Caterpillar's little brother research

[HartmutHolzwart]

Additionally to the helix, you also need quite a sophisticated mechanism to multiply the one gilder transported by the helix into the 24 gliders needed to build the two rows of six blinkers needed to support the caterpillars front end.

Also for every *WSS to be build, much more than the minimum four gliders for one sided construction, due to the heavy use of kickback reactions. So overall it comes out to about 80 *WSS and 600 to 800 gliders produced and consumed per cycle.

In the thread, various options are discussed how to get a smaller caterpillar by reducing these numbers, but so far none of these was really implemented.

All in all, the existing caterpillar already is highly optimized and in my view best possible given the design.

[dvgrn]

In the thread, various options are discussed how to get a smaller caterpillar by reducing these numbers, but so far none of these was really implemented.

I'm still fairly optimistic about one of the options, based on experience with 31c/240 self-supporting spaceships. It seems quite likely that slow-salvo recipes can be designed, that build the standard 6x Caterpillar helix, and that can be regenerated by structures traveling on some number of blinker trails (no idea how many yet).

Even though it will take a lot more gliders to produce each *WSS, the resulting caterpillar will probably be shorter. Parallel streams of gliders can be packed together much more tightly than the huge triangle structures in the current Caterpillar.

Also, slow salvos can construct a helix closer to the blinker trails, because it won't be necessary to leave space for long chains of rephasers between the NE and SE edges of the triangles. And slow-salvo construction is convenient because there's no need for the precise timing needed to get kickbacks to work.

There's still the rephasing problem associated with generating gliders on demand for the slow salvos, on 102 different lanes -- relative to the blinkers in the blinker trails, or rather, relative to the output gliders from the 6x period-multiplier mechanism.

I guess it remains to be seen whether the lane rephasing problem can be solved with just a few pi climbers plus throw-and-catch trickery making a variety of rake types, similar to the collection of rakes used in the Centipede.

[muzik]

This is kind of unrelated, but how did the program that assembled the original caterpillar work; did it simply piece together some existing parts, or did it actually generate the caterpillar somehow?

If the latter is true, couldn't you just run it again and hope for a caterpillar with 100 or so less cells than the existing one?

It would be a *really* trivial improvement, but it's definitely an improvement, especially seeing that Daniel apparently got a smaller than 232815-cell caterloopillar from running the caterloopillar-generating script (I am yet to test that assertion).


Although I heard that getting the thing that made the caterpillar up and running wasn't exactly the most pleasant thing ever.

[dvgrn]

This is kind of unrelated, but how did the program that assembled the original caterpillar work; did it simply piece together some existing parts, or did it actually generate the caterpillar somehow?

If the latter is true, couldn't you just run it again and hope for a caterpillar with 100 or so less cells than the existing one?

If you run robocat again, not surprisingly, you'll get exactly the same Caterpillar. You'd have to reprogram it to put the pieces together differently, to have any hope of an improvement.

However, it's easy enough to optimize the Caterpillar by hand and end up with a smaller population and/or bounding box. The robocat program often just put together pieces without optimizing the phasing, because it would have taken forever to run (and write) the robocat code, if every possible rephasing optimization had to be tested.

As an experiment, I just made a smaller Caterpillar by moving the bottom 575 cells of the last four blinker trails up by 34 cells, along with the rephaser column just above it (third blinker trail from the left). That makes a Caterpillar that fits inside a 4195x330683 bounding box, with a population that's smaller by 24 cells.

Then that whole cleanup mechanism could be rephased one tick at a time, to bring it even closer to the last p45 glider rake above it. One of those phases will turn out to give the whole Caterpillar the lowest population (at one of its 270 possible phases). That may or may not be the same phase that allows for the smallest possible bounding box, so you have to decide what you want to optimize.

And then you could repeat that micro-optimization in probably several hundred places along the length of the Caterpillar, and you'll have... well, still not a very interesting amount of improvement, percentage-wise, compared to a thorough Little-Brother rebuild.

We should probably run competitions to find shorter *WSS-building components, for starters -- the two-part HWSS synthesis is especially worth improving. Anything that can be constructed incrementally with backward slow salvos, should be, because you can pack slow-salvo components much closer together... no long empty stretches of blinker trails needed any more, to give enough space between backward rakes and their matching forward rakes.

Another tangential idea: it's probably possible to build a Caterpillar with a significantly smaller population, just by rephasing the pi heptominoes wherever possible so that a large fraction of them are in their lowest-population phase simultaneously. It's not possible to get them all synchronized that way, or even nearly, but paying attention to that detail during a rebuild could still make a sizable difference.

[muzik]

Since I'm far (like, pretty damn far) from being engineered-spaceship savvy, I probably won't be of much help for the new ship's construction.

One thing that kind of strikes me is that the structure of the main body of the caterpillar looks pretty repetitive (emphasis here on "looks"), with a lot of triangles in it. Although these probably aren't exact clones of each other except in different generations, so that doesn't look to be a good enough method of compression.


Say, in the nearish future, we do find the smaller 17c/45. What would it look like? I'd assume just like the caterpillar (using the same main reaction), but not quite as tall. More importantly, how many cells would it have? Would we be able to knock it down into the hundreds of thousands range, maybe even smaller than the centipede? Or would it still be a multi-million cell beast?

[gmc_nxtman]

To my understanding, the reason that the caterpillar "looks" repetitive is that each segment that looks almost the same as the last one is used to build a part of the helix, which then lays down the tracks, which then build the helix, etc. So it's a self-sustaining loop. In order to compress the repetitive parts, one would have to use a smaller helix (which, luckily, already exists). But it's not a trivial process to reassemble the caterpillar with a smaller helix.

[Kazyan]

The Little Brother would probably not have triangles--there's been talk of using slow-salvos to build the helix, which can pack more tightly. So you'd have a string of closely-spaced "rakes" with the glider streams all pointing in the same direction towards the helix, instead of several triangles (composed of two different rakes pointing in different directions) trying to build the helix with synchronized shots.

[muzik]

I'm assuming this version is focused more on the bounding box than the population?

[dvgrn]

I'm assuming this version is focused more on the bounding box than the population?

Not sure you can really assume anything at this point, since nobody has quite picked up all the pieces and started the re-assembly. Larger size means longer strings of gliders and *WSSes and blinkers, so population and bounding box will both definitely be reduced. As I mentioned, just paying a lot of attention to pi-heptomino phasing could cut down the population by a very large amount -- it's mostly just a matter of whether the rebuilder cares enough about minimizing the population to do the extra work.

The switch to slow-salvo construction could allow the Little Brother to be much narrower. I believe the current width is dictated by the necessity of rephasing the blinker trails between each backward rake and its paired forward rake. Depending on what rephasing is needed, it can take ridiculously tall columns of pi climbers to get the spacing and timing just right, and in the original design those have to fit in the vertical edge of each of those large triangles.

-- More or less, anyway. I bet that's an oversimplification. I definitely haven't memorized what each of those 25-tracks and 32-tracks is actually used for... The main point is that if we're not using any forward rakes, or not very many, then we can construct the upward *WSS streams very close to the blinker trails on both sides. Slow salvos don't care how far they travel before they do their work.

And we might not really need as many blinker trails as the original Caterpillar has. For making slow salvos, we could get away with just two blinker trails, except that we still need the downward MWSS filter streams, or some equivalent mechanism, to cut the pi-climber rakes' output down from period 45 to period 270. So we have to have enough blinker trails to conveniently build those downward MWSSes.

-- I suppose it might turn out that those MWSSes could be built with "not-so-slow" salvos using p45 backrakes lined up on just the right lanes. In that case, the minimum might be back down to two blinker trails again -- or maybe six trails, if we need catch-and-throw 25-tracks on either side, to get the construction timing right.

[Oddly enough, for most slow-salvo gliders, we won't need the catch-and-throw trick -- the timing of the middle gliders in a slow-salvo recipe don't matter. But we'll still need very precise timing to produce the glider that triggers each *WSS seed to build the upward streams in the helix.]

Or maybe eight trails will be better, so we can run leftward and rightward backrakes on separate trails up the middle, without the rakes having to wait for each other to get out of the way. Or more, for further increases in efficiency... and pretty soon we'll be right back up to the Caterpillar's trail count.

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

The simplest rebuild would involve copying the top 17,000 rows of the Caterpillar exactly -- that's a lot of very hard design work that it would be convenient not to have to re-do! Or maybe just move the left and right sides in by 1000 cells or so, since that's mostly just a copy-and-paste adjustment. Then attach rakes to those existing blinker trails to make slow salvos that build all those upward *WSS streams, using slow salvos or other new tricks.

