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Engineered Spaceships Q&A

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Engineered Spaceships Q&A

Postby biggiemac » April 11th, 2016, 4:43 am

There have been a couple times I wish I had a general "engineered spaceships" thread here, for my reference and to refer others, so here it is. I hope frequent lifeviewer examples make this more digestible..

Engineered spaceships families currently known:
Gabriel Nivasch's 17c/45 Caterpillar
Andrew Wade's Gemini
Half-Baked knightships
31c/240 Centipede/shield bug
Waterbear
Demonoid
simsim314's caterloopillar

Proposed:
13131 (13,1)c/31 oblique caterpillar
(27,1)c/72 oblique caterpillar
1D spaceship
others..?

History and Terminology
For a while, "engineered spaceship" was synonymous with "caterpillar," which in turn was synonymous with Gabriel Nivasch's 17c/45 Caterpillar spaceship. A great reference for the technology specific to that caterpillar is found on his website here. In particular, it defines a few pretty common terms:

climber/crawler: A chainable natural reaction, typically a reburnable fuse, that moves at a certain velocity. This velocity defines the spaceship velocity. The reaction itself is known as a climber or crawler (I prefer climber), and the trail it climbs on is referred to as a "track."
x = 23, y = 126, rule = B3/S23
10b3o16$11bo$11bo$11bo16$10b3o16$11bo$11bo$11bo16$10b3o4$11bo$10bobo$
10bobo$10bobo3$2b2o2b3o5b3o2b2o$bobo2b2o7b2o2bobo$2o6bo5bo6b2o$b2ob3o
9b3ob2o$2b3o2bo7bo2b3o$3bo3b2o5b2o3bo$4b2o2b2o3b2o2b2o$4bo2b2obobob2o
2bo$5bo2b2o3b2o2bo$6b3o5b3o4$10b3o16$11bo$11bo$11bo16$10b3o!


helix: An engineered periodic assortment of parallel LWSS, MWSS or HWSS (collectively, *WSS), plus a single defect at the top, usually a glider. This defect interacts with the *WSS, destroying one period worth while moving the exact same distance that the climber does. It is named "helix" because if you graph the position of the defect over time it vaguely resembles a spiral, looping but moving.

The helix defines the spaceship period, always a multiple of the period of the climber, so it's usually referred to as xN, where N is the multiple. For the Caterpillar, Gabriel Nivasch used a x6 helix. Observe that the helix keeps pace exactly with the climber, and completes a cycle every 6 climber periods.
x = 133, y = 290, rule = B3/S23
10bo$10bo$10bo16$9b3o16$10bo$10bo$10bo16$9b3o16$10bo$10bo$10bo16$9b3o
16$10bo$10bo$10bo16$9b3o16$10bo$10bo$10bo16$9b3o16$10bo$10bo$10bo16$9b
3o16$10bo$10bo$10bo$114bo$100bo12b3o$86bo12b3o4b3o3b2obo4b2o$9b3o60bo
12b3o4b3o3b2obo3bo2bo3b3o5bobo$9b3o59b3o4b3o3b2obo3bo2bo3b3o7bo4b2o5bo
$64b3o3b2obo3bo2bo3b3o7bo4b2o3bo3bo$9bobo51bo2bo3b3o7bo4b2o3bo3bo9bo3b
o$66bo4b2o3bo3bo9bo3bo13bo$b2o2b2o7b2o2b2o42bo3bo9bo3bo13bo10bobo$obo
3bobo3bobo3bobo41bo3bo13bo10bobo$o6bo5bo6bo45bo10bobo$o3bo5bo5bo3bo36b
3o3bobo$bob3o9b3obo37bo2bo$2bo2b2o7b2o2bo38bo$4bo2b2o3b2o2bo40bo3bo$4b
2o3bobo3b2o40bo$4b2o2bo3bo2b2o41bobo6b3o$6b2o5b2o52bo2bo4bo5b3o$67bo6b
3o4bo2bo4bo5b3o$61b3o3bo5b2obo4bo6b3o4bo2bo4bo$10bo50bo2bo3bobo2b3o5bo
5b2obo4bo6b3o5b3o$10bo50bo11b3o6bobo2b3o5bo5b2obo5bo2bo4bo$10bo38b3o9b
o11b3o11b3o6bobo2b3o6bo6b3o$48bo2bo10bobo9b2o11b3o11b3o6bo5b2obo$51bo
36b2o11b3o7bobo2b3o$47bo3bo50b2o12b3o$47bo3bo64b3o$51bo65b2o$48bobo4$
129b3o$114bo13bo2bo$100bo12b3o4b3o8bo$86bo12b3o4b3o4bob2o3bo2bo7bo$72b
o12b3o4b3o4bob2o3bo2bo4b3o3bo7bobo$71b3o4b3o4bob2o3bo2bo4b3o3bo7b2o4bo
3bo$64b3o4bob2o3bo2bo4b3o3bo7b2o4bo3bo9bo3bo$64bo2bo4b3o3bo7b2o4bo3bo
9bo3bo9bo$64bo7b2o4bo3bo9bo3bo9bo14bobo$64bo3bo9bo3bo9bo14bobo$64bo3bo
9bo14bobo$64bo14bobo$57b3o5bobo$56bo2bo$59bo$55bo3bo$59bo$56bobo8b3o$
66bo2bo5bo5b3o$69bo4b3o3bo2bo5bo5b3o$61b3o5bo4bob2o5bo4b3o3bo2bo5bo$
60bo2bo2bobo6b3o5bo4bob2o5bo4b3o5b3o$63bo11b3o2bobo6b3o5bo4bob2o3bo2bo
5bo$49b3o11bo11b3o11b3o2bobo6b3o6bo4b3o$49bo2bo7bobo12b2o12b3o11b3o6bo
4bob2o$49bo39b2o12b3o3bobo6b3o$49bo3bo49b2o13b3o$49bo3bo64b3o$49bo68b
2o$50bobo4$129b3o$114bo14bo2bo$100bo12b3o4b3o6bo$86bo12b3o4b3o3b2obo3b
o2bo6bo$72bo12b3o4b3o3b2obo3bo2bo3b3o7bo7bobo$71b3o4b3o3b2obo3bo2bo3b
3o7bo4b2o3bo3bo$64b3o3b2obo3bo2bo3b3o7bo4b2o3bo3bo9bo3bo$63bo2bo3b3o7b
o4b2o3bo3bo9bo3bo13bo$66bo4b2o3bo3bo9bo3bo13bo10bobo$62bo3bo9bo3bo13bo
10bobo$62bo3bo13bo10bobo$66bo10bobo$57b3o3bobo$57bo2bo$57bo$57bo3bo$
57bo$58bobo!


Important note, the helix is engineered. There are available tools to build helices for any velocity with orthogonal speed strictly less than 11c/24, though the periods get larger and larger the closer to the speed limit you get. SInce the waterbear is slower than the caterpillar, there was a x2 helix available. Since the (13,1)c/31 project is very near the speed limit, the best known helix is x16.

Why are "climbers" and "helices" important?
A spaceship in CGOL is basically a perpetual motion machine. It goes forever without being slowed, altered, or destroyed. The climbers accomplish this for free as long as the front is supported. The whole point of the helix is to provide support at the front of the ship to get the climbers started. However, the support comes at a cost: the *WSS are destroyed.

In general, we have to make up for this by coming out ahead somewhere else. I always refer to it as an "overunity" reaction - something that not only shows perpetual motion, but actually free energy. This is fundamental to any engineered spaceship, not just caterpillars.

In the context of a caterpillar, one major design challenge is turning copies of the climber into an appropriate set of overunity reactions, and another is connecting them to the helix.

