Thread for basic questions

[hkoenig]

If "methuselah" was Latin, then perhaps the plural would be "methuselae".

But it's not Latin (the giveaway is the final 'h'). How Semitic languages form plurals is an exercise for the student.

[rattlesnake]

Catagolue does not appear to automatically reorient guns at the moment, so please be aware of the convention when submitting patterns to the box:

1) The gliders travel to the lower right.
2) The pattern is in the last phase before a glider leaves the bounding box.
3) The width is greater than or equal to the height.

What is the reason for these conventions?

[GUYTU6J]

Catagolue does not appear to automatically reorient guns at the moment, so please be aware of the convention when submitting patterns to the box:

1) The gliders travel to the lower right.
2) The pattern is in the last phase before a glider leaves the bounding box.
3) The width is greater than or equal to the height.

What is the reason for these conventions?

See readme.txt on Jason Summer's page for Dieter and Peter’s gun collection.

EDIT: wait, why did the post above receive a like

[mniemiec]

Catagolue does not appear to automatically reorient guns at the moment, so please be aware of the convention when submitting patterns to the box:
1) The gliders travel to the lower right.
2) The pattern is in the last phase before a glider leaves the bounding box.
3) The width is greater than or equal to the height.

What is the reason for these conventions?

In any large pattern collection, it's much locate a sample pattern in the collection by doing a simple string comparison between its representation and that of every pattern in the collection. This is facilitated by having exactly one canonical representation of each pattern. It doesn't particularly matter WHAT convention is used, as long as there is an unambiguous convention. It's also usually better to have a convention that offers some additional mechanical advantages, as well, if possible.

[confocaloid]

EDIT: wait, why did the post above receive a like :roll:

Because it is a good question -- it is not at all obvious why these particular conventions exist / where they come from, and it seems interesting to know that. It seems a good idea to question non-obvious things and not just blindly follow rules.

By the way, it is still not obvious to me what is the reason to follow these conventions when submitting guns to Catagolue. As I understand, they were helpful in maintaining gun collections manually -- but now that guns are processed automatically, I think it should not be particularly important to submit them in any "canonical" form, as long as the submission is accepted and processed correctly.

[mniemiec]

By the way, it is still not obvious to me what is the reason to follow these conventions when submitting guns to Catagolue. As I understand, they were helpful in maintaining gun collections manually -- but now that guns are processed automatically, I think it should not be particularly important to submit them in any "canonical" form, as long as the submission is accepted and processed correctly.

For Catagolue to accept non-canonical forms, it would need to be able to convert such forms to canonical forms. It's easy to do that for oscillators and spaceships, because the algorithm for generating apgs of those is fairly easy. It's not so easy for guns.

[confocaloid]

It seems like there are many examples where Catagolue shows something different from what would be a canonical form of the gun according to conventions for other pattern collections. I just checked a few periods around 200 and found several examples.

I could not find any evidence that these conventions are "official" on Catagolue. The submission page does not mention them, for example.

If guns can indeed be submitted to Catagolue in any orientation/phase, and are accepted and processed anyway (as seems to be the case), then I do not see any reason to follow conventions for other pattern collections (although on the other hand I do not see any reason to not follow them).

Current gun_204 breaks (1):

Code: Select all

#C [[ GRID MAXGRIDSIZE 14 THEME Catagolue ]]
#CSYNTH gun_204 costs 1925 cells.
#C period 204 fullperiod 204 bbox 55 by 35
#CLL state-numbering golly
x = 55, y = 35, rule = LifeHistory
21.A$21.3A7.A$24.A5.A.A$23.2A4.2BAB$23.6B.2B$25.6B$4.2A18.8B$5.A
17.B.9B$5.A.AB14.11B$6.2AB11.B.6B2A2B.B2A$8.3B7.10B2A2B.BA.A$8.4B
3.2B.4BA9B4.A$2.2A5.12BA3BA6B4.2A$3.A5.14B4A3B.B2A$3.A.AB.3BA2B3A
4B3A2BA3B.BA.A4.2A$4.2AB.3B4A14B5.A3.A2.A$2A4.6BA3BA12B5.2A2.A.A.A
B$.A4.9BA4B.2B3.4B9.A.3A$.A.AB.2B2A10B7.4B9.B3A$2.2AB.2B2A6B.B10.
4B8.3B$4.11B14.4B5.2B$4.9B.B15.BABA3.3B$6.8B17.B2A2B.2AB9.2A$7.6B
19.A3BA2BAB8.A.A$6.2B.6B18.4B2A2B.B8.A$5.BA2B4.2A19.9BAB3.B.BA.2A$
5.A.A5.A20.9B3A.B2A.A.A$6.A7.3A17.10B2A2B2A.A.A$16.A17.9BA5B2.A.2A
$32.2AB.8BA3B4A2.A$31.A.AB.8BAB.BAB2.2A$31.A5.7B6.2A$30.2A5.A3B.2B
7.A$36.A3B9.A$35.B3A10.2A!

gun_216 also breaks (1):

Code: Select all

#C [[ GRID MAXGRIDSIZE 14 THEME Catagolue ]]
#CSYNTH gun_216 costs 1400 cells.
#C period 216 fullperiod 216 bbox 35 by 40
#CLL state-numbering golly
x = 35, y = 40, rule = LifeHistory
A9.A14.A$3A5.3A12.3A$3.A3.A14.A$2.2A.B.2A13.2A$2.7B3.3B4.5B$4.BAB
3.6B3.3B$3.2BA2B2.6B2.6B$2.2BABA2B2.13B$2.3BA3B.5BA8B$.4BA7B3A9B$.
4BA7B2A10B$2.3BA3B2.4BA9B$2.2BABA2B2.3BA8B.B2A$3.2BA2B3.3BA8B.BA.A
2.2A$4.BAB4.11B5.A2.A$2.7B3.5B.3BA5.3A2.A$2.2A.B.2A4.3B3.3BA7.3A$
3.A3.A5.3B4.3AB5.A$.A.A.A.A.A3.3B5.4B4.2A$.2A.A.A.2A2.2A.2A5.9B$4.
A.A5.2A.2A5.7B5.B$4.A.A6.BAB7.A7B2.2A$5.A5.ABAB6.BABA7BABA$10.4BA
5.2BABA9BA$10.BA2BAB4.3BA10B$8.B4ABA5.B2.10B$7.B4A2B5.2B4.7B$4.2A.
BA2BA6.3B3.9B$4.ABA2B2AB6.B2A2B2.2ABA4B$6.3B2A6.AB2A2B2.B2AB2A$4.A
BA2.B6.A.4B4.2A3B$4.2A8.4B.A7.3B$13.2B2ABA7.5B$13.2B2AB7.B2AB2A$
15.3B4.2A2.2A.AB2.2A$15.2B5.A2.B3.A.A2.A$23.7A.2A$30.A$25.4A.A$25.
A2.2A!

Current gun_102 breaks (3):

Code: Select all

#C [[ GRID MAXGRIDSIZE 14 THEME Catagolue ]]
#CSYNTH gun_102 costs 1599 cells.
#C period 102 fullperiod 102 bbox 39 by 41
#CLL state-numbering golly
x = 39, y = 41, rule = LifeHistory
22.A$20.3A$19.A6.A$19.2A3.3A$17.4B2.A8.A$12.AB3.2B4.2A5.3A$11.A.AB
.9B4.A$12.A4BA5B6.2A$13.B.2AB2A5B2.3AB$14.B2AB2A7B2A$14.12BABA$14.
3B2A9B$14.3BA9B$12.A2B.A.A8B$11.A.2A2.B2A7B$11.A7.4BA4B$10.2A8.2AB
A4B$19.2BABA3B$13.B6.9B$12.3A5.9B$11.5B6.3BABA2B$9.7BA4.4BAB2A8.2A
$9.7BAB3.4BA4B7.A$8.6B3AB4.7B2AB2.2A.A$7.2AB.2B2AB6.8BA.A.2BA$6.A.
AB2.B2A7.9BA3B$6.A6.3B5.9B2A3B$5.2A6.2B5.ABA12B$13.3B3.B2A7B2AB2AB
$13.B2A.4BA2.5B2AB2A.B$2A.2A7.BA2BA4B5.5BA4BA$2A.A8.2B2A4B4.9B.BA.
A$3.A.B3.2A8B5.2A4.2B3.BA$3.2A2B.3BA7B6.A2.4B$.2A2.A2BAB2A7B3.3A3.
2A$A2.AB2A12B3.A6.A$2A.A.AB3.7B.B2A.A3.3A$.A2.3AB2.7B.BA.A.2A2.A$.
A5.A4.2BAB5.A2.2A3.A$2.5A5.3BA5.2A5.2A$4.A8.3AB!

gun_189 also breaks (3):

Code: Select all

#C [[ GRID MAXGRIDSIZE 14 THEME Catagolue ]]
#CSYNTH gun_189 costs 2040 cells.
#C period 189 fullperiod 189 bbox 40 by 51
#CLL state-numbering golly
x = 40, y = 51, rule = LifeHistory
22.2A$3.2A5.2A5.BA2.A.A$2.B2AB3.B2AB3.B6A$3.2B5.2B4.2ABAB$4.2B3.2B
4.B5A$3.A2B3.2BA3.ABAB2AB$.2B2A2B.2B2A2B.2BAB2AB$.2B2ABA.AB2A2B.2B
A4B$2BA2B2A.2A2BA2B2.5B$.AB2A.A.A.2ABA2.2BA3B$.BABA.A.A.ABAB2.ABA
3B5.BA3.AB$4.BA3.AB5.3BABA2.BABA.A.A.ABAB$16.3BA2B2.AB2A.A.A.2ABA$
16.5B2.2BA2B2A.2A2BA2B$16.4BA2B.2B2ABA.AB2A2B$8.2A6.B2ABA2B.2B2A2B
.2B2A2B$9.A6.B2ABABA3.A2B3.2BA$9.A.AB4.5AB4.2B3.2B$10.2AB4.BAB2A4.
2B5.2B$12.B2A2B.3AB3.B2AB3.B2AB$11.2BABA3BA2B4.2A5.2A$12.BABAB2.5B
$11.BA.BA4.4B$11.2ABA.2A3.5B3.2A5.2A$7.2A.A.A.A.2A4.4B.2B2A5.A$7.A
.2A.A.A8.7B3.BA.A$13.2A9.8B.B2A$25.5B2A2B$11.4A10.5BABAB$10.A4.A8.
7BAB$10.2A2.2A7.8B$14.5B3.4B3.B.A$5.2A9.3B2.4B5.BAB$4.A.A8.9B6.3B$
4.A8.B.4BABAB6.A3BA$.2A.AB.B3.8B2AB5.3A.A.3A$2.A.A.2AB.10BAB4.A4.A
B3.A$2.A.A.2A14B5.4A.ABABA$.2A.A2.5B2A8B8.A.A.B2.2A$.A2.4A3BA2BA5B
.B2A3.2A.A.BAB2A2.A$2.2A2.BAB.2B2A6B.BA.A2.2A.A3BA.A.2A$4.2A6.7B5.
A6.A3B.A.A$4.A7.2B.4B5.2A6.4BA2.A$6.A9.4B12.A2B2.3A$5.2A10.4B12.4A
$18.4B11.2B2.A$19.4B6.2A.A.A.2A$20.4B5.A.2A.2A$21.3BA8.A3.3A$22.3B
A7.A.2A2.A$23.3AB7.A.A!

gun_184 breaks (2) and reports 34x30 (instead of expected 34x31). I do not know whether it would say 34x31 if the pattern was submitted in a different phase/orientation, or whether it would still say 34x30 no matter what.

Code: Select all

#C [[ GRID MAXGRIDSIZE 14 THEME Catagolue ]]
#CSYNTH gun_184 costs 1020 cells.
#C period 184 fullperiod 184 bbox 34 by 30
#CLL state-numbering golly
x = 34, y = 30, rule = LifeHistory
19.A$17.3A$16.A$16.2A$13.5B9.BA$12.4B10.2A.B$11.3A3B2.B6.B.2A$11.A
BA3B.4B5.AB$9.4BA9B2.B$8.4B2A9B.4B$8.4B2ABA6B.5B$6.6BA3BA12B$5.9BA
B2A13B$4.9B2ABA15B$4.10B2A15B$4.10B3A12B$2.2AB.6BA4BA10B2.B2A$.A.A
B3.3BA3B2ABA4B2A5.3AB$.A5.4BAB2ABAB2A3B2A4.A.2AB$2A4.6BA5BA5B4.A.A
.2B$7.16B5.A2.A$7.16B6.2A$8.2B.11B$10.2BA7B$9.2BABA5B$8.2BA6B$5.AB
2.BA3B2AB$4.BA.A.7BA$4.A.AB3.A3BA$5.BA5.3AB!

Catagolue does not appear to automatically reorient guns at the moment, so please be aware of the convention when submitting patterns to the box:

1) The gliders travel to the lower right.
2) The pattern is in the last phase before a glider leaves the bounding box.
3) The width is greater than or equal to the height.

What is the reason for these conventions?

See readme.txt on Jason Summer's page for Dieter and Peter’s gun collection.

EDIT: wait, why did the post above receive a like :roll:

By the way, it is still not obvious to me what is the reason to follow these conventions when submitting guns to Catagolue. As I understand, they were helpful in maintaining gun collections manually -- but now that guns are processed automatically, I think it should not be particularly important to submit them in any "canonical" form, as long as the submission is accepted and processed correctly.

For Catagolue to accept non-canonical forms, it would need to be able to convert such forms to canonical forms. It's easy to do that for oscillators and spaceships, because the algorithm for generating apgs of those is fairly easy. It's not so easy for guns.

[confocaloid]

There was no gun_2023 on Catagolue and I thought I'd submit one as a test.

I submitted the following RLE pattern (which I got by modifying gun_2039). Note that it breaks conventions for previous gun collections in several distinct ways. (The output glider stream goes in the opposite direction; height exceeds width; the phase is different from the one where the output glider is about to leave the bounding box.)

The submitted RLE appeared unchanged in the log (#3542807487).

Code: Select all

x = 227, y = 258, rule = B3/S23
74b2o$74bobo$76bo4b2o$72b4ob2o2bo2bo$66b2o4bo2bobobobob2o$66bo8bobobob
o$68bo7b2obobo$64b5o11bo$64bo$67b4o$67bo2bo4b2o$75b2o$62b2o$62bo2bob2o
$64b2ob2o5$78b2o$78bo$79b3o$81bo12$37b2o$37b2o2$19bo$17b3o$16bo$15bobo
$15bobo$16bo4$51b2o$2o49bobo$2o51bo$53b2o3$20b2o$20bobo$22bo$13b2o7b2o
8b2o$13b2o18bo$30b3o$3bob2o23bo$b3ob2o$o$b3ob2o$3b2o2bo40b2o$6bobo39bo
bo89bo$2bob2obobo16bo23bo89b3o$2b2obo2bo15b3o23b2o91bo$5bo17bo118bobo$
5b2o16b2o117bobo$3b2o2bobo133bo$2bo2bo2b2o$3b2o2$40b2o$40b2o116b2o$28b
2o128b2o$28bo5bo$26bobo3b3o$26b2o3bo$31b2o105b2o$51b2o84bobo$12b2o37bo
85bo$11bobo35bobo84b2o7b2o$11bo37b2o94b2o$10b2o$30b2o121b2obo$31bo3b2o
116b2ob3o$28b3o3bobo122bo$28bo5bo118b2ob3o$33b2o117bo2b2o$21b2o128bobo
$21b2o110bo16bobob2obo$133b3o15bo2bob2o$58b2o76bo17bo$53b2o2bo2bo74b2o
16b2o$53bobo2b2o90bobo2b2o$38b2o16b2o92b2o2bo2bo$39bo17bo97b2o$11b2o
23b3o15bo2bob2o$12bo23bo16bobob2obo$12bobo39bobo$13b2o40bo2b2o$56b2ob
3o$62bo$56b2ob3o$32bo23b2obo67b2o19b2o$30b3o94b2o19b2o$29bo18b2o$29b2o
8b2o7b2o$40bo108b2o$40bobo106bo$41b2o107b3o$152bo3$61b2o$61b2o2$9b2o$
9b2o2$46bo$45bobo$45bobo$46bo$43b3o$43bo$135b2o3b2o$18b2o4b2o108bo2bob
o2bo$19bo4b2o103bo5b2o3b2o5bo$17bo110bobo15bobo$17b5o14b2o91bo17bo$22b
o13bo$19b3o12bobo$18bo15b2o$18b4o$16b2o3bo3b2o$15bo2b3o4b2o$15b2obo$
18bo$18b2o3$26b2o$27bo$24b3o$24bo$89bo$89b3o$92bo$91b2o7$101b2o$94b2o
5bobo$94b2o7bo$103b2o2$90bo$89bobob2o$89bobobobo$86b2obobobobo2bo$86bo
2bo2b2ob4o$88b2o4bo$94bobo$95b2o5$217bo$215b3o$214bo$214b2o3$222b2o$
75b2o146bo$75bobo145bob2o$75bo139b2o4b3o2bo$215b2o3bo3b2o$220b4o$206b
2o15bo$205bobo12b3o$205bo13bo$204b2o14b5o$224bo$222bo$222b2o37$135bo$
133b3o$132bo$132b2o10b2o$144bo$121b2o19bobo$122bo19b2o10bo$122bobo29b
3o$123b2o32bo$156b2o$171b2o$171bo$123b2o43b2obo$122bobo42bo2bo$122bo
45b2o$121b2o4b2o24b2o$126bobo24b2o$126bo$125b2o2$140b2o3bo$140bo3bobo$
141bo3bobo$142bo3bobob2o$140bob4o2bob2o$139bobo3bobo$139bobo2bo2b2ob2o
$140bo3b2o2bobo$148bobo10b2o$149bo11b2o!

