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Challenges

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Re: Challenges

Postby 83bismuth38 » July 3rd, 2017, 10:43 am

is a c/1 knightship possible?
x = 8, y = 10, rule = B3/S23
3b2o$3b2o$2b3o$4bobo$2obobobo$3bo2bo$2bobo2bo$2bo4bo$2bo4bo$2bo!

No football of any dui mauris said that.
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Re: Challenges

Postby Saka » July 3rd, 2017, 11:25 am

83bismuth38 wrote:is a c/1 knightship possible?

x = 11, y = 19, rule = R5,C4,M0,S83..98,B10..108,NN:T1000,1000
$4.C$5.CB$5.2CBA$5.2C2BA$5.2C2B2A$5.2C2B2A$5.2C2B2A$5.2C2B2A$4.3C2B2A
$4.2C3B2A$3.3C2B3A$2.3C3B2A$.3C3B3A$2.C3B3A$4.B3A$6.A!
Proud owner and founder of Sakagolue
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

(Check gen 2)
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Re: Challenges

Postby gameoflifemaniac » July 9th, 2017, 6:04 am

p1 puffer
https://www.youtube.com/watch?v=q6EoRBvdVPQ
One big dirty Oro. Yeeeeeeeeee...
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Re: Challenges

Postby drc » July 9th, 2017, 6:12 am

gameoflifemaniac wrote:p1 puffer

x = 8, y = 8, rule = B2ace5-er/S2ae3aeir4q5i
4bo$3b2obo$bo4b2o$ob3obo$ob3obo$bo4b2o$3b2obo$4bo!
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Re: Challenges

Postby dvgrn » July 10th, 2017, 10:13 am

Possible isotropic rule example for Golly 3.0: find a 16x16 soup in B2-a5/S1e2-a35678 -- a distant Just Friends relative -- that displays the most different kinds of reactions before stabilizing inside a finite bounding box.

Here's my first candidate --
x = 16, y = 16, rule = B2-a5/S1e2-a35678
2bobobob4obobo$bob2obo2bo2b2o$2bobo4b3ob3o$3obo5bob2o$3o4b2o4b3o$2o5b
8o$bo2bo5b3o$o2b2o4bo2b2o$o2bobob3o4bo$2o2b4o3b3o$3o2b2obo3b4o$3bo5bob
2ob2o$o4b6o2b2o$4ob3obob2o$2b4ob2o3bobo$ob2o4b4ob2o!

-- but I don't like it all that much. It starts out well, but then it turns out that its huge final population is all due to one trick at the end.

Here's the script that found it. Hit 'q' to stop searching and display the soup with the highest population found so far:

from __future__ import division
import golly as g

best=0
bestpat = []
count=0

while 1:
  g.new(str(count)+": "+str(best))
  g.select([0,0,16,16])
  g.randfill(50)
  clist = g.getcells(g.getselrect())
  g.run(16384)
  r = g.getrect()
  if r==[]: r=[0,0,1,1]
  g.run(4096)
  r2 = g.getrect()
  if r2==[]: r2=[0,0,1,1]
  if r2[2]>r[2] or r2[3]>r[3]:
    continue
# if 1000*int(g.getpop())/r[2]/r[3]+r[2]+r[3]>best:
  if int(g.getpop())>best:
    best = int(g.getpop())
    bestpat = clist[:]
  count+=1
  g.fit()
  g.update()
  k = g.getevent()
  if k=="key q none":
    g.new("Best")
    g.putcells(bestpat)
    g.exit()

I tried a couple other metrics, like highest density and largest bounding box, and different run times -- presumably this script will throw away occasional methuselahs with >16384 run times, which would be great candidates for the challenge. But the search gets a lot slower if you bump that number up too high.
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Re: Challenges

Postby drc » July 14th, 2017, 8:24 am

Challenge: Find a garden of eden in B8/S012345678, in which these two patterns are mapped to the same configuration:
x = 8, y = 3, rule = B8/S012345678
3o2b3o$obo2b3o$3o2b3o!
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Re: Challenges

Postby calcyman » July 18th, 2017, 4:16 am

drc wrote:Challenge: Find a garden of eden in B8/S012345678, in which these two patterns are mapped to the same configuration:
x = 8, y = 3, rule = B8/S012345678
3o2b3o$obo2b3o$3o2b3o!


Done:

x = 3, y = 3, rule = B8/S012345678
3o$obo$3o!


