4 glider syntheses

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
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Ian07
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Re: 4 glider syntheses

Post by Ian07 » February 1st, 2020, 3:18 pm

#230: xs16_0ggca96z3443

Code: Select all

x = 9, y = 12, rule = B3/S23
4bobo$5b2o$5bo$2bo$obo3b2o$b2o3bobo$6bo3$2b2o$2bobo$2bo!
EDIT: #231: Longhorn

Code: Select all

x = 30, y = 18, rule = B3/S23
27bo$27bobo$27b2o6$13bo$13bobo$13b2o2$5bo$6b2o$5b2o$3o$2bo$bo!
Bonus: 4G cis-beacon on dock:

Code: Select all

x = 30, y = 18, rule = B3/S23
27bo$27bobo$27b2o6$9bo$8bo$8b3o2$10bo$9b2o$9bobo$bo$b2o$obo!

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Re: 4 glider syntheses

Post by GUYTU6J » February 4th, 2020, 2:04 am

Almost xs19_wmm0e952z643

Code: Select all

x = 18, y = 24, rule = B3/S23
17bo$15b2o$16b2o7$14bo$12b2o$13b2o2$11b3o$11bo$12bo6$2o$b2o$o!
Bullet51 wrote:
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Ian07
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Re: 4 glider syntheses

Post by Ian07 » February 4th, 2020, 7:18 am

GUYTU6J wrote:
February 4th, 2020, 2:04 am
Almost xs19_wmm0e952z643

Code: Select all

RLE
5G:

Code: Select all

x = 56, y = 60, rule = B3/S23
53bobo$53b2o$54bo23$43bo$42bo$42b3o4$30bo$31b2o$30b2o3$30b3o$32bo$31bo
19$bo$b2o$obo!

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GUYTU6J
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Re: 4 glider syntheses

Post by GUYTU6J » February 4th, 2020, 1:23 pm

Ian07 wrote:
February 4th, 2020, 7:18 am
GUYTU6J wrote:
February 4th, 2020, 2:04 am
Almost xs19_wmm0e952z643

Code: Select all

Failed 4G synth
5G:

Code: Select all

x = 56, y = 60, rule = B3/S23
53bobo$53b2o$54bo23$43bo$42bo$42b3o4$30bo$31b2o$30b2o3$30b3o$32bo$31bo
19$bo$b2o$obo!
Good. Can every reaction initiated by two invalid gliders be started via valid 2~3G pathway(s)?
Bullet51 wrote:
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没想到你就这样和我们说再见了。你寒假还会回来吗?
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Re: 4 glider syntheses

Post by mniemiec » February 4th, 2020, 2:49 pm

GUYTU6J wrote:
February 4th, 2020, 1:23 pm
Good. Can every reaction initiated by two invalid gliders be started via valid 2~3G pathway(s)?
This one, in particular, does not do so by creating one glider that suddenly appears next to an approaching one (which would likely provide a recipe for creating many such "impossible" collisions); that would likely require 3 gliders in addition to the approaching one.

To properly answer your question, it would probably be necessary to explicitly enumerate all the "impossible" 2-glider collisions, and then examine each one to see whether the result a few generations down the road occurs from some known 3-glider collision.

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Re: 4 glider syntheses

Post by dvgrn » February 4th, 2020, 3:07 pm

mniemiec wrote:
February 4th, 2020, 2:49 pm
To properly answer your question, it would probably be necessary to explicitly enumerate all the "impossible" 2-glider collisions, and then examine each one to see whether the result a few generations down the road occurs from some known 3-glider collision.
Even then, there might be cases where the gliders making up the replacement 3-glider collision might get in the way of the remaining (valid) gliders in the recipe, so that the replacement couldn't actually be made to work. I'd guess there are two- to four-glider replacements for a majority of the invalid cases, though.

