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Spiral Growth Geminoid Challenge

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

Spiral Growth Geminoid Challenge

Postby dvgrn » December 10th, 2013, 12:39 pm

It's now fairly straightforward to use Geminoid technology to put together a spiral-growth Life pattern. I can think of a couple of obvious designs:

1) Start with four pre-built spiral corners plus just one glider-stream-encoded recipe. Each spiral corner consists of a 90-degree stable reflector attached to a Geminoid universal constructor. The UC will use the recipe to build a copy of itself one step farther from the center of the spiral; at the same time, it will reflect the recipe to the next UC in the spiral. If the spiral is big enough, the fifth UC corner will be complete in time to accept the incoming glider stream after its trip around the first four corners.

The cycle will continue indefinitely, in at least a somewhat space-filling fashion -- it won't exercise every cell in the Life plane or anything like that, but at least any chosen location will eventually be no more than a few hundred cells away from a live cell.

2) Start with a high-period salvo shotgun that repeatedly emits the above glider-stream recipe. As before, each spiral corner will construct an offset copy of itself. However, the 90-degree output will be blocked until the end of the construction process, when a one-time-turner chain will remove the output-blocking eater and also block off the universal-constructor part of the circuitry, leaving only a stable reflector. The next recipe from the salvo gun will then activate the UC at the next corner.

The salvo gun can be folded into a relatively small two-dimensional space, which allows for an initial pattern with a much smaller bounding box. In absolute terms the population increase will be much slower, but it will get to all the same places eventually.

Here's a 62-still-life 9hd Geminoid universal constructor that Calcyman put together a while back:

x = 400, y = 272, rule = LifeHistory
110.2A194.2E$80.2A28.2A194.E$80.2A222.E.E$304.2E$92.A19.2A$90.3A19.2A
$89.A35.2A$89.2A34.A$123.A.A$123.2A$127.2A$127.2A3$63.2A$62.A2.A$63.
2A2$114.2A$114.2A$58.2A$57.A.A$57.2A$95.A$66.2A26.A.A$66.2A27.2A5$
121.2A$121.2A2$66.2A$67.A$2A65.A.A$2A66.2A3$82.2A$82.A.A$84.A$84.2A3$
66.2A$65.A.A$65.A$64.2A7.2A$73.2A5$172.2A$172.2A11$152.2A4.2A$93.2A
57.A4.A.A$86.2A5.2A16.A38.A.A4.A$86.2A21.3A29.2A7.2A4.2A$108.A11.A20.
2A$108.2A10.3A$88.2A33.A$88.2A32.2A$82.2A$70.2A10.2A93.2A$69.A2.A104.
A$70.2A85.2A19.3A$157.2A21.A$119.2A$119.2A25.2A$146.2A2$150.A$150.3A$
153.A$126.2A24.2A$79.A47.A12.2A$79.3A42.3A6.A6.2A$82.A41.A7.A.A54.A
34.A$81.2A50.A55.3A32.3A$192.A34.A$169.2A20.2A33.2A$169.2A7.2A56.2A$
178.A57.A$176.A.A55.A.A$176.2A4.2A44.2A4.2A$119.2A39.2A20.A44.A2.A$
119.A41.A18.A.A45.2A$120.3A38.A.A16.2A34.2A$101.2A19.A39.2A52.2A$101.
2A126.3A$229.A$230.A5$191.2A32.2A3.2A$191.2A11.2A20.A3.A$86.2A116.A
18.3A5.3A$86.2A80.2A35.3A15.A9.A$164.2A2.2A37.A$163.A.A$163.A23.2A$
162.2A23.A$188.3A$190.A23$92.2A$93.A$93.A.A$94.2A2$109.2A$109.2A3$92.
2A$92.2A5.2A$99.2A2$105.A$104.A.A$97.2A6.2A$98.A$95.3A$95.A111$397.3A
$397.A$398.A!

This would finally make some use of some of Guam's impressive Herschel technology from a few years back -- the 4hd transceiver and the R126 turn.

EDIT: Here's the 10hd version of Calcyman's universal constructor, with the same still-life count:

x = 395, y = 322, rule = LifeHistory
112.2A143.2E$82.2A28.2A143.E$82.2A171.E.E$255.2E$94.A19.2A$92.3A19.2A
$91.A35.2A$91.2A34.A$125.A.A$125.2A$129.2A$129.2A3$65.2A$64.A2.A$65.
2A2$116.2A$116.2A$60.2A$59.A.A$59.2A$97.A$68.2A26.A.A$68.2A27.2A5$
123.2A$123.2A2$68.2A$2E67.A$2E67.A.A$70.2A3$84.2A$84.A.A$86.A$86.2A3$
68.2A$67.A.A$67.A$66.2A7.2A$75.2A13$176.A$174.3A$152.2A19.A$93.2A57.A
20.2A$86.2A5.2A16.A38.A.A51.A$86.2A21.3A29.2A7.2A52.3A$108.A11.A20.2A
64.A14.A$108.2A10.3A83.2A12.3A$88.2A33.A95.A$88.2A32.2A95.2A$82.2A$
82.2A$218.2A$72.2A83.2A40.2A17.2A$71.A2.A82.2A40.2A$72.2A45.2A$119.2A
25.2A13.2A$146.2A13.2A2$150.A$150.3A49.2A$153.A28.2A19.A$126.2A24.2A
28.A.A15.3A$79.A47.A12.2A42.A15.A$79.3A42.3A6.A6.2A42.2A19.2A$82.A41.
A7.A.A71.A$81.2A50.A69.3A$203.A4$221.2A$221.A.A$119.2A75.2A25.A$119.A
77.A25.2A$120.3A74.A.A15.2A$101.2A19.A75.2A15.2A$101.2A9$86.2A$86.2A$
216.2A$216.A.A$218.A$218.2A9$206.2A$206.2A6$217.2A$196.2A19.A$197.A
17.A.A$197.A.A15.2A$198.2A4.A$203.A.A$203.A.A2.2C$204.A3.C.C4.2A$208.
C6.A.A$217.A$217.2A$202.2A$203.A$200.3A$200.A34$130.2A$131.A$131.A.A$
132.2A2$147.2A$147.2A3$130.2A$130.2A5.2C$137.2C2$143.A$142.A.A$135.2A
6.2A$136.A$133.3A$133.A124$393.C$392.2C$392.C.C!

The pieces don't fit together quite as tightly, but that has the nice side effect of allowing about twice as many different glider-pair timings for negative offsets, without any extra adjustment. By "negative offset" I mean the direction of adjustment that is eventually limited by the compression rating of the circuitry. In this kind of design, it's generally possible to have glider pairs with arbitrarily large positive offsets, just by delaying the second glider by the right amount.

As I mentioned on the old Geminoid Challenge thread, the jury is still officially out on whether 9hd or 10hd ultimately has a better set of elbow operations, but so far it looks like the 10hd toolkit is about thirty percent more efficient (!).
dvgrn
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Re: Spiral Growth Geminoid Challenge

Postby dvgrn » December 10th, 2013, 2:05 pm

Here's a more complete template for the spiral-growth pattern. Just imagine that the four quarters start out much farther apart, to leave room for a full encoded recipe stream. The copy of the corner in red at the far left has to be constructed by the universal constructor immediately to its right:

x = 919, y = 791, rule = LifeHistory
640.2A$640.2A56$654.2A$654.A.A$655.2A3$661.A$660.A.A$628.A31.A.A$628.
3A30.A$631.A11.A7.2A$630.2A9.3A7.2A$640.A$600.A39.2A$599.A.A$599.A.A$
600.A$627.2A$627.2A5$588.2A$588.A85.2A$586.A.A85.2A$586.2A13.2A33.2A$
601.2A34.A$634.3A$634.A$565.2A40.2A$565.2A40.2A$603.2A$603.2A64.2A$
669.A.A$671.A$526.2A8.A134.2A$526.2A6.3A71.2A$533.A74.2A42.A$518.2A
13.2A116.A.A$519.A131.2A$519.A.A$520.2A$525.2A$525.2A$575.2A$575.2A2$
522.A$521.A.A$521.2A2$605.2A$530.2A73.A.A$530.2A75.A67.2A$607.2A66.2A
$671.2A$671.2A$657.2A$657.2A4$578.2A16.2A$577.A.A16.2A7.2A$577.A27.A
39.2A$576.2A25.A.A39.2A$603.2A62.2A$587.2A78.A$588.A79.3A$588.A.A79.A
$589.2A74.2A$665.2A4$587.A$586.A.A$587.A6$588.2A$588.2A16.2A$606.2A4$
595.2A$595.2A3$592.2A13.2A$592.A14.A$590.A.A15.3A$590.2A18.A3$607.A$
598.2A7.3A$598.2A10.A$609.2A$579.A$577.3A$561.A14.A$561.3A12.2A$564.A
$563.2A3$564.2A$564.2A17.2A$583.2A2$621.2A$621.2A3$580.2A$580.A19.2A$
581.3A15.A.A$583.A15.A$577.2A19.2A$577.A$578.3A$580.A4$561.2A$560.A.A
$560.A25.2A$559.2A25.A$567.2A15.A.A$567.2A15.2A12$566.2A$565.A.A$565.
A$564.2A9$576.2A$576.2A6$565.2A$566.A19.2A$566.A.A17.A$567.2A15.A.A$
579.A4.2A$578.A.A$578.A.A$567.2A10.A$566.A.A$566.A$565.2A$580.2A$580.
A$581.3A$583.A5$110.2D254.2A$80.2D28.2D224.2A28.2A$80.2D254.2A2$92.D
19.2D234.A19.2A$90.3D19.2D232.3A19.2A$89.D35.2D218.A35.2A$89.2D34.D
219.2A34.A$123.D.D253.A.A$123.2D254.2A$127.2D254.2A$127.2D254.2A3$63.
2D254.2A$62.D2.D252.A2.A$63.2D254.2A2$114.2D254.2A$114.2D254.2A$58.2D
254.2A507.A$57.D.D253.A.A505.3A$57.2D254.2A505.A$95.D255.A460.2A6.2A$
66.2D26.D.D225.2A26.A.A459.A.A$66.2D27.2D225.2A27.2A460.A2$818.2A$
818.2A5.2A$825.2A$121.2D254.2A$121.2D254.2A$808.2A$66.2D254.2A484.2A$
67.D255.A$2D65.D.D186.2A65.A.A497.2A$2D66.2D186.2A66.2A497.A.A$825.A$
825.2A$82.2D254.2A$82.D.D253.A.A$84.D255.A$84.2D254.2A3$66.2D254.2A$
65.D.D253.A.A$65.D255.A$64.2D7.2D245.2A7.2A$73.2D254.2A5$172.2D254.2A
$172.2D254.2A6$728.A$728.3A$731.A23.2A$730.2A23.A$753.A.A$152.2D4.2D
248.2A4.2A295.A37.2A2.2A$93.2D57.D4.D.D189.2A57.A4.A.A269.A9.A15.3A
35.2A80.2A$86.2D5.2D16.D38.D.D4.D184.2A5.2A16.A38.A.A4.A271.3A5.3A18.
A116.2A$86.2D21.3D29.2D7.2D4.2D184.2A21.3A29.2A7.2A4.2A274.A3.A20.2A
11.2A$108.D11.D20.2D221.A11.A20.2A288.2A3.2A32.2A$108.2D10.3D241.2A
10.3A$88.2D33.D220.2A33.A$88.2D32.2D220.2A32.2A$82.2D254.2A$70.2D10.
2D93.2D147.2A10.2A93.2A$69.D2.D104.D147.A2.A104.A$70.2D85.2D19.3D145.
2A85.2A19.3A379.2A$157.2D21.D232.2A21.A264.2A52.2A39.A19.2A$119.2D
254.2A324.2A34.2A16.A.A38.3A$119.2D25.2D227.2A25.2A285.2A45.A.A18.A
41.A$146.2D254.2A284.A2.A44.A20.2A39.2A$683.2A4.2A44.2A4.2A$150.D255.
A275.A.A55.A.A$150.3D253.3A273.A57.A$153.D255.A271.2A56.2A7.2A$126.2D
24.2D228.2A24.2A281.2A33.2A20.2A$79.D47.D12.2D193.A47.A12.2A293.A34.A
$79.3D42.3D6.D6.2D193.3A42.3A6.A6.2A294.3A32.3A55.A50.2A$82.D41.D7.D.
D54.D34.D113.A41.A7.A.A54.A34.A213.A34.A54.A.A7.A41.A$81.2D50.D55.3D
32.3D110.2A50.A55.3A32.3A294.2A6.A6.3A42.3A$192.D34.D220.A34.A293.2A
12.A47.A$169.2D20.2D33.2D197.2A20.2A33.2A281.2A24.2A$169.2D7.2D56.2D
187.2A7.2A56.2A271.A$178.D57.D197.A57.A273.3A$176.D.D55.D.D195.A.A55.
A.A275.A$176.2D4.2D44.2D4.2D196.2A4.2A44.2A4.2A$119.2D39.2D20.D44.D2.
D144.2A39.2A20.A44.A2.A284.2A$119.D41.D18.D.D45.2D145.A41.A18.A.A45.
2A285.2A25.2A$120.3D38.D.D16.2D34.2D158.3A38.A.A16.2A34.2A324.2A$101.
2D19.D39.2D52.2D139.2A19.A39.2A52.2A264.A21.2A$101.2D254.2A126.3A250.
3A19.2A85.2A$485.A255.A104.A2.A$486.A253.2A93.2A10.2A$835.2A$795.2A
32.2A$795.A33.2A$796.3A10.2A$191.2D32.2D3.2D215.2A32.2A3.2A288.2A20.A
11.A$191.2D11.2D20.D3.D216.2A11.2A20.A3.A274.2A4.2A7.2A29.3A21.2A$86.
2D116.D18.3D5.3D108.2A116.A18.3A5.3A271.A4.A.A38.A16.2A5.2A$86.2D80.
2D35.3D15.D9.D108.2A80.2A35.3A15.A9.A269.A.A4.A57.2A$164.2D2.2D37.D
212.2A2.2A37.A295.2A4.2A$163.D.D253.A.A$163.D23.2D230.A23.2A$162.2D
23.D230.2A23.A$188.3D253.3A$190.D255.A6$745.2A$745.2A5$844.2A$844.2A
7.2A$853.A$851.A.A$851.2A3$833.2A$834.A$834.A.A$835.2A$92.2D254.2A$
93.D255.A$93.D.D253.A.A497.2A66.2A$94.2D254.2A497.A.A65.2A$851.A$109.
2D254.2A484.2A$109.2D254.2A$796.2A$796.2A$92.2D254.2A$92.2D5.2D247.2A
5.2A$99.2D254.2A2$105.D255.A460.2A27.2A$104.D.D253.A.A459.A.A26.2A$
97.2D6.2D246.2A6.2A460.A$98.D255.A505.2A$95.3D253.3A505.A.A$95.D255.A
507.2A$803.2A$803.2A2$854.2A$853.A2.A$854.2A3$790.2A$790.2A$794.2A$
793.A.A$793.A34.2A$792.2A35.A$805.2A19.3A$805.2A19.A2$837.2A$807.2A
28.2A$807.2A91$653.3A$653.A$654.A40$463.A$463.3A$466.A$465.2A$480.2A$
480.A$478.A.A$467.A10.2A$466.A.A$466.A.A$461.2A4.A$460.A.A15.2A$460.A
17.A.A$459.2A19.A$480.2A6$469.2A$469.2A9$481.2A$481.A$479.A.A$479.2A
12$461.2A15.2A$460.A.A15.2A$460.A25.2A$459.2A25.A$484.A.A$484.2A4$
466.A$466.3A$469.A$447.2A19.2A$447.A15.A$445.A.A15.3A$445.2A19.A$465.
2A3$424.2A$424.2A2$462.2A$462.2A17.2A$481.2A3$482.2A$482.A$469.2A12.
3A$470.A14.A$467.3A$467.A$436.2A$436.A10.2A$437.3A7.2A$439.A3$436.A
18.2A$436.3A15.A.A$439.A14.A$438.2A13.2A3$450.2A$450.2A4$439.2A$439.
2A16.2A$457.2A6$459.A$458.A.A$459.A4$380.2A$380.2A74.2A$376.A79.A.A$
376.3A79.A$379.A78.2A$378.2A62.2A$400.2A39.A.A25.2A$400.2A39.A27.A$
440.2A7.2A16.A.A$449.2A16.2A4$388.2A$388.2A$374.2A$374.2A$370.2A66.2A
$370.2A67.A75.2A$439.A.A73.2A$440.2A2$524.2A$523.A.A$524.A2$470.2A$
470.2A$520.2A$520.2A$525.2A$525.A.A$394.2A131.A$393.A.A116.2A13.2A$
394.A42.2A74.A$437.2A71.3A6.2A$374.2A134.A8.2A$375.A$375.A.A$376.2A
64.2A$442.2A$438.2A40.2A$438.2A40.2A$412.A$410.3A$409.A34.2A$409.2A
33.2A13.2A$371.2A85.A.A$371.2A85.A$457.2A5$418.2A$418.2A$446.A$445.A.
A$445.A.A$405.2A39.A$406.A$394.2A7.3A9.2A$394.2A7.A11.A$385.A30.3A$
384.A.A31.A$384.A.A$385.A3$390.2A$390.A.A$391.2A56$405.2A$405.2A!

Some trivial adjustment of the Herschel transceiver will almost certainly be needed, by the way, to allow a wider variety of glider-pair recipes to work. Moving the trombone-slide component in the NW by thirty or forty cells diagonally should be enough. Looks like that will mean increasing the offset to the new corner, maybe to 512 instead of 256 if we want to stick with powers of two for Hashlife's sake, but that's also a trivial change.

Can anyone come up with a significantly simpler design for a spiral-growth replicator unit?

I'd also be very interested in a more efficient universal constructor -- a two-arm design, for example, might allow for a much shorter total recipe stream. But I think it's someone else's turn to figure out the synchronization and programming details...!
dvgrn
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Re: Spiral Growth Geminoid Challenge

Postby towerator » December 10th, 2013, 5:00 pm

Those spirals UC are awesome, not because their function, but because they look like acutal cells. It is like a langton loop in GoL.
This is game of life, this is game of life!
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Joined: September 2nd, 2013, 3:03 pm

Re: Spiral Growth Geminoid Challenge

Postby dvgrn » December 10th, 2013, 5:32 pm

towerator wrote:Those spirals UC are awesome, not because their function, but because they look like acutal cells. It is like a langton loop in GoL.

