## Building a reverse caber-tosser

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

### Re: Building a reverse caber-tosser

Yes, it can construct itself, by roughly the following sequence of operations:

• Construct a universal computer with some binary stream B.
• Feed a binary stream A into the computer, where A is the integer len(B) encoded in some universal prefix-free coding.
• Feed B into the computer.
• Feed a prefix-free 'cleanup' program C into the computer.

So the overall recipe is BABC, and it produces a universal computer initialised with binary tapes containing A, B and C. The computer then runs the cleanup program C to remove all of the detritus (the Cordership has crashed by this point) to leave just itself and these tapes A, B, C. It then concatenates them to form BABC (the original recipe, in binary) and converts this into unary. Using this, it constructs an immense Blockic seed of OTTs which, when activated, produces the original glider synthesis. Finally, it self-destructs and fires a single glider at the Blockic seed, triggering it.

For 'practicality', B should bootstrap the construction of a block-keeper, followed by a DBCA (decoder + better construction arm), then finally the universal computer-constructor.

Your conclusion is correct: if your glider count of 324 is valid, then there are huge sprawling SMOGs with minimum population 1620 of every velocity strictly lower than the vacuum speed limit.
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calcyman

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### Re: Building a reverse caber-tosser

this design is for a constructor with a one time tape and a construction arm, but no tape copier.

first you read the tape to do a bunch of important things
- get a better construction arm
- destroy BLSE
- get a cordership catcher
- get a constructor that builds a still life everytime the cordership hits
- get a pusher component that can emit twice the number of push instructions for every input given
*1st input: outputs 1 push, 2nd input: outputs 2 pushes, 3rd input: 4 pushes
*the computer must only start testing still lives after the cordership catcher detects the approaching cordership

second the next part of the tape just repeats itself so the newly constructed tape copier can copy it.

when the tape ends, signalled by a destroyed cordership, the pusher component reads the line of still lives made by the constructor, and pushes an elbow the corresponding amount of times each time it reads a still life.

if we modify the constructor to have a tape copier, it would be easy-ish. it just keeps on pushing a still life until the cordership arrives, then constructs a cordership.
Last edited by Redstoneboi on June 8th, 2018, 8:29 am, edited 1 time in total.
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Redstoneboi

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### Re: Building a reverse caber-tosser

The upper speed limit for these would be c/4 due to the usage of gliders, right, similarly to the Caterloopillars?

77topaz

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### Re: Building a reverse caber-tosser

77topaz wrote:The upper speed limit for these would be c/4 due to the usage of gliders, right, similarly to the Caterloopillars?

that is WAY up. it uses corderships, which are c/12.
c(>^x^<c)~
This is Fluffy the cat.
Fluffy wants to discover new things that everyone likes.
Fluffy likes to watch spaceship guns in Golly.

There’s one problem,

Fluffy doesn’t exist :(

Redstoneboi

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### Re: Building a reverse caber-tosser

77topaz wrote:The upper speed limit for these would be c/4 due to the usage of gliders, right, similarly to the Caterloopillars?
The speed limit would just be the speed limit for ships in general, which is c/4 diagonally and c/2 orthogonally. The use of gliders and corderships doesn't really make a difference, since they can be used to create a new constructor.

Macbi

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### Re: Building a reverse caber-tosser

Macbi wrote:
77topaz wrote:The upper speed limit for these would be c/4 due to the usage of gliders, right, similarly to the Caterloopillars?
The speed limit would just be the speed limit for ships in general, which is c/4 diagonally and c/2 orthogonally. The use of gliders and corderships doesn't really make a difference, since they can be used to create a new constructor.

At least that's the argument: the limit speed of a Spaceship Made of Gliders is the fastest speed that you can push an object away from your location, without it getting away from you permanently. For c/2 orthogonal, that involves something like starting a blinker puffer, then burning it when it gets long enough and leaving a target for unidirectional construction (with *WSSes) (?!?).

For c/4, you could do the same, then send a *WSS from that target sideways to intersect with a glider, again leaving a target but this time for a more conventional construction with a unidirectional glider salvo. These aren't necessarily slow salvos, but slow salvos work and are the easiest to encode.

calcyman wrote:Your conclusion is correct: if your glider count of 324 is valid, then there are huge sprawling SMOGs with minimum population 1620 of every velocity strictly lower than the vacuum speed limit.

Is it really certain that your "immense Blockic seed of OTTs" that build, among other things, a Very^{ridiculousnumber} Far Away Cordership, can be constructed and triggered in an amount of time that's negligible relative to the time needed to push out that initial faraway target? That's a requirement for approaching the vacuum speed limit, I think.

I guess there's no reason why that couldn't be done, with a sufficiently clever computer built at some point to do all the bit-collecting and waiting around to light the blinker fuses at the exact right times.

Seems like the lowest possible period of one of these SMOGs is proportional to 2^(number of bits in the total recipe), at the least. So... um... I don't think oscar.lua is going to be verifying the period of one of these any time soon.

dvgrn
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### Re: Building a reverse caber-tosser

dvgrn wrote:Is it really certain that your "immense Blockic seed of OTTs" that build, among other things, a Very^{ridiculousnumber} Far Away Cordership, can be constructed and triggered in an amount of time that's negligible relative to the time needed to push out that initial faraway target? That's a requirement for approaching the vacuum speed limit, I think.

Yes, for much the same reason as your following paragraph:

I guess there's no reason why that couldn't be done, with a sufficiently clever computer built at some point to do all the bit-collecting and waiting around to light the blinker fuses at the exact right times.

This would be an engineering nightmare, of course. By this point, the 'how about a unidimensional spaceship?' challenge seems incredibly tame by comparison.
What do you do with ill crystallographers? Take them to the mono-clinic!

calcyman

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### Re: Building a reverse caber-tosser

calcyman wrote:This would be an engineering nightmare, of course. By this point, the 'how about a unidimensional spaceship?' challenge seems incredibly tame by comparison.

Yes, and then a minimal SMOG is incredibly tame in comparison with that. And a mere quadratic-growth replicator is quite a bit easier still.

That last one we actually know how to do now. Mostly it's just a matter of stringing the pieces together. I wish someone would get their act together and do that, so I don't have to...

Anyway, congratulations all round! It looks like we're collectively cleverer than Gustavo's MIT hackers, since they needed several dozen more gliders to build their universal constructor.

I can see why the pattern was too big for Gustavo to post, now. I thought at the time that RLE for 386 gliders would have to be a fairly reasonable size -- but if they were using a faraway object to encode a recipe, a couple of the numbers in the RLE would have been several gigabytes each. That should teach me not to be so smug and self-assured about dismissing crazy-sounding ideas as impossible.

Those big run lengths would have made it tough to fit the pattern into canonical RLE, come to think of it, given the 70-character-per-line limit.

dvgrn
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### Re: Building a reverse caber-tosser

> 70 characters per line

Huh, wut?

Majestas32

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### Re: Building a reverse caber-tosser

Is there really one canonical line-length for RLEs? Because I've noticed that the line-length is different for RLEs from Catagolue compared to those from Golly, for example.

77topaz

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### Re: Building a reverse caber-tosser

77topaz wrote:Is there really one canonical line-length for RLEs? Because I've noticed that the line-length is different for RLEs from Catagolue compared to those from Golly, for example.

Catagolue makes very strange soup RLEs -- really more a form of ASCII format than real RLE, since there aren't any run lengths. The RLE definition on the LifeWiki mentions the 70-character maximum line lengths. The lines may be shorter, to avoid breaking a number in half or separating a number from a "b", "o", or "\$".

Really pretty much every RLE reader in existence can handle longer lines as input, though.

dvgrn
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### Re: Building a reverse caber-tosser

mostly useless and expensive eater1 pull/dFire reaction that we probably won’t use

`x = 34, y = 19, rule = LifeHistoryE\$.2E\$2E\$5.E\$6.E5.C\$4.3E6.2C\$12.2C2\$16.A15.A\$17.A15.A\$15.3A3.D9.3A\$19.3D\$18.D\$18.2D\$31.D\$16.2A13.DCA\$15.A.A12.DADA\$15.A15.A\$14.2A14.2A!`

this might be possible using semi snarks

`x = 32, y = 33, rule = LifeHistory7.D\$8.2D\$7.2D5\$C\$.2C\$2C\$11.A\$12.A\$10.3A6.C\$20.2C\$19.2C5\$12.D\$13.2D\$12.2D17.D\$23.A5.3D\$24.A3.D\$22.3A3.2D5\$23.2A\$22.A.A\$22.A\$21.2A!`

WHAT THE...
`x = 61, y = 41, rule = LifeHistory7.D\$8.2D\$7.2D5\$C\$.2C\$2C\$11.A\$12.A\$10.3A4\$23.C27.D\$24.2C26.2D\$23.2C26.2D5\$16.D27.C\$17.2D26.2C\$16.2D17.D8.2C\$27.A5.3D19.A\$28.A3.D23.A\$26.3A3.2D20.3A4\$26.2D26.D\$25.D.CA25.DCA\$25.DA.A24.DADA\$24.2DA27.A\$25.2A26.2A\$31.2C26.2A\$30.C.C25.A.A\$30.C27.A\$29.2C26.2A!`

The question is:
Does anyone know a cheap eater1 puffer glider synth that puffs eaters in the right orientation?
something like the one in infinite binary ruler generator?

The problem is:
it will take twice as many signals to pull this thing, plus how do you even get to both sides of the reaction?
Last edited by Redstoneboi on June 9th, 2018, 5:05 pm, edited 1 time in total.
c(>^x^<c)~
This is Fluffy the cat.
Fluffy wants to discover new things that everyone likes.
Fluffy likes to watch spaceship guns in Golly.

There’s one problem,

Fluffy doesn’t exist :(

Redstoneboi

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### Re: Building a reverse caber-tosser

When the synthesis of the crab-barge-stretcher thing was completed, I made this suggestion, and I'd probably make a similar suggestion here.
succ

blah

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### Re: Building a reverse caber-tosser

blah wrote:When the synthesis of the crab-barge-stretcher thing was completed, I made this suggestion, and I'd probably make a similar suggestion here.

All kinds of announcements will be in the works as soon there's an official synthesis -- LifeWiki article, something on the ConwayLife home page, submissions to Hacker News or Reddit or Slashdot or whatever, and no doubt a Did You Know.

I don't quite trust the count until the continuous synthesis has been assembled -- it seems likely that there's a blocked lane or two in there somewhere that may need a kickback to complete correctly.

dvgrn
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### Re: Building a reverse caber-tosser

Would it be possible to actually build the RLE for the synthesis of a very simple object (e.g. one that would normally take only two or three gliders) just to act as an example/proof of the method, or would even that get too large?

77topaz

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### Re: Building a reverse caber-tosser

77topaz wrote:Would it be possible to actually build the RLE for the synthesis of a very simple object (e.g. one that would normally take only two or three gliders) just to act as an example/proof of the method, or would even that get too large?

It's going to be pretty easy to show the universal-constructor mechanism in operation, just by building a SE-traveling glider salvo that simulates the glider pairs what will be coming back from the Cordership -- but doing it enormously faster, suppressing the outgoing glider pairs if necessary.

We can then calculate the position of the Cordership that would return the first N of those glider pairs, and see at what point Golly starts having trouble running the full pattern. I suspect it will be slow but doable for the first few gliders of a slow-salvo recipe for whatever the target is -- let's say a pulsar.

I think by the time the tenth glider of the output slow salvo is generated, we'll pretty definitely have exceeded some practical limit or other, but I'm not sure which one!

I tried putting together the continuous synthesis. Had no trouble with adding the second stage to the first, just one sub-synthesis where the timing had to be changed by 160 ticks I think.

But there are some problems with the third stage that I think might increase the glider count. There's a p8 bumper where the leftover beehive is slightly in the way of a glider for a future construction -- and the upper block of the blocker is just barely in the way also.

Maybe that can be fixed by changing the build order, I'm not sure yet. There are some other collisions when I rewind the third stage, but maybe they can be fixed just by adjusting the timing. Am going to stop working on it for a while, so I'll post the version of Stage 1 + Stage 2 + Stage 3 that I'm looking at right now:

