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Solution Counts For Inhomogeneous Sets

These are configuration counts for various inhomogeneous dice sets (as found via exhaustive computer search), either with mirror-symmetry or no such restriction (note that column-grouped and column-paired symmetry can only happen with homogeneous sets). These counts avoid equivalent sets where the dice are simply relabeled. In other words, these counts assume that, if a and b are equal sized dice, then in the string representation of a solution the first “a” appears before the first “b”.

Tallies marked with the notation “ASA” denote counts that were found using the high performance computing cluster at the Alabama Supercompter Authority (this work was made possible in part by a grant of high performance computing resources and technical support from the Alabama Supercomputer Authority).

	Mirrored	Unmirrored
2-2	1	1
2-2-3	0	0
2-2-6	0	0
2-2-12	0	0
2-2-15	0	0
2-2-18	0	0
2-2-24	0	0
2-2-30	0	0
2-2-36	0	0
2-2-40	0	0
2-2-48	0	0
2-2-60	0	0
2-2-72	0	0
2-2-120	0	0
2-3	2	2
2-3-4	0	0
2-3-6	0	0
2-3-8	0	0
2-3-10	0	0
2-3-12	0	0
2-3-20	0	0
2-3-24	0	0
2-3-30	0	0
2-3-40	0	0
2-3-48	0	0
2-3-60	0	0
2-3-120	0	0
2-4	3	3
2-4-5	0	0
2-4-6	3	3
2-4-6-6	0	0
2-4-6-12	0	0
2-4-6-15	0	0
2-4-6-24	0	0
2-4-6-30	0	0
2-4-6-48	0	0
2-4-6-60	0	0
2-4-6-120	0	0
2-4-12	5	5
2-4-12-12	0	0
2-4-12-15	0	0
2-4-12-24	0	0
2-4-12-30	0	0
2-4-12-48	0	0
2-4-12-60	0	0
2-4-12-120	0	0
2-4-15	0	0
2-4-24	9	9
2-4-24-24	0	0
2-4-24-30	0	0
2-4-24-48	0	0
2-4-24-60	0	0
2-4-24-120	0	0
2-4-30	11	11
2-4-30-30	0	0
2-4-30-48	0	0
2-4-30-60	0	0
2-4-30-120	0	0
2-4-48	17	17
2-4-48-48	0	0
2-4-48-60	0	0
2-4-48-120	0	0
2-4-60	21	21
2-4-60-60	0	0
2-4-60-120	0
2-4-120	41	41
2-4-120-120	0
2-5	3	3
2-5-6	0	0
2-5-12	0	0
2-5-18	0	70
2-5-24	0	0
2-5-30	0	0
2-5-48	0	0
2-5-60	0	0
2-5-120	0	0
2-6	4	4
2-6-6	0	0
2-6-8	6	8
2-6-8-12	0	0
2-6-8-15	0	0
2-6-8-24	0	0
2-6-8-30	0	0
2-6-8-48	0	0
2-6-8-60	0	0
2-6-8-120	0	0
2-6-9	0	0
2-6-10	0	0
2-6-12	10	18
2-6-12-12	0	0
2-6-12-15	0	0
2-6-12-20	0	0
2-6-12-24	0	0
2-6-12-30	0	0
2-6-12-40	0	0
2-6-12-48	0	0
2-6-12-60	0	0
2-6-12-120	0	0
2-6-15	0	0
2-6-20	21	55
2-6-20-24	0	0
2-6-20-30	0	0
2-6-20-48	0	0
2-6-20-60	0	0
2-6-20-120	0
2-6-24	28	86
2-6-24-24	0	0
2-6-24-30	0	0
2-6-24-40	0	0
2-6-24-48	0	0
2-6-24-60	0	0
2-6-24-120	0	0
2-6-30	0	0
2-6-40	66	318
2-6-40-48	0	0
2-6-40-60	0	0
2-6-40-120	0
2-6-48	91	519
2-6-48-48	0
2-6-48-60	0
2-6-48-120	0
2-6-60	136	956
2-6-60-60	0
2-6-60-120
2-6-120		6786
2-6-120-120
2-7	0	4
2-8		5
2-8-12		33
2-8-12-12	0	0
2-8-12-15	0	0
2-8-12-24	0	0
2-8-12-30	0	0
2-8-12-48	0	0
2-8-12-60	0	0
2-8-12-120	0	0
2-8-15	0	0
2-8-24		177
2-8-24-24	0	0
2-8-24-30	0	0
2-8-24-48	0	0
2-8-24-60	0	0
2-8-24-120
2-8-30		318
2-8-30-30	0	0
2-8-30-48	0	0
2-8-30-60
2-8-30-120
2-8-48		1143
2-8-48-48
2-8-48-60
2-8-48-120
2-8-60		2135
2-8-60-60
2-8-60-120
2-8-120		15603
2-8-120-120
2-9		5
2-9-10		186
2-10	6	6
2-10-12	0	0
2-10-15	0	0
2-10-18	112	7672
2-10-24	0	0
2-10-30	0	0
2-10-48	0	0
2-10-60	0	0