And here is the displayed gun_2023 from Catagolue object page:

Code: Select all

#C [[ GRID MAXGRIDSIZE 14 THEME Catagolue ]]
#CSYNTH gun_2023 costs 58566 cells.
#C period 2023 fullperiod 2023 bbox 227 by 258
#CLL state-numbering golly
x = 227, y = 258, rule = LifeHistory
31.B3A39.2A$32.A3B38.A.A$33.A3B39.A4.2A$34.4B34.4A.2A2.A2.A$35.4B
27.2A4.A2.A.A.A.A.2A$36.4B26.A7.BABABA.A$37.4B27.A6.B2ABA.A$38.4B
22.5A7.2B.BA$39.4B21.A10.3B$40.4B22.B4A3.4B$41.4B21.BA2.A3.B2A3B$
42.4B20.4B4.B2A3B$43.4B15.2A3.15B$44.4B14.A2.A.2A14B$45.4B15.2A.2A
15B$46.4B18.B.15B$47.4B20.9B2.4B$48.4B19.7B5.4B$49.4B18.9B4.4B$50.
4B16.4B4.2A5.4B$51.4B14.4B5.A7.4B$52.4B12.4B7.3A5.4B$53.4B10.4B10.
A6.4B$54.4B8.4B19.4B$55.4B6.4B21.4B$56.4B4.4B23.4B$57.4B2.4B25.4B$
58.8B27.4B$59.6B29.4B$60.4B31.4B$59.6B31.4B$58.8B31.4B$57.4B2.4B
31.4B$56.4B4.4B31.4B$37.2A16.4B6.4B31.4B$36.B2AB14.4B8.4B31.4B$30.
B6.2B14.4B10.4B31.4B$19.A9.3B4.2B14.4B12.4B31.4B$17.3A5.14B12.4B
14.4B31.4B$16.A8.14B11.4B16.4B31.4B$15.A.A7.17B5.B.4B18.4B31.4B$
14.BA.A6.28B20.4B31.4B$13.3BA5.30B21.4B31.4B$11.4B6.31B22.4B31.4B$
9.6B5.32B23.4B31.4B$8.7B4.32B25.4B31.4B$.B.4B.8B2.4B3.23B2.B2A24.
4B31.4B$2AB.17B7.16B.B4.BA.A24.4B31.4B$2A18B9.2B.10B11.A25.4B31.4B
$.2B.16B12.9B12.2A25.4B31.4B$4.16B13.11B37.4B31.4B$5.15B13.12B37.
4B31.4B$6.12B.B2A11.12B38.4B31.4B$6.11B2.BA.A11.11B39.4B31.4B$7.
10B5.A9.4B.8B40.4B31.4B$7.6B2A2B5.2A8.2A4.7B41.4B31.4B$7.6B2A3B15.
A4.7B42.4B31.4B$7.10B13.3A6.6B43.4B31.4B$3.A.2AB.8B13.A8.7B43.4B
31.4B$.3AB2AB3.7B21.8B43.4B31.4B$A4.B6.6B22.8B43.4B31.4B$.3A.2A4.
6B23.8B44.4B31.4B$3.2A2.A4.5B22.6B2.B2A43.4B31.4B$6.A.A.8B21.7B.BA
.A43.4B31.4B7.A$2.A.2A.A.A8B8.A13.6B4.A44.4B31.4B6.3A$2.2A.A.BA2B.
6B6.3A13.6B4.2A44.4B31.4B8.A$5.A2.2B2.7B4.A16.6B51.4B31.4B6.A.A$5.
2A.B3.7B4.2A14.8B51.4B31.4B5.A.AB$3.2A2.A.A2.8B.4B13.8B53.4B31.4B
5.A3B$2.A2.A2.2A2.11B15.9B53.4B31.4B6.4B$3.2A7.12B14.9B54.4B31.4B
5.6B$12.12B13.10B55.4B31.4B4.7B$13.11B13.3B2A5B56.4B31.4B2.8B.4B.B
$16.7B13.4B2A5B57.4B31.17B.B2A$15.8B5.2A6.11B58.4B31.18B2A$14.8B6.
A5.A12B59.4B30.16B.2B$15.8B2.BA.A3.3A2.8B62.4B29.16B$14.10B.B2A3.A
6.7B63.4B28.15B$14.12B5.2A7.5B64.4B25.2AB.12B$14.12B14.6B5.2A57.4B
23.A.AB2.11B$12.2AB2.9B13.6B6.A59.4B22.A5.10B$11.A.AB2.8B13.8B2.BA
.A60.4B20.2A5.2B2A6B$11.A6.6B13.9B2.B2A62.4B25.3B2A6B$10.2A5.6B14.
12B65.4B25.10B$18.5B7.2A5.12B66.4B24.8B.B2A.A$18.7B6.A3.2AB.10B67.
4B22.7B3.B2AB3A$18.8B2.3A3.A.AB2.8B69.4B21.6B6.B4.A$16.12BA5.A6.8B
69.4B21.6B4.2A.3A$16.11B6.2A5.8B71.4B20.5B4.A2.2A$16.5B2A4B13.7B
73.4B18.8B.A.A$16.5B2A3B13.11B71.4B8.A8.8BA.A.2A.A$16.10B13.12B71.
4B7.3A6.6B.2BAB.A.2A$16.9B14.12B7.2A63.4B9.A4.7B2.2B2.A$16.9B15.
11B2.2A2.A2.A63.4B7.2A4.7B3.B.2A$17.8B13.4B.8B2.A.A2.2A65.4B6.4B.
8B2.A.A2.2A$16.8B14.2A4.7B3.B.2A68.4B7.11B2.2A2.A2.A$17.6B16.A4.7B
2.2B2.A69.4B5.12B7.2A$11.2A4.6B13.3A6.6B.2BAB.A.2A67.4B4.12B$12.A
4.6B13.A8.8BA.A.2A.A68.4B3.11B$12.A.AB.7B21.8B.A.A73.4B3.7B$13.2AB
2.6B22.5B4.A2.2A71.4B2.8B$15.8B23.6B4.2A.3A70.14B$15.8B22.6B6.B4.A
68.16B$16.8B21.7B3.B2AB3A66.B.17B.B$17.7B8.A13.8B.B2A.A67.2AB.17B
2A$18.6B6.3A13.10B71.2A19B2A$18.7B4.A15.3B2A6B72.2B.18B$18.7B4.2A
8.2A5.2B2A6B75.13B2.5B$18.8B.4B9.A5.10B77.10B6.2A$18.11B11.A.AB2.
11B76.9B7.A$18.12B11.2AB.12B76.9B8.3A$18.12B13.15B75.11B8.A$19.11B
13.16B73.13B$22.9B12.5B2A9B.2B67.2B.13B.2B$21.10B.2B9.2A2B2A12B2A
65.21B$10.3B4.B.15BA7.2B2A3BA9B.B2A63.25B$10.23B2A3B3.2BAB2.8B.4B.
B64.25B$9.2A11B2A8B2A10B4.7B70.27B$9.2A10B2ABA10B3A5B5.7B70.27B$
10.B.9B2ABA13BA3B6.8B68.29B$12.9B2AB2A3B3A2B3A4B5.A3B3.4B68.27B$
14.8B4A4B2AB2A5B5.A.AB5.4B67.6B2.11B2.6B$15.B5.2B4AB3ABAB2A3B6.A.A
7.4B65.4B.B4.9B4.B.4B$24.B4A2B2A2B3A8.A9.4B63.4B9.5B9.4B$24.2B2A8B
2A5.3A11.4B61.4B9.7B9.4B$25.2B4.5B7.A14.4B59.4B8.11B8.4B$24.2B5.4B
24.4B57.4B8.3B2A3B2A3B8.4B$18.2A3.B2AB3.4B26.4B55.4B7.B.2BA2BABA2B
A2B.B7.4B$19.A4.2A3.4B28.4B53.4B7.A5B2A3B2A5BA7.4B$17.A10.4B30.4B
51.4B7.A.A2B.9B.2BA.A7.4B$17.5A5.4B5.2A25.4B49.4B9.AB3.9B3.BA9.4B$
22.A4.4B5.A27.4B47.4B15.9B15.4B$19.3AB2.7B.BA.A28.4B45.4B17.B5.B
17.4B$18.A.2B3.7B.B2A30.4B43.4B43.4B$18.4A12B33.4B41.4B45.4B$16.2A
2.BA3B2A7B34.4B39.4B47.4B$15.A2.3AB.2B2A7B35.4B37.4B49.4B$15.2A.A.
B3.10B36.4B35.4B51.4B$18.A8.8B36.4B33.4B53.4B$18.2A7.9B36.4B31.4B
55.4B$28.3B2.4B36.4B29.4B57.4B$26.5B3.4B36.4B27.4B59.4B$26.2A7.4B
36.4B25.4B61.4B$27.A8.4B36.4B23.4B63.4B$24.3A10.4B36.4B21.4B65.4B$
24.A13.4B36.4B19.4B67.4B$39.4B36.4B6.A10.4B69.4B$40.4B36.4B5.3A7.
4B71.4B$41.4B36.4B7.A5.4B73.4B$42.4B36.4B5.2A4.4B75.4B$43.4B36.4B
4.9B77.4B$44.4B36.4B5.6B79.4B$45.4B36.4B2.8B80.4B$46.4B36.15B79.4B
$47.4B36.14B80.4B$48.4B36.13B81.4B$49.4B36.10B.B2A80.4B$50.4B37.3B
2AB3.BA.A80.4B$51.4B36.3B2AB6.A81.4B$52.4B37.4B6.2A81.4B$53.4B36.
3B91.4B$54.4B32.AB.2B93.4B$55.4B30.A.AB2AB93.4B$56.4B29.A.ABABAB
93.4B$57.4B25.2A.A.A.A.A2.A92.4B$58.4B24.A2.A2.2A.4A93.4B$59.4B25.
2A4.A98.4B$60.4B30.A.A97.4B$61.4B30.2A98.4B$62.4B130.4B$63.4B130.
4B$64.4B130.4B$65.4B130.4B$66.4B130.4B13.A$67.4B130.4B10.3A$68.4B
130.4B8.A$69.4B130.4B7.2A$70.4B130.4B3.5B$71.4B130.4B2.3B$72.4B
130.9B7.2A$73.4B130.8B8.A$74.4B130.10B3.B.A.2A$75.4B129.7B2A2B.B3A
2.A$76.4B128.7B2A3BAB2.2A$77.4B127.12B4A$78.4B124.2AB.7B3.2B.A$79.
4B122.A.AB.7B2.B3A$80.4B121.A5.4B4.A$81.4B119.2A5.4B5.5A$82.4B124.
4B10.A$83.4B122.4B9.A$84.4B120.4B10.2A$85.4B118.4B$86.4B116.4B$87.
4B114.4B$88.4B112.4B$89.4B110.4B$90.4B108.4B$91.4B106.BA2B$92.4B
104.2A2B$93.4B102.2B2A$94.4B100.4B$95.4B98.4B$96.4B96.4B$97.4B94.
4B$98.4B92.4B$99.4B90.4B$100.4B88.4B$101.4B86.4B$102.4B84.4B$103.
4B82.4B$104.4B80.4B$105.4B78.4B$106.4B76.4B$107.4B74.4B$108.4B72.
4B$109.4B70.4B$110.4B68.4B$111.4B66.4B$112.4B64.4B$113.4B62.4B$
114.4B60.4B$115.4B58.4B$116.4B56.4B$117.4B54.4B$118.4B52.4B$119.4B
50.4B$120.4B48.4B$121.4B10.A35.4B$122.4B7.3A34.4B$123.4B5.A36.4B$
124.4B4.2A10.2A22.4B$125.9B10.A22.4B$121.2A3.6B9.BA.A21.4B$122.A4.
6B4.3B.B2A10.A10.4B$122.A.AB.7B.7B12.3A7.4B$123.2AB.15B15.A5.4B$
125.16B15.2A4.4B$124.18B14.9B6.2A$125.19B14.6B7.A$123.2AB.20B2.2B
2.B3.6B5.2A.A$122.A.AB4.33B4.A2.A$122.A6.7B.27B3.B2A$121.2A4.2AB.
2B.B2.16B2A14B$126.A.AB7.16B2A13B$126.A11.29B$125.2A18.2B.B.17B$
144.3B4.15B$140.2A.2BA5.15B$140.A.2BA.A5.13B$141.A2.BA.A2.13B$142.
A3.A.A.2A4.8B$140.A.4A2.AB2A6.6B$139.A.A3.A.A2.B8.5B$139.A.A2.A2.
2A.2A9.B.B$140.A3.2A2.A.A9.3B$148.A.A9.B2AB$149.A11.2A!

Note that the displayed RLE is in the same orientation as the submitted RLE, but the phase is automatically changed to one where the glider is about to escape the bounding box.

[calcyman]

There was no gun_2023 on Catagolue and I thought I'd submit one as a test.

143-by-84, using Kazyan's method to multiply the period of the drive gun by 17:

Code: Select all

x = 143, y = 84, rule = LifeHistory
34.2A$34.A.A$36.A4.2A$32.4A.2A2.A2.A$26.2A4.A2.A.A.A.A.2A$26.A7.BABAB
A.A$28.A6.B2ABA.A52.A.A21.2A$24.5A7.2B.BA52.A.2A2.A17.A.A$24.A10.3B
55.A3.3A11.2A4.A$26.B4A3.4B51.A.2A.2A13.A2.A2.2A.4A$26.BA2.A3.B2A3B
49.2A.A.A.2A11.2A.A.A.A.A2.A$26.4B4.B2A3B53.2B2.A14.A.ABABAB$22.2A3.
15B51.AB2A15.A.AB2AB$22.A2.A.2A14B49.BAB2.3A13.AB.2B$24.2A.2A3BA11B
48.3B2A2.A16.3B$28.B.BABA11B46.4B.A.A17.4B6.2A$31.BA7B2.4B41.2A.2AB2A
.A.2A14.3B2AB6.A$31.7B5.4B40.2A.A.A3BA2.A5.A8.3B2AB3.BA.A$31.9B4.4B
42.A.A.B2.2A4.3A6.10B.B2A$30.4B4.2A5.4B38.4A.5A5.A8.13B$29.4B5.A7.4B
36.A4.AB3.A4.A.A6.14B$28.4B7.3A5.4B36.3A.A.3A4.BA.A5.15B$27.4B10.A6.
4B37.2AB2A5.3BA5.4B2.8B$26.4B19.4B37.3B4.4B6.4B5.6B$25.4B21.4B36.3B2.
6B5.4B4.9B$24.4B23.4B36.B2.7B4.4B5.2A4.4B$23.4B25.4B35.2B.8B2.4B7.A5.
4B$22.4B27.4B34.16B5.3A7.4B$21.4B29.4B32.8B3A5B6.A10.3BA$20.4B31.4B
30.9B3A5B18.B2AB10.2A$19.4B33.4B28.9BA3BA4B19.ABAB9.A$18.4B35.4B26.
10B2AB2A4B20.4B10.A$17.4B37.4B24.4B2.12B.B2A12.2A5.4B5.5A$4.2A10.4B
39.4B22.4B3.11B2.BA.A12.A5.4B4.A$5.A9.4B41.4B20.4B5.10B5.A12.A.AB.7B
2.B3A$3.A7.2B.4B5.2A36.4B18.4B6.10B5.2A12.2AB.7B3.2B.A$3.2A6.7B5.A38.
4B16.4B7.11B20.12B4A$.2A2.BAB.2B2A6B.BA.A39.4B14.4B8.10B21.7B2A3BAB2.
2A$A2.4A3BA2BA5B.B2A41.4B12.4B5.A.2AB.8B21.7B2A2B.B3A2.A$2A.A2.5B2A8B
44.4B10.4B4.3AB2AB3.7B20.10B3.B.A.2A$.A.A.2A14B45.4B8.4B4.A4.B6.6B19.
8B8.A$.A.A.2AB.12B46.4B6.4B6.3A.2A4.6B19.9B7.2A$2A.AB.B3.11B47.4B4.4B
9.2A2.A4.5B18.4B2.3B$3.A8.B.8B47.4B2.4B13.A.A.8B16.4B3.5B$3.A.A8.9B
47.8B10.A.2A.A.A8B15.4B7.2A$4.2A8.10B43.2B.7B11.2A.A.BA2B.6B7.2A5.4B
8.A$11.2A.4B3.4B41.2A8B15.A2.2B2.7B6.A5.4B10.3A$11.A.4B5.4B40.2A7B16.
2A.B3.7B3.BA.A4.4B13.A$8.2A.A.2B2AB5.4B40.B.5B15.2A2.A.A2.8B2.B2A4.4B
$6.A2.A.2A2B2A7.4B41.5B14.A2.A2.2A2.11B5.4B$6.2A.A.3B11.4B39.7B14.2A
7.11B4.4B$9.A5.2A9.4B37.4B.4B22.11B3.4B$9.2A5.A10.4B35.A3B3.4B22.11B.
4B$14.A13.4B33.BABA5.4B13.2A9.7B.4B$14.2A13.4B31.2B2A7.4B12.A.A7.12B$
30.4B29.4B9.4B13.A5.B3A9B$31.4B27.4B11.4B12.2AB.2B5A7B$32.4B25.4B13.
4B13.3BAB2A2BA2B2A2B$33.4B23.4B15.4B10.2AB.2AB4A3BABAB.B$34.4B21.4B
17.4B8.A2.A2B5A6BA2B2A$35.4B19.4B19.4B5.A2.2A4BA6BA2BA2B2A$36.4B6.A
10.4B21.4B4.2A.A.2B5.B2A3BA4B$37.4B5.3A7.4B23.4B6.A.B5.A5B2.4B$38.4B
7.A5.4B25.4B5.2A6.6B$39.4B5.2A4.4B27.4B11.A.A3B$40.4B4.9B29.4B8.3A.A.
A.A$41.4B5.7B30.4B6.A4.A.2A.A$42.4B2.9B31.4B5.2A3.A4.A$43.15B.B29.4B
8.2A4.2A$44.15B2A.2A26.4B$45.14B2A.A2.A25.4B$46.15B3.2A26.4B$48.3B2AB
4.4B31.4B$48.3B2AB3.A2.AB32.4B$50.4B3.4AB33.4B$50.3B10.A32.4B$47.AB.
2B7.5A33.4B$46.A.AB2AB6.A38.4B$46.A.ABABAB7.A37.4B$43.2A.A.A.A.A2.A4.
2A38.4B$43.A2.A2.2A.4A45.4B$45.2A4.A50.3BA$51.A.A49.3BA$52.2A50.3AB!

[confocaloid]

A phoenix is a pattern all of whose cells die in every generation, but that never dies as a whole. What happens if the requirement "in every generation" is relaxed to "in at least one generation"? Are there non-phoenix oscillators where all alive cells simultaneously die in some generation?

[Macbi]

A phoenix is a pattern all of whose cells die in every generation, but that never dies as a whole. What happens if the requirement "in every generation" is relaxed to "in at least one generation"? Are there non-phoenix oscillators where all alive cells simultaneously die in some generation?

These are called oscillators with volatility 1. I don't know if there are any where every cell is alive in some generation.

