Vendredi 17 Juin 2016 Rencontres SMAI Mathématiques - Industrie

Vendredi 17 Juin 2016

 Rencontres SMAI Mathématiques - Industrie

 

La 20ème Rencontre SMAI Mathématiques-Industrie aura lieu le Vendredi 17 Juin à l'INSA Rouen :
de 9h30 à 17h (Dumont d'Urville, Amphi Curie, B-RJ-02-CURIE).

 

Lire la suite : http://lmi.insa-rouen.fr/64.html

Premier Prix Bull-Joseph Fourier 2015 : des simulations numériques pour un diagnostic d’AVC plus rapide

"Fruit de la collaboration entre Atos et GENCI, le Prix Bull-Joseph Fourier 2015 a récompensé le 12 avril 2016 une équipe de mathématiciens et d’informaticiens de plusieurs laboratoires CNRS pour leurs travaux innovants de simulation numérique. Grâce à eux, la définition du type d’accident vasculaire cérébral (AVC) affectant un patient devient possible en quelques minutes, ce qui assure une meilleure prise en charge.

Chaque année, le Prix Bull-Joseph Fourier, décerné par Atos et GENCI, distingue les travaux de recherche d’équipes académiques et industrielles dans les domaines de la simulation informatique et du calcul haute performance en France. Cette année, pour sa 6e édition, le premier prix Bull-Joseph Fourier a..."

Lire la suite : http://www.cnrs.fr/cnrsinnovation-lalettre/actus.php?nume...

PGMO a reçu le grand prix AEF des meilleures initiatives partagées le 24 mars 2016

"Le Programme Gaspard Monge pour l’optimisation et la recherche opérationnelle (PGMO), créé par EDF R&D et la FMJH (Fondation Mathématique Jacques Hadamard) de Paris-Saclay, a reçu le Grand prix AEF des meilleures initiatives partagées le 24 mars 2016 à Paris. Ce prix récompense les bonnes pratiques en cours dans la catégorie « Recherche & Innovation », reposant sur une collaboration entre établissements de l’enseignement supérieur et entreprises. PGMO est un projet de recherche commun entre des laboratoires académiques spécialisés en Optimisation Mathématique et la R&D du groupe EDF (département OSIRIS). C’est une belle reconnaissance pour la communauté scientifique de Paris-Saclay à l’heure où la R&D d’EDF la rejoint !

La R&D d’EDF était représentée par Sandrine Charousset, ingénieur chercheur et responsable de l'Initiative de Recherche Optimisation et Énergie, et la fondation Mathématique Jacques Hadamard par Pierre Pansu, professeur à l’Université Paris-Sud et Directeur de la FMJH.

« PGMO permet d’établir..."

 

Lire la suite : http://chercheurs.edf.com/organisation/partenariats/pgmo-...

http://culturemath.ens.fr/

http://culturemath.ens.fr/

Quand des objets ‪#‎mathématiques‬ abstraits donnent des images étonnantes..

Diaporama ‪#‎CNRSleJournal‬ : Quand des objets ‪#‎mathématiques‬ abstraits donnent des images étonnantes...

Des équations aux objets

Quand les chercheurs veulent représenter visuellement des objets mathématiques aussi abstraits que des équations, des images virtuelles étonnantes, à la limite du...

LEJOURNAL.CNRS.FR

 

Conjecture de Dickson

 

 

En théorie des nombres, la conjecture de Dickson est une conjecture émise par Leonard Eugene Dickson, selon laquelle pour un ensemble fini de k suites arithmétiquesa₁ + nb₁, a₂ + nb₂, ..., a_k + nb_k avec b_i ≥ 1, il existe une infinité d'entiers positifs n pour lesquels les nombres correspondants sont tous premiers, excepté s'il existe une condition de congruence qui empêche cela (Ribenboim 1996, 6.I). Le cas k=1 est le théorème de Dirichlet.

Deux cas particuliers sont des conjectures célèbres et non résolues : l'existence d'une infinité de nombres premiers jumeaux (n et n+2 sont premiers), et d'une infinité denombres premiers de Sophie Germain (n et 2n+1 sont premiers).

La conjecture de Dickson a été par la suite généralisée par l'hypothèse H de Schinzel.

Références[modifier | modifier le code]

• (en) Cet article est partiellement ou en totalité issu de l’article de Wikipédia en anglais intitulé « Dickson's conjecture » (voir la liste des auteurs).
• (en) L. E. Dickson, A new extension of Dirichlet's theorem on prime numbers, vol. 33 : Messenger of mathematics, Macmillan and Co,‎ 1904, 155-161 p. (lire en ligne)
• (en) Paulo Ribenboim, The new book of prime number records, Berlin, New York, Springer-Verlag,‎ 1996 (ISBN 978-0-387-94457-9, lire en ligne)

Voir aussi[modifier | modifier le code]

Théorème de Green-Tao

• Portail de l’arithmétique et de la théorie des nombres

Catégories :

• Nombre premier
• Conjecture non résolue

| [+]

Liste des 20 000 premiers couples de nombres premiers jumeaux (p, p+2)

Source : http://arnflo.se/~site_files/Other/twinprimes

 