2-10-120
2-12	7	7
2-12-12	35	151
2-12-12-12	0	0
2-12-12-20	0	0
2-12-12-24	0	0
2-12-12-30	0	0
2-12-12-40	0	0
2-12-12-48	0	0
2-12-12-60	0	0
2-12-12-120
2-12-15	0	0
2-12-18	84	676
2-12-20		1514
2-12-20-24	0	0
2-12-20-30	0	0
2-12-20-48	0	0
2-12-20-60
2-12-20-120
2-12-24		5925
2-12-24-24	0	0
2-12-24-30	0	0
2-12-24-40
2-12-24-48
2-12-24-60
2-12-24-120
2-12-30		5444
2-12-30-30
2-12-30-40
2-12-30-48
2-12-30-60
2-12-30-120
2-12-40		61731
2-12-40-48
2-12-40-60
2-12-40-120
2-12-48		221825
2-12-48-48
2-12-48-60
2-12-48-120
2-12-60
2-12-60-60
2-12-60-120
2-12-120
2-12-120-120
2-15		8
2-15-20	0	0
2-15-24	0	0
2-15-30	0	0
2-15-40
2-15-48
2-15-60
2-15-120
2-20	11	11
2-20-24
2-20-30
2-20-48
2-20-60
2-20-120
2-24	13	13
2-24-24	3003	553981
2-24-24-24	0	0
2-24-24-30
2-24-30
2-24-40
2-24-48
2-24-60	720544
2-24-60-60	0
2-24-60-120
2-24-120
2-30	16	16
2-30-30	0
2-30-40
2-30-48
2-30-60
2-30-120
2-40	21	21
2-40-48
2-40-60
2-40-120
2-48	25	25
2-48-48
2-48-60
2-48-120
2-60	31	31
2-60-60
2-60-120
2-120	61	61
2-120-120
3-4		5
3-4-4		0
3-4-6		12
3-4-6-6		0
3-4-6-8		0
3-4-6-10		0
3-4-6-12		0
3-4-6-20		0
3-4-6-24		0
3-4-6-30		0
3-4-6-40		0
3-4-6-48		0
3-4-6-60		0
3-4-6-120		0
3-4-8		0
3-4-10		0
3-4-12		44
3-4-12-12		0
3-4-12-20		0
3-4-12-24		0
3-4-12-30		0
3-4-12-40		0
3-4-12-48		0
3-4-12-60		0
3-4-12-120
3-4-20		0
3-4-24		206
3-4-24-24		0
3-4-24-30		0
3-4-24-40		0
3-4-24-48
3-4-24-60
3-4-24-120
3-4-30		354
3-4-30-30
3-4-30-40
3-4-30-48
3-4-30-60
3-4-30-120
3-4-40		0
3-4-48		1226
3-4-48-48
3-4-48-60
3-4-48-120
3-4-60		2252
3-4-60-60
3-4-60-120
3-4-120		15902
3-4-120-120
3-6		8
3-6-6		0
3-6-8		33
3-6-8-8		0
3-6-8-10		0
3-6-8-12		0
3-6-8-20		0
3-6-8-24		0
3-6-8-30		0
3-6-8-40		0
3-6-8-48		0
3-6-8-60		0
3-6-8-120
3-6-10		0
3-6-12		74
3-6-12-12		0
3-6-12-20		0
3-6-12-24		0
3-6-12-30		0
3-6-12-40		0
3-6-12-48		0
3-6-12-60
3-6-12-120
3-6-20		320
3-6-20-20		0
3-6-20-24		0
3-6-20-30		0
3-6-20-40
3-6-20-48
3-6-20-60
3-6-20-120
3-6-24		592
3-6-24-24
3-6-24-30		0
3-6-24-40
3-6-24-48
3-6-24-60
3-6-24-120
3-6-30		0
3-6-40		4099
3-6-40-40
3-6-40-48
3-6-40-60
3-6-40-120
3-6-48		8719
3-6-48-48
3-6-48-60
3-6-48-120
3-6-60		22730
3-6-60-60
3-6-60-120
3-6-120		529798
3-6-120-120
3-8		13
3-8-8		0
3-8-10		10
3-8-10-12		0
3-8-10-24		0
3-8-10-30		0
3-8-10-48		0
3-8-10-60		0
3-8-10-120
3-8-12		429
3-8-12-12		0
3-8-12-20		0
3-8-12-24		0
3-8-12-30		0
3-8-12-40
3-8-12-48
3-8-12-60
3-8-12-120
3-8-20		30
3-8-20-24		0
3-8-20-30		0
3-8-20-48
3-8-20-60
3-8-20-120
3-8-24		8435
3-8-24-24
3-8-24-30
3-8-24-40
3-8-24-48
3-8-24-60
3-8-24-120
3-8-30		30334
3-8-30-30
3-8-30-40
3-8-30-48
3-8-30-60
3-8-30-120
3-8-40		22968
3-8-40-48
3-8-40-60
3-8-40-120
3-8-48		400548
3-8-48-48
3-8-48-60
3-8-48-120
3-8-60
3-8-60-60
3-8-60-120
3-8-120
3-8-120-120
3-10		18
3-10-12		827
3-10-12-12		0
3-10-12-20		0
3-10-12-24		0
3-10-12-30		0
3-10-12-40
3-10-12-48
3-10-12-60
3-10-12-120
3-10-20		8962
3-10-20-24
3-10-20-30
3-10-20-48
3-10-20-60
3-10-20-120
3-10-24		121097
3-10-24-24
3-10-24-30
3-10-24-40
3-10-24-48