Since a xN helix needs to support N iterations of the climbing reaction each cycle, "fanouts" are used to take some spark from the helix and fan it out into N usable targets. This is typically accomplished with additional *WSS, making effectively a bigger helix. This can make the difficulty grow very quickly.: you don't know how many *WSS you are destroying each cycle until you can show an overunity reaction successfully climbing the debris. A condensed version of this for the caterpillar is shown below - that is a lot of *WSS.
x = 894, y = 1502, rule = B3/S23
822b2o$818bo3b2o$817bobo$817bobo9bo$818bo9b3o12bo$828bob2o3b3o4b3o12bo
$823bo5b3o3bo2bo3bob2o3b3o4b3o$822b3o4b2o4bo7b3o3bo2bo3bob2o3b3o6bo$
822bob2o9bo3bo3b2o4bo7b3o3bo2bo4b3o$811bo11b3o9bo3bo9bo3bo3b2o4bo7bob
2o3b3o$810b3o10b2o10bo13bo3bo9bo3bo4b3o3bo2bo$809b2obo23bobo10bo13bo3b
o4b2o4bo$809b3o38bobo10bo14bo3bo$809b3o52bobo11bo3bo$809b3o66bo$810b2o
67bobo4$891bo$890b3o$874b3o5bo6b2obo$860b3o5bo4bo2bo4b3o5b3o$846b3o5bo
4bo2bo4b3o6bo4bob2o5b2o$832b3o5bo4bo2bo4b3o6bo4bob2o5bo5b3o$826bo4bo2b
o4b3o6bo4bob2o5bo5b3o2bobo6b3o$825b3o6bo4bob2o5bo5b3o2bobo6b3o11b3o$
825bob2o5bo5b3o2bobo6b3o11b3o11b2o$826b3o2bobo6b3o11b3o11b2o$826b3o11b
3o11b2o$826b3o11b2o$819bo6b2o$818b3o$817b2obo$817b3o$817b3o$818b2o9bo$
828b3o12bo$827b2obo4b3o4b3o12bo$823bo3b3o4bo2bo3b2obo4b3o4b3o$822b3o3b
2o7bo3b3o4bo2bo3b2obo4b3o6bo$821b2obo8bo3bo4b2o7bo3b3o4bo2bo5b3o$811bo
9b3o9bo3bo9bo3bo4b2o7bo4b2obo4b3o$756b2o52b3o9b2o13bo9bo3bo9bo3bo4b3o
4bo2bo$756bobo51bob2o20bobo14bo9bo3bo5b2o7bo$756bo54b3o34bobo14bo10bo
3bo$811b3o48bobo11bo3bo$811b3o66bo$811b2o64bobo4$891bo$890b3o$750b3o
121b3o5bo7bob2o$749bo2bo107b3o5bo5bo2bo3b3o7b3o$752bo93b3o5bo5bo2bo3b
3o4bo5b2obo7b2o$748bo3bo79b3o5bo5bo2bo3b3o4bo5b2obo4bo5b3o$752bo73bo5b
o2bo3b3o4bo5b2obo4bo5b3o6bobo2b3o$749bobo73b3o4bo5b2obo4bo5b3o6bobo2b
3o11b3o$824b2obo4bo5b3o6bobo2b3o11b3o12b2o$824b3o6bobo2b3o11b3o12b2o$
824b3o11b3o12b2o$736b3o85b3o12b2o$736bo2bo79bo5b2o$736bo81b3o$736bo3bo
77bob2o$736bo82b3o$737bobo79b3o$819b2o8bo$828b3o12bo$828bob2o3b3o4b3o
12bo$823bo5b3o3bo2bo3bob2o3b3o4b3o$822b3o4b2o4bo7b3o3bo2bo3bob2o3b3o6b
o$822bob2o9bo3bo3b2o4bo7b3o3bo2bo4b3o$811bo11b3o9bo3bo9bo3bo3b2o4bo7bo
b2o3b3o$810b3o10b2o10bo13bo3bo9bo3bo4b3o3bo2bo$809b2obo23bobo10bo13bo
3bo4b2o4bo$809b3o38bobo10bo14bo3bo$809b3o52bobo11bo3bo$809b3o66bo$810b
2o67bobo2$684bo$683b2o$683bobo205bo$890b3o$750b3o121b3o5bo6b2obo$750bo
2bo106b3o5bo4bo2bo4b3o5b3o$750bo95b3o5bo4bo2bo4b3o6bo4bob2o5b2o$750bo
3bo77b3o5bo4bo2bo4b3o6bo4bob2o5bo5b3o$750bo75bo4bo2bo4b3o6bo4bob2o5bo
5b3o2bobo6b3o$751bobo71b3o6bo4bob2o5bo5b3o2bobo6b3o11b3o$825bob2o5bo5b
3o2bobo6b3o11b3o11b2o$826b3o2bobo6b3o11b3o11b2o$826b3o11b3o11b2o$736b
3o87b3o11b2o$735bo2bo80bo6b2o$738bo79b3o$734bo3bo78b2obo$738bo78b3o$
735bobo79b3o$818b2o9bo$828b3o12bo$827b2obo4b3o4b3o12bo$823bo3b3o4bo2bo
3b2obo4b3o4b3o$822b3o3b2o7bo3b3o4bo2bo3b2obo4b3o6bo$821b2obo8bo3bo4b2o
7bo3b3o4bo2bo5b3o$811bo9b3o9bo3bo9bo3bo4b2o7bo4b2obo4b3o$810b3o9b2o13b
o9bo3bo9bo3bo4b3o4bo2bo$810bob2o20bobo14bo9bo3bo5b2o7bo$811b3o34bobo
14bo10bo3bo$811b3o48bobo11bo3bo$811b3o66bo$811b2o64bobo4$616b2o273bo$
615b2o273b3o$617bo132b3o121b3o5bo7bob2o$749bo2bo107b3o5bo5bo2bo3b3o7b
3o$752bo93b3o5bo5bo2bo3b3o4bo5b2obo7b2o$748bo3bo79b3o5bo5bo2bo3b3o4bo
5b2obo4bo5b3o$752bo73bo5bo2bo3b3o4bo5b2obo4bo5b3o6bobo2b3o$749bobo73b
3o4bo5b2obo4bo5b3o6bobo2b3o11b3o$824b2obo4bo5b3o6bobo2b3o11b3o12b2o$
824b3o6bobo2b3o11b3o12b2o$824b3o11b3o12b2o$736b3o85b3o12b2o$736bo2bo
79bo5b2o$736bo81b3o$736bo3bo77bob2o$736bo82b3o$737bobo79b3o$819b2o8bo$
828b3o12bo$828bob2o3b3o4b3o12bo$823bo5b3o3bo2bo3bob2o3b3o4b3o$822b3o4b
2o4bo7b3o3bo2bo3bob2o3b3o6bo$822bob2o9bo3bo3b2o4bo7b3o3bo2bo4b3o$811bo
11b3o9bo3bo9bo3bo3b2o4bo7bob2o3b3o$810b3o10b2o10bo13bo3bo9bo3bo4b3o3bo
2bo$809b2obo23bobo10bo13bo3bo4b2o4bo$809b3o38bobo10bo14bo3bo$809b3o52b
obo11bo3bo$809b3o66bo$810b2o67bobo4$891bo$549bo340b3o$548b2o200b3o121b
3o5bo6b2obo$548bobo199bo2bo106b3o5bo4bo2bo4b3o5b3o$750bo95b3o5bo4bo2bo
4b3o6bo4bob2o5b2o$750bo3bo77b3o5bo4bo2bo4b3o6bo4bob2o5bo5b3o$750bo75bo
4bo2bo4b3o6bo4bob2o5bo5b3o2bobo6b3o$751bobo71b3o6bo4bob2o5bo5b3o2bobo
6b3o11b3o$825bob2o5bo5b3o2bobo6b3o11b3o11b2o$826b3o2bobo6b3o11b3o11b2o
$826b3o11b3o11b2o$736b3o87b3o11b2o$735bo2bo80bo6b2o$738bo79b3o$734bo3b
o78b2obo$738bo78b3o$735bobo79b3o$818b2o9bo$828b3o12bo$827b2obo4b3o4b3o
12bo$823bo3b3o4bo2bo3b2obo4b3o4b3o$822b3o3b2o7bo3b3o4bo2bo3b2obo4b3o6b
o$821b2obo8bo3bo4b2o7bo3b3o4bo2bo5b3o$811bo9b3o9bo3bo9bo3bo4b2o7bo4b2o
bo4b3o$810b3o9b2o13bo9bo3bo9bo3bo4b3o4bo2bo$810bob2o20bobo14bo9bo3bo5b
2o7bo$811b3o34bobo14bo10bo3bo$811b3o48bobo11bo3bo$811b3o66bo$811b2o64b
obo4$891bo$690bo199b3o$689bo60b3o121b3o5bo7bob2o$481b2o206b3o57bo2bo
107b3o5bo5bo2bo3b3o7b3o$480b2o270bo93b3o5bo5bo2bo3b3o4bo5b2obo7b2o$
482bo265bo3bo79b3o5bo5bo2bo3b3o4bo5b2obo4bo5b3o$752bo73bo5bo2bo3b3o4bo
5b2obo4bo5b3o6bobo2b3o$749bobo73b3o4bo5b2obo4bo5b3o6bobo2b3o11b3o$824b
2obo4bo5b3o6bobo2b3o11b3o12b2o$824b3o6bobo2b3o11b3o12b2o$824b3o11b3o
12b2o$736b3o85b3o12b2o$736bo2bo79bo5b2o$736bo81b3o$736bo3bo77bob2o$
736bo82b3o$737bobo79b3o$819b2o8bo$828b3o12bo$828bob2o3b3o4b3o12bo$823b
o5b3o3bo2bo3bob2o3b3o4b3o$822b3o4b2o4bo7b3o3bo2bo3bob2o3b3o6bo$822bob
2o9bo3bo3b2o4bo7b3o3bo2bo4b3o$811bo11b3o9bo3bo9bo3bo3b2o4bo7bob2o3b3o$
810b3o10b2o10bo13bo3bo9bo3bo4b3o3bo2bo$809b2obo23bobo10bo13bo3bo4b2o4b
o$809b3o38bobo10bo14bo3bo$809b3o52bobo11bo3bo$809b3o66bo$810b2o67bobo
4$891bo$890b3o$750b3o121b3o5bo6b2obo$750bo2bo106b3o5bo4bo2bo4b3o5b3o$
414bo335bo95b3o5bo4bo2bo4b3o6bo4bob2o5b2o$413b2o335bo3bo77b3o5bo4bo2bo
4b3o6bo4bob2o5bo5b3o$413bobo334bo75bo4bo2bo4b3o6bo4bob2o5bo5b3o2bobo6b
3o$751bobo71b3o6bo4bob2o5bo5b3o2bobo6b3o11b3o$825bob2o5bo5b3o2bobo6b3o
11b3o11b2o$826b3o2bobo6b3o11b3o11b2o$826b3o11b3o11b2o$736b3o87b3o11b2o
$735bo2bo80bo6b2o$738bo79b3o$734bo3bo78b2obo$738bo78b3o$735bobo79b3o$
818b2o9bo$828b3o12bo$827b2obo4b3o4b3o12bo$823bo3b3o4bo2bo3b2obo4b3o4b
3o$822b3o3b2o7bo3b3o4bo2bo3b2obo4b3o6bo$821b2obo8bo3bo4b2o7bo3b3o4bo2b
o5b3o$811bo9b3o9bo3bo9bo3bo4b2o7bo4b2obo4b3o$810b3o9b2o13bo9bo3bo9bo3b
o4b3o4bo2bo$810bob2o20bobo14bo9bo3bo5b2o7bo$811b3o34bobo14bo10bo3bo$
811b3o48bobo11bo3bo$811b3o66bo$811b2o64bobo4$891bo$890b3o$750b3o121b3o
5bo7bob2o$749bo2bo107b3o5bo5bo2bo3b3o7b3o$752bo93b3o5bo5bo2bo3b3o4bo5b
2obo7b2o$748bo3bo79b3o5bo5bo2bo3b3o4bo5b2obo4bo5b3o$346b2o404bo73bo5bo
2bo3b3o4bo5b2obo4bo5b3o6bobo2b3o$345b2o402bobo73b3o4bo5b2obo4bo5b3o6bo
bo2b3o11b3o$347bo476b2obo4bo5b3o6bobo2b3o11b3o12b2o$824b3o6bobo2b3o11b
3o12b2o$824b3o11b3o12b2o$736b3o85b3o12b2o$736bo2bo79bo5b2o$736bo81b3o$
736bo3bo77bob2o$736bo82b3o$737bobo79b3o$819b2o8bo$828b3o12bo$828bob2o
3b3o4b3o12bo$823bo5b3o3bo2bo3bob2o3b3o4b3o$822b3o4b2o4bo7b3o3bo2bo3bob
2o3b3o6bo$822bob2o9bo3bo3b2o4bo7b3o3bo2bo4b3o$811bo11b3o9bo3bo9bo3bo3b
2o4bo7bob2o3b3o$810b3o10b2o10bo13bo3bo9bo3bo4b3o3bo2bo$809b2obo23bobo
10bo13bo3bo4b2o4bo$809b3o38bobo10bo14bo3bo$809b3o52bobo11bo3bo$809b3o
66bo$810b2o67bobo4$891bo$890b3o$750b3o121b3o5bo6b2obo$750bo2bo106b3o5b
o4bo2bo4b3o5b3o$750bo95b3o5bo4bo2bo4b3o6bo4bob2o5b2o$750bo3bo77b3o5bo
4bo2bo4b3o6bo4bob2o5bo5b3o$750bo75bo4bo2bo4b3o6bo4bob2o5bo5b3o2bobo6b
3o$279bo471bobo71b3o6bo4bob2o5bo5b3o2bobo6b3o11b3o$278b2o545bob2o5bo5b
3o2bobo6b3o11b3o11b2o$278bobo545b3o2bobo6b3o11b3o11b2o$826b3o11b3o11b
2o$736b3o87b3o11b2o$735bo2bo80bo6b2o$738bo79b3o$734bo3bo78b2obo$738bo
78b3o$735bobo79b3o$818b2o9bo$828b3o12bo$827b2obo4b3o4b3o12bo$823bo3b3o
4bo2bo3b2obo4b3o4b3o$822b3o3b2o7bo3b3o4bo2bo3b2obo4b3o6bo$821b2obo8bo
3bo4b2o7bo3b3o4bo2bo5b3o$811bo9b3o9bo3bo9bo3bo4b2o7bo4b2obo4b3o$810b3o
9b2o13bo9bo3bo9bo3bo4b3o4bo2bo$810bob2o20bobo14bo9bo3bo5b2o7bo$811b3o
34bobo14bo10bo3bo$811b3o48bobo11bo3bo$811b3o66bo$811b2o64bobo4$891bo$
890b3o$750b3o121b3o5bo7bob2o$749bo2bo107b3o5bo5bo2bo3b3o7b3o$752bo93b
3o5bo5bo2bo3b3o4bo5b2obo7b2o$748bo3bo79b3o5bo5bo2bo3b3o4bo5b2obo4bo5b
3o$752bo73bo5bo2bo3b3o4bo5b2obo4bo5b3o6bobo2b3o$749bobo73b3o4bo5b2obo
4bo5b3o6bobo2b3o11b3o$824b2obo4bo5b3o6bobo2b3o11b3o12b2o$211b2o611b3o
6bobo2b3o11b3o12b2o$210b2o612b3o11b3o12b2o$212bo523b3o85b3o12b2o$736bo
2bo79bo5b2o$736bo81b3o$736bo3bo77bob2o$736bo82b3o$737bobo79b3o$819b2o
8bo$828b3o12bo$828bob2o3b3o4b3o12bo$823bo5b3o3bo2bo3bob2o3b3o4b3o$822b
3o4b2o4bo7b3o3bo2bo3bob2o3b3o6bo$822bob2o9bo3bo3b2o4bo7b3o3bo2bo4b3o$
811bo11b3o9bo3bo9bo3bo3b2o4bo7bob2o3b3o$810b3o10b2o10bo13bo3bo9bo3bo4b
3o3bo2bo$809b2obo23bobo10bo13bo3bo4b2o4bo$809b3o38bobo10bo14bo3bo$809b
3o52bobo11bo3bo$809b3o66bo$810b2o67bobo4$891bo$890b3o$750b3o121b3o5bo
6b2obo$750bo2bo106b3o5bo4bo2bo4b3o5b3o$750bo95b3o5bo4bo2bo4b3o6bo4bob
2o5b2o$750bo3bo77b3o5bo4bo2bo4b3o6bo4bob2o5bo5b3o$622bo127bo75bo4bo2bo
4b3o6bo4bob2o5bo5b3o2bobo6b3o$622bobo126bobo71b3o6bo4bob2o5bo5b3o2bobo
6b3o11b3o$622b2o201bob2o5bo5b3o2bobo6b3o11b3o11b2o$826b3o2bobo6b3o11b
3o11b2o$144bo681b3o11b3o11b2o$143b2o591b3o87b3o11b2o$143bobo589bo2bo
80bo6b2o$738bo79b3o$734bo3bo78b2obo$738bo78b3o$735bobo79b3o$818b2o9bo$
828b3o12bo$827b2obo4b3o4b3o12bo$823bo3b3o4bo2bo3b2obo4b3o4b3o$822b3o3b
2o7bo3b3o4bo2bo3b2obo4b3o6bo$821b2obo8bo3bo4b2o7bo3b3o4bo2bo5b3o$811bo
9b3o9bo3bo9bo3bo4b2o7bo4b2obo4b3o$810b3o9b2o13bo9bo3bo9bo3bo4b3o4bo2bo
$810bob2o20bobo14bo9bo3bo5b2o7bo$811b3o34bobo14bo10bo3bo$617b3o191b3o
48bobo11bo3bo$616bo2bo191b3o66bo$619bo191b2o64bobo$619bo$616bobo2$891b
