ConwayLife.com

Posted: **April 28th, 2019, 11:39 am**

I've looked on LifeWiki and the sites it listed as references, but none of them seem to have any explanation of how the 0E0P metacell was constructed or how its signalling processes work. While Goucher's page mentioned he would make an article describing the process, it does not seem like he has gotten around to it. Would someone here be able to give me at least a broad overview of how it functions? Details aren't necessary, but would be appreciated nevertheless.

Posted: **April 28th, 2019, 12:18 pm**

This thread might be useful to look at.

Posted: **April 28th, 2019, 1:53 pm**

I took a look at the linked topic, but it didn't say anything about the metacell's inner workings; I know that it simulates an eight-state, four-neighbor CA able to communicate with its neighbors via signals, but I can't seem to find any information as to how exactly it does either of those things.

I did also take a look at Golly, and while I can recognize some pieces of the circuitry I can't figure out the mechanism that allows it to be programmed or how it receives/sends signals from other metacells. dvgrn mentioned that he was going to try and make a blueprint of the individual components of the metacell, but it doesn't seem like anything came of that effort.

Posted: **April 28th, 2019, 2:20 pm**

Ch91 wrote:Would someone here be able to give me at least a broad overview of how it functions? Details aren't necessary, but would be appreciated nevertheless.

Yeah, I've been meaning to get the next stage of writeup done for the 0E0P LifeWiki article -- if nothing else, then just to get calcyman to correct me when I get details wrong! It's quite a bit of work, so it's not too surprising that everybody's been avoiding the job.

More soon. Please feel free to remind me here in a couple of days if you don't see any new progress.

Posted: **May 2nd, 2019, 10:54 pm**

dvgrn wrote:
Ch91 wrote:Would someone here be able to give me at least a broad overview of how it functions? Details aren't necessary, but would be appreciated nevertheless.
Yeah, I've been meaning to get the next stage of writeup done for the 0E0P LifeWiki article -- if nothing else, then just to get calcyman to correct me when I get details wrong! It's quite a bit of work, so it's not too surprising that everybody's been avoiding the job.

More soon. Please feel free to remind me here in a couple of days if you don't see any new progress.

Thanks. Bumping this as a reminder, as requested.

Posted: **May 3rd, 2019, 2:56 pm**

Ch91 wrote:Bumping this as a reminder, as requested.

Okay here goes. For a start, I have a nice text explanation of the BCC-automaton emulation layer, direct from calcyman, which will look nice in LifeViewer. This is how the period-2^35 0E0P metacell, which runs on a body-centered-cubic lattice where each metacell has only four neighbors, successfully emulates whatever period-2^36 Moore neighborhood rule it's programmed for.

To step through the stages, click in the LifeViewer window, then hit j repeatedly to move to the next point of interest. (Shift+J moves you backwards if you need to do that.)

Code: Select all

#C [[ COLOR 1 Yellow COLOR 2 Orange COLOR 3 Pink COLOR 4 Gray COLOR 5 Purple ]]

#C [[ COLOR 6 Blue COLOR 7 Cyan COLOR 8 Red COLOR 9 Green ]]

#C [[ LABELSIZE 12 LABELALPHA 1 COLOR LABEL White ]]

#C [[ POI X -150 Y -20 Z 32 POITRANS 0 ]]

#C [[ LABEL 15 14 24 "Here's where it all starts\n-- one cell, in Stage E\n(shown in purple)" ]]

#C [[ POI X -120 Y -20 Z 32 POITRANS 0 ]]

#C [[ LABEL 45 14 24 "Cell moves to Stage F (blue)\n-- ready to start constructing children, SE first" ]]

#C [[ POI X -90 Y -20 Z 32 POITRANS 0 ]]

#C [[ LABEL 75 14 24 "Cell remains in Stage F (blue)\n-- child #1 constructed in SE\n(yellow cell, Stage A)" ]]

#C [[ POI X -60 Y -20 Z 32 POITRANS 0 ]]

#C [[ LABEL 105 14 24 "Cell remains in Stage F (blue)\n-- child #2 constructed in NE\n(yellow cell, Stage A)" ]]

#C [[ POI X -30 Y -20 Z 32 POITRANS 0 ]]

#C [[ LABEL 135 14 24 "Cell remains in Stage F (blue)\n-- child #3 constructed in NW\n(yellow cell, Stage A)" ]]

#C [[ POI X 0 Y -20 Z 32 POITRANS 0 ]]

#C [[ LABEL 165 14 24 "Cell remains in Stage F (blue)\n-- child #4 constructed in SW\n(yellow cell, Stage A)" ]]

#C [[ POI X 30 Y -20 Z 32 POITRANS 0 ]]

#C [[ LABEL 195 14 24 "Cell moves to Stage G (cyan)\n-- central parent cell sends its own state to each neighbor" ]]

#C [[ POI X 60 Y -20 Z 32 POITRANS 0 ]]

#C [[ LABEL 225 14 24 "Cell moves to Stage H (red)\nThe cycle is complete.  The original central cell self-destructs.\nThe state signals from the center cell are collected and stored in registers\nin each neighbor/child cell, which have all now moved to Stage B (orange)" ]]

#C [[ POI X 90 Y -20 Z 32 POITRANS 0 ]]

#C [[ LABEL 255 14 24 "The central cell is gone now -- green is the background state, completely empty.\nThe four child cells move to Stage C (pink)\nIn each cell, the collected values in four registers, one for each neighbor,\nare used to calculate the future state of the cell." ]]

#C [[ POI X 120 Y -20 Z 32 POITRANS 0 ]]

#C [[ LABEL 285 14 24 "The four child cells move to Stage D (gray)\nIf the cell's calculated state is 0, the cell self-destructs immediately.\nIn this particular case, all four child cells survive (this is what always happens\nin the first half-cycle when emulating a Moore-neighborhood rule)" ]]

#C [[ POI X 150 Y -20 Z 32 POITRANS 0 ]]

#C [[ LABEL 315 14 24 "The four child cells move to Stage E (purple)\nThe construction/signal/collect/decide cycle begins again.\n\nThis cycle happens *twice* in each 2^36 0E0P metacell cycle." ]]

#C [[ POI X -150 Y 20 Z 32 POITRANS 0 ]]

#C [[ LABEL 15 54 24 "The cycle restarts.\nNow there are four cells, all in Stage E\n(shown in purple)" ]]

#C [[ POI X -120 Y 20 Z 32 POITRANS 0 ]]

#C [[ LABEL 45 54 24 "The four cells move to Stage F (blue)\n-- ready to start constructing children, SE first" ]]

#C [[ POI X -90 Y 20 Z 32 POITRANS 0 ]]

#C [[ LABEL 75 54 24 "The four cells remain in Stage F (blue)\n-- four children constructed in SE\n(yellow cells, Stage A)" ]]

#C [[ POI X -60 Y 20 Z 32 POITRANS 0 ]]

#C [[ LABEL 105 54 24 "The four cells remain in Stage F (blue)\n-- two more children constructed in NE\n(yellow cells, Stage A)" ]]

#C [[ POI X -30 Y 20 Z 32 POITRANS 0 ]]

#C [[ LABEL 135 54 24 "The four cells remain in Stage F (blue)\n-- two more children constructed in NW\n(yellow cells, Stage A)" ]]

#C [[ POI X 0 Y 20 Z 32 POITRANS 0 ]]

#C [[ LABEL 165 54 24 "The four cells remain in Stage F (blue)\n-- one more child constructed in SW\n(yellow cells, Stage A)" ]]

#C [[ POI X 30 Y 20 Z 32 POITRANS 0 ]]

#C [[ LABEL 195 54 24 "Cells move to Stage G (cyan)\n-- each parent cell sends its own state to each neighbor" ]]

#C [[ POI X 60 Y 20 Z 32 POITRANS 0 ]]

#C [[ LABEL 225 54 24 "Cells move to Stage H (red)\nThe cycle is complete.  The parent cells self-destruct, as always.\nThe state signals from the parent cell are collected and stored in registers\nin the neighbor cells, which have all now moved to Stage B (orange)" ]]

#C [[ POI X 90 Y 20 Z 32 POITRANS 0 ]]

#C [[ LABEL 255 54 24 "The parent cells are gone now -- back to the green background state, completely empty.\nThe nine child cells move to Stage C (pink)\nIn each cell, the collected values in four registers, one for each neighbor,\nare used to calculate the future state of the cell." ]]

#C [[ POI X 120 Y 20 Z 32 POITRANS 0 ]]

#C [[ LABEL 285 54 24 "The nine child cells move to Stage D (gray)\nIf a child cell's calculated state is 0, the cell self-destructs immediately.\nIn this particular case, where the rule being simulated is S0,\nonly one of the nine child cells survive." ]]

#C [[ POI X 150 Y 20 Z 32 POITRANS 0 ]]

#C [[ LABEL 315 54 24 "The one remaining cell moves to Stage E (purple).\nEmpty background locations are shown in green." ]]



#C [[ WIDTH 656 ]]

x = 331, y = 62, rule = none

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The dark green checkerboard is empty space -- all the locations where a metacell may be constructed at some point.

Important note: The state of an 0E0P metacell is always a number between 0 and 7, where 0 is the empty space left behind by complete self-destruction. Each 0E0P metacell, no matter what its state, goes through a series of Stages in the course of its period-2^35 lifespan. The Stages are color-coded in the LifeViewer pattern above, and explained in detail below.

Stage A (yellow). The cell is constructed by one of its neighbours (parents).
Stage B (orange). Signals from between 1 and 4 parents enter the cell, destroying the 'initial eater' and placing the parent states into four registers {P1, P2, P3, P4}.
Stage C (pink). The states of those four registers are combined into a single value P1P2P3P4 (between 1 and 4095), and used to index into a rule-table. The result of this indexing calculation is stored in a register R.
Stage D (gray). If R == 0, the cell self-destructs.
Stage E (purple). Otherwise, if 1 <= R <= 7, the cell waits a while in this phase.
Stage F (blue). The cell constructs four neighbouring cells (SE, NE, NW, SW). This corresponds to Stage A in the childrens' lifecycles.
Stage G (cyan). The cell sends its own state R to the four neighbours (this corresponds to Stage B in their lifecycles).
Stage H (red). The cell self-destructs.

I'll be making some edits to this summary when I can fix the Stage H color -- there's a minor bug in the current build of LifeViewer. (EDIT: Fixed in Build 325. Corrected colors above.)

Please ask questions if anything is unclear. I'll probably work on making improvements here, then move the whole summary over to the LifeWiki article.

Posted: **May 4th, 2019, 2:04 am**

Thanks. Here are my first few questions.

1. How are the signals sent out from one metacell to its neighbors? I assume it involves gliders given the alignment of the metacells, but that's all I can deduce.
2. In Adam Goucher's animation of the metacell's reproduction cycle(as seen on [url]https://cp4space.wordpress.com/2018/11/ ... plication/[/url), it seems like the self-destruct left behind part of the metacell circuitry instead of being erased cleanly. Is this intentional, or is it merely an artifact of how the animation was rendered?
3. What part of the metacell holds the "program" for which rule it will follow?
4. What is the mechanism that the metacell uses uses for its construction and self-destruction processes?

Posted: **May 4th, 2019, 4:44 am**

Ch91 wrote:Thanks. Here are my first few questions.

1. How are the signals sent out from one metacell to its neighbors? I assume it involves gliders given the alignment of the metacells, but that's all I can deduce.
2. In Adam Goucher's animation of the metacell's reproduction cycle(as seen on [url]https://cp4space.wordpress.com/2018/11/ ... plication/[/url), it seems like the self-destruct left behind part of the metacell circuitry instead of being erased cleanly. Is this intentional, or is it merely an artifact of how the animation was rendered?
3. What part of the metacell holds the "program" for which rule it will follow?
4. What is the mechanism that the metacell uses uses for its construction and self-destruction processes?

1. Correct, yes: the metacell emits an almost-unary encoding of its state (using {0, 2, 3, 4, 5, 6, 7, 8} gliders to represent states {0, 1, 2, 3, 4, 5, 6, 7}, respectively), and broadcasts that signal to its neighbours.
2. The latter; the remnants cleanly self-destruct very close to the end of the .mp4 (which I expected would seamlessly loop in the way that a GIF does).
3. A segment of the tape contains 4096 'memory locations', each of which contains between 0 and 7 gliders (as a unary encoding). Some of the circuitry in the south corner is responsible for retrieving a value from that array according to the four states of its neighbours.
4. Single-channel slow-salvo construction (see http://b3s23life.blogspot.com/2018/11/n ... ction.html for some examples that can be run in Golly at a reasonable speed) and one-time circuitry for destruction.

Posted: **May 4th, 2019, 4:37 pm**

calcyman wrote:
Ch91 wrote:Thanks. Here are my first few questions.

1. How are the signals sent out from one metacell to its neighbors? I assume it involves gliders given the alignment of the metacells, but that's all I can deduce.
2. In Adam Goucher's animation of the metacell's reproduction cycle(as seen on [url]https://cp4space.wordpress.com/2018/11/ ... plication/[/url), it seems like the self-destruct left behind part of the metacell circuitry instead of being erased cleanly. Is this intentional, or is it merely an artifact of how the animation was rendered?
3. What part of the metacell holds the "program" for which rule it will follow?
4. What is the mechanism that the metacell uses uses for its construction and self-destruction processes?
1. Correct, yes: the metacell emits an almost-unary encoding of its state (using {0, 2, 3, 4, 5, 6, 7, 8} gliders to represent states {0, 1, 2, 3, 4, 5, 6, 7}, respectively), and broadcasts that signal to its neighbours.
2. The latter; the remnants cleanly self-destruct very close to the end of the .mp4 (which I expected would seamlessly loop in the way that a GIF does).
3. A segment of the tape contains 4096 'memory locations', each of which contains between 0 and 7 gliders (as a unary encoding). Some of the circuitry in the south corner is responsible for retrieving a value from that array according to the four states of its neighbours.
4. Single-channel slow-salvo construction (see http://b3s23life.blogspot.com/2018/11/n ... ction.html for some examples that can be run in Golly at a reasonable speed) and one-time circuitry for destruction.

Interesting. I assume you used slsparse to design the one-time circuitry in a way that it wouldn't leave any ash behind. Can I ask why the encoding skips from zero gliders to two?

I also recall in another topic that there was work on a schematic outlining the composition of the different parts- it's too big to quote here, but it's in the "0E0P Constructions" topic. Do you think you could expand on that in LifeWiki?

Also, how would the "birth" process work for a metacell pattern- would it be identical to your original animation but with multiple metacells present at the end of a metatick, or am I mistaken? I attempted to look at the metaglider pattern posted in the LifeWiki entry to get an idea, but I doubt I can run it on my computer in a reasonable time frame. At the minimum, I assume the slow-salvos are set up to ensure that the metacells don't end up close enough to affect each other's growth.

Again, thanks for the information. I'm relatively new to Life, so it's not easy for me to recognize what everything does at a glance.

Posted: **May 5th, 2019, 8:00 am**

Ch91 wrote:Interesting. I assume you used slsparse to design the one-time circuitry in a way that it wouldn't leave any ash behind.

I used Simon Ekstroem's GoL_destroy script for that.

Can I ask why the encoding skips from zero gliders to two?

Boring technical reasons -- the first glider received is removed to trigger the metacell's life cycle, leaving the correct number for unary encoding.

I also recall in another topic that there was work on a schematic outlining the composition of the different parts- it's too big to quote here, but it's in the "0E0P Constructions" topic. Do you think you could expand on that in LifeWiki?

I think Dave Greene is working on that.

At the minimum, I assume the slow-salvos are set up to ensure that the metacells don't end up close enough to affect each other's growth.

Yes, exactly. You can see this somewhat in the original animation, because after the first 2^35 generations there are four metacells in close proximity.

Posted: **May 5th, 2019, 3:00 pm**

Ch91 wrote:Also, how would the "birth" process work for a metacell pattern- would it be identical to your original animation but with multiple metacells present at the end of a metatick...?

Yes, the original animation shows a metacell programmed for a rule where a single isolated cell survives. It happens to be B2-an3-eiky4aiqw5ijnr6ak/S012ik3-acir4kqw5acq6ack7c8, but it could just as well be plain B/S0 or any other rule with S0 in it -- the pattern of evolution will look the same for a single cell.

Adding B1c or B1e, or both, would have made a difference. Either four or all eight of the child cells toward the end of the cycle would have stayed alive instead of dying off as soon as they were constructed. Any other additions to the rule wouldn't change how a single isolated cell behaves.*

All the details about Stages A to H in my previous post might not really be necessary to understand the basic design. And I think I'd better rework the pattern and turn the view 45 degrees, so that the individual cells look like diamonds, same as in an actual 0E0P pattern.

Here's an attempt at a higher-level summary. It still won't be short... but at least it will avoid worrying about so many of the staging details.

In a healthy 0E0P metacell pattern, metacells could be thought of as living on a diagonally-oriented checkerboard. They're allowed to be present on the dark squares of the checkerboard only on even metaticks, and on the light squares of the checkerboard only on even ticks.
Every period-2^36 cycle of an 0E0P metacell consists of two period-2^35 half-cycles. In each half-cycle, all metacells make sure that there are child metacells all around them, on the other checkerboard square color -- either by building them, or by attempting to build them and having the construction recipe cleanly eaten by an eater that's part of an already existing child in that location.
Switching checkerboard colors and expanding to four surrounding metacells twice (for two half-cycles) effectively ensures that all eight metacells surrounding any given ON metacell on the same checkerboard square color are occupied by child metacells. These are all the neighbor locations for that particular metacell.
No effect can travel faster than lightspeed in the range-1 Moore-neighborhood rules that the 0E0P metacell can emulate, so at the end of two half-cycles, metacells are present in every location where a metacell could possibly be needed to turn ON in the next metatick.
There's no direct communication between an 0E0P metacell and its nearest possible living neighbor metacells to the north, south, east, and west -- i.e., the nearest same-color squares on the 45-degree-angled checkerboard -- let alone between it and the other possibly-living neighbor cells, two checkerboard squares away diagonally.
However, by the end of each full cycle, communication between parent and child metacells during each half-cycle has effectively transmitted neighbor state information from one dark-square metacell to all its dark-square neighbors.
This means that at the end of each full cycle, every "potentially alive" 0E0P metacell has all the information it needs to decide whether it should transition to a "fully alive" state and start building child metacells, or if it should self-destruct.

* Adding B0 might make a difference eventually. But 0E0P metacells can't support B0 rules for obvious reasons, except in the odd cases where you do the anti-strobing trick and simulate equivalent non-B0 rules instead.

Posted: **May 5th, 2019, 5:25 pm**

dvgrn wrote:... I'd better rework the pattern and turn the view 45 degrees, so that the individual cells look like diamonds, same as in an actual 0E0P pattern.

Here's an exploration of how 0E0P metacells work when they're programmed with standard B3/S23 Life rules, and with LifeViewer oriented to display colored regions that match what 0E0P metacells actually look like in the Life universe. Maybe this will be a little easier to follow than the previous example, which showed what happened to one lonely immortal ON cell in a non-Life rule.

One cycle of a 0E0P Conway's Life metaglider looks like this:

Code: Select all

#C [[ COLOR 1 Yellow COLOR 2 Orange COLOR 3 Pink COLOR 4 Gray COLOR 5 Purple ]]

#C [[ COLOR 6 Blue COLOR 7 Cyan COLOR 8 Red COLOR 9 Green ]]

#C [[ LABELSIZE 12 LABELALPHA 1 LABELANGLE 315 COLOR LABEL White ]]

#C [[ GRID ANGLE 45 HEIGHT 600 THEME MCell GRIDMAJOR 0 ]]

#C [[ POI X -108 Y 92 Z 32 POITRANS 0 ]] Point of interest #1

#C [[ LABEL 11 211 16 "Here's where it all starts\n-- five metacells forming a glider, in Stage E\n(shown in purple)" ]]

#C [[ POI X -88 Y 72 Z 32 POITRANS 0 ]] POI #2

#C [[ LABEL 31 191 16 "Metacells move to Stage F (blue).\n-- ready to start constructing children, SE first" ]]

#C [[ POI X -68 Y 52 Z 32 POITRANS 0 ]] POI #3

#C [[ LABEL 51 171 16 "Metacells remain in Stage F (blue).\nChildren constructed SE of each metacell\n(yellow cells, Stage A)" ]]

#C [[ POI X -48 Y 32 Z 32 POITRANS 0 ]] POI #4

#C [[ LABEL 71 151 16 "Metacells remain in Stage F (blue).\nChildren constructed NE of each metacell\n(yellow cells, Stage A)" ]]

#C [[ POI X -28 Y 12 Z 32 POITRANS 0 ]] POI #5

#C [[ LABEL 91 131 16 "Metacells remain in Stage F (blue).\nChildren constructed NW of each metacell\n(yellow cells, Stage A)" ]]

#C [[ POI X -8 Y -8 Z 32 POITRANS 0 ]] POI #6

#C [[ LABEL 111 111 16 "Metacells remain in Stage F (blue).\nChildren constructed SW of each metacell\n(yellow cells, Stage A)" ]]

#C [[ POI X 12 Y -28 Z 32 POITRANS 0 ]] POI #7

#C [[ LABEL 130 90 16 "Original metacells move to Stage G (cyan).\nParent metacells send their own states\nto each immediate neighbor.  All receiving neighbors\nare recently constructed child metacells." ]]

#C [[ POI X 32 Y -48 Z 32 POITRANS 0 ]] POI #8

#C [[ LABEL 150 70 16 "Metacells move to Stage H (red)\nThe cycle is complete. The original metacells self-destruct.\nState signals from the original metacells are collected and\nstored in registers in each neighboring child cell,\nwhich have all now moved to Stage B (orange)" ]]

#C [[ POI X 52 Y -68 Z 32 POITRANS 0 ]] POI #9

#C [[ LABEL 170 50 16 "Original metacells are gone now\n(green is the background state, completely empty).\nThe four child metacells move to Stage C (pink)\nIn each metacell, the collected state values from each\nneighbor are used to calculate the future state of the cell." ]]

#C [[ POI X 72 Y -88 Z 32 POITRANS 0 ]] POI #10

#C [[ LABEL 190 30 16 "The child metacells move to Stage D (gray)\nIf a child metacell's new calculated state is 0, it\nself-destructs. Here all 13 child metacells survive.\nThis is what always happens in the first\nhalf-cycle, when a Moore-neighborhood rule\nis being emulated." ]]

#C [[ POI X 92 Y -108 Z 32 POITRANS 0 ]] POI #11

#C [[ LABEL 211 11 16 "The thirteen child metacells move to Stage E (purple)\nThe construction/signal/collect/decide cycle begins again.\nThis cycle happens twice in each 2^36 0E0P metacell cycle." ]]

#C [[ POI X -88 Y 112 Z 32 POITRANS 0 ]] POI #12

#C [[ LABEL 30 230 16 "The cycle restarts.\nNow there are thirteen metacells, all in Stage E\n(shown in purple)" ]]

#C [[ POI X -68 Y 92 Z 32 POITRANS 0 ]] POI #13

#C [[ LABEL 50 210 16 "The thirteen metacells move to Stage F (blue)\n-- ready to start constructing children, SE first" ]]

#C [[ POI X -48 Y 72 Z 32 POITRANS 0 ]] POI #14

#C [[ LABEL 70 190 16 "The thirteen metacells remain in Stage F (blue).\nThirteen children are constructed in the SE\n(yellow metacells, Stage A)" ]]

#C [[ POI X -28 Y 52 Z 32 POITRANS 0 ]] POI #15

#C [[ LABEL 90 170 16 "The thirteen metacells remain in Stage F (blue).\nFour more children are constructed in the NE\n(yellow metacells, Stage A)" ]]

#C [[ POI X -8 Y 32 Z 32 POITRANS 0 ]] POI #16

#C [[ LABEL 110 150 16 "The thirteen metacells remain in Stage F (blue).\nFour more children are constructed in the NW\n(yellow metacells, Stage A)" ]]

#C [[ POI X 12 Y 12 Z 32 POITRANS 0 ]] POI #17

#C [[ LABEL 130 130 16 "The thirteen metacells remain in Stage F (blue).\nOne more child is constructed in the SW\n(yellow metacell, Stage A)" ]]

#C [[ POI X 32 Y -8 Z 32 POITRANS 0 ]] POI #18

#C [[ LABEL 150 110 16 "Metacells move to Stage G (cyan).\nEach parent metacell sends its own state to each neighbor." ]]

#C [[ POI X 52 Y -28 Z 32 POITRANS 0 ]] POI #19

#C [[ LABEL 170 90 16 "Parent metacells move to Stage H (red).\nChild metacells move to stage B (orange).\nThe parent metacells self-destruct, as always.\nState signals from the parent cell are stored in registers\nin the new child cells." ]]

#C [[ POI X 72 Y -48 Z 32 POITRANS 0 ]] POI #20

#C [[ LABEL 190 70 16 "The thirteen parent metacells are gone now -- back to the\ngreen background state, completely empty.\nThe twenty-two child metacells move to Stage C (pink)\nIn each metacell, the collected neighbor states\nare used to calculate the future state of the metacell." ]]

#C [[ POI X 92 Y -68 Z 32 POITRANS 0 ]] POI #21

#C [[ LABEL 210 50 16 "The twenty-two child metacells move to Stage D (gray)\nIf a child metacell's calculated state is 0, it self-destructs.\nIn this case, where a B3/S23 glider is being emulated,\nonly five of the twenty-two child metacells survive." ]]

#C [[ POI X 112 Y -88 Z 32 POITRANS 0 ]] POI #22

#C [[ LABEL 230 30 16 "The five remaining metacells move to Stage E (purple).\nEmpty background locations are shown in green." ]]

#C [[ POI INITIAL X 132 Y -108 Z 32 POITRANS 0 ]] POI #23 (initial position, because of INITIAL keyword)

#C [[ LABEL 245 6 16 "Press 'J' to move forward through 0E0P stages,\nor 'Shift+J' to move backwards." ]]

x = 233, y = 233, rule = none

206.I$205.3I$204.5I$203.7I$202.3IEIE3I$201.3IEIEIE3I$200.5IEIEIE3I$

201.5IEIE3I$202.3IEIE3I$203.3IE3I$204.5I$205.3I$206.I8$186.I39.I$185.

