For general discussion about Conway's Game of Life.
Haycat2009
Posts: 843
Joined: April 26th, 2023, 5:47 am
Location: Bahar Junction, Zumaland

Mathemagician314 wrote:
June 16th, 2024, 4:49 pm
Is there any stable lifelike rule with a minimum speed limit?
The only rules with a minimum speed limit I know about have B2a and B3i but no B2e, so likely not. Determination has a minimum speed limit of c, but it is B2a3i/S12, so it does not count for your question.
~ Haycat Durnak, a hard-working editor
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b-engine
Posts: 1901
Joined: October 26th, 2023, 4:11 am
Location: Somewhere on earth

Mathemagician314 wrote:
June 16th, 2024, 4:49 pm
Is there any stable lifelike rule with a minimum speed limit?
If considering non-stable rules, add sufficiently enough conditions (B/S condition, as I refers a requirement of a cellstate to transform into another state as transitions) and support a single spaceship would work:

Code: Select all

``````#R B245678/S0345678
b2o\$o2bo!
``````
b-rules100th post: 18 November 2023 1000th post: 8 March 2024 10000th post:

tommyaweosme
Posts: 1096
Joined: January 15th, 2024, 9:37 am
Location: platformer mode
Contact:

Code: Select all

``````#R B23-j45678/S01e2-k345678
b2o\$o2bo!``````

Code: Select all

``````#R B23-j45678/S01e2-k345678
!
[[ RANDOMIZE ]]``````
isotropified
i can solve a rubix cube in 3 minutes or less with my new speedcube

Supersuthiastic
Posts: 26
Joined: March 14th, 2024, 8:55 pm

Is this p3 known? I originally conjectured that all oscillators have period 2 in this rule.

Code: Select all

``````x = 3, y = 5, rule = B34/S23
b2o\$b2o2\$2o\$2o!
``````

confocaloid
Posts: 3524
Joined: February 8th, 2022, 3:15 pm

Supersuthiastic wrote:
June 17th, 2024, 2:06 pm
Is this p3 known? I originally conjectured that all oscillators have period 2 in this rule.

Code: Select all

``````x = 3, y = 5, rule = B34/S23
b2o\$b2o2\$2o\$2o!
``````
Drelectron8 wrote:
June 17th, 2024, 7:39 pm
How do I know if a spaceship is already discovered? I mean like for just Life (B3/S23) and not the David Eppstein Glider Database.
If you have RLE of a small still life or a low-period oscillator or a spaceship, then you can try "Search for pattern" on the page https://conwaylife.com/ref/mniemiec/lifesrch.htm (Mark Niemiec's database).

Alternatively, you may copy and paste the RLE into the form on the page https://catagolue.hatsya.com/object and click the button "Identify". Currently this works for two-state isotropic CA that use the range-1 Moore neighbourhood.

I just did the latter for the RLE above, and reached the object page https://catagolue.hatsya.com/object/xp3_3ro/b34s23
Just because that page exists, doesn't mean the pattern is known. However, there's a comment from 2021 on the linked page:
/object/xp3_3ro/b34s23#comment wrote: On 2021-10-01 at 10:52:19 UTC, Ignacy.Jackl wrote:

Block eating block
So the oscillator is (almost certainly[1]) known.

[1]: "almost certainly" because there's the possibility of having a different oscillator in another CA, with the same apgcode but differing evolution. In that case, the Catagolue comments will get mixed together on the same page.
Last edited by confocaloid on June 17th, 2024, 7:55 pm, edited 5 times in total.
127:1 B3/S234c User:Confocal/R (isotropic CA, incomplete)
Unlikely events happen.
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Drelectron8
Posts: 92
Joined: March 5th, 2023, 4:54 am
Location: Queenstown, Singapore

How do I know if a spaceship is already discovered? I mean like for just Life (B3/S23) and not the David Eppstein Glider Database.

Code: Select all

``````x = 4, y = 4, rule = B01356/S012345
ob2o\$2obo2\$obo!
#C [[ THEME Book AUTOFIT LAYERS 5 DEPTH 0.50 ]]
``````
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otismo
Posts: 1368
Joined: August 18th, 2010, 1:41 pm
Location: Florida
Contact:

I seem to remember an "on-off" Brice Due MetaPixel that came with Golly.

It would be useful for study but I no longer have it.

Can anyone please post the file -

Thank You !
"One picture is worth 1000 words; but one thousand words, carefully crafted, can paint an infinite number of pictures."
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dvgrn
Moderator
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otismo wrote:
June 17th, 2024, 9:16 pm
I seem to remember an "on-off" Brice Due MetaPixel that came with Golly.

It would be useful for study but I no longer have it.

Can anyone please post the file -

Thank You !
Those files are generated by metafier.py the first time you run it, in Golly's data directory.

On Windows it's

C:\Users\{your_user_name}\AppData\Roaming\Golly\metapixel-OFF.rle and metapixel-ON.rle

If you don't find them there, or if you're on another OSes, just run this to see where the data directory is:

Code: Select all

``````local g = golly()
local OFFcellFileName = g.getdir("data").."metapixel-OFF.rle"
g.setclipstr(OFFcellFileName)
g.note("Sent to clipboard: "..OFFcellFileName)``````
metapixel-ON.rle
metapixel-OFF.rle

otismo
Posts: 1368
Joined: August 18th, 2010, 1:41 pm
Location: Florida
Contact:

here is an OFF CELL

Code: Select all

