Incomplete search patterns - try to complete

[knightlife]

That's the most promising result. It's a shame that the block is displaced by (3,0).

I found a simple Hershel reaction that can move a block by (3,0)!

Code: Select all

x = 9, y = 12, rule = B3/S23
7b2o$7b2o8$3o$bo$b3o!

With this reaction a stable reflector becomes much easier to make, which I will describe here.
A simple Herschel conduit should be able to restore the moved block, using the output Herschel and looping around to the required position.
Fortunately, all the mirror images of the reaction are available because of the all-way symmetry of the block.

Here is the partial construction:

Code: Select all

x = 66, y = 59, rule = B3/S23
bo$2b2o$b2o10$2o$bo$bobo$2b2o11$36bo$35bobo$35bobo$36bo3$20b3o$20bo$
19b3o6$16bo$16bo28b2o$14b3o9b2o17b2o$14bo11b2o5$56b2o$55bo2bo2b2o$55bo
bo4bo$36b2o18bo5bob2o$35bobo21b2obobo$35bo23bo2bo2bo$34b2o20bo4bo2b2o$
56b5o2$58b2obo$58bob2o!

The final reconstruction happens first in this demo, and the extra glider from the reaction is stopped with an eater. The ghosted Herschel is the position of the output glider, which needs to be looped around clockwise to produce the final reconstruction (the (3,0) block move).

The only tricky part might be allowing a clear path for the input glider.

The speed of recovery looks fairly good, because the output Herschel is generated quickly from the initial pi reaction.
I would love to complete this stable reflector myself but I don't think I would get to it for quite a while.
Someone with Hersrch should be able to find the right conduit in short order (hopefully).
Oh, yeah... the output glider for this reflector has to come from the Hershel conduit, which should not be a problem.

It won't win any prizes, but it might beat the record, who knows?

[calcyman]

There aren't many ways to allow the input glider to reach its destination. However, I managed to find one solution:

Code: Select all

x = 126, y = 109, rule = B3/S23
90bo$88boo$89boo5$64boo$57boo5boo$57boo$94bo$92b3o$59boo30bo$59boo30b
oo$53boo$53boo5$99boo$99bo$97bobo$97boo3$104bo$102b3o$50boo49bo$51bo
49boo14boo$51bobo63boo$52boo$44bo$44b3o76boo$47bo75boo$46boo71boo$67b
oo50boo$67bo$34boo29bobo$35bo29boo$35bobo86boo$36boo55boo29boo$93bo$
94b3o$96bo8$29bo$28bobo$28bobo27boo$29bo28boo5boo$65boo3$63boo$63boo$
69boo$69boo$$96boo$38boo55bobo$38boo55bo16boo$19boo73boo16boo7boo$19b
oo100bo$119bobo$119boo3$105boo$8boo63bo30bobo$3boobbobbo60b3o30bo$3bo
4bobo59bo32boo$oobo5bo18boo40boo$boboboo21bobo45bo$obbobbo23bo43b3o$oo
bbo4bo20boo41bo$5b5o63boo$$4boboo$4boobo3$76boo$57boo17boo$57boo38boo$
97boo$$56boo$57bo$54b3o12boo$54bo14bo51boo$70b3o48boo$72bo3$121boo$
121boo$107boo$106bobo$106bo$105boo8boo$115bo$116b3o$118bo!

Notice that the Herschel track is only composed of blocks and eaters (the beehive and eater3 being part of the rectifier).

It produces eight gliders, one of which returns on the exact same lane as the input glider. This facilitates this (very silly) pattern:

Code: Select all

x = 202, y = 202, rule = B3/S23
170boboo$170boobo$$168b5o$168bo4bobboo$171bobbobbo$171boobobo$168bo5bo
boo$167bobo4bo$167bobbobboo$168boo9$160boo$160boo8$146boo22boo$145bobb
o21bo$146boo23b3o$173bo3$131bo$131b3o$134bo$133boo$158boo$158boo5$125b
oo$126bo$126bobo$127boo$$133b3o$121bo13bo$121b3o10bo$124bo$107boo14boo
$107boo78boo$187bo$185bobo$101boo78boobboo$101boo44boo32boo$105boo40b
oo$105boo3$152boo$100boo50boo$100boo29boo15boo$132bo15boo$129b3o$129bo
$154boo31boo$154boo13boo16bobo$168bobo18bo$168bo20boo$167boo4boo$172bo
bo$172bo$171boo7boo$180boo14$105boo$104bobo$104bo29boo$103boo29bobo23b
o$136bo21b3o$136boo19bo$115boo40boo23boo$116bo65boo$113b3o$64boo47bo$
57boo5boo55boo$57boo44boo15bobo$94bo7bobbo14bo48bo$92b3o8bobo13boo46b
3o$59boo30bo12bo61bo31bo$59boo30boo73boo28b3o$53boo140bo$53boo140boo4$
159boo$99boo58boo$99bo$97bobo98boo$97boo99bobo$122boo76bo$122boo76boo$
104bo23boo32boo$102b3o23boo33bo$50boo49bo58b3o25boo3boo$51bo49boo14boo
41bo27boo3boo$51bobo63boo7boo$52boo72boo5boo$44bo88boo$44b3o76boo$47bo
75boo$46boo71boo$67boo50boo$67bo$34boo29bobo$35bo29boo$35bobo86boo$36b
oo55boo29boo$93bo$94b3o$96bo8$29bo$28bobo$28bobo27boo$29bo28boo5boo$
65boo3$63boo$63boo$69boo$69boo$$96boo$38boo55bobo$38boo55bo16boo$19boo
73boo16boo7boo$19boo100bo$119bobo$119boo3$105boo$8boo63bo30bobo$3boobb
obbo60b3o30bo$3bo4bobo59bo32boo$oobo5bo18boo40boo$boboboo21bobo45bo$o
bbobbo23bo43b3o$oobbo4bo20boo41bo$5b5o63boo$$4boboo$4boobo3$76boo$57b
oo17boo$57boo38boo$97boo$$56boo$57bo$54b3o12boo$54bo14bo51boo$70b3o48b
oo$72bo3$121boo$121boo$107boo$106bobo$106bo$105boo8boo$115bo$116b3o$
118bo!

[calcyman]

Here's a much better solution, which has a custom Herschel conduit inside it. In other words, this could not have been found by a simple Hersrch search:

Code: Select all

x = 162, y = 75, rule = B3/S23
75bo47boo$73b3o47boo$72bo28bo$72boo27b3o$60bo43bo$43boo15b3o40boo39boo
$4boobo36bo18bo80boo5boo$4boboo36bobo15boo20bo66boo$45boo37b3o$5b5o77b
o$oobbo4bo20boo44boo8boo11boo48boo$obbobbo23bo45boo21boo48boo$boboboo
21bobo124boo$oobo5bo18boo125boo$3bo4bobo$3boobbobbo$8boo3$124boo$111b
oo11boo$53boo57bo$19boo32boo54b3o$19boo88bo$38boo43bo3boo$38boo42bobo
3bo39boo$77boobbobo3bo12boo27bo$77bo3bo4bo13bobo23b3o$78b4o5b3o12bo23b
o$89bo12boo17boo$80boo40bo$80boo24bo15bobo$104b3o16boo$103bo$103boo$
29bo$28bobo52bo76boo$28bobo50b3o76boo$29bo50bo$67boo11boo$67boo$155boo
$155boo$159boo$159boo$$36boo$36boo86boo27boo$42boo80boo11boo14boo$42b
oo93bo$138b3o$140bo$40boo$40boo5boo71boo$47boo39boo30bo$88bo5boo25b3o$
89b3obobo27bo$91bobo7boo$68boo22boo7boo$68boo13$73boo$72boo$74bo!

The recovery time is less than 1000, which is better than infinity.


The reason for the custom Herschel conduit is the excess glider from the Herschel that enters the R64 conduit. It would collide with a normal F166, so the final block+snake combination has been removed. This leaves an extra block from the output B-heptomino, which is converted into a pi by the nuisance glider. However, the pi is in just the right place to be eaten by a standard eater. Unfortunately, this generated another problem -- the eater was in the way of the FNG from the output Herschel. This needed to be cleaned up with a special eater5 combo, which welds elegantly to the standard eater.

[calcyman]

And, at 60 cells wide, this is officially the thinnest 90° stable reflector!

[knightlife]

The recovery time is less than 1000, which is better than infinity.

Well, at least it's completed. Thanks, calcyman. [The thinnest... hehe]

[Sokwe]

MikeP,

might your search program be able to find a replacement for the block in this pattern?

Code: Select all

x = 62, y = 79, rule = B3/S23
31b2o2$29bo3bo$29bo4bo$31bobobo$32bobobo$33bo4bo$28b2o4bo3bo$29bo$29bo
bo3b2o8b3o$30b2o12bo3bo7bo$43bo5bo5bobo$43bo5bo4bo3bo$26bo16bo5bo5bo3b
o$25bobo16bo3bo7bo3bo$24bo3bo9b3o4b3o9bo3bo$25bo3bo7bo3bo16bobo$26bo3b
o5bo5bo16bo$27bo3bo4bo5bo$22b2o4bobo5bo5bo$23bo5bo7bo3bo12b2o$23bobo
12b3o8b2o3bobo$24b2o30bo$28bo18bo3bo4b2o$19b2o6b2o18bo4bo$27bobo19bobo
bo$17bo3bo28bobobo$17bo4bo28bo4bo$19bobobo28bo3bo$20bobobo19bobo$21bo
4bo18b2o6b2o$16b2o4bo3bo18bo$17bo$17bobo3b2o8b3o$18b2o12bo3bo$31bo5bo$
31bo5bo$14bo16bo5bo$13bobo16bo3bo$12bo3bo9b3o4b3o18bobo$13bo3bo7bo3bo
9b2o14b2o$14bo3bo5bo5bo8b2o14bo$15bo3bo4bo5bo$10b2o4bobo5bo5bo$11bo5bo
7bo3bo$11bobo12b3o8b2o$12b2o$16bo18bo3bo$7b2o6b2o18bo4bo$15bobo19bobob
o$5bo3bo28bobobo$5bo4bo28bo4bo$7bobobo28bo3bo$8bobobo19bobo$9bo4bo18b
2o6b2o$4b2o4bo3bo18bo$5bo30b2o$5bobo3b2o8b3o12bobo$6b2o12bo3bo7bo5bo$
19bo5bo5bobo4b2o$19bo5bo4bo3bo$2bo16bo5bo5bo3bo$bobo16bo3bo7bo3bo$o3bo
9b3o4b3o9bo3bo$bo3bo7bo3bo16bobo$2bo3bo5bo5bo16bo$3bo3bo4bo5bo$4bobo5b
o5bo$5bo7bo3bo12b2o$14b3o8b2o3bobo$32bo$23bo3bo4b2o$23bo4bo$25bobobo$
26bobobo$27bo4bo$28bo3bo2$29b2o!

It's a bit of a long shot, but it could allow the construction of a period-40 gun, so it might be worth a try.

Another interesting possibility would be to find still lifes to replace the glider streams in this glider-supported p43 oscillator:

Code: Select all

x = 213, y = 96, rule = B3/S23
67bo$66bo$66b3o$149bobo$150b2o$150bo6$57bo$55b2o$56b2o103bo$162bo$160b
3o7$45bo$45bobo$45b2o124bo$172b2o$171b2o$2bo$obo152bo$b2o152b3o54bo$
158bo51b2o$157b2o52b2o3$48bob2o116bob2o$47b2ob2o115b2ob2o14b2o$48bo2bo
116bo2bo14bo$184bobo$11bobo170b2o$12b2o$12bo187bo$200bobo$145bo54b2o$
145b2o$34b3o107bobo7b3o$34b2o35b3o80b2o$71bo$34b3o23bo11bo81b3o23bo$
23bo11bo23b3o93bo23b3o$24bo$22b3o35b2o118b2o$59b3o117b3o7bobo$189b2o$
134b2o54bo$133bobo$83bo51bo$82b2o$82bobo65b2o$149bobo$44bo2bo101bo14bo
2bo$44b2ob2o99b2o14b2ob2o$44b2obo116b2obo3$123b2o52b2o$124b2o51bo$93b
2o28bo54b3o$93bobo84bo$93bo$163b2o$162b2o$49b2o113bo$48bobo$50bo7$173b
3o$173bo$38b2o134bo$39b2o$38bo6$185bo$184b2o$184bobo$27b3o$29bo$28bo!