`x = 3137, y = 3440, rule = B3/S233076bo\$3075bo\$3075b3o6\$3069bobo\$3069b2o\$3070bo\$49bo\$47bobo16bo\$48b2o17bo\$58bo6b3o\$59bo\$50bo6b3o\$51bo\$49b3o22\$100bo\$101bo\$99b3o7\$3124bo\$3123bo\$3118bo4b3o\$3118bobo\$3118b2o2\$103bo\$101bobo\$102b2o2\$3120bo\$3120bobo\$3120b2o4\$107bobo\$108b2o\$108bo3013bo\$3122bobo\$3122b2o5\$20bo\$21bo\$19b3o2\$32bobo\$33b2o\$33bo4\$3089bo\$3089bobo\$3089b2o\$44bo\$45b2o\$44b2o2\$3093bo\$3093bobo\$3093b2o\$3071bo\$3070bo\$3070b3o5\$3091bo\$64bo3024b2o12bobo\$65bo3024b2o11b2o\$63b3o3038bo6\$67bo\$65bobo\$66b2o5\$73bobo\$63bobo8b2o\$64b2o8bo\$59bo4bo\$59b2o\$58bobo53\$bo\$2b2o\$b2o\$14bo\$12bobo\$13b2o6\$10bobo\$obo8b2o\$b2o8bo\$bo146\$3114bo\$3114bobo\$3114b2o4\$3119bo\$3118bo\$3118b3o37\$3065bo\$3063b2o\$3064b2o\$3072bo\$3071bo\$3071b3o3\$3061bobo\$3061b2o\$14bo3047bo\$12bobo\$13b2o10\$3047bo\$3046bo\$3046b3o3\$12bo\$13b2o\$12b2o3041bo\$3054bo\$3054b3o8\$3036bo\$3036bobo\$3036b2o2\$3031bo\$3031bobo\$27bo3003b2o\$28b2o\$27b2o3012bo\$3040bo\$3040b3o221\$496bo\$494bobo\$495b2o27\$442bobo\$443b2o\$443bo\$446bo\$447b2o\$446b2o5\$462bobo\$463b2o15bo17bo\$463bo17bo14bobo\$479b3o15b2o2042bobo\$2541b2o\$484bo2057bo12bo\$482bobo2068b2o\$483b2o30bo2038b2o\$516bo\$514b3o\$508bobo\$509b2o19bo\$473bo35bo21bo\$474bo54b3o\$472b3o2\$2543bo\$2541b2o\$2542b2o3\$518bo2062bo\$418bobo95bobo2056bobo2bo\$419b2o96b2o2056b2o3b3o\$419bo2156bo2\$436bo83bobo\$434bobo84b2o\$435b2o84bo3\$445bo\$446bo\$444b3o\$519bo2046bo\$520b2o2044bobo\$519b2o2045b2o4\$516bo\$517b2o\$516b2o5\$523bo\$524bo\$522b3o2\$2596bobo\$2580bo15b2o\$2578b2o17bo\$2579b2o6bo\$2586bo\$2586b3o6bo\$2594bo\$2594b3o212\$2714bo\$2713bo\$2713b3o6\$2716bo\$2715bo\$2715b3o12\$680bobo\$681b2o\$681bo2\$685bobo\$686b2o\$686bo2017bo\$683bo2020bobo\$676bo7bo2019b2o\$677b2o3b3o\$676b2o2\$2696bobo\$2696b2o\$2697bo173\$869bo\$870bo\$868b3o3\$865bo\$863bobo\$864b2o3\$2877bobo\$2877b2o\$2878bo66\$2009bo\$2008bo\$2008b3o6\$2002bobo\$2002b2o\$2003bo\$1182bo\$1180bobo16bo\$1181b2o17bo\$1191bo6b3o\$1192bo\$1183bo6b3o\$1184bo\$1182b3o55\$1265bobo\$1266b2o\$1266bo2\$1261bo\$1262b2o\$1261b2o3\$2102bo\$2102bobo\$2102b2o3\$1266bo\$1267bo\$1265b3o2\$1271bo\$1272bo\$1270b3o\$2093bobo\$2093b2o\$1262bo831bo\$1260bobo\$1261b2o173\$1796bobo\$1796b2o\$1797bo2\$1802bo\$1800b2o\$1801b2o3\$961bo\$959bobo\$960b2o3\$1797bo\$1796bo\$1796b3o2\$1792bo\$1791bo\$1791b3o\$968bobo\$969b2o\$969bo831bo\$1801bobo\$1801b2o27\$1850bo\$1850bobo\$1038bo811b2o\$1039b2o\$1038b2o64\$1166bo\$1167bo\$1165b3o4\$1165bobo\$1166b2o889bobo\$1166bo890b2o8bo\$2058bo6b2o\$2066b2o21\$2020bo\$1128bo891bobo\$1129bo890b2o\$1127b3o108\$1465bo\$1463bobo\$1464b2o2\$1470bo\$1468bobo\$1469b2o803bo\$2272b2o\$1460bo812b2o\$1461bo\$1459b3o68\$2182bo\$2181bo18bobo\$2181b3o16b2o\$2201bo2\$2190bo15bo\$2190bobo11b2o\$2190b2o13b2o3\$2186bo\$2186bobo\$2186b2o79\$1380bo\$1379bobo\$1379bo\$1378b2o122\$1196b2o\$1197b2o\$1196bo4\$1186b3o\$1188bo\$1172b2o13bo\$1171bobo\$1173bo78\$2101bo\$2087b2o11b2o\$2086b2o12bobo\$2088bo195\$962bo\$962b2o11b2o\$961bobo12b2o\$975bo169\$2057b3o\$1165b2o890bo\$1164bobo891bo\$1166bo21\$1119b2o\$1120b2o6bo\$1119bo8b2o890bo\$1127bobo889b2o\$2019bobo4\$2019b3o\$2019bo\$2020bo23\$2267bo\$2266b2o\$2266bobo93\$1362bo\$1362b2o\$1361bobo5\$2184b2o\$2183b2o\$2185bo5\$1362b2o\$1363b2o\$1362bo832b3o\$2195bo\$2196bo32\$506b3o\$508bo\$507bo2\$488bo\$488b2o12b3o\$487bobo14bo\$503bo2\$492b2o17b2o\$493b2o15bobo\$492bo19bo2\$532bo\$532b2o\$531bobo7\$2601b2o\$2601bobo\$477b2o2122bo\$478b2o\$477bo12\$480b2o\$479bobo\$481bo5\$451b2o\$450bobo14b2o6bo\$452bo13bobo6b2o\$468bo5bobo5\$452b2o\$453b2o\$452bo\$2567b2o\$2566b2o\$2568bo12\$2562b3o\$2562bo\$2563bo\$2566b2o\$2566bobo\$2566bo14b2o\$2581bobo\$2581bo4\$2590b3o\$2590bo\$2591bo14bo\$2605b2o\$2605bobo12\$431b2o\$430bobo\$432bo6b2o\$438bobo\$440bo6bo\$447b2o\$446bobo\$428bo\$428b2o\$427bobo2\$2551b3o\$2551bo\$2552bo5\$2558b2o\$2557b2o\$2559bo150\$2711b2o\$2710b2o\$2712bo4\$2714b2o\$2714bobo\$2714bo2\$2723b3o\$2723bo\$2724bo\$2720b2o\$2720bobo\$2720bo12\$63b2o\$64b2o\$63bo4\$53b3o\$55bo\$39b2o13bo\$38bobo\$40bo34\$3127b2o\$3126b2o\$3128bo4\$3134b2o\$3134bobo\$3134bo19\$3069bo\$3068b2o\$3068bobo3\$82b2o\$81bobo\$83bo3013bo\$3096b2o\$3096bobo\$91b3o\$93bo\$92bo2\$86b3o\$88bo\$87bo3\$3105b2o\$3105bobo\$3105bo\$69b3o\$71bo\$70bo11b2o\$83b2o\$82bo2\$87bo\$87b2o\$86bobo3\$3101b2o\$3101bobo\$71bo3029bo\$71b2o\$70bobo3\$60b3o\$62bo\$61bo\$68b2o\$69b2o\$68bo41\$2875b3o\$2875bo\$2876bo\$6b3o\$8bo\$7bo4\$11b2o\$10bobo\$12bo146\$3125bo\$3115bo8b2o\$3114b2o8bobo\$3114bobo6\$3112b2o\$3112bobo\$3112bo\$3124b2o\$3123b2o\$3125bo58\$3061bo\$3051bo8b2o\$3050b2o8bobo\$3050bobo3\$3041b2o\$3040b2o\$3042bo2\$18b2o\$17bobo\$19bo3\$34bo\$34b2o3030b2o\$33bobo3030bobo\$3066bo3\$14b2o\$13bobo\$15bo\$3068b3o\$3068bo\$3069bo!`

dvgrn
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### Re: Building a reverse caber-tosser

dvgrn wrote:I tried putting together the continuous synthesis. Had no trouble with adding the second stage to the first, just one sub-synthesis where the timing had to be changed by 160 ticks I think.

But there are some problems with the third stage that I think might increase the glider count. There's a p8 bumper where the leftover beehive is slightly in the way of a glider for a future construction -- and the upper block of the blocker is just barely in the way also.

Maybe that can be fixed by changing the build order, I'm not sure yet. There are some other collisions when I rewind the third stage, but maybe they can be fixed just by adjusting the timing. Am going to stop working on it for a while, so I'll post the version of Stage 1 + Stage 2 + Stage 3 that I'm looking at right now:...

Yeah, sorry about those errors. There were so many gliders in each stage that I had basically resigned myself to the fact that there would be errors in the synthesis that would have to be fixed by kickbacks. Unfortunately, I was already doing the synthesis assembly independently of dvgrn.

I've done the first 4 stages (but I have to fix some minor issues before moving on to the final stage). So far I've used 2 extra kickbacks. I believe they are necessary but I'm not completely sure. It should become more clear to me once I've completed the synthesis...
Things to work on:
• Work on the snowflakes orthogonoid

Goldtiger997

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### Re: Building a reverse caber-tosser

Okay, here's a complete uncompressed continuous synthesis for the Universal Constructor (Cordership and BLSE not included):

Code: Select all
`x = 4202, y = 4190, rule = B3/S23o\$b2o\$2o233\$48bo\$46bobo\$47b2o35\$98bo\$99bo\$97b3o6\$88bo\$89b2o\$88b2o15\$101bo\$102b2o\$101b2o\$114bo\$112bobo\$113b2o6\$110bobo\$100bobo8b2o\$101b2o8bo\$101bo295\$3282bo\$3281bo\$3281b3o\$671bo\$672bo\$670b3o14bo\$688b2o\$687b2o\$540bo\$541b2o\$540b2o2\$688bobo2600bobo\$689b2o2600b2o\$548bo140bo2602bo\$549bo\$547b3o11\$555bobo\$556b2o\$556bo13\$572bo\$573b2o\$572b2o2\$584bobo\$585b2o\$585bo16\$588bobo\$589b2o\$589bo4\$597bo\$595bobo\$596b2o23\$677bo\$678bo\$676b3o6\$617bo\$618b2o\$617b2o32\$661bo\$662bo\$660b3o2\$674bo\$672bobo\$673b2o138\$3336bobo\$3336b2o\$3337bo4\$3329bo\$3329bobo\$3329b2o38\$699bo2193bo\$697bobo2192bo\$698b2o2192b3o412bo\$3305b2o\$3306b2o4\$2886bobo\$2886b2o\$2887bo\$1060bo\$1058bobo16bo\$1059b2o17bo\$1069bo6b3o\$1070bo\$1061bo6b3o\$1062bo\$1060b3o23\$3267bobo\$3267b2o\$3258bobo7bo\$3258b2o\$645bo2613bo\$643bobo\$644b2o2626bobo\$3272b2o\$3273bo13\$666bo\$667b2o\$666b2o466bo\$1135b2o\$1134b2o4\$651bobo\$652b2o\$652bo\$2918bo\$2916b2o\$2911bobo3b2o\$2911b2o\$661bo2250bo\$662b2o\$661b2o473bobo\$1137b2o\$1137bo2\$2913bobo\$2913b2o\$2914bo3\$1045bo97bo\$1046bo97bo\$1044b3o95b3o\$2915bobo\$1057bobo1855b2o\$1058b2o1856bo\$1058bo4\$2892bo\$2892bobo\$2892b2o\$1069bo\$1070b2o\$1069b2o2\$2896bobo\$2896b2o\$2897bo\$2875bo\$2873b2o\$2874b2o5\$2893bo13bo\$1088bo1804bobo10bo\$1089b2o1802b2o11b3o\$1088b2o6\$1090bobo\$1091b2o\$1091bo4\$1099bo\$1089bo10bo\$1090bo7b3o\$1088b3o55\$1025bo\$1026b2o\$1025b2o\$1038bo\$1036bobo\$1037b2o6\$1034bobo\$1024bobo8b2o\$1025b2o8bo\$1025bo36\$3028bo\$3028bobo\$3028b2o4\$3033bo\$3032bo\$3032b3o38\$2977bobo\$2977b2o\$2978bo\$2985bo\$2985bobo\$2985b2o2\$2976bo\$2974b2o\$928bo2046b2o\$929bo\$927b3o11\$2960bo\$2960bobo\$2960b2o3\$926bobo\$927b2o\$927bo2040bo\$2968bobo\$2968b2o12\$2945bo\$2944bo\$2944b3o2\$2940bo\$2939bo\$2939b3o\$946bobo\$947b2o\$947bo2001bo\$2949bobo\$2949b2o16\$1209bobo\$1210b2o\$1210bo13\$2703bo\$2702bo\$2702b3o6\$2696bobo\$2696b2o\$2697bo\$1316bo\$1314bobo\$1158bo156b2o\$1159bo\$1157b3o\$2684bo\$1162bo1521bobo\$1160bobo1521b2o\$1161b2o\$1307bo\$1308b2o\$1307b2o\$1178bo\$1179bo\$1177b3o14bo16bobo\$1195b2o15b2o1441bo\$1194b2o16bo1441bo\$2654b3o\$1197bobo1467bo\$1198b2o1467bobo\$1198bo30bo1437b2o\$1230b2o\$1224bo4b2o\$1225bo\$1223b3o18bo\$1187bo57b2o\$1188b2o54b2o\$1187b2o2\$2655bo\$2655bobo\$2655b2o3\$1134bo96bobo1455bo5bo\$1135bo96b2o1454bo4b2o\$1133b3o96bo1455b3o3b2o2\$1236bo\$1149bobo85bo\$1150b2o83b3o\$1150bo3\$1159bo\$1160b2o\$1159b2o\$1235bo1443bobo\$1233bobo1443b2o\$1234b2o1444bo4\$1232bo\$1230bobo\$1231b2o5\$1237bo\$1238b2o\$1237b2o\$2710bo\$2709bo\$2692bo16b3o\$2692bobo\$2692b2o7bo\$2699b2o\$2700b2o7bo\$2707b2o\$2708b2o62\$2618bo\$2616b2o\$2617b2o3\$2621bobo\$2621b2o\$2622bo2\$968bo\$969bo\$967b3o4\$2617bo\$2617bobo\$2617b2o2\$2612bo\$2612bobo\$976bo1635b2o\$977b2o\$976b2o1644bo\$2621bo\$2621b3o83\$1573bo\$1574bo\$1565bo6b3o\$1566bo\$1557bo6b3o\$1558bo\$1556b3o35\$2829bo\$2827b2o\$2828b2o6\$2831bo\$2829b2o\$2830b2o11\$1395bo\$1396bo\$1394b3o2\$1400bo\$1401bo\$1399b3o\$2818bobo\$1396bo1421b2o\$1391bo5b2o1420bo\$1389bobo4b2o\$1390b2o\$2811bo\$2810bo\$2810b3o25\$1679bobo\$1680b2o\$1680bo2\$1675bo\$1676b2o\$1675b2o3\$2516bo\$2516bobo\$2516b2o3\$1680bo\$1681bo\$1679b3o2\$1685bo\$1686bo\$1684b3o\$2507bobo\$2507b2o\$1676bo831bo\$1674bobo\$1675b2o128\$2345bo\$2344bo\$2344b3o4\$1404bo\$1405bo\$1403b3o\$1379bo\$1380bo\$1378b3o4\$1403bo1181bobo\$1382bo18bobo1181b2o\$1380bobo19b2o1182bo\$1381b2o\$1392bobo\$1393b2o\$1393bo212bobo\$1607b2o\$1607bo2\$1602bo\$1603b2o\$1602b2o3\$2967bo\$2967bobo\$2967b2o11\$1414bo\$1412bobo\$1413b2o5\$1424bo\$1425b2o1187bo4bobo\$1424b2o1188bobo2b2o\$2614b2o4bo44\$2264bo\$2264bobo\$1452bo811b2o\$1453b2o\$1452b2o104\$1620bo\$1621bo\$1619b3o4\$1619bobo\$1620b2o809bobo\$1620bo810b2o8bo\$2432bo6b2o\$2440b2o21\$2394bo\$1582bo811bobo\$1583bo810b2o\$1581b3o25\$1590bo\$1591bo\$1589b3o41\$1879bo\$1877bobo\$1878b2o2\$1884bo\$1882bobo\$1883b2o803bo\$2686b2o\$1874bo812b2o\$1875bo\$1873b3o68\$2597bo17bo\$2595b2o17bo\$2596b2o16b3o3\$2604bobo12bo\$2604b2o13bobo\$2605bo13b2o3\$2600bobo\$2600b2o\$2601bo174\$1500b2o\$1499bobo\$1501bo813bo\$2314b2o\$2314bobo66\$1570b2o\$1571b2o\$1570bo4\$1560b3o\$1562bo\$1561bo40\$2515bo\$2501b2o11b2o\$2500b2o12bobo\$2502bo266\$1074b2o\$1075b2o\$1074bo146b2o\$1222b2o\$1221bo2\$1064b3o\$1066bo135b3o12b2o\$1050b2o13bo138bo13b2o\$1049bobo151bo13bo\$1051bo\$1207b2o17bo\$1206bobo17b2o\$1208bo16bobo\$1050b2o\$1049bobo323b2o\$1051bo194b3o127b2o1345bo\$1248bo126bo1346b2o\$1247bo1474bobo2\$2920b2o\$1368b2o1550bobo\$1367bobo21bo1528bo\$1369bo21b2o\$1390bobo1322bo\$2714b2o\$1192b2o1520bobo211bo\$1191bobo1733b2o\$1193bo1733bobo12\$1195bo\$1195b2o\$1194bobo5\$1166bo\$1166b2o14bo\$1165bobo14b2o5b3o\$1181bobo7bo\$1190bo4\$1167b2o\$1166bobo\$1168bo\$2680b2o189b3o\$2680bobo188bo\$2680bo191bo\$2431b3o\$1107bo511b2o810bo\$1107b2o509bobo811bo\$1106bobo511bo\$2899b3o\$2899bo\$1116b2o1782bo\$1117b2o\$1116bo2\$1111b2o\$1112b2o1562b2o\$1111bo1563b2o\$2677bo\$2680bo\$2679b2o228bo\$2679bobo13bo212b2o\$2694b2o212bobo\$1094b2o1598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[[ THEME 2 STEP 8 PAUSE 1 ZOOM 1 T 5000 ZOOM -3 ]]`

It costs 316 gliders. (3 of the 7 extra gliders come from additional kickbacks, and the other 4 come from two eaters which I previously completely failed to notice and synthesize.) So all synthesisable patterns cost at most 316+4+9 = 331 gliders!

