Thread for basic questions

[BlinkerSpawn]

What's wrong with Sokwe's 45-degree MWSS converter? That should count "small and fast" if anything does...

The only thing wrong with it is that I forgot about it.

[AbhpzTa]

Does there exist a stable 45 degree reflector?

Yes. Simply connect the 135-degree reflector to a Snark.
Does there exist a *small* or *fast* 45 degree reflector? The only one I know of is the P6 LWSS-to-G that was posted (Osc Discoveries thread?) a while ago.

What's wrong with Sokwe's 45-degree MWSS converter? That should count "small and fast" if anything does:

Code: Select all

x = 9, y = 15, rule = B3/S23
b2o$2bo3b2o$bo4b2o$b2o$3bo$b3o$o$2o2$6b3o$5bo2bo$8bo$4bo3bo$8bo$5bobo!
#C [[ THUMBNAIL STOP 35 ]]

Doesn't work for LWSSes, though. The only converter that works for all three *WSSes is definitely not small or fast -- I should probably look it up and see if new technology can make it any smaller.

If you want a 45-degree converter starting from a glider, the fastest in terms of recovery time is probably syringe + (a couple of Herschel conduits) + Kazyan's H-to-MWSS, and the smallest stable mechanism I think is currently

Code: Select all

x = 81, y = 58, rule = B3/S23
49bo11b2o$16bo31bobo10b2o$14b3o5b2o24bobo$13bo7bobo22b3ob2o$13b2o7bo
22bo$46b3ob2o$48bob2o3$8b2o$7bo2bo$7bo2bo$8b2o10bo$19bobo16b2o13b2o$
19bobo16b2o13b2o$20bo47b2o$67bo2bo$68b2obo$71bo$71b2o$56b2o18b2o$57bo
18bo$54b3o21bo$54bo2b3o14b5o$56bo2bo13bo$55b2o2bobo12b3o$60b2o15bo$74b
4o$69b2o3bo3b2o$69b2o4b3o2bo$3o74bob2o$2bo74bo$bo74b2o3$50bo17b2o$48b
3o17bo$47bo21b3o$47b2o22bo7$37b2o$36bobo5b2o$36bo7b2o$35b2o2$49bo$45b
2obobo$44bobobobo$41bo2bobobobob2o$41b4ob2o2bo2bo$45bo4b2o$43bobo$43b
2o!
#C [[ THUMBNAIL STEP 5 STOP 555 ]]

I think those are 135-degree converters and codeholic's LWSS/MWSS-to-G is a 45-degree converter:

Code: Select all

x = 62, y = 26, rule = B3/S23
48bob2o4bo$48b2obo3bobo$55bobo$46b5o3b2ob3o$45bo2bo2bo8bo$45b2o3b2o2b
2ob3o$54b2obo$61bo$59b3o$2bo55bo$o3bo32bo2bo17b2o$5bo35bo$o4bo31bo3bo$
b5o32b4o2$55b2o$54bo2bo$55b2o$47b2o$46bobo$46bo$45b2o$58b2o$58bo$59b3o
$61bo!
#C [[ THUMBNAIL ZOOM 5 STOP 160 ]]

[BlinkerSpawn]

That converter deflects the path by an angle of 45 degrees; the other reflectors have an angle of 45 degrees between the paths (135-degree deflection).

[dvgrn]

I think those are 135-degree converters and codeholic's LWSS/MWSS-to-G is a 45-degree converter...

Come to think of it, you're probably right! I'll have to adjust the new Life Lexicon entries accordingly -- unless someone can convince me the current terminology is correct after all.

There's no ambiguity about 90-degree left and right turns, but we need a clear standard when we move to 45 degrees and 135 degrees.

Fortunately we have an old standard naming convention that we can check against:

• A "0-degree reflector" is one where the output signal keeps going in the same direction as the input signal.
• For a 180-degree reflector (like the rectifier) the output signal goes back in the opposite direction from the input signal.

Hmm.

Obviously a 45-degree reflector had better be an output signal that bisects the 0-degree and 90-degree directions, and a 135-degree reflector's output should bisect the 90-degree and 180-degree directions.

That's not the way we've been applying the terms to Sokwe's and codeholic's reflectors, but I think we should probably start now...!

[calcyman]

Seconded.

[drc]

Should 8x32 soups be counted as natural?

[muzik]

Are there any c/4 diagonal glider backrakes?

[dvgrn]

Should 8x32 soups be counted as natural?

I'd vote that they should be. The symmetric soups are definitely not quite natural, but there's no particular bias toward complex structures in an 8x32 soup.

The "no particular bias" criterion suggests that the results of Calcyman's slow-salvo soup experiments could also be considered natural -- but that's kind of stretching the definition of "random soup" all out of shape.

[chris_c]

Are there any c/4 diagonal glider backrakes?

Yes. You could take the siderake from here and add this reflector:

Code: Select all

x = 51, y = 36, rule = B3/S23
28bo10b2o$27b5o6b2o$27bo2b2o8bo7b2o$29b2obo5b2o6b3obo$38b2o3bob2o$32bo
bo6b2o$37b3obo4bo$34b3o3bo4bo$35bo7bo$35bo6bo2$38bo2$2o$b2o$o4$30bo$
29b2o$29bobo2$32b2o$32b2o2$28bob2o$27b4o$27bo3b2o$32bo2bo2$31b2o3bo$
31b2o3bo$32bo$32bo$33b2o!

[Rhombic]

Any proof for how no evolved pattern (say, more than 5 generations from a random soup) in Seeds can have a live cell with 7 or 8 neighbours? i.e. B2/S78, B2/S8 and B2/S7 are equivalent to B2/S

And how any 100x100 torus 50% random soup evolves into a xpN where N is a multiple of 21 in B2c345678/S02i:T100,100

[_zM]

A live cell in Seeds has to be born from two live cells around it. These cells have to be dead in the next generation, because there is no survival condition in Seeds. Thus, any live cell has less than seven live neighbors.

[drc]

Could a true infinite novelty generator be produced by making a puffer that fires snakes, then extends the snakes by creating rakes via breeder? I don't know if that makes sense.

[dvgrn]

Could a true infinite novelty generator be produced by making a puffer that fires snakes, then extends the snakes by creating rakes via breeder? I don't know if that makes sense.

Infinite novelty in the sense of building every different length of snake? It seems likely that that could be managed somehow, maybe with slide guns building the successive rakes.

Assuming that there is a constructible puffer/rake that can lengthen an evenly-spaced series of snake heads -- which seems like a fairly good assumption -- then at least there's a universal-constructor-based solution, that moves an elbow/hand combination by (X, 1) before each new puffer/rake construction... if there's an odd-X puffer/rake, then it's a little easier, but even with even distances it's just a matter of alternating two recipes.

[Saka]

I know that there exists a c4 diagonal backwards glider rake. Could someone post the rle for me?

[dvgrn]

I know that there exists a c4 diagonal backwards glider rake. Could someone post the rle for me?

See chris_c's post a few messages back in this thread:

Code: Select all

x = 3308, y = 3306, rule = B3/S23
19bo$18b2o$18bobo2$21b2o$21b2o2$12bo6b2o$11b2o5bo2bo$11bobo3b2obo$15bo
$8b2o4bo$7b2o5bo2b2o27b2obo$9bo9bo26bo3bo$11b2o5bobo25bo4bo$10bo8bobo
26b2o$20bobo27bobo$9bo2bo8bobo$b2o5b2o2bobo7bobo20bo6b2o$2o5bo5bobo7bo
bo18b5o4bo2bo$2bo4bobo4bobo7bobo11b2o4bo6b2o$4b2o2bo6bobo7bobo10bobo
11bo$4b2o10bobo7bobo9bo5bob2o6bobo$17bobo7bobo9b2o4bo4bobo$18bobo7bobo
8bo2bo6b3o$19bobo7bobo7bo6b2ob2o23bo$20bobo7bobo8bobobo2bo24b5o$21bobo
7bobo39bo2b2o$22bobo7bobo8bo4bo26b2obo$23bobo7bobo8b4o$24bobo7bobo41bo
bo$25bobo7bobo$26bobo7bobo32b3o6b3o$27bobo7bobo26bo4bo2b3o4b3o$28bobo
7bobo24b2o5b2ob5ob3o$29bobo7bobo23bobo3b3o4b2ob2o$30bobo7bobo34bobo$
31bobo7bobo23b3o6bo2bo$20b3o9bobo7bobo21b3o7bo$20bo2b3o7bobo7bobo22bob
ob4o2bo$21bobo10bobo7bobo23b2ob2o$26bo8bobo7bobo22b6o$24bo11bobo7bobo$
26bobo8bobo7bobo$19b2obo6bo8bobo7bobo$18b2o3bo2bo2bo9bobo7bobo$12b3o4b
o2bo2bo3bo10bobo7bobo$12bo6bo2bo2bo3bo11bobo7bobo$15bo3bo6bobo13bobo7b
obo$12bo2bo8b2o17bobo7bobo374bo$13bo2bo6b3o18bobo7bobo372b2o$14bo5bo3b
o20bobo7bobo365bo5bobo$16bobob2obo22bobo7bobo363b2o$18b2o27bobo7bobo
362bobo3b2obobo$22bo25bobo7bobo365bo7b2o$49bobo7bobo363bo4bo5b2o$19bo
2bo27bobo7bobo362bo2bo2b6o$51bobo7bobo$52bobo7bobo$53bobo7bobo365b2o2b
2o$54bobo7bobo364bob4o$55bobo7bobo363bo4bobo$56bobo7bobo370bo$57bobo7b
obo368b3o$58bobo7bobo$34b2o23bobo7bobo366bo$33b2o3bo21bobo7bobo$35bob
2o22bobo7bobo364b2obo$37b3o22bobo7bobo363b2ob4o$37bo25bobo7bobo363bo2b
4o$39b3o22bobo7bobo363b2o$32b2obo4b2o23bobo7bobo$32bob2o3bobo24bobo7bo
bo$26b2o4bob2o3b3o25bobo7bobo$25b2o6bo5b3o26bobo7bobo$26bobo4b2o4bobo
27bobo7bobo$26b3o4b2o2b2o31bobo7bobo$26b2o6bobo34bobo7bobo$28bobo3b2o
3bo32bobo7bobo$34b4o35bobo7bobo$30bobo41bobo7bobo$32b4o39bobo7bobo$32b
4o40bobo7bobo$33b2o42bobo7bobo$78bobo7bobo$79bobo7bobo$80bobo7bobo$81b
obo7bobo$82bobo7bobo$83bobo7bobo$84bobo7bobo$85bobo7bobo$86bobo7bobo$
87bobo7bobo$88bobo7bobo$89bobo7bobo$90bobo7bobo398bo10b2o$91bobo7bobo
396b5o6b2o$92bobo7bobo395bo2b2o8bo7b2o$93bobo7bobo348b2o46b2obo5b2o6b
3obo$94bobo7bobo347bobo54b2o3bob2o$95bobo7bobo346bo50bobo6b2o$96bobo7b
obo346b2o53b3obo4bo$97bobo7bobo345bo2bo48b3o3bo4bo$98bobo7bobo344bo52b
o7bo$99bobo7bobo345bobo48bo6bo$100bobo7bobo348bo$101bobo7bobo345bo2bo
48bo$102bobo7bobo344bo2bo67bo$103bobo7bobo345b3o65b2o$104bobo7bobo340b
3ob3o59bo5bobo$105bobo7bobo335b3ob2o2b3o58b2o$106bobo7bobo334bo7b2o59b
obo3b2obobo$107bobo7bobo334bo6b2o63bo7b2o$108bobo7bobo336b5o63bo4bo5b
2o$109bobo7bobo337b2o64bo2bo2b6o$110bobo7bobo335b2o$111bobo7bobo334b2o
$112bobo7bobo332bobo71b2o2b2o$113bobo7bobo330b2o73bob4o$114bobo7bobo
329bobo72bo4bobo$115bobo7bobo327bo83bo$116bobo7bobo327b2o80b3o$117bobo
7bobo$118bobo7bobo407bo$119bobo7bobo$120bobo7bobo405b2obo$121bobo7bobo
332b3o69b2ob4o$122bobo7bobo331bo9b2o61bo2b4o$123bobo7bobo331bo6b3obo
61b2o$124bobo7bobo332b2o2b2o$125bobo7bobo332bo$126bobo7bobo335bo$127bo
bo7bobo330b2o3bo$128bobo7bobo328bobob2o5b2o2bob2obo$129bobo7bobo327bob
o2bob2ob2o3bob2obo$130bobo7bobo325bo4b2o6bobo6bo$131bobo7bobo324b2o9bo
7b2obo$132bobo7bobo323b2o7b3o10bo$133bobo7bobo330bo10bo2bo$134bobo7bob
o327bo4bo10bo$135bobo7bobo325b2o2bo10b2o$136bobo7bobo325b2o$137bobo7bo
bo324b2o$138bobo7bobo323b3o$139bobo7bobo$140bobo7bobo321bobo$141bobo7b
obo320bobo$142bobo7bobo319bob2obo$143bobo7bobo318b2o2bobo$144bobo7bobo
318bo5bo$145bobo7bobo317bo$146bobo7bobo321bo$147bobo7bobo318bo$148bobo
7bobo$149bobo7bobo439bo10b2o$150bobo7bobo437b5o6b2o$151bobo7bobo436bo
2b2o8bo7b2o$152bobo7bobo389b2o46b2obo5b2o6b3obo$153bobo7bobo388bobo54b
2o3bob2o$154bobo7bobo387bo50bobo6b2o$155bobo7bobo387b2o53b3obo4bo$156b
obo7bobo386bo2bo48b3o3bo4bo$157bobo7bobo385bo52bo7bo$158bobo7bobo386bo
bo48bo6bo$159bobo7bobo389bo$160bobo7bobo386bo2bo48bo$161bobo7bobo341bo
43bo2bo67bo$162bobo7bobo339b5o42b3o65b2o$163bobo7bobo338bo2b2o38b3ob3o
59bo5bobo$164bobo7bobo339b2obo33b3ob2o2b3o58b2o$165bobo7bobo375bo7b2o
59bobo3b2obobo$166bobo7bobo340bobo32bo6b2o63bo7b2o$167bobo7bobo377b5o
63bo4bo5b2o$168bobo7bobo331b3o6b3o35b2o64bo2bo2b6o$169bobo7bobo325bo4b
o2b3o4b3o33b2o$170bobo7bobo323b2o5b2ob5ob3o33b2o$171bobo7bobo322bobo3b
3o4b2ob2o33bobo71b2o2b2o$172bobo7bobo333bobo35b2o73bob4o$173bobo7bobo
322b3o6bo2bo35bobo72bo4bobo$174bobo7bobo320b3o7bo37bo83bo$175bobo7bobo
321bobob4o2bo36b2o80b3o$176bobo7bobo322b2ob2o$177bobo7bobo321b6o121bo$
178bobo7bobo$179bobo7bobo446b2obo$180bobo7bobo373b3o69b2ob4o$181bobo7b
obo372bo9b2o61bo2b4o$182bobo7bobo372bo6b3obo61b2o$183bobo7bobo373b2o2b
2o$184bobo7bobo373bo$185bobo7bobo376bo$186bobo7bobo371b2o3bo$187bobo7b
obo369bobob2o5b2o2bob2obo$188bobo7bobo368bobo2bob2ob2o3bob2obo$189bobo
7bobo366bo4b2o6bobo6bo$190bobo7bobo365b2o9bo7b2obo$191bobo7bobo364b2o
7b3o10bo$192bobo7bobo371bo10bo2bo$193bobo7bobo368bo4bo10bo$194bobo7bob
o366b2o2bo10b2o$195bobo7bobo366b2o$196bobo7bobo365b2o$197bobo7bobo364b
3o$198bobo7bobo$199bobo7bobo362bobo$200bobo7bobo361bobo$201bobo7bobo
360bob2obo$202bobo7bobo359b2o2bobo$203bobo7bobo359bo5bo$204bobo7bobo
358bo$205bobo7bobo362bo$206bobo7bobo359bo$207bobo7bobo$208bobo7bobo
480bo10b2o$209bobo7bobo478b5o6b2o$210bobo7bobo477bo2b2o8bo7b2o$211bobo
7bobo430b2o46b2obo5b2o6b3obo$212bobo7bobo429bobo54b2o3bob2o$213bobo7bo
bo428bo50bobo6b2o$214bobo7bobo428b2o53b3obo4bo$215bobo7bobo427bo2bo48b
3o3bo4bo$216bobo7bobo426bo52bo7bo$217bobo7bobo427bobo48bo6bo$218bobo7b
obo430bo$219bobo7bobo427bo2bo48bo$220bobo7bobo382bo43bo2bo67bo$221bobo
7bobo380b5o42b3o65b2o$222bobo7bobo379bo2b2o38b3ob3o59bo5bobo$223bobo7b
obo380b2obo33b3ob2o2b3o58b2o$224bobo7bobo416bo7b2o59bobo3b2obobo$225bo
bo7bobo381bobo32bo6b2o63bo7b2o$226bobo7bobo418b5o63bo4bo5b2o$227bobo7b
obo372b3o6b3o35b2o64bo2bo2b6o$228bobo7bobo366bo4bo2b3o4b3o33b2o$229bob
o7bobo364b2o5b2ob5ob3o33b2o$230bobo7bobo363bobo3b3o4b2ob2o33bobo71b2o
2b2o$231bobo7bobo374bobo35b2o73bob4o$232bobo7bobo363b3o6bo2bo35bobo72b
o4bobo$233bobo7bobo361b3o7bo37bo83bo$234bobo7bobo362bobob4o2bo36b2o80b
3o$235bobo7bobo363b2ob2o$236bobo7bobo362b6o121bo$237bobo7bobo$238bobo
7bobo487b2obo$239bobo7bobo414b3o69b2ob4o$240bobo7bobo413bo9b2o61bo2b4o
$241bobo7bobo413bo6b3obo61b2o$242bobo7bobo414b2o2b2o$243bobo7bobo414bo
$244bobo7bobo417bo$245bobo7bobo412b2o3bo$246bobo7bobo410bobob2o5b2o2bo
b2obo$247bobo7bobo409bobo2bob2ob2o3bob2obo$248bobo7bobo407bo4b2o6bobo
6bo$249bobo7bobo406b2o9bo7b2obo$250bobo7bobo405b2o7b3o10bo$251bobo7bob
o412bo10bo2bo$252bobo7bobo409bo4bo10bo$253bobo7bobo407b2o2bo10b2o$254b
obo7bobo407b2o$255bobo7bobo406b2o$256bobo7bobo405b3o$257bobo7bobo$258b
obo7bobo403bobo$259bobo7bobo402bobo$260bobo7bobo401bob2obo$261bobo7bob
o400b2o2bobo$262bobo7bobo400bo5bo$263bobo7bobo399bo$264bobo7bobo403bo$
265bobo7bobo400bo$266bobo7bobo$267bobo7bobo521bo10b2o$268bobo7bobo519b
5o6b2o$269bobo7bobo518bo2b2o8bo7b2o$270bobo7bobo471b2o46b2obo5b2o6b3ob
o$271bobo7bobo470bobo54b2o3bob2o$272bobo7bobo469bo50bobo6b2o$273bobo7b
obo469b2o53b3obo4bo$274bobo7bobo468bo2bo48b3o3bo4bo$275bobo7bobo467bo
52bo7bo$276bobo7bobo468bobo48bo6bo$277bobo7bobo471bo$278bobo7bobo468bo
2bo48bo$279bobo7bobo423bo43bo2bo$280bobo7bobo421b5o42b3o$281bobo7bobo
420bo2b2o38b3ob3o$282bobo7bobo421b2obo33b3ob2o2b3o$283bobo7bobo457bo7b
2o$284bobo7bobo422bobo32bo6b2o$285bobo7bobo459b5o99bo$286bobo7bobo413b
3o6b3o35b2o99b5o$287bobo7bobo407bo4bo2b3o4b3o33b2o100bo2b2o$288bobo7bo
bo405b2o5b2ob5ob3o33b2o74b2o26b2obo$289bobo7bobo404bobo3b3o4b2ob2o33bo
bo73b2o$290bobo7bobo415bobo35b2o69b2o5bo30bobo$291bobo7bobo404b3o6bo2b
o35bobo67b2o5b2o$292bobo7bobo402b3o7bo37bo72bo4bobo2b2o18b3o6b3o$293bo
bo7bobo403bobob4o2bo36b2o72b2o3b2ob4o11bo4bo2b3o4b3o$294bobo7bobo404b
2ob2o114b2o10bo9b2o5b2ob5ob3o$295bobo7bobo403b6o125bo9bobo3b3o4b2ob2o$
296bobo7bobo527bo27bobo$297bobo7bobo528bo15b3o6bo2bo$298bobo7bobo455b
3o70b2obob3o6b3o7bo$299bobo7bobo454bo9b2o64bo4b2o6bobob4o2bo$300bobo7b
obo454bo6b3obo60bo2b6o9b2ob2o$301bobo7bobo455b2o2b2o65bo16b6o$302bobo
7bobo455bo$303bobo7bobo458bo$304bobo7bobo453b2o3bo$305bobo7bobo451bobo
b2o5b2o2bob2obo$306bobo7bobo450bobo2bob2ob2o3bob2obo$307bobo7bobo448bo
4b2o6bobo6bo94b2o$308bobo7bobo447b2o9bo7b2obo82b3o9bobo$309bobo7bobo
446b2o7b3o10bo82bo2b3o6bo9bo$310bobo7bobo453bo10bo2bo83bobo16b2obo$
311bobo7bobo450bo4bo10bo88bo4b2o2bo3b2o2bo$312bobo7bobo448b2o2bo10b2o
87bo6b2o2bob2o2bo$313bobo7bobo448b2o103bob2obo3b5o$314bobo7bobo447b2o
112b2o$315bobo7bobo446b3o103bo2b6o$316bobo7bobo552b7o$317bobo7bobo444b
obo106b3o$318bobo7bobo443bobo$319bobo7bobo442bob2obo$320bobo7bobo441b
2o2bobo$321bobo7bobo441bo5bo$322bobo7bobo440bo$323bobo7bobo444bo$324bo
bo7bobo441bo$325bobo7bobo$326bobo7bobo$327bobo7bobo$328bobo7bobo$329bo
bo7bobo$330bobo7bobo509b3o$331bobo7bobo508bo$332bobo7bobo510bo$333bobo
7bobo506bo2bo$334bobo7bobo506bo2bo$335bobo7bobo506bo$336bobo7bobo507bo
bo$337bobo7bobo508b2o$338bobo7bobo464bo43bo$339bobo7bobo462b5o39b2o$
340bobo7bobo461bo2b2o38b3o$341bobo7bobo462b2obo32b2ob2ob2o$342bobo7bob
o497bo3bob2o$343bobo7bobo463bobo30bob3o2bo$344bobo7bobo500b2o$345bobo
7bobo454b3o6b3o32b3o$346bobo7bobo448bo4bo2b3o4b3o$347bobo7bobo446b2o5b
2ob5ob3o$348bobo7bobo445bobo3b3o4b2ob2o31b3o$349bobo7bobo456bobo34b3o$
350bobo7bobo445b3o6bo2bo$351bobo7bobo443b3o7bo36b2o$352bobo7bobo444bob
ob4o2bo34bo$353bobo7bobo445b2ob2o$354bobo7bobo444b6o$355bobo7bobo$356b
obo7bobo$357bobo7bobo$358bobo7bobo$359bobo7bobo$360bobo7bobo$361bobo7b
obo$362bobo7bobo$363bobo7bobo$364bobo7bobo$365bobo7bobo$366bobo7bobo
507bo$367bobo7bobo505b5o$368bobo7bobo504bo2b2o$369bobo7bobo505b2obo$
370bobo7bobo$371bobo7bobo506bobo$372bobo7bobo$373bobo7bobo497b3o6b3o$
374bobo7bobo491bo4bo2b3o4b3o$375bobo7bobo489b2o5b2ob5ob3o$376bobo7bobo
488bobo3b3o4b2ob2o$377bobo7bobo499bobo$378bobo7bobo488b3o6bo2bo$379bob
o7bobo486b3o7bo$380bobo7bobo487bobob4o2bo$381bobo7bobo488b2ob2o$382bob
o7bobo487b6o$383bobo7bobo$384bobo7bobo$385bobo7bobo$386bobo7bobo$387bo
bo7bobo$388bobo7bobo$389bobo7bobo558b3o$390bobo7bobo557bo$391bobo7bobo
557bo$392bobo7bobo558b2o$393bobo7bobo558bo3b2o$394bobo7bobo560b2o$395b
obo7bobo562b2o$396bobo7bobo555b6o$397bobo7bobo554bo2b2obo$398bobo7bobo
540b2o13bo4bo$399bobo7bobo539bobo10bo6bo$400bobo7bobo538bo11bo$401bobo
