Strangest CA-related mathematical coincidences?

[confocaloid]

What are the strangest known CA-related mathematical coincidences?
E.g. two or more apparently unrelated reactions with the same effect, without any obvious explanation for why that would be the case.

LoM-based 8c/96d reaction
(posted in "Spaceship Discussion Thread")

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#C https://conwaylife.com/forums/viewtopic.php?p=160357#p160357
#C https://conwaylife.com/forums/viewtopic.php?p=160345#p160345
#C https://conwaylife.com/forums/viewtopic.php?p=143269#p143269
x = 171, y = 171, rule = B3/S23
28bo$20bo7bo$20b3o5bo$22bobo3b2o$20bo2bo$20b2o2bo$8b2o$8b2o7$2o$2o$14b
2o3b2o$13bobo3b4o3bo$13bo3bo2bo2b2obo$13b2o3bo4b2obo$18bo3bo$17bo3$27b
o6b3o$27bob2o3b2o$27bobo5b2o$27bob3o$27b2o14$28bo$29b2ob2o12bo$29b2obo
12bobo$31bo12bo3bo$44bo3bo$42b3obobo$41bo2bob2o$41bobo$42b2o8$24b2o$
20bo$22bo$20bobo$65b2o6bo$64bo3bo3bobo$35b3o26b2o3bobo3bo$34bo4bo8bo
15b2obobo2bobo$38b2o8b4o13b2o2bo3bo$34bo3bo25bo4bo$34bo30bo2bo$34bobo
29bo$34bo11bobo$32bo3b2o9bo$36b2o10b2o$35bobo8bo2bo$30bo5bo9b2ob2o2$
30b2ob2o$32b3o24bo$57bo2bo7b3o$56bo3bo5b2obobo$56bo3bo5b2obobo$56bo3b
2o5bo3bo$57bo2bo7bobo$69bo4$65bo$64bobo$64bobo$65bo5$57bo48bo$56bobo
46bobo$56bobo45bo3bo$57bo47bobo$89b3o14bo$88bo3bo$87bo2b3o10b4o$88bo3b
o9bo4bo$49bo39b3o13bo$48bobo30b2o7b2o9bo2bo3bo$48bobo29bo2bo18bob3obo$
49bo31b2o20bob3o3$89bo$88b5o$93bo$73b2o$40bo31bo2bo12bo3bo$40bo32b2o
14b3o2$38b3o$40bo$21bo3b2o10bob2o$21b2o13b2o66bo$37b2o26b2o29bo7bo$37b
ob2o23bo2bo28b3o5bo$24bo12b5o23b2o31bobo3b2o17b3o$23bobo10bobo2b2o53bo
2bo22bo3bo$23bo12b2o3b3o52b2o2bo21b2o3bo$24bo2bo13b2o83bo$13b2o9bo3bo
11b2o80b4o$13b2o9b2obo12bo5bo73b2obo$24bo20b3o72bo2bo$24b3o17b5o72b2o$
14b2o27b2o3b2o2b3ob2o$14b2o32b2o2bobo49b2o$47b2obo3bo48b2o$46bob5o44b
3o6bo$46b2o3bo44bob2obo4bo37bobo$97bo8bo37b3o$93b2o5b4obo39b2o$93b2o
32bo$93bo5bo26b2o$94bo30bo17bo$94bobo29b2o15bobo$126b2o15b3o21bo$44bo
83bo13bo24b4o$43bobo96b5o$41bo10bo98b3o$41bobo3bo4bo59bo$41b5o2bo63bo
38b2o12bobo$46b2o103b2o13bo$51bo57b2o39bo2bo13b2o$51b2o100bo11bo2bo$
109bobo40b3o10b2ob2o$153b2o$150b2o$149bo2bo2$39b2o112b2o$39b2o2b2o106b
o2bo$43b2o106b3o4$163b2o$163b2o7$155b2o$155b2o!

F117 + L156_1 and F176 + L112
(posted in "Herschel conduits and other stable circuits")
F117 + L156_1 and F176 + L112 perform the same relocation of a Herschel, only with 15-tick time difference:

Code: Select all

x = 77, y = 69, rule = TripleLife
62.2F$61.F2.F$62.2F8$67.2F$67.F$65.3F6$73.2F$73.F.F$75.F$75.2F7$65.2F
$56.2F7.2F$57.F$57.F.F$52.2B4.2F$53.B20.2B$31.2B20.B.B18.B$32.B6.2B
13.2B16.B.B$32.B.B4.2B31.2B$33.2B$29.B27.D$29.3B25.3D$21.2B9.B15.D11.
D$21.2B4.2D2.2B15.3D8.2D14.D$27.D.D21.D22.D.D$17.D11.D20.2D23.D$17.3D
9.2D12.2B$20.D22.2B$7.2F10.2D$8.F57.2B4.2D$8.F.F55.2B2.2BD.D$9.2F41.B
3.2B12.B.B.D$32.2D17.B.B3.B14.B.2D$32.2D16.B.B3.B13.2D2B$51.B3.B14.D$
46.2B4.4B.B5.2D6.3D$46.B.B7.B.B4.D9.D$48.B3.2B2.B.B5.3D$9.F38.2B2.2B
3.B8.D$9.F.F$9.3F30.2D$11.F11.2D18.D$23.D16.3D$21.2B.3D12.BF$21.2B2.B
F13.B$25.B.B12.B.2B$2.2F23.B7.B2.B.B2.B$3.F23.2B6.4B.2B$3F36.B$F36.B.
B$37.2B!

SE38T127
(posted in "Thread For Your Useless Discoveries")
There are two different Herschel-to-glider converters with systematic description "SE38T127", i.e. two different ways to produce an output glider on the same lane with the same timing:

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x = 44, y = 52, rule = TripleLife
15.2B$16.B$16.B.B$17.2B6$33.2B$33.B$31.B.B$10.D20.2B8.D$9.D.D27.3D$9.
2D27.D$29.2B4.2B.2D$9.2D18.2B5.B$9.D.D21.3B$10.D22.B$35.2D$35.2D3$12.
2D$11.D.D26.2D$11.D28.D$10.2D29.3D$43.D2$7.2F$8.F$8.F.F$9.2F17.2F.2F$
28.2F.F.F$33.F$33.2F4$9.F$9.F.F18.2F$9.3F18.2F$11.F5$2.2F$3.F19.2F$3F
20.F$F23.3F$26.F!
#C [[ T 75 PAUSE 1 T 162 PAUSE 1 STOP 257 ]]

2c/11d in B2n3-e/S234c

(edit: it turns out there are two different natural 2c/11d spaceships. Are these mechanisms related in any way, or this is a coincidence?)

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#C [[ ZOOM 8 TRACK 2/11 2/11 ]]
x = 25, y = 5, rule = B2n3-e/S234c
2o2bobo14bobo$2o2bo15bo2b2o$3bo$2b3o15b2o2bo$3bo17bob2o!

[H. H. P. M. P. Cole]

There is absolutely no reason I have come across that explains why there are 40 4-cell objects in Factorio. This is probably not a coincidence. Here's why I posted it in this thread:

- The rulestring is relatively short.
- All the objects are, remarkably, mod 1.

The mystery of the treasure trove of 4-cell pbjects is still intriguing to me despite investigating Factorio for quite a long time.

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x = 149, y = 80, rule = R3,C2,S2,B3,N+
2o13bobo13bo2bo$2o13bobo13bo2bo9$15bobo13bo2bo2$15bobo13bo2bo9$31bo2b
o3$31bo2bo17$2b2o11b2o14b2o12bobo15bobo15b2o15b2o10bobo9b2o12b2o8bobo
$bo2bo9bo3bo10bo4bo9bo3bo13bobo14b2o16bobo9bo2bo7bo2bo11b2o8b2o9$2b2o
11b2o14b2o12bobo15bobo15b2o15b2o10bobo9b2o12b2o8bobo2$bo2bo9bo3bo10bo
4bo9bo3bo13bobo14b2o16bobo9bo2bo7bo2bo11b2o8b2o9$2b2o11b2o14b2o12bobo
15bobo15b2o15b2o10bobo9b2o12b2o8bobo3$bo2bo9bo3bo10bo4bo9bo3bo13bobo14b
2o16bobo9bo2bo7bo2bo11b2o8b2o14$bo2b3o!

[Haycat2009]

I do not know wheteher this counts, but there are 4 F Herschel-accepting conduits with step between 110 and 117: HF110B, F114, F116 and F117

[confocaloid]

I do not know wheteher this counts, but there are 4 F Herschel-accepting conduits with step between 110 and 117: HF110B, F114, F116 and F117

Maybe there are no particular reasons why that could not count for someone else. But for me at least, that does not count. First, it is not a coincidence. All four mentioned conduits have different steps. Second, it is not very strange. Even for Herschel-to-Herschel conduits specifically, there are different conduits for each of steps 156, 198, 200 e.g., listed in the old collection "h-to-h-collection-26Aug2017.rle".

[confocaloid]

There are several different period-46 gun mechanisms, and reactions at multiples of 46. This may not be the strangest one, but it is certainly a coincidence, acknowledged by others --

I am utterly speechless at the moment... Behold, the new smallest period-46 glider gun with a 555-cell bounding box (37x15):

Code: Select all

x = 37, y = 15, rule = B3/S23
24b2o$24b2o$36bo$10b2o22b3o$2o7bobo13b2o6bo$2o7bo15b2o6b2o$9b3o4$9b3o
21b3o$2o7bo20b2o$2o7bobo13bo4b2o$10b2o11bobo4bobo$24b2o!

I'm utterly speechless at the moment... Behold, a brand-new period-46 glider gun without any Snarks, twin-bees shuttles or Tanner's P46s:

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x = 30, y = 31, rule = B3/S23
13b2o$8b2o3bo2bobo$2o5b2o6b2ob3o$bo7bo11bo$bobo11b2ob3o$2b2o11b2obo2$
20b2o$20bo$18bobo$2o5b2o9b2o$2o5bobo$7bobo$8b2o4$20b2o$20bobo$20bobo5b
2o$10b2o9b2o5b2o$9bobo$9bo$8b2o2$11bob2o11b2o$9b3ob2o11bobo$8bo11bo7bo
$9b3ob2o6b2o5b2o$11bobo2bo3b2o$15b2o!

Is the allusion intentional?

It is indeed intentional; both posts involve absolutely-enormous discoveries pertaining to period-46 glider guns.

I find it very interesting that the two earliest known simple guns (p30 GGG and p46 twin bees gun) both have comparably simple but unrelated guns at multiples of their period, 30 x 4 = 120 for the Simkin gun and 46 * 4 = 184 for this gun. Furthermore, while the originals are based upon shuttles, the latter are based upon Herschel conduits.

Also the p138 gun based on Gabriel Nivasch's p138 is 46 x 3. Many a strange coincidence.

[confocaloid]

There is a composite F154 (made out of two Fx77) and an elementary L154, where the active reactions converge at T = 135 ignoring a dying noninteracting spark:

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#C https://conwaylife.com/forums/viewtopic.php?p=170678#p170678
#C https://conwaylife.com/forums/viewtopic.php?p=170750#p170750
#C [[ STOP 135 ]]
x = 70, y = 78, rule = LifeHistory
42.2A$43.A$43.A.A$44.2A$45.3B$45.3B.B$47.4B.B$47.8B$49.6B$49.2B3C2B3.
2B3.2A$49.2BC4B3.4BA2BA$49.B3C4B.5B2A.A$49.14B.B.A.2A$49.14B2A2.A.A$
49.13BA2.2A$50.12B.2A$51.10B3.A$51.11B2.A.A$49.12B2.2A.3A$48.11B5.B4.
A$41.2A6.9B4.B2AB3A$42.A6.12B.B2A.A$42.A.AB2.11B2A2B$43.2AB.10B.BA.AB
$45.12B3.2A$45.12B$46.9B.B2A$45.12BA.A$45.11B3.A$46.10B3.2A$46.9B$46.
9B$47.7B$46.9B.2B$46.13BD$44.15BDBD$43.5B2E9B3DB$43.5B2E11BD$44.16B$
47.6B.B$49.B7$51.A$49.3A$25.A22.A$25.3A20.2A$28.A17.4B$27.2A16.3B$27.
4B14.4B$8.A20.3B12.5B$8.3A12.B.3B.4B11.6B$11.A10.18B2.8B$10.2A3.B5.2B
2E11BD14B$10.8B3.2B2E9B3D13B$12.8B.13BDBD4B.7B$12.22BD15B$11.15B.2B2.
19B$9.17B8.17B$7.18B11.15B.2B2.2B$7.2BC15B12.22BD$6.3BCBC4B.7B13.8B.
13BDBD$7.2B3C13B10.8B3.2B2E9B3DB$6.5BC14B9.2A3.B5.2B2E11BD$5.10B2.8B
11.A10.13B$4.4B11.6B8.3A12.B.3B.B$4.3B12.5B9.A$2.4B14.4B$2.2A16.3B$3.
A17.4B$3A20.2A$A22.A$24.3A$26.A!

[confocaloid]

[...]
LoM-based 8c/96d reaction
[...]
2c/11d in B2n3-e/S234c
[...]

Along the same lines, I didn't see a reason why the following two reactions (found in a cellular automaton located midway between Life-like CA B3/S23 and B35/S23) must have the same simplified speed (orthogonal 4c/31 in both cases):

Code: Select all

#C An orthogonal 8c/62 spaceship and an orthogonal 16c/124 puffer
x = 39, y = 25, rule = B35cejkr/S23
2bo23b2o$bobo21b2obo$o2bo22bob2o8bo$3bo22bobo9bo$obo25bo$bo36bo$38bo$
30b2o$30b2o7$23b2o$23b2o7$30b2o$30b2o!

Is there a common mechanism that I failed to notice? Or this is an example of a mathematical coincidence?

