ConwayLife.com

Posted: **May 27th, 2014, 4:51 pm**

I've written a script for Golly to filter edge-shooters required for building a 31c/240 ship.

Here are the results. There are still not perfect, because there are some syntheses that leave a lot of junk on the right, which will prevent from building them in into an existing spaceship stream.

Code: Select all

#P 0 0
#C Start-RLE: o$b2o$2o3$4bo$3bobo$4bo6$10b2o$9bo2bo$5b2o3bobo$5b2o4bo3$12b3o!
#C [167]: DELAY 1 TICKS, FIRE R1L0B
#C [3313]: REPHASE BY 9 LANES, DELAY 1 TICKS, FIRE R2L7B
#C [53781]: FIRE R2L7B
#C [252428]: FIRE R1L2B
#C [285297]: FIRE R1L2B
#C [23008669]: REPHASE BY 9 LANES, DELAY 1 TICKS, FIRE R3L1B
.........***
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#P 200 0
#C Start-RLE: 8bo$8bo$8bo2$4b3o3b3o5$o$b2o$2o2b3o3b3o2$8bo$8bo$8bo!
#C [290]: DELAY 1 TICKS, FIRE R1L0B
#C [3938]: FIRE R3L1B
#C [20073]: FIRE R1L0B
#C [82180]: FIRE R1L0B
#C [119811]: DELAY 1 TICKS, FIRE R1L0B
#C [641251]: FIRE R1L2B
#C [4827451]: REPHASE BY 9 LANES, FIRE R1L0B
#C [92875403]: DELAY 1 TICKS, FIRE R3L26B
...*..........
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#P 400 0
#C Start-RLE: 2bo$3b2o$2b2o3$10bo$10bo$10bo2$2b2o4bo$2b2o3bobo$6bo2bo$7b2o6$bo$obo$bo!
#C [368]: FIRE R1L0B
#C [1007]: FIRE R1L0B
#C [6177]: FIRE R2L7B
#C [23448]: FIRE R1L0B
#C [437846]: REPHASE BY 9 LANES, FIRE R2L7B
#C [1967564]: DELAY 1 TICKS, FIRE R1L0B
#C [6736895]: FIRE R1L2B
#C [21163042]: FIRE R1L0B
#C [138177752]: REPHASE BY 9 LANES, FIRE R1L0B
.*..........................
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#P 600 0
#C Start-RLE: o$b2o$2o4$6b3o2$4bo5bo$4bo5bo$4bo5bo2$6b3o!
#C [435]: FIRE R1L0B
#C [4659]: REPHASE BY 9 LANES, FIRE R2L7B
#C [21200]: DELAY 1 TICKS, FIRE R1L2B
#C [421246]: FIRE R3L26B
#C [23794874]: REPHASE BY 9 LANES, DELAY 1 TICKS, FIRE R3L21B
#C [142245676]: FIRE R1L0B
.........*.......
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#P 800 0
#C Start-RLE: o$b2o$2o4$6b3o2$4bo5bo$4bo5bo$4bo5bo2$6b3o!
#C [435]: FIRE R1L0B
#C [4661]: FIRE R3L19B
#C [21214]: DELAY 1 TICKS, FIRE R1L2B
#C [421343]: FIRE R3L26B
#C [23795675]: REPHASE BY 9 LANES, DELAY 1 TICKS, FIRE R3L21B
#C [142246524]: FIRE R1L0B
.........*.......
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#P 1000 0
#C Start-RLE: o$b2o$2o3$11bo$11bo$11bo2$3b2o4bo$3b2o3bobo$7bo2bo$8b2o6$2bo$bobo$2bo!
#C [365]: FIRE R1L0B
#C [1003]: FIRE R1L0B
#C [2709]: FIRE R1L0B
#C [8849]: FIRE R1L2B
#C [28307]: DELAY 1 TICKS, FIRE R1L2B
#C [37263]: DELAY 1 TICKS, FIRE R1L0B
#C [231368]: DELAY 1 TICKS, FIRE R1L0B
#C [797765]: DELAY 1 TICKS, FIRE R1L0B
#C [5180587]: REPHASE BY 9 LANES, DELAY 1 TICKS, FIRE R1L2B
*.......................
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#P 1200 0
#C Start-RLE: o$b2o$2o3$11bo$11bo$11bo2$3b2o4bo$3b2o3bobo$7bo2bo$8b2o6$2bo$bobo$2bo!
#C [365]: FIRE R1L0B
#C [1003]: FIRE R1L0B
#C [2709]: FIRE R1L0B
#C [8849]: FIRE R1L2B
#C [28307]: DELAY 1 TICKS, FIRE R1L2B
#C [37263]: DELAY 1 TICKS, FIRE R1L0B
#C [231368]: DELAY 1 TICKS, FIRE R1L0B
#C [797765]: DELAY 1 TICKS, FIRE R1L0B
#C [833162]: FIRE R1L2B
#C [5238363]: DELAY 1 TICKS, FIRE R1L2B
....**.
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#P 1400 0
#C Start-RLE: 4bo$5b2o$4b2o3$4bo$4bo$4bo2$3o3b3o7$3o3b3o2$4bo$4bo$4bo!
#C [312]: DELAY 1 TICKS, FIRE R1L0B
#C [911]: FIRE R1L2B
#C [2559]: DELAY 1 TICKS, FIRE R1L0B
#C [8588]: DELAY 1 TICKS, FIRE R1L2B
#C [27923]: DELAY 1 TICKS, FIRE R1L2B
#C [468004]: REPHASE BY 18 LANES, DELAY 1 TICKS, FIRE R1L2B
#C [2009984]: FIRE R1L0B
#C [33438447]: FIRE R3L21B
*..................**.
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#P 1600 0
#C Start-RLE: 7b3o$o$b2o2bo5bo$2o3bo5bo$5bo5bo5$5bo5bo$5bo5bo$5bo5bo2$7b3o!
#C [266]: FIRE R1L0B
#C [3695]: FIRE R3L21B
#C [54584]: REPHASE BY 9 LANES, DELAY 1 TICKS, FIRE R1L0B
#C [253329]: DELAY 1 TICKS, FIRE R1L2B
#C [1720364]: DELAY 1 TICKS, FIRE R2L7B
#C [6387957]: FIRE R1L0B
#C [20671123]: DELAY 1 TICKS, FIRE R1L0B
#C [64907171]: DELAY 1 TICKS, FIRE R1L0B
*...................
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...*..*.............
...*..*......*......
....**.......*......
.............*......


#P 1800 0
#C Start-RLE: 8bo$8bo$8bo2$4b3o3b3o5$o$b2o$2o2b3o3b3o2$8bo$8bo$8bo!
#C [290]: DELAY 1 TICKS, FIRE R1L0B
#C [856]: FIRE R1L0B
#C [2417]: FIRE R1L2B
#C [49751]: FIRE R3L19B
#C [247452]: DELAY 1 TICKS, FIRE R1L2B
#C [277145]: FIRE R1L2B
#C [9015322]: REPHASE BY 18 LANES, FIRE R1L0B
#C [48366996]: FIRE R1L2B
#C [174236101]: FIRE R1L2B
..........*.........
...........**.......
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*.........*.........
*.........*......**.
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........**..........


#P 2000 0
#C Start-RLE: o$b2o$2o3$12bo$12bo$12bo2$4b2o4bo$4b2o3bobo$8bo2bo$9b2o6$3bo$2bobo$3bo!
#C [364]: FIRE R1L0B
#C [4432]: DELAY 1 TICKS, FIRE R3L19B
#C [146709]: REPHASE BY 18 LANES, FIRE R1L2B
#C [3320252]: FIRE R3L4B
#C [37907017]: REPHASE BY 9 LANES, DELAY 1 TICKS, FIRE R1L2B
......*..............
.......**............
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....*.*..............
....*.*...........**.
.....*...........*..*
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#P 2200 0
#C Start-RLE: 8bo$o7bo$b2o5bo$2o$4b3o3b3o2$8bo$8bo$8bo!
#C [450]: DELAY 1 TICKS, FIRE R1L0B
#C [1894]: REPHASE BY 9 LANES, FIRE R1L0B
#C [16408]: DELAY 1 TICKS, FIRE R2L7B
#C [76570]: FIRE R1L2B
#C [1295643]: FIRE R3L3B
#C [13113966]: REPHASE BY 9 LANES, FIRE R1L0B
#C [53553602]: FIRE R1L0B
......*.............
.......**...........
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...........**....***
..........*..*......
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#P 2400 0
#C Start-RLE: 8bo$o7bo$b2o5bo$2o$4b3o3b3o2$8bo$8bo$8bo!
#C [450]: DELAY 1 TICKS, FIRE R1L0B
#C [1894]: REPHASE BY 9 LANES, FIRE R1L0B
#C [16408]: DELAY 1 TICKS, FIRE R2L7B
#C [76570]: FIRE R1L2B
#C [1295652]: DELAY 1 TICKS, FIRE R3L3B
#C [13113996]: REPHASE BY 9 LANES, FIRE R1L0B
#C [53553638]: FIRE R1L0B
.......*.............
........**...........
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#P 2600 0
#C Start-RLE: o$b2o$2o3$12bo$12bo$12bo2$4b2o4bo$4b2o3bobo$8bo2bo$9b2o6$3bo$2bobo$3bo!
#C [364]: FIRE R1L0B
#C [4432]: DELAY 1 TICKS, FIRE R3L19B
#C [146709]: REPHASE BY 18 LANES, FIRE R1L2B
#C [3320252]: FIRE R3L4B
#C [16470208]: DELAY 1 TICKS, FIRE R1L0B
#C [58515147]: DELAY 1 TICKS, FIRE R1L2B
.......*..............
........**............
.......**.............
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............**....***.
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.....*.*...........**.
......*...........*..*
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#P 2800 0
#C Start-RLE: o$b2o$2o3$12bo$12bo$12bo2$4b2o4bo$4b2o3bobo$8bo2bo$9b2o6$3bo$2bobo$3bo!
#C [364]: FIRE R1L0B
#C [4432]: DELAY 1 TICKS, FIRE R3L19B
#C [146709]: REPHASE BY 18 LANES, FIRE R1L2B
#C [3320252]: FIRE R3L4B
#C [16470211]: FIRE R1L2B
#C [58515151]: DELAY 1 TICKS, FIRE R1L2B
......*.............
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#P 3000 0
#C Start-RLE: 8bo$o7bo$b2o5bo$2o$4b3o3b3o2$8bo$8bo$8bo!
#C [450]: DELAY 1 TICKS, FIRE R1L0B
#C [1894]: REPHASE BY 9 LANES, FIRE R1L0B
#C [16408]: DELAY 1 TICKS, FIRE R2L7B
#C [76570]: FIRE R1L2B
#C [1295643]: FIRE R3L3B
#C [5804153]: FIRE R1L0B
#C [19798868]: FIRE R1L0B
#C [63643080]: FIRE R1L0B
.......*.............
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#P 3200 0
#C Start-RLE: 8bo$8bo$8bo2$4b3o3b3o4$o$b2o$2o$4b3o3b3o2$8bo$8bo$8bo!
#C [291]: DELAY 1 TICKS, FIRE R1L0B
#C [863]: FIRE R1L2B
#C [12905]: REPHASE BY 9 LANES, DELAY 1 TICKS, FIRE R2L7B
#C [72154]: FIRE R1L0B
#C [1266656]: DELAY 1 TICKS, FIRE R3L26B
#C [13056919]: REPHASE BY 9 LANES, FIRE R1L0B
#C [53485594]: FIRE R1L0B
#C [181853536]: FIRE R1L2B
*..................***
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....*..*..............
.....*.*..............
......*...............

P. S. There is no single HWSS synthesis

Posted: **May 29th, 2014, 1:12 pm**

codeholic wrote:I've written a script for Golly to filter edge-shooters required for building a 31c/240 ship.

Here are the results. There are still not perfect, because there are some syntheses that leave a lot of junk on the right, which will prevent from building them in into an existing spaceship stream.

Also, even without the junk, all the MWSS recipes seem to have the same "spark signature", which extends a long way to the right and would also prevent some combinations from being built. It might be worth looking at some of the more expensive recipes from earlier runs, to pick up more "edgy" MWSS and HWSS recipes. Really none of the recipes found by sscs are all that expensive, now that we have all these rakes.

I do like this LWSS recipe, though:

Code: Select all

x = 20, y = 23, rule = LifeHistory
C$.2C$2C3$17.C$17.C$17.C3$18.C$17.C.C$17.C.C$18.C$13.C$13.C$13.C2$4.
2C3.3C3.3C$3.C2.C$3.C2.C6.C$4.2C7.C$13.C!

Posted: **May 29th, 2014, 3:11 pm**

dvgrn wrote:I do like this LWSS recipe, though:

Yep. This one is probably the only one that is usable in a tight spaceship stream. But a tight spaceship stream might be not needed, if one can find a front that uses the spaceship streams only to produce initial pair of orthogonal middleweight spaceships.

Code: Select all

x = 259, y = 379, rule = B3/S23
17bo$16b2o$16bobo4$2b3o$bo2bo$4bo$o3bo$o3bo$4bo$bobo4$10bo$9b3o$9bob2o
$10b3o$10b3o$10b3o$10b2o7$77bo$76b2o$76bobo27$137bo$136b2o$136bobo27$
197bo$196b2o$196bobo6$2b3o$bo2bo$4bo$o3bo$o3bo$4bo$bobo4$10bo$9b3o$9bo
b2o$10b3o$10b3o$10b3o$10b2o5$257bo$256b2o$256bobo66$2b3o$bo2bo$4bo$o3b
o$o3bo$4bo$bobo4$10bo$9b3o$9bob2o$10b3o$10b3o$10b3o$10b2o73$2b3o$bo2bo
$4bo$o3bo$o3bo$4bo$bobo4$10bo$9b3o$9bob2o$10b3o$10b3o$10b3o$10b2o73$2b
3o$bo2bo$4bo$o3bo$o3bo$4bo$bobo4$10bo$9b3o$9bob2o$10b3o$10b3o$10b3o$
10b2o!

Posted: **May 29th, 2014, 6:03 pm**

codeholic wrote:But a tight spaceship stream might be not needed, if one can find a front that uses the spaceship streams only to produce initial pair of orthogonal middleweight spaceships.

I like the looks of the 2HWSS+G->MWSS reaction. I'll build that in to the trial front end I've been working on (making it much wider, obviously!) and then see what it costs to build those two HWSSes on each side, with known slow-salvo recipes and rakes.

That will leave just the five reverse forward lateral streams on the right side, unless someone comes up with a way to reduce or remove those. Blocks could be built in the correct place with just two more 2HWSS+G->MWSS reactions, I suppose, no other supporting streams needed -- so it will be good to get a sense of the total cost for that HWSS pair. Looks like there should be plenty of room for a few forward glider streams to pass through the lateral MWSS streams, if that becomes necessary.

Posted: **May 30th, 2014, 3:37 am**

dvgrn wrote:That will leave just the five reverse forward lateral streams on the right side, unless someone comes up with a way to reduce or remove those.

Since the distance between them is not fixed, you can build them with slow forward glider salvos, coming from the very bottom of the front, where you have fully functional forward rakes and rephasers. The initial target for slow salvos can be constructed by colliding a glider stream from an extra pair of Herschels on the initial trails with a forward glider stream. Though pretty straightforward, that will increase the spaceship's width quite significantly (though the length will be probably even greater than that anyway).

Posted: **May 30th, 2014, 11:19 am**

codeholic wrote:Since the distance between them is not fixed, you can build them with slow forward glider salvos, coming from the very bottom of the front, where you have fully functional forward rakes and rephasers. The initial target for slow salvos can be constructed by colliding a glider stream from an extra pair of Herschels on the initial trails with a forward glider stream. Though pretty straightforward, that will increase the spaceship's width quite significantly (though the length will be probably even greater than that anyway).

Right -- that's sort of the standard backup way to get those support streams, with maybe three to six forerakes per forward stream, plus rephasers between the forerakes. But given that you're starting with two-glider collisions, it may well make more sense to use simple kickbacks instead, plus maybe a few rephasers to get the block trails lined up.