7bobo540bo7b2o3bo$402bobo7bobo539b2o2b2obo2b3o$403bobo7bobo542bo5bo17b
2o$404bobo7bobo541bobo3bo5b3o9bobo$405bobo7bobo538bob2o3bo6bo2b3o6bo9b
o$406bobo7bobo536b2ob2o11bobo16b2obo$407bobo7bobo535bo2bo17bo4b2o2bo3b
2o2bo$408bobo7bobo536bobo14bo6b2o2bob2o2bo$409bobo7bobo535bo2b2o14bob
2obo3b5o$410bobo7bobo562b2o$411bobo6b2obo553bo2b6o$412bobo6bob3o552b7o
$413bobo5b2o2b2o553b3o$414bob2o4b5o$415bob3o4b4o$52b2o362bo2b2o4b2obo$
51b2o364b2obo3bo2bo$53bo364bob2obob2o$55b2o361b5obo$54bo364b4obo4b2o$
421bobo4b2obo$53bo2bo365bo4bo4bo$50b2obo372b2o4b2o$49b2o4bo370bo5b2o$
51bobo2bo2b3o365bo5bob2o$56bo2bo368b3o6bo$53bo2bo3bo368b3o5b3o$54bobo
3bo376bo2bo$54bobo2b2o370bo5b2o$55b2o2b3o369bo5b2o2bo$55bo376b5obo2bo$
61bobobob2o364bob3o$62b2o3b3o363bo10b2o$63bo6bo363bo11bo$67b2obo365b2o
$68b2o375bo$68b2o374bo$68b2o369bo3bo$69bo369bo2bo$440bo6$1001b2o$111b
2o887b2o$99b3o9bobo880b2o5bo$99bo2b3o6bo9bo871b2o5b2o$100bobo16b2obo
872bo4bobo2b2o$105bo4b2o2bo3b2o2bo874b2o3b2ob4o$103bo6b2o2bob2o2bo876b
2o10bo$105bob2obo3b5o890bo$114b2o887bo$106bo2b6o888bo3bo$107b7o888b2ob
2o$109b3o890bo3bob2o$1003b2ob4o$1008b2o2bo$127b2o880b2obo43b2o$127bobo
880bo44b2o$127bo8b3o828b2o41b2o45bo$130bo3b2ob2o828bobo40b3o46b2o$130b
2obo833bo42b2o2bo43bo5bo$133b3o832b2o44bobo45b2obo$968bo2bo39bo3bobo
45bo3bo$130bo3bobo4bo826bo42b6o42b2o2b3o$129b2obob3o3b5ob4o820bobo40b
3o43b2obo$129bo3bo8b3o4b3o822bo72bo13bo3bo$128b2o5bo3bo4bob3o823bo2bo
70b2o11b2o5b2o$128bo6bo2bo2bo6bo823bo2bo70bobo10b3o$129bo8bo10bo3bo
820b3o73bo7bob2o$135bob2obo7bo821b3ob3o72bo3b2ob2obo2bo$134b2o13bo2bo
813b3ob2o2b3o72bo3b2ob3o$134bobo13bo815bo7b2o79bob2o$967bo6b2o31bo43bo
2bo4bo$136bo833b5o31b2o43b3o$134b2o836b2o32bobo41bo2bo$971b2o78bobobo$
134b2o835b2o36b2o45bo$134b2obobo830bobo36b2o41bo3bo$137bo3bo827b2o33b
2o$134b2o5bo827bobo32bo2b2o$136b5o827bo35bo3bo$969b2o34b2obo$1004bo3b
2o$1001b2o$983b2o16bo7bo$982b2o17bo$984bo18b3o$986b2o15b6o75b2o$985bo
5bo11bo68b3o9bobo$989b2obo10b2o3bo63bo2b3o6bo9bo$97b2o891bo3bo8b2o2bo
65bobo16b2obo$96b2o888b2o2b3o11b3o2b3o66bo4b2o2bo3b2o2bo$97bobo886b2ob
o16bo4bobo11b3o48bo6b2o2bob2o2bo$97b3o874bo13bo3bo13b4obobo11bo52bob2o
bo3b5o$97b2o874b2o11b2o5b2o11b4obobo14bo58b2o$99bobo871bobo10b3o20bo
15bo2bo50bo2b6o$176b2o799bo7bob2o37bo2bo50b7o$101bobo71b2o3bo795bo3b2o
b2obo2bo37bo54b3o$103b3o71bob2o795bo3b2ob3o43bobo$103bo75b3o800bob2o
45b2o$102bo76bo798bo2bo4bo45bo$97bob2obo4bo73b3o794b3o50b2o$96b2ob2obo
71b2obo4b2o793bo2bo49b3o$96bobo4bo70bob2o3bobo794bobobo42b2ob2ob2o$
101b2o65b2o4bob2o3b3o799bo41bo3bob2o$101bo3bo61b2o6bo5b3o795bo3bo41bob
3o2bo$100bo3bo63bobo4b2o4bobo846b2o$168b3o4b2o2b2o848b3o$100bo2bo64b2o
6bobo$99b2obo67bobo3b2o3bo$99bo76b4o848b3o$98b2o72bobo853b3o$98bo12b2o
61b4o$99bo10b2o62b4o849b2o80bo$112bo62b2o850bo69b2o9b2o$114b2o980b2o3b
o6bobo$113bo984bob2o15b3o$1100b3o5bobo4b2ob2o$112bo2bo984bo6b2obobobo$
109b2obo925b2o62b3obo6bob2o$108b2o4bo923bobo62b2o7bo$110bobo2bo2b3o
917bo8b3o53b2o5b2o$115bo2bo922bo3b2ob2o55b5o$112bo2bo3bo921b2obo$113bo
bo3bo924b3o$113bobo2b2o$114b2o2b3o920bo3bobo4bo$114bo925b2obob3o3b5ob
4o$120bobobob2o912bo3bo8b3o4b3o$121b2o3b3o910b2o5bo3bo4bob3o$122bo6bo
909bo6bo2bo2bo6bo$126b2obo910bo8bo10bo3bo$127b2o917bob2obo7bo$127b2o
916b2o13bo2bo$127b2o916bobo13bo$128bo$1047bo$1045b2o2$1045b2o$1045b2ob
obo$1048bo3bo$1045b2o5bo$170b2o875b5o$158b3o9bobo$158bo2b3o6bo9bo$159b
obo16b2obo$164bo4b2o2bo3b2o2bo$162bo6b2o2bob2o2bo$164bob2obo3b5o$173b
2o$165bo2b6o$166b7o$168b3o3$186b2o$186bobo$186bo8b3o$189bo3b2ob2o$189b
2obo893b2o$192b3o890b2o3bo$1087bob2o$189bo3bobo4bo888b3o$188b2obob3o3b
5ob4o880bo$188bo3bo8b3o4b3o880b3o$187b2o5bo3bo4bob3o876b2obo4b2o$187bo
6bo2bo2bo6bo876bob2o3bobo$188bo8bo10bo3bo865b2o4bob2o3b3o$194bob2obo7b
o869b2o6bo5b3o73b3o$193b2o13bo2bo866bobo4b2o4bobo73bo2b3o$193bobo13bo
868b3o4b2o2b2o77bobo$1078b2o6bobo84bo$195bo884bobo3b2o3bo79bo$193b2o
891b4o83bobo$1082bobo81b2obo6bo$193b2o889b4o77b2o3bo2bo2bo$193b2obobo
885b4o71b3o4bo2bo2bo3bo$196bo3bo884b2o72bo6bo2bo2bo3bo$193b2o5bo961bo
3bo6bobo$195b5o959bo2bo8b2o$1160bo2bo6b3o15bo$1161bo5bo3bo4b2o9b2o$
1163bobob2obo4b2o3bo6bobo$1165b2o10bob2o15b3o$1169bo9b3o5bobo4b2ob2o$
1179bo6b2obobobo$1166bo2bo11b3obo6bob2o$1182b2o7bo$1147b2obo31b2o5b2o$
156b2o989bo3bo32b5o$155b2o990bo4bo$156bobo990b2o$156b3o992bobo$156b2o$
158bobo985bo6b2o$235b2o908b5o4bo2bo$160bobo71b2o3bo899b2o4bo6b2o$162b
3o71bob2o899bobo11bo$162bo75b3o898bo5bob2o6bobo$161bo76bo901b2o4bo4bob
o$156bob2obo4bo73b3o897bo2bo6b3o$155b2ob2obo71b2obo4b2o897bo6b2ob2o$
155bobo4bo70bob2o3bobo899bobobo2bo$160b2o65b2o4bob2o3b3o$160bo3bo61b2o
6bo5b3o901bo4bo$159bo3bo63bobo4b2o4bobo902b4o$227b3o4b2o2b2o$159bo2bo
64b2o6bobo$158b2obo67bobo3b2o3bo$158bo76b4o$157b2o72bobo$157bo12b2o61b
4o$158bo10b2o62b4o$171bo62b2o$173b2o$172bo2$171bo2bo$168b2obo$167b2o4b
o$169bobo2bo2b3o$174bo2bo$171bo2bo3bo$172bobo3bo$172bobo2b2o$173b2o2b
3o$173bo$179bobobob2o$180b2o3b3o$181bo6bo$185b2obo$186b2o$186b2o$186b
2o$187bo8$229b2o$217b3o9bobo$217bo2b3o6bo9bo$218bobo16b2obo$223bo4b2o
2bo3b2o2bo$221bo6b2o2bob2o2bo$223bob2obo3b5o$232b2o$224bo2b6o$225b7o$
227b3o3$245b2o$245bobo$245bo8b3o$248bo3b2ob2o$248b2obo$251b3o2$248bo3b
obo4bo$247b2obob3o3b5ob4o$247bo3bo8b3o4b3o$246b2o5bo3bo4bob3o$246bo6bo
2bo2bo6bo$247bo8bo10bo3bo$253bob2obo7bo$252b2o13bo2bo$252bobo13bo2$
254bo$252b2o2$252b2o$252b2obobo$255bo3bo$252b2o5bo$254b5o10$215b2o$
214b2o$215bobo$215b3o$215b2o$217bobo$294b2o$219bobo71b2o3bo$221b3o71bo
b2o$221bo75b3o$220bo76bo$215bob2obo4bo73b3o$214b2ob2obo71b2obo4b2o$
214bobo4bo70bob2o3bobo$219b2o65b2o4bob2o3b3o$219bo3bo61b2o6bo5b3o$218b
o3bo63bobo4b2o4bobo$286b3o4b2o2b2o$218bo2bo64b2o6bobo$217b2obo67bobo3b
2o3bo$217bo76b4o$216b2o72bobo$216bo12b2o61b4o$217bo10b2o62b4o$230bo62b
2o$232b2o$231bo2$230bo2bo$227b2obo$226b2o4bo$228bobo2bo2b3o$233bo2bo$
230bo2bo3bo$231bobo3bo$231bobo2b2o$232b2o2b3o$232bo$238bobobob2o$239b
2o3b3o$240bo6bo$244b2obo$245b2o$245b2o$245b2o$246bo8$288b2o$276b3o9bob
o$276bo2b3o6bo9bo$277bobo16b2obo$282bo4b2o2bo3b2o2bo$280bo6b2o2bob2o2b
o$282bob2obo3b5o$291b2o$283bo2b6o$284b7o$286b3o3$304b2o$304bobo$304bo
8b3o$307bo3b2ob2o$307b2obo$310b3o2$307bo3bobo4bo$306b2obob3o3b5ob4o$
306bo3bo8b3o4b3o$305b2o5bo3bo4bob3o$305bo6bo2bo2bo6bo$306bo8bo10bo3bo$
312bob2obo7bo$311b2o13bo2bo$311bobo13bo2$313bo$311b2o2$311b2o$311b2obo
bo$314bo3bo$311b2o5bo$313b5o10$274b2o$273b2o$274bobo$274b3o$274b2o$
276bobo$353b2o$278bobo71b2o3bo$280b3o71bob2o$280bo75b3o$279bo76bo$274b
ob2obo4bo73b3o$273b2ob2obo71b2obo4b2o$273bobo4bo70bob2o3bobo$278b2o65b
2o4bob2o3b3o$278bo3bo61b2o6bo5b3o$277bo3bo63bobo4b2o4bobo$345b3o4b2o2b
2o$277bo2bo64b2o6bobo$276b2obo67bobo3b2o3bo$276bo76b4o$275b2o72bobo$
275bo75b4o$276bo74b4o$352b2o2$297bo$296b2o$296bobo2$299b2o$299b2o2$
295bob2o$294b4o$294bo3b2o$299bo2bo2$298b2o3bo$298b2o4bobo$299bo4bo2bo$
299bo$300b2o2b3o$306bo$304bobo$304bobo$304bobo$305b2o$305bo4$300b2o34b
2obo7b3o$299b2o3bo31bo3bo6bo$301bob2o31bo4bo7bo7b2o$303b3o32b2o7bobo4b
2obo$303bo36bobo4b3obo2b2o$305b3o38bo3b2o2b2o$298b2obo4b2o34b2ob4ob2o$
298bob2o3bobo35b7o$292b2o4bob2o3b3o$291b2o6bo5b3o$292bobo4b2o4bobo$
292b3o4b2o2b2o$292b2o6bobo$294bobo3b2o3bo$300b4o$296bobo$298b4o$298b4o
$299b2o3$314b2o$314bobo$314bo$315b2o$315bo2bo62b2o$315bo64b2o3bo$317bo
bo62bob2o$321bo62b3o$319bo2bo61bo$319bo2bo63b3o$321b3o55b2obo4b2o$317b
3ob3o55bob2o3bobo$313b3ob2o2b3o49b2o4bob2o3b3o$313bo7b2o49b2o6bo5b3o$
314bo6b2o50bobo4b2o4bobo$317b5o51b3o4b2o2b2o$319b2o52b2o6bobo$318b2o
55bobo3b2o3bo$318b2o61b4o$317bobo57bobo$316b2o61b4o$316bobo60b4o$315bo
64b2o$316b2o55$404b3o$404bo$405bo$407b2o$408bo3b2o$411b2o$414b2o$408b
6o$408bo2b2obo$395b2o13bo4bo$395bobo10bo6bo$395bo11bo$398bo7b2o3bo$
398b2o2b2obo2b3o$402bo5bo$402bobo3bo71b2o$400bob2o3bo60b3o9bobo$399b2o
b2o64bo2b3o6bo9bo$399bo2bo66bobo16b2obo$401bobo6b2o62bo4b2o2bo3b2o2bo$
401bo2b2o4bobo59bo6b2o2bob2o2bo$410bo63bob2obo3b5o$411b2o70b2o19b2o$
411bo2bo60bo2b6o19b2o$411bo64b7o22bo$413bobo62b3o26b2o$417bo88bo5bo$
415bo2bo91b2obo$415bo2bo92bo3bo$417b3o87b2o2b3o$413b3ob3o87b2obo$409b
3ob2o2b3o75bo13bo3bo$409bo7b2o75b2o11b2o5b2o$410bo6b2o75bobo10b3o$413b
5o80bo7bob2o$415b2o80bo3b2ob2obo2bo$414b2o81bo3b2ob3o$414b2o87bob2o$
413bobo83bo2bo4bo$412b2o85b3o$412bobo83bo2bo$411bo87bobobo$412b2o41bo
48bo$454b2o44bo3bo$454bobo2$457b2o$457b2o2$453bob2o$452b4o37b3o$452bo
3b2o4b2o29bo$457bo2b3obo31b5o$464bo23b3obo3b2ob3o$456b2o4bo25bo2bo4b2o
3bo$456b2o4b3o18b2o6bo5bo3b4o$457bo3bo2bo17b2o5bo7bo2bo2b2o$457bo5b3o
18bo4b4o4bobo3b2o$458b2o3b4o19b2o4bobo6bob3o$466b5o15b2o13bo$468b3ob2o
27b4o$465b2o2bo3bo$473b2o27b3o$470b2ob2o$472b3o$471bobo$472bo8$502b2ob
o7b3o$502bo3bo6bo$502bo4bo7bo7b2o$504b2o7bobo4b2obo$506bobo4b3obo2b2o$
512bo3b2o2b2o$508b2ob4ob2o$509b7o6$529b3o$529bo9b2o$530bo6b3obo$532b2o
2b2o$533bo$537bo$533b2o3bo$532bobob2o5b2o2bob2obo$476b2o54bobo2bob2ob
2o3bob2obo$475b2o54bo4b2o6bobo6bo$477bo53b2o9bo7b2obo$479b2o50b2o7b3o
10bo$478bo5bo54bo10bo2bo$482b2obo51bo4bo10bo$483bo3bo48b2o2bo10b2o$
479b2o2b3o51b2o$479b2obo54b2o$467bo13bo3bo51b3o$466b2o11b2o5b2o$466bob
o10b3o55bobo$470bo7bob2o55bobo$469bo3b2ob2obo2bo54bob2obo$469bo3b2ob3o
58b2o2bobo$475bob2o59bo5bo$471bo2bo4bo58bo$471b3o69bo$470bo2bo67bo$
471bobobo$476bo$472bo3bo5$498b2o$498bobo$498bo$499b2o$499bo2bo$499bo
79bo$501bobo74b5o$505bo72bo2b2o$503bo2bo73b2obo$503bo2bo$505b3o75bobo$
501b3ob3o$497b3ob2o2b3o68b3o6b3o$497bo7b2o64bo4bo2b3o4b3o$498bo6b2o63b
2o5b2ob5ob3o$501b5o64bobo3b3o4b2ob2o$503b2o77bobo$502b2o68b3o6bo2bo$
502b2o67b3o7bo$501bobo69bobob4o2bo$500b2o73b2ob2o$500bobo72b6o$499bo$
500b2o$525bo$524b2o$524bobo2$526b3o$525b3o$527bobo$529b3o$529b3o$532bo
$529bo2bo$528bo3bo606b2o$524b2ob2o3bo605b2o$523b2o7bo599b2o5bo$525bob
2o2bo599b2o5b2o$531bo601bo4bobo2b2o$528bobo604b2o3b2ob4o$529bo605b2o
10bo$528bo618bo$527bobo611bo$527bobo611bo3bo$526bo613b2ob2o$526b2o612b
o3bob2o$526b2o613b2ob4o$1146b2o2bo$1147b2obo$1148bo$1148b2o$1148b3o$
1148b2o2bo$1152bobo$1149bo3bobo$1149b6o$1151b3o2$1110bo$1109b2o$1109bo
bo99b2o$1211bobo$1112b2o90b2o5bo$1112b2o90bobo3b2o2bo$1204bo11bo$1108b
ob2o95bo3b2o3b3o$607b3o497b4o96b2o4b2o4bo$607bo2b3o494bo3b2o4b2o94b7o$