3I37.3I$184.5I35.5I$183.7I33.7I$182.3IDID3I31.9I$181.3IDIDID3I29.6IE

4I$180.5IDIDID3I27.8IE4I$181.5IDID3I29.4IEIE4I$182.3IDID3I31.6IE2I$

183.3ID3I33.7I$184.5I35.5I$185.3I37.3I$186.I39.I8$166.I39.I$165.3I37.

3I$164.5I35.5I$163.7I33.2IHIH2I$162.3ICIC3I31.2IHIHIH2I$161.3ICICIC3I

29.2IHIHIDIH2I$160.5ICICIC3I27.4IHIHIDIH2I$161.5ICIC3I29.4IDIDIH2I$

162.3ICIC3I31.2IHIHID2I$163.3IC3I33.2IHIH2I$164.5I35.2IH2I$165.3I37.

3I$166.I39.I8$146.I39.I$145.3I37.3I$144.5I35.5I$143.7I33.2ICIC2I$142.

3IBIB3I31.2ICICIC2I$141.3IBHBHB3I29.2ICICICIC2I$140.5IBIBHB3I27.4ICIC

ICIC2I$141.5IBHB3I29.4ICICIC2I$142.3IBHB3I31.2ICICIC2I$143.3IB3I33.2I

CIC2I$144.5I35.2IC2I$145.3I37.3I$146.I39.I8$126.I39.I$125.3I37.3I$

124.5I35.5I$123.7I33.2IBIB2I$122.3IAIA3I31.2IBHBHB2I$121.3IAGAGA3I29.

2IBHBHBHB2I$120.5IAIAGA3I27.4IBHBHBHB2I$121.5IAGA3I29.4IBHBHB2I$122.

3IAGA3I31.2IBHBHB2I$123.3IA3I33.2IBHB2I$124.5I35.2IB2I$125.3I37.3I$

126.I39.I8$106.I39.I$105.3I37.3I$104.5I35.5I$103.7I33.2IAIA2I$102.3IA

IA3I31.2IAGAGA2I$101.3IAFAFA3I29.2IAGAGAGA2I$100.5IAIAFA3I27.4IAGAGAG

A2I$101.5IAFA3I29.4IAGAGA2I$102.3IAFA3I31.2IAGAGA2I$103.3IA3I33.2IAGA

2I$104.5I35.2IA2I$105.3I37.3I$106.I39.I8$86.I39.I$85.3I37.3I$84.5I35.

5I$83.7I33.2IAIA2I$82.3IAIA3I31.2IAFAFA2I$81.3IAFAFA3I29.2IAFAFAFA2I$

80.7IAFA3I27.4IAFAFAFA2I$81.5IAFA3I29.4IAFAFA2I$82.3IAFA3I31.2IAFAFA

2I$83.7I33.2IAFA2I$84.5I35.2IA2I$85.3I37.3I$86.I39.I8$66.I39.I$65.3I

37.3I$64.5I35.5I$63.7I33.2IAIA2I$62.3IAIA3I31.2IAFAFA2I$61.4IFAFA3I

29.2IAFAFAFA2I$60.7IAFA3I27.4IAFAFAFA2I$61.5IAFA3I29.4IAFAFA2I$62.4IF

A3I31.2IAFAFA2I$63.7I33.2IAFA2I$64.5I35.5I$65.3I37.3I$66.I39.I8$46.I

39.I$45.3I37.3I$44.5I35.5I$43.7I33.2IAIA2I$42.9I31.2IAFAFA2I$41.4IFAF

A3I29.3IFAFAFA2I$40.8IFA3I27.5IFAFAFA2I$41.6IFA3I29.4IAFAFA2I$42.4IFA

3I31.3IFAFA2I$43.7I33.3IFA2I$44.5I35.5I$45.3I37.3I$46.I39.I8$26.I39.I

$25.3I37.3I$24.5I35.5I$23.7I33.7I$22.9I31.3IFAFA2I$21.4IFIF4I29.3IFAF

AFA2I$20.8IF4I27.5IFAFAFA2I$21.6IF4I29.5IFAFA2I$22.4IF4I31.3IFAFA2I$

23.7I33.3IFA2I$24.5I35.5I$25.3I37.3I$26.I39.I8$6.I39.I$5.3I37.3I$4.5I

35.5I$3.7I33.7I$2.9I31.3IFIF3I$.4IEIE4I29.3IFIFIF3I$8IE4I27.5IFIFIF3I

$.6IE4I29.5IFIF3I$2.4IE4I31.3IFIF3I$3.7I33.3IF3I$4.5I35.5I$5.3I37.3I$

6.I39.I8$26.I$25.3I$24.5I$23.7I$22.3IEIE3I$21.3IEIEIE3I$20.5IEIEIE3I$

21.5IEIE3I$22.3IEIE3I$23.3IE3I$24.5I$25.3I$26.I!

Important note: The state of an 0E0P metacell is always a number between 0 and 7, where 0 is the empty space left behind by complete self-destruction. Each 0E0P metacell, no matter what its state, goes through a series of Stages in the course of its period-2^35 lifespan. The Stages are color-coded in the LifeViewer pattern above, and explained in detail below.

Stage A (yellow). A metacell is constructed by one of its neighbours (parents).
Stage B (orange). Signals from between 1 and 4 parents enter the metacell, destroying the 'initial eater' and placing the parent states into four registers {P1, P2, P3, P4}.
Stage C (pink). The states of those four registers are combined into a single value P1P2P3P4 (between 1 and 4095), and used to index into a rule-table. The result of this indexing calculation is stored in a register R.
Stage D (gray). If R == 0, the metacell self-destructs immediately (before building any child metacells).
Stage E (purple). Otherwise, if 1 <= R <= 7, the metacell waits a while in this phase.
Stage F (blue). Each metacell constructs four neighbouring cells (SE, NE, NW, SW). This corresponds to Stage A in the children's lifecycles.
Stage G (cyan). Each parent metacell sends its own state R to the four child neighbours (this corresponds to Stage B in the children's lifecycles).
Stage H (red). All parent cells self-destruct.

If anything is unclear, please keep asking questions. I'll probably continue to work on making improvements here, then move the whole summary over to the LifeWiki article.

... And yes, this is definitely only one tiny corner of the explanations that ought to be written up eventually. The above assumes that the metacells are programmed correctly to simulate Life or whatever other isotropic Moore-neighborhood rule is wanted, but doesn't explain how that's done. Each metacell is still a black box, with no explanation of the construction and destruction mechanisms inside it -- and so on. One piece at a time --

Posted: **May 5th, 2019, 6:01 pm**

dvgrn wrote:
dvgrn wrote:... I'd better rework the pattern and turn the view 45 degrees, so that the individual cells look like diamonds, same as in an actual 0E0P pattern.
Here's an exploration of how 0E0P metacells work when they're programmed with standard B3/S23 Life rules, and with LifeViewer oriented to display colored regions that match what 0E0P metacells actually look like in the Life universe. Maybe this will be a little easier to follow than the previous example, which showed what happened to one lonely immortal ON cell in a non-Life rule.
...
And yes, this is definitely only one tiny corner of the explanations that ought to be written up eventually. The above assumes that the metacells are programmed correctly to simulate Life or whatever other isotropic Moore-neighborhood rule is wanted, but doesn't explain how that's done. Each metacell is still a black box, with no explanation of the construction and destruction mechanisms inside it -- and so on. One piece at a time --

The new explanation makes way more sense now that it's a more practical example. With the zoom at the right level, the gap between the two glider cells that would normally be orthogonally adjacent wouldn't even be visible. Clever.

Take as much time as you need. I'm sure it's not going to be an easy task.

Posted: **May 5th, 2019, 10:19 pm**

Ch91 wrote:With the zoom at the right level, the gap between the two glider cells that would normally be orthogonally adjacent wouldn't even be visible. Clever.

Yup, when the zoom level in Golly is one (or even four) pixels per metacell, there's no way to tell them apart visually from regular single cells... as long as you pick the right phase and don't take any smaller steps than 2^36, anyway.
You'll certainly see lots of weird effects at smaller step sizes.

Ch91 wrote:Take as much time as you need. I'm sure it's not going to be an easy task.

There are definitely some things I could use help with. One item is that calcyman has kindly sent me his collection of 563 snapshots from the trial single-metacell run -- the frames from which the CP4space 0E0P video was made.

The collection is almost 3.4GB in compressed format, so it's not particularly easy to share the whole thing. But most of the frames are kind of boring anyway.

I can definitely compress and attach individual snapshots here. I'm hoping to sort out a series of custom snapshots of times where something interesting is just about to happen -- switching between stages, key moments in the construction, the very beginning of the main self-destruct sequence, etc. -- and post those snapshots along with the coordinates where the exciting stuff is going on.

Posted: **May 7th, 2019, 1:51 pm**

Here's something to start with. Call this attached snapshot the "T=0" point:

rrocell_backup100087.mc.gz: compressed macrocell version of calcyman's first snapshot; (6.64 MiB) Downloaded 443 times

7.5 billion ticks later (!), the initial single metacell will have created four child copies of itself, on all the adjacent opposite-color checkerboard squares. It will have copied its single-channel glider instruction tape and its rule lookup table to each child's memory block. And it will have disabled its own memory loop, so that the huge number of back-and-forth gliders are gradually being absorbed by an eater.

rrocell_backup128756.mc.gz: Macrocell format is awesome. 5 0E0P metacells only need 49K more than 1 metacell.; (6.69 MiB) Downloaded 420 times

Technical note: The snapshots were taken at intervals of an hour, with a step size of 2^18 = 262144 ticks. The number suffix on the file name records the number of steps. So if we're calling the first 100087 snapshot T=0, then this one is T=(128756-100087)*262144=7515406336. There are 160 snapshots in the range between 100087 and 128756 inclusive. Sometimes StreamLife got through a lot more steps in an hour than other times -- see next post.

First An Orderly Memory-Loop Shutdown...
If we extract just the parent cell out of this snapshot and run it a little longer, we get this mostly-stable configuration at T=7,621,050,368:

Code: Select all

[M2] (golly 3.2)
#R B3/S23
#G 7621050368
$$$$$$.....*$....*.*$
4 0 0 1 0
5 0 0 2 0
6 0 0 3 0
7 0 0 4 0
8 0 0 0 5
9 0 0 6 0
10 0 0 0 7
$$$$$$....*$...*.*$
4 0 0 0 9
....**$
4 0 11 0 0
5 0 10 0 12
6 0 0 13 0
7 0 14 0 0
4 11 0 0 0
5 16 0 0 0
$$$$$$$....**$
4 0 18 0 11
5 0 0 0 19
6 17 0 0 20
$$$$$$$......**$
......**$
$$$$.....**$.....**$
4 22 0 23 24
5 0 25 0 0
6 0 26 0 0
7 21 0 27 0
8 15 28 0 0
$$$.....**$.....*.*$.......*$...****$...*..*$
$$$$.....**$......*$......*$.......*$
......*$.......*$$$$......**$*.....**$*$
4 0 30 31 32
$$$$$....**$**..*..*$*.*.*.**$
*.*.*$*.*.*$...*$
4 34 0 35 0
5 0 0 33 36
6 0 0 0 37
$$......*$.....*.*$.....**$
4 39 0 0 0
5 0 40 0 0
6 0 0 41 0
7 0 0 38 42
8 0 0 43 0
$$$$$$.**$.*$
..***$....*$
4 45 0 46 0
5 0 47 0 0
6 0 48 0 0
7 49 0 0 0
8 50 0 0 0
9 29 44 0 51
10 0 52 0 0
11 0 8 0 53
12 0 0 0 54
13 0 55 0 0
14 0 56 0 0
15 0 57 0 0
$$$$$$$.....**$
4 0 0 59 0
5 0 0 60 0
6 0 0 61 0
7 0 0 62 0
8 0 0 0 63
9 0 0 0 64
10 0 0 65 0
11 0 0 66 0
12 0 0 0 67
13 0 0 68 0
14 0 0 69 0
15 0 0 70 0
16 0 58 71 0
$$....*$...*.*$...**$
4 0 73 0 0
5 0 74 0 0
6 0 75 0 0
7 0 0 0 76
8 0 0 0 77
9 0 0 0 78
$$....**$.....*$.....*.*$......*$.......*$
4 0 80 0 0
5 0 0 0 81
6 0 82 0 0
7 0 0 0 83
8 0 84 0 84
9 0 0 0 85
$$.......*$$$..*$..***$.....*$
$$$$$$$.......*$
....**$$$.....**$.....**$$$*$
4 0 87 88 89
$$*$*$*.*$.**$
$**$**$
$$$$$......**$......*$
4 91 92 0 93
5 0 0 90 94
6 0 0 0 95
$$$$$$*$*$
4 0 0 97 0
5 0 0 98 0
$$$$$$......*$.....*.*$
.....**$
4 0 100 0 101
5 0 0 0 102
6 0 0 99 103
7 0 0 96 104
8 0 0 105 0
......*$.......*$
*$
$$$$$$..**$.*.*$
4 107 108 0 109
$$$$$$$..**$
..*$...***$.....*$
4 0 111 0 112
.*$**$
$$$$$$$*$
4 0 114 88 115
..**$..**$
$...**$...*$.*.*$.**$
4 0 0 117 118
5 110 113 116 119
.......*$.......*$$$$..*$.*.*$.*.*$
..*$
4 0 121 0 122
$$$$$$....**$....**$
$$$$$$..*$.*.*$
$$$$$..**$..**$
4 124 0 125 126
5 0 123 0 127
*$*$$$$$$...*$
*$*.*$.**$
..*.*$..**$
4 129 130 131 0
$$$$$.......*$.......*$
$$$$$*$.*$.*$
.**$
4 133 134 18 135
$$$$$$....**$...*.*$
...*$..**$
4 137 0 138 0
....*$.....***$.......*$
4 140 0 0 0
5 132 136 139 141
6 0 120 128 142
**$
$$$$$.*$*.*$*..*$
....**$...*..*$...*.*$....*$
4 144 145 146 135
$$$$.......*$.......*$
$$$*$.*$*$
$$$$$$.*$*.*$
4 148 149 150 0
5 147 0 151 0
..*$.*.*$.*.*$..*$
4 135 0 153 0
.......*$....***$....*$
4 22 0 155 0
5 154 156 0 0
6 152 0 157 0
$$$$$$......*$....***$
4 0 0 0 159
*..*$.**$$.......*$......*$..*....*$.*.*$.*..*$
$$$*$*$
..**$
4 161 162 163 0
$$$$*$.*$*$
...*$...**$$$$$$......**$
4 165 166 0 23
$$$$$$$.**.*$
.....**$$$$$$$...**$
4 0 59 168 169
5 160 164 167 170
....**$....**$
....*.*$....*$...**$
4 59 172 173 0
$.....**$.....*$...*.*$...**$
$$$$$......**$.....*$.....*.*$
......*$
4 175 176 0 177
$$$$$.....**$.....**$
$$$....**$....*$.....***$.......*$
4 0 0 179 180
5 174 178 0 181
$$$$......**$......**$
$$$$$....*$...*.*$..*..*$
4 183 0 0 184
.**.***$.......*$.**.***$..*.*$..*.*$...*$
..*.*$..*$.**$
4 186 187 0 0
...**$
4 0 189 0 0
5 185 188 190 0
$$$$.......*$......*$......*$.....**$
$$$$*$*$$.......*$
.......*$
4 192 193 0 194
$$.....**$.....**$$$$*$
$***$..*$
4 196 0 197 0
5 195 198 90 94
6 171 182 191 199
$$$$$$*$
4 201 0 0 0
$$$$$....**$....**$
4 0 0 0 203
5 202 0 0 204
$$$$$......**$......**$
4 0 0 206 0
$$.....**$.....**$
4 0 208 0 0
5 0 207 98 209
6 205 0 210 0
7 143 158 200 211
$$$.**$.**$
4 0 0 213 0
$$$...**$...**$
4 0 0 0 215
5 0 214 216 0
6 0 0 0 217
4 208 0 92 0
.....**$.....**$
4 0 0 220 0
5 219 221 0 0
6 0 0 222 0
4 117 0 0 0
5 0 224 0 0
$$$$.**$.**$
4 0 0 0 226
$$$$...**$...**$
4 0 0 228 0
5 0 227 0 229
6 0 225 230 0
4 148 149 0 0
5 0 0 232 0
6 233 0 0 0
7 218 223 231 234
5 154 0 0 0
6 152 0 236 0
5 202 0 0 0
4 203 0 0 0
5 0 0 0 239
6 238 0 99 240
7 143 237 200 241
$..**$..**$
4 0 243 0 0
5 0 244 0 0
4 0 206 0 0
5 0 0 246 0
6 245 0 0 247
4 0 0 0 208
5 249 239 0 0
6 0 250 0 0
7 248 0 251 0
8 212 235 242 252
$$$$$$......**$......*$
4 0 0 254 115
5 0 0 255 0
4 194 0 0 0
5 257 0 0 0
6 256 0 258 0
7 0 0 259 0
$$$.......*$
4 0 261 0 0
$$*$.*$**$
4 263 0 0 0
5 262 264 0 0
6 0 0 0 265
$$.......*$.......*$
$*$.*$*$
4 267 268 0 0
5 269 0 0 0
6 270 0 0 0
7 266 0 0 271
8 260 0 272 0
9 106 0 253 273
10 0 79 86 274
9 0 85 0 0
4 0 0 208 0
5 246 277 0 0
6 152 278 236 0
5 204 0 207 0
6 238 0 99 280
7 143 279 200 281
5 207 0 204 0
6 0 0 0 283
4 208 0 0 0
5 285 0 0 0
6 0 286 0 0
7 284 0 287 0
5 209 0 0 0
6 152 289 236 0
5 195 198 0 0
6 171 182 191 291
$$$.**$.*.*$..*$
4 0 293 0 0
5 202 0 294 0
6 295 0 0 0
7 143 290 292 296
$$$.*$*.*$**$
4 0 0 0 298
5 0 0 299 0
6 300 0 0 0
7 301 0 0 0
8 282 288 297 302
$$$$$$$...*$
4 0 0 0 304
5 0 0 0 305
4 0 131 0 0
5 0 307 0 0
6 0 306 0 308
7 0 0 0 309
8 0 0 0 310
9 303 311 0 0
$$$$$$.*$**$
......*$......**$$$$$$.......*$
$$$$......**$.......*$.......*$*....***$
4 88 313 314 315
5 0 0 0 316
$$$$$$.**$..*$
4 0 0 318 0
5 0 0 319 0
$$......**$.....*.*$.....*$....**$
4 0 321 0 0
*...*$....****$.......*$....***$...*$....****$$......*$
4 194 323 0 23
5 322 324 0 0
**$$$$$*$*$
4 326 0 0 0
5 327 0 0 0
6 317 320 325 328
7 0 329 0 0
8 0 0 0 330
9 0 0 0 331
$.......*$
*$.*$**$
4 0 0 333 334
5 335 0 0 0
6 0 0 0 336
7 0 0 0 337
$$$$$$.....**$......*$
4 0 0 339 0
5 0 0 340 0
6 0 0 0 341
$.....**$.....*.*$......*$
4 0 0 0 343
5 0 0 0 344
6 0 0 0 345
....*$....****$$......**$.....*$.....***$...**$..*..***$
$*$.*$*$$*$*...**$....**$
..**.*$.....*$.....**$
$$$$$.....**$......*$...***$
4 347 348 349 350
$.......*$.......*$.....*.*$.....**$
$*$
4 352 353 0 0
...*$
4 0 355 0 0
5 351 354 356 0
$$$$....*$...*.*$...**$
4 358 0 0 0
5 0 0 359 0
6 0 357 360 0
7 0 342 346 361
$$$$$$.....**$.....*$
4 0 0 363 0
5 0 0 0 364
6 0 0 0 365
7 0 0 366 0
$$$......*$.....*.*$....*..*$....*.*$.....*$
$..**$..*.*$...**$
4 0 368 0 369
5 370 0 0 0
6 0 371 0 0
4 0 0 0 228
5 0 19 0 373
6 0 0 0 374
7 372 0 0 375
8 338 362 367 376
$....**$....*.*$.....*.*$......*$
4 0 0 0 378
5 0 379 0 0
$..**$..*.*$...*.*$....*$
4 0 0 381 0
5 382 0 0 0
$$$$$$.......*$.......*$
4 384 97 0 215
5 0 385 0 0
6 380 383 0 386
7 0 0 366 387
4 0 0 18 0
5 0 0 389 0
....*.*$.....*.*$......*$
4 391 0 0 0
5 392 0 0 0
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At (176000, 218000) is a short stream of gliders, the very last contents of memory loop to be destroyed. At T=7,621,225,667 the last of those gliders will get eaten by an eater2 at (133000, 261090).