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Re: 4 glider syntheses

Post by muzik » February 11th, 2020, 4:17 pm

4-glider synthesis of a bach:

Code: Select all

x = 20, y = 29, rule = B3/S23
2$9bo$7bobo$8b2o3bo$12bo$12b3o14$15b2o$4bo10bobo$4b2o9bo$3bobo!
It may be possible to knock this down to 3 though:

Code: Select all

x = 14, y = 5, rule = B3/S23
11bo$11bobo$11b2o2$7o!
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Re: 4 glider syntheses

Post by dvgrn » February 11th, 2020, 7:43 pm

muzik wrote:
February 11th, 2020, 4:17 pm
4-glider synthesis of a bach...
It may be possible to knock this down to 3 though...
Yup, synthesise-constellation-ee9.py knows about four ways to produce that constellation:

Code: Select all

x = 201, y = 41, rule = B3/S23
153bo$151bobo$152b2o24$2bo$obo$b2o98bo92bo$102b2o7bo83b2o$59bo41b2o7bo
83b2o$60bo49b3o86bo$58b3o137b2o$198bobo$12bo96bo$7b2o2b2o48bo46b2o$6bo
bo2bobo47b2o45bobo$8bo51bobo$51b2o$52b2o$51bo!
If you're interested in glider syntheses in general, it's really worth getting the synthesise-patt and synthesise-constellation scripts working on your computer, if at all possible. They make searching for this kind of thing very nearly trivial -- just select and run, and see what comes back.

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Re: 4 glider syntheses

Post by muzik » February 11th, 2020, 8:55 pm

Seems to work for me but turned up no results for chopin, schumann or stravinsky, so it seems they'll have to go unsynthesized for now:

Code: Select all

x = 31, y = 8, rule = B3/S23
24b2o3b2o$b2o3b2o16b2o3b2o$o2bobo2bo3bo5bo$obo3bobo2bobo3bobo$bo5bo4bo
5bo8bo$4bo10bo10bobo$4bo10bo10bobo$4bo10bo11bo!
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Re: 4 glider syntheses

Post by Entity Valkyrie 2 » February 12th, 2020, 1:22 am

What's the smallest number of gliders for a bartok?
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Re: 4 glider syntheses

Post by Ian07 » February 12th, 2020, 7:19 am

muzik wrote:
February 11th, 2020, 8:55 pm
Seems to work for me but turned up no results for chopin, schumann or stravinsky, so it seems they'll have to go unsynthesized for now:

Code: Select all

RLE
Since it looks like you got Python scripts to work, I'd suggest getting this apgcode script by biggiemac so you can check these yourself.

4G Chopin:

Code: Select all

x = 19, y = 7, rule = B3/S23
bo11bo$2bo9bo$3o9b3o2$4bo11b3o$4b2o10bo$3bobo11bo!
4G Schumann:

Code: Select all

x = 14, y = 15, rule = B3/S23
11bo$11bobo$11b2o2$bo$2bo$3o$5bo$4bo$4b3o3$3bo$bobo$2b2o!
Stravinsky doesn't currently have a synth on Catagolue.

(Disclaimer: I may have mixed up some of the names; I just assumed they were in the order you showed the constellations)

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Re: 4 glider syntheses

Post by dvgrn » February 12th, 2020, 9:16 am

Ian07 wrote:
February 12th, 2020, 7:19 am
Stravinsky doesn't currently have a synth on Catagolue.
It does now. If it wasn't there when Ian07's message was posted, that was quick work on somebody's part.

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Re: 4 glider syntheses

Post by mniemiec » February 12th, 2020, 3:33 pm

Entity Valkyrie 2 wrote:
February 12th, 2020, 1:22 am
What's the smallest number of gliders for a bartok?
That would depend on what a "bartok" is. Do you have a RLE or APGcode? I can find no mention of it on the forums or the wiki.
EDIT: I would suspect that Chopin, Schumann, and Stravinsky also occur fairly often from 3-glider collisions.

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Re: 4 glider syntheses

Post by dvgrn » February 12th, 2020, 4:39 pm

mniemiec wrote:
February 12th, 2020, 3:33 pm
I would suspect that Chopin, Schumann, and Stravinsky also occur fairly often from 3-glider collisions.
I think Ian07 probably checked that, but I just rechecked those three, and the 3G search script doesn't give any results. Looks like 4G is the best available for all of them.

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Re: 4 glider syntheses

Post by GUYTU6J » February 13th, 2020, 8:10 am

dvgrn wrote:
February 4th, 2020, 3:07 pm
mniemiec wrote:
February 4th, 2020, 2:49 pm
To properly answer your question, it would probably be necessary to explicitly enumerate all the "impossible" 2-glider collisions, and then examine each one to see whether the result a few generations down the road occurs from some known 3-glider collision.
Even then, there might be cases where the gliders making up the replacement 3-glider collision might get in the way of the remaining (valid) gliders in the recipe, so that the replacement couldn't actually be made to work. I'd guess there are two- to four-glider replacements for a majority of the invalid cases, though.
How about this example?

