[2,2,2,2] generating graphics... => 120
[2,2,2,1,1] generating graphics... => 108
[2,2,1,1,1,1] generating graphics... => 84
[2,1,1,1,1,1,1] generating graphics... => 48
[1,1,1,1,1,1,1,1] generating graphics... => 0
[9] generating graphics... => 0
[8,1] generating graphics... => 63
[7,2] generating graphics... => 112
[7,1,1] generating graphics... => 108
[6,3] generating graphics... => 147
[6,2,1] generating graphics... => 144
[6,1,1,1] generating graphics... => 135
[5,4] generating graphics... => 168
[5,3,1] generating graphics... => 168
[5,2,2] generating graphics... => 168
[5,2,1,1] generating graphics... => 160
[5,1,1,1,1] generating graphics... => 144
[4,4,1] generating graphics... => 180
[4,3,2] generating graphics... => 183
[4,3,1,1] generating graphics... => 175
[4,2,2,1] generating graphics... => 175
[4,2,1,1,1] generating graphics... => 160
[4,1,1,1,1,1] generating graphics... => 135
[3,3,3] generating graphics... => 192
[3,3,2,1] generating graphics... => 183
[3,3,1,1,1] generating graphics... => 168
[3,2,2,2] generating graphics... => 180
[3,2,2,1,1] generating graphics... => 168
[3,2,1,1,1,1] generating graphics... => 144
[3,1,1,1,1,1,1] generating graphics... => 108
[2,2,2,2,1] generating graphics... => 168
[2,2,2,1,1,1] generating graphics... => 147
[2,2,1,1,1,1,1] generating graphics... => 112
[2,1,1,1,1,1,1,1] generating graphics... => 63
[1,1,1,1,1,1,1,1,1] generating graphics... => 0
[10] generating graphics... => 0
[9,1] generating graphics... => 80
[8,2] generating graphics... => 144
[8,1,1] generating graphics... => 140
[7,3] generating graphics... => 192
[7,2,1] generating graphics... => 189
[7,1,1,1] generating graphics... => 180
[6,4] generating graphics... => 224
[6,3,1] generating graphics... => 224
[6,2,2] generating graphics... => 224
[6,2,1,1] generating graphics... => 216
[6,1,1,1,1] generating graphics... => 200
[5,5] generating graphics... => 240
[5,4,1] generating graphics... => 245
[5,3,2] generating graphics... => 248
[5,3,1,1] generating graphics... => 240
[5,2,2,1] generating graphics... => 240
[5,2,1,1,1] generating graphics... => 225
[5,1,1,1,1,1] generating graphics... => 200
[4,4,2] generating graphics... => 260
[4,4,1,1] generating graphics... => 252
[4,3,3] generating graphics... => 264
[4,3,2,1] generating graphics... => 255
[4,3,1,1,1] generating graphics... => 240
[4,2,2,2] generating graphics... => 252
[4,2,2,1,1] generating graphics... => 240
[4,2,1,1,1,1] generating graphics... => 216
[4,1,1,1,1,1,1] generating graphics... => 180
[3,3,3,1] generating graphics... => 264
[3,3,2,2] generating graphics... => 260
[3,3,2,1,1] generating graphics... => 248
[3,3,1,1,1,1] generating graphics... => 224
[3,2,2,2,1] generating graphics... => 245
[3,2,2,1,1,1] generating graphics... => 224
[3,2,1,1,1,1,1] generating graphics... => 189
[3,1,1,1,1,1,1,1] generating graphics... => 140
[2,2,2,2,2] generating graphics... => 240
[2,2,2,2,1,1] generating graphics... => 224
[2,2,2,1,1,1,1] generating graphics... => 192
[2,2,1,1,1,1,1,1] generating graphics... => 144
[2,1,1,1,1,1,1,1,1] generating graphics... => 80
[1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[11] generating graphics... => 0
[10,1] generating graphics... => 99
[9,2] generating graphics... => 180
[9,1,1] generating graphics... => 176
[8,3] generating graphics... => 243
[8,2,1] generating graphics... => 240
[8,1,1,1] generating graphics... => 231
[7,4] generating graphics... => 288
[7,3,1] generating graphics... => 288
[7,2,2] generating graphics... => 288
[7,2,1,1] generating graphics... => 280
[7,1,1,1,1] generating graphics... => 264
[6,5] generating graphics... => 315
[6,4,1] generating graphics... => 320
[6,3,2] generating graphics... => 323
[6,3,1,1] generating graphics... => 315
[6,2,2,1] generating graphics... => 315
[6,2,1,1,1] generating graphics... => 300
[6,1,1,1,1,1] generating graphics... => 275
[5,5,1] generating graphics... => 336
[5,4,2] generating graphics... => 344
[5,4,1,1] generating graphics... => 336
[5,3,3] generating graphics... => 348
[5,3,2,1] generating graphics... => 339
[5,3,1,1,1] generating graphics... => 324
[5,2,2,2] generating graphics... => 336
[5,2,2,1,1] generating graphics... => 324
[5,2,1,1,1,1] generating graphics... => 300
[5,1,1,1,1,1,1] generating graphics... => 264
[4,4,3] generating graphics... => 360
[4,4,2,1] generating graphics... => 351
[4,4,1,1,1] generating graphics... => 336
[4,3,3,1] generating graphics... => 355
[4,3,2,2] generating graphics... => 351
[4,3,2,1,1] generating graphics... => 339
[4,3,1,1,1,1] generating graphics... => 315
[4,2,2,2,1] generating graphics... => 336
[4,2,2,1,1,1] generating graphics... => 315
[4,2,1,1,1,1,1] generating graphics... => 280
[4,1,1,1,1,1,1,1] generating graphics... => 231
[3,3,3,2] generating graphics... => 360
[3,3,3,1,1] generating graphics... => 348
[3,3,2,2,1] generating graphics... => 344
[3,3,2,1,1,1] generating graphics... => 323
[3,3,1,1,1,1,1] generating graphics... => 288
[3,2,2,2,2] generating graphics... => 336
[3,2,2,2,1,1] generating graphics... => 320
[3,2,2,1,1,1,1] generating graphics... => 288
[3,2,1,1,1,1,1,1] generating graphics... => 240
[3,1,1,1,1,1,1,1,1] generating graphics... => 176
[2,2,2,2,2,1] generating graphics... => 315
[2,2,2,2,1,1,1] generating graphics... => 288
[2,2,2,1,1,1,1,1] generating graphics... => 243
[2,2,1,1,1,1,1,1,1] generating graphics... => 180
[2,1,1,1,1,1,1,1,1,1] generating graphics... => 99
[1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[12] generating graphics... => 0
[11,1] generating graphics... => 120
[10,2] generating graphics... => 220
[10,1,1] generating graphics... => 216
[9,3] generating graphics... => 300
[9,2,1] generating graphics... => 297
[9,1,1,1] generating graphics... => 288
[8,4] generating graphics... => 360
[8,3,1] generating graphics... => 360
[8,2,2] generating graphics... => 360
[8,2,1,1] generating graphics... => 352
[8,1,1,1,1] generating graphics... => 336
[7,5] generating graphics... => 400
[7,4,1] generating graphics... => 405
[7,3,2] generating graphics... => 408
[7,3,1,1] generating graphics... => 400
[7,2,2,1] generating graphics... => 400
[7,2,1,1,1] generating graphics... => 385
[7,1,1,1,1,1] generating graphics... => 360
[6,6] generating graphics... => 420
[6,5,1] generating graphics... => 432
[6,4,2] generating graphics... => 440