# 20000 first twin primes
# Calculated: 12/09-10 By Oscar Arnflo
# Processing time: 626.478574038 seconds

3,5 #1
5,7 #2
11,13 #3
17,19 #4
29,31 #5
41,43 #6
59,61 #7
71,73 #8
101,103 #9
107,109 #10
137,139 #11
149,151 #12
179,181 #13
191,193 #14
197,199 #15
227,229 #16
239,241 #17
269,271 #18
281,283 #19
311,313 #20
347,349 #21
419,421 #22
431,433 #23
461,463 #24
521,523 #25
569,571 #26
599,601 #27
617,619 #28
641,643 #29
659,661 #30
809,811 #31
821,823 #32
827,829 #33
857,859 #34
881,883 #35
1019,1021 #36
1031,1033 #37
1049,1051 #38
1061,1063 #39
1091,1093 #40
1151,1153 #41
1229,1231 #42
1277,1279 #43
1289,1291 #44
1301,1303 #45
1319,1321 #46
1427,1429 #47
1451,1453 #48
1481,1483 #49
1487,1489 #50
1607,1609 #51
1619,1621 #52
1667,1669 #53
1697,1699 #54
1721,1723 #55
1787,1789 #56
1871,1873 #57
1877,1879 #58
1931,1933 #59
1949,1951 #60
1997,1999 #61
2027,2029 #62
2081,2083 #63
2087,2089 #64
2111,2113 #65
2129,2131 #66
2141,2143 #67
2237,2239 #68
2267,2269 #69
2309,2311 #70
2339,2341 #71
2381,2383 #72
2549,2551 #73
2591,2593 #74
2657,2659 #75
2687,2689 #76
2711,2713 #77
2729,2731 #78
2789,2791 #79
2801,2803 #80
2969,2971 #81
2999,3001 #82
3119,3121 #83
3167,3169 #84
3251,3253 #85
3257,3259 #86
3299,3301 #87
3329,3331 #88
3359,3361 #89
3371,3373 #90
3389,3391 #91
3461,3463 #92
3467,3469 #93
3527,3529 #94
3539,3541 #95
3557,3559 #96
3581,3583 #97
3671,3673 #98
3767,3769 #99
3821,3823 #100
3851,3853 #101
3917,3919 #102
3929,3931 #103
4001,4003 #104
4019,4021 #105
4049,4051 #106
4091,4093 #107
4127,4129 #108
4157,4159 #109
4217,4219 #110
4229,4231 #111
4241,4243 #112
4259,4261 #113
4271,4273 #114
4337,4339 #115
4421,4423 #116
4481,4483 #117
4517,4519 #118
4547,4549 #119
4637,4639 #120
4649,4651 #121
4721,4723 #122
4787,4789 #123
4799,4801 #124
4931,4933 #125
4967,4969 #126
5009,5011 #127
5021,5023 #128
5099,5101 #129
5231,5233 #130
5279,5281 #131
5417,5419 #132
5441,5443 #133
5477,5479 #134
5501,5503 #135
5519,5521 #136
5639,5641 #137
5651,5653 #138
5657,5659 #139
5741,5743 #140
5849,5851 #141
5867,5869 #142
5879,5881 #143
6089,6091 #144
6131,6133 #145
6197,6199 #146
6269,6271 #147
6299,6301 #148
6359,6361 #149
6449,6451 #150
6551,6553 #151
6569,6571 #152
6659,6661 #153
6689,6691 #154
6701,6703 #155
6761,6763 #156
6779,6781 #157
6791,6793 #158
6827,6829 #159
6869,6871 #160
6947,6949 #161
6959,6961 #162
7127,7129 #163
7211,7213 #164
7307,7309 #165
7331,7333 #166
7349,7351 #167
7457,7459 #168
7487,7489 #169
7547,7549 #170
7559,7561 #171
7589,7591 #172
7757,7759 #173
7877,7879 #174
7949,7951 #175
8009,8011 #176
8087,8089 #177
8219,8221 #178
8231,8233 #179
8291,8293 #180
8387,8389 #181
8429,8431 #182
8537,8539 #183
8597,8599 #184
8627,8629 #185
8819,8821 #186
8837,8839 #187
8861,8863 #188
8969,8971 #189
8999,9001 #190
9011,9013 #191
9041,9043 #192
9239,9241 #193
9281,9283 #194
9341,9343 #195
9419,9421 #196
9431,9433 #197
9437,9439 #198
9461,9463 #199
9629,9631 #200
9677,9679 #201
9719,9721 #202
9767,9769 #203
9857,9859 #204
9929,9931 #205
10007,10009 #206
10037,10039 #207
10067,10069 #208
10091,10093 #209
10139,10141 #210
10271,10273 #211
10301,10303 #212
10331,10333 #213
10427,10429 #214
10457,10459 #215
10499,10501 #216
10529,10531 #217
10709,10711 #218
10859,10861 #219
10889,10891 #220
10937,10939 #221
11057,11059 #222
11069,11071 #223
11117,11119 #224
11159,11161 #225
11171,11173 #226
11351,11353 #227
11489,11491 #228
11549,11551 #229
11699,11701 #230
11717,11719 #231
11777,11779 #232
11831,11833 #233
11939,11941 #234
11969,11971 #235
12041,12043 #236
12071,12073 #237
12107,12109 #238
12161,12163 #239
12239,12241 #240
12251,12253 #241
12377,12379 #242
12539,12541 #243
12611,12613 #244
12821,12823 #245
12917,12919 #246
13001,13003 #247
13007,13009 #248
13217,13219 #249
13337,13339 #250
13397,13399 #251
13679,13681 #252
13691,13693 #253
13709,13711 #254
13721,13723 #255
13757,13759 #256
13829,13831 #257
13877,13879 #258
13901,13903 #259
13931,13933 #260
13997,13999 #261
14009,14011 #262
14081,14083 #263
14249,14251 #264
14321,14323 #265
14387,14389 #266
14447,14449 #267
14549,14551 #268
14561,14563 #269
14591,14593 #270
14627,14629 #271
14867,14869 #272
15137,15139 #273
15269,15271 #274
15287,15289 #275
15329,15331 #276
15359,15361 #277
15581,15583 #278
15641,15643 #279
15647,15649 #280
15731,15733 #281
15737,15739 #282
15887,15889 #283
15971,15973 #284
16061,16063 #285
16067,16069 #286
16139,16141 #287
16187,16189 #288
16229,16231 #289
16361,16363 #290
16451,16453 #291
16631,16633 #292
16649,16651 #293
16691,16693 #294
16829,16831 #295
16901,16903 #296
16979,16981 #297
17027,17029 #298
17189,17191 #299
17207,17209 #300
17291,17293 #301
17387,17389 #302
17417,17419 #303
17489,17491 #304
17579,17581 #305
17597,17599 #306
17657,17659 #307
17681,17683 #308
17747,17749 #309
17789,17791 #310
17837,17839 #311
17909,17911 #312
17921,17923 #313
17957,17959 #314
17987,17989 #315
18041,18043 #316
18047,18049 #317
18059,18061 #318
18119,18121 #319
18131,18133 #320
18251,18253 #321
18287,18289 #322
18311,18313 #323
18521,18523 #324
18539,18541 #325
18911,18913 #326
18917,18919 #327
19079,19081 #328
19139,19141 #329
19181,19183 #330
19211,19213 #331
19379,19381 #332
19421,19423 #333
19427,19429 #334
19469,19471 #335
19541,19543 #336
19697,19699 #337
19751,19753 #338
19841,19843 #339
19889,19891 #340
19961,19963 #341
19991,19993 #342
20021,20023 #343
20147,20149 #344
20231,20233 #345
20357,20359 #346
20441,20443 #347
20477,20479 #348
20507,20509 #349
20549,20551 #350
20639,20641 #351
20717,20719 #352
20747,20749 #353
20771,20773 #354
20807,20809 #355
20897,20899 #356
20981,20983 #357
21011,21013 #358
21017,21019 #359
21059,21061 #360
21191,21193 #361
21317,21319 #362
21377,21379 #363
21491,21493 #364
21521,21523 #365
21557,21559 #366
21587,21589 #367
21599,21601 #368
21611,21613 #369
21647,21649 #370
21737,21739 #371
21839,21841 #372
22037,22039 #373
22091,22093 #374
22109,22111 #375
22157,22159 #376
22271,22273 #377
22277,22279 #378
22367,22369 #379
22481,22483 #380
22541,22543 #381
22571,22573 #382
22619,22621 #383
22637,22639 #384
22697,22699 #385
22739,22741 #386
22859,22861 #387
22961,22963 #388
23027,23029 #389
23039,23041 #390
23057,23059 #391
23201,23203 #392
23291,23293 #393
23369,23371 #394
23537,23539 #395
23561,23563 #396
23627,23629 #397
23669,23671 #398
23687,23689 #399
23741,23743 #400
23831,23833 #401
23909,23911 #402
24107,24109 #403
24179,24181 #404
24371,24373 #405
24419,24421 #406
24917,24919 #407
24977,24979 #408
25031,25033 #409
25169,25171 #410
25301,25303 #411
25307,25309 #412
25409,25411 #413
25469,25471 #414
25577,25579 #415
25601,25603 #416
25799,25801 #417
25847,25849 #418
25931,25933 #419
25997,25999 #420
26111,26113 #421
26249,26251 #422
26261,26263 #423
26681,26683 #424
26699,26701 #425
26711,26713 #426
26729,26731 #427
26861,26863 #428
26879,26881 #429
26891,26893 #430
26951,26953 #431
27059,27061 #432
27107,27109 #433
27239,27241 #434
27281,27283 #435
27407,27409 #436
27479,27481 #437
27527,27529 #438
27539,27541 #439
27581,27583 #440
27689,27691 #441
27737,27739 #442
27749,27751 #443
27791,27793 #444
27917,27919 #445
27941,27943 #446
28097,28099 #447
28109,28111 #448
28181,28183 #449
28277,28279 #450
28307,28309 #451
28349,28351 #452
28409,28411 #453
28547,28549 #454
28571,28573 #455
28619,28621 #456
28661,28663 #457
28751,28753 #458
29021,29023 #459
29129,29131 #460
29207,29209 #461
29387,29389 #462
29399,29401 #463
29567,29569 #464
29669,29671 #465
29759,29761 #466
29879,29881 #467
30011,30013 #468
30089,30091 #469
30137,30139 #470
30269,30271 #471
30389,30391 #472
30467,30469 #473
30491,30493 #474
30557,30559 #475
30839,30841 #476
30851,30853 #477
30869,30871 #478
31079,31081 #479
31121,31123 #480
31151,31153 #481
31181,31183 #482
31247,31249 #483
31319,31321 #484
31391,31393 #485
31511,31513 #486
31541,31543 #487
31721,31723 #488
31727,31729 #489
31769,31771 #490
31847,31849 #491
32027,32029 #492
32057,32059 #493
32117,32119 #494
32141,32143 #495
32189,32191 #496
32297,32299 #497
32321,32323 #498
32369,32371 #499
32411,32413 #500
32441,32443 #501
32531,32533 #502
32561,32563 #503
32609,32611 #504
32717,32719 #505
32801,32803 #506
32831,32833 #507
32909,32911 #508
32939,32941 #509
32969,32971 #510
33071,33073 #511
33149,33151 #512
33179,33181 #513
33287,33289 #514
33329,33331 #515
33347,33349 #516
33587,33589 #517
33599,33601 #518
33617,33619 #519
33749,33751 #520
33767,33769 #521
33809,33811 #522
33827,33829 #523
34031,34033 #524
34127,34129 #525
34157,34159 #526
34211,34213 #527
34259,34261 #528
34301,34303 #529
34367,34369 #530
34469,34471 #531
34499,34501 #532
34511,34513 #533
34589,34591 #534
34649,34651 #535
34757,34759 #536
34841,34843 #537
34847,34849 #538
34961,34963 #539
35051,35053 #540
35081,35083 #541
35279,35281 #542
35447,35449 #543
35507,35509 #544
35531,35533 #545
35591,35593 #546
35729,35731 #547
35801,35803 #548
35837,35839 #549
35897,35899 #550
36011,36013 #551
36107,36109 #552
36341,36343 #553
36467,36469 #554
36527,36529 #555
36779,36781 #556
36791,36793 #557
36899,36901 #558
36929,36931 #559
37019,37021 #560
37199,37201 #561
37307,37309 #562
37337,37339 #563
37361,37363 #564
37547,37549 #565
37571,37573 #566
37589,37591 #567
37691,37693 #568
37781,37783 #569
37811,37813 #570
37991,37993 #571
38237,38239 #572
38327,38329 #573
38447,38449 #574
38459,38461 #575
38567,38569 #576
38609,38611 #577
38651,38653 #578
38669,38671 #579
38711,38713 #580
38747,38749 #581
38921,38923 #582
39041,39043 #583
39161,39163 #584
39227,39229 #585
39239,39241 #586
39341,39343 #587
39371,39373 #588
39509,39511 #589
39827,39829 #590
39839,39841 #591
40037,40039 #592
40127,40129 #593
40151,40153 #594
40427,40429 #595
40529,40531 #596
40637,40639 #597
40697,40699 #598
40847,40849 #599
41141,41143 #600
41177,41179 #601
41201,41203 #602
41231,41233 #603
41387,41389 #604
41411,41413 #605
41519,41521 #606
41609,41611 #607
41759,41761 #608
41849,41851 #609
41957,41959 #610
41981,41983 #611
42017,42019 #612
42071,42073 #613
42179,42181 #614
42221,42223 #615
42281,42283 #616
42407,42409 #617
42461,42463 #618
42569,42571 #619
42641,42643 #620
42701,42703 #621
42839,42841 #622
42899,42901 #623
43049,43051 #624
43319,43321 #625
43397,43399 #626
43541,43543 #627
43577,43579 #628
43607,43609 #629
43649,43651 #630
43781,43783 #631
43787,43789 #632
43889,43891 #633
43961,43963 #634
44027,44029 #635
44087,44089 #636
44129,44131 #637
44201,44203 #638
44267,44269 #639
44279,44281 #640
44381,44383 #641
44531,44533 #642
44621,44623 #643
44699,44701 #644
44771,44773 #645
45119,45121 #646
45137,45139 #647
45179,45181 #648
45317,45319 #649
45341,45343 #650
45587,45589 #651
45821,45823 #652
46049,46051 #653
46091,46093 #654
46181,46183 #655
46271,46273 #656
46307,46309 #657
46349,46351 #658
46439,46441 #659
46589,46591 #660
46679,46681 #661
46769,46771 #662
46817,46819 #663
46829,46831 #664
47057,47059 #665
47147,47149 #666
47351,47353 #667
47387,47389 #668
47417,47419 #669
47657,47659 #670
47699,47701 #671
47711,47713 #672
47741,47743 #673
47777,47779 #674
47807,47809 #675
48119,48121 #676
48311,48313 #677
48407,48409 #678
48479,48481 #679
48539,48541 #680
48647,48649 #681
48677,48679 #682
48731,48733 #683
48779,48781 #684
48821,48823 #685
48857,48859 #686
48869,48871 #687
48989,48991 #688
49031,49033 #689
49121,49123 #690
49169,49171 #691
49199,49201 #692
49277,49279 #693
49331,49333 #694
49367,49369 #695
49391,49393 #696
49409,49411 #697
49529,49531 #698
49547,49549 #699
49667,49669 #700
49739,49741 #701
49787,49789 #702
49919,49921 #703
49937,49939 #704
49991,49993 #705
50021,50023 #706
50051,50053 #707
50129,50131 #708
50261,50263 #709
50459,50461 #710
50549,50551 #711
50591,50593 #712
50891,50893 #713
50969,50971 #714
51059,51061 #715
51131,51133 #716
51197,51199 #717
51239,51241 #718
51341,51343 #719
51347,51349 #720
51419,51421 #721
51437,51439 #722
51479,51481 #723
51719,51721 #724
51767,51769 #725
51827,51829 #726
51869,51871 #727
51971,51973 #728
52067,52069 #729
52181,52183 #730
52289,52291 #731
52361,52363 #732
52541,52543 #733
52709,52711 #734
52859,52861 #735
52901,52903 #736
53087,53089 #737
53147,53149 #738
53171,53173 #739
53231,53233 #740
53267,53269 #741
53279,53281 #742
53549,53551 #743
53591,53593 #744
53609,53611 #745
53717,53719 #746
53897,53899 #747
54011,54013 #748
54401,54403 #749
54419,54421 #750
54497,54499 #751
54539,54541 #752
54581,54583 #753
54629,54631 #754
54917,54919 #755
55049,55051 #756
55217,55219 #757
55331,55333 #758
55337,55339 #759
55439,55441 #760
55619,55621 #761
55631,55633 #762
55661,55663 #763
55817,55819 #764
55901,55903 #765
55931,55933 #766
56039,56041 #767
56099,56101 #768
56207,56209 #769
56237,56239 #770
56267,56269 #771
56477,56479 #772
56501,56503 #773
56531,56533 #774
56597,56599 #775
56711,56713 #776
56807,56809 #777
56891,56893 #778
56909,56911 #779
56921,56923 #780
57191,57193 #781
57221,57223 #782
57269,57271 #783
57329,57331 #784
57347,57349 #785
57527,57529 #786
57557,57559 #787
57791,57793 #788
57899,57901 #789
58109,58111 #790
58151,58153 #791
58169,58171 #792
58229,58231 #793
58367,58369 #794
58391,58393 #795
58439,58441 #796
58451,58453 #797
58601,58603 #798
58787,58789 #799
58907,58909 #800
59009,59011 #801
59021,59023 #802
59051,59053 #803
59207,59209 #804
59219,59221 #805
59357,59359 #806
59417,59419 #807
59441,59443 #808
59471,59473 #809
59627,59629 #810
59669,59671 #811
60089,60091 #812
60101,60103 #813
60167,60169 #814
60257,60259 #815
60647,60649 #816
60659,60661 #817
60761,60763 #818
60887,60889 #819
60899,60901 #820
60917,60919 #821
61151,61153 #822
61331,61333 #823
61379,61381 #824
61469,61471 #825
61559,61561 #826
61979,61981 #827
62129,62131 #828
62141,62143 #829
62189,62191 #830
62297,62299 #831
62927,62929 #832
62969,62971 #833
62981,62983 #834
62987,62989 #835
63029,63031 #836
63197,63199 #837
63311,63313 #838
63389,63391 #839
63419,63421 #840
63587,63589 #841
63599,63601 #842
63647,63649 #843
63689,63691 #844
63839,63841 #845
64151,64153 #846
64187,64189 #847
64301,64303 #848
64451,64453 #849
64577,64579 #850
64661,64663 #851
64781,64783 #852
64877,64879 #853
64919,64921 #854
65027,65029 #855
65099,65101 #856
65171,65173 #857
65267,65269 #858
65447,65449 #859
65519,65521 #860
65537,65539 #861
65579,65581 #862
65699,65701 #863
65717,65719 #864
65729,65731 #865
65837,65839 #866
65927,65929 #867
65981,65983 #868
66107,66109 #869
66359,66361 #870
66569,66571 #871
66749,66751 #872
66851,66853 #873
66947,66949 #874
67139,67141 #875
67187,67189 #876
67211,67213 #877
67217,67219 #878
67271,67273 #879
67409,67411 #880
67427,67429 #881
67577,67579 #882
67757,67759 #883
67931,67933 #884
68111,68113 #885
68207,68209 #886
68279,68281 #887
68447,68449 #888
68489,68491 #889
68711,68713 #890
68819,68821 #891
68879,68881 #892
68897,68899 #893
69029,69031 #894
69149,69151 #895
69191,69193 #896
69257,69259 #897
69401,69403 #898
69491,69493 #899
69497,69499 #900
69737,69739 #901
69761,69763 #902
69827,69829 #903
69857,69859 #904
69929,69931 #905
70001,70003 #906
70121,70123 #907
70139,70141 #908
70181,70183 #909
70199,70201 #910
70379,70381 #911
70457,70459 #912
70487,70489 #913
70571,70573 #914
70619,70621 #915
70841,70843 #916
70877,70879 #917
70919,70921 #918
70949,70951 #919
70979,70981 #920
70997,70999 #921
71261,71263 #922
71327,71329 #923
71339,71341 #924
71387,71389 #925
71411,71413 #926
71471,71473 #927
71549,71551 #928
71711,71713 #929
71807,71809 #930
71879,71881 #931
72089,72091 #932
72101,72103 #933
72167,72169 #934
72221,72223 #935
72227,72229 #936
72251,72253 #937
72269,72271 #938
72467,72469 #939
72647,72649 #940
72671,72673 #941
72869,72871 #942
73037,73039 #943
73061,73063 #944
73361,73363 #945
73607,73609 #946
73679,73681 #947
73847,73849 #948
74099,74101 #949
74159,74161 #950
74201,74203 #951
74381,74383 #952
74411,74413 #953
74507,74509 #954
74609,74611 #955
74717,74719 #956
74729,74731 #957
74759,74761 #958
75011,75013 #959
75167,75169 #960
75209,75211 #961
75389,75391 #962
75401,75403 #963
75539,75541 #964
75617,75619 #965
75707,75709 #966
75989,75991 #967
76001,76003 #968
76079,76081 #969
76157,76159 #970
76259,76261 #971
76367,76369 #972
76421,76423 #973
76541,76543 #974
76649,76651 #975
76829,76831 #976
76871,76873 #977
76961,76963 #978
77237,77239 #979
77261,77263 #980
77267,77269 #981
77417,77419 #982
77477,77479 #983
77489,77491 #984
77549,77551 #985
77687,77689 #986
77711,77713 #987
78137,78139 #988
78191,78193 #989
78437,78439 #990
78509,78511 #991
78539,78541 #992
78569,78571 #993
78779,78781 #994
78887,78889 #995
78977,78979 #996
79151,79153 #997
79229,79231 #998
79397,79399 #999
79559,79561 #1000
79631,79633 #1001
79691,79693 #1002
79697,79699 #1003
79811,79813 #1004
79841,79843 #1005
79901,79903 #1006
79997,79999 #1007
80147,80149 #1008
80207,80209 #1009
80231,80233 #1010
80447,80449 #1011
80471,80473 #1012
80489,80491 #1013
80627,80629 #1014
80669,80671 #1015
80681,80683 #1016
80747,80749 #1017
80777,80779 #1018
80831,80833 #1019
80909,80911 #1020
81017,81019 #1021
81041,81043 #1022
81047,81049 #1023
81197,81199 #1024
81281,81283 #1025
81371,81373 #1026
81551,81553 #1027
81647,81649 #1028
81701,81703 #1029
81899,81901 #1030
81929,81931 #1031
81971,81973 #1032
82007,82009 #1033
82037,82039 #1034
82139,82141 #1035
82217,82219 #1036
82349,82351 #1037
82469,82471 #1038
82529,82531 #1039
82559,82561 #1040
82721,82723 #1041
82727,82729 #1042
82757,82759 #1043
82811,82813 #1044
82889,82891 #1045
83219,83221 #1046
83231,83233 #1047
83267,83269 #1048
83339,83341 #1049
83399,83401 #1050
83561,83563 #1051
83639,83641 #1052
83717,83719 #1053
84059,84061 #1054
84179,84181 #1055
84221,84223 #1056
84317,84319 #1057
84347,84349 #1058
84389,84391 #1059
84521,84523 #1060
84629,84631 #1061
84809,84811 #1062
84857,84859 #1063
84869,84871 #1064
84977,84979 #1065
85091,85093 #1066
85199,85201 #1067
85331,85333 #1068
85361,85363 #1069
85427,85429 #1070
85451,85453 #1071
85619,85621 #1072
85667,85669 #1073
85817,85819 #1074
85829,85831 #1075
85931,85933 #1076
86027,86029 #1077
86111,86113 #1078
86291,86293 #1079
86351,86353 #1080
86369,86371 #1081
86531,86533 #1082
86627,86629 #1083
86927,86929 #1084
87011,87013 #1085
87119,87121 #1086
87149,87151 #1087
87179,87181 #1088
87221,87223 #1089
87251,87253 #1090
87509,87511 #1091
87539,87541 #1092
87557,87559 #1093
87587,87589 #1094
87629,87631 #1095
87641,87643 #1096
87719,87721 #1097
87959,87961 #1098
88001,88003 #1099
88259,88261 #1100
88337,88339 #1101
88469,88471 #1102
88589,88591 #1103
88607,88609 #1104
88661,88663 #1105
88799,88801 #1106
88811,88813 #1107
88817,88819 #1108
89069,89071 #1109
89519,89521 #1110
89561,89563 #1111
89597,89599 #1112
89657,89659 #1113
89669,89671 #1114
89819,89821 #1115
89897,89899 #1116
90017,90019 #1117
90071,90073 #1118
90197,90199 #1119
90371,90373 #1120
90401,90403 #1121
90437,90439 #1122
90527,90529 #1123
90617,90619 #1124
90677,90679 #1125
90821,90823 #1126
91079,91081 #1127
91097,91099 #1128
91127,91129 #1129
91139,91141 #1130
91151,91153 #1131
91367,91369 #1132
91457,91459 #1133
91571,91573 #1134
91811,91813 #1135
91967,91969 #1136
92177,92179 #1137
92219,92221 #1138
92381,92383 #1139
92399,92401 #1140
92459,92461 #1141
92567,92569 #1142
92639,92641 #1143
92669,92671 #1144
92681,92683 #1145
92789,92791 #1146
92861,92863 #1147
92957,92959 #1148
93131,93133 #1149
93239,93241 #1150
93251,93253 #1151
93281,93283 #1152
93479,93481 #1153
93491,93493 #1154
93557,93559 #1155
93701,93703 #1156
93761,93763 #1157
93809,93811 #1158
93887,93889 #1159
93911,93913 #1160
94007,94009 #1161
94109,94111 #1162
94151,94153 #1163
94307,94309 #1164
94349,94351 #1165
94397,94399 #1166
94439,94441 #1167
94529,94531 #1168
94541,94543 #1169
94559,94561 #1170
94649,94651 #1171
94847,94849 #1172
94949,94951 #1173
95087,95089 #1174
95189,95191 #1175
95231,95233 #1176
95441,95443 #1177
95789,95791 #1178
95801,95803 #1179
95957,95959 #1180
95987,95989 #1181
96179,96181 #1182
96221,96223 #1183
96329,96331 #1184
96587,96589 #1185
96737,96739 #1186
96797,96799 #1187
96821,96823 #1188
97001,97003 #1189
97157,97159 #1190
97169,97171 #1191
97301,97303 #1192
97367,97369 #1193
97379,97381 #1194
97499,97501 #1195
97547,97549 #1196
97577,97579 #1197
97607,97609 #1198
97649,97651 #1199
97787,97789 #1200
97841,97843 #1201
97847,97849 #1202
97859,97861 #1203
98009,98011 #1204
98297,98299 #1205
98321,98323 #1206
98387,98389 #1207
98561,98563 #1208
98639,98641 #1209
98711,98713 #1210
98729,98731 #1211
98807,98809 #1212
98867,98869 #1213
98897,98899 #1214
98909,98911 #1215
98927,98929 #1216
99131,99133 #1217
99137,99139 #1218
99257,99259 #1219
99347,99349 #1220
99527,99529 #1221
99707,99709 #1222
99719,99721 #1223
99989,99991 #1224
100151,100153 #1225
100361,100363 #1226
100391,100393 #1227
100517,100519 #1228
100547,100549 #1229
100799,100801 #1230
101111,101113 #1231
101117,101119 #1232
101159,101161 #1233
101207,101209 #1234
101279,101281 #1235
101501,101503 #1236
101531,101533 #1237
101747,101749 #1238
101837,101839 #1239
101999,102001 #1240
102059,102061 #1241
102077,102079 #1242
102101,102103 #1243
102197,102199 #1244
102251,102253 #1245
102299,102301 #1246
102407,102409 #1247
102497,102499 #1248
102677,102679 #1249
102761,102763 #1250
102911,102913 #1251
102929,102931 #1252
103067,103069 #1253
103091,103093 #1254
103289,103291 #1255
103391,103393 #1256
103421,103423 #1257
103811,103813 #1258
103841,103843 #1259
103967,103969 #1260
103979,103981 #1261
103991,103993 #1262
104087,104089 #1263
104147,104149 #1264
104231,104233 #1265
104309,104311 #1266
104381,104383 #1267
104471,104473 #1268
104549,104551 #1269
104681,104683 #1270
104759,104761 #1271
104801,104803 #1272
104849,104851 #1273
105227,105229 #1274
105251,105253 #1275
105359,105361 #1276
105527,105529 #1277
105767,105769 #1278
106031,106033 #1279
106121,106123 #1280
106187,106189 #1281
106217,106219 #1282
106277,106279 #1283
106319,106321 #1284
106451,106453 #1285
106541,106543 #1286
106619,106621 #1287
106661,106663 #1288
106751,106753 #1289
106781,106783 #1290
106859,106861 #1291
106961,106963 #1292
107069,107071 #1293
107099,107101 #1294
107507,107509 #1295
107717,107719 #1296
107837,107839 #1297
108011,108013 #1298
108107,108109 #1299
108191,108193 #1300
108287,108289 #1301
108377,108379 #1302
108461,108463 #1303
108497,108499 #1304
108707,108709 #1305
108791,108793 #1306
108881,108883 #1307
108947,108949 #1308
108959,108961 #1309
109139,109141 #1310
109169,109171 #1311
109199,109201 #1312
109451,109453 #1313
109469,109471 #1314
109517,109519 #1315
109619,109621 #1316
109661,109663 #1317
109829,109831 #1318
109841,109843 #1319
109847,109849 #1320
110321,110323 #1321
110477,110479 #1322
110501,110503 #1323
110567,110569 #1324
110729,110731 #1325
110819,110821 #1326
110879,110881 #1327
110921,110923 #1328
111029,111031 #1329
111119,111121 #1330
111227,111229 #1331
111269,111271 #1332
111491,111493 #1333
111731,111733 #1334
111779,111781 #1335
111827,111829 #1336
111869,111871 #1337
112067,112069 #1338
112247,112249 #1339
112289,112291 #1340
112337,112339 #1341
112361,112363 #1342
112571,112573 #1343
112601,112603 #1344
112757,112759 #1345
112919,112921 #1346
113021,113023 #1347
113039,113041 #1348
113081,113083 #1349
113147,113149 #1350
113159,113161 #1351
113171,113173 #1352
113327,113329 #1353
113357,113359 #1354
113381,113383 #1355
113537,113539 #1356
113621,113623 #1357
113717,113719 #1358
113759,113761 #1359
113777,113779 #1360
114041,114043 #1361
114197,114199 #1362
114599,114601 #1363
114641,114643 #1364
114659,114661 #1365
114689,114691 #1366
114797,114799 #1367
115019,115021 #1368
115151,115153 #1369
115301,115303 #1370
115319,115321 #1371
115361,115363 #1372
115469,115471 #1373
115601,115603 #1374
115769,115771 #1375
115781,115783 #1376
115859,115861 #1377
115877,115879 #1378
115901,115903 #1379
115931,115933 #1380
115979,115981 #1381
116099,116101 #1382
116189,116191 #1383
116531,116533 #1384
116537,116539 #1385
116687,116689 #1386
116789,116791 #1387
116927,116929 #1388
117041,117043 #1389
117191,117193 #1390
117239,117241 #1391
117329,117331 #1392
117371,117373 #1393
117497,117499 #1394
117539,117541 #1395
117617,117619 #1396
117671,117673 #1397
117701,117703 #1398
117809,117811 #1399
117839,117841 #1400
117881,117883 #1401
117977,117979 #1402
117989,117991 #1403
118169,118171 #1404
118211,118213 #1405
118247,118249 #1406
118409,118411 #1407
118619,118621 #1408
118799,118801 #1409
118901,118903 #1410
119087,119089 #1411
119099,119101 #1412
119129,119131 #1413
119291,119293 #1414
119297,119299 #1415
119417,119419 #1416
119549,119551 #1417
119657,119659 #1418
119687,119689 #1419
119699,119701 #1420
119771,119773 #1421
119849,119851 #1422
119921,119923 #1423
119981,119983 #1424
120047,120049 #1425
120077,120079 #1426
120689,120691 #1427
120737,120739 #1428
120917,120919 #1429
120941,120943 #1430
121019,121021 #1431
121061,121063 #1432
121169,121171 #1433
121349,121351 #1434
121367,121369 #1435
121439,121441 #1436
121577,121579 #1437
121607,121609 #1438
121631,121633 #1439
121787,121789 #1440
121949,121951 #1441
122027,122029 #1442
122039,122041 #1443
122051,122053 #1444
122147,122149 #1445
122201,122203 #1446
122207,122209 #1447
122321,122323 #1448
122387,122389 #1449
122399,122401 #1450
122501,122503 #1451
122597,122599 #1452
122609,122611 #1453
122651,122653 #1454
122741,122743 #1455
122867,122869 #1456
123377,123379 #1457
123491,123493 #1458
123551,123553 #1459
123581,123583 #1460
123731,123733 #1461
124121,124123 #1462
124181,124183 #1463
124247,124249 #1464
124301,124303 #1465
124337,124339 #1466
124349,124351 #1467
124427,124429 #1468
124541,124543 #1469
124769,124771 #1470
124781,124783 #1471
124907,124909 #1472
124979,124981 #1473
125117,125119 #1474
125219,125221 #1475
125507,125509 #1476
125639,125641 #1477
125789,125791 #1478
125897,125899 #1479
125927,125929 #1480
126011,126013 #1481
126227,126229 #1482
126491,126493 #1483
126611,126613 #1484
126857,126859 #1485
127031,127033 #1486
127079,127081 #1487
127217,127219 #1488
127247,127249 #1489
127289,127291 #1490
127607,127609 #1491
127679,127681 #1492
127709,127711 #1493
127817,127819 #1494
128111,128113 #1495
128201,128203 #1496
128237,128239 #1497
128339,128341 #1498
128411,128413 #1499
128519,128521 #1500
128549,128551 #1501
128657,128659 #1502
128747,128749 #1503
128831,128833 #1504
128939,128941 #1505
128969,128971 #1506
128981,128983 #1507
129119,129121 #1508
129221,129223 #1509
129287,129289 #1510
129401,129403 #1511
129497,129499 #1512
129527,129529 #1513
129587,129589 #1514
129629,129631 #1515
129641,129643 #1516
129917,129919 #1517
130199,130201 #1518
130259,130261 #1519
130367,130369 #1520
130409,130411 #1521
130619,130621 #1522
130631,130633 #1523
130649,130651 #1524
130841,130843 #1525
131009,131011 #1526
131111,131113 #1527
131249,131251 #1528
131447,131449 #1529
131477,131479 #1530
131639,131641 #1531
131711,131713 #1532
131777,131779 #1533
131837,131839 #1534
131891,131893 #1535
131939,131941 #1536
132047,132049 #1537
132329,132331 #1538
132437,132439 #1539
132527,132529 #1540
132707,132709 #1541
132749,132751 #1542
132761,132763 #1543
132857,132859 #1544
132947,132949 #1545
133277,133279 #1546
133319,133321 #1547
133349,133351 #1548
133541,133543 #1549
133631,133633 #1550
133709,133711 #1551
133811,133813 #1552
133979,133981 #1553
134087,134089 #1554
134291,134293 #1555
134339,134341 #1556
134369,134371 #1557
134399,134401 #1558
134591,134593 #1559
134681,134683 #1560
134837,134839 #1561
134921,134923 #1562
135017,135019 #1563
135209,135211 #1564
135281,135283 #1565
135347,135349 #1566
135389,135391 #1567
135431,135433 #1568
135461,135463 #1569
135467,135469 #1570
135599,135601 #1571
135647,135649 #1572
135719,135721 #1573
135911,135913 #1574
135977,135979 #1575
136067,136069 #1576
136397,136399 #1577
136481,136483 #1578
136601,136603 #1579
136649,136651 #1580
136691,136693 #1581
136709,136711 #1582
136751,136753 #1583
136811,136813 #1584
136859,136861 #1585
136949,136951 #1586
136991,136993 #1587
137087,137089 #1588
137117,137119 #1589
137339,137341 #1590
137867,137869 #1591
137909,137911 #1592
138077,138079 #1593
138179,138181 #1594
138239,138241 #1595
138371,138373 #1596
138401,138403 #1597
138449,138451 #1598
138569,138571 #1599
138797,138799 #1600
139121,139123 #1601
139199,139201 #1602
139301,139303 #1603
139367,139369 #1604
139457,139459 #1605
139589,139591 #1606
139661,139663 #1607
139967,139969 #1608
140069,140071 #1609
140417,140419 #1610
140549,140551 #1611
140627,140629 #1612
140681,140683 #1613
140729,140731 #1614
140759,140761 #1615
140837,140839 #1616
140867,140869 #1617
140891,140893 #1618
141179,141181 #1619
141221,141223 #1620
141497,141499 #1621
141509,141511 #1622
141677,141679 #1623
141707,141709 #1624
141767,141769 #1625
141851,141853 #1626
141959,141961 #1627
142097,142099 #1628
142157,142159 #1629
142589,142591 #1630
142607,142609 #1631
142697,142699 #1632
142757,142759 #1633
142787,142789 #1634
142871,142873 #1635
142979,142981 #1636
143111,143113 #1637
143261,143263 #1638
143501,143503 #1639
143567,143569 #1640
143651,143653 #1641
143831,143833 #1642
143879,143881 #1643
144071,144073 #1644
144161,144163 #1645
144167,144169 #1646
144407,144409 #1647
144479,144481 #1648
144539,144541 #1649
144887,144889 #1650
145007,145009 #1651
145511,145513 #1652
145547,145549 #1653
145601,145603 #1654
145679,145681 #1655
145721,145723 #1656
145757,145759 #1657
145931,145933 #1658
145967,145969 #1659
146009,146011 #1660
146021,146023 #1661
146057,146059 #1662
146297,146299 #1663
146381,146383 #1664
146519,146521 #1665
146681,146683 #1666
146891,146893 #1667
146987,146989 #1668
147029,147031 #1669
147137,147139 #1670
147209,147211 #1671
147227,147229 #1672
147449,147451 #1673
147671,147673 #1674
148061,148063 #1675
148151,148153 #1676
148199,148201 #1677
148301,148303 #1678
148469,148471 #1679
148667,148669 #1680
148691,148693 #1681
148721,148723 #1682
148781,148783 #1683
148859,148861 #1684
148931,148933 #1685
149057,149059 #1686
149099,149101 #1687
149111,149113 #1688
149159,149161 #1689
149249,149251 #1690
149417,149419 #1691
149489,149491 #1692
149519,149521 #1693
149531,149533 #1694
149561,149563 #1695
149627,149629 #1696
149711,149713 #1697
149729,149731 #1698
149837,149839 #1699
149909,149911 #1700
149969,149971 #1701
150089,150091 #1702
150209,150211 #1703
150221,150223 #1704
150299,150301 #1705
150377,150379 #1706
150587,150589 #1707
150767,150769 #1708
150881,150883 #1709
150959,150961 #1710
150989,150991 #1711
151007,151009 #1712
151049,151051 #1713
151169,151171 #1714
151241,151243 #1715
151337,151339 #1716
151379,151381 #1717
151607,151609 #1718
151769,151771 #1719
151847,151849 #1720
151901,151903 #1721
151937,151939 #1722
151967,151969 #1723
152027,152029 #1724
152039,152041 #1725
152081,152083 #1726
152417,152419 #1727
152441,152443 #1728
152459,152461 #1729
152531,152533 #1730
152597,152599 #1731
152639,152641 #1732
152819,152821 #1733
152837,152839 #1734
152897,152899 #1735
152939,152941 #1736
153071,153073 #1737
153269,153271 #1738
153407,153409 #1739
153509,153511 #1740
153521,153523 #1741
153887,153889 #1742
153911,153913 #1743
153947,153949 #1744
154079,154081 #1745
154157,154159 #1746
154181,154183 #1747
154211,154213 #1748
154277,154279 #1749
154571,154573 #1750
154589,154591 #1751
154619,154621 #1752
154667,154669 #1753
154787,154789 #1754
154871,154873 #1755
155081,155083 #1756
155201,155203 #1757
155381,155383 #1758
155537,155539 #1759
155579,155581 #1760
155717,155719 #1761
155849,155851 #1762
155861,155863 #1763
155891,155893 #1764
156059,156061 #1765
156227,156229 #1766
156257,156259 #1767
156419,156421 #1768
156491,156493 #1769
156677,156679 #1770
156797,156799 #1771
156899,156901 #1772
156941,156943 #1773
157049,157051 #1774
157217,157219 #1775
157229,157231 #1776
157271,157273 #1777
157277,157279 #1778
157349,157351 #1779
157427,157429 #1780
157559,157561 #1781
157637,157639 #1782
157667,157669 #1783
157769,157771 #1784
157931,157933 #1785
158141,158143 #1786
158231,158233 #1787
158357,158359 #1788
158747,158749 #1789
158759,158761 #1790
159167,159169 #1791
159191,159193 #1792
159347,159349 #1793
159539,159541 #1794
159569,159571 #1795
159629,159631 #1796
159671,159673 #1797
159737,159739 #1798
159791,159793 #1799
159869,159871 #1800
159977,159979 #1801
160031,160033 #1802
160079,160081 #1803
160091,160093 #1804
160481,160483 #1805
160619,160621 #1806
160637,160639 #1807
160649,160651 #1808
160709,160711 #1809
160751,160753 #1810
160877,160879 #1811
160967,160969 #1812
161339,161341 #1813
161459,161461 #1814
161561,161563 #1815
161639,161641 #1816
161729,161731 #1817
161741,161743 #1818
161771,161773 #1819
161879,161881 #1820
161921,161923 #1821
161969,161971 #1822
162287,162289 #1823
162389,162391 #1824
162527,162529 #1825
162749,162751 #1826
162821,162823 #1827
162971,162973 #1828
163019,163021 #1829
163061,163063 #1830
163127,163129 #1831
163169,163171 #1832
163307,163309 #1833
163409,163411 #1834
163481,163483 #1835
163859,163861 #1836
163979,163981 #1837
163991,163993 #1838
164147,164149 #1839
164231,164233 #1840
164249,164251 #1841
164429,164431 #1842
164447,164449 #1843
164621,164623 #1844
164837,164839 #1845
164999,165001 #1846
165047,165049 #1847
165311,165313 #1848
165551,165553 #1849
165587,165589 #1850
165701,165703 #1851
165707,165709 #1852
165719,165721 #1853
166301,166303 #1854
166349,166351 #1855
166601,166603 #1856
166667,166669 #1857
166739,166741 #1858
166781,166783 #1859
166841,166843 #1860
166847,166849 #1861
167021,167023 #1862
167117,167119 #1863
167267,167269 #1864
167309,167311 #1865
167339,167341 #1866
167441,167443 #1867
167621,167623 #1868
167777,167779 #1869
167861,167863 #1870
168449,168451 #1871
168599,168601 #1872
168629,168631 #1873
168899,168901 #1874
169007,169009 #1875
169067,169069 #1876
169217,169219 #1877
169241,169243 #1878
169319,169321 #1879
169691,169693 #1880
169751,169753 #1881
169889,169891 #1882
170099,170101 #1883
170351,170353 #1884
170369,170371 #1885
170537,170539 #1886
170759,170761 #1887
171047,171049 #1888
171077,171079 #1889
171161,171163 #1890
171167,171169 #1891
171251,171253 #1892
171401,171403 #1893
171467,171469 #1894
171539,171541 #1895
171671,171673 #1896
171761,171763 #1897
172169,172171 #1898
172217,172219 #1899
172421,172423 #1900
172439,172441 #1901
172517,172519 #1902
173021,173023 #1903
173189,173191 #1904
173207,173209 #1905
173291,173293 #1906
173357,173359 #1907
173429,173431 #1908
173669,173671 #1909
173741,173743 #1910
173777,173779 #1911
174017,174019 #1912
174047,174049 #1913
174077,174079 #1914
174257,174259 #1915
174329,174331 #1916
174467,174469 #1917
174569,174571 #1918
174761,174763 #1919
174929,174931 #1920
174989,174991 #1921
175067,175069 #1922
175079,175081 #1923
175391,175393 #1924
175631,175633 #1925
175757,175759 #1926
175781,175783 #1927
175937,175939 #1928
175961,175963 #1929
175991,175993 #1930
176021,176023 #1931
176051,176053 #1932
176087,176089 #1933
176159,176161 #1934
176327,176329 #1935
176417,176419 #1936
176459,176461 #1937
176507,176509 #1938
176549,176551 #1939
176597,176599 #1940
176609,176611 #1941
176711,176713 #1942
176777,176779 #1943
176789,176791 #1944
176807,176809 #1945
176921,176923 #1946
177011,177013 #1947
177209,177211 #1948
177431,177433 #1949
177677,177679 #1950
177761,177763 #1951
177839,177841 #1952
177887,177889 #1953
178037,178039 #1954
178067,178069 #1955
178091,178093 #1956
178247,178249 #1957
178259,178261 #1958
178349,178351 #1959
178439,178441 #1960
178487,178489 #1961
178559,178561 #1962
178601,178603 #1963
178691,178693 #1964
178817,178819 #1965
178907,178909 #1966
178931,178933 #1967
179381,179383 #1968
179579,179581 #1969
179591,179593 #1970
179657,179659 #1971
179687,179689 #1972
179717,179719 #1973
179819,179821 #1974
179897,179899 #1975
179951,179953 #1976
179999,180001 #1977
180071,180073 #1978
180179,180181 #1979
180239,180241 #1980
180287,180289 #1981
180539,180541 #1982
180749,180751 #1983
180797,180799 #1984
181001,181003 #1985
181061,181063 #1986
181199,181201 #1987
181211,181213 #1988
181301,181303 #1989
181397,181399 #1990
181457,181459 #1991
181499,181501 #1992
181607,181609 #1993
181667,181669 #1994
181757,181759 #1995
181787,181789 #1996
181871,181873 #1997
181889,181891 #1998
182009,182011 #1999
182027,182029 #2000
182057,182059 #2001
182099,182101 #2002
182129,182131 #2003
182177,182179 #2004
182339,182341 #2005
182387,182389 #2006
182471,182473 #2007
182639,182641 #2008
182657,182659 #2009
182711,182713 #2010
182927,182929 #2011
183089,183091 #2012
183299,183301 #2013
183317,183319 #2014
183437,183439 #2015
183497,183499 #2016
183509,183511 #2017
183569,183571 #2018
183707,183709 #2019
183761,183763 #2020
183917,183919 #2021
183971,183973 #2022
184187,184189 #2023
184271,184273 #2024
184487,184489 #2025
184607,184609 #2026
184631,184633 #2027
184649,184651 #2028
184829,184831 #2029
184901,184903 #2030
184967,184969 #2031
184997,184999 #2032
185069,185071 #2033
185369,185371 #2034
185531,185533 #2035
185567,185569 #2036
185681,185683 #2037
185747,185749 #2038
185819,185821 #2039
185831,185833 #2040
185957,185959 #2041
186161,186163 #2042
186227,186229 #2043
186299,186301 #2044
186377,186379 #2045
186479,186481 #2046
186581,186583 #2047
186647,186649 #2048
186707,186709 #2049
186761,186763 #2050
186869,186871 #2051
187067,187069 #2052
187127,187129 #2053
187139,187141 #2054
187217,187219 #2055
187337,187339 #2056
187469,187471 #2057
187631,187633 #2058
187637,187639 #2059
187907,187909 #2060
188831,188833 #2061
188861,188863 #2062
188939,188941 #2063
189017,189019 #2064
189041,189043 #2065
189149,189151 #2066
189251,189253 #2067
189347,189349 #2068
189389,189391 #2069
189437,189439 #2070
189491,189493 #2071
189617,189619 #2072
189797,189799 #2073
189851,189853 #2074
189947,189949 #2075
190367,190369 #2076
190577,190579 #2077
190667,190669 #2078
190709,190711 #2079
190889,190891 #2080
191141,191143 #2081
191249,191251 #2082
191297,191299 #2083
191339,191341 #2084
191447,191449 #2085
191459,191461 #2086
191507,191509 #2087
191531,191533 #2088
191561,191563 #2089
191669,191671 #2090
191747,191749 #2091
191801,191803 #2092
191831,191833 #2093
192191,192193 #2094
192317,192319 #2095
192341,192343 #2096
192461,192463 #2097
192497,192499 #2098
192581,192583 #2099
192611,192613 #2100
192629,192631 #2101
192887,192889 #2102
192977,192979 #2103
193181,193183 #2104
193379,193381 #2105
193601,193603 #2106
193811,193813 #2107
193859,193861 #2108
193871,193873 #2109
193937,193939 #2110
194069,194071 #2111
194267,194269 #2112
194681,194683 #2113
194861,194863 #2114
194867,194869 #2115
195047,195049 #2116
195161,195163 #2117
195341,195343 #2118
195539,195541 #2119
195731,195733 #2120
195737,195739 #2121
195929,195931 #2122
195971,195973 #2123
196169,196171 #2124
196277,196279 #2125
196499,196501 #2126
196541,196543 #2127
196661,196663 #2128
196769,196771 #2129
196871,196873 #2130
196991,196993 #2131
197159,197161 #2132
197297,197299 #2133
197339,197341 #2134
197369,197371 #2135
197381,197383 #2136
197567,197569 #2137
197597,197599 #2138
197711,197713 #2139
197891,197893 #2140
197957,197959 #2141
197969,197971 #2142
198221,198223 #2143
198257,198259 #2144
198347,198349 #2145
198437,198439 #2146
198461,198463 #2147
198827,198829 #2148
198839,198841 #2149
198899,198901 #2150
198941,198943 #2151
199037,199039 #2152
199151,199153 #2153
199487,199489 #2154
199499,199501 #2155
199601,199603 #2156
199739,199741 #2157
199751,199753 #2158
199811,199813 #2159
199931,199933 #2160
200381,200383 #2161
200867,200869 #2162
200927,200929 #2163
200987,200989 #2164
201119,201121 #2165
201209,201211 #2166
201401,201403 #2167
201449,201451 #2168
201491,201493 #2169
201497,201499 #2170
201767,201769 #2171
201821,201823 #2172
201827,201829 #2173
202061,202063 #2174
202127,202129 #2175
202289,202291 #2176
202637,202639 #2177
202751,202753 #2178
202877,202879 #2179
202931,202933 #2180
203207,203209 #2181
203309,203311 #2182
203321,203323 #2183
203339,203341 #2184
203351,203353 #2185
203381,203383 #2186
203417,203419 #2187
203429,203431 #2188
203459,203461 #2189
203657,203659 #2190
203771,203773 #2191
203807,203809 #2192
203909,203911 #2193
203969,203971 #2194
204161,204163 #2195
204299,204301 #2196
204329,204331 #2197
204359,204361 #2198
204437,204439 #2199
204509,204511 #2200
204599,204601 #2201
204749,204751 #2202
204791,204793 #2203
204857,204859 #2204
205031,205033 #2205
205211,205213 #2206
205397,205399 #2207
205421,205423 #2208
205661,205663 #2209
205949,205951 #2210
205991,205993 #2211
206081,206083 #2212
206177,206179 #2213
206249,206251 #2214
206279,206281 #2215
206411,206413 #2216
206639,206641 #2217
206819,206821 #2218
206909,206911 #2219
206951,206953 #2220
207197,207199 #2221
207239,207241 #2222
207329,207331 #2223
207341,207343 #2224
207479,207481 #2225
207509,207511 #2226
207521,207523 #2227
207671,207673 #2228
207719,207721 #2229
207797,207799 #2230
207971,207973 #2231
208001,208003 #2232
208139,208141 #2233
208277,208279 #2234
208391,208393 #2235
208457,208459 #2236
208499,208501 #2237
208511,208513 #2238
208589,208591 #2239
208697,208699 #2240
208889,208891 #2241
208931,208933 #2242
208961,208963 #2243
208991,208993 #2244
209201,209203 #2245
209267,209269 #2246
209357,209359 #2247
209567,209569 #2248
209579,209581 #2249
209621,209623 #2250
209717,209719 #2251
209819,209821 #2252
209927,209929 #2253
210191,210193 #2254
210317,210319 #2255
210359,210361 #2256
210401,210403 #2257
210599,210601 #2258
210809,210811 #2259
210911,210913 #2260
211049,211051 #2261
211061,211063 #2262
211151,211153 #2263
211217,211219 #2264
211229,211231 #2265
211499,211501 #2266
211571,211573 #2267
211661,211663 #2268
211691,211693 #2269
211877,211879 #2270
211889,211891 #2271
211931,211933 #2272
212207,212209 #2273
212669,212671 #2274
212867,212869 #2275
213131,213133 #2276
213287,213289 #2277
213359,213361 #2278
213611,213613 #2279
213947,213949 #2280
214007,214009 #2281
214031,214033 #2282
214211,214213 #2283
214481,214483 #2284
214517,214519 #2285
214559,214561 #2286
214787,214789 #2287
215141,215143 #2288
215351,215353 #2289
215459,215461 #2290
215687,215689 #2291
215981,215983 #2292
216317,216319 #2293
216371,216373 #2294
216551,216553 #2295
216569,216571 #2296
216647,216649 #2297
216779,216781 #2298
216899,216901 #2299
216917,216919 #2300
217001,217003 #2301
217199,217201 #2302
217307,217309 #2303
217337,217339 #2304
217361,217363 #2305
217367,217369 #2306
217409,217411 #2307
217517,217519 #2308
217559,217561 #2309
217577,217579 #2310
217907,217909 #2311
217979,217981 #2312
218081,218083 #2313
218417,218419 #2314
218459,218461 #2315
218549,218551 #2316
218627,218629 #2317
218717,218719 #2318
218969,218971 #2319
218987,218989 #2320
219017,219019 #2321
219311,219313 #2322
219407,219409 #2323
219647,219649 #2324
219677,219679 #2325
219761,219763 #2326
219797,219799 #2327
219941,219943 #2328
219977,219979 #2329
220019,220021 #2330
220469,220471 #2331
220511,220513 #2332
220859,220861 #2333
220877,220879 #2334
220901,220903 #2335
220931,220933 #2336
221069,221071 #2337
221171,221173 #2338
221201,221203 #2339
221399,221401 #2340
221411,221413 #2341
221537,221539 #2342
221621,221623 #2343
221657,221659 #2344
221717,221719 #2345
221951,221953 #2346
221987,221989 #2347
222041,222043 #2348
222107,222109 #2349
222149,222151 #2350
222161,222163 #2351
222197,222199 #2352
222347,222349 #2353
222791,222793 #2354
222839,222841 #2355
222977,222979 #2356
223007,223009 #2357
223049,223051 #2358
223061,223063 #2359
223217,223219 #2360
223241,223243 #2361
223337,223339 #2362
223439,223441 #2363
223547,223549 #2364
223679,223681 #2365
223757,223759 #2366
223829,223831 #2367
223841,223843 #2368
223919,223921 #2369
224069,224071 #2370
224129,224131 #2371
224909,224911 #2372
225077,225079 #2373
225161,225163 #2374
225221,225223 #2375
225287,225289 #2376
225341,225343 #2377
225347,225349 #2378
225371,225373 #2379
225527,225529 #2380
225581,225583 #2381
225611,225613 #2382
225749,225751 #2383
225767,225769 #2384
225779,225781 #2385
225941,225943 #2386
226199,226201 #2387
226379,226381 #2388
226451,226453 #2389
226547,226549 #2390
226817,226819 #2391
226901,226903 #2392
227111,227113 #2393
227189,227191 #2394
227231,227233 #2395
227471,227473 #2396
227531,227533 #2397
227567,227569 #2398
227609,227611 #2399
227627,227629 #2400
227651,227653 #2401
228197,228199 #2402
228299,228301 #2403
228419,228421 #2404
228509,228511 #2405
228521,228523 #2406
228617,228619 #2407
228731,228733 #2408
228797,228799 #2409
228881,228883 #2410
228911,228913 #2411
228959,228961 #2412
229247,229249 #2413
229547,229549 #2414
229589,229591 #2415
229637,229639 #2416
229751,229753 #2417
229769,229771 #2418
229847,229849 #2419
229937,229939 #2420
229961,229963 #2421
229979,229981 #2422
230309,230311 #2423
230339,230341 #2424
230387,230389 #2425
230561,230563 #2426
230771,230773 #2427
230861,230863 #2428
230939,230941 #2429
230999,231001 #2430
231017,231019 #2431
231107,231109 #2432
231269,231271 #2433
231347,231349 #2434
231431,231433 #2435
231461,231463 #2436
231479,231481 #2437
231611,231613 #2438
231821,231823 #2439
231839,231841 #2440
232049,232051 #2441
232079,232081 #2442
232187,232189 #2443
232409,232411 #2444
232457,232459 #2445
232709,232711 #2446
232751,232753 #2447
232961,232963 #2448
233069,233071 #2449
233141,233143 #2450
233159,233161 #2451
233327,233329 #2452
233417,233419 #2453
233549,233551 #2454
233687,233689 #2455
233879,233881 #2456
233921,233923 #2457
233939,233941 #2458
234191,234193 #2459
234317,234319 #2460
234341,234343 #2461
234461,234463 #2462
234527,234529 #2463
234539,234541 #2464
234587,234589 #2465
234809,234811 #2466
234959,234961 #2467
234977,234979 #2468
235007,235009 #2469
235241,235243 #2470
235307,235309 #2471
235439,235441 #2472
235661,235663 #2473
235787,235789 #2474
235811,235813 #2475
235889,235891 #2476
236207,236209 #2477
236477,236479 #2478
236699,236701 #2479
236771,236773 #2480
236867,236869 #2481
236879,236881 #2482
236891,236893 #2483
236981,236983 #2484
237071,237073 #2485
237089,237091 #2486
237161,237163 #2487
237689,237691 #2488
237857,237859 #2489
237971,237973 #2490
238037,238039 #2491
238079,238081 #2492
238157,238159 #2493
238361,238363 #2494
238529,238531 #2495
238727,238729 #2496
238877,238879 #2497
238919,238921 #2498
239231,239233 #2499
239387,239389 #2500
239429,239431 #2501
239711,239713 #2502
239849,239851 #2503
240041,240043 #2504
240047,240049 #2505
240257,240259 #2506
240347,240349 #2507
240587,240589 #2508
240881,240883 #2509
241049,241051 #2510
241067,241069 #2511
241259,241261 #2512
241361,241363 #2513
241391,241393 #2514
241511,241513 #2515
241559,241561 #2516
241601,241603 #2517
241781,241783 #2518
241919,241921 #2519
241979,241981 #2520
242057,242059 #2521
242171,242173 #2522
242447,242449 #2523
242519,242521 #2524
242729,242731 #2525
243119,243121 #2526
243401,243403 #2527
243431,243433 #2528
243587,243589 #2529
243671,243673 #2530
243701,243703 #2531
243707,243709 #2532
244157,244159 #2533
244217,244219 #2534
244301,244303 #2535
244379,244381 #2536
244637,244639 #2537
244667,244669 #2538
244841,244843 #2539
244859,244861 #2540
245129,245131 #2541
245171,245173 #2542
245417,245419 #2543
245471,245473 #2544
245519,245521 #2545
245561,245563 #2546
245591,245593 #2547
245627,245629 #2548
245681,245683 #2549
245849,245851 #2550
245897,245899 #2551
245909,245911 #2552
245981,245983 #2553
246119,246121 #2554
246131,246133 #2555
246317,246319 #2556
246509,246511 #2557
246611,246613 #2558
246641,246643 #2559
246707,246709 #2560
246809,246811 #2561
246929,246931 #2562
247067,247069 #2563
247337,247339 #2564
247391,247393 #2565
247529,247531 #2566
247601,247603 #2567
247607,247609 #2568
247649,247651 #2569
247691,247693 #2570
247769,247771 #2571
247811,247813 #2572
247991,247993 #2573
247997,247999 #2574
248117,248119 #2575
248177,248179 #2576
248201,248203 #2577
248291,248293 #2578
248639,248641 #2579
248867,248869 #2580
248891,248893 #2581
249131,249133 #2582
249419,249421 #2583
249437,249439 #2584
249497,249499 #2585
249539,249541 #2586
249857,249859 #2587
249971,249973 #2588
250049,250051 #2589
250499,250501 #2590
250739,250741 #2591
250751,250753 #2592
250949,250951 #2593
250967,250969 #2594
251057,251059 #2595
251177,251179 #2596
251201,251203 #2597
251219,251221 #2598
251231,251233 #2599
251261,251263 #2600
251429,251431 #2601
251609,251611 #2602
251621,251623 #2603
251789,251791 #2604
251831,251833 #2605
251939,251941 #2606
251969,251971 #2607
252827,252829 #2608
252911,252913 #2609
253157,253159 #2610
253367,253369 #2611
253607,253609 #2612
253637,253639 #2613
253679,253681 #2614
253787,253789 #2615
253907,253909 #2616
253949,253951 #2617
254039,254041 #2618
254207,254209 #2619
254279,254281 #2620
254489,254491 #2621
254729,254731 #2622
254831,254833 #2623
254927,254929 #2624
255179,255181 #2625
255191,255193 #2626
255251,255253 #2627
255467,255469 #2628
255587,255589 #2629
255839,255841 #2630
255917,255919 #2631
255971,255973 #2632
256019,256021 #2633
256031,256033 #2634
256187,256189 #2635
256391,256393 #2636
256469,256471 #2637
256577,256579 #2638
256721,256723 #2639
256799,256801 #2640
256901,256903 #2641
257219,257221 #2642
257351,257353 #2643
257399,257401 #2644
257501,257503 #2645
257687,257689 #2646
257711,257713 #2647
257861,257863 #2648
257867,257869 #2649
257987,257989 #2650
258107,258109 #2651
258317,258319 #2652
258329,258331 #2653
258611,258613 #2654
258917,258919 #2655
259121,259123 #2656
259157,259159 #2657
259211,259213 #2658
259379,259381 #2659
259451,259453 #2660
259619,259621 #2661
259781,259783 #2662
259991,259993 #2663
260009,260011 #2664
260189,260191 #2665
260207,260209 #2666
260411,260413 #2667
260417,260419 #2668
260549,260551 #2669
260807,260809 #2670
260861,260863 #2671
261011,261013 #2672
261059,261061 #2673
261167,261169 #2674
261431,261433 #2675
261641,261643 #2676
261971,261973 #2677
262049,262051 #2678
262109,262111 #2679
262151,262153 #2680
262349,262351 #2681
262511,262513 #2682
262541,262543 #2683
262649,262651 #2684
262739,262741 #2685
262781,262783 #2686
263267,263269 #2687
263399,263401 #2688
263489,263491 #2689
263519,263521 #2690
263609,263611 #2691
263759,263761 #2692
263819,263821 #2693
263867,263869 #2694
263909,263911 #2695
263951,263953 #2696
264029,264031 #2697
264137,264139 #2698
264167,264169 #2699
264527,264529 #2700
264599,264601 #2701
264791,264793 #2702
264827,264829 #2703
264959,264961 #2704
265091,265093 #2705
265247,265249 #2706
265271,265273 #2707
265337,265339 #2708
265511,265513 #2709
265541,265543 #2710
265619,265621 #2711
265709,265711 #2712
265871,265873 #2713
266027,266029 #2714
266051,266053 #2715
266081,266083 #2716
266291,266293 #2717
266351,266353 #2718
266447,266449 #2719
266477,266479 #2720
266489,266491 #2721
266681,266683 #2722
266687,266689 #2723
266837,266839 #2724
266897,266899 #2725
267131,267133 #2726
267227,267229 #2727
267299,267301 #2728
267389,267391 #2729
267401,267403 #2730
267431,267433 #2731
267479,267481 #2732
267521,267523 #2733
267611,267613 #2734
267647,267649 #2735
267677,267679 #2736
267719,267721 #2737
267737,267739 #2738
267899,267901 #2739
267959,267961 #2740
268517,268519 #2741
268529,268531 #2742
268757,268759 #2743
268781,268783 #2744
268811,268813 #2745
268817,268819 #2746
268841,268843 #2747
268997,268999 #2748
269039,269041 #2749
269177,269179 #2750
269219,269221 #2751
269387,269389 #2752
269429,269431 #2753
270029,270031 #2754
270071,270073 #2755
270131,270133 #2756
270239,270241 #2757
270269,270271 #2758
270461,270463 #2759
270551,270553 #2760
270761,270763 #2761
270797,270799 #2762
271127,271129 #2763
271277,271279 #2764
271499,271501 #2765
271571,271573 #2766
271637,271639 #2767
271769,271771 #2768
271967,271969 #2769
272009,272011 #2770
272189,272191 #2771
272201,272203 #2772
272267,272269 #2773
272351,272353 #2774
272381,272383 #2775
272537,272539 #2776
272717,272719 #2777
272759,272761 #2778
272807,272809 #2779
272981,272983 #2780
272999,273001 #2781
273059,273061 #2782
273269,273271 #2783
273281,273283 #2784
273311,273313 #2785
273641,273643 #2786
273899,273901 #2787
273941,273943 #2788
274121,274123 #2789
274199,274201 #2790
274451,274453 #2791
274709,274711 #2792
274829,274831 #2793
275129,275131 #2794
275159,275161 #2795
275321,275323 #2796
275447,275449 #2797
275459,275461 #2798
275489,275491 #2799
275579,275581 #2800
275591,275593 #2801
275921,275923 #2802
275939,275941 #2803
276041,276043 #2804
276047,276049 #2805
276371,276373 #2806
276587,276589 #2807
276671,276673 #2808
276779,276781 #2809
276821,276823 #2810
276917,276919 #2811
277097,277099 #2812
277259,277261 #2813
277427,277429 #2814
277547,277549 #2815
277577,277579 #2816
277601,277603 #2817
277637,277639 #2818
277787,277789 #2819
277889,277891 #2820
278147,278149 #2821
278207,278209 #2822
278489,278491 #2823
278501,278503 #2824
278561,278563 #2825
278609,278611 #2826
278687,278689 #2827
278741,278743 #2828
278807,278809 #2829
278879,278881 #2830
278909,278911 #2831
279119,279121 #2832
279479,279481 #2833
279551,279553 #2834
279707,279709 #2835
280097,280099 #2836
280337,280339 #2837
280409,280411 #2838
280547,280549 #2839
280589,280591 #2840
280697,280699 #2841
280769,280771 #2842
281189,281191 #2843
281249,281251 #2844
281429,281431 #2845
281549,281551 #2846
281579,281581 #2847
281621,281623 #2848
281651,281653 #2849
281717,281719 #2850
281837,281839 #2851
281921,281923 #2852
282089,282091 #2853
282101,282103 #2854
282239,282241 #2855
282311,282313 #2856
282389,282391 #2857
282407,282409 #2858
282677,282679 #2859
282767,282769 #2860
282911,282913 #2861
283007,283009 #2862
283097,283099 #2863
283181,283183 #2864
283487,283489 #2865
283571,283573 #2866
283607,283609 #2867
283637,283639 #2868
283769,283771 #2869
283859,283861 #2870
284057,284059 #2871
284129,284131 #2872
284159,284161 #2873
284231,284233 #2874
284267,284269 #2875
284507,284509 #2876
284591,284593 #2877
284657,284659 #2878
284729,284731 #2879
284741,284743 #2880
284747,284749 #2881
284831,284833 #2882
284897,284899 #2883
285119,285121 #2884
285281,285283 #2885
285287,285289 #2886
285557,285559 #2887
285611,285613 #2888
285629,285631 #2889
285641,285643 #2890
285707,285709 #2891
285839,285841 #2892
285977,285979 #2893
286061,286063 #2894
286367,286369 #2895
286457,286459 #2896
286541,286543 #2897
286589,286591 #2898
286751,286753 #2899
287057,287059 #2900
287237,287239 #2901
287279,287281 #2902
287501,287503 #2903
287669,287671 #2904
287849,287851 #2905
288179,288181 #2906
288359,288361 #2907
288527,288529 #2908
288647,288649 #2909
288731,288733 #2910
288851,288853 #2911
288929,288931 #2912
288989,288991 #2913
289019,289021 #2914
289031,289033 #2915
289109,289111 #2916
289127,289129 #2917
289139,289141 #2918
289169,289171 #2919
289241,289243 #2920
289841,289843 #2921
290021,290023 #2922
290039,290041 #2923
290441,290443 #2924
290471,290473 #2925
290531,290533 #2926
290621,290623 #2927
290657,290659 #2928
290669,290671 #2929
290837,290839 #2930
291041,291043 #2931
291101,291103 #2932
291167,291169 #2933
291371,291373 #2934
291437,291439 #2935
291647,291649 #2936
291689,291691 #2937
291899,291901 #2938
292079,292081 #2939
292091,292093 #2940
292181,292183 #2941
292469,292471 #2942
292709,292711 #2943
293147,293149 #2944
293177,293179 #2945
293261,293263 #2946
293861,293863 #2947
293999,294001 #2948
294167,294169 #2949
294179,294181 #2950
294311,294313 #2951
294317,294319 #2952
294647,294649 #2953
294947,294949 #2954
294989,294991 #2955
295037,295039 #2956
295079,295081 #2957
295199,295201 #2958
295439,295441 #2959
295871,295873 #2960
295877,295879 #2961
295901,295903 #2962
295949,295951 #2963
296249,296251 #2964
296477,296479 #2965
296507,296509 #2966
296561,296563 #2967
296579,296581 #2968
296729,296731 #2969
296771,296773 #2970
296831,296833 #2971
296909,296911 #2972
296969,296971 #2973
296981,296983 #2974
297467,297469 #2975
297809,297811 #2976
297989,297991 #2977
298157,298159 #2978
298169,298171 #2979
298211,298213 #2980
298409,298411 #2981
298679,298681 #2982
298691,298693 #2983
298757,298759 #2984
298799,298801 #2985
298817,298819 #2986
299027,299029 #2987
299357,299359 #2988
299417,299419 #2989
299471,299473 #2990
299477,299479 #2991
299567,299569 #2992
299681,299683 #2993
299699,299701 #2994
300149,300151 #2995
300191,300193 #2996
300299,300301 #2997
300317,300319 #2998
300491,300493 #2999
300497,300499 #3000
300581,300583 #3001
300647,300649 #3002
300719,300721 #3003
300821,300823 #3004
300929,300931 #3005
301181,301183 #3006
301241,301243 #3007
301331,301333 #3008
301361,301363 #3009
301487,301489 #3010
301577,301579 #3011
301751,301753 #3012
301841,301843 #3013
301991,301993 #3014
301997,301999 #3015
302171,302173 #3016
302189,302191 #3017
302297,302299 #3018
302579,302581 #3019
302831,302833 #3020
302969,302971 #3021
303011,303013 #3022
303089,303091 #3023
303377,303379 #3024
303491,303493 #3025
303551,303553 #3026
303617,303619 #3027
303647,303649 #3028
303689,303691 #3029
304067,304069 #3030
304151,304153 #3031
304301,304303 #3032
304391,304393 #3033
304457,304459 #3034
304559,304561 #3035
304847,304849 #3036
304901,304903 #3037
304979,304981 #3038
305021,305023 #3039
305111,305113 #3040
305351,305353 #3041
305411,305413 #3042
305477,305479 #3043
305717,305719 #3044
305741,305743 #3045
305759,305761 #3046
306167,306169 #3047
306191,306193 #3048
306329,306331 #3049
306347,306349 #3050
306419,306421 #3051
306587,306589 #3052
306701,306703 #3053
306827,306829 #3054
306947,306949 #3055
307031,307033 #3056
307091,307093 #3057
307169,307171 #3058
307187,307189 #3059
307259,307261 #3060
307337,307339 #3061
307397,307399 #3062
307631,307633 #3063
307691,307693 #3064
307871,307873 #3065
308291,308293 #3066
308309,308311 #3067
308489,308491 #3068
308507,308509 #3069
308519,308521 #3070
308639,308641 #3071
308849,308851 #3072
308927,308929 #3073
309011,309013 #3074
309107,309109 #3075
309269,309271 #3076
309311,309313 #3077
309479,309481 #3078
309521,309523 #3079
309539,309541 #3080
309779,309781 #3081
309851,309853 #3082
309929,309931 #3083
310019,310021 #3084
310127,310129 #3085
310229,310231 #3086
310361,310363 #3087
310727,310729 #3088
310829,310831 #3089
311291,311293 #3090
311537,311539 #3091
311567,311569 #3092
311681,311683 #3093
311711,311713 #3094
311747,311749 #3095
311867,311869 #3096
312029,312031 #3097
312071,312073 #3098
312197,312199 #3099
312209,312211 #3100
312251,312253 #3101
312281,312283 #3102
312311,312313 #3103
312551,312553 #3104
312581,312583 #3105
312617,312619 #3106
312677,312679 #3107
312701,312703 #3108
312839,312841 #3109
312929,312931 #3110
312941,312943 #3111
313127,313129 #3112
313151,313153 #3113
313331,313333 #3114
313637,313639 #3115
313739,313741 #3116
313931,313933 #3117
313979,313981 #3118
313991,313993 #3119
314159,314161 #3120
314261,314263 #3121
314357,314359 #3122
314399,314401 #3123
314597,314599 #3124
314777,314779 #3125
315011,315013 #3126
315179,315181 #3127
315407,315409 #3128
315449,315451 #3129
315527,315529 #3130
315701,315703 #3131
315881,315883 #3132
316031,316033 #3133
316241,316243 #3134
316469,316471 #3135
316499,316501 #3136
316661,316663 #3137
316697,316699 #3138
316817,316819 #3139
316859,316861 #3140
317087,317089 #3141
317267,317269 #3142
317321,317323 #3143
317351,317353 #3144
317489,317491 #3145
317591,317593 #3146
317729,317731 #3147
317741,317743 #3148
317771,317773 #3149
317921,317923 #3150
317957,317959 #3151
317969,317971 #3152
318179,318181 #3153
318209,318211 #3154
318287,318289 #3155
318299,318301 #3156
318347,318349 #3157
318557,318559 #3158
318677,318679 #3159
318749,318751 #3160
318809,318811 #3161
318881,318883 #3162
318917,318919 #3163
319127,319129 #3164
319439,319441 #3165
319589,319591 #3166
319679,319681 #3167
319727,319729 #3168
319817,319819 #3169
319829,319831 #3170
320009,320011 #3171
320039,320041 #3172
320081,320083 #3173
320141,320143 #3174
320237,320239 #3175
320267,320269 #3176
320291,320293 #3177
320387,320389 #3178
320561,320563 #3179
320609,320611 #3180
320657,320659 #3181
320939,320941 #3182
321311,321313 #3183
321329,321331 #3184
321467,321469 #3185
321569,321571 #3186
321617,321619 #3187
321707,321709 #3188
321821,321823 #3189
321947,321949 #3190
322037,322039 #3191
322109,322111 #3192
322169,322171 #3193
322247,322249 #3194
322349,322351 #3195
322571,322573 #3196
322589,322591 #3197
322631,322633 #3198
322769,322771 #3199
322781,322783 #3200
322919,322921 #3201
322997,322999 #3202
323249,323251 #3203
323339,323341 #3204
323369,323371 #3205
323381,323383 #3206
323441,323443 #3207
323471,323473 #3208
323507,323509 #3209
323579,323581 #3210
323597,323599 #3211
323801,323803 #3212
324209,324211 #3213
324299,324301 #3214
324437,324439 #3215
324449,324451 #3216
324587,324589 #3217
324617,324619 #3218
324809,324811 #3219
324869,324871 #3220
324977,324979 #3221
325019,325021 #3222
325079,325081 #3223
325187,325189 #3224
325217,325219 #3225
325229,325231 #3226
325307,325309 #3227
325541,325543 #3228
325691,325693 #3229
325751,325753 #3230
325781,325783 #3231
325889,325891 #3232
326099,326101 #3233
326141,326143 #3234
326147,326149 #3235
326351,326353 #3236
326537,326539 #3237
326561,326563 #3238
326609,326611 #3239
326657,326659 #3240
326867,326869 #3241
326939,326941 #3242
326999,327001 #3243
327209,327211 #3244
327317,327319 #3245
327407,327409 #3246
327419,327421 #3247
327491,327493 #3248
327557,327559 #3249
327581,327583 #3250
327737,327739 #3251
327797,327799 #3252
327827,327829 #3253
327851,327853 #3254
327869,327871 #3255
328061,328063 #3256
328127,328129 #3257
328331,328333 #3258
328379,328381 #3259
328511,328513 #3260
328589,328591 #3261
328619,328621 #3262
328637,328639 #3263
328787,328789 #3264
328847,328849 #3265
328919,328921 #3266
329081,329083 #3267
329207,329209 #3268
329267,329269 #3269
329297,329299 #3270
329471,329473 #3271
329627,329629 #3272
329801,329803 #3273
330017,330019 #3274
330131,330133 #3275
330227,330229 #3276
330287,330289 #3277
330311,330313 #3278
330329,330331 #3279
330431,330433 #3280
330641,330643 #3281
330719,330721 #3282
330791,330793 #3283
330821,330823 #3284
330857,330859 #3285
331337,331339 #3286
331367,331369 #3287
331547,331549 #3288
331577,331579 #3289
331691,331693 #3290
331841,331843 #3291
331907,331909 #3292
331997,331999 #3293
332009,332011 #3294
332159,332161 #3295
332201,332203 #3296
332219,332221 #3297
332471,332473 #3298
332567,332569 #3299
332987,332989 #3300
333029,333031 #3301
333101,333103 #3302
333269,333271 #3303
333449,333451 #3304
333491,333493 #3305
333719,333721 #3306
333791,333793 #3307
334331,334333 #3308
334421,334423 #3309
334427,334429 #3310
334511,334513 #3311
334547,334549 #3312
334751,334753 #3313
334889,334891 #3314
334991,334993 #3315
335171,335173 #3316
335381,335383 #3317
335807,335809 #3318
336029,336031 #3319
336101,336103 #3320
336221,336223 #3321
336251,336253 #3322
336527,336529 #3323
336767,336769 #3324
336827,336829 #3325
336899,336901 #3326
337217,337219 #3327
337277,337279 #3328
337367,337369 #3329
337487,337489 #3330
337541,337543 #3331
337607,337609 #3332
337859,337861 #3333
337871,337873 #3334
337901,337903 #3335
338159,338161 #3336
338267,338269 #3337
338321,338323 #3338
338339,338341 #3339
338411,338413 #3340
338579,338581 #3341
339137,339139 #3342
339671,339673 #3343
339749,339751 #3344
339839,339841 #3345
340061,340063 #3346
340127,340129 #3347
340337,340339 #3348
340451,340453 #3349
340577,340579 #3350
340787,340789 #3351
340931,340933 #3352
340937,340939 #3353
341057,341059 #3354
341321,341323 #3355
341459,341461 #3356
341771,341773 #3357
341951,341953 #3358
342047,342049 #3359
342059,342061 #3360
342071,342073 #3361
342239,342241 #3362
342281,342283 #3363
342341,342343 #3364
342371,342373 #3365
342449,342451 #3366
342467,342469 #3367
342869,342871 #3368
343307,343309 #3369
343379,343381 #3370
343391,343393 #3371
343529,343531 #3372
343559,343561 #3373
343589,343591 #3374
343769,343771 #3375
343799,343801 #3376
343829,343831 #3377
344171,344173 #3378
344207,344209 #3379
344249,344251 #3380
344291,344293 #3381
344681,344683 #3382
344819,344821 #3383
344957,344959 #3384
345017,345019 #3385
345227,345229 #3386
345461,345463 #3387
345599,345601 #3388
345731,345733 #3389
345887,345889 #3390
346139,346141 #3391
346259,346261 #3392
346391,346393 #3393
346397,346399 #3394
346439,346441 #3395
346559,346561 #3396
346649,346651 #3397
346667,346669 #3398
346961,346963 #3399
347057,347059 #3400
347069,347071 #3401
347129,347131 #3402
347141,347143 #3403
347297,347299 #3404
347561,347563 #3405
347729,347731 #3406
347771,347773 #3407
347957,347959 #3408
347981,347983 #3409
347987,347989 #3410
348239,348241 #3411
348419,348421 #3412
348431,348433 #3413
348461,348463 #3414
348917,348919 #3415
348989,348991 #3416
349079,349081 #3417
349379,349381 #3418
349397,349399 #3419
349409,349411 #3420
349829,349831 #3421
349931,349933 #3422
350087,350089 #3423
350429,350431 #3424
350561,350563 #3425
350729,350731 #3426
350981,350983 #3427
351059,351061 #3428
351077,351079 #3429
351257,351259 #3430
351287,351289 #3431
351341,351343 #3432
351359,351361 #3433
351731,351733 #3434
351749,351751 #3435
351929,351931 #3436
352109,352111 #3437
352271,352273 #3438
352367,352369 #3439
352409,352411 #3440
352421,352423 #3441
352481,352483 #3442
352739,352741 #3443
352817,352819 #3444
352907,352909 #3445
352949,352951 #3446
353147,353149 #3447
353201,353203 #3448
353471,353473 #3449
353627,353629 #3450
353867,353869 #3451
354041,354043 #3452
354251,354253 #3453
354257,354259 #3454
354371,354373 #3455
354461,354463 #3456
354551,354553 #3457
354701,354703 #3458
354881,354883 #3459
354971,354973 #3460
355007,355009 #3461
355037,355039 #3462
355109,355111 #3463
355361,355363 #3464
355499,355501 #3465
355517,355519 #3466
355571,355573 #3467
355721,355723 #3468
355937,355939 #3469
355967,355969 #3470
356141,356143 #3471
356171,356173 #3472
356261,356263 #3473
356441,356443 #3474
356561,356563 #3475
356819,356821 #3476
356927,356929 #3477
357107,357109 #3478
357197,357199 #3479
357239,357241 #3480
357281,357283 #3481
357347,357349 #3482
357569,357571 #3483
357611,357613 #3484
357659,357661 #3485
357737,357739 #3486
357779,357781 #3487
358157,358159 #3488
358277,358279 #3489
358289,358291 #3490
358427,358429 #3491
358571,358573 #3492
358667,358669 #3493
358859,358861 #3494
358877,358879 #3495
358901,358903 #3496
358907,358909 #3497
359207,359209 #3498
359297,359299 #3499
359417,359419 #3500
359477,359479 #3501
359561,359563 #3502
360089,360091 #3503
360167,360169 #3504
360287,360289 #3505
360509,360511 #3506
360779,360781 #3507
360821,360823 #3508
360851,360853 #3509
360947,360949 #3510
360977,360979 #3511
361001,361003 #3512
361091,361093 #3513
361211,361213 #3514
361217,361219 #3515
361349,361351 #3516
361409,361411 #3517
361649,361651 #3518
361787,361789 #3519
361871,361873 #3520
361901,361903 #3521
362051,362053 #3522
362291,362293 #3523
362429,362431 #3524
362741,362743 #3525
362951,362953 #3526
363017,363019 #3527
363059,363061 #3528
363149,363151 #3529
363269,363271 #3530
363359,363361 #3531
363371,363373 #3532
363401,363403 #3533
363437,363439 #3534
363887,363889 #3535
363947,363949 #3536
364127,364129 #3537
364289,364291 #3538
364541,364543 #3539
364751,364753 #3540
364919,364921 #3541
365249,365251 #3542
365291,365293 #3543
365411,365413 #3544
365471,365473 #3545
365507,365509 #3546
365567,365569 #3547
365639,365641 #3548
365747,365749 #3549
365837,365839 #3550
366029,366031 #3551
366167,366169 #3552
366341,366343 #3553
366437,366439 #3554
366461,366463 #3555
366701,366703 #3556
366851,366853 #3557
367019,367021 #3558
367121,367123 #3559
367229,367231 #3560
367259,367261 #3561
367307,367309 #3562
367559,367561 #3563
367649,367651 #3564
368231,368233 #3565
368651,368653 #3566
368789,368791 #3567
368801,368803 #3568
369077,369079 #3569
369407,369409 #3570
369659,369661 #3571
369791,369793 #3572
369827,369829 #3573
369959,369961 #3574
370421,370423 #3575
370439,370441 #3576
370661,370663 #3577
370871,370873 #3578
371027,371029 #3579
371069,371071 #3580
371141,371143 #3581
371177,371179 #3582
371249,371251 #3583
371339,371341 #3584
371387,371389 #3585
371927,371929 #3586
371939,371941 #3587
372059,372061 #3588
372269,372271 #3589
372311,372313 #3590
372611,372613 #3591
372707,372709 #3592
372941,372943 #3593
372971,372973 #3594
373181,373183 #3595
373211,373213 #3596
373229,373231 #3597
373361,373363 #3598
373487,373489 #3599
373859,373861 #3600
374039,374041 #3601
374291,374293 #3602
374441,374443 #3603
374639,374641 #3604
374681,374683 #3605
374837,374839 #3606
374987,374989 #3607
375017,375019 #3608
375101,375103 #3609
375119,375121 #3610
375251,375253 #3611
375257,375259 #3612
375281,375283 #3613
375371,375373 #3614
375449,375451 #3615
375509,375511 #3616
375707,375709 #3617
375899,375901 #3618
376001,376003 #3619
376097,376099 #3620
376469,376471 #3621
376529,376531 #3622
376631,376633 #3623
376757,376759 #3624
376889,376891 #3625
376931,376933 #3626
377171,377173 #3627
377327,377329 #3628
377369,377371 #3629
377561,377563 #3630
378149,378151 #3631
378239,378241 #3632
378569,378571 #3633
378821,378823 #3634
379007,379009 #3635
379187,379189 #3636
379397,379399 #3637
379439,379441 #3638
379499,379501 #3639
379571,379573 #3640
379679,379681 #3641
379721,379723 #3642
379997,379999 #3643
380129,380131 #3644
380201,380203 #3645
380267,380269 #3646
380309,380311 #3647
380327,380329 #3648
380459,380461 #3649
380621,380623 #3650
380837,380839 #3651
380867,380869 #3652
380879,380881 #3653
381167,381169 #3654
381221,381223 #3655
381287,381289 #3656
381371,381373 #3657
381527,381529 #3658
381629,381631 #3659
381737,381739 #3660
381791,381793 #3661
381989,381991 #3662
382001,382003 #3663
382229,382231 #3664
382427,382429 #3665
382661,382663 #3666
382727,382729 #3667
382871,382873 #3668
383081,383083 #3669
383099,383101 #3670
383219,383221 #3671
383417,383419 #3672
383519,383521 #3673
383609,383611 #3674
383657,383659 #3675
383681,383683 #3676
383837,383839 #3677
384257,384259 #3678
384287,384289 #3679
384299,384301 #3680
384479,384481 #3681
385079,385081 #3682
385127,385129 #3683
385139,385141 #3684
385289,385291 #3685
385391,385393 #3686
385571,385573 #3687
385589,385591 #3688
385661,385663 #3689
385739,385741 #3690
386039,386041 #3691
386117,386119 #3692
386129,386131 #3693
386159,386161 #3694
386297,386299 #3695
386369,386371 #3696
386381,386383 #3697
386411,386413 #3698
386429,386431 #3699
386609,386611 #3700
386987,386989 #3701
387197,387199 #3702
387677,387679 #3703
387911,387913 #3704
387971,387973 #3705
388109,388111 #3706
388181,388183 #3707
388481,388483 #3708
388691,388693 #3709
388697,388699 #3710
388901,388903 #3711
388931,388933 #3712
388961,388963 #3713
389027,389029 #3714
389171,389173 #3715
389297,389299 #3716
389399,389401 #3717
389531,389533 #3718
389561,389563 #3719
389567,389569 #3720
389999,390001 #3721
390107,390109 #3722
390191,390193 #3723
390209,390211 #3724
390389,390391 #3725
390419,390421 #3726
390491,390493 #3727
390671,390673 #3728
390737,390739 #3729
390959,390961 #3730
390989,390991 #3731
391019,391021 #3732
391217,391219 #3733
391247,391249 #3734
391397,391399 #3735
391451,391453 #3736
391691,391693 #3737
391751,391753 #3738
391889,391891 #3739
392099,392101 #3740
392111,392113 #3741
392261,392263 #3742
392267,392269 #3743
392279,392281 #3744
392297,392299 #3745
392759,392761 #3746
392807,392809 #3747
392849,392851 #3748
392927,392929 #3749
392981,392983 #3750
393077,393079 #3751
393299,393301 #3752
393401,393403 #3753
393539,393541 #3754
393581,393583 #3755
393857,393859 #3756
393929,393931 #3757
394367,394369 #3758
394409,394411 #3759
394577,394579 #3760
394631,394633 #3761
394727,394729 #3762
394811,394813 #3763
394817,394819 #3764
394967,394969 #3765
395111,395113 #3766
395189,395191 #3767
395321,395323 #3768
395429,395431 #3769
395849,395851 #3770
396029,396031 #3771
396041,396043 #3772
396197,396199 #3773
396299,396301 #3774
396377,396379 #3775
396629,396631 #3776
396881,396883 #3777
397151,397153 #3778
397181,397183 #3779
397301,397303 #3780
397427,397429 #3781
397517,397519 #3782
397541,397543 #3783
397547,397549 #3784
397589,397591 #3785
397721,397723 #3786
397751,397753 #3787
397757,397759 #3788
398117,398119 #3789
398339,398341 #3790
398471,398473 #3791
398609,398611 #3792
398681,398683 #3793
398729,398731 #3794
398819,398821 #3795
399149,399151 #3796
399239,399241 #3797
399281,399283 #3798
399389,399391 #3799
399401,399403 #3800
399491,399493 #3801
399689,399691 #3802
399851,399853 #3803
399911,399913 #3804
400031,400033 #3805
400067,400069 #3806
400247,400249 #3807
400679,400681 #3808
400721,400723 #3809
401309,401311 #3810
401537,401539 #3811
401627,401629 #3812
401669,401671 #3813
401771,401773 #3814
401957,401959 #3815
402089,402091 #3816
402131,402133 #3817
402137,402139 #3818
402221,402223 #3819
402329,402331 #3820
402341,402343 #3821
402359,402361 #3822
402527,402529 #3823
402581,402583 #3824
402761,402763 #3825
402767,402769 #3826
402947,402949 #3827
403001,403003 #3828
403061,403063 #3829
403241,403243 #3830
403547,403549 #3831
403679,403681 #3832
403829,403831 #3833
403979,403981 #3834
404009,404011 #3835
404189,404191 #3836
404249,404251 #3837
404267,404269 #3838
404321,404323 #3839
404387,404389 #3840
404429,404431 #3841
404531,404533 #3842
404849,404851 #3843
404981,404983 #3844
405047,405049 #3845
405071,405073 #3846
405089,405091 #3847
405239,405241 #3848
405341,405343 #3849
405437,405439 #3850
405497,405499 #3851
405527,405529 #3852
405677,405679 #3853
405701,405703 #3854
405827,405829 #3855
405869,405871 #3856
405947,405949 #3857
405989,405991 #3858
406169,406171 #3859
406499,406501 #3860
406559,406561 #3861
406577,406579 #3862
406631,406633 #3863
406697,406699 #3864
407177,407179 #3865
407219,407221 #3866
407357,407359 #3867
407501,407503 #3868
407789,407791 #3869
407969,407971 #3870
408209,408211 #3871
408431,408433 #3872
408689,408691 #3873
408701,408703 #3874
408911,408913 #3875
409259,409261 #3876
409289,409291 #3877
409349,409351 #3878
409691,409693 #3879
409709,409711 #3880
409889,409891 #3881
410117,410119 #3882
410141,410143 #3883
410171,410173 #3884
410231,410233 #3885
410279,410281 #3886
410339,410341 #3887
410411,410413 #3888
410489,410491 #3889
410621,410623 #3890
410747,410749 #3891
410999,411001 #3892
411011,411013 #3893
411251,411253 #3894
411527,411529 #3895
411611,411613 #3896
411707,411709 #3897
411737,411739 #3898
411821,411823 #3899
412031,412033 #3900
412037,412039 #3901
412187,412189 #3902
412211,412213 #3903
412589,412591 #3904
412637,412639 #3905
412901,412903 #3906
413069,413071 #3907
413087,413089 #3908
413111,413113 #3909
413141,413143 #3910
413681,413683 #3911
413711,413713 #3912
413867,413869 #3913
414017,414019 #3914
414107,414109 #3915
414311,414313 #3916
414329,414331 #3917
414431,414433 #3918
414641,414643 #3919
414677,414679 #3920
414707,414709 #3921
414767,414769 #3922
415109,415111 #3923
415187,415189 #3924
415271,415273 #3925
415379,415381 #3926
415607,415609 #3927
415799,415801 #3928
415949,415951 #3929
416147,416149 #3930
416387,416389 #3931
416399,416401 #3932
416417,416419 #3933
416441,416443 #3934
416501,416503 #3935
416621,416623 #3936
416849,416851 #3937
417017,417019 #3938
417377,417379 #3939
417491,417493 #3940
417509,417511 #3941
417581,417583 #3942
417719,417721 #3943
417731,417733 #3944
417881,417883 #3945
417959,417961 #3946
418007,418009 #3947
418337,418339 #3948
418349,418351 #3949
418601,418603 #3950
418631,418633 #3951
418811,418813 #3952
419051,419053 #3953
419057,419059 #3954
419189,419191 #3955
419561,419563 #3956
419597,419599 #3957
419789,419791 #3958
419801,419803 #3959
419927,419929 #3960
419999,420001 #3961
420191,420193 #3962
420269,420271 #3963
420317,420319 #3964
420419,420421 #3965
420479,420481 #3966
420569,420571 #3967
420779,420781 #3968
420809,420811 #3969
420851,420853 #3970
420857,420859 #3971
421079,421081 #3972
421121,421123 #3973
421469,421471 #3974
421607,421609 #3975
421697,421699 #3976
421709,421711 #3977
421739,421741 #3978
422087,422089 #3979
422099,422101 #3980
422111,422113 #3981
422309,422311 #3982
422549,422551 #3983
422759,422761 #3984
422867,422869 #3985
422879,422881 #3986
422897,422899 #3987
423257,423259 #3988
423287,423289 #3989
423461,423463 #3990
423557,423559 #3991
423749,423751 #3992
423779,423781 #3993
423989,423991 #3994
424001,424003 #3995
424091,424093 #3996
424271,424273 #3997
424547,424549 #3998
424727,424729 #3999
424769,424771 #4000
424817,424819 #4001
424841,424843 #4002
424889,424891 #4003
425057,425059 #4004
425147,425149 #4005
425279,425281 #4006
425417,425419 #4007
425441,425443 #4008
425471,425473 #4009
425519,425521 #4010
425837,425839 #4011
425987,425989 #4012
426089,426091 #4013
426161,426163 #4014
426551,426553 #4015
426707,426709 #4016
426737,426739 #4017
426761,426763 #4018
426917,426919 #4019
426971,426973 #4020
427067,427069 #4021
427079,427081 #4022
427241,427243 #4023
427247,427249 #4024
427307,427309 #4025
427379,427381 #4026
427421,427423 #4027
427619,427621 #4028
427787,427789 #4029
427877,427879 #4030
427949,427951 #4031
427967,427969 #4032
427991,427993 #4033
428039,428041 #4034
428147,428149 #4035
428249,428251 #4036
428297,428299 #4037
428471,428473 #4038
428567,428569 #4039
428807,428809 #4040
429137,429139 #4041
429281,429283 #4042
429347,429349 #4043
429467,429469 #4044
429509,429511 #4045
429587,429589 #4046
429659,429661 #4047
429677,429679 #4048
429731,429733 #4049
429851,429853 #4050
429887,429889 #4051
429899,429901 #4052
429929,429931 #4053
429971,429973 #4054
430007,430009 #4055
430091,430093 #4056
430277,430279 #4057
430511,430513 #4058
430601,430603 #4059
430697,430699 #4060
430739,430741 #4061
430751,430753 #4062
430907,430909 #4063
430979,430981 #4064
431267,431269 #4065
431447,431449 #4066
431657,431659 #4067
431729,431731 #4068
431801,431803 #4069
431831,431833 #4070
431867,431869 #4071
432137,432139 #4072
432161,432163 #4073
432389,432391 #4074
432557,432559 #4075
432587,432589 #4076
432659,432661 #4077
432797,432799 #4078
432959,432961 #4079
433049,433051 #4080
433259,433261 #4081
433469,433471 #4082
433661,433663 #4083
433679,433681 #4084
433859,433861 #4085
434009,434011 #4086
434111,434113 #4087
434387,434389 #4088
434459,434461 #4089
434561,434563 #4090
434717,434719 #4091
434921,434923 #4092
435107,435109 #4093
435179,435181 #4094
435221,435223 #4095
435401,435403 #4096
435437,435439 #4097
435569,435571 #4098
435647,435649 #4099
435731,435733 #4100
435857,435859 #4101
435947,435949 #4102
436307,436309 #4103
436481,436483 #4104
436529,436531 #4105
436547,436549 #4106
436649,436651 #4107
436727,436729 #4108
436739,436741 #4109
437111,437113 #4110
437387,437389 #4111
437471,437473 #4112
437651,437653 #4113
438047,438049 #4114
438131,438133 #4115
438521,438523 #4116
438827,438829 #4117
439007,439009 #4118
439427,439429 #4119
440177,440179 #4120
440441,440443 #4121
440507,440509 #4122
440549,440551 #4123
440567,440569 #4124
440579,440581 #4125
440651,440653 #4126
440681,440683 #4127
440807,440809 #4128
440939,440941 #4129
440987,440989 #4130
441041,441043 #4131
441107,441109 #4132
441191,441193 #4133
441359,441361 #4134
441797,441799 #4135
441827,441829 #4136
441839,441841 #4137
442007,442009 #4138
442031,442033 #4139
442397,442399 #4140
442487,442489 #4141
442499,442501 #4142
442571,442573 #4143
442577,442579 #4144
442829,442831 #4145
442961,442963 #4146
443039,443041 #4147
443057,443059 #4148
443159,443161 #4149
443291,443293 #4150
443561,443563 #4151
443687,443689 #4152
443759,443761 #4153
443867,443869 #4154
443879,443881 #4155
443939,443941 #4156
443999,444001 #4157
444179,444181 #4158
444287,444289 #4159
444341,444343 #4160
444347,444349 #4161
444401,444403 #4162
444461,444463 #4163
444527,444529 #4164
444791,444793 #4165
445019,445021 #4166
445031,445033 #4167
445631,445633 #4168
445769,445771 #4169
445967,445969 #4170
446189,446191 #4171
446261,446263 #4172
446387,446389 #4173
446399,446401 #4174
446891,446893 #4175
446909,446911 #4176
447257,447259 #4177
447449,447451 #4178
447569,447571 #4179
447701,447703 #4180
447791,447793 #4181
447827,447829 #4182
448139,448141 #4183
448157,448159 #4184
448631,448633 #4185
448871,448873 #4186
448997,448999 #4187
449129,449131 #4188
449171,449173 #4189
449201,449203 #4190
449261,449263 #4191
449417,449419 #4192
449567,449569 #4193
449987,449989 #4194
450101,450103 #4195
450257,450259 #4196
450299,450301 #4197
450479,450481 #4198
450599,450601 #4199
450641,450643 #4200
450797,450799 #4201
450809,450811 #4202
450839,450841 #4203
450881,450883 #4204
451181,451183 #4205
451277,451279 #4206
451301,451303 #4207
451439,451441 #4208
451667,451669 #4209
451679,451681 #4210
451901,451903 #4211
451937,451939 #4212
452159,452161 #4213
452519,452521 #4214
452531,452533 #4215
452537,452539 #4216
452687,452689 #4217
453197,453199 #4218
453377,453379 #4219
453569,453571 #4220
453599,453601 #4221
453641,453643 #4222
453707,453709 #4223
453797,453799 #4224
454031,454033 #4225
454061,454063 #4226
454211,454213 #4227
454229,454231 #4228
454451,454453 #4229
454541,454543 #4230
454577,454579 #4231
454709,454711 #4232
454721,454723 #4233
454847,454849 #4234
454889,454891 #4235
454919,454921 #4236
454967,454969 #4237
455261,455263 #4238
455339,455341 #4239
455471,455473 #4240
455489,455491 #4241
455597,455599 #4242
455681,455683 #4243
456107,456109 #4244
456149,456151 #4245
456557,456559 #4246
456611,456613 #4247
456647,456649 #4248
456767,456769 #4249
456809,456811 #4250
456899,456901 #4251
457001,457003 #4252
457097,457099 #4253
457151,457153 #4254
457277,457279 #4255
457397,457399 #4256
457607,457609 #4257
457979,457981 #4258
458189,458191 #4259
458399,458401 #4260
458531,458533 #4261
458567,458569 #4262
458789,458791 #4263
458957,458959 #4264
459029,459031 #4265
459089,459091 #4266
459167,459169 #4267
459341,459343 #4268
459467,459469 #4269
459521,459523 #4270
459647,459649 #4271
460079,460081 #4272
460709,460711 #4273
460841,460843 #4274
460949,460951 #4275
460979,460981 #4276
461009,461011 #4277
461051,461053 #4278
461297,461299 #4279
461411,461413 #4280
461441,461443 #4281
461687,461689 #4282
461801,461803 #4283
462419,462421 #4284
462491,462493 #4285
462569,462571 #4286
462641,462643 #4287
462899,462901 #4288
463031,463033 #4289
463247,463249 #4290
463319,463321 #4291
463451,463453 #4292
463457,463459 #4293
463511,463513 #4294
463829,463831 #4295
463889,463891 #4296
463919,463921 #4297
464129,464131 #4298
464141,464143 #4299
464171,464173 #4300
464279,464281 #4301
464309,464311 #4302
464381,464383 #4303
464537,464539 #4304
464747,464749 #4305
464771,464773 #4306
464801,464803 #4307
464939,464941 #4308
464951,464953 #4309
465011,465013 #4310
465077,465079 #4311
465161,465163 #4312
465167,465169 #4313
465209,465211 #4314
465317,465319 #4315
465797,465799 #4316
465929,465931 #4317
466181,466183 #4318
466649,466651 #4319
467081,467083 #4320
467237,467239 #4321
467471,467473 #4322
467477,467479 #4323
467627,467629 #4324
467669,467671 #4325
467867,467869 #4326
467879,467881 #4327
467897,467899 #4328
468107,468109 #4329
468239,468241 #4330
468491,468493 #4331
468737,468739 #4332
468887,468889 #4333
469367,469369 #4334
469541,469543 #4335
469877,469879 #4336
470081,470083 #4337
470087,470089 #4338
470207,470209 #4339
470297,470299 #4340
470411,470413 #4341
470471,470473 #4342
470597,470599 #4343
470651,470653 #4344
470957,470959 #4345
471089,471091 #4346
471137,471139 #4347
471281,471283 #4348
471299,471301 #4349
471389,471391 #4350
471617,471619 #4351
471671,471673 #4352
471719,471721 #4353
471929,471931 #4354
472247,472249 #4355
472331,472333 #4356
472391,472393 #4357
472541,472543 #4358
472559,472561 #4359
472709,472711 #4360
472907,472909 #4361
472937,472939 #4362
473201,473203 #4363
473351,473353 #4364
473381,473383 #4365
473441,473443 #4366
473477,473479 #4367
473531,473533 #4368
473741,473743 #4369
473927,473929 #4370
473951,473953 #4371
474389,474391 #4372
474497,474499 #4373
474569,474571 #4374
474581,474583 #4375
474707,474709 #4376
474809,474811 #4377
475091,475093 #4378
475271,475273 #4379
475331,475333 #4380
475367,475369 #4381
475379,475381 #4382
475427,475429 #4383
475619,475621 #4384
475637,475639 #4385
475679,475681 #4386
475691,475693 #4387
475751,475753 #4388
475877,475879 #4389
476027,476029 #4390
476039,476041 #4391
476087,476089 #4392
476477,476479 #4393
476681,476683 #4394
476849,476851 #4395
477011,477013 #4396
477017,477019 #4397
477359,477361 #4398
477551,477553 #4399
477767,477769 #4400
477809,477811 #4401
477821,477823 #4402
478067,478069 #4403
478169,478171 #4404
478241,478243 #4405
478271,478273 #4406
478451,478453 #4407
478481,478483 #4408
478571,478573 #4409
478727,478729 #4410
478739,478741 #4411
478811,478813 #4412
479027,479029 #4413
479189,479191 #4414
479429,479431 #4415
479879,479881 #4416
479951,479953 #4417
480017,480019 #4418
480047,480049 #4419
480059,480061 #4420
480167,480169 #4421
480341,480343 #4422
480449,480451 #4423
480461,480463 #4424
481001,481003 #4425
481301,481303 #4426
481697,481699 #4427
481751,481753 #4428
481847,481849 #4429
482099,482101 #4430
482231,482233 #4431
482399,482401 #4432
482507,482509 #4433
482687,482689 #4434
482717,482719 #4435
482861,482863 #4436
482897,482899 #4437
483209,483211 #4438
483407,483409 #4439
483809,483811 #4440
483827,483829 #4441
484151,484153 #4442
484301,484303 #4443
484457,484459 #4444
484487,484489 #4445
484607,484609 #4446
485207,485209 #4447
485729,485731 #4448
485831,485833 #4449
486041,486043 #4450
486179,486181 #4451
486221,486223 #4452
486329,486331 #4453
486377,486379 #4454
486389,486391 #4455
486509,486511 #4456
486641,486643 #4457
486677,486679 #4458
486767,486769 #4459
486947,486949 #4460
487049,487051 #4461
487211,487213 #4462
487427,487429 #4463
487469,487471 #4464
487601,487603 #4465
487649,487651 #4466
487829,487831 #4467
487889,487891 #4468
488009,488011 #4469
488207,488209 #4470
488231,488233 #4471
488261,488263 #4472
488309,488311 #4473
488399,488401 #4474
488417,488419 #4475
488639,488641 #4476
488687,488689 #4477
489239,489241 #4478
489407,489409 #4479
489551,489553 #4480
489677,489679 #4481
489689,489691 #4482
489791,489793 #4483
489869,489871 #4484
489911,489913 #4485
489941,489943 #4486
489959,489961 #4487
490001,490003 #4488
490031,490033 #4489
490247,490249 #4490
490541,490543 #4491
490571,490573 #4492
490577,490579 #4493
490661,490663 #4494
490769,490771 #4495
