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Thread for basic questions

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Re: Thread for basic questions

Postby biggiemac » October 18th, 2016, 1:20 am

By only collecting noninteracting objects, there are a few very interesting things missed, but that's just how the project was designed. I know in the past I've wished that close-but-not-interacting *WSS pairs were catagolued in case they allow for nice paired helix syntheses in caterpillar-like projects. Unfortunately those are impossible to get from the sample soups for *WSS because the *WSS themselves are too common to keep accruing sample soups.
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Re: Thread for basic questions

Postby calcyman » October 18th, 2016, 4:53 am

Caenbe wrote:Ok, I'll just call it a blinkross.
Suppose I want to know if a blinkross has appeared naturally in apgsearch. Do I have to look through all 300 sample soups in Catagolue containing a cross 2, and check if they have a blinker inside them?


You don't need to check the soups with diagonal symmetry (such as D8_1, D4_x1 or D2_x). The most promising symmetry class is that of the blinkross itself, namely D4_+1.
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Re: Thread for basic questions

Postby A for awesome » October 18th, 2016, 3:34 pm

Are there any existing fast iterators for non-totalistic rules on an infinite universe written in universal C++, or any Life ones that could be modified relatively easily to handle non-totalistic rules?
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

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Re: Thread for basic questions

Postby calcyman » October 18th, 2016, 4:29 pm

A for awesome wrote:Are there any existing fast iterators for non-totalistic rules on an infinite universe written in universal C++, or any Life ones that could be modified relatively easily to handle non-totalistic rules?


Golly's hlife and qlife seem to fit that description.

I've also implemented a HashLife variant which uses SSE/AVX acceleration in the leaf nodes. Performance is quite promising on my rather primitive laptop for the following benchmark:

Benchmark wrote:Run the Caterpillar for 256 generations and report its population


  • Golly qlife: 41 seconds
  • Golly hlife: 17 seconds
  • New algorithm: 12 seconds

At the moment it's limited to outer-totalistic 2-state cellular automata, plus optional history, co-history, and annotation layers (so it can run LifeHistory without the grey cells). And it has the same limitation as apgmera that it relies on rule2asm, which only works on x86_64 processors.

There's not really anything novel in this new algorithm; it just combines the best parts of HashLife with the low-level iterator from apgmera. Specifically:

  • The universe is represented as a quadtree.
  • A leaf node is a 16-by-16 square of cells.
  • A 'leaf iteration' takes four leaf nodes forming a 32-by-32 square, advances it by n <= 8 generations using a fast SSE/AVX implementation, and returns a leaf node forming the 16-by-16 interior.
  • For higher levels, it works recursively like Gosper's HashLife, caching results in a hashtable.

I've almost finished writing a high-level API for this, allowing you to manipulate patterns (shift/transform/combine/select) and iterate them in various rules. Morally like GoLGrid or LifeAPI, but for infinite universes and with HashLife capabilities.

Notably, HashLife computations from one universe are cached for later use in other universes in the 'multiverse' -- so if you run the HBK and subsequently run the HBK gun, the latter will benefit from cached results generated by the former. A caveat is that the hashtables aren't threadsafe, so you need a separate multiverse for each thread.
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Re: Thread for basic questions

Postby A for awesome » October 18th, 2016, 4:36 pm

calcyman wrote:Golly's hlife and qlife seem to fit that description.

Is it possible to use the source code for the Golly 2.8 versions of these, or is it impossible/illegal?
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

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Re: Thread for basic questions

Postby calcyman » October 18th, 2016, 4:51 pm

A for awesome wrote:
calcyman wrote:Golly's hlife and qlife seem to fit that description.

Is it possible to use the source code for the Golly 2.8 versions of these, or is it impossible/illegal?


Yes, it's possible (Golly is open-source):

https://sourceforge.net/p/golly/code/ci/master/tree/gollybase/
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Re: Thread for basic questions

Postby M. I. Wright » October 20th, 2016, 1:00 am

wildmyron wrote:@M. I. Wright: I believe you misunderstood the question.

Caenbe wrote:Are there any 2-state inner-totalistic rules with still lives, oscillators, and spaceships?

Indeed I did (confused inner- and outer-totalistic)... I'm not sure I understand it even now, though. Wouldn't regular Life satisfy the question's conditions?
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Re: Thread for basic questions

Postby wildmyron » October 20th, 2016, 2:47 am

M. I. Wright wrote:Wouldn't regular Life satisfy the question's conditions?

It doesn't, because S3 corresponds to the transition [count = 4 -> 1] which also corresponds to B4.

In other words, to convert from inner-totalistic to B/S outer-totalistic (aka semi-totalistic) notation:

1) The rule is specified as a list of cell counts {c_i} where each c_i is one of [0-9]. Each count corresponds to a transition rule which maps any 3x3 neighbourhood with c_i On cells to the central cell being On.
2) For each c_i, include Bc_i in the transition rule (excluding c_i = 9)
3) For each c_i, include S(c_i - 1) in the transition rule (excluding c_i = 0)

Please excuse my very sloppy notation.

Warning - confusing side tangent ahead:
To be honest, I find the label outer-totalistic to describe Life-like CA to be very confusing. Semi-totalistic seems much more appropriate as the resulting state of the cell depends on the current cell state as well as the total of outer cells. Totalistic could then refer to transition rules dependent only on the total number of On cells, and outer-totalistic could refer to transition rules dependent on the total of neighbouring (outer) cells independent of the current cell state. However, that's all by the by as those terms were defined long ago and won't be changing.

Edit: spelling.
Last edited by wildmyron on October 20th, 2016, 10:23 am, edited 1 time in total.
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Re: Thread for basic questions

Postby shouldsee » October 20th, 2016, 9:59 am

Under wildmyron's classification, B35/S24 would be a totalistic (all9) rule. B0125/S0125 would be a outer-totalistic rule. I don't think inner-totalistic rule should refer to anything specific.

EDIT: But let's reserve such usage for conventions.
Here is my guess of how the convention works:

    inner-totalistic => you should include inner-cell when you count the total ,aka k=9, and this should not result in a B/S notation.

    outer-totalistic => you should only include the outer-cell when you count the total. This leads to 2 natural extension:

      absolute-outer-totalistic=> don't worry about the inner cell, only use the outer-total to update, this will not give a B/S notation

      semi-outer-totalistic => the state of inner cell is considered, but in a non-totalistic fashion, i.e. B string and S string are independent from each other. These rules generally have to be expressed in B/S notation, due to two distinct strings.

In other words, except for the last category, all other categories can be viewed as special cases of B/S rules. i.e. the B string and S string are the same thing -- once you know one of them, the other is also fixed.
x = 64, y = 35, rule = B0125/S0125
8$36bobo$36b3o$35b5o$18bo16b5o$17b3o14b7o$16b5o13b7o$15bob3obo13b5o$
15bob3obo11bob5obo$16b5o13b7o$17b3o15b5o$18bo17b3o$37bo!
Last edited by shouldsee on October 20th, 2016, 11:01 am, edited 2 times in total.
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Re: Thread for basic questions

Postby wildmyron » October 20th, 2016, 10:26 am

shouldsee wrote:Under wildmyron's classification, B35/S24 would be a totalistic (all9) rule. B0125/S0125 would be a outer-totalistic rule. I don't think inner-totalistic rule should refer to anything specific.


Well yes, but please don't start using that interpretation of the terminology as it will be very confusing.
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Re: Thread for basic questions

Postby drc » October 25th, 2016, 1:04 am

Are there infinite sparks?

I'd assume so, because you can make beautiful patterns like this:

x = 23, y = 16, rule = B35j/S23
11bo$11bo$10b3o$8b7o$6b11o$bo2b4o2b3o2b4o2bo$bo4bob7obo4bo$7ob7ob7o$7o
b7ob7o$bo4bob7obo4bo$bo2b4o2b3o2b4o2bo$6b11o$8b7o$10b3o$11bo$11bo!


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Re: Thread for basic questions

Postby wildmyron » October 25th, 2016, 2:10 am

drc wrote:Are there infinite sparks?

Can you define the domain of your question? i.e. do you mean in CGOL or rules similar to CGOL or any Life-like rule? What kind of patterns would constitute an infinite spark (connected, polyomino, or other?)

Without these details both of the following would seem to satisfy your request:
x = 20, y = 3, rule = B3/S23:T20,0
obobobobobobobobobo2$obobobobobobobobobo!

x = 20, y = 1, rule = B2/S:T20,0
20o!
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Re: Thread for basic questions

Postby muzik » October 28th, 2016, 9:05 am

I'd assume they would have to be connected.


An infinite 2D grid of diagonally touching blocks would instantly die.
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Re: Thread for basic questions