Don't Forget to Tell The Kids...
Completely independent of this cleanup operation, even though it looks related from a distance, a nearby high-period gun will shortly afterward (T=7,621,233,000) produce a glider at (131860, 260356). This glider will be routed through some one-time circuitry to produce a stream of eight output gliders representing the state of the parent metacell. The state in this case is 8-1 = 7.

If the metacell's state had been something different, then there would be some junk lying around to absorb some of those gliders, or maybe those gliders wouldn't have gotten created in the first place. (Details in some future exciting installment of 0E0P Metacells, Season One -- watch this space...)

The eight state gliders are duplicated, once in each center-edge mechanism of the parent metacell, and copies are sent outward to be caught and collected by the child metacells. Normally those gliders will only travel a short distance, because there's always a child center-edge mechanism waiting on the adjacent checkerboard square to catch them almost as soon as they're emitted. But that, too, is another story and will be told another time.

...And Then Comes Armageddon
The state-glider duplication and transmission is all done by T=7,623,050,000 or so. Meanwhile, the high-period gun is still counting powers of two. Nothing exciting happens for half a billion generations -- if generations were years, this would be like watching algal mats evolve on the early Earth.

At T=8,158,100,200, there's a glider at (131600, 260280) that is destined to make it out of the p256 gun and through all 21 of the period doublers in the chain to the southeast. It cleans up... some stuff. Must be some important stuff since it gets priority over the entire rest of the parent metacell.

Faster and Faster
For now, discovering the purpose of that Important Stuff is mostly left as an exercise for the enterprising reader. But one of those cleaned-up still lifes is an eater removed from an alternate gun output path, before the last four period doublers. The gun effectively just got sixteen times faster, so now we only have to wait 2^25 ticks for the next significant glider.

At T=8,191,654,632 that lucky glider starts its journey through the remaining 17 period doublers. It's a good time to set Golly's base step to 2 instead of the default 8 for HashLife, set the step size to 2^22, and start hitting the TAB key (and then Ctrl+Z if you want to go back and maybe zoom in or out and see more of the effects.)

TAB #1, to T=8,195,848,936: that glider activates the self-destruct sequence on three more period doublers. The gun has just gotten eight times faster again, so now a glider gets out every 2^22 ticks. Also, the output is now pointed at a row of ten one-time turners: nine boats, then a two-block 180-degree turner. Wonder what that last one does...

TAB #2, to T=8,200,043,240: self-destruct sequence activated for the four outermost period-doubling semi-Snarks in the original now-defunct p2^29 gun... plus one plain Snark that happened to be in the wrong place at the wrong time.

TAB #3, to T=8,204,237,544: a lot of circuitry to the east-southeast self-destructs.

TAB #4, to T=8,208,431,848: the splitter that was attached to the semi-Snarks from TAB #2 now gets cleaned up.

TAB #5, to T=8,212,626,152: four extra-dangerous still lifes get shot down. I'm guessing these might be some optional switching circuitry, since the central block and eater will still get shot down the same way even if the outer boat and block are missing. No idea what those might sometimes get used for, so that's another problem for The Enterprising Reader.

TAB #6, to T=8,216,820,456: a circuit to the south goes away. (I might edit in names for all these pieces later.)

TAB #7, to T=8,221,014,760: a bunch more circuitry to the southwest and farther south disappears.

TAB #8, to T=8,225,209,064: apparently a single lonely eater down in the southwest needs some extra care and attention -- it gets its own separate line in the cleanup microprogram.

TAB #9, to T=8,229,403,368: another unusually important eater, to the southeast this time, bites the dust.

TAB #10, to T=8,233,597,672: Golly needs a moment for this one, because almost the entire rest of the metacell self-destructs, including all the Snark chains in the central memory area. It takes over two million ticks for a signal glider to make the trip around the whole metacell clockwise, spreading destruction everywhere it goes. At T=8,231,470,096 the glider's rampage is finally stopped by a brave and lonely block back at (13601,260929), near where it all started. The gun has survived, and so has a mysterious constellation off to the northwest -- let's call it "Area 51". (Apparently the NE half is a merge circuit, and the SW half is a glider color corrector.)

TAB #11, to T=8,233,597,672: the final two-block 180-degree turner has its fun, destroys the gun and Area 51. We're finally done.

(The gun actually orchestrates its own disappearance in several more stages, with a final burst of activity at T=8,234,403,560. This narration seemed more than long enough already so I'm skipping those details.)

Posted: **May 8th, 2019, 5:20 pm**

Despite not having StreamLife myself, I was able to run the self-destruct process to its conclusion. A shame there's no way to have Golly track the glider causing that massive swathe of destruction for me, it would have been interesting to track exactly how it destroys everything so cleanly.

Would I be correct in guessing that the white section of the cell's interior (in the first screenshot) is the part of the tape being actively read? I assume something's being coded there and in the gaps between the gliders.

Posted: **May 9th, 2019, 5:41 pm**

Ch91 wrote:Despite not having StreamLife myself, I was able to run the self-destruct process to its conclusion. A shame there's no way to have Golly track the glider causing that massive swathe of destruction for me, it would have been interesting to track exactly how it destroys everything so cleanly.

If you change the HashLife step size from 8 to 2, skip ahead (maybe using goto.lua) to T=8229403368, and hit Ctrl+H to switch the pattern over to LifeHistory, you can run the pattern starting at a step size around 2^4, zoomed in to the south corner. Hit [Enter] to start running, and [Enter] every now and then to give Golly a stopping point that you can undo back to if necessary.

When the glider heads off to the northeast, zoom out and hit + to speed up the simulation until you can see the growing glider track coming from the south corner. Whenever the track gets close to a new piece of mechanism, hit [Enter], maybe [Tab] to get the glider as close as possible and Ctrl+Z to undo if you overshoot, and then zoom in and hit the - key enough times to slow down the simulation to something watchable.

Run and undo multiple times until you've seen all the action, then hit + to speed things up again to get to the next piece of self-destructing circuitry that you want to watch. It's a little annoying that the blue background states in LifeHistory turn green when you zoom out too far, so you can't see anything... but really that's just a sign that you're too far out to see all of the details anyway.

Ch91 wrote:Would I be correct in guessing that the white section of the cell's interior (in the first screenshot) is the part of the tape being actively read? I assume something's being coded there and in the gaps between the gliders.

Yes, the white region contains, mostly, the single-channel recipe to construct the entire 0E0P metacell. There's also a state lookup table that tells the metacell what its output state should be, given the incoming state signals from its four neighbors.

All that data just cycles around and around in that memory area until the clock in the south corner executes some piece of microprogram that opens switches to let copies of at data out to do construction tasks, or to replicate the data into each constructed child metacell.

Posted: **May 10th, 2019, 11:17 pm**

I'm a bit embarrassed to admit that I didn't even realize the lifehistory conversion script existed until you pointed it out to me.

dvgrn wrote: Yes, the white region contains, mostly, the single-channel recipe to construct the entire 0E0P metacell. There's also a state lookup table that tells the metacell what its output state should be, given the incoming state signals from its four neighbors.

All that data just cycles around and around in that memory area until the clock in the south corner executes some piece of microprogram that opens switches to let copies of at data out to do construction tasks, or to replicate the data into each constructed child metacell.

Admittedly, I had mistakenly thought single-channel constructors would have been less massive in size- but that probably says more about my lack of expertise in the matter than anything else. I did get the feeling the section in the south was important, but I wouldn't have guessed it was a clock. Now that I think of it, the article on the syringe mentioned that a modified variant of it was used in the metacell; I couldn't see any in the self-destruct process though, so I assume it was removed at a prior step (either that, or it's not using the eater2-eater5 weld still life normally used in the syringe).

Posted: **May 11th, 2019, 9:41 am**

Ch91 wrote:I'm a bit embarrassed to admit that I didn't even realize the lifehistory conversion script existed until you pointed it out to me.

Alt+H for moving to LifeHistory, and Alt+J for moving back again, are relatively new additions to Golly, and they're not advertised particularly well. They probably ought to get mentioned in more places in the Help, and wherever they're relevant in tutorials on the LifeWiki and so on. Suggestions welcome.

Ch91 wrote:Admittedly, I had mistakenly thought single-channel constructors would have been less massive in size- but that probably says more about my lack of expertise in the matter than anything else...

The 0E0P is really a highly unusual project -- the most ambitiously huge construction Conway's Life has ever seen, by a fairly wide margin. Granted, the Caterpillar is a bit bigger in one dimension, but its population is much lower and its mechanisms are much simpler to explain and understand in detail.

The construction method calcyman generally follows can be summarized as "The Best Is The Enemy of the Good", or "Get It Done!". So the 0E0P metacell is full of mechanisms that could be reworked to make them cheaper to construct, or faster to execute -- but stopping to optimize every detail would have prevented the project from ever being completed at all. As a result, the construction recipe is much longer than it theoretically needs to be.

Ch91 wrote:Now that I think of it, the article on the syringe mentioned that a modified variant of it was used in the metacell; I couldn't see any in the self-destruct process though, so I assume it was removed at a prior step (either that, or it's not using the eater2-eater5 weld still life normally used in the syringe).

Those modified syringes are actually all over the place in the metacell, used whenever one glider signal has to be reflected, converted into two signals, etc. If the G-to-H stage is followed by a dependent conduit, you don't need to weld the eater5 stage onto the eater2. Here's a sample of the variant in question, from "Area 51":

Code: Select all

x = 184, y = 144, rule = LifeHistory
120.A$118.3A$117.A$107.2A8.2A$108.A5.5B$76.2A11.A18.A.AB.4B$75.B2AB9.
A.A18.2AB.6B4.B$76.3B9.A.A20.10B.B2A$75.B.B9.2A.3A2.2A14.12B2A$75.5B
8.B4.A2.A14.11B.B$75.6B6.2AB3A3.A.AB2.4B3.13B$75.8B4.2A.A6.2AB2.5B2.
12B.2B$76.13B10.24B2A$74.13B12.24B2A7.2A$73.15B12.20B.B.B8.A$73.15B
10.B2.20B8.BA.A$72.17B.B5.26B7.B2A$72.51B4.3B$71.13B2A13B2A21B4.4B$
70.14B2A13B2A21B3.4B$69.2AB3.46B3.4B$68.A2.A4.45B2.4B$67.A.2A5.6B3.B
2.2B2.29B.4B$67.A7.6B13.4B2.7B.17B$66.2A6.9B17.6B2.16B$73.4B4.2A19.3B
3.10B.4B$72.4B5.A21.B4.14B$71.4B7.3A24.12B$70.4B10.A24.11B$69.4B36.
11B$68.4B38.9B$67.4B39.9B$66.4B35.2A3.9B$65.4B37.A3.9B$64.4B38.A.A9B$
63.4B40.2A2.6B$62.4B45.6B$61.4B46.7B$60.4B47.8B2.2A$59.4B46.12BA.A$
58.4B47.11B3.A$57.4B48.5B2A4B3.2A$56.4B49.5B2A3B$55.4B50.10B$54.4B51.
9B$53.4B52.9B$52.4B54.8B$51.4B54.8B$50.4B56.6B$49.4B51.2A4.6B$48.4B
53.A4.6B$47.4B54.A.AB.7B$46.4B56.2AB2.6B$45.4B59.8B$44.4B60.8B43.A$
43.4B62.8B41.A.A$42.4B64.7B8.A32.BA2B2.2A$41.4B66.6B6.3A33.2B3.2A$40.
4B67.7B4.A34.3B$39.4B68.7B4.2A20.A12.4B3.4A$38.4B69.8B.4B4.A15.3A10.
5B.BA2.A$37.4B70.11B4.3A18.A6.8B.B.2B$36.4B71.12B2.A20.2A3.B.8B2.3B$
35.4B72.12B2.2A19.22B$34.4B74.11B3.B21.20B$33.4B78.7B4.3B19.19B2A$32.
4B78.8B3.6B16.20B2A$31.4B78.9B2.10B11.21B.B$30.4B78.23B3.2B2.24B$29.
4B77.B.16B2A30B3.4B$28.4B77.2A17B2A22B.6B5.4B$27.4B78.2A41B2.B.5B4.4B
$26.4B80.42B7.2A5.4B$25.4B42.2A35.5B2.36B8.A7.4B$24.4B43.A36.2A6.5B5.
13B.4B16.3A5.4B$23.4B41.BA.A37.A7.2B.3B3.7B.B4.4B19.A6.4B$22.4B42.B2A
35.3A12.2A16.3B28.4B$21.4B41.3B37.A14.A15.4B30.4B$20.4B41.4B53.3A12.
2A33.4B$19.4B41.4B56.A13.A34.4B$5.A12.4B41.4B68.3A36.4B$5.3A9.4B41.4B
69.A39.4B$8.A7.4B41.4B111.4B$7.2A6.4B41.4B113.4B$7.5B2.4B6.2A33.4B
115.4B$9.8B7.A15.A17.4B6.2A3.2A104.4B$8.8B5.BA.A15.3A14.4B6.B2AB.B2AB
104.4B$7.8B2.3B.B2A19.A12.4B4.B3.3B2.2B$6.16B20.2A11.4B3.4B.3B.3B$4.
18B20.B11.13B.7B5.2A$4.17B19.3B9.23B5.A$2.2AB.16B16.6B4.8B.19B.BA.A$.
A.AB2.17B11.10B2.29B.B2A$.A5.20B2.2B3.44B$2A6.31B2A37B$9.7B.22B2A37B$
9.6B2.60B$8.6B3.58B$8.4B6.59B$8.2B2AB12.4B.13B4.25B3.2A$6.2AB.2A14.3B
5.B.7B4.B4.20B3.A$5.A.AB18.4B15.2A7.15B6.3A$5.A23.2A15.A12.11B8.A$4.
2A23.A17.3A8.13B$30.3A16.A7.15B$32.A23.16B$55.17B$56.16B$57.13B$57.5B
2A2B.3B$59.3B2A2B2.4B$59.8B3.2A$58.8B4.A$58.8B5.3A$58.7B8.A$58.7B$59.
6B7.A$59.6B6.A.A$60.5B6.A.A$60.6B4.2A.3A$59.6B6.B4.A$59.7B3.B2AB3A$
60.8B.B2A.A$60.10B$59.3B2A6B$53.2A5.2B2A6B$54.A5.10B$54.A.AB2.11B$55.
2AB.12B$57.15B$57.16B$57.16B.2B$57.18B2A$56.17B.B2A$55.4B2.8B.4B.B$
54.4B4.7B$53.4B5.6B$52.4B6.4B$51.4B5.A3B$50.4B5.A.AB$49.4B6.A.A$48.2A
2B8.A$47.A.AB6.3A$49.A7.A!

Posted: **May 13th, 2019, 10:18 pm**

dvgrn wrote: Alt+H for moving to LifeHistory, and Alt+J for moving back again, are relatively new additions to Golly, and they're not advertised particularly well. They probably ought to get mentioned in more places in the Help, and wherever they're relevant in tutorials on the LifeWiki and so on. Suggestions welcome.

I'll go and add that to the LifeWiki tutorial now, not sure why it wasn't already there.

dvgrn1 wrote: Those modified syringes are actually all over the place in the metacell, used whenever one glider signal has to be reflected, converted into two signals, etc. If the G-to-H stage is followed by a dependent conduit, you don't need to weld the eater5 stage onto the eater2.

I had noticed a few of those, but didn't recognize them for what they were. That explains why they seemed to be so common.

Posted: **May 21st, 2019, 3:34 pm**

I'm still very slowly documenting 0E0P construction and destruction stages. Meanwhile, here's a note from calcyman pointing out an interesting detail I didn't include in my 0E0P self-destruct summary:

calcyman wrote:One possibly-notable detail that was missing happens around generation 8 216 830 000: an ostentatious salvo of three southbound MWSSes are produced to clean up a single Snark.

This is the uppermost of a vertical line of 6 equally-spaced Snarks on the south corner of the metacell. However, note that as much as this Snark pretends to be like the others, it is a very different animal: the other three corners of the metacell each have a line of only 5 equally-spaced Snarks, and it's those five that are deleted.

This mysterious extra Snark therefore has to be deleted using asymmetric circuitry, and asymmetric circuitry is only allowed to be in the kernel of the metacell -- which is why the cleanup has no choice but to fire it down using long-range orthogonal spaceships.

The creation of the mysterious extra Snark is equally as unique as its destruction: rather than being built by slmake with the other surrounding circuitry, it's actually created using the Snarkmaker recipe. Its purpose, along with any connections to the mysterious Area 51, is left as an exercise to the reader.

So... are there in fact any readers out there that want some exercise? It turns out that the Mysterious Snark does connect, with a long delay mechanism, to Area 51. Area 51 is a simple merge circuit for the memory loop, sneakily set up between glider lanes in the middle of one edge of the big diamond, so that it doesn't require any customization to the Snark chains (since those are built by re-running the same recipes many times, to save space in the construction recipe).

Finding the connection to Area 51 is a fairly easy tracking job. However, that connection was only active during an earlier stage of the metacell's activity, and a key piece of it (first block in a syringe) at (132132, 262000) has gotten disabled by the time of the T = 7621050368 pattern.

The block is not there at T = 7515406336 in rrocell_backup128756.mc.gz either. It doesn't seem very easy to pinpoint when the disabling operation happened. I haven't done any further hunting yet, but I'm guessing there's a micro-instruction that knocks out the block in that syringe at some point.

If anyone wants access to more of the 563 snapshots, let me know. Looks like I could get half of them on Dropbox, at least, and that would include the majority of the interesting ones.

Posted: **May 26th, 2019, 4:01 pm**

dvgrn wrote:It turns out that the Mysterious Snark does connect, with a long delay mechanism, to Area 51...

Speaking of the Mysterious Snark:

Thanks to Chris Rowett's continuing incredible work on LifeViewer, the scripting system now has a way to support fairly large single-channel recipes, even if they're larger than LifeViewer's boundaries. Gliders (or whatever) can be pasted in at the correct intervals to simulate a long single-channel recipe in a small space:

Code: Select all

x = 65798, y = 65794, rule = B3/S23

2o2b2o$2o2bobo$4bo25$32bo$31b2o$31bobo21$54b2o$54bobo$54bo21$78bo$77b

2o$77bobo21$100b2o$99b2o$101bo31$133b2o$132b2o$134bo27$161b3o$161bo$

162bo29$194bo$193b2o$193bobo21$216b2o$216bobo$216bo21$238b3o$238bo$

239bo20$262bo$261b2o$261bobo22$285b2o$285bobo$285bo21$307b3o$307bo$

308bo26$336b2o$336bobo$336bo39$376b3o$376bo$377bo56$435b2o$434b2o$436b

o38$474b3o$474bo$475bo20$497b2o$497bobo$497bo37$536b2o$535b2o$537bo29$

568bo$567b2o$567bobo22$590b3o$590bo$591bo27$620b2o$620bobo$620bo21$

642b3o$642bo$643bo20$666bo$665b2o$665bobo21$688b2o$687b2o$689bo276$

967bo$966b2o$966bobo26$993b3o$993bo$994bo20$1017bo$1016b2o$1016bobo22$

1040b2o$1039b2o$1041bo21$1062b3o$1062bo$1063bo20$1086bo$1085b2o$1085bo

bo21$1109bo$1108b2o$1108bobo21$1131b2o$1130b2o$1132bo40$1173b2o$1173bo

bo$1173bo21$1196b2o$1195b2o$1197bo20$1219bo$1218b2o$1218bobo27$1248bo$

1247b2o$1247bobo21$1270b2o$1269b2o$1271bo26$1298b2o$1298bobo$1298bo

277$1576b3o$1576bo$1577bo25$1604b2o$1603b2o$1605bo21$1626b3o$1626bo$

1627bo21$1650b2o$1649b2o$1651bo21$1672b3o$1672bo$1673bo37$1711b3o$

1711bo$1712bo20$1735bo$1734b2o$1734bobo21$1757b2o$1757bobo$1757bo22$

1780b3o$1780bo$1781bo20$1803b2o$1803bobo$1803bo21$1826b2o$1825b2o$

1827bo33$1861b2o$1860b2o$1862bo21$1883b3o$1883bo$1884bo23$1910bo$1909b

2o$1909bobo21$1932b2o$1932bobo$1932bo21$1955b2o$1954b2o$1956bo31$1988b

2o$1987b2o$1989bo276$2267bo$2266b2o$2266bobo26$2293b3o$2293bo$2294bo

20$2316b2o$2316bobo$2316bo21$2340bo$2339b2o$2339bobo21$2362b2o$2362bob

o$2362bo21$2385b2o$2384b2o$2386bo20$2408bo$2407b2o$2407bobo21$2430b2o$

2429b2o$2431bo23$2455b2o$2454b2o$2456bo20$2478bo$2477b2o$2477bobo21$

2500b2o$2499b2o$2501bo34$2537bo$2536b2o$2536bobo22$2561bo$2560b2o$

2560bobo21$2583b2o$2582b2o$2584bo20$2606bo$2605b2o$2605bobo21$2628b2o$

2627b2o$2629bo21$2651b2o$2650b2o$2652bo37$2690b2o$2689b2o$2691bo34$

2726b2o$2725b2o$2727bo276$3005bo$3004b2o$3004bobo26$3031b3o$3031bo$

3032bo20$3055bo$3054b2o$3054bobo22$3077b3o$3077bo$3078bo20$3101bo$

3100b2o$3100bobo31$3134bo$3133b2o$3133bobo27$3162b2o$3162bobo$3162bo

24$3187b3o$3187bo$3188bo20$3210b2o$3210bobo$3210bo21$3233b2o$3232b2o$

3234bo21$3255b3o$3255bo$3256bo20$3279bo$3278b2o$3278bobo21$3301b2o$

3300b2o$3302bo20$3324bo$3323b2o$3323bobo37$3362b2o$3361b2o$3363bo278$

3643bo$3642b2o$3642bobo22$3665b3o$3665bo$3666bo20$3689bo$3688b2o$3688b

obo28$3718b2o$3717b2o$3719bo21$3740b3o$3740bo$3741bo35$3779bo$3778b2o$

3778bobo21$3801b2o$3800b2o$3802bo38$3840b3o$3840bo$3841bo20$3864bo$

3863b2o$3863bobo21$3887bo$3886b2o$3886bobo21$3909b2o$3908b2o$3910bo32$

3943b2o$3942b2o$3944bo20$3966bo$3965b2o$3965bobo21$3988b2o$3987b2o$

3989bo36$4027bo$4026b2o$4026bobo21$4049b2o$4048b2o$4050bo23$4074b2o$

4074bobo$4074bo24$4100b2o$4100bobo$4100bo39$4142bo$4141b2o$4141bobo31$

4173b3o$4173bo$4174bo20$4197bo$4196b2o$4196bobo26$4223b3o$4223bo$4224b

o20$4247bo$4246b2o$4246bobo22$4269b3o$4269bo$4270bo20$4293bo$4292b2o$

4292bobo23$4316b3o$4316bo$4317bo20$4339b2o$4339bobo$4339bo21$4362b2o$

4361b2o$4363bo26$4389b3o$4389bo$4390bo20$4413bo$4412b2o$4412bobo27$

4442bo$4441b2o$4441bobo21$4464b2o$4464bobo$4464bo22$4487b3o$4487bo$

4488bo80$4570b2o$4570bobo$4570bo21$4593b2o$4592b2o$4594bo20$4616bo$

4615b2o$4615bobo22$4639b2o$4639bobo$4639bo21$4662b2o$4661b2o$4663bo20$

4685bo$4684b2o$4684bobo21$4707b2o$4706b2o$4708bo21$4729b3o$4729bo$

4730bo28$4761bo$4760b2o$4760bobo21$4783b2o$4782b2o$4784bo21$4805b3o$

4805bo$4806bo36$4843b3o$4843bo$4844bo20$4866b2o$4866bobo$4866bo21$

4888b3o$4888bo$4889bo21$4912b2o$4911b2o$4913bo21$4934b3o$4934bo$4935bo

27$4963b3o$4963bo$4964bo20$4987bo$4986b2o$4986bobo31$5019b2o$5019bobo$

5019bo21$5042b2o$5041b2o$5043bo22$5065b3o$5065bo$5066bo45$5112b3o$

5112bo$5113bo26$5141b2o$5140b2o$5142bo21$5163b3o$5163bo$5164bo20$5187b

o$5186b2o$5186bobo35$5223b2o$5223bobo$5223bo29$5253b3o$5253bo$5254bo

20$5277bo$5276b2o$5276bobo42$5319b3o$5319bo$5320bo20$5343bo$5342b2o$

5342bobo21$5365b2o$5365bobo$5365bo31$5399bo$5398b2o$5398bobo60$5460b2o

$5460bobo$5460bo21$5483b2o$5483bobo$5483bo21$5505b3o$5505bo$5506bo25$

5533b2o$5532b2o$5534bo21$5555b3o$5555bo$5556bo21$5579b2o$5578b2o$5580b

o21$5601b3o$5601bo$5602bo30$5634b2o$5633b2o$5635bo35$5671b2o$5670b2o$

5672bo21$5693b3o$5693bo$5694bo21$5717b2o$5716b2o$5718bo36$5756bo$5755b

2o$5755bobo21$5778b2o$5777b2o$5779bo31$5812bo$5811b2o$5811bobo21$5834b

2o$5834bobo$5834bo21$5857b2o$5856b2o$5858bo20$5880bo$5879b2o$5879bobo

21$5902b2o$5902bobo$5902bo21$5925b2o$5924b2o$5926bo26$5952b3o$5952bo$

5953bo20$5976bo$5975b2o$5975bobo21$5998b2o$5998bobo$5998bo21$6021b2o$

6020b2o$6022bo21$6043b3o$6043bo$6044bo20$6067bo$6066b2o$6066bobo26$

6093b3o$6093bo$6094bo20$6116b2o$6116bobo$6116bo21$6140bo$6139b2o$6139b

obo21$6162b2o$6162bobo$6162bo21$6185b2o$6184b2o$6186bo37$6225bo$6224b

2o$6224bobo22$6248b2o$6247b2o$6249bo26$6276b2o$6276bobo$6276bo21$6299b

2o$6298b2o$6300bo20$6322bo$6321b2o$6321bobo21$6344b2o$6344bobo$6344bo

22$6368b2o$6368bobo$6368bo21$6390b3o$6390bo$6391bo33$6426b2o$6426bobo$

6426bo21$6449b2o$6448b2o$6450bo25$6476b2o$6476bobo$6476bo21$6499b2o$

6498b2o$6500bo21$6523bo$6522b2o$6522bobo21$6545b2o$6545bobo$6545bo21$

6568b2o$6567b2o$6569bo43$6612b3o$6612bo$6613bo20$6636bo$6635b2o$6635bo

bo21$6658b2o$6657b2o$6659bo21$6682bo$6681b2o$6681bobo21$6704b2o$6704bo

bo$6704bo27$6732b3o$6732bo$6733bo20$6755b2o$6755bobo$6755bo40$6796b3o$

6796bo$6797bo20$6819b2o$6819bobo$6819bo21$6841b3o$6841bo$6842bo20$

6864b2o$6864bobo$6864bo21$6887b2o$6886b2o$6888bo27$6916b2o$6916bobo$

6916bo21$6938b3o$6938bo$6939bo22$6962b3o$6962bo$6963bo20$6985b2o$6985b

obo$6985bo21$7007b3o$7007bo$7008bo21$7032bo$7031b2o$7031bobo21$7054b2o

$7054bobo$7054bo21$7077b2o$7076b2o$7078bo25$7104b2o$7104bobo$7104bo21$

7127b2o$7126b2o$7128bo21$7150b2o$7150bobo$7150bo21$7172b3o$7172bo$

7173bo37$7211b3o$7211bo$7212bo20$7235bo$7234b2o$7234bobo21$7257b2o$

7257bobo$7257bo22$7280b3o$7280bo$7281bo20$7304bo$7303b2o$7303bobo21$

7326b2o$7325b2o$7327bo35$7362b3o$7362bo$7363bo27$7392b2o$7391b2o$7393b

o21$7414b3o$7414bo$7415bo34$7450b3o$7450bo$7451bo20$7473b2o$7473bobo$

7473bo21$7496b2o$7495b2o$7497bo30$7528b2o$7527b2o$7529bo23$7553b2o$

7552b2o$7554bo21$7575b3o$7575bo$7576bo20$7598b2o$7598bobo$7598bo24$

7625bo$7624b2o$7624bobo21$7647b2o$7647bobo$7647bo21$7670b2o$7669b2o$

7671bo25$7697b2o$7697bobo$7697bo21$7720b2o$7719b2o$7721bo21$7744bo$

7743b2o$7743bobo21$7766b2o$7766bobo$7766bo21$7789b2o$7788b2o$7790bo29$

7820b2o$7819b2o$7821bo21$7842b3o$7842bo$7843bo24$7869b2o$7868b2o$7870b

o20$7892bo$7891b2o$7891bobo41$7933b3o$7933bo$7934bo20$7957bo$7956b2o$

7956bobo21$7979b2o$7978b2o$7980bo27$8008b2o$8007b2o$8009bo21$8030b3o$

8030bo$8031bo33$8066b2o$8066bobo$8066bo21$8088b3o$8088bo$8089bo20$

8111b2o$8111bobo$8111bo21$8134b2o$8133b2o$8135bo25$8161b2o$8161bobo$

8161bo21$8184b2o$8183b2o$8185bo21$8207b2o$8207bobo$8207bo21$8230b2o$

8229b2o$8231bo21$8253b2o$8252b2o$8254bo21$8275b3o$8275bo$8276bo20$

8298b2o$8298bobo$8298bo21$8320b3o$8320bo$8321bo21$8345bo$8344b2o$8344b

obo24$8370b2o$8369b2o$8371bo21$8392b3o$8392bo$8393bo20$8416bo$8415b2o$

8415bobo21$8438b2o$8438bobo$8438bo31$8470b3o$8470bo$8471bo20$8494bo$

8493b2o$8493bobo21$8516b2o$8515b2o$8517bo32$8550b2o$8549b2o$8551bo21$

8572b3o$8572bo$8573bo20$8596bo$8595b2o$8595bobo28$8625b2o$8625bobo$

8625bo26$8654bo$8653b2o$8653bobo21$8676b2o$8675b2o$8677bo21$8698b3o$

8698bo$8699bo26$8727b2o$8727bobo$8727bo21$8749b3o$8749bo$8750bo25$

8777b2o$8776b2o$8778bo21$8799b3o$8799bo$8800bo21$8823b2o$8823bobo$

8823bo21$8846b2o$8845b2o$8847bo21$8868b3o$8868bo$8869bo42$8914bo$8913b

2o$8913bobo21$8936b2o$8936bobo$8936bo21$8958b3o$8958bo$8959bo21$8982b

2o$8982bobo$8982bo21$9005b2o$9004b2o$9006bo23$9031bo$9030b2o$9030bobo

21$9053b2o$9053bobo$9053bo36$9091b2o$9090b2o$9092bo20$9114bo$9113b2o$

9113bobo21$9136b2o$9135b2o$9137bo23$9161b2o$9161bobo$9161bo21$9183b3o$

9183bo$9184bo20$9207bo$9206b2o$9206bobo30$9237b3o$9237bo$9238bo44$

9283b3o$9283bo$9284bo20$9306b2o$9306bobo$9306bo21$9328b3o$9328bo$9329b

o20$9351b2o$9351bobo$9351bo25$9379bo$9378b2o$9378bobo21$9401b2o$9401bo

bo$9401bo22$9424b3o$9424bo$9425bo20$9448bo$9447b2o$9447bobo21$9470b2o$

9470bobo$9470bo43$9515b2o$9514b2o$9516bo21$9537b3o$9537bo$9538bo20$

9560b2o$9560bobo$9560bo22$9583b3o$9583bo$9584bo20$9607bo$9606b2o$9606b

obo24$9632b2o$9631b2o$9633bo21$9654b3o$9654bo$9655bo35$9693bo$9692b2o$

9692bobo21$9715b2o$9714b2o$9716bo20$9738bo$9737b2o$9737bobo24$9762b3o$

9762bo$9763bo20$9785b2o$9785bobo$9785bo21$9808b2o$9807b2o$9809bo29$

9839b2o$9839bobo$9839bo44$9885b2o$9885bobo$9885bo21$9907b3o$9907bo$

9908bo20$9930b2o$9930bobo$9930bo21$9952b3o$9952bo$9953bo25$9980b2o$

9979b2o$9981bo21$10002b3o$10002bo$10003bo21$10026b2o$10025b2o$10027bo

20$10049bo$10048b2o$10048bobo33$10084bo$10083b2o$10083bobo36$10121b2o$

10120b2o$10122bo31$10154b2o$10153b2o$10155bo51$10207b2o$10206b2o$

10208bo24$10232b3o$10232bo$10233bo20$10255b2o$10255bobo$10255bo23$

10279b3o$10279bo$10280bo20$10302b2o$10302bobo$10302bo35$10339b2o$

10339bobo$10339bo21$10361b3o$10361bo$10362bo20$10384b2o$10384bobo$

10384bo21$10407b2o$10406b2o$10408bo21$10429b3o$10429bo$10430bo20$

10453bo$10452b2o$10452bobo28$10482b2o$10482bobo$10482bo23$10508bo$

10507b2o$10507bobo25$10535bo$10534b2o$10534bobo21$10557b2o$10556b2o$

10558bo21$10579b3o$10579bo$10580bo20$10603bo$10602b2o$10602bobo28$

10632b2o$10632bobo$10632bo21$10654b3o$10654bo$10655bo25$10682b2o$

10681b2o$10683bo21$10704b3o$10704bo$10705bo21$10728b2o$10728bobo$

10728bo21$10751b2o$10750b2o$10752bo20$10774bo$10773b2o$10773bobo23$

10798b2o$10798bobo$10798bo21$10820b3o$10820bo$10821bo26$10848b3o$

10848bo$10849bo20$10871b2o$10871bobo$10871bo21$10894b2o$10893b2o$

10895bo24$10920b2o$10920bobo$10920bo21$10942b3o$10942bo$10943bo28$

10973b2o$10972b2o$10974bo27$11003bo$11002b2o$11002bobo24$11028b2o$

11028bobo$11028bo21$11050b3o$11050bo$11051bo34$11086b3o$11086bo$11087b

o27$11116b2o$11115b2o$11117bo22$11139b3o$11139bo$11140bo20$11163bo$

11162b2o$11162bobo26$11189b3o$11189bo$11190bo20$11213bo$11212b2o$

11212bobo22$11235b3o$11235bo$11236bo20$11259bo$11258b2o$11258bobo21$

11282bo$11281b2o$11281bobo21$11304b2o$11304bobo$11304bo21$11326b3o$

11326bo$11327bo20$11349b2o$11349bobo$11349bo22$11373b2o$11372b2o$

11374bo23$11399bo$11398b2o$11398bobo21$11421b2o$11421bobo$11421bo21$

11444b2o$11443b2o$11445bo21$11466b3o$11466bo$11467bo30$11499b2o$11499b

obo$11499bo21$11522b2o$11521b2o$11523bo20$11545bo$11544b2o$11544bobo

32$11579bo$11578b2o$11578bobo21$11601b2o$11601bobo$11601bo21$11624b2o$

11623b2o$11625bo28$11653b3o$11653bo$11654bo26$11682b2o$11681b2o$11683b

o20$11705bo$11704b2o$11704bobo21$11727b2o$11727bobo$11727bo27$11755b3o

$11755bo$11756bo20$11779bo$11778b2o$11778bobo26$11805b3o$11805bo$

11806bo20$11828b2o$11828bobo$11828bo21$11852bo$11851b2o$11851bobo21$

11874b2o$11874bobo$11874bo21$11897b2o$11896b2o$11898bo43$11942b2o$

11942bobo$11942bo21$11964b3o$11964bo$11965bo21$11989bo$11988b2o$11988b

obo26$12016b2o$12015b2o$12017bo26$12045bo$12044b2o$12044bobo23$12070bo

$12069b2o$12069bobo38$12110bo$12109b2o$12109bobo21$12132b2o$12131b2o$

12133bo34$12167b3o$12167bo$12168bo20$12191bo$12190b2o$12190bobo28$

12220b2o$12220bobo$12220bo21$12242b3o$12242bo$12243bo24$12269b2o$

12269bobo$12269bo30$12302bo$12301b2o$12301bobo26$12328b3o$12328bo$

12329bo20$12352bo$12351b2o$12351bobo22$12374b3o$12374bo$12375bo20$

12398bo$12397b2o$12397bobo21$12421bo$12420b2o$12420bobo21$12443b2o$

12443bobo$12443bo21$12465b3o$12465bo$12466bo20$12488b2o$12488bobo$

12488bo39$12528b3o$12528bo$12529bo20$12552bo$12551b2o$12551bobo21$

12574b2o$12574bobo$12574bo21$12596b3o$12596bo$12597bo30$12629b2o$

12628b2o$12630bo21$12651b3o$12651bo$12652bo26$12680b2o$12679b2o$12681b

o20$12703bo$12702b2o$12702bobo21$12725b2o$12724b2o$12726bo20$12748bo$

12747b2o$12747bobo21$12770b2o$12769b2o$12771bo25$12797b2o$12797bobo$

12797bo21$12820b2o$12819b2o$12821bo21$12843b2o$12843bobo$12843bo21$

12865b3o$12865bo$12866bo33$12900b3o$12900bo$12901bo35$12938b2o$12938bo

bo$12938bo34$12973b3o$12973bo$12974bo20$12997bo$12996b2o$12996bobo21$

13019b2o$13018b2o$13020bo26$13046b3o$13046bo$13047bo20$13070bo$13069b

2o$13069bobo21$13092b2o$13092bobo$13092bo46$13141bo$13140b2o$13140bobo

23$13164b3o$13164bo$13165bo20$13188bo$13187b2o$13187bobo21$13210b2o$

13210bobo$13210bo37$13249b2o$13248b2o$13250bo20$13272bo$13271b2o$

13271bobo23$13296b2o$13295b2o$13297bo20$13319bo$13318b2o$13318bobo21$

13341b2o$13341bobo$13341bo21$13365bo$13364b2o$13364bobo21$13387b2o$

13387bobo$13387bo36$13425b2o$13424b2o$13426bo20$13448bo$13447b2o$

13447bobo33$13482b2o$13482bobo$13482bo43$13527b2o$13527bobo$13527bo24$

13553b2o$13552b2o$13554bo27$13581b3o$13581bo$13582bo39$13624bo$13623b

2o$13623bobo21$13646b2o$13646bobo$13646bo28$13676b2o$13676bobo$13676bo

33$13711b2o$13710b2o$13712bo32$13744b3o$13744bo$13745bo20$13768bo$

13767b2o$13767bobo21$13790b2o$13790bobo$13790bo41$13832b3o$13832bo$

13833bo25$13860b2o$13859b2o$13861bo21$13882b3o$13882bo$13883bo21$

13906b2o$13905b2o$13907bo20$13929bo$13928b2o$13928bobo37$13967b2o$

13967bobo$13967bo25$13993b3o$13993bo$13994bo20$14017bo$14016b2o$14016b

obo29$14046b3o$14046bo$14047bo20$14069b2o$14069bobo$14069bo21$14091b3o

$14091bo$14092bo20$14115bo$14114b2o$14114bobo33$14148b3o$14148bo$

14149bo20$14171b2o$14171bobo$14171bo56$14229b2o$14229bobo$14229bo21$

14251b3o$14251bo$14252bo20$14275bo$14274b2o$14274bobo21$14297b2o$

14297bobo$14297bo22$14320b3o$14320bo$14321bo20$14343b2o$14343bobo$

14343bo41$14386b2o$14385b2o$14387bo20$14409bo$14408b2o$14408bobo21$

14431b2o$14431bobo$14431bo24$14457b2o$14456b2o$14458bo23$14483bo$

14482b2o$14482bobo26$14509b3o$14509bo$14510bo20$14533bo$14532b2o$

14532bobo22$14555b3o$14555bo$14556bo20$14579bo$14578b2o$14578bobo33$

14612b3o$14612bo$14613bo20$14635b2o$14635bobo$14635bo40$14676b3o$

14676bo$14677bo20$14700bo$14699b2o$14699bobo24$14725b2o$14724b2o$

14726bo20$14748bo$14747b2o$14747bobo24$14774bo$14773b2o$14773bobo21$

14796b2o$14796bobo$14796bo22$14820b2o$14820bobo$14820bo22$14844b2o$

14844bobo$14844bo21$14867b2o$14866b2o$14868bo20$14890bo$14889b2o$

14889bobo21$14912b2o$14911b2o$14913bo20$14935bo$14934b2o$14934bobo40$

14976b2o$14975b2o$14977bo20$14999bo$14998b2o$14998bobo21$15021b2o$

15020b2o$15022bo21$15044b2o$15044bobo$15044bo21$15066b3o$15066bo$

15067bo20$15090bo$15089b2o$15089bobo26$15116b3o$15116bo$15117bo20$

15140bo$15139b2o$15139bobo22$15163b2o$15162b2o$15164bo21$15185b3o$

15185bo$15186bo20$15209bo$15208b2o$15208bobo29$15240bo$15239b2o$15239b

obo21$15262b2o$15262bobo$15262bo24$15289bo$15288b2o$15288bobo21$15311b

2o$15311bobo$15311bo28$15341b2o$15340b2o$15342bo21$15363b3o$15363bo$

15364bo31$15396b3o$15396bo$15397bo22$15422bo$15421b2o$15421bobo21$

15444b2o$15443b2o$15445bo20$15467bo$15466b2o$15466bobo21$15489b2o$

15488b2o$15490bo35$15527bo$15526b2o$15526bobo38$15567bo$15566b2o$

15566bobo27$15596bo$15595b2o$15595bobo21$15618b2o$15618bobo$15618bo21$

15641b2o$15640b2o$15642bo21$15663b3o$15663bo$15664bo20$15686b2o$15686b

obo$15686bo22$15710b2o$15710bobo$15710bo21$15732b3o$15732bo$15733bo20$

15755b2o$15755bobo$15755bo25$15783bo$15782b2o$15782bobo21$15805b2o$

15805bobo$15805bo21$15829bo$15828b2o$15828bobo21$15851b2o$15850b2o$

15852bo41$15893b3o$15893bo$15894bo20$15916b2o$15916bobo$15916bo21$

15938b3o$15938bo$15939bo20$15962bo$15961b2o$15961bobo21$15984b2o$

15983b2o$15985bo21$16006b3o$16006bo$16007bo20$16029b2o$16029bobo$

16029bo21$16052b2o$16051b2o$16053bo30$16084b2o$16084bobo$16084bo34$

16120b2o$16120bobo$16120bo21$16142b3o$16142bo$16143bo20$16165b2o$

16165bobo$16165bo28$16195b2o$16195bobo$16195bo21$16217b3o$16217bo$

16218bo20$16241bo$16240b2o$16240bobo21$16263b2o$16263bobo$16263bo40$

16306bo$16305b2o$16305bobo21$16328b2o$16327b2o$16329bo21$16350b3o$

16350bo$16351bo25$16378b2o$16377b2o$16379bo21$16400b3o$16400bo$16401bo

21$16424b2o$16423b2o$16425bo21$16446b3o$16446bo$16447bo27$16476b2o$

16476bobo$16476bo21$16498b3o$16498bo$16499bo20$16522bo$16521b2o$16521b

obo21$16544b2o$16544bobo$16544bo21$16567b2o$16566b2o$16568bo24$16593b

2o$16592b2o$16594bo53$16647b3o$16647bo$16648bo20$16671bo$16670b2o$

16670bobo32$16704b2o$16704bobo$16704bo24$16731bo$16730b2o$16730bobo37$

16769b2o$16768b2o$16770bo20$16792bo$16791b2o$16791bobo21$16814b2o$

16814bobo$16814bo39$16855b2o$16855bobo$16855bo21$16878b2o$16877b2o$

16879bo31$16911b2o$16910b2o$16912bo20$16934bo$16933b2o$16933bobo21$

16956b2o$16955b2o$16957bo33$16991b2o$16990b2o$16992bo21$17015bo$17014b