The best bet for a quadratic-growth spacefilling replicator in Conway's Life seems to be something along the lines of Langton's Loop. But nobody has seen one of those in action yet, and I'm afraid they'll mostly be empty space, so they'll just look like skinny diamonds.

You might be thinking of the loafer-seed gun variant with a double-spiral memory loop -- which is definitely fun to watch, but it doesn't necessarily have much to do with a spiral-growth universal constructor. The second design described in the original post could have a double-spiral memory loop in the center, to save space... but that object wouldn't get replicated out to the corner UCs in any recognizable form, so you wouldn't end up with anything resembling Langton's Loops.

Here are a few more experiments with 9hd and 10hd universal constructors that could be used in a spiral-growth pattern. Technically they're an improvement on Calcyman's design in terms of the number of still lifes -- these four are all about the same (I believe it's 55, 56, 57 and 58 still lifes). But they all require a semi-Snark pair quite a distance away:

x = 1102, y = 1177, rule = LifeHistory
304.2E$304.E$302.E.E$302.2E$724.2E$724.E$722.E.E$722.2E35$89.2A$82.2A
5.2A$82.2A3$84.2A17.2A8.2A$84.2A17.A9.2A$78.2A21.A.A$78.2A21.2A$119.
2A$119.2A$115.2A$115.2A4$120.2A$120.2A2$2E$2E73.A$75.3A$78.A$77.2A5$
504.A21.2A$502.3A21.2A$72.2A427.A35.2A$73.A427.2A34.A$73.A.A24.2A433.
A.A$74.2A23.A.A376.A56.2A$99.A370.A7.3A$98.2A370.3A8.A$88.2A16.2A365.
A6.2A$88.A.A15.2A17.2A345.2A$90.A34.2A384.2A11.2C12.2A$90.2A419.2A11.
2C12.A$70.2A464.A.A$70.A465.2A$71.3A$73.A$523.2A$79.2A387.2A44.2A6.A.
A$79.2A387.2A23.2A20.A6.A$95.A382.2D13.A18.3A6.2A$93.3A382.2D4.2A8.3A
15.A$92.A12.2A377.A11.A$92.2A10.A.A378.3A$104.A382.A$67.A35.2A$67.3A
455.2A$70.A453.A.A$69.2A453.A$401.2E120.2A$401.2E82.2A$485.A.A$487.A$
64.2A43.2A367.2A7.2A$65.A43.2A4.2A361.2A$65.A.A47.2A$66.2A$76.2A3.2A
446.2A$76.2A3.2A446.2A4.2A$114.2A350.2A67.2A$110.2A2.2A351.A$109.A.A
355.A.A$109.A12.2A344.2A$108.2A11.A.A410.2A$121.A408.2A2.2A$120.2A
407.A.A$91.2A244.3D46.3D140.A12.2A$91.2A189.2D26.6D19.5D44.5D139.2A
11.A.A$280.4D24.10D15.7D42.7D152.A$278.6D23.4D4.5D10.10D39.10D99.2A
50.2A$122.2A152.8D22.4D7.4D9.10D39.10D99.A$121.A.A150.10D21.4D8.4D13.
6D43.6D97.A.A$121.A155.7D20.4D10.4D12.6D43.6D97.2A$120.2A156.6D19.5D
10.5D11.6D43.6D$278.6D19.4D12.5D10.6D43.6D153.2A$279.5D18.5D12.5D10.
6D43.6D152.A.A$76.2A201.5D18.5D12.6D9.6D43.6D152.A$76.2A107.A93.5D17.
6D13.5D9.6D43.6D151.2A$185.3A91.5D17.5D14.5D9.6D43.6D$188.A90.5D17.5D
14.6D8.6D43.6D$130.2A55.2A90.5D16.6D14.6D8.6D43.6D$130.2A7.2A56.2A80.
5D16.6D14.6D8.6D6.6D21.7D3.6D216.A$139.A57.A81.5D16.6D14.6D8.6D4.9D
18.11D.6D216.3A$137.A.A55.A.A81.5D16.6D14.6D8.6D3.11D16.4D5.10D219.A$
137.2A4.2A44.2A4.2A82.5D16.6D14.7D7.6D2.13D13.5D7.9D79.2A15.2A63.2A
55.2A$121.2A20.A44.A2.A87.5D15.7D14.7D7.6D.3D5.6D12.5D9.8D78.A.A15.2A
63.2A7.2A56.2A$122.A18.A.A45.2A88.5D15.7D14.7D7.8D8.6D11.4D11.7D78.A
25.2A64.A57.A$122.A.A16.2A34.2A100.5D15.7D14.7D7.7D9.6D10.4D12.7D77.
2A25.A63.A.A55.A.A$123.2A52.2A100.5D15.7D14.7D7.6D11.5D9.5D13.6D102.A
.A63.2A4.2A44.2A4.2A$190.3C86.5D15.7D14.7D7.6D11.5D9.5D13.6D102.2A48.
2A20.A44.A2.A$190.C88.5D15.7D14.7D7.6D11.5D8.5D14.6D153.A18.A.A45.2A$
191.C87.5D15.7D14.7D7.6D11.5D8.5D14.6D153.A.A16.2A34.2A$279.5D15.7D
14.7D7.6D11.5D8.5D14.6D154.2A52.2A$279.5D15.7D14.7D7.6D11.5D8.5D14.6D
84.A136.3C$279.5D15.7D14.6D8.6D11.5D7.6D14.6D84.3A134.C$279.5D16.6D
14.6D8.6D11.5D7.6D14.6D87.A134.C$152.2A32.2A3.2A86.5D16.6D14.6D8.6D
11.5D7.6D14.6D86.2A$152.2A11.2A20.A3.A87.5D16.6D14.6D8.6D11.5D7.6D14.
6D$165.A18.3A5.3A84.5D16.6D14.6D8.6D11.5D7.6D14.6D$129.2A35.3A15.A9.A
84.5D17.5D14.5D9.6D11.5D7.6D14.6D$125.2A2.2A37.A110.5D17.5D14.5D9.6D
11.5D7.7D13.6D183.2A32.2A3.2A$124.A.A152.5D17.6D12.6D9.6D11.5D7.7D13.
6D183.2A11.2A20.A3.A$124.A154.5D18.5D12.5D10.6D11.5D8.6D13.6D196.A18.
3A5.3A$123.2A154.5D18.5D12.5D10.6D11.5D8.7D12.6D160.2A35.3A15.A9.A$
279.5D19.4D12.4D11.6D11.5D8.8D11.6D156.2A2.2A37.A$279.5D19.5D10.5D11.
6D11.5D9.7D11.6D155.A.A$279.5D20.4D10.4D12.6D11.6D8.9D8.7D106.2A47.A$
278.6D20.5D8.4D13.6D11.6D9.9D5.13D102.2A46.2A$278.6D21.5D6.5D13.6D11.
6D10.25D$277.9D20.5D4.4D13.9D8.9D10.14D.7D$273.16D19.10D12.14D2.15D8.
11D3.5D$310.6D56.6D5.3D5$480.2A$480.2A85$259.2A$259.2A3$268.2A$267.A.
A410.2A$268.A411.2A3$262.2C425.2A$262.2C2D422.A.A$264.2D423.A$269.2A$
269.A.A$271.A411.2C$256.2A13.2A410.2C2D$257.A427.2D$254.3A6.2A425.2A$
254.A8.2A425.A.A$692.A$677.2A13.2A$678.A$675.3A6.2A$675.A8.2A14$214.
2A$215.A$215.A.A$216.2A2$231.2A$231.2A2$222.2C$214.2A6.2C$214.2A5.2D$
221.2D2$227.A$226.A.A$219.2A6.2A$220.A$217.3A$217.A3$362.2C$362.C.C$
362.C3$784.C$783.2C$783.C.C3$609.2A$610.A$610.A.A$611.2A2$626.2A$626.
2A2$617.2C$609.2A6.2C$609.2A5.2D$616.2D2$622.A$621.A.A$614.2A6.2A$
615.A$612.3A$612.A101$490.3C$490.C$491.C3$911.3C$911.C$912.C92$301.2E
$301.E$299.E.E$299.2E10$727.2E$727.E$725.E.E$725.2E13$618.3C$618.C$
619.C3$1039.3C$1039.C$1040.C$108.2A$101.2A5.2A$101.2A3$103.2A17.2A8.
2A$103.2A17.A9.2A$97.2A21.A.A$97.2A21.2A$138.2A$138.2A$134.2A$134.2A
4$139.2A$139.2A3$21.2E71.A$21.2E71.3A$97.A$96.2A7$91.2A$92.A$92.A.A
24.2A209.3D46.3D$93.2A23.A.A181.7D19.5D44.5D$118.A181.11D15.7D42.7D$
117.2A179.5D4.6D10.10D39.10D$107.2A16.2A170.4D8.5D9.10D39.10D$107.A.A
15.2A17.2A150.4D10.5D12.6D43.6D147.A21.2A$109.A34.2A150.3D12.5D11.6D
43.6D145.3A21.2A$109.2A184.4D12.5D11.6D43.6D144.A35.2A$89.2A203.5D13.
5D10.6D43.6D144.2A34.A$89.A204.4D14.5D10.6D43.6D178.A.A$90.3A200.5D
14.6D9.6D43.6D121.A56.2A$92.A200.5D15.5D9.6D43.6D113.A7.3A$293.5D15.
6D8.6D43.6D113.3A8.A$98.2A193.5D15.6D8.6D43.6D116.A6.2A$98.2A193.5D
15.6D8.6D43.6D115.2A$114.A177.6D15.6D8.6D6.6D21.7D3.6D154.2A11.2C12.
2A$112.3A177.6D15.6D8.6D4.9D18.11D.6D154.2A11.2C12.A$111.A12.2A167.5D
15.6D8.6D3.11D16.4D5.10D179.A.A$111.2A10.A.A167.6D14.6D8.6D2.13D13.5D
7.9D179.2A$123.A169.6D14.6D8.6D.3D5.6D12.5D9.8D$86.A35.2A169.6D14.6D
8.8D8.6D11.4D11.7D$86.3A204.7D13.6D8.7D9.6D10.4D12.7D166.2A$89.A204.
6D13.6D8.6D11.5D9.5D13.6D111.2A44.2A6.A.A$88.2A204.7D12.6D8.6D11.5D9.
5D13.6D111.2A23.2A20.A6.A$295.7D9.8D8.6D11.5D8.5D14.6D121.2D13.A18.3A
6.2A$296.8D5.10D8.6D11.5D8.5D14.6D121.2D4.2A8.3A15.A$297.14D.6D9.6D
11.5D8.5D14.6D127.A11.A$115.2A181.11D3.6D9.6D11.5D8.5D14.6D128.3A$83.
2A31.A183.7D4.7D9.6D11.5D7.6D14.6D130.A$84.A31.A.A15.2A175.6D10.6D11.
5D7.6D14.6D$84.A.A30.2A15.2A175.6D10.6D11.5D7.6D14.6D168.2A$85.2A223.
6D11.6D11.5D7.6D14.6D167.A.A$95.2A3.2A208.6D11.6D11.5D7.6D14.6D44.2A
121.A$95.2A3.2A207.6D12.6D11.5D7.6D14.6D44.2A120.2A$309.6D12.6D11.5D
7.7D13.6D128.2A$308.6D13.6D11.5D7.7D13.6D128.A.A$307.6D14.6D11.5D8.6D
13.6D130.A$307.5D15.6D11.5D8.7D12.6D121.2A7.2A$306.5D16.6D11.5D8.8D
11.6D121.2A$305.5D17.6D11.5D9.7D11.6D$304.5D18.6D11.6D8.9D8.7D159.2A$
110.2A191.5D19.6D11.6D9.9D5.13D156.A$110.2A23.2A165.4D21.6D11.6D10.
25D157.A.A15.2A$135.A.A162.5D20.9D8.9D10.14D.7D160.2A15.2A$137.A159.
6D20.14D2.15D8.11D3.5D$137.2A154.7D65.6D5.3D114.2A$494.A$494.A.A$495.
2A2$119.2A$95.2A21.A.A$95.2A21.A$117.2A394.2A$513.A$511.A.A47.2A$511.
2A48.A.A$147.A34.A380.A$147.3A32.3A378.2A$150.A34.A$127.2A20.2A33.2A$
127.2A7.2A56.2A$136.A57.A$134.A.A55.A.A350.2A$134.2A4.2A44.2A4.2A350.
A.A$118.2A20.A44.A2.A355.A$119.A18.A.A45.2A355.2A$119.A.A16.2A34.2A$
120.2A52.2A317.2A15.2A$187.3C302.A.A15.2A$187.C304.A25.2A53.A34.A$
188.C302.2A25.A54.3A32.3A$516.A.A57.A34.A$516.2A35.2A20.2A33.2A$553.
2A7.2A56.2A$562.A57.A$149.2A32.2A3.2A370.A.A55.A.A$149.2A11.2A20.A3.A
309.A61.2A4.2A44.2A4.2A$162.A18.3A5.3A306.3A43.2A20.A44.A2.A$126.2A
35.3A15.A9.A309.A43.A18.A.A45.2A$122.2A2.2A37.A334.2A43.A.A16.2A34.2A
$121.A.A422.2A52.2A$121.A491.3C$120.2A491.C$614.C5$575.2A32.2A3.2A$
520.2A53.2A11.2A20.A3.A$520.2A66.A18.3A5.3A$552.2A35.3A15.A9.A$548.2A
2.2A37.A$547.A.A$547.A$546.2A4$505.2A$505.2A81$256.2A$256.2A3$265.2A$
264.A.A$265.A3$259.2C$259.2C2D$261.2D$266.2A$266.A.A$268.A414.2A$253.
2A13.2A413.2A$254.A$251.3A6.2A$251.A8.2A430.2A$691.A.A$692.A3$225.2A
459.2C$226.A459.2C2D$226.A.A459.2D$227.2A464.2A$693.A.A$242.2A451.A$
242.2A436.2A13.2A$681.A$233.2C443.3A6.2A$225.2A6.2C443.A8.2A$225.2A5.
2D$232.2D2$238.A$237.A.A$230.2A6.2A$231.A$228.3A$228.A10$352.2C$352.C
.C$352.C10$626.2A$627.A$627.A.A150.C$628.2A149.2C$779.C.C$643.2A$643.
2A2$634.2C$626.2A6.2C$626.2A5.2D$633.2D2$639.A$638.A.A$631.2A6.2A$
632.A$629.3A$629.A130$511.3C$511.C$512.C13$939.3C$939.C$940.C143$671.
3C$671.C$672.C13$1099.3C$1099.C$1100.C!

It may be possible to tighten these up somehow by using different settings on the period quadruplers, but I don't think so. Also, Calcyman's design has a huge efficiency advantage: all of the input gliders code for construction-arm gliders. In the above designs, two gliders out of every group of four are non-coding -- they serve only to reset the semi-Snarks and the period quadrupler (or period doublers).

Is there any simpler way to get the right amount of delay between the input gliders, to allow a wide range of glider-pair outputs... but use only one semi-Snark or period doubler on each construction lane?
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Re: Spiral Growth Geminoid Challenge

Postby dvgrn » August 1st, 2014, 4:40 pm

Finally took some time off of other half-baked projects, and cleaned up the last few details of a 10hd Geminoid universal constructor. This makes it possible to complete a relatively compact spiral growth pattern... less than 1.6 million cells on a side (sheesh):

Spiral-growth-pattern.png
Spiral-growth pattern overview
Spiral-growth-pattern.png (2.92 KiB) Viewed 4720 times

Life-spiral.mc.gz
Four 10hd Geminoid universal constructors programmed for spiral growth
(45.32 KiB) Downloaded 250 times

"10hd" means that the pairs of gliders aimed at the construction elbow are spaced 10 half-diagonals apart, instead of 9hd as in the linear Life replicator. 10hd still appears to be significantly more efficient, but I haven't done a side-by-side compilation of two identical recipes yet.

Here's a minimal version of the spiral-growth pattern with the input gliders in a single stream:

Spiral-in-Life-straightline-min.mc.gz
B3/S23 spiral-growth pattern with straight-line input recipe
(16.77 KiB) Downloaded 208 times
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Re: Spiral Growth Geminoid Challenge

Postby simsim314 » August 4th, 2014, 12:51 pm

Nice this one is simpler than any Geminoid or replicator, but still an interesting construction.

I think the question is: how can we use this construction in some more complex constellation, say quadratic growth, or something of a kind.
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Re: Spiral Growth Geminoid Challenge

Postby dvgrn » June 3rd, 2017, 6:42 am

An update to an old thread: the last spiral growth pattern had a bounding box of slightly over 1.5 million pixels on a side. With simeks' single-channel toolkit and Calcyman's "slmake" slow-salvo compiler, that can now easily be reduced by a factor of 100.

The new version fits inside 145102x145022 -- though its population is only a few thousand cells smaller than the old version, assuming you don't count the decorative Snarkbox that holds the initial recipe.

single-channel-spiral-centered.mc.gz
spiral growth pattern, with recipe packed into the center -- slow start in Golly
(50.18 KiB) Downloaded 26 times

Single-channel recipes can be packed a lot tighter than the old 10hd constructor arm recipes, and single-channel construction arms are much simpler -- but they're also much less efficient in terms of the number of gliders on the tape needed to encode a slow-salvo construction recipe for a given piece of circuitry.

Here's a version that runs better in Golly at step sizes around 2^15 (8^5), showing the full length of the required single-channel recipe:

single-channel-spiral-straightinput.mc.gz
spiral growth pattern, minimal version (file is smaller due to better macrocell encoding of repetition in the recipe)
(45.64 KiB) Downloaded 25 times

On May 17th it actually became possible to build a much smaller spiral-growth pattern than this one, with another 100-fold reduction in bounding box and population. Details are left as an exercise for the reader...!
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Re: Spiral Growth Geminoid Challenge

Postby fluffykitty » June 3rd, 2017, 6:30 pm

Is a sub-1Kx1K replicator possible now?
I like making rules
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Re: Spiral Growth Geminoid Challenge

Postby dvgrn » June 3rd, 2017, 9:49 pm

fluffykitty wrote:Is a sub-1Kx1K replicator possible now?

