3
[1, 2, 3, 5, 7, 10, 13, 18, 23, 30, 37, 47, 57, 70] [6]
[1, 2, 3, 5, 7, 10, 13, 17, 22, 27, 33, 41, 48, 57] [5, 1]
[1, 2, 3, 5, 7, 10, 13, 17, 21, 26, 31, 37, 43, 50] [4, 2]
[1, 2, 3, 5, 7, 10, 13, 17, 21, 26, 31, 37, 43, 50] [4, 1, 1]
[1, 2, 3, 5, 7, 10, 13, 17, 21, 26, 31, 37, 43, 50] [3, 3]
[1, 2, 3, 5, 7, 10, 13, 17, 20, 26, 29, 35, 39, 48] [3, 2, 1]
[1, 2, 3, 5, 7, 10, 13, 17, 21, 26, 31, 37, 43, 50] [3, 1, 1, 1]
[1, 2, 3, 5, 7, 10, 13, 17, 21, 26, 31, 37, 43, 50] [2, 2, 2]
[1, 2, 3, 5, 7, 10, 13, 17, 21, 26, 31, 37, 43, 50] [2, 2, 1, 1]
[1, 2, 3, 5, 7, 10, 13, 17, 22, 27, 33, 41, 48, 57] [2, 1, 1, 1, 1]
[1, 2, 3, 5, 7, 10, 13, 18, 23, 30, 37, 47, 57, 70] [1, 1, 1, 1, 1, 1]
['NE', 'E']
-(x^4 - x^3 + x)/(x^4 - 2*x^3 + 2*x - 1)
[1, 2, 3, 5, 7, 10, 13, 17, 21, 26, 31, 37, 43, 50, 57, 65, 73, 82, 91, 101, 111, 122, 133, 145, 157, 170, 183, 197, 211, 226, 241, 257, 273, 290, 307, 325, 343, 362, 381, 401, 421, 442, 463, 485, 507, 530, 553, 577, 601, 626, 651, 677, 703, 730, 757, 785, 813, 842, 871, 901, 931, 962, 993, 1025, 1057, 1090, 1123, 1157, 1191, 1226, 1261, 1297, 1333, 1370, 1407, 1445, 1483, 1522, 1561, 1601, 1641, 1682, 1723, 1765, 1807, 1850, 1893, 1937, 1981, 2026, 2071, 2117, 2163, 2210, 2257, 2305, 2353, 2402, 2451, 2501]
(x + 1)*(x - 1)^3
['NE', 'E', 'NE']
Error in lines 1-1
Traceback (most recent call last):
File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1044, in execute
exec compile(block+'\n', '', 'single', flags=compile_flags) in namespace, locals
File "", line 1, in <module>
File "./PartitionAvoidanceGF.py", line 99, in Test
F = GFTree(L,1)
File "./PartitionAvoidanceGF.py", line 60, in GFTree
F0 = GFTree(L[1:], 0)
File "./PartitionAvoidanceGF.py", line 54, in GFTree
G = (GFTree(L[1:],1) - x*t*GFTree(L[1:],x*t))/(1-x*t)
File "./PartitionAvoidanceGF.py", line 60, in GFTree
F0 = GFTree(L[1:], 0)
File "./PartitionAvoidanceGF.py", line 70, in GFTree
return x*t/(1-x*t)
TypeError: unsupported operand type(s) for *: 'Partitions_n_with_category.element_class' and 'int'
1 , 2 , 3 , 5 , 7 , 11 , 14 , 20 , 25 , 32 , 39 , 49 , 56 , 68 , 79 , 91 , 103 , 119 , 132 , 150 , 165 , 183 , 202 , 224 , 241 , 264 , 287 , 311 , 334 , 362 , 385 , 415 , 442 , 472 , 503 , 535 , 563 , 599 , 634 , 670 , 703 , 743 , 778 , 820 , 859 , 899 , 942 , 988 , 1027 , 1074 , 1119 , 1167 , 1214 , 1266 , 1313 , 1365 , 1414 , 1468 , 1523 , 1581 , 1630 , 1690 , 1749 , 1807 , 1865 , 1927 , 1986 , 2052 , 2115 , 2181 , 2244 , 2314 , 2375 , 2447 , 2518 , 2588 , 2659 , 2733 , 2804 , 2882 , 2953 , 3030 , 3109 , 3191 , 3264 , 3346 , 3429 , 3513 , 