Postby GUYTU6J » October 29th, 2016, 9:44 pm

x = 3356, y = 1088, rule = B3/S23
3o$o2bo$ob2o$4b2o5bo$4b2o4b3o$10bob2o$4b2o8bo$4b2o8b2o4b3o$10bo9bo2bo$
14b2o8bo$11bo2bo7bobo6bo$8bo11bo3bo4b2ob2o$19bob5o6b2o$17bo3b2o9bobo6b
o$17bobo13b2o5bobo$29b4o2b2o2b2ob2o$27b3obo7b2obo8bo$27b2o11bo2bobo4bo
bo4b2o$40b3o2bo3bo2bo$37b2o6bo4bobo14bo$6bo30b2o11b2o8b3o5bo$6bo44b2ob
3o3b3o4bo$2b2o2b3o38b2o11bo16bo$2b2o3b2o6b2o30b2o12bo3bo5bo4bobo$o3bob
obo8bo43bo3bo4b3o5bo$o3b5o3b2o43b2o3bo2bo8bo$2bob4o4bo2bob2o7bo30b2o
12b3o12b3o$10b2o6bo4bob2o45b4o4b3o3b3o$10b5o2bo5bob2o10bo29b2o4b2o6bo
2b3o$12bobob2o5bobob2o8bo29b2o12bo3bo5bo3bob2o$20b2o3bo2bo5b2o46bob2o
5bo3bo2bo$19bo2b6o5b3o12bo28b2o4bo7bo$26bo10b2o6b2obo28b2o13b2ob2o5b2o
3bo$22bo7b2o2bo3bo53b3o6b8o$29bo2bo2b3o5b2o13bo28b2o12bo3bobo$7b2o21bo
2bo10b2ob2o7b3o28b2o13b2obo2bo4bo$7b2o31b2o2b2ob2o5bob2o45b2o6b2obob3o
$o30bobo5bobo4bo7bo2bo9bobo27b2o12bo3bobobo$17b2o21bobo11b2ob2o7bo2bo
22b2o3b2o13b2obo$9bo7b2o22b3o6bo4bobo6b3o47bo2bo4b3o2bo$9bo32b2o5bob2o
3bo7bo2bo9b2o24bo3b2o10b2ob2obob2o$9bo17b2o21bo14bobo2bo2bo3b3o22bo4b
2o14b3o2b2o6bo$27b2o23bo6bo5b3o2bo3bobo26bo23b3o3bo3bo$18b3o31b2o5bob
2o12bobo3bo6bo24b2o2b2o10bobob2o3bo$37b2o21b2o8bo4b2o2bo2bo4b2o23bo4b
2o15b2o2bo$29bo7b2o23bo6bo6bo4b3o2bo2bo23b2o22b2o3bo2b3o$29bo32bo6bobo
bo3bo3b3obob5o31b2o2b2o11bo2b5o$29bo17b2o14bo6b2o10b2obo3bo2bo4b3o23b
2o2b2o11bo7bo$47b2o23bo6b2o3bo7bo3bo26bo9bo13bo8bo$38b3o31bo6b3ob3obo
4bo2bobo2bo34bob2o9bo2b3ob3o$57b2o14b2obo8b3o4bo3b2ob3o5b2o23bobo3bo3b
o7b4o4bo$49bo7b2o23b4ob3ob2o3b2o2b3o3bob2o23bo12bo6bob3o$2b2o45bo32b7o
2b5obob2o4bob2obo31bobo2bobobob4o8b3o$2b2o45bo17b2o17bo12b3o3bo3bobo5b
o24bobo3bo3b3o2b2ob6o2bo$67b2o22b2obo2b2o2b2o5bo3bo3bob2o23bo13b3obo3b
3o$12b2o44b3o32bob3o7bob3o2bo3bo3bo31b3o2b3obo14b2o$12b2o63b2o23bob2ob
obob4o4bobo5b2o23b3o7b3o5bo2b2ob2o$69bo7b2o23bob2ob2o3bo3bo2b3o4bo36bo
2b6obo3bo$22b2o45bo32bo3bo12b3o4bo2b2o32bo7bob2o8bo2bo$22b2o45bo17b2o
26b3o4bob2o5bo6bo24bo9b2o8bo2b2o$87b2o22b3ob3obo3bob2o3bo6b2o24bo5bo9b
3obo4bo$5b2o25b2o44b3o42b2o4b2o5b2ob2o25b2o6b5obo2b2o9b2o$4bo2bo24b2o
63b2o21bob2ob2o3bo2bo3bo3bo7bo23b7o3bo6bo2b4o$4bobo82bo7b2o22b2o3b2o2b
2obob4obo6b2o24bob4o11bo2bo3b2o$5bo9b2o25b2o45bo40b2o2bo3b2o7bo3bo38bo
3bob3o$14bo2bo24b2o45bo17b2o22b2o3b2o3bob2o2bob2o9bo22b7o4b3ob2o3b4o$
14bobo90b2o23bo3b2o3bob4ob3o7bobo22bo10b3ob3o2bo3bo$o14bo9b2o25b2o44b
3o40bo15b2o9bo26b2ob2o4b2ob2o$24bo2bo24b2o63b2o22bo4b2o4b2o3bob3o7bo
22bo2bo2bo10bo4b2o$9bo14bobo82bo7b2o23bo3bo4b3ob2o11b3o21bobo10bo4bob
2ob2o$9bo15bo9b2o25b2o45bo33bo7bo4bobo8bo2bo7bo25b2obobo5b3o$9bo24bo2b
o24b2o45bo17b2o23b6o8bo3b2o5bobo22b3o3bo9b2o$34bobo90b2o23b3o6b4o3bo
10bo22b2o11b3obo3b4o$18b3o14bo9b2o25b2o44b3o40bo4b2o8bo3bo34bob3o2b2ob
o2bo$44bo2bo24b2o63b2o23b3ob2o8bobobo6b3o22b2o8b2o4bo$29bo14bobo82bo7b
2o24bo7b2obobo3bo6b3o23bo9b5obo4bo$29bo15bo9b2o25b2o45bo41bo2b5o6b2o
36bobo2b2o2b2ob3o$29bo24bo2bo24b2o45bo17b2o23b3o13b3o7bo23b2o9bo2b3o$
54bobo90b2o32b2obobob2o7b3o24bo9b2o3bo3bobo$38b3o14bo9b2o25b2o44b3o40b
2ob2obo8bo4bo31bo5bo3bo2bo$64bo2bo24b2o63b2o24bo11b2ob2obo31bobo2bo4bo
2b2obo6bobo$49bo14bobo82bo7b2o32b2obob3o8b3o23bo10b2o3bo3bobo$2b2o45bo
15bo9b2o25b2o45bo42bobo13bobobo32bob2o4b2o4bo$2b2o45bo24bo2bo24b2o45bo
17b2o24bo7bo3b2obo3bo30b6o5b3o2bo6b2o$74bobo90b2o33bobo2bo8bobo24bo11b
ob2o7b3o$12b2o44b3o14bo9b2o25b2o44b3o41b3o4bo2bo2bo2b2o2bo22b2o10b2o3b
3o2b2o$12b2o70bo2bo24b2o63b2o31bo2bo4bob3o30b3o8bobo2bo6b2o$69bo14bobo
82bo7b2o33b3ob2o2b2o6bo4bo20bo2bo9b2o4bo3bo$22b2o45bo15bo9b2o25b2o45bo
43bo6b3o2b4o2bo3bo19b2o7bo8bo4bo$22b2o45bo24bo2bo24b2o45bo17b2o31bo4b
2obo2bo32bo2bo5bo2bo2bo6bo$94bobo90b2o32bob2ob2o3bo5bo26bo2bo7bob2o5b
4o$32b2o44b3o14bo9b2o25b2o44b3o42bo7b2o5b2o2b3o20b2o7b3o6b3o2bo$32b2o
70bo2bo24b2o63b2o24bo6bo3b3o4b5o28bobo6bo2bo2bo$89bo14bobo82bo7b2o31bo
5b2o5b5o27b2o8bob2o6b3o$42b2o45bo15bo9b2o25b2o45bo42b2o8bo2bo2bo26b2o
7b2o7b2o3bo$42b2o45bo24bo2bo24b2o45bo17b2o25bo4bob2ob3ob2ob5o37bo3b2o$
114bobo90b2o31bob2o4b4o4bo28b2o8bob2o7bo$52b2o44b3o14bo9b2o25b2o44b3o
42bobo3b3o5b2o27bo7b2o8b2ob2o$3b2o47b2o70bo2bo24b2o63b2o25bo4b3o3b4o
36bo5b2ob2ob2o12bo$3b2o104bo14bobo82bo7b2o34b2o5b7o28b3o7bo9bo5bo6b2ob
o$62b2o45bo15bo9b2o25b2o45bo43b3o2bo2bob3obo37bo2bo3bo2bobo$13b2o47b2o
45bo24bo2bo24b2o45bo17b2o29bo8b2o36b2o4bo3bob2o6bo6bo$13b2o119bobo90b
2o31b2ob2o3bo6b2o29b2o4bo2bobo7bo4b2o9bo$72b2o44b3o14bo9b2o25b2o44b3o
43bo3b7o2bo38bobo3b2obobo9b5o$23b2o47b2o70bo2bo24b2o63b2o26bo3bobobo3b
o38b2o3bo3b3o7b8o$23b2o104bo14bobo82bo7b2o31b2obo4bo2b2o3bo29bo5b2o3bo
7bob2o$82b2o45bo15bo9b2o25b2o45bo44bo4bo5b2o3bo35bo5b2obo8bo5b3o$33b2o
47b2o45bo24bo2bo24b2o45bo17b2o26bo3bo2bob2obo38b3o3b2o2bo9b4o$33b2o
119bobo90b2o27bo3b2o2b3obo2bo40b2o2bobo6bo7bo$92b2o44b3o14bo9b2o25b2o
44b3o44b3o3b2o2b3o2b2o25b2o13bo2bo7bo7bo$43b2o47b2o70bo2bo24b2o63b2o
27b4ob2o2bo3bo36b2o4b2obobobo5bo4b3o$43b2o104bo14bobo82bo7b2o28b2obo4b
o2b4o35bobo3bo7bo4b4obobo$102b2o45bo15bo9b2o25b2o45bo45bo3bobo4b2o2bo
26b2o5bo2bo4bo3b4obobo$53b2o47b2o45bo24bo2bo24b2o45bo17b2o27bob2obo3b
2o3b2o37bo3bobo3b4ob2o4b3o$53b2o119bobo90b2o28bo3bo3bobo2b2o4bo2bo26b
2obo3bobo5bob2obo2bo3bo$112b2o44b3o14bo9b2o25b2o44b3o45b3o7bo3bo27bo5b
3o7bobob2o3bo$63b2o47b2o70bo2bo24b2o63b2o27b3o3bo2b2o4bo34b2obo3bobo4b
3ob2o5bo$63b2o104bo14bobo82bo7b2o31b2o3bo5bo5b2o28b3o3b2o9bobo3b3o$
122b2o45bo15bo9b2o25b2o45bo46b2o3b2o3b4o35bo10bo2b5o$73b2o47b2o45bo24b
o2bo24b2o45bo17b2o28bobob2o3bo2b2o35b2obo3bobob2o5bo$73b2o119bobo90b2o
31bo4bo2b4o5bo30b2o3b2ob3o5b2o4b3o$132b2o44b3o14bo9b2o25b2o44b3o45b4ob
o5b2o37b2o7b2o2bo3bo$83b2o47b2o70bo2bo24b2o63b2o30bo2bo3bo2b2o36bobo3b
obo2bo5bo$83b2o104bo14bobo82bo7b2o30bobo4b2o2bo6bo30b2o3b2o2bo3bo3bo5b
o$142b2o45bo15bo9b2o25b2o45bo46b2o3bo4bobo38bo7bo4b3o$93b2o47b2o45bo
24bo2bo24b2o45bo17b2o30b3o7bo2bo34bobo3bobo3b5o$93b2o119bobo90b2o31b2o
4b2ob2o37b2o3b2o3b2o3b2o$152b2o44b3o14bo9b2o25b2o44b3o46b3o6b3o3bo34b
2o5b2o4b3o$103b2o47b2o70bo2bo24b2o63b2o30b2obo4b2o3bo35b2o3b2o4bo3bo$
103b2o104bo14bobo82bo7b2o32bo5bo2b2o37bo3bo4bo5bo$162b2o45bo15bo9b2o
25b2o45bo46bo2bob2o4bo40bo5bo6bo$113b2o47b2o45bo24bo2bo24b2o45bo17b2o
29bob3o2bob2o2b3o34b3ob3o5b3o$113b2o119bobo90b2o36bo3bo18bo30b2ob2o$
172b2o44b3o14bo9b2o25b2o44b3o46bo3bo5bo5bo34b2o3b2o6bo$123b2o47b2o70bo
2bo24b2o63b2o28bob2ob2ob3o4bo5bo30b2ob2o6bobo$123b2o104bo14bobo82bo7b
2o37bo2bob2o13b2o31bo3bo$182b2o45bo15bo9b2o25b2o45bo47b3ob2obo9b5o30bo
3bo$133b2o47b2o45bo24bo2bo24b2o45bo17b2o29b2o3bo2b3o4b3ob2o7b2o21b2ob
2o6b3o$133b2o119bobo90b2o37bo5b2o46b3o$192b2o44b3o14bo9b2o25b2o44b3o
46b2obobo12bo2bo8bo21bo3bo$143b2o47b2o70bo2bo24b2o63b2o30bo3b2o2b2o5b
2ob2o7bo22b2ob2o7bo$143b2o104bo14bobo82bo7b2o37b2o2bob2o2bo9bo33b3o$
202b2o45bo15bo9b2o25b2o45bo48bobobo2b2o8b3o9bo21bo3bo$153b2o47b2o45bo
24bo2bo24b2o45bo17b2o30bo3b2ob2o9b2o2b2o3bobo20b2ob2o$153b2o119bobo90b
2o38bob2ob2obo10bo33b3o$212b2o44b3o14bo9b2o25b2o44b3o47b3ob2obo9b2o10b
o21bo3bo$163b2o47b2o70bo2bo24b2o63b2o35bo2b2o8bo3b2o3bobo12bo7b2ob2o$
163b2o104bo14bobo82bo7b2o38b4o2b3ob2o2b2o3bo2bo12bo18bo$222b2o45bo15bo
9b2o25b2o45bo51bob3ob6ob3o4bo5bo21b2ob2o$173b2o47b2o45bo24bo2bo24b2o
45bo17b2o39bobobo6bobo4bobo11b2o7b2ob2o$173b2o119bobo90b2o42b6obo2bo4b
obo9bo3bo18bo$232b2o44b3o14bo9b2o25b2o44b3o46b2o2bo6b2obo2b2o4b2o5bo4b
o17bobo$183b2o47b2o70bo2bo24b2o63b2o43bo2bo3b3o5b2o20b2ob2o$183b2o104b
o14bobo82bo7b2o38bo3b2ob2obo8bobo10b4o$242b2o45bo15bo9b2o25b2o45bo47bo
2bo8b2o4bobo3bo6b3obo17b3o$193b2o47b2o45bo24bo2bo24b2o45bo17b2o29bo10b
3obob6obo4b2o21bobo$193b2o119bobo90b2o38b2ob2o3bobobo6bo13b2o8bobo$
252b2o44b3o14bo9b2o25b2o44b3o46b2o11bobo4bo2b2o7b2ob2o17bo$203b2o47b2o
70bo2bo24b2o63b2o30bo10b2o2bob2o4bo2bob2o21b3o$203b2o104bo14bobo82bo7b
2o38b2o5bo3bobobo5bo12bo8bobo$262b2o45bo15bo9b2o25b2o45bo48bobo9bo6bob
2obo6b2obo$213b2o47b2o45bo24bo2bo24b2o45bo17b2o30bo8bob2obo3b3o2bo2bo
2bo3b2o16b3o$213b2o119bobo90b2o39bobo3b2o4b3obobobo3b2o16bo2bo$272b2o
44b3o14bo9b2o25b2o44b3o47b3o9bo2b5ob2obo4bo2b3o$223b2o47b2o70bo2bo24b
2o63b2o39bobo2b3o3bo2bobobo2b2obo18bo$223b2o104bo14bobo82bo7b2o39b3o5b
o4bo2bo4b2obo7bo8b2ob2o$282b2o45bo15bo9b2o25b2o45bo49bo10bobob3o2bo2bo
8bo2bo7b2o$233b2o47b2o45bo24bo2bo24b2o45bo17b2o38bo2bo6b2o3b3ob3o2bobo
5b2obo8bo$233b2o119bobo90b2o39b3o2bo3b2o4b2ob4o12b2o6bobo$292b2o44b3o
14bo9b2o25b2o44b3o56b2obobo4bo3bo9b3o5b2ob2o$243b2o47b2o70bo2bo24b2o
63b2o39b3obobo3bo3b2ob2o5b2o5b2obo$243b2o104bo14bobo82bo7b2o40bo4bo2bo
5bo3b3o12bo7b3o$302b2o45bo15bo9b2o25b2o45bo58bo2bo8bo11bo7bobo$253b2o
47b2o45bo24bo2bo24b2o45bo17b2o39b3o2bo4b4o2b2o2bo3bo7bobo$253b2o119bob
o90b2o44bobobo2b2ob3obo2bobo7b2o9bo$312b2o44b3o14bo9b2o25b2o44b3o57b3o
2bo2b2o2bo8b3o8b3o$263b2o47b2o70bo2bo24b2o63b2o40bo3b3ob2obo3bo3bobobo
7bobo$263b2o104bo14bobo82bo7b2o45b2obo3bo2b2o2bob3o$322b2o45bo15bo9b2o
25b2o45bo58bobo2bo2bo12bobo8b3o$273b2o47b2o45bo24bo2bo24b2o45bo17b2o
40bo4b2o2bobo7bobobo7bo2bo$273b2o119bobo90b2o45bo3b3o2b3o2bo2b2o$332b
2o44b3o14bo9b2o25b2o44b3o57b3o4bo3bo10bo10bo$283b2o47b2o70bo2bo24b2o
63b2o45b2o12bobob2o6b3o$283b2o104bo14bobo82bo7b2o44bo4b3o2b2o3b2obo9b
3o$342b2o45bo15bo9b2o25b2o45bo59bo4b2o3bo10bob2o7bo$293b2o47b2o45bo24b
o2bo24b2o45bo17b2o43bobo4bobo5bo2bobo7bobo$293b2o119bobo90b2o44bo4b3o
3bo3b2o9bo3bo$352b2o44b3o14bo9b2o25b2o44b3o62b2o4bobo10bo$303b2o47b2o
70bo2bo24b2o63b2o43bobo2bobobo8b3o7b3o$303b2o104bo14bobo82bo7b2o43bo6b
2o5b3o2bo8b3o$362b2o45bo15bo9b2o25b2o45bo63b5obobo7bo2bo$313b2o47b2o