o$890b3o$750b3o121b3o5bo7bob2o$749bo2bo107b3o5bo5bo2bo3b3o7b3o$752bo
93b3o5bo5bo2bo3b3o4bo5b2obo7b2o$748bo3bo79b3o5bo5bo2bo3b3o4bo5b2obo4bo
5b3o$752bo73bo5bo2bo3b3o4bo5b2obo4bo5b3o6bobo2b3o$749bobo73b3o4bo5b2ob
o4bo5b3o6bobo2b3o11b3o$824b2obo4bo5b3o6bobo2b3o11b3o12b2o$824b3o6bobo
2b3o11b3o12b2o$623b3o198b3o11b3o12b2o$622bo2bo110b3o85b3o12b2o$76b2o
547bo110bo2bo79bo5b2o$75b2o548bo110bo81b3o$77bo544bobo111bo3bo77bob2o$
736bo82b3o$737bobo79b3o$819b2o8bo$828b3o12bo$828bob2o3b3o4b3o12bo$823b
o5b3o3bo2bo3bob2o3b3o4b3o$822b3o4b2o4bo7b3o3bo2bo3bob2o3b3o6bo$822bob
2o9bo3bo3b2o4bo7b3o3bo2bo4b3o$811bo11b3o9bo3bo9bo3bo3b2o4bo7bob2o3b3o$
810b3o10b2o10bo13bo3bo9bo3bo4b3o3bo2bo$809b2obo23bobo10bo13bo3bo4b2o4b
o$809b3o38bobo10bo14bo3bo$617b3o189b3o52bobo11bo3bo$617bo2bo188b3o66bo
$617bo192b2o67bobo$617bo$618bobo2$891bo$890b3o$750b3o121b3o5bo6b2obo$
750bo2bo106b3o5bo4bo2bo4b3o5b3o$750bo95b3o5bo4bo2bo4b3o6bo4bob2o5b2o$
750bo3bo77b3o5bo4bo2bo4b3o6bo4bob2o5bo5b3o$750bo75bo4bo2bo4b3o6bo4bob
2o5bo5b3o2bobo6b3o$751bobo71b3o6bo4bob2o5bo5b3o2bobo6b3o11b3o$825bob2o
5bo5b3o2bobo6b3o11b3o11b2o$826b3o2bobo6b3o11b3o11b2o$623b3o200b3o11b3o
11b2o$623bo2bo109b3o87b3o11b2o$623bo111bo2bo80bo6b2o$9bo613bo114bo79b
3o$8b2o614bobo107bo3bo78b2obo$8bobo727bo78b3o$735bobo79b3o$818b2o9bo$
828b3o12bo$827b2obo4b3o4b3o12bo$823bo3b3o4bo2bo3b2obo4b3o4b3o$822b3o3b
2o7bo3b3o4bo2bo3b2obo4b3o6bo$b3o817b2obo8bo3bo4b2o7bo3b3o4bo2bo5b3o$bo
2bo806bo9b3o9bo3bo9bo3bo4b2o7bo4b2obo4b3o$bo808b3o9b2o13bo9bo3bo9bo3bo
4b3o4bo2bo$bo808bob2o20bobo14bo9bo3bo5b2o7bo$2bobo806b3o34bobo14bo10bo
3bo$617b3o191b3o48bobo11bo3bo$616bo2bo191b3o66bo$619bo191b2o64bobo$
619bo$616bobo2$7b3o881bo$7bo2bo879b3o$7bo742b3o121b3o5bo7bob2o$7bo741b
o2bo107b3o5bo5bo2bo3b3o7b3o$8bobo741bo93b3o5bo5bo2bo3b3o4bo5b2obo7b2o$
748bo3bo79b3o5bo5bo2bo3b3o4bo5b2obo4bo5b3o$752bo73bo5bo2bo3b3o4bo5b2ob
o4bo5b3o6bobo2b3o$749bobo73b3o4bo5b2obo4bo5b3o6bobo2b3o11b3o$824b2obo
4bo5b3o6bobo2b3o11b3o12b2o$824b3o6bobo2b3o11b3o12b2o$609bo13b3o198b3o
11b3o12b2o$608bobo11bo2bo110b3o85b3o12b2o$608bobo14bo110bo2bo79bo5b2o$
609bo15bo110bo81b3o$622bobo111bo3bo77bob2o$736bo82b3o$737bobo79b3o$
819b2o8bo$828b3o12bo$828bob2o3b3o4b3o12bo$823bo5b3o3bo2bo3bob2o3b3o4b
3o$822b3o4b2o4bo7b3o3bo2bo3bob2o3b3o6bo$b3o818bob2o9bo3bo3b2o4bo7b3o3b
o2bo4b3o$o2bo807bo11b3o9bo3bo9bo3bo3b2o4bo7bob2o3b3o$3bo806b3o10b2o10b
o13bo3bo9bo3bo4b3o3bo2bo$3bo805b2obo23bobo10bo13bo3bo4b2o4bo$obo806b3o
38bobo10bo14bo3bo$617b3o189b3o52bobo11bo3bo$617bo2bo188b3o66bo$617bo
192b2o67bobo$617bo$618bobo2$7b3o881bo$6bo2bo880b3o$9bo740b3o121b3o5bo
6b2obo$9bo740bo2bo106b3o5bo4bo2bo4b3o5b3o$6bobo741bo95b3o5bo4bo2bo4b3o
6bo4bob2o5b2o$750bo3bo77b3o5bo4bo2bo4b3o6bo4bob2o5bo5b3o$750bo75bo4bo
2bo4b3o6bo4bob2o5bo5b3o2bobo6b3o$751bobo71b3o6bo4bob2o5bo5b3o2bobo6b3o
11b3o$825bob2o5bo5b3o2bobo6b3o11b3o11b2o$826b3o2bobo6b3o11b3o11b2o$
623b3o200b3o11b3o11b2o$623bo2bo109b3o87b3o11b2o$623bo111bo2bo80bo6b2o$
623bo114bo79b3o$624bobo107bo3bo78b2obo$738bo78b3o$603b3o129bobo79b3o$
603bo2bo211b2o9bo$21b3o579bo224b3o12bo$21bo2bo578bo3bo219b2obo4b3o4b3o
12bo$21bo581bo219bo3b3o4bo2bo3b2obo4b3o4b3o$21bo582bobo215b3o3b2o7bo3b
3o4bo2bo3b2obo4b3o6bo$b3o18bobo796b2obo8bo3bo4b2o7bo3b3o4bo2bo5b3o$bo
2bo806bo9b3o9bo3bo9bo3bo4b2o7bo4b2obo4b3o$bo808b3o9b2o13bo9bo3bo9bo3bo
4b3o4bo2bo$bo15b3o790bob2o20bobo14bo9bo3bo5b2o7bo$2bobo12bo2bo790b3o
34bobo14bo10bo3bo$17bo599b3o191b3o48bobo11bo3bo$17bo36b3o559bo2bo191b
3o66bo$18bobo35bo562bo191b2o64bobo$55bo563bo$616bobo2$7b3o881bo$7bo2bo
879b3o$7bo742b3o121b3o5bo7bob2o$7bo741bo2bo107b3o5bo5bo2bo3b3o7b3o$8bo
bo741bo93b3o5bo5bo2bo3b3o4bo5b2obo7b2o$748bo3bo79b3o5bo5bo2bo3b3o4bo5b
2obo4bo5b3o$752bo73bo5bo2bo3b3o4bo5b2obo4bo5b3o6bobo2b3o$749bobo73b3o
4bo5b2obo4bo5b3o6bobo2b3o11b3o$824b2obo4bo5b3o6bobo2b3o11b3o12b2o$824b
3o6bobo2b3o11b3o12b2o$623b3o198b3o11b3o12b2o$622bo2bo110b3o85b3o12b2o$
625bo110bo2bo79bo5b2o$625bo110bo81b3o$622bobo111bo3bo77bob2o$736bo82b
3o$603b3o131bobo79b3o$602bo2bo213b2o8bo$21b3o581bo222b3o12bo$20bo2bo
577bo3bo222bob2o3b3o4b3o12bo$23bo581bo217bo5b3o3bo2bo3bob2o3b3o4b3o$
23bo578bobo217b3o4b2o4bo7b3o3bo2bo3bob2o3b3o6bo$b3o16bobo799bob2o9bo3b
o3b2o4bo7b3o3bo2bo4b3o$o2bo585b3o219bo11b3o9bo3bo9bo3bo3b2o4bo7bob2o3b
3o$3bo584bo2bo218b3o10b2o10bo13bo3bo9bo3bo4b3o3bo2bo$3bo13b3o571bo217b
2obo23bobo10bo13bo3bo4b2o4bo$obo13bo2bo571bo217b3o38bobo10bo14bo3bo$
19bo568bobo26b3o189b3o52bobo11bo3bo$19bo597bo2bo188b3o66bo$16bobo103b
2o436b3o54bo192b2o67bobo$53b3o65bobo436bo32b3o21bo$55bo67bo437bo30bo2b
o22bobo$54bo540bo$7b3o585bo295bo$6bo2bo582bobo295b3o$9bo740b3o121b3o5b
o6b2obo$9bo740bo2bo106b3o5bo4bo2bo4b3o5b3o$6bobo741bo95b3o5bo4bo2bo4b
3o6bo4bob2o5b2o$38b3o709bo3bo77b3o5bo4bo2bo4b3o6bo4bob2o5bo5b3o$38bo2b
o708bo75bo4bo2bo4b3o6bo4bob2o5bo5b3o2bobo6b3o$38bo712bobo71b3o6bo4bob
2o5bo5b3o2bobo6b3o11b3o$38bo786bob2o5bo5b3o2bobo6b3o11b3o11b2o$39bobo
784b3o2bobo6b3o11b3o11b2o$623b3o200b3o11b3o11b2o$623bo2bo109b3o87b3o
11b2o$34b3o586bo111bo2bo80bo6b2o$34bo2bo585bo114bo79b3o$34bo589bobo
107bo3bo78b2obo$34bo703bo78b3o$35bobo565b3o129bobo79b3o$603bo2bo211b2o
9bo$21b3o579bo224b3o12bo$21bo2bo578bo3bo219b2obo4b3o4b3o12bo$21bo581bo
219bo3b3o4bo2bo3b2obo4b3o4b3o$21bo582bobo215b3o3b2o7bo3b3o4bo2bo3b2obo
4b3o6bo$b3o18bobo796b2obo8bo3bo4b2o7bo3b3o4bo2bo5b3o$bo2bo584b3o219bo
9b3o9bo3bo9bo3bo4b2o7bo4b2obo4b3o$bo587bo2bo217b3o9b2o13bo9bo3bo9bo3bo
4b3o4bo2bo$bo15b3o569bo220bob2o20bobo14bo9bo3bo5b2o7bo$2bobo12bo2bo
568bo221b3o34bobo14bo10bo3bo$17bo572bobo24b3o191b3o48bobo11bo3bo$17bo
598bo2bo191b3o66bo$18bobo33bo564bo191b2o64bobo$53bobo437b2o98b3o23bo$
53bobo65b2o66b3o301bobo65b3o29bo2bo19bobo$54bo65bobo68bo301bo67bo31bo$
7b3o48b3o61bo67bo371bo30bo$7bo2bo47bo2bo532bobo$7bo50bo691b3o$7bo50bo
3bo686bo2bo$8bobo37b3o7bo693bo$38b3o7bo2bo7bobo686bo3bo$37bo2bo7bo703b
o$40bo7bo700bobo$40bo8bobo$37bobo$572b3o48b3o$571bo2bo47bo2bo110b3o$
34b3o537bo50bo110bo2bo$33bo2bo537bo50bo110bo$36bo534bobo48bobo111bo3bo
$36bo699bo$33bobo567b3o131bobo$576b3o23bo2bo$21b3o551bo2bo26bo$20bo2bo
554bo22bo3bo$23bo554bo26bo$23bo551bobo24bobo$b3o16bobo$o2bo585b3o$3bo
584bo2bo$3bo13b3o29b3o507bo31bo$obo13bo2bo29bo2bo506bobo29bo$19bo29bo
509b2o27bobo26b3o$19bo29bo567bo2bo$16bobo31bobo564bo$561b3o29b3o21bo$
561bo2bo27bo2bo22bobo$257b2o166b3o66b2o65bo33bo$7b3o48b3o127b3o65bobo
166bo68bobo64bo33bo$6bo2bo47bo2bo129bo67bo167bo67bo67bobo27bobo$9bo50b
o128bo560b3o$9bo46bo3bo689bo2bo$6bobo39b3o9bo689bo$38b3o6bo2bo6bobo
492b3o195bo3bo$38bo2bo8bo500bo2bo195bo$38bo11bo503bo196bobo$38bo8bobo
62b2o436bo3bo$39bobo69bobo440bo7b3o$113bo437bobo7bo2bo7b3o48b3o$564bo
7bo2bo47bo2bo109b3o$34b3o527bo7bo50bo111bo2bo$34bo2bo523bobo8bo50bo
114bo$34bo538bobo48bobo107bo3bo$34bo703bo$35bobo565b3o129bobo$576b3o
24bo2bo$21b3o552bo2bo23bo$21bo2bo551bo26bo3bo$21bo554bo26bo$21bo555bob
o24bobo$b3o18bobo$bo2bo584b3o$bo587bo2bo$bo15b3o29b3o537bo$2bobo12bo2b
o27bo2bo537bo$17bo33bo538bobo24b3o$17bo33bo564bo2bo$18bobo27bobo568bo$
561b3o29b3o23bo$560bo2bo29bo2bo19bobo$563bo29bo$7b3o48b3o297b2o203bo
29bo$7bo2bo47bo2bo194b2o66b3o31bobo65b3o131bobo31bobo$7bo50bo196bobo
68bo31bo67bo323b3o$7bo50bo3bo194bo67bo101bo321bo2bo$8bobo37b3o7bo693bo
$38b3o7bo2bo7bobo490b3o193bo3bo$37bo2bo7bo503bo2bo196bo$40bo7bo503bo
196bobo$40bo8bobo32bo467bo3bo$37bobo43b3o417b2o47bo9b3o$78bo4bob2o92b
3o321bobo47bobo6bo2bo6b3o48b3o$77b3o4b3o94bo321bo58bo8bo2bo47bo2bo110b
3o$34b3o40bob2o3b2o94bo381bo11bo50bo110bo2bo$33bo2bo41b3o482bobo8bo50b
o110bo$36bo41b2o491bobo48bobo111bo3bo$36bo699bo$33bobo567b3o131bobo$
576b3o23bo2bo$21b3o551bo2bo26bo$20bo2bo554bo22bo3bo$23bo94bo459bo26bo$
23bo94b2o455bobo24bobo$b3o16bobo94bobo$o2bo585b3o$3bo584bo2bo$3bo13b3o
29b3o539bo$obo13bo2bo29bo2bo538bo$19bo29bo538bobo26b3o$19bo29bo567bo2b
o$16bobo31bobo564bo$561b3o29b3o21bo$561bo2bo27bo2bo22bobo$561bo33bo$7b
3o48b3o500bo33bo$6bo2bo47bo2bo501bobo27bobo$9bo50bo298b2o$9bo46bo3bo
262b3o33bobo$6bobo39b3o9bo264bo33bo$38b3o6bo2bo6bobo264bo227b3o$38bo2b
o8bo500bo2bo$38bo11bo503bo$38bo8bobo34bo465bo3bo$39bobo41b3o468bo7b3o$
78bo3b2obo465bobo7bo2bo7b3o48b3o$77b3o2b3o162b2o186b3o126bo7bo2bo47bo
2bo$34b3o39b2obo3b2o161bobo186bo128bo7bo50bo$34bo2bo38b3o169bo187bo91b
o32bobo8bo50bo$34bo42b2o448b3o43bobo48bobo$34bo491b2obo4bo$35bobo488b
3o4b3o67b3o$527b2o3b2obo40b3o24bo2bo$21b3o97b2o409b3o41bo2bo23bo$21bo
2bo97b2o409b2o41bo26bo3bo$21bo79bo19bo454bo26bo$21bo78b3o395bo78bobo
24bobo$b3o18bobo75bob2o81b2o310b2o$bo2bo96b3o82b2o309bobo89b3o$bo99b2o
82bo403bo2bo$bo15b3o29b3o537bo$2bobo12bo2bo27bo2bo537bo$17bo33bo45bo
492bobo24b3o$17bo33bo44b3o517bo2bo$18bobo27bobo45bob2o519bo$97b3o461b
3o29b3o23bo$97b2o461bo2bo29bo2bo19bobo$563bo29bo$7b3o48b3o502bo29bo$7b
o2bo47bo2bo498bobo31bobo$7bo50bo$7bo50bo3bo$8bobo37b3o7bo$38b3o7bo2bo
7bobo490b3o$37bo2bo7bo503bo2bo$40bo7bo503bo$40bo8bobo32bo467bo3bo$37bo
bo43b3o466bo9b3o$78bo4bob2o466bobo6bo2bo6b3o48b3o$77b3o4b3o475bo8bo2bo
47bo2bo$34b3o40bob2o3b2o282b2o192bo11bo50bo$33bo2bo41b3o233b3o51bobo
157bo34bobo8bo50bo$36bo41b2o236bo51bo158b3o41bobo48bobo$36bo278bo211bo
b2o3bo$33bobo492b3o2b3o67b3o$528b2o3bob2o39b3o23bo2bo$21b3o510b3o38bo
2bo26bo$20bo2bo165bo304b2o38b2o42bo22bo3bo$23bo77bo18b2o67b2o302b2o83b
o26bo$23bo76b3o18b2o65bobo304bo79bobo24bobo$b3o16bobo76b2obo17bo217b3o
$o2bo95b3o151bo176b2o157b3o$3bo96b2o151b2o174b2o157bo2bo$3bo13b3o29b3o