Well, not with this technology, I'd say. Look at the center of the first spiral-growth pattern.

It's not packed quite as tightly as it could be, and more efficient slow salvo construction recipes could be found (e.g., with glider triplets, quadruplets, etc., instead of just glider pairs in the single-channel recipes).

But as of right now, a bounding box of well over 4000x4000 is needed to encode the construction of less than two dozen still lifes. All possible optimizations together might well add up to a factor of two improvement over this, but a factor of twenty seems like a little much to hope for -- not counting the fact that a replicator's mechanism probably has to be a little more complicated than just one minimal constructor/reflector.

Now, there are lots of possible ways to mix and match this with other technology, and maybe get some more improvements. In particular, not a whole lot has been done with Andrew Wade's original idea from the Gemini spaceship, of building circuitry with two synchronized constructor arms. That's maybe an order of magnitude more efficient... but then you have to build more than twice as much circuitry, and spend some time waiting around to keep the two arms synchronized, so you lose a good part of that.

There may well be a natural self-replicator inside a million-cell bounding box, but I don't see how known mechanisms provide even a glimmer of a hope of an engineered replicator anywhere near that small.
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Re: Spiral Growth Geminoid Challenge

Postby dvgrn » June 21st, 2017, 2:25 pm

dvgrn wrote:On May 17th it actually became possible to build a much smaller spiral-growth pattern than this one, with another 100-fold reduction in bounding box and population.

Okay, I lied. It's not even a factor of four reduction in population -- at least not without reworking the Snarkbox, which I'm not inclined to do. This one is too much fun to watch in Golly.

However, the bounding-box area reduction is something like a factor of 5000 -- and the pattern fits in a forum post and in LifeViewer:

x = 1966, y = 2007, rule = B3/S23
926b2o$926bobo$928bo4b2o$924b4ob2o2bo2bo$924bo2bobobobob2o$927bobobobo
$927bo3bobo$932bo$927bobo$918b2o$919bo6bobobo$919bobo4b5o$920b2o2b2obo
4b2o$925b2o2bo4bo54b2o$926bobo60b2o$926b2o5b2o$926b5o$928bo2$930b2o$
930bo$931b3o$933bo5$935b2o$934bobo$928b2o4bo$926bo2bo2b2ob4o$910b2o14b
2obobobobo2bo$909bobo17bobobobo$911bo17bobob2o$930bo24bo$956bo$943b2o
9b3o$934b2o7bo$934b2o5bobo$941b2o7$931b2o$921bo10bo$920bo8b3o$920b3o6b
o13bo$942b2o$942bobo3$926b2o$926bobo$928bo4b2o$924b4ob2o2bo2bo$924bo2b
obobobob2o42bo$927bobobobo43bobo$928b2obobo44b2o$932bo$879b2o$878bobo
37b2o$880bo38bo7b2o$919bobo5b2o$920b2o4$898bo$898bobo$898b2o65b2o$930b
2o32b2o$930bo35bo$931b3o$933bo9bo$941bobo$942b2o3$935b2o63bobo$934bobo
64b2o$928b2o4bo66bo$926bo2bo2b2ob4o$856b2o68b2obobobo4bo$857b2o70bobo
3bo$856bo72bo5bo$930b2o$933bobo$935bo7b2o$904bo26bo2b2o7bo$904b2o35bob
o$903bobo23bo3bo7b2o$928bo4bo54bo$928b3o56b2o$987bobo3$869bo94bobo$
868bo62b2o32b2o$868b3o61bo32bo$929b3o$929bo4$834bo$834b2o90b2o101bo$
833bobo90bobo98bobo$928bo4b2o93b2o$924b4ob2o2bo2bo$924bo2bobobobob2o$
927bobobobo$881b2o45b2obobo$880bobo49bo$882bo$905bobo10b2o$905b2o12bo
7b2o$906bo12bobo5b2o$920b2o2$1014b3o$845bobo166bo$845b2o168bo$846bo2$
930b2o34b2o$930bo35bobo26bo$931b3o32bo26bobo$811b2o120bo60b2o$810bobo
130bo106bobo$812bo131b2o105b2o$943b2o106bo2$935b2o$934bobo$928b2o4bo$
926bo2bo2b2ob4o$883bo42b2obobobobo2bo$882bo46bobobobo$882b3o44bobob2o$
930bo2$905b3o35b2o92b2o$907bo35bo93bobo$849b3o54bo34bobo93bo$851bo82bo
6b2o$850bo81b2ob2o$932b2ob2o$932bo2b2o51b3o$933b2o53bo$989bo$788b2o
228bobo$789b2o24bo115b2o34bo51b2o$788bo24b2o117bo32bobo51bo$814b2o113b
3o34b2o$929bo5$926b2o$926bobo$928bo4b2o$924b4ob2o2bo2bo$883b2o39bo2bob
obobob2o149bo$882bobo24bo17bobobobo127bo25b2o$827b2o55bo24bobo16b2obob
o20bo105b2o24b2o$826bobo80b2o21bo20b2o105bobo$828bo124bobo$918b2o$919b
o7b2o$919bobo5b2o$920b2o$766bo274bo$766b2o78bo195b2o$765bobo77bo195b2o
$845b3o2$993bo$930b2o62bo$930bo61b3o$920b2o9b3o88b2o$921b2o10bo88bobo$
920bo101bo4$935b2o11bo$934bobo9bobo134b2o$804b3o121b2o4bo12b2o134bobo$
806bo119bo2bo2b2ob4o38b2o104bo$775bo29bo50b3o67b2obobobobo2bo37b2o$
775bobo80bo70bobobobo42bo$775b2o80bo71bobob2o181bo$930bo183bobo$1115b
2o$743b2o198b2o118bobo$742bobo189b2o7bo120b2o$744bo189b2o5bobo120bo$
941b2o2$1015bo$1016b2o$1015b2o$897b3o37b2o106b2o$899bo36b2o106b2o$898b
o32b2o5bo107bo$813bobo116bo$813b2o114b3o$814bo114bo$864bobo102bobo$
782bo81b2o104b2o134b2o$782b2o81bo104bo134b2o$753bo27bobo50b2o163b3o
105bo$752bo80bobo90b2o71bo$752b3o80bo90bobo71bo137bo$928bo4b2o204bo$
924b4ob2o2bo2bo200b3o$924bo2bobobobob2o$720b3o204bobobobo$722bo205b2ob
obo$721bo210bo2$918b2o$919bo7b2o$919bobo5b2o$875bo44b2o38bo$875b2o82b
2o106b3o$874bobo82bobo105bo$791bo276bo$790bo253bo$790b3o145bo106b2o$
842bo96bo53bo50b2o55bo$841bo88b2o5b3o54bo107bo26bo$841b3o86bo61b3o105b
3o25b2o$893bo37b3o194bobo$892bo40bo$892b3o$1025b2o133bo$1025bobo133b2o
$1025bo134b2o$935b2o$913b3o18bobo$915bo12b2o4bo$914bo11bo2bo2b2ob4o$
926b2obobobobo2bo$929bobobobo$929bobob2o$930bo$852b2o236b2o$851bobo89b
2o38b2o105bobo$742bo110bo80b2o7bo39bobo104bo$742b2o190b2o5bobo39bo$
714bo26bobo23bobo171b2o125bo$685b2o25b2o53b2o191bo105bobo$686b2o25b2o
53bo23b2o26bo140b2o53bo50b2o55bo$685bo107b2o23b2o140b2o52bobo105bobo
26b2o$792bo26b2o114b3o77b2o106b2o25b2o$871bo63bo216bo$869b2o65bo$870b
2o59b2o$932bo115b2o$929b3o115b2o$929bo119bo$891bo$891b2o$890bobo2$926b
2o$926bobo263bo$928bo4b2o255bobo$911bo12b4ob2o2bo2bo254b2o$829b2o80bob
o10bo2bobobobob2o176b2o$830b2o79b2o14bobobobo178b2o$719b2o108bo98b2obo
bo180bo$720b2o23bo186bo$663bo55bo24bo345bo$663b2o79b3o23bo147b2o62bobo
106b2o$662bobo105b2o147bo7b2o54b2o25b3o24bobo50b2o$769bobo23bobo121bob
o5b2o29b2o23bo26bo27b2o$795b2o123b2o36bobo50bo26bo$796bo50bo110bo217b
2o$847bobo325b2o$847b2o328bo4$930b2o$930bo$931b3o$933bo223bobo$864b3o
75bobo213b2o54bo$866bo76b2o213bo56bo$865bo50b3o24bo269b3o$807bo80bobo
27bo$807b2o79b2o27bo17b2o198b3o$806bobo80bo44bobo198bo$696b3o229b2o4bo
201bo$698bo227bo2bo2b2ob4o$697bo228b2obobobobo2bo146b3o26bo$747b2o180b
obobobo125bo23bo26bobo$748b2o23bo155bobob2o127bo23bo26b2o$747bo24bo
157bo129b3o$717bobo52b3o424bo$717b2o106bo117b2o253b2o$718bo104b2o109b
2o7bo40b2o212bobo$824b2o108b2o5bobo40bobo52b2o$941b2o41bo54bobo$1039bo
3$655bo360bobo$654bo362b2o162bo$654b3o185bo122bo51bo164bo$842b2o87b2o
33b2o212b3o$841bobo50b2o36bo32b2o270bo$893bobo33b3o306b2o$895bo33bo12b
2o293b2o$918bo23bobo$620bo53bo243bobo21bo$620b2o52b2o242b2o$619bobo51b
obo432b2o$779b3o144b2o180bobo24bobo26bo$724b3o54bo144bobo179bo27b2o25b
2o$726bo53bo147bo4b2o201bo26bobo$696bo28bo198b4ob2o2bo2bo$694b2o228bo
2bobobobob2o284b2o$695b2o104bobo123bobobobo286b2o$801b2o125b2obobo73b
2o213bo$745bobo54bo129bo73b2o$745b2o261bo$746bo171b2o144b2o$919bo7b2o
135bobo$919bobo5b2o135bo$920b2o173bo$848bo244bobo107bo$846b2o139bobo
104b2o108b2o$847b2o139b2o213b2o$871bo116bo270bobo$871b2o387b2o$870bobo
387bo$922bo7b2o$597b2o52b2o269b2o6bo$596bobo51bobo268bobo7b3o$598bo53b
o104bo175bo36bo159b3o$757b2o210b2o159bo55b2o$756bobo210bobo159bo54bobo
$1054bo131bo$673bo378bobo108bo$671b2o262b2o9bobo104b2o106bobo$672b2o
260bobo10b2o213b2o$724bo203b2o4bo12bo$614bo107b2o79b3o120bo2bo2b2ob4o
92b2o$614bobo106b2o80bo120b2obobobobo2bo91b2o$614b2o158bo29bo124bobobo
bo96bo$774bobo152bobob2o$774b2o154bo186bo$1118bo$824bobo52bo63b2o171b
3o$824b2o51b2o55b2o7bo68bo215bo$687b3o135bo52b2o54b2o5bobo66bobo213bob
o$689bo158b2o91b2o68b2o214b2o$688bo158bobo408bo$849bo407b2o$899b2o25bo
330bobo$900b2o23bo$899bo25b3o$992b2o$733b3o195b2o59bobo214b2o$735bo
196bo59bo83bo79b2o50b2o$623b2o109bo194b3o145bo77b2o28bo24bo$624b2o303b
o145b3o26b2o51bo28bo$623bo480bobo77b3o$1104bo$781bo$781b2o$780bobo143b
2o20bo106b2o$751bobo172bobo18b2o105b2o$751b2o175bo4b2o12bobo106bo$752b
o171b4ob2o2bo2bo$586bo107bobo227bo2bobobobob2o$585bo108b2o159bobo69bob
obobo100bo215bo$557bo27b3o107bo159b2o71b2obobo101bo215bo$557b2o297bo
75bo100b3o213b3o$556bobo266b2o$826b2o90b2o$825bo51bo41bo7b2o353bo$877b
2o40bobo5b2o352b2o$876bobo41b2o359bobo$986bobo$657bo53bo275b2o27bo$
657b2o52b2o274bo27b2o162bo51b3o$601bo54bobo51bobo77bo107bobo114bobo
160b2o51bo$601b2o187bobo105b2o278bobo26bo24bo$600bobo187b2o107bo226b3o
79b2o$930b2o194bo29bo50b2o$921b2o7bo196bo26bobo$758b2o160bobo8b3o221b
2o$759b2o161bo10bo9bo$758bo185bo132b3o242bo$942b3o25b3o104bo28bo213bob
o$970bo107bo28b2o212b2o$672bo298bo134b2o$563bo107bo162bo100b2o$563bobo
105b3o158b2o100bobo120bo214bo$534b2o27b2o159bo108b2o93b2o4bo120bobo
215b2o$535b2o185b2o202bo2bo2b2ob4o117b2o214b2o$534bo188b2o201b2obobobo
bo2bo$929bobobobo$854b2o73bobob2o369b2o$610bo242bobo74bo372b2o$610bobo
242bo153bo295bo$610b2o331b2o65b2o$934b2o7bo65b2o27b2o215bo$877bo55bo2b
o4bobo94bobo160b2o51b2o$578b2o187bobo105b2o64b2o95bo162bobo50bobo$579b
2o186b2o24b2o81b2o55bo267bo$578bo189bo25b2o136b2o$629b2o162bo140bo243b
o53bo$628bobo548b2o52b2o$630bo547b2o52b2o$966bo133b2o$931b2o31bobo26b
2o105bobo$678b3o251bo32b2o26bobo104bo243bobo$680bo248b3o61bo351b2o$
649bo29bo249bo415bo$649bobo$539bobo107b2o645bo$539b2o159bo596bo$540bo
159bobo460bo131b3o$700b2o224b2o234b2o$926bobo233bobo162bo$831b2o95bo4b
2o391b2o$722b2o108b2o90b4ob2o2bo2bo389bobo$721bobo107bo92bo2bobobobob
2o204bo$723bo158b3o42bobobobo208bo$884bo43b2obobo127b2o77b3o134b2o$
883bo23bo24bo128bobo213bobo$744bo26bo134bo154bo215bo$744bobo24b2o133b
3o9b2o35b3o$744b2o24bobo23bo122bo7b2o26bo$795bo123bobo5b2o27bo245bo$
795b3o122b2o278bobo$550b2o26bo622b2o$549bobo24b2o544b3o$551bo25b2o519b
o23bo110bo133bo$1099bo23bo108b2o134b2o$492b2o603b3o132bobo132b2o$491bo
bo$493bo23bo412b2o$516bo161bo251bo333bo54bo$516b3o158bo242b3o8b3o115bo
215b2o50bobo$677b3o242bo10bo116b2o133b2o77b2o52b2o$622bo298bo127b2o
134bobo$620b2o215bo106bo81bo158bo163b2o$621b2o212b2o108b2o51bobo24b2o
321b2o$836b2o106b2o53b2o24bobo322bo$590b2o214b2o52b2o73b2o62bo$591b2o
212bobo51bobo72bobo228bo$590bo216bo53bo66b2o4bo149b2o77bobo$641b2o283b
o2bo2b2ob4o144b2o79b2o$642b2o77bobo202b2obobobobo2bo146bo$641bo79b2o
206bobobobo43b2o$722bo51bo106bobo45bobob2o44bobo323bo$772b2o107b2o47bo
48bo324b2o$773b2o107bo421bobo$527b3o24bo388b2o200b2o$529bo24bobo377b2o
7bo201bobo$528bo25b2o378b2o5bobo177bo23bo$941b2o176bobo$1120b2o2$494bo
188b2o710bo$494bobo187b2o50b2o160b2o388bo107bo$494b2o187bo51bobo159bob
o171bobo212bobo105b3o$737bo161bo172b2o213b2o$931b2o139bo$932bo33bobo
376bo26b2o$920bo8b3o9b2o24b2o270bo106b2o23b2o$649bobo267bo9bo11bobo23b
o269bobo105b2o26bo$567b3o79b2o186b2o80b3o19bo245bo50b2o$569bo80bo187b
2o267bo80bo$568bo239bobo26bo268b2o78b3o26b2o$591bo26b3o187b2o296bobo
105b2o$591bobo26bo188bo116b2o288bo$591b2o26bo306bobo73b2o$750bobo175bo
4b2o66b2o324b2o$750b2o172b4ob2o2bo2bo66bo28bo293b2o$505bo188bo56bo104b
o67bo2bobobobob2o96bo294bo$505b2o24bobo160bobo158bo71bobobobo97b3o$
504bobo24b2o161b2o159b3o70b2obobo209bo$532bo399bo130bo80bo134bo$771b2o
289b2o78b3o133b2o$772b2o144b2o142bobo213bobo$771bo147bo7b2o$471bobo
445bobo5b2o381bo106bo$471b2o240b2o205b2o389bo106b2o$472bo241b2o593b3o
105b2o$713bo$656b2o331bo$655bobo332b2o375bobo$657bo240bo25bo64b2o377b
2o$896b2o26b2o442bo$814b3o80b2o24bobo4b2o278bo$435b2o379bo113bo198b2o
77bobo27bo$434bobo159b2o217bo115b3o194b2o79b2o26b2o$436bo104b2o25bobo
24bobo335bo196bo106bobo$542b2o24b2o27bo$541bo27bo50bo108bo294b3o159b3o
$619bo107b2o216bo78bo161bo163b2o$619b3o106b2o216b2o77bo29bo131bo82bo
79bobo$834bo100b2o8b2o106bobo215b2o77bo$832b2o100bobo117b2o214b2o$669b
o163b2o93b2o4bo41b2o188bo$668bo188bo68bo2bo2b2ob4o37bobo106b2o77bobo
134b2o$668b3o77b3o106b2o67b2obobobobo2bo37bo107b2o28bo50b2o133b2o$477b
3o270bo105bobo70bobobobo150bo28bo186bo108b2o$479bo269bo179bobob2o178b
3o294b2o$478bo212bo81bo156bo481bo26bobo$691b2o78b2o667b2o$690bobo79b2o
169b2o495bo$934b2o7bo$633b3o298b2o5bobo67bobo$635bo305b2o69b2o$634bo
266b2o109bo$792bo109b2o328bo$440bo351b2o107bo331bo$412b3o24bo351bobo
142b2o293b3o$414bo24b3o77bo26bo26b3o359b2o$413bo105b2o24bo29bo361bo$
518bobo24b3o26bo356b2o276b2o$598bo333bo276bobo52b2o80bo$488bo107b2o
107bo223b3o35bobo239bo53b2o82bo25b2o$488bobo106b2o104b2o224bo38b2o295b
o28bo50b3o24b2o$488b2o214b2o104bobo155bo323bobo79bo$810b2o348b2o131b2o
107bobo$811bo347b2o26bobo134bo78b2o$726b2o272b2o106b2o51bo26b2o133b2o
78bo$455bo269bobo198b2o71b2o107bobo77bo134bobo$455b2o187bo82bo198bobo
72bo106bo$454bobo185b2o284bo4b2o527bo$643b2o104bo174b4ob2o2bo2bo526b2o
$749bobo104bobo65bo2bobobobob2o121b3o401b2o$666b3o80b2o105b2o69bobobob
o124bo$668bo158b2o28bo70b2obobo100bo24bo$610b2o55bo158bobo103bo102b2o$
611b2o215bo205b2o$610bo307b2o$905bo13bo7b2o$903b2o14bobo5b2o$904b2o14b
2o36b3o$496b2o376b2o82bo$497b2o374bobo83bo190bo296b2o$496bo267b2o109bo
275b2o78b3o212b2o$385b2o187bo188bobo384b2o79bo136bo79bo$386b2o24bo52bo
bo106bobo104bobo81bo225bo240bo136b2o24b3o$385bo24b2o53b2o107b2o105b2o
309b2o322bo51b2o25bo$411b2o53bo215bo239b3o5b2o59b2o269bobo52b2o77bo28b
o$924bo5bo251b3o78b2o51b2o108b2o$923bo7b3o248bo80bo82b2o77b2o$933bo
196b3o50bo27bobo131b2o$1130bo81b2o133bo$431b2o79bo107bo510bo80bo$432b
2o77bo26b2o80bobo673b2o186bobo$431bo79b3o23bobo80b2o213bo191b2o53bo
213bobo186b2o$539bo104bo188b2o100b2o90bobo51b2o213bo188bo$644b2o188b2o
98bobo90bo53bobo$643bobo158b3o121b2o4bo121bobo$587b3o216bo119bo2bo2b2o
b4o118b2o$589bo215bo120b2obobobobo2bo118bo$588bo131bo208bobobobo$692b
2o25bo161bobo45bobob2o180bo$691bobo25b3o159b2o47bo185b2o$693bo188bo
232b2o$473b2o376b2o90b2o525bo$474b2o376b2o80b2o7bo228bobo294b2o$473bo
267b3o24bo82bo82b2o5bobo13bobo213b2o80b2o212bobo$362b3o378bo23bo173b2o
15b2o26b2o185bo80b2o$364bo293bo83bo24b3o188bo26b2o26bobo240bo$363bo
294bobo326bo26b2o269bo54bo$658b2o354bo271b2o50bobo$1285b2o52b2o2$1398b
o$598bo332b2o302bobo161bo$408b3o25bo52bo107bo334bo303b2o159b3o107bo$
410bo23b2o53bobo105b3o329b3o304bo136b2o133b2o$409bo25b2o52b2o438bo174b
2o267bobo131b2o$379bo160bo563bobo266bo$377b2o161bobo536bo24bo$378b2o
160b2o23bo514b2o242bo$565b2o488bo23b2o242b2o$564bobo359b2o126b2o267bob
o$697bo80b2o146bobo125bobo161b2o241bo$697bobo77bobo148bo4b2o283bobo
214b2o25b2o$697b2o80bo144b4ob2o2bo2bo203bo26bo50bo216bobo23b2o$451bo
161bo310bo2bobobobob2o201bobo25b2o267bo$451b2o160b2o213bo98bobobobo
205b2o25bobo27bo$450bobo159bobo104b2o107b2o98b2obobo47bo215bo80bo$718b
obo24bo53bobo25bobo102bo49bo212b3o79b2o$339b2o379bo24bobo51b2o179b3o
25b3o266bobo$338bobo294bo109b2o53bo77b2o38b2o88bo$340bo293bo242bobo39b
o7b2o80bo486b3o$634b3o23bo218bo39bobo4bo2bo566bo$660b2o258b2o118bo456b
o$659bobo267bo111b2o$929b2o109b2o217bo106bo$386b2o540bo331bo106b2o$
385bobo78bobo789b3o105b2o$387bo78b2o376bo551b2o$467bo50bo323b2o282b3o
266b2o$355bobo159bo325b2o85b2o194bo270bo$355b2o160b3o410bo196bo$356bo
574b3o412b2o$933bo34b3o106b2o267bobo$968bo108bobo266bo$755b3o211bo107b
o162b3o240bobo$757bo404bo77bo243b2o$483b2o271bo406bo77bo216b3o23bo$
484b2o449b2o173bo50b3o27bo266bo$483bo321b2o127bobo174bo78b2o242bo24bo$
696b2o80bo25bobo121b2o4bo68bo105b3o78bobo26bo80b2o133b2o107bo$398bo
298b2o23bo53b2o28bo77bobo39bo2bo2b2ob4o65b2o214b2o78bobo131b2o106bobo$
316b2o80bobo295bo24bo55b2o105b2o40b2obobobobo2bo64b2o27b2o185b2o79bo
242b2o$317b2o79b2o266bobo52b3o131b2o28bo43bobobobo96bobo485bo$316bo
349b2o188b2o71bobob2o97bo486b2o$637b2o28bo187bo74bo588bobo$420bo107bo
27bo81b2o266bo$420b2o106b2o24b2o81bo268b2o35b2o$419bobo105bobo25b2o
348bobo26b2o7bo444bobo$934b2o5bobo445b2o$941b2o446bo$361b2o457bo464bo
134bo$362b2o132bo323bobo463bo132b2o$332bo28bo132b2o324b2o462b3o132bobo
$332bobo160b2o$332b2o239b3o24bo769bo$575bo23bo501bo267b2o$574bo24b3o
131b2o196b2o167b2o161b2o104bobo$732bobo197bo167bobo160bobo$435bo25bo
272bo194b3o64bo79bo186bo$433b2o26b2o466bo12b2o51b2o80b2o$434b2o24bobo
478b2o26bobo23bobo78b2o54bo81bo$782b2o159bo26b2o161b2o78b2o241bobo$
673b3o107b2o131bobo51bo161b2o79bobo25bobo213b2o106bobo$375bobo297bo24b
o81bo133b2o270bobo51b2o213bo108b2o$293b3o79b2o267bo29bo23b2o217bo8b2o
127b2o132b2o51bo244b2o77bo$295bo80bo266bo55b2o225bobo99bobo23b2o133bo
162bobo131b2o$294bo348b3o282bo4b2o94b2o25bo271bo24b2o133bo53b3o$924b4o
b2o2bo2bo92bo297b2o24bo188bo$397b2o106b2o25bobo321bobo24b2o39bo2bobobo
bob2o390bobo213bo$398b2o104bobo25b2o322b2o26b2o41bobobobo478bo$397bo
108bo26bo323bo25bo44b2obobo234b3o242bo$610b2o214b3o103bo235bo242b3o$
339bo269bobo216bo340bo$339b2o270bo215bo90b2o388bo133b2o$338bobo578bo7b
2o377bobo133bobo$309bobo607bobo5b2o378b2o133bo$309b2o240bo368b2o$310bo
240b2o24bo215bo598b2o$550bobo24bobo212bo330b2o267bobo$577b2o131b2o25bo
54b3o328bobo160b2o104bo$711b2o23bo386bo161b2o$411bo298bo25b3o548bo$
411bobo578bo106bobo$411b2o23b2o492b2o35bo25b2o105b2o54bo79b2o242bo$
435bobo24bobo430bo34bo35b2o24b2o106bo53bobo78b2o28bo215bo$353bo83bo24b
2o429b2o36b3o32bobo53b2o131b2o55bo24bo28bo212b3o108bo$352bo110bo212bo
217b2o37bo87b2o190bo50b3o324bo$270b2o80b3o321bobo263bobo78bo28bo24b3o
131b3o295b3o77b3o$271b2o403b2o265b2o108bo23bo431bo56bo$270bo672bo107b
3o24bo271b2o158bo54b2o$1350bobo212bobo$374b3o105b3o25bo349b3o72b2o413b
o$376bo107bo23b2o241b2o109bo71bobo254b2o241bo$375bo107bo25b2o241b2o50b
2o55bo66b2o4bo256bobo241b2o$587b2o25bobo24b3o107bo51bobo120bo2bo2b2ob
4o252bo242b2o$588b2o24b2o27bo161bo120b2obobobobo2bo445bo161bo$587bo27b