2o$17014bobo22$17037b3o$17037bo$17038bo20$17060b2o$17060bobo$17060bo

22$17084b2o$17084bobo$17084bo21$17106b3o$17106bo$17107bo20$17129b2o$

17129bobo$17129bo21$17152b2o$17151b2o$17153bo35$17189b2o$17189bobo$

17189bo21$17211b3o$17211bo$17212bo20$17234b2o$17234bobo$17234bo38$

17275bo$17274b2o$17274bobo23$17300bo$17299b2o$17299bobo26$17326b3o$

17326bo$17327bo20$17350bo$17349b2o$17349bobo22$17372b3o$17372bo$17373b

o20$17396bo$17395b2o$17395bobo21$17419bo$17418b2o$17418bobo21$17441b2o

$17441bobo$17441bo21$17463b3o$17463bo$17464bo20$17486b2o$17486bobo$

17486bo29$17517b2o$17517bobo$17517bo21$17540b2o$17539b2o$17541bo33$

17576bo$17575b2o$17575bobo21$17598b2o$17597b2o$17599bo20$17621bo$

17620b2o$17620bobo21$17643b2o$17643bobo$17643bo21$17666b2o$17665b2o$

17667bo26$17694b2o$17693b2o$17695bo20$17717bo$17716b2o$17716bobo24$

17742b2o$17741b2o$17743bo23$17768bo$17767b2o$17767bobo24$17793b2o$

17793bobo$17793bo21$17815b3o$17815bo$17816bo20$17838b2o$17838bobo$

17838bo21$17860b3o$17860bo$17861bo27$17890b2o$17889b2o$17891bo26$

17918b2o$17917b2o$17919bo20$17941bo$17940b2o$17940bobo46$17987b3o$

17987bo$17988bo20$18010b2o$18010bobo$18010bo21$18032b3o$18032bo$18033b

o25$18060b2o$18059b2o$18061bo21$18082b3o$18082bo$18083bo21$18106b2o$

18105b2o$18107bo21$18128b3o$18128bo$18129bo21$18151b3o$18151bo$18152bo

20$18175bo$18174b2o$18174bobo21$18197b2o$18196b2o$18198bo20$18220bo$

18219b2o$18219bobo39$18260b2o$18259b2o$18261bo21$18282b3o$18282bo$

18283bo20$18306bo$18305b2o$18305bobo21$18328b2o$18327b2o$18329bo30$

18360b2o$18360bobo$18360bo21$18383b2o$18382b2o$18384bo26$18411b2o$

18411bobo$18411bo21$18433b3o$18433bo$18434bo20$18456b2o$18456bobo$

18456bo21$18478b3o$18478bo$18479bo20$18501b2o$18501bobo$18501bo25$

18529bo$18528b2o$18528bobo21$18551b2o$18551bobo$18551bo21$18575bo$

18574b2o$18574bobo21$18597b2o$18597bobo$18597bo21$18620b2o$18620bobo$

18620bo21$18642b3o$18642bo$18643bo22$18667b2o$18666b2o$18668bo21$

18689b3o$18689bo$18690bo27$18718b3o$18718bo$18719bo20$18742bo$18741b2o

$18741bobo35$18777b3o$18777bo$18778bo20$18800b2o$18800bobo$18800bo21$

18823b2o$18822b2o$18824bo22$18848bo$18847b2o$18847bobo21$18870b2o$

18869b2o$18871bo20$18893bo$18892b2o$18892bobo45$18940bo$18939b2o$

18939bobo21$18962b2o$18962bobo$18962bo21$18985b2o$18984b2o$18986bo21$

19007b3o$19007bo$19008bo20$19030b2o$19030bobo$19030bo27$19059b2o$

19058b2o$19060bo21$19081b3o$19081bo$19082bo25$19109b2o$19108b2o$19110b

o21$19131b3o$19131bo$19132bo21$19155b2o$19154b2o$19156bo21$19177b3o$

19177bo$19178bo22$19202b2o$19201b2o$19203bo21$19224b3o$19224bo$19225bo

20$19247b2o$19247bobo$19247bo21$19270b2o$19269b2o$19271bo28$19300b2o$

19299b2o$19301bo21$19322b3o$19322bo$19323bo27$19352b2o$19351b2o$19353b

o21$19374b3o$19374bo$19375bo28$19406bo$19405b2o$19405bobo21$19428b2o$

19427b2o$19429bo27$19458bo$19457b2o$19457bobo21$19480b2o$19480bobo$

19480bo35$19516b3o$19516bo$19517bo25$19544b2o$19544bobo$19544bo38$

19584b2o$19584bobo$19584bo21$19606b3o$19606bo$19607bo25$19634b2o$

19633b2o$19635bo21$19656b3o$19656bo$19657bo21$19680b2o$19679b2o$19681b

o20$19703bo$19702b2o$19702bobo31$19734b3o$19734bo$19735bo35$19771b3o$

19771bo$19772bo20$19794b2o$19794bobo$19794bo21$19818bo$19817b2o$19817b

obo21$19840b2o$19839b2o$19841bo34$19875b3o$19875bo$19876bo22$19899b3o$

19899bo$19900bo21$19922b3o$19922bo$19923bo20$19945b2o$19945bobo$19945b

o39$19987bo$19986b2o$19986bobo21$20009b2o$20008b2o$20010bo27$20039bo$

20038b2o$20038bobo21$20061b2o$20060b2o$20062bo20$20084bo$20083b2o$

20083bobo21$20106b2o$20106bobo$20106bo21$20129b2o$20128b2o$20130bo25$

20156b2o$20156bobo$20156bo21$20179b2o$20178b2o$20180bo21$20203bo$

20202b2o$20202bobo21$20225b2o$20225bobo$20225bo21$20248b2o$20247b2o$

20249bo21$20271b2o$20271bobo$20271bo21$20293b3o$20293bo$20294bo37$

20333b2o$20333bobo$20333bo21$20355b3o$20355bo$20356bo20$20379bo$20378b

2o$20378bobo21$20401b2o$20400b2o$20402bo20$20424bo$20423b2o$20423bobo

27$20453bo$20452b2o$20452bobo24$20479bo$20478b2o$20478bobo26$20505b3o$

20505bo$20506bo20$20529bo$20528b2o$20528bobo22$20552b2o$20551b2o$

20553bo21$20574b3o$20574bo$20575bo20$20598bo$20597b2o$20597bobo40$

20639b2o$20639bobo$20639bo21$20661b3o$20661bo$20662bo20$20684b2o$

20684bobo$20684bo21$20707b2o$20706b2o$20708bo22$20730b3o$20730bo$

20731bo20$20753b2o$20753bobo$20753bo21$20775b3o$20775bo$20776bo35$

20812b3o$20812bo$20813bo20$20835b2o$20835bobo$20835bo36$20873b2o$

20872b2o$20874bo20$20896bo$20895b2o$20895bobo21$20918b2o$20917b2o$

20919bo32$20952b2o$20951b2o$20953bo31$20986bo$20985b2o$20985bobo37$

21024b2o$21024bobo$21024bo27$21053b2o$21052b2o$21054bo24$21078b3o$

21078bo$21079bo20$21102bo$21101b2o$21101bobo26$21128b3o$21128bo$21129b

o20$21152bo$21151b2o$21151bobo22$21174b3o$21174bo$21175bo20$21197b2o$

21197bobo$21197bo37$21236b2o$21235b2o$21237bo24$21263bo$21262b2o$

21262bobo21$21285b2o$21285bobo$21285bo28$21316bo$21315b2o$21315bobo21$

21338b2o$21337b2o$21339bo20$21361bo$21360b2o$21360bobo21$21383b2o$

21383bobo$21383bo32$21418bo$21417b2o$21417bobo21$21440b2o$21439b2o$

21441bo56$21498b2o$21497b2o$21499bo20$21521bo$21520b2o$21520bobo21$

21543b2o$21543bobo$21543bo21$21566b2o$21565b2o$21567bo21$21590bo$

21589b2o$21589bobo21$21612b2o$21611b2o$21613bo41$21654b3o$21654bo$

21655bo20$21677b2o$21677bobo$21677bo21$21700b2o$21699b2o$21701bo24$

21725b3o$21725bo$21726bo23$21751b2o$21750b2o$21752bo25$21778b2o$21778b

obo$21778bo21$21801b2o$21800b2o$21802bo21$21825bo$21824b2o$21824bobo

21$21847b2o$21847bobo$21847bo21$21870b2o$21869b2o$21871bo32$21904b2o$

21903b2o$21905bo21$21926b3o$21926bo$21927bo20$21950bo$21949b2o$21949bo

bo21$21972b2o$21971b2o$21973bo40$22014b2o$22013b2o$22015bo20$22037bo$

22036b2o$22036bobo21$22059b2o$22058b2o$22060bo25$22087bo$22086b2o$

22086bobo21$22109b2o$22108b2o$22110bo20$22132bo$22131b2o$22131bobo22$

22154b3o$22154bo$22155bo20$22178bo$22177b2o$22177bobo26$22205b2o$

22205bobo$22205bo21$22228b2o$22227b2o$22229bo21$22250b3o$22250bo$

22251bo20$22273b2o$22273bobo$22273bo31$22306b2o$22306bobo$22306bo21$

22329b2o$22328b2o$22330bo21$22351b3o$22351bo$22352bo21$22375b2o$22374b

2o$22376bo21$22397b3o$22397bo$22398bo27$22427b2o$22427bobo$22427bo21$

22449b3o$22449bo$22450bo32$22484b2o$22483b2o$22485bo21$22506b3o$22506b

o$22507bo41$22550b2o$22549b2o$22551bo21$22573b2o$22573bobo$22573bo38$

22612b3o$22612bo$22613bo20$22635b2o$22635bobo$22635bo21$22657b3o$

22657bo$22658bo20$22680b2o$22680bobo$22680bo28$22709b3o$22709bo$22710b

o20$22732b2o$22732bobo$22732bo21$22755b2o$22754b2o$22756bo20$22778bo$

22777b2o$22777bobo36$22815b2o$22815bobo$22815bo37$22853b3o$22853bo$

22854bo39$22896bo$22895b2o$22895bobo21$22918b2o$22918bobo$22918bo31$

22952bo$22951b2o$22951bobo21$22974b2o$22973b2o$22975bo28$23003b3o$

23003bo$23004bo42$23048b2o$23048bobo$23048bo37$23087b2o$23086b2o$

23088bo20$23110bo$23109b2o$23109bobo21$23132b2o$23131b2o$23133bo20$

23155bo$23154b2o$23154bobo26$23181b3o$23181bo$23182bo20$23205bo$23204b

2o$23204bobo22$23228b2o$23227b2o$23229bo21$23250b3o$23250bo$23251bo20$

23274bo$23273b2o$23273bobo22$23297b2o$23297bobo$23297bo21$23320b2o$

23319b2o$23321bo20$23343bo$23342b2o$23342bobo22$23365b3o$23365bo$

23366bo52$23420b2o$23420bobo$23420bo34$23455b3o$23455bo$23456bo20$

23478b2o$23478bobo$23478bo21$23501b2o$23500b2o$23502bo38$23541b2o$

23541bobo$23541bo21$23563b3o$23563bo$23564bo32$23598b2o$23598bobo$

23598bo21$23620b3o$23620bo$23621bo38$23661b2o$23661bobo$23661bo21$

23684b2o$23683b2o$23685bo20$23707bo$23706b2o$23706bobo33$23742bo$

23741b2o$23741bobo22$23765b2o$23765bobo$23765bo25$23793bo$23792b2o$

23792bobo26$23819b3o$23819bo$23820bo20$23843bo$23842b2o$23842bobo22$

23865b3o$23865bo$23866bo20$23889bo$23888b2o$23888bobo21$23912bo$23911b

2o$23911bobo21$23934b2o$23934bobo$23934bo23$23958b3o$23958bo$23959bo

48$24009b2o$24008b2o$24010bo21$24031b3o$24031bo$24032bo30$24064b2o$

24063b2o$24065bo20$24087bo$24086b2o$24086bobo21$24109b2o$24108b2o$

24110bo20$24132bo$24131b2o$24131bobo21$24154b2o$24153b2o$24155bo20$

24177bo$24176b2o$24176bobo24$24202b2o$24202bobo$24202bo21$24224b3o$

24224bo$24225bo25$24251b3o$24251bo$24252bo20$24274b2o$24274bobo$24274b

o24$24300b2o$24300bobo$24300bo21$24322b3o$24322bo$24323bo25$24350b2o$

24349b2o$24351bo21$24372b3o$24372bo$24373bo21$24396b2o$24395b2o$24397b

o20$24419bo$24418b2o$24418bobo31$24450b3o$24450bo$24451bo35$24487b3o$

24487bo$24488bo20$24510b2o$24510bobo$24510bo21$24534bo$24533b2o$24533b

obo21$24556b2o$24555b2o$24557bo34$24591b3o$24591bo$24592bo22$24615b3o$

24615bo$24616bo21$24638b3o$24638bo$24639bo20$24661b2o$24661bobo$24661b

o39$24703bo$24702b2o$24702bobo21$24725b2o$24724b2o$24726bo27$24755bo$

24754b2o$24754bobo21$24777b2o$24776b2o$24778bo20$24800bo$24799b2o$

24799bobo21$24822b2o$24822bobo$24822bo21$24845b2o$24844b2o$24846bo25$

24872b2o$24872bobo$24872bo21$24895b2o$24894b2o$24896bo21$24919bo$

24918b2o$24918bobo21$24941b2o$24941bobo$24941bo21$24964b2o$24963b2o$

24965bo43$25008b3o$25008bo$25009bo20$25032bo$25031b2o$25031bobo21$

25054b2o$25053b2o$25055bo21$25078bo$25077b2o$25077bobo21$25100b2o$

25100bobo$25100bo26$25128b2o$25127b2o$25129bo20$25151bo$25150b2o$

25150bobo21$25173b2o$25172b2o$25174bo20$25196bo$25195b2o$25195bobo41$

25238b2o$25238bobo$25238bo21$25261b2o$25260b2o$25262bo25$25289bo$

25288b2o$25288bobo21$25311b2o$25311bobo$25311bo37$25349b3o$25349bo$

25350bo20$25372b2o$25372bobo$25372bo31$25405b2o$25405bobo$25405bo21$

25428b2o$25427b2o$25429bo25$25455b2o$25455bobo$25455bo21$25478b2o$

25477b2o$25479bo21$25502bo$25501b2o$25501bobo21$25524b2o$25524bobo$

25524bo21$25547b2o$25546b2o$25548bo29$25578b2o$25577b2o$25579bo20$

25601bo$25600b2o$25600bobo34$25637bo$25636b2o$25636bobo21$25659b2o$

25658b2o$25660bo20$25682bo$25681b2o$25681bobo21$25704b2o$25703b2o$

25705bo39$25745b2o$25745bobo$25745bo28$25775b2o$25774b2o$25776bo20$

25798bo$25797b2o$25797bobo24$25824bo$25823b2o$25823bobo21$25846b2o$

25845b2o$25847bo23$25871b2o$25870b2o$25872bo20$25894bo$25893b2o$25893b

obo21$25916b2o$25915b2o$25917bo21$25938b3o$25938bo$25939bo25$25966b2o$

25965b2o$25967bo21$25988b3o$25988bo$25989bo21$26012b2o$26011b2o$26013b

o21$26034b3o$26034bo$26035bo21$26057b3o$26057bo$26058bo20$26081bo$

26080b2o$26080bobo21$26103b2o$26102b2o$26104bo20$26126bo$26125b2o$

26125bobo39$26166b2o$26165b2o$26167bo21$26188b3o$26188bo$26189bo20$

26212bo$26211b2o$26211bobo21$26234b2o$26233b2o$26235bo30$26266b2o$

26266bobo$26266bo21$26289b2o$26288b2o$26290bo26$26317b2o$26317bobo$

26317bo21$26339b3o$26339bo$26340bo20$26362b2o$26362bobo$26362bo21$

26384b3o$26384bo$26385bo20$26408bo$26407b2o$26407bobo26$26434b3o$

26434bo$26435bo20$26458bo$26457b2o$26457bobo22$26481b2o$26480b2o$

26482bo21$26503b3o$26503bo$26504bo20$26527bo$26526b2o$26526bobo22$

26550b2o$26550bobo$26550bo21$26573b2o$26572b2o$26574bo20$26596bo$

26595b2o$26595bobo22$26618b3o$26618bo$26619bo52$26673b2o$26673bobo$

26673bo41$26716b2o$26716bobo$26716bo21$26738b3o$26738bo$26739bo20$

26761b2o$26761bobo$26761bo21$26783b3o$26783bo$26784bo27$26812b3o$

26812bo$26813bo26$26840b3o$26840bo$26841bo83$26926b2o$26925b2o$26927bo

25$26952b3o$26952bo$26953bo24$26979b2o$26979bobo$26979bo21$27001b3o$

27001bo$27002bo38$27043bo$27042b2o$27042bobo21$27065b2o$27065bobo$

27065bo21$27087b3o$27087bo$27088bo25$27115b2o$27114b2o$27116bo21$

27137b3o$27137bo$27138bo21$27161b2o$27160b2o$27162bo20$27184bo$27183b

2o$27183bobo41$27225b3o$27225bo$27226bo20$27248b2o$27248bobo$27248bo

21$27271b2o$27270b2o$27272bo24$27296b3o$27296bo$27297bo20$27320bo$

27319b2o$27319bobo32$27352b3o$27352bo$27353bo20$27375b2o$27375bobo$

27375bo21$27397b3o$27397bo$27398bo20$27421bo$27420b2o$27420bobo21$

27443b2o$27443bobo$27443bo21$27465b3o$27465bo$27466bo25$27493b2o$

27493bobo$27493bo21$27516b2o$27515b2o$27517bo21$27539b2o$27539bobo$

27539bo21$27561b3o$27561bo$27562bo26$27589b3o$27589bo$27590bo40$27633b

o$27632b2o$27632bobo21$27655b2o$27654b2o$27656bo25$27682b2o$27682bobo$

27682bo21$27705b2o$27704b2o$27706bo21$27729bo$27728b2o$27728bobo21$

27751b2o$27751bobo$27751bo21$27774b2o$27773b2o$27775bo41$27816b3o$

27816bo$27817bo20$27840bo$27839b2o$27839bobo21$27862b2o$27861b2o$

27863bo26$27890b2o$27890bobo$27890bo21$27912b3o$27912bo$27913bo22$

27937b2o$27936b2o$27938bo26$27966bo$27965b2o$27965bobo21$27988b2o$

27987b2o$27989bo24$28014b2o$28014bobo$28014bo21$28036b3o$28036bo$

28037bo32$28072bo$28071b2o$28071bobo21$28094b2o$28093b2o$28095bo26$

28122b2o$28122bobo$28122bo21$28144b3o$28144bo$28145bo24$28171b2o$

28171bobo$28171bo23$28195b3o$28195bo$28196bo28$28226b2o$28225b2o$

28227bo20$28249bo$28248b2o$28248bobo26$28275b3o$28275bo$28276bo20$

28299bo$28298b2o$28298bobo22$28322b2o$28321b2o$28323bo21$28344b3o$

28344bo$28345bo20$28368bo$28367b2o$28367bobo29$28399bo$28398b2o$28398b

obo21$28421b2o$28420b2o$28422bo33$28457bo$28456b2o$28456bobo21$28479b

2o$28478b2o$28480bo20$28502bo$28501b2o$28501bobo35$28538b2o$28537b2o$

28539bo21$28560b3o$28560bo$28561bo36$28599b2o$28598b2o$28600bo20$

28622bo$28621b2o$28621bobo24$28647b2o$28646b2o$28648bo21$28669b3o$

28669bo$28670bo36$28707b3o$28707bo$28708bo25$28734b3o$28734bo$28735bo

22$28759b2o$28758b2o$28760bo21$28781b3o$28781bo$28782bo25$28809b2o$

28808b2o$28810bo21$28831b3o$28831bo$28832bo21$28855b2o$28855bobo$

28855bo21$28878b2o$28877b2o$28879bo21$28900b3o$28900bo$28901bo29$

28931b3o$28931bo$28932bo20$28954b2o$28954bobo$28954bo41$28996b3o$

28996bo$28997bo20$29019b2o$29019bobo$29019bo21$29041b3o$29041bo$29042b

o20$29065bo$29064b2o$29064bobo21$29087b2o$29086b2o$29088bo23$29111b3o$

29111bo$29112bo20$29135bo$29134b2o$29134bobo21$29157b2o$29156b2o$

29158bo21$29179b3o$29179bo$29180bo25$29207b2o$29207bobo$29207bo28$

29238bo$29237b2o$29237bobo39$29277b3o$29277bo$29278bo27$29307b2o$

29306b2o$29308bo27$29335b3o$29335bo$29336bo32$29370b2o$29369b2o$29371b

o20$29393bo$29392b2o$29392bobo21$29415b2o$29415bobo$29415bo21$29437b3o

$29437bo$29438bo25$29465b2o$29464b2o$29466bo20$29488bo$29487b2o$29487b

obo22$29510b3o$29510bo$29511bo20$29534bo$29533b2o$29533bobo21$29556b2o

$29556bobo$29556bo30$29588b2o$29588bobo$29588bo21$29610b3o$29610bo$

29611bo32$29646bo$29645b2o$29645bobo21$29668b2o$29668bobo$29668bo21$

29690b3o$29690bo$29691bo22$29715b2o$29714b2o$29716bo21$29737b3o$29737b

o$29738bo29$29768b3o$29768bo$29769bo37$29808b2o$29807b2o$29809bo21$

29830b3o$29830bo$29831bo20$29853b2o$29853bobo$29853bo21$29875b3o$

29875bo$29876bo30$29908b2o$29907b2o$29909bo34$29944b2o$29943b2o$29945b

o21$29966b3o$29966bo$29967bo20$29990bo$29989b2o$29989bobo35$30026b2o$

30026bobo$30026bo31$30058b3o$30058bo$30059bo20$30082bo$30081b2o$30081b

obo21$30104b2o$30103b2o$30105bo20$30127bo$30126b2o$30126bobo21$30149b

2o$30149bobo$30149bo21$30171b3o$30171bo$30172bo33$30206b3o$30206bo$

30207bo20$30229b2o$30229bobo$30229bo21$30252b2o$30252bobo$30252bo21$

30274b3o$30274bo$30275bo20$30297b2o$30297bobo$30297bo25$30325bo$30324b

2o$30324bobo21$30347b2o$30347bobo$30347bo21$30371bo$30370b2o$30370bobo

21$30393b2o$30392b2o$30394bo37$30432b2o$30431b2o$30433bo21$30454b3o$

30454bo$30455bo20$30478bo$30477b2o$30477bobo24$30503b2o$30502b2o$

30504bo21$30525b3o$30525bo$30526bo20$30549bo$30548b2o$30548bobo21$

30571b2o$30570b2o$30572bo20$30594bo$30593b2o$30593bobo25$30620b2o$

30619b2o$30621bo21$30642b3o$30642bo$30643bo39$30684b2o$30684bobo$

30684bo21$30706b3o$30706bo$30707bo29$30738b2o$30737b2o$30739bo21$

30760b3o$30760bo$30761bo20$30783b2o$30783bobo$30783bo30$30814b3o$

30814bo$30815bo20$30838bo$30837b2o$30837bobo26$30864b3o$30864bo$30865b

o20$30888bo$30887b2o$30887bobo22$30911b2o$30910b2o$30912bo21$30933b3o$

30933bo$30934bo20$30957bo$30956b2o$30956bobo43$31001b2o$31001bobo$

31001bo21$31024b2o$31023b2o$31025bo20$31047bo$31046b2o$31046bobo22$

31070b2o$31069b2o$31071bo21$31092b3o$31092bo$31093bo23$31118b2o$31118b

obo$31118bo21$31141b2o$31140b2o$31142bo36$31178b3o$31178bo$31179bo20$

31201b2o$31201bobo$31201bo21$31223b3o$31223bo$31224bo23$31249b2o$

31248b2o$31250bo20$31272bo$31271b2o$31271bobo21$31294b2o$31294bobo$

31294bo29$31326bo$31325b2o$31325bobo44$31372bo$31371b2o$31371bobo21$

31394b2o$31393b2o$31395bo20$31417bo$31416b2o$31416bobo21$31439b2o$

31438b2o$31440bo21$31462b2o$31462bobo$31462bo21$31485b2o$31484b2o$

31486bo36$31522b3o$31522bo$31523bo20$31545b2o$31545bobo$31545bo33$

31580b2o$31579b2o$31581bo43$31625b2o$31624b2o$31626bo24$31650b3o$

31650bo$31651bo26$31680bo$31679b2o$31679bobo40$31721b2o$31721bobo$

31721bo21$31744b2o$31743b2o$31745bo28$31774b2o$31773b2o$31775bo33$