Edit: I may have found a more plausible alternative for the p40 gun. I think it could work if someone could complete this period-5 sparker:

Code: Select all

x = 62, y = 79, rule = B3/S23
31b2o2$29bo3bo$29bo4bo$31bobobo$32bobobo$33bo4bo$28b2o4bo3bo$29bo$29bo
bo3b2o8b3o$30b2o12bo3bo7bo$43bo5bo5bobo$43bo5bo4bo3bo$26bo16bo5bo5bo3b
o$25bobo16bo3bo7bo3bo$24bo3bo9b3o4b3o9bo3bo$25bo3bo7bo3bo16bobo$26bo3b
o5bo5bo16bo$27bo3bo4bo5bo$22b2o4bobo5bo5bo$23bo5bo7bo3bo12b2o$23bobo
12b3o8b2o3bobo$24b2o30bo$28bo18bo3bo4b2o$19b2o6b2o18bo4bo$27bobo19bobo
bo$17bo3bo28bobobo$17bo4bo28bo4bo$19bobobo28bo3bo$20bobobo19bobo$21bo
4bo18b2o6b2o$16b2o4bo3bo18bo$17bo$17bobo3b2o8b3o$18b2o12bo3bo$31bo5bo$
31bo5bo5bo$14bo16bo5bo5b3o$13bobo16bo3bo9bo$12bo3bo9b3o4b3o8bo9bobo$
13bo3bo7bo3bo13bo2b3o6b2o$14bo3bo5bo5bo12b4o2bo5bo$15bo3bo4bo5bo10b2o
3b2o2bo$10b2o4bobo5bo5bo10bo2b4o3bo$11bo5bo7bo3bo12bobo4bob3o$11bobo
12b3o8b2o4bob4obo3bo$12b2o30bo3bobo2b2o$16bo18bo3bo4bobobobobo$7b2o6b
2o18bo4bo7bobobob3o$15bobo19bobobo4bo3b2obobobo$5bo3bo28bobobo5b2o3bo
3bo$5bo4bo28bo4bo2b3o2b3o2b2o$7bobobo28bo3bo2b3o7bo$8bobobo19bobo17b5o
$9bo4bo18b2o6b2o12bo$4b2o4bo3bo18bo19bo$5bo30b2o15bo$5bobo3b2o8b3o12bo
bo15bo$6b2o12bo3bo7bo5bo$19bo5bo5bobo4b2o$19bo5bo4bo3bo$2bo16bo5bo5bo
3bo$bobo16bo3bo7bo3bo$o3bo9b3o4b3o9bo3bo$bo3bo7bo3bo16bobo$2bo3bo5bo5b
o16bo$3bo3bo4bo5bo$4bobo5bo5bo$5bo7bo3bo12b2o$14b3o8b2o3bobo$32bo$23bo
3bo4b2o$23bo4bo$25bobobo$26bobobo$27bo4bo$28bo3bo2$29b2o!

Edit 2: Calcyman provided this p40 gun:

