Thread for basic questions

[calcyman]

Basically, I guess you can say that it’s really almost impossible to prove that there is no glider synthesis for something, and the easiest way to prove that there is is to show a synthesis for the object.

Yes, it's a Pi^0_1 statement: does there exist a finite glider synthesis and a finite time t such that, after t ticks, those gliders evolve into a copy of Sir Robin? There isn't a good reason to suppose these sorts of questions are algorithmically answerable (indeed, a general Pi^0_1 statement is undecidable).

I lack any intuition whatsoever about whether Sir Robin can be synthesised.

[dvgrn]

Is Sir Robin synthesisable? Is there a way to disprove glider syntheses besides checking GoE?

Dvgrn probably has a better answer that’s also conveniently divided up into sections.

I don't know about "better", and I'm even going to try to avoid "longer", because I don't really know what I"m talking about. Maybe my usual five paragraphs would be a good limit... except I'll cheat with a multi-section attempt at answering a somewhat related question.

I think Sir Robin probably has a glider synthesis Somewhere Out There, but that's definitely just my opinion. The hardest thing to construct tends to be "space dust" that's inaccessible because it's surrounded by lots of other space dust. Sir Robin has some of that, for sure, but luckily it's fairly long and thin, so it has a reasonable amount of surface area.

(Actually luck has nothing to do with it: a shorter rounder cousin of Sir Robin is also probably Somewhere Out There, but we can't find it yet because we haven't figured out how to manage the ridiculously huge search space that medium-sized blob-shaped spaceships sit in.)

I was thinking something along the lines of 'there would need to be too many gliders in one place at the final step, and no ash could last that long.'

Yeah, there's definitely an information-flow component to this kind of problem, isn't there? There's only room to crash a certain maximum number of gliders together in a given region of spacetime. On the other hand, it often seems to be possible to work around that limitation to a very large extent, by building what are essentially complex fuses that carry information in toward the center of a construction, faster than a glider can travel.

Possibly we could someday crunch the numbers enough to say "IF there are more than {pick a very large number} 25x25 SuperBlobShips, then some of them must not have glider syntheses, because there aren't enough distinct useful glider syntheses to go around". That wouldn't help in figuring out which ones are constructible and which aren't, though. And with all the possible pre-built fuse and still-life and oscillator trickery out there, I think the limit number would have to be really uselessly large anyway.

[Moosey]

Is Sir Robin synthesisable? Is there a way to disprove glider syntheses besides checking GoE?

Dvgrn probably has a better answer that’s also conveniently divided up into sections.

I don't know about "better", and I'm even going to try to avoid "longer", because I don't really know what I"m talking about. Maybe my usual five paragraphs would be a good limit... except I'll cheat with a multi-section attempt at answering a somewhat related question.

I think Sir Robin probably has a glider synthesis Somewhere Out There, but that's definitely just my opinion. The hardest thing to construct tends to be "space dust" that's inaccessible because it's surrounded by lots of other space dust. Sir Robin has some of that, for sure, but luckily it's fairly long and thin, so it has a reasonable amount of surface area.

(Actually luck has nothing to do with it: a shorter rounder cousin of Sir Robin is also probably Somewhere Out There, but we can't find it yet because we haven't figured out how to manage the ridiculously huge search space that medium-sized blob-shaped spaceships sit in.)
...

Kind of unrelated, except for the last paragraph I quoted, but:
Can anyone search for smaller knightships based on similar partials?
On the bright side, because we are looking for smaller spaceships, we can have an upper limit to how big we want the target ship to be before we can terminate the search.

[toroidalet]

I noticed that engineered spaceships tend to have lots of empty space, so could engineered and elementary spaceships be differentiated based on some density-based metric?

I don't really know what the point of this is, seeming as it's pretty easy to tell what's engineered and what's elementary with your eyes.

[Moosey]

Why is long boat more common than barge? Especially considering barge is more common than long ship?

[dvgrn]

Why is long boat more common than barge? Especially considering barge is more common than long ship?

Just the luck of the draw as to which of them has more "bottleneck" predecessors -- low population active reactions, reachable via some fairly common collision.

The first two long-boat soups on Catagolue both have the following predecessor, though they get there in different ways. So that might (or might not) be the configuration that happens to be more common than any barge predecessor:

Code: Select all

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

[77topaz]

It's also worth remembering that boats are more common than tubs. So, if there's some reaction that could extend boats to longboats and tubs to barges (and I'm pretty sure such reactions exist), we'd expect that to result in more longboats than barges. Of course, longboats and barges also have predecessors not involving their smaller counterparts, whose relative frequencies are harder to predict.

[Moosey]

How does one notate HROT rules in lifeviewer?

[muzik]

viewtopic.php?f=3&t=1622&p=67121#p67121 .

[rowett]

viewtopic.php?f=3&t=1622&p=67121#p67121 .

And also this post where the neighbourhood support was added.

[Moosey]

What is this strict still life called?

Code: Select all

#C the first RLE I typed by hand
2o$obo$2b3o$bo3bo$b2ob2o

[Ian07]

What is this strict still life called?

Code: Select all

#C the first RLE I typed by hand
2o$obo$2b3o$bo3bo$b2ob2o

That would be a house siamese shillelagh.

[Moosey]

While looking through the caterloopillar thread, I found myself wondering, “Shouldn’t it be possible to build a spaceship that shoots XWSS groups up, then uses them to shoot gliders, then reflects the gliders down and produces more of the same XWSSes, while moving the whole thing?
Here’s a sketch I made in golly:

Code: Select all

x = 15, y = 37, rule = LifeHistory
10.2C$9.4C$8.6C$7.8C$10.2C$10.2C$10.2C$10.2C$10.2C$10.2C$10.2C$10.2C$
10.2C$10.2C$.E8.2C$.D8.2C$.DA7.2C$.D.D$.D2.D$.D3.D$.D4.D$.D5.D$.DA5.D
$.D.D5.D$.DA.D5.DB$.D.D.D4.DB$.DA.D.D3.DB$.D.D.D.D2.DB$.D2.D.D.D.DB$.
D3.D.D.2DB$.D4.D.D.DB$.D5.D.2DB$.D6.D.DB$.D7.2DB$.D8.DB$2A8D2A$2A8.2A
!
#C [[ VIEWONLY ]]

Red lines represent spaceships, green dots represent data that can be moved and used to nondestructively produce gliders. The yellow thing on top is a sort of “cap”. The blue line is a thing that “pulls” gliders down to the reflecting things below. (My drawing is of course not a working concept, you’d need a lot more code.)