-- Or another lateral MWSS stream, for that matter. One thing I'd like to look at is whether it's possible to produce forward glider streams somehow from very close to the front of the ship, to feed the MWSS-producing collisions. That would keep the overall width down to something more reasonable.

It's also probably worthwhile to put together a more organized collection of ways to build block trails. A two-glider collision plus a single (2,1) block pull seems reasonable, but the two-block-pull correction gets me thinking that there might be something more efficient.

Posted: **May 30th, 2014, 11:25 am**

dvgrn wrote:But given that you're starting with two-glider collisions, it may well make more sense to use simple kickbacks instead, plus maybe a few rephasers to get the block trails lined up.

Ah, right, kickbacks will also work. I forgot for a second, that the thing is moving

Posted: **May 30th, 2014, 7:20 pm**

oblique wrote:Update (I didn't have too much time on my hands lately ...):

I ran a such with all your latest back rakes up to a level of 12...

Are PRUNE_SX and PRUNE_SY still set at 35 and 28? I'd still be very interested in the results of a search inside a 20x20 bounding box or so, with a somewhat higher maximum cost. Did you try any runs along those lines?

The resulting seeds would tend to be easier to build one piece at a time, in cases where it doesn't make any particular sense to do slow-salvo constructions. And the odds shouldn't be too bad that good HWSS seeds would show up again this time...! (They'll be really handy for the 2HWSS+G->lateral MWSS reaction.)

Posted: **June 11th, 2014, 12:35 pm**

dvgrn wrote:
oblique wrote:Update (I didn't have too much time on my hands lately ...):

I ran a such with all your latest back rakes up to a level of 12...
Are PRUNE_SX and PRUNE_SY still set at 35 and 28? I'd still be very interested in the results of a search inside a 20x20 bounding box or so, with a somewhat higher maximum cost. Did you try any runs along those lines?

The resulting seeds would tend to be easier to build one piece at a time, in cases where it doesn't make any particular sense to do slow-salvo constructions. And the odds shouldn't be too bad that good HWSS seeds would show up again this time...! (They'll be really handy for the 2HWSS+G->lateral MWSS reaction.)

I reran with 20x20 upto level 14 - I hope to have the results wrapped up by tomorrow (with some 220 reactions in the db a simple dump or "optimize table" can run for quite a time, so ...)

Since you missed some nice HWSS seeds ... how about this for a teaser?

Code: Select all

#P 0 0                                                                           
#C Start-RLE: o$b2o$2o$7b3o2$5bo5bo$5bo5bo$5bo5bo5$5bo5bo$5bo5bo$5bo5bo2$7b3o!
#C [270]: FIRE R1L0B
#C [755]: DELAY 1 TICKS, FIRE R1L2B
#C [18544]: REPHASE BY 9 LANES, DELAY 1 TICKS, FIRE R3L21B
#C [51227]: DELAY 1 TICKS, FIRE R1L2B
#C [568619]: REPHASE BY 9 LANES, FIRE R1L0B
#C [4076431]: REPHASE BY 9 LANES, FIRE R1L0B
#C [25692761]: REPHASE BY 9 LANES, DELAY 1 TICKS, FIRE R1L2B
#C [153720441]: FIRE R2L7B
....**.......
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Posted: **June 11th, 2014, 1:57 pm**

oblique wrote:Since you missed some nice HWSS seeds ... how about this for a teaser?

Wow! That is indeed a wondrous discovery -- especially since it leaves just a nice simple block behind, out of the upship lane (for slow-salvo constructions this is perfect, significantly better than a clean seed). And the seed can be built either with a slow salvo or with two independent forerake/backrake pairs (i.e., the pairs of gliders can be sent in either order). Like so:

Code: Select all

x = 43, y = 49, rule = LifeHistory
.A$2.A$3A6$17.A$15.A.A$16.2A17$34.2D$34.2D2.2D$38.2D5$33.A.A$34.2A$
34.A5$40.3D2$31.2A$32.2A$31.A$19.3A$21.A$20.A!

I look forward to seeing the full report! I'm fairly sure that just this result all by itself can allow a very significantly smaller 17c/45 "Caterpillar's little brother" to be constructed.

Posted: **June 12th, 2014, 1:28 pm**

Here are the seeds of my latest run (20x20, all known back rakes, up to COST=14)

sample_n.pat.gz: (63.48 KiB) Downloaded 877 times

sample_s.pat.gz: (67.91 KiB) Downloaded 851 times

sample_e.pat.gz: (59.92 KiB) Downloaded 855 times

Posted: **June 12th, 2014, 1:29 pm**

sample_w.pat.gz: (76.84 KiB) Downloaded 839 times

Posted: **June 12th, 2014, 6:20 pm**

dvgrn wrote:And the seed can be built either with a slow salvo or with two independent forerake/backrake pairs (i.e., the pairs of gliders can be sent in either order).

Spoke a little too soon. Only the independent-pair construction will work; a slow salvo won't, unless we come up with a new recipe for this seed. Just took a look at the intermediate targets, and five of them get in the way of the HWSS stream. Will try filtering the new collection with codeholic's script, and see what passes the test.

Here's another detail that came up. I'm writing a script to convert REPHASE / DELAY / FIRE comments into a simple slow-salvo recipe -- i.e., just a simple list of lanes and glider parities. But the parities aren't working out as I expected -- I seem to have only a 50% chance of getting the right glider phase for each rake. I can calculate the correct lanes with no problem, but have to test each type of rake separately to see what its default parity is.

Am I right in guessing that some of the rakes in the sscs database put out even-phase gliders, and some put out odd phases? Are the rake patterns stored in a database table now? I didn't see the new rakes specified in the code anywhere, and the collection in the "parts" subfolder looks incomplete.

EDIT: Ah, no, I see the problem -- three interdependent bad assumptions on my part... Everything works if the rakes all emit o$b2o$2o! gliders by default. This gives a slow salvo of

Code: Select all

x = 131, y = 135, rule = B3/S23
o$b2o$2o4$24bo$25bo$23b3o36$41bo$42b2o$41b2o5$61bo$62b2o$61b2o16$64bo$
65bo$63b3o3$92bo$93bo$91b3o17$105bo$106bo$104b3o18$113bo$114b2o$113b2o
12$129bo$130bo$128b3o3$128b3o$130bo$129bo!

I've attached the rake implied by the REPHASE / DELAY / FIRE instructions, in case anyone wants to look at where the intermediate targets go wrong.

Posted: **June 13th, 2014, 8:09 am**

dvgrn wrote:I'm writing a script to convert REPHASE / DELAY / FIRE comments into a simple slow-salvo recipe -- i.e., just a simple list of lanes and glider parities...

Here's the script so far. Copy to the clipboard a set of sscs rake-building instructions starting with the #P line. Running this script in Golly will process the string and put a simple EO-recipe on the clipboard in its place. No warranty express or implied, etc., etc. -- this is very quick-and-dirty without much syntax checking:

Code: Select all

# Interpret-sscs-recipe.py  version 0.1
# Interpret a recipe from sscs, produce a slow salvo lane list in EO-format
import golly as g

lines=g.getclipstr().split("\n")+["END"]
ptr,curlane,curphase=0,0,0

if lines[ptr][:3]!="#P ":
  g.exit("Nonstandard recipe on clipobard.")
ptr+=1
if lines[ptr][:14]!="#C Start-RLE: ":
  g.exit("Can't find starting RLE.")

# g.new("Full recipe from clipboard")
# g.putcells(g.parse(lines[ptr][14:]))

ptr+=1
currentlane,recipe=0,"EOrecipe:"
while lines[ptr][:3]=="#C ":
  instrlist=lines[ptr].replace("\r","").split(":")[1].split(",")
  parity, rephasebefore, rephaseafter=0,0,0
  for item in instrlist:
    instr=item.strip().split(" ")
    if instr[0]=="REPHASE":
      rephasebefore=int(instr[2])
    elif instr[0]=="DELAY":
      parity=int(instr[1])
    elif instr[0]=="FIRE":
      rloc=instr[1].find("R")
      lloc=instr[1].find("L")
      bloc=instr[1].find("B")
      rephaseafter=int(instr[1][rloc+1:lloc])*9
      firelane=int(instr[1][lloc+1:bloc])
  recipe+="E" if parity==0 else "O"
  currentlane+=rephasebefore
  recipe+=str(2*((currentlane+firelane)%31)+1)+" "
  currentlane+=rephaseafter
  ptr+=1
g.setclipstr(recipe[:-1])
g.exit(recipe)

Currently the script will report minimum positive lane numbers -- odd numbers in the range 1 through 61, corresponding to lanes 0 through 30. Because the target can drift up or down as the slow salvo modifies it, occasionally the true recipe lane will be +62 or -62 from where the script reports it. For example, the "teaser" HWSS recipe comes out to

E1 O23 O35 O51 E21 E57 O35 E1

-- but to work correctly it should be

E1 O23 O35 O-11 E21 E-5 O35 E1

If and when I get around to improving this script to fix this +/-62 offset problem, use the "Start-RLE" initial target, and actually build a slow-salvo pattern in the current layer, I'll edit the code above and update the version number to 1.0.

Posted: **June 13th, 2014, 8:35 am**

dvgrn wrote:Will try filtering the new collection with codeholic's script, and see what passes the test.

The 20x20 search results include a nice little collection of edge shooters. There's at least one of each *WSS type with a fairly minimal rightward spark and no debris left in the lane. Here's a stamp collection with the reaction envelopes shown in blue:

Code: Select all

x = 2032, y = 141, rule = LifeHistory
1222.3D197.3D197.3D397.3D$1222.D2.D196.D2.D196.D2.D396.D2.D$1222.D
199.D199.D399.D$1222.D3.D195.D3.D195.D3.D395.D3.D$1222.D199.D199.D
399.D$1223.D.D197.D.D197.D.D397.D.D21$417.D$416.3D$415.2D.D$415.3D$
415.3D$415.3D$416.2D$1818.3D$1818.D2.D$1818.D$1818.D3.D$1818.D$1819.D
.D6$824.D$823.3D$822.2D.D$25.D199.D596.3D$24.3D197.3D596.2D$23.2D.D
196.2D.D$23.3D197.3D$23.3D197.3D$23.3D197.3D$24.2D198.2D397.D$622.3D
401.D$622.D.2D399.3D$623.3D398.2D.D$623.2D399.3D$1025.2D39$22.7B193.
7B185.7B200.5B196.5B197.5B192.6B194.6B194.6B189.6B199.6B$22.7B193.7B
185.7B200.5B196.5B197.5B191.6B194.6B194.6B191.6B197.6B$22.7B193.7B
185.7B195.2D3.5B196.5B197.5B192.6B190.BD2.6B190.BD2.6B189.6B195.BD2.
6B$22.7B193.7B185.7B181.2B11.BDBD2.5B196.5B197.5B190.7B190.BDBD6B190.
BDBD6B191.6B193.BDBD6B$22.7B193.7B185.7B179.4B.2B6.4BD8B196.5B197.5B
182.2B4.10B184.2B.4B2D7B184.2B.4B2D7B182.D6.6B189.2B.4B2D7B$22.7B193.
7B185.7B178.27B196.5B180.2B.2B2.3B6.6B180.17B183.B2D14B183.B2D14B182.
BDB2.2B2.6B186.B2D14B$CB20.7B171.CB20.7B175.2CB.B5.7B176.3BC25B174.CB
20.5B179.4BC6B6.6B179.2D6B3C8B181.2B2D4B3C8B181.2B2D4B3C8B181.BDB.3C
7B186.2B2D4B3C8B$B2C19.7B171.B2C19.7B175.2C2B2C4.7B175.5B2C6B2C15B
174.B2C19.5B179.5B2C6B2.9B178.DEC17B180.B2C19B178.B2C19B176.10B.6B
185.B2C19B$2C2B18.7B171.2C2B18.7B176.B.B2CB3.7B175.4B2C2B2C2BCBC15B
174.2C7B13.5B179.4B2C18B170.CB6.B2C17B172.CB6.B2C21B168.CB6.B2C21B
168.22B178.CB6.B2C21B$.4B17.7B172.4B17.7B171.CB6.2DB3.7B176.7B2C2B2C
16B172.2B.7B2DB11.5B179.24B170.B2CB.2C.5BC10B2D174.B2CB.2C.5BC18B168.
B2CB.2C.5BC18B168.23B177.B2CB.2C.5BC18B$2.4B16.7B173.4B16.7B171.B2C4.
B2D4.7B178.27B171.D12BDB10.5B179.24B170.2C2BC2BC5BC10B2D174.2C2BC2BC
5BC17B169.2C2BC2BC5BC17B167.24B178.2C2BC2BC5BC17B$3.4B5.2CB.B5.7B174.
4B5.2CB.B5.7B171.2C2B2.14B179.27B170.D11B2D3B4.CB3.5B177.8B2C16B171.B
.2BCBC5BC7B.2B177.B.2BCBC5BC16B171.B.2BCBC5BC16B168.25B178.B.2BCBC5BC
16B$4.4B4.2C2B2C4.7B175.4B4.2C2B2C4.7B172.4B.14B180.25B169.3BD15B2.2B
C3B.5B176.8BC2BC17B172.2BC12B185.2BC23B174.2BC23B167.13B2C11B181.2BC
23B$5.4B4.B.B2CB3.7B176.4B4.B.B2CB3.7B173.4B.12B181.23B170.24BC3B.5B
175.10B2C3B2C13B173.4B3C7B186.4B3C3B2D12B176.4B3C3B2D12B168.13B2C10B
183.4B3C3B2D12B$6.4B6.2DB3.7B177.4B6.2DB3.7B174.15B183.7BC14B171.33B
175.14BC2BC13B175.12B188.7B2D3B3.3B182.7B2D3B3.3B172.9B2D11B188.7B2D
3B3.3B$7.4B4.B2D4.7B178.4B4.B2D4.7B175.15B185.4BC7B2D4B173.26B.5B174.
16BCBC13B176.10B190.12B3.B184.12B3.B173.9B2D11B187.14B3.B$8.4B2.14B
180.4B2.14B177.15B185.3BCB.4BD2BDB173.25BC8B174.17BC13B176.11B190.12B
188.12B176.22B188.14B$9.4B.14B181.4B.14B178.13B186.5B2.4B2D173.26BCBC
7B173.B2D12B2D15B176.10B192.11B189.11B176.22B187.3B2C10B$10.4B.12B
183.4B.12B180.12B194.B175.28BCBC7B173.B2E11BD2BD13B175.BC7B3C192.5B3C
2B185.2E3.5B3C2B177.12B2C8B188.BCBC4B3C2B$11.15B185.15B182.10B371.29B
C8B172.BC2BC10BD2BD13B175.BC9B193.7B2D185.E2.E2.7B2D178.3BC7BC2BC6B
189.B2C7B2D$12.15B185.15B181.2B3C4B373.4B2D17BC13B173.BCBC11B2D4B2.3B
.2B177.DED.3BCB195.3BC3B2D185.E2.E2.3BC3B2D179.3B2C2BC3B2C7B190.B.3BC
3B2D$13.15B185.15B181.6B377.2B2D13B2D2BC13B173.2BC3D8B3C3B4.B182.B4.B
CB197.BCB190.2E5.BCB182.3B2C2BCBC10B195.BCB$14.13B187.13B183.4B379.
16B2D2BC13B173.18B195.C199.C199.C183.7BCBC8B198.C$15.12B188.12B184.B
384.31B172.21B778.7BC6B$16.10B190.10B570.8B2C3B3C3B3C9B172.22B778.4B
2.5B$16.2B3C4B191.2B3C4B573.5BC2BC18B175.3BD16B780.2B5.B$12.2E3.6B
194.6B575.5BC2BC6BC10B176.3BD15B$.2E9.E.E3.4B179.2E4.2E9.4B575.7B2C7B
C9B177.3BD15B$.2E10.E5.B181.2E4.2E10.B578.15BC9B177.17B$799.23B179.
16B$800.2D20B179.14B$800.2D14B2.3B181.13B$802.13B188.B.10B$803.11B
191.12B$805.8B187.2B.14B$807.5B188.16B$999.17B$999.17B$1000.16B$1002.
14B$1003.11B$1006.8B$1009.4B$1010.B!