[confocaloid]

A phoenix is a pattern all of whose cells die in every generation, but that never dies as a whole. What happens if the requirement "in every generation" is relaxed to "in at least one generation"? Are there non-phoenix oscillators where all alive cells simultaneously die in some generation?

These are called oscillators with volatility 1. I don't know if there are any where every cell is alive in some generation.

Not quite -- I'm looking for a pattern where at least one phase consists of newborn cells (without any cells surviving from the previous phase). "Volatility 1" is weaker than this requirement, which in turn is weaker than "phoenix". For example, pentadecathlon has volatility 1, but it does not qualify, because in every generation there are some surviving cells.

[KtT]

What is the type of this quadratic growth pattern?

Code: Select all

x = 700, y = 6166, rule = B3/S23
27b3o3b3o$27bo2bobo2bo$19b3o5bo2bobo2bo5b3o$19bo2bo4b2obobob2o4bo2bo$
19bo8b2o3b2o8bo76bo5bo260b3o3b3o$19bo3bo2b4o3b4o2bo3bo75b3o3b3o258bo2b
o3bo2bo$19bo6b11o6bo68bo6bob2ob2obo6bo244b3o8bobo8b3o$20bo2b2o4b5o4b2o
2bo68b3o6bobobobo6b3o242bo2bo6b3ob3o6bo2bo$27bo7bo75bob2o5bo5bo5b2obo
160bo5bo78bo5bob2ob2obo5bo$112b3o3b2o7b2o3b3o160b3o3b3o73bo3bo4b2o2bo
bo2b2o4bo3bo$112b3o2bo3b2ob2o3bo2b3o153bo5b2o2bobo2b2o5bo70bo2bob2o3b
o3b2obo2bo$31bo80b2o6bo2bo2bo6b2o152b3o4b2o2bobo2b2o4b3o66bobo3bob2o7b
2obo3bobo$31bo83b2o13b2o154b2obo5bo2bobo2bo5bob2o71bobo9bobo$31bo86b2o
7b2o157b3o5bo3bobo3bo5b3o$286b3o5bo4bo4bo5b3o78bo$31bo255b2o2b4o9b4o2b
2o79bo$31bo90b3o169bo9bo86bo$31bo$391bo$31bo266b3o90bo$31bo90b3o266bo
$31bo$21bo19bo349bo$20b3o8bo8b3o255b3o90bo$20bob2o7bo7b2obo79b3o266bo
$21b3o7bo7b3o$21b3o15b3o339bo9bo9bo$21b3o7bo7b3o70b3o17b3o163b3o79b3o
8bo8b3o$21b2o8bo8b2o69bo2bo7b3o7bo2bo243b2obo8bo8bob2o$31bo82bo17bo246b
3o19b3o$110bo3bo17bo3bo242b3o9bo9b3o$31bo78bo3bo17bo3bo151b3o7b3o7b3o
68b3o9bo9b3o$31bo82bo7b3o7bo155bo2bo15bo2bo69b2o9bo9b2o$31bo79bobo19b
obo152bo21bo$288bo3bo13bo3bo80bo$31bo256bo3bo5b3o5bo3bo80bo$31bo90b3o
163bo21bo80bo$31bo257bobo15bobo$391bo$31bo266b3o90bo$18bo12bo12bo77b3o
266bo$2bo14b3o11bo11b3o14bo$b3o6bo5b2obo23bob2o5bo6b3o329bo$2obo5b3o4b
3o12bo12b3o4b3o5bob2o235b3o90bo$3o5b2o2bo3b3o12bo12b3o3bo2b2o5b3o59b3o
253bo12bo12bo$3o5bo2bobo2b3o12bo12b3o2bobo2bo5b3o46b3o23b3o224bo14b3o
23b3o14bo$b2o2b3obo7b2o25b2o7bob3o2b2o31b3o13bo2bo21bo2bo13b3o207b3o6b
o6bob2o10bo10b2obo6bo6b3o$b2o3b2o6b2o15bo15b2o6b2o3b2o31bo2bo4b3o5bo27b
o5b3o4bo2bo144b3o60bob2o4b3o6b3o10bo10b3o6b3o4b2obo$2b2o3bo6bo2bo13bo
13bo2bo6bo3b2o32bo7bo2bo4bo3bo8b3o8bo3bo4bo2bo7bo208b3o3bo2b2o5b3o10b
o10b3o5b2o2bo3b3o$6bo11bo12bo12bo11bo36bo3bo2bo3bo4bo3bo19bo3bo4bo3bo
2bo3bo131b3o23b3o48b3o2bobo2bo5b3o21b3o5bo2bobo2b3o$18bo25bo48bo6bobo
3bo2bo27bo2bo3bobo6bo115b3o12bo2bo23bo2bo12b3o32b2o7bob3o2b2o11bo11b2o
2b3obo7b2o$31bo62bo2b2o8bobo27bobo8b2o2bo115bo2bo5b3o7bo10b3o10bo7b3o
5bo2bo34b2o6b2o3b2o11bo11b2o3b2o6b2o$31bo62b5o8bo14b3o14bo8b5o118bo4b
o2bo3bo3bo23bo3bo3bo2bo4bo35bo2bo6bo3b2o12bo12b2o3bo6bo2bo$19bo11bo11b
o53b2o6bo3b3o23b3o3bo6b2o117bo3bo4bo3bo2bo3bo23bo3bo2bo3bo4bo3bo30bo11b
o33bo11bo$3bo14b3o21b3o14bo34b2o55b2o118bo2bo3bobo6bo23bo6bobo3bo2bo34b
o28bo28bo$2b3o6bo5b2obo10bo10bob2o5bo6b3o210bobo8b2o2bo11b3o11bo2b2o8b
obo63bo$b2obo5b3o4b3o11bo11b3o4b3o5bob2o60b3o148bo8b5o25b5o8bo65bo$b3o
5b2o2bo3b3o10bobo10b3o3bo2b2o5b3o207b3o3bo6b2o31b2o6bo3b3o49bo23bo$b3o
5bo2bobo2b3o10bobo10b3o2bobo2bo5b3o48b3o21b3o148b2o25b2o49bo14b3o10bo
10b3o14bo$2b2o2b3obo7b2o9b2ob2o9b2o7bob3o2b2o33b3o13bo2bo19bo2bo13b3o
145b3o61b3o6bo6bob2o9bo9b2obo6bo6b3o$2b2o3b2o6b2o12bo3bo12b2o6b2o3b2o
33bo2bo4b3o5bo11b3o11bo5b3o4bo2bo209bob2o4b3o6b3o9bo9b3o6b3o4b2obo$3b
2o3bo6bo2bo10b2ob2o10bo2bo6bo3b2o34bo7bo2bo4bo3bo17bo3bo4bo2bo7bo210b
3o3bo2b2o5b3o19b3o5b2o2bo3b3o$7bo11bo23bo11bo38bo3bo2bo3bo4bo3bo7bobo
7bo3bo4bo3bo2bo3bo133b3o21b3o50b3o2bobo2bo5b3o8b3o8b3o5bo2bobo2b3o$19b
o9b2ob2o9bo50bo6bobo3bo2bo11b3o11bo2bo3bobo6bo117b3o12bo2bo9b3o9bo2bo
12b3o34b2o7bob3o2b2o8bo3bo8b2o2b3obo7b2o$30bobo62bo2b2o8bobo10bo3bo10b
obo8b2o2bo117bo2bo5b3o7bo21bo7b3o5bo2bo36b2o6b2o3b2o8b2ob2o8b2o3b2o6b
2o$95b5o8bo12b2ob2o12bo8b5o120bo4bo2bo3bo3bo21bo3bo3bo2bo4bo37bo2bo6b
o3b2o23b2o3bo6bo2bo$29b2ob2o9bo54b2o6bo3b3o21b3o3bo6b2o119bo3bo4bo3bo
2bo3bo10bo10bo3bo2bo3bo4bo3bo32bo11bo13b2ob2o13bo11bo$42b3o50b2o24b2o
b2o24b2o120bo2bo3bobo6bo8b2ob2o8bo6bobo3bo2bo36bo26bobo26bo$42bob2o76b
obo147bobo8b2o2bo9b2ob2o9bo2b2o8bobo63bobo$17b3o23b3o76bobo149bo8b5o23b
5o8bo64b2ob2o$16bo2bo23b3o224b3o3bo6b2o12b2ob2o12b2o6bo3b3o50bo9b2ob2o
$19bo23b3o64b3o8b2ob2o160b2o8bobobobo8b2o65b3o$15bo3bo23b2o65bo2bo264b
ob2o$19bo90bo25bo160b2ob2o77b3o21b3o$16bobo91bo3bo20b3o159b2ob2o77b3o
20bo2bo$110bo3bo20bob2o171b3o66b3o23bo$110bo25b3o171bo2bo65b2o20bo3bo
$111bobo22b3o147bo10b2ob2o8bo94bo$136b2o147b3o22bo3bo87bobo$285bob2o21b
o3bo$286b3o21bo$286b3o22bobo$286b2o3$44bo$43b3o$17b3o22b2obo$16bo2bo22b
3o$19bo22b3o333bo$15bo3bo22b3o64b3o265b3o$19bo23b2o63bo2bo24bo239b2ob
o23b3o$16bobo92bo23b3o238b3o23bo2bo$107bo3bo23bob2o237b3o26bo$40b3o64b
o3bo24b3o172b3o62b3o22bo3bo$40bo2bo67bo24b3o147bo23bo2bo63b2o26bo$40b
o67bobo25b2o147b3o25bo88bobo$40bo3bo240bob2o20bo3bo$40bo3bo68bo172b3o
20bo3bo66b3o$40bo71b3o171b3o24bo66bo2bo$41bobo67b2obo171b2o22bobo67bo
$111b3o266bo3bo$111b3o195bo70bo3bo$111b3o194b3o69bo$112b2o193b2obo70b
obo$307b3o$307b3o$307b3o$308b2o2$13b3o$13bo2bo$13bo$13bo$14bobo123bo266b
3o$139b3o265bo2bo$138b2obo265bo$138b3o266bo$139b2o141bo125bobo$281b3o
$280b2obo$280b3o$281b2o12$15b3o$15bo2bo$15bo$15bo$16bobo119bo266b3o$137b
3o265bo2bo$136b2obo265bo$136b3o266bo$137b2o145bo121bobo$283b3o$32b3o247b
2obo$32bo2bo246b3o$32bo250b2o$32bo3bo$32bo88bo266b3o$33bobo84b3o265bo
2bo$119b2obo265bo$119b3o266bo$119b3o179bo86bo3bobo$120b2o3bo174b3o86b
obo2bo$125bo173b2obo$299b3o$52b2o241bobob3o$51bobo242bo3b2o$53bo2$102b
o266b3o$101b2o266bo$101bobo266bo2$319b2o$320b2o$319bo38$505bo5bo$504b
3o3b3o$497bo5b2o2bobo2b2o5bo$496b3o4b2o2bobo2b2o4b3o$495b2obo5bo2bobo
2bo5bob2o$412b3o3b3o74b3o5bo3bobo3bo5b3o$412bo2bobo2bo74b3o5bo4bo4bo5b
3o$404b3o5bo2bobo2bo5b3o67b2o2b4o9b4o2b2o$404bo2bo4b2obobob2o4bo2bo74b
o9bo$404bo8b2o3b2o8bo78b3o$404bo3bo2b4o3b4o2bo3bo$404bo6b11o6bo$405bo
2b2o4b5o4b2o2bo$412bo7bo86b3o3$416bo$416bo90b3o$416bo2$416bo$416bo90b
3o$416bo$497b3o17b3o$416bo80bo2bo15bo2bo$416bo80bo9b3o9bo$416bo80bo3b
o13bo3bo$406bo19bo70bo3bo13bo3bo$405b3o8bo8b3o69bo21bo$405bob2o7bo7b2o
bo70bobo6b3o6bobo$406b3o7bo7b3o$406b3o15b3o$406b3o7bo7b3o$406b2o8bo8b
2o80b3o$416bo2$416bo$416bo90b3o$416bo2$416bo$416bo77b3o10b3o10b3o$416b
o61b3o12bo2bo23bo2bo12b3o$477bo2bo5b3o7bo23bo7b3o5bo2bo$416bo63bo4bo2b
o3bo3bo23bo3bo3bo2bo4bo$403bo12bo12bo46bo3bo4bo3bo2bo3bo10b3o10bo3bo2b
o3bo4bo3bo$387bo14b3o11bo11b3o14bo34bo2bo3bobo6bo23bo6bobo3bo2bo$386b
3o6bo5b2obo23bob2o5bo6b3o33bobo8b2o2bo25bo2b2o8bobo$385b2obo5b3o4b3o12b
o12b3o4b3o5bob2o34bo8b5o25b5o8bo$385b3o5b2o2bo3b3o12bo12b3o3bo2b2o5b3o
30b3o3bo6b2o14b3o14b2o6bo3b3o$385b3o5bo2bobo2b3o12bo12b3o2bobo2bo5b3o
46b2o25b2o$386b2o2b3obo7b2o25b2o7bob3o2b2o$386b2o3b2o6b2o15bo15b2o6b2o
3b2o$387b2o3bo6bo2bo13bo13bo2bo6bo3b2o61b3o$391bo11bo12bo12bo11bo53b3o
21b3o$403bo25bo49b3o12bo2bo21bo2bo12b3o$416bo61bo2bo5b3o7bo21bo7b3o5b
o2bo$416bo64bo4bo2bo3bo3bo9b3o9bo3bo3bo2bo4bo$404bo11bo11bo48bo3bo4bo
3bo2bo3bo21bo3bo2bo3bo4bo3bo$388bo14b3o21b3o14bo36bo2bo3bobo6bo21bo6b
obo3bo2bo$387b3o6bo5b2obo10bo10bob2o5bo6b3o35bobo8b2o2bo23bo2b2o8bobo
$386b2obo5b3o4b3o11bo11b3o4b3o5bob2o36bo8b5o10b3o10b5o8bo$386b3o5b2o2b
o3b3o11bo11b3o3bo2b2o5b3o32b3o3bo6b2o13bobo13b2o6bo3b3o$386b3o5bo2bob
o2b3o23b3o2bobo2bo5b3o48b2o10bobo10b2o$387b2o2b3obo7b2o11bo11b2o7bob3o
2b2o60b2ob2o$387b2o3b2o6b2o14bo14b2o6b2o3b2o59bo5bo$388b2o3bo6bo2bo11b
obo11bo2bo6bo3b2o61b2ob2o$392bo11bo10bobo10bo11bo54b3o$404bo9b2ob2o9b
o65bo2bo8b2ob2o$414bo3bo78bo9bobo11bo$414b2ob2o74bo3bo9bobo10b3o$428b
o64bo3bo9bobo9b2obo$414b2ob2o8b3o67bo9bobo9b3o$415bobo9bob2o63bobo22b
3o$402b3o10bobo10b3o89b2o$401bo2bo9b2ob2o9b3o$404bo8bobobobo8b3o$400b
o3bo23b2o$404bo$401bobo7$494b3o$494bo2bo23bo$494bo25b3o$494bo3bo20b2o
bo$429bo64bo3bo20b3o$428b3o63bo24b3o$402b3o22b2obo64bobo22b2o$401bo2b
o22b3o$404bo22b3o68bo$400bo3bo22b3o67b3o$404bo23b2o67bob2o$401bobo94b
3o$498b3o$425b3o70b3o$425bo2bo69b2o$425bo$425bo3bo$425bo3bo$425bo$426b
obo5$525bo$524b3o$524bob2o$525b3o$525b2o$398b3o$398bo2bo$398bo$398bo$
399bobo15$523bo$522b3o$522bob2o$511b2o10b3o$511b2o10b2o$400b3o$400bo2b
o$400bo11b2o$400bo11b2o$401bobo$506bo$505b3o$505bob2o$506b3o$506b3o$417b
3o86b2o$417bo2bo$417bo74b2o$417bo3bo69b2o$417bo75bo$418bobo$431b2o$430b
obo$432bo207$203bobo$204b2o$204bo14bo$217b2o$218b2o183$340bo$340bobo$
340b2o41$413bo5bo$412b3o3b3o$405bo6bob2ob2obo6bo$404b3o6bobobobo6b3o$
404bob2o5bo5bo5b2obo$405b3o3b2o7b2o3b3o$405b3o2bo3b2ob2o3bo2b3o$405b2o
6bo2bo2bo6b2o$408b2o13b2o$411b2o7b2o$415b3o4$415b3o4$415b3o2$415bobo$
415b3o$414bo3bo$405b3o6b2ob2o6b3o$404bo2bo17bo2bo$407bo6b2ob2o6bo$403b
o3bo7bobo7bo3bo$403bo3bo7bobo7bo3bo$407bo6b2ob2o6bo$404bobo6bo5bo6bob
o$414bo3bo11$402b3o23b3o$386b3o13bo2bo21bo2bo13b3o$386bo2bo4b3o5bo27b
o5b3o4bo2bo$386bo7bo2bo4bo3bo19bo3bo4bo2bo7bo$386bo3bo2bo3bo4bo3bo19b
o3bo4bo3bo2bo3bo$386bo6bobo3bo2bo27bo2bo3bobo6bo$387bo2b2o8bobo27bobo
8b2o2bo$387b5o8bo31bo8b5o$390b2o6bo3b3o23b3o3bo6b2o$387b2o55b2o4$403b
3o21b3o$387b3o13bo2bo19bo2bo13b3o$387bo2bo4b3o5bo25bo5b3o4bo2bo$387bo
7bo2bo4bo3bo17bo3bo4bo2bo7bo$387bo3bo2bo3bo4bo3bo17bo3bo4bo3bo2bo3bo$
387bo6bobo3bo2bo25bo2bo3bobo6bo$388bo2b2o8bobo25bobo8b2o2bo$388b5o8bo
29bo8b5o$391b2o6bo3b3o21b3o3bo6b2o$388b2o53b2o4$403b3o$403bo2bo$403bo