Perhaps it would be easier to do away with the “cap” and just make a forerake.
I suppose that this is basically a 1-“engine” caterloopillar.
Anyways, I’ll leave the macrospaceship engineering to the experts.

[dvgrn]

While looking through the caterloopillar thread, I found myself wondering, “Shouldn’t it be possible to build a spaceship that shoots XWSS groups up, then uses them to shoot gliders, then reflects the gliders down and produces more of the same XWSSes, while moving the whole thing?
...
I suppose that this is basically a 1-“engine” caterloopillar.
Anyways, I’ll leave the macrospaceship engineering to the experts.

"The experts" (which is really just simsim314 at the moment, for caterloopillars) seem to think that the best generalizable caterloopillar design they can think of looks pretty much like a caterloopillar.

Your diagram has four "magical" points -- the yellow dot, the two larger green squares, and the blue line -- where the green squares and blue line are doing some kind of mysterious reflection operation, and the yellow end cap is more of an eater. If they were just reflecting and eating then it would be relatively easy to make some circuitry with the functionality that's wanted in those places, but they actually also have to move by the right distance while they're doing it.

That seriously limits what you can put in those four places, especially if you want the whole mechanism to be adjustable in any way. The caterloopillar design has four magical points -- front cap, back cap, and the lines of loaves on each side for information storage -- so this new design doesn't really seem to be an improvement.

If you rearrange those four magical pieces and their inputs and outputs, so that they can all be replaced with mechanisms that we actually know how to build, you might end up with an interesting variant of chris_c's recent camelship -- or possibly something more like the Golly-friendly quadratic replicator that I hope to get around to putting together later this year.

[Moosey]

While looking through the caterloopillar thread, I found myself wondering, “Shouldn’t it be possible to build a spaceship that shoots XWSS groups up, then uses them to shoot gliders, then reflects the gliders down and produces more of the same XWSSes, while moving the whole thing?
...
I suppose that this is basically a 1-“engine” caterloopillar.
Anyways, I’ll leave the macrospaceship engineering to the experts.

"The experts" (which is really just simsim314 at the moment, for caterloopillars) seem to think that the best generalizable caterloopillar design they can think of looks pretty much like a caterloopillar.

...

Would it perhaps be possible to make a gun based on this design, sort of like Abhpzta's rake gun in pedestrian life?

This would of course be a zillion times easier.

(Of course, our data couldn't move)

Or we could just build an "engineless" rake gun, which is precisely what that post contained anyways.

EDIT:
related:
viewtopic.php?f=12&t=3813#p70858

[dvgrn]

Would it perhaps be possible to make a gun based on this design, sort of like Abhpzta's rake gun in pedestrian life?

This would of course be a zillion times easier.

(Of course, our data couldn't move)

Sure... though again it might be more "vaguely like this design" than "based on this design", since the design is kind of unclear.

It's not impossible in principle to put together some kind of caterloopillar-like oscillator, but there are some pretty big changes that would have to be made. Caterloopillars rely on slow salvos, and slow salvos only work because each data point in the line of loaf data is gradually moving past a long line of construction sites. If the whole thing is standing still, it's not clear how a bunch of parallel gliders are really going to build anything useful.

So you could actually build a moving caterloopillar-puffer quite a bit more easily, by extending the trailing side of a working caterloopillar and adding more loaves. There's a little problem involving the question of where the initial target comes from, so actually I think both sides have to be extended, and then instead of the target getting cleaned up by the reverse-side slow salvo, it would leave behind whatever you wanted to build -- which might be a seed for a spaceship, with some mechanism to trigger it at the last minute to get a rake.

Another part of your idea -- a string of reusable stationary data markers encoding a slow salvo -- was implemented many years ago in calcyman's Osqrtlogt pattern -- see Golly's Help > Online Archives > Very Large Patterns. There are a couple of columns of honeybits and intermittent eaters, which encode the slow salvos that maintain the triangular 2D grid of boats that do the binary-counting trick.

[Moosey]

Are there any variants of Riley's Breeder that create glider producing switch engines?

[dvgrn]

Are there any variants of Riley's Breeder that create glider producing switch engines?

Define "variant". It's easy to make a GPSE breeder out of high-period rakes, or (I think -- haven't looked up the necessary rake period to know for sure) modify Mitchell Riley's breeder with high-period rakes to convert some of the block-laying switch engines to the glider-producing variety:

Code: Select all

x = 49, y = 52, rule = B3/S23
2$20b2o$20b2o$33b2o$33b2o3$37b2o$37b2o$12b2o5b3ob2o$12b2o8b3o$20b2o2$
25b2o13b2o$25b2o13b2o7$32b2o$13bo18b2o$22b3o$8bob2o10bobo$8bobo6bo2b2o
2bo$7bo4b2o3bo2b3o$8bo8bo2b3o$8bo7bo2$12bo10$38bo$37b2o$37bobo!

But it would be a major modification, especially since there isn't room for GPSEs to fit next to each other as closely as the BLSEs do. It's probably fairly tricky, but may be possible, to come up with a GPSE breeder with the same population as Riley's BLSE breeder -- just the luck of the draw whether a peturbation is available somewhere in that search space.

[77topaz]

Are there any variants of Riley's Breeder that create glider producing switch engines?

Mosquito 3 produces glider-producing switch engines.

[Hunting]

With a 4-barreled gun, how can I make a gun that is 1-barreled? Still no eaters.

[dvgrn]

With a 4-barreled gun, how can I make a gun that is 1-barreled? Still no eaters.

Use reflectors to crash three of the gliders together? Otherwise it seems like you're out of luck; multiple copies of the gun will mostly just make the problem worse, right?

[Moosey]

How are soups scored in apgsearch?

[Ian07]

How are soups scored in apgsearch?