Here's the actual output from sscs filtered by codeholic's script, in case anyone wants to extract slow-salvo recipes for non-31c/240 purposes:

Code: Select all

#P 0 0
#C Start-RLE: 2bo$3b2o$2b2o3$4bo$4bo$4bo2$3o3b3o7$3o3b3o2$4bo$4bo$4bo!
#C [310]: DELAY 1 TICKS, FIRE R1L0B
#C [847]: DELAY 1 TICKS, FIRE R1L2B
#C [1961]: FIRE R1L0B
#C [5811]: FIRE R1L2B
#C [16797]: FIRE R1L2B
#C [209101]: FIRE R3L19B
#C [767295]: FIRE R1L0B
#C [4378295]: DELAY 1 TICKS, FIRE R2L7B
#C [100054740]: REPHASE BY 9 LANES, FIRE R3L3B
*....................
.**..................
**...................
.....................
.....................
............**.......
............**..**...
................**...
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
..................***
............**.......
.**.........*.*......
.**..........*.......


#P 200 0
#C Start-RLE: 2bo$3b2o$2b2o3$4bo$4bo$4bo2$3o3b3o7$3o3b3o2$4bo$4bo$4bo!
#C [310]: DELAY 1 TICKS, FIRE R1L0B
#C [847]: DELAY 1 TICKS, FIRE R1L2B
#C [1961]: FIRE R1L0B
#C [5811]: FIRE R1L2B
#C [16797]: FIRE R1L2B
#C [209101]: FIRE R3L19B
#C [767295]: FIRE R1L0B
#C [4378295]: DELAY 1 TICKS, FIRE R2L7B
#C [13213617]: DELAY 1 TICKS, FIRE R1L0B
#C [134998257]: FIRE R3L3B
*....................
.**..................
**...................
.....................
.....................
............**.......
............**..**...
................**...
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
.....................
..................***
.....................
.**....**............
.**....**............


#P 400 0
#C Start-RLE: o$b2o$2o$7b3o2$5bo5bo$5bo5bo$5bo5bo5$5bo5bo$5bo5bo$5bo5bo2$7b3o!
#C [270]: FIRE R1L0B
#C [755]: DELAY 1 TICKS, FIRE R1L2B
#C [18544]: REPHASE BY 9 LANES, DELAY 1 TICKS, FIRE R3L21B
#C [51227]: DELAY 1 TICKS, FIRE R1L2B
#C [568619]: REPHASE BY 9 LANES, FIRE R1L0B
#C [4076431]: REPHASE BY 9 LANES, FIRE R1L0B
#C [25692761]: REPHASE BY 9 LANES, DELAY 1 TICKS, FIRE R1L2B
#C [153720441]: FIRE R2L7B
....**.......
....**..**...
........**...
*............
.**..........
**...........
.............
.............
.............
.............
.............
.............
.............
.............
..........***


#P 600 0
#C Start-RLE: o$b2o$2o4$6b3o2$4bo5bo$4bo5bo$4bo5bo5$4bo5bo$4bo5bo$4bo5bo2$6b3o!
#C [274]: FIRE R1L0B
#C [6699]: REPHASE BY 9 LANES, FIRE R3L21B
#C [33847]: FIRE R1L2B
#C [69790]: DELAY 1 TICKS, FIRE R1L0B
#C [285483]: DELAY 1 TICKS, FIRE R1L0B
#C [3500500]: DELAY 1 TICKS, FIRE R3L21B
#C [12383965]: DELAY 1 TICKS, FIRE R1L0B
#C [34440573]: DELAY 1 TICKS, FIRE R1L0B
#C [86509257]: DELAY 1 TICKS, FIRE R1L2B
*..........
.**......**
**..**..*.*
....**..**.
...........
...........
...........
...........
........*..
........*..
........*..


#P 800 0
#C Start-RLE: 7b3o$o$b2o2bo5bo$2o3bo5bo$5bo5bo5$5bo5bo$5bo5bo$5bo5bo2$7b3o!
#C [266]: FIRE R1L0B
#C [2736]: FIRE R3L21B
#C [26482]: REPHASE BY 9 LANES, DELAY 1 TICKS, FIRE R1L0B
#C [61028]: DELAY 1 TICKS, FIRE R1L2B
#C [584915]: DELAY 1 TICKS, FIRE R2L7B
#C [2015475]: FIRE R1L0B
#C [5567611]: DELAY 1 TICKS, FIRE R1L0B
#C [14444743]: DELAY 1 TICKS, FIRE R1L0B
*...................
.**.................
**..................
....................
....................
.................*..
.................*..
.................*..
....................
....................
..................*.
.................*.*
.................*.*
..................*.
.............*......
.............*......
.............*......
....................
....**...***...***..
...*..*.............
...*..*......*......
....**.......*......
.............*......


#P 1000 0
#C Start-RLE: o$b2o$2o$7b3o2$5bo5bo$5bo5bo$5bo5bo5$5bo5bo$5bo5bo$5bo5bo2$7b3o!
#C [270]: FIRE R1L0B
#C [757]: FIRE R1L2B
#C [1806]: DELAY 1 TICKS, FIRE R1L2B
#C [5450]: FIRE R1L0B
#C [16234]: FIRE R1L0B
#C [45271]: FIRE R1L2B
#C [255518]: REPHASE BY 9 LANES, FIRE R1L2B
#C [815263]: FIRE R1L2B
#C [4453384]: REPHASE BY 9 LANES, FIRE R1L2B
#C [26295543]: REPHASE BY 9 LANES, FIRE R1L0B
#C [78938820]: DELAY 1 TICKS, FIRE R1L0B
#C [203447516]: FIRE R1L0B
..........*.........
...........**.......
..........**........
....................
....................
............**......
...........*..*.....
............**...**.
................*..*
.................*.*
..................*.
....................
.**.................
*..*................
.*.*................
..*...........***...


#P 1200 0
#C Start-RLE: o6b3o$b2o$2o3bo5bo$5bo5bo$5bo5bo5$5bo5bo$5bo5bo$5bo5bo2$7b3o!
#C [267]: FIRE R1L0B
#C [742]: FIRE R1L0B
#C [8072]: DELAY 1 TICKS, FIRE R3L26B
#C [35074]: DELAY 1 TICKS, FIRE R1L0B
#C [71334]: DELAY 1 TICKS, FIRE R1L0B
#C [1198765]: FIRE R3L4B
#C [4818740]: DELAY 1 TICKS, FIRE R1L0B
#C [13660870]: FIRE R1L2B
#C [68507199]: REPHASE BY 9 LANES, DELAY 1 TICKS, FIRE R1L2B
................***
.........**........
*........**........
.**..**......*.....
**..*..*.....*.....
.....*.*.....*.....
......*............
.........***.......
...................
...................
...................
...................
.......*.......***.
.......*...........
.......*.....*.....
.............*.....
.............*.....


#P 1400 0
#C Start-RLE: o6b3o$b2o$2o3bo5bo$5bo5bo$5bo5bo5$5bo5bo$5bo5bo$5bo5bo2$7b3o!
#C [267]: FIRE R1L0B
#C [742]: FIRE R1L0B
#C [8072]: DELAY 1 TICKS, FIRE R3L26B
#C [35074]: DELAY 1 TICKS, FIRE R1L0B
#C [71337]: FIRE R1L2B
#C [1198838]: FIRE R3L4B
#C [4818826]: DELAY 1 TICKS, FIRE R1L0B
#C [13661060]: FIRE R1L2B
#C [68507517]: REPHASE BY 9 LANES, DELAY 1 TICKS, FIRE R1L2B
................***
.........**........
*........**........
.**..**......*.....
**..*..*.....*.....
.....*.*.....*.....
......*............
.........***.......
...................
...................
...................
...................
...............***.
...................
.............*.....
.............*.....
.............*.....


#P 1600 0
#C Start-RLE: o6b3o$b2o$2o3bo5bo$5bo5bo$5bo5bo5$5bo5bo$5bo5bo$5bo5bo2$7b3o!
#C [267]: FIRE R1L0B
#C [742]: FIRE R1L0B
#C [8072]: DELAY 1 TICKS, FIRE R3L26B
#C [35074]: DELAY 1 TICKS, FIRE R1L0B
#C [71334]: DELAY 1 TICKS, FIRE R1L0B
#C [1198765]: FIRE R3L4B
#C [4818740]: DELAY 1 TICKS, FIRE R1L0B
#C [13660870]: FIRE R1L2B
#C [35877614]: FIRE R1L2B
#C [87752591]: DELAY 1 TICKS, FIRE R1L2B
................***
.........**........
*........**........
.**..**......*.....
**..*..*.....*.....
.....*.*.....*.....
......*............
.........***.......
...................
...................
...................
...................
.....**........***.
....*..*...........
....*..*.....*.....
.....**......*.....
.............*.....


#P 1800 0
#C Start-RLE: o$b2o$2o3$7bo$7bo$7bo2$3b3o3b3o7$3b3o3b3o2$7bo$7bo$7bo!
#C [305]: DELAY 1 TICKS, FIRE R1L0B
#C [1407]: REPHASE BY 9 LANES, FIRE R1L0B
#C [4958]: DELAY 1 TICKS, FIRE R1L2B
#C [15503]: FIRE R1L0B
#C [44510]: FIRE R1L2B
#C [254197]: DELAY 1 TICKS, FIRE R2L7B
#C [813906]: FIRE R1L2B
#C [9120059]: FIRE R3L4B
#C [117946362]: FIRE R3L26B
............***
...............
...............
...............
...............
...............
..........**...
..........**...
...............
...............
...............
...............
.........**....
*.......*..*...
.**..*...**....
**..*.*........
....*.*........
.....*.........


#P 2000 0
#C Start-RLE: 7b3o2$5bo5bo$5bo5bo$5bo5bo5$o4bo5bo$b2o2bo5bo$2o3bo5bo2$7b3o!
#C [258]: FIRE R1L0B
#C [718]: FIRE R1L0B
#C [1700]: FIRE R1L0B
#C [22815]: FIRE R3L21B
#C [56337]: DELAY 1 TICKS, FIRE R1L0B
#C [2501301]: REPHASE BY 9 LANES, FIRE R3L4B
#C [11565150]: DELAY 1 TICKS, FIRE R1L0B
#C [33550818]: FIRE R1L2B
#C [164289519]: REPHASE BY 9 LANES, DELAY 1 TICKS, FIRE R1L2B
................***
.........**........
*........**........
.**..**......*.....
**..*..*.....*.....
.....*.*.....*.....
......*............
.........***.......
...................
...................
...................
.........**........
........*.*....***.
........**.........
.............*.....
.............*.....
.............*.....

EDIT: The HWSS recipes (first three above) are all variants of the #153720441 teaser recipe that oblique posted. This must mean that codeholic's script is one lane too generous in diagnosing HWSS edge shooters -- the HWSS spark knocks out a blinker and a block in the intermediate targets as it goes by them... all without affecting the HWSS, but the damage is done when higher recipes attempt to continue from the modified targets.

So for now we're still stuck building this seed in some other way, until we dig up some of the slightly more expensive true HWSS edge-shooters from previous search runs. Maybe this weekend I'll check and see if the MWSS recipes are really workable -- MWSS sparks would affect blocks at similar offsets, but not blinkers.

EDIT 2: MWSS recipe #117946362 should work okay, anyway:

Code: Select all

x = 1244, y = 1231, rule = B3/S23
2bo$obo$b2o135$152bo$150bobo$151b2o159$302bo$300bobo$301b2o130$451bo$
452b2o$451b2o162$602bo$600bobo$601b2o159$783bo$781bobo$782b2o124$901bo
$902b2o$901b2o159$1052bo$1050bobo$1051b2o166$1232bo$1233b2o$1232b2o3$
1239bo$1239bo$1239bo2$1235b3o3b3o7$1235b3o3b3o2$1239bo$1239bo$1239bo!

An intermediate blinker ends up on the closest safe lane, but there's nothing permanent to the right of that.

... This brings up some interesting possibilities for HWSS and MWSS streams modifying their own intermediate targets in passing. There may be a few recipes that don't currently produce *WSSes, but that would actually produce them once an upship stream got started, because the feedback from the *WSS sparks would modify the intermediates in just the right way.

It'd be a nightmare to actually find these with sscs, of course; it's not worth spending any time on, but it would be an impressive trick if one happened to show up. No doubt a sample could be built based on the teaser HWSS seed.

Posted: **June 13th, 2014, 12:20 pm**

dvgrn wrote:EDIT: The HWSS recipes (first three above) are all variants of the #153720441 teaser recipe that oblique posted. This must mean that codeholic's script is one lane too generous in diagnosing HWSS edge shooters -- the HWSS spark knocks out a blinker and a block in the intermediate targets as it goes by them... all without affecting the HWSS, but the damage is done when higher recipes attempt to continue from the modified targets.

My script doesn't take intermediate steps into account (partly because I didn't know how to read the recipes).

Posted: **June 13th, 2014, 1:33 pm**

codeholic wrote:My script doesn't take intermediate steps into account (partly because I didn't know how to read the recipes).

Ah, got it. Obviously I didn't read the Perl script very closely... but it's certainly still a good initial filter, to get rid of all the recipes that obviously aren't edge-shooters.

Maybe I should extend my Interpret-sscs-recipe.py to go through and build all the recipes in the edge-shooters.life output file. It's pretty easy to spot potential problems by running recipes in LifeHistory. There's already code in oblique's project to build an actual 31c/240 rake for any recipe, but it's still kind of annoying to extract the slow salvos if someone wants to use them for a non-31c/240 purpose -- especially since the code needs the whole database to do its work...!

The first two LWSS edge-shooters are quite nice -- the first one pushes its leftover ash over ten cells to the right, which will make it cheaper to do chained slow-salvo LWSS constructions:

Code: Select all

#C LWSS edge-shooter, #86509257
x = 172, y = 175, rule = B3/S23
2bo$obo$b2o27$42bo$40bobo$22bo18b2o$20bobo$21b2o22$62bo$60bobo$61b2o
17$82bo$80bobo$81b2o27$102bo$100bobo$101b2o22$141bo$142b2o$141b2o$121b
o$122b2o$121b2o23$161bo$162b2o$161b2o4$167b3o2$165bo5bo$165bo5bo$165bo
5bo5$165bo5bo$165bo5bo$165bo5bo2$167b3o!

Code: Select all

#C LWSS edge-shooter, #14444743
x = 153, y = 159, rule = B3/S23
2bo$obo$b2o27$22bo$20bobo$21b2o27$41bo20bo$42b2o16bobo$41b2o18b2o32$
82bo19bo$80bobo17bobo$81b2o18b2o33$121bo$122b2o$121b2o16$148b3o$141bo$
142b2o2bo5bo$141b2o3bo5bo$146bo5bo5$146bo5bo$146bo5bo$146bo5bo2$148b3o!

The third one (#203447516) has an intermediate blinker in the way of the LWSS lane. With four expensive objects in the constellation and a complex LWSS-generating explosion, it's probably not worth finding another way to build that seed.

The MWSS edge-shooters should be safe also -- they're crazy-looking recipes, but clean up fairly nicely, with the first one leaving a block in the MWSS lane to continue a slow-salvo construction:

Code: Select all

#C MWSS edge-shooter, #68507199
x = 173, y = 169, rule = B3/S23
2bo$obo$b2o5$21bo$22b2o$21b2o29$42bo$40bobo$41b2o10$61bo$62b2o$61b2o
29$102bo$100bobo$82bo18b2o$80bobo$81b2o17$122bo$120bobo$121b2o22$141bo
$142b2o$141b2o27$161bo6b3o$162b2o$161b2o3bo5bo$166bo5bo$166bo5bo5$166b
o5bo$166bo5bo$166bo5bo2$168b3o!