3594 , 3682 , 3761 , 3849 , 3936 , 4026 , 4117 , 4209 , 4294 , 4390 , 4483 , 4577 , 4669 , 4769 , 4864 , 4966 , 5063 , 5161 , 5264 , 5370 , 5467 , 5575 , 5678 , 5786 , 5889 , 6001 , 6108 , 6220 , 6331 , 6443 , 6558 , 6674 , 6779 , 6898 , 7017 , 7137 , 7256 , 7378 , 7493 , 7619 , 7740 , 7866 , 7989 , 8119 , 8240 , 8370 , 8501 , 8629 , 8758 , 8894 , 9025 , 9163 , 9292 , 9430 , 9569 , 9709 , 9839 , 9981 , 10124 , 10266 , 10409 , 10557 , 10696 , 10846 , 10991 , 11139 , 11286 , 11438 , 11583 , 11739 , 11894 , 12050 , 12199 , 12357 , 12510 , 12672 , 12831 , 12989 , 13152 , 13318 , 13471 , 13638 , 13801 , 13967 , 14134 , 14306 , 14473 , 14643 , 14810 , 14984 , 15159 , 15337 , 15500 , 15680 , 15855 , 16035 , 16212 , 16394 , 16573 , 16757 , 16940 , 17122 , 17305 , 17495 , 17674 , 17866 , 18057 , 18245 , 18433 , 18629 , 18816 , 19014 , 19203 , 19401 , 19600 , 19800 , 19993 , 20195 , 20398 , 20600 , 20799 , 21005 , 21200 , 21410 , 21617 , 21827 , 22038 , 22250 , 22451 , 22665 , 22880 , 23096 , 23305 , 23523 , 23738 , 23960 , 24173 , 24390 , 24613 , 24839 , 25056 , 25284 , 25507 , 25731 , 25956 , 26188 , 26411 , 26643 , 26874 , 27108 , 27339 , 27577 , 27798 , 28038 , 28275 , 28513 , 28752 , 28992 , 29231 , 29475 , 29716 , 29962 , 30205 , 30455 , 30690 , 30940 , 31191 , 31439 , 31687 , 31943 , 32194 , 32450 , 32699 , 32955 , 33214 , 33476 , 33725 , 33987 , 34246 , 34510 , 34773 , 35041 , 35296 , 35566 , 35829 , 36095 , 36366 , 36636 , 36901 , 37177 , 37452 , 37726 , 37991 , 38271 , 38546 , 38828 , 39107 , 39385 , 39664 , 39948 , 40219 , 40506 , 40789 , 41077 , 41364 , 41656 , 41939 , 42231 , 42520 , 42810 , 43105 , 43401 , 43684 , 43982 , 44281 , 44581 , 44876 , 45178 , 45473 , 45779 , 46076 , 46382 , 46685 , 46995 , 47292 , 47604 , 47915 , 48219 , 48530 , 48846 , 49157 , 49473 , 49780 , 50098 , 50413 , 50733 , 51043 , 51363 , 51686 , 52010 , 52331 , 52657 , 52972 , 53302 , 53629 , 53957 , 54288 , 54620 , 54937 , 55273 , 55606 , 55942 , 56271 , 56609 , 56940 , 57280 , 57617 , 57955 , 58298 , 58644 , 58981 , 59329 , 59668 , 60012 , 60353 , 60705 , 61052 , 61404 , 61755 , 62105 , 62460 , 62818 , 63155 , 63514 , 63873 , 64231 , 64584 , 64946 , 65305 , 65671 , 66030 , 66394 , 66757 , 67125 , 67486 , 67858 , 68225 , 68593 , 68962 , 69336 , 69699 , 70077 , 70446 , 70824 , 71203 , 71585 , 71954 , 72332 , 72715 , 73097 , 73480 , 73868 , 74243 , 74631 , 75012 , 75402 , 75793 , 76185 , 76564 , 76960 , 77355 , 77747 , 78133 ,
Too many output messages: 257 (at most 256 per cell -- type 'smc?' to learn how to raise this limit): attempting to terminate...