o26bo286bobobobo449bo79b2o80bo$827bobo99bobob2o448b3o78b2o79b3o$827b2o
101bo402bo132bo$528b2o25bo272bo77b2o426bo$311bo217b2o23bo216bo133bobo
35b2o387b3o80b2o$311b2o215bo25b3o212b2o136bo26b2o7bo202b2o267bobo$282b
o27bobo402bo54b2o162b2o5bobo202bobo159b3o104bo$282bobo428b2o226b2o203b
o161bo$282b2o104bobo323b2o406bo186bo$388b2o733b2o$389bo23b2o25bo242b2o
437b2o55bo$414b2o23bo242bobo360bo134bo323bo$413bo25b3o212bo29bo359b2o
132b3o54bo53bo212bobo108bo$248bo404bo270bo119bobo186bobo51bobo213b2o
27b2o77bobo$248b2o403b3o266b2o7b2o301b2o52b2o242bobo77b2o$247bobo673b
2o7bo599bo$866bo62b3o$838b2o25bo63bo93bo349b3o$324bobo159bo350bobo25b
3o128b3o25b2o347bo$324b2o160bobo239b3o108bo156bo26b2o188b3o158bo83bo$
325bo160b2o104bo26bo110bo50b3o213bo215bo242bobo$564b2o25bo27b2o108bo
53bo430bo242b2o$347b2o214bobo25b3o24bobo161bo143b2o180b3o296bo$348b2o
215bo240bo119bobo179bo296bobo$347bo456b2o122bo4b2o174bo296b2o$506bo
298b2o117b4ob2o2bo2bo418bo243bo$506b2o416bo2bobobobob2o419b2o240b2o$
288b2o215bobo419bobobobo18b2o401b2o81b2o158bobo$289b2o590b2o45b2obobo
18bobo134bo79b2o106b2o158b2o134bobo$288bo402bobo188b2o48bo19bo137bo77b
2o107bobo159bo134b2o$366bo324b2o188bo100bo105b3o79bo106bo296bo$365bo
326bo225b2o63b2o159bobo$365b3o77bo473bo7b2o53b2o161b2o$418bo26b2o213b
2o257bobo5b2o216bo55bo$416b2o26bobo214b2o257b2o280b2o132b3o186bobo$
417b2o241bo540b2o107bobo23bo189b2o$225b2o295bo788b2o24bo188bo28b2o$
224bobo159b2o133bo789bo242b2o$226bo158bobo133b3o1032bo$387bo455bo553bo
$843bobo173b2o26bo348b2o$463bobo377b2o50bobo32b2o87bobo23bobo348bobo$
463b2o294bo53b2o80b2o33bo88bo26b2o431bobo161bo$464bo294b2o53b2o80bo34b
3o546b2o159bobo$541b2o52bo162bobo52bo119bo197b2o296bo50bo161b2o$324b3o
215b2o51b2o105b2o427bobo296bo78b3o$326bo214bo52bobo106b2o77bobo346bo
109b2o185b3o78bo$325bo376bo24bo54b2o457bobo266bo$727bobo53bo457bo$727b
2o206b2o524bo$265b3o294bo371bobo523b2o135bo$267bo293bo296b3o67b2o4bo
364b3o158bobo135bo$266bo294b3o296bo65bo2bo2b2ob4o146b2o107bo104bo296b
3o$859bo66b2obobobobo2bo12bo133bobo80bo24b2o105bo$929bobobobo16b2o131b
o83bo23bobo80bo350b2o$422b2o505bobob2o16b2o214b3o107b2o348bobo$340bo
53bo28b2o212bo292bo345b2o81b2o188bo77bo$340bobo51bobo25bo214b2o720bobo
188bo$340b2o52b2o77b3o160bobo304b2o414bo188b3o$202b2o271bo24bo433b2o7b
o$203b2o269bo23b2o434b2o5bobo285bo349b2o$202bo296b2o440b2o177bobo107bo
347b2o$934bo186b2o105b3o108bo79b2o159bo$442bo430bo59b2o133bobo50bo215b
obo79bobo$440b2o215bo214bo60bobo133b2o267b2o79bo$277bobo161b2o212b2o
133b3o79b3o23b3o115bobo50bo594bobo$222bo54b2o78b2o297b2o134bo107bo116b
2o646b2o$222bobo53bo79b2o212b2o106bo110bo107bo93bo23bo29bo348bobo134bo
131bo$222b2o77b2o54bo213bobo106b2o51bo27bo169b2o59b2o52b2o349b2o133b2o
$300bobo270bo105bobo23bo27b2o24b2o171bo59bobo51bobo214b3o131bo110bo23b
obo$302bo293bo107bo27bobo25b2o167b3o331bo245bo$595bo108b3o222bo334bo
242b3o$595b3o885b2o$540bo941b2o$538b2o268bobo648bo24bo$510b3o26b2o267b
2o298b2o347bobo$239b2o271bo296bo116b2o179b2o349b2o$240b2o269bo414bobo
180bo190bo$239bo159b3o429b3o94bo4b2o363bobo$401bo212b2o217bo90b4ob2o2b
o2bo362b2o$316bobo81bo212bobo216bo91bo2bobobobob2o230b2o160b2o295bo25b
3o$180bo135b2o51bo245bo311bobobobo233bobo24bobo132bobo295b2o23bo$180b
2o135bo50bo559b2obobo233bo27b2o132bo54b3o215bo23b2o25bo$179bobo186b3o
561bo210bo51bo56bo131bo216b2o$1144b2o104bobo132bo215bobo$918b2o36b2o
185b2o106b2o107bobo$850bo68bo7b2o27bobo133bo268b2o$768b2o80bobo66bobo
5b2o27bo136b2o266bo325bo$254bo512bobo80b2o51bo16b2o170b2o594b2o$253bo
80b2o433bo131b2o85bo430bo267b2o$253b3o79b2o565b2o29bobo53bo79b2o349b2o
133b2o$278b2o54bo375b2o222b2o51b3o79bobo214b2o131b2o133b2o$279b2o401bo
28b2o221bo134bo216bobo241bo25bo$278bo294bo108bobo25bo159b2o414bo163b2o
79b2o$437b3o105bo27bobo106b2o185bobo578bobo77b2o$439bo105b2o26b2o296bo
58b2o518bo137bo$438bo77bobo25bobo240bo142bo550bo107bo$488bo27b2o267b2o
144b3o87b3o107bo350bo104b3o$217bo270b2o27bo268b2o145bo87bo108b2o348b3o
$217b2o268bobo532bo29bo77bobo$216bobo240bo593bo267bobo$457b2o592b3o
268b2o$186bo108bo162b2o131b2o214bo514bo352b2o$185bo107b2o297b2o213b2o
126b2o252b3o25bo25b3o105b3o294bobo24bobo$185b3o106b2o295bo214bobo125bo
bo252bo28b2o23bo107bo297b2o24bo$346bo565b2o14b2o4bo255bo26b2o25bo29bo
77bo296bo$155bo188b2o565bobo12bo2bo2b2ob4o228bo107bo$155b2o188b2o566bo
12b2obobobobo2bo229bo104b3o107bo26b2o$154bobo772bobobobo42b3o185b3o
215b2o24bobo$827bobo99bobob2o43bo137bo266b2o25bo$637b3o105b2o80b2o101b
o48bo134bobo594bo$232bo406bo78bo27b2o80bo286b2o592bobo$230b2o406bo77b
2o27bo197b2o65bo513bo185b2o$231b2o455bo28b2o215b2o7bo67b2o510b2o54bo$
255b3o402bo27b2o244b2o5bobo15bo50b2o80b3o215bo212bobo52b2o$257bo401bo
27bobo251b2o14bobo132bo216b2o243bo23bobo$256bo158bo243b3o185b2o109b2o
133bo215bobo161b2o77bobo$415b2o105b2o324b2o622b2o79b2o$359bo54bobo77bo
26bobo323bo87b2o537bo136bo25b2o$359b2o132bo29bo77bobo330b2o568bo104bob
o24b2o$358bobo132b3o105b2o333bo565bobo105b2o26bo$384bo217bo900b2o$382b
2o376bo170b2o141bo269bo$383b2o50bo323bo172bo142b2o268b2o107bo$435bobo
321b3o167b3o142b2o268b2o109bo$164bo106bobo161b2o131b2o214b2o79bo63bo
121bo105b3o52b2o53bo106b2o77b3o215bo26b2o$162b2o107b2o294bobo213bobo
79bobo182b2o105bo54bobo51b2o106bobo295b2o23b2o$163b2o107bo185b2o80bo
28bo215bo79b2o183bobo105bo53bo53bobo105bo296b2o26bo$322bobo134b2o77b2o
$132b2o52b3o133b2o134bo80b2o648bo$133b2o53bo134bo602b2o73b2o187b2o105b
obo105bobo$132bo54bo738bobo72bobo185b2o107b2o106b2o$615bo312bo4b2o66bo
296bo107bo$615b2o186bo120b4ob2o2bo2bo499b2o$614bobo185bo121bo2bobobobo
b2o498b2o297bo$288b2o512b3o122bobobobo100bo402bo108b2o187b2o$287bobo
375bo215b2o45b2obobo47bo53bo80bo25bo403bobo52b2o131b2o$232bo56bo375b2o
51bo161bobo49bo49bo50b3o79b2o26b2o187b2o212bo29bo24bobo$232b2o430bobo
51b2o162bo97b3o132bobo24b2o188bobo242bo23bo$231bobo158b2o323bobo198b2o
412bo242b3o$391bobo525bo7b2o29bo$393bo104b3o418bobo5b2o28b2o297bo376bo
25b3o$500bo77bo54bo286b2o35bobo294bobo242b2o133b2o23bo$469bobo27bo78bo
bo50b2o622b2o242bobo131b2o25bo$198bo161bobo106b2o107b2o52b2o865bo$198b
obo131bo27b2o51bo56bo266bo$198b2o132b2o27bo50bo324bobo77b2o657bo$249bo
81bobo78b3o322b2o77bobo362bo295b2o53bo$140bobo105bo296b3o213b3o54bo23b
obo335b2o52b3o160b2o77b2o55bo159bobo24b3o$140b2o106b3o185bo110bo215bo
78b2o86b2o248bobo51bo161b2o133b3o160b2o24bo$141bo159bo134b2o78bo29bo
215bo80bo50bobo33bo304bo162bo295bo26bo$299b2o134bobo78bobo375b2o35b3o$
109bo190b2o214b2o377bo37bo386bo53bo$109b2o913b2o295b2o52b2o$108bobo
912b2o295b2o52b2o53bobo$592b2o431bo404b2o27bo$593b2o185bo166bo269bo
212bo27b2o$592bo187bobo152b2o8bobo270bo239bobo297bo$157b2o106b2o513b2o
152bobo9b2o108bo54bo104b3o79b3o268b2o185bobo$156bobo107b2o660b2o4bo68b
o53b2o50bobo26b2o158bo269b2o187b2o$158bo50b2o54bo660bo2bo2b2ob4o65b2o
50b2o26b3o23b2o26bobo158bo270bo27bo$208bobo715b2obobobobo2bo64b2o79bo
53bo460b2o$210bo718bobobobo149bo512b2o26b3o$476bo452bobob2o691bo$476b
2o78bo373bo696bo29bo$447bo27bobo77bo53bo750b2o160b2o131bobo$446bo108b
3o51bobo50bobo240b2o36b2o414b2o160b2o133b2o$175bobo268b3o160b2o51b2o
242b2o26b2o7bo417bo161bo$175b2o486bo23b3o215bo28b2o5bobo743b2o$176bo
512bo104b2o145b2o557bo185b2o$226bo461bo50bo55b2o23bo680bo52bo133bo55bo
$225bo296bo216b2o53bo24bo383b3o213b3o77b3o53b2o186b2o$116bobo106b3o
185b2o79bo27b2o214bobo78b3o50bo63bo51b3o186bobo23bo215bo134b2o187bobo$
116b2o159bo134bobo78bo27bobo185bo161bo63b2o51bo189b2o24bo215bo$117bo
159bobo134bo78b3o212bo162b3o61bobo51bo188bo$86b2o189b2o429b3o131bo204b
o296bo51bobo$87b2o266b2o485b2o87b2o113b2o294bobo52b2o54bo$86bo269b2o
483bobo88bo113bobo294b2o52bo56bo$326bo28bo573b3o520b3o26b2o$326bobo
428bobo169bo550b2o$326b2o429b2o562b2o159bo109bo187bo$758bo536bo25bobo
267b2o188b2o$1107b2o134bo52b2o23bo269bobo186b2o$186b3o105b2o811bobo
131bobo51b2o325bo$131b2o55bo104bobo78bo188b2o349bo11b2o179bo134b2o376b
obo27bo$132b2o53bo50b2o55bo78bobo187b2o347bo12bobo45bobo107bo536b2o26b
2o$131bo105bobo134b2o77b2o108bo349b3o12bo4b2o40b2o108bo563bobo$239bo
212bobo79bo389b4ob2o2bo2bo38bo107b3o$454bo77b2o52bo337bo2bobobobob2o
445b3o$423bobo107b2o50bo53bo242b3o42bobobobo342b2o104bo$423b2o160b3o
51bobo242bo43b2obobo235b2o104b2o106bo$424bo214b2o242bo44b2o2bo211bo24b
obo105bo405bo25b3o24bobo$13b2o912b3o212bobo24bo352bo161b2o23bo27b2o$
13b2o189bo511b2o200b2o223b2o81b2o295b2o51bobo104b2o25bo26bo28b2o$95bo
106b2o295b2o214bobo201bo6bobobo81bo26bo160bo25bobo293b2o53b2o186b2o$
93b2o108b2o266bo28b2o215bo201bob2o3b2ob2o80b2o24bobo161b2o23bo324b3o
23bo189bo$94b2o50bobo105bo216bobo25bo420bo3b2o5b2o78bobo24b2o160b2o
349bo$146b2o106bobo214b2o452bo2b4ob2o431bo52bo132bo$147bo106b2o428bobo
132b2o104bo4b5o26b2o404bo52b2o25b2o$386b2o214b3o79b2o132bobo24bo76bo4b
o2b2obo26b2o403b3o51b2o25b2o28bo$385bobo216bo80bo134bo24bobo79b3o32bo
485bo25bobo27bo$303bobo81bo215bo132bo108b2o77b2o549b2o26b2o$59b2o242b
2o429b2o767bobo$60b2o242bo430b2o193b2o411b3o458bo$59bo870bo386bobo23bo
458bobo$931b3o196b2o186b2o24bo458b2o$109bo647bo26bo148bo195b2o187bo$
109b2o51b2o376b3o214b2o24bo347bo$108bobo52b2o50b3o105bo218bo104b2o107b
obo24b3o104bo216bo159bobo$162bo54bo105b2o216bo106b2o240bobo212bobo160b
2o$216bo105bobo24bo297bo242b2o44b2o63bo80bo23b2o160bo137bo$266b2o79b2o
52bo107bo53bo53bo317bobo64bo78b2o322b2o$265bobo80b2o50bo108bobo51bobo
50bo312b2o4bo64b3o78bobo321bobo$267bo132b3o106b2o52b2o51b3o308bo2bo2b
2ob4o226bo24b3o429b3o133bo$927b2obobobobo2bo227bo23bo431bo83bo25b2o25b
2o$910b2o18bobobobo228b3o24bo407bo23bo80bobo25bobo23b2o28bo$180bo512b
3o213bobo18bobob2o125bo539bo53bo50b2o25bo54b2o$71bo107bo242b2o271bo
215bo19bo102b2o26bo161bo350bo23b3o54bo131bobo$71bobo50bo54b3o239bobo
270bo260bo77b2o25b3o159bobo349b2o78b3o$71b2o50bo107bobo189bo428b3o89b
2o7bobo79bo187b2o80b3o242bo23bobo$123b3o105b2o430bo190bo80b2o7bo9b2o
349bo245bo$232bo347b2o79b2o133b3o24bo29bo81b2o5bobo27bo10b3o40bo53bo
53bo53bo53bo53bo9bo43bo53bo53bo10b3o40bo36b3o14bo53bo53bo53bo53bo53bo$
363b2o106b2o106bobo80b2o134bo23bo119b2o26b3o10bo40b3o51b3o51b3o51b3o
51b3o51b3o51b3o51b3o51b3o10bo40b3o51b3o51b3o51b3o12b2o37b3o51b3o51b3o$
282bo81b2o104bobo108bo215bo24b3o144bo14bo38bo53bo53bo53bo53bo53bo53bo
53bo53bo14bo38bo53bo53bo53bo15bobo35bo53bo53bo$37bo242b2o81bo108bo239b
obo254b2o52b2o52b2o52b2o52b2o52b2o52b2o52b2o52b2o52b2o52b2o52b2o52b2o
52b2o14bo37b2o52b2o52b2o$37b2o242b2o159bo269b2o652b2o$36bobo401b2o271b
o652bobo$441b2o534b2o52b2o52b2o52b2o12bo39b2o52b2o52b2o44bo7b2o9bo42b
2o52b2o52b2o52b2o52b2o52b2o52b2o52b2o52b2o$978bo53bo53bo53bo11b2o40bo
53bo53bo43b2o8bo53bo42bo10bo53bo53bo53bo53bo53bo53bo53bo$734b2o187bo8b
2o18b2o24bob2o22b2o26bob2o22b2o26bob2o22b2o26bob2o8bobo11b2o26bob2o22b
2o26bob2o22b2o26bob2o22b2o13b4ob2o6bob2o22b2o26bob2o22b2o14b3o9bob2o
22b2o26bob2o22b2o26bob2o22b2o26bob2o22b2o26bob2o22b2o26bob2o22b2o24bob
ob2o22b2o26bob2o$733bobo132bo54bobo7bo18bo17b2o4b3o2bo22bo19b2o4b3o2bo
22bo19b2o4b3o2bo22bo16bob3o4b3o2bo22bo19b2o4b3o2bo22bo19b2o4b3o2bo22bo
16bob3o4b3o2bo22bo14b2o2b2o2bob4o2bo22bo16bo2b2o4b3o2bo22bo14b2ob2o6b
3o2bo22bo19b2o4b3o2bo10b3o9bo19b2o4b3o2bo22bo19b2o4b3o2bo22bo19b2o4b3o
2bo22bo19bo5b3o2bo22bo21b2o2bobo2bo22bo15bo3b2o4b3o2bo$192b2o106b2o
433bo131bo55b2o5b3o21bo15b2o3bo3b2o25bo17b2o3bo3b2o25bo17b2o3bo3b2o25b
o15b4o3bo3b2o25bo17b2o3bo3b2o25bo17b2o3bo3b2o25bo15b4o3bo3b2o25bo11b2o
bo2b2o7b2o25bo12bobo2b2o3bo3b2o25bo11b3ob3o4bo3b2o25bo17b2o3bo3b2o11bo
13bo17b2o3bo3b2o25bo17b2o3bo3b2o25bo17b2o3bo3b2o25bo17b2o3bo3b2o25bo
18b2o2bo3b2o25bo14b2ob2o3bo3b2o$193b2o104bobo565b3o60bo2b3o14b5o20b4o
7b2o14b5o22b4o7b2o14b5o22b4o7b2o6bo7b5o13b3o6b4o7b2o14b5o22b4o7b2o14b
5o22b4o7b2o14b5o13b3o6b4o7b2o14b5o12bo2bobo2bo2b3o7b2o14b5o13b2o7b4o7b
2o6bo7b5o12b2ob2o5b4o7b2o14b5o22b4o7b2o5bo8b5o22b4o7b2o14b5o22b4o7b2o
14b5o22b4o7b2o14b5o22b2obo7b2o14b5o15b2o2b7o7b2o14b5o13b2o7b4o$192bo
108bo630bo2bo13bo11b2o15bo8bo13bo13b2o15bo8bo13bo13b2o15bo8bo5b3o5bo
13b2o15bo8bo13bo13b2o15bo8bo13bo13b2o15bo8bo13bo13b2o15bo8bo13bo13b2o
2bo4b2o6bo8bo13bo13b2o15bo8bo5b3o5bo13b2o3b3o9bo8bo13bo13b2o15bo8bo13b
o13b2o15bo8bo13bo13b2o15bo8bo13bo13b2o15bo8bo13bo13b2o15bo8bo13bo13b2o
6b3o3bo2bo8bo13bo13b2o15bo$486bobo51bobo52bo335b2o2bobo4bo7b3o7bobo12b
3o9bobo12b3o9bobo12b3o9bobo12b3o9bobo12b3o9bobo3b4o5b3o9bobo12b3o9bobo
12b3o9bobo12b3o9bobo12b3o9bobo12b3o9bobo12b3o9bobo12b3o9bobo12b3o9bobo
12b3o9bobo12b3o9bobo12b3o9bobo3b4o5b3o9bobo4bo7b3o9bobo12b3o9bobo12b3o
9bobo12b3o9bobo12b3o9bobo12b3o9bobo12b3o9bobo12b3o9bobo12b3o9bobo12b3o
9bobo12b3o9bobo12b3o9bobo6b3o2b4o9bobo12b3o9bobo12b3o$486b2o52b2o51b2o
341b2o3b3o9bo6bo13bo13b2o15bo8bo13bo13b2o15bo8bo13bo13b2o7bo7bo8bo13bo
13b2o15bo8bo13bo13b2o15bo8bo13bo13b2o3bo11bo8bo13bo13b2o15bo8bo8bo4bo
13b2o15bo8bo13bo13b2o7bo7bo8bo13bo13b2o15bo8bo13bo13b2o15bo8bo13bo13b
2o15bo8bo13bo13b2o3bo11bo8bo13bo13b2o15bo8bo13bo13b2o15bo8bo7b2o4bo13b
2o15bo8bo13bo$487bo53bo52b2o344b2ob2o5b4o5b2o14b5o22b4o7b2o14b5o22b4o
7b2o14b5o14bo2b2o3b4o7b2o14b5o22b4o7b2o14b5o22b4o7b2o14b5o12bo2bo6b4o
7b2o14b5o22b4o7b2o5bo2bo5b5o22b4o7b2o14b5o14bo2b2o3b4o7b2o14b5o22b4o7b
2o14b5o22b4o7b2o14b5o22b4o7b2o14b5o12bo2bo6b4o7b2o14b5o22b4o7b2o5bo8b
5o13b2o7b4o7b2o6b2o6b5o22b4o7b2o14b5o$618b2o319b3ob3o4bo3b2o23bo17b2o
3bo3b2o25bo17b2o3bo3b2o25bo13bobob3o2bo3b2o25bo17b2o3bo3b2o25bo17b2o3b
o3b2o25bo12bo2bo6bo3b2o25bo17b2o3bo3b2o12bobo10bo17b2o3bo3b2o25bo13bob
ob3o2bo3b2o25bo17b2o3bo3b2o25bo17b2o3bo3b2o25bo17b2o3bo3b2o25bo12bo2bo
6bo3b2o25bo17b2o3bo3b2o12bobo10bo14b2ob2o3bo3b2o13bo11bo17b2o3bo3b2o
25bo$36bo53bo53bo53bo53bo53bo53bo53bo53bo53bo53bo40bobo10bo40bo12bo53b
o53bo53bo40b3o10bo39b2ob2o6b3o2bo20bo19b2o4b3o2bo22bo19b2o4b3o2bo22bo
16bo2b2o4b3o2bo22bo19b2o4b3o2bo22bo19b2o4b3o2bo9bo12bo15bobo7b3o2bo22b
o19b2o4b3o2bo22bo19b2o4b3o2bo22bo16bo2b2o4b3o2bo22bo19b2o4b3o2bo9bo12b
o19b2o4b3o2bo22bo19b2o4b3o2bo22bo15bobo7b3o2bo9bo12bo19b2o4b3o2bo11b2o
9bo15bo3b2o4b3o2bo22bo19b2o4b3o2bo22bo$36b3o51b3o51b3o11bo39b3o51b3o
51b3o51b3o10bobo38b3o51b3o51b3o51b3o40bo10b3o38b2o11b3o51b3o10bobo38b
3o51b3o40bo10b3o38b3o9bob2o20b2o26bob2o22b2o26bob2o22b2o12bo5bo7bob2o
22b2o26bob2o22b2o26bob2o8bo13b2o26bob2o22b2o26bob2o22b2o26bob2o22b2o
12bo5bo7bob2o22b2o26bob2o9bobo10b2o26bob2o22b2o26bob2o8bobo11b2o26bob
2o9bobo10b2o26bob2o22b2o26bob2o22b2o26bob2o22b2o$39bo8bo44bo53bo8b2o
43bo53bo53bo53bo9b2o24b2o16bo53bo53bo53bo53bo36bobo14bo53bo9b2o42bo53b
o38bo14bo38bo10bo51bo53bo40b5o8bo53bo53bo11b3o39bo37b2o14bo53bo40b5o8b
o53bo12b2o39bo53bo11b2o40bo12b2o39bo53bo53bo$38b2o7bo44b2o52b2o9b2o41b
2o52b2o52b2o52b2o10bo25b2o14b2o52b2o52b2o52b2o52b2o52b2o52b2o10bo41b2o
52b2o52b2o48b2o50b2o52b2o41b3o8b2o52b2o52b2o52b2o36bobo13b2o52b2o41b3o
8b2o52b2o52b2o10bo41b2o12bo39b2o52b2o52b2o52b2o$47b3o23bo26bobo105bo
190bo105b2o595bo211bo111bo127b2o$73b2o25b2o24b3o79bobo293bobo267b2o
128b3o565b2o81b2o$30b2o40bobo9b2o15bo26bo9b2o52b2o14b2o36b2o52b2o12bo
39b2o52b2o52b2o42bo9b2o39b3o10b2o52b2o52b2o52b2o39bobo10b2o12bo39b2o
52b2o7bo3bo36b2o50b2o52b2o52b2o52b2o52b2o52b2o52b2o52b2o52b2o41bobo8b
2o52b2o52b2o52b2o41b3o8b2o52b2o52b2o$30bo53bo42bo10bo53bo53bo53bo13bob
o23b3o11bo53bo39b3o11bo53bo42bo10bo53bo53bo53bo42bo10bo13bobo37bo53bo
8bo3bo36bo51bo53bo53bo53bo53bo53bo53bo53bo53bo44bo8bo53bo53bo53bo44bo
8bo53bo53bo$3b2o22b2obo26b2o22b2obo26b2o22b2obo26b2o22b2obo26b2o22b2ob
