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Spaceship Discussion Thread

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.

Re: Spaceship Discussion Thread

Postby moebius » June 11th, 2016, 5:11 pm

Sokwe,

It is really cool that you found a way to use my ship to support Stephen Silver's 16 year old wave.

I did complete a c/7 width 19 gutter search with no ships found. I don't have the longest partial handy, but I believe it was about 100 rows. This means that the minimum width for c/7 gutter ships is 21, and a small example would be two reflected loafers.

In regards to c/4 ships I have run every search with knightt that completes in less than a few days. These are vast collections of ships, most of which a very large.


Muzik,

There are almost certainly 3c/7 ships that are findable in a reasonable length of time and half the size of the ship I posted. This will involve in running much longer odd symmetric width 25 searches which run 10 times slower than the width 23 search that ultimately found this ship.

I think it is entirely appropriate to split the spaceship section between elementary and engineered spaceships. I would characterize the elementary class as the strictly search oriented ships. This ship is definitely in the elementary class even though it is quite large. The key difference in my mind is that all engineered spaceships have the equivalent of an instruction tape that is read in order to continue the ship.


drc,

I have thought about how to construct a search program oriented towards finding a 3c/7 rake. It will be a while before I write up said search program. In the meantime getting lucky is the course to find one.


simsim314,

The total amount of cpu time invested in the path that actually found the ship was one or two months. I had other related and investigatory searches running in parallel.


As for a name, I was looking at the phase of the ship that I posted and it made me think of the "Spaghetti Monster". The very front looked like two eyes, and it is definitely trailed by a long jumble of spaghetti.


Have a happy day,

-Tim Coe
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Re: Spaceship Discussion Thread

Postby Sokwe » June 11th, 2016, 5:43 pm

moebius wrote:I did complete a c/7 width 19 gutter search with no ships found. I don't have the longest partial handy, but I believe it was about 100 rows.

I imagine it looked something like this:
x = 19, y = 113, rule = B3/S23
6bo5bo$5bobo3bobo$5bobo3bobo$6bo5bo2$3bo3b2ob2o3bo$3bo3b2ob2o3bo$3bo
11bo3$2b3ob2o3b2ob3o$bo6bobo6bo$6bobobobo$2bo5bobo5bo$5b2obobob2o$6bob
obobo$5b2obobob2o$5b3o3b3o$5bo7bo$3bobo7bobo$2bo2bo7bo2bo$2b2o4bobo4b
2o$2b3o2b2ob2o2b3o$3bobo7bobo$2b2ob2o5b2ob2o$7bo3bo$4b3o5b3o$3bo2bobob
obo2bo$2bobo3bobo3bobo$2bo3bobobobo3bo$bo2b2obo3bob2o2bo$bo2bo9bo2bo$
2bo13bo2$3bo11bo$b2obo9bob2o$b2o4b2ob2o4b2o$b4o3bobo3b4o$3b2o3bobo3b2o
$6b3ob3o$7b2ob2o$7b2ob2o$6bo5bo$6b3ob3o$7b2ob2o$6bo5bo$2b3obobobobob3o
$6bo5bo$6b2o3b2o2$3b2o9b2o$4bo9bo$3b2ob2o3b2ob2o$5bobo3bobo$5bob2ob2ob
o$6bobobobo$b2o5bobo5b2o$o2bo11bo2bo$b2o3bobobobo3b2o$b2o2b3o3b3o2b2o$
2bo4bo3bo4bo$b6o5b6o$2bo13bo$4b3o5b3o$4b3o5b3o$4b2ob2ob2ob2o$5bobo3bob
o$4b2obo3bob2o$5bobo3bobo$6bo5bo$3bobobo3bobobo$b2ob2o7b2ob2o$4b3o5b3o
2$6bobobobo$4bo3bobo3bo$4b3o5b3o$4b3o5b3o$2b2obo7bob2o$bobob2o5b2obobo
$o4bo7bo4bo$o2bo11bo2bo2$2b2o11b2o$4b3o5b3o$5b2o5b2o2$2b2o11b2o$2b3o9b
3o$4bo9bo$b2ob2o7b2ob2o$bob3o2bobo2b3obo$bob3o2bobo2b3obo$2b2o4bobo4b
2o$2b3o3bobo3b3o$bo3bo2bobo2bo3bo$bo15bo2$b3o3bo3bo3b3o$bo2bob2o3b2obo
2bo$2b2o2bo5bo2b2o$2b5o5b5o$3bo2bo5bo2bo$3b2ob2o3b2ob2o$3bo2bo5bo2bo$
2bo2bo7bo2bo$b3ob3o3b3ob3o$3bo3b2ob2o3bo$o6b2ob2o6bo$bobo11bobo$bobo2b
o5bo2bobo$bo5b2ob2o5bo$2bo13bo!

I found this partial after trying to extend the longest width-17 partial at width 19.
-Matthias Merzenich
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Re: Spaceship Discussion Thread

Postby muzik » June 12th, 2016, 6:19 am

moebius wrote:I think it is entirely appropriate to split the spaceship section between elementary and engineered spaceships. I would characterize the elementary class as the strictly search oriented ships. This ship is definitely in the elementary class even though it is quite large. The key difference in my mind is that all engineered spaceships have the equivalent of an instruction tape that is read in order to continue the ship.

So corderships would be considered as elementary spaceships? That's pretty reassuring.



Anyway, dug up this old quote:

biggiemac wrote:It just makes me sad to think of a loafer or a tiny c/18 ship or something crashing into a blinker in the middle of a forgotten apgnano search..


Anyone up for searching for this hypothetical tiny c/18 ship (with a spaceship search program that does not let spaceships crash into blinkers)?
Image This jump is annoying. Let's fix it.

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Re: Spaceship Discussion Thread

Postby thunk » June 14th, 2016, 1:45 am

Congratulations, Tim Coe.

This spaceship is pretty neat!
"What's purple and commutes?
The Evanston Express."
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Re: Spaceship Discussion Thread

Postby Kazyan » June 14th, 2016, 2:39 am

Late, but, congratulations! Many heads have been beaten against the wall to find a 3c/7 ship--it's only fitting that newer algorithms are the ones to finally find it. All possible speeds of spaceships with period ≤7 have now been found, with the exception of (2,1)/X knightships.
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Re: Spaceship Discussion Thread

Postby muzik » June 14th, 2016, 3:40 am

Well, looks like that 3c/7 orthogonal and 2c/9 diagonal thread has ondirectly accomplished something.

Of course, we should probably start of using more on the 2c/9 diagonal.

Or the c/18 orthogonal. We may never know.


The FOMO is real here. But in all seriousness, we've advanced a lot in 50 years. Here's a (relatively large) stamp collection of the smallest of each spaceship speed, excluding engineered spaceships:

x = 395, y = 204, rule = B3/S23
256bo$256bo$248bo5bo$246bobo6bo$249bo2bo3bo$247b2obobo2bo$247b2obo$
235b2o$235b2o7$227b2o$227b2o$242bo3b2o$241b2o4b3o$240b2o8bob3o$241b5o
2bobo$243b3o3bo3$262bo$254bo7bo$254b3o5bo$256bobo3b2o$254bo2bo$254b2o
2bo10$275bo$275b4o54bo$332bobo$332bo2b2o2$273bobo61bo$274bo60b2o2b2o$
275b2o21bo2b2o36b2o$273bo2bo20bobo40bo$273b2ob2o5bo16bo39bobo$283bo57b
2o$283bo13b2o22b3o17bo2bo$323bo16bo4bo$282b2o12b2o20b2o2bo17bo5bo$281b
o2bo13bo19b2o25bo3bo13b2o$282bobo11b2ob2o21b2o19b2o3bobo12b2o$284b2o
10b2o23b2o24b2ob2o10bo2bo$285bo13bo20bo2bo20bobo4b2o9bo2bob2o$281b2o
61bo7b2o8bo$281b2o35bo2bo22bo9bo7bo2bo3b2o$281b2o34bo3bo30b2o9bo5b2o$
282bob2o30bob3o31bo10b5obo$282b3o30bo35bo3bo12bo$283bo31bo13bobo2b2o
18bobo$316bo13b2obobo13b3obo3bo$311b2o13b2o2bo4bo17bo15b3o$310bo2b2o2b
2o6bo3bo28b2o11bo$294b2o19bo2bo6bo6b2o23b2o13b2o$b3o8bo7bo16bo19b2obo
9bo12bo5bo30bo7bo17b3o10b3o9bo13b2o107b2o23b2o4bobo4b2o21b2o2b4o10bo4b
2o$o2bo7bobo5bobo14b3o15b2obob2ob3o5bo12bo5bo8bo15b2obobob2o3b2obobob
2o6b3obo7b2o7bob3o3bobo11b4o124bo3bo3bo5bo34b2o10bo3b3o$3bo6b2ob2o3b2o
b2o12b2ob2o11b4o2b2o6bo3bobo10bobo3bobo5bo3bo10b3obob3o9b3obob3o7bo3bo
2bo2bo2bo3bo7bo2bo142b2o4bo2bo50bo4bo$3bo7bobo5bobo28bo4bo3bo3b2o5bo
12bo12bo3b2o9bo3bobo5bobo5bobo3bo7bo5bo4bo5bo8b2o10b6o122bobo5bo3b2o
38bo13bo3bo$obo6bob2o3bo3b2obo10bobobobo2bo7b2o17bo12bo9bob2o5b2o11b2o
6bobo6b2o17b2o2b2o27b4o122b2o8bo41bo2bo11bo$9b7ob7o9b2o3bo3b3o26bo3b4o
3bo6b6o2bo6bo7b2o9bobo9b2o11bo3bo2bo3bo10bo5bo138bo4bo41bo2bo11bobob2o
$13b7o13b2o3bo6bo29b4o11b2o6bo3b3o7b2ob2o15b2ob2o11bobo6bobo11bo3bobo
5b2o2b2o128bo3bo44bo10bo5b2o8b2o$12bob2ob2obo22bobo25b4o4b4o15bo3bob2o
10bo15bo16b10o11b2o3bo2bo2b2obo2bob2o95b2o26b2o5bo45bo9b2o4b2o7bobo$9b
2obo7bob2o17bobo57bo49bo4bo13bo3b2o2bo5bo2bo98b2o26bo5bo44b2o12b4o11bo
$8b3ob2o5b2ob3o17bo2bo27bo6bo25bo42bo8bo$7bo17bo19bo28b2o2b2o25bo42bo
10bo$10bob2o5b2obo82bo43bo8bo26b2o$185b2o$14bo3bo$9bob3o5b3obo$10bob3o
3b3obo$14bo3bo$13b2o3b2o$12b2o5b2o$11b3o5b3o$8b4o9b4o$7bo17bo$6b2o3b2o
7b2o3b2o$7bobobobo5bobobobo$7b3o2b3o3b3o2b3o$12bo7bo$7bo17bo2$7bobobo
9bobobo$9b3o9b3o$6bob3o2bo5bo2b3obo$7b2ob3o7b3ob2o$11b2o7b2o$11bob2o3b
2obo$11bo3bobo3bo$3b3o5bo3bobo3bo5b3o$3bob2o6bo5bo6b2obo$3bo2bo3b2ob2o
3b2ob2o3bo2bo$6bo2b2o3bo3bo3b2o2bo$10bo2bo5bo2bo$5bobobobo9bobobobo$3b
2obo19bob2o$9bo13bo$6b2o17b2o2$5bo21bo$4b2o21b2o$3b2o23b2o2$3b2o23b2o$
4bo23bo$5bo4bobo7bobo4bo$4b3o4bob2o3b2obo4b3o$4b3o2bobob2o3b2obobo2b3o
$9bo2b2o5b2o2bo$8b4o9b4o2$6b2o17b2o$6b2o2b2o9b2o2b2o$7bo2bobo7bobo2bo$
4bo2bobo2bo3bo3bo2bobo2bo$4bo4bo3bob3obo3bo4bo$5bobobo4bobobo4bobobo$
7bobo4bo3bo4bobo$5b4o2bobo5bobo2b4o$5b3ob2ob2ob3ob2ob2ob3o$14b5o$11bob
o5bobo$11bob2o3b2obo$16bo$16bo$10b2o9b2o$10b2obo5bob2o$10bob2obobob2ob
o$12b2obobob2o$9bobobobobobobobo$9b2o2bo5bo2b2o$10bob2o5b2obo$12b2o5b
2o$11bo9bo$11b3o5b3o4$12bo7bo$11b2obo3bob2o$11bo2bo3bo2bo$11b3o5b3o$
13b3ob3o$14b2ob2o$15bobo$14b2ob2o$12b2o2bo2b2o$16bo$11b2o7b2o$10b3obo
3bob3o$9bo2bo7bo2bo$10bo11bo$11bo9bo$8b2ob2o7b2ob2o$11bo9bo$7bo3b2o7b
2o3bo$8b6o5b6o$12bo7bo$11b2obo3bob2o$12bob2ob2obo$11bo9bo$12bobo3bobo$
10bobobo3bobobo$12bob5obo$11b2ob2ob2ob2o$11b4o3b4o$10bo2bo5bo2bo$9bo2b
o7bo2bo$10bob2o5b2obo$8bob2o9b2obo$8b2o13b2o$8b2o13b2o$9b2o2b3ob3o2b2o
$9b2o2b2o3b2o2b2o$12b2o5b2o$9bo2bo7bo2bo$9bo2bo7bo2bo$8b2obo9bob2o$8bo
2bo3b3o3bo2bo$8bo2bo3b3o3bo2bo$11bo2bo3bo2bo$7b2obo4b3o4bob2o$6b6o3bob
o3b6o$6bo19bo$10bo2b3ob3o2bo$10bo3bo3bo3bo$10bo11bo$15b3o$16bo$13b3ob
3o$14b2ob2o!




