## Incomplete search patterns - try to complete

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

### Re: Incomplete search patterns - try to complete

calcyman wrote: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)!
`x = 9, y = 12, rule = B3/S237b2o\$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:
`x = 66, y = 59, rule = B3/S23bo\$2b2o\$b2o10\$2o\$bo\$bobo\$2b2o11\$36bo\$35bobo\$35bobo\$36bo3\$20b3o\$20bo\$19b3o6\$16bo\$16bo28b2o\$14b3o9b2o17b2o\$14bo11b2o5\$56b2o\$55bo2bo2b2o\$55bobo4bo\$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?
knightlife

Posts: 566
Joined: May 31st, 2009, 12:08 am

### Re: Incomplete search patterns - try to complete

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

`x = 126, y = 109, rule = B3/S2390bo\$88boo\$89boo5\$64boo\$57boo5boo\$57boo\$94bo\$92b3o\$59boo30bo\$59boo30boo\$53boo\$53boo5\$99boo\$99bo\$97bobo\$97boo3\$104bo\$102b3o\$50boo49bo\$51bo49boo14boo\$51bobo63boo\$52boo\$44bo\$44b3o76boo\$47bo75boo\$46boo71boo\$67boo50boo\$67bo\$34boo29bobo\$35bo29boo\$35bobo86boo\$36boo55boo29boo\$93bo\$94b3o\$96bo8\$29bo\$28bobo\$28bobo27boo\$29bo28boo5boo\$65boo3\$63boo\$63boo\$69boo\$69boo\$\$96boo\$38boo55bobo\$38boo55bo16boo\$19boo73boo16boo7boo\$19boo100bo\$119bobo\$119boo3\$105boo\$8boo63bo30bobo\$3boobbobbo60b3o30bo\$3bo4bobo59bo32boo\$oobo5bo18boo40boo\$boboboo21bobo45bo\$obbobbo23bo43b3o\$oobbo4bo20boo41bo\$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:

`x = 202, y = 202, rule = B3/S23170boboo\$170boobo\$\$168b5o\$168bo4bobboo\$171bobbobbo\$171boobobo\$168bo5boboo\$167bobo4bo\$167bobbobboo\$168boo9\$160boo\$160boo8\$146boo22boo\$145bobbo21bo\$146boo23b3o\$173bo3\$131bo\$131b3o\$134bo\$133boo\$158boo\$158boo5\$125boo\$126bo\$126bobo\$127boo\$\$133b3o\$121bo13bo\$121b3o10bo\$124bo\$107boo14boo\$107boo78boo\$187bo\$185bobo\$101boo78boobboo\$101boo44boo32boo\$105boo40boo\$105boo3\$152boo\$100boo50boo\$100boo29boo15boo\$132bo15boo\$129b3o\$129bo\$154boo31boo\$154boo13boo16bobo\$168bobo18bo\$168bo20boo\$167boo4boo\$172bobo\$172bo\$171boo7boo\$180boo14\$105boo\$104bobo\$104bo29boo\$103boo29bobo23bo\$136bo21b3o\$136boo19bo\$115boo40boo23boo\$116bo65boo\$113b3o\$64boo47bo\$57boo5boo55boo\$57boo44boo15bobo\$94bo7bobbo14bo48bo\$92b3o8bobo13boo46b3o\$59boo30bo12bo61bo31bo\$59boo30boo73boo28b3o\$53boo140bo\$53boo140boo4\$159boo\$99boo58boo\$99bo\$97bobo98boo\$97boo99bobo\$122boo76bo\$122boo76boo\$104bo23boo32boo\$102b3o23boo33bo\$50boo49bo58b3o25boo3boo\$51bo49boo14boo41bo27boo3boo\$51bobo63boo7boo\$52boo72boo5boo\$44bo88boo\$44b3o76boo\$47bo75boo\$46boo71boo\$67boo50boo\$67bo\$34boo29bobo\$35bo29boo\$35bobo86boo\$36boo55boo29boo\$93bo\$94b3o\$96bo8\$29bo\$28bobo\$28bobo27boo\$29bo28boo5boo\$65boo3\$63boo\$63boo\$69boo\$69boo\$\$96boo\$38boo55bobo\$38boo55bo16boo\$19boo73boo16boo7boo\$19boo100bo\$119bobo\$119boo3\$105boo\$8boo63bo30bobo\$3boobbobbo60b3o30bo\$3bo4bobo59bo32boo\$oobo5bo18boo40boo\$boboboo21bobo45bo\$obbobbo23bo43b3o\$oobbo4bo20boo41bo\$5b5o63boo\$\$4boboo\$4boobo3\$76boo\$57boo17boo\$57boo38boo\$97boo\$\$56boo\$57bo\$54b3o12boo\$54bo14bo51boo\$70b3o48boo\$72bo3\$121boo\$121boo\$107boo\$106bobo\$106bo\$105boo8boo\$115bo\$116b3o\$118bo!`
What do you do with ill crystallographers? Take them to the mono-clinic!