Code: Select all

#C MWSS edge-shooter, #117946362
x = 173, y = 160, rule = B3/S23
2bo$obo$b2o5$22bo$20bobo$21b2o29$42bo$40bobo$41b2o18bo$62b2o$61b2o32$
82bo19bo$80bobo17bobo$81b2o18b2o25$121bo$122b2o$121b2o29$142bo$140bobo
$141b2o5$161bo$162b2o$161b2o3$168bo$168bo$168bo2$164b3o3b3o7$164b3o3b
3o2$168bo$168bo$168bo!

That's it for this run, I think. The other MWSS edge-shooters are all trivial variants of the first one.

The next line of investigation might be an unweighted search at 20x20 (for Caterpillar's little brother and suchlike), or maybe even something like a 15x15 search, to try to reach out into some new HWSS search territory...?

Probably the next thing I can do is go back and look at older HWSS recipes again, and see how expensive they are with new rakes. I'll also build the "teaser" HWSS rake eventually, using two synchronized pairs of gliders, and see what that looks like.

Posted: **June 14th, 2014, 12:46 am**

dvgrn wrote:
dvgrn wrote:And the seed can be built either with a slow salvo or with two independent forerake/backrake pairs (i.e., the pairs of gliders can be sent in either order).
Spoke a little too soon. Only the independent-pair construction will work; a slow salvo won't, unless we come up with a new recipe for this seed. Just took a look at the intermediate targets, and five of them get in the way of the HWSS stream.

That's a pitty. Most salvos I looked at more closely by now had a tendency to move slowly *away* from the glider source ... of course this has to be an exception.

dvgrn wrote: Am I right in guessing that some of the rakes in the sscs database put out even-phase gliders, and some put out odd phases? Are the rake patterns stored in a database table now? I didn't see the new rakes specified in the code anywhere, and the collection in the "parts" subfolder looks incomplete.

EDIT: Ah, no, I see the problem -- three interdependent bad assumptions on my part... Everything works if the rakes all emit o$b2o$2o! gliders by default. This gives a slow salvo of [...]

That's about what I meant a few pages before when I said I'd have to normalize your rakes before my own recipe generator could work: yes the rakes are (or rather: should be) stored in the DB.

Currently only as stubs because I have not yet find the brain-time to properly align anything and rephase them so my recipe.c can easily stitch them together.

Sscs itself of course does not need the patterns for finding stuff - it just assumes, that all rakes are aligned and phased properly.

Besides: I just noticed that anything but still lifes, P2, and P4 will be a real pain when it comes to getting the DELAY part right. I made sure the bullets of all rakes are in the same x-offset from the track - but since the construction site wanders around, I would have to take the x-component of this movement into account too ... so: either sscs should stick to P1,2,4 or implement the forward rakes also (because that needs about the same amount of additional work).

Posted: **June 14th, 2014, 12:58 am**

dvgrn wrote: Maybe I should extend my Interpret-sscs-recipe.py to go through and build all the recipes in the edge-shooters.life output file. It's pretty easy to spot potential problems by running recipes in LifeHistory. There's already code in oblique's project to build an actual 31c/240 rake for any recipe, but it's still kind of annoying to extract the slow salvos if someone wants to use them for a non-31c/240 purpose -- especially since the code needs the whole database to do its work...!

Worse. Since it's an ordered search space and the calculations are based on the fact, that the ship itself moves in a well defined way the results themselfs are about guarantied to be suboptimal for any other purpose.

And you would have to convert them to slow salvo form (like in one of your recent posts) before they make any sense.

I should be able to build a modified script that just illustrates the collision-sequence for all the recipes ... the resulting stamp collection would be some 3-10 times larger i think.

On the other hand: if I filtered out all non edge shooters before exporting them ... should be not tooo huge to be usefull.

dvgrn wrote: The next line of investigation might be an unweighted search at 20x20 (for Caterpillar's little brother and suchlike), or maybe even something like a 15x15 search, to try to reach out into some new HWSS search territory...?

Probably the next thing I can do is go back and look at older HWSS recipes again, and see how expensive they are with new rakes. I'll also build the "teaser" HWSS rake eventually, using two synchronized pairs of gliders, and see what that looks like.

An unweighted search for 20x20 will explode rather quick. I don't think I would be able to go any deeper then about 10 or 12 gliders. Since I tended to be over optimistic in the past I would rather say 9 or even just 8.

The 15x15 search should reach some depth of about ... 16? 18?

There won't be to much P3 or P15 in there I think

Posted: **June 14th, 2014, 8:00 am**

oblique wrote:Besides: I just noticed that anything but still lifes, P2, and P4 will be a real pain when it comes to getting the DELAY part right. I made sure the bullets of all rakes are in the same x-offset from the track - but since the construction site wanders around, I would have to take the x-component of this movement into account too ... so: either sscs should stick to P1,2,4 or implement the forward rakes also (because that needs about the same amount of additional work).

I suppose there would be a lot of overlap between the location-tracking work needed to handle P3 and P5+ targets correctly, and the location-tracking work needed to handle forward rakes. On the other hand, if recipe.c gets a backrake timing wrong for a P3 target, the fix involves selecting the rake and hitting Ctrl+Space once or twice in Golly -- not very painful at all, considering how rarely the problem will come up anyway.

Forward rakes are a somewhat weirder problem, even if you stick to your "one at a time" rule. In building a rake, recipe.c would have to worry about adding a vertical block-trail distance proportional to the x-offset to make sure that the forerake and backrake streams don't cross. I just wrote a long summary of all the strange search-space-expanding things that happen if the streams are allowed to cross, but then remembered that the topic came up already.

oblique wrote:I should be able to build a modified script that just illustrates the collision-sequence for all the recipes ... the resulting stamp collection would be some 3-10 times larger i think.

Another option might be to just list an EO-format slow salvo recipe in a comment -- basically the information that comes out of the script I posted above, but with the right +/-31N corrections when the target drifts one way or the other. It's not actually all that hard to fix the script to figure out those corrections, but it would be easier if that information were never lost in the first place. If you include the lane list in some form, it won't make the stamp collections much bigger, and I can easily fix up my slow-salvo builder script to reconstitute an RLE pattern from that plus the Start-RLE.

Right now, mostly because of codeholic's recent discovery of a workable knightship mechanism, I have to say that there's something I'm a lot more interested in than forerake/backrake combinations at the moment. Might it be possible to dig out a good reference collection of monochromatic slow-salvo target-move operations from the sscs database?

The weighting for Half-Baked Knightship slow salvos is very strange and interesting. Probably I could just sort known block-move recipes according to the number of scans needed to complete them, and then compose atomic recipes to get longer-distance moves... but as codeholic points out, going back to a block every time is arbitrary and horribly inefficient. Ideally we'd just build a really big database of slow salvos that create different simple objects at different offsets, and then do a quick search to find the move-plus-glider-turn combination that's most efficient for a given 90-degree glider output.

Except for the "monochromatic" part, this is basically the same database that's needed as a good next step in building the 31c/240 spaceship. If and when we dig up a reasonable slow-salvo HWSS recipe, we'll need a way to look up the most efficient slow salvo that moves leftover junk J@(x,y) from HWSS Construction #N, to produce different junk a little farther away that can serve as a target to start HWSS Construction #N+1.

This construction model doesn't work too terribly well with interchanges and similar two-glider-collision objects as initial targets, though. I don't think it's very cheap to get back to an interchange with a slow salvo, starting from random ash...?

So if our HWSS recipes all start from things like interchanges, we'll be stuck building new initial targets for each HWSS, using relatively expensive forerake/backrake pairs. I guess it's quite possible that that's an all-around simpler way to do things anyway!

Posted: **June 14th, 2014, 2:33 pm**

dvgrn wrote:
oblique wrote:Besides: I just noticed that anything but still lifes, P2, and P4 will be a real pain when it comes to getting the DELAY part right. I made sure the bullets of all rakes are in the same x-offset from the track - but since the construction site wanders around, I would have to take the x-component of this movement into account too ... so: either sscs should stick to P1,2,4 or implement the forward rakes also (because that needs about the same amount of additional work).
I suppose there would be a lot of overlap between the location-tracking work needed to handle P3 and P5+ targets correctly, and the location-tracking work needed to handle forward rakes. On the other hand, if recipe.c gets a backrake timing wrong for a P3 target, the fix involves selecting the rake and hitting Ctrl+Space once or twice in Golly -- not very painful at all, considering how rarely the problem will come up anyway.

The more I think about P3+ stuff, the more I tend to believe it ain't worth the trouble anyway.
The only patterns I have *ever* found in any of my numerous runs are:

pulsar
pentadecathlon
mold
figure eight (very rare)

Anything beyound pentadecathlon is much to rare a beast to expect it to be usefull.
And pulsar / pentadecathlon need pretty much space.

dvgrn wrote: Another option might be to just list an EO-format slow salvo recipe in a comment -- basically the information that comes out of the script I posted above, but with the right +/-31N corrections when the target drifts one way or the other. It's not actually all that hard to fix the script to figure out those corrections, but it would be easier if that information were never lost in the first place. If you include the lane list in some form, it won't make the stamp collections much bigger, and I can easily fix up my slow-salvo builder script to reconstitute an RLE pattern from that plus the Start-RLE.

I'm currently not realy tracking the absolute lane numbers, rather the programs readjusts after each step. Or are you taking about fly-by situations? Where may recipe seems to fire on say lane 1 and the glider hits 32 (of the neighbouring pattern) instead? This would be infact easy to mention in the output.

dvgrn wrote: Right now, mostly because of codeholic's recent discovery of a workable knightship mechanism, I have to say that there's something I'm a lot more interested in than forerake/backrake combinations at the moment. Might it be possible to dig out a good reference collection of monochromatic slow-salvo target-move operations from the sscs database?

Last time I looked there where not to many movers - besides the well-known ones (atomic block, loaf and blinker move by something like (+2,+1) or (-3,+1))

Monochromatic means: use every other lane, right? If the first glider came on an even lane, the EVERY glider has to be on an even lane.

What are the starting patterns to look shoot at? What is the maximum size of an intermediate target allowed?

Are you only interessted in classical movers, or more like "build a blinker at (+x,y) by starting with a glider at (0,0)"

dvgrn wrote: The weighting for Half-Baked Knightship slow salvos is very strange and interesting. Probably I could just sort known block-move recipes according to the number of scans needed to complete them, and then compose atomic recipes to get longer-distance moves... but as codeholic points out, going back to a block every time is arbitrary and horribly inefficient. Ideally we'd just build a really big database of slow salvos that create different simple objects at different offsets, and then do a quick search to find the move-plus-glider-turn combination that's most efficient for a given 90-degree glider output.

I didn't follow this thread too closely - yet

dvgrn wrote: Except for the "monochromatic" part, this is basically the same database that's needed as a good next step in building the 31c/240 spaceship. If and when we dig up a reasonable slow-salvo HWSS recipe, we'll need a way to look up the most efficient slow salvo that moves leftover junk J@(x,y) from HWSS Construction #N, to produce different junk a little farther away that can serve as a target to start HWSS Construction #N+1.

This construction model doesn't work too terribly well with interchanges and similar two-glider-collision objects as initial targets, though. I don't think it's very cheap to get back to an interchange with a slow salvo, starting from random ash...?

So if our HWSS recipes all start from things like interchanges, we'll be stuck building new initial targets for each HWSS, using relatively expensive forerake/backrake pairs. I guess it's quite possible that that's an all-around simpler way to do things anyway!

Hmm.
Since a block is easily killed by half the block/glider reactions anyway, and you seemed to be able to build an - say - interchange with a single FWD+BACK combo - it might be cheaper to do this right away, then try to push-along-and-reconstruct ...
(Even if we took the switching malus into account ...)

Posted: **June 14th, 2014, 6:58 pm**

oblique wrote:I'm currently not realy tracking the absolute lane numbers, rather the programs readjusts after each step. Or are you taking about fly-by situations? Where may recipe seems to fire on say lane 1 and the glider hits 32 (of the neighbouring pattern) instead? This would be infact easy to mention in the output.

I guess the goal is just to know as easily as possible what stream of gliders produces the advertised result... partly because some people will likely end up using these various *WSS recipes to build other things besides 31c/240 spaceships. Absolute lanes, relative lanes, full-recipe RLE, anything that carries that information should be good.

oblique wrote:Last time I looked there [were not too] many movers - besides the well-known ones (atomic block, loaf and blinker move by something like (+2,+1) or (-3,+1))

Right, that's the full list of atomic moves with the same start and end objects... which you've actually posted earlier on this thread. If you ever run into, say, a two-object constellation that gets displaced by a glider collision, that will be a real surprise.

There are lots and lots of non-atomic move recipes, though. In previous slow-salvo-based patterns I've limited my recipes to ones where the start and end objects are both blocks -- an inefficient but convenient simplification, which helped keep my brain from overloading during last year's mostly-solo effort to put together a Life replicator.

oblique wrote:Monochromatic means: use every other lane, right? If the first glider came on an even lane, the EVERY glider has to be on an even lane.

What are the starting patterns to look shoot at? What is the maximum size of an intermediate target allowed?

Are you only interessted in classical movers, or more like "build a blinker at (+x,y) by starting with a glider at (0,0)"?

Just for the record, since I posted here last, codeholic seems to be maybe gearing up to tackle the problem of a a weighted monochromatic search specific to half-bakery knightships. So it might make more sense to keep sscs focused on polychromatic slow salvos -- but there are similar target-move questions that still might be worth looking at.

Start patterns and maximum size are somewhat open to negotiation -- I suppose the general idea is "whatever junk you'll most often find lying around after making a 90-degree glider". But even if the limit is, say, ten ON cells or less, that's many hundreds of possible targets. The key is going to be figuring out how to get the most useful lookup table for moving a "slow elbow" target around, with the least amount of painful math and programming. We probably could be quite happy with a mere multi-megabyte lookup table, if an unwieldy multi-gigabyte table would really only improve slow-salvo construction efficiency by a few percent.

Here's one suggestion: allow only relatively few really common objects as initial or final objects. The list of glider turners that codeholic posted implies that allowable objects could be block, blinker, traffic light, honeyfarm, and beehive. I'd be tempted to arbitrarily disallow beehives because they're not as symmetrical. Could just as arbitrarily allow ponds and tubs, because they _are_ symmetrical... I'm not sure that much can be done with them using monochromatic salvos, but they work well with polychromatic recipes.

If we get really ambitious we could include anything in Achim Flammenkamp's top ten objects, which would allow loaves, boats, ships, longboats, and toads into the club -- but all the different orientations might be too much of a headache.

Here again, monochromaticity adds a new level of strangeness: each non-symmetrical object will have two totally different sets of possible slow-salvo transformations, depending on which color squares it's on. Arbitrarily we might call an object's location "black"=even or "white"=odd depending (let's say) on the sum of the X and Y coordinates of the upper left corner of its bounding box. Objects with diagonal symmetry will at least have mirror-image move recipes for their "black" and "white" versions.

oblique wrote:
dvgrn wrote:So if our HWSS recipes all start from things like interchanges, we'll be stuck building new initial targets for each HWSS, using relatively expensive forerake/backrake pairs. I guess it's quite possible that that's an all-around simpler way to do things anyway!
Hmm.
Since a block is easily killed by half the block/glider reactions anyway, and you seemed to be able to build an - say - interchange with a single FWD+BACK combo - it might be cheaper to do this right away, then try to push-along-and-reconstruct ...

For our current 31c/240 purposes, I think you're right. The forerake+backrake combo can get a bit expensive in terms of spaceship length, when upship streams are being built a long distance from the block trails -- you end up with a lot of empty trail between the two rakes. It might be worth revisiting this if we end up with a really wide front end or something like that. I also think push-along-and-reconstruct could be key to eventually making a much smaller "Caterpillar's little brother"... but for now, let's assume that we'll collide gliders to build whatever targets we need to build.

Posted: **June 15th, 2014, 3:01 pm**

This simple loaf-and-blinker MWSS seed seems like a promisingly adaptable result from codeholic's May 27th edge-shooter results:

Code: Select all

x = 105, y = 67, rule = B3/S23
9bo$10bo$8b3o$o$b2o$2o30$31bo$29bobo$30b2o5$91bo$92b2o$91b2o4$96b2o4b
3o$95bo2bo$96bobo$97bo13$34b3o$36bo$35bo!