So, back on topic (how many times have I said that sentence? Yet another mystery of life.), has anyone seriously looked into a 3c/14 orthogonal using the pre-pulsar partial? I would put my money on there being a 3c/14 orthogonal with fewer than 250 live cells (problem is, being a lazy 14 year old I don't really have entirely that much money)

x = 15, y = 7, rule = B3/S23
3b3o3b3o$2bo3bobo3bo$2bo3bobo3bo$2bo3bobo3bo$o2b3o3b3o2bo$o13bo$o13bo!
Image This jump is annoying. Let's fix it.

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Re: Spaceship Discussion Thread

Postby Sokwe » June 14th, 2016, 11:48 pm

I don't have any new discoveries to report, but I just finished compiling the credits for the small c/4 orthogonal ship collection, so I thought I should post it.
#C All known c/4 orthogonal ships up to 70 bits.
#C
#C Discovery credits:
#C BU = "Bullet51"
#C DH = Dean Hickerson
#C HH = Hartmut Holzwart
#C JB = Josh Ball
#C JS = Jason Summers
#C MM = Matthias Merzenich
#C RM = "rmmh"
#C SS = Stephen Silver
#C TC = Tim Coe
#C
#C 37 JB 15 Apr 2012
#C 41 JB 19 Apr 2013
#C 43 MM 18 Apr 2012
#C 45 MM 20 Apr 2012
#C    MM 20 Apr 2012
#C 46 TC  3 May 1996
#C    MM 20 Apr 2012
#C 47 SS  9 Oct 2000
#C    SS  9 Oct 2000
#C 48 TC    Dec 2015
#C    TC    Dec 2015
#C 50 MM 20 Apr 2012
#C    MM 20 Apr 2012
#C 51 TC  3 May 1996
#C    SS 11 Nov 2000
#C    SS 11 Nov 2000
#C 53 TC  6 Aug 1995
#C    SS 10 Nov 2000
#C 54 TC Between Dec 2015 and 21 Apr 2016
#C 55 HH  2 Jan 2004
#C    MM 20 Apr 2012
#C    TC    Dec 2015
#C    TC Between Dec 2015 and 21 Apr 2016 (tag)
#C 56 MM 18 Apr 2012
#C    TC    Dec 2015
#C 57 TC Between Dec 2015 and 21 Apr 2016
#C    TC Between Dec 2015 and 21 Apr 2016
#C    MM 20 Apr 2012
#C    MM 20 Apr 2012
#C    JB 15 Apr 2012 (tag by HH 18 Aug 1992)
#C    JB 15 Apr 2012 (tag by HH 18 Aug 1992)
#C    JB 15 Apr 2012 (tag by HH 18 Aug 1992)
#C    JB 15 Apr 2012 (tag by HH 18 Aug 1992)
#C    JB 15 Apr 2012 (tag by JS  1 Oct 2000)
#C 58 MM 20 Apr 2012
#C    TC Between Dec 2015 and 21 Apr 2016 (tag)
#C    JB 19 Apr 2013 (tag by HH 18 Aug 1992)
#C    JB 19 Apr 2013 (tag by HH 18 Aug 1992)
#C    JB 19 Apr 2013 (tag by HH 18 Aug 1992)
#C    JB 19 Apr 2013 (tag by HH 18 Aug 1992)
#C    JB 19 Apr 2013 (tag by HH 18 Aug 1992)
#C    JB 19 Apr 2013 (tag by HH 18 Aug 1992)
#C 59 MM 20 Apr 2012
#C 60 TC Between Dec 2015 and 19 Mar 2016
#C 61 JS 22 Sep 2000
#C    MM 20 Apr 2012
#C    TC Between Dec 2015 and 21 Apr 2016 (tag)
#C 62 MM  2 Aug 2015
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    TC Between Dec 2015 and 21 Apr 2016 (tag)
#C 63 MM 20 Apr 2012
#C    MM 20 Apr 2012 (tag by HH 18 Aug 1992)
#C    MM 20 Apr 2012 (tag by HH 18 Aug 1992)
#C    TC Between Dec 2015 and 21 Apr 2016
#C 64 TC Between Dec 2015 and 19 Mar 2016
#C    TC Between Dec 2015 and 19 Mar 2016
#C    TC Between Dec 2015 and 19 Mar 2016
#C    MM 18 Apr 2012
#C    MM  4 Aug 2015 (tag)
#C    MM  4 Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    TC Between Dec 2015 and 21 Apr 2016 (tag)
#C 65 TC Between Dec 2015 and 19 Mar 2016
#C    BU 19 Mar 2016 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    TC    Dec 2015 (tag by HH 18 Aug 1992)
#C    TC Between Dec 2015 and 21 Apr 2016 (tag)
#C 66 HH 11 Aug 1992
#C    TC Between Dec 2015 and 19 Mar 2016
#C    TC Between Dec 2015 and 19 Mar 2016
#C    TC Between Dec 2015 and 19 Mar 2016
#C    JB 15 Apr 2013 (tag by DH Dec 1989)
#C    JB 15 Apr 2013 (tag by DH Dec 1989)
#C    TC Between Dec 2015 and 21 Apr 2016 (tag)
#C    TC Between Dec 2015 and 21 Apr 2016 (tag)
#C    TC Between Dec 2015 and 21 Apr 2016 (tag)
#C    TC Between Dec 2015 and 21 Apr 2016 (tag)
#C 67 HH 17 May 1994
#C    HH  2 Mar 2006 (as part of a grayship)
#C    TC Between Dec 2015 and 19 Mar 2016
#C    SS  7 Oct 2000
#C    SS  7 Oct 2000
#C    TC Between Dec 2015 and 21 Apr 2016 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM 20 Apr 2012 (tag by HH 18 Aug 1992)
#C    MM 20 Apr 2012 (tag by HH 18 Aug 1992)
#C    HH  2 Jan 2004
#C    SS  9 Oct 2000 (tag by JS  1 Oct 2000)
#C    SS  9 Oct 2000 (tag by JS  1 Oct 2000)
#C    TC Between Dec 2015 and 21 Apr 2016 (tag)
#C    TC Between Dec 2015 and 21 Apr 2016 (tag)
#C    TC Between Dec 2015 and 21 Apr 2016 (tag)
#C 68 RM  9 Mar 2016
#C    HH center: 5 Feb 1993; wings: no later than 2 Mar 2006
#C    MM  2 Aug 2015
#C    MM  2 Aug 2015
#C    HH (tag found as part of a grayship no later than 2 Mar 2006)
#C    MM    Aug 2015
#C    MM    Aug 2015
#C    MM    Aug 2015
#C    TC    Dec 2015 (tag by JS  1 Oct 2000)
#C    TC Between Dec 2015 and 19 Mar 2016
#C    TC Between Dec 2015 and 21 Apr 2016
#C 69 JS 22 Sep 2000
#C    JS 22 Sep 2000
#C    JS 22 Sep 2000
#C    TC Between Dec 2015 and 19 Mar 2016
#C    TC Between Dec 2015 and 21 Apr 2016
#C    SS  7 Oct 2000
#C    SS  7 Oct 2000
#C    TC  3 May 1996 (tag by HH 18 Aug 1992)
#C    TC  3 May 1996 (tag by HH 18 Aug 1992)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM    Aug 2015 (tag)
#C    MM 20 Apr 2012 (tag by DH    Dec 1989)
#C    TC    Dec 2015 (tag by JS  1 Oct 2000)
#C    TC Between Dec 2015 and 21 Apr 2016 (tag)
#C    TC Between Dec 2015 and 21 Apr 2016 (tag)
#C    TC Between Dec 2015 and 21 Apr 2016 (tag)
#C 70 MM 18 Apr 2012
#C    TC    Dec 2015
#C    SS 11 Nov 2000 (tag by SS 9 Oct 2000 based on a ship by HH 5 Feb 1993)
#C    SS 11 Nov 2000 (tag by SS 9 Oct 2000 based on a ship by HH 5 Feb 1993)
#C    JB 15 Apr 2012 (tags by HH 18 Aug 1992 and 2 Mar 2006)
#C    JB 15 Apr 2012 (tags by HH 18 Aug 1992 and 2 Mar 2006)
#C    BU 19 Mar 2016 (tag)
x = 1095, y = 585, rule = B3/S23
163bo$161b2o$163bo$165bobo$164bo2bo83bo$30bo133bo2bo81b2o$28bo2b2o131b
obo25bobo56bo$26b3o137bo25bo3bo48bo3b2o$25bobo136b2o26bo4b2o12b2o30bo
2b2obobo$25bob2o135b2o28bo3bo2b2o7b3o5bobo4b2o14b3o6b2o$obobo3bobobo
11bo4bo110bobobo3bobobo15bob2o23b2o3bo10bo6bo7bo2bo10bobo7b2o$23b2o
142b2o43bo5bo2b3o5bo10bob2o9bo$4bo7bo127bo7bo42b4o18b2o5bo5bo2bo9bo4bo
8bo$22bo4b2o138b2obo18b2obo2bo16b3o10b2o11b2o11bo$obobo7bo13bo113bobob
o3bobobo14b2obo18b4o2bo13bo2b2o4b2o29b2o$23b3o143bo8bo2b2o10bo15b2o4b
2o20bo4b2o7bo$4bo7bo12bo118bo7bo13bo2b2o7b2o2bo26bo3b2obo2bo21bo$26bo
140b3o8bo3b3o2b3o23b3o22b3o$obobo7bo12b2o113bobobo3bobobo29b2obo2b2o
23b2ob2obobo18bo$26bo139bo16bo33bo3bo19bo$26b2o138b2o16b2o31bo22b2o$
23bo2b2o137bo2b2o15bo3bo51bo$21b2o3bo140bobo16bo2bo51b2o$23bo139b2o3bo
18bobo48bo2b2o$164b3o69b2o3bo$165b2o71bo$168bo$166bobo$167bo6$35bo$26b
3o4bobo$o3bo4bo11bo2b2o4b2obobo126bobo$21b2o7bo131bo3bo19bo$o3bo4bo11b
o3bo6b3o127bo2b2o17bo2b2o$26b2o4bo2bo128bobo15b3o$obobo4bo21b2o2bo130b
o14bobo$28b3o4bo129b2obo12bob2o$4bo4bo25bo130bobo11bo4bo$34b2o128bo14b
2o$4bo4bo22bo2b2o103bobobo3bobobo10b2o$30b2o146bo4b2o$32bo107bo7bo13b