I suspect that just with this kind of minimal rebuild, the Little Brother could end up at half the original Caterpillar's population and length (and bounding box), maybe somewhat less. But I have no hard evidence to back up this crackpot theory. Can't really measure Little Brother until somebody actually finishes building it; there are too many unsolved problems and unknown unknowns. It might not end up being any smaller at all...!

[biggiemac]

The bounding box is generally a more useful metric for optimization, because as dvgrn said above, just changing the phase of pis so that they all reach a low population in sync could drastically reduce the minimum population.

I feel like the caterpillar is an order of magnitude more complicated than the Waterbear, just looking at Gabriel's page about it. I presume filters and catch/throw retiming are still going to be necessary in the slow salvo version as well?

Also, I was not under the impression that slow salvos could get more helix spaceships built per unit height - so to optimize bounding box they should only being used when the helix ship couldn't be put into place by a standard synthesis; am I wrong? I guess I might be out of date on the contents of this thread.

[dvgrn]

I feel like the caterpillar is an order of magnitude more complicated than the Waterbear, just looking at Gabriel's page about it.

I dunno. I don't know a whole lot of the details about either one, but at this point I think I'd personally get fewer and smaller headaches building Little Brother, than trying to rebuild the waterbear. Maybe I kinda sorta think I understand what's going on in the Caterpillar because of experience with 31c/240. Orthogonal designs seem a lot easier to break down into independent pieces, whereas some of the waterbear's mechanisms just seem like black magic.

I presume filters and catch/throw retiming are still going to be necessary in the slow salvo version as well?

Filters, yes, because pi climbers inevitably throw out p45 glider streams, and nobody has come up with anything near a p45-repeatable helix reaction.

Catch/throw, probably, or at least maybe -- but just for the trigger glider in each slow-salvo recipe. The other gliders in a slow salvo don't need timing adjustments, but the last glider's timing will determine how the newly constructed *WSS lines up with the rest of the helix.

... Right now it seems to me that it might be possible to substitute a spatial offset for a temporal one. That is, if you wait long enough before sending the trigger glider stream, it will turn out that the *WSS stream lines up correctly with the helix. But too much of that kind of waiting around and you end up with an oversized bounding box again.

Also, I was not under the impression that slow salvos could get more helix spaceships built per unit height - so to optimize bounding box they should only being used when the helix ship couldn't be put into place by a standard synthesis; am I wrong? I guess I might be out of date on the contents of this thread.

I might be out of date also.

My recollection is that it was very hard to find a reasonable slow-salvo recipe that could build some of the closely spaced *WSSes in codeholic's 5x helix (at the top of this thread). The original 6x helix didn't seem to be as much of a problem.

Now, the current rakes for building helix LWSS and MWSS streams seem to be roughly 5000 cells high, and HWSS streams need 9000+ cells and a double rake (two triangles).

There seems to be no trouble packing backrakes about 200 cells apart on average in the existing Caterpillar, with gliders in exactly the right spacetime locations for the current multi-kickback synchronized constructions. That might mean that a LWSS or MWSS-creating slow salvo should have no more than 25 or 30 gliders, and a HWSS-creating salvo would stop being competitive at around 50 gliders. Very roughly.

I'm hoping that at least the HWSS double-rake construction can be replaced cost-effectively by slow salvos. Ideally I guess we'd run a new search that checks slow salvo recipes in order of cost, measured in pi climbers.

[simsim314]

How about using the universal helix? I think it somewhat simpler, but the period is higher...

An example:

Code: Select all

x = 118, y = 390, rule = B3/S23
9$29b2o$28bo2bo$28bobo$29bo6$54bo4b3o$53b3o3bo2bo$46b3o3b2obo3bo$46bo
2bo2b3o4bo3bo$46bo5b3o4bo$46bo3bob3o5bobo$46bo3bob2o$46bo6b2o$47bobo8b
3o$58bo2bo$53bo4bo$53bo4bo3bo$53bo4bo3bo$58bo$53bo5bobo$53bo$53bo2$53b
o$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo
$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo
2$53bo$53bo$53bo8b3o$62bo2bo$53bo8bo$53bo8bo3bo$53bo8bo3bo$62bo$53bo9b
obo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$
53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo18b3o$53bo18bo2bo$
72bo$53bo18bo$53bo19bobo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$
53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo$40b3o$40bo2b
o9bo$40bo12bo$40bo12bo$41bobo$20bo32bo$19b3o31bo$19bob2o30bo$20b3o$20b
3o30bo$20b2o31bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo
2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo
$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$
53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$
53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$
53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$
53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$27bo25bo$26b3o24bo$25b2obo24bo$
25b3o$26b2o25bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$
53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$
53bo$53bo$53bo2$36b3o14bo$36bo2bo13bo$36bo16bo$36bo3bo$36bo16bo$37bobo
13bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$53bo$53bo$53bo2$47bo5bo$46b
3o4bo$46bob2o3bo$47b3o$47b3o3bo$47b3o3bo$47b2o40$64b3o$63bo2bo$66bo$
62bo3bo$66bo$63bobo!

[dvgrn]

How about using the universal helix? I think it somewhat simpler, but the period is higher...

Looks simpler enough to me that it might be worth switching over to it, if it weren't for the higher-period issue. I'd love to see one of these in action, but I'm not sure that it would make very good support for a standard 17c/45 Caterpillar.

The sample you posted seems like it could be cut down to a period of about 1700, roughly. Filter streams could turn p45 rakes into p1710 rakes with no problem -- but that would be 38x instead of the current 6x. That means a factor of six increase in the number of fanout devices. Those are the secondary streams of more widely spaced LWSS and MWSS streams, separate from the actual helix at the far right. Their job is to build the initial 32-track -- two blinker trails -- for the first pi climbers to run on.

The original Caterpillar has a 6x helix, so that means building twelve blinkers for each p270 period of the spaceship. A 38x helix would mean building 76 blinkers in each p1710 cycle, assuming that the universal helix can really be cut down that to that low a period -- I'm not sure how quickly those blinker puffers can really be constructed with one-sided recipes, for example.

EDIT: I'm a little nervous about the idea of constructing any other c/2 objects as part of a helix, besides the standard *WSSes. HWSSes, at least close to anything else, have turned out to be plenty hard enough to handle.

-- It's quite possible I'm missing something, though. Is there a different approach that might work better for supporting a Caterpillar front end?

[Sphenocorona]

Well, this is more of the known approaches, but I think it might be possible to create a 4x helix if a high forward displacement turner can be found that is faster than and of comparable size to the recent one I found that chains at 16c/43... There's ones I've found that would work but are too big just because they refuse to clean up nicely...

[muzik]

Since we've managed to reduce the centipede down to the water strider and have it even fit in a LifeViewer window, and also reduced the (34,7)c/156 macroship which exceeded the caterpillar's population and bounding box, how about we set some effort back into this project? I have enough confidence that we can knock off a digit or possibly even two off the base-10 cell count with modern technology.

[shuich01]

Since we've managed to reduce the centipede down to the water strider and have it even fit in a LifeViewer window, and also reduced the (34,7)c/156 macroship which exceeded the caterpillar's population and bounding box, how about we set some effort back into this project? I have enough confidence that we can knock off a digit or possibly even two off the base-10 cell count with modern technology.

Leaf bug-like technology seems to be adaptable. maybe we can have a try with similar technologies, I guess.

[dvgrn]

Leaf bug-like technology seems to be adaptable. maybe we can have a try with similar technologies, I guess.

The big unavoidable differences between 31c/240 leaf bugs and 17c/45 caterpillars are that

1) leaf bugs can use gliders to build trails in front of themselves, but caterpillars are too fast -- so the only option for reaching the front is some kind of relatively expensive helix.

There have been some interesting experiments with using unconventional helix components like Schick engines, but I think the details haven't been worked out to build a 17c/45 compatible helix yet, so it's not clear if a new helix would end up being cheaper to construct or not.

2) 240 is a big enough period that the entire leaf bug spaceship can easily work at that period. A "Caterpillar's little brother" is still going to need a filter mechanism to multiply 45 by some N to get a workable period -- and then basically build N times more of everything at the front end.

The current 6x filter is one possible target for optimization -- if all the necessary mechanisms can work with a lower multiple of 45, the whole structure should get correspondingly simpler. (But that's a pretty big "if". At least, nobody has been able to get a lower period working so far.)

[Resu]

The big unavoidable differences between 31c/240 leaf bugs and 17c/45 caterpillars are that

1) leaf bugs can use gliders to build trails in front of themselves, but caterpillars are too fast -- so the only option for reaching the front is some kind of relatively expensive helix.

What is the maximum speed that gliders are able to construct a trail for?

[PK22]

What is the maximum speed that gliders are able to construct a trail for?