[Anivec]

Here’s a strange occurrence, the timings for SE and NE have the most conduits for t = 4 mod(8) and the least is t = 6 mod(8)

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x = 2382, y = 1382, rule = LifeHistory
979.D$978.D.D$319.D172.D484.D.D.D434.D3.D.5D8.3D2.5D.5D3.D3.5D2.3D86.
D3.D.D3.D2.3D4.D3.5D3.D4.3D3.3D105.D3.D.5D9.D6.D2.5D3.D4.3D3.3D99.D3.
D.5D9.D4.3D2.5D2.3D3.3D3.3D83.D3.D.5D.5D.5D10.D199.D3.D.5D3.D4.3D2.5D
3.D6.D75.D3.D.5D.5D.5D3.D4.3D3.3D$318.D.D170.D.D482.D5.D433.2D2.D.D11.
D3.D5.D3.D4.2D7.D.D89.2D2.D.D3.D.D3.D2.2D5.D4.2D3.D3.D.D3.D104.2D2.D.
D12.2D5.2D4.D4.2D3.D3.D.D3.D98.2D2.D.D12.2D3.D7.D3.D3.D.D3.D.D3.D82.2D
2.D.D5.D7.D11.2D199.2D2.D.D6.2D3.D7.D4.2D5.2D75.2D2.D.D9.D3.D4.2D3.D3.
D.D3.D$317.D.D.D168.D.D.D484.D436.D.D.D.D15.D4.D4.D5.D6.D2.D89.D.D.D.
D3.D5.D3.D5.D5.D7.D.D2.2D104.D.D.D.D13.D4.D.D4.D5.D7.D.D3.D98.D.D.D.D
13.D3.D7.D7.D.D2.2D5.D82.D.D.D.D5.D7.D10.D.D199.D.D.D.D7.D3.D7.D5.D4.
D.D75.D.D.D.D8.D4.D5.D3.D3.D5.D$316.D5.D166.D5.D920.D2.2D.3D3.5D4.D4.
D5.D5.D5.D3.4D86.D2.2D.D.D.D3.2D4.D5.D5.D6.D2.D.D.D104.D2.2D.3D3.5D3.
D3.D2.D4.D5.D5.2D3.3D99.D2.2D.3D3.5D3.D3.4D4.D6.D2.D.D.D3.2D83.D2.2D.
3D4.3D4.D3.5D.D2.D199.D2.2D.3D5.D3.4D4.D5.D3.D2.D75.D2.2D.3D5.D5.D5.D
4.3D4.2D$319.D172.D486.D436.D3.D.D13.D4.D6.D5.D4.D4.D3.D85.D3.D.D.D.D
5.D3.D5.D5.D5.D3.2D2.D104.D3.D.D13.D3.5D3.D5.D7.D.D3.D98.D3.D.D13.D3.
D3.D3.D5.D3.2D2.D5.D82.D3.D.D9.D3.D9.5D198.D3.D.D7.D3.D3.D3.D5.D3.5D74.
D3.D.D6.D6.D5.D3.D3.D5.D$1416.D3.D.D12.D4.D7.D5.D3.D5.D3.D85.D3.D.2D.
2D.D3.D3.D5.D5.D4.D4.D3.D104.D3.D.D13.D6.D4.D5.D3.D3.D.D3.D98.D3.D.D13.
D3.D3.D3.D4.D4.D3.D.D3.D82.D3.D.D5.D3.D3.D12.D199.D3.D.D7.D3.D3.D3.D5.
D6.D75.D3.D.D5.D7.D5.D3.D3.D.D3.D$319.D172.D486.D436.D3.D.5D7.5D.D7.D
4.3D2.D6.3D86.D3.D.D3.D2.3D3.3D4.D4.3D2.5D2.3D105.D3.D.5D8.3D5.D4.D4.
3D3.3D3.3D99.D3.D.5D8.3D3.3D4.D3.5D2.3D3.3D83.D3.D.5D2.3D4.D12.D199.D
3.D.5D2.3D3.3D4.D4.3D5.D75.D3.D.5D.D7.D4.3D3.3D3.3D2$319.D172.D2$1417.
3D2.5D.5D.5D2.3D3.3D104.D3.D.5D8.3D3.3D2.5D3.D4.3D3.3D100.3D2.D3.D8.3D
2.5D2.3D4.D113.3D2.5D2.3D2.5D.5D3.D6.D3.3D338.B13.4B$1416.D3.D.D5.D7.
D3.D3.D.D3.D103.2D2.D.D11.D3.D.D3.D3.D4.2D3.D3.D.D3.D98.D3.D.D3.D7.D3.
D3.D3.D3.D2.2D112.D3.D.D5.D3.D5.D3.D4.2D5.2D2.D3.D332.B3.3B11.4B$1416.
D5.D5.D7.D7.D5.D103.D.D.D.D15.D.D3.D3.D5.D3.D3.D5.D98.D5.D3.D11.D3.D7.
D3.D112.D5.D9.D4.D4.D5.D4.D.D6.D331.2B.6B8.5B$1417.3D2.3D4.3D4.D6.D4.
2D104.D2.2D.3D3.5D4.D3.3D4.D5.D4.4D3.2D100.3D2.D.D.D.5D4.D4.D6.D4.D113.
3D2.3D5.2D4.D5.D5.D3.D2.D4.2D329.5B.7B3.8B113.A$1420.D.D9.D3.D5.D7.D103.
D3.D.D13.D3.D3.D3.D5.D7.D5.D102.D.D.D.D9.D5.D5.D5.D116.D.D9.D2.D6.D5.
D3.5D5.D326.A25B111.3A$1416.D3.D.D5.D3.D3.D4.D4.D3.D103.D3.D.D12.D4.D
3.D3.D5.D7.D.D3.D98.D3.D.2D.2D8.D6.D4.D6.D112.D3.D.D5.D3.D.D7.D5.D4.B
.D2.D3.D324.3B2AD23B109.A$1417.3D2.5D2.3D4.D3.5D2.3D104.D3.D.5D7.5D2.
3D4.D4.3D3.3D3.3D100.3D2.D3.D7.5D3.D3.5D2.3D112.3D2.5D2.3D2.D7.D4.3D2.
2B.D3.3D118.4B203.4BACBD21B.3B105.2A11.B$1874.2A15.3B125.4B204.5BDCDB
2A22B102.5B10.2B$14.D3.D.D3.D8.3D2.5D3.D4.3D3.3D558.D3.D.D3.D2.3D3.3D
2.5D2.3D3.3D3.3D127.3D2.5D2.3D2.5D.5D3.D4.3D3.3D296.3D2.5D.5D.5D2.3D3.
3D708.B2AB13.4B124.4B205.B5ABDB2A21B2A86.A12.5B11.3B$14.2D2.D.D3.D7.D
3.D3.D4.2D3.D3.D.D3.D557.2D2.D.D3.D.D3.D.D3.D3.D3.D3.D.D3.D.D3.D125.D
3.D.D5.D3.D5.D3.D4.2D3.D3.D.D3.D120.3D2.5D10.D3.3D2.5D3.D4.3D3.3D123.
D3.D.D5.D7.D3.D3.D.D3.D708.2B13.4B124.4B206.4BA25B.B2A86.3A9.9B7.4B$14.
D.D.D.D3.D7.D3.D3.D5.D7.D.D3.D557.D.D.D.D3.D5.D.D3.D3.D7.D.D2.2D5.D125.
D5.D9.D4.D4.D5.D3.D3.D.D3.D119.D3.D.D13.2D2.D3.D3.D4.2D3.D3.D.D3.D122.
D5.D5.D7.D7.D5.D709.2B11.4B124.4B207.4B2.23B3.B90.A7.14B2.4B$14.D2.2D
.D.D.D.5D2.4D3.D5.D6.D3.4D234.3D2.5D8.3D3.3D2.5D3.D4.3D3.3D120.3D2.5D
10.D3.3D2.5D2.3D5.D3.3D101.D2.2D.D.D.D3.2D3.4D3.D6.D2.D.D.D3.2D127.3D
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10B3.7B118.B.21B137.8B8.2A115.A4.17B453.10B3.7B$28.9B3D3B117.A14.13B121.
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2BD19B.B12.4B$27.15B2.2A139.4B108.8B5.4B157.10BA6B144.11B154.20B12.4B
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20B119.13B3D9B119.2B3D4B2.12B2A13.3B$26.15B4.3A139.4B107.3B4.2A5.4B157.
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5B7.4B146.D3.D.5D8.3D3.3D4.D3.5D2.3D3.3D392.2A.9B2.2B125.9B4.A120.3A20.
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3A7.3B128.8B.B2A6.A143.A350.D3.D.D9.D.D3.D3.D5.D5.D$27.3BA4B12.4B271.
4B170.4B129.17B142.3A20.A154.2B12.4B585.A7.5B127.9B2.B502.D3.D.D5.D3.
D.D3.D3.D4.D5.D$26.10B3.B8.4B271.4B170.4B128.18B141.A23.3A152.2B12.4B
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5D.5D$24.B2A10B.B2A8.4B271.4B170.4B125.20B167.A151.B2AB12.4B141.D3.D.
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25.11B2.B13.4B569.6B3D9B488.D.D9.D2.D6.D5.D3.5D5.D532.2B516.3D2.5D.5D
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4B$295.3D2.3D3.5D3.2D2.D.D.D3.D5.D4.3D2.D2.D118.D5.D12.D.D4.D5.D7.D5.
D.D109.A4.4BABA3B9.4B303.D3.D.D14.D2.D3.D3.D5.D7.D.D3.D137.7B6.4B$298.
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11.D3.D.D3.D3.D5.D3.D3.D4.D122.D.D11.5D3.D5.D5.D7.D5.D110.5BA5B10.4B489.
11B2.4B1084.B2A2B$295.3D2.5D8.3D3.3D4.D4.3D3.3D5.D118.D3.D.D14.D4.D5.
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3D3.3D110.13B11.2B484.20B1082.3B3.4B$626.13B12.B482.21B1083.9B$627.12B
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3A290.5B.B2A.A341.A15.A137.18B.B1070.B3.3B3.10B.BA.A13.4B$320.A15.A291.
4B.B2.B2AB3A339.3A13.2A4.2A129.18B1072.2B.6B2.10B.B2A13.4B$320.3A13.2A
4.2A284.2A8.B4.A341.A9.5B4.A130.17B1070.5B.7B.12B14.4B$323.A9.5B4.A154.
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4.D$324.16B159.2A4.B133.A145.D5.D6.D.D4.D5.D5.D4.D.D2.D3.D154.16B132.
18B1066.5BDCDB2A21B8.4B80.2D2.D.D5.D3.D3.D3.D3.D2.2D$324.16B159.8B279.
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.D.D.D5.D3.D3.D7.D3.D$323.17B161.8B5.2A273.D.D5.5D3.D5.D5.D3.5D5.D151.
18B132.20B1065.4BA29B4.4B82.D2.2D.3D4.4D3.D5.2D4.D$159.3D2.5D3.D4.3D2.
5D2.3D129.18B161.9B6.A269.D3.D.D8.D4.D5.D5.D6.D6.D149.19B134.18B825.D
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3.D.D9.D3.D3.D3.D3.D$158.D5.D7.D3.D3.D3.D3.D3.D126.2BD15B161.14BA467.
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D4.3D3.3D$159.3D2.3D5.D4.3D4.D4.4D125.3BDBD13B160.15B469.2B3D13B134.16B
828.D2.2D.D.D.D3.D5.D5.D4.3D5.D210.30B$162.D.D7.D3.D3.D3.D7.D126.2B3D
13B159.15B469.5BD12B134.18B827.D3.D.D.D.D2.D6.D5.D3.D3.D3.D211.32B$158.
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154.10B3.6B133.21B825.D3.D.2D.2D.D7.D5.D3.D3.D2.D210.2A2B.29B$159.3D2.
5D2.3D3.3D4.D4.3D125.10B3.6B158.6BDBD10B272.D3.D.D5.D3.D.D3.D3.D3.D5.
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8B$316.8B6.7B156.4B.2B3D4B.B2AB2A271.D5.D9.D.D3.D3.D3.D5.D3.D151.8B9.
5B132.21B1072.A10.16B2A9B$315.8B9.5B155.4B.5BD4B2.A3.A272.3D2.3D5.2D3.
4D3.D4.3D3.4D150.8B11.4B132.19B713.D3.D.5D2.3D2.5D2.3D332.2A10.27B$13.
3D2.5D8.3D2.5D2.3D3.3D262.8B11.4B154.4B.10B4.3A276.D.D9.D5.D3.D7.D5.D
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3A273.3D2.5D2.3D3.3D4.D4.3D3.3D148.8B147.A.A18B408.D.D.D.D15.D3.D5.D3.
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A4.17B407.D2.2D.3D3.5D4.D4.D5.D4.4D3.2D102.D3.D.5D2.3D2.5D.5D3.D4.3D3.
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$16.D.D13.D5.D3.D3.D.2D2.D251.2A4.8B169.4B.4B13.2A.2A450.3A4.8B148.2A
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12.D3.D.D12.D6.D3.D3.D.D3.D250.B2AB2.8B169.4B.4B468.A6.8B155.12B3.4B405.
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226.19B96.6B3.4B$166.A137.10B169.4B.4B297.2BAB168.2B4.8B150.A8.10B7.4B
550.D3.D.D6.D4.D3.D3.D5.D4.D5.D146.4B343.19B97.12B$165.A.A4.2A128.11B
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2.5D.5D142.4B344.19B90.A6.11B$32.2B131.A.A3.B2AB124.13B163.2A4.4B.4B301.
3B.B163.B2A11B153.2AB.3B.11B2A.2A3.4B736.4B343.2AB.3B2.12B90.3A4.10B$
32.BA2B128.2A.2A2.3B7.A112.B3.13B163.B2AB2.4B.4B296.2A3.9B160.13B156.
17B2ABA.A3.4B734.4B343.A.AB7.10B82.A11.A2.10B.B$31.BABA2B127.A2.B3.2B
6.3A111.2AB.9BA4B163.4B.4B.4B296.B2AB.11B10.2A146.13B157.19B3.A4.4B732.
4B145.B198.A8.12B82.3A8.2A3.8B.2BA$30.2BABA2B128.AB2AB.3B4.A114.2A10B
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15BA.A$30.3BA2B127.A.A.2A5B4.2A114.B.9BA2BA4B162.6B.4B292.A5.3B2.16B2.
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2B2A.7B86.8B2.13B$30.7B133.8B120.11B2.4B155.14B295.2AB.2B2A21B147.2A16B
2A149.21B14.4B420.BABAB7.3A4.4B99.D2.2D.3D4.3D4.2D4.D4.3D4.D133.2A8.4B
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149.B3.14B298.4B2A22B147.15B.B2A149.2BD19B.B12.4B420.B2AB.2B3.A6.4B100.
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4B86.20B$31.7B.B2A127.5B2A2B121.10B4.4B147.2AB.9B2A3B299.28B149.13B2.
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D122.A12.5B.4B81.4B9.16B35.4B211.3B5.4B84.19B.B2A$32.8B2A126.6B2A2B122.
3B4.2A5.4B146.2A10BA2BA3B298.29B9.2A137.14B152.2B3D4B2.12B2A13.3B418.