2o2b2o14bo$162b3ob2o11b3o$140bobobo3bobobo12bob2o12bo$164b2o16bo$144bo
3bo3bo11bo16b2ob2o$164bob2o12b2o2bo$140bobobo3bobobo11bo3bo11b2o3bo$
164bo14bobo3b2o$165bo13b2o4b2o$169bobo8b3obo$166b2o3bo9b2ob3o$30bo134b
obo3bo7bo$28bo2b2o132b2obo10bo$26b3o132bobo15bobo$25bobo133bo$25bob2o
132bobo$o3bo3bobobo11bo4bo$23b2o$o3bo7bo$22bo4b2o$obobo3bobobo13bo$23b
3o$4bo7bo12bo$26bo4bo$4bo3bobobo12b2ob2obo$24bo3bo$24b4o219bo$21bo3b2o
213bobob2obo25bobobo18bo24bo24bo24bo24bo$21b2o215bo3bobo26bo3bob2obo
13bo2b2o20bo2b2o20bo2b2o20bo2b2o20bo2b2o$21bo192bo22bo32bo9bo11b3o22b
3o22b3o22b3o22b3o$168b2o8bobobo14b2o8bobob2obo21bo3b2o27bo3b2o16bobo
22bobo22bobo22bobo22bobo$166b2o12bob2obo9b2o12bobo24bob2o29bob2o18bob
2o21bob2o21bob2o21bob2o21bob2o$140bobobo3bobobo10bobob2o6bo9bo6bobob2o
6bo32bo32bo19bo4bo19bo4bo19bo4bo19bo4bo19bo4bo$163bo14b2o12bo14b2o26bo
32bo20b2o23b2o23b2o23b2o23b2o$140bo11bo10bo4bo4b2ob2o14bo4bo4b2ob2o27b
obo30bobo$165b2obo3b3o19b2obo3b3o27bo2bobo27bo2bobo18bo4b2o18bo4b2o18b
o4b2o18bo4b2o18bo4b2o$140bobobo7bo17b3o7bo18b3o7bo20bobo30bobo26bo24bo
24bo24bo24bo$175b2o3bo23b2o3bo19bo2bo29bo2bo23b3o22b3o22b3o22b3o22b3o$
144bo7bo23bo2bo25bo2bo21bo32bo27bo24bo24bo24bo24bo$174b3o2b2o22b3o2b2o
11bo2b2o5b2o21bo2b2o5b2o26bo12bo11bo24bo24bo24bo$140bobobo7bo20bo2bo2b
2o21bo2bo2b2o11b2o2bo5bo22b2o2bo5bo26b2o7bo2b3o10b2o7bo2b2o11b2o23b2o
23b2o$74bo99bobo2bo23bobo2bo12bo3b3o2b2o22bo3b3o2b2o27bo7bo2b2o12bo7bo
2b3o11bo24bo24bo$37bobobo25bobob2obo99bobo3bo22bobo3bo15b2obo3bo25b2ob
o3bo26b2ob2o3bo16b2ob2o3bo4bo11b2o23b2o23b2o$35bo3bob2obo20bo3bobo108b
o28bo16bo4bo27bo4bo24bo2b2obob3o14bo2b2obob3o14bo2b2o3bo16bo2b2o3bo16b
o2b2o$o3bo3bobobo21bo9bo19bo162b2o31b2o25b2o3bo3b4o12b2o3bo3b4o12b2o3b
o3b4o12b2o3bo3b4o12b2o3bo3bobo$33bo3b2o24bo3b2o159bo3bo28bo3bo23bo7bo
16bo7bo16bo5bob3o14bo5bob3o14bo8bo3bo$o3bo3bo24bob2o26bob2o162bo2bo29b
o2bo79b2o3bo4bo14b2o3bo19b2ob3obo$22b2ob2o7bo17b2ob2o7bo165bobo30bobo
84bo2b3o19bo2b2o15bo6bo$obobo3bobobo8b3o8bo18b3o8bo287bo2b2o20bo2b3o
12bo6b3o$22b2obo2bo2bobo18b2obo2bo2bobo316bo12b2o6bo$4bo7bo18bobo27bob
o329bo$26b2obo26b2obo$4bo3bobobo15b2o28b2o$28b3o27b3o$30bo2b2o25bo2b2o
$32bo29bo2$205bo$204b2o$174bo$172bo2b2o23b2obo$170b3o26b3obobo$198b2o
2b2obo$171b2o26bo4bo$166b4o2bo23bobo27bo35bo35bo35bo35bo34bo13bo$163bo
b3o3b3o18bo3bo20b3o4bobo26b3o4bobo26b3o4bobo26b3o4bobo26b3o4bobo5b2obo
bo14b3o4bobo5b2obob2obo$140bobobo3bobobo9b2o7b4o15bo2b2o17bo2b2o4b2obo
bo21bo2b2o4b2obobo21bo2b2o4b2obobo21bo2b2o4b2obobo14bo6bo2b2o4b2obobo
3bo4bob2obo6bo2b2o4b2obobo3bo4bobo$174bo13b3o21b2o7bo26b2o7bo26b2o7bo
11b2obobo9b2o7bo11b2obob2obo6b2o7bo7bo10bo6b2o7bo7bo$140bo7bo3bo9bob2o
bo19bobo22bo3bo6b3o22bo3bo6b3o22bo3bo6b3o5bo4bob2obo6bo3bo6b3o5bo4bobo
9bo3bo6b3o3bo3b2o12bo3bo6b3o3bo3b2o$27b3o23bo108b2o3bo19bob2o26b2o4bo
2bo26b2o4bo2bo26b2o4bo2bo3bo10bo11b2o4bo2bo3bo22b2o4bo2bo3b3o19b2o4bo
2bo3b3o$25b2o3bo21bobo85bobobo3bobobo14bo18bo4bo30b2o2bo31b2o2bo31b2o
2bo3bo3b2o22b2o2bo3bo3b2o22b2o2bo30b2o2bo$23bo27b2o109b2o21b2o32b3o4bo
4b3o21b3o4bo4b3o21b3o4bo4b3o21b3o4bo4b3o21b3o4bo27b3o4bo$21b2o3bo3bo
22bo90bo3bo3bo9bo63bo3bo3b2o26bo3bo3b2o26bo35bo35bo34bo$23bo2bo3bo22bo
108b3o19bo4b2o34b2o3bo10bo19b2o3bo30b2o34b2o34b2o33b2o$o3bo3bobobo12b
2o113bobobo3bobobo10b2o3bo19bo34bo2b2o3bo4bob2obo17bo2b2o3bo4bobo20bo
2b2o31bo2b2o31bo2b2o30bo2b2o$26bo3bo21b2o115bo15b3o33b2o10b2obobo18b2o
10b2obob2obo15b2o34b2o34b2o33b2o$o3bo3bo17bo3bo19b2o114b2o19bo35bo35bo
17bo17bo35bo35bo34bo$26b3o19b2o2bo112bob2o19bo$obobo3bobobo35b3o114b2o
20b2o$26b3o8bo2b2o9b2o108bobo24bo$4bo3bo3bo13bo3bo6b2o2bo119bo26b2o$
26bo3bo6bo3b3o2b3o112bobo21bo2b2o$4bo3bobobo12b2o14b2obo2b2o134b2o3bo$
23bo2bo3bo11bo142bo$21b2o3bo3bo12b2o$23bo20bo3bo$25b2o3bo14bo2bo$27b3o
16bobo5$181bo$180bobo$180bobo$180bo2$180bobo2$178b3o$140bobobo3bobobo
24bo$176b2obo$140bo7bo3bo27bo$22b2o29b2o125bo$o3bo3bobobo8b3o20bo7b3o
85bobobo3bobobo22bobo$22bo20bo9bo15b2o101bob2o$o3bo7bo10b2ob2o15b2o9b
2ob2o10b3ob2obo67bo7bo17b2ob2o$28bo5bo6bo17bo5bob3o6bo93b2ob2o$obobo7b
o10b2o7bobob3o6bo8b2o7bobo6bo67bobobo3bobobo20bo$24bo6bobo4b3ob2obo9bo
6bobo9b2o85bob2o6bobo$4bo7bo12bo2bo9b2o16bo2bo14bo86bo3b2o$26bobobob2o
23bobobob2o10bo85bob2o6bobo$4bo7bo12b2o3bo25b2o3bo104b3ob2obo$27bo30bo
108bob2o2$168bobo$170b2obo$173bo9$26bo$26b2o$26bo$28bo$28bo$27b2o18bo$
45b2o130b2o$29bo17bo129b4o$o3bo3bobobo15bobo9bo8bobo88bobobo3bobobo17b
o5bo3bo$27b4o9b2o6bo2bo118b2ob2o2bo$o3bo3bo3bo10b2o2bo12bo7bo2bo88bo7b
o3bo13bobo2bo2bo3bobo$23b2obobo13bo5bobo112bo2bo7b3o3bo$obobo3bobobo
10b2o2bo14bo7bo89bobobo3bo3bo8b2o3b2o14bo$22b2o17b2o120bo2b2o10bo2bo4b
3o$4bo3bo3bo8bo17bo2bo2bobo92bo3bo3bo3bo12bo2bo7b2o3bo2bob3o$21bo5bo9b
2o6bob2o117b2o6bo8b2o$4bo3bobobo9bob3o12bo5b4o91bobobo3bobobo21bo11bo$
27bo13b4o129bobo10bobo$24b4o18bo3bo137bo$24bo2bo18b5o$27bo19b2o$26bo$
26bobo$26bobo$27bo12$164bobo29bobo29bo$162b2o3b2o27bo3bo25b2o$162bobo
31bo4b2o25bo$164bo33bo3bo2b2o15bo3b2o$161bo37b2o3bo15bo2b2obobo$161b2o
3bo51b3o6b2o$o3bo3bobobo127bobobo4bo19b2o24b4o18bobo7b2o$164b2o3bo23b
2obo2bo17bob2o9bo$o3bo3bo3bo127bo8bo15bobo4b2o19b4o2bo16bo4bo8bo$165b
7obo23bo17b2o11bo$obobo3bobobo127bobobo4bo14bo61b2o$165b7obo17b3o20bo
4b2o7bo$4bo7bo127bo3bo4bo15bobo4b2o17b3o24bo$164b2o3bo10bo2b2o30b3o$4b
o3bobobo127bobobo4bo19b2o9b2o2bo32bo$161b2o3bo13bo3b3o2b3o26bo4bo$161b
o22b2obo2b2o25b2ob2obo$164bo20bo30bo3bo$162bobo21b2o28b4o$162b2o3b2o
18bo3bo21bo3b2o$164bobo21bo2bo21b2o$189bobo21bo11$173bo$59bo111b2o96b
2o31b2o$32b2o24bobo112bo94bo32bo5bo178bo$31bo26bobo114bobo15bo3b2o27bo
3b2o35b2ob3o27b2ob3o2b2o175bobo$31b2o25bo115bo2bo13bo2b2obobo24bo2b2ob
obo31b7obo2b2o20b7obo105b2o34b2o35bo$31b2o141bo2bo11b3o6bo3bo19b3o6bo
3bo5bo22bo3bo5bo22bo3bo108bobo4bo28bobo32b2o$26b4obo26bobo113bobo11bob
o7b7obo14bobo7b7obo2b2o15bo3bobo26bo3bobo35bo35bo36bo2bob2obobo25bo2bo
b2obobo25bo2bob3o$23bob3o148bo11bob2o9b2ob3o2b2o10bob2o9b2ob3o17bo2b2o
b2o25bo2b2ob2o32bo3bo31bo3bo39b2o3bobo28b2o3bobo25bo4b3o$obobo3bobobo
9b2o7b2o23b3o81bobobo3bobobo34bo4bo9bo5bo11bo4bo9bo19b3o30b3o30b3o4bob
o2bo23b3o4bobo2bo36b2obo32b2obo7bo24b2o$55bo117bobo10b2o15b2o14b2o15b
2o16bobo30bobo26bo2b2o4b2obobo3b2obo14bo2b2o4b2obobo3b2obo7bo20bo2bo
32bo2bo36b2o$o7bo3bo9bob2obo26b2obo82bo11bo16b3ob2obo77bob2o29bob2o25b
2o7bo12b2o3bobo6b2o7bo12b2o3bobo11b3o4bobo3bo22b3o4bobo3bo31bo2bo$22b
2o3bo30bo111bob2obo9bo4b2o26bo4b2o28bo4bo27bo4bo24bo3bo6b3o5bo2bob2obo
bo6bo3bo6b3o5bo2bob2obobo6bo2b2o4b2obobo3bo17bo2b2o4b2obobo3bo22b3o4bo
bo2bo$obobo3bo3bo14bo30bo81bobobo3bobobo14bo2bobo16bo32bo29b2o31b2o34b
2o4bo2bo7bobo4bo11b2o4bo2bo7bobo11b2o7bo26b2o7bo26bo2b2o4b2obobo$22b2o
29bo111bo2bo2b2o13b3o30b3o104b2o2bo8b2o21b2o2bo8b2o11bo3bo6b3o22bo3bo
6b3o22b2o7bo$4bo3bo3bo9bo29b2obo84bo3bo3bo15bo2bo2bo17bo32bo29bo4b2o