608bobo501bo2b3obo94b4o$613bo505bo$611bo499b2o4bo95b3o2bo$613bobo495b
2o4b3o92b2ob2o$606b2obo6bo495bo3bo2bo94bobob2o$605b2o3bo2bo2bo495bo5b
3o98bo2bo$599b3o4bo2bo2bo3bo496b2o3b4o98b3o$599bo6bo2bo2bo3bo504b5o94b
o$602bo3bo6bobo507b3ob2o$599bo2bo8b2o507b2o2bo3bo91b2o$600bo2bo6b3o
515b2o90b2obobo$601bo5bo3bo513b2ob2o93bo3bo$603bobob2obo516b3o90b2o5bo
$605b2o519bobo93b5o$609bo517bo2$606bo2bo2$587b2obo$587bo3bo$587bo4bo$
589b2o$591bobo2$586bo6b2o$585b5o4bo2bo$579b2o4bo6b2o$579bobo11bo$579bo
5bob2o6bobo$580b2o4bo4bobo$580bo2bo6b3o$580bo6b2ob2o$582bobobo2bo2$
584bo4bo3bo$585b4o3b2o$592bobo2$594b3o$593b3o686b2obo7b3o$595bobo684bo
3bo6bo$597b3o682bo4bo7bo7b2o$597b3o636b2o46b2o7bobo4b2obo$600bo634b2o
49bobo4b3obo2b2o$597bo2bo635bobo53bo3b2o2b2o$596bo3bo635b3o49b2ob4ob2o
$592b2ob2o3bo635b2o51b7o$591b2o7bo637bobo$593bob2o2bo$599bo640bobo$
596bobo643b3o$597bo644bo$596bo644bo$595bobo638bob2obo4bo$595bobo637b2o
b2obo$594bo640bobo4bo$594b2o644b2o$594b2o644bo3bo$1239bo3bo2$1239bo2bo
$1238b2obo$1238bo$1135b3o99b2o113bo$1135bo101bo102b2o9b2o$1136bo101bo
100b2o3bo6bobo$1138b2o201bob2o15b3o$1139bo203b3o5bobo4b2ob2o$1343bo6b
2obobobo$1136bo112bo95b3obo6bob2o$1133b4obo109b2o96b2o7bo$1133bo4bo5bo
103bobo7b2o86b2o5b2o$1134bo4b2o2b2o110b2obo89b5o$1136bo2b3obobo105b2o
2b2o$1140b2ob2o106b2o2b2o$1137b2ob2o2b2o106b2o$1138bob2o110b4obo$1138b
obo2bobo105bobob2obo2b3o4b2o$1139b2o4b2o103b2o9bo2b3ob2ob2o$1147b2ob2o
bo96bobo2b3o2b2o6bo3bo$1147bo2b2obo95bo11b2o9b2o$1146b2o6bo95b2o7b3o7b
2ob2o$1151b2obo104bobo9b3o$1154bo100b3o12bobo$1151bo2bo100bo15bo$1154b
o103bo$1152b2o101bo$1256bobo$1256bobo2$1255b2obo$1255b2ob4o$1256bo2b4o
$1257b2o$1184bo10b2o$1183b5o6b2o$1183bo2b2o8bo7b2o$1185b2obo5b2o6b3obo
$1194b2o3bob2o$1188bobo6b2o$1193b3obo4bo$1190b3o3bo4bo$1191bo7bo$1191b
o6bo2$1194bo2$1211b2o$1210b2o9bo$1212bo6b2obo$1214b2o2b2o2bo73b2obo$
1214b4o2bo75bo3bo$1216b3o77bo4bo74b2o$1217bo80b2o76bobo$1213b3ob2obo3b
2obo3b2o67bobo66b2o5bo$1213b3o2bobo3bo3b2ob3o135bobo3b2o2bo$1217bo2bo
3bo9bo60bo6b2o65bo11bo$1212b2o4bo7bob2ob2obo59b5o4bo2bo65bo3b2o3b3o$
1212bo9b2o8b2o54b2o4bo6b2o69b2o4b2o4bo38b2o$1220bobo9b2o54bobo11bo75b
7o38bobo$1218b6o8b2o54bo5bob2o6bobo72b4o40bo$1218bo2bo11bo55b2o4bo4bob
o123bo$1218bo70bo2bo6b3o76b3o2bo42b2o3bo$1219bo69bo6b2ob2o76b2ob2o44b
2o2bobo$1219bo71bobobo2bo80bobob2o42bob2o2bo$1219bo164bo2bo39b2obob3o$
1293bo4bo86b3o39bobo3b2o$1218b3o73b4o87bo41bo5bo$1218b2o2bo114bo75b3o
17b2o$1222bobo111b2o47b2o26bo12b2o$1219bo3bobo110bobo46b2obobo23bo10bo
b2o$1219b6o163bo3bo23b3o5bo4bo$1221b3o114b3o44b2o5bo24b6ob2o3bo$1337b
3o47b5o28bo4bo$1339bobo77bobo4b2o$1341b3o74b3o$1341b3o73bo$1344bo73bob
o$1341bo2bo74b5o$1340bo3bo75b2obo$1336b2ob2o3bo$1180b3o152b2o7bo$1180b
o156bob2o2bo$1183bo159bo31b3o$1180bo2bo156bobo32bo$1181bo2bo156bo34bo$
1182bo157bo37b2o$1184bobo72b3o77bobo37bo$1186b2o71bo2b3o74bobo32bo$
1187bo72bobo75bo34b4o37bo$1186b2o77bo72b2o33bo2b2o36bo$1185b3o75bo74b
2o35bo38bo$1180b2ob2ob2o77bobo106bo2bo$1180bo3bob2o70b2obo6bo102bob6o$
1180bob3o2bo69b2o3bo2bo2bo83b2o16b6ob2o$1185b2o64b3o4bo2bo2bo3bo83bobo
15bo2bo39bo$1184b3o64bo6bo2bo2bo3bo83bo19b2o38b3o$1254bo3bo6bobo87bo
17bo2b2o33b2o3b3o41bo$1251bo2bo8b2o90b2o3bo9bo4b2o33b3o5bo29b2o9b2o$
1183b3o66bo2bo6b3o90b2o2bobo9bobob2o39bo30b2o3bo6bobo$1183b3o67bo5bo3b
o92bob2o2bo10b2obo2bo35b2o32bob2o15b3o$1255bobob2obo93b2obob3o10bo4bo
35bo35b3o5bobo4b2ob2o$1182b2o73b2o97bobo3b2o15bo21b2o10b2obo34bo6b2obo
bobo$1182bo78bo94bo5bo11bobo4b3o16b2o11bo2bo36b3obo6bob2o$1342b3o17b2o
12b2obo21bobo9bo40b2o7bo$1258bo2bo80bo12b2o22bo21b3o9bo2bo37b2o5b2o$
1343bo10bob2o43b2o9b2obo40b5o$1345b3o5bo4bo44bobo5b3o$1346b6ob2o3bo53b
2ob2o$1349bo4bo50bobo4bo2b2o$1348bobo4b2o50b3o3b3o$1347b3o57bo6bo$
1346bo59bo$1347bobo51bob2obo4bo$1348b5o47b2ob2obo$1349b2obo47bobo4bo$
1405b2o$1405bo3bo$1404bo3bo2$1404bo2bo$1403b2obo$1403bo$1402b2o285bo$
1402bo274b2o9b2o$1403bo272b2o3bo6bobo$1465b2o211bob2o15b3o$1465b2o213b
3o5bobo4b2ob2o$1680bo6b2obobobo$1414bo267b3obo6bob2o$1413b2o268b2o7bo$
1413bobo7b2o258b2o5b2o$1420b2obo261b5o$1416b2o2b2o$1282bo133b2o2b2o$
1270b2o9b2o134b2o$1269b2o3bo6bobo133b4obo$1271bob2o15b3o123bobob2obo2b
3o4b2o$1206bo66b3o5bobo4b2ob2o122b2o9bo2b3ob2ob2o$1205b2o66bo6b2obobob
o127bobo2b3o2b2o6bo3bo$1205bobo67b3obo6bob2o124bo11b2o9b2o$1276b2o7bo
19b2o108b2o7b3o7b2ob2o$1207b3o66b2o5b2o20bobo116bobo9b3o$1206b3o69b5o
22bo114b3o12bobo$1208bobo97bo111bo15bo$1210b3o95b2o3bo109bo$1210b3o95b
2o2bobo105bo$1213bo95bob2o2bo105bobo$1210bo2bo95b2obob3o104bobo$1209bo
3bo95bobo3b2o$1205b2ob2o3bo95bo5bo104b2obo$1204b2o7bo81b3o17b2o103b2ob
4o$1206bob2o2bo82bo12b2o111bo2b4o$1212bo83bo10bob2o111b2o$1209bobo86b
3o5bo4bo$1210bo88b6ob2o3bo$1209bo92bo4bo$1208bobo90bobo4b2o$1208bobo
89b3o$1207bo91bo$1207b2o91bobo$1207b2o92b5o$1302b2obo6$1255b3o$1255bo
39b2o2bo$1256bo37b2o4bo160b2obo$1258b2o35bobo163bo3bo$1259bo30b2o2b5ob
2o159bo4bo$1289b2o2b3o5b2obo158b2o$1256bo27b2o4bobob2o3b2o164bobo$
1253b4obo25bobo3b2o2bo3b4o2b2o$1253bo4bo5bo19bo6bob3o2bo6bo154bo6b2o$
1254bo4b2o2b2o22bo6b2o163b5o4bo2bo69b2o$1256bo2b3obobo21b2o12b3ob2o
146b2o4bo6b2o72b2o3bo$1260b2ob2o188bobo11bo74bob2o$1257b2ob2o2b2o38bo
148bo5bob2o6bobo72b3o$1258bob2o42bo149b2o4bo4bobo76bo$1258bobo2bobo38b
o149bo2bo6b3o79b3o$1259b2o4b2o187bo6b2ob2o73b2obo4b2o39b3o$1267b2ob2ob
o182bobobo2bo75bob2o3bobo39bo2b3o$1267bo2b2obo113b2o144b2o4bob2o3b3o
13b2o25bobo$1266b2o6bo111bobo69bo4bo68b2o6bo5b3o13bobo29bo$1271b2obo
111b2o7bo63b4o70bobo4b2o4bobo6b2o5bo29bo$1274bo119bobo136b3o4b2o2b2o9b
obo3b2o2bo28bobo$1271bo2bo119bobo136b2o6bobo11bo11bo19b2obo6bo$1274bo
120bo5b3o131bobo3b2o3bo11bo3b2o3b3o16b2o3bo2bo2bo$1272b2o267b4o13b2o4b
2o4bo9b3o4bo2bo2bo3bo$1537bobo24b7o9bo6bo2bo2bo3bo$1389b2o148b4o22b4o
14bo3bo6bobo$1388bo2bo147b4o37bo2bo8b2o$1389b2o149b2o26b3ob2o7bo2bo6b
3o$1567b2obob2ob2o5bo5bo3bo$1521bo45b2o2bo2b2obo6bobob2obo$1520b5o44bo
16b2o$1304bo10b2o203bo2b2o65bo$1303b5o6b2o75bo130b2obo$1303bo2b2o8bo7b
2o65bo195bo2bo$1305b2obo5b2o6b3obo64bo26b2o105bobo$1314b2o3bob2o94bo2b
o$1308bobo6b2o99bobo97b3o6b3o84bo$1313b3obo4bo96bo93bo4bo2b3o4b3o71b2o
9b2o$1310b3o3bo4bo101b2o87b2o5b2ob5ob3o70b2o3bo6bobo$1311bo7bo103b2o
87bobo3b3o4b2ob2o73bob2o15b3o$1311bo6bo91bo113bobo78b3o5bobo4b2ob2o$
1299bo109bobo2b2o98b3o6bo2bo78bo6b2obobobo$1298b2o8bo5bo95bo2bo2bo96b
3o7bo83b3obo6bob2o$1297b3o7b4o103b2o99bobob4o2bo82b2o7bo$1269b2o25b2o
5b7obo19b2o78bo105b2ob2o86b2o5b2o$1269bobo18b3o4bo5bo7b2o17b2o9bo68bob
o104b6o87b5o$1269bo31b2o4bob3o20bo6b2obo67bobo112b3o$1272bo25bob2ob2ob
o2b2o23b2o2b2o2bo68bo113bo$1272b2o3bo20bo35b4o2bo63bo123bo$1272b2o2bob
o19b2o36b3o64bobo119bo2bo$1273bob2o2bo57bo65bo2bo119bo2bo$1273b2obob3o
52b3ob2obo3b2obo3b2o51b2o121bo$1273bobo3b2o52b3o2bobo3bo3b2ob3o175bobo
$1273bo5bo57bo2bo3bo9bo176b2o$1259b3o17b2o51b2o4bo7bob2ob2obo52b2o123b
o$1259bo12b2o58bo9b2o8b2o53b2o122b2o$1260bo10bob2o65bobo9b2o78bo97b3o$
1262b3o5bo4bo62b6o8b2o77bobo91b2ob2ob2o$1263b6ob2o3bo62bo2bo11bo77bobo
91bo3bob2o$1266bo4bo66bo93bo92bob3o2bo$1265bobo4b2o65bo190b2o$1264b3o
72bo189b3o$1263bo75bo86b2o343b2o$1264bobo158bo2bo342bobo$1265b5o68b3o
85b2o100b3o233b2o5bo$1266b2obo68b2o2bo185b3o233bobo3b2o2bo$1342bobo96b
2o321bo11bo$1339bo3bobo94bo2bo83b2o238bo3b2o3b3o$1339b6o96b2o84bo239b
2o4b2o4bo$1341b3o429b7o$1774b4o$1436bo$1435bobo335b3o2bo$1435bobo334b
2ob2o$1436bo337bobob2o$1779bo2bo$1780b3o$1780bo$1300bo373bo$1299b2o
372b2o105b2o$1299bobo371bobo104b2obobo44b2o$1783bo3bo42bobo$1301b3o
371b3o102b2o5bo42bo$1300b3o371b3o105b5o46bo$1302bobo74b3o294bobo154b2o
3bo$1304b3o72bo2b3o293b3o152b2o2bobo$1304b3o73bobo295b3o153bob2o2bo$
1307bo77bo295bo152b2obob3o$1304bo2bo75bo294bo2bo152bobo3b2o$1303bo3bo
77bobo289bo3bo152bo5bo$1299b2ob2o3bo70b2obo6bo284b2ob2o3bo138b3o17b2o$
1298b2o7bo69b2o3bo2bo2bo283b2o7bo138bo12b2o$1300bob2o2bo64b3o4bo2bo2bo
3bo285bob2o2bo140bo10bob2o$1306bo64bo6bo2bo2bo3bo291bo31b3o108b3o5bo4b
o$1303bobo68bo3bo6bobo289bobo32bo111b6ob2o3bo$1304bo66bo2bo8b2o293bo
34bo113bo4bo$1303bo23b2o43bo2bo6b3o292bo37b2o109bobo4b2o$1302bobo22b2o
44bo5bo3bo231bo60bobo37bo108b3o$1302bobo70bobob2obo231b5o57bobo32bo
112bo$1301bo75b2o235bo2b2o56bo34b4o111bobo$1301b2o78bo234b2obo55b2o33b
o2b2o111b5o$1301b2o372b2o35bo114b2obo$1378bo2bo237bobo89bo2bo$1708bob
6o$1612b3o6b3o65b2o16b6ob2o$1607bo4bo2b3o4b3o64bobo15bo2bo$1606b2o5b2o
b5ob3o64bo19b2o$1606bobo3b3o4b2ob2o68bo17bo2b2o140bo$1618bobo71b2o3bo
9bo4b2o129b2o9b2o$1608b3o6bo2bo71b2o2bobo9bobob2o128b2o3bo6bobo$1607b
3o7bo75bob2o2bo10b2obo2bo127bob2o15b3o$1609bobob4o2bo73b2obob3o10bo4bo
129b3o5bobo4b2ob2o$1611b2ob2o77bobo3b2o15bo79b2o48bo6b2obobobo$1611b6o
76bo5bo11bobo4b3o74b2o51b3obo6bob2o$1679b3o17b2o12b2obo79bobo50b2o7bo$
1679bo12b2o22bo79b3o50b2o5b2o$1680bo10bob2o101b2o53b5o$1682b3o5bo4bo
102bobo$1683b6ob2o3bo$1686bo4bo108bobo$1685bobo4b2o108b3o$1684b3o115bo
$1683bo117bo$1684bobo109bob2obo4bo$1685b5o105b2ob2obo$1686b2obo105bobo
4bo$1800b2o$1800bo3bo$1799bo3bo2$1799bo2bo$1798b2obo$1798bo$1797b2o
287bo$1659bo137bo276b2o9b2o$1658b5o135bo274b2o3bo6bobo$1658bo2b2o412bo
b2o15b3o$1660b2obo413b3o5bobo4b2ob2o$2077bo6b2obobobo$1663bobo143bo
269b3obo6bob2o$1808b2o270b2o7bo$1656b3o6b3o140bobo7b2o260b2o5b2o$1651b
o4bo2b3o4b3o146b2obo263b5o$1407b2o241b2o5b2ob5ob3o142b2o2b2o$1406b2o3b
o238bobo3b3o4b2ob2o143b2o2b2o$1408bob2o250bobo147b2o$1410b3o239b3o6bo
2bo147b4obo$1410bo240b3o7bo149bobob2obo2b3o4b2o$1412b3o238bobob4o2bo
146b2o9bo2b3ob2ob2o$1405b2obo4b2o240b2ob2o150bobo2b3o2b2o6bo3bo$1405bo
b2o3bobo240b6o148bo11b2o9b2o$1399b2o4bob2o3b3o395b2o7b3o7b2ob2o$1398b
2o6bo5b3o404bobo9b3o$1399bobo4b2o4bobo400b3o12bobo$1399b3o4b2o2b2o403b
o15bo$1399b2o6bobo408bo$1401bobo3b2o3bo2b2obo7b3o386bo$1407b4o4bo3bo6b
o389bobo$1403bobo9bo4bo7bo7b2o378bobo$1405b4o8b2o7bobo4b2obo$1405b4o
10bobo4b3obo2b2o380b2obo$1406b2o17bo3b2o2b2o380b2ob4o$1421b2ob4ob2o
385bo2b4o$1387bo34b7o388b2o$1386b5o$1386bo2b2o$1388b2obo2$1391bobo2$
1384b3o6b3o$1379bo4bo2b3o4b3o$1378b2o5b2ob5ob3o$1378bobo3b3o4b2ob2o$
1390bobo$1380b3o6bo2bo$1379b3o7bo$1381bobob4o2bo$1383b2ob2o$1383b6o$
1856b2obo$1856bo3bo$1856bo4bo$1858b2o$1860bobo2$1388b3o464bo6b2o$1388b