The scoring system isn't actually used anymore, but the Python script used it to determine which soups were the most "interesting." Every sufficiently rare object is given a point value which is added on to the soup's overall score if it appears. For example, a soup producing both a pulsar and an MWSS would have a score of 17, as determined by this list:

Code: Select all

# A dict of objects in the form {"identifier": ("common name", points)}
#
# As a rough heuristic, an object is worth 15 + log2(n) points if it
# is n times rarer than the pentadecathlon.
#
# Still-lifes are limited to 10 points.
# p2 oscillators are limited to 20 points.
# p3 and p4 oscillators are limited to 30 points.
self.commonnames = {"xp3_co9nas0san9oczgoldlo0oldlogz1047210127401": ("pulsar", 8),
                "xp15_4r4z4r4": ("pentadecathlon", 15),
                "xp2_2a54": ("clock", 16),
                "xp2_31ago": ("bipole", 17),
                "xp2_0g0k053z32": ("quadpole", 18),
                "xp2_g8gid1e8z1226": ("great on-off", 19),
                "xp2_rhewehr": ("spark coil", 19),
                "xp8_gk2gb3z11": ("figure-8", 20),
                "xp4_37bkic": ("mold", 21),
                "xp2_31a08zy0123cko": ("quadpole on ship", 20),
                "xp2_g0k053z11": ("tripole", 20),
                "xp4_ssj3744zw3": ("mazing", 23),
                "xp8_g3jgz1ut": ("blocker", 24),
                "xp3_695qc8zx33": ("jam", 24),
                "xp30_w33z8kqrqk8zzzw33": ("cis-queen-bee-shuttle", 24),
                "xp30_w33z8kqrqk8zzzx33": ("trans-queen-bee-shuttle", 24),
                "xp4_8eh5e0e5he8z178a707a871": ("cloverleaf", 25),
                "xp5_idiidiz01w1": ("octagon II", 26),
                "xp6_ccb7w66z066": ("unix", 26),
                "xp14_j9d0d9j": ("tumbler", 27),
                "xp3_025qzrq221": ("trans-tub-eater", 28),
                "xp3_4hh186z07": ("caterer", 29),
                "xp3_025qz32qq1": ("cis-tub-eater", 30),
                "xp8_wgovnz234z33": ("Tim Coe's p8", 31),
                "xp5_3pmwmp3zx11": ("fumarole", 33),
                "xp46_330279cx1aad3y833zx4e93x855bc": ("cis-twin-bees-shuttle", 35),
                "xp46_330279cx1aad3zx4e93x855bcy8cc": ("trans-twin-bees-shuttle", 35),
                "yl144_1_16_afb5f3db909e60548f086e22ee3353ac": ("block-laying switch engine", 16),
                "yl384_1_59_7aeb1999980c43b4945fb7fcdb023326": ("glider-producing switch engine", 17),
                "xp10_9hr": ("[HighLife] p10", 6),
                "xp7_13090c8": ("[HighLife] p7", 9),
                "xq48_07z8ca7zy1e531": ("[HighLife] bomber", 9),
                "xq4_153": ("glider", 0),
                "xq4_6frc": ("lightweight spaceship", 7),
                "xq4_27dee6": ("middleweight spaceship", 9),
                "xq4_27deee6": ("heavyweight spaceship", 12),
                "xq7_3nw17862z6952": ("loafer", 70),
                "xp2_7": ("blinker", 0),
                "xs4_33": ("block", 0),
                "xs4_252": ("tub", 0),
                "xs5_253": ("boat", 0),
                "xs6_bd": ("snake", 0),
                "xs6_356": ("ship", 0),
                "xs6_696": ("beehive", 0),
                "xs6_25a4": ("barge", 0),
                "xs6_39c": ("carrier", 0),
                "xp2_7e": ("toad", 0),
                "xp2_318c": ("beacon", 0),
                "xs7_3lo": ("long snake", 0),
                "xs7_25ac": ("long boat", 0),
                "xs7_178c": ("eater", 0),
                "xs7_2596": ("loaf", 0),
                "xs8_178k8": ("twit", 0),
                "xs8_32qk": ("hook with tail", 0),
                "xs8_69ic": ("mango", 0),
                "xs8_6996": ("pond", 0),
                "xs8_25ak8": ("long barge", 0),
                "xs8_3pm": ("shillelagh", 0),
                "xs8_312ko": ("canoe", 0),
                "xs8_31248c": ("very long snake", 0),
                "xs8_35ac": ("long ship", 0),
                "xs12_g8o653z11": ("ship-tie", 0),
                "xs14_g88m952z121": ("half-bakery", 0),
                "xs14_69bqic": ("paperclip", 0),
                "xs9_31ego": ("integral sign", 0),
                "xs10_g8o652z01": ("boat-tie", 0),
                "xs14_g88b96z123": ("big ess", 0),
                "xs16_g88m996z1221": ("bipond", 0),
                "xs12_raar": ("table on table", 0),