calcyman

Posts: 2088
Joined: June 1st, 2009, 4:32 pm

### Re: Incomplete search patterns - try to complete

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:

`x = 162, y = 75, rule = B3/S2375bo47boo\$73b3o47boo\$72bo28bo\$72boo27b3o\$60bo43bo\$43boo15b3o40boo39boo\$4boobo36bo18bo80boo5boo\$4boboo36bobo15boo20bo66boo\$45boo37b3o\$5b5o77bo\$oobbo4bo20boo44boo8boo11boo48boo\$obbobbo23bo45boo21boo48boo\$boboboo21bobo124boo\$oobo5bo18boo125boo\$3bo4bobo\$3boobbobbo\$8boo3\$124boo\$111boo11boo\$53boo57bo\$19boo32boo54b3o\$19boo88bo\$38boo43bo3boo\$38boo42bobo3bo39boo\$77boobbobo3bo12boo27bo\$77bo3bo4bo13bobo23b3o\$78b4o5b3o12bo23bo\$89bo12boo17boo\$80boo40bo\$80boo24bo15bobo\$104b3o16boo\$103bo\$103boo\$29bo\$28bobo52bo76boo\$28bobo50b3o76boo\$29bo50bo\$67boo11boo\$67boo\$155boo\$155boo\$159boo\$159boo\$\$36boo\$36boo86boo27boo\$42boo80boo11boo14boo\$42boo93bo\$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.
What do you do with ill crystallographers? Take them to the mono-clinic!

calcyman

Posts: 2088
Joined: June 1st, 2009, 4:32 pm

### Re: Incomplete search patterns - try to complete

And, at 60 cells wide, this is officially the thinnest 90° stable reflector!
What do you do with ill crystallographers? Take them to the mono-clinic!