Could someone create a nice demonstration case so we can see the technology in action?...
Things to work on:
• Work on the snowflakes orthogonoid

Goldtiger997

Posts: 481
Joined: June 21st, 2016, 8:00 am
Location: 11.329903°N 142.199305°E

### Re: Building a reverse caber-tosser

Impressive! I think it needs 5 gliders for the BLSE; I can't see any way to remove the kickback:

`x = 4202, y = 4190, rule = B3/S23o\$b2o\$2o233\$48bo\$46bobo\$47b2o35\$98bo\$99bo\$97b3o6\$88bo\$89b2o\$88b2o15\$101bo\$102b2o\$101b2o\$114bo\$112bobo\$113b2o6\$110bobo\$100bobo8b2o\$101b2o8bo\$101bo295\$3282bo\$3281bo\$3281b3o\$671bo\$672bo\$670b3o14bo\$688b2o\$687b2o\$540bo\$541b2o\$540b2o2\$688bobo2600bobo\$689b2o2600b2o\$548bo140bo2602bo\$549bo\$547b3o11\$555bobo\$556b2o\$556bo13\$572bo\$573b2o\$572b2o2\$584bobo\$585b2o\$585bo16\$588bobo\$589b2o\$589bo4\$597bo\$595bobo\$596b2o23\$677bo\$678bo\$676b3o6\$617bo\$618b2o\$617b2o32\$661bo\$662bo\$660b3o2\$674bo\$672bobo\$673b2o138\$3336bobo\$3336b2o\$3337bo4\$3329bo\$3329bobo\$3329b2o38\$699bo2193bo\$697bobo2192bo\$698b2o2192b3o412bo\$3305b2o\$3306b2o4\$2886bobo\$2886b2o\$2887bo\$1060bo\$1058bobo16bo\$1059b2o17bo\$1069bo6b3o\$1070bo\$1061bo6b3o\$1062bo\$1060b3o23\$3267bobo\$3267b2o\$3258bobo7bo\$3258b2o\$645bo2613bo\$643bobo\$644b2o2626bobo\$3272b2o\$3273bo13\$666bo\$667b2o\$666b2o466bo\$1135b2o\$1134b2o4\$651bobo\$652b2o\$652bo\$2918bo\$2916b2o\$2911bobo3b2o\$2911b2o\$661bo2250bo\$662b2o\$661b2o473bobo\$1137b2o\$1137bo2\$2913bobo\$2913b2o\$2914bo3\$1045bo97bo\$1046bo97bo\$1044b3o95b3o\$2915bobo\$1057bobo1855b2o\$1058b2o1856bo\$1058bo4\$2892bo\$2892bobo\$2892b2o\$1069bo\$1070b2o\$1069b2o2\$2896bobo\$2896b2o\$2897bo\$2875bo\$2873b2o\$2874b2o5\$2893bo13bo\$1088bo1804bobo10bo\$1089b2o1802b2o11b3o\$1088b2o6\$1090bobo\$1091b2o\$1091bo4\$1099bo\$1089bo10bo\$1090bo7b3o\$1088b3o55\$1025bo\$1026b2o\$1025b2o\$1038bo\$1036bobo\$1037b2o6\$1034bobo\$1024bobo8b2o\$1025b2o8bo\$1025bo36\$3028bo\$3028bobo\$3028b2o4\$3033bo\$3032bo\$3032b3o38\$2977bobo\$2977b2o\$2978bo\$2985bo\$2985bobo\$2985b2o2\$2976bo\$2974b2o\$928bo2046b2o\$929bo\$927b3o11\$2960bo\$2960bobo\$2960b2o3\$926bobo\$927b2o\$927bo2040bo\$2968bobo\$2968b2o12\$2945bo\$2944bo\$2944b3o2\$2940bo\$2939bo\$2939b3o\$946bobo\$947b2o\$947bo2001bo\$2949bobo\$2949b2o16\$1209bobo\$1210b2o\$1210bo13\$2703bo\$2702bo\$2702b3o6\$2696bobo\$2696b2o\$2697bo\$1316bo\$1314bobo\$1158bo156b2o\$1159bo\$1157b3o\$2684bo\$1162bo1521bobo\$1160bobo1521b2o\$1161b2o\$1307bo\$1308b2o\$1307b2o\$1178bo\$1179bo\$1177b3o14bo16bobo\$1195b2o15b2o1441bo\$1194b2o16bo1441bo\$2654b3o\$1197bobo1467bo\$1198b2o1467bobo\$1198bo30bo1437b2o\$1230b2o\$1224bo4b2o\$1225bo\$1223b3o18bo\$1187bo57b2o\$1188b2o54b2o\$1187b2o2\$2655bo\$2655bobo\$2655b2o3\$1134bo96bobo1455bo5bo\$1135bo96b2o1454bo4b2o\$1133b3o96bo1455b3o3b2o2\$1236bo\$1149bobo85bo\$1150b2o83b3o\$1150bo3\$1159bo\$1160b2o\$1159b2o\$1235bo1443bobo\$1233bobo1443b2o\$1234b2o1444bo4\$1232bo\$1230bobo\$1231b2o5\$1237bo\$1238b2o\$1237b2o\$2710bo\$2709bo\$2692bo16b3o\$2692bobo\$2692b2o7bo\$2699b2o\$2700b2o7bo\$2707b2o\$2708b2o62\$2618bo\$2616b2o\$2617b2o3\$2621bobo\$2621b2o\$2622bo2\$968bo\$969bo\$967b3o4\$2617bo\$2617bobo\$2617b2o2\$2612bo\$2612bobo\$976bo1635b2o\$977b2o\$976b2o1644bo\$2621bo\$2621b3o83\$1573bo\$1574bo\$1565bo6b3o\$1566bo\$1557bo6b3o\$1558bo\$1556b3o35\$2829bo\$2827b2o\$2828b2o6\$2831bo\$2829b2o\$2830b2o11\$1395bo\$1396bo\$1394b3o2\$1400bo2216bo\$1401bo2214bo\$1399b3o2214b3o\$2818bobo\$1396bo1421b2o\$1391bo5b2o1420bo\$1389bobo4b2o\$1390b2o\$2811bo\$2810bo\$2810b3o25\$1679bobo\$1680b2o\$1680bo2\$1675bo\$1676b2o\$1675b2o3\$2516bo\$2516bobo\$2516b2o3\$1680bo\$1681bo\$1679b3o2\$1685bo\$1686bo\$1684b3o\$2507bobo\$2507b2o\$1676bo831bo\$1674bobo\$1675b2o128\$2345bo\$2344bo\$2344b3o4\$1404bo\$1405bo\$1403b3o\$1379bo\$1380bo\$1378b3o4\$1403bo1181bobo\$1382bo18bobo1181b2o\$1380bobo19b2o1182bo\$1381b2o\$1392bobo\$1393b2o\$1393bo212bobo\$1607b2o\$1607bo2\$1602bo\$1603b2o\$1602b2o3\$2967bo\$2967bobo\$2967b2o11\$1414bo\$1412bobo\$1413b2o5\$1424bo\$1425b2o1187bo4bobo\$1424b2o1188bobo2b2o\$2614b2o4bo44\$2264bo\$2264bobo\$1452bo811b2o\$1453b2o\$1452b2o104\$1620bo\$1621bo\$1619b3o4\$1619bobo\$1620b2o809bobo\$1620bo810b2o8bo\$2432bo6b2o\$2440b2o21\$2394bo\$1582bo811bobo\$1583bo810b2o\$1581b3o25\$1590bo\$1591bo\$1589b3o41\$1879bo\$1877bobo\$1878b2o2\$1884bo\$1882bobo\$1883b2o803bo\$2686b2o\$1874bo812b2o\$1875bo\$1873b3o68\$2597bo17bo\$2595b2o17bo\$2596b2o16b3o3\$2604bobo12bo\$2604b2o13bobo\$2605bo13b2o3\$2600bobo\$2600b2o\$2601bo174\$1500b2o\$1499bobo\$1501bo813bo\$2314b2o\$2314bobo66\$1570b2o\$1571b2o\$1570bo4\$1560b3o\$1562bo\$1561bo40\$2515bo\$2501b2o11b2o\$2500b2o12bobo\$2502bo266\$1074b2o\$1075b2o\$1074bo146b2o\$1222b2o\$1221bo2\$1064b3o\$1066bo135b3o12b2o\$1050b2o13bo138bo13b2o\$1049bobo151bo13bo\$1051bo\$1207b2o17bo\$1206bobo17b2o\$1208bo16bobo\$1050b2o\$1049bobo323b2o\$1051bo194b3o127b2o1345bo\$1248bo126bo1346b2o\$1247bo1474bobo2\$2920b2o\$1368b2o1550bobo\$1367bobo21bo1528bo\$1369bo21b2o\$1390bobo1322bo\$2714b2o\$1192b2o1520bobo211bo\$1191bobo1733b2o\$1193bo1733bobo12\$1195bo\$1195b2o\$1194bobo5\$1166bo\$1166b2o14bo\$1165bobo14b2o5b3o\$1181bobo7bo\$1190bo4\$1167b2o\$1166bobo\$1168bo\$2680b2o189b3o\$2680bobo188bo\$2680bo191bo\$2431b3o\$1107bo511b2o810bo\$1107b2o509bobo811bo\$1106bobo511bo\$2899b3o\$2899bo\$1116b2o1782bo\$1117b2o\$1116bo2\$1111b2o\$1112b2o1562b2o\$1111bo1563b2o\$2677bo\$2680bo\$2679b2o228bo\$2679bobo13bo212b2o\$2694b2o212bobo\$1094b2o1598bobo\$1083b3o9b2o\$1085bo8bo12b2o\$1084bo21bobo\$1108bo1595b2o\$2703b2o\$1573b2o1130bo\$1111b3o460b2o6bo1135b3o\$1113bo459bo8b2o810bo323bo\$1112bo468bobo809b2o324bo\$2393bobo\$2905bo\$2904b2o\$2904bobo\$1095b3o1295b3o\$1097bo1295bo\$1096bo1297bo2\$1085b2o\$1086b2o\$1085bo60bo\$1093b2o51b2o\$1092bobo50bobo6bo\$1094bo59b2o\$1153bobo\$1161b3o\$1163bo\$1162bo\$1142b3o\$1144bo\$1143bo\$1592bo1072b2o\$1592b2o1070b2o\$1591bobo1072bo5\$2671b2o\$2671bobo\$2671bo28\$1030b3o\$1032bo\$1031bo4\$1035b2o\$1034bobo\$1036bo3\$2681bo\$2680b2o\$2680bobo13\$2195b2o\$2195b2o71\$1396bo4b2o\$1396b2o2bobo1184b2o\$1395bobo4bo1183b2o\$2588bo6\$1775b3o\$1777bo\$1776bo4\$2598b2o\$2598bobo\$2598bo5\$1776b2o\$1775bobo\$1777bo832b2o\$2609b2o214b2o\$2611bo213bobo\$2825bo3\$1410b3o\$1412bo1416bo\$1411bo1416b2o\$2828bobo2\$2838b2o\$2837b2o\$2839bo\$2835bo\$2834b2o\$1426bo1186b2o219bobo\$1426b2o1185bobo\$1425bobo1185bo7\$2611b3o\$2611bo\$2612bo40\$969b2o12bo\$970b2o11b2o\$969bo12bobo73\$3039bo\$3029bo8b2o\$3028b2o8bobo\$3028bobo6\$3026b2o\$3026bobo\$3026bo\$3038b2o\$3037b2o\$3039bo4\$2966bo\$2965b2o\$2965bobo35\$671b2o\$670bobo\$672bo15\$2974b2o\$2964b2o7b2o\$2963b2o10bo\$2965bo2\$2955bo\$672b2o2280b2o\$673b2o2279bobo\$672bo2\$932b3o18b2o\$934bo19b2o\$933bo19bo4\$2979b3o\$2979bo\$2980bo3\$928b3o\$583bo346bo\$583b2o344bo2052b2o\$582bobo2397bobo\$2982bo21\$551bo\$551b2o46b2o\$550bobo47b2o\$599bo5\$560b2o\$559bobo\$561bo2660b2o\$3221b2o\$3223bo10\$614b2o\$613bobo\$615bo4\$607bo\$607b2o\$606bobo156\$3326b2o\$3325b2o\$3327bo7\$735b2o\$736b2o\$735bo40\$686b3o\$688bo\$687bo\$3251b2o\$687bo2562b2o\$687b2o2563bo\$686bobo2\$678b3o\$680bo2571b2o\$679bo2572bobo\$3241b3o8bo\$3241bo\$3242bo38\$3283b2o\$3263b2o18bobo\$3263bobo17bo\$3263bo3\$3276bo\$3275b2o\$3275bobo14\$647b2o\$646bobo\$648bo2621bo\$3269b2o\$3269bobo3\$655bo\$655b2o\$654bobo2\$648b2o\$647bobo\$649bo2609bo\$3258b2o24b3o\$3258bobo23bo\$3285bo2\$666b2o\$665bobo\$667bo4\$659b2o\$658bobo\$660bo\$648b3o\$650bo\$649bo\$3251b3o\$3251bo\$3252bo5\$663b3o\$665bo\$664bo\$3266b3o\$3266bo\$3267bo25\$1534b2o\$1535b2o\$1534bo2\$3591b2o\$3591bobo\$3591bo3\$726b2o\$727b2o\$726bo2\$3185b2o\$3185bobo\$3185bo5\$763b2o\$762bobo\$764bo7\$758b2o\$757bobo\$759bo\$743b2o\$744b2o\$743bo2489b2o\$3232b2o\$3234bo385bo\$3619b2o\$3619bobo6\$740b3o\$742bo\$734b2o5bo\$733bobo\$735bo\$3226bo\$3225b2o\$3225bobo6\$3231b3o125b2o\$3231bo127bobo\$3232bo126bo47\$1464b2o\$1463bobo\$1465bo29\$182b3o\$184bo\$183bo11\$3437b2o\$3437bobo\$3437bo49\$118b3o\$120bo\$119bo3\$93b2o\$94b2o\$93bo\$106b3o\$108bo\$107bo4\$111b2o\$110bobo\$112bo\$85b2o\$84bobo\$86bo4\$78bo\$78b2o\$77bobo8\$44b2o\$43bobo\$45bo279\$4200b2o\$4199b2o\$4201bo!`

Fortunately, we don't need to separately construct an elbow. After using Dave's DFIRE to delete the first boat, there's a monochromatic* P1 salvo which turns the other boat into a block and gradually pushes it away from the critical zone:

`x = 1355, y = 1814, rule = B3/S231352bo\$1352bobo\$1352b2o37\$1303bo\$1302bo\$1302b3o12\$1323bo\$1322bo\$1322b3o4\$1293bo\$1292bo\$1292b3o22\$1269bo\$1269bobo\$1269b2o18\$1283bo\$1283bobo\$1283b2o8\$1263bo\$1263bobo\$1263b2o7\$1220bo\$1219bo\$1219b3o12\$1240bo\$1239bo\$1239b3o4\$1210bo\$1209bo\$1209b3o22\$1186bo\$1186bobo\$1186b2o18\$1200bo\$1200bobo\$1200b2o8\$1180bo\$1180bobo\$1180b2o7\$1137bo\$1136bo\$1136b3o12\$1157bo\$1156bo\$1156b3o4\$1127bo\$1126bo\$1126b3o22\$1103bo\$1103bobo\$1103b2o18\$1117bo\$1117bobo\$1117b2o8\$1097bo\$1097bobo\$1097b2o7\$1054bo\$1053bo\$1053b3o12\$1074bo\$1073bo\$1073b3o4\$1044bo\$1043bo\$1043b3o22\$1020bo\$1020bobo\$1020b2o18\$1034bo\$1034bobo\$1034b2o8\$1014bo\$1014bobo\$1014b2o7\$971bo\$970bo\$970b3o12\$991bo\$990bo\$990b3o4\$961bo\$960bo\$960b3o22\$937bo\$937bobo\$937b2o18\$951bo\$951bobo\$951b2o8\$931bo\$931bobo\$931b2o7\$888bo\$887bo\$887b3o12\$908bo\$907bo\$907b3o4\$878bo\$877bo\$877b3o22\$854bo\$854bobo\$854b2o18\$868bo\$868bobo\$868b2o8\$848bo\$848bobo\$848b2o7\$805bo\$804bo\$804b3o12\$825bo\$824bo\$824b3o4\$795bo\$794bo\$794b3o22\$771bo\$771bobo\$771b2o18\$785bo\$785bobo\$785b2o8\$765bo\$765bobo\$765b2o7\$722bo\$721bo\$721b3o12\$742bo\$741bo\$741b3o4\$712bo\$711bo\$711b3o22\$688bo\$688bobo\$688b2o18\$702bo\$702bobo\$702b2o8\$682bo\$682bobo\$682b2o7\$639bo\$638bo\$638b3o12\$659bo\$658bo\$658b3o4\$629bo\$628bo\$628b3o22\$605bo\$605bobo\$605b2o18\$619bo\$619bobo\$619b2o8\$599bo\$599bobo\$599b2o7\$556bo\$555bo\$555b3o12\$576bo\$575bo\$575b3o4\$546bo\$545bo\$545b3o22\$522bo\$522bobo\$522b2o18\$536bo\$536bobo\$536b2o8\$516bo\$516bobo\$516b2o7\$473bo\$472bo\$472b3o12\$493bo\$492bo\$492b3o4\$463bo\$462bo\$462b3o22\$439bo\$439bobo\$439b2o18\$453bo\$453bobo\$453b2o8\$433bo\$433bobo\$433b2o7\$390bo\$389bo\$389b3o12\$410bo\$409bo\$409b3o4\$380bo\$379bo\$379b3o22\$356bo\$356bobo\$356b2o18\$370bo\$370bobo\$370b2o8\$350bo\$350bobo\$350b2o7\$307bo\$306bo\$306b3o12\$327bo\$326bo\$326b3o4\$297bo\$296bo\$296b3o22\$273bo\$273bobo\$273b2o18\$287bo\$287bobo\$287b2o8\$267bo\$267bobo\$267b2o7\$224bo\$223bo\$223b3o12\$244bo\$243bo\$243b3o4\$214bo\$213bo\$213b3o22\$190bo\$190bobo\$190b2o18\$204bo\$204bobo\$204b2o8\$184bo\$184bobo\$184b2o7\$141bo\$140bo\$140b3o12\$161bo\$160bo\$160b3o4\$131bo\$130bo\$130b3o22\$107bo\$107bobo\$107b2o18\$121bo\$121bobo\$121b2o8\$101bo\$101bobo\$101b2o7\$58bo\$57bo\$57b3o12\$78bo\$77bo\$77b3o4\$48bo\$47bo\$47b3o42\$38bo\$38bobo\$38b2o13\$11bo\$11bobo\$11b2o5\$bo\$obo\$b2o6\$36b2o\$36b2o2\$30b2o\$30b2o2\$12b3o\$26b2o\$26b2o16b2o\$44b2o3\$16b2o\$16b2o5\$39b2o\$39b2o3\$35b2o\$35b2o\$60b2o\$60b2o2\$54b2o\$32b2o20b2o\$32b2o2\$50b2o\$50b2o16b2o\$68b2o3\$40b2o\$40b2o5\$63b2o\$63b2o3\$59b2o\$59b2o\$84b2o\$84b2o2\$78b2o\$56b2o20b2o\$56b2o2\$74b2o\$74b2o16b2o\$92b2o3\$64b2o\$64b2o5\$87b2o\$87b2o3\$83b2o\$83b2o\$108b2o\$108b2o2\$102b2o\$80b2o20b2o\$80b2o2\$98b2o\$98b2o16b2o\$116b2o3\$88b2o\$88b2o5\$111b2o\$111b2o3\$107b2o\$107b2o\$132b2o\$132b2o2\$126b2o\$104b2o20b2o\$104b2o2\$122b2o\$122b2o16b2o\$140b2o3\$112b2o\$112b2o5\$135b2o\$135b2o3\$131b2o\$131b2o\$156b2o\$156b2o2\$150b2o\$128b2o20b2o\$128b2o2\$146b2o\$146b2o16b2o\$164b2o3\$136b2o\$136b2o5\$159b2o\$159b2o3\$155b2o\$155b2o\$180b2o\$180b2o2\$174b2o\$152b2o20b2o\$152b2o2\$170b2o\$170b2o16b2o\$188b2o3\$160b2o\$160b2o5\$183b2o\$183b2o3\$179b2o\$179b2o\$204b2o\$204b2o2\$198b2o\$176b2o20b2o\$176b2o2\$194b2o\$194b2o16b2o\$212b2o3\$184b2o\$184b2o5\$207b2o\$207b2o3\$203b2o\$203b2o\$228b2o\$228b2o2\$222b2o\$200b2o20b2o\$200b2o2\$218b2o\$218b2o16b2o\$236b2o3\$208b2o\$208b2o5\$231b2o\$231b2o3\$227b2o\$227b2o\$252b2o\$252b2o2\$246b2o\$224b2o20b2o\$224b2o2\$242b2o\$242b2o16b2o\$260b2o3\$232b2o\$232b2o5\$255b2o\$255b2o3\$251b2o\$251b2o\$276b2o\$276b2o2\$270b2o\$248b2o20b2o\$248b2o2\$266b2o\$266b2o16b2o\$284b2o3\$256b2o\$256b2o5\$279b2o\$279b2o3\$275b2o\$275b2o\$300b2o\$300b2o2\$294b2o\$272b2o20b2o\$272b2o2\$290b2o\$290b2o16b2o\$308b2o3\$280b2o\$280b2o5\$303b2o\$303b2o3\$299b2o\$299b2o\$324b2o\$324b2o2\$318b2o\$296b2o20b2o\$296b2o2\$314b2o\$314b2o16b2o\$332b2o3\$304b2o\$304b2o5\$327b2o\$327b2o3\$323b2o\$323b2o\$348b2o\$348b2o2\$342b2o\$320b2o20b2o\$320b2o2\$338b2o\$338b2o16b2o\$356b2o3\$328b2o\$328b2o5\$351b2o\$351b2o3\$347b2o\$347b2o\$372b2o\$372b2o2\$366b2o\$344b2o20b2o\$344b2o2\$362b2o\$362b2o16b2o\$380b2o3\$352b2o\$352b2o5\$375b2o\$375b2o3\$371b2o\$371b2o\$396b2o\$396b2o2\$390b2o\$368b2o20b2o\$368b2o2\$386b2o\$386b2o16b2o\$404b2o3\$376b2o\$376b2o5\$399b2o\$399b2o3\$395b2o\$395b2o\$420b2o\$420b2o2\$414b2o\$392b2o20b2o\$392b2o2\$410b2o\$410b2o16b2o\$428b2o3\$400b2o\$400b2o3\$436b2o\$436b2o\$423b2o\$423b2o3\$419b2o15b2o\$419b2o15bobo\$438b2o4b2o\$437bo6b2o\$435bobo\$434b2o\$416b2o18bo\$416b2o14bo\$431b2o\$430bo2bo\$430b2o14bobo\$431bobo11bo2bo\$431b3o11bo2b2o\$446b3ob2o\$424b2o22bo2bo\$424b2o7bo\$431b2o\$447bo2bo\$448bobo\$449bo3\$432b2o\$432b2o\$447b2o\$446b3o\$447b2o\$449bo\$449bo\$449bo!`

* with the same glider colour as those emitted by the DFIREs.

We also can duplicate blocks with monophase monochromatic gliders, so the remaining task is to be able to move them around to assemble the four requisite OTTs. Then we inherit full universal construction capabilities from slmake.
What do you do with ill crystallographers? Take them to the mono-clinic!

calcyman

Posts: 1897
Joined: June 1st, 2009, 4:32 pm

### Re: Building a reverse caber-tosser

329 gliders in total:

`x = 5379, y = 5173, rule = 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What do you do with ill crystallographers? Take them to the mono-clinic!

calcyman

Posts: 1897
Joined: June 1st, 2009, 4:32 pm

### Re: Building a reverse caber-tosser

EDIT: Fixed double post.
dvgrn wrote:
calcyman wrote:Impressive! I think it needs 5 gliders for the BLSE; I can't see any way to remove the kickback...[/code]
I think that's right. I checked both the BLSE and Cordership syntheses. Didn't see any way to cut the number of gliders in either location -- though I could certainly have missed something.

calcyman wrote:Fortunately, we don't need to separately construct an elbow. After using Dave's DFIRE to delete the first boat, there's a monochromatic* P1 salvo which turns the other boat into a block and gradually pushes it away from the critical zone.

I think there are more efficient monochromatic block pushes, but that's more of a job for a search utility. Is a block-move library already available, from the half-baked knightship project? I didn't do any of that part of the HBKs.

Using this elbow push method, we'd need close to 300 bits on the tape -- 294, I think -- just to make the elbow block and push it back the first 1fd. Each additional push would take more bits than that, but just doing this much already increases the size of the pattern by a factor of something over 10^88.

`x = 5871, y = 5868, rule = 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5748.D.D\$5749.2D2\$5740.C\$5741.2C5.C\$5740.2C7.C\$5747.3C13\$5770.D\$5768.D.D\$5769.2D2\$5760.C\$5761.2C5.C\$5760.2C7.C\$5767.3C13\$5790.D\$5788.D.D\$5789.2D2\$5780.C\$5781.2C5.C\$5780.2C7.C\$5787.3C13\$5810.D\$5808.D.D\$5809.2D2\$5800.C\$5801.2C5.C\$5800.2C7.C\$5807.3C13\$5830.D\$5828.D.D\$5829.2D2\$5820.C\$5821.2C5.C\$5820.2C7.C\$5827.3C13\$5850.D\$5848.D.D\$5849.2D2\$5840.C\$5841.2C5.C\$5840.2C7.C\$5847.3C13\$5870.D\$5868.D.D\$5869.2D2\$5860.C\$5861.2C5.C\$5860.2C7.C\$5867.3C!`

Anyone want to try calculating the Cordership position that will return those bits in that order, and see how much trouble Golly has running the thing? In macrocell format the file size shouldn't be too bad yet -- or even in RLE, I guess, if you don't mind a bunch of numbers here and there with 90-plus digits. The RLE would end up a lot smaller if we rotated the whole synthesis pattern by 180 degrees, or reflected it across the Y axis.

294 bits needed to fire just half a dozen gliders -- ouch!

Maybe a better construction sample would be whatever the cleanest rare object is that can be built with less than ten monochrome-slow gliders. Seems like there ought to be a pulsar at about that cost, anyway. Can just build it close to the BLSE, there's probably no need to push the hand block away first.

Maybe one easy starting point would be to filter Paul Chapman's original P1 block-move table -- recipes here:

2004 Glue block-move table for P1 bichromatic slow salvos
blockmov.png (86.15 KiB) Viewed 8913 times

Any of those recipes that happen to be all even lanes or all odd lanes can be used to move hand blocks around. Luckily the (2,1) block pull changes the color of a block. So it's mostly just a matter of finding the edgiest block move recipes, to place one-time-turner constellation blocks near each other.

I seem to recall that the 2-glider block splitter in the above recipe is actually pretty good for block placement. You just keep the hand block a short distance off to the side, and place new blocks by reaching around behind blocks that have already been placed. The loafer gun in Golly's HashLife folder uses that trick a lot.

dvgrn
Moderator

Posts: 5209
Joined: May 17th, 2009, 11:00 pm

### Re: Building a reverse caber-tosser

Here's another piece of the puzzle. This should be a slightly better option than the old P1 block-move recipes. Looking back at old emails, I stumbled on a filtered list of P2 block-move recipes that use all monochrome monoparity gliders. This was from June 2014, the early days of HBK construction.

In standard slow-salvo recipe format, this restriction means that the parities are all "E", and the quarter-diagonal lane numbers are all 3 (mod 4). To interpret these recipes, copy a line and paste it into build-EO-lane-slow-salvo.py.

This allows blinkers, traffic lights, beacons, toads, and so on to be included as intermediate targets in the block-move recipes. I double-checked that all the numbers in the recipes below are in fact 4N+3 values, for integer N:

`1m2  ,1  :E113m5  ,12 :E-9 E-29 E313m5  ,12 :E-9 E-29 E353m5  ,12 :E-9 E-29 E273m7  ,-8 :E-9 E-29 E-93m7  ,-8 :E-9 E-29 E-173m7  ,-8 :E-9 E-29 E-134m-3 ,1  :E-9 E-13 E-9 E-134m1  ,-2 :E-9 E-13 E-29 E-54m5  ,12 :E-9 E-29 E19 E234m5  ,12 :E-9 E-29 E19 E274m5  ,12 :E-9 E-29 E19 E314m6  ,14 :E-9 E-29 E-25 E274m6  ,14 :E-9 E-29 E-25 E314m6  ,14 :E-9 E-29 E-25 E354m7  ,-8 :E-9 E-29 E-25 E-214m7  ,-8 :E-9 E-29 E-25 E-174m7  ,-8 :E-9 E-29 E-25 E-134m8  ,-6 :E-9 E-29 E19 E-134m8  ,-6 :E-9 E-29 E19 E-174m8  ,-6 :E-9 E-29 E19 E-95m-8 ,7  :E-9 E7 E-21 E-5 E-295m-5 ,3  :E-9 E-13 E-9 E-21 E-215m-5 ,4  :E-9 E-13 E-13 E-29 E75m-2 ,10 :E-9 E7 E-21 E3 E-95m-1 ,4  :E-9 E-13 E-9 E-1 E-15m-1 ,9  :E-9 E7 E-17 E-25 E35m1  ,12 :E-9 E-1 E-1 E19 E235m4  ,0  :E-9 E7 E11 E-29 E75m5  ,12 :E-9 E-29 E19 E39 E315m5  ,12 :E-9 E-29 E39 E43 E275m5  ,12 :E-9 E-29 E19 E39 E355m5  ,12 :E-9 E-29 E19 E39 E275m7  ,-8 :E-9 E-29 E-5 E-1 E-175m7  ,-8 :E-9 E-29 E-25 E-5 E-135m7  ,-8 :E-9 E-29 E-25 E-5 E-95m7  ,-8 :E-9 E-29 E-25 E-5 E-175m8  ,15 :E-9 E-29 E-25 E-5 E275m8  ,15 :E-9 E-29 E-25 E-5 E355m8  ,15 :E-9 E-29 E-25 E-5 E315m10 ,-5 :E-9 E-29 E19 E39 E-135m10 ,-5 :E-9 E-29 E19 E39 E-95m10 ,-5 :E-9 E-29 E19 E39 E-176m-16,11 :E-9 E7 E-9 E-25 E-21 E-776m-16,11 :E-9 E7 E-9 E-25 E-21 E-816m-8 ,7  :E-9 E7 E-21 E-5 E-37 E-256m-6 ,7  :E-9 E7 E-17 E11 E-1 E196m-5 ,4  :E-9 E7 E7 E11 E-29 E196m-5 ,4  :E-9 E7 E7 E11 E-29 E156m-4 ,-10:E-9 E11 E11 E19 E7 E276m-4 ,-10:E-9 E11 E11 E19 E7 E356m-4 ,6  :E-9 E-13 E-13 E-29 E-29 E76m-3 ,11 :E-9 E7 E-17 E-33 E-33 E36m-2 ,-5 :E-9 E-13 E-13 E-1 E-13 E116m-2 ,0  :E-9 E-1 E-5 E7 E3 E-216m-2 ,0  :E-9 E-1 E-5 E7 E3 E-136m-1 ,-1 :E-9 E-29 E39 E59 E39 E-136m-1 ,-1 :E-9 E-29 E39 E59 E39 E-176m-1 ,-1 :E-9 E-29 E39 E59 E39 E-96m-1 ,8  :E-9 E7 E7 E-17 E3 E-576m-1 ,8  :E-9 E7 E7 E-17 E3 E-536m-1 ,8  :E-9 E7 E7 E-17 E3 E-496m-1 ,8  :E-9 E7 E7 E-17 E-49 E36m0  ,8  :E-9 E-13 E-17 E-5 E-37 E-416m0  ,8  :E-9 E7 E-5 E11 E7 E-336m0  ,11 :E-9 E7 E-21 E3 E-13 E-96m1  ,6  :E-9 E-13 E-17 E-21 E-41 E-96m1  ,6  :E-9 E-13 E-17 E-21 E-41 E-296m1  ,7  :E-9 E-13 E-13 E-9 E3 E116m1  ,7  :E-9 E-13 E-13 E-9 E3 E156m1  ,28 :E-9 E7 E7 E-17 E-5 E156m1  ,28 :E-9 E7 E7 E-17 E3 E-176m1  ,28 :E-9 E7 E7 E-17 E-13 E36m1  ,28 :E-9 E7 E7 E-17 E3 E-136m1  ,28 :E-9 E7 E7 E-17 E-5 E-56m1  ,28 :E-9 E7 E7 E-17 E3 E-216m4  ,9  :E-9 E7 E-5 E-17 E-1 E-256m4  ,9  :E-9 E7 E-5 E-17 E-1 E-336m4  ,9  :E-9 E7 E-17 E-29 E-25 E36m5  ,12 :E-9 E-29 E39 E27 E27 E356m5  ,12 :E-9 E-29 E39 E43 E39 E396m5  ,12 :E-9 E-29 E39 E43 E39 E356m5  ,12 :E-9 E-29 E39 E43 E31 E396m5  ,12 :E-9 E-29 E39 E27 E27 E556m5  ,12 :E-9 E-29 E39 E59 E39 E36m5  ,12 :E-9 E-29 E39 E59 E39 E-16m5  ,12 :E-9 E-29 E39 E59 E-1 E476m5  ,12 :E-9 E-29 E39 E59 E-1 E436m5  ,12 :E-9 E-29 E39 E23 E59 E316m5  ,12 :E-9 E-29 E39 E23 E59 E396m5  ,12 :E-9 E-29 E39 E59 E-1 E396m5  ,12 :E-9 E-29 E39 E43 E31 E596m6  ,14 :E-9 E-29 E39 E43 E-25 E276m7  ,-8 :E-9 E-29 E-5 E-21 E15 E-56m7  ,-8 :E-9 E-29 E-5 E-1 E-13 E-56m7  ,-8 :E-9 E-29 E-5 E-17 E-17 E-96m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E-56m7  ,-8 :E-9 E-29 E-5 E-17 E-17 E116m7  ,-8 :E-9 E-29 E-5 E-21 E15 E-136m7  ,-8 :E-9 E-29 E-5 E-1 E-13 E156m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E-96m8  ,-6 :E-9 E-29 E-5 E-1 E19 E-176m8  ,4  :E-9 E-1 E-17 E3 E-9 E-216m8  ,4  :E-9 E-1 E-17 E3 E-9 E-136m11 ,3  :E-9 E7 E-17 E11 E-9 E36m14 ,-16:E-9 E7 E-5 E-9 E-9 E596m19 ,-3 :E-9 E-29 E39 E59 E-1 E-96m19 ,-3 :E-9 E-29 E39 E59 E-1 E-176m19 ,-3 :E-9 E-29 E39 E59 E-1 E-136m24 ,2  :E-9 E11 E11 E23 E-21 E-17m-25,13 :E-9 E-13 E-17 E-33 E-17 E-37 E77m-25,13 :E-9 E-13 E-17 E-33 E-17 E-21 E117m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E157m-25,13 :E-9 E-13 E-17 E-33 E-17 E-37 E-137m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E-17m-25,13 :E-9 E-13 E-17 E-33 E-17 E3 E-257m-25,13 :E-9 E-13 E-17 E-33 E-17 E3 E-297m-18,6  :E-9 E7 E-9 E-57 E-53 E-25 E-497m-18,6  :E-9 E7 E-9 E-57 E-53 E-25 E-577m-16,11 :E-9 E7 E-9 E-25 E-21 E-89 E-937m-12,9  :E-9 E7 E-5 E11 E3 E-53 E117m-12,16 :E-9 E-1 E-17 E-9 E19 E7 E-297m-11,4  :E-9 E7 E-9 E-37 E-41 E-53 E-337m-11,4  :E-9 E7 E-9 E-57 E-53 E-45 E-577m-11,4  :E-9 E7 E-9 E-57 E-53 E-45 E-497m-10,16 :E-9 E7 E-17 E-29 E-41 E-45 E37m-9 ,9  :E-9 E7 E-17 E-29 E-41 E-45 E-217m-8 ,0  :E-9 E-13 E-13 E-29 E-29 E-9 E-177m-8 ,0  :E-9 E-13 E-13 E-29 E-29 E-9 E-217m-8 ,0  :E-9 E-13 E-13 E-29 E-29 E-9 E-257m-8 ,3  :E-9 E11 E11 E23 E39 E11 E397m-8 ,3  :E-9 E11 E11 E23 E39 E11 E477m-8 ,3  :E-9 E11 E11 E23 E39 E11 E357m-8 ,4  :E-9 E-1 E-17 E11 E-25 E-37 E277m-8 ,4  :E-9 E-1 E-17 E11 E-25 E-37 E237m-8 ,12 :E-9 E7 E-5 E3 E23 E3 E117m-8 ,12 :E-9 E7 E-5 E3 E23 E3 E157m-8 ,12 :E-9 E7 E-5 E3 E23 E3 E197m-8 ,17 :E-9 E-1 E-1 E19 E19 E-17 E-257m-8 ,17 :E-9 E-1 E-1 E19 E19 E-17 E-297m-6 ,-8 :E-9 E11 E11 E19 E-1 E-1 E357m-6 ,-8 :E-9 E11 E11 E19 E-1 E-1 E277m-6 ,-5 :E-9 E7 E-5 E-29 E-9 E-1 E-177m-6 ,-5 :E-9 E7 E-5 E-29 E-9 E-29 E-137m-6 ,9  :E-9 E11 E11 E-29 E-29 E-17 E37m-6 ,11 :E-9 E11 E11 E-29 E-29 E3 E77m-5 ,4  :E-9 E-13 E-13 E-1 E-1 E-29 E-57m-5 ,4  :E-9 E7 E7 E11 E-29 E11 E117m-5 ,4  :E-9 E7 E7 E11 E-29 E11 E157m-5 ,4  :E-9 E7 E7 E11 E-29 E3 E157m-5 ,4  :E-9 E7 E7 E11 E-29 E11 E197m-5 ,4  :E-9 E7 E7 E11 E-29 E23 E157m-5 ,4  :E-9 E7 E7 E11 E-29 E23 E197m-5 ,4  :E-9 E7 E7 E11 E-29 E23 E37m-5 ,7  :E-9 E11 E11 E3 E-5 E-21 E197m-5 ,11 :E-9 E-13 E-17 E-33 E-17 E-81 E77m-5 ,11 :E-9 E-13 E-17 E-33 E-17 E-81 E-137m-4 ,-10:E-9 E11 E11 E19 E7 E23 E237m-4 ,-10:E-9 E11 E11 E19 E31 E7 E197m-4 ,-10:E-9 E11 E11 E19 E31 E7 E237m-4 ,-10:E-9 E11 E11 E19 E31 E7 E157m-4 ,6  :E-9 E7 E7 E11 E-29 E-29 E157m-4 ,6  :E-9 E7 E7 E11 E-29 E-29 E197m-4 ,7  :E-9 E-13 E-17 E-5 E-5 E-33 E-297m-4 ,7  :E-9 E-13 E-17 E-5 E-5 E-33 E-497m-4 ,10 :E-9 E11 E11 E-1 E27 E-33 E-97m-3 ,-9 :E-9 E-13 E-13 E-29 E-29 E-13 E-137m-3 ,5  :E-9 E7 E-21 E-13 E-1 E-9 E-17m-3 ,5  :E-9 E7 E-21 E-13 E-1 E-9 E117m-3 ,16 :E-9 E-9 E19 E-1 E-1 E7 E397m-3 ,16 :E-9 E-9 E19 E-1 E-1 E7 E197m-2 ,5  :E-9 E-13 E-13 E-1 E-1 E-29 E-97m-2 ,10 :E-9 E7 E-21 E11 E19 E-5 E117m-2 ,12 :E-9 E-9 E-5 E-17 E-25 E-5 E157m-2 ,17 :E-9 E-1 E15 E-5 E-5 E35 E-217m-2 ,17 :E-9 E-1 E15 E-5 E-5 E-21 E357m-1 ,-1 :E-9 E-29 E39 E59 E39 E-25 E-137m-1 ,-1 :E-9 E-29 E39 E59 E39 E-25 E-177m-1 ,-1 :E-9 E-29 E39 E59 E39 E-25 E-217m-1 ,1  :E-9 E7 E-17 E-25 E11 E3 E-97m-1 ,1  :E-9 E7 E-17 E-25 E11 E3 E-297m-1 ,4  :E-9 E7 E-21 E-21 E11 E-29 E77m-1 ,5  :E-9 E7 E-5 E11 E3 E-5 E-497m-1 ,5  :E-9 E7 E-5 E11 E3 E-5 E-577m-1 ,8  :E-9 E7 E7 E-17 E-65 E3 E-537m-1 ,8  :E-9 E7 E7 E-17 E-65 E3 E-577m-1 ,8  :E-9 E7 E7 E-17 E-65 E3 E-617m-1 ,12 :E-9 E7 E-17 E11 E7 E-1 E117m-1 ,12 :E-9 E7 E-17 E11 E7 E-1 E197m-1 ,28 :E-9 E11 E11 E-1 E27 E-29 E-417m0  ,-10:E-9 E7 E-17 E-29 E-25 E23 E-57m0  ,-10:E-9 E7 E-17 E-29 E-25 E23 E-97m0  ,-10:E-9 E7 E-17 E-29 E-25 E23 E-137m0  ,19 :E-9 E-1 E15 E-5 E-29 E35 E-137m0  ,19 :E-9 E-1 E15 E-5 E-29 E35 E-97m0  ,19 :E-9 E-1 E15 E-5 E-29 E-9 E357m1  ,-2 :E-9 E7 E7 E-13 E-29 E-5 E277m1  ,0  :E-9 E-29 E39 E59 E39 E11 E-97m1  ,0  :E-9 E-29 E39 E59 E39 E11 E-177m1  ,0  :E-9 E-29 E39 E59 E39 E11 E-137m1  ,0  :E-9 E7 E11 E7 E11 E-5 E-297m1  ,0  :E-9 E-13 E-13 E-9 E15 E-1 E-177m1  ,7  :E-9 E-13 E-13 E-9 E3 E3 E-17m1  ,7  :E-9 E-13 E-13 E-9 E3 E19 E157m1  ,7  :E-9 E-13 E-13 E-9 E3 E19 E117m1  ,7  :E-9 E-13 E-13 E-9 E3 E19 E-17m1  ,12 :E-9 E-1 E-1 E19 E27 E-5 E317m1  ,28 :E-9 E7 E7 E-17 E11 E-5 E277m1  ,28 :E-9 E7 E7 E-17 E-13 E-9 E-57m1  ,28 :E-9 E7 E7 E-17 E-13 E-9 E-97m1  ,28 :E-9 E7 E7 E-17 E11 E-5 E317m1  ,28 :E-9 E7 E7 E-17 E11 E-5 E357m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-537m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-577m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-497m2  ,-14:E-9 E7 E-17 E11 E-5 E-33 E-137m2  ,8  :E-9 E-1 E15 E-5 E-17 E35 E-337m2  ,8  :E-9 E-1 E15 E-5 E-17 E35 E-377m2  ,8  :E-9 E-1 E15 E-5 E-17 E35 E-497m2  ,12 :E-9 E-9 E-5 E-17 E-25 E-21 E157m2  ,30 :E-9 E7 E7 E-17 E-65 E3 E-137m2  ,30 :E-9 E7 E7 E-17 E-65 E-13 E37m2  ,30 :E-9 E7 E7 E-17 E-65 E-5 E-57m2  ,30 :E-9 E7 E7 E-17 E-65 E3 E-217m2  ,30 :E-9 E7 E7 E-17 E-65 E-5 E157m2  ,30 :E-9 E7 E7 E-17 E-65 E3 E-177m3  ,-2 :E-9 E-13 E-13 E-9 E-9 E-9 E-137m3  ,-2 :E-9 E-13 E-13 E-9 E-9 E-9 E-177m3  ,8  :E-9 E-9 E-5 E-17 E-25 E-25 E157m3  ,9  :E-9 E-13 E-17 E-21 E-5 E-41 E77m4  ,0  :E-9 E7 E-5 E11 E7 E-29 E-257m4  ,0  :E-9 E7 E-5 E11 E7 E-29 E-137m4  ,9  :E-9 E7 E-17 E-29 E-25 E15 E117m4  ,9  :E-9 E7 E-17 E-29 E-25 E11 E197m4  ,9  :E-9 E7 E-17 E-29 E-25 E23 E157m4  ,9  :E-9 E7 E-17 E-29 E-25 E11 E117m4  ,9  :E-9 E7 E-17 E-29 E-25 E23 E197m4  ,9  :E-9 E7 E-17 E-29 E-25 E23 E237m4  ,14 :E-9 E7 E-5 E-17 E11 E3 E-57m5  ,-2 :E-9 E11 E11 E-1 E19 E-53 E-497m5  ,11 :E-9 E7 E-17 E-29 E-25 E-21 E37m5  ,12 :E-9 E-29 E39 E43 E47 E71 E597m5  ,12 :E-9 E-29 E39 E43 E47 E71 E637m5  ,12 :E-9 E-29 E19 E39 E39 E43 E277m5  ,12 :E-9 E-29 E39 E43 E19 E19 E357m5  ,12 :E-9 E-29 E39 E43 E47 E35 E637m5  ,12 :E-9 E-29 E39 E43 E43 E23 E637m5  ,12 :E-9 E-29 E39 E23 E35 E55 E637m5  ,12 :E-9 E-29 E19 E19 E-1 E19 E637m5  ,12 :E-9 E-29 E39 E59 E39 E11 E37m5  ,12 :E-9 E-29 E39 E59 E39 E11 E-17m5  ,12 :E-9 E-29 E39 E59 E55 E-1 E517m5  ,12 :E-9 E-29 E39 E59 E55 E-1 E477m5  ,12 :E-9 E-29 E39 E59 E55 E-1 E437m5  ,12 :E-9 E-29 E39 E59 E39 E11 E77m5  ,12 :E-9 E-29 E19 E19 E-1 E19 E597m5  ,12 :E-9 E-29 E39 E43 E43 E59 E397m5  ,12 :E-9 E-29 E39 E23 E47 E27 E477m5  ,12 :E-9 E-29 E39 E23 E51 E43 E437m5  ,12 :E-9 E-29 E39 E31 E23 E19 E517m5  ,12 :E-9 E-29 E39 E43 E39 E47 E517m5  ,12 :E-9 E-29 E39 E23 E47 E27 E517m5  ,12 :E-9 E-29 E39 E43 E19 E19 E117m5  ,12 :E-9 E-29 E39 E43 E39 E51 E397m5  ,12 :E-9 E-29 E39 E43 E43 E23 E557m5  ,12 :E-9 E-29 E39 E31 E23 E19 E557m5  ,12 :E-9 E-29 E19 E19 E39 E31 E37m5  ,12 :E-9 E-29 E19 E19 E-1 E19 E557m5  ,12 :E-9 E-29 E19 E19 E39 E31 E237m5  ,12 :E-9 E-29 E39 E23 E35 E55 E397m5  ,12 :E-9 E-29 E39 E23 E35 E55 E557m6  ,-9 :E-9 E-13 E-13 E-9 E19 E23 E37m6  ,-9 :E-9 E-13 E-13 E-9 E19 E23 E-177m6  ,-4 :E-9 E11 E11 E19 E31 E3 E-17m6  ,-4 :E-9 E11 E11 E19 E31 E7 E77m6  ,-1 :E-9 E7 E-17 E-13 E11 E-25 E-97m6  ,7  :E-9 E11 E11 E23 E7 E-29 E397m6  ,7  :E-9 E11 E11 E23 E39 E7 E-297m6  ,7  :E-9 E11 E11 E23 E7 E-29 E437m6  ,7  :E-9 E11 E11 E23 E7 E-29 E477m6  ,12 :E-9 E7 E-21 E-13 E3 E-21 E77m6  ,14 :E-9 E-29 E39 E27 E-25 E27 E357m6  ,14 :E-9 E-29 E39 E43 E-25 E59 E317m6  ,14 :E-9 E-29 E39 E43 E-25 E59 E397m6  ,14 :E-9 E-29 E39 E43 E-25 E39 E397m6  ,14 :E-9 E-29 E39 E59 E-1 E-25 E397m6  ,14 :E-9 E-29 E39 E59 E39 E-25 E37m6  ,14 :E-9 E-29 E39 E59 E39 E-25 E-17m6  ,14 :E-9 E-29 E39 E43 E-25 E39 E357m6  ,14 :E-9 E-29 E39 E59 E-1 E-25 E477m6  ,14 :E-9 E-29 E39 E59 E-1 E-25 E437m6  ,14 :E-9 E-29 E39 E27 E-25 E27 E557m7  ,-8 :E-9 E-29 E-5 E-21 E3 E-17 E77m7  ,-8 :E-9 E-29 E-5 E-1 E-25 E-25 E-97m7  ,-8 :E-9 E-29 E-5 E-1 E3 E27 E197m7  ,-8 :E-9 E-29 E-5 E-21 E7 E-1 E-17m7  ,-8 :E-9 E-29 E-5 E-21 E-9 E11 E117m7  ,-8 :E-9 E-29 E-5 E-1 E-1 E-21 E117m7  ,-8 :E-9 E-29 E-5 E-21 E-9 E11 E197m7  ,-8 :E-9 E-29 E-5 E-1 E3 E27 E157m7  ,-8 :E-9 E-29 E-5 E-21 E-9 E11 E-57m7  ,-8 :E-9 E-29 E-5 E-21 E15 E-17 E-177m7  ,-8 :E-9 E-29 E-25 E-25 E-5 E-13 E-417m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E3 E77m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E7 E-57m7  ,-8 :E-9 E-29 E-25 E-25 E-45 E19 E-297m7  ,-8 :E-9 E-29 E-25 E-25 E-45 E19 E-337m7  ,-8 :E-9 E-29 E-5 E-1 E-25 E-25 E-337m7  ,-8 :E-9 