Code: Select all

x = 752, y = 510, rule = B3/S23
345bo60bo$343b3o60b3o$342bo66bo$342b2o64b2o2$339b3o68b3o$341bo68bo$
340bo70bo8$329b3o88b3o$331bo88bo$330bo90bo8$319b3o108b3o$321bo108bo$
320bo110bo4$195b3o356b3o$195b3o356b3o$195b3o10bo334bo10b3o$198b3o5b3o
334b3o5b3o$198b3o4bo103b3o128b3o103bo4b3o$198b3o4b2o104bo128bo104b2o4b
3o$204b2o104bo130bo104b2o$203b2o342b2o$202b3o342b3o$207b2o334b2o$205bo
2bo334bo2bo$174bo29bo342bo29bo$202bo4bo336bo4bo$172bob3o25bo3bo338bo3b
o25b3obo$174b2obo8bo15b2o95b3o148b3o95b2o15bo8bob2o$174bob2o6b3o114bo
148bo114b3o6b2obo$175b3obo3bo116bo150bo116bo3bob3o$183b2o43b2o292b2o
43b2o$177bo48bob2o292b2obo48bo$181bo43bo300bo43bo$180bobo29b2o14bo294b
o14b2o29bobo$181b2o2b2o24b2o11b2obo296bob2o11b2o24b2o2b2o$185b2o5bo20b
o10b2o300b2o10bo20bo5b2o$192bobo362bobo$183bo8b2o27bo67b3o168b3o67bo
27b2o8bo$182b2o36bobo68bo168bo68bobo36b2o$182bobo35b2o68bo170bo68b2o
35bobo$224b2o300b2o$224bobo298bobo$219b2o5bo298bo5b2o$211b3o5b2o5b2o
296b2o5b2o5b3o$173bo16b2o21bo324bo21b2o16bo$172bo13b2o2b2o20bo326bo20b
2o2b2o13bo$172b3o10bobo376bobo10b3o$186bo92b3o188b3o92bo$181b3o97bo
188bo97b3o$184bo3b2o90bo190bo90b2o3bo$180bo3bo3bo374bo3bo3bo$179bobo2b
o4b3o368b3o4bo2bobo$177bo2bobo8bo368bo8bobo2bo$147b2o28bo3bo19b3o344b
3o19bo3bo28b2o$144bo18bo13bo25bo344bo25bo13bo18bo$143bobo2b2o12bo15b3o
21bo346bo21b3o15bo12b2o2bobo$141bobob3o2bo11b3o56bo308bo56b3o11bo2b3ob
obo$141bo2b6o70bobo46b3o208b3o46bobo70b6o2bo$144b2ob2o72bo6b2o41bo208b
o41b2o6bo72b2ob2o$143b6o2bo14bo61bobo39bo210bo39bobo61bo14bo2b6o$142bo
2b3obobo57bo9b5ob2obobo290bobob2ob5o9bo57bobob3o2bo$143b2o2bobo14b3obo
39bobo8bo3bobo2bob2o288b2obo2bobo3bo8bobo39bob3o14bobo2b2o$148bo14bob
2o41bobo10bobobobo4bo286bo4bobobobo10bobo41b2obo14bo$144b2o17b2obo7bo
16b3o13b2ob2o7bob3o3bobobobo284bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17b
2o$153bo7bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo284bobobo3b3o5bo3bo3bo2b
o12bo18b3o6b3obo7bo$152bo18bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo286bo4bo
4b7o2bob2o2bo2b2ob2o7bo13bo6bo18bo$152b3o8bo7b2o4b3o19bob2o4bo2b2o3b4o
3b10o288b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo8b3o$176bob3o15bo2bobob3o7b3o
43b3o228b3o43b3o7b3obobo2bo15b3obo$164bo10bo3bo16b3obo10bo4bo7b2o2b2o
31bo228bo31b2o2b2o7bo4bo10bob3o16bo3bo10bo$162b3o9bo3bo15b2o4bo10b5obo
6b2o2b2o30bo230bo30b2o2b2o6bob5o10bo4b2o15bo3bo9b3o$161bobobo7b3obo15b
o2b5o9bo6bo316bo6bo9b5o2bo15bob3o7bobobo$149bo11bo3bo8b3o15bo2bo5b3o7b
3o3b2o314b2o3b3o7b3o5bo2bo15b3o8bo3bo11bo$149b2o8b2o5b2o7bo15bo4b4ob3o
9bo107b2o106b2o107bo9b3ob4o4bo15bo7b2o5b2o8b2o$148bobo7bo4bo4bo12b3o7b
ob2obo5b2o344b2o5bob2obo7b3o12bo4bo4bo7bobo$157b3o2bobo3b2o13bo5bob4ob
obobo119bo3bo102bo3bo119bobobob4obo5bo13b2o3bobo2b3o$158bo4bo5bo12bo5b
o3bobobo122bo4bo102bo4bo122bobobo3bo5bo12bo5bo4bo$159b2o9bo17bobobob2o
b2o110bo8bobobo106bobobo8bo110b2ob2obobobo17bo9b2o$161bo8b2o15b2o2b2o
3bo5bo46b3o57b3o5bobobo108bobobo5b3o57b3o46bo5bo3b2o2b2o15b2o8bo$161b
2o8bo21bobo5b3o47bo60bo2bo4bo110bo4bo2bo60bo47b3o5bobo21bo8b2o$162bo9b
2o19b2o5bob3o45bo60b2o2bo3bo112bo3bo2b2o60bo45b3obo5b2o19b2o9bo$150bo
12bo5bo4bo13bo10bo3bo65bo212bo65bo3bo10bo13bo4bo5bo12bo$139bo9bo13b2o
3bobo2b3o10b3o9bo3bo7bo57bobo43bo2b2o114b2o2bo43bobo57bo7bo3bo9b3o10b
3o2bobo3b2o13bo9bo$139b2o8b3o12bo4bo4bo10bobobo7b3obo6b3o58bo6b2o35bob
o120bobo35b2o6bo58b3o6bob3o7bobobo10bo4bo4bo12b3o8b2o$138bobo16bo7b2o
5b2o11bo3bo8b3o6bo6bo61bobo30b2o2b2o122b2o2b2o30bobo61bo6bo6b3o8bo3bo
11b2o5b2o7bo16bobo$156b3o8bo3bo11b2o5b2o7bo7b2o48bo9b5ob2obobo30b2o
130b2o30bobob2ob5o9bo48b2o7bo7b2o5b2o11bo3bo8b3o$155bob3o7bobobo10bo4b
o4bo19b3obo39bobo8bo3bobo2bob2o192b2obo2bobo3bo8bobo39bob3o19bo4bo4bo
10bobobo7b3obo$154bo3bo9b3o10b3o2bobo3b2o17bob2o41bobo10bobobobo4bo
190bo4bobobobo10bobo41b2obo17b2o3bobo2b3o10b3o9bo3bo$153bo3bo10bo13bo
4bo5bo17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo188bobobobo3b3obo7b2ob2o
13b3o16bo7bob2o17bo5bo4bo13bo10bo3bo$152b3obo26b2o9bo14bob3o6b3o18bo
12bo2bo3bo3bo5b3o3bobobo188bobobo3b3o5bo3bo3bo2bo12bo18b3o6b3obo14bo9b
2o26bob3o$153b3o4b2o7bo15bo8b2o23bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo
36bo116bo36bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo23b2o8bo15bo7b2o4b3o$
141b2o11bo6bo23b2o8bo15bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o38b2o112b2o38b
10o3b4o3b2o2bo4b2obo19b3o4b2o7bo15bo8b2o23bo6bo11b2o$129bo12bo15b3o6b
3obo14bo9b2o26bob3o15bo2bobob3o7b3o43b3o7b2o114b2o7b3o43b3o7b3obobo2bo
15b3obo26b2o9bo14bob3o6b3o15bo12bo$129b2o8b3o16bo7bob2o17bo5bo4bo13bo
10bo3bo16b3obo10bo4bo7b2o2b2o31bo132bo31b2o2b2o7bo4bo10bob3o16bo3bo10b
o13bo4bo5bo17b2obo7bo16b3o8b2o$128bobo8bo26b2obo17b2o3bobo2b3o10b3o9bo
3bo15b2o4bo10b5obo6b2o2b2o30bo134bo30b2o2b2o6bob5o10bo4b2o15bo3bo9b3o
10b3o2bobo3b2o17bob2o26bo8bobo$164bob3o19bo4bo4bo10bobobo7b3obo15bo2b
5o9bo6bo220bo6bo9b5o2bo15bob3o7bobobo10bo4bo4bo19b3obo$172b2o7bo7b2o5b
2o11bo3bo8b3o15bo2bo5b3o7b3o3b2o218b2o3b3o7b3o5bo2bo15b3o8bo3bo11b2o5b
2o7bo7b2o$166bo6bo6b3o8bo3bo11b2o5b2o7bo15bo4b4ob3o9bo228bo9b3ob4o4bo
15bo7b2o5b2o11bo3bo8b3o6bo6bo$170b3o6bob3o7bobobo10bo4bo4bo12b3o7bob2o
bo5b2o248b2o5bob2obo7b3o12bo4bo4bo10bobobo7b3obo6b3o$170bo7bo3bo9b3o
10b3o2bobo3b2o13bo5bob4obobobo254bobobob4obo5bo13b2o3bobo2b3o10b3o9bo
3bo7bo$177bo3bo10bo13bo4bo5bo12bo5bo3bobobo82bo96bo82bobobo3bo5bo12bo
5bo4bo13bo10bo3bo$176b3obo26b2o9bo17bobobob2ob2o81b2o92b2o81b2ob2obobo
bo17bo9b2o26bob3o$119bo57b3o4b2o7bo15bo8b2o15b2o2b2o3bo5bo46b3o27b2o
94b2o27b3o46bo5bo3b2o2b2o15b2o8bo15bo7b2o4b3o57bo$119b2o57bo6bo23b2o8b
o21bobo5b3o47bo152bo47b3o5bobo21bo8b2o23bo6bo57b2o$118bobo61b3o6b3obo
14bo9b2o19b2o5bob3o45bo154bo45b3obo5b2o19b2o9bo14bob3o6b3o61bobo$182bo
7bob2o17bo5bo4bo13bo10bo3bo65bo116bo65bo3bo10bo13bo4bo5bo17b2obo7bo$
190b2obo17b2o3bobo2b3o10b3o9bo3bo7bo57bobo114bobo57bo7bo3bo9b3o10b3o2b
obo3b2o17bob2o$188bob3o19bo4bo4bo10bobobo7b3obo6b3o58bo6b2o100b2o6bo
58b3o6bob3o7bobobo10bo4bo4bo19b3obo$196b2o7bo7b2o5b2o11bo3bo8b3o6bo6bo
61bobo98bobo61bo6bo6b3o8bo3bo11b2o5b2o7bo7b2o$73bo116bo6bo6b3o8bo3bo
11b2o5b2o7bo7b2o48bo9b5ob2obobo98bobob2ob5o9bo48b2o7bo7b2o5b2o11bo3bo
8b3o6bo6bo116bo$73b2o119b3o6bob3o7bobobo10bo4bo4bo19b3obo39bobo8bo3bob
o2bob2o9bo76bo9b2obo2bobo3bo8bobo39bob3o19bo4bo4bo10bobobo7b3obo6b3o
119b2o$72b2obo118bo7bo3bo9b3o10b3o2bobo3b2o17bob2o41bobo10bobobobo4bo
9b2o72b2o9bo4bobobobo10bobo41b2obo17b2o3bobo2b3o10b3o9bo3bo7bo118bob2o
$71bo2b3o32bo91bo3bo10bo13bo4bo5bo17b2obo7bo16b3o13b2ob2o7bob3o3bobobo
bo7b2o74b2o7bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17bo5bo4bo13bo10bo3bo
91bo32b3o2bo$61bo8bobobo34b2o89b3obo5b2o19b2o9bo14bob3o6b3o18bo12bo2bo
3bo3bo5b3o3bobobo92bobobo3b3o5bo3bo3bo2bo12bo18b3o6b3obo14bo9b2o19b2o
5bob3o89b2o34bobobo8bo$61b3o5bobobo34bobo90b3o5bobo21bo8b2o23bo6bo13bo
7b2ob2o2bo2b2obo2b7o4bo4bo94bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo23b2o8b
o21bobo5b3o90bobo34bobobo5b3o$34bo29bo2b3o2bo129bo5bo3b2o2b2o15b2o8bo
15bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o96b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo
15bo8b2o15b2o2b2o3bo5bo129bo2b3o2bo29bo$33b3o27b2o3bob2o134b2ob2obobob
o17bo9b2o26bob3o15bo2bobob3o7b3o128b3o7b3obobo2bo15b3obo26b2o9bo17bobo
bob2ob2o134b2obo3b2o27b3o$32bob3o32b2o137bobobo3bo5bo12bo5bo4bo13bo10b
o3bo16b3obo10bo4bo7b2o2b2o100b2o2b2o7bo4bo10bob3o16bo3bo10bo13bo4bo5bo
12bo5bo3bobobo137b2o32b3obo$22bo8bo3bo30bo3bo133bobobob4obo5bo13b2o3bo
bo2b3o10b3o9bo3bo15b2o4bo10b5obo6b2o2b2o100b2o2b2o6bob5o10bo4b2o15bo3b
o9b3o10b3o2bobo3b2o13bo5bob4obobobo133bo3bo30bo3bo8bo$22b3o5bo3bo30bob
o133b2o5bob2obo7b3o12bo4bo4bo10bobobo7b3obo15bo2b5o9bo6bo124bo6bo9b5o
2bo15bob3o7bobobo10bo4bo4bo12b3o7bob2obo5b2o133bobo30bo3bo5b3o$25bo3b
3obo27b2o2b2o124bo9b3ob4o4bo15bo7b2o5b2o11bo3bo8b3o15bo2bo5b3o7b3o3b2o
32bo56bo32b2o3b3o7b3o5bo2bo15b3o8bo3bo11b2o5b2o7bo15bo4b4ob3o9bo124b2o
2b2o27bob3o3bo$24b2o4b3o28b2o123b2o3b3o7b3o5bo2bo15b3o8bo3bo11b2o5b2o
7bo15bo4b4ob3o9bo38b2o52b2o38bo9b3ob4o4bo15bo7b2o5b2o11bo3bo8b3o15bo2b
o5b3o7b3o3b2o123b2o28b3o4b2o$31bo67bo87bo6bo9b5o2bo15bob3o7bobobo10bo
4bo4bo12b3o7bob2obo5b2o47b2o54b2o47b2o5bob2obo7b3o12bo4bo4bo10bobobo7b
3obo15bo2b5o9bo6bo87bo67bo$27bo71b2o74b2o2b2o6bob5o10bo4b2o15bo3bo9b3o
10b3o2bobo3b2o13bo5bob4obobobo158bobobob4obo5bo13b2o3bobo2b3o10b3o9bo
3bo15b2o4bo10b5obo6b2o2b2o74b2o71bo$26bobo69bobo74b2o2b2o7bo4bo10bob3o
16bo3bo10bo13bo4bo5bo12bo5bo3bobobo166bobobo3bo5bo12bo5bo4bo13bo10bo3b
o16b3obo10bo4bo7b2o2b2o74bobo69bobo$22b2o2b2o161b3o7b3obobo2bo15b3obo
26b2o9bo17bobobob2ob2o162b2ob2obobobo17bo9b2o26bob3o15bo2bobob3o7b3o
161b2o2b2o$22b2o46bo102b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo15bo8b2o15b2o
2b2o3bo5bo154bo5bo3b2o2b2o15b2o8bo15bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o
102bo46b2o$68bobo101bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo23b2o8bo21bobo
5b3o152b3o5bobo21bo8b2o23bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo101bobo$
59b2o8b2o100bobobo3b3o5bo3bo3bo2bo12bo18b3o6b3obo14bo9b2o19b2o5bob3o
150b3obo5b2o19b2o9bo14bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo100b2o8b2o$
60b2o109bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17bo5bo4bo13bo10bo3bo152bo
3bo10bo13bo4bo5bo17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo109b2o$30bo28bo
112bo4bobobobo10bobo41b2obo17b2o3bobo2b3o10b3o9bo3bo7bo50bo36bo50bo7bo
3bo9b3o10b3o2bobo3b2o17bob2o41bobo10bobobobo4bo112bo28bo$31bo141b2obo
2bobo3bo8bobo39bob3o19bo4bo4bo10bobobo7b3obo6b3o51b2o32b2o51b3o6bob3o
7bobobo10bo4bo4bo19b3obo39bobo8bo3bobo2bob2o141bo$2bo26b3o57bo84bobob
2ob5o9bo48b2o7bo7b2o5b2o11bo3bo8b3o6bo6bo46b2o34b2o46bo6bo6b3o8bo3bo
11b2o5b2o7bo7b2o48bo9b5ob2obobo84bo57b3o26bo$bobo16bo68b2o83bobo61bo6b
o6b3o8bo3bo11b2o5b2o7bo7b2o142b2o7bo7b2o5b2o11bo3bo8b3o6bo6bo61bobo83b
2o68bo16bobo$o3bo15b2o66bobo84b2o6bo58b3o6bob3o7bobobo10bo4bo4bo19b3ob
o126bob3o19bo4bo4bo10bobobo7b3obo6b3o58bo6b2o84bobo66b2o15bo3bo$bo3bo
13bobo160bobo57bo7bo3bo9b3o10b3o2bobo3b2o17bob2o130b2obo17b2o3bobo2b3o
10b3o9bo3bo7bo57bobo160bobo13bo3bo$2bo3bo73bo102bo65bo3bo10bo13bo4bo5b
o17b2obo7bo114bo7bob2o17bo5bo4bo13bo10bo3bo65bo102bo73bo3bo$3bo3bo70bo
bo121bo45b3obo5b2o19b2o9bo14bob3o6b3o114b3o6b3obo14bo9b2o19b2o5bob3o
45bo121bobo70bo3bo$4bobo42b2o28b2o120bo47b3o5bobo21bo8b2o23bo6bo106bo
6bo23b2o8bo21bobo5b3o47bo120b2o28b2o42bobo$5bo44b2o149b3o46bo5bo3b2o2b
2o15b2o8bo15bo7b2o4b3o104b3o4b2o7bo15bo8b2o15b2o2b2o3bo5bo46b3o149b2o
44bo$9bo30bo8bo204b2ob2obobobo17bo9b2o26bob3o42bo16bo42b3obo26b2o9bo
17bobobob2ob2o204bo8bo30bo$8bobo30bo214bobobo3bo5bo12bo5bo4bo13bo10bo
3bo44b2o12b2o44bo3bo10bo13bo4bo5bo12bo5bo3bobobo214bo30bobo$9b2o28b3o
36b2o172bobobob4obo5bo13b2o3bobo2b3o10b3o9bo3bo7bo36b2o14b2o36bo7bo3bo
9b3o10b3o2bobo3b2o13bo5bob4obobobo172b2o36b3o28b2o$5b2o8b2o61b2o2b2o
165b2o5bob2obo7b3o12bo4bo4bo10bobobo7b3obo6b3o90b3o6bob3o7bobobo10bo4b
o4bo12b3o7bob2obo5b2o165b2o2b2o61b2o8b2o$4bobo8bobo64bobo154bo9b3ob4o