``````x = 2058, y = 2058, rule = B3/S23
bo2054bo\$obo2052bobo\$bo2054bo2\$4b2o2046b2o\$4b2o8b4o157b2o829b2o41b2o
1001b2o\$13bo3bo41b2o35b2o77b2o829b2o41bo\$17bo41b2o35b2o949bobo\$13bo2bo
1030b2o\$2016b2o5b2o20b2o\$58b2o2b2o27b2o2b2o1915b2o2b2o5b2o2b2o15bobo\$
9b2o3bo5bo5bo5bo5bo5bo5bo7b2o2b2o27b2o2b2o1915b2o13b2o14bo\$9bo3bobo3bo
bo3bobo3bobo3bobo3bobo3bobo1990bo\$10bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2b
o2bo2bo2bo1740bo249b3o3bobo\$11bobo3bobo3bobo3bobo3bobo3bobo3bobo3bo5b
2o18b2o4b3o1703bo2bo251bo5bo\$12bo5bo5bo5bo5bo5bo5bo5bo3bobo18b2o3bo3bo
1702b5o249bo6bo\$55bo2bo25b2ob2o1702b3ob2o16b2o229bo4bo2bo\$56bobo26bobo
1694bo9b2obo16bo230bo6b3o\$57bo110b3o3b3o1603b3o10b2o16bo2b2o226bo\$85bo
bo80b3o3b3o1602bo31bo2bo228b3o\$84b2ob2o78bob2o3b2obo1602b3o10b2o16bobo
10bo221bo\$84bo3bo78bob2o3b2obo1604bo9b2obo16b2o10b3o189b3o3b3o20bo\$85b
3o80b2o5b2o1614b3ob2o30bo188bo2bobo2bo19bo\$169bo5bo1615b5o16b2o10b3o
189b2obobob2o18bo\$184b2o8b3o14b2o1578bo2bo16bobo10bo191b2o5b2o17bo\$
184b2o8bo3bo12b2o1580bo17bo2bo228b3o\$194bo4bo1611bo2b2o230bo\$195bo3bo
1612bo232bo\$1777bo16bo18b2o229bo\$10b2o152b2o13b2o14bo3bo7b3o1567b3o14b
obo221b2ob2o20bo\$10b2o152b2o2b2o5b2o2b2o13bo4bo5b2obob2o1568bo13b2o
220bo2bobo2bo17bo\$78b3o5b3o79b2o5b2o7b2o8bo3bo5bo5b2o1567b2o235bobo3bo
bo18b3o\$15bo3b2o57bo2b2ob2o2bo95b2o8b3o8b2obob2o1804b3o3b3o21bo\$9b2o2b
2obob3o13b2o43b3o3b3o119b3o1813b2o20bo\$9b2o2bo4b3o13b2o44bo5bo1936b2o
19bo\$13bo3bo2005b2o18bo\$14b3o2025bo\$28b2o3b2o2008b3o\$14b3o10b3o3b3o39b
2o13b2o1954bo\$13bo3bo7b3o7b3o37b2o2b2o5b2o2b2o1953bo\$9b2o2bo4b3o4b3o7b
3o41b2o5b2o1701b2o253bo\$9b2o2b2obob3o4b3o7b3o1743b2o6bobo251bo\$15bo3b
2o6b3o3b3o1744bobo6bo252bo\$28b2o3b2o1745bo191b2o5b2o62b3o\$10b2o1767b2o
187b2o2b2o5b2o2b2o61bo\$10b2o958b2o967b2o27b2o13b2o60bo\$224b2o743bo2bo
832bo3b2o127bo2bo102bo\$224b2o744b2o831b2obob3o128b2o102bo\$1803bo4b3o
231bo\$1792bobo2b2o4bo3bo14bo220b3o\$1791bo3bob3o4b3o15b3o221bo\$65b2o5b
2o1718bo6b2o24bo219bo\$61b2o2b2o5b2o2b2o1702bo12b5obo4b3o15b3o219bo\$61b
2o2b2o5b2o2b2o1700b3o15b3o4bo3bo14bo150bo5bo63bo\$65b3o3b3o1703bo25bo4b
3o161bobo3bobo61bo\$64bo2bo3bo2bo1703b3o15b3o4b2obob3o160bo3bobo3bo59bo
\$68bobo1709bo12b5obo5bo3b2o160bo3bobo3bo58bo\$64b2o7b2o26b2o115bo5bo
756b2o809bo6b2o170bo9bo57bo\$64b2o7b2o26bo2bobo110b3o3b3o755bo2bobo804b
o3bob3o240b3o3b2o\$67bo3bo31b2ob3o107b2o2bobo2b2o756b2ob3o803bobo2b2o
173b2o5b2o62bo2b2o2b2o\$67b2ob2o37bo105bob4ob4obo761bo1052b2o6b2o\$65b3o
3b3o29b2ob3o108b3o3b3o757b2ob3o1015b2o\$65b2o5b2o16bo3bo8b2obo109b3o5b
3o750b2obo2b2obo995bo21b2o40b2o\$65bo7bo15bo5bo876b3o2b2o2bo992bo3bob2o
2bo8b2o51b2o\$95bo877b2o6bo997bo4bo10bo\$81bo8bo3b2o865bo12b3o3b2o988b2o
3bobo2bo2bob2o5b2o2bo8b2o\$79b3o9b3o865b3o13bo3bo995bobo3b2o3bo6bo2bo8b
2o\$78bo879bo1019bob7o7bobo\$79b3o9b3o19bo845b3o13bo3bo13bo976bo2bo8b3o
9b2o\$81bo8bo3b2o7bo7b3o847bo12b3o3b2o9b3o978b2o\$95bo4bo2bob2o3bo102b2o
13b2o743b2o6bo8bo992b2o9b2o\$89bo5bo10bo4bo101b2o2b2o5b2o2b2o742b3o2b2o
2bo9bo989bo3b2o7bobo\$90bo3bo10bo4b2o105b2o5b2o751b2obo9b2o989bo4bo6bo
2bo8b2o\$44b2o27b2o1906bo3b2o5b2o2bo8b2o\$44b2o25b2ob2o25b5o1877b2o10bo\$
69bo2bobo27b4o1887b2o23b2o\$49bo3b2o14bo34bo1899b2o12b2o\$43b2o2b2obob3o
14bo4bo1929b2o29bo\$43b2o2bo4b3o15bo3bo1915bo39bo3bo\$47bo3bo15b2o2b3o
1915bobo25b2o10bo8b2o2b2o\$48b3o16b2o1920bobo25b2o10bo2b2o5bo2b2o\$1988b
2ob2o37b2o5bobo\$48b3o1980b3o3b2o\$47bo3bo\$43b2o2bo4b3o13b2o150b2o5b2o
31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b
2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o
5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b
2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o
31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b2o31b2o5b
2o31b2o5b2o31b2o5b2o31b2o5b2o78bo5bo37b3o3b2o\$43b2o2b2obob3o13b2o146b
2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2o
2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2obo
2bo3bo2bob2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2obo
bo5bobob2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2o2b2o
5b2o2b2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2o2b2o5b
2o2b2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o
2b2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b
2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2obo2bo3bo2bob2o23b2o2b2o5b2o2b
2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2obobo5bobob2o23b2o2b2o5b2o2b2o
23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o
23b2o2b2o5b2o2b2o23b2o2b2o5b2o2b2o73b3o3b3o35b2o5bobo\$49bo3b2o161b2o
13b2o23b2o13b2o23b2o13b2o23b2o13b2o23b2o13b2o23b2o13b2o23b2o13b2o23b2o
13b2o23b2obo9bob2o23b2o13b2o23b2o13b2o23b2o13b2o23bo15bo23b2o13b2o23b
2o13b2o23b2o13b2o23bo15bo23b2o13b2o23b2o13b2o23b2o13b2o23b2o13b2o23b2o
13b2o23b2o13b2o23b2o13b2o23b2o13b2o23b2o13b2o23b2o13b2o23b2o13b2o23b2o
13b2o23b2o13b2o23b2o13b2o23b2obo9bob2o23b2o13b2o23b2o13b2o23b2o13b2o
23bo15bo23b2o13b2o23b2o13b2o23b2o13b2o23bo15bo23b2o13b2o23b2o13b2o23b
2o13b2o72bo2b2ob2o2bo21b2o10bo2b2o5bo\$381bo5bo151bo2bo3bo2bo147b2o4bob
o4b2o589bo5bo151bo2bo3bo2bo147b2o4bobo4b2o353bo3bobo3bo21b2o10bo8b2o\$
44b2o175bo5bo152b3o3b3o151bob2ob2obo151bo2bobo2bo432bo5bo152b3o3b3o
151bob2ob2obo151bo2bobo2bo358bobobobo36bo3bo\$44b2o174b3o3b3o150b2o2bob
o2b2o149b2o7b2o431bo5bo152b3o3b3o150b2o2bobo2b2o149b2o7b2o431bo5bo127b
o\$219bo2b2ob2o2bo149b2ob2ob2ob2o149b2o7b2o271bo5bo152b3o3b3o150bo2b2ob
2o2bo149b2ob2ob2ob2o149b2o7b2o271bo5bo152b3o3b3o75b2ob2o3b2ob2o21b2o\$
219bo3bobo3bo152b2ob2o152b3o5b3o111bo5bo152b3o3b3o150b2o2bobo2b2o149bo
3bobo3bo152b2ob2o152b3o5b3o111bo5bo152b3o3b3o150b2o2bobo2b2o76bo7bo23b
2o26b2o\$132b2o23b2o62bobobobo152bobo3bobo112bo5bo33b3ob3o112b3o3b3o31b
o7bo110bo2b2ob2o2bo149bo3bobo3bo30b2o5b2o112bobobobo152bobo3bobo112bo
5bo33b3ob3o112b3o3b3o31bo7bo110bo2b2ob2o2bo149bo3bobo3bo136b2o\$133bo
22bobo182bo5bo31bo2bo3bo2bo30bo7bo71b3o3b3o34bobo113b2obo3bob2o31bobob
obo111b3o5b3o30b3o3b3o110bob2o3b2obo271bo5bo31bo2bo3bo2bo30bo7bo71b3o
3b3o34bobo113b2obo3bob2o31bobobobo111b3o5b3o30b3o3b3o110bob2o3b2obo\$
133bobo82b2ob2o3b2ob2o29bo7bo71b3o3b3o33bo3bo32bo2bo3bo2bo70bob2ob2obo
31bo2bobo2bo152bobobobo151bo9bo109b2o7b2o29bo9bo71bo5bo30b2ob2o3b2ob2o
29bo7bo71b3o3b3o33bo3bo32bo2bo3bo2bo70bob2ob2obo31bo2bobo2bo152bobobob
o151bo9bo109b2o7b2o\$134b2o84bo7bo29bob2o5b2obo68b2o2bobo2b2o29bobo5bob
o33bobo76b2ob2o32bo2bo3bo2bo32b2ob2o113bob2ob2obo150bo3bobo3bo70b3o3b
3o70bo3bobo3bo70b3o3b3o31bo7bo29bob2o5b2obo68b2o2bobo2b2o29bobo5bobo
33bobo76b2ob2o32bo2bo3bo2bo32b2ob2o113bob2ob2obo150bo3bobo3bo70b3o3b3o
177b2o\$147b4o8bo98bo3b2ob2o3bo67bob4ob4obo29bo7bo34bobo34bo7bo33b2ob2o
33b2o5b2o32bo5bo32b2o5b2o33bo3bo33b2o5b2o71b3o3b3o71b3o3b3o71b3o3b3o
70bo3bobo3bo69b2ob2ob2ob2o68bo3b2ob2o3bo67bob4ob4obo29bo7bo34bobo34bo
7bo33b2ob2o33b2o5b2o32bo5bo32b2o5b2o33bo3bo33b2o5b2o71b3o3b3o71b3o3b3o
71b3o3b3o177b2o2b2o\$147bob2o7b2o99bo3bobo3bo29b3o5b3o30b3o3b3o74bobo
34b2o5b2o33b2ob2o112bo2bo3bo2bo32bo3bo113bo2bobo2bo72bo5bo71bob2o3b2ob
o70bobo3bobo69b3o7b3o68bo3bobo3bo29b3o5b3o30b3o3b3o74bobo34b2o5b2o33b
2ob2o112bo2bo3bo2bo32bo3bo113bo2bobo2bo72bo5bo71bob2o3b2obo180b2o\$147b
o112b3o3b3o30b3o5b3o29b3o5b3o69bo2bo3bo2bo30b3o3b3o111bo7bo33b2ob2o
153b2obobob2o111bo7bo30bob2o3b2obo71bo5bo31b3o5b3o110b3o3b3o30b3o5b3o
29b3o5b3o69bo2bo3bo2bo30b3o3b3o111bo7bo33b2ob2o153b2obobob2o111bo7bo
30bob2o3b2obo\$148b2o150b2o5b2o111b3o3b3o33b2ob2o113bo2bobo2bo32bobobob
o111b2obo3bob2o30b2o5b2o110b4o3b4o30b2o5b2o109b2ob2o3b2ob2o29bo7bo111b
2o5b2o111b3o3b3o33b2ob2o113bo2bobo2bo32bobobobo111b2obo3bob2o30b2o5b2o
110b4o3b4o30b2o5b2o\$302bo3bo155bo3bo113b3o3b3o32bobobobo111bo2bo3bo2bo
149bo3bobo3bo31bo5bo110b2obobobobob2o151bo3bo155bo3bo113b3o3b3o32bobob
obo111bo2bo3bo2bo149bo3bobo3bo31bo5bo116b2o\$148b2o150bo2bobo2bo150b2o
7b2o149bo9bo110b3o3b3o151bo2bobo2bo150bo3bobo3bo150bo2bobo2bo150b2o7b
2o149bo9bo110b3o3b3o151bo2bobo2bo155bo14b2o\$147bo151bo3bobo3bo53b2o41b
o42bo9b2o7b2o17b2o78bo50bo11bo210bo58b3o3b3o150bo2bo3bo2bo149bo3bobo3b
o53b2o41bo42bo9b2o7b2o17b2o78bo50bo11bo210bo58b3o3b3o154b2o15bo\$118b2o
2bobo22bob2o7b2o43b2o40b2o42b4o7bo2bobo2bo18b3o31b5o40b2o41bo2b2o9bobo
20bo11b4o19bo3b2o38bo2bo39bobo2b2o30bo3bo29bob2o85bo3b3o67bo3bo43bo72b
2o85b2o8b3o3b3o19b2o33b2o40b2o42b4o7bo2bobo2bo18b3o31b5o40b2o41bo2b2o
9bobo20bo11b4o19bo3b2o38bo2bo39bobo2b2o30bo3bo29bob2o85bo3b3o67bo3bo
43bo72b2o99bo2bo7b2obo\$111b2o4b3obo3bo21b4o8bo41b2ob2o38bo2b2o40bo2b2o
6b3o3b3o17bo4bo5b3obo18bo4bo38bob3o39bo5bo4bo2bo3bo2bo15bo2b2o7b6o16b
2obob3o38b5o37bo3bob3o6b2ob2o17bo5bo5bo21bo2b2o2b3o41b2o36bobo2b5o5b2o
b2o16b3o33bo7bo42b2o35b2o2bo4b2o4b2ob2o15bobo39b4o42bobo34bo2bo9b2o19b
2ob2o38bo2b2o40bo2b2o6b3o3b3o17bo4bo5b3obo18bo4bo38bob3o39bo5bo4bo2bo
3bo2bo15bo2b2o7b6o16b2obob3o38b5o37bo3bob3o6b2ob2o17bo5bo5bo21bo2b2o2b
3o41b2o36bobo2b5o5b2ob2o16b3o33bo7bo42b2o35b2o2bo4b2o4b2ob2o15bobo100b
3o7b2ob2o\$111b2o3b2o6bo76bo2bo38b6o41bo2b2o30bo5bo5b2obob2o16bo2b3o42b
2o39bobo2b2o4b3o3b3o16bo2bo7b2o2b3o16bo4b3o38b3ob2o37bo6b2o3bo2bobo2bo
15bo33bo6b2o43b2o35bo3b2o3b2o2bo2bobo2bo14bo3bo29bo5b2o2bo43b2o34bob2o
6bo3bo5bo14bo35bo5b2obo42bob2o32b2o2bo6b2ob3o18bo2bo38b6o41bo2b2o30bo
5bo5b2obob2o16bo2b3o42b2o39bobo2b2o4b3o3b3o16bo2bo7b2o2b3o16bo4b3o38b
3ob2o37bo6b2o3bo2bobo2bo15bo33bo6b2o43b2o35bo3b2o3b2o2bo2bobo2bo14bo3b
o29bo5b2o2bo43b2o34bob2o6bo3bo5bo14bo102b3o\$117bob5o72bo4bo2bo31bo3bo
4b4o27bo13bo2bo22bo9bo9bob2ob3o12bo3b2o2bo31bobobo6b2o27bo12bo3b2o21bo
8bobo7b3o4b2o12bo2bo3bo32bo9b2obo26bo12b5obo4b3o3b3o7bo7b2o3bo26b4o3b
3o30bo9b5o25bo11bo2bo3b2o3bobo3bobo7bo6bo4bo27bob2o5b2o29bo9b2o2b2o24b
o11bo6bob4ob2ob5o6bo5b3o31bo2b2o6bo28bo14b2o23bo10bo2bo4bob2obobo13bo
4bo2bo31bo3bo4b4o27bo13bo2bo22bo9bo9bob2ob3o12bo3b2o2bo31bobobo6b2o27b
o12bo3b2o21bo8bobo7b3o4b2o12bo2bo3bo32bo9b2obo26bo12b5obo4b3o3b3o7bo7b
2o3bo26b4o3b3o30bo9b5o25bo11bo2bo3b2o3bobo3bobo7bo6bo4bo27bob2o5b2o29b
o9b2o2b2o24bo11bo6bob4ob2ob5o6bo5b3o110b2ob2o\$118b3o35bobo35b3o5b2o15b
o14b7o33b3o14b2o21b3o10b2o7b3obobo11b3o5b2o11b3o16b3obobo6bo26b3o14b3o
20b3o9b2o7b2o5b2o10b3o3b3o12bo18b3o10b2o25b3o15b3o19b3o9b3o25b3o3bo3bo
10bo18b3o9b4o24b3o12b3o3bo4b3o3b3o5b3o7bo3bo25b3ob2o3b3o9bo18b3o37b3o
11b3o4b2o2b2ob2ob3ob2o3b3o22bo14b6o5b2o6b2obo17b3o14bo22b3o11bo6bobo3b
obo10b3o5b2o15bo14b7o33b3o14b2o21b3o10b2o7b3obobo11b3o5b2o11b3o16b3obo
bo6bo26b3o14b3o20b3o9b2o7b2o5b2o10b3o3b3o12bo18b3o10b2o25b3o15b3o19b3o
9b3o25b3o3bo3bo10bo18b3o9b4o24b3o12b3o3bo4b3o3b3o5b3o7bo3bo25b3ob2o3b
3o9bo18b3o37b3o11b3o4b2o2b2ob2ob3ob2o3b3o22bo96bobo\$157b2o34bo21b5o13b
o18b2o2b2o15bo39bo23b4o12bo21b6o12bo39bo39bo20b3o4b3o9bo20b2o3b2o12bo
39bo39bo22b2o15bo20bob2obo13bo39bo33b2o4bo22bob2o13bo19b2o18bo39bo27bo
6b3o2bo21b2o2bo13bo19b5o15bo39bo23bo3b2o10bo21b5o13bo18b2o2b2o15bo39bo
23b4o12bo21b6o12bo39bo39bo20b3o4b3o9bo20b2o3b2o12bo39bo39bo22b2o15bo
20bob2obo13bo39bo33b2o4bo22bob2o13bo19b2o18bo39bo27bo6b3o2bo21b2o2bo
30bo65bobo\$118b3o73b3o5b2o10bo2b3o7b2o5b7o26b2o5b3o14b2o14b2o5b3o10b2o
5b2o3b4o4b2o5b3o5b2o10bo3b2o7b2o5b3obobo6bo19b2o5b3o14b3o13b2o5b3o9b2o
13b2o4b2o5b3o3b3o11b2o3b2o6b2o5b3o10b2o18b2o5b3o15b3o12b2o5b3o9b3o6b3o
bo7b2o5b3o3bo3bo9bob3o8b2o5b3o9b4o17b2o5b3o12b3o3bo11b2o5b3o7bo3bo5b2o
3b2o6b2o5b3ob2o3b3o7bo2b3o8b2o5b3o30b2o5b3o11b3o4b2o10bobo4b3o17bo2bo
2bo6b2o5b6o5b2o5bo2b3o9b2o5b3o14bo15b2o5b3o11bo6b3o3bo5b2o5b3o5b2o10bo
2b3o7b2o5b7o26b2o5b3o14b2o14b2o5b3o10b2o5b2o3b4o4b2o5b3o5b2o10bo3b2o7b
2o5b3obobo6bo19b2o5b3o14b3o13b2o5b3o9b2o13b2o4b2o5b3o3b3o11b2o3b2o6b2o
5b3o10b2o18b2o5b3o15b3o12b2o5b3o9b3o6b3obo7b2o5b3o3bo3bo9bob3o8b2o5b3o
9b4o17b2o5b3o12b3o3bo11b2o5b3o7bo3bo5b2o3b2o6b2o5b3ob2o3b3o7bo2b3o8b2o
5b3o30b2o5b3o11b3o4b2o10bobo4b3o17bo2bo2bo6b2o21b3o64bo\$117bob5o14b2o
56bo4bo2bo10b2o10b2o7bo3bo4b4o18b2o7bo13bo2bo13b2o7bo9bo8bob2o8b2o7bo
3b2o2bo10b4o8b2o7bobobo6b2o18b2o7bo12bo3b2o12b2o7bo8bobo9b2obo6b2o7bo
2bo3bo10b2o3bo7b2o7bo9b2obo17b2o7bo12b5obo11b2o7bo7b2o3bo8bob2o5b2o7b
4o3b3o8b2o3bo7b2o7bo9b5o16b2o7bo11bo2bo3b2o10b2o7bo6bo4bo7bob3o6b2o7bo
b2o5b2o6b6o8b2o7bo9b2o2b2o15b2o7bo11bo6bobo9b2o7bo5b3o10b2o10b2o7bo2b
2o6bo19b2o7bo14b2o14b2o7bo10bo2bo4bob2o8b2o7bo4bo2bo10b2o10b2o7bo3bo4b
4o18b2o7bo13bo2bo13b2o7bo9bo8bob2o8b2o7bo3b2o2bo10b4o8b2o7bobobo6b2o
18b2o7bo12bo3b2o12b2o7bo8bobo9b2obo6b2o7bo2bo3bo10b2o3bo7b2o7bo9b2obo
17b2o7bo12b5obo11b2o7bo7b2o3bo8bob2o5b2o7b4o3b3o8b2o3bo7b2o7bo9b5o16b
2o7bo11bo2bo3b2o10b2o7bo6bo4bo7bob3o6b2o7bob2o5b2o6b6o8b2o7bo9b2o2b2o
15b2o7bo11bo6bobo9b2o7bo5b3o10b2o10b2o24bo51bobo\$111b2o3b2o6bo8bo5bo
61bo2bo38b6o41bo2b2o30bo5bo4bo2bo20bo2b3o10b2o30b2o39bobo2b2o29bo2bo5b
o4b2o18bo4b3o38b3ob2o37bo6b2o27bo10bo4b2o16bo6b2o43b2o35bo3b2o3b2o25bo
3bo9b2o18bo5b2o2bo7b3o33b2o34bob2o6b2o23bo35bo5b2obo42bob2o32b2o2bo8bo
21bo2bo38b6o41bo2b2o30bo5bo4bo2bo20bo2b3o10b2o30b2o39bobo2b2o29bo2bo5b
o4b2o18bo4b3o38b3ob2o37bo6b2o27bo10bo4b2o16bo6b2o43b2o35bo3b2o3b2o25bo
3bo9b2o18bo5b2o2bo7b3o33b2o34bob2o6b2o23bo49b2o51b2obo\$111b2o4b3obo3bo
7bo4bo4b2o56b2ob2o38bo2b2o40bo2b2o32bo4bo4bo2bo20bo4bo38bob3o39bo5bo
30bo2b2o5b2o2bo19b2obob3o38b5o37bo3bob3o28bo5bo8b2o17bo2b2o2b3o41b2o
36bobo2b5o26b3o12bobo18bo7bo42b2o35b2o2bo4b2o24bobo39b4o42bobo34bo2bo
6b2o22b2ob2o38bo2b2o40bo2b2o32bo4bo4bo2bo20bo4bo38bob3o39bo5bo30bo2b2o
5b2o2bo19b2obob3o38b5o37bo3bob3o28bo5bo8b2o17bo2b2o2b3o41b2o36bobo2b5o
26b3o12bobo18bo7bo42b2o35b2o2bo4b2o24bobo103bo\$118b2o2bobo12b3o3b2o58b
2o40b2o42b4o34b3o7b2o22b5o40b2o41bo2b2o32bo10b2o22bo3b2o38bo2bo39bobo
2b2o30bo3bo5bo2b2o19bob2o85bo3b3o42b2obo21bo3bo43bo72b2o12bobo70b2o36b
2o7bo25b2o40b2o42b4o34b3o7b2o22b5o40b2o41bo2b2o32bo10b2o22bo3b2o38bo2b
o39bobo2b2o30bo3bo5bo2b2o19bob2o85bo3b3o42b2obo21bo3bo43bo72b2o12bobo
88b2o\$134bob2ob2o77bo144b2o41bo42bo37b2o78bo89bo160bo22bo135bobo158bo
144b2o41bo42bo37b2o78bo89bo160bo22bo135bobo\$136bo81bo759bo159bo759bo\$
46bo86bo2b3o11b2o\$45bobo65b2o18b2o2b2o9bo4bo\$45bobo65b2o20bo2bo15bo\$
46bo88b3o10bo5bo\$127b2o20b6o\$112b2o13bobo\$112b2o13bob2o\$128b2o\$128bo
13b2o1802b2o\$141bobo1802bobo\$128bo13bo67b2o1736bo\$128b2o80b2o1736b2o\$
112b2o13bob2o29b2o2bo4b2o16b2o3b2o8bo\$112b2o13bobo30bob2o6b2o14bo2bobo
2bo7bo2b2o\$127b2o20bo11bo6bobo14bo9bo5bo5bo3b2o\$147b3o11b3o4b2o14b2o9b
2o5bobo2b2o2b2o\$113b2o31bo38bo9bo6bo3b2o\$113b2o32b3o11b3o4b2o16bo2bobo
2bo9b3o\$149bo11bo6bobo16b2o3b2o\$135bo24bob2o6b2o32b3o\$134b3o23b2o2bo4b
2o31bo3b2o\$134bob2o35bo12b2o14bobo2b2o2b2o\$135b3o11b2o22b2o11b2o13bo5b
o3b2o\$135b3o11bobo20bobo27bo2b2o\$131b3ob3o13bo50bo\$135b3o11b3o5bo52b2o
\$135b2o20b3o50b2o\$113b2o45bo\$113b2o19bo22b3o\$122bo10bo15b3o5bo1813b2o\$
118b2o2bo10bo17bo1819b2o\$112b2o3bo5bo25bobo\$112b2o2b2o2bobo12bo13b2o
1812b4o\$117b2o3bo38b2o1784b2o14bo2b2o4b2o\$118b3o41b2o1783b2o15bo2b2o3b
2o\$161bo1802bo2bo\$118b3o1844b2o\$117b2o3bo\$112b2o2b2o2bobo1842b2o\$112b
2o3bo5bo48b2o1790bo2bo\$118b2o2bo13b2o34b2o1790bo2b2o3b2o\$122bo13bobo
1809bo14bo2b2o4b2o\$113b2o23bo16b3o3bo1781b2o4b2o12b4o\$113b2o23b2o13b5o
2bobo10b2o1767bo\$152b2o3b2o3bo10b2o1768b2o3bo22b2o\$153b2o3bo2bo1785bob
o21b2o\$154bo3b3o1786bobo\$1948bo\$154bo3b3o1866b2o\$153b2o3bo2bo1865b2o\$
152b2o3b2o3bo10b2o1873bo\$153b5o2bobo10b2o1859b2o9b2o3bo\$153bob3o3bo
1864b2o5bobo9b2obob2o\$151b2o1873b2o5bo10bo6b2o\$145b2o4b3o18b2o1859b3o
9b2obob2o\$145b2o3bo3bo17b2o1871b2o3bo\$149bo5bo1892bo\$150b2ob2o1789b2ob
o3bob2o\$1944bo2bo3bo2bo78b3o\$150b2ob2o1790b3o3b3o72b2o5bo17b2o\$149bo5b
o1870b2o5bobo15b2o\$150bo3bo1879b2o\$151b3o\$151b3o1873b2o\$2027b2o\$1947b
2ob2o\$1948bobo\$1948bobo\$1949bo75b2o5b2o\$1971b2o52b2o5b2o\$144b2o7b2o
1816b2o\$144bob2o3b2obo1794b2o\$144bo3bobo3bo1793b4o7b2o\$144b2o2bobo2b2o
1792bobobo6bo2b2o9b2o\$145b3o3b3o1793b2ob3o4b6o9b2o\$146bo5bo1797b2obo5b
4o\$1950b2obo2\$1950b2obo\$1950b2obo5b4o\$1949bo2bo4b6o9b2o\$145b2o5b2o
1796b2o6bo2b2o9b2o\$145b2o5b2o1796b2o7b2o\$1946bo4bo\$1945b3o3b3o17b2o51b
3o5b3o\$151bo2bo1790bo2bobo2bo17b2o50b2ob2o3b2ob2o\$141b3o7bo1795b2ob2o
71b2obobobobob2o\$127b2o11bo4bo9bo1868bo3bobo3bo\$127b2o10bo5bo8b2o1868b
o2bo3bo2bo\$140bo8bo1875b3o3b3o\$141b2o8b2o1792bo7bo\$1946bobobobo\$141b2o
8b2o1793bobobobo\$140bo8bo3bo1791bob2ob2obo\$127b2o10bo5bo4bo2bo1791b2o
5b2o\$127b2o11bo4bo4bo2bo1878b2o\$141b3o7b2o1879b2o\$1986b2o\$1986b2o2\$
190b2o1801b2o9b2o3b2o\$189bo2bo1792b2o5bobo8bob2ob2obo\$184bo7bo1792b2o
4b2obo8bo7bo\$183bobo3bo2bo1799b2o9bob2ob2obo\$133bo48b2ob2ob2ob2o1800bo
10b2o3b2o\$131b3o52bobo1758b2ob2o\$130bo54b2ob2o1758bobo42bo\$130b2o1816b
obo41b2o\$144bo1804bo35b2o4b2obo15b2o\$142b3o1826b2o12b2o5bobo15b2o\$125b
2o14bo1829b2o20b2o\$126bo14b2o40b3o3b3o\$126b2obo17b2o33bo9bo1764b2o27b
2o\$129bo17bo34bo3bobo3bo1754b2o6b2ob2o12b2o12b2o\$130b2o13bobo35b3o3b3o
1755b2o6bo2bo13b2o\$126b3o2b2o12b2o37bo5bo1764bo2bo\$128b2o1826b2o\$126bo
2bo4bo\$125bobobo3bo1822b2o\$124bo4bo1825bo2bo\$116b2o6bo2bob3o5bo1817bo
2bo13b2o\$115bobo7bo3b3ob2o3bo64b2o5b2o1743b2ob2o12b2o\$115bo10b2o5bo4bo
64b2o5b2o1745b2o\$114b2o10b2o3b2o2bobo\$126bo4bo1839b2o\$131b3o51b2ob2o
1781b2o\$127b2o57bobo\$186bobo\$123b2o2b3o57bo\$124bobobo1817bo5bo\$125b4o
1816b3o3b3o\$120b2o4bo1817b2obo3bob2o\$119bobo\$119bo\$118b2o7bobo1817bo3b
o\$128b2o1817bo3bo\$128bo\$202b2o7b2o\$202bob2o3b2obo\$118b2o82bo3bobo3bo\$
119bo51b2o5b2o22b2o2bobo2b2o\$119bobo49b2o5b2o23b3o3b3o\$120b2o82bo5bo2\$
124bob2o\$124bob2o1819b2ob2o\$172bo5bo1769bobo\$133bo37b3o3b3o1768bobo\$
123b2o4bob2obo35bo2b2ob2o2bo22b2o1744bo\$123b2o2bo5bo36bo3bobo3bo22b2o
1766b2o\$114b2o11bo5bo38bobobobo1793bo\$115bo7b2o6b2o4b2o\$115bobo5b2o4bo
bo5b2o30b2ob2o3b2ob2o1780b2o\$116b2o11b2o40bo7bo1767b2o12bo2bo7b2o\$
1947b2o11b2o2bo7b2o\$1961bo2bo\$1962bo2\$145b2o25bo1789bo\$145bobo23b3o
1787bo2bo\$147bo22bo3bo1785b2o2bo7b2o\$147b2o20bo5bo1785bo2bo7b2o\$141b2o
26bo5bo1786b2o\$141bo28bo3bo1772b2o\$142b3o1801b3o23bo\$144bo25bo3bo1771b
3o22b2o\$130b2o37bo5bo1770b2o2bo\$130bo38bo5bo2b2o1767bobo\$131b3o36bo3bo
3b2o1767b3o\$133bo37b3o\$145b2o7b2o16bo\$143b2o2bo6b2o\$143b6o4bo2bo\$133bo