490949,490951 #4496
490967,490969 #4497
490991,490993 #4498
491039,491041 #4499
491081,491083 #4500
491297,491299 #4501
491327,491329 #4502
491339,491341 #4503
491501,491503 #4504
491537,491539 #4505
491591,491593 #4506
491651,491653 #4507
492059,492061 #4508
492251,492253 #4509
492617,492619 #4510
492629,492631 #4511
492671,492673 #4512
492719,492721 #4513
492761,492763 #4514
493109,493111 #4515
493121,493123 #4516
493217,493219 #4517
493277,493279 #4518
493397,493399 #4519
493709,493711 #4520
493811,493813 #4521
493937,493939 #4522
494267,494269 #4523
494381,494383 #4524
494441,494443 #4525
494519,494521 #4526
494561,494563 #4527
494759,494761 #4528
495041,495043 #4529
495149,495151 #4530
495359,495361 #4531
495557,495559 #4532
495569,495571 #4533
495587,495589 #4534
495611,495613 #4535
495617,495619 #4536
495749,495751 #4537
495797,495799 #4538
495827,495829 #4539
496229,496231 #4540
496289,496291 #4541
496889,496891 #4542
496997,496999 #4543
497111,497113 #4544
497279,497281 #4545
497507,497509 #4546
497771,497773 #4547
497867,497869 #4548
498101,498103 #4549
498257,498259 #4550
498401,498403 #4551
498467,498469 #4552
498521,498523 #4553
498611,498613 #4554
498689,498691 #4555
498779,498781 #4556
498857,498859 #4557
499127,499129 #4558
499139,499141 #4559
499157,499159 #4560
499181,499183 #4561
499361,499363 #4562
499481,499483 #4563
499661,499663 #4564
499691,499693 #4565
500111,500113 #4566
500177,500179 #4567
500231,500233 #4568
500237,500239 #4569
500471,500473 #4570
500807,500809 #4571
500909,500911 #4572
500921,500923 #4573
501029,501031 #4574
501131,501133 #4575
501341,501343 #4576
501701,501703 #4577
501827,501829 #4578
502079,502081 #4579
502259,502261 #4580
502499,502501 #4581
502631,502633 #4582
502769,502771 #4583
502919,502921 #4584
503231,503233 #4585
503381,503383 #4586
503549,503551 #4587
503609,503611 #4588
503621,503623 #4589
503777,503779 #4590
503819,503821 #4591
503927,503929 #4592
504149,504151 #4593
504377,504379 #4594
504521,504523 #4595
504617,504619 #4596
504797,504799 #4597
504851,504853 #4598
504989,504991 #4599
505031,505033 #4600
505049,505051 #4601
505157,505159 #4602
505277,505279 #4603
505319,505321 #4604
505367,505369 #4605
505409,505411 #4606
505511,505513 #4607
505691,505693 #4608
505709,505711 #4609
506171,506173 #4610
506327,506329 #4611
506459,506461 #4612
506531,506533 #4613
506591,506593 #4614
506687,506689 #4615
506729,506731 #4616
507077,507079 #4617
507137,507139 #4618
507149,507151 #4619
507347,507349 #4620
507359,507361 #4621
507497,507499 #4622
507779,507781 #4623
507917,507919 #4624
508019,508021 #4625
508271,508273 #4626
508577,508579 #4627
508619,508621 #4628
508901,508903 #4629
509147,509149 #4630
509687,509689 #4631
509909,509911 #4632
510047,510049 #4633
510077,510079 #4634
510401,510403 #4635
510449,510451 #4636
510551,510553 #4637
510581,510583 #4638
510611,510613 #4639
510617,510619 #4640
510707,510709 #4641
510941,510943 #4642
511109,511111 #4643
511151,511153 #4644
511169,511171 #4645
511211,511213 #4646
511631,511633 #4647
511961,511963 #4648
512009,512011 #4649
512249,512251 #4650
512579,512581 #4651
512591,512593 #4652
512711,512713 #4653
512819,512821 #4654
512927,512929 #4655
512999,513001 #4656
513101,513103 #4657
513167,513169 #4658
513311,513313 #4659
513479,513481 #4660
513509,513511 #4661
513767,513769 #4662
513839,513841 #4663
514049,514051 #4664
514079,514081 #4665
514247,514249 #4666
514529,514531 #4667
514637,514639 #4668
514649,514651 #4669
514739,514741 #4670
515087,515089 #4671
515231,515233 #4672
515369,515371 #4673
515651,515653 #4674
515771,515773 #4675
516161,516163 #4676
516251,516253 #4677
516359,516361 #4678
516431,516433 #4679
516539,516541 #4680
516587,516589 #4681
516617,516619 #4682
516947,516949 #4683
516977,516979 #4684
517079,517081 #4685
517241,517243 #4686
517457,517459 #4687
517469,517471 #4688
517499,517501 #4689
517511,517513 #4690
517547,517549 #4691
517637,517639 #4692
518057,518059 #4693
518099,518101 #4694
518129,518131 #4695
518207,518209 #4696
518237,518239 #4697
518387,518389 #4698
518429,518431 #4699
518471,518473 #4700
518741,518743 #4701
518759,518761 #4702
518801,518803 #4703
518807,518809 #4704
518981,518983 #4705
519089,519091 #4706
519119,519121 #4707
519227,519229 #4708
519371,519373 #4709
519521,519523 #4710
519551,519553 #4711
519917,519919 #4712
520019,520021 #4713
520307,520309 #4714
520361,520363 #4715
520379,520381 #4716
520409,520411 #4717
520547,520549 #4718
520607,520609 #4719
520631,520633 #4720
520967,520969 #4721
521021,521023 #4722
521039,521041 #4723
521177,521179 #4724
521357,521359 #4725
521399,521401 #4726
521537,521539 #4727
521657,521659 #4728
521669,521671 #4729
521789,521791 #4730
521879,521881 #4731
522059,522061 #4732
522227,522229 #4733
522281,522283 #4734
522371,522373 #4735
522521,522523 #4736
522659,522661 #4737
522677,522679 #4738
522761,522763 #4739
522827,522829 #4740
522881,522883 #4741
522959,522961 #4742
523349,523351 #4743
523487,523489 #4744
523541,523543 #4745
523571,523573 #4746
523637,523639 #4747
523667,523669 #4748
524201,524203 #4749
524219,524221 #4750
524351,524353 #4751
524387,524389 #4752
524411,524413 #4753
524507,524509 #4754
524519,524521 #4755
524591,524593 #4756
524681,524683 #4757
524801,524803 #4758
524939,524941 #4759
524957,524959 #4760
524969,524971 #4761
524981,524983 #4762
524999,525001 #4763
525191,525193 #4764
525359,525361 #4765
525377,525379 #4766
525431,525433 #4767
525491,525493 #4768
525869,525871 #4769
525947,525949 #4770
526049,526051 #4771
526067,526069 #4772
526157,526159 #4773
526289,526291 #4774
526499,526501 #4775
526571,526573 #4776
526649,526651 #4777
526679,526681 #4778
526739,526741 #4779
526829,526831 #4780
527069,527071 #4781
527159,527161 #4782
527207,527209 #4783
527699,527701 #4784
527981,527983 #4785
528041,528043 #4786
528401,528403 #4787
528509,528511 #4788
528629,528631 #4789
528707,528709 #4790
528821,528823 #4791
528881,528883 #4792
528971,528973 #4793
529049,529051 #4794
529127,529129 #4795
529181,529183 #4796
529271,529273 #4797
529421,529423 #4798
529517,529519 #4799
529577,529579 #4800
529691,529693 #4801
529811,529813 #4802
529979,529981 #4803
530249,530251 #4804
530531,530533 #4805
530597,530599 #4806
530711,530713 #4807
530741,530743 #4808
531101,531103 #4809
531569,531571 #4810
531611,531613 #4811
531821,531823 #4812
532331,532333 #4813
532451,532453 #4814
532529,532531 #4815
532601,532603 #4816
532619,532621 #4817
532781,532783 #4818
532949,532951 #4819
533009,533011 #4820
533051,533053 #4821
533189,533191 #4822
533261,533263 #4823
533711,533713 #4824
533969,533971 #4825
534047,534049 #4826
534629,534631 #4827
534647,534649 #4828
534659,534661 #4829
534839,534841 #4830
535349,535351 #4831
535487,535489 #4832
535571,535573 #4833
535607,535609 #4834
535859,535861 #4835
535937,535939 #4836
536057,536059 #4837
536099,536101 #4838
536147,536149 #4839
536189,536191 #4840
536279,536281 #4841
536441,536443 #4842
536447,536449 #4843
536531,536533 #4844
536561,536563 #4845
536717,536719 #4846
536771,536773 #4847
536777,536779 #4848
536801,536803 #4849
536867,536869 #4850
536999,537001 #4851
537401,537403 #4852
538049,538051 #4853
538121,538123 #4854
538157,538159 #4855
538199,538201 #4856
538247,538249 #4857
538301,538303 #4858
538331,538333 #4859
538397,538399 #4860
538511,538513 #4861
538649,538651 #4862
538709,538711 #4863
538721,538723 #4864
538799,538801 #4865
539111,539113 #4866
539267,539269 #4867
539309,539311 #4868
539321,539323 #4869
539447,539449 #4870
539501,539503 #4871
539507,539509 #4872
539639,539641 #4873
539711,539713 #4874
539837,539839 #4875
539897,539899 #4876
540119,540121 #4877
540179,540181 #4878
540269,540271 #4879
540347,540349 #4880
540389,540391 #4881
540509,540511 #4882
540539,540541 #4883
540557,540559 #4884
540611,540613 #4885
540677,540679 #4886
540689,540691 #4887
540779,540781 #4888
541361,541363 #4889
541529,541531 #4890
541547,541549 #4891
541577,541579 #4892
541991,541993 #4893
542021,542023 #4894
542081,542083 #4895
542117,542119 #4896
542261,542263 #4897
542537,542539 #4898
542921,542923 #4899
543017,543019 #4900
543161,543163 #4901
543287,543289 #4902
543311,543313 #4903
543551,543553 #4904
543659,543661 #4905
543791,543793 #4906
543857,543859 #4907
543887,543889 #4908
544007,544009 #4909
544097,544099 #4910
544277,544279 #4911
544721,544723 #4912
544757,544759 #4913
544877,544879 #4914
544961,544963 #4915
545087,545089 #4916
545141,545143 #4917
545549,545551 #4918
545747,545749 #4919
545789,545791 #4920
546017,546019 #4921
546101,546103 #4922
546149,546151 #4923
546239,546241 #4924
546617,546619 #4925
547271,547273 #4926
547361,547363 #4927
547397,547399 #4928
547499,547501 #4929
547661,547663 #4930
547817,547819 #4931
548459,548461 #4932
548501,548503 #4933
548519,548521 #4934
548831,548833 #4935
549011,549013 #4936
549089,549091 #4937
549161,549163 #4938
549167,549169 #4939
549257,549259 #4940
549509,549511 #4941
549551,549553 #4942
549587,549589 #4943
549641,549643 #4944
549737,549739 #4945
549749,549751 #4946
549977,549979 #4947
550007,550009 #4948
550061,550063 #4949
550127,550129 #4950
550211,550213 #4951
550439,550441 #4952
550469,550471 #4953
550607,550609 #4954
550661,550663 #4955
550811,550813 #4956
550841,550843 #4957
550859,550861 #4958
550937,550939 #4959
551231,551233 #4960
551651,551653 #4961
551729,551731 #4962
551909,551911 #4963
552029,552031 #4964
552089,552091 #4965
552239,552241 #4966
552401,552403 #4967
552491,552493 #4968
552581,552583 #4969
552707,552709 #4970
552749,552751 #4971
552791,552793 #4972
553097,553099 #4973
553139,553141 #4974
553277,553279 #4975
553589,553591 #4976
553757,553759 #4977
553919,553921 #4978
553961,553963 #4979
554087,554089 #4980
554207,554209 #4981
554417,554419 #4982
554639,554641 #4983
554789,554791 #4984
554837,554839 #4985
554891,554893 #4986
555041,555043 #4987
555251,555253 #4988
555419,555421 #4989
555521,555523 #4990
555827,555829 #4991
556067,556069 #4992
556271,556273 #4993
556607,556609 #4994
556691,556693 #4995
556817,556819 #4996
556859,556861 #4997
557057,557059 #4998
557369,557371 #4999
557519,557521 #5000
557729,557731 #5001
557741,557743 #5002
557759,557761 #5003
557801,557803 #5004
557861,557863 #5005
558251,558253 #5006
558287,558289 #5007
558497,558499 #5008
558539,558541 #5009
558791,558793 #5010
558827,558829 #5011
559049,559051 #5012
559211,559213 #5013
559217,559219 #5014
559367,559369 #5015
559511,559513 #5016
559547,559549 #5017
559631,559633 #5018
560081,560083 #5019
560171,560173 #5020
560237,560239 #5021
560297,560299 #5022
560477,560479 #5023
560489,560491 #5024
560501,560503 #5025
560639,560641 #5026
560891,560893 #5027
560939,560941 #5028
561059,561061 #5029
561101,561103 #5030
561551,561553 #5031
562019,562021 #5032
562271,562273 #5033
562349,562351 #5034
562517,562519 #5035
562577,562579 #5036
562589,562591 #5037
562631,562633 #5038
562691,562693 #5039
563009,563011 #5040
563039,563041 #5041
563117,563119 #5042
563357,563359 #5043
563411,563413 #5044
563417,563419 #5045
563447,563449 #5046
563501,563503 #5047
564059,564061 #5048
564227,564229 #5049
564269,564271 #5050
564299,564301 #5051
564371,564373 #5052
564407,564409 #5053
564701,564703 #5054
564917,564919 #5055
565109,565111 #5056
565259,565261 #5057
565379,565381 #5058
565391,565393 #5059
565427,565429 #5060
565517,565519 #5061
565769,565771 #5062
565889,565891 #5063
565907,565909 #5064
565919,565921 #5065
566231,566233 #5066
566429,566431 #5067
566441,566443 #5068
566537,566539 #5069
566549,566551 #5070
566717,566719 #5071
567011,567013 #5072
567179,567181 #5073
567449,567451 #5074
567527,567529 #5075
567659,567661 #5076
567881,567883 #5077
567947,567949 #5078
568151,568153 #5079
568187,568189 #5080
568439,568441 #5081
569081,569083 #5082
569159,569161 #5083
569249,569251 #5084
569267,569269 #5085
569321,569323 #5086
569417,569419 #5087
569579,569581 #5088
569711,569713 #5089
569729,569731 #5090
569771,569773 #5091
570041,570043 #5092
570047,570049 #5093
570077,570079 #5094
570107,570109 #5095
570389,570391 #5096
570419,570421 #5097
570461,570463 #5098
570497,570499 #5099
570509,570511 #5100
570527,570529 #5101
570839,570841 #5102
570851,570853 #5103
570959,570961 #5104
571199,571201 #5105
571229,571231 #5106
571397,571399 #5107
571601,571603 #5108
571799,571801 #5109
571871,571873 #5110
572051,572053 #5111
572177,572179 #5112
572321,572323 #5113
572417,572419 #5114
572519,572521 #5115
572597,572599 #5116
572651,572653 #5117
572657,572659 #5118
572879,572881 #5119
572939,572941 #5120
573107,573109 #5121
573161,573163 #5122
573341,573343 #5123
573479,573481 #5124
573509,573511 #5125
573569,573571 #5126
573737,573739 #5127
573761,573763 #5128
573899,573901 #5129
574031,574033 #5130
574157,574159 #5131
574181,574183 #5132
574307,574309 #5133
574619,574621 #5134
574799,574801 #5135
574967,574969 #5136
575129,575131 #5137
575249,575251 #5138
575369,575371 #5139
575429,575431 #5140
575579,575581 #5141
575591,575593 #5142
575921,575923 #5143
575957,575959 #5144
576029,576031 #5145
576221,576223 #5146
576377,576379 #5147
576551,576553 #5148
576647,576649 #5149
576701,576703 #5150
576881,576883 #5151
577007,577009 #5152
577067,577069 #5153
577151,577153 #5154
577331,577333 #5155
577349,577351 #5156
577397,577399 #5157
577529,577531 #5158
577637,577639 #5159
577937,577939 #5160
577979,577981 #5161
578297,578299 #5162
578309,578311 #5163
578399,578401 #5164
578687,578689 #5165
578777,578779 #5166
578819,578821 #5167
578957,578959 #5168
579197,579199 #5169
579281,579283 #5170
579407,579409 #5171
579497,579499 #5172
579539,579541 #5173
579569,579571 #5174
579611,579613 #5175
579641,579643 #5176
579881,579883 #5177
579947,579949 #5178
580031,580033 #5179
580079,580081 #5180
580301,580303 #5181
580379,580381 #5182
580631,580633 #5183
580691,580693 #5184
580757,580759 #5185
580889,580891 #5186
581069,581071 #5187
581099,581101 #5188
581171,581173 #5189
581237,581239 #5190
581261,581263 #5191
581351,581353 #5192
581549,581551 #5193
581597,581599 #5194
581699,581701 #5195
581729,581731 #5196
581981,581983 #5197
582011,582013 #5198
582137,582139 #5199
582221,582223 #5200
582317,582319 #5201
582509,582511 #5202
582689,582691 #5203
582719,582721 #5204
582761,582763 #5205
582851,582853 #5206
582971,582973 #5207
583019,583021 #5208
583169,583171 #5209
583337,583339 #5210
583619,583621 #5211
583859,583861 #5212
584279,584281 #5213
584357,584359 #5214
584471,584473 #5215
584789,584791 #5216
585041,585043 #5217
585071,585073 #5218
585269,585271 #5219
585839,585841 #5220
585881,585883 #5221
585911,585913 #5222
585917,585919 #5223
586121,586123 #5224
586361,586363 #5225
586457,586459 #5226
586499,586501 #5227
586541,586543 #5228
586601,586603 #5229
586631,586633 #5230
586811,586813 #5231
586919,586921 #5232
586979,586981 #5233
587051,587053 #5234
587267,587269 #5235
587549,587551 #5236
587621,587623 #5237
587747,587749 #5238
587771,587773 #5239
587969,587971 #5240
587987,587989 #5241
588167,588169 #5242
588239,588241 #5243
588359,588361 #5244
588569,588571 #5245
588647,588649 #5246
588947,588949 #5247
589109,589111 #5248
589187,589189 #5249
589241,589243 #5250
589289,589291 #5251
589451,589453 #5252
589529,589531 #5253
589607,589609 #5254
589751,589753 #5255
589859,589861 #5256
590129,590131 #5257
590267,590269 #5258
590321,590323 #5259
590657,590659 #5260
590717,590719 #5261
590921,590923 #5262
591089,591091 #5263
591161,591163 #5264
591287,591289 #5265
591317,591319 #5266
591599,591601 #5267
591749,591751 #5268
592217,592219 #5269
592307,592309 #5270
592367,592369 #5271
592391,592393 #5272
592451,592453 #5273
592661,592663 #5274
593081,593083 #5275
593141,593143 #5276
593207,593209 #5277
593231,593233 #5278
593291,593293 #5279
593321,593323 #5280
593399,593401 #5281
593447,593449 #5282
593627,593629 #5283
594161,594163 #5284
594281,594283 #5285
594311,594313 #5286
594401,594403 #5287
594467,594469 #5288
594521,594523 #5289
594569,594571 #5290
594749,594751 #5291
594821,594823 #5292
594827,594829 #5293
594929,594931 #5294
594959,594961 #5295
595037,595039 #5296
595139,595141 #5297
595157,595159 #5298
595181,595183 #5299
595379,595381 #5300
595451,595453 #5301
595547,595549 #5302
595577,595579 #5303
595709,595711 #5304
595949,595951 #5305
595961,595963 #5306
596081,596083 #5307
596117,596119 #5308
596291,596293 #5309
596669,596671 #5310
596861,596863 #5311
596927,596929 #5312
597131,597133 #5313
597269,597271 #5314
597407,597409 #5315
597521,597523 #5316
597671,597673 #5317
597677,597679 #5318
597767,597769 #5319
597899,597901 #5320
598049,598051 #5321
598187,598189 #5322
598487,598489 #5323
598649,598651 #5324
598727,598729 #5325
598931,598933 #5326
599021,599023 #5327
599147,599149 #5328
599477,599479 #5329
599699,599701 #5330
599939,599941 #5331
600071,600073 #5332
600167,600169 #5333
600239,600241 #5334
600317,600319 #5335
600359,600361 #5336
600401,600403 #5337
600449,600451 #5338
600701,600703 #5339
600881,600883 #5340
600947,600949 #5341
600959,600961 #5342
601037,601039 #5343
601187,601189 #5344
601541,601543 #5345
601589,601591 #5346
602081,602083 #5347
602141,602143 #5348
602267,602269 #5349
602309,602311 #5350
602477,602479 #5351
602687,602689 #5352
602711,602713 #5353
603011,603013 #5354
603101,603103 #5355
603131,603133 #5356
603389,603391 #5357
603521,603523 #5358
603791,603793 #5359
603851,603853 #5360
603899,603901 #5361
603917,603919 #5362
603947,603949 #5363
604649,604651 #5364
604697,604699 #5365
604727,604729 #5366
604859,604861 #5367
605021,605023 #5368
605069,605071 #5369
605237,605239 #5370
605411,605413 #5371
605531,605533 #5372
605597,605599 #5373
605639,605641 #5374
606029,606031 #5375
606077,606079 #5376
606299,606301 #5377
606311,606313 #5378
606587,606589 #5379
606731,606733 #5380
606959,606961 #5381
607001,607003 #5382
607091,607093 #5383
607127,607129 #5384
607151,607153 #5385
607301,607303 #5386
607307,607309 #5387
607337,607339 #5388
607421,607423 #5389
607667,607669 #5390
607721,607723 #5391
607931,607933 #5392
607991,607993 #5393
608087,608089 #5394
608129,608131 #5395
608297,608299 #5396
608357,608359 #5397
608369,608371 #5398
608429,608431 #5399
608519,608521 #5400
608591,608593 #5401
608609,608611 #5402
608897,608899 #5403
608987,608989 #5404
609359,609361 #5405
609599,609601 #5406
609617,609619 #5407
609779,609781 #5408
609911,609913 #5409
609989,609991 #5410
610217,610219 #5411
610541,610543 #5412
610739,610741 #5413
610781,610783 #5414
610847,610849 #5415
610877,610879 #5416
610919,610921 #5417
611069,611071 #5418
611111,611113 #5419
611549,611551 #5420
611801,611803 #5421
611837,611839 #5422
611951,611953 #5423
612041,612043 #5424
612107,612109 #5425
612317,612319 #5426
612371,612373 #5427
612611,612613 #5428
612809,612811 #5429
613007,613009 #5430
613097,613099 #5431
613229,613231 #5432
613439,613441 #5433
613469,613471 #5434
613607,613609 #5435
613967,613969 #5436
614177,614179 #5437
614291,614293 #5438
614561,614563 #5439
614609,614611 #5440
614657,614659 #5441
614741,614743 #5442
614849,614851 #5443
614981,614983 #5444
615101,615103 #5445
615341,615343 #5446
615401,615403 #5447
615491,615493 #5448
615677,615679 #5449
615749,615751 #5450
615827,615829 #5451
616139,616141 #5452
616169,616171 #5453
616391,616393 #5454
616409,616411 #5455
616787,616789 #5456
616841,616843 #5457
616997,616999 #5458
617051,617053 #5459
617129,617131 #5460
617189,617191 #5461
617231,617233 #5462
617339,617341 #5463
617471,617473 #5464
617717,617719 #5465
617759,617761 #5466
618029,618031 #5467
618227,618229 #5468
618269,618271 #5469
618347,618349 #5470
618437,618439 #5471
618587,618589 #5472
618857,618859 #5473
619007,619009 #5474
619187,619189 #5475
619277,619279 #5476
619739,619741 #5477
619811,619813 #5478
619979,619981 #5479
620159,620161 #5480
620237,620239 #5481
620567,620569 #5482
620771,620773 #5483
620909,620911 #5484
621029,621031 #5485
621239,621241 #5486
621617,621619 #5487
621629,621631 #5488
621701,621703 #5489
621869,621871 #5490
622049,622051 #5491
622157,622159 #5492
622187,622189 #5493
622241,622243 #5494
622247,622249 #5495
622331,622333 #5496
622397,622399 #5497
622481,622483 #5498
622547,622549 #5499
622619,622621 #5500
622637,622639 #5501
623057,623059 #5502
623261,623263 #5503
623279,623281 #5504
623351,623353 #5505
623669,623671 #5506
623681,623683 #5507
623717,623719 #5508
623867,623869 #5509
623879,623881 #5510
624047,624049 #5511
624311,624313 #5512
624329,624331 #5513
624467,624469 #5514
624539,624541 #5515
624599,624601 #5516
624707,624709 #5517
625109,625111 #5518
625169,625171 #5519
625367,625369 #5520
625589,625591 #5521
625661,625663 #5522
625697,625699 #5523
626009,626011 #5524
626189,626191 #5525
626597,626599 #5526
626609,626611 #5527
626621,626623 #5528
626627,626629 #5529
626711,626713 #5530
627071,627073 #5531
627089,627091 #5532
627269,627271 #5533
627377,627379 #5534
627479,627481 #5535
627617,627619 #5536
627659,627661 #5537
627797,627799 #5538
628049,628051 #5539
628217,628219 #5540
628679,628681 #5541
628757,628759 #5542
628781,628783 #5543
628799,628801 #5544
628937,628939 #5545
629009,629011 #5546
629339,629341 #5547
629381,629383 #5548
629567,629569 #5549
629591,629593 #5550
629609,629611 #5551
629687,629689 #5552
629897,629899 #5553
629927,629929 #5554
629987,629989 #5555
630167,630169 #5556
630521,630523 #5557
630587,630589 #5558
630899,630901 #5559
631151,631153 #5560
631247,631249 #5561
631271,631273 #5562
631457,631459 #5563
631469,631471 #5564
631529,631531 #5565
631679,631681 #5566
631751,631753 #5567
631817,631819 #5568
631859,631861 #5569
631901,631903 #5570
631991,631993 #5571
632081,632083 #5572
632087,632089 #5573
632297,632299 #5574
632321,632323 #5575
632327,632329 #5576
632351,632353 #5577
632501,632503 #5578
632627,632629 #5579
632939,632941 #5580
633377,633379 #5581
633461,633463 #5582
633467,633469 #5583
633569,633571 #5584
633791,633793 #5585
633797,633799 #5586
634157,634159 #5587
634649,634651 #5588
634679,634681 #5589
634757,634759 #5590
634859,634861 #5591
634901,634903 #5592
634937,634939 #5593
635147,635149 #5594
635249,635251 #5595
635291,635293 #5596
635351,635353 #5597
635387,635389 #5598
635729,635731 #5599
635891,635893 #5600
635981,635983 #5601
636059,636061 #5602
636071,636073 #5603
636107,636109 #5604
636407,636409 #5605
636539,636541 #5606
636719,636721 #5607
636761,636763 #5608
636917,636919 #5609
637001,637003 #5610
637199,637201 #5611
637319,637321 #5612
637337,637339 #5613
637421,637423 #5614
637529,637531 #5615
637601,637603 #5616
637709,637711 #5617
637727,637729 #5618
637781,637783 #5619
637829,637831 #5620
637937,637939 #5621
638159,638161 #5622
638177,638179 #5623
638717,638719 #5624
639167,639169 #5625
639257,639259 #5626
639491,639493 #5627
639599,639601 #5628
639677,639679 #5629
639701,639703 #5630
639851,639853 #5631
640007,640009 #5632
640151,640153 #5633
640229,640231 #5634
640247,640249 #5635
640259,640261 #5636
640529,640531 #5637
640667,640669 #5638
641129,641131 #5639
641411,641413 #5640
641519,641521 #5641
641549,641551 #5642
641579,641581 #5643
641747,641749 #5644
641789,641791 #5645
641819,641821 #5646
642011,642013 #5647
642077,642079 #5648
642149,642151 #5649
642197,642199 #5650
642359,642361 #5651
642527,642529 #5652
642737,642739 #5653
642797,642799 #5654
642869,642871 #5655
643301,643303 #5656
643649,643651 #5657
643691,643693 #5658
643847,643849 #5659
644051,644053 #5660
644129,644131 #5661
644141,644143 #5662
644381,644383 #5663
644489,644491 #5664
644597,644599 #5665
644669,644671 #5666
644729,644731 #5667
644867,644869 #5668
644909,644911 #5669
645011,645013 #5670
645431,645433 #5671
645497,645499 #5672
645527,645529 #5673
645581,645583 #5674
645647,645649 #5675
645737,645739 #5676
646157,646159 #5677
646181,646183 #5678
646271,646273 #5679
646307,646309 #5680
646421,646423 #5681
646571,646573 #5682
646979,646981 #5683
646991,646993 #5684
647111,647113 #5685
647261,647263 #5686
647357,647359 #5687
647399,647401 #5688
647741,647743 #5689
647837,647839 #5690
647891,647893 #5691
647951,647953 #5692
648059,648061 #5693
648257,648259 #5694
648341,648343 #5695
648377,648379 #5696
648617,648619 #5697
648629,648631 #5698
648887,648889 #5699
649079,649081 #5700
649277,649279 #5701
649379,649381 #5702
649421,649423 #5703
649469,649471 #5704
649499,649501 #5705
649631,649633 #5706
649769,649771 #5707
649799,649801 #5708
649877,649879 #5709
650327,650329 #5710
650477,650479 #5711
650759,650761 #5712
650861,650863 #5713
651017,651019 #5714
651179,651181 #5715
651191,651193 #5716
651221,651223 #5717
651437,651439 #5718
651647,651649 #5719
651731,651733 #5720
651767,651769 #5721
651809,651811 #5722
651839,651841 #5723
652079,652081 #5724
652241,652243 #5725
652319,652321 #5726
652451,652453 #5727
652541,652543 #5728
652607,652609 #5729
652739,652741 #5730
652931,652933 #5731
652997,652999 #5732
653111,653113 #5733
653207,653209 #5734
653501,653503 #5735
653537,653539 #5736
653561,653563 #5737
653621,653623 #5738
653711,653713 #5739
653879,653881 #5740
653927,653929 #5741
654161,654163 #5742
654167,654169 #5743
654221,654223 #5744
654527,654529 #5745
654539,654541 #5746
654611,654613 #5747
654779,654781 #5748
655001,655003 #5749
655241,655243 #5750
655559,655561 #5751
655649,655651 #5752
655847,655849 #5753
656321,656323 #5754
656597,656599 #5755
656681,656683 #5756
657047,657049 #5757
657089,657091 #5758
657311,657313 #5759
657491,657493 #5760
657497,657499 #5761
657581,657583 #5762
657659,657661 #5763
657929,657931 #5764
658277,658279 #5765
658319,658321 #5766
658349,658351 #5767
658547,658549 #5768
658589,658591 #5769
658751,658753 #5770
658871,658873 #5771
658961,658963 #5772
659171,659173 #5773
659609,659611 #5774
659669,659671 #5775
659759,659761 #5776
659999,660001 #5777
660071,660073 #5778
660197,660199 #5779
660347,660349 #5780
660377,660379 #5781
660557,660559 #5782
660599,660601 #5783
660617,660619 #5784
660659,660661 #5785
660731,660733 #5786
660809,660811 #5787
660851,660853 #5788
660899,660901 #5789
661091,661093 #5790
661097,661099 #5791
661187,661189 #5792
661481,661483 #5793
661877,661879 #5794
661949,661951 #5795
662141,662143 #5796
662351,662353 #5797
662537,662539 #5798
662771,662773 #5799
662897,662899 #5800
662939,662941 #5801
662951,662953 #5802
662999,663001 #5803
663161,663163 #5804
663239,663241 #5805
663281,663283 #5806
663407,663409 #5807
663539,663541 #5808
663569,663571 #5809
663581,663583 #5810
663587,663589 #5811
663599,663601 #5812
663659,663661 #5813
663821,663823 #5814
663959,663961 #5815
663977,663979 #5816
664121,664123 #5817
664271,664273 #5818
664379,664381 #5819
664619,664621 #5820
664661,664663 #5821
664667,664669 #5822
664691,664693 #5823
664847,664849 #5824
665051,665053 #5825
665111,665113 #5826
665177,665179 #5827
665501,665503 #5828
665801,665803 #5829
665921,665923 #5830
665981,665983 #5831
666089,666091 #5832
666431,666433 #5833
666437,666439 #5834
666527,666529 #5835
666557,666559 #5836
666647,666649 #5837
666749,666751 #5838
666821,666823 #5839
667019,667021 #5840
667127,667129 #5841
667241,667243 #5842
667361,667363 #5843
667421,667423 #5844
667547,667549 #5845
667559,667561 #5846
667697,667699 #5847
667817,667819 #5848
667859,667861 #5849
668201,668203 #5850
668531,668533 #5851
668579,668581 #5852
668609,668611 #5853
668867,668869 #5854
669089,669091 #5855
669287,669289 #5856
669377,669379 #5857
669479,669481 #5858
669659,669661 #5859
669677,669679 #5860
669857,669859 #5861
670037,670039 #5862
670049,670051 #5863
670097,670099 #5864
670487,670489 #5865
670541,670543 #5866
670727,670729 #5867
671159,671161 #5868
671777,671779 #5869
671939,671941 #5870
671969,671971 #5871
672041,672043 #5872
672167,672169 #5873
672227,672229 #5874
672377,672379 #5875
672641,672643 #5876
672779,672781 #5877
672869,672871 #5878
673091,673093 #5879
673109,673111 #5880
673199,673201 #5881
673271,673273 #5882
673397,673399 #5883
673427,673429 #5884
673457,673459 #5885
673637,673639 #5886
673667,673669 #5887
674057,674059 #5888
674159,674161 #5889
674699,674701 #5890
674717,674719 #5891
674759,674761 #5892
674831,674833 #5893
675131,675133 #5894
675161,675163 #5895
675251,675253 #5896
675539,675541 #5897
675551,675553 #5898
675839,675841 #5899
675929,675931 #5900
675977,675979 #5901
676007,676009 #5902
676217,676219 #5903
676337,676339 #5904
676409,676411 #5905
676859,676861 #5906
676979,676981 #5907
677111,677113 #5908
677231,677233 #5909
677309,677311 #5910
677321,677323 #5911
677459,677461 #5912
677471,677473 #5913
677531,677533 #5914
677561,677563 #5915
677681,677683 #5916
678101,678103 #5917
678341,678343 #5918
678407,678409 #5919
678479,678481 #5920
678647,678649 #5921
678719,678721 #5922
678761,678763 #5923
678941,678943 #5924
679037,679039 #5925
679169,679171 #5926
679277,679279 #5927
679361,679363 #5928
679517,679519 #5929
679751,679753 #5930
679907,679909 #5931
680081,680083 #5932
680159,680161 #5933
680291,680293 #5934
680297,680299 #5935
680399,680401 #5936
680441,680443 #5937
680507,680509 #5938
680567,680569 #5939
680879,680881 #5940
680987,680989 #5941
681047,681049 #5942
681089,681091 #5943
681251,681253 #5944
681257,681259 #5945
681407,681409 #5946
681449,681451 #5947
681521,681523 #5948
681839,681841 #5949
681977,681979 #5950
682151,682153 #5951
682289,682291 #5952
682697,682699 #5953
683477,683479 #5954
683651,683653 #5955
683699,683701 #5956
683819,683821 #5957
683831,683833 #5958
683861,683863 #5959
683909,683911 #5960
684119,684121 #5961
684287,684289 #5962
684347,684349 #5963
684557,684559 #5964
684767,684769 #5965
684791,684793 #5966
685247,685249 #5967
685337,685339 #5968
685367,685369 #5969
685427,685429 #5970
685511,685513 #5971
686009,686011 #5972
686027,686029 #5973
686039,686041 #5974
686087,686089 #5975
686141,686143 #5976
686267,686269 #5977
686669,686671 #5978
686729,686731 #5979
686891,686893 #5980
686969,686971 #5981
687017,687019 #5982
687107,687109 #5983
687161,687163 #5984
687341,687343 #5985
687431,687433 #5986
687521,687523 #5987
688451,688453 #5988
689459,689461 #5989
689597,689599 #5990
689867,689869 #5991
689891,689893 #5992
689957,689959 #5993
690269,690271 #5994
690491,690493 #5995
690509,690511 #5996
690719,690721 #5997
690839,690841 #5998
690869,690871 #5999
690887,690889 #6000
691109,691111 #6001
691151,691153 #6002
691181,691183 #6003
691589,691591 #6004
691721,691723 #6005
691727,691729 #6006
691841,691843 #6007
691919,691921 #6008
692147,692149 #6009
692297,692299 #6010
692387,692389 #6011
692399,692401 #6012
692537,692539 #6013
692927,692929 #6014
693167,693169 #6015
693401,693403 #6016
693527,693529 #6017
693569,693571 #6018
693659,693661 #6019
693689,693691 #6020
693731,693733 #6021
693827,693829 #6022
694079,694081 #6023
694259,694261 #6024
694271,694273 #6025
694481,694483 #6026
694511,694513 #6027
694649,694651 #6028
694781,694783 #6029
694829,694831 #6030
694871,694873 #6031
694997,694999 #6032
695087,695089 #6033
695327,695329 #6034
695369,695371 #6035
695687,695689 #6036
695879,695881 #6037
696077,696079 #6038
696107,696109 #6039
696359,696361 #6040
696719,696721 #6041
696809,696811 #6042
696851,696853 #6043
696887,696889 #6044
696989,696991 #6045
697259,697261 #6046
697379,697381 #6047
697397,697399 #6048
697511,697513 #6049
697601,697603 #6050
697691,697693 #6051
697727,697729 #6052
697757,697759 #6053
698051,698053 #6054
698249,698251 #6055
698261,698263 #6056
698417,698419 #6057
699287,699289 #6058
699527,699529 #6059
699539,699541 #6060
699791,699793 #6061
700079,700081 #6062
700127,700129 #6063
700199,700201 #6064
700277,700279 #6065
700361,700363 #6066
700391,700393 #6067
700571,700573 #6068
701009,701011 #6069
701177,701179 #6070
701219,701221 #6071
701357,701359 #6072
701399,701401 #6073
701417,701419 #6074
701507,701509 #6075
701579,701581 #6076
701609,701611 #6077
701627,701629 #6078
701669,701671 #6079
702137,702139 #6080
702281,702283 #6081
702311,702313 #6082
702347,702349 #6083
702431,702433 #6084
702587,702589 #6085
702731,702733 #6086
702851,702853 #6087
703121,703123 #6088
703139,703141 #6089
703229,703231 #6090
703559,703561 #6091
703709,703711 #6092
704027,704029 #6093
704279,704281 #6094
704447,704449 #6095
704549,704551 #6096
704567,704569 #6097
704579,704581 #6098
704777,704779 #6099
704861,704863 #6100
705011,705013 #6101
705161,705163 #6102
705167,705169 #6103
705491,705493 #6104
705779,705781 #6105
705827,705829 #6106
706001,706003 #6107
706049,706051 #6108
706157,706159 #6109
706631,706633 #6110
706751,706753 #6111
706919,706921 #6112
707027,707029 #6113
707429,707431 #6114
707561,707563 #6115
707669,707671 #6116
707951,707953 #6117
707981,707983 #6118
708047,708049 #6119
708137,708139 #6120
708161,708163 #6121
708221,708223 #6122
708359,708361 #6123
708479,708481 #6124
708599,708601 #6125
708857,708859 #6126
708989,708991 #6127
709139,709141 #6128
709151,709153 #6129
709271,709273 #6130
709349,709351 #6131
709451,709453 #6132
709607,709609 #6133
709649,709651 #6134
709691,709693 #6135
709739,709741 #6136
710051,710053 #6137
710219,710221 #6138
710321,710323 #6139
710441,710443 #6140
710621,710623 #6141
710777,710779 #6142
710837,710839 #6143
710849,710851 #6144
710909,710911 #6145
710987,710989 #6146
711017,711019 #6147
711131,711133 #6148
711497,711499 #6149
711707,711709 #6150
711749,711751 #6151
712169,712171 #6152
712301,712303 #6153
712319,712321 #6154
712427,712429 #6155
712571,712573 #6156
712601,712603 #6157
712841,712843 #6158
712889,712891 #6159
713147,713149 #6160
713189,713191 #6161
713309,713311 #6162
713351,713353 #6163
713597,713599 #6164
713831,713833 #6165
713861,713863 #6166
713939,713941 #6167
714479,714481 #6168
714839,714841 #6169
714851,714853 #6170
714947,714949 #6171
715151,715153 #6172
715157,715159 #6173
715301,715303 #6174
715439,715441 #6175
715577,715579 #6176
715679,715681 #6177
715877,715879 #6178
715961,715963 #6179
716171,716173 #6180
716411,716413 #6181
716447,716449 #6182
716477,716479 #6183
716741,716743 #6184
716897,716899 #6185
716951,716953 #6186
717089,717091 #6187
717149,717151 #6188
717527,717529 #6189
717917,717919 #6190
718049,718051 #6191
718169,718171 #6192
718379,718381 #6193
718511,718513 #6194
719009,719011 #6195
719177,719179 #6196
719237,719239 #6197
719351,719353 #6198
719567,719569 #6199
719597,719599 #6200
719681,719683 #6201
720089,720091 #6202
720281,720283 #6203
720299,720301 #6204
720359,720361 #6205
720569,720571 #6206
720617,720619 #6207
720791,720793 #6208
720899,720901 #6209
721109,721111 #6210
721139,721141 #6211
721319,721321 #6212
721379,721381 #6213
721619,721621 #6214
721661,721663 #6215
722147,722149 #6216
722537,722539 #6217
723029,723031 #6218
723101,723103 #6219
723167,723169 #6220
723257,723259 #6221
723269,723271 #6222
723407,723409 #6223
723491,723493 #6224
723551,723553 #6225
723587,723589 #6226
723797,723799 #6227
723857,723859 #6228
724121,724123 #6229
724517,724519 #6230
724721,724723 #6231
724781,724783 #6232
724901,724903 #6233
724991,724993 #6234
725111,725113 #6235
725147,725149 #6236
725159,725161 #6237
725321,725323 #6238
725357,725359 #6239
725447,725449 #6240
725861,725863 #6241
725981,725983 #6242
726107,726109 #6243
726137,726139 #6244
726287,726289 #6245
726377,726379 #6246
726599,726601 #6247
726809,726811 #6248
726839,726841 #6249
726989,726991 #6250
727019,727021 #6251
727061,727063 #6252
727121,727123 #6253
727157,727159 #6254
727247,727249 #6255
727271,727273 #6256
727499,727501 #6257
727877,727879 #6258
728129,728131 #6259
728207,728209 #6260
728267,728269 #6261
728381,728383 #6262
728699,728701 #6263
728729,728731 #6264
728837,728839 #6265
728867,728869 #6266
728927,728929 #6267
728969,728971 #6268
729269,729271 #6269
729329,729331 #6270
729371,729373 #6271
729557,729559 #6272
729569,729571 #6273
729941,729943 #6274
729977,729979 #6275
730397,730399 #6276
730571,730573 #6277
730589,730591 #6278
730781,730783 #6279
731189,731191 #6280
731249,731251 #6281
731501,731503 #6282
731681,731683 #6283
731711,731713 #6284
731909,731911 #6285
731921,731923 #6286
732077,732079 #6287
732209,732211 #6288
732491,732493 #6289
732827,732829 #6290
733097,733099 #6291
733331,733333 #6292
733391,733393 #6293
733517,733519 #6294
733559,733561 #6295
733751,733753 #6296
733847,733849 #6297
733919,733921 #6298
733937,733939 #6299
734429,734431 #6300
734471,734473 #6301
734477,734479 #6302
734957,734959 #6303
735071,735073 #6304
735107,735109 #6305
735209,735211 #6306
735389,735391 #6307
735419,735421 #6308
735731,735733 #6309
736037,736039 #6310
736061,736063 #6311
736091,736093 #6312
736247,736249 #6313
736277,736279 #6314
736361,736363 #6315
736367,736369 #6316
736469,736471 #6317
737039,737041 #6318
737129,737131 #6319
737279,737281 #6320
737291,737293 #6321
737351,737353 #6322
737411,737413 #6323
737507,737509 #6324
737531,737533 #6325
737591,737593 #6326
737717,737719 #6327
737927,737929 #6328
738107,738109 #6329
738317,738319 #6330
738401,738403 #6331
738581,738583 #6332
738917,738919 #6333
739199,739201 #6334
739301,739303 #6335
739391,739393 #6336
739397,739399 #6337
739511,739513 #6338
739601,739603 #6339
739631,739633 #6340
739859,739861 #6341
739967,739969 #6342
740021,740023 #6343
740141,740143 #6344
740189,740191 #6345
740321,740323 #6346
740651,740653 #6347
740711,740713 #6348
740891,740893 #6349
741077,741079 #6350
741119,741121 #6351
741227,741229 #6352
741341,741343 #6353
741467,741469 #6354
741491,741493 #6355
741677,741679 #6356
741857,741859 #6357
742151,742153 #6358
742199,742201 #6359
742211,742213 #6360
742241,742243 #6361
742697,742699 #6362
742757,742759 #6363
742991,742993 #6364
743129,743131 #6365
743159,743161 #6366
743177,743179 #6367
743549,743551 #6368
743669,743671 #6369
743777,743779 #6370
743849,743851 #6371
743921,743923 #6372
743987,743989 #6373
744251,744253 #6374
744389,744391 #6375
744407,744409 #6376
744659,744661 #6377
745187,745189 #6378
745247,745249 #6379
745529,745531 #6380
745697,745699 #6381
745709,745711 #6382
745751,745753 #6383
745931,745933 #6384
746099,746101 #6385
746231,746233 #6386
746411,746413 #6387
746477,746479 #6388
746507,746509 #6389
746531,746533 #6390
746561,746563 #6391
746747,746749 #6392
746957,746959 #6393
747449,747451 #6394
747497,747499 #6395
747827,747829 #6396
747839,747841 #6397
747869,747871 #6398
747917,747919 #6399
747977,747979 #6400
748019,748021 #6401
748091,748093 #6402
748217,748219 #6403
748271,748273 #6404
748337,748339 #6405
748637,748639 #6406
748817,748819 #6407
748829,748831 #6408
749081,749083 #6409
749297,749299 #6410
749429,749431 #6411
749807,749809 #6412
749891,749893 #6413
749939,749941 #6414
750119,750121 #6415
750131,750133 #6416
750161,750163 #6417
750311,750313 #6418
750719,750721 #6419
751139,751141 #6420
751181,751183 #6421
751319,751321 #6422
751631,751633 #6423
752201,752203 #6424
752291,752293 #6425
752447,752449 #6426
752681,752683 #6427
752699,752701 #6428
752819,752821 #6429
752831,752833 #6430
753437,753439 #6431
753461,753463 #6432
753497,753499 #6433
753587,753589 #6434
753617,753619 #6435
753677,753679 #6436
753689,753691 #6437
753719,753721 #6438
754109,754111 #6439
754121,754123 #6440
754181,754183 #6441
754379,754381 #6442
754709,754711 #6443
754937,754939 #6444
754967,754969 #6445
754979,754981 #6446
754991,754993 #6447
755171,755173 #6448
755309,755311 #6449
755399,755401 #6450
755567,755569 #6451
755717,755719 #6452
755789,755791 #6453
755861,755863 #6454
756251,756253 #6455
756419,756421 #6456
757109,757111 #6457
757241,757243 #6458
757577,757579 #6459
757709,757711 #6460
757751,757753 #6461
758099,758101 #6462
758201,758203 #6463
758267,758269 #6464
758339,758341 #6465
758501,758503 #6466
758519,758521 #6467
758711,758713 #6468
758729,758731 #6469
758741,758743 #6470
758969,758971 #6471
759179,759181 #6472
759431,759433 #6473
759557,759559 #6474
759569,759571 #6475
759797,759799 #6476
759959,759961 #6477
760229,760231 #6478
760619,760621 #6479
760841,760843 #6480
761177,761179 #6481
761249,761251 #6482
761261,761263 #6483
761441,761443 #6484
761531,761533 #6485
761669,761671 #6486
761711,761713 #6487
761777,761779 #6488
761807,761809 #6489
761861,761863 #6490
762239,762241 #6491
762371,762373 #6492
762407,762409 #6493
762821,762823 #6494
762899,762901 #6495
762917,762919 #6496
763157,763159 #6497
763619,763621 #6498
763751,763753 #6499
764051,764053 #6500
764249,764251 #6501
764339,764341 #6502
764591,764593 #6503
764627,764629 #6504
764717,764719 #6505
764837,764839 #6506
764891,764893 #6507
764969,764971 #6508
765041,765043 #6509
765137,765139 #6510
765209,765211 #6511
765227,765229 #6512
765437,765439 #6513
765857,765859 #6514
766109,766111 #6515
766229,766231 #6516
766541,766543 #6517
766637,766639 #6518
766811,766813 #6519
766937,766939 #6520
767321,767323 #6521
767357,767359 #6522
767537,767539 #6523
767549,767551 #6524
767747,767749 #6525
767759,767761 #6526
767867,767869 #6527
768167,768169 #6528
768191,768193 #6529
768197,768199 #6530
768371,768373 #6531
768629,768631 #6532
768641,768643 #6533
768851,768853 #6534
769259,769261 #6535
769421,769423 #6536
769541,769543 #6537
769577,769579 #6538
769589,769591 #6539
769661,769663 #6540
769961,769963 #6541
769997,769999 #6542
770039,770041 #6543
770057,770059 #6544
770111,770113 #6545
770177,770179 #6546
770309,770311 #6547
770447,770449 #6548
770639,770641 #6549
770837,770839 #6550
770927,770929 #6551
771011,771013 #6552
771047,771049 #6553
771179,771181 #6554
771299,771301 #6555
771401,771403 #6556
771437,771439 #6557
771887,771889 #6558
771971,771973 #6559
772001,772003 #6560
772229,772231 #6561
772379,772381 #6562
772391,772393 #6563
772439,772441 #6564
772571,772573 #6565
772661,772663 #6566
772907,772909 #6567
773021,773023 #6568
773027,773029 #6569
773081,773083 #6570
773207,773209 #6571
773249,773251 #6572
773567,773569 #6573
773609,773611 #6574
773657,773659 #6575
773681,773683 #6576
773777,773779 #6577
773867,773869 #6578
773951,773953 #6579
773987,773989 #6580
773999,774001 #6581
774071,774073 #6582
774131,774133 #6583
774797,774799 #6584
774929,774931 #6585
775361,775363 #6586
775601,775603 #6587
775739,775741 #6588
775937,775939 #6589
776057,776059 #6590
776117,776119 #6591
776177,776179 #6592
776219,776221 #6593
776561,776563 #6594
777011,777013 #6595
777167,777169 #6596
777389,777391 #6597
777419,777421 #6598
777431,777433 #6599
777617,777619 #6600
777641,777643 #6601
777857,777859 #6602
777977,777979 #6603
778049,778051 #6604
778079,778081 #6605
778109,778111 #6606
778121,778123 #6607
778361,778363 #6608
778511,778513 #6609
778697,778699 #6610
778871,778873 #6611
779327,779329 #6612
779351,779353 #6613
779561,779563 #6614
779591,779593 #6615
779657,779659 #6616
779747,779749 #6617
779981,779983 #6618
780047,780049 #6619
780191,780193 #6620
780719,780721 #6621
780851,780853 #6622
780887,780889 #6623
780971,780973 #6624
781127,781129 #6625
781307,781309 #6626
781367,781369 #6627
781397,781399 #6628
781481,781483 #6629
781511,781513 #6630
781631,781633 #6631
781799,781801 #6632
781817,781819 #6633
781967,781969 #6634
781997,781999 #6635
782009,782011 #6636
782147,782149 #6637
782189,782191 #6638
782387,782389 #6639
782669,782671 #6640
782687,782689 #6641
782981,782983 #6642
783119,783121 #6643
783149,783151 #6644
783191,783193 #6645
783257,783259 #6646
783359,783361 #6647
783527,783529 #6648
783569,783571 #6649
783689,783691 #6650
783701,783703 #6651
783719,783721 #6652
783779,783781 #6653
783791,783793 #6654
784181,784183 #6655
784211,784213 #6656
784307,784309 #6657
784349,784351 #6658
784409,784411 #6659
784541,784543 #6660
785219,785221 #6661
785459,785461 #6662
785501,785503 #6663
785777,785779 #6664
785801,785803 #6665
785921,785923 #6666
786059,786061 #6667
786431,786433 #6668
786551,786553 #6669
786587,786589 #6670
786659,786661 #6671
786701,786703 #6672
786887,786889 #6673
787067,787069 #6674
787331,787333 #6675
787427,787429 #6676
787517,787519 #6677
787769,787771 #6678
788087,788089 #6679
788351,788353 #6680
788561,788563 #6681
788867,788869 #6682
788999,789001 #6683
789029,789031 #6684
789389,789391 #6685
789491,789493 #6686
789587,789589 #6687
789671,789673 #6688
789959,789961 #6689
789977,789979 #6690
790169,790171 #6691
790199,790201 #6692
790289,790291 #6693
790331,790333 #6694
790649,790651 #6695
790817,790819 #6696
790967,790969 #6697
791309,791311 #6698
791561,791563 #6699
791627,791629 #6700
791801,791803 #6701
791849,791851 #6702
791897,791899 #6703
791927,791929 #6704
791969,791971 #6705
792107,792109 #6706
792227,792229 #6707
792299,792301 #6708
792479,792481 #6709
792551,792553 #6710
792641,792643 #6711
792689,792691 #6712
792989,792991 #6713
793187,793189 #6714
793487,793489 #6715
793517,793519 #6716
793787,793789 #6717
793841,793843 #6718
793979,793981 #6719
794009,794011 #6720
794039,794041 #6721
794111,794113 #6722
794201,794203 #6723
794471,794473 #6724
794657,794659 #6725
794741,794743 #6726
794879,794881 #6727
794921,794923 #6728
794999,795001 #6729
795077,795079 #6730
795101,795103 #6731
795251,795253 #6732
795647,795649 #6733
795659,795661 #6734
795761,795763 #6735
795791,795793 #6736
795797,795799 #6737
795827,795829 #6738
795941,795943 #6739
796139,796141 #6740
796337,796339 #6741
796361,796363 #6742
796709,796711 #6743
796799,796801 #6744
796847,796849 #6745
796931,796933 #6746
796967,796969 #6747
797051,797053 #6748
797309,797311 #6749
797507,797509 #6750
797549,797551 #6751
797567,797569 #6752
797579,797581 #6753
797591,797593 #6754
798197,798199 #6755
798221,798223 #6756
798647,798649 #6757
799061,799063 #6758
799091,799093 #6759
799217,799219 #6760
799301,799303 #6761
799361,799363 #6762
799481,799483 #6763
799619,799621 #6764
799739,799741 #6765
799991,799993 #6766
800117,800119 #6767
800159,800161 #6768
800417,800419 #6769
800519,800521 #6770
800537,800539 #6771
800621,800623 #6772
800729,800731 #6773
800741,800743 #6774
800999,801001 #6775
801077,801079 #6776
801419,801421 #6777
801569,801571 #6778
801707,801709 #6779
801809,801811 #6780
801947,801949 #6781
802127,802129 #6782
802181,802183 #6783
802649,802651 #6784
802829,802831 #6785
803057,803059 #6786
803441,803443 #6787
803447,803449 #6788
803609,803611 #6789
803729,803731 #6790
803987,803989 #6791
804281,804283 #6792
804521,804523 #6793
804611,804613 #6794
804941,804943 #6795
805031,805033 #6796
805097,805099 #6797
805109,805111 #6798
805331,805333 #6799
805499,805501 #6800
806009,806011 #6801
806261,806263 #6802
806369,806371 #6803
806381,806383 #6804
806579,806581 #6805
806789,806791 #6806
807407,807409 #6807
807491,807493 #6808
807509,807511 #6809
807731,807733 #6810
807869,807871 #6811
807941,807943 #6812
808019,808021 #6813
808307,808309 #6814
808349,808351 #6815
808361,808363 #6816
808439,808441 #6817
808601,808603 #6818
808679,808681 #6819
808991,808993 #6820
809141,809143 #6821
809201,809203 #6822
809357,809359 #6823
809399,809401 #6824
809579,809581 #6825
809747,809749 #6826
809801,809803 #6827
809981,809983 #6828
810149,810151 #6829
810191,810193 #6830
810377,810379 #6831
810389,810391 #6832
810539,810541 #6833
810581,810583 #6834
811037,811039 #6835
811649,811651 #6836
811931,811933 #6837
812297,812299 #6838
812351,812353 #6839
812501,812503 #6840
812597,812599 #6841
812639,812641 #6842
812699,812701 #6843
812759,812761 #6844
813089,813091 #6845
813299,813301 #6846
814061,814063 #6847
814067,814069 #6848
814127,814129 #6849
814211,814213 #6850
814241,814243 #6851
814379,814381 #6852
814577,814579 #6853
814601,814603 #6854
814631,814633 #6855
814901,814903 #6856
814937,814939 #6857
815411,815413 #6858
815621,815623 #6859
815669,815671 #6860
815819,815821 #6861
816131,816133 #6862
816161,816163 #6863
816587,816589 #6864
816689,816691 #6865
816839,816841 #6866
816857,816859 #6867
816917,816919 #6868
817049,817051 #6869
817151,817153 #6870
817277,817279 #6871
817319,817321 #6872
817709,817711 #6873
817721,817723 #6874
817889,817891 #6875
818099,818101 #6876
818171,818173 #6877
818339,818341 #6878
818579,818581 #6879
818687,818689 #6880
818819,818821 #6881
818999,819001 #6882
819029,819031 #6883
819239,819241 #6884
819251,819253 #6885
819317,819319 #6886
819389,819391 #6887
819407,819409 #6888
819491,819493 #6889
819617,819619 #6890
819737,819739 #6891
819827,819829 #6892
819911,819913 #6893
819989,819991 #6894
820241,820243 #6895
820271,820273 #6896
820319,820321 #6897
820331,820333 #6898
820409,820411 #6899
820427,820429 #6900
820679,820681 #6901
820907,820909 #6902
821099,821101 #6903
821207,821209 #6904
821459,821461 #6905
821477,821479 #6906
821801,821803 #6907
821939,821941 #6908
822011,822013 #6909
822161,822163 #6910
822167,822169 #6911
822221,822223 #6912
822389,822391 #6913
822431,822433 #6914
822539,822541 #6915
822551,822553 #6916
822587,822589 #6917
822671,822673 #6918
822761,822763 #6919
822791,822793 #6920
822821,822823 #6921
822881,822883 #6922
822971,822973 #6923
823001,823003 #6924
823127,823129 #6925
823241,823243 #6926
823349,823351 #6927
823481,823483 #6928
823619,823621 #6929
823721,823723 #6930
823727,823729 #6931
823787,823789 #6932
823829,823831 #6933
823841,823843 #6934
823967,823969 #6935
824189,824191 #6936
824231,824233 #6937
824399,824401 #6938
824669,824671 #6939
824699,824701 #6940
824777,824779 #6941
824981,824983 #6942
825047,825049 #6943
825107,825109 #6944
825191,825193 #6945
825281,825283 #6946
825551,825553 #6947
825611,825613 #6948
825827,825829 #6949
825959,825961 #6950
826037,826039 #6951
826151,826153 #6952
826169,826171 #6953
826349,826351 #6954
826379,826381 #6955
826391,826393 #6956
826559,826561 #6957
826667,826669 #6958
826697,826699 #6959
827039,827041 #6960
827129,827131 #6961
827537,827539 #6962
827927,827929 #6963
827987,827989 #6964
828011,828013 #6965
828131,828133 #6966
828407,828409 #6967
828701,828703 #6968
828809,828811 #6969
828899,828901 #6970
829121,829123 #6971
829637,829639 #6972
829721,829723 #6973
829727,829729 #6974
829811,829813 #6975
829847,829849 #6976
830309,830311 #6977
830327,830329 #6978
830339,830341 #6979
830411,830413 #6980
830447,830449 #6981
830549,830551 #6982
830741,830743 #6983
831071,831073 #6984
831161,831163 #6985
831371,831373 #6986
831407,831409 #6987
831431,831433 #6988
831539,831541 #6989
831617,831619 #6990
831659,831661 #6991
831707,831709 #6992
831911,831913 #6993
832079,832081 #6994
832121,832123 #6995
832157,832159 #6996
832367,832369 #6997
832631,832633 #6998
832679,832681 #6999
833099,833101 #7000
833177,833179 #7001
833477,833479 #7002
833711,833713 #7003
833717,833719 #7004
834131,834133 #7005
834149,834151 #7006
834257,834259 #7007
834569,834571 #7008
834641,834643 #7009
834809,834811 #7010
834857,834859 #7011
834947,834949 #7012
834959,834961 #7013
835097,835099 #7014
835139,835141 #7015
835319,835321 #7016
835451,835453 #7017
835607,835609 #7018
835661,835663 #7019
835817,835819 #7020
836159,836161 #7021
836189,836191 #7022
836567,836569 #7023
836609,836611 #7024
836699,836701 #7025
836747,836749 #7026
836861,836863 #7027
836879,836881 #7028
837071,837073 #7029
837077,837079 #7030
837377,837379 #7031
837677,837679 #7032
837929,837931 #7033
838037,838039 #7034
838091,838093 #7035
838139,838141 #7036
838169,838171 #7037
838247,838249 #7038
838349,838351 #7039
838391,838393 #7040
838631,838633 #7041
838769,838771 #7042
838949,838951 #7043
838991,838993 #7044
839351,839353 #7045
839471,839473 #7046
839609,839611 #7047
839651,839653 #7048
839897,839899 #7049
839957,839959 #7050
840137,840139 #7051
840179,840181 #7052
840239,840241 #7053
840821,840823 #7054
840839,840841 #7055
840941,840943 #7056
840989,840991 #7057
841019,841021 #7058
841079,841081 #7059
841457,841459 #7060
841661,841663 #7061
841931,841933 #7062
842087,842089 #7063
842111,842113 #7064
842159,842161 #7065
842291,842293 #7066
842321,842323 #7067
842339,842341 #7068
842351,842353 #7069
842417,842419 #7070
842447,842449 #7071
842519,842521 #7072
843179,843181 #7073
843209,843211 #7074
843299,843301 #7075
843377,843379 #7076
843587,843589 #7077
843677,843679 #7078
843779,843781 #7079
843881,843883 #7080
844139,844141 #7081
844199,844201 #7082
844427,844429 #7083
844511,844513 #7084
844601,844603 #7085
844619,844621 #7086
844769,844771 #7087
845489,845491 #7088
845657,845659 #7089
845879,845881 #7090
845981,845983 #7091
845987,845989 #7092
846059,846061 #7093
846341,846343 #7094
846359,846361 #7095
846401,846403 #7096
846749,846751 #7097
846869,846871 #7098
846917,846919 #7099
847277,847279 #7100
847727,847729 #7101
847787,847789 #7102
847967,847969 #7103
847991,847993 #7104
848201,848203 #7105
848591,848593 #7106
848789,848791 #7107
848849,848851 #7108
848921,848923 #7109
849047,849049 #7110
849221,849223 #7111
849347,849349 #7112
849599,849601 #7113
849701,849703 #7114
849731,849733 #7115
850061,850063 #7116
850271,850273 #7117
850301,850303 #7118
850349,850351 #7119
851801,851803 #7120
852011,852013 #7121
852149,852151 #7122
852197,852199 #7123
852287,852289 #7124
852557,852559 #7125
852581,852583 #7126
852671,852673 #7127
852749,852751 #7128
852827,852829 #7129
853031,853033 #7130
853187,853189 #7131
853289,853291 #7132
853427,853429 #7133
853667,853669 #7134
853901,853903 #7135
854039,854041 #7136
854351,854353 #7137
854417,854419 #7138
854459,854461 #7139
854897,854899 #7140
854921,854923 #7141
854927,854929 #7142
855059,855061 #7143
855269,855271 #7144
855719,855721 #7145
855731,855733 #7146
855737,855739 #7147
855887,855889 #7148
856277,856279 #7149
856391,856393 #7150
856547,856549 #7151
856697,856699 #7152
856787,856789 #7153
856811,856813 #7154
856901,856903 #7155
857009,857011 #7156
857027,857029 #7157
857081,857083 #7158
857201,857203 #7159
857567,857569 #7160
857579,857581 #7161
857669,857671 #7162
857711,857713 #7163
857741,857743 #7164
857951,857953 #7165
857957,857959 #7166
858101,858103 #7167
858239,858241 #7168
858707,858709 #7169
859049,859051 #7170
859091,859093 #7171
859277,859279 #7172
859361,859363 #7173
859559,859561 #7174
859601,859603 #7175
859667,859669 #7176
859679,859681 #7177
859799,859801 #7178
860009,860011 #7179
860087,860089 #7180
860309,860311 #7181
860381,860383 #7182
860579,860581 #7183
860789,860791 #7184
860927,860929 #7185
860939,860941 #7186
860969,860971 #7187
861437,861439 #7188
861491,861493 #7189
861701,861703 #7190
861797,861799 #7191
861899,861901 #7192
861977,861979 #7193
862031,862033 #7194
862157,862159 #7195
862229,862231 #7196
862259,862261 #7197
862397,862399 #7198
862481,862483 #7199
862571,862573 #7200
862649,862651 #7201
862907,862909 #7202
862919,862921 #7203
863537,863539 #7204
863801,863803 #7205
863867,863869 #7206
863897,863899 #7207
864011,864013 #7208
864047,864049 #7209
864077,864079 #7210
864119,864121 #7211
864167,864169 #7212
864221,864223 #7213
864299,864301 #7214
864359,864361 #7215
864509,864511 #7216
864581,864583 #7217
864629,864631 #7218
865001,865003 #7219
865211,865213 #7220
865259,865261 #7221
865481,865483 #7222
865637,865639 #7223
865769,865771 #7224
865817,865819 #7225
866009,866011 #7226
866051,866053 #7227
866081,866083 #7228
866309,866311 #7229
866639,866641 #7230
866849,866851 #7231
867257,867259 #7232
867509,867511 #7233
867617,867619 #7234
867677,867679 #7235
867827,867829 #7236
868121,868123 #7237
868379,868381 #7238
868451,868453 #7239
868487,868489 #7240
868529,868531 #7241
868559,868561 #7242
868739,868741 #7243
868799,868801 #7244
868937,868939 #7245
868997,868999 #7246
869249,869251 #7247
869291,869293 #7248
869369,869371 #7249
869597,869599 #7250
869777,869779 #7251
869807,869809 #7252
870047,870049 #7253
870239,870241 #7254
870431,870433 #7255
870641,870643 #7256
870809,870811 #7257
870929,870931 #7258
871229,871231 #7259
871679,871681 #7260
872141,872143 #7261
872159,872161 #7262
872351,872353 #7263
872381,872383 #7264
872477,872479 #7265
872561,872563 #7266
872609,872611 #7267
872621,872623 #7268
872657,872659 #7269
872747,872749 #7270
872789,872791 #7271
872951,872953 #7272
873317,873319 #7273
873419,873421 #7274
873461,873463 #7275
873527,873529 #7276
873539,873541 #7277
873569,873571 #7278
873617,873619 #7279
873641,873643 #7280
873707,873709 #7281
873989,873991 #7282
874301,874303 #7283
874457,874459 #7284
874637,874639 #7285
874721,874723 #7286
874889,874891 #7287
875261,875263 #7288
875267,875269 #7289
875297,875299 #7290
875339,875341 #7291
875417,875419 #7292
875519,875521 #7293
875591,875593 #7294
875627,875629 #7295
875681,875683 #7296
875759,875761 #7297
875981,875983 #7298
876011,876013 #7299
876017,876019 #7300
876077,876079 #7301
876191,876193 #7302
876329,876331 #7303
876371,876373 #7304
876431,876433 #7305
876479,876481 #7306
876719,876721 #7307
876749,876751 #7308
876851,876853 #7309
877109,877111 #7310
877397,877399 #7311
877619,877621 #7312
877871,877873 #7313
877907,877909 #7314
877937,877939 #7315
878021,878023 #7316
878039,878041 #7317
878411,878413 #7318
878831,878833 #7319
878987,878989 #7320
879167,879169 #7321
879269,879271 #7322
879341,879343 #7323
879581,879583 #7324
879689,879691 #7325
879707,879709 #7326
879797,879799 #7327
879917,879919 #7328
880067,880069 #7329
880151,880153 #7330
880247,880249 #7331
880301,880303 #7332
880421,880423 #7333
880541,880543 #7334
880571,880573 #7335
880727,880729 #7336
880799,880801 #7337
880907,880909 #7338
880949,880951 #7339
881141,881143 #7340
881171,881173 #7341
881471,881473 #7342
881477,881479 #7343
881537,881539 #7344
881897,881899 #7345
882017,882019 #7346
882029,882031 #7347
882239,882241 #7348
882251,882253 #7349
882389,882391 #7350
882449,882451 #7351
882701,882703 #7352
882881,882883 #7353
883109,883111 #7354
883229,883231 #7355
883247,883249 #7356
883409,883411 #7357
883577,883579 #7358
883697,883699 #7359
883781,883783 #7360
884129,884131 #7361
884267,884269 #7362
884309,884311 #7363
884369,884371 #7364
884489,884491 #7365
884591,884593 #7366
884789,884791 #7367
885161,885163 #7368
885551,885553 #7369
885791,885793 #7370
885821,885823 #7371
885881,885883 #7372
885959,885961 #7373
886019,886021 #7374
886181,886183 #7375
886241,886243 #7376
886337,886339 #7377
886427,886429 #7378
886469,886471 #7379
886517,886519 #7380
886547,886549 #7381
886607,886609 #7382
886967,886969 #7383
886979,886981 #7384
887057,887059 #7385
887141,887143 #7386
887267,887269 #7387
887399,887401 #7388
887567,887569 #7389
887657,887659 #7390
887669,887671 #7391
887837,887839 #7392
887921,887923 #7393
887987,887989 #7394
888059,888061 #7395
888161,888163 #7396
888359,888361 #7397
888659,888661 #7398
888689,888691 #7399
888779,888781 #7400
888869,888871 #7401
888917,888919 #7402
888959,888961 #7403
889037,889039 #7404
889349,889351 #7405
889697,889699 #7406
889871,889873 #7407
889877,889879 #7408
889907,889909 #7409
890117,890119 #7410
890159,890161 #7411
890861,890863 #7412
890999,891001 #7413
891047,891049 #7414
891101,891103 #7415
891377,891379 #7416
891389,891391 #7417
891491,891493 #7418
891521,891523 #7419
891557,891559 #7420
891659,891661 #7421
891677,891679 #7422
891797,891799 #7423
891827,891829 #7424
891887,891889 #7425
892091,892093 #7426
892781,892783 #7427
893117,893119 #7428
893147,893149 #7429
893339,893341 #7430
893381,893383 #7431
894137,894139 #7432
894191,894193 #7433
894209,894211 #7434
894407,894409 #7435
894449,894451 #7436
894611,894613 #7437
894791,894793 #7438
894869,894871 #7439
895007,895009 #7440
895049,895051 #7441
895157,895159 #7442
895241,895243 #7443
895421,895423 #7444
895469,895471 #7445
895649,895651 #7446
895667,895669 #7447
895787,895789 #7448
895799,895801 #7449
895901,895903 #7450
896111,896113 #7451
896297,896299 #7452
896447,896449 #7453
896717,896719 #7454
897101,897103 #7455
897269,897271 #7456
897317,897319 #7457
897467,897469 #7458
897497,897499 #7459
897647,897649 #7460
897707,897709 #7461
897779,897781 #7462
898067,898069 #7463
898211,898213 #7464
898241,898243 #7465
898421,898423 #7466
898481,898483 #7467
898661,898663 #7468
899159,899161 #7469
899177,899179 #7470
899849,899851 #7471
899891,899893 #7472
900089,900091 #7473
900329,900331 #7474
900551,900553 #7475
900587,900589 #7476
900671,900673 #7477
900761,900763 #7478
900929,900931 #7479
900971,900973 #7480
901007,901009 #7481
901169,901171 #7482
901211,901213 #7483
901247,901249 #7484
901427,901429 #7485
901499,901501 #7486
901739,901741 #7487
901907,901909 #7488
902087,902089 #7489
902261,902263 #7490
902597,902599 #7491
903389,903391 #7492
903449,903451 #7493
904067,904069 #7494
904217,904219 #7495
904511,904513 #7496
904661,904663 #7497
904679,904681 #7498
904901,904903 #7499
904931,904933 #7500
904997,904999 #7501
905207,905209 #7502
905297,905299 #7503
905759,905761 #7504
906011,906013 #7505
906119,906121 #7506
906329,906331 #7507
906539,906541 #7508
906749,906751 #7509
906929,906931 #7510
907019,907021 #7511
907139,907141 #7512
907211,907213 #7513
907367,907369 #7514
907391,907393 #7515
907397,907399 #7516
907469,907471 #7517
907691,907693 #7518
907757,907759 #7519
907811,907813 #7520
907967,907969 #7521
907997,907999 #7522
908417,908419 #7523
908489,908491 #7524
908669,908671 #7525
908819,908821 #7526
908849,908851 #7527
908861,908863 #7528
908879,908881 #7529
908909,908911 #7530
909089,909091 #7531
909239,909241 #7532
909287,909289 #7533
909299,909301 #7534
909317,909319 #7535
909329,909331 #7536
909341,909343 #7537
909539,909541 #7538
909611,909613 #7539
909899,909901 #7540
909971,909973 #7541
910097,910099 #7542
910139,910141 #7543
910199,910201 #7544
910277,910279 #7545
910451,910453 #7546
910619,910621 #7547
910709,910711 #7548
911087,911089 #7549
911159,911161 #7550
911171,911173 #7551
911231,911233 #7552
911291,911293 #7553
911357,911359 #7554
911681,911683 #7555
911837,911839 #7556
911957,911959 #7557
912047,912049 #7558
912449,912451 #7559
912467,912469 #7560
912521,912523 #7561
912647,912649 #7562
912797,912799 #7563
912851,912853 #7564
912869,912871 #7565
912971,912973 #7566
913037,913039 #7567
913571,913573 #7568
913637,913639 #7569
914189,914191 #7570
914237,914239 #7571
914357,914359 #7572
914369,914371 #7573
914519,914521 #7574
914579,914581 #7575
914609,914611 #7576
914789,914791 #7577
915197,915199 #7578
915221,915223 #7579
915251,915253 #7580
915587,915589 #7581
915611,915613 #7582
915917,915919 #7583
915947,915949 #7584
916031,916033 #7585
916127,916129 #7586
916187,916189 #7587
916217,916219 #7588
916259,916261 #7589
916337,916339 #7590
916469,916471 #7591
916649,916651 #7592
916931,916933 #7593
917039,917041 #7594
917051,917053 #7595
917237,917239 #7596
917459,917461 #7597
917591,917593 #7598
917687,917689 #7599
917771,917773 #7600
918257,918259 #7601
918431,918433 #7602
918581,918583 #7603
918677,918679 #7604
918947,918949 #7605
919019,919021 #7606
919031,919033 #7607
919109,919111 #7608
919229,919231 #7609
919349,919351 #7610
919421,919423 #7611
919691,919693 #7612
919757,919759 #7613
919901,919903 #7614
919937,919939 #7615
919949,919951 #7616
920147,920149 #7617
920201,920203 #7618
920279,920281 #7619
920441,920443 #7620
920651,920653 #7621
920741,920743 #7622
920789,920791 #7623
920999,921001 #7624
921029,921031 #7625
921197,921199 #7626
921257,921259 #7627
921407,921409 #7628
921497,921499 #7629
921749,921751 #7630
921839,921841 #7631
921887,921889 #7632
921911,921913 #7633
922037,922039 #7634
922067,922069 #7635
922079,922081 #7636
922289,922291 #7637
922331,922333 #7638
922487,922489 #7639
922511,922513 #7640
922637,922639 #7641
922679,922681 #7642
922739,922741 #7643
923051,923053 #7644
923177,923179 #7645
923201,923203 #7646
923309,923311 #7647
923369,923371 #7648
923579,923581 #7649
923849,923851 #7650
924041,924043 #7651
924281,924283 #7652
924359,924361 #7653
924401,924403 #7654
924419,924421 #7655
924527,924529 #7656
924641,924643 #7657
924659,924661 #7658
924809,924811 #7659
924827,924829 #7660
925079,925081 #7661
925271,925273 #7662
925499,925501 #7663
925577,925579 #7664
925619,925621 #7665
926087,926089 #7666
926111,926113 #7667
926129,926131 #7668
926351,926353 #7669
926657,926659 #7670
926669,926671 #7671
927629,927631 #7672
928097,928099 #7673
928139,928141 #7674
928157,928159 #7675
928271,928273 #7676
928427,928429 #7677
928469,928471 #7678
928559,928561 #7679
928619,928621 #7680
928649,928651 #7681
928769,928771 #7682
928817,928819 #7683
929009,929011 #7684
929057,929059 #7685
929207,929209 #7686
929417,929419 #7687
929627,929629 #7688
929639,929641 #7689
929741,929743 #7690
929807,929809 #7691
930071,930073 #7692
930077,930079 #7693
930197,930199 #7694
930287,930289 #7695
930467,930469 #7696
930569,930571 #7697
930617,930619 #7698
930989,930991 #7699
931127,931129 #7700
931571,931573 #7701
931727,931729 #7702
931781,931783 #7703
932117,932119 #7704
932207,932209 #7705
932219,932221 #7706
932417,932419 #7707
932471,932473 #7708
932681,932683 #7709
932801,932803 #7710
932999,933001 #7711
933059,933061 #7712
933551,933553 #7713
933809,933811 #7714
933851,933853 #7715
934049,934051 #7716
934067,934069 #7717
934487,934489 #7718
934721,934723 #7719
934889,934891 #7720
934907,934909 #7721
934979,934981 #7722
935021,935023 #7723
935147,935149 #7724
935591,935593 #7725
935651,935653 #7726
935687,935689 #7727
935717,935719 #7728
936179,936181 #7729
936281,936283 #7730
936737,936739 #7731
936917,936919 #7732
937007,937009 #7733
937031,937033 #7734
937229,937231 #7735
937241,937243 #7736
937589,937591 #7737
937637,937639 #7738
937661,937663 #7739
937679,937681 #7740
937901,937903 #7741
938051,938053 #7742
938057,938059 #7743
938879,938881 #7744
938981,938983 #7745
939089,939091 #7746
939119,939121 #7747
939179,939181 #7748
939347,939349 #7749
939359,939361 #7750
939611,939613 #7751
939737,939739 #7752
939767,939769 #7753
939791,939793 #7754
939971,939973 #7755
940001,940003 #7756
940349,940351 #7757
940529,940531 #7758
940547,940549 #7759
940781,940783 #7760
941009,941011 #7761
941117,941119 #7762
941207,941209 #7763
941249,941251 #7764
941489,941491 #7765
941669,941671 #7766
942041,942043 #7767
942167,942169 #7768
942311,942313 #7769
942437,942439 #7770
942659,942661 #7771
942857,942859 #7772
942899,942901 #7773
943079,943081 #7774
943301,943303 #7775
943541,943543 #7776
943601,943603 #7777
943781,943783 #7778
943799,943801 #7779
943841,943843 #7780
944147,944149 #7781
944261,944263 #7782
944387,944389 #7783
944429,944431 #7784
944519,944521 #7785
944561,944563 #7786
944687,944689 #7787
944729,944731 #7788
944897,944899 #7789
945209,945211 #7790
945389,945391 #7791
945479,945481 #7792
945587,945589 #7793
945629,945631 #7794
945671,945673 #7795
945731,945733 #7796
945809,945811 #7797
945881,945883 #7798
945941,945943 #7799
946079,946081 #7800
946091,946093 #7801
946109,946111 #7802
946367,946369 #7803
946487,946489 #7804
946511,946513 #7805
946661,946663 #7806
946667,946669 #7807
946859,946861 #7808
947381,947383 #7809
947411,947413 #7810
947741,947743 #7811
948089,948091 #7812
948149,948151 #7813
948401,948403 #7814
948797,948799 #7815
948971,948973 #7816
949019,949021 #7817
949211,949213 #7818
949241,949243 #7819
949439,949441 #7820
949451,949453 #7821
949607,949609 #7822
949631,949633 #7823
949649,949651 #7824
949889,949891 #7825
949937,949939 #7826
950039,950041 #7827
950177,950179 #7828
950231,950233 #7829
950459,950461 #7830
950837,950839 #7831
950867,950869 #7832
951059,951061 #7833
951089,951091 #7834
951107,951109 #7835
951281,951283 #7836
951341,951343 #7837
951581,951583 #7838
951647,951649 #7839
951941,951943 #7840
952277,952279 #7841
952379,952381 #7842
952667,952669 #7843
952739,952741 #7844
952811,952813 #7845
952979,952981 #7846
953039,953041 #7847
953501,953503 #7848
953789,953791 #7849
954131,954133 #7850
954257,954259 #7851
954377,954379 #7852
954827,954829 #7853
954851,954853 #7854
954869,954871 #7855
954971,954973 #7856
954977,954979 #7857
955037,955039 #7858
955061,955063 #7859
955091,955093 #7860
955307,955309 #7861
955439,955441 #7862
955481,955483 #7863
955709,955711 #7864
955727,955729 #7865
955937,955939 #7866
955991,955993 #7867
956399,956401 #7868
956951,956953 #7869
957041,957043 #7870
957107,957109 #7871
957431,957433 #7872
957599,957601 #7873
957641,957643 #7874
957701,957703 #7875
957821,957823 #7876
958049,958051 #7877
958121,958123 #7878
958259,958261 #7879
958367,958369 #7880
958499,958501 #7881
958541,958543 #7882
958547,958549 #7883
958667,958669 #7884
958931,958933 #7885
959207,959209 #7886
959267,959269 #7887
959471,959473 #7888
959477,959479 #7889
959867,959869 #7890
960017,960019 #7891
960119,960121 #7892
960137,960139 #7893
960329,960331 #7894
960497,960499 #7895
960521,960523 #7896
960647,960649 #7897
960989,960991 #7898
961067,961069 #7899
961097,961099 #7900
961139,961141 #7901
961157,961159 #7902
961187,961189 #7903
961241,961243 #7904
961397,961399 #7905
961451,961453 #7906
961529,961531 #7907
961547,961549 #7908
961661,961663 #7909
961811,961813 #7910
961991,961993 #7911
962009,962011 #7912
962459,962461 #7913
962669,962671 #7914
962681,962683 #7915
962789,962791 #7916
962837,962839 #7917
962867,962869 #7918
962909,962911 #7919
963239,963241 #7920
963299,963301 #7921
963341,963343 #7922
963497,963499 #7923
963689,963691 #7924
963707,963709 #7925
963761,963763 #7926
963839,963841 #7927
963899,963901 #7928
964151,964153 #7929
964217,964219 #7930
964259,964261 #7931
964499,964501 #7932
964517,964519 #7933
964967,964969 #7934
965087,965089 #7935
965177,965179 #7936
965189,965191 #7937
965399,965401 #7938
965621,965623 #7939
965777,965779 #7940
966011,966013 #7941
966209,966211 #7942
966377,966379 #7943
966617,966619 #7944
966659,966661 #7945
966869,966871 #7946
967259,967261 #7947
967319,967321 #7948
967361,967363 #7949
967427,967429 #7950
967751,967753 #7951
968111,968113 #7952
968237,968239 #7953
968501,968503 #7954
968519,968521 #7955
968729,968731 #7956
968909,968911 #7957
969179,969181 #7958
969257,969259 #7959
969341,969343 #7960
969431,969433 #7961
969677,969679 #7962
969719,969721 #7963
970061,970063 #7964
970217,970219 #7965
970259,970261 #7966
970421,970423 #7967
970787,970789 #7968
970859,970861 #7969
970967,970969 #7970
970997,970999 #7971
971027,971029 #7972
971051,971053 #7973
971141,971143 #7974
971279,971281 #7975
971387,971389 #7976
971561,971563 #7977
971651,971653 #7978
972029,972031 #7979
972119,972121 #7980
972131,972133 #7981
972161,972163 #7982
972197,972199 #7983
972227,972229 #7984
972407,972409 #7985
972611,972613 #7986
972899,972901 #7987
972941,972943 #7988
973001,973003 #7989
973031,973033 #7990
973067,973069 #7991
973277,973279 #7992
973331,973333 #7993
973409,973411 #7994
973757,973759 #7995
973787,973789 #7996
974159,974161 #7997
974177,974179 #7998
974417,974419 #7999
974537,974539 #8000
974651,974653 #8001
974711,974713 #8002
974747,974749 #8003
974819,974821 #8004
974861,974863 #8005
974957,974959 #8006
974969,974971 #8007
975257,975259 #8008
975521,975523 #8009
975551,975553 #8010
975899,975901 #8011
975941,975943 #8012
976091,976093 #8013
976301,976303 #8014
976307,976309 #8015
976559,976561 #8016
976637,976639 #8017
977021,977023 #8018
977147,977149 #8019
977357,977359 #8020
977411,977413 #8021
977591,977593 #8022
977609,977611 #8023
978071,978073 #8024
978077,978079 #8025
978149,978151 #8026
978179,978181 #8027
978347,978349 #8028
978617,978619 #8029
978797,978799 #8030
978851,978853 #8031
979061,979063 #8032
979541,979543 #8033
979919,979921 #8034
980069,980071 #8035
980489,980491 #8036
980591,980593 #8037
980687,980689 #8038
980717,980719 #8039
980729,980731 #8040
980801,980803 #8041
980897,980899 #8042
980909,980911 #8043
981137,981139 #8044
981287,981289 #8045
981437,981439 #8046
981599,981601 #8047
981809,981811 #8048
981887,981889 #8049
981947,981949 #8050
982061,982063 #8051
982097,982099 #8052
982211,982213 #8053
982271,982273 #8054
982337,982339 #8055
982571,982573 #8056
982841,982843 #8057
983327,983329 #8058
983429,983431 #8059
983441,983443 #8060
983447,983449 #8061
983531,983533 #8062
983579,983581 #8063
983699,983701 #8064
983789,983791 #8065
983861,983863 #8066
984119,984121 #8067
984299,984301 #8068
984539,984541 #8069
984701,984703 #8070
984911,984913 #8071
985277,985279 #8072
985529,985531 #8073
985781,985783 #8074
985979,985981 #8075
985991,985993 #8076
986147,986149 #8077
986189,986191 #8078
986507,986509 #8079
986567,986569 #8080
986597,986599 #8081
986717,986719 #8082
986849,986851 #8083
986927,986929 #8084
986981,986983 #8085
987191,987193 #8086
987209,987211 #8087
987911,987913 #8088
988067,988069 #8089
988109,988111 #8090
988217,988219 #8091
988319,988321 #8092
988577,988579 #8093
988649,988651 #8094
988859,988861 #8095
989171,989173 #8096
989249,989251 #8097
989321,989323 #8098
989477,989479 #8099
989579,989581 #8100
989837,989839 #8101
989999,990001 #8102
990179,990181 #8103
990287,990289 #8104
990329,990331 #8105
990359,990361 #8106
990797,990799 #8107
990887,990889 #8108
991127,991129 #8109
991427,991429 #8110
991619,991621 #8111
991871,991873 #8112
991979,991981 #8113
992021,992023 #8114
992111,992113 #8115
992267,992269 #8116
992357,992359 #8117
992861,992863 #8118
993197,993199 #8119
993479,993481 #8120
993779,993781 #8121
993821,993823 #8122
994067,994069 #8123
994181,994183 #8124
994247,994249 #8125
994307,994309 #8126
994319,994321 #8127
994337,994339 #8128
994391,994393 #8129
994559,994561 #8130
994709,994711 #8131
994811,994813 #8132
995051,995053 #8133
995117,995119 #8134
995327,995329 #8135
995339,995341 #8136
995549,995551 #8137
995591,995593 #8138
995957,995959 #8139
995987,995989 #8140
996167,996169 #8141
996209,996211 #8142
996407,996409 #8143
996599,996601 #8144
996629,996631 #8145
996647,996649 #8146
996857,996859 #8147
996881,996883 #8148
997019,997021 #8149
997097,997099 #8150
997109,997111 #8151
997121,997123 #8152
997151,997153 #8153
997307,997309 #8154
997649,997651 #8155
997739,997741 #8156
997811,997813 #8157
997877,997879 #8158
997889,997891 #8159
997961,997963 #8160
998027,998029 #8161
998069,998071 #8162
998537,998539 #8163
998651,998653 #8164
998687,998689 #8165
999329,999331 #8166
999431,999433 #8167
999611,999613 #8168
999959,999961 #8169
1000037,1000039 #8170
1000211,1000213 #8171
1000289,1000291 #8172
1000427,1000429 #8173
1000577,1000579 #8174
1000619,1000621 #8175
1000667,1000669 #8176
1000721,1000723 #8177
1000847,1000849 #8178
1000859,1000861 #8179
1000919,1000921 #8180
1001087,1001089 #8181
1001321,1001323 #8182
1001387,1001389 #8183
1001549,1001551 #8184
1001807,1001809 #8185
1001981,1001983 #8186
1002149,1002151 #8187
1002257,1002259 #8188
1002341,1002343 #8189
1002347,1002349 #8190
1002359,1002361 #8191
1002719,1002721 #8192
1002767,1002769 #8193
1002851,1002853 #8194
1002929,1002931 #8195
1003001,1003003 #8196
1003109,1003111 #8197
1003199,1003201 #8198
1003349,1003351 #8199
1003361,1003363 #8200
1003367,1003369 #8201
1003619,1003621 #8202
1003817,1003819 #8203
1003907,1003909 #8204
1004117,1004119 #8205
1004657,1004659 #8206
1004669,1004671 #8207
1004747,1004749 #8208
1005071,1005073 #8209
1005131,1005133 #8210
1005239,1005241 #8211
1005371,1005373 #8212
1005437,1005439 #8213
1005551,1005553 #8214
1005617,1005619 #8215
1005677,1005679 #8216
1005911,1005913 #8217
1006151,1006153 #8218
1006169,1006171 #8219
1006217,1006219 #8220
1006301,1006303 #8221
1006307,1006309 #8222
1006331,1006333 #8223
1006337,1006339 #8224
1006391,1006393 #8225
1006469,1006471 #8226
1006781,1006783 #8227
1006877,1006879 #8228
1007021,1007023 #8229
1007117,1007119 #8230
1007297,1007299 #8231
1007597,1007599 #8232
1007681,1007683 #8233
1007729,1007731 #8234
1007957,1007959 #8235
1008041,1008043 #8236
1008407,1008409 #8237
1008419,1008421 #8238
1008587,1008589 #8239
1008611,1008613 #8240
1008779,1008781 #8241
1008851,1008853 #8242
1008857,1008859 #8243
1008911,1008913 #8244
1008989,1008991 #8245
1009157,1009159 #8246
1009199,1009201 #8247
1009289,1009291 #8248
1009301,1009303 #8249
1009319,1009321 #8250
1009499,1009501 #8251
1009649,1009651 #8252
1009991,1009993 #8253
1010081,1010083 #8254
1010129,1010131 #8255
1010201,1010203 #8256
1010717,1010719 #8257
1010747,1010749 #8258
1010897,1010899 #8259
1010981,1010983 #8260
1011077,1011079 #8261
1011137,1011139 #8262
1011587,1011589 #8263
1011599,1011601 #8264
1011797,1011799 #8265
1012007,1012009 #8266
1012259,1012261 #8267
1012397,1012399 #8268
1012421,1012423 #8269
1012547,1012549 #8270
1012631,1012633 #8271
1012769,1012771 #8272
1012829,1012831 #8273
1013237,1013239 #8274
1013399,1013401 #8275
1013429,1013431 #8276
1013501,1013503 #8277
1013531,1013533 #8278
1013627,1013629 #8279
1013711,1013713 #8280
1013891,1013893 #8281
1013921,1013923 #8282
1014197,1014199 #8283
1014257,1014259 #8284
1014317,1014319 #8285
1014359,1014361 #8286
1014719,1014721 #8287
1014887,1014889 #8288
1015361,1015363 #8289
1015367,1015369 #8290
1015451,1015453 #8291
1015499,1015501 #8292
1015559,1015561 #8293
1015601,1015603 #8294
1016009,1016011 #8295
1016051,1016053 #8296
1016201,1016203 #8297
1016339,1016341 #8298
1016357,1016359 #8299
1016399,1016401 #8300
1016567,1016569 #8301
1016597,1016599 #8302
1016879,1016881 #8303
1016927,1016929 #8304
1017041,1017043 #8305
1017299,1017301 #8306
1017437,1017439 #8307
1017479,1017481 #8308
1017551,1017553 #8309
1017647,1017649 #8310
1017719,1017721 #8311
1017857,1017859 #8312
1018019,1018021 #8313
1018649,1018651 #8314
1018709,1018711 #8315
1018811,1018813 #8316
1019069,1019071 #8317
1019351,1019353 #8318
1019411,1019413 #8319
1019531,1019533 #8320
1019699,1019701 #8321
1019729,1019731 #8322
1020011,1020013 #8323
1020077,1020079 #8324
1020707,1020709 #8325
1020821,1020823 #8326
1020839,1020841 #8327
1020959,1020961 #8328
1020977,1020979 #8329
1020989,1020991 #8330
1021091,1021093 #8331
1021127,1021129 #8332
1021157,1021159 #8333
1021259,1021261 #8334
1021289,1021291 #8335
1021301,1021303 #8336
1021331,1021333 #8337
1021367,1021369 #8338
1021661,1021663 #8339
1021961,1021963 #8340
1022249,1022251 #8341
1022381,1022383 #8342
1022387,1022389 #8343
1022501,1022503 #8344
1022507,1022509 #8345
1023227,1023229 #8346
1023257,1023259 #8347
1023299,1023301 #8348
1023311,1023313 #8349
1023389,1023391 #8350
1023719,1023721 #8351
1023731,1023733 #8352
1023941,1023943 #8353
1023947,1023949 #8354
1024319,1024321 #8355
1024337,1024339 #8356
1024577,1024579 #8357
1024589,1024591 #8358
1025111,1025113 #8359
1025147,1025149 #8360
1025279,1025281 #8361
1025417,1025419 #8362
1025621,1025623 #8363
1025747,1025749 #8364
1025909,1025911 #8365
1026029,1026031 #8366
1026041,1026043 #8367
1026197,1026199 #8368
1026227,1026229 #8369
1026251,1026253 #8370
1026479,1026481 #8371
1026581,1026583 #8372
1026677,1026679 #8373
1026911,1026913 #8374
1026941,1026943 #8375
1027001,1027003 #8376
1027127,1027129 #8377
1027319,1027321 #8378
1027487,1027489 #8379
1027547,1027549 #8380
1027751,1027753 #8381
1027757,1027759 #8382
1028099,1028101 #8383
1028189,1028191 #8384
1028327,1028329 #8385
1028471,1028473 #8386
1028579,1028581 #8387
1028681,1028683 #8388
1028747,1028749 #8389
1028939,1028941 #8390
1028999,1029001 #8391
1029359,1029361 #8392
1029407,1029409 #8393
1029839,1029841 #8394
1029881,1029883 #8395
1030019,1030021 #8396
1030031,1030033 #8397
1030067,1030069 #8398
1030439,1030441 #8399
1030637,1030639 #8400
1030739,1030741 #8401
1030949,1030951 #8402
1031117,1031119 #8403
1031279,1031281 #8404
1031411,1031413 #8405
1031477,1031479 #8406
1031531,1031533 #8407
1031729,1031731 #8408
1031759,1031761 #8409
1032047,1032049 #8410
1032191,1032193 #8411
1032347,1032349 #8412
1032509,1032511 #8413
1032839,1032841 #8414
1032851,1032853 #8415
1032959,1032961 #8416
1033061,1033063 #8417
1033271,1033273 #8418
1033337,1033339 #8419
1033421,1033423 #8420
1033601,1033603 #8421
1033661,1033663 #8422
1033841,1033843 #8423
1034027,1034029 #8424
1034069,1034071 #8425
1034219,1034221 #8426
1034237,1034239 #8427
1034249,1034251 #8428
1034357,1034359 #8429
1034477,1034479 #8430
1034489,1034491 #8431
1034597,1034599 #8432
1034651,1034653 #8433
1034729,1034731 #8434
1034861,1034863 #8435
1034951,1034953 #8436
1035341,1035343 #8437
1035449,1035451 #8438
1035467,1035469 #8439
1035761,1035763 #8440
1036001,1036003 #8441
1036067,1036069 #8442
1036247,1036249 #8443
1036349,1036351 #8444
1036367,1036369 #8445
1036667,1036669 #8446
1036757,1036759 #8447
1036829,1036831 #8448
1036991,1036993 #8449
1037087,1037089 #8450
1037327,1037329 #8451
1037681,1037683 #8452
1038017,1038019 #8453
1038041,1038043 #8454
1038209,1038211 #8455
1038251,1038253 #8456
1038599,1038601 #8457
1038617,1038619 #8458
1038689,1038691 #8459
1039037,1039039 #8460
1039067,1039069 #8461
1039109,1039111 #8462
1039349,1039351 #8463
1039427,1039429 #8464
1040057,1040059 #8465
1040069,1040071 #8466
1040159,1040161 #8467
1040189,1040191 #8468
1040447,1040449 #8469
1040579,1040581 #8470
1040657,1040659 #8471
1040747,1040749 #8472
1040777,1040779 #8473
1041119,1041121 #8474
1041149,1041151 #8475
1041167,1041169 #8476
1041221,1041223 #8477
1041239,1041241 #8478
1041281,1041283 #8479
1041449,1041451 #8480
1041617,1041619 #8481
1041671,1041673 #8482
1042121,1042123 #8483
1042241,1042243 #8484
1042271,1042273 #8485
1042331,1042333 #8486
1042607,1042609 #8487
1042631,1042633 #8488
1042901,1042903 #8489
1043111,1043113 #8490
1043291,1043293 #8491
1043591,1043593 #8492
1043597,1043599 #8493
1043759,1043761 #8494
1043837,1043839 #8495
1043897,1043899 #8496
1043921,1043923 #8497
1044179,1044181 #8498
1044287,1044289 #8499
1044737,1044739 #8500
1044749,1044751 #8501
1044779,1044781 #8502
1044809,1044811 #8503
1045061,1045063 #8504
1045151,1045153 #8505
1045307,1045309 #8506
1045391,1045393 #8507
1045409,1045411 #8508
1045547,1045549 #8509
1045571,1045573 #8510
1045727,1045729 #8511
1045799,1045801 #8512
1046051,1046053 #8513
1046189,1046191 #8514
1046237,1046239 #8515
1046369,1046371 #8516
1046447,1046449 #8517
1046597,1046599 #8518
1046657,1046659 #8519
1047041,1047043 #8520
1047131,1047133 #8521
1047197,1047199 #8522
1047281,1047283 #8523
1047311,1047313 #8524
1047467,1047469 #8525
1047587,1047589 #8526
1047647,1047649 #8527
1047689,1047691 #8528
1047701,1047703 #8529
1047881,1047883 #8530
1048007,1048009 #8531
1048049,1048051 #8532
1048127,1048129 #8533
1048217,1048219 #8534
1048571,1048573 #8535
1048889,1048891 #8536
1049129,1049131 #8537
1049141,1049143 #8538
1049171,1049173 #8539
1049471,1049473 #8540
1049681,1049683 #8541
1049861,1049863 #8542
1049897,1049899 #8543
1050011,1050013 #8544
1050167,1050169 #8545
1050239,1050241 #8546
1050449,1050451 #8547
1050737,1050739 #8548
1050851,1050853 #8549
1050899,1050901 #8550
1051007,1051009 #8551
1051079,1051081 #8552
1051151,1051153 #8553
1051469,1051471 #8554
1051619,1051621 #8555
1051847,1051849 #8556
1052039,1052041 #8557
1052279,1052281 #8558
1052327,1052329 #8559
1052531,1052533 #8560
1052561,1052563 #8561
1052801,1052803 #8562
1052897,1052899 #8563
1053179,1053181 #8564
1053257,1053259 #8565
1053509,1053511 #8566
1053581,1053583 #8567
1053737,1053739 #8568
1053989,1053991 #8569
1054169,1054171 #8570
1054199,1054201 #8571
1054301,1054303 #8572
1054439,1054441 #8573
1054607,1054609 #8574
1054721,1054723 #8575
1055141,1055143 #8576
1055189,1055191 #8577
1055231,1055233 #8578
1055267,1055269 #8579
1055501,1055503 #8580
1055609,1055611 #8581
1056047,1056049 #8582
1056071,1056073 #8583
1056269,1056271 #8584
1056371,1056373 #8585
1056479,1056481 #8586
1056719,1056721 #8587
1057181,1057183 #8588
1057391,1057393 #8589
1057487,1057489 #8590
1057577,1057579 #8591
1057631,1057633 #8592
1057739,1057741 #8593
1058009,1058011 #8594
1058147,1058149 #8595
1058339,1058341 #8596
1058381,1058383 #8597
1058591,1058593 #8598
1058747,1058749 #8599
1058807,1058809 #8600
1058999,1059001 #8601
1059059,1059061 #8602
1059257,1059259 #8603
1059437,1059439 #8604
1059701,1059703 #8605
1060019,1060021 #8606
1060349,1060351 #8607
1060391,1060393 #8608
1060571,1060573 #8609
1060721,1060723 #8610
1060991,1060993 #8611
1061141,1061143 #8612
1061771,1061773 #8613
1061867,1061869 #8614
1061909,1061911 #8615
1062251,1062253 #8616
1062407,1062409 #8617
1062599,1062601 #8618
1062671,1062673 #8619
1062779,1062781 #8620
1062869,1062871 #8621
1062911,1062913 #8622
1062947,1062949 #8623
1062977,1062979 #8624
1063157,1063159 #8625
1063241,1063243 #8626
1063397,1063399 #8627
1063847,1063849 #8628
1063871,1063873 #8629
1063919,1063921 #8630
1063961,1063963 #8631
1063967,1063969 #8632
1064177,1064179 #8633
1064339,1064341 #8634
1064471,1064473 #8635
1064519,1064521 #8636
1064669,1064671 #8637
1064939,1064941 #8638
1064951,1064953 #8639
1065011,1065013 #8640
1065017,1065019 #8641
1065089,1065091 #8642
1065131,1065133 #8643
1065527,1065529 #8644
1065899,1065901 #8645
1066139,1066141 #8646
1066157,1066159 #8647
1066409,1066411 #8648
1066619,1066621 #8649
1066979,1066981 #8650
1067327,1067329 #8651
1067489,1067491 #8652
1067567,1067569 #8653
1067747,1067749 #8654
1067849,1067851 #8655
1068101,1068103 #8656
1068251,1068253 #8657
1068257,1068259 #8658
1068407,1068409 #8659
1068437,1068439 #8660
1068497,1068499 #8661
1068629,1068631 #8662
1068701,1068703 #8663
1068707,1068709 #8664
1068719,1068721 #8665
1068887,1068889 #8666
1069127,1069129 #8667
1069217,1069219 #8668
1069427,1069429 #8669
1069499,1069501 #8670
1069571,1069573 #8671
1069919,1069921 #8672
1069931,1069933 #8673
1069949,1069951 #8674
1070009,1070011 #8675
1070231,1070233 #8676
1070339,1070341 #8677
1070429,1070431 #8678
1070567,1070569 #8679
1070681,1070683 #8680
1071149,1071151 #8681
1071227,1071229 #8682
1071311,1071313 #8683
1071377,1071379 #8684
1071569,1071571 #8685
1071641,1071643 #8686
1071659,1071661 #8687
1071977,1071979 #8688
1072229,1072231 #8689
1072457,1072459 #8690
1072829,1072831 #8691
1072931,1072933 #8692
1072997,1072999 #8693
1073141,1073143 #8694
1073351,1073353 #8695
1073381,1073383 #8696
1073507,1073509 #8697
1073711,1073713 #8698
1073789,1073791 #8699
1073879,1073881 #8700
1073909,1073911 #8701
1073951,1073953 #8702
1074107,1074109 #8703
1074251,1074253 #8704
1074287,1074289 #8705
1074377,1074379 #8706
1074509,1074511 #8707
1074641,1074643 #8708
1074707,1074709 #8709
1074761,1074763 #8710
1074917,1074919 #8711
1074971,1074973 #8712
1074989,1074991 #8713
1075091,1075093 #8714
1075169,1075171 #8715
1075337,1075339 #8716
1075619,1075621 #8717
1075649,1075651 #8718
1075691,1075693 #8719
1075727,1075729 #8720
1075757,1075759 #8721
1075769,1075771 #8722
1076111,1076113 #8723
1076279,1076281 #8724
1076399,1076401 #8725
1076501,1076503 #8726
1076771,1076773 #8727
1077299,1077301 #8728
1077539,1077541 #8729
1077719,1077721 #8730
1077761,1077763 #8731
1077821,1077823 #8732
1077911,1077913 #8733
1078109,1078111 #8734
1078151,1078153 #8735