A more fun solution, which works for *any* rule with two 3-by-3 configurations P and Q mapping to the same configuration, is as follows:

  • Consider a pattern of size (5n - 2) by (5n - 2). If it occurs within generation 1 of a pattern, then that 'father' can be assumed to be 5n by 5n. (We take 'father' more liberally to allow junk outside the target 'child'.)
  • Suppose the father exists. Divide it into n^2 5-by-5 regions. If any of them is P with an empty border, replace it with Q with an empty border.
  • This means there are only (2^25 - 1) ^ (n^2) putative fathers worth considering.
  • However, there are 2^((5n-2)^2) patterns of size (5n - 2) by (5n - 2). Whenever n >= 232581596, this is greater than the previous value.
  • Hence there exists a GoE of size 1162907980 by 1162907980.
  • An explicit GoE is therefore obtained by tiling together all possible patterns of this size, in lexicographical order, into an immense square. The resulting pattern is a colossal square of side-length 1162907980 * 2 ^ 676177484973840200.
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Re: Challenges

Postby drc » July 18th, 2017, 4:25 am

Alright, does this count for B8/S01234567?:
x = 10, y = 3, rule = B8/S01234567
4o2b4o$o2bo2b4o$4o2b4o!

I'm trying to find a rule that's REALLY difficult to find a GoE for.
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Re: Challenges

Postby calcyman » July 19th, 2017, 3:43 am

drc wrote:I'm trying to find a rule that's REALLY difficult to find a GoE for.


B13578/S02468 should be excruciatingly difficult. Without the B8, this is the Fredkin replicator rule (which is reversible ergo has no GoEs), but the B8 makes it irreversible. In particular, the following two patterns have the same descendant:

x = 129, y = 29, rule = B13578/S02468
11o7b11o71b11o7b11o$11o7b11o71b11o7b11o$11o7b11o71b11o7b11o$3ob3ob3o7b
3ob3ob3o71b3ob3ob3o7b3ob3ob3o$4o2bobo3b2ob2o3bobo2b4o71b11o7b11o$4o2bo
bo3b2ob2o3bobo2b4o71b11o7b11o$11o7b11o71b11o7b11o$3o3b3o3b2ob2o3b3o3b
3o71b3ob3ob3o7b3ob3ob3o$11o7b11o71b11o7b11o$4o2bobo3b2ob2o3bobo2b4o71b
11o7b11o$4o2bobo3b2ob2o3bobo2b4o71b11o7b11o2$4b2obob2ob2ob2ob2obob2o$
4b2obob2ob2ob2ob2obob2o2$4b2obob2ob2ob2ob2obob2o$4b2obob2ob2ob2ob2obob
2o2$4o2bobo3b2ob2o3bobo2b4o71b11o7b11o$4o2bobo3b2ob2o3bobo2b4o71b11o7b
11o$11o7b11o71b11o7b11o$3o3b3o3b2ob2o3b3o3b3o71b3ob3ob3o7b3ob3ob3o$11o
7b11o71b11o7b11o$4o2bobo3b2ob2o3bobo2b4o71b11o7b11o$4o2bobo3b2ob2o3bob
o2b4o71b11o7b11o$3ob3ob3o7b3ob3ob3o71b3ob3ob3o7b3ob3ob3o$11o7b11o71b
11o7b11o$11o7b11o71b11o7b11o$11o7b11o71b11o7b11o!
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Re: Challenges

Postby dvgrn » July 19th, 2017, 1:40 pm

calcyman wrote:B13578/S02468 should be excruciatingly difficult. Without the B8, this is the Fredkin replicator rule (which is reversible ergo has no GoEs), but the B8 makes it irreversible. In particular, the following two patterns have the same descendant...

That 30x30 pattern with two 28x28 predecessors implies at least a 28x28 with two 26x26 predecessors:

x = 127, y = 27, rule = B13578/S02468
11o4b11o31b11o4b11o$
11o4b11o31b11o4b11o$
11o4b11o31b11o4b11o$
3ob3ob3o4b3ob3ob3o31b3ob3ob3o4b3ob3ob3o$
4o2bobo3b2o3bobo2b4o31b11o4b11o$
4o2bobo3b2o3bobo2b4o31b11o4b11o$
11o4b11o31b11o4b11o$
3o3b3o3b2o3b3o3b3o31b3ob3ob3o4b3ob3ob3o$
11o4b11o31b11o4b11o$
4o2bobo3b2o3bobo2b4o31b11o4b11o$
4o2bobo3b2o3bobo2b4o31b11o4b11o$
$
4b2obob2ob2ob2obob2o$
4b2obob2ob2ob2obob2o$
$
4o2bobo3b2o3bobo2b4o31b11o4b11o$
4o2bobo3b2o3bobo2b4o31b11o4b11o$
11o4b11o31b11o4b11o$
3o3b3o3b2o3b3o3b3o31b3ob3ob3o4b3ob3ob3o$
11o4b11o31b11o4b11o$
4o2bobo3b2o3bobo2b4o31b11o4b11o$
4o2bobo3b2o3bobo2b4o31b11o4b11o$
3ob3ob3o4b3ob3ob3o31b3ob3ob3o4b3ob3ob3o$
11o4b11o31b11o4b11o$
11o4b11o31b11o4b11o$
11o4b11o31b11o4b11o!

(sorry for the weird RLE, I'm away from Golly at the moment).

So what is the smallest MxN bounding box in this rule that contains a pattern with two possible parents? Once that's known, a much larger version of the "more fun solution" described above will give a truly ludicrous upper bound for an explicitly constructible Garden of Eden in B13578/S02468.
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Re: Challenges

Postby Gamedziner » July 19th, 2017, 6:17 pm

calcyman wrote:
drc wrote:I'm trying to find a rule that's REALLY difficult to find a GoE for.


B13578/S02468 should be excruciatingly difficult. Without the B8, this is the Fredkin replicator rule (which is reversible ergo has no GoEs), but the B8 makes it irreversible.


Actually, the Fredkin replicator rule has the smallest possible GoE: a single cell. Since it has b1, cells are always born around the corners of any pattern. The amount of cells in the next generation then is greater than or equal to the number of corners around the pattern. Almost every pattern has multiple corners, with the only exceptions being zero cells and some infinite-cell patterns. Since infinite patterns need not be proved that they aren't parents for a pattern to be a GoE (see the page on gardens of eden), they need not be considered here. Since no cells can be born from zero cells without b0, the pattern with zero cells cannot become a pattern other than itself, and thus is not a parent of a single cell (Even with b0, it would make a pattern with infinite cells and still not be a parent to the single cell.). As for the remaining finite patterns, since they have multiple corners, they give birth to multiple cells (that is, more than 1). Even if every other cell dies off, these cells will still cause the population to be greater than 1. However, a single cell has a population of exactly 1, so at least 1 cell exists in the resulting pattern that doesn't exist in the single-cell pattern, making it a different pattern. Therefore, the starting patterns do not give birth to the single-cell pattern, and are not parents of the single-cell pattern. Consequently, there are no finite patterns in this rule that give birth to a single cell, making a single cell a GoE.

Since the logic used here only required that a rule have b1, the related B13578/S02468 also has a single cell as a GoE.
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Re: Challenges

Postby gameoflifeboy » July 19th, 2017, 9:15 pm

A single cell has this as its predecessor (imagine extending it infinitely):
x = 256, y = 256, rule = B1357/S02468:T256,256
$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o!

When Calcyman mentioned a bijective correspondence between each pattern and its next generation, I believe he wasn't only referring to finite patterns...

However, under the standard definition you are right, a single cell would be a Garden of Eden. When I noticed this, rather than reporting it, I suspected there was an unconventional solution, because Calcyman usually isn't wrong about these things. :D Eventually I solved it.

I would like to see a proof that there is a one-to-one correspondence between patterns and their predecessors in Fredkin. It makes for an interesting bi-deterministic rule, yet as you can see from the example, the reverse CA would have infinite neighborhood size as changing a single cell results in differences arbitrarily far away in the previous generation. For this reason, I don't think that the previous generation of an infinite pattern is even well-defined unless the states of all cells are already known, because when building the pattern up cell by cell a change in just one cell can completely alter the previous generation, as you just saw, so doing it repeatedly wouldn't make the previous generation converge to anything.