25bo$403bo3bo20b3o$403bo3bo20bob2o$403bo25b3o$404bobo22b3o$429b2o11$212b
2o$212b2o188b3o$401bo2bo24bo$404bo23b3o$400bo3bo23bob2o$400bo3bo24b3o
$404bo24b3o$401bobo25b2o2$406bo$405b3o$404b2obo$404b3o$404b3o$404b3o$
405b2o10$433bo$432b3o$431b2obo$431b3o$432b2o20$431bo$430b3o$429b2obo$
429b3o$430b2o6$414bo$413b3o$412b2obo$412b3o$412b3o$413b2o64$338bo$337b
2o$337bobo218$44bo5bo$43b3o3b3o$36bo5b2o2bobo2b2o5bo$35b3o4b2o2bobo2b
2o4b3o$34b2obo5bo2bobo2bo5bob2o343bo5bo$34b3o5bo3bobo3bo5b3o74b3o3b3o
259b3o3b3o$34b3o5bo4bo4bo5b3o74bo2bobo2bo252bo6bob2ob2obo6bo$35b2o2b4o
9b4o2b2o67b3o5bo2bobo2bo5b3o243b3o6bobobobo6b3o$42bo9bo74bo2bo4b2obob
ob2o4bo2bo243bob2o5bo5bo5b2obo$46b3o78bo8b2o3b2o8bo159b3o3b3o76b3o3b2o
7b2o3b3o$127bo3bo2b4o3b4o2bo3bo158bo2bo3bo2bo75b3o2bo3b2ob2o3bo2b3o$127b
o6b11o6bo151b3o8bobo8b3o68b2o6bo2bo2bo6b2o$128bo2b2o4b5o4b2o2bo151bo2b
o6b3ob3o6bo2bo70b2o13b2o$46b3o86bo7bo66bobo92bo5bob2ob2obo5bo76b2o7b2o
$213bo87bo3bo4b2o2bobo2b2o4bo3bo$213bo91bo2bob2o3bo3b2obo2bo$139bo70b
o2bo88bobo3bob2o7b2obo3bobo77b3o$46b3o90bo71b3o94bobo9bobo$139bo$315b
o$139bo175bo90b3o$46b3o90bo175bo$139bo$36b3o17b3o256bo$36bo2bo15bo2bo
80bo175bo90b3o$36bo9b3o9bo80bo175bo$36bo3bo13bo3bo80bo$36bo3bo13bo3bo
70bo19bo165bo80b3o17b3o$36bo21bo69b3o8bo8b3o164bo79bo2bo7b3o7bo2bo$37b
obo6b3o6bobo70bob2o7bo7b2obo164bo82bo17bo$129b3o7bo7b3o244bo3bo17bo3b
o$129b3o15b3o155bo9bo9bo68bo3bo17bo3bo$129b3o7bo7b3o154b3o8bo8b3o71bo
7b3o7bo$46b3o80b2o8bo8b2o153b2obo8bo8bob2o67bobo19bobo$139bo163b3o19b
3o$303b3o9bo9b3o$139bo163b3o9bo9b3o78b3o$46b3o90bo164b2o9bo9b2o$139bo
$315bo$139bo175bo90b3o$33b3o10b3o10b3o77bo175bo$17b3o12bo2bo23bo2bo12b
3o61bo$16bo2bo5b3o7bo23bo7b3o5bo2bo236bo$19bo4bo2bo3bo3bo23bo3bo3bo2b
o4bo63bo175bo90b3o$15bo3bo4bo3bo2bo3bo10b3o10bo3bo2bo3bo4bo3bo46bo12b
o12bo162bo77b3o23b3o$19bo2bo3bobo6bo23bo6bobo3bo2bo34bo14b3o11bo11b3o
14bo208b3o13bo2bo21bo2bo13b3o$19bobo8b2o2bo25bo2b2o8bobo33b3o6bo5b2ob
o23bob2o5bo6b3o145bo61bo2bo4b3o5bo27bo5b3o4bo2bo$21bo8b5o25b5o8bo34b2o
bo5b3o4b3o12bo12b3o4b3o5bob2o144bo61bo7bo2bo4bo3bo8b3o8bo3bo4bo2bo7bo
$17b3o3bo6b2o14b3o14b2o6bo3b3o30b3o5b2o2bo3b3o12bo12b3o3bo2b2o5b3o131b
o12bo12bo48bo3bo2bo3bo4bo3bo19bo3bo4bo3bo2bo3bo$33b2o25b2o46b3o5bo2bo
bo2b3o12bo12b3o2bobo2bo5b3o115bo14b3o23b3o14bo32bo6bobo3bo2bo27bo2bo3b
obo6bo$109b2o2b3obo7b2o25b2o7bob3o2b2o115b3o6bo6bob2o10bo10b2obo6bo6b
3o32bo2b2o8bobo27bobo8b2o2bo$109b2o3b2o6b2o15bo15b2o6b2o3b2o115bob2o4b
3o6b3o10bo10b3o6b3o4b2obo32b5o8bo14b3o14bo8b5o$46b3o61b2o3bo6bo2bo13b
o13bo2bo6bo3b2o117b3o3bo2b2o5b3o10bo10b3o5b2o2bo3b3o36b2o6bo3b3o23b3o
3bo6b2o$34b3o21b3o53bo11bo12bo12bo11bo121b3o2bobo2bo5b3o21b3o5bo2bobo
2b3o33b2o55b2o$18b3o12bo2bo21bo2bo12b3o49bo25bo133b2o7bob3o2b2o11bo11b
2o2b3obo7b2o$17bo2bo5b3o7bo21bo7b3o5bo2bo61bo149b2o6b2o3b2o11bo11b2o3b
2o6b2o64b3o$20bo4bo2bo3bo3bo9b3o9bo3bo3bo2bo4bo64bo147bo2bo6bo3b2o12b
o12b2o3bo6bo2bo$16bo3bo4bo3bo2bo3bo9bobo9bo3bo2bo3bo4bo3bo48bo11bo11b
o134bo11bo33bo11bo49b3o21b3o$20bo2bo3bobo6bo9bobo9bo6bobo3bo2bo36bo14b
3o21b3o14bo118bo28bo28bo33b3o13bo2bo19bo2bo13b3o$20bobo8b2o2bo9b2ob2o
9bo2b2o8bobo35b3o6bo5b2obo10bo10bob2o5bo6b3o146bo62bo2bo4b3o5bo11b3o11b
o5b3o4bo2bo$22bo8b5o8bo5bo8b5o8bo36b2obo5b3o4b3o11bo11b3o4b3o5bob2o145b
o62bo7bo2bo4bo3bo17bo3bo4bo2bo7bo$18b3o3bo6b2o12b2ob2o12b2o6bo3b3o32b
3o5b2o2bo3b3o10bobo10b3o3bo2b2o5b3o133bo23bo50bo3bo2bo3bo4bo3bo7bobo7b
o3bo4bo3bo2bo3bo$34b2o23b2o48b3o5bo2bobo2b3o10bobo10b3o2bobo2bo5b3o117b
o14b3o10bo10b3o14bo34bo6bobo3bo2bo11b3o11bo2bo3bobo6bo$45b2ob2o60b2o2b
3obo7b2o9b2ob2o9b2o7bob3o2b2o117b3o6bo6bob2o9bo9b2obo6bo6b3o34bo2b2o8b
obo10bo3bo10bobo8b2o2bo$45b2ob2o60b2o3b2o6b2o12bo3bo12b2o6b2o3b2o117b
ob2o4b3o6b3o9bo9b3o6b3o4b2obo34b5o8bo12b2ob2o12bo8b5o$45b2ob2o61b2o3b
o6bo2bo10b2ob2o10bo2bo6bo3b2o119b3o3bo2b2o5b3o19b3o5b2o2bo3b3o38b2o6b
o3b3o21b3o3bo6b2o$58b3o54bo11bo23bo11bo123b3o2bobo2bo5b3o8b3o8b3o5bo2b
obo2b3o35b2o24b2ob2o24b2o$58bo2bo65bo9b2ob2o9bo135b2o7bob3o2b2o8bo3bo
8b2o2b3obo7b2o62bobo$34bo23bo79bobo149b2o6b2o3b2o8b2ob2o8b2o3b2o6b2o65b
obo$33b3o22bo3bo225bo2bo6bo3b2o23b2o3bo6bo2bo$33bob2o21bo3bo64bo9b2ob
2o145bo11bo13b2ob2o13bo11bo50b3o8b2ob2o$34b3o21bo67b3o158bo26bobo26bo
50bo2bo$34b3o22bobo63b2obo185bobo77bo25bo$34b2o89b3o23b3o159b2ob2o76b
o3bo20b3o$125b3o23bo2bo158b2ob2o9bo66bo3bo20bob2o$125b3o23bo174b3o65b
o25b3o$126b2o23bo3bo169b2obo66bobo22b3o$151bo149b3o21b3o92b2o$152bobo
146bo2bo20b3o$301bo23b3o$301bo3bo20b2o$301bo$302bobo3$59b3o$34bo23bo2b
o$33b3o25bo$33bob2o20bo3bo$34b3o20bo3bo64bo266b3o$34b3o24bo63b3o264bo
2bo24bo$34b2o22bobo64bob2o22b3o241bo23b3o$126b3o22bo2bo236bo3bo23bob2o
$57bo68b3o22bo176bo62bo3bo24b3o$56b3o67b3o22bo3bo171b3o65bo24b3o$55b2o
bo67b2o23bo149b3o23bob2o61bobo25b2o$55b3o94bobo146bo2bo23b3o$55b3o243b
o26b3o66bo$55b3o70b3o170bo3bo22b3o65b3o$56b2o69bo2bo170bo26b2o65b2obo
$130bo171bobo90b3o$126bo3bo264b3o$126bo3bo193b3o68b3o$130bo192bo2bo69b
2o$127bobo196bo$322bo3bo$322bo3bo$326bo$323bobo$30bo$29b3o$28b2obo$28b
3o$29b2o393bo$155b3o265b3o$154bo2bo264b2obo$157bo264b3o$157bo265b2o$154b
obo140b3o$296bo2bo$299bo$299bo$296bobo11$32bo$31b3o$30b2obo$30b3o$31b
2o389bo$153b3o265b3o$152bo2bo264b2obo$155bo264b3o$155bo265b2o$152bobo
144b3o$49bo248bo2bo$48b3o250bo$47b2obo250bo$47b3o248bobo$47b3o355bo$48b
2o86b3o265b3o$135bo2bo264b2obo$138bo264b3o$134bo3bo264b3o$138bo177b3o
85b2o3bo$135bobo177bo2bo90bo$318bo$318bo$68b2o242bobo3bo$69b2o241bo2b
obo$68bo$386bo$117b2o266b2o$117bobo265bobo$117bo2$335b3o$337bo$336bo38$
520b3o3b3o$519bo2bo3bo2bo$512b3o8bobo8b3o$511bo2bo6b3ob3o6bo2bo$429bo
5bo78bo5bob2ob2obo5bo$428b3o3b3o73bo3bo4b2o2bobo2b2o4bo3bo$421bo5b2o2b
obo2b2o5bo70bo2bob2o3bo3b2obo2bo$420b3o4b2o2bobo2b2o4b3o66bobo3bob2o7b
2obo3bobo$419b2obo5bo2bobo2bo5bob2o71bobo4bo4bobo$419b3o5bo3bobo3bo5b
3o78bo$419b3o5bo4bo4bo5b3o78bo$420b2o2b4o9b4o2b2o$427bo9bo86bo$431b3o
90bo$524bo2$524bo$431b3o90bo$524bo2$524bo$431b3o90bo$514bo9bo9bo$513b
3o17b3o$512b2obo8bo8bob2o$431b3o78b3o9bo9b3o$512b3o9bo9b3o$421b3o17b3o
68b3o19b3o$421bo2bo15bo2bo69b2o9bo9b2o$421bo9b3o9bo80bo$421bo3bo13bo3b
o80bo$421bo3bo13bo3bo$421bo21bo80bo$422bobo6b3o6bobo81bo$524bo2$524bo
$431b3o90bo$524bo2$511bo12bo12bo$431b3o61bo14b3o11bo11b3o14bo$494b3o6b
o6bob2o10bo10b2obo6bo6b3o$494bob2o4b3o6b3o21b3o6b3o4b2obo$495b3o3bo2b
2o5b3o10bo10b3o5b2o2bo3b3o$418b3o10b3o10b3o48b3o2bobo2bo5b3o10bo10b3o
5bo2bobo2b3o$402b3o12bo2bo23bo2bo12b3o32b2o7bob3o2b2o11bo11b2o2b3obo7b
2o$401bo2bo5b3o7bo23bo7b3o5bo2bo34b2o6b2o3b2o23b2o3b2o6b2o$404bo4bo2b
o3bo3bo23bo3bo3bo2bo4bo35bo2bo6bo3b2o12bo12b2o3bo6bo2bo$400bo3bo4bo3b
o2bo3bo10b3o10bo3bo2bo3bo4bo3bo30bo11bo16bo16bo11bo$404bo2bo3bobo6bo23b
o6bobo3bo2bo34bo28bo28bo$404bobo8b2o2bo25bo2b2o8bobo$406bo8b5o25b5o8b
o65bo$402b3o3bo6b2o14b3o14b2o6bo3b3o49bo11bo11bo$418b2o25b2o49bo14b3o
10bo10b3o14bo$495b3o6bo6bob2o19b2obo6bo6b3o$495bob2o4b3o6b3o9bo9b3o6b
3o4b2obo$431b3o62b3o3bo2b2o5b3o9bo9b3o5b2o2bo3b3o$419b3o21b3o50b3o2bo
bo2bo5b3o9bo9b3o5bo2bobo2b3o$403b3o12bo2bo21bo2bo12b3o34b2o7bob3o2b2o
21b2o2b3obo7b2o$402bo2bo5b3o7bo21bo7b3o5bo2bo36b2o6b2o3b2o10bo10b2o3b
2o6b2o$405bo4bo2bo3bo3bo9b3o9bo3bo3bo2bo4bo37bo2bo6bo3b2o10bobo10b2o3b
o6bo2bo$401bo3bo4bo3bo2bo3bo21bo3bo2bo3bo4bo3bo32bo11bo13b2ob2o13bo11b
o$405bo2bo3bobo6bo21bo6bobo3bo2bo36bo26bobo26bo$405bobo8b2o2bo23bo2b2o
8bobo62b2ob2o$407bo8b5o10b3o10b5o8bo63bo5bo$403b3o3bo6b2o13bobo13b2o6b
o3b3o50bo9bo3bo$419b2o10bobo10b2o65b3o$430b2ob2o76bob2o7b2ob2o$429bo5b
o76b3o8bobo10b3o$430b2ob2o77b3o7b2ob2o8bo2bo$443b3o66b3o7b2ob2o11bo$430b
2ob2o8bo2bo65b2o20bo3bo$419bo11bobo9bo94bo$418b3o10bobo9bo3bo87bobo$418b
ob2o9bobo9bo3bo$419b3o9bobo9bo$419b3o22bobo$419b2o7$511bo$510b3o$509b
2obo23b3o$509b3o23bo2bo$509b3o26bo$444b3o62b3o22bo3bo$419bo23bo2bo63b
2o26bo$418b3o25bo88bobo$418bob2o20bo3bo$419b3o20bo3bo66b3o$419b3o24bo
66bo2bo$419b2o22bobo67bo$513bo3bo$442bo70bo3bo$441b3o69bo$440b2obo70b
obo$440b3o$440b3o$440b3o$441b2o6$540b3o$540bo2bo$540bo$540bo$415bo125b
obo$414b3o$413b2obo$413b3o$414b2o16$538b3o$538bo2bo$538bo$527b2o9bo$417b
o109b2o10bobo$416b3o$415b2obo$415b3o10b2o$416b2o10b2o2$521b3o$521bo2b
o$521bo$521bo3bo$434bo86bo$433b3o86bobo$432b2obo$432b3o72b3o$432b3o72b
o$433b2o73bo2$447b2o$448b2o$447bo207$221bo$219bobo$220b2o12bo$233bo$233b
3o52$210bobo$213bo$213bo$210bo2bo$211b3o127$357bo$355b2o$356b2o41$428b
3o3b3o$428bo2bobo2bo$420b3o5bo2bobo2bo5b3o$420bo2bo4b2obobob2o4bo2bo$
420bo8b2o3b2o8bo$420bo3bo2b4o3b4o2bo3bo$420bo6b11o6bo$421bo2b2o4b5o4b
2o2bo$428bo7bo$432bo$432bo$432bo2$432bo$432bo$432bo2$432bo$432bo$431b
obo$431bobo$430b2ob2o$422bo7bo3bo7bo$421b3o6b2ob2o6b3o$421bob2o15b2ob
o$422b3o5b2ob2o5b3o$422b3o6bobo6b3o$422b3o6bobo6b3o$422b2o6b2ob2o6b2o
$429bobobobo11$419bo25bo$403bo14b3o23b3o14bo$402b3o6bo5b2obo23bob2o5b
o6b3o$401b2obo5b3o4b3o25b3o4b3o5bob2o$401b3o5b2o2bo3b3o25b3o3bo2b2o5b
3o$401b3o5bo2bobo2b3o25b3o2bobo2bo5b3o$402b2o2b3obo7b2o25b2o7bob3o2b2o
$402b2o3b2o6b2o31b2o6b2o3b2o$403b2o3bo6bo2bo27bo2bo6bo3b2o$407bo11bo25b
o11bo$419bo25bo3$420bo23bo$404bo14b3o21b3o14bo$403b3o6bo5b2obo21bob2o
5bo6b3o$402b2obo5b3o4b3o23b3o4b3o5bob2o$402b3o5b2o2bo3b3o23b3o3bo2b2o
5b3o$402b3o5bo2bobo2b3o23b3o2bobo2bo5b3o$403b2o2b3obo7b2o23b2o7bob3o2b
2o$403b2o3b2o6b2o29b2o6b2o3b2o$404b2o3bo6bo2bo25bo2bo6bo3b2o$408bo11b
o23bo11bo$420bo23bo3$420bo$419b3o$418b2obo$418b3o23b3o$418b3o23bo2bo$
418b3o23bo$419b2o23bo3bo$444bo$445bobo11$228b2o189bo$228b2o188b3o$418b
ob2o22b3o$419b3o22bo2bo$419b3o22bo$419b3o22bo3bo$419b2o23bo$445bobo2$
421b3o$420bo2bo$423bo$419bo3bo$419bo3bo$423bo$420bobo10$448b3o$447bo2b
o$450bo$450bo$447bobo20$446b3o$445bo2bo$448bo$448bo$445bobo6$429b3o$428b
o2bo$431bo$427bo3bo$431bo$428bobo64$353b2o$353bobo$353bo218$29b3o3b3o