13B3.4B102.D3.D.5D2.3D3.3D4.D4.3D3.3D121.A.AB7.11B83.4B8.16B34.4B213.
B7.4B81.21B.BA.A$32.6B.2B127.9B.B3.2B115.4B4.A7.4B146.B.10BABA4B124.D
3.D.D3.D2.3D4.D3.5D3.D4.3D3.3D129.29B7.A140.12B151.5BD4B2.11B.B15.2B417.
12B4.4B265.2AB.3B3.13B82.4B5.17B34.4B223.4B78.23B4.A$31.7B130.8B.3B.4B
113.4B6.3A5.4B148.10BA6B123.2D2.D.D3.D.D3.D2.2D5.D4.2D3.D3.D.D3.D126.
31B4.BA.A140.2B2A9B149.10B3.9B20.B252.D3.D.5D8.3D2.5D.5D3.D3.5D2.3D113.
12B3.4B268.20B2A82.4B3.18B33.4B225.4B77.2BD14B4.4B2.2A$30.8B131.17B113.
B2AB7.A6.4B148.11B2.4B122.D.D.D.D3.D5.D3.D5.D5.D7.D.D2.2D124.A.2A32B.
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4B269.20B2A83.4B.20B31.4B227.4B75.3BDBD4B.6B7.2A$20.2A8.8B131.17B114.
2A16.4B148.8B5.4B121.D2.2D.D.D.D3.2D4.D5.D5.D6.D2.D.D.D122.3AB2AB6.27B
144.9B.4B146.3B12.5B276.D.D.D.D15.D4.D4.D5.D6.D2.D111.2A4.16B271.20B85.
24B19.A10.4B229.4B75.2B3D4B2.B.5B5.A$21.A9.8B131.17B132.4B147.10B4.4B
120.D3.D.D.D.D5.D3.D5.D5.D5.D3.2D2.D121.A4.B9.8B2A16B144.9B2.4B143.4B
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7.4B231.4B73.5BD4B7.2A6.3A$21.A.AB4.10B131.16B134.4B147.3B4.2A5.4B119.
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138.3A20.A276.D3.D.5D7.5D.D7.D4.3D2.D6.3D107.4B5.10B270.2BD15B.4B88.24B
2A18.9B237.B71.3B19.A$24.17B125.2BD18B136.4B143.B2AB7.A6.4B288.A16.14B
3.4B139.2A3.6B8.4B137.A23.3A431.19B270.3BDBD4B.7B4.2A86.27B9.B11.6B308.
4B$25.17B.B121.3BDBD4B.7B.4B136.4B143.2A16.4B305.12B5.4B144.4B10.4B162.
A431.18B272.2B3D4B2.6B4.A87.2BD17B.6B7.2A2B4.2B4.5B309.2A$24.19B2A121.
2B3D4B.7B2.4B136.4B161.4B114.D3.D.D3.D2.3D3.3D2.5D3.D4.3D3.3D145.12B5.
4B144.2B12.4B592.18B272.5BD4B3.6B4.3A83.3BDBD17B10.2B2A10B.7B309.A$22.
19B.B2A120.5BD4B.7B3.4B136.4B161.4B113.2D2.D.D3.D.D3.D.D7.D4.2D3.D5.D
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21B2.B120.10B3.5B5.4B301.4B112.D.D.D.D3.D5.D.D7.D5.D3.D9.D147.11B5.4B
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7B4.4B301.4B111.D2.2D.D.D.D4.D2.4D4.D5.D3.4D4.2D150.10B5.4B142.2A14.4B
590.16B271.3B14.2A.B2A87.10B2.43B$19.3BDBD4B.9B124.3B10.2B4.2A5.4B301.
4B110.D3.D.D.D.D3.D3.D3.D3.D5.D3.D3.D5.D150.B.B3.4B5.3B159.4B445.4B141.
15B123.2A144.4B18.BA.A85.4B3.B5.43B$20.2B3D4B.8B123.4B11.2AB3.A7.4B301.
4B109.D3.D.2D.2D2.D4.D3.D3.D5.D3.D3.D.D3.D151.3B3.4B167.4B443.4B143.16B
120.B2AB5.2A136.2A23.A85.3B3.3B3.44B4.2A$19.5BD4B.8B123.2A9.2A.A.A5.3A
5.3B302.4B108.D3.D.D3.D.5D2.3D4.D4.3D3.3D3.3D151.B2AB4.4B167.4B441.4B
144.16B121.3B5.A138.A23.2A82.4B4.2A3B.45B2.A.A$18.10B.9B124.A9.A.2A.A
.A5.A6.2B303.4B305.2A5.5B167.4B439.4B145.2A12B.B2A120.B3.BA.A135.3A108.
2A4.BA.A49B2.BA$17.4B6.10B.2B119.3A16.2A13.B619.5B8.2B158.4B437.4B146.
2A11B2.BA.A115.7B.B2A136.A111.A3.2B2A.23B2.27B$17.3B5.14B2A118.A652.9B
4.4B158.4B435.4B148.11B6.A114.10B28.4B215.3A5.4B.16B3.2B5.25B$15.4B5.
15B2A568.3D2.5D2.3D3.3D2.5D3.D4.3D3.3D153.B4.9B4.4B159.4B433.4B150.8B
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29B587.7BABA2B14.A111.A8.2A8.5B2AB125.16B12.4B238.B.2B5.2A22.13B$32.4B
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3D2.5D3.D4.3D3.3D322.D2.2D.3D5.2D2.4D4.D6.D5.D$317.A15.A161.A129.17B170.
4B165.16B425.4B13.6B103.18B4.B157.5B5.13B104.2D2.D.D3.D2.2D3.D3.D3.D4.
2D3.D3.D.D3.D321.D3.D.D9.D.D3.D3.D5.D5.D$317.3A13.2A4.2A153.2A4.B125.
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4B.26B68.3BDBD4B.31B2.4B$26.A9.12B130.A117.11B2.4B148.B.10BABA4B476.12B
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4B470.2A.8B3.4B160.17B2ABA.A4.4B1078.21B64.4B12.7B13.10B$29.23B118.8B
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19B2.2A5.4B1076.22B64.A15.A3.A7.2A5.2B.6B$25.24B115.B4.9B139.4B145.B2A
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5D2.3D2.5D3.D4.3D3.3D494.10B.10B61.A15.A9.A5.A.AB.11B$24.3BDBD4B.9B117.
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8B99.13B$24.5BD4B.8B110.A27B140.4B163.4B468.B2AB12.4B148.3BDBD4B.13B2A
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9B364.3B8.A96.2BA2BA9B$21.A7.13B115.32B2A791.4B138.4B13.4B711.4B7.2A9.
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2D123.8B125.2A7.23B3.4B463.A7.4B.2A$38.4B114.4B8.14B5.4B1360.D3.D.D13.
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9B5.A124.21B3D9BA4B$173.6B2.BA.A6.2B414.D3.D.D5.D3.D.D3.D3.D3.D3.D.D3.
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2B2AD24B123.19B2.12B2.2BA4B$172.A6.3A107.3D2.5D8.3D3.3D2.5D3.D4.3D3.3D
268.3D2.5D.5D2.3D4.D3.5D2.3D301.D3.D.D11.D3.D.D7.D4.2D7.D3.2D420.D2.2D
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4B$169.A118.D5.D15.D.D7.D5.D7.D.D3.D608.3D2.3D3.5D3.2D2.4D4.D5.D5.D3.
D2.D420.D3.D.D7.D3.D3.D3.D3.D3.D2.D114.4B13.4B108.5ABDB2A22B9.A110.2B
3D4B2.6B7.7B7.2B$289.3D2.3D3.5D4.D2.4D4.D5.D5.2D3.3D612.D.D15.D.D3.D3.
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111.10B6.4B5.10B5.A.A$288.D3.D.D12.D4.D3.D3.D5.D3.D3.D.D3.D266.D3.D.D
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118.B2.24B4.2A109.4B12.B2A2B6.8B7.A$289.3D2.5D7.5D2.3D4.D4.3D3.3D3.3D
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2A5.8B$608.3D2.D.D.D4.D3.3D4.D5.D5.D4.4D786.A.A118.A.AB3.12B4.4B121.30B
109.4B18.BA.A4.9B$611.D.D.D.D3.D7.D3.D5.D4.D8.D786.A.A119.2AB2.13B3.4B
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22B121.2AB2.29B106.3B23.2A7.B2.4B$608.3D2.D3.D.5D2.3D4.D4.3D2.D6.3D784.
A4.B121.21B121.A.AB2.4B.25B105.2B37.4B$1438.3AB2AB119.20B122.A10.25B105.
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3D2.5D.5D2.3D2.5D3.D4.3D3.3D261.A10.6B113.B.20B135.24B147.4B$317.A15.
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3D263.3A13.2A4.2A266.D3.D.D3.D2.2D3.D3.D3.D4.2D3.D3.D.D3.D318.A15.A135.
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17B5.4B103.22B138.22B$15.3D2.3D6.D5.D4.D3.5D2.3D265.8B.7B.B2A272.D.D.
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2A23B$15.3D2.5D.5D.5D3.D10.3D266.17B639.16B438.20B2.4B107.10B2.11B135.
2B.21B$318.18B639.17B438.2BD22B108.10B3.12B136.20B$316.19B295.A342.18B
438.3BDBD4B.14B108.10B5.6BA5B137.18B$316.2BD15B296.3A338.19B155.A284.
2B3D4B2.12B109.10B5.5BABA3B138.12B3.2B$315.3BDBD13B299.A337.2BD15B156.
3A281.5BD4B2.12B101.2A6.10B7.3B2A4B137.8B.3B$316.2B3D13B290.A7.2A336.
3BDBD13B159.A279.10B4.12B101.A7.9B8.B2.4B139.13B$315.5BD12B291.3A5.4B
335.2B3D13B158.2AB6.2A269.4B10.12B102.A.AB4.9B.2B4.3B144.7B4.2A$314.10B
3.6B294.A6.4B332.5BD12B159.5B4.A270.3B12.9B105.2AB.14B2A3.B2AB143.7B4.
A$313.8B6.7B292.2A3.8B330.10B3.6B161.3B.BA.A268.4B13.8B108.16B2A4.2A145.
7B4.3A$312.8B9.5B131.3D2.5D3.D4.3D2.5D3.D4.3D117.B4.3B.9B329.8B6.7B145.
A12.5B.B2A269.2A16.6B109.14B.2B152.6B7.A$311.8B11.4B130.D3.D.D6.2D3.D
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17.B$310.8B11.B2A2B130.D5.D7.D3.D2.2D3.D5.D3.D3.D113.6B3.16B323.8B11.
4B148.A7.9B269.3A15.2A4.2B109.14B.2B151.7B16.2B$303.2A4.8B13.2A133.3D
2.3D5.D3.D.D.D3.D5.D4.4D107.4B2.7B2.16B322.8B11.B2A2B147.2A4.12B269.A
18.A3.B2AB106.18B2A145.2A2.8B15.3B$302.B2AB2.8B152.D.D7.D3.2D2.D3.D5.
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4B$302.4B.8B149.D3.D.D7.D3.D3.D3.D5.D7.D104.B2ABD28B314.3A4.8B165.22B
281.A114.2BD15B2.B145.A3.11B11.4B$32.A270.2B.8B151.3D2.5D2.3D3.3D4.D4.
3D3.3D105.3ABCAD27B312.A6.8B165.23B395.3BDBD4B.8B147.2A3.4B2A5B10.4B$
32.3A268.10B296.B2AB3CB2A25B311.2A4.8B165.25B395.2B3D4B2.7B153.3B2A5B
9.4B$23.A11.A265.11B297.3AB2ADB2A21B.4B308.4B3.8B167.24B394.5BD4B2.7B
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4B162.A10.2A131.B2.19B6.3B304.B2A11B162.2AB.30B390.3B12.7B153.8B6.4B109.
D3.D.5D2.3D3.3D2.5D2.3D$25.8B2.11B2A99.3D2.3D3.D2.D5.D4.D5.D3.D2.D3.3D
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4B110.2D2.D.D5.D3.D.D3.D3.D3.D3.D$27.19B2A102.D.D5.5D3.D5.D5.D3.5D5.D
100.B.9BA2BA4B163.A8.A.2A129.21B8.B303.13B165.B.30B389.2A16.5B156.6B4.
4B111.D.D.D.D9.D.D2.2D3.D7.D$27.20B99.D3.D.D8.D3.D6.D5.D6.D2.D3.D103.
9B2A6B161.2A3.B5.A.A128.9B2.11B310.3B2A9B168.31B389.A14.6B157.6B3.4B112.
D2.2D.3D5.2D2.D.D.D3.D5.2D$26.20B101.3D2.5D4.D2.5D3.D4.3D5.D3.3D105.11B
2.4B160.8B4.B128.4B.5B2.11B310.3B2A10B167.12B.18B386.3A15.6B157.6B2.4B
113.D3.D.D9.D.2D2.D3.D7.D$24.21B253.8B5.4B161.8B.3B126.4B2.4B3.9B.B2A
307.2A14B.2B164.31B386.A17.4B158.7B.4B114.D3.D.D5.D3.D.D3.D3.D3.D3.D$
22.24B252.10B4.4B160.13B124.4B11.8B.BA.A306.2A16B2A163.12B.19B403.2B2A
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.2B120.4B11.9B4.A307.15B.B2A163.10B3.20B404.2A159.9B$21.3BDBD4B.6B6.4B
250.4B4.A7.4B155.18B2A118.4B11.9B5.2A308.13B2.B164.10B4.15B.4B564.8B$
22.2B3D4B2.B.5B5.4B248.4B6.3A5.4B152.18B.B2A117.4B11.4B2.3B316.14B165.
10B6.14B2.4B562.8B$21.5BD4B7.2A6.4B248.B2AB7.A6.4B151.2BD15B2.B117.4B
11.4B4.B319.12B165.10B7.9B7.4B561.7B120.3D2.5D2.3D3.3D2.5D8.3D$20.10B
8.A8.4B248.2A16.4B149.3BDBD4B.7B120.4B11.4B325.2B2A9B156.2A6.10B8.5B11.
3B561.6B120.D3.D.D5.D3.D.D3.D3.D9.D3.D$19.4B16.3A6.3B267.4B149.2B3D12B
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2B10.2A11.B560.7B121.3D2.3D6.D5.D4.D3.5D2.3D$17.4B299.4B145.19B.3B6.A