9b4o5bob2o\$131b3o18bob2o1789b2o5b2o\$130bo1813bo2bo3bo2bo\$131b3o18bob2o
1791b2ob2o\$133bo9b4o5bob2o14b2o1774bobobobo\$143b6o4b3ob2o11bo1775bobob
obo\$143b2o2bo6bobobo12b3o1770bo9bo\$145b2o7b4o15bo1769bo11bo\$155b2o\$
1945bob2ob2obo\$1947b2ob2o\$1946bo5bo\$1947b2ob2o\$1948bobo\$1948bobo\$1949b
o\$1971b2o\$1971b2o2\$1964b2o\$1947b2o15bobo5b2o\$1947b2o15bob2o4b2o\$1965b
2o\$1965bo2\$1965bo\$1965b2o\$138b2o1824bob2o4b2o\$140bo1803b2ob2o15bobo5b
2o\$125b2o10b2o2bo10b2o1793b3o14b2o\$125b2o11bo2bo10b2o1789b5obo\$139bobo
1802bobo24b2o\$139b2o1806bobo21b2o\$1948bo\$139b2o1807bo\$139bobo\$125b2o
11bo2bo\$125b2o10b2o2bo\$140bo\$138b2o\$1947b2ob2o\$1946bo5bo2\$1945bo7bo\$
1945bo2bobo2bo\$1945b3o3b3o6\$172b4o\$171b2o2bo14b2o1755b2ob2o\$170b2o2bo
15b2o1756bobo\$171bo2bo1773bobo\$172b2o1775bo\$1971b2o\$172b2o1797b2o\$171b
o2bo\$163b2o5b2o2bo15b2o\$163b2o6b2o2bo14b2o1755b6o5b4o10b2o\$172b4o1771b
4o7b2obo10b2o\$1950b2obo7bo\$1952b2o5b2o2\$1952b2o5b2o\$1950b2obo7bo\$1950b
o7b2obo10b2o\$1950b3o5b4o10b2o3\$1946bo5bo18b2o\$1945b3o3b3o17b2o\$1945bob
2ob2obo\$1944b2o7b2o\$1944b2o7b2o\$1944b3o5b3o\$1946b3ob3o\$1948bobo\$1945bo
2bobo2bo\$1944bo2bo3bo2bo\$1945b2o5b2o11\$1947b2ob2o\$1948bobo\$1948bobo\$
1949bo\$1971b2o\$1971b2o2\$1957b2o\$1947b2o7bobo13b2o\$1947b2o7bo15b2o\$
1956b3o4\$1956b3o\$1956bo15b2o\$1956bobo13b2o\$1957b2o2\$1971b2o\$1971b2o5\$
91b2o13bo7bo1831bo5bo\$90bo2bo10b3o5b3o1830b3o3b3o\$89bobobo9bo7bo14b2o
1817bob2ob2obo\$88b3obo10b2o6b2o13bobo1818b2ob2o\$88b3o29bo6b3o1817b2ob
2o\$118b2ob2ob3ob2o1817b2ob2o\$118b2ob2ob5o\$120bo5bo\$90b2o29b2ob2o\$90b2o
3\$120bo5bo\$119b2o5b2o\$118bob2o3b2obo\$118bob2o3b2obo1818b2ob2o\$119b3o3b
3o1820bobo\$119b3o3b3o1820bobo\$1949bo\$1971b2o\$1970bobo\$109bo1860bo\$107b
3o1862bo\$106bo1840b2o12b2o2bo3bo3bo\$106b2o1839b2o12bob2o7b2o\$1962bo\$
1962b3o4b2o\$121b2ob2o\$122bobo1837b3o4b2o\$109bo12bobo1837bo\$107b3o13bo
1837bob2o7b2o\$106bo1854b2o2bo3bo3bo\$106b2o1839bobo22bo\$1948bo21bo\$
1948b2o20bobo\$1948b2o21b2o\$1947bo2bo\$109bo1837b3o\$107b3o\$106bo\$106b2o
4\$1945bo7bo\$109bo1835b2o5b2o\$107b3o1835b3o3b3o\$106bo1840b2ob2o\$106b2o
1839bo3bo\$1944b2o7b2o\$1944b2o7b2o\$1948bobo\$1944bo2bo3bo2bo\$109bo1835b
3o3b3o\$107b3o1837bo3bo\$106bo1840b2ob2o\$106b2o1840bobo\$1948bobo\$1949bo\$
1971b2o\$1971b2o\$109bo\$107b3o1854bo\$106bo1840b2o15b2o6b2o\$106b2o1839b2o
16b2o5b2o\$1960b2o2b2o4\$109bo1850b2o2b2o\$107b3o1836b2o17b2o5b2o\$106bo
1838b3o16b2o6b2o\$106b2o1836b2o2bo15bo\$1944bo2bo\$1943bo4b2o21b2o\$1948b
2o3bo17b2o\$1944bobobo\$109bo\$107b3o\$106bo\$106b2o\$1945bo7bo\$1944bo2bo3bo
2bo\$1948bobo\$1948bobo\$109bo1838bobo\$107b3o1834bo2bo3bo2bo\$106bo1838b3o
3b3o\$106b2o5\$109bo\$107b3o\$106bo1840b2ob2o\$106b2o1840bobo\$1948bobo\$
1949bo\$1971b2o\$1971b2o\$109bo1845bo\$107b3o1846bo3bo\$106bo1840b2o2b2o8bo
10b2o\$106b2o1839b2o2bo5b2o2bo10b2o\$1951bobo5b2o\$1952b2o3b3o2\$1952b2o3b
3o\$109bo1841bobo5b2o\$107b3o1841bo5b2o2bo10b2o\$106bo1844b2o8bo10b2o\$
106b2o1848bo3bo\$1955bo\$1971b2o\$1946bo5bo18b2o\$1945b3o3b3o\$109bo1834b2o
2bobo2b2o\$107b3o1834b2ob2ob2ob2o\$106bo1840b2ob2o\$106b2o1837bobo3bobo\$
1944bo2bo3bo2bo\$1947bo3bo\$1944bobo5bobo\$1945bo7bo\$109bo\$107b3o\$106bo\$
106b2o5\$109bo\$107b3o\$106bo1840b2ob2o\$106b2o1840bobo\$1948bobo\$1949bo\$
1971b2o\$1971b2o\$109bo\$107b3o\$106bo1840b2o8b3o12b2o\$106b2o1839b2o8bo3bo
10b2o\$1957bo4bo\$1958bo3bo2\$1958bo3bo\$109bo1847bo4bo\$107b3o1847bo3bo10b
2o\$106bo1850b3o12b2o\$106b2o2\$1971b2o\$1971b2o2\$109bo\$107b3o\$106bo\$106b
2o\$1946bo5bo\$1945b3o3b3o\$1944b2o2bobo2b2o\$1943bob4ob4obo\$109bo1835b3o
3b3o\$107b3o1834b3o5b3o\$106bo\$106b2o5\$109bo\$107b3o\$106bo1840b2ob2o\$106b
2o1840bobo\$1948bobo\$1949bo\$1971b2o\$1971b2o\$109bo\$107b3o1852bo3b3ob3o\$
106bo1840b2o12bobo2b4o3bo\$106b2o1839b2o12bo3b2o6bo\$1962bo2bo3b2obo\$
1963b3o3bo2\$1963b3o3bo\$109bo1852bo2bo3b2obo\$107b3o1851bo3b2o6bo\$106bo
1841b2o11bobo2b4o3bo\$106b2o1839b3o12bo3b3ob3o2\$1971b2o\$1971b2o\$1947b4o
\$109bo1837b3o\$107b3o\$106bo\$106b2o5\$109bo1834b3o5b3o\$107b3o1834b3o5b3o\$
106bo1838b2o5b2o\$106b2o1839bo3bo\$1945bo2bobo2bo\$1944bo3bobo3bo\$1945bo
2bobo2bo\$1945b3o3b3o\$109bo\$107b3o\$106bo1840b2ob2o\$106b2o1840bobo\$1948b
obo\$1949bo\$1971b2o\$1971b2o\$109bo\$107b3o\$106bo1840b2o14b2o7b2o\$106b2o
1839b2o15b2o6b2o\$1960b5o\$1960b4o2\$1949b3o8b4o\$109bo1838b6o6b5o\$107b3o
1838b2o2b3o9b2o6b2o\$106bo1839b2o4b3o8b2o7b2o\$106b2o1837b2o6b2o\$1944bo
2bo5b2o\$1944bo2bo3b3o17b2o\$1945bo3b4o18b2o\$1945bo3b3o\$109bo1836bo2bo\$
107b3o\$106bo\$106b2o2\$1945bo7bo\$1943bob2o5b2obo\$1943bo3b2ob2o3bo\$109bo
1834bo3bobo3bo\$107b3o1835b3o3b3o\$106bo\$106b2o5\$109bo\$107b3o\$106bo1840b
2ob2o\$106b2o1840bobo\$1948bobo\$1949bo\$1971b2o\$1971b2o\$109bo\$107b3o1843b
ob2o\$106bo1840b2o3bo2b2o2b3o10b2o\$106b2o1839b2o3bo6b2o11b2o\$1952b2o3b
3o\$1954bo3bo2\$1954bo3bo\$109bo1842b2o3b3o\$107b3o1842bo6b2o11b2o\$106bo
1845bo2b2o2b3o10b2o\$106b2o1845bob2o2\$1971b2o\$1971b2o\$1946bo5bo\$109bo
1835b3o3b3o\$107b3o1834bo2b2ob2o2bo\$106bo1837bo3bobo3bo\$106b2o1838bobob
obo2\$1943b2ob2o3b2ob2o\$1945bo7bo2\$109bo\$107b3o\$106bo\$106b2o5\$109bo\$
107b3o\$106bo1840b2ob2o\$106b2o1840bobo\$1948bobo\$1949bo\$1971b2o\$1971b2o\$
109bo\$107b3o1849bo3bo\$106bo1840b2o9bo5bo7b2o\$106b2o1839b2o9bo13b2o\$
1958b2o3bo\$1960b3o2\$1960b3o\$109bo7bo7bo37b2o1793b2o3bo\$107b3o5b3o5b3o
39bo1792bo13b2o\$106bo7bo7bo27b2o10b2o2bo1791bo5bo7b2o\$106b2o6b2o6b2o
26b2o11bo2bo1792bo3bo\$164bobo8bo\$164b2o9b3o1793b2o\$178bo1792b2o\$153b2o
9b2o9b3o\$151bo3b2o7bobo8bo\$151bo4bo6bo2bo\$151bo3b2o5b2o2bo\$153b2o10bo\$
163b2o\$1946bo5bo\$1945b3o3b3o\$24b2o1918b2ob2ob2ob2o\$24b2o1917b3o7b3o\$
30b3o132bo\$29bo3bo131b3o1777bo7bo\$29b2ob2o134bo\$167b2o\$29b2ob2o120bo\$
31bo122b3o1790b2ob2o\$114b2o5b2o34bo\$109bo4b2o5b2o33b2o1789b2ob2o\$107b
3o\$24bo7bo73bo1840b2ob2o\$23bo2bo3bo2bo72b2o50b2o1788bobo\$27bobo126bo3b
o5b2o9b2o1769bobo\$27bobo125bo5bo3bo2bo4b3o2bo1770bo\$27bobo125bo4bo5bo
4bo2b5o1792b2o\$23bo2bo3bo2bo121bo2bo7bo2b4o1798b2o\$24b3o3b3o76bo46bobo
8bob2o3bo\$107b3o47bo8b2obob3o7b2o1779bobo2b2o\$106bo61bo3bo8bobo1763b2o
12bo3bob3o2b2o\$106b2o57b3o15bo1763b2o13bo6b2ob2o\$166bo16b2o1778b5obo\$
114bo7bo1843b3o\$114b2o5b2o\$114b3o3b3o1843b3o\$26b2ob2o78bo6b2ob2o45b2o
1795b5obo\$27bobo77b3o6bo3bo22b2o21b2o1794bo6b2ob2o\$27bobo76bo6b2o7b2o
20bo1804bo11bo3bob3o2b2o\$28bo77b2o5b2o7b2o17b3o1804b2o12bobo2b2o\$117bo
bo21bo35b2o1768b3o\$113bo2bo3bo2bo53bobo1766b2ob2o20b2o\$114b3o3b3o56bo
1766b2ob2o20b2o\$179b2o1766bob2o\$109bo63b2o1773bo\$107b3o63bo\$106bo7b2o
25b2o31b3o\$106b2o6b2o25b2o33bo2\$132b2o\$130b2o2bo7b2o\$130b6o6b2o\$109bo
20b4o\$107b3o1834b3o5b3o\$106bo1836b2ob2o3b2ob2o\$106b2o1835b2obobobobob
2o\$130b4o1810bo3bobo3bo\$130b6o6b2o1800bo2bo3bo2bo\$130b2o2bo7b2o1801b3o
3b3o\$132b2o\$109bo\$107b3o31b2o\$106bo18bobo13b2o1804b2ob2o\$106b2o18b2o
1820bobo\$126bo1821bobo\$1949bo\$1971b2o\$1971b2o\$109bo1851bo\$107b3o20b2o
1827bo2bo\$106bo23b2o1815b2o10b5o8b2o\$106b2o1839b2o10b3ob2o7b2o\$1960b2o
bo\$1961b2o2\$1951b2o8b2o\$109bo1838bob3o7b2obo\$107b3o1838bo2bobo5b3ob2o
7b2o\$106bo1841b3obo6b5o8b2o\$106b2o1837b2ob2obobo5bo2bo\$1944bo2bob5o7bo
\$1944bo2bob2ob2o17b2o\$1945b2o3b2o19b2o\$1947b2o\$109bo1838bo\$107b3o\$106b
o\$106b2o1837b2o5b2o2\$162bo3b3o1775bo9bo\$161bobo2b5o3b2o1768bo3bobo3bo\$
161bo3b2o3b2o2b2o1768bo3bobo3bo\$109bo52bo2bo3b2o1774bobo3bobo\$107b3o
53b3o3bo1776bo5bo\$106bo\$106b2o55b3o3bo\$162bo2bo3b2o\$147b2o12bo3b2o3b2o
2b2o\$147b2o12bobo2b5o3b2o\$162bo3b3o3\$1947b2ob2o\$1948bobo\$152bo1795bobo
\$130b3o19b3o1794bo\$130bo2bo21bo1815b2o\$130bo23b2o1815b2o\$130bo10bo\$
131bobo7b3o1811bo3b2o\$144bo1802b2o4b2obob3o11b2o\$143b2o1802b2o4bo4b3o
11b2o\$156bo3bo1792bo3bo\$155b5obo1792b3o\$154b3o4b2o\$154b2ob5o1792b3o\$
156b3o1794bo3bo\$1953bo4b3o11b2o\$158bo1794b2obob3o11b2o\$154bo2b3o1795bo
3b2o\$153b2obo3bo7b2o\$147b2o3b2ob3obo2b2o4bobo1800b2o\$147b2o3b3ob2o4b2o
6bo1800b2o\$152b3o15b2o\$109bo1836bo5bo\$107b3o1835b3o3b3o\$106bo1837b2o2b
obo2b2o\$106b2o46bo1789bo3bobo3bo\$154bob3o1785bob2o3b2obo\$155bo3bo1784b
2o7b2o\$126b2o3b2o8bo17bo\$125bo2bobo2bo7bo2b2o10b2obo4b2o\$109bo14bo9bo
5bo5bo11bo5bobo\$107b3o13b2o9b2o5bobo2b2o18bo\$106bo17bo9bo6bo3b2o3bo15b
2o\$106b2o17bo2bobo2bo9b3o4b3o7b2o\$126b2o3b2o20bo6bo\$143b3o4b3o8b3o\$
141bo3b2o3bo12bo\$125b2o14bobo2b2o\$109bo15b2o13bo5bo\$107b3o31bo2b2o\$
106bo34bo1805b2ob2o\$106b2o1840bobo\$1948bobo\$1949bo\$1971b2o\$1971b2o\$
109bo1851b2o\$107b3o1850bo\$106bo1840b2o10bo2b2o8b2o\$106b2o1839b2o10bo2b
o9b2o\$1959bobo\$1960b2o2\$1960b2o\$109bo1849bobo\$107b3o1849bo2bo9b2o\$106b
o1852bo2b2o8b2o\$106b2o1852bo\$1961b2o\$1949bo21b2o\$1949bo21b2o2\$109bo\$
107b3o1839bo\$106bo1842bo\$106b2o3\$1945b3o3b3o\$1945b3o3b3o\$109bo1834bob
2o3b2obo\$107b3o1834bob2o3b2obo\$106bo1838b2o5b2o\$106b2o1838bo5bo3\$1947b
2ob2o\$1948bobo\$109bo1838bobo\$107b3o1838bobo\$106bo1840b2ob2o\$106b2o
1840bobo\$1948bobo\$1949bo\$1971b2o\$1971b2o\$109bo1853bo\$107b3o1853bo2b2o\$
106bo1840b2o13bo5bo3b2o\$106b2o1839b2o14bobo2b2o2b2o\$1963bo3b2o\$1965b3o
2\$1965b3o\$109bo1853bo3b2o\$107b3o1853bobo2b2o2b2o\$106bo1855bo5bo3b2o\$
106b2o1840b3o12bo2b2o\$1942b2o4b2o13bo\$1948b2o21b2o\$1947bobo21b2o\$1947b
obo\$109bo1838bo\$107b3o\$106bo\$106b2o5\$109bo\$107b3o1835bo7bo\$106bo1837b
4o3b4o\$106b2o1836bo3bobo3bo\$1945bo2bobo2bo\$1945b3o3b3o3\$109bo\$107b3o\$
106bo1840b2ob2o\$106b2o1840bobo\$1948bobo\$1949bo\$1971b2o\$1971b2o\$109bo
1850bo\$107b3o1850b2o\$106bo1840b2o9bob3o9b2o\$106b2o1839b2o13b2o8b2o\$
1961b2o\$1961bo2\$1950bo10bo\$109bo1839bob2o8b2o\$107b3o1838b3ob2o8b2o8b2o
\$106bo1844b3o4bob3o9b2o\$106b2o1838bo13b2o28bo\$1945bobo3b2o7bo28bobo\$
1944b2ob6o18b2o16bobo\$1948bo22b2o15b2ob2o\$1947b2ob2o\$109bo46b2o5b2o\$
107b3o46b2o5b2o\$106bo\$106b2o\$1945b3o3b3o\$1944bo9bo\$1944bo3bobo3bo56bo\$
1945b3o3b3o32bo7bo15bobo\$109bo47bo5bo1782bo5bo31bob2o5b2obo13bobo\$107b
3o46b3o3b3o1819bo3b2ob2o3bo14bo\$106bo48bo2b2ob2o2bo1819bo3bobo3bo\$106b
2o47b3o5b3o1820b3o3b3o4\$28bo\$27b2o80bo7bo7bo\$26b3obo9b2o65b3o5b3o5b3o\$
25b2o13b2o64bo7bo7bo1824b2ob2o32b4o11b2o\$16bo9b2o78b2o6b2o6b2o1824bobo
32b2o3bo11bo\$14b3o10bo128b3o1789bobo32bo11b2obo\$13bo141bo3bo1789bo33b
4ob2o5b2ob2o\$14b3o10bo10bo116b2ob2o1811b2o10b2o\$16bo9b2o8b2obo116bobo
1812b2o10b2obo8b2ob2o\$25b2o8b2ob3o1916b2o26b3o8bobo\$26b3obo5bo2bo116bo
bo1796b5o25b3o8bobo\$27b2o8b2o116b2ob2o1787b2o5bo4bo12b2o12bo10bo\$28bo
126bo3bo3b2o1782b2o5bo2b3o12b2o11bobo\$156b3o4b2o1789b2o2bo26b2obo\$
1956b2o30bo\$1988b2o\$1956b2o\$1954b2o2bo\$1954bo2b3o12b2o\$1954bo4bo12b2o\$
1955b5o\$1957b2o\$1971b2o\$1971b2o2\$109bo60b2o\$107b3o50b2o6b2ob2o14b2o
1757bo5bo\$106bo53b2o6bo2bo15b2o1756b3o3b3o\$106b2o60bo2bo1772bo2b2ob2o
2bo96b2o\$5bo163b2o1773b3o5b3o96b2o\$5b3o\$8bo160b2o\$7b2o159bo2bo\$109bo
58bo2bo15b2o\$107b3o58b2ob2o14b2o\$106bo27bobo2b2o29b2o\$106b2o11b2o12bo
3bob3o4b2o\$119b2o13bo6b2o3b2o\$135b5obo\$138b3o2\$109bo28b3o\$107b3o25b5ob
o\$106bo12b2o13bo6b2o1804b2ob2o\$106b2o11b2o12bo3bob3o1806bobo\$134bobo2b
2o1807bobo\$1949bo\$1971b2o\$1971b2o\$109bo\$107b3o1851b3o\$106bo40b2o1798b
2o11bo4bo6b2o\$106b2o39b2o1798b2o10bo5bo6b2o\$1960bo\$1961b2o2\$1961b2o\$
109bo1850bo\$107b3o1849bo5bo6b2o\$106bo1853bo4bo6b2o\$106b2o1853b3o2\$
1948b2o21b2o\$148bo5bo1793b3o20b2o\$147bobo3bobo1792b2o\$109bo36bo3bobo3b
o1792b2o\$107b3o36bo3bobo3bo1792b2o\$106bo39bo9bo1791bo\$106b2o\$147b2o5b
2o1893b2o\$2049bo\$2050b3o\$5b2o142b2ob2o1791b3o3b3o98bo\$5b2o102bo40bobo
1792bo2bobo2bo\$107b3o39b2ob2o1791b2obobob2o\$106bo43bobo1792b2o5b2o\$
106b2o41b2ob2o\$150bobo\$150bobo\$151bo1795bo3bo\$1947b2ob2o\$109bo1836bobo
bobo\$107b3o1838bobo\$106bo1840b2ob2o\$106b2o1840bobo\$1948bobo\$68b2o23bo
41bo1813bo\$69bo22b3o40b3o1833b2o\$69bob2o18b2obo43bo1832b2o\$70bobo18b3o
15bo27b2o50bo\$60bo30b3o13b3o21b2o54b3o1773b4o\$59bobo30b2o12bo25bo53bo
1760b2o14bo2b2o4b2o\$59bobo39bo4b2o24bobo51b2o1759b2o15bo2b2o3b2o\$58b2o
b2o37b3o30b2o57b2o1770bo2bo\$61bo37b2obo66b2o21bo1772b2o\$58b2o2bo7bo28b
3o67bo20bobo\$59bo2bo7bobo27b2o52bo12bobo20b2o1773b2o\$57bo8b3o40bo44b3o
10b2o1795bo2bo\$57b2o9b3o2bo33b3o47bo1806bo2b2o3b2o\$66b2o4b2o32bo49b2o
1790bo14bo2b2o4b2o\$70b2o34b2o1835b2o4b2o12b4o\$127b2o1813bo\$128bo22bo
1791b2o3bo22b2o\$128bobo19b2o1795bobo21b2o\$129b2o10bo4bo49b2o1749bobo\$
109bo30b2o3b2o30bo18bo1751bo\$65bo3bo37b3o29b2o3b2o29b4o15bobo\$65bo3bo
36bo33b2o4bo27b2o3b2o13b2o\$106b2o33b2o34bo3bo\$177bo3bo\$62b2obo3bob2o
104bo2b2o\$63b3o3b3o103bo3bo\$64bo5bo\$52bo56bo44b2o\$51bobo53b3o44bo\$51bo
bo52bo48b3o1786b2obo3bob2o\$52bo53b2o49bo11b2o1773bo2bo3bo2bo\$143b2o25b
o1774b3o3b3o\$65b2ob2o73bo23b3o\$66bobo71bo3b3o20bo\$66bobo69b3o5bo33b2o\$
67bo41bo27bo43bo\$107b3o27b2o39b3o8bo\$106bo44bo26bo8b3o1757b2ob2o\$106b
2o41b3o34bo1761bobo\$148bo37b2o1760bobo\$148b2o42b2o1755bo\$169b2o21bo
1778b2o\$138b2ob2o26bo20bobo1778b2o\$109bo28b2ob2o11bo12bobo20b2o1757b2o
\$107b3o44b3o10b2o1779b4o7b2o\$106bo38b2o10bo1789bobobo6bo2b2o9b2o\$106b
2o37b2o9b2o21b2o1766b2ob3o4b6o9b2o\$179b2o1769b2obo5b4o\$137b2o1811b2obo
\$123b2o11b2obo15bo\$122bobo12bob4o13bo1793b2obo\$109bo12bo15bo2b3o10b3o
39b2o1752b2obo5b4o\$107b3o11b2o16bo3bo52bo1752bo2bo4b6o9b2o\$106bo32b4o
51bobo1753b2o6bo2b2o9b2o\$106b2o33bo8b3o34b2o5b2o1754b2o7b2o\$152bo21b3o
7bo2b3o1756bo4bo\$138b2o11bo21b2ob2o2b4o2bo2bo1755b3o3b3o17b2o\$138b2o
15b2o15bo4b2ob4ob2o2bo1755bo2bobo2bo17b2o\$155b2o16b6o6b2obo1758b2ob2o\$
109bo64b2o2bo8bo\$107b3o17b2o49b2obo\$106bo19bobo50bobo\$106b2o18bo52bo
1765bo7bo\$125b2o42b2o1775bobobobo\$131b2o37bo1775bobobobo\$132bo34b3o
1775bob2ob2obo\$129b3o35bo1777b2o5b2o\$109bo19bo50b2o\$107b3o71bo\$106bo
71b3o\$106b2o21bo48bo\$127bobo\$128bobo\$128bo2\$109bo30b2o\$107b3o30b2o\$
106bo1840b2ob2o\$106b2o1840bobo\$1948bobo\$123b2o13b2o1809bo\$124bo11bo2bo
1831b2o\$124bobo9bo2bo1831b2o\$109bo15b2o8b2ob2o\$107b3o24b2ob2o1818b2o\$
106bo26b2o3b2o1807b2o6b2ob2o12b2o\$106b2o26b3o2bo1807b2o6bo2bo13b2o\$
139bo1815bo2bo\$136bobo15b2o1800b2o\$137bo16bobo\$156bo1799b2o\$109bo46b2o
1797bo2bo\$93bo13b3o40b2o1803bo2bo13b2o\$92b3o11bo43bo1804b2ob2o12b2o\$
56bo34b2obo11b2o43b3o1803b2o\$55bobo33b3o59bo\$27bo27bobo33b3o45b2o1830b
2o\$26bobo25b2ob2o33b2o45bo1831b2o\$26bobo72bo33bo4b3o\$25b2ob2o70b3o6bo
25b3o4bo\$99b2obo4b3o28bo\$99b3o4bo30b2o50bo1756bo5bo\$100b2o4b2o23b2o54b
3o1755b3o3b3o\$132bo53bo1757b2obo3bob2o\$132bobo51b2o\$133b2o57b2o\$169b2o
21bo1754bo3bo\$24bo5bo78bo59bo20bobo1754bo3bo\$23b3o3b3o75b3o34b2o8bo12b
obo20b2o\$22b2o2bobo2b2o18b3o5b3o44bo37b2o8b3o10b2o\$21bob4ob4obo17b3o5b
3o44b2o49bo\$23b3o3b3o20b2o5b2o95b2o21b2o\$22b3o5b3o21bo3bo120b2o\$52bo2b
obo2bo66b2o16bo\$51bo3bobo3bo66bo15b3o\$52bo2bobo2bo48bo18bobo8bo3bo\$52b
3o3b3o46b3o19b2o7b3obob2o8bo41b2o\$106bo30bo3b2obo8bobo19bo20bo1750b2ob
2o\$106b2o31b4o2bo7bo2bo17bobo3bobo4bo6bobo1751bobo\$56bo5bo70b5o2bo4bo
5bo4bo16bo3b3obobo2bobo5b2o1752bobo\$55b3o3b3o69bo2b3o4bo2bo3bo5bo15b2o
2bo4bobobo3b2o1758bo\$54b2o2bobo2b2o68b2o9b2o5bo3bo15b2ob3o5bo3b2o1783b
2o\$29bo24b2ob2ob2ob2o87b2o16bo4bo1796bo\$27bobo27b2ob2o47bo61b4o6b2o4bo
2bo\$28b2o25bobo3bobo43b3o62b2o6bo6bobo1772b2o\$54bo2bo3bo2bo41bo47b2o
24b3o4b2o1758b2o12bo2bo7b2o\$57bo3bo44b2o46bo24b2o1766b2o11b2o2bo7b2o\$
20bo7bo25bobo5bobo90b3o21bo1781bo2bo\$19bo2bo3bo2bo16bo8bo7bo93bo11b2o
1791bo\$23bobo19bo89bo7b2o25bo\$23bobo19b3o87b3o5bo23b3o1792bo\$23bobo83b
o28bo5b3o20bo1793bo2bo\$19bo2bo3bo2bo77b3o27b2o7bo33b2o7bo1770b2o2bo7b
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1775b2o\$39b3o90bobo43bo7b2o1759b2o\$133b2o57b2o1752b3o23bo\$169b2o21bo
1753b3o22b2o\$139b2o28bo20bobo1753b2o2bo\$36b2o19b2ob2o47bo29b2o13bo12bo
bo20b2o1755bobo\$37bo20bobo46b3o44b3o10b2o1778b3o\$22b2ob2o7b3o10b2o9bob
o45bo34bo15bo26b2o\$23bobo8bo12bobo9bo46b2o27b3o3b2ob2o10b2o26b2o\$23bob
o23bo85b2o5bobobo32bo\$24bo24b2o76b2o8bo4bob2o31b2obo\$128bo12b3o37bo5b
2o\$128bobo6b2o2bobo33b2o2bo5b2o1756b2o5b2o\$109bo19b2o6b6o37bob2o12b2o
1746bo2bo3bo2bo\$107b3o27b3o4b2o32bobob2o3b2o7bo1750b2ob2o\$106bo37b2o
34bo2bo3b2o5bobo1749bobobobo\$106b2o70bob2o12b2o1750bobobobo\$180bob2o
1760bo9bo\$181b2o1760bo11bo2\$1945bob2ob2obo\$109bo1837b2ob2o\$107b3o44b2o
1790bo5bo\$106bo47bo1792b2ob2o\$16b2o5b2o81b2o47b3o1790bobo\$16b2o5b2o
132bo11b2o1777bobo\$135bo7b2o25bo1778bo\$135b3o5bo23b3o1801b2o\$138bo5b3o
20bo1803b2o\$109bo27b2o7bo33b2o7bo\$107b3o21b2o48bo5b3o1774b2o\$106bo25bo
45b3o5bo1760b2o15bobo5b2o\$106b2o24bobo43bo7b2o1759b2o15bob2o4b2o\$133b
2o57b2o1771b2o\$169b2o21bo1772bo\$169bo20bobo\$154bo12bobo20b2o1773bo\$
109bo44b3o10b2o1796b2o\$107b3o47bo1806bob2o4b2o\$106bo49b2o1786b2ob2o15b
obo5b2o\$106b2o1839b3o14b2o\$15b3o5b3o101b2o1814b5obo\$15bo2b2ob2o2bo102b
o10b3o8b2o1792bobo24b2o\$16b3o3b3o103bobo7bo2bo4bo3b2o1795bobo21b2o\$17b
o5bo105b2o6bo3bo3bobo48b2o1750bo\$109bo27bo7bobo25bo22bo1751bo\$107b3o
30bo32b2o19bobo\$106bo30b2obo37bo4bo10b2o\$106b2o70b2o3b2o\$179b2o3b2o\$
93bo46bob2o34bo4b2o\$16b2o74b3o45b3o39b2o1763b2ob2o\$16b2o73b2obo46bo
1804bo5bo\$91b3o15bo44b2o\$91b3o13b3o44bo1790bo7bo\$92b2o12bo48b3o1787bo
2bobo2bo\$101bo4b2o49bo11b2o1774b3o3b3o\$100b3o40b2o25bo\$99b2obo40bo23b
3o\$99b3o38bo3b3o20bo\$100b2o36b3o5bo33b2o\$109bo27bo43bo\$107b3o27b2o39b
3o8bo\$106bo44bo26bo8b3o1757b2ob2o\$106b2o41b3o34bo1761bobo\$148bo37b2o
1760bobo\$148b2o42b2o1755bo\$169b2o21bo1778b2o\$138b2ob2o26bo20bobo1778b
2o\$109bo28b2ob2o11bo12bobo20b2o\$107b3o44b3o10b2o\$106bo30b2o6b2o10bo
1789b6o5b4o10b2o\$106b2o27bo3bo5b2o9b2o21b2o1766b4o7b2obo10b2o\$134bo4b
2o38b2o1769b2obo7bo\$134bo5bo1811b2o5b2o\$123b2o\$44bo77bobo10bo4bo1811b
2o5b2o\$42b5o10bo51bo12bo12b2obob2obo34b3o15b2o1752b2obo7bo\$41bo2bob2o
9b2o8b2o38b3o11b2o30bo2b3o19b4o14bo1753bo7b2obo10b2o\$40bo7bo9b2o7b2o
37bo45bo3bobo14b2o3b2ob2o3b2o6bobo1753b3o5b4o10b2o\$41bo2bob2o5b2o2b2o
47b2o45bob3o14bo7bo5b3o5b2o\$42b5o123bo2bo5b3o3bob3o\$44bo125bo2bo5b2obo
2b2obo1757bo5bo18b2o\$155b2o12bo3bo8b2ob2obo1756b3o3b3o17b2o\$53b2o2b2o