26bo4b2o32b3o4bo28b3o4bo26b2o4bo2bo26b2o4bo2bo21bo3bo6b3o$22b3o17bob2o
118bo3bob3o16bo32bo32bo32bo41bo35bo31b2o2bo31b2o2bo26b2o4bo2bo$obobo3b
obobo10b2o3bo11b2o3bo94bobobo3bobobo12b3obo2bo15b2o31b2o29b3o30b3o41b
2o34b2o28b3o4bo28b3o4bo31b2o2bo$29bo12bobo6bobo111bobo21bo32bo31bo32bo
39bo2b2o31bo2b2o34bo35bo28b3o4bo$26b2o18b3ob2o112b2o23b2o31b2o31bo32bo
36b2o34b2o38b2o34b2o35bo$25bob2o17b2ob2o135bo2b2o28bo2b2o30b2o31b2o38b
o35bo35bo2b2o31bo2b2o33b2o$25b2o21bobo110b2o3bo17b2o3bo27b2o3bo32bo32b
o108b2o34b2o36bo2b2o$21bobo25b3o109bo24bo32bo35b2o31b2o109bo35bo33b2o$
21bo27b4o111bo87bo2b2o28bo2b2o181bo$21bobo28bo109bobo85b2o3bo27b2o3bo$
162b2o3b2o83bo32bo$164bobo7$183bo$182bobo$24bo3bo153bobo$23bob2obo153b
o$23bobo249bo$24bo157bobo23bo36bo26b4o$22b2o183bobo34bobo25b3o$22b2o
156b3o24bobo34bobo22b2o2bo$26bob2o149bo27bo36bo23bo3b2o$25b2o9bobo25bo
bo111b2obo89b3o$obobo4bo26bo27bo75bobobo3bobobo29bo24bobo34bobo20bo2bo
$25b2obo7bobo2bo2bo19bobo2bo2bo109bo85b2o$o8bo15b2obo10bo27bo72bo11bo
24bo27b3o3b3o28b3o3b3o17bobobo$27bo12bob2obo22bob2obo102b2obo24bo5bo3b
2o25bo5bo3b2o15bo3bo7b2o$obobo4bo14bo2b2o12b3obo23b3obo66bobobo3bobobo
50b2obo3bo29b2obo3bo10bo9bo10bo$25b3o12bo4bo2bob2o16bo4bo2bob2o113bob
2o10bo3bo4bobo11bob2o10bo3bo4bob2obo10bo8b2o$4bo4bo27bo3b2o3bob4o13bo
3b2o3bob4o60bo3bo7bo22bobo13b2o3bo10bo5b2obob2obo6b2o3bo10bo5b2obobo
17bobo2b2o3bo$24bo12b2o2bo2bob2o4bo12b2o2bo2bob2o4bo4bo86bob2o17bobo6b
obo16bo8bobo6bobo28b2o3bo7bo$obobo4bo14b2o11bo8b2o4bo2b2o8bo8b2o4bo2b
3o54bobobo3bobobo17b2ob2o22b3ob2o31b3ob2o29bobo3bo3b2o$23bo2b2o14b2o3b
2o3bo2b3o12b2o3b2o3bo2b2o85b2ob2o22b2ob2o32b2ob2o30b2obo6bo$25bobo29bo
115bo25bobo34bobo26bobo15bo$21b2o3bo134bob2o6bobo26b3o34b3o25bo15b2o$
22b3o136bo3b2o33b4o33b4o24bobo11bo$23b2o136bob2o6bobo29bo36bo38bo$26bo
139b3ob2obo105bobo$24bobo140bob2o$25bo$168bobo$170b2obo$173bo6$669bo$
668b2o2$264bo399b2obo$262bo2b2o396b3obobo$260b3o68bo330b2o2b2obo$259bo
bo60b3o4bobo331bo4bo$173bobo18bob2o7bo29bobo21bob2o44bo9bo2b2o4b2obobo
33bo36bo36bo36bo36bo36bo36bo36bo35bobo$176bo15b2o3bo4b2o3bo26bo2bo20bo
4bo41b2o10b2o7bo29b3o4bobo27b3o4bobo27b3o4bobo27b3o4bobo27b3o4bobo27b
3o4bobo27b3o4bobo9bo17b3o4bobo9bo21bo3bo$obobo3bobobo127bobobo3bo3bo
18b2obob5o13bobo3b3o2bobo6bo20bo12b2o7b2o38bo9bo9bo3bo6b3o20bo2b2o4b2o
bobo22bo2b2o4b2obobo22bo2b2o4b2obobo22bo2b2o4b2obobo22bo2b2o4b2obobo9b
o12bo2b2o4b2obobo9bo12bo2b2o4b2obobo9b2o4bo6bo2b2o4b2obobo9b2o18bo2b2o
$170b2o4b3o19b3o2bo3bo6b2o20b2o10b2o38b3o4bobo11bo12b2o4bo2bo19b2o7bo
27b2o7bo27b2o7bo27b2o7bo27b2o7bo14b2o4bo6b2o7bo14b2o11b2o7bo10b2obobo
2b3o6b2o7bo10b2obobo2b2o12b3o$o11bo127bo7bo3bo10bo34b3o13bo8bob2o9bobo
9bo7bo4b2o20bo2b2o4b2obobo10bo18b2o2bo19bo3bo6b3o23bo3bo6b3o23bo3bo6b
3o23bo3bo6b3o23bo3bo6b3o6b2obobo2b3o6bo3bo6b3o6b2obobo2b2o7bo3bo6b3o6b
3o2bo2b2o7bo3bo6b3o6b3o2bo2b3o10bobo$161b2o3b3o2bo9bo34bo6bo3b2o5bobo
8bo2bo11bo22b2o7bo8b3o4bobo13b3o4bo4bo3bo15b2o4bo2bo27b2o4bo2bo27b2o4b
o2bo4bo22b2o4bo2bo4bo22b2o4bo2bo5b3o2bo2b2o12b2o4bo2bo5b3o2bo2b3o11b2o
4bo2bo3b2o2bo19b2o4bo2bo3b2o2bo7bo10bob2o$obobo3bobobo127bobobo3bobobo
10bo2bo4bo7b2o2bo17bo9bo4bo6bob2o6bo2b4o2bo4bo9b3o23bo3bo6b3o11b2o21bo
3bobobobo19b2o2bo4bo27b2o2bo4bo27b2o2bo3bobo26b2o2bo3bobo26b2o2bo3b2o
2bo24b2o2bo3b2o2bo7bo16b2o2bo32b2o2bo25bo4bo$165b3o10b3o3bo11b2o6b3o3b
4ob2o11b3obo5b2o2b2ob3obo9bo28b2o4bo2bo2bo2bobo3bo20b2o2bo2bobo3bo14b
3o4bo3bobo23b3o4bo3bobo23b3o4bo29b3o4bo29b3o4bo29b3o4bo29b3o4bo3bobo
23b3o4bo3bobo18b2o$4bo3bo131bo3bo7bo16bo11bo15bobobo2bo4bo6bo12bob2o5b
3o6b2o12bo31b2o2bo3bobobobo20bo2b2o9b2o21bo36bo36bo3b2o2bo28bo3b2o2bo
7bo20bo3bobo30bo3bobo30bo4bo31bo4bo$168b2obo3bobo3bo3bo11bo4bo3bo2bo5b
o45bo28b3o4bo4bo3bo19b2o7b3o4bobo19b2o3b2o2bo27b2o3b2o2bo7bo19b2o5b3o
2bo2b2o20b2o5b3o2bo2b3o19b2o4bo30b2o4bo30b2o35b2o23bo4b2o$obobo3bobobo
127bobobo7bo16b4o3b2o3bo3bo11bo3bo6b2obo2bo15bobo7bo19bo8b2o26bo30bo
13bo19bo2b2o4b3o2bo2b2o18bo2b2o4b3o2bo2b3o17bo2b2o4b2obobo2b3o17bo2b2o
4b2obobo2b2o18bo2b2o32bo2b2o32bo2b2o32bo2b2o26bo$170b4ob2o6bobo12bo9bo
23b2obob3o20bobo6b4ob3o19b2o45bo16b2o9b2obobo2b3o15b2o9b2obobo2b2o16b
2o13b2o4bo15b2o13b2o20b2o35b2o35b2o35b2o28b3o$177b2o20bo35bo24bo2b3o6b
obo19bo2b2o42bo20bo12b2o4bo17bo12b2o22bo12bo23bo12bo23bo36bo36bo36bo
29bo$265bo3bo4bo17b2o45b2o34bo36bo239bo4bo$264bob3obobob3o17bo46bo309b
2ob2obo$265b2o2b4o377bo3bo$269bo2bo377b4o$647bo3b2o$647b2o$647bo8$22bo
167b3o$22b2o2b2o138bo21b2o3bo139bo$22bo2bo138b2o20bo146b2o$25bo140bo
17b2o3bo3bo139bo$168b4o14bo2bo3bo15bo31bo31bo31bo29bo28bo$25b3o141bo2b
o15b2o17bo2b2o27bo2b2o27bo2b2o27bo2b2o27bo26bo2b2o$26bo143b2o17bo3bo
11b3o29b3o29b3o29b3o30b2o24b3o$23bobo145b2o16bo3bo10bobo29bobo29bobo
29bobo56bobo$22bo14bo128bobo20b3o12bob2o28bob2o28bob2o28bob2o32bo22bob
2o13b2o$obobo3bobobo9bo3bo8b2o17bobo83bobobo3bobobo13bobo34bo4bo26bo4b
o26bo4bo26bo4bo30bobo20bo4bo12b2o$21b2obobo10bo10b2o2b2o2bo108bo2bo20b
3o10b2o30b2o30b2o30b2o34b4o19b2o17bo$o11bo11bo3bo10b5o3b3o6bo83bo7bo
17b2o21bo3bo89bo31bo14b2o2bo36bobo2bo$23b2ob2o12bo4bo4bobo118bo17bo3bo
7bo4b2o25bo4b2o25bo4b2o9b2o6bo7bo4b2o9b2o15b2obobo20bo4b2o7bo4bo$obobo
3bobobo10b2obo13bo4bob3o2bo87bobobo3bobobo13b3o2b2o15b2o15bo31bo31bo9b
o4bob2obo11bo9bo4bobo11b2o2bo25bo9bo2b3obo$26b2o12bo4bo6b2o112bob5o13b
o2bo3bo8b3o29b3o29b3o9b3o3bobo11b3o9b3o3bob2obo7b2o26b3o9bobo3b2o$4bo
7bo9bo3b2o11b2obo3b3o3b3o85bo3bo7bo13bobo15b2o3bo3bo10bo31bo31bo8bo4bo
17bo8bo4bo6bo6bo30bo9bo$26bo14bo4b3o117bo2bo16bo18bo4bob3o22bo4bob3o
22bo4bob2obo21bo4bob2obo16bo5bo25bo4bobobo$obobo3bobobo10b3o17b2o2b2o
91bobobo3bobobo13bo21b2o3bo10b2ob2obob2obo20b2ob2obob2obo20b2ob2obob3o
21b2ob2obob3o18bob3o6b2obobo13b2ob2obo$25bo18b2o122b2o20b3o10bo3bo5bo
4bo16bo3bo5bo4bo6bo9bo3bo27bo3bo30bo3bo4bob2obo9bo3bo$26bo176b4o7b3o3b
obo12b4o7b3o3bob2obo9b4o28b4o28b4o2bo10bo9b4o$25b2o140b2o16b3o12bo3b2o
9bo4bob2obo6bo3b2o9bo4bobo9bo3b2o26bo3b2o29bo2bo2bo3b2o12bo3b2o$26bo
139bobo19bobo9b2o15b2o6bo6b2o15b2o13b2o30b2o36bo3b3o14b2o$26b2o137b2o
3bo3bo9bo2bobo10bo18bo12bo18bo12bo31bo36bo21bo$23bo2b2o133bo3b2obo3bo
2b2o6bo3bo145bobo$21b2o3bo134b2o2bo4b3o11bo148bobo$23bo137bo2b2o19b2o
147bo$186b3o$186b3o9$481bo$443bobobo26bobob2obo$382bo58bo3bob2obo21bo
3bobo$382b2o34bo21bo9bo20bo$382bo35b2o19bo3b2o25bo3b2o$29b4obo162bo31b
o38b2o33bo32bo47bo34bo19bob2o27bob2o$28b4o4bo6bo127b2obo22b2ob2o27b2ob
2o34b4o22b3o4bobo23b3o4bobo47bo29bob2obo8b2ob2o7bo18b2ob2o7bo$obobo3bo
3bo12b2o7bo2b2ob2o2b2o94bobobo3bobobo14b3obob3o17bobo2bo26bobo2bo30bo
5bo3bo17bo2b2o4b2obobo8b2obo6bo2b2o4b2obobo45b3o22bobob2obob2obo7b3o8b
o19b3o8bo$23bo2bo3bo3b3o4bo121bobo10bo3b2o8bo2bo6bo3bo17bo2bo6bo3bo24b
2ob2o2bo20b2o7bo12bob3o6b2o7bo39bobobo5bo2bo20bo3bobo5bo2bo7b2obo2bo2b
obo19b2obo2bo2bobo$o7bo3bo8b2o3bo3bo3bo2bo2bo99bo7bo12b2o4b2o5bo3b4o6b
2o3b2o9b2o14b2o3b2o9b2o19bobo2bo2bo3bobo17bo3bo6b3o8b2o9bo3bo6b3o33bo