Strictly less than c/4 - if a self-supporting spaceship is moving at greater than or equal to c/4 orthogonal, gliders cannot be reflected back to the front to rebuild the track since they travel at c/4 diagonal.
The leaf bug moves at 31c/240, which is about 0.129c, so you can reflect gliders to the front to rebuilt the track.
The caterpillar moves at 17c/45, which is about 0.378c, so gliders cannot be reflected to the front - you have to use xWSSes to rebuilt the track.

[shuich01]

The big unavoidable differences between 31c/240 leaf bugs and 17c/45 caterpillars are that

1) leaf bugs can use gliders to build trails in front of themselves, but caterpillars are too fast -- so the only option for reaching the front is some kind of relatively expensive helix.

What is the maximum speed that gliders are able to construct a trail for?

ahh i forgot that building a trail like that requires speed slower than c/4, otherwise the glider trail would not keep up with the spaceship

[shuich01]

Speaking of doing a minor reduction to the original Caterpillar, we can just do some fine-tune to some parts, which do nothing but changing the blinkers' phase, from this:

clipboard0.png (2.49 KiB) Viewed 1445 times

to like this:

clipboard1.png (1.58 KiB) Viewed 1445 times

I am not sure if it all works, but it may help reduce a little to the original spaceship

[codeholic]

I've posted some of my recent results in the Helix thread, but I think I'd better use this topic, because it's too specific.

I've just found out that there is a glider duplicating convoy that works at x3 period, so it seems one could overclock fanout devices, halving their number:

Code: Select all

x = 145, y = 422, rule = B3/S23
144bo$142b2o$143b2o83$109bo$109bobo$109b2o83$75bobo$75b2o$76bo82$42bo$
41bo$41b3o83$9bo$7b2o$8b2o8$3bo7bo$2b3o5b3o$b2obo4b2obo$b3o5b3o$b3o5b
3o$2b2o5b3o$10b2o11$2b3o5b3o$bo2bo4bo2bo$4bo7bo$o3bo3bo3bo$4bo3bo3bo$b
obo8bo$9bobo10$3bo7bo$2b3o5b3o$2bob2o4bob2o$3b3o5b3o$3b3o5b3o$3b2o6b3o
$11b2o11$2b3o5b3o$2bo2bo4bo2bo$2bo7bo$2bo3bo3bo3bo$2bo7bo3bo$3bobo4bo$
11bobo10$3bo7bo$2b3o5b3o$b2obo4b2obo$b3o5b3o$b3o5b3o$2b2o5b3o$10b2o!

I wonder if one can split an x6 glider stream into two and then through some trickery merge them back to get an x3 one.

[codeholic]

It looks like it may be possible by making use of the spaceship stream on the opposite side. This would, however, result in a huge distance between the helix and fanout devices, as well as large triangles of gliders in the front. That said, if the slow salvo approach is used, the distance to the spaceship streams may turn out to be not as important. Here's the sketch of the idea (distance between spaceship streams is understated, and the math isn't quite mathing):