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17.2A144.B16.A140.4B143.4B7.15B.BA.A452.2A.8B3.4B156.16B2A10.3A564.13B
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145.4B139.4B11.15B453.A.A3.5B7.4B155.13B579.15B$15.A146.12B3.2A145.4B
138.2A13.15B453.2A3.6B8.4B153.14B.2B576.14B$162.12B2.3B146.4B138.A14.
14B459.4B10.4B150.18B2A576.13B$163.14B287.3A15.13B461.2B12.4B147.18B.
B2A576.14B$163.16B285.A18.11B463.2B12.4B146.2BD15B2.B578.12B$161.19B302.
14B460.B2AB12.4B144.3BDBD4B.8B583.3B2A3B151.A$160.2A.16B.2B301.14B460.
2A14.4B144.2B3D4B2.7B584.BA2BA2B149.3A$160.2A19B2A300.15B476.4B142.5B
D4B2.7B586.2AB150.A$161.2B.17B2A299.17B476.4B140.10B3.7B728.A10.2A$164.
15B.2B298.A.2AB.8B2.4B476.4B138.4B11.7B726.A.A6.5B$164.16B298.3AB2AB.
6B5.4B476.4B137.3B12.7B726.A.A5.4B$165.15B297.A4.B6.5B4.4B476.4B134.4B
13.6B725.3A.2A3.6B11.A$165.16B297.3A.2A8.2A5.4B476.4B133.2A16.5B724.A
4.B4.6B9.3A9.B$164.18B298.A.A9.A7.4B476.4B133.A14.6B719.A6.3AB2AB.7B8.
A11.2B$163.21B296.A.A10.3A5.3B477.4B129.3A15.6B719.3A6.A.2AB2.6B.2B5.
2A9.3B$163.22B296.A13.A6.2B610.A17.4B724.A7.21B8.4B$163.21B319.B628.2B
2AB722.2A3.B5.17B9.4B$163.20B951.2A723.8B2.15B2A2B7.4B$163.21B1677.22B
A2BA2B5.4B$161.2A17B.4B1676.23B2A3B4.4B$160.A.A17B2.4B1674.19B3.9B.4B
$160.A4.15B3.4B1671.21B4.12B$159.2A5.13B5.4B416.3D2.5D2.3D4.D3.5D2.3D
3.3D1213.24B4.10B$165.12B8.4B414.D3.D.D5.D3.D2.2D5.D3.D5.D3.D1212.2BD
14B4.4B3.9B$165.12B9.4B413.D5.D9.D3.D5.D3.D5.D2.2D1211.3BDBD4B.6B6.4B
.9B$156.2A7.10B12.4B413.3D2.3D5.2D4.D5.D3.4D2.D.D.D1212.2B3D4B2.B.5B5.
4B.7B$157.A8.10B6.2A4.4B415.D.D9.D3.D5.D3.D3.D.2D2.D1211.5BD4B7.2A6.10B
$157.A.AB6.11B5.A5.3B411.D3.D.D5.D3.D3.D5.D3.D3.D.D3.D1210.10B8.A8.4B
.2B$158.2AB.3B.11B2A.3A7.2B412.3D2.5D2.3D3.3D4.D4.3D3.3D1210.4B16.3A6.
4B$160.17B2ABA10.B95.3D2.5D9.D3.5D.5D3.D4.3D3.3D1515.3B19.A7.4B$160.19B
107.D3.D.D12.2D7.D3.D4.2D3.D3.D.D1516.4B29.4B$161.19B106.D5.D13.D6.D4.
D5.D3.D2.2D.D1516.2A32.4B$14.3D2.D3.D.5D.5D3.D4.3D3.3D107.20B107.3D2.
3D3.5D3.D5.D5.D5.D3.D.D.D.4D1514.A33.4B$13.D3.D.D3.D.D7.D4.2D3.D5.D3.
D104.20B112.D.D13.D4.D6.D5.D3.2D2.D.D3.D1510.3A35.4B$13.D5.D3.D.D7.D5.
D3.D5.D2.2D102.21B109.D3.D.D13.D3.D7.D5.D3.D3.D.D3.D1510.A38.4B$14.3D
2.D.D.D2.3D4.D5.D3.4D2.D.D.D102.2BD19B.B107.3D2.5D8.3D2.D7.D4.3D3.3D3.
3D1551.4B$17.D.D.D.D5.D3.D5.D3.D3.D.2D2.D101.3BDBD4B.13B2A444.B1264.4B
$13.D3.D.2D.2D.D3.D3.D5.D3.D3.D.D3.D102.2B3D4B2.12B2A443.2AB.2B$14.3D
2.D3.D2.3D4.D4.3D3.3D3.3D102.5BD4B2.11B.B444.2A5B$154.10B3.9B449.7B$153.
4B10.6B.B450.8B490.3D2.5D2.3D5.D2.5D2.3D3.3D$153.3B12.5B453.7B489.D3.
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.D5.D3.D.5D3.D3.D3.D3.D$14.3D2.3D6.D5.D4.D3.5D2.3D96.3A20.A453.9B487.
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3B3.10B.4B$305.7B6.2A293.2B.6B2.16B517.A$304.8B6.A291.5B.7B.17B516.3A
$303.10B2.BA.A289.A28B.4B518.A8.2A$33.A269.7BD3B.B2A288.3B2AD25B2.4B491.
2A7.B15.2A8.A$32.A.A9.A259.6BDBD3B290.4BACBD23B3.4B491.A5.4B14.5B2.BA
.A383.D3.D.5D2.3D3.3D2.5D3.D3.5D$32.A.A7.3A258.7B3D3B290.5BDCDB2A21B3.
3B491.A.AB.5B5.B10.4B.B2A384.2D2.D.D5.D3.D.D3.D3.D4.2D7.D$30.3A.2A5.A
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2D3.D5.D6.D$29.A4.B6.2A256.17B290.4BA28B480.2A6.B2AB7.8B.8B.11B386.D2.
2D.3D5.2D2.D.D.D3.D5.D5.D$30.3AB2AB2.4B256.16B291.4B2.26B320.3D2.5D.5D
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2.6B5.32B384.D3.D.5D2.3D3.3D4.D4.3D2.D$28.3A4.9B259.13B299.24B2A317.3D
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16B2.A147.D2.2D.3D5.2D2.4D4.D6.D5.D105.2A14.12B2A477.36B.6B10.4B393.B
2AB$23.22B255.13B2AB150.D3.D.D9.D.D3.D3.D5.D5.D122.10B.B2A477.36B18.4B
393.3B$23.22B255.9B3.A2BA150.D3.D.D5.D3.D.D3.D3.D4.D5.D121.2AB.6B4.B334.
2B143.34B20.4B391.B.B281.D3.D.5D2.3D3.3D2.5D3.D4.3D3.3D$22.19B2.B254.
2AB.8B3.2A151.D3.D.5D2.3D3.3D4.D3.5D.5D117.A.AB.4B341.BA2B140.33B23.4B
390.5B279.2D2.D.D5.D3.D.D3.D3.D4.2D3.D3.D.D3.D$20.21B256.A.AB.9B313.A
5.5B338.BABA2B137.31B28.3B389.6B279.D.D.D.D9.D.D3.D3.D5.D7.D5.D$18.24B
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2D3.4D3.D5.D6.D4.2D$18.2BD14B4.4B253.2A11.4B320.A338.3BA2B136.2BD15B5.
11B29.B389.7B278.D3.D.D9.D5.D3.D5.D5.D7.D$17.3BDBD11B6.4B266.4B153.3D
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5BD4B3.6B8.10B2A414.8B$16.11B7.A8.4B266.4B150.3D2.3D4.3D4.D6.D5.D4.D468.
7B.B2A128.10B6.4B6.10B.2B404.2A10.7B$15.4B3.4B9.3A6.4B266.4B152.D.D9.
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410.A.AB7.6B4.A18.B$13.4B3.4B22.4B266.4B147.3D2.5D2.3D4.D3.5D.5D.D470.
7B6.A122.4B18.BA.A.3A418.2AB.3B3.6B.BA.A17.2B299.A$13.2A4.4B24.4B266.
4B651.8B4.3A122.2A23.A.A422.14B.B2A17.3B297.3A$14.A3.4B26.4B910.2A8.8B
3.A126.A23.2A423.16B18.4B296.A$11.3A3.4B28.4B910.A9.8B2.2A122.3A450.14B
18.4B297.2A11.B$11.A4.4B30.4B432.2A475.A.AB4.14B122.A451.16B16.4B295.
5B10.2B$15.4B32.4B430.B2A2B474.2AB.15B574.18B15.4B294.5B11.3B$14.4B34.
4B430.4B476.19B570.19B15.4B282.A11.9B7.4B$13.4B36.3B425.3B3.4B475.21B
568.2BD15B15.4B264.BA17.3A8.14B2.4B$481.9B477.22B565.3BDBD15B2.3B7.4B
264.BABA19.A6.15B.4B$481.9B21.B454.23B566.2B3D4B.10B2.4B5.4B265.BABA13.
2A3.2A5.20B$480.9B21.2B452.24B566.5BD4B2.16B3.4B267.BA2B12.A.A2.5B2.19B
$480.8B5.2A14.3B450.19B.B.2B567.10B4.21B266.5B14.AB4.4B.18B$474.B4.9B
5.A14.4B450.2BD15B573.3B11.20B266.9B2.6B.3B4.5B.18B$469.B3.3B3.10B.BA
.A13.4B450.3BDBD4B.9B570.4B12.19B267.22B2.25B$468.2B.6B2.10B.B2A13.4B
452.2B3D4B2.7B571.2A14.18B269.47B$16.D3.D.5D2.3D3.3D2.5D2.3D415.5B.7B
.12B14.4B452.5BD4B2.7B572.A14.17B269.18B2A28B$16.2D2.D.D5.D3.D.D3.D3.
D3.D3.D412.A27B13.4B452.10B4.6B569.3A16.B2A14B266.20B2A29B$16.D.D.D.D
9.D.D2.2D3.D7.D410.3B2AD24B12.4B452.4B10.7B569.A18.B2A6B3.3B.B2A262.52B
$16.D2.2D.3D5.2D2.D.D.D3.D5.2D411.4BACBD23B10.4B453.3B12.6B591.8B5.BA
.A261.2BD48B$16.D3.D.D9.D.2D2.D3.D7.D410.5BDCDB2A21B8.4B452.4B13.7B596.
2A8.A260.3BDBD20B2.24B$16.D3.D.D5.D3.D.D3.D3.D3.D3.D410.B5ABDB2A22B6.
4B453.2A16.5B597.A9.2A260.2B3D17B.B2.25B$16.D3.D.5D2.3D3.3D4.D4.3D411.
4BA29B4.4B104.3D2.5D2.3D3.3D2.5D3.D4.3D312.A16.6B597.3A267.5BD16B6.23B
$461.4B2.29B2.4B104.D3.D.D5.D3.D.D3.D3.D4.2D3.D3.D308.3A15.9B598.A266.
21B9.22B$469.B2.24B.4B105.D5.D9.D.D3.D3.D5.D7.D308.A17.2A.7B863.4B5.14B
8.17B.2B$471.29B107.3D2.3D6.D3.4D3.D5.D6.D328.A5.4B862.3B4.17B7.2A4.12B
$17.3D2.5D2.3D3.3D2.5D8.3D414.30B110.D.D7.D7.D3.D5.D5.D326.3A7.4B859.
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17.3D2.3D6.D5.D4.D3.5D2.3D411.A.AB2.4B.16B2A8B480.4B854.3A6.A6.15B17.
3B.BA.A$20.D.D7.D5.D5.D9.D3.D410.A10.16B2A9B480.4B853.A16.13B16.5B4.A
$16.D3.D.D6.D5.D6.D9.D3.D409.2A10.27B481.4B871.5B3.2B17.2AB6.2A$17.3D
2.5D.5D.5D3.D10.3D423.27B1353.6B3.2B19.A$480.26B1353.2A.B4.B2AB15.3A$
480.25B119.4B1232.A7.2A16.A$481.23B119.5B354.A874.3A$482.22B112.2A4.3B
2A2B2.2A348.A.A873.A$482.23B111.A5.2BA2BAB.B2A2B346.A.A$484.22B111.3A
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106.2B3D4B2.10B.B2A5.4B316.19B$17.8B2.15B2A2B7.4B446.4B104.5BD4B2.9B2.
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4B452.4B99.3B13.6B15.B314.5BD4B2.7B$16.21B4.12B454.3B97.4B12.5B2.2B328.
10B4.6B$14.24B4.10B456.2B97.2A12.A.2A4.B2A327.4B10.7B$14.2BD14B4.4B3.
9B458.B98.A10.3AB2A5.A.A326.3B12.6B$13.3BDBD4B.6B6.4B.9B555.3A10.A4.B
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15.5B$13.5BD4B7.2A6.10B253.2A318.A.A10.2A322.A16.6B$12.10B8.A8.4B.2B254.
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4B250.10B664.A10.4B$10.A33.4B249.7B2AB$7.3A35.4B248.6BA2BA$7.A38.4B245.
2AB.5B2AB$47.4B243.A.AB.8B$48.4B242.A4.8B3.2B1540.D3.D.5D4.D3.3D2.5D8.
3D$293.2A5.12B665.AB873.2D2.D.D7.2D2.D7.D9.D3.D$300.14B662.A.AB.B870.
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4.D3.5D3.2D$298.18B645.A11.6B.B2A869.D3.D.D5.5D.D3.D3.D13.D$296.21B644.
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3.D.5D4.D3.3D4.D10.3D$295.3BDBD17B646.16B$296.2B3D17B646.16B$295.5BD20B
644.15B567.D3.D.5D2.3D2.5D.5D3.D4.3D3.3D312.4B$294.10B.16B.BA640.16B567.
2D2.D.D5.D3.D.D7.D4.2D3.D3.D.D3.D310.4B$293.4B9.16BA.A637.18B567.D.D.
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5.D309.4B$290.4B13.13B639.3BDBD4B.9B568.D3.D.D6.D4.D3.D3.D5.D4.D5.D267.
3B39.4B$289.4B15.13B639.2B3D4B2.7B569.D3.D.5D.5D2.3D4.D4.3D2.5D.5D264.
5B36.4B$288.4B17.7B2.4B637.5BD4B2.7B879.6B35.4B$287.4B18.7B3.4B635.10B
4.6B879.8B21.A10.4B$286.4B21.4B5.4B633.4B10.7B879.8B21.3A7.4B$286.3B20.
8B4.4B632.3B12.6B569.D3.D.5D.5D2.3D2.5D2.3D4.D265.B4.9B24.A5.4B$286.2B
21.2A4.2A5.4B629.4B13.7B568.2D2.D.D5.D5.D3.D3.D3.D3.D2.2D264.3B3.11B21.
2A.7B$286.B23.A4.A7.4B628.2A16.5B569.D.D.D.D5.D9.D3.D3.D3.D3.D262.6B2.
13B19.9B$307.3A6.3A5.4B628.A16.6B568.D2.2D.3D4.3D4.2D4.D4.3D4.D256.4B
2.7B.13B9.B11.6B$307.A10.A6.4B624.3A15.9B567.D3.D.D9.D5.D3.D3.D3.D3.D
254.A27B8.2A2B4.2B4.5B$326.4B623.A17.2A.7B566.D3.D.D5.D3.D.D3.D3.D3.D
3.D3.D253.2B2AD25B5.2B2A10B.7B$327.4B641.A5.4B565.D3.D.5D2.3D3.3D4.D4.
3D3.3D252.3BACBD23B2.24B$328.4B637.3A7.4B856.4BDCDB2A46B$329.4B636.A10.