45bo24bo2bo24b2o45bo17b2o43bobo2bob2o10bo9bo$313b2o119bobo90b2o43bo3bo
3bo6bo3bo8b3o$372b2o44b3o14bo9b2o25b2o44b3o52bo9b2ob2ob2o8bo$323b2o47b
2o70bo2bo24b2o63b2o36bo5bo2bo2bob2o8b3o2bo$323b2o104bo14bobo82bo7b2o
43bo2b2o8bo2b2obo2bo5b3o$382b2o45bo15bo9b2o25b2o45bo53b3o5bobo3b3o9bo
2bo$333b2o47b2o45bo24bo2bo24b2o45bo17b2o36bo6b2o3bo7bo3bo2b2o$333b2o
119bobo90b2o43b2o6b2o3bo2b2o2b3o6bo$392b2o44b3o14bo9b2o25b2o44b3o53b3o
6bob2o2bobobo6b3o$343b2o47b2o70bo2bo24b2o63b2o43b2ob2o3b5o4b2o2bo$343b
2o104bo14bobo82bo7b2o44bob2o4bob3o3bo4bo$402b2o45bo15bo9b2o25b2o45bo
54b2o7bobo3bobobo6b3o$353b2o47b2o45bo24bo2bo24b2o45bo17b2o44bobo4b3o7b
o2bo$353b2o119bobo90b2o44bobo8b2o3bo2b2o$412b2o44b3o14bo9b2o25b2o44b3o
53b2o8b2o3bob3o7bo$363b2o47b2o70bo2bo24b2o63b2o44bo6bo9b3o$363b2o104bo
14bobo82bo7b2o44bobo9bo3bo2b2o$422b2o45bo15bo9b2o25b2o45bo54b2o8b2o3bo
4bo$373b2o47b2o45bo24bo2bo24b2o45bo17b2o44bo6b2o8b3o$373b2o119bobo90b
2o45b2o9bo3bo2bo$432b2o44b3o14bo9b2o25b2o44b3o53b2o7b3o3bo3bo$383b2o
47b2o70bo2bo24b2o63b2o51b5o6bo$383b2o104bo14bobo82bo7b2o45b2o6b2obo4b
3o$442b2o45bo15bo9b2o25b2o45bo54b2o8b2o3b2o2bo$393b2o47b2o45bo24bo2bo
24b2o45bo17b2o52b3o$393b2o119bobo90b2o45b2o9bo4b3o$452b2o44b3o14bo9b2o
25b2o44b3o53b2o8b2o4bo2bo$403b2o47b2o70bo2bo24b2o63b2o51bob2o$403b2o
104bo14bobo82bo7b2o45b2o8b2o5bo$462b2o45bo15bo9b2o25b2o45bo54b2o8b2o4b
3o$413b2o47b2o45bo24bo2bo24b2o45bo17b2o51bob2o$413b2o119bobo90b2o45b2o
8bo$472b2o44b3o14bo9b2o25b2o44b3o53b2o8b2o4b3o$423b2o47b2o70bo2bo24b2o
63b2o41bo9bo2bo$423b2o104bo14bobo82bo7b2o45b2o8bo$482b2o45bo15bo9b2o
25b2o45bo51bo2bo7bobo6bo$433b2o47b2o45bo24bo2bo24b2o45bo17b2o29bo11bo
3bo4b2ob2o$433b2o119bobo90b2o40bob5o6b2o$492b2o44b3o14bo9b2o25b2o39bo
4b3o10b2o34bo3b2o9bobo6bo$443b2o47b2o70bo2bo24b2o39bo23b2o28bobo13b2o
5bobo$443b2o104bo14bobo82bo7b2o40b4o2b2o2b2ob2o$502b2o45bo15bo9b2o25b
2o39b2o4bo11bo35b3obo7b2obo8bo$453b2o47b2o45bo24bo2bo24b2o38bo6bo11b2o
4bo29b2o11bo2bobo4bobo4b2o$453b2o119bobo76bo5bob2o4b2obo39b3o2bo3bo2bo
$512b2o44b3o14bo9b2o25b2o36bo2bo5b3o9bo35b2o6bo4bobo14bo$463b2o47b2o
70bo2bo24b2o37bobo6b2o10bo34b2o11b2o8b3o5bo$463b2o104bo14bobo74b2o5bo
2bo4b3obo40b2ob3o3b3o4bo$522b2o45bo15bo9b2o25b2o37b3o5b3o6b2obo35b2o
11bo16bo$473b2o47b2o45bo24bo2bo24b2o37b2o15b2o2bo3b2o29b2o12bo3bo5bo4b
obo$473b2o119bobo75bo6b3o7b2o40bo3bo4b3o5bo$532b2o44b3o14bo9b2o25b2o
37b2o7bo6bo3bo35b2o3bo2bo8bo$483b2o47b2o70bo2bo24b2o38bo16bo2bo3b2o29b
2o12b3o12b3o$483b2o104bo14bobo75bo6b3o5b3o42b4o4b3o3b3o$542b2o45bo15bo
9b2o25b2o37bobo10bo2bo2b2o5bo29b2o4b2o6bo2b3o$493b2o47b2o45bo24bo2bo
24b2o25b2o9bo18b2o6bo29b2o12bo3bo5bo3bob2o$493b2o119bobo66bo16b2ob2o2b
3o42bob2o5bo3bo2bo$552b2o44b3o14bo9b2o25b2o25bo2bo8b3o16bo7bo28b2o4bo
7bo$503b2o47b2o70bo2bo24b2o37b2o12bo2bob2o4bobo28b2o13b2ob2o5b2o3bo$
503b2o104bo14bobo52b2o10bobo8bobo6b3o48b3o6b8o$562b2o45bo15bo9b2o25b2o
26b3o20b2o2bob2o7bo28b2o12bo3bobo$513b2o47b2o45bo24bo2bo24b2o25b2o10b
2o10b2o6bo4b3o28b2o13b2obo2bo4bo$513b2o119bobo52b2o10b2o9b3o2bo4bobo2b
o45b2o6b2obob3o$572b2o44b3o14bo9b2o25b2o29bo8bo4bo3bobo3bo9bobo27b2o
12bo3bobobo$523b2o47b2o70bo2bo24b2o25b2o10b2o10bo4b4o4bo2bo22b2o3b2o
13b2obo$523b2o104bo14bobo52b2o11bobobo6bo3b5o2b3o47bo2bo4b3o2bo$582b2o
45bo15bo9b2o25b2o30bobo4bo2bo6bo2b2obo9b2o24bo3b2o10b2ob2obob2o$533b2o
47b2o45bo24bo2bo24b2o25b2o10bo6bo5b2obo2bo2bo3b3o22bo4b2o14b3o2b2o6bo$
533b2o119bobo52b2o11bo2bobo3bo2b2o3b3o2bobo26bo23b3o3bo3bo$592b2o44b3o
14bo9b2o25b2o29bobo5bo2bob2o7bobo3bo6bo24b2o2b2o10bobob2o3bo$543b2o47b
2o70bo2bo24b2o25b2o11b2o2b3obo4bobo4bo4b2o23bo4b2o15b2o2bo$543b2o104bo
14bobo52b2o11b4o6bo2bob3ob3o2bo2bo23b2o22b2o3bo2b3o$602b2o45bo15bo9b2o
25b2o31bo5bo2bo2b3o2b2obob5o31b2o2b2o11bo2b5o$553b2o47b2o45bo24bo2bo
24b2o25b2o11b2o6bob2obo3bo2bo4b3o23b2o2b2o11bo7bo$553b2o119bobo52bo14b
3o3bobo2bo2bo3bo3bo26bo9bo13bo8bo$612b2o44b3o14bo9b2o25b2o27bo10bo2b3o
bo2bo2bobo2bo34bob2o9bo2b3ob3o$563b2o47b2o70bo2bo24b2o24bobo14b2o3bobo
3b2ob3o5b2o23bobo3bo3bo7b4o4bo$563b2o104bo14bobo52bo12b2ob2o4b2o3b2o2b
3o3bob2o23bo12bo6bob3o$622b2o45bo15bo9b2o25b2o24bobo9bo5bo3bo4bob2obo
31bobo2bobobob4o8b3o$573b2o47b2o45bo24bo2bo24b2o24bobo11bo2bo4b2o3bo3b
obo5bo24bobo3bo3b3o2b2ob6o2bo$573b2o119bobo52bo13bo2bo4b2o5bo3bo3bob2o
23bo13b3obo3b3o$632b2o44b3o14bo9b2o25b2o24b2o2bo3bo2bo5bob3o2bo3bo3bo
31b3o2b3obo14b2o$583b2o47b2o70bo2bo24b2o24b3o10b2o3bob2ob4o4bobo5b2o
23b3o7b3o5bo2b2ob2o$583b2o104bo14bobo60bo2b3o3b3o3bo3bo2b3o4bo36bo2b6o
bo3bo$642b2o45bo15bo9b2o24bo2bo24bob2o5bo10b3o4bo2b2o32bo7bob2o8bo2bo$
593b2o47b2o45bo24bo2bo24b2o25bo7b2o6b3o4bob2o5bo6bo24bo9b2o8bo2b2o$
593b2o119bobo34bo2bo13bo8b2ob4o5bo3bob2o3bo6b2o24bo5bo9b3obo4bo$652b2o
44b3o14bo9b2o24bo2bo24bo8bo4b2o4b2o5b2ob2o25b2o6b5obo2b2o9b2o$603b2o
47b2o70bo2bo24b2o25bo5bo2bobob2ob2o3bo2bo3bo3bo7bo23b7o3bo6bo2b4o$603b
2o104bo14bobo34b2obo10bob2o6bo2bo2b2o3b2o2b2obob4obo6b2o24bob4o11bo2bo
3b2o$662b2o45bo15bo9b2o24b4o23b2o6b2o2b2o2bo3b2o7bo3bo38bo3bob3o$613b
2o47b2o45bo24bo2bo49b2o6b3o3b2o3b2o3bob2o2bob2o9bo22b7o4b3ob2o3b4o$
613b2o119bobo34b2ob2o7bob3o7bo2bo3bo3b2o3bob4ob3o7bobo22bo10b3ob3o2bo
3bo$672b2o44b3o14bo9b2o25b2o10b2o12bo12bo15b2o9bo26b2ob2o4b2ob2o$623b
2o47b2o70bo2bo34bob2o11b2o7bo4bo4b2o4b2o3bob3o7bo22bo2bo2bo10bo4b2o$
623b2o104bo14bobo35bobo7bo3bo8b3o4bo3bo4b3ob2o11b3o21bobo10bo4bob2ob2o
$682b2o45bo15bo9b2o25b2o8bob2o9bob2o4bo7bo4bobo8bo2bo7bo25b2obobo5b3o$
633b2o47b2o45bo24bo2bo36bo9b2obo14b6o8bo3b2o5bobo22b3o3bo9b2o$633b2o
119bobo35b2o8b3obo8b3o4b3o6b4o3bo10bo22b2o11b3obo3b4o$692b2o44b3o14bo
9b2o25b2o8b3o9bo2bo13bo4b2o8bo3bo34bob3o2b2obo2bo$643b2o47b2o70bo2bo
49bo14b3ob2o8bobobo6b3o22b2o8b2o4bo$643b2o104bo14bobo35b2o9bob2o9bo6bo
7b2obobo3bo6b3o23bo9b5obo4bo$702b2o45bo15bo9b2o25b2o8b2o11b3o13bo2b5o
6b2o36bobo2b2o2b2ob3o$653b2o47b2o45bo24bo2bo46b2obo14b3o13b3o7bo23b2o
9bo2b3o$653b2o119bobo35b2o9bobo25b2obobob2o7b3o24bo9b2o3bo3bobo$712b2o
44b3o14bo9b2o25b2o9b2o10b3o13b2ob2obo8bo4bo31bo5bo3bo2bo$663b2o47b2o
70bo2bo35bo10bo2bo15bo11b2ob2obo31bobo2bo4bo2b2obo6bobo$663b2o104bo14b
obo35b2obo7bo27b2obob3o8b3o23bo10b2o3bo3bobo$722b2o45bo15bo9b2o26bobo
8b2o10b2o14bobo13bobobo32bob2o4b2o4bo$673b2o47b2o45bo24bo2bo35bo10b2ob
o15bo7bo3b2obo3bo30b6o5b3o2bo6b2o$673b2o119bobo36b3o8b2o26bobo2bo8bobo
24bo11bob2o7b3o$732b2o44b3o14bo9b2o26bobo8b2o10b2o14b3o4bo2bo2bo2b2o2b
o22b2o10b2o3b3o2b2o$683b2o47b2o70bo2bo47bobo22bo2bo4bob3o30b3o8bobo2bo
6b2o$683b2o104bo14bobo35bob2o8b2o26b3ob2o2b2o6bo4bo20bo2bo9b2o4bo3bo$
742b2o45bo15bo9b2o26bobo10bo9b2o15bo6b3o2b4o2bo3bo19b2o7bo8bo4bo$693b
2o47b2o45bo24bo2bo35bo11bo2bo21bo4b2obo2bo32bo2bo5bo2bo2bo6bo$693b2o
119bobo35bo3bo8bo25bob2ob2o3bo5bo26bo2bo7bob2o5b4o$752b2o44b3o14bo9b2o
25bob2o9b2o26bo7b2o5b2o2b3o20b2o7b3o6b3o2bo$703b2o47b2o70bo2bo10b2o24b
2o9b4o14bo6bo3b3o4b5o28bobo6bo2bo2bo$703b2o104bo14bobo35b2ob2o9b2obo
20bo5b2o5b5o27b2o8bob2o6b3o$762b2o45bo15bo9b2o11bo13bobo19bo17b2o8bo2b
o2bo26b2o7b2o7b2o3bo$713b2o47b2o45bo24bo2bo10bo20bo4b2o11b2o15bo4bob2o
b3ob2ob5o37bo3b2o$713b2o119bobo12bo5bo15bobobo8bob2obob2o17bob2o4b4o4b
o28b2o8bob2o7bo$772b2o44b3o14bo9b2o10bo14bo2bo2bo10b6o18bobo3b3o5b2o
27bo7b2o8b2ob2o$723b2o47b2o70bobo3bo7b2o20b2o3b7obo3b2o15bo4b3o3b4o36b
o5b2ob2ob2o12bo$723b2o104bo14b3o14b2o2bo6bo5bo4bob2ob2ob2obo2bobo23b2o
5b7o28b3o7bo9bo5bo6b2obo$782b2o45bo21bo4bo3b8o14b2o7b3obo3b5obo17b3o2b
o2bob3obo37bo2bo3bo2bobo$733b2o47b2o45bo22bo2b2o3b2o2b3obo5bo8b2o4b3ob
6o4bo3b2o19bo8b2o36b2o4bo3bob2o6bo6bo$733b2o119b2o6b2o2bob2o5bo6b3o8bo
11bob2o21b2ob2o3bo6b2o29b2o4bo2bobo7bo4b2o9bo$792b2o44b3o21b3ob9o2b2o
4bo4b2o3bo4bob3o2bo3bo5bo18bo3b7o2bo38bobo3b2obobo9b5o$743b2o47b2o68b
2obo10bo3b5o8b2o8b2ob3ob8o17bo3bobobo3bo38b2o3bo3b3o7b8o$743b2o104bo
14bo3bo4bo2bo2b4o2bo5b2o2bo3bo3bo4bob2obobob2o21b2obo4bo2b2o3bo29bo5b
2o3bo7bob2o$802b2o45bo14bo7b2o3b2o4b2o3b2o8bo5b7o2bo5bo24bo4bo5b2o3bo
35bo5b2obo8bo5b3o$753b2o47b2o45bo23bo3bo6bobob3ob2o4bo5b3o8b4o3bob3o
18bo3bo2bob2obo38b3o3b2o2bo9b4o$753b2o112b2o5b4o5b4o2bo2bob2o5b2o6b5o
4bob2obobob2o17bo3b2o2b3obo2bo40b2o2bobo6bo7bo$812b2o44b3o14b3o5bo3bo
6b2o2bo2bo7b4ob3o2bo3bo4bo26b3o3b2o2b3o2b2o25b2o13bo2bo7bo7bo$763b2o
47b2o63b2o4bo2b2o8b3ob3o5bo2bo3bo2bo4b6o3b2ob2o19b4ob2o2bo3bo36b2o4b2o
bobobo5bo4b3o$763b2o104bo7b2o5b3o6bo2bo5bob2o3bobo10b2o7bo3bobo19b2obo
4bo2b4o35bobo3bo7bo4b4obobo$822b2o45bo23b2o2b2o3bobo6bo7b3o3b3o2b2obo
3b2o26bo3bobo4b2o2bo26b2o5bo2bo4bo3b4obobo$773b2o47b2o45bo17b2o5b3o10b
2o2b2o2bo3bo5bo3b2ob6o4b2ob2o19bob2obo3b2o3b2o37bo3bobo3b4ob2o4b3o$
773b2o112b2o6bo10b2obo4bo4b2o8b3o9bobobobo19bo3bo3bobo2b2o4bo2bo26b2ob
o3bobo5bob2obo2bo3bo$832b2o44b3o21b3o2bo5b2o5b2o3bo4bo4b3o3bob2o2bo28b
3o7bo3bo27bo5b3o7bobob2o3bo$783b2o47b2o63b2o5b3o5b2o4bo2bo13bo2bobobo
2b3o4b2ob2o19b3o3bo2b2o4bo34b2obo3bobo4b3ob2o5bo$783b2o104bo7b2o13b2o
3b3o3b3o2b2o6bo3b2o10b2ob2o23b2o3bo5bo5b2o28b3o3b2o9bobo3b3o$842b2o45b
o23bobobo12b2o13b3o3bo5bo28b2o3b2o3b4o35bo10bo2b5o$793b2o47b2o45bo17b
2o7bo5bo5b2o2bob2o3bo6bobobobo2b3o5bobo21bobob2o3bo2b2o35b2obo3bobob2o
5bo$793b2o112b2o6bo6b2o4b2o9bo7b2ob2o2bo7b5o23bo4bo2b4o5bo30b2o3b2ob3o
5b2o4b3o$852b2o44b3o25bo7bo2bo2b2o5b2o7b2o3bo5bo28b4obo5b2o37b2o7b2o2b
o3bo$803b2o47b2o63b2o5bobo4bo2bo3b2o2bob2ob2o6bo2bobobob4o7bo23bo2bo3b
o2b2o36bobo3bobo2bo5bo$803b2o104bo7b2o6bo5bob3o3bo2bob2ob2o9bob2o10b4o
23bobo4b2o2bo6bo30b2o3b2o2bo3bo3bo5bo$862b2o45bo24bobo7bo2bo2b2o3bo2bo