Code: Select all

x = 12, y = 36, rule = B3/S23
10bo$9bo$9b3o20$b2o$bobo$bo2$3o$2bo$bo5$4b3o$4bo$5bo!
Synthesise_patt_v1.2.py cannot replace the central glider pair with 3G. Does either of the 2G-to-G reflection work?
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Re: 4 glider syntheses

Post by dvgrn » February 13th, 2020, 5:53 pm

GUYTU6J wrote:
February 13th, 2020, 8:10 am
Synthesise_patt_v1.2.py cannot replace the central glider pair with 3G. Does either of the 2G-to-G reflection work?
I think glider kickbacks are pretty hopeless for this kind of thing, but let's go ahead and do the tests. Kickbacks are confusing, but they're not exactly rocket surgery. Here are the two kickback reactions from two-glider-syntheses.rle:

Code: Select all

x = 33, y = 21, rule = LifeHistory
13.2D$14.2D$13.D2$30.3D$32.D$31.D$7.A$6.A20.A$6.3A17.A$26.3A7$23.A$.
2A19.2A$A.A19.A.A$2.A!
When the green gliders collide, they'll end up in the red marked locations in 60 ticks. So all you have to do is rewind three of the gliders in the invalid 4G collision -- i.e., move each of the gliders backwards by 60 ticks, which is 15 cells diagonally -- and then drop in one of these recipes in the place of the remaining glider (so the red marked cells cover up the glider).

Here's a test page that could be used to try all sixteen combinations of kickback and orientation:

Code: Select all

x = 339, y = 766, rule = LifeHistory
134.A129.A$133.A129.A$133.3A127.3A13$119.D129.D$118.D129.D$118.3D127.
3D19$108.A$10.2D98.2E128.2D$10.D.D97.E.E127.D.D$10.D99.E129.D.A2$16.A
92.3D127.3E77.3D$14.A.A94.D129.E79.D$15.2A93.D129.E79.D2$25.A310.3D$
23.2A313.D$24.2A311.D$113.3D127.3D$113.D129.D68.A.A18.A$114.D129.D67.
2A18.A$313.A18.3A$255.2A$255.A.A$6.2D247.A$6.D.D$6.D87.3A$96.A$95.A
233.A$307.2A19.2A$308.2A18.A.A$14.A292.A$15.2A$14.2A112.3A127.3A$128.
A129.A$129.A129.A$25.A$24.2A$24.A.A32$134.A129.A$133.A129.A$133.3A
127.3A13$119.D129.D$118.D129.D$118.3D127.3D19$108.A$110.2E128.2D$110.
E.E127.D.D$110.E129.D.A2$109.3D127.3E$111.D129.E$110.D129.E5$113.3D
127.3D$113.D129.D$114.D129.D2$255.2A$255.A.A$255.A2$94.3A$96.A$95.A5$
128.3A127.3A$128.A129.A$129.A129.A35$134.A129.A$133.A129.A$133.3A127.
3A13$119.D129.D$118.D129.D$118.3D127.3D19$108.A$110.2E128.2D$110.E.E
127.D.D$110.E129.D.A2$109.3D127.3E$111.D129.E$110.D129.E5$113.3D127.
3D$113.D129.D$114.D129.D2$255.2A$255.A.A$255.A2$94.3A$96.A$95.A5$128.
3A127.3A$128.A129.A$129.A129.A35$134.A129.A$133.A129.A$133.3A127.3A
13$119.D129.D$118.D129.D$118.3D127.3D19$108.A$110.2E128.2D$110.E.E
127.D.D$110.E129.D.A2$109.3D127.3E$111.D129.E$110.D129.E5$113.3D127.
3D$113.D129.D$114.D129.D2$255.2A$255.A.A$255.A2$94.3A$96.A$95.A5$128.
3A127.3A$128.A129.A$129.A129.A35$134.A129.A$133.A129.A$133.3A127.3A
13$119.D129.D$118.D129.D$118.3D127.3D16$17.2D$17.D.D$17.D$108.A$2D
108.2E128.2D$D.D107.E.E127.D.D$D109.E129.D.A2$109.3D127.3E77.3D$25.A
85.D129.E79.D$6.A19.2A82.D129.E79.D$4.A.A18.2A$5.2A307.A$313.A$313.3A
$113.3D127.3D$113.D129.D$114.D129.D60.A.A$9.2A19.A275.2A$8.2E2A17.2A
224.2A49.A$8.EAE18.A.A223.A.A$255.A2$94.3A$96.A$95.A227.3D$325.D$324.
D3$128.3A127.3A$128.A129.A$129.A129.A$314.A.A$314.2A$315.A2$305.2A$
306.2A$305.A28$134.A129.A$133.A129.A$133.3A127.3A13$119.D129.D$118.D
129.D$118.3D127.3D19$108.A$110.2E128.2D$110.E.E127.D.D$110.E129.D.A2$
109.3D127.3E$111.D129.E$110.D129.E5$113.3D127.3D$113.D129.D$114.D129.
D2$255.2A$255.A.A$255.A2$94.3A$96.A$95.A5$128.3A127.3A$128.A129.A$
129.A129.A35$134.A129.A$133.A129.A$133.3A127.3A13$119.D129.D$118.D
129.D$118.3D127.3D19$108.A$110.2E128.2D$110.E.E127.D.D$110.E129.D.A2$
109.3D127.3E$111.D129.E$110.D129.E5$113.3D127.3D$113.D129.D$114.D129.
D2$255.2A$255.A.A$255.A2$94.3A$96.A$95.A5$128.3A127.3A$128.A129.A$
129.A129.A35$134.A129.A$133.A129.A$133.3A127.3A13$119.D129.D$118.D
129.D$118.3D127.3D19$108.A$110.2E128.2D$110.E.E127.D.D$110.E129.D.A2$
109.3D127.3E$111.D129.E$110.D129.E5$113.3D127.3D$113.D129.D$114.D129.
D2$255.2A$255.A.A$255.A2$94.3A$96.A$95.A5$128.3A127.3A$128.A129.A$
129.A129.A!
There's a third set of adjustments, though. To have any chance of success, the kickback has to happen at the last possible moment. So let's take the upper left corner case in the test page:

Code: Select all

x = 130, y = 69, rule = LifeHistory
128.A$127.A$127.3A13$113.D$112.D$112.3D19$102.A$4.2D98.2E$4.D.D97.E.E
$4.D99.E2$10.A92.3D$8.A.A94.D$9.2A93.D2$19.A$17.2A$18.2A$107.3D$107.D
$108.D4$2D$D.D$D87.3A$90.A$89.A3$8.A$9.2A$8.2A112.3A$122.A$123.A$19.A
$18.2A$18.A.A!
Drop one of the red gliders in one of the groups of three on the left, directly on top of the yellow sabotaged glider, and you'll end up with five gliders that would make that invalid 4G collision -- if the gliders didn't interact too soon:

Code: Select all

x = 42, y = 66, rule = LifeHistory
40.A$39.A$39.3A13$25.D$24.D$24.3D19$14.A$16.2D$16.D.D$16.D2$15.3D4.A$
17.D2.A.A$16.D4.2A2$31.A$29.2A$30.2A$19.3D$19.D$20.D6$3A$2.A$.A5$34.
3A$34.A$35.A!
So we want to make the kicked-back glider appear at the last possible minute. It turns out that we can delay the kickback recipe gliders in time by multiples of 4 -- i.e., move them each two steps diagonally backwards -- and then move both gliders in whatever direction is "forwards" from the point of view of the kicked-back glider. This is the part I find a little confusing: I have to mumble things to myself, like "Okay, I moved both gliders backward, so now they're going to get where they're going too late, so to make up for that by moving the location where they're going to collide, by the same distance."