[6,4,1,1] generating graphics... => 432
[6,3,3] generating graphics... => 444
[6,3,2,1] generating graphics... => 435
[6,3,1,1,1] generating graphics... => 420
[6,2,2,2] generating graphics... => 432
[6,2,2,1,1] generating graphics... => 420
[6,2,1,1,1,1] generating graphics... => 396
[6,1,1,1,1,1,1] generating graphics... => 360
[5,5,2] generating graphics... => 456
[5,5,1,1] generating graphics... => 448
[5,4,3] generating graphics... => 465
[5,4,2,1] generating graphics... => 456
[5,4,1,1,1] generating graphics... => 441
[5,3,3,1] generating graphics... => 460
[5,3,2,2] generating graphics... => 456
[5,3,2,1,1] generating graphics... => 444
[5,3,1,1,1,1] generating graphics... => 420
[5,2,2,2,1] generating graphics... => 441
[5,2,2,1,1,1] generating graphics... => 420
[5,2,1,1,1,1,1] generating graphics... => 385
[5,1,1,1,1,1,1,1] generating graphics... => 336
[4,4,4] generating graphics... => 480
[4,4,3,1] generating graphics... => 472
[4,4,2,2] generating graphics... => 468
[4,4,2,1,1] generating graphics... => 456
[4,4,1,1,1,1] generating graphics... => 432
[4,3,3,2] generating graphics... => 472
[4,3,3,1,1] generating graphics... => 460
[4,3,2,2,1] generating graphics... => 456
[4,3,2,1,1,1] generating graphics... => 435
[4,3,1,1,1,1,1] generating graphics... => 400
[4,2,2,2,2] generating graphics... => 448
[4,2,2,2,1,1] generating graphics... => 432
[4,2,2,1,1,1,1] generating graphics... => 400
[4,2,1,1,1,1,1,1] generating graphics... => 352
[4,1,1,1,1,1,1,1,1] generating graphics... => 288
[3,3,3,3] generating graphics... => 480
[3,3,3,2,1] generating graphics... => 465
[3,3,3,1,1,1] generating graphics... => 444
[3,3,2,2,2] generating graphics... => 456
[3,3,2,2,1,1] generating graphics... => 440
[3,3,2,1,1,1,1] generating graphics... => 408
[3,3,1,1,1,1,1,1] generating graphics... => 360
[3,2,2,2,2,1] generating graphics... => 432
[3,2,2,2,1,1,1] generating graphics... => 405
[3,2,2,1,1,1,1,1] generating graphics... => 360
[3,2,1,1,1,1,1,1,1] generating graphics... => 297
[3,1,1,1,1,1,1,1,1,1] generating graphics... => 216
[2,2,2,2,2,2] generating graphics... => 420
[2,2,2,2,2,1,1] generating graphics... => 400
[2,2,2,2,1,1,1,1] generating graphics... => 360
[2,2,2,1,1,1,1,1,1] generating graphics... => 300
[2,2,1,1,1,1,1,1,1,1] generating graphics... => 220
[2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 120
[1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[13] generating graphics... => 0
[12,1] generating graphics... => 143
[11,2] generating graphics... => 264
[11,1,1] generating graphics... => 260
[10,3] generating graphics... => 363
[10,2,1] generating graphics... => 360
[10,1,1,1] generating graphics... => 351
[9,4] generating graphics... => 440
[9,3,1] generating graphics... => 440
[9,2,2] generating graphics... => 440
[9,2,1,1] generating graphics... => 432
[9,1,1,1,1] generating graphics... => 416
[8,5] generating graphics... => 495
[8,4,1] generating graphics... => 500
[8,3,2] generating graphics... => 503
[8,3,1,1] generating graphics... => 495
[8,2,2,1] generating graphics... => 495
[8,2,1,1,1] generating graphics... => 480
[8,1,1,1,1,1] generating graphics... => 455
[7,6] generating graphics... => 528
[7,5,1] generating graphics... => 540
[7,4,2] generating graphics... => 548
[7,4,1,1] generating graphics... => 540
[7,3,3] generating graphics... => 552
[7,3,2,1] generating graphics... => 543
[7,3,1,1,1] generating graphics... => 528
[7,2,2,2] generating graphics... => 540
[7,2,2,1,1] generating graphics... => 528
[7,2,1,1,1,1] generating graphics... => 504
[7,1,1,1,1,1,1] generating graphics... => 468
[6,6,1] generating graphics... => 560
[6,5,2] generating graphics... => 575
[6,5,1,1] generating graphics... => 567
[6,4,3] generating graphics... => 584
[6,4,2,1] generating graphics... => 575
[6,4,1,1,1] generating graphics... => 560
[6,3,3,1] generating graphics... => 579
[6,3,2,2] generating graphics... => 575
[6,3,2,1,1] generating graphics... => 563
[6,3,1,1,1,1] generating graphics... => 539
[6,2,2,2,1] generating graphics... => 560
[6,2,2,1,1,1] generating graphics... => 539
[6,2,1,1,1,1,1] generating graphics... => 504
[6,1,1,1,1,1,1,1] generating graphics... => 455
[5,5,3] generating graphics... => 600
[5,5,2,1] generating graphics... => 591
[5,5,1,1,1] generating graphics... => 576
[5,4,4] generating graphics... => 608
[5,4,3,1] generating graphics... => 600
[5,4,2,2] generating graphics... => 596
[5,4,2,1,1] generating graphics... => 584
[5,4,1,1,1,1] generating graphics... => 560
[5,3,3,2] generating graphics... => 600
[5,3,3,1,1] generating graphics... => 588
[5,3,2,2,1] generating graphics... => 584
[5,3,2,1,1,1] generating graphics... => 563
[5,3,1,1,1,1,1] generating graphics... => 528
[5,2,2,2,2] generating graphics... => 576
[5,2,2,2,1,1] generating graphics... => 560
[5,2,2,1,1,1,1] generating graphics... => 528
[5,2,1,1,1,1,1,1] generating graphics... => 480
[5,1,1,1,1,1,1,1,1] generating graphics... => 416
[4,4,4,1] generating graphics... => 615
[4,4,3,2] generating graphics... => 612
[4,4,3,1,1] generating graphics... => 600
[4,4,2,2,1] generating graphics... => 596
[4,4,2,1,1,1] generating graphics... => 575
[4,4,1,1,1,1,1] generating graphics... => 540
[4,3,3,3] generating graphics... => 615
[4,3,3,2,1] generating graphics... => 600
[4,3,3,1,1,1] generating graphics... => 579
[4,3,2,2,2] generating graphics... => 591
[4,3,2,2,1,1] generating graphics... => 575
[4,3,2,1,1,1,1] generating graphics... => 543
[4,3,1,1,1,1,1,1] generating graphics... => 495
[4,2,2,2,2,1] generating graphics... => 567
[4,2,2,2,1,1,1] generating graphics... => 540
[4,2,2,1,1,1,1,1] generating graphics... => 495
[4,2,1,1,1,1,1,1,1] generating graphics... => 432
[4,1,1,1,1,1,1,1,1,1] generating graphics... => 351
[3,3,3,3,1] generating graphics... => 608
[3,3,3,2,2] generating graphics... => 600
[3,3,3,2,1,1] generating graphics... => 584
[3,3,3,1,1,1,1] generating graphics... => 552
[3,3,2,2,2,1] generating graphics... => 575
[3,3,2,2,1,1,1] generating graphics... => 548
[3,3,2,1,1,1,1,1] generating graphics... => 503
[3,3,1,1,1,1,1,1,1] generating graphics... => 440
[3,2,2,2,2,2] generating graphics... => 560
[3,2,2,2,2,1,1] generating graphics... => 540
[3,2,2,2,1,1,1,1] generating graphics... => 500
[3,2,2,1,1,1,1,1,1] generating graphics... => 440