$28bo2bo3bo2bo$21b3o8bobo8b3o$20bo2bo6b3ob3o6bo2bo$23bo5bob2ob2obo5bo
78bo5bo260b3o3b3o$19bo3bo4b2o2bobo2b2o4bo3bo73b3o3b3o80bobo176bo2bobo
2bo$23bo2bob2o3bo3b2obo2bo70bo5b2o2bobo2b2o5bo76bo167b3o5bo2bobo2bo5b
3o$20bobo3bob2o7b2obo3bobo66b3o4b2o2bobo2b2o4b3o75bo167bo2bo4b2obobob
2o4bo2bo$26bobo4bo4bobo71b2obo5bo2bobo2bo5bob2o71bo2bo84bo5bo76bo8b2o
3b2o8bo$33bo78b3o5bo3bobo3bo5b3o72b3o83b3o3b3o75bo3bo2b4o3b4o2bo3bo$33b
o78b3o5bo4bo4bo5b3o151bo6bob2ob2obo6bo68bo6b11o6bo$113b2o2b4o9b4o2b2o
151b3o6bobobobo6b3o68bo2b2o4b5o4b2o2bo$33bo86bo9bo158bob2o5bo5bo5b2ob
o75bo7bo$33bo90b3o163b3o3b2o7b2o3b3o$33bo194b2o60b3o2bo3b2ob2o3bo2b3o
$228b3o59b2o6bo2bo2bo6b2o80bo$33bo193bob2o62b2o13b2o83bo$33bo90b3o100b
3o66b2o7b2o86bo$33bo194bo$393bo$33bo266b3o90bo$33bo90b3o266bo$23bo9bo
9bo$22b3o17b3o348bo$21b2obo8bo8bob2o254b3o90bo$21b3o9bo9b3o78b3o266bo
$21b3o9bo9b3o337bo19bo$21b3o19b3o68b3o17b3o245b3o8bo8b3o$22b2o9bo9b2o
69bo2bo15bo2bo163b3o79bob2o7bo7b2obo$33bo80bo9b3o9bo246b3o7bo7b3o$33b
o80bo3bo13bo3bo246b3o15b3o$114bo3bo13bo3bo153b3o17b3o70b3o7bo7b3o$33b
o80bo21bo152bo2bo7b3o7bo2bo69b2o8bo8b2o$33bo81bobo6b3o6bobo156bo17bo82b
o$33bo254bo3bo17bo3bo$288bo3bo17bo3bo78bo$33bo258bo7b3o7bo82bo$33bo90b
3o162bobo19bobo79bo$33bo$393bo$20bo12bo12bo253b3o90bo$4bo14b3o11bo11b
3o14bo61b3o266bo$3b3o6bo6bob2o10bo10b2obo6bo6b3o$3bob2o4b3o6b3o21b3o6b
3o4b2obo329bo$4b3o3bo2b2o5b3o10bo10b3o5b2o2bo3b3o237b3o77bo12bo12bo$4b
3o2bobo2bo5b3o10bo10b3o5bo2bobo2b3o48b3o10b3o10b3o224bo14b3o11bo11b3o
14bo$4b2o7bob3o2b2o11bo11b2o2b3obo7b2o32b3o12bo2bo23bo2bo12b3o207b3o6b
o5b2obo23bob2o5bo6b3o$7b2o6b2o3b2o23b2o3b2o6b2o34bo2bo5b3o7bo23bo7b3o
5bo2bo205b2obo5b3o4b3o12bo12b3o4b3o5bob2o$5bo2bo6bo3b2o12bo12b2o3bo6b
o2bo35bo4bo2bo3bo3bo23bo3bo3bo2bo4bo146b3o59b3o5b2o2bo3b3o12bo12b3o3b
o2b2o5b3o$4bo11bo16bo16bo11bo30bo3bo4bo3bo2bo3bo10b3o10bo3bo2bo3bo4bo
3bo129b3o23b3o46b3o5bo2bobo2b3o12bo12b3o2bobo2bo5b3o$4bo28bo28bo34bo2b
o3bobo6bo23bo6bobo3bo2bo117b3o13bo2bo21bo2bo13b3o31b2o2b3obo7b2o25b2o
7bob3o2b2o$97bobo8b2o2bo25bo2b2o8bobo117bo2bo4b3o5bo27bo5b3o4bo2bo31b
2o3b2o6b2o15bo15b2o6b2o3b2o$33bo65bo8b5o25b5o8bo119bo7bo2bo4bo3bo8b3o
8bo3bo4bo2bo7bo32b2o3bo6bo2bo13bo13bo2bo6bo3b2o$21bo11bo11bo49b3o3bo6b
2o14b3o14b2o6bo3b3o115bo3bo2bo3bo4bo3bo19bo3bo4bo3bo2bo3bo36bo11bo12b
o12bo11bo$5bo14b3o10bo10b3o14bo49b2o25b2o131bo6bobo3bo2bo27bo2bo3bobo
6bo48bo25bo$4b3o6bo6bob2o19b2obo6bo6b3o209bo2b2o8bobo27bobo8b2o2bo62b
o$4bob2o4b3o6b3o9bo9b3o6b3o4b2obo209b5o8bo14b3o14bo8b5o62bo$5b3o3bo2b
2o5b3o8bobo8b3o5b2o2bo3b3o62b3o148b2o6bo3b3o23b3o3bo6b2o53bo11bo11bo$
5b3o2bobo2bo5b3o7b2ob2o7b3o5bo2bobo2b3o50b3o21b3o133b2o55b2o34bo14b3o
21b3o14bo$5b2o7bob3o2b2o9bobo9b2o2b3obo7b2o34b3o12bo2bo21bo2bo12b3o209b
3o6bo5b2obo10bo10bob2o5bo6b3o$8b2o6b2o3b2o8b2ob2o8b2o3b2o6b2o36bo2bo5b
3o7bo21bo7b3o5bo2bo144b3o60b2obo5b3o4b3o11bo11b3o4b3o5bob2o$6bo2bo6bo
3b2o8bo5bo8b2o3bo6bo2bo37bo4bo2bo3bo3bo9b3o9bo3bo3bo2bo4bo210b3o5b2o2b
o3b3o10bobo10b3o3bo2b2o5b3o$5bo11bo13bo3bo13bo11bo32bo3bo4bo3bo2bo3bo
9bobo9bo3bo2bo3bo4bo3bo131b3o21b3o48b3o5bo2bobo2b3o10bobo10b3o2bobo2b
o5b3o$5bo55bo36bo2bo3bobo6bo9bobo9bo6bobo3bo2bo119b3o13bo2bo19bo2bo13b
3o33b2o2b3obo7b2o9b2ob2o9b2o7bob3o2b2o$31b2ob2o62bobo8b2o2bo9b2ob2o9b
o2b2o8bobo119bo2bo4b3o5bo11b3o11bo5b3o4bo2bo33b2o3b2o6b2o12bo3bo12b2o
6b2o3b2o$30bo5bo63bo8b5o8bo5bo8b5o8bo121bo7bo2bo4bo3bo17bo3bo4bo2bo7b
o34b2o3bo6bo2bo10b2ob2o10bo2bo6bo3b2o$31b2ob2o9bo50b3o3bo6b2o12b2ob2o
12b2o6bo3b3o117bo3bo2bo3bo4bo3bo7bobo7bo3bo4bo3bo2bo3bo38bo11bo23bo11b
o$44b3o65b2o23b2o133bo6bobo3bo2bo11b3o11bo2bo3bobo6bo50bo9b2ob2o9bo$43b
2obo76b2ob2o145bo2b2o8bobo10bo3bo10bobo8b2o2bo62bobo$19b3o21b3o77b2ob
2o145b5o8bo12b2ob2o12bo8b5o$19bo2bo20b3o77b2ob2o148b2o6bo3b3o21b3o3bo
6b2o54bo9b2ob2o$19bo23b3o66b3o158b2o24b2ob2o24b2o50b3o$19bo3bo20b2o65b
o2bo185bobo76b2obo$19bo94bo23bo161bobo76b3o23b3o$20bobo87bo3bo22b3o239b
3o23bo2bo$110bo3bo21b2obo159b2ob2o8b3o64b3o23bo$114bo21b3o172bo2bo65b
2o23bo3bo$111bobo22b3o149bo25bo90bo$137b2o148b3o20bo3bo91bobo$286b2ob
o20bo3bo$286b3o25bo$286b3o22bobo$287b2o3$46bo$45b3o$19b3o23bob2o$19bo
2bo23b3o$19bo26b3o331bo$19bo3bo22b3o62b3o265b3o$19bo26b2o63bo2bo23bo240b
ob2o22b3o$20bobo88bo25b3o240b3o22bo2bo$111bo3bo20b2obo240b3o22bo$42b3o
66bo3bo20b3o174b3o64b3o22bo3bo$41bo2bo66bo24b3o149bo24bo2bo63b2o23bo$
44bo67bobo22b2o148b3o23bo92bobo$40bo3bo241b2obo23bo3bo$40bo3bo70bo170b
3o24bo3bo64b3o$44bo69b3o169b3o24bo67bo2bo$41bobo70bob2o169b2o25bobo67b
o$115b3o262bo3bo$115b3o193bo68bo3bo$115b3o192b3o71bo$115b2o193bob2o67b
obo$311b3o$311b3o$311b3o$311b2o2$15b3o$14bo2bo$17bo$17bo$14bobo125bo266b
3o$141b3o264bo2bo$141bob2o266bo$142b3o266bo$142b2o140bo123bobo$283b3o
$283bob2o$284b3o$284b2o12$17b3o$16bo2bo$19bo$19bo$16bobo121bo266b3o$139b
3o264bo2bo$139bob2o266bo$140b3o266bo$140b2o144bo119bobo$285b3o$34b3o248b
ob2o$33bo2bo249b3o$36bo249b2o$32bo3bo$36bo86bo266b3o$33bobo86b3o264bo
2bo$122bob2o266bo$123b3o262bo3bo$123b3o177bo88bo$123b2o177b3o84bobo$302b
ob2o$303b3o$303b3o$54b3o242bo3b2o$56bo242bo$55bo$371b2o$103b2o266bobo
$102b2o267bo$104bo$322bo$322b2o$321bobo38$507bo5bo$506b3o3b3o$499bo6b
ob2ob2obo6bo$498b3o6bobobobo6b3o$498bob2o5bo5bo5b2obo$414b3o3b3o76b3o
3b2o7b2o3b3o$413bo2bo3bo2bo75b3o2bo3b2ob2o3bo2b3o$406b3o8bobo8b3o68b2o
6bo2bo2bo6b2o$405bo2bo6b3ob3o6bo2bo70b2o13b2o$408bo5bob2ob2obo5bo76b2o
7b2o$404bo3bo4b2o2bobo2b2o4bo3bo76b3o$408bo2bob2o3bo3b2obo2bo$405bobo
3bob2o7b2obo3bobo$411bobo4bo4bobo$418bo90b3o$418bo2$418bo$418bo90b3o$
418bo2$418bo$418bo90b3o$418bo80b3o17b3o$498bo2bo17bo2bo$418bo82bo17bo
$418bo78bo3bo7b3o7bo3bo$408bo9bo9bo68bo3bo17bo3bo$407b3o17b3o71bo17bo
$406b2obo8bo8bob2o67bobo19bobo$406b3o9bo9b3o78b3o$406b3o9bo9b3o$406b3o
19b3o$407b2o9bo9b2o$418bo90b3o$418bo2$418bo$418bo90b3o$418bo2$418bo77b
3o23b3o$418bo61b3o13bo2bo9b3o9bo2bo13b3o$418bo61bo2bo4b3o5bo27bo5b3o4b
o2bo$480bo7bo2bo4bo3bo19bo3bo4bo2bo7bo$405bo12bo12bo48bo3bo2bo3bo4bo3b
o19bo3bo4bo3bo2bo3bo$389bo14b3o11bo11b3o14bo32bo6bobo3bo2bo12b3o12bo2b
o3bobo6bo$388b3o6bo6bob2o10bo10b2obo6bo6b3o32bo2b2o8bobo27bobo8b2o2bo
$388bob2o4b3o6b3o21b3o6b3o4b2obo32b5o8bo31bo8b5o$389b3o3bo2b2o5b3o10b
o10b3o5b2o2bo3b3o36b2o6bo3b3o23b3o3bo6b2o$389b3o2bobo2bo5b3o10bo10b3o
5bo2bobo2b3o33b2o26b3o26b2o$389b2o7bob3o2b2o11bo11b2o2b3obo7b2o$392b2o
6b2o3b2o23b2o3b2o6b2o$390bo2bo6bo3b2o12bo12b2o3bo6bo2bo$389bo11bo16bo
16bo11bo49b3o9b3o9b3o$389bo28bo28bo33b3o13bo2bo19bo2bo13b3o$481bo2bo4b
3o5bo25bo5b3o4bo2bo$418bo62bo7bo2bo4bo3bo17bo3bo4bo2bo7bo$406bo11bo11b
o50bo3bo2bo3bo4bo3bo7b3o7bo3bo4bo3bo2bo3bo$390bo14b3o10bo10b3o14bo34b
o6bobo3bo2bo25bo2bo3bobo6bo$389b3o6bo6bob2o19b2obo6bo6b3o34bo2b2o8bob
o25bobo8b2o2bo$389bob2o4b3o6b3o9bo9b3o6b3o4b2obo34b5o8bo14bo14bo8b5o$
390b3o3bo2b2o5b3o9bo9b3o5b2o2bo3b3o38b2o6bo3b3o8b2ob2o8b3o3bo6b2o$390b
3o2bobo2bo5b3o9bo9b3o5bo2bobo2b3o35b2o24b2ob2o24b2o$390b2o7bob3o2b2o21b
2o2b3obo7b2o$393b2o6b2o3b2o10bo10b2o3b2o6b2o64b2ob2o$391bo2bo6bo3b2o10b
obo10b2o3bo6bo2bo61bobobobo$390bo11bo13b2ob2o13bo11bo50b3o$390bo26bob
o26bo50bo2bo7b2ob2o$416b2ob2o76bo10b2ob2o10bo$415bo5bo75bo3bo20b3o$416b
o3bo9bo66bo3bo20bob2o$429b3o65bo10b2ob2o10b3o$416b2ob2o7b2obo66bobo22b
3o$404b3o10bobo8b3o92b2o$404bo2bo8b2ob2o7b3o$404bo11b2ob2o7b3o$404bo3b
o20b2o$404bo$405bobo7$496b3o$495bo2bo24bo$498bo23b3o$494bo3bo23bob2o$
431bo62bo3bo24b3o$430b3o65bo24b3o$404b3o23bob2o61bobo25b2o$404bo2bo23b
3o$404bo26b3o66bo$404bo3bo22b3o65b3o$404bo26b2o65b2obo$405bobo90b3o$498b
3o$427b3o68b3o$426bo2bo69b2o$429bo$425bo3bo$425bo3bo$429bo$426bobo5$527b
o$526b3o$525b2obo$525b3o$526b2o$400b3o$399bo2bo$402bo$402bo$399bobo15$
525bo$524b3o$523b2obo$523b3o$513b2o9b2o$402b3o108b2o$401bo2bo$404bo$404b
o9b2o$401bobo10b2o$508bo$507b3o$506b2obo$506b3o$506b3o$419b3o85b2o$418b
o2bo$421bo72bo$417bo3bo71b2o$421bo71bobo$418bobo2$433b3o$435bo$434bo207$
206bo$207b2o$206b2o$219bobo$219b2o$220bo43$210bobo$213bo$213bo$210bo2b
o$211b3o5$228b2o$228b3o$227bob2o$227b3o$228bo126$342bo$341bo$341b3o40$
415bo5bo$414b3o3b3o$407bo5b2o2bobo2b2o5bo$406b3o4b2o2bobo2b2o4b3o$405b
2obo5bo2bobo2bo5bob2o$405b3o5bo3bobo3bo5b3o$405b3o5bo4bo4bo5b3o$406b2o
2b4o9b4o2b2o$413bo9bo3$417b3o4$417b3o4$417b3o$417bobo$417bobo$416b2ob
2o$407b3o5bo5bo5b3o$407bo2bo5b2ob2o5bo2bo$407bo21bo$407bo3bo4b2ob2o4b
o3bo$407bo3bo5bobo5bo3bo$407bo9bobo9bo$408bobo6bobo6bobo$417bobo11$404b
3o23b3o$388b3o12bo2bo23bo2bo12b3o$387bo2bo5b3o7bo23bo7b3o5bo2bo$390bo
4bo2bo3bo3bo23bo3bo3bo2bo4bo$386bo3bo4bo3bo2bo3bo23bo3bo2bo3bo4bo3bo$
390bo2bo3bobo6bo23bo6bobo3bo2bo$390bobo8b2o2bo25bo2b2o8bobo$392bo8b5o
25b5o8bo$388b3o3bo6b2o31b2o6bo3b3o$404b2o25b2o4$405b3o21b3o$389b3o12b
o2bo21bo2bo12b3o$388bo2bo5b3o7bo21bo7b3o5bo2bo$391bo4bo2bo3bo3bo21bo3b
o3bo2bo4bo$387bo3bo4bo3bo2bo3bo21bo3bo2bo3bo4bo3bo$391bo2bo3bobo6bo21b
o6bobo3bo2bo$391bobo8b2o2bo23bo2b2o8bobo$393bo8b5o23b5o8bo$389b3o3bo6b
2o29b2o6bo3b3o$405b2o23b2o4$405b3o$404bo2bo$407bo23bo$403bo3bo22b3o$403b
o3bo21b2obo$407bo21b3o$404bobo22b3o$430b2o12$214b2o188b3o$214b2o188bo
2bo23bo$404bo25b3o$404bo3bo20b2obo$404bo3bo20b3o$404bo24b3o$405bobo22b
2o2$408bo$407b3o$407bob2o$408b3o$408b3o$408b3o$408b2o10$435bo$434b3o$
434bob2o$435b3o$435b2o20$433bo$432b3o$432bob2o$433b3o$433b2o6$416bo$415b
3o$415bob2o$416b3o$416b3o$416b2o65$339b2o$338b2o$340bo210$35b3o3b3o$34b
o2bo3bo2bo$27b3o8bobo8b3o$26bo2bo6b3ob3o6bo2bo$29bo5bob2ob2obo5bo78bo
5bo260b3o3b3o$25bo3bo4b2o2bobo2b2o4bo3bo73b3o3b3o74bobo182bo2bobo2bo$
29bo2bob2o3bo3b2obo2bo70bo5b2o2bobo2b2o5bo70bo173b3o5bo2bobo2bo5b3o$26b
obo3bob2o7b2obo3bobo66b3o4b2o2bobo2b2o4b3o69bo173bo2bo4b2obobob2o4bo2b
o$32bobo4bo4bobo71b2obo5bo2bobo2bo5bob2o65bo2bo90bo5bo76bo8b2o3b2o8bo
$39bo78b3o5bo3bobo3bo5b3o66b3o89b3o3b3o75bo3bo2b4o3b4o2bo3bo$39bo78b3o