Unfortunately it isn't quite the loaf-and-blinker constellation that you can get by colliding two gliders, and there's no really short simple conversion salvo to move the blinker and/or the loaf to the right relative locations -- as shown by the experimental four-glider collision at the left.

Probably the simplest non-slow-salvo construction would be to create loaf-and-blinker, delete the blinker, rebuild it at a small offset with two more gliders, and shove it into the right place with a final glider -- six gliders in all. Might it be worth looking for a two-glider reaction that adjusts the blinker instead, or an additional block or other object that will catalyze the leftover ash into something less messy?

Another two-object LWSS seed implied by the May 27th results is this block and boat combination:

Code: Select all

x = 12, y = 13, rule = B3/S23
3bo$4b2o$3b2o4$2o$2o3$9b2o$9bobo$10bo!

Still haven't found any slow-salvo-constructed HWSS seeds that quite work. This one, from an earlier search, again has just one blinker in the wrong phase and one cell too far right:

Code: Select all

x = 372, y = 592, rule = B3/S23
bo$2bo$3o27$20bo$21b2o$20b2o27$40bo$41b2o$40b2o17$81bo$82bo$60bo19b3o$
61b2o$60b2o25$100bo$101b2o$100b2o27$121bo$122bo$120b3o5$141bo$142bo$
140b3o27$160bo$161b2o$160b2o14$180bo$181b2o$180b2o14$200bo$201b2o$200b
2o156$367b3o2$365bo5bo$365bo5bo$365bo5bo5$365bo5bo$365bo5bo$365bo5bo2$
367b3o3$161bo$162bo$160b3o27$180bo$181b2o$180b2o27$200bo$201b2o$200b2o
17$241bo$242bo$220bo19b3o$221b2o$220b2o25$260bo$261b2o$260b2o27$281bo$
282bo$280b3o5$301bo$302bo$300b3o27$320bo$321b2o$320b2o14$340bo$341b2o$
340b2o12$367b3o2$360bo4bo5bo$361b2o2bo5bo$360b2o3bo5bo5$365bo5bo$365bo
5bo$365bo5bo2$367b3o!

EDIT: At least the above answers my worry about making an interchange out of leftover ash, using just a slow salvo. Turns out it's just a few gliders away from a traffic light.

There are a few HWSS seeds from even farther back that could maybe be constructed one piece at a time, but they'd be very inefficient as I recall -- three or four objects per seed, and not always the easy two-glider object constructions. So I think we're still hoping for a lucky HWSS recipe, from some odd corner of the search space that hasn't been checked yet.

EDIT 2: The seeds for other directions certainly keep me hoping that there's a good cheap HWSS seed out there somewhere. This one could be turned into a decent north HWSS recipe with the addition of a 180-degree one-time turner, or better some cheaper way of creating a pi in that location and orientation:

Code: Select all

x = 11, y = 15, rule = LifeHistory
.2C5.2C$.2C4.C2.C$8.2C5$2C$2C4$9.2C$8.2C$10.C!

[Oops, I see the same HWSS seed has caught my eye before. Might be time to do a complete survey of the S, E, and W collections, in case there's anything else like this.]

EDIT 3: Even with a turner added, this won't work in a 31c/240 ship, as codeholic points out.

Posted: **June 18th, 2014, 5:31 pm**

dvgrn wrote:Still haven't found any slow-salvo-constructed HWSS seeds that quite work.

I think I've been through all the old HWSS seeds now, including the ones that use the wrong cost metrics. All of the slow-salvo ways of building HWSS seeds seem to have intermediate targets that extend too far to the right -- usually by just one cell.

This isn't really too surprising. Many recipes are really just variants of each other. The "teaser" blinker-plus-half-blockade HWSS recipe is actually a version of the blinker-plus-eater seed that we knew about way back, that the old HWSS rake from January is based on. In fact codeholic even posted that seed pattern once upon a time.

It seems to be surprisingly tricky to generate the half-blockade in the obvious way, with a cheap LOM recipe. If the blinker or one of its obvious predecessors is already present, the LOM explosion hits it. And only one of the LOM half-blockades can be used; if you try to work with the other one, you end up with an illegal intermediate target. You could move the unused half-blockade around and turn it into the blinker, but that's a long distance for that kind of conversion.

There's probably a way to do it somehow. Here's a sample salvo using an inexpensive LOM recipe, which is just a bit too tall to work in a 31c/240 context but may be useful elsewhere -- 16 gliders from a block, 15 from a honeyfarm:

Code: Select all

#C block+16G -> blinker+half-blockade HWSS seed (plus trigger glider)
#C (can't be used with a 31c/240 block column)
x = 377, y = 403, rule = B3/S23
o$b2o$2o42$64bobo$65b2o$65bo43$91bo$89bobo$90b2o28$112bo$110bobo$111b
2o13$135bo$133bobo$134b2o24$164bo$162bobo$163b2o9$183bo$184bo$182b3o
16$183bo$184bo$182b3o10$203bo$204bo$202b3o18$223bo$224bo$222b3o15$243b
o$244bo$242b3o14$252bo$250bobo$251b2o25$271bobo$272b2o$272bo28$297bo$
295bobo$296b2o43$336bo$334bobo$335b2o28$358bo$356bobo$357b2o8$376bo$
374bobo$375b2o3$375b2o$375b2o!

With a more expensive way of building the blocks, it's easy to string together a workable 18-glider HWSS seed recipe:

Code: Select all

#C block+18G -> blinker+half-blockade HWSS seed
#C (31c/240 compatible; trigger glider also shown)
x = 340, y = 351, rule = B3/S23
bo$2bo$3o11$27bobo$28b2o$28bo21$45bo$46bo$44b3o18$72bo$73bo$71b3o19$
84bobo$85b2o$85bo18$96bobo$97b2o$97bo18$119bobo$120b2o$120bo22$142bo$
143bo$141b3o18$169bo$170bo$168b3o18$186bo$187bo$185b3o29$196bobo$197b
2o$197bo8$223bobo$224b2o$224bo18$235bobo$236b2o$236bo13$254bo$255bo$
253b3o13$267bo$268b2o$267b2o23$278bo$279bo$277b3o7$298bo$299bo$297b3o
18$318bo$319bo$317b3o15$338bo$339bo$337b3o4$338b2o$338b2o!

Just for the record, here's the proof of 31c/240 compatibility:

Code: Select all

x = 7039, y = 9189, rule = B3/S23
bo$2bo$3o89$61bo$62bo$60b3o30$137bobo$138b2o$138bo57$121bo$122bo$120b
3o30$197bobo$198b2o$198bo57$181bo$182bo$180b3o$285bo$286bo$284b3o27$
257bobo$258b2o$258bo57$241bo$242bo$240b3o$345bo$346bo$344b3o27$317bobo
$318b2o$318bo28$442bo$443bo$441b3o27$301bo$302bo$300b3o$405bo$406bo$
404b3o27$377bobo$378b2o$378bo28$502bo$503bo$501b3o27$361bo$362bo$360b
3o$465bo$466bo$464b3o26$584bobo$437bobo145b2o$438b2o145bo$438bo28$562b
o$563bo$561b3o27$421bo$422bo$420b3o$525bo$526bo$524b3o26$644bobo$497bo
bo145b2o$498b2o145bo$498bo28$622bo$623bo$621b3o26$726bobo$481bo245b2o$
482bo244bo$480b3o$585bo$586bo$584b3o26$704bobo$557bobo145b2o$558b2o
145bo$558bo28$682bo$683bo$681b3o26$786bobo$541bo245b2o$542bo244bo$540b
3o$645bo$646bo$644b3o26$764bobo$617bobo145b2o$618b2o145bo$618bo24$879b
obo$880b2o$880bo2$742bo$743bo$741b3o26$846bobo$601bo245b2o$602bo244bo$
600b3o$705bo$706bo$704b3o26$824bobo$677bobo145b2o$678b2o145bo$678bo24$
939bobo$940b2o$940bo2$802bo$803bo$801b3o26$906bobo$661bo245b2o$662bo
244bo$660b3o$765bo$766bo$764b3o26$884bobo$737bobo145b2o$738b2o145bo$
738bo24$999bobo$1000b2o$1000bo2$862bo$863bo$861b3o26$966bobo$721bo245b
2o$722bo244bo$720b3o$825bo$826bo$824b3o26$944bobo$797bobo145b2o$798b2o
145bo$798bo15$1142bo$1143bo$1141b3o7$1059bobo$1060b2o$1060bo2$922bo$
923bo$921b3o26$1026bobo$781bo245b2o$782bo244bo$780b3o$885bo$886bo$884b
3o26$1004bobo$857bobo145b2o$858b2o145bo$858bo15$1202bo$1203bo$1201b3o
7$1119bobo$1120b2o$1120bo2$982bo$983bo$981b3o26$1086bobo$841bo245b2o$
842bo244bo$840b3o$945bo$946bo$944b3o12$1299bo$1300bo$1298b3o12$1064bob
o$917bobo145b2o$918b2o145bo$918bo15$1262bo$1263bo$1261b3o7$1179bobo$
1180b2o$1180bo2$1042bo$1043bo$1041b3o26$1146bobo$901bo245b2o$902bo244b
o$900b3o$1005bo$1006bo$1004b3o12$1359bo$1360bo$1358b3o12$1124bobo$977b
obo145b2o$978b2o145bo$978bo15$1322bo$1323bo$1321b3o7$1239bobo$1240b2o$
1240bo2$1102bo$1103bo$1101b3o12$1446bo$1447bo$1445b3o12$1206bobo$961bo
245b2o$962bo244bo$960b3o$1065bo$1066bo$1064b3o12$1419bo$1420bo$1418b3o
12$1184bobo$1037bobo145b2o$1038b2o145bo$1038bo15$1382bo$1383bo$1381b3o
7$1299bobo$1300b2o$1300bo2$1162bo$1163bo$1161b3o12$1506bo$1507bo$1505b
3o12$1266bobo$1021bo245b2o$1022bo244bo$1020b3o$1125bo$1126bo$1124b3o
12$1479bo$1480bo$1478b3o12$1244bobo$1097bobo145b2o$1098b2o145bo$1098bo
11$1576bobo$1577b2o$1577bo2$1442bo$1443bo$1441b3o7$1359bobo$1360b2o$
1360bo2$1222bo$1223bo$1221b3o12$1566bo$1567bo$1565b3o12$1326bobo$1081b
o245b2o$1082bo244bo$1080b3o$1185bo$1186bo$1184b3o12$1539bo$1540bo$
1538b3o12$1304bobo$1157bobo145b2o$1158b2o145bo$1158bo11$1636bobo$1637b
2o$1637bo2$1502bo$1503bo$1501b3o7$1419bobo$1420b2o$1420bo2$1282bo$
1283bo$1281b3o12$1626bo$1627bo$1625b3o12$1386bobo$1141bo245b2o$1142bo
244bo$1140b3o$1245bo$1246bo$1244b3o8$1743bobo$1744b2o$1744bo2$1599bo$
1600bo$1598b3o12$1364bobo$1217bobo145b2o$1218b2o145bo$1218bo11$1696bob
o$1697b2o$1697bo2$1562bo$1563bo$1561b3o7$1479bobo$1480b2o$1480bo2$
1342bo$1343bo$1341b3o12$1686bo$1687bo$1685b3o12$1446bobo$1201bo245b2o$
1202bo244bo$1200b3o$1305bo$1306bo$1304b3o8$1803bobo$1804b2o$1804bo2$
1659bo$1660bo$1658b3o12$1424bobo$1277bobo145b2o$1278b2o145bo$1278bo11$
1756bobo$1757b2o$1757bo2$1622bo$1623bo$1621b3o7$1539bobo$1540b2o$1540b
o2$1402bo$1403bo$1401b3o8$1885bobo$1886b2o$1886bo2$1746bo$1747bo$1745b
3o12$1506bobo$1261bo245b2o$1262bo244bo$1260b3o$1365bo$1366bo$1364b3o8$
1863bobo$1864b2o$1864bo2$1719bo$1720bo$1718b3o12$1484bobo$1337bobo145b
2o$1338b2o145bo$1338bo11$1816bobo$1817b2o$1817bo2$1682bo$1683bo$1681b
3o7$1599bobo$1600b2o$1600bo2$1462bo$1463bo$1461b3o8$1945bobo$1946b2o$
1946bo2$1806bo$1807bo$1805b3o12$1566bobo$1321bo245b2o$1322bo244bo$
1320b3o$1425bo$1426bo$1424b3o8$1923bobo$1924b2o$1924bo2$1779bo$1780bo$
1778b3o12$1544bobo$1397bobo145b2o$1398b2o145bo$1398bo11$1876bobo$1877b
2o$1877bo2$1742bo$1743bo$1741b3o7$1659bobo$1660b2o$1660bo2$1522bo$
1523bo$1521b3o8$2005bobo$2006b2o$2006bo2$1866bo$1867bo$1865b3o12$1626b
obo$1381bo245b2o$1382bo244bo$1380b3o$1485bo$1486bo$1484b3o8$1983bobo$
1984b2o$1984bo2$1839bo$1840bo$1838b3o5$2114bo$2115bo$2113b3o5$1604bobo
$1457bobo145b2o$1458b2o145bo$1458bo11$1936bobo$1937b2o$1937bo2$1802bo$
1803bo$1801b3o7$1719bobo$1720b2o$1720bo2$1582bo$1583bo$1581b3o8$2065bo
bo$2066b2o$2066bo2$1926bo$1927bo$1925b3o12$1686bobo$1441bo245b2o$1442b
o244bo$1440b3o$1545bo$1546bo$1544b3o8$2043bobo$2044b2o$2044bo2$1899bo$
1900bo$1898b3o5$2174bo$2175bo$2173b3o5$1664bobo$1517bobo145b2o$1518b2o
145bo$1518bo11$1996bobo$1997b2o$1997bo2$1862bo$1863bo$1861b3o7$1779bob
o$1780b2o$1780bo2$1642bo$1643bo$1641b3o8$2125bobo$2126b2o$2126bo2$
1986bo$1987bo$1985b3o12$1746bobo$1501bo245b2o$1502bo244bo$1500b3o$
1605bo$1606bo$1604b3o2$2277bo$2278b2o$2277b2o4$2103bobo$2104b2o$2104bo
2$1959bo$1960bo$1958b3o5$2234bo$2235bo$2233b3o5$1724bobo$1577bobo145b
2o$1578b2o145bo$1578bo11$2056bobo$2057b2o$2057bo2$1922bo$1923bo$1921b
3o7$1839bobo$1840b2o$1840bo2$1702bo$1703bo$1701b3o8$2185bobo$2186b2o$
2186bo2$2046bo$2047bo$2045b3o12$1806bobo$1561bo245b2o$1562bo244bo$
1560b3o$1665bo$1666bo$1664b3o2$2337bo$2338b2o$2337b2o4$2163bobo$2164b
2o$2164bo2$2019bo$2020bo$2018b3o5$2294bo$2295bo$2293b3o5$1784bobo$
1637bobo145b2o$1638b2o145bo$1638bo11$2116bobo$2117b2o$2117bo2$1982bo$
1983bo$1981b3o7$1899bobo$1900b2o$1900bo2$1762bo$1763bo$1761b3o8$2245bo
bo$2246b2o$2246bo2$2106bo$2107bo$2105b3o3$2428bo$2429bo$2427b3o7$1866b
obo$1621bo245b2o$1622bo244bo$1620b3o$1725bo$1726bo$1724b3o2$2397bo$
2398b2o$2397b2o4$2223bobo$2224b2o$2224bo2$2079bo$2080bo$2078b3o5$2354b
o$2355bo$2353b3o5$1844bobo$1697bobo145b2o$1698b2o145bo$1698bo11$2176bo
bo$2177b2o$2177bo2$2042bo$2043bo$2041b3o7$1959bobo$1960b2o$1960bo2$
1822bo$1823bo$1821b3o8$2305bobo$2306b2o$2306bo2$2166bo$2167bo$2165b3o
3$2488bo$2489bo$2487b3o7$1926bobo$1681bo245b2o$1682bo244bo$1680b3o$
1785bo$1786bo$1784b3o2$2457bo$2458b2o$2457b2o4$2283bobo$2284b2o$2284bo
2$2139bo$2140bo$2138b3o5$2414bo$2415bo$2413b3o5$1904bobo$1757bobo145b
2o$1758b2o145bo$1758bo4$2578bo$2579bo$2577b3o5$2236bobo$2237b2o$2237bo
2$2102bo$2103bo$2101b3o7$2019bobo$2020b2o$2020bo2$1882bo$1883bo$1881b
3o8$2365bobo$2366b2o$2366bo2$2226bo$2227bo$2225b3o3$2548bo$2549bo$
2547b3o7$1986bobo$1741bo245b2o$1742bo244bo$1740b3o$1845bo$1846bo$1844b
3o2$2517bo$2518b2o$2517b2o4$2343bobo$2344b2o$2344bo2$2199bo$2200bo$
2198b3o5$2474bo$2475bo$2473b3o5$1964bobo$1817bobo145b2o$1818b2o145bo$
1818bo4$2638bo$2639bo$2637b3o5$2296bobo$2297b2o$2297bo2$2162bo$2163bo$
2161b3o7$2079bobo$2080b2o$2080bo2$1942bo$1943bo$1941b3o8$2425bobo$
2426b2o$2426bo2$2286bo$2287bo$2285b3o3$2608bo$2609bo$2607b3o7$2046bobo
$1801bo245b2o$1802bo244bo$1800b3o$1905bo$1906bo$1904b3o$2728bo$2577bo
151bo$2578b2o147b3o$2577b2o4$2403bobo$2404b2o$2404bo2$2259bo$2260bo$
2258b3o5$2534bo$2535bo$2533b3o5$2024bobo$1877bobo145b2o$1878b2o145bo$
1878bo4$2698bo$2699bo$2697b3o5$2356bobo$2357b2o$2357bo2$2222bo$2223bo$
2221b3o7$2139bobo$2140b2o$2140bo2$2002bo$2003bo$2001b3o8$2485bobo$
2486b2o$2486bo2$2346bo$2347bo$2345b3o3$2668bo$2669bo$2667b3o7$2106bobo
$1861bo245b2o$1862bo244bo$1860b3o$1965bo$1966bo$1964b3o$2788bo$2637bo
151bo$2638b2o147b3o$2637b2o4$2463bobo$2464b2o$2464bo2$2319bo$2320bo$
2318b3o5$2594bo$2595bo$2593b3o5$2084bobo$1937bobo145b2o$1938b2o145bo$
1938bo4$2758bo$2759bo$2757b3o5$2416bobo$2417b2o$2417bo2$2282bo$2283bo$
2281b3o7$2199bobo$2200b2o$2200bo2$2062bo815bo$2063bo815bo$2061b3o813b
3o8$2545bobo$2546b2o$2546bo2$2406bo$2407bo$2405b3o3$2728bo$2729bo$
2727b3o7$2166bobo$1921bo245b2o$1922bo244bo$1920b3o$2025bo$2026bo$2024b
3o$2848bo$2697bo151bo$2698b2o147b3o$2697b2o4$2523bobo$2524b2o$2524bo2$
2379bo$2380bo$2378b3o5$2654bo$2655bo$2653b3o5$2144bobo$1997bobo145b2o$
1998b2o145bo$1998bo4$2818bo$2819bo$2817b3o5$2476bobo$2477b2o$2477bo2$
2342bo$2343bo$2341b3o7$2259bobo$2260b2o$2260bo2$2122bo815bo$2123bo815b
o$2121b3o813b3o8$2605bobo$2606b2o$2606bo2$2466bo$2467bo$2465b3o3$2788b
o$2789bo$2787b3o7$2226bobo$1981bo245b2o$1982bo244bo$1980b3o$2085bo$
2086bo$2084b3o$2908bo$2757bo151bo$2758b2o147b3o$2757b2o4$2583bobo$
2584b2o$2584bo2$2439bo$2440bo$2438b3o5$2714bo$2715bo$2713b3o5$2204bobo
$2057bobo145b2o$2058b2o145bo$2058bo4$2878bo$2879bo$2877b3o5$2536bobo$
2537b2o$2537bo2$2402bo$2403bo$2401b3o7$2319bobo$2320b2o$2320bo2$2182bo
815bo$2183bo815bo$2181b3o813b3o8$2665bobo$2666b2o$2666bo2$2526bo$2527b
o$2525b3o3$2848bo$2849bo$2847b3o7$2286bobo$2041bo245b2o$2042bo244bo$
2040b3o$2145bo$2146bo$2144b3o$2968bo$2817bo151bo$2818b2o147b3o$2817b2o
4$2643bobo$2644b2o$2644bo2$2499bo$2500bo$2498b3o5$2774bo$2775bo$2773b
3o5$2264bobo$2117bobo145b2o$2118b2o145bo$2118bo4$2938bo$2939bo$2937b3o
5$2596bobo$2597b2o$2597bo2$2462bo$2463bo$2461b3o7$2379bobo$2380b2o$
2380bo2$2242bo815bo$2243bo815bo$2241b3o813b3o8$2725bobo$2726b2o$2726bo
2$2586bo$2587bo$2585b3o3$2908bo$2909bo$2907b3o7$2346bobo$2101bo245b2o$
2102bo244bo$2100b3o$2205bo$2206bo$2204b3o$3028bo$2877bo151bo$2878b2o
147b3o$2877b2o4$2703bobo$2704b2o$2704bo2$2559bo$2560bo$2558b3o5$2834bo
$2835bo$2833b3o5$2324bobo$2177bobo145b2o$2178b2o145bo$2178bo4$2998bo$
2999bo$2997b3o5$2656bobo$2657b2o$2657bo2$2522bo$2523bo$2521b3o7$2439bo
bo$2440b2o$2440bo2$2302bo815bo$2303bo815bo$2301b3o813b3o8$2785bobo$
2786b2o$2786bo2$2646bo$2647bo$2645b3o3$2968bo$2969bo$2967b3o7$2406bobo
$2161bo245b2o$2162bo244bo$2160b3o$2265bo$2266bo$2264b3o$3088bo$2937bo
151bo$2938b2o147b3o$2937b2o4$2763bobo$2764b2o$2764bo2$2619bo$2620bo$
2618b3o5$2894bo$2895bo$2893b3o5$2384bobo$2237bobo145b2o$2238b2o145bo$
2238bo4$3058bo$3059bo$3057b3o5$2716bobo$2717b2o$2717bo2$2582bo$2583bo$
2581b3o7$2499bobo$2500b2o$2500bo2$2362bo815bo$2363bo815bo$2361b3o813b
3o8$2845bobo$2846b2o$2846bo2$2706bo$2707bo$2705b3o3$3028bo$3029bo$
3027b3o7$2466bobo$2221bo245b2o$2222bo244bo$2220b3o$2325bo$2326bo$2324b
3o$3148bo$2997bo151bo$2998b2o147b3o$2997b2o4$2823bobo$2824b2o$2824bo2$
2679bo$2680bo$2678b3o5$2954bo$2955bo$2953b3o5$2444bobo$2297bobo145b2o$
2298b2o145bo$2298bo4$3118bo$3119bo$3117b3o5$2776bobo$2777b2o$2777bo2$
2642bo$2643bo$2641b3o7$2559bobo$2560b2o$2560bo2$2422bo815bo$2423bo815b
o$2421b3o813b3o8$2905bobo$2906b2o$2906bo2$2766bo$2767bo$2765b3o3$3088b
o$3089bo$3087b3o7$2526bobo$2281bo245b2o$2282bo244bo$2280b3o$2385bo$
2386bo$2384b3o$3208bo$3057bo151bo$3058b2o147b3o$3057b2o4$2883bobo$
2884b2o$2884bo2$2739bo$2740bo$2738b3o5$3014bo$3015bo$3013b3o5$2504bobo
$2357bobo145b2o$2358b2o145bo$2358bo4$3178bo$3179bo$3177b3o5$2836bobo$
2837b2o$2837bo2$2702bo$2703bo$2701b3o7$2619bobo$2620b2o$2620bo2$2482bo
815bo$2483bo815bo$2481b3o813b3o8$2965bobo$2966b2o$2966bo2$2826bo$2827b
o$2825b3o3$3148bo$3149bo$3147b3o7$2586bobo$2341bo245b2o$2342bo244bo$
2340b3o$2445bo$2446bo$2444b3o$3268bo$3117bo151bo$3118b2o147b3o$3117b2o
4$2943bobo$2944b2o$2944bo2$2799bo$2800bo$2798b3o5$3074bo$3075bo$3073b
3o5$2564bobo$2417bobo145b2o$2418b2o145bo$2418bo4$3238bo$3239bo$3237b3o
5$2896bobo$2897b2o$2897bo2$2762bo$2763bo$2761b3o7$2679bobo$2680b2o$
2680bo2$2542bo815bo$2543bo815bo$2541b3o813b3o8$3025bobo$3026b2o$3026bo
2$2886bo$2887bo$2885b3o3$3208bo$3209bo$3207b3o7$2646bobo$2401bo245b2o$
2402bo244bo$2400b3o$2505bo$2506bo$2504b3o$3328bo$3177bo151bo$3178b2o
147b3o$3177b2o4$3003bobo$3004b2o$3004bo2$2859bo$2860bo$2858b3o5$3134bo
$3135bo$3133b3o5$2624bobo$2477bobo145b2o$2478b2o145bo$2478bo4$3298bo$
3299bo$3297b3o5$2956bobo$2957b2o$2957bo2$2822bo$2823bo$2821b3o7$2739bo
bo$2740b2o$2740bo2$2602bo815bo$2603bo815bo$2601b3o813b3o8$3085bobo$
3086b2o$3086bo2$2946bo$2947bo$2945b3o3$3268bo$3269bo$3267b3o7$2706bobo
$2461bo245b2o$2462bo244bo$2460b3o$2565bo$2566bo$2564b3o$3388bo$3237bo
151bo$3238b2o147b3o$3237b2o4$3063bobo$3064b2o$3064bo2$2919bo$2920bo$
2918b3o5$3194bo$3195bo$3193b3o5$2684bobo$2537bobo145b2o$2538b2o145bo$
2538bo4$3358bo$3359bo$3357b3o5$3016bobo$3017b2o$3017bo2$2882bo$2883bo$
2881b3o7$2799bobo$2800b2o$2800bo2$2662bo815bo$2663bo815bo$2661b3o813b
3o8$3145bobo$3146b2o$3146bo2$3006bo$3007bo$3005b3o3$3328bo$3329bo$
3327b3o7$2766bobo$2521bo245b2o$2522bo244bo$2520b3o$2625bo$2626bo$2624b
3o$3448bo$3297bo151bo$3298b2o147b3o$3297b2o4$3123bobo$3124b2o$3124bo2$
2979bo$2980bo$2978b3o5$3254bo$3255bo$3253b3o5$2744bobo$2597bobo145b2o$
2598b2o145bo$2598bo4$3418bo$3419bo$3417b3o5$3076bobo$3077b2o$3077bo2$
2942bo$2943bo$2941b3o7$2859bobo$2860b2o$2860bo2$2722bo815bo$2723bo815b
o$2721b3o813b3o8$3205bobo$3206b2o$3206bo2$3066bo$3067bo$3065b3o3$3388b
o$3389bo$3387b3o7$2826bobo$2581bo245b2o$2582bo244bo$2580b3o$2685bo$
2686bo$2684b3o$3508bo$3357bo151bo$3358b2o147b3o$3357b2o4$3183bobo$
3184b2o$3184bo2$3039bo$3040bo$3038b3o5$3314bo$3315bo$3313b3o5$2804bobo
$2657bobo145b2o$2658b2o145bo$2658bo4$3478bo$3479bo$3477b3o5$3136bobo$
3137b2o$3137bo2$3002bo$3003bo$3001b3o7$2919bobo$2920b2o$2920bo2$2782bo
815bo$2783bo815bo$2781b3o813b3o8$3265bobo$3266b2o$3266bo2$3126bo$3127b
o$3125b3o3$3448bo$3449bo$3447b3o7$2886bobo$2641bo245b2o$2642bo244bo$
2640b3o$2745bo$2746bo$2744b3o$3568bo$3417bo151bo$3418b2o147b3o$3417b2o
4$3243bobo$3244b2o$3244bo2$3099bo$3100bo$3098b3o5$3374bo$3375bo$3373b
3o5$2864bobo$2717bobo145b2o$2718b2o145bo$2718bo4$3538bo$3539bo$3537b3o
5$3196bobo$3197b2o$3197bo2$3062bo$3063bo$3061b3o7$2979bobo$2980b2o$
2980bo2$2842bo815bo$2843bo815bo$2841b3o813b3o8$3325bobo$3326b2o$3326bo
2$3186bo$3187bo$3185b3o3$3508bo$3509bo$3507b3o7$2946bobo$2701bo245b2o$
2702bo244bo$2700b3o$2805bo$2806bo$2804b3o$3628bo$3477bo151bo$3478b2o
147b3o$3477b2o4$3303bobo$3304b2o$3304bo2$3159bo$3160bo$3158b3o5$3434bo
$3435bo$3433b3o5$2924bobo$2777bobo145b2o$2778b2o145bo$2778bo4$3598bo$
3599bo$3597b3o5$3256bobo$3257b2o$3257bo2$3122bo$3123bo$3121b3o7$3039bo
bo$3040b2o$3040bo2$2902bo815bo$2903bo815bo$2901b3o813b3o8$3385bobo$
3386b2o$3386bo2$3246bo$3247bo$3245b3o3$3568bo$3569bo$3567b3o7$3006bobo
$2761bo245b2o$2762bo244bo$2760b3o$2865bo$2866bo$2864b3o$3688bo$3537bo
151bo$3538b2o147b3o$3537b2o4$3363bobo$3364b2o$3364bo2$3219bo$3220bo$
3218b3o5$3494bo$3495bo$3493b3o5$2984bobo$2837bobo145b2o$2838b2o145bo$
2838bo4$3658bo$3659bo$3657b3o5$3316bobo$3317b2o$3317bo2$3182bo$3183bo$
3181b3o7$3099bobo$3100b2o$3100bo2$2962bo815bo$2963bo815bo$2961b3o813b
3o8$3445bobo$3446b2o$3446bo2$3306bo$3307bo$3305b3o3$3628bo$3629bo$
3627b3o7$3066bobo$2821bo245b2o$2822bo244bo$2820b3o$2925bo$2926bo$2924b
3o$3748bo$3597bo151bo$3598b2o147b3o$3597b2o4$3423bobo$3424b2o$3424bo2$
3279bo$3280bo$3278b3o5$3554bo$3555bo$3553b3o5$3044bobo$2897bobo145b2o$
2898b2o145bo$2898bo4$3718bo$3719bo$3717b3o5$3376bobo$3377b2o$3377bo2$
3242bo$3243bo$3241b3o7$3159bobo$3160b2o$3160bo2$3022bo815bo$3023bo815b
o$3021b3o813b3o8$3505bobo$3506b2o$3506bo2$3366bo$3367bo$3365b3o3$3688b
o$3689bo$3687b3o7$3126bobo$2881bo245b2o$2882bo244bo$2880b3o$2985bo$
2986bo$2984b3o$3808bo$3657bo151bo$3658b2o147b3o$3657b2o4$3483bobo$
3484b2o$3484bo2$3339bo$3340bo$3338b3o5$3614bo$3615bo$3613b3o5$3104bobo
$2957bobo145b2o$2958b2o145bo$2958bo4$3778bo$3779bo$3777b3o5$3436bobo$
3437b2o$3437bo2$3302bo$3303bo$3301b3o7$3219bobo$3220b2o$3220bo2$3082bo
815bo$3083bo815bo$3081b3o813b3o8$3565bobo$3566b2o$3566bo2$3426bo$3427b
o$3425b3o3$3748bo$3749bo$3747b3o7$3186bobo$2941bo245b2o$2942bo244bo$
2940b3o$3045bo$3046bo$3044b3o$3868bo$3717bo151bo$3718b2o147b3o$3717b2o
4$3543bobo$3544b2o$3544bo2$3399bo$3400bo$3398b3o5$3674bo$3675bo$3673b
3o5$3164bobo$3017bobo145b2o$3018b2o145bo$3018bo4$3838bo$3839bo$3837b3o
5$3496bobo$3497b2o$3497bo2$3362bo$3363bo$3361b3o7$3279bobo$3280b2o$
3280bo2$3142bo815bo$3143bo815bo$3141b3o813b3o8$3625bobo$3626b2o$3626bo
2$3486bo$3487bo$3485b3o3$3808bo$3809bo$3807b3o7$3246bobo$3001bo245b2o$
3002bo244bo$3000b3o$3105bo$3106bo$3104b3o$3928bo$3777bo151bo$3778b2o
147b3o$3777b2o4$3603bobo$3604b2o$3604bo2$3459bo$3460bo$3458b3o5$3734bo
$3735bo$3733b3o5$3224bobo$3077bobo145b2o$3078b2o145bo$3078bo4$3898bo$
3899bo$3897b3o5$3556bobo$3557b2o$3557bo2$3422bo$3423bo$3421b3o7$3339bo
bo$3340b2o$3340bo2$3202bo815bo$3203bo815bo$3201b3o813b3o8$3685bobo$
3686b2o$3686bo2$3546bo$3547bo$3545b3o3$3868bo$3869bo$3867b3o7$3306bobo
$3061bo245b2o$3062bo244bo$3060b3o$3165bo$3166bo$3164b3o$3988bo$3837bo
151bo$3838b2o147b3o$3837b2o4$3663bobo$3664b2o$3664bo2$3519bo$3520bo$
3518b3o5$3794bo$3795bo$3793b3o5$3284bobo$3137bobo145b2o$3138b2o145bo$
3138bo4$3958bo$3959bo$3957b3o5$3616bobo$3617b2o$3617bo2$3482bo$3483bo$
3481b3o7$3399bobo$3400b2o$3400bo2$3262bo815bo$3263bo815bo$3261b3o813b