In this case the final result is that one glider moves by (-2N, -2N) and the other moves by (0,-2N):

Code: Select all

x = 42, y = 66, rule = LifeHistory
40.A$39.A$39.3A13$25.D$24.D$24.3D19$14.A$16.2D$16.D.D$16.D3.A$18.A.A$
15.3D.2A.B$17.D2.B.B$16.D4.2B8.A$29.2A$30.2A$29.2B$30.2B$19.3D$19.D$
20.D6$3A$2.A$.A5$34.3A$34.A$35.A!
Keep moving the gliders until just before the kickback doesn't work any more, and you'll find out that... even the last-possible-moment kickback still doesn't work:

Code: Select all

x = 42, y = 66, rule = LifeHistory
40.A$39.A$39.3A13$25.D$24.D$24.3D10$8.A$6.A.A$7.2A2$31.A$29.2A$30.2A
4$16.2D$16.D.D$16.D2$15.3D4.B$17.D2.B.B$16.D4.2B2$31.B$29.2B$30.2B$
19.3D$19.D$20.D6$3A$2.A$.A5$34.3A$34.A$35.A!
Trying the other fifteen possibilities would probably be good practice for working with kickbacks. But I think the kickback reaction will always get mixed up with the other glider somehow.

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Re: 4 glider syntheses

Post by dvgrn » February 13th, 2020, 6:11 pm

dvgrn wrote:
February 13th, 2020, 5:53 pm
Trying the other fifteen possibilities would probably be good practice for working with kickbacks. But I think the kickback reaction will always get mixed up with the other glider somehow.
I was a little surprised to see that that invalid 2-glider collision didn't have a 3G synthesis. Did you try checking the 4G database?

Alternatively, there's a stage very late in the construction reaction where the active pattern resolves into two pieces that look like they ought to be constructible:

Code: Select all

x = 15, y = 15, rule = LifeHistory
2$6.A6.D$5.2A5.D$4.2A5.D$3.2A5.2D$4.3A3.D$11.D$4.A2$7.D$6.D.D$5.2D$7.
D!
Run six ticks, then draw active cells over the red cells and keep running.

The 3G database reports a couple of matches for the eastern cluster of red cells, but they're all false positives I think:

Code: Select all

x = 160, y = 11, rule = B3/S23
2bo72bo77bo$2bobo71b2o76b2o$2b2o71b2o76b2o$81bo76bo$79b2o69b2o5b2o$80b
2o69b2o4bobo$bo148bo$2bo$3o2bo70bo$5bobo68b2o$5b2o68bobo!
The southern cluster is really common and has lots of 3G solutions, though they mostly won't fit with whatever builds the western green cluster. But anyway if you experiment with it you'll find out that you just need a single dot spark at the right generation (T=9) down there in the south.

Anyway, no doubt someone in the Synth Department who really knows what they're doing will come up with a better approach, maybe using one of the other zillion soups for that still life. Really I just wanted to write a walkthrough about kickbacks.

EDIT: Yeah, please ignore the above. The 4G may be invalid, and several of the 5Gs produce the same basic reaction, a TL plus whatever that seven-cell "block tie blinker" thing is that the eater+glider makes -- does it have a name?

Code: Select all

x = 25, y = 32, rule = B3/S23
12bobo$7bobo2b2o$8b2o3bo$8bo11$2bo$obo$b2o19bo$22bobo$22b2o11$20b2o$
19b2o$21bo!
However, the sixth of the 5G searches produces a beautiful 6G recipe. Can't hope for much better than that:

Code: Select all

x = 48, y = 48, rule = B3/S23
2bo$obo$b2o22$38bo$36bobo$37b2o11$33b2o$32bobo10b3o$34bo10bo$46bo$21b
2o$22b2o$21bo2$19bo$19b2o$18bobo!

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Re: 4 glider syntheses

Post by Entity Valkyrie 2 » February 14th, 2020, 7:00 pm

mniemiec wrote:
February 12th, 2020, 3:33 pm
Entity Valkyrie 2 wrote:
February 12th, 2020, 1:22 am
What's the smallest number of gliders for a bartok?
That would depend on what a "bartok" is. Do you have a RLE or APGcode? I can find no mention of it on the forums or the wiki.
EDIT: I would suspect that Chopin, Schumann, and Stravinsky also occur fairly often from 3-glider collisions.
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Ian07
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Re: 4 glider syntheses

Post by Ian07 » February 14th, 2020, 7:07 pm

Entity Valkyrie 2 wrote:
February 14th, 2020, 7:00 pm
It is in my user page.
(To be more specific, it's this)

Don't know how to make a synthesis from the reaction you showed; it doesn't have a 3G, and even the weird object at the top doesn't have a 3G either.