1078331,1078333 #8736
1078367,1078369 #8737
1078409,1078411 #8738
1078787,1078789 #8739
1079009,1079011 #8740
1079357,1079359 #8741
1079471,1079473 #8742
1079669,1079671 #8743
1079777,1079779 #8744
1079927,1079929 #8745
1080089,1080091 #8746
1080269,1080271 #8747
1080449,1080451 #8748
1080479,1080481 #8749
1080557,1080559 #8750
1080647,1080649 #8751
1080899,1080901 #8752
1080941,1080943 #8753
1080971,1080973 #8754
1081097,1081099 #8755
1081121,1081123 #8756
1081229,1081231 #8757
1081277,1081279 #8758
1081679,1081681 #8759
1081709,1081711 #8760
1081721,1081723 #8761
1081937,1081939 #8762
1081979,1081981 #8763
1082141,1082143 #8764
1082231,1082233 #8765
1082381,1082383 #8766
1082531,1082533 #8767
1082579,1082581 #8768
1082969,1082971 #8769
1083077,1083079 #8770
1083191,1083193 #8771
1083287,1083289 #8772
1083317,1083319 #8773
1083449,1083451 #8774
1083611,1083613 #8775
1083911,1083913 #8776
1083947,1083949 #8777
1084217,1084219 #8778
1084469,1084471 #8779
1085111,1085113 #8780
1085141,1085143 #8781
1085351,1085353 #8782
1085429,1085431 #8783
1086089,1086091 #8784
1086101,1086103 #8785
1086191,1086193 #8786
1086257,1086259 #8787
1086299,1086301 #8788
1086389,1086391 #8789
1086509,1086511 #8790
1086557,1086559 #8791
1086989,1086991 #8792
1087379,1087381 #8793
1087451,1087453 #8794
1087517,1087519 #8795
1087589,1087591 #8796
1087787,1087789 #8797
1087841,1087843 #8798
1088159,1088161 #8799
1088237,1088239 #8800
1088387,1088389 #8801
1088447,1088449 #8802
1088621,1088623 #8803
1088639,1088641 #8804
1088669,1088671 #8805
1088957,1088959 #8806
1089461,1089463 #8807
1089677,1089679 #8808
1089917,1089919 #8809
1089941,1089943 #8810
1090097,1090099 #8811
1090127,1090129 #8812
1090151,1090153 #8813
1090211,1090213 #8814
1090421,1090423 #8815
1090457,1090459 #8816
1090469,1090471 #8817
1090709,1090711 #8818
1090757,1090759 #8819
1090877,1090879 #8820
1090889,1090891 #8821
1090937,1090939 #8822
1091021,1091023 #8823
1091147,1091149 #8824
1091159,1091161 #8825
1091219,1091221 #8826
1091261,1091263 #8827
1091267,1091269 #8828
1091369,1091371 #8829
1091399,1091401 #8830
1091411,1091413 #8831
1091549,1091551 #8832
1091729,1091731 #8833
1091807,1091809 #8834
1092041,1092043 #8835
1092059,1092061 #8836
1092389,1092391 #8837
1092461,1092463 #8838
1092731,1092733 #8839
1092827,1092829 #8840
1092851,1092853 #8841
1092989,1092991 #8842
1093061,1093063 #8843
1093067,1093069 #8844
1093109,1093111 #8845
1093199,1093201 #8846
1093529,1093531 #8847
1093637,1093639 #8848
1093679,1093681 #8849
1093751,1093753 #8850
1093991,1093993 #8851
1093997,1093999 #8852
1094057,1094059 #8853
1094099,1094101 #8854
1094129,1094131 #8855
1094549,1094551 #8856
1094669,1094671 #8857
1094801,1094803 #8858
1094831,1094833 #8859
1094921,1094923 #8860
1095047,1095049 #8861
1095221,1095223 #8862
1095401,1095403 #8863
1095581,1095583 #8864
1095779,1095781 #8865
1095791,1095793 #8866
1095839,1095841 #8867
1095959,1095961 #8868
1096097,1096099 #8869
1096349,1096351 #8870
1096559,1096561 #8871
1096829,1096831 #8872
1096859,1096861 #8873
1096967,1096969 #8874
1097111,1097113 #8875
1097141,1097143 #8876
1097321,1097323 #8877
1097441,1097443 #8878
1097651,1097653 #8879
1097849,1097851 #8880
1097891,1097893 #8881
1098191,1098193 #8882
1098311,1098313 #8883
1098479,1098481 #8884
1098509,1098511 #8885
1098707,1098709 #8886
1099079,1099081 #8887
1099247,1099249 #8888
1099391,1099393 #8889
1099409,1099411 #8890
1099487,1099489 #8891
1099619,1099621 #8892
1099727,1099729 #8893
1099841,1099843 #8894
1100039,1100041 #8895
1100147,1100149 #8896
1100441,1100443 #8897
1100681,1100683 #8898
1100831,1100833 #8899
1100837,1100839 #8900
1101407,1101409 #8901
1101431,1101433 #8902
1101509,1101511 #8903
1101671,1101673 #8904
1101689,1101691 #8905
1101929,1101931 #8906
1102427,1102429 #8907
1102481,1102483 #8908
1102679,1102681 #8909
1102691,1102693 #8910
1102727,1102729 #8911
1102901,1102903 #8912
1103279,1103281 #8913
1103339,1103341 #8914
1103579,1103581 #8915
1103987,1103989 #8916
1104137,1104139 #8917
1104377,1104379 #8918
1104557,1104559 #8919
1104659,1104661 #8920
1104737,1104739 #8921
1104749,1104751 #8922
1104767,1104769 #8923
1104821,1104823 #8924
1105061,1105063 #8925
1105337,1105339 #8926
1105547,1105549 #8927
1105607,1105609 #8928
1105649,1105651 #8929
1105691,1105693 #8930
1105757,1105759 #8931
1105961,1105963 #8932
1105997,1105999 #8933
1106099,1106101 #8934
1106177,1106179 #8935
1106447,1106449 #8936
1106489,1106491 #8937
1106627,1106629 #8938
1106687,1106689 #8939
1106837,1106839 #8940
1107047,1107049 #8941
1107107,1107109 #8942
1107317,1107319 #8943
1107569,1107571 #8944
1107581,1107583 #8945
1107677,1107679 #8946
1107791,1107793 #8947
1107851,1107853 #8948
1108169,1108171 #8949
1108361,1108363 #8950
1108487,1108489 #8951
1108559,1108561 #8952
1108571,1108573 #8953
1108691,1108693 #8954
1108727,1108729 #8955
1108817,1108819 #8956
1108907,1108909 #8957
1108997,1108999 #8958
1109159,1109161 #8959
1109399,1109401 #8960
1109489,1109491 #8961
1109531,1109533 #8962
1109609,1109611 #8963
1109789,1109791 #8964
1110269,1110271 #8965
1110311,1110313 #8966
1110521,1110523 #8967
1110539,1110541 #8968
1110587,1110589 #8969
1110917,1110919 #8970
1110929,1110931 #8971
1110971,1110973 #8972
1111181,1111183 #8973
1111211,1111213 #8974
1111637,1111639 #8975
1112129,1112131 #8976
1112141,1112143 #8977
1112339,1112341 #8978
1112381,1112383 #8979
1112567,1112569 #8980
1112651,1112653 #8981
1112729,1112731 #8982
1112777,1112779 #8983
1112831,1112833 #8984
1112897,1112899 #8985
1113197,1113199 #8986
1113317,1113319 #8987
1113401,1113403 #8988
1113701,1113703 #8989
1114037,1114039 #8990
1114271,1114273 #8991
1114301,1114303 #8992
1114721,1114723 #8993
1114907,1114909 #8994
1115027,1115029 #8995
1115237,1115239 #8996
1115267,1115269 #8997
1115297,1115299 #8998
1115327,1115329 #8999
1115417,1115419 #9000
1115447,1115449 #9001
1115531,1115533 #9002
1115579,1115581 #9003
1115711,1115713 #9004
1115771,1115773 #9005
1116317,1116319 #9006
1116569,1116571 #9007
1116749,1116751 #9008
1116851,1116853 #9009
1116887,1116889 #9010
1117031,1117033 #9011
1117307,1117309 #9012
1117481,1117483 #9013
1117601,1117603 #9014
1117607,1117609 #9015
1117679,1117681 #9016
1117757,1117759 #9017
1117811,1117813 #9018
1117817,1117819 #9019
1117931,1117933 #9020
1118009,1118011 #9021
1118021,1118023 #9022
1118147,1118149 #9023
1118567,1118569 #9024
1118807,1118809 #9025
1118861,1118863 #9026
1118867,1118869 #9027
1119047,1119049 #9028
1119527,1119529 #9029
1119821,1119823 #9030
1119947,1119949 #9031
1120157,1120159 #9032
1120289,1120291 #9033
1120319,1120321 #9034
1120499,1120501 #9035
1120517,1120519 #9036
1120541,1120543 #9037
1120547,1120549 #9038
1120661,1120663 #9039
1120739,1120741 #9040
1120781,1120783 #9041
1121189,1121191 #9042
1121387,1121389 #9043
1121831,1121833 #9044
1121837,1121839 #9045
1122089,1122091 #9046
1122131,1122133 #9047
1122137,1122139 #9048
1122179,1122181 #9049
1122281,1122283 #9050
1123079,1123081 #9051
1123217,1123219 #9052
1123349,1123351 #9053
1123427,1123429 #9054
1123667,1123669 #9055
1123691,1123693 #9056
1123739,1123741 #9057
1124267,1124269 #9058
1124351,1124353 #9059
1124441,1124443 #9060
1124831,1124833 #9061
1124867,1124869 #9062
1125167,1125169 #9063
1125359,1125361 #9064
1125431,1125433 #9065
1125557,1125559 #9066
1125569,1125571 #9067
1125911,1125913 #9068
1126031,1126033 #9069
1126397,1126399 #9070
1126439,1126441 #9071
1126457,1126459 #9072
1126577,1126579 #9073
1126661,1126663 #9074
1126667,1126669 #9075
1126859,1126861 #9076
1127309,1127311 #9077
1127381,1127383 #9078
1127801,1127803 #9079
1127981,1127983 #9080
1128089,1128091 #9081
1128107,1128109 #9082
1128287,1128289 #9083
1128299,1128301 #9084
1128371,1128373 #9085
1128497,1128499 #9086
1128599,1128601 #9087
1128641,1128643 #9088
1128761,1128763 #9089
1128779,1128781 #9090
1128821,1128823 #9091
1128899,1128901 #9092
1128947,1128949 #9093
1128977,1128979 #9094
1129109,1129111 #9095
1129211,1129213 #9096
1129439,1129441 #9097
1129487,1129489 #9098
1129559,1129561 #9099
1129787,1129789 #9100
1129859,1129861 #9101
1130429,1130431 #9102
1130579,1130581 #9103
1130627,1130629 #9104
1130639,1130641 #9105
1130807,1130809 #9106
1130951,1130953 #9107
1131047,1131049 #9108
1131077,1131079 #9109
1131131,1131133 #9110
1131269,1131271 #9111
1131329,1131331 #9112
1131341,1131343 #9113
1131419,1131421 #9114
1131749,1131751 #9115
1131827,1131829 #9116
1131881,1131883 #9117
1131917,1131919 #9118
1131959,1131961 #9119
1132139,1132141 #9120
1132601,1132603 #9121
1132991,1132993 #9122
1133147,1133149 #9123
1133189,1133191 #9124
1133261,1133263 #9125
1133357,1133359 #9126
1133477,1133479 #9127
1133621,1133623 #9128
1133651,1133653 #9129
1133681,1133683 #9130
1134149,1134151 #9131
1134239,1134241 #9132
1134311,1134313 #9133
1134389,1134391 #9134
1134479,1134481 #9135
1134557,1134559 #9136
1135007,1135009 #9137
1135019,1135021 #9138
1135061,1135063 #9139
1135091,1135093 #9140
1135427,1135429 #9141
1135859,1135861 #9142
1135919,1135921 #9143
1135997,1135999 #9144
1136087,1136089 #9145
1136327,1136329 #9146
1136459,1136461 #9147
1136717,1136719 #9148
1136831,1136833 #9149
1136981,1136983 #9150
1136999,1137001 #9151
1137137,1137139 #9152
1137161,1137163 #9153
1137527,1137529 #9154
1137551,1137553 #9155
1137611,1137613 #9156
1137809,1137811 #9157
1137881,1137883 #9158
1137887,1137889 #9159
1138367,1138369 #9160
1138391,1138393 #9161
1138409,1138411 #9162
1138427,1138429 #9163
1138589,1138591 #9164
1138637,1138639 #9165
1138679,1138681 #9166
1138829,1138831 #9167
1138997,1138999 #9168
1139141,1139143 #9169
1139291,1139293 #9170
1139471,1139473 #9171
1139519,1139521 #9172
1139681,1139683 #9173
1139771,1139773 #9174
1139849,1139851 #9175
1139861,1139863 #9176
1139909,1139911 #9177
1140101,1140103 #9178
1140569,1140571 #9179
1140677,1140679 #9180
1140911,1140913 #9181
1141031,1141033 #9182
1141241,1141243 #9183
1141277,1141279 #9184
1141289,1141291 #9185
1141319,1141321 #9186
1141379,1141381 #9187
1141529,1141531 #9188
1141571,1141573 #9189
1141631,1141633 #9190
1141967,1141969 #9191
1142039,1142041 #9192
1142129,1142131 #9193
1142159,1142161 #9194
1142357,1142359 #9195
1142507,1142509 #9196
1142969,1142971 #9197
1143047,1143049 #9198
1143071,1143073 #9199
1143089,1143091 #9200
1143281,1143283 #9201
1143587,1143589 #9202
1144139,1144141 #9203
1144277,1144279 #9204
1144439,1144441 #9205
1144721,1144723 #9206
1144877,1144879 #9207
1144901,1144903 #9208
1145057,1145059 #9209
1145141,1145143 #9210
1145189,1145191 #9211
1145327,1145329 #9212
1145369,1145371 #9213
1145537,1145539 #9214
1145621,1145623 #9215
1145741,1145743 #9216
1145801,1145803 #9217
1145897,1145899 #9218
1146329,1146331 #9219
1146419,1146421 #9220
1146779,1146781 #9221
1146791,1146793 #9222
1146797,1146799 #9223
1147187,1147189 #9224
1147229,1147231 #9225
1147247,1147249 #9226
1147271,1147273 #9227
1147451,1147453 #9228
1147637,1147639 #9229
1147709,1147711 #9230
1147841,1147843 #9231
1148087,1148089 #9232
1148261,1148263 #9233
1148291,1148293 #9234
1148729,1148731 #9235
1148837,1148839 #9236
1149059,1149061 #9237
1149191,1149193 #9238
1149227,1149229 #9239
1149857,1149859 #9240
1149917,1149919 #9241
1149989,1149991 #9242
1150139,1150141 #9243
1150211,1150213 #9244
1150349,1150351 #9245
1150421,1150423 #9246
1150649,1150651 #9247
1150739,1150741 #9248
1150871,1150873 #9249
1151177,1151179 #9250
1151399,1151401 #9251
1151441,1151443 #9252
1151471,1151473 #9253
1151651,1151653 #9254
1151879,1151881 #9255
1152077,1152079 #9256
1152119,1152121 #9257
1152161,1152163 #9258
1152419,1152421 #9259
1152629,1152631 #9260
1152761,1152763 #9261
1152791,1152793 #9262
1153247,1153249 #9263
1153457,1153459 #9264
1153751,1153753 #9265
1154297,1154299 #9266
1154537,1154539 #9267
1154561,1154563 #9268
1154579,1154581 #9269
1154651,1154653 #9270
1154819,1154821 #9271
1154969,1154971 #9272
1155017,1155019 #9273
1155149,1155151 #9274
1155377,1155379 #9275
1155527,1155529 #9276
1155611,1155613 #9277
1155617,1155619 #9278
1155629,1155631 #9279
1155701,1155703 #9280
1155821,1155823 #9281
1155899,1155901 #9282
1156031,1156033 #9283
1156037,1156039 #9284
1156229,1156231 #9285
1156367,1156369 #9286
1156427,1156429 #9287
1156451,1156453 #9288
1156709,1156711 #9289
1156847,1156849 #9290
1157201,1157203 #9291
1157339,1157341 #9292
1157489,1157491 #9293
1157669,1157671 #9294
1157699,1157701 #9295
1157711,1157713 #9296
1157747,1157749 #9297
1157771,1157773 #9298
1157831,1157833 #9299
1157837,1157839 #9300
1158539,1158541 #9301
1158611,1158613 #9302
1158821,1158823 #9303
1159187,1159189 #9304
1159199,1159201 #9305
1159229,1159231 #9306
1159241,1159243 #9307
1159337,1159339 #9308
1159421,1159423 #9309
1159661,1159663 #9310
1159787,1159789 #9311
1159811,1159813 #9312
1160039,1160041 #9313
1160219,1160221 #9314
1160447,1160449 #9315
1160567,1160569 #9316
1160837,1160839 #9317
1160987,1160989 #9318
1161239,1161241 #9319
1161401,1161403 #9320
1161437,1161439 #9321
1161497,1161499 #9322
1161551,1161553 #9323
1161617,1161619 #9324
1161929,1161931 #9325
1161947,1161949 #9326
1162079,1162081 #9327
1162277,1162279 #9328
1162541,1162543 #9329
1162571,1162573 #9330
1162619,1162621 #9331
1162727,1162729 #9332
1162751,1162753 #9333
1162877,1162879 #9334
1163081,1163083 #9335
1163231,1163233 #9336
1163609,1163611 #9337
1163627,1163629 #9338
1163651,1163653 #9339
1163711,1163713 #9340
1163717,1163719 #9341
1163969,1163971 #9342
1164179,1164181 #9343
1164431,1164433 #9344
1164587,1164589 #9345
1165049,1165051 #9346
1165079,1165081 #9347
1165187,1165189 #9348
1165301,1165303 #9349
1165361,1165363 #9350
1165397,1165399 #9351
1165529,1165531 #9352
1165727,1165729 #9353
1165919,1165921 #9354
1165949,1165951 #9355
1165991,1165993 #9356
1166411,1166413 #9357
1166531,1166533 #9358
1166567,1166569 #9359
1166927,1166929 #9360
1167011,1167013 #9361
1167209,1167211 #9362
1167347,1167349 #9363
1167701,1167703 #9364
1167707,1167709 #9365
1167821,1167823 #9366
1167839,1167841 #9367
1168241,1168243 #9368
1168247,1168249 #9369
1168337,1168339 #9370
1168397,1168399 #9371
1168619,1168621 #9372
1168637,1168639 #9373
1168829,1168831 #9374
1168877,1168879 #9375
1168931,1168933 #9376
1169009,1169011 #9377
1169027,1169029 #9378
1169381,1169383 #9379
1169417,1169419 #9380
1169591,1169593 #9381
1169759,1169761 #9382
1170107,1170109 #9383
1170131,1170133 #9384
1170137,1170139 #9385
1170581,1170583 #9386
1170707,1170709 #9387
1170779,1170781 #9388
1171031,1171033 #9389
1171109,1171111 #9390
1171199,1171201 #9391
1171241,1171243 #9392
1171811,1171813 #9393
1171967,1171969 #9394
1171979,1171981 #9395
1172021,1172023 #9396
1172027,1172029 #9397
1172531,1172533 #9398
1172537,1172539 #9399
1172657,1172659 #9400
1172681,1172683 #9401
1172957,1172959 #9402
1173281,1173283 #9403
1173539,1173541 #9404
1173551,1173553 #9405
1173581,1173583 #9406
1173587,1173589 #9407
1173827,1173829 #9408
1173881,1173883 #9409
1173959,1173961 #9410
1174091,1174093 #9411
1174211,1174213 #9412
1174337,1174339 #9413
1174487,1174489 #9414
1174601,1174603 #9415
1174781,1174783 #9416
1174949,1174951 #9417
1175351,1175353 #9418
1175387,1175389 #9419
1175411,1175413 #9420
1175789,1175791 #9421
1175819,1175821 #9422
1176029,1176031 #9423
1176221,1176223 #9424
1176599,1176601 #9425
1176671,1176673 #9426
1176869,1176871 #9427
1176947,1176949 #9428
1177157,1177159 #9429
1177541,1177543 #9430
1177619,1177621 #9431
1177739,1177741 #9432
1177919,1177921 #9433
1178039,1178041 #9434
1178159,1178161 #9435
1178237,1178239 #9436
1178369,1178371 #9437
1178621,1178623 #9438
1178699,1178701 #9439
1178717,1178719 #9440
1179149,1179151 #9441
1179251,1179253 #9442
1179287,1179289 #9443
1179317,1179319 #9444
1179329,1179331 #9445
1179419,1179421 #9446
1179551,1179553 #9447
1179569,1179571 #9448
1179977,1179979 #9449
1179989,1179991 #9450
1180241,1180243 #9451
1180547,1180549 #9452
1180691,1180693 #9453
1180721,1180723 #9454
1180847,1180849 #9455
1180901,1180903 #9456
1181051,1181053 #9457
1181267,1181269 #9458
1181309,1181311 #9459
1181471,1181473 #9460
1181561,1181563 #9461
1181699,1181701 #9462
1181729,1181731 #9463
1181771,1181773 #9464
1181879,1181881 #9465
1182281,1182283 #9466
1182287,1182289 #9467
1182341,1182343 #9468
1182437,1182439 #9469
1182449,1182451 #9470
1182677,1182679 #9471
1182689,1182691 #9472
1182737,1182739 #9473
1182917,1182919 #9474
1183031,1183033 #9475
1183121,1183123 #9476
1183157,1183159 #9477
1183199,1183201 #9478
1183211,1183213 #9479
1183277,1183279 #9480
1183409,1183411 #9481
1183769,1183771 #9482
1183811,1183813 #9483
1184081,1184083 #9484
1184171,1184173 #9485
1184411,1184413 #9486
1184459,1184461 #9487
1184471,1184473 #9488
1184537,1184539 #9489
1184549,1184551 #9490
1184837,1184839 #9491
1184957,1184959 #9492
1185179,1185181 #9493
1185659,1185661 #9494
1185929,1185931 #9495
1186049,1186051 #9496
1186349,1186351 #9497
1186439,1186441 #9498
1186517,1186519 #9499
1186697,1186699 #9500
1186739,1186741 #9501
1186811,1186813 #9502
1187309,1187311 #9503
1187339,1187341 #9504
1187411,1187413 #9505
1187507,1187509 #9506
1187687,1187689 #9507
1187699,1187701 #9508
1187801,1187803 #9509
1187819,1187821 #9510
1187939,1187941 #9511
1187999,1188001 #9512
1188071,1188073 #9513
1188149,1188151 #9514
1188167,1188169 #9515
1188287,1188289 #9516
1188359,1188361 #9517
1188527,1188529 #9518
1188557,1188559 #9519
1188839,1188841 #9520
1189061,1189063 #9521
1189469,1189471 #9522
1189481,1189483 #9523
1189577,1189579 #9524
1189631,1189633 #9525
1189649,1189651 #9526
1189757,1189759 #9527
1190069,1190071 #9528
1190261,1190263 #9529
1190489,1190491 #9530
1190507,1190509 #9531
1190699,1190701 #9532
1190807,1190809 #9533
1190897,1190899 #9534
1190951,1190953 #9535
1191011,1191013 #9536
1191077,1191079 #9537
1191107,1191109 #9538
1191611,1191613 #9539
1191767,1191769 #9540
1192097,1192099 #9541
1192151,1192153 #9542
1192181,1192183 #9543
1192199,1192201 #9544
1192337,1192339 #9545
1192559,1192561 #9546
1192967,1192969 #9547
1193237,1193239 #9548
1193429,1193431 #9549
1193501,1193503 #9550
1193741,1193743 #9551
1193837,1193839 #9552
1193867,1193869 #9553
1193909,1193911 #9554
1194161,1194163 #9555
1194209,1194211 #9556
1194251,1194253 #9557
1194341,1194343 #9558
1194731,1194733 #9559
1194797,1194799 #9560
1194899,1194901 #9561
1194959,1194961 #9562
1195037,1195039 #9563
1195121,1195123 #9564
1195169,1195171 #9565
1195547,1195549 #9566
1195679,1195681 #9567
1195721,1195723 #9568
1196087,1196089 #9569
1196267,1196269 #9570
1196357,1196359 #9571
1196399,1196401 #9572
1196471,1196473 #9573
1196519,1196521 #9574
1196537,1196539 #9575
1196717,1196719 #9576
1196729,1196731 #9577
1196861,1196863 #9578
1197011,1197013 #9579
1197197,1197199 #9580
1197347,1197349 #9581
1197407,1197409 #9582
1197617,1197619 #9583
1197827,1197829 #9584
1198049,1198051 #9585
1198187,1198189 #9586
1198259,1198261 #9587
1198289,1198291 #9588
1198361,1198363 #9589
1198397,1198399 #9590
1198511,1198513 #9591
1198607,1198609 #9592
1198997,1198999 #9593
1199087,1199089 #9594
1199369,1199371 #9595
1199459,1199461 #9596
1199507,1199509 #9597
1199591,1199593 #9598
1199621,1199623 #9599
1200359,1200361 #9600
1200371,1200373 #9601
1200581,1200583 #9602
1200809,1200811 #9603
1200887,1200889 #9604
1201001,1201003 #9605
1201019,1201021 #9606
1201307,1201309 #9607
1201481,1201483 #9608
1201841,1201843 #9609
1202027,1202029 #9610
1202219,1202221 #9611
1202471,1202473 #9612
1202627,1202629 #9613
1202741,1202743 #9614
1203149,1203151 #9615
1203329,1203331 #9616
1203359,1203361 #9617
1203689,1203691 #9618
1203731,1203733 #9619
1203791,1203793 #9620
1203899,1203901 #9621
1203929,1203931 #9622
1204139,1204141 #9623
1204169,1204171 #9624
1204451,1204453 #9625
1204781,1204783 #9626
1204871,1204873 #9627
1204967,1204969 #9628
1205117,1205119 #9629
1205471,1205473 #9630
1205537,1205539 #9631
1205627,1205629 #9632
1206059,1206061 #9633
1206701,1206703 #9634
1206767,1206769 #9635
1207121,1207123 #9636
1207307,1207309 #9637
1207439,1207441 #9638
1207979,1207981 #9639
1208021,1208023 #9640
1208237,1208239 #9641
1208297,1208299 #9642
1208789,1208791 #9643
1208939,1208941 #9644
1209629,1209631 #9645
1209707,1209709 #9646
1209779,1209781 #9647
1209809,1209811 #9648
1210019,1210021 #9649
1210037,1210039 #9650
1210049,1210051 #9651
1210397,1210399 #9652
1210409,1210411 #9653
1210439,1210441 #9654
1210637,1210639 #9655
1210799,1210801 #9656
1210817,1210819 #9657
1210871,1210873 #9658
1210877,1210879 #9659
1211057,1211059 #9660
1211081,1211083 #9661
1211279,1211281 #9662
1211501,1211503 #9663
1211597,1211599 #9664
1211657,1211659 #9665
1211921,1211923 #9666
1212119,1212121 #9667
1212437,1212439 #9668
1212611,1212613 #9669
1212851,1212853 #9670
1212917,1212919 #9671
1213019,1213021 #9672
1213151,1213153 #9673
1213481,1213483 #9674
1213631,1213633 #9675
1213757,1213759 #9676
1213907,1213909 #9677
1214219,1214221 #9678
1214639,1214641 #9679
1214657,1214659 #9680
1214669,1214671 #9681
1214957,1214959 #9682
1215299,1215301 #9683
1215437,1215439 #9684
1215497,1215499 #9685
1215629,1215631 #9686
1215647,1215649 #9687
1215917,1215919 #9688
1216067,1216069 #9689
1216337,1216339 #9690
1216349,1216351 #9691
1216559,1216561 #9692
1216601,1216603 #9693
1216847,1216849 #9694
1216937,1216939 #9695
1217141,1217143 #9696
1217297,1217299 #9697
1217471,1217473 #9698
1217831,1217833 #9699
1218197,1218199 #9700
1218209,1218211 #9701
1218557,1218559 #9702
1218911,1218913 #9703
1218989,1218991 #9704
1219109,1219111 #9705
1219301,1219303 #9706
1219487,1219489 #9707
1219649,1219651 #9708
1219787,1219789 #9709
1219847,1219849 #9710
1219859,1219861 #9711
1219877,1219879 #9712
1219949,1219951 #9713
1219961,1219963 #9714
1220027,1220029 #9715
1220249,1220251 #9716
1220489,1220491 #9717
1220801,1220803 #9718
1220981,1220983 #9719
1221221,1221223 #9720
1221557,1221559 #9721
1221749,1221751 #9722
1221791,1221793 #9723
1221821,1221823 #9724
1222157,1222159 #9725
1222229,1222231 #9726
1222409,1222411 #9727
1222601,1222603 #9728
1222679,1222681 #9729
1222829,1222831 #9730
1223177,1223179 #9731
1223279,1223281 #9732
1223309,1223311 #9733
1223447,1223449 #9734
1223489,1223491 #9735
1223687,1223689 #9736
1223939,1223941 #9737
1224029,1224031 #9738
1224077,1224079 #9739
1224131,1224133 #9740
1224257,1224259 #9741
1224269,1224271 #9742
1224437,1224439 #9743
1224479,1224481 #9744
1224701,1224703 #9745
1224857,1224859 #9746
1224887,1224889 #9747
1225097,1225099 #9748
1225109,1225111 #9749
1225127,1225129 #9750
1225577,1225579 #9751
1225589,1225591 #9752
1225727,1225729 #9753
1225907,1225909 #9754
1225997,1225999 #9755
1226189,1226191 #9756
1226297,1226299 #9757
1226339,1226341 #9758
1226501,1226503 #9759
1226609,1226611 #9760
1226681,1226683 #9761
1226711,1226713 #9762
1226801,1226803 #9763
1227101,1227103 #9764
1227131,1227133 #9765
1227299,1227301 #9766
1227701,1227703 #9767
1227977,1227979 #9768
1228391,1228393 #9769
1228397,1228399 #9770
1228457,1228459 #9771
1228541,1228543 #9772
1228691,1228693 #9773
1228889,1228891 #9774
1228949,1228951 #9775
1228961,1228963 #9776
1229021,1229023 #9777
1229201,1229203 #9778
1229309,1229311 #9779
1229351,1229353 #9780
1229519,1229521 #9781
1229561,1229563 #9782
1229939,1229941 #9783
1230167,1230169 #9784
1230329,1230331 #9785
1230347,1230349 #9786
1230371,1230373 #9787
1230377,1230379 #9788
1230629,1230631 #9789
1230869,1230871 #9790
1231001,1231003 #9791
1231049,1231051 #9792
1231091,1231093 #9793
1231127,1231129 #9794
1231199,1231201 #9795
1231229,1231231 #9796
1231301,1231303 #9797
1231337,1231339 #9798
1231379,1231381 #9799
1231421,1231423 #9800
1231457,1231459 #9801
1231511,1231513 #9802
1231577,1231579 #9803
1231829,1231831 #9804
1232069,1232071 #9805
1232351,1232353 #9806
1232657,1232659 #9807
1232849,1232851 #9808
1232981,1232983 #9809
1233179,1233181 #9810
1233371,1233373 #9811
1233431,1233433 #9812
1233437,1233439 #9813
1233761,1233763 #9814
1233779,1233781 #9815
1234001,1234003 #9816
1234241,1234243 #9817
1234349,1234351 #9818
1234391,1234393 #9819
1234757,1234759 #9820
1234787,1234789 #9821
1234841,1234843 #9822
1234967,1234969 #9823
1235249,1235251 #9824
1235417,1235419 #9825
1235447,1235449 #9826
1235501,1235503 #9827
1235651,1235653 #9828
1235789,1235791 #9829
1235831,1235833 #9830
1236161,1236163 #9831
1236479,1236481 #9832
1236659,1236661 #9833
1237211,1237213 #9834
1237499,1237501 #9835
1237529,1237531 #9836
1237961,1237963 #9837
1238087,1238089 #9838
1238177,1238179 #9839
1238267,1238269 #9840
1238381,1238383 #9841
1238429,1238431 #9842
1238597,1238599 #9843
1238681,1238683 #9844
1238717,1238719 #9845
1238747,1238749 #9846
1238759,1238761 #9847
1238999,1239001 #9848
1239377,1239379 #9849
1239737,1239739 #9850
1239911,1239913 #9851
1240007,1240009 #9852
1240271,1240273 #9853
1240361,1240363 #9854
1240667,1240669 #9855
1240739,1240741 #9856
1240859,1240861 #9857
1241159,1241161 #9858
1241267,1241269 #9859
1241489,1241491 #9860
1241507,1241509 #9861
1241549,1241551 #9862
1241741,1241743 #9863
1241921,1241923 #9864
1241939,1241941 #9865
1242119,1242121 #9866
1242167,1242169 #9867
1242191,1242193 #9868
1242359,1242361 #9869
1242419,1242421 #9870
1242641,1242643 #9871
1242929,1242931 #9872
1242977,1242979 #9873
1243271,1243273 #9874
1243367,1243369 #9875
1243391,1243393 #9876
1243481,1243483 #9877
1243577,1243579 #9878
1243841,1243843 #9879
1243967,1243969 #9880
1244027,1244029 #9881
1244039,1244041 #9882
1244057,1244059 #9883
1244141,1244143 #9884
1244261,1244263 #9885
1244357,1244359 #9886
1244531,1244533 #9887
1244609,1244611 #9888
1244627,1244629 #9889
1244819,1244821 #9890
1244909,1244911 #9891
1244987,1244989 #9892
1245017,1245019 #9893
1245449,1245451 #9894
1245527,1245529 #9895
1245617,1245619 #9896
1245689,1245691 #9897
1245719,1245721 #9898
1245779,1245781 #9899
1245971,1245973 #9900
1246241,1246243 #9901
1246247,1246249 #9902
1246361,1246363 #9903
1246367,1246369 #9904
1246499,1246501 #9905
1246589,1246591 #9906
1246961,1246963 #9907
1247117,1247119 #9908
1247327,1247329 #9909
1247417,1247419 #9910
1247759,1247761 #9911
1247879,1247881 #9912
1248017,1248019 #9913
1248059,1248061 #9914
1248101,1248103 #9915
1248209,1248211 #9916
1248239,1248241 #9917
1248347,1248349 #9918
1248449,1248451 #9919
1248551,1248553 #9920
1248671,1248673 #9921
1248857,1248859 #9922
1248977,1248979 #9923
1249139,1249141 #9924
1249319,1249321 #9925
1249361,1249363 #9926
1249487,1249489 #9927
1249691,1249693 #9928
1249739,1249741 #9929
1249817,1249819 #9930
1249847,1249849 #9931
1250021,1250023 #9932
1250147,1250149 #9933
1250201,1250203 #9934
1250519,1250521 #9935
1250609,1250611 #9936
1250771,1250773 #9937
1250969,1250971 #9938
1250981,1250983 #9939
1251431,1251433 #9940
1251461,1251463 #9941
1251527,1251529 #9942
1251581,1251583 #9943
1251869,1251871 #9944
1252217,1252219 #9945
1252661,1252663 #9946
1252817,1252819 #9947
1253249,1253251 #9948
1253519,1253521 #9949
1253849,1253851 #9950
1253909,1253911 #9951
1253951,1253953 #9952
1254059,1254061 #9953
1254371,1254373 #9954
1254467,1254469 #9955
1254527,1254529 #9956
1254731,1254733 #9957
1254791,1254793 #9958
1255181,1255183 #9959
1255391,1255393 #9960
1255451,1255453 #9961
1255757,1255759 #9962
1255799,1255801 #9963
1255829,1255831 #9964
1256531,1256533 #9965
1256819,1256821 #9966
1257041,1257043 #9967
1257071,1257073 #9968
1257077,1257079 #9969
1257239,1257241 #9970
1257251,1257253 #9971
1257461,1257463 #9972
1257491,1257493 #9973
1257587,1257589 #9974
1257689,1257691 #9975
1257719,1257721 #9976
1257827,1257829 #9977
1257959,1257961 #9978
1258097,1258099 #9979
1258139,1258141 #9980
1258181,1258183 #9981
1258217,1258219 #9982
1258421,1258423 #9983
1258469,1258471 #9984
1258637,1258639 #9985
1258709,1258711 #9986
1258781,1258783 #9987
1259051,1259053 #9988
1259537,1259539 #9989
1260167,1260169 #9990
1260317,1260319 #9991
1260359,1260361 #9992
1260437,1260439 #9993
1260641,1260643 #9994
1260731,1260733 #9995
1260767,1260769 #9996
1260797,1260799 #9997
1260827,1260829 #9998
1260899,1260901 #9999
1260989,1260991 #10000
1261079,1261081 #10001
1261259,1261261 #10002
1261487,1261489 #10003
1261697,1261699 #10004
1261829,1261831 #10005
1261889,1261891 #10006
1262081,1262083 #10007
1262099,1262101 #10008
1262291,1262293 #10009
1262621,1262623 #10010
1262669,1262671 #10011
1262711,1262713 #10012
1262927,1262929 #10013
1262939,1262941 #10014
1263077,1263079 #10015
1263107,1263109 #10016
1263179,1263181 #10017
1263191,1263193 #10018
1263461,1263463 #10019
1263539,1263541 #10020
1263629,1263631 #10021
1263929,1263931 #10022
1263947,1263949 #10023
1264061,1264063 #10024
1264259,1264261 #10025
1264301,1264303 #10026
1264559,1264561 #10027
1264649,1264651 #10028
1264979,1264981 #10029
1265051,1265053 #10030
1265081,1265083 #10031
1265111,1265113 #10032
1265177,1265179 #10033
1265279,1265281 #10034
1265477,1265479 #10035
1265519,1265521 #10036
1265777,1265779 #10037
1265861,1265863 #10038
1265909,1265911 #10039
1265921,1265923 #10040
1266077,1266079 #10041
1266269,1266271 #10042
1266371,1266373 #10043
1266491,1266493 #10044
1266761,1266763 #10045
1266779,1266781 #10046
1266929,1266931 #10047
1267157,1267159 #10048
1267529,1267531 #10049
1267577,1267579 #10050
1267709,1267711 #10051
1267787,1267789 #10052
1268051,1268053 #10053
1268357,1268359 #10054
1268621,1268623 #10055
1268789,1268791 #10056
1269041,1269043 #10057
1269221,1269223 #10058
1269239,1269241 #10059
1269377,1269379 #10060
1269641,1269643 #10061
1269731,1269733 #10062
1269869,1269871 #10063
1270559,1270561 #10064
1270571,1270573 #10065
1270649,1270651 #10066
1270667,1270669 #10067
1270859,1270861 #10068
1271027,1271029 #10069
1271087,1271089 #10070
1271201,1271203 #10071
1271351,1271353 #10072
1271399,1271401 #10073
1271657,1271659 #10074
1271747,1271749 #10075
1271927,1271929 #10076
1271999,1272001 #10077
1272281,1272283 #10078
1272287,1272289 #10079
1272377,1272379 #10080
1272629,1272631 #10081
1272881,1272883 #10082
1272917,1272919 #10083
1272989,1272991 #10084
1273037,1273039 #10085
1273157,1273159 #10086
1273289,1273291 #10087
1273331,1273333 #10088
1273409,1273411 #10089
1273421,1273423 #10090
1273541,1273543 #10091
1273637,1273639 #10092
1273889,1273891 #10093
1274087,1274089 #10094
1274111,1274113 #10095
1274291,1274293 #10096
1274771,1274773 #10097
1274939,1274941 #10098
1275359,1275361 #10099
1275539,1275541 #10100
1275707,1275709 #10101
1275749,1275751 #10102
1275977,1275979 #10103
1276619,1276621 #10104
1276967,1276969 #10105
1277039,1277041 #10106
1277069,1277071 #10107
1277207,1277209 #10108
1277321,1277323 #10109
1277357,1277359 #10110
1277741,1277743 #10111
1277909,1277911 #10112
1278029,1278031 #10113
1278287,1278289 #10114
1278371,1278373 #10115
1278437,1278439 #10116
1278479,1278481 #10117
1278617,1278619 #10118
1279181,1279183 #10119
1279307,1279309 #10120
1279319,1279321 #10121
1279457,1279459 #10122
1279547,1279549 #10123
1279919,1279921 #10124
1280129,1280131 #10125
1280159,1280161 #10126
1280399,1280401 #10127
1280759,1280761 #10128
1280789,1280791 #10129
1280987,1280989 #10130
1281041,1281043 #10131
1281281,1281283 #10132
1281431,1281433 #10133
1281521,1281523 #10134
1281779,1281781 #10135
1281821,1281823 #10136
1282007,1282009 #10137
1282031,1282033 #10138
1282079,1282081 #10139
1282277,1282279 #10140
1282469,1282471 #10141
1282511,1282513 #10142
1282637,1282639 #10143
1282781,1282783 #10144
1282907,1282909 #10145
1283171,1283173 #10146
1283537,1283539 #10147
1283717,1283719 #10148
1283879,1283881 #10149
1283939,1283941 #10150
1283981,1283983 #10151
1284209,1284211 #10152
1284551,1284553 #10153
1284737,1284739 #10154
1284791,1284793 #10155
1285049,1285051 #10156
1285511,1285513 #10157
1285517,1285519 #10158
1285547,1285549 #10159
1285811,1285813 #10160
1286147,1286149 #10161
1286189,1286191 #10162
1286267,1286269 #10163
1286489,1286491 #10164
1286819,1286821 #10165
1286837,1286839 #10166
1286939,1286941 #10167
1286981,1286983 #10168
1287059,1287061 #10169
1287131,1287133 #10170
1287197,1287199 #10171
1287371,1287373 #10172
1287467,1287469 #10173
1287551,1287553 #10174
1287749,1287751 #10175
1288169,1288171 #10176
1288247,1288249 #10177
1288361,1288363 #10178
1288421,1288423 #10179
1288541,1288543 #10180
1288697,1288699 #10181
1288709,1288711 #10182
1288829,1288831 #10183
1288871,1288873 #10184
1288919,1288921 #10185
1289597,1289599 #10186
1289621,1289623 #10187
1289711,1289713 #10188
1289747,1289749 #10189
1289801,1289803 #10190
1289969,1289971 #10191
1290167,1290169 #10192
1290257,1290259 #10193
1290431,1290433 #10194
1290467,1290469 #10195
1290629,1290631 #10196
1291007,1291009 #10197
1291019,1291021 #10198
1291217,1291219 #10199
1291481,1291483 #10200
1291817,1291819 #10201
1291907,1291909 #10202
1292141,1292143 #10203
1292591,1292593 #10204
1292657,1292659 #10205
1292999,1293001 #10206
1293317,1293319 #10207
1293419,1293421 #10208
1293491,1293493 #10209
1293839,1293841 #10210
1293947,1293949 #10211
1293977,1293979 #10212
1294019,1294021 #10213
1294037,1294039 #10214
1294121,1294123 #10215
1294199,1294201 #10216
1294301,1294303 #10217
1294367,1294369 #10218
1294649,1294651 #10219
1294721,1294723 #10220
1294757,1294759 #10221
1295069,1295071 #10222
1295219,1295221 #10223
1295297,1295299 #10224
1295321,1295323 #10225
1295387,1295389 #10226
1295549,1295551 #10227
1295561,1295563 #10228
1295867,1295869 #10229
1296341,1296343 #10230
1296521,1296523 #10231
1297001,1297003 #10232
1297061,1297063 #10233
1297169,1297171 #10234
1297271,1297273 #10235
1297367,1297369 #10236
1297397,1297399 #10237
1297631,1297633 #10238
1297649,1297651 #10239
1298111,1298113 #10240
1298117,1298119 #10241
1298489,1298491 #10242
1298651,1298653 #10243
1298909,1298911 #10244
1299059,1299061 #10245
1299209,1299211 #10246
1299341,1299343 #10247
1299377,1299379 #10248
1299437,1299439 #10249
1299449,1299451 #10250
1299917,1299919 #10251
1300127,1300129 #10252
1300139,1300141 #10253
1300307,1300309 #10254
1300421,1300423 #10255
1300571,1300573 #10256
1300709,1300711 #10257
1300769,1300771 #10258
1300841,1300843 #10259
1301021,1301023 #10260
1301147,1301149 #10261
1301171,1301173 #10262
1301219,1301221 #10263
1301387,1301389 #10264
1301849,1301851 #10265
1301939,1301941 #10266
1301957,1301959 #10267
1302017,1302019 #10268
1302179,1302181 #10269
1302347,1302349 #10270
1302491,1302493 #10271
1302737,1302739 #10272
1302839,1302841 #10273
1303241,1303243 #10274
1303409,1303411 #10275
1303667,1303669 #10276
1303739,1303741 #10277
1303787,1303789 #10278
1303871,1303873 #10279
1303931,1303933 #10280
1303961,1303963 #10281
1304111,1304113 #10282
1304129,1304131 #10283
1304207,1304209 #10284
1304981,1304983 #10285
1305011,1305013 #10286
1305149,1305151 #10287
1305251,1305253 #10288
1305287,1305289 #10289
1305371,1305373 #10290
1305587,1305589 #10291
1305959,1305961 #10292
1306157,1306159 #10293
1306241,1306243 #10294
1306517,1306519 #10295
1306661,1306663 #10296
1306691,1306693 #10297
1306757,1306759 #10298
1306817,1306819 #10299
1306829,1306831 #10300
1306889,1306891 #10301
1307081,1307083 #10302
1307309,1307311 #10303
1307729,1307731 #10304
1308191,1308193 #10305
1308299,1308301 #10306
1308497,1308499 #10307
1308521,1308523 #10308
1308581,1308583 #10309
1308611,1308613 #10310
1308647,1308649 #10311
1308707,1308709 #10312
1308917,1308919 #10313
1309127,1309129 #10314
1309337,1309339 #10315
1309349,1309351 #10316
1309589,1309591 #10317
1309829,1309831 #10318
1309961,1309963 #10319
1310039,1310041 #10320
1310117,1310119 #10321
1310327,1310329 #10322
1310369,1310371 #10323
1310381,1310383 #10324
1310627,1310629 #10325
1310807,1310809 #10326
1310999,1311001 #10327
1311029,1311031 #10328
1311239,1311241 #10329
1311617,1311619 #10330
1311689,1311691 #10331
1311767,1311769 #10332
1311797,1311799 #10333
1311899,1311901 #10334
1312187,1312189 #10335
1312301,1312303 #10336
1312391,1312393 #10337
1312559,1312561 #10338
1312601,1312603 #10339
1312667,1312669 #10340
1312889,1312891 #10341
1313237,1313239 #10342
1313357,1313359 #10343
1313447,1313449 #10344
1313567,1313569 #10345
1313621,1313623 #10346
1313699,1313701 #10347
1313957,1313959 #10348
1314161,1314163 #10349
1314359,1314361 #10350
1314569,1314571 #10351
1314671,1314673 #10352
1314767,1314769 #10353
1314821,1314823 #10354
1314851,1314853 #10355
1315211,1315213 #10356
1315229,1315231 #10357
1315289,1315291 #10358
1315397,1315399 #10359
1315451,1315453 #10360
1315889,1315891 #10361
1315967,1315969 #10362
1316039,1316041 #10363
1316321,1316323 #10364
1316507,1316509 #10365
1316591,1316593 #10366
1316669,1316671 #10367
1316741,1316743 #10368
1316921,1316923 #10369
1317191,1317193 #10370
1317227,1317229 #10371
1317257,1317259 #10372
1317299,1317301 #10373
1317317,1317319 #10374
1317359,1317361 #10375
1317521,1317523 #10376
1317761,1317763 #10377
1318409,1318411 #10378
1318487,1318489 #10379
1318661,1318663 #10380
1318697,1318699 #10381
1318727,1318729 #10382
1318781,1318783 #10383
1318829,1318831 #10384
1318859,1318861 #10385
1318901,1318903 #10386
1319207,1319209 #10387
1319321,1319323 #10388
1319399,1319401 #10389
1319741,1319743 #10390
1319777,1319779 #10391
1320377,1320379 #10392
1320749,1320751 #10393
1320887,1320889 #10394
1320929,1320931 #10395
1321139,1321141 #10396
1321169,1321171 #10397
1321247,1321249 #10398
1321301,1321303 #10399
1321349,1321351 #10400
1321457,1321459 #10401
1321679,1321681 #10402
1321757,1321759 #10403
1322147,1322149 #10404
1322159,1322161 #10405
1322171,1322173 #10406
1322177,1322179 #10407
1322219,1322221 #10408
1322327,1322329 #10409
1322357,1322359 #10410
1322591,1322593 #10411
1322597,1322599 #10412
1322747,1322749 #10413
1322939,1322941 #10414
1323041,1323043 #10415
1323107,1323109 #10416
1323137,1323139 #10417
1323197,1323199 #10418
1323689,1323691 #10419
1323797,1323799 #10420
1323869,1323871 #10421
1324199,1324201 #10422
1324511,1324513 #10423
1324571,1324573 #10424
1324577,1324579 #10425
1324619,1324621 #10426
1324649,1324651 #10427
1324679,1324681 #10428
1324949,1324951 #10429
1325417,1325419 #10430
1325579,1325581 #10431
1325657,1325659 #10432
1325771,1325773 #10433
1325939,1325941 #10434
1326047,1326049 #10435
1326251,1326253 #10436
1326461,1326463 #10437
1326821,1326823 #10438
1326887,1326889 #10439
1327199,1327201 #10440
1327349,1327351 #10441
1327901,1327903 #10442
1328099,1328101 #10443
1328447,1328449 #10444
1328477,1328479 #10445
1328729,1328731 #10446
1328861,1328863 #10447
1328891,1328893 #10448
1328909,1328911 #10449
1329437,1329439 #10450
1329701,1329703 #10451
1329707,1329709 #10452
1329719,1329721 #10453
1329761,1329763 #10454
1330001,1330003 #10455
1330211,1330213 #10456
1330499,1330501 #10457
1330601,1330603 #10458
1330787,1330789 #10459
1330961,1330963 #10460
1331039,1331041 #10461
1331249,1331251 #10462
1331327,1331329 #10463
1331381,1331383 #10464
1331597,1331599 #10465
1331921,1331923 #10466
1331987,1331989 #10467
1332167,1332169 #10468
1332281,1332283 #10469
1332431,1332433 #10470
1332587,1332589 #10471
1332671,1332673 #10472
1332767,1332769 #10473
1333139,1333141 #10474
1333151,1333153 #10475
1333271,1333273 #10476
1333289,1333291 #10477
1333721,1333723 #10478
1333991,1333993 #10479
1334117,1334119 #10480
1334327,1334329 #10481
1334339,1334341 #10482
1334369,1334371 #10483
1334561,1334563 #10484
1334717,1334719 #10485
1335209,1335211 #10486
1335239,1335241 #10487
1335287,1335289 #10488
1335407,1335409 #10489
1335617,1335619 #10490
1335749,1335751 #10491
1335989,1335991 #10492
1336019,1336021 #10493
1336037,1336039 #10494
1336169,1336171 #10495
1336187,1336189 #10496
1336271,1336273 #10497
1336337,1336339 #10498
1336799,1336801 #10499
1336961,1336963 #10500
1337261,1337263 #10501
1337267,1337269 #10502
1337591,1337593 #10503
1337627,1337629 #10504
1337729,1337731 #10505
1337801,1337803 #10506
1337909,1337911 #10507
1337969,1337971 #10508
1337981,1337983 #10509
1338107,1338109 #10510
1338479,1338481 #10511
1338749,1338751 #10512
1338791,1338793 #10513
1338809,1338811 #10514
1339001,1339003 #10515
1339109,1339111 #10516
1339337,1339339 #10517
1339409,1339411 #10518
1339691,1339693 #10519
1339901,1339903 #10520
1339907,1339909 #10521
1340039,1340041 #10522
1340069,1340071 #10523
1340321,1340323 #10524
1340327,1340329 #10525
1340357,1340359 #10526
1340489,1340491 #10527
1340747,1340749 #10528
1341017,1341019 #10529
1341071,1341073 #10530
1341101,1341103 #10531
1341257,1341259 #10532
1341467,1341469 #10533
1341491,1341493 #10534
1341551,1341553 #10535
1341617,1341619 #10536
1341839,1341841 #10537
1341869,1341871 #10538
1341881,1341883 #10539
1342049,1342051 #10540
1342067,1342069 #10541
1342109,1342111 #10542
1342259,1342261 #10543
1342277,1342279 #10544
1342499,1342501 #10545
1342571,1342573 #10546
1342667,1342669 #10547
1342697,1342699 #10548
1342739,1342741 #10549
1342751,1342753 #10550
1342799,1342801 #10551
1342907,1342909 #10552
1343057,1343059 #10553
1343387,1343389 #10554
1343477,1343479 #10555
1343567,1343569 #10556
1343651,1343653 #10557
1343789,1343791 #10558
1344401,1344403 #10559
1344461,1344463 #10560
1344599,1344601 #10561
1344779,1344781 #10562
1344797,1344799 #10563
1344821,1344823 #10564
1344857,1344859 #10565
1344899,1344901 #10566
1344947,1344949 #10567
1345229,1345231 #10568
1345241,1345243 #10569
1345271,1345273 #10570
1345301,1345303 #10571
1345451,1345453 #10572
1345649,1345651 #10573
1345691,1345693 #10574
1345781,1345783 #10575
1345931,1345933 #10576
1346117,1346119 #10577
1346159,1346161 #10578
1346309,1346311 #10579
1346537,1346539 #10580
1346591,1346593 #10581
1346951,1346953 #10582
1346999,1347001 #10583
1347209,1347211 #10584
1347221,1347223 #10585
1347287,1347289 #10586
1347329,1347331 #10587
1347389,1347391 #10588
1347767,1347769 #10589
1348379,1348381 #10590
1348547,1348549 #10591
1348619,1348621 #10592
1348847,1348849 #10593
1348871,1348873 #10594
1348889,1348891 #10595
1348937,1348939 #10596
1349147,1349149 #10597
1349471,1349473 #10598
1349531,1349533 #10599
1349669,1349671 #10600
1349807,1349809 #10601
1350047,1350049 #10602
1350059,1350061 #10603
1350317,1350319 #10604
1350341,1350343 #10605
1350467,1350469 #10606
1350509,1350511 #10607
1350551,1350553 #10608
1350749,1350751 #10609
1350959,1350961 #10610
1351037,1351039 #10611
1351121,1351123 #10612
1351169,1351171 #10613
1351241,1351243 #10614
1351247,1351249 #10615
1351289,1351291 #10616
1351421,1351423 #10617
1351541,1351543 #10618
1351781,1351783 #10619
1351841,1351843 #10620
1351919,1351921 #10621
1351979,1351981 #10622
1352201,1352203 #10623
1352207,1352209 #10624
1352291,1352293 #10625
1352369,1352371 #10626
1352441,1352443 #10627
1352597,1352599 #10628
1352777,1352779 #10629
1352861,1352863 #10630
1353089,1353091 #10631
1353221,1353223 #10632
1353239,1353241 #10633
1353257,1353259 #10634
1354007,1354009 #10635
1354019,1354021 #10636
1354229,1354231 #10637
1354289,1354291 #10638
1354391,1354393 #10639
1354499,1354501 #10640
1354601,1354603 #10641
1354649,1354651 #10642
1354811,1354813 #10643
1354937,1354939 #10644
1355129,1355131 #10645
1355267,1355269 #10646
1355279,1355281 #10647
1355309,1355311 #10648
1355399,1355401 #10649
1355447,1355449 #10650
1355657,1355659 #10651
1355741,1355743 #10652
1355987,1355989 #10653
1356077,1356079 #10654
1356167,1356169 #10655
1356461,1356463 #10656
1356497,1356499 #10657
1356869,1356871 #10658
1356911,1356913 #10659
1357001,1357003 #10660
1357061,1357063 #10661
1357427,1357429 #10662
1357547,1357549 #10663
1358057,1358059 #10664
1358297,1358299 #10665
1358477,1358479 #10666
1358507,1358509 #10667
1358741,1358743 #10668
1358801,1358803 #10669
1358807,1358809 #10670
1359179,1359181 #10671
1359311,1359313 #10672
1359731,1359733 #10673
1359857,1359859 #10674
1359977,1359979 #10675
1360067,1360069 #10676
1360277,1360279 #10677
1360439,1360441 #10678
1360529,1360531 #10679
1360589,1360591 #10680
1360781,1360783 #10681
1360787,1360789 #10682
1361021,1361023 #10683
1361051,1361053 #10684
1361387,1361389 #10685
1361441,1361443 #10686
1361741,1361743 #10687
1361957,1361959 #10688
1362017,1362019 #10689
1362209,1362211 #10690
1362299,1362301 #10691
1362341,1362343 #10692
1362407,1362409 #10693
1362461,1362463 #10694
1362521,1362523 #10695
1362629,1362631 #10696
1362707,1362709 #10697
1362761,1362763 #10698
1362929,1362931 #10699
1363331,1363333 #10700
1363511,1363513 #10701
1363751,1363753 #10702
1364177,1364179 #10703
1364201,1364203 #10704
1364327,1364329 #10705
1364399,1364401 #10706
1364717,1364719 #10707
1364771,1364773 #10708
1364969,1364971 #10709
1365107,1365109 #10710
1365137,1365139 #10711
1365311,1365313 #10712
1365731,1365733 #10713
1365911,1365913 #10714
1365977,1365979 #10715
1366019,1366021 #10716
1366289,1366291 #10717
1366481,1366483 #10718
1366529,1366531 #10719
1366661,1366663 #10720
1366829,1366831 #10721
1367057,1367059 #10722
1367159,1367161 #10723
1367339,1367341 #10724
1367459,1367461 #10725
1367519,1367521 #10726
1367579,1367581 #10727
1367711,1367713 #10728
1368077,1368079 #10729
1368119,1368121 #10730
1368161,1368163 #10731
1368251,1368253 #10732
1368329,1368331 #10733
1368461,1368463 #10734
1368467,1368469 #10735
1368527,1368529 #10736
1368737,1368739 #10737
1368791,1368793 #10738
1368839,1368841 #10739
1369019,1369021 #10740
1369097,1369099 #10741
1369217,1369219 #10742
1369337,1369339 #10743
1369391,1369393 #10744
1369427,1369429 #10745
1369559,1369561 #10746
1369787,1369789 #10747
1370051,1370053 #10748
1370099,1370101 #10749
1370111,1370113 #10750
1370321,1370323 #10751
1370459,1370461 #10752
1370519,1370521 #10753
1370531,1370533 #10754
1370597,1370599 #10755
1370819,1370821 #10756
1371119,1371121 #10757
1371581,1371583 #10758
1371911,1371913 #10759
1371947,1371949 #10760
1371989,1371991 #10761
1372079,1372081 #10762
1372757,1372759 #10763
1372961,1372963 #10764
1372979,1372981 #10765
1373159,1373161 #10766
1373189,1373191 #10767
1373369,1373371 #10768
1373417,1373419 #10769
1373849,1373851 #10770
1374209,1374211 #10771
1374299,1374301 #10772
1374311,1374313 #10773
1374377,1374379 #10774
1374557,1374559 #10775
1374617,1374619 #10776
1374719,1374721 #10777
1375019,1375021 #10778
1375037,1375039 #10779
1375109,1375111 #10780
1375637,1375639 #10781
1375679,1375681 #10782
1375727,1375729 #10783
1375817,1375819 #10784
1375877,1375879 #10785
1375949,1375951 #10786
1376171,1376173 #10787
1376447,1376449 #10788
1376621,1376623 #10789
1376699,1376701 #10790
1376897,1376899 #10791
1377041,1377043 #10792
1377347,1377349 #10793
1377377,1377379 #10794
1377749,1377751 #10795
1377791,1377793 #10796
1377851,1377853 #10797
1377911,1377913 #10798
1378007,1378009 #10799
1378031,1378033 #10800
1378187,1378189 #10801
1378217,1378219 #10802
1378337,1378339 #10803
1378439,1378441 #10804
1378499,1378501 #10805
1378589,1378591 #10806
1378679,1378681 #10807
1378799,1378801 #10808
1378841,1378843 #10809
1378997,1378999 #10810
1379069,1379071 #10811
1379237,1379239 #10812
1379447,1379449 #10813
1379489,1379491 #10814
1379639,1379641 #10815
1379657,1379659 #10816
1379801,1379803 #10817
1379867,1379869 #10818
1380317,1380319 #10819
1380677,1380679 #10820
1380779,1380781 #10821
1380887,1380889 #10822
1380947,1380949 #10823
1381109,1381111 #10824
1381229,1381231 #10825
1381271,1381273 #10826
1381277,1381279 #10827
1381409,1381411 #10828
1381439,1381441 #10829
1381487,1381489 #10830
1381517,1381519 #10831
1381967,1381969 #10832
1381997,1381999 #10833
1382021,1382023 #10834
1382177,1382179 #10835
1382189,1382191 #10836
1382501,1382503 #10837
1382891,1382893 #10838
1382957,1382959 #10839
1382987,1382989 #10840
1383377,1383379 #10841
1383449,1383451 #10842
1383797,1383799 #10843
1383959,1383961 #10844
1384067,1384069 #10845
1384247,1384249 #10846
1384349,1384351 #10847
1384499,1384501 #10848
1384697,1384699 #10849
1384847,1384849 #10850
1384919,1384921 #10851
1384961,1384963 #10852
1385099,1385101 #10853
1385147,1385149 #10854
1385387,1385389 #10855
1385399,1385401 #10856
1385477,1385479 #10857
1385561,1385563 #10858
1385777,1385779 #10859
1385861,1385863 #10860
1386179,1386181 #10861
1386311,1386313 #10862
1386377,1386379 #10863
1386731,1386733 #10864
1386821,1386823 #10865
1386881,1386883 #10866
1386947,1386949 #10867
1387037,1387039 #10868
1387121,1387123 #10869
1387259,1387261 #10870
1387499,1387501 #10871
1387667,1387669 #10872
1387781,1387783 #10873
1387847,1387849 #10874
1387877,1387879 #10875
1388477,1388479 #10876
1388789,1388791 #10877
1389209,1389211 #10878
1389431,1389433 #10879
1389587,1389589 #10880
1389809,1389811 #10881
1389851,1389853 #10882
1389917,1389919 #10883
1389989,1389991 #10884
1390157,1390159 #10885
1390469,1390471 #10886
1390619,1390621 #10887
1390757,1390759 #10888
1390901,1390903 #10889
1390967,1390969 #10890
1391081,1391083 #10891
1391519,1391521 #10892
1391561,1391563 #10893
1391627,1391629 #10894
1391651,1391653 #10895
1392101,1392103 #10896
1392269,1392271 #10897
1392449,1392451 #10898
1392539,1392541 #10899
1392731,1392733 #10900
1393121,1393123 #10901
1393331,1393333 #10902
1393451,1393453 #10903
1393661,1393663 #10904
1393919,1393921 #10905
1393937,1393939 #10906
1393967,1393969 #10907
1393979,1393981 #10908
1394021,1394023 #10909
1394147,1394149 #10910
1394297,1394299 #10911
1394669,1394671 #10912
1394681,1394683 #10913
1394711,1394713 #10914
1394747,1394749 #10915
1394891,1394893 #10916
1395179,1395181 #10917
1395467,1395469 #10918
1395551,1395553 #10919
1395659,1395661 #10920
1395671,1395673 #10921
1395869,1395871 #10922
1396049,1396051 #10923
1396301,1396303 #10924
1396427,1396429 #10925
1396529,1396531 #10926
1396559,1396561 #10927
1396751,1396753 #10928
1396817,1396819 #10929
1396847,1396849 #10930
1397021,1397023 #10931
1397057,1397059 #10932
1397117,1397119 #10933
1397159,1397161 #10934
1397441,1397443 #10935
1397579,1397581 #10936
1397717,1397719 #10937
1397951,1397953 #10938
1398209,1398211 #10939
1398281,1398283 #10940
1398347,1398349 #10941
1398557,1398559 #10942
1398779,1398781 #10943
1398977,1398979 #10944
1399037,1399039 #10945
1399199,1399201 #10946
1399271,1399273 #10947
1399439,1399441 #10948
1399469,1399471 #10949
1399547,1399549 #10950
1399577,1399579 #10951
1399817,1399819 #10952
1400141,1400143 #10953
1400249,1400251 #10954
1400297,1400299 #10955
1400687,1400689 #10956
1400801,1400803 #10957
1400807,1400809 #10958
1400879,1400881 #10959
1400939,1400941 #10960
1401317,1401319 #10961
1401401,1401403 #10962
1401737,1401739 #10963
1401791,1401793 #10964
1401809,1401811 #10965
1401821,1401823 #10966
1401977,1401979 #10967
1402127,1402129 #10968
1402361,1402363 #10969
1402367,1402369 #10970
1402397,1402399 #10971
1402697,1402699 #10972
1402799,1402801 #10973
1402871,1402873 #10974
1403249,1403251 #10975
1403459,1403461 #10976
1403489,1403491 #10977
1403531,1403533 #10978
1403651,1403653 #10979
1403681,1403683 #10980
1403789,1403791 #10981
1403921,1403923 #10982
1403951,1403953 #10983
1404059,1404061 #10984
1404131,1404133 #10985
1404287,1404289 #10986
1404437,1404439 #10987
1404581,1404583 #10988
1404881,1404883 #10989
1404959,1404961 #10990
1405007,1405009 #10991
1405097,1405099 #10992
1405247,1405249 #10993
1405361,1405363 #10994
1405511,1405513 #10995
1405529,1405531 #10996
1406159,1406161 #10997
1406387,1406389 #10998
1406441,1406443 #10999
1406591,1406593 #11000
1406771,1406773 #11001
1407017,1407019 #11002
1407251,1407253 #11003
1407317,1407319 #11004
1407389,1407391 #11005
1407557,1407559 #11006
1407611,1407613 #11007
1407827,1407829 #11008
1408007,1408009 #11009
1408217,1408219 #11010
1408409,1408411 #11011
1408619,1408621 #11012
1408661,1408663 #11013
1408697,1408699 #11014
1408787,1408789 #11015
1408871,1408873 #11016
1408961,1408963 #11017
1408991,1408993 #11018
1409207,1409209 #11019
1409327,1409329 #11020
1409489,1409491 #11021
1409531,1409533 #11022
1409579,1409581 #11023
1409789,1409791 #11024
1410707,1410709 #11025
1410809,1410811 #11026
1410971,1410973 #11027
1410977,1410979 #11028
1411181,1411183 #11029
1411427,1411429 #11030
1411607,1411609 #11031
1411829,1411831 #11032
1412009,1412011 #11033
1412051,1412053 #11034
1412219,1412221 #11035
1412471,1412473 #11036
1412711,1412713 #11037
1412777,1412779 #11038
1412861,1412863 #11039
1413029,1413031 #11040
1413077,1413079 #11041
1413131,1413133 #11042
1413479,1413481 #11043
1413521,1413523 #11044
1413677,1413679 #11045
1413689,1413691 #11046
1413749,1413751 #11047
1413827,1413829 #11048
1414319,1414321 #11049
1415081,1415083 #11050
1415339,1415341 #11051
1415567,1415569 #11052
1415831,1415833 #11053
1416029,1416031 #11054
1416071,1416073 #11055
1416197,1416199 #11056
1416209,1416211 #11057
1416629,1416631 #11058
1417217,1417219 #11059
1417301,1417303 #11060
1417487,1417489 #11061
1417541,1417543 #11062
1417769,1417771 #11063
1417991,1417993 #11064
1418117,1418119 #11065
1418159,1418161 #11066
1418297,1418299 #11067
1418447,1418449 #11068
1418567,1418569 #11069
1418579,1418581 #11070
1418687,1418689 #11071
1418867,1418869 #11072
1418951,1418953 #11073
1419161,1419163 #11074
1419371,1419373 #11075
1419641,1419643 #11076
1419827,1419829 #11077
1420037,1420039 #11078
1420091,1420093 #11079
1420121,1420123 #11080
1420259,1420261 #11081
1420301,1420303 #11082
1420631,1420633 #11083
1420817,1420819 #11084
1420919,1420921 #11085
1420931,1420933 #11086
1421039,1421041 #11087
1421291,1421293 #11088
1421471,1421473 #11089
1421909,1421911 #11090
1422011,1422013 #11091
1422191,1422193 #11092
1422227,1422229 #11093
1422437,1422439 #11094
1422521,1422523 #11095
1422599,1422601 #11096
1422977,1422979 #11097
1423127,1423129 #11098
1423181,1423183 #11099
1423319,1423321 #11100
1423379,1423381 #11101
1423439,1423441 #11102
1423451,1423453 #11103
1423481,1423483 #11104
1423757,1423759 #11105
1423967,1423969 #11106
1424021,1424023 #11107
1424261,1424263 #11108
1424441,1424443 #11109
1424699,1424701 #11110
1424849,1424851 #11111
1425077,1425079 #11112
1425251,1425253 #11113
1425299,1425301 #11114
1425881,1425883 #11115
1425911,1425913 #11116
1426109,1426111 #11117
1426127,1426129 #11118
1426151,1426153 #11119
1426169,1426171 #11120
1426211,1426213 #11121
1426289,1426291 #11122
1426301,1426303 #11123
1426427,1426429 #11124
1426541,1426543 #11125
1426751,1426753 #11126
1426889,1426891 #11127
1426949,1426951 #11128
1427141,1427143 #11129
1427399,1427401 #11130
1427561,1427563 #11131
1427747,1427749 #11132
1428197,1428199 #11133
1428671,1428673 #11134
1428767,1428769 #11135
1428851,1428853 #11136
1429061,1429063 #11137
1429247,1429249 #11138
1429367,1429369 #11139
1429397,1429399 #11140
1429529,1429531 #11141
1429859,1429861 #11142
1430237,1430239 #11143
1430279,1430281 #11144
1430291,1430293 #11145
1430711,1430713 #11146
1430879,1430881 #11147
1430969,1430971 #11148
1431191,1431193 #11149
1431377,1431379 #11150
1431569,1431571 #11151
1431917,1431919 #11152
1432019,1432021 #11153
1432271,1432273 #11154
1432439,1432441 #11155
1432547,1432549 #11156
1432589,1432591 #11157
1432679,1432681 #11158
1432799,1432801 #11159
1433057,1433059 #11160
1433351,1433353 #11161
1433741,1433743 #11162
1433819,1433821 #11163
1434107,1434109 #11164
1434131,1434133 #11165
1434281,1434283 #11166
1434491,1434493 #11167
1434539,1434541 #11168
1434677,1434679 #11169
1434791,1434793 #11170
1434911,1434913 #11171
1434941,1434943 #11172
1435139,1435141 #11173
1435457,1435459 #11174
1435559,1435561 #11175
1435571,1435573 #11176
1435739,1435741 #11177
1435829,1435831 #11178
1435919,1435921 #11179
1436021,1436023 #11180
1436087,1436089 #11181
1436249,1436251 #11182
1436429,1436431 #11183
1436441,1436443 #11184
1436801,1436803 #11185
1437011,1437013 #11186
1437047,1437049 #11187
1437347,1437349 #11188
1437389,1437391 #11189
1437851,1437853 #11190
1438067,1438069 #11191
1438751,1438753 #11192
1438847,1438849 #11193
1438937,1438939 #11194
1438961,1438963 #11195
1438991,1438993 #11196
1439369,1439371 #11197
1439699,1439701 #11198
1439717,1439719 #11199
1440209,1440211 #11200
1440581,1440583 #11201
1440587,1440589 #11202
1440851,1440853 #11203
1441007,1441009 #11204
1441049,1441051 #11205
1441199,1441201 #11206
1441589,1441591 #11207
1441679,1441681 #11208
1441721,1441723 #11209
1441877,1441879 #11210
1441931,1441933 #11211
1442069,1442071 #11212
1442921,1442923 #11213
1442939,1442941 #11214
1443437,1443439 #11215
1443857,1443859 #11216
1444109,1444111 #11217
1444271,1444273 #11218
1444481,1444483 #11219
1444787,1444789 #11220
1444901,1444903 #11221
1444979,1444981 #11222
1445177,1445179 #11223
1445237,1445239 #11224
1445417,1445419 #11225
1445567,1445569 #11226
1445669,1445671 #11227
1446041,1446043 #11228
1446089,1446091 #11229
1446167,1446169 #11230
1446617,1446619 #11231
1446701,1446703 #11232
1446899,1446901 #11233
1446917,1446919 #11234
1447001,1447003 #11235
1447007,1447009 #11236
1447151,1447153 #11237
1447217,1447219 #11238
1447331,1447333 #11239
1447349,1447351 #11240
1447427,1447429 #11241
1447559,1447561 #11242
1447811,1447813 #11243
1447889,1447891 #11244
1447949,1447951 #11245
1448189,1448191 #11246
1448219,1448221 #11247
1448801,1448803 #11248
1449167,1449169 #11249
1449191,1449193 #11250
1449209,1449211 #11251
1449521,1449523 #11252
1449587,1449589 #11253
1449599,1449601 #11254
1449647,1449649 #11255
1449671,1449673 #11256
1449827,1449829 #11257
1449977,1449979 #11258
1450019,1450021 #11259
1450199,1450201 #11260
1450331,1450333 #11261
1450487,1450489 #11262
1450571,1450573 #11263
1450637,1450639 #11264
1450697,1450699 #11265
1450739,1450741 #11266
1450847,1450849 #11267
1450871,1450873 #11268
1451039,1451041 #11269
1451057,1451059 #11270
1451081,1451083 #11271
1451717,1451719 #11272
1451741,1451743 #11273
1451831,1451833 #11274
1451837,1451839 #11275
1451909,1451911 #11276
1452221,1452223 #11277
1452299,1452301 #11278
1452419,1452421 #11279
1452557,1452559 #11280
1452851,1452853 #11281
1453091,1453093 #11282
1453169,1453171 #11283
1453337,1453339 #11284
1453427,1453429 #11285
1453547,1453549 #11286
1453607,1453609 #11287
1454207,1454209 #11288
1454417,1454419 #11289
1454441,1454443 #11290
1454459,1454461 #11291
1454567,1454569 #11292
1454597,1454599 #11293
1454699,1454701 #11294
1454897,1454899 #11295
1454939,1454941 #11296
1454987,1454989 #11297
1455029,1455031 #11298
1455119,1455121 #11299
1455197,1455199 #11300
1455359,1455361 #11301
1455437,1455439 #11302
1456121,1456123 #11303
1456157,1456159 #11304
1456241,1456243 #11305
1456391,1456393 #11306
1456517,1456519 #11307
1456919,1456921 #11308
1457147,1457149 #11309
1457501,1457503 #11310
1457957,1457959 #11311
1458167,1458169 #11312
1458461,1458463 #11313
1458599,1458601 #11314
1458629,1458631 #11315
1458881,1458883 #11316
1458971,1458973 #11317
1459109,1459111 #11318
1459259,1459261 #11319
1459427,1459429 #11320
1459949,1459951 #11321
1460027,1460029 #11322
1460087,1460089 #11323
1460099,1460101 #11324
1460267,1460269 #11325
1460651,1460653 #11326
1460729,1460731 #11327
1460741,1460743 #11328
1461077,1461079 #11329
1461179,1461181 #11330
1461209,1461211 #11331
1461287,1461289 #11332
1461401,1461403 #11333
1461407,1461409 #11334
1461599,1461601 #11335
1461659,1461661 #11336
1461701,1461703 #11337
1461851,1461853 #11338
1462037,1462039 #11339
1462061,1462063 #11340
1462169,1462171 #11341
1462247,1462249 #11342
1462337,1462339 #11343
1462397,1462399 #11344
1462421,1462423 #11345
1462619,1462621 #11346
1462691,1462693 #11347
1462871,1462873 #11348
1463177,1463179 #11349
1463219,1463221 #11350
1463261,1463263 #11351
1463507,1463509 #11352
1463597,1463599 #11353
1463897,1463899 #11354
1463981,1463983 #11355
1464101,1464103 #11356
1464257,1464259 #11357
1464269,1464271 #11358
1464371,1464373 #11359
1464401,1464403 #11360
1464731,1464733 #11361
1464809,1464811 #11362
1464899,1464901 #11363
1464959,1464961 #11364
1465019,1465021 #11365
1465127,1465129 #11366
1465229,1465231 #11367
1465391,1465393 #11368
1465421,1465423 #11369
1465439,1465441 #11370
1465547,1465549 #11371
1465559,1465561 #11372
1465661,1465663 #11373
1465691,1465693 #11374
1465727,1465729 #11375
1465991,1465993 #11376
1466291,1466293 #11377
1466459,1466461 #11378
1466657,1466659 #11379
1466711,1466713 #11380
1466999,1467001 #11381
1467209,1467211 #11382
1467281,1467283 #11383
1467749,1467751 #11384
1467887,1467889 #11385
1467911,1467913 #11386
1468211,1468213 #11387
1468457,1468459 #11388
1468559,1468561 #11389
1468631,1468633 #11390
1468637,1468639 #11391
1468739,1468741 #11392
1468799,1468801 #11393
1468967,1468969 #11394
1469129,1469131 #11395
1469357,1469359 #11396
1469519,1469521 #11397
1469621,1469623 #11398
1469729,1469731 #11399
1470149,1470151 #11400
1470611,1470613 #11401
1470839,1470841 #11402
1470869,1470871 #11403
1470947,1470949 #11404
1471031,1471033 #11405
1471277,1471279 #11406
1471409,1471411 #11407
1471499,1471501 #11408
1471511,1471513 #11409
1471619,1471621 #11410
1471667,1471669 #11411
1471817,1471819 #11412
1471907,1471909 #11413
1472411,1472413 #11414
1472687,1472689 #11415
1472789,1472791 #11416
1472927,1472929 #11417
1472951,1472953 #11418
1473047,1473049 #11419
1473191,1473193 #11420
1473341,1473343 #11421
1473389,1473391 #11422
1473419,1473421 #11423
1473551,1473553 #11424
1473959,1473961 #11425
1473971,1473973 #11426
1474127,1474129 #11427
1474241,1474243 #11428
1474259,1474261 #11429
1474439,1474441 #11430
1474589,1474591 #11431
1474859,1474861 #11432
1475237,1475239 #11433
1475399,1475401 #11434
1475561,1475563 #11435
1475729,1475731 #11436
1476149,1476151 #11437
1476191,1476193 #11438
1476401,1476403 #11439
1476647,1476649 #11440
1476689,1476691 #11441
1476701,1476703 #11442
1476791,1476793 #11443
1476857,1476859 #11444
1476911,1476913 #11445
1477109,1477111 #11446
1477319,1477321 #11447
1477337,1477339 #11448
1477361,1477363 #11449
1477499,1477501 #11450
1477769,1477771 #11451
1477787,1477789 #11452
1478207,1478209 #11453
1478591,1478593 #11454
1478837,1478839 #11455
1478861,1478863 #11456
1479011,1479013 #11457
1479209,1479211 #11458
1479251,1479253 #11459
1479341,1479343 #11460
1479449,1479451 #11461
1479479,1479481 #11462
1479557,1479559 #11463
1479761,1479763 #11464
1479857,1479859 #11465
1479911,1479913 #11466
1480019,1480021 #11467
1480319,1480321 #11468
1480517,1480519 #11469
1480541,1480543 #11470
1480571,1480573 #11471
1480781,1480783 #11472
1480907,1480909 #11473
1480931,1480933 #11474
1481537,1481539 #11475
1481717,1481719 #11476
1481747,1481749 #11477
1481897,1481899 #11478
1482581,1482583 #11479
1482659,1482661 #11480
1482737,1482739 #11481
1482851,1482853 #11482
1483019,1483021 #11483
1483169,1483171 #11484
1483331,1483333 #11485
1483451,1483453 #11486
1483631,1483633 #11487
1483967,1483969 #11488
1484141,1484143 #11489
1484207,1484209 #11490
1484927,1484929 #11491
1485017,1485019 #11492
1485047,1485049 #11493
1485191,1485193 #11494
1485557,1485559 #11495
1485719,1485721 #11496
1485761,1485763 #11497
1486139,1486141 #11498
1486181,1486183 #11499
1486409,1486411 #11500
1486607,1486609 #11501
1486841,1486843 #11502
1486907,1486909 #11503
1487051,1487053 #11504
1487399,1487401 #11505
1487459,1487461 #11506
1487579,1487581 #11507
1487711,1487713 #11508
1487777,1487779 #11509
1487819,1487821 #11510
1487951,1487953 #11511
1487987,1487989 #11512
1488119,1488121 #11513
1488131,1488133 #11514
1488209,1488211 #11515
1488239,1488241 #11516
1488761,1488763 #11517
1488791,1488793 #11518
1488869,1488871 #11519
1489067,1489069 #11520
1489097,1489099 #11521
1489259,1489261 #11522
1489511,1489513 #11523
1489529,1489531 #11524
1489667,1489669 #11525
1489721,1489723 #11526
1489751,1489753 #11527
1489781,1489783 #11528
1490117,1490119 #11529
1490297,1490299 #11530
1490327,1490329 #11531
1490351,1490353 #11532
1490369,1490371 #11533
1490477,1490479 #11534
1490639,1490641 #11535
1490999,1491001 #11536
1491239,1491241 #11537
1491401,1491403 #11538
1491419,1491421 #11539
1491437,1491439 #11540
1491491,1491493 #11541
1491641,1491643 #11542
1491911,1491913 #11543
1491977,1491979 #11544
1491989,1491991 #11545
1492187,1492189 #11546
1492457,1492459 #11547
1492499,1492501 #11548
1492871,1492873 #11549
1493099,1493101 #11550
1493279,1493281 #11551
1493291,1493293 #11552
1493447,1493449 #11553
1493489,1493491 #11554
1493537,1493539 #11555
1493621,1493623 #11556
1493717,1493719 #11557
1493729,1493731 #11558
1493741,1493743 #11559
1493927,1493929 #11560
1494047,1494049 #11561
1494347,1494349 #11562
1494371,1494373 #11563
1494401,1494403 #11564
1494461,1494463 #11565
1494509,1494511 #11566
1494641,1494643 #11567
1494677,1494679 #11568
1494707,1494709 #11569
1495157,1495159 #11570
1495379,1495381 #11571
1495631,1495633 #11572
1495829,1495831 #11573
1495859,1495861 #11574
1496069,1496071 #11575
1496477,1496479 #11576
1496489,1496491 #11577
1496567,1496569 #11578
1496639,1496641 #11579
1496939,1496941 #11580
1497149,1497151 #11581
1497227,1497229 #11582
1497281,1497283 #11583
1497719,1497721 #11584
1498139,1498141 #11585
1498349,1498351 #11586
1498529,1498531 #11587
1498619,1498621 #11588
1498799,1498801 #11589
1498811,1498813 #11590
1499219,1499221 #11591
1499357,1499359 #11592
1499549,1499551 #11593
1499567,1499569 #11594
1499609,1499611 #11595
1499681,1499683 #11596
1500041,1500043 #11597
1500071,1500073 #11598
1500347,1500349 #11599
1500407,1500409 #11600
1500467,1500469 #11601
1500647,1500649 #11602
1500701,1500703 #11603
1500767,1500769 #11604
1500797,1500799 #11605
1500857,1500859 #11606
1500929,1500931 #11607
1501427,1501429 #11608
1501481,1501483 #11609
1501499,1501501 #11610
1501679,1501681 #11611
1501781,1501783 #11612
1501847,1501849 #11613
1502021,1502023 #11614
1502099,1502101 #11615
1502141,1502143 #11616
1502201,1502203 #11617
1502327,1502329 #11618
1502687,1502689 #11619
1502717,1502719 #11620
1502861,1502863 #11621
1503317,1503319 #11622
1503371,1503373 #11623
1503611,1503613 #11624
1503659,1503661 #11625
1503881,1503883 #11626
1503959,1503961 #11627
1504409,1504411 #11628
1504469,1504471 #11629
1504661,1504663 #11630
1504691,1504693 #11631
1504859,1504861 #11632
1504967,1504969 #11633
1505087,1505089 #11634
1505291,1505293 #11635
1505519,1505521 #11636
1505657,1505659 #11637
1505681,1505683 #11638
1505849,1505851 #11639
1506077,1506079 #11640
1506389,1506391 #11641
1506497,1506499 #11642
1506509,1506511 #11643
1506551,1506553 #11644
1506611,1506613 #11645
1506731,1506733 #11646
1506779,1506781 #11647
1506887,1506889 #11648
1506977,1506979 #11649
1507139,1507141 #11650
1507421,1507423 #11651
1507481,1507483 #11652
1507607,1507609 #11653
1507697,1507699 #11654
1507769,1507771 #11655
1508249,1508251 #11656
1508279,1508281 #11657
1508321,1508323 #11658
1508471,1508473 #11659
1508621,1508623 #11660
1508627,1508629 #11661
1508909,1508911 #11662
1508951,1508953 #11663
1509059,1509061 #11664
1509437,1509439 #11665
1509551,1509553 #11666
1509587,1509589 #11667
1510217,1510219 #11668
1510307,1510309 #11669
1510319,1510321 #11670
1510337,1510339 #11671
1510361,1510363 #11672
1510391,1510393 #11673
1510427,1510429 #11674
1510679,1510681 #11675
1510757,1510759 #11676
1510961,1510963 #11677
1511099,1511101 #11678
1511231,1511233 #11679
1511327,1511329 #11680
1511441,1511443 #11681
1511597,1511599 #11682
1511687,1511689 #11683
1511819,1511821 #11684
1512221,1512223 #11685
1512281,1512283 #11686
1512479,1512481 #11687
1512557,1512559 #11688
1512689,1512691 #11689
1512827,1512829 #11690
1513019,1513021 #11691
1513067,1513069 #11692
1513091,1513093 #11693
1513121,1513123 #11694
1513271,1513273 #11695
1513319,1513321 #11696
1513397,1513399 #11697
1513427,1513429 #11698
1513487,1513489 #11699
1513529,1513531 #11700
1513619,1513621 #11701
1513667,1513669 #11702
1513739,1513741 #11703
1514099,1514101 #11704
1514321,1514323 #11705
1514327,1514329 #11706
1514549,1514551 #11707
1514561,1514563 #11708
1514657,1514659 #11709
1515719,1515721 #11710
1515821,1515823 #11711
1515971,1515973 #11712
1516127,1516129 #11713
1516187,1516189 #11714
1516259,1516261 #11715
1516391,1516393 #11716
1516589,1516591 #11717
1516607,1516609 #11718
1516661,1516663 #11719
1516817,1516819 #11720
1517051,1517053 #11721
1517099,1517101 #11722
1517141,1517143 #11723
1517519,1517521 #11724
1517567,1517569 #11725
1517651,1517653 #11726
1517687,1517689 #11727
1517939,1517941 #11728
1518089,1518091 #11729
1518311,1518313 #11730
1518551,1518553 #11731
1518677,1518679 #11732
1518707,1518709 #11733
1518731,1518733 #11734
1518947,1518949 #11735
1518971,1518973 #11736
1519097,1519099 #11737
1519121,1519123 #11738
1519421,1519423 #11739
1519517,1519519 #11740
1519547,1519549 #11741
1519709,1519711 #11742
1520009,1520011 #11743
1520339,1520341 #11744
1520357,1520359 #11745
1520501,1520503 #11746
1520537,1520539 #11747
1520681,1520683 #11748
1521029,1521031 #11749
1521227,1521229 #11750
1521671,1521673 #11751
1522019,1522021 #11752
1522049,1522051 #11753
1522361,1522363 #11754
1522457,1522459 #11755
1522691,1522693 #11756
1522769,1522771 #11757
1523087,1523089 #11758
1523099,1523101 #11759
1523441,1523443 #11760
1523567,1523569 #11761
1523651,1523653 #11762
1523939,1523941 #11763
1523981,1523983 #11764
1524071,1524073 #11765
1524077,1524079 #11766
1524137,1524139 #11767
1524179,1524181 #11768
1524359,1524361 #11769
1524377,1524379 #11770
1524401,1524403 #11771
1524431,1524433 #11772
1524569,1524571 #11773
1524629,1524631 #11774
1524701,1524703 #11775
1524827,1524829 #11776
1524839,1524841 #11777
1525031,1525033 #11778
1525217,1525219 #11779
1525331,1525333 #11780
1525421,1525423 #11781
1525607,1525609 #11782
1525637,1525639 #11783
1525961,1525963 #11784
1525967,1525969 #11785
1526069,1526071 #11786
1526087,1526089 #11787
1526267,1526269 #11788
1526339,1526341 #11789
1526639,1526641 #11790
1527107,1527109 #11791
1527287,1527289 #11792
1527311,1527313 #11793
1527347,1527349 #11794
1527521,1527523 #11795
1527551,1527553 #11796
1527677,1527679 #11797
1527791,1527793 #11798
1527857,1527859 #11799
1527899,1527901 #11800
1527971,1527973 #11801
1528139,1528141 #11802
1528937,1528939 #11803
1529027,1529029 #11804
1529069,1529071 #11805
1529189,1529191 #11806
1529387,1529389 #11807
1529501,1529503 #11808
1529531,1529533 #11809
1529849,1529851 #11810
1530071,1530073 #11811
1530227,1530229 #11812
1530311,1530313 #11813
1530521,1530523 #11814
1530539,1530541 #11815
1530827,1530829 #11816
1530869,1530871 #11817
1530911,1530913 #11818
1531091,1531093 #11819
1531331,1531333 #11820
1531631,1531633 #11821
1531811,1531813 #11822
1532351,1532353 #11823
1532579,1532581 #11824
1533107,1533109 #11825
1533137,1533139 #11826
1533197,1533199 #11827
1533437,1533439 #11828
1533461,1533463 #11829
1533797,1533799 #11830
1533899,1533901 #11831
1534019,1534021 #11832
1534067,1534069 #11833
1534151,1534153 #11834
1534217,1534219 #11835
1534451,1534453 #11836
1534787,1534789 #11837
1534961,1534963 #11838
1535069,1535071 #11839
1535291,1535293 #11840
1535351,1535353 #11841
1535669,1535671 #11842
1535717,1535719 #11843
1535969,1535971 #11844
1536011,1536013 #11845
1536047,1536049 #11846
1536581,1536583 #11847
1536641,1536643 #11848
1536677,1536679 #11849
1536809,1536811 #11850
1536959,1536961 #11851
1536989,1536991 #11852
1537397,1537399 #11853
1537439,1537441 #11854
1537559,1537561 #11855
1537799,1537801 #11856
1537967,1537969 #11857
1537997,1537999 #11858
1538027,1538029 #11859
1538057,1538059 #11860
1538081,1538083 #11861
1538501,1538503 #11862
1538597,1538599 #11863
1538609,1538611 #11864
1538627,1538629 #11865
1538837,1538839 #11866
1539257,1539259 #11867
1539449,1539451 #11868
1539719,1539721 #11869
1539971,1539973 #11870
1540151,1540153 #11871
1540169,1540171 #11872
1540541,1540543 #11873
1540619,1540621 #11874
1540697,1540699 #11875
1540709,1540711 #11876
1540751,1540753 #11877
1540787,1540789 #11878
1540871,1540873 #11879
1540961,1540963 #11880
1540967,1540969 #11881
1541117,1541119 #11882
1541357,1541359 #11883
1541429,1541431 #11884
1541819,1541821 #11885
1541921,1541923 #11886
1542029,1542031 #11887
1542041,1542043 #11888
1542089,1542091 #11889
1542347,1542349 #11890
1542509,1542511 #11891
1542521,1542523 #11892
1542689,1542691 #11893
1543391,1543393 #11894
1543511,1543513 #11895
1543637,1543639 #11896
1543811,1543813 #11897
1543979,1543981 #11898
1544129,1544131 #11899
1544507,1544509 #11900
1545041,1545043 #11901
1545239,1545241 #11902
1545389,1545391 #11903
1545431,1545433 #11904
1545617,1545619 #11905
1545701,1545703 #11906
1545809,1545811 #11907
1545911,1545913 #11908
1546217,1546219 #11909
1546229,1546231 #11910
1546271,1546273 #11911
1546547,1546549 #11912
1546757,1546759 #11913
1546901,1546903 #11914
1546967,1546969 #11915
1547129,1547131 #11916
1547477,1547479 #11917
1547519,1547521 #11918
1547591,1547593 #11919
1547657,1547659 #11920
1547717,1547719 #11921
1547771,1547773 #11922
1547837,1547839 #11923
1547879,1547881 #11924
1547927,1547929 #11925
1547939,1547941 #11926
1548179,1548181 #11927
1548539,1548541 #11928
1548719,1548721 #11929
1548761,1548763 #11930
1548947,1548949 #11931
1549319,1549321 #11932
1549367,1549369 #11933
1549529,1549531 #11934
1549547,1549549 #11935
1549739,1549741 #11936
1550051,1550053 #11937
1550207,1550209 #11938
1550231,1550233 #11939
1550441,1550443 #11940
1550777,1550779 #11941
1550999,1551001 #11942
1551497,1551499 #11943
1551617,1551619 #11944
1551659,1551661 #11945
1551731,1551733 #11946
1551791,1551793 #11947
1551887,1551889 #11948
1551917,1551919 #11949
1551959,1551961 #11950
1552121,1552123 #11951
1552379,1552381 #11952
1552541,1552543 #11953
1553009,1553011 #11954
1553309,1553311 #11955
1553507,1553509 #11956
1553807,1553809 #11957
1554101,1554103 #11958
1554281,1554283 #11959
1554347,1554349 #11960
1554611,1554613 #11961
1554737,1554739 #11962
1554779,1554781 #11963
1555157,1555159 #11964
1555187,1555189 #11965
1555247,1555249 #11966
1555259,1555261 #11967
1555289,1555291 #11968
1555469,1555471 #11969
1555571,1555573 #11970
1555637,1555639 #11971
1555691,1555693 #11972
1555817,1555819 #11973
1555997,1555999 #11974
1556327,1556329 #11975
1556369,1556371 #11976
1556561,1556563 #11977
1556669,1556671 #11978
1556717,1556719 #11979
1556759,1556761 #11980
1556771,1556773 #11981
1556837,1556839 #11982
1557041,1557043 #11983
1557089,1557091 #11984
1557287,1557289 #11985
1557341,1557343 #11986
1557707,1557709 #11987
1557947,1557949 #11988
1558307,1558309 #11989
1558559,1558561 #11990
1558727,1558729 #11991
1558757,1558759 #11992
1558787,1558789 #11993
1558811,1558813 #11994
1558829,1558831 #11995
1558937,1558939 #11996
1558979,1558981 #11997
1559057,1559059 #11998
1559447,1559449 #11999
1559477,1559479 #12000
1559609,1559611 #12001
1559849,1559851 #12002
1559891,1559893 #12003
1560047,1560049 #12004
1560131,1560133 #12005
1560239,1560241 #12006
1560407,1560409 #12007
1560707,1560709 #12008
1561037,1561039 #12009
1561121,1561123 #12010
1561421,1561423 #12011
1561577,1561579 #12012
1561757,1561759 #12013
1562051,1562053 #12014
1562087,1562089 #12015
1562129,1562131 #12016
1562291,1562293 #12017
1562357,1562359 #12018
1562591,1562593 #12019
1563017,1563019 #12020
1563227,1563229 #12021
1563257,1563259 #12022
1563281,1563283 #12023
1563407,1563409 #12024
1563431,1563433 #12025
1563467,1563469 #12026
1563629,1563631 #12027
1563971,1563973 #12028
1564307,1564309 #12029
1564361,1564363 #12030
1564499,1564501 #12031
1564571,1564573 #12032
1564907,1564909 #12033
1564991,1564993 #12034
1565189,1565191 #12035
1565381,1565383 #12036
1565489,1565491 #12037
1565519,1565521 #12038
1565561,1565563 #12039
1565609,1565611 #12040
1565741,1565743 #12041
1565789,1565791 #12042
1565867,1565869 #12043
1566197,1566199 #12044
1566209,1566211 #12045
1566281,1566283 #12046
1566401,1566403 #12047
1566449,1566451 #12048
1566749,1566751 #12049
1566767,1566769 #12050
1566821,1566823 #12051
1566881,1566883 #12052
1567001,1567003 #12053
1567037,1567039 #12054
1567169,1567171 #12055
1567259,1567261 #12056
1567301,1567303 #12057
1567409,1567411 #12058
1567901,1567903 #12059
1568141,1568143 #12060
1568351,1568353 #12061
1568519,1568521 #12062
1568561,1568563 #12063
1568921,1568923 #12064
1568969,1568971 #12065
1569011,1569013 #12066
1569257,1569259 #12067
1569317,1569319 #12068
1569329,1569331 #12069
1569551,1569553 #12070
1570097,1570099 #12071
1570451,1570453 #12072
1570631,1570633 #12073
1570769,1570771 #12074
1570871,1570873 #12075
1571027,1571029 #12076
1571237,1571239 #12077
1571417,1571419 #12078
1571681,1571683 #12079
1571741,1571743 #12080
1571747,1571749 #12081
1571957,1571959 #12082
1572251,1572253 #12083
1572281,1572283 #12084
1572377,1572379 #12085
1572509,1572511 #12086
1572587,1572589 #12087
1572677,1572679 #12088
1572749,1572751 #12089
1572869,1572871 #12090
1573079,1573081 #12091
1573109,1573111 #12092
1573139,1573141 #12093
1573151,1573153 #12094
1573301,1573303 #12095
1573541,1573543 #12096
1573547,1573549 #12097
1573667,1573669 #12098
1573811,1573813 #12099
1573907,1573909 #12100
1573931,1573933 #12101
1573937,1573939 #12102
1574009,1574011 #12103
1574057,1574059 #12104
1574159,1574161 #12105
1574369,1574371 #12106
1575029,1575031 #12107
1575137,1575139 #12108
1575281,1575283 #12109
1575479,1575481 #12110
1575641,1575643 #12111
1575731,1575733 #12112
1575989,1575991 #12113
1576037,1576039 #12114
1576241,1576243 #12115
1576499,1576501 #12116
1576649,1576651 #12117
1576721,1576723 #12118
1576889,1576891 #12119
1577099,1577101 #12120
1577117,1577119 #12121
1577201,1577203 #12122
1577291,1577293 #12123
1577297,1577299 #12124
1577507,1577509 #12125
1577531,1577533 #12126
1577657,1577659 #12127
1577699,1577701 #12128
1577999,1578001 #12129
1578821,1578823 #12130
1578851,1578853 #12131
1579139,1579141 #12132
1579217,1579219 #12133
1579397,1579399 #12134
1579619,1579621 #12135
1579637,1579639 #12136
1579931,1579933 #12137
1580417,1580419 #12138
1580429,1580431 #12139
1580459,1580461 #12140
1580651,1580653 #12141
1580771,1580773 #12142
1580849,1580851 #12143
1580921,1580923 #12144
1581077,1581079 #12145
1581191,1581193 #12146
1581707,1581709 #12147
1581719,1581721 #12148
1581857,1581859 #12149
1582079,1582081 #12150
1582169,1582171 #12151
1582391,1582393 #12152
1582577,1582579 #12153
1582811,1582813 #12154
1582961,1582963 #12155
1583291,1583293 #12156
1583357,1583359 #12157
1583651,1583653 #12158
1583807,1583809 #12159
1583861,1583863 #12160
1583927,1583929 #12161
1583999,1584001 #12162
1584101,1584103 #12163
1584137,1584139 #12164
1584257,1584259 #12165
1584431,1584433 #12166
1584437,1584439 #12167
1584641,1584643 #12168
1584701,1584703 #12169
1584827,1584829 #12170
1584899,1584901 #12171
1584929,1584931 #12172
1584941,1584943 #12173
1585007,1585009 #12174
1585289,1585291 #12175
1585481,1585483 #12176
1585697,1585699 #12177
1586111,1586113 #12178
1586309,1586311 #12179
1586537,1586539 #12180
1586621,1586623 #12181
1586771,1586773 #12182
1586789,1586791 #12183
1586867,1586869 #12184
1586951,1586953 #12185
1587737,1587739 #12186
1587869,1587871 #12187
1587959,1587961 #12188
1588049,1588051 #12189
1588187,1588189 #12190
1588511,1588513 #12191
1588661,1588663 #12192
1588751,1588753 #12193
1588757,1588759 #12194
1588859,1588861 #12195
1588877,1588879 #12196
1588901,1588903 #12197
1588931,1588933 #12198
1589207,1589209 #12199
1589249,1589251 #12200
1589297,1589299 #12201
1589387,1589389 #12202
1589501,1589503 #12203
1589561,1589563 #12204
1589669,1589671 #12205
1589849,1589851 #12206
1590047,1590049 #12207
1590077,1590079 #12208
1590131,1590133 #12209
1590539,1590541 #12210
1590551,1590553 #12211
1590791,1590793 #12212
1591097,1591099 #12213
1591871,1591873 #12214
1592111,1592113 #12215
1592321,1592323 #12216
1592429,1592431 #12217
1592579,1592581 #12218
1592621,1592623 #12219
1592777,1592779 #12220
1592861,1592863 #12221
1592867,1592869 #12222
1592879,1592881 #12223
1593197,1593199 #12224
1593269,1593271 #12225
1593377,1593379 #12226
1593497,1593499 #12227
1593539,1593541 #12228
1593797,1593799 #12229
1593857,1593859 #12230
1594127,1594129 #12231
1594259,1594261 #12232
1594631,1594633 #12233
1595051,1595053 #12234
1595309,1595311 #12235
1595729,1595731 #12236
1595831,1595833 #12237
1595861,1595863 #12238
1595927,1595929 #12239
1596059,1596061 #12240
1596311,1596313 #12241
1596347,1596349 #12242
1596377,1596379 #12243
1596629,1596631 #12244
1596737,1596739 #12245
1596869,1596871 #12246
1597067,1597069 #12247
1597109,1597111 #12248
1597619,1597621 #12249
1597721,1597723 #12250
1598237,1598239 #12251
1598447,1598449 #12252
1598501,1598503 #12253
1598789,1598791 #12254
1598897,1598899 #12255
1598951,1598953 #12256
1599461,1599463 #12257
1599509,1599511 #12258
1599707,1599709 #12259
1599839,1599841 #12260
1600097,1600099 #12261
1600217,1600219 #12262
1600241,1600243 #12263
1600631,1600633 #12264
1600787,1600789 #12265
1600811,1600813 #12266
1600889,1600891 #12267
1600967,1600969 #12268
1601207,1601209 #12269
1601267,1601269 #12270
1601441,1601443 #12271
1601627,1601629 #12272
1601729,1601731 #12273
1601777,1601779 #12274
1601867,1601869 #12275
1602077,1602079 #12276
1602101,1602103 #12277
1602119,1602121 #12278
1602281,1602283 #12279
1602527,1602529 #12280
1602551,1602553 #12281
1602719,1602721 #12282
1602749,1602751 #12283
1602827,1602829 #12284
1602899,1602901 #12285
1602941,1602943 #12286
1602959,1602961 #12287
1603079,1603081 #12288
1603331,1603333 #12289
1603337,1603339 #12290
1603361,1603363 #12291
1603517,1603519 #12292
1603529,1603531 #12293
1603697,1603699 #12294
1603709,1603711 #12295
1603799,1603801 #12296
1604129,1604131 #12297
1604147,1604149 #12298
1604177,1604179 #12299
1604297,1604299 #12300
1604609,1604611 #12301
1605029,1605031 #12302
1605419,1605421 #12303
1605431,1605433 #12304
1605509,1605511 #12305
1605551,1605553 #12306
1605629,1605631 #12307
1605887,1605889 #12308
1606151,1606153 #12309
1606247,1606249 #12310
1606259,1606261 #12311
1606289,1606291 #12312
1606541,1606543 #12313
1606739,1606741 #12314
1606751,1606753 #12315
1607141,1607143 #12316
1607477,1607479 #12317
1607699,1607701 #12318
1607831,1607833 #12319
1608107,1608109 #12320
1608239,1608241 #12321
1608461,1608463 #12322
1608569,1608571 #12323
1608821,1608823 #12324
1608911,1608913 #12325
1609061,1609063 #12326
1609247,1609249 #12327
1609667,1609669 #12328
1609691,1609693 #12329
1609871,1609873 #12330
1609901,1609903 #12331
1609997,1609999 #12332
1610177,1610179 #12333
1610237,1610239 #12334
1610309,1610311 #12335
1610429,1610431 #12336
1610471,1610473 #12337
1610657,1610659 #12338
1610771,1610773 #12339
1611689,1611691 #12340
1611761,1611763 #12341
1611851,1611853 #12342
1611899,1611901 #12343
1611947,1611949 #12344
1612181,1612183 #12345
1612211,1612213 #12346
1612307,1612309 #12347
1612361,1612363 #12348
1612619,1612621 #12349
1612997,1612999 #12350
1613321,1613323 #12351
1613411,1613413 #12352
1613639,1613641 #12353
1613669,1613671 #12354
1614329,1614331 #12355
1614461,1614463 #12356
1614491,1614493 #12357
1614629,1614631 #12358
1614647,1614649 #12359
1614659,1614661 #12360
1614719,1614721 #12361
1614911,1614913 #12362
1615181,1615183 #12363
1615331,1615333 #12364
1615499,1615501 #12365
1615631,1615633 #12366
1615841,1615843 #12367
1615847,1615849 #12368
1615919,1615921 #12369
1616609,1616611 #12370
1616621,1616623 #12371
1616687,1616689 #12372
1616801,1616803 #12373
1616807,1616809 #12374
1616897,1616899 #12375
1617137,1617139 #12376
1617347,1617349 #12377
1617437,1617439 #12378
1617689,1617691 #12379
1617767,1617769 #12380
1618049,1618051 #12381
1618079,1618081 #12382
1618091,1618093 #12383
1618187,1618189 #12384
1618367,1618369 #12385
1618457,1618459 #12386
1618679,1618681 #12387
1618739,1618741 #12388
1618829,1618831 #12389
1619069,1619071 #12390
1619207,1619209 #12391
1619327,1619329 #12392
1619339,1619341 #12393
1619381,1619383 #12394
1619417,1619419 #12395
1619549,1619551 #12396
1619669,1619671 #12397
1619687,1619689 #12398
1620329,1620331 #12399
1620467,1620469 #12400
1620569,1620571 #12401
1620611,1620613 #12402
1620629,1620631 #12403
1620677,1620679 #12404
1621031,1621033 #12405
1621349,1621351 #12406
1621421,1621423 #12407
1621469,1621471 #12408
1621619,1621621 #12409
1621637,1621639 #12410
1621721,1621723 #12411
1621727,1621729 #12412
1621769,1621771 #12413
1621931,1621933 #12414
1622039,1622041 #12415
1622141,1622143 #12416
1622207,1622209 #12417
1622471,1622473 #12418
1622639,1622641 #12419
1622669,1622671 #12420
1623161,1623163 #12421
1623287,1623289 #12422
1623827,1623829 #12423
1623929,1623931 #12424
1624169,1624171 #12425
1624199,1624201 #12426
1624277,1624279 #12427
1624349,1624351 #12428
1624589,1624591 #12429
1624661,1624663 #12430
1624811,1624813 #12431
1624967,1624969 #12432
1624991,1624993 #12433
1625177,1625179 #12434
1625207,1625209 #12435
1625417,1625419 #12436
1625717,1625719 #12437
1625747,1625749 #12438
1625807,1625809 #12439
1625837,1625839 #12440
1626071,1626073 #12441
1626089,1626091 #12442
1626281,1626283 #12443
1626377,1626379 #12444
1626431,1626433 #12445
1626479,1626481 #12446
1626617,1626619 #12447
1627061,1627063 #12448
1627487,1627489 #12449
1627601,1627603 #12450
1627607,1627609 #12451
1627649,1627651 #12452
1627727,1627729 #12453
1627781,1627783 #12454
1627859,1627861 #12455
1627979,1627981 #12456
1628057,1628059 #12457
1628171,1628173 #12458
1628381,1628383 #12459
1628489,1628491 #12460
1628591,1628593 #12461
1628987,1628989 #12462
1629011,1629013 #12463
1629107,1629109 #12464
1629209,1629211 #12465
1629317,1629319 #12466
1629359,1629361 #12467
1629449,1629451 #12468
1629557,1629559 #12469
1629581,1629583 #12470
1629599,1629601 #12471
1629851,1629853 #12472
1630019,1630021 #12473
1630049,1630051 #12474
1630091,1630093 #12475
1630127,1630129 #12476
1630379,1630381 #12477
1630427,1630429 #12478
1630457,1630459 #12479
1630547,1630549 #12480
1630619,1630621 #12481
1630841,1630843 #12482
1631027,1631029 #12483
1631051,1631053 #12484
1631057,1631059 #12485
1631261,1631263 #12486
1631297,1631299 #12487
1631489,1631491 #12488
1631519,1631521 #12489
1631657,1631659 #12490
1631897,1631899 #12491
1632311,1632313 #12492
1632467,1632469 #12493
1632479,1632481 #12494
1632569,1632571 #12495
1632647,1632649 #12496
1632749,1632751 #12497
1632767,1632769 #12498
1632779,1632781 #12499
1633127,1633129 #12500
1633169,1633171 #12501
1633319,1633321 #12502
1633337,1633339 #12503
1633361,1633363 #12504
1633559,1633561 #12505
1633691,1633693 #12506
1633787,1633789 #12507
1633991,1633993 #12508
1634051,1634053 #12509
1634069,1634071 #12510
1634201,1634203 #12511
1634231,1634233 #12512
1634291,1634293 #12513
1634441,1634443 #12514
1634681,1634683 #12515
1634879,1634881 #12516
1634951,1634953 #12517
1635371,1635373 #12518
1635497,1635499 #12519
1635971,1635973 #12520
1636007,1636009 #12521
1636067,1636069 #12522
1636331,1636333 #12523
1636541,1636543 #12524
1636667,1636669 #12525
1636697,1636699 #12526
1636757,1636759 #12527