E-29 E-25 E-5 E-5 E-1 E-177m7  ,-8 :E-9 E-29 E-5 E-1 E-1 E-21 E197m7  ,-8 :E-9 E-29 E-25 E-25 E-45 E19 E-257m7  ,-8 :E-9 E-29 E-5 E-21 E3 E-17 E37m7  ,-8 :E-9 E-29 E-5 E-1 E-1 E15 E-57m7  ,-8 :E-9 E-29 E-25 E-25 E-5 E-13 E-217m7  ,-8 :E-9 E-29 E-5 E-1 E3 E-9 E197m8  ,-6 :E-9 E-29 E-5 E-1 E-5 E19 E-97m8  ,-6 :E-9 E-29 E-5 E-1 E19 E15 E-57m8  ,-6 :E-9 E-29 E-5 E-17 E-17 E19 E117m8  ,-6 :E-9 E-29 E-5 E-17 E-17 E19 E-97m8  ,-6 :E-9 E-29 E-5 E-1 E-5 E19 E-57m8  ,-6 :E-9 E-29 E-5 E-1 E19 E15 E-137m8  ,-3 :E-9 E7 E-5 E3 E-5 E-41 E-177m8  ,6  :E-9 E-1 E-17 E15 E19 E7 E-137m8  ,8  :E-9 E11 E11 E3 E-17 E-41 E-377m8  ,12 :E-9 E11 E11 E-1 E7 E11 E117m9  ,10 :E-9 E-13 E-17 E-21 E-21 E-41 E-177m10 ,-5 :E-9 E-29 E-5 E-1 E19 E39 E-177m10 ,2  :E-9 E7 E-5 E11 E-1 E11 E-497m10 ,2  :E-9 E7 E-5 E11 E-1 E11 E-417m10 ,2  :E-9 E7 E-5 E11 E-1 E-41 E117m10 ,5  :E-9 E-1 E-17 E3 E19 E-9 E-217m10 ,5  :E-9 E-1 E-17 E3 E19 E-9 E-137m10 ,12 :E-9 E-13 E-17 E-13 E-33 E-33 E-217m11 ,-7 :E-9 E-1 E-17 E-1 E55 E3 E-137m11 ,-7 :E-9 E-1 E-17 E-1 E55 E3 E-217m11 ,3  :E-9 E7 E7 E11 E-29 E11 E-217m11 ,3  :E-9 E7 E7 E11 E-29 E11 E-177m11 ,3  :E-9 E7 E7 E11 E-29 E11 E-137m11 ,4  :E-9 E7 E-5 E3 E23 E3 E-377m11 ,4  :E-9 E7 E-5 E3 E23 E3 E-417m11 ,4  :E-9 E7 E-5 E3 E23 E3 E-457m11 ,26 :E-9 E-29 E-25 E-25 E-45 E19 E277m11 ,26 :E-9 E-29 E-25 E-25 E-45 E19 E317m11 ,26 :E-9 E-29 E-25 E-25 E-45 E19 E357m12 ,0  :E-9 E-1 E-17 E11 E-25 E11 E-217m12 ,0  :E-9 E-1 E-17 E11 E-25 E11 E-257m14 ,22 :E-9 E-9 E19 E-9 E11 E11 E37m15 ,-14:E-9 E-29 E19 E19 E-1 E19 E-177m15 ,-14:E-9 E-29 E19 E19 E-1 E19 E-97m15 ,-14:E-9 E-29 E19 E19 E-1 E19 E-137m17 ,6  :E-9 E11 E11 E23 E-21 E15 E437m17 ,6  :E-9 E11 E11 E23 E-21 E15 E477m19 ,-3 :E-9 E-29 E39 E59 E-1 E-25 E-137m19 ,-3 :E-9 E-29 E39 E59 E-1 E-25 E-177m19 ,-3 :E-9 E-29 E39 E59 E-1 E-25 E-217m20 ,2  :E-9 E-9 E3 E11 E3 E23 E37m21 ,-2 :E-9 E-29 E39 E59 E55 E-1 E-97m21 ,-2 :E-9 E-29 E39 E59 E55 E-1 E-177m21 ,-2 :E-9 E-29 E39 E59 E55 E-1 E-137m24 ,2  :E-9 E11 E11 E23 E-21 E15 E237m24 ,2  :E-9 E11 E11 E23 E7 E-29 E-17m24 ,2  :E-9 E11 E11 E23 E7 E-29 E37m24 ,2  :E-9 E11 E11 E23 E-13 E-21 E-97m24 ,2  :E-9 E11 E11 E23 E-21 E15 E197m24 ,2  :E-9 E11 E11 E23 E7 E-29 E-57m24 ,2  :E-9 E11 E11 E23 E-13 E-29 E117m26 ,3  :E-9 E11 E11 E23 E55 E-21 E-18m-25,13 :E-9 E-13 E-17 E-33 E-17 E11 E-45 E-138m-25,13 :E-9 E-13 E-17 E-33 E-17 E11 E-13 E-458m-25,13 :E-9 E-13 E-17 E-33 E-17 E11 E-45 E38m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E3 E-98m-25,13 :E-9 E-13 E-17 E-33 E-17 E-21 E-41 E-58m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E19 E198m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E19 E118m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E19 E-18m-25,13 :E-9 E-13 E-17 E-33 E-17 E3 E-5 E-58m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E3 E-178m-25,13 :E-9 E-13 E-17 E-33 E-17 E3 E-5 E-98m-25,13 :E-9 E-13 E-17 E-33 E-17 E3 E-5 E-138m-25,13 :E-9 E-13 E-17 E-33 E-17 E3 E-13 E-178m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E7 E-18m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E7 E78m-25,13 :E-9 E-13 E-17 E-33 E-17 E11 E-13 E-298m-23,14 :E-9 E-13 E-17 E-33 E-17 E-37 E-65 E-138m-23,14 :E-9 E-13 E-17 E-33 E-17 E-9 E-65 E-18m-23,14 :E-9 E-13 E-17 E-33 E-17 E3 E-65 E-258m-23,14 :E-9 E-13 E-17 E-33 E-17 E-37 E-65 E78m-23,14 :E-9 E-13 E-17 E-33 E-17 E3 E-65 E-298m-23,14 :E-9 E-13 E-17 E-33 E-17 E-21 E-65 E118m-23,14 :E-9 E-13 E-17 E-33 E-17 E-9 E-65 E158m-18,6  :E-9 E7 E-9 E-41 E-33 E-33 E-25 E-458m-18,6  :E-9 E7 E-9 E-45 E-29 E-37 E-41 E-458m-18,6  :E-9 E7 E-9 E-57 E-37 E-49 E-25 E-538m-18,6  :E-9 E7 E-9 E-57 E-37 E-49 E-25 E-498m-18,6  :E-9 E7 E-9 E-57 E-37 E-49 E-25 E-458m-18,6  :E-9 E7 E-9 E-57 E-29 E-21 E-21 E-418m-18,6  :E-9 E7 E-9 E-57 E-29 E-21 E-21 E-218m-18,6  :E-9 E7 E-9 E-57 E-53 E-61 E-25 E-618m-18,6  :E-9 E7 E-9 E-41 E-33 E-33 E-25 E-378m-16,7  :E-9 E7 E-9 E-57 E-53 E-25 E-37 E-498m-16,7  :E-9 E7 E-9 E-57 E-53 E-25 E-37 E-578m-16,10 :E-9 E-13 E-17 E-21 E-25 E-9 E-61 E-298m-16,11 :E-9 E7 E-9 E-25 E-21 E-89 E-97 E-1018m-16,11 :E-9 E7 E-9 E-25 E-21 E-89 E-101 E-898m-16,11 :E-9 E7 E-9 E-25 E-21 E-89 E-97 E-1058m-15,14 :E-9 E-13 E-17 E-21 E-25 E-9 E-41 E-298m-13,-3 :E-9 E11 E11 E19 E3 E-9 E-13 E278m-13,-3 :E-9 E11 E11 E19 E3 E-9 E-13 E358m-13,4  :E-9 E7 E7 E11 E-29 E-25 E-21 E-498m-13,4  :E-9 E7 E7 E11 E-29 E-25 E-21 E-578m-13,11 :E-9 E7 E-9 E-37 E-29 E-57 E-37 E-298m-12,16 :E-9 E-1 E-17 E-9 E19 E23 E-29 E-138m-12,16 :E-9 E-1 E-17 E-9 E19 E23 E-29 E78m-12,16 :E-9 E-1 E-17 E-9 E19 E19 E-29 E238m-11,-12:E-9 E-13 E-17 E-33 E-53 E-37 E-21 E358m-11,4  :E-9 E7 E-9 E-37 E-41 E-25 E-53 E-378m-11,4  :E-9 E7 E-9 E-37 E-41 E-29 E-53 E-218m-11,4  :E-9 E7 E-9 E-37 E-41 E-29 E-53 E-258m-11,4  :E-9 E7 E-9 E-37 E-41 E-53 E-25 E-378m-11,4  :E-9 E7 E-9 E-29 E-29 E-53 E-53 E-338m-11,4  :E-9 E7 E-9 E-57 E-53 E-61 E-45 E-618m-10,6  :E-9 E7 E-9 E-57 E-53 E-45 E-41 E-498m-10,6  :E-9 E7 E-9 E-57 E-53 E-45 E-41 E-578m-10,9  :E-9 E7 E11 E-29 E-9 E-13 E-41 E198m-10,16 :E-9 E7 E-17 E-29 E-41 E-45 E-9 E-58m-10,16 :E-9 E7 E-17 E-29 E-41 E-45 E-9 E-98m-10,18 :E-9 E7 E-5 E11 E-1 E11 E-45 E198m-10,18 :E-9 E7 E-5 E11 E-1 E11 E-45 E158m-10,18 :E-9 E7 E-5 E11 E-1 E11 E-45 E118m-9 ,-5 :E-9 E7 E-9 E-57 E-29 E-21 E-33 E-418m-9 ,8  :E-9 E-1 E-17 E11 E-25 E-13 E-21 E278m-9 ,8  :E-9 E-1 E-17 E11 E-25 E-13 E-21 E238m-9 ,14 :E-9 E-29 E-5 E-1 E-25 E-9 E15 E358m-9 ,14 :E-9 E-29 E-5 E-1 E-25 E-9 E15 E318m-9 ,14 :E-9 E-29 E-5 E-1 E-25 E-9 E15 E278m-8 ,0  :E-9 E7 E7 E-13 E-13 E-33 E-9 E278m-8 ,3  :E-9 E11 E11 E23 E55 E11 E-21 E-178m-8 ,4  :E-9 E-1 E-17 E11 E-25 E3 E-37 E238m-8 ,4  :E-9 E-1 E-17 E11 E-25 E35 E-37 E238m-8 ,12 :E-9 E7 E-5 E3 E23 E3 E3 E118m-8 ,12 :E-9 E7 E-5 E3 E23 E3 E3 E158m-8 ,12 :E-9 E7 E-5 E3 E23 E3 E3 E78m-7 ,-2 :E-9 E-17 E19 E-5 E11 E31 E-41 E-218m-7 ,-2 :E-9 E-17 E19 E-5 E11 E31 E-41 E-258m-7 ,5  :E-9 E7 E-21 E11 E-1 E7 E31 E198m-7 ,14 :E-9 E11 E11 E-1 E-9 E7 E-45 E-218m-6 ,-5 :E-9 E7 E-5 E-29 E-9 E-29 E-29 E-138m-6 ,-5 :E-9 E7 E-5 E-29 E-9 E-29 E-5 E-138m-6 ,-4 :E-9 E-1 E-5 E7 E3 E-9 E7 E-18m-6 ,5  :E-9 E-1 E-17 E11 E-25 E-13 E-37 E278m-6 ,5  :E-9 E-1 E-17 E11 E-25 E-13 E-37 E238m-6 ,9  :E-9 E7 E-5 E-29 E3 E-1 E7 E118m-6 ,9  :E-9 E7 E-5 E-29 E3 E-1 E11 E118m-6 ,9  :E-9 E7 E-5 E-29 E3 E-1 E-5 E158m-6 ,11 :E-9 E11 E11 E-29 E3 E-1 E-29 E38m-6 ,11 :E-9 E11 E11 E-29 E3 E-1 E-29 E-138m-6 ,11 :E-9 E7 E11 E7 E-29 E-5 E-5 E-178m-6 ,11 :E-9 E-13 E-13 E-1 E-17 E-17 E-21 E-98m-5 ,4  :E-9 E7 E7 E11 E-29 E3 E23 E198m-5 ,4  :E-9 E7 E7 E11 E-29 E3 E23 E358m-5 ,7  :E-9 E11 E11 E3 E-5 E-21 E15 E118m-5 ,7  :E-9 E11 E11 E3 E-5 E-21 E15 E78m-4 ,6  :E-9 E7 E7 E11 E-29 E23 E-29 E38m-4 ,6  :E-9 E7 E7 E11 E-29 E23 E-29 E198m-4 ,6  :E-9 E7 E7 E11 E-29 E23 E-29 E158m-3 ,-9 :E-9 E-13 E-13 E-29 E-29 E-13 E-21 E-98m-3 ,-9 :E-9 E-13 E-13 E-29 E-29 E-13 E-17 E-258m-3 ,-9 :E-9 E-13 E-13 E-29 E-29 E-13 E-17 E-218m-3 ,1  :E-9 E-13 E-17 E-33 E-17 E3 E-5 E-818m-3 ,1  :E-9 E-13 E-17 E-33 E-17 E3 E-5 E-778m-3 ,1  :E-9 E-13 E-17 E-33 E-17 E3 E-5 E-738m-2 ,-19:E-9 E7 E11 E-29 E-9 E7 E-1 E358m-2 ,5  :E-9 E7 E-17 E11 E-9 E-29 E-5 E-298m-2 ,5  :E-9 E7 E-17 E11 E-9 E-29 E-5 E-458m-2 ,5  :E-9 E-9 E-5 E-13 E-17 E-29 E-13 E-618m-2 ,10 :E-9 E7 E-21 E11 E19 E-5 E3 E158m-2 ,10 :E-9 E7 E-21 E11 E19 E7 E-5 E-18m-2 ,10 :E-9 E7 E-21 E11 E19 E7 E-5 E38m-2 ,15 :E-9 E11 E11 E-29 E3 E-1 E7 E-58m-1 ,0  :E-9 E7 E-17 E11 E-1 E-13 E-33 E238m-1 ,0  :E-9 E7 E-17 E11 E-1 E-13 E-33 E38m-1 ,4  :E-9 E7 E-21 E-21 E11 E11 E-29 E158m-1 ,4  :E-9 E7 E-21 E-21 E11 E11 E-29 E118m-1 ,11 :E-9 E11 E11 E-1 E27 E-25 E-33 E-98m-1 ,19 :E-9 E-1 E15 E-5 E-5 E-21 E-49 E358m-1 ,19 :E-9 E-29 E-5 E-21 E15 E-17 E-33 E358m-1 ,19 :E-9 E-29 E-5 E-21 E15 E-17 E-33 E278m-1 ,19 :E-9 E-29 E-5 E-21 E15 E-17 E-33 E318m-1 ,28 :E-9 E11 E11 E-1 E27 E-29 E-33 E-458m0  ,9  :E-9 E7 E-9 E-41 E-21 E-29 E-25 E-498m0  ,9  :E-9 E7 E-9 E-41 E-21 E-29 E-25 E-418m0  ,13 :E-9 E-9 E-5 E-17 E-25 E-5 E-17 E158m0  ,19 :E-9 E-1 E15 E-5 E-9 E11 E-29 E398m0  ,19 :E-9 E-1 E15 E-5 E-5 E35 E-29 E-138m0  ,19 :E-9 E-1 E15 E-5 E-5 E35 E-29 E-98m0  ,19 :E-9 E-1 E15 E-5 E-5 E35 E-29 E-258m0  ,19 :E-9 E-1 E15 E-5 E-9 E11 E-29 E198m1  ,-2 :E-9 E7 E-21 E-13 E-29 E-17 E-5 E-218m1  ,-2 :E-9 E-9 E19 E-5 E27 E-29 E-5 E318m1  ,0  :E-9 E11 E11 E-1 E7 E-13 E23 E-138m1  ,0  :E-9 E11 E11 E-1 E7 E-17 E23 E-58m1  ,0  :E-9 E11 E11 E-1 E7 E-13 E23 E-218m1  ,0  :E-9 E11 E11 E-1 E7 E-1 E23 E-218m1  ,6  :E-9 E7 E-5 E11 E3 E-5 E-1 E-578m1  ,6  :E-9 E7 E-5 E11 E3 E-5 E-1 E-498m1  ,12 :E-9 E-1 E-1 E19 E27 E35 E-5 E438m1  ,12 :E-9 E-1 E-1 E19 E27 E35 E-5 E398m1  ,12 :E-9 E-1 E-1 E19 E27 E39 E-5 E278m1  ,21 :E-9 E-1 E15 E-5 E-29 E-49 E-9 E358m1  ,21 :E-9 E7 E-17 E-33 E-25 E-37 E-21 E78m1  ,21 :E-9 E7 E-17 E-33 E-25 E-37 E-21 E38m1  ,21 :E-9 E7 E-17 E-33 E-25 E-37 E7 E-218m1  ,28 :E-9 E7 E7 E-17 E-13 E-17 E-41 E-338m1  ,28 :E-9 E7 E7 E-17 E-13 E-13 E-25 E78m1  ,28 :E-9 E7 E7 E-17 E-13 E-17 E-41 E-298m1  ,28 :E-9 E7 E7 E-17 E11 E-5 E43 E398m1  ,28 :E-9 E7 E7 E-17 E11 E-5 E43 E318m1  ,28 :E-9 E7 E7 E-17 E11 E-5 E43 E358m2  ,-18:E-9 E-13 E-13 E-9 E-5 E55 E-13 E-178m2  ,-14:E-9 E7 E-17 E11 E-5 E-13 E-25 E-338m2  ,-14:E-9 E7 E-17 E11 E-5 E-13 E-25 E-258m2  ,-14:E-9 E7 E-17 E11 E-5 E-9 E-13 E-338m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-65 E-538m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-65 E-578m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-65 E-618m2  ,-14:E-9 E7 E-17 E11 E-5 E-9 E-9 E-218m2  ,-14:E-9 E7 E-17 E11 E-5 E-9 E-9 E-178m2  ,-14:E-9 E7 E7 E11 E-13 E-5 E-29 E278m2  ,0  :E-9 E7 E7 E-13 E-29 E-5 E-5 E278m2  ,2  :E-9 E11 E11 E-29 E-29 E-29 E19 E78m2  ,12 :E-9 E-13 E-13 E-9 E3 E3 E-17 E-58m2  ,14 :E-9 E-1 E-1 E19 E27 E-5 E-33 E318m2  ,30 :E-9 E7 E7 E-17 E11 E-5 E-65 E358m2  ,30 :E-9 E7 E7 E-17 E11 E-5 E-65 E318m2  ,30 :E-9 E7 E7 E-17 E11 E-5 E-65 E278m2  ,30 :E-9 E7 E7 E-17 E-65 E-13 E-9 E-98m2  ,30 :E-9 E7 E7 E-17 E-65 E-13 E-9 E-58m3  ,0  :E-9 E-1 E15 E-13 E-29 E-21 E-1 E-178m3  ,0  :E-9 E-1 E15 E-13 E-29 E-21 E-1 E-218m3  ,0  :E-9 E-1 E15 E-13 E-29 E-21 E-1 E-258m4  ,-13:E-9 E7 E-17 E11 E-5 E-33 E43 E-138m4  ,-13:E-9 E7 E7 E-17 E11 E-5 E43 E-498m4  ,-13:E-9 E7 E7 E-17 E11 E-5 E43 E-538m4  ,-13:E-9 E7 E7 E-17 E11 E-5 E43 E-578m4  ,-3 :E-9 E11 E11 E-29 E-29 E-29 E19 E38m4  ,0  :E-9 E-13 E-13 E-9 E-9 E-9 E-1 E-138m4  ,0  :E-9 E-13 E-13 E-9 E-9 E-9 E-1 E-178m4  ,9  :E-9 E-1 E15 E-5 E-17 E-1 E35 E-498m4  ,9  :E-9 E-1 E15 E-5 E-17 E-1 E35 E-378m4  ,9  :E-9 E-1 E15 E-5 E-17 E-1 E35 E-338m4  ,9  :E-9 E7 E-17 E-29 E-25 E15 E15 E38m4  ,9  :E-9 E7 E-17 E-29 E-25 E15 E15 E158m4  ,9  :E-9 E7 E-17 E-29 E-25 E11 E7 E78m4  ,10 :E-9 E7 E-17 E11 E7 E-1 E-1 E-178m4  ,11 :E-9 E-1 E15 E-5 E-5 E-5 E-33 E358m5  ,-9 :E-9 E11 E11 E3 E-5 E15 E31 E-18m5  ,1  :E-9 E-13 E-13 E-9 E19 E-9 E15 E-178m5  ,2  :E-9 E-9 E3 E23 E-1 E-1 E7 E198m5  ,2  :E-9 E-9 E3 E23 E-1 E-1 E7 E238m5  ,11 :E-9 E-1 E15 E-5 E-17 E-1 E35 E-218m5  ,11 :E-9 E-1 E15 E-5 E-17 E-1 E-21 E358m5  ,11 :E-9 E7 E-17 E-29 E-25 E-21 E15 E118m5  ,12 :E-9 E-29 E39 E31 E23 E19 E47 E558m5  ,12 :E-9 E-29 E39 E23 E51 E27 E39 E558m5  ,12 :E-9 E-29 E39 E31 E23 E19 E59 E598m5  ,12 :E-9 E-29 E39 E31 E23 E19 E59 E558m5  ,12 :E-9 E-29 E39 E31 E23 E19 E59 E518m5  ,12 :E-9 E-29 E39 E43 E19 E35 E3 E598m5  ,12 :E-9 E-29 E39 E43 E39 E47 E59 E478m5  ,12 :E-9 E-29 E19 E39 E39 E27 E27 E558m5  ,12 :E-9 E-29 E39 E43 E19 E19 E59 E358m5  ,12 :E-9 E-29 