200bobo176bo79bo79bo$obo13bo2bo29bo2bo457b3o78bo$19bo29bo47bo411b2obo
75bobo26b3o$19bo29bo46b3o410b3o105bo2bo$16bobo31bobo42b2obo411b2o105bo
$95b3o463b3o29b3o21bo$96b2o24bobo436bo2bo27bo2bo22bobo$123b2o390bo45bo
33bo$7b3o48b3o62bo390b3o44bo33bo$6bo2bo47bo2bo452b2obo45bobo27bobo$9bo
50bo452b3o$9bo46bo3bo453b2o$6bobo39b3o9bo$38b3o6bo2bo6bobo492b3o$38bo
2bo8bo500bo2bo$38bo11bo67bo435bo$38bo8bobo34bo32b3o430bo3bo$39bobo41b
3o31bob2o433bo7b3o$78bo3b2obo32b3o430bobo7bo2bo7b3o48b3o$77b3o2b3o33b
2o444bo7bo2bo47bo2bo$34b3o39b2obo3b2o479bo7bo50bo$34bo2bo38b3o449bo32b
obo8bo50bo$34bo42b2o35bo412b3o43bobo48bobo$34bo78b3o410b2obo4bo$35bobo
75bob2o409b3o4b3o67b3o$114b3o410b2o3b2obo40b3o24bo2bo$21b3o90b2o416b3o
41bo2bo23bo$21bo2bo508b2o41bo26bo3bo$21bo79bo325bo148bo26bo$21bo78b3o
25bo59bo67b2o168b2o67bo81bobo24bobo$b3o18bobo75bob2o23b3o58b2o67b2o
167bobo65b3o$bo2bo96b3o23bob2o56bobo66bo81b3o152b4o92b3o$bo99b2o25b3o
232bo128bobo94bo2bo$bo15b3o29b3o76b2o190b2o40b2o128b2o17bo77bo$2bobo
12bo2bo27bo2bo269b2o39bobo128bo16b3o76bo$17bo33bo45bo222bo189bob2o76bo
bo24b3o$17bo33bo44b3o412b3o102bo2bo$18bobo27bobo45bob2o411b2o106bo$97b
3o461b3o29b3o23bo$97b2o461bo2bo29bo2bo19bobo$515bo47bo29bo$7b3o48b3o
453b3o46bo29bo$7bo2bo47bo2bo452bob2o42bobo31bobo$7bo50bo456b3o$7bo50bo
3bo452b2o$8bobo37b3o7bo$38b3o7bo2bo7bobo490b3o$37bo2bo7bo503bo2bo$40bo
7bo69bo16b3o414bo$40bo8bobo32bo32b3o15bo2bo413bo3bo$37bobo43b3o30b2obo
15bo416bo9b3o$78bo4bob2o29b3o16bo417bobo6bo2bo6b3o48b3o$77b3o4b3o30b2o
17bobo423bo8bo2bo47bo2bo$34b3o40bob2o3b2o408bo67bo11bo50bo$33bo2bo41b
3o412b3o32bo34bobo8bo50bo$36bo41b2o34bo377b2obo31b3o41bobo48bobo$36bo
76b3o376b3o32bob2o3bo$33bobo76b2obo377b2o33b3o2b3o67b3o$112b3o413b2o3b
ob2o39b3o23bo2bo$21b3o89b2o419b3o38bo2bo26bo$20bo2bo474bo35b2o42bo22bo
3bo$23bo77bo395b3o78bo26bo$23bo76b3o25bo367b2obo75bobo24bobo$b3o16bobo
76b2obo24b3o194bo34b2o67bo67b3o$o2bo95b3o24b2obo125b2o67b2o32b2o67b2o
68b2o90b3o$3bo96b2o24b3o127b2o65bobo12b3o19bo66bobo158bo2bo$3bo13b3o
29b3o75b2o126bo255bo79bo$obo13bo2bo29bo2bo457b3o78bo$19bo29bo47bo411b
2obo75bobo26b3o$19bo29bo46b3o410b3o105bo2bo$16bobo31bobo42b2obo411b2o
105bo$95b3o463b3o29b3o21bo$96b2o463bo2bo27bo2bo22bobo$515bo45bo33bo$7b
3o48b3o453b3o44bo33bo$6bo2bo47bo2bo452b2obo45bobo27bobo$9bo50bo452b3o$
9bo46bo3bo453b2o$6bobo39b3o9bo$38b3o6bo2bo6bobo492b3o$38bo2bo8bo500bo
2bo$38bo11bo67bo16b3o416bo$38bo8bobo34bo32b3o14bo2bo412bo3bo$39bobo41b
3o31bob2o16bo416bo7b3o$78bo3b2obo32b3o16bo413bobo7bo2bo7b3o48b3o$77b3o
2b3o33b2o14bobo427bo7bo2bo47bo2bo$34b3o39b2obo3b2o409bo69bo7bo50bo$34b
o2bo38b3o414b3o32bo32bobo8bo50bo$34bo42b2o35bo378bob2o30b3o43bobo48bob
o$34bo78b3o378b3o29b2obo4bo$35bobo75bob2o377b2o30b3o4b3o67b3o$114b3o
354bo55b2o3b2obo40b3o24bo2bo$21b3o90b2o354b3o59b3o41bo2bo23bo$21bo2bo
445bob2o24bo34b2o41bo26bo3bo$21bo79bo369b3o23b3o76bo26bo$21bo78b3o25bo
342b2o24bob2o76bobo24bobo$b3o18bobo75bob2o23b3o368b3o$bo2bo96b3o23bob
2o367b2o89b3o$bo99b2o25b3o192bo36b2o113bo113bo2bo$bo15b3o29b3o76b2o
193b2o13b3o18b2o113b3o34bo77bo$2bobo12bo2bo27bo2bo270bobo36bo112bob2o
32b3o76bo$17bo33bo45bo377b3o32bob2o76bobo24b3o$17bo33bo44b3o376b2o34b
3o102bo2bo$18bobo27bobo45bob2o411b2o106bo$97b3o461b3o29b3o23bo$97b2o
53bo407bo2bo29bo2bo19bobo$151b3o361bo47bo29bo$7b3o48b3o90bob2o359b3o
46bo29bo$7bo2bo47bo2bo90b3o359bob2o42bobo31bobo$7bo50bo93b2o361b3o$7bo
50bo3bo116b2o248bo85b2o$8bobo37b3o7bo121b2o246b2o$38b3o7bo2bo7bobo86bo
30bo248bobo121b3o$37bo2bo7bo98b3o402bo2bo$40bo7bo69bo16b3o9bob2o401bo$
40bo8bobo32bo32b3o15bo2bo9b3o188bo212bo3bo$37bobo43b3o30b2obo15bo12b2o
189bo212bo9b3o$78bo4bob2o29b3o16bo203bo213bobo6bo2bo6b3o48b3o$77b3o4b
3o30b2o17bobo423bo8bo2bo47bo2bo$34b3o40bob2o3b2o408bo67bo11bo50bo$33bo
2bo41b3o412b3o32bo34bobo8bo50bo$36bo41b2o34bo377b2obo31b3o41bobo48bobo
$36bo76b3o376b3o32bob2o3bo$33bobo76b2obo377b2o33b3o2b3o67b3o$112b3o
356bo56b2o3bob2o39b3o23bo2bo$21b3o89b2o355b3o61b3o38bo2bo26bo$20bo2bo
445b2obo25bo35b2o42bo22bo3bo$23bo77bo367b3o25b3o78bo26bo$23bo76b3o25bo
341b2o24b2obo75bobo24bobo$b3o16bobo76b2obo24b3o366b3o$o2bo95b3o24b2obo
367b2o90b3o$3bo96b2o24b3o346bo112bo2bo$3bo13b3o29b3o75b2o345b3o34bo79b
o$obo13bo2bo29bo2bo285b3o132b2obo33b3o78bo$19bo29bo47bo375b3o33b2obo
75bobo26b3o$19bo29bo46b3o375b2o33b3o105bo2bo$16bobo31bobo42b2obo411b2o
105bo$95b3o463b3o29b3o21bo$96b2o54bo408bo2bo27bo2bo22bobo$151b3o361bo
45bo33bo$7b3o48b3o89b2obo360b3o44bo33bo$6bo2bo47bo2bo89b3o360b2obo45bo
bo27bobo$9bo50bo90b2o360b3o$9bo46bo3bo453b2o$6bobo39b3o9bo186bo206bo$
38b3o6bo2bo6bobo88bo29b2o67b2o112b2o67bo22b3o96b3o$38bo2bo8bo96b3o29b
2o65bobo111b2o67b2o22bob2o94bo2bo$38bo11bo67bo16b3o8b2obo28bo183bo66bo
bo22b3o97bo$38bo8bobo34bo32b3o14bo2bo8b3o305b2o94bo3bo$39bobo41b3o31bo
b2o16bo9b2o190bo214bo7b3o$78bo3b2obo32b3o16bo201bo211bobo7bo2bo7b3o48b
3o$77b3o2b3o33b2o14bobo202bo118bo105bo7bo2bo47bo2bo$34b3o39b2obo3b2o
372b3o34bo69bo7bo50bo$34bo2bo38b3o378bob2o32b3o32bo32bobo8bo50bo$34bo
42b2o35bo343b3o32bob2o30b3o43bobo48bobo$34bo78b3o342b2o34b3o29b2obo4bo
$35bobo75bob2o377b2o30b3o4b3o67b3o$114b3o354bo55b2o3b2obo40b3o24bo2bo$
21b3o90b2o53bo300b3o59b3o41bo2bo23bo$21bo2bo143b3o299bob2o24bo34b2o41b
o26bo3bo$21bo79bo66bob2o299b3o23b3o76bo26bo$21bo78b3o25bo40b3o299b2o
24bob2o76bobo24bobo$b3o18bobo75bob2o23b3o39b2o327b3o$bo2bo96b3o23bob2o
367b2o89b3o$bo99b2o25b3o344bo113bo2bo$bo15b3o29b3o76b2o35bo308b3o34bo
77bo$2bobo12bo2bo27bo2bo112b3o307bob2o32b3o76bo$17bo33bo45bo66bob2o
170b3o134b3o32bob2o76bobo24b3o$17bo33bo44b3o66b3o307b2o34b3o102bo2bo$
18bobo27bobo45bob2o65b2o344b2o106bo$97b3o80bobo378b3o29b3o23bo$97b2o
53bo28b2o377bo2bo29bo2bo19bobo$151b3o27bo333bo47bo29bo$7b3o48b3o90bob
2o359b3o46bo29bo$7bo2bo47bo2bo90b3o359bob2o42bobo31bobo$7bo50bo93b2o
361b3o$7bo50bo3bo452b2o$8bobo37b3o7bo395bo$38b3o7bo2bo7bobo86bo31bo
272b3o96b3o$37bo2bo7bo98b3o29b3o64bo205b2obo96bo2bo$40bo7bo69bo16b3o9b
ob2o27b2obo64b2o114b2o88b3o97bo$40bo8bobo32bo32b3o15bo2bo9b3o27b3o64bo
bo113b2o90b2o97bo3bo$37bobo43b3o30b2obo15bo12b2o29b2o182bo188bo9b3o$
78bo4bob2o29b3o16bo203bo213bobo6bo2bo6b3o$77b3o4b3o30b2o17bobo200bo
118bo103bo8bo2bo$34b3o40bob2o3b2o253bo117b3o34bo67bo11bo$33bo2bo41b3o
108bo266b2obo33b3o32bo34bobo8bo$36bo41b2o34bo73b3o265b3o33b2obo31b3o
41bobo$36bo76b3o72bob2o247bo17b2o33b3o32bob2o3bo$33bobo76b2obo73b3o
246b2o53b2o33b3o2b3o67b3o$112b3o64bo9b3o246bobo30bo56b2o3bob2o39b3o23b
o2bo$21b3o89b2o54bo8b3o8b2o116bo162b3o61b3o38bo2bo26bo$20bo2bo144b3o7b
ob2o125bo161b2obo25bo35b2o42bo22bo3bo$23bo77bo65b2obo8b3o125bo121bo39b
3o25b3o78bo26bo$23bo76b3o25bo38b3o9b2o246b2o41b2o24b2obo75bobo24bobo$b
3o16bobo76b2obo24b3o38b2o258b2o66b3o$o2bo95b3o24b2obo367b2o90b3o$3bo
96b2o24b3o314bo31bo112bo2bo$3bo13b3o29b3o75b2o36bo276b3o29b3o34bo79bo$
obo13bo2bo29bo2bo111b3o275bob2o27b2obo33b3o78bo$19bo29bo47bo65b2obo
276b3o27b3o33b2obo75bobo$19bo29bo46b3o64b3o172b3o102b2o29b2o33b3o$16bo
bo31bobo42b2obo65b2o344b2o$95b3o463b3o29b3o$96b2o54bo408bo2bo27bo2bo$
151b3o280bo80bo45bo33bo$7b3o48b3o89b2obo279b3o78b3o44bo33bo$6bo2bo47bo
2bo89b3o279b2obo77b2obo45bobo27bobo$9bo50bo90b2o279b3o78b3o$9bo46bo3bo
371b3o9bo69b2o$6bobo39b3o9bo372b2o8b3o8bo$38b3o6bo2bo6bobo88bo31bo261b
2obo7b3o96b3o$38bo2bo8bo96b3o29b3o260b3o8bob2o94bo2bo$38bo11bo67bo16b
3o8b2obo29bob2o260b2o9b3o97bo$38bo8bobo34bo32b3o14bo2bo8b3o31b3o271b2o
94bo3bo$39bobo41b3o31bob2o16bo9b2o31b2o372bo7b3o$78bo3b2obo32b3o16bo
413bobo7bo2bo7b3o$77b3o2b3o33b2o14bobo202bo118bo105bo7bo2bo$34b3o39b2o
bo3b2o254bo117b3o34bo69bo7bo$34bo2bo38b3o110bo149bo117bob2o32b3o32bo
32bobo8bo$34bo42b2o35bo73b3o267b3o32bob2o30b3o43bobo$34bo78b3o71b2obo
267b2o34b3o29b2obo4bo$35bobo75bob2o70b3o47bo256b2o30b3o4b3o$114b3o62bo
7b3o47b2o132b2o98bo55b2o3b2obo40b3o$114b2o53bo8b3o7b2o46bobo131b2o98b
3o59b3o41bo2bo$168b3o6b2obo126bo64bo97bob2o24bo34b2o41bo$101bo66bob2o
5b3o127bo163b3o23b3o76bo$100b3o25bo40b3o6b2o127bo163b2o24bob2o76bobo$
100bob2o23b3o39b2o327b3o$101b3o23bob2o367b2o$101b2o25b3o312bo31bo$49b
3o76b2o35bo276b3o29b3o34bo$48bo2bo112b3o274b2obo29bob2o32b3o$51bo45bo
66bob2o273b3o31b3o32bob2o$51bo44b3o66b3o274b2o31b2o34b3o$48bobo45bob2o
65b2o171b3o170b2o$97b3o461b3o$97b2o53bo407bo2bo$151b3o280bo80bo47bo$
58b3o90bob2o278b3o78b3o46bo$58bo2bo90b3o278bob2o77bob2o42bobo$58bo93b
2o280b3o78b3o$58bo3bo371b3o7bo70b2o$48b3o7bo375b2o7b3o8bo$38b3o7bo2bo
7bobo86bo31bo262bob2o6b3o96b3o$37bo2bo7bo98b3o29b3o262b3o5b2obo96bo2bo
$40bo7bo69bo16b3o9bob2o27b2obo262b2o6b3o97bo$40bo8bobo32bo32b3o15bo2bo
9b3o27b3o227b3o42b2o97bo3bo$37bobo43b3o30b2obo15bo12b2o29b2o226bo2bo
141bo9b3o$78bo4bob2o29b3o16bo274bo3b3o136bobo6bo2bo6b3o$77b3o4b3o30b2o
17bobo271bo2bo2bo41bo103bo8bo2bo$34b3o40bob2o3b2o253bo67bobo6bo40b3o
34bo67bo11bo$33bo2bo41b3o108bo149bo76bo39b2obo33b3o32bo34bobo8bo$36bo
41b2o34bo73b3o148bo73bobo40b3o33b2obo31b3o41bobo$36bo76b3o72bob2o265b
2o33b3o32bob2o3bo$33bobo76b2obo73b3o301b2o33b3o2b3o$112b3o64bo9b3o279b
o56b2o3bob2o39b3o$113b2o54bo8b3o8b2o279b3o61b3o38bo2bo$168b3o7bob2o
287b2obo25bo35b2o42bo$101bo65b2obo8b3o125bo161b3o25b3o78bo$100b3o25bo
38b3o9b2o126bo162b2o24b2obo75bobo$99b2obo24b3o38b2o43b3o91bo188b3o$99b
3o24b2obo82bo2bo281b2o$100b2o24b3o78b3o5bo227bo31bo$127b2o36bo40bo2bo
5bo226b3o29b3o34bo$164b3o42bo2bobo227bob2o27b2obo33b3o$97bo65b2obo42bo
233b3o27b3o33b2obo$96b3o64b3o40bobo234b2o29b2o33b3o$95b2obo65b2o76b3o
120b2o143b2o$95b3o146bo93b3o24bobo193b3o$96b2o54bo90bo121bo195bo2bo$