1637549,1637551 #12528
1637639,1637641 #12529
1638059,1638061 #12530
1638209,1638211 #12531
1638347,1638349 #12532
1638797,1638799 #12533
1639151,1639153 #12534
1639199,1639201 #12535
1639241,1639243 #12536
1639511,1639513 #12537
1639577,1639579 #12538
1639607,1639609 #12539
1640057,1640059 #12540
1640621,1640623 #12541
1640927,1640929 #12542
1640939,1640941 #12543
1641089,1641091 #12544
1641359,1641361 #12545
1641377,1641379 #12546
1641587,1641589 #12547
1641797,1641799 #12548
1641929,1641931 #12549
1642031,1642033 #12550
1642049,1642051 #12551
1642481,1642483 #12552
1642517,1642519 #12553
1642631,1642633 #12554
1642811,1642813 #12555
1643219,1643221 #12556
1643231,1643233 #12557
1643597,1643599 #12558
1643639,1643641 #12559
1643819,1643821 #12560
1643867,1643869 #12561
1643891,1643893 #12562
1643987,1643989 #12563
1644197,1644199 #12564
1644371,1644373 #12565
1644437,1644439 #12566
1644491,1644493 #12567
1644689,1644691 #12568
1644899,1644901 #12569
1644947,1644949 #12570
1644989,1644991 #12571
1645559,1645561 #12572
1645601,1645603 #12573
1645667,1645669 #12574
1645727,1645729 #12575
1645769,1645771 #12576
1645907,1645909 #12577
1645937,1645939 #12578
1646147,1646149 #12579
1646171,1646173 #12580
1646219,1646221 #12581
1646717,1646719 #12582
1646921,1646923 #12583
1647251,1647253 #12584
1647377,1647379 #12585
1647551,1647553 #12586
1647599,1647601 #12587
1647857,1647859 #12588
1648067,1648069 #12589
1648259,1648261 #12590
1648289,1648291 #12591
1648481,1648483 #12592
1648529,1648531 #12593
1649099,1649101 #12594
1649147,1649149 #12595
1649171,1649173 #12596
1649309,1649311 #12597
1649771,1649773 #12598
1649801,1649803 #12599
1649861,1649863 #12600
1650107,1650109 #12601
1650611,1650613 #12602
1651211,1651213 #12603
1651409,1651411 #12604
1651511,1651513 #12605
1651589,1651591 #12606
1651691,1651693 #12607
1652351,1652353 #12608
1652489,1652491 #12609
1652771,1652773 #12610
1652837,1652839 #12611
1652879,1652881 #12612
1652897,1652899 #12613
1652921,1652923 #12614
1653059,1653061 #12615
1653101,1653103 #12616
1653107,1653109 #12617
1653191,1653193 #12618
1653329,1653331 #12619
1653341,1653343 #12620
1653497,1653499 #12621
1653917,1653919 #12622
1654019,1654021 #12623
1654031,1654033 #12624
1654199,1654201 #12625
1654649,1654651 #12626
1654787,1654789 #12627
1654979,1654981 #12628
1655021,1655023 #12629
1655177,1655179 #12630
1655207,1655209 #12631
1655279,1655281 #12632
1655321,1655323 #12633
1655807,1655809 #12634
1655891,1655893 #12635
1656047,1656049 #12636
1656119,1656121 #12637
1656167,1656169 #12638
1656227,1656229 #12639
1656311,1656313 #12640
1656647,1656649 #12641
1656791,1656793 #12642
1656827,1656829 #12643
1656839,1656841 #12644
1656899,1656901 #12645
1657037,1657039 #12646
1657571,1657573 #12647
1657697,1657699 #12648
1657937,1657939 #12649
1658051,1658053 #12650
1658201,1658203 #12651
1658309,1658311 #12652
1658387,1658389 #12653
1658411,1658413 #12654
1658441,1658443 #12655
1659101,1659103 #12656
1659107,1659109 #12657
1659347,1659349 #12658
1659569,1659571 #12659
1659809,1659811 #12660
1659881,1659883 #12661
1660037,1660039 #12662
1660229,1660231 #12663
1660259,1660261 #12664
1660409,1660411 #12665
1660469,1660471 #12666
1660661,1660663 #12667
1660697,1660699 #12668
1660721,1660723 #12669
1660739,1660741 #12670
1660871,1660873 #12671
1661159,1661161 #12672
1661249,1661251 #12673
1661831,1661833 #12674
1662119,1662121 #12675
1662161,1662163 #12676
1662629,1662631 #12677
1662641,1662643 #12678
1662779,1662781 #12679
1662839,1662841 #12680
1662959,1662961 #12681
1662977,1662979 #12682
1663217,1663219 #12683
1663301,1663303 #12684
1663349,1663351 #12685
1663379,1663381 #12686
1663547,1663549 #12687
1664459,1664461 #12688
1664561,1664563 #12689
1664651,1664653 #12690
1664711,1664713 #12691
1664867,1664869 #12692
1665071,1665073 #12693
1665107,1665109 #12694
1665527,1665529 #12695
1665569,1665571 #12696
1665581,1665583 #12697
1665647,1665649 #12698
1665929,1665931 #12699
1665941,1665943 #12700
1666037,1666039 #12701
1666211,1666213 #12702
1666307,1666309 #12703
1666727,1666729 #12704
1666781,1666783 #12705
1667051,1667053 #12706
1667249,1667251 #12707
1667357,1667359 #12708
1667441,1667443 #12709
1667507,1667509 #12710
1667597,1667599 #12711
1667639,1667641 #12712
1667747,1667749 #12713
1667777,1667779 #12714
1667789,1667791 #12715
1667957,1667959 #12716
1668131,1668133 #12717
1668299,1668301 #12718
1668479,1668481 #12719
1668551,1668553 #12720
1668617,1668619 #12721
1668647,1668649 #12722
1668911,1668913 #12723
1669097,1669099 #12724
1669469,1669471 #12725
1669541,1669543 #12726
1669649,1669651 #12727
1669781,1669783 #12728
1669931,1669933 #12729
1670057,1670059 #12730
1670411,1670413 #12731
1670489,1670491 #12732
1670531,1670533 #12733
1670561,1670563 #12734
1670567,1670569 #12735
1670657,1670659 #12736
1670831,1670833 #12737
1671209,1671211 #12738
1671347,1671349 #12739
1671641,1671643 #12740
1672079,1672081 #12741
1672337,1672339 #12742
1672379,1672381 #12743
1672421,1672423 #12744
1672469,1672471 #12745
1672499,1672501 #12746
1672607,1672609 #12747
1672637,1672639 #12748
1672751,1672753 #12749
1672961,1672963 #12750
1673069,1673071 #12751
1673207,1673209 #12752
1673279,1673281 #12753
1673627,1673629 #12754
1673807,1673809 #12755
1673951,1673953 #12756
1673981,1673983 #12757
1674161,1674163 #12758
1674269,1674271 #12759
1674557,1674559 #12760
1674599,1674601 #12761
1674767,1674769 #12762
1674887,1674889 #12763
1674917,1674919 #12764
1674947,1674949 #12765
1674989,1674991 #12766
1675109,1675111 #12767
1675181,1675183 #12768
1675577,1675579 #12769
1675769,1675771 #12770
1675787,1675789 #12771
1675799,1675801 #12772
1676027,1676029 #12773
1676069,1676071 #12774
1676471,1676473 #12775
1676627,1676629 #12776
1676711,1676713 #12777
1676891,1676893 #12778
1677197,1677199 #12779
1677251,1677253 #12780
1677281,1677283 #12781
1677461,1677463 #12782
1677521,1677523 #12783
1678067,1678069 #12784
1678091,1678093 #12785
1678151,1678153 #12786
1678217,1678219 #12787
1678319,1678321 #12788
1678361,1678363 #12789
1678421,1678423 #12790
1678601,1678603 #12791
1678751,1678753 #12792
1678757,1678759 #12793
1678769,1678771 #12794
1678877,1678879 #12795
1678889,1678891 #12796
1679057,1679059 #12797
1679099,1679101 #12798
1679471,1679473 #12799
1679681,1679683 #12800
1679831,1679833 #12801
1680101,1680103 #12802
1680179,1680181 #12803
1680269,1680271 #12804
1680317,1680319 #12805
1680359,1680361 #12806
1680527,1680529 #12807
1680821,1680823 #12808
1681259,1681261 #12809
1681571,1681573 #12810
1681619,1681621 #12811
1681649,1681651 #12812
1681721,1681723 #12813
1681871,1681873 #12814
1681877,1681879 #12815
1682249,1682251 #12816
1682477,1682479 #12817
1682537,1682539 #12818
1682669,1682671 #12819
1682831,1682833 #12820
1683041,1683043 #12821
1683467,1683469 #12822
1683839,1683841 #12823
1684097,1684099 #12824
1684169,1684171 #12825
1684229,1684231 #12826
1684301,1684303 #12827
1684607,1684609 #12828
1684691,1684693 #12829
1685111,1685113 #12830
1685207,1685209 #12831
1685267,1685269 #12832
1685441,1685443 #12833
1685447,1685449 #12834
1685477,1685479 #12835
1685711,1685713 #12836
1685777,1685779 #12837
1685819,1685821 #12838
1685861,1685863 #12839
1685951,1685953 #12840
1686257,1686259 #12841
1686341,1686343 #12842
1686701,1686703 #12843
1687451,1687453 #12844
1687667,1687669 #12845
1687757,1687759 #12846
1687781,1687783 #12847
1687799,1687801 #12848
1688261,1688263 #12849
1688327,1688329 #12850
1688369,1688371 #12851
1688411,1688413 #12852
1688969,1688971 #12853
1689197,1689199 #12854
1689377,1689379 #12855
1689551,1689553 #12856
1689659,1689661 #12857
1689911,1689913 #12858
1689929,1689931 #12859
1690079,1690081 #12860
1690097,1690099 #12861
1690187,1690189 #12862
1690217,1690219 #12863
1690229,1690231 #12864
1690571,1690573 #12865
1690691,1690693 #12866
1690781,1690783 #12867
1690847,1690849 #12868
1691099,1691101 #12869
1691411,1691413 #12870
1691531,1691533 #12871
1691861,1691863 #12872
1691867,1691869 #12873
1692137,1692139 #12874
1692239,1692241 #12875
1692827,1692829 #12876
1692947,1692949 #12877
1693091,1693093 #12878
1693169,1693171 #12879
1693271,1693273 #12880
1693331,1693333 #12881
1693427,1693429 #12882
1693577,1693579 #12883
1693631,1693633 #12884
1693661,1693663 #12885
1693889,1693891 #12886
1694027,1694029 #12887
1694081,1694083 #12888
1694309,1694311 #12889
1694351,1694353 #12890
1694447,1694449 #12891
1695347,1695349 #12892
1695401,1695403 #12893
1695437,1695439 #12894
1695509,1695511 #12895
1695641,1695643 #12896
1695761,1695763 #12897
1695779,1695781 #12898
1696421,1696423 #12899
1696577,1696579 #12900
1696691,1696693 #12901
1696859,1696861 #12902
1697039,1697041 #12903
1697411,1697413 #12904
1697459,1697461 #12905
1697621,1697623 #12906
1697741,1697743 #12907
1697867,1697869 #12908
1697957,1697959 #12909
1697987,1697989 #12910
1698119,1698121 #12911
1698131,1698133 #12912
1698311,1698313 #12913
1698377,1698379 #12914
1698509,1698511 #12915
1698797,1698799 #12916
1698857,1698859 #12917
1698869,1698871 #12918
1698881,1698883 #12919
1699067,1699069 #12920
1699109,1699111 #12921
1699331,1699333 #12922
1699391,1699393 #12923
1699469,1699471 #12924
1699499,1699501 #12925
1699679,1699681 #12926
1699739,1699741 #12927
1699781,1699783 #12928
1699799,1699801 #12929
1699877,1699879 #12930
1699937,1699939 #12931
1700141,1700143 #12932
1700267,1700269 #12933
1700339,1700341 #12934
1700591,1700593 #12935
1700759,1700761 #12936
1700849,1700851 #12937
1700981,1700983 #12938
1701017,1701019 #12939
1701041,1701043 #12940
1701059,1701061 #12941
1701179,1701181 #12942
1701389,1701391 #12943
1701437,1701439 #12944
1701521,1701523 #12945
1701641,1701643 #12946
1701827,1701829 #12947
1701857,1701859 #12948
1701899,1701901 #12949
1701911,1701913 #12950
1702319,1702321 #12951
1702637,1702639 #12952
1702661,1702663 #12953
1702709,1702711 #12954
1702739,1702741 #12955
1702781,1702783 #12956
1702817,1702819 #12957
1702901,1702903 #12958
1702931,1702933 #12959
1702991,1702993 #12960
1703267,1703269 #12961
1703717,1703719 #12962
1704119,1704121 #12963
1704587,1704589 #12964
1704611,1704613 #12965
1704671,1704673 #12966
1704929,1704931 #12967
1705127,1705129 #12968
1705139,1705141 #12969
1705271,1705273 #12970
1705397,1705399 #12971
1705817,1705819 #12972
1705859,1705861 #12973
1706249,1706251 #12974
1706291,1706293 #12975
1706489,1706491 #12976
1706567,1706569 #12977
1706657,1706659 #12978
1706687,1706689 #12979
1706741,1706743 #12980
1706867,1706869 #12981
1707071,1707073 #12982
1707161,1707163 #12983
1707521,1707523 #12984
1707647,1707649 #12985
1707707,1707709 #12986
1707887,1707889 #12987
1707941,1707943 #12988
1708037,1708039 #12989
1708409,1708411 #12990
1708541,1708543 #12991
1708571,1708573 #12992
1708781,1708783 #12993
1708961,1708963 #12994
1708979,1708981 #12995
1709261,1709263 #12996
1709339,1709341 #12997
1709507,1709509 #12998
1709711,1709713 #12999
1709861,1709863 #13000
1709969,1709971 #13001
1710197,1710199 #13002
1710341,1710343 #13003
1710407,1710409 #13004
1710617,1710619 #13005
1710689,1710691 #13006
1710851,1710853 #13007
1710869,1710871 #13008
1711049,1711051 #13009
1711091,1711093 #13010
1711277,1711279 #13011
1711289,1711291 #13012
1711397,1711399 #13013
1711517,1711519 #13014
1711811,1711813 #13015
1711817,1711819 #13016
1711889,1711891 #13017
1711979,1711981 #13018
1712171,1712173 #13019
1712369,1712371 #13020
1712549,1712551 #13021
1712567,1712569 #13022
1712759,1712761 #13023
1712927,1712929 #13024
1713221,1713223 #13025
1713317,1713319 #13026
1713557,1713559 #13027
1713599,1713601 #13028
1713977,1713979 #13029
1714157,1714159 #13030
1714187,1714189 #13031
1714409,1714411 #13032
1714421,1714423 #13033
1714439,1714441 #13034
1714631,1714633 #13035
1714787,1714789 #13036
1714859,1714861 #13037
1715471,1715473 #13038
1715711,1715713 #13039
1715849,1715851 #13040
1716047,1716049 #13041
1716107,1716109 #13042
1716311,1716313 #13043
1716359,1716361 #13044
1716389,1716391 #13045
1716497,1716499 #13046
1716941,1716943 #13047
1717361,1717363 #13048
1718027,1718029 #13049
1718291,1718293 #13050
1718369,1718371 #13051
1718447,1718449 #13052
1718471,1718473 #13053
1718699,1718701 #13054
1718711,1718713 #13055
1718747,1718749 #13056
1718789,1718791 #13057
1718861,1718863 #13058
1718867,1718869 #13059
1718879,1718881 #13060
1719239,1719241 #13061
1719299,1719301 #13062
1719491,1719493 #13063
1719719,1719721 #13064
1719857,1719859 #13065
1720181,1720183 #13066
1720217,1720219 #13067
1720289,1720291 #13068
1720361,1720363 #13069
1720427,1720429 #13070
1720709,1720711 #13071
1720931,1720933 #13072
1720949,1720951 #13073
1721009,1721011 #13074
1721147,1721149 #13075
1721507,1721509 #13076
1721567,1721569 #13077
1721717,1721719 #13078
1721807,1721809 #13079
1721891,1721893 #13080
1722029,1722031 #13081
1722209,1722211 #13082
1722599,1722601 #13083
1722647,1722649 #13084
1722737,1722739 #13085
1722989,1722991 #13086
1723451,1723453 #13087
1723487,1723489 #13088
1723619,1723621 #13089
1723637,1723639 #13090
1723721,1723723 #13091
1724027,1724029 #13092
1724447,1724449 #13093
1724507,1724509 #13094
1724579,1724581 #13095
1724741,1724743 #13096
1724927,1724929 #13097
1724969,1724971 #13098
1725011,1725013 #13099
1725077,1725079 #13100
1725089,1725091 #13101
1725221,1725223 #13102
1725497,1725499 #13103
1725539,1725541 #13104
1725929,1725931 #13105
1726031,1726033 #13106
1726199,1726201 #13107
1726409,1726411 #13108
1726601,1726603 #13109
1726691,1726693 #13110
1726757,1726759 #13111
1726937,1726939 #13112
1727021,1727023 #13113
1727069,1727071 #13114
1727189,1727191 #13115
1727261,1727263 #13116
1727291,1727293 #13117
1727771,1727773 #13118
1727777,1727779 #13119
1727939,1727941 #13120
1727987,1727989 #13121
1728017,1728019 #13122
1728119,1728121 #13123
1728317,1728319 #13124
1728539,1728541 #13125
1728581,1728583 #13126
1728689,1728691 #13127
1728737,1728739 #13128
1728821,1728823 #13129
1729127,1729129 #13130
1729307,1729309 #13131
1729709,1729711 #13132
1729757,1729759 #13133
1729841,1729843 #13134
1730087,1730089 #13135
1730147,1730149 #13136
1730429,1730431 #13137
1730471,1730473 #13138
1730579,1730581 #13139
1730789,1730791 #13140
1730849,1730851 #13141
1731179,1731181 #13142
1731251,1731253 #13143
1731311,1731313 #13144
1731491,1731493 #13145
1731701,1731703 #13146
1731731,1731733 #13147
1731929,1731931 #13148
1732037,1732039 #13149
1732271,1732273 #13150
1732319,1732321 #13151
1732331,1732333 #13152
1732397,1732399 #13153
1732499,1732501 #13154
1732529,1732531 #13155
1732901,1732903 #13156
1733141,1733143 #13157
1733309,1733311 #13158
1733651,1733653 #13159
1733909,1733911 #13160
1734041,1734043 #13161
1734371,1734373 #13162
1734737,1734739 #13163
1734767,1734769 #13164
1735397,1735399 #13165
1735421,1735423 #13166
1735829,1735831 #13167
1735847,1735849 #13168
1735931,1735933 #13169
1736099,1736101 #13170
1736177,1736179 #13171
1736219,1736221 #13172
1736387,1736389 #13173
1736417,1736419 #13174
1736459,1736461 #13175
1736687,1736689 #13176
1736849,1736851 #13177
1736879,1736881 #13178
1737101,1737103 #13179
1737401,1737403 #13180
1737431,1737433 #13181
1737521,1737523 #13182
1737611,1737613 #13183
1737677,1737679 #13184
1738019,1738021 #13185
1738127,1738129 #13186
1738169,1738171 #13187
1738379,1738381 #13188
1738421,1738423 #13189
1738589,1738591 #13190
1738901,1738903 #13191
1738967,1738969 #13192
1738991,1738993 #13193
1739039,1739041 #13194
1739207,1739209 #13195
1739357,1739359 #13196
1739399,1739401 #13197
1739471,1739473 #13198
1739579,1739581 #13199
1739867,1739869 #13200
1740047,1740049 #13201
1740119,1740121 #13202
1740197,1740199 #13203
1740257,1740259 #13204
1740437,1740439 #13205
1740521,1740523 #13206
1740689,1740691 #13207
1740701,1740703 #13208
1741151,1741153 #13209
1741319,1741321 #13210
1741379,1741381 #13211
1741697,1741699 #13212
1741877,1741879 #13213
1742171,1742173 #13214
1742537,1742539 #13215
1742591,1742593 #13216
1742771,1742773 #13217
1742969,1742971 #13218
1743461,1743463 #13219
1743527,1743529 #13220
1743629,1743631 #13221
1743659,1743661 #13222
1743737,1743739 #13223
1743827,1743829 #13224
1743869,1743871 #13225
1744007,1744009 #13226
1744361,1744363 #13227
1744817,1744819 #13228
1744991,1744993 #13229
1745111,1745113 #13230
1745141,1745143 #13231
1745351,1745353 #13232
1745459,1745461 #13233
1745921,1745923 #13234
1745969,1745971 #13235
1746167,1746169 #13236
1746179,1746181 #13237
1746209,1746211 #13238
1746299,1746301 #13239
1746419,1746421 #13240
1746539,1746541 #13241
1746599,1746601 #13242
1746761,1746763 #13243
1746947,1746949 #13244
1747001,1747003 #13245
1747061,1747063 #13246
1747169,1747171 #13247
1747301,1747303 #13248
1747721,1747723 #13249
1747727,1747729 #13250
1748027,1748029 #13251
1748039,1748041 #13252
1748051,1748053 #13253
1748177,1748179 #13254
1748237,1748239 #13255
1748267,1748269 #13256
1748471,1748473 #13257
1748477,1748479 #13258
1748489,1748491 #13259
1749029,1749031 #13260
1749047,1749049 #13261
1749071,1749073 #13262
1749089,1749091 #13263
1749149,1749151 #13264
1749257,1749259 #13265
1749269,1749271 #13266
1749467,1749469 #13267
1749491,1749493 #13268
1749497,1749499 #13269
1749701,1749703 #13270
1749959,1749961 #13271
1750127,1750129 #13272
1750181,1750183 #13273
1750379,1750381 #13274
1750499,1750501 #13275
1750871,1750873 #13276
1750979,1750981 #13277
1751039,1751041 #13278
1751291,1751293 #13279
1751411,1751413 #13280
1751567,1751569 #13281
1752011,1752013 #13282
1752029,1752031 #13283
1752227,1752229 #13284
1752269,1752271 #13285
1752599,1752601 #13286
1752629,1752631 #13287
1752701,1752703 #13288
1752719,1752721 #13289
1752941,1752943 #13290
1752977,1752979 #13291
1753049,1753051 #13292
1753289,1753291 #13293
1753439,1753441 #13294
1753517,1753519 #13295
1753559,1753561 #13296
1753649,1753651 #13297
1753901,1753903 #13298
1753979,1753981 #13299
1754171,1754173 #13300
1754579,1754581 #13301
1754801,1754803 #13302
1755041,1755043 #13303
1755179,1755181 #13304
1755491,1755493 #13305
1755569,1755571 #13306
1755821,1755823 #13307
1755827,1755829 #13308
1756229,1756231 #13309
1756331,1756333 #13310
1756787,1756789 #13311
1756817,1756819 #13312
1756919,1756921 #13313
1757087,1757089 #13314
1757309,1757311 #13315
1757447,1757449 #13316
1758389,1758391 #13317
1758401,1758403 #13318
1758437,1758439 #13319
1758539,1758541 #13320
1758737,1758739 #13321
1759361,1759363 #13322
1759397,1759399 #13323
1759649,1759651 #13324
1760069,1760071 #13325
1760279,1760281 #13326
1760567,1760569 #13327
1760657,1760659 #13328
1760699,1760701 #13329
1760777,1760779 #13330
1760921,1760923 #13331
1761101,1761103 #13332
1761299,1761301 #13333
1761689,1761691 #13334
1761941,1761943 #13335
1762259,1762261 #13336
1762427,1762429 #13337
1762601,1762603 #13338
1762907,1762909 #13339
1762919,1762921 #13340
1762931,1762933 #13341
1763147,1763149 #13342
1763429,1763431 #13343
1763549,1763551 #13344
1763717,1763719 #13345
1763849,1763851 #13346
1764221,1764223 #13347
1764227,1764229 #13348
1764251,1764253 #13349
1764461,1764463 #13350
1764557,1764559 #13351
1764731,1764733 #13352
1764809,1764811 #13353
1764899,1764901 #13354
1764977,1764979 #13355
1765061,1765063 #13356
1765121,1765123 #13357
1765787,1765789 #13358
1765997,1765999 #13359
1766159,1766161 #13360
1766459,1766461 #13361
1766507,1766509 #13362
1766537,1766539 #13363
1766579,1766581 #13364
1766627,1766629 #13365
1766717,1766719 #13366
1766747,1766749 #13367
1766801,1766803 #13368
1766879,1766881 #13369
1767041,1767043 #13370
1767089,1767091 #13371
1767329,1767331 #13372
1767419,1767421 #13373
1767737,1767739 #13374
1767917,1767919 #13375
1768001,1768003 #13376
1768229,1768231 #13377
1768241,1768243 #13378
1768379,1768381 #13379
1768421,1768423 #13380
1768439,1768441 #13381
1768607,1768609 #13382
1768757,1768759 #13383
1769099,1769101 #13384
1769111,1769113 #13385
1769291,1769293 #13386
1769399,1769401 #13387
1769891,1769893 #13388
1770491,1770493 #13389
1771421,1771423 #13390
1771457,1771459 #13391
1771877,1771879 #13392
1772291,1772293 #13393
1772399,1772401 #13394
1772579,1772581 #13395
1772591,1772593 #13396
1772711,1772713 #13397
1772987,1772989 #13398
1773179,1773181 #13399
1773227,1773229 #13400
1773281,1773283 #13401
1773587,1773589 #13402
1773641,1773643 #13403
1773677,1773679 #13404
1773719,1773721 #13405
1773881,1773883 #13406
1773977,1773979 #13407
1774007,1774009 #13408
1774301,1774303 #13409
1774637,1774639 #13410
1774697,1774699 #13411
1774937,1774939 #13412
1775171,1775173 #13413
1775201,1775203 #13414
1775489,1775491 #13415
1775549,1775551 #13416
1775687,1775689 #13417
1775729,1775731 #13418
1775867,1775869 #13419
1776011,1776013 #13420
1776239,1776241 #13421
1776317,1776319 #13422
1776419,1776421 #13423
1776791,1776793 #13424
1777079,1777081 #13425
1777481,1777483 #13426
1777541,1777543 #13427
1777751,1777753 #13428
1777859,1777861 #13429
1777931,1777933 #13430
1778009,1778011 #13431
1778069,1778071 #13432
1778219,1778221 #13433
1778261,1778263 #13434
1778321,1778323 #13435
1778459,1778461 #13436
1778471,1778473 #13437
1778549,1778551 #13438
1778729,1778731 #13439
1778927,1778929 #13440
1779131,1779133 #13441
1779161,1779163 #13442
1779287,1779289 #13443
1779299,1779301 #13444
1779647,1779649 #13445
1779689,1779691 #13446
1779821,1779823 #13447
1780001,1780003 #13448
1780067,1780069 #13449
1780169,1780171 #13450
1780307,1780309 #13451
1780349,1780351 #13452
1780379,1780381 #13453
1780481,1780483 #13454
1780487,1780489 #13455
1780577,1780579 #13456
1780967,1780969 #13457
1781027,1781029 #13458
1781357,1781359 #13459
1781567,1781569 #13460
1781777,1781779 #13461
1782167,1782169 #13462
1782197,1782199 #13463
1782239,1782241 #13464
1782269,1782271 #13465
1782377,1782379 #13466
1782461,1782463 #13467
1782497,1782499 #13468
1782509,1782511 #13469
1782551,1782553 #13470
1782929,1782931 #13471
1782959,1782961 #13472
1783427,1783429 #13473
1783499,1783501 #13474
1783517,1783519 #13475
1783667,1783669 #13476
1783781,1783783 #13477
1783799,1783801 #13478
1783841,1783843 #13479
1784021,1784023 #13480
1784171,1784173 #13481
1784579,1784581 #13482
1785101,1785103 #13483
1785149,1785151 #13484
1785689,1785691 #13485
1785851,1785853 #13486
1786217,1786219 #13487
1786331,1786333 #13488
1786439,1786441 #13489
1786457,1786459 #13490
1786637,1786639 #13491
1787039,1787041 #13492
1787087,1787089 #13493
1787249,1787251 #13494
1787339,1787341 #13495
1787519,1787521 #13496
1787699,1787701 #13497
1787717,1787719 #13498
1788011,1788013 #13499
1788509,1788511 #13500
1788767,1788769 #13501
1789001,1789003 #13502
1789091,1789093 #13503
1789217,1789219 #13504
1789481,1789483 #13505
1789517,1789519 #13506
1790051,1790053 #13507
1790231,1790233 #13508
1790291,1790293 #13509
1790309,1790311 #13510
1790357,1790359 #13511
1790417,1790419 #13512
1790669,1790671 #13513
1791017,1791019 #13514
1791089,1791091 #13515
1791191,1791193 #13516
1791551,1791553 #13517
1791731,1791733 #13518
1791737,1791739 #13519
1791791,1791793 #13520
1791899,1791901 #13521
1791941,1791943 #13522
1791989,1791991 #13523
1792031,1792033 #13524
1792247,1792249 #13525
1792277,1792279 #13526
1792337,1792339 #13527
1792379,1792381 #13528
1792601,1792603 #13529
1792709,1792711 #13530
1792757,1792759 #13531
1792787,1792789 #13532
1792979,1792981 #13533
1793117,1793119 #13534
1793171,1793173 #13535
1793357,1793359 #13536
1793417,1793419 #13537
1793717,1793719 #13538
1793927,1793929 #13539
1794179,1794181 #13540
1794269,1794271 #13541
1794521,1794523 #13542
1794587,1794589 #13543
1794647,1794649 #13544
1794677,1794679 #13545
1794731,1794733 #13546
1794761,1794763 #13547
1795007,1795009 #13548
1795151,1795153 #13549
1795271,1795273 #13550
1795331,1795333 #13551
1795529,1795531 #13552
1795559,1795561 #13553
1795601,1795603 #13554
1795697,1795699 #13555
1795811,1795813 #13556
1795889,1795891 #13557
1796129,1796131 #13558
1796189,1796191 #13559
1796477,1796479 #13560
1796759,1796761 #13561
1796777,1796779 #13562
1796801,1796803 #13563
1797239,1797241 #13564
1797371,1797373 #13565
1797377,1797379 #13566
1797539,1797541 #13567
1797779,1797781 #13568
1797821,1797823 #13569
1798001,1798003 #13570
1798127,1798129 #13571
1798187,1798189 #13572
1798271,1798273 #13573
1798427,1798429 #13574
1798631,1798633 #13575
1798637,1798639 #13576
1798721,1798723 #13577
1798919,1798921 #13578
1798997,1798999 #13579
1799009,1799011 #13580
1799177,1799179 #13581
1799309,1799311 #13582
1799801,1799803 #13583
1800119,1800121 #13584
1800257,1800259 #13585
1800311,1800313 #13586
1800341,1800343 #13587
1800551,1800553 #13588
1800707,1800709 #13589
1800809,1800811 #13590
1800959,1800961 #13591
1801361,1801363 #13592
1801529,1801531 #13593
1801769,1801771 #13594
1801817,1801819 #13595
1801871,1801873 #13596
1802081,1802083 #13597
1802597,1802599 #13598
1802651,1802653 #13599
1802657,1802659 #13600
1802837,1802839 #13601
1803029,1803031 #13602
1803077,1803079 #13603
1803101,1803103 #13604
1803167,1803169 #13605
1803209,1803211 #13606
1803251,1803253 #13607
1803419,1803421 #13608
1803509,1803511 #13609
1803551,1803553 #13610
1803677,1803679 #13611
1804547,1804549 #13612
1804709,1804711 #13613
1804799,1804801 #13614
1804919,1804921 #13615
1804937,1804939 #13616
1804961,1804963 #13617
1804991,1804993 #13618
1805261,1805263 #13619
1805357,1805359 #13620
1805369,1805371 #13621
1805579,1805581 #13622
1805591,1805593 #13623
1805651,1805653 #13624
1805819,1805821 #13625
1806059,1806061 #13626
1806191,1806193 #13627
1806221,1806223 #13628
1806839,1806841 #13629
1806899,1806901 #13630
1806941,1806943 #13631
1807061,1807063 #13632
1807187,1807189 #13633
1807511,1807513 #13634
1807607,1807609 #13635
1807691,1807693 #13636
1807997,1807999 #13637
1808039,1808041 #13638
1808117,1808119 #13639
1808489,1808491 #13640
1808801,1808803 #13641
1808921,1808923 #13642
1809167,1809169 #13643
1809209,1809211 #13644
1809419,1809421 #13645
1809527,1809529 #13646
1809551,1809553 #13647
1809581,1809583 #13648
1809671,1809673 #13649
1809851,1809853 #13650
1810217,1810219 #13651
1810241,1810243 #13652
1810421,1810423 #13653
1810577,1810579 #13654
1810607,1810609 #13655
1810931,1810933 #13656
1810967,1810969 #13657
1810979,1810981 #13658
1811081,1811083 #13659
1811321,1811323 #13660
1811387,1811389 #13661
1811567,1811569 #13662
1811681,1811683 #13663
1812059,1812061 #13664
1812089,1812091 #13665
1812269,1812271 #13666
1812359,1812361 #13667
1812401,1812403 #13668
1812509,1812511 #13669
1812821,1812823 #13670
1812869,1812871 #13671
1812947,1812949 #13672
1813001,1813003 #13673
1813319,1813321 #13674
1813367,1813369 #13675
1813739,1813741 #13676
1813937,1813939 #13677
1813991,1813993 #13678
1814117,1814119 #13679
1814381,1814383 #13680
1814429,1814431 #13681
1814507,1814509 #13682
1814609,1814611 #13683
1814639,1814641 #13684
1814651,1814653 #13685
1814807,1814809 #13686
1814819,1814821 #13687
1814927,1814929 #13688
1815101,1815103 #13689
1815221,1815223 #13690
1815269,1815271 #13691
1815347,1815349 #13692
1815557,1815559 #13693
1815629,1815631 #13694
1815731,1815733 #13695
1815839,1815841 #13696
1815881,1815883 #13697
1815941,1815943 #13698
1816187,1816189 #13699
1817267,1817269 #13700
1817279,1817281 #13701
1817447,1817449 #13702
1817687,1817689 #13703
1818077,1818079 #13704
1818107,1818109 #13705
1818161,1818163 #13706
1818407,1818409 #13707
1818527,1818529 #13708
1818977,1818979 #13709
1818989,1818991 #13710
1819061,1819063 #13711
1819271,1819273 #13712
1819709,1819711 #13713
1819757,1819759 #13714
1819841,1819843 #13715
1819847,1819849 #13716
1819931,1819933 #13717
1820087,1820089 #13718
1820279,1820281 #13719
1820339,1820341 #13720
1820387,1820389 #13721
1820549,1820551 #13722
1820669,1820671 #13723
1820699,1820701 #13724
1821137,1821139 #13725
1821371,1821373 #13726
1821551,1821553 #13727
1821707,1821709 #13728
1821731,1821733 #13729
1822019,1822021 #13730
1822187,1822189 #13731
1822319,1822321 #13732
1822391,1822393 #13733
1822439,1822441 #13734
1822547,1822549 #13735
1822661,1822663 #13736
1823009,1823011 #13737
1823051,1823053 #13738
1823117,1823119 #13739
1823189,1823191 #13740
1823291,1823293 #13741
1823429,1823431 #13742
1823531,1823533 #13743
1823579,1823581 #13744
1823669,1823671 #13745
1823681,1823683 #13746
1823999,1824001 #13747
1824167,1824169 #13748
1824269,1824271 #13749
1824371,1824373 #13750
1824461,1824463 #13751
1824479,1824481 #13752
1824677,1824679 #13753
1824827,1824829 #13754
1824839,1824841 #13755
1824857,1824859 #13756
1824917,1824919 #13757
1824971,1824973 #13758
1825079,1825081 #13759
1825139,1825141 #13760
1825331,1825333 #13761
1825379,1825381 #13762
1825457,1825459 #13763
1826171,1826173 #13764
1826519,1826521 #13765
1826609,1826611 #13766
1826687,1826689 #13767
1826897,1826899 #13768
1827101,1827103 #13769
1827179,1827181 #13770
1827227,1827229 #13771
1827269,1827271 #13772
1827731,1827733 #13773
1828271,1828273 #13774
1828301,1828303 #13775
1828397,1828399 #13776
1828499,1828501 #13777
1828667,1828669 #13778
1828829,1828831 #13779
1828901,1828903 #13780
1829141,1829143 #13781
1829549,1829551 #13782
1829621,1829623 #13783
1829699,1829701 #13784
1829801,1829803 #13785
1830011,1830013 #13786
1830077,1830079 #13787
1830341,1830343 #13788
1830347,1830349 #13789
1830419,1830421 #13790
1830557,1830559 #13791
1830887,1830889 #13792
1831001,1831003 #13793
1831127,1831129 #13794
1831169,1831171 #13795
1831481,1831483 #13796
1831589,1831591 #13797
1831679,1831681 #13798
1831967,1831969 #13799
1832177,1832179 #13800
1832219,1832221 #13801
1832291,1832293 #13802
1832459,1832461 #13803
1832861,1832863 #13804
1833257,1833259 #13805
1833317,1833319 #13806
1833341,1833343 #13807
1833437,1833439 #13808
1833521,1833523 #13809
1833527,1833529 #13810
1833677,1833679 #13811
1833749,1833751 #13812
1833761,1833763 #13813
1834031,1834033 #13814
1834037,1834039 #13815
1834067,1834069 #13816
1834109,1834111 #13817
1834139,1834141 #13818
1834307,1834309 #13819
1834601,1834603 #13820
1834667,1834669 #13821
1834751,1834753 #13822
1834907,1834909 #13823
1834967,1834969 #13824
1834991,1834993 #13825
1835081,1835083 #13826
1835129,1835131 #13827
1835297,1835299 #13828
1835399,1835401 #13829
1835411,1835413 #13830
1835591,1835593 #13831
1835861,1835863 #13832
1835921,1835923 #13833
1836059,1836061 #13834
1836299,1836301 #13835
1836449,1836451 #13836
1836689,1836691 #13837
1836761,1836763 #13838
1836929,1836931 #13839
1836971,1836973 #13840
1837007,1837009 #13841
1837271,1837273 #13842
1837391,1837393 #13843
1837397,1837399 #13844
1837727,1837729 #13845
1837739,1837741 #13846
1838141,1838143 #13847
1838297,1838299 #13848
1838519,1838521 #13849
1838717,1838719 #13850
1838741,1838743 #13851
1838909,1838911 #13852
1838987,1838989 #13853
1838999,1839001 #13854
1839359,1839361 #13855
1839491,1839493 #13856
1839767,1839769 #13857
1839911,1839913 #13858
1839947,1839949 #13859
1840049,1840051 #13860
1840259,1840261 #13861
1840457,1840459 #13862
1840649,1840651 #13863
1841069,1841071 #13864
1841087,1841089 #13865
1841111,1841113 #13866
1841249,1841251 #13867
1841291,1841293 #13868
1841639,1841641 #13869
1841657,1841659 #13870
1841699,1841701 #13871
1841711,1841713 #13872
1842131,1842133 #13873
1842287,1842289 #13874
1842479,1842481 #13875
1842767,1842769 #13876
1842779,1842781 #13877
1842809,1842811 #13878
1842887,1842889 #13879
1842899,1842901 #13880
1843139,1843141 #13881
1843421,1843423 #13882
1843487,1843489 #13883
1843547,1843549 #13884
1843997,1843999 #13885
1844567,1844569 #13886
1844681,1844683 #13887
1844747,1844749 #13888
1845047,1845049 #13889
1845209,1845211 #13890
1845419,1845421 #13891
1845539,1845541 #13892
1845581,1845583 #13893
1845719,1845721 #13894
1845827,1845829 #13895
1846331,1846333 #13896
1846847,1846849 #13897
1847357,1847359 #13898
1847471,1847473 #13899
1847537,1847539 #13900
1847687,1847689 #13901
1847777,1847779 #13902
1847861,1847863 #13903
1847969,1847971 #13904
1848029,1848031 #13905
1848167,1848169 #13906
1849049,1849051 #13907
1849187,1849189 #13908
1849229,1849231 #13909
1849271,1849273 #13910
1849511,1849513 #13911
1849577,1849579 #13912
1849721,1849723 #13913
1849829,1849831 #13914
1849847,1849849 #13915
1849919,1849921 #13916
1850129,1850131 #13917
1850267,1850269 #13918
1850489,1850491 #13919
1850687,1850689 #13920
1850837,1850839 #13921
1850939,1850941 #13922
1851299,1851301 #13923
1851371,1851373 #13924
1851401,1851403 #13925
1851539,1851541 #13926
1851557,1851559 #13927
1851761,1851763 #13928
1851779,1851781 #13929
1851917,1851919 #13930
1852049,1852051 #13931
1852241,1852243 #13932
1852271,1852273 #13933
1852427,1852429 #13934
1852679,1852681 #13935
1852817,1852819 #13936
1853081,1853083 #13937
1853207,1853209 #13938
1853669,1853671 #13939
1853711,1853713 #13940
1853807,1853809 #13941
1854269,1854271 #13942
1854407,1854409 #13943
1854527,1854529 #13944
1854659,1854661 #13945
1854701,1854703 #13946
1854779,1854781 #13947
1854791,1854793 #13948
1855031,1855033 #13949
1855097,1855099 #13950
1855169,1855171 #13951
1855421,1855423 #13952
1855517,1855519 #13953
1855589,1855591 #13954
1855757,1855759 #13955
1855811,1855813 #13956
1855949,1855951 #13957
1855979,1855981 #13958
1856147,1856149 #13959
1856441,1856443 #13960
1856819,1856821 #13961
1856969,1856971 #13962
1856999,1857001 #13963
1857281,1857283 #13964
1857671,1857673 #13965
1857677,1857679 #13966
1857929,1857931 #13967
1858091,1858093 #13968
1858187,1858189 #13969
1858529,1858531 #13970
1858691,1858693 #13971
1858739,1858741 #13972
1858889,1858891 #13973
1858919,1858921 #13974
1859201,1859203 #13975
1859279,1859281 #13976
1859327,1859329 #13977
1859489,1859491 #13978
1859519,1859521 #13979
1859651,1859653 #13980
1860179,1860181 #13981
1860251,1860253 #13982
1860569,1860571 #13983
1860581,1860583 #13984
1860641,1860643 #13985
1860707,1860709 #13986
1860851,1860853 #13987
1860977,1860979 #13988
1861019,1861021 #13989
1861337,1861339 #13990
1861469,1861471 #13991
1861589,1861591 #13992
1861661,1861663 #13993
1861709,1861711 #13994
1861757,1861759 #13995
1861859,1861861 #13996
1862219,1862221 #13997
1862249,1862251 #13998
1862381,1862383 #13999
1862519,1862521 #14000
1862591,1862593 #14001
1862981,1862983 #14002
1863089,1863091 #14003
1863269,1863271 #14004
1863401,1863403 #14005
1863479,1863481 #14006
1863581,1863583 #14007
1863647,1863649 #14008
1864001,1864003 #14009
1864151,1864153 #14010
1864361,1864363 #14011
1864547,1864549 #14012
1864589,1864591 #14013
1864691,1864693 #14014
1864859,1864861 #14015
1864871,1864873 #14016
1865159,1865161 #14017
1865261,1865263 #14018
1865327,1865329 #14019
1865417,1865419 #14020
1865489,1865491 #14021
1865837,1865839 #14022
1865957,1865959 #14023
1865999,1866001 #14024
1866281,1866283 #14025
1866341,1866343 #14026
1866437,1866439 #14027
1866677,1866679 #14028
1866857,1866859 #14029
1866869,1866871 #14030
1866971,1866973 #14031
1867001,1867003 #14032
1867211,1867213 #14033
1867319,1867321 #14034
1867421,1867423 #14035
1867709,1867711 #14036
1867727,1867729 #14037
1867751,1867753 #14038
1867769,1867771 #14039
1867847,1867849 #14040
1867949,1867951 #14041
1868057,1868059 #14042
1868567,1868569 #14043
1868639,1868641 #14044
1868717,1868719 #14045
1868747,1868749 #14046
1868987,1868989 #14047
1869071,1869073 #14048
1869191,1869193 #14049
1870019,1870021 #14050
1870247,1870249 #14051
1870667,1870669 #14052
1870709,1870711 #14053
1870859,1870861 #14054
1871081,1871083 #14055
1871447,1871449 #14056
1871459,1871461 #14057
1871627,1871629 #14058
1871711,1871713 #14059
1871927,1871929 #14060
1871981,1871983 #14061
1872287,1872289 #14062
1872419,1872421 #14063
1872461,1872463 #14064
1872587,1872589 #14065
1873019,1873021 #14066
1873217,1873219 #14067
1873409,1873411 #14068
1873679,1873681 #14069
1873769,1873771 #14070
1873967,1873969 #14071
1874099,1874101 #14072
1874207,1874209 #14073
1874261,1874263 #14074
1874441,1874443 #14075
1874627,1874629 #14076
1874657,1874659 #14077
1874837,1874839 #14078
1874921,1874923 #14079
1875059,1875061 #14080
1875161,1875163 #14081
1875239,1875241 #14082
1875371,1875373 #14083
1875449,1875451 #14084
1875479,1875481 #14085
1876181,1876183 #14086
1876247,1876249 #14087
1876289,1876291 #14088
1876331,1876333 #14089
1876451,1876453 #14090
1876517,1876519 #14091
1876949,1876951 #14092
1877009,1877011 #14093
1877177,1877179 #14094
1877231,1877233 #14095
1877297,1877299 #14096
1877399,1877401 #14097
1877459,1877461 #14098
1877501,1877503 #14099
1877669,1877671 #14100
1878047,1878049 #14101
1878059,1878061 #14102
1878089,1878091 #14103
1878221,1878223 #14104
1878419,1878421 #14105
1878491,1878493 #14106
1878557,1878559 #14107
1878839,1878841 #14108
1878887,1878889 #14109
1878911,1878913 #14110
1878977,1878979 #14111
1879067,1879069 #14112
1879847,1879849 #14113
1879937,1879939 #14114
1880321,1880323 #14115
1880339,1880341 #14116
1880831,1880833 #14117
1880939,1880941 #14118
1881161,1881163 #14119
1881197,1881199 #14120
1881221,1881223 #14121
1881389,1881391 #14122
1881401,1881403 #14123
1881461,1881463 #14124
1881617,1881619 #14125
1881749,1881751 #14126
1881767,1881769 #14127
1881821,1881823 #14128
1881851,1881853 #14129
1882037,1882039 #14130
1882169,1882171 #14131
1882367,1882369 #14132
1882457,1882459 #14133
1882469,1882471 #14134
1883051,1883053 #14135
1883381,1883383 #14136
1883501,1883503 #14137
1883669,1883671 #14138
1883879,1883881 #14139
1883939,1883941 #14140
1883969,1883971 #14141
1884011,1884013 #14142
1884119,1884121 #14143
1884341,1884343 #14144
1884479,1884481 #14145
1884527,1884529 #14146
1884599,1884601 #14147
1884677,1884679 #14148
1884791,1884793 #14149
1884887,1884889 #14150
1885151,1885153 #14151
1885307,1885309 #14152
1885391,1885393 #14153
1885601,1885603 #14154
1885907,1885909 #14155
1885979,1885981 #14156
1885991,1885993 #14157
1886231,1886233 #14158
1886327,1886329 #14159
1886411,1886413 #14160
1886447,1886449 #14161
1886657,1886659 #14162
1886699,1886701 #14163
1886867,1886869 #14164
1887131,1887133 #14165
1887167,1887169 #14166
1887209,1887211 #14167
1887419,1887421 #14168
1887617,1887619 #14169
1888121,1888123 #14170
1888169,1888171 #14171
1888349,1888351 #14172
1888559,1888561 #14173
1888979,1888981 #14174
1889009,1889011 #14175
1889051,1889053 #14176
1889099,1889101 #14177
1889219,1889221 #14178
1889309,1889311 #14179
1889387,1889389 #14180
1889399,1889401 #14181
1889651,1889653 #14182
1889801,1889803 #14183
1890401,1890403 #14184
1890521,1890523 #14185
1890527,1890529 #14186
1890599,1890601 #14187
1890641,1890643 #14188
1891187,1891189 #14189
1891499,1891501 #14190
1891661,1891663 #14191
1891859,1891861 #14192
1891907,1891909 #14193
1891949,1891951 #14194
1892309,1892311 #14195
1892699,1892701 #14196
1892771,1892773 #14197
1893191,1893193 #14198
1893209,1893211 #14199
1893347,1893349 #14200
1893371,1893373 #14201
1893467,1893469 #14202
1893587,1893589 #14203
1893779,1893781 #14204
1893971,1893973 #14205
1894001,1894003 #14206
1894049,1894051 #14207
1894337,1894339 #14208
1894601,1894603 #14209
1894727,1894729 #14210
1894931,1894933 #14211
1895009,1895011 #14212
1895081,1895083 #14213
1895189,1895191 #14214
1895261,1895263 #14215
1895357,1895359 #14216
1895711,1895713 #14217
1896017,1896019 #14218
1896149,1896151 #14219
1896227,1896229 #14220
1896527,1896529 #14221
1896887,1896889 #14222
1896899,1896901 #14223
1896989,1896991 #14224
1897097,1897099 #14225
1897139,1897141 #14226
1897277,1897279 #14227
1897667,1897669 #14228
1898009,1898011 #14229
1898051,1898053 #14230
1898417,1898419 #14231
1898591,1898593 #14232
1898759,1898761 #14233
1898861,1898863 #14234
1899047,1899049 #14235
1899197,1899199 #14236
1899341,1899343 #14237
1899419,1899421 #14238
1899509,1899511 #14239
1899659,1899661 #14240
1900487,1900489 #14241
1900499,1900501 #14242
1900529,1900531 #14243
1900541,1900543 #14244
1900607,1900609 #14245
1900709,1900711 #14246
1901087,1901089 #14247
1901357,1901359 #14248
1901369,1901371 #14249
1901717,1901719 #14250
1901831,1901833 #14251
1901897,1901899 #14252
1902287,1902289 #14253
1902389,1902391 #14254
1902611,1902613 #14255
1902617,1902619 #14256
1902881,1902883 #14257
1903061,1903063 #14258
1903379,1903381 #14259
1903511,1903513 #14260
1903787,1903789 #14261
1903859,1903861 #14262
1904027,1904029 #14263
1904471,1904473 #14264
1904477,1904479 #14265
1904519,1904521 #14266
1904531,1904533 #14267
1904939,1904941 #14268
1905179,1905181 #14269
1905359,1905361 #14270
1905689,1905691 #14271
1905779,1905781 #14272
1906241,1906243 #14273
1906379,1906381 #14274
1906391,1906393 #14275
1906691,1906693 #14276
1906829,1906831 #14277
1907231,1907233 #14278
1907369,1907371 #14279
1907447,1907449 #14280
1907471,1907473 #14281
1907747,1907749 #14282
1907861,1907863 #14283
1907909,1907911 #14284
1907987,1907989 #14285
1908041,1908043 #14286
1908089,1908091 #14287
1908167,1908169 #14288
1908449,1908451 #14289
1908521,1908523 #14290
1908659,1908661 #14291
1908869,1908871 #14292
1909079,1909081 #14293
1909109,1909111 #14294
1909307,1909309 #14295
1909487,1909489 #14296
1909799,1909801 #14297
1909907,1909909 #14298
1909949,1909951 #14299
1910177,1910179 #14300
1910261,1910263 #14301
1910267,1910269 #14302
1910399,1910401 #14303
1911029,1911031 #14304
1911101,1911103 #14305
1911209,1911211 #14306
1911251,1911253 #14307
1911317,1911319 #14308
1911617,1911619 #14309
1911671,1911673 #14310
1911839,1911841 #14311
1912061,1912063 #14312
1912067,1912069 #14313
1912451,1912453 #14314
1912457,1912459 #14315
1912487,1912489 #14316
1912529,1912531 #14317
1912541,1912543 #14318
1912679,1912681 #14319
1912739,1912741 #14320
1912829,1912831 #14321
1912919,1912921 #14322
1912949,1912951 #14323
1913291,1913293 #14324
1913831,1913833 #14325
1913939,1913941 #14326
1913957,1913959 #14327
1913999,1914001 #14328
1914509,1914511 #14329
1914707,1914709 #14330
1914767,1914769 #14331
1914947,1914949 #14332
1914959,1914961 #14333
1915469,1915471 #14334
1915481,1915483 #14335
1915757,1915759 #14336
1915811,1915813 #14337
1915841,1915843 #14338
1915931,1915933 #14339
1915937,1915939 #14340
1916021,1916023 #14341
1916249,1916251 #14342
1916279,1916281 #14343
1916309,1916311 #14344
1916351,1916353 #14345
1916687,1916689 #14346
1916729,1916731 #14347
1916951,1916953 #14348
1917077,1917079 #14349
1917341,1917343 #14350
1917521,1917523 #14351
1917569,1917571 #14352
1917731,1917733 #14353
1917737,1917739 #14354
1917959,1917961 #14355
1918517,1918519 #14356
1918769,1918771 #14357
1918919,1918921 #14358
1919039,1919041 #14359
1919297,1919299 #14360
1919429,1919431 #14361
1919459,1919461 #14362
1920011,1920013 #14363
1920221,1920223 #14364
1920377,1920379 #14365
1920599,1920601 #14366
1920911,1920913 #14367
1921481,1921483 #14368
1921529,1921531 #14369
1921691,1921693 #14370
1921769,1921771 #14371
1921847,1921849 #14372
1921919,1921921 #14373
1922351,1922353 #14374
1922561,1922563 #14375
1922771,1922773 #14376
1923107,1923109 #14377
1923137,1923139 #14378
1923167,1923169 #14379
1923401,1923403 #14380
1923611,1923613 #14381
1923707,1923709 #14382
1923749,1923751 #14383
1923791,1923793 #14384
1923869,1923871 #14385
1923989,1923991 #14386
1924031,1924033 #14387
1924079,1924081 #14388
1924289,1924291 #14389
1924457,1924459 #14390
1924649,1924651 #14391
1924751,1924753 #14392
1925039,1925041 #14393
1925057,1925059 #14394
1925177,1925179 #14395
1925321,1925323 #14396
1925381,1925383 #14397
1925387,1925389 #14398
1925459,1925461 #14399
1925507,1925509 #14400
1925531,1925533 #14401
1925717,1925719 #14402
1925837,1925839 #14403
1926077,1926079 #14404
1926341,1926343 #14405
1926359,1926361 #14406
1926437,1926439 #14407
1926521,1926523 #14408
1926569,1926571 #14409
1926647,1926649 #14410
1927031,1927033 #14411
1927109,1927111 #14412
1927349,1927351 #14413
1927397,1927399 #14414
1927481,1927483 #14415
1927571,1927573 #14416
1927631,1927633 #14417
1927691,1927693 #14418
1927901,1927903 #14419
1927967,1927969 #14420
1928321,1928323 #14421
1928369,1928371 #14422
1928447,1928449 #14423
1928567,1928569 #14424
1928621,1928623 #14425
1928741,1928743 #14426
1928807,1928809 #14427
1928957,1928959 #14428
1929047,1929049 #14429
1929071,1929073 #14430
1929119,1929121 #14431
1929197,1929199 #14432
1929227,1929229 #14433
1929287,1929289 #14434
1929329,1929331 #14435
1929647,1929649 #14436
1929749,1929751 #14437
1929839,1929841 #14438
1929869,1929871 #14439
1929971,1929973 #14440
1930079,1930081 #14441
1930259,1930261 #14442
1930307,1930309 #14443
1930349,1930351 #14444
1930427,1930429 #14445
1930517,1930519 #14446
1930541,1930543 #14447
1930937,1930939 #14448
1930961,1930963 #14449
1931051,1931053 #14450
1931297,1931299 #14451
1931339,1931341 #14452
1931381,1931383 #14453
1931537,1931539 #14454
1931771,1931773 #14455
1931819,1931821 #14456
1931987,1931989 #14457
1932059,1932061 #14458
1932107,1932109 #14459
1932839,1932841 #14460
1932869,1932871 #14461
1932947,1932949 #14462
1933469,1933471 #14463
1933511,1933513 #14464
1933661,1933663 #14465
1933781,1933783 #14466
1933859,1933861 #14467
1934297,1934299 #14468
1934417,1934419 #14469
1934519,1934521 #14470
1934627,1934629 #14471
1934687,1934689 #14472
1935047,1935049 #14473
1935251,1935253 #14474
1935341,1935343 #14475
1936397,1936399 #14476
1936631,1936633 #14477
1936721,1936723 #14478
1936817,1936819 #14479
1937057,1937059 #14480
1937489,1937491 #14481
1937657,1937659 #14482
1937729,1937731 #14483
1937939,1937941 #14484
1937987,1937989 #14485
1938071,1938073 #14486
1938161,1938163 #14487
1938197,1938199 #14488
1938269,1938271 #14489
1938449,1938451 #14490
1938887,1938889 #14491
1938971,1938973 #14492
1939541,1939543 #14493
1939571,1939573 #14494
1939631,1939633 #14495
1939937,1939939 #14496
1939967,1939969 #14497
1940219,1940221 #14498
1940399,1940401 #14499
1940597,1940599 #14500
1940711,1940713 #14501
1940747,1940749 #14502
1940777,1940779 #14503
1941089,1941091 #14504
1941101,1941103 #14505
1941257,1941259 #14506
1941419,1941421 #14507
1941479,1941481 #14508
1941557,1941559 #14509
1941671,1941673 #14510
1942139,1942141 #14511
1942151,1942153 #14512
1942307,1942309 #14513
1942319,1942321 #14514
1942361,1942363 #14515
1942481,1942483 #14516
1942727,1942729 #14517
1942751,1942753 #14518
1943021,1943023 #14519
1943237,1943239 #14520
1943411,1943413 #14521
1943531,1943533 #14522
1943651,1943653 #14523
1943657,1943659 #14524
1943861,1943863 #14525
1944011,1944013 #14526
1944377,1944379 #14527
1944779,1944781 #14528
1944797,1944799 #14529
1944881,1944883 #14530
1945091,1945093 #14531
1945301,1945303 #14532
1945607,1945609 #14533
1945649,1945651 #14534
1945709,1945711 #14535
1946171,1946173 #14536
1946207,1946209 #14537
1946297,1946299 #14538
1946471,1946473 #14539
1946561,1946563 #14540
1946627,1946629 #14541
1946669,1946671 #14542
1946699,1946701 #14543
1947107,1947109 #14544
1947149,1947151 #14545
1947227,1947229 #14546
1947497,1947499 #14547
1947731,1947733 #14548
1947851,1947853 #14549
1947971,1947973 #14550
1947989,1947991 #14551
1948097,1948099 #14552
1948229,1948231 #14553
1948517,1948519 #14554
1948601,1948603 #14555
1948799,1948801 #14556
1948907,1948909 #14557
1949111,1949113 #14558
1949357,1949359 #14559
1949471,1949473 #14560
1949579,1949581 #14561
1949819,1949821 #14562
1950071,1950073 #14563
1950269,1950271 #14564
1950761,1950763 #14565
1951049,1951051 #14566
1951097,1951099 #14567
1951457,1951459 #14568
1951601,1951603 #14569
1951949,1951951 #14570
1952021,1952023 #14571
1952087,1952089 #14572
1952129,1952131 #14573
1952219,1952221 #14574
1952477,1952479 #14575
1953041,1953043 #14576
1953491,1953493 #14577
1953557,1953559 #14578
1953821,1953823 #14579
1954151,1954153 #14580
1954157,1954159 #14581
1954289,1954291 #14582
1954361,1954363 #14583
1954367,1954369 #14584
1954487,1954489 #14585
1955279,1955281 #14586
1955489,1955491 #14587
1955507,1955509 #14588
1955531,1955533 #14589
1955771,1955773 #14590
1955957,1955959 #14591
1956047,1956049 #14592
1956089,1956091 #14593
1956287,1956289 #14594
1956431,1956433 #14595
1956527,1956529 #14596
1956611,1956613 #14597
1956761,1956763 #14598
1956881,1956883 #14599
1957049,1957051 #14600
1957097,1957099 #14601
1957301,1957303 #14602
1957517,1957519 #14603
1957799,1957801 #14604
1957847,1957849 #14605
1957859,1957861 #14606
1957937,1957939 #14607
1957997,1957999 #14608
1958639,1958641 #14609
1958681,1958683 #14610
1958897,1958899 #14611
1959017,1959019 #14612
1959149,1959151 #14613
1959239,1959241 #14614
1959311,1959313 #14615
1959317,1959319 #14616
1959521,1959523 #14617
1959647,1959649 #14618
1959719,1959721 #14619
1959941,1959943 #14620
1960199,1960201 #14621
1960289,1960291 #14622
1960529,1960531 #14623
1960769,1960771 #14624
1960787,1960789 #14625
1960877,1960879 #14626
1960919,1960921 #14627
1960991,1960993 #14628
1961129,1961131 #14629
1961249,1961251 #14630
1961327,1961329 #14631
1961411,1961413 #14632
1961549,1961551 #14633
1961651,1961653 #14634
1961669,1961671 #14635
1962011,1962013 #14636
1962209,1962211 #14637
1962449,1962451 #14638
1962809,1962811 #14639
1962941,1962943 #14640
1963319,1963321 #14641
1963457,1963459 #14642
1963469,1963471 #14643
1963691,1963693 #14644
1963811,1963813 #14645
1964117,1964119 #14646
1964789,1964791 #14647
1964981,1964983 #14648
1965389,1965391 #14649
1965449,1965451 #14650
1965461,1965463 #14651
1965629,1965631 #14652
1965641,1965643 #14653
1965851,1965853 #14654
1966007,1966009 #14655
1966301,1966303 #14656
1966397,1966399 #14657
1966427,1966429 #14658
1966667,1966669 #14659
1966817,1966819 #14660
1966841,1966843 #14661
1966871,1966873 #14662
1966931,1966933 #14663
1967261,1967263 #14664
1967297,1967299 #14665
1967417,1967419 #14666
1967891,1967893 #14667
1968017,1968019 #14668
1968059,1968061 #14669
1968137,1968139 #14670
1968359,1968361 #14671
1968401,1968403 #14672
1968539,1968541 #14673
1968611,1968613 #14674
1968749,1968751 #14675
1968977,1968979 #14676
1969181,1969183 #14677
1969829,1969831 #14678
1969967,1969969 #14679
1970261,1970263 #14680
1970429,1970431 #14681
1970459,1970461 #14682
1970597,1970599 #14683
1970627,1970629 #14684
1970711,1970713 #14685
1970921,1970923 #14686
1970957,1970959 #14687
1971251,1971253 #14688
1971467,1971469 #14689
1971479,1971481 #14690
1971707,1971709 #14691
1971887,1971889 #14692
1972097,1972099 #14693
1972121,1972123 #14694
1972247,1972249 #14695
1972379,1972381 #14696
1972589,1972591 #14697
1972739,1972741 #14698
1972847,1972849 #14699
1972889,1972891 #14700
1973051,1973053 #14701
1973297,1973299 #14702
1973507,1973509 #14703
1973687,1973689 #14704
1973747,1973749 #14705
1974647,1974649 #14706
1974779,1974781 #14707
1974881,1974883 #14708
1975019,1975021 #14709
1975121,1975123 #14710
1975199,1975201 #14711
1975691,1975693 #14712
1975817,1975819 #14713
1975931,1975933 #14714
1976069,1976071 #14715
1976729,1976731 #14716
1976747,1976749 #14717
1976759,1976761 #14718
1976789,1976791 #14719
1976927,1976929 #14720
1976939,1976941 #14721
1977089,1977091 #14722
1977359,1977361 #14723
1977719,1977721 #14724
1977749,1977751 #14725
1977821,1977823 #14726
1978157,1978159 #14727
1978199,1978201 #14728
1978421,1978423 #14729
1978439,1978441 #14730
1978589,1978591 #14731
1978661,1978663 #14732
1979051,1979053 #14733
1979141,1979143 #14734
1979147,1979149 #14735
1979207,1979209 #14736
1979321,1979323 #14737
1979489,1979491 #14738
1979891,1979893 #14739
1979897,1979899 #14740
1980029,1980031 #14741
1980101,1980103 #14742
1980227,1980229 #14743
1980281,1980283 #14744
1980521,1980523 #14745
1980659,1980661 #14746
1980701,1980703 #14747
1980761,1980763 #14748
1980947,1980949 #14749
1981619,1981621 #14750
1981667,1981669 #14751
1981919,1981921 #14752
1982291,1982293 #14753
1982609,1982611 #14754
1982639,1982641 #14755
1982837,1982839 #14756
1982879,1982881 #14757
1982987,1982989 #14758
1983227,1983229 #14759
1983341,1983343 #14760
1983437,1983439 #14761
1983491,1983493 #14762
1983599,1983601 #14763
1983647,1983649 #14764
1983851,1983853 #14765
1983929,1983931 #14766
1984181,1984183 #14767
1984259,1984261 #14768
1984361,1984363 #14769
1984397,1984399 #14770
1984457,1984459 #14771
1984709,1984711 #14772
1984727,1984729 #14773
1984979,1984981 #14774
1985237,1985239 #14775
1985591,1985593 #14776
1985741,1985743 #14777
1985987,1985989 #14778
1986167,1986169 #14779
1986497,1986499 #14780
1986539,1986541 #14781
1986629,1986631 #14782
1986779,1986781 #14783
1986869,1986871 #14784
1986989,1986991 #14785
1987121,1987123 #14786
1987481,1987483 #14787
1987547,1987549 #14788
1987619,1987621 #14789
1987679,1987681 #14790
1987889,1987891 #14791
1988087,1988089 #14792
1988219,1988221 #14793
1988249,1988251 #14794
1988297,1988299 #14795
1988339,1988341 #14796
1988531,1988533 #14797
1988549,1988551 #14798
1988561,1988563 #14799
1988669,1988671 #14800
1988837,1988839 #14801
1989131,1989133 #14802
1989551,1989553 #14803
1989959,1989961 #14804
1990031,1990033 #14805
1990187,1990189 #14806
1990277,1990279 #14807
1990319,1990321 #14808
1990379,1990381 #14809
1990577,1990579 #14810
1990691,1990693 #14811
1990829,1990831 #14812
1991279,1991281 #14813
1991357,1991359 #14814
1991387,1991389 #14815
1991489,1991491 #14816
1991861,1991863 #14817
1991879,1991881 #14818
1992257,1992259 #14819
1992407,1992409 #14820
1992437,1992439 #14821
1992761,1992763 #14822
1992839,1992841 #14823
1992917,1992919 #14824
1993037,1993039 #14825
1993217,1993219 #14826
1993259,1993261 #14827
1993529,1993531 #14828
1993601,1993603 #14829
1993631,1993633 #14830
1993679,1993681 #14831
1993697,1993699 #14832
1993757,1993759 #14833
1993931,1993933 #14834
1994051,1994053 #14835
1994339,1994341 #14836
1994477,1994479 #14837
1994519,1994521 #14838
1994567,1994569 #14839
1994621,1994623 #14840
1994777,1994779 #14841
1995011,1995013 #14842
1995107,1995109 #14843
1995221,1995223 #14844
1995527,1995529 #14845
1995689,1995691 #14846
1995977,1995979 #14847
1995989,1995991 #14848
1996217,1996219 #14849
1996277,1996279 #14850
1996301,1996303 #14851
1996721,1996723 #14852
1996901,1996903 #14853
1997057,1997059 #14854
1997087,1997089 #14855
1997267,1997269 #14856
1997339,1997341 #14857
1997771,1997773 #14858
1998107,1998109 #14859
1998221,1998223 #14860
1998329,1998331 #14861
1998341,1998343 #14862
1998587,1998589 #14863
1998641,1998643 #14864
1998947,1998949 #14865
1999301,1999303 #14866
1999511,1999513 #14867
1999559,1999561 #14868
1999631,1999633 #14869
1999817,1999819 #14870
1999889,1999891 #14871
2000081,2000083 #14872
2000291,2000293 #14873
2000351,2000353 #14874
2000387,2000389 #14875
2000519,2000521 #14876
2000939,2000941 #14877
2001407,2001409 #14878
2001449,2001451 #14879
2001509,2001511 #14880
2001539,2001541 #14881
2001581,2001583 #14882
2001617,2001619 #14883
2002157,2002159 #14884
2002331,2002333 #14885
2002337,2002339 #14886
2002577,2002579 #14887
2002667,2002669 #14888
2002937,2002939 #14889
2002967,2002969 #14890
2003009,2003011 #14891
2003081,2003083 #14892
2003591,2003593 #14893
2003801,2003803 #14894
2003861,2003863 #14895
2003999,2004001 #14896
2004131,2004133 #14897
2004269,2004271 #14898
2004347,2004349 #14899
2004461,2004463 #14900
2004809,2004811 #14901
2005019,2005021 #14902
2005037,2005039 #14903
2005181,2005183 #14904
2005229,2005231 #14905
2005427,2005429 #14906
2005877,2005879 #14907
2006297,2006299 #14908
2006339,2006341 #14909
2006441,2006443 #14910
2006489,2006491 #14911
2006657,2006659 #14912
2006897,2006899 #14913
2007011,2007013 #14914
2007077,2007079 #14915
2007149,2007151 #14916
2007389,2007391 #14917
2007431,2007433 #14918
2007491,2007493 #14919
2007611,2007613 #14920
2007617,2007619 #14921
2007659,2007661 #14922
2007701,2007703 #14923
2007767,2007769 #14924
2007869,2007871 #14925
2007881,2007883 #14926
2007911,2007913 #14927
2007917,2007919 #14928
2007959,2007961 #14929
2008049,2008051 #14930
2008079,2008081 #14931
2008439,2008441 #14932
2008481,2008483 #14933
2009171,2009173 #14934
2009867,2009869 #14935
2009879,2009881 #14936
2009921,2009923 #14937
2009981,2009983 #14938
2010137,2010139 #14939
2010581,2010583 #14940
2010971,2010973 #14941
2011019,2011021 #14942
2011127,2011129 #14943
2011199,2011201 #14944
2011391,2011393 #14945
2011439,2011441 #14946
2011697,2011699 #14947
2012009,2012011 #14948
2012159,2012161 #14949
2012447,2012449 #14950
2012531,2012533 #14951
2012639,2012641 #14952
2012711,2012713 #14953
2012741,2012743 #14954
2012819,2012821 #14955
2013227,2013229 #14956
2013287,2013289 #14957
2013299,2013301 #14958
2013617,2013619 #14959
2013707,2013709 #14960
2013749,2013751 #14961
2014097,2014099 #14962
2014139,2014141 #14963
2014217,2014219 #14964
2014301,2014303 #14965
2014457,2014459 #14966
2014799,2014801 #14967
2014811,2014813 #14968
2014919,2014921 #14969
2015087,2015089 #14970
2015177,2015179 #14971
2015201,2015203 #14972
2015267,2015269 #14973
2015441,2015443 #14974
2015777,2015779 #14975
2015831,2015833 #14976
2015861,2015863 #14977
2016029,2016031 #14978
2016137,2016139 #14979
2016197,2016199 #14980
2016359,2016361 #14981
2016401,2016403 #14982
2016407,2016409 #14983
2016671,2016673 #14984
2016821,2016823 #14985
2016851,2016853 #14986
2017187,2017189 #14987
2017469,2017471 #14988
2017709,2017711 #14989
2017751,2017753 #14990
2018111,2018113 #14991
2018171,2018173 #14992
2018249,2018251 #14993
2018381,2018383 #14994
2018591,2018593 #14995
2018747,2018749 #14996
2018897,2018899 #14997
2019011,2019013 #14998
2019131,2019133 #14999
2019401,2019403 #15000
2019461,2019463 #15001
2019707,2019709 #15002
2019767,2019769 #15003
2020001,2020003 #15004
2020391,2020393 #15005
2020409,2020411 #15006
2020661,2020663 #15007
2020721,2020723 #15008
2020727,2020729 #15009
2020817,2020819 #15010
2021081,2021083 #15011
2021597,2021599 #15012
2021627,2021629 #15013
2021651,2021653 #15014
2021777,2021779 #15015
2021837,2021839 #15016
2022017,2022019 #15017
2022047,2022049 #15018
2022101,2022103 #15019
2022281,2022283 #15020
2022329,2022331 #15021
2022401,2022403 #15022
2022617,2022619 #15023
2022659,2022661 #15024
2022749,2022751 #15025
2022989,2022991 #15026
2023157,2023159 #15027
2023529,2023531 #15028
2023577,2023579 #15029
2023829,2023831 #15030
2023841,2023843 #15031
2024177,2024179 #15032
2024219,2024221 #15033
2024261,2024263 #15034
2024327,2024329 #15035
2024369,2024371 #15036
2024417,2024419 #15037
2024597,2024599 #15038
2024831,2024833 #15039
2024861,2024863 #15040
2025251,2025253 #15041
2025347,2025349 #15042
2025629,2025631 #15043
2025641,2025643 #15044
2025719,2025721 #15045
2025899,2025901 #15046
2026151,2026153 #15047
2026181,2026183 #15048
2026391,2026393 #15049
2026469,2026471 #15050
2026727,2026729 #15051
2027021,2027023 #15052
2027099,2027101 #15053
2027159,2027161 #15054
2027237,2027239 #15055
2027447,2027449 #15056
2027567,2027569 #15057
2027897,2027899 #15058
2027951,2027953 #15059
2028107,2028109 #15060
2028119,2028121 #15061
2028137,2028139 #15062
2028197,2028199 #15063
2028239,2028241 #15064
2028371,2028373 #15065
2028701,2028703 #15066
2028779,2028781 #15067
2029019,2029021 #15068
2029121,2029123 #15069
2029241,2029243 #15070
2029439,2029441 #15071
2029499,2029501 #15072
2029667,2029669 #15073
2029721,2029723 #15074
2029799,2029801 #15075
2029829,2029831 #15076
2029871,2029873 #15077
2029889,2029891 #15078
2030051,2030053 #15079
2030099,2030101 #15080
2030309,2030311 #15081
2030381,2030383 #15082
2030459,2030461 #15083
2030657,2030659 #15084
2030879,2030881 #15085
2030909,2030911 #15086
2031569,2031571 #15087
2031977,2031979 #15088
2032109,2032111 #15089
2032157,2032159 #15090
2032271,2032273 #15091
2032361,2032363 #15092
2032559,2032561 #15093
2032619,2032621 #15094
2032649,2032651 #15095
2032661,2032663 #15096
2032859,2032861 #15097
2032937,2032939 #15098
2032967,2032969 #15099
2033201,2033203 #15100
2033279,2033281 #15101
2033357,2033359 #15102
2033441,2033443 #15103
2033459,2033461 #15104
2033531,2033533 #15105
2033609,2033611 #15106
2033951,2033953 #15107
2034209,2034211 #15108
2034491,2034493 #15109
2034839,2034841 #15110
2035067,2035069 #15111
2035211,2035213 #15112
2035301,2035303 #15113
2035511,2035513 #15114
2035667,2035669 #15115
2035841,2035843 #15116
2036129,2036131 #15117
2036339,2036341 #15118
2036807,2036809 #15119
2036831,2036833 #15120
2036861,2036863 #15121
2036891,2036893 #15122
2036939,2036941 #15123
2037017,2037019 #15124
2037071,2037073 #15125
2037149,2037151 #15126
2037251,2037253 #15127
2037281,2037283 #15128
2037377,2037379 #15129
2037491,2037493 #15130
2037851,2037853 #15131
2038019,2038021 #15132
2038427,2038429 #15133
2038577,2038579 #15134
2038637,2038639 #15135
2038919,2038921 #15136
2039171,2039173 #15137
2039351,2039353 #15138
2039621,2039623 #15139
2039909,2039911 #15140
2039927,2039929 #15141
2040107,2040109 #15142
2040149,2040151 #15143
2040191,2040193 #15144
2040251,2040253 #15145
2040431,2040433 #15146
2040539,2040541 #15147
2040557,2040559 #15148
2040917,2040919 #15149
2041199,2041201 #15150
2042399,2042401 #15151
2042849,2042851 #15152
2042981,2042983 #15153
2043191,2043193 #15154
2043257,2043259 #15155
2043539,2043541 #15156
2043719,2043721 #15157
2043749,2043751 #15158
2043761,2043763 #15159
2044067,2044069 #15160
2044127,2044129 #15161
2044277,2044279 #15162
2044487,2044489 #15163
2044787,2044789 #15164
2044841,2044843 #15165
2044919,2044921 #15166
2045009,2045011 #15167
2045189,2045191 #15168
2045357,2045359 #15169
2045567,2045569 #15170
2045609,2045611 #15171
2045651,2045653 #15172
2045759,2045761 #15173
2045837,2045839 #15174
2046047,2046049 #15175
2046311,2046313 #15176
2046389,2046391 #15177
2046719,2046721 #15178
2046827,2046829 #15179
2046971,2046973 #15180
2047037,2047039 #15181
2047061,2047063 #15182
2047091,2047093 #15183
2047181,2047183 #15184
2047217,2047219 #15185
2047349,2047351 #15186
2047811,2047813 #15187
2048327,2048329 #15188
2049041,2049043 #15189
2049119,2049121 #15190
2049347,2049349 #15191
2049407,2049409 #15192
2049449,2049451 #15193
2049491,2049493 #15194
2049611,2049613 #15195
2049821,2049823 #15196
2050031,2050033 #15197
2050229,2050231 #15198
2050331,2050333 #15199
2050337,2050339 #15200
2050511,2050513 #15201
2050817,2050819 #15202
2051111,2051113 #15203
2051171,2051173 #15204
2051249,2051251 #15205
2051279,2051281 #15206
2051321,2051323 #15207
2051417,2051419 #15208
2051459,2051461 #15209
2051477,2051479 #15210
2051627,2051629 #15211
2051891,2051893 #15212
2052047,2052049 #15213
2052179,2052181 #15214
2052329,2052331 #15215
2052749,2052751 #15216
2052857,2052859 #15217
2053067,2053069 #15218
2053109,2053111 #15219
2053211,2053213 #15220
2053421,2053423 #15221
2053619,2053621 #15222
2053769,2053771 #15223
2053871,2053873 #15224
2054009,2054011 #15225
2054021,2054023 #15226
2054231,2054233 #15227
2054249,2054251 #15228
2054579,2054581 #15229
2054627,2054629 #15230
2054849,2054851 #15231
2055101,2055103 #15232
2055197,2055199 #15233
2055479,2055481 #15234
2055509,2055511 #15235
2055707,2055709 #15236
2056079,2056081 #15237
2056139,2056141 #15238
2056277,2056279 #15239
2056751,2056753 #15240
2056841,2056843 #15241
2056907,2056909 #15242
2056961,2056963 #15243
2057021,2057023 #15244
2057177,2057179 #15245
2057381,2057383 #15246
2057399,2057401 #15247
2057477,2057479 #15248
2057597,2057599 #15249
2057609,2057611 #15250
2057777,2057779 #15251
2058011,2058013 #15252
2058191,2058193 #15253
2058557,2058559 #15254
2058701,2058703 #15255
2058839,2058841 #15256
2058869,2058871 #15257
2059271,2059273 #15258
2059709,2059711 #15259
2059721,2059723 #15260
2059817,2059819 #15261
2059859,2059861 #15262
2059931,2059933 #15263
2060099,2060101 #15264
2060159,2060161 #15265
2060249,2060251 #15266
2060447,2060449 #15267
2060561,2060563 #15268
2060579,2060581 #15269
2060627,2060629 #15270
2060801,2060803 #15271
2060879,2060881 #15272
2061077,2061079 #15273
2061179,2061181 #15274
2061287,2061289 #15275
2061599,2061601 #15276
2062001,2062003 #15277
2062007,2062009 #15278
2062061,2062063 #15279
2062199,2062201 #15280
2062517,2062519 #15281
2062757,2062759 #15282
2062871,2062873 #15283
2062889,2062891 #15284
2063057,2063059 #15285
2063249,2063251 #15286
2063291,2063293 #15287
2063459,2063461 #15288
2063561,2063563 #15289
2063729,2063731 #15290
2063771,2063773 #15291
2063777,2063779 #15292
2063861,2063863 #15293
2064149,2064151 #15294
2064371,2064373 #15295
2064527,2064529 #15296
2064581,2064583 #15297
2064761,2064763 #15298
2064947,2064949 #15299
2065571,2065573 #15300
2065577,2065579 #15301
2065667,2065669 #15302
2065727,2065729 #15303
2065799,2065801 #15304
2066081,2066083 #15305
2066177,2066179 #15306
2066201,2066203 #15307
2066507,2066509 #15308
2066549,2066551 #15309
2066681,2066683 #15310
2066759,2066761 #15311
2066969,2066971 #15312
2067071,2067073 #15313
2067209,2067211 #15314
2067719,2067721 #15315
2067797,2067799 #15316
2067851,2067853 #15317
2068037,2068039 #15318
2068061,2068063 #15319
2068487,2068489 #15320
2068499,2068501 #15321
2068637,2068639 #15322
2068751,2068753 #15323
2068811,2068813 #15324
2069381,2069383 #15325
2069531,2069533 #15326
2069909,2069911 #15327
2069957,2069959 #15328
2069987,2069989 #15329
2070041,2070043 #15330
2070179,2070181 #15331
2070239,2070241 #15332
2070317,2070319 #15333
2070461,2070463 #15334
2070611,2070613 #15335
2070641,2070643 #15336
2070797,2070799 #15337
2071259,2071261 #15338
2071427,2071429 #15339
2071721,2071723 #15340
2071799,2071801 #15341
2071997,2071999 #15342
2072129,2072131 #15343
2072207,2072209 #15344
2072429,2072431 #15345
2072489,2072491 #15346
2072699,2072701 #15347
2073101,2073103 #15348
2073119,2073121 #15349
2073347,2073349 #15350
2073359,2073361 #15351
2073389,2073391 #15352
2073647,2073649 #15353
2073809,2073811 #15354
2074139,2074141 #15355
2074199,2074201 #15356
2074349,2074351 #15357
2074481,2074483 #15358
2074517,2074519 #15359
2074871,2074873 #15360
2074949,2074951 #15361
2075261,2075263 #15362
2075537,2075539 #15363
2075657,2075659 #15364
2075741,2075743 #15365
2075831,2075833 #15366
2075837,2075839 #15367
2075867,2075869 #15368
2075999,2076001 #15369
2076407,2076409 #15370
2076419,2076421 #15371
2076617,2076619 #15372
2077319,2077321 #15373
2077637,2077639 #15374
2077709,2077711 #15375
2077769,2077771 #15376
2077811,2077813 #15377
2078159,2078161 #15378
2078309,2078311 #15379
2078339,2078341 #15380
2078507,2078509 #15381
2078927,2078929 #15382
2079017,2079019 #15383
2079071,2079073 #15384
2079167,2079169 #15385
2079191,2079193 #15386
2079197,2079199 #15387
2079239,2079241 #15388
2079401,2079403 #15389
2079461,2079463 #15390
2079599,2079601 #15391
2079629,2079631 #15392
2079941,2079943 #15393
2080451,2080453 #15394
2080541,2080543 #15395
2080847,2080849 #15396
2080961,2080963 #15397
2081159,2081161 #15398
2081249,2081251 #15399
2081351,2081353 #15400
2081921,2081923 #15401
2082131,2082133 #15402
2082497,2082499 #15403
2082737,2082739 #15404
2082851,2082853 #15405
2082887,2082889 #15406
2083019,2083021 #15407
2083421,2083423 #15408
2083451,2083453 #15409
2083511,2083513 #15410
2083517,2083519 #15411
2083769,2083771 #15412
2083847,2083849 #15413
2084231,2084233 #15414
2084441,2084443 #15415
2084447,2084449 #15416
2084501,2084503 #15417
2084567,2084569 #15418
2084609,2084611 #15419
2084981,2084983 #15420
2085131,2085133 #15421
2085227,2085229 #15422
2085287,2085289 #15423
2085701,2085703 #15424
2085737,2085739 #15425
2085929,2085931 #15426
2086079,2086081 #15427
2086109,2086111 #15428
2086211,2086213 #15429
2086349,2086351 #15430
2086361,2086363 #15431
2086421,2086423 #15432
2086457,2086459 #15433
2086547,2086549 #15434
2086571,2086573 #15435
2086757,2086759 #15436
2086829,2086831 #15437
2087219,2087221 #15438
2087231,2087233 #15439
2087381,2087383 #15440
2087387,2087389 #15441
2087669,2087671 #15442
2087711,2087713 #15443
2087807,2087809 #15444
2088011,2088013 #15445
2088131,2088133 #15446
2088341,2088343 #15447
2088407,2088409 #15448
2088419,2088421 #15449
2088587,2088589 #15450
2088599,2088601 #15451
2088641,2088643 #15452
2088719,2088721 #15453
2088731,2088733 #15454
2088869,2088871 #15455
2088971,2088973 #15456
2089037,2089039 #15457
2089049,2089051 #15458
2089091,2089093 #15459
2089271,2089273 #15460
2089391,2089393 #15461
2089541,2089543 #15462
2090069,2090071 #15463
2090279,2090281 #15464
2090327,2090329 #15465
2090351,2090353 #15466
2090717,2090719 #15467
2091149,2091151 #15468
2091239,2091241 #15469
2091281,2091283 #15470
2091317,2091319 #15471
2091707,2091709 #15472
2092019,2092021 #15473
2092427,2092429 #15474
2092589,2092591 #15475
2092661,2092663 #15476
2092721,2092723 #15477
2092799,2092801 #15478
2092859,2092861 #15479
2092997,2092999 #15480
2093321,2093323 #15481
2093489,2093491 #15482
2093699,2093701 #15483
2094107,2094109 #15484
2094341,2094343 #15485
2094359,2094361 #15486
2094749,2094751 #15487
2094809,2094811 #15488
2095361,2095363 #15489
2095397,2095399 #15490
2095697,2095699 #15491
2096009,2096011 #15492
2096231,2096233 #15493
2096399,2096401 #15494
2096429,2096431 #15495
2096597,2096599 #15496
2096789,2096791 #15497
2096909,2096911 #15498
2096957,2096959 #15499
2097131,2097133 #15500
2097257,2097259 #15501
2097287,2097289 #15502
2097449,2097451 #15503
2097479,2097481 #15504
2097671,2097673 #15505
2097857,2097859 #15506
2098079,2098081 #15507
2098169,2098171 #15508
2098277,2098279 #15509
2098697,2098699 #15510
2098739,2098741 #15511
2098781,2098783 #15512
2099219,2099221 #15513
2099477,2099479 #15514
2099939,2099941 #15515
2100191,2100193 #15516
2100227,2100229 #15517
2100407,2100409 #15518
2100587,2100589 #15519
2101091,2101093 #15520
2101247,2101249 #15521
2101259,2101261 #15522
2101481,2101483 #15523
2101499,2101501 #15524
2101667,2101669 #15525
2101871,2101873 #15526
2101907,2101909 #15527
2102171,2102173 #15528
2102249,2102251 #15529
2102459,2102461 #15530
2102531,2102533 #15531
2103149,2103151 #15532
2103611,2103613 #15533
2103791,2103793 #15534
2104019,2104021 #15535
2104757,2104759 #15536
2105069,2105071 #15537
2105267,2105269 #15538
2105357,2105359 #15539
2105417,2105419 #15540
2105729,2105731 #15541
2106197,2106199 #15542
2106227,2106229 #15543
2106341,2106343 #15544
2106617,2106619 #15545
2106677,2106679 #15546
2106779,2106781 #15547
2106917,2106919 #15548
2106989,2106991 #15549
2107319,2107321 #15550
2107529,2107531 #15551
2107601,2107603 #15552
2107661,2107663 #15553
2107667,2107669 #15554
2108087,2108089 #15555
2108549,2108551 #15556
2108597,2108599 #15557
2108759,2108761 #15558
2108807,2108809 #15559
2108879,2108881 #15560
2108927,2108929 #15561
2109011,2109013 #15562
2109101,2109103 #15563
2109617,2109619 #15564
2109797,2109799 #15565
2109869,2109871 #15566
2110019,2110021 #15567
2110151,2110153 #15568
2110187,2110189 #15569
2110289,2110291 #15570
2110529,2110531 #15571
2110751,2110753 #15572
2110859,2110861 #15573
2110877,2110879 #15574
2110949,2110951 #15575
2111309,2111311 #15576
2111357,2111359 #15577
2111507,2111509 #15578
2111531,2111533 #15579
2111729,2111731 #15580
2111801,2111803 #15581
2111969,2111971 #15582
2112191,2112193 #15583
2112569,2112571 #15584
2112827,2112829 #15585
2113037,2113039 #15586
2113289,2113291 #15587
2113469,2113471 #15588
2113511,2113513 #15589
2113667,2113669 #15590
2113679,2113681 #15591
2113757,2113759 #15592
2114039,2114041 #15593
2114087,2114089 #15594
2114249,2114251 #15595
2114507,2114509 #15596
2114531,2114533 #15597
2114711,2114713 #15598
2114741,2114743 #15599
2114969,2114971 #15600
2115077,2115079 #15601
2115131,2115133 #15602
2115227,2115229 #15603
2115317,2115319 #15604
2115431,2115433 #15605
2116019,2116021 #15606
2116097,2116099 #15607
2116559,2116561 #15608
2116571,2116573 #15609
2116577,2116579 #15610
2116691,2116693 #15611
2116799,2116801 #15612
2116811,2116813 #15613
2116901,2116903 #15614
2116949,2116951 #15615
2116967,2116969 #15616
2117039,2117041 #15617
2117051,2117053 #15618
2117237,2117239 #15619
2117429,2117431 #15620
2117651,2117653 #15621
2117699,2117701 #15622
2118029,2118031 #15623
2118089,2118091 #15624
2118119,2118121 #15625
2118299,2118301 #15626
2119259,2119261 #15627
2119307,2119309 #15628
2119589,2119591 #15629
2119877,2119879 #15630
2119919,2119921 #15631
2119937,2119939 #15632
2119967,2119969 #15633
2120099,2120101 #15634
2120351,2120353 #15635
2120549,2120551 #15636
2120849,2120851 #15637
2121191,2121193 #15638
2121239,2121241 #15639
2121737,2121739 #15640
2121941,2121943 #15641
2122511,2122513 #15642
2122709,2122711 #15643
2122721,2122723 #15644
2122961,2122963 #15645
2123081,2123083 #15646
2123237,2123239 #15647
2123279,2123281 #15648
2123741,2123743 #15649
2123879,2123881 #15650
2123969,2123971 #15651
2124011,2124013 #15652
2124041,2124043 #15653
2124359,2124361 #15654
2124401,2124403 #15655
2124467,2124469 #15656
2124839,2124841 #15657
2125469,2125471 #15658
2125601,2125603 #15659
2125679,2125681 #15660
2125691,2125693 #15661
2126027,2126029 #15662
2126039,2126041 #15663
2126147,2126149 #15664
2126429,2126431 #15665
2126849,2126851 #15666
2126897,2126899 #15667
2127269,2127271 #15668
2127287,2127289 #15669
2127341,2127343 #15670
2127647,2127649 #15671
2127689,2127691 #15672
2127947,2127949 #15673
2127971,2127973 #15674
2128547,2128549 #15675
2128559,2128561 #15676
2128601,2128603 #15677
2128667,2128669 #15678
2128781,2128783 #15679
2128871,2128873 #15680
2128991,2128993 #15681
2129261,2129263 #15682
2129291,2129293 #15683
2129399,2129401 #15684
2129507,2129509 #15685
2129549,2129551 #15686
2129597,2129599 #15687
2129819,2129821 #15688
2129849,2129851 #15689
2130239,2130241 #15690
2130341,2130343 #15691
2130437,2130439 #15692
2130617,2130619 #15693
2130671,2130673 #15694
2130701,2130703 #15695
2130767,2130769 #15696
2131319,2131321 #15697
2131427,2131429 #15698
2131601,2131603 #15699
2131691,2131693 #15700
2131979,2131981 #15701
2132231,2132233 #15702
2132279,2132281 #15703
2132309,2132311 #15704
2132321,2132323 #15705
2132591,2132593 #15706
2132657,2132659 #15707
2132759,2132761 #15708
2132981,2132983 #15709
2133029,2133031 #15710
2133251,2133253 #15711
2133431,2133433 #15712
2133539,2133541 #15713
2133587,2133589 #15714
2133611,2133613 #15715
2133797,2133799 #15716
2134019,2134021 #15717
2134241,2134243 #15718
2134259,2134261 #15719
2134961,2134963 #15720
2135099,2135101 #15721
2135519,2135521 #15722
2135687,2135689 #15723
2135699,2135701 #15724
2135717,2135719 #15725
2136107,2136109 #15726
2136131,2136133 #15727
2136137,2136139 #15728
2136191,2136193 #15729
2136287,2136289 #15730
2136311,2136313 #15731
2136359,2136361 #15732
2136389,2136391 #15733
2136437,2136439 #15734
2136557,2136559 #15735
2136599,2136601 #15736
2136731,2136733 #15737
2136989,2136991 #15738
2137151,2137153 #15739
2137409,2137411 #15740
2137547,2137549 #15741
2137979,2137981 #15742
2138249,2138251 #15743
2138399,2138401 #15744
2138501,2138503 #15745
2138831,2138833 #15746
2138987,2138989 #15747
2139407,2139409 #15748
2139461,2139463 #15749
2139497,2139499 #15750
2139539,2139541 #15751
2139659,2139661 #15752
2139857,2139859 #15753
2140001,2140003 #15754
2140601,2140603 #15755
2140847,2140849 #15756
2140967,2140969 #15757
2141057,2141059 #15758
2141297,2141299 #15759
2141591,2141593 #15760
2141801,2141803 #15761
2141807,2141809 #15762
2141897,2141899 #15763
2142167,2142169 #15764
2142227,2142229 #15765
2142251,2142253 #15766
2142521,2142523 #15767
2142641,2142643 #15768
2143199,2143201 #15769
2143259,2143261 #15770
2143481,2143483 #15771
2143487,2143489 #15772
2143541,2143543 #15773
2143571,2143573 #15774
2143829,2143831 #15775
2143859,2143861 #15776
2144249,2144251 #15777
2144369,2144371 #15778
2144477,2144479 #15779
2144489,2144491 #15780
2144501,2144503 #15781
2144507,2144509 #15782
2144687,2144689 #15783
2144717,2144719 #15784
2144729,2144731 #15785
2144897,2144899 #15786
2144951,2144953 #15787
2145191,2145193 #15788
2145287,2145289 #15789
2145329,2145331 #15790
2145359,2145361 #15791
2145629,2145631 #15792
2145641,2145643 #15793
2145707,2145709 #15794
2145821,2145823 #15795
2146091,2146093 #15796
2146139,2146141 #15797
2146691,2146693 #15798
2146787,2146789 #15799
2147021,2147023 #15800
2147051,2147053 #15801
2147279,2147281 #15802
2147501,2147503 #15803
2147861,2147863 #15804
2147909,2147911 #15805
2147987,2147989 #15806
2148071,2148073 #15807
2148401,2148403 #15808
2148449,2148451 #15809
2148527,2148529 #15810
2148659,2148661 #15811
2148737,2148739 #15812
2149139,2149141 #15813
2149247,2149249 #15814
2149349,2149351 #15815
2149619,2149621 #15816
2149991,2149993 #15817
2150009,2150011 #15818
2150207,2150209 #15819
2150417,2150419 #15820
2150639,2150641 #15821
2150717,2150719 #15822
2150879,2150881 #15823
2151011,2151013 #15824
2151137,2151139 #15825
2151269,2151271 #15826
2151509,2151511 #15827
2151701,2151703 #15828
2152229,2152231 #15829
2152307,2152309 #15830
2152427,2152429 #15831
2152481,2152483 #15832
2152817,2152819 #15833
2152847,2152849 #15834
2153057,2153059 #15835
2153069,2153071 #15836
2153111,2153113 #15837
2153297,2153299 #15838
2153561,2153563 #15839
2154041,2154043 #15840
2154329,2154331 #15841
2154539,2154541 #15842
2154641,2154643 #15843
2154791,2154793 #15844
2154851,2154853 #15845
2155007,2155009 #15846
2155271,2155273 #15847
2155511,2155513 #15848
2155961,2155963 #15849
2156039,2156041 #15850
2156309,2156311 #15851
2156459,2156461 #15852
2156597,2156599 #15853
2156681,2156683 #15854
2156849,2156851 #15855
2157119,2157121 #15856
2157149,2157151 #15857
2157341,2157343 #15858
2157557,2157559 #15859
2157677,2157679 #15860
2157731,2157733 #15861
2157737,2157739 #15862
2157767,2157769 #15863
2157821,2157823 #15864
2157899,2157901 #15865
2158181,2158183 #15866
2158367,2158369 #15867
2158547,2158549 #15868
2158577,2158579 #15869
2158589,2158591 #15870
2158601,2158603 #15871
2158697,2158699 #15872
2158769,2158771 #15873
2158841,2158843 #15874
2159081,2159083 #15875
2159231,2159233 #15876
2159237,2159239 #15877
2159249,2159251 #15878
2159327,2159329 #15879
2159669,2159671 #15880
2159819,2159821 #15881
2159957,2159959 #15882
2160029,2160031 #15883
2160131,2160133 #15884
2160209,2160211 #15885
2160461,2160463 #15886
2160617,2160619 #15887
2160881,2160883 #15888
2161127,2161129 #15889
2161301,2161303 #15890
2161637,2161639 #15891
2161697,2161699 #15892
2162057,2162059 #15893
2162087,2162089 #15894
2162189,2162191 #15895
2162351,2162353 #15896
2162507,2162509 #15897
2162579,2162581 #15898
2162957,2162959 #15899
2163011,2163013 #15900
2163041,2163043 #15901
2163221,2163223 #15902
2163347,2163349 #15903
2163479,2163481 #15904
2163569,2163571 #15905
2163671,2163673 #15906
2163827,2163829 #15907
2163881,2163883 #15908
2164037,2164039 #15909
2164607,2164609 #15910
2164619,2164621 #15911
2165027,2165029 #15912
2165081,2165083 #15913
2165321,2165323 #15914
2165531,2165533 #15915
2165591,2165593 #15916
2165771,2165773 #15917
2165957,2165959 #15918
2166119,2166121 #15919
2166509,2166511 #15920
2166917,2166919 #15921
2166947,2166949 #15922
2167019,2167021 #15923
2167091,2167093 #15924
2167259,2167261 #15925
2167367,2167369 #15926
2167439,2167441 #15927
2167469,2167471 #15928
2167769,2167771 #15929
2167937,2167939 #15930
2168057,2168059 #15931
2168291,2168293 #15932
2168519,2168521 #15933
2168651,2168653 #15934
2168657,2168659 #15935
2168669,2168671 #15936
2168687,2168689 #15937
2168711,2168713 #15938
2168861,2168863 #15939
2168951,2168953 #15940
2168987,2168989 #15941
2169029,2169031 #15942
2169071,2169073 #15943
2169311,2169313 #15944
2169359,2169361 #15945
2169467,2169469 #15946
2169509,2169511 #15947
2169617,2169619 #15948
2170109,2170111 #15949
2170241,2170243 #15950
2170409,2170411 #15951
2170937,2170939 #15952
2171159,2171161 #15953
2171621,2171623 #15954
2171759,2171761 #15955
2172089,2172091 #15956
2172227,2172229 #15957
2172239,2172241 #15958
2172827,2172829 #15959
2172851,2172853 #15960
2172869,2172871 #15961
2172977,2172979 #15962
2173079,2173081 #15963
2173151,2173153 #15964
2173361,2173363 #15965
2173529,2173531 #15966
2173571,2173573 #15967
2173649,2173651 #15968
2173727,2173729 #15969
2173877,2173879 #15970
2174399,2174401 #15971
2174591,2174593 #15972
2174609,2174611 #15973
2174699,2174701 #15974
2174771,2174773 #15975
2175449,2175451 #15976
2175599,2175601 #15977
2175659,2175661 #15978
2175791,2175793 #15979
2175851,2175853 #15980
2176409,2176411 #15981
2176547,2176549 #15982
2176631,2176633 #15983
2176637,2176639 #15984
2176829,2176831 #15985
2176871,2176873 #15986
2177009,2177011 #15987
2177237,2177239 #15988
2177321,2177323 #15989
2177429,2177431 #15990
2177447,2177449 #15991
2177501,2177503 #15992
2177507,2177509 #15993
2177519,2177521 #15994
2177597,2177599 #15995
2177687,2177689 #15996
2178131,2178133 #15997
2178149,2178151 #15998
2178257,2178259 #15999
2178641,2178643 #16000
2178677,2178679 #16001
2178731,2178733 #16002
2179139,2179141 #16003
2179607,2179609 #16004
2179649,2179651 #16005
2180177,2180179 #16006
2180219,2180221 #16007
2180681,2180683 #16008
2180921,2180923 #16009
2181071,2181073 #16010
2181227,2181229 #16011
2181329,2181331 #16012
2181461,2181463 #16013
2181539,2181541 #16014
2181869,2181871 #16015
2182007,2182009 #16016
2182097,2182099 #16017
2182559,2182561 #16018
2182601,2182603 #16019
2182811,2182813 #16020
2182991,2182993 #16021
2183339,2183341 #16022
2183507,2183509 #16023
2183579,2183581 #16024
2183681,2183683 #16025
2183771,2183773 #16026
2183789,2183791 #16027
2183807,2183809 #16028
2183957,2183959 #16029
2184197,2184199 #16030
2184317,2184319 #16031
2184359,2184361 #16032
2184407,2184409 #16033
2184647,2184649 #16034
2184989,2184991 #16035
2185187,2185189 #16036
2185199,2185201 #16037
2185427,2185429 #16038
2185697,2185699 #16039
2185871,2185873 #16040
2185919,2185921 #16041
2186099,2186101 #16042
2186837,2186839 #16043
2187959,2187961 #16044
2187971,2187973 #16045
2188031,2188033 #16046
2188157,2188159 #16047
2188169,2188171 #16048
2188409,2188411 #16049
2188607,2188609 #16050
2188787,2188789 #16051
2188871,2188873 #16052
2189027,2189029 #16053
2189219,2189221 #16054
2189321,2189323 #16055
2189417,2189419 #16056
2189459,2189461 #16057
2189741,2189743 #16058
2189879,2189881 #16059
2189987,2189989 #16060
2190077,2190079 #16061
2190191,2190193 #16062
2190269,2190271 #16063
2190479,2190481 #16064
2190521,2190523 #16065
2190581,2190583 #16066
2190821,2190823 #16067
2191067,2191069 #16068
2191169,2191171 #16069
2191337,2191339 #16070
2191457,2191459 #16071
2191949,2191951 #16072
2192051,2192053 #16073
2192129,2192131 #16074
2192249,2192251 #16075
2192339,2192341 #16076
2192621,2192623 #16077
2192651,2192653 #16078
2192789,2192791 #16079
2192849,2192851 #16080
2193311,2193313 #16081
2193419,2193421 #16082
2193479,2193481 #16083
2193599,2193601 #16084
2193641,2193643 #16085
2193701,2193703 #16086
2193881,2193883 #16087
2193887,2193889 #16088
2193941,2193943 #16089
2194019,2194021 #16090
2194319,2194321 #16091
2194529,2194531 #16092
2194721,2194723 #16093
2194901,2194903 #16094
2194991,2194993 #16095
2195117,2195119 #16096
2195339,2195341 #16097
2195381,2195383 #16098
2195441,2195443 #16099
2195579,2195581 #16100
2195729,2195731 #16101
2195861,2195863 #16102
2196287,2196289 #16103
2196539,2196541 #16104
2196611,2196613 #16105
2196869,2196871 #16106
2196977,2196979 #16107
2197409,2197411 #16108
2197631,2197633 #16109
2197847,2197849 #16110
2198291,2198293 #16111
2198759,2198761 #16112
2198879,2198881 #16113
2199179,2199181 #16114
2199311,2199313 #16115
2199521,2199523 #16116
2199959,2199961 #16117
2200139,2200141 #16118
2200589,2200591 #16119
2200619,2200621 #16120
2200727,2200729 #16121
2200811,2200813 #16122
2200841,2200843 #16123
2201189,2201191 #16124
2201201,2201203 #16125
2201531,2201533 #16126
2201597,2201599 #16127
2201669,2201671 #16128
2202047,2202049 #16129
2202131,2202133 #16130
2202311,2202313 #16131
2202377,2202379 #16132
2202437,2202439 #16133
2202791,2202793 #16134
2202797,2202799 #16135
2202857,2202859 #16136
2202929,2202931 #16137
2203301,2203303 #16138
2203631,2203633 #16139
2203961,2203963 #16140
2203967,2203969 #16141
2204009,2204011 #16142
2204471,2204473 #16143
2204831,2204833 #16144
2205011,2205013 #16145
2205449,2205451 #16146
2205587,2205589 #16147
2205611,2205613 #16148
2205659,2205661 #16149
2205947,2205949 #16150
2206121,2206123 #16151
2206151,2206153 #16152
2206247,2206249 #16153
2206439,2206441 #16154
2206469,2206471 #16155
2206619,2206621 #16156
2206817,2206819 #16157
2207201,2207203 #16158
2207279,2207281 #16159
2207321,2207323 #16160
2207537,2207539 #16161
2207831,2207833 #16162
2207981,2207983 #16163
2208257,2208259 #16164
2208707,2208709 #16165
2208797,2208799 #16166
2208887,2208889 #16167
2209001,2209003 #16168
2209061,2209063 #16169
2209169,2209171 #16170
2209547,2209549 #16171
2209661,2209663 #16172
2209787,2209789 #16173
2209841,2209843 #16174
2209901,2209903 #16175
2209937,2209939 #16176
2210009,2210011 #16177
2210027,2210029 #16178
2210057,2210059 #16179
2210279,2210281 #16180
2210387,2210389 #16181
2210567,2210569 #16182
2210651,2210653 #16183
2210777,2210779 #16184
2211257,2211259 #16185
2211929,2211931 #16186
2212097,2212099 #16187
2212181,2212183 #16188
2212349,2212351 #16189
2212631,2212633 #16190
2212781,2212783 #16191
2213201,2213203 #16192
2213399,2213401 #16193
2213411,2213413 #16194
2213591,2213593 #16195
2213837,2213839 #16196
2214101,2214103 #16197
2214269,2214271 #16198
2214479,2214481 #16199
2214491,2214493 #16200
2215097,2215099 #16201
2215307,2215309 #16202
2215349,2215351 #16203
2215469,2215471 #16204
2215529,2215531 #16205
2215667,2215669 #16206
2215691,2215693 #16207
2215901,2215903 #16208
2216321,2216323 #16209
2216609,2216611 #16210
2216657,2216659 #16211
2216699,2216701 #16212
2216759,2216761 #16213
2216999,2217001 #16214
2217491,2217493 #16215
2217539,2217541 #16216
2217569,2217571 #16217
2217581,2217583 #16218
2217641,2217643 #16219
2217671,2217673 #16220
2218091,2218093 #16221
2218127,2218129 #16222
2218199,2218201 #16223
2218427,2218429 #16224
2218547,2218549 #16225
2218607,2218609 #16226
2218901,2218903 #16227
2218967,2218969 #16228
2219081,2219083 #16229
2219279,2219281 #16230
2219351,2219353 #16231
2219489,2219491 #16232
2219681,2219683 #16233
2219771,2219773 #16234
2220527,2220529 #16235
2220551,2220553 #16236
2220917,2220919 #16237
2220971,2220973 #16238
2221127,2221129 #16239
2221229,2221231 #16240
2221379,2221381 #16241
2221631,2221633 #16242
2221859,2221861 #16243
2221907,2221909 #16244
2222249,2222251 #16245
2222501,2222503 #16246
2223161,2223163 #16247
2223281,2223283 #16248
2223449,2223451 #16249
2223467,2223469 #16250
2223497,2223499 #16251
2223671,2223673 #16252
2223677,2223679 #16253
2223839,2223841 #16254
2224457,2224459 #16255
2224667,2224669 #16256
2224679,2224681 #16257
2225051,2225053 #16258
2225057,2225059 #16259
2225231,2225233 #16260
2225387,2225389 #16261
2225567,2225569 #16262
2225579,2225581 #16263