o465b5o4bo2bo$1389bo458b2o4bo6b2o$1391b2o455bobo11bo$1392bo455bo5bob2o
6bobo$1849b2o4bo4bobo$1389bo459bo2bo6b3o$1386b4obo457bo6b2ob2o$1386bo
4bo459bobobo2bo$1387bo4b2o$1389bo2b3o458bo4bo$1393b2o459b4o$1390b2ob2o
2b2o$1391bob2ob3o$1391bobo2bo2bo$1392b2o2b2o$1398bo$1396b2o$1396b2o$
1398bo$1397b2o$1397bo$1398bo3$1392b2obo$1392bo3bo$1392bo4bo$1394b2o$
1396bobo2$1391bo6b2o$1390b5o4bo2bo$1384b2o4bo6b2o$1384bobo11bo$1384bo
5bob2o6bobo$1385b2o4bo4bobo$1385bo2bo6b3o$1385bo6b2ob2o$1387bobobo2bo
2$1389bo4bo$1390b4o4$1407bo$1406b2o$1406bobo2$1408b3o$1407b3o65b2o$
1409bobo62b2o3bo$1411b3o62bob2o$1411b3o64b3o$1414bo63bo$1411bo2bo65b3o
$1410bo3bo58b2obo4b2o$1406b2ob2o3bo58bob2o3bobo$1405b2o7bo52b2o4bob2o
3b3o$1407bob2o2bo52b2o6bo5b3o$1413bo53bobo4b2o4bobo$1410bobo54b3o4b2o
2b2o$1411bo55b2o6bobo$1410bo58bobo3b2o3bo$1409bobo63b4o$1409bobo59bobo
$1408bo64b4o$1408b2o63b4o$1408b2o64b2o2$2006b2o$2005b2o3bo$2007bob2o$
2009b3o$2009bo$2011b3o$2004b2obo4b2o$2004bob2o3bobo$1998b2o4bob2o3b3o$
1997b2o6bo5b3o$1998bobo4b2o4bobo$1998b3o4b2o2b2o$1998b2o6bobo11bo10b2o
$2000bobo3b2o3bo7b5o6b2o166b2o$2006b4o9bo2b2o8bo7b2o156bobo$2002bobo
16b2obo5b2o6b3obo148b2o5bo$2004b4o22b2o3bob2o152bobo3b2o2bo$2004b4o16b
obo6b2o156bo11bo$2005b2o22b3obo4bo155bo3b2o3b3o$2026b3o3bo4bo16b3o137b
2o4b2o4bo$1986bo40bo7bo18bo145b7o$1985b5o37bo6bo20bo145b4o$1985bo2b2o
67b2o$1987b2obo39bo27bo3b2o136b3o2bo$1512b2o547b2o136b2ob2o$1511b2o3bo
473bobo71b2o135bobob2o$1513bob2o541b6o142bo2bo$1515b3o465b3o6b3o63bo2b
2obo142b3o$1515bo462bo4bo2b3o4b3o49b2o13bo4bo141bo$1517b3o457b2o5b2ob
5ob3o49bobo10bo6bo5bo183b2o$1510b2obo4b2o457bobo3b3o4b2ob2o50bo11bo12b
2o135b2o46bobo$1510bob2o3bobo469bobo56bo7b2o3bo8bobo134b2obobo42bo$
1504b2o4bob2o3b3o459b3o6bo2bo56b2o2b2obo2b3o149bo3bo43bo$1503b2o6bo5b
3o458b3o7bo63bo5bo13b3o132b2o5bo43b2o3bo$1504bobo4b2o4bobo460bobob4o2b
o61bobo3bo12b3o135b5o44b2o2bobo$1504b3o4b2o2b2o465b2ob2o63bob2o3bo15bo
bo183bob2o2bo$1504b2o6bobo467b6o61b2ob2o21b3o181b2obob3o$1506bobo3b2o
3bo472b3o56bo2bo22b3o181bobo3b2o$1512b4o474bo60bobo24bo180bo5bo$1508bo
bo482bo57bo2b2o19bo2bo166b3o17b2o$1510b4o476bo2bo80bo3bo166bo12b2o$
1510b4o477bo2bo75b2ob2o3bo167bo10bob2o$1511b2o479bo76b2o7bo169b3o5bo4b
o$1994bobo74bob2o2bo171b6ob2o3bo$1996b2o79bo31b3o140bo4bo$1997bo76bobo
32bo141bobo4b2o$1460bo535b2o47bo29bo34bo139b3o$1448b2o9b2o534b3o46b2o
28bo37b2o135bo$1447b2o3bo6bobo528b2ob2ob2o46bob5o22bobo37bo136bobo$
1449bob2o15b3o519bo3bob2o42bo6bo4bo20bobo32bo142b5o$1326bo124b3o5bobo
4b2ob2o519bob3o2bo41b4o3bo5bo19bo34b4o141b2obo$1325b2o124bo6b2obobobo
529b2o42bo2b2o10bo17b2o33bo2b2o$1325bobo125b3obo6bob2o526b3o36b3o5bo6b
2ob2o2bo16b2o35bo$1454b2o7bo19b2o548bo6bo2bo3b2o2b2o3bo51bo2bo$1327b3o
124b2o5b2o20bobo548bo4b6o4bobo53bob6o$1326b3o127b5o22bo509b3o40b4obob
2o6bo2bobo29b2o16b6ob2o$1328bobo155bo506b3o41b2o12b2o3bo29bobo15bo2bo$
1330b3o153b2o3bo560b3o31bo19b2o$1330b3o153b2o2bobo499b2o58bo36bo17bo2b
2o170bo$1333bo153bob2o2bo498bo61bo34b2o3bo9bo4b2o159b2o9b2o$1330bo2bo
153b2obob3o559bo34b2o2bobo9bobob2o158b2o3bo6bobo$1329bo3bo153bobo3b2o
595bob2o2bo10b2obo2bo157bob2o15b3o$1325b2ob2o3bo153bo5bo596b2obob3o10b
o4bo159b3o5bobo4b2ob2o$1324b2o7bo139b3o17b2o595bobo3b2o15bo109b2o48bo
6b2obobobo$1326bob2o2bo140bo12b2o602bo5bo11bobo4b3o104b2o51b3obo6bob2o
$1332bo141bo10bob2o587b3o17b2o12b2obo109bobo50b2o7bo$1329bobo144b3o5bo
4bo586bo12b2o22bo109b3o50b2o5b2o$1330bo146b6ob2o3bo587bo10bob2o131b2o
53b5o$1329bo150bo4bo593b3o5bo4bo132bobo$1328bobo148bobo4b2o592b6ob2o3b
o$1328bobo147b3o602bo4bo138bobo$1327bo149bo604bobo4b2o138b3o$1327b2o
149bobo600b3o145bo$1327b2o150b5o596bo147bo$1480b2obo597bobo139bob2obo
4bo$2082b5o135b2ob2obo$2083b2obo135bobo4bo$2227b2o$2227bo3bo$2226bo3bo
2$1473b2o2bo748bo2bo$1472b2o4bo746b2obo$1473bobo749bo$1468b2o2b5ob2o
744b2o105bo$1467b2o2b3o5b2obo741bo94b2o9b2o$1462b2o4bobob2o3b2o746bo
92b2o3bo6bobo$1462bobo3b2o2bo3b4o2b2o836bob2o15b3o$1462bo6bob3o2bo6bo
838b3o5bobo4b2ob2o$1465bo6b2o848bo6b2obobobo$1465b2o12b3ob2o751bo87b3o
bo6bob2o$2235b2o88b2o7bo$1482bo752bobo7b2o78b2o5b2o$1482bo759b2obo81b
5o$1482bo755b2o2b2o$2238b2o2b2o$2239b2o$2239b4obo$2238bobob2obo2b3o4b
2o$2237b2o9bo2b3ob2ob2o$2237bobo2b3o2b2o6bo3bo$2236bo11b2o9b2o$2237b2o
7b3o7b2ob2o$2246bobo9b3o$2242b3o12bobo$2242bo15bo$2245bo$2242bo$2243bo
bo$2243bobo2$2242b2obo$2242b2ob4o$2243bo2b4o$2244b2o17$2283b2obo$2283b
o3bo$2283bo4bo$2285b2o$2287bobo2$2282bo6b2o$1433b3o845b5o4bo2bo$1433bo
841b2o4bo6b2o$1434bo840bobo11bo$1436b2o837bo5bob2o6bobo$1437bo838b2o4b
o4bobo$2276bo2bo6b3o$1434bo841bo6b2ob2o$1431b4obo841bobobo2bo$1431bo4b
o5bo$1432bo4b2o2b2o837bo4bo$1434bo2b3obobo837b4o$1438b2ob2o$1435b2ob2o
2b2o$1436bob2o$1436bobo2bobo$1437b2o4b2o$1445b2ob2obo$1445bo2b2obo$
1444b2o6bo$1449b2obo$1452bo$1449bo2bo$1452bo$1450b2o8$1482bo10b2o$
1481b5o6b2o$1481bo2b2o8bo7b2o$1483b2obo5b2o6b3obo$1492b2o3bob2o$1486bo
bo6b2o$1491b3obo4bo$1488b3o3bo4bo$1489bo7bo$1489bo6bo2$1492bo2$1509b2o
$1508b2o9bo$1510bo6b2obo$1512b2o2b2o2bo$1512b4o2bo$1514b3o$1515bo$
1511b3ob2obo3b2obo3b2o$1511b3o2bobo3bo3b2ob3o$1515bo2bo3bo9bo$1510b2o
4bo7bob2ob2obo$1510bo9b2o8b2o$1459b2o57bobo9b2o$1459bobo54b6o8b2o$
1459bo56bo2bo11bo$1462bo53bo$1462b2o3bo49bo$1462b2o2bobo48bo$1463bob2o
2bo47bo$1463b2obob3o$1463bobo3b2o45b3o$1463bo5bo46b2o2bo$1449b3o17b2o
49bobo$1449bo12b2o53bo3bobo$1450bo10bob2o52b6o$1452b3o5bo4bo53b3o$
1453b6ob2o3bo$1456bo4bo$1455bobo4b2o$1454b3o$1453bo$1454bobo$1455b5o$
1456b2obo$1478bo$1477b2o$1477bobo2$1479b3o$1478b3o$1480bobo74b3o$1482b
3o72bo2b3o$1482b3o73bobo$1485bo77bo$1482bo2bo75bo$1481bo3bo77bobo$
1477b2ob2o3bo70b2obo6bo$1476b2o7bo69b2o3bo2bo2bo$1478bob2o2bo64b3o4bo
2bo2bo3bo$1484bo64bo6bo2bo2bo3bo$1481bobo68bo3bo6bobo$1482bo66bo2bo8b
2o$1481bo68bo2bo6b3o$1480bobo68bo5bo3bo$1480bobo70bobob2obo900b2o$
1479bo75b2o903b2o3bo$1479b2o78bo902bob2o$1479b2o983b3o$1556bo2bo904bo$
2466b3o$2459b2obo4b2o$2459bob2o3bobo$2453b2o4bob2o3b3o$2452b2o6bo5b3o$
2453bobo4b2o4bobo$2453b3o4b2o2b2o$2453b2o6bobo$2455bobo3b2o3bo24b2obo
7b3o$2461b4o26bo3bo6bo$2457bobo31bo4bo7bo7b2o$2459b4o30b2o7bobo4b2obo$
2459b4o32bobo4b3obo2b2o$2460b2o39bo3b2o2b2o$2497b2ob4ob2o$2441bo56b7o$
2440b5o$2440bo2b2o$2442b2obo2$2445bobo2$2438b3o6b3o$2433bo4bo2b3o4b3o$
2432b2o5b2ob5ob3o$2432bobo3b3o4b2ob2o$2444bobo$2434b3o6bo2bo$2433b3o7b
o$2435bobob4o2bo$2437b2ob2o$2437b6o21$2515b2o$2515bobo$2508b2o5bo$
2508bobo3b2o2bo$2508bo11bo$2511bo3b2o3b3o$2511b2o4b2o4bo$2517b7o$2518b
4o2$2517b3o2bo$2516b2ob2o$2518bobob2o$2523bo2bo$2524b3o$2524bo$2316bo
255b2o$2315b2o207b2o46bobo$2315bobo206b2obobo42bo$2527bo3bo43bo$2317b
3o204b2o5bo43b2o3bo$2316b3o207b5o44b2o2bobo$2318bobo255bob2o2bo$2320b
3o253b2obob3o$2320b3o253bobo3b2o$2323bo252bo5bo$2320bo2bo238b3o17b2o$
2319bo3bo238bo12b2o$2315b2ob2o3bo239bo10bob2o$2314b2o7bo241b3o5bo4bo$
2316bob2o2bo243b6ob2o3bo$2322bo31b3o212bo4bo$2319bobo32bo213bobo4b2o$
2320bo34bo211b3o$2319bo37b2o207bo$2318bobo37bo208bobo$2318bobo32bo214b
5o$2317bo34b4o213b2obo$2317b2o33bo2b2o$2317b2o35bo$2353bo2bo$2350bob6o
$2331b2o16b6ob2o$2331bobo15bo2bo$2331bo19b2o$2334bo17bo2b2o242bo$2334b
2o3bo9bo4b2o231b2o9b2o$2334b2o2bobo9bobob2o230b2o3bo6bobo$2335bob2o2bo
10b2obo2bo229bob2o15b3o$2335b2obob3o10bo4bo231b3o5bobo4b2ob2o$2335bobo
3b2o15bo181b2o48bo6b2obobobo$2335bo5bo11bobo4b3o176b2o51b3obo6bob2o$
2321b3o17b2o12b2obo181bobo50b2o7bo$2321bo12b2o22bo181b3o50b2o5b2o$
2322bo10bob2o203b2o53b5o$2324b3o5bo4bo204bobo$2325b6ob2o3bo$2328bo4bo
210bobo$1655b2o670bobo4b2o210b3o$1654b2o3bo666b3o217bo$1656bob2o665bo
219bo$1658b3o665bobo211bob2obo4bo$1658bo668b5o207b2ob2obo$1660b3o665b
2obo207bobo4bo$1653b2obo4b2o881b2o$1653bob2o3bobo881bo3bo$1647b2o4bob
2o3b3o880bo3bo$1646b2o6bo5b3o$1647bobo4b2o4bobo880bo2bo$1647b3o4b2o2b
2o882b2obo$1647b2o6bobo884bo$1649bobo3b2o3bo2b2obo7b3o864b2o105bo$
1655b4o4bo3bo6bo866bo94b2o9b2o$1651bobo9bo4bo7bo7b2o856bo92b2o3bo6bobo
$1653b4o8b2o7bobo4b2obo952bob2o15b3o$1653b4o10bobo4b3obo2b2o956b3o5bob
o4b2ob2o$1654b2o17bo3b2o2b2o956bo6b2obobobo$1669b2ob4ob2o874bo87b3obo
6bob2o$1635bo34b7o875b2o88b2o7bo$1634b5o913bobo7b2o78b2o5b2o$1634bo2b
2o920b2obo81b5o$1636b2obo915b2o2b2o$2555b2o2b2o$1639bobo914b2o$2556b4o
bo$1632b3o6b3o911bobob2obo2b3o4b2o$1627bo4bo2b3o4b3o909b2o9bo2b3ob2ob
2o$1626b2o5b2ob5ob3o909bobo2b3o2b2o6bo3bo$1626bobo3b3o4b2ob2o909bo11b
2o9b2o$1638bobo913b2o7b3o7b2ob2o$1628b3o6bo2bo922bobo9b3o$1627b3o7bo
921b3o12bobo$1629bobob4o2bo919bo15bo$1631b2ob2o926bo$1631b6o922bo$
2560bobo$2560bobo2$2559b2obo$2559b2ob4o$1639b2o919bo2b4o$1638b2o921b2o
$1639bobo$1639b3o$1639b2o$1641bobo2$1643bobo$1645b3o$1645bo$1644bo$
1639bob2obo4bo$1638b2ob2obo$1638bobo4bo$1643b2o33b2o$1643bo3bo30bobo$
1642bo3bo31bo$1681bo$1642bo2bo35b2o917b2obo$1641b2obo36b2o917bo3bo$
1641bo34b2o2b2o918bo4bo$1640b2o33b2o2b2o921b2o$1640bo35bobob2o922bobo$
1641bo34b2o2bo$1677bob3o917bo6b2o$1673b2o5b2o916b5o4bo2bo$1654b3o15b2o
918b2o4bo6b2o$1654bo19bobo915bobo11bo$1655bo18b2o3bo912bo5bob2o6bobo$
1657b2o15bo3b2o913b2o4bo4bobo$1658bo3b2o10bo3bobo912bo2bo6b3o$1661b2o
11bo918bo6b2ob2o$1664b2o12b5o912bobobo2bo$1658b6o11b2ob2o2b3o$1658bo2b
2obo18bo913bo4bo$1645b2o13bo4bo11bo3bobob2o911b4o$1645bobo10bo6bo12bo$
1645bo11bo21bob2o$1648bo7b2o3bo$1648b2o2b2obo2b3o$1652bo5bo$1652bobo3b
o$1650bob2o3bo$1649b2ob2o$1649bo2bo$1651bobo$1651bo2b2o4$1668bo$1656b
2o9b2o$1655b2o3bo6bobo$1657bob2o15b3o$1504bo154b3o5bobo4b2ob2o$1503b2o
154bo6b2obobobo$1503bobo155b3obo6bob2o$1662b2o7bo19b2o$1505b3o154b2o5b
2o20bobo$1504b3o157b5o22bo$1506bobo185bo$1508b3o183b2o3bo$1508b3o183b
2o2bobo$1511bo183bob2o2bo$1508bo2bo183b2obob3o$1507bo3bo183bobo3b2o$
1503b2ob2o3bo183bo5bo$1502b2o7bo169b3o17b2o$1504bob2o2bo170bo12b2o$
1510bo171bo10bob2o$1507bobo174b3o5bo4bo$1508bo176b6ob2o3bo$1507bo180bo
4bo$1506bobo178bobo4b2o$1506bobo177b3o$1505bo179bo$1505b2o179bobo$
1505b2o180b5o$1688b2obo7$1681b2o2bo$1680b2o4bo$1681bobo$1676b2o2b5ob2o
$1675b2o2b3o5b2obo$1670b2o4bobob2o3b2o$1670bobo3b2o2bo3b4o2b2o$1670bo
6bob3o2bo6bo$1673bo6b2o$1673b2o12b3ob2o2$1690bo$1690bo$1690bo74$1641b
3o$1641bo$1642bo$1644b2o$1645bo2$1642bo$1639b4obo$1639bo4bo5bo$1640bo