6b3o3bo5bo28b2o3bo4bobo38bo7bo4b3o$813b2o47b2o45bo17b2o5bobo3bo3bo2bob
2o4bo2bo8bo2bo2b5o31b3o7bo2bo34bobo3bobo3b5o$813b2o112b2o6bo4bob2o6b3o
2bobo3bo4b2o2b2o10bob3o23b2o4b2ob2o37b2o3b2o3b2o3b2o$872b2o44b3o23bobo
4bo3b3o2bo5b2o7b3o3bobo33b3o6b3o3bo34b2o5b2o4b3o$823b2o47b2o63b2o5b3o
3b3o2b2o3bo5b2o6bo2bo2bo2b5o31b2obo4b2o3bo35b2o3b2o4bo3bo$823b2o104bo
7b2o12b2o2bo4b2ob2o2bo4b5o3b2o4bo8b2obo22bo5bo2b2o37bo3bo4bo5bo$882b2o
45bo24b3o4bo4bo4b3o2bo8b2o4b3ob2obo27bo2bob2o4bo40bo5bo6bo$833b2o47b2o
45bo17b2o6bo5bo4bo3b2o4bo10bo3b2o2b2o31bob3o2bob2o2b3o34b3ob3o5b3o$
833b2o112b2o12bo3bo5bob4o7b3o3bo13bo3bo26bo3bo18bo30b2ob2o$892b2o44b3o
21bo2b2o5bo2b2o4b3obo3bo4bobo5bo2b4o28bo3bo5bo5bo34b2o3b2o6bo$843b2o
47b2o63b2o5bo7b3o6bo2bo10bobo3b2o3bo30bob2ob2ob3o4bo5bo30b2ob2o6bobo$
843b2o104bo7b2o13b4o5bob4o7b3o3bo18bo26bo2bob2o13b2o31bo3bo$902b2o45bo
22bo2bo6bo4bo3b2o7b2obo3bo5b3ob2o28b3ob2obo9b5o30bo3bo$853b2o47b2o45bo
17b2o4bobo7bo7b2o7b2obob2o5b3obo31b2o3bo2b3o4b3ob2o7b2o21b2ob2o6b3o$
853b2o112b2o14b2obo6b3o5bo3b2o3b2o4bo12b2o25bo5b2o46b3o$912b2o44b3o21b
o3bo5bo3b2o3b2o7b2ob2o10bo2bo28b2obobo12bo2bo8bo21bo3bo$863b2o47b2o63b
2o3bo8bo2bob2o4bo10b5o4b3obobo30bo3b2o2b2o5b2ob2o7bo22b2ob2o7bo$863b2o
104bo7b2o5b2o8bobo8bo5bo9bobo2b5o8bo26b2o2bob2o2bo9bo33b3o$922b2o45bo
21bo2bobo6b2obo4b3o6b2o2bo3bo10b2o27bobobo2b2o8b3o9bo21bo3bo$873b2o47b
2o45bo17b2o3b4o6b3ob2o13bobob3o4bob3o2b2o7bo20bo3b2ob2o9b2o2b2o3bobo
20b2ob2o$873b2o112b2o5bo6b2o3bo14b2o8bobob2o2bo6bo2bo27bob2ob2obo10bo
33b3o$932b2o44b3o20b2obobo7b3o5bob2o5bo6bo11bo27b3ob2obo9b2o10bo21bo3b
o$883b2o47b2o63b2o4b3o7b2obo14bo3b3o7bo4bo33bo2b2o8bo3b2o3bobo12bo7b2o
b2o$883b2o104bo7b2o12b2o3bo15b4o5b3ob2o2bo7b3o27b4o2b3ob2o2b2o3bo2bo
12bo18bo$942b2o45bo22bob2o9bo6bobo6bob2o3bo7b3obo30bob3ob6ob3o4bo5bo
21b2ob2o$893b2o47b2o45bo17b2o5b2o6bob3o15bo2b3o7bob2obo37bobobo6bobo4b
obo11b2o7b2ob2o$893b2o112b2o13bo3bo15b2o7b2o2b2o2bo8b2o31b6obo2bo4bobo
9bo3bo18bo$952b2o44b3o21b4o19bo5bob2o3bo7b2o2bo26b2o2bo6b2obo2b2o4b2o
5bo4bo17bobo$903b2o47b2o63b2o5bo7bob3o4bo3bo6bo2b3o7bo4bo41bo2bo3b3o5b
2o20b2ob2o$903b2o104bo7b2o13b2o2bo3bo12bo7b2o2bo2b2o8b2o27bo3b2ob2obo
8bobo10b4o$962b2o45bo23b3o17b3o5b2o3bo10bo2bo26bo2bo8b2o4bobo3bo6b3obo
17b3o$913b2o47b2o45bo17b2o12bo3b2o4b2ob2o7bob3o8b2o2bo27bo10b3obob6obo
4b2o21bobo$913b2o112b2o13b2ob2o4b3o21b2ob2o8b2o27b2ob2o3bobobo6bo13b2o
8bobo$972b2o44b3o23bo6b3o8bob2o4b4o2bo10bo2bo26b2o11bobo4bo2b2o7b2ob2o
17bo$923b2o47b2o63b2o13b2ob2o5bo2bo10bo10bo2bo28bo10b2o2bob2o4bo2bob2o
21b3o$923b2o104bo7b2o14bobo6bo9bo3bo3b2o3bo2b2o9bo27b2o5bo3bobobo5bo
12bo8bobo$982b2o45bo24bo7bo2bo6bo10b3o11b2obo27bobo9bo6bob2obo6b2obo$
933b2o47b2o45bo17b2o13bo2bo7b3o5bo2bobo6b2o3b2o29bo8bob2obo3b3o2bo2bo
2bo3b2o16b3o$933b2o112b2o14bobo7b2o7b3obo3b2o7bo8bobo27bobo3b2o4b3obob
obo3b2o16bo2bo$992b2o44b3o23bo8b2o8b3o5b5o7bo4bo29b3o9bo2b5ob2obo4bo2b
3o$943b2o47b2o63b2o13bo2bo8bo6bo4bo3bo3bo3b3o37bobo2b3o3bo2bobobo2b2ob
o18bo$943b2o104bo7b2o14bobo16bo3bo3bo3bo14b2o27b3o5bo4bo2bo4b2obo7bo8b
2ob2o$1002b2o45bo24bo8b2o8b3o5bo10b2o4b3o28bo10bobob3o2bo2bo8bo2bo7b2o
$953b2o47b2o45bo17b2o14bobo16b2ob2o3b4o5bo37bo2bo6b2o3b3ob3o2bobo5b2ob
o8bo$953b2o112b2o14b3o16b5o4b3o8bo6bo28b3o2bo3b2o4b2ob4o12b2o6bobo$
1012b2o44b3o32bo19bo5bo3bo5b2o36b2obobo4bo3bo9b3o5b2ob2o$963b2o47b2o
63b2o14b2o17b2ob2o2bo2bo6bo38b3obobo3bo3b2ob2o5b2o5b2obo$963b2o104bo7b
2o15b2o17bo2bo4b2o7b3o6bo29bo4bo2bo5bo3b3o12bo7b3o$1022b2o45bo53bobo3b
4o5bobo37bo2bo8bo11bo7bobo$973b2o47b2o45bo17b2o13b3o13bo4bobo4b3o8bo
36b3o2bo4b4o2b2o2bo3bo7bobo$973b2o112b2o15bo2bo11bo3b3o12bo44bobobo2b
2ob3obo2bobo7b2o9bo$1032b2o44b3o25bo6bo10b2o7bobo3bob2o5b3o37b3o2bo2b
2o2bo8b3o8b3o$983b2o47b2o63b2o14bo3bo6b2ob2o4b3o4bo2bo5b2o38bo3b3ob2ob
o3bo3bobobo7bobo$983b2o104bo7b2o14bo3bo7bo3bo4bo14b2o8bo34b2obo3bo2b2o
2bob3o$1042b2o45bo25b2o7b2o3bo12bo2bo3b3o7bo38bobo2bo2bo12bobo8b3o$
993b2o47b2o45bo17b2o14b4o7b2ob2o4b3o6b2o5bo39bo4b2o2bobo7bobobo7bo2bo$
993b2o112b2o15bob2o7b2o2bo12b2o6bo8bo34bo3b3o2b3o2bo2b2o$1052b2o44b3o
24bo7bo3b3o13b2o4bo2bo5bobo37b3o4bo3bo10bo10bo$1003b2o47b2o63b2o14bo2b
2o7bob2o5b2o4bo2bo50b2o12bobob2o6b3o$1003b2o104bo7b2o15bobo6bob2o2bo
13bo6bo42bo4b3o2b2o3b2obo9b3o$1062b2o45bo25bo7bo4b2o13b3o4b3o5b3o38bo
4b2o3bo10bob2o7bo$1013b2o47b2o45bo17b2o15b3o8bobo12b3o5b3o41bobo4bobo
5bo2bobo7bobo$1013b2o112b2o15b3o6b4ob2o6bo6bo3b3o43bo4b3o3bo3b2o9bo3bo
$1072b2o44b3o32bo4b2o6bo5bo2b3o11bo43b2o4bobo10bo$1023b2o47b2o63b2o15b
3o17bobobob4o4b3o41bobo2bobobo8b3o7b3o$1023b2o104bo7b2o16bo7b2obobo8b
3o7bo44bo6b2o5b3o2bo8b3o$1082b2o45bo33bo2b3obo6b6o3bo56b5obobo7bo2bo$
1033b2o47b2o45bo17b2o15b3o9bobob2o2bobo3b2obo4b3o41bobo2bob2o10bo9bo$
1033b2o112b2o24b2o3b3o2b3ob4obobo4bo42bo3bo3bo6bo3bo8b3o$1092b2o44b3o
33b3obob6o5b6ob2o9bo33bo9b2ob2ob2o8bo$1043b2o47b2o63b2o16bo6bo3bo7bob
5obo6bo35bo5bo2bo2bob2o8b3o2bo$1043b2o104bo7b2o24bo2b4obo10bobo3bobo
41bo2b2o8bo2b2obo2bo5b3o$1102b2o45bo34b3o3bo2b2o6bo2b3o46b3o5bobo3b3o
9bo2bo$1053b2o47b2o45bo17b2o21bo2b2obobo2bo5b2o2bobo4b3o34bo6b2o3bo7bo
3bo2b2o$1053b2o112b2o24b2ob2o6bo3b2obo2bo47b2o6b2o3bo2b2o2b3o6bo$1112b
2o44b3o34bo3b3o4bob2o5bo2bo2bo42b3o6bob2o2bobobo6b3o$1063b2o47b2o63b2o
24b2obo2b3o3b2o4bo7bo42b2ob2o3b5o4b2o2bo$1063b2o104bo7b2o25b3o3b2o2b2o
bobob4o3b3o42bob2o4bob3o3bo4bo$1122b2o45bo38bobo3bo4b2o2b2o3b2obo42b2o
7bobo3bobobo6b3o$1073b2o47b2o45bo17b2o24b2obo3bo4bo4b2o51bobo4b3o7bo2b
o$1073b2o112b2o26bobo3bo3bobobobob2o3b3o42bobo8b2o3bo2b2o$1132b2o44b3o
40bo2bobob2o4bo2bo3bo42b2o8b2o3bob3o7bo$1083b2o47b2o63b2o19b2o4bob3o
12bo51bo6bo9b3o$1083b2o104bo7b2o25bo4b2o3bobo4bobo5b2o42bobo9bo3bo2b2o
$1142b2o45bo39b3o4bob3o2b2o2b2obo43b2o8b2o3bo4bo$1093b2o47b2o45bo17b2o
19b2o4b3o2bob2obo2b3obo51bo6b2o8b3o$1093b2o112b2o25bo5b5ob4ob3o5bo44b
2o9bo3bo2bo$1152b2o44b3o37bo7bo3bo2bo4bob2o42b2o7b3o3bo3bo$1103b2o47b
2o63b2o20bo3b3o5bo2bo2b2o61b5o6bo$1103b2o104bo7b2o20bo7bob2o2b2o7bo51b
2o6b2obo4b3o$1162b2o45bo41bo3b2o2b2ob2o4b3o43b2o8b2o3b2o2bo$1113b2o47b
2o45bo17b2o19bob4ob2o4bobo4bob2o59b3o$1113b2o112b2o20bob2o4b3o2b2o2bo
2b2obo51b2o9bo4b3o$1172b2o44b3o33b2o2b2o3bo6bobo5b2o44b2o8b2o4bo2bo$
1123b2o47b2o63b2o19b3ob2ob2o4bobo3bo2b2o58bob2o$1123b2o104bo7b2o23bo2b
o2bo3bo2bo4bo53b2o8b2o5bo$1182b2o45bo34b2o2b2o3bobo4bob2o50b2o8b2o4b3o
$1133b2o47b2o45bo17b2o20bo2b2o7bo5b4o59bob2o$1133b2o112b2o22bo2b2obo4b
o3bob3obo51b2o8bo$1192b2o44b3o33b2obob4o2b4o3bo51b2o8b2o4b3o$1143b2o
47b2o63b2o21b3o2bo2bobobo4bo3bo4bo43bo9bo2bo$1143b2o104bo7b2o25b2ob3o
6bob3o2bo2bo47b2o8bo$1202b2o45bo35bobo2b3o3bo6bo47bo2bo7bobo6bo$1153b
2o47b2o45bo17b2o22bo3bo3bobo14bo31bo11bo3bo4b2ob2o$1153b2o112b2o26b4o
2bo4b3ob3o2bobo41bob5o6b2o$1212b2o44b3o34bo4b3o3b3o2b3o43bo3b2o9bobo6b
o$1163b2o47b2o63b2o29bo2bo7bo37bobo13b2o5bobo$1163b2o104bo7b2o26b3obob
o5bo2bo4b3o41b4o2b2o2b2ob2o$1222b2o45bo35bo5b2o3b2o3b3o2b2o39b3obo7b2o
bo8bo$1173b2o47b2o45bo17b2o27bo2bobo2b2o2b2o37b2o11bo2bobo4bobo4b2o$
1173b2o112b2o25b3obo2bob3o2b2o5b2o43b3o2bo3bo2bo$1232b2o44b3o39bob3o3b
2o2b2o2bobo38b2o6bo4bobo14bo$1183b2o47b2o63b2o25b2obobob2ob2o3bo6bo30b
2o11b2o8b3o5bo$1183b2o104bo7b2o25b2o3bobo2bo4bo6bo44b2ob3o3b3o4bo$
1242b2o45bo41bo6bo3b2o2b3o38b2o11bo16bo$1193b2o47b2o45bo17b2o24b2o3bo
3b2o3b2o6b2o30b2o12bo3bo5bo4bobo$1193b2o112b2o26b2o3bo3bobobo8bo43bo3b
o4b3o5bo$1252b2o44b3o39bo3b5o3b2o43b2o3bo2bo8bo$1203b2o47b2o63b2o23bob
4o4bo2bob2o7bo30b2o12b3o12b3o$1203b2o104bo7b2o31b2o6bo4bob2o45b4o4b3o
3b3o$1262b2o45bo40b5o2bo5bob2o10bo29b2o4b2o6bo2b3o$1213b2o47b2o45bo17b
2o23bobob2o5bobob2o8bo29b2o12bo3bo5bo3bob2o$1213b2o112b2o31b2o3bo2bo5b
2o46bob2o5bo3bo2bo$1272b2o44b3o38bo2b6o5b3o12bo28b2o4bo7bo$1223b2o47b
2o63b2o27bo10b2o6b2obo28b2o13b2ob2o5b2o3bo$1223b2o104bo7b2o23bo7b2o2bo
3bo53b3o6b8o$1282b2o45bo39bo2bo2b3o5b2o13bo28b2o12bo3bobo$1233b2o47b2o
45bo17b2o21bo2bo10b2ob2o7b3o28b2o13b2obo2bo4bo$1233b2o112b2o31b2o2b2ob
2o5bob2o45b2o6b2obob3o$1292b2o44b3o30bobo5bobo4bo7bo2bo9bobo27b2o12bo
3bobobo$1243b2o47b2o63b2o21bobo11b2ob2o7bo2bo22b2o3b2o13b2obo$1243b2o
104bo7b2o22b3o6bo4bobo6b3o47bo2bo4b3o2bo$1302b2o45bo32b2o5bob2o3bo7bo
2bo9b2o24bo3b2o10b2ob2obob2o$1253b2o47b2o45bo17b2o21bo14bobo2bo2bo3b3o
22bo4b2o14b3o2b2o6bo$1253b2o112b2o23bo6bo5b3o2bo3bobo26bo23b3o3bo3bo$
1312b2o44b3o31b2o5bob2o12bobo3bo6bo24b2o2b2o10bobob2o3bo$1263b2o47b2o
63b2o21b2o8bo4b2o2bo2bo4b2o23bo4b2o15b2o2bo$1263b2o104bo7b2o23bo6bo6bo
4b3o2bo2bo23b2o22b2o3bo2b3o$1322b2o45bo32bo6bobobo3bo3b3obob5o31b2o2b
2o11bo2b5o$1273b2o47b2o45bo17b2o14bo6b2o10b2obo3bo2bo4b3o23b2o2b2o11bo
7bo$1273b2o112b2o23bo6b2o3bo7bo3bo26bo9bo13bo8bo$1332b2o44b3o31bo6b3ob
3obo4bo2bobo2bo34bob2o9bo2b3ob3o$1283b2o47b2o63b2o14b2obo8b3o4bo3b2ob
3o5b2o23bobo3bo3bo7b4o4bo$1283b2o104bo7b2o23b4ob3ob2o3b2o2b3o3bob2o23b
o12bo6bob3o$1342b2o45bo32b7o2b5obob2o4bob2obo31bobo2bobobob4o8b3o$
1293b2o47b2o45bo17b2o17bo12b3o3bo3bobo5bo24bobo3bo3b3o2b2ob6o2bo$1293b
2o112b2o22b2obo2b2o2b2o5bo3bo3bob2o23bo13b3obo3b3o$1352b2o44b3o32bob3o
7bob3o2bo3bo3bo31b3o2b3obo14b2o$1303b2o47b2o63b2o23bob2obobob4o4bobo5b
2o23b3o7b3o5bo2b2ob2o$1303b2o104bo7b2o23bob2ob2o3bo3bo2b3o4bo36bo2b6ob
o3bo$1362b2o45bo32bo3bo12b3o4bo2b2o32bo7bob2o8bo2bo$1313b2o47b2o45bo
17b2o26b3o4bob2o5bo6bo24bo9b2o8bo2b2o$1313b2o112b2o22b3ob3obo3bob2o3bo
6b2o24bo5bo9b3obo4bo$1372b2o44b3o42b2o4b2o5b2ob2o25b2o6b5obo2b2o9b2o$
1323b2o47b2o63b2o21bob2ob2o3bo2bo3bo3bo7bo23b7o3bo6bo2b4o$1323b2o104bo
7b2o22b2o3b2o2b2obob4obo6b2o24bob4o11bo2bo3b2o$1382b2o45bo40b2o2bo3b2o