3bob2obob2obo20bo13b3o16bobo28bobo$23bo13bo125bob2o2bo4b3obo11bo2b2o4b
2obo19bo2b2o4b2obo10bo8bo2bo7b3o3bo7bobo12b2o4bo2bo6bobo14b2o4bo2bo6b
2o23bo9bob2obo19bo3b2o11bo11b2obo27b2obo$obobo3bobobo12b2o3bo5bo103bob
obo3bobobo16bo4bo17bo2bo2bo3bo5bo2b2o11bo2bo2bo3bo5bo2b3o6b2o3b2o14bo
4bo2bo17b2o2bo3b3ob3o18b2o2bo4b3obo21bo3b2o10bo19bob2o13bo13b2o29b2o$
27b3o6b3o124bob2o2bo4b3obo14b2o7bo5bo2b3o11b2o7bo5bo2b2o9bo2b2o10bo2bo
4bo3bo14b3o4bo3bo4bo16b3o4bo3bo4bo21bob2o11b2o8b2ob2o7bo13bo15b3o28b3o
$4bo7bo24b2o101bo3bo3bo3bo8b2o4b2o5bo3b4o16bo4b2o3bo4bo16bo4b2o3bo15bo
2bo7b2o3bo2bobo25bo4b3obo23bo3b3ob3o9b2ob2o7bo13bo8b3o8bo15b2o16bo2b2o
26bo2b2o$37bo125bobo10bo3b2o15b2o4bob3o21b2o4bob3o17b2o6bo8b2o2b2o22b
2o6b2o23b2o6bobo9b3o8bo25b2obo2bo2bobo14bo19bo3bo26bo3bo$obobo7bo23bob
o101bobobo3bobobo14b3obob3o16bob2o3bo4b4o16bob2o3bo4b4o25bo11bo22bo2b
2o28bo2b2o6b2o10b2obo2bo2bobo33bobo38bobo28bobo$36bobo132b2obo17bo3b2o
2b2o3bo18bo3b2o2b2o3bo27bobo10b2o18b2o31b2o11bob3o16bobo28b2obo45bo4bo
25bo4bo$37bo154bob2o28bob2o51b2obo17bo32bo11b2obo11b2obo34b2o44b2o2b2o
bo23b2o2b2obo$282bo79b2o34b3o44b3obobo24b3obobo$362b3o35bo2b2o41b2obo
27b2obo$364bo2b2o33bo$366bo83b2o29b2o$451bo30bo36$56bo$55bobo$54b2o$
56bo$56bo140bo804bo$194b4o705bobo95bobo$54b2obo136b3o451bo31bo94bo32bo
35bo38bo19bo96b2o91b2o$39b2o12b3o137bo454b2o4bo25b2o92bobo30bobo33bobo
36bobo18bo2bo95bo90b2o$39b2o12bo3bo132b2ob2o312bo44bo26bo31bo32b2obobo
2b3o21b2obobo2b2o23bo32bo30b2o31b2o35bobo36bobo20bo3bo92bo90bo$39bo13b
ob2o132b3obo133bo44bo132b2o6bo36b2o23bo2bobo26bo2bobo31b3o2bo2b2o22b3o
2bo2b3o21bobo30bobo31bo32bo34bo38bo24bobo16bo30bo130bobo2bo$36bo2bo
148b2o2b3o130b2o6bo36b2o36bob3o40bob3o45bo4bob2obo34bo4bobo16b4o28b4o
34b2o2bo27b2o2bo7bo20b2o31b2o33bo32bo96b2o19b2o6bo22b2o6bo35b2o84bo4bo
$33bo4bo14bo2bo9bo122bo4bo2b2o22bobobo40bobobo52bo4bob2obo34bo4bobo25b
obob2obob2obo32bobob2obob2obo43b3o3bobo36b3o3bob2obo13b3o3b2o2bo21b3o
3b2o2bo7bo16bo31bo37bo32bo100bobo36bobo20b3o18bo6b3o21bo6b3o32b2o32bob
obo49bo2b3obo$29b2o2b2ob3obo11b2o10b2o22bo97bobo7bo22bo3bob2obob3o31bo
3bob2obob3o44b3o3bobo36b3o3bob2obo20bo3bobo5bo4bo27bo3bobo5bo4bo6bo32b
o4bo39bo4bo6bo10b2o2bo6b3o2bo2b2o11b2o2bo6b3o2bo2b3o13b4o2bobo23b4o2bo
bo32bo32bo31b2o31b2o119bo6bo23bo6bo30b2o2bo29bo3bob2obo45bobo3b2o$obob
o3bobobo15bo2bo6b2o8bo3b2o12bo19b2obo23b2o35b2o30bo3bo31bo9bob2obo29bo
9bob2obo32bobobo5bo4bo29bobobo5bo4bo6bo19bo13b3o3bobo22bo13b3o3bob2obo
29bob2obo39bob2obo19bo3b2o6b2obobo2b3o9bo3b2o6b2obobo2b2o14b3o4bo24b3o
4bo96b2o31b2o34b3o3b3o30b3o3b3o16b2o21b2ob3obo23b2ob3obo30b3o30bo9bobo
bo41bo$21b4obo21bo19bo5b3o7b2o3bo14bo3b3o2b3o25bo3b3o2b3o27bo2b2o32bo
3b2o8bo4bo25bo3b2o8bo4bo6bo20bo3bob2obob2obo30bo3bob2obob2obo28bo3b2o
10bo4bob2obo18bo3b2o10bo4bobo25bobob2obob3o33bobob2obob3o23b3o10b2o4bo
12b3o10b2o15b2o2bo27b2o2bo38b2o31b2o27b2o2bo28b2o2bo32bo5bo3b2o27bo5bo
3b2o14b2o3bo20bo3bo26bo3bo19bo2b2o9b2o27bo3b2o9bo37bobobo$o11bo8bo2b4o
bo17b2o2bo15bo5bo10b2obo14b2obo4bo2b2obobo4bo15b2obo4bo2b2obobo4bo17b
3o36bob2o11b3o3bobo21bob2o11b3o3bob2obo19bo9bob3o30bo9bob3o29bob2o14b
2o6bo18bob2o14b2o27bo3bobo38bo3bobo26bo2bo13bo14bo2bo13bo15bo3b2o26bo
3b2o36b2o31b2o29b3o30b3o33b2obo3bo31b2obo3bo10bo16b2o10b2o2bobo24b2o2b
obo23b2o2bo38bob2o11bobo3b2o23bobob2obo$48bob2o15bobo3bo3b2o2b2o4b2o
10bobob2o3b2o5b3o6bo11bobob2o3b2o5b3o6bo15bobo26b2ob2o7bo14bo4bob2obo
7b2ob2o7bo14bo4bobo21bo3b2o39bo3b2o28b2ob2o7bo18bo13b2ob2o7bo18bo25bo
44bo34b2o30b2o33b3o29b3o34b2o2bo28b2o2bo17bo2b2o9b2o17bo2b2o9b2o35bo3b
o4bobo27bo3bo4bob2obo11b2o3bo10b3o28b3o20bo7bo3b3o2b3o20b2ob2o7bo14bo
2b3obo20bo3bobo$obobo7bo8b3o24bob2o15bobobo3bo4b2ob2o3b3obo6bo7bo3b3ob
o3b4obo11bo7bo3b3obo3b4obo4bo10bob2o24b3o8bo18b2o6bo6b3o8bo18b2o25bob
2o41bob2o29b3o8bo33b3o8bo45bo3b2o39bo3b2o30bobobo27bobobo26bo2bo28bo2b
o37b3o30b3o19b2o2bo28b2o2bo46bo5b2obob2obo24bo5b2obobo15bobo4b2o7bo15b
2o13bo20bo12b2obo2b2o19b3o8bo16bo4bo21bo$48bob2o19b5obo2bob3o4bobo7bo
4b2ob2o4bo4b2o3b3obobo6bo4b2ob2o4bo4b2o3b3obobo9bo4bo24b2obo2bo2bobo
19bo13b2obo2bo2bobo19bo13b2ob2o7bo32b2ob2o7bo32b2obo2bo2bobo33b2obo2bo
2bobo44bob2o41bob2o32bo3bo27bo3bo27b2o30b2o27bo2b2o9b2o17bo2b2o9b2o17b
o3b3o2b3o21bo3b3o2b3o34bo18bo19bo31b7obo8b2ob2o10b3ob2obo8b2ob2o15b2o
12bo26b2obo2bo2bobo16bobo2bo19bo3b2o$o3bo7bo8bo2b4obo17b2o2bo15bo10bo
22b2obobo11bo8bobo8b2obobo11bo8bobo8b2o38bobo42bobo32b3o8bo33b3o8bo43b
obo42bobo33b2ob2o7bo32b2ob2o7bo34bo31bo31bobobo27bobobo24b2o2bo28b2o2b
o32b2obo2b2o25b2obo2b2o33b2obo35b2obo28bo22bo5bob3o6bo13bo5bo6bo16b2o
33bobo21bo19bob2o$21b4obo21bo17bo4b2o32b2o22bo12b2o66b2obo41b2obo37b2o
bo2bo2bobo33b2obo2bo2bobo37b2obo41b2obo36b3o8bo33b3o8bo37bo31bo30bo3bo
27bo3bo24bo3b3o2b3o8b2o11bo3b3o2b3o8b2o16bo32bo29bob2o35bob2o39b7obo8b
2o7bobo6bo12b2o7bobob3o6bo13bo3bo24b2obo25b2o7b2ob2o7bo$obobo7bo15bo2b
o6b2o8bo3b2o13bo2bo2bo32b4o33b4o27bo4b2o31b2o43b2o46bobo42bobo39b2o43b
2o37b2obo2bo2bobo33b2obo2bo2bobo40bobo29bobo24bo31bo32b2obo2b2o7bobo4b
o10b2obo2b2o7bobo17b2o31b2o25b2o3bo33b2o3bo39bobo4b2o9bo6bobo9b2o10bo
6bobo4b3ob2obo14bo2bo2bo23b2o25b2o6b3o8bo$29b2o2b2ob3obo11b2o13b3obobo
34bo36bo32bo33b3o42b3o40b2obo41b2obo43b3o42b3o45bobo42bobo37b2o3bo26b
2o3bo25bo31bo32bo10bo2bob2obobo11bo10bo2bob2obobo13bo3bo3bo24bo3bo3bo
19bobo6bobo27bobo6bobo30b2o3bo14bo2bo14bo12bo2bo9b2o21bobo2bo23b3o33b
2obo2bo2bobo$33bo4bo14bo2bo16bo101b3o36bo2b2o40bo2b2o38b2o43b2o45bo2b
2o40bo2b2o36b2obo41b2obo40bobo3bo25bobo3bo29bobo29bobo27b2o11b2o3bobo
12b2o11b2o3bobo14bo2bo3bo25bo2bo3bo23b3ob2o33b3ob2o37b2o14bobobob2o10b
o12bobobob2o33b2o23bo2b2o38bobo$36bo2bo137bo38bo44bo40b3o42b3o46bo44bo
40b2o43b2o40b2obo28b2obo29b2o3bo26b2o3bo28bo3bo3b2obo21bo3bo3b2obo7bo
15bobo2bo27bobo2bo24b2ob2o34b2ob2o30b2o3bo17b2o3bo25b2o3bo36b2o25bo35b
2obo$39bo13bob2o121bo125bo2b2o40bo2b2o128b3o42b3o35bobo29bobo33bobo3bo
25bobo3bo29bo2bo2bo26bo2bo2bo33b2obo29b2obo7bo14bobo36bobo30bo24bo30bo
40bo4b3o56b2o$39b2o12bo3bo119b2o127bo44bo132bo2b2o40bo2b2o31bo31bo35b
2obo28b2obo33bobo3bo26bobo3bo36b2o3bobo25b2o3bobo15b3o36b3o32bo93bo2bo
b3o56b3o$39b2o12b3o122bo307bo44bo33bobo29bobo29bobo29bobo44bo32bo33bo
2bob2obobo22bo2bob2obobo15b4o35b4o29bobo95b2o62bo2b2o$54b2obo120b2o
449bo31bo116bobo4bo25bobo23bo38bo29b2o3b2o94bo62bo$175bo2b2o449bobo29b
obo115b2o31b2o94bobo97bobo$56bo116b2o3bo830bo$56bo118bo$54b2o$55bobo$
56bo6$287bo7bo$73bo211b2o7bo$71b2o214bo6b2o$48bo24bo218bo$21bobo22b2o
27bobo210b2o6bo$21bo26bo25bo2bo18bobo4b2o184b3ob2obo70bo$21bo28bobo21b
o2bo18bo7bo2bo11b2o26b2o136bo3b2o73b2obo$23b2o24bo2bo21bobo19bo2b3o5bo
10b3o25b3o43bo64bo27b2o76b2o$22b3o24bo2bo23bo21bo5bo2bo11bo27bo42b2o
37bo18b3o4bobo27bo76bo$21b2o7bobo16bobo51b2o15b2ob2o23b2ob2o39bo34b2o
14bo2b2o4b2obobo29bo27bobo41b2o2b2o$21bo3b2o2bo2bo12bo5bo21bobo17bob2o