31808b3o$31808bo$31809bo31$31843bo$31842b2o$31842bobo21$31865b2o$

31865bobo$31865bo21$31888b2o$31887b2o$31889bo40$31931bo$31930b2o$

31930bobo26$31957b3o$31957bo$31958bo20$31980b2o$31980bobo$31980bo21$

32004bo$32003b2o$32003bobo21$32026b2o$32026bobo$32026bo21$32049b2o$

32048b2o$32050bo30$32081b2o$32080b2o$32082bo20$32104bo$32103b2o$32103b

obo33$32138b2o$32138bobo$32138bo21$32161b2o$32160b2o$32162bo20$32184bo

$32183b2o$32183bobo23$32207b3o$32207bo$32208bo20$32231bo$32230b2o$

32230bobo29$32262bo$32261b2o$32261bobo38$32300b3o$32300bo$32301bo20$

32324bo$32323b2o$32323bobo21$32346b2o$32345b2o$32347bo20$32369bo$

32368b2o$32368bobo31$32400b3o$32400bo$32401bo34$32436b3o$32436bo$

32437bo20$32460bo$32459b2o$32459bobo21$32482b2o$32482bobo$32482bo35$

32519b2o$32518b2o$32520bo30$32552bo$32551b2o$32551bobo21$32574b2o$

32574bobo$32574bo21$32596b3o$32596bo$32597bo20$32619b2o$32619bobo$

32619bo21$32642b2o$32641b2o$32643bo20$32665bo$32664b2o$32664bobo33$

32700bo$32699b2o$32699bobo21$32722b2o$32721b2o$32723bo21$32745b2o$

32744b2o$32746bo20$32768bo$32767b2o$32767bobo21$32790b2o$32789b2o$

32791bo25$32817b2o$32817bobo$32817bo21$32840b2o$32839b2o$32841bo21$

32863b2o$32863bobo$32863bo21$32886b2o$32885b2o$32887bo34$32922b2o$

32922bobo$32922bo52$32976b2o$32975b2o$32977bo26$33005bo$33004b2o$

33004bobo21$33027b2o$33027bobo$33027bo28$33058bo$33057b2o$33057bobo21$

33080b2o$33080bobo$33080bo36$33117b3o$33117bo$33118bo20$33141bo$33140b

2o$33140bobo21$33163b2o$33163bobo$33163bo36$33202bo$33201b2o$33201bobo

21$33224b2o$33224bobo$33224bo33$33260bo$33259b2o$33259bobo21$33282b2o$

33281b2o$33283bo21$33304b3o$33304bo$33305bo20$33328bo$33327b2o$33327bo

bo21$33350b2o$33349b2o$33351bo29$33380b3o$33380bo$33381bo20$33404bo$

33403b2o$33403bobo26$33430b3o$33430bo$33431bo20$33453b2o$33453bobo$

33453bo23$33479bo$33478b2o$33478bobo41$33520b3o$33520bo$33521bo51$

33574b2o$33573b2o$33575bo31$33607b2o$33607bobo$33607bo47$33656b2o$

33655b2o$33657bo20$33679bo$33678b2o$33678bobo31$33712bo$33711b2o$

33711bobo34$33747b2o$33747bobo$33747bo21$33770b2o$33769b2o$33771bo33$

33804b3o$33804bo$33805bo32$33839b2o$33839bobo$33839bo38$33878b3o$

33878bo$33879bo35$33917bo$33916b2o$33916bobo23$33941b2o$33941bobo$

33941bo21$33964b2o$33963b2o$33965bo25$33991b2o$33990b2o$33992bo23$

34015b3o$34015bo$34016bo20$34039bo$34038b2o$34038bobo21$34061b2o$

34060b2o$34062bo21$34083b3o$34083bo$34084bo20$34107bo$34106b2o$34106bo

bo21$34129b2o$34128b2o$34130bo21$34151b3o$34151bo$34152bo30$34185bo$

34184b2o$34184bobo21$34207b2o$34207bobo$34207bo25$34235bo$34234b2o$

34234bobo21$34257b2o$34257bobo$34257bo21$34281bo$34280b2o$34280bobo21$

34303b2o$34302b2o$34304bo37$34342b2o$34341b2o$34343bo21$34364b3o$

34364bo$34365bo20$34388bo$34387b2o$34387bobo22$34412bo$34411b2o$34411b

obo31$34445bo$34444b2o$34444bobo21$34467b2o$34467bobo$34467bo21$34490b

2o$34489b2o$34491bo24$34517bo$34516b2o$34516bobo21$34539b2o$34539bobo$

34539bo21$34561b3o$34561bo$34562bo27$34592bo$34591b2o$34591bobo45$

34637b3o$34637bo$34638bo20$34661bo$34660b2o$34660bobo22$34685bo$34684b

2o$34684bobo21$34707b2o$34706b2o$34708bo31$34740b2o$34739b2o$34741bo

20$34763bo$34762b2o$34762bobo21$34785b2o$34785bobo$34785bo21$34807b3o$

34807bo$34808bo33$34843b2o$34843bobo$34843bo25$34871bo$34870b2o$34870b

obo21$34893b2o$34893bobo$34893bo22$34916b3o$34916bo$34917bo20$34940bo$

34939b2o$34939bobo21$34962b2o$34962bobo$34962bo29$34993b2o$34993bobo$

34993bo21$35015b3o$35015bo$35016bo40$35058b2o$35058bobo$35058bo21$

35080b3o$35080bo$35081bo20$35103b2o$35103bobo$35103bo21$35126b2o$

35125b2o$35127bo20$35149bo$35148b2o$35148bobo23$35173b2o$35173bobo$

35173bo21$35196b2o$35195b2o$35197bo20$35219bo$35218b2o$35218bobo21$

35241b2o$35241bobo$35241bo26$35268b3o$35268bo$35269bo28$35299b2o$

35298b2o$35300bo38$35339b2o$35339bobo$35339bo27$35369bo$35368b2o$

35368bobo27$35397b2o$35397bobo$35397bo32$35432bo$35431b2o$35431bobo21$

35454b2o$35453b2o$35455bo21$35476b3o$35476bo$35477bo20$35499b2o$35499b

obo$35499bo25$35527bo$35526b2o$35526bobo21$35549b2o$35549bobo$35549bo

21$35573bo$35572b2o$35572bobo21$35595b2o$35594b2o$35596bo37$35633b3o$

35633bo$35634bo24$35660b2o$35660bobo$35660bo21$35683b2o$35682b2o$

35684bo28$35713b2o$35713bobo$35713bo21$35735b3o$35735bo$35736bo20$

35758b2o$35758bobo$35758bo21$35781b2o$35780b2o$35782bo32$35815b2o$

35815bobo$35815bo21$35837b3o$35837bo$35838bo56$35895b3o$35895bo$35896b

o20$35918b2o$35918bobo$35918bo21$35941b2o$35940b2o$35942bo21$35963b3o$

35963bo$35964bo21$35987b2o$35987bobo$35987bo21$36009b3o$36009bo$36010b

o40$36053bo$36052b2o$36052bobo21$36075b2o$36074b2o$36076bo21$36097b3o$

36097bo$36098bo23$36124bo$36123b2o$36123bobo24$36149b2o$36148b2o$

36150bo25$36176b2o$36176bobo$36176bo21$36199b2o$36198b2o$36200bo21$

36222b2o$36222bobo$36222bo21$36244b3o$36244bo$36245bo30$36277b2o$

36276b2o$36278bo35$36314b2o$36313b2o$36315bo21$36336b3o$36336bo$36337b

o23$36362b2o$36362bobo$36362bo21$36385b2o$36384b2o$36386bo21$36407b3o$

36407bo$36408bo34$36444b2o$36443b2o$36445bo42$36489bo$36488b2o$36488bo

bo21$36511b2o$36511bobo$36511bo27$36540b2o$36539b2o$36541bo20$36563bo$

36562b2o$36562bobo21$36585b2o$36584b2o$36586bo21$36607b3o$36607bo$

36608bo24$36633b3o$36633bo$36634bo20$36656b2o$36656bobo$36656bo21$

36678b3o$36678bo$36679bo21$36701b3o$36701bo$36702bo60$36764b2o$36763b

2o$36765bo20$36787bo$36786b2o$36786bobo21$36809b2o$36808b2o$36810bo21$

36831b3o$36831bo$36832bo25$36859b2o$36858b2o$36860bo21$36881b3o$36881b

o$36882bo21$36905b2o$36905bobo$36905bo21$36928b2o$36927b2o$36929bo20$

36951bo$36950b2o$36950bobo36$36989bo$36988b2o$36988bobo21$37011b2o$

37011bobo$37011bo21$37033b3o$37033bo$37034bo20$37057bo$37056b2o$37056b

obo28$37085b3o$37085bo$37086bo20$37108b2o$37108bobo$37108bo21$37131b2o

$37130b2o$37132bo26$37158b3o$37158bo$37159bo20$37182bo$37181b2o$37181b

obo21$37204b2o$37204bobo$37204bo28$37233b3o$37233bo$37234bo20$37256b2o

$37256bobo$37256bo34$37293bo$37292b2o$37292bobo21$37315b2o$37314b2o$

37316bo23$37340b2o$37339b2o$37341bo27$37369b2o$37368b2o$37370bo20$

37392bo$37391b2o$37391bobo21$37414b2o$37413b2o$37415bo23$37438b3o$

37438bo$37439bo20$37461b2o$37461bobo$37461bo25$37489bo$37488b2o$37488b

obo21$37511b2o$37511bobo$37511bo22$37534b3o$37534bo$37535bo20$37558bo$

37557b2o$37557bobo21$37580b2o$37580bobo$37580bo30$37612b2o$37612bobo$

37612bo30$37643b3o$37643bo$37644bo20$37666b2o$37666bobo$37666bo38$

37707bo$37706b2o$37706bobo36$37744b2o$37744bobo$37744bo21$37766b3o$

37766bo$37767bo25$37794b2o$37793b2o$37795bo21$37816b3o$37816bo$37817bo

20$37839b2o$37839bobo$37839bo21$37861b3o$37861bo$37862bo21$37885b2o$

37885bobo$37885bo34$37921b2o$37921bobo$37921bo25$37947b3o$37947bo$

37948bo20$37970b2o$37970bobo$37970bo22$37993b3o$37993bo$37994bo20$

38016b2o$38016bobo$38016bo21$38038b3o$38038bo$38039bo20$38061b2o$

38061bobo$38061bo25$38089bo$38088b2o$38088bobo21$38111b2o$38111bobo$

38111bo22$38134b3o$38134bo$38135bo20$38158bo$38157b2o$38157bobo21$

38180b2o$38180bobo$38180bo29$38211b2o$38211bobo$38211bo21$38234b2o$

38233b2o$38235bo24$38260b2o$38260bobo$38260bo21$38282b3o$38282bo$

38283bo40$38325b2o$38324b2o$38326bo21$38347b3o$38347bo$38348bo20$

38370b2o$38370bobo$38370bo27$38399b2o$38399bobo$38399bo21$38422b2o$

38421b2o$38423bo33$38458bo$38457b2o$38457bobo21$38480b2o$38479b2o$

38481bo20$38503bo$38502b2o$38502bobo21$38525b2o$38525bobo$38525bo25$

38553bo$38552b2o$38552bobo21$38575b2o$38575bobo$38575bo21$38599bo$

38598b2o$38598bobo21$38621b2o$38620b2o$38622bo33$38656b2o$38655b2o$

38657bo35$38694bo$38693b2o$38693bobo25$38721bo$38720b2o$38720bobo21$

38743b2o$38743bobo$38743bo21$38765b3o$38765bo$38766bo25$38794bo$38793b

2o$38793bobo21$38816b2o$38816bobo$38816bo21$38839b2o$38838b2o$38840bo

46$38888bo$38887b2o$38887bobo23$38912b2o$38911b2o$38913bo20$38935bo$

38934b2o$38934bobo41$38976b3o$38976bo$38977bo20$38999b2o$38999bobo$

38999bo25$39027bo$39026b2o$39026bobo21$39049b2o$39049bobo$39049bo22$

39072b3o$39072bo$39073bo20$39096bo$39095b2o$39095bobo21$39118b2o$

39118bobo$39118bo33$39154bo$39153b2o$39153bobo21$39176b2o$39175b2o$

39177bo41$39218b3o$39218bo$39219bo20$39241b2o$39241bobo$39241bo37$

39280b2o$39279b2o$39281bo20$39303bo$39302b2o$39302bobo26$39330b2o$

39330bobo$39330bo21$39353b2o$39352b2o$39354bo20$39376bo$39375b2o$

39375bobo31$39408b2o$39407b2o$39409bo20$39431bo$39430b2o$39430bobo21$

39453b2o$39453bobo$39453bo21$39475b3o$39475bo$39476bo22$39500b2o$

39499b2o$39501bo20$39523bo$39522b2o$39522bobo21$39545b2o$39544b2o$

39546bo25$39572b2o$39572bobo$39572bo21$39595b2o$39594b2o$39596bo21$

39619bo$39618b2o$39618bobo21$39641b2o$39641bobo$39641bo21$39664b2o$

39663b2o$39665bo28$39694b2o$39694bobo$39694bo21$39716b3o$39716bo$

39717bo20$39739b2o$39739bobo$39739bo21$39761b3o$39761bo$39762bo20$

39784b2o$39784bobo$39784bo21$39806b3o$39806bo$39807bo20$39829b2o$

39829bobo$39829bo23$39854b2o$39853b2o$39855bo20$39877bo$39876b2o$

39876bobo40$39917b3o$39917bo$39918bo27$39948bo$39947b2o$39947bobo21$

39970b2o$39969b2o$39971bo24$39997bo$39996b2o$39996bobo21$40019b2o$

40018b2o$40020bo20$40042bo$40041b2o$40041bobo21$40064b2o$40064bobo$

40064bo25$40092bo$40091b2o$40091bobo21$40114b2o$40114bobo$40114bo22$

40137b3o$40137bo$40138bo20$40161bo$40160b2o$40160bobo21$40183b2o$

40183bobo$40183bo21$40207bo$40206b2o$40206bobo21$40229b2o$40228b2o$

40230bo22$40252b3o$40252bo$40253bo20$40275b2o$40275bobo$40275bo26$

40304bo$40303b2o$40303bobo21$40326b2o$40325b2o$40327bo23$40350b3o$

40350bo$40351bo20$40373b2o$40373bobo$40373bo37$40412b2o$40412bobo$

40412bo21$40434b3o$40434bo$40435bo20$40457b2o$40457bobo$40457bo21$

40479b3o$40479bo$40480bo32$40514b2o$40514bobo$40514bo41$40556b3o$

40556bo$40557bo25$40584b2o$40583b2o$40585bo21$40606b3o$40606bo$40607bo

21$40630b2o$40630bobo$40630bo21$40653b2o$40652b2o$40654bo21$40675b3o$

40675bo$40676bo21$40698b3o$40698bo$40699bo20$40721b2o$40721bobo$40721b

o40$40764bo$40763b2o$40763bobo21$40786b2o$40785b2o$40787bo20$40809bo$

40808b2o$40808bobo21$40831b2o$40830b2o$40832bo25$40857b3o$40857bo$

40858bo20$40880b2o$40880bobo$40880bo21$40902b3o$40902bo$40903bo20$

40926bo$40925b2o$40925bobo21$40948b2o$40947b2o$40949bo22$40971b3o$

40971bo$40972bo20$40995bo$40994b2o$40994bobo21$41017b2o$41017bobo$

41017bo25$41045bo$41044b2o$41044bobo21$41067b2o$41067bobo$41067bo21$

41091bo$41090b2o$41090bobo21$41113b2o$41112b2o$41114bo41$41155b3o$

41155bo$41156bo20$41178b2o$41178bobo$41178bo21$41200b3o$41200bo$41201b

o20$41224bo$41223b2o$41223bobo21$41246b2o$41245b2o$41247bo21$41268b3o$

41268bo$41269bo20$41291b2o$41291bobo$41291bo21$41314b2o$41313b2o$

41315bo30$41346b2o$41346bobo$41346bo34$41382b2o$41382bobo$41382bo21$

41404b3o$41404bo$41405bo20$41427b2o$41427bobo$41427bo28$41457b2o$

41457bobo$41457bo21$41479b3o$41479bo$41480bo20$41503bo$41502b2o$41502b

obo21$41525b2o$41525bobo$41525bo40$41568bo$41567b2o$41567bobo21$41590b

2o$41589b2o$41591bo21$41612b3o$41612bo$41613bo25$41640b2o$41639b2o$

41641bo20$41663bo$41662b2o$41662bobo22$41686b2o$41686bobo$41686bo59$

41748bo$41747b2o$41747bobo21$41770b2o$41769b2o$41771bo31$41802b3o$

41802bo$41803bo31$41837bo$41836b2o$41836bobo21$41859b2o$41858b2o$

41860bo20$41882bo$41881b2o$41881bobo37$41920b2o$41919b2o$41921bo20$

41943bo$41942b2o$41942bobo21$41965b2o$41965bobo$41965bo21$41988b2o$

41987b2o$41989bo21$42010b3o$42010bo$42011bo25$42039bo$42038b2o$42038bo

bo21$42061b2o$42060b2o$42062bo20$42084bo$42083b2o$42083bobo21$42106b2o

$42106bobo$42106bo21$42129b2o$42128b2o$42130bo30$42161b2o$42160b2o$

42162bo21$42183b3o$42183bo$42184bo22$42207b3o$42207bo$42208bo20$42231b

o$42230b2o$42230bobo26$42257b3o$42257bo$42258bo20$42281bo$42280b2o$

42280bobo22$42304b2o$42303b2o$42305bo21$42326b3o$42326bo$42327bo20$

42350bo$42349b2o$42349bobo29$42381bo$42380b2o$42380bobo21$42403b2o$

42403bobo$42403bo24$42430bo$42429b2o$42429bobo21$42452b2o$42452bobo$

42452bo28$42482b2o$42481b2o$42483bo21$42504b3o$42504bo$42505bo31$

42537b3o$42537bo$42538bo22$42563bo$42562b2o$42562bobo21$42585b2o$

42584b2o$42586bo20$42608bo$42607b2o$42607bobo21$42630b2o$42629b2o$

42631bo35$42668bo$42667b2o$42667bobo38$42708bo$42707b2o$42707bobo27$

42737bo$42736b2o$42736bobo21$42759b2o$42759bobo$42759bo21$42782b2o$

42781b2o$42783bo21$42804b3o$42804bo$42805bo20$42827b2o$42827bobo$

42827bo22$42851b2o$42851bobo$42851bo21$42873b3o$42873bo$42874bo20$

42897bo$42896b2o$42896bobo22$42919b3o$42919bo$42920bo20$42943bo$42942b

2o$42942bobo27$42972bo$42971b2o$42971bobo21$42994b2o$42994bobo$42994bo

36$43032b2o$43031b2o$43033bo20$43055bo$43054b2o$43054bobo26$43081b3o$

43081bo$43082bo25$43110bo$43109b2o$43109bobo30$43141b2o$43141bobo$

43141bo21$43164b2o$43163b2o$43165bo26$43192b2o$43192bobo$43192bo21$

43215b2o$43214b2o$43216bo40$43257b2o$43257bobo$43257bo45$43303b3o$

43303bo$43304bo20$43326b2o$43326bobo$43326bo21$43348b3o$43348bo$43349b

o37$43388b2o$43388bobo$43388bo21$43411b2o$43410b2o$43412bo20$43434bo$

43433b2o$43433bobo21$43456b2o$43455b2o$43457bo20$43479bo$43478b2o$

43478bobo28$43507b3o$43507bo$43508bo20$43531bo$43530b2o$43530bobo38$

43571bo$43570b2o$43570bobo21$43593b2o$43592b2o$43594bo21$43615b3o$

43615bo$43616bo22$43639b3o$43639bo$43640bo20$43662b2o$43662bobo$43662b

o21$43684b3o$43684bo$43685bo20$43708bo$43707b2o$43707bobo26$43734b3o$

43734bo$43735bo20$43758bo$43757b2o$43757bobo22$43781b2o$43780b2o$

43782bo21$43803b3o$43803bo$43804bo20$43826b2o$43826bobo$43826bo22$

43850b2o$43849b2o$43851bo21$43872b3o$43872bo$43873bo20$43895b2o$43895b

obo$43895bo35$43932b2o$43931b2o$43933bo40$43973b3o$43973bo$43974bo20$

43996b2o$43996bobo$43996bo38$44036b2o$44036bobo$44036bo21$44058b3o$

44058bo$44059bo38$44098b3o$44098bo$44099bo24$44124b3o$44124bo$44125bo

20$44147b2o$44147bobo$44147bo21$44169b3o$44169bo$44170bo20$44193bo$

44192b2o$44192bobo21$44215b2o$44215bobo$44215bo23$44241bo$44240b2o$

44240bobo33$44275b2o$44275bobo$44275bo21$44298b2o$44297b2o$44299bo20$

44321bo$44320b2o$44320bobo32$44355bo$44354b2o$44354bobo31$44386b3o$

44386bo$44387bo20$44409b2o$44409bobo$44409bo25$44437bo$44436b2o$44436b

obo21$44459b2o$44459bobo$44459bo21$44483bo$44482b2o$44482bobo21$44505b

2o$44505bobo$44505bo29$44536b2o$44535b2o$44537bo21$44558b3o$44558bo$

44559bo27$44588b2o$44588bobo$44588bo21$44610b3o$44610bo$44611bo20$

44634bo$44633b2o$44633bobo25$44661bo$44660b2o$44660bobo21$44683b2o$

44683bobo$44683bo21$44706b2o$44705b2o$44707bo20$44729bo$44728b2o$

44728bobo21$44751b2o$44750b2o$44752bo20$44774bo$44773b2o$44773bobo21$

44796b2o$44795b2o$44797bo34$44831b3o$44831bo$44832bo20$44855bo$44854b

2o$44854bobo21$44878bo$44877b2o$44877bobo43$44921b3o$44921bo$44922bo

30$44954b2o$44953b2o$44955bo23$44979b2o$44979bobo$44979bo40$45021b2o$

45020b2o$45022bo21$45043b3o$45043bo$45044bo20$45066b2o$45066bobo$

45066bo21$45088b3o$45088bo$45089bo20$45112bo$45111b2o$45111bobo31$

45144b2o$45143b2o$45145bo30$45175b3o$45175bo$45176bo20$45198b2o$45198b

obo$45198bo32$45233bo$45232b2o$45232bobo21$45255b2o$45255bobo$45255bo

21$45279bo$45278b2o$45278bobo21$45301b2o$45300b2o$45302bo21$45323b3o$

45323bo$45324bo20$45347bo$45346b2o$45346bobo22$45370b2o$45369b2o$

45371bo55$45427b2o$45427bobo$45427bo25$45454b2o$45453b2o$45455bo21$

45476b3o$45476bo$45477bo20$45499b2o$45499bobo$45499bo24$45525b2o$

45525bobo$45525bo21$45548b2o$45547b2o$45549bo21$45570b3o$45570bo$

45571bo23$45596b2o$45595b2o$45597bo21$45618b3o$45618bo$45619bo20$

45642bo$45641b2o$45641bobo22$45664b3o$45664bo$45665bo20$45687b2o$

45687bobo$45687bo28$45717b2o$45716b2o$45718bo20$45740bo$45739b2o$

45739bobo32$45772b3o$45772bo$45773bo20$45795b2o$45795bobo$45795bo21$

45818b2o$45817b2o$45819bo21$45841b2o$45841bobo$45841bo34$45878bo$

45877b2o$45877bobo21$45900b2o$45900bobo$45900bo31$45933b2o$45933bobo$

45933bo21$45956b2o$45955b2o$45957bo25$45983b2o$45983bobo$45983bo21$

46006b2o$46005b2o$46007bo21$46029b2o$46029bobo$46029bo21$46052b2o$

46051b2o$46053bo32$46086b2o$46086bobo$46086bo21$46108b3o$46108bo$

46109bo39$46150b2o$46150bobo$46150bo21$46173b2o$46172b2o$46174bo23$

46199bo$46198b2o$46198bobo21$46221b2o$46220b2o$46222bo24$46247b2o$

46246b2o$46248bo21$46269b3o$46269bo$46270bo22$46293b3o$46293bo$46294bo

22$46317b3o$46317bo$46318bo20$46341bo$46340b2o$46340bobo21$46363b2o$

46362b2o$46364bo20$46386bo$46385b2o$46385bobo21$46408b2o$46407b2o$

46409bo39$46450bo$46449b2o$46449bobo21$46472b2o$46471b2o$46473bo20$

46495bo$46494b2o$46494bobo22$46517b3o$46517bo$46518bo20$46540b2o$

46540bobo$46540bo21$46562b3o$46562bo$46563bo25$46590b2o$46589b2o$

46591bo20$46613bo$46612b2o$46612bobo22$46635b3o$46635bo$46636bo20$