...Wait, I just found another infinite predecessor of a single cell. So I guess that the set of patterns in the bijective correspondence doesn't include all infinite repeating patterns...
x = 230, y = 225, rule = B1357/S02468
229bo10$o$212bo7$12bo7$199bo3$20bo20$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2o$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2o$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2o$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2o$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2o$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2o$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2o$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2o$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$
45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bo
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$46b
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45b2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$46b2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45b2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$46b2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45b2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$46b2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45b2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$46b2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2o$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2o$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2o$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2o$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2o$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2o$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2o$45b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$
45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
$46b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45b
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$46b2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45b2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$46b2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45b2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$46b2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45b2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$46b2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45b2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$45bob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$45bob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$45bob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$45bob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$45bob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$45bob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$45bob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$45bob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bo
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$
45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2o2$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2o2$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2o2$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2o2$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2o2$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2o2$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2o2$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2o2$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2o2$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$45bob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$45bob2ob2ob2ob2ob2ob2ob2ob2ob2o
b2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o25$23bo9$13bo11$5bo!

If anyone knows the rules for which patterns are included in the set of patterns that make this rule reversible, I really want to be informed.
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Re: Challenges

Postby calcyman » July 20th, 2017, 3:37 am

I was using the stricter definition of a pattern that cannot appear as a subpattern of generation 1 of any other pattern.

(Formally, you stipulate finitely many ON cells, finitely many OFF cells, and the rest of the universe comprises 'DON'T CARE' cells.)

I seem to recall Achim Flammenkamp uses 'orphan' to refer to the stricter definition and 'GoE' for the weaker definition.

No pattern in Fredkin is an orphan, since running that pattern for 2^n generations (where n is large) will result in multiple well-separated copies of the original pattern. Hence why I suggested B13578/S02468, which does have orphans by the GoE theorem.
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Re: Challenges

Postby dvgrn » July 20th, 2017, 8:45 am

dvgrn wrote:
calcyman wrote:B13578/S02468 should be excruciatingly difficult. Without the B8, this is the Fredkin replicator rule (which is reversible ergo has no GoEs), but the B8 makes it irreversible. In particular, the following two patterns have the same descendant...

That 30x30 pattern with two 28x28 predecessors implies at least a 28x28 with two 26x26 predecessors...
(sorry for the weird RLE, I'm away from Golly at the moment).

So what is the smallest MxN bounding box in this rule that contains a pattern with two possible parents?

It's much easier to experiment in Golly than to do the required hard thinking about this (or experimenting in LifeViewer). A more reasonable upper bound seems to be 8x8:

x = 27, y = 27, rule = B13578/S02468
b6o13b6o$bob2obo13bob2obo$b2o2b2o13b6o$b2o2b2o13b6o$bob2obo13bob2obo$b
6o13b6o14$ob4obo11bob4obo$b6o13b6o$3o2b3o11b3o2b3o$2o4b2o11b2o4b2o$2o
4b2o11b2o4b2o$3o2b3o11b3o2b3o$b6o13b6o$ob4obo11bob4obo!

This pair of arrangements allows a birth on B7 in one case and a birth on B8 in the other, while the cells that turn OFF do so because of 5 neighbors in one case and 7 neighbors in the other.

Offhand I don't see how to manage a similar trick without the block of four cells in the center, so maybe 8x8 is minimal. Certainly it seems as if any two patterns with differences in their outside ring of cells can't have the same descendant, so that limits the possibilities quite a bit.

I'll leave someone else to figure out what value of n makes (2^100-1)^(n^2) < 2^((10n-2)^2) -- if I've done the substitution right. Looks like it will take a bit more than an easy afternoon to enumerate all patterns in a square that size, whatever it is...!

No doubt that upper bound can be tightened up quite a bit, just as it can in B3/S23 where the upper bound guarantees a GoE inside 1162907980 by 1162907980 but there's actually one in 10x10.
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Re: Challenges

Postby wildmyron » July 20th, 2017, 8:55 am

gameoflifeboy wrote:If anyone knows the rules for which patterns are included in the set of patterns that make this rule reversible, I really want to be informed.

The patterns you posted are not in Fredkin, but in the very similar rule calcyman posted as a challenge - which is not reversible.

Edit: Please ignore - dvgrn pointed out that these patterns are in Fredkin - I was confused.
Last edited by wildmyron on July 20th, 2017, 11:58 pm, edited 1 time in total.
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Re: Challenges

Postby dvgrn » July 20th, 2017, 10:58 pm

wildmyron wrote:
gameoflifeboy wrote:If anyone knows the rules for which patterns are included in the set of patterns that make this rule reversible, I really want to be informed.

The patterns you posted are not in Fredkin, but in the very similar rule calcyman posted as a challenge - which is not reversible.