Code: Select all

x = 1198, y = 2352, rule = B3/S23
1184b3o4bo$1154b3o27bo2bo2b3o$1153bo2bo5bo5b3o13bo4b2obo$1156bo4b3o3bo
2bo5bo7bo3b4o$1150bobo3bo4bob2o5bo4b3o6bo5b2o$1150b4obo6b3o5bo4bob2o5b
o2bo$1149bobo10b3o2bobo6b3o6b2o$1162b3o11b3o5bo$1162b2o12b3o$1176b2o5b
o3b2o$1185bob2o$1184b2o2bo$1185b3o2$1180bo12b3o$1179b3o10bo2bo$1179bob
2o12bo$1180b3o8bo3bo$1180b3o8bo3bo$1125bo54b2o13bo$1124bo67bobo$1124b
3o28b3o$1139bo9bo4bo2bo$1138b3o7b3o6bo$1137b2obo7bob2o5bo$1137b3o9b3o
2bobo$1137b3o9b3o$1128b3o6b3o9b3o$1128bo2bo6b2o9b2o$1128bo$1128bo$
1129bobo2$1184b3o4bo$1144b3o7b3o26bo2bo3b3o$1143bo2bo7bo2bo4bo5b3o15bo
3bob2o$1146bo7bo6b3o4bo2bo4bo5bo3bo4b3o$1142bo3bo7bo5b2obo4bo6b3o4bo3b
o4b2o$1142bo3bo8bobo2b3o5bo5b2obo8b2o$1146bo13b3o6bobo2b3o9b2o$1143bob
o14b3o11b3o7bobo$1161b2o11b3o7b3o$1175b2o9b2o$1186b3o$1140bo44b2o2bo$
1139b3o42bo2b2o$1138b2obo42bob2o$1138b3o39bo5b2o5b3o$1139b2o38b3o11bo
2bo$1178b2obo11bo$1178b3o12bo3bo$1178b3o12bo3bo$1179b2o12bo$1194bobo$
1155b3o$1139bo9bo5bo2bo$1138b3o7b3o4bo$1138bob2o5b2obo4bo$1139b3o5b3o
6bobo$1139b3o5b3o$1128b3o8b3o5b3o$1127bo2bo8b2o7b2o$1130bo$1130bo$
1127bobo2$1184b3o4bo$1144b3o7b3o27bo2bo2b3o$1144bo2bo5bo2bo5bo5b3o13bo
4b2obo$1144bo11bo4b3o3bo2bo5bo7bo3b4o$1144bo3bo7bo4bob2o5bo4b3o6bo5b2o
$1144bo3bo4bobo6b3o5bo4bob2o5bo2bo$1144bo17b3o2bobo6b3o6b2o$1145bobo
14b3o11b3o$1162b2o12b3o$1176b2o2$1140bo47b2o$1139b3o46b2o$1139bob2o$
1140b3o37bo4b3o5b3o$1140b2o37b3o4bo5bo2bo$1179bob2o3bo8bo$1180b3o8bo3b
o$1180b3o8bo3bo$1180b2o13bo$1192bobo$1155b3o$1139bo9bo4bo2bo$1138b3o7b
3o6bo$1137b2obo7bob2o5bo$1137b3o9b3o2bobo$1137b3o9b3o$1128b3o6b3o9b3o$
1128bo2bo6b2o9b2o$1128bo$1128bo$1129bobo2$1184b3o4bo$1144b3o7b3o26bo2b
o3b3o$1143bo2bo7bo2bo4bo5b3o15bo3bob2o$1146bo7bo6b3o4bo2bo4bo5bo3bo4b
3o$1142bo3bo7bo5b2obo4bo6b3o4bo3bo4b2o$1142bo3bo8bobo2b3o5bo5b2obo8b2o
$1146bo13b3o6bobo2b3o6bo2b2o$1143bobo14b3o11b3o8b2o$1161b2o11b3o$1175b
2o2$1140bo$1139b3o46b2o$1138b2obo$1138b3o39bo4bo3bo3b3o$1139b2o38b3o3b
o2bo4bo2bo$1178b2obo4bo6bo$1178b3o12bo3bo$1178b3o12bo3bo$1179b2o12bo$
1194bobo$1155b3o$1139bo9bo5bo2bo$1138b3o7b3o4bo$1138bob2o5b2obo4bo$
1139b3o5b3o6bobo$1139b3o5b3o$1128b3o8b3o5b3o$1127bo2bo8b2o7b2o$1130bo$
1130bo$1127bobo2$1184b3o4bo$1144b3o7b3o27bo2bo2b3o$1144bo2bo5bo2bo5bo
5b3o13bo4b2obo$1144bo11bo4b3o3bo2bo5bo7bo3b4o$1144bo3bo7bo4bob2o5bo4b
3o6bo5b2o$1144bo3bo4bobo6b3o5bo4bob2o5bo2bo$1144bo17b3o2bobo6b3o6b2o$
1145bobo14b3o11b3o6bo$1162b2o12b3o7bo$1176b2o8bo2$1140bo$1139b3o$1139b
ob2o$1140b3o37bo12b3o$1140b2o37b3o10bo2bo$1179bob2o12bo$1180b3o8bo3bo$
1180b3o8bo3bo$1180b2o13bo$1192bobo$1155b3o$1139bo9bo4bo2bo$1138b3o7b3o
6bo$1137b2obo7bob2o5bo$1137b3o9b3o2bobo$1137b3o9b3o$1128b3o6b3o9b3o$
1128bo2bo6b2o9b2o$1128bo$1128bo$1129bobo2$1184b3o4bo$1144b3o7b3o26bo2b
o3b3o$1143bo2bo7bo2bo4bo5b3o15bo3bob2o$1146bo7bo6b3o4bo2bo4bo5bo3bo4b
3o$1142bo3bo7bo5b2obo4bo6b3o4bo3bo4b2o$1142bo3bo8bobo2b3o5bo5b2obo8b2o
$1146bo13b3o6bobo2b3o9b2o$1143bobo14b3o11b3o7bobo$1161b2o11b3o$1175b2o
8b2o2$1140bo$1139b3o$1138b2obo$1138b3o39bo12b3o$1139b2o38b3o11bo2bo$
1178b2obo11bo$1178b3o12bo3bo$1178b3o12bo3bo$1179b2o12bo$1194bobo$1155b
3o$1139bo9bo5bo2bo$1138b3o7b3o4bo$1057bo80bob2o5b2obo4bo$1057bobo79b3o
5b3o6bobo$1057b2o80b3o5b3o$1128b3o8b3o5b3o$1127bo2bo8b2o7b2o$1130bo$
1130bo$1127bobo2$1184b3o4bo$1144b3o7b3o27bo2bo2b3o$1144bo2bo5bo2bo5bo
5b3o13bo4b2obo$1144bo11bo4b3o3bo2bo5bo7bo3b4o$1144bo3bo7bo4bob2o5bo4b
3o6bo5b2o$1144bo3bo4bobo6b3o5bo4bob2o5bo2bo$1144bo17b3o2bobo6b3o6b2o$
1145bobo14b3o11b3o6bo$1162b2o12b3o6b3o$1176b2o7b3o2$1140bo$1139b3o$
1139bob2o$1140b3o37bo12b3o$1140b2o37b3o10bo2bo$1179bob2o12bo$1180b3o8b
o3bo$1180b3o8bo3bo$1180b2o13bo$1192bobo$1155b3o$1139bo9bo4bo2bo$1138b
3o7b3o6bo$1137b2obo7bob2o5bo$1137b3o9b3o2bobo$1137b3o9b3o$1128b3o6b3o
9b3o$1128bo2bo6b2o9b2o$1128bo$1128bo$1129bobo2$1184b3o4bo$1144b3o7b3o
26bo2bo3b3o$1143bo2bo7bo2bo4bo5b3o15bo3bob2o$1146bo7bo6b3o4bo2bo4bo5bo
3bo4b3o$1142bo3bo7bo5b2obo4bo6b3o4bo3bo4b2o$1142bo3bo8bobo2b3o5bo5b2ob
o8b2o$1146bo13b3o6bobo2b3o9b2o$1143bobo14b3o11b3o6b2ob2o$1161b2o11b3o
6b2o2bo$1175b2o7b2ob2o$1185bobo$1140bo45bo$1139b3o$1138b2obo$1138b3o
39bo12b3o$1139b2o38b3o11bo2bo$1178b2obo11bo$1178b3o12bo3bo$1178b3o12bo
3bo$1179b2o12bo$1194bobo$1155b3o$1139bo9bo5bo2bo$1138b3o7b3o4bo$1138bo
b2o5b2obo4bo$1139b3o5b3o6bobo$1139b3o5b3o$1128b3o8b3o5b3o$1127bo2bo8b
2o7b2o$1130bo$1130bo$1127bobo2$1184b3o4bo$1144b3o7b3o27bo2bo2b3o$1144b
o2bo5bo2bo5bo5b3o13bo4b2obo$1144bo11bo4b3o3bo2bo5bo7bo3b4o$1144bo3bo7b
o4bob2o5bo4b3o6bo5b2o$1144bo3bo4bobo6b3o5bo4bob2o5bo2bo$1144bo17b3o2bo
bo6b3o6b2o$1145bobo14b3o11b3o5bo$1162b2o12b3o$1176b2o5bo3b2o$1185bob2o
$1140bo43b2o2bo$1139b3o43b3o$1139bob2o$1140b3o37bo12b3o$1140b2o37b3o
10bo2bo$1179bob2o12bo$1180b3o8bo3bo$1180b3o8bo3bo$1180b2o13bo$1192bobo
$1155b3o$1139bo9bo4bo2bo$1138b3o7b3o6bo$1137b2obo7bob2o5bo$1137b3o9b3o
2bobo$1137b3o9b3o$1128b3o6b3o9b3o$1128bo2bo6b2o9b2o$1128bo$1128bo$
1129bobo2$1184b3o4bo$1144b3o7b3o26bo2bo3b3o$1143bo2bo7bo2bo4bo5b3o15bo
3bob2o$1146bo7bo6b3o4bo2bo4bo5bo3bo4b3o$1142bo3bo7bo5b2obo4bo6b3o4bo3b
o4b2o$1142bo3bo8bobo2b3o5bo5b2obo8b2o$1146bo13b3o6bobo2b3o9b2o$1143bob
o14b3o11b3o7bobo$1161b2o11b3o7b3o$1175b2o9b2o$1186b3o$1140bo44b2o2bo$
1139b3o42bo2b2o$1138b2obo42bob2o$1138b3o39bo5b2o5b3o$1139b2o38b3o11bo
2bo$1178b2obo11bo$1178b3o12bo3bo$1178b3o12bo3bo$1179b2o12bo$1194bobo$
1155b3o$1139bo9bo5bo2bo$1138b3o7b3o4bo$1138bob2o5b2obo4bo$1139b3o5b3o
6bobo$1139b3o5b3o$1128b3o8b3o5b3o$1127bo2bo8b2o7b2o$1130bo$1130bo$
1127bobo2$1184b3o4bo$1144b3o7b3o27bo2bo2b3o$1144bo2bo5bo2bo5bo5b3o13bo
4b2obo$1144bo11bo4b3o3bo2bo5bo7bo3b4o$1144bo3bo7bo4bob2o5bo4b3o6bo5b2o
$1144bo3bo4bobo6b3o5bo4bob2o5bo2bo$1144bo17b3o2bobo6b3o6b2o$1145bobo
14b3o11b3o$1162b2o12b3o$1176b2o2$1140bo47b2o$1139b3o46b2o$1139bob2o$
1140b3o37bo4b3o5b3o$1140b2o37b3o4bo5bo2bo$1179bob2o3bo8bo$1180b3o8bo3b
o$1180b3o8bo3bo$1180b2o13bo$1192bobo$1155b3o$1139bo9bo4bo2bo$1138b3o7b
3o6bo$1137b2obo7bob2o5bo$1137b3o9b3o2bobo$1137b3o9b3o$1128b3o6b3o9b3o$