4bo15bo7b2o5b2o11bo3bo8b3o6bo6bo82bo6bo6b3o8bo3bo11b2o5b2o7bo15bo4b4ob
3o9bo154bobo64bobo8bobo$4bo5b2o3bo67bo150b2o3b3o7b3o5bo2bo15b3o8bo3bo
11b2o5b2o7bo7b2o94b2o7bo7b2o5b2o11bo3bo8b3o15bo2bo5b3o7b3o3b2o150bo67b
o3b2o5bo$3b2o5b2o223bo6bo9b5o2bo15bob3o7bobobo10bo4bo4bo19b3obo78bob3o
19bo4bo4bo10bobobo7b3obo15bo2b5o9bo6bo223b2o5b2o$39b2o39b2o4b2o104bo
30b2o2b2o6bob5o10bo4b2o15bo3bo9b3o10b3o2bobo3b2o17bob2o26bo8bobo6bobo
8bo26b2obo17b2o3bobo2b3o10b3o9bo3bo15b2o4bo10b5obo6b2o2b2o30bo104b2o4b
2o39b2o$39b2o2b2o36bo4b2obo101bo31b2o2b2o7bo4bo10bob3o16bo3bo10bo13bo
4bo5bo17b2obo7bo16b3o8b2o8b2o8b3o16bo7bob2o17bo5bo4bo13bo10bo3bo16b3ob
o10bo4bo7b2o2b2o31bo101bob2o4bo36b2o2b2o$43bobo32b3o9bo100b3o43b3o7b3o
bobo2bo15b3obo26b2o9bo14bob3o6b3o15bo12bo8bo12bo15b3o6b3obo14bo9b2o26b
ob3o15bo2bobob3o7b3o43b3o100bo9b3o32bobo$44bo2b2o29bo8bo133b10o3b4o3b
2o2bo4b2obo19b3o4b2o7bo15bo8b2o23bo6bo11b2o32b2o11bo6bo23b2o8bo15bo7b
2o4b3o19bob2o4bo2b2o3b4o3b10o133bo8bo29b2o2bo$88bob2o128bo4bo4b7o2bob
2o2bo2b2ob2o7bo13bo6bo23b2o8bo15bo7b2o4b3o27b2o27b3o4b2o7bo15bo8b2o23b
o6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo128b2obo$41b2o2bo3bo40b2o127bobobo3b
3o5bo3bo3bo2bo12bo18b3o6b3obo14bo9b2o26bob3o26b2o26b3obo26b2o9bo14bob
3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo127b2o40bo3bo2b2o$25b2o15bo2bo4bo
168bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17bo5bo4bo13bo10bo3bo56bo3bo10b
o13bo4bo5bo17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo168bo4bo2bo15b2o$25bo
bo11b3o5bobobo168bo4bobobobo10bobo41b2obo17b2o3bobo2b3o10b3o9bo3bo58bo
3bo9b3o10b3o2bobo3b2o17bob2o41bobo10bobobobo4bo168bobobo5b3o11bobo$25b
o13bo8bobobo168b2obo2bobo3bo8bobo39bob3o19bo4bo4bo10bobobo7b3obo60bob
3o7bobobo10bo4bo4bo19b3obo39bobo8bo3bobo2bob2o168bobobo8bo13bo$49bo4bo
167bobob2ob5o9bo48b2o7bo7b2o5b2o11bo3bo8b3o62b3o8bo3bo11b2o5b2o7bo7b2o
48bo9b5ob2obobo167bo4bo$50bo3bo127bo39bobo61bo6bo6b3o8bo3bo11b2o5b2o7b
o16bobo26bobo16bo7b2o5b2o11bo3bo8b3o6bo6bo61bobo39bo127bo3bo$181bo41b
2o6bo58b3o6bob3o7bobobo10bo4bo4bo12b3o8b2o28b2o8b3o12bo4bo4bo10bobobo
7b3obo6b3o58bo6b2o41bo$51b2o128b3o46bobo57bo7bo3bo9b3o10b3o2bobo3b2o
13bo9bo28bo9bo13b2o3bobo2b3o10b3o9bo3bo7bo57bobo46b3o128b2o$231bo65bo
3bo10bo13bo4bo5bo12bo50bo12bo5bo4bo13bo10bo3bo65bo$250bo45b3obo5b2o19b
2o9bo74bo9b2o19b2o5bob3o45bo$249bo47b3o5bobo21bo8b2o72b2o8bo21bobo5b3o
47bo$35b2o212b3o46bo5bo3b2o2b2o15b2o8bo72bo8b2o15b2o2b2o3bo5bo46b3o
212b2o$35bobo264b2ob2obobobo17bo9b2o68b2o9bo17bobobob2ob2o264bobo$35bo
268bobobo3bo5bo12bo5bo4bo66bo4bo5bo12bo5bo3bobobo268bo$300bobobob4obo
5bo13b2o3bobo2b3o64b3o2bobo3b2o13bo5bob4obobobo$172bo124b2o5bob2obo7b
3o12bo4bo4bo7bobo46bobo7bo4bo4bo12b3o7bob2obo5b2o124bo$171bo115bo9b3ob
4o4bo15bo7b2o5b2o8b2o48b2o8b2o5b2o7bo15bo4b4ob3o9bo115bo$171b3o108b2o
3b3o7b3o5bo2bo15b3o8bo3bo11bo48bo11bo3bo8b3o15bo2bo5b3o7b3o3b2o108b3o$
283bo6bo9b5o2bo15bob3o7bobobo72bobobo7b3obo15bo2b5o9bo6bo$240bo30b2o2b
2o6bob5o10bo4b2o15bo3bo9b3o74b3o9bo3bo15b2o4bo10b5obo6b2o2b2o30bo$239b
o31b2o2b2o7bo4bo10bob3o16bo3bo10bo78bo10bo3bo16b3obo10bo4bo7b2o2b2o31b
o$45b2o192b3o43b3o7b3obobo2bo15b3obo102bob3o15bo2bobob3o7b3o43b3o192b
2o$45bobo221b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo8b3o54b3o8bo7b2o4b3o19bob
2o4bo2b2o3b4o3b10o221bobo$45bo222bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo
18bo54bo18bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo222bo$267bobobo3b3o5bo3bo
3bo2bo12bo18b3o6b3obo7bo56bo7bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo$
162bo104bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17b2o38b2o17b2obo7bo16b3o
13b2ob2o7bob3o3bobobobo104bo$161bo106bo4bobobobo10bobo41b2obo14bo46bo
14bob2o41bobo10bobobobo4bo106bo$161b3o68b2o35b2obo2bobo3bo8bobo39bob3o
14bobo2b2o36b2o2bobo14b3obo39bobo8bo3bobo2bob2o35b2o68b3o$231bobo36bob
ob2ob5o9bo57bobob3o2bo34bo2b3obobo57bo9b5ob2obobo36bobo$231bo38bobo61b
o14bo2b6o36b6o2bo14bo61bobo38bo$230b2o39b2o6bo72b2ob2o38b2ob2o72bo6b2o
39b2o$55b2o221bobo70b6o2bo32bo2b6o70bobo221b2o$55bobo221bo56b3o11bo2b
3obobo32bobob3o2bo11b3o56bo221bobo$55bo242bo21b3o15bo12b2o2bobo36bobo
2b2o12bo15b3o21bo242bo$297bo25bo13bo18bo38bo18bo13bo25bo$152bo144b3o
19bo3bo28b2o44b2o28bo3bo19b3o144bo$151bo157bo8bobo2bo104bo2bobo8bo157b
o$151b3o155b3o4bo2bobo108bobo2bo4b3o155b3o$312bo3bo3bo110bo3bo3bo$311b
2o3bo118bo3b2o$317b3o112b3o$65b2o247bo122bo247b2o$65bobo245bobo10b3o
94b3o10bobo245bobo$65bo222bo20b2o2b2o13bo94bo13b2o2b2o20bo222bo$287bo
21b2o16bo96bo16b2o21bo$142bo130b2o5b2o5b3o172b3o5b2o5b2o130bo$141bo
132bo5b2o188b2o5bo132bo$141b3o130bobo198bobo130b3o$275b2o198b2o$279b2o
35bobo114bobo35b2o$278bobo36b2o114b2o36bobo$75b2o202bo27b2o8bo116bo8b
2o27bo202b2o$75bobo228bobo134bobo228bobo$75bo199b2o10bo20bo5b2o120b2o
5bo20bo10b2o199bo$273bob2o11b2o24b2o2b2o112b2o2b2o24b2o11b2obo$132bo
139bo14b2o29bobo110bobo29b2o14bo139bo$131bo143bo43bo112bo43bo143bo$
131b3o137b2obo48bo104bo48bob2o137b3o$271b2o43b2o116b2o43b2o$317bo3bob
3o100b3obo3bo$314b3o6b2obo98bob2o6b3o$85b2o210b2o15bo8bob2o98b2obo8bo
15b2o210b2o$85bobo206bo3bo25b3obo94bob3o25bo3bo206bobo$85bo207bo4bo
154bo4bo207bo$296bo29bo98bo29bo$122bo169bo2bo160bo2bo169bo$121bo170b2o
164b2o170bo$121b3o172b3o154b3o172b3o$296b2o156b2o$295b2o158b2o$294b2o
4b3o146b3o4b2o$95b2o198bo4b3o146b3o4bo198b2o$95bobo194b3o5b3o146b3o5b
3o194bobo$95bo196bo10b3o140b3o10bo196bo$303b3o140b3o$112bo190b3o140b3o
190bo$111bo528bo$111b3o524b3o4$104b2o540b2o$103bob2o538b2obo$103bo544b
o$104bo542bo$100b2o548b2o$100b2o548b2o$104bo542bo$103bo544bo$103bob2o
538b2obo$104b2o540b2o4$111b3o524b3o$111bo528bo$112bo190b3o140b3o190bo$
303b3o140b3o$95bo196bo10b3o140b3o10bo196bo$95bobo194b3o5b3o146b3o5b3o
194bobo$95b2o198bo4b3o146b3o4bo198b2o$294b2o4b3o146b3o4b2o$295b2o158b
2o$296b2o156b2o$121b3o172b3o154b3o172b3o$121bo170b2o164b2o170bo$122bo
169bo2bo160bo2bo169bo$296bo29bo98bo29bo$85bo207bo4bo154bo4bo207bo$85bo
bo206bo3bo25b3obo94bob3o25bo3bo206bobo$85b2o210b2o15bo8bob2o98b2obo8bo
15b2o210b2o$314b3o6b2obo98bob2o6b3o$317bo3bob3o100b3obo3bo$271b2o43b2o
116b2o43b2o$131b3o137b2obo48bo104bo48bob2o137b3o$131bo143bo43bo112bo
43bo143bo$132bo139bo14b2o29bobo110bobo29b2o14bo139bo$273bob2o11b2o24b
2o2b2o112b2o2b2o24b2o11b2obo$75bo199b2o10bo20bo5b2o120b2o5bo20bo10b2o
199bo$75bobo228bobo134bobo228bobo$75b2o202bo27b2o8bo116bo8b2o27bo202b
2o$278bobo36b2o114b2o36bobo$279b2o35bobo114bobo35b2o$275b2o198b2o$141b
3o130bobo198bobo130b3o$141bo132bo5b2o188b2o5bo132bo$142bo130b2o5b2o5b
3o172b3o5b2o5b2o130bo$287bo21b2o16bo96bo16b2o21bo$65bo222bo20b2o2b2o
13bo94bo13b2o2b2o20bo222bo$65bobo245bobo10b3o94b3o10bobo245bobo$65b2o
247bo122bo247b2o$317b3o112b3o$311b2o3bo118bo3b2o$312bo3bo3bo110bo3bo3b
o$151b3o155b3o4bo2bobo108bobo2bo4b3o155b3o$151bo157bo8bobo2bo104bo2bob
o8bo157bo$152bo144b3o19bo3bo28b2o44b2o28bo3bo19b3o144bo$297bo25bo13bo
18bo38bo18bo13bo25bo$55bo242bo21b3o15bo12b2o2bobo36bobo2b2o12bo15b3o
21bo242bo$55bobo221bo56b3o11bo2b3obobo32bobob3o2bo11b3o56bo221bobo$55b
2o221bobo70b6o2bo32bo2b6o70bobo221b2o$230b2o39b2o6bo72b2ob2o38b2ob2o
72bo6b2o39b2o$231bo38bobo61bo14bo2b6o36b6o2bo14bo61bobo38bo$231bobo36b
obob2ob5o9bo57bobob3o2bo34bo2b3obobo57bo9b5ob2obobo36bobo$161b3o68b2o
35b2obo2bobo3bo8bobo39bob3o14bobo2b2o36b2o2bobo14b3obo39bobo8bo3bobo2b
ob2o35b2o68b3o$161bo106bo4bobobobo10bobo41b2obo14bo46bo14bob2o41bobo
10bobobobo4bo106bo$162bo104bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17b2o
38b2o17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo104bo$267bobobo3b3o5bo3bo3b
o2bo12bo18b3o6b3obo7bo56bo7bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo$45bo
222bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo18bo54bo18bo6bo13bo7b2ob2o2bo2b
2obo2b7o4bo4bo222bo$45bobo221b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo8b3o54b
3o8bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o221bobo$45b2o192b3o43b3o7b3obobo2b
o15b3obo102bob3o15bo2bobob3o7b3o43b3o192b2o$239bo31b2o2b2o7bo4bo10bob
3o16bo3bo10bo78bo10bo3bo16b3obo10bo4bo7b2o2b2o31bo$240bo30b2o2b2o6bob
5o10bo4b2o15bo3bo9b3o74b3o9bo3bo15b2o4bo10b5obo6b2o2b2o30bo$283bo6bo9b
5o2bo15bob3o7bobobo72bobobo7b3obo15bo2b5o9bo6bo$171b3o108b2o3b3o7b3o5b
o2bo15b3o8bo3bo11bo48bo11bo3bo8b3o15bo2bo5b3o7b3o3b2o108b3o$171bo115bo
9b3ob4o4bo15bo7b2o5b2o8b2o48b2o8b2o5b2o7bo15bo4b4ob3o9bo115bo$172bo
124b2o5bob2obo7b3o12bo4bo4bo7bobo46bobo7bo4bo4bo12b3o7bob2obo5b2o124bo
$300bobobob4obo5bo13b2o3bobo2b3o64b3o2bobo3b2o13bo5bob4obobobo$35bo
268bobobo3bo5bo12bo5bo4bo66bo4bo5bo12bo5bo3bobobo268bo$35bobo264b2ob2o
bobobo17bo9b2o68b2o9bo17bobobob2ob2o264bobo$35b2o212b3o46bo5bo3b2o2b2o
15b2o8bo72bo8b2o15b2o2b2o3bo5bo46b3o212b2o$249bo47b3o5bobo21bo8b2o72b
2o8bo21bobo5b3o47bo$250bo45b3obo5b2o19b2o9bo74bo9b2o19b2o5bob3o45bo$
231bo65bo3bo10bo13bo4bo5bo12bo50bo12bo5bo4bo13bo10bo3bo65bo$51b2o128b
3o46bobo57bo7bo3bo9b3o10b3o2bobo3b2o13bo9bo28bo9bo13b2o3bobo2b3o10b3o
9bo3bo7bo57bobo46b3o128b2o$181bo41b2o6bo58b3o6bob3o7bobobo10bo4bo4bo
12b3o8b2o28b2o8b3o12bo4bo4bo10bobobo7b3obo6b3o58bo6b2o41bo$50bo3bo127b
o39bobo61bo6bo6b3o8bo3bo11b2o5b2o7bo16bobo26bobo16bo7b2o5b2o11bo3bo8b
3o6bo6bo61bobo39bo127bo3bo$49bo4bo167bobob2ob5o9bo48b2o7bo7b2o5b2o11bo
3bo8b3o62b3o8bo3bo11b2o5b2o7bo7b2o48bo9b5ob2obobo167bo4bo$25bo13bo8bob
obo168b2obo2bobo3bo8bobo39bob3o19bo4bo4bo10bobobo7b3obo60bob3o7bobobo
10bo4bo4bo19b3obo39bobo8bo3bobo2bob2o168bobobo8bo13bo$25bobo11b3o5bobo
bo168bo4bobobobo10bobo41b2obo17b2o3bobo2b3o10b3o9bo3bo58bo3bo9b3o10b3o
2bobo3b2o17bob2o41bobo10bobobobo4bo168bobobo5b3o11bobo$25b2o15bo2bo4bo
168bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17bo5bo4bo13bo10bo3bo56bo3bo10b
o13bo4bo5bo17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo168bo4bo2bo15b2o$41b
2o2bo3bo40b2o127bobobo3b3o5bo3bo3bo2bo12bo18b3o6b3obo14bo9b2o26bob3o
26b2o26b3obo26b2o9bo14bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo127b2o40bo
3bo2b2o$88bob2o128bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo23b2o8bo15bo7b2o
4b3o27b2o27b3o4b2o7bo15bo8b2o23bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo128b
2obo$44bo2b2o29bo8bo133b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo15bo8b2o23bo6b
o11b2o32b2o11bo6bo23b2o8bo15bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o133bo8bo
29b2o2bo$43bobo32b3o9bo100b3o43b3o7b3obobo2bo15b3obo26b2o9bo14bob3o6b
3o15bo12bo8bo12bo15b3o6b3obo14bo9b2o26bob3o15bo2bobob3o7b3o43b3o100bo
9b3o32bobo$39b2o2b2o36bo4b2obo101bo31b2o2b2o7bo4bo10bob3o16bo3bo10bo
13bo4bo5bo17b2obo7bo16b3o8b2o8b2o8b3o16bo7bob2o17bo5bo4bo13bo10bo3bo
16b3obo10bo4bo7b2o2b2o31bo101bob2o4bo36b2o2b2o$39b2o39b2o4b2o104bo30b
2o2b2o6bob5o10bo4b2o15bo3bo9b3o10b3o2bobo3b2o17bob2o26bo8bobo6bobo8bo
26b2obo17b2o3bobo2b3o10b3o9bo3bo15b2o4bo10b5obo6b2o2b2o30bo104b2o4b2o
39b2o$3b2o5b2o223bo6bo9b5o2bo15bob3o7bobobo10bo4bo4bo19b3obo78bob3o19b
o4bo4bo10bobobo7b3obo15bo2b5o9bo6bo223b2o5b2o$4bo5b2o3bo67bo150b2o3b3o
7b3o5bo2bo15b3o8bo3bo11b2o5b2o7bo7b2o94b2o7bo7b2o5b2o11bo3bo8b3o15bo2b