o11bobo12b2o22b2obo13b2o11b2o13bo8b2obo26b2o22b2obo26b2o13bo8b2obo26b
2o22b2obo26b2o13bo8b2obo26b2o22b2obo26b2o22b2obo26b2o22b2obo26b2o22b2o
bo13b2o11b2o22b2obo5bo20b2o22b2obo6b2o4bo11b2o24b3o49b3o51b3o51b3o51b
3o51b3o51b3o51b3o51b3o51b3o51b3o51b3o51b3o51b3o40bo10b3o51b3o51b3o$4bo
9b2o11bo2b3o4b2o19bo22bo2b3o4b2o19bo22bo2b3o4b2o19bo22bo2b3o4b2o19bo9b
2o11bo2b3o4b2o3b2o14bo22bo2b3o4b2o19bo12bo9bo2b3o4b2o19bo22bo2b3o4b2o
19bo12bo9bo2b3o4b2o19bo22bo2b3o4b2o19bo22bo2b3o4b2o19bo22bo2b3o4bo2b2o
16bo22bo2b3o4b2o19bo22bo2b3o4b2o19bo22bo2b3o4b2o19bo22bo2b2o4b2o20bo
22bo2b3o3bo4bo14bo26bo51bo36bo16bo9bo43bo53bo36b2o15bo53bo53bo36b3o14b
o53bo53bo53bo53bo53bo53bo53bo53bo$2bo10bobo12b2o3bo3b2o17bo25b2o3bo3b
2o17bo25b2o3bo3b2o17bo25b2o3bo3b2o17bo10bobo12b2o3bo3b2o4bo12bo25b2o3b
o3b2o17bo25b2o3bo3b2o17bo25b2o3bo3b2o2bo14bo25b2o3bo3b2o17bo25b2o3bo3b
2o17bo25b2o3bo3b2o17bo25b2o3bo3bo2b3o13bo25b2o3bo3b2o17bo25b2o3bo3b2o
17bo25b2o3bo3b2o17bo25b2o2bob2ob2o17bo25b2o3bo2bo3bobo11bo117b2o24bo
134bobo162bo$2b5o8bo5b2o7b4o22b5o14b2o7b4o22b5o14b2o7b4o22b5o14b2o7b4o
22b5o8bo5b2o7b4o22b5o14b2o7b4o22b5o14b2o7b4o22b5o14b2o7b4o6b3o13b5o14b
2o7b4o22b5o14b2o7b4o22b5o14b2o7b4o22b5o14b2o7b4o8b2o12b5o14b2o7b4o22b
5o14b2o7b4o22b5o14b2o7b4o22b5o14b2o7b2o24b5o14b2o7b4o2bo4bo12b5o14b2o
96bobo24b3o134bo161bo212bo$7bo13bo8bo15b2o13bo13bo8bo15b2o13bo13bo8bo
15b2o13bo13bo8bo15b2o13bo13bo8bo15b2o13bo13bo8bo15b2o13bo13bo8bo15b2o
13bo13bo8bo9b2o4b2o13bo13bo8bo15b2o13bo13bo8bo15b2o13bo13bo8bo15b2o13b
o13bo8bo10bo4b2o13bo13bo8bo15b2o13bo13bo8bo15b2o13bo13bo8bo15b2o13bo
13bo8bobo13b2o13bo13bo8bo6b2o3bo3b2o11bo13bo2bo633b2o$4b3o12bobo9b3o
12bobo9b3o12bobo9b3o12bobo9b3o12bobo9b3o12bobo9b3o12bobo9b3o12bobo9b3o
12bobo9b3o12bobo9b3o12bobo9b3o12bobo9b3o12bobo9b3o12bobo9b3o12bobo9b3o
12bobo9b3o12bobo9b3o12bobo9b3o12bobo9b3o12bobo9b3o12bobo9b3o12bobo9b3o
12bobo9b3o12bobo9b3o12bobo9b3o12bobo9b3o12bobo9b3o12bobo9b3o12bobo9b3o
12bobo9b3o12bobo9bobo12bobo9b3o12bobo9b3o5bo2bo3bobo7b3o12bobob2o442bo
189bobo$3bo15b2o13bo13bo8bo15b2o13bo13bo8bo15b2o13bo13bo8bo15b2o13bo
13bo8bo15b2o13bo13bo8bo15b2o13bo13bo8bo15b2o13bo13bo8bo15b2o13bo13bo8b
o15b2o13bo13bo8bo15b2o13bo13bo8bo15b2o13bo13bo8bo15b2o13bo13bo8bo15b2o
13bo13bo8bo11bo3b2o13bo13bo8bo15b2o13bo13bo8bo10bo4b2o13bo5bo7bo8bo15b
2o13bo4bo8bo6bo15b2obo173bo161bo107bo431bo$3bob2o22b5o14b2o7b4o22b5o
14b2o7b4o22b5o14b2o7b4o6b3o13b5o14b2o7bob2o22b5o14b2o7b4o6b3o13b5o14b
2o7b4o22b5o14b2o7b4o22b5o14b2o7b4o22b5o14b2o7b4o22b5o14b2o7b4o22b5o14b
2o7b4o22b5o14b2o7b4o22b5o14b2o7b4o6b2obo12b5o14b2o7b4o22b5o14b2o7b4o4b
ob2o14b5o7b2o5b2o7b4o22b5o6b3o5b2o5b4o15bo172bo162bobo105b3o401b2o26bo
bo$b2o3bo3b2o17bo25b2o3bo3b2o17bo25b2o3bo3b2o17bo25b2o3bo3b4o15bo25b2o
3bo3b2o17bo25b2o3bo3b4o15bo25b2o3bo3b2o17bo25b2o3bo3b2o17bo25b2o3bo3b
2o17bo25b2o3bo3b2o17bo25b2o3bo3b2o17bo25b2o3bo3b2o17bo25b2o3bo3b2o17bo
25b2o3bo6bo2bo12bo25b2o3bo3b2o17bo25b2o3bo3bo4bo13bo10b2o13b2o3bo3b2o
17bo23b2o3bo3b2o10b3o61bo108b3o23b3o134b2o511b2o25b2o$o2b3o5bo19bo22bo
2b3o4b2o19bo22bo2b3o4b2o19bo22bo2b3o4b3obo16bo22bo2b3o5bo19bo22bo2b3o
4b3obo16bo22bo2b3o4b2o19bo22bo2b3o4b2o19bo22bo2b3o4b2o19bo12bo9bo2b3o
4b2o19bo22bo2b3o4b2o19bo22bo2b3o4b2o19bo22bo2b3o4b2o19bo22bo2b3o7b3o
15bo22bo2b3o4b2o19bo22bo2b3o4bo20bo22bo2b3o4b2o19bo20bo2b3o4b2o13bo59b
o80b2o55bo646bo$2obo26b2o22b2obo26b2o22b2obo26b2o22b2obo26b2o22b2obo
26b2o22b2obo26b2o22b2obo26b2o22b2obo26b2o22b2obo26b2o13bo8b2obo26b2o
22b2obo26b2o22b2obo26b2o22b2obo26b2o22b2obo26b2o22b2obo26b2o22b2obo7bo
18b2o22b2obo26b2o20b2obo20b2o59b3o79b2o53bo$3bo53bo53bo53bo53bo53bo53b
o53bo53bo39b3o11bo53bo42bo10bo53bo53bo53bo53bo53bo51bo52bo109bo159b2o
268b3o241bo$3b2o52b2o52b2o52b2o52b2o52b2o52b2o52b2o52b2o52b2o52b2o39bo
bo10b2o52b2o52b2o52b2o52b2o52b2o50b2o21b3o27b2o269b2o269bo239b2o$585b
2o354bo3bo25bobo268bo270bo212b3o26b2o$373bo376bo134b2o53bo5bo781bo$11b
2o52b2o52b2o52b2o52b2o52b2o52b2o37bo14b2o52b2o52b2o52b2o52b2o52b2o52b
2o36b2o14b2o52b2o52b2o7b2o41b2o11bo5bo211bo322bobo106bo136bo$12bo37bo
15bo53bo53bo53bo53bo53bo35b3o15bo53bo53bo53bo53bo53bo53bo35b2o16bo53bo
53bo9bo41bo11bo5bo209b2o323b2o105b2o$9b3o39b2o10b3o39bo11b3o51b3o51b3o
51b3o51b3o51b3o51b3o51b3o51b3o51b3o51b3o51b3o51b3o51b3o51b3o49b3o13bo
3bo4b2o205b2o323bo106b2o23b3o$9bo40b2o11bo42b2o9bo53bo41bobo9bo53bo53b
o53bo53bo53bo14b3o36bo53bo53bo53bo53bo53bo53bo51bo16b3o5bobo471bo191bo
$105b2o55bo51b2o188b2o104bo56bo52b2o79bo250bo443b2o25bo191bo$163bo50bo
108bobo25b2o51bobo104bo54b2o51b2o81b2o105bobo140b2o333b2o26bo81b2o24b
3o23b2o214b2o$161b3o160b2o25bobo50bo161bobo52bo79b2o107b2o474bobo24b2o
81bo53b2o212bobo$324bo26bo110bo347bo128bo348bo25b2o133bo216bo168b2o$
30b2o213b3o213b2o475bobob2o394b2o492b2o2bo$29b2o214bo215bobo189bo25b2o
257bobobobo68b2o26bo133b3o159bobo490b3ob2o11bo$31bo53b3o158bo404bobo
25bobo253b2obobobobo2bo64bobo24b2o136bo23bo137bo489bo15b3o$85bo566b2o
25bo255bo2bo2b2ob4o66bo25b2o134bo23bo603b2o11bo12b3ob2o8bo$86bo353bo
496b2o4bo256b3o601b2o10bobo13bob2o8b2o$441bo350bo150bobo415bo161bo25b
2o265bobo$199bo80bo25b2o131b3o349b2o151b2o143bo269b2o160b2o25bobo264b
2ob3o$198b2o78bobo25bobo482bobo133bobo159bobo23b2o243b2o160b2o26bo77bo
192bo$198bobo78b2o25bo245bo375b2o130bo28b2o23bobo510bo134bo52b2ob3o$
553bo374bo131b2o54bo510b3o132b2o24bo26b2obo$500bo50b3o389bo115bobo428b
2o269bobo24bobo$498bobo106bobo331b3o5b2o268b3o267bobo296b2o$499b2o107b
2o330bo9b2o269bo269bo$608bo331b2o7bo270bo$772bobo132b3o$154bo618b2o
132bo942b2o$153b2o618bo134bo683b2o218b2o13b2o21b2o$127bobo23bobo377b2o
322b2o732bobo218b2o13b2o$128b2o403bobo321bobo542bo190bo203b2o$128bo55b
o242b2o104bo189bobo107bo23bo515b3o24b2o394bo2bo$78bo106b2o186b3o25bo
24b2o296b2o26b2o80bo95b2o36bo295b3o24bo83bo25b2o23b3o295bo70bob2o$79bo
104b2o187bo28b2o24bo295bo27bobo77b3o94bobo5b2o27b2o298bo24bobo80bo53bo
23bo269b2o71bo$77b3o162bo131bo26b2o81b2o266bo176bo7b2o28b2o296bo25b2o
134bo24bobo185bo82b2o69b2o$240bobo240b2o443b2o223b2o297b2o186b2o167b2o
$241b2o242bo107b3o78bobo25b2o313bo134bobo484bobo167bo$110bo482bo81b2o
24b2o239bo74bobo104bo29bo23bo631b3o$109b2o483bo80bo27bo234b2obobo73b2o
104bo54bobo50bobo78b2o498bo$109bobo825bobobobo179b3o52b2o51b2o80b2o$
896bo37bo2bobobobob2o39bo245bo79bo186bo26b3o$301bobo25b2o563bobo37b4ob
2o2bo2bo39b2o511bobo26bo131bobo$59b3o240b2o24b2o324b2o239b2o41bo4b2o
40bobo104bo406b2o26bo132b2o$59bo242bo27bo243bo79bobo279bobo98b2o53b2o
510bobo54bo104bo$60bo514b2o77bo281b2o100b2o51bobo510b2o159bo$521bobo
50b2o55bo405bo294bo216bo55bo159b3o$522b2o108bo699bobo212b2o133bo$522bo
107b3o699b2o214b2o132b2o$796bo397bo486bobo50b3o$283b2o512bo141bo254b2o
540bo$176b2o104b2o511b3o141b3o251bobo539bo$175b2o107bo657bo626b3o$177b
o378b2o322b2o59b2o628bo$555b2o271bo50b2o173bo296bo26bobo189bo$206bobo
25b2o160b2o159bo269b2o52bo172bobo294b2o25b2o$207b2o24b2o161bobo24bobo
52bo296b2o50bobo114bobo107b2o212bobo79bobo26bo23b2o25bo$207bo27bo160bo
27b2o53b2o293b2o168b2o322b2o134b2o23bo$263bobo158bo53b2o296bo82bo85bo
293b3o27bo133bo25b3o185b2o$264b2o351bo239bobo381bo376b2o$264bo351b2o
240b2o91b2o42bo244bo376bo$132b2o482bobo325b2o5bobo39b2o215bo79bo$132bo
bo321b3o485b2o7bo40b2o158bo53b2o80b2o$132bo323bo297bobo196b2o199bobo
52b2o78bobo212b2o$352bo26bo77bo271b2o24b2o160bobo43b2o189b2o347bobo
186bo190bo$82b2o267b2o27bo348bobo23bo162b2o20bo21bobo540bo185bo191b3o$
82bobo266bobo24b3o295b3o50bo188bo20bobob2o19bo104b2o511bo108b3o192bo$
82bo515bo77bo262bobobobo122bobo510bo303bobo$165bobo160bo267bobo78bo
258b2obobobobo2bo121bo239bo270b3o301bobo$166b2o161b2o266b2o337bo2bo2b
2ob4o360bo215bo360bo$166bo161b2o325bo282b2o4bo364b3o131bo81bobo131b2o$
653bobo288bobo63b2o431b2o80b2o131bobo51bo$306bo347b2o289b2o62bobo159b
2o269bobo215bo51b2o25bo$305b2o243bo460bo104b3o51bobo538bobo23b2o$305bo
bo215b2o23bobo567bo53bo374b2o189b2o161b2o$522b2o25b2o566bo428bobo78bo
273b2o$524bo377b3o127bo323bo191bo78bobo$202b2o25bo27bo592b2o50bo40bo
87bo323bo108bo162b2o$202bobo25b2o24b2o160b3o26bo402bobo50bo37b3o87b3o
293b3o25b3o23bo80b2o$202bo26b2o25bobo159bo29bo51bobo215bo131bo89bo305b
o82bo51b2o24bo55b2o416b2o$125bo293bo26b3o52b2o80b2o134bo220b2o275b2o
25b2o82bo51bobo24bobo470bobo$126bo161bo212bo81bobo131b3o160bobo333bobo
26b2o160b2o185b3o283bo$124b3o162bo293bo297b2o335bo377bo282b2o7b2o$287b
3o350b2o239bo55b3o31bobo621bo292b2o$480bo158b2o295bo3bo30b2o$479b2o
160bo136bo156bo5bo30bo158bobo51bobo708b2obo$479bobo297bo156bo3bo190b2o
52b2o294b3o412b2ob3o$752b2o23b3o150b2o5b3o192bo53bo296bo418bo$160bo
539bo50b2o176bobo331bo218bo186bo226b2ob3o$159b2o538b2o52bo80bobo92bo
116b2o215b2o402b2o226bo2b2o$159bobo27bo215bo215bo77bobo133b2o91b2o117b
2o213bobo403b2o224bobo$190bo215bo215bo187b2o23bo210bo846bobob2obo$110b
o77b3o213b3o213b3o187bobo129bo127bobo803b2o16bo2bob2o$109b2o565bobo
131bo127b2obobo126b2o348b2o80bo133b3o238bo19bo$109bobo565b2o258bobobob
o43b2o82bo349b2o77b2o136bo238bobo16b2o$328b2o242bo104bo256bo2bobobobob
2o41b2o104bo325bo80b2o134bo50b3o24bo162b2o13bobo2b2o$327b2o217bo26bo
360b4ob2o2bo2bo40bo106b2o594bo24bobo175b2o2bo2bo$329bo215b2o24b3o364bo
4b2o148bobo428b3o162bo25b2o181b2o$545bobo388bobo587bo77bobo$387bo548b
2o72bo322bo191bo78b2o$224b3o159b2o485b2o133b2o295bo27bobo104bo164bo$
224bo161bobo80bo402b2o135b2o294b2o26b2o50bo53bo$225bo55b2o187b2o53bo
214bo133bo347bo81bobo77bo54b3o$280b2o187b2o52bobo80b2o133b2o161bo289b
3o25bobo159b3o158bo$147bobo132bo241b2o79b2o133b2o163bo33bo256bo25b2o
320bo$148b2o457bo295b3o33b3o196bo56bo348b3o$148bo513b3o277bo195b2o$
368bo293bo278b2o194bobo23bo108bo606b2o$366bobo294bo136bo361bo107b2o
607b2o14b2o$367b2o432b2o359b3o106b2o598b2o22bo$775b2o23b2o142bo927bo
23b3o$182b2o132bobo403b2o51bobo166bobo293b2o403bo226bobo23bo$182bobo
132b2o402b2o52bo168b2o295b2o320b2o80bobo225b2o$182bo29bo51bobo50bo109b
o27bo187bo79bo516bo323b2o79b2o$210bobo52b2o161b2o24b2o188b2o186b3o116b
2o610bo$132b2o77b2o52bo161b2o25bobo186b2o187bo111b2o5bobo444bo344b2o$
132bobo698bo110b2o7bo444b2o213b2o127bobo$132bo380bo439b2o9b2o431bobo
212bobo51bo69b2o4bo148b2o$512b2o81bo367bobo375b2o271bo51b2o66bo2bo2b2o
b4o144bo$512bobo53b2o23bobo344bo24bo376b2o321bobo66b2obobobobo2bo142bo
bo$352b3o212b2o25b2o109bo159bobo71bobob2o396bo240bo154bobobobo145b2o$
352bo216bo133bobo160b2o71bobobobo68b2o565bo155bobob2o$248bo104bo55b2o
293b2o160bo69b2obobobobo2bo37bobo26b2o293bobo268b3o154bo$247b2o159b2o
526bo2bo2b2ob4o37b2o26bo295b2o106bo25b2o$247bobo54bo105bo82bo444b2o4bo
42bo323bo51bo52b2o25bobo51b2o187bo64b2o$303b2o186bobo52bobo215bo179bob
o225bo188b2o54b2o26bo52b2o185bo56b2o7bo$170bo132bobo186b2o53b2o80b2o
131bobo180b2o225b2o188b2o104bobo26bo187b3o54b2o5bobo$171b2o374bo81bobo
131b2o406bobo294b2o279b2o$170b2o457bo55b2o428b2o352bo$390bo294bobo428b
2o78bo$391bo293bo429bo25bo52b2o52bobo24b2o$389b3o551bo141bo53b2o54b2o
51b2o26b2o$823bobo115b3o141bobo52b2o107bo25bo612b2o$797b3o24b2o114bo
144b2o785b2o14b2o$797bo26bo115b2o86bo26b3o681b2o132bo22b2o$205b3o80bo
509bo229bobo26bo682bo129b3o23bo$205bo83bo161bo25b2o377bo77b2o92b2o26bo
455bobo222b3o130bo23bobo$206bo80b3o159bobo25bobo375b2o52b3o25b3o274b2o
296b2o223bo156b2o$450b2o25bo271b2o104bobo51bo22bo4bo2b2obo271b2o296bo
105bo$156b2o591bobo158bo24bo4b5o269bo375b2o25b2o$155b2o460bo53bo77bo
185bo2b4ob2o374bo271b2o25b2o$157bo433bo26bo53bo257bo3b2o5b2o376b2o269b
o$375b2o160b2o51b2o24b3o51b3o216bo39bob2o3b2ob2o377bobo555b2o$375bobo
159bobo50bobo133bobo161bo38bo6bobobo51bo377b3o504bo$241bobo131bo161bo
189b2o159b3o37b2o35bo26b2o295bo82bo504bobo$242b2o188b2o293bo209b3o23b
2o26bobo293b2o82bo506b2o$242bo188b2o505b2o2bo21b2o322b2o104bobo$326b2o
24bobo78bo504b2obobo450b2o78b3o186bo$326bobo24b2o432bo149bobobobo451bo
80bo186bobo$192bobo131bo26bo297b3o134bo145bo2bobobobob2o528bo187b2o$
193b2o456bo134b3o145b4ob2o2bo2bo146bo350bobo$193bo458bo285bo4b2o148b2o
349b2o$575bo360bobo153bobo77bobo78bo191bo$412bobo158bobo360b2o179bobo
24b3o25b2o79b2o$413b2o159b2o271bo269b2o27bo26bo78bobo$413bo434bo269bo
26bo$846b3o184b2o592bo$229bo802bobo592b2o250b2o$228b2o54bo654bo94bo
455bo26b2o107bobo250b2o14b2o$228bobo52b2o187bobo25b2o376b2o59b3o62bo
187bo296bo28b2o351b2o22bo$283bobo187b2o25bobo375bobo61bo59b2o188b2o
295b3o25bo354bo23b3o$473bo26bo271b2o104bo62b2o60b2o50bobo133bobo401bob
o274bobo23bo$771b2o282b2o538b2o276b2o$693bo79bo282bo239b2o106b2o190bo$
317bo376b2o247b2o350bobo24bobo78bobo132bobo$318bo240b3o131b2o54bo192bo
2bo351bo24b2o24bo56bo132b2o$265bo50b3o240bo163b2o25b2o190b2ob2o376bo
24b2o189bo$184b2o80bo188bo104bo162bobo23b2o161bobo28bobo319bobo79bobo
212bo328b2o$184bobo77b3o187b2o267bo189b2o29bo6b2o312b2o295b2o327bo$
184bo190bo27bo50bobo456bo37bobo312bo294bobo325bobo72b2o$376b2o24b2o
549bo497b2o436b2o73b2o$375b2o25bobo135bo268bo143b2o497b2o$538bobo269b
2o24b3o367bo216bo27bo$539b2o268b2o25bo103bo129b2o133bo215b2o$837bo101b
obob2o124bobo133b3o214b2o$220bo215bo159bobo340bobobobo125bo50bo$221bo
215bo159b2o26b2o309b2obobobobo2bo173b2o24bo$219b3o213b3o159bo26b2o310b
o2bo2b2ob4o172bobo23bo$358bo267bo311b2o4bo12b2o188b3o$357b2o296bo288bo
bo9bobo402bo242b2o$251b2o104bobo296b2o287b2o11bo402bobo131bo107bobo$
251bobo52b2o187bo159b2o704b2o132b2o108bo$251bo54bobo187b2o375bobo24b3o
77bobo24b3o456bobo25bobo391b2o$306bo188b2o377b2o24bo79b2o27bo24bo431b
2o106bo297b2o14b2o$686b3o106b2o77bo26bo79bo26bo23b2o433bo104b2o299bo
22b2o$686bo108bobo145bo89b2o538b2o295b3o23bo$687bo29bo77bo145b3o329b3o
25bo214bo353bo23bobo$340bo241b2o131bobo222bo223b3o51b3o54bo23b2o214bo
378b2o$338bobo241bobo131b2o53bobo166b2o224bo53bo53bo25b2o213b3o$288bo
50b2o241bo163b2o24b2o161bo229bo53bo104b3o$206b3o77bobo188b2o266b2o25bo
163b2o388bo212b2o79bobo$206bo80b2o188bobo267bo187b2o388bo214b2o78b2o$
207bo217b2o50bo897b2o52bo109bo81bo254b2o$425bobo134bo811bobo52b2o446bo
$425bo137bo296bo515bo51bobo446bobo$402bo158b3o295b2o69b2o251bo215bo
478b2o$400bobo456bobo67bobo5b2o108b2o134bobo213bobo$401b2o526bo7b2o
109b2o133b2o214b2o$837bo90b2o117bo$838bo259b3o24bo$243bobo377bo212b3o
103bo157bo24bobo$244b2o378bo313b2obobo155bo25b2o212bo$244bo377b3o312bo
bobobo394bo242b2o$462bobo80bo388bo2bobobobob2o391b3o131b2o108b2o$328b
3o132b2o79b2o351bo36b4ob2o2bo2bo38bo458bo28b2o106bo$328bo134bo80bobo
351bo39bo4b2o40b2o456bo28bo$329bo566b3o37bobo45bobo23bo432b3o104bobo$
386b2o429b3o116b2o72bobo537b2o327b2o$385b2o352bo77bo192b2o239b2o298bo
327b2o14b2o$387bo352bo77bo134bo188bo53bo26bo26bobo24bobo591b2o22bo$
361bobo240b3o131b3o53bo158bobo186b2o52b2o24bo29bo24b2o593bo23b3o$282b
2o26bo51b2o160bobo77bo164bo25b2o156b2o104bobo79bobo51bobo24b3o53bo23bo
569bobo23bo$282bobo26bo50bo162b2o78bo162b2o24b2o136bo6bo119b2o241b2o
295bo273b2o$282bo26b3o213bo242bobo160b2o6b3o118bo240bobo293b2o$931bobo
8bo655b2o$941b2o409b2o$448b3o134bo767b2o$448bo134bobo296b2o468bo132bo
405b2o$449bo134b2o82bo213bobo140bo350bobo106bobo403bo$667b2o213bo142b
2o349b2o107b2o402bobo$667bobo354bobo350bo511b2o$508b2o214b2o134bo215bo
26bo$267bo239b2o215bobo131bobo90b2o123b2o24bo$240b2o26bo240bo214bo134b
2o83b2o5bobo121bobo24b3o$240bobo23b3o162bo267bobo242b2o7bo$240bo191bo
267b2o251b2o495bo107bo$351b2o77b3o267bo749b2o106b2o$351bobo586bo453bo
54bobo105bobo$351bo587bobob2o449b2o$651bo268bobo16bobobobo447bobo$652b
2o267b2o13b2obobobobo2bo200bo$651b2o109bo158bo14bo2bo2b2ob4o198b2o161b
o187bo$760bobo175b2o4bo39bo163b2o50bo107b2o106bobo79b2o388b2o$548bo