3o8$3745bobo$3746b2o$3746bo2$3606bo$3607bo$3605b3o3$3928bo$3929bo$
3927b3o7$3366bobo$3121bo245b2o$3122bo244bo$3120b3o$3225bo$3226bo$3224b
3o$4048bo$3897bo151bo$3898b2o147b3o$3897b2o4$3723bobo$3724b2o$3724bo2$
3579bo$3580bo$3578b3o5$3854bo$3855bo$3853b3o5$3344bobo$3197bobo145b2o$
3198b2o145bo$3198bo4$4018bo$4019bo$4017b3o5$3676bobo$3677b2o$3677bo2$
3542bo$3543bo$3541b3o7$3459bobo$3460b2o$3460bo2$3322bo815bo$3323bo815b
o$3321b3o813b3o8$3805bobo$3806b2o$3806bo2$3666bo$3667bo$3665b3o3$3988b
o$3989bo$3987b3o7$3426bobo$3181bo245b2o$3182bo244bo$3180b3o$3285bo$
3286bo$3284b3o$4108bo$3957bo151bo$3958b2o147b3o$3957b2o4$3783bobo$
3784b2o$3784bo2$3639bo$3640bo$3638b3o5$3914bo$3915bo$3913b3o5$3404bobo
$3257bobo145b2o$3258b2o145bo$3258bo4$4078bo$4079bo$4077b3o5$3736bobo$
3737b2o$3737bo2$3602bo$3603bo$3601b3o7$3519bobo$3520b2o$3520bo2$3382bo
815bo$3383bo815bo$3381b3o813b3o8$3865bobo$3866b2o$3866bo2$3726bo$3727b
o$3725b3o3$4048bo$4049bo$4047b3o7$3486bobo$3241bo245b2o$3242bo244bo$
3240b3o$3345bo$3346bo$3344b3o$4168bo$4017bo151bo$4018b2o147b3o$4017b2o
4$3843bobo$3844b2o$3844bo2$3699bo$3700bo$3698b3o5$3974bo$3975bo$3973b
3o5$3464bobo$3317bobo145b2o$3318b2o145bo$3318bo4$4138bo$4139bo$4137b3o
5$3796bobo$3797b2o$3797bo2$3662bo$3663bo$3661b3o7$3579bobo$3580b2o$
3580bo2$3442bo815bo$3443bo815bo$3441b3o813b3o8$3925bobo$3926b2o$3926bo
2$3786bo$3787bo$3785b3o3$4108bo$4109bo$4107b3o7$3546bobo$3301bo245b2o$
3302bo244bo$3300b3o$3405bo$3406bo$3404b3o$4228bo$4077bo151bo$4078b2o
147b3o$4077b2o4$3903bobo$3904b2o$3904bo2$3759bo$3760bo$3758b3o5$4034bo
$4035bo$4033b3o5$3524bobo$3377bobo145b2o$3378b2o145bo$3378bo4$4198bo$
4199bo$4197b3o5$3856bobo$3857b2o$3857bo2$3722bo$3723bo$3721b3o7$3639bo
bo$3640b2o$3640bo2$3502bo815bo$3503bo815bo$3501b3o813b3o8$3985bobo$
3986b2o$3986bo2$3846bo$3847bo$3845b3o3$4168bo$4169bo$4167b3o7$3606bobo
$3361bo245b2o$3362bo244bo$3360b3o$3465bo$3466bo$3464b3o$4288bo$4137bo
151bo$4138b2o147b3o$4137b2o4$3963bobo$3964b2o$3964bo2$3819bo$3820bo$
3818b3o5$4094bo$4095bo$4093b3o5$3584bobo$3437bobo145b2o$3438b2o145bo$
3438bo4$4258bo$4259bo$4257b3o5$3916bobo$3917b2o$3917bo2$3782bo$3783bo$
3781b3o7$3699bobo$3700b2o$3700bo2$3562bo815bo$3563bo815bo$3561b3o813b
3o8$4045bobo$4046b2o$4046bo2$3906bo$3907bo$3905b3o3$4228bo$4229bo$
4227b3o7$3666bobo$3421bo245b2o$3422bo244bo$3420b3o$3525bo$3526bo$3524b
3o$4348bo$4197bo151bo$4198b2o147b3o$4197b2o4$4023bobo$4024b2o$4024bo2$
3879bo$3880bo$3878b3o5$4154bo$4155bo$4153b3o5$3644bobo$3497bobo145b2o$
3498b2o145bo$3498bo4$4318bo$4319bo$4317b3o5$3976bobo$3977b2o$3977bo2$
3842bo$3843bo$3841b3o7$3759bobo$3760b2o$3760bo2$3622bo815bo$3623bo815b
o$3621b3o813b3o8$4105bobo$4106b2o$4106bo2$3966bo$3967bo$3965b3o3$4288b
o$4289bo$4287b3o7$3726bobo$3481bo245b2o$3482bo244bo$3480b3o$3585bo$
3586bo$3584b3o$4408bo$4257bo151bo$4258b2o147b3o$4257b2o4$4083bobo$
4084b2o$4084bo2$3939bo$3940bo$3938b3o5$4214bo$4215bo$4213b3o5$3704bobo
$3557bobo145b2o$3558b2o145bo$3558bo4$4378bo$4379bo$4377b3o5$4036bobo$
4037b2o$4037bo2$3902bo$3903bo$3901b3o7$3819bobo$3820b2o$3820bo2$3682bo
815bo$3683bo815bo$3681b3o813b3o8$4165bobo$4166b2o$4166bo2$4026bo$4027b
o$4025b3o3$4348bo$4349bo$4347b3o7$3786bobo$3541bo245b2o$3542bo244bo$
3540b3o$3645bo$3646bo$3644b3o$4468bo$4317bo151bo$4318b2o147b3o$4317b2o
4$4143bobo$4144b2o$4144bo2$3999bo$4000bo$3998b3o5$4274bo$4275bo$4273b
3o5$3764bobo$3617bobo145b2o$3618b2o145bo$3618bo4$4438bo$4439bo$4437b3o
5$4096bobo$4097b2o$4097bo2$3962bo$3963bo$3961b3o7$3879bobo$3880b2o$
3880bo2$3742bo815bo$3743bo815bo$3741b3o813b3o8$4225bobo$4226b2o$4226bo
2$4086bo$4087bo$4085b3o3$4408bo$4409bo$4407b3o7$3846bobo$3601bo245b2o$
3602bo244bo$3600b3o$3705bo$3706bo$3704b3o$4528bo$4377bo151bo$4378b2o
147b3o$4377b2o4$4203bobo$4204b2o$4204bo2$4059bo$4060bo$4058b3o5$4334bo
$4335bo$4333b3o5$3824bobo$3677bobo145b2o$3678b2o145bo$3678bo4$4498bo$
4499bo$4497b3o5$4156bobo$4157b2o$4157bo2$4022bo$4023bo$4021b3o7$3939bo
bo$3940b2o$3940bo2$3802bo815bo$3803bo815bo$3801b3o813b3o8$4285bobo$
4286b2o$4286bo2$4146bo$4147bo$4145b3o3$4468bo$4469bo$4467b3o7$3906bobo
$3661bo245b2o$3662bo244bo$3660b3o$3765bo$3766bo$3764b3o$4588bo$4437bo
151bo$4438b2o147b3o$4437b2o4$4263bobo$4264b2o$4264bo2$4119bo$4120bo$
4118b3o5$4394bo$4395bo$4393b3o5$3884bobo$3737bobo145b2o$3738b2o145bo$
3738bo4$4558bo$4559bo$4557b3o5$4216bobo$4217b2o$4217bo2$4082bo$4083bo$
4081b3o7$3999bobo$4000b2o$4000bo2$3862bo815bo$3863bo815bo$3861b3o813b
3o8$4345bobo$4346b2o$4346bo2$4206bo$4207bo$4205b3o3$4528bo$4529bo$
4527b3o7$3966bobo$3721bo245b2o$3722bo244bo$3720b3o$3825bo$3826bo$3824b
3o$4648bo$4497bo151bo$4498b2o147b3o$4497b2o4$4323bobo$4324b2o$4324bo2$
4179bo$4180bo$4178b3o5$4454bo$4455bo$4453b3o5$3944bobo$3797bobo145b2o$
3798b2o145bo$3798bo4$4618bo$4619bo$4617b3o5$4276bobo$4277b2o$4277bo2$
4142bo$4143bo$4141b3o7$4059bobo$4060b2o$4060bo2$3922bo815bo$3923bo815b
o$3921b3o813b3o8$4405bobo$4406b2o$4406bo2$4266bo$4267bo$4265b3o3$4588b
o$4589bo$4587b3o7$4026bobo$3781bo245b2o$3782bo244bo$3780b3o$3885bo$
3886bo$3884b3o$4708bo$4557bo151bo$4558b2o147b3o$4557b2o4$4383bobo$
4384b2o$4384bo2$4239bo$4240bo$4238b3o5$4514bo$4515bo$4513b3o5$4004bobo
$3857bobo145b2o$3858b2o145bo$3858bo4$4678bo$4679bo$4677b3o5$4336bobo$
4337b2o$4337bo2$4202bo$4203bo$4201b3o7$4119bobo$4120b2o$4120bo2$3982bo
815bo$3983bo815bo$3981b3o813b3o8$4465bobo$4466b2o$4466bo2$4326bo$4327b
o$4325b3o3$4648bo$4649bo$4647b3o7$4086bobo$3841bo245b2o$3842bo244bo$
3840b3o$3945bo$3946bo$3944b3o$4768bo$4617bo151bo$4618b2o147b3o$4617b2o
4$4443bobo$4444b2o$4444bo2$4299bo$4300bo$4298b3o5$4574bo$4575bo$4573b
3o5$4064bobo$3917bobo145b2o$3918b2o145bo$3918bo4$4738bo$4739bo$4737b3o
5$4396bobo$4397b2o$4397bo2$4262bo$4263bo$4261b3o7$4179bobo$4180b2o$
4180bo2$4042bo815bo$4043bo815bo$4041b3o813b3o8$4525bobo$4526b2o$4526bo
2$4386bo$4387bo$4385b3o3$4708bo$4709bo$4707b3o7$4146bobo$3901bo245b2o$
3902bo244bo$3900b3o$4005bo$4006bo$4004b3o$4828bo$4677bo151bo$4678b2o
147b3o$4677b2o4$4503bobo$4504b2o$4504bo2$4359bo$4360bo$4358b3o5$4634bo
$4635bo$4633b3o5$4124bobo$3977bobo145b2o$3978b2o145bo$3978bo4$4798bo$
4799bo$4797b3o5$4456bobo$4457b2o$4457bo2$4322bo$4323bo$4321b3o7$4239bo
bo$4240b2o$4240bo2$4102bo815bo$4103bo815bo$4101b3o813b3o8$4585bobo$
4586b2o$4586bo2$4446bo$4447bo$4445b3o3$4768bo$4769bo$4767b3o7$4206bobo
$3961bo245b2o$3962bo244bo$3960b3o$4065bo$4066bo$4064b3o$4888bo$4737bo
151bo$4738b2o147b3o$4737b2o4$4563bobo$4564b2o$4564bo2$4419bo$4420bo$
4418b3o5$4694bo$4695bo$4693b3o5$4184bobo$4037bobo145b2o$4038b2o145bo$
4038bo4$4858bo$4859bo$4857b3o5$4516bobo$4517b2o$4517bo2$4382bo$4383bo$
4381b3o7$4299bobo$4300b2o$4300bo2$4162bo815bo$4163bo815bo$4161b3o813b
3o8$4645bobo$4646b2o$4646bo2$4506bo$4507bo$4505b3o3$4828bo$4829bo$
4827b3o7$4266bobo$4021bo245b2o$4022bo244bo$4020b3o$4125bo$4126bo$4124b
3o$4948bo$4797bo151bo$4798b2o147b3o$4797b2o4$4623bobo$4624b2o$4624bo2$
4479bo$4480bo$4478b3o5$4754bo$4755bo$4753b3o5$4244bobo$4097bobo145b2o$
4098b2o145bo$4098bo4$4918bo$4919bo$4917b3o5$4576bobo$4577b2o$4577bo2$
4442bo$4443bo$4441b3o7$4359bobo$4360b2o$4360bo2$4222bo815bo$4223bo815b
o$4221b3o813b3o8$4705bobo$4706b2o$4706bo2$4566bo$4567bo$4565b3o3$4888b
o$4889bo$4887b3o7$4326bobo$4081bo245b2o$4082bo244bo$4080b3o$4185bo$
4186bo$4184b3o$5008bo$4857bo151bo$4858b2o147b3o$4857b2o4$4683bobo$
4684b2o$4684bo2$4539bo$4540bo$4538b3o5$4814bo$4815bo$4813b3o5$4304bobo
$4157bobo145b2o$4158b2o145bo$4158bo4$4978bo$4979bo$4977b3o5$4636bobo$
4637b2o$4637bo2$4502bo$4503bo$4501b3o7$4419bobo$4420b2o$4420bo2$4282bo
815bo$4283bo815bo$4281b3o813b3o8$4765bobo$4766b2o$4766bo2$4626bo$4627b
o$4625b3o3$4948bo$4949bo$4947b3o7$4386bobo$4141bo245b2o$4142bo244bo$
4140b3o$4245bo$4246bo$4244b3o$5068bo$4917bo151bo$4918b2o147b3o$4917b2o
4$4743bobo$4744b2o$4744bo2$4599bo$4600bo$4598b3o5$4874bo$4875bo$4873b
3o5$4364bobo$4217bobo145b2o$4218b2o145bo$4218bo4$5038bo$5039bo$5037b3o
5$4696bobo$4697b2o$4697bo2$4562bo$4563bo$4561b3o7$4479bobo$4480b2o$
4480bo2$4342bo815bo$4343bo815bo$4341b3o813b3o8$4825bobo$4826b2o$4826bo
2$4686bo$4687bo$4685b3o3$5008bo$5009bo$5007b3o7$4446bobo$4447b2o$4447b
o2$4305bo$4306bo$4304b3o$5128bo$4977bo151bo$4978b2o147b3o$4977b2o4$
4803bobo$4804b2o$4804bo2$4659bo$4660bo$4658b3o5$4934bo$4935bo$4933b3o
5$4424bobo$4277bobo145b2o$4278b2o145bo$4278bo4$5098bo$5099bo$5097b3o5$
4756bobo$4757b2o$4757bo2$4622bo$4623bo$4621b3o7$4539bobo$4540b2o$4540b
o2$4402bo815bo$4403bo815bo$4401b3o813b3o8$4885bobo$4886b2o$4886bo2$
4746bo$4747bo$4745b3o3$5068bo$5069bo$5067b3o7$4506bobo$4507b2o$4507bo
2$4365bo$4366bo$4364b3o$5188bo$5037bo151bo$5038b2o147b3o$5037b2o4$
4863bobo$4864b2o$4864bo2$4719bo$4720bo$4718b3o5$4994bo$4995bo$4993b3o
5$4484bobo$4485b2o$4485bo5$5158bo$5159bo$5157b3o5$4816bobo$4817b2o$
4817bo2$4682bo$4683bo$4681b3o7$4599bobo$4600b2o$4600bo2$4462bo815bo$
4463bo815bo$4461b3o813b3o8$4945bobo$4946b2o$4946bo2$4806bo$4807bo$
4805b3o3$5128bo$5129bo$5127b3o7$4566bobo$4567b2o$4567bo2$4425bo$4426bo
$4424b3o$5248bo$5097bo151bo$5098b2o147b3o$5097b2o4$4923bobo$4924b2o$
4924bo2$4779bo$4780bo$4778b3o5$5054bo$5055bo$5053b3o5$4544bobo$4545b2o
$4545bo5$5218bo$5219bo$5217b3o5$4876bobo$4877b2o$4877bo2$4742bo$4743bo
$4741b3o7$4659bobo$4660b2o$4660bo2$4522bo815bo$4523bo815bo$4521b3o813b
3o8$5005bobo$5006b2o$5006bo2$4866bo$4867bo$4865b3o3$5188bo$5189bo$
5187b3o7$4626bobo$4627b2o$4627bo5$5308bo$5157bo151bo$5158b2o147b3o$
5157b2o4$4983bobo$4984b2o$4984bo2$4839bo$4840bo$4838b3o5$5114bo$5115bo
$5113b3o5$4604bobo$4605b2o$4605bo5$5278bo$5279bo$5277b3o5$4936bobo$
4937b2o$4937bo2$4802bo$4803bo$4801b3o7$4719bobo$4720b2o$4720bo2$4582bo
815bo$4583bo815bo$4581b3o813b3o8$5065bobo$5066b2o$5066bo2$4926bo$4927b
o$4925b3o3$5248bo$5249bo$5247b3o7$4686bobo$4687b2o$4687bo5$5368bo$
5217bo151bo$5218b2o147b3o$5217b2o4$5043bobo$5044b2o$5044bo2$4899bo$
4900bo$4898b3o5$5174bo$5175bo$5173b3o5$4664bobo$4665b2o$4665bo5$5338bo
$5339bo$5337b3o5$4996bobo$4997b2o$4997bo2$4862bo$4863bo$4861b3o7$4779b
obo$4780b2o$4780bo2$5458bo$5459bo$5457b3o8$5125bobo$5126b2o$5126bo2$
4986bo$4987bo$4985b3o3$5308bo$5309bo$5307b3o7$4746bobo$4747b2o$4747bo
5$5428bo$5277bo151bo$5278b2o147b3o$5277b2o4$5103bobo$5104b2o$5104bo2$
4959bo$4960bo$4958b3o5$5234bo$5235bo$5233b3o5$4724bobo$4725b2o$4725bo
5$5398bo$5399bo$5397b3o5$5056bobo$5057b2o$5057bo2$4922bo$4923bo$4921b
3o7$4839bobo$4840b2o$4840bo2$5518bo$5519bo$5517b3o8$5185bobo$5186b2o$
5186bo2$5046bo$5047bo$5045b3o3$5368bo$5369bo$5367b3o7$4806bobo$4807b2o
$4807bo5$5488bo$5337bo151bo$5338b2o147b3o$5337b2o4$5163bobo$5164b2o$
5164bo2$5019bo$5020bo$5018b3o5$5294bo$5295bo$5293b3o12$5458bo$5459bo$
5457b3o5$5116bobo$5117b2o$5117bo2$4982bo$4983bo$4981b3o7$4899bobo$
4900b2o$4900bo2$5578bo$5579bo$5577b3o8$5245bobo$5246b2o$5246bo2$5106bo
$5107bo$5105b3o3$5428bo$5429bo$5427b3o7$4866bobo$4867b2o$4867bo5$5548b
o$5397bo151bo$5398b2o147b3o$5397b2o4$5223bobo$5224b2o$5224bo2$5079bo$
5080bo$5078b3o5$5354bo$5355bo$5353b3o12$5518bo$5519bo$5517b3o$7037b2o$
7037b2o3$5176bobo$5177b2o$5177bo2$5042bo$5043bo$5041b3o7$4959bobo$
4960b2o$4960bo2$5638bo$5639bo$5637b3o8$5305bobo1729b2o$5306b2o1729b2o$
5306bo2$5166bo$5167bo$5165b3o3$5488bo$5489bo$5487b3o14$5608bo$5457bo
151bo$5458b2o147b3o$5457b2o3$7037b2o$5283bobo1751b2o$5284b2o$5284bo2$
5139bo$5140bo$5138b3o5$5414bo$5415bo$5413b3o12$5578bo$5579bo$5577b3o3$
7037b2o$7037b2o$5236bobo$5237b2o$5237bo2$5102bo$5103bo$5101b3o7$5019bo
bo$5020b2o$5020bo2$5698bo$5699bo$5697b3o8$5365bobo$5366b2o$5366bo1670b
2o$7037b2o$5226bo$5227bo$5225b3o3$5548bo$5549bo$5547b3o14$5668bo$5517b
o151bo$5518b2o147b3o$5517b2o4$5343bobo$5344b2o1691b2o$5344bo1692b2o2$
5199bo$5200bo$5198b3o5$5474bo$5475bo$5473b3o12$5638bo$5639bo$5637b3o5$
5296bobo1738b2o$5297b2o1738b2o$5297bo2$5162bo$5163bo$5161b3o11$5758bo$
5759bo$5757b3o8$5425bobo$5426b2o$5426bo2$5286bo1750b2o$5287bo1749b2o$
5285b3o3$5608bo$5609bo$5607b3o14$5728bo$5577bo151bo$5578b2o147b3o$
5577b2o4$5403bobo$5404b2o$5404bo$7037b2o$5259bo1777b2o$5260bo$5258b3o
5$5534bo$5535bo$5533b3o12$5698bo$5699bo$5697b3o5$5356bobo$5357b2o$
5357bo1679b2o$7037b2o$5222bo$5223bo$5221b3o11$5818bo$5819bo$5817b3o8$
5485bobo$5486b2o$5486bo2$5346bo$5347bo$5345b3o1689b2o$7037b2o2$5668bo$
5669bo$5667b3o14$5788bo$5637bo151bo$5638b2o147b3o$5637b2o4$5463bobo$
5464b2o$5464bo2$5319bo$5320bo1716b2o$5318b3o1716b2o5$5594bo$5595bo$
5593b3o12$5758bo$5759bo$5757b3o5$5416bobo$5417b2o$5417bo2$5282bo1754b
2o$5283bo1753b2o$5281b3o11$5878bo$5879bo$5877b3o8$5545bobo$5546b2o$
5546bo2$5406bo$5407bo$5405b3o2$7037b2o$5728bo1308b2o$5729bo$5727b3o14$
5848bo$5697bo151bo$5698b2o147b3o$5697b2o4$5523bobo$5524b2o$5524bo2$
5379bo$5380bo$5378b3o$7037b2o$7037b2o3$5654bo$5655bo$5653b3o12$5818bo$
5819bo$5817b3o5$5476bobo$5477b2o$5477bo4$7037b2o$7037b2o10$5938bo$
5939bo$5937b3o8$5605bobo$5606b2o$5606bo2$5466bo$5467bo$5465b3o3$5788bo
$5789bo1247b2o$5787b3o1247b2o14$5908bo$5757bo151bo$5758b2o147b3o$5757b
2o4$5583bobo$5584b2o$5584bo2$5439bo$5440bo$5438b3o3$7037b2o$7037b2o$
5714bo$5715bo$5713b3o12$5878bo$5879bo$5877b3o5$5536bobo$5537b2o$5537bo
6$7037b2o$7037b2o8$5998bo$5999bo$5997b3o8$5665bobo$5666b2o$5666bo2$
5526bo$5527bo$5525b3o3$5848bo$5849bo$5847b3o$7037b2o$7037b2o12$5968bo$
5817bo151bo$5818b2o147b3o$5817b2o4$5643bobo$5644b2o$5644bo9$5774bo
1262b2o$5775bo1261b2o$5773b3o12$5938bo$5939bo$5937b3o5$5596bobo$5597b
2o$5597bo8$7037b2o$7037b2o6$6058bo$6059bo$6057b3o8$5725bobo$5726b2o$
5726bo2$5586bo$5587bo$5585b3o3$5908bo$5909bo$5907b3o3$7037b2o$7037b2o
10$6028bo$5877bo151bo$5878b2o147b3o$5877b2o4$5703bobo$5704b2o$5704bo9$
5834bo$5835bo$5833b3o1201b2o$7037b2o11$5998bo$5999bo$5997b3o5$5656bobo
$5657b2o$5657bo10$7037b2o$7037b2o4$6118bo$6119bo$6117b3o8$5785bobo$
5786b2o$5786bo7$5968bo$5969bo$5967b3o5$7037b2o$7037b2o8$6088bo$5937bo
151bo$5938b2o147b3o$5937b2o4$5763bobo$5764b2o$5764bo9$5894bo$5895bo$
5893b3o2$7037b2o$7037b2o9$6058bo$6059bo$6057b3o5$5716bobo$5717b2o$
5717bo12$7037b2o$7037b2o2$6178bo$6179bo$6177b3o8$5845bobo$5846b2o$
5846bo7$6028bo$6029bo$6027b3o7$7037b2o$7037b2o6$6148bo$5997bo151bo$
5998b2o147b3o$5997b2o4$5823bobo$5824b2o$5824bo9$5954bo$5955bo$5953b3o
4$7037b2o$7037b2o7$6118bo$6119bo$6117b3o21$7037b2o$6238bo798b2o$6239bo
$6237b3o8$5905bobo$5906b2o$5906bo7$6088bo$6089bo$6087b3o9$7037b2o$
7037b2o4$6208bo$6057bo151bo$6058b2o147b3o$6057b2o4$5883bobo$5884b2o$
5884bo9$6014bo$6015bo$6013b3o6$7037b2o$7037b2o5$6178bo$6179bo$6177b3o
22$6298bo$6299bo737b2o$6297b3o737b2o8$5965bobo$5966b2o$5966bo7$6148bo$
6149bo$6147b3o11$7037b2o$7037b2o2$6268bo$6117bo151bo$6118b2o147b3o$
6117b2o15$6074bo$6075bo$6073b3o8$7037b2o$7037b2o3$6238bo$6239bo$6237b
3o22$6358bo$6359bo$6357b3o$7037b2o$7037b2o6$6025bobo$6026b2o$6026bo7$
6208bo$6209bo$6207b3o13$7037b2o$6328bo708b2o$6177bo151bo$6178b2o147b3o
$6177b2o15$6134bo$6135bo$6133b3o10$7037b2o$7037b2o$6298bo$6299bo$6297b
3o22$6418bo$6419bo$6417b3o3$7037b2o$7037b2o13$6268bo$6269bo$6267b3o14$
6388bo$6237bo151bo647b2o$6238b2o147b3o647b2o$6237b2o15$6194bo$6195bo$
6193b3o12$6358bo678b2o$6359bo677b2o$6357b3o22$6478bo$6479bo$6477b3o5$
7037b2o$7037b2o11$6328bo$6329bo$6327b3o14$6448bo$6297bo151bo$6298b2o
147b3o$6297b2o738b2o$7037b2o14$6254bo$6255bo$6253b3o12$6418bo$6419bo$
6417b3o617b2o$7037b2o21$6538bo$6539bo$6537b3o7$7037b2o$7037b2o9$6388bo
$6389bo$6387b3o14$6508bo$6357bo151bo$6358b2o147b3o$6357b2o2$7037b2o$
7037b2o26$6478bo$6479bo$6477b3o2$7037b2o$7037b2o19$6598bo$6599bo$6597b
3o9$7037b2o$7037b2o7$6448bo$6449bo$6447b3o14$6568bo$6417bo151bo$6418b
2o147b3o$6417b2o4$7037b2o$7037b2o24$6538bo$6539bo$6537b3o4$7037b2o$
7037b2o17$6658bo$6659bo$6657b3o11$7037b2o$7037b2o5$6508bo$6509bo$6507b
3o14$6628bo$6629bo$6627b3o7$7037b2o$7037b2o22$6598bo$6599bo$6597b3o6$
7037b2o$7037b2o15$6718bo$6719bo$6717b3o13$7037b2o$7037b2o3$6568bo$
6569bo$6567b3o14$6688bo$6689bo$6687b3o9$7037b2o$7037b2o20$6658bo$6659b
o$6657b3o8$7037b2o$7037b2o13$6778bo$6779bo$6777b3o15$7037b2o$7037b2o
17$6748bo$6749bo$6747b3o11$7037b2o$7037b2o18$6718bo$6719bo$6717b3o10$
7037b2o$7037b2o11$6838bo$6839bo$6837b3o17$7037b2o$7037b2o15$6808bo$
6809bo$6807b3o13$7037b2o$7037b2o30$7037b2o$7037b2o9$6898bo$6899bo$
6897b3o19$7037b2o$7037b2o13$6868bo$6869bo$6867b3o15$7037b2o$7037b2o30$
7037b2o$7037b2o7$6958bo$6959bo$6957b3o21$7037b2o$7037b2o30$7037b2o$
7037b2o30$7037b2o$7037b2o5$7018bo$7019bo$7017b3o23$7037b2o$7037b2o!