                "xs9_4aar": ("hat", 0),
                "xs10_35ako": ("very long ship", 0),
                "xs9_178ko": ("trans boat with tail", 0),
                "xs15_354cgc453": ("moose antlers", 0),
                "xs14_6970796": ("cis-mirrored r-bee", 0),
                "xs10_32qr": ("block on table", 0),
                "xs16_j1u0696z11": ("beehive on dock", 0),
                "xs14_j1u066z11": ("block on dock", 0),
                "xs11_g8o652z11": ("boat tie ship", 0),
                "xs9_25ako": ("very long boat", 0),
                "xs16_69egmiczx1": ("scorpion", 0),
                "xs18_rhe0ehr": ("dead spark coil", 0),
                "xs17_2ege1ege2": ("twinhat", 0),
                "xs10_178kk8": ("beehive with tail", 0),
                "xs10_69ar": ("loop", 0),
                "xs14_69bo8a6": ("fourteener", 0),
                "xs14_39e0e93": ("bookends", 0),
                "xs9_178kc": ("cis boat with tail", 0),
                "xs12_330f96": ("block and cap", 0),
                "xs10_358gkc": ("10.003",0),
                "xs12_330fho": ("trans block and longhook", 0),
                "xs10_g0s252z11": ("prodigal sign", 0),
                "xs11_g0s453z11": ("elevener", 0),
                "xs14_6is079c": ("cis-rotated hook", 0),
                "xs14_69e0eic": ("trans-mirrored R-bee", 0),
                "xs11_ggm952z1": ("trans loaf with tail", 0),
                "xs15_j1u06a4z11": ("cis boat and dock", 0),
                "xs20_3lkkl3z32w23": ("mirrored dock", 0),
                "xs12_178br": ("12.003",0),
                "xs12_3hu066": ("cis block and longhook", 0),
                "xs12_178c453": ("eater with nine", 0),
                "xs10_0drz32": ("broken snake", 0),
                "xs9_312453": ("long shillelagh", 0),
                "xs10_3215ac": ("boat with long tail", 0),
                "xs14_39e0e96": ("cis-hook and R-bee", 0),
                "xs13_g88m96z121": ("beehive at loaf", 0),
                "xs14_39e0eic": ("trans hook and R-bee", 0),
                "xs10_3542ac": ("S-ten", 0),
                "xs15_259e0eic": ("trans R-bee and R-loaf", 0),
                "xs11_178jd": ("11-loop", 0),
                "xs9_25a84c": ("tub with long tail", 0),
                "xs15_3lkm96z01": ("bee-hat", 0),
                "xs14_g8o0e96z121": ("cis-rotated R-bee", 0),
                "xs13_69e0mq": ("R-bee and snake", 0),
                "xs11_69lic": ("11.003", 0),
                "xs12_6960ui": ("beehive and table", 0),
                "xs16_259e0e952": ("cis-mirrored R-loaf", 0),
                "xs10_1784ko": ("8-snake-eater", 0),
                "xs13_4a960ui": ("ortho loaf and table", 0),
                "xs9_g0g853z11": ("long canoe", 0),
                "xs18_69is0si96": ("[cis-mirrored R-mango]", 0),
                "xs11_178kic": ("cis loaf with tail", 0),
                "xs16_69bob96": ("symmetric scorpion", 0),
                "xs13_0g8o653z121": ("longboat on ship", 0),
                "xs12_o4q552z01": ("beehive at beehive", 0),
                "xs10_ggka52z1": ("trans barge with tail", 0),
                "xs12_256o8a6": ("eater on boat", 0),
                "xs14_6960uic": ("beehive with cap", 0),
                "xs12_2egm93": ("snorkel loop", 0),
                "xs12_2egm96": ("beehive bend tail", 0),
                "xs11_g0s253z11": ("trans boat with nine", 0),
                "xs15_3lk453z121": ("trans boat and dock", 0),
                "xs19_69icw8ozxdd11": ("[mango with block on dock]", 0),
                "xs13_2530f96": ("[cis boat and cap]", 0),
                "xs11_2530f9": ("cis boat and table", 0),
                "xs14_4a9m88gzx121": ("[bi-loaf2]", 0),
                "xs11_ggka53z1": ("trans longboat with tail", 0),
                "xs18_2egm9a4zx346": ("[loaf eater tail]", 0),
                "xs15_4a9raic": ("[15-bent-paperclip]", 0),
                "xs11_3586246": ("[11-snake]",0),
                "xs11_178b52": ("[11-boat wrap tail]", 0),
                "xs14_08u1e8z321": ("[hat join hook]", 0),
                "xs14_g4s079cz11": ("[cis-mirrored offset hooks]", 0),
                "xs13_31egma4": ("[13-boat wrap eater]", 0),
                "xs14_69960ui": ("pond and table", 0),
                "xs13_255q8a6": ("[eater tie beehive]", 0),
                "xs15_09v0ccz321": ("[hook join table and block]",0)}