7bo3bo38bo3bob3o$1333b2o47b2o45bo17b2o22b2o3b2o3bob2o2bob2o9bo22b7o4b
3ob2o3b4o$1333b2o112b2o23bo3b2o3bob4ob3o7bobo22bo10b3ob3o2bo3bo$1392b
2o44b3o40bo15b2o9bo26b2ob2o4b2ob2o$1343b2o47b2o63b2o22bo4b2o4b2o3bob3o
7bo22bo2bo2bo10bo4b2o$1343b2o104bo7b2o23bo3bo4b3ob2o11b3o21bobo10bo4bo
b2ob2o$1402b2o45bo33bo7bo4bobo8bo2bo7bo25b2obobo5b3o$1353b2o47b2o45bo
17b2o23b6o8bo3b2o5bobo22b3o3bo9b2o$1353b2o112b2o23b3o6b4o3bo10bo22b2o
11b3obo3b4o$1412b2o44b3o40bo4b2o8bo3bo34bob3o2b2obo2bo$1363b2o47b2o63b
2o23b3ob2o8bobobo6b3o22b2o8b2o4bo$1363b2o104bo7b2o24bo7b2obobo3bo6b3o
23bo9b5obo4bo$1422b2o45bo41bo2b5o6b2o36bobo2b2o2b2ob3o$1373b2o47b2o45b
o17b2o23b3o13b3o7bo23b2o9bo2b3o$1373b2o112b2o32b2obobob2o7b3o24bo9b2o
3bo3bobo$1432b2o44b3o40b2ob2obo8bo4bo31bo5bo3bo2bo$1383b2o47b2o63b2o
24bo11b2ob2obo31bobo2bo4bo2b2obo6bobo$1383b2o104bo7b2o32b2obob3o8b3o
23bo10b2o3bo3bobo$1442b2o45bo42bobo13bobobo32bob2o4b2o4bo$1393b2o47b2o
45bo17b2o24bo7bo3b2obo3bo30b6o5b3o2bo6b2o$1393b2o112b2o33bobo2bo8bobo
24bo11bob2o7b3o$1452b2o44b3o41b3o4bo2bo2bo2b2o2bo22b2o10b2o3b3o2b2o$
1403b2o47b2o63b2o31bo2bo4bob3o30b3o8bobo2bo6b2o$1403b2o104bo7b2o33b3ob
2o2b2o6bo4bo20bo2bo9b2o4bo3bo$1462b2o45bo43bo6b3o2b4o2bo3bo19b2o7bo8bo
4bo$1413b2o47b2o45bo17b2o31bo4b2obo2bo32bo2bo5bo2bo2bo6bo$1413b2o112b
2o32bob2ob2o3bo5bo26bo2bo7bob2o5b4o$1472b2o44b3o42bo7b2o5b2o2b3o20b2o
7b3o6b3o2bo$1423b2o47b2o63b2o24bo6bo3b3o4b5o28bobo6bo2bo2bo$1423b2o
104bo7b2o31bo5b2o5b5o27b2o8bob2o6b3o$1482b2o45bo42b2o8bo2bo2bo26b2o7b
2o7b2o3bo$1433b2o47b2o45bo17b2o25bo4bob2ob3ob2ob5o37bo3b2o$1433b2o112b
2o31bob2o4b4o4bo28b2o8bob2o7bo$1492b2o44b3o42bobo3b3o5b2o27bo7b2o8b2ob
2o$1443b2o47b2o63b2o25bo4b3o3b4o36bo5b2ob2ob2o12bo$1443b2o104bo7b2o34b
2o5b7o28b3o7bo9bo5bo6b2obo$1502b2o45bo43b3o2bo2bob3obo37bo2bo3bo2bobo$
1453b2o47b2o45bo17b2o29bo8b2o36b2o4bo3bob2o6bo6bo$1453b2o112b2o31b2ob
2o3bo6b2o29b2o4bo2bobo7bo4b2o9bo$1512b2o44b3o43bo3b7o2bo38bobo3b2obobo
9b5o$1463b2o47b2o63b2o26bo3bobobo3bo38b2o3bo3b3o7b8o$1463b2o104bo7b2o
31b2obo4bo2b2o3bo29bo5b2o3bo7bob2o$1522b2o45bo44bo4bo5b2o3bo35bo5b2obo
8bo5b3o$1473b2o47b2o45bo17b2o26bo3bo2bob2obo38b3o3b2o2bo9b4o$1473b2o
112b2o27bo3b2o2b3obo2bo40b2o2bobo6bo7bo$1532b2o44b3o44b3o3b2o2b3o2b2o
25b2o13bo2bo7bo7bo$1483b2o47b2o63b2o27b4ob2o2bo3bo36b2o4b2obobobo5bo4b
3o$1483b2o104bo7b2o28b2obo4bo2b4o35bobo3bo7bo4b4obobo$1542b2o45bo45bo
3bobo4b2o2bo26b2o5bo2bo4bo3b4obobo$1493b2o47b2o45bo17b2o27bob2obo3b2o
3b2o37bo3bobo3b4ob2o4b3o$1493b2o112b2o28bo3bo3bobo2b2o4bo2bo26b2obo3bo
bo5bob2obo2bo3bo$1552b2o44b3o45b3o7bo3bo27bo5b3o7bobob2o3bo$1503b2o47b
2o63b2o27b3o3bo2b2o4bo34b2obo3bobo4b3ob2o5bo$1503b2o104bo7b2o31b2o3bo
5bo5b2o28b3o3b2o9bobo3b3o$1562b2o45bo46b2o3b2o3b4o35bo10bo2b5o$1513b2o
47b2o45bo17b2o28bobob2o3bo2b2o35b2obo3bobob2o5bo$1513b2o31bo80b2o31bo
4bo2b4o5bo30b2o3b2ob3o5b2o4b3o$1546bo25b2o44b3o45b4obo5b2o37b2o7b2o2bo
3bo$1523b2o47b2o63b2o30bo2bo3bo2b2o36bobo3bobo2bo5bo$1523b2o31bo72bo7b
2o30bobo4b2o2bo6bo30b2o3b2o2bo3bo3bo5bo$1555bobo24b2o45bo46b2o3bo4bobo
38bo7bo4b3o$1533b2o47b2o45bo17b2o30b3o7bo2bo34bobo3bobo3b5o$1533b2o31b
o80b2o31b2o4b2ob2o37b2o3b2o3b2o3b2o$1565bobo24b2o44b3o46b3o6b3o3bo34b
2o5b2o4b3o$1543b2o20bobo24b2o63b2o30b2obo4b2o3bo35b2o3b2o4bo3bo$1543b
2o31bo72bo7b2o32bo5bo2b2o37bo3bo4bo5bo$1575bobo24b2o45bo46bo2bob2o4bo
40bo5bo6bo$1553b2o20bo2bo23b2o45bo17b2o29bob3o2bob2o2b3o34b3ob3o5b3o$
1553b2o21bo90b2o36bo3bo18bo30b2ob2o$1585b3o24b2o44b3o46bo3bo5bo5bo34b
2o3b2o6bo$1563b2o20b2o2bo22b2o63b2o28bob2ob2ob3o4bo5bo30b2ob2o6bobo$
1563bo23bo81bo7b2o37bo2bob2o13b2o31bo3bo$1595b2o25b2o45bo47b3ob2obo9b
5o30bo3bo$1573b2o21bobob2o20b2o45bo17b2o29b2o3bo2b3o4b3ob2o7b2o21b2ob
2o6b3o$1573bo24bo7bo80b2o37bo5b2o46b3o$1575bo24b2o4bo25b2o44b3o46b2obo
bo12bo2bo8bo21bo3bo$1583b2o21b3ob2o20b2o63b2o30bo3b2o2b2o5b2ob2o7bo22b
2ob2o7bo$1583bo2bo21bob2o77bo7b2o37b2o2bob2o2bo9bo33b3o$1584bobo21bobo
4b3o6bo17b2o45bo48bobobo2b2o8b3o9bo21bo3bo$1593b2o25b2o20b2o45bo17b2o
30bo3b2ob2o9b2o2b2o3bobo20b2ob2o$1594b3o21b3o86b2o38bob2ob2obo10bo33b
3o$1595b2o7bo13bo7bo7b2o16b2o44b3o47b3ob2obo9b2o10bo21bo3bo$1603bo17bo
2bob2o2b2obo18b2o63b2o35bo2b2o8bo3b2o3bobo12bo7b2ob2o$1603bo2bo18b3o2b
ob3obo72bo7b2o38b4o2b3ob2o2b2o3bo2bo12bo18bo$1605b2o19b2o2bob3obo4bo2b
o17b2o45bo51bob3ob6ob3o4bo5bo21b2ob2o$1613b3o10b2o5b2ob2o3bo2b2o16b2o
45bo17b2o39bobobo6bobo4bobo11b2o7b2ob2o$1611bo2b4o4b2o3b2o2bo8bo3b2o
81b2o42b6obo2bo4bobo9bo3bo18bo$1627b2o7bo3b3o3bo5b2o18b2o44b3o46b2o2bo
6b2obo2b2o4b2o5bo4bo17bobo$1622b4obo4bo3b2o3bobo2bo4b4o17b2o63b2o43bo
2bo3b3o5b2o20b2ob2o$1626b2o9bo3bob2obo3bo4b2o72bo7b2o38bo3b2ob2obo8bob
o10b4o$1621b2o9b2o3bo4b3o6b2o10bo18b2o45bo47bo2bo8b2o4bobo3bo6b3obo17b
3o$1635b3o5b4o4bo5bo3b2obo17b2o45bo17b2o29bo10b3obob6obo4b2o21bobo$
1631bo2bobo7bob2o4b2ob2o4bo3bo81b2o38b2ob2o3bobobo6bo13b2o8bobo$1643bo
3bo4b2o7b3ob2o6bo18b2o44b3o46b2o11bobo4bo2b2o7b2ob2o17bo$1631b2o9b2ob
2o18b2o5bobo17b2o63b2o30bo10b2o2bob2o4bo2bob2o21b3o$1642b3obo7b4o4b2o
2bo4b2o2bo73bo7b2o38b2o5bo3bobobo5bo12bo8bobo$1642bo11b2o2bo3bo9b4o7bo
18b2o45bo48bobo9bo6bob2obo6b2obo$1641b2o6bo3bobo19bo6bobo17b2o45bo17b
2o30bo8bob2obo3b3o2bo2bo2bo3b2o16b3o$1646bo5b2o3bo14b2o2bo5bo2bo81b2o
39bobo3b2o4b3obobobo3b2o16bo2bo$1648bo2bo5bo5b6o3bo4bo4b3o8bo18b2o44b
3o47b3o9bo2b5ob2obo4bo2b3o$1656b4o5bob2o5bo10bo6bobo17b2o63b2o39bobo2b
3o3bo2bobobo2b2obo18bo$1651b2o3b3o4bo3bo10bo3b4o6bo2bo73bo7b2o39b3o5bo
4bo2bo4b2obo7bo8b2ob2o$1658bo3b5o2bo4bo2bo3bo2bobo6b2o8bo18b2o45bo49bo
10bobob3o2bo2bo8bo2bo7b2o$1661b2o2b2o6b3obo7b3o5bo8bobo17b2o45bo17b2o
38bo2bo6b2o3b3ob3o2bobo5b2obo8bo$1661b2o5b2o3b2o2bo7b3o4b3obo6b2o82b2o
39b3o2bo3b2o4b2ob4o12b2o6bobo$1667bo7b2ob2o6b2o3bo4bo6b2o8bo18b2o44b3o
56b2obobo4bo3bo9b3o5b2ob2o$1671b2o5b2o3b2o6bo2bob2o14bobo17b2o63b2o39b
3obobo3bo3b2ob2o5b2o5b2obo$1671b2o3bobo5bo3bo14bobo7b2o74bo7b2o40bo4bo
2bo5bo3b3o12bo7b3o$1677bo7b2obo3bo3bo5b2o2b2o15bo18b2o45bo58bo2bo8bo
11bo7bobo$1681b2o3bobo5b4o3b3o10bo7bobo17b2o45bo17b2o39b3o2bo4b4o2b2o
2bo3bo7bobo$1681b2o3b3o5bobobo3b2o2bo6bo2bo6b2o82b2o44bobobo2b2ob3obo
2bobo7b2o9bo$1697bo4b3o7bo3bo16bo18b2o44b3o57b3o2bo2b2o2bo8b3o8b3o$
1691b2o3bobo5b2obo4bo4bo14bobo17b2o63b2o40bo3b3ob2obo3bo3bobobo7bobo$
1691b2o4bo8bobo3bo10b3o7b2o74bo7b2o45b2obo3bo2b2o2bob3o$1697bo7bo2bo4b
ob2o6b4o16bo18b2o45bo58bobo2bo2bo12bobo8b3o$1701b2o10bo8bo3bo15bobo17b
2o45bo17b2o40bo4b2o2bobo7bobobo7bo2bo$1701b2o3b3o7b2o5b3obo6bo8b2o82b
2o45bo3b3o2b3o2bo2b2o$1712bo3b3o4b3o7b3o17bo18b2o44b3o57b3o4bo3bo10bo
10bo$1711bo4b2o14bo3b2o14bobo17b2o63b2o45b2o12bobob2o6b3o$1711bo5b2o4b
o3bo5b2o18b2o74bo7b2o44bo4b3o2b2o3b2obo9b3o$1712bo9bo3b2o6bo3bo4b3o17b
o18b2o45bo59bo4b2o3bo10bob2o7bo$1721bo6bo6bobo5bo2bo15bobo17b2o45bo17b
2o43bobo4bobo5bo2bobo7bobo$1721bobobo17b2ob2o15b2o82b2o44bo4b3o3bo3b2o
9bo3bo$1722bo4b2o3b6o7b3o6b2o17bo18b2o44b3o62b2o4bobo10bo$1731bob3o2bo
7b2o5b2o17bobo17b2o63b2o43bobo2bobobo8b3o7b3o$1731b3ob3o16bob2o15b2o
74bo7b2o43bo6b2o5b3o2bo8b3o$1737b2o4bo2b2o8b2o6bo18bo18b2o45bo63b5obob
o7bo2bo$1742b2ob2o17b2o16bobo17b2o45bo17b2o43bobo2bob2o10bo9bo$1741b2o
3bob2o7bo6bobo16b2o82b2o43bo3bo3bo6bo3bo8b3o$1754bo2bo8b2o5b2o18bo18b
2o44b3o52bo9b2ob2ob2o8bo$1747bo4b2o2bo6bo2bo4bo3bo16bobo17b2o63b2o36bo
5bo2bo2bob2o8b3o2bo$1752bo3bobo6b2o9bo16b2o74bo7b2o43bo2b2o8bo2b2obo2b
o5b3o$1749bo2bo4b3o4b2obo6b3o6b2o18bo18b2o45bo53b3o5bobo3b3o9bo2bo$
1758bobobo3bo4b2o3bo5bob3o15bobo17b2o45bo17b2o36bo6b2o3bo7bo3bo2b2o$
1759b4o3bobo5b2o5b3o19b2o82b2o43b2o6b2o3bo2b2o2b3o6bo$1760b2o5b2o8bo3b
2ob2o7bo19bo18b2o44b3o53b3o6bob2o2bobobo6b3o$1770bo2bo2b2o4bobob2o4bob
2o16bobo17b2o63b2o43b2ob2o3b5o4b2o2bo$1769b4o3bob2o3b2o7bo2b2o16b2o74b
o7b2o44bob2o4bob3o3bo4bo$1777bo4b2o7bo3b2o26bo18b2o45bo54b2o7bobo3bobo
bo6b3o$1782b2o2b3obo2bo3b2o3b3o17bobo17b2o45bo17b2o44bobo4b3o7bo2bo$
1779b3o4bo6bo8bob2o17b2o82b2o44bobo8b2o3bo2b2o$1780bo7bo3b2o9bobobo25b
o18b2o44b3o53b2o8b2o3bob3o7bo$1780bo7bo3bo4b2obob2o4bo3b2o18bobo17b2o
63b2o44bo6bo9b3o$1796b2ob3obo4bo3bob2o17b2o74bo7b2o44bobo9bo3bo2b2o$
1789b3o6bobobo12bo27bo18b2o45bo54b2o8b2o3bo4bo$1798bobobo2bobo5bo2b3o
3b2o18bobo17b2o45bo17b2o44bo6b2o8b3o$1799b3o4b2ob3ob4obo3bobo18b2o82b
2o45b2o9bo3bo2bo$1800bo7bo3bo2b2o7b2o27bo18b2o44b3o53b2o7b3o3bo3bo$
1808bo3bo3b2o5b2o2b2o3b2o18bobo17b2o63b2o51b5o6bo$1809b3o5bo5bo2bobo3b
obo18b2o74bo7b2o45b2o6b2obo4b3o$1818b5o3bo7bo28bo18b2o45bo54b2o8b2o3b
2o2bo$1819b3o4bo3bo3bo3bo3bo19bobo17b2o45bo17b2o52b3o$1820bo6bo5bo3b2o
3b2o19b2o82b2o45b2o9bo4b3o$1828bo3bo3b2o5b2o28bo18b2o44b3o53b2o8b2o4bo
2bo$1829b3o5b2o3b2o28bobo17b2o63b2o51bob2o$1838b5o4b3ob3o19b2o74bo7b2o
45b2o8b2o5bo$1839b3o5bo5bo29bo18b2o45bo54b2o8b2o4b3o$1840bo6bo5bo28bob
o17b2o45bo17b2o51bob2o$1848bo3bo5b2ob2o20b2o82b2o45b2o8bo$1849b3o5b2o
3b2o29bo18b2o44b3o53b2o8b2o4b3o$1858b2ob2o29bobo17b2o63b2o41bo9bo2bo$
1859b3o6b2ob2o20b2o74bo7b2o45b2o8bo$1860bo7bo3bo30bo18b2o45bo51bo2bo7b
obo6bo$1868bo3bo29bobo17b2o45bo17b2o29bo11bo3bo4b2ob2o$1869bobo6b2ob2o
20b2o82b2o40bob5o6b2o$1870bo7bo3bo30bo18b2o39bo4b3o10b2o34bo3b2o9bobo
6bo$1879b3o30bobo17b2o39bo23b2o28bobo13b2o5bobo$1879b3o6b2ob2o20b2o74b
o7b2o40b4o2b2o2b2ob2o$1888bo3bo30bo18b2o39b2o4bo11bo35b3obo7b2obo8bo$
1889b3o30bobo17b2o38bo6bo11b2o4bo29b2o11bo2bobo4bobo4b2o$1890bo7b2ob2o
20b2o68bo5bob2o4b2obo39b3o2bo3bo2bo$1898bo3bo30bo18b2o36bo2bo5b3o9bo
35b2o6bo4bobo14bo$1899b3o30bobo17b2o37bobo6b2o10bo34b2o11b2o8b3o5bo$
1908b2ob2o20b2o66b2o5bo2bo4b3obo40b2ob3o3b3o4bo$1908b2ob2o30bo18b2o37b