151b3o280bo80bo45bo$150b2obo279b3o78b3o44bo$150b3o279b2obo77b2obo45bob
o$151b2o279b3o78b3o$432b3o9bo69b2o$433b2o8b3o8bo$148bo31bo261b2obo7b3o
96b3o$147b3o29b3o260b3o8bob2o94bo2bo$118bo16b3o8b2obo29bob2o260b2o9b3o
97bo$84bo32b3o14bo2bo8b3o31b3o225b3o43b2o94bo3bo$83b3o31bob2o16bo9b2o
31b2o226bo2bo142bo7b3o$78bo3b2obo32b3o16bo270bo5b3o134bobo7bo2bo$77b3o
2b3o33b2o14bobo271bo5bo2bo40bo105bo$76b2obo3b2o324bobo2bo42b3o34bo69bo
$76b3o110bo149bo74bo42bob2o32b3o32bo32bobo$77b2o35bo73b3o148bo75bobo
40b3o32bob2o30b3o$113b3o71b2obo148bo118b2o34b3o29b2obo4bo$113bob2o70b
3o304b2o30b3o4b3o$114b3o62bo7b3o281bo55b2o3b2obo$114b2o53bo8b3o7b2o
280b3o59b3o$168b3o6b2obo289bob2o24bo34b2o$101bo66bob2o5b3o211b3o77b3o
23b3o$100b3o25bo40b3o6b2o127bo82bo2bo77b2o24bob2o$100bob2o23b3o39b2o
42b3o91bo85bo104b3o$101b3o23bob2o82bo2bo90bo85bo104b2o$101b2o25b3o76b
3o3bo176bobo50bo31bo$128b2o35bo41bo2bo2bo228b3o29b3o34bo$164b3o40bo6bo
bo29b2o193b2obo29bob2o32b3o$97bo66bob2o39bo37bobo113b3o31b3o43b3o31b3o
32bob2o$96b3o66b3o40bobo36bo113bo32bo2bo44b2o31b2o34b3o$96bob2o65b2o
195bo34bo113b2o$97b3o297bo$97b2o53bo185b3o53bobo$151b3o280bo80bo$151bo
b2o278b3o78b3o$152b3o75b3o200bob2o77bob2o$152b2o75bo2bo201b3o78b3o$
232bo201b3o7bo70b2o$232bo201b2o7b3o8bo$148bo31bo48bobo211bob2o6b3o$
147b3o29b3o124b3o135b3o5b2obo$118bo16b3o9bob2o27b2obo262b2o6b3o$117b3o
15bo2bo9b3o27b3o45b3o179b3o42b2o$116b2obo15bo12b2o29b2o44bo2bo178bo2bo
$116b3o16bo92bo181bo3b3o$117b2o17bobo89bo181bo2bo2bo41bo$225bobo179bob
o6bo40b3o34bo$189bo226bo39b2obo33b3o32bo$114bo73b3o148bo73bobo40b3o33b
2obo31b3o$113b3o72bob2o147bo117b2o33b3o32bob2o3bo$112b2obo73b3o147bo
153b2o33b3o2b3o$112b3o64bo9b3o279bo56b2o3bob2o$113b2o54bo8b3o8b2o279b
3o61b3o$168b3o7bob2o287b2obo25bo35b2o$167b2obo8b3o209b3o75b3o25b3o$
128bo38b3o9b2o210bo2bo75b2o24b2obo$127b3o38b2o43b3o91bo83bo104b3o$126b
2obo82bo2bo91bo83bo105b2o$126b3o78b3o5bo91bo84bobo48bo31bo$127b2o36bo
40bo2bo5bo226b3o29b3o34bo$164b3o42bo2bobo227bob2o27b2obo33b3o$163b2obo
42bo36bo148b3o45b3o27b3o33b2obo$163b3o40bobo36bo149bo2bo44b2o29b2o33b
3o$164b2o78bo3b2o112b3o30bo114b2o$244bo3bobo111bo32bo$152bo92bo3b2o
112bo32bobo$151b3o184b3o93bo80bo$150b2obo279b3o78b3o$150b3o77b3o199b2o
bo77b2obo$151b2o77bo2bo198b3o78b3o$230bo201b3o9bo69b2o$230bo202b2o8b3o
8bo$148bo31bo50bobo208b2obo7b3o$147b3o29b3o260b3o8bob2o$135b3o8b2obo
29bob2o123b3o65b3o66b2o9b3o$134bo2bo8b3o31b3o43b3o144bo2bo31b3o43b2o$
137bo9b2o31b2o44bo2bo146bo31bo2bo$137bo88bo149bo31bo5b3o$134bobo89bo
146bobo32bo5bo2bo40bo$227bobo179bobo2bo42b3o34bo$189bo224bo42bob2o32b
3o32bo$188b3o187b3o34bobo40b3o32bob2o30b3o$187b2obo148bo37bo2bo77b2o
34b3o29b2obo4bo$187b3o149bo40bo113b2o30b3o4b3o$179bo7b3o149bo40bo90bo
55b2o3b2obo$169bo8b3o7b2o187bobo90b3o59b3o$168b3o6b2obo289bob2o24bo34b
2o$168bob2o5b3o211b3o77b3o23b3o$128bo40b3o6b2o67b3o140bo2bo77b2o24bob
2o$127b3o39b2o42b3o30bo2bo143bo104b3o$127bob2o82bo2bo32bo57bo85bo104b
2o$128b3o76b3o3bo35bo57bo82bobo50bo31bo$128b2o35bo41bo2bo2bo32bobo58bo
52bo81b3o29b3o34bo$164b3o40bo6bobo143bobo78b2obo29bob2o32b3o$164bob2o
39bo152b3o32b3o43b3o31b3o32bob2o$165b3o40bobo32b3o117bo30bo2bo44b2o31b
2o34b3o$165b2o75bo2bo114bo2bo33bo113b2o$245bo117bo33bo$152bo92bo117bo
30bobo$151b3o88bobo115bobo71bo80bo$151bob2o183b3o92b3o78b3o$152b3o75b
3o200bob2o77bob2o$152b2o75bo2bo201b3o78b3o$232bo201b3o7bo70b2o$232bo
201b2o7b3o8bo$148bo31bo48bobo211bob2o6b3o$147b3o29b3o125bo136b3o5b2obo
$135b3o9bob2o27b2obo124b3o65b3o67b2o6b3o$135bo2bo9b3o27b3o45b3o75b2obo
b2o63bo2bo30b3o42b2o$135bo12b2o29b2o44bo2bo75b2o3b2o63bo32bo2bo$135bo
92bo75bobobobo63bo35bo3b3o$136bobo89bo78bo59b3o5bobo32bo2bo2bo41bo$
225bobo74b3o5b3o53bo2bo37bobo6bo40b3o34bo$189bo112b3o5b3o56bo46bo39b2o
bo33b3o$188b3o112bobo3bobo57bo8b3o32bobo40b3o33b2obo$188bob2o110b3o5b
3o53bobo9bo2bo75b2o33b3o$189b3o109b3o7b3o25bo38bo114b2o$179bo9b3o111bo
7bo27bo38bo92bo$169bo8b3o8b2o105bo21bo20bo39bobo88b3o$168b3o7bob2o113b
obo3b2o9b2o3bobo149b2obo25bo$167b2obo8b3o114b2o3b2o2bo3bo2b2o3b2o72b3o
75b3o25b3o$167b3o9b2o66b3o14b3o28b3o3b2obobobobob2o3b3o71bo2bo75b2o24b
2obo$168b2o43b3o31bo2bo12bo2bo26b5o3bo11bo3b5o69bo104b3o$212bo2bo31bo
18bo27b4o4b2ob2ob2ob2o4b4o70bo105b2o$207b3o5bo31bo18bo28b2obo5bo5bo5bo
b2o72bobo48bo31bo$165bo40bo2bo5bo32bobo12bobo30b2o19b2o123b3o29b3o$
164b3o42bo2bobo227bob2o27b2obo$163b2obo42bo185b3o45b3o27b3o$163b3o40bo
bo34b3o115b3o31bo2bo44b2o29b2o$164b2o77bo2bo114bo2bo30bo$243bo117bo33b
o$152bo90bo62b3o52bo34bobo$151b3o90bobo115bobo69bo$150b2obo279b3o$150b
3o77b3o105b3o91b2obo$151b2o77bo2bo198b3o$230bo76bo124b3o9bo$230bo27b3o
45b3o124b2o8b3o8bo$148bo31bo50bobo23bo2bo44bo3bo132b2obo7b3o$147b3o29b
3o78bo46bo134b3o8bob2o$146b2obo29bob2o77bo42bo3bo3bo62b3o66b2o9b3o$
146b3o31b3o43b3o28bobo38b2o3bo7bo3b2o56bo2bo31b3o43b2o$147b2o31b2o44bo
2bo68b2o3bob5obo3b2o59bo31bo2bo$226bo70bo6bob3obo6bo58bo31bo5b3o$226bo
71b2o15b2o50b3o3bobo32bo5bo2bo40bo$227bobo68b5o9b5o50bo2bo38bobo2bo42b
3o$189bo112bo9bo54bo46bo42bob2o$188b3o110bo2b2o3b2o2bo53bo10b3o34bobo
40b3o$187b2obo110b2ob2o3b2ob2o54bobo6bo2bo77b2o$187b3o112bo2bo3bo2bo
67bo$179bo7b3o113b2o5b2o27bo40bo90bo$169bo8b3o7b2o149bo37bobo90b3o$
168b3o6b2obo158bo130bob2o$168bob2o5b3o211b3o77b3o$169b3o6b2o67b3o14b3o
39b3o81bo2bo77b2o$169b2o42b3o30bo2bo14bo2bo125bo$213bo2bo32bo14bo128bo
$207b3o3bo35bo14bo125bobo50bo31bo$165bo41bo2bo2bo32bobo16bobo174b3o29b
3o$164b3o40bo6bobo224b2obo29bob2o$164bob2o39bo187b3o43b3o31b3o$165b3o
40bobo32b3o115b3o30bo2bo44b2o31b2o$165b2o75bo2bo114bo2bo33bo$245bo117b
o33bo$245bo117bo30bobo$242bobo115bobo71bo$433b3o$230b3o200bob2o$229bo
2bo105b3o93b3o$232bo201b3o7bo$232bo25b3o46bo126b2o7b3o8bo$180bo48bobo
26bo2bo45bo135bob2o6b3o$179b3o76bo48bo136b3o5b2obo$178b2obo76bo115b3o
67b2o6b3o$178b3o45b3o30bobo112bo2bo30b3o42b2o$179b2o44bo2bo145bo32bo2b
o$228bo145bo35bo3b3o$228bo138b3o5bobo32bo2bo2bo41bo$225bobo46bo91bo2bo
37bobo6bo40b3o$189bo83bobo93bo46bo39b2obo$188b3o82bobo93bo8b3o32bobo
40b3o$188bob2o82bo91bobo9bo2bo75b2o$189b3o186bo$179bo9b3o186bo$178b3o
8b2o148bo39bobo$178bob2o157bo$179b3o157bo51b3o$179b2o66b3o14b3o124bo2b
o$213b3o31bo2bo12bo2bo39b3o82bo$212bo2bo31bo18bo86bo37bo$207b3o5bo31bo
18bo85bobo37bobo48bo$206bo2bo5bo32bobo12bobo86bobo87b3o$209bo2bobo138b
o88bob2o$209bo185b3o45b3o$206bobo34b3o115b3o31bo2bo44b2o$243bo2bo114bo
2bo30bo$243bo117bo33bo$243bo117bo34bobo$244bobo115bobo69bo$433b3o$230b
3o199b2obo$230bo2bo198b3o$230bo107b3o91b3o9bo$230bo27b3o172b2o8b3o$
231bobo23bo2bo46bo134b2obo$260bo46bo134b3o$260bo46bo66b3o66b2o$226b3o
28bobo113bo2bo31b3o$226bo2bo146bo31bo2bo$226bo149bo31bo5b3o$226bo140b
3o3bobo32bo5bo2bo$227bobo137bo2bo38bobo2bo$367bo46bo$367bo10b3o34bobo$
368bobo6bo2bo$380bo$380bo$377bobo$339bo$339bo51b3o$247b3o14b3o72bo50bo
2bo$213b3o30bo2bo14bo2bo125bo$213bo2bo32bo14bo41b3o84bo$207b3o3bo35bo
14bo125bobo$207bo2bo2bo32bobo16bobo$207bo6bobo$207bo187b3o$208bobo32b
3o115b3o30bo2bo$242bo2bo114bo2bo33bo$245bo117bo33bo$245bo117bo30bobo$
242bobo115bobo2$230b3o$229bo2bo$232bo$232bo25b3o77b3o$229bobo26bo2bo$
258bo48bo$258bo48bo66b3o$226b3o30bobo45bo66bo2bo30b3o$225bo2bo145bo32b
o2bo$228bo145bo35bo3b3o$228bo138b3o5bobo32bo2bo2bo$225bobo138bo2bo37bo
bo6bo$369bo46bo$369bo8b3o32bobo$366bobo9bo2bo$378bo$378bo$379bobo2$
339bo51b3o$247b3o14b3o72bo51bo2bo$213b3o31bo2bo12bo2bo72bo51bo$212bo2b
o31bo18bo124bo$207b3o5bo31bo18bo39b3o83bobo$206bo2bo5bo32bobo12bobo$
209bo2bobo$209bo185b3o$206bobo34b3o115b3o31bo2bo$243bo2bo114bo2bo30bo$
243bo117bo33bo$243bo117bo34bobo$244bobo115bobo2$230b3o$230bo2bo$230bo$
230bo27b3o$231bobo23bo2bo77b3o$260bo$260bo46bo66b3o$226b3o28bobo47bo
65bo2bo$226bo2bo77bo68bo$226bo149bo$226bo140b3o3bobo$227bobo137bo2bo$
367bo$367bo10b3o$368bobo6bo2bo$380bo$380bo$377bobo2$391b3o$247b3o14b3o
72bo50bo2bo$246bo2bo14bo2bo71bo53bo$249bo14bo74bo53bo$249bo14bo125bobo
$246bobo16bobo38b3o$353bo$352bobo40b3o$243b3o106bobo6b3o30bo2bo$242bo
2bo93bo13bo6bo2bo33bo$245bo93bo23bo33bo$245bo92b3o22bo30bobo$242bobo
115bobo$306b3o27bo5bo$230b3o101bo9bo$229bo2bo72bo3bo23b2o4bo4b2o$232bo
72bo3bo22b2o4b3o4b2o$232bo25b3o42bo7bo21bo2b3ob3o2bo$229bobo26bo2bo39b
2o4bo4b2o20b2obo3bob2o$258bo42bo4bobo4bo21b2o5b2o$258bo42bo3bo3bo3bo
60b3o$226b3o30bobo40b2obo3bob2o61bo2bo$225bo2bo75bo5bo63bo$228bo145bo$
228bo110bo27b3o5bobo$225bobo104b2o5bo5b2o19bo2bo$333b2o4bo4b2o23bo$
328b3o17b3o18bo8b3o$300b2o4b3o4b2o51bobo9bo2bo$297bo3bo11bo3bo60bo$
297bo3bo11bo3bo8bo51bo$297bo19bo7b4o50bobo$324bo4bo$324bo3b4o4b2o3b2o
5bo$247b3o14b3o34b2o9b2obo8bo4bo6b3ob3o$247bo2bo12bo2bo32bo4bo5bo5bo3b
2o7bo5b3o3b3o4bo$247bo18bo38bo3bo7bo2b2o2b2o3bo5bo7bo$247bo18bo29b2obo
5bo3bo6bo6bo5bo$248bobo12bobo36bo2bo3bo2bo3b2o8b3o$296b2o4bobo5bobo4b
2o7b3o$317bo2b2o$243b3o72b3o40b3o$243bo2bo72bo18b3o20bo2bo$243bo117bo$
243bo63bo53bo$244bobo60bo54bobo$307bo4$258b3o$257bo2bo$260bo$260bo113b
3o$257bobo113bo2bo$376bo$376bo$367b3o3bobo$339bo27bo2bo$339bo27bo$339b
o27bo10b3o$368bobo6bo2bo$306b3o71bo$380bo$377bobo$337bo$338b2o$247b3o
14b3o70b2o$246bo2bo14bo2bo$249bo14bo$249bo14bo$246bobo16bobo3$243b3o
115b3o$242bo2bo114bo2bo$245bo92b3o22bo$245bo117bo$242bobo62bo52bobo$
307bo$307bo10$367b3o$366bo2bo$339bo29bo$339bo9bo19bo$339bo10bo15bobo$
348b3o$306b3o14$338b3o2$307bo$307bo$307bo12$339bo$339bo$339bo2$306b3o
14$338b3o2$307bo$307bo$307bo2$372bo$370bobo$371b2o26$382bo$383b2o$382b
2o26$394bo$395bo$393b3o!