This isn't anywhere near minimal, just the most obvious thing that I could string together from existing pieces. It's also not optimized for 31c/240, so it would be equally useful for the Caterpillar's-little-brother project.

I guess it works as an extreme upper bound for the HWSS problem, anyway. Hopefully cheaper recipes will still show up somewhere in the search space; we could use a few more alternatives. I checked this reaction against the original Caterpillar, and there seems to be one HWSS in the helix that it can't build.

Posted: **July 3rd, 2014, 4:55 pm**

dvgrn wrote:With a more expensive way of building the blocks, it's easy to string together a workable 18-glider HWSS seed recipe.

Looks like the lack of a decent HWSS recipe has stalled progress on the 31c/240 ship for the last couple of weeks. Think I should just go ahead and build an HWSS rake with the horribly inefficient 18-glider recipe (which didn't come from the search program, so it will end up having a ridiculously high cost in rephasers)?

-- Or is there another search still in the works that might turn up a more reasonable HWSS seed or two? I suggested cutting the bounding box to maybe 15x15, both to find smaller seeds and to reach out into the COST=15..20 space that hasn't been searched much yet (I don't think). But the Half-Baked Knightship project has been distracting me, so I haven't gotten desperate enough yet to download the latest sscs and try it myself...!

Another question while I'm at it: what exactly does sscs do with patterns that never settle? A new discussion has brought up the question of when the first switch engine makes an appearance in the slow-salvo search tree? Presumably this would be an unweighted search starting from just a blonk (block or blinker), with a bounding box probably at least big enough to hold a pi explosion.

Technically it wouldn't matter much if the intermediate reactions emitted gliders, as long as the output gliders didn't get in the way of input gliders -- but that starts to get more complicated to code, unless you just ignore output gliders and check recipes for consistency later. Just the simplest possible search would probably give useful results. I'm betting there's a switch engine within six slow gliders of a blonk -- but now I'm wondering if I'm being too conservative and I should bet on a five-glider recipe instead...!

ConwayLife.com

Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program

Re: Prototype / demo for a (weighted) collision search program