96b2o13b3o7bobo3bobo1756bob2ob2obo\$40b2o16b2o7b2o40bo71bo4bo2bo1754b2o
7b2o\$40b2o15b2o8b2o38b3o17b2o57b3o1755b2o7b2o\$57bo48bo19bobo50b2o6bo
1756b3o5b3o\$106b2o18bo52b2o1765b3ob3o\$125b2o42b2o1777bobo\$131b2o37bo
1774bo2bobo2bo\$132bo34b3o1774bo2bo3bo2bo\$129b3o35bo1777b2o5b2o\$109bo
19bo50b2o\$107b3o71bo\$106bo71b3o\$106b2o21bo48bo\$127bobo\$128bobo\$128bo2\$
109bo30b2o\$107b3o30b2o\$106bo1840b2ob2o\$106b2o1840bobo\$1948bobo\$123b2o
1824bo\$124bo1846b2o\$124bobo1844b2o\$109bo15b2o4b4o\$107b3o20b2o2bo5b2o
1815b2o\$106bo22b2o2bo4bobob2o1803b2o7bobo13b2o\$106b2o22bo2bo2b2o5bo
1803b2o7bo15b2o\$131b2o6bo3bo1812b3o\$136bo5bo11b2o\$137b4o13bobo\$139bo
16bo\$109bo46b2o1798b3o\$107b3o40b2o1804bo15b2o\$106bo43bo1805bobo13b2o\$
106b2o43b3o1803b2o\$153bo\$139b2o1830b2o\$139bo1831b2o\$140b3o4bo\$109bo32b
o3bobo\$107b3o36bobo\$106bo38b2ob2o\$106b2o1838bo5bo\$1945b3o3b3o\$1945bob
2ob2obo\$1947b2ob2o\$1947b2ob2o\$109bo1837b2ob2o\$107b3o\$106bo\$106b2o2\$
143bo7bo22b2o5b2o\$62bo2bo76bobo5bobo21b2o5b2o\$52b3o7bo82bo3bo\$51bo4bo
9bo42bo7bo7bo16bo2bo3bo2bo\$50bo5bo8b2o26bo13b3o5b3o5b3o17bobo3bobo\$41b
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2o8b2o27b3o49b3o3b3o1797bo\$41bo9bo8bo3bo27b2o50bo5bo23b3o3b3o1788b2o\$
50bo5bo4bo2bo36bo71bo2bo3bo2bo1786bobo\$51bo4bo4bo2bo35b3o70b2obo3bob2o
1786bo\$52b3o7b2o35b2obo1869bo\$99b3o48b2o1795b2o12b2o2bo3bo3bo\$100b2o
48b2o1795b2o12bob2o7b2o\$1962bo\$1962b3o4b2o\$44b2o5b2o\$40b2o2b2o5b2o2b2o
1905b3o4b2o\$40b2o13b2o1905bo\$175bo1785bob2o7b2o\$44b3o3b3o120b2ob2o
1783b2o2bo3bo3bo\$44bo2bobo2bo120b2ob2o15b2o5b2o1745bobo22bo\$43bo3bobo
3bo139b2o5b2o1746bo21bo\$44bo2bobo2bo119bobobobo1769b2o20bobo\$46bo3bo
1897b2o21b2o\$44b2o5b2o120b2ob2o1769bo2bo\$43b3o5b3o55bo64b3o4b2o1764b3o
\$43b3o5b3o53b3o65bo5b2o\$106bo\$106b2o2\$194bo5bo\$50b3o140b3o3b3o\$50b3o
140bob2ob2obo1743bo7bo\$49b5o55bo7bo77b2ob2o1745b2o5b2o\$48b2o3b2o52b3o
5b3o77b2ob2o1745b3o3b3o\$48b2o3b2o51bo7bo80b2ob2o1747b2ob2o\$106b2o6b2o
1831bo3bo\$1944b2o7b2o\$1944b2o7b2o\$48b2o3b2o1893bobo\$44b2o2b2o3b2o1889b
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\$200b2o1769b2o\$109bo\$107b3o1854bo\$106bo22bo1817b2o15b2o6b2o\$106b2o20bo
bo1816b2o16b2o5b2o\$128bobo1829b2o2b2o\$129bo3\$109bo1850b2o2b2o\$107b3o
13bobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobobo
bobobobo1748b2o17b2o5b2o\$106bo1838b3o16b2o6b2o\$106b2o15bo73bo1746b2o2b
o15bo\$129bo1814bo2bo\$123bo4bobo66bo1745bo4b2o21b2o\$128bobo12bobobo
1800b2o3bo17b2o\$123bo5bo67bo1746bobobo\$109bo33bo3bo36bobobobo\$107b3o
13bo73bo\$106bo36bobobo34bobobobobobo\$106b2o15bo26bo22bobobo19bo\$143bo
3bo2b3o29bobo5bobo1752bo7bo\$123bo29bo19bo3bo19bo1746bo2bo3bo2bo\$129bo
13bobobo4bo29bobo1763bobo\$123bo4bobo42bobobo19bo1750bobo\$109bo18bobo
37bo15bobobobo1757bobo\$107b3o13bo5bo37bo5bo3bo19bo1746bo2bo3bo2bo\$106b
o61b3o19bobo1752b3o3b3o\$106b2o15bo19bobobo22bo2bobobo19bo\$128bobobobob
o45bobo5bobo\$123bo23bo2bo46bo\$128bobobobobobo11b3o29bobobobobobo\$123bo
23bo5bo43bo\$109bo18bobo5bobo13bo20bobobo6bobobobo\$107b3o13bo23bo49bo\$
106bo21bobo5bobo29bo8bo1769b2ob2o\$106b2o15bo23bo19bo29bo1750bobo\$128bo
bobobobo31b3o6bo8bo1761bobo\$123bo46bo14bobo9bo1751bo\$128bobo5bobo38bo
7bobo1783b2o\$123bo26bo35bo10bo1773b2o\$109bo18bobo5bobo4bobobo2b3o24bo
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3o1852bo\$99b2obo20bo49bobobo19bo1773b2o\$99b3o1844bo5bo18b2o\$100b2o21bo
73bo1747b3o3b3o\$109bo76bo1757b2o2bobo2b2o\$107b3o13bo61bobo9bo1746b2ob
2ob2ob2o\$23bobobobobobobobobobobobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobo4bo22bo55bobo1759b2ob2o\$106b2o15bo4bobo55bo10bo
1747bobo3bobo\$23bo77bo26bobo12bobobo1796bo2bo3bo2bo\$123bo5bo67bo1749bo
3bo\$23bo22bobobobo7bobo5bobo30bo41bo40bobobobo1753bobo5bobo\$123bo73bo
1747bo7bo\$23bo20bobobobobobo5bobo5bobo11bobobobo12bo7bo33bobobo34bobob
obobobo\$107b3o13bo26bo22bobobo19bo\$23bo20bobo5bobo5bobobo3bobo11bobobo
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bobo3bobo11bobo16bo27bo13bobobo4bo29bobo\$123bo4bobo42bobobo19bo\$23bo
20bobo5bobo5bobo2bo2bobo11bobo16bo26bobo37bo15bobobobo\$123bo5bo37bo9bo
19bo\$23bo20bobo5bobo5bobo3bobobo15bobobobobobo4bo7bo58b3o19bobo\$107b3o
13bo19bo3bo22bo2bobobo19bo\$23bo20bobo5bobo5bobo3bobobo15bobobobobobo4b
o4bo21bobobobobo45bobo5bobo1754b2ob2o\$106b2o15bo19bo3bo2bo46bo1750bobo
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o1755bobo\$123bo19bobobo5bo43bo1751bo\$23bo22bobobobo7bobo5bobo23bobo4bo
26bobo5bobo13bo20bo3bo6bobobobo1780b2o\$123bo23bo49bo1773b2o\$23bo77bo7b
o18bobo5bobo29bo4bo3bo\$107b3o13bo23bo19bo29bo\$23bo77bo4bo21bobobobobo
31b3o2bobobo8bo1760b2o8b3o12b2o\$106b2o15bo46bo14bobo9bo1749b2o8bo3bo
10b2o\$23bo77bo26bobo5bobo38bo7bobo1769bo4bo\$123bo26bo35bo10bo1760bo3bo
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obo12bo7bo18bobobobobobo8bo4bo1804bo4bo\$107b3o13bo73bo1759bo3bo10b2o\$
23bo4bobo5bobo5bobo13bobo23bobo12bo4bo21bobobobobo6bobobo20bo1788b3o
12b2o\$106b2o15bo43bo5bobobo19bo\$23bo4bobo5bobo5bobobobobo7bobobobobo
13bobo16bo45bo20b3o15bo\$123bo46bo6bo7bobo9bo1773b2o\$23bo4bobo5bobo5bob
obobobo7bobobobobo13bobo16bo27bo13bobobo37bobo1783b2o\$123bo4bobo42bobo
bo8bo10bo\$23bo4bobo5bobo5bobo13bobo23bobobobobobo4bo7bo18bobo\$107b3o
13bo5bo47bo19bo\$23bo4bobo5bobo5bobo13bobo23bobobobobobo4bo4bo\$106b2o
15bo49bobobo19bo\$23bo4bobobobobobo5bobo13bobo31bobo4bo1844bo5bo\$123bo
73bo1747b3o3b3o\$23bo6bobobobo7bobo13bobo31bobo4bo84bo1757b2o2bobo2b2o\$
123bo61bobo9bo1745bob4ob4obo\$23bo77bo7bo19bo55bobo1757b3o3b3o\$107b3o
13bo4bobo55bo10bo1746b3o5b3o\$23bobobobobobobobobobobobobobobobobobobob
obobobobobobobobobobobobobobobobobobobobo4bo21bobo12bobobo\$106b2o15bo
5bo67bo\$147bo36bobobobo\$123bo73bo\$143bobobo34bobobobobobo\$123bo26bo22b
obobo19bo\$109bo33bo6b3o29bobo5bobo\$107b3o13bo29bo23bo19bo\$106bo22bo13b
obobo4bo29bobo1762b2ob2o\$106b2o15bo4bobo42bobobo19bo1750bobo\$128bobo
37bo15bobobobo1757bobo\$123bo5bo37bo5bo23bo1751bo\$168b3o19bobo1778b2o\$
123bo21bo24bo2bobobo19bo1773b2o\$109bo18bobobobobo45bobo5bobo\$107b3o13b
o21bo4bo46bo1764bo3b3ob3o\$106bo21bobobobobobo11b3o29bobobobobobo1754b
2o12bobo2b4o3bo\$106b2o15bo21bo7bo43bo1749b2o12bo3b2o6bo\$128bobo5bobo
13bo22bo8bobobobo1771bo2bo3b2obo\$123bo21bo51bo1765b3o3bo\$128bobo5bobo
29bo6bo\$123bo21bo21bo29bo1765b3o3bo\$109bo18bobobobobo31b3o4bo10bo1775b
o2bo3b2obo\$107b3o13bo46bo14bobo9bo1763bo3b2o6bo\$106bo21bobo5bobo36bo9b
obo1760b2o11bobo2b4o3bo\$106b2o15bo26bo35bo10bo1749b3o12bo3b3ob3o\$128bo
bo5bobo4bobobo2b3o22bo\$123bo29bo43bo1773b2o\$128bobobobobobo4bo3bo4bo
1818b2o\$123bo73bo1749b4o\$109bo18bobobobobo6bo3bo20bo1778b3o\$93bo13b3o
13bo43bo5bobobo19bo\$92b3o11bo36bo3bo20b3o15bo\$91b2obo11b2o15bo46bo2bo
3bo7bobo9bo\$91b3o49bobobo37bobo\$91b3o29bo49bo3bo8bo10bo\$92b2o\$101bo21b
o49bo3bo19bo\$100b3o6bo1834b3o5b3o\$99b2obo4b3o13bo49bobobo19bo1746b3o5b
3o\$99b3o4bo1838b2o5b2o\$100b2o4b2o15bo73bo1749bo3bo\$186bo1758bo2bobo2bo
\$123bo61bobo9bo1746bo3bobo3bo\$185bobo1757bo2bobo2bo\$123bobobobobobobob
obobobobobobobobobobobobobobobobobobobobobobo4bo4bobobobo1747b3o3b3o\$
109bo\$107b3o\$106bo1840b2ob2o\$106b2o56b2o1782bobo\$164bo26b3o1754bobo\$
165b3o23b3o4b2o1749bo\$167bo22bo3bo3b2o1771b2o\$189bo5bo1775b2o\$109bo80b
2ob2o\$107b3o\$106bo83b2ob2o1752b2o14b2o7b2o\$106b2o81bo5bo1751b2o15b2o6b
2o\$146b2o42bo3bo1765b5o\$145bo2bo42b3o1766b4o\$145bo7bo37b3o\$145bo2bo3bo
bo1794b3o8b4o\$109bo35b2ob2ob2ob2o1792b6o6b5o\$107b3o39bobo1796b2o2b3o9b
2o6b2o\$106bo41b2ob2o1793b2o4b3o8b2o7b2o\$106b2o1837b2o6b2o\$1944bo2bo5b
2o\$190b2o7b2o1743bo2bo3b3o17b2o\$190bob2o3b2obo1744bo3b4o18b2o\$146b3o3b
3o35bo3bobo3bo1744bo3b3o\$109bo35bo9bo34b2o2bobo2b2o1745bo2bo\$107b3o35b
o3bobo3bo35b3o3b3o\$106bo39b3o3b3o37bo5bo\$106b2o39bo5bo2\$1945bo7bo\$
1943bob2o5b2obo\$1943bo3b2ob2o3bo\$109bo81b2o5b2o1744bo3bobo3bo\$107b3o
81b2o5b2o1745b3o3b3o\$106bo\$106b2o2\$148b2ob2o\$149bobo\$149bobo\$109bo40bo
\$107b3o\$106bo1840b2ob2o\$106b2o1840bobo\$1948bobo\$1949bo\$164bo1806b2o\$
163bobo1805b2o\$109bo53bobo\$107b3o52b2ob2o1786bob2o\$106bo1840b2o3bo2b2o
2b3o10b2o\$106b2o1839b2o3bo6b2o11b2o\$1952b2o3b3o\$1954bo3bo2\$1954bo3bo\$
109bo1842b2o3b3o\$107b3o1842bo6b2o11b2o\$106bo1845bo2b2o2b3o10b2o\$106b2o
1845bob2o2\$1971b2o\$160bo7bo1802b2o\$159b4o3b4o1776bo5bo\$109bo49bo3bobo
3bo1775b3o3b3o\$107b3o50bo2bobo2bo1775bo2b2ob2o2bo\$106bo53b3o3b3o1775bo
3bobo3bo\$106b2o1838bobobobo2\$1943b2ob2o3b2ob2o\$1945bo7bo2\$109bo\$107b3o
50b2o\$106bo53b2o\$106b2o2\$93bo\$92b3o\$91b2obo\$91b3o15bo\$91b3o13b3o\$92b2o
12bo1840b2ob2o\$101bo4b2o67b3ob3o9b2o1755bobo\$100b3o71bob2ob2obo7b2ob2o
6b2o1745bobo\$99b2obo70b2o7b2o7bo2bo6b2o1746bo\$99b3o72bob2ob2obo8bo2bo
1776b2o\$100b2o73b3ob3o10b2o1777b2o2\$192b2o1765bo3bo\$191bo2bo1752b2o9bo
5bo7b2o\$174b2o15bo2bo6b2o1744b2o9bo13b2o\$174b2o14b2ob2o6b2o1755b2o3bo\$
191b2o1767b3o2\$1960b3o\$109bo1848b2o3bo\$107b3o1848bo13b2o\$106bo86b2o5b
2o1756bo5bo7b2o\$106b2o85b2o5b2o1757bo3bo2\$1971b2o\$1971b2o2\$109bo\$107b
3o\$106bo\$106b2o2\$1946bo5bo\$194bo5bo1744b3o3b3o\$193bobo3bobo1742b2ob2ob
2ob2o\$109bo7bo7bo66bo3bobo3bo1740b3o7b3o\$107b3o5b3o5b3o66bo3bobo3bo\$
106bo7bo7bo69bo9bo1742bo7bo\$106b2o6b2o6b2o\$193b2o5b2o2\$1947b2ob2o2\$
195bo3bo1747b2ob2o\$193b2o\$192bo3bobo3b2o1743b2ob2o\$192bo3bobo1749bobo\$
193b3o1752bobo\$200bo2bo1745bo\$200b2o1769b2o\$30b2o1939b2o\$30b2o\$1962bob
o2b2o\$42bobo2b2o1898b2o12bo3bob3o2b2o\$29b2o10bo3bob3o1897b2o13bo6b2ob
2o\$29b2o11bo6b2o1912b5obo\$43b5obo1916b3o\$46b3o\$1966b3o\$46b3o1914b5obo\$
43b5obo1912bo6b2ob2o\$29b2o11bo6b2o3b2o65b2o1826bo11bo3bob3o2b2o\$29b2o
10bo3bob3o4b2o65b2o1825b2o12bobo2b2o\$42bobo2b2o1898b3o\$1946b2ob2o20b2o
\$30b2o1914b2ob2o20b2o\$30b2o1915bob2o\$1948bo\$55b2o\$55b2o6\$109bo4b2o5b2o
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2o9bobo1823b2obobobobob2o\$115b3ob3o1822bo3bobo3bo\$113b3o5b3o1820bo2bo
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b3o\$63bob2o403b3o212bob2o3b2obo869b2o6bo3bo5bo5b2o50b2ob2o11b2o11bo6b
2o54bo5bo\$62b2o2bo499bo7bo111b2o5b2o878bo4bo5b2obob2o80b5obo54b3o3b3o\$
62b2ob2o403b3o214bo5bo401b2o5b2o470bo3bo7b3o52b2ob2o28b3o55bob2ob2obo\$
63bobo403bob5o619b2o5b2o539bo87b2o7b2o\$64bo403b2o6bo13b2o103b3o3b3o65b
3o5b3o894bo3bo95b3o54b2o7b2o\$469b3obo3bo12b2o102bo2bo3bo2bo63b2ob2o3b
2ob2o892bo4bo92b5obo53b3o5b3o\$57b2o411b2o2bobo90bo26b2obo3bob2o63b2obo
bobobob2o7b2ob2o872b2o6bo3bo12b2o65b2o11bo6b2o3b2o49b3ob3o\$56bobo507b
3o100bo3bobo3bo7bo5bo871b2o6b3o14b2o50bo7bo6b2o10bo3bob3o4b2o51bobo\$
56bo508bo2bo66b2o32bo2bo3bo2bo5b5ob2ob2o945bo2bo3bo2bo18bobo2b2o55bo2b
obo2bo\$55b2o301b2o205bobobo65bo2bobo29b3o3b3o5b2ob3ob2ob2o949bobo83bo
2bo3bo2bo\$6b2o53b2o36bo6b2o215b3o3b3o22bobo2bo206b3o68b2ob3o41b3o6bo
872b2o77bobo10b2o72b2o5b2o\$6b2o2b2o50bo37b2o4b2o215bo2bobo2bo20b3ob2o
79b2o128bo5b2o68bo41bobo878b2o77bobo10b2o\$10b2o47b3o37b2o222b2obobob2o
19bo84bo2bo133b2o62b2ob3o43b2o263b4o5b6o675bo2bo3bo2bo\$59bo263b2o5b2o
20b4o80bo7bo179bo3bo8b2obo31b2ob2o219b6o5b4o40bob2o7b4o676b3o3b3o\$108b
o245bob2o13bo64bo2bo3bobo177bo5bo43bobo220b4o7b2obo40bo7bob2o\$10b2o54b
2o39bobo261b2o63b2ob2ob2ob2o182bo43bobo84b2o46b2o89b2obo7bo41b2o5b2o\$
10b2o26b2o25bobo15b2o23bo263b2o66bobo172bo8bo3b2o44bo84bo2bo44bo2bo90b
2o5b2o\$38b2o24b2obo15b2o24b3o63b2o190b2o2b2o6bo42b2o15b2ob2o169b3o9b3o
132b2o46b2o142b2o5b2o\$59bo5b2o44bo63b2o148b2ob2o28bobo18b3o40b2o70bo
117bo288b2o5b2o41bo7bob2o1049b2o\$28b3o26b3o6bo256bo2bobo2bo26bobo21bo
3bo98b2o5b3o118b3o9b3o19bo251b2obo7bo26b2o12bob2o7b4o1046b2o\$27bo4bo6b
2o15bo112bo5bo147bobo3bobo15bo10b2o19b3o4b3o5b2o11b4o53b3o14b2o3bo4bo
83b2o20b2ob2o13bo8bo3b2o7bo7b3o248b4o7b2obo12b2o12b2o12b4o5b6o672b2o
13b2o73b2o13b2o\$26bo5bo6b2o16b3o6bo15b2o84b3o3b3o146b3o3b3o15b3o9bo7b
2o2b2o6bo9bo4bo3b2o6b2o2bo12b2o39bo3bo12b2o3bobo3bo82bo22bobo28bo4bo2b
ob2o3bo251b6o5b4o12b2o713b2o2b2o5b2o2b2o73b2o2b2o5b2o2b2o253b2o\$27bo
31bo5b2o15b2o20b2o62bo2bobo2bo146b2o5b2o18bo5b2obobo10b2o14bo3bobo3b2o
5b2o2bo13b2o12b3o3b3o11bo6bo4bo17bobo3bo82bo21bobo22bo5bo10bo4bo996b2o
5b2o81b2o5b2o247b2o7bobo13b2o\$28b2o34b2obo35b2ob2o62b2ob2o148b2o5b2o
17bo11bo9b2o14bo3bobo12bo2bo26bo9bo8b3o7bo3bo18bo3b2o81b2o22bo24bo3bo
10bo4b2o1342b2o6b2obo13b2o\$65bobo18b3o15b4o215b2o5b2o17b2o6bo2bo10bo
15b2ob2o15b2o27bo3bobo3bo7bo1542b2o\$28b2o36b2o18bobo16b2o252b2o76b3o3b
3o9b3o7bo3bo7b3o95b2o58b5o1358bo\$27bo58bobo318b2o29bo5bo12bo6bo4bo5b2o
bob2o92bobo59b4o1341bo\$14b2o10bo5bo6b2o46bobo78bo7bo229bo2bo54bo3bo5bo
5b2o93bo62bo1341b3o15bo\$14b2o11bo4bo6b2o48bo79bobobobo229b2o2bo13b2o
39b3o8b2obob2o45b5o1448b2obo13b2o\$28b3o90bo47bobobobo230b2o2bo12b2o52b
3o46bo4bo1464b2obo13b2o\$121b3o44bob2ob2obo230b4o120bo1465bobo13b2o\$38b
2o48bo35bo43b2o5b2o317bo31bo3bo1467b2o\$38b2o48bo34b2o20b2o47b2o226b2o
69b2o33bo\$110bo35bo46bobo226b2o69bobo1516b2o\$110b3o33bobo44bo30b2o852b
o933b2o\$113bo33b2o43b2o30b2o226b2o5b2o605b2o5b6o8b4o293b2o5b2o439b2o5b
2o105b2o6b2o7b2o\$112b2o102b2o4bo13bo3b3o55b2o63b2o74b2ob2o4b2obobo5bob
ob2o45b2o554bo6bobobo9bo2b2o288b2o2b2o5b2o2b2o431b2o2b2o5b2o2b2o101bo
7b2o6bo2b2o\$216bo3b3o12bobo2b5o53bo7b3o5b4o35b2o6b2ob2o15b2o57bobo5b2o
b2o7b2ob2o44b2o33bobo2b2o19b2o495bo5bo4bo9bo2b2o287b2o13b2o431b2o13b2o
102bo5bo2bo4b6o18bo5bo\$217bo3bobo11bo3b2o58bo6bo7b2obo35b2o6bo2bo17b2o
34b2o5b2o13bobo7b6ob6o47b5o9bo18bo3bob3o19bo492b3o7bo13bo2bo4bo847b3o
7b2obo5b4o9bo7b3o3b3o\$214b3o5b2o12bo2bo3b2obo49b3o7b2obo7bo10bo32bo2bo
16bo7b4o21b2o2b2o5b2o2b2o10bo10bob2ob2obo34b3o13b4o9b3o17bo6b2o15b3o
493bo11b2o11b2o5b3o845bo9b2obo18b3o4b2o2bobo2b2o\$79b2o7b2o11bo24bo87bo
22b3o3b2ob3o47bo11b2o5b2o11b3o31b2o25bo2b2o20b2o13b2o62bo3bo29bo4bo12b
5obo16bo530bo855bo23bo3bo3bobo3bo\$79bob2o3b2obo10b3o22b3o121bo81bo58bo
2b2o55bo11bo19bo9bo4bo13b4o9b3o3b3o15b3o538b2o5b3o285b3o3b3o563b2o18b
3o4bob2o3b2obo\$79bo3bobo3bo9b2obo21b2o2bo41b2ob2o62b3o3b2ob3o59b2o5b2o
11b3o31b2o26bo2bo4bo52bo9bo18b3o9bo3bo13b5o9bo4bo558bo2bo4bo287bo2bobo
2bo563b2o5b4o9bo6b2o7b2o\$79b2o2bobo2b2o9b3o21b2o3b2o11b2o28bobo62bo2bo
3b2obo61b2o7bo10bo32bo2bo26b2o5b3o52bobobobo19bo29b2o19b3o15b3o537bo2b
2o290bo3bobo3bo567b6o\$10b2o68b3o3b3o11b2o19bobo2bobo13bo10b3o8b2o5bobo
61bo3b2o73b2obo35b2o6bo2bo36bo51bobobobo20b3o9bo3bo13b2o20bo12b5obo
535bo2b2o291b4o3b4o568bo2b2o\$10b2o69bo5bo33b2o3b2o9b2o3bobo7bo2bo4bo3b
2o6bo62bobo2b5o69b4o35b2o6b2ob2o25b2o5b3o53b2ob2o23bo9bo4bo46bo6b2o3b
2o513bob2o12b4o293bo7bo558bob2o8b2o\$116b2o19bobo3b2o6bo3bo3bobo59bob2o
11bo3b3o60bo59b2o25bo2bo4bo52bo2bo3bo2bo31bo3bo45bo3bob3o4b2o511b3ob2o
874b3ob2o\$6b2o6b2o100b2o21bo11bo7bobo57b3ob2o76b6o83bo2b2o23bo7bo25b2o
5b2o34b3o46bobo2b2o517bo763bo7bo107bo\$6b2o2b2o2bo61b2o13b2o46b2o13bo
63bo81bo4bo83bo2b2o675b3ob2o756bobo5bobo107b3ob2o\$10b2o3b3o58b2o2b2o5b
2o2b2o58b2obo64b3ob2o76b3ob2o82b4o23b3o7b3o642bobo2bo757bo3bo112bobo2b
o\$18bo61b2o5b2o132bobo2bo32bo43bobo2bo108b2ob2ob2ob2o647b2o754bo2bo3bo
2bo113b2o\$17bo154b2o51b2o31b2o47b2o109b3o3b3o1405bobo3bobo\$16bo137bob
2o14bobo82b2o160bo5bo959bo448b2ob2o\$15bo138b3o17bo83b2o2b2o9bo1110b3o
444b2ob2ob2ob2o\$14bo76bo63bo18b2o68b3o26b3o21bo1085bo3bo443b2o2bobo2b
2o138b2o13b2o\$13bo77bo2b2o72b2o23b2o9b3ob3o31bo3bo29bo16b2o2bo1085b2ob
2o444b3o3b3o139b2o2b2o5b2o2b2o\$12bo77bo5bo36b2o33bo22b2ob2o7bob2ob2obo
19bo9bo4bo26b3o16bo5bo1084b2ob2o445bo5bo144b2o5b2o\$11bo79bobo2b2o35bob
o33b3o19bo2bo7b2o7b2o16b3o9bo3bo12b2o2b2o9bo17b2o2bobo\$12b3o63bo12bo3b
2o38bo35bo14bo4bo2bo8bob2ob2obo16bo28b2o33b2o3bo12bo1072b2ob2o\$15bo60b
3o14b3o39b2o20b2o25b3o5b2o10b3ob3o18b3o9bo3bo12b2o33b3o14b3o1070b2ob2o
\$14bo60bo41b2o10b2o26bo25bo47bo9bo4bo12bo53bo138b2o632b2o295bo3bo3b2o
439b2o\$13bo62b3o14b3o20bo2bo9bo28b3o23b3o5b2o48bo3bo46b3o14b3o107b2ob
2o27b2o631bo2bo295b3o4b2o439b2o\$12bo65bo12bo3b2o20b2o11b3o27bo25bo4bo
2bo49b3o45b2o3bo12bo110bobo662b2o297bo660b2o\$11bo79bobo2b2o4b2o28bo58b
o2bo15b2o59bo13b2o4b2o2bobo123bobo1622b2o\$12b3o75bo5bo5b2o87b2ob2o14b
2o57b3o13b2o5bo5bo123bo1613bo\$15bo75bo2b2o97b2o67bo5bo24b2o2bo1737bo2b
o\$14bo76bo168bobo5b2o27bo1736b5o8b2o\$13bo247b2o1707b2o5b2o54b2ob3o8b2o
\$12bo1953b2o2b2o5b2o2b2o51bob2o\$11bo1954b2o13b2o52b2o\$12b3o\$15bo2019b
2o\$14bo18b2o4b3o1992bob2o\$13bo19b2o3bo3bo1822bo156b2o9b2ob3o8b2o\$12bo
25b2ob2o1817bo3bo157b2o10b5o8b2o\$11bo27bobo1817bo8b2o2b2o161bo2bo\$12b
3o224bo31b2o1586bo2b2o5bo2b2o7b2o5b2o80bo7bo57bo\$15bo23bobo193b2o2bo
16b2o13bo1588b2o5bobo7b2o2b2o5b2o2b2o75bo2bo3bo2bo66b2o\$14bo23b2ob2o
191bo5bo14bobo14b3o1586b3o3b2o8b2o13b2o79bobo70b2o\$13bo24bo3bo190b2o2b
obo17bo16bo78b2o2b2o4bo2b2o12b2o1591bobo\$12bo26b3o188bo3b2o3bo22b2o3bo
85b2ob2o6b2obo12b2o1479b3o3b2o104bobo\$11bo216b3o4b3o24b3obob2o87bobo6b
o1493b2o5bobo99bo2bo3bo2bo\$12b3o212bo34b3o4bo88b2o4b3o1478b2o12bo2b2o
5bo2b2o96b3o3b3o\$15bo212b3o4b3o27bo3bo2bo1572b2o12bo8b2o2b2o\$14bo215bo
3b2o3bo26b3o3b3o83b2o4b3o1493bo3bo\$13bo219b2o2bobo35bo81bobo6bo1498bo\$
12bo221bo5bo25b3o3b3o78b2ob2o6b2obo\$11bo223b2o2bo25bo3bo2bo80b2o2b2o4b
o2b2o\$12b3o224bo22b3o4bo635b2o974b2o5b2o\$15bo16b3o5b3o219b3obob2o633b
2o2bo972bo2bo3bo2bo109bo\$5b3o6bo17bo2b2ob2o2bo219b2o3bo635b6o972bo2bob
o2bo109bobo\$5bo2bo4bo19b3o3b3o861b4o4bo3bo968bobo112bo2bo\$5bo6bo21bo5b
o870b7o964b3ob3o88b2o18bobo3bo5bo5bo5bo5bo5bo5bo5bo\$5bo5bo906bo961b3o
5b3o86b2o18b2o5bo3bobo3bobo3bobo3bobo3bobo3bobo3bobo\$6bobo3b3o896b7o
962b2o7b2o114bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo\$15bo887b4o4b
o3bo964b2o7b2o115bobo3bobo3bobo3bobo3bobo3bobo3bobo3bo\$14bo14b2o13b2o
844b2o11b6o972bob2ob2obo71b2o2b2o27b2o2b2o7bo5bo5bo5bo5bo5bo5bo3b2o\$
11bobo15b2o2b2o5b2o2b2o844b2o11b2o2bo973b3o3b3o71b2o2b2o27b2o2b2o\$11b
2o20b2o5b2o863b2o975bo5bo\$1009b2o1030bo2bo\$1008bobo949b2o35b2o41bo\$
1008bo41b2o829b2o77b2o35b2o41bo3bo\$4b2o1001b2o41b2o829b2o157b4o8b2o\$4b
2o2046b2o2\$bo2054bo\$obo2052bobo\$bo2054bo!

``````
<3
here is how to make it a Blinker Cell

Code: Select all

