Challenges
 83bismuth38
 Posts: 453
 Joined: March 2nd, 2017, 4:23 pm
 Location: Still sitting around in Sagittarius A...
 Contact:
Re: Challenges
is a c/1 knightship possible?
Code: Select all
x = 8, y = 10, rule = B3/S23
3b2o$3b2o$2b3o$4bobo$2obobobo$3bo2bo$2bobo2bo$2bo4bo$2bo4bo$2bo!

 Posts: 3138
 Joined: June 19th, 2015, 8:50 pm
 Location: In the kingdom of Sultan Hamengkubuwono X
Re: Challenges
83bismuth38 wrote:is a c/1 knightship possible?
Code: Select all
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!
Airy Clave White It Nay
(Check gen 2)
Code: Select all
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
 gameoflifemaniac
 Posts: 774
 Joined: January 22nd, 2017, 11:17 am
 Location: There too
Re: Challenges
p1 puffer
https://www.youtube.com/watch?v=q6EoRBvdVPQ
One big dirty Oro. Yeeeeeeeeee...
One big dirty Oro. Yeeeeeeeeee...
Re: Challenges
gameoflifemaniac wrote:p1 puffer
Code: Select all
x = 8, y = 8, rule = B2ace5er/S2ae3aeir4q5i
4bo$3b2obo$bo4b2o$ob3obo$ob3obo$bo4b2o$3b2obo$4bo!
This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.)
Current rule interest: B2ce3ir4a5y/S2c3y
Current rule interest: B2ce3ir4a5y/S2c3y
Re: Challenges
Possible isotropic rule example for Golly 3.0: find a 16x16 soup in B2a5/S1e2a35678  a distant Just Friends relative  that displays the most different kinds of reactions before stabilizing inside a finite bounding box.
Here's my first candidate 
 but I don't like it all that much. It starts out well, but then it turns out that its huge final population is all due to one trick at the end.
Here's the script that found it. Hit 'q' to stop searching and display the soup with the highest population found so far:
I tried a couple other metrics, like highest density and largest bounding box, and different run times  presumably this script will throw away occasional methuselahs with >16384 run times, which would be great candidates for the challenge. But the search gets a lot slower if you bump that number up too high.
Here's my first candidate 
Code: Select all
x = 16, y = 16, rule = B2a5/S1e2a35678
2bobobob4obobo$bob2obo2bo2b2o$2bobo4b3ob3o$3obo5bob2o$3o4b2o4b3o$2o5b
8o$bo2bo5b3o$o2b2o4bo2b2o$o2bobob3o4bo$2o2b4o3b3o$3o2b2obo3b4o$3bo5bob
2ob2o$o4b6o2b2o$4ob3obob2o$2b4ob2o3bobo$ob2o4b4ob2o!
Here's the script that found it. Hit 'q' to stop searching and display the soup with the highest population found so far:
Code: Select all
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()
Re: Challenges
Challenge: Find a garden of eden in B8/S012345678, in which these two patterns are mapped to the same configuration:
Code: Select all
x = 8, y = 3, rule = B8/S012345678
3o2b3o$obo2b3o$3o2b3o!
This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.)
Current rule interest: B2ce3ir4a5y/S2c3y
Current rule interest: B2ce3ir4a5y/S2c3y
Re: Challenges
Done:drc wrote:Challenge: Find a garden of eden in B8/S012345678, in which these two patterns are mapped to the same configuration:Code: Select all
x = 8, y = 3, rule = B8/S012345678 3o2b3o$obo2b3o$3o2b3o!
Code: Select all
x = 3, y = 3, rule = B8/S012345678
3o$obo$3o!
 Consider a pattern of size (5n  2) by (5n  2). If it occurs within generation 1 of a pattern, then that 'father' can be assumed to be 5n by 5n. (We take 'father' more liberally to allow junk outside the target 'child'.)
 Suppose the father exists. Divide it into n^2 5by5 regions. If any of them is P with an empty border, replace it with Q with an empty border.
 This means there are only (2^25  1) ^ (n^2) putative fathers worth considering.
 However, there are 2^((5n2)^2) patterns of size (5n  2) by (5n  2). Whenever n >= 232581596, this is greater than the previous value.
 Hence there exists a GoE of size 1162907980 by 1162907980.
 An explicit GoE is therefore obtained by tiling together all possible patterns of this size, in lexicographical order, into an immense square. The resulting pattern is a colossal square of sidelength 1162907980 * 2 ^ 676177484973840200.
What do you do with ill crystallographers? Take them to the monoclinic!
Re: Challenges
Alright, does this count for B8/S01234567?:
I'm trying to find a rule that's REALLY difficult to find a GoE for.
Code: Select all
x = 10, y = 3, rule = B8/S01234567
4o2b4o$o2bo2b4o$4o2b4o!
This post was brought to you by the letter D, for dishes that Andrew J. Wade won't do. (Also Daniel, which happens to be me.)