Objects not in the list are scored as follows:

• Still-lifes are worth 1 point for every living cell, up to a maximum of 20 points.
• p2 oscillators are worth 20 points.
• p3 and p4 oscillators are worth 30 points.
• p5+ oscillators are worth 40 points.
• Spaceships are worth 50 points.
• Linear growth patterns are worth 60 points.

[dani]

Does this pattern ever reach a population of 16 again after generation 55?

Code: Select all

x = 6, y = 1, rule = B2ac/S
2o2b2o!

[Ian07]

Does this pattern ever reach a population of 16 again after generation 55?

Code: Select all

x = 6, y = 1, rule = B2ac/S
2o2b2o!

Its population plot seems to consistently grow linearly, so no.

Code: Select all

x = 552, y = 536, rule = B3/S23
261b3o2bo6b3o2b4o2b4o3b3o3b3o2b4o2b4o$260bo3bobo7bo3bo3bobo3bobo3bobo
3bobo3bobo3bo$260bo5bo7bo3bo3bobo3bobo3bobo3bobo3bobo3bo$260bo5bo7bo3b
4o2b4o2bo3bob5ob4o2bo3bo$260bo5bo7bo3bo5bo3bobo3bobo3bobo2bo2bo3bo$
260bo3bobo7bo3bo5bo3bobo3bobo3bobo3bobo3bo$261b3o2b5o2b3o2bo5b4o3b3o2b
o3bobo3bob4o8$bo4b3o2b5o2b3o3b3o$2o3bo3bo5bobo3bobo3bo$bo3bo2b2o4bo6bo
bo3bo$bo3bobobo3bo6bo3b3o10bo495bo$bo3b2o2bo2bo6bo3bo3bo9bo495bo$bo3bo
3bobo6bo4bo3bo9bo495bo$3o3b3o2bo5b5o2b3o10bo495bo$37bo495bo$37bo495bo$
37bo495bo2bo$37bo495bo2bo$37bo495bo2bo$37bo495bo2bo$37bo495b2obo$37bo
495b2obo$37bo495b2obo$37bo495b2obo$37bo495b2obo$37bo495b2obo$37bo495b
2obo$37bo489bo5b2obo$37bo489bo3bob2obo$37bo489bo3bob2obo$37bo489bo3bob
4o$37bo489bo3bob4o$37bo489bo3bob4o$37bo489bo3bob4o$37bo489bo3bob4o$37b
o489bo3bob4o$37bo489bo3b6o$37bo489b2o2b6o$37bo486bo2b3ob6o$37bo486bo2b
3ob6o$37bo473bo7bo4bo2b10o$37bo473bo7b2o3bo2b10o$37bo473bo6b3o3bo2b10o
$37bo473bo6b3o3bo2b10o$37bo463bo9bo4b5o3bob11o$37bo463bo8b2ob2ob5o3bob
11o$37bo463bo8b2ob2ob5obobob11o$37bo463bo8b2ob2ob5ob3ob11o$37bo463bo8b
2ob2ob5ob3ob11o$37bo463bo8b2ob2ob5ob15o$37bo463bo8b2ob2ob21o$37bo463bo
8b2ob2ob21o$37bo463bo8b2ob2ob21o$37bo463bo4bo3b2ob2ob21o$37bo457bo5bob
o2b2o2b2ob2ob21o$37bo457bo5bobo2b2o2b2ob2ob21o$37bo457bo5bobo2b2o2b5ob
21o$37bo456b2o5bobo2b2o2b27o$37bo456b2o5bobo2b2o2b27o$37bo456b2o2bob2o
bo2b2o2b27o$37bo456b2o2bob2obo2b31o$37bo456b2ob2ob2obo2b31o$37bo456b2o
b2ob2obo2b31o$37bo456b2ob2ob2obo2b31o$37bo456b2ob2ob2obob32o$37bo456b
2ob2ob4ob32o$37bo456b2ob2ob37o$37bo456b2ob2ob37o$37bo456b2ob2ob37o$37b
o452bo3b2ob2ob37o$37bo452bo2b3ob2ob37o$37bo452bo2b3ob2ob37o$37bo444bo
7bo2b6ob37o$37bo444bo7b2ob6ob37o$37bo444bo4bo2b2ob6ob37o$37bo433bo10bo
4bo2b2ob6ob37o$37bo433bo10bo4bo2b2ob6ob37o$37bo433bo10bo4bo2b2ob6ob37o
$37bo433bo10bo3b2o2b9ob37o$37bo433bo10bo3b2o2b47o$37bo433bo7bo2bo3b2o
2b47o$37bo431bobo7bo2bo3b2o2b47o$37bo431bobo6b2o2b2ob3o2b47o$37bo431bo
bo4bob2o2b2ob3o2b47o$37bo431bobo4bob2o2b6ob48o$37bo431bobo4bob2o2b55o$
37bo431bobo4bob2o2b55o$37bo431bobo4bob2o2b55o$37bo431bobo4bob2o2b55o$
37bo428bo2bobo4bob2o2b55o$37bo428bo2b3o4b4o2b55o$37bo428bo2b3o4b4o2b
55o$37bo428bo2b3o4b5ob55o$37bo424bo3bob4o4b61o$37bo424bo3bob4o4b61o$
37bo424b2o2bob4o4b61o$37bo424b2o2bob4o4b61o$37bo411bo5bo6b2o2bob4o2bob
61o$37bo411bo5bo6b2ob2ob5obob61o$37bo411bo5bo6b2ob2ob69o$37bo411bo5bo
6b5ob69o$37bo411bo5bo6b5ob69o$37bo411bo5bo6b5ob69o$37bo411bo5bo6b75o$
37bo411bo5bobo4b75o$37bo411bo5bobo3b76o$37bo408bo2bo5bobo3b76o$37bo
400bo7bo2b2o4bobo3b76o$37bo400bo7bo2b2obo2bobo3b76o$37bo400bo5bobo2b2o
bo2bobob78o$37bo400bo2bo2bob2ob2obo2bobob78o$37bo400bo2bo2bob2ob4o2b3o
b78o$37bo400bo2bo2bob2ob4ob83o$37bo400bo2bob2ob2ob4ob83o$37bo400bo2bob
2ob2ob4ob83o$37bo400bo2bob10ob83o$37bo400bo2bob10ob83o$37bo400bo2b96o$
37bo400bo2b96o$37bo400bo2b96o$37bo384bo10bo4bo2b96o$37bo384bo10bo4bo2b