991bobo134bo2bo6b2o9b2o$989bo3bo134bo$989b2ob2o134bo$990b2o137bobo2$
993bo190b3o4bo$993bo150b3o7b3o26bo2bo3b3o$1143bo2bo7bo2bo4bo5b3o15bo3b
ob2o$1146bo7bo6b3o4bo2bo4bo5bo3bo4b3o$1142bo3bo7bo5b2obo4bo6b3o4bo3bo
4b2o$1142bo3bo8bobo2b3o5bo5b2obo8b2o$1146bo13b3o6bobo2b3o6bo2b2o$1143b
obo14b3o11b3o8b2o$1161b2o11b3o$1175b2o2$1140bo$1139b3o46b2o$1138b2obo$
1138b3o39bo4bo3bo3b3o$1139b2o38b3o3bo2bo4bo2bo$1178b2obo4bo6bo$1178b3o
12bo3bo$1178b3o12bo3bo$1179b2o12bo$1194bobo$1155b3o$1139bo9bo5bo2bo$
989b3o146b3o7b3o4bo$989bo2bo145bob2o5b2obo4bo$989bo149b3o5b3o6bobo$
989bo149b3o5b3o$990bobo135b3o8b3o5b3o$1127bo2bo8b2o7b2o$1130bo$993b3o
134bo$925b3o65bo2bo130bobo$925bo67bo$926bo66bo190b3o4bo$994bobo147b3o
7b3o27bo2bo2b3o$1144bo2bo5bo2bo5bo5b3o13bo4b2obo$1144bo11bo4b3o3bo2bo
5bo7bo3b4o$1144bo3bo7bo4bob2o5bo4b3o6bo5b2o$1144bo3bo4bobo6b3o5bo4bob
2o5bo2bo$1144bo17b3o2bobo6b3o6b2o$1145bobo14b3o11b3o6bo$1162b2o12b3o7b
o$1176b2o8bo2$1140bo$1139b3o$1139bob2o$1140b3o37bo12b3o$1140b2o37b3o
10bo2bo$1179bob2o12bo$1180b3o8bo3bo$1180b3o8bo3bo$1180b2o13bo$1192bobo
$1155b3o$1139bo9bo4bo2bo$989b3o146b3o7b3o6bo$988bo2bo145b2obo7bob2o5bo
$991bo145b3o9b3o2bobo$991bo145b3o9b3o$988bobo137b3o6b3o9b3o$1128bo2bo
6b2o9b2o$1128bo$993b3o132bo$992bo2bo133bobo$858b2o135bo$858bobo134bo
188b3o4bo$858bo133bobo149b3o7b3o26bo2bo3b3o$1143bo2bo7bo2bo4bo5b3o15bo
3bob2o$1146bo7bo6b3o4bo2bo4bo5bo3bo4b3o$1142bo3bo7bo5b2obo4bo6b3o4bo3b
o4b2o$1142bo3bo8bobo2b3o5bo5b2obo8b2o$1146bo13b3o6bobo2b3o9b2o$1143bob
o14b3o11b3o7bobo$1161b2o11b3o$1175b2o8b2o2$1140bo$1139b3o$1138b2obo$
1138b3o39bo12b3o$1139b2o38b3o11bo2bo$1178b2obo11bo$1178b3o12bo3bo$
1178b3o12bo3bo$1179b2o12bo$1194bobo$1155b3o$1139bo9bo5bo2bo$989b3o146b
3o7b3o4bo$989bo2bo145bob2o5b2obo4bo$989bo149b3o5b3o6bobo$989bo149b3o5b
3o$990bobo135b3o8b3o5b3o$1127bo2bo8b2o7b2o$1130bo$993b3o134bo$993bo2bo
130bobo$993bo$993bo190b3o4bo$790b3o201bobo147b3o7b3o27bo2bo2b3o$790bo
353bo2bo5bo2bo5bo5b3o13bo4b2obo$791bo352bo11bo4b3o3bo2bo5bo7bo3b4o$
1144bo3bo7bo4bob2o5bo4b3o6bo5b2o$1144bo3bo4bobo6b3o5bo4bob2o5bo2bo$
1144bo17b3o2bobo6b3o6b2o$1145bobo14b3o11b3o6bo$1162b2o12b3o6b3o$1176b
2o7b3o2$1140bo$1139b3o$1139bob2o$1140b3o37bo12b3o$1140b2o37b3o10bo2bo$
1179bob2o12bo$1180b3o8bo3bo$1180b3o8bo3bo$1180b2o13bo$1192bobo$1155b3o
$1139bo9bo4bo2bo$989b3o146b3o7b3o6bo$988bo2bo145b2obo7bob2o5bo$991bo
145b3o9b3o2bobo$991bo145b3o9b3o$988bobo137b3o6b3o9b3o$1128bo2bo6b2o9b
2o$1128bo$993b3o132bo$992bo2bo133bobo$995bo$995bo188b3o4bo$992bobo149b
3o7b3o26bo2bo3b3o$723b2o418bo2bo7bo2bo4bo5b3o15bo3bob2o$723bobo420bo7b
o6b3o4bo2bo4bo5bo3bo4b3o$723bo418bo3bo7bo5b2obo4bo6b3o4bo3bo4b2o$1142b
o3bo8bobo2b3o5bo5b2obo8b2o$1146bo13b3o6bobo2b3o9b2o$1143bobo14b3o11b3o
6b2ob2o$1161b2o11b3o6b2o2bo$1175b2o7b2ob2o$1185bobo$1140bo45bo$1139b3o
$1138b2obo$1138b3o39bo12b3o$1139b2o38b3o11bo2bo$1178b2obo11bo$1178b3o
12bo3bo$1178b3o12bo3bo$1179b2o12bo$1194bobo$1155b3o$1139bo9bo5bo2bo$
989b3o146b3o7b3o4bo$989bo2bo145bob2o5b2obo4bo$989bo149b3o5b3o6bobo$
989bo149b3o5b3o$990bobo135b3o8b3o5b3o$1127bo2bo8b2o7b2o$1130bo$993b3o
134bo$993bo2bo130bobo$923bo69bo$923bobo67bo190b3o4bo$923b2o69bobo147b
3o7b3o27bo2bo2b3o$1144bo2bo5bo2bo5bo5b3o13bo4b2obo$1144bo11bo4b3o3bo2b
o5bo7bo3b4o$655b3o486bo3bo7bo4bob2o5bo4b3o6bo5b2o$655bo488bo3bo4bobo6b
3o5bo4bob2o5bo2bo$656bo487bo17b3o2bobo6b3o6b2o$1145bobo14b3o11b3o5bo$
1162b2o12b3o$1176b2o5bo3b2o$1185bob2o$1140bo43b2o2bo$1139b3o43b3o$
1139bob2o$1140b3o37bo12b3o$1140b2o37b3o10bo2bo$1179bob2o12bo$1180b3o8b
o3bo$1180b3o8bo3bo$1180b2o13bo$1192bobo$1155b3o$1139bo9bo4bo2bo$989b3o
146b3o7b3o6bo$988bo2bo145b2obo7bob2o5bo$991bo145b3o9b3o2bobo$991bo145b
3o9b3o$988bobo137b3o6b3o9b3o$1128bo2bo6b2o9b2o$1128bo$993b3o132bo$992b
o2bo133bobo$995bo$995bo188b3o4bo$992bobo149b3o7b3o26bo2bo3b3o$1143bo2b
o7bo2bo4bo5b3o15bo3bob2o$1146bo7bo6b3o4bo2bo4bo5bo3bo4b3o$1142bo3bo7bo
5b2obo4bo6b3o4bo3bo4b2o$588b2o552bo3bo8bobo2b3o5bo5b2obo8b2o$588bobo
555bo13b3o6bobo2b3o9b2o$588bo554bobo14b3o11b3o7bobo$1161b2o11b3o7b3o$
1175b2o9b2o$1186b3o$1140bo44b2o2bo$1139b3o42bo2b2o$1138b2obo42bob2o$
1138b3o39bo5b2o5b3o$1139b2o38b3o11bo2bo$1178b2obo11bo$1178b3o12bo3bo$
1178b3o12bo3bo$1179b2o12bo$1194bobo$1155b3o$1139bo9bo5bo2bo$989b3o146b
3o7b3o4bo$989bo2bo145bob2o5b2obo4bo$989bo149b3o5b3o6bobo$989bo149b3o5b
3o$990bobo135b3o8b3o5b3o$1127bo2bo8b2o7b2o$1130bo$993b3o134bo$993bo2bo
130bobo$993bo$993bo190b3o4bo$994bobo147b3o7b3o27bo2bo2b3o$1144bo2bo5bo
2bo5bo5b3o13bo4b2obo$1144bo11bo4b3o3bo2bo5bo7bo3b4o$1144bo3bo7bo4bob2o
5bo4b3o6bo5b2o$1144bo3bo4bobo6b3o5bo4bob2o5bo2bo$1144bo17b3o2bobo6b3o
6b2o$520b3o622bobo14b3o11b3o$520bo641b2o12b3o$521bo654b2o2$1140bo47b2o
$1139b3o46b2o$1139bob2o$1140b3o37bo4b3o5b3o$1140b2o37b3o4bo5bo2bo$
1179bob2o3bo8bo$1180b3o8bo3bo$1180b3o8bo3bo$1180b2o13bo$1192bobo$1155b
3o$1139bo9bo4bo2bo$1138b3o7b3o6bo$1137b2obo7bob2o5bo$1137b3o9b3o2bobo$
1137b3o9b3o$1128b3o6b3o9b3o$1128bo2bo6b2o9b2o$1128bo$1128bo$1129bobo2$
1184b3o4bo$1144b3o7b3o26bo2bo3b3o$1143bo2bo7bo2bo4bo5b3o15bo3bob2o$
1146bo7bo6b3o4bo2bo4bo5bo3bo4b3o$1142bo3bo7bo5b2obo4bo6b3o4bo3bo4b2o$
1142bo3bo8bobo2b3o5bo5b2obo8b2o$1146bo13b3o6bobo2b3o6bo2b2o$1143bobo
14b3o11b3o8b2o$453b2o706b2o11b3o$453bobo719b2o$453bo$1140bo$1139b3o46b
2o$1138b2obo$1138b3o39bo4bo3bo3b3o$1139b2o38b3o3bo2bo4bo2bo$1178b2obo
4bo6bo$1178b3o12bo3bo$1178b3o12bo3bo$1179b2o12bo$1194bobo$1155b3o$
1139bo9bo5bo2bo$1138b3o7b3o4bo$1138bob2o5b2obo4bo$1139b3o5b3o6bobo$
1139b3o5b3o$1128b3o8b3o5b3o$1127bo2bo8b2o7b2o$1130bo$1130bo$1127bobo2$
1184b3o4bo$1144b3o7b3o27bo2bo2b3o$1144bo2bo5bo2bo5bo5b3o13bo4b2obo$
1144bo11bo4b3o3bo2bo5bo7bo3b4o$1144bo3bo7bo4bob2o5bo4b3o6bo5b2o$1144bo
3bo4bobo6b3o5bo4bob2o5bo2bo$1144bo17b3o2bobo6b3o6b2o$1145bobo14b3o11b
3o6bo$1162b2o12b3o7bo$1176b2o8bo$385b3o$385bo754bo$386bo752b3o$1139bob
2o$1140b3o37bo12b3o$1140b2o37b3o10bo2bo$1179bob2o12bo$1180b3o8bo3bo$
1180b3o8bo3bo$1180b2o13bo$1192bobo$1155b3o$1139bo9bo4bo2bo$1138b3o7b3o
6bo$1137b2obo7bob2o5bo$1137b3o9b3o2bobo$1137b3o9b3o$1128b3o6b3o9b3o$