``````x = 217, y = 207, rule = LifeHistory
D5.D8.D9.4D2.D13.D5.3D3.D10.D12.3D9.D4.D3.D15.D5.D3.2D9.D3.D.D8.D23.
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3.D.D3.D3.D5.D2.D3.5D3.D3.D.D2.3D3.D3.D3.D.D4.D3.D3.D3.D2.D.D2.5D.D4.
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D3.D2.D.D2.D5.D4.D5.D2.2D.D2.2D\$D5.D2.3D4.2D2.2D.D.D5.D.D3.D2.3D3.D4.
3D4.2D2.2D.D3.2D2.3D5.3D3.3D4.2D3.2D.D.D3.D2.2D.D3.5D.D2.D4.3D4.D3.D.
D.4D4.2D2.3D2.D5.2D.D4.3D4.D4.3D2.D4.5D2.2D.D2.2D.D\$114.D58.D42.D\$
111.3D56.3D40.3D20\$108.A\$106.3A13.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D
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D.D.D.D.D11.3A29.D.D.D.D.D.D\$122.D19.D.D.D5.A43.D\$22.D22.D.D.D.D7.D.D
5.D.D23.D.D4.D26.D.D5.D.D13.A20.D3.D6.D.D.D.D\$122.D23.D49.D\$22.D77.D
7.A18.D.D5.D.D29.A4.D3.D\$106.3A13.D23.D19.A29.D\$22.D77.D4.A21.D.D.D.D
.D31.3A2.D.D.D8.A\$105.2A15.D46.A14.A.A9.D\$22.D77.D26.D.D5.D.D38.D7.A.
A\$122.D26.A35.A10.D\$22.D6.D.D.D.D7.D.D.D.D.D.D5.D.D.D.D.D.D30.D26.D.D
5.D.D4.D.D.D2.3A24.D\$122.D29.A43.D\$22.D4.D.D.D.D.D.D5.D.D.D.D.D.D5.D.
D.D.D.D.D15.D.D12.D7.A18.D.D.D.D.D.D8.D4.A\$106.3A13.D73.D\$22.D4.D.D5.
D.D5.D.D13.D.D23.D.D12.D4.A21.D.D.D.D.D6.D.D.D20.A\$105.2A15.D43.A5.D.
D.D19.D\$22.D4.D.D5.D.D5.D.D.D.D.D7.D.D.D.D.D13.D.D16.D45.D20.3A15.A\$
122.D46.A6.D7.A.A9.D\$22.D4.D.D5.D.D5.D.D.D.D.D7.D.D.D.D.D13.D.D16.D
27.A13.D.D.D37.A.A\$122.D4.A.A42.D.D.D8.A10.D\$22.D4.D.D5.D.D5.D.D13.D.
D23.D.D.D.D.D.D4.D7.A18.A.A\$106.3A13.D5.A47.D19.D\$22.D4.D.D5.D.D5.D.D
13.D.D23.D.D.D.D.D.D4.D4.A\$105.2A15.D49.D.D.D19.D\$22.D4.D.D.D.D.D.D5.
D.D13.D.D31.D.D4.D\$122.D73.D\$22.D6.D.D.D.D7.D.D13.D.D31.D.D4.D84.A\$
122.D61.A.A9.D\$22.D77.D7.A19.A55.A.A\$106.3A13.D4.A.A55.A10.D\$22.D.D.D
.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.
D.D.D4.A21.A.A12.D.D.D\$105.2A15.D5.A67.D\$146.D36.D.D.D.D\$122.D73.D\$
142.D.D.D34.D.D.D.D.D.D\$122.D26.A22.D.D.D19.D\$108.A33.D6.3A29.D.D5.D.
D\$106.3A13.D29.A23.D19.D\$105.A22.A13.D.D.D4.A29.D.D\$105.2A15.D4.A.A
42.D.D.D19.D\$127.A.A37.A15.D.D.D.D\$122.D5.A37.A5.D23.D\$167.3A19.D.D\$
122.D21.D24.A2.D.D.D19.D\$108.A18.D.D.D.D.D45.D.D5.D.D\$106.3A13.D21.D
4.A46.D\$105.A21.D.D.D.D.D.D11.3A29.D.D.D.D.D.D\$105.2A15.D21.D7.A43.D\$
127.D.D5.D.D13.A22.D8.D.D.D.D\$122.D21.D51.D\$127.D.D5.D.D28.2D6.D\$122.
D21.D21.D29.D\$108.A18.D.D.D.D.D31.3D4.D10.A\$106.3A13.D46.D14.A.A9.D\$
105.A21.D.D5.D.D36.D9.A.A\$105.2A15.D26.D35.A10.D\$127.D.D5.D.D4.D.D.D
2.3D22.D\$122.D29.D43.D\$127.D.D.D.D.D.D4.D3.D4.2D\$122.D73.D\$108.A18.D.
D.D.D.D6.D3.D20.A\$92.A13.3A13.D43.A5.D.D.D19.D\$91.3A11.A36.D3.D20.3A
15.A\$90.2A.A11.2A15.D46.A2.D3.D7.A.A9.D\$90.3A49.D.D.D37.A.A\$90.3A29.D
49.D3.D8.A10.D\$91.2A\$100.A21.D49.D3.D19.D\$99.3A6.A\$98.2A.A4.3A13.D49.
D.D.D19.D\$98.3A4.A\$99.2A4.2A15.D73.D\$185.A\$122.D61.A.A9.D\$184.A.A\$
122.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D.D4.A4.D
.D.D.D29\$81.3D9.D5.5D9.4D5.3D5.3D5.D4.5D14.4D2.D2.D7.D18.3D8.D2.D\$80.
D3.D8.D7.D11.D3.D3.D3.D3.D3.D3.2D4.D18.D3.D.D10.D17.D3.D7.D2.D\$80.D6.
3D2.4D5.D4.3D4.D3.D3.D3.D3.D8.D4.D6.3D2.D.2D3.D3.D.D2.D.D.2D2.D2.D2.
3D2.D.2D3.D6.3D2.D2.D\$81.3D2.D3.D2.D7.D3.D3.D3.4D4.D.D.D4.3D5.D4.4D2.
D3.D.2D5.4D2.D2.D.2D2.D.D.D2.D3.D.2D5.D5.D3.D.D2.D\$84.D.5D2.D7.D3.D3.
D3.D3.D3.D3.D7.D4.D4.D5.D3.D.D6.D3.D.D2.D.D3.D.2D3.5D.D6.D5.5D.D2.D\$
80.D3.D.D6.D7.D3.D3.D3.D3.D3.D3.D3.D3.D4.D4.D5.D3.D.D6.D3.D.D2.D.D3.D
.D.D2.D5.D6.D3.D.D5.D2.D\$81.3D3.3D4.2D5.D4.3D4.4D5.3D5.3D4.3D3.D6.3D
2.D6.4D3.D.D.D3.D.D2.D2.3D2.D7.3D3.3D3.D2.D!
``````
"One picture is worth 1000 words; but one thousand words, carefully crafted, can paint an infinite number of pictures."
- autonomic writing
forFUN : http://gol.jct.onl
Art Gallery : http://cgol.art
Video WebSite : http://conway.life

H. H. P. M. P. Cole
Posts: 236
Joined: July 15th, 2023, 9:36 pm

H. H. P. M. P. Cole wrote:
February 7th, 2024, 11:12 pm
Reaction between phi spark and pi heptomino produces a trans-block on long bookend and a LWSS. Known?

Code: Select all