bo26bo27bo40b5o21bo8bo13b2o7bo34bo26bo2bo11bobo25bo2bobo$obobo3bobobo
11bobobo3bo6bo3bo2bo22b3ob2obo15b3o4bo20b2o26b2o34bo10bo3bo11b3o4bobo
10b5o7bo3bo6b3o29b2o27bo12bo2bo25bo4bo3bo$24bo3bo10b2o2bo4bobo19bob2ob
o22bo22bo2bo24bo2bo22b3o4bobo4b2o3bo4bo6bo2b2o4b2obobo11bo3bo11b2o4bo
2bo58b2o9bo3bo24b2o5bo2bo$o7bo3bo11bobo2b2o8bo3bo2b4obo15bo2bobo19b2o
29bo27bo18bo2b2o4b2obobo2b2o6bobo8b2o7bo10b2o3bo4bo16b2o2bo30bo14bob2o
9bobo7b2o28b2o6bobo$26b2o19b2obo14bo2bo2b2o16b5obo18bobo4bo20bobo4bo
20b2o7bo13b2o11bo3bo6b3o4b2o6bobo15b3o4bo4bo3bo20bobo13bo3b2o5bobo8bob
2o23bo2bo$obobo3bobobo10b2ob2o16b2o18bo2bo2bo16b2ob2obo20bo27bo27bo3bo
6b3o3bobob2o18b2o4bo2bo9b2o25bo3bobob2o19b4o13bob2o6bo2b4o2bo20b3o4bob
o2bo$23b2ob2o16b2o18bo3bob3o14bo3bobobo18bobo2bo2bo19bobo2bo2bo24b2o4b
o2bo3bo3bo23b2o2bo3bobob2o26b2o9b2o13b2o2bo21b3obo5b2o2b2ob2obo9bo2b2o
4b2obobo$o3bo3bo3bo13b2o19b2obo14b3obo2bo14b2obob2obo21bo27bo34b2o2bo
28b3o4bo4bo3bo24bo2b2o2b2o6bobo10b2obobo21bob2o5b3o7b2obo6b2o7bo$24bob
o2b2o8bo3bo2b4obo13bobo22b2o26bob2obo22bob2obo25b3o4bo35bo31b2o9b2o3bo
4bo8b2o2bo44bo6bo3bo6b3o$obobo3bobobo11bo3bo10b2o2bo4bobo13b2o21b3o29b
3obo23b3obo32bo34b2o33bo14bo3bo7b2o27bobo7bo22b2o4bo2bo$24bobobo3bo6bo
3bo2bo41bo29bo4bo2bob2o16bo4bo2bob2o25b2o32bo2b2o46b5o7bo31b2obob3o28b
2o2bo$21bo3b2o2bo2bo12bo5bo9b2o3bo17b2o29bo3b2o3bob4o13bo3b2o3bob4o23b
o2b2o29b2o49bo13bo5bo28bo29b3o4bo$21b2o7bobo16bobo9b2o21b2o29b2o2bo2bo
b2o4bo12b2o2bo2bob2o4bo4bo15b2o36bo46b2o15bob3o66bo$22b3o24bo2bo33bo
28bo8b2o4bo2b2o8bo8b2o4bo2b3o17bo84bo19bo64b2o$23b2o24bo2bo8b3o21bobo
32b2o3b2o3bo2b3o12b2o3b2o3bo2b2o120b4o62bo2b2o$21bo28bobo8b2o22bob2obo
44bo147bo2bo60b2o$21bo26bo14bobo20bo3bo195bo62bo$21bobo22b2o13bo3bo
219bo$48bo10bo2bo222bobo$59bo225bobo$59bobo224bo6$99bo$98bobo$97b2o$
99bo$99bo$218bo3bo22bo3bo$97b2obo116bob2obo21bob2obo12bo$23bo3bo18bo3b
o18bo3bo22b3o118bobo13bobo8bobo13bobo$22bob2obo17bob2obo17bob2obo22bo
3bo117bo10b3obobo9bo10b3obobo28bo33bo228b2o5b2obo16bobo6bo$22bobo20bob
o20bobo25bob2o116b2o7b4obo4bo7b2o7b4obo28bo2b3o28bo2b3o98bo2b2o29bo2b
2o90bo6bo2b2o16bo7bobo$23bo22bo22bo146b2o7bo4bo12b2o7bo4bo28bo2b2o29bo
2b2o99bo2b3o28bo2b3o89b2o5bo20bo7bo78bo$21b2o14bo6b2o21b2o14bo12bo2bo
20bo99bob2o5bo17bob2o5bo25bo3bo29bo3bo40bo33bo24bo3bo4bo24bo3bo4bo89b
2o6bo21bo3b2o77bo2b2o$21b2o7bobob2obo6b2o7bobobo9b2o7bobob2obo11b2o22b
2o3bo5b2o87b2o5b2o18b2o5b2o26bob3o29bob3o36bo2b3o28bo2b3o23bob3o29bob
3o34bo2b2o29bo2b2o17b4obo3b2ob2o25b2obobo50bo20b3o$obobo3bobobo12b3o4b
obo13b3o4bob2obo10b3o4bobo10bo3b2o21b2o3bob2o5bo20b2o6bo29b2o6bo81bob
3o29bob3o36bo2b2o29bo2b2o24bob3o29bob3o34bo2b3o28bo2b3o13bob3o6b2o3bo
21b2o3bo2bo21bo5b2o13b3o4bobo19bobo15bobo$24b2o21b2o11bo9b2o19bo19b4o
2b3o3bo4bobo13bo3b3o2b3o26bo3b3o2b3o25b2obo23b2obo19bob2o8b3o19bob2o8b
3o34bo3bo29bo3bo16bob2o8b3o19bob2o8b3o32bo3bo4bo24bo3bo4bo12b2o7b2o3b
2o21bo3b2o17b3o4bobo4b3o8bo2b2o4b2obobo19bob2o13bo2bo$o7bo3bo17b2o21b
2o21b2o12b2o2bo14bo5b2o4bo4bobo13b2obo4bo2b2obobo5bo15b2obo4bo2b2obobo
5bo16b2obo23b2obo19bo3b2o5b2o21bo3b2o5b2o35bob3o29bob3o17bo3b2o5b2o21b
o3b2o5b2o33bob3o29bob3o34b2o17b2o18bo2b2o4b2obobo5bo9b2o7bo10b2o11bo4b
o11bo3bo$24b6o17b6o17b6o15bob2o12b2o6bobo3bo6bo10bobob2o3b2o5b3o7bo11b
obob2o3b2o5b3o7bo17bo26bo20bob2o6bobo21bob2o6bobo35bob3o29bob3o17bob2o
6bobo21bob2o6bobo33bob3o29bob3o18bob2obo31bo17b2o7bo11bo8bo3bo6b3o6b2o
10b2o15b2o$obobo3bobobo11bo22bo22bo20bob2o14bo2bo2bo6bo16bo7bo3b3obo3b
5obo11bo7bo3b3obo3b5obo4bo9bo2b2o22bo2b2o24b3obo29b3obo26bob2o8b3o19bo
b2o8b3o24b3obo29b3obo24bob2o8b3o19bob2o8b3o20b2o3bo24bo8bobo13bo3bo6b
3o8b2o11b2o4bo2bo4bob2o23bobob2o$24b6o17b6o17b6o15bob2o16b2o4b2obobo
16bo4b2ob2o4bo4b2o4b3obobo6bo4b2ob2o4bo4b2o4b3obobo10b3o24b3o26bob2o
30bob2o26bo3b2o5b2o21bo3b2o5b2o27bob2o30bob2o24bo3b2o5b2o21bo3b2o5b2o
27bo24b2o6bo2bo18b2o4bo2bo5bob2o16b2o2bo3b2ob2o8bo4b2o7bo$o3bo7bo17b2o
21b2o21b2o12b2o2bo17bo5bo3bobo16b2obobo11bo9bobo8b2obobo11bo9bobo130bo
b2o6bobo8bo12bob2o6bobo8bo80bob2o6bobo8bo12bob2o6bobo8bo13b2o28bo7bo2b
o23b2o2bo3b2o2bo14b3o4bo6b2o12bo9bo2b2obo$24b2o21b2o11bo9b2o11bo7bo4bo
15bo4b2o2bo23b2o23bo12b2o33bo26bo30bobo31bobo31b3obo9b2o18b3obo9b2o6bo
13bobo31bobo29b3obo9b2o18b3obo9b2o6bo7bo31bo5bobo21b3o4bo6b2o21bo3b2o
2bo9b3o9bobo4b2obo$obobo3bobobo12b3o4bobo13b3o4bob2obo10b3o4bob2obo7bo
3b3o12bo8b3obobo20b4o34b4o30b2o25b2o31b2obob3o26b2obob3o25bob2o7bo4bob
o15bob2o7bo4bob2obo15b2obob3o26b2obob3o23bob2o7bo4bobo15bob2o7bo4bob2o
bo7b3o29bo7bo28bo3b2ob2o20b2o5bob2o10bo9bo9bo$21b2o7bobob2obo6b2o7bobo
bo9b2o7bobobo15b2o12b2o8b2ob2o23bo37bo30bo2b2o22bo2b2o32bob2obo28bob2o
bo34b3o3bob2obo22b3o3bobo21bob2obo28bob2obo32b3o3bob2obo22b3o3bobo11b
2o3bo24b2o35b2o4bob2o18bo2b2o6b2o11bo4bobobo$21b2o14bo6b2o21b2o41bo9b
3obo94bobo24bobo35bo4bo6bo21bo4bo22bobo5bo4bo6bo13bobo5bo4bo28bo4bo6bo
21bo4bo20bobo5bo4bo6bo13bobo5bo4bo21bo21bo2bo2bobo28bo2b2o4b2o17b2o10b
o12b2ob2obo$23bo22bo22bo27b3o115b2o3bo21b2o3bo37b3o3bob2obo22b3o3bobo
20b2obob2obo25b2obob2obo32b3o3bob2obo22b3o3bobo18b2obob2obo25b2obob2ob
o21b2o21b2o6bob2o25b2o9b2o19bo8bo12bo3bo$22bobo20bobo20bobo26bobo116b
3o24b3o40bo4bobo26bo4bob2obo20bob3o29bob3o34bo4bobo26bo4bob2obo18bob3o
29bob3o21bob2o22bo5b4o27bo37b3o11b4o$22bob2obo17bob2obo17bob2obo21b2o
120b2o25b2o42b2o32b2o6bo95b2o32b2o6bo78b2o26b4o70b2o8bo3b2o$23bo3bo18b
o3bo18bo3bo22bobo121bo26bo42bo33bo103bo33bo80bobo34bo3bo74b2o$96bob2o
118bobo24bobo295bo36b5o74bo$98b2o119bo26bo296bobo35b2o2$99bo$97b2o$97b
2o$99bo4$29bo$27bo2b2o136bobo$25b3o138b2o3b2o$24bobo13bo125bobo$24bob
2o10b2o3bo77bo24bo21bo$23bo4bo11bo2b2o74bo2b2o20bo2b2o16bo$22b2o19b2o
72b3o22b3o20b2o3bo$43bo72bobo22bobo27bo$21bo4b2o14b2o72bob2o21bob2o23b
2ob2o$25bo17bo71bo4bo19bo4bo23bob2o$22b3o15b3o17bobo4b2o20bobo4b2o16b
2o23b2o27b2obo$24bo15b2o18bo7bo2bo17bo7bo2bo70bo$26bo12bobo18bo2b3o5bo
17bo2b3o5bo12bo4b2o18bo4b2o22bo2bo$obobo3bobobo13bo12bob4o17bo5bo2bo
19bo5bo2bo16bo24bo24bo2b2o$25bo3b2o8bobo13b2o10b2o15b2o10b2o16b3o22b3o
26b2o$4bo3bo3bo12bobo16b2o8b3o3b2o21b3o3b2o25bo24bo$25bo3bo11b3o11b2ob
o4bo20b2obo4bo24bo12bo11bo$4bo3bo3bo16b2o9b2obo14bo4bo23bo4bo23b2o7bo
2b3o10b2o7bo2b2o11b3o$29b2o9b2o2bo72bo7bo2b2o12bo7bo2b3o13bobo$4bo3bo
3bo12bo3bo10b2o2bo13b6o23b6o24b2ob2o3bo16b2ob2o3bo4bo9bo2bobo$25bobo
13b2o19b2o2bobo22b2o2bobo16bo2b2obob3o14bo2b2obob3o14bo3bo$4bo3bobobo
12bo3b2o25bo2b2o5b2ob2o14bo2b2o5b2ob2o12b2o3bo3b4o12b2o3bo3b4o15bo$26b
o16bo10b2o3bob2ob2o17b2o3bob2ob2o10bo8bo7bo16bo7bo18b2o$26bo16b3obo8bo
3b2o3bo5bobo11bo3b2o3bo5bob2obo61b3o$24bo17bo2bo15bo6b2obob2obo13bo6b
2obobo21bo24bo17b3o$22b3o16b2o4bo17b2o9bo17b2o26bobo22bobo$25bo14bo6bo
74bo2bo21bo2bo$21bo4b2o12b2o4bo75bo2bo21bo2bo13b3o$46bo76bobo22bobo16b
obo$22b2o18b3o76bo24bo16bo2bobo$23bo4bo12bo4b2o71b2o23b2o16bo3bo$24bob
2o12b3o78bo24bo16bo$24bobo14b2o121b2o$25b3o137b3o$27bo2b2o133b3o$29bo!