3o5b3o6b2obo35b2o11bo16bo$1910bo31bobo17b2o37b2o15b2o2bo3b2o29b2o12bo
3bo5bo4bobo$1918b2ob2o20b2o5bo61bo6b3o7b2o40bo3bo4b3o5bo$1919bobo30b2o
18b2o37b2o7bo6bo3bo35b2o3bo2bo8bo$1920bo8bobo16bo5bo17b2o38bo16bo2bo3b
2o29b2o12b3o12b3o$1929bobo21b2o5b2o60bo6b3o5b3o42b4o4b3o3b3o$1929b3o
17bo10b4o18b2o37bobo10bo2bo2b2o5bo29b2o4b2o6bo2b3o$1938bo2bo16b2o4bo
17b2o25b2o9bo18b2o6bo29b2o12bo3bo5bo3bob2o$1939b3o16b2obobo7bo51bo16b
2ob2o2b3o42bob2o5bo3bo2bo$1940bo7bo10bobobo6b4o18b2o25bo2bo8b3o16bo7bo
28b2o4bo7bo$1948bo2bo7bo9bo4bo17b2o37b2o12bo2bob2o4bobo28b2o13b2ob2o5b
2o3bo$1949b3o6b3o7b2ob3obo43b2o10bobo8bobo6b3o48b3o6b8o$1958b3o8bobobo
6b3o19b2o26b3o20b2o2bob2o7bo28b2o12bo3bobo$1960b2o7bo4bo4bo3b2o17b2o
25b2o10b2o10b2o6bo4b3o28b2o13b2obo2bo4bo$1959b2o6bobo9b5obo43b2o10b2o
9b3o2bo4bobo2bo45b2o6b2obob3o$1970bo8bo5bo5b2o19b2o29bo8bo4bo3bobo3bo
9bobo27b2o12bo3bobobo$1967bo2bo12bo6b2obo18b2o25b2o10b2o10bo4b4o4bo2bo
22b2o3b2o13b2obo$1969b2o6b3o4bo4b2o2bobo43b2o11bobobo6bo3b5o2b3o47bo2b
o4b3o2bo$1977b3o14b2o5b2o19b2o30bobo4bo2bo6bo2b2obo9b2o24bo3b2o10b2ob
2obob2o$1978bobo7bo4b2o6bobo18b2o25b2o10bo6bo5b2obo2bo2bo3b3o22bo4b2o
14b3o2b2o6bo$1979b2o7bo6bo4bo2bo45b2o11bo2bobo3bo2b2o3b3o2bobo26bo23b
3o3bo3bo$1988bo10b2obob3o5bo19b2o29bobo5bo2bob2o7bobo3bo6bo24b2o2b2o
10bobob2o3bo$1988bo2bo7b2o3bo6b2o19b2o25b2o11b2o2b3obo4bobo4bo4b2o23bo
4b2o15b2o2bo$1989b2o8b3o3b2o4bobo45b2o11b4o6bo2bob3ob3o2bo2bo23b2o22b
2o3bo2b3o$1998bob2o8bobo2b2o25b2o31bo5bo2bo2b3o2b2obob5o31b2o2b2o11bo
2b5o$1999b2o8b2o4b2o4b3o18b2o25b2o11b2o6bob2obo3bo2bo4b3o23b2o2b2o11bo
7bo$1999bo8bo3bo2bo5bo47bo14b3o3bobo2bo2bo3bo3bo26bo9bo13bo8bo$2011bo
10bo2b2o25b2o27bo10bo2b3obo2bo2bobo2bo34bob2o9bo2b3ob3o$2008b3o9b2o3b
2o5b2o18b2o24bobo14b2o3bobo3b2ob3o5b2o23bobo3bo3bo7b4o4bo$2018b2ob2o8b
2o46bo12b2ob2o4b2o3b2o2b3o3bob2o23bo12bo6bob3o$2018b3o3bo7bo2b2obo23b
2o24bobo9bo5bo3bo4bob2obo31bobo2bobobob4o8b3o$2019bo11bo4bobo3b2o18b2o
24bobo11bo2bo4b2o3bo3bobo5bo24bobo3bo3b3o2b2ob6o2bo$2029bobobo8bobo44b
o13bo2bo4b2o5bo3bo3bob2o23bo13b3obo3b3o$2028b3o4bo6bo3b2o24b2o24b2o2bo
3bo2bo5bob3o2bo3bo3bo31b3o2b3obo14b2o$2035bo4bobo3b3o3b2o18b2o24b3o10b
2o3bob2ob4o4bobo5b2o23b3o7b3o5bo2b2ob2o$2039bo12bobo52bo2b3o3b3o3bo3bo
2b3o4bo36bo2b6obo3bo$2038bo3bob3o7bo2bo23bo2bo24bob2o5bo10b3o4bo2b2o
32bo7bob2o8bo2bo$2039bobo10b5obo3bo19b2o25bo7b2o6b3o4bob2o5bo6bo24bo9b
2o8bo2b2o$2049b4o2bo3bo2b2o27bo2bo13bo8b2ob4o5bo3bob2o3bo6b2o24bo5bo9b
3obo4bo$2049b3o3bo7b2o26bo2bo24bo8bo4b2o4b2o5b2ob2o25b2o6b5obo2b2o9b2o
$2049b2o4bo7bo2b3o23b2o25bo5bo2bobob2ob2o3bo2bo3bo3bo7bo23b7o3bo6bo2b
4o$2062bo3b3o2b3o27b2obo10bob2o6bo2bo2b2o3b2o2b2obob4obo6b2o24bob4o11b
o2bo3b2o$2058b4o3bo2bo4bo27b4o23b2o6b2o2b2o2bo3b2o7bo3bo38bo3bob3o$
2065b7obo3bo49b2o6b3o3b2o3b2o3bob2o2bob2o9bo22b7o4b3ob2o3b4o$2067b6o3b
3o2b2o28b2ob2o7bob3o7bo2bo3bo3b2o3bob4ob3o7bobo22bo10b3ob3o2bo3bo$
2075bo6b2o28b2o10b2o12bo12bo15b2o9bo26b2ob2o4b2ob2o$2075bo2bo2b2o5bo
33bob2o11b2o7bo4bo4b2o4b2o3bob3o7bo22bo2bo2bo10bo4b2o$2076bob2obo4b2o
3b2o29bobo7bo3bo8b3o4bo3bo4b3ob2o11b3o21bobo10bo4bob2ob2o$2085bobo4bo
29b2o8bob2o9bob2o4bo7bo4bobo8bo2bo7bo25b2obobo5b3o$2085b4o3bo5bo35bo9b
2obo14b6o8bo3b2o5bobo22b3o3bo9b2o$2088bo2bo5bobob2o29b2o8b3obo8b3o4b3o
6b4o3bo10bo22b2o11b3obo3b4o$2090bo3b2obo4bo29b2o8b3o9bo2bo13bo4b2o8bo
3bo34bob3o2b2obo2bo$2096bob4o55bo14b3ob2o8bobobo6b3o22b2o8b2o4bo$2099b
3o3bob3ob2o29b2o9bob2o9bo6bo7b2obobo3bo6b3o23bo9b5obo4bo$2105bob2o3bo
29b2o8b2o11b3o13bo2b5o6b2o36bobo2b2o2b2ob3o$2105bo3b3o52b2obo14b3o13b
3o7bo23b2o9bo2b3o$2110bo7b2ob2o29b2o9bobo25b2obobob2o7b3o24bo9b2o3bo3b
obo$2114b3obo3bo29b2o9b2o10b3o13b2ob2obo8bo4bo31bo5bo3bo2bo$2119b3o41b
o10bo2bo15bo11b2ob2obo31bobo2bo4bo2b2obo6bobo$2125bo2b2ob2o29b2obo7bo
27b2obob3o8b3o23bo10b2o3bo3bobo$2125bo2b2ob2o30bobo8b2o10b2o14bobo13bo
bobo32bob2o4b2o4bo$2125bo4bo42bo10b2obo15bo7bo3b2obo3bo30b6o5b3o2bo6b
2o$2138b2ob2o30b3o8b2o26bobo2bo8bobo24bo11bob2o7b3o$2134b3o2bobo31bobo
8b2o10b2o14b3o4bo2bo2bo2b2o2bo22b2o10b2o3b3o2b2o$2140bo8bobo6bo36bobo
22bo2bo4bob3o30b3o8bobo2bo6b2o$2145bo3bobo6bo23bob2o8b2o26b3ob2o2b2o6b
o4bo20bo2bo9b2o4bo3bo$2145bo3b3o31bobo10bo9b2o15bo6b3o2b4o2bo3bo19b2o
7bo8bo4bo$2145bo13bobo6b2o23bo11bo2bo21bo4b2obo2bo32bo2bo5bo2bo2bo6bo$
2159b3o5bo24bo3bo8bo25bob2ob2o3bo5bo26bo2bo7bob2o5b4o$2154b3o3bo31bob
2o9b2o26bo7b2o5b2o2b3o20b2o7b3o6b3o2bo$2168bo2bo6b2o24b2o9b4o14bo6bo3b
3o4b5o28bobo6bo2bo2bo$2165bo3b3o6b2o22b2ob2o9b2obo20bo5b2o5b5o27b2o8bo
b2o6b3o$2165bo12b3o7bo13bobo19bo17b2o8bo2bo2bo26b2o7b2o7b2o3bo$2165bo
13b2o7bo20bo4b2o11b2o15bo4bob2ob3ob2ob5o37bo3b2o$2180bo8bo5bo15bobobo
8bob2obob2o17bob2o4b4o4bo28b2o8bob2o7bo$2174b3o4bo7bo7bo14bo2bo2bo10b
6o18bobo3b3o5b2o27bo7b2o8b2ob2o$2189bo8b2o20b2o3b7obo3b2o15bo4b3o3b4o
36bo5b2ob2ob2o12bo$2185bo4bo10b2o2bo6bo5bo4bob2ob2ob2obo2bobo23b2o5b7o
28b3o7bo9bo5bo6b2obo$2185bo5bo4bo3b8o14b2o7b3obo3b5obo17b3o2bo2bob3obo
37bo2bo3bo2bobo$2185bo6bo6b3o2b3obo5bo8b2o4b3ob6o4bo3b2o19bo8b2o36b2o
4bo3bob2o6bo6bo$2202b2o2bob2o5bo6b3o8bo11bob2o21b2ob2o3bo6b2o29b2o4bo
2bobo7bo4b2o9bo$2194b3o5b3ob9o2b2o4bo4b2o3bo4bob3o2bo3bo5bo18bo3b7o2bo
38bobo3b2obobo9b5o$2202b2obo10bo3b5o8b2o8b2ob3ob8o17bo3bobobo3bo38b2o
3bo3b3o7b8o$2204b2obo5bo2bo2b4o2bo5b2o2bo3bo3bo4bob2obobob2o21b2obo4bo
2b2o3bo29bo5b2o3bo7bob2o$2204b2o6b2o3b2o4b2o3b2o8bo5b7o2bo5bo24bo4bo5b
2o3bo35bo5b2obo8bo5b3o$2213bo3bo6bobob3ob2o4bo5b3o8b4o3bob3o18bo3bo2bo
b2obo38b3o3b2o2bo9b4o$2214b4o5b4o2bo2bob2o5b2o6b5o4bob2obobob2o17bo3b
2o2b3obo2bo40b2o2bobo6bo7bo$2215bo7bo3bo6b2o2bo2bo7b4ob3o2bo3bo4bo26b
3o3b2o2b3o2b2o25b2o13bo2bo7bo7bo$2223bo2b2o8b3ob3o5bo2bo3bo2bo4b6o3b2o
b2o19b4ob2o2bo3bo36b2o4b2obobobo5bo4b3o$2224b3o6bo2bo5bob2o3bobo10b2o
7bo3bobo19b2obo4bo2b4o35bobo3bo7bo4b4obobo$2233b2o2b2o3bobo6bo7b3o3b3o
2b2obo3b2o26bo3bobo4b2o2bo26b2o5bo2bo4bo3b4obobo$2234b3o10b2o2b2o2bo3b
o5bo3b2ob6o4b2ob2o19bob2obo3b2o3b2o37bo3bobo3b4ob2o4b3o$2235bo10b2obo
4bo4b2o8b3o9bobobobo19bo3bo3bobo2b2o4bo2bo26b2obo3bobo5bob2obo2bo3bo$
2242b3o2bo5b2o5b2o3bo4bo4b3o3bob2o2bo28b3o7bo3bo27bo5b3o7bobob2o3bo$
2244b3o5b2o4bo2bo13bo2bobobo2b3o4b2ob2o19b3o3bo2b2o4bo34b2obo3bobo4b3o
b2o5bo$2252b2o3b3o3b3o2b2o6bo3b2o10b2ob2o23b2o3bo5bo5b2o28b3o3b2o9bobo
3b3o$2253bobobo12b2o13b3o3bo5bo28b2o3b2o3b4o35bo10bo2b5o$2256bo5bo5b2o
2bob2o3bo6bobobobo2b3o5bobo21bobob2o3bo2b2o35b2obo3bobob2o5bo$2255bo6b
2o4b2o9bo7b2ob2o2bo7b5o23bo4bo2b4o5bo30b2o3b2ob3o5b2o4b3o$2266bo7bo2bo
2b2o5b2o7b2o3bo5bo28b4obo5b2o37b2o7b2o2bo3bo$2264bobo4bo2bo3b2o2bob2ob
2o6bo2bobobob4o7bo23bo2bo3bo2b2o36bobo3bobo2bo5bo$2265bo5bob3o3bo2bob
2ob2o9bob2o10b4o23bobo4b2o2bo6bo30b2o3b2o2bo3bo3bo5bo$2274bobo7bo2bo2b
2o3bo2bo6b3o3bo5bo28b2o3bo4bobo38bo7bo4b3o$2274bobo3bo3bo2bob2o4bo2bo
8bo2bo2b5o31b3o7bo2bo34bobo3bobo3b5o$2275bo4bob2o6b3o2bobo3bo4b2o2b2o
10bob3o23b2o4b2ob2o37b2o3b2o3b2o3b2o$2284bobo4bo3b3o2bo5b2o7b3o3bobo
33b3o6b3o3bo34b2o5b2o4b3o$2284b3o3b3o2b2o3bo5b2o6bo2bo2bo2b5o31b2obo4b
2o3bo35b2o3b2o4bo3bo$2291b2o2bo4b2ob2o2bo4b5o3b2o4bo8b2obo22bo5bo2b2o
37bo3bo4bo5bo$2294b3o4bo4bo4b3o2bo8b2o4b3ob2obo27bo2bob2o4bo40bo5bo6bo
$2295bo5bo4bo3b2o4bo10bo3b2o2b2o31bob3o2bob2o2b3o34b3ob3o5b3o$2301bo3b
o5bob4o7b3o3bo13bo3bo26bo3bo18bo30b2ob2o$2302bo2b2o5bo2b2o4b3obo3bo4bo
bo5bo2b4o28bo3bo5bo5bo34b2o3b2o6bo$2304bo7b3o6bo2bo10bobo3b2o3bo30bob
2ob2ob3o4bo5bo30b2ob2o6bobo$2312b4o5bob4o7b3o3bo18bo26bo2bob2o13b2o31b
o3bo$2312bo2bo6bo4bo3b2o7b2obo3bo5b3ob2o28b3ob2obo9b5o30bo3bo$2313bobo
7bo7b2o7b2obob2o5b3obo31b2o3bo2b3o4b3ob2o7b2o21b2ob2o6b3o$2323b2obo6b
3o5bo3b2o3b2o4bo12b2o25bo5b2o46b3o$2322bo3bo5bo3b2o3b2o7b2ob2o10bo2bo
28b2obobo12bo2bo8bo21bo3bo$2322bo8bo2bob2o4bo10b5o4b3obobo30bo3b2o2b2o
5b2ob2o7bo22b2ob2o7bo$2324b2o8bobo8bo5bo9bobo2b5o8bo26b2o2bob2o2bo9bo
33b3o$2331bo2bobo6b2obo4b3o6b2o2bo3bo10b2o27bobobo2b2o8b3o9bo21bo3bo$
2332b4o6b3ob2o13bobob3o4bob3o2b2o7bo20bo3b2ob2o9b2o2b2o3bobo20b2ob2o$
2334bo6b2o3bo14b2o8bobob2o2bo6bo2bo27bob2ob2obo10bo33b3o$2341b2obobo7b
3o5bob2o5bo6bo11bo27b3ob2obo9b2o10bo21bo3bo$2343b3o7b2obo14bo3b3o7bo4b
o33bo2b2o8bo3b2o3bobo12bo7b2ob2o$2351b2o3bo15b4o5b3ob2o2bo7b3o27b4o2b
3ob2o2b2o3bo2bo12bo18bo$2352bob2o9bo6bobo6bob2o3bo7b3obo30bob3ob6ob3o
4bo5bo21b2ob2o$2354b2o6bob3o15bo2b3o7bob2obo37bobobo6bobo4bobo11b2o7b
2ob2o$2362bo3bo15b2o7b2o2b2o2bo8b2o31b6obo2bo4bobo9bo3bo18bo$2362b4o
19bo5bob2o3bo7b2o2bo26b2o2bo6b2obo2b2o4b2o5bo4bo17bobo$2364bo7bob3o4bo
3bo6bo2b3o7bo4bo41bo2bo3b3o5b2o20b2ob2o$2372b2o2bo3bo12bo7b2o2bo2b2o8b
2o27bo3b2ob2obo8bobo10b4o$2373b3o17b3o5b2o3bo10bo2bo26bo2bo8b2o4bobo3b
o6b3obo17b3o$2381bo3b2o4b2ob2o7bob3o8b2o2bo27bo10b3obob6obo4b2o21bobo$
2382b2ob2o4b3o21b2ob2o8b2o27b2ob2o3bobobo6bo13b2o8bobo$2384bo6b3o8bob
2o4b4o2bo10bo2bo26b2o11bobo4bo2b2o7b2ob2o17bo$2392b2ob2o5bo2bo10bo10bo
2bo28bo10b2o2bob2o4bo2bob2o21b3o$2393bobo6bo9bo3bo3b2o3bo2b2o9bo27b2o
5bo3bobobo5bo12bo8bobo$2394bo7bo2bo6bo10b3o11b2obo27bobo9bo6bob2obo6b
2obo$2402bo2bo7b3o5bo2bobo6b2o3b2o29bo8bob2obo3b3o2bo2bo2bo3b2o16b3o$
2403bobo7b2o7b3obo3b2o7bo8bobo27bobo3b2o4b3obobobo3b2o16bo2bo$2404bo8b
2o8b3o5b5o7bo4bo29b3o9bo2b5ob2obo4bo2b3o$2412bo2bo8bo6bo4bo3bo3bo3b3o
37bobo2b3o3bo2bobobo2b2obo18bo$2413bobo16bo3bo3bo3bo14b2o27b3o5bo4bo2b
o4b2obo7bo8b2ob2o$2414bo8b2o8b3o5bo10b2o4b3o28bo10bobob3o2bo2bo8bo2bo
7b2o$2423bobo16b2ob2o3b4o5bo37bo2bo6b2o3b3ob3o2bobo5b2obo8bo$2423b3o
16b5o4b3o8bo6bo28b3o2bo3b2o4b2ob4o12b2o6bobo$2433bo19bo5bo3bo5b2o36b2o