212b2o181bobo36bo54bo79b3o79bobo106b2o105b2o79bobo372b2o14b2o$304b3o
25bo216bo241b2o152b2o36b3o50b2o82bo79b2o77bo137bo455bo$304bo28b2o212b
3o241bobo243b2o80bo159b2o294bo294b3o$305bo26b2o242b3o212bo486bobo294bo
bo292bo$576bo645b2o351b2o$472bo104bo245bo397bobo105b3o$417b3o51b2o351b
o118bo279bo107bo$417bo53bobo135bo212b3o116b3o386bo24bo$418bo191bo295b
2o32bo412b2o$608b3o295bobo31b2o5bo406b2o520b2o$906bo40b2o928bo$946bobo
104bo458bo364bobo$505bo351bo195b2o457bobo363b2o$262b3o241b2o186b3o159b
2o139b2o53bobo457b2o$262bo242b2o135b2o50bo161bobo139b2o$263bo378bobo
50bo55b2o244bo537b2o$373b3o266bo108bobo176b2o604b2o$373bo377bo177bobo
5b2o135bo460bo$374bo554bo7b2o134bo$297bo107bo522b2o143b3o$298bo104bobo
324bo394bo26b3o267b3o$296b3o105b2o325bo210bo182bobo26bo131bobo105bo29b
o23bobo24b2o$460bobo266b3o206b2obobo18bo133b2o27b2o26bo24bo53bo53b2o
105bo29bo24b2o26b2o$461b2o474bobobobo16b2o133bobo78b2o52b2o55bo105b3o
53bo25bo$461bo108bobo361bo2bobobobob2o14b2o134bo79b2o52b2o23b2o295bo
325b2o$357bo213b2o361b4ob2o2bo2bo308bobo294bo326b2o14b2o$355bobo213bo
366bo4b2o312bo294b3o340bo$356b2o433bo144bobo368bo588b3o$440b2o52b2o
106b2o188bo52bo90b2o369b2o589bo$440bobo51bobo104b2o187b3o53b2o458bobo$
440bo53bo108bo27bo189bo23b2o349b2o$632b2o186b2o79bobo291bobo$631b2o
187bobo79b2o293bo158b2o$902bo36bo417b2o$939b3o61bo26b2o324bo132bobo$
529bo161bo26bo223bo59bo26bobo457b2o$527bobo159bobo25b2o222b2o31b3o25b
3o26bo458bo$340b3o185b2o160b2o25bobo256bo$340bo433b2o168bo30bo536b3o$
341bo55b2o374b2o108b2o58bo2bo567bo$397bobo375bo106b2o63bo565bo$397bo
29bo456bo53b2o4bo$320bo107bo510bo4bo3bo100bo269bo80bo$318bobo105b3o
324bo185bo2bo5bo2b2o95bo53bobo24b2o188bobo78b2o24bo26bo$319b2o162bo
267bobo187b2o8bobo94b3o51b2o26b2o131bo55b2o78bobo23bo27b2o$484b2o266b
2o188bobobo6bo149bo25bo24bo108bobo159b3o24bobo429b2o$483b2o109bo348b3o
7b2o199bobo106b2o105bo512bo2bo$379bo215bo558b2o77b3o132b2o514b2o$380bo
212b3o344bo3bo290bo133b2o$378b3o558bob2obo289bo$814bo124bobo3b2o337b2o
$812bobo121b2obobobobo2bo336b2o$813b2o121bo2bo2b2ob4o335bo$653bobo187b
2o93b2o4bo$654b2o26b2o158b2o100bobo117bo$576bo77bo27bobo159bo100b2o
117b2o$468b2o105b2o105bo380bobo$467b2o106bobo403bo25b3o159bo$469bo80bo
bo426b2o28bo159b2o$363b2o160b2o24b2o188b2o186bobo19b2o27b2o26bo159bobo
347bo$363bobo159bobo23bo188b2o55bo80bo51b2o11bo8b2o563bo$363bo161bo
216bo53b2o81bo50bo10b3o7bo510bo54b3o$419b3o374bobo78b3o25b3o32bo520bo$
419bo485bo34b2o519b3o$420bo485bo282bo$1026bo161bo107bobo$344bo681bobo
51bo107b3o105b2o78b3o25bo25b2o$342bobo681b2o50b2o160bobo54bo23bo56bo
23b2o27b2o$343b2o107bobo269bo354b2o159b2o79b2o54bo25b2o25bo$453b2o270b
o485b2o28bo78bobo23bo$401bo51bo56bo132b3o77b3o204b2o278bobo133bobo$
402b2o107bo131bo285bobo5b2o273bo133b2o$401b2o106b3o132bo284bo7b2o189bo
$928b2o196b2o349b3o$620bobo504b2o131b2o217bo$621b2o319bo318b2o215bo$
621bo163bo79b3o70b2obobo316bo$786b2o77bo71bobobobo$491bo106b2o185b2o
79bo67bo2bobobobob2o$490b2o105b2o335b4ob2o2bo2bo38b2o$490bobo106bo338b
o4b2o12bobo24bobo159b2o$936bobo18b2o27bo158bobo$385b3o160b2o213b3o170b
2o20bo131bo56bo347bo$385bo161b2o162b2o50bo137bo188b2o403bobo$386bo55b
2o105bo161bobo50bo134bobo187bobo347bo55b2o$442bobo266bo188b2o537bobo$
442bo996b2o$939bo227bo$824b2o113b3o223b2o106bobo78b2o$691bo132bobo115b
o113bo109b2o50bo54b2o78bobo51b3o$476bo212bobo132bo116b2o113bobo158bo
56bo23b2o55bo53bo$477bo107bo104b2o162bo172bo28b2o159b3o77bobo108bo$
475b3o108bo80bo187b2o79b2o89b2o270bo$532bo51b3o79b2o186b2o79b2o89bobo$
533b2o131bobo268bo437bo$532b2o570bo269bo80bo$644bo459bobo131bo135b3o
78b2o$645bo305b2o151b2o132b2o78bo135bobo$643b3o298b2o5bobo283bobo78bob
o$809bo134b2o7bo364b2o$807bobo143b2o$808b2o181bo$758bo181bo48b2o$759bo
134bo44bobob2o45b2o$408b2o347b3o27bo105b2o44bobobobo176b3o$382bo25bobo
375b2o105bobo40b2obobobobo2bo118b2o55bo$383b2o23bo108b3o214b2o50bobo
133bobo11bo2bo2b2ob4o119b2o53bo293bo$382b2o80b3o50bo215b2o188b2o13b2o
4bo122bo348bo$464bo53bo216bo187bo20bobo469b3o$465bo163b2o314b2o$629bob
o538b3o78bo$629bo217b2o323bo77bo$712bobo131b2o323bo78b3o$580bo132b2o
133bo426b3o$579b2o132bo162bobo64bo60b2o271bo$579bobo107b2o186b2o62b3o
61b2o131bo53bobo81bo$554bobo131b2o187bo62bo63bo25bo106bo54b2o$555b2o
133bo249b2o86b2o107b3o53bo$555bo473b2o50bobo294b2o$667bo413b2o132b2o
79bo82b2o77bo$665bobo276b3o135bo133b2o77bo82bo78bo$507bo158b2o278bo
268bo79b3o131b2o26b3o$508bo436bo482bobo$506b3o810b2o109bo$930b2o35bobo
348bobo$781bo147bobo5b2o28b2o351bo$619bo159bobo134b2o11bo7b2o29bo131bo
$620b2o158b2o28bo105bobo9b2o115bo54b2o$541bo77b2o188b2o105bo128b2o52bo
bo$540b2o214b3o50bobo130bo101bobo$540bobo213bo181b2obobo$757bo179bobob
obo449bo$651b3o280bo2bobobobob2o201bo242b2o$651bo282b4ob2o2bo2bo201b2o
242b2o$492b2o158bo216b3o66bo4b2o202bobo77bobo$491b2o376bo66bobo288b2o$
493bo108b2o266bo65b2o290bo$602bobo107bo186bobo79b2o187bo$602bo108b2o
187b2o78bobo133bo52bo$711bobo186bo81bo23bobo105b2o53b3o$416bobo587b2o
107b2o131bo107bo$417b2o322bobo105bobo87bo67bo50bo189b2o78bo27b2o$417bo
324b2o106b2o87b3o115bo189bobo77bo27bobo77bo$742bo107bo91bo114b3o267b3o
105bobo$529bo52bobo356b2o463b2o27b2o$450bo79b2o51b2o822b2o$449b2o78b2o
52bo604b2o216bo$449bobo351bo383bobo$804bo384bo$802b3o133b2o137b2o187bo
$832b2o105b2o2bo78b2o52bobo186bo$780bo50b2o107b4o7b2o70b2o53bo186b3o$
563b3o213b2o52bo107b2o8bobo68bo$483bobo77bo215bobo159b2obo8bo$484b2o
78bo109b2o267b3o7b2o$484bo189bobo266bobo179b2o$649bo24bo265b2obo180bob
o78bo$514b3o133b2o287bob4o181bo77bo$514bo134b2o288bobobob2o257b3o$515b
o420b2obobobo4bo$734b2o200bo2bo2b2ob4o9b3o187bo$708bo25bobo186bobo12b
2o4bo15bo185b2o133b3o$440bo268b2o23bo189b2o18bobo12bo187b2o134bo$441bo
266b2o55bo158bo20b2o278b2o55bo$439b3o324bo268bo188bobo105bo$764b3o268b
obo188bo78bo26b2o24bo53bobo$605bo429b2o266b2o26bobo23bo54b2o$553bo52b
2o696b2o51b3o23b3o27bo$551bobo51b2o336bo441bo$552b2o387b3o221b2o217bo$
940bo142bo82b2o$637b2o301b2o141bobo79bo$637bobo443b2o158bo$637bo605bob
o$587bo214b2o439b2o$479b2o105b2o213b2o$479bobo25bo78bobo214bo$479bo28b
2o186b3o$507b2o187bo233b2o170b3o$673bo23bo190bo40bobo5b2o54bo110bo$
538b2o131bobo215b2o38bo7b2o54b2o108bo$537b2o133b2o214b2o38b2o34bo27bob
o$539bo378b2o44bobo$918bobo21bo21b2o$732bo185bo19b2obobo233bobo$462bo
267bobo107bo96bobobobo233b2o$463b2o266b2o108b2o91bo2bobobobob2o175bo
55bo23b2o$462b2o376b2o92b4ob2o2bo2bo65bobo105b2o81b2o104b2o$788bobo
147bo4b2o67b2o107b2o79bo78bo28b2o23bo53bo$789b2o145bobo74bo267bobo25bo
25bobo50bo$576bo212bo146b2o343b2o52b2o51b3o$577bo53bo403b2o$575b3o51bo
bo242b2o160b2o104b2o$630b2o134b3o105bobo158bo105bobo$766bo107bo268bo
77bo26b3o$767bo171bo280bo29bo$939b3o278b3o26bo$942bo$501b3o322b2o113b
2o112bobo$501bo29bo293b2o228b2o$502bo26bobo188b2o105bo228bo293b3o$530b
2o188bobo220b2o407bo$720bo222b2o25b2o379bo$560b3o380bobo25b2o$560bo
383bo25bo$561bo382bo6b2o$951bobo$619b2o132bobo197bo$618b2o134b2o106bob
o88b2o$487bo132bo133bo108b2o126bo106bobo186bo$485bobo323bo51bo76bo48b
2o79b2o26b2o187b2o$486b2o324b2o125bobob2o45b2o79b2o26bo186bobo23bobo
52bo$677b3o131b2o126bobobobo124bo241b2o51b2o$598bo54bo23bo258b2obobobo
bo2bo64bo299bo52b2o$599b2o53bo23bo257bo2bo2b2ob4o64b2o$598b2o52b3o241b
3o39b2o4bo67bobo104b3o$896bo47bobo174bo$897bo29bo17b2o173bo$925bobo$
926b2o$849bo$713bobo132b2o398bobo$714b2o132bobo92bo195bo108b2o78b2o$
714bo226b3o194bo110bo77bobo$527b3o269bo140bo197b3o188bo$527bo270b2o
140b2o5b3o78bo$528bo54b3o212bobo148bo78bobo$583bo364bo79b2o$560bo23bo$
558bobo215bo$559b2o80b3o133b2o$509bo131bo134b2o298bo$510bo131bo287b2o
35bobo105bo$508b3o323bo94bobo5b2o28b2o78b3o25b3o104bo80b2o25bo$755bo
79b2o92bo7b2o29bo80bo104b2o25bo80bobo24bo53bo$754b2o78b2o92b2o118bo
104bobo25b3o80bo24b3o51bobo$675bo78bobo233b2o163bo187b2o$676b2o241b2o
21bo48b2o$675b2o242bobo16b2obobo46bo$919bo17bobobobo$626bo307bo2bobobo
bob2o$627bo306b4ob2o2bo2bo$625b3o310bo4b2o$871b2o63bobo287bo$871bobo
62b2o287bo$871bo27bobo323b3o77bo$550b2o348b2o403b2o$550bobo268b2o77bo
105bo188b3o106bobo$550bo55b2o212b2o183bo191bo$606bobo105b3o26bo78bo
116bo65b3o188bo$606bo107bo29bo194b3o$581bobo131bo26b3o197bo$582b2o80b
2o275b2o$582bo81bobo$531bo132bo$532b2o409b3o$531b2o325bo83bo3bo212bo
80b2o26bo$856bobo82bo5bo129bo81bobo79b2o23b2o52bo$857b2o83bo3bo103bo
26b2o51bo28b2o79bo26b2o50bo$806bo136b3o5b2o14b3o78b2o26bobo23bobo25b2o
187b3o$698bobo106b2o142bobo15bo79b2o51b2o25bobo$699b2o105b2o145bo14bo
50b2o82bo$699bo253b2o65b2o$648bo370bo$649b2o289bo$648b2o135b2o152bobob
2o$785bobo107bo43bobobobo$785bo108b2o26bo13b2obobobobo2bo$894bobo26b2o
11bo2bo2b2ob4o333b2o$922b2o14b2o4bo336bobo$944bobo336bo$575b2o160b2o
206b2o$575bobo159bobo430bo26bo$575bo161bo432b2o24bo$1169bobo24b3o$768b
o$769b2o172bo$555bo212b2o171b3o$556bo53bo329bo$554b3o54bo268bo59b2o
275b3o$609b3o269b2o171b2o163bo78bo$855b2o23b2o173b2o24bo25b2o109bo77b
2o$722bo105bobo24bobo86bo109bo24b2o25bobo188b2o$723bo105b2o24bo88b2o
51bo82b2o26bo23bo$721b3o105bo113bobo51b2o133bobo$969bo26bobo133b2o$
672bo24b3o230b2o35b2o$670bobo24bo231bobo5b2o29b2o$645b3o23b2o25bo108b
3o119bo7b2o296bo$645bo161bo109b2o9b2o304bo$646bo161bo108bobo314b3o$
917bo24bo$938b2obobo$937bobobobo$597b3o159b3o172bo2bobobobob2o$597bo
161bo174b4ob2o2bo2bo200b2o26bo$598bo161bo177bo4b2o203b2o23b2o$936bobo
208bo26b2o$936b2o314b3o$1254bo$578bo674bo$576bobo53bo$577b2o54b2o269bo
127bo$632b2o268bobo34bo92b2o$851bo26b2o23b2o34b3o89bobo23bo26b2o$852b
2o23b2o63bo114bobo25b2o$851b2o26bo61b2o31b2o81b2o25bo24bobo78b2o$975b
2o132b2o80b2o77bo$720b2o223bo28bo135bo79bo78bo$720bobo222bobo321b3o$
668b2o50bo27bobo194b2o$668bobo78b2o461bo$668bo28bo51bo462bobo$698b2o
251b2o259b2o$697b2o245b2o5bobo$944b2o7bo38bo$620b2o331b2o36bo$620bobo
368b3o$620bo319bo210bo$939bobob2o178bo26bo$813bo125bobobobo177b2o25b3o
77bo$814b2o120b2obobobobo2bo173bobo105b2o$813b2o121bo2bo2b2ob4o280bobo
$790bo147b2o4bo$654bobo132b2o53b2o98bobo$655b2o132bobo51b2o100b2o62b2o
$655bo189bo162bobo$604bo296b2o107bo$605b2o294bobo48bo135bo$604b2o295bo
28bo21b2o132b2o79b3o$931b2o10bo7bobo133b2o80bo78bo$742b3o185b2o9b3o
224bo77b2o$742bo28bo168bo306b2o$743bo28b2o166b2o$691b3o77b2o$691bo27bo
bo$692bo27b2o$720bo2$642b3o323bo$642bo244bo42b2o36bobo$643bo244b2o39bo
bo5b2o29b2o159bo$887b2o40bo7b2o81bo79b2o25b2o$928b2o88b2o25b3o53b2o25b
2o$1019b2o26bo52bo$942bo103bo$812b2o124b2obobo$811b2o124bobobobo$680bo
132bo120bo2bobobobob2o39b3o$678bobo253b4ob2o2bo2bo41bo$679b2o242b3o12b
o4b2o42bo$923bo12bobo125bobo105bo$924bo11b2o126b2o78b2o25bo$1065bo79b
2o24b3o50bo$1144bo79bobo$849bo374b2o$769bo77bobo$743bo24b2o78b2o89bo$
744bo23bobo107b2o59b3o250b2o$742b3o132b2o63bo248bobo$879bo61b2o250bo2$
802bo142bobo$800bobo142b2o$801b2o143bo158bobo$996bo26b2o80b2o$670b2o
324bobo23bobo81bo$669b2o280b2o43b2o26bo$671bo272b2o5bobo$834b3o107b2o
7bo$834bo118b2o9bo$701bobo131bo128b2o$702b2o216bo19bo22bobo$702bo218bo
17bobob2o$651bo267b3o17bobobobo176bo26bo$652b2o282b2obobobobo2bo91bobo
79b2o25bobo$651b2o283bo2bo2b2ob4o91b2o79bobo25b2o$871bo66b2o4bo96bo
158bobo$872bo71bobo253b2o$870b3o72b2o116b2o136bo$901bo162b2o$900b2o
161bo105b3o$768bo131bobo268bo$769bo400bo$767b3o173bo$823bobo115b3o$
824b2o114bo$799b2o23bo115b2o$798b2o282bo$692b3o105bo134bo144b2o$692bo
241b2o62b3o80b2o$693bo239bob6obo28bo28bo$932b3o2bob2o2b2o24b2o28bo$
932b2o4bo4bo26b2o$726bo203b3ob2o5b2o$724bobo202bobo4bo3bo$725b2o135b2o
65bo6bobobo$675bo185b2o65b2o7b3o78bo107bo$676bo186bo74bo78bo108bobo$
674b3o265bo74b3o106b2o51bo$938b2obobo233b2o$759b2o176bobobobo97bo136b
2o$759bobo172bo2bobobobob2o94b2o$759bo163b2o9b4ob2o2bo2bo93bobo$923bob
o12bo4b2o$923bo12bobo$936b2o$847bo$848bo$846b3o2$939bo118bobo$716b2o
221b3o34b2o80b2o$716bobo223bo32bobo81bo23bo$716bo83bo140b2o4bo29bo105b
2o$801bo106bo38bobo132bobo$799b3o107b2o36b2o$747bobo158b2o$748b2o$748b
o135b3o$698bo185bo111bo106bobo24bo$696bobo186bo65b2o41b2o107b2o25b2o$
697b2o245b2o5bobo41b2o107bo24bobo23bobo$944b2o7bo201b2o$953b2o63b2o
136bo$1019b2o$838b2o100bo77bo$837b2o100bobob2o$839bo99bobobobo$936b2ob
obobobo2bo$870bo65bo2bo2b2ob4o$868bobo67b2o4bo$869b2o73bobo$945b2o2$
739b2o212b2o$738b2o214b2o104b2o$740bo81bo130bo105bobo$823b2o107bo10bo
117bo$822b2o106bobo8b3o$931b2o7bo$940b2o$720bo187b2o$721bo185b2o171bo
26b2o$719b3o54bo25b2o105bo170bobo23bobo$774bobo25bobo275b2o26bo$775b2o
25bo220bo107bobo$968bobo24b3o25bobo105b2o$930b2o36b2o27bo25b2o107bo$
929bobo5b2o30bo26bo$929bo7b2o$928b2o2$942bo$866b2o70b2obobo$865b2o70bo
bobobo$867bo66bo2bobobobob2o$897bo36b4ob2o2bo2bo$761b3o131bobo40bo4b2o
$761bo134b2o38bobo98b2o$762bo81bobo89b2o100b2o$845b2o190bo$845bo3$930b
3o6bo$930bo8b3o115bobo24b2o$797bobo131bo10bo114b2o24bobo$798b2o141b2o
115bo26bo24bo$746bo51bo174bo134b2o$747b2o224b2o134b2o$746b2o224bobo3$
1130b2o$951b2o176bobo$889bo54b2o5bobo177bo$834b3o51b2o54b2o7bo$834bo
53bobo62b2o$835bo$940bo$939bobob2o$921bo17bobobobo68bo$922b2o12b2obobo
bobo2bo65b2o$921b2o13bo2bo2b2ob4o36bo27bobo$938b2o4bo40bobo$944bobo38b
2o$945b2o2$1061b3o$1063bo$1062bo$943bo6b2o$771bo169b3o5bobo78bo$772bo
167bo10bo78bobo$770b3o167b2o88b2o$880bobo$881b2o197bo$881bo197bo$831bo
25b2o220b3o$829bobo25bobo$830b2o25bo245bo$807bo122b2o171b2o$806b2o121b
obo5b2o163bobo$806bobo120bo7b2o$928b2o61b2o$990bobo$942bo19bobo27bo$
938b2obobo18b2o$937bobobobo19bo$934bo2bobobobob2o$934b4ob2o2bo2bo$938b
o4b2o$936bobo$936b2o2$793bo213bobo$794b2o211b2o$793b2o109bo103bo$905bo
33bo$903b3o33b3o116bo$942bo113b2o$880b2o52b2o5b2o114b2o$879b2o53bobo
90b3o$881bo52bo94bo50b2o$829b2o197bo52b2o$829bobo248bo$829bo$968b3o$
951b2o17bo$944b2o5bobo15bo$944b2o7bo$953b2o2$940bo$939bobob2o$939bobob
obo$936b2obobobobo2bo$936bo2bo2b2ob4o$938b2o4bo$871bo72bobo$872b2o71b
2o$871b2o$1034bobo$1034b2o$902b3o100b2o28bo$823bo78bo40bo60bobo$824b2o
77bo37b3o62bo50b2o$823b2o26b3o78bobo5bo115bobo$851bo81b2o5b2o116bo$
852bo80bo2$971bo$970bo$970b3o2$930b2o$929bobo5b2o$929bo7b2o$928b2o2$
942bo$938b2obobo$937bobobobo$934bo2bobobobob2o$934b4ob2o2bo2bo66bo$
897bo40bo4b2o66b2o$898b2o36bobo73b2o$897b2o37b2o44b3o$845bobo78b3o55bo
$846b2o78bo56bo50b2o$846bo28b2o50bo107b2o$875bobo156bo$875bo63bo$939b
3o$942bo5bo$941b2o5bobo$948b2o6$951b2o$944b2o5bobo$944b2o7bo$953b2o2$
940bo48bobo$939bobob2o44b2o$939bobobobo44bo$923bo12b2obobobobo2bo$924b
o11bo2bo2b2ob4o63bo$869bobo50b3o13b2o4bo67b2o$870b2o26b2o44bobo64bobo$
870bo26b2o46b2o$899bo4$943bo$941b3o$940bo$940b2o3$944b2o$943bobo$945bo
2$930b2o$929bobo5b2o$929bo7b2o$928b2o2$942bo$938b2obobo44b2o$937bobobo
bo43bobo$934bo2bobobobob2o42bo$934b4ob2o2bo2bo$938bo4b2o$936bobo$927bo
8b2o$926b2o$926bobo3$939bo$939b3o$942bo6bo$941b2o4b2o$948b2o$910bo$
908bobo$909b2o3$951b2o$944b2o5bobo$944b2o7bo11b2o$953b2o11b2o$965bo$
940bo$939bobob2o$939bobobobo$936b2obobobobo2bo$936bo2bo2b2ob4o$938b2o
4bo$944bobo$945b2o5$943bo$941b3o$940bo$940b2o5$942b3o$939bo4bo$930b2o
7bo3bo$929bobo$929bo7b2o2bo$928b2o7bo$937bobo$941b2o$937bo5bo$937bo3bo
bo$934bo4bobobob2o$934b4ob2o2bo2bo$938bo4b2o$936bobo$936b2o5$939bo$
939b3o$942bo$941b2o7$951b2o$944b2o5bobo$944b2o7bo$953b2o2$940bo$939bob
ob2o$939bobobobo$936b2obobobobo2bo$936bo2bo2b2ob4o$938b2o4bo$944bobo$
945b2o5$943bo$941b3o$940bo$940b2o125$1029b2o$1029b2o!
#C [[ STEP 50 ]]
dvgrn
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Re: Spiral Growth Geminoid Challenge