``````x = 7, y = 9, rule = B3/S23
o2b2o\$2obo3\$2b2ob2o\$2bo3bo\$2bo3bo\$3bobo\$4bo!
``````
Are there any uses of this reaction?
Harfordson Parker-Cole

Factorio
Speciation (by NimbleRogue)

Drelectron8
Posts: 92
Joined: March 5th, 2023, 4:54 am
Location: Queenstown, Singapore

Has this c/4 spaceship been found?

Code: Select all

``````x = 83, y = 27, rule = B3/S23
8\$55bo\$28bo25bo3b3o14b2o\$15b2o8b4o8b2o13b2o4bo9b2o3b3o\$15bo2b3o2b4o5b
4obo6bo7b2o2bob4o4b3obobo3bo\$14bo7b2o2bo4bo7bobobobo4bobobo5b2o2bo3bo
3bo2bo\$13b4obobo3bo2bo4b2o4b4obob2ob2o9b3obo2bo2bo2bo3bo\$13b2o8bo2b2o
bo2bo2bobobobobo4b3o10bobo5bo5b2o\$12bo10b2obo9bo2bo3bobo2bo12bo7b2o5b
3obo\$9b3obo5bobo5bobob3o6b5o2bo9bobobobo5b2o6bobo\$8bo2bo7bo9bob3o23bo
\$9b3obo5bobo5bobob3o6b5o2bo9bobobobo5b2o6bobo\$12bo10b2obo9bo2bo3bobo2b
o12bo7b2o5b3obo\$13b2o8bo2b2obo2bo2bobobobobo4b3o10bobo5bo5b2o\$13b4obo
bo3bo2bo4b2o4b4obob2ob2o9b3obo2bo2bo2bo3bo\$14bo7b2o2bo4bo7bobobobo4bo
bobo5b2o2bo3bo3bo2bo\$15bo2b3o2b4o5b4obo6bo7b2o2bob4o4b3obobo3bo\$15b2o
8b4o8b2o13b2o4bo9b2o3b3o\$28bo25bo3b3o14b2o\$55bo!``````
It would be called 309P4H1V0 or something like that.