@Tim Coe:
Would it be possible for you to narrow down the discovery dates of the c/4 orthogonal ships in this post and this post? Just the year would be sufficient. Currently, they're labeled as being discovered "between Dec 2015 and 19 Mar 2016" and "Between Dec 2015 and 21 Apr 2016" respectively.

muzik wrote:has anyone seriously looked into a 3c/14 orthogonal using the pre-pulsar partial?

It's a good place to start, but it will still probably be very difficult to find a 3c/14 ship. First, period-14 tends to be too high to search at directly. A search-width of 5 completes relatively quickly with zfind, but based on results at other speeds, we're not likely to find anything until we get to a search-width of 9, and that search will take much longer. Second, as the period goes up, the number of potential spaceship components seems to go down. Third, as the speed goes up, the number of potential spaceship components seems to go down. 3c/14 isn't very fast, but it's still faster than c/5. This could also reduce the probability of finding a spaceship.

So it might be possible to find a 3c/14 ship by using the pre-pulsar push to expand the reasonable search space, but you'll still need a bit of luck. Of course, I don't want to discourage anyone from exploring this idea. As we've seen recently, there could still be several small ships that are within our reach that we just haven't looked for yet.
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Re: Spaceship Discussion Thread

Postby muzik » June 15th, 2016, 3:37 am

Sokwe wrote:...

muzik wrote:has anyone seriously looked into a 3c/14 orthogonal using the pre-pulsar partial?

It's a good place to start, but it will still probably be very difficult to find a 3c/14 ship. First, period-14 tends to be too high to search at directly. A search-width of 5 completes relatively quickly with zfind, but based on results at other speeds, we're not likely to find anything until we get to a search-width of 9, and that search will take much longer. Second, as the period goes up, the number of potential spaceship components seems to go down. Third, as the speed goes up, the number of potential spaceship components seems to go down. 3c/14 isn't very fast, but it's still faster than c/5. This could also reduce the probability of finding a spaceship.

So it might be possible to find a 3c/14 ship by using the pre-pulsar push to expand the reasonable search space, but you'll still need a bit of luck. Of course, I don't want to discourage anyone from exploring this idea. As we've seen recently, there could still be several small ships that are within our reach that we just haven't looked for yet.


It seems that things that are small enough to memorise how to build given a few minutes or so, but slow enough that they won't be seen escaping from soup, tend to be the best way to go. Copperhead of course is period 10 and kind of fragile (not really that much at the front and back), and loafer, a slightly earlier discovery, is even smaller and period 7. And similarly, we have the c/98 HighLife ship, which is pretty damn high period.


So searching for exotic speeds such as 3c/14 (which would actually lengthen some sort of chain, as we technically have 2c/14, 4c/14 and 6c/14) is probably our best bet. Since c/8 and c/9 have been quite thoroughly searched with no elementary spaceships popping up, we can tell that any ones of those speed are probably not going to be small. There are some really nice partials there though. Then there are some other potentially elementary speeds that don't seem to have been looked into like c/18 and c/67.


tl:dr c/98 is astronomically slow for such a small spaceship, which is unfortunately not in regular Life, so let's find an even weirder elementary speed which is in regular Life. Also I state the obvious too much
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Re: Spaceship Discussion Thread

Postby Scorbie » June 15th, 2016, 7:54 am

muzik wrote:
Sokwe wrote:...

muzik wrote:has anyone seriously looked into a 3c/14 orthogonal using the pre-pulsar partial?

It's a good place to start, but it will still probably be very difficult to find a 3c/14 ship. First, period-14 tends to be too high to search at directly. A search-width of 5 completes relatively quickly with zfind, but based on results at other speeds, we're not likely to find anything until we get to a search-width of 9, and that search will take much longer. Second, as the period goes up, the number of potential spaceship components seems to go down. Third, as the speed goes up, the number of potential spaceship components seems to go down. 3c/14 isn't very fast, but it's still faster than c/5. This could also reduce the probability of finding a spaceship.

So it might be possible to find a 3c/14 ship by using the pre-pulsar push to expand the reasonable search space, but you'll still need a bit of luck. Of course, I don't want to discourage anyone from exploring this idea. As we've seen recently, there could still be several small ships that are within our reach that we just haven't looked for yet.


It seems that things that are small enough to memorise how to build given a few minutes or so, but slow enough that they won't be seen escaping from soup, tend to be the best way to go. Copperhead of course is period 10 and kind of fragile (not really that much at the front and back), and loafer, a slightly earlier discovery, is even smaller and period 7. And similarly, we have the c/98 HighLife ship, which is pretty damn high period.