[3,2,1,1,1,1,1,1,1,1] generating graphics... => 360
[3,1,1,1,1,1,1,1,1,1,1] generating graphics... => 260
[2,2,2,2,2,2,1] generating graphics... => 528
[2,2,2,2,2,1,1,1] generating graphics... => 495
[2,2,2,2,1,1,1,1,1] generating graphics... => 440
[2,2,2,1,1,1,1,1,1,1] generating graphics... => 363
[2,2,1,1,1,1,1,1,1,1,1] generating graphics... => 264
[2,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 143
[1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[14] generating graphics... => 0
[13,1] generating graphics... => 168
[12,2] generating graphics... => 312
[12,1,1] generating graphics... => 308
[11,3] generating graphics... => 432
[11,2,1] generating graphics... => 429
[11,1,1,1] generating graphics... => 420
[10,4] generating graphics... => 528
[10,3,1] generating graphics... => 528
[10,2,2] generating graphics... => 528
[10,2,1,1] generating graphics... => 520
[10,1,1,1,1] generating graphics... => 504
[9,5] generating graphics... => 600
[9,4,1] generating graphics... => 605
[9,3,2] generating graphics... => 608
[9,3,1,1] generating graphics... => 600
[9,2,2,1] generating graphics... => 600
[9,2,1,1,1] generating graphics... => 585
[9,1,1,1,1,1] generating graphics... => 560
[8,6] generating graphics... => 648
[8,5,1] generating graphics... => 660
[8,4,2] generating graphics... => 668
[8,4,1,1] generating graphics... => 660
[8,3,3] generating graphics... => 672
[8,3,2,1] generating graphics... => 663
[8,3,1,1,1] generating graphics... => 648
[8,2,2,2] generating graphics... => 660
[8,2,2,1,1] generating graphics... => 648
[8,2,1,1,1,1] generating graphics... => 624
[8,1,1,1,1,1,1] generating graphics... => 588
[7,7] generating graphics... => 672
[7,6,1] generating graphics... => 693
[7,5,2] generating graphics... => 708
[7,5,1,1] generating graphics... => 700
[7,4,3] generating graphics... => 717
[7,4,2,1] generating graphics... => 708
[7,4,1,1,1] generating graphics... => 693
[7,3,3,1] generating graphics... => 712
[7,3,2,2] generating graphics... => 708
[7,3,2,1,1] generating graphics... => 696
[7,3,1,1,1,1] generating graphics... => 672
[7,2,2,2,1] generating graphics... => 693
[7,2,2,1,1,1] generating graphics... => 672
[7,2,1,1,1,1,1] generating graphics... => 637
[7,1,1,1,1,1,1,1] generating graphics... => 588
[6,6,2] generating graphics... => 728
[6,6,1,1] generating graphics... => 720
[6,5,3] generating graphics... => 744
[6,5,2,1] generating graphics... => 735
[6,5,1,1,1] generating graphics... => 720
[6,4,4] generating graphics... => 752
[6,4,3,1] generating graphics... => 744
[6,4,2,2] generating graphics... => 740
[6,4,2,1,1] generating graphics... => 728
[6,4,1,1,1,1] generating graphics... => 704
[6,3,3,2] generating graphics... => 744
[6,3,3,1,1] generating graphics... => 732
[6,3,2,2,1] generating graphics... => 728
[6,3,2,1,1,1] generating graphics... => 707
[6,3,1,1,1,1,1] generating graphics... => 672
[6,2,2,2,2] generating graphics... => 720
[6,2,2,2,1,1] generating graphics... => 704
[6,2,2,1,1,1,1] generating graphics... => 672
[6,2,1,1,1,1,1,1] generating graphics... => 624
[6,1,1,1,1,1,1,1,1] generating graphics... => 560
[5,5,4] generating graphics... => 768
[5,5,3,1] generating graphics... => 760
[5,5,2,2] generating graphics... => 756
[5,5,2,1,1] generating graphics... => 744
[5,5,1,1,1,1] generating graphics... => 720
[5,4,4,1] generating graphics... => 768
[5,4,3,2] generating graphics... => 765
[5,4,3,1,1] generating graphics... => 753
[5,4,2,2,1] generating graphics... => 749
[5,4,2,1,1,1] generating graphics... => 728
[5,4,1,1,1,1,1] generating graphics... => 693
[5,3,3,3] generating graphics... => 768
[5,3,3,2,1] generating graphics... => 753
[5,3,3,1,1,1] generating graphics... => 732
[5,3,2,2,2] generating graphics... => 744
[5,3,2,2,1,1] generating graphics... => 728
[5,3,2,1,1,1,1] generating graphics... => 696
[5,3,1,1,1,1,1,1] generating graphics... => 648
[5,2,2,2,2,1] generating graphics... => 720
[5,2,2,2,1,1,1] generating graphics... => 693
[5,2,2,1,1,1,1,1] generating graphics... => 648
[5,2,1,1,1,1,1,1,1] generating graphics... => 585
[5,1,1,1,1,1,1,1,1,1] generating graphics... => 504
[4,4,4,2] generating graphics... => 780
[4,4,4,1,1] generating graphics... => 768
[4,4,3,3] generating graphics... => 780
[4,4,3,2,1] generating graphics... => 765
[4,4,3,1,1,1] generating graphics... => 744
[4,4,2,2,2] generating graphics... => 756
[4,4,2,2,1,1] generating graphics... => 740
[4,4,2,1,1,1,1] generating graphics... => 708
[4,4,1,1,1,1,1,1] generating graphics... => 660
[4,3,3,3,1] generating graphics... => 768
[4,3,3,2,2] generating graphics... => 760
[4,3,3,2,1,1] generating graphics... => 744
[4,3,3,1,1,1,1] generating graphics... => 712
[4,3,2,2,2,1] generating graphics... => 735
[4,3,2,2,1,1,1] generating graphics... => 708
[4,3,2,1,1,1,1,1] generating graphics... => 663
[4,3,1,1,1,1,1,1,1] generating graphics... => 600
[4,2,2,2,2,2] generating graphics... => 720
[4,2,2,2,2,1,1] generating graphics... => 700
[4,2,2,2,1,1,1,1] generating graphics... => 660
[4,2,2,1,1,1,1,1,1] generating graphics... => 600
[4,2,1,1,1,1,1,1,1,1] generating graphics... => 520
[4,1,1,1,1,1,1,1,1,1,1] generating graphics... => 420
[3,3,3,3,2] generating graphics... => 768
[3,3,3,3,1,1] generating graphics... => 752
[3,3,3,2,2,1] generating graphics... => 744
[3,3,3,2,1,1,1] generating graphics... => 717
[3,3,3,1,1,1,1,1] generating graphics... => 672
[3,3,2,2,2,2] generating graphics... => 728
[3,3,2,2,2,1,1] generating graphics... => 708
[3,3,2,2,1,1,1,1] generating graphics... => 668
[3,3,2,1,1,1,1,1,1] generating graphics... => 608
[3,3,1,1,1,1,1,1,1,1] generating graphics... => 528
[3,2,2,2,2,2,1] generating graphics... => 693
[3,2,2,2,2,1,1,1] generating graphics... => 660
[3,2,2,2,1,1,1,1,1] generating graphics... => 605
[3,2,2,1,1,1,1,1,1,1] generating graphics... => 528
[3,2,1,1,1,1,1,1,1,1,1] generating graphics... => 429
[3,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 308
[2,2,2,2,2,2,2] generating graphics... => 672
[2,2,2,2,2,2,1,1] generating graphics... => 648
[2,2,2,2,2,1,1,1,1] generating graphics... => 600
[2,2,2,2,1,1,1,1,1,1] generating graphics... => 528
[2,2,2,1,1,1,1,1,1,1,1] generating graphics... => 432
[2,2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 312
[2,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 168