o5b3o7b3o3b2o150bo67bo3b2o5bo$4bobo8bobo64bobo154bo9b3ob4o4bo15bo7b2o
5b2o11bo3bo8b3o6bo6bo82bo6bo6b3o8bo3bo11b2o5b2o7bo15bo4b4ob3o9bo154bob
o64bobo8bobo$5b2o8b2o61b2o2b2o165b2o5bob2obo7b3o12bo4bo4bo10bobobo7b3o
bo6b3o90b3o6bob3o7bobobo10bo4bo4bo12b3o7bob2obo5b2o165b2o2b2o61b2o8b2o
$9b2o28b3o36b2o172bobobob4obo5bo13b2o3bobo2b3o10b3o9bo3bo7bo36b2o14b2o
36bo7bo3bo9b3o10b3o2bobo3b2o13bo5bob4obobobo172b2o36b3o28b2o$8bobo30bo
214bobobo3bo5bo12bo5bo4bo13bo10bo3bo44b2o12b2o44bo3bo10bo13bo4bo5bo12b
o5bo3bobobo214bo30bobo$9bo30bo8bo204b2ob2obobobo17bo9b2o26bob3o42bo16b
o42b3obo26b2o9bo17bobobob2ob2o204bo8bo30bo$5bo44b2o149b3o46bo5bo3b2o2b
2o15b2o8bo15bo7b2o4b3o104b3o4b2o7bo15bo8b2o15b2o2b2o3bo5bo46b3o149b2o
44bo$4bobo42b2o28b2o120bo47b3o5bobo21bo8b2o23bo6bo106bo6bo23b2o8bo21bo
bo5b3o47bo120b2o28b2o42bobo$3bo3bo70bobo121bo45b3obo5b2o19b2o9bo14bob
3o6b3o114b3o6b3obo14bo9b2o19b2o5bob3o45bo121bobo70bo3bo$2bo3bo73bo102b
o65bo3bo10bo13bo4bo5bo17b2obo7bo114bo7bob2o17bo5bo4bo13bo10bo3bo65bo
102bo73bo3bo$bo3bo13bobo160bobo57bo7bo3bo9b3o10b3o2bobo3b2o17bob2o130b
2obo17b2o3bobo2b3o10b3o9bo3bo7bo57bobo160bobo13bo3bo$o3bo15b2o66bobo
84b2o6bo58b3o6bob3o7bobobo10bo4bo4bo19b3obo126bob3o19bo4bo4bo10bobobo
7b3obo6b3o58bo6b2o84bobo66b2o15bo3bo$bobo16bo68b2o83bobo61bo6bo6b3o8bo
3bo11b2o5b2o7bo7b2o142b2o7bo7b2o5b2o11bo3bo8b3o6bo6bo61bobo83b2o68bo
16bobo$2bo26b3o57bo84bobob2ob5o9bo48b2o7bo7b2o5b2o11bo3bo8b3o6bo6bo46b
2o34b2o46bo6bo6b3o8bo3bo11b2o5b2o7bo7b2o48bo9b5ob2obobo84bo57b3o26bo$
31bo141b2obo2bobo3bo8bobo39bob3o19bo4bo4bo10bobobo7b3obo6b3o51b2o32b2o
51b3o6bob3o7bobobo10bo4bo4bo19b3obo39bobo8bo3bobo2bob2o141bo$30bo28bo
112bo4bobobobo10bobo41b2obo17b2o3bobo2b3o10b3o9bo3bo7bo50bo36bo50bo7bo
3bo9b3o10b3o2bobo3b2o17bob2o41bobo10bobobobo4bo112bo28bo$60b2o109bobob
obo3b3obo7b2ob2o13b3o16bo7bob2o17bo5bo4bo13bo10bo3bo152bo3bo10bo13bo4b
o5bo17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo109b2o$59b2o8b2o100bobobo3b
3o5bo3bo3bo2bo12bo18b3o6b3obo14bo9b2o19b2o5bob3o150b3obo5b2o19b2o9bo
14bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo100b2o8b2o$68bobo101bo4bo4b7o2b
ob2o2bo2b2ob2o7bo13bo6bo23b2o8bo21bobo5b3o152b3o5bobo21bo8b2o23bo6bo
13bo7b2ob2o2bo2b2obo2b7o4bo4bo101bobo$22b2o46bo102b10o3b4o3b2o2bo4b2ob
o19b3o4b2o7bo15bo8b2o15b2o2b2o3bo5bo154bo5bo3b2o2b2o15b2o8bo15bo7b2o4b
3o19bob2o4bo2b2o3b4o3b10o102bo46b2o$22b2o2b2o161b3o7b3obobo2bo15b3obo
26b2o9bo17bobobob2ob2o162b2ob2obobobo17bo9b2o26bob3o15bo2bobob3o7b3o
161b2o2b2o$26bobo69bobo74b2o2b2o7bo4bo10bob3o16bo3bo10bo13bo4bo5bo12bo
5bo3bobobo166bobobo3bo5bo12bo5bo4bo13bo10bo3bo16b3obo10bo4bo7b2o2b2o
74bobo69bobo$27bo71b2o74b2o2b2o6bob5o10bo4b2o15bo3bo9b3o10b3o2bobo3b2o
13bo5bob4obobobo158bobobob4obo5bo13b2o3bobo2b3o10b3o9bo3bo15b2o4bo10b
5obo6b2o2b2o74b2o71bo$31bo67bo87bo6bo9b5o2bo15bob3o7bobobo10bo4bo4bo
12b3o7bob2obo5b2o47b2o54b2o47b2o5bob2obo7b3o12bo4bo4bo10bobobo7b3obo
15bo2b5o9bo6bo87bo67bo$24b2o4b3o28b2o123b2o3b3o7b3o5bo2bo15b3o8bo3bo
11b2o5b2o7bo15bo4b4ob3o9bo38b2o52b2o38bo9b3ob4o4bo15bo7b2o5b2o11bo3bo
8b3o15bo2bo5b3o7b3o3b2o123b2o28b3o4b2o$25bo3b3obo27b2o2b2o124bo9b3ob4o
4bo15bo7b2o5b2o11bo3bo8b3o15bo2bo5b3o7b3o3b2o32bo56bo32b2o3b3o7b3o5bo
2bo15b3o8bo3bo11b2o5b2o7bo15bo4b4ob3o9bo124b2o2b2o27bob3o3bo$22b3o5bo
3bo30bobo133b2o5bob2obo7b3o12bo4bo4bo10bobobo7b3obo15bo2b5o9bo6bo124bo
6bo9b5o2bo15bob3o7bobobo10bo4bo4bo12b3o7bob2obo5b2o133bobo30bo3bo5b3o$
22bo8bo3bo30bo3bo133bobobob4obo5bo13b2o3bobo2b3o10b3o9bo3bo15b2o4bo10b
5obo6b2o2b2o100b2o2b2o6bob5o10bo4b2o15bo3bo9b3o10b3o2bobo3b2o13bo5bob
4obobobo133bo3bo30bo3bo8bo$32bob3o32b2o137bobobo3bo5bo12bo5bo4bo13bo
10bo3bo16b3obo10bo4bo7b2o2b2o100b2o2b2o7bo4bo10bob3o16bo3bo10bo13bo4bo
5bo12bo5bo3bobobo137b2o32b3obo$33b3o27b2o3bob2o134b2ob2obobobo17bo9b2o
26bob3o15bo2bobob3o7b3o128b3o7b3obobo2bo15b3obo26b2o9bo17bobobob2ob2o
134b2obo3b2o27b3o$34bo29bo2b3o2bo129bo5bo3b2o2b2o15b2o8bo15bo7b2o4b3o
19bob2o4bo2b2o3b4o3b10o96b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo15bo8b2o15b
2o2b2o3bo5bo129bo2b3o2bo29bo$61b3o5bobobo34bobo90b3o5bobo21bo8b2o23bo
6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo94bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo
23b2o8bo21bobo5b3o90bobo34bobobo5b3o$61bo8bobobo34b2o89b3obo5b2o19b2o
9bo14bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo92bobobo3b3o5bo3bo3bo2bo12bo
18b3o6b3obo14bo9b2o19b2o5bob3o89b2o34bobobo8bo$71bo2b3o32bo91bo3bo10bo
13bo4bo5bo17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo7b2o74b2o7bobobobo3b3o
bo7b2ob2o13b3o16bo7bob2o17bo5bo4bo13bo10bo3bo91bo32b3o2bo$72b2obo118bo
7bo3bo9b3o10b3o2bobo3b2o17bob2o41bobo10bobobobo4bo9b2o72b2o9bo4bobobob
o10bobo41b2obo17b2o3bobo2b3o10b3o9bo3bo7bo118bob2o$73b2o119b3o6bob3o7b
obobo10bo4bo4bo19b3obo39bobo8bo3bobo2bob2o9bo76bo9b2obo2bobo3bo8bobo
39bob3o19bo4bo4bo10bobobo7b3obo6b3o119b2o$73bo116bo6bo6b3o8bo3bo11b2o
5b2o7bo7b2o48bo9b5ob2obobo98bobob2ob5o9bo48b2o7bo7b2o5b2o11bo3bo8b3o6b
o6bo116bo$196b2o7bo7b2o5b2o11bo3bo8b3o6bo6bo61bobo98bobo61bo6bo6b3o8bo
3bo11b2o5b2o7bo7b2o$188bob3o19bo4bo4bo10bobobo7b3obo6b3o58bo6b2o100b2o
6bo58b3o6bob3o7bobobo10bo4bo4bo19b3obo$190b2obo17b2o3bobo2b3o10b3o9bo
3bo7bo57bobo114bobo57bo7bo3bo9b3o10b3o2bobo3b2o17bob2o$182bo7bob2o17bo
5bo4bo13bo10bo3bo65bo116bo65bo3bo10bo13bo4bo5bo17b2obo7bo$118bobo61b3o
6b3obo14bo9b2o19b2o5bob3o45bo154bo45b3obo5b2o19b2o9bo14bob3o6b3o61bobo
$119b2o57bo6bo23b2o8bo21bobo5b3o47bo152bo47b3o5bobo21bo8b2o23bo6bo57b
2o$119bo57b3o4b2o7bo15bo8b2o15b2o2b2o3bo5bo46b3o27b2o94b2o27b3o46bo5bo
3b2o2b2o15b2o8bo15bo7b2o4b3o57bo$176b3obo26b2o9bo17bobobob2ob2o81b2o
92b2o81b2ob2obobobo17bo9b2o26bob3o$177bo3bo10bo13bo4bo5bo12bo5bo3bobob
o82bo96bo82bobobo3bo5bo12bo5bo4bo13bo10bo3bo$170bo7bo3bo9b3o10b3o2bobo
3b2o13bo5bob4obobobo254bobobob4obo5bo13b2o3bobo2b3o10b3o9bo3bo7bo$170b
3o6bob3o7bobobo10bo4bo4bo12b3o7bob2obo5b2o248b2o5bob2obo7b3o12bo4bo4bo
10bobobo7b3obo6b3o$166bo6bo6b3o8bo3bo11b2o5b2o7bo15bo4b4ob3o9bo228bo9b
3ob4o4bo15bo7b2o5b2o11bo3bo8b3o6bo6bo$172b2o7bo7b2o5b2o11bo3bo8b3o15bo
2bo5b3o7b3o3b2o218b2o3b3o7b3o5bo2bo15b3o8bo3bo11b2o5b2o7bo7b2o$164bob
3o19bo4bo4bo10bobobo7b3obo15bo2b5o9bo6bo220bo6bo9b5o2bo15bob3o7bobobo
10bo4bo4bo19b3obo$128bobo8bo26b2obo17b2o3bobo2b3o10b3o9bo3bo15b2o4bo
10b5obo6b2o2b2o30bo134bo30b2o2b2o6bob5o10bo4b2o15bo3bo9b3o10b3o2bobo3b
2o17bob2o26bo8bobo$129b2o8b3o16bo7bob2o17bo5bo4bo13bo10bo3bo16b3obo10b
o4bo7b2o2b2o31bo132bo31b2o2b2o7bo4bo10bob3o16bo3bo10bo13bo4bo5bo17b2ob
o7bo16b3o8b2o$129bo12bo15b3o6b3obo14bo9b2o26bob3o15bo2bobob3o7b3o43b3o
7b2o114b2o7b3o43b3o7b3obobo2bo15b3obo26b2o9bo14bob3o6b3o15bo12bo$141b
2o11bo6bo23b2o8bo15bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o38b2o112b2o38b10o
3b4o3b2o2bo4b2obo19b3o4b2o7bo15bo8b2o23bo6bo11b2o$153b3o4b2o7bo15bo8b
2o23bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo36bo116bo36bo4bo4b7o2bob2o2bo2b
2ob2o7bo13bo6bo23b2o8bo15bo7b2o4b3o$152b3obo26b2o9bo14bob3o6b3o18bo12b
o2bo3bo3bo5b3o3bobobo188bobobo3b3o5bo3bo3bo2bo12bo18b3o6b3obo14bo9b2o
26bob3o$153bo3bo10bo13bo4bo5bo17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo
188bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17bo5bo4bo13bo10bo3bo$154bo3bo
9b3o10b3o2bobo3b2o17bob2o41bobo10bobobobo4bo190bo4bobobobo10bobo41b2ob
o17b2o3bobo2b3o10b3o9bo3bo$155bob3o7bobobo10bo4bo4bo19b3obo39bobo8bo3b
obo2bob2o192b2obo2bobo3bo8bobo39bob3o19bo4bo4bo10bobobo7b3obo$156b3o8b
o3bo11b2o5b2o7bo7b2o48bo9b5ob2obobo30b2o130b2o30bobob2ob5o9bo48b2o7bo
7b2o5b2o11bo3bo8b3o$138bobo16bo7b2o5b2o11bo3bo8b3o6bo6bo61bobo30b2o2b
2o122b2o2b2o30bobo61bo6bo6b3o8bo3bo11b2o5b2o7bo16bobo$139b2o8b3o12bo4b
o4bo10bobobo7b3obo6b3o58bo6b2o35bobo120bobo35b2o6bo58b3o6bob3o7bobobo
10bo4bo4bo12b3o8b2o$139bo9bo13b2o3bobo2b3o10b3o9bo3bo7bo57bobo43bo2b2o
114b2o2bo43bobo57bo7bo3bo9b3o10b3o2bobo3b2o13bo9bo$150bo12bo5bo4bo13bo
10bo3bo65bo212bo65bo3bo10bo13bo4bo5bo12bo$162bo9b2o19b2o5bob3o45bo60b
2o2bo3bo112bo3bo2b2o60bo45b3obo5b2o19b2o9bo$161b2o8bo21bobo5b3o47bo60b
o2bo4bo110bo4bo2bo60bo47b3o5bobo21bo8b2o$161bo8b2o15b2o2b2o3bo5bo46b3o
57b3o5bobobo108bobobo5b3o57b3o46bo5bo3b2o2b2o15b2o8bo$159b2o9bo17bobob
ob2ob2o110bo8bobobo106bobobo8bo110b2ob2obobobo17bo9b2o$158bo4bo5bo12bo
5bo3bobobo122bo4bo102bo4bo122bobobo3bo5bo12bo5bo4bo$157b3o2bobo3b2o13b
o5bob4obobobo119bo3bo102bo3bo119bobobob4obo5bo13b2o3bobo2b3o$148bobo7b
o4bo4bo12b3o7bob2obo5b2o344b2o5bob2obo7b3o12bo4bo4bo7bobo$149b2o8b2o5b
2o7bo15bo4b4ob3o9bo107b2o106b2o107bo9b3ob4o4bo15bo7b2o5b2o8b2o$149bo
11bo3bo8b3o15bo2bo5b3o7b3o3b2o314b2o3b3o7b3o5bo2bo15b3o8bo3bo11bo$161b
obobo7b3obo15bo2b5o9bo6bo316bo6bo9b5o2bo15bob3o7bobobo$162b3o9bo3bo15b
2o4bo10b5obo6b2o2b2o30bo230bo30b2o2b2o6bob5o10bo4b2o15bo3bo9b3o$164bo
10bo3bo16b3obo10bo4bo7b2o2b2o31bo228bo31b2o2b2o7bo4bo10bob3o16bo3bo10b
o$176bob3o15bo2bobob3o7b3o43b3o228b3o43b3o7b3obobo2bo15b3obo$152b3o8bo
7b2o4b3o19bob2o4bo2b2o3b4o3b10o288b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo8b
3o$152bo18bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo286bo4bo4b7o2bob2o2bo2b2o
b2o7bo13bo6bo18bo$153bo7bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo284bobobo
3b3o5bo3bo3bo2bo12bo18b3o6b3obo7bo$144b2o17b2obo7bo16b3o13b2ob2o7bob3o
3bobobobo284bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17b2o$148bo14bob2o41bo
bo10bobobobo4bo286bo4bobobobo10bobo41b2obo14bo$143b2o2bobo14b3obo39bob
o8bo3bobo2bob2o288b2obo2bobo3bo8bobo39bob3o14bobo2b2o$142bo2b3obobo57b
o9b5ob2obobo290bobob2ob5o9bo57bobob3o2bo$143b6o2bo14bo61bobo39bo210bo
39bobo61bo14bo2b6o$144b2ob2o72bo6b2o41bo208bo41b2o6bo72b2ob2o$141bo2b
6o70bobo46b3o208b3o46bobo70b6o2bo$141bobob3o2bo11b3o56bo308bo56b3o11bo
2b3obobo$143bobo2b2o12bo15b3o21bo346bo21b3o15bo12b2o2bobo$144bo18bo13b
o25bo344bo25bo13bo18bo$147b2o28bo3bo19b3o344b3o19bo3bo28b2o$177bo2bobo
8bo368bo8bobo2bo$179bobo2bo4b3o368b3o4bo2bobo$180bo3bo3bo374bo3bo3bo$
184bo3b2o90bo190bo90b2o3bo$181b3o97bo188bo97b3o$186bo92b3o188b3o92bo$
172b3o10bobo376bobo10b3o$172bo13b2o2b2o20bo326bo20b2o2b2o13bo$173bo16b
2o21bo324bo21b2o16bo$211b3o5b2o5b2o296b2o5b2o5b3o$219b2o5bo298bo5b2o$
224bobo298bobo$224b2o300b2o$182bobo35b2o68bo170bo68b2o35bobo$182b2o36b
obo68bo168bo68bobo36b2o$183bo8b2o27bo67b3o168b3o67bo27b2o8bo$192bobo
362bobo$185b2o5bo20bo10b2o300b2o10bo20bo5b2o$181b2o2b2o24b2o11b2obo
296bob2o11b2o24b2o2b2o$180bobo29b2o14bo294bo14b2o29bobo$181bo43bo300bo
43bo$177bo48bob2o292b2obo48bo$183b2o43b2o292b2o43b2o$175b3obo3bo116bo
150bo116bo3bob3o$174bob2o6b3o114bo148bo114b3o6b2obo$174b2obo8bo15b2o
95b3o148b3o95b2o15bo8bob2o$172bob3o25bo3bo338bo3bo25b3obo$202bo4bo336b
o4bo$174bo29bo342bo29bo$205bo2bo334bo2bo$207b2o334b2o$202b3o342b3o$
203b2o342b2o$204b2o104bo130bo104b2o$198b3o4b2o104bo128bo104b2o4b3o$
198b3o4bo103b3o128b3o103bo4b3o$198b3o5b3o334b3o5b3o$195b3o10bo334bo10b
3o$195b3o356b3o$195b3o356b3o4$320bo110bo$321bo108bo$319b3o108b3o8$330b
o90bo$331bo88bo$329b3o88b3o8$340bo70bo$341bo68bo$339b3o68b3o2$408b2o$
409bo$406b3o$406bo!