3-10-24-60
3-10-24-120
3-10-30		155200
3-10-30-30
3-10-30-40
3-10-30-48
3-10-30-60
3-10-30-120
3-10-40		1106314
3-10-40-48
3-10-40-60
3-10-40-120
3-10-48		19765498
3-10-48-48
3-10-48-60
3-10-48-120
3-10-60
3-10-60-60
3-10-60-120
3-10-120
3-10-120-120
3-12		25
3-20		61
3-24		85
3-30		128
3-40		221
3-48		313
3-60		481
3-120		1861
4	1	1
4-4	3	4
4-4-6	3	4
4-4-6-6	0	0
4-4-6-12	0	0
4-4-6-18	0	0
4-4-6-18-30	0	0
4-4-6-24	0	0
4-4-6-30	0	0
4-4-9		10
4-4-12	5	15
4-4-12-12	0	0
4-4-12-18	0	0
4-4-12-18-30	0	0
4-4-12-24	0	0
4-4-12-30	0	0
4-4-18	7	68
4-4-18-18	0	0
4-4-18-24	0	0
4-4-18-30	0	0
4-4-24	9	118
4-4-24-24	0	0
4-4-24-30	0	0
4-4-24-30-30	0	0
4-4-30	11	211
4-4-30-30	0	0
4-4-30-30-30	0	0
4-4-30-36	0
4-4-30-36-36	0
4-6	10	18
4-5-6	0	2
4-5-6-6	0	0
4-5-6-12	0	0
4-5-6-18	0	0
4-5-6-24	0	0
4-5-6-30	0	0
4-5-6-36	0	0
4-6-6	6	35
4-6-6-6	0	0
4-6-6-7	0	0
4-6-6-8	0	0
4-6-6-10	0	0
4-6-6-12	0	0
4-6-6-18	0	0
4-6-6-20	0	0
4-6-6-24	0	0
4-6-6-30	0	0
4-6-7	0	8
4-6-7-8		0
4-6-7-10		0
4-6-7-12		0
4-6-7-18		0
4-6-7-24		0
4-6-7-30		0
4-6-7-36		0
4-6-7-48		0
4-6-7-60		0
4-6-8	15	37
4-6-8-12	9	27
4-6-8-18	0	0
4-6-8-24	30	200
4-6-8-30	0	0
4-6-9		142
4-6-10	15	59
4-6-10-12	0	0
4-6-10-18	0	0
4-6-10-24	0	0
4-6-10-30	0	0
4-6-10-36	383
4-6-10-36-36	0
4-6-12	35	601
4-6-12-12	0	0
4-6-12-18	0	0
4-6-12-20	0	0
4-6-12-24	54	972
4-6-12-30	0	0
4-6-18	59	2775
4-6-18-18	0	0
4-6-18-18-20	0	0
4-6-18-18-30	0	0
4-6-18-20	645	83061
4-6-18-20-24	0	0
4-6-18-20-30	0	0
4-6-18-20-36	0
4-6-18-24	0	0
4-6-18-24-30	0	0
4-6-18-30	0	0
4-6-18-30-30	0	0
4-6-20	73	873
4-6-20-24	0	0
4-6-20-30	0	0
4-6-20-36	30406
4-6-20-36-36	0
4-6-24	119	10191
4-6-24-24	906	205209
4-6-24-24-30	0	0
4-6-24-30	0	0
4-6-24-30-30	0	0
4-6-30	168	28616
4-6-30-30	0	0
4-6-30-30-30	0	0
4-6-30-36	1041053
4-6-30-36-36	0
4-8	15	33
4-8-9		372
4-8-12	41	577
4-8-12-12	15	45
4-8-12-12-30	0	0
4-8-12-18	21	63
4-8-12-18-30	0	0
4-8-12-24	102	906
4-8-12-24-30	0	0
4-8-12-30	33	99
4-8-12-30-30	0	0
4-8-12-30-36	0
4-8-18	115	7509
4-8-18-18	0	0
4-8-18-18-30	0	0
4-8-18-24	704	16286
4-8-18-24-30	0	0
4-8-18-30	0	0
4-8-18-30-30	0	0
4-8-18-30-36	0	0
4-8-24	156	28878
4-8-24-24	225	4425
4-8-24-24-30	0	0
4-8-24-30	330
4-8-24-30-30	0
4-8-24-30-36	0
4-8-30	275	122419
4-8-30-30	5464
4-8-30-30-30	0
4-8-30-30-36	0
4-8-30-36	2002
4-8-30-36-36	0
4-9		43
4-9-10		1041
4-10	21	55
4-10-12	83	2755
4-10-12-12	0	0
4-10-12-12-12	0	0
4-10-12-12-18	0	0
4-10-12-12-24	0	0
4-10-12-12-30	0	0
4-10-12-18	0	0
4-10-12-18-18	0	0
4-10-12-18-24	0	0
4-10-12-18-30	0	0
4-10-12-24	0	0
4-10-12-24-24	0	0
4-10-12-24-30	0	0
4-10-12-30	486
4-10-12-30-30	0
4-10-12-30-36	0
4-10-12-36	1040
4-10-12-36-36	0
4-10-18	314	70002
4-10-18-18	44	724
4-10-18-18-18	0
4-10-18-18-24	0
4-10-18-18-30	0
4-10-18-18-36	0
4-10-18-24	0
4-10-18-24-24	0
4-10-18-24-30	0
4-10-18-24-36	0
4-10-18-30	0
4-10-18-30-30	0
4-10-18-30-36	0
4-10-18-36	3204
4-10-18-36-36	0
4-10-24	619	261413
4-10-24-24	0
4-10-24-24-24	0
4-10-24-24-30	0
4-10-24-24-36	0
4-10-24-30	26961
4-10-24-30-30	0
4-10-24-30-36	0
4-10-24-36	3930