Don't know if those two patterns got edited, but they certainly work in Fredkin, and the rule header specifies Fredkin now -- no B8 to be seen.

I'm also curious about the best way to state the inverse rule, for either Fredkin or the related B1357/S1357 (which makes eight copies of any pattern at sufficiently high 2^k-tick intervals, instead of nine copies.)

It seems fairly simple to reverse any pattern that is in fact Generation N of some other pattern: just run it for the lowest power-of-two number of ticks that's larger than the largest diameter of the pattern, inspecting it after each tick to see if it's made up of eight (Replicator) or nine (Fredkin) copies of some smaller pattern. The number of cells separating copies at opposite edges is twice the number of ticks that have passed since the smaller pattern appeared at the center of gravity between those copies. Any tick between then and now can be trivially reconstructed.

But there are a lot of patterns that can't be run backward -- right? What would the T=-1 generation of something asymmetrical be, like

Code: Select all
x = 5, y = 5, rule = B13578/S02468
obo2$obobo2$obobo!
#C [[ THUMBNAIL THUMBSIZE 2 ]]

?
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Re: Challenges

Postby wildmyron » July 20th, 2017, 11:57 pm

dvgrn wrote:
wildmyron wrote:
gameoflifeboy wrote:If anyone knows the rules for which patterns are included in the set of patterns that make this rule reversible, I really want to be informed.

The patterns you posted are not in Fredkin, but in the very similar rule calcyman posted as a challenge - which is not reversible.

Don't know if those two patterns got edited, but the certainly work in Fredkin, and the rule header specifies Fredkin now -- no B8 to be seen.

Whoops, my mistake, I confused B8 with S8.
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Re: Challenges

Postby toroidalet » July 22nd, 2017, 12:58 pm

drc wrote:A glider that reaches its maximum population 1 generation before its minimum

Done:
x = 23, y = 6, rule = B34e5y7e/S23
bo5bo6b3o3b3o$2obobob2o8bobo$9o$bo2bo2bo10bo$b2o3b2o7b3ob3o$2bo3bo8b2o
3b2o!
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Re: Challenges

Postby gameoflifemaniac » August 16th, 2017, 1:09 pm

Find the slowest spaceship in ANY rule.
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Re: Challenges

Postby AforAmpere » August 16th, 2017, 1:57 pm

That would just mean using AbhpzTa's rule, or A For Awesome's variant for many millions of cells, and that would already beat all records. There is no slowest ship, because any n for C/n is possible.
Things to work on:
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- Find a C/10 in Day and Night
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Re: Challenges

Postby gameoflifemaniac » August 16th, 2017, 2:15 pm

I meant the slowest speed you CAN make. Extending the c/2n(+1) is trivial, you have to keep the population low.
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Re: Challenges

Postby dvgrn » August 16th, 2017, 8:55 pm

gameoflifemaniac wrote:I meant the slowest speed you CAN make. Extending the c/2n(+1) is trivial, you have to keep the population low.

If you don't say exactly how low to keep the population, there's still no good way to answer this challenge.

Constructs like the Parallel HBK, not to mention the Demonoid and Orthogonoid spaceships, can be made arbitrarily slow by separating the two parts of the ship -- and there's no increase in population, only in bounding box.
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Re: Challenges

Postby Saka » August 16th, 2017, 9:20 pm

Is there a slowest possible spaceship for n cells?
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x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!

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Re: Challenges

Postby dvgrn » August 17th, 2017, 8:27 am

Saka wrote:Is there a slowest possible spaceship for n cells?

Well, yes, for small N these do exist, of course. But there's not ever going to be a discoverable algorithm where you input N and get back the relevant slowest possible spaceship.

Above some value Nmax < pop(0hd Demonoid) there isn't any slowest possible spaceship, and we'll never know what Nmax is -- we'll just have an upper bound based on the lowest-population Demonoid/Orthogonoid-ish thing that anyone has built so far.

It will always be possible that there's an incredibly lucky/clever shortcut for self-construction that nobody has happened to come across yet -- maybe one that would take an exhaustive search of 1000x1000 bounding boxes to find. (Even a million-qubit quantum computer might not be up to that search task, in practice...!)
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Re: Challenges

Postby toroidalet » August 22nd, 2017, 11:09 am

Challenge: Find a pattern that doesn't die out in R6,C0,M1,S34..58,B34..45,NM, which I am terming "Bugs but I literally changed the range to 6 and it's still miraculously stable."
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