It could probably be reduced in size. It might be worthwhile to reduce the size of the period-5 sparker first (so that adjacent glider streams can be released).

[dvgrn]

Here's a list of specific incomplete patterns from an old (2008) open-problems list:

• - p7 mono sparker that can perform the TL push demonstrated here:
  EDIT: done -- see below.

  Code: Select all

  x = 19, y = 14, rule = B3/S23
  bboo3boo$bobbobobbo$bobooboobo$oobbobobboo$bbobobobobbo$bbooboobob3o4b
  oo$oo10bo3b3o$boboobobo3bo4boo$bobbo7bo$bbo3bobo3bo$3b3obooboo$5bo4bo$
  6b3obo$8boo!

  - A p36 (16+20) traffic light hassler oscillator. (Replace the figure-8s
  in this pattern with something whose period is a factor of 36:
  EDIT: done -- see below.

  Code: Select all

  x = 32, y = 35, rule = B3/S23
  17boo5boo$4boo11boo5boboboo$26bobobo$bbo3bo8b4o3b5obobo$bbo4bo7bo3bobo
  bo3booboo$4bobobo8bobobo3bo5bo$5bobobo6bobboo4b3ob3o$6bo4bo4b3o7boobo$
  7bo3bo$bbobo$5bobboo$bobbo$obobo5bo$obbo5bobo$boo5bo3bo9boo$9bobo8bobb
  o$10bo9b3o$$10bo9b3o$9bobo8bobbo$boo5bo3bo9boo$obbo5bobo$obobo5bo$bobb
  o$5bobboo$bbobo$7bo3bo$6bo4bo4b3o7boobo$5bobobo6bobboo4b3ob3o$4bobobo
  8bobobo3bo5bo$bbo4bo7bo3bobobo3booboo$bbo3bo8b4o3b5obobo$26bobobo$4boo
  11boo5boboboo$17boo5boo!

  - A p6 fencepost to complete this wickstretcher:
  EDIT: done -- see below.

  Code: Select all

  x = 44, y = 44, rule = B3/S23
  32bo7bo$31boo5boobo$31bobo3boobbo$35boobbo$33b5o$25b3oboob3o$20b3obbo
  bboboboo$20bo5b3oboo$21bo$17bo6boo$16boo4bobo$16bobo3b4o$23bo$19boo$
  19boo$$10boo9bo$9boo9b3o$11bo7bobo$13boo3booboo$6boo5boobbobboo$6bobo
  7b6o$6bo3boo5bobo3b3o$11boo9b3o$9b3o10b3o$5boobbobo10bo3b3o$5bobo17b3o
  $5bobo17b3o$6boo17bo3b3o$5bo22b3o$5b3o20b3o$boo4bo20bo3b3o$oo3boo24b3o
  $bbob3o24b3o$4boo25bo3b3o$3boo29b3o$3boo29b3o$bbobo29bo3b3o$boo34b3o$b
  obo33b3o$o36bo3b3o$boo37b3o$40b3o$40bo!

  - A c/5 orthogonal "spaceship" to complete this wavestretcher. (c/6 diagonal would also work.)
  EDIT: done -- see below.

  Code: Select all

  x = 90, y = 42, rule = B3/S23
  32bo$31boo$31bobo$$26boo5b3o$25boobboob5obooboo$27bobbob3o3boo3booboo$
  29b3obbo8boo3booboo$28bo5bo6boo5boo3booboo$22boo9bo3bo8boo5boo3booboo$
  22bobo3boobbo3bo14boo5boo3booboo$22bo4boobo25boo5boo3booboo$25bobb3ob
  oobo25boo5boo3booboo$14boo9boob3o35boo5boo3booboo$14bobo3bo4bobo43boo
  5boo3booboo$14bo3b3oboo3boo47boo5boo3boo$17boo8boo52boo5boo$20b3o4bo
  58boo$18bo3b3o$17bo6bo$17bobboboo$16boobo$16bobo$15b4o$14bo3boo$13boo
  3boo$13boboobo$13b4obo$11boob3obo$11bobo$10bo$9boobbo$8boo3bo$7boobbo$
  8bobboo$8bobbo$$3o$o9bo$bobb6o$3bo$4boo!

  - More investigation of possible (23,5)c/79 spaceship based on:

  Code: Select all

  x = 59, y = 98, rule = B3/S23
  58bo$56boo$57boo41$32bo$32bobo$32boo15$18bo$16booboo$16booboo$17bob3o$
  16b3o4$17boo$17boo$$16bo$15bobooboo$14boo4boo$14booboo$16bo8$23bo$24bo
  $22b3o10$bbo$oo$boo!

  - 2c/5 terminations for this wave:
  EDIT: One side completed -- see below.

  Code: Select all

  x = 44, y = 20, rule = B3/S23
  oo$bboo$bbooboo$oo5boo$7booboo$5boo5boo$12booboo$10boo5boo$17booboo$
  15boo5boo$22booboo$20boo5boo$27booboo$25boo5boo$32booboo$30boo5boo$37b
  ooboo$35boo5boo$42boo$40boo!

  - An extensible stabilisation for this p2 agar:

  Code: Select all

  x = 43, y = 43, rule = S23/B3
  19booboo$13boo5bobobboo$14bo3bo4bobobbo$14bob3oboobo3boo$15bo5bobbo$
  17b3oboobbo$16boobbobo8boo$10bo4bo3bo5boo3bobbo$9bobo3bo5boo7boobo$7b
  3obo5boo7b3obobboo$6bo6boo7boo4bobbo3bo$6bobobo7boo5bo3bo3boo$7b3o4boo
  5bo3bo$11bo5bo3bo5boo3bo8bo$bboo5boobbo3bo5boo5bobo6b3o$3bo5bo3bo5boo
  5bo3bo3boobbo$bo5bobo5boo5bo3bo9bobbo$boobbobo3boo5bo3bo5boo3bobboobo$
  4bo9bo3bo5boo5bobo3boboo$oboo6bo3bo5boo5bo3bo3bobo4bo$oo3boobobo5boo5b
  o3bo8bobboboo$3b3obbo3boo5bo3bo5boo3bobb3o$oobobbo8bo3bo5boo5boboboo3b
  oo$o4bobo3bo3bo5boo5bo3bo6boobo$bboobo3bobo5boo5bo3bo9bo$3boboobbo3boo
  5bo3bo5boo3bobobboo$3bobbo9bo3bo5boo5bobo5bo$4bobboo3bo3bo5boo5bo3bo5b
  o$b3o6bobo5boo5bo3bobboo5boo$bo8bo3boo5bo3bo5bo$17bo3bo5boo4b3o$8boo3b
  o3bo5boo7bobobo$7bo3bobbo4boo7boo6bo$8boobbob3o7boo5bob3o$9boboo7boo5b
  o3bobo$9bobbo3boo5bo3bo4bo$10boo8bobobboo$17bobboob3o$18bobbo5bo$14boo
  3boboob3obo$14bobbobo4bo3bo$16boobbobo5boo$19booboo!

  - A caterpillar-like c/3 orthogonal spaceship including the following p69 reaction (this ship would be much easier than other caterpillar variants because we have well-developed c/3 technology):

  Code: Select all

  x = 9, y = 14, rule = S23/B3
  7boo$7boo10$bbo$b3o$oobbo!