[1, 2, 3, 5, 7, 11, 15, 22, 29, 40, 51, 67, 83, 105, 127, 156, 185, 222, 259, 305]
[1, 2, 3, 5, 7, 11, 15, 21, 28, 37, 46, 59, 72, 87, 104, 124, 144, 168, 192, 220, 250, 282, 314, 352, 391]
[1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676]
1 2 4 5 8 9 13 15 20 22 30 32 41 44 57 58 74 75 95 97 117 117 147 144 176 172
[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 1 17 0
[2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 2 1 15
[2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 2 3 13
[3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 3 1 14
[2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 2 5 11
[4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 4 1 13
[2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 2 7 9
[3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 3 4 11
[5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 5 1 12
[2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1] 2 9 7
[6, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 6 1 11
[2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1] 2 11 5
[3, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1] 3 7 8
[4, 4, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 4 5 9
[7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 7 1 10
[2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1] 2 13 3
[8, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1] 8 1 9
[2, 2, 2, 2, 2, 2, 2, 2, 1, 1] 2 15 1
[3, 3, 3, 3, 1, 1, 1, 1, 1, 1] 3 10 5
[5, 5, 1, 1, 1, 1, 1, 1, 1, 1] 5 6 7
[9, 1, 1, 1, 1, 1, 1, 1, 1, 1] 9 1 8
[2, 2, 2, 2, 2, 2, 2, 2, 2] 2 16 0
[3, 2, 2, 2, 2, 2, 2, 2, 1] 3 2 13
[4, 4, 4, 1, 1, 1, 1, 1, 1] 4 9 5
[10, 1, 1, 1, 1, 1, 1, 1, 1] 10 1 7
[3, 3, 2, 2, 2, 2, 2, 2] 3 5 10
[4, 2, 2, 2, 2, 2, 2, 2] 4 2 12
[3, 3, 3, 2, 2, 2, 2, 1] 3 8 7
[5, 2, 2, 2, 2, 2, 2, 1] 5 2 11
[3, 3, 3, 3, 3, 1, 1, 1] 3 13 2
[6, 6, 1, 1, 1, 1, 1, 1] 6 7 5
[11, 1, 1, 1, 1, 1, 1, 1] 11 1 6
[3, 3, 3, 3, 2, 2, 2] 3 11 4
[4, 4, 2, 2, 2, 2, 2] 4 6 8
[6, 2, 2, 2, 2, 2, 2] 6 2 10
[3, 3, 3, 3, 3, 2, 1] 3 14 1
[7, 2, 2, 2, 2, 2, 1] 7 2 9
[12, 1, 1, 1, 1, 1, 1] 12 1 5
[3, 3, 3, 3, 3, 3] 3 15 0
[4, 3, 3, 3, 3, 2] 4 3 11
[4, 4, 4, 2, 2, 2] 4 10 4
[5, 5, 2, 2, 2, 2] 5 7 6
[8, 2, 2, 2, 2, 2] 8 2 8
[4, 4, 3, 3, 3, 1] 4 7 7
[5, 3, 3, 3, 3, 1] 5 3 10
[9, 2, 2, 2, 2, 1] 9 2 7
[4, 4, 4, 4, 1, 1] 4 13 1
[5, 5, 5, 1, 1, 1] 5 11 2
[7, 7, 1, 1, 1, 1] 7 8 3
[13, 1, 1, 1, 1, 1] 13 1 4
[4, 4, 4, 3, 3] 4 11 3
[6, 3, 3, 3, 3] 6 3 9
[4, 4, 4, 4, 2] 4 14 0
[5, 5, 3, 3, 2] 5 8 5
[7, 3, 3, 3, 2] 7 3 8
[6, 6, 2, 2, 2] 6 8 4
[10, 2, 2, 2, 2] 10 2 6
[5, 4, 4, 4, 1] 5 4 9
[8, 3, 3, 3, 1] 8 3 7
[5, 5, 5, 2, 1] 5 12 1
[11, 2, 2, 2, 1] 11 2 5
[14, 1, 1, 1, 1] 14 1 3
[5, 5, 4, 4] 5 9 4
[6, 4, 4, 4] 6 4 8
[5, 5, 5, 3] 5 13 0
[7, 4, 4, 3] 7 4 7
[6, 6, 3, 3] 6 9 3
[9, 3, 3, 3] 9 3 6
[6, 5, 5, 2] 6 5 7
[6, 6, 4, 2] 6 10 2
[8, 4, 4, 2] 8 4 6
[10, 3, 3, 2] 10 3 5
[7, 7, 2, 2] 7 9 2
[12, 2, 2, 2] 12 2 4
[6, 6, 5, 1] 6 11 1
[7, 5, 5, 1] 7 5 6
[9, 4, 4, 1] 9 4 5
[7, 7, 3, 1] 7 10 1
[11, 3, 3, 1] 11 3 4
[13, 2, 2, 1] 13 2 3
[8, 8, 1, 1] 8 9 1
[15, 1, 1, 1] 15 1 2
[6, 6, 6] 6 12 0
[7, 6, 5] 7 6 5
[8, 5, 5] 8 5 5
[7, 7, 4] 7 11 0
[8, 6, 4] 8 6 4
[9, 5, 4] 9 5 4
[10, 4, 4] 10 4 4
[8, 7, 3] 8 7 3
[9, 6, 3] 9 6 3
[10, 5, 3] 10 5 3
[11, 4, 3] 11 4 3
[12, 3, 3] 12 3 3
[8, 8, 2] 8 10 0
[9, 7, 2] 9 7 2
[10, 6, 2] 10 6 2
[11, 5, 2] 11 5 2
[12, 4, 2] 12 4 2
[13, 3, 2] 13 3 2
[14, 2, 2] 14 2 2
[9, 8, 1] 9 8 1
[10, 7, 1] 10 7 1
[11, 6, 1] 11 6 1
[12, 5, 1] 12 5 1