4-10-24-36-36	0
4-10-30	519	1349357
4-10-30-30	0
4-10-30-30-30	0
4-10-30-30-36	0
4-10-30-36	526410
4-10-30-36-36	0
4-10-36	5971
4-10-36-36	21588
4-10-36-36-36	0
4-12	28	86
4-12-12	66	11857
4-12-12-12	0	0
4-12-12-12-20	0	0
4-12-12-12-30	0	0
4-12-12-18	0
4-12-12-18-20	0	0
4-12-12-18-30	0
4-12-12-20	0	0
4-12-12-20-24	0	0
4-12-12-20-30	0	0
4-12-12-24	90
4-12-12-24-30	0
4-12-12-30	0
4-12-12-30-30	0
4-12-12-30-36	0
4-12-18	503	447159
4-12-18-18	0
4-12-18-18-20	0
4-12-18-18-30	0
4-12-18-20	1220
4-12-18-20-24	0
4-12-18-20-30	0
4-12-18-20-36	0
4-12-18-24	126
4-12-18-24-30	0
4-12-18-30	0
4-12-18-30-30	0
4-12-18-30-36	0
4-12-20	1038	430356
4-12-20-24	0
4-12-20-24-24	0
4-12-20-24-30	0
4-12-20-24-36	0
4-12-20-30	28955
4-12-20-30-30	0
4-12-20-30-36	0
4-12-20-36	64860
4-12-20-36-36	0
4-12-24	1192	4748150
4-12-24-24	2427
4-12-24-24-30	0
4-12-24-30	198
4-12-24-30-30	0
4-12-24-30-36	0
4-12-30	5545	38757705
4-12-30-30	468120
4-12-30-30-30	0
4-12-30-30-36	0
4-12-30-36	2245680
4-12-30-36-36	0
4-18	55	241
4-18-18	766	10940539
4-18-18-18	0
4-18-18-18-20	0
4-18-18-18-30	0
4-18-18-20	2615
4-18-18-20-24	0
4-18-18-20-30	0
4-18-18-20-36	0
4-18-18-24	0
4-18-18-24-30	0
4-18-18-30	2080
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8-10-12-24-24	0
8-10-12-24-30	0
8-10-12-24-36	0
8-10-12-30	3888
8-10-12-30-30	0
8-10-12-30-36	0
8-10-12-36	15089
8-10-12-36-36	0
8-10-18	2531
8-10-18-18	974
8-10-18-18-18	0
8-10-18-18-24	0
8-10-18-18-30	0
8-10-18-18-36	0
8-10-18-24	8440
8-10-18-24-24	0
8-10-18-24-30	0
8-10-18-24-36	0
8-10-18-30	19562
8-10-18-30-30	0
8-10-18-30-36	0
8-10-18-36	178587
8-10-18-36-36	0
8-10-24	6445
8-10-24-24	13363
8-10-24-24-24	0
8-10-24-24-30	0
8-10-24-24-36	0
8-10-24-30	260452
8-10-24-30-30	0
8-10-24-30-36	0
8-10-24-36	1131835
8-10-24-36-36	0
8-10-30	18327
8-10-30-30	518420
8-10-30-30-30	0
8-10-30-30-36	0
8-10-30-36	11137990
8-10-30-36-36
8-10-36	74384
8-10-36-36	52121489
8-10-36-36-36
8-12	210	3788
8-12-12	625	307548
8-12-12-12	328	6965
8-12-12-12-20	0	0
8-12-12-12-30	0
8-12-12-18	2767
8-12-12-18-20	0
8-12-12-18-30	0
8-12-12-20	653
8-12-12-20-24	0
8-12-12-20-30	0
8-12-12-20-36	0
8-12-12-24	12248
8-12-12-24-30	0
8-12-12-30	29938
8-12-12-30-30	0
8-12-12-30-36	0
8-12-18	6542
8-12-18-18	11963
8-12-18-18-20	0
8-12-18-18-30	0
8-12-18-20	12371
8-12-18-20-24	0
8-12-18-20-30	0
8-12-18-20-36	0
8-12-18-24	165849
8-12-18-24-30	0
8-12-18-30	439913
8-12-18-30-30	0
8-12-18-30-36	0
8-12-20	8658
8-12-20-24	39687
8-12-20-24-24	0
8-12-20-24-30	0
8-12-20-24-36	0
8-12-20-30	283889
8-12-20-30-30	0
8-12-20-30-36	0
8-12-20-36	1073339
8-12-20-36-36	0
8-12-24	24198
8-12-24-24	485145
8-12-24-24-30	0
8-12-24-30	5253540
8-12-24-30-30	0
8-12-24-30-36	0
8-12-30	89350
8-12-30-30	16397774
8-12-30-30-30
8-12-30-30-36
8-12-30-36
8-12-30-36-36
8-18	715	33885
8-18-18	22605
8-18-18-18	23386
8-18-18-18-20	0
8-18-18-18-30	0
8-18-18-20	79277
8-18-18-20-24	0
8-18-18-20-30	0
8-18-18-20-36	0
8-18-18-24	814841
8-18-18-24-30	0
8-18-18-30	2956398
8-18-18-30-30	0
8-18-18-30-36
8-18-20	90268