96o$37bo384bo2bo7bo4bo2b96o$37bo384bo2bo7bo4bo2b96o$37bo384bo2bo7bo3b
2ob97o$37bo384bo2bo7bobob2ob97o$37bo384bo2bo7bobob100o$37bo384bo2bo7bo
bob100o$37bo382bobo2bo7bob102o$37bo382bobo2bo3bo3bob102o$37bo382bobo2b
o3bo2b2ob102o$37bo382bobo2bo3b108o$37bo382bobo2bo3b108o$37bo382bobo2bo
2b109o$37bo382bobo2bo2b109o$37bo382bobo2bo2b109o$37bo382bobo2bo2b109o$
37bo379bob2obo2bo2b109o$37bo365bo13bob2obo2bo2b109o$37bo365bo12b2ob2ob
o2bo2b109o$37bo365bo12b2ob4o2bo2b109o$37bo365b2o9b9o2bo2b109o$37bo365b
2o9b10obo2b109o$37bo365b2o9b10obo2b109o$37bo365b2o9b10obob110o$37bo
365b2o9b123o$37bo365b2o9b123o$37bo365b2o8b124o$37bo365b2o3b2o2b125o$
37bo360bo4b2o3b2o2b125o$37bo360bo4b2o3b129o$37bo355bo4bo4b2o3b129o$37b
o355bo4bo4b2o3b129o$37bo355bo4bo4b2o3b129o$37bo355bo4bo4b2o2b130o$37bo
355bo4bo4b3ob130o$37bo355bo4bo4b3ob130o$37bo355bo4bo4b134o$37bo355bo2b
obobo2b134o$37bo355bo2bobobo2b134o$37bo355bo2bobob137o$37bo355bo2bobob
137o$37bo343bo2bo8bob2obob137o$37bo343bo2bo8bob2obob137o$37bo343bo2bob
o6b6ob137o$37bo343bo2bobo4bob6ob137o$37bo343bo2bobo4bob144o$37bo343bo
2bobo4bob144o$37bo343bo2bobo3b2ob144o$37bo343bo2bobo3b147o$37bo343bo2b
obo3b147o$37bo343bo2b4o2b147o$37bo343b2ob4ob148o$37bo341bob2ob4ob148o$
37bo341bob7ob148o$37bo341bob156o$37bo322bo7bo10bob156o$37bo322bo7bo10b
ob156o$37bo322bo7bo10bob156o$37bo322bo7bo2bo7bob156o$37bo322bo7bo2bo7b
ob156o$37bo322bo7bo2bo7bob156o$37bo322bo4bo2bo2bo3bo3bob156o$37bo322bo
bo2bo2b2obo3bobobob156o$37bo322bobo2bo2b2obo3bobobob156o$37bo309bo12bo
bo2bo2b2obo3bobobob156o$37bo309bo12bobo2b5obo3bobobob156o$37bo309bo12b
obo2b5obo3bobob158o$37bo309bo8bo3bobo2b5obo2b2obob158o$37bo309bo8bo3bo
bo2b5obo2b2obob158o$37bo309bo4bo3bo3bobo2b5ob2ob2obob158o$37bo309bo4bo
3bo3bobo2b5ob5ob160o$37bo309bo4bo3bo3bob2ob5ob5ob160o$37bo309bo4bo3bo
3bob2ob11ob160o$37bo309bo4bo3bo3bob2ob172o$37bo309bo4bo3bo3bob2ob172o$
37bo309bo4bo3bo3bob2ob172o$37bo309bo4bo3bo3bob2ob172o$37bo309bo4bo3bo
3bob2ob173o$37bo309bo4bo3bo3bob2ob173o$37bo309bo4bo3bo3bob176o$37bo
309b2o3b2o2b3obob176o$37bo309b2o3b3ob3obob176o$37bo309b2o3b3ob3obob
176o$37bo309b2o3b3ob5ob176o$37bo309b2o3b3ob5ob176o$37bo309b2o2b4ob182o
$37bo307bob2o2b4ob182o$37bo306b2ob2o2b4ob182o$37bo303bo2b5o2b187o$37bo
302b2o2b5o2b187o$37bo302b2o2b5o2b187o$37bo302b2o2b194o$37bo302b3ob194o
$37bo302b3ob194o$37bo302b3ob194o$37bo298bo2b4ob194o$37bo298bo2b4ob194o
$37bo294bo2b2o2b4ob194o$37bo292bobo2b2ob5ob194o$37bo292bobo2b2ob5ob
194o$37bo292bobo2b2ob200o$37bo292bobo2b2ob200o$37bo292bob2ob2ob200o$
37bo292bob2ob2ob200o$37bo289b7ob203o$37bo284bo3b8ob203o$37bo284bo3b8ob
203o$37bo284bo2b9ob203o$37bo284bo2b9ob203o$37bo284bo2b9ob203o$20b7o10b
o268bo15bo2b9ob203o$23bo13bo268bo15bo2b9ob203o$22bo14bo268bo10bo2bobo
2b9ob203o$21bo15bo268bo10bo2bobo2b9ob203o$20b7o10bo268bo5bo4bo2bob2ob
213o$37bo268bo5bo4bob2ob2ob213o$21b5o11bo262bo5bo5bo4bob2ob2ob213o$20b
o5bo10bo262bo5bo5bo2b3ob2ob2ob213o$20bo5bo10bo262bo5bo3bobo2b3ob5ob
212o$20bo5bo10bo262bo5bo3bobo2b3ob218o$21b5o11bo262bo5bo3bobo2b3ob218o
$37bo262bo3bobo3bobo2b3ob218o$37bo262bo3bobo3bobo2b3ob218o$20bo5bo10bo
262bo3bobo3bobob4ob218o$20b7o10bo262bo3bobo3bob225o$20bo5bo10bo262bo3b
obobob227o$37bo262bo3bobob229o$37bo262b2o2bobob229o$20bo16bo255bo6b2ob
2obob229o$20bo16bo255bo6b2ob4ob229o$20b7o10bo255bo4bob2ob4ob229o$20bo
16bo255b2o3bob2ob234o$20bo16bo255b2o3bob2ob234o$37bo255b3o2bob2ob234o$
21b6o10bo255b3o2bob2ob234o$20bo2bo13bo255b3o2bob2ob234o$20bo2bo13bo
247bo7b3o2bob2ob234o$20bo2bo13bo247bo7b3o2bob2ob234o$21b6o10bo247bo4bo
2b3o2bob2ob234o$37bo247bo4bo2b3ob2ob237o$26bo10bo246b3o3bo2b6ob237o$
26bo10bo246b3o3bo2b6ob237o$26bo10bo246b3o2b2o2b6ob237o$26bo10bo238bo7b