46659bo$46658b2o$46658bobo21$46681b2o$46681bobo$46681bo30$46713b2o$

46713bobo$46713bo21$46735b3o$46735bo$46736bo32$46771bo$46770b2o$46770b

obo21$46793b2o$46793bobo$46793bo21$46815b3o$46815bo$46816bo22$46840b2o

$46839b2o$46841bo21$46862b3o$46862bo$46863bo29$46893b3o$46893bo$46894b

o37$46933b2o$46932b2o$46934bo21$46955b3o$46955bo$46956bo20$46978b2o$

46978bobo$46978bo21$47000b3o$47000bo$47001bo30$47033b2o$47032b2o$

47034bo34$47069b2o$47068b2o$47070bo21$47091b3o$47091bo$47092bo20$

47115bo$47114b2o$47114bobo35$47151b2o$47151bobo$47151bo31$47183b3o$

47183bo$47184bo20$47207bo$47206b2o$47206bobo21$47229b2o$47228b2o$

47230bo20$47252bo$47251b2o$47251bobo21$47274b2o$47274bobo$47274bo21$

47296b3o$47296bo$47297bo33$47331b3o$47331bo$47332bo20$47354b2o$47354bo

bo$47354bo21$47377b2o$47377bobo$47377bo21$47399b3o$47399bo$47400bo20$

47423bo$47422b2o$47422bobo29$47453b2o$47453bobo$47453bo66$47520b3o$

47520bo$47521bo20$47543b2o$47543bobo$47543bo29$47575bo$47574b2o$47574b

obo21$47597b2o$47596b2o$47598bo20$47620bo$47619b2o$47619bobo21$47642b

2o$47641b2o$47643bo21$47666bo$47665b2o$47665bobo33$47699b3o$47699bo$

47700bo28$47731bo$47730b2o$47730bobo21$47753b2o$47752b2o$47754bo34$

47789b2o$47789bobo$47789bo32$47823b2o$47823bobo$47823bo21$47845b3o$

47845bo$47846bo20$47869bo$47868b2o$47868bobo23$47894bo$47893b2o$47893b

obo21$47916b2o$47916bobo$47916bo24$47943bo$47942b2o$47942bobo21$47965b

2o$47965bobo$47965bo36$48004bo$48003b2o$48003bobo21$48026b2o$48026bobo

$48026bo21$48048b3o$48048bo$48049bo34$48085b2o$48084b2o$48086bo37$

48123b3o$48123bo$48124bo25$48151b2o$48150b2o$48152bo21$48173b3o$48173b

o$48174bo21$48197b2o$48196b2o$48198bo21$48219b3o$48219bo$48220bo21$

48242b3o$48242bo$48243bo20$48266bo$48265b2o$48265bobo33$48300b2o$

48300bobo$48300bo21$48322b3o$48322bo$48323bo20$48346bo$48345b2o$48345b

obo21$48368b2o$48368bobo$48368bo21$48390b3o$48390bo$48391bo22$48414b3o

$48414bo$48415bo30$48447b2o$48447bobo$48447bo22$48472bo$48471b2o$

48471bobo21$48494b2o$48494bobo$48494bo39$48535b2o$48535bobo$48535bo21$

48557b3o$48557bo$48558bo22$48582b2o$48581b2o$48583bo21$48604b3o$48604b

o$48605bo20$48627b2o$48627bobo$48627bo21$48650b2o$48649b2o$48651bo26$

48679bo$48678b2o$48678bobo21$48701b2o$48700b2o$48702bo20$48724bo$

48723b2o$48723bobo28$48753b2o$48752b2o$48754bo20$48776bo$48775b2o$

48775bobo21$48798b2o$48797b2o$48799bo29$48828b3o$48828bo$48829bo65$

48896b2o$48896bobo$48896bo21$48918b3o$48918bo$48919bo29$48950b2o$

48949b2o$48951bo20$48973bo$48972b2o$48972bobo21$48995b2o$48994b2o$

48996bo20$49018bo$49017b2o$49017bobo22$49041b2o$49040b2o$49042bo32$

49075b2o$49075bobo$49075bo29$49106b2o$49105b2o$49107bo20$49129bo$

49128b2o$49128bobo35$49164b3o$49164bo$49165bo32$49198b3o$49198bo$

49199bo20$49221b2o$49221bobo$49221bo21$49244b2o$49243b2o$49245bo23$

49269b2o$49268b2o$49270bo21$49291b3o$49291bo$49292bo24$49318b2o$49317b

2o$49319bo21$49340b3o$49340bo$49341bo36$49379b2o$49378b2o$49380bo21$

49401b3o$49401bo$49402bo20$49424b2o$49424bobo$49424bo34$49461bo$49460b

2o$49460bobo37$49499b2o$49499bobo$49499bo25$49527bo$49526b2o$49526bobo

21$49549b2o$49548b2o$49550bo21$49572b2o$49572bobo$49572bo21$49595b2o$

49594b2o$49596bo21$49617b3o$49617bo$49618bo35$49654b3o$49654bo$49655bo

20$49678bo$49677b2o$49677bobo21$49700b2o$49699b2o$49701bo36$49737b3o$

49737bo$49738bo20$49760b2o$49760bobo$49760bo21$49783b2o$49782b2o$

49784bo39$49823b3o$49823bo$49824bo25$49850b3o$49850bo$49851bo35$49889b

o$49888b2o$49888bobo26$49917bo$49916b2o$49916bobo34$49953bo$49952b2o$

49952bobo21$49975b2o$49974b2o$49976bo35$50012b2o$50012bobo$50012bo21$

50034b3o$50034bo$50035bo20$50057b2o$50057bobo$50057bo23$50082b2o$

50081b2o$50083bo20$50105bo$50104b2o$50104bobo26$50131b3o$50131bo$

50132bo20$50155bo$50154b2o$50154bobo22$50178b2o$50177b2o$50179bo21$

50200b3o$50200bo$50201bo20$50224bo$50223b2o$50223bobo29$50255bo$50254b

2o$50254bobo21$50277b2o$50277bobo$50277bo30$50308b3o$50308bo$50309bo

20$50332bo$50331b2o$50331bobo33$50367bo$50366b2o$50366bobo39$50407b2o$

50406b2o$50408bo35$50444b2o$50443b2o$50445bo20$50467bo$50466b2o$50466b

obo21$50489b2o$50488b2o$50490bo28$50518b3o$50518bo$50519bo20$50541b2o$

50541bobo$50541bo21$50564b2o$50563b2o$50565bo25$50591b2o$50591bobo$

50591bo21$50614b2o$50613b2o$50615bo21$50637b2o$50637bobo$50637bo21$

50660b2o$50659b2o$50661bo37$50698b3o$50698bo$50699bo24$50725b2o$50725b

obo$50725bo21$50748b2o$50747b2o$50749bo21$50770b3o$50770bo$50771bo22$

50794b3o$50794bo$50795bo20$50817b2o$50817bobo$50817bo21$50839b3o$

50839bo$50840bo20$50863bo$50862b2o$50862bobo25$50890bo$50889b2o$50889b

obo21$50912b2o$50911b2o$50913bo37$50951b2o$50950b2o$50952bo20$50974bo$

50973b2o$50973bobo21$50996b2o$50995b2o$50997bo28$51026b2o$51025b2o$

51027bo20$51049bo$51048b2o$51048bobo26$51077bo$51076b2o$51076bobo21$

51099b2o$51099bobo$51099bo23$51124b2o$51123b2o$51125bo21$51146b3o$

51146bo$51147bo25$51174b2o$51173b2o$51175bo21$51196b3o$51196bo$51197bo

21$51220b2o$51219b2o$51221bo21$51242b3o$51242bo$51243bo30$51275b2o$

51274b2o$51276bo35$51312b2o$51311b2o$51313bo21$51334b3o$51334bo$51335b

o21$51358b2o$51357b2o$51359bo36$51397bo$51396b2o$51396bobo21$51419b2o$

51418b2o$51420bo31$51453bo$51452b2o$51452bobo21$51475b2o$51475bobo$

51475bo21$51498b2o$51497b2o$51499bo20$51521bo$51520b2o$51520bobo21$

51543b2o$51543bobo$51543bo21$51566b2o$51565b2o$51567bo26$51593b3o$

51593bo$51594bo20$51617bo$51616b2o$51616bobo21$51639b2o$51639bobo$

51639bo21$51662b2o$51661b2o$51663bo21$51684b3o$51684bo$51685bo20$

51707b2o$51707bobo$51707bo25$51735bo$51734b2o$51734bobo21$51757b2o$

51757bobo$51757bo21$51781bo$51780b2o$51780bobo21$51803b2o$51803bobo$

51803bo30$51836bo$51835b2o$51835bobo35$51873bo$51872b2o$51872bobo21$

51895b2o$51895bobo$51895bo21$51919bo$51918b2o$51918bobo37$51957b2o$

51956b2o$51958bo20$51980bo$51979b2o$51979bobo32$52013b2o$52012b2o$

52014bo21$52035b3o$52035bo$52036bo20$52059bo$52058b2o$52058bobo21$

52081b2o$52080b2o$52082bo21$52103b3o$52103bo$52104bo20$52127bo$52126b

2o$52126bobo26$52154b2o$52154bobo$52154bo21$52177b2o$52176b2o$52178bo

21$52199b3o$52199bo$52200bo20$52223bo$52222b2o$52222bobo21$52245b2o$

52245bobo$52245bo21$52267b3o$52267bo$52268bo25$52295b2o$52294b2o$

52296bo21$52317b3o$52317bo$52318bo21$52341b2o$52340b2o$52342bo21$

52363b3o$52363bo$52364bo30$52396b2o$52395b2o$52397bo35$52433b2o$52433b

obo$52433bo21$52456b2o$52455b2o$52457bo20$52479bo$52478b2o$52478bobo

21$52501b2o$52500b2o$52502bo33$52537bo$52536b2o$52536bobo53$52591b2o$

52591bobo$52591bo21$52613b3o$52613bo$52614bo22$52639bo$52638b2o$52638b

obo21$52661b2o$52661bobo$52661bo25$52689bo$52688b2o$52688bobo27$52717b

2o$52717bobo$52717bo21$52740b2o$52740bobo$52740bo44$52787bo$52786b2o$

52786bobo21$52809b2o$52809bobo$52809bo25$52837bo$52836b2o$52836bobo21$

52859b2o$52858b2o$52860bo21$52882b2o$52882bobo$52882bo21$52905b2o$

52904b2o$52906bo21$52927b3o$52927bo$52928bo33$52963b2o$52963bobo$

52963bo21$52985b3o$52985bo$52986bo22$53010b2o$53010bobo$53010bo21$

53032b3o$53032bo$53033bo20$53056bo$53055b2o$53055bobo30$53086b3o$

53086bo$53087bo26$53115b2o$53115bobo$53115bo30$53147b2o$53146b2o$

53148bo20$53170bo$53169b2o$53169bobo26$53197b2o$53197bobo$53197bo21$

53219b3o$53219bo$53220bo25$53247b2o$53246b2o$53248bo21$53269b3o$53269b

o$53270bo21$53293b2o$53292b2o$53294bo21$53315b3o$53315bo$53316bo30$

53348b2o$53348bobo$53348bo21$53371b2o$53370b2o$53372bo20$53394bo$

53393b2o$53393bobo32$53427b2o$53426b2o$53428bo20$53450bo$53449b2o$

53449bobo21$53472b2o$53471b2o$53473bo24$53497b3o$53497bo$53498bo28$

53528b2o$53528bobo$53528bo37$53567b2o$53567bobo$53567bo26$53595b2o$

53595bobo$53595bo21$53617b3o$53617bo$53618bo43$53664bo$53663b2o$53663b

obo28$53692b3o$53692bo$53693bo20$53716bo$53715b2o$53715bobo36$53754bo$

53753b2o$53753bobo34$53788b3o$53788bo$53789bo20$53811b2o$53811bobo$

53811bo23$53835b3o$53835bo$53836bo20$53858b2o$53858bobo$53858bo21$

53881b2o$53880b2o$53882bo21$53904b2o$53904bobo$53904bo21$53927b2o$

53926b2o$53928bo27$53956b2o$53955b2o$53957bo21$53978b3o$53978bo$53979b

o30$54012bo$54011b2o$54011bobo21$54034b2o$54034bobo$54034bo22$54058b2o

$54057b2o$54059bo45$54105b2o$54104b2o$54106bo26$54133b2o$54133bobo$

54133bo21$54156b2o$54155b2o$54157bo21$54178b3o$54178bo$54179bo34$

54216bo$54215b2o$54215bobo29$54246b2o$54245b2o$54247bo21$54268b3o$

54268bo$54269bo41$54312b2o$54311b2o$54313bo21$54334b3o$54334bo$54335bo

20$54358bo$54357b2o$54357bobo32$54390b3o$54390bo$54391bo59$54453bo$

54452b2o$54452bobo21$54476bo$54475b2o$54475bobo21$54498b2o$54498bobo$

54498bo25$54526bo$54525b2o$54525bobo21$54548b2o$54548bobo$54548bo21$

54572bo$54571b2o$54571bobo21$54594b2o$54593b2o$54595bo37$54633b2o$

54632b2o$54634bo21$54655b3o$54655bo$54656bo20$54679bo$54678b2o$54678bo

bo22$54702b2o$54701b2o$54703bo21$54724b3o$54724bo$54725bo20$54747b2o$

54747bobo$54747bo35$54784b2o$54783b2o$54785bo27$54813b2o$54813bobo$

54813bo21$54836b2o$54835b2o$54837bo34$54872b2o$54871b2o$54873bo20$

54895bo$54894b2o$54894bobo21$54917b2o$54917bobo$54917bo30$54949b2o$

54949bobo$54949bo23$54974b2o$54974bobo$54974bo21$54997b2o$54996b2o$

54998bo20$55020bo$55019b2o$55019bobo25$55045b3o$55045bo$55046bo20$

55069bo$55068b2o$55068bobo21$55091b2o$55091bobo$55091bo21$55115bo$

55114b2o$55114bobo21$55137b2o$55137bobo$55137bo27$55166b2o$55166bobo$

55166bo21$55189b2o$55188b2o$55190bo24$55216bo$55215b2o$55215bobo21$

55238b2o$55238bobo$55238bo37$55277b2o$55276b2o$55278bo20$55300bo$

55299b2o$55299bobo25$55326b2o$55325b2o$55327bo20$55349bo$55348b2o$

55348bobo40$55390b2o$55390bobo$55390bo21$55412b3o$55412bo$55413bo20$

55435b2o$55435bobo$55435bo21$55458b2o$55457b2o$55459bo35$55495b2o$

55494b2o$55496bo29$55525b3o$55525bo$55526bo25$55554bo$55553b2o$55553bo

bo37$55592b2o$55592bobo$55592bo21$55615b2o$55614b2o$55616bo24$55641b2o

$55641bobo$55641bo21$55663b3o$55663bo$55664bo20$55686b2o$55686bobo$

55686bo21$55709b2o$55709bobo$55709bo21$55731b3o$55731bo$55732bo29$

55762b3o$55762bo$55763bo20$55785b2o$55785bobo$55785bo21$55808b2o$

55807b2o$55809bo25$55835b2o$55835bobo$55835bo21$55858b2o$55857b2o$

55859bo21$55882bo$55881b2o$55881bobo21$55904b2o$55904bobo$55904bo21$

55927b2o$55926b2o$55928bo22$55950b3o$55950bo$55951bo20$55974bo$55973b

2o$55973bobo21$55996b2o$55995b2o$55997bo22$56020b2o$56020bobo$56020bo

34$56056b2o$56055b2o$56057bo41$56098b3o$56098bo$56099bo20$56121b2o$

56121bobo$56121bo24$56148bo$56147b2o$56147bobo21$56170b2o$56169b2o$

56171bo21$56192b3o$56192bo$56193bo34$56228b3o$56228bo$56229bo20$56252b

o$56251b2o$56251bobo21$56274b2o$56273b2o$56275bo20$56297bo$56296b2o$

56296bobo21$56319b2o$56318b2o$56320bo21$56343bo$56342b2o$56342bobo21$

56365b2o$56364b2o$56366bo20$56388bo$56387b2o$56387bobo21$56410b2o$

56409b2o$56411bo25$56437b2o$56437bobo$56437bo21$56460b2o$56459b2o$

56461bo21$56483b2o$56483bobo$56483bo21$56506b2o$56505b2o$56507bo21$

56529b2o$56528b2o$56530bo20$56552bo$56551b2o$56551bobo38$56591b2o$

56590b2o$56592bo20$56614bo$56613b2o$56613bobo22$56637b2o$56636b2o$

56638bo65$56705bo$56704b2o$56704bobo41$56748bo$56747b2o$56747bobo31$

56780b2o$56779b2o$56781bo20$56803bo$56802b2o$56802bobo21$56825b2o$

56825bobo$56825bo21$56848b2o$56847b2o$56849bo22$56872b2o$56871b2o$

56873bo20$56895bo$56894b2o$56894bobo21$56917b2o$56916b2o$56918bo35$

56953b3o$56953bo$56954bo20$56977bo$56976b2o$56976bobo26$57003b3o$

57003bo$57004bo20$57027bo$57026b2o$57026bobo22$57049b3o$57049bo$57050b

o20$57073bo$57072b2o$57072bobo21$57096bo$57095b2o$57095bobo21$57118b2o

$57117b2o$57119bo38$57159bo$57158b2o$57158bobo21$57181b2o$57180b2o$

57182bo30$57213b2o$57213bobo$57213bo21$57236b2o$57235b2o$57237bo21$

57258b3o$57258bo$57259bo20$57282bo$57281b2o$57281bobo21$57304b2o$

57303b2o$57305bo32$57338b2o$57338bobo$57338bo23$57363b2o$57362b2o$

57364bo20$57386bo$57385b2o$57385bobo21$57408b2o$57407b2o$57409bo26$

57435b3o$57435bo$57436bo20$57459bo$57458b2o$57458bobo37$57496b3o$

57496bo$57497bo20$57519b2o$57519bobo$57519bo21$57541b3o$57541bo$57542b

o20$57564b2o$57564bobo$57564bo25$57592bo$57591b2o$57591bobo21$57614b2o

$57614bobo$57614bo22$57638b2o$57637b2o$57639bo29$57669b2o$57669bobo$

57669bo30$57701b2o$57701bobo$57701bo21$57723b3o$57723bo$57724bo20$

57746b2o$57746bobo$57746bo21$57768b3o$57768bo$57769bo41$57811b3o$

57811bo$57812bo20$57834b2o$57834bobo$57834bo21$57856b3o$57856bo$57857b

o20$57879b2o$57879bobo$57879bo28$57909b2o$57908b2o$57910bo21$57931b3o$

57931bo$57932bo26$57960b2o$57959b2o$57961bo60$58021b3o$58021bo$58022bo

20$58044b2o$58044bobo$58044bo34$58080b2o$58080bobo$58080bo21$58102b3o$

58102bo$58103bo33$58137b3o$58137bo$58138bo20$58160b2o$58160bobo$58160b

o25$58188bo$58187b2o$58187bobo21$58210b2o$58209b2o$58211bo21$58233b2o$

58233bobo$58233bo21$58256b2o$58255b2o$58257bo20$58279bo$58278b2o$

58278bobo22$58302b2o$58302bobo$58302bo21$58325b2o$58324b2o$58326bo21$

58347b3o$58347bo$58348bo32$58383bo$58382b2o$58382bobo21$58405b2o$

58404b2o$58406bo35$58441b3o$58441bo$58442bo20$58464b2o$58464bobo$

58464bo21$58486b3o$58486bo$58487bo22$58512bo$58511b2o$58511bobo28$

58540b3o$58540bo$58541bo20$58564bo$58563b2o$58563bobo38$58602b3o$

58602bo$58603bo20$58626bo$58625b2o$58625bobo30$58657b2o$58656b2o$

58658bo20$58680bo$58679b2o$58679bobo21$58702b2o$58701b2o$58703bo21$

58724b3o$58724bo$58725bo38$58764b3o$58764bo$58765bo20$58787b2o$58787bo

bo$58787bo21$58810b2o$58809b2o$58811bo21$58832b3o$58832bo$58833bo20$

58856bo$58855b2o$58855bobo26$58883b2o$58883bobo$58883bo21$58905b3o$

58905bo$58906bo20$58928b2o$58928bobo$58928bo26$58957bo$58956b2o$58956b

obo21$58979b2o$58978b2o$58980bo21$59001b3o$59001bo$59002bo25$59029b2o$

59028b2o$59030bo21$59051b3o$59051bo$59052bo21$59075b2o$59075bobo$

59075bo21$59098b2o$59097b2o$59099bo20$59121bo$59120b2o$59120bobo23$

59145b2o$59145bobo$59145bo21$59167b3o$59167bo$59168bo26$59195b3o$

59195bo$59196bo20$59218b2o$59218bobo$59218bo21$59241b2o$59240b2o$

59242bo24$59267b2o$59267bobo$59267bo21$59289b3o$59289bo$59290bo28$

59320b2o$59319b2o$59321bo27$59350bo$59349b2o$59349bobo24$59375b2o$

59375bobo$59375bo21$59397b3o$59397bo$59398bo34$59433b3o$59433bo$59434b

o27$59463b2o$59462b2o$59464bo22$59486b3o$59486bo$59487bo20$59510bo$

59509b2o$59509bobo26$59536b3o$59536bo$59537bo20$59560bo$59559b2o$

59559bobo22$59583b2o$59582b2o$59584bo21$59605b3o$59605bo$59606bo20$

59629bo$59628b2o$59628bobo29$59660bo$59659b2o$59659bobo21$59682b2o$

59681b2o$59683bo34$59718b2o$59717b2o$59719bo20$59741bo$59740b2o$59740b

obo21$59763b2o$59762b2o$59764bo20$59786bo$59785b2o$59785bobo40$59826b

3o$59826bo$59827bo27$59857bo$59856b2o$59856bobo21$59879b2o$59878b2o$

59880bo24$59905b2o$59904b2o$59906bo20$59928bo$59927b2o$59927bobo23$

59953bo$59952b2o$59952bobo21$59975b2o$59974b2o$59976bo20$59998bo$

59997b2o$59997bobo21$60020b2o$60019b2o$60021bo25$60047b2o$60047bobo$

60047bo21$60070b2o$60069b2o$60071bo21$60094bo$60093b2o$60093bobo21$

60116b2o$60116bobo$60116bo21$60139b2o$60138b2o$60140bo43$60183b3o$

60183bo$60184bo20$60207bo$60206b2o$60206bobo21$60229b2o$60228b2o$

60230bo21$60253bo$60252b2o$60252bobo21$60275b2o$60275bobo$60275bo27$

60303b3o$60303bo$60304bo20$60326b2o$60326bobo$60326bo40$60367b3o$

60367bo$60368bo20$60390b2o$60390bobo$60390bo21$60412b3o$60412bo$60413b

o20$60435b2o$60435bobo$60435bo21$60458b2o$60457b2o$60459bo27$60487b2o$

60487bobo$60487bo21$60509b3o$60509bo$60510bo22$60533b3o$60533bo$60534b

o20$60556b2o$60556bobo$60556bo21$60578b3o$60578bo$60579bo21$60603bo$

60602b2o$60602bobo21$60625b2o$60625bobo$60625bo21$60648b2o$60647b2o$

60649bo25$60675b2o$60675bobo$60675bo21$60698b2o$60697b2o$60699bo21$

60722bo$60721b2o$60721bobo21$60744b2o$60744bobo$60744bo21$60767b2o$

60766b2o$60768bo22$60790b3o$60790bo$60791bo20$60814bo$60813b2o$60813bo

bo21$60836b2o$60835b2o$60837bo35$60874bo$60873b2o$60873bobo21$60896b2o

$60895b2o$60897bo33$60931b2o$60930b2o$60932bo20$60954bo$60953b2o$

60953bobo21$60976b2o$60976bobo$60976bo21$60998b3o$60998bo$60999bo40$

61042bo$61041b2o$61041bobo21$61064b2o$61063b2o$61065bo27$61094bo$

61093b2o$61093bobo21$61116b2o$61116bobo$61116bo26$61144b2o$61143b2o$

61145bo20$61167bo$61166b2o$61166bobo24$61193bo$61192b2o$61192bobo21$

61215b2o$61215bobo$61215bo25$61243bo$61242b2o$61242bobo21$61265b2o$

61265bobo$61265bo21$61289bo$61288b2o$61288bobo21$61311b2o$61311bobo$

61311bo22$61336bo$61335b2o$61335bobo21$61358b2o$61358bobo$61358bo21$

61380b3o$61380bo$61381bo20$61404bo$61403b2o$61403bobo28$61434bo$61433b

2o$61433bobo21$61456b2o$61455b2o$61457bo22$61479b3o$61479bo$61480bo20$