8-18-20-24	589197
8-18-20-24-24	0
8-18-20-24-30	0
8-18-20-24-36	0
8-18-20-30	2743669
8-18-20-30-30
8-18-20-30-36
8-18-20-36
8-18-20-36-36
8-18-24	306739
8-18-24-24	6670064
8-18-24-24-30	0
8-18-24-30	91892106
8-18-24-30-30
8-18-24-30-36
8-18-30	1400864
8-18-30-30
8-18-30-30-30
8-18-30-30-36
8-18-30-36
8-18-30-36-36
8-20	1001	61731
8-20-24	504860
8-20-24-24	1381310
8-20-24-24-24	0
8-20-24-24-30	0
8-20-24-24-36	0
8-20-24-30	34725072
8-20-24-30-30
8-20-24-30-36
8-20-24-36
8-20-24-36-36
8-20-30	2673462
8-20-30-30
8-20-30-30-30
8-20-30-30-36
8-20-30-36
8-20-30-36-36
8-20-36
8-20-36-36
8-20-36-36-36
8-24	1820	178870
8-24-24	1238512
8-24-24-24	23371502
8-24-24-24-30
8-24-24-30
8-24-24-30-30
8-24-24-30-36
8-24-30	17164839
8-24-30-30
8-24-30-30-30
8-24-30-30-36
8-24-30-36
8-24-30-36-36
8-30	3876	684572
8-30-30	68381201
8-30-30-30
8-30-30-30-30
8-30-30-30-36
8-30-30-36
8-30-30-36-36
8-30-36
8-30-36-36
8-30-36-36-36
9-10		2934
9-10-10		30520
9-10-10-12		0
9-10-12		295001
9-10-12-12		5
9-10-12-12-12		0
9-10-12-12-16		0
9-10-12-12-18		0
9-10-12-16		2
9-12		8150
9-12-12		737488
9-12-12-12		8
9-12-12-12-20		0
10	1	1
10-10	126	2724
10-10-12	311	360112
10-10-12-12	45	127
10-10-12-12-12	0	0
10-10-12-12-18	0
10-10-12-12-24	0	0
10-10-12-12-30	0
10-10-12-12-36	0
10-10-12-18	212
10-10-12-18-18	0
10-10-12-18-24	0
10-10-12-18-30	0
10-10-12-18-36	0
10-10-12-24	1359
10-10-12-24-24	0
10-10-12-24-30	0
10-10-12-24-36	0
10-10-12-30	3604
10-10-12-30-30	0
10-10-12-30-36	0
10-10-12-36	13469
10-10-12-36-36	0
10-10-18	1758
10-10-18-18	681
10-10-18-18-18	0
10-10-18-18-24	0
10-10-18-18-30	0
10-10-18-18-36	0
10-10-18-24	5733
10-10-18-24-24	0
10-10-18-24-30	0
10-10-18-24-36	0
10-10-18-30	21435
10-10-18-30-30	0
10-10-18-30-36	0
10-10-18-36	108526
10-10-18-36-36	0
10-10-24	9243
10-10-24-24	33671
10-10-24-24-24	0
10-10-24-24-30	0
10-10-24-24-36	0
10-10-24-30	265021
10-10-24-30-30	0
10-10-24-30-36	0
10-10-24-36	1859255
10-10-24-36-36	0
10-10-30	17223
10-10-30-30	896500
10-10-30-30-30	0
10-10-30-30-36
10-10-30-36	9610260
10-10-30-36-36
10-10-36	122475
10-10-36-36	81438096
10-10-36-36-36
10-12	462	16660
10-12-12	1343	1842313
10-12-12-12	176	1946
10-12-12-12-12	0	0
10-12-12-12-14	0	0
10-12-12-12-16	0	0
10-12-12-12-18	0
10-12-12-12-20	0
10-12-12-12-24	0
10-12-12-12-30	0
10-12-12-12-36	0
10-12-12-18	1072
10-12-12-18-18	0
10-12-12-18-20	0
10-12-12-18-24	0
10-12-12-18-30	0
10-12-12-18-36	0
10-12-12-20	1600
10-12-12-20-24	0
10-12-12-20-30	0
10-12-12-20-36	0
10-12-12-24	8801
10-12-12-24-24	0
10-12-12-24-30	0
10-12-12-24-36	0
10-12-12-30	0
10-12-12-30-30	0
10-12-12-30-36	0
10-12-12-36	80751
10-12-12-36-36	0
10-12-18	12268
10-12-18-18	3010
10-12-18-18-18	0
10-12-18-18-20	0
10-12-18-18-24	0
10-12-18-18-30	0
10-12-18-18-36	0
10-12-18-20	15895
10-12-18-20-24	0
10-12-18-20-30	0
10-12-18-20-36	0
10-12-18-24	62657
10-12-18-24-24	0
10-12-18-24-30	0
10-12-18-24-36	0
10-12-18-30	206668
10-12-18-30-30	0
10-12-18-30-36	0
10-12-18-36	1107945
10-12-18-36-36
10-12-20	20818
10-12-20-24	136581