4b2o2b2o$1642bo2b3obobo$1646b2ob2o$1643b2ob2o2b2o$1644bob2o$1644bobo2b
obo$1645b2o4b2o$1653b2ob2obo$1653bo2b2obo$1652b2o6bo$1657b2obo$1660bo$
1657bo2bo$1660bo$1658b2o1190b2o$2849b2o3bo$2851bob2o$2853b3o$2853bo$
2855b3o$2848b2obo4b2o$2848bob2o3bobo$1690bo10b2o1139b2o4bob2o3b3o$
1689b5o6b2o1139b2o6bo5b3o$1689bo2b2o8bo7b2o1130bobo4b2o4bobo$1691b2obo
5b2o6b3obo1129b3o4b2o2b2o$1700b2o3bob2o1133b2o6bobo$1694bobo6b2o1139bo
bo3b2o3bo24b2obo7b3o$1699b3obo4bo1141b4o26bo3bo6bo$1696b3o3bo4bo1138bo
bo31bo4bo7bo7b2o$1697bo7bo1142b4o30b2o7bobo4b2obo$1697bo6bo1143b4o32bo
bo4b3obo2b2o$2849b2o39bo3b2o2b2o$1700bo1185b2ob4ob2o$2830bo56b7o$1717b
2o1110b5o$1716b2o9bo1101bo2b2o$1718bo6b2obo1102b2obo$1720b2o2b2o2bo$
1720b4o2bo1107bobo$1722b3o$1723bo1103b3o6b3o$1719b3ob2obo3b2obo3b2o
1083bo4bo2b3o4b3o$1719b3o2bobo3bo3b2ob3o1081b2o5b2ob5ob3o$1723bo2bo3bo
9bo1080bobo3b3o4b2ob2o$1665b2o51b2o4bo7bob2ob2obo1092bobo$1665bobo50bo
9b2o8b2o1083b3o6bo2bo$1665bo60bobo9b2o1082b3o7bo$1668bo55b6o8b2o1084bo
bob4o2bo$1668b2o3bo50bo2bo11bo1086b2ob2o$1668b2o2bobo49bo1101b6o$1669b
ob2o2bo49bo$1669b2obob3o48bo$1669bobo3b2o48bo1160b2o$1669bo5bo1210bobo
$1655b3o17b2o47b3o1152b2o5bo$1655bo12b2o54b2o2bo1150bobo3b2o2bo$1656bo
10bob2o57bobo1148bo11bo$1658b3o5bo4bo53bo3bobo1150bo3b2o3b3o$1659b6ob
2o3bo53b6o1151b2o4b2o4bo$1662bo4bo59b3o1158b7o$1661bobo4b2o1219b4o$
1660b3o$1659bo1228b3o2bo$1660bobo1224b2ob2o$1661b5o1223bobob2o$1662b2o
bo1228bo2bo$2895b3o$2895bo$1686bo946bo309b2o$1685b2o945b2o261b2o46bobo
$1685bobo944bobo260b2obobo42bo$2898bo3bo43bo$1687b3o944b3o258b2o5bo43b
2o3bo$1686b3o944b3o261b5o44b2o2bobo$1688bobo74b3o867bobo309bob2o2bo$
1690b3o72bo2b3o866b3o307b2obob3o$1690b3o73bobo868b3o307bobo3b2o$1693bo
77bo868bo306bo5bo$1690bo2bo75bo867bo2bo292b3o17b2o$1689bo3bo77bobo862b
o3bo292bo12b2o$1685b2ob2o3bo70b2obo6bo857b2ob2o3bo293bo10bob2o$1684b2o
7bo69b2o3bo2bo2bo856b2o7bo295b3o5bo4bo$1686bob2o2bo64b3o4bo2bo2bo3bo
858bob2o2bo297b6ob2o3bo$1692bo64bo6bo2bo2bo3bo864bo31b3o266bo4bo$1689b
obo68bo3bo6bobo862bobo32bo267bobo4b2o$1690bo66bo2bo8b2o866bo34bo265b3o
$1689bo68bo2bo6b3o865bo37b2o261bo$1688bobo68bo5bo3bo865bobo37bo262bobo
$1688bobo70bobob2obo866bobo32bo268b5o$1687bo75b2o869bo34b4o267b2obo$
1687b2o78bo866b2o33bo2b2o$1687b2o945b2o35bo$1764bo2bo902bo2bo$2667bob
6o$2648b2o16b6ob2o$2648bobo15bo2bo$2648bo19b2o$2651bo17bo2b2o296bo$
2651b2o3bo9bo4b2o285b2o9b2o$2651b2o2bobo9bobob2o284b2o3bo6bobo$2652bob
2o2bo10b2obo2bo283bob2o15b3o$2652b2obob3o10bo4bo285b3o5bobo4b2ob2o$
2652bobo3b2o15bo235b2o48bo6b2obobobo$2652bo5bo11bobo4b3o230b2o51b3obo
6bob2o$2638b3o17b2o12b2obo235bobo50b2o7bo$2638bo12b2o22bo235b3o50b2o5b
2o$2639bo10bob2o257b2o53b5o$2641b3o5bo4bo258bobo$2642b6ob2o3bo$2645bo
4bo264bobo$2644bobo4b2o264b3o$2643b3o271bo$2642bo273bo$1948bo694bobo
265bob2obo4bo$1936b2o9b2o695b5o261b2ob2obo$1935b2o3bo6bobo695b2obo261b
obo4bo$1937bob2o15b3o956b2o$1712bo226b3o5bobo4b2ob2o956bo3bo$1711b2o
226bo6b2obobobo960bo3bo$1711bobo227b3obo6bob2o$1942b2o7bo19b2o941bo2bo
$1713b3o226b2o5b2o20bobo939b2obo$1712b3o229b5o22bo941bo$1714bobo257bo
937b2o$1716b3o255b2o3bo932bo69b2obo7b3o$1716b3o255b2o2bobo932bo68bo3bo
6bo$1719bo255bob2o2bo1000bo4bo7bo7b2o$1716bo2bo255b2obob3o1001b2o7bobo
4b2obo$1715bo3bo255bobo3b2o1003bobo4b3obo2b2o$1711b2ob2o3bo255bo5bo
942bo67bo3b2o2b2o$1710b2o7bo241b3o17b2o940b2o63b2ob4ob2o$1712bob2o2bo
242bo12b2o947bobo7b2o54b7o$1718bo243bo10bob2o953b2obo$1715bobo246b3o5b
o4bo948b2o2b2o$1716bo248b6ob2o3bo948b2o2b2o$1715bo252bo4bo953b2o$1714b
obo250bobo4b2o951b4obo$1714bobo249b3o957bobob2obo2b3o4b2o$1713bo251bo
959b2o9bo2b3ob2ob2o$1713b2o251bobo956bobo2b3o2b2o6bo3bo$1713b2o252b5o
952bo11b2o9b2o$1968b2obo953b2o7b3o7b2ob2o$2934bobo9b3o$2930b3o12bobo$
2930bo15bo$2933bo$2930bo$2931bobo$1961b2o2bo965bobo$1960b2o4bo$1961bob
o966b2obo$1956b2o2b5ob2o962b2ob4o$1955b2o2b3o5b2obo960bo2b4o$1950b2o4b
obob2o3b2o965b2o$1950bobo3b2o2bo3b4o2b2o$1950bo6bob3o2bo6bo$1953bo6b2o
$1953b2o12b3ob2o2$1970bo$1970bo$1970bo9$2971b2obo$2971bo3bo$2971bo4bo$
2973b2o$2975bobo2$2970bo6b2o$2969b5o4bo2bo$2963b2o4bo6b2o$2963bobo11bo
$2963bo5bob2o6bobo$2964b2o4bo4bobo$2964bo2bo6b3o$2964bo6b2ob2o$2966bob
obo2bo2$2968bo4bo$2969b4o44$1891b2o$1890b2o3bo$1892bob2o$1894b3o$1894b
o$1896b3o$1889b2obo4b2o$1889bob2o3bobo$1883b2o4bob2o3b3o$1882b2o6bo5b
3o$1883bobo4b2o4bobo$1883b3o4b2o2b2o$1883b2o6bobo$1885bobo3b2o3bo$
1891b4o$1887bobo$1889b4o$1889b4o$1890b2o2$1871bo$1870b5o$1870bo2b2o$
1872b2obo2$1875bobo2$1868b3o6b3o$1863bo4bo2b3o4b3o$1862b2o5b2ob5ob3o$
1862bobo3b3o4b2ob2o$1874bobo$1864b3o6bo2bo$1863b3o7bo$1865bobob4o2bo$
1867b2ob2o$1867b6o23$1875b3o$1875bo$1878bo$1875bo2bo$1876bo2bo$1877bo$
1879bobo$1881b2o$1882bo$1881b2o$1880b3o$1875b2ob2ob2o$1875bo3bob2o$
1875bob3o2bo$1880b2o$1879b3o2$1921b3o$1878b3o40bo$1878b3o41bo$1924b2o$
1877b2o46bo$1877bo$1922bo$1919b4obo$1919bo4bo5bo$1920bo4b2o2b2o$1922bo
2b3obobo$1926b2ob2o$1923b2ob2o2b2o$1924bob2o$1924bobo2bobo$1925b2o4b2o
$1933b2ob2obo$1933bo2b2obo$1932b2o6bo$1937b2obo$1940bo$1937bo2bo$1940b
o$1938b2o8$1970bo10b2o$1969b5o6b2o$1969bo2b2o8bo7b2o$1971b2obo5b2o6b3o
bo$1980b2o3bob2o$1974bobo6b2o$1979b3obo4bo$1976b3o3bo4bo$1977bo7bo$
1977bo6bo2$1980bo2$1997b2o$1996b2o9bo$1998bo6b2obo$2000b2o2b2o2bo$
2000b4o2bo$2002b3o$2003bo$1999b3ob2obo3b2obo3b2o$1999b3o2bobo3bo3b2ob
3o$2003bo2bo3bo9bo$1945b2o51b2o4bo7bob2ob2obo$1945bobo50bo9b2o8b2o$
1945bo60bobo9b2o$1948bo55b6o8b2o$1948b2o3bo50bo2bo11bo$1948b2o2bobo49b
o$1949bob2o2bo49bo$1949b2obob3o48bo$1949bobo3b2o48bo$1949bo5bo$1935b3o
17b2o47b3o$1935bo12b2o54b2o2bo$1936bo10bob2o57bobo$1938b3o5bo4bo53bo3b
obo$1939b6ob2o3bo53b6o$1942bo4bo59b3o$1941bobo4b2o$1940b3o$1939bo$
1940bobo$1941b5o$1942b2obo3$1966bo$1965b2o$1965bobo2$1967b3o$1966b3o$
1968bobo74b3o$1970b3o72bo2b3o$1970b3o73bobo$1973bo77bo$1970bo2bo75bo$
1969bo3bo77bobo$1965b2ob2o3bo70b2obo6bo$1964b2o7bo69b2o3bo2bo2bo$1966b
ob2o2bo64b3o4bo2bo2bo3bo$1972bo64bo6bo2bo2bo3bo$1969bobo68bo3bo6bobo
1221b2o$1970bo66bo2bo8b2o1223b2o3bo$1969bo68bo2bo6b3o1225bob2o$1968bob
o68bo5bo3bo1228b3o$1968bobo70bobob2obo1229bo$1967bo75b2o1235b3o$1967b
2o78bo1225b2obo4b2o$1967b2o1304bob2o3bobo$2044bo2bo1219b2o4bob2o3b3o$
3266b2o6bo5b3o$3267bobo4b2o4bobo$3267b3o4b2o2b2o$3267b2o6bobo7bo10b2o$
3269bobo3b2o3bo3b5o6b2o$3275b4o5bo2b2o8bo7b2o$3271bobo12b2obo5b2o6b3ob
o$3273b4o18b2o3bob2o$3273b4o12bobo6b2o$3274b2o18b3obo4bo$3291b3o3bo4bo
$3255bo36bo7bo$3254b5o33bo6bo$3254bo2b2o$3256b2obo35bo2$3259bobo$3293b
obobobo$3252b3o6b3o29b2o3b2o$3247bo4bo2b3o4b3o29bo3bo$2282bo963b2o5b2o
b5ob3o$2270b2o9b2o963bobo3b3o4b2ob2o$2269b2o3bo6bobo974bobo26bo$2271bo
b2o15b3o955b3o6bo2bo25b2o$1992bo280b3o5bobo4b2ob2o954b3o7bo28bobo$
1991b2o280bo6b2obobobo961bobob4o2bo$1991bobo281b3obo6bob2o961b2ob2o33b
2o$2276b2o7bo19b2o944b6o32b2o$1993b3o280b2o5b2o20bobo$1992b3o283b5o22b
o979bob2o$1994bobo311bo975b4o$1996b3o309b2o3bo970bo3b2o$1996b3o309b2o
2bobo974bo2bo$1999bo309bob2o2bo$1996bo2bo309b2obob3o971b2o3bo$1995bo3b
o309bobo3b2o971b2o3bo$1991b2ob2o3bo309bo5bo973bo$1990b2o7bo295b3o17b2o
972bo$1992bob2o2bo296bo12b2o980b2o$1998bo297bo10bob2o$1995bobo300b3o5b
o4bo$1996bo302b6ob2o3bo$1995bo306bo4bo963bobo$1994bobo304bobo4b2o961b
2o$1994bobo303b3o969bo$1993bo305bo$1993b2o305bobo$1993b2o306b5o$2302b
2obo7$2295b2o2bo$2294b2o4bo$2295bobo$2290b2o2b5ob2o$2289b2o2b3o5b2obo$
2284b2o4bobob2o3b2o$2284bobo3b2o2bo3b4o2b2o$2284bo6bob3o2bo6bo$2287bo
6b2o$2287b2o12b3ob2o2$2304bo$2304bo$2304bo142$2243b2o$2242b2o3bo$2244b
ob2o$2246b3o$2246bo$2248b3o$2241b2obo4b2o$2241bob2o3bobo$2235b2o4bob2o
3b3o$2234b2o6bo5b3o$2235bobo4b2o4bobo$2235b3o4b2o2b2o$2235b2o6bobo$
2237bobo3b2o3bo$2243b4o$2239bobo$2241b4o$2241b4o$2242b2o2$2223bo$2222b
5o$2222bo2b2o$2224b2obo2$2227bobo2$2220b3o6b3o$2215bo4bo2b3o4b3o$2214b
2o5b2ob5ob3o$2214bobo3b3o4b2ob2o$2226bobo$2216b3o6bo2bo$2215b3o7bo$
2217bobob4o2bo$2219b2ob2o$2219b6o22$2255b3o$2227b3o25bo$2227bo28bo$
2230bo27b2o$2227bo2bo28bo$2228bo2bo$2229bo26bo$2231bobo19b4obo$2233b2o
18bo4bo5bo$2234bo19bo4b2o2b2o$2233b2o21bo2b3obobo$2232b3o25b2ob2o$
2227b2ob2ob2o22b2ob2o2b2o$2227bo3bob2o23bob2o$2227bob3o2bo23bobo2bobo$
2232b2o25b2o4b2o$2231b3o33b2ob2obo$2267bo2b2obo$2266b2o6bo$2230b3o38b
2obo$2230b3o41bo$2271bo2bo$2229b2o43bo$2229bo42b2o8$2304bo10b2o$2303b
5o6b2o$2303bo2b2o8bo7b2o$2305b2obo5b2o6b3obo$2314b2o3bob2o$2308bobo6b
2o$2313b3obo4bo$2310b3o3bo4bo$2311bo7bo$2311bo6bo2$2314bo2$2331b2o$
2330b2o9bo$2332bo6b2obo$2334b2o2b2o2bo$2334b4o2bo$2336b3o$2337bo$2333b
3ob2obo3b2obo3b2o$2333b3o2bobo3bo3b2ob3o$2337bo2bo3bo9bo$2279b2o51b2o
4bo7bob2ob2obo$2279bobo50bo9b2o8b2o$2279bo60bobo9b2o$2282bo55b6o8b2o$
2282b2o3bo50bo2bo11bo$2282b2o2bobo49bo$2283bob2o2bo49bo$2283b2obob3o
48bo$2283bobo3b2o48bo$2283bo5bo$2269b3o17b2o47b3o$2269bo12b2o54b2o2bo$
2270bo10bob2o57bobo$2272b3o5bo4bo53bo3bobo$2273b6ob2o3bo53b6o$2276bo4b
o59b3o$2275bobo4b2o$2274b3o$2273bo$2274bobo$2275b5o$2276b2obo3$2300bo$
2299b2o$2299bobo2$2301b3o$2300b3o665b2o$2302bobo74b3o585bo2bo$2304b3o
72bo2b3o583b2o$2304b3o73bobo$2307bo77bo$2304bo2bo75bo579bo$2303bo3bo
77bobo574bobo$2299b2ob2o3bo70b2obo6bo573bobo$2298b2o7bo69b2o3bo2bo2bo
574bo$2300bob2o2bo64b3o4bo2bo2bo3bo$2306bo64bo6bo2bo2bo3bo$2303bobo68b
o3bo6bobo$2304bo66bo2bo8b2o$2303bo68bo2bo6b3o$2302bobo68bo5bo3bo$2302b
obo70bobob2obo$2301bo75b2o$2301b2o78bo$2301b2o$2378bo2bo$2325b3o$2325b
o$2328bo$2325bo2bo$2326bo2bo$2327bo$2329bobo$2331b2o$2332bo$2331b2o$
2330b3o$2325b2ob2ob2o$2325bo3bob2o$2325bob3o2bo$2330b2o$2329b3o3$2328b
3o$2328b3o2$2327b2o$2327bo242$2631b2o$2630b2o3bo$2632bob2o$2634b3o$
2634bo$2636b3o$2629b2obo4b2o$2629bob2o3bobo$2623b2o4bob2o3b3o$2622b2o
6bo5b3o$2623bobo4b2o4bobo$2623b3o4b2o2b2o$2623b2o6bobo$2625bobo3b2o3bo
$2631b4o$2627bobo$2629b4o$2629b4o$2630b2o2$2611bo$2610b5o$2610bo2b2o$
2612b2obo2$2615bobo35b2o$2654b2o$2608b3o6b3o33bo$2603bo4bo2b3o4b3o$
2602b2o5b2ob5ob3o$2602bobo3b3o4b2ob2o$2614bobo$2604b3o6bo2bo$2603b3o7b
o$2605bobob4o2bo$2607b2ob2o$2607b6o$2615b3o$2615bo$2618bo$2615bo2bo$
2616bo2bo$2617bo$2619bobo$2621b2o$2622bo$2621b2o$2620b3o$2615b2ob2ob2o
$2615bo3bob2o$2615bob3o2bo$2620b2o$2619b3o3$2618b3o$2618b3o2$2617b2o$
2617bo!