2225681,2225683 #16264
2225747,2225749 #16265
2225999,2226001 #16266
2226149,2226151 #16267
2226197,2226199 #16268
2226227,2226229 #16269
2226311,2226313 #16270
2226407,2226409 #16271
2226461,2226463 #16272
2226527,2226529 #16273
2226569,2226571 #16274
2226617,2226619 #16275
2226767,2226769 #16276
2226941,2226943 #16277
2227031,2227033 #16278
2227061,2227063 #16279
2227259,2227261 #16280
2227367,2227369 #16281
2227397,2227399 #16282
2227439,2227441 #16283
2227499,2227501 #16284
2227607,2227609 #16285
2227649,2227651 #16286
2228117,2228119 #16287
2228321,2228323 #16288
2228507,2228509 #16289
2228519,2228521 #16290
2228531,2228533 #16291
2228657,2228659 #16292
2228711,2228713 #16293
2228981,2228983 #16294
2229041,2229043 #16295
2229119,2229121 #16296
2229167,2229169 #16297
2229389,2229391 #16298
2229587,2229589 #16299
2229767,2229769 #16300
2229791,2229793 #16301
2230157,2230159 #16302
2230409,2230411 #16303
2230511,2230513 #16304
2230871,2230873 #16305
2231309,2231311 #16306
2231429,2231431 #16307
2231477,2231479 #16308
2231819,2231821 #16309
2232509,2232511 #16310
2232749,2232751 #16311
2232779,2232781 #16312
2232887,2232889 #16313
2232929,2232931 #16314
2233079,2233081 #16315
2233199,2233201 #16316
2233379,2233381 #16317
2233499,2233501 #16318
2233529,2233531 #16319
2233571,2233573 #16320
2233709,2233711 #16321
2233877,2233879 #16322
2233937,2233939 #16323
2234117,2234119 #16324
2234159,2234161 #16325
2234207,2234209 #16326
2234339,2234341 #16327
2234501,2234503 #16328
2234591,2234593 #16329
2234717,2234719 #16330
2234927,2234929 #16331
2235047,2235049 #16332
2235137,2235139 #16333
2235227,2235229 #16334
2235509,2235511 #16335
2235731,2235733 #16336
2235809,2235811 #16337
2235941,2235943 #16338
2235971,2235973 #16339
2236007,2236009 #16340
2236049,2236051 #16341
2236079,2236081 #16342
2236187,2236189 #16343
2236517,2236519 #16344
2236709,2236711 #16345
2236769,2236771 #16346
2237399,2237401 #16347
2237561,2237563 #16348
2237771,2237773 #16349
2238011,2238013 #16350
2238161,2238163 #16351
2238209,2238211 #16352
2238287,2238289 #16353
2238359,2238361 #16354
2238419,2238421 #16355
2238527,2238529 #16356
2238569,2238571 #16357
2238809,2238811 #16358
2238959,2238961 #16359
2239007,2239009 #16360
2239217,2239219 #16361
2239229,2239231 #16362
2239331,2239333 #16363
2239649,2239651 #16364
2239709,2239711 #16365
2239751,2239753 #16366
2240111,2240113 #16367
2240321,2240323 #16368
2240477,2240479 #16369
2240531,2240533 #16370
2240657,2240659 #16371
2240699,2240701 #16372
2240807,2240809 #16373
2240837,2240839 #16374
2241011,2241013 #16375
2241047,2241049 #16376
2241119,2241121 #16377
2241191,2241193 #16378
2241299,2241301 #16379
2241311,2241313 #16380
2241359,2241361 #16381
2241389,2241391 #16382
2241521,2241523 #16383
2241779,2241781 #16384
2241917,2241919 #16385
2242127,2242129 #16386
2242187,2242189 #16387
2242211,2242213 #16388
2242379,2242381 #16389
2242517,2242519 #16390
2242727,2242729 #16391
2242781,2242783 #16392
2242811,2242813 #16393
2242841,2242843 #16394
2242871,2242873 #16395
2242949,2242951 #16396
2243207,2243209 #16397
2243429,2243431 #16398
2243621,2243623 #16399
2243741,2243743 #16400
2243819,2243821 #16401
2243909,2243911 #16402
2244257,2244259 #16403
2244587,2244589 #16404
2244659,2244661 #16405
2244689,2244691 #16406
2244719,2244721 #16407
2244881,2244883 #16408
2245427,2245429 #16409
2245457,2245459 #16410
2245541,2245543 #16411
2245679,2245681 #16412
2245721,2245723 #16413
2245811,2245813 #16414
2246051,2246053 #16415
2246141,2246143 #16416
2246147,2246149 #16417
2246357,2246359 #16418
2246687,2246689 #16419
2246789,2246791 #16420
2246969,2246971 #16421
2247101,2247103 #16422
2247227,2247229 #16423
2247461,2247463 #16424
2247521,2247523 #16425
2247809,2247811 #16426
2247851,2247853 #16427
2247899,2247901 #16428
2248019,2248021 #16429
2248067,2248069 #16430
2248241,2248243 #16431
2248247,2248249 #16432
2248331,2248333 #16433
2248529,2248531 #16434
2248637,2248639 #16435
2248661,2248663 #16436
2248679,2248681 #16437
2248691,2248693 #16438
2248847,2248849 #16439
2249309,2249311 #16440
2249411,2249413 #16441
2249981,2249983 #16442
2250041,2250043 #16443
2250089,2250091 #16444
2250401,2250403 #16445
2250419,2250421 #16446
2250761,2250763 #16447
2250929,2250931 #16448
2250977,2250979 #16449
2251199,2251201 #16450
2251211,2251213 #16451
2251727,2251729 #16452
2251901,2251903 #16453
2251979,2251981 #16454
2252009,2252011 #16455
2252219,2252221 #16456
2252231,2252233 #16457
2252309,2252311 #16458
2252387,2252389 #16459
2252681,2252683 #16460
2252951,2252953 #16461
2253257,2253259 #16462
2253281,2253283 #16463
2253479,2253481 #16464
2253497,2253499 #16465
2253971,2253973 #16466
2254097,2254099 #16467
2254157,2254159 #16468
2254409,2254411 #16469
2254781,2254783 #16470
2254799,2254801 #16471
2254871,2254873 #16472
2255021,2255023 #16473
2255159,2255161 #16474
2255249,2255251 #16475
2255549,2255551 #16476
2255567,2255569 #16477
2255969,2255971 #16478
2255987,2255989 #16479
2256029,2256031 #16480
2256179,2256181 #16481
2256311,2256313 #16482
2256341,2256343 #16483
2256347,2256349 #16484
2256377,2256379 #16485
2256467,2256469 #16486
2256557,2256559 #16487
2256911,2256913 #16488
2257049,2257051 #16489
2257439,2257441 #16490
2257529,2257531 #16491
2257691,2257693 #16492
2257859,2257861 #16493
2258327,2258329 #16494
2258519,2258521 #16495
2258651,2258653 #16496
2258741,2258743 #16497
2258819,2258821 #16498
2259029,2259031 #16499
2259137,2259139 #16500
2259197,2259199 #16501
2259239,2259241 #16502
2259527,2259529 #16503
2260169,2260171 #16504
2260499,2260501 #16505
2260547,2260549 #16506
2260631,2260633 #16507
2260649,2260651 #16508
2260787,2260789 #16509
2260889,2260891 #16510
2261267,2261269 #16511
2261471,2261473 #16512
2261801,2261803 #16513
2261837,2261839 #16514
2262641,2262643 #16515
2262857,2262859 #16516
2262971,2262973 #16517
2262977,2262979 #16518
2263067,2263069 #16519
2263139,2263141 #16520
2263169,2263171 #16521
2263319,2263321 #16522
2263439,2263441 #16523
2263517,2263519 #16524
2263559,2263561 #16525
2263739,2263741 #16526
2263841,2263843 #16527
2264201,2264203 #16528
2264357,2264359 #16529
2264567,2264569 #16530
2264609,2264611 #16531
2264861,2264863 #16532
2264957,2264959 #16533
2265269,2265271 #16534
2265467,2265469 #16535
2265587,2265589 #16536
2265749,2265751 #16537
2265941,2265943 #16538
2266037,2266039 #16539
2266289,2266291 #16540
2266469,2266471 #16541
2266499,2266501 #16542
2266631,2266633 #16543
2266637,2266639 #16544
2266709,2266711 #16545
2266991,2266993 #16546
2267051,2267053 #16547
2267129,2267131 #16548
2267141,2267143 #16549
2267297,2267299 #16550
2267381,2267383 #16551
2267561,2267563 #16552
2267981,2267983 #16553
2268197,2268199 #16554
2268221,2268223 #16555
2268269,2268271 #16556
2268317,2268319 #16557
2268449,2268451 #16558
2268587,2268589 #16559
2268647,2268649 #16560
2268839,2268841 #16561
2268941,2268943 #16562
2268977,2268979 #16563
2269217,2269219 #16564
2269439,2269441 #16565
2269457,2269459 #16566
2269877,2269879 #16567
2269901,2269903 #16568
2270111,2270113 #16569
2270171,2270173 #16570
2270249,2270251 #16571
2270267,2270269 #16572
2270309,2270311 #16573
2270339,2270341 #16574
2270447,2270449 #16575
2270549,2270551 #16576
2270687,2270689 #16577
2270771,2270773 #16578
2270837,2270839 #16579
2271161,2271163 #16580
2271221,2271223 #16581
2271341,2271343 #16582
2271497,2271499 #16583
2271551,2271553 #16584
2271569,2271571 #16585
2271749,2271751 #16586
2271881,2271883 #16587
2272199,2272201 #16588
2272217,2272219 #16589
2272451,2272453 #16590
2272547,2272549 #16591
2272727,2272729 #16592
2272859,2272861 #16593
2273069,2273071 #16594
2273309,2273311 #16595
2273501,2273503 #16596
2273567,2273569 #16597
2273669,2273671 #16598
2274269,2274271 #16599
2274287,2274289 #16600
2274407,2274409 #16601
2274521,2274523 #16602
2274689,2274691 #16603
2274761,2274763 #16604
2275199,2275201 #16605
2275391,2275393 #16606
2275529,2275531 #16607
2275769,2275771 #16608
2276231,2276233 #16609
2276399,2276401 #16610
2276429,2276431 #16611
2276999,2277001 #16612
2277551,2277553 #16613
2277617,2277619 #16614
2277659,2277661 #16615
2277731,2277733 #16616
2277809,2277811 #16617
2277857,2277859 #16618
2278019,2278021 #16619
2278091,2278093 #16620
2278139,2278141 #16621
2278259,2278261 #16622
2278301,2278303 #16623
2278517,2278519 #16624
2278691,2278693 #16625
2278811,2278813 #16626
2278961,2278963 #16627
2278979,2278981 #16628
2279117,2279119 #16629
2279351,2279353 #16630
2279489,2279491 #16631
2279567,2279569 #16632
2279741,2279743 #16633
2279897,2279899 #16634
2280071,2280073 #16635
2280167,2280169 #16636
2280401,2280403 #16637
2280671,2280673 #16638
2281001,2281003 #16639
2281229,2281231 #16640
2281379,2281381 #16641
2281661,2281663 #16642
2282321,2282323 #16643
2282381,2282383 #16644
2282897,2282899 #16645
2283137,2283139 #16646
2283317,2283319 #16647
2283497,2283499 #16648
2283581,2283583 #16649
2283707,2283709 #16650
2283731,2283733 #16651
2283887,2283889 #16652
2284211,2284213 #16653
2284277,2284279 #16654
2284367,2284369 #16655
2284487,2284489 #16656
2284871,2284873 #16657
2284949,2284951 #16658
2285069,2285071 #16659
2285159,2285161 #16660
2285219,2285221 #16661
2285249,2285251 #16662
2285357,2285359 #16663
2285399,2285401 #16664
2285639,2285641 #16665
2285741,2285743 #16666
2285861,2285863 #16667
2285891,2285893 #16668
2285951,2285953 #16669
2286197,2286199 #16670
2286377,2286379 #16671
2286797,2286799 #16672
2286881,2286883 #16673
2287247,2287249 #16674
2287289,2287291 #16675
2287421,2287423 #16676
2287529,2287531 #16677
2287667,2287669 #16678
2287991,2287993 #16679
2288057,2288059 #16680
2288261,2288263 #16681
2288747,2288749 #16682
2288771,2288773 #16683
2288807,2288809 #16684
2288831,2288833 #16685
2288927,2288929 #16686
2289149,2289151 #16687
2289179,2289181 #16688
2289431,2289433 #16689
2289641,2289643 #16690
2289647,2289649 #16691
2289839,2289841 #16692
2290031,2290033 #16693
2290037,2290039 #16694
2290151,2290153 #16695
2290571,2290573 #16696
2290829,2290831 #16697
2291351,2291353 #16698
2291477,2291479 #16699
2291657,2291659 #16700
2291747,2291749 #16701
2291801,2291803 #16702
2291909,2291911 #16703
2291999,2292001 #16704
2292359,2292361 #16705
2292461,2292463 #16706
2292947,2292949 #16707
2293139,2293141 #16708
2293301,2293303 #16709
2293391,2293393 #16710
2293481,2293483 #16711
2293631,2293633 #16712
2293727,2293729 #16713
2293799,2293801 #16714
2293829,2293831 #16715
2293847,2293849 #16716
2294009,2294011 #16717
2294051,2294053 #16718
2294057,2294059 #16719
2294249,2294251 #16720
2294309,2294311 #16721
2294429,2294431 #16722
2294489,2294491 #16723
2295077,2295079 #16724
2295479,2295481 #16725
2295539,2295541 #16726
2295719,2295721 #16727
2295911,2295913 #16728
2295947,2295949 #16729
2296079,2296081 #16730
2296517,2296519 #16731
2296727,2296729 #16732
2296781,2296783 #16733
2296871,2296873 #16734
2296907,2296909 #16735
2297039,2297041 #16736
2297369,2297371 #16737
2297591,2297593 #16738
2297717,2297719 #16739
2297747,2297749 #16740
2297759,2297761 #16741
2298011,2298013 #16742
2298071,2298073 #16743
2298209,2298211 #16744
2298311,2298313 #16745
2298377,2298379 #16746
2298389,2298391 #16747
2298761,2298763 #16748
2298839,2298841 #16749
2298869,2298871 #16750
2298887,2298889 #16751
2299481,2299483 #16752
2299601,2299603 #16753
2299937,2299939 #16754
2299949,2299951 #16755
2300201,2300203 #16756
2300267,2300269 #16757
2300279,2300281 #16758
2300609,2300611 #16759
2300951,2300953 #16760
2301029,2301031 #16761
2301197,2301199 #16762
2301281,2301283 #16763
2301491,2301493 #16764
2301569,2301571 #16765
2301599,2301601 #16766
2301707,2301709 #16767
2302217,2302219 #16768
2302301,2302303 #16769
2302379,2302381 #16770
2302451,2302453 #16771
2302679,2302681 #16772
2303531,2303533 #16773
2303591,2303593 #16774
2303597,2303599 #16775
2303627,2303629 #16776
2304017,2304019 #16777
2304317,2304319 #16778
2304689,2304691 #16779
2304791,2304793 #16780
2305109,2305111 #16781
2305337,2305339 #16782
2305361,2305363 #16783
2305409,2305411 #16784
2305481,2305483 #16785
2305607,2305609 #16786
2305649,2305651 #16787
2305967,2305969 #16788
2306039,2306041 #16789
2306327,2306329 #16790
2306387,2306389 #16791
2306567,2306569 #16792
2306639,2306641 #16793
2307161,2307163 #16794
2307449,2307451 #16795
2307467,2307469 #16796
2308001,2308003 #16797
2308049,2308051 #16798
2308181,2308183 #16799
2308529,2308531 #16800
2308679,2308681 #16801
2308721,2308723 #16802
2308841,2308843 #16803
2309231,2309233 #16804
2309339,2309341 #16805
2309759,2309761 #16806
2309891,2309893 #16807
2310221,2310223 #16808
2310479,2310481 #16809
2310491,2310493 #16810
2310701,2310703 #16811
2310731,2310733 #16812
2310767,2310769 #16813
2310899,2310901 #16814
2311409,2311411 #16815
2311469,2311471 #16816
2311667,2311669 #16817
2311739,2311741 #16818
2311817,2311819 #16819
2312201,2312203 #16820
2312747,2312749 #16821
2312897,2312899 #16822
2313161,2313163 #16823
2313347,2313349 #16824
2313401,2313403 #16825
2313431,2313433 #16826
2313539,2313541 #16827
2313599,2313601 #16828
2313629,2313631 #16829
2313767,2313769 #16830
2313797,2313799 #16831
2313929,2313931 #16832
2314061,2314063 #16833
2314589,2314591 #16834
2314721,2314723 #16835
2314841,2314843 #16836
2314931,2314933 #16837
2314997,2314999 #16838
2315057,2315059 #16839
2315231,2315233 #16840
2315657,2315659 #16841
2315771,2315773 #16842
2315981,2315983 #16843
2316329,2316331 #16844
2316371,2316373 #16845
2316449,2316451 #16846
2317121,2317123 #16847
2317169,2317171 #16848
2317499,2317501 #16849
2317787,2317789 #16850
2317811,2317813 #16851
2317919,2317921 #16852
2318189,2318191 #16853
2318387,2318389 #16854
2318597,2318599 #16855
2318609,2318611 #16856
2318807,2318809 #16857
2318819,2318821 #16858
2318957,2318959 #16859
2319179,2319181 #16860
2319407,2319409 #16861
2319431,2319433 #16862
2320361,2320363 #16863
2320397,2320399 #16864
2320649,2320651 #16865
2320697,2320699 #16866
2320739,2320741 #16867
2321087,2321089 #16868
2321147,2321149 #16869
2321381,2321383 #16870
2321507,2321509 #16871
2321747,2321749 #16872
2322077,2322079 #16873
2322107,2322109 #16874
2322119,2322121 #16875
2322401,2322403 #16876
2322491,2322493 #16877
2322569,2322571 #16878
2322629,2322631 #16879
2323001,2323003 #16880
2323037,2323039 #16881
2323229,2323231 #16882
2323259,2323261 #16883
2323367,2323369 #16884
2323379,2323381 #16885
2323421,2323423 #16886
2323457,2323459 #16887
2323691,2323693 #16888
2323817,2323819 #16889
2324351,2324353 #16890
2324501,2324503 #16891
2324681,2324683 #16892
2325317,2325319 #16893
2325437,2325439 #16894
2325509,2325511 #16895
2326019,2326021 #16896
2326097,2326099 #16897
2326211,2326213 #16898
2326277,2326279 #16899
2326367,2326369 #16900
2326481,2326483 #16901
2326661,2326663 #16902
2326769,2326771 #16903
2326991,2326993 #16904
2327027,2327029 #16905
2327051,2327053 #16906
2327399,2327401 #16907
2327597,2327599 #16908
2327639,2327641 #16909
2327651,2327653 #16910
2327681,2327683 #16911
2327711,2327713 #16912
2327849,2327851 #16913
2327867,2327869 #16914
2327909,2327911 #16915
2327951,2327953 #16916
2327987,2327989 #16917
2328281,2328283 #16918
2328617,2328619 #16919
2328761,2328763 #16920
2328827,2328829 #16921
2328971,2328973 #16922
2329337,2329339 #16923
2329469,2329471 #16924
2329517,2329519 #16925
2329667,2329669 #16926
2330099,2330101 #16927
2330201,2330203 #16928
2330387,2330389 #16929
2330687,2330689 #16930
2330927,2330929 #16931
2330957,2330959 #16932
2331377,2331379 #16933
2331419,2331421 #16934
2331647,2331649 #16935
2331689,2331691 #16936
2331779,2331781 #16937
2331869,2331871 #16938
2332397,2332399 #16939
2332511,2332513 #16940
2332661,2332663 #16941
2332829,2332831 #16942
2332931,2332933 #16943
2333081,2333083 #16944
2333237,2333239 #16945
2333321,2333323 #16946
2333531,2333533 #16947
2333867,2333869 #16948
2333951,2333953 #16949
2333999,2334001 #16950
2334257,2334259 #16951
2334401,2334403 #16952
2334767,2334769 #16953
2334779,2334781 #16954
2334947,2334949 #16955
2335217,2335219 #16956
2335241,2335243 #16957
2335367,2335369 #16958
2335547,2335549 #16959
2335637,2335639 #16960
2335691,2335693 #16961
2335967,2335969 #16962
2336207,2336209 #16963
2336309,2336311 #16964
2336471,2336473 #16965
2336861,2336863 #16966
2337089,2337091 #16967
2337149,2337151 #16968
2337317,2337319 #16969
2337479,2337481 #16970
2337539,2337541 #16971
2337869,2337871 #16972
2337899,2337901 #16973
2337911,2337913 #16974
2338079,2338081 #16975
2338151,2338153 #16976
2338541,2338543 #16977
2338871,2338873 #16978
2338949,2338951 #16979
2339039,2339041 #16980
2339369,2339371 #16981
2339609,2339611 #16982
2339669,2339671 #16983
2339681,2339683 #16984
2339927,2339929 #16985
2340251,2340253 #16986
2340257,2340259 #16987
2340419,2340421 #16988
2340491,2340493 #16989
2340659,2340661 #16990
2340719,2340721 #16991
2341217,2341219 #16992
2341301,2341303 #16993
2341457,2341459 #16994
2341817,2341819 #16995
2341979,2341981 #16996
2341991,2341993 #16997
2342027,2342029 #16998
2342099,2342101 #16999
2342189,2342191 #17000
2342201,2342203 #17001
2342237,2342239 #17002
2342399,2342401 #17003
2342537,2342539 #17004
2342609,2342611 #17005
2342771,2342773 #17006
2342777,2342779 #17007
2342981,2342983 #17008
2343239,2343241 #17009
2343359,2343361 #17010
2343527,2343529 #17011
2343611,2343613 #17012
2343641,2343643 #17013
2343791,2343793 #17014
2343881,2343883 #17015
2344259,2344261 #17016
2344469,2344471 #17017
2344649,2344651 #17018
2344709,2344711 #17019
2344751,2344753 #17020
2344787,2344789 #17021
2345039,2345041 #17022
2345129,2345131 #17023
2345459,2345461 #17024
2345477,2345479 #17025
2345657,2345659 #17026
2345729,2345731 #17027
2345807,2345809 #17028
2345867,2345869 #17029
2345921,2345923 #17030
2345969,2345971 #17031
2346269,2346271 #17032
2346347,2346349 #17033
2346521,2346523 #17034
2346779,2346781 #17035
2346857,2346859 #17036
2347151,2347153 #17037
2347271,2347273 #17038
2347337,2347339 #17039
2347439,2347441 #17040
2347451,2347453 #17041
2347559,2347561 #17042
2347997,2347999 #17043
2348081,2348083 #17044
2348237,2348239 #17045
2348471,2348473 #17046
2348579,2348581 #17047
2348741,2348743 #17048
2348807,2348809 #17049
2348909,2348911 #17050
2348999,2349001 #17051
2349161,2349163 #17052
2349251,2349253 #17053
2349497,2349499 #17054
2349869,2349871 #17055
2350067,2350069 #17056
2350217,2350219 #17057
2350289,2350291 #17058
2350331,2350333 #17059
2350589,2350591 #17060
2350631,2350633 #17061
2351099,2351101 #17062
2351147,2351149 #17063
2351351,2351353 #17064
2351507,2351509 #17065
2351597,2351599 #17066
2351747,2351749 #17067
2351759,2351761 #17068
2352041,2352043 #17069
2352149,2352151 #17070
2352479,2352481 #17071
2352641,2352643 #17072
2352671,2352673 #17073
2352899,2352901 #17074
2353049,2353051 #17075
2353499,2353501 #17076
2353649,2353651 #17077
2353697,2353699 #17078
2353991,2353993 #17079
2354351,2354353 #17080
2354489,2354491 #17081
2354501,2354503 #17082
2354591,2354593 #17083
2354621,2354623 #17084
2354897,2354899 #17085
2354951,2354953 #17086
2355137,2355139 #17087
2355209,2355211 #17088
2355557,2355559 #17089
2355761,2355763 #17090
2355971,2355973 #17091
2356127,2356129 #17092
2356139,2356141 #17093
2356349,2356351 #17094
2356379,2356381 #17095
2356427,2356429 #17096
2356661,2356663 #17097
2356901,2356903 #17098
2357027,2357029 #17099
2357057,2357059 #17100
2357351,2357353 #17101
2357417,2357419 #17102
2357741,2357743 #17103
2357807,2357809 #17104
2357921,2357923 #17105
2357939,2357941 #17106
2358329,2358331 #17107
2358371,2358373 #17108
2358401,2358403 #17109
2358737,2358739 #17110
2358779,2358781 #17111
2358899,2358901 #17112
2358911,2358913 #17113
2359031,2359033 #17114
2359391,2359393 #17115
2359559,2359561 #17116
2359829,2359831 #17117
2360021,2360023 #17118
2360087,2360089 #17119
2360201,2360203 #17120
2360417,2360419 #17121
2360591,2360593 #17122
2360849,2360851 #17123
2361041,2361043 #17124
2361089,2361091 #17125
2361629,2361631 #17126
2361911,2361913 #17127
2361941,2361943 #17128
2362109,2362111 #17129
2362247,2362249 #17130
2362271,2362273 #17131
2362277,2362279 #17132
2362571,2362573 #17133
2362637,2362639 #17134
2362649,2362651 #17135
2362751,2362753 #17136
2362769,2362771 #17137
2362817,2362819 #17138
2362961,2362963 #17139
2363027,2363029 #17140
2363189,2363191 #17141
2363399,2363401 #17142
2363651,2363653 #17143
2363741,2363743 #17144
2363939,2363941 #17145
2363981,2363983 #17146
2364077,2364079 #17147
2364119,2364121 #17148
2364161,2364163 #17149
2364221,2364223 #17150
2364287,2364289 #17151
2364407,2364409 #17152
2364599,2364601 #17153
2365007,2365009 #17154
2365241,2365243 #17155
2365421,2365423 #17156
2365457,2365459 #17157
2365469,2365471 #17158
2365589,2365591 #17159
2365637,2365639 #17160
2365787,2365789 #17161
2365997,2365999 #17162
2366057,2366059 #17163
2366207,2366209 #17164
2366387,2366389 #17165
2366489,2366491 #17166
2366627,2366629 #17167
2366669,2366671 #17168
2367119,2367121 #17169
2367329,2367331 #17170
2367509,2367511 #17171
2367929,2367931 #17172
2367971,2367973 #17173
2368127,2368129 #17174
2368211,2368213 #17175
2368271,2368273 #17176
2368391,2368393 #17177
2368439,2368441 #17178
2368577,2368579 #17179
2368601,2368603 #17180
2368757,2368759 #17181
2368799,2368801 #17182
2369201,2369203 #17183
2369231,2369233 #17184
2369537,2369539 #17185
2369639,2369641 #17186
2369837,2369839 #17187
2370239,2370241 #17188
2370299,2370301 #17189
2370629,2370631 #17190
2370671,2370673 #17191
2370941,2370943 #17192
2371307,2371309 #17193
2371709,2371711 #17194
2371847,2371849 #17195
2371877,2371879 #17196
2372099,2372101 #17197
2372369,2372371 #17198
2372441,2372443 #17199
2372507,2372509 #17200
2372561,2372563 #17201
2372597,2372599 #17202
2372681,2372683 #17203
2372759,2372761 #17204
2372987,2372989 #17205
2372999,2373001 #17206
2373167,2373169 #17207
2373227,2373229 #17208
2373401,2373403 #17209
2373407,2373409 #17210
2373821,2373823 #17211
2374061,2374063 #17212
2374289,2374291 #17213
2374397,2374399 #17214
2374529,2374531 #17215
2375039,2375041 #17216
2375339,2375341 #17217
2375759,2375761 #17218
2375771,2375773 #17219
2376161,2376163 #17220
2376167,2376169 #17221
2376329,2376331 #17222
2376419,2376421 #17223
2376641,2376643 #17224
2377019,2377021 #17225
2377379,2377381 #17226
2377787,2377789 #17227
2377799,2377801 #17228
2378069,2378071 #17229
2378219,2378221 #17230
2378291,2378293 #17231
2378357,2378359 #17232
2378669,2378671 #17233
2378771,2378773 #17234
2378951,2378953 #17235
2379077,2379079 #17236
2379149,2379151 #17237
2379239,2379241 #17238
2379449,2379451 #17239
2379569,2379571 #17240
2379929,2379931 #17241
2380121,2380123 #17242
2380421,2380423 #17243
2380487,2380489 #17244
2380517,2380519 #17245
2380619,2380621 #17246
2381081,2381083 #17247
2381087,2381089 #17248
2381147,2381149 #17249
2381189,2381191 #17250
2381339,2381341 #17251
2381789,2381791 #17252
2381879,2381881 #17253
2381891,2381893 #17254
2381969,2381971 #17255
2381999,2382001 #17256
2382299,2382301 #17257
2382449,2382451 #17258
2382461,2382463 #17259
2382557,2382559 #17260
2382857,2382859 #17261
2382881,2382883 #17262
2382977,2382979 #17263
2383571,2383573 #17264
2383679,2383681 #17265
2383751,2383753 #17266
2383811,2383813 #17267
2383919,2383921 #17268
2384381,2384383 #17269
2384579,2384581 #17270
2384609,2384611 #17271
2384951,2384953 #17272
2385209,2385211 #17273
2385599,2385601 #17274
2385701,2385703 #17275
2385827,2385829 #17276
2385881,2385883 #17277
2385959,2385961 #17278
2385989,2385991 #17279
2386061,2386063 #17280
2386289,2386291 #17281
2386469,2386471 #17282
2386661,2386663 #17283
2386859,2386861 #17284
2387039,2387041 #17285
2387051,2387053 #17286
2387417,2387419 #17287
2387447,2387449 #17288
2387909,2387911 #17289
2387951,2387953 #17290
2387969,2387971 #17291
2388101,2388103 #17292
2388161,2388163 #17293
2388257,2388259 #17294
2388359,2388361 #17295
2388557,2388559 #17296
2388677,2388679 #17297
2388899,2388901 #17298
2389181,2389183 #17299
2389241,2389243 #17300
2389481,2389483 #17301
2389529,2389531 #17302
2389589,2389591 #17303
2389661,2389663 #17304
2389967,2389969 #17305
2390021,2390023 #17306
2390051,2390053 #17307
2390429,2390431 #17308
2390471,2390473 #17309
2390909,2390911 #17310
2391041,2391043 #17311
2391089,2391091 #17312
2391437,2391439 #17313
2391449,2391451 #17314
2391539,2391541 #17315
2392001,2392003 #17316
2392139,2392141 #17317
2392517,2392519 #17318
2392571,2392573 #17319
2393021,2393023 #17320
2393177,2393179 #17321
2393759,2393761 #17322
2393927,2393929 #17323
2394149,2394151 #17324
2394239,2394241 #17325
2394317,2394319 #17326
2394419,2394421 #17327
2394479,2394481 #17328
2394629,2394631 #17329
2394641,2394643 #17330
2395397,2395399 #17331
2395739,2395741 #17332
2395847,2395849 #17333
2395871,2395873 #17334
2396039,2396041 #17335
2396129,2396131 #17336
2396237,2396239 #17337
2396309,2396311 #17338
2396591,2396593 #17339
2396741,2396743 #17340
2396921,2396923 #17341
2397179,2397181 #17342
2397821,2397823 #17343
2397851,2397853 #17344
2397947,2397949 #17345
2398157,2398159 #17346
2398169,2398171 #17347
2398181,2398183 #17348
2398259,2398261 #17349
2398367,2398369 #17350
2398481,2398483 #17351
2398679,2398681 #17352
2399027,2399029 #17353
2399039,2399041 #17354
2399387,2399389 #17355
2399477,2399479 #17356
2399597,2399599 #17357
2399627,2399629 #17358
2399711,2399713 #17359
2399807,2399809 #17360
2400107,2400109 #17361
2400161,2400163 #17362
2401547,2401549 #17363
2401667,2401669 #17364
2401967,2401969 #17365
2402087,2402089 #17366
2402201,2402203 #17367
2402261,2402263 #17368
2402291,2402293 #17369
2402381,2402383 #17370
2402789,2402791 #17371
2402837,2402839 #17372
2403209,2403211 #17373
2403551,2403553 #17374
2403587,2403589 #17375
2403677,2403679 #17376
2403689,2403691 #17377
2403881,2403883 #17378
2403887,2403889 #17379
2403911,2403913 #17380
2404067,2404069 #17381
2404289,2404291 #17382
2404541,2404543 #17383
2404877,2404879 #17384
2404931,2404933 #17385
2404991,2404993 #17386
2405069,2405071 #17387
2405147,2405149 #17388
2405339,2405341 #17389
2405441,2405443 #17390
2405561,2405563 #17391
2405747,2405749 #17392
2405831,2405833 #17393
2405981,2405983 #17394
2406461,2406463 #17395
2406617,2406619 #17396
2406629,2406631 #17397
2407001,2407003 #17398
2407577,2407579 #17399
2408009,2408011 #17400
2408279,2408281 #17401
2408309,2408311 #17402
2408501,2408503 #17403
2408561,2408563 #17404
2408759,2408761 #17405
2408771,2408773 #17406
2408969,2408971 #17407
2408981,2408983 #17408
2409131,2409133 #17409
2409191,2409193 #17410
2409269,2409271 #17411
2409299,2409301 #17412
2409311,2409313 #17413
2409389,2409391 #17414
2409467,2409469 #17415
2410181,2410183 #17416
2410271,2410273 #17417
2410337,2410339 #17418
2410517,2410519 #17419
2410829,2410831 #17420
2410937,2410939 #17421
2410997,2410999 #17422
2411009,2411011 #17423
2411027,2411029 #17424
2411207,2411209 #17425
2411219,2411221 #17426
2411291,2411293 #17427
2411639,2411641 #17428
2411867,2411869 #17429
2412197,2412199 #17430
2412299,2412301 #17431
2412407,2412409 #17432
2412797,2412799 #17433
2412959,2412961 #17434
2413259,2413261 #17435
2413421,2413423 #17436
2413427,2413429 #17437
2413469,2413471 #17438
2413517,2413519 #17439
2413601,2413603 #17440
2413637,2413639 #17441
2414099,2414101 #17442
2414129,2414131 #17443
2414177,2414179 #17444
2414261,2414263 #17445
2414411,2414413 #17446
2414549,2414551 #17447
2414591,2414593 #17448
2414849,2414851 #17449
2414981,2414983 #17450
2415407,2415409 #17451
2415557,2415559 #17452
2415629,2415631 #17453
2415689,2415691 #17454
2415701,2415703 #17455
2416229,2416231 #17456
2416241,2416243 #17457
2416301,2416303 #17458
2416859,2416861 #17459
2417027,2417029 #17460
2417087,2417089 #17461
2417117,2417119 #17462
2417201,2417203 #17463
2417339,2417341 #17464
2417741,2417743 #17465
2417771,2417773 #17466
2417939,2417941 #17467
2417981,2417983 #17468
2417999,2418001 #17469
2418077,2418079 #17470
2418347,2418349 #17471
2418509,2418511 #17472
2418671,2418673 #17473
2418677,2418679 #17474
2419601,2419603 #17475
2419619,2419621 #17476
2419721,2419723 #17477
2419799,2419801 #17478
2419871,2419873 #17479
2419979,2419981 #17480
2420111,2420113 #17481
2420567,2420569 #17482
2420609,2420611 #17483
2420687,2420689 #17484
2420699,2420701 #17485
2421281,2421283 #17486
2421449,2421451 #17487
2421467,2421469 #17488
2421821,2421823 #17489
2421917,2421919 #17490
2422169,2422171 #17491
2422241,2422243 #17492
2422421,2422423 #17493
2422487,2422489 #17494
2422559,2422561 #17495
2422697,2422699 #17496
2422757,2422759 #17497
2422997,2422999 #17498
2423021,2423023 #17499
2423039,2423041 #17500
2423147,2423149 #17501
2423411,2423413 #17502
2423417,2423419 #17503
2423567,2423569 #17504
2423801,2423803 #17505
2424089,2424091 #17506
2424491,2424493 #17507
2424971,2424973 #17508
2425019,2425021 #17509
2425229,2425231 #17510
2425259,2425261 #17511
2425361,2425363 #17512
2425457,2425459 #17513
2425697,2425699 #17514
2426057,2426059 #17515
2426267,2426269 #17516
2426381,2426383 #17517
2426441,2426443 #17518
2426777,2426779 #17519
2426819,2426821 #17520
2426951,2426953 #17521
2427287,2427289 #17522
2427461,2427463 #17523
2427587,2427589 #17524
2427779,2427781 #17525
2428157,2428159 #17526
2428169,2428171 #17527
2428241,2428243 #17528
2428451,2428453 #17529
2428649,2428651 #17530
2428889,2428891 #17531
2428997,2428999 #17532
2429057,2429059 #17533
2429267,2429269 #17534
2429597,2429599 #17535
2429729,2429731 #17536
2429771,2429773 #17537
2430011,2430013 #17538
2430089,2430091 #17539
2430731,2430733 #17540
2430761,2430763 #17541
2431061,2431063 #17542
2431439,2431441 #17543
2431577,2431579 #17544
2431841,2431843 #17545
2432237,2432239 #17546
2432657,2432659 #17547
2432669,2432671 #17548
2432999,2433001 #17549
2433059,2433061 #17550
2433251,2433253 #17551
2433491,2433493 #17552
2433521,2433523 #17553
2434049,2434051 #17554
2434097,2434099 #17555
2434277,2434279 #17556
2434841,2434843 #17557
2434967,2434969 #17558
2435051,2435053 #17559
2435201,2435203 #17560
2435339,2435341 #17561
2435567,2435569 #17562
2435729,2435731 #17563
2436059,2436061 #17564
2436209,2436211 #17565
2436407,2436409 #17566
2436611,2436613 #17567
2436701,2436703 #17568
2436977,2436979 #17569
2437007,2437009 #17570
2437427,2437429 #17571
2437637,2437639 #17572
2437691,2437693 #17573
2437847,2437849 #17574
2437997,2437999 #17575
2438081,2438083 #17576
2438339,2438341 #17577
2438459,2438461 #17578
2438507,2438509 #17579
2438627,2438629 #17580
2439179,2439181 #17581
2439317,2439319 #17582
2439497,2439499 #17583
2439737,2439739 #17584
2439989,2439991 #17585
2440019,2440021 #17586
2440211,2440213 #17587
2440391,2440393 #17588
2440577,2440579 #17589
2440589,2440591 #17590
2440679,2440681 #17591
2440817,2440819 #17592
2441207,2441209 #17593
2441267,2441269 #17594
2441561,2441563 #17595
2441639,2441641 #17596
2441807,2441809 #17597
2442017,2442019 #17598
2442197,2442199 #17599
2442287,2442289 #17600
2442497,2442499 #17601
2442941,2442943 #17602
2443031,2443033 #17603
2443211,2443213 #17604
2443781,2443783 #17605
2443787,2443789 #17606
2443997,2443999 #17607
2444081,2444083 #17608
2444129,2444131 #17609
2444159,2444161 #17610
2444357,2444359 #17611
2444471,2444473 #17612
2445347,2445349 #17613
2445461,2445463 #17614
2445647,2445649 #17615
2445767,2445769 #17616
2445827,2445829 #17617
2446097,2446099 #17618
2446151,2446153 #17619
2446331,2446333 #17620
2446811,2446813 #17621
2446889,2446891 #17622
2447021,2447023 #17623
2447327,2447329 #17624
2447351,2447353 #17625
2447519,2447521 #17626
2447567,2447569 #17627
2447579,2447581 #17628
2447759,2447761 #17629
2447831,2447833 #17630
2448071,2448073 #17631
2448107,2448109 #17632
2448827,2448829 #17633
2448869,2448871 #17634
2448881,2448883 #17635
2449169,2449171 #17636
2449439,2449441 #17637
2449691,2449693 #17638
2449787,2449789 #17639
2449859,2449861 #17640
2450141,2450143 #17641
2450291,2450293 #17642
2450549,2450551 #17643
2450597,2450599 #17644
2450711,2450713 #17645
2450807,2450809 #17646
2451221,2451223 #17647
2451257,2451259 #17648
2451467,2451469 #17649
2451539,2451541 #17650
2451641,2451643 #17651
2451719,2451721 #17652
2451767,2451769 #17653
2451809,2451811 #17654
2452337,2452339 #17655
2452517,2452519 #17656
2452529,2452531 #17657
2452757,2452759 #17658
2452829,2452831 #17659
2452859,2452861 #17660
2452949,2452951 #17661
2453051,2453053 #17662
2453177,2453179 #17663
2453291,2453293 #17664
2453417,2453419 #17665
2453441,2453443 #17666
2453459,2453461 #17667
2453651,2453653 #17668
2453921,2453923 #17669
2454119,2454121 #17670
2454251,2454253 #17671
2454869,2454871 #17672
2455001,2455003 #17673
2455127,2455129 #17674
2455307,2455309 #17675
2455337,2455339 #17676
2455379,2455381 #17677
2455469,2455471 #17678
2455511,2455513 #17679
2455679,2455681 #17680
2455907,2455909 #17681
2456087,2456089 #17682
2456357,2456359 #17683
2456429,2456431 #17684
2456747,2456749 #17685
2456801,2456803 #17686
2456981,2456983 #17687
2456999,2457001 #17688
2457317,2457319 #17689
2457347,2457349 #17690
2457731,2457733 #17691
2457899,2457901 #17692
2458061,2458063 #17693
2458151,2458153 #17694
2458367,2458369 #17695
2458409,2458411 #17696
2458457,2458459 #17697
2458607,2458609 #17698
2458661,2458663 #17699
2458667,2458669 #17700
2458679,2458681 #17701
2458901,2458903 #17702
2459027,2459029 #17703
2459141,2459143 #17704
2459291,2459293 #17705
2459381,2459383 #17706
2459489,2459491 #17707
2459621,2459623 #17708
2459657,2459659 #17709
2459789,2459791 #17710
2459921,2459923 #17711
2460179,2460181 #17712
2460299,2460301 #17713
2460431,2460433 #17714
2460509,2460511 #17715
2460641,2460643 #17716
2460719,2460721 #17717
2460881,2460883 #17718
2460917,2460919 #17719
2460959,2460961 #17720
2461091,2461093 #17721
2461169,2461171 #17722
2461229,2461231 #17723
2461337,2461339 #17724
2461397,2461399 #17725
2461577,2461579 #17726
2461727,2461729 #17727
2461871,2461873 #17728
2462639,2462641 #17729
2462699,2462701 #17730
2462741,2462743 #17731
2463029,2463031 #17732
2463161,2463163 #17733
2463311,2463313 #17734
2463761,2463763 #17735
2463947,2463949 #17736
2464211,2464213 #17737
2464589,2464591 #17738
2464799,2464801 #17739
2464919,2464921 #17740
2464937,2464939 #17741
2465159,2465161 #17742
2465537,2465539 #17743
2466491,2466493 #17744
2466881,2466883 #17745
2467019,2467021 #17746
2467217,2467219 #17747
2467391,2467393 #17748
2467607,2467609 #17749
2467709,2467711 #17750
2467901,2467903 #17751
2467919,2467921 #17752
2467961,2467963 #17753
2467979,2467981 #17754
2468099,2468101 #17755
2468129,2468131 #17756
2468447,2468449 #17757
2468951,2468953 #17758
2468969,2468971 #17759
2469281,2469283 #17760
2469317,2469319 #17761
2469407,2469409 #17762
2469431,2469433 #17763
2469557,2469559 #17764
2469581,2469583 #17765
2469869,2469871 #17766
2470001,2470003 #17767
2470121,2470123 #17768
2470199,2470201 #17769
2470241,2470243 #17770
2470331,2470333 #17771
2470337,2470339 #17772
2470691,2470693 #17773
2470889,2470891 #17774
2471057,2471059 #17775
2471087,2471089 #17776
2471321,2471323 #17777
2471471,2471473 #17778
2471531,2471533 #17779
2472179,2472181 #17780
2472539,2472541 #17781
2472557,2472559 #17782
2472851,2472853 #17783
2472929,2472931 #17784
2472959,2472961 #17785
2473127,2473129 #17786
2473181,2473183 #17787
2473421,2473423 #17788
2473451,2473453 #17789
2473607,2473609 #17790
2473631,2473633 #17791
2474051,2474053 #17792
2474117,2474119 #17793
2474207,2474209 #17794
2474711,2474713 #17795
2474861,2474863 #17796
2475089,2475091 #17797
2475287,2475289 #17798
2475437,2475439 #17799
2475797,2475799 #17800
2475857,2475859 #17801
2475959,2475961 #17802
2476037,2476039 #17803
2476079,2476081 #17804
2476391,2476393 #17805
2476421,2476423 #17806
2476751,2476753 #17807
2477129,2477131 #17808
2477159,2477161 #17809
2477171,2477173 #17810
2477309,2477311 #17811
2477327,2477329 #17812
2477411,2477413 #17813
2477609,2477611 #17814
2477639,2477641 #17815
2478239,2478241 #17816
2478269,2478271 #17817
2478347,2478349 #17818
2478521,2478523 #17819
2478527,2478529 #17820
2478587,2478589 #17821
2479487,2479489 #17822
2479661,2479663 #17823
2479667,2479669 #17824
2479691,2479693 #17825
2479847,2479849 #17826
2479901,2479903 #17827
2480081,2480083 #17828
2480207,2480209 #17829
2480501,2480503 #17830
2480717,2480719 #17831
2480909,2480911 #17832
2481137,2481139 #17833
2481179,2481181 #17834
2481317,2481319 #17835
2481497,2481499 #17836
2481839,2481841 #17837
2481887,2481889 #17838
2481977,2481979 #17839
2482349,2482351 #17840
2482619,2482621 #17841
2482769,2482771 #17842
2483519,2483521 #17843
2483669,2483671 #17844
2483711,2483713 #17845
2483867,2483869 #17846
2484017,2484019 #17847
2484197,2484199 #17848
2484569,2484571 #17849
2484731,2484733 #17850
2484899,2484901 #17851
2484917,2484919 #17852
2484959,2484961 #17853
2484971,2484973 #17854
2485001,2485003 #17855
2485121,2485123 #17856
2485277,2485279 #17857
2485391,2485393 #17858
2485667,2485669 #17859
2485937,2485939 #17860
2485997,2485999 #17861
2486039,2486041 #17862
2486147,2486149 #17863
2486189,2486191 #17864
2486219,2486221 #17865
2486381,2486383 #17866
2486579,2486581 #17867
2486591,2486593 #17868
2486831,2486833 #17869
2486969,2486971 #17870
2487071,2487073 #17871
2487137,2487139 #17872
2487227,2487229 #17873
2487521,2487523 #17874
2487599,2487601 #17875
2487671,2487673 #17876
2487809,2487811 #17877
2488217,2488219 #17878
2488397,2488399 #17879
2488427,2488429 #17880
2488469,2488471 #17881
2488907,2488909 #17882
2488961,2488963 #17883
2489159,2489161 #17884
2489237,2489239 #17885
2489339,2489341 #17886
2489411,2489413 #17887
2489717,2489719 #17888
2489759,2489761 #17889
2489867,2489869 #17890
2490659,2490661 #17891
2490809,2490811 #17892
2491007,2491009 #17893
2491607,2491609 #17894
2491757,2491759 #17895
2491961,2491963 #17896
2492069,2492071 #17897
2492459,2492461 #17898
2493077,2493079 #17899
2493107,2493109 #17900
2493329,2493331 #17901
2493347,2493349 #17902
2493707,2493709 #17903
2493719,2493721 #17904
2493851,2493853 #17905
2493947,2493949 #17906
2494031,2494033 #17907
2494169,2494171 #17908
2494379,2494381 #17909
2494421,2494423 #17910
2494439,2494441 #17911
2494829,2494831 #17912
2494949,2494951 #17913
2494979,2494981 #17914
2494991,2494993 #17915
2495321,2495323 #17916
2495459,2495461 #17917
2496077,2496079 #17918
2496251,2496253 #17919
2496269,2496271 #17920
2496491,2496493 #17921
2496827,2496829 #17922
2496917,2496919 #17923
2497211,2497213 #17924
2497421,2497423 #17925
2497511,2497513 #17926
2497631,2497633 #17927
2497751,2497753 #17928
2497877,2497879 #17929
2497931,2497933 #17930
2499059,2499061 #17931
2499137,2499139 #17932
2499149,2499151 #17933
2499641,2499643 #17934
2499779,2499781 #17935
2499941,2499943 #17936
2499947,2499949 #17937
2500049,2500051 #17938
2500439,2500441 #17939
2500637,2500639 #17940
2500781,2500783 #17941
2500889,2500891 #17942
2501099,2501101 #17943
2501249,2501251 #17944
2501591,2501593 #17945
2501789,2501791 #17946
2501897,2501899 #17947
2501957,2501959 #17948
2501999,2502001 #17949
2502209,2502211 #17950
2502341,2502343 #17951
2502359,2502361 #17952
2502371,2502373 #17953
2502389,2502391 #17954
2502581,2502583 #17955
2502779,2502781 #17956
2503139,2503141 #17957
2503181,2503183 #17958
2503211,2503213 #17959
2503511,2503513 #17960
2503637,2503639 #17961
2503871,2503873 #17962
2503997,2503999 #17963
2504009,2504011 #17964
2504069,2504071 #17965
2504429,2504431 #17966
2504501,2504503 #17967
2505119,2505121 #17968
2505161,2505163 #17969
2505539,2505541 #17970
2505791,2505793 #17971
2505857,2505859 #17972
2505989,2505991 #17973
2506199,2506201 #17974
2506277,2506279 #17975
2506409,2506411 #17976
2506547,2506549 #17977
2506979,2506981 #17978
2507147,2507149 #17979
2507387,2507389 #17980
2507627,2507629 #17981
2507861,2507863 #17982
2508041,2508043 #17983
2508047,2508049 #17984
2508089,2508091 #17985
2508281,2508283 #17986
2508557,2508559 #17987
2508689,2508691 #17988
2508899,2508901 #17989
2509061,2509063 #17990
2509517,2509519 #17991
2509961,2509963 #17992
2510447,2510449 #17993
2510531,2510533 #17994
2510549,2510551 #17995
2510579,2510581 #17996
2510741,2510743 #17997
2510801,2510803 #17998
2511107,2511109 #17999
2511149,2511151 #18000
2511167,2511169 #18001
2511791,2511793 #18002
2511809,2511811 #18003
2512019,2512021 #18004
2512217,2512219 #18005
2512511,2512513 #18006
2512637,2512639 #18007
2512721,2512723 #18008
2512841,2512843 #18009
2513087,2513089 #18010
2513309,2513311 #18011
2513351,2513353 #18012
2513549,2513551 #18013
2513591,2513593 #18014
2513657,2513659 #18015
2513801,2513803 #18016
2514089,2514091 #18017
2514227,2514229 #18018
2514437,2514439 #18019
2514467,2514469 #18020
2514527,2514529 #18021
2514947,2514949 #18022
2514959,2514961 #18023
2514989,2514991 #18024
2515319,2515321 #18025
2515451,2515453 #18026
2515529,2515531 #18027
2515571,2515573 #18028
2515697,2515699 #18029
2515871,2515873 #18030
2516411,2516413 #18031
2517131,2517133 #18032
2517269,2517271 #18033
2517467,2517469 #18034
2517677,2517679 #18035
2517701,2517703 #18036
2517797,2517799 #18037
2518067,2518069 #18038
2518079,2518081 #18039
2518289,2518291 #18040
2518559,2518561 #18041
2518727,2518729 #18042
2518949,2518951 #18043
2519087,2519089 #18044
2519159,2519161 #18045
2519639,2519641 #18046
2519729,2519731 #18047
2519939,2519941 #18048
2520149,2520151 #18049
2520431,2520433 #18050
2520611,2520613 #18051
2520629,2520631 #18052
2520779,2520781 #18053
2521019,2521021 #18054
2521037,2521039 #18055
2521271,2521273 #18056
2521499,2521501 #18057
2521721,2521723 #18058
2521919,2521921 #18059
2522057,2522059 #18060
2522087,2522089 #18061
2522657,2522659 #18062
2522669,2522671 #18063
2522759,2522761 #18064
2522789,2522791 #18065
2522909,2522911 #18066
2522981,2522983 #18067
2523011,2523013 #18068
2523041,2523043 #18069
2523149,2523151 #18070
2523161,2523163 #18071
2523527,2523529 #18072
2523641,2523643 #18073
2523707,2523709 #18074
2524031,2524033 #18075
2524199,2524201 #18076
2524217,2524219 #18077
2524259,2524261 #18078
2524349,2524351 #18079
2524469,2524471 #18080
2524649,2524651 #18081
2524679,2524681 #18082
2524859,2524861 #18083
2524937,2524939 #18084
2525177,2525179 #18085
2525189,2525191 #18086
2525219,2525221 #18087
2525267,2525269 #18088
2525387,2525389 #18089
2525669,2525671 #18090
2526299,2526301 #18091
2526581,2526583 #18092
2526647,2526649 #18093
2527097,2527099 #18094
2527277,2527279 #18095
2527451,2527453 #18096
2527559,2527561 #18097
2527961,2527963 #18098
2528231,2528233 #18099
2528627,2528629 #18100
2528819,2528821 #18101
2528831,2528833 #18102
2528861,2528863 #18103
2528891,2528893 #18104
2529227,2529229 #18105
2529251,2529253 #18106
2529347,2529349 #18107
2529419,2529421 #18108
2529689,2529691 #18109
2529911,2529913 #18110
2530109,2530111 #18111
2530139,2530141 #18112
2530457,2530459 #18113
2530571,2530573 #18114
2530961,2530963 #18115
2530991,2530993 #18116
2531099,2531101 #18117
2531369,2531371 #18118
2531609,2531611 #18119
2531687,2531689 #18120
2531699,2531701 #18121
2531831,2531833 #18122
2531981,2531983 #18123
2532107,2532109 #18124
2532197,2532199 #18125
2532401,2532403 #18126
2532449,2532451 #18127
2532707,2532709 #18128
2532989,2532991 #18129
2533007,2533009 #18130
2533031,2533033 #18131
2533301,2533303 #18132
2534039,2534041 #18133
2534267,2534269 #18134
2534501,2534503 #18135
2534561,2534563 #18136
2534879,2534881 #18137
2534951,2534953 #18138
2535017,2535019 #18139
2535101,2535103 #18140
2535107,2535109 #18141
2535161,2535163 #18142
2535917,2535919 #18143
2536241,2536243 #18144
2536307,2536309 #18145
2536361,2536363 #18146
2536379,2536381 #18147
2536559,2536561 #18148
2536577,2536579 #18149
2536799,2536801 #18150
2536811,2536813 #18151
2536907,2536909 #18152
2537081,2537083 #18153
2537111,2537113 #18154
2537459,2537461 #18155
2537501,2537503 #18156
2538059,2538061 #18157
2538101,2538103 #18158
2538299,2538301 #18159
2538449,2538451 #18160
2538509,2538511 #18161
2538617,2538619 #18162
2538707,2538709 #18163
2538749,2538751 #18164
2538917,2538919 #18165
2539319,2539321 #18166
2539349,2539351 #18167
2539529,2539531 #18168
2539571,2539573 #18169
2539631,2539633 #18170
2539961,2539963 #18171
2540177,2540179 #18172
2540201,2540203 #18173
2540339,2540341 #18174
2540441,2540443 #18175
2540537,2540539 #18176
2540687,2540689 #18177
2540981,2540983 #18178
2541527,2541529 #18179
2541701,2541703 #18180
2541941,2541943 #18181
2541947,2541949 #18182
2542049,2542051 #18183
2542481,2542483 #18184
2542511,2542513 #18185
2542607,2542609 #18186
2542619,2542621 #18187
2543111,2543113 #18188
2543141,2543143 #18189
2543237,2543239 #18190
2543459,2543461 #18191
2543507,2543509 #18192
2543621,2543623 #18193
2544131,2544133 #18194
2544161,2544163 #18195
2544209,2544211 #18196
2544299,2544301 #18197
2544359,2544361 #18198
2544629,2544631 #18199
2544767,2544769 #18200
2544791,2544793 #18201
2544809,2544811 #18202
2544929,2544931 #18203
2545451,2545453 #18204
2545679,2545681 #18205
2545757,2545759 #18206
2545769,2545771 #18207
2545889,2545891 #18208
2546177,2546179 #18209
2546231,2546233 #18210
2546237,2546239 #18211
2546561,2546563 #18212
2546657,2546659 #18213
2546669,2546671 #18214
2546837,2546839 #18215
2546909,2546911 #18216
2547029,2547031 #18217
2547581,2547583 #18218
2547971,2547973 #18219
2548277,2548279 #18220
2548289,2548291 #18221
2548499,2548501 #18222
2548571,2548573 #18223
2548751,2548753 #18224
2548769,2548771 #18225
2548877,2548879 #18226
2549291,2549293 #18227
2549357,2549359 #18228
2549381,2549383 #18229
2549429,2549431 #18230
2549621,2549623 #18231
2550179,2550181 #18232
2550467,2550469 #18233
2550857,2550859 #18234
2550971,2550973 #18235
2551097,2551099 #18236
2551247,2551249 #18237
2551499,2551501 #18238
2551979,2551981 #18239
2552111,2552113 #18240
2552117,2552119 #18241
2552357,2552359 #18242
2552621,2552623 #18243
2552651,2552653 #18244
2552657,2552659 #18245
2552777,2552779 #18246
2553149,2553151 #18247
2553431,2553433 #18248
2553539,2553541 #18249
2553599,2553601 #18250
2553869,2553871 #18251
2554247,2554249 #18252
2554271,2554273 #18253
2554337,2554339 #18254
2554397,2554399 #18255
2554457,2554459 #18256
2554787,2554789 #18257
2554829,2554831 #18258
2555009,2555011 #18259
2555129,2555131 #18260
2555171,2555173 #18261
2555261,2555263 #18262
2555549,2555551 #18263
2556161,2556163 #18264
2556791,2556793 #18265
2557169,2557171 #18266
2557199,2557201 #18267
2557277,2557279 #18268
2557367,2557369 #18269
2557517,2557519 #18270
2557601,2557603 #18271
2558009,2558011 #18272
2558249,2558251 #18273
2558321,2558323 #18274
2558471,2558473 #18275
2558531,2558533 #18276
2558951,2558953 #18277
2559041,2559043 #18278
2559077,2559079 #18279
2559287,2559289 #18280
2559437,2559439 #18281
2559617,2559619 #18282
2559827,2559829 #18283
2560169,2560171 #18284
2560211,2560213 #18285
2560601,2560603 #18286
2560637,2560639 #18287
2560739,2560741 #18288
2560847,2560849 #18289
2560937,2560939 #18290
2561021,2561023 #18291
2561231,2561233 #18292
2561261,2561263 #18293
2561267,2561269 #18294
2561387,2561389 #18295
2561549,2561551 #18296
2561651,2561653 #18297
2561681,2561683 #18298
2561729,2561731 #18299
2561759,2561761 #18300
2561927,2561929 #18301
2562029,2562031 #18302
2562251,2562253 #18303
2562347,2562349 #18304
2562431,2562433 #18305
2562557,2562559 #18306
2562611,2562613 #18307
2562689,2562691 #18308
2562941,2562943 #18309
2562977,2562979 #18310
2563007,2563009 #18311
2563151,2563153 #18312
2563367,2563369 #18313
2563907,2563909 #18314
2564249,2564251 #18315
2564321,2564323 #18316
2564327,2564329 #18317
2564519,2564521 #18318
2565047,2565049 #18319
2565149,2565151 #18320
2565347,2565349 #18321
2565389,2565391 #18322
2565461,2565463 #18323
2566019,2566021 #18324
2566049,2566051 #18325
2566127,2566129 #18326
2566139,2566141 #18327
2566259,2566261 #18328
2566517,2566519 #18329
2566589,2566591 #18330
2567111,2567113 #18331
2567177,2567179 #18332
2567351,2567353 #18333
2567447,2567449 #18334
2567531,2567533 #18335
2567819,2567821 #18336
2568029,2568031 #18337
2568119,2568121 #18338
2568497,2568499 #18339
2568701,2568703 #18340
2568869,2568871 #18341
2568911,2568913 #18342
2569421,2569423 #18343
2569739,2569741 #18344
2569751,2569753 #18345
2569937,2569939 #18346
2570201,2570203 #18347
2570219,2570221 #18348
2570369,2570371 #18349
2570387,2570389 #18350
2570429,2570431 #18351
2570507,2570509 #18352
2570537,2570539 #18353
2570609,2570611 #18354
2570849,2570851 #18355
2571071,2571073 #18356
2571449,2571451 #18357
2571551,2571553 #18358
2571731,2571733 #18359
2572079,2572081 #18360
2572091,2572093 #18361
2572121,2572123 #18362
2572397,2572399 #18363
2572487,2572489 #18364
2572517,2572519 #18365
2572649,2572651 #18366
2572679,2572681 #18367
2572697,2572699 #18368
2572937,2572939 #18369
2573057,2573059 #18370
2573099,2573101 #18371
2573357,2573359 #18372
2574029,2574031 #18373
2574149,2574151 #18374
2574179,2574181 #18375
2574587,2574589 #18376
2574851,2574853 #18377
2575019,2575021 #18378
2575061,2575063 #18379
2575091,2575093 #18380
2575799,2575801 #18381
2575817,2575819 #18382
2575877,2575879 #18383
2575919,2575921 #18384
2576219,2576221 #18385
2576261,2576263 #18386
2576549,2576551 #18387
2576591,2576593 #18388
2576597,2576599 #18389
2576729,2576731 #18390
2576771,2576773 #18391
2577077,2577079 #18392
2577437,2577439 #18393
2577569,2577571 #18394
2577917,2577919 #18395
2577941,2577943 #18396
2578109,2578111 #18397
2578349,2578351 #18398
2578391,2578393 #18399
2578451,2578453 #18400
2578517,2578519 #18401
2578757,2578759 #18402
2578799,2578801 #18403
2578817,2578819 #18404
2578991,2578993 #18405
2579177,2579179 #18406
2579387,2579389 #18407
2579651,2579653 #18408
2579807,2579809 #18409
2580167,2580169 #18410
2580287,2580289 #18411
2580419,2580421 #18412
2580467,2580469 #18413
2580509,2580511 #18414
2580647,2580649 #18415
2580659,2580661 #18416
2580671,2580673 #18417
2580689,2580691 #18418
2580701,2580703 #18419
2580839,2580841 #18420
2580857,2580859 #18421
2581079,2581081 #18422
2581121,2581123 #18423
2581211,2581213 #18424
2581391,2581393 #18425
2581559,2581561 #18426
2581697,2581699 #18427
2581769,2581771 #18428
2581919,2581921 #18429
2581961,2581963 #18430
2582087,2582089 #18431
2582159,2582161 #18432
2582399,2582401 #18433
2582441,2582443 #18434
2582609,2582611 #18435
2582729,2582731 #18436
2582771,2582773 #18437
2583017,2583019 #18438
2583101,2583103 #18439
2583179,2583181 #18440
2583239,2583241 #18441
2583389,2583391 #18442
2583461,2583463 #18443
2583629,2583631 #18444
2583767,2583769 #18445
2583857,2583859 #18446
2584007,2584009 #18447
2584031,2584033 #18448
2584079,2584081 #18449
2584367,2584369 #18450
2584787,2584789 #18451
2584889,2584891 #18452
2584949,2584951 #18453
2585111,2585113 #18454
2585351,2585353 #18455
2585507,2585509 #18456
2585837,2585839 #18457
2585951,2585953 #18458
2585969,2585971 #18459
2585981,2585983 #18460
2586137,2586139 #18461
2586167,2586169 #18462
2586341,2586343 #18463
2586377,2586379 #18464
2586629,2586631 #18465
2586719,2586721 #18466
2586767,2586769 #18467
2586797,2586799 #18468
2586821,2586823 #18469
2587127,2587129 #18470
2587157,2587159 #18471
2587421,2587423 #18472
2587547,2587549 #18473
2587967,2587969 #18474
2588357,2588359 #18475
2588669,2588671 #18476
2588819,2588821 #18477
2588897,2588899 #18478
2589227,2589229 #18479
2589341,2589343 #18480
2589551,2589553 #18481
2589677,2589679 #18482
2589701,2589703 #18483
2589791,2589793 #18484
2590031,2590033 #18485
2590127,2590129 #18486
2590769,2590771 #18487
2590871,2590873 #18488
2591261,2591263 #18489
2591681,2591683 #18490
2591747,2591749 #18491
2591777,2591779 #18492
2591819,2591821 #18493
2591969,2591971 #18494
2592521,2592523 #18495
2592587,2592589 #18496
2592647,2592649 #18497
2592761,2592763 #18498
2592851,2592853 #18499
2592899,2592901 #18500
2593247,2593249 #18501
2593361,2593363 #18502
2593397,2593399 #18503
2593607,2593609 #18504
2593691,2593693 #18505
2593751,2593753 #18506
2593991,2593993 #18507
2594531,2594533 #18508
2594567,2594569 #18509
2594609,2594611 #18510
2594951,2594953 #18511
2594957,2594959 #18512
2594981,2594983 #18513
2594987,2594989 #18514
2595029,2595031 #18515
2595629,2595631 #18516
2595641,2595643 #18517
2596127,2596129 #18518
2596439,2596441 #18519
2596499,2596501 #18520
2596577,2596579 #18521
2596619,2596621 #18522
2596637,2596639 #18523
2596661,2596663 #18524
2596667,2596669 #18525
2596679,2596681 #18526
2596871,2596873 #18527
2597057,2597059 #18528
2597081,2597083 #18529
2597297,2597299 #18530
2597627,2597629 #18531
2597867,2597869 #18532
2597897,2597899 #18533
2597909,2597911 #18534
2598119,2598121 #18535
2598179,2598181 #18536
2598509,2598511 #18537
2598521,2598523 #18538
2598599,2598601 #18539
2598731,2598733 #18540
2598857,2598859 #18541
2599109,2599111 #18542
2599187,2599189 #18543
2599631,2599633 #18544
2599739,2599741 #18545
2600327,2600329 #18546
2600567,2600569 #18547
2601089,2601091 #18548
2601299,2601301 #18549
2601437,2601439 #18550
2601479,2601481 #18551
2601761,2601763 #18552
2602007,2602009 #18553
2602331,2602333 #18554
2602349,2602351 #18555
2602571,2602573 #18556
2602679,2602681 #18557
2602781,2602783 #18558
2602877,2602879 #18559
2602937,2602939 #18560
2603141,2603143 #18561
2603231,2603233 #18562
2603369,2603371 #18563
2603441,2603443 #18564
2603561,2603563 #18565
2603789,2603791 #18566
2603849,2603851 #18567
2603927,2603929 #18568
2604011,2604013 #18569
2604521,2604523 #18570
2604557,2604559 #18571
2604731,2604733 #18572
2604737,2604739 #18573
2605019,2605021 #18574
2605409,2605411 #18575
2605481,2605483 #18576
2605529,2605531 #18577
2605661,2605663 #18578
2605751,2605753 #18579
2605847,2605849 #18580
2606039,2606041 #18581
2606267,2606269 #18582
2606939,2606941 #18583
2607107,2607109 #18584
2607167,2607169 #18585
2607179,2607181 #18586
2607587,2607589 #18587
2607599,2607601 #18588
2607791,2607793 #18589
2607989,2607991 #18590
2608127,2608129 #18591
2608349,2608351 #18592
2608367,2608369 #18593
2608517,2608519 #18594
2608559,2608561 #18595
2609027,2609029 #18596
2609069,2609071 #18597
2609081,2609083 #18598
2609207,2609209 #18599
2609261,2609263 #18600
2609309,2609311 #18601
2609489,2609491 #18602
2609597,2609599 #18603
2609699,2609701 #18604
2610131,2610133 #18605
2610191,2610193 #18606
2610341,2610343 #18607
2610449,2610451 #18608
2610497,2610499 #18609
2610611,2610613 #18610
2610677,2610679 #18611
2610719,2610721 #18612
2610821,2610823 #18613
2611157,2611159 #18614
2611667,2611669 #18615
2611799,2611801 #18616
2611907,2611909 #18617
2611979,2611981 #18618
2612249,2612251 #18619
2612411,2612413 #18620
2612429,2612431 #18621
2612537,2612539 #18622
2612789,2612791 #18623
2612879,2612881 #18624
2613041,2613043 #18625
2613227,2613229 #18626
2613647,2613649 #18627
2613671,2613673 #18628
2613761,2613763 #18629
2613899,2613901 #18630
2613977,2613979 #18631
2614061,2614063 #18632
2614067,2614069 #18633
2614121,2614123 #18634
2614301,2614303 #18635
2614361,2614363 #18636
2614427,2614429 #18637
2614517,2614519 #18638
2614697,2614699 #18639
2614769,2614771 #18640
2615111,2615113 #18641
2615279,2615281 #18642
2615357,2615359 #18643
2615447,2615449 #18644
2615531,2615533 #18645
2615651,2615653 #18646
2615957,2615959 #18647
2615969,2615971 #18648
2615981,2615983 #18649
2616191,2616193 #18650
2616671,2616673 #18651
2616701,2616703 #18652
2616881,2616883 #18653
2617091,2617093 #18654
2617169,2617171 #18655
2617187,2617189 #18656
2617259,2617261 #18657
2617409,2617411 #18658
2617427,2617429 #18659
2617631,2617633 #18660
2618261,2618263 #18661
2618279,2618281 #18662
2618531,2618533 #18663
2618879,2618881 #18664
2619011,2619013 #18665
2619299,2619301 #18666
2619389,2619391 #18667
2619557,2619559 #18668
2619917,2619919 #18669
2620019,2620021 #18670
2620097,2620099 #18671
2620139,2620141 #18672
2620439,2620441 #18673
2620529,2620531 #18674
2620589,2620591 #18675
2620661,2620663 #18676
2621369,2621371 #18677
2621921,2621923 #18678
2622119,2622121 #18679
2622341,2622343 #18680
2623331,2623333 #18681
2623529,2623531 #18682
2623571,2623573 #18683
2623589,2623591 #18684
2623721,2623723 #18685
2623757,2623759 #18686
2623937,2623939 #18687
2623991,2623993 #18688
2624051,2624053 #18689
2624177,2624179 #18690
2624267,2624269 #18691
2624309,2624311 #18692
2624561,2624563 #18693
2624957,2624959 #18694
2625251,2625253 #18695
2625521,2625523 #18696
2625617,2625619 #18697
2625641,2625643 #18698
2625809,2625811 #18699
2625947,2625949 #18700
2626049,2626051 #18701
2626751,2626753 #18702
2626901,2626903 #18703
2626931,2626933 #18704
2627057,2627059 #18705
2627201,2627203 #18706
2627477,2627479 #18707
2627507,2627509 #18708
2627561,2627563 #18709
2627699,2627701 #18710
2627789,2627791 #18711
2627981,2627983 #18712
2628167,2628169 #18713
2628539,2628541 #18714
2628779,2628781 #18715
2628809,2628811 #18716
2629091,2629093 #18717
2629127,2629129 #18718
2629307,2629309 #18719
2629421,2629423 #18720
2629481,2629483 #18721
2629589,2629591 #18722
2629721,2629723 #18723
2629811,2629813 #18724
2629901,2629903 #18725
2629931,2629933 #18726
2630237,2630239 #18727
2630321,2630323 #18728
2630429,2630431 #18729
2630489,2630491 #18730
2630741,2630743 #18731
2630861,2630863 #18732
2630921,2630923 #18733
2631281,2631283 #18734
2631467,2631469 #18735
2631509,2631511 #18736
2631527,2631529 #18737
2631647,2631649 #18738
2631689,2631691 #18739
2631917,2631919 #18740
2631947,2631949 #18741
2631971,2631973 #18742
2632151,2632153 #18743
2632247,2632249 #18744
2632829,2632831 #18745
2632919,2632921 #18746
2633129,2633131 #18747
2633219,2633221 #18748
2633261,2633263 #18749
2633441,2633443 #18750
2633537,2633539 #18751
2633639,2633641 #18752
2633711,2633713 #18753
2634011,2634013 #18754
2634629,2634631 #18755
2634689,2634691 #18756
2634941,2634943 #18757
2635097,2635099 #18758
2635481,2635483 #18759
2635487,2635489 #18760
2635691,2635693 #18761
2635877,2635879 #18762
2635907,2635909 #18763
2637197,2637199 #18764
2637251,2637253 #18765
2637539,2637541 #18766
2637671,2637673 #18767
2637797,2637799 #18768
2637959,2637961 #18769
2638199,2638201 #18770
2638367,2638369 #18771
2638631,2638633 #18772
2638841,2638843 #18773
2639069,2639071 #18774
2639177,2639179 #18775
2639489,2639491 #18776
2639699,2639701 #18777
2639759,2639761 #18778
2639939,2639941 #18779
2639969,2639971 #18780
2640137,2640139 #18781
2640347,2640349 #18782
2640509,2640511 #18783
2640707,2640709 #18784
2640821,2640823 #18785
2640917,2640919 #18786
2641061,2641063 #18787
2641151,2641153 #18788
2641277,2641279 #18789
2641367,2641369 #18790
2641421,2641423 #18791
2641517,2641519 #18792
2641547,2641549 #18793
2641631,2641633 #18794
2641799,2641801 #18795
2641829,2641831 #18796
2641907,2641909 #18797
2642039,2642041 #18798
2642147,2642149 #18799
2642201,2642203 #18800
2642357,2642359 #18801
2642789,2642791 #18802
2643059,2643061 #18803
2643131,2643133 #18804
2643239,2643241 #18805
2643341,2643343 #18806
2643581,2643583 #18807
2643659,2643661 #18808
2643671,2643673 #18809
2644091,2644093 #18810
2644139,2644141 #18811
2644151,2644153 #18812
2644181,2644183 #18813
2644727,2644729 #18814
2644847,2644849 #18815
2644919,2644921 #18816
2645099,2645101 #18817
2645129,2645131 #18818
2645189,2645191 #18819
2645219,2645221 #18820
2645429,2645431 #18821
2645477,2645479 #18822
2645519,2645521 #18823
2645549,2645551 #18824
2645567,2645569 #18825
2645777,2645779 #18826
2645891,2645893 #18827
2646011,2646013 #18828
2646107,2646109 #18829
2646989,2646991 #18830
2647079,2647081 #18831
2647157,2647159 #18832
2647319,2647321 #18833
2647361,2647363 #18834
2647571,2647573 #18835
2647889,2647891 #18836
2648081,2648083 #18837
2648099,2648101 #18838
2648507,2648509 #18839
2648531,2648533 #18840
2648909,2648911 #18841
2649137,2649139 #18842
2649497,2649499 #18843
2649551,2649553 #18844
2649611,2649613 #18845
2649677,2649679 #18846
2649929,2649931 #18847
2650007,2650009 #18848
2650091,2650093 #18849
2650229,2650231 #18850
2650379,2650381 #18851
2650577,2650579 #18852
2650619,2650621 #18853
2650787,2650789 #18854
2650931,2650933 #18855
2651039,2651041 #18856
2651189,2651191 #18857
2651237,2651239 #18858
2651291,2651293 #18859
2651489,2651491 #18860
2651501,2651503 #18861
2651741,2651743 #18862
2651819,2651821 #18863
2652029,2652031 #18864
2652101,2652103 #18865
2652149,2652151 #18866
2652371,2652373 #18867
2652407,2652409 #18868
2652437,2652439 #18869
2652941,2652943 #18870
2653109,2653111 #18871
2653619,2653621 #18872
2653697,2653699 #18873
2653811,2653813 #18874
2653967,2653969 #18875
2654387,2654389 #18876
2654501,2654503 #18877
2654651,2654653 #18878
2654801,2654803 #18879
2654831,2654833 #18880
2654879,2654881 #18881
2655047,2655049 #18882
2655407,2655409 #18883
2655437,2655439 #18884
2655461,2655463 #18885
2655479,2655481 #18886
2655797,2655799 #18887
2655941,2655943 #18888
2656271,2656273 #18889
2656319,2656321 #18890
2656361,2656363 #18891
2656499,2656501 #18892
2656727,2656729 #18893
2656919,2656921 #18894
2656991,2656993 #18895
2657069,2657071 #18896
2657189,2657191 #18897
2657201,2657203 #18898
2657327,2657329 #18899
2657339,2657341 #18900
2657399,2657401 #18901
2657561,2657563 #18902
2658077,2658079 #18903
2658287,2658289 #18904
2658377,2658379 #18905
2658449,2658451 #18906
2658659,2658661 #18907
2658701,2658703 #18908
2658881,2658883 #18909
2658977,2658979 #18910
2659091,2659093 #18911
2659337,2659339 #18912
2659439,2659441 #18913
2659451,2659453 #18914
2659469,2659471 #18915
2659859,2659861 #18916
2660069,2660071 #18917
2660087,2660089 #18918
2660351,2660353 #18919
2660657,2660659 #18920
2661641,2661643 #18921
2661731,2661733 #18922
2661779,2661781 #18923
2661929,2661931 #18924
2661947,2661949 #18925
2661959,2661961 #18926
2662067,2662069 #18927
2662157,2662159 #18928
2662769,2662771 #18929
2662787,2662789 #18930
2662811,2662813 #18931
2662901,2662903 #18932
2662949,2662951 #18933
2663027,2663029 #18934
2663357,2663359 #18935
2663429,2663431 #18936
2663459,2663461 #18937
2663567,2663569 #18938
2663579,2663581 #18939
2663669,2663671 #18940
2664041,2664043 #18941
2664059,2664061 #18942
2664071,2664073 #18943
2664227,2664229 #18944
2664449,2664451 #18945
2664551,2664553 #18946
2664689,2664691 #18947
2664707,2664709 #18948
2664899,2664901 #18949
2664929,2664931 #18950
2665007,2665009 #18951
2665319,2665321 #18952
2665499,2665501 #18953
2665667,2665669 #18954
2665799,2665801 #18955
2665841,2665843 #18956
2665931,2665933 #18957
2666087,2666089 #18958
2666381,2666383 #18959
2666537,2666539 #18960
2666747,2666749 #18961
2666861,2666863 #18962
2667059,2667061 #18963
2667191,2667193 #18964
2667359,2667361 #18965
2667461,2667463 #18966
2667569,2667571 #18967
2667881,2667883 #18968
2667947,2667949 #18969
2668091,2668093 #18970
2668217,2668219 #18971
2668229,2668231 #18972
2668241,2668243 #18973
2668247,2668249 #18974
2668637,2668639 #18975
2668877,2668879 #18976
2668907,2668909 #18977
2669201,2669203 #18978
2669267,2669269 #18979
2669339,2669341 #18980
2669417,2669419 #18981
2669507,2669509 #18982
2669801,2669803 #18983
2670719,2670721 #18984
2670791,2670793 #18985
2671169,2671171 #18986
2671181,2671183 #18987
2671367,2671369 #18988
2671649,2671651 #18989
2671661,2671663 #18990
2671679,2671681 #18991
2672387,2672389 #18992
2673059,2673061 #18993
2673257,2673259 #18994
2673329,2673331 #18995
2673521,2673523 #18996
2673527,2673529 #18997
2673761,2673763 #18998
2673791,2673793 #18999
2673857,2673859 #19000
2673989,2673991 #19001
2674121,2674123 #19002
2674367,2674369 #19003
2674541,2674543 #19004
2674547,2674549 #19005
2674577,2674579 #19006
2674979,2674981 #19007
2675009,2675011 #19008
2675087,2675089 #19009
2675129,2675131 #19010
2675147,2675149 #19011
2675201,2675203 #19012
2675327,2675329 #19013
2675831,2675833 #19014
2675921,2675923 #19015
2676239,2676241 #19016
2676407,2676409 #19017
2676491,2676493 #19018
2676719,2676721 #19019
2677097,2677099 #19020
2677151,2677153 #19021
2677289,2677291 #19022
2677817,2677819 #19023
2677901,2677903 #19024
2678147,2678149 #19025
2678321,2678323 #19026
2678381,2678383 #19027
2678549,2678551 #19028
2678747,2678749 #19029
2679239,2679241 #19030
2679401,2679403 #19031
2679461,2679463 #19032
2679491,2679493 #19033
2679497,2679499 #19034
2679617,2679619 #19035
2679641,2679643 #19036
2679869,2679871 #19037
2680607,2680609 #19038
2680877,2680879 #19039
2680967,2680969 #19040
2681387,2681389 #19041
2681681,2681683 #19042
2681879,2681881 #19043
2681927,2681929 #19044
2682011,2682013 #19045
2682101,2682103 #19046
2682269,2682271 #19047
2682299,2682301 #19048
2682539,2682541 #19049
2682947,2682949 #19050
2683061,2683063 #19051
2683097,2683099 #19052
2683319,2683321 #19053
2683361,2683363 #19054
2683517,2683519 #19055
2683589,2683591 #19056
2683781,2683783 #19057
2683787,2683789 #19058
2684021,2684023 #19059
2684081,2684083 #19060
2684177,2684179 #19061
2684807,2684809 #19062
2685017,2685019 #19063
2685257,2685259 #19064
2685407,2685409 #19065
2685509,2685511 #19066
2685521,2685523 #19067
2685581,2685583 #19068
2685911,2685913 #19069
2685959,2685961 #19070
2686037,2686039 #19071
2686217,2686219 #19072
2686667,2686669 #19073
2686811,2686813 #19074
2686889,2686891 #19075
2687141,2687143 #19076
2687219,2687221 #19077
2687549,2687551 #19078
2687609,2687611 #19079
2687777,2687779 #19080
2687897,2687899 #19081
2688017,2688019 #19082
2688221,2688223 #19083
2688419,2688421 #19084
2688527,2688529 #19085
2688731,2688733 #19086
2688797,2688799 #19087
2688947,2688949 #19088
2688977,2688979 #19089
2689187,2689189 #19090
2689259,2689261 #19091
2689499,2689501 #19092
2689571,2689573 #19093
2689649,2689651 #19094
2689889,2689891 #19095
2690351,2690353 #19096
2690579,2690581 #19097
2690657,2690659 #19098
2690717,2690719 #19099
2690957,2690959 #19100
2691041,2691043 #19101
2691191,2691193 #19102
2691431,2691433 #19103
2691587,2691589 #19104
2691719,2691721 #19105
2691839,2691841 #19106
2692637,2692639 #19107
2692799,2692801 #19108
2693057,2693059 #19109
2693111,2693113 #19110
2693237,2693239 #19111
2693261,2693263 #19112
2693357,2693359 #19113
2693441,2693443 #19114
2693501,2693503 #19115
2693651,2693653 #19116
2693729,2693731 #19117
2693849,2693851 #19118
2693891,2693893 #19119
2694047,2694049 #19120
2694299,2694301 #19121
2694689,2694691 #19122
2694869,2694871 #19123
2695139,2695141 #19124
2695181,2695183 #19125
2695409,2695411 #19126
2695697,2695699 #19127
2695787,2695789 #19128
2695997,2695999 #19129
2696009,2696011 #19130
2696051,2696053 #19131
2696921,2696923 #19132
2696927,2696929 #19133
2697059,2697061 #19134
2697239,2697241 #19135
2697437,2697439 #19136
2697767,2697769 #19137
2697911,2697913 #19138
2697971,2697973 #19139
2698097,2698099 #19140
2698181,2698183 #19141
2698229,2698231 #19142
2698277,2698279 #19143
2698571,2698573 #19144
2698607,2698609 #19145
2698649,2698651 #19146
2698679,2698681 #19147
2699297,2699299 #19148
2699339,2699341 #19149
2699369,2699371 #19150
2699621,2699623 #19151
2699657,2699659 #19152
2699687,2699689 #19153
2699867,2699869 #19154
2700119,2700121 #19155
2700209,2700211 #19156
2700389,2700391 #19157
2700611,2700613 #19158
2700809,2700811 #19159
2700851,2700853 #19160
2701007,2701009 #19161
2701409,2701411 #19162
2701577,2701579 #19163
2701661,2701663 #19164
2701847,2701849 #19165
2701967,2701969 #19166
2702057,2702059 #19167
2702081,2702083 #19168
2702837,2702839 #19169
2703011,2703013 #19170
2703047,2703049 #19171
2703137,2703139 #19172
2703191,2703193 #19173
2703269,2703271 #19174
2703401,2703403 #19175
2703599,2703601 #19176
2703761,2703763 #19177
2703887,2703889 #19178
2704019,2704021 #19179
2704109,2704111 #19180
2704127,2704129 #19181
2704391,2704393 #19182
2704769,2704771 #19183
2704901,2704903 #19184
2704907,2704909 #19185
2704937,2704939 #19186
2704979,2704981 #19187
2705069,2705071 #19188
2705111,2705113 #19189
2705249,2705251 #19190
2705537,2705539 #19191
2705627,2705629 #19192
2705819,2705821 #19193
2705849,2705851 #19194
2706059,2706061 #19195
2706167,2706169 #19196
2706677,2706679 #19197
2706971,2706973 #19198
2707037,2707039 #19199
2707127,2707129 #19200
2707319,2707321 #19201
2707457,2707459 #19202
2707499,2707501 #19203
2707589,2707591 #19204
2707739,2707741 #19205
2707799,2707801 #19206
2707841,2707843 #19207
2708261,2708263 #19208
2708309,2708311 #19209
2708681,2708683 #19210
2708819,2708821 #19211
2709167,2709169 #19212
2709197,2709199 #19213
2709269,2709271 #19214
2709359,2709361 #19215
2709479,2709481 #19216
2709599,2709601 #19217
2709737,2709739 #19218
2709821,2709823 #19219
2710007,2710009 #19220
2710187,2710189 #19221
2710397,2710399 #19222
2710439,2710441 #19223
2710451,2710453 #19224
2710679,2710681 #19225
2710907,2710909 #19226
2710931,2710933 #19227
2711087,2711089 #19228
2711327,2711329 #19229
2711339,2711341 #19230
2711459,2711461 #19231
2711939,2711941 #19232
2712131,2712133 #19233
2712179,2712181 #19234
2712251,2712253 #19235
2712371,2712373 #19236
2712377,2712379 #19237
2712767,2712769 #19238
2712971,2712973 #19239
2713649,2713651 #19240
2713811,2713813 #19241
2713871,2713873 #19242
2713937,2713939 #19243
2714009,2714011 #19244
2714027,2714029 #19245
2714279,2714281 #19246
2714627,2714629 #19247
2714729,2714731 #19248
2715281,2715283 #19249
2715287,2715289 #19250
2715437,2715439 #19251
2715521,2715523 #19252
2715617,2715619 #19253
2715857,2715859 #19254
2715929,2715931 #19255
2715959,2715961 #19256
2716157,2716159 #19257
2716451,2716453 #19258
2716541,2716543 #19259
2716709,2716711 #19260
2716997,2716999 #19261
2717087,2717089 #19262
2717129,2717131 #19263
2717147,2717149 #19264
2717249,2717251 #19265
2717291,2717293 #19266
2717411,2717413 #19267
2717651,2717653 #19268
2717711,2717713 #19269
2717831,2717833 #19270
2718059,2718061 #19271
2718101,2718103 #19272
2718137,2718139 #19273
2718227,2718229 #19274
2718557,2718559 #19275
2718671,2718673 #19276
2718839,2718841 #19277
2718887,2718889 #19278
2718971,2718973 #19279
2719139,2719141 #19280
2719151,2719153 #19281
2719391,2719393 #19282
2719529,2719531 #19283
2719667,2719669 #19284
2720147,2720149 #19285
2720189,2720191 #19286
2720297,2720299 #19287
2720381,2720383 #19288
2720897,2720899 #19289
2721317,2721319 #19290
2721419,2721421 #19291
2721449,2721451 #19292
2721869,2721871 #19293
2722061,2722063 #19294
2722469,2722471 #19295
2722799,2722801 #19296
2722877,2722879 #19297
2723339,2723341 #19298
2723351,2723353 #19299
2723549,2723551 #19300
2723561,2723563 #19301
2723717,2723719 #19302
2723759,2723761 #19303
2723837,2723839 #19304
2723879,2723881 #19305
2723909,2723911 #19306
2724119,2724121 #19307
2724479,2724481 #19308
2724719,2724721 #19309
2725001,2725003 #19310
2725367,2725369 #19311
2725451,2725453 #19312
2725517,2725519 #19313
2725691,2725693 #19314
2725781,2725783 #19315
2725817,2725819 #19316
2726387,2726389 #19317
2726741,2726743 #19318
2726819,2726821 #19319
2726837,2726839 #19320
2727119,2727121 #19321
2727299,2727301 #19322
2727311,2727313 #19323
2727449,2727451 #19324
2727839,2727841 #19325
2728169,2728171 #19326
2728259,2728261 #19327
2728541,2728543 #19328
2728547,2728549 #19329
2728751,2728753 #19330
2728769,2728771 #19331
2728931,2728933 #19332
2729099,2729101 #19333
2729117,2729119 #19334
2729381,2729383 #19335
2729591,2729593 #19336
2729651,2729653 #19337
2729957,2729959 #19338
2730179,2730181 #19339
2730239,2730241 #19340
2730569,2730571 #19341
2730599,2730601 #19342
2730989,2730991 #19343
2731061,2731063 #19344
2731187,2731189 #19345
2731241,2731243 #19346
2731277,2731279 #19347
2731427,2731429 #19348
2731607,2731609 #19349
2731667,2731669 #19350
2731691,2731693 #19351
2731697,2731699 #19352
2731901,2731903 #19353
2731907,2731909 #19354
2732207,2732209 #19355
2732381,2732383 #19356
2732489,2732491 #19357
2732501,2732503 #19358
2732537,2732539 #19359
2732579,2732581 #19360
2732759,2732761 #19361
2733041,2733043 #19362
2733257,2733259 #19363
2733329,2733331 #19364
2733371,2733373 #19365
2733461,2733463 #19366
2733539,2733541 #19367
2733779,2733781 #19368
2734007,2734009 #19369
2734097,2734099 #19370
2734607,2734609 #19371
2734817,2734819 #19372
2734967,2734969 #19373
2735021,2735023 #19374
2735189,2735191 #19375
2735267,2735269 #19376
2735279,2735281 #19377
2735441,2735443 #19378
2735609,2735611 #19379
2735921,2735923 #19380
2736497,2736499 #19381
2736581,2736583 #19382
2736689,2736691 #19383
2737127,2737129 #19384
2737169,2737171 #19385
2737211,2737213 #19386
2737409,2737411 #19387
2737487,2737489 #19388
2737871,2737873 #19389
2737979,2737981 #19390
2738117,2738119 #19391
2738387,2738389 #19392
2738621,2738623 #19393
2738651,2738653 #19394
2739239,2739241 #19395
2739281,2739283 #19396
2739419,2739421 #19397
2739557,2739559 #19398
2739719,2739721 #19399
2739731,2739733 #19400
2740037,2740039 #19401
2740139,2740141 #19402
2740187,2740189 #19403
2740217,2740219 #19404
2740511,2740513 #19405
2740601,2740603 #19406
2741351,2741353 #19407
2741579,2741581 #19408
2741657,2741659 #19409
2741729,2741731 #19410
2741927,2741929 #19411
2741939,2741941 #19412
2742029,2742031 #19413
2742161,2742163 #19414
2742197,2742199 #19415
2742407,2742409 #19416
2742461,2742463 #19417
2742671,2742673 #19418
2742737,2742739 #19419
2742809,2742811 #19420
2742917,2742919 #19421
2742977,2742979 #19422
2742989,2742991 #19423
2743547,2743549 #19424
2743709,2743711 #19425
2743859,2743861 #19426
2743931,2743933 #19427
2744081,2744083 #19428
2744447,2744449 #19429
2744591,2744593 #19430
2745047,2745049 #19431
2745371,2745373 #19432
2745569,2745571 #19433
2745929,2745931 #19434
2746031,2746033 #19435
2746199,2746201 #19436
2746421,2746423 #19437
2746481,2746483 #19438
2746607,2746609 #19439
2746661,2746663 #19440
2746787,2746789 #19441
2747021,2747023 #19442
2747117,2747119 #19443
2747177,2747179 #19444
2747321,2747323 #19445
2747357,2747359 #19446
2747447,2747449 #19447
2747711,2747713 #19448
2748059,2748061 #19449
2748131,2748133 #19450
2748281,2748283 #19451
2748467,2748469 #19452
2748827,2748829 #19453
2748857,2748859 #19454
2748971,2748973 #19455
2749067,2749069 #19456
2749301,2749303 #19457
2749361,2749363 #19458
2749709,2749711 #19459
2749847,2749849 #19460
2749919,2749921 #19461
2750159,2750161 #19462
2750261,2750263 #19463
2750399,2750401 #19464
2750771,2750773 #19465
2750789,2750791 #19466
2750981,2750983 #19467
2751101,2751103 #19468
2751251,2751253 #19469
2751479,2751481 #19470
2751809,2751811 #19471
2751821,2751823 #19472
2752049,2752051 #19473
2752151,2752153 #19474
2752199,2752201 #19475
2752229,2752231 #19476
2752637,2752639 #19477
2752667,2752669 #19478
2752721,2752723 #19479
2752877,2752879 #19480
2753129,2753131 #19481
2753549,2753551 #19482
2753939,2753941 #19483
2753999,2754001 #19484
2754047,2754049 #19485
2755031,2755033 #19486
2755199,2755201 #19487
2755211,2755213 #19488
2755301,2755303 #19489
2755661,2755663 #19490
2755859,2755861 #19491
2756009,2756011 #19492
2756069,2756071 #19493
2756099,2756101 #19494
2756267,2756269 #19495
2756519,2756521 #19496
2756561,2756563 #19497
2756627,2756629 #19498
2756681,2756683 #19499
2757119,2757121 #19500
2757191,2757193 #19501
2757257,2757259 #19502
2757317,2757319 #19503
2757659,2757661 #19504
2758241,2758243 #19505
2758517,2758519 #19506
2758529,2758531 #19507
2758541,2758543 #19508
2758631,2758633 #19509
2758841,2758843 #19510
2759171,2759173 #19511
2759291,2759293 #19512
2759297,2759299 #19513
2759411,2759413 #19514
2759441,2759443 #19515
2759459,2759461 #19516
2759819,2759821 #19517
2759879,2759881 #19518
2760221,2760223 #19519
2760629,2760631 #19520
2760671,2760673 #19521
2760761,2760763 #19522
2760881,2760883 #19523
2761007,2761009 #19524
2761091,2761093 #19525
2761151,2761153 #19526
2761181,2761183 #19527
2761277,2761279 #19528
2761301,2761303 #19529
2761721,2761723 #19530
2761727,2761729 #19531
2761901,2761903 #19532
2762027,2762029 #19533
2762117,2762119 #19534
2762171,2762173 #19535
2762759,2762761 #19536
2762777,2762779 #19537
2762939,2762941 #19538
2762951,2762953 #19539
2763587,2763589 #19540
2763599,2763601 #19541
2763659,2763661 #19542
2763779,2763781 #19543
2763881,2763883 #19544
2764121,2764123 #19545
2764127,2764129 #19546
2764649,2764651 #19547
2764787,2764789 #19548
2764871,2764873 #19549
2764901,2764903 #19550
2765207,2765209 #19551
2765297,2765299 #19552
2765471,2765473 #19553
2765837,2765839 #19554
2765927,2765929 #19555
2766329,2766331 #19556
2766581,2766583 #19557
2766677,2766679 #19558
2766791,2766793 #19559
2767067,2767069 #19560
2767229,2767231 #19561
2767319,2767321 #19562
2767361,2767363 #19563
2767409,2767411 #19564
2767571,2767573 #19565
2768069,2768071 #19566
2768177,2768179 #19567
2768189,2768191 #19568
2768201,2768203 #19569
2768417,2768419 #19570
2768429,2768431 #19571
2768609,2768611 #19572
2768681,2768683 #19573
2768789,2768791 #19574
2768957,2768959 #19575
2769257,2769259 #19576
2769551,2769553 #19577
2769617,2769619 #19578
2769887,2769889 #19579
2770091,2770093 #19580
2770169,2770171 #19581
2770589,2770591 #19582
2770769,2770771 #19583
2770841,2770843 #19584
2770991,2770993 #19585
2771141,2771143 #19586
2771177,2771179 #19587
2771381,2771383 #19588
2771609,2771611 #19589
2771861,2771863 #19590
2771957,2771959 #19591
2772017,2772019 #19592
2772191,2772193 #19593
2772569,2772571 #19594
2772629,2772631 #19595
2772827,2772829 #19596
2772881,2772883 #19597
2773019,2773021 #19598
2773079,2773081 #19599
2773319,2773321 #19600
2773679,2773681 #19601
2773697,2773699 #19602
2773817,2773819 #19603
2773919,2773921 #19604
2773997,2773999 #19605
2774141,2774143 #19606
2774309,2774311 #19607
2774477,2774479 #19608
2774501,2774503 #19609
2774729,2774731 #19610
2774867,2774869 #19611
2775041,2775043 #19612
2775161,2775163 #19613
2775389,2775391 #19614
2775611,2775613 #19615
2775737,2775739 #19616
2775989,2775991 #19617
2776001,2776003 #19618
2776061,2776063 #19619
2776181,2776183 #19620
2776649,2776651 #19621
2776799,2776801 #19622
2776841,2776843 #19623
2776979,2776981 #19624
2777111,2777113 #19625
2777141,2777143 #19626
2777231,2777233 #19627
2777309,2777311 #19628
2777837,2777839 #19629
2778107,2778109 #19630
2778341,2778343 #19631
2778647,2778649 #19632
2778827,2778829 #19633
2778911,2778913 #19634
2779487,2779489 #19635
2779631,2779633 #19636
2779769,2779771 #19637
2779781,2779783 #19638
2780177,2780179 #19639
2780207,2780209 #19640
2780597,2780599 #19641
2780621,2780623 #19642
2780777,2780779 #19643
2781017,2781019 #19644
2781059,2781061 #19645
2781209,2781211 #19646
2781347,2781349 #19647
2781377,2781379 #19648
2782061,2782063 #19649
2782097,2782099 #19650
2782691,2782693 #19651
2782859,2782861 #19652
2782937,2782939 #19653
2782991,2782993 #19654
2783321,2783323 #19655
2783579,2783581 #19656
2783657,2783659 #19657
2783687,2783689 #19658
2783771,2783773 #19659
2784167,2784169 #19660
2784281,2784283 #19661
2784347,2784349 #19662
2784371,2784373 #19663
2784569,2784571 #19664
2784911,2784913 #19665
2785019,2785021 #19666
2785031,2785033 #19667
2785511,2785513 #19668
2785577,2785579 #19669
2785589,2785591 #19670
2785631,2785633 #19671
2785901,2785903 #19672
2785961,2785963 #19673
2786081,2786083 #19674
2786219,2786221 #19675
2786429,2786431 #19676
2786477,2786479 #19677
2786741,2786743 #19678
2787017,2787019 #19679
2787119,2787121 #19680
2787227,2787229 #19681
2787329,2787331 #19682
2787479,2787481 #19683
2787527,2787529 #19684
2787557,2787559 #19685
2787749,2787751 #19686
2787767,2787769 #19687
2788529,2788531 #19688
2788781,2788783 #19689
2788829,2788831 #19690
2789117,2789119 #19691
2789327,2789329 #19692
2789489,2789491 #19693
2789627,2789629 #19694
2790101,2790103 #19695
2790251,2790253 #19696
2790257,2790259 #19697
2790449,2790451 #19698
2790479,2790481 #19699
2790647,2790649 #19700
2790857,2790859 #19701
2791037,2791039 #19702
2791091,2791093 #19703
2791121,2791123 #19704
2791181,2791183 #19705
2791559,2791561 #19706
2791637,2791639 #19707
2791697,2791699 #19708
2791967,2791969 #19709
2791979,2791981 #19710
2792087,2792089 #19711
2792159,2792161 #19712
2792171,2792173 #19713
2792189,2792191 #19714
2792399,2792401 #19715
2792429,2792431 #19716
2792747,2792749 #19717
2792771,2792773 #19718
2792831,2792833 #19719
2792861,2792863 #19720
2792987,2792989 #19721
2793071,2793073 #19722
2793101,2793103 #19723
2793179,2793181 #19724
2793731,2793733 #19725
2793809,2793811 #19726
2793941,2793943 #19727
2794217,2794219 #19728
2794241,2794243 #19729
2794301,2794303 #19730
2794397,2794399 #19731
2794541,2794543 #19732
2794787,2794789 #19733
2795267,2795269 #19734
2795321,2795323 #19735
2795381,2795383 #19736
2795561,2795563 #19737
2796221,2796223 #19738
2796527,2796529 #19739
2796707,2796709 #19740
2797211,2797213 #19741
2797337,2797339 #19742
2797439,2797441 #19743
2798141,2798143 #19744
2798459,2798461 #19745
2798597,2798599 #19746
2798639,2798641 #19747
2798867,2798869 #19748
2798921,2798923 #19749
2799131,2799133 #19750
2799149,2799151 #19751
2799449,2799451 #19752
2799497,2799499 #19753
2799749,2799751 #19754
2799791,2799793 #19755
2799911,2799913 #19756
2799989,2799991 #19757
2800001,2800003 #19758
2800139,2800141 #19759
2800247,2800249 #19760
2800331,2800333 #19761
2800781,2800783 #19762
2800949,2800951 #19763
2800979,2800981 #19764
2801219,2801221 #19765
2801441,2801443 #19766
2801597,2801599 #19767
2801801,2801803 #19768
2802011,2802013 #19769
2802089,2802091 #19770
2802311,2802313 #19771
2802599,2802601 #19772
2802641,2802643 #19773
2802857,2802859 #19774
2802929,2802931 #19775
2803067,2803069 #19776
2803121,2803123 #19777
2803571,2803573 #19778
2803637,2803639 #19779
2803649,2803651 #19780
2803781,2803783 #19781
2803817,2803819 #19782
2803937,2803939 #19783
2804027,2804029 #19784
2804057,2804059 #19785
2804141,2804143 #19786
2804237,2804239 #19787
2804309,2804311 #19788
2804519,2804521 #19789
2804567,2804569 #19790
2804729,2804731 #19791
2804831,2804833 #19792
2804939,2804941 #19793
2805041,2805043 #19794
2805161,2805163 #19795
2805167,2805169 #19796
2806121,2806123 #19797
2806247,2806249 #19798
2806367,2806369 #19799
2806379,2806381 #19800
2806457,2806459 #19801
2806691,2806693 #19802
2806787,2806789 #19803
2806847,2806849 #19804
2806961,2806963 #19805
2807087,2807089 #19806
2807177,2807179 #19807
2807477,2807479 #19808
2807549,2807551 #19809
2807591,2807593 #19810
2807657,2807659 #19811
2807879,2807881 #19812
2807927,2807929 #19813
2807969,2807971 #19814
2808059,2808061 #19815
2808359,2808361 #19816
2808497,2808499 #19817
2808719,2808721 #19818
2808761,2808763 #19819
2808809,2808811 #19820
2808917,2808919 #19821
2809271,2809273 #19822
2809307,2809309 #19823
2809349,2809351 #19824
2809451,2809453 #19825
2809487,2809489 #19826
2810009,2810011 #19827
2810369,2810371 #19828
2810411,2810413 #19829
2810501,2810503 #19830
2810579,2810581 #19831
2810711,2810713 #19832
2810909,2810911 #19833
2810957,2810959 #19834
2811089,2811091 #19835
2811161,2811163 #19836
2811227,2811229 #19837
2811617,2811619 #19838
2811629,2811631 #19839
2811659,2811661 #19840
2811707,2811709 #19841
2812421,2812423 #19842
2812751,2812753 #19843
2812811,2812813 #19844
2813339,2813341 #19845
2813411,2813413 #19846
2813477,2813479 #19847
2813507,2813509 #19848
2813579,2813581 #19849
2813807,2813809 #19850
2813819,2813821 #19851
2813849,2813851 #19852
2814167,2814169 #19853
2814431,2814433 #19854
2814839,2814841 #19855
2815739,2815741 #19856
2816057,2816059 #19857
2816087,2816089 #19858
2816171,2816173 #19859
2816291,2816293 #19860
2816531,2816533 #19861
2817077,2817079 #19862
2817167,2817169 #19863
2817251,2817253 #19864
2817467,2817469 #19865
2817671,2817673 #19866
2818157,2818159 #19867
2818391,2818393 #19868
2818469,2818471 #19869
2818997,2818999 #19870
2819021,2819023 #19871
2819051,2819053 #19872
2819099,2819101 #19873
2819147,2819149 #19874
2819471,2819473 #19875
2819489,2819491 #19876
2819519,2819521 #19877
2819627,2819629 #19878
2819681,2819683 #19879
2819741,2819743 #19880
2820017,2820019 #19881
2820359,2820361 #19882
2820401,2820403 #19883
2820479,2820481 #19884
2820707,2820709 #19885
2820749,2820751 #19886
2820887,2820889 #19887
2820941,2820943 #19888
2821151,2821153 #19889
2821769,2821771 #19890
2821829,2821831 #19891
2821979,2821981 #19892
2821997,2821999 #19893
2822009,2822011 #19894
2822189,2822191 #19895
2822297,2822299 #19896
2822711,2822713 #19897
2822717,2822719 #19898
2822879,2822881 #19899
2823437,2823439 #19900
2823521,2823523 #19901
2823671,2823673 #19902
2823809,2823811 #19903
2823971,2823973 #19904
2824187,2824189 #19905
2824649,2824651 #19906
2825099,2825101 #19907
2825411,2825413 #19908
2825477,2825479 #19909
2825489,2825491 #19910
2825819,2825821 #19911
2825861,2825863 #19912
2825957,2825959 #19913
2825981,2825983 #19914
2826071,2826073 #19915
2826149,2826151 #19916
2826179,2826181 #19917
2826737,2826739 #19918
2826851,2826853 #19919
2826917,2826919 #19920
2827211,2827213 #19921
2827547,2827549 #19922
2827631,2827633 #19923
2827679,2827681 #19924
2828297,2828299 #19925
2828429,2828431 #19926
2828597,2828599 #19927
2828627,2828629 #19928
2828741,2828743 #19929
2828867,2828869 #19930
2829569,2829571 #19931
2829677,2829679 #19932
2829707,2829709 #19933
2829887,2829889 #19934
2830097,2830099 #19935
2830151,2830153 #19936
2830349,2830351 #19937
2830871,2830873 #19938
2830937,2830939 #19939
2830967,2830969 #19940
2831657,2831659 #19941
2831669,2831671 #19942
2831789,2831791 #19943
2831861,2831863 #19944
2831951,2831953 #19945
2831999,2832001 #19946
2832131,2832133 #19947
2832257,2832259 #19948
2832329,2832331 #19949
2832629,2832631 #19950
2833319,2833321 #19951
2833331,2833333 #19952
2833799,2833801 #19953
2833811,2833813 #19954
2834261,2834263 #19955
2834411,2834413 #19956
2834651,2834653 #19957
2834717,2834719 #19958
2834747,2834749 #19959
2835137,2835139 #19960
2835221,2835223 #19961
2835269,2835271 #19962
2835587,2835589 #19963
2835671,2835673 #19964
2835689,2835691 #19965
2836079,2836081 #19966
2836241,2836243 #19967
2836259,2836261 #19968
2836367,2836369 #19969
2836487,2836489 #19970
2836607,2836609 #19971
2836619,2836621 #19972
2836961,2836963 #19973
2836991,2836993 #19974
2837057,2837059 #19975
2837069,2837071 #19976
2837279,2837281 #19977
2837501,2837503 #19978
2837711,2837713 #19979
2837801,2837803 #19980
2837951,2837953 #19981
2837981,2837983 #19982
2838137,2838139 #19983
2838149,2838151 #19984
2838287,2838289 #19985
2838461,2838463 #19986
2838629,2838631 #19987
2838767,2838769 #19988
2838851,2838853 #19989
2838917,2838919 #19990
2839469,2839471 #19991
2839547,2839549 #19992
2839841,2839843 #19993
2839931,2839933 #19994
2839937,2839939 #19995
2840039,2840041 #19996
2840237,2840239 #19997
2840261,2840263 #19998
2840267,2840269 #19999
2840417,2840419 #20000