A similar process for the Waterbear, only 10 *WSS per period.
x = 287, y = 622, rule = B3/S23
96bo$95b3o$94b2obo2$94b2o$94bo2bo$94bo2bo$95bobo5b3o$103bo2bo$103bo$
97bo5bo$82bo13b3o5bobo$81b3o12bob2o$80b2obo13b3o$80b3o14b2o$81b2o7$80b
3o$79bo2bo$82bo$65bobo14bo$60b2o3bo2bo10bobo$59b3o$58bo$60bo6bo13b3o$
64bo2bo13bo2bo$59b2o2bo2bo14bo$59b2obo3bo14bo$61bo3bo16bobo20b3o$61bo
2bo40bo2bo$105bo$105bo$106bobo2$69bo$67b2o44b3o$68b2o42bo2bo$115bo$
107bo7bo$74bo17bo13b3o3bobo$73b3o15b3o11b2obo$73bob2o14bob2o10b3o$74b
3o15b3o11b2o$74b3o15b2o$74b2o6$90b3o$90bo2bo$90bo$90bo$83b3o5bobo$82bo
2bo$85bo$85bo5b3o$82bobo5bo2bo$93bo$93bo$90bobo22b3o$114bo2bo$117bo$
117bo$114bobo3$123b3o$123bo2bo$123bo$117bo5bo$84bo17bo13b3o5bobo$83b3o
15b3o12bob2o$45b2o35b2obo14b2obo13b3o$45bob2o33b3o15b3o14b2o$47b2o33b
3o16b2o$47b2o34b2o$44b2o2$47b2o3$100b3o$99bo2bo$102bo$37bo64bo$36bo56b
3o3bobo$36b3o54bo2bo$93bo$93bo7b3o$94bobo4bo2bo$101bo$101bo$102bobo20b
3o$125bo2bo$125bo$125bo$126bobo3$133b3o$132bo2bo$135bo$127bo7bo$94bo
17bo13b3o3bobo$93b3o15b3o11b2obo$93bob2o14bob2o10b3o$94b3o15b3o11b2o$
94b3o15b2o$94b2o2$52bo$51bobo$51bobo$52bo$110b3o$58bo51bo2bo$57b3o50bo
$56b2obo50bo$56b3o44b3o5bobo$57b2o43bo2bo$105bo$105bo5b3o$102bobo5bo2b
o$113bo$113bo$110bobo22b3o$134bo2bo$13bo123bo$11b2o124bo$12b2o120bobo
3$62b3o78b3o$47bo13bo2bo78bo2bo$46bobo15bo78bo$2bobo41bobo15bo72bo5bo$
o4bo41bo13bobo40bo17bo13b3o5bobo$o4bo97b3o15b3o12bob2o$4b2o96b2obo14b
2obo13b3o$102b3o15b3o14b2o$2o2b2o96b3o16b2o$2o2b2o33b3o61b2o$bob3o32bo
3bo$4bo38bo$3bo$38b2o3bo$40b3o$120b3o$68bo50bo2bo$67b3o52bo$67bob2o51b
o$68b3o42b3o3bobo$68b2o43bo2bo$113bo$113bo7b3o$114bobo4bo2bo$121bo$
121bo$122bobo20b3o$145bo2bo$145bo$145bo$146bobo3$72b3o78b3o$72bo2bo76b
o2bo$72bo82bo$10bobo59bo74bo7bo$11b2o60bobo38bo17bo13b3o3bobo$11bo36bo
64b3o15b3o11b2obo$46bobo64bob2o14bob2o10b3o$47b2o65b3o15b3o11b2o$114b
3o15b2o$24b3o87b2o$24bo2bo$24bo2bo2$27b2o$26bo2bo$26bo2bo100b3o$26bo
51bo51bo2bo$77b3o50bo$76b2obo50bo$76b3o44b3o5bobo$77b2o43bo2bo$125bo$
125bo5b3o$122bobo5bo2bo$133bo$133bo$15bo114bobo22b3o$13b2o139bo2bo$14b
2o141bo$157bo$154bobo3$82b3o78b3o$81bo2bo78bo2bo$18bo65bo78bo$17bobo
64bo72bo5bo$17bobo61bobo40bo17bo13b3o5bobo$18bo104b3o15b3o12bob2o$122b
2obo14b2obo13b3o$122b3o15b3o14b2o$122b3o16b2o$123b2o6$61bobo76b3o$62b
2o24bo50bo2bo$62bo24b3o52bo$87bob2o51bo$88b3o42b3o3bobo$88b2o43bo2bo$
133bo$133bo7b3o$134bobo4bo2bo$38bo102bo$13bo25b2o100bo$12bobo23b2o102b
obo20b3o$12bobo150bo2bo$13bo151bo$165bo$166bobo3$92b3o78b3o$92bo2bo76b
o2bo$92bo82bo$92bo74bo7bo$93bobo38bo17bo13b3o3bobo$133b3o15b3o11b2obo$
133bob2o14bob2o10b3o$134b3o15b3o11b2o$134b3o15b2o$134b2o6$150b3o$98bo
51bo2bo$97b3o50bo$96b2obo50bo$96b3o44b3o5bobo$97b2o43bo2bo$145bo$145bo
5b3o$142bobo5bo2bo$77bo75bo$78bo74bo$76b3o71bobo22b3o$174bo2bo$177bo$
177bo$174bobo3$102b3o78b3o$54bo46bo2bo78bo2bo$52bobo49bo78bo$53b2o49bo
72bo5bo$101bobo40bo17bo13b3o5bobo$143b3o15b3o12bob2o$142b2obo14b2obo
13b3o$142b3o15b3o14b2o$142b3o16b2o$143b2o6$160b3o$108bo50bo2bo$107b3o
52bo$107bob2o51bo$108b3o42b3o3bobo$108b2o43bo2bo$153bo$153bo7b3o$154bo
bo4bo2bo$161bo$161bo$162bobo20b3o$185bo2bo$185bo$185bo$186bobo3$112b3o
78b3o$91bo20bo2bo76bo2bo$92b2o18bo82bo$91b2o19bo74bo7bo$113bobo38bo17b
o13b3o3bobo$153b3o15b3o11b2obo$153bob2o14bob2o10b3o$154b3o15b3o11b2o$
154b3o15b2o$154b2o2$67bobo$68b2o$68bo2$170b3o$118bo51bo2bo$117b3o50bo$
116b2obo50bo$116b3o44b3o5bobo$117b2o43bo2bo$165bo$165bo5b3o$162bobo5bo
2bo$173bo$173bo$170bobo22b3o$194bo2bo$197bo$197bo$194bobo3$122b3o78b3o
$121bo2bo78bo2bo$124bo78bo$124bo72bo5bo$121bobo40bo17bo13b3o5bobo$163b
3o15b3o12bob2o$162b2obo14b2obo13b3o$162b3o15b3o14b2o$162b3o16b2o$163b
2o2$107bo$105bobo$106b2o2$180b3o$128bo50bo2bo$127b3o52bo$127bob2o51bo$
128b3o42b3o3bobo$83bo44b2o43bo2bo$84bo88bo$82b3o88bo7b3o$174bobo4bo2bo
$181bo$181bo$182bobo20b3o$205bo2bo$205bo$205bo$206bobo3$132b3o78b3o$
132bo2bo76bo2bo$132bo82bo$132bo74bo7bo$133bobo38bo17bo13b3o3bobo$173b
3o15b3o11b2obo$173bob2o14bob2o10b3o$174b3o15b3o11b2o$174b3o15b2o$174b
2o6$190b3o$138bo51bo2bo$137b3o50bo$136b2obo50bo$136b3o44b3o5bobo$137b
2o43bo2bo$120bobo62bo$121b2o62bo5b3o$121bo60bobo5bo2bo$193bo$193bo$
190bobo22b3o$214bo2bo$217bo$217bo$97bo116bobo$98b2o$97b2o$142b3o78b3o$
141bo2bo78bo2bo$144bo78bo$144bo72bo5bo$141bobo40bo17bo13b3o5bobo$183b
3o15b3o12bob2o$182b2obo14b2obo13b3o$182b3o15b3o14b2o$182b3o16b2o$183b
2o6$200b3o$148bo50bo2bo$147b3o52bo$147bob2o51bo$148b3o42b3o3bobo$148b
2o43bo2bo$193bo$193bo7b3o$194bobo4bo2bo$201bo$201bo$202bobo20b3o$225bo
2bo$225bo$225bo$136bo89bobo$137bo$135b3o$152b3o78b3o$152bo2bo76bo2bo$
152bo82bo$152bo74bo7bo$153bobo38bo17bo13b3o3bobo$193b3o15b3o11b2obo$
193bob2o14bob2o10b3o$113bo80b3o15b3o11b2o$111bobo80b3o15b2o$112b2o80b
2o6$210b3o$158bo51bo2bo$157b3o50bo$156b2obo50bo$156b3o44b3o5bobo$157b
2o43bo2bo$205bo$205bo5b3o$202bobo5bo2bo$213bo$213bo$210bobo22b3o$234bo
2bo$237bo$237bo$234bobo3$162b3o78b3o$161bo2bo78bo2bo$164bo78bo$164bo
72bo5bo$161bobo40bo17bo13b3o5bobo$203b3o15b3o12bob2o$202b2obo14b2obo
13b3o$150bo51b3o15b3o14b2o$151b2o49b3o16b2o$150b2o51b2o6$220b3o$168bo
50bo2bo$126bobo38b3o52bo$127b2o38bob2o51bo$127bo40b3o42b3o3bobo$168b2o
43bo2bo$213bo$213bo7b3o$214bobo4bo2bo$221bo$221bo$222bobo20b3o$245bo2b
o$245bo$245bo$246bobo3$172b3o78b3o$172bo2bo76bo2bo$172bo82bo$172bo74bo
7bo$173bobo38bo17bo13b3o3bobo$213b3o15b3o11b2obo$213bob2o14bob2o10b3o$
214b3o15b3o11b2o$214b3o15b2o$214b2o6$230b3o$178bo51bo2bo$166bo10b3o50b
o$164bobo9b2obo50bo$165b2o9b3o44b3o5bobo$177b2o43bo2bo$225bo$225bo5b3o
$222bobo5bo2bo$233bo$233bo$142bo87bobo22b3o$143bo110bo2bo$141b3o113bo$
257bo$254bobo3$182b3o78b3o$181bo2bo78bo2bo$184bo78bo$184bo72bo5bo$181b
obo40bo17bo13b3o5bobo$223b3o15b3o12bob2o$222b2obo14b2obo13b3o$222b3o
15b3o14b2o$222b3o16b2o$223b2o6$240b3o$188bo50bo2bo$187b3o52bo$187bob2o
51bo$188b3o42b3o3bobo$188b2o43bo2bo$233bo$233bo7b3o$234bobo4bo2bo$241b
o$241bo$242bobo20b3o$179bobo83bo2bo$180b2o83bo$180bo84bo$266bobo3$192b
3o78b3o$192bo2bo76bo2bo$192bo82bo$156bo35bo74bo7bo$157b2o34bobo38bo17b
o13b3o3bobo$156b2o75b3o15b3o11b2obo$233bob2o14bob2o10b3o$234b3o15b3o
11b2o$234b3o15b2o$234b2o6$250b3o$198bo51bo2bo$197b3o50bo$196b2obo50bo$
196b3o44b3o5bobo$197b2o43bo2bo$245bo$245bo5b3o$242bobo5bo2bo$253bo$
253bo$250bobo22b3o$274bo2bo$277bo$277bo$274bobo3$202b3o78b3o$201bo2bo
78bo2bo$204bo78bo$195bo8bo72bo5bo$196bo4bobo40bo17bo13b3o5bobo$194b3o
46b3o15b3o12bob2o$242b2obo14b2obo13b3o$242b3o15b3o14b2o$242b3o16b2o$
243b2o4$172bo$170bobo$171b2o$208bo$207b3o$207bob2o$208b3o$208b2o!