Current rule interest: B2ce3ir4a5y/S2c3y
Current rule interest: B2ce3ir4a5y/S2c3y
Re: Challenges
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:drc wrote:I'm trying to find a rule that's REALLY difficult to find a GoE for.
Code: Select all
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$11o7b11o71b11o7b11o!
What do you do with ill crystallographers? Take them to the monoclinic!
Re: Challenges
That 30x30 pattern with two 28x28 predecessors implies at least a 28x28 with two 26x26 predecessors:calcyman wrote:B13578/S02468 should be excruciatingly difficult. Without the B8, this is the Fredkin replicator rule (which is reversible ergo has no GoEs), but the B8 makes it irreversible. In particular, the following two patterns have the same descendant...
Code: Select all
x = 127, y = 27, rule = B13578/S02468
11o4b11o31b11o4b11o$
11o4b11o31b11o4b11o$
11o4b11o31b11o4b11o$
3ob3ob3o4b3ob3ob3o31b3ob3ob3o4b3ob3ob3o$
4o2bobo3b2o3bobo2b4o31b11o4b11o$
4o2bobo3b2o3bobo2b4o31b11o4b11o$
11o4b11o31b11o4b11o$
3o3b3o3b2o3b3o3b3o31b3ob3ob3o4b3ob3ob3o$
11o4b11o31b11o4b11o$
4o2bobo3b2o3bobo2b4o31b11o4b11o$
4o2bobo3b2o3bobo2b4o31b11o4b11o$
$
4b2obob2ob2ob2obob2o$
4b2obob2ob2ob2obob2o$
$
4o2bobo3b2o3bobo2b4o31b11o4b11o$
4o2bobo3b2o3bobo2b4o31b11o4b11o$
11o4b11o31b11o4b11o$
3o3b3o3b2o3b3o3b3o31b3ob3ob3o4b3ob3ob3o$
11o4b11o31b11o4b11o$
4o2bobo3b2o3bobo2b4o31b11o4b11o$
4o2bobo3b2o3bobo2b4o31b11o4b11o$
3ob3ob3o4b3ob3ob3o31b3ob3ob3o4b3ob3ob3o$
11o4b11o31b11o4b11o$
11o4b11o31b11o4b11o$
11o4b11o31b11o4b11o!
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.

 Posts: 796
 Joined: May 30th, 2016, 8:47 pm
 Location: Milky Way Galaxy: Planet Earth
Re: Challenges
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 infinitecell 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 singlecell pattern, making it a different pattern. Therefore, the starting patterns do not give birth to the singlecell pattern, and are not parents of the singlecell pattern. Consequently, there are no finite patterns in this rule that give birth to a single cell, making a single cell a GoE.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.drc wrote:I'm trying to find a rule that's REALLY difficult to find a GoE for.
Since the logic used here only required that a rule have b1, the related B13578/S02468 also has a single cell as a GoE.
Code: Select all
x = 81, y = 96, rule = LifeHistory
58.2A$58.2A3$59.2A17.2A$59.2A17.2A3$79.2A$79.2A2$57.A$56.A$56.3A4$27.
A$27.A.A$27.2A21$3.2A$3.2A2.2A$7.2A18$7.2A$7.2A2.2A$11.2A11$2A$2A2.2A
$4.2A18$4.2A$4.2A2.2A$8.2A!
 gameoflifeboy
 Posts: 474
 Joined: January 15th, 2015, 2:08 am
Re: Challenges
A single cell has this as its predecessor (imagine extending it infinitely):
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. Eventually I solved it.
I would like to see a proof that there is a onetoone correspondence between patterns and their predecessors in Fredkin. It makes for an interesting bideterministic 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 welldefined 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...
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.
Code: Select all
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
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
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
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
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
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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
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2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
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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
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
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2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
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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
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2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o$2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2o2$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
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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$2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob3ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob
2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2ob2o!
However, under the standard definition you are right, a single cell would be a Garden of Eden. When I noticed this, rather than reporting it, I suspected there was an unconventional solution, because Calcyman usually isn't wrong about these things. Eventually I solved it.
I would like to see a proof that there is a onetoone correspondence between patterns and their predecessors in Fredkin. It makes for an interesting bideterministic rule, yet as you can see from the example, the reverse CA would have infinite neighborhood size as changing a single cell results in differences arbitrarily far away in the previous generation. For this reason, I don't think that the previous generation of an infinite pattern is even welldefined unless the states of all cells are already known, because when building the pattern up cell by cell a change in just one cell can completely alter the previous generation, as you just saw, so doing it repeatedly wouldn't make the previous generation converge to anything.
...Wait, I just found another infinite predecessor of a single cell. So I guess that the set of patterns in the bijective correspondence doesn't include all infinite repeating patterns...
Code: Select all
x = 230, y = 225, rule = B1357/S02468
229bo10$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!