Source : http://numbers.computation.free.fr/Constants/Primes/twin.html

 

Introduction to twin primes and Brun's constant computation

 

(Click here for a Postscript version of this page and here for a pdf version)

 

1  Introduction

It's a very old fact (Euclid 325-265 B.C., in Book IX of the Elements) that the set of primes is infinite and a much more recent and famous result (by Jacques Hadamard (1865-1963) and Charles-Jean de la Vallee Poussin (1866-1962)) that the density of primes is ruled by the law

p(n) ~

n log(n)

where the prime counting function p(n) is the number of prime numbers less than a given integer n. This result proved in 1896 is the celebrated prime numbers theorem and was conjectured earlier, in 1792, by young Carl Friedrich Gauss (1777-1855) and by Adrien-Marie Legendre (1752-1833) who studied the repartition of those numbers in published tables of primes.

This approximation may be usefully replaced by the more accurate logarithmic integral Li(n):

p(n) ~ Li(n)=

ó õ

n 2

dt log(t)

.

However among the deeply studied set of primes there is a famous and fascinating subset for which very little is known and has generated some famous conjectures: the twin primes (the term prime pairs was used before [5]).

Definition 1 A couple of primes (p,q) are said to be twins if q=p+2. Except for the couple (2,3), this is clearly the smallest possible distance between two primes.

Example 2 (3,5),(5,7),(11,13),(17,19),(29,31),...,(419,421),... are twin primes.

 

2  Counting twin primes

As for the set of primes the most natural question is wether the set of twin primes is finite or not. But unlike prime numbers for which numerous and elementary proofs exist [10], the answer to this natural question is still unknown for twin primes ! Today, this problem remains one of the greatest challenge in mathematics and has occupied numbers of mathematicians. Of course, as we will see, there are some empirical and numerical results suggesting an answer and most mathematicians believe that there are infinitely many twin primes.

In 1849, Alphonse de Polignac (1817-1890) made the general conjecture that there are infinitely many primes distant from 2k. The case for which k=1 is the twin primes case.

It's now natural to introduce the twin prime counting function p₂(n) which is the number of twin primes smaller than a given n.

 

2.1  Numerical results

Using huge table of primes (Glaisher 1878 [5], before computer age, enumerated p₂(10⁵)) and with intensive computations during modern period (Shanks and Wrench 1974 [12], Brent 1976 [1], Nicely 1996-2002 [9], Sebah 2001-2002 [11], see also [10]) it's possible to compute the exact values of p₂(n) for large n and its conjectured approximation 2C₂Li₂(n) (see next section for the definition).

The following array includes the relative error e (in %) between the approximation and the real value.

 

n	p2(n)	2C2Li2(n)	e
10	2	5	150.00
102	8	14	75.00
103	35	46	31.43
104	205	214	4.39
105	1224	1249	2.04
106	8169	8248	0.97
107	58980	58754	-0.38
108	440312	440368	0.013
109	3424506	3425308	0.023
1010	27412679	27411417	-0.0046
1011	224376048	224368865	-0.0032
1012	1870585220	1870559867	-0.0013
1013	15834664872	15834598305	-0.00042
1014	135780321665	135780264894	-0.000042
1015	1177209242304	1177208491861	-0.000064
1016	10304195697298	10304192554496	-0.000031

At present time (2002), Pascal Sebah has reached p₂(10¹⁶) and his values are confirmed by Thomas Nicely up to p₂(4.10¹⁵) who used an independent approach and implementation.

 

2.1.1  Sieving twin primes

Because the most convenient (in fact the only available) way to compute p₂(n) is to find all twin primes and just count them, it's of great importance to improve as much as possible such an algorithm. All known methods use variations on the historical Eratosthenes sieve.

In order to accelerate the sieve, a possible idea is to represent integers modulo a base m, so that any integer has the form mk+r with 0 £ r < m. Primes numbers are such as m and r are relatively primes and for any value of m, there are f(m) numbers r which are prime with m (this is the definition of Euler's f totient function).

Modulo 6  

For example modulo 6 all integers have one of the form

6k,6k+1,6k+2,6k+3,6k+4,6k+5

but 6k may not be prime, 6k+2 and 6k+4 are divisible by 2, 6k+3 is divisible by 3, therefore primes (except 2 and 3) must be of the form

6k+1,6k+5

or which is more convenient to sieve twin primes

( 6k+5,6k+7) .

This allows to sieve a proportion of only f(m)/m=2/6 or 33.3% of all the numbers.

Modulo 30  

The same kind of approach modulo 30 gives for candidates

30k+1,30k+7,30k+11,30k+13,30k+17,30k+19,30k+23,30k+29

and here we need to sieve only f(m)/m=8/30 or 26.66% of the integers to find all primes (except 2,3 and 5).

But remember that we are only trying to sieve twin primes hence are left only the candidate couples

( 30k+11,30k+13) ,( 30k+17,30k+19) ,(30k+29,30k+31)

and the proportion drops to 6/30 or 20% of all integers.

This suggest to introduce the function f₂(m) which is the number of pairs of integer 0 £ r < m such as r and r+2 are relatively prime with m. We observe from the last two examples that

f₂(6)=1,f₂(30)=3.

   Example  

Let's illustrate this on a numerical example. The enumeration of twin primes modulo 30 up to 10¹⁰ gives, respectively, for each of the 3 previous couples:

9137078,9138015,9137584

twin primes. So that (don't forget to count the two couples (3,5) and (5,7)!)

p₂(10¹⁰)=9137078+9138015+9137584+2=27412679.

And, for the same couples, up to 10¹²:

623517830,623557143,623510245

which produces

p₂(10¹²)=623517830+623557143+623510245+2=1870585220.

It's interesting to observe that the contribution to the enumeration of the twin primes of each couple is almost equivalent. This was also observed during all numerical estimations for other modulo like 210, 2310, 30030, ... [11].

This result is well known when enumerating just prime numbers but may be conjectured for twin primes.

Other modulo  

In this table we show the proportion 2f₂(m)/m of integer to sieve in order to count twin primes as a function of the modulo m:

 

m	f2(m)	%
2	.	50.0
6	1	33.3
30	3	20.0
210	15	14.3
2310	135	11.7
30030	1485	9.9
510510	22275	8.7

The smallest ratios are obtained for values of m which are the product of the first primes (2#=2,3#=2×3,5#=2×3×5,7#=2×3×5×7,...), that is the first values of the primorial # function. For example in [11], the sieves were made modulo 30030 and 510510, therefore less than 10% of the set of integers were considered by the algorithm. In some others implementations sieves modulo 6 or 30 are used.

 

2.2  Twin prime conjecture

Based on heuristic considerations, a law (the twin prime conjecture) was developed, in 1922, by Godfrey Harold Hardy (1877-1947) and John Edensor Littlewood (1885-1977) to estimate the density of twin primes.

According to the prime number theorem the probability that a number n is prime is about 1/log(n), therefore, if the probability that n+2 is also prime was independent of the probability for n, we should have the approximation

p2(n) ~

n log2(n)

,

but a more careful analysis shows that this model is too simplified (an argument is given in [6]). In fact we have the following and more accurate conjecture (called conjecture B in[7]).

Conjecture 3 [Twin prime conjecture]For large values of n, the two following equivalent approximations are conjectured

p2(n) ~ 2C2Li2(n)=2C2

ó õ

n 2

dt log2(t)

(1)

or

p2(n) ~ 2C2

n log2(n)

(2)

Note that C₂ is the twin prime constant and is defined by

C2=

Õ p ³ 3

æ è

p(p-2) (p-1)2

ö ø

=0.6601618158468695739278121100145...

This last constant occurs in some asymptotic estimations involving primes and it's interesting to observe that it may be estimated using properties of the Riemann Zeta function to thousand of digits (Sebah computed it to more than 5000 digits).

 

Figure 1: p₂(n) and 2C₂Li₂(n)

Remark 4 The function Li₂(n) occuring in (1) may be related to the logarithmic integral Li(n) by the trivial relation

Li2(n)=Li(n)+

2 log(2)

-

n log(n)

.

 

2.2.1  Generalizations

In fact, Hardy and Littlewood made a more general conjecture on the primes separated by a gap of d. A natural generalization of the twin primes is to search for primes distant of d=2k (which should be infinite for any d according to Polignac's conjecture). The case d=2 is the twin primes set, d=4 forms the cousin primes set, d=6 is the sexy primes set, ...

If we denote p_d(n) the number of primes p £ n such as p+d is also prime (observe that here p and p+d may not be consecutive), Hardy-Littlewood's conjecture states (in [7]) that for d ³ 2:

pd(n) ~ 2C2Rd

ó õ

n 2

dt log2(t)

,

with R_d ³ 1 being the rational number

Rd=

Õ p|d,p > 2

p-1 p-2

,       p is prime.

The first values of the function R_d are

 

d	2	4	6	8	10	12	14	16	18	20
Rd	1	1	2	1	4/3	2	6/5	1	2	4/3

According to this conjecture the density of twin primes is equivalent to the density of cousin primes. For example, the exact computed values up to 10¹² are: 

p₂(10¹²) =1870585220
p₄(10¹²) =1870585458, 

which can be compared to the predicted value 1870559867 by the conjecture. Marek Wolf has studied the function

W(n)=p₂(n)-p₄(n)

and its fractal properties and approximate dimension of 1.48 ([13]).

 

3  Brun's constant

 

3.1  From Euler's constant to Brun's constant

Euler's constant  

It's very natural to understand the nature of the harmonic numbers

H(n)=1+

1 2

+

1 3

+

1 4

+...+

1 n

when n becomes large and the sum takes all integers in account. We know since Euler, for instance, that

ê ê ê

H(n) ~ log(n) H(n)-log(n) ~ g

so that the harmonic numbers tends to infinite like log(n). Note that g is Euler's constant and may be evaluated to million of digits.

Mertens' constant  

The next step is to take in account only the primes numbers in the sum that is

P(p)=1+

1 2

+

1 3

+

1 5

+...+

1 p

and we have the beautiful results that

ê ê ê

P(p) ~ log( log(p)) P(p)-log( log(p)) ~ M

Therefore the sum diverges (this was also observed by Euler) but at the very low rate log(log(p)) and M is the interesting Mertens' constant which may be evaluated to much less digits than g, say a few thousands.

Brun's Constant  

In the last step we only take in account the twin primes less than p in the sum

B2(p)=

æ è

1 3

+

1 5

ö ø

+

æ è

1 5

+

1 7

ö ø

+

æ è

1 11

+

1 13

ö ø

+...

and here comes the remarkable result due to Norwegian Mathematician Viggo Brun (1885-1978) in 1919 [2].

Theorem 5 The sum of the inverse of the twin primes converges to a finite constant B₂.

We write this result as

lim p®¥

B2(p)=B2.

Note that this theorem doesn't answer to the question of the infinitude of twin primes, it just says that the limit exists (and may or may not contains a finite number of terms !). The proof is rather complex and based on a majoration of the density of twin primes ; a more modern one may also be found in [8].

Unlike Euler's constant or Mertens' constant, Brun's constant is one of the hardest to evaluate and we are not even sure to know 9 digits of it. By mean of very intensive computations, we only have guaranteed minorations !

 

3.2  Estimation of Brun's constant

 

3.2.1  Direct estimation

In the following table we have try to estimate this constant by computing the partial sums B₂(p) up to different values of p.

 

p	B2(p)
102	1.330990365719...
104	1.616893557432...
106	1.710776930804...
108	1.758815621067...
1010	1.787478502719...
1012	1.806592419175...
1014	1.820244968130...
1015	1.825706013240...
1016	1.830484424658...

From this, we observe that the convergence is extremely slow and irregular. If we expect to find even just a few digits, we have to make some assumptions.

 

3.2.2  Extrapolation

An easy consequence of the twin prime conjecture is that we may write the numbers B₂(p) as (see [4] and [9])

B2(p)=B2-

4C2 log(p)

+O

æ è

1 Öplog(p)

ö ø

and thanks to this relation, the extrapolated value

B2*(p)=B2(p)+

4C2 log(p)

converges much faster to Brun's constant B₂.

Let's take a look to numerical values:

 

p	B2*(p)
102	1.904399633290...
104	1.903598191217...
106	1.901913353327...
108	1.902167937960...
1010	1.902160356233...
1012	1.902160630437...
1014	1.902160577783...
1015	1.902160582249...
1016	1.902160583104...

which suggest that the value of B₂ should be around 1.902160583... (a similar value was first proposed by Nicely after intensive computations and checked later by Sebah, see [9] and [11]).

The relation

B2(p) ~ B2-

4C2 log(p)

invites us to draw the function B₂(p)=f( 1/log(p)) (see Figure 2) which should be a line with a negative slop with a value near -4C₂ » -2.64064726.

 

Figure 2: B₂(p)=f( [ 1/log(p)])

The intersection of the line with the vertical axis (that is p=¥) is Brun's constant if the twin prime conjecture is valid. And according to this line the direct estimation B₂(p) should reach 1.9 not before the value p ~ 10⁵³⁰ which is far beyond any computational project !

 

4  Twin prime characterization

There is a result from Clement (1949, [3]) which permits to see if a couple (p,p+2) is a twin primes pair. This theorem extends Wilson's famous theorem on prime numbers.

Theorem 6 Let p ³ 3, the integers (p,p+2) form a twin primes pair if and only if

4( (p-1)!+1) º -p mod p(p+2)

Example 7 For p=17, 4( (p-1)!+1) = 83691159552004 º 306 mod 323 and -p º 306 mod 323, therefore (17,19) is a twin prime pair.

The huge value of the factorial makes this theorem of no practical use to find large twin primes.

 

4.1  Large twin primes

Today, thanks to modern computers, a lot of huge twin primes are known. Many of those primes are of the form k×2ⁿ±1 because there are efficient primality testing algorithms for such numbers when k is not too large.

The following theorem due to the French farmer François Proth (1852-1879) may be used.

Theorem 8 [Proth's theorem - 1878]Let N=k.2ⁿ+1 with k < 2ⁿ, if there is an integer a such as

a^(N-1)/2 º -1 mod N

then N is prime.

To help finding large pairs, an idea is to take a value for n and then to start a sieve in order to reduce the set of possible values for the k. It should take a few hours to find twin primes with a few thousands digits.

For example the following numbers are twin prime pairs (some are given from [10]): 

		459.28529±1       Dubner, 1993
		594501.29999±1
		6797727.215328±1       Forbes, 1995
		697053813.216352±1       Indlekofer & Janai, 1994
		318032361.2107001±1       Underbakke & Carmody & ..., 2001

The last one is a twin primes pair of more than 32000 digits !

 

References

[1]

R.P. Brent, Tables Concerning Irregularities in the Distribution of Primes and Twin Primes Up to 10¹¹, Math. Comput., (1976), vol. 30, p. 379

 

[2]

V. Brun, La série 1/5+1/7+1/11+1/13+1/17+1/19+1/29+1/31+1/41+1/43+1/59+1/61+..., où les dénominateurs sont nombres premiers jumeaux est convergente ou finie, Bulletin des sciences mathématiques, (1919), vol. 43, p. 100-104 and p. 124-128

 

[3]

P.A. Clement, Congruences for sets of primes, American Mathematical Monthly, (1949), vol. 56, p. 23-25

 

[4]

C.E. Fröberg, On the sum of inverses of primes and twin primes, Nordisk Tidskr. Informationsbehandling (BIT), (1961), vol. 1, p. 15-20.

 

[5]

J.W.L. Glaisher, An enumeration of prime-pairs, Messenger of Mathematics, (1878), vol. 8, p. 28-33

 

[6]

G.H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, Oxford Science Publications, (1979)

 

[7]

G.H. Hardy and J.E. Littlewood, Some problems of 'Partitio Numerorum' III : On the expression of a number as a sum of primes, Acta Mathematica, (1922), vol. 44, p. 1-70

 

[8]

W.J. LeVeque, Fundamentals of Number Theory, New York, Dover, (1996)

 

[9]

T. Nicely, Enumeration to 10¹⁴ of the Twin Primes and Brun's Constant, Virginia J. Sci., (1996), vol. 46, p. 195-204

 

[10]

P. Ribenboim, The new Book of Prime Number Records, Springer, (1996)

 

[11]

P. Sebah, Counting Twin Primes and estimation of Brun's Constant up to 10¹⁶, Computational project at http://numbers.computation.free.fr/Constants/constants.html, (2002)

 

[12]

D. Shanks and J.W. Wrench, Brun's Constant, (1974), Math. Comput., vol. 28, p. 293-299

 

[13]

M. Wolf, On the Twin and Cousin primes, (1996), See http://www.ift.uni.wroc.pl/~mwolf/

---

File translated from T_EX by T_TH, version 3.01.
On 29 Jul 2002, 14:41.

L'union fait la force des mathématiciens LE MONDE SCIENCE ET TECHNO | 24.06.2013 à 15h40 | En savoir plus sur http://www.lemonde.fr/sciences/article/2013/06/24/l-union-fait-la-force-des-mathematiciens_3435624_1650684.html#64byvQVhFuDDXMoA.99

L'union fait la force des mathématiciens

LE MONDE SCIENCE ET TECHNO | 24.06.2013 à 15h40 |

 

"Peut-on collaborer massivement en mathématiques, faisant interagir des centaines de chercheurs vers un but unique ? C'est l'objectif de la plate-forme collaborative Polymath, lancée en 2009 par le mathématicien britannique Tim Gowers, qui a déjà plusieurs succès à son actif. L'amélioration en cours d'un récent résultat de théorie des nombres illustre l'efficacité de ce type de collaboration.

Le résultat en question, accepté pour publication en mai 2013 par les prestigieuses Annals of Mathematics, annonce..."

En savoir plus sur http://www.lemonde.fr/sciences/article/2013/06/24/l-union-fait-la-force-des-mathematiciens_3435624_1650684.html#64byvQVhFuDDXMoA.99

En savoir plus sur http://www.lemonde.fr/sciences/article/2013/06/24/l-union-fait-la-force-des-mathematiciens_3435624_1650684.html#64byvQVhFuDDXMoA.99

 

 

Nombres premiers jumeaux

 

 

En mathématiques, deux nombres premiers jumeaux sont deux nombres premiers qui ne diffèrent que de 2. Hormis pour le couple (2, 3), cet écart entre nombres premiers de 2 est le plus petit possible. Les plus petits nombres premiers jumeaux sont 3 et 5, 5 et 7, 11 et 13.

Au 25 décembre 2011, les plus grands nombres premiers jumeaux connus, découverts dans le cadre du projet de calcul distribué PrimeGrid, sont 3 756 801 695 685 × 2^666 669 ± 1 ; ils possèdent 200 700 chiffres en écriture décimale.

Selon la conjecture des nombres premiers jumeaux, il existe une infinité de nombres premiers jumeaux ; les observations numériques et des raisonnements heuristiquesjustifient la conjecture, mais aucune démonstration n'en a encore été faite.

 

Sommaire

 [masquer] 

• 1Définition
• 2Liste des premiers nombres premiers jumeaux
• 3Quelques propriétés
• 4Records
• 5Conjecture des nombres premiers jumeaux
  • 5.1Résultats partiels
  • 5.2La conjecture de Hardy-Littlewood
• 6Notes et références
• 7Voir aussi
  • 7.1Articles connexes
  • 7.2Liens externes

 

Définition[modifier | modifier le code]

Soient p et q deux nombres premiers. On dit que (p, q) forme un couple de nombres premiers jumeaux si q = p + 2.

Liste des premiers nombres premiers jumeaux[modifier | modifier le code]

L'ensemble des nombres premiers jumeaux jusqu'à 1000 :

(3, 5)	(5, 7)	(11, 13)	(17, 19)	(29, 31)
(41, 43)	(59, 61)	(71, 73)	(101, 103)	(107, 109)
(137, 139)	(149, 151)	(179, 181)	(191, 193)	(197, 199)
(227, 229)	(239, 241)	(269, 271)	(281, 283)	(311, 313)
(347, 349)	(419 , 421)	(431 , 433)	(461 , 463)	(521 , 523)
(569 , 571)	(599 , 601)	(617 , 619)	(641 , 643)	(659 , 661)
(809 , 811)	(821 , 823)	(827 , 829)	(857 , 859)	(881 , 883)

Quelques propriétés[modifier | modifier le code]

• Le couple (2, 3) est le seul couple de nombres premiers consécutifs.
• Si l'on omet le couple (2, 3), la plus petite distance possible entre deux nombres premiers est 2 ; deux nombres premiers jumeaux sont ainsi deux nombres impairsconsécutifs.
• Tout couple de nombres premiers jumeaux, à l'exception du couple (3, 5), est de la forme (6n – 1, 6n + 1) pour un certain entier n. En effet, tout triplet d'entiers consécutifs comporte au moins un multiple de 2 (éventuellement deux) et un seul multiple de 3 ; l'entier qui se trouve entre les deux nombres premiers jumeaux est à la fois ce multiple de 2 et ce multiple de 3, car cela ne peut pas être l'un des nombres premiers.
• Pour tout entier m ≥ 2, le couple (m, m + 2) est constitué de nombres premiers jumeaux si et seulement si 4[(m - 1)! + 1] + m est divisible par m(m + 2). Cette caractérisation des nombres premiers jumeaux, remarquée par P. A. Clement en 1949¹, résulte du théorème de Wilson.
• Alors que la série des inverses des nombres premiers est divergente, la série des inverses de nombres premiers jumeaux est convergente (vers un nombre appelé constante de Brun). Cette propriété fut démontrée par Viggo Brun en 1919².

Records[modifier | modifier le code]

Le 15 janvier 2007, les deux projets de calcul distribué Twin Prime Search et PrimeGrid ont découvert le plus grand couple de nombres premiers jumeaux connu à l'époque, de 58 711 chiffres en écriture décimale. Le découvreur était le Français Éric Vautier³.

Le 25 décembre 2011, le couple record³ est 3 756 801 695 685 × 2^666 669 ± 1 ; les deux nombres possèdent 200 700 chiffres.

Conjecture des nombres premiers jumeaux[modifier | modifier le code]

La conjecture des nombres premiers jumeaux affirme qu'il existe une infinité de nombres premiers jumeaux:

Il existe une infinité de nombres premiers p tels que p + 2 soit aussi premier.

Cette conjecture partage avec l'hypothèse de Riemann et la conjecture de Goldbach le numéro 8 des problèmes de Hilbert, énoncés par ce dernier en 1900. Bien que la plupart des chercheurs en théorie des nombres pensent que cette conjecture est vraie, elle n'a jamais été démontrée. Ils se basent sur des observations numériques et des raisonnements heuristiques utilisant la distribution probabiliste des nombres premiers.

En 1849, Alphonse de Polignac émit une conjecture plus générale : la conjecture de Polignac :

Tout nombre pair est égal à la différence de deux nombres premiers consécutifs d'une infinité de manières.

dont le cas n = 2 correspond à la conjecture des nombres premiers jumeaux.

Il existe également une version plus forte de cette conjecture : la première conjecture de Hardy-Littlewood (cf. infra), qui fournit une loi de distribution des nombres premiers jumeaux et qui s'inspire du théorème des nombres premiers.

La conjecture des nombres premiers jumeaux est un cas particulier de la conjecture de Schinzel.

Résultats partiels[modifier | modifier le code]

En 1940, Paul Erdős démontra l'existence d'une constante positive c < 1 pour laquelle l'ensemble des nombres premiers p tels que p' – p < c ln(p) est infini, où p' désigne le nombre premier suivant immédiatement p.

Ce résultat fut plusieurs fois amélioré ; en 1986, Helmut Maier montra que c peut être choisi inférieur à 1/4. En 2005, Daniel Goldston, János Pintz et Cem Yıldırım démontrèrent que c peut être choisi arbitrairement petit.

Par ailleurs, en 1966, Chen Jingrun démontra l'existence d'une infinité de « nombres premiers de Chen », c'est-à-dire de nombres premiers p tels que p + 2 soit premier ou semi-premier (un nombre semi-premier est le produit de deux nombres premiers). Son approche est celle de la théorie des cribles, qu'il a utilisée pour traiter de façon similaire la conjecture des nombres premiers jumeaux et la conjecture de Goldbach (voir Théorème de Chen).

À partir de 2009, à la suite de la découverte d'une optimisation du crible d'Eratosthène, Zhang Yitang établit qu'il existe une infinité de nombres premiers consécutifs dont l'écart est inférieur à 70 000 000, résultat qui constitue une forme faible de la conjecture des nombres premiers jumeaux. Début 2013, le projet Polymath, un projet de mathématiques collaboratives mené par Tim Gowers et Terence Tao, a proposé de réduire progressivement cet écart N = 70 millions pour le faire tendre vers 2 : en septembre 2013 l'écart a été réduit à N = 4 680^4,5. En novembre 2013, une amélioration significative de ces résultats est annoncée indépendamment par James Maynard (en) et Terence Tao⁶ : non seulement l'écart entre deux nombres premiers consécutifs est inférieur ou égal à 600 infiniment souvent, mais un résultat équivalent est valable pour m nombres premiers consécutifs, quel que soit m ≥ 2. Une nouvelle amélioration est annoncée par le projet Polymath (section Polymath8) début 2014 : d'une part, l'écart serait inférieur à 270 infiniment souvent, d'autre part, en admettant une version généralisée de la conjecture d'Elliott-Halberstam, l'écart serait alors inférieur ou égal à 6⁷.

Le résultat de Zhang a été publié dans les Annals of Mathematics⁸. Dans un premier temps il a été difficile de trouver des relecteurs acceptant d'évaluer le travail⁹.

La conjecture de Hardy-Littlewood[modifier | modifier le code]

Il existe aussi une généralisation de la conjecture des nombres premiers jumeaux, connue sous le nom de première¹⁰ conjecture de Hardy-Littlewood, en rapport avec la distribution des premiers jumeaux, par analogie avec le théorème des nombres premiers. Soit π₂(x) le nombre de nombres premiers p ≤ x tels que p + 2 soit aussi premier.

On note C₂ le nombre obtenu de la façon suivante :

¹¹

(ici le produit s'étend à l'ensemble des nombres premiers p ≥ 3). C₂ est appelé constante des nombres premiers jumeaux¹² ou constante de Shah et Wilson¹³.

Alors la conjecture de Hardy-Littlewood s'énonce de la façon suivante :

(ce qui signifie que le quotient des deux expressions tend vers 1 quand x tend vers l'infini).

Comme le second membre a une limite infinie quand x tend vers l'infini, cette conjecture démontrerait que le nombre de nombres premiers jumeaux est bien infini.

Cette conjecture peut être justifiée (mais pas démontrée) en supposant que 1/ln(t) est la fonction de densité de la distribution des nombres premiers, une hypothèse suggérée par le théorème des nombres premiers. Cette conjecture est un cas particulier d'une conjecture plus générale appelée conjecture des n-uplets premiers de Hardy-Littlewood¹⁴utilisée dans les recherches sur la conjecture de Goldbach.

Notes et références[modifier | modifier le code]

1. ↑ (en) P. A. Clement, « Congruences for sets of primes », American Mathematical Monthly, vol. 56,‎ 1949, p. 23-25 (lire en ligne [archive])
2. ↑ Viggo Brun, « La série 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/29 + 1/31 + 1/41 + 1/43 + 1/59 + 1/61 + ... où les dénominateurs sont « nombres premiers jumeaux » est convergente ou finie », Bulletin des Sciences Mathématiques, vol. 43,‎ 1919, p. 100-104 et 124-128
3. ↑ ^{a et b} (en) « Twin Primes » [archive], sur Top Twenty
4. ↑ L'union fait la force des mathématiciens [archive], Le Monde, 24/06/2013.
5. ↑ (en) Bounded gaps between primes [archive].
6. ↑ (en) Polymath8b: Bounded intervals with many primes, after Maynard [archive], sur le blog de Terence Tao.
7. ↑ (en) Annonce de ce résultat [archive] sur le blog de Gil Kalai (en)
8. ↑ Y. Zhang, « Bounded gaps between primes », Annals of Mathematics, 179 (2014), p. 1121–1174
9. ↑ John Friedlander, « Prime Numbers: A Much Needed Gap Is Finally Found », Notices of the American Mathematical Society, vol. 62, n^o 6,‎ juin 2015 (lire en ligne [archive]).
10. ↑ Il existe une seconde conjecture de Hardy-Littlewood
11. ↑ suite A005597 de l'OEIS des décimales de cette constante.
12. ↑ (en) Eric W. Weisstein, « Twin Primes Constant [archive] », MathWorld
13. ↑ François Le Lionnais, Les nombres remarquables, Hermann, 1983, p. 30 [archive]
14. ↑ (en) Eric W. Weisstein, « Twin Prime Conjecture [archive] », MathWorld

Voir aussi[modifier | modifier le code]

Articles connexes[modifier | modifier le code]

• Conjecture de Dickson
• Conjecture de Dubner
• Conjecture d'Elliott-Halberstam
• Nombres premiers cousins
• Nombres premiers sexy

Liens externes[modifier | modifier le code]

• (en) Twin Primes (Chris Caldwell)
• (en) Introduction to Twin Primes and Brun's Constant (Xavier Gourdon, Pascal Sebah)
• Liste des 20 000 premiers couples de nombres premiers jumeaux (p, p+2)
• (en) http://www.twinprimesearch.org
• (en) Projet Polymath 8 : le projet Polymath correspondant.

 [afficher]

v · m

Nombres premiers

• Portail de l’arithmétique et de la théorie des nombres

Catégories :

• Nombre premier
• Conjecture non résolue

| [+]

 

Source : wikipedia

A Short Biography of A.N. Kolmogorov

Source : http://homepages.cwi.nl/~paulv/KOLMOGOROV.BIOGRAPHY.html

 

A Short Biography of A.N. Kolmogorov

(``Andrei Nikolaevich Kolmogorov,'' CWI Quarterly, 1(1988), pp. 3-18.)
by Paul M.B. Vitanyi, CWI and University of Amsterdam

 

---

Andrei Nikolaevich Kolmogorov, born 25 April 1903 in Tambov, Russia, died 20 October 1987 in Moscow. He was perhaps the foremost contemporary Soviet mathematician and counts as one of the great mathematicians of this century. His many creative and fundamental contributions to a vast variety of mathematical fields are so wide-ranging that I cannot even attempt to treat them either completely or in any detail.
For now let me mention a non-exhaustive list of areas he enriched by his fundamental research: The theory of trigonometric series, measure theory, set theory, the theory of integration, constructive logic (intuitionism), topology, approximation theory, probability theory, the theory of random processes, information theory, mathematical statistics, dynamical systems, automata theory, theory of algorithms, mathematical linguistics, turbulence theory, celestial mechanics, differential equations, Hilbert's 13th problem, ballistics, and applications of mathematics to problems of biology, geology, and the crystallization of metals.
In over 300 research papers, textbooks and monographs, Kolmogorov covered almost every area of mathematics except number theory. In all of these areas even his short contributions did not just study an isolated question, but in contrast exposed fundamental insights and deep relations, and started whole new fields of investigations.
Apart from his penetrating work in Mathematics and the Sciences, he devoted much of his time to improving the teaching of mathematics in secondary schools in the Soviet Union, and in providing special schools for the mathematically gifted - which were very successful. Famous are also his efforts to capture in quantitative form some aspects of Russian poetry, especially that of Pushkin. It is told that ``it was fascinating to hear him lecture on this, whether one understood Russian or not.'' In 1942 Kolmogorov married Anna Dmitriyevna Egorov. He did not have children of his own.
Apart from being acknowledged without question in science, Kolmogorov was also blessed with social recognition. The USSR conferred to him seven orders of Lenin, the Order of the October Revolution, and also the high title of Hero of Socialist Labour; he gained Lenin prizes and State prizes. He occupies the first place among all Soviet mathematicians in the number of foreign academies and scientific societies that have elected him as member. These number over twenty, among them the Royal Netherlands Academy of Sciences (1963), the London Royal Society (1964), the USA National Society (1967), the Paris Academy of Sciences (1968), the Polish Academy of Sciences, the Rumanian Academy of Sciences (1956), the German Academy of Sciences Leopoldina (1959), the American Academy of Sciences and Arts in Boston (1959).
He was presented with honorary doctorates from the universities of Paris, Berlin, Warsaw, Stockholm, etc. He was elected a honorary member of the Moscow, London, Indian, and Calcutta Mathematical Societies, of the London Royal Statistical Society, the International Statistical Institute, and the American Meteorological Society. In 1963 he was awarded the International Bolzano prize.
Let me state here that I do not claim any personal relations with Kolmogorov. These remarks are based on second hand information, and primarily on sources in the Russian Mathematical Surveys, other references, and to a much lesser extent on personal communications. My credentials for writing about Kolmogorov's achievements are founded solely on my interests in that excellent notion we call``Kolmogorov complexity''. Since Kolmogorov was a man of many aspects, it is a pleasure to share some of these with the reader. This writeup was originally published as an obituary: P.M.B. Vitanyi, Andrei Nikolaevich Kolmogorov, CWI Quarterly, 1(1988), pp. 3-18. See also references in Section 1.6 of M. Li and P.M.B. Vitányi, An Introduction to Kolmogorov Complexity and its Applications, Springer-Verlag, New York, 1993 (xx + 546 pp). (This is Section 1.13 in the Second Edition of 1997.)

Early Years: 1903-1933

Kolmogorov was born on 25 April 1903 in the town of Tambov, where his mother Mariya Yakovlevna Kolmogorova had been delayed on her way from the Crimea. She died in childbed, and the responsibility to bring up the child was taken over by her sister Vera Yakovlevna Kolmogorova, ``an independent woman who held high social ideals. She passed this over to her nephew, raising him in the sense of responsibility, independence of opinion, intolerance towards idleness and poorly performed tasks, and the desire to understand and not just to memorize.''
K. treated her as his mother until her death in 1950 at Komarovka (his dacha) at the age of 87. From his mother's side K. was of aristocratic stock, his grandfather Yakov Stephanovitch Kolmogorov was a district head of the nobles in Uglich.
He spent his early years (before the revolution of 1917) at the family estate. The sources are less clear about his father. Apparently, K.'s father was the son of a clergyman, and was himself an agronomist with highly specialized training, what they called at the time ``a learned agronomist.''
K. started to work already at an early age (but presumably after the revolution); and before he became a student at Moscow University, he worked for some time as a railway conductor. He arrived at the University in autumn 1920, with already a fair knowledge of mathematics, gleaned from a book called ``New Ideas in Mathematics.'' Students at the time received grants that had little material value, but at the second course received, in addition, a ration of 16 kilos of baked bread and a kilo of fat. Hence, K. lost little time to check the minimum requirements for moving to the second course (lecture attendance being noncompulsory).
Conditions were generally harsh, and lecture rooms cold and unheated in the winter of 1920/1921. The following (unattributed) lines describe it:
``That grim year, nineteen twenty-one,
the scientific march began
Of Moscow University.
Though I was not then very old,
Though sheepskin coats enveloped me,
I still recall that beastly cold.''
For some time K. was interested in Russian history as well as mathematics. He did serious scientific research on XV-XVI century manuscripts concerning agrarian relations in ancient Novgorod. In the twenties he made a hypothesis on the way the upper Pinega was settled, and this conjecture was later confirmed by an expedition to that area.
In this early post-October revolution period the mathematical life in Moscow was dominated by ``young Luzitania'' (1920-1923) and ``post-Luzitania'' (1923-1927), a nickname for the school of real function theory headed by N.N. Luzin. This legendary personality apparently created either enthusiastic admiration or, in their struggle for independence, one-sided negation in his pupils. Among the first subjects in mathematics K. took were set theory, projective geometry, and theory of analytic functions. In 1921-1922 he obtained his first independent mathematical result (the existence of Fourier-Lebesgue series with arbitrarily slowly decreasing Fourier coefficients), and he became a pupil of N.N. Luzin. During this time he was also approached by P.S. Urysohn, who tried to interest him in topological problems. Since K. had obtained some results on the descriptive theory of functions, work that did not fit into Luzin's plans, Urysohn brought him into contact with P.S. Alexandrov whose research interests were better related to this topic. However, at about this time K. constructed a Fourier series divergent everywhere, a result that attracted international attention, and brought him for the time being in Luzin's orbit again. For this reason K.'s initial contacts with Aleksandrov stayed very limited at the time.
K. got interested in mathematical logic, and in 1925 published a paper in Mathematicheskii Sbornik on the law of the excluded middle, which has been a continuous source for later work in mathematical logic. This was the first Soviet publication on mathematical logic containing (very substantial) new results, and the first systematic research in the world on intuitionistic logic. K. anticipated to a large extentA. Heyting 's formalization of intuitionistic reasoning, and made a more definite correlation between classical and intuitionistic mathematics. K. defined an operation for `embedding' one logical theory in another. Using this - historically the first such operation, now called the `Kolmogorov operation' - to embed classical logic in intuitionistic logic, he proved that application of the law of the excluded middle in itself cannot lead to a contradiction. In 1932 K. published a second paper on intuitionistic logic, in which for the first time a semantics was proposed (for this logic), free from the philosophical aims of intuitionism. This paper made it possible to treat intuitionistic logic as constructive logic.
His interest in probability theory originated in 1924. His first steps in this area were performed jointly with A.Y. Khinchin. In 1928 he succeeded in finding necessary and sufficient conditions for the strong law of large numbers to hold, and proved the law of the iterated logarithm for sums of independent random variables, under very general conditions on the summands. In "A general theory of measure and the calculus of probabilities", 1929, he put forward a first draft of an axiom system for probability theory based on the theory of measure and the theory of functions of a real variable. Such a theory had been first suggested by E. Borel in 1909, was further developed by Lomnicki in 1923, and received its so successful final form with K.'s classic treatment of 1933. Much important work on probability theory had already been done without benefit of foundations, but this little book ``Foundations of the Calculus of Probabilities,'' published in German in 1933, immediately became the definitive formulation of the subject. This determined not only a new stage in the development of probability theory as a branch of mathematics, but also gave the necessary basis for the creation of the theory of random processes - the subject of his 1931 paper below. It was here that the basic theorems on infinite-dimensional distributions, now the logical foundations for the rigorous construction of the theory of random functions and sequences of random variables, were first formulated. The involved ideas lie at the heart of the modern theory of random processes; they form essential concepts in the very idea of control theory, and play a vital role in K.'s later synthesis of information theory and ergodic theory. K.'s many contributions in the theory of probability and statistics made him generally acknowledged as the foremost representative of this discipline.
In 1931 K.'s paper ``Analytical methods in probability theory'' appeared, in which he laid the foundations for the modern theory of Markov processes. According to Gnedenko: "In the history of probability theory it is difficult to find other works that changed the established points of view and basic trends in research work in such a decisive way. In fact, this work could be considered as the beginning of a new stage in the development of the whole theory".
The theory had a few forerunners: A.A. Markov, Poincaré and Bashelier, Fokker, Planck, Smolukhovski and Chapman. Their particular equations for individual problems in physics, informally obtained, followed as special cases in K.'s theory. A long series of subsequent publications followed, by K. and his followers, among which a paper by K. dealing with one of the basic problems of mathematical statistics, where he introduces his famous criterion (Kolmogorov's test) for using the empirical distribution function of observed random variables to test the validity of an hypothesis about their true distribution. In general K.'s ideas on probability and statistics have led to numerous theoretic developments, and to numerous applications in present-day physical sciences.
After graduation in 1925, K. stretched his stay at the University for four more years as a research student, but finally in 1928-1929 stricter control on the number of years a student had for research was enforced. An unprecedented number of 70 students finished in 1929, including K. This raised the problem of where to continue his research. Aleksandrov was instrumental in securing for K. the single available vacancy in 1929 at the Institute of Mathematics and Mechanics of Moscow University, against heavy competition.

Youth: 1929-1940

From 1930-1940 K. published more than sixty papers on probability theory, projective geometry, mathematical statistics, the theory of functions of a real variable, topology, mathematical logic, mathematical biology, philosophy and the history of mathematics. In 1931 K. was made professor at Moscow University, and from 1937 held the chair of theory of probability. From this time dates the life long friendship between K. and Aleksandrov. Says Aleksandrov: ``in 1979 this friendship [with K.] celebrated its fiftieth anniversary and over the whole of this half century there was not only never any breach in it, there was also never any quarrel, in all this time there was never any misunderstanding between us on any question, no matter how important for our lives and our philosophy; even when our opinions on one of these questions differed, we showed complete understanding and sympathy for the views of each other.''
Says K.: ``for me these 53 years of close and indissoluble friendship were the reason why all my life was on the whole full of happiness, and the basis of that happiness was the unceasing thoughtfulness on the part of Aleksandrov.''
K. describes how this friendship started in 1929 during a sailing trip on the Volga. At that time, the ``Society for Proletarian Tourism and Excursions'' offered active vacations: one obtained a boat and camping equipment at one city on the Volga which could be handed in at other cities downstream. K., already experienced in boating, decided to organize such a trip, and asked (besides two others) Aleksandrov to join. The young men bought the then popular ``Jungsturm'' suits for all of the crew. By way of books they took along only a steamboat timetable and a copy of the Odyssey (and also manuscripts to work on and a folding writing desk). They started out at June 16, and covered 1300 kilometers before handing in the boat at Samar downstream. K. and Aleksandrov then proceeded together to the Caucasus by steamer. After some more wandering, they set up residence in an unused cell of a monastery on a small peninsula in Lake Savan. Whiling their time away at secluded bays, in between swimming and sun bathing they also managed to get some work done: K. in the shadows on integration theory and analytic description of Markov processes in continuous time, and Aleksandrov dressed only in dark glasses and white panama hat in the burning sun on his Topology book with Hopf. They stayed in these idyllic surroundings for about three weeks, then set off partly on foot, partly by other means of transport, and eventually climbed the Alagez mountain (4100m). They wound up at Tiflis, from where Aleksandrov proceeded alone to a prearranged appointment with a group of mathematicians. K. continued hiking and mountain climbing. (By this time it was August.) Later, they joined up again at Gagra, on the Black Sea, and spent some more time there, sunbathing and swimming and doing mathematics. At about this time they decided to share a house together.
After returning to Moscow they forthwith rented the first in a series of houses in the nearby vacation village of Klyaz'm, and moved in together with K.'s aunt Vera Yakovlevna. A short time later, Masha Barbanova, who had been K.'s nanny at the family estate near Jaroslavl' before the revolution, joined as housekeeper. In 1935 they acquired (initially part of) an old manor house at Komarovka, with room for a large library and several guests. This `house at Komarovka' became a meeting place for mathematicians. One of them said ``It is just like Oberwolfach (a mathematical institute in the Black Forest), except that here Kolmogorov buys all the drinks.''
It is perhaps instructive to see a glimpse of the mathematicians' country life:
``As a rule,'' says K., ``of the seven days a week, four were spent in Komarovka, one of which was devoted entirely to physical recreation - skiing, rowing, long excursions on foot (these long walks covered on average about 30 kilometers, rising to 50; on sunny March days we went out on skis wearing nothing but shorts, for as much as four hours on a stretch. On the other days, morning exercise was compulsory, supplemented in the winter by a 10 kilometer ski run ... Especially did we love swimming in the river just as it began to melt ... I swam only short distances in icy water but Aleksandrov swam much further. It was I however who skied naked for considerably longer distances.'' As P. Halmos, visiting K. in Moscow in 1965 tells it:
``Kolmogorov [had] five rooms [apartment in the University]. ... stacks of reprints in one corner, a collection of theatrical masks somewhere, and a couple of skis somewhere else. "Is this where you work? I asked. "No, no", he said: "I work out at the dacha; I am here only three days a week."'' (At the celebration meeting of K's seventieth birthday, a skiing trip was organized where K. clad only in shorts outskied every other participant.)
In 1930-1931 K. and Aleksandrov were mainly abroad. The year 1930 they spent both at Gottingen. Here K. had contacts with R. Courant on limit theorems, with H. Weyl on intuitionistic logic, and with E. Landau on function theory. K. relates the story that he solved a problem Landau much liked to be solved, and wrote it up in detail. Landau being very pleased told everybody about the success and invited a paper on the subject, but, to his embarrassment, K. discovered a few weeks later exactly the same result with the same proof by Besicovitch in Fundamenta Mathematicae. The summer both K. and Aleksandrov visited Caratheodory at Munich (measure theory), and were invited to stay with Frechet on the Mediterranean (to work on probability theory in K.'s case). The journey there involved hiking through Bavaria, staying with Frechet for about a month, visiting P.S. Urysohn's grave in Normandy, and continuing on to Paris. Aleksandrov left Paris by the end of September for Goettingen, and K. stayed on until December, and had some meetings with Borel and P. Lévy, especially the last. While K. returned to Goettingen, Aleksandrov spent the spring 1931 semester in the U.S.A.
As another highlight of this period the article "Mathematics" for the second edition of the Great Soviet Encyclopaedia is often mentioned. Another area he turned to at the time was topology. Simultaneously with the U.S. topologist J.W. Alexander and independently of him, K. discovered the notion of cohomology and founded the theory of cohomological operations. The work of K. and his school on the deep connections between topology, the theory of ordinary differential equations, celestial mechanics and the theory of dynamical systems, determined to a considerable extent its present state.
At the end of the thirties, K.'s attention was drawn to the mechanics of turbulence. In the hands of K. and his school the theory of turbulence obtained an accurate mathematical form as an applied chapter in the theory of measure of function spaces. With great physical intuition, in two short papers in 1941, K. posited in concise mathematical form ideas about the structure of the small-scale components of turbulent motion of fluids and gasses, latent in earlier experimental work, particularly by G.I. Taylor. These hypotheses imply many qualitative results that are widely applicable - what goes on, for instance, within the turbulence that occurs in the wake of a jet aircraft. Some of the quantitative relations arising have the character of new laws of nature - like K.'s law of "2/3": in each developed turbulent flow the mean square difference of the velocities at two points is proportional to the 2/3rd power of their distance (if the distance is not too small or not too large). K. made also quantitative predictions on the basis of his theories, that were later confirmed by experiments, e.g., the stratified structure of the ocean, an effect known as "pancakes". K.'s 1941 contributions to the theory of turbulence are perhaps the most important ones in the long and unfinished history of the theory of turbulence.

Middle Years: 1940-1960

He was interested in every branch of science, he and his pupils wrote about crystal growth, about geometry of the interaction of plants, and also made significant contributions to ``birth and death'' processes and to genetics. One of these papers brought him to a head-on confrontation with Lysenko. In a courageous stand in emphasizing scientific truth, in a paper published in 1940 in the "Genetics" section of Dokl. Akad. Nauk SSSR , K. showed that the material gathered by followers of Stalin's proteg e Academician Lysenko, contrary to opinion, supported Mendel's laws. Another joint work (with Piscounov andPetrovsky) treated the rate of advance of an advantageous gene in a linear environment, (a topic studied independently by R.A. Fisher, for whom K. had high regard). This was later adapted to describe spreading of epidemics of innovations, and rumours.
The theory of smoothing and prediction of stationary time-series is usually associated with the name of Norbert Wiener but in fact it was developed simultaneously by Wiener and K. during the second world war.
In the post-war period K. turned again to turbulence, and made small improvements on laws he discovered before, that were experimentally verified as well. Topics in the vast range of classical mechanics, ergodic theory, function theory, information theory and the theory of algorithms belong to this period. He managed to find links between totally unconnected fields, and published a small number of papers, but quite fundamental ones, on each topic. In his work on dynamical systems one can distinguish two periods. In 1953-1954 he made a seminal contribution to the fundamental problem of classical mechanics, identified fifty years earlier by H. Poincare in his study of the motion of planets around the sun. Neglecting all but one planet one deals with an ``integrable'' problem that is well understood. However, the small effects associated with gravitational interaction between the planets introduces a profound qualitative change related to the fact that the equations are now ``nonintegrable.'' In attacking this problem, K.'s great achievement was to develop a general theory of Hamiltonian systems under small perturbations, which has several practical applications, among others in the study of magnetic fields and plasma physics. This work also spawned, together with improvements of K.'s pupil Arnol'd and by Moser, what is now known as the study of ``KAM-tori.'' Subsequent computational studies aptly confirm K.'s insights and have opened up the enormously fruitful field of ``chaos in dynamical systems,'' which is currently attracting much attention. These studies lead, for example, to better weather forecasting.
At this time he also started to work on the theory of automata and the theory of algorithms. Together with his pupil Uspenskii he formulated the important notion of Kolmogorov-Uspenskii machine. He supported the up and coming field of cybernetics (theory of computation) against heavy initial antagonism (in the USSR). Many USSR computer scientists are K.'s pupils or pupils of K.'s pupils.
The second period from 1955-1959 consisted in applications from information theory to the ergodic theory of dynamical systems. He introduced the fruitful idea of informational (entropic) characteristics in the study of metric spaces and of dynamical systems. Together with Arnol'd, K. settled in 1956-1957 Hilbert's 13th problem, disproving the conjectured outcome, by showing that a continuous function in any number of variables can be represented as a composition of continuous functions of a single variable and addition. The ideas of introducing entropic characteristics in the theory of dynamical systems opened up a large new area. Another important concept, that of a quasi-regular system (now called K-system), plays a very important role in the analysis of classical dynamic systems with strong stochastic properties, such as in physics, biology and chemistry. In the years 1958-1959 K. applied ergodic theory to phenomena of the type of turbulence, which had a great influence on subsequent work.

Later Years: 1960-1987

While in previous years K. used concepts of information theory in mathematical sciences, now it was the turn of information theory to be reconstructed using the theory of algorithms, incidentally closing the circle of his research by giving logico-algorithmic foundations to the theory of probability. Algorithmic information theory, or " Kolmogorov complexity theory", originated with the discovery of universal descriptions of finite objects, and a recursively invariant approach to the concepts of complexity of description, randomness and a priori probability. Historically, it is firmly rooted in R. von Mises' notion of random infinite sequences ( Kollektivs ), proposed from 1919 onwards as foundation for the theory of probability in the spirit of a physical theory (according to the program outlined in D. Hilbert's 6th problem), using the frequency interpretation of probability. In 1940 A. Church proposed an algorithmic version of von Mises random sequences, but the results were not yet satisfactory.
In his 1933 booklet K. had in some sense executed Hilbert's suggestion in his 6th problem: "To treat (in the same manner as geometry) by means of axioms, those physical sciences in which mathematics plays an important part; in the first rank are the theory of probability ..", in 1963 K. observes: "This theory [K's 1933 set theoretic axiomatic approach] was so successful, that the problem of finding the basis of real applications of the results of the mathematical theory of probability became rather secondary to many investigators. ..[However] the basis for the applicability of the results of the mathematical theory of probability to real 'random' phenomena must depend in some form on the frequency concept of probability , the unavoidable nature of which has been established by von Mises in a spirited manner."
However, von Mises based his approach on axiomatically postulated infinite random sequences, representing repetitious independent trials with a limiting frequency. To this K. objects: "The frequency concept based on the notion of limiting frequency as the number of trials increases to infinity, does not contribute anything to substantiate the application of the results of probability theory to real practical problems where we always have to deal with a finite number of trials."
Following a four decades long controversy on von Mises' intended notion of an infinite random sequence, in a 1965 paper K. used the theory of algorithms to describe the complexity of a finite object as the length of the smallest description (algorithm to reconstruct it). This would seem to make the definition depend on the algorithmic method used. However, it turns out that there are optimal and universal methods for which the complexities of the objects described are asymptotically optimal. Although there are many optimal methods, the corresponding complexities differ by no more than an additive constant. It is natural to call a finite object random if it has no description of complexity less than it has itself. It is seductive to define an random infinite sequence as one of which the growth of complexity if the initial segments with the length is sufficiently fast, thus relating to von Mises' earlier approach. Due to unavoidable oscillations of the complexity of prefixes as function of their length this did not work out. However, P. Martin-Loef, a Swedish mathematician visiting K. in Moscow in 1964-1965, was able to show that under appropriate axiomatic definitions of randomness, one can prove once and for all that the thus defined sequences satisfy all effective tests for randomness, and have measure one in the set of all such infinite sequences. This rigorously defined an appropriate class, intuitively satisfactory as well, to qualify as von Mises' Kollektivs. Later it was shown by L.A. Levin, P. Gacs and G.J. Chaitin that one can refine the notion of complexity by defining it relative to a set of admissible descriptions. If admissible descriptions are restricted such that no description is a proper prefix of any other description, then an infinite sequence is Martin-L of random if and only if each of its finite initial sequences has a complexity that equals (up to a fixed constant) its length.
With the advent of electronic computers in the 1950's, a new emphasis on computer algorithms, and a maturing general recursive function theory, ideas tantamount to Kolmogorov complexity came to many people's minds, because ``when the time is ripe for certain things, these things appear in different places in the manner of violets coming to light in early spring,'' in the phrase of Wolfgang Bolyai in another famous context. Thus, R. Solomonoff in Cambridge, Massachusetts, had formulated the same ideas already in 1960. and had published his truly innovative work on the subject already in 1964 in `Information and Control'.
According to Solomonoff his work got far more attention after K. started to refer to it from 1968 onward, even though the attribution ``Kolmogorov'' complexity seems to have stuck. Says K.: ``I came to similar conclusions before becoming aware of Solomonoff's work, in 1963-1964.''
Yet a third independent inventor entered slightly later, Gregory Chaitin who was an 18 year old undergraduate in New York when he submitted a very similar set of inventions for publication end 1965 for publication in `J. Assoc. Comp. Mach.' (published in 1966 and 1969, the last paper containing the definition of Kolmogorov complexity and results thereof, while the 1966 paper extends C.E. Shannon's non-invariant notion of state-symbol measure for the complexity of Turing machines). Says Chaitin: ``this definition [of Kolmogorov complexity] was independently proposed about 1965 by A.N. Kolmogorov and me ... Both Kolmogorov and I were then unaware of related proposals made in 1960 by Ray Solomonoff.''
One of the last papers of K. was on the topic of algorithmic information theory - a paper together with Uspenskii published in 1987. For a comprehensive introduction and a survey of the astonishing range of applications of Kolmogorov complexity, see M. Li and P.M.B. Vitányi, An Introduction to Kolmogorov Complexity and its Applications, Springer-Verlag, New York, 1993 (xx + 546 pp).

As a Teacher

K.'s pedagogical activities began in 1922, when he became teacher at the experimental model school of the People's Commissariat for Education. He taught there until 1925. From 1925 till 1929 he was instructor at the University. Passing on knowledge and scientific ideas was very important for K. His interests in this subject ranged over the full scale from earliest education to higher education, and occupied much of his time. He actively took part in organizing mathematical Olympiads in schools and gave talks to school children. Thus he wrote a booklet on the topic ``Mathematics as a Profession'', which circulated in tens of thousands of copies. He put special emphasis on selection of mathematically gifted adolescents, since even the nonmathematicians will need such training in their later career
According to K., by 14-15 years about half of the pupils have come to the conclusion that mathematics and physics will be of little use to them. In recognition of that fact a special simplified program should be followed by such pupils. ``The mechanically understood principles of uniformity of schools providing general education, which excludes schools with a more detailed study of individual subjects, has outlived itself. As applied to mathematics it has already been destroyed by the creation of schools giving special training to computer operators and computer programmers.'' And: ``At 14-16 everything changes. At this age interest in mathematics usually becomes apparent, which quickly and painlessly leads the student to concentrated work and then to the real research work of the young scientist (at 18-20 years). ... For the beginners, the young people entering science for the first time, it is important to be convinced as soon as possible that they are capable of doing something original, their very own. When offering a subject for research to a graduate or a research student, the supervisor must not think only about the objective importance, or urgency of the subject, but also whether the work on the subject will stimulate the development of the young scientist, and whether it is within his powers to carry out, and at the same time demand the maximal effort of which he is capable.'' The ability to offer the students exactly what is most important and ripe in the development of science, and avoid pursuing dead-ends, and what is at the same time in their powers to accomplish is very characteristic for K.
The number of Kolmogorov's research students who have obtained their Ph.D. exceeds sixty. He was instrumental in substantial transformation (in the Soviet Union) of the very character of university education in mathematics, in particular the organization of practical work in mathematics, and updating the contents of mathematics. He also engaged in the search for new contents of mathematics in secondary schools, the founding of mathematical boarding schools, gave cycles of lectures for teachers on the structure of modern mathematics, and so on. Finally, he created an author's collective, and took part himself in writing textbooks on geometry, algebra and analysis for 6th through 10th grades. At the mathematical boarding school No. 18 at the University of Moscow, otherwise known as the ``Kolmogorov school'', he gave for years lessons up to 26 hours a week, and wrote accompanying syllabi. He also gave lectures to the students on music, art and literature. He felt that intellectual development must be evenly balanced. The former pupils of this school are very successful and systematically take the first places in All-Union and International Mathematical Olympiads.
In 1964 K. became head of the mathematical section of a joint syllabus committee of the USSR Academy of Sciences and that of Pedagogical Sciences. K. also organized a Statistical Laboratory at the University of Moscow, and succeeded in upgrading the budding library by obtaining large funds, and also international literature through partial use of money he received as part of the international Bolzano prize. In 1972 on K.'s initiative a compulsory course in mathematical logic was introduced for the first time in the Department of Mechanics and Mathematics at Moscow State University. He wrote the syllabus (which was still followed in 1983) and was the first to teach it.
According to V.I. Arnol'd, ``K. never explained anything, just posed problems, and didn't chew them over. He gave the student complete independence and never forced one to do anything, always waiting to hear from the student something remarkable. He stood out from the other professors I met by his complete respect for the personality of the student. I remember only one case where he interfered with my work: in 1959 he asked me to omit from the paper on self-maps of the circle the section on applications to heartbeats, adding "That is not one of the classical problems one ought to work on". The application to the theory of heartbeats was published by L. Glass 25 years later, while I had to concentrate my efforts on the celestial-mechanical applications of the same theory.''
L.S. Pontryagin relates: ``Kolmogorov gave me an interesting task..: to study [some problems in] locally compact algebraic fields in which multiplication is not necessarily commutative... A week later I reported to Aleksandrov that I had solved it in the case of commutative fields. Directly afterwards the three of us, Aleksandrov, Kolmogorov and I, met in Aleksandrov's flat. With a shade of ironical doubt, Kolmogorov said: "Well now, Lev Semenovich, I hear you have already solved my problem, let's hear you." Kolmogorov declared my very first statement to be false, but I immediately refuted him. Then he said: "Yes, it seems that the problem turned out to be much easier than I supposed." None of the rest of my answer aroused doubt. For the case of the noncommutative field the problem was immeasurably more difficult. It took me a whole year to work it out.'' It is also said that K. was one of the very few non-political mathematicians in the Soviet Union with yet real power. He quietly helped talented people with otherwise unfashionable views.
K.'s pupils included in the early years: Millionshchikov (later Vice-President of the USSR Academy of Sciences), Mal'tsev, Nikol'skii, Gnedenko, Gel'fand, Bavli and Verchenko. The subjects ranged from theoretical geophysics, mathematical logic, functional analysis, probability theory, function theory. During and after the war: Shilov, Fage, Sevast'yanov, Sirazhdinov, Pinsker, Prikhorov, Barenblatt, Bol'shev, Dobrushin, Medvedev, Mikhalevich, Uspenskii, Borovkov, Zolotarev, Alekseev, Belyaev, Mehhalkin, Epokhin, Rozanov, Sinai, Tikhomirov, Shiryaev, Arnol'd, Bassalygo, and Ofman. Later also Prokhorov, L.A. Levin, Kozlov, Zhurbenko, Abramov, and Bulinskii. His pupils include a number of well-known foreign mathematicians, among who the Swede P. Martin-L of. Pupils who became member of the USSR Academy of Sciences: A.I. Mal'tsev (algebra, mathematical logic), S.M. Nikol'skii (function theory), A.M. Obukhov (physics of the atmosphere), I.M. Gel'fand (functional analysis), Yu.V. Prokhorov (probability theory); and corresponding member: L.N. Bol'shev (mathematical statistics), A.A. Borovokov (probability theory, mathematical statistics), A.S. Monin (oceanology), and V.I. Arnol'd. The Ukrainian Academy of Sciences: B.V. Gnedenko (probability theory, history of mathematics), V.M. Mikhalevich (cybernetics), etc.