The technology for making these things is, well, somewhat less than satisfactory...!

[muzik]

Are there any glider gins built entirely out of gliders? Are there any reactions that require only gliders and put out more gliders than used, for that matter?

[dvgrn]

Are there any glider gins built entirely out of gliders? Are there any reactions that require only gliders and put out more gliders than used, for that matter?

1) No, not that I can think of. The closest match would be something along the lines of an elbow ladder -- see Golly's Patterns/Life/Miscellaneous/elbow-ladders.rle. But that's not a very good match -- you clearly need a surplus of gliders coming from outside a reaction like that, because all the kickbacks eat up gliders like crazy.

2) Yes, over-unity glider recipes have been known for a long time. Dean Hickerson's Cyclotron is an example from 1992. I seem to recall there's also a 4-glider collision that produces 5 (clean?) output gliders, that has been used to build a similar gun pattern. Looks like it will take me a little longer to dig that one up.

EDIT: Ah, here it is:

Code: Select all

#C 4 gliders synthesize 5 gliders
#C reaction #1, left (Dietrich Leithner, 19 Jul 1992)
#C reaction #2, right (Dietrich Leithner, 21 Sep 1996)
x = 120, y = 65, rule = B3/S23
60bo2$60bo2$60bo2$60bo2$obo57bo$b2o$bo58bo2$60bo2$60bo2$60bo2$60bo2$
60bo2$60bo$117bobo$60bo56b2o$118bo$60bo2$60bo2$60bo2$17bo42bo$15bobo2b
o$16b2o2bobo20bo16bo$20b2o20b2o$42bobo15bo2$60bo2$60bo2$60bo2$60bo2$
60bo$92bo$60bo29bobo2bo$76bo14b2o2bobo$60bo15b2o17b2o$75bobo$60bo2$60b
o2$60bo2$60bo2$60bo2$60bo2$60bo!

There's a gun somewhere that uses one of these, with oscillating reflectors. A P1 version could be put together using Snarks and syringes nowadays; I don't remember if that has actually been done. If someone did it, I hope it wasn't me...!