3o2b2o2b6ob237o$20b7o10bo238b2o6b3ob3ob245o$37bo238b2o6b3ob3ob245o$20b
6o11bo238b2o6b3ob3ob245o$26bo10bo238b2o6b3ob3ob245o$26bo10bo238b2o4bob
3ob249o$26bo10bo238b2o4bob253o$20b6o11bo232bo5b2o4bob253o$37bo232bo5b
2o4bob253o$21b2o14bo232bo5b3o2b256o$20bo2bo13bo232bo5b3o2b256o$20bo2bo
13bo229bo2bo5b3o2b256o$20bo2bo13bo229bo2bo3bob3o2b256o$20b7o10bo225bo
3bo2bo3bob3o2b256o$37bo225bo3bo2b2ob2ob261o$21b5o11bo225bo3bo2b2ob2ob
261o$20bo5bo10bo225bo3bo2b2ob2ob261o$20bo5bo10bo221bo3bo3bo2b2ob260ob
3o$20bo5bo10bo221bo3bo3bo2b2ob260ob3o$21b5o11bo221bo3bo3bo2b2ob260ob3o
$37bo221b2o2bo3bob3ob254ob5ob3o$21b2o14bo221b2o2bo3b5ob254ob5ob3o$20bo
2bo13bo221b2o2bo3b252ob7obob3obo$20bo2bo13bo221b2o2bo3b252ob6o2bob3obo
$20bo2bo13bo221b2o2bo3b252ob6o2bob2o2bo$20b7o10bo221b2o2bo3b247ob4ob6o
$37bo221b3obo3b247ob4ob6o$37bo221b3obobob247ob2obob2ob3o$37bo206bo14b
3ob3ob247ob2obob2o2bo$37bo206bo14b3ob3ob245obob2obobo$37bo206bo14b3ob
3ob245obob2obobo$37bo206bo13b4ob3ob236ob8obo2bobo$37bo206bo4bo8b4ob3ob
236ob7o2bo2bo$37bo206bo4bo7b5ob240ob7o2bo$37bo206bo4bo4b2ob244o3b3o2bo
$37bo206bo4b2o3b241ob5o3b3o2bo$37bo206bo4b4ob241o2bob2o$37bo205b2o4b4o
b241o2bob2o$37bo205b2o4b4ob241o2bob2o$37bo205b2ob2ob4ob236ob2obo2bo$
37bo205b2ob2ob240o2b2obo2bo$37bo201bo2b3ob2ob240o2bo2bo$37bo201bo2b3ob
2ob237obo3bo2bo$37bo201bo2b3ob2ob237o$37bo198bo2bo2b3ob2ob234o2bo$37bo
198bo2bo2b3ob2ob232obo2bo$37bo198bob2ob7ob228o2b2o4bo$37bo198bob2ob7ob
213ob5ob7o3b2o$37bo198bob2ob221ob5ob3ob3o3b2o$37bo197b2ob224ob2ob2ob3o
bobo3b2o$37bo192bo4b227ob2ob2obobobobo$37bo192bo4b227ob2ob2o3bobobo$
37bo192bo4b227ob2ob2o5bobo$37bo192bo4b226o2b2obo8bo$37bo192bo4b226o5bo
$37bo192bob222ob6o$37bo190bobob222obo2b3o$37bo190bobob217ob4obo2bobo$
37bo189b2obob214ob2o2b3obo2bo$37bo189b2obob209ob4ob2o3bo2bo2bo$37bo
184bo4b214ob4obo7bo$37bo184bob2ob214ob4o9bo$37bo174bo9bob2ob214ob2obo$
37bo174bo6bo2bob2ob208ob4o2b2obo$37bo174bo6b2obob211ob4o2bo2bo$37bo
174bobo4b2obob210o5bo2bo2bo$37bo174bobo4b2obob206ob3o8bo2bo$37bo174bob
2o3b211obobo11bo$37bo174bob2o3b203ob5o3bobo$37bo173b2ob2o3b203ob5o3bo$
37bo170b2ob2ob3ob204ob4o$37bo170b2ob2ob205ob2ob4o$37bo170b5ob203obob2o
b4o$37bo167bo2b5ob199obobobo2bob4o$37bo167bo2b5ob199obobobo2bo2bobo$
37bo167bo2b5ob192ob6obo3bo2bo2bo$37bo167bo2b5ob189o2bob6o5bo5bo$37bo
164bo2b2ob195o2bob2ob3o11bo$37bo163b2o2b2ob195o2bo2bobobo$37bo163b2o2b
2ob195o5bobobo$37bo163b2o2b2ob195o7bobo$37bo157bo5b2o2b2ob190ob3o8bobo
$37bo157bo5b3ob191obob2o$37bo157bo5b3ob191obo2bo$37bo157bo2bob192ob3ob
o$37bo157bob2ob184ob7ob3obo$37bo157bob2ob184ob7ob3o$37bo153bo3bob2ob
182obob4ob2obo$37bo153bo3bob2ob182obob3o2b2obo$37bo153bo3bob2ob182obob
3o2bo2bo$37bo153bobobob2ob179obo2bo2b2o5bo$37bo153bobobob2ob179obo2bo
9bo$37bo153bob3ob2ob179obo2bo9bo$37bo151b3ob6ob179obo$37bo151b3ob6ob
177obo$37bo148bo2b3ob6ob165ob9obo$37bo148bo2b10ob165o2b8o$37bo144bo3bo
b177o2b2obobo$37bo133bo10bo3b174ob4o2b2o$37bo133bo7bo2bo2b175ob4o2bo$
37bo133bo2bo4bo2b2ob175obobo$37bo133bo2bo4bo2b2ob169o3b3o3bo$37bo133bo
2bo4b2ob2ob169o3b3o3bo$37bo133bo2bo4b2ob2ob165ob3o4b2o$37bo133bo2bo4b
2ob2ob165o3bo4b2o$37bo133bo2bo4b2ob2ob165o9bo$37bo133bo2bo3b3ob2ob160o
b4o$37bo133bo2bo3b3ob158o2b2o2b4o$37bo133bo2bob162obo2bo3b4o$37bo133bo
2bob162obo2bo5b2o$37bo133bo2bob161o2bo2bo5b2o$37bo132b2o2bob157obobo2b
o2bo5bo$37bo132b2ob2ob151ob5obo4bo$37bo132b2ob2ob151ob2o2bo6bo$37bo
131b3ob2ob151ob2o2bo6bo$37bo128bob4ob2ob146ob4ob2o2bo6bo$37bo125bo2bob
4ob2ob146ob2obo2bo$37bo125bob7ob146ob2o2bo4bo$37bo125bob7ob143ob2obo$
37bo123bobob7ob141obob2o$37bo120bo2b3ob7ob141obob2o$37bo117bo2bo2b3ob
7ob136ob4obob2o$37bo114bo2bo2bo2b3ob144ob4obob2o$37bo114bo2bo2bob4ob