4B855.5ABDB2A46B$330.3B648.4B854.3BA52B$331.2B649.4B858.51B4.2A$332.B
650.4B859.B2.47B2.A.A$1848.48B2.BA$10.D3.D.D3.D.5D3.D3.5D2.3D3.3D2.5D
1790.24B.27B$10.2D2.D.D3.D.D6.2D5.D3.D3.D.D3.D.D1794.24B3.25B$10.D.D.
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D3.3D1788.A.AB2.18B7.26B$10.D3.D.D.D.D5.D3.D5.D5.D5.D7.D1787.A6.18B.B
4.25B$10.D3.D.2D.2D.D3.D3.D5.D4.D5.D4.D3.D1786.2A7.18B2A3.3B2.20B$10.
D3.D.D3.D2.3D3.3D4.D3.5D.5D2.3D1796.18B2A4.B4.16B$1852.3B3.13B11.14B$
1556.2A295.B2.3B.11B12.13B$1555.B2AB5.2A290.2A2.9B14.13B$11.3D2.5D2.3D
3.3D2.5D8.3D1506.3B5.A292.A3.7B15.14B$10.D3.D.D5.D3.D.D3.D3.D9.D3.D1506.
B3.BA.A289.3A5.4B17.14B$10.D5.D9.D5.D3.D9.D3.D1502.7B.B2A290.A8.5B15.
14B$11.3D2.3D6.D5.D4.D3.5D2.3D416.D3.D.D3.D3.D4.3D2.5D3.D4.3D3.3D1040.
10B28.4B272.2A13.2A14B$14.D.D7.D5.D5.D9.D3.D415.2D2.D.D3.D2.2D3.D3.D3.
D4.2D3.D3.D.D3.D438.D3.D.D3.D2.3D3.3D2.5D3.D3.5D.5D554.7B2AB27.4B273.
A13.A.AB2.2B2.6BAB$10.D3.D.D6.D5.D6.D9.D3.D415.D.D.D.D3.D3.D3.D3.D3.D
5.D3.D2.2D5.D438.2D2.D.D3.D.D3.D.D7.D4.2D3.D9.D554.6BA2BA26.4B275.3A10.
A4.4B2.4BABA$11.3D2.5D.5D.5D3.D10.3D416.D2.2D.D.D.D3.D4.4D3.D5.D3.D.D
.D4.D439.D.D.D.D3.D5.D.D7.D5.D3.D8.D553.2AB.5B2AB25.4B278.A9.2A4.B2AB
3.3B2A$466.D3.D.D.D.D3.D7.D3.D5.D3.2D2.D3.D440.D2.2D.D.D.D4.D2.4D4.D5.
D4.3D4.D553.A.AB.8B24.4B296.2A4.3B$4.4B458.D3.D.2D.2D3.D7.D3.D5.D3.D3.
D2.D441.D3.D.D.D.D3.D3.D3.D3.D5.D7.D2.D554.A4.8B3.2B18.4B304.4B$5.4B457.
D3.D.D3.D2.3D3.3D4.D4.3D3.3D2.5D438.D3.D.2D.2D2.D4.D3.D3.D5.D3.D3.D.D
554.2A5.12B17.4B307.2A$6.4B941.D3.D.D3.D.5D2.3D4.D4.3D3.3D2.D561.14B14.
4B308.A$7.4B1543.16B12.4B310.3A$8.4B1541.18B10.4B313.A$9.4B453.D3.D.5D
3.D4.3D2.5D4.D3.3D1045.21B8.4B$10.4B452.2D2.D.D6.2D3.D3.D3.D5.2D2.D3.
D445.3D2.5D.5D.5D3.D6.D566.2BD19B6.4B$11.4B451.D.D.D.D7.D3.D2.2D3.D4.
D.D6.D444.D3.D.D9.D3.D4.2D5.2D565.3BDBD19B3.5B$12.4B11.2A4.B432.D2.2D
.3D5.D3.D.D.D3.D3.D2.D4.2D445.D5.D8.D4.D5.D4.D.D566.2B3D20B.7B$13.4B10.
A.A2.4B430.D3.D.D7.D3.2D2.D3.D3.5D5.D445.3D2.3D5.D5.D5.D3.D2.D565.5BD
29B2.B$14.4B10.A7B15.2A234.3D2.5D3.D4.3D2.5D4.D3.3D140.D3.D.D7.D3.D3.
D3.D6.D2.D3.D448.D.D6.D6.D5.D3.5D563.10B.25B.B2A$15.4B11.6B8.BA5.A234.
D3.D.D6.2D3.D3.D3.D5.2D2.D3.D139.D3.D.5D2.3D3.3D4.D6.D3.3D445.D3.D.D5.
D7.D5.D6.D563.4B4.2B3.26B2A$16.4B10.7B3.4BABA.BA.A234.D5.D7.D3.D3.D3.
D4.D.D6.D625.3D2.5D.D7.D4.3D5.D562.4B10.24B.2B$17.4B.B5.17B2A.B2A236.
3D2.3D5.D4.4D3.D3.D2.D5.D1220.4B12.23B$18.31B241.D.D7.D7.D3.D3.5D3.D1221.
2A14.24B$18.31B237.D3.D.D7.D7.D3.D6.D3.D143.3D2.5D2.3D5.D2.5D4.D3.3D1041.
A16.23B$18.30B239.3D2.5D2.3D3.3D4.D6.D2.5D139.D3.D.D5.D3.D3.2D4.D5.2D
2.D3.D445.3D2.D3.D8.3D2.5D2.3D4.D554.3A17.24B9.B$18.28B420.D5.D9.D2.D
.D4.D4.D.D6.D444.D3.D.D3.D7.D3.D3.D3.D3.D2.2D554.A19.23B9.2B$19.26B422.
3D2.3D6.D2.D2.D4.D3.D2.D4.2D445.D5.D3.D11.D3.D7.D3.D573.25B7.3B$17.2A
B2.22B426.D.D7.D3.5D3.D3.5D5.D445.3D2.D.D.D.5D4.D4.D6.D4.D573.24B7.4B
$16.A.AB3.21B422.D3.D.D6.D7.D4.D6.D2.D3.D448.D.D.D.D9.D5.D5.D5.D574.23B
6.4B$16.A5.23B422.3D2.5D.5D4.D4.D6.D3.3D445.D3.D.2D.2D8.D6.D4.D6.D574.
25B3.4B$15.2A5.22B908.3D2.D3.D7.5D3.D3.5D2.3D575.29B$21.23B1524.8B2.16B
$21.22B1526.7B3.14B$22.19B.3B422.3D2.D3.D8.3D2.5D2.3D4.D443.4B618.5B5.
13B$22.16B5.2A421.D3.D.D3.D7.D3.D3.D3.D3.D2.2D444.4B619.2B7.12B$22.14B
7.A422.D5.D3.D11.D3.D7.D3.D445.4B626.12B$22.14B8.3A420.3D2.D.D.D.5D4.
D4.D6.D4.D446.4B621.15B$21.14B11.A256.A166.D.D.D.D9.D5.D5.D5.D447.4B619.
16B$20.15B257.A9.A.A161.D3.D.2D.2D8.D6.D4.D6.D448.4B618.15B$21.2A13B256.
3A7.A.A162.3D2.D3.D7.5D3.D3.5D2.3D448.4B617.14B$21.2A14B258.A5.2A.3A648.
4B614.2AB.10B$22.14B258.2A6.B4.A648.4B22.A589.A.AB2.7B$22.11B261.5B.B
2AB3A650.4B12.2A5.3A589.A6.6B$23.8B265.3B.B2A.A653.4B10.B2AB3.A591.2A
9.2B$23.8B263.9B656.4B9.3B4.2A$23.7B4.2A255.B.9B163.4B38.4B449.4B.2B2.
2B2.B2.5B$24.6B4.A255.2A3B2A5B164.4B36.4B451.18B$24.6B.BA.A255.2A3B2A
5B165.4B34.4B452.17B2A$23.7B.B2A257.2B.8B166.4B32.4B453.12B2A3B2A$24.
8B263.7B167.4B30.4B454.12B2A2B.B871.D3.D.5D.5D2.3D2.5D3.D4.3D2.5D$17.
A6.7B256.B3.11B168.4B25.B2.4B453.2AB.14B873.2D2.D.D5.D5.D3.D3.D4.2D3.
D3.D5.D$17.3A4.7B255.A2B.13B168.4B22.8B453.A.AB4.7B877.D.D.D.D5.D5.D2.
2D3.D5.D3.D2.2D4.D$8.A11.A2.7B4.B250.A.A16B168.4B19.9B454.A8.7B876.D2.
2D.3D4.3D2.D.D.D3.D5.D3.D.D.D3.D$8.3A8.2A3.6B.B.2BA250.AB.15B169.4B7.
2A9.8B454.2A8.7B876.D3.D.D9.D.2D2.D3.D5.D3.2D2.D2.D$11.A7.15BA.A252.16B
169.4B5.B2AB7.8B7.A456.9B875.D3.D.D5.D3.D.D3.D3.D5.D3.D3.D.D$10.2A3.B
5.12B.BA254.16B169.4B5.3B6.10B5.A.A454.11B874.D3.D.5D2.3D3.3D4.D4.3D3.
3D2.D$10.8B2.13B256.18B169.4B3.B.B7.9B5.2BAB444.2A8.11B$12.21B257.17B
170.4B.6B6.7B7.2B446.A9.10B$12.20B258.18B170.10B4.9B5.4B446.A.AB4.14B
$11.19B260.19B161.2A7.23B3.4B448.2AB.17B$9.21B261.12B2A5B161.A8.23B2.
2BA4B447.20B$7.24B261.11B2A5B161.A.AB6.22B.2BABA4B446.20B$7.2BD14B4.4B
261.18B161.2AB.3B2.25BABA3B448.20B$6.3BDBD4B.6B6.4B259.20B162.33BA4B447.
21B$7.2B3D4B2.B.5B5.4B258.20B162.38B445.23B$6.5BD4B7.2A6.4B258.B.18B162.
32BA4B443.19B.B.B.B2A$5.10B8.A8.4B258.20B.B158.32BABA3B443.2BD15B6.BA
.A893.A$4.4B16.3A6.4B258.18B.B2A155.31B.2BABA4B441.3BDBD4B.9B8.A893.3A
$4.3B19.A7.4B255.22B2A153.19B2.12B2.2BA4B443.2B3D4B2.7B9.2A878.A16.A$
2.4B29.4B254.2A.17B.2B154.2BD15B3.11B3.4B445.5BD4B2.7B889.3A13.2A$2.2A
32.4B254.A3.15B156.3BDBD4B.7B5.9B5.4B443.10B4.6B892.A12.4B$3.A33.4B250.
3A5.9B.4B157.2B3D4B2.6B7.7B7.2B442.4B10.7B879.2A10.2A8.2A4.B2A$3A35.4B
249.A7.8B3.4B155.5BD4B3.6B5.9B5.2BAB440.4B12.6B880.A10.5B4.B2AB2.BA.A
$A38.4B258.5B5.4B153.10B6.4B5.10B5.A.A439.4B13.7B879.A.AB9.4B3.B.B3.B
2A$40.4B257.6B2.7B151.4B12.B2A2B6.8B7.A439.4B15.5B881.2AB.3B4.13B.3B$
41.4B256.15B150.4B14.2A.B2A5.8B445.4B16.6B882.7B.17B$42.4B256.2B.12B148.
4B18.BA.A4.9B443.4B15.9B881.25B$300.4B2.14B144.4B22.A6.8B442.3B16.2A.
7B881.25B$300.2A3.16B142.4B23.2A7.B2.4B441.2B18.A5.4B879.26B$301.A3.17B
140.4B37.4B440.B16.3A7.4B876.28B$298.3A4.17B140.3B39.4B456.A10.4B873.
18B.B.9B$298.A7.17B139.2B41.4B467.4B872.2BD15B2.10B.BA$299.2A5.17B139.
B514.4B870.3BDBD4B.7B3.11BA.A$300.A5.18B654.4B870.2B3D4B2.7B3.6B.B.2B
A$300.A.AB3.18B654.4B868.5BD4B4.2B2A3.7B4.B$301.2AB.19B656.4B866.10B3.
4B2A4.7B$303.21B657.4B864.4B10.2A8.7B$303.20B659.4B863.3B12.A8.8B$304.
19B660.4B860.4B10.3A8.7B.B2A$303.20B1524.2A12.A11.6B.BA.A$301.22B1525.
A24.6B4.A$299.24B.2B1519.3A24.7B4.2A$299.2BD23B2A1518.A21.2A2.8B$298.
3BDBD19B.B2A1539.A.A12B12.B$299.2B3D4B.14B2.B1540.A3.11B11.2B$298.5BD
4B2.14B1541.2A3.4B2A5B10.3B$297.10B2.9B.6B1546.3B2A5B9.4B$296.4B9.11B
2.4B1545.10B8.4B$296.3B9.13B2.4B1545.9B7.4B$294.4B10.13B3.4B1544.9B6.
4B$294.2A11.13B5.4B1543.8B6.4B$295.A10.14B6.4B1543.8B4.4B$292.3A11.13B
8.4B1543.6B4.4B$292.A13.13B9.3B1543.6B3.4B$306.13B10.2B1543.6B2.4B$307.
11B12.B1542.7B.4B$1873.6B.4B$1874.9B$1874.8B$1873.8B$1873.7B$1873.6B$
1872.7B$1872.7B$1867.3B.8B$1866.13B$1865.14B$1864.15B$1864.14B$1865.13B
$1865.14B$1866.12B$955.D3.D.D3.D2.3D4.D3.5D3.D4.3D3.3D867.3B2A3B$955.
2D2.D.D3.D.D3.D2.2D5.D4.2D3.D3.D.D3.D867.BA2BA2B$955.D.D.D.D3.D5.D3.D
5.D5.D7.D.D2.2D869.2AB$955.D2.2D.D.D.D3.2D4.D5.D5.D6.D2.D.D.D$955.D3.
D.D.D.D5.D3.D5.D5.D5.D3.2D2.D$955.D3.D.2D.2D.D3.D3.D5.D5.D4.D4.D3.D$955.
D3.D.D3.D2.3D3.3D4.D4.3D2.5D2.3D4$956.3D2.5D.5D.5D3.D6.D$292.D3.D.D3.
D2.3D4.D3.5D3.D4.3D3.3D617.D3.D.D9.D3.D4.2D5.2D$292.2D2.D.D3.D.D3.D2.
2D5.D4.2D3.D3.D.D3.D616.D5.D8.D4.D5.D4.D.D$292.D.D.D.D3.D5.D3.D5.D5.D
7.D.D2.2D617.3D2.3D5.D5.D5.D3.D2.D$292.D2.2D.D.D.D3.2D4.D5.D5.D6.D2.D
.D.D620.D.D6.D6.D5.D3.5D$292.D3.D.D.D.D5.D3.D5.D5.D5.D3.2D2.D616.D3.D
.D5.D7.D5.D6.D$292.D3.D.2D.2D.D3.D3.D5.D5.D4.D4.D3.D617.3D2.5D.D7.D4.
3D5.D$292.D3.D.D3.D2.3D3.3D4.D4.3D2.5D2.3D2$969.4B$970.4B$293.3D2.5D2.
3D3.3D2.5D.5D4.D639.4B$292.D3.D.D5.D3.D.D3.D3.D7.D3.2D640.4B$292.D5.D
9.D5.D3.D6.D3.D.D641.4B$293.3D2.3D6.D5.D4.D5.D3.D2.D642.4B$296.D.D7.D
5.D5.D4.D4.5D137.3D2.5D2.3D3.3D2.5D.5D2.3D466.4B$292.D3.D.D6.D5.D6.D3.
D8.D137.D3.D.D5.D3.D.D3.D3.D3.D5.D3.D465.4B$293.3D2.5D.5D.5D3.D3.D8.D
137.D5.D9.D.D3.D3.D3.D5.D3.D465.5B$470.3D2.3D5.2D3.4D3.D4.3D3.4D464.9B
$473.D.D9.D5.D3.D7.D5.D464.9B$469.D3.D.D5.D3.D5.D3.D3.D3.D5.D464.9B$470.
3D2.5D2.3D3.3D4.D4.3D3.3D464.10B$301.4B667.12B$302.4B656.2A8.13B$303.
4B656.A9.11B$304.4B174.A480.A.AB4.12B865.D3.D.5D.5D2.3D2.5D2.3D2.5D$305.
4B173.3A479.2AB.15B865.2D2.D.D9.D.D3.D3.D3.D3.D.D$306.4B175.A480.17B865.
D.D.D.D8.D2.D2.2D3.D7.D.D$307.4B173.2AB479.17B865.D2.2D.3D5.D3.D.D.D3.
D5.2D3.3D$308.4B172.4B479.17B.B862.D3.D.D6.D4.2D2.D3.D7.D5.D$309.4B8.
A163.4B477.19B2A861.D3.D.D5.D5.D3.D3.D3.D3.D.D3.D$302.2A6.4B5.3A163.5B
474.19B.B2A861.D3.D.5D.D6.3D4.D4.3D3.3D$303.A7.4B3.A166.5B8.2B462.19B
4.B$303.A.AB4.4B3.2A164.9B4.4B461.2BD16B$304.2AB.2B.5B.3B159.B4.9B4.4B
460.3BDBD4B.9B$306.12B160.2AB.11B3.6B460.2B3D4B2.7B$306.14B158.2A22B459.
5BD4B2.7B$306.14B159.B.22B457.10B4.6B$307.14B151.2A8.22B455.4B10.7B$308.
14B151.A7.24B454.3B12.6B$298.2A8.13B152.A.AB4.25B451.4B13.7B887.A$299.
A9.11B154.2AB.29B450.2A16.5B888.3A$299.A.AB4.14B155.32B450.A16.6B873.
A16.A$300.2AB.18B154.27B2.4B446.3A15.9B872.3A13.2A$302.20B155.26B3.4B
445.A17.2A.7B874.A12.4B$302.19B155.26B5.4B463.A5.4B860.2A10.2A8.2A4.B