[skomick]

- A c/5 orthogonal "spaceship" to complete this wavestretcher. (c/6 diagonal would also work.)

c/5 part by Matthias Merzenich, 15 Apr 2011:

Code: Select all

x = 103, y = 75, rule = B3/S23
70bo$68b2ob2o$67b3o$64b2o3bo$64bo3bo2$60bo3b3o$59bobo$58bo2bo$60b2o$
57bo2bo4bo$58b3o2bobo$63b3o$58bob4o$57bo$58bo$55bo2bobo$55b2o$51b2o4bo
$50b3obobo$50bo$52b2o$52b2o2$49b3o$51bo$48bo3bo$48bo4bo$48bo29b2o5b2o
5b2o5b2o$48b5o23bo3bo3bo2bo3bo2bo3bo3bo$76bo3bobob3o5b3obobo3bo$76bo5b
2o2b3ob3o2b2o5bo$46b2o21b2o5b2ob3o15b3ob2o$40bobo3bobo20bobo4bo25bo$
31b2o6b2o2b2o2bo21bobo5bo3bo15bo3bo$30b2o10bobo24bo3b2o3bo2bo15bo2bo$
31bobo9bobo5bo7bob4obo6b2o$26bo4b3o9b2o4b4o4bob3obobobo6bo$25b5ob3o2bo
bob2o2b3ob2o3b4o12bo$25bo2b2o6bo4bo2bo2bo3bo2b2o5bobo3bob2o$35bo3bo4bo
3b4obo3bo4b7o$27b2o2b2ob2o2bo10b2ob2o4bo4bo$35bo28bo$21b3o3bo5b2o18bo$
21bo5bo2bob2o17b2o$22bo3b2obo$25b2o3bobo$13b3o10bo$13bo5b3o2b2o$14bo2b
2ob3ob2o$16bo10bo$17bobob2o4bo$19b2obo$17b2o3bobo$16b2o$18bo$15b2o$14b
3o$13b2obo$12b4obo$17b3o$18b2o$10b3ob2o$9bo3b3o$12b3o$8bobobo$7b4o$7bo
$8b2o$9bo2bo$2o$obo3b3o$o3bo4bo$3b2o$3bo5bo!

[Sokwe]

c/5 part by Matthias Merzenich, 15 Apr 2011

I also found this alternate c/5 part two days later:

Code: Select all

x = 112, y = 50, rule = B3/S23
51b2o5b2o5b2o5b2o$49bo3bo3bo2bo3bo2bo3bo3bo$49bo3bobob3o5b3obobo3bo$
49bo5b2o2b3ob3o2b2o5bo$49b2ob3o15b3ob2o$49bo25bo$50bo3bo15bo3bo$46b2o
3bo2bo15bo2bo$40bobo3bobo$31b2o6b2o2b2o2bo$30b2o10bobo31bo10bo3b3o5b3o
3bo$31bobo9bobo5bo7bob4obo8bo2bo5b2ob5ob2o3b2ob5ob2o$26bo4b3o9b2o4b4o
4bob3obobobo2b2o3bo2bo3bob2obo5bobobobo5bob2obo$25b5ob3o2bobob2o2b3ob
2o3b4o12bobo2bo4bobo3bobo3b5ob5o3bobo3bo$25bo2b2o6bo4bo2bo2bo3bo2b2o5b
obo3bob2o3bo4bo5b3o5b2o3b2o5b3o$35bo3bo4bo3b4obo3bo4b7o10bo2bo2bob3o
13b3obo2bo$27b2o2b2ob2o2bo10b2ob2o4bo4bo9b2obobo5bo23bo$35bo28bo8bo$
21b3o3bo5b2o18bo$21bo5bo2bob2o17b2o$22bo3b2obo$25b2o3bobo$13b3o10bo$
13bo5b3o2b2o$14bo2b2ob3ob2o$16bo10bo$17bobob2o4bo$19b2obo$17b2o3bobo$
16b2o$18bo$15b2o$14b3o$13b2obo$12b4obo$17b3o$18b2o$10b3ob2o$9bo3b3o$
12b3o$8bobobo$7b4o$7bo$8b2o$9bo2bo$2o$obo3b3o$o3bo4bo$3b2o$3bo5bo!

A p6 fencepost to complete this wickstretcher

By Jason Summers and me, January 2013:

Code: Select all

x = 61, y = 61, rule = B3/S23
38b2o$37b2o$39bo$41b2o$40bo$32b2o$32bo2b2o2bo2bo$32bob3o2bo$33bo4bo2bo
$27bo5bo6bo$26b2o5bo2bo$26bobo$33bo$23bo5bob3obo$22b2o4b2o3bo23b2o$22b
obo2b2o2bobobo5b4o11b4o$26bo6bobo4bo4bo9bo2bobo$25b2ob2o10bo3bobo7bobo
2b2o$26bo14bo3bobo5bobo$47bo4b2o$26bo20bo4b3o$24b2o18bo2bo5bobo$14b2o
7bobo19b2o7b2o$13b2o7bo27bo$15bo5bo2b2obo21b3o$17bo3b2obo3bo20b3o$10b
2o4b3obo28b3o$9b2o4bo8bo2b2obo10b2o6b3o$11bo2b2obo7bobo3bo8b4o6bo$13b
2o2bo21bobo2bo$27bo2b2obo5b2o2bobo$13bobo12bobo3bo9bobo2b2o$5b3o5bo32b
2o2b2o$5bo2b3ob5o13bo2b2obo8b3ob3o$7bo23bobo3bo6bobo2b3o$6b2o5bob2o27b
2o3b3o$6b2o2bo22bo2b2obo10bo$bo32bobo3bo$2o6bo$obo3b2o21b2o5bo2b2obo$
4bo4bo6b2o10bobo6bobo3bo3b5o$3bo4bo6bo2bo8b3o$3bo2bo8bo11b2o10bo2b2ob
2ob2o$15bo12bobo9bobo5bo$15bobo3bo7bobo2b2o10bo$16bobo3bo7bo2bobo6bo2b
o$17bo4bo8b4o7bobo$18b4o10b2o6bo$40bob2o$24b4o3bob3o4bobo$23b6o2b6o3bo
$24b4o4b4o4bo$19b2o$18b4o$17bo2bobo$16bobo2b2o$15bobo$14b2o$14b3o$15bo
bo$16b2o!

2c/5 terminations for this wave

One side of the waveguide by Nicolay Beluchenko, November 2008

Code: Select all

x = 64, y = 59, rule = B3/S23
26bo$18bo5b2ob2o$17b3o4b2o2bob2o$16bo5b2ob2o5b2o$16b3o3bob2o6b2ob2o$
18b2o2bo7b2o5b2o$9bo13b3o11b2ob2o$8b3o4b5o5b2o8b2o5b2o$8bo3b2ob4o3bo4b
o14b2ob2o$5b5o4bo7bo4bo12b2o5b2o$3b2ob4o2bo2b2o8b3o19b2ob2o$6bo2b3o13b
2o18b2o5b2o$7bo4bo39b2ob2o$9b6o11b2o22b2o5b2o$4bob3o6bo41b2ob2o$11bo3b
2o38b2o5b2o$4bobo4bo3bo46b2o$3b3o4bo4bo44b2o$3bo6b6o$10bo4bo$10bob2o$
11b2o$4bo6b3o$3b3o2b3o$2b2o2b2o6b2o$3bo2bo3b3ob3o$3bo7bo2b3o$3bo6b2o2b
2o$4b2o$10b2o$10b3o$7b2o3b2o$6bob2o4bo$6b4ob2o2bo$8b3o4bo$6bobob4ob2o$
6bo8b2o$6bobob2ob3o$6bo3bo2bo$5b2obob2o$5b2o3bo$7bob2o$7bo2$5b2o$4b2o$
7bo$2b6ob3o$2o5bo4bo$3o4b2obobo$2o2bob3obo$2bob3o$2b2ob3o2bo$bob2o2bob
o2$6b2o$5b5o$5b2o2bo$8bo!

[Kasuha]

- A p36 (16+20) traffic light hassler oscillator. (Replace the figure-8s
in this pattern with something whose period is a factor of 36:

Here you are. I think it has a lot of improvement potential, though:

Code: Select all

x = 75, y = 43, rule = B3/S23
32b2o7b2o$32bobo5bobo$27b2ob2o2bo5bo2b2ob2o$28bobo3b2o3b2o3bobo$28bo2b
3o2bobo2b3o2bo$26b2obobob2obobob2obobob2o$27bobobo3bo3bo3bobobo$26bo2b
o4bo5bo4bo2bo$26bobob3o9b3obobo$27b2o4b2o5b2o4b2o$29b2obo9bob2o$10b2o
4b2o7b6o13b6o7b2o4b2o$10bobo4bo3b2obo25bob2o3bo4bobo$6b2o4bo3bo3bobobo
bo5b2o7b2o5bobobobo3bo3bo4b2o$6bobo2bob2o2b4o2bobobo4b2o7b2o4bobobo2b
4o2b2obo2bobo$3bo4b4obob2o4bobo2b2obobo11bobob2o2bobo4b2obob4o4bo$3b5o
10b4ob2o2b2obo13bob2o2b2ob4o10b5o$8bo2b2obob3obo3bo2bo2bo13bo2bo2bo3bo
b3obob2o2bo$3b2o2bo2bobobo4bo4bo2bo19bo2bo4bo4bobobo2bo2b2o$3bo2bo7bo
2b2o8bo2bo3bo5bo3bo2bo8b2o2bo7bo2bo$8bobo2b2o3bo3bo2bobo2bo2bobo3bobo
2bo2bobo2bo3bo3b2o2bobo$4bob2obo4b2o2bo3b2obob2o3bo3bobo3bo3b2obob2o3b
o2b2o4bob2obo$2o2bo8b2o2b5o11bobo3bobo11b5o2b2o8bo2b2o$bo3b2o7bo3bobo
13bo5bo13bobo3bo7b2o3bo$bobobo3b2obobob2o39b2obobob2o3bobobo$2b2o2bo2b
ob2obobo41bobob2obo2bo2b2o$5b2o7bobo3b2ob2o25b2ob2o3bobo7b2o$14b2o4b2o
bo2b2o19b2o2bob2o4b2o$23bobobo19bobobo$23bo3bo19bo3bo$24b3o21b3o$26bo
8b2ob2o8bo$24b2o10bobo10b2o$23bo10bobobobo10bo$23b2o9b2o3b2o9b2o$20b2o
bo27bob2o$20bo2bob2o21b2obo2bo$21b3o2b2o19b2o2b3o$24bob2o19b2obo$21b4o
25b4o$21bo4b2o19b2o4bo$22b3obo21bob3o$24b3o21b3o!

[Sokwe]

The T-nosed p4 gives a little more room to work in some cases:

Code: Select all

x = 75, y = 36, rule = B3/S23
32b2o7b2o$32bobo5bobo$27b2ob2o2bo5bo2b2ob2o$28bobo3b2o3b2o3bobo$28bo2b
3o2bobo2b3o2bo$26b2obobob2obobob2obobob2o$27bobobo3bo3bo3bobobo$26bo2b
o4bo5bo4bo2bo$26bobob3o9b3obobo$27b2o4b2o5b2o4b2o$29b2obo9bob2o$10b2o
4b2o7b6o13b6o7b2o4b2o$10bobo4bo3b2obo25bob2o3bo4bobo$6b2o4bo3bo3bobobo
bo5b2o7b2o5bobobobo3bo3bo4b2o$6bobo2bob2o2b4o2bobobo4b2o7b2o4bobobo2b
4o2b2obo2bobo$3bo4b4obob2o4bobo2b2obobo11bobob2o2bobo4b2obob4o4bo$3b5o
10b4ob2o2b2obo13bob2o2b2ob4o10b5o$8bo2b2obob3obo3bo2bo2bo13bo2bo2bo3bo
b3obob2o2bo$3b2o2bo2bobobo4bo4bo2bo19bo2bo4bo4bobobo2bo2b2o$3bo2bo7bo
2b2o8bo2bo3bo5bo3bo2bo8b2o2bo7bo2bo$8bobo2b2o3bo3bo2bobo2bo2bobo3bobo
2bo2bobo2bo3bo3b2o2bobo$4bob2obo4b2o2bo3b2obob2o3bo3bobo3bo3b2obob2o3b
o2b2o4bob2obo$2o2bo8b2o2b5o11bobo3bobo11b5o2b2o8bo2b2o$bo3b2o7bo3bobo
13bo5bo13bobo3bo7b2o3bo$bobobo3b2obobob2o39b2obobob2o3bobobo$2b2o2bo2b
ob2obobo9bo21bo9bobob2obo2bo2b2o$5b2o7bobo8b3o19b3o8bobo7b2o$14b2o9b3o
19b3o9b2o$25bobo19bobo$25b3o19b3o$24b5o17b5o$23bo5bo5b2ob2o5bo5bo$23bo
5bo6bobo6bo5bo$22b2obobob2o3bobobobo3b2obobob2o$21bo2b2ob2o2bo2b2o3b2o
2bo2b2ob2o2bo$21b2o7b2o11b2o7b2o!

[Kasuha]

- p7 mono sparker that can perform the TL push demonstrated here:

Code: Select all

x = 19, y = 14, rule = B3/S23
bboo3boo$bobbobobbo$bobooboobo$oobbobobboo$bbobobobobbo$bbooboobob3o4b
oo$oo10bo3b3o$boboobobo3bo4boo$bobbo7bo$bbo3bobo3bo$3b3obooboo$5bo4bo$
6b3obo$8boo!

Here. I guess it counts as a new p14 oscillator?