141ob2ob4o3b2o$37bo114bo2bo2bob4ob138ob2ob2o2bo$37bo114bo2bo2bob4ob
138ob2ob2o2bo$37bo114bo2bo2bob4ob136obob2obo$37bo114bo2b2ob6ob136obobo
2bo$37bo114bo2b2ob6ob135o4bo2bo$37bo111bo2bo2b138ob4obo4bo2bo$37bo111b
o2b141ob4o$37bo111bob142ob4o$37bo109bobob140obob4o$37bo109bobob130ob5o
bobo3b3o$37bo101bo7bobob130ob5obo6bo$37bo101bo5b3ob132ob2ob2o8bo$37bo
101bo3bob3ob132ob2ob2o$37bo101bo3bob3ob125obo2b2o5b2o$37bo101bobob5ob
125obo3bo6bo$37bo101bobob5ob125obo$37bo99bobobob5ob125obo$37bo99bobobo
b5ob118ob2obobobo$37bo98b4obob5ob118ob2o$37bo98b6ob5ob118o2bo$37bo98b
129obo$37bo93bo4b124o2b3obo$37bo93bo4b119o2bobo2b2o$37bo90bo2bo4b119o
2bobo2b2o$37bo87bo2bo2b4ob118o5bo3bo$37bo87b2obo2b4ob118o5bo$37bo87b2o
bo2b120o2bo$37bo87b2obo2b113ob5o3bo$37bo87b2obo2b113obob3o$37bo87b2ob
2ob113obob3o$37bo87b2ob2ob110ob2obobobo$37bo85bob2ob113ob2obo$37bo85bo
b2ob110ob2obo2bo$37bo82bob2ob2ob110obo2bo2bo$37bo82bob2ob112o2bo$37bo
82bob105ob2obobo$37bo82bob105ob2obobo$37bo82bob100ob4o2bobobo$37bo69bo
6bo2bo2bob100ob4o6bo$37bo69bo6bo2bo2bob100ob2obo$37bo69bo6bo2bo2b102o
2bobo$37bo69bo6bo2bob100ob2o2bo$37bo69bo6bo2bob99o2b2o2bo$37bo69bo6bob
2ob90obob4o8bo$37bo69bobo4bob2ob90obob2obo8bo$37bo69bobo2bobob2ob86ob
2o2bob2obo$37bo69bobo2bobob2ob86o2bo2bo2bobo$37bo69bobo2b6ob85o3bo2bo
2bobo$37bo68b2obo2b92o6bo4bo$37bo67b3ob95o$37bo67b99o$37bo63bo3b92ob3o
b2o$37bo62b2o3b91o3bo2bo$37bo58bo3b3o2b88obo$37bo58bo3b3o2b82obob3obo$
37bo58bo3b3o2b82obo2b2obo$37bo58bo3b3o2b81o2bo2bo$37bo57b2o3b3ob82o2bo
$37bo52bo2bob2o3b3ob77o2b3o$37bo52bo2b4obob81o2b2o$37bo52bo2b4obob71ob
8o3b2o$37bo52bo2b4ob73ob5o6bo$37bo52bob5ob72o2b5o$37bo52bob5ob72o2b5o$
37bo52bob5ob72o2bo2b2o$37bo52bob5ob72o2bo2bo$37bo52bob5ob71o3bo2bo$37b
o52bob5ob62obob4o8bo$37bo52b7ob62obo3b2o8bo$37bo47bo2b70obobo4bo$37bo
43bo2b2o2b70o3bo4bo$37bo39bo2b2o2b2ob65o4b2o8bo$37bo39bo2b2o2b68o$37bo
39bo2b3ob67o$37bo39bo2b3ob66o$37bo39bo2b3ob57obob3obo$37bo39bo2b61obo
2b2o$37bo39bo2b61obo3bo$37bo36bo2bo2b57obo3bo$37bo36bo2bo2b56o$37bo34b
obob2ob57o$37bo34bob4ob51ob2o2bo$37bo34b6ob46ob2o4bo$37bo34b6ob46obo$
37bo34b6ob43obo2bo$37bo31bo2b50obo$37bo28bo2bob51obo$37bo28bob2ob51o$
37bo25bo2bob2ob43ob2ob2o$37bo23bob2obob2ob43obo2b2o$37bo23bob7ob41obo
4bo$37bo20bo2bob7ob35ob5o$37bo20bob2ob43ob2obo$37bo20bob2ob43ob2o$37bo
20bob2ob42o2b2o$37bo20bob2ob40o4bo$37bo20bob2ob35ob4o$37bo20bob38obo2b
o$37bo19b2ob30ob4ob2o$37bo15bobob2ob30ob3o2b2o$37bo15bobob33o6bo$37bo
15bob34o$37bo14b2ob29ob4o$37bo12bob32obob2o$37bo12bob30obo4bo$37bo11b
2ob29o$37bo9bob31o$37bo9bob24obo2b2o$37bo6bo2bob22obo4bo$37bo6b2ob24ob
o4bo$37bo3b2ob24ob2o$37bo3b2ob22o3b2o$37bo3b2ob19obo4bo$37bo3b2ob18o7b
o$37bo3b2ob16o9bo$37bo3b16o$37bo3b14o$37bob13ob2o$25bo11bob10ob2o$24b
2o11b12o$23bobo11b7ob4o$22bo2bo11b7obo$22b5o10b501o$25bo$25bo8$35b3o
185b3o2b5obo3bob5ob4o3b3o2b5o2b3o3b3o2bo3bo10bo34bo4b3o4bo4b3o3bo175bo
4b3o3b3o3b3o3b3o$34bo3bo183bo3bobo5b2o2bobo5bo3bobo3bo3bo5bo3bo3bob2o
2bo9bo11bo22b2o3bo3bo2bobo2bo3bo3bo173b2o3bo3bobo3bobo3bobo3bo$34bo2b
2o183bo5bo5bobobobo5bo3bobo3bo3bo5bo3bo3bobobobo9bo4b4ob5o2b3o2b4o2b5o
3bo3bo2b2obo3bobo2b2o3bo174bo3bo2b2obo2b2obo2b2obo2b2o$34bobobo183bo2b
2ob3o3bo2b2ob3o3b4o2b5o3bo5bo3bo3bobo2b2o9bo3bo7bo3bo3bobo3bo9bo3bobob
o7bobobo3bo174bo3bobobobobobobobobobobobo$34b2o2bo183bo3bobo5bo3bobo5b
o2bo2bo3bo3bo5bo3bo3bobo3bo9bo4b3o4bo3b5obo3bob5o3bo3b2o2bo7b2o2bo3bo
174bo3b2o2bob2o2bob2o2bob2o2bo$34bo3bo183bo3bobo5bo3bobo5bo3bobo3bo3bo
5bo3bo3bobo3bo9bo7bo3bo3bo5bo3bo9bo3bo3bo7bo3bo3bo174bo3bo3bobo3bobo3b
obo3bo$35b3o185b3o2b5obo3bob5obo3bobo3bo3bo4b3o3b3o2bo3bo10bo2b4o5b2o
2b4ob4o9b3o3b3o9b3o3bo174b3o3b3o3b3o3b3o3b3o$312bo$312bo!