2A$303.20B151.25B9.4B459.3A7.4B860.A10.5B4.B2AB2.BA.A$302.22B148.27B10.
4B458.A10.4B859.A.AB9.4B3.B.B3.B2A$300.23B149.2BD26B9.3B470.4B859.2AB
.3B4.13B.3B$298.24B149.3BDBD4B.13B4.2A10.2B471.4B860.7B.17B$298.2BD22B
149.2B3D4B.8B3.B5.A485.4B859.25B$297.3BDBD4B.10B2.4B147.5BD4B.8B10.3A
483.4B859.25B$298.2B3D4B2.7B5.4B145.10B.9B12.A484.4B857.26B$297.5BD4B
2.8B5.4B143.4B6.10B.2B496.4B854.28B$296.10B2.11B4.4B142.3B5.14B2A496.
4B851.18B.B.9B$295.4B9.11B5.4B139.4B5.15B2A1351.2BD15B2.10B.BA$295.3B
11.11B5.4B138.2A6.17B1351.3BDBD4B.7B3.11BA.A$293.4B11.B.10B6.4B138.A7.
13B1355.2B3D4B2.7B3.6B.B.2BA$293.2A12.2B.9B8.3B135.3A11.10B1354.5BD4B
4.2B2A3.7B4.B$294.A9.2B.12B9.2B135.A13.11B1352.10B3.4B2A4.7B$291.3A9.
2A13B11.B149.10B1352.4B10.2A8.7B$291.A11.2A13B162.8B1353.3B12.A8.8B$304.
2B.13B163.3B1353.4B10.3A8.7B.B2A$308.6B4.2A164.4B1351.2A12.A11.6B.BA.
A$318.A167.2A1352.A24.6B4.A$319.3A164.A1350.3A24.7B4.2A$321.A165.3A1347.
A26.8B$489.A1374.8B$1863.11B$1863.14B$1862.2A14B$1862.2A13B$1861.15B$
1862.16B$1863.15B$1863.16B$1863.17B$1853.2A8.17B$1854.A7.19B$1854.A.A
B4.20B$1855.2AB5.21B8.B$1856.5B.23B6.2B$1857.29B4.3B$1857.31B.4B$1858.
34B$1858.33B$1858.32B$1856.2AB.29B$1855.A.AB3.27B$1855.A7.B5.20B$1854.
2A14.18B$1868.14B.4B$1865.2A.14B3.B$1865.A.A13B$1866.AB.8B.5B$1870.5B
6.2A$1872.3B6.A$960.3D2.5D2.3D3.3D2.5D8.3D874.B8.3A$959.D3.D.D5.D3.D.
D3.D3.D9.D888.A$959.D5.D9.D5.D3.D9.D$960.3D2.3D6.D4.2D4.D3.5D.4D$963.
D.D7.D7.D3.D9.D3.D$959.D3.D.D6.D4.D3.D3.D9.D3.D$960.3D2.5D.5D2.3D4.D10.
3D6$987.A$985.3A$984.A$471.3D2.5D4.D3.3D2.5D.5D2.3D474.2A$470.D3.D.D7.
2D2.D3.D3.D3.D5.D3.D456.2A12.5B$470.D5.D6.D.D6.D3.D3.D5.D3.D457.A11.4B
$471.3D2.3D3.D2.D4.2D4.D4.3D3.4D457.A.AB7.6B$474.D.D5.5D5.D3.D7.D5.D458.
2AB.3B3.7B$470.D3.D.D8.D2.D3.D3.D3.D3.D5.D460.16B$471.3D2.5D4.D3.3D4.
D4.3D3.3D461.17B$972.17B$971.19B$969.17B.4B$967.19B2.4B$500.A466.2BD15B
4.4B$498.3A465.3BDBD4B.7B6.4B$497.A469.2B3D4B2.6B7.4B$484.A7.4B.2A467.
5BD4B2.6B8.4B$484.3A3.9B466.10B3.5B10.3B$487.A2.7B467.4B8.9B9.2B$486.
2A2.9B465.3B9.2AB4.2A10.B$486.14B462.4B11.A5.A$488.12B462.2A10.3A7.3A
$487.4B2A8B462.A10.A11.A$488.2BA2BA9B457.3A$490.B2A12B455.A$490.16B$489.
16B$489.14B$490.13B$489.13B$487.2AB.11B$486.A.AB.11B$486.A4.10B$485.2A
5.2B.6B$495.7B$479.A12.10B$479.3A8.13B$482.A6.15B$469.2A10.2A6.16B$470.
A10.5B3.12B.4B$470.A.AB9.4B2.13B.4B$471.2AB.3B4.20B2.4B$473.7B.23B.4B
$473.28BA8B$474.26BABA8B$473.27BABA4B.3B$471.30BA4B3.2B445.D3.D.D3.D2.
3D4.D3.5D3.D4.3D3.3D$469.18B.B3.B.2B3.5B6.B445.2D2.D.D3.D.D3.D2.2D5.D
4.2D3.D3.D.D3.D$469.2BD13B6.3B7.B454.D.D.D.D3.D5.D3.D5.D5.D7.D.D2.2D$
468.3BDBD4B.6B6.B2AB5.3B453.D2.2D.D.D.D3.2D4.D5.D5.D6.D2.D.D.D$469.2B
3D4B2.B.5B5.2A6.B2AB452.D3.D.D.D.D5.D3.D5.D5.D5.D3.2D2.D$468.5BD4B7.2A
14.2A453.D3.D.2D.2D.D3.D3.D5.D5.D4.D4.D3.D$467.10B8.A470.D3.D.D3.D2.3D
3.3D4.D4.3D2.5D2.3D$466.4B16.3A$466.3B19.A$464.4B$464.2A491.3D2.5D2.3D
3.3D2.5D2.3D4.D6.D$465.A490.D3.D.D5.D3.D.D7.D3.D3.D2.2D5.2D$462.3A491.
D5.D9.D.D7.D7.D3.D4.D.D$462.A494.3D2.3D5.2D2.4D4.D6.D4.D3.D2.D$960.D.
D9.D.D3.D3.D5.D5.D3.5D$956.D3.D.D5.D3.D.D3.D3.D4.D6.D6.D$957.3D2.5D2.
3D3.3D4.D3.5D2.3D5.D4$957.3D2.D3.D8.3D2.5D2.3D4.D$956.D3.D.D3.D7.D3.D
3.D3.D3.D2.2D$956.D5.D3.D11.D3.D7.D3.D$957.3D2.D.D.D.5D4.D4.D6.D4.D$960.
D.D.D.D9.D5.D5.D5.D$956.D3.D.2D.2D8.D6.D4.D6.D$957.3D2.D3.D7.5D3.D3.5D
2.3D2$966.4B$967.4B$968.4B$969.4B$970.4B$971.4B$972.4B$973.4B$974.4B10.
2A$975.4B8.A.A$968.2A6.4B5.3A.A.AB$969.A7.4B3.A5.2AB.2B$969.A.AB4.4B3.
2A6.5B$970.2AB.2B.5B.3B6.7B$972.12B8.7B$972.14B6.7B$972.14B3.10B$973.
14B.13B5.2A$974.28B4.A$964.2A8.24B.3B.BA.A$965.A9.11B.15B.B2A$965.A.A
B4.31B$966.2AB.35B$968.34B2A4.2A$968.34B2A5.A$969.35B2.3A$968.38BA$966.
39B$964.41B$964.2BC38B$963.3BCBC4B.31B$964.2B3C4B2.31B$963.5BC4B2.31B
$962.10B2.33B$961.4B9.34B$960.4B11.21B.12B$959.4B11.B.20B3.6B.4B$958.
4B11.2B.19B6.2B4.4B$465.3D2.5D4.D5.D2.5D2.3D4.D454.4B9.2B.22B13.4B$464.
D3.D.D7.2D4.2D4.D3.D3.D2.2D453.4B9.2A23B15.4B$464.D5.D6.D.D3.D.D4.D3.
D3.D3.D453.3B10.2A21B18.4B$465.3D2.3D3.D2.D2.D2.D4.D4.4D3.D453.2B12.2B
.19B19.4B$468.D.D5.5D.5D3.D7.D3.D453.B17.17B21.4B$464.D3.D.D8.D5.D4.D
7.D3.D476.10B24.4B$465.3D2.5D4.D5.D4.D4.3D3.3D475.10B25.4B$978.11B26.
3B$974.A.2A2B.8B27.2B$972.3AB2AB2.7B29.B$971.A4.B4.7B$972.3A.2A4.5B$481.
2AB490.A.A5.5B$479.BA2BA2B488.A.A6.2B.B2A$478.3B2A3B489.A10.BA.A$476.
12B501.A$475.14B500.2A$475.13B$474.14B$474.15B$475.14B$476.13B$477.3B
.8B$482.7B$482.7B$483.6B$483.7B$483.8B$484.8B$484.9B$483.6B.4B$483.7B
.4B$484.6B2.4B$484.6B3.4B$484.6B4.4B$483.8B4.4B$482.8B6.4B$482.9B6.4B
$482.9B7.4B$481.10B8.4B$481.3B2A5B9.3B$475.2A3.4B2A5B10.2B$476.A3.11B
11.B$476.A.A12B$471.2A4.2A2.8B$472.A9.7B4.2A$472.A.AB7.6B4.A$473.2AB.
3B3.6B.BA.A$475.14B.B2A$475.16B$476.14B$475.16B$473.18B$471.19B$471.2B
D15B$470.3BDBD4B.7B$471.2B3D4B2.6B$470.5BD4B3.6B$469.10B6.4B$468.4B12.
B2A2B$468.3B14.2A.B2A$466.4B18.BA.A$466.2A23.A$467.A23.2A$464.3A$464.
A48$463.3D2.5D4.D2.5D.5D3.D4.3D3.3D$462.D3.D.D7.2D6.D3.D4.2D3.D3.D.D3.
D$462.D5.D6.D.D5.D4.D5.D7.D5.D$463.3D2.3D3.D2.D4.D5.D5.D6.D4.2D$466.D
.D5.5D2.D6.D5.D5.D7.D$462.D3.D.D8.D2.D7.D5.D4.D4.D3.D$463.3D2.5D4.D2.
D7.D4.3D2.5D2.3D5$495.A$495.3A$498.A$497.2AB6.2A$497.5B4.A$499.3B.BA.
A$497.5B.B2A$484.A11.8B$465.BA17.3A8.9B$464.BABA19.A4.12B$464.BABA13.
2A3.2A2.13B.2B$465.BA2B12.A.A2.22B$463.5B14.AB4.20B$462.9B2.6B.3B4.22B
$462.22B2.23B$463.46B$462.18B2A28B$460.20B2A29B$458.52B$458.2BD49B$457.
3BDBD20B2.26B$458.2B3D17B.B2.27B$457.5BD16B6.26B$456.21B9.26B$455.4B5.
14B8.27B$455.3B4.17B7.2A6.15B.4B$453.4B5.2A2.14B7.A7.14B2.4B$453.2A8.
A2.15B3.3A9.9B7.4B$454.A5.3A3.15B3.A12.5B11.3B$451.3A6.A6.15B17.5B10.
2B$451.A16.13B21.2A11.B$470.5B3.2B22.A$468.6B3.2B24.3A$468.2A.B4.B2AB
25.A$469.A7.2A$466.3A$466.A46$465.3D2.5D.5D.5D.5D3.D5.D3.5D$464.D3.D.
D5.D9.D3.D4.2D4.2D3.D$464.D5.D5.D8.D4.D5.D5.D3.D$465.3D2.3D4.3D4.D5.D
5.D5.D4.3D$468.D.D9.D2.D6.D5.D5.D7.D$464.D3.D.D5.D3.D.D7.D5.D5.D3.D3.
D$465.3D2.5D2.3D2.D7.D4.3D3.3D3.3D4$465.3D2.5D2.3D3.3D2.5D8.3D$464.D3.
D.D5.D3.D.D3.D3.D9.D3.D$464.D5.D9.D5.D3.D9.D3.D$465.3D2.3D6.D5.D4.D3.
5D2.3D$468.D.D7.D5.D5.D9.D3.D$464.D3.D.D6.D5.D6.D9.D3.D$465.3D2.5D.5D
.5D3.D10.3D7$486.2AB$484.BA2BA2B$483.3B2A3B$481.12B$480.14B$480.13B$479.
14B$479.15B$480.14B$481.13B$482.3B.8B$487.7B$487.7B$488.6B$488.7B$488.
8B$489.8B$489.9B$488.6B.4B$488.7B.4B$489.6B2.4B$489.6B3.4B$489.6B4.4B
$488.8B4.4B$487.8B6.4B$487.9B6.4B$487.9B7.4B$486.10B8.4B$486.3B2A5B9.
4B$480.2A3.4B2A5B10.3B$481.A3.11B11.2B$481.A.A12B12.B$482.2A2.8B$487.
7B4.2A$488.6B4.A$488.6B.BA.A$487.7B.B2A$488.8B$481.A6.7B$481.3A4.7B$472.
A11.A2.7B4.B$472.3A8.2A3.6B.B.2BA$475.A7.15BA.A$474.2A3.B5.12B.BA$474.
8B2.13B$476.21B$476.20B$475.19B$473.21B$471.24B$471.2BD14B4.4B$470.3B
DBD4B.6B6.4B$471.2B3D4B2.B.5B5.4B$470.5BD4B7.2A6.4B$469.10B8.A8.4B$468.
4B16.3A6.4B$468.3B19.A7.4B$466.4B29.4B$466.2A32.4B$467.A33.4B$464.3A35.
4B$464.A38.4B$504.4B$505.4B$506.3B$507.2B$508.B38$472.3D2.5D2.3D5.D2.
5D3.D4.3D$471.D3.D.D5.D7.2D4.D4.2D3.D3.D$471.D5.D5.D6.D.D4.D5.D3.D3.D
$472.3D2.3D3.4D2.D2.D4.D5.D4.4D$475.D.D5.D3.D.5D3.D5.D7.D$471.D3.D.D5.
D3.D4.D4.D5.D7.D$472.3D2.5D2.3D5.D4.D4.3D3.3D10$499.A$488.B8.3A$487.3B
6.A$485.5B6.2A$481.AB.8B.5B$480.A.A13B$480.2A.14B3.B$483.14B.4B$469.2A
14.18B$470.A7.B5.20B$470.A.AB3.27B$471.2AB.29B$473.32B$473.33B$473.34B
$472.31B.4B$472.29B4.3B$471.5B.23B6.2B$470.2AB5.21B8.B$469.A.AB4.20B$
469.A7.19B$468.2A8.17B$478.17B$478.16B$478.15B$477.16B$476.15B$477.2A
13B$477.2A14B$478.14B$478.11B$479.8B$468.2A9.8B$469.A9.7B4.2A$469.A.A
B7.6B4.A$470.2AB.3B3.6B.BA.A$472.14B.B2A$472.16B$473.14B$472.16B$470.
18B$468.19B$468.2BD15B$467.3BDBD4B.7B$468.2B3D4B2.6B$467.5BD4B3.6B$466.
10B6.4B$465.4B12.B2A2B$465.3B14.2A.B2A$463.4B18.BA.A$463.2A23.A$464.A
23.2A$461.3A$461.A26$465.3D2.5D.5D.5D.5D4.D3.3D$464.D3.D.D9.D5.D3.D5.
2D2.D3.D$464.D5.D8.D5.D4.D4.D.D6.D$465.3D2.3D5.D5.D5.D3.D2.D4.2D$468.
D.D6.D5.D6.D3.5D5.D$464.D3.D.D5.D5.D7.D6.D2.D3.D$465.3D2.5D.D5.D7.D6.
D3.3D4$465.3D2.5D2.3D3.3D2.5D8.3D$464.D3.D.D5.D3.D.D3.D3.D9.D3.D$464.
D5.D9.D5.D3.D9.D3.D$465.3D2.3D6.D5.D4.D3.5D2.3D$468.D.D7.D5.D5.D9.D3.
D$464.D3.D.D6.D5.D6.D9.D3.D$465.3D2.5D.5D.5D3.D10.3D2$497.A$486.B8.3A
$485.3B6.A$483.5B6.2A$479.AB.8B.5B$478.A.A13B$478.2A.14B3.B$481.14B.4B
$467.2A14.18B$468.A7.B5.20B$468.A.AB3.27B$469.2AB.29B$471.32B$471.33B
$471.34B$470.31B.4B$470.29B4.3B$469.5B.23B6.2B$468.2AB5.21B8.B$467.A.
AB4.20B$467.A7.19B$466.2A8.17B$476.17B$476.16B$476.15B$475.16B$474.15B
$475.2A13B$475.2A14B$476.14B$476.11B$477.8B$477.8B$477.7B4.2A$478.6B4.
A$478.6B.BA.A$477.7B.B2A$478.8B$471.A6.7B$471.3A4.7B$462.A11.A2.7B4.B
$462.3A8.2A3.6B.B.2BA$465.A7.15BA.A$464.2A3.B5.12B.BA$464.8B2.13B$466.
21B$466.20B$465.19B$463.21B$461.24B$461.2BD14B4.4B$460.3BDBD4B.6B6.4B
$461.2B3D4B2.B.5B5.4B$460.5BD4B7.2A6.4B$459.10B8.A8.4B$458.4B16.3A6.4B
$458.3B19.A7.4B$456.4B29.4B$456.2A32.4B$457.A33.4B$454.3A35.4B$454.A38.
4B$494.4B$495.4B$496.4B$497.4B$498.4B$499.4B$500.4B$501.4B!