Postby calcyman » June 22nd, 2017, 11:32 am

You can reduce the spacing between streams from 27hd to 23hd with a non-obvious weld:

Code: Select all
x = 27, y = 142, rule = B3/S23
12b2o$12bo$13b3o$15bo$15bob2o$14b2o2bo$10b2o4bo$8bo2bo2b2ob4o$8b2obobo
bobo2bo$11bobobobo$11bobob2o$12bo2$25b2o$16b2o7bo$16b2o5bobo$23b2o7$
13b2o$14bo$11b3o$11bo$8b2obo$8bo2b2o$10bo4b2o$6b4ob2o2bo2bo$6bo2bobobo
bob2o$9bobobobo$10b2obobo$14bo2$2o$bo7b2o$bobo5b2o$2b2o7$12b2o$12bo$
13b3o$15bo$15bob2o$14b2o2bo$10b2o4bo$8bo2bo2b2ob4o$8b2obobobobo2bo$11b
obobobo$11bobob2o$12bo2$25b2o$16b2o7bo$16b2o5bobo$23b2o7$13b2o$14bo$
11b3o$11bo$8b2obo$8bo2b2o$10bo4b2o$6b4ob2o2bo2bo$6bo2bobobobob2o$9bobo
bobo$10b2obobo$14bo2$2o$bo7b2o$bobo5b2o$2b2o7$12b2o$12bo$13b3o$15bo$
15bob2o$14b2o2bo$10b2o4bo$8bo2bo2b2ob4o$8b2obobobobo2bo$11bobobobo$11b
obob2o$12bo2$25b2o$16b2o7bo$16b2o5bobo$23b2o7$13b2o$14bo$11b3o$11bo$8b
2obo$8bo2b2o$10bo4b2o$6b4ob2o2bo2bo$6bo2bobobobob2o$9bobobobo$10b2obob
o$14bo2$2o$bo7b2o$bobo5b2o$2b2o7$12b2o$12bo$13b3o$15bo!
What do you do with ill crystallographers? Take them to the mono-clinic!
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Re: Spiral Growth Geminoid Challenge

Postby dvgrn » June 22nd, 2017, 11:59 am

calcyman wrote:You can reduce the spacing between streams from 27hd to 23hd with a non-obvious weld...

Thanks! I'd been looking at that, but hadn't found a good weld yet. The double-spiral glider Snarkbox storage unit was copied wholesale from the old Blockic loafer gun, with no attempt to rework it for the modern age. There might be some other options where the lines of Snarks are slightly oblique instead of vertical, but that may not work well given the double-spiral structure.

If anyone decides to do the rebuild to get the size below 2000x2000*, it may be worth keeping in mind that the pattern runs much better (after the first cycle in Golly) if the period is an exact power of two. Right now it's 2^18. If the storage unit is made more efficient, it's still a good idea to keep the same length of empty space in the spiral. Of course there are tighter H-to-2G connections available than the simple chain of Fx77's -- I just threw that in there to get the timing right without running a Hersrch search.

It would take some serious optimization of the 0-degree elbow recipes to reduce the recipe length by half, so that it would fit in a 2^17-length loop and presumably about a 1400^2 bounding box. That's probably possible, but it might require fairly time-consuming searches using single-channel glider triplets, quadruplets, etc., as well as glider pairs.

-------------------------------------

* The rebuild is surprisingly easy to do, so no one should let the apparent complexity scare them off -- it could be something like half an hour of work:

-- Build an empty double spiral with calcyman's weld
-- Add the current pattern's H-to-2G end-cap back at some random location
-- Put one glider in the loop and see how long it takes to get back to its initial location
-- Move the endcap by (N, -N) to adjust the timing by 8N to get a period of 2^18
-- Remove the first elbow from the current spiral-growth pattern and let one full-length recipe escape
-- Feed that stream of gliders into the new smaller double spiral (the H-to-G after the Fx77 chain is transparent)
-- Put elbows back wherever you want them
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Re: Spiral Growth Geminoid Challenge

Postby wwei23 » June 23rd, 2017, 11:41 am

If a 2-directional synthesis of a snark is possible(down-right and down-left from the top, for example), and it is positioned correctly, then perhaps a glider gun in the middle could make this work.
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x = 3, y = 3, rule = B3/S234y
2bo$3o$bo!
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