calcyman

Posts: 2088
Joined: June 1st, 2009, 4:32 pm

### Re: Incomplete search patterns - try to complete

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

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

Posts: 566
Joined: May 31st, 2009, 12:08 am

### Re: Incomplete search patterns - try to complete

MikeP,

might your search program be able to find a replacement for the block in this pattern?
`x = 62, y = 79, rule = B3/S2331b2o2\$29bo3bo\$29bo4bo\$31bobobo\$32bobobo\$33bo4bo\$28b2o4bo3bo\$29bo\$29bobo3b2o8b3o\$30b2o12bo3bo7bo\$43bo5bo5bobo\$43bo5bo4bo3bo\$26bo16bo5bo5bo3bo\$25bobo16bo3bo7bo3bo\$24bo3bo9b3o4b3o9bo3bo\$25bo3bo7bo3bo16bobo\$26bo3bo5bo5bo16bo\$27bo3bo4bo5bo\$22b2o4bobo5bo5bo\$23bo5bo7bo3bo12b2o\$23bobo12b3o8b2o3bobo\$24b2o30bo\$28bo18bo3bo4b2o\$19b2o6b2o18bo4bo\$27bobo19bobobo\$17bo3bo28bobobo\$17bo4bo28bo4bo\$19bobobo28bo3bo\$20bobobo19bobo\$21bo4bo18b2o6b2o\$16b2o4bo3bo18bo\$17bo\$17bobo3b2o8b3o\$18b2o12bo3bo\$31bo5bo\$31bo5bo\$14bo16bo5bo\$13bobo16bo3bo\$12bo3bo9b3o4b3o18bobo\$13bo3bo7bo3bo9b2o14b2o\$14bo3bo5bo5bo8b2o14bo\$15bo3bo4bo5bo\$10b2o4bobo5bo5bo\$11bo5bo7bo3bo\$11bobo12b3o8b2o\$12b2o\$16bo18bo3bo\$7b2o6b2o18bo4bo\$15bobo19bobobo\$5bo3bo28bobobo\$5bo4bo28bo4bo\$7bobobo28bo3bo\$8bobobo19bobo\$9bo4bo18b2o6b2o\$4b2o4bo3bo18bo\$5bo30b2o\$5bobo3b2o8b3o12bobo\$6b2o12bo3bo7bo5bo\$19bo5bo5bobo4b2o\$19bo5bo4bo3bo\$2bo16bo5bo5bo3bo\$bobo16bo3bo7bo3bo\$o3bo9b3o4b3o9bo3bo\$bo3bo7bo3bo16bobo\$2bo3bo5bo5bo16bo\$3bo3bo4bo5bo\$4bobo5bo5bo\$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:
`x = 213, y = 96, rule = B3/S2367bo\$66bo\$66b3o\$149bobo\$150b2o\$150bo6\$57bo\$55b2o\$56b2o103bo\$162bo\$160b3o7\$45bo\$45bobo\$45b2o124bo\$172b2o\$171b2o\$2bo\$obo152bo\$b2o152b3o54bo\$158bo51b2o\$157b2o52b2o3\$48bob2o116bob2o\$47b2ob2o115b2ob2o14b2o\$48bo2bo116bo2bo14bo\$184bobo\$11bobo170b2o\$12b2o\$12bo187bo\$200bobo\$145bo54b2o\$145b2o\$34b3o107bobo7b3o\$34b2o35b3o80b2o\$71bo\$34b3o23bo11bo81b3o23bo\$23bo11bo23b3o93bo23b3o\$24bo\$22b3o35b2o118b2o\$59b3o117b3o7bobo\$189b2o\$134b2o54bo\$133bobo\$83bo51bo\$82b2o\$82bobo65b2o\$149bobo\$44bo2bo101bo14bo2bo\$44b2ob2o99b2o14b2ob2o\$44b2obo116b2obo3\$123b2o52b2o\$124b2o51bo\$93b2o28bo54b3o\$93bobo84bo\$93bo\$163b2o\$162b2o\$49b2o113bo\$48bobo\$50bo7\$173b3o\$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:
`x = 62, y = 79, rule = B3/S2331b2o2\$29bo3bo\$29bo4bo\$31bobobo\$32bobobo\$33bo4bo\$28b2o4bo3bo\$29bo\$29bobo3b2o8b3o\$30b2o12bo3bo7bo\$43bo5bo5bobo\$43bo5bo4bo3bo\$26bo16bo5bo5bo3bo\$25bobo16bo3bo7bo3bo\$24bo3bo9b3o4b3o9bo3bo\$25bo3bo7bo3bo16bobo\$26bo3bo5bo5bo16bo\$27bo3bo4bo5bo\$22b2o4bobo5bo5bo\$23bo5bo7bo3bo12b2o\$23bobo12b3o8b2o3bobo\$24b2o30bo\$28bo18bo3bo4b2o\$19b2o6b2o18bo4bo\$27bobo19bobobo\$17bo3bo28bobobo\$17bo4bo28bo4bo\$19bobobo28bo3bo\$20bobobo19bobo\$21bo4bo18b2o6b2o\$16b2o4bo3bo18bo\$17bo\$17bobo3b2o8b3o\$18b2o12bo3bo\$31bo5bo\$31bo5bo5bo\$14bo16bo5bo5b3o\$13bobo16bo3bo9bo\$12bo3bo9b3o4b3o8bo9bobo\$13bo3bo7bo3bo13bo2b3o6b2o\$14bo3bo5bo5bo12b4o2bo5bo\$15bo3bo4bo5bo10b2o3b2o2bo\$10b2o4bobo5bo5bo10bo2b4o3bo\$11bo5bo7bo3bo12bobo4bob3o\$11bobo12b3o8b2o4bob4obo3bo\$12b2o30bo3bobo2b2o\$16bo18bo3bo4bobobobobo\$7b2o6b2o18bo4bo7bobobob3o\$15bobo19bobobo4bo3b2obobobo\$5bo3bo28bobobo5b2o3bo3bo\$5bo4bo28bo4bo2b3o2b3o2b2o\$7bobobo28bo3bo2b3o7bo\$8bobobo19bobo17b5o\$9bo4bo18b2o6b2o12bo\$4b2o4bo3bo18bo19bo\$5bo30b2o15bo\$5bobo3b2o8b3o12bobo15bo\$6b2o12bo3bo7bo5bo\$19bo5bo5bobo4b2o\$19bo5bo4bo3bo\$2bo16bo5bo5bo3bo\$bobo16bo3bo7bo3bo\$o3bo9b3o4b3o9bo3bo\$bo3bo7bo3bo16bobo\$2bo3bo5bo5bo16bo\$3bo3bo4bo5bo\$4bobo5bo5bo\$5bo7bo3bo12b2o\$14b3o8b2o3bobo\$32bo\$23bo3bo4b2o\$23bo4bo\$25bobobo\$26bobobo\$27bo4bo\$28bo3bo2\$29b2o!`