61503bo$61502b2o$61502bobo34$61538b2o$61538bobo$61538bo21$61560b3o$

61560bo$61561bo20$61583b2o$61583bobo$61583bo21$61605b3o$61605bo$61606b

o20$61628b2o$61628bobo$61628bo21$61651b2o$61650b2o$61652bo25$61678b2o$

61678bobo$61678bo21$61700b3o$61700bo$61701bo21$61725bo$61724b2o$61724b

obo60$61785b3o$61785bo$61786bo20$61808b2o$61808bobo$61808bo22$61832b2o

$61831b2o$61833bo20$61855bo$61854b2o$61854bobo29$61885b2o$61885bobo$

61885bo21$61908b2o$61907b2o$61909bo20$61931bo$61930b2o$61930bobo27$

61959b2o$61959bobo$61959bo34$61994b3o$61994bo$61995bo20$62018bo$62017b

2o$62017bobo26$62044b3o$62044bo$62045bo20$62068bo$62067b2o$62067bobo

22$62091b2o$62090b2o$62092bo21$62113b3o$62113bo$62114bo20$62137bo$

62136b2o$62136bobo29$62168bo$62167b2o$62167bobo21$62190b2o$62190bobo$

62190bo21$62212b3o$62212bo$62213bo20$62236bo$62235b2o$62235bobo21$

62258b2o$62258bobo$62258bo21$62280b3o$62280bo$62281bo20$62304bo$62303b

2o$62303bobo21$62326b2o$62325b2o$62327bo33$62361b2o$62361bobo$62361bo

21$62383b3o$62383bo$62384bo41$62426b3o$62426bo$62427bo20$62450bo$

62449b2o$62449bobo39$62489b3o$62489bo$62490bo20$62512b2o$62512bobo$

62512bo40$62555bo$62554b2o$62554bobo55$62612bo$62611b2o$62611bobo21$

62634b2o$62633b2o$62635bo25$62661b2o$62661bobo$62661bo21$62684b2o$

62683b2o$62685bo21$62708bo$62707b2o$62707bobo21$62730b2o$62730bobo$

62730bo21$62753b2o$62752b2o$62754bo21$62776b2o$62776bobo$62776bo21$

62798b3o$62798bo$62799bo20$62822bo$62821b2o$62821bobo21$62844b2o$

62844bobo$62844bo21$62866b3o$62866bo$62867bo23$62891b3o$62891bo$62892b

o20$62914b2o$62914bobo$62914bo22$62937b3o$62937bo$62938bo20$62960b2o$

62960bobo$62960bo25$62987b2o$62987bobo$62987bo21$63009b3o$63009bo$

63010bo20$63033bo$63032b2o$63032bobo21$63055b2o$63055bobo$63055bo28$

63085b2o$63084b2o$63086bo276$63364bo$63363b2o$63363bobo26$63390b3o$

63390bo$63391bo20$63414bo$63413b2o$63413bobo22$63437b2o$63437bobo$

63437bo26$63466bo$63465b2o$63465bobo21$63488b2o$63487b2o$63489bo31$

63522bo$63521b2o$63521bobo21$63544b2o$63543b2o$63545bo276$63823bo$

63822b2o$63822bobo26$63849b3o$63849bo$63850bo20$63872b2o$63872bobo$

63872bo21$63896bo$63895b2o$63895bobo21$63918b2o$63918bobo$63918bo21$

63940b3o$63940bo$63941bo21$63965bo$63964b2o$63964bobo21$63987b2o$

63987bobo$63987bo21$64010b2o$64009b2o$64011bo32$64045bo$64044b2o$

64044bobo38$64083b3o$64083bo$64084bo22$64107b3o$64107bo$64108bo20$

64130b2o$64130bobo$64130bo28$64160b2o$64160bobo$64160bo21$64183b2o$

64182b2o$64184bo22$64207b2o$64207bobo$64207bo25$64234b2o$64233b2o$

64235bo20$64257bo$64256b2o$64256bobo21$64279b2o$64278b2o$64280bo21$

64302b2o$64302bobo$64302bo45$64349b2o$64349bobo$64349bo25$64377bo$

64376b2o$64376bobo21$64399b2o$64398b2o$64400bo21$64422b2o$64422bobo$

64422bo21$64445b2o$64444b2o$64446bo20$64468bo$64467b2o$64467bobo22$

64491b2o$64491bobo$64491bo21$64514b2o$64513b2o$64515bo21$64536b3o$

64536bo$64537bo32$64571b2o$64571bobo$64571bo37$64611bo$64610b2o$64610b

obo22$64635bo$64634b2o$64634bobo21$64657b2o$64656b2o$64658bo28$64687b

2o$64686b2o$64688bo21$64709b3o$64709bo$64710bo22$64734b2o$64733b2o$

64735bo25$64760b3o$64760bo$64761bo20$64783b2o$64783bobo$64783bo21$

64805b3o$64805bo$64806bo21$64829b2o$64828b2o$64830bo45$64876b2o$64875b

2o$64877bo25$64903b2o$64903bobo$64903bo21$64925b3o$64925bo$64926bo21$

64949b2o$64948b2o$64950bo21$64971b3o$64971bo$64972bo20$64994b2o$64994b

obo$64994bo22$65018b2o$65017b2o$65019bo21$65040b3o$65040bo$65041bo20$

65064bo$65063b2o$65063bobo33$65098b2o$65097b2o$65099bo37$65137b2o$

65137bobo$65137bo22$65161b2o$65161bobo$65161bo21$65183b3o$65183bo$

65184bo28$65213b3o$65213bo$65214bo20$65237bo$65236b2o$65236bobo23$

65260b3o$65260bo$65261bo24$65288bo$65287b2o$65287bobo21$65310b2o$

65309b2o$65311bo20$65333bo$65332b2o$65332bobo22$65355b3o$65355bo$

65356bo45$65402b3o$65402bo$65403bo25$65430b2o$65429b2o$65431bo21$

65452b3o$65452bo$65453bo21$65476b2o$65475b2o$65477bo21$65498b3o$65498b

o$65499bo21$65521b3o$65521bo$65522bo20$65544b2o$65544bobo$65544bo22$

65569bo$65568b2o$65568bobo21$65591b2o$65591bobo$65591bo27$65620b2o$

65620bobo$65620bo21$65643b2o$65642b2o$65644bo21$65666b2o$65666bobo$

65666bo27$65695b2o$65694b2o$65696bo20$65718bo$65717b2o$65717bobo21$

65740b2o$65740bobo$65740bo31$65772b3o$65772bo$65773bo19$65793bo$65795b

2o$65795bobo$65795bo!

#C [[ X 40 Y 10 Z 2 STEP 9 WIDTH 600 HEIGHT 600 ]]

#C [[ COLOR LABEL Orange LABELSIZE 32 ]]

#C [[ LABELT 0 1000 0 LABEL 110 -20 2 "Snarkmaker\nSnarkmaker,\nmake me a Snark --" ]]

#C [[ COLOR LABEL LightGreen LABELSIZE 28 ]]

#C [[ LABELT 0 3000 100 LABEL -10 100 2 "recipe to create an offset block" ]]

#C [[ LABELT 4000 9000 100 LABEL -10 100 2 "line up elbow with new block\n(two parts)" ]]

#C [[ LABELT 9500 12000 100 LABEL -10 100 2 "duplicate the elbow,\ncreate a 0-degree elbow" ]]

#C [[ LABELT 12800 14600 100 LABEL -10 100 2 "move 0-degree elbow\naway from the block target" ]]

#C [[ LABELT 15500 252000 100 LABEL -10 100 2 "0-degree slow salvo recipe" ]]

#C [[ LABELT 253000 255000 100 LABEL -10 100 2 "remove 0-degree elbow" ]]

#C [[ LABELT 256000 263000 100 LABEL -10 100 2 "push new elbow back\n(optional)" ]]

#C Define block pattern

#C [[ RLE block 2o$2o! ]]

#C [[ RLE glider 2o$obo$o! ]]

#C [[ PASTE block ]]

#C [[ PASTEMODE OR ]]

#C [[ RLE elbow_to_block 2o$obo$o25$28bo$27b2o$27bobo21$50b2o$50bobo$50bo21$74bo$73b2o$73bobo21$96b2o$95b2o$97bo31$129b2o$128b2o$130bo27$157b3o$157bo$158bo29$190bo$189b2o$189bobo21$212b2o$212bobo$212bo21$234b3o$234bo$235bo20$258bo$257b2o$257bobo22$281b2o$281bobo$281bo21$303b3o$303bo$304bo26$332b2o$332bobo$332bo39$372b3o$372bo$373bo56$431b2o$430b2o$432bo38$470b3o$470bo$471bo20$493b2o$493bobo$493bo37$532b2o$531b2o$533bo29$564bo$563b2o$563bobo22$586b3o$586bo$587bo27$616b2o$616bobo$616bo21$638b3o$638bo$639bo20$662bo$661b2o$661bobo21$684b2o$683b2o$685bo! ]]

#C [[ PASTE elbow_to_block 4 0 ]]

#C elbow_to_block = 0 109 91 93 90 132 115 127 91 90 91 95 90 114 162 233 159 90 155 126 93 118 90 91 90 1114

[[ PASTET 4000 109 91 94 91 91 92 90 169 91 90 116 90 113 1114 109 91 93 91 156 91 91 94 90 91 140 91 103 91 91 132 1114 109 90 93 91 91 90 90 100 90 90 146 96 90 90 90 92 156 144 1114 109 91 93 91 132 115 102 90 91 91 91 90 90 154 1122 93 91 118 91 151 90 159 91 92 90 136 90 90 154 90 101 104 165 129 91 109 91 93 91 97 90 91 111 91 116 91 94 330 91 90 95 91 90 90 91 123 90 91 152 90 90 93 91 116 91 131 91 95 188 113 91 91 147 122 91 173 91 91 133 247 92 90 109 91 93 91 129 148 91 93 154 90 134 91 91 90 91 91 111 91 91 91 91 91 109 90 93 91 91 158 94 113 91 90 91 96 90 142 91 109 91 94 91 91 179 91 90 94 91 114 90 166 90 90 90 91 117 90 96 90 90 95 91 91 109 91 93 90 156 91 91 94 91 90 147 117 91 144 90 91 128 100 91 90 105 91 91 109 91 94 91 91 124 91 105 90 169 91 90 116 91 142 90 90 91 109 91 93 91 92 91 90 90 95 102 91 91 91 130 91 90 136 91 91 119 113 90 91 114 90 109 91 94 91 91 179 91 90 94 91 102 91 151 90 90 101 90 91 125 184 90 90 90 109 91 94 91 91 179 91 90 94 91 102 91 151 90 90 101 90 91 125 184 90 90 90 109 91 93 90 140 150 132 212 103 90 98 90 148 90 90 91 91 91 119 101 108 90 91 91 119 90 109 91 94 91 90 99 90 112 90 91 105 90 121 118 103 90 144 117 95 91 109 91 93 91 92 91 90 90 95 102 91 91 91 130 91 90 136 91 91 119 113 90 91 114 91 109 90 93 91 91 181 90 95 110 114 100 160 90 143 91 119 90 106 129 109 91 93 91 92 91 90 90 162 91 91 90 129 91 113 90 90 90 90 109 91 93 90 140 150 142 91 90 111 91 91 193 97 91 91 155 90 98 90 91 93 91 151 90 139 180 103 115 167 91 120 139 135 91 91 170 109 91 93 90 155 106 91 121 90 90 91 137 90 232 90 91 91 94 90 171 90 91 103 102 109 91 93 91 137 90 166 91 102 90 104 91 96 96 91 90 90 90 166 90 90 93 90 91 109 91 94 91 91 124 91 105 91 119 91 132 99 90 90 90 150 160 116 91 91 91 90 96 90 90 109 91 93 90 171 90 90 91 90 91 90 91 129 144 90 90 120 90 91 91 169 90 91 109 91 93 91 118 90 91 91 91 104 219 91 135 105 154 90 91 164 91 132 90 90 140 94 93 90 96 90 90 91 149 90 90 161 100 109 91 93 91 92 91 90 90 124 91 142 90 90 91 91 112 90 102 102 103 90 90 90 117 112 90 189 90 90 109 91 93 91 92 91 90 90 162 91 91 90 129 91 113 90 90 90 90 109 91 93 91 92 90 97 91 116 91 145 90 91 98 90 90 188 91 91 91 90 115 91 109 91 93 91 97 91 90 91 120 91 117 91 123 90 118 91 146 110 160 90 109 91 93 90 129 148 90 93 90 143 96 92 90 165 90 118 90 90 91 91 109 91 94 91 91 93 90 158 90 91 90 90 116 104 109 91 94 91 91 167 90 90 91 95 90 90 148 90 151 90 90 136 134 155 115 103 91 109 91 93 90 155 106 91 121 90 90 91 137 90 232 90 91 91 94 90 171 90 91 103 101 109 91 94 91 91 136 91 91 90 168 90 90 110 90 90 93 91 111 91 91 90 132 91 91 93 91 118 90 137 91 173 93 158 90 90 90 118 90 91 90 151 154 167 91 133 90 119 178 155 90 90 90 109 91 94 91 91 95 91 90 93 218 142 90 91 161 90 138 90 162 91 90 140 95 109 109 91 93 91 92 91 98 201 91 129 90 90 90 90 90 103 90 108 90 104 90 109 91 93 90 129 148 90 93 90 143 96 92 90 165 90 118 90 90 91 91 109 91 94 91 91 179 91 90 94 91 111 90 90 90 171 91 110 91 154 90 132 91 109 91 94 91 91 124 90 144 90 90 90 165 119 90 104 90 100 90 90 91 109 91 93 91 92 91 90 90 162 91 91 90 129 91 113 90 90 90 91 109 91 94 91 91 95 91 90 93 218 172 90 90 90 116 112 341 107 106 90 163 91 90 109 91 93 90 169 90 91 103 91 133 90 90 91 91 90 110 91 93 90 112 171 90 109 91 94 91 91 171 91 90 113 90 97 114 90 105 90 139 90 113 90 106 98 121 90 109 91 94 91 91 124 90 142 90 90 146 91 153 90 102 91 152 108 97 91 109 91 94 91 91 124 90 170 90 90 91 90 99 91 90 91 110 121 161 117 115 137 90 91 90 109 90 93 91 91 128 90 139 91 90 97 91 124 157 91 90 90 129 144 91 91 147 130 91 90 90 91 90 140 90 92 90 90 109 91 93 90 156 91 91 102 91 91 90 90 106 91 166 90 125 91 90 126 91 109 91 94 91 91 179 91 90 94 91 102 91 151 90 90 101 90 91 125 184 90 90 90 93 91 151 90 139 180 103 115 167 91 120 139 135 91 91 170 109 90 93 91 91 128 90 139 91 90 97 91 124 157 91 90 90 129 144 91 91 147 130 91 90 90 91 90 140 90 92 90 90 109 91 93 91 145 215 114 91 121 91 150 91 91 153 91 141 90 91 91 90 123 91 109 90 101 169 213 133 195 90 132 143 91 139 138 158 151 99 91 108 99 91 90 91 91 90 91 131 91 109 91 93 90 156 91 91 96 132 91 91 106 91 90 119 185 91 96 90 132 90 91 90 142 109 91 94 91 91 124 90 170 90 90 91 90 99 91 90 91 110 121 161 117 115 137 90 91 90 109 91 93 90 155 106 91 121 90 90 91 137 90 232 90 91 91 94 90 171 90 91 103 102 109 91 93 90 129 148 91 102 91 91 145 178 91 115 90 90 91 104 90 90 92 249 90 90 91 109 91 94 91 90 152 91 90 91 117 90 91 111 91 91 118 90 145 90 100 116 90 90 99 90 109 91 94 91 91 128 126 90 161 151 90 109 91 90 90 94 144 106 90 94 90 90 90 109 91 94 91 91 124 91 105 90 169 91 90 116 91 142 90 90 91 109 91 93 90 140 150 108 91 90 111 91 91 194 98 90 169 90 109 91 94 91 91 141 90 171 90 155 90 111 91 90 130 90 91 90 97 90 90 109 91 94 91 91 121 90 90 90 90 90 90 99 90 165 119 90 106 90 90 91 109 91 94 91 91 93 90 95 90 113 90 99 90 156 90 90 90 138 170 109 91 94 91 91 92 90 169 90 90 90 107 90 90 91 90 95 91 91 109 91 93 90 171 90 90 91 90 91 90 91 129 144 90 90 120 90 91 91 169 90 91 109 90 95 245 90 131 135 90 90 154 90 91 91 91 111 90 90 91 91 128 91 96 91 109 91 94 91 91 124 91 105 91 119 91 132 99 90 90 90 150 160 116 91 91 91 90 96 90 91 93 91 116 91 151 90 109 111 127 91 113 91 169 186 90 90 158 91 90 90 90 117 91 160 90 91 96 90 90 91 109 91 94 91 90 95 91 90 147 167 90 160 90 160 104 90 90 91 91 101 139 91 90 136 129 90 109 91 93 91 123 91 118 90 91 108 91 91 90 90 90 90 143 91 92 177 129 101 167 91 90 90 91 130 127 90 137 91 93 90 91 91 94 229 107 91 90 104 91 91 101 91 91 93 90 119 90 133 90 91 93 145 91 132 91 109 91 93 91 137 90 166 91 102 90 104 91 96 96 91 90 90 90 166 90 90 93 90 90 109 90 93 91 91 128 90 139 91 90 97 91 124 157 91 90 90 129 144 91 91 147 130 91 90 90 91 90 140 90 92 90 91 123 270 90 125 90 90 90 94 137 123 90 145 136 90 91 100 91 105 91 153 91 90 145 155 109 91 93 91 92 91 139 90 91 91 90 96 130 97 91 164 90 97 91 90 91 114 90 90 118 90 90 123 270 90 125 90 90 90 94 137 123 90 145 136 90 91 100 91 105 91 153 91 90 145 155 109 90 93 91 91 148 91 90 151 90 91 163 108 151 112 144 90 149 90 90 99 90 109 91 94 91 91 124 91 126 91 140 162 148 90 90 119 90 91 109 91 93 91 155 106 91 91 96 90 90 91 108 90 156 90 90 120 90 112 91 99 91 109 91 93 91 129 148 91 93 154 90 134 91 91 90 91 91 111 91 91 91 91 90 109 91 93 91 129 148 91 93 154 90 134 91 91 90 91 91 111 91 91 91 91 90 109 91 93 91 129 149 91 90 90 142 219 90 99 91 109 115 92 185 91 109 90 93 91 91 142 90 98 90 91 125 114 127 90 111 90 109 91 93 91 130 91 90 134 90 90 103 122 156 112 90 183 117 91 152 141 90 98 90 91 93 91 116 91 131 91 95 188 113 91 91 147 122 91 173 91 91 133 247 92 91 109 91 93 90 156 91 91 94 91 90 147 117 91 144 90 91 128 100 91 90 105 91 91 93 91 116 91 106 91 155 90 106 90 167 90 90 91 148 123 111 155 91 105 90 90 92 90 124 90 91 109 91 94 91 91 95 91 90 97 143 171 90 105 90 91 144 91 90 90 90 94 90 90 90 109 91 93 91 92 90 158 90 94 270 172 130 90 91 91 96 90 90 147 91 109 91 93 91 92 90 162 90 129 91 91 91 90 137 99 90 90 111 91 153 90 90 90 109 91 95 125 128 90 90 90 172 90 90 90 119 91 113 247 90 144 90 140 90 109 90 93 91 90 95 91 91 139 90 147 90 90 99 117 91 157 91 126 90 90 91 160 90 91 91 91 111 90 90 113 90 91 109 91 94 91 90 99 90 112 90 91 105 90 121 118 103 90 144 117 95 91 109 91 94 91 91 124 90 144 90 90 90 165 119 90 104 90 100 90 90 90 109 91 94 91 91 179 91 90 94 91 114 90 166 90 90 90 91 117 90 96 90 90 95 91 91 109 91 94 91 91 95 91 90 150 90 140 90 91 90 171 90 118 91 111 90 104 91 109 91 93 91 97 91 90 91 120 90 95 91 143 90 90 90 90 91 109 90 95 245 90 95 90 123 91 90 115 142 91 109 91 94 91 91 124 91 90 91 91 90 91 90 141 90 172 91 161 90 169 228 90 109 91 94 91 91 93 90 91 91 90 100 90 94 90 108 90 91 91 119 1114 109 91 95 113 90 134 90 1114 109 90 93 91 90 95 91 91 138 157 96 90 120 91 97 107 90 90 93 188 109 90 93 91 90 95 91 91 138 157 96 90 120 91 97 107 90 90 93 188 109 90 93 91 90 95 91 91 138 157 96 90 120 91 97 107 90 90 93 188 109 91 93 91 92 90 97 91 116 91 93 115 90 91 130 ]]

#C a trailing "90" would mark a safe location for the first glider in a following copy of the recipe

[[ PASTE glider 254 250 ]]

[[ T 15500 ]]

[[ T 15501 STEP 64 ]]

[[ T 253000 ]]

[[ T 253001 STEP 9 ]]

This is more or less the recipe used in the 0E0P metacell to create the Mysterious Snark. Other Snarks in 0E0P circuitry are generally produced with more conventional slow salvos, sent at 90 degrees from a construction elbow, rather than straight out at 0 degrees.

To copy out the entire Snarkmaker slow salvo, rather than just the part of it that's visible at any given moment, type Ctrl+Shift+C in LifeViewer.

Posted: **May 29th, 2019, 2:07 am**

dvgrn wrote:If anyone wants access to more of the 563 snapshots, let me know. Looks like I could get half of them on Dropbox, at least, and that would include the majority of the interesting ones.

I'd like to see them. Link it when you're ready.

Posted: **May 29th, 2019, 6:46 am**

Ch91 wrote:
dvgrn wrote:If anyone wants access to more of the 563 snapshots, let me know. Looks like I could get half of them on Dropbox, at least, and that would include the majority of the interesting ones.
I'd like to see them. Link it when you're ready.

There's also a new HD video of the construction of the daughter metacell:

http://files.hatsya.co.uk/gol/metacell_1920x1080.mp4

Posted: **May 29th, 2019, 9:02 am**

calcyman wrote:There's also a new HD video of the construction of the daughter metacell:

http://files.hatsya.co.uk/gol/metacell_1920x1080.mp4

I've been wondering if it might be possible to make a single timeline .mc.gz out of the snapshots that were used to make that video. The timeline macrocell format allows hashtiles that are shared between snapshots (which is almost all of them) to be stored only once.

Does lifelib have any options for doing this kind of thing? It's not a task that can be done very easily with a Golly script, because Golly's default assumption is that any pattern that the script is working with will get converted to a cell list, and that's pretty much deadly here. The conversion process would probably just read the snapshot .mc files directly and collapse duplicate hashtile definitions whenever it finds them, without using any Golly functionality at all.

ConwayLife.com

How does the 0E0P metacell work?

How does the 0E0P metacell work?

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