The long slog afterwards is using the overunity reactions as constructors to rebuild the entire helix + fanouts. That is what makes these things so large - they need to compensate for destroying the helix by rebuilding it, and the construction process is arduous.

How difficult that task turns out to be depends a lot on modular arithmetic. Vector math can tell us how many distinct types of outputs we have to deal with, and that sets up a group structure, generated by the climber. The specifics of the group are quite dependent on what the over-unity reaction is, but basically the happiest situations are when everything is relatively prime, because then any given track can produce any given output. I can continue with specifics of the waterbear but I hope this thread stays more general.

Other Engineered Spaceships
All this technology is specific to caterpillar type spaceships, those that support a basic reaction via a helix. Things changed with the Gemini. No longer was there a short-period reaction powering the ship. But many principles remained. There was a basic over-unity reaction in the construction arm technology - with a glider quartet as input, one could get the same glider quartet as output in the other direction, plus a programmed construction glider pair. Also, since the over-unity reaction is stationary, it doesn't rely on a track. It waits as long as is needed for all its orchestrated phases to complete, and then construction proceeds to the next unit.

A similarly patient engineered family of spaceships are the half-baked knightships. This is essentially a caterpillar, in that it has a track and climbers, but the track is a single glider, and the climbers are HBs. Since the HBs are stationary, the period can be as large as it needs to be. But of course, we don't get anywhere without an over-unity reaction. Here, it's the extra glider made when two HBs rub together during the climbing phase (see codeholic's avatar). These react to make the synchronized tracks all begin at the front again next period.