5bo4bo4bo5b3o151bo6bob2ob2obo6bo68bo6b11o6bo$119b2o2b4o9b4o2b2o151b3o
6bobobobo6b3o68bo2b2o4b5o4b2o2bo$39bo86bo9bo158bob2o5bo5bo5b2obo75bo7b
o$39bo90b3o163b3o3b2o7b2o3b3o$39bo188b2o66b3o2bo3b2ob2o3bo2b3o$228b3o
65b2o6bo2bo2bo6b2o80bo$39bo187bob2o68b2o13b2o83bo$39bo90b3o94b3o72b2o
7b2o86bo$39bo188bo$399bo$39bo266b3o90bo$39bo90b3o266bo$29bo9bo9bo164b
obo$28b3o17b3o162bo185bo$27b2obo8bo8bob2o161bo92b3o90bo$27b3o9bo9b3o78b
3o80bo2bo182bo$27b3o9bo9b3o161b3o173bo19bo$27b3o19b3o68b3o17b3o245b3o
8bo8b3o$28b2o9bo9b2o69bo2bo15bo2bo163b3o79bob2o7bo7b2obo$39bo80bo9b3o
9bo246b3o7bo7b3o$39bo80bo3bo13bo3bo246b3o15b3o$120bo3bo13bo3bo153b3o17b
3o70b3o7bo7b3o$39bo80bo21bo152bo2bo7b3o7bo2bo69b2o8bo8b2o$39bo81bobo6b
3o6bobo156bo17bo82bo$39bo254bo3bo17bo3bo$294bo3bo17bo3bo78bo$39bo258b
o7b3o7bo82bo$39bo90b3o162bobo19bobo79bo$39bo$399bo$26bo12bo12bo253b3o
90bo$10bo14b3o11bo11b3o14bo61b3o266bo$9b3o6bo6bob2o10bo10b2obo6bo6b3o
$9bob2o4b3o6b3o21b3o6b3o4b2obo329bo$10b3o3bo2b2o5b3o10bo10b3o5b2o2bo3b
3o237b3o77bo12bo12bo$10b3o2bobo2bo5b3o10bo10b3o5bo2bobo2b3o48b3o10b3o
10b3o224bo14b3o11bo11b3o14bo$10b2o7bob3o2b2o11bo11b2o2b3obo7b2o32b3o12b
o2bo23bo2bo12b3o207b3o6bo5b2obo23bob2o5bo6b3o$13b2o6b2o3b2o23b2o3b2o6b
2o34bo2bo5b3o7bo23bo7b3o5bo2bo205b2obo5b3o4b3o12bo12b3o4b3o5bob2o$11b
o2bo6bo3b2o12bo12b2o3bo6bo2bo35bo4bo2bo3bo3bo23bo3bo3bo2bo4bo146b3o59b
3o5b2o2bo3b3o12bo12b3o3bo2b2o5b3o$10bo11bo16bo16bo11bo30bo3bo4bo3bo2b
o3bo10b3o10bo3bo2bo3bo4bo3bo129b3o23b3o46b3o5bo2bobo2b3o12bo12b3o2bob
o2bo5b3o$10bo28bo28bo34bo2bo3bobo6bo23bo6bobo3bo2bo117b3o13bo2bo21bo2b
o13b3o31b2o2b3obo7b2o25b2o7bob3o2b2o$103bobo8b2o2bo25bo2b2o8bobo117bo
2bo4b3o5bo27bo5b3o4bo2bo31b2o3b2o6b2o15bo15b2o6b2o3b2o$39bo65bo8b5o25b
5o8bo119bo7bo2bo4bo3bo8b3o8bo3bo4bo2bo7bo32b2o3bo6bo2bo13bo13bo2bo6bo
3b2o$27bo11bo11bo49b3o3bo6b2o14b3o14b2o6bo3b3o115bo3bo2bo3bo4bo3bo19b
o3bo4bo3bo2bo3bo36bo11bo12bo12bo11bo$11bo14b3o10bo10b3o14bo49b2o25b2o
131bo6bobo3bo2bo27bo2bo3bobo6bo48bo25bo$10b3o6bo6bob2o19b2obo6bo6b3o209b
o2b2o8bobo27bobo8b2o2bo62bo$10bob2o4b3o6b3o9bo9b3o6b3o4b2obo209b5o8bo
14b3o14bo8b5o62bo$11b3o3bo2b2o5b3o8bobo8b3o5b2o2bo3b3o62b3o148b2o6bo3b
3o23b3o3bo6b2o53bo11bo11bo$11b3o2bobo2bo5b3o7b2ob2o7b3o5bo2bobo2b3o50b
3o21b3o133b2o55b2o34bo14b3o21b3o14bo$11b2o7bob3o2b2o9bobo9b2o2b3obo7b
2o34b3o12bo2bo21bo2bo12b3o209b3o6bo5b2obo10bo10bob2o5bo6b3o$14b2o6b2o
3b2o8b2ob2o8b2o3b2o6b2o36bo2bo5b3o7bo21bo7b3o5bo2bo144b3o60b2obo5b3o4b
3o11bo11b3o4b3o5bob2o$12bo2bo6bo3b2o8bo5bo8b2o3bo6bo2bo37bo4bo2bo3bo3b
o9b3o9bo3bo3bo2bo4bo210b3o5b2o2bo3b3o10bobo10b3o3bo2b2o5b3o$11bo11bo13b
o3bo13bo11bo32bo3bo4bo3bo2bo3bo9bobo9bo3bo2bo3bo4bo3bo131b3o21b3o48b3o
5bo2bobo2b3o10bobo10b3o2bobo2bo5b3o$11bo55bo36bo2bo3bobo6bo9bobo9bo6b
obo3bo2bo119b3o13bo2bo19bo2bo13b3o33b2o2b3obo7b2o9b2ob2o9b2o7bob3o2b2o
$37b2ob2o62bobo8b2o2bo9b2ob2o9bo2b2o8bobo119bo2bo4b3o5bo11b3o11bo5b3o
4bo2bo33b2o3b2o6b2o12bo3bo12b2o6b2o3b2o$36bo5bo63bo8b5o8bo5bo8b5o8bo121b
o7bo2bo4bo3bo17bo3bo4bo2bo7bo34b2o3bo6bo2bo10b2ob2o10bo2bo6bo3b2o$37b
2ob2o9bo50b3o3bo6b2o12b2ob2o12b2o6bo3b3o117bo3bo2bo3bo4bo3bo7bobo7bo3b
o4bo3bo2bo3bo38bo11bo23bo11bo$50b3o65b2o23b2o133bo6bobo3bo2bo11b3o11b
o2bo3bobo6bo50bo9b2ob2o9bo$49b2obo76b2ob2o145bo2b2o8bobo10bo3bo10bobo
8b2o2bo62bobo$25b3o21b3o77b2ob2o145b5o8bo12b2ob2o12bo8b5o$25bo2bo20b3o
77b2ob2o148b2o6bo3b3o21b3o3bo6b2o54bo9b2ob2o$25bo23b3o66b3o158b2o24b2o
b2o24b2o50b3o$25bo3bo20b2o65bo2bo185bobo76b2obo$25bo94bo23bo161bobo76b
3o23b3o$26bobo87bo3bo22b3o239b3o23bo2bo$116bo3bo21b2obo159b2ob2o8b3o64b
3o23bo$120bo21b3o172bo2bo65b2o23bo3bo$117bobo22b3o149bo25bo90bo$143b2o
148b3o20bo3bo91bobo$292b2obo20bo3bo$292b3o25bo$292b3o22bobo$293b2o3$52b
o$51b3o$25b3o23bob2o$25bo2bo23b3o$25bo26b3o331bo$25bo3bo22b3o62b3o265b
3o$25bo26b2o63bo2bo23bo240bob2o22b3o$26bobo88bo25b3o240b3o22bo2bo$117b
o3bo20b2obo240b3o22bo$48b3o66bo3bo20b3o174b3o64b3o22bo3bo$47bo2bo66bo
24b3o149bo24bo2bo63b2o23bo$50bo67bobo22b2o148b3o23bo92bobo$46bo3bo241b
2obo23bo3bo$46bo3bo70bo170b3o24bo3bo64b3o$50bo69b3o169b3o24bo67bo2bo$
47bobo70bob2o169b2o25bobo67bo$121b3o262bo3bo$121b3o193bo68bo3bo$121b3o
192b3o71bo$121b2o193bob2o67bobo$317b3o$317b3o$317b3o$317b2o2$21b3o$20b
o2bo$23bo$23bo$20bobo125bo266b3o$147b3o264bo2bo$147bob2o266bo$148b3o266b
o$148b2o140bo123bobo$289b3o$289bob2o$290b3o$290b2o12$23b3o$22bo2bo$25b
o$25bo$22bobo121bo266b3o$145b3o264bo2bo$145bob2o266bo$146b3o266bo$146b
2o144bo119bobo$291b3o$40b3o248bob2o$39bo2bo249b3o$42bo249b2o$38bo3bo$
42bo86bo266b3o$39bobo86b3o264bo2bo$128bob2o266bo$129b3o262bo3bo$129b3o
177bo88bo$129b2o177b3o84bobo$308bob2o$309b3o$309b3o$60b3o242bo3b2o$62b
o242bo$61bo$377b2o$109b2o266bobo$108b2o267bo$110bo$328bo$328b2o$327bo
bo38$513bo5bo$512b3o3b3o$505bo6bob2ob2obo6bo$504b3o6bobobobo6b3o$504b
ob2o5bo5bo5b2obo$420b3o3b3o76b3o3b2o7b2o3b3o$419bo2bo3bo2bo75b3o2bo3b
2ob2o3bo2b3o$412b3o8bobo8b3o68b2o6bo2bo2bo6b2o$411bo2bo6b3ob3o6bo2bo70b
2o13b2o$414bo5bob2ob2obo5bo76b2o7b2o$410bo3bo4b2o2bobo2b2o4bo3bo76b3o
$414bo2bob2o3bo3b2obo2bo$411bobo3bob2o7b2obo3bobo$417bobo4bo4bobo$424b
o90b3o$424bo2$424bo$424bo90b3o$424bo2$424bo$424bo90b3o$424bo80b3o17b3o
$504bo2bo17bo2bo$424bo82bo17bo$424bo78bo3bo7b3o7bo3bo$414bo9bo9bo68bo
3bo17bo3bo$413b3o17b3o71bo17bo$412b2obo8bo8bob2o67bobo19bobo$412b3o9b
o9b3o78b3o$412b3o9bo9b3o$412b3o19b3o$413b2o9bo9b2o$424bo90b3o$424bo2$
424bo$424bo90b3o$424bo2$424bo77b3o23b3o$424bo61b3o13bo2bo9b3o9bo2bo13b
3o$424bo61bo2bo4b3o5bo27bo5b3o4bo2bo$486bo7bo2bo4bo3bo19bo3bo4bo2bo7b
o$411bo12bo12bo48bo3bo2bo3bo4bo3bo19bo3bo4bo3bo2bo3bo$395bo14b3o11bo11b
3o14bo32bo6bobo3bo2bo12b3o12bo2bo3bobo6bo$394b3o6bo6bob2o10bo10b2obo6b
o6b3o32bo2b2o8bobo27bobo8b2o2bo$394bob2o4b3o6b3o21b3o6b3o4b2obo32b5o8b
o31bo8b5o$395b3o3bo2b2o5b3o10bo10b3o5b2o2bo3b3o36b2o6bo3b3o23b3o3bo6b
2o$395b3o2bobo2bo5b3o10bo10b3o5bo2bobo2b3o33b2o26b3o26b2o$395b2o7bob3o
2b2o11bo11b2o2b3obo7b2o$398b2o6b2o3b2o23b2o3b2o6b2o$396bo2bo6bo3b2o12b
o12b2o3bo6bo2bo$395bo11bo16bo16bo11bo49b3o9b3o9b3o$395bo28bo28bo33b3o
13bo2bo19bo2bo13b3o$487bo2bo4b3o5bo25bo5b3o4bo2bo$424bo62bo7bo2bo4bo3b
o17bo3bo4bo2bo7bo$412bo11bo11bo50bo3bo2bo3bo4bo3bo7b3o7bo3bo4bo3bo2bo
3bo$396bo14b3o10bo10b3o14bo34bo6bobo3bo2bo25bo2bo3bobo6bo$395b3o6bo6b
ob2o19b2obo6bo6b3o34bo2b2o8bobo25bobo8b2o2bo$395bob2o4b3o6b3o9bo9b3o6b
3o4b2obo34b5o8bo14bo14bo8b5o$396b3o3bo2b2o5b3o9bo9b3o5b2o2bo3b3o38b2o
6bo3b3o8b2ob2o8b3o3bo6b2o$396b3o2bobo2bo5b3o9bo9b3o5bo2bobo2b3o35b2o24b
2ob2o24b2o$396b2o7bob3o2b2o21b2o2b3obo7b2o$399b2o6b2o3b2o10bo10b2o3b2o
6b2o64b2ob2o$397bo2bo6bo3b2o10bobo10b2o3bo6bo2bo61bobobobo$396bo11bo13b
2ob2o13bo11bo50b3o$396bo26bobo26bo50bo2bo7b2ob2o$422b2ob2o76bo10b2ob2o
10bo$421bo5bo75bo3bo20b3o$422bo3bo9bo66bo3bo20bob2o$435b3o65bo10b2ob2o
10b3o$422b2ob2o7b2obo66bobo22b3o$410b3o10bobo8b3o92b2o$410bo2bo8b2ob2o
7b3o$410bo11b2ob2o7b3o$410bo3bo20b2o$410bo$411bobo7$502b3o$501bo2bo24b
o$504bo23b3o$500bo3bo23bob2o$437bo62bo3bo24b3o$436b3o65bo24b3o$410b3o
23bob2o61bobo25b2o$410bo2bo23b3o$410bo26b3o66bo$410bo3bo22b3o65b3o$410b
o26b2o65b2obo$411bobo90b3o$504b3o$433b3o68b3o$432bo2bo69b2o$435bo$431b
o3bo$431bo3bo$435bo$432bobo5$533bo$532b3o$531b2obo$531b3o$532b2o$406b
3o$405bo2bo$408bo$408bo$405bobo15$531bo$530b3o$529b2obo$529b3o$519b2o
9b2o$408b3o108b2o$407bo2bo$410bo$410bo9b2o$407bobo10b2o$514bo$513b3o$
512b2obo$512b3o$512b3o$425b3o85b2o$424bo2bo$427bo72bo$423bo3bo71b2o$427b
o71bobo$424bobo2$439b3o$441bo$440bo207$212bo$213b2o$212b2o$225bobo$225b
2o$226bo43$210bobo$213bo$213bo$210bo2bo$211b3o5$228b2o$228b3o$227bob2o
$227b3o$228bo4$214bobo$213bo$213bo$213bo2bo$213b3o118$348bo$347bo$347b
3o40$421bo5bo$420b3o3b3o$413bo5b2o2bobo2b2o5bo$412b3o4b2o2bobo2b2o4b3o
$411b2obo5bo2bobo2bo5bob2o$411b3o5bo3bobo3bo5b3o$411b3o5bo4bo4bo5b3o$
412b2o2b4o9b4o2b2o$419bo9bo3$423b3o4$423b3o4$423b3o$423bobo$423bobo$422b
2ob2o$413b3o5bo5bo5b3o$413bo2bo5b2ob2o5bo2bo$413bo21bo$413bo3bo4b2ob2o
4bo3bo$413bo3bo5bobo5bo3bo$413bo9bobo9bo$414bobo6bobo6bobo$423bobo11$
410b3o23b3o$394b3o12bo2bo23bo2bo12b3o$393bo2bo5b3o7bo23bo7b3o5bo2bo$396b
o4bo2bo3bo3bo23bo3bo3bo2bo4bo$392bo3bo4bo3bo2bo3bo23bo3bo2bo3bo4bo3bo
$396bo2bo3bobo6bo23bo6bobo3bo2bo$396bobo8b2o2bo25bo2b2o8bobo$398bo8b5o
25b5o8bo$394b3o3bo6b2o31b2o6bo3b3o$410b2o25b2o4$411b3o21b3o$395b3o12b
o2bo21bo2bo12b3o$394bo2bo5b3o7bo21bo7b3o5bo2bo$397bo4bo2bo3bo3bo21bo3b
o3bo2bo4bo$393bo3bo4bo3bo2bo3bo21bo3bo2bo3bo4bo3bo$397bo2bo3bobo6bo21b
o6bobo3bo2bo$397bobo8b2o2bo23bo2b2o8bobo$399bo8b5o23b5o8bo$395b3o3bo6b
2o29b2o6bo3b3o$411b2o23b2o4$411b3o$410bo2bo$413bo23bo$409bo3bo22b3o$409b
o3bo21b2obo$413bo21b3o$410bobo22b3o$436b2o12$220b2o188b3o$220b2o188bo
2bo23bo$410bo25b3o$410bo3bo20b2obo$410bo3bo20b3o$410bo24b3o$411bobo22b
2o2$414bo$413b3o$413bob2o$414b3o$414b3o$414b3o$414b2o10$441bo$440b3o$
440bob2o$441b3o$441b2o20$439bo$438b3o$438bob2o$439b3o$439b2o6$422bo$421b
3o$421bob2o$422b3o$422b3o$422b2o65$345b2o$344b2o$346bo210$43b3o3b3o$42b
o2bo3bo2bo$35b3o8bobo8b3o$34bo2bo6b3ob3o6bo2bo$37bo5bob2ob2obo5bo78bo
5bo260b3o3b3o$33bo3bo4b2o2bobo2b2o4bo3bo73b3o3b3o66bobo190bo2bobo2bo$
37bo2bob2o3bo3b2obo2bo70bo5b2o2bobo2b2o5bo62bo181b3o5bo2bobo2bo5b3o$34b
obo3bob2o7b2obo3bobo66b3o4b2o2bobo2b2o4b3o61bo181bo2bo4b2obobob2o4bo2b
o$40bobo4bo4bobo71b2obo5bo2bobo2bo5bob2o57bo2bo98bo5bo76bo8b2o3b2o8bo
$47bo78b3o5bo3bobo3bo5b3o58b3o97b3o3b3o75bo3bo2b4o3b4o2bo3bo$47bo78b3o
5bo4bo4bo5b3o151bo6bob2ob2obo6bo68bo6b11o6bo$127b2o2b4o9b4o2b2o151b3o
6bobobobo6b3o68bo2b2o4b5o4b2o2bo$47bo86bo9bo158bob2o5bo5bo5b2obo75bo7b
o$47bo90b3o163b3o3b2o7b2o3b3o$47bo180b2o74b3o2bo3b2ob2o3bo2b3o$228b3o
73b2o6bo2bo2bo6b2o80bo$47bo179bob2o76b2o13b2o83bo$47bo90b3o86b3o80b2o
7b2o86bo$47bo180bo$407bo$47bo266b3o90bo$47bo90b3o266bo$37bo9bo9bo156b