[13, 4, 1] 13 4 1
[14, 3, 1] 14 3 1
[15, 2, 1] 15 2 1
[16, 1, 1] 16 1 1
[9, 9] 9 9 0
[10, 8] 10 8 0
[11, 7] 11 7 0
[12, 6] 12 6 0
[13, 5] 13 5 0
[14, 4] 14 4 0
[15, 3] 15 3 0
[16, 2] 16 2 0
[17, 1] 17 1 0
[18] 18 0 0
0
1
4
8
14
20
28
37
44
58
6
35
1 1 1
2 2 3
3 3 6
4 5 11
5 7 18
6 10 28
7 13 41
8 17 58
9 20 78
10 26 104
11 29 133
12 35 168
13 39 207
14 48 255
15 48 303
16 60 363
17 61 424
18 74 498
19 73 571
20 87 658
21 86 744
22 106 850
23 99 949
24 120 1069
25 112 1181
26 140 1321
27 130 1451
28 155 1606
29 143 1749
30 176 1925
31 159 2084
32 194 2278
33 180 2458
34 216 2674
35 186 2860
36 240 3100
37 209 3309
38 258 3567
39 234 3801
40 274 4075
41 243 4318
42 308 4626
43 261 4887
44 325 5212
45 289 5501
46 348 5849
47 297 6146
48 383 6529
49 314 6843
50 392 7235
51 356 7591
52 423 8014
53 355 8369
54 460 8829
55 372 9201
56 468 9669
57 422 10091
58 496 10587
59 415 11002
60 548 11550
61 437 11987
62 548 12535
63 481 13016
64 579 13595
65 478 14073
66 632 14705
67 501 15206
68 639 15845
69 560 16405
70 648 17053
71 543 17596
72 727 18323
73 567 18890
74 714 19604
75 635 20239
76 757 20996
77 602 21598
78 816 22414
79 633 23047
80 811 23858
81 707 24565
82 830 25395
83 679 26074
84 926 27000
85 708 27708
86 890 28598
87 788 29386
88 932 30318
89 749 31067
90 1010 32077
91 768 32845
92 1009 33854
93 870 34724
94 1012 35736
95 828 36564
96 1136 37700
97 847 38547
98 1068 39615
99 941 40556
100 1144 41700
101 897 42597
102 1224 43821
103 921 44742
104 1196 45938
105 1042 46980
106 1204 48184
107 971 49155
108 1358 50513
109 997 51510
110 1272 52782
111 1122 53904
112 1331 55235
113 1049 56284
114 1444 57728
115 1090 58818
116 1415 60233
117 1197 61430
118 1402 62832
119 1120 63952
120 1602 65554
121 1150 66704
122 1474 68178
123 1300 69478
124 1557 71035
125 1226 72261
126 1656 73917
127 1233 75150
128 1623 76773
129 1390 78163
130 1622 79785
131 1285 81070
132 1836 82906
133 1312 84218
134 1682 85900
135 1498 87398
136 1774 89172
137 1369 90541
138 1908 92449
139 1395 93844
140 1870 95714
141 1576 97290
142 1824 99114
143 1436 100550
144 2077 102627
145 1514 104141
146 1900 106041
147 1673 107714
148 2009 109723
149 1535 111258
150 2174 113432
151 1563 114995
152 2080 117075
153 1757 118832
154 2032 120864
155 1660 122524
156 2350 124874
157 1651 126525
158 2120 128645
159 1864 130509
160 2268 132777
161 1710 134487
162 2398 136885
163 1737 138622
164 2325 140947
165 1994 142941
166 2270 145211
167 1791 147002
168 2616 149618
169 1818 151436
170 2384 153820
171 2059 155879
172 2489 158368
173 1883 160251
174 2664 162915
175 1969 164884
176 2551 167435
177 2168 169603
178 2500 172103
179 1969 174072
180 2925 176997
181 2003 179000
182 2576 181576
183 2270 183846
184 2736 186582
185 2120 188702
186 2932 191634
187 2076 193710
188 2819 196529
189 2374 198903
190 2788 201691
191 2153 203844
192 3175 207019
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194 2818 212022
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200 3135 228379
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202 2982 233947
203 2350 236297
204 3464 239761
205 2440 242201
206 3060 245261
207 2683 247944
208 3231 251175
209 2416 253591
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211 2467 259606
212 3339 262945
213 2800 265745
214 3226 268971
215 2602 271573
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217 2576 277909
218 3310 281219
219 2906 284125
220 3572 287697
221 2602 290299
222 3764 294063
223 2651 296714