I wasn’t paying much attention to which conduits go where and these conduits are all spartan.

[confocaloid]

Crosspost from "Thread For Your Accidental Discoveries"; overlapped in Rule:TripleLife:

Code: Select all

x = 48, y = 39, rule = TripleLife
26.2F$26.F.F$28.F4.2F$24.4F.2F2.F2.F$24.F2.F.F.F.F.2F$27.F.F.F.F$28.
2F.F.F$32.F$G$.2G15.2F$2G17.F7.2F$19.F.F5.2F9.A$20.2F15.A.A$30.2A.2A
2.A.3A$18.A12.A.A.A.A4.A$16.3AF11.A2.A.A.A.A.A$15.A.3F9.A.A4.A.A.2A4.
2A$15.AG8.2A2.2A4.A.A8.A$2A14.2F7.2A9.A7.A.A$.A28.2F12.2A$.A.2A25.F$
2.A2.A25.3F$3.2A28.GA$18.2A12.A2.A$18.2A13.2A$6.2F$5.F.F5.2F$5.F7.2F$
4.2F2$18.F22.2A$14.2F.F.F.2A.2A2.2A10.A.A$13.F.F.F.F.2A.A2.A.A10.2A$
10.F2.F.F.F.F.2F3.2A.A.A$10.4F.2F2.FA.G3A2.A.2A3.2A3.4A$14.F4.FGA4.A.
A6.2A4.A2.A$10.2AF.F8.2A.A.A10.A3.2A$10.2A2F6.3A.A.2A11.2A$20.A!

Identical shift to the snark pair (might be of use for clearance issues)

Code: Select all

x = 431, y = 340, rule = LifeHistory
23$20.C63.C63.C63.C$21.C63.C63.C63.C$19.3C61.3C61.3C61.3C62$84.C63.C
63.C63.C$85.C63.C63.C63.C$83.3C61.3C61.3C61.3C51$298.2A$298.A.A$300.A
4.2A$296.4A.2A2.A2.A$296.A2.A.A.A.A.2A$298.BABABA.A$299.B2ABA.A$300.
2B.BA$299.3B$290.2A6.4B$291.A6.B2A3B$148.C63.C62.BC14.A.AB3.B2A3B36.C
33.A$149.C63.C61.2BC14.2AB.10B33.2BC31.A.A$147.3C61.3C61.3CB15.13B32.
3CB23.2A.2A2.A.3A$276.4B14.5B3D6B32.4B10.A12.A.A.A.A4.A$277.4B10.A2.
7BD7B32.4B7.3A12.A2.A.A.ABABA$278.4B7.3A4.4BD3B2.4B32.4B5.A12.BA.A4.A
.A.2A4.2A$279.4B5.A7.6B5.4B32.4B4.2A8.2A.B2A4.ABA4B4.A$280.4B4.2A5.9B
4.4B24.2A6.9B7.B2A2B4.3BA2B4.BA.A$281.9B4.4B4.2A5.4B24.A7.6B10.5B2.5B
4.B.B2A$282.6B5.4B5.A7.4B23.A.2A5.6B3.B2.2B2.5B.6B2.4B$282.4BD3B2.4B
7.3A5.4B23.A2.A4.4B.14BD14B$280.7BD7B10.A6.4B23.2AB3.5B2.13BDBDB2A9B$
280.5B3D6B19.4B23.9B3.2B2A9B3DA2BA9B$280.13B21.3B24.13B2A11BDB2A6B.4B
$278.2AB.10B23.2B25.34B3.4B$277.A.AB3.B2A4B25.B25.17B.B.12B6.4B$277.A
6.B2A3B53.15B5.11B7.4B$276.2A6.4B55.15B6.10B8.4B$285.3B56.13B8.11B7.
4B$286.2B.BA55.13B5.3B.8B.2A5.4B$285.B2ABA.A53.8B4.2A.2A2.2AB2.7BA.A
6.4B$284.BABABA.A53.6B6.2ABA2.A.A5.B.2B.2A8.3B$282.A2.A.A.A.A.2A50.5B
8.B3.2A.A.A2.3B2.B11.2B$282.4A.2A2.A2.A50.B.B8.A.4A2.A.2A2.B2AB2.4A8.
B$286.A4.2A53.3B7.2A4.A.A6.2A4.A2.A$284.A.A58.B2AB10.2A.A.A10.A3.2A$
284.2A60.2A8.3A.A.2A11.2A$356.A90$298.2A$298.A.A$300.A4.2A$296.4A.2A
2.A2.A$296.A2.A.A.A.A.2A$298.BABABA.A$299.B2ABA.A$300.2B.BA$299.3B$
290.2A6.4B$291.A6.B2A3B$291.A.AB3.B2A3B70.A$292.2AB.10B67.A.A$294.13B
59.2A.2A2.A.3A$294.5B3D6B46.A12.A.A.A.A4.A$291.A2.7BD7B43.3A12.A2.A.A
.ABABA$278.4B7.3A4.4BD3B2.4B32.4B5.A12.BA.A4.A.A.2A4.2A$279.4B5.A7.6B
5.4B32.4B4.2A8.2A.B2A4.ABA4B4.A$280.4B4.2A5.9B4.4B24.2A6.9B7.B2A2B4.
3BA2B4.BA.A$281.9B4.4B4.2A5.4B24.A7.2B14.5B2.5B4.B.B2A$282.6B5.4B5.A
7.4B23.A.2A5.B8.B2.2B2.5B.6B2.4B$282.4BD3B2.4B7.3A5.4B23.A2.A4.B5.13B
D14B$280.7BD7B10.A6.4B23.2AB3.2B5.13BDBDB2A9B$280.5B3D6B19.4B23.7B5.
2B2A9B3DA2BA9B$280.13B21.3B24.6B5.2B2A11BDB2A6B.4B$278.2AB.10B23.2B
25.34B3.4B$277.A.AB3.B2A4B25.B25.17B.B.12B6.4B$277.A6.B2A3B53.15B5.
11B7.4B$276.2A6.4B55.15B6.10B8.4B$285.3B56.13B8.11B7.4B$286.2B.BA55.
13B5.3B.8B.2A5.4B$285.B2ABA.A53.8B4.2A.2A2.2AB2.7BA.A6.4B$284.BABABA.
A53.6B6.2ABA2.A.A5.B.2B.2A8.3B$282.A2.A.A.A.A.2A50.5B8.B3.2A.A.A2.3B
2.B11.2B$282.4A.2A2.A2.A50.B.B8.A.4A2.A.2A2.B2AB2.4A8.B$286.A4.2A53.
3B7.2A4.A.A6.2A4.A2.A$284.A.A58.B2AB10.2A.A.A10.A3.2A$284.2A60.2A8.3A
.A.2A11.2A$356.A!