10-12-20-24-24	0
10-12-20-24-30	0
10-12-20-24-36	0
10-12-20-30	496931
10-12-20-30-30	0
10-12-20-30-36	0
10-12-20-36	3506563
10-12-20-36-36
10-12-24	73661
10-12-24-24	352140
10-12-24-24-24	0
10-12-24-24-30	0
10-12-24-24-36	0
10-12-24-30	3008637
10-12-24-30-30	0
10-12-24-30-36
10-12-24-36	19972152
10-12-24-36-36
10-12-30	217719
10-12-30-30	10101362
10-12-30-30-30	0
10-12-30-30-36
10-12-30-36	159273797
10-12-30-36-36
10-12-36
10-12-36-36	683904763
10-12-36-36-36
10-18	2002	246448
10-18-18	40658
10-18-18-18	11127
10-18-18-18-18	0
10-18-18-18-20	0
10-18-18-18-24	0
10-18-18-18-30	0
10-18-18-18-36	0
10-18-18-20	58443
10-18-18-20-24	0
10-18-18-20-30	0
10-18-18-20-36	0
10-18-18-24	228720
10-18-18-24-24	0
10-18-18-24-30	0
10-18-18-24-36	0
10-18-18-30	1451605
10-18-18-30-30	0
10-18-18-30-36
10-18-18-36
10-18-18-36-36
10-18-20	235477
10-18-20-24	1107386
10-18-20-24-24
10-18-20-24-30
10-18-20-24-36
10-18-20-30
10-18-20-30-30
10-18-20-30-36
10-18-20-36
10-18-20-36-36
10-18-24	921427
10-18-24-24	3261714
10-18-24-24-24	0
10-18-24-24-30
10-18-24-24-36
10-18-24-30
10-18-24-30-30
10-18-24-30-36
10-18-24-36
10-18-24-36-36
10-18-30	3405656
10-18-30-30
10-18-30-30-30
10-18-30-30-36
10-18-30-36
10-18-30-36-36
10-18-36
10-18-36-36
10-18-36-36-36
10-20	3003	517971
10-20-24	1863769
10-20-24-24
10-20-24-24-24
10-20-24-24-30
10-20-24-24-36
10-20-24-30
10-20-24-30-30
10-20-24-30-36
10-20-24-36
10-20-24-36-36
10-20-30	9919366
10-20-30-30
10-20-30-30-30
10-20-30-30-36
10-20-30-36
10-20-30-36-36
10-20-36
10-20-36-36
10-20-36-36-36
10-24	6188	1943488
10-24-24	4308149
10-24-24-24
10-24-24-24-24
10-24-24-24-30
10-24-24-24-36
10-24-24-30
10-24-24-30-30
10-24-24-30-36
10-24-24-36
10-24-24-36-36
10-24-30	62895459
10-24-30-30
10-24-30-30-30
10-24-30-30-36
10-24-30-36
10-24-30-36-36
10-24-36
10-24-36-36
10-24-36-36-36
10-30	15504	10388788
10-30-30	230472861
10-30-30-30
10-30-30-30-30
10-30-30-30-36
10-30-30-36
10-30-30-36-36
10-30-36
10-30-36-36
10-30-36-36-36
10-36
10-36-36
10-36-36-36
10-36-36-36-36
12	1	1
12-12	462	30554
12-12-12	916	3304324
12-12-12-12	187	3374
12-12-12-12-20	0	0
12-12-12-12-30	0	0
12-12-12-12-60	0
12-12-12-12-120	0
12-12-12-18	1984
12-12-12-18-20	0
12-12-12-18-30	0
12-12-12-20	4066
12-12-12-20-20	0
12-12-12-20-24	0
12-12-12-20-30	0
12-12-12-20-36	0
12-12-12-24	14112
12-12-12-24-30	0
12-12-12-30	32311
12-12-12-30-30	0
12-12-12-30-36	0
12-12-18	19574
12-12-18-18	6745
12-12-18-18-20	0
12-12-18-18-30	0
12-12-18-20	51451
12-12-18-20-20	0
12-12-18-20-24	0
12-12-18-20-30	0
12-12-18-20-36	0
12-12-18-24	187225
12-12-18-24-30	0
12-12-18-30	337217
12-12-18-30-30	0
12-12-18-30-36	0
12-12-20	37726
12-12-20-20	37621
12-12-20-20-24	0
12-12-20-20-30	0
12-12-20-20-36	0
12-12-20-24	373295
12-12-20-24-24	0
12-12-20-24-30	0
12-12-20-24-36	0
12-12-20-30	1600757
12-12-20-30-30	0
12-12-20-30-36	0
12-12-20-36	8097247
12-12-20-36-36
12-12-24	99029
12-12-24-24	833330
12-12-24-24-30	0
12-12-24-30	7528135
12-12-24-30-30	0
12-12-24-30-36
12-12-30	457830
12-12-30-30	16339852