bobo4bo3bo9b3o5b2ob2o$2433b2o17b2ob2o2bo2bo6bo38b3obobo3bo3b2ob2o5b2o
5b2obo$2434b2o17bo2bo4b2o7b3o6bo29bo4bo2bo5bo3b3o12bo7b3o$2463bobo3b4o
5bobo37bo2bo8bo11bo7bobo$2442b3o13bo4bobo4b3o8bo36b3o2bo4b4o2b2o2bo3bo
7bobo$2444bo2bo11bo3b3o12bo44bobobo2b2ob3obo2bobo7b2o9bo$2446bo6bo10b
2o7bobo3bob2o5b3o37b3o2bo2b2o2bo8b3o8b3o$2453bo3bo6b2ob2o4b3o4bo2bo5b
2o38bo3b3ob2obo3bo3bobobo7bobo$2453bo3bo7bo3bo4bo14b2o8bo34b2obo3bo2b
2o2bob3o$2455b2o7b2o3bo12bo2bo3b3o7bo38bobo2bo2bo12bobo8b3o$2463b4o7b
2ob2o4b3o6b2o5bo39bo4b2o2bobo7bobobo7bo2bo$2464bob2o7b2o2bo12b2o6bo8bo
34bo3b3o2b3o2bo2b2o$2465bo7bo3b3o13b2o4bo2bo5bobo37b3o4bo3bo10bo10bo$
2473bo2b2o7bob2o5b2o4bo2bo50b2o12bobob2o6b3o$2474bobo6bob2o2bo13bo6bo
42bo4b3o2b2o3b2obo9b3o$2475bo7bo4b2o13b3o4b3o5b3o38bo4b2o3bo10bob2o7bo
$2484b3o8bobo12b3o5b3o41bobo4bobo5bo2bobo7bobo$2484b3o6b4ob2o6bo6bo3b
3o43bo4b3o3bo3b2o9bo3bo$2493bo4b2o6bo5bo2b3o11bo43b2o4bobo10bo$2494b3o
17bobobob4o4b3o41bobo2bobobo8b3o7b3o$2495bo7b2obobo8b3o7bo44bo6b2o5b3o
2bo8b3o$2503bo2b3obo6b6o3bo56b5obobo7bo2bo$2504b3o9bobob2o2bobo3b2obo
4b3o41bobo2bob2o10bo9bo$2513b2o3b3o2b3ob4obobo4bo42bo3bo3bo6bo3bo8b3o$
2514b3obob6o5b6ob2o9bo33bo9b2ob2ob2o8bo$2515bo6bo3bo7bob5obo6bo35bo5bo
2bo2bob2o8b3o2bo$2523bo2b4obo10bobo3bobo41bo2b2o8bo2b2obo2bo5b3o$2524b
3o3bo2b2o6bo2b3o46b3o5bobo3b3o9bo2bo$2530bo2b2obobo2bo5b2o2bobo4b3o34b
o6b2o3bo7bo3bo2b2o$2533b2ob2o6bo3b2obo2bo47b2o6b2o3bo2b2o2b3o6bo$2535b
o3b3o4bob2o5bo2bo2bo42b3o6bob2o2bobobo6b3o$2543b2obo2b3o3b2o4bo7bo42b
2ob2o3b5o4b2o2bo$2544b3o3b2o2b2obobob4o3b3o42bob2o4bob3o3bo4bo$2548bob
o3bo4b2o2b2o3b2obo42b2o7bobo3bobobo6b3o$2553b2obo3bo4bo4b2o51bobo4b3o
7bo2bo$2555bobo3bo3bobobobob2o3b3o42bobo8b2o3bo2b2o$2561bo2bobob2o4bo
2bo3bo42b2o8b2o3bob3o7bo$2558b2o4bob3o12bo51bo6bo9b3o$2564bo4b2o3bobo
4bobo5b2o42bobo9bo3bo2b2o$2569b3o4bob3o2b2o2b2obo43b2o8b2o3bo4bo$2568b
2o4b3o2bob2obo2b3obo51bo6b2o8b3o$2574bo5b5ob4ob3o5bo44b2o9bo3bo2bo$
2578bo7bo3bo2bo4bob2o42b2o7b3o3bo3bo$2579bo3b3o5bo2bo2b2o61b5o6bo$
2579bo7bob2o2b2o7bo51b2o6b2obo4b3o$2591bo3b2o2b2ob2o4b3o43b2o8b2o3b2o
2bo$2588bob4ob2o4bobo4bob2o59b3o$2589bob2o4b3o2b2o2bo2b2obo51b2o9bo4b
3o$2594b2o2b2o3bo6bobo5b2o44b2o8b2o4bo2bo$2598b3ob2ob2o4bobo3bo2b2o58b
ob2o$2602bo2bo2bo3bo2bo4bo53b2o8b2o5bo$2604b2o2b2o3bobo4bob2o50b2o8b2o
4b3o$2609bo2b2o7bo5b4o59bob2o$2611bo2b2obo4bo3bob3obo51b2o8bo$2614b2ob
ob4o2b4o3bo51b2o8b2o4b3o$2620b3o2bo2bobobo4bo3bo4bo43bo9bo2bo$2624b2ob
3o6bob3o2bo2bo47b2o8bo$2625bobo2b3o3bo6bo47bo2bo7bobo6bo$2631bo3bo3bob
o14bo31bo11bo3bo4b2ob2o$2635b4o2bo4b3ob3o2bobo41bob5o6b2o$2635bo4b3o3b
3o2b3o43bo3b2o9bobo6bo$2648bo2bo7bo37bobo13b2o5bobo$2645b3obobo5bo2bo
4b3o41b4o2b2o2b2ob2o$2645bo5b2o3b2o3b3o2b2o39b3obo7b2obo8bo$2656bo2bob
o2b2o2b2o37b2o11bo2bobo4bobo4b2o$2654b3obo2bob3o2b2o5b2o43b3o2bo3bo2bo
$2660bob3o3b2o2b2o2bobo38b2o6bo4bobo14bo$2664b2obobob2ob2o3bo6bo30b2o
11b2o8b3o5bo$2664b2o3bobo2bo4bo6bo44b2ob3o3b3o4bo$2671bo6bo3b2o2b3o38b
2o11bo16bo$2673b2o3bo3b2o3b2o6b2o30b2o12bo3bo5bo4bobo$2675b2o3bo3bobob
o8bo43bo3bo4b3o5bo$2680bo3b5o3b2o43b2o3bo2bo8bo$2682bob4o4bo2bob2o7bo
30b2o12b3o12b3o$2690b2o6bo4bob2o45b4o4b3o3b3o$2690b5o2bo5bob2o10bo29b
2o4b2o6bo2b3o$2692bobob2o5bobob2o8bo29b2o12bo3bo5bo3bob2o$2700b2o3bo2b
o5b2o46bob2o5bo3bo2bo$2699bo2b6o5b3o12bo28b2o4bo7bo$2706bo10b2o6b2obo
28b2o13b2ob2o5b2o3bo$2702bo7b2o2bo3bo53b3o6b8o$2709bo2bo2b3o5b2o13bo
28b2o12bo3bobo$2710bo2bo10b2ob2o7b3o28b2o13b2obo2bo4bo$2720b2o2b2ob2o
5bob2o45b2o6b2obob3o$2711bobo5bobo4bo7bo2bo9bobo27b2o12bo3bobobo$2720b
obo11b2ob2o7bo2bo22b2o3b2o13b2obo$2721b3o6bo4bobo6b3o47bo2bo4b3o2bo$
2722b2o5bob2o3bo7bo2bo9b2o24bo3b2o10b2ob2obob2o$2730bo14bobo2bo2bo3b3o
22bo4b2o14b3o2b2o6bo$2732bo6bo5b3o2bo3bobo26bo23b3o3bo3bo$2732b2o5bob
2o12bobo3bo6bo24b2o2b2o10bobob2o3bo$2740b2o8bo4b2o2bo2bo4b2o23bo4b2o
15b2o2bo$2742bo6bo6bo4b3o2bo2bo23b2o22b2o3bo2b3o$2742bo6bobobo3bo3b3ob
ob5o31b2o2b2o11bo2b5o$2743bo6b2o10b2obo3bo2bo4b3o23b2o2b2o11bo7bo$
2752bo6b2o3bo7bo3bo26bo9bo13bo8bo$2752bo6b3ob3obo4bo2bobo2bo34bob2o9bo
2b3ob3o$2753b2obo8b3o4bo3b2ob3o5b2o23bobo3bo3bo7b4o4bo$2762b4ob3ob2o3b
2o2b3o3bob2o23bo12bo6bob3o$2762b7o2b5obob2o4bob2obo31bobo2bobobob4o8b
3o$2766bo12b3o3bo3bobo5bo24bobo3bo3b3o2b2ob6o2bo$2771b2obo2b2o2b2o5bo
3bo3bob2o23bo13b3obo3b3o$2773bob3o7bob3o2bo3bo3bo31b3o2b3obo14b2o$
2782bob2obobob4o4bobo5b2o23b3o7b3o5bo2b2ob2o$2782bob2ob2o3bo3bo2b3o4bo
36bo2b6obo3bo$2782bo3bo12b3o4bo2b2o32bo7bob2o8bo2bo$2795b3o4bob2o5bo6b
o24bo9b2o8bo2b2o$2791b3ob3obo3bob2o3bo6b2o24bo5bo9b3obo4bo$2803b2o4b2o
5b2ob2o25b2o6b5obo2b2o9b2o$2800bob2ob2o3bo2bo3bo3bo7bo23b7o3bo6bo2b4o$
2801b2o3b2o2b2obob4obo6b2o24bob4o11bo2bo3b2o$2810b2o2bo3b2o7bo3bo38bo
3bob3o$2811b2o3b2o3bob2o2bob2o9bo22b7o4b3ob2o3b4o$2812bo3b2o3bob4ob3o
7bobo22bo10b3ob3o2bo3bo$2821bo15b2o9bo26b2ob2o4b2ob2o$2821bo4b2o4b2o3b
ob3o7bo22bo2bo2bo10bo4b2o$2822bo3bo4b3ob2o11b3o21bobo10bo4bob2ob2o$
2823bo7bo4bobo8bo2bo7bo25b2obobo5b3o$2832b6o8bo3b2o5bobo22b3o3bo9b2o$
2832b3o6b4o3bo10bo22b2o11b3obo3b4o$2841bo4b2o8bo3bo34bob3o2b2obo2bo$
2842b3ob2o8bobobo6b3o22b2o8b2o4bo$2843bo7b2obobo3bo6b3o23bo9b5obo4bo$
2851bo2b5o6b2o36bobo2b2o2b2ob3o$2852b3o13b3o7bo23b2o9bo2b3o$2861b2obob
ob2o7b3o24bo9b2o3bo3bobo$2861b2ob2obo8bo4bo31bo5bo3bo2bo$2863bo11b2ob
2obo31bobo2bo4bo2b2obo6bobo$2871b2obob3o8b3o23bo10b2o3bo3bobo$2872bobo
13bobobo32bob2o4b2o4bo$2873bo7bo3b2obo3bo30b6o5b3o2bo6b2o$2882bobo2bo
8bobo24bo11bob2o7b3o$2882b3o4bo2bo2bo2b2o2bo22b2o10b2o3b3o2b2o$2890bo
2bo4bob3o30b3o8bobo2bo6b2o$2892b3ob2o2b2o6bo4bo20bo2bo9b2o4bo3bo$2893b
o6b3o2b4o2bo3bo19b2o7bo8bo4bo$2900bo4b2obo2bo32bo2bo5bo2bo2bo6bo$2901b
ob2ob2o3bo5bo26bo2bo7bob2o5b4o$2903bo7b2o5b2o2b3o20b2o7b3o6b3o2bo$
2903bo6bo3b3o4b5o28bobo6bo2bo2bo$2910bo5b2o5b5o27b2o8bob2o6b3o$2912b2o
8bo2bo2bo26b2o7b2o7b2o3bo$2914bo4bob2ob3ob2ob5o37bo3b2o$2920bob2o4b4o
4bo28b2o8bob2o7bo$2923bobo3b3o5b2o27bo7b2o8b2ob2o$2924bo4b3o3b4o36bo5b
2ob2ob2o12bo$2933b2o5b7o28b3o7bo9bo5bo6b2obo$2933b3o2bo2bob3obo37bo2bo
3bo2bobo$2938bo8b2o36b2o4bo3bob2o6bo6bo$2940b2ob2o3bo6b2o29b2o4bo2bobo
7bo4b2o9bo$2944bo3b7o2bo38bobo3b2obobo9b5o$2945bo3bobobo3bo38b2o3bo3b
3o7b8o$2950b2obo4bo2b2o3bo29bo5b2o3bo7bob2o$2954bo4bo5b2o3bo35bo5b2obo
8bo5b3o$2955bo3bo2bob2obo38b3o3b2o2bo9b4o$2956bo3b2o2b3obo2bo40b2o2bob
o6bo7bo$2965b3o3b2o2b3o2b2o25b2o13bo2bo7bo7bo$2966b4ob2o2bo3bo36b2o4b
2obobobo5bo4b3o$2967b2obo4bo2b4o35bobo3bo7bo4b4obobo$2975bo3bobo4b2o2b
o26b2o5bo2bo4bo3b4obobo$2976bob2obo3b2o3b2o37bo3bobo3b4ob2o4b3o$2977bo
3bo3bobo2b2o4bo2bo26b2obo3bobo5bob2obo2bo3bo$2986b3o7bo3bo27bo5b3o7bob
ob2o3bo$2986b3o3bo2b2o4bo34b2obo3bobo4b3ob2o5bo$2990b2o3bo5bo5b2o28b3o
3b2o9bobo3b3o$2996b2o3b2o3b4o35bo10bo2b5o$2997bobob2o3bo2b2o35b2obo3bo
bob2o5bo$3000bo4bo2b4o5bo30b2o3b2ob3o5b2o4b3o$3006b4obo5b2o37b2o7b2o2b
o3bo$3009bo2bo3bo2b2o36bobo3bobo2bo5bo$3009bobo4b2o2bo6bo30b2o3b2o2bo
3bo3bo5bo$3016b2o3bo4bobo38bo7bo4b3o$3019b3o7bo2bo34bobo3bobo3b5o$
3020b2o4b2ob2o37b2o3b2o3b2o3b2o$3027b3o6b3o3bo34b2o5b2o4b3o$3029b2obo
4b2o3bo35b2o3b2o4bo3bo$3031bo5bo2b2o37bo3bo4bo5bo$3036bo2bob2o4bo40bo
5bo6bo$3038bob3o2bob2o2b3o34b3ob3o5b3o$3045bo3bo18bo30b2ob2o$3047bo3bo
5bo5bo34b2o3b2o6bo$3047bob2ob2ob3o4bo5bo30b2ob2o6bobo$3056bo2bob2o13b
2o31bo3bo$3057b3ob2obo9b5o30bo3bo$3058b2o3bo2b3o4b3ob2o7b2o21b2ob2o6b
3o$3066bo5b2o46b3o$3067b2obobo12bo2bo8bo21bo3bo$3069bo3b2o2b2o5b2ob2o
7bo22b2ob2o7bo$3076b2o2bob2o2bo9bo33b3o$3078bobobo2b2o8b3o9bo21bo3bo$
3079bo3b2ob2o9b2o2b2o3bobo20b2ob2o$3087bob2ob2obo10bo33b3o$3088b3ob2ob
o9b2o10bo21bo3bo$3094bo2b2o8bo3b2o3bobo12bo7b2ob2o$3097b4o2b3ob2o2b2o
3bo2bo12bo18bo$3101bob3ob6ob3o4bo5bo21b2ob2o$3108bobobo6bobo4bobo11b2o
7b2ob2o$3111b6obo2bo4bobo9bo3bo18bo$3107b2o2bo6b2obo2b2o4b2o5bo4bo17bo
bo$3122bo2bo3b3o5b2o20b2ob2o$3117bo3b2ob2obo8bobo10b4o$3117bo2bo8b2o4b
obo3bo6b3obo17b3o$3118bo10b3obob6obo4b2o21bobo$3127b2ob2o3bobobo6bo13b
2o8bobo$3127b2o11bobo4bo2b2o7b2ob2o17bo$3129bo10b2o2bob2o4bo2bob2o21b
3o$3137b2o5bo3bobobo5bo12bo8bobo$3138bobo9bo6bob2obo6b2obo$3139bo8bob
2obo3b3o2bo2bo2bo3b2o16b3o$3148bobo3b2o4b3obobobo3b2o16bo2bo$3148b3o9b
o2b5ob2obo4bo2b3o$3158bobo2b3o3bo2bobobo2b2obo18bo$3158b3o5bo4bo2bo4b
2obo7bo8b2ob2o$3159bo10bobob3o2bo2bo8bo2bo7b2o$3167bo2bo6b2o3b3ob3o2bo
bo5b2obo8bo$3168b3o2bo3b2o4b2ob4o12b2o6bobo$3177b2obobo4bo3bo9b3o5b2ob
2o$3178b3obobo3bo3b2ob2o5b2o5b2obo$3179bo4bo2bo5bo3b3o12bo7b3o$3188bo
2bo8bo11bo7bobo$3188b3o2bo4b4o2b2o2bo3bo7bobo$3193bobobo2b2ob3obo2bobo
7b2o9bo$3198b3o2bo2b2o2bo8b3o8b3o$3199bo3b3ob2obo3bo3bobobo7bobo$3204b
2obo3bo2b2o2bob3o$3208bobo2bo2bo12bobo8b3o$3209bo4b2o2bobo7bobobo7bo2b
o$3214bo3b3o2b3o2bo2b2o$3218b3o4bo3bo10bo10bo$3224b2o12bobob2o6b3o$
3223bo4b3o2b2o3b2obo9b3o$3229bo4b2o3bo10bob2o7bo$3232bobo4bobo5bo2bobo
7bobo$3233bo4b3o3bo3b2o9bo3bo$3243b2o4bobo10bo$3242bobo2bobobo8b3o7b3o
$3242bo6b2o5b3o2bo8b3o$3253b5obobo7bo2bo$3252bobo2bob2o10bo9bo$3252bo
3bo3bo6bo3bo8b3o$3253bo9b2ob2ob2o8bo$3255bo5bo2bo2bob2o8b3o2bo$3262bo
2b2o8bo2b2obo2bo5b3o$3263b3o5bobo3b3o9bo2bo$3265bo6b2o3bo7bo3bo2b2o$
3272b2o6b2o3bo2b2o2b3o6bo$3274b3o6bob2o2bobobo6b3o$3282b2ob2o3b5o4b2o
2bo$3283bob2o4bob3o3bo4bo$3284b2o7bobo3bobobo6b3o$3293bobo4b3o7bo2bo$
3293bobo8b2o3bo2b2o$3294b2o8b2o3bob3o7bo$3303bo6bo9b3o$3303bobo9bo3bo
2b2o$3304b2o8b2o3bo4bo$3313bo6b2o8b3o$3314b2o9bo3bo2bo$3314b2o7b3o3bo
3bo$3330b5o6bo$3324b2o6b2obo4b3o$3324b2o8b2o3b2o2bo$3341b3o$3334b2o9bo
4b3o$3334b2o8b2o4bo2bo$3350bob2o$3344b2o8b2o$3344b2o8b2o2$3354b2o$
3354b2o!