obo3bobo$36b3o17b3o154bo5bo187bo$35b2obo8bo8bob2o153bo5bo94b3o90bo$35b
3o9bo9b3o78b3o72bo2bo2bo2bo184bo$35b3o9bo9b3o153b3o3b3o175bo19bo$35b3o
19b3o68b3o17b3o245b3o8bo8b3o$36b2o9bo9b2o69bo2bo15bo2bo163b3o79bob2o7b
o7b2obo$47bo80bo9b3o9bo246b3o7bo7b3o$47bo80bo3bo13bo3bo246b3o15b3o$128b
o3bo13bo3bo153b3o17b3o70b3o7bo7b3o$47bo80bo21bo152bo2bo7b3o7bo2bo69b2o
8bo8b2o$47bo81bobo6b3o6bobo156bo17bo82bo$47bo254bo3bo17bo3bo$302bo3bo
17bo3bo78bo$47bo258bo7b3o7bo82bo$47bo90b3o162bobo19bobo79bo$47bo$407b
o$34bo12bo12bo253b3o90bo$18bo14b3o11bo11b3o14bo61b3o266bo$17b3o6bo6bo
b2o10bo10b2obo6bo6b3o$17bob2o4b3o6b3o21b3o6b3o4b2obo329bo$18b3o3bo2b2o
5b3o10bo10b3o5b2o2bo3b3o237b3o77bo12bo12bo$18b3o2bobo2bo5b3o10bo10b3o
5bo2bobo2b3o48b3o10b3o10b3o224bo14b3o11bo11b3o14bo$18b2o7bob3o2b2o11b
o11b2o2b3obo7b2o32b3o12bo2bo23bo2bo12b3o207b3o6bo5b2obo23bob2o5bo6b3o
$21b2o6b2o3b2o23b2o3b2o6b2o34bo2bo5b3o7bo23bo7b3o5bo2bo205b2obo5b3o4b
3o12bo12b3o4b3o5bob2o$19bo2bo6bo3b2o12bo12b2o3bo6bo2bo35bo4bo2bo3bo3b
o23bo3bo3bo2bo4bo146b3o59b3o5b2o2bo3b3o12bo12b3o3bo2b2o5b3o$18bo11bo16b
o16bo11bo30bo3bo4bo3bo2bo3bo10b3o10bo3bo2bo3bo4bo3bo129b3o23b3o46b3o5b
o2bobo2b3o12bo12b3o2bobo2bo5b3o$18bo28bo28bo34bo2bo3bobo6bo23bo6bobo3b
o2bo117b3o13bo2bo21bo2bo13b3o31b2o2b3obo7b2o25b2o7bob3o2b2o$111bobo8b
2o2bo25bo2b2o8bobo117bo2bo4b3o5bo27bo5b3o4bo2bo31b2o3b2o6b2o15bo15b2o
6b2o3b2o$47bo65bo8b5o25b5o8bo119bo7bo2bo4bo3bo8b3o8bo3bo4bo2bo7bo32b2o
3bo6bo2bo13bo13bo2bo6bo3b2o$35bo11bo11bo49b3o3bo6b2o14b3o14b2o6bo3b3o
115bo3bo2bo3bo4bo3bo19bo3bo4bo3bo2bo3bo36bo11bo12bo12bo11bo$19bo14b3o
10bo10b3o14bo49b2o25b2o131bo6bobo3bo2bo27bo2bo3bobo6bo48bo25bo$18b3o6b
o6bob2o19b2obo6bo6b3o209bo2b2o8bobo27bobo8b2o2bo62bo$18bob2o4b3o6b3o9b
o9b3o6b3o4b2obo209b5o8bo14b3o14bo8b5o62bo$19b3o3bo2b2o5b3o8bobo8b3o5b
2o2bo3b3o62b3o148b2o6bo3b3o23b3o3bo6b2o53bo11bo11bo$19b3o2bobo2bo5b3o
7b2ob2o7b3o5bo2bobo2b3o50b3o21b3o133b2o55b2o34bo14b3o21b3o14bo$19b2o7b
ob3o2b2o9bobo9b2o2b3obo7b2o34b3o12bo2bo21bo2bo12b3o209b3o6bo5b2obo10b
o10bob2o5bo6b3o$22b2o6b2o3b2o8b2ob2o8b2o3b2o6b2o36bo2bo5b3o7bo21bo7b3o
5bo2bo144b3o60b2obo5b3o4b3o11bo11b3o4b3o5bob2o$20bo2bo6bo3b2o8bo5bo8b
2o3bo6bo2bo37bo4bo2bo3bo3bo9b3o9bo3bo3bo2bo4bo210b3o5b2o2bo3b3o10bobo
10b3o3bo2b2o5b3o$19bo11bo13bo3bo13bo11bo32bo3bo4bo3bo2bo3bo9bobo9bo3b
o2bo3bo4bo3bo131b3o21b3o48b3o5bo2bobo2b3o10bobo10b3o2bobo2bo5b3o$19bo
55bo36bo2bo3bobo6bo9bobo9bo6bobo3bo2bo119b3o13bo2bo19bo2bo13b3o33b2o2b
3obo7b2o9b2ob2o9b2o7bob3o2b2o$45b2ob2o62bobo8b2o2bo9b2ob2o9bo2b2o8bob
o119bo2bo4b3o5bo11b3o11bo5b3o4bo2bo33b2o3b2o6b2o12bo3bo12b2o6b2o3b2o$
44bo5bo63bo8b5o8bo5bo8b5o8bo121bo7bo2bo4bo3bo17bo3bo4bo2bo7bo34b2o3bo
6bo2bo10b2ob2o10bo2bo6bo3b2o$45b2ob2o9bo50b3o3bo6b2o12b2ob2o12b2o6bo3b
3o117bo3bo2bo3bo4bo3bo7bobo7bo3bo4bo3bo2bo3bo38bo11bo23bo11bo$58b3o65b
2o23b2o133bo6bobo3bo2bo11b3o11bo2bo3bobo6bo50bo9b2ob2o9bo$57b2obo76b2o
b2o145bo2b2o8bobo10bo3bo10bobo8b2o2bo62bobo$33b3o21b3o77b2ob2o145b5o8b
o12b2ob2o12bo8b5o$33bo2bo20b3o77b2ob2o148b2o6bo3b3o21b3o3bo6b2o54bo9b
2ob2o$33bo23b3o66b3o158b2o24b2ob2o24b2o50b3o$33bo3bo20b2o65bo2bo185bo
bo76b2obo$33bo94bo23bo161bobo76b3o23b3o$34bobo87bo3bo22b3o239b3o23bo2b
o$124bo3bo21b2obo159b2ob2o8b3o64b3o23bo$128bo21b3o172bo2bo65b2o23bo3b
o$125bobo22b3o149bo25bo90bo$151b2o148b3o20bo3bo91bobo$300b2obo20bo3bo
$300b3o25bo$300b3o22bobo$301b2o3$60bo$59b3o$33b3o23bob2o$33bo2bo23b3o
$33bo26b3o331bo$33bo3bo22b3o62b3o265b3o$33bo26b2o63bo2bo23bo240bob2o22b
3o$34bobo88bo25b3o240b3o22bo2bo$125bo3bo20b2obo240b3o22bo$56b3o66bo3b
o20b3o174b3o64b3o22bo3bo$55bo2bo66bo24b3o149bo24bo2bo63b2o23bo$58bo67b
obo22b2o148b3o23bo92bobo$54bo3bo241b2obo23bo3bo$54bo3bo70bo170b3o24bo
3bo64b3o$58bo69b3o169b3o24bo67bo2bo$55bobo70bob2o169b2o25bobo67bo$129b
3o262bo3bo$129b3o193bo68bo3bo$129b3o192b3o71bo$129b2o193bob2o67bobo$325b
3o$325b3o$325b3o$325b2o2$29b3o$28bo2bo$31bo$31bo$28bobo125bo266b3o$155b
3o264bo2bo$155bob2o266bo$156b3o266bo$156b2o140bo123bobo$297b3o$297bob
2o$298b3o$298b2o12$31b3o$30bo2bo$33bo$33bo$30bobo121bo266b3o$153b3o264b
o2bo$153bob2o266bo$154b3o266bo$154b2o144bo119bobo$299b3o$48b3o248bob2o
$47bo2bo249b3o$50bo249b2o$46bo3bo$50bo86bo266b3o$47bobo86b3o264bo2bo$
136bob2o266bo$137b3o262bo3bo$137b3o177bo88bo$137b2o177b3o84bobo$316bo
b2o$317b3o$317b3o$68b3o242bo3b2o$70bo242bo$69bo$385b2o$117b2o266bobo$
116b2o267bo$118bo$336bo$336b2o$335bobo38$521bo5bo$520b3o3b3o$513bo6bo
b2ob2obo6bo$512b3o6bobobobo6b3o$512bob2o5bo5bo5b2obo$428b3o3b3o76b3o3b
2o7b2o3b3o$427bo2bo3bo2bo75b3o2bo3b2ob2o3bo2b3o$420b3o8bobo8b3o68b2o6b
o2bo2bo6b2o$419bo2bo6b3ob3o6bo2bo70b2o13b2o$422bo5bob2ob2obo5bo76b2o7b
2o$418bo3bo4b2o2bobo2b2o4bo3bo76b3o$422bo2bob2o3bo3b2obo2bo$419bobo3b
ob2o7b2obo3bobo$425bobo4bo4bobo$432bo90b3o$432bo2$432bo$432bo90b3o$432b
o2$432bo$432bo90b3o$432bo80b3o17b3o$512bo2bo17bo2bo$432bo82bo17bo$432b
o78bo3bo7b3o7bo3bo$422bo9bo9bo68bo3bo17bo3bo$421b3o17b3o71bo17bo$420b
2obo8bo8bob2o67bobo19bobo$420b3o9bo9b3o78b3o$420b3o9bo9b3o$420b3o19b3o
$421b2o9bo9b2o$432bo90b3o$432bo2$432bo$432bo90b3o$432bo2$432bo77b3o23b
3o$432bo61b3o13bo2bo9b3o9bo2bo13b3o$432bo61bo2bo4b3o5bo27bo5b3o4bo2bo
$494bo7bo2bo4bo3bo19bo3bo4bo2bo7bo$419bo12bo12bo48bo3bo2bo3bo4bo3bo19b
o3bo4bo3bo2bo3bo$403bo14b3o11bo11b3o14bo32bo6bobo3bo2bo12b3o12bo2bo3b
obo6bo$402b3o6bo6bob2o10bo10b2obo6bo6b3o32bo2b2o8bobo27bobo8b2o2bo$402b
ob2o4b3o6b3o21b3o6b3o4b2obo32b5o8bo31bo8b5o$403b3o3bo2b2o5b3o10bo10b3o
5b2o2bo3b3o36b2o6bo3b3o23b3o3bo6b2o$403b3o2bobo2bo5b3o10bo10b3o5bo2bo
bo2b3o33b2o26b3o26b2o$403b2o7bob3o2b2o11bo11b2o2b3obo7b2o$406b2o6b2o3b
2o23b2o3b2o6b2o$404bo2bo6bo3b2o12bo12b2o3bo6bo2bo$403bo11bo16bo16bo11b
o49b3o9b3o9b3o$403bo28bo28bo33b3o13bo2bo19bo2bo13b3o$495bo2bo4b3o5bo25b
o5b3o4bo2bo$432bo62bo7bo2bo4bo3bo17bo3bo4bo2bo7bo$420bo11bo11bo50bo3b
o2bo3bo4bo3bo7b3o7bo3bo4bo3bo2bo3bo$404bo14b3o10bo10b3o14bo34bo6bobo3b
o2bo25bo2bo3bobo6bo$403b3o6bo6bob2o19b2obo6bo6b3o34bo2b2o8bobo25bobo8b
2o2bo$403bob2o4b3o6b3o9bo9b3o6b3o4b2obo34b5o8bo14bo14bo8b5o$404b3o3bo
2b2o5b3o9bo9b3o5b2o2bo3b3o38b2o6bo3b3o8b2ob2o8b3o3bo6b2o$404b3o2bobo2b
o5b3o9bo9b3o5bo2bobo2b3o35b2o24b2ob2o24b2o$404b2o7bob3o2b2o21b2o2b3ob
o7b2o$407b2o6b2o3b2o10bo10b2o3b2o6b2o64b2ob2o$405bo2bo6bo3b2o10bobo10b
2o3bo6bo2bo61bobobobo$404bo11bo13b2ob2o13bo11bo50b3o$404bo26bobo26bo50b
o2bo7b2ob2o$430b2ob2o76bo10b2ob2o10bo$429bo5bo75bo3bo20b3o$430bo3bo9b
o66bo3bo20bob2o$443b3o65bo10b2ob2o10b3o$430b2ob2o7b2obo66bobo22b3o$418b
3o10bobo8b3o92b2o$418bo2bo8b2ob2o7b3o$418bo11b2ob2o7b3o$418bo3bo20b2o
$418bo$419bobo7$510b3o$509bo2bo24bo$512bo23b3o$508bo3bo23bob2o$445bo62b
o3bo24b3o$444b3o65bo24b3o$418b3o23bob2o61bobo25b2o$418bo2bo23b3o$418b
o26b3o66bo$418bo3bo22b3o65b3o$418bo26b2o65b2obo$419bobo90b3o$512b3o$441b
3o68b3o$440bo2bo69b2o$443bo$439bo3bo$439bo3bo$443bo$440bobo5$541bo$540b
3o$539b2obo$539b3o$540b2o$414b3o$413bo2bo$416bo$416bo$413bobo15$539bo
$538b3o$537b2obo$537b3o$527b2o9b2o$416b3o108b2o$415bo2bo$418bo$418bo9b
2o$415bobo10b2o$522bo$521b3o$520b2obo$520b3o$520b3o$433b3o85b2o$432bo
2bo$435bo72bo$431bo3bo71b2o$435bo71bobo$432bobo2$447b3o$449bo$448bo207$
220bo$221b2o$220b2o$233bobo$233b2o$234bo43$210bobo$213bo$213bo$210bo2b
o$211b3o5$228b2o$228b3o$227bob2o$227b3o$228bo4$214bobo3bobo$213bo5bo$
213bo5bo$213bo2bo2bo2bo$213b3o3b3o66$565bo25bo20bo$565b3o21b3o11bo7bo
bo$568bo19bo14b3o6bo$567b2o19b2o16bo16bo$605b2o14b3o$620bo$620b2o3$561b
2o$560bobo35b2o25b2o$556b2o2bo37b2o25bo$556bobobobo60bobo$558bobo2bo59b
2o$555bo2bo5bo$555b3o2bo$558b4o48b2o$557bo5bo37b2o6bobo$558b6o38bo6bo
$601bo6b2o$560b2o39b2o$560b2o4$612b2o$611bobo$557b2o52bo$558bo51b2o$558b
obo$559b2o5$603b2o$604bo$604bobo15b2o$605b2o15b2o2$553b2o$554bo$553bo
6b2o15b2o$553b2o5b2o15bobo$579bo$579b2o4$560bo$559b5o59b2o$564bo58bob
o$356bo215b2o51bo$355bo203bo3bo8bo52b2o$355b3o202b3o7bobo$570b2o4$622b
2o$581b2o39b2o$574b2o6bo$574bo6bo38b6o$572bobo6b2o37bo5bo$572b2o48b4o
$623bo2b3o$619bo5bo2bo$559b2o59bo2bobo$558bobo60bobobobo$558bo25b2o37b
o2b2o$557b2o25b2o35bobo$621b2o3$562b2o$563bo$560b3o14b2o$560bo16bo16b
2o19b2o$571bo6b3o14bo19bo$570bobo7bo11b3o21b3o$571bo20bo25bo$686b2o$686b
2o3$695b2o$694bobo$695bo3$689b2o$689b2o2$696b2o$429bo5bo260bobo$428b3o
3b3o261bo$421bo5b2o2bobo2b2o5bo239b2o13b2o$420b3o4b2o2bobo2b2o4b3o239b
o$419b2obo5bo2bobo2bo5bob2o235b3o6b2o$419b3o5bo3bobo3bo5b3o235bo8b2o$
419b3o5bo4bo4bo5b3o$420b2o2b4o9b4o2b2o$427bo9bo3$431b3o4$431b3o4$431b
3o$431bobo$431bobo$430b2ob2o$421b3o5bo5bo5b3o$421bo2bo5b2ob2o5bo2bo$421b
o21bo$421bo3bo4b2ob2o4bo3bo$421bo3bo5bobo5bo3bo$421bo9bobo9bo$422bobo
6bobo6bobo$431bobo11$418b3o23b3o$402b3o12bo2bo23bo2bo12b3o$401bo2bo5b
3o7bo23bo7b3o5bo2bo$404bo4bo2bo3bo3bo23bo3bo3bo2bo4bo$400bo3bo4bo3bo2b
o3bo23bo3bo2bo3bo4bo3bo$404bo2bo3bobo6bo23bo6bobo3bo2bo$404bobo8b2o2b
o25bo2b2o8bobo$406bo8b5o25b5o8bo$402b3o3bo6b2o31b2o6bo3b3o$418b2o25b2o
4$419b3o21b3o$403b3o12bo2bo21bo2bo12b3o$402bo2bo5b3o7bo21bo7b3o5bo2bo
$405bo4bo2bo3bo3bo21bo3bo3bo2bo4bo$401bo3bo4bo3bo2bo3bo21bo3bo2bo3bo4b
o3bo$405bo2bo3bobo6bo21bo6bobo3bo2bo$405bobo8b2o2bo23bo2b2o8bobo$407b
o8b5o23b5o8bo$403b3o3bo6b2o29b2o6bo3b3o$419b2o23b2o4$419b3o$418bo2bo$
421bo23bo$417bo3bo22b3o$417bo3bo21b2obo$421bo21b3o$418bobo22b3o$444b2o
12$228b2o188b3o$228b2o188bo2bo23bo$418bo25b3o$418bo3bo20b2obo$418bo3b
o20b3o$418bo24b3o$419bobo22b2o2$422bo$421b3o$421bob2o$422b3o$422b3o$422b
3o$422b2o10$449bo$448b3o$448bob2o$449b3o$449b2o20$447bo$446b3o$446bob
2o$447b3o$447b2o6$430bo$429b3o$429bob2o$430b3o$430b3o95bobo$430b2o96b
2o$529bo64$353b2o$352b2o$354bo215$210bobo$213bo$213bo$210bo2bo$211b3o
5$228b2o$228b3o$227bob2o$227b3o$228bo4$214bobo3bobo5bobo$213bo5bo7bo$
213bo5bo7bo$213bo2bo2bo2bo4bo2bo$213b3o3b3o5b3o2$222bobo$222b2o$223bo
!