Code: Select all

``````x = 4, y = 4, rule = B01356/S012345
ob2o\$2obo2\$obo!
#C [[ THEME Book AUTOFIT LAYERS 5 DEPTH 0.50 ]]
``````
OCA:Wickstretcher And The Parasites← Check this cool rule out!

Wickstretcher And The Parasites forums. ← Check the forums as well!

Gamer729
Posts: 11
Joined: June 23rd, 2023, 5:51 am

If I found some random reaction smashing together basic stuff, where would I go to see if it is already found?

confocaloid
Posts: 3524
Joined: February 8th, 2022, 3:15 pm

Gamer729 wrote:
June 20th, 2024, 4:43 pm
If I found some random reaction smashing together basic stuff, where would I go to see if it is already found?
Determining which reactions of a certain type are known will likely require some amount of searching by keywords, reading through web pages / forum threads, and looking through pattern collections. Category:Pattern collections and databases

There are software tools (lifesrch, Catagolue / "Identify pattern", octohash) which work for some types of reactions or patterns.

For most kinds of reactions or patterns, there's no quick automated test. There are some forum threads where you can post the reaction (if you do, please write what it is/what it does, and how you found it). There are also lots of threads for specific types of patterns.

In cases when it's straightforward to enumerate all possible reactions of certain kind, and there are at most a few dozens of possibilities (for example two-glider collisions), that likely means people already did the enumeration. Some reactions of that kind can be found in Lifeline.

On the other hand, "enumerated all possibilities" doesn't mean "explored every possibility". Reusing the same example, just because the complete list of possible 2G collisions was known long ago, doesn't mean there's nothing left to discover, say, by trying to influence a collision by placing catalysts and/or sparkers around it.
127:1 B3/S234c User:Confocal/R (isotropic CA, incomplete)
Unlikely events happen.
My silence does not imply agreement, nor indifference. If I disagreed with something in the past, then please do not construe my silence as something that could change that.

b-engine
Posts: 1901
Joined: October 26th, 2023, 4:11 am
Location: Somewhere on earth

Drelectron8 wrote:
June 20th, 2024, 5:30 am
Has this c/4 spaceship been found?
...
It would be called 309P4H1V0 or something like that.
According to Catagolue page
[catagolue]xq4_y2gse1esgzwcepw2x2wpeczw2itg0g434g0gti2z0801ompfxfpmo108z011g8phc929chp8g11zwrr01p91219p10rrzw10a883s0s388a01zx2dtdg303gdtd2zwg0q941x149q0gz032iy1oy1i23z23891288l0l88219832zy0c3y33czw3oh331606133ho3z0c38d844o0o448d83czy332023/b3s23[/catagolue], there's no comments in that, so it's likely new.
b-rules100th post: 18 November 2023 1000th post: 8 March 2024 10000th post:

confocaloid
Posts: 3524
Joined: February 8th, 2022, 3:15 pm

How that spaceship was found, again? Looks like it was probably found by running a search program, but which program and which inputs remains unknown (unless people remember to explain how they found the patterns/reactions they post). That also can affect likelihood in "it's likely new", as well as likelihood in "we'll likely never know whether or not it was new", because it's plausible that someone else already ran the same search program earlier and found the same spaceship but didn't post it anywhere.
Drelectron8 wrote:
June 20th, 2024, 5:30 am
Has this c/4 spaceship been found? [...]
b-engine wrote:
June 20th, 2024, 6:34 pm
[...] there's no comments in that, so it's likely new.

Drelectron8
Posts: 92
Joined: March 5th, 2023, 4:54 am
Location: Queenstown, Singapore

confocaloid wrote:
June 20th, 2024, 6:41 pm
How that spaceship was found, again? Looks like it was probably found by running a search program, but which program and which inputs remains unknown (unless people remember to explain how they found the patterns/reactions they post). That also can affect likelihood in "it's likely new", as well as likelihood in "we'll likely never know whether or not it was new", because it's plausible that someone else already ran the same search program earlier and found the same spaceship but didn't post it anywhere.
Drelectron8 wrote:
June 20th, 2024, 5:30 am
Has this c/4 spaceship been found? [...]
b-engine wrote:
June 20th, 2024, 6:34 pm
[...] there's no comments in that, so it's likely new.

I used rlifesrc. The inputs, I don't quite remember, but I can give an estimate.

Width: 75

Height: 21

Period: 4

dx: 1

Symmetry: D2-

Code: Select all

``````x = 4, y = 4, rule = B01356/S012345
ob2o\$2obo2\$obo!
#C [[ THEME Book AUTOFIT LAYERS 5 DEPTH 0.50 ]]
``````
OCA:Wickstretcher And The Parasites← Check this cool rule out!

Wickstretcher And The Parasites forums. ← Check the forums as well!

tommyaweosme
Posts: 1096
Joined: January 15th, 2024, 9:37 am
Location: platformer mode
Contact:

the fite reaction was already known (enumerated) but we found it ourselves and made a partial (and full) reflector
i can solve a rubix cube in 3 minutes or less with my new speedcube

confocaloid
Posts: 3524
Joined: February 8th, 2022, 3:15 pm

tommyaweosme wrote:
June 20th, 2024, 7:52 pm
the fite reaction was already known (enumerated) but we found it ourselves and made a partial (and full) reflector
Depends what you mean.

The boat can serve as one-time turner for a glider; that reaction was definitely known and used long ago, in many diferent contexts. See for example these links:
Demultiplexer
viewtopic.php?f=2&t=1828&start=25
viewtopic.php?p=52920#p52920
viewtopic.php?p=137205#p137205
viewtopic.php?p=150112#p150112
viewtopic.php?p=153587#p153587

Now, before June 2024, did anyone complete a working stable reflector that uses the same reaction to turn the input glider into the output glider, while using some spark to reconstruct the boat later? Maybe someone already did that; I don't know for sure.