Scientific Career

K. entered Moscow University in 1920, graduated in 1925, and got his (equivalent of) Ph.D. in 1929, when he also got a position on the faculty. In 1931 K. became professor at Moscow University, and from 1933-1939 he also became Director of the Scientific Research Institute of Mathematics at the Moscow State University. Apparently, he was involved with the scientific research of all graduate students at the institute, not only his own. Most of them mention the unforgettable hikes on Sundays when K. invited all his own students (graduates and undergraduates) as well as students from other supervisors. These 40 km walks in the environment of Bolshevo, Klyaz'm, later Komarovka, are remembered as intellectually stimulating and culturally wide ranging experiences, ending when he and Aleksandrov treated the whole company to dinner in their dacha. In 1939 K. was elected as an Academician of the All-Union Academy of Sciences and as Academician-Secretary of the Physics-Mathematical Section. He also did enormous work as head of the mathematics editorial board of the Publishing House of Foreign Literature and as editor of the mathematics section of the Great Soviet Encyclopaedia. During the second world war K. engaged in the war effort by solving problems in ballistics and began research on problems of quality control of mass industrial production. From 1964 to 1966, and from 1976 till at least 1983 K. has been President of the Moscow Mathematical Society; from 1946 to 1954 and from 1983 on Editor-in-chief of Uspekhi Math. Nauk (Russian Mathematical Surveys). At the University of Moscow, K. held from 1938 to 1966 the chair of probability theory. From 1966 till 1976 he was the head of the Interdepartmental Laboratory of Statistical Methods, and from 1976 to 1980 he held the chair of mathematical statistics, which he organized. From 1980 on K. held the chair of mathematical logic. From 1951 to 1953 he was Director of the Institute of Mathematics and Mechanics of the Moscow State University; from 1954 to 1956 and from 1978 to at least 1983 the head of the mathematics section of the Faculty of Mechanics and Mathematics. From 1954 to 1958 he was Dean of the Faculty of Mechanics and Mathematics of the University.

---

---

This page is maintained by Paul Vitanyi, at CWI and was last modified on January 24, 1996.

http://www.kolmogorov.com/

http://www.kolmogorov.com/

Mathematics Genealogy Project

Voir le site : http://genealogy.math.ndsu.nodak.edu/

2003 Steele Prizes

Voir le pdf : http://www.ams.org/notices/200304/comm-steele.pdf

 

2003 Steele Prizes 462 NOTICES OF THE AMS VOLUME 50, NUMBER 4 The 2003 Leroy P. Steele Prizes were awarded at the 109th Annual Meeting of the AMS in Baltimore in January 2003. The Steele Prizes were established in 1970 in honor of George David Birkhoff, William Fogg Osgood, and William Caspar Graustein. Osgood was president of the AMS during 1905–06, and Birkhoff served in that capacity during 1925–26. The prizes are endowed under the terms of a bequest from Leroy P. Steele. Up to three prizes are awarded each year in the following categories: (1) Mathematical Exposition: for a book or substantial survey or expository-research paper; (2) Seminal Contribution to Research (limited for 2003 to the field of logic): for a paper, whether recent or not, that has proved to be of fundamental or lasting importance in its field or a model of important research; and (3) Lifetime Achievement: for the cumulative influence of the total mathematical work of the recipient, high level of research over a period of time, particular influence on the development of a field, and influence on mathematics through Ph.D. students. Each Steele Prize carries a cash award of $5,000. The Steele Prizes are awarded by the AMS Council acting on the recommendation of a selection committee. For the 2003 prizes, the members of the selection committee were: M. S. Baouendi, Andreas R. Blass, Sun-Yung Alice Chang, Michael G. Crandall, Constantine M. Dafermos, Daniel J. Kleitman, Barry Simon, Lou P. van den Dries, and Herbert S. Wilf (chair). The list of previous recipients of the Steele Prize may be found in the November 2001 issue of the Notices, pages 1216–20, or on the World Wide Web, http://www.ams.org/prizes-awards. The 2003 Steele Prizes were awarded to JOHN B. GARNETT for Mathematical Exposition, to RONALD JENSEN and to MICHAEL D. MORLEY for a Seminal Contribution to Research, and to RONALD GRAHAM and to VICTOR GUILLEMIN for Lifetime Achievement. The text that follows presents, for each awardee, the selection committee’s citation, a brief biographical sketch, and the awardee’s response upon receiving the prize. Mathematical Exposition: John B. Garnett Citation An important development in harmonic analysis was the discovery, by C. Fefferman and E. Stein, in the early seventies, that the space of functions of bounded mean oscillation (BMO) can be realized as the limit of the Hardy spaces Hp as p tends to infinity. A crucial link in their proof is the use of “Carleson measure”—a quadratic norm condition introduced by Carleson in his famous proof of the “Corona” problem in complex analysis. In his book Bounded Analytic Functions (Pure and Applied Mathematics, 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981, xvi + 467 pp.), Garnett brings together these far-reaching ideas by adopting the techniques of singular integrals of the Calderón-Zygmund school and combining them with techniques in complex analysis. The book, which covers a wide range of beautiful topics in analysis, is extremely well organized and well written, with elegant, detailed proofs. The book has educated a whole generation of mathematicians with backgrounds in complex analysis and function algebras. It has had a great impact on the early careers of many leading analysts and has been widely adopted as a textbook for graduate courses and learning seminars in both the U.S. and abroad. Biographical Sketch John B. Garnett was born in Seattle in 1940. He received a B.A. degree from the University of Notre Dame in 1962 and a Ph.D. degree in mathematics APRIL 2003 NOTICES OF THE AMS 463 from the University of Washington in 1966. His thesis advisor at Washington was Irving Glicksberg. In 1968, following a two-year appointment as C.L.E. Moore Instructor at the Massachusetts Institute of Technology, Garnett became assistant professor at the University of California, Los Angeles, where he has worked ever since. At UCLA, Garnett was promoted to tenure in 1970 and to professor in 1974. In 1989 he received the UCLA Distinguished Teaching Award primarily for his work with Ph.D. students, and from 1995 to 1997 he served as department chairman. Garnett’s research focuses on complex analysis and harmonic analysis. He has held visiting positions at Institut Mittag-Leffler; Université de Paris-Sud; Eidgenössische Technische Hochschule, Zurich; Yale University; Institut des Hautes Études Scientifiques; and Centre de Recerca Matemática, Barcelona. He gave invited lectures to the AMS in 1979 and to the International Congress of Mathematicians in 1986. Response I am honored to receive the Steele Prize for the book Bounded Analytic Functions. It is especially satisfying because the prize had previously been awarded for some of the classic books in analysis by L. Ahlfors, Y. Katznelson, W. Rudin, and E. M. Stein, from which I first learned much mathematics and to which I still return frequently. I wrote Bounded Analytic Functions around 1980 to explain an intricate subject that was rapidly growing in surprising ways, to teach students techniques in their simplest cases, and to argue that the subject, which had become an offshoot of abstract mathematics, was better understood using the concrete methods of harmonic analysis and geometric function theory. I want to thank several mathematicians: L. Carleson, C. Fefferman, K. Hoffman, and D. Sarason, whose ideas prompted the development of the subject; and S.-Y. A. Chang, P. Jones, D. Marshall, and the late T. Wolff, whose exciting new results at the time were some of the book’s highlights. Encouragement is critical to the younger mathematician, and from that time I owe much to my mentors I. Glicksberg, K. Hoffman, and L. Carleson, and to my contemporaries T. W. Gamelin, P. Koosis, and N. Varopoulos. I also want to thank the young mathematicians who over the years have told me that they learned from the book. Seminal Contribution to Research: Ronald Jensen Citation Ronald Jensen’s paper “The fine structure of the constructible hierarchy” (Annals of Mathematical Logic 4 (1972) 229–308) has been of seminal importance for two different directions of research in contemporary set theory: the inner model program and the use of combinatorial principles of the sort that Jensen established for the constructible universe. The inner model program, one of the most active parts of set theory nowadays, has as its goals the understanding of very large cardinals and their use to measure the consistency strength of assertions about John B. Garnett Ronald Jensen Michael D. Morley Ronald Graham Victor Guillemin 464 NOTICES OF THE AMS VOLUME 50, NUMBER 4 much smaller sets. A central ingredient of this program is to build, for a given large cardinal axiom, a model of set theory that either is just barely large enough to contain that type of cardinal or is just barely too small to contain it. The fine structure techniques introduced in Jensen’s paper are the foundation of the more recent work of Mitchell, Steel, Jensen himself, and others constructing such models. The paradigm, initiated by Jensen, for relating large cardinals to combinatorial properties of smaller sets is first to show that the desired properties hold in these inner models and then to show that, if they failed to hold in the universe of all sets, then that universe and the inner model would differ so strongly that a large cardinal that is barely missing from the inner model would be present in the universe. The paper cited here contains the first steps in this direction, establishing for the first time combinatorial properties of an inner model, in this case Gödel’s constructible sets, that go far beyond Gödel’s proof of the generalized continuum hypothesis in this model. The second direction initiated by Jensen’s paper involves applying these combinatorial principles to problems arising in other parts of mathematics. The principle , which Jensen proved to hold in the constructible universe, has been particularly useful in such applications. A good example is Shelah’s solution of the Whitehead problem in abelian group theory; half of the solution was to show that a positive answer to the problem follows from . By now, has become part of the standard tool kit of several branches of mathematics, ranging from general topology to module theory. Biographical Sketch Ronald Jensen received his Ph.D. in 1964 from the University of Bonn. He continued his research at Bonn as a scientific assistant (1964–69). From 1969 until 1973 Jensen was a professor of mathematics at the University of Oslo. During this period he held concurrent positions at Rockefeller University (1969–71) and the University of California, Berkeley (1971–73). At the University of Bonn he was awarded the Humboldt Prize (1974–75) and served as a professor of mathematics (1976–78). He was a visiting fellow at Oxford University’s Wolfson College (1978–79), a professor of mathematics at the University of Freiburg (1979–81), and a senior research fellow at Oxford University’s All Souls College (1981–94). He moved to Humboldt University of Berlin, where he was a professor of mathematics (1994–2001). His areas of research interest include set theory. Response I feel deeply honored that on the basis of my paper “The fine structure of the constructible hierarchy”, I was chosen to share the Steele Prize for seminal research with Michael Morley. I came to set theory in the wake of Cohen’s discovery of the forcing method, together with a group of other young mathematicians such as Bob Solovay, Tony Martin, and Jack Silver, all of whom influenced my work. It was an exciting time. Much of the work centered on independence proofs using Cohen’s method, but the research on the consequences of strong existence axioms, such as large cardinals and determinacy, was also beginning. The theory of inner models—in particular Gödel’s model L—was comparatively underdeveloped. After discovering that the axiom V = L settles Souslin’s problem, I began developing a body of methods, now known as “fine structure theory”, for investigating the structure L. Much of this work was done in 1969–71 at Rockefeller University and the University of Oslo. The above-mentioned paper was subsequently written at Berkeley. In the ensuing years it became apparent that these methods were also applicable to larger inner models in which strong existence axioms are realized. The most important breakthrough in this direction was made by John Steel. He and Hugh Woodin have applied the methods widely. This work is being extended by a very capable group of younger mathematicians, such as Itay Neeman, Ernest Schimmerling, and Martin Zeman. I feel privileged to have worked in such gifted company. Seminal Contribution to Research: Michael D. Morley Citation Michael Morley’s paper “Categoricity in power” (Transactions of the AMS 114 (1965) 514–538) set in motion an extensive development of pure model theory by proving the first deep theorem in this subject and introducing in the process completely new tools to analyze theories (sets of first-order axioms) and their models. When does a theory have (up to isomorphism) a unique model? An early result in mathematical logic is that, for basic cardinality reasons, a theory never has a unique infinite model. The next question is: when does a theory have exactly one model of some specified infinite cardinality? An important example is the theory of algebraically closed fields of any given characteristic, which has a unique model in every uncountable cardinality. Answering a question of L
os´, Morley proved that a countable theory which is categorical (has a unique model) in one uncountable cardinality is categorical in every uncountable cardinality. Morley used most of the then-existing model theory, but what makes his paper seminal are its new techniques, which involve a systematic study of Stone spaces of Boolean algebras of definable sets, called type spaces. For the theories under consideration, these type spaces admit a CantorBendixson analysis, yielding the key notions of Morley rank and ω-stability. This property of ω-stability of a theory was the first of many to APRIL 2003 NOTICES OF THE AMS 465 follow that are of an intrinsic nature, that is, invariant under biinterpretability. Morley’s work set the stage for studying the difficult problem of the possible isomorphism types of models of a given theory. This was pursued with great success by Shelah, who vastly generalized Morley’s methods. Also, the recognition grew that categoricity properties and notions like Morley rank and ω-stability are intimately tied to underlying combinatorial geometries (Baldwin-Lachlan, Zil ber). In combination with the fact that an infinite field with uncountably categorical theory has to be algebraically closed (Macintyre), this led to the geometric orientation of current model theory. In the last ten years, the development started by Morley enabled remarkable applications by Hrushovski and others to questions of diophantine character, with impact on areas such as differential and difference algebra. Biographical Sketch Michael Morley was born in Youngstown, Ohio, in 1930. In 1951 he received a B.S. degree in mathematics from Case Institute of Technology and began graduate work at the University of Chicago. There was a five-and-one-half year hiatus (1955–61) in his graduate education, during which he worked as a mathematician at the Laboratories for Applied Sciences of the University of Chicago. After returning to graduate school, he received his Ph.D. from the University of Chicago in 1962, though the last year of his graduate work was done at the University of California, Berkeley. He was an instructor for one year at Berkeley, an assistant professor for three years at the University of Wisconsin, and joined the Cornell faculty in 1966. He was associate chairman and director of undergraduate studies for the mathematics department at Cornell from 1984–95. He achieved emeritus status at the end of 2002. He served as president of the Association for Symbolic Logic in 1986–89. Response I am grateful for this award. By definition, a paper is judged seminal because of work that follows it. Therefore, I am aware that I am being honored in large part for the work of other people. This paper was written just over forty years ago. At that time most mathematicians considered mathematical logic as philosophically very interesting but mathematically not very deep. (After all, some of the work was done by professors of philosophy.) There was some justification for this attitude. However, in the early 1960s several papers appeared that obtained spectacular results by applying nontrivial mathematics to logic. This attracted many of the best young mathematicians to mathematical logic. Today there is a large body of mathematically deep and lovely work in logic. One worries that we may have lost some of the philosophical significance. The paper was my doctoral dissertation written under the supervision of Professor Robert Vaught. Bob Vaught died last spring. I must express the gratitude that I, and indeed many of his students, felt towards Robert Vaught, not just for his mathematical direction, but for his great personal kindness and generosity of spirit. He was a fine mathematician and a truly good man. Lifetime Achievement: Ronald Graham Citation Ron Graham has been one of the principal architects of the rapid development worldwide of discrete mathematics in recent years. He has made many important research contributions to this subject, including the development, with Fan Chung, of the theory of quasirandom combinatorial and graphical families, Ramsey theory, the theory of packing and covering, etc., as well as to the theory of numbers, and seminal contributions to approximation algorithms and computational geometry (the “Graham scan”). Furthermore, his talks and his writings have done much to shape the positive public image of mathematical research in the USA, as well as to inspire young people to enter the subject. He was chief scientist at Bell Labs for many years and built it into a world-class center for research in discrete mathematics and theoretical computer science. He served as president of the AMS in 1993–94. Biographical Sketch Ronald Graham’s undergraduate training included three years at the University of Chicago (in Robert Maynard Hutchins’ Great Books program); a year at Berkeley as an electrical engineering major; and four years in the U.S. Air Force, three of which were spent in Fairbanks, Alaska, where he concurrently received a B.S. in physics in 1959. He subsequently was awarded a Ph.D. in mathematics from the University of California, Berkeley, in 1962. He spent the next thirty-seven years at Bell Labs as a researcher, leaving from what is now AT&T Labs in 1999 as chief scientist. During that time he also held visiting positions at Princeton University, Stanford University, the California Institute of Technology, and the University of California, Los Angeles, and was a (part-time) University Professor at Rutgers for ten years. He currently holds the Irwin and Joan Jacobs Chair of Computer and Information Science at the University of California at San Diego. Graham has received the Pólya Prize in Combinatorics from the Society for Industrial and Applied Mathematics, the Euler Medal from the Institute of Combinatorics and Its Applications, the Lester R. Ford Award from the Mathematical Association of America (MAA), and the Carl Allendoerfer Award 466 NOTICES OF THE AMS VOLUME 50, NUMBER 4 from the MAA. He is currently treasurer of the National Academy of Sciences, a foreign member of the Hungarian Academy of Sciences, a fellow of the American Academy of Arts and Sciences, a fellow of the American Association for the Advancement of Science, and past president of the International Jugglers Association. He was an invited speaker at the International Congress of Mathematicians in Warsaw in 1983 and was the AMS Gibbs Lecturer in 2000. Response from Professor Graham I must say that it is a great honor and pleasure for me to receive this award in recognition of a life in mathematics, and I would like to express my deep appreciation to the American Mathematical Society and to the Steele Prize Committee for their selection. When I was first notified, my initial reaction was to recall the famous quote of Mark Twain, who, upon seeing his obituary printed in a local newspaper, wrote that “the reports of my death are greatly exaggerated.” I can’t remember a time when I didn’t love doing mathematics, and that desire has not dimmed over the years (yet!). But I also get great pleasure sharing mathematical discoveries and insights with others, even though this can present a special challenge for mathematicians talking to nonmathematicians. However, I really believe that this type of communication will become increasingly important in the future. As an undergraduate at Berkeley, a one-year course in number theory taught by D. H. Lehmer fired my imagination for the subject and formed the basis for my Ph.D. dissertation under him (after a slight detour of four years in the military and Alaska). Although I never took another course from Dick Lehmer, he taught me the value of independence of thought and an appreciation for the algorithmic issues in mathematics. I feel that I have been very lucky to have been at the right place and time in history for participating in the rapid and exciting current developments in combinatorics. No doubt, all mathematicians in every generation feel this way! In particular, I have had the good fortune to work with, and be inspired by, such giants as Paul Erdo˝s and Gian-Carlo Rota, who, though different in many ways, were both driven by grand visions which have helped guide the paths of many combinatorial researchers today. Number theory and combinatorics are especially rife with simple-looking problems which, like Socratic gadflies, constantly remind us how little we really know. (For example, are there infinitely many pairs of primes which differ by 2? The answer, of course, is yes! However, at present we don’t have a clue how to prove this.) I recall the story of a civilization so advanced that a prize was awarded to the first mathematician who realized that the Riemann Hypothesis actually needed a proof. Perhaps more imminent (and more likely?) is the related version in which the Great Computer a hundred years from now, when asked whether the Riemann Hypothesis is true, pauses for a moment and then says, “Yes, it is true. But you wouldn’t be able to understand the proof!” Still, I am a firm believer in Hilbert’s famous dictum “Wir müssen wissen, wir werden wissen” (“We must know, we shall know”). And with this thought in mind, I will happily continue to keep hammering pitons into the sides of the infinite mountain of mathematical truth, as we all slowly inch our way up its irresistible slopes. Lifetime Achievement: Victor Guillemin Citation Victor Guillemin has played a critical role in the development of a number of important areas in analysis and geometry. In particular, he has made fundamental contributions to microlocal analysis, symplectic group actions, and spectral theory of elliptic operators on manifolds. His work on generalizations of the Poisson and Selberg trace formulae has been particularly influential. Moreover, Guillemin has greatly advanced these areas, and mathematics in general, by mentoring many graduate students and postdoctoral fellows, some of whom have become leading mathematicians in their own right. Biographical Sketch Victor Guillemin was born in Cambridge, Massachusetts, on October 15, 1937. He received his B.A. from Harvard in 1959, his M.A. from the University of Chicago in 1960, and his Ph.D. from Harvard in 1962. He was an instructor at Columbia from 1963 to 1966 and an assistant professor at the Massachusetts Institute of Technology from 1966 to 1969. He was promoted to associate professor in 1969 and to full professor in 1973. He has held a Sloan fellowship (1969–70), a Guggenheim grant (1988–89), and an Alexander Humboldt fellowship (1998). He was elected to the American Academy of Arts and Sciences in 1984 and to the National Academy of Sciences in 1985. Response I want to thank the AMS Steele Prize Committee for the wonderful honor of being selected as corecipient, with Ron Graham, of this year’s Steele Lifetime Achievement award. For me personally, my main “lifetime achievement” has been to have had, over the course of my career, some remarkable mentors, collaborators, and students. In particular, as a graduate student I had the good fortune to have Raoul Bott and Shlomo Sternberg as teachers at a time when Morse theory, index theory, and K-theory were revolutionizing differential topology. It was also a time when Raoul Bott was, for Shlomo and me, not only a teacher and mentor but APRIL 2003 NOTICES OF THE AMS 467 a greater-than-life role model. I can’t speak for Shlomo, but “greater-than-life” remains my view of Raoul to this day. In the collaborations I’ve been involved in, I feel I have been extraordinarily lucky. I was Shlomo Sternberg’s Ph.D. student when we wrote our first paper together in 1962, neither of us imagining that this was going to be the first of thirty papers and six books that we would produce together or that we would still be actively working together four decades later. These four decades have tempered somewhat the awe I felt in his presence when I first started working with him, but not my awe for the range and depth of his understanding of mathematics. When I met Richard Melrose at a conference in Nice in 1973, he seemed, with his scruffy beard and ponytail, the embodiment of the 1970s counterculture Zeitgeist. He had, however, just settled an important special case of one of the main open problems in physical optics, the glancing ray problem; and two years later, together with Mike Taylor, he solved this problem in complete generality (a result for which he won the Bôcher Prize in 1979). Thirty years later the ponytail is gone and the beard marginally less scruffy, and when the occasion requires, he can pass himself off as a respectable middle-aged academic. However, he is still, with his many students and collaborators (of whom I am fortunate to be one), exploring the consequences of this result and the beautiful ideas to which it has led in microlocal analysis on manifolds-with-corners and singular spaces. One of the most rewarding collaborations of my life was working with Hans Duistermaat on the Poisson formula for elliptic operators; however, at the time it was also one of the most exasperating. I enjoy writing mathematical papers but find it hard to edit and revise and am often content with efforts that give one a glimpse of, without entirely embodying, the good, the true, and the beautiful. Hans is the opposite: With the fiercely competitive instincts of the accomplished chess player that he is, he is content with nothing short of perfection, and our paper went through many rewrites before he was completely happy with it. With each rewrite my exasperation mounted, and when we finally sent it off, I recalled his once warning me that Duistermaat is Dutch for “dark mate”. The early 1990s saw a curious blip in the demographics of the population of Generation-X mathematicians of that era. Jobs in theoretical physics became hard to come by, and as a consequence many would-be graduate students in physics gravitated to adjoining areas of mathematics. My own field of symplectic geometry was one of the beneficiaries of this development, and in the early and mid-1990s there were a large number of exceptionally talented postdocs in our department at MIT, some of whom became my collaborators and many of whom became cherished friends. Among them were Jiang-Hua Lu, Reyer Sjamaar, Sue Tolman, Yael Karshon, Jaap Kalkman, and Eckhard Meinrenken. I like to believe that they learned a little symplectic geometry from me, but I suspect I learned much, much more from them. (In particular, I learned from Eckhard Meinrenken that, as Shlomo and I had conjectured fifteen years before, “quantization and reduction commute”.) My first student, in 1968, was Marty Golubitsky, and my last student, in 2002, Tara Holm. To them and to the students in between I owe everything that has made my life in mathematics worthwhile.

Préface : CONCRETE MATHEMATICS: A Foundation for Computer Science

Source : http://cs.ioc.ee/yik/lib/1/Graham1pre.html

 

CONCRETE MATHEMATICS: A Foundation for Computer Science
2nd ed
by Ronald L. Graham, Donald Ervin Knuth, and Oren Patashnik

Addison-Wesley Publishing Co. - Reading, Mass.
ISBN: 0-201-55802-5 * Hardcover * 657 p. * © 1994

---

This book is based on a course of the same name that has been taught annually at Stanford University since 1970. About fifty students have taken it each year juniors and seniors, but mostly graduate students - and alumni of these classes have begun to spawn similar courses elsewhere. Thus the time seems ripe to present the material to a wider audience (including sophomores).

It was dark and stormy decade when Concrete Mathematics was born. Long-held values were constantly being questioned during those turbulent years; college campuses were hotbeds of controversy. The college curriculum itself was challenged, and mathematics did not escape scrutiny. John Hammersley had just written a thought-provoking article "On the enfeeblement of mathematical skills by 'Modern Mathematics' and by similar soft intellectual trash in schools and universities" [176] ; other worried mathematicians [332] even asked, "Can mathematics be saved?" One of the present authors had embarked on a series of books called The Art of Computer Programming, and in writing the first volume he (DEK) had found that there were mathematical tools missing from his repertoire; the mathematics he needed for a thorough, well-grounded understanding of computer programs was quite different from what he'd learned as a mathematics major in college. So he introduced a new course, teaching what he wished somebody had taught him.

The course title "Concrete Mathematics" was originally intended as an antidote to "Abstract Mathematics," since concrete classical results were rapidly being swept out of the modern mathematical curriculum by a new wave of abstract ideas popularly called the "New Math." Abstract mathematics is a wonderful subject, and there's nothing wrong with it: It's beautiful, general, and useful. But its adherents had become deluded that the rest of mathematics was inferior and no longer worthy of attention. The goal of generalization had become so fashionable that a generation of mathematicians had become unable to relish beauty in the particular, to enjoy the challenge of solving quantitative problems, or to appreciate the value of technique. Abstract mathematics was becoming inbred and losing touch with reality; mathematical education needed a concrete counterweight in order to restore a healthy balance.

When DEK taught Concrete Mathematics at Stanford for the first time he explained the somewhat strange title by saying that it was his attempt to teach a math course that was hard instead of soft. He announced that, contrary to the expectations of some of his colleagues, he was not going to teach the Theory of Aggregates, not Stone's Embedding Theorem, nor even the Stone-Cech compactification. (Several students from the civil engineering department got up and quietly left the room.)

Although Concrete Mathematics began as a reaction against other trends, the main reasons for its existence were positive instead of negative. And as the course continued its popular place in the curriculum, its subject matter "solidified" and proved to be valuable in a variety of new applications. Meanwhile, independent confirmation for the appropriateness of the name came from another direction, when Z.A. Melzak published two volumes entitled Companion to Concrete Mathematics [267].

The material of concrete mathematics may seem at first to be a disparate bag of tricks, but practice makes it into a disciplined set of tools. Indeed, the techniques have an underlying unity and a strong appeal for many people. When another one of the authors (RLG) first taught the course in 1979, the students had such fun that they decided to hold a class reunion a year later.

But what exactly is Concrete Mathematics? It is a blend of continuous and discrete mathematics. More concretely, it is the controlled manipulation of mathematical formulas, using a collection of techniques for solving problems. Once you, the reader, have learned the material in this book, all you will need is a cool head, a large sheet of paper, and fairly decent handwriting in order to evaluate horrendous-looking sums, to solve complex recurrence relations, and to discover subtle patterns in data. You will be so fluent in algebraic techniques that you will often find it easier to obtain exact results than to settle for approximate answers that are valid only in a limiting sense.

The major topics treated in this book include sums, recurrences, elementary number theory, binomial coefficients, generating functions, discrete probability, and asymptotic methods. The emphasis is on manipulative techniques rather than on existence theorems or combinatorial reasoning; the goal is for each reader to become as familiar with discrete operation (like the greatest integer function and finite summation) as a student of calculus is familiar with continuous operations (like the absolute-value function and infinite integration)

Notice that this list of topics is quite different from what is usually taught nowadays in undergraduate course entitled "Discrete Mathematics." Therefore the subject needs a distinctive name, and "Concrete Mathematics" has proved to be as suitable as another

The original textbook for Stanford's course on concrete mathematics was the "Mathematical Preliminaries" section in The Art of Computer Programming [207]. But the presentation in those 110 pages is quite terse, so another author (OP) was inspired to draft a lengthy set of supplementary notes. The present book is an outgrowth of those notes; it is an expansion of, and a more leisurely introduction to, the material if Mathematical Preliminaries. Some of the more advanced parts have been omitted; on the other hand, several topics not found there have been included here so that the story will be complete

The authors have enjoyed putting this book together because the subject began to jell and to take on a life of its own before our eyes; this book almost seemed to write itself. Moreover, the somewhat unconventional approaches we have adopted in several places have seemed to fit together so well, after these years of experience, that we can't help feeling that this book is a kind of manifesto about our favorite way to do mathematics. So we think the book has turned out to be a tale of mathematical beauty and surprise, and we hope that our readers will share at least of the pleasure we had while writing it

Since this book was born in a university setting, we have tried to capture the spirit of a contemporary classroom by adopting an informal style. Some people think that mathematics is a serious business that must always be cold and dry; but we think mathematics is fun, and we aren't ashamed to admit the fact. Why should a strict boundary line be drawn between work and play? Concrete mathematics is full of appealing patterns; the manipulations are not always easy, but the answers can be astonishingly attractive. The joy and sorrows of mathematical work are reflected explicitly in this book because they are part of our lives.

Students always know better than their teachers, so we have asked the first students of this material to contribute their frank opinions, as "graffiti" in the margins. Some of these marginal markings are merely corny, some are profound; some of them warn about ambiguities or obscurities, others are typical comments made by wise guys in the back row; some are positive, some are negative, some are zero. But they all are real indications of feelings that should make the text material easier to assimilate. (the inspiration for such marginal notes comes from a student handbook entitled Approaching Stanford, where the official university line is counterbalanced by the remarks of outgoing students. For example, Stanford says, "There are a few things you cannot miss in this amorphous .. what the h*** does that mean? Typical of the pseudo-intellectualism around her." Stanford: There is no end to the potential of a group of students living together." Graffito: "Stanford dorms are like zoos without a keeper."

The margins also include direct quotations from famous mathematicians of past generations, giving the actual words in which they announced some of their fundamental discoveries. Somehow it seems appropriate to mix the words of Leibniz, Euler, Gauss, and others with those of the people who will be continuing the work. Mathematics is an ongoing endeavor for people everywhere; many strands are being woven into one rich fabric.

This book contains more than 500 exercises, divided into six categories:

1. Warmups are exercises that every reader should try to do when first reading the material.
2. Basics are exercises to develop facts that are best learned by trying one's own derivation rather than by reading somebody else's.
3. Homework exercises are problems intended to deepen an understanding of material in the current chapter.
4. Exam problems typically involve ideas from two or more chapters simultaneously; they are generally intended for use in take-home exams (not for in-class exams under time pressure).
5. Bonus problems go beyond what an average student of concrete mathematics is expected to handle while taking a course based on this book; they extend the text in interesting ways.
6. Research problems may or may not be humanly solvable, but the ones presented here seen to be worth a try (without time pressure).

Answers to all the exercises appear in Appendix A, often with additional information about related results. (Of course the "answers" to research problems are incomplete; but even in these cases, partial results or hints are given that might prove to be helpful.) Readers are encouraged to look at the answers especially the answers to the warmup problems, but only after making a serious attempt to solve the problems without peeking.

We have tried in Appendix C to give proper credit to the sources of each exercise, since a great deal of creativity and/or luck often goes into the design of an instructive problem. Mathematicians have unfortunately developed a tradition of borrowing exercises without an acknowledgment; we believe that the opposite tradition, practiced for example books and magazines about chess (where names, dates, and location of original chess problems are routinely specified) is far superior. However, we have not been able to pin down the sources of many problems that have become part of the folklore. If any reader knows the origin of an exercise for which our citation is missing or inaccurate, we would be glad to learn the details so that we can correct the omission in subsequent editions of this book.

The typeface used for mathematics throughout this book is a new design by Hermann Zapf [227], commissioned by the American Mathematical Society and developed with the help of a committee that included B. Beeton, R.P. Boas. L.K. Durst, D. E. Knuth, P. Murdock, R.S. Palais, P Renz, E. Swanson, S.B. Whidden and W.B. Woolf. The underlying philosophy of Zapf's design is to capture the flavor of mathematics as it might be written by a mathematician with excellent handwriting. A handwritten rather than mechanical style is appropriate because people generally create mathematics with pen, pencil, or chalk. (For example, one of the trademarks of the new design is the symbol for zero, 'O', which is slightly pointed at the top because a handwritten zero rarely closes together smoothly when the curve returns to its starting point.) The letters are upright, not italic, so the subscripts, superscripts, and accents are more easily fitted with ordinary symbols. This new type of family has been named AMS Euler, after the great Swiss mathematician Leonhard Euler (1707-1783) who discovered so much of mathematics as we know it today. The alphabets include Euler Text, Euler Fraktur, and Euler Script Capitals, as well as Euler Greek and special symbols such as <p> and <N>. We are especially pleased to be able to inaugurate the Euler Family of typefaces in this book, because Leonhard Euler's spirit truly lives on every pare: Concrete mathematics is Eulerian mathematics.

The authors are extremely grateful to Andrei Broder, Ernst Mayr, Andrew Yao, and Frances Yao, who contributed greatly to this book during the years that they taught Concrete Mathematics at Stanford. Furthermore we offer 1024 thanks to the teaching assistants who creatively transcribed what took place in class each year and who helped to design the examination questions; their names are listed in Appendix C. This book, which is essentially a compendium of sixteen years' worth of lecture notes, would have been impossible without their first-rate work.

Many other people have helped to make this book a reality. For examples, we wish to commend the students at Brown, Columbia, CUNY, Princeton, Rice, and Stanford who contributed the choice of graffiti and helped to debug our first drafts. Our contacts at Addison-Wesley were especially efficient and helpful; in particular, we wish to thank our publisher (Peter Gordon), production supervisor (Bette Aaronson), designer (Roy Brown), and copy editor (Lyn Dupré). The National Science Foundation and the Office of Naval Research have given invaluable support. Cheryl Graham was tremendously helpful as we prepared the index. An above all, we wish to thank our wives (fan, Jill, and Amy) for their patience, support, encouragement, and ideas.

This second edition features a new Section 5.8, which describes some important ideas that Doron Zeilberger discovered shortly after the first edition went to press. Additional improvements to the first printing can also be found on almost every page.

We have tried to produce a perfect book, but we are imperfect authors. Therefore we solicit help in correcting any mistakes that we've made. A reward of $2.56 will gratefully be paid to the first finder if any error, whether it is mathematical, historical, or typographical.

Murray Hill, New Jersey	RLG
and Stanford California	DEK
May 1988 and October 1993	OP

---

Concrete Mathematics

 

 

Concrete Mathematics: A Foundation for Computer Science
Auteur	Ronald Graham, Donald Knuth, etOren Patashnik
Pays	États-Unis
Genre	Mathématiques Informatique
Éditeur	Addison–Wesley
Nombre de pages	657 pp (seconde édition)
ISBN	0-201-55802-5
modifier

Concrete Mathematics, sous-titré A Foundation for Computer Science (Mathématiques concrètes : Fondations pour l'informatique) est un manuel de cours écrit par Ronald Graham, Donald Knuth et Oren Patashnik (en), fréquemment utilisé dans l'enseignement de l'informatique.

 

Sommaire

 [masquer] 

• 1Historique et contenu
• 2Typographie
• 3Table des matières
• 4Éditions
• 5Notes
• 6Liens externes

 

Historique et contenu[modifier | modifier le code]

Concrete Mathematics a pour objectif d'exposer les connaissances et les compétences mathématiques nécessaires en informatique (théorique), et plus particulièrement celles permettant l'analyse de l'efficacité des algorithmes. La préface précise que les sujets abordés « combinent des mathématiques CONtinues et disCRÈTES. » ; bien que les méthodes employées soit essentiellement celles de la combinatoire (dénombrements, raisonnement par récurrence, etc.) et de la théorie des nombres (arithmétique modulaire), les explications et les exercices utilisent fréquemment des outils provenant de l'analyse, comme les intégrales ou les développements asymptotiques. L'expression « concrete mathematics (mathématiques concrètes) » fait contraste avec abstract mathematics (mathématiques pures) et se rapproche de mathématiques constructives ; de plus, elle contient un jeu de mot intraduisible, concrete signifiant également béton en anglais, ce qui renvoie à l'idée de fondations (d'un bâtiment), et explique la couverture de l'ouvrage, représentant le symbole somme imprimé dans du béton.

Le livre est basé sur un cours donné par Donald Knuth à partir de 1970 à l'université Stanford. Il développe le matériel exposé dans la section Mathematical Preliminaries(Préliminaires mathématiques) du livre de Knuth, The Art of Computer Programming, et peut être utilisé comme une introduction à cette célèbre série d'ouvrages.

Concrete Mathematics est écrit dans un langage informel et souvent humoristique, les auteurs rejetant ce qu'ils voient comme le style aride de la plupart des manuels de mathématiques. Les marges contiennent des « graffitis mathématiques », commentaires proposés par les premiers lecteurs du manuscrit : les étudiants de Knuth et de Patashnik à Stanford.

Comme pour la plupart des livres de Knuth, les lecteurs se voient proposé une récompense (en) pour toute erreur qu'ils découvriraient dans le texte, que cela soit « techniquement, historiquement, typographiquement, ou politiquement incorrect »¹.

Le livre est à l'origine de la popularité de nombreuses notations en combinatoire, par exemple les crochets de Iverson, les notations de la partie entière et de la partie fractionnaire, et celles des factorielles croissantes et décroissantes.

Typographie[modifier | modifier le code]

Donald Knuth utilisa la première édition de Concrete Mathematics comme un test en grandeur réelle de la police d'écriture AMS Euler (en) et de la fonte de caractères Concrete Roman (en)².

Table des matières[modifier | modifier le code]

1. Relations de récurrence
2. Sommations
3. Fonctions entières
4. Théorie des nombres
5. Coefficients binomiaux
6. Suites d'entiers remarquables
7. Séries génératrices
8. Probabilités discrètes
9. Comparaison asymptotique

Éditions[modifier | modifier le code]

• Première édition (septembre 1988) : (en) Ronald Graham, Donald Knuth et Oren Patashnik, Concrete Mathematics, Reading, MA, First, coll. « Advanced Book Program »,‎1989, xiv+625 p. (ISBN 0-201-14236-8)
• Deuxième édition (février 1994) : (en) Ronald Graham, Donald Knuth et Oren Patashnik, Concrete Mathematics, Reading, MA, Second,‎ 1994, xiv+657 p. (ISBN 0-201-55802-5)
• Traduction en français de la deuxième édition (octobre 2003) : (en) Ronald Graham, Donald Knuth et Oren Patashnik (trad. Alain Denise), Mathématiques concrètes : Fondations pour l'informatique, Paris, deuxième,‎ 2003, xiv+688 p. (ISBN 978-2711748242)

Notes[modifier | modifier le code]

1. ↑ (en) Graham, Knuth and Patashnik : Concrete Mathematics [archive]
2. ↑ Donald E. Knuth. Typesetting Concrete Mathematics [archive], TUGboat 10 (1989), 31–36, 342. Réimprimé comme le chapitre 18 du livre Digital Typography.

Liens externes[modifier | modifier le code]

• (en) Cet article est partiellement ou en totalité issu de l’article de Wikipédia en anglais intitulé « Concrete Mathematics » (voir la liste des auteurs).

• (en) Table des matières détaillée
• (en) Préface de Concrete Mathematics, 2ème édition.

[masquer] v · m Donald Knuth
Publications	The Art of Computer Programming · The Complexity of Songs · Computers and Typesetting · Concrete Mathematics · Things a Computer Scientist Rarely Talks About ·Selected papers series
Logiciels	TEX · MIXAL (MIX · MMIX · GNU MDK)
Polices d’écriture	AMS Euler · Computer Modern · Metafont
Programmation lettrée	WEB · CWEB
Algorithmes	Algorithme X de Knuth · Algorithme de Knuth-Bendix · Algorithme de Knuth-Morris-Pratt · Knuth shuffle · Correspondance de Robinson-Schensted-Knuth ·Trabb Pardo–Knuth algorithm
Autres	Dancing Links · Knuth reward check · Prix Donald E. Knuth · Man or boy test · Système quater-imaginaire · Nombre surréel · -yllion ·Potrzebie system of weights and measures

• Portail des mathématiques
• Portail de l’informatique

Catégories :

• Livre de mathématiques
• Livre d'informatique
• Donald Knuth

| [+]

Beaux ordres et graphes Bastien Le Gloannec 21 avril 2009

Voir le pdf : http://perso.ens-lyon.fr/eric.thierry/Graphes2009/bastien...

 

Beaux ordres et graphes Bastien Le Gloannec 21 avril 2009 1 Introduction L’´etude des beaux ordres n’est pas sp´ecifique `a la th´eorie des graphes. Ces ordres apparaissent en effet `a de tr`es nombreuses occasions et l’on peut les voir comme une forme affaiblie des bons ordres. En th´eorie des graphes, l’embl´ematique th´eor`eme des mineurs de Robertson et Seymour a notamment contribu´e `a mettre en avant certaines notions comme les d´ecompositions arborescentes et les beaux ordres. Ces derniers ´etaient toutefois ´etudi´es depuis longtemps, y compris en th´eorie des graphes, ce que nous illustrerons notamment avec le th´eor`eme de Kruskal, qui a lui-mˆeme ´egalement publi´e un survey ayant pour objet la th´eorie des beaux pr´eordres en 1970 ([3]). Nous pr´esenterons dans ce rapport une approche tout d’abord g´en´erale, puis centr´ee sur la th´eorie des graphes, de la notion de bel ordre. Cela nous offrira l’occasion de nous int´eresser finalement au th´eor`eme des mineurs, dont les enjeux et cons´equences ont notamment ´et´e synth´etis´ees dans un survey de Lovasz sur la th´eorie des mineurs ([5]), et de le mettre en relation avec la notion de bel ordre. Enfin, il convient de faire remarquer au lecteur qu’un nombre non n´egligeable de preuves ou exemples de ce rapport sont issus d’exercices (non corrig´es) de [1]. Il n’est par cons´equent pas impossible que des erreurs ou impr´ecisions y figurent malencontreusement. Le lecteur est donc invit´e `a rester vigilant. 2 G´en´eralit´es 2.1 D´efinitions et caract´erisation Commen¸cons par rappeler qu’´etant donn´e un ensemble X quelconque, on appelle pr´eordre sur X toute relation binaire r´eflexive et transitive sur X. Si X est muni d’un pr´eordre, nous parlerons d’anti-chaˆıne pour d´esigner un sous-ensemble de X dans lequel tous les ´el´ements distincts sont deux `a deux incomparables. On appelle beau pr´eordre tout pr´eordre 6 sur X tel que pour toute suite infinie (xn)n∈N d’´el´ements de X, il existe deux indices i < j tels que xi 6 xj . Le couple (xi , xj ) est dans ce cas appel´e bonne paire et toute suite contenant une bonne paire sera appel´ee bonne suite. A l’inverse, une suite qui n’est pas bonne sera ` 1 Beaux ordres et graphes Bastien Le Gloannec dite mauvaise. Ainsi, tout pr´eordre sur X est un beau pr´eordre si et seulement si toute suite infinie de X est bonne. On donne le th´eor`eme de caract´erisation des beaux pr´eordres suivant. Th´eor`eme 1 (Caract´erisation des beaux pr´eordres) Les propositions suivantes sont ´equivalentes : (i) 6 est un beau pr´eordre sur X. (ii) De toute suite infinie d’´el´ements de X, on peut extraire une sous-suite croissante. (iii) X ne contient ni anti-chaˆıne infinie, ni suite infinie strictement d´ecroissante. Bien qu’il soit assez simple de donner une preuve directe de cette caract´erisation, il existe une jolie d´emonstration passant par un th´eor`eme de Ramsey ´enonc´e et d´emontr´e ciapr`es. Mais avant, d´efinissons quelques notations utiles. Etant donn´e un ensemble ´ X, nous noterons Pk(X) l’ensemble des parties finies de X `a exactement k ´el´ements. Pour c > 1, on appelle c-coloration de X toute fonction de X dans {0, . . . , c−1}, qui `a chaque ´el´ement de X associe une couleur parmi c couleurs possibles. Si X est muni d’une c-coloration, on dira qu’un ensemble Y ⊆ X est monocromatique si tous les ´el´ements de Y ont la mˆeme couleur. Th´eor`eme 2 (Ramsey) Soit X un ensemble infini, k > 1, c > 1 et l’on suppose donn´ee une c-coloration de Pk(X). Alors il existe une partie infinie Y ⊆ X telle que Pk(Y ) soit monochromatique. Preuve (Ramsey) On proc`ede par r´ecurrence sur k `a c fix´e. Pour k = 1, quel que soit X infini et une c-coloration de P1(X) (singletons) que l’on assimilera `a une coloration de X, il n’y a qu’un nombre fini de couleurs attribu´ees `a un nombre infini d’´el´ements donc au moins une couleur est affect´ee `a une infinit´e d’´el´ements. Pour k > 1 on suppose que pour tout ensemble Z infini et toute c-coloration de Pk−1(X), il existe une partie infinie Z 0 ⊆ Z telle que Pk−1(Z 0 ) soit monochromatique. Nous allons construire une suite (xn)n∈N d’´el´ements de X ainsi qu’une suite (Xn)n∈N strictement d´ecroissante de parties infinies de X v´erifiant les conditions suivantes (pour tout i) : (i) xi ∈ Xi (ii) Xi+1 ⊆ Xi{xi} (iii) L’ensemble {S∪{xi}, S ∈ Pk−1(Xi{xi})} (i.e. l’ensemble des parties `a k ´el´ements de X contenant xi et dont tous les autres ´el´ements sont pris dans Xi) est monochromatique, et l’on note ci sa couleur. On commence par poser X0 = X et x0 ∈ X quelconque. 2/16 Beaux ordres et graphes Bastien Le Gloannec Supposons construite la suite jusqu’au rang i. On consid`ere l’ensemble Pk−1(Xi{xi}) et l’on d´efinit une c-coloration sur cet ensemble ainsi : pour tout S ∈ Pk−1(Xi{xi}), on pose la couleur de S comme ´etant la couleur de S ∪ {xi} (ensemble `a k ´el´ements car xi ∈/ Xi) dans la c-coloration de Pk(X). Par hypoth`ese de r´ecurrence, il existe Xi+1 ⊆ Xi{xi} ((ii) est v´erifi´ee) tel que Pk−1(Xi+1) soit monochromatique ((iii) est v´erifi´ee) et l’on pose ci la couleur correspondante1 . On choisit alors xi+1 ∈ Xi+1 quelconque ((i) est v´erifi´ee). La suite ´etant maintenant construite, on remarque que la suite des couleurs associ´ees ne prend qu’un nombre fini de valeurs, il en existe donc une extraction ϕ telle que le suite infinie (cϕ(n) )n∈N soit constante, notons C sa valeur. Il ne reste plus qu’`a poser Y = {xϕ(n) , n ∈ N} ⊆ X. Y v´erifie (on a tout fait pour) la propri´et´e attendue : Pk(Y ) est monochromatique. En effet, quel que soit S ∈ Pk(Y ), S est constitu´e d’´el´ements de la suite (xϕ(n) ) et posons xi l’´el´ement de plus petit indice de S. Par construction, S{xi} ∈ Pk−1(Xi+1), et donc, par (iii), S est de couleur ci = C (car xi est issu de le suite extraite (xϕ(n) )) et ce pour tout S, donc Pk(Y ) est monochromatique. D’o`u le r´esultat. On peut maintenant d´emontrer le th´eor`eme de caract´erisation qui nous int´eresse. Preuve (Caract´erisation) Remarquons tout d’abord que les implications (ii) ⇒ (i) et (i) ⇒ (iii) sont ´evidentes. Pour la premi`ere, si pour toute suite il existe une soussuite croissante, alors il existe une infinit´e de bonnes paires et a fortiori la suite est bonne. Pour la seconde, toute suite d’´el´ements distincts d’une anti-chaˆıne infinie, ainsi que toute suite infinie strictement d´ecroissante est une mauvaise suite, ce qui n’existe pas par d´efinition mˆeme d’un beau pr´eordre. Consid´erons maintenant l’implication (iii) ⇒ (i). Soit (xn)n∈N une suite d’´el´ements de X. Consid´erons le graphe infini dont les sommets sont les indices de la suite et les arˆetes les couples (i, j) pour i < j. Pour tous i < j, on colorie l’arˆete (i, j) de la fa¸con suivante : • si xi et xj sont incomparables, on colorie l’arˆete (i, j) en gris. • sinon, si xi 6 xj , i.e. (xi , xj ) est une bonne paire, on colorie l’arˆete (i, j) en vert. • sinon, on a xi > xj et l’on colorie l’arˆete (i, j) en rouge. Par th´eor`eme de Ramsey (pour k = 2 et c = 3 sur les paires d’´el´ements de n, la paire {i, j} avec i < j se voyant attribu´ee la couleur de l’arˆete (i, j) de notre graphe), il existe un sous-graphe infini monochrome. S’il ´etait gris alors on aurait form´e une anti-chaˆıne infinie. S’il ´etait rouge, on aurait trouv´e une sous-suite infinie strictement d´ecroissante. Il ne peut donc qu’ˆetre vert : c’est une sous-suite infinie croissante et donc bonne a fortiori. On notera au passage que par cette mˆeme m´ethode on peut extraire de toute suite de X une sous-suite croissante, i.e. l’implication (i) ⇒ (ii) est d´emontr´ee du mˆeme coup. 3/16 Beaux ordres et graphes Bastien Le Gloannec Dans la suite, nous appellerons bel ordre tout beau pr´eordre qui est en plus un ordre (i.e. anti-sym´etrique). 2.2 Exemples et premi`eres propri´et´es Nous allons exposer ici quelques exemples de beaux pr´eordres et beaux ordres ainsi que quelques propri´et´es simples, naturelles et utiles. Voici tout d’abord quelques remarques imm´ediates sur les beaux pr´eordres. Proposition 1 (Beau pr´eordre induit) Soit 6 est un beau pr´eordre (resp. bel ordre) sur X et Y ⊆ X, le pr´eordre (resp. ordre) induit par 6 sur Y est un beau pr´eordre (resp. bel ordre). Preuve Tout mauvaise suite sur Y muni de l’ordre induit serait aussi une mauvaise suite sur X, or il n’en existe pas par hypoth`ese. Proposition 2 (Ordres et sous-ordres) Soient 61 et 62 sont deux pr´eordres sur X v´erifiant 61⊆62, i.e. ∀x, y ∈ X, x 61 y ⇒ x 62 y. Alors on a 61 beau pr´eordre ⇒ 62 beau pr´eordre mais la r´eciproque est fausse. Preuve Toute bonne suite pour 61 est encore bonne pour 62. Toute suite est donc bonne pour 62 qui est donc un beau pr´eordre. Pour la r´eciproque, comme nous le verrons, la relation de mineur est un bel ordre sur les graphes finis mais pas la relation de mineur topologique. Exemple 1 Les ordres sur N. 1. L’ordre usuel sur N est un bel ordre (car il est total et qu’il n’existe pas de chaˆıne infinie strictement d´ecroissante). 2. L’ordre produit usuel (composante par composante) sur N k est aussi un bel ordre. En effet, de toute suite de N k , on peut extraire une sous-suite croissante ainsi : on extrait une sous-suite croissante (pour l’ordre usuel, bon ordre sur N) suivant la premi`ere composante ; de cette suite on extrait une sous-suite croissante suivant la deuxi`eme composante, et on it`ere ainsi sur toutes les composantes. . . On arrive finalement `a une suite de N k simultan´ement croissante sur toutes les composantes, i.e. croissante pour l’ordre produit. Il est int´eressant de constater qu’`a travers de l’exemple de N k , nous avons donn´e une m´ethode de preuve qui assure imm´ediatement le r´esultat suivant. Proposition 3 (Bel ordre produit) Pour tout n > 1 et tous ensembles X1, . . . , Xn munis respectivement de beaux pr´eordres (resp. beaux ordres) 61, . . . , 6n, le pr´eordre (resp. l’ordre) produit sur X = Qn k=1 Xk, d´efinit par (x1, . . . , xn) 6 (y1, . . . , yn) si et seulement si ∀1 6 k 6 n, xk 6 yk, est un beau pr´eordre (resp. bel ordre) sur X. 4/16 Beaux ordres et graphes Bastien Le Gloannec La preuve est imm´ediate par la m´ethode que nous avons propos´e pour l’exemple 1. Dans la mˆeme veine, ce r´esultat sur le produit cart´esien est ´egalement trivialement valable pour l’union disjointe. Proposition 4 (Bel ordre sur l’union) Pour tout n > 1 et tous ensembles X1, . . . , Xn disjoints munis respectivement de beaux pr´eordres (resp. beaux ordres) 61, . . . , 6n, le pr´eordre (resp. l’ordre) union sur X = Sn k=1 Xk, d´efini par 6= Sn k=1 6k, est un beau pr´eordre (resp. bel ordre) sur X. Exemple 2 Bons ordres et beaux ordres. Une question brˆule certainement les l`evres du lecteur avis´e qui a certainement d´ej`a entendu parler de bons ordres, de relations bien fond´ees et se demande s’il existe un lien avec ces beaux ordres qu’il vient de d´ecouvrir. Une relation bien fond´ee sur un ensemble X est une relation binaire sur X2 telle que tout sous-ensemble non vide de X admette un ´el´ement “minimal” (au sens d’un ´el´ement sans ant´ec´edent par la relation ; en particulier, il n’y a pas n´ecessairement unicit´e de cet ´el´ement). Modulo l’axiome du choix d´ependant, cette d´efinition est ´equivalente `a la non existence de suite infinie d´ecroissante (on dit aussi que la relation est nœuth´erienne en th´eorie de la r´e´ecriture). Ainsi donc un pr´eordre est un beau pr´eordre si et seulement si l’ordre strict associ´e est bien fond´e et qu’il n’existe pas d’anti-chaˆıne infinie. Qu’en est-il des bons ordres ? Un bon ordre sur X est une ordre sur X tel que tout sousensemble non vide de X admette un plus petit ´el´ement (au sens d’un ´el´ement inf´erieur ou ´egal `a tous les autres). En particulier un tel ordre est total. L`a encore, modulo l’axiome du choix d´ependant, cette d´efinition est en fait ´equivalente `a dire que l’ordre est total et la relation d’ordre strict associ´ee est bien fond´ee. Un bon ordre est donc un bel ordre : il n’existe par d’anti-chaˆıne par totalit´e et la relation stricte est bien fond´ee. Ainsi donc tout ensemble bien ordonn´e est ´egalement muni d’un bel ordre. C’´etait par exemple le cas de N pour l’ordre usuel, mais c’est par exemple aussi le cas des N k pour l’ordre lexicographique. Quelques contre-exemples • L’ordre usuel sur Z, Q, R n’est pas un bel ordre (suites infinies strictement d´ecroissantes). • Les ordres produit et lexicographique sur Z k , Qk , R k (suites infinies strictement d´ecroissantes, ou anti-chaˆınes infinies dans le cas de l’ordre produit). • L’inclusion ⊆ sur un ensemble infini : les singletons forment une anti-chaˆıne infinie. 5/16 Beaux ordres et graphes Bastien Le Gloannec 3 Quelques r´esultats 3.1 Lemme de Higman Un r´esultat remarquable est que l’on peut ´etendre tout beau pr´eordre sur X `a l’ensemble X<ω des parties finies de X. On d´efinit en effet la relation 6 sur X<ω ainsi : pour tous A, B ∈ X<ω , A 6 B si et seulement s’il existe une injection f de A dans B telle que pour tout a ∈ A, a 6 f(a). On v´erifie ais´ement que cette relation est un pr´eordre sur X<ω : • R´eflexivit´e : il suffit de prendre f = idA. • Transitivit´e : si A 6 B par une injection f et B 6 C par une injection g, alors ∀a ∈ A, f(a) ∈ B donc g(f(a)) > f(a) > a et g ◦ f compos´ee d’injections reste injective. Dans le cas o`u l’on dispose initialement d’un bel ordre sur X, on obtient ´egalement un bel ordre sur X<ω. En effet, on h´erite de l’anti-sym´etrie : si A 6 B via f et B 6 A via g, alors ∀a ∈ A, g(f(a)) > a. g ◦ f est une bijection de A dans A et cette in´egalit´e exprime le fait que tout ´el´ement de a doive ˆetre envoy´e sur un ´el´ement depuis lequel il est accessible dans le DAG fini (car A fini) de la relation d’ordre (partielle) > sur A. Ainsi, les sources de ce DAG (´el´ements maximaux de A) sont n´ecessairement envoy´ees sur elles-mˆemes. Comme l’application est injective, on ne peut plus r´eutiliser ces sources pour continuer `a construire g ◦ f, on peut donc les retirer du graphe, faisant ainsi apparaˆıtre de nouvelles sources `a leur tour envoy´ees sur elles-mˆemes, et l’on it`ere. . . Finalement, ∀a ∈ A, g(f(a)) = a. Mais a = g(f(a)) > f(a) > a (par B 6 A puis A 6 B) donc f(a) = a et donc A = B. Lemme 1 (Higman – version ensembles) Soit X un ensemble muni d’un beau pr´eordre 6 alors le pr´eordre induit par 6 sur X<ω est un beau pr´eordre. Preuve Par l’absurde, supposons qu’il existe des mauvaises suites sur X<ω. On va construire une suite (Xn)n∈N d’´el´ements de X<ω par r´ecurrence. Supposons construite la suite jusqu’au rang i et supposons qu’elle v´erifie l’hypoth`ese suivante : X0, . . . , Xi est le d´ebut d’au moins une mauvaise suite sur X<ω. On alors choisit Xi+1 ∈ X<ω de cardinal minimal tel que X0, . . . , Xi , Xi+1 soit le d´ebut d’une mauvaise suite. La suite ainsi form´ee est bien sˆur une mauvaise suite (sinon il existe i < j tels que Xi 6 Xj et donc X0, . . . , Xi , . . . , Xj ne saurait ˆetre le d´ebut d’une mauvaise suite). A fortiori, on a donc ∀n ∈ N, Xn 6= ∅ (en remarquant que ∀A ∈ X<ω , ∅ 6 A). Pour tout n, on peut donc choisir xn ∈ Xn quelconque et poser Yn = Xn{an}. Par caract´erisation (iii) dans X muni d’un bel ordre, la suite (xn)n∈N admet une sous-suite (xϕ(n) )n∈N croissante. Par minimalit´e du cardinal dans le choix Aϕ(0), la suite X0, . . . , Xϕ(0)−1 , Yϕ(0), Yϕ(1), Yϕ(2), . . . est bonne et contient donc une bonne paire. Une telle paire ne peut ˆetre ni de la forme (Xi , Xj ) (puisque (Xn)n∈N est mauvaise) ni (Xi , Yj ) puisque Xj > Yj (et on aurait Xi 6 Yj < Xj ). Une bonne paire est donc de la forme (Yi , Yj ) et donc Yi 6 Yj via une 6/16 Beaux ordres et graphes Bastien Le Gloannec injection f de Yi vers Yj . On prolonge alors f en f 0 de Xi vers Xj en posant f 0 (xi) = xj (on a bien xj > xi car xi et xj sont issus de la suite (xϕ(n) )n∈N) on a construit une injection assurant que Xi 6 Xj , ce qui est absurde car la suite (Xn)n∈N est mauvaise. La r´eciproque du lemme de Higman est ´egalement vraie : il suffit de consid´erer les singletons. Il existe ´egalement une version mots du lemme de Higman que nous allons maintenant consid´erer. Si Σ un alphabet muni d’un beau pr´eordre 6, on peut ´etendre ce pr´eordre `a Σ∗ en posant, pour tous mots u = u1 . . . up et v = v1 . . . vq, u 6 v si et seulement si il existe une injection f de {1, . . . , p} dans {1, . . . , q} telle que pour tout 1 6 i 6 p, ui 6 vf(i) . Lemme 2 (Higman – version mots) Si Σ un alphabet muni d’un beau pr´eordre 6, alors le pr´eordre induit par 6 sur Σ ∗ est beau pr´eordre. Ce r´esultat pourrait se d´emontrer par une preuve totalement analogue `a la pr´ec´edente. Nous allons plutˆot proc´eder en r´eutilisant le r´esultat pr´ec´edent. Nous allons mˆeme montrer un peu plus : l’´equivalence des deux versions du lemme de Higman. Preuve (´equivalence des versions ensembles/mots) Il suffit de remarquer que pour toute permutation σ de {1, . . . , p} et toute permutation σ 0 de {1, . . . , q}, si l’on pose u 0 = uσ(1) . . . uσ(p) et v 0 = vσ0(1) . . . vσ0(q) alors si l’on a u 6 v via une injection f, on a ´egalement u 0 6 v 0 via l’injection σ 0−1 ◦ f ◦ σ. En d’autres termes, l’ordre des lettres n’a aucune importance, on peut les voir comme des ensembles finis de lettres, i.e. des ´el´ements de Σ∗<ω. L’´equivalence des ´enonc´es est alors imm´ediate. Il est `a noter que l’ordre des lettres n’´etant pas important, pour tout mot u et toute permutation u 0 de u, u 0 6= u, on aura tout de mˆeme u 6 u 0 et u 0 6 u sans avoir u = u 0 : l’anti-sym´etrie n’est pas v´erifi´ee, on ne peut avoir qu’un pr´eordre ici et pas d’ordre. Enfin, il existe en combinatoire sur les mots une autre version usuelle du lemme de Higman. On utilise pour cette derni`ere l’ordre suivant : u 6 v si et seulement si u est un sous-mot de v (au sens d’une suite extraite, aux lettres non n´ecessairement cons´ecutives dans v). On v´erifie ais´ement que cette relation sur les mots est cette fois un ordre et pas seulement un pr´eordre. Lemme 3 (Higman – version sous-mots) La relation de sous-mot 6 est un bel ordre sur Σ ∗ . Cela revient `a prendre l’´egalit´e comme relation et `a imposer de plus `a l’injection d’ˆetre croissante dans la version mots du lemme de Higman. On peut en fait montrer que le lemme de Higman est encore vrai si l’on impose `a l’injection d’ˆetre croissante. Il implique alors directement la version sous-mots (que l’on pourrait aussi d´emontrer directement en adaptant la preuve du th´eor`eme de Higman en une preuve plus simple par certains aspects, puisque l’on ne dispose plus d’un beau pr´eordre sur Σ, mais en assurant la croissance de l’injection). 7/16 Beaux ordres et graphes Bastien Le Gloannec 3.2 Th´eor`eme de Kruskal Dans cette section, nous allons ´etudier le th´eor`eme de Kruskal sur la classe des arbres finis. Avant toute chose, une remarque pr´eliminaire et importante pour toute la suite s’impose : les relations de mineur (not´ee 4) et mineur topologique sont des relations d’ordre (partielles) sur la classe des graphes finis. Ce fait est tr`es simple `a v´erifier. Th´eor`eme 3 (Kruskal, [2]) La relation de mineur topologique est un bel ordre sur les arbres finis. Il est `a noter que ce r´esultat ne restera cependant pas vrai sur la classe des graphes finis quelconques toute enti`ere comme nous allons le voir dans la section suivante. Afin de d´emontrer ce th´eor`eme, nous allons renforcer la notion de mineur topologique en d´efinissant la notion de mineur topologique enracin´e sur la classe des arbres. Rappelons si n´ecessaire les d´efinitions de la notions de mineur topologique. On dit qu’un graphe H est une subdivision d’un graphe G si H peut ˆetre obtenu `a partir de G en “subdivisant” des arˆetes, i.e. en rempla¸cant une arˆete de G par une chaˆıne de longueur arbitraire. On dit alors qu’un graphe G est un mineur topologique d’un graphe H s’il existe un sous-graphe H0 de H tel que H0 soit une subdivision de G. En d’autres termes, G est obtenu `a partir de H en supprimant des arˆetes, des sommets, et en contractant des chaˆınes. Etant donn´es ´ deux arbres enracin´es T et T 0 , de racines respectives r et r 0 (rappelons que l’enracinement induit un ordre naturel sur l’arbre), on dira que T 6 T 0 si et seulement s’il existe une isomorphisme ϕ d’une subdivision T0 de T (pour la mˆeme racine, ce qui induit un ordre sur T0) vers un sous-arbre T1 de T 0 qui pr´eserve l’ordre, i.e. telle que si x < y dans T alors ϕ(x) < ϕ(y) dans T1 ⊆ T 0 . Il est ais´e de v´erifier que l’on d´efinit bien un pr´eordre sur les arbres enracin´es ainsi. Essentiellement, la relation d´efinie est en tout points similaire `a la notion de mineur topologique, si ce n’est qu’elle pr´eserve l’orientation pour des arbres enracin´es. La Fig. 1 illustre cette notion. La m´ethode de preuve qui suit est totalement similaire `a celle mise en œuvre pour d´emontrer le lemme de Higman. D’ailleurs, nous n’h´esiterons pas `a renvoyer par endroit le lecteur `a cette derni`ere dans la preuve qui suit. Preuve (Kruskal, m´ethode de Nash-Williams, [6]) Nous allons d´emontrer que la relation de mineur topologique enracin´e est un beau pr´eordre sur les arbres finis enracin´es, ce qui implique naturellement ce que l’on veut d´emontrer du fait de l’´equivalence suivante : T 0 est un mineur topologique de T si et seulement si il existe un enracinement de T et un enracinement de T 0 tels que T 0 soit un mineur topologique enracin´e de T pour ces enracinements. Par l’absurde (i.e. on suppose l’existence de mauvaises suites), on proc`ede comme dans la preuve du lemme de Higman (s’y reporter si n´ecessaire) en construisant une suite (Tn)n∈N d’arbres enracin´es (de racines respectives les ´el´ements de la suite (rn)n∈N) en choisissant `a chaque ´etape i un plus petit arbre (en nombre de sommets) Ti de racine ri 8/16 Beaux ordres et graphes Bastien Le Gloannec Fig. 1 – Mineur topologique enracin´e, [1] tel que T0, . . . , Ti soit le d´ebut d’une mauvaise suite. L`a encore, (Tn)n∈N est une mauvaise suite. Pour tout i ∈ N, on pose Si l’ensemble des composantes connexes du graphe Ti dont on a retir´e la racine ri , chacune de ces composantes ´etant enracin´ee en le voisin de ri dans la composante, de sorte que l’ordre induit par l’enracinement reste exactement le mˆeme que dans Ti . On pose S = S n∈N Sn. Montrons alors que l’on a un beau pr´eordre sur S. Soit (tn)n∈N une suite quelconque de S en prenant, pour tout n, tn ∈ Sin . Soit m tel que im soit minimal parmi les in. D`es lors, la suite T0, . . . , Tim−1, tm, tm+1, tm+2, . . . est bonne (car tm ∈ Sim est une composante connexe issue de la suppression de rim dans Tim et a au moins un sommet de moins que Tim) et contient donc une bonne paire qui ne peut ˆetre que de la forme (ti , tj ) avec i < j. En effet, comme (Tn) est mauvaise, cela ne peut ˆetre (Ti , Tj ) et si c’´etait (Ti , tj ), alors Ti 6 tj < Tij avec i 6 im − 1 et par choix de m on a ij > im donc i < ij ce qui contredirait le fait que (Tn) soit mauvaise. On a donc trouv´e en (ti , tj ) une bonne paire dans la suite (tn) (a priori quelconque) de S qui est donc bien muni d’un beau pr´eordre. Puisque chaque Sn est une partie finie de S muni d’un beau pr´eordre, alors par lemme de Higman la suite (Sn) est bonne et admet donc une bonne paire (Si , Sj ), i < j, et donc Si 6 Sj via une injection f de Si dans Sj v´erifiant, pour tout t ∈ Si , t 6 f(t) via un certain isomorphisme ϕt . On pose ϕ le morphisme r´ealisant l’union de sous ces ϕt et on le prolonge `a Ti en posant ϕ(ri) = rj . L’ordre est ainsi pr´eserv´e (car on avait d´ej`a remarqu´e que l’ordre restait inchang´e dans les composantes connexes lorsque l’on effectuait la suppression de ri) et ϕ d´efinit naturellement un isomorphisme assurant Ti 6 Tj : on a trouv´e une bonne paire dans la mauvaise s´equence (Tn), d’o`u la 9/16 Beaux ordres et graphes Bastien Le Gloannec contradiction. 3.3 Contre-exemples On consid`ere dans cette section deux contre-exemples instructifs. Le premier montre que le th´eor`eme de Kruskal ne tient plus si l’on restreint la relation `a celle de sous-graphe connexe, et le second que le th´eor`eme des mineurs ne reste pas non plus vrai si l’on se limite `a la relation de mineur topologique. Contre-exemple 1 La relation de sous-graphe connexe n’est pas un bel ordre pour la classe des arbres finis. Notons que les propri´et´es de r´eflexivit´e, de transitivit´e et d’anti-sym´etrie sont trivialement v´erifi´ees pour cette relation. Remarquons ´egalement qu’un graphe n’a qu’un nombre fini de sous-graphes connexes (et ils sont tous de taille inf´erieure ou ´egale), par cons´equent il est inutile d’esp´erer obtenir une suite strictement d´ecroissante ici. Nous allons maintenant exhiber une anti-chaˆıne infinie de d’arbres. La Fig. 2 pr´esente une telle famille d’arbres deux `a deux incomparables pour la relation de sous graphe connexe. (a) T1 (b) T2 (c) T3 n arˆetes (d) Tn Fig. 2 – Anti-chaˆıne infinie pour la relation de sous-graphe connexe sur les arbres finis Contre exemple 2 La relation de mineur topologique n’est pas un bel ordre sur la classe des graphes finis. Rappelons que ce qui ´etait vrai sur la classe des arbres finis ne l’est donc plus lorsque l’on passe aux graphes quelconques. Mais cela sera par contre vrai sur la classe des graphes fini en ´elargissant la relation aux mineurs. L`a encore, comme dans l’exemple pr´ec´edent, il est inutile d’esp´erer obtenir une suite infinie strictement d´ecroissante, un graphe n’ayant qu’un nombre fini de mineurs topologiques. On cherche donc une anti-chaˆıne infinie, ce qui 10/16 Beaux ordres et graphes Bastien Le Gloannec est moins ´evident `a obtenir que dans le cas pr´ec´edent. L’id´ee est que pour montrer qu’un graphe H est un mineur topologique d’un graphe G, on peut exhiber un isomorphisme de graphe d’une subdivision de H vers une sous-graphe de G. Il n’est pas difficile de remarquer que ce morphisme envoie n´ecessairement tout sommet de H vers un sommet de degr´e sup´erieur ou ´egal dans G. Organiser judicieusement les degr´es est un moyen de forcer tel sommet `a ˆetre envoy´e sur tel autre sommet, en agen¸cant les sommets entre-eux de fa¸con `a ce qu’il ne soit pas possible qu’un graphe soit le mineur d’un autre (ici il y a 2 sommets de degr´es 6 par graphe qui sont forc´ement envoy´es les uns sur les autres, la chaine les s´eparant n’´etant pas bien contractable) on construit une anti-chaˆıne infinie d´ecrite sur la Fig. 3, et bas´ee sur une adaptation naturelle de l’exemple pr´ec´edent. (a) T1 (b) T2 (c) T3 n blocs (d) Tn Fig. 3 – Anti-chaˆıne infinie pour la relation de mineur topologique sur les graphes quelconques 4 Autour du th´eor`eme des mineurs Dans cette section, nous allons nous int´eresser au fameux th´eor`eme des mineurs et voir en quoi il est fondamentalement li´e `a la notion de bel ordre. Mais avant, pr´ecisons que nous dirons dans tout ce qui suit qu’une classe de graphes C est ferm´ee par mineurs si et seulement si tout mineur d’un graphe de C est encore dans C, i.e. la classe est stable par passage `a un mineur. 4.1 Approche et ´enonc´e Un r´esultat bien connu en th´eorie des graphes est que l’on peut caract´eriser la classe des graphes planaires comme l’ensemble des graphes n’admettant ni K5 ni K3,3 comme mineur. Ce r´esultat de 1930 est connu sous le nom de th´eor`eme de Kuratowski. 11/16 Beaux ordres et graphes Bastien Le Gloannec Th´eor`eme 4 (Kuratowski, [4]) Un graphe est planaire si et seulement s’il n’admet ni K5 ni K3,3 comme mineur. Ce r´esultat a particuli`erement marqu´e les th´eoriciens des graphes qui en ont longtemps cherch´e des g´en´eralisations. Il est en effet tr`es commode de disposer d’une telle caract´erisation par une famille finie de mineurs interdits : d’une part on peut montrer la non appartenance `a la classe d’un graphe en donnant pour certificat une s´equence de transformations conduisant au mineur interdit et d’autre part l’on peut tester l’appartenance `a la classe en temps polynomial. Malheureusement, encore auourd’hui bien peu de r´esultats explicites de ce genre sont connus et le th´eor`eme de Kuratowski reste de loin le plus embl´ematique. Toutefois, Wagner aurait conjectur´e d`es 1970 que toute classe de graphes ferm´ee par mineurs (i.e. telle que tout mineur d’un graphe de la classe est encore dedans) pouvait ˆetre caract´eris´ee par une famille finie de mineurs interdits, `a la mani`ere du th´eor`eme de Kuratowski. Ce r´esultat a ´et´e finalement ´et´e d´emontr´e par Robertson et Seymour `a travers une s´erie de vingts articles publi´es entre 1983 ([8]) et 2004 ([10]). Th´eor`eme 5 (Robertson & Seymour, [10]) Toute classe de graphes ferm´ee par mineurs peut ˆetre caract´eris´ee par une famille finie de mineurs interdits. Pour bien comprendre les enjeux de ce th´eor`eme, il est a noter que c’est bel et bien l’aspect fini de la famille de mineurs qui en est l’´el´ement important. Ce mˆeme r´esultat pour une famille infinie est une propri´et´e basique et bien connue ´enonc´e ci-dessous. Introduisons tout d’abord une notation utile. Pour K un ensemble de graphes, on d´efinit la classe Forb4(K) comme l’ensemble des graphes n’admettant aucun des ´el´ements de K comme mineur, i.e. la classe de graphes caract´eris´ee par un ensemble de mineurs interdits K. On rappelle que l’on note 4 la relation de mineur (et ≺ la relation stricte associ´ee). Inversement, pour tout classe C, on appelle ensemble de Kuratowski de C l’ensemble KC = {G graphe/G /∈ C et ∀H ≺ G, H ∈ C} i.e. l’ensemble des ´el´ements minimaux pour 4 dans le compl´ementaire C de C. Par construction mˆeme, les ´el´ements de KC forment une anti-chaˆıne pour 4. Proposition 5 Une classe de graphes est ferm´ee par mineurs si et seulement si on peut la caract´eriser par une famille (´eventuellement infinie) de mineurs interdits, auquel cas KC est une famille qui convient et c’est la famille minimale pour l’inclusion unique `a convenir. Preuve Si C est une classe de graphes ferm´ee par mineurs, il suffit de remarquer que C = Forb4(C) (pour C le compl´ementaire de la classe). Par ailleurs, KC est incluse dans toute autre famille K `a convenir car si un ´el´ement G de KC n’y ´etais pas, alors il serait interdit (car il doit l’ˆetre) en faisant intervenir un ´el´ement de K qui serait un mineur strict de G. Or par d´efinition mˆeme de KC, tout mineur strict de ses ´el´ements est dans C. D’o`u 12/16 Beaux ordres et graphes Bastien Le Gloannec la contradiction et donc KC ⊆ K. Par ailleurs KC convient ´egalement car s’il existait un ´el´ement G de C non interdit par KC, alors aucun de ses mineurs ne serait dans KC. Imaginons l’arbre des mineurs de G sur lequel G est la racine, suivent tous les mineurs stricts directs (issus d’une op´eration), puis les mineurs stricts directs des mineurs,etc (on autorise les r´ep´etitions de sommets correspondant `a un mˆeme graphe). Toutes les feuilles de l’arbre correspondent au graphe `a un sommet qui appartient ´evidemment `a tout classe de graphes ferm´ee par mineurs (suppos´ee implicitement non vide). Mais alors il existe dans le graphe des sommets appartenant `a C (ainsi qu’au moins la racine appartenant `a C). Par stabilit´e par mineurs de C, ces sommets ont tous leurs descendants dans C. Consid´erons un sommet S de profondeur maximale dans l’arbre parmi ceux correspondant `a un graphe de C. Tous ses descendants sont donc dans C. Ce sommet est donc dans KC et est un mineur de G. D’o`u la contradiction. R´eciproquement, tout Forb4(K) est trivialement ferm´e par mineurs. 4.2 Mineurs et beaux ordres Le th´eor`eme des mineurs a une autre formulation mettant plus en valeur ce qui nous pr´eoccupe, `a savoir les beaux ordres. Th´eor`eme 6 (des mineurs – deuxi`eme version) La relation de mineur est un bel ordre sur la classe des graphes finis. Il est int´eressant de montrer l’´equivalence des deux ´enonc´es de ce th´eor`eme. Preuve (´equivalence des ´enonc´es) Comme nous l’avons d´ej`a vu, si une classe C est ferm´ee par mineurs, alors C = Forb4(KC) o`u KC est une anti-chaˆıne pour 4. Mais alors, si KC n’est pas fini, alors on a trouv´e une anti-chaˆıne infinie et donc 4 ne saurait ˆetre un bel ordre sur la classe des graphes finis. On a montr´e par contrapos´ee que la deuxi`eme version implique la premi`ere (qui est clairement ´equivalente `a la finitude de KC en utilisant la proposition 5). R´eciproquement, supposons un instant par l’absurde qu’il existe une anti-chaˆıne infinie K. La classe C = Forb4(K) est close par mineurs et admet donc un ensemble de Kuratowski KC fini tel que C = Forb4(KC). Mais alors, KC est un ensemble de mineurs qui interdit l’ensemble des ´el´ements K. Et surtout, par proposition 5, KC ⊆ K. Il y a donc dans K infini une infinit´e d’´el´ements `a ne pas ˆetre dans KC et `a pourtant admettre pour mineur un ´el´ement de KC et donc de K, qui ne saurait donc ˆetre une anti-chaˆıne. D’o`u le r´esultat. 4.3 Aspects algorithmiques Le th´eor`eme suivant constitue une cons´equence algorithmique non n´egligeable du th´eor`eme des mineurs. 13/16 Beaux ordres et graphes Bastien Le Gloannec Th´eor`eme 7 L’appartenance d’un graphe `a une classe de ferm´ees par mineurs peut toujours ˆetre test´ee en temps polynomial. Ce r´esultat tr`es fort et g´en´eral repose sur une m´ethode algorithmique en O(n 3 ) (Seymour & Robertson, [9]). Toutefois la constante est ´enorme et d´epend fortement de la liste des mineurs exclus. Nous n’entrerons cependant pas dans les d´etails algorithmiques ici. 4.4 Une conjecture plus forte Dans les ann´ees 1980, Seymour a conjectur´e l’´enonc´e suivant. Conjecture 1 (Seymour) Tout graphe infini d´enombrable est un mineur strict de luimˆeme. Pr´ecisons le sens `a donner `a la notion de mineur strict ici : G infini est un mineur strict de lui mˆeme s’il existe une s´equence de transformations, parmi les suppressions de sommets, d’arˆetes et les contractions d’arˆetes, non vide et finie telle que le graphe obtenu soit isomorphe `a G. Cela peut sembler ´etonnant de prime abord, puisque l’on s’int´eresse ici `a des graphes infinis d´enombrables (un contre-exemple ind´enombrable a ´et´e d´ecouvert en 1990 par Oporowski, [7]), mais ce r´esultat impliquerait le th´eor`eme des mineurs. Preuve (le th´eor`eme des mineurs est un corollaire de la conjecture) Pour la classe des graphes connexes Par l’absurde, supposons la conjecture v´erifi´ee mais pas le th´eor`eme des mineurs. Comme nous l’avons d´ej`a vu, il n’y a jamais de suite infinie strictement d´ecroissante pour la relation 4. Par cons´equent, c’est qu’il existe une anti-chaˆıne infinie de graphes finis {G0, G1, . . .} (d´enombrable car l’ensemble des graphes finis est lui-mˆeme d´enombrable). Posons alors G = S i∈N Gi (sans cr´eer d’arˆetes entre-eux). G est un mineur strict de lui-mˆeme donc il existe une s´equence non vide de transformations qui produisent finalement un graphe G0 isomorphe `a G. Comme il y a au moins une transformation, au moins un graphe Gi est modifi´e. Mais Gi ne peut avoir ´et´e supprim´e compl`etement. En effet, s’il l’avait ´et´e, alors comme il est pr´esent dans G’, et qu’il est connexe, c’est qu’il a ´et´e obtenu `a partir d’un autre graphe (et d’un seul car on est dans le cas connexe) de l’anti-chaˆıne, graphe dont il serait donc mineur, ce qui est impossible par hypoth`ese. Mais alors il a ´et´e r´eduit sans totalement disparaˆıtre. Chaque composante connexe d’apr`es r´eduction (et il y en a au moins une) ´etant isomorphe `a un graphe de l’anti-chaˆıne, graphe qui est donc un mineur de G, ce qui est absurde. D’o`u le r´esultat dans le cas connexe. 14/16 Beaux ordres et graphes Bastien Le Gloannec Et dans le cas g´en´eral On peut voir un graphe fini quelconque comme l’ensemble de ses composantes connexes, i.e. comme une partie finie de la classe des graphes connexes. Il n’est pas difficile alors de remarquer que l’on a H 4 G avec H et G non n´ecessairement connexes si et seulement si G a au moins autant de composantes connexes que H et il existe une injection de H vers G envoyant chaque composante connexe c 0 de H vers une composante c de G telle que c 0 4 c, autrement dit c 0 4 f(c 0 ) (on r´eduit alors G en H en supprimant toutes les composantes qui n’appartiennent pas `a l’image de f, et en r´eduisant chaque f(c 0 ) en la composante c 0 de H). La relation de mineur sur les graphes finis est donc exactement la relation induite par la relation de mineur pour la classe graphes connexes (qui est un bel ordre) sur l’ensemble de ses parties finies. Par lemme de Higman, on en d´eduit que la relation 4 est un bel ordre sur la classe des graphes quelconques. 5 Conclusion L’´etude des beaux ordres a permis d’´etablir un certain nombre de th´eor`emes int´eressants, notamment, pour ce qui est de l’informatique fondamentale, en combinatoire sur les mots et en th´eorie des graphes comme nous avons pu l’illustrer tout au long de ce rapport. Le th´eor`eme des mineurs de Robertson et Seymour, qui est probablement le plus gros r´esultat de la th´eorie des graphes en l’´etat actuel de l’art, se ram`ene ainsi `a d´emontrer que la relation de mineur est un bel ordre sur la classe des graphes finis. Sur des structures combinatoires peu contraintes comme les graphes ou les mots, les beaux ordres peuvent ˆetre vus comme une alternative faible `a des notions plus fortes telles que les bons ordres, omnipr´esents en th´eorie des ensembles. C’est finalement un moyen fructueux de ramener des probl`emes combinatoires `a des objets math´ematiques bien connus et ´etudi´es. R´ef´erences [1] R. Diestel. Graph theory. Springer, 2005. [2] JB Kruskal. Well-quasi-ordering, the tree theorem, and Vazsonyi’s conjecture. Transactions of the American Mathematical Society, pages 210–225, 1960. [3] J.B. Kruskal. The theory of well-quasi-ordering : A frequently discovered concept. J. Combinatorial Theory Ser. A, 13(3) :297–305, 1972. [4] K. Kuratowski. Sur le probleme des courbes gauches en topologie. Fund. Math, 15(27) :1–283, 1930. [5] L. Lov´asz. Graph minor theory. Bulletin-American Mathematical Society, 43(1) :75, 2006. [6] C. Nash-Williams. On well-quasi-ordering finite trees. In Mathematical Proceedings of the Cambridge Philosophical Society, volume 59, 1963. 15/16 Beaux ordres et graphes Bastien Le Gloannec [7] B. Oporowski. A counterexample to Seymour’s self-minor conjecture. Journal of Graph Theory, 14(5), 1990. [8] Neil Robertson and Paul D. Seymour. Graph minors. i. excluding a forest. J. Comb. Theory, Ser. B, 35(1) :39–61, 1983. [9] Neil Robertson and Paul D. Seymour. Graph minors .xiii. the disjoint paths problem. J. Comb. Theory, Ser. B, 63(1) :65–110, 1995. [10] Neil Robertson and Paul D. Seymour. Graph minors. xx. wagner’s conjecture. J. Comb. Theory, Ser. B, 92(2) :325–357, 2004. 16/16

Graham Higman

 

 

Cet article est une ébauche concernant un mathématicien. Vous pouvez partager vos connaissances en l’améliorant (comment ?) selon les recommandations des projets correspondants.

Graham Higman

G. Higman en 1960

Naissance	19 janvier 1917 + Louth (en) +
Décès	8 avril 2008 + Oxford +
Nationalité	britannique +
Formation	Balliol College +
Activité	mathématicien +
A travaillé pour	Magdalen College +
Domaine	théorie des groupes +
Membre de	Royal Society +
Distinction	membre de la Royal Society (d) +

modifier - modifier le code - modifier Wikidata

Graham Higman (né le 19 janvier 1917, mort le 8 avril 2008) est un mathématicien britannique connu pour ses contributions à la théorie des groupes. Il est connu notamment pour le lemme de Higman qui donne une propriété sur la notion de sous-mot, analogue au théorème de Kruskal.

Il a fondé le Journal of Algebra (en) dont il a été le rédacteur de 1964 à 1984.

 

Sommaire

 [masquer] 

• 1Distinctions
• 2Annexes
  • 2.1Articles connexes
  • 2.2Lien externe

 

Distinctions[modifier | modifier le code]

• 1962 : Prix Senior Berwick
• 1977 : Médaille De Morgan
• 1979 : Médaille Sylvester

Annexes[modifier | modifier le code]

Articles connexes[modifier | modifier le code]

• Extension HNN
• Groupe de Higman-Sims, nommé en l'honneur de Donald G. Higman (en) et Charles Sims (en) mais également étudié par Graham Higman
• Lemme de Higman

Lien externe[modifier | modifier le code]

• Notices d’autorité : Fichier d’autorité international virtuel • International Standard Name Identifier •Système universitaire de documentation • Bibliothèque du Congrès • Gemeinsame Normdatei • WorldCat

Source : wikipedia