Other similar efforts mostly used catalysts to produce the gliders -- like this one from 1995, which was based on an earlier version by David Buckingham in 1992, using four copies of the same reaction:

Code: Select all

#C p460 glider gun based on a reaction found by Buckingham which converts
#C 2 gliders to 3 gliders with the help of 3 blocks, a snake, a ship, and
#C an eater.  One glider escapes; the others are reflected by p46 shuttles
#C to repeat the reaction.  Given a period P oscillator which can reflect
#C a glider 90 degrees, we can build a gun whose period is any multiple
#C of P that's >= 452.
#C Dean Hickerson, 1/95
x = 152, y = 92, rule = B3/S23
37b2o5b2o$37b2o5b2o2$96b2o5b2o$96b2o5b2o9$38bo5bo52bo5bo$37b3o3b3o50b
3o3b3o$36bo3bobo3bo49bob2ob2obo$36bo9bo51b2ob2o$37b3o3b3o52b2ob2o$98b
2ob2o3$77b2o$39b2ob2o33bobo$40bobo35b2o$36b2ob2ob2ob2o55b3o$36bo2bo3bo
bo11b2o43b3o$36bo7bo13bo$36bo2bo18bobo40b2ob2o$37b2o20b2o40bo3bo$102b
3o$96b2o5bo$96b2o3$84b2o$84b2o$41b2o$41b2o2$134bo$123b2o8b2o15b2o$123b
2o7b2o16b2o$133b2o2b2o3$17b2o$2o15bobo113b2o2b2o$2o17bo112b2o16b2o$17b
3o113b2o15b2o$134bo3$17b3o$2o17bo7b2o$2o15bobo7b2o$17b2o4$25b2o14b3o8b
2o$25b2o12bo3bo8b2o21bobo$38bo4bo32b2o$38bo3bo33bo2$38bo3bo$38bo4bo$
25b2o12bo3bo$25b2o14b3o$78b2o$78b2o2$69b2obo10b3o$69bob2o10bo$84bo9$
87b3o$64b2o8b3o8b2obob2o$64b2o8bo3bo5bo5b2o$74bo4bo5b2obob2o$75bo3bo7b
3o2$75bo3bo$74bo4bo$64b2o8bo3bo12b2o$64b2o8b3o14b2o!

This was put together before stable reflectors or Herschel tracks existed. It probably doesn't look so interesting any more -- it's doing a 2-glider-to-3-glider magic trick, where a Silver reflector can do 1 glider to 4 gliders, plus a fifth internally recycled, and we can get as many more as we want by sticking on more Herschel conduits.

It seems possible that some of knightlife's one-time Blockic splitters could be adapted to make over-unity reactions, by building some block constellations via glider collisions and replacing other blocks directly with gliders. Without some research it's not clear that you'll get out more than you put in there, though.

[Ethanagor]

Is there a way to convert a block into a glider?

related question: what is the most compact way to convert a herschel into a glider?

[dvgrn]

Is there a way to convert a block into a glider?

Sure, lots of different ways. It depends on what kind of signal you want to use to do the converting. Here's an old example with a Herschel signal. As it's wired here, the same signal then rebuilds the block. You don't have to connect to the Herschel-to-block converter, though -- you could use a block generated by some other reaction instead:

Code: Select all

x = 61, y = 70, rule = LifeHistory
4.D3.D.D3.D.D3.D2.3D5.D2.5D2.3D3.3D5.D$4.D3.D.2D2.D.D3.D.D3.D3.2D4.D
3.D3.D.D3.D3.2D$4.D3.D.D.D.D.D3.D5.D2.D.D4.D7.D.D2.2D2.D.D$4.5D.D2.2D
.D.D.D3.2D2.D2.D4.D6.D2.D.D.D.D2.D$4.D3.D.D3.D.D.D.D5.D.5D3.D5.D3.2D
2.D.5D$4.D3.D.D3.D.2D.2D.D3.D4.D4.D4.D4.D3.D4.D$4.D3.D.D3.D.D3.D2.3D
5.D4.D3.5D2.3D5.D10$28.2E$21.2E3.2B2EB$20.B2EB2.4B$21.2B3.6B.B$22.2B
2.10B$21.2B2E11B16.2E$18.B.3B2E12B14.B2EB$17.2E18B15.2B$17.2EB.15B17.
2B3.B$18.B3.15B15.4B.B2E$22.17B11.8B2E$23.19B2.2B2.6B2EB.B$23.31B2E$
24.7B.24B$24.6B2.28B$18.2B3.7B2.28B$18.3B2.6B4.26B2E$18.4B2.6B10.4B.
14B2E$19.4B.5B12.4B2.11B.B$20.4B2E3B13.4B2.10B$21.3B2E2B15.14B$16.E5.
8B14.14B$16.3E4.3B2.2E14.13B$19.E.4B3.E15.13B$18.E.E5B3.3E12.8B.2B$
18.BE2B.4B4.E12.8B$19.2B3.4B16.9B$20.2B3.4B15.9B$19.B2EB3.4B13.7B2.B
2E$20.2E5.4B11.8B2.BE.E$8.E19.4B9.8B6.E$8.3E12.B.3B.4B7.9B6.2E$11.E
10.21B.6B$10.2E3.B5.2B2E17B.7B$10.8B3.2B2E16B2.6B$12.8B.20B.7B$12.38B
$11.15B.2B2.19B$9.17B7.18B$7.18B8.18B3.B$7.2BC15B6.4B2.15B.B2E$6.3BCB
C4B.7B7.2E3.18B2E$7.2B3C13B7.E3.12B2E3B.B$6.5BC14B3.3E5.11B2E2B$5.10B
2.8B4.E7.10B2.2B$4.4B11.6B14.B.6B3.2B$3.4B12.5B19.4B2.B2EB$2.4B14.4B
18.B2E2B3.2E$2.2E16.3B20.2E$3.E17.4B$3E20.2E$E22.E$24.3E$26.E!

This is one of the H-to-Gs in the Elementary Conduits Collection (even though it's actually a composite circuit, which is why it's color-coded yellow instead of green).

related question: what is the most compact way to convert a herschel into a glider?

There's actually a more comprehensive collection of H-to-Gs than what's in the Elementary Conduits collection. The current record holder depends on whether you count the Herschel's first natural glider or not. If so, one of the SW-2T21's will certainly win. If not, then there are several other small candidates with outputs in various directions:

Code: Select all

x = 160, y = 133, rule = LifeHistory
5.D3.D.5D3.D3.5D2.3D3.3D19.3D2.D3.D4.D2.5D4.D5.D30.3D2.D3.D8.3D2.5D2.
3D4.D$5.2D2.D.D6.2D5.D3.D3.D.D3.D17.D3.D.D3.D3.2D4.D5.2D4.2D29.D3.D.D
3.D7.D3.D3.D3.D3.D2.2D$5.D.D.D.D7.D5.D7.D5.D17.D5.D3.D2.D.D4.D4.D.D3.
D.D29.D5.D3.D11.D3.D7.D3.D$5.D2.2D.3D5.D5.D6.D5.D19.3D2.D.D.D.D2.D4.D
3.D2.D2.D2.D30.3D2.D.D.D.5D4.D4.D6.D4.D$5.D3.D.D7.D5.D5.D5.D23.D.D.D.
D.5D3.D3.5D.5D32.D.D.D.D9.D5.D5.D5.D$5.D3.D.D7.D5.D4.D5.D20.D3.D.2D.
2D4.D4.D6.D5.D29.D3.D.2D.2D8.D6.D4.D6.D$5.D3.D.5D2.3D4.D3.5D.5D18.3D
2.D3.D4.D4.D6.D5.D30.3D2.D3.D7.5D3.D3.5D2.3D3$38.B$37.2B$36.3B$35.4B$
34.4B103.2B$33.4B103.5B$17.2A13.4B40.A62.7B$18.A12.4B39.3A61.8B$17.A
12.4B39.A64.9B$17.2A2.2A6.4B40.2A63.10B$20.A.A5.4B36.7B6.2A56.8BA$15.
4A.A6.4B36.8B6.A56.8BABA$15.A2.A.2A4.4B36.10B2.BA.A54.10BABA$18.5B2.
4B37.7BC3B.B2A53.13BAB$19.9B39.6BCBC3B55.2BC11B$19.8B39.7B3C3B54.3BCB
C9B$18.8B37.12BC3B55.2B3C7B$7.2A9.7B37.17B54.5BC7B$8.A10.6B4.2A31.16B
54.10B2.B$8.A.AB7.6B4.A33.15B53.4B$9.2AB.3B3.6B.BA.A37.11B52.4B$11.
14B.B2A37.11B52.4B$11.16B40.9B52.4B$12.14B42.7B52.4B$11.16B40.8B65.2A
$9.18B40.8B64.B2A2B$7.19B40.8B66.4B$7.2BC16B39.4B2.3B67.4B$6.3BCBC4B.
9B38.4B3.B2A66.4B$7.2B3C4B2.7B38.4B4.BA.A64.7B$6.5BC4B2.7B37.4B6.B2A
64.7B$5.10B4.6B36.4B5.4B64.7B2A$4.4B10.7B35.4B6.2A64.9B2A$4.3B12.6B
35.3B8.A62.10B.B$2.4B13.7B34.2B6.3A63.2BC6B$2.2A16.5B35.B7.A64.3BCBC
4B$3.A16.5B109.2B3C4B$3A15.7B108.5BC4B$A17.2A.3B108.10B$19.A111.4B$
16.3A111.4B$16.A113.3B$130.2B$130.B2$143.3B$142.5B$139.9B$138.10B$15.
D3.D.D3.D3.D3.5D.5D3.D5.D4.3D77.10B2.BA$15.2D2.D.D3.D2.2D3.D7.D4.2D4.
2D3.D3.D77.11BA.A$15.D.D.D.D3.D3.D3.D7.D5.D5.D7.D76.13B2A$15.D2.2D.D.
D.D3.D4.3D4.D5.D5.D5.2D75.14B$15.D3.D.D.D.D3.D7.D3.D5.D5.D7.D72.17B2A
$15.D3.D.2D.2D3.D3.D3.D3.D5.D5.D3.D3.D72.2BC11B.BA.A$15.D3.D.D3.D2.3D
3.3D4.D4.3D3.3D3.3D72.3BCBC4B.3B3.BA$134.2B3C4B2.B$133.5BC4B$132.10B$
16.3D2.5D.5D.5D2.3D3.3D82.4B11.2A$15.D3.D.D5.D7.D3.D3.D.D3.D80.4B12.A
$15.D5.D5.D7.D7.D5.D79.4B10.BA.A$16.3D2.3D4.3D4.D6.D4.2D79.4B8.2A.B2A
$19.D.D9.D3.D5.D7.D78.3B8.B2A2B$15.D3.D.D5.D3.D3.D4.D4.D3.D78.2B10.4B
$8.4B4.3D2.5D2.3D4.D3.5D2.3D79.B12.2B$9.4B127.2AB$10.4B125.B2A6B$11.
4B124.9B$12.4B123.10B$13.4B121.11B$14.4B119.13B$15.4B117.15B$16.4B18.
A95.16B$17.4B11.2A3.A.A94.2BC10B$18.4B11.A3.A2.A92.3BCBC4B.3B$19.4B
10.A.2A.A.A93.2B3C4B$20.4B10.A.A.A.2A91.5BC4B$21.4B10.2B2A.A2.A88.10B
$22.4B10.4B2.2A87.4B$23.4B6.7B90.4B$24.4B3.8B90.4B$20.2A3.4B.8B$21.A
4.12B105.2A$21.A.AB2.11B.2B102.A$22.2AB.14B2A98.BA.A$24.16B2A95.B.BA.
A$24.14B.2B95.2A3BA$25.13B98.2AB.7B$24.14B.2B96.B3.6B$22.18B2A97.12B$
20.18B.B2A96.14B$20.2BC15B2.B95.16B$19.3BCBC4B.8B96.17B$20.2B3C4B2.7B
96.2BC12B$19.5BC4B2.7B95.3BCBC10B$18.10B3.7B96.2B3C4B.4B$17.4B11.6B.B
A92.5BC4B3.B$17.3B12.7BA.A90.10B$15.4B13.8BA90.4B$15.2A15.6B.B90.4B$
16.A15.5B92.4B$13.3A16.6B90.4B$13.A16.2AB.5B$29.A.AB3.4B$29.A7.4B94.A
$28.2A8.4B93.3A$39.4B95.A$40.4B93.2A2.3B$41.4B92.9B$42.4B93.7B$43.4B
91.7B2A$44.4B88.9B2A$45.4B81.B2.11B.B$46.4B80.6BC6B$130.6BCBC4B$130.
6B3C4B$130.8BC4B$130.12B$131.4B$130.4B$130.3B$130.2B$130.B!

[drc]

What if we programmed apgsearch in life

[gameoflifeboy]

It would be cool if there was a way to start with a pattern (probably confined to an oscillator or still life) and make it out of metapixels by feeding it into a machine. In Life.

It's probably impossible to make one that works for all oscillators, though, even if it was supplied with an infinite grid of metapixels.

Or maybe there could be a pattern that starts with the user inputting an oscillator as data (not data from a synthesis but instead taken straight from the cell states of the finished pattern), and the pattern would construct that oscillator. This seems slightly more likely to be possible, but still pretty far fetched.

[Saka]

Is it possible to make a copying machine that copies a still life by scanning the cells?

[dvgrn]

Is it possible to make a copying machine that copies a still life by scanning the cells?

Almost certainly not (in my opinion). A copying machine has no possible way to "see" the second row of a still life, without taking apart the first row, probably bit by bit -- seems like it would have to "feel" its way along, checking at each location if there's an ON bit, and then somehow re-stabilizing the still life without that bit.

But there are a lot of different ways to arrange row 2 and row 3 and so on, for a given first row of a (large enough) still life. It seems highly optimistic to think that there's a stabilization method that can remove Row#1 and somehow keep Row #2 stable and readable enough to be copied.

Really it's highly optimistic to think that there's even a set of reactions that could reliably figure out what the first row of a large still life looks like, let alone the inside part. All the beams of light that can be bounced off a still life to figure out its structure, are potentially highly destructive, and therefore not very useful...!

[simsim314]

I would ask this differently: given an infinite array of the same SL can we scan it? I would also add that they are placed in a way that any glider/*WSS shoot out from them will very probably not destroy any other SL in the array (knight arrangement, distant enough from each other).

EDIT Another formulation: could we know the SL by shooting all possible glider salvos at it from all direction - and see only the stabilized results, and if yes what is the number of salvos needed to know the SL?

[dvgrn]

I would ask this differently: given an infinite array of the same SL can we scan it? I would also add that they are placed in a way that any glider/*WSS shoot out from them will very probably not destroy any other SL in the array (knight arrangement, distant enough from each other).

EDIT Another formulation: could we know the SL by shooting all possible glider salvos at it from all direction - and see only the stabilized results, and if yes what is the number of salvos needed to know the SL?

Without a limitation on the size of the still life, I wouldn't want to work on finding an algorithm for this -- but I think it would be an interesting challenge to break whatever algorithm someone might come up with.

It doesn't seem too unlikely that there's a way to construct some variant of

Code: Select all

x = 65, y = 65, rule = LifeHistory
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-- maybe with longer diagonal fuses in the central area, that can't be incrementally disassembled... and that is guaranteed to lose at least one bit of information as it collapses.

This question has come up before somewhere -- I'll see if I can find the link. Of course it all ended up with hand-waving and wild speculation on both sides last time, too...!

EDIT: Ah, there it is -- a topic from just a year ago. It seems I took the other side of the bet that time, so I'm not doing too well on consistency but at least all my options are covered --