Re: Challenges
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 wellseparated copies of the original pattern. Hence why I suggested B13578/S02468, which does have orphans by the GoE theorem.
(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 wellseparated copies of the original pattern. Hence why I suggested B13578/S02468, which does have orphans by the GoE theorem.
What do you do with ill crystallographers? Take them to the monoclinic!
Re: Challenges
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:dvgrn wrote:That 30x30 pattern with two 28x28 predecessors implies at least a 28x28 with two 26x26 predecessors...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...
(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?
Code: Select all
x = 27, y = 27, rule = B13578/S02468
b6o13b6o$bob2obo13bob2obo$b2o2b2o13b6o$b2o2b2o13b6o$bob2obo13bob2obo$b
6o13b6o14$ob4obo11bob4obo$b6o13b6o$3o2b3o11b3o2b3o$2o4b2o11b2o4b2o$2o
4b2o11b2o4b2o$3o2b3o11b3o2b3o$b6o13b6o$ob4obo11bob4obo!
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 (2^1001)^(n^2) < 2^((10n2)^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.
Re: Challenges
The patterns you posted are not in Fredkin, but in the very similar rule calcyman posted as a challenge  which is not reversible.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.
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.
The latest version of the 5S Project contains over 221,000 spaceships. Tabulated pages up to period 160 are available on the LifeWiki.
Re: Challenges
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.wildmyron wrote:The patterns you posted are not in Fredkin, but in the very similar rule calcyman posted as a challenge  which is not reversible.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.
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^ktick 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 poweroftwo 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 ]]
Re: Challenges
Whoops, my mistake, I confused B8 with S8.dvgrn wrote: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.wildmyron wrote:The patterns you posted are not in Fredkin, but in the very similar rule calcyman posted as a challenge  which is not reversible.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 latest version of the 5S Project contains over 221,000 spaceships. Tabulated pages up to period 160 are available on the LifeWiki.
 toroidalet
 Posts: 1019
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Re: Challenges
Done:drc wrote:A glider that reaches its maximum population 1 generation before its minimum
Code: Select all
x = 23, y = 6, rule = B34e5y7e/S23
bo5bo6b3o3b3o$2obobob2o8bobo$9o$bo2bo2bo10bo$b2o3b2o7b3ob3o$2bo3bo8b2o
3b2o!
"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."
Terry Pratchett
Terry Pratchett
 gameoflifemaniac
 Posts: 774
 Joined: January 22nd, 2017, 11:17 am
 Location: There too
Re: Challenges
Find the slowest spaceship in ANY rule.
https://www.youtube.com/watch?v=q6EoRBvdVPQ
One big dirty Oro. Yeeeeeeeeee...
One big dirty Oro. Yeeeeeeeeee...

 Posts: 1049
 Joined: July 1st, 2016, 3:58 pm
Re: Challenges
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.
I and wildmyron manage the 5S project, which collects all known spaceship speeds in Isotropic Nontotalistic rules.
Things to work on:
 Find a (7,1)c/8 ship in a Nontotalistic rule
 Finish a rule with ships with period >= f_e_0(n) (in progress)
Things to work on:
 Find a (7,1)c/8 ship in a Nontotalistic rule
 Finish a rule with ships with period >= f_e_0(n) (in progress)
 gameoflifemaniac
 Posts: 774
 Joined: January 22nd, 2017, 11:17 am
 Location: There too
Re: Challenges
I meant the slowest speed you CAN make. Extending the c/2n(+1) is trivial, you have to keep the population low.
https://www.youtube.com/watch?v=q6EoRBvdVPQ
One big dirty Oro. Yeeeeeeeeee...
One big dirty Oro. Yeeeeeeeeee...
Re: Challenges
If you don't say exactly how low to keep the population, there's still no good way to answer this challenge.gameoflifemaniac wrote:I meant the slowest speed you CAN make. Extending the c/2n(+1) is trivial, you have to keep the population low.
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.

 Posts: 3138
 Joined: June 19th, 2015, 8:50 pm
 Location: In the kingdom of Sultan Hamengkubuwono X
Re: Challenges
Is there a slowest possible spaceship for n cells?
Airy Clave White It Nay
(Check gen 2)
Code: Select all
x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
Re: Challenges
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.Saka wrote:Is there a slowest possible spaceship for n cells?
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 lowestpopulation Demonoid/Orthogonoidish thing that anyone has built so far.
It will always be possible that there's an incredibly lucky/clever shortcut for selfconstruction that nobody has happened to come across yet  maybe one that would take an exhaustive search of 1000x1000 bounding boxes to find. (Even a millionqubit quantum computer might not be up to that search task, in practice...!)
 toroidalet
 Posts: 1019
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Re: Challenges
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."
"Build a man a fire and he'll be warm for a day. Set a man on fire and he'll be warm for the rest of his life."
Terry Pratchett
Terry Pratchett