The front of this pattern is rakes that generate LWSSes and back of this pattern is a glider gun.

[dvgrn]

Not quite -- I'm looking for a pattern where at least one phase consists of newborn cells (without any cells surviving from the previous phase). "Volatility 1" is weaker than this requirement...

If these hypothetical patterns are supposed to be volatility 1 (no stator) _and_ all rotor cells simultaneously die in some generation, then ... where are any newborn cells going to come from?

The same question would apply in any isotropic rule, let alone in Life. Even a B0 rule wouldn't be able to help much in unscrewing the inscrutable here, unless you're interested in the infinitely large strobing oscillator in B0/S.

(??)

[silversmith]

What is the type of this quadratic growth pattern?

As far as I can tell, the reaction which creates the rakes is stationary so the pattern overall would be SMM.

Edit:

Not quite -- I'm looking for a pattern where at least one phase consists of newborn cells (without any cells surviving from the previous phase). "Volatility 1" is weaker than this requirement, which in turn is weaker than "phoenix". For example, pentadecathlon has volatility 1, but it does not qualify, because in every generation there are some surviving cells.

Something like this? All cells die after an odd generation, and some survive after an even generation.

Code: Select all

x = 3, y = 1, rule = B2ci/S1e
3o!

[confocaloid]

Not quite -- I'm looking for a pattern where at least one phase consists of newborn cells (without any cells surviving from the previous phase). "Volatility 1" is weaker than this requirement, which in turn is weaker than "phoenix". For example, pentadecathlon has volatility 1, but it does not qualify, because in every generation there are some surviving cells.

Something like this? All cells die after an odd generation, and some survive after an even generation.

Code: Select all

x = 3, y = 1, rule = B2ci/S1e
3o!

Yes, this is a valid example!

If these hypothetical patterns are supposed to be volatility 1 (no stator) _and_ all rotor cells simultaneously die in some generation, then ... where are any newborn cells going to come from?

The same question would apply in any isotropic rule, let alone in Life. Even a B0 rule wouldn't be able to help much in unscrewing the inscrutable here, unless you're interested in the infinitely large strobing oscillator in B0/S.

(??)

Well, then the question "where are any newborn cells going to come from" would apply for a proper phoenix as well. There is no stator and all rotor cells simultaneously die, yet phoenices exist:

Code: Select all

x = 8, y = 8, rule = B3/S23
4bo$2bobo$6bo$2o$6b2o$bo$3bobo$3bo!

The p4 posted by silversmith above is a valid example of what I'm looking for:

Code: Select all

x = 3, y = 1, rule = B2ci/S1e
3o!

Here's another way to formulate this. For an arbitrary oscillator it is possible to count the number of phases that consist of newborn cells only (i.e. phases without any "old" cells). For a phoenix, this number equals the period. For an oscillator with a nonempty stator, this number equals zero. I'm looking for patterns where this number is greater than 0 but less than the period.

[HartmutHolzwart]

So you essentially want an oscillator in B3/s23 that has only p2 and p4 cells, no stator? As a simple example, I mean.

[confocaloid]

Not quite -- I'm looking for a pattern where at least one phase consists of newborn cells (without any cells surviving from the previous phase). "Volatility 1" is weaker than this requirement, which in turn is weaker than "phoenix". For example, pentadecathlon has volatility 1, but it does not qualify, because in every generation there are some surviving cells.

The p4 posted by silversmith above is a valid example of what I'm looking for:

Code: Select all

x = 3, y = 1, rule = B2ci/S1e
3o!

Here's another way to formulate this. For an arbitrary oscillator it is possible to count the number of phases that consist of newborn cells only (i.e. phases without any "old" cells). For a phoenix, this number equals the period. For an oscillator with a nonempty stator, this number equals zero. I'm looking for patterns where this number is greater than 0 but less than the period.

This number is also =0 for the pentadecathlon, because each of its 15 phases has some "old" cells:

Two different phases of the pentadecathlon have =12 new cells and =10 old cells.
Each of 15 phases has cells of both types. One phase has 2 new cells and 16 old cells. One phase has 16 new cells and 2 old cells.

Code: Select all

#C The number of phases with (row) new cells and (column) old cells
#C    |  2  4  6  8 10 12 14 16 18 20
#C ---+------------------------------
#C  2 |  .  .  .  .  .  .  .  1  .  .
#C  8 |  .  1  .  1  1  1  1  .  .  1
#C 12 |  .  .  .  1  2  .  .  .  .  .
#C 14 |  .  1  1  .  .  .  .  .  .  .
#C 16 |  1  1  .  .  .  .  .  .  .  .
#C 22 |  .  .  .  .  .  .  .  .  1  .
x = 94, y = 36, rule = //3
85.2A$64.4A15.A4.A$43.6A14.6B13.A6.A$3.A4.A13.AB4ABA12.B6.B12.B6AB11.
A8.A$.BA.B2AB.AB11.B.4B.B11.A8.A10.BA6.AB10.B8.B$3.A4.A13.AB4ABA12.B
6.B12.B6AB11.A8.A$43.6A14.6B13.A6.A$64.4A15.A4.A$85.2A9$2.B6.B11.AB6.
BA10.2B6.2B10.2B6.2B$.BA6.AB9.A2.A4.A2.A8.B2.B4.B2.B7.A4.A2.A4.A7.A2.
A4.A2.A$ABA6.ABA8.B2.A4.A2.B7.AB2ABA2.AB2ABA6.B4.B2.B4.B5.ABA2.AB2ABA
2.ABA$.BA6.AB9.A2.A4.A2.A8.B2.B4.B2.B7.A4.A2.A4.A7.A2.A4.A2.A$2.B6.B
11.AB6.BA10.2B6.2B10.2B6.2B12$B2.B.2A.B2.B8.B2.B.2B.B2.B7.AB3.A2.A3.B
A6.B2.2A4.2A2.B9.B.A2.A.B$B2AB.2B.B2AB7.AB2.B4.B2.BA6.2B2AB4.B2A2B5.A
3.2BA2.A2B3.A4.BA.A2.B2.B2.A.AB$B2.B.2A.B2.B8.B2.B.2B.B2.B7.AB3.A2.A
3.BA6.B2.2A4.2A2.B9.B.A2.A.B!
#C [[ VIEWONLY ]]

[dani]

I feel like such a pattern exists, and could possibly be done via some weird UC encoding that somehow ends up constructing its recipe but with glider predecessors like this:

Code: Select all

x = 12, y = 5, rule = B3/S23
bobo6bo$o3bo3bo$2bo4bo2bo$bo7bo$3bo3bo3bo!

...But that feels less satisfying than a small example. Cross and star get pretty close, though.

I wonder if LLS could find an example, or a similar SAT-solver based approach. I don't think LLS allows one to specify cells that can only be the same state if they're dead.

[confocaloid]

I feel like such a pattern exists, and could possibly be done via some weird UC encoding that somehow ends up constructing its recipe but with glider predecessors like this:

Code: Select all

x = 12, y = 5, rule = B3/S23
bobo6bo$o3bo3bo$2bo4bo2bo$bo7bo$3bo3bo3bo!

...But that feels less satisfying than a small example. Cross and star get pretty close, though.

I wonder if LLS could find an example, or a similar SAT-solver based approach. I don't think LLS allows one to specify cells that can only be the same state if they're dead.

I 'm not quite up to the task of constructing an UC-based solution, but in case these can be useful, here are ways to construct glider predecessors for both shapes. At T = 47, neither of marked (red) cells is on; at T = 48, the marked cells are the only alive cells.

Code: Select all

x = 74, y = 43, rule = LifeHistory
62.A$60.2A$61.2A8$49.2A$48.A.A$49.A$11.A32.A$10.A.A32.A27.A$4.A4.A.A
31.3A25.2A$3.A.A3.2A43.2A16.2A$4.2A48.A.A$56.A$56.2A$3.D13.2A35.D$2.D
13.2A34.2D$.AC2D13.A34.2D$A2.A$A.A43.2A3.2A3.D2A$.A44.2A3.2A4.A.A$58.
A2$2.A$.A.A48.2A$2.A.A47.2A$3.2A9$8.2A$7.2A$9.A!

[dvgrn]

I 'm not quite up to the task of constructing an UC-based solution, but in case these can be useful, here are ways to construct glider predecessors for both shapes. At T = 47, neither of marked (red) cells is on; at T = 48, the marked cells are the only alive cells.

For the hand-waving theoretical solution that's actually not too terribly hard to complete at this point, it would work to build three 1G seeds for groups of RCT gliders using these glider predecessors, 15 gliders in all -- and then add a few short recipes to the "cleanup" stages of an RCT, so that it builds those three seeds in the right places instead of doing a complete cleanup.

Then the ATBC, Actual Thing Being Constructed, would be a splitter constellation that creates the three activation gliders at the epicentre, aimed at the three 1G seeds with the correct relative timing.

It's a measurably easier project to build an RCT15 oscillator than it would have been to build an RCT16 oscillator, because we don't have to create a glider way out in empty space to the northeast where there's no junk to clean up (and therefore no target to aim at to build a seed).

[Book]

I'd like to take crack at labelling the Cambrian Explosion rle. Any existing information on the patterns therein that might help save some work on this would be appreciated.

[dvgrn]

I'd like to take crack at labelling the Cambrian Explosion rle. Any existing information on the patterns therein that might help save some work on this would be appreciated.

I put together Cambrian Explosion for Golly release 1.1, in late 2006. The comments in the Golly pattern give some good pointers about where to look:

#C Based on 'a-plus.lif' from Alan Hensel's 'lifebc' collection.
#C Most additional patterns are from 2004-2006, and were selected
#C (somewhat at random) from Koenig's Life News weblog. For details
#C on individual patterns, see http://pentadecathlon.com/lifeNews .
#C Press 'm' in Golly to center the view on the column of spaceships
#C of different speeds. A new speed (c/6) has been added.
#C To the NE are diagonal spaceships with some new speeds (c/5, c/6).

"A-plus.lif" can be found in "Alan Hensel's Pattern Collection" in Golly's Online Archives. It looks like this, but doesn't have any comments:

Code: Select all

x = 152, y = 91, rule = B3/S23
7bo71bo$6b3o69b3o24bo10bo$4b2ob3o20b3o9b3o9b3o20b3ob2o23b2o8bobo$5bo2b
ob2o4bo4bo7bo3bo7bo3bo7bo3bo7bo4bo4b2obo2bo18b2o3b2o9b2o$2b2obo4bobob
2ob2ob3o5b2o3b2o5b2o3b2o5b2o3b2o5b3ob2ob2obobo4bob2o14b2o$2b2obobo2bob
o7b4o3b2obobob2o3b2obobob2o3b2obobob2o3b4o7bobo2bobob2o10bo5bo$2bo8b3o
bobob2o2b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2b2obobob3o8bo8bobo
22bo$b2o7b2o12bobo3bobo3bobo3bobo3bobo3bobo3bobo12b2o7b2o8b2o2b2o5b3o
6b2o2bobo$97bobo7bo7b2ob2o$5b3o15b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2o15b3o17bo6bo7bo$4bo3bo69bo3bo25b3o$3b2o4bo11b45o11bo4b2o24bo$2bob
ob2ob2o3b3o2b2obo4bo8bo6bo6bo8bo4bob2o2b3o3b2ob2obobo24bo$b2obo4bob2ob
3obo49bob3ob2obo4bob2o40bo$o4bo3bo4bobo4bo4bobob4obobob2obobob2obobob
4obobo4bo4bobo4bo3bo4bo40bo$12bo5b2o47b2o5bo50b3o$2o7b2o65b2o7b2o64bo$
110bo26bobo9b2o$42b3o63bobo26b2o11b2o$13bo17b2o9bobo9b2o39bo13b2o27bo$
12b3o16b2o9bobo9b2o38bobo$11b2ob2o78bobo$92b3ob2o$10bobobobo2bo71bo$9b
2o3bo3b3o71b3ob2o$9b2o3bo6bo72bob2o$19bobo$17bobo47b3o7bob2o$18bo2bo
47bo6bo3bo31b2o$21bo27b2o7b2o7bo7bo4bo18b3o9bobo$50b2o7bob2o4bobo7b2o
22bo11bo27bo$14bo34bo11b2o2bob3o4bobo23bo21bo17b2o$13bobo24b3o4bo13b2o
2b2o3bo50b2o17bobo$12bo3bo22b2o4b3o17b2ob4ob2o46bobo$13b3o24bobob3o20b
7o$39bo$11b2o3b2o26bobo81b2o$9bo3bobo3bo24bob2o37b2o41b2o5b2o$8b2o3bob
o3b2o25bo21bo15bobo48b2o$7bo5bobo5bo23bob2o18bobo$8bob2obobob2obo24bo
22bo13bobo$46b2o41b2o13b2o27b2o$32b3o4b3o38bobo7bo13b2o27b2o11b2o$7bo
12bo67bo50b2o5b2o$7bo12bo11bobo4bobo13bo22bobo5bobo50b2o$6bobo10bobo
10bobo4bobo12bobo41b2o$7bo12bo33bobo3b2o14bobo5bobo11b2o46b2o$7bo12bo
12bo2b2o2bo10b2obob2o3bo13bo26b2o42bobo$8bo3b4o3bo12b2obo2bob2o10bobo
6bob2o10b2o5bobo17b2o44bo$12b4o16bo8bo8bo2bobob3obo2bo83bob2o$8b4o4b4o
14bo4bo10b2obobo4bobo18b2o64b2ob2o$33b2o4b2o12bobo2b2o2b2o15bo$10bo6bo
35bobo3bobo17b2o16b2o$11b2o2b2o15bobo4bobo12b2obobobo35b2o$31bo2bo4bo
2bo13bobobo$30b2o10b2o12bobo$8bo11bo9b2o3bo2bo3b2o13b2o$8bo11bo11bo3b
2o3bo34b3o$7bobo9bobo9b2o8b2o40b2o2b2o$29bo2bobob2obobo2bo29bo4bobo4bo
bo$6bo3bo7bo3bo6bo2b2o6b2o2bo29bo4bobo2bobo$6bob6ob6obo7bo12bo30bo4bob
o5bo$5bo7bobo7bo8b2o6b2o34b3o3b5o$5bo7bobo7bo9bo6bo43bo$5bo17bo8b2o2b
2o2b2o32b3o$6bob2ob2o3b2ob2obo13b2o20b3o7b3o2bo4bo$36b2o10b2o2b2o19bo
4bo$48bobo4bobo4bo3bo4bobo4bo65b2o$10bo7bo18bo12bobo2bobo4bo3bo4bo72b
2o$4b2obobob2o3b2obobob2o7b2o3bo11bo5bobo4bo3bo4bo2b3o44bo$b3obob3o9b
3obob3o4bo2b2ob2o10b5o3b3o7b3o50b3o$bo3bobo5bobo5bobo3bo6b2ob2o13bo68b
obo$5b2o6bobo6b2o17bo18b3o3b3o13b2o5b2o32bo15b2o$2b2o9bobo9b2o11bobobo
15bo4bobo4bo12bo5b2o48b2o$2b2ob2o15b2ob2o6bo3bo3bo16bo4bobo4bo12bobo
57b2o$6bo15bo10b2ob2o20bo4bobo4bo13b2o57b2o$88b2o12b2o$33b3ob2obo19b3o
3b3o18bobo12b2o$32bo3bobo2bo46bo19b2o27b2o$6b3o10b3o10bobo2bobob3o40bo
23b2o27b2o$b3obo7b2o7bob3o6b4o2bo4bo$5bo3bo2bo2bo2bo3bo17bob2o38b3obo$
5bo5bo4bo5bo10b4o2b2obo38bob2o14b2o5b2o$11b2o2b2o16bo2b3o3bo38b2obo14b
2o5b2o5b2o9b2o$8bo3bo2bo3bo14bobob4o37bob3o29b2o9b2o3bo$8bobo6bobo13b
2o63bob3o25bobo$9b10o16bobobo41bo16b2o3bo25bobo$11bo4bo18bobob3o59b2o
28bo$9bo8bo17bo5bo54bob2o30b2o$8bo10bo17b5o55b2obo$9bo8bo20bo!

The Cambrian Explosion pattern was completed by November 17th, 2006. I'm finding a rumor in my old emails that I really started from something called "a-plus-plus.lif" -- here's an email describing it from October 20, 2006:

I'm thinking about building one really crazy
pattern, along the lines of Alan Hensel's old introductory
"a-plus-plus.lif". Maybe I should call it "A-Cambrian-Explosion"...
greyships going off in three different directions, different-speed
spaceships racing each other, multi-line wickstretchers, anteaters,
antstretchers, linestretchers, David Bell's double-barrelled
Cordership... and down in the half-universe that a-plus-plus.lif
didn't use, HALFMAX.

I suspect "a-plus-plus.lif" is the default pattern shown in Alan Hensel's online Java applet, if anyone can find it in the source code or get the applet running in a sandbox somewhere.

Some of the contents are easy to recognize, and/or biggiemac's script or Catagolue's search page can help with the spaceships.

If you can get started and supply a template, I can probably dig up sources and edit in labels for the weirder stuff.

[AlbertArmStain]

Can I have a collection of edgy clean p1 eater 3 object seeds?

[ohennel]

Hi folks,

After a looong time I revisited the site and found some interest in my humble "achievements".
Now that CPUs are much faster, a soup search might bring results faster.

I think that seeding based on 64-bit int values instead of 32-bit would be nice.

But, is there a better (totally superior) soup search program now?
I would not like to invest my time in a goner.

Best regards,
Andrzej Okrasinski