Code: Select all

x = 65, y = 19, rule = B3/S23
21b2o19b2o$12b2o7bo21bo7b2o$3bobo4bo2bo2b2o5bo17bo5b2o2bo2bo4bobo$3b2o
bo3b2obobobo4b2o17b2o4bobobob2o3bob2o$6bo6bobo33bobo6bo$b4ob2o2b2obob
2o3bo23bo3b2obob2o2b2ob4o$o3bo4bobobo4b2obo2bob2o9b2obo2bob2o4bobobo4b
o3bo$obo2bob3obo2bo2bobo4bobo11bobo4bobo2bo2bob3obo2bobo$b3obo5b3ob3ob
obob2obo11bob2obobob3ob3o5bob3o$11bo2b2o3bo3bob2o4b2o5b2obo3bo3b2o2bo$
b3obo5b3ob3obobob2obo3b3o5bob2obobob3ob3o5bob3o$obo2bob3obo2bo2bobo4bo
bo4b2o5bobo4bobo2bo2bob3obo2bobo$o3bo4bobobo4b2obo2bob2o9b2obo2bob2o4b
obobo4bo3bo$b4ob2o2b2obob2o3bo23bo3b2obob2o2b2ob4o$6bo6bobo33bobo6bo$
3b2obo3b2obobobo4b2o17b2o4bobobob2o3bob2o$3bobo4bo2bo2b2o5bo17bo5b2o2b
o2bo4bobo$12b2o7bo21bo7b2o$21b2o19b2o!

[Sokwe]

I guess it counts as a new p14 oscillator?

Very nice! It can be extended in the obvious way:

Code: Select all

x = 100, y = 19, rule = B3/S23
21b2o54b2o$12b2o7bo56bo7b2o$3bobo4bo2bo2b2o5bo52bo5b2o2bo2bo4bobo$3b2o
bo3b2obobobo4b2o11b2o5b2o5b2o5b2o5b2o11b2o4bobobob2o3bob2o$6bo6bob2o5b
o12b2o5b2o5b2o5b2o5b2o12bo5b2obo6bo$b4ob2o2b2obobo5b2o54b2o5bobob2o2b
2ob4o$o3bo4bobobo5bob4ob2o4bo6bo6bo6bo6bo6bo4b2ob4obo5bobobo4bo3bo$obo
bob4obob2o3b2o4bobo4bo8bo4bo8bo4bo8bo4bobo4b2o3b2obob4obobobo$b2o9b2o
2b2obob2o3bo4bo8bo4bo8bo4bo8bo4bo3b2obob2o2b2o9b2o$6b2ob2o4bo4bo3b2o5b
o8bo4bo8bo4bo8bo5b2o3bo4bo4b2ob2o$b2o9b2o2b2obob2o3bo5bo6bo6bo6bo6bo6b
o5bo3b2obob2o2b2o9b2o$obobob4obob2o3b2o4bobo46bobo4b2o3b2obob4obobobo$
o3bo4bobobo5bob4ob2o7b2o5b2o5b2o5b2o5b2o7b2ob4obo5bobobo4bo3bo$b4ob2o
2b2obobo5b2o12b2o5b2o5b2o5b2o5b2o12b2o5bobob2o2b2ob4o$6bo6bob2o5bo54bo
5b2obo6bo$3b2obo3b2obobobo4b2o52b2o4bobobob2o3bob2o$3bobo4bo2bo2b2o5bo
52bo5b2o2bo2bo4bobo$12b2o7bo56bo7b2o$21b2o54b2o!

[codeholic]

More investigation of possible (23,5)c/79 spaceship

A caterpillar-like spaceship based on this reaction seems quite plausible. I wonder, if anyone has got a copy of the script and the collision table that were used by Gabriel Nivasch & Co. for building the burning helix for the caterpillar. Another problem is track multiplication.

[codeholic]

I built a naive 5/4 track multiplication as a proof of concept. One could probably find something more effective.

Code: Select all

x = 258, y = 379, rule = B3/S23
249bobo$206bo42b2o$204b2o44bo$205b2o4$219bobo$219b2o$220bo15$257bo$
255b2o$256b2o16$225bo$224bo$180bo43b3o$180bobo$180b2o3$195bo$194bo$
194b3o16$231bo$231bobo$231b2o16$201bo$199b2o$155bobo42b2o$155b2o$156bo
3$171bo$169b2o$170b2o16$206bobo$206b2o$207bo16$175bo$131bo43bobo$130bo
44b2o$130b3o4$145bo$145bobo$145b2o15$182bo$181bo$181b3o17$150bobo$107b
o42b2o$105b2o44bo$106b2o4$120bobo$120b2o$121bo15$158bo$156b2o$157b2o
16$126bo$125bo$81bo43b3o$81bobo$81b2o3$96bo$95bo$95b3o16$132bo$132bobo
$132b2o16$102bo$100b2o$56bobo42b2o$56b2o$57bo3$72bo$70b2o$71b2o$45bobo
$45bo2bo$44bo3b2o$44bo2$44bo2b3o$44b2o$46b3o$46b3o7$107bobo$107b2o$
108bo15$54bo$55b2o19bo$54b2o20bobo$76b2o5$46bo$46bobo$46b2o$64b3o$25bo
41bo$25bobo36bo2bo$25b2o38b2o$40bo24b2o$40b2o22bo2bo$42bo21bo$40b2o24b
2o$39bobo$40bo$38bobo$36bo$36bobo2$83bo$82bo$80b2ob2o$79b5o$78b2o2bo$
78bob4o$78bo4bo$78bo2b2o$80b2o2$60b2o14bo$59bobo14bobo$60bo15b2o11$47b
o$48bo$46b3o3$46bo$44b2o$obo42b2o$2o$bo$55b2o$54bobo$16bo38bo$14b2o$
15b2o4$89bo$87bobo$54b2o32b2o$55b2o$54bo$69b2o$68bobo$70bo$84bo$84b2o$
83bobo2$51bobo$51b2o$52bo!

EDIT: It seems feasible to me to use just 2 tracks instead of 4, having put Herschels from tracks 1-2 and 3-4 on the same track pairwise and probably using more Herschels in the middle to adjust the track period.

EDIT: I opened a follow-up topic.

[knightlife]

Small glider duplicator needs a catalyst instead of a ship:

Code: Select all

x = 19, y = 15, rule = B3/S23
6bo10b2o$7b2o8bo$6b2o7bobo$15b2o2$2o$2o2$9b2o$9b2o3$10b2o$10bobo$11b2o
!

[calcyman]

Can Bellman find a stabilisation for this beautiful period-41 wick by Achim Flammenkamp?

Code: Select all

x = 397, y = 21, rule = B3/S23
6bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo$6bo31bo31bo31bo31b
o31bo31bo31bo31bo31bo31bo31bo31bo$6bo31bo31bo31bo31bo31bo31bo31bo31bo
31bo31bo31bo31bo5$2bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo
7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo$2ob2o3b2ob2o19b2ob2o3b2ob2o19b
2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob
2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o
3b2ob2o19b2ob2o3b2ob2o$2bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7b
o23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo2$2bo7bo23bo7bo23bo7bo23bo
7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo$2ob
2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o
19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b
2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o$2bo7bo23bo7bo23bo7b
o23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7b
o5$6bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo$6bo31bo31bo31bo
31bo31bo31bo31bo31bo31bo31bo31bo31bo$6bo31bo31bo31bo31bo31bo31bo31bo
31bo31bo31bo31bo31bo!

That would leave just three unknown oscillator periods, namely 19, 23 and 38.

[Freywa]

Can Bellman find a stabilisation for this beautiful period-41 wick by Achim Flammenkamp?

I have already tested out this wick and there's no solution! Please concentrate on glider syntheses instead.

[MikeP]

I have already tested out this wick and there's no solution!

That's a bold statement. I doubt Bellman could prove this in a reasonable time. I imagine you had max-live and max-active parameters set, which will have excluded most of the search space from consideration; all you've proved is that there's no solution which is consistent with the constraints you placed on the search.

[Freywa]

p41-critical.png (1.63 KiB) Viewed 87171 times

Here's an argument lending weight to the idea that the p41 wick (it's also in the Summers collection, by the way) has no stable stabilisation.

This wick operates via a suppression mechanism: for each unit in it, four cells that would normally become alive at generation 26 (relative to the phase Goucher posted) remain dead because of the adjacent units, and this keeps things going. I've highlighted this above at the critical moment. Now suppose there exists a stable catalyst that acts as a fencepost; because it prevents said cells from becoming alive and does not cause the birth of neighbouring cells that destroy the oscillator, it must have a certain configuration of cells two rows away from the above highlighted unit's left edge (call this E). But then over the next few generations, more patterns of cells turn up at E, and no configuration by itself can ensure the unit returns to its original "four pre-TLs" state. Thus the fencepost must be dynamic. Bellman can't find dynamic things, only still-life catalysts.

[calcyman]

That proof can't work for fundamental reasons. In particular, your proof would theoretically generalise to a similar reaction, which operates at p1000041 instead of p41. However, it is trivial (by which I mean it can be done) to construct a set of bait still lifes, which (when impacted by the reaction) release gliders, which then pass through a complicated network of stable Herschel tracks to produce more gliders, which are aimed at the reaction and restore it.

And that arrangement of still lifes is a stable catalyst, conceptually no different from those found by Bellman (other than being orders of magnitude larger).

[Kasuha]

You don't have to make the reaction go exactly the same way, you only need to make it end up at the beginning of the cycle. For instance this sacrificial eater works for exactly one cycle so technically all we need is to replace the two blocks with something that will reappear at the place again:

Code: Select all

x = 121, y = 27, rule = B3/S23
118bo$116b3o$115bo$6bo31bo31bo31bo12b2o$6bo31bo31bo31bo$6bo31bo31bo31b
o2$119b2o$119b2o2$2bo7bo23bo7bo23bo7bo23bo7bo$2ob2o3b2ob2o19b2ob2o3b2o
b2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o$2bo7bo23bo7bo23bo7bo23bo7bo2$2bo7bo
23bo7bo23bo7bo23bo7bo$2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob
2o3b2ob2o$2bo7bo23bo7bo23bo7bo23bo7bo2$119b2o$119b2o2$6bo31bo31bo31bo$
6bo31bo31bo31bo$6bo31bo31bo31bo12b2o$115bo$116b3o$118bo!

But of course if the Bellman search was done exhaustively then there likely is no such thing.

[Freywa]

That works, in fact. The Summers collection has a set of "supported oscillator" patterns which require some gliders to keep going. The p41 wick is in there, and I've been analysing how the interaction between oscillator core and glider happens. I am not saying that a catalyst does not exist at all, but rather that it would have to be fundamentally different from "normal" Bellman catalysts.

On a side note, I've also been investigating on how to use JavaLifeSearch to construct glider syntheses.

[Sphenocorona]

If you place an object like a tub slightly behind and directly inbetween the two blocks in Kashua's design, it becomes possible to turn the blocks into more permanent eater 1's or eater 2's, like so:

Code: Select all

x = 123, y = 27, rule = B3/S23
118bo$116b3o$115bo$6bo31bo31bo31bo12b2o$6bo31bo31bo31bo$6bo31bo31bo31b
o18b2o$121bo$119bobo$119b2o2$2bo7bo23bo7bo23bo7bo23bo7bo$2ob2o3b2ob2o
19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o$2bo7bo23bo7bo23bo7bo23bo
7bo14bo$120bobo$2bo7bo23bo7bo23bo7bo23bo7bo14bo$2ob2o3b2ob2o19b2ob2o3b
2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o$2bo7bo23bo7bo23bo7bo23bo7bo2$119b
2o$119bobo$121bo$6bo31bo31bo31bo18b2o$6bo31bo31bo31bo$6bo31bo31bo31bo
12b2o$115bo$116b3o$118bo!

Alternately, replacing the blocks with hives results in a similar effect to using blocks, except that there is also some leftover reaction that may be able to be manipulated back into hives again:

Code: Select all

x = 128, y = 27, rule = B3/S23
118bo$116b3o$115bo$6bo31bo31bo31bo12b2o$6bo31bo31bo31bo$6bo31bo31bo31b
o2$120b2o$119bo2bo$120b2o$2bo7bo23bo7bo23bo7bo23bo7bo19b2o$2ob2o3b2ob
2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o17b2o$2bo7bo23bo7bo23bo
7bo23bo7bo2$2bo7bo23bo7bo23bo7bo23bo7bo$2ob2o3b2ob2o19b2ob2o3b2ob2o19b
2ob2o3b2ob2o19b2ob2o3b2ob2o17b2o$2bo7bo23bo7bo23bo7bo23bo7bo19b2o$120b
2o$119bo2bo$120b2o2$6bo31bo31bo31bo$6bo31bo31bo31bo$6bo31bo31bo31bo12b
2o$115bo$116b3o$118bo!

Here I added two blocks which quickly turn the reaction into gliders; without them it produces two blinkers. Maybe a Bellman search might find a catalyst to restore the hives?

[Freywa]

Here's the Bellman input file I concocted for finding the p41. If anyone uses this and manages to find the fencepost, please credit me and Playle as contributors.

Code: Select all

#S first-encounter 4
#S last-encounter 34
#S repair-interval 31
#P 2 2
.............??????????????????
.............??????????????????
.............??????????????????
.............??????????????????
.............??????????????????
.............??????????????????
........@..........????????????
.@.......@.....@@..????????????
.@...@@..@....@..@.????????????
@@....@....@@..@@..????????????
........@@..@......????????????
..@........@@......????????????
..@.@@@@@@@........????????????
...................????????????
..@.@@@@@@@........????????????
..@........@@......????????????
........@@..@......????????????
@@....@....@@..@@..????????????
.@...@@..@....@..@.????????????
.@.......@.....@@..????????????
........@..........????????????
.............??????????????????
.............??????????????????
.............??????????????????
.............??????????????????
.............??????????????????
.............??????????????????
#F 35 15 8
......
..**..
.*..*.
..**..
......
??????
??????
??????
??????
??????
??????
??????
......
..**..
.*..*.
..**..
......