[1,1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[15] generating graphics... => 0
[14,1] generating graphics... => 195
[13,2] generating graphics... => 364
[13,1,1] generating graphics... => 360
[12,3] generating graphics... => 507
[12,2,1] generating graphics... => 504
[12,1,1,1] generating graphics... => 495
[11,4] generating graphics... => 624
[11,3,1] generating graphics... => 624
[11,2,2] generating graphics... => 624
[11,2,1,1] generating graphics... => 616
[11,1,1,1,1] generating graphics... => 600
[10,5] generating graphics... => 715
[10,4,1] generating graphics... => 720
[10,3,2] generating graphics... => 723
[10,3,1,1] generating graphics... => 715
[10,2,2,1] generating graphics... => 715
[10,2,1,1,1] generating graphics... => 700
[10,1,1,1,1,1] generating graphics... => 675
[9,6] generating graphics... => 780
[9,5,1] generating graphics... => 792
[9,4,2] generating graphics... => 800
[9,4,1,1] generating graphics... => 792
[9,3,3] generating graphics... => 804
[9,3,2,1] generating graphics... => 795
[9,3,1,1,1] generating graphics... => 780
[9,2,2,2] generating graphics... => 792
[9,2,2,1,1] generating graphics... => 780
[9,2,1,1,1,1] generating graphics... => 756
[9,1,1,1,1,1,1] generating graphics... => 720
[8,7] generating graphics... => 819
[8,6,1] generating graphics... => 840
[8,5,2] generating graphics... => 855
[8,5,1,1] generating graphics... => 847
[8,4,3] generating graphics... => 864
[8,4,2,1] generating graphics... => 855
[8,4,1,1,1] generating graphics... => 840
[8,3,3,1] generating graphics... => 859
[8,3,2,2] generating graphics... => 855
[8,3,2,1,1] generating graphics... => 843
[8,3,1,1,1,1] generating graphics... => 819
[8,2,2,2,1] generating graphics... => 840
[8,2,2,1,1,1] generating graphics... => 819
[8,2,1,1,1,1,1] generating graphics... => 784
[8,1,1,1,1,1,1,1] generating graphics... => 735
[7,7,1] generating graphics... => 864
[7,6,2] generating graphics... => 888
[7,6,1,1] generating graphics... => 880
[7,5,3] generating graphics... => 904
[7,5,2,1] generating graphics... => 895
[7,5,1,1,1] generating graphics... => 880
[7,4,4] generating graphics... => 912
[7,4,3,1] generating graphics... => 904
[7,4,2,2] generating graphics... => 900
[7,4,2,1,1] generating graphics... => 888
[7,4,1,1,1,1] generating graphics... => 864
[7,3,3,2] generating graphics... => 904
[7,3,3,1,1] generating graphics... => 892
[7,3,2,2,1] generating graphics... => 888
[7,3,2,1,1,1] generating graphics... => 867
[7,3,1,1,1,1,1] generating graphics... => 832
[7,2,2,2,2] generating graphics... => 880
[7,2,2,2,1,1] generating graphics... => 864
[7,2,2,1,1,1,1] generating graphics... => 832
[7,2,1,1,1,1,1,1] generating graphics... => 784
[7,1,1,1,1,1,1,1,1] generating graphics... => 720
[6,6,3] generating graphics... => 924
[6,6,2,1] generating graphics... => 915
[6,6,1,1,1] generating graphics... => 900
[6,5,4] generating graphics... => 939
[6,5,3,1] generating graphics... => 931
[6,5,2,2] generating graphics... => 927
[6,5,2,1,1] generating graphics... => 915
[6,5,1,1,1,1] generating graphics... => 891
[6,4,4,1] generating graphics... => 939
[6,4,3,2] generating graphics... => 936
[6,4,3,1,1] generating graphics... => 924
[6,4,2,2,1] generating graphics... => 920
[6,4,2,1,1,1] generating graphics... => 899
[6,4,1,1,1,1,1] generating graphics... => 864
[6,3,3,3] generating graphics... => 939
[6,3,3,2,1] generating graphics... => 924
[6,3,3,1,1,1] generating graphics... => 903
[6,3,2,2,2] generating graphics... => 915
[6,3,2,2,1,1] generating graphics... => 899
[6,3,2,1,1,1,1] generating graphics... => 867
[6,3,1,1,1,1,1,1] generating graphics... => 819
[6,2,2,2,2,1] generating graphics... => 891
[6,2,2,2,1,1,1] generating graphics... => 864
[6,2,2,1,1,1,1,1] generating graphics... => 819
[6,2,1,1,1,1,1,1,1] generating graphics... => 756
[6,1,1,1,1,1,1,1,1,1] generating graphics... => 675
[5,5,5] generating graphics... => 960
[5,5,4,1] generating graphics... => 955
[5,5,3,2] generating graphics... => 952
[5,5,3,1,1] generating graphics... => 940
[5,5,2,2,1] generating graphics... => 936
[5,5,2,1,1,1] generating graphics... => 915
[5,5,1,1,1,1,1] generating graphics... => 880
[5,4,4,2] generating graphics... => 960
[5,4,4,1,1] generating graphics... => 948
[5,4,3,3] generating graphics... => 960
[5,4,3,2,1] generating graphics... => 945
[5,4,3,1,1,1] generating graphics... => 924
[5,4,2,2,2] generating graphics... => 936
[5,4,2,2,1,1] generating graphics... => 920
[5,4,2,1,1,1,1] generating graphics... => 888
[5,4,1,1,1,1,1,1] generating graphics... => 840
[5,3,3,3,1] generating graphics... => 948
[5,3,3,2,2] generating graphics... => 940
[5,3,3,2,1,1] generating graphics... => 924
[5,3,3,1,1,1,1] generating graphics... => 892
[5,3,2,2,2,1] generating graphics... => 915
[5,3,2,2,1,1,1] generating graphics... => 888
[5,3,2,1,1,1,1,1] generating graphics... => 843
[5,3,1,1,1,1,1,1,1] generating graphics... => 780
[5,2,2,2,2,2] generating graphics... => 900
[5,2,2,2,2,1,1] generating graphics... => 880
[5,2,2,2,1,1,1,1] generating graphics... => 840
[5,2,2,1,1,1,1,1,1] generating graphics... => 780
[5,2,1,1,1,1,1,1,1,1] generating graphics... => 700
[5,1,1,1,1,1,1,1,1,1,1] generating graphics... => 600
[4,4,4,3] generating graphics... => 975
[4,4,4,2,1] generating graphics... => 960
[4,4,4,1,1,1] generating graphics... => 939
[4,4,3,3,1] generating graphics... => 960
[4,4,3,2,2] generating graphics... => 952
[4,4,3,2,1,1] generating graphics... => 936
[4,4,3,1,1,1,1] generating graphics... => 904
[4,4,2,2,2,1] generating graphics... => 927
[4,4,2,2,1,1,1] generating graphics... => 900
[4,4,2,1,1,1,1,1] generating graphics... => 855
[4,4,1,1,1,1,1,1,1] generating graphics... => 792
[4,3,3,3,2] generating graphics... => 955
[4,3,3,3,1,1] generating graphics... => 939
[4,3,3,2,2,1] generating graphics... => 931
[4,3,3,2,1,1,1] generating graphics... => 904
[4,3,3,1,1,1,1,1] generating graphics... => 859
[4,3,2,2,2,2] generating graphics... => 915
[4,3,2,2,2,1,1] generating graphics... => 895
[4,3,2,2,1,1,1,1] generating graphics... => 855
[4,3,2,1,1,1,1,1,1] generating graphics... => 795
[4,3,1,1,1,1,1,1,1,1] generating graphics... => 715
[4,2,2,2,2,2,1] generating graphics... => 880
[4,2,2,2,2,1,1,1] generating graphics... => 847
[4,2,2,2,1,1,1,1,1] generating graphics... => 792
[4,2,2,1,1,1,1,1,1,1] generating graphics... => 715