224 3610 300324
225 3095 303419
226 3480 306899
227 2717 309616
228 4062 313678
229 2749 316427
230 3644 320071
231 3138 323209
232 3788 326997
233 2815 329812
234 4032 333844
235 2942 336786
236 3871 340657
237 3238 343895
238 3736 347631
239 2907 350538
240 4454 354992
241 2945 357937
242 3810 361747
243 3353 365100
244 4057 369157
245 3141 372298
246 4348 376646
247 3022 379668
248 4156 383824
249 3464 387288
250 4090 391378
251 3103 394481
252 4695 399176
253 3130 402306
254 4080 406386
255 3676 410062
256 4338 414400
257 3207 417607
258 4644 422251
259 3274 425525
260 4518 430043
261 3699 433742
262 4254 437996
263 3305 441301
264 5004 446305
265 3464 449769
266 4360 454129
267 3812 457941
268 4613 462554
269 3403 465957
270 5052 471009
271 3439 474448
272 4709 479157
273 3950 483107
274 4522 487629
275 3631 491260
276 5328 496588
277 3543 500131
278 4610 504741
279 4049 508790
280 5074 513864
281 3613 517477
282 5256 522733
283 3643 526376
284 4993 531369
285 4280 535649
286 4760 540409
287 3756 544165
288 5662 549827
289 3742 553569
290 5030 558599
291 4286 562885
292 5193 568078
293 3815 571893
294 5594 577487
295 4000 581487
296 5310 586797
297 4402 591199
298 5062 596261
299 3900 600161
300 6119 606280
301 4010 610290
302 5156 615446
303 4524 619970
304 5487 625457
305 4184 629641
306 5872 635513
307 4059 639572
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309 4646 649828
310 5508 655336
311 4127 659463
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313 4165 669968
314 5436 675404
315 4984 680388
316 5783 686171
317 4233 690404
318 6200 696604
319 4260 700864
320 6065 706929
321 4888 711817
322 5660 717477
323 4320 721797
324 6671 728468
325 4545 733013
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328 6116 749861
329 4512 754373
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331 4487 765548
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334 5900 782782
335 4742 787524
336 7072 794596
337 4591 799187
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389 5541 1123734
390 8428 1132162
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392 7879 1145595
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431 6333 1432711
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435 7624 1465176
436 8933 1474109
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438 9596 1490131
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444 10302 1539102
445 6924 1546026
446 8680 1554706
447 7604 1562310
448 9429 1571739
449 6685 1578424
450 10308 1588732
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453 7742 1612589
454 8886 1621475
455 7246 1628721
456 10736 1639457
457 6841 1646298
458 8988 1655286
459 7902 1663188
460 9930 1673118
461 6917 1680035
462 10424 1690459
463 6959 1697418
464 9775 1707193
465 8340 1715533
466 9202 1724735
467 7035 1731770
468 11093 1742863
469 7214 1750077
470 9684 1759761
471 8154 1767915
472 10024 1777939
473 7164 1785103
474 10676 1795779
475 7511 1803290
476 10148 1813438
477 8347 1821785
478 9508 1831293
479 7265 1838558
480 11876 1850434
481 7308 1857742
482 9622 1867364
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967 17903 9508667
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977 18139 9737750
978 27884 9765634
979 18330 9783964
980 27817 9811781
981 21503 9833284
982 24278 9857562
983
Too many output messages: 257 (at most 256 per cell -- type 'smc?' to learn how to raise this limit): attempting to terminate...