1128bo2bo6b2o9b2o$1128bo$1128bo$1129bobo2$1184b3o4bo$1144b3o7b3o26bo2b
o3b3o$1143bo2bo7bo2bo4bo5b3o15bo3bob2o$856bo289bo7bo6b3o4bo2bo4bo5bo3b
o4b3o$855bo286bo3bo7bo5b2obo4bo6b3o4bo3bo4b2o$855b3o284bo3bo8bobo2b3o
5bo5b2obo8b2o$1146bo13b3o6bobo2b3o9b2o$1143bobo14b3o11b3o7bobo$1161b2o
11b3o$1175b2o8b2o2$318b2o820bo$318bobo818b3o$318bo819b2obo$1138b3o39bo
12b3o$1139b2o38b3o11bo2bo$1178b2obo11bo$1178b3o12bo3bo$1178b3o12bo3bo$
1179b2o12bo$1194bobo$1155b3o$1139bo9bo5bo2bo$1138b3o7b3o4bo$1138bob2o
5b2obo4bo$1139b3o5b3o6bobo$1139b3o5b3o$1128b3o8b3o5b3o$1127bo2bo8b2o7b
2o$1130bo$1130bo$1127bobo2$1184b3o4bo$1144b3o7b3o27bo2bo2b3o$1144bo2bo
5bo2bo5bo5b3o13bo4b2obo$1144bo11bo4b3o3bo2bo5bo7bo3b4o$1144bo3bo7bo4bo
b2o5bo4b3o6bo5b2o$1144bo3bo4bobo6b3o5bo4bob2o5bo2bo$1144bo17b3o2bobo6b
3o6b2o$1145bobo14b3o11b3o6bo$1162b2o12b3o6b3o$1176b2o7b3o2$1140bo$
1139b3o$250b3o886bob2o$250bo889b3o37bo12b3o$251bo888b2o37b3o10bo2bo$
1179bob2o12bo$1180b3o8bo3bo$1180b3o8bo3bo$1180b2o13bo$1192bobo$1155b3o
$1139bo9bo4bo2bo$1138b3o7b3o6bo$1137b2obo7bob2o5bo$1137b3o9b3o2bobo$
1137b3o9b3o$1128b3o6b3o9b3o$1128bo2bo6b2o9b2o$1128bo$1128bo$1129bobo2$
1184b3o4bo$1144b3o7b3o26bo2bo3b3o$1143bo2bo7bo2bo4bo5b3o15bo3bob2o$
1146bo7bo6b3o4bo2bo4bo5bo3bo4b3o$1142bo3bo7bo5b2obo4bo6b3o4bo3bo4b2o$
1142bo3bo8bobo2b3o5bo5b2obo8b2o$1146bo13b3o6bobo2b3o9b2o$1143bobo14b3o
11b3o6b2ob2o$1161b2o11b3o6b2o2bo$1175b2o7b2ob2o$1185bobo$1140bo45bo$
1139b3o$1138b2obo$183b2o953b3o39bo12b3o$183bobo953b2o38b3o11bo2bo$183b
o994b2obo11bo$1178b3o12bo3bo$1178b3o12bo3bo$1179b2o12bo$1194bobo$1155b
3o$1139bo9bo5bo2bo$1138b3o7b3o4bo$1138bob2o5b2obo4bo$1139b3o5b3o6bobo$
1139b3o5b3o$1128b3o8b3o5b3o$1127bo2bo8b2o7b2o$1130bo$1130bo$1127bobo2$
1184b3o4bo$1144b3o7b3o27bo2bo2b3o$1144bo2bo5bo2bo5bo5b3o13bo4b2obo$
1144bo11bo4b3o3bo2bo5bo7bo3b4o$1144bo3bo7bo4bob2o5bo4b3o6bo5b2o$1144bo
3bo4bobo6b3o5bo4bob2o5bo2bo$1144bo17b3o2bobo6b3o6b2o$1145bobo14b3o11b
3o5bo$1162b2o12b3o$1176b2o5bo3b2o$1185bob2o$1140bo43b2o2bo$1139b3o43b
3o$1139bob2o$1140b3o37bo12b3o$1140b2o37b3o10bo2bo$115b3o1061bob2o12bo$
115bo1064b3o8bo3bo$116bo1063b3o8bo3bo$1180b2o13bo$1192bobo$1155b3o$
1139bo9bo4bo2bo$1138b3o7b3o6bo$1137b2obo7bob2o5bo$1137b3o9b3o2bobo$
1137b3o9b3o$1128b3o6b3o9b3o$1128bo2bo6b2o9b2o$1128bo$1128bo$1129bobo2$
1184b3o4bo$1144b3o7b3o26bo2bo3b3o$1143bo2bo7bo2bo4bo5b3o15bo3bob2o$
1146bo7bo6b3o4bo2bo4bo5bo3bo4b3o$1142bo3bo7bo5b2obo4bo6b3o4bo3bo4b2o$
1142bo3bo8bobo2b3o5bo5b2obo8b2o$1146bo13b3o6bobo2b3o9b2o$1143bobo14b3o
11b3o7bobo$1161b2o11b3o7b3o$1175b2o9b2o$1186b3o$1140bo44b2o2bo$1139b3o
42bo2b2o$1138b2obo42bob2o$1138b3o39bo5b2o5b3o$1139b2o38b3o11bo2bo$
1178b2obo11bo$48b2o1128b3o12bo3bo$48bobo1127b3o12bo3bo$48bo1130b2o12bo
$1194bobo$1155b3o$1139bo9bo5bo2bo$1138b3o7b3o4bo$1138bob2o5b2obo4bo$
1139b3o5b3o6bobo$1139b3o5b3o$1128b3o8b3o5b3o$1127bo2bo8b2o7b2o$1130bo$
1130bo$1127bobo2$1184b3o4bo$1144b3o7b3o27bo2bo2b3o$1144bo2bo5bo2bo5bo
5b3o13bo4b2obo$1144bo11bo4b3o3bo2bo5bo7bo3b4o$1144bo3bo7bo4bob2o5bo4b
3o6bo5b2o$1144bo3bo4bobo6b3o5bo4bob2o5bo2bo$1144bo17b3o2bobo6b3o6b2o$
1145bobo14b3o11b3o$1162b2o12b3o$1176b2o2$1140bo47b2o$1139b3o46b2o$
1139bob2o$1140b3o37bo4b3o5b3o$1140b2o37b3o4bo5bo2bo$1179bob2o3bo8bo$
1180b3o8bo3bo$1180b3o8bo3bo$1180b2o13bo$1192bobo$1155b3o$1139bo9bo4bo
2bo$1138b3o7b3o6bo$1137b2obo7bob2o5bo$1137b3o9b3o2bobo$1137b3o9b3o$
1128b3o6b3o9b3o$1128bo2bo6b2o9b2o$1128bo$2bo1125bo$b3o1125bobo$2obo$3o
1181b3o4bo$b2o1141b3o7b3o26bo2bo3b3o$1143bo2bo7bo2bo4bo5b3o15bo3bob2o$
1146bo7bo6b3o4bo2bo4bo5bo3bo4b3o$1142bo3bo7bo5b2obo4bo6b3o4bo3bo4b2o$
1142bo3bo8bobo2b3o5bo5b2obo8b2o$1146bo13b3o6bobo2b3o6bo2b2o$1143bobo
14b3o11b3o8b2o$9bo1151b2o11b3o$8bobo1164b2o$8bobo$9bo1130bo$1139b3o46b
2o$1138b2obo$1138b3o39bo4bo3bo3b3o$1139b2o38b3o3bo2bo4bo2bo$1178b2obo
4bo6bo$1178b3o12bo3bo$1178b3o12bo3bo$1179b2o12bo$1194bobo$1155b3o$
1139bo9bo5bo2bo$1138b3o7b3o4bo$1138bob2o5b2obo4bo$1139b3o5b3o6bobo$
1139b3o5b3o$1128b3o8b3o5b3o$1127bo2bo8b2o7b2o$1130bo$2bo1127bo$b3o
1123bobo$bob2o$2b3o1179b3o4bo$2b2o1140b3o7b3o27bo2bo2b3o$1144bo2bo5bo
2bo5bo5b3o13bo4b2obo$1144bo11bo4b3o3bo2bo5bo7bo3b4o$1144bo3bo7bo4bob2o
5bo4b3o6bo5b2o$1144bo3bo4bobo6b3o5bo4bob2o5bo2bo$1144bo17b3o2bobo6b3o
6b2o$1145bobo14b3o11b3o6bo$1162b2o12b3o7bo$1176b2o8bo2$1140bo$768bo
370b3o$767bo371bob2o$767b3o370b3o37bo12b3o$1140b2o37b3o10bo2bo$1179bob
2o12bo$1180b3o8bo3bo$1180b3o8bo3bo$1180b2o13bo$1192bobo$1155b3o$1139bo
9bo4bo2bo$1138b3o7b3o6bo$1137b2obo7bob2o5bo$1137b3o9b3o2bobo$1137b3o9b
3o$1128b3o6b3o9b3o$1128bo2bo6b2o9b2o$1128bo$2bo1125bo$b3o1125bobo$2obo
$3o1181b3o4bo$b2o1141b3o7b3o26bo2bo3b3o$1143bo2bo7bo2bo4bo5b3o15bo3bob
2o$1146bo7bo6b3o4bo2bo4bo5bo3bo4b3o$1142bo3bo7bo5b2obo4bo6b3o4bo3bo4b
2o$1142bo3bo8bobo2b3o5bo5b2obo8b2o$1146bo13b3o6bobo2b3o9b2o$1143bobo
14b3o11b3o7bobo$1161b2o11b3o$1175b2o8b2o2$1140bo$1139b3o$1138b2obo$
1138b3o39bo12b3o$1139b2o38b3o11bo2bo$1178b2obo11bo$1178b3o12bo3bo$
1178b3o12bo3bo$1179b2o12bo$1194bobo$1155b3o$1139bo9bo5bo2bo$1138b3o7b
3o4bo$1138bob2o5b2obo4bo$1139b3o5b3o6bobo$1139b3o5b3o$1128b3o8b3o5b3o$
1127bo2bo8b2o7b2o$1130bo$2bo1127bo$b3o1123bobo$bob2o$2b3o1179b3o4bo$2b
2o1140b3o7b3o27bo2bo2b3o$1144bo2bo5bo2bo5bo5b3o13bo4b2obo$1144bo11bo4b
3o3bo2bo5bo7bo3b4o$1144bo3bo7bo4bob2o5bo4b3o6bo5b2o$1144bo3bo4bobo6b3o
5bo4bob2o5bo2bo$1144bo17b3o2bobo6b3o6b2o$1145bobo14b3o11b3o6bo$1162b2o
12b3o6b3o$1176b2o7b3o2$9bo1130bo$8bobo1128b3o$8bobo1128bob2o$9bo1130b
3o37bo12b3o$1140b2o37b3o10bo2bo$1179bob2o12bo$1180b3o8bo3bo$1180b3o8bo
3bo$1180b2o13bo$1192bobo$1155b3o$1139bo9bo4bo2bo$1138b3o7b3o6bo$1137b
2obo7bob2o5bo$1137b3o9b3o2bobo$1137b3o9b3o$1128b3o6b3o9b3o$1128bo2bo6b
2o9b2o$1128bo$2bo1125bo$b3o1125bobo$2obo$3o1181b3o4bo$b2o1141b3o7b3o
26bo2bo3b3o$1143bo2bo7bo2bo4bo5b3o15bo3bob2o$1146bo7bo6b3o4bo2bo4bo5bo
3bo4b3o$1142bo3bo7bo5b2obo4bo6b3o4bo3bo4b2o$1142bo3bo8bobo2b3o5bo5b2ob
o8b2o$1146bo13b3o6bobo2b3o9b2o$1143bobo14b3o11b3o6b2ob2o$1161b2o11b3o
6b2o2bo$1175b2o7b2ob2o$1185bobo$1140bo45bo$1139b3o$1138b2obo$1138b3o