E39 E23 E51 E27 E39 E598m5  ,12 :E-9 E-29 E19 E39 E39 E43 E31 E598m5  ,12 :E-9 E-29 E19 E39 E39 E27 E27 E358m5  ,12 :E-9 E-29 E39 E43 E47 E35 E59 E518m5  ,12 :E-9 E-29 E39 E23 E47 E27 E63 E518m5  ,12 :E-9 E-29 E39 E23 E47 E27 E59 E638m5  ,12 :E-9 E-29 E39 E23 E47 E27 E43 E638m5  ,12 :E-9 E-29 E39 E31 E23 E19 E67 E558m5  ,12 :E-9 E-29 E39 E31 E23 E19 E47 E678m5  ,12 :E-9 E-29 E39 E31 E23 E19 E63 E678m5  ,12 :E-9 E-29 E39 E23 E51 E27 E39 E518m5  ,12 :E-9 E-29 E39 E23 E47 E27 E43 E518m5  ,12 :E-9 E-29 E39 E43 E39 E51 E31 E198m5  ,12 :E-9 E-29 E39 E43 E39 E51 E31 E358m5  ,12 :E-9 E-29 E39 E43 E47 E35 E71 E598m5  ,12 :E-9 E-29 E39 E43 E47 E35 E71 E678m5  ,12 :E-9 E-29 E39 E43 E47 E35 E59 E718m5  ,12 :E-9 E-29 E39 E43 E43 E23 E51 E518m5  ,12 :E-9 E-29 E39 E31 E23 E19 E47 E518m5  ,12 :E-9 E-29 E19 E39 E39 E43 E31 E398m5  ,12 :E-9 E-29 E39 E43 E19 E35 E3 E438m5  ,12 :E-9 E-29 E39 E23 E39 E51 E83 E798m5  ,12 :E-9 E-29 E39 E23 E39 E51 E83 E718m5  ,12 :E-9 E-29 E39 E23 E47 E27 E43 E478m6  ,14 :E-9 E-29 E39 E43 E39 E51 E-25 E398m6  ,14 :E-9 E-29 E39 E23 E47 E27 E-25 E518m6  ,14 :E-9 E-29 E39 E23 E35 E55 E-25 E558m6  ,14 :E-9 E-29 E39 E23 E35 E55 E-25 E398m6  ,14 :E-9 E-29 E39 E31 E23 E19 E-25 E558m6  ,14 :E-9 E-29 E39 E43 E43 E23 E-25 E558m6  ,14 :E-9 E-29 E39 E31 E23 E19 E-25 E518m6  ,14 :E-9 E-29 E39 E23 E47 E27 E-25 E478m6  ,14 :E-9 E-29 E39 E43 E43 E23 E-25 E638m6  ,14 :E-9 E-29 E39 E23 E35 E55 E-25 E638m6  ,14 :E-9 E-29 E39 E43 E-25 E43 E63 E238m6  ,14 :E-9 E-29 E39 E43 E47 E71 E-25 E638m6  ,14 :E-9 E-29 E39 E43 E47 E71 E-25 E598m7  ,-8 :E-9 E-29 E-5 E-1 E-25 E-9 E15 E-498m7  ,-8 :E-9 E-29 E-25 E-5 E-5 E-17 E-17 E-98m7  ,-8 :E-9 E-29 E-5 E-21 E15 E-17 E-33 E-458m7  ,-8 :E-9 E-29 E-5 E-1 E-25 E-9 E15 E-458m7  ,-8 :E-9 E-29 E-25 E-25 E-9 E-33 E-13 E-338m7  ,-8 :E-9 E-29 E-5 E-1 E-25 E-9 E15 E-418m7  ,-8 :E-9 E-29 E-5 E-1 E-25 E-9 E-41 E158m7  ,-8 :E-9 E-29 E-5 E-1 E3 E-9 E27 E158m7  ,-8 :E-9 E-29 E-5 E-1 E3 E-9 E27 E238m7  ,-8 :E-9 E-29 E-5 E-21 E15 E-17 E-33 E-418m7  ,-8 :E-9 E-29 E-5 E-17 E-17 E15 E7 E-418m7  ,-8 :E-9 E-29 E-5 E-21 E15 E-17 E-33 E-378m7  ,-8 :E-9 E-29 E-5 E-21 E3 E-17 E-1 E198m7  ,-8 :E-9 E-29 E-5 E-21 E3 E-17 E15 E198m7  ,-8 :E-9 E-29 E-5 E-17 E-17 E15 E-25 E78m7  ,-8 :E-9 E-29 E-5 E-17 E-17 E15 E-25 E-98m7  ,-8 :E-9 E-29 E-5 E-17 E-17 E15 E7 E-258m7  ,-8 :E-9 E-29 E-5 E-1 E-25 E-25 E15 E-98m7  ,-8 :E-9 E-29 E-5 E-21 E3 E-17 E-1 E38m7  ,-8 :E-9 E-29 E-5 E-1 E-1 E-21 E7 E78m7  ,-8 :E-9 E-29 E-5 E-21 E3 E-17 E-1 E78m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E-98m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E-258m7  ,-8 :E-9 E-29 E-5 E-1 E-25 E-9 E-41 E-18m7  ,-8 :E-9 E-29 E-5 E-21 E-9 E11 E-1 E-58m7  ,-8 :E-9 E-29 E-25 E-5 E-5 E-17 E-17 E118m7  ,-8 :E-9 E-29 E-5 E-21 E-9 E11 E-1 E-258m7  ,-8 :E-9 E-29 E-25 E-25 E-9 E-33 E-13 E-378m7  ,-7 :E-9 E-13 E-13 E-9 E19 E23 E19 E38m7  ,-7 :E-9 E-13 E-13 E-9 E19 E23 E19 E-178m7  ,-2 :E-9 E-1 E-5 E7 E-1 E-9 E-25 E78m7  ,10 :E-9 E7 E-21 E-13 E3 E3 E27 E-18m7  ,12 :E-9 E7 E-17 E-29 E-25 E-21 E-1 E38m8  ,-6 :E-9 E-29 E-5 E-1 E19 E-1 E-21 E118m8  ,-6 :E-9 E-29 E-5 E-1 E19 E-1 E-21 E198m8  ,-6 :E-9 E-29 E-5 E-1 E-5 E19 E-13 E-58m8  ,-6 :E-9 E-29 E-5 E-1 E-5 E19 E-13 E78m8  ,-6 :E-9 E-29 E-5 E-1 E-5 E19 E-13 E-98m8  ,-6 :E-9 E-29 E-5 E-1 E-5 E7 E19 E-58m8  ,-6 :E-9 E-29 E-5 E-21 E19 E3 E-17 E78m8  ,-6 :E-9 E-29 E-5 E-21 E19 E3 E-17 E38m8  ,-6 :E-9 E-29 E-5 E-21 E15 E-17 E19 E-178m8  ,-6 :E-9 E-29 E-5 E-1 E19 E3 E27 E198m8  ,-6 :E-9 E-29 E-5 E-1 E19 E3 E27 E158m8  ,-3 :E-9 E7 E-5 E3 E-5 E-13 E-41 E-58m8  ,-3 :E-9 E7 E-5 E3 E-5 E-13 E-41 E-98m8  ,11 :E-9 E-29 E39 E31 E47 E27 E23 E438m8  ,11 :E-9 E-29 E39 E31 E47 E27 E23 E518m8  ,14 :E-9 E7 E-17 E11 E7 E19 E-29 E38m8  ,15 :E-9 E-29 E39 E59 E-1 E-25 E-5 E398m8  ,15 :E-9 E-29 E39 E59 E-1 E-25 E-5 E478m8  ,15 :E-9 E-29 E39 E59 E-1 E-25 E-5 E438m9  ,3  :E-9 E-1 E-17 E-9 E19 E3 E-9 E-178m9  ,7  :E-9 E7 E11 E3 E-9 E-33 E31 E-58m10 ,-5 :E-9 E-29 E-5 E-1 E19 E39 E-5 E-58m10 ,-5 :E-9 E-29 E-5 E-1 E19 E39 E-5 E-98m10 ,2  :E-9 E7 E-5 E11 E-1 E11 E-45 E-538m10 ,2  :E-9 E7 E-5 E11 E-1 E11 E-53 E-538m10 ,2  :E-9 E7 E-5 E11 E-1 E11 E-45 E-578m10 ,2  :E-9 E7 E-5 E11 E-1 E11 E-45 E-618m10 ,7  :E-9 E7 E11 E-29 E-5 E-5 E-33 E-298m10 ,7  :E-9 E7 E11 E-29 E-5 E-5 E-33 E-458m10 ,12 :E-9 E-13 E-17 E-21 E-21 E-13 E-41 E-178m11 ,-16:E-9 E-29 E39 E31 E23 E19 E59 E-98m11 ,-16:E-9 E-29 E39 E31 E23 E19 E59 E-178m11 ,-16:E-9 E-29 E39 E31 E23 E19 E59 E-138m11 ,4  :E-9 E-1 E-17 E11 E-25 E35 E27 E-218m11 ,4  :E-9 E-1 E-17 E11 E-25 E35 E27 E-258m11 ,22 :E-9 E-1 E15 E-13 E-29 E-21 E-1 E118m11 ,22 :E-9 E-1 E15 E-13 E-29 E-21 E-1 E38m11 ,22 :E-9 E-1 E15 E-13 E-29 E-21 E-1 E78m11 ,22 :E-9 E-1 E15 E-13 E-29 E-21 E23 E278m12 ,0  :E-9 E-1 E-17 E11 E-25 E11 E-45 E-258m12 ,0  :E-9 E-1 E-17 E11 E-25 E11 E-13 E-258m12 ,6  :E-9 E7 E-5 E3 E23 E3 E3 E-378m12 ,6  :E-9 E7 E-5 E3 E23 E3 E3 E-418m12 ,6  :E-9 E7 E-5 E3 E23 E3 E3 E-458m12 ,13 :E-9 E-13 E-17 E-13 E-33 E-33 E7 E-218m13 ,0  :E-9 E7 E11 E3 E-9 E-33 E15 E118m15 ,0  :E-9 E7 E-5 E3 E23 E15 E3 E-498m15 ,0  :E-9 E7 E-5 E3 E23 E15 E-49 E118m15 ,0  :E-9 E7 E-5 E3 E23 E15 E3 E-298m15 ,0  :E-9 E7 E-5 E3 E23 E15 E-49 E38m16 ,-1 :E-9 E7 E-21 E11 E-1 E7 E-29 E198m17 ,-10:E-9 E-29 E39 E23 E51 E27 E39 E-98m17 ,-10:E-9 E-29 E39 E23 E51 E27 E39 E-138m17 ,-10:E-9 E-29 E39 E23 E51 E27 E39 E-178m19 ,-3 :E-9 E-29 E39 E59 E-1 E-25 E-5 E-138m19 ,-3 :E-9 E-29 E39 E59 E-1 E-25 E-5 E-178m19 ,-3 :E-9 E-29 E39 E59 E-1 E-25 E-5 E-98m20 ,2  :E-9 E-9 E3 E11 E3 E23 E-1 E-298m20 ,2  :E-9 E-9 E3 E11 E3 E23 E-1 E-98m21 ,1  :E-9 E-1 E-5 E7 E-5 E-17 E47 E358m23 ,5  :E-9 E-29 E-5 E-21 E-5 E31 E7 E198m24 ,2  :E-9 E7 E-17 E11 E23 E-5 E-9 E-218m24 ,2  :E-9 E11 E11 E23 E-13 E-29 E3 E158m24 ,2  :E-9 E7 E-17 E11 E23 E-5 E-9 E-178m26 ,7  :E-9 E11 E11 E23 E-21 E23 E35 E318m26 ,7  :E-9 E11 E11 E23 E-21 E23 E35 E518m28 ,-5 :E-9 E-1 E15 E-5 E-25 E19 E-5 E-138m28 ,-5 :E-9 E-1 E15 E-5 E-25 E19 E-5 E-178m28 ,33 :E-9 E-9 E19 E-9 E11 E-1 E-9 E38m31 ,18 :E-9 E-9 E19 E-9 E11 E-5 E7 E39m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E19 E15 E119m-25,13 :E-9 E-13 E-17 E-33 E-17 E-9 E19 E15 E159m-23,14 :E-9 E-13 E-17 E-33 E-17 E-9 E19 E-65 E119m-23,14 :E-9 E-13 E-17 E-33 E-17 E-9 E19 E-65 E-19m-23,14 :E-9 E-13 E-17 E-33 E-17 E-9 E7 E-65 E79m-23,14 :E-9 E-13 E-17 E-33 E-17 E-9 E7 E-65 E-19m-23,14 :E-9 E-13 E-17 E-33 E-17 E-9 E19 E-65 E199m-22,16 :E-9 E-13 E-17 E-33 E-17 E-65 E-85 E-9 E159m-22,16 :E-9 E-13 E-17 E-33 E-17 E-65 E-85 E-9 E-19m-18,6  :E-9 E7 E-9 E-57 E-29 E-21 E-13 E-69 E-419m-18,6  :E-9 E7 E-9 E-57 E-29 E-21 E-13 E-69 E-259m-18,6  :E-9 E7 E-9 E-57 E-37 E-49 E-61 E-25 E-579m-18,6  :E-9 E7 E-9 E-57 E-37 E-49 E-61 E-25 E-539m-18,6  :E-9 E7 E-9 E-57 E-37 E-49 E-61 E-25 E-499m-15,4  :E-9 E-9 E3 E23 E-1 E-17 E31 E-41 E359m-11,4  :E-9 E7 E-9 E-25 E-49 E-37 E-49 E-53 E-139m-11,4  :E-9 E7 E7 E-13 E-17 E-5 E-41 E-41 E279m-7 ,-2 :E-9 E-17 E19 E-5 E11 E-5 E-41 E-17 E-419m-7 ,-2 :E-9 E-17 E19 E-5 E11 E-5 E-41 E-17 E-339m-6 ,1  :E-9 E7 E7 E-13 E-13 E-33 E-9 E-5 E279m-6 ,9  :E-9 E7 E-5 E-29 E3 E-1 E23 E-1 E119m-5 ,3  :E-9 E-1 E-17 E11 E-13 E15 E15 E-21 E-579m-5 ,3  :E-9 E-1 E-17 E11 E-13 E15 E15 E-21 E-419m-4 ,-8 :E-9 E7 E-5 E-29 E3 E3 E-1 E3 E279m-4 ,-8 :E-9 E7 E-5 E-29 E3 E3 E-1 E3 E319m-4 ,18 :E-9 E-13 E-13 E-1 E-17 E7 E7 E-33 E-259m-3 ,2  :E-9 E-1 E-5 E7 E-1 E11 E-17 E-5 E279m-3 ,2  :E-9 E-1 E-5 E7 E-1 E11 E-17 E-5 E319m-3 ,2  :E-9 E-1 E-5 E7 E-1 E11 E-17 E-5 E359m-3 ,2  :E-9 E-1 E-5 E7 E-1 E11 E-17 E-5 E399m-3 ,2  :E-9 E-1 E-5 E7 E-1 E11 E-17 E-5 E439m-3 ,23 :E-9 E-17 E-33 E15 E-1 E-5 E-45 E-5 E199m-3 ,23 :E-9 E-17 E-33 E15 E-1 E-5 E-45 E-5 E279m-1 ,10 :E-9 E7 E7 E-13 E-17 E-5 E-25 E-41 E279m1  ,-16:E-9 E-17 E-33 E15 E15 E23 E-29 E-5 E-179m1  ,-16:E-9 E-17 E-33 E15 E15 E23 E-29 E-5 E-99m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-65 E-45 E-499m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-65 E-45 E-539m2  ,-14:E-9 E7 E7 E-17 E11 E-5 E-65 E-45 E-579m2  ,30 :E-9 E7 E7 E-17 E11 E-5 E-65 E43 E359m2  ,30 :E-9 E7 E7 E-17 E11 E-5 E-65 E43 E399m2  ,30 :E-9 E7 E7 E-17 E11 E-5 E-65 E43 E319m2  ,30 :E-9 E7 E7 E-17 E-13 E-17 E-41 E-65 E-339m2  ,30 :E-9 E7 E7 E-17 E-13 E-17 E-41 E-65 E-299m4  ,-13:E-9 E7 E-17 E11 E-5 E-13 E43 E-25 E-339m4  ,-13:E-9 E7 E7 E11 E-13 E-5 E43 E-29 E279m4  ,-13:E-9 E7 E-17 E11 E-5 E-13 E43 E-25 E-259m4  ,-13:E-9 E7 E7 E-17 E11 E-5 E-65 E43 E-539m4  ,-13:E-9 E7 E7 E-17 E11 E-5 E-65 E43 E-619m4  ,-13:E-9 E7 E7 E-17 E11 E-5 E-65 E43 E-579m4  ,31 :E-9 E7 E7 E-17 E11 E-5 E-65 E-45 E279m4  ,31 :E-9 E7 E7 E-17 E11 E-5 E-65 E-45 E319m4  ,31 :E-9 E7 E7 E-17 E11 E-5 E-65 E-45 E359m5  ,12 :E-9 E-29 E39 E31 E23 E19 E67 E47 E359m5  ,12 :E-9 E-29 E39 E31 E23 E19 E67 E47 E519m5  ,12 :E-9 E-29 E39 E23 E47 E27 E63 E43 E479m5  ,12 :E-9 E-29 E39 E23 E47 E27 E63 E43 E319m5  ,12 :E-9 E-29 E39 E43 E19 E35 E3 E39 E399m5  ,12 :E-9 E-29 E39 E23 E47 E39 E59 E47 E479m5  ,12 :E-9 E-29 E39 E43 E19 E35 E3 E39 E599m5  ,12 :E-9 E-29 E39 E43 E19 E35 E3 E39 E479m5  ,12 :E-9 E-29 E39 E43 E39 E51 E31 E39 E199m5  ,12 :E-9 E-29 E39 E43 E39 E51 E31 E39 E319m5  ,12 :E-9 E-29 E39 E43 E39 E51 E31 E39 E399m6  ,14 :E-9 E-29 E39 E23 E47 E27 E43 E-25 E479m6  ,14 :E-9 E-29 E39 E31 E23 E19 E47 E-25 E679m6  ,14 :E-9 E-29 E39 E43 E19 E35 E-25 E3 E439m6  ,14 :E-9 E-29 E39 E31 E23 E19 E47 E-25 E519m6  ,14 :E-9 E-29 E39 E43 E39 E51 E-25 E31 E199m6  ,14 :E-9 E-29 E39 E23 E47 E27 E43 E-25 E639m6  ,14 :E-9 E-29 E39 E43 E39 E51 E-25 E31 E359m6  ,14 :E-9 E-29 E39 E23 E47 E27 E43 E-25 E519m6  ,14 :E-9 E-29 E39 E43 E19 E35 E-25 E3 E599m6  ,14 :E-9 E-29 E39 E43 E47 E35 E71 E-25 E679m6  ,14 :E-9 E-29 E39 E43 E47 E35 E71 E-25 E599m6  ,14 :E-9 E-29 E39 E31 E23 E19 E47 E-25 E559m7  ,-8 :E-9 E-29 E-5 E-21 E3 E-5 E15 E3 E39m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E-21 E-419m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E-21 E-339m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E-5 E-59m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E-5 E-259m7  ,-8 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E-5 E-139m7  ,1  :E-9 E7 E-17 E-33 E11 E19 E3 E-5 E-139m7  ,1  :E-9 E7 E-17 E-33 E11 E19 E3 E-5 E-179m8  ,-6 :E-9 E-29 E-5 E-1 E-25 E-9 E19 E-41 E159m8  ,-6 :E-9 E-29 E-5 E-1 E-25 E-9 E19 E-41 E-19m8  ,-6 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E19 E-99m8  ,-6 :E-9 E-29 E-5 E-1 E-5 E7 E-13 E19 E-259m8  ,15 :E-9 E-29 E39 E43 E47 E71 E-25 E-5 E639m8  ,15 :E-9 E-29 E39 E43 E47 E71 E-25 E-5 E599m8  ,15 :E-9 E-29 E39 E43 E43 E23 E-25 E-5 E639m8  ,15 :E-9 E-29 E39 E43 E43 E23 E-25 E-5 E559m10 ,-5 :E-9 E-29 E-5 E-1 E19 E3 E27 E39 E199m10 ,-5 :E-9 E-29 E-5 E-1 E19 E3 E27 E39 E159m10 ,7  :E-9 E7 E11 E-29 E-5 E-5 E-33 E-25 E-259m10 ,7  :E-9 E7 E11 E-29 E-5 E-5 E-33 E-25 E-339m10 ,7  :E-9 E7 E11 E-29 E-5 E-5 E-33 E-25 E-459m11 ,2  :E-9 E-1 E-1 E19 E-1 E-9 E-5 E23 E-619m13 ,9  :E-9 E7 E11 E-29 E-5 E11 E7 E-33 E-299m13 ,9  :E-9 E7 E11 E-29 E-5 E11 E7 E-33 E-459m13 ,26 :E-9 E-29 E-25 E-25 E-5 E-45 E-25 E11 E-99m21 ,12 :E-9 E7 E-21 E-13 E3 E3 E3 E27 E-19m28 ,-5 :E-9 E-1 E15 E-5 E-25 E19 E-5 E-21 E-139m28 ,-5 :E-9 E-1 E15 E-5 E-25 E19 E-5 E-21 E-179m28 ,-5 :E-9 E-1 E15 E-5 E-25 E19 E-5 E-21 E-19m31 ,18 :E-9 E-9 E19 E-9 E11 E-5 E7 E-9 E-99m31 ,18 :E-9 E-9 E19 E-9 E11 E-5 E7 E-9 E-59m31 ,18 :E-9 E-9 E19 E-9 E11 E-5 E7 E-29 E-19m31 ,18 :E-9 E-9 E19 E-9 E11 E-5 E7 E-29 E-9`