The caterloopillar manages to use very specific helices that bounce signals around on their sparks only, and don't get destroyed except at the very end. Whenever another signal gets out to contribute to the constructions in the center, that is over-unity.

Construction types
Using very limited categories of outputs to build a target helix / construction arm / HBK glider seed as the case may be brings up the question: how do you store information about what you are building and how to build it in the tracks?

Basically everything is built from collisions of gliders, *WSS or ash. If multiple moving parts arrive together it's a salvo, and if only one glider arrives at a time, it's a slow salvo. Slow salvos are especially simple, because all that needs to be programmed is which lane the glider needs to come from. For the caterloopillar this is stored in the interim position of the signals bouncing around. For the HBK it is stored in the timing delay between glider generation on the top lane and the bottom lane. For the Gemini and Demonoid construction arms, there's kind of a meta salvo technology: the timing of the incoming glider tape encodes the timing of a salvo pair, and successive salvo pairs aimed at an "elbow" slowly accomplish a slow salvo construction.

Salvos (non-slow) are a bit more complicated, because you need to encode the lane and the timing to fire. The original Caterpillar used the "catch and throw" technology in Gabriel's link to get both right. I used a lot of modular arithmetic and reaction-specific tricks to get it to work for the Waterbear. The analogous tricks for other knightship caterpillars could be really challenging. However, if an oblique caterpillar is supported by a *WSS helix, then slow salvos are impossible because ash won't ever stay close to the helix, so for every oblique caterpillar we need some ingenuity to accomplish the constructions.


I'll continute to update this thread with whatever I know if people show interest, and anyone is welcome to ask questions, propose their own spaceship reactions, contribute. I want more such things to exist!
Physics: sophistication from simplicity.
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biggiemac
 
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Re: Engineered Spaceships Q&A

Postby HartmutHolzwart » April 11th, 2016, 5:51 am

Good Job!

I was thinking on something along this lines as well!

It should be stressed that the classical helices are all destructive (caterpillar, centipede, waterbear). The *WSS convoys used in the caterloopillar are no Helices in the original sense.
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Re: Engineered Spaceships Q&A

Postby codeholic » April 11th, 2016, 6:16 am

Well, I would argue, that centipede's frontend is not a helix. I used to propose a helical frontend for a 31c/240 spaceship, but it required much more spaceships than there are in the final design.
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Re: Engineered Spaceships Q&A

Postby dvgrn » April 11th, 2016, 9:42 am

biggiemac wrote:The reaction itself is known as a climber or crawler (I prefer climber), and the trail it climbs on is referred to as a "track."

I also prefer "climber". In the 31c/240 project I found I didn't like "track" so much, because of the sort-of conflict with "Herschel track" (though really it's a very similar idea -- support for a signal). I think early discussions of the Caterpillar used both "blinker tracks" and "blinker trails", so I always tried to refer to 31c/240 supporting blocks as "block trails".

HartmutHolzwart wrote:It should be stressed that the classical helices are all destructive (caterpillar, centipede, waterbear). The *WSS convoys used in the caterloopillar are no Helices in the original sense.

Well... those *WSS convoys *are* destroyed at the front end, resulting in an active reaction that moves at the speed of the spaceship. It spends some time as a glider, and some time as a honeyfarm-loaf-pond constellation, but that doesn't disqualify it as a helix. Even the sample reaction in the Life Lexicon spends a little time as a block.

A new innovation in the Caterloopillar is the "negative helix", which pulls a reaction instead of pushing it. Again it's a destructive reaction. The strange thing about both of them is the double function -- they move the front end and back end at the appropriate speed, as helices should, but the only output generated is a glider from the front end to contribute to making a block target for the following slow salvos. The slow salvos are generated by side effects of passing helix components -- we've never had a helix with side effects before, right?

codeholic wrote:Well, I would argue, that centipede's frontend is not a helix.

Agreed. When the overall speed is less than c/4, it seems as if it will usually end up being more efficient to construct the front-end support directly with streams of gliders, reflected off of upward streams of *WSSes as necessary. Those upward *WSSes don't quite count as a helix in my book.
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Re: Engineered Spaceships Q&A

Postby simsim314 » April 11th, 2016, 6:58 pm

dvgrn wrote:Well... those *WSS convoys *are* destroyed at the front end, resulting in an active reaction that moves at the speed of the spaceship. It spends some time as a glider, and some time as a honeyfarm-loaf-pond constellation, but that doesn't disqualify it as a helix... The slow salvos are generated by side effects of passing helix components -- we've never had a helix with side effects before, right?


I think there are two logical components inside caterlopoillar reading heads design.

1. Is the non-destructive part that convert SL into glider and back into SL. I wouldn't call this part helix - but something that related to reading a tape of slow salvo operations in SL form. In a sense it's just another implementation of universal construction using moving components, that somehow by "accident" turned out to be *WSSs.

2. The destructive mechanism that moves SL by some distance - while destroying the universal construction part. This is definitely a universal helix mechanism that works for any speed < c/4. It consist of SL+*WSS reaction to make a glider, fanout, and another *WSS to bring it back into the same SL after some distance. It's minimalistic design of 4 *WSS that can move with any slow enough speed.

The current design incorporates both of the components pretty well into single monolithic design, which is part of its elegancy, but logically speaking many other ways to implements each "logical" part can be suggested. For starters we can destroy *WSS reading head with gliders instead with helix. This was strongly suggested by codeholic in the discussions, and should work fine. This will minimize the *WSS count and will replace the *WSS helix with gliders, but on the other hand will add complexity.
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Re: Engineered Spaceships Q&A

Postby dvgrn » April 14th, 2016, 5:16 pm

biggiemac wrote:Basically everything is built from collisions of gliders, *WSS or ash. If multiple moving parts arrive together it's a salvo, and if only one glider arrives at a time, it's a slow salvo. Slow salvos are especially simple, because all that needs to be programmed is which lane the glider needs to come from. For the caterloopillar this is stored in the interim position of the signals bouncing around. For the HBK it is stored in the timing delay between glider generation on the top lane and the bottom lane. For the Gemini and Demonoid construction arms, there's kind of a meta salvo technology:..

A minor note: if you mention Geminoid/Demonoid technology, the sentence I've marked in red is a fairly good approximation, but not quite true.

The meta-salvo in those cases is, or can be, a "P2 slow" salvo. That means that to record the recipe correctly, you have to keep track of the parity of the glider (even or odd phase) as well as the lane the glider is traveling on.

You don't have to worry about parity in the Caterloopillar, because the parity of the output gliders can't be easily controlled for all possible spaceship speeds, so it's simpler to use only P1 slow salvos in the design.

I seem to recall the HBKs were a little more complicated -- you could get either parity of glider, because the glider available on a given lane changes parity after each reset cycle. You just have to wait a cycle sometimes, if the parity actually matters in the recipe you're using.
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Re: Engineered Spaceships Q&A

Postby simsim314 » April 15th, 2016, 7:39 pm

Speaking of slow salvo - there was some concern about monochromatic slow salvo, or P2 with same parity. Turned out to be absolutely fine - the recipes are maybe 10% longer at worst.

So there is absolutely no need to optimize a design to allow some more complex slow salvo options. Even monochromatic same parity will work for all needs with minor costs.

It was somewhat bold decision in caterloopillar to let go of half of the lanes, and the internal states - and just trust the statistic of exponential growth to cover for it. This allowed to gain some amount of generality otherwise impossible to get.
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Re: Engineered Spaceships Q&A

Postby muzik » April 16th, 2016, 4:34 am

This is the kind of reaction I'm looking for:

- A glider hits a still life or collection of still lifes. This triggers a reaction.

- After the reaction, the same arrangement appears, except all moved to the side a bit, and the reaction also throws off a glider in the opposite direction it came in from.

- The glider does this very same reaction, moving the other arrangement the same way, etc.


With this, we could make engineered spaceships with controllable speed
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Re: Engineered Spaceships Q&A

Postby Sokwe » April 16th, 2016, 5:03 am

muzik wrote:This is the kind of reaction I'm looking for:

- A glider hits a still life or collection of still lifes. This triggers a reaction.

- After the reaction, the same arrangement appears, except all moved to the side a bit, and the reaction also throws off a glider in the opposite direction it came in from.

These are very hard conditions to meet. I'm not sure if we will ever find a small constellation that does this. The closest thing we have is the half-bakery reaction:
x = 13, y = 14, rule = B3/S23
10bo$10bobo$10b2o5$4b2o$3bo2bo$3bobo$b2obo$o2bo$obo$bo!

And this was already used to construct the half-baked ships.

One place to start looking for this would be in the ash of common chaotic patterns (such as the R-pentomino). For example, you might be able to crash a glider into the ash of an R-pentomino to get a new R-penomino and some extra gliders. Then another glider can crash into the ash of the new R-pentomino (like the half-bakery reaction, but much messier). I'm not sure if anyone would be interested in this, as you probably won't find a reaction as clean or as elegant as the half-bakery reaction.
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Re: Engineered Spaceships Q&A

Postby codeholic » April 16th, 2016, 11:42 am

This is a pretty old idea. Gabriel Nivasch even wrote an exhaustive search program for this particular purpose 16 years ago, but there's been no luck so far.
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Re: Engineered Spaceships Q&A

Postby dvgrn » April 16th, 2016, 1:33 pm

muzik wrote:- The glider does this very same reaction, moving the other arrangement the same way, etc.

codeholic wrote:This is a pretty old idea. Gabriel Nivasch even wrote an exhaustive search program for this particular purpose 16 years ago, but there's been no luck so far.

Or replace "glider" with "long long stream of gliders", and there are known ways to get a (Spartan circuitry) constellation to move by any (x,y) you want -- including (2,1), for a super-slow adjustable-period true knightship, or (0,0), for a thoroughly ridiculous adjustable-period oscillator.

The Demonoid is the only example constructed so far, and it's a special case -- you need a constellation about twice as big for non-diagonal movement, because you need different Spartan circuitry at the two ends to avoid moving the ends in mirror-image directions.
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Re: Engineered Spaceships Q&A

Postby muzik » April 18th, 2016, 11:26 am

Sokwe wrote:One place to start looking for this would be in the ash of common chaotic patterns (such as the R-pentomino). For example, you might be able to crash a glider into the ash of an R-pentomino to get a new R-penomino and some extra gliders. Then another glider can crash into the ash of the new R-pentomino (like the half-bakery reaction, but much messier). I'm not sure if anyone would be interested in this, as you probably won't find a reaction as clean or as elegant as the half-bakery reaction.


That was easy. Here is something that produces the hexomino successor of the R-pentomino:

x = 11, y = 9, rule = B3/S23
8bo$8bobo$8b2o3$bo$obo$obo$bo!


However, it can't go on forever:

x = 11, y = 161, rule = B3/S23
8bo$8bobo$8b2o3$bo$obo$obo$bo16$bo$obo$obo$bo16$bo$obo$obo$bo16$bo$obo
$obo$bo16$bo$obo$obo$bo16$bo$obo$obo$bo16$bo$obo$obo$bo16$bo$obo$obo$b
o16$bo$obo$obo$bo!


Now to find something that happens when you actually do it inside the ashes.

Of course finding applications for this is the hard part.
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Re: Engineered Spaceships Q&A

Postby Sphenocorona » June 27th, 2016, 7:25 pm

I feel that this thread is the right place to post this.

I like the idea of dividing up the non-elementary spaceships into fixed velocity and adjustable velocity categories, but I think that calling them "engineered" and "engineerable" ships is a bit confusing; I understand the terminology fine, but as both categories have historically referred to together as "engineered" for a very long time, to me it stands as a more glaring ambiguity than using the term 'caterpillar' to describe both a specific spaceship and describe an entire category.
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Re: Engineered Spaceships Q&A

Postby dvgrn » July 4th, 2016, 1:07 pm

Sphenocorona wrote:I feel that this thread is the right place to post this.

I like the idea of dividing up the non-elementary spaceships into fixed velocity and adjustable velocity categories, but I think that calling them "engineered" and "engineerable" ships is a bit confusing...

Second that. The two terms are just too close to each other, along the same lines as my original silly idea that there would be a distinction between "half-baked knightships" and "half-bakery knightships".

I wonder if it's too late to re-engineer the terminology. Could the main category be simply "engineered spaceships", with a subcategory of "adjustable spaceships"?
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Re: Engineered Spaceships Q&A

Postby codeholic » July 4th, 2016, 6:59 pm

I don't think there is a need for a special term, especially "adjustable" can mean different things, so it's better to be more descriptive, i. e. "with adjustable period", "with adjustable velocity", "with adjustable period, velocity and slope".

P. S. I think that was you who proposed to categorize engineered spaceships into "self-constructing" and "self-supporting". This classification might be also occasionally useful, but sometimes the difference may be vague.
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