39bo12b3o$1139b2o38b3o11bo2bo$1178b2obo11bo$1178b3o12bo3bo$1178b3o12bo
3bo$1179b2o12bo$1194bobo$1155b3o$1139bo9bo5bo2bo$1138b3o7b3o4bo$1138bo
b2o5b2obo4bo$1139b3o5b3o6bobo$1139b3o5b3o$1128b3o8b3o5b3o$1127bo2bo8b
2o7b2o$1130bo$2bo1127bo$b3o1123bobo$bob2o$2b3o1179b3o4bo$2b2o1140b3o7b
3o27bo2bo2b3o$1144bo2bo5bo2bo5bo5b3o13bo4b2obo$1144bo11bo4b3o3bo2bo5bo
7bo3b4o$1144bo3bo7bo4bob2o5bo4b3o6bo5b2o$1144bo3bo4bobo6b3o5bo4bob2o5b
o2bo$1144bo17b3o2bobo6b3o6b2o$1145bobo14b3o11b3o5bo$1162b2o12b3o$1176b
2o5bo3b2o$1185bob2o$1140bo43b2o2bo$1139b3o43b3o$1139bob2o$1140b3o37bo
12b3o$1140b2o37b3o10bo2bo$1179bob2o12bo$1180b3o8bo3bo$1180b3o8bo3bo$
1180b2o13bo$1192bobo$1155b3o$1139bo9bo4bo2bo$1138b3o7b3o6bo$1137b2obo
7bob2o5bo$1137b3o9b3o2bobo$1137b3o9b3o$1128b3o6b3o9b3o$1128bo2bo6b2o9b
2o$1128bo$2bo1125bo$b3o1125bobo$2obo$3o1181b3o4bo$b2o1141b3o7b3o26bo2b
o3b3o$1143bo2bo7bo2bo4bo5b3o15bo3bob2o$1146bo7bo6b3o4bo2bo4bo5bo3bo4b
3o$1142bo3bo7bo5b2obo4bo6b3o4bo3bo4b2o$1142bo3bo8bobo2b3o5bo5b2obo8b2o
$1146bo13b3o6bobo2b3o9b2o$1143bobo14b3o11b3o7bobo$1161b2o11b3o7b3o$
1175b2o9b2o$1186b3o$1140bo44b2o2bo$1139b3o42bo2b2o$1138b2obo42bob2o$9b
o1128b3o39bo5b2o5b3o$8bobo1128b2o38b3o11bo2bo$8bobo1167b2obo11bo$9bo
690bo477b3o12bo3bo$700bobo475b3o12bo3bo$700b2o477b2o12bo$1194bobo$
1155b3o$1139bo9bo5bo2bo$1138b3o7b3o4bo$1138bob2o5b2obo4bo$1139b3o5b3o
6bobo$1139b3o5b3o$1128b3o8b3o5b3o$1127bo2bo8b2o7b2o$1130bo$2bo1127bo$b
3o1123bobo$bob2o$2b3o1179b3o4bo$2b2o1140b3o7b3o27bo2bo2b3o$1144bo2bo5b
o2bo5bo5b3o13bo4b2obo$1144bo11bo4b3o3bo2bo5bo7bo3b4o$1144bo3bo7bo4bob
2o5bo4b3o6bo5b2o$1144bo3bo4bobo6b3o5bo4bob2o5bo2bo$1144bo17b3o2bobo6b
3o6b2o$1145bobo14b3o11b3o$1162b2o12b3o$1176b2o2$1140bo47b2o$1139b3o46b
2o$1139bob2o$1140b3o37bo4b3o5b3o$1140b2o37b3o4bo5bo2bo$1179bob2o3bo8bo
$1180b3o8bo3bo$1180b3o8bo3bo$1180b2o13bo$1192bobo$1155b3o$1139bo9bo4bo
2bo$1138b3o7b3o6bo$1137b2obo7bob2o5bo$1137b3o9b3o2bobo$1137b3o9b3o$
1128b3o6b3o9b3o$1128bo2bo6b2o9b2o$1128bo$2bo1125bo$b3o1125bobo$2obo$3o
1181b3o4bo$b2o1141b3o7b3o26bo2bo3b3o$1143bo2bo7bo2bo4bo5b3o15bo3bob2o$
1146bo7bo6b3o4bo2bo4bo5bo3bo4b3o$1142bo3bo7bo5b2obo4bo6b3o4bo3bo4b2o$
1142bo3bo8bobo2b3o5bo5b2obo8b2o$1146bo13b3o6bobo2b3o6bo2b2o$1143bobo
14b3o11b3o8b2o$1161b2o11b3o$1175b2o2$1140bo$1139b3o46b2o$1138b2obo$
1138b3o39bo4bo3bo3b3o$1139b2o38b3o3bo2bo4bo2bo$1178b2obo4bo6bo$1178b3o
12bo3bo$1178b3o12bo3bo$1179b2o12bo$1194bobo$1155b3o$1139bo9bo5bo2bo$
1138b3o7b3o4bo$1138bob2o5b2obo4bo$1139b3o5b3o6bobo$1139b3o5b3o$1128b3o
8b3o5b3o$1127bo2bo8b2o7b2o$1130bo$2bo1127bo$b3o1123bobo$bob2o$2b3o
1179b3o4bo$2b2o1140b3o7b3o27bo2bo2b3o$1144bo2bo5bo2bo5bo5b3o13bo4b2obo
$1144bo11bo4b3o3bo2bo5bo7bo3b4o$1144bo3bo7bo4bob2o5bo4b3o6bo5b2o$1144b
o3bo4bobo6b3o5bo4bob2o5bo2bo$1144bo17b3o2bobo6b3o6b2o$1145bobo14b3o11b
3o6bo$1162b2o12b3o7bo$1176b2o8bo2$1140bo$1139b3o$1139bob2o$1140b3o37bo
12b3o$1140b2o37b3o10bo2bo$1179bob2o12bo$9bo1170b3o8bo3bo$8bobo1169b3o
8bo3bo$8bobo1169b2o13bo$9bo1182bobo$1155b3o$1139bo9bo4bo2bo$1138b3o7b
3o6bo$1137b2obo7bob2o5bo$1137b3o9b3o2bobo$1137b3o9b3o$1128b3o6b3o9b3o$
1128bo2bo6b2o9b2o$1128bo$2bo1125bo$b3o1125bobo$2obo$3o$b2o1141b3o$
1143bo2bo$1146bo$1142bo3bo$1142bo3bo$1146bo$1143bobo4$1140bo$14bo1124b
3o$13b3o1122b2obo$13bob2o1121b3o$14b3o1122b2o$14b3o$14b2o13$2bo$b3o$bo
b2o$2b3o$2b2o11$14bo$13b3o$12b2obo$12b3o$12b3o$13b2o4$633bo$632bo$632b
3o7$2bo$b3o$2obo$3o$b2o11$14bo$13b3o$13bob2o$14b3o$14b3o$14b2o13$2bo$b
3o$bob2o$2b3o$2b2o11$14bo$13b3o$12b2obo$12b3o$12b3o$13b2o13$2bo$b3o$2o
bo$3o$b2o5$65bo$66b2o$65b2o4$14bo$13b3o$13bob2o$14b3o$14b3o$14b2o13$2b
o$b3o$bob2o$2b3o$2b2o11$14bo$13b3o$12b2obo$12b3o$12b3o$13b2o13$2bo$b3o
$2obo$3o$b2o11$14bo$13b3o$13bob2o$14b3o$14b3o$14b2o9$565bo$565bobo$
565b2o2$2bo$b3o$bob2o$2b3o$2b2o11$14bo$13b3o$12b2obo$12b3o$12b3o$13b2o
13$2bo$b3o$2obo$3o$b2o11$14bo$13b3o$13bob2o$14b3o$14b3o$14b2o13$2bo$b
3o$bob2o$2b3o$2b2o10$132bobo$14bo118b2o$13b3o117bo$12b2obo$12b3o$12b3o
$13b2o13$2bo$b3o$2obo$3o$b2o11$14bo$13b3o$13bob2o$14b3o$14b3o$14b2o13$
2bo$b3o$bob2o$2b3o$2b2o11$14bo$13b3o$12b2obo$12b3o$12b3o$13b2o13$498bo
$497bo$497b3o13$14bo$13b3o$13bob2o$14b3o$14b3o$14b2o28$14bo$13b3o$12b
2obo$12b3o$12b3o$13b2o28$14bo$13b3o$13bob2o$14b3o183bo$14b3o184b2o$14b
2o184b2o28$14bo$13b3o$12b2obo$12b3o$12b3o$13b2o28$14bo$13b3o$13bob2o$
14b3o$14b3o$14b2o18$430bo$430bobo$430b2o8$14bo$13b3o$12b2obo$12b3o$12b
3o$13b2o28$14bo$13b3o$13bob2o$14b3o$14b3o$14b2o28$14bo$13b3o$12b2obo$
12b3o$12b3o$13b2o3$267bobo$268b2o$268bo23$14bo$13b3o$13bob2o$14b3o$14b
3o$14b2o28$14bo$13b3o$12b2obo$12b3o$12b3o$13b2o22$363bo$362bo$362b3o
83$330bo$328b2o$329b2o25$333bo$332b3o$331b2obo$331b3o$332b2o29$333bo$
332b3o$332bob2o$333b3o$333b2o21$295bo$295bobo$295b2o6$290b3o5b3o32bo$
290bo2bo4bo2bo30b3o$290bo7bo32b2obo$290bo3bo3bo3bo28b3o$290bo7bo3bo29b
2o$291bobo4bo$299bobo7$268bo$267b2o$267bobo$291bo7bo$290b3o5b3o$289b2o
bo4b2obo$289b3o5b3o$289b3o5b3o$290b2o5b3o$298b2o9$233b3o$233bo$234bo
55b3o5b3o32bo$289bo2bo4bo2bo31b3o$292bo7bo31bob2o$288bo3bo3bo3bo32b3o$
292bo3bo3bo32b2o$289bobo8bo$297bobo10$291bo7bo$290b3o5b3o$290bob2o4bob
2o$291b3o5b3o$291b3o5b3o$291b2o6b3o$299b2o11$290b3o5b3o32bo$290bo2bo4b
o2bo30b3o$290bo7bo32b2obo$290bo3bo3bo3bo28b3o$290bo7bo3bo29b2o$291bobo
4bo$299bobo2$259bo$258bo$258b3o6$291bo7bo$290b3o5b3o$289b2obo4b2obo$
289b3o5b3o$289b3o5b3o$290b2o5b3o$298b2o11$290b3o5b3o$289bo2bo4bo2bo$
292bo7bo$288bo3bo3bo3bo$292bo3bo3bo$289bobo8bo$297bobo10$291bo7bo$290b
3o5b3o$290bob2o4bob2o$291b3o5b3o$291b3o5b3o$291b2o6b3o$299b2o11$290b3o
5b3o$290bo2bo4bo2bo$290bo7bo$290bo3bo3bo3bo$290bo7bo3bo$291bobo4bo$
299bobo10$291bo7bo$290b3o5b3o$289b2obo4b2obo$289b3o5b3o$289b3o5b3o$
290b2o5b3o$298b2o5$226bo$224b2o$225b2o4$290b3o5b3o$289bo2bo4bo2bo$292b
o7bo$288bo3bo3bo3bo$292bo3bo3bo$289bobo8bo$297bobo10$291bo7bo$290b3o5b
3o$290bob2o4bob2o$291b3o5b3o$291b3o5b3o$291b2o6b3o$299b2o11$290b3o5b3o
$290bo2bo4bo2bo$290bo7bo$290bo3bo3bo3bo$290bo7bo3bo$291bobo4bo$299bobo
10$291bo7bo$290b3o5b3o$289b2obo4b2obo$289b3o5b3o$289b3o5b3o$290b2o5b3o
$298b2o!
[pattern]