12-12-30-30-30	0
12-12-30-30-36
12-12-30-36	344518964
12-12-30-36-36
12-14	1716
12-14-16	33963
12-14-16-18	15412
12-14-16-18-30	0
12-14-18	74268
12-14-18-18	21856
12-14-18-18-20	0
12-14-18-18-30	0
12-16	3003
12-16-16	39998
12-16-16-18	39159
12-16-16-18-30	0
12-16-18	192526
12-16-18-18	72513
12-16-18-18-20	0
12-16-18-18-30	0
12-18	5005	1437269
12-18-18	173402
12-18-18-18	28178
12-18-18-18-20	0
12-18-18-18-30	0
12-18-18-20	221505
12-18-18-20-20	0
12-18-18-20-24	0
12-18-18-20-30	0
12-18-18-20-36	0
12-18-18-24	1016185
12-18-18-24-30	0
12-18-18-30	3881336
12-18-18-30-30
12-18-18-30-36
12-18-20	816859
12-18-20-20	629205
12-18-20-20-24	0
12-18-20-20-30	0
12-18-20-20-36	0
12-18-20-24	5788394
12-18-20-24-24	0
12-18-20-24-30	0
12-18-20-24-36	0
12-18-20-30	22189274
12-18-20-30-30
12-18-20-30-36
12-18-20-36
12-18-20-36-36
12-18-24	3121342
12-18-24-24
12-18-24-24-30
12-18-24-30
12-18-24-30-30
12-18-24-30-36
12-18-30	16384598
12-18-30-30
12-18-30-30-30
12-18-30-30-36
12-18-30-36
12-18-30-36-36
12-20	8008	3451798
12-20-20	784320
12-20-20-24	6494305
12-20-20-24-24	0
12-20-20-24-30
12-20-20-24-36
12-20-20-30	50928390
12-20-20-30-30
12-20-20-30-36
12-20-20-36
12-20-20-36-36
12-20-24	7364896
12-20-24-24
12-20-24-24-24
12-20-24-24-30
12-20-24-24-36
12-20-24-30
12-20-24-30-30
12-20-24-30-36
12-20-24-36
12-20-24-36-36
12-20-30	45806720
12-20-30-30
12-20-30-30-30
12-20-30-30-36
12-20-30-36
12-20-30-36-36
12-20-36
12-20-36-36
12-20-36-36-36
12-24	18564	16509188
12-24-24	16250482
12-24-24-24	64924738
12-24-24-24-30
12-24-24-30
12-24-24-30-30
12-24-24-30-36
12-24-30	264300628
12-24-30-30
12-24-30-30-30
12-24-30-30-36
12-24-30-36
12-24-30-36-36
12-30	54264	121095602
12-30-30	1271061347
12-30-30-30
12-30-30-30-30
12-30-30-30-36
12-30-30-36
12-30-30-36-36
12-30-36
12-30-36-36
12-30-36-36-36
18	1	1
18-18	24310
18-18-18	767975
18-18-18-18	84588
18-18-18-18-20	0
18-18-18-18-30	0
18-18-18-20	668130
18-18-18-20-20	0
18-18-18-20-24	0
18-18-18-20-30	0
18-18-18-20-36	0
18-18-18-24	3159772
18-18-18-24-30	0 (ECH/ASA, 27 Feb 2023)
18-18-18-30	23795548
18-18-18-30-30	0
18-18-18-30-36	0 (ECH/ASA, 19 Mar 2023)
18-18-20	6658201
18-18-20-20	3232120
18-18-20-20-24	0 (ECH/ASA, 20 Mar 2023)
18-18-20-20-30	0 (ECH/ASA, 21 Mar 2023)
18-18-20-20-36	0 (ECH/ASA, 21 Mar 2023)
18-18-20-24	30352708
18-18-20-24-24	0 (ECH/ASA, 26 Mar 2023)
18-18-20-24-30	0 (ECH/ASA, 19 May 2023)
18-18-20-24-36	0 (ECH/ASA, 11 June 2023)
18-18-20-30	185097098 (ECH/ASA, 29 Mar 2023)
18-18-20-30-30	0 (ECH/ASA, 2 Jun 2023)
18-18-20-30-36
18-18-20-36	1935926005 (ECH/ASA, 30 Mar 2023)
18-18-20-36-36
18-18-24	32458818
18-18-24-24	94842699 (ECH/ASA, 27 Mar 2023)
18-18-24-24-30
18-18-24-30	1152297001 (ECH/ASA, 7 Apr 2023)
18-18-24-30-30
18-18-24-30-36
18-18-30	219417378
18-18-30-30
18-18-30-30-30
18-18-30-30-36
18-18-30-36
18-18-30-36-36
18-20	92378
18-20-20	16451144
18-20-20-24	74600925 (ECH/ASA, 26 Mar 2023)
18-20-20-24-24	0 (ECH/ASA, 9 Jun 2023)
18-20-20-24-30	0 (ECH/ASA, 5 Apr 2023)
18-20-20-24-36	0?