To show that the current reverse caber tosser really can construct anything that slmake can compile, we just have to show that these block moves can reach any location on the Life plane, and then combine these recipes with the cheap two-glider monochromatic block splitter (and other splitters if necessary) to build these four Blockic splitters.

-- Unless someone wants to run a proper search for the actual cheapest monochromatic monoparity recipes that produce each of the four glider types starting from a block, and returning to a block afterwards. It's clear that this can be done somehow, but it would be nice to have an actual working toolkit available.

EDIT: There's an article started about the 329-glider upper limit on the conwaylife.com home page. Am planning to add a bullet list at the bottom of the article, explaining all the steps the mechanism will have to go through to build something big like a Gemini spaceship with 329 gliders.

EDIT2: Turned the detailed summary into a second blog posting.

dvgrn
Moderator

Posts: 5209
Joined: May 17th, 2009, 11:00 pm

### Re: Building a reverse caber-tosser

Congratulations on 329 glider universal constructor! Now let's see if we can do it in under 20 gliders.

I don't think this is as ridiculous as it sounds. Look at how low the population for a quadratic growth pattern got, compared to the population of the first breeder. It seems likely to me that some Nick-Gotts-style pattern of carefully interacting switch engine puffers could also exhibit universal construction at a lower glider-count or starting population. These puffers may even emit gliders, as long as there's a distant block-layer to absorb them.

Come to think of it, I have a more concrete suggestion: Why can't the approaching Cordership be replaced by a switch engine puffer? The universal constructor can just clean up the debris later.
itaibn

Posts: 11
Joined: October 31st, 2013, 8:45 am

### Re: Building a reverse caber-tosser

itaibn wrote:It seems likely to me that some Nick-Gotts-style pattern of carefully interacting switch engine puffers could also exhibit universal construction at a lower glider-count or starting population. These puffers may even emit gliders, as long as there's a distant block-layer to absorb them.

Aha! The distant block-layers are the key here!

I can believe that there exists a 20-glider solution somewhere out there, but I doubt that we'll ever find it. Essentially, it would boil down to finding a low-glider collision which just happens to produce an infinite novelty generator.

itaibn wrote:Come to think of it, I have a more concrete suggestion: Why can't the approaching Cordership be replaced by a switch engine puffer? The universal constructor can just clean up the debris later.

Good idea, although it will require Extrementhusiast to rediscover an analogous reflection reaction which works with the BLSE instead of the 2-engine Cordership.

itaibn wrote:Look at how low the population for a quadratic growth pattern got, compared to the population of the first breeder.

Well, the correct analogue of 'the first breeder' in this case would be a pair of P1 sliding-block memories attached to a Chapman-Greene construction arm; I'd estimate a total cost of maybe 10000 gliders. 329 is impressively lower than this.
What do you do with ill crystallographers? Take them to the mono-clinic!

calcyman

Posts: 1897
Joined: June 1st, 2009, 4:32 pm

### Re: Building a reverse caber-tosser

Just a silly question, is there a periodic constraint that disallow to use the following ? If not, I think it might be possible to reduce the need for glider turners and use p120 guns instead. And if we cant, we have 6 glider turners instead of 8 glider turners. I know that life hash loves power of 2, but the "minimal" example might not care.

`x = 116, y = 153, rule = LifeHistory2\$4.A\$5.2A\$4.2A22.A.A\$25.D2.2A\$25.3D.A\$16.A11.D\$17.2A8.2D\$16.2A\$30.3A\$30.A\$26.D4.A\$16.ED5.2D.2D14.A.A\$16.DE5.2D2.2D14.2A\$26.2D15.A\$20.2D21.B\$20.2D\$45.A\$45.A.A\$33.2A10.2A\$33.A.A7.2D\$12.A8.B11.A3.B5.2D\$12.2A\$11.A.A26.2D5.ED\$40.2D5.DE\$36.2A5.2A\$24.2A9.A.A5.A.A\$24.ABA10.A5.A\$24.A\$55.2A\$55.A.A\$55.A39\$103.A\$101.2A\$102.2A\$83.2A\$84.2A\$83.A7.2A\$91.A.A\$91.A7.2A11.A\$98.2A11.2A\$100.A10.A.A\$94.2A\$93.A.A\$95.A38\$61.A\$61.A.A\$61.2A\$30.A\$30.ABA10.A5.A\$30.2A9.A.A5.A.A\$42.2A5.2A\$46.2D5.DE\$17.A.A26.2D5.ED\$18.2A\$18.A8.B11.A3.B5.2D\$39.A.A7.2D\$39.2A10.2A\$51.A.A\$51.A\$26.2D\$26.2D21.B\$32.2D15.A\$22.DE5.2D2.2D14.2A\$22.ED5.2D.2D14.A.A\$32.D4.A\$36.A\$36.3A\$22.2A\$23.2A8.2D\$22.A11.D\$31.3D.A\$31.D2.2A\$10.2A22.A.A\$11.2A\$10.A!`
Jormungant

Posts: 78
Joined: May 27th, 2016, 1:01 am

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