[HartmutHolzwart]

I‘m still struggling how to synthesize a Coe ship using standard methods.

It must be done in three steps due to the timing constraints

1) insert an LWSS in the helix. This is standard

Code: Select all

x = 56, y = 115, rule = B3/S23
9$50b3o$50bo2bo$50bo$50bo$51bobo9$10bobo$11b2o$11bo2$12bo$13bo$11b3o
14$50b3o$49bo2bo$52bo$52bo$49bobo29$50b3o$50bo2bo$50bo$50bo$51bobo21$
14b2o$13bobo$15bo4$8b2o$7bobo$9bo40b3o$49bo2bo$52bo$52bo$49bobo!

2) amend that to an MWSS on LWSS 3 convoy
3) convert the convoy to the Coe ship using a two glider collision. This is also standard:

Code: Select all

x = 28, y = 25, rule = B3/S23
$9bo$7bobo$8b2o$27bo$27bo10$20bo$19b3o3b3o$9b2o7b2obo2bo2bo$8bobo7b3o
6bo$10bo7b3o2bo3bo$19b2o2bo2bo!

The issue is with step 2). The usual methods to build the MWSS collide with the existing LWSS. The one method known that works is via a boat and has two issues:
A) I don’t know how to place the boat in that orientiation one-sided. Kickback is way too slow for the purpose.
B) Even if I could find another way to create that boat, I must be very quick

Alternatively, edge-shooting MWSS seeds could help, but I couldn’t find any so far.

Would it be possible to use QuFince to come up with a replacement for the boat based synthesis method that is quick enough?

[HartmutHolzwart]

tobe more concrete on step 2. I'd need a quick enough replacement for the following reaction:

Code: Select all

x = 27, y = 24, rule = B3/S23
$19bo$18b3o$17b2obo$8bo8b3o$9bo7b3o$7b3o8b2o5$10b2o$10bobo$11bo$16b3o$
4b2o10bo2bo$5b2o9bo$4bo11bo$17bobo!