18-20-20-30	659882464 (ECH/ASA, 3 Apr 2023)
18-20-20-30-30
18-20-20-30-36
18-20-20-36	5938634866 (ECH/ASA, 10 Apr 2023)
18-20-20-36-36
18-20-24	169959966
18-20-24-24	450051891 (ECH/ASA, 13 Jul 2023)
18-20-24-24-24	0 (ECH/ASA, 13 Jul 2023)
18-20-24-24-30
18-20-24-24-36
18-20-24-30
18-20-24-30-30
18-20-24-30-36
18-20-24-36
18-20-24-36-36
18-20-24-36-48
18-20-30	1441808340 (ECH/ASA, 2 Apr 2023)
18-20-30-30
18-20-30-30-30
18-20-30-30-36
18-20-30-36
18-20-30-36-36
18-20-36	10083162174 (ECH/ASA, 2 Apr 2023)
18-20-36-36
18-20-36-36-36
18-24	293930
18-24-24	486415107
18-24-24-24
18-24-24-24-30
18-24-24-24-36
18-24-24-30
18-24-24-30-30
18-24-24-30-36
18-24-30
18-24-30-30
18-24-30-30-30
18-24-30-30-36
18-24-30-36
18-24-30-36-36
18-30	1307504
18-30-30
18-30-30-30
18-30-30-30-30
18-30-30-30-36
18-30-30-36
18-30-30-36-36
18-30-36
18-30-36-36
18-30-36-36-36
20	1	1
20-20	92378	735298671
20-20-24	215789595
20-20-24-24
20-20-24-24-24
20-20-24-24-30
20-20-24-24-36
20-20-24-30
20-20-24-30-30
20-20-24-30-36
20-20-24-36
20-20-24-36-36
20-20-30	2086967332
20-20-30-30
20-20-30-30-30
20-20-30-30-36
20-20-30-36
20-20-30-36-36
20-20-36
20-20-36-36
20-20-36-36-36
20-24	646646	16385965086
20-24-24	1377626279
20-24-24-24
20-24-24-24-24
20-24-24-24-30
20-24-24-24-36
20-24-24-30
20-24-24-30-30
20-24-24-30-36
20-24-24-36
20-24-24-36-36
20-24-30	31457860136
20-24-30-30
20-24-30-30-30
20-24-30-30-36
20-24-30-36
20-24-30-36-36
20-24-36
20-24-36-36
20-24-36-36-36
20-30	3268760
20-30-30
20-30-30-30
20-30-30-30-30
20-30-30-30-36
20-30-30-36
20-30-30-36-36
20-30-36
20-30-36-36
20-30-36-36-36
20-36
20-36-36
20-36-36-36
20-36-36-36-36
24	1	1
24-24	1352078	131377492010
24-24-24	3163085576
24-24-24-24
24-24-24-24-30
24-24-24-30
24-24-24-30-30
24-24-24-30-36
24-24-30
24-24-30-30
24-24-30-30-30
24-24-30-30-36
24-24-30-36
24-24-30-36-36
24-30	17383860
24-30-30
24-30-30-30
24-30-30-30-30
24-30-30-30-36
24-30-30-36
24-30-30-36-36
24-30-36
24-30-36-36
24-30-36-36-36
30	1	1
30-30	77558760
30-30-30	15,050,285,682,919 (ECH/ASA, 17 Apr 2023)
30-30-30-30
30-30-30-30-30
30-30-30-30-36
30-30-30-36
30-30-30-36-36
30-30-36
30-30-36-36
30-30-36-36-36
30-36
30-36-36
30-36-36-36
30-36-36-36-36

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