Was that particular boat+biblock bait known or used before?
confocaloid wrote:
June 12th, 2024, 3:34 pm
tommyaweosme wrote:
June 12th, 2024, 12:38 pm
but could someone turn it into a glider reflector (and call it the fite reflector) please? [...]
confocaloid wrote:
June 12th, 2024, 1:02 pm
Here's a partial. It remains to remove the leftover beehive and to restore the damaged bi-block, and hey presto, have a fite reflector: [...]
Here's a completed fite reflector, with bounding box 211-by-173:

Code: Select all

``````x = 211, y = 173, rule = B3/S23
91b2o\$91b2o12b2obob2o\$98bob2obo2bob2o2bo\$98b2obob2obo4bobo\$106b5obo\$
102b2obo4bo\$102b2obobo3bo\$106bobo3bo10b2o\$107bo3b2o8bo2bo\$121b3o\$130b
2o\$121b3o5bobo\$121bo2bo4bo\$99b2o11bo10b2o3b2o\$99b2o9b3o22b2o\$84b2o24bo
24bo26bo\$83bo2bo23bo22bobo25bobo\$82bob2o47b2o26bob3o\$82bo75b2obo4bo\$
81b2o75bobobobobo\$96b2o62bobob2o4b2o\$96bo55b2o5bobo8bo\$97b3o52b2o6bo7b
obo\$99bo10b2o56b2o\$109bobo\$109bo\$108b2o32bo14b2o\$140b3o13bo2bo\$120b2o
8b3o6bo17b2o\$121bo8bo8b2o\$118b3o8b2o\$118bo3\$165b2o\$152b2o10bobo\$148b2o
bobo10b2o\$148bob2obobo\$154b2o3b2o3b4o\$159b2o4bo2bo\$126b2o19b2o14bo3b2o
\$126b2o19b2o14b2o2\$176b2o\$125b2o50bo\$82b2o42bo49bo\$72bo9bobob2o35b3o
50b2o\$72b3o9bobo36bo54bo12b2o\$75bo7b2obo89b3o12b2o\$74b2o10bob2o85bo\$
48b2o19b2o7bo4b4o2bo85b2o\$47bo2bo17bobo6bobo3bo3b2o47bobo47bo\$40b2o5bo
2bo15b3obobo4bo2bo3b3o49bobo46bobo\$40b2o6b2o15bo5b2o5b2o6bo49b2o47bobo
6b2o\$24b2o39b2o19bobo85b2o10bo5bo2bo13bo\$17b2o5b2o61b2o85b2o15bob2o13b
o\$17b2o173bo2b3o10b3o\$193b2o3bo\$172b2o22b2o\$19b2o17b2o17bo11b2o101bo2b
ob2o14b2obo\$19b2o17bo18b3o9b2o103b2obobo13bo2bo\$13b2o21bobo20bo115bo2b
2o14b2o\$13b2o21b2o21bo74b2o3b2o32bobo\$133bo2bobo2bo31b2o15b2o\$77bo50bo
5b2o3b2o5bo43bo\$76bobo48bobo15bobo43b3o\$34bo35b2o4bobo4b2o43bo17bo46bo
\$34bo35bo2bo3bo3bo2bo\$32b3o9b2o25b3o7b3o\$32bo11b2o11b2o\$57bo11b7o3b7o\$
6b2o50b3o8bo6bobo6bo\$3b2o2bo52bo9bobob2o3b2obobo\$b3ob2o64b2obo5bob2o\$o
39b2o34bobo\$b3ob2o33bo34b2ob2o\$3bob2o13b3o18b3o\$22bo20bo\$22b2o2\$b2o25b
2o\$b2o25bo\$10b2o17bo\$10b2o16b2o\$27bo\$27b3o\$5b2o23bo\$4bobo22b2o\$4bo\$3b
2o\$26b2o\$26bobo\$28bo\$28b2o4\$69b2o133b2o\$70bo133bo\$70bobo129bobo\$71b2o
129b2o3\$95bo83bo\$94bobo81bobo\$73b2o19bobo81bobo19b2o\$68b2o3b2o20bo83bo
20b2o3b2o\$67bo2bo133bo2bo\$67bobobo52b2o23b2o52bobobo\$66b2obobo52bobo
21bobo52bobob2o\$67bo2bo55bo21bo55bo2bo\$67bo58b2o19b2o58bo\$65bob2o137b
2obo\$64bobo2bobo63b2ob2o63bobo2bobo\$64bo2bo2b2o28b2o33b2ob2o33b2o28b2o
2bo2bo\$65b2o7bob2o22b2o71b2o22b2obo7b2o\$70b5obo121bob5o\$70bo5bobo40b2o
33b2o40bobo5bo\$72bo3b2obo39bo35bo39bob2o3bo\$71b2o6bo40b3o29b3o40bo6b2o
\$79b2o9b2o30bo5b2o22bo30b2o9b2o\$90b2o17bo17bobo35bo17b2o\$108bobo16bo
12bo23bobo\$109bo16b2o11bobo23bo\$140b2o4\$128b2o\$129bo\$129bobo\$130b2o14b
2o\$146b2o6\$113bo\$113b3o\$116bo\$115b2o2\$96bo\$96b3o\$99bo\$86bo11b2o11b2o
11bo\$84b3o24b2o9b3o22b2o\$83bo38bo24bo\$83b2o37bo22bobo\$68b2o75b2o\$69bo\$
69bob2o\$70bo2bo23bo\$71b2o24bo\$86b2o9b3o\$86b2o11bo22b2o\$121bobo\$121bo\$
120b2o2\$94bo3b2o\$93bobo3bo\$89b2obobo3bo12b2o\$89b2obo4bo13bo27bo\$93b5ob
o12b3o23bobo\$85b2obob2obo4bobo13bo23b2o\$85bob2obo2bob2o2bo\$78b2o12b2ob
ob2o\$78b2o58b2o\$138bo\$139b3o\$141bo!
``````
The contraption involves a number of components, including Snark64, Speed Tunnel, syringe, HF95P, a Spartan version of the pi splitter, some Herschel conduits (Fx77, R64, Lx86), a H-to-G converter (SE18T9), a glider reflector from December 2023, and a H-to-boat still life factory.
[...]
127:1 B3/S234c User:Confocal/R (isotropic CA, incomplete)
Unlikely events happen.
My silence does not imply agreement, nor indifference. If I disagreed with something in the past, then please do not construe my silence as something that could change that.

TigerCub414
Posts: 10
Joined: March 25th, 2024, 9:51 pm

Is Adam P. Goucher's Thessalonic G-to-H the cheapest known G-to-H to construct with a slow salvo?

dvgrn
Moderator
Posts: 10872
Joined: May 17th, 2009, 11:00 pm
Contact:

TigerCub414 wrote:
June 22nd, 2024, 4:39 pm
Is Adam P. Goucher's Thessalonic G-to-H the cheapest known G-to-H to construct with a slow salvo?
I think that's a definite "maybe" at the moment. There are only 11 still lifes in the Thessalonic G-to-H, mostly eaters -- but some of them are quite close to other eaters, which will make them more expensive to construct. The cost in slow-salvo might change quite a bit depending on the orientation of the G-to-H. There's no way to tell for sure what's "cheapest known" without running a recent pslmake build against all orientations, and ... averaging? adding up? ... the costs.

The dependent form of the syringe only has five objects in it, and they're separated just far enough from each other that construction isn't hampered by other existing objects nearby. The objects include an eater2 and a beehive-with-tail, which are expensive to slow-salvo construct, but not terribly expensive. Seems like the dependent syringe is still in the running until proven otherwise.

For that matter, there's really not a lot of point in constructing either the Thessalonic G-to-H or the dependent syringe without also constructing whatever it's attached to, to suppress the output Herschel's first natural glider.

So maybe the measurements to check could be the total cost of all orientations of

1) a Callahan G-to-H, capped with a beehive to make it a G-to-G,
2) a dependent syringe with some minimal dependent H-to-G attached to make it a working G-to-G,
3) the Thessalonic G-to-H with (the same?) minimal dependent H-to-G attached.

(?)

confocaloid
Posts: 3524
Joined: February 8th, 2022, 3:15 pm

TigerCub414 wrote:
June 22nd, 2024, 4:39 pm
Is Adam P. Goucher's Thessalonic G-to-H the cheapest known G-to-H to construct with a slow salvo?
dvgrn wrote:
June 22nd, 2024, 6:13 pm
I think that's a definite "maybe" at the moment. [...]
For Callahan G-to-H, there are also several known ways to complete it:
viewtopic.php?p=166003#p166003
viewtopic.php?p=183223#p183223

confocaloid
Posts: 3524
Joined: February 8th, 2022, 3:15 pm

dvgrn wrote:
June 23rd, 2024, 6:46 am
[...]
There are any number of rules where you can set up ways for information to move from point A to point B in the same way that the "logic gates" are doing in that B78/S012345 thread -- once but not repeatably. The thread shows how structures can be built that will collapse in a predictable way into a permanently broken state while doing some things that can be interpreted as logical operations. We could do that in all kinds of different ways in Conway's Life, too -- but we don't spend much of any time on it, because it just plain doesn't seem to be all that interesting compared to repeatable-use circuitry.
One possible use of one-time logic would be to provide a way of configuring repeatable circuitry, once at the start.
There is some pattern that can be configured (before running) in some understandable way, and will evolve into one of a number of possible contraptions, for example depending on which initially present blocks you remove. The configuration part will be destroyed in a predictable way while reading it at the start.
What are good existing examples of this?
127:1 B3/S234c User:Confocal/R (isotropic CA, incomplete)
Unlikely events happen.
My silence does not imply agreement, nor indifference. If I disagreed with something in the past, then please do not construe my silence as something that could change that.

dvgrn
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confocaloid wrote:
June 23rd, 2024, 9:27 am
One possible use of one-time logic would be to provide a way of configuring repeatable circuitry, once at the start.
There is some pattern that can be configured (before running) in some understandable way, and will evolve into one of a number of possible contraptions, for example depending on which initially present blocks you remove. The configuration part will be destroyed in a predictable way while reading it at the start.
What are good existing examples of this?
The example that comes to mind is the one-time circuitry that Brice Due designed for the OTCAMP project. Objects are arranged at the corners and edges of the metapixel so that whenever connections need to be made at the corners between four neighboring metacells, four fuses are lit that burn off a key two-block LWSS eater, and a temporary LWSS escapes. A third block is added behind another two-block eater so that it mutually annihilates with the LWSS from the opposite direction.

If the fuses don't get lit, that two-block eater remains in place and automatically seals off the edges of the metacell area so that signals to neighbors aren't always being sent out into empty space.

It's kind of a shame that metafier.py hides all of this startup activity by running the metafied pattern for one cycle. Probably a lot of people have never seen that complicated fuse trickery in the corners... if anyone wants to have a look at these things in context, just disable the "g.step()" line at the very end of metafier.lua.

Those fuses are probably hugely over-engineered -- I wouldn't be surprised if there was a much much simpler solution -- but they're fun to look at:

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``````x = 186, y = 186, rule = B3/S23
94b2o\$94b2o2b2o\$98b2o3\$98b2o\$98b2o28\$98b2o\$98b2o2\$94b2o6b2o\$94b2o2b2o
2bo\$98b2o3b3o\$106bo\$105bo\$104bo\$103bo\$102bo\$101bo\$100bo\$99bo\$100b3o\$
103bo\$102bo\$101bo\$100bo\$99bo\$100b3o\$103bo\$102bo\$101bo\$100bo\$99bo\$100b
3o\$103bo\$102bo\$101bo\$100bo\$99bo\$100b3o\$103bo\$102bo\$101bo\$100bo\$99bo\$
100b3o\$103bo\$102bo\$101bo\$100bo\$99bo\$100b3o\$40bo62bo\$39bobo51b3o6bo\$39b
o2bo50bo2bo4bo\$37bobo3bo5bo5bo5bo5bo5bo5bo5bo7bo6bo\$37b2o5bo3bobo3bobo
3bobo3bobo3bobo3bobo3bobo6bo5bo\$45bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo
2bo2bo2bo6bobo3b3o\$46bobo3bobo3bobo3bobo3bobo3bobo3bobo3bo14bo\$b2o2b2o
27b2o2b2o7bo5bo5bo5bo5bo5bo5bo3b2o13bo\$b2o2b2o27b2o2b2o59bobo\$89bo6bo
2b2o\$81bo2bo3bobo4bobo\$2o35b2o41bo8bo6bo\$2o35b2o41bo3bo\$80b4o8b2o\$92b
2o8b4o\$101bo3bo41b2o35b2o\$89bo6bo8bo41b2o35b2o\$88bobo4bobo3bo2bo\$85b2o
2bo6bo\$84bobo59b2o2b2o27b2o2b2o\$83bo13b2o3bo5bo5bo5bo5bo5bo5bo7b2o2b2o
27b2o2b2o\$82bo14bo3bobo3bobo3bobo3bobo3bobo3bobo3bobo\$83b3o3bobo6bo2bo
2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo2bo\$86bo5bo6bobo3bobo3bobo3bobo3bo
bo3bobo3bobo3bo5b2o\$85bo6bo7bo5bo5bo5bo5bo5bo5bo5bo3bobo\$84bo4bo2bo50b
o2bo\$83bo6b3o51bobo\$82bo62bo\$83b3o\$86bo\$85bo\$84bo\$83bo\$82bo\$83b3o\$86bo
\$85bo\$84bo\$83bo\$82bo\$83b3o\$86bo\$85bo\$84bo\$83bo\$82bo\$83b3o\$86bo\$85bo\$
84bo\$83bo\$82bo\$83b3o\$86bo\$85bo\$84bo\$83bo\$82bo\$83b3o\$86bo\$85bo\$84bo\$83b
o\$82bo\$81bo\$80bo\$79bo\$80b3o3b2o\$83bo2b2o2b2o\$82b2o6b2o2\$86b2o\$86b2o28\$
86b2o\$86b2o3\$86b2o\$86b2o2b2o\$90b2o!``````
There are also "proximity fuses" at the orthogonal edges between metacells, but those are much less interesting-looking -- just simple fishhook eaters sabotaged by a nearby block from the next metacell.

confocaloid
Posts: 3524
Joined: February 8th, 2022, 3:15 pm

Roughly how many different synthesis components are currently known?

vilc
Posts: 68
Joined: March 20th, 2024, 4:36 pm

confocaloid wrote:
June 24th, 2024, 3:40 pm
Roughly how many different synthesis components are currently known?
It depends on the criterias used to differentiate components. If we take Shinkuku's definition of "template component", then there are around 22000 of them, but this definition wouldn't match that of a human being for many reasons:
• The useful "component" below is to my knowledge the cheapest way to perform a very elementary transformation, but it consists in multiple stages that involve other components. Should we count it as a component or some kind of metacomponent ?

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``````x = 70, y = 68, rule = LifeHistory
9.A.A\$10.2A\$10.A56.A.A\$67.2A\$4.A59.A3.A\$2.A.A57.2A\$3.2A58.2A2\$7.A\$5.A
.A\$6.2A2\$18.A\$16.A.A39.A\$17.2A39.A.A\$58.2A3\$48.A7.A.A\$48.A.A5.2A\$48.
2A7.A5\$8.A30.A\$6.A.A8.A19.A.A\$7.2A6.A.A9.A10.2A\$16.2A10.2A\$27.2A12.2A
\$41.A.A\$41.A4\$43.A\$38.D3.2A\$17.2A15.2A3D3.A.A\$16.A.A16.C\$18.A16.C.2C\$
34.2C.C\$36.C2.C\$36.C.2C12.2A\$35.2C.C12.2A\$38.C14.A\$38.2C20\$.2A\$A.A\$2.
A!``````
There are perhaps only a few thousands of elementary components.
• I don't know if this "component" has any other application on a single object, but it can be used to build complex constellations incrementally:

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``````x = 41, y = 43, rule = LifeHistory
3\$15.A\$16.A20.A\$14.3A18.2A\$36.2A5\$33.A.A\$33.2A\$34.A2\$14.A2.2D\$14.2A.D
32.2A\$31.2A\$4.3A26.A\$6.A19.2A\$5.A20.A.A\$26.A!
``````
In the same order of ideas, a synthesis of any object starting from vacuum can or cannot be considered as a component.
• The following reactions would usually be considered distinct components, but they perform the same transformation.

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``````x = 29, y = 17, rule = LifeHistory
2\$19.A\$6.A.A11.A\$7.2A3.A5.3A\$7.A2.2A11.2A\$11.2A9.2A\$24.A\$5.CD13.CD\$4.
C.C12.C.C\$5.C14.C!
``````
And what if they had the same clearance ? If they used the same reaction and differed only in cleanup ?
• The answer could be infinity if we allow infinite chains of fast components :

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``````x = 48, y = 32, rule = LifeHistory
41.A\$41.A.A\$41.2A\$46.A\$45.A\$24.A9.A10.3A\$23.A9.A\$23.3A7.3A2\$3.A.A\$4.
2A30.2A\$4.A30.A2.A\$35.A2.A\$18.A9.A7.2A\$16.A.A7.A.A\$17.2A8.2A\$40.2C\$
17.2D.2D2.D2.2D.2D2.D2.DC2.C\$15.D2.D.D2.D.D2.D.D2.D.D2.2C\$15.2D2.D2.
2D.2D2.D2.2D.2D2\$12.2A8.2A\$11.A.A7.A.A\$13.A9.A\$.A\$.2A4.A\$A.A4.2A\$6.A.
A2\$28.3A7.3A\$28.A9.A\$29.A9.A!
``````
If we restrict ourselves to small, non-trivial, elementary components with good reusability and include a few useful variants (like most components in components_v4), then I would say the answer lies between a few hundreds and a thousand, although I can't accurately measure it. That would be the most reasonnable way to count in my opinion.