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Re: 4 glider syntheses

Post by Entity Valkyrie 2 » February 14th, 2020, 7:13 pm

Ian07 wrote:
February 14th, 2020, 7:07 pm
Entity Valkyrie 2 wrote:
February 14th, 2020, 7:00 pm
It is in my user page.
(To be more specific, it's this)

Don't know how to make a synthesis from the reaction you showed; it doesn't have a 3G, and even the weird object at the top doesn't have a 3G either.
It's really just a honey farm with a few cells from the top removed. The weird thing on the top is just one way to do it; I have advanced a few generations and removed it.

UPDATE: Better mozart predecessor.
Bx222 IS MY WORST ENEMY.

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Re: 4 glider syntheses

Post by dvgrn » February 14th, 2020, 10:40 pm

Entity Valkyrie 2 wrote:
February 14th, 2020, 7:13 pm
It's really just a honey farm with a few cells from the top removed. The weird thing on the top is just one way to do it; I have advanced a few generations and removed it.
I'm really kind of surprised that there isn't a 3G bartok, given that it's just a damaged pre-HF. But apparently these composers are all 4G.

The damage can be done with a pre-blinker or another pre-honeyfarm, according to wildmyron's 4G script:

Code: Select all

x = 225, y = 29, rule = B3/S23
obo$b2o$bo102bo$17bo87bo$15b2o86b3o117bo$16b2o204bo$120bo101b3o$118b2o
$119b2o83bobo$205b2o$205bo2$221bo$221bobo$221b2o2$15b2o$15bobo$15bo$
117b2o$116b2o90b2o$118bo88bobo$209bo$125b2o$125bobo$125bo$27b2o$26b2o$
28bo!

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Re: 4 glider syntheses

Post by mniemiec » February 15th, 2020, 3:02 am

dvgrn wrote:
February 14th, 2020, 10:40 pm
The damage can be done with a pre-blinker or another pre-honeyfarm, according to wildmyron's 4G script: ...
Bartok and Mozart can be easily be synthesized artificially from 4 gliders too:

Code: Select all

x = 70, y = 21, rule = B3/S23
36bo$37boo9bo$4bobo29boo8boo$4boo41boo$5bo4$8boo$8bobo$8bo$$bo$boo38bo
$obobboo11b3o7b3o10boo16boo7boo$4boo34bobobboo12boo7boo$6bo37boo$24bo
21bo17bo$23bobo37bobo$23bobo37bobo$24bo39bo!

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Re: 4 glider syntheses

Post by Entity Valkyrie 2 » February 15th, 2020, 6:37 am

Y'all probably don't know that Entity Valkyrie 2 is also a (junior) composer, but giving you an example piece would show you my real name so I wouldn't do it.

EDIT: That's probably a random post.
Bx222 IS MY WORST ENEMY.

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Re: 4 glider syntheses

Post by mniemiec » February 15th, 2020, 7:25 am

Entity Valkyrie 2 wrote:
February 15th, 2020, 6:37 am
Y'all probably don't know that Entity Valkyrie 2 is also a (junior) composer, but giving you an example piece would show you my real name so I wouldn't do it.

EDIT: That's probably a random post.
This would be more appropriate for the sandbox, rather than added to a totally unrelated thread. Also, posts of the form "I have information that I think might be of interest to you (otherwise I wouldn't be talking about it), but I'm not going to give it to you" are generally not useful. I also don't understand why people are afraid to mention discoveries under their real names. Is there some kind of stigma associated with CA that I'm not aware of?

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Re: 4 glider syntheses

Post by Extrementhusiast » February 15th, 2020, 3:31 pm

mniemiec wrote:
February 15th, 2020, 7:25 am
Entity Valkyrie 2 wrote:
February 15th, 2020, 6:37 am
Y'all probably don't know that Entity Valkyrie 2 is also a (junior) composer, but giving you an example piece would show you my real name so I wouldn't do it.

EDIT: That's probably a random post.
This would be more appropriate for the sandbox, rather than added to a totally unrelated thread. Also, posts of the form "I have information that I think might be of interest to you (otherwise I wouldn't be talking about it), but I'm not going to give it to you" are generally not useful. I also don't understand why people are afraid to mention discoveries under their real names. Is there some kind of stigma associated with CA that I'm not aware of?
No, but in this era of everything tracking you, I can see why somebody would want to keep themselves private.
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