[4,2,1,1,1,1,1,1,1,1,1] generating graphics... => 616
[4,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 495
[3,3,3,3,3] generating graphics... => 960
[3,3,3,3,2,1] generating graphics... => 939
[3,3,3,3,1,1,1] generating graphics... => 912
[3,3,3,2,2,2] generating graphics... => 924
[3,3,3,2,2,1,1] generating graphics... => 904
[3,3,3,2,1,1,1,1] generating graphics... => 864
[3,3,3,1,1,1,1,1,1] generating graphics... => 804
[3,3,2,2,2,2,1] generating graphics... => 888
[3,3,2,2,2,1,1,1] generating graphics... => 855
[3,3,2,2,1,1,1,1,1] generating graphics... => 800
[3,3,2,1,1,1,1,1,1,1] generating graphics... => 723
[3,3,1,1,1,1,1,1,1,1,1] generating graphics... => 624
[3,2,2,2,2,2,2] generating graphics... => 864
[3,2,2,2,2,2,1,1] generating graphics... => 840
[3,2,2,2,2,1,1,1,1] generating graphics... => 792
[3,2,2,2,1,1,1,1,1,1] generating graphics... => 720
[3,2,2,1,1,1,1,1,1,1,1] generating graphics... => 624
[3,2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 504
[3,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 360
[2,2,2,2,2,2,2,1] generating graphics... => 819
[2,2,2,2,2,2,1,1,1] generating graphics... => 780
[2,2,2,2,2,1,1,1,1,1] generating graphics... => 715
[2,2,2,2,1,1,1,1,1,1,1] generating graphics... => 624
[2,2,2,1,1,1,1,1,1,1,1,1] generating graphics... => 507
[2,2,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 364
[2,1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 195
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[16] generating graphics... => 0
[15,1] generating graphics... => 224
[14,2] generating graphics... => 420
[14,1,1] generating graphics... => 416
[13,3] generating graphics... => 588
[13,2,1] generating graphics... => 585
[13,1,1,1] generating graphics... => 576
[12,4] generating graphics... => 728
[12,3,1] generating graphics... => 728
[12,2,2] generating graphics... => 728
[12,2,1,1] generating graphics... => 720
[12,1,1,1,1] generating graphics... => 704
[11,5] generating graphics... => 840
[11,4,1] generating graphics... => 845
[11,3,2] generating graphics... => 848
[11,3,1,1] generating graphics... => 840
[11,2,2,1] generating graphics... => 840
[11,2,1,1,1] generating graphics... => 825
[11,1,1,1,1,1] generating graphics... => 800
[10,6] generating graphics... => 924
[10,5,1] generating graphics... => 936
[10,4,2] generating graphics... => 944
[10,4,1,1] generating graphics... => 936
[10,3,3] generating graphics... => 948
[10,3,2,1] generating graphics... => 939
[10,3,1,1,1] generating graphics... => 924
[10,2,2,2] generating graphics... => 936
[10,2,2,1,1] generating graphics... => 924
[10,2,1,1,1,1] generating graphics... => 900
[10,1,1,1,1,1,1] generating graphics... => 864
[9,7] generating graphics... => 980
[9,6,1] generating graphics... => 1001
[9,5,2] generating graphics... => 1016
[9,5,1,1] generating graphics... => 1008
[9,4,3] generating graphics... => 1025
[9,4,2,1] generating graphics... => 1016
[9,4,1,1,1] generating graphics... => 1001
[9,3,3,1] generating graphics... => 1020
[9,3,2,2] generating graphics... => 1016
[9,3,2,1,1] generating graphics... => 1004
[9,3,1,1,1,1] generating graphics... => 980
[9,2,2,2,1] generating graphics... => 1001
[9,2,2,1,1,1] generating graphics... => 980
[9,2,1,1,1,1,1] generating graphics... => 945
[9,1,1,1,1,1,1,1] generating graphics... => 896
[8,8] generating graphics... => 1008
[8,7,1] generating graphics... => 1040
[8,6,2] generating graphics... => 1064
[8,6,1,1] generating graphics... => 1056
[8,5,3] generating graphics... => 1080
[8,5,2,1] generating graphics... => 1071
[8,5,1,1,1] generating graphics... => 1056
[8,4,4] generating graphics... => 1088
[8,4,3,1] generating graphics... => 1080
[8,4,2,2] generating graphics... => 1076
[8,4,2,1,1] generating graphics... => 1064
[8,4,1,1,1,1] generating graphics... => 1040
[8,3,3,2] generating graphics... => 1080
[8,3,3,1,1] generating graphics... => 1068
[8,3,2,2,1] generating graphics... => 1064
[8,3,2,1,1,1] generating graphics... => 1043
[8,3,1,1,1,1,1] generating graphics... => 1008
[8,2,2,2,2] generating graphics... => 1056
[8,2,2,2,1,1] generating graphics... => 1040
[8,2,2,1,1,1,1] generating graphics... => 1008
[8,2,1,1,1,1,1,1] generating graphics... => 960
[8,1,1,1,1,1,1,1,1] generating graphics... => 896
[7,7,2] generating graphics... => 1088
[7,7,1,1] generating graphics... => 1080
[7,6,3] generating graphics... => 1113
[7,6,2,1] generating graphics... => 1104
[7,6,1,1,1] generating graphics... => 1089
[7,5,4] generating graphics... => 1128
[7,5,3,1] generating graphics... => 1120
[7,5,2,2] generating graphics... => 1116
[7,5,2,1,1] generating graphics... => 1104
[7,5,1,1,1,1] generating graphics... => 1080
[7,4,4,1] generating graphics... => 1128
[7,4,3,2] generating graphics... => 1125
[7,4,3,1,1] generating graphics... => 1113
[7,4,2,2,1] generating graphics... => 1109
[7,4,2,1,1,1] generating graphics... => 1088
[7,4,1,1,1,1,1] generating graphics... => 1053
[7,3,3,3] generating graphics... => 1128
[7,3,3,2,1] generating graphics... => 1113
[7,3,3,1,1,1] generating graphics... => 1092
[7,3,2,2,2] generating graphics... => 1104
[7,3,2,2,1,1] generating graphics... => 1088
[7,3,2,1,1,1,1] generating graphics... => 1056
[7,3,1,1,1,1,1,1] generating graphics... => 1008
[7,2,2,2,2,1] generating graphics... => 1080
[7,2,2,2,1,1,1] generating graphics... => 1053
[7,2,2,1,1,1,1,1] generating graphics... => 1008
[7,2,1,1,1,1,1,1,1] generating graphics... => 945
[7,1,1,1,1,1,1,1,1,1] generating graphics... => 864
[6,6,4] generating graphics... => 1148
[6,6,3,1] generating graphics... => 1140
[6,6,2,2] generating graphics... => 1136
[6,6,2,1,1] generating graphics... => 1124
[6,6,1,1,1,1] generating graphics... => 1100
[6,5,5] generating graphics... => 1160
[6,5,4,1] generating graphics... => 1155
[6,5,3,2] generating graphics... => 1152
[6,5,3,1,1] generating graphics... => 1140
[6,5,2,2,1] generating graphics... => 1136
[6,5,2,1,1,1] generating graphics... => 1115
[6,5,1,1,1,1,1] generating graphics... => 1080
[6,4,4,2] generating graphics... => 1160
[6,4,4,1,1] generating graphics... => 1148
[6,4,3,3] generating graphics... => 1160
[6,4,3,2,1] generating graphics... => 1145
[6,4,3,1,1,1] generating graphics... => 1124
[6,4,2,2,2] generating graphics... => 1136
[6,4,2,2,1,1] generating graphics... => 1120
[6,4,2,1,1,1,1] generating graphics... => 1088