So searching for exotic speeds such as 3c/14 (which would actually lengthen some sort of chain, as we technically have 2c/14, 4c/14 and 6c/14) is probably our best bet. Since c/8 and c/9 have been quite thoroughly searched with no elementary spaceships popping up, we can tell that any ones of those speed are probably not going to be small. There are some really nice partials there though. Then there are some other potentially elementary speeds that don't seem to have been looked into like c/18 and c/67.


tl:dr c/98 is astronomically slow for such a small spaceship, which is unfortunately not in regular Life, so let's find an even weirder elementary speed which is in regular Life. Also I state the obvious too much
I would like to say: don't lose hope. New searches are coming along and maybe that 3c/14 ship is right on the corner of the new search utilities. Currently, row-based searches look pretty impractical as Sokwe said, but if there is a ship small enough, I would say we could bet on coppersearch.
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Re: Spaceship Discussion Thread

Postby muzik » June 15th, 2016, 8:23 am

Scorbie wrote:I would like to say: don't lose hope. New searches are coming along and maybe that 3c/14 ship is right on the corner of the new search utilities. Currently, row-based searches look pretty impractical as Sokwe said, but if there is a ship small enough, I would say we could bet on coppersearch.

Just wanting to know, do different search programs have advantages over each other?

Also I was considering possibly using/getting a bunch of people to use apgsearch (symmetrical with an odd number of cells in between) and see if it pops out of there. It would be a boring process, but hey, Copperhead appeared from a symmetrical soup soon after its discovery. Even then, apgsearch maybe isn't our best bet.


Anyway, whichever search program is best. Everyone go ahead and start the search!
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Re: Spaceship Discussion Thread

Postby Scorbie » June 15th, 2016, 11:36 am

muzik wrote:Just wanting to know, do different search programs have advantages over each other?
Of course. That is why there are different programs.
muzik wrote:Anyway, whichever search program is best. Everyone go ahead and start the search!
Sadly I don't have computing power :( But I hope others keep on with searching.
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Re: Spaceship Discussion Thread

Postby muzik » June 15th, 2016, 12:09 pm

That's unfortunate...

Everyone except Scorbie go ahead and start the search!



On a slightly unrelated note, I asked about there being the possibili of a smaller Cordership and got what I interpret as a "pretty likely" from Dave: viewtopic.php?f=7&t=2036&start=100#p31928

It seems like a tricky task to search for one, but it might be something else worth looking into.
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Re: Spaceship Discussion Thread

Postby muzik » June 18th, 2016, 8:09 am

Should I compile a list of known partials for each speed?
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Re: Spaceship Discussion Thread

Postby muzik » June 26th, 2016, 5:00 am

Stupid question that's been floating about my head for a while, but could a 17c/45, 31c/240 or 23,5c/79 ship with <10000 cells exist?
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Re: Spaceship Discussion Thread

Postby biggiemac » June 26th, 2016, 9:55 am

muzik wrote:Stupid question that's been floating about my head for a while, but could a 17c/45, 31c/240 or 23,5c/79 ship with <10000 cells exist?


I think yes, such a thing definitely should exist. What got the caterpillar kinds discovered first is that they were built from convenient puzzle pieces instead of discovered all at once. As soon as one gets big enough, I'm confident any possible speed of spaceship exists, but the huge number of possibilities are impossible to weed through. So, yes, but engineered spaceships are what we will be seeing instead for those high-periods and large cell counts.

Each could probably take some order of magnitude incremental improvement with more time spent engineering. The 'caterpillar's younger brother' thread has existed for a while but nobody explicitly made the improved ship.
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Re: Spaceship Discussion Thread

Postby muzik » June 26th, 2016, 3:55 pm

I feel like the caterpillar's repetitive structure should make it possible to crimp down a bit and save on about 10000 or so cells, but that's most likely a trick of the eye.


Any ways, this thread should probably be renamed "Elementary Spaceship Discussion Thread" because it's mostly about elementary spaceships. There should also be an "Engineered Spaceship Discussion Thread" because there's a good few threads on engineered and engineerable spaceships.



Anyway, how about elementary knightships?

We know this guy:

x = 13, y = 19, rule = b3/s23
11bob$6b2o2bo2b$6bob2o3b$5bo5b2o$bobo2bo6b$o12b$o3bo2b3ob2o$o3bo4bo3b$
5bob2o4b$bo3bob2o4b$2ob3o7b$4b2obo5b$2o2b3o6b$2obo9b$3b2o4b2o2b$b3o9b$
2bo2b3ob2o2b$3b2o2b2o4b$4b3o!


who is disqualified from spaceshiphood by 2 cells. However, it was discovered in 2004, and I'm pretty sure we have more powerful searches these days. So maybe try running this through a search of some sort?
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Re: Spaceship Discussion Thread

Postby Sokwe » June 26th, 2016, 7:05 pm

muzik wrote:"Engineered Spaceship Discussion Thread" because there's a good few threads on engineered and engineerable spaceships.

I worry that an "Engineered Spaceship Discussion Thread" would intertwine multiple complicated discussions, making them more difficult to follow.

muzik wrote:how about elementary knightships?

The spaceship search status page has information on the status of some of the completed searches for obliquely-traveling ships. In particular, Tim Coe searched for p6 knightships up to a "width" of 15 (see here). This only represents searches where the long dimension is the same as the 2-cell direction of travel. "Short" knightship searches have not been focused on as much. Another possibility is to run diagonal searches for knightships. I did a bit of this at p6 several years ago, but I can't find my notes on it. I think that I searched up to a diagonal width of 19 for a "long" spaceship and a diagonal width of 13 for a "short" spaceship.

Knightship searches at periods above 6 have not been explored as much. For all we know, it might actually be easier to find a p7 knightship.
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Re: Spaceship Discussion Thread

Postby muzik » June 27th, 2016, 6:57 am

Sokwe wrote:
muzik wrote:how about elementary knightships?

The spaceship search status page has information on the status of some of the completed searches for obliquely-traveling ships. In particular, Tim Coe searched for p6 knightships up to a "width" of 15 (see here). This only represents searches where the long dimension is the same as the 2-cell direction of travel. "Short" knightship searches have not been focused on as much. Another possibility is to run diagonal searches for knightships. I did a bit of this at p6 several years ago, but I can't find my notes on it. I think that I searched up to a diagonal width of 19 for a "long" spaceship and a diagonal width of 13 for a "short" spaceship.

Knightship searches at periods above 6 have not been explored as much. For all we know, it might actually be easier to find a p7 knightship.


I barely understood any of that.

My understanding is that there are probably no 2,1c/6 knightwise ships that are less than 15 cells wide, and we haven't tapped into the realm of knightships with a restricted height. And you searched for knightships with a diagonal symmetry of some sort?
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Re: Spaceship Discussion Thread

Postby Sokwe » June 27th, 2016, 7:36 am

muzik wrote:My understanding is that there are probably no 2,1c/6 knightwise ships that are less than 15 cells wide

There are no (2,1)c/6 knightships that are less than or equal to 15 cells wide over all phases.

muzik wrote:we haven't tapped into the realm of knightships with a restricted height

I think I searched for "short" p6 knightships up to a height of 12 using WLS, but I might be misremembering. Such searches tend to take longer than the "long" knightship searches. Also, gfind-pt and knight2 are incapable of searching for "short" knightships.

muzik wrote:you searched for p6 knightships with a diagonal symmetry of some sort?

I searched for knightships with a diagonal shape. Unfortunately, I can't find any of my knightship partials, but here is a c/4 orthogonal ship to show the idea:
x = 30, y = 31, rule = B3/S23
4b2o$b2ob2o$o2bo$b2o4bobo$bo4b4o$10bo$2o4bobo$6bobo2b2o$12b2o$12b2o2$
12b2o$14bo$13b2o2$11b2o$11bo4b3ob3o$13bobo6bo$13bo3bo3bo$18bobobobo$
22bob2o$20b2o$22bob3o$23bobo$25b3o$27bo$28b2o$27b2o$27bo2$26b2o!
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Re: Spaceship Discussion Thread

Postby muzik » June 27th, 2016, 7:45 am

Sokwe wrote:
muzik wrote:you searched for p6 knightships with a diagonal symmetry of some sort?

I searched for knightships with a diagonal shape. Unfortunately, I can't find any of my knightship partials, but here is a c/4 orthogonal ship to show the idea:
x = 30, y = 31, rule = B3/S23
4b2o$b2ob2o$o2bo$b2o4bobo$bo4b4o$10bo$2o4bobo$6bobo2b2o$12b2o$12b2o2$
12b2o$14bo$13b2o2$11b2o$11bo4b3ob3o$13bobo6bo$13bo3bo3bo$18bobobobo$
22bob2o$20b2o$22bob3o$23bobo$25b3o$27bo$28b2o$27b2o$27bo2$26b2o!

Although I'm assuming it's asymmetric, and only looks diagonal?
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Re: Spaceship Discussion Thread

Postby BlinkerSpawn » June 27th, 2016, 8:26 am

muzik wrote:
Sokwe wrote:
muzik wrote:you searched for p6 knightships with a diagonal symmetry of some sort?

I searched for knightships with a diagonal shape. Unfortunately, I can't find any of my knightship partials, but here is a c/4 orthogonal ship to show the idea:
rle

Although I'm assuming it's asymmetric, and only looks diagonal?

Diagonally-symmetric reactions can only travel diagonally.
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Re: Spaceship Discussion Thread

Postby muzik » June 27th, 2016, 9:31 am

BlinkerSpawn wrote:
muzik wrote:Although I'm assuming it's asymmetric, and only looks diagonal?

Diagonally-symmetric reactions can only travel diagonally.

Of course, that's why I suggested it would be asymmetric
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Re: Spaceship Discussion Thread

Postby Gamedziner » June 27th, 2016, 11:22 am

Is there any "small" (less than 1000 cells) means by which those two cells could be prevented from appearing, thus allowing a sort of flotilla knightship?
A base-2 ruler for all your measuring needs in CGOL:
32b32o$16b16o16b16o$8b8o8b8o8b8o8b8o$4b4o4b4o4b4o4b4o4b4o4b4o4b4o4b4o$2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
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Re: Spaceship Discussion Thread

Postby dvgrn » June 27th, 2016, 11:30 am

Gamedziner wrote:Is there any "small" (less than 1000 cells) means by which those two cells could be prevented from appearing, thus allowing a sort of flotilla knightship?

If something like that existed, it would have to move at the same speed as the knightship to keep doing its suppression work, and so it would be a very good candidate knightship on its own.

It might work to start a new search for a "support" ship that suppresses those two cells in the almost-knightship, and see if any solutions happen to come up for the different possible searchable shapes. I would expect that one or more people have already tried something along those lines, but I don't know for sure.
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Re: Spaceship Discussion Thread

Postby Gamedziner » June 27th, 2016, 11:58 am

#N Backrake 2
#O David Buckingham
#C A period 12 orthogonal c/2 backrake.
#C www.conwaylife.com/wiki/index.php?title=Backrake_2
x = 19, y = 26, rule = 23/3
3bo15b$2b3o14b$b2obo5bo8b$b3o5b3o7b$2b2o4bo2b2o3b3o$8b3o4bo2bo$18bo$
18bo$18bo$2b3o12bob$2bo2bo13b$2bo16b$2bo16b$3bo15b7$3o16b$o2bo11bo3b$o
13b3o2b$o12b2obo2b$o12b3o3b$bo12b2o!


If only there was a way to make this backrake's stream of gliders work... It seems to have the right period, but if used, it would make an expanding knightship, at best! (At worst, it would just fail)
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32b32o$16b16o16b16o$8b8o8b8o8b8o8b8o$4b4o4b4o4b4o4b4o4b4o4b4o4b4o4b4o$2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o2b2o$bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
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