Could such pattern be added into Lifewiki along with those block-laying waves and clean waves ?
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Measure-preserving

Postby shouldsee » November 4th, 2016, 11:29 am

Semi-outer-totalistic CA is not measure-preserving transformation. (Due to the existence of Garden of Eden) Is there a simple way to make it measure-preserving?
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Re: Measure-preserving

Postby BlinkerSpawn » November 4th, 2016, 4:00 pm

shouldsee wrote:Semi-outer-totalistic CA is not measure-preserving transformation. (Due to the existence of Garden of Eden) Is there a simple way to make it measure-preserving?

A reversible rule would match your specifications (correct?) but construction of a semi-totalistic reversible rule is likely impossible, given that I'm correctly understanding what that is.
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Re: Measure-preserving

Postby shouldsee » November 4th, 2016, 6:28 pm

BlinkerSpawn wrote:
shouldsee wrote:Semi-outer-totalistic CA is not measure-preserving transformation. (Due to the existence of Garden of Eden) Is there a simple way to make it measure-preserving?

A reversible rule would match your specifications (correct?) but construction of a semi-totalistic reversible rule is likely impossible, given that I'm correctly understanding what that is.


Reversible would eliminate garden of Eden states, but do not necessarily guarantee a strong-connected state-space (since you can have many cycles isolated from each other). But in terms of measure-preserving, I think such system should be adequate. If we assign equal probability to every state within the same cycle, then any set would have a preserved measure under the transformation, (which ,however, make a dull topology, restricted to loops only.)
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Re: Thread for basic questions

Postby rahul25 » November 6th, 2016, 6:28 am

Can anyone tell me some good online archives or encyclopaedia other than wiki
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Re: Thread for basic questions

Postby Rich Holmes » November 6th, 2016, 8:14 am

rahul25 wrote:Can anyone tell me some good online archives or encyclopaedia other than wiki

See this thread: viewtopic.php?f=7&t=20

But forums, even with sticky posts, are lousy reference resources. There's a "Books and articles" category on the Wiki; there should be a "Websites" category too. There's a Wiki page, http://www.conwaylife.com/w/index.php?t ... Life_links but it isn't in any category and nothing links to it, making it very hard to find.
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Re: Thread for basic questions

Postby muzik » November 11th, 2016, 12:42 pm

Does this (and the other such patterns from the thread) actually count as SS infinite growth? I kind of doubted it originally when I pointed it out, since it's mainly composed of moving objects (spaceships) rather than still objects such as the bricklayer (blocks).

And if it is indeed a record-holder for this category of patterns, does it deserve a wiki article?
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Re: Thread for basic questions

Postby blah » November 11th, 2016, 5:39 pm

musik wrote:Does this (and the other such patterns from the thread) actually count as SS infinite growth?

As I asked in that thread, doesn't it make sense to classify it as a really weird wickstretcher? I guess by that definition any gun might be a wickstretcher, but it seems especially applicable to this.
Last edited by blah on November 18th, 2016, 6:05 am, edited 1 time in total.
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Re: Thread for basic questions

Postby Scorbie » November 11th, 2016, 10:37 pm

blah wrote:As I asked in that thread, doesn't it make sense to classify it as a really weird wickstretcher? I guess by that definition any gun might be a wickstretcher, but it seems especially applicable to this.
I do think it *looks* like a wickstretcher... BTW, I was a little amused to see that back-and-forth glider isn't part of the wick, but rather acts as a c/61 stabilizing end of the "glider stream" wick.
On the other hand, I am not sure if Impush(it's in jslife; LWSS streams push a LoM in there) or elbowladder counts as a wickstretcher. I guess regular stablilized patterns are technically a wick but not called as a wick.

There are some terms for similar patterns. Elbow ladder (using slide guns), elbow, etc.
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Re: Thread for basic questions

Postby muzik » November 12th, 2016, 2:21 pm

I don't think bricklayer counts as a wickstretcher though.
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Re: Thread for basic questions

Postby Gamedziner » November 14th, 2016, 7:31 pm

Are there any known guns that produce rakes?
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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!
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Re: Thread for basic questions

Postby muzik » November 14th, 2016, 7:47 pm

Many of them, classed as SMM breeders.
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