[wwei47]

What about acorn and multum in parvo having the same final population and glider count?

[confocaloid]

What about acorn and multum in parvo having the same final population and glider count?

That's certainly on-topic (although may or may not lead to further interesting mathematics):

Acorn

Code: Select all

#C Acorn
#C lifespan 5206 ticks, final population 633 alive cells including 13 escaping gliders
x = 7, y = 3, rule = B3/S23
bo$3bo$2o2b3o!

Multum in parvo

Code: Select all

#C Multum in parvo
#C lifespan 3933 ticks, final population 633 alive cells including 13 escaping gliders
x = 6, y = 4, rule = B3/S23
3b3o$2bo2bo$bo$o!

[Citation needed]

ColorfulGalaxy has a page on LifeWiki that records interesting numbers. You can find some entries that may interest you.

[confocaloid]

ColorfulGalaxy has a page on LifeWiki that records interesting numbers. You can find some entries that may interest you.

Many of entries in that page aren't really mathematical coincidences.
Many of entries in that page aren't related to Conway's Life or other cellular automata.
See the forum post viewtopic.php?p=196717#p196717

It isn't particularly hard to generate many "apparent coincidences" that are Life/CA-related, but which don't immediately lead to further interesting mathematics or Life/CA constructions, and are merely "numeric curiosities". For example:

• Did you know that the numbers 19 and 41, the last two periods for which an oscillator was discovered in Conway's Life, are largest prime factors of (2^9 + 1 = 513 = 3 x 3 x 3 x 19) and (2^10 + 1 = 1025 = 5 x 5 x 41) respectively?
• Did you know that the same two numbers 19 and 41 are primes that are concatenations of two squares, when written in decimal notation?
• ... primes such that the sum of the predecessor and successor primes is divisible by 5?
• ... primes sandwiched between two numbers having same number of divisors (another such prime number being 137)?

In contrast, what I'm looking for in this forum thread are primarily those mathematical coincidences that do lead to some further interesting observations, further mathematics, further constructions, or otherwise escape the state of being "merely a curiosity".

For example, when two apparently-unrelated moving reactions just so happen to move at the same simplified speed, that can be useful for making patterns moving at that speed (a coincidence within a speed-specific technology).

Likewise, when two apparently-unrelated stable conduits just so happen to perform the same conversion of one active object (in a specific location) into another active object (in a specific location), that can be useful because one conduit could then be replaced by another conduit, changing the clearance and/or the timing.

[confocaloid]

[...] 2c/11d in B2n3-e/S234c [...]

Along the same lines, I didn't see a reason why the following two reactions (found in a cellular automaton located midway between Life-like CA B3/S23 and B35/S23) must have the same simplified speed (orthogonal 4c/31 in both cases): [...]

Here is another example.

Is there an explanation of why there are two different period-328 mod-164 mechanisms in this CA? One of two mechanisms is stationary, and another is moving.

• There is a p656 mod164 statorless rotating oscillator (xp656_3t), which is 2-loopable so it is possible to make a p328 mod164 oscillator (xp328_yeonzzzz8oz7).
• There is a p328 mod164 diagonal 23c/328 puffer (yl164_1_18_091f29656b82b9db44b202dc0b0172a4).

As far as I can tell this is a coincidence, but I might be missing some explanation:

Code: Select all

x = 664, y = 641, rule = B34eqz6ei7c8/S234e5e
107bob3o$107b2o17$87b2o$84b3obo27$153bob3o$153b2o14$19bo$19bo$19bo$18b
o114b2o$18b2o110b3obo19$2o$bo$o$o$o4$199bob3o$199b2o14$65bo$65bo$65bo$
64bo114b2o$64b2o110b3obo19$46b2o$47bo$46bo$46bo$46bo4$245bob3o$245b2o
4$185bo$184bobo$184bobo$185bo2$187b2o$176b3o8b2o3$181bo$111bo68bobo$
111bo68b2o$111bo$110bo114b2o$110b2o110b3obo9$208bo$207bobo$207bobo$
208bo2$210b2o$199b3o8b2o3$204bo$92b2o78bo30bobo$93bo78bo30b2o$92bo79bo
$92bo$92bo83b2o$175bobo$176bo2$167b2o122bob3o$166bo2bo121b2o$167b2o$
171b2o$171b2o$231bo$230bobo$230bobo$231bo2$233b2o$222b3o8b2o3$227bo$
157bo37bo30bobo$157bo37bo30b2o$157bo37bo$156bo114b2o$156b2o41b2o67b3ob
o$198bobo$199bo2$190b2o$189bo2bo$190b2o$194b2o$194b2o7$245b3o2$251bo$
250b3o$138b2o78bo31b3o$139bo78bo31bo$138bo79bo32bobo$138bo110bo$138bo
83b2o28bo$221bobo27bo$222bo23b2obo$245b3o5b2o$213b2o31bo3bo2b3o81bob3o
$212bo2bo31b3o3bobo81b2o$213b2o26bo11b3o$217b2o21bo6b2ob2obo$217b2o20b
o2bo4b2obo$240bobo4bo$241bo6b2o$240b3o5b2o$240b3o$251b2o$250bo2bo$251b
2o3$240b2o$203bo35bo2bo$203bo36bobo$203bo37bo$202bo114b2o$202b2o110b3o
bo19$184b2o$185bo$184bo$184bo$184bo4$383bob3o$383b2o14$249bo$249bo$
249bo$248bo114b2o$248b2o110b3obo19$230b2o$231bo$230bo$230bo$230bo4$
429bob3o$429b2o14$295bo$295bo$295bo$294bo114b2o$294b2o110b3obo19$276b
2o$277bo$276bo$276bo$276bo4$475bob3o$475b2o14$341bo$341bo$341bo$340bo
114b2o$340b2o110b3obo19$322b2o$323bo$322bo$322bo$322bo4$521bob3o$521b
2o14$387bo$387bo$387bo$386bo114b2o$386b2o110b3obo19$368b2o$369bo$368bo
$368bo$368bo4$567bob3o$567b2o14$433bo$433bo$433bo$432bo114b2o$432b2o
110b3obo19$414b2o$415bo$414bo$414bo$414bo4$613bob3o$613b2o14$479bo$
479bo$479bo$478bo114b2o$478b2o110b3obo19$460b2o$461bo$460bo$460bo$460b
o4$659bob3o$659b2o14$525bo$525bo$525bo$524bo114b2o$524b2o110b3obo19$
506b2o$507bo$506bo$506bo$506bo19$571bo$571bo$571bo$570bo$570b2o19$552b
2o$553bo$552bo$552bo$552bo!
#C [[ THEME MCell ZOOM 2 X -90 Y -90 TRACKLOOP 328 23/328 23/328 ]]

[...]
EDIT 1 (2024-12-27): the ear is a 2-loopable p656 mod164 statorless rotating oscillator, endemic to this CA within the space of 2-state isotropic CA with range-1 Moore neighbourhood:

Code: Select all

x = 88, y = 20, rule = B34eqz6ei7c8/S234e5e
23bob3o55bob3o$23b2o58b2o17$3b2o$3obo!
#C [[ GRID THEME MCell ]]

[...]

[eRroR_6o6]

B34c5ae/S234e has a few oscillators, but two of them stand out for being the same period and having high periods, more than 100.
(By the way, this rule is known, and is called "SwirlyLife". I learned that the hard way, by finding out there was a thread for it while exploring it thinking it was new.)

P104

Code: Select all

x = 48, y = 45, rule = B34c5ae/S234e
23b2o$25bo$23b2o2$16b2o$15bo2bo$15bo2bo$15bo2bo$16b2o2$23b2o$25bo$8b3o
12b2o$7bo3bo$7bo3bo$8b3o3$32bo9bo$31bobo7bobo$3bobo7bobo15bobo7bobo$3b
obo7bobo$4bo9bo3$36b3o$35bo3bo$35bo3bo$22b2o12b3o$21bo$22b2o2$29b2o$
28bo2bo$28bo2bo$28bo2bo$29b2o2$22b2o$21bo$22b2o!

Much more natural P104

Code: Select all

x = 5, y = 4, rule = B34c5ae/S234e
b2o$o2bo$o2bo$bobo!

[hotcrystal0]

The repeat time of the speed tunnel (61) is the same as the lowest period where stable FNG suppression works.

[squareroot12621]

The repeat time of the speed tunnel (61) is the same as the lowest period where stable FNG suppression works.

I don't think so—Simkin's p60 is one tick faster than that.

[confocaloid]

Crosspost from "Thread For Your Accidental Discoveries"; overlapped in Rule:TripleLife: [...]

Identical shift to the snark pair (might be of use for clearance issues) [...]

Here is another coincidence, found by Tawal in viewtopic.php?p=209233#p209233

Two different Herschel-to-glider converters with description NE22T108; one of them has a transparent output glider lane:

Code: Select all

x = 44, y = 46, rule = DoubleB3S23
27.2A$27.A$24.A4.A2.2A$24.5A.A2.A$10.2A18.2A.A.2A$11.A10.4A.3A3.A2.A$
11.A.A8.A2.A.A3.2A.A$12.2A.B16.A.2A$13.3B16.A$12.B18.2A$12.2B$20.2B$
20.B$18.B.B$12.C5.2B$12.C.C$12.3C$14.C27.2A$42.A$40.A.A$40.2A2$5.2A$
6.A$3.3A35.2A$3.A38.A$41.A$40.A$41.3A$43.A5$35.2A$2.2B31.2A$.B.B$.B
17.2B$2B9.B7.B.B$10.B.B8.B$11.B.B.2B4.2B$9.B.B.B.B.B13.A$9.2B.B4.B12.
A.A$12.B.3B14.A$12.B.B$13.B!

[WhiteHawk]

While I wait for a computer repairman to try and fix my malfunctioning keyboard, here are some more CA-related mathematical coincidences not yet mentioned here.

Weak: The fact that there are two P177 oscillators in life with the same minipop of 104 cells.

Code: Select all

x = 109, y = 46, rule = B3/S23
16bo12bo$9b2o24b2o$8b3o3b2o14b2o3b3o49b2o$14b2ob2o8b2ob2o47bo8bo$16bo
12bo49bo8bobo3bo$79bo9b2o3bo$78b2o14bo$76bo$2bo40bo31bo4bo$b2o40b2o30b
o$b2o40b2o32b3o12bo$91bobo$91bobo$92bo$2b2o38b2o44b2o$2b2o38b2o43bo2b
o$o3bo36bo3bo22b3o16bo$3bo38bo32b2o11b2o$3bo38bo31bo2bo$75b2o$68b2o9b
o$69bo8bo2bo$66b3o9bo2bo$66bo12b2o13b2o12bo$93bo2bo9b3o$93bo2bo8bo$95b
o9b2o$3bo38bo55b2o$3bo38bo54bo2bo$o3bo36bo3bo39b2o11b2o$2b2o38b2o43bo
16b3o$2b2o38b2o40bo2bo$85b2o$82bo$81bobo$b2o40b2o36bobo$b2o40b2o37bo$
2bo40bo3$80bo$16bo12bo50bo3b2o$14b2ob2o8b2ob2o48bo3bobo$8b3o3b2o14b2o
3b3o48bo$9b2o24b2o49b2o$16bo12bo!

Moderate: The presence of two completely different p23 oscillators in EightLife which trigger the s8 condition.

Code: Select all

x = 52, y = 26, rule = B3/S238
11b4o26b2o$9b8o18bob2obobo4bo$8b10o17b2obobo4b3o$7b2o8b2o20b2o3bo$7b3o
6b3o25b2o$8b3o4b3o15b2o7b3o5b2o$10bo4bo18bo6b3o6bo$3b2o16b2o11bobo3b5o
3bobo$2b4o14b4o11b3obo5bob3o$b2ob2o14b2ob2o12b3o2bo2b3o$b2o2b2o12b2o2b
2o12b3obobob3o$3o20b3o11b3o2bo2b3o$3o20b3o9b3obo5bob3o$3o20b3o8bobo3b
5o3bobo$3o20b3o8bo6b3o6bo$b2o2b2o12b2o2b2o8b2o5b3o7b2o$b2ob2o14b2ob2o
14b2o$2b4o14b4o16bo3b2o$3b2o16b2o14b3o4bobob2o$10bo4bo21bo4bobob2obo$
8b3o4b3o24b2o$7b3o6b3o$7b2o8b2o$8b10o$9b8o$11b4o!

Moderate: The presence of four completely different p7 oscillators in regular life with minimum population of 28 cells

[roee.s]

I want to add three coincidences that have amazed me for years.
The first two are related to HighLife: First the fact that the two most useful technologies, the replicator and the shuttle, have basic period 24, and second that the replicator can react with a loaf producing the same result as happens in Life's Eater-3, but with a different sequence: (shown in B36-e/S23 to preserve life's reaction of a loaf with a glider)

Code: Select all

x = 85, y = 94, rule = B36-e/S23
4b2o$4b2o2$43b2o$43b2o$6bo$5bo$6bo$47bo$42b3o3bo$41bo$41bo$41bo2bo2bo$
47bo$47bo$40bo3b3o$41bo13bo$50b3o3bo$18bo30bo$17b3o29bo$16b2ob2o28bo2b
o2bo$15b2ob2o35bo$14b2ob2o36bo$15b3o30bo3b3o$16bo32bo4$68b2o$26b2o40b
2o$25bo2bo$25bobo$26bo3$54bo$53bo7b2o3bo$53b3o5b2o4b2o$65b2o$67bo14$
48b3o$48bo$49bo4$54b3o$54bo$55bo4$60b3o$60bo$61bo4$66b3o5b3o$56b2o8bo
7bob2o$56bobobobo5bo5b3o$56b2o23b2o$50b2o29bobo$49bobo31bo$49bo33b2o$
48b2o4$68bo$67bobo$66bo3bo$67bobo$67b3o4$65b2o$66bo$63b3o$63bo!

The last is that the loafer, the only natural spaceship apart from the glider that isn't c/2o, contains (and of course is named after) the loaf, which has 7 cells, and has speed c/7.