[6,4,1,1,1,1,1,1] generating graphics... => 1040
[6,3,3,3,1] generating graphics... => 1148
[6,3,3,2,2] generating graphics... => 1140
[6,3,3,2,1,1] generating graphics... => 1124
[6,3,3,1,1,1,1] generating graphics... => 1092
[6,3,2,2,2,1] generating graphics... => 1115
[6,3,2,2,1,1,1] generating graphics... => 1088
[6,3,2,1,1,1,1,1] generating graphics... => 1043
[6,3,1,1,1,1,1,1,1] generating graphics... => 980
[6,2,2,2,2,2] generating graphics... => 1100
[6,2,2,2,2,1,1] generating graphics... => 1080
[6,2,2,2,1,1,1,1] generating graphics... => 1040
[6,2,2,1,1,1,1,1,1] generating graphics... => 980
[6,2,1,1,1,1,1,1,1,1] generating graphics... => 900
[6,1,1,1,1,1,1,1,1,1,1] generating graphics... => 800
[5,5,5,1] generating graphics... => 1176
[5,5,4,2] generating graphics... => 1176
[5,5,4,1,1] generating graphics... => 1164
[5,5,3,3] generating graphics... => 1176
[5,5,3,2,1] generating graphics... => 1161
[5,5,3,1,1,1] generating graphics... => 1140
[5,5,2,2,2] generating graphics... => 1152
[5,5,2,2,1,1] generating graphics... => 1136
[5,5,2,1,1,1,1] generating graphics... => 1104
[5,5,1,1,1,1,1,1] generating graphics... => 1056
[5,4,4,3] generating graphics... => 1184
[5,4,4,2,1] generating graphics... => 1169
[5,4,4,1,1,1] generating graphics... => 1148
[5,4,3,3,1] generating graphics... => 1169
[5,4,3,2,2] generating graphics... => 1161
[5,4,3,2,1,1] generating graphics... => 1145
[5,4,3,1,1,1,1] generating graphics... => 1113
[5,4,2,2,2,1] generating graphics... => 1136
[5,4,2,2,1,1,1] generating graphics... => 1109
[5,4,2,1,1,1,1,1] generating graphics... => 1064
[5,4,1,1,1,1,1,1,1] generating graphics... => 1001
[5,3,3,3,2] generating graphics... => 1164
[5,3,3,3,1,1] generating graphics... => 1148
[5,3,3,2,2,1] generating graphics... => 1140
[5,3,3,2,1,1,1] generating graphics... => 1113
[5,3,3,1,1,1,1,1] generating graphics... => 1068
[5,3,2,2,2,2] generating graphics... => 1124
[5,3,2,2,2,1,1] generating graphics... => 1104
[5,3,2,2,1,1,1,1] generating graphics... => 1064
[5,3,2,1,1,1,1,1,1] generating graphics... => 1004
[5,3,1,1,1,1,1,1,1,1] generating graphics... => 924
[5,2,2,2,2,2,1] generating graphics... => 1089
[5,2,2,2,2,1,1,1] generating graphics... => 1056
[5,2,2,2,1,1,1,1,1] generating graphics... => 1001
[5,2,2,1,1,1,1,1,1,1] generating graphics... => 924
[5,2,1,1,1,1,1,1,1,1,1] generating graphics... => 825
[5,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 704
[4,4,4,4] generating graphics... => 1200
[4,4,4,3,1] generating graphics... => 1184
[4,4,4,2,2] generating graphics... => 1176
[4,4,4,2,1,1] generating graphics... => 1160
[4,4,4,1,1,1,1] generating graphics... => 1128
[4,4,3,3,2] generating graphics... => 1176
[4,4,3,3,1,1] generating graphics... => 1160
[4,4,3,2,2,1] generating graphics... => 1152
[4,4,3,2,1,1,1] generating graphics... => 1125
[4,4,3,1,1,1,1,1] generating graphics... => 1080
[4,4,2,2,2,2] generating graphics... => 1136
[4,4,2,2,2,1,1] generating graphics... => 1116
[4,4,2,2,1,1,1,1] generating graphics... => 1076
[4,4,2,1,1,1,1,1,1] generating graphics... => 1016
[4,4,1,1,1,1,1,1,1,1] generating graphics... => 936
[4,3,3,3,3] generating graphics... => 1176
[4,3,3,3,2,1] generating graphics... => 1155
[4,3,3,3,1,1,1] generating graphics... => 1128
[4,3,3,2,2,2] generating graphics... => 1140
[4,3,3,2,2,1,1] generating graphics... => 1120
[4,3,3,2,1,1,1,1] generating graphics... => 1080
[4,3,3,1,1,1,1,1,1] generating graphics... => 1020
[4,3,2,2,2,2,1] generating graphics... => 1104
[4,3,2,2,2,1,1,1] generating graphics... => 1071
[4,3,2,2,1,1,1,1,1] generating graphics... => 1016
[4,3,2,1,1,1,1,1,1,1] generating graphics... => 939
[4,3,1,1,1,1,1,1,1,1,1] generating graphics... => 840
[4,2,2,2,2,2,2] generating graphics... => 1080
[4,2,2,2,2,2,1,1] generating graphics... => 1056
[4,2,2,2,2,1,1,1,1] generating graphics... => 1008
[4,2,2,2,1,1,1,1,1,1] generating graphics... => 936
[4,2,2,1,1,1,1,1,1,1,1] generating graphics... => 840
[4,2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 720
[4,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 576
[3,3,3,3,3,1] generating graphics... => 1160
[3,3,3,3,2,2] generating graphics... => 1148
[3,3,3,3,2,1,1] generating graphics... => 1128
[3,3,3,3,1,1,1,1] generating graphics... => 1088
[3,3,3,2,2,2,1] generating graphics... => 1113
[3,3,3,2,2,1,1,1] generating graphics... => 1080
[3,3,3,2,1,1,1,1,1] generating graphics... => 1025
[3,3,3,1,1,1,1,1,1,1] generating graphics... => 948
[3,3,2,2,2,2,2] generating graphics... => 1088
[3,3,2,2,2,2,1,1] generating graphics... => 1064
[3,3,2,2,2,1,1,1,1] generating graphics... => 1016
[3,3,2,2,1,1,1,1,1,1] generating graphics... => 944
[3,3,2,1,1,1,1,1,1,1,1] generating graphics... => 848
[3,3,1,1,1,1,1,1,1,1,1,1] generating graphics... => 728
[3,2,2,2,2,2,2,1] generating graphics... => 1040
[3,2,2,2,2,2,1,1,1] generating graphics... => 1001
[3,2,2,2,2,1,1,1,1,1] generating graphics... => 936
[3,2,2,2,1,1,1,1,1,1,1] generating graphics... => 845
[3,2,2,1,1,1,1,1,1,1,1,1] generating graphics... => 728
[3,2,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 585
[3,1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 416
[2,2,2,2,2,2,2,2] generating graphics... => 1008
[2,2,2,2,2,2,2,1,1] generating graphics... => 980
[2,2,2,2,2,2,1,1,1,1] generating graphics... => 924
[2,2,2,2,2,1,1,1,1,1,1] generating graphics... => 840
[2,2,2,2,1,1,1,1,1,1,1,1] generating graphics... => 728
[2,2,2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 588
[2,2,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 420
[2,1,1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 224
[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 0
[17] generating graphics... => 0
[16,1] generating graphics... => 255
[15,2] generating graphics... => 480
[15,1,1] generating graphics... => 476
[14,3] generating graphics... => 675
[14,2,1] generating graphics... => 672
[14,1,1,1] generating graphics... => 663
[13,4] generating graphics... => 840
[13,3,1] generating graphics... => 840
[13,2,2] generating graphics... => 840
[13,2,1,1] generating graphics... => 832
[13,1,1,1,1] generating graphics... => 816
[12,5] generating graphics... => 975
[12,4,1] generating graphics... => 980
[12,3,2] generating graphics... => 983
[12,3,1,1] generating graphics... => 975
[12,2,2,1] generating graphics... => 975
[12,2,1,1,1] generating graphics... => 960
[12,1,1,1,1,1] generating graphics... => 935
[11,6] generating graphics... => 1080
[11,5,1] generating graphics... => 1092
[11,4,2] generating graphics... => 1100
[11,4,1,1] generating graphics... => 1092
[11,3,3] generating graphics... => 1104
[11,3,2,1] generating graphics... => 1095
[11,3,1,1,1] generating graphics... => 1080
[11,2,2,2] generating graphics... => 1092
[11,2,2,1,1] generating graphics... => 1080
[11,2,1,1,1,1] generating graphics... => 1056
[11,1,1,1,1,1,1] generating graphics... => 1020
[10,7] generating graphics... => 1155
[10,6,1] generating graphics... => 1176
[10,5,2] generating graphics... => 1191
[10,5,1,1] generating graphics... => 1183
[10,4,3] generating graphics... => 1200
[10,4,2,1] generating graphics... => 1191
[10,4,1,1,1] generating graphics... => 1176
[10,3,3,1] generating graphics... => 1195
[10,3,2,2] generating graphics... => 1191
[10,3,2,1,1] generating graphics... => 1179
[10,3,1,1,1,1] generating graphics... => 1155
[10,2,2,2,1] generating graphics... => 1176
[10,2,2,1,1,1] generating graphics... => 1155
[10,2,1,1,1,1,1] generating graphics... => 1120
[10,1,1,1,1,1,1,1] generating graphics... => 1071
[9,8] generating graphics... => 1200
[9,7,1] generating graphics... => 1232
[9,6,2] generating graphics... => 1256
[9,6,1,1] generating graphics... => 1248
[9,5,3] generating graphics... => 1272
[9,5,2,1] generating graphics... => 1263
[9,5,1,1,1] generating graphics... => 1248
[9,4,4] generating graphics... => 1280
[9,4,3,1] generating graphics... => 1272
[9,4,2,2] generating graphics... => 1268
[9,4,2,1,1] generating graphics... => 1256
[9,4,1,1,1,1] generating graphics... => 1232
[9,3,3,2] generating graphics... => 1272
[9,3,3,1,1] generating graphics... => 1260
[9,3,2,2,1] generating graphics... => 1256
[9,3,2,1,1,1] generating graphics... => 1235
[9,3,1,1,1,1,1] generating graphics... => 1200
[9,2,2,2,2] generating graphics... => 1248
[9,2,2,2,1,1] generating graphics... => 1232
[9,2,2,1,1,1,1] generating graphics... => 1200
[9,2,1,1,1,1,1,1] generating graphics... => 1152
[9,1,1,1,1,1,1,1,1] generating graphics... => 1088
[8,8,1] generating graphics... => 1260
[8,7,2] generating graphics... => 1295
[8,7,1,1] generating graphics... => 1287
[8,6,3] generating graphics... => 1320
[8,6,2,1] generating graphics... => 1311
[8,6,1,1,1] generating graphics... => 1296
[8,5,4] generating graphics... => 1335
[8,5,3,1] generating graphics... => 1327
[8,5,2,2] generating graphics... => 1323
[8,5,2,1,1] generating graphics... => 1311
[8,5,1,1,1,1] generating graphics... => 1287
[8,4,4,1] generating graphics... => 1335
[8,4,3,2] generating graphics... => 1332
[8,4,3,1,1] generating graphics... => 1320
[8,4,2,2,1] generating graphics... => 1316
[8,4,2,1,1,1] generating graphics... => 1295
[8,4,1,1,1,1,1] generating graphics... => 1260
[8,3,3,3] generating graphics... => 1335
[8,3,3,2,1] generating graphics... => 1320
[8,3,3,1,1,1] generating graphics... => 1299
[8,3,2,2,2] generating graphics... => 1311
[8,3,2,2,1,1] generating graphics... => 1295
[8,3,2,1,1,1,1] generating graphics... => 1263
[8,3,1,1,1,1,1,1] generating graphics... => 1215
[8,2,2,2,2,1] generating graphics... => 1287
[8,2,2,2,1,1,1] generating graphics... => 1260
[8,2,2,1,1,1,1,1] generating graphics... => 1215
[8,2,1,1,1,1,1,1,1] generating graphics... => 1152
[8,1,1,1,1,1,1,1,1,1] generating graphics... => 1071
[7,7,3] generating graphics... => 1344
[7,7,2,1] generating graphics... => 1335
[7,7,1,1,1] generating graphics... => 1320
[7,6,4] generating graphics... => 1368
[7,6,3,1] generating graphics... => 1360
[7,6,2,2] generating graphics... => 1356
[7,6,2,1,1] generating graphics... => 1344
[7,6,1,1,1,1] generating graphics... => 1320
[7,5,5] generating graphics... => 1380
[7,5,4,1] generating graphics... => 1375
[7,5,3,2] generating graphics... => 1372
[7,5,3,1,1] generating graphics... => 1360
[7,5,2,2,1] generating graphics... => 1356
[7,5,2,1,1,1] generating graphics... => 1335
[7,5,1,1,1,1,1] generating graphics... => 1300
[7,4,4,2] generating graphics... => 1380
[7,4,4,1,1] generating graphics... => 1368
[7,4,3,3] generating graphics... => 1380
[7,4,3,2,1] generating graphics... => 1365
[7,4,3,1,1,1] generating graphics... => 1344
[7,4,2,2,2] generating graphics... => 1356
[7,4,2,2,1,1] generating graphics... => 1340
[7,4,2,1,1,1,1] generating graphics... => 1308
[7,4,1,1,1,1,1,1] generating graphics... => 1260
[7,3,3,3,1] generating graphics... => 1368
[7,3,3,2,2] generating graphics... => 1360
[7,3,3,2,1,1] generating graphics... => 1344
[7,3,3,1,1,1,1] generating graphics... => 1312
[7,3,2,2,2,1] generating graphics... => 1335
[7,3,2,2,1,1,1] generating graphics... => 1308
[7,3,2,1,1,1,1,1] generating graphics... => 1263
[7,3,1,1,1,1,1,1,1] generating graphics... => 1200
[7,2,2,2,2,2] generating graphics... => 1320
[7,2,2,2,2,1,1] generating graphics... => 1300
[7,2,2,2,1,1,1,1] generating graphics... => 1260
[7,2,2,1,1,1,1,1,1] generating graphics... => 1200
[7,2,1,1,1,1,1,1,1,1] generating graphics... => 1120
[7,1,1,1,1,1,1,1,1,1,1] generating graphics... => 1020
[6,6,5] generating graphics... => 1400
[6,6,4,1] generating graphics... => 1395
[6,6,3,2] generating graphics... => 1392
[6,6,3,1,1] generating graphics... => 1380
[6,6,2,2,1] generating graphics... => 1376
[6,6,2,1,1,1] generating graphics... => 1355
[6,6,1,1,1,1,1] generating graphics... => 1320
[6,5,5,1] generating graphics... => 1407
[6,5,4,2] generating graphics... => 1407
[6,5,4,1,1] generating graphics... => 1395
[6,5,3,3] generating graphics... => 1407
[6,5,3,2,1] generating graphics... => 1392
[6,5,3,1,1,1] generating graphics... => 1371
[6,5,2,2,2] generating graphics... => 1383
[6,5,2,2,1,1] generating graphics... => 1367
[6,5,2,1,1,1,1] generating graphics... => 1335
[6,5,1,1,1,1,1,1] generating graphics... => 1287
[6,4,4,3] generating graphics... => 1415
[6,4,4,2,1] generating graphics... => 1400
[6,4,4,1,1,1] generating graphics... => 1379
[6,4,3,3,1] generating graphics... => 1400
[6,4,3,2,2] generating graphics... => 1392
[6,4,3,2,1,1] generating graphics... => 1376
[6,4,3,1,1,1,1] generating graphics... => 1344
[6,4,2,2,2,1] generating graphics... => 1367
[6,4,2,2,1,1,1] generating graphics... => 1340
[6,4,2,1,1,1,1,1] generating graphics... => 1295
[6,4,1,1,1,1,1,1,1] generating graphics... => 1232
[6,3,3,3,2] generating graphics... => 1395
[6,3,3,3,1,1] generating graphics... => 1379
[6,3,3,2,2,1] generating graphics... => 1371
[6,3,3,2,1,1,1] generating graphics... => 1344
[6,3,3,1,1,1,1,1] generating graphics... => 1299
[6,3,2,2,2,2] generating graphics... => 1355
[6,3,2,2,2,1,1] generating graphics... => 1335
[6,3,2,2,1,1,1,1] generating graphics... => 1295
[6,3,2,1,1,1,1,1,1] generating graphics... => 1235
[6,3,1,1,1,1,1,1,1,1] generating graphics... => 1155
[6,2,2,2,2,2,1] generating graphics... => 1320
[6,2,2,2,2,1,1,1] generating graphics... => 1287
[6,2,2,2,1,1,1,1,1] generating graphics... => 1232
[6,2,2,1,1,1,1,1,1,1] generating graphics... => 1155
[6,2,1,1,1,1,1,1,1,1,1] generating graphics... => 1056
[6,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 935
[5,5,5,2] generating graphics... => 1428
[5,5,5,1,1] generating graphics... => 1416
[5,5,4,3] generating graphics... => 1431
[5,5,4,2,1] generating graphics... => 1416
[5,5,4,1,1,1] generating graphics... => 1395
[5,5,3,3,1] generating graphics... => 1416
[5,5,3,2,2] generating graphics... => 1408
[5,5,3,2,1,1] generating graphics... => 1392
[5,5,3,1,1,1,1] generating graphics... => 1360
[5,5,2,2,2,1] generating graphics... => 1383
[5,5,2,2,1,1,1] generating graphics... => 1356
[5,5,2,1,1,1,1,1] generating graphics... => 1311
[5,5,1,1,1,1,1,1,1] generating graphics... => 1248
[5,4,4,4] generating graphics... => 1440
[5,4,4,3,1] generating graphics... => 1424
[5,4,4,2,2] generating graphics... => 1416
[5,4,4,2,1,1] generating graphics... => 1400
[5,4,4,1,1,1,1] generating graphics... => 1368
[5,4,3,3,2] generating graphics... => 1416
[5,4,3,3,1,1] generating graphics... => 1400
[5,4,3,2,2,1] generating graphics... => 1392
[5,4,3,2,1,1,1] generating graphics... => 1365
[5,4,3,1,1,1,1,1] generating graphics... => 1320
[5,4,2,2,2,2] generating graphics... => 1376
[5,4,2,2,2,1,1] generating graphics... => 1356
[5,4,2,2,1,1,1,1] generating graphics... => 1316
[5,4,2,1,1,1,1,1,1] generating graphics... => 1256
[5,4,1,1,1,1,1,1,1,1] generating graphics... => 1176
[5,3,3,3,3] generating graphics... => 1416
[5,3,3,3,2,1] generating graphics... => 1395
[5,3,3,3,1,1,1] generating graphics... => 1368
[5,3,3,2,2,2] generating graphics... => 1380
[5,3,3,2,2,1,1] generating graphics... => 1360
[5,3,3,2,1,1,1,1] generating graphics... => 1320
[5,3,3,1,1,1,1,1,1] generating graphics... => 1260
[5,3,2,2,2,2,1] generating graphics... => 1344
[5,3,2,2,2,1,1,1] generating graphics... => 1311
[5,3,2,2,1,1,1,1,1] generating graphics... => 1256
[5,3,2,1,1,1,1,1,1,1] generating graphics... => 1179
[5,3,1,1,1,1,1,1,1,1,1] generating graphics... => 1080
[5,2,2,2,2,2,2] generating graphics... => 1320
[5,2,2,2,2,2,1,1] generating graphics... => 1296
[5,2,2,2,2,1,1,1,1] generating graphics... => 1248
[5,2,2,2,1,1,1,1,1,1] generating graphics... => 1176
[5,2,2,1,1,1,1,1,1,1,1] generating graphics... => 1080
[5,2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 960
[5,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 816
[4,4,4,4,1] generating graphics... => 1440
[4,4,4,3,2] generating graphics... => 1431
[4,4,4,3,1,1] generating graphics... => 1415
[4,4,4,2,2,1] generating graphics... => 1407
[4,4,4,2,1,1,1] generating graphics... => 1380
[4,4,4,1,1,1,1,1] generating graphics... => 1335
[4,4,3,3,3] generating graphics... => 1428
[4,4,3,3,2,1] generating graphics... => 1407
[4,4,3,3,1,1,1] generating graphics... => 1380
[4,4,3,2,2,2] generating graphics... => 1392
[4,4,3,2,2,1,1] generating graphics... => 1372
[4,4,3,2,1,1,1,1] generating graphics... => 1332
[4,4,3,1,1,1,1,1,1] generating graphics... => 1272
[4,4,2,2,2,2,1] generating graphics... => 1356
[4,4,2,2,2,1,1,1] generating graphics... => 1323
[4,4,2,2,1,1,1,1,1] generating graphics... => 1268
[4,4,2,1,1,1,1,1,1,1] generating graphics... => 1191
[4,4,1,1,1,1,1,1,1,1,1] generating graphics... => 1092
[4,3,3,3,3,1] generating graphics... => 1407
[4,3,3,3,2,2] generating graphics... => 1395
[4,3,3,3,2,1,1] generating graphics... => 1375
[4,3,3,3,1,1,1,1] generating graphics... => 1335
[4,3,3,2,2,2,1] generating graphics... => 1360
[4,3,3,2,2,1,1,1] generating graphics... => 1327
[4,3,3,2,1,1,1,1,1] generating graphics... => 1272
[4,3,3,1,1,1,1,1,1,1] generating graphics... => 1195
[4,3,2,2,2,2,2] generating graphics... => 1335
[4,3,2,2,2,2,1,1] generating graphics... => 1311
[4,3,2,2,2,1,1,1,1] generating graphics... => 1263
[4,3,2,2,1,1,1,1,1,1] generating graphics... => 1191
[4,3,2,1,1,1,1,1,1,1,1] generating graphics... => 1095
[4,3,1,1,1,1,1,1,1,1,1,1] generating graphics... => 975
[4,2,2,2,2,2,2,1] generating graphics... => 1287
[4,2,2,2,2,2,1,1,1] generating graphics... => 1248
[4,2,2,2,2,1,1,1,1,1] generating graphics... => 1183
[4,2,2,2,1,1,1,1,1,1,1] generating graphics... => 1092
[4,2,2,1,1,1,1,1,1,1,1,1] generating graphics... => 975
[4,2,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 832
[4,1,1,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 663
[3,3,3,3,3,2] generating graphics... => 1400
[3,3,3,3,3,1,1] generating graphics... => 1380
[3,3,3,3,2,2,1] generating graphics... => 1368
[3,3,3,3,2,1,1,1] generating graphics... => 1335
[3,3,3,3,1,1,1,1,1] generating graphics... => 1280
[3,3,3,2,2,2,2] generating graphics... => 1344
[3,3,3,2,2,2,1,1] generating graphics... => 1320
[3,3,3,2,2,1,1,1,1] generating graphics... => 1272
[3,3,3,2,1,1,1,1,1,1] generating graphics... => 1200
[3,3,3,1,1,1,1,1,1,1,1] generating graphics... => 1104
[3,3,2,2,2,2,2,1] generating graphics... => 1295
[3,3,2,2,2,2,1,1,1] generating graphics... => 1256
[3,3,2,2,2,1,1,1,1,1] generating graphics... => 1191
[3,3,2,2,1,1,1,1,1,1,1] generating graphics... => 1100
[3,3,2,1,1,1,1,1,1,1,1,1] generating graphics... => 983
[3,3,1,1,1,1,1,1,1,1,1,1,1] generating graphics... => 840
[3,2,2,2,2,2,2,2] generating graphics... => 1260
[3,2,2,2,2,2,2,1,1] generating graphics... => 1232
[3,2,2,2,2,2,1,1,1,1] generating graphics... => 1176
[3,2,2,2,2,1,1,1,1,1,1] generating graphics... => 1092
[3,2,2,2,1,1,1,1,1,1,1,1] generating graphics... => 980
[3,2,2,1,1,1,1,1,1,1,1,1,1] generating graphics... => 840
click to show generating function       
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)

Created
May 07, 2018 at 20:47 by Christian Stump
Updated
May 07, 2018 at 20:47 by Christian Stump