Edit 2: Calcyman provided this p40 gun:
`x = 752, y = 510, rule = B3/S23345bo60bo\$343b3o60b3o\$342bo66bo\$342b2o64b2o2\$339b3o68b3o\$341bo68bo\$340bo70bo8\$329b3o88b3o\$331bo88bo\$330bo90bo8\$319b3o108b3o\$321bo108bo\$320bo110bo4\$195b3o356b3o\$195b3o356b3o\$195b3o10bo334bo10b3o\$198b3o5b3o334b3o5b3o\$198b3o4bo103b3o128b3o103bo4b3o\$198b3o4b2o104bo128bo104b2o4b3o\$204b2o104bo130bo104b2o\$203b2o342b2o\$202b3o342b3o\$207b2o334b2o\$205bo2bo334bo2bo\$174bo29bo342bo29bo\$202bo4bo336bo4bo\$172bob3o25bo3bo338bo3bo25b3obo\$174b2obo8bo15b2o95b3o148b3o95b2o15bo8bob2o\$174bob2o6b3o114bo148bo114b3o6b2obo\$175b3obo3bo116bo150bo116bo3bob3o\$183b2o43b2o292b2o43b2o\$177bo48bob2o292b2obo48bo\$181bo43bo300bo43bo\$180bobo29b2o14bo294bo14b2o29bobo\$181b2o2b2o24b2o11b2obo296bob2o11b2o24b2o2b2o\$185b2o5bo20bo10b2o300b2o10bo20bo5b2o\$192bobo362bobo\$183bo8b2o27bo67b3o168b3o67bo27b2o8bo\$182b2o36bobo68bo168bo68bobo36b2o\$182bobo35b2o68bo170bo68b2o35bobo\$224b2o300b2o\$224bobo298bobo\$219b2o5bo298bo5b2o\$211b3o5b2o5b2o296b2o5b2o5b3o\$173bo16b2o21bo324bo21b2o16bo\$172bo13b2o2b2o20bo326bo20b2o2b2o13bo\$172b3o10bobo376bobo10b3o\$186bo92b3o188b3o92bo\$181b3o97bo188bo97b3o\$184bo3b2o90bo190bo90b2o3bo\$180bo3bo3bo374bo3bo3bo\$179bobo2bo4b3o368b3o4bo2bobo\$177bo2bobo8bo368bo8bobo2bo\$147b2o28bo3bo19b3o344b3o19bo3bo28b2o\$144bo18bo13bo25bo344bo25bo13bo18bo\$143bobo2b2o12bo15b3o21bo346bo21b3o15bo12b2o2bobo\$141bobob3o2bo11b3o56bo308bo56b3o11bo2b3obobo\$141bo2b6o70bobo46b3o208b3o46bobo70b6o2bo\$144b2ob2o72bo6b2o41bo208bo41b2o6bo72b2ob2o\$143b6o2bo14bo61bobo39bo210bo39bobo61bo14bo2b6o\$142bo2b3obobo57bo9b5ob2obobo290bobob2ob5o9bo57bobob3o2bo\$143b2o2bobo14b3obo39bobo8bo3bobo2bob2o288b2obo2bobo3bo8bobo39bob3o14bobo2b2o\$148bo14bob2o41bobo10bobobobo4bo286bo4bobobobo10bobo41b2obo14bo\$144b2o17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo284bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17b2o\$153bo7bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo284bobobo3b3o5bo3bo3bo2bo12bo18b3o6b3obo7bo\$152bo18bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo286bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo18bo\$152b3o8bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o288b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo8b3o\$176bob3o15bo2bobob3o7b3o43b3o228b3o43b3o7b3obobo2bo15b3obo\$164bo10bo3bo16b3obo10bo4bo7b2o2b2o31bo228bo31b2o2b2o7bo4bo10bob3o16bo3bo10bo\$162b3o9bo3bo15b2o4bo10b5obo6b2o2b2o30bo230bo30b2o2b2o6bob5o10bo4b2o15bo3bo9b3o\$161bobobo7b3obo15bo2b5o9bo6bo316bo6bo9b5o2bo15bob3o7bobobo\$149bo11bo3bo8b3o15bo2bo5b3o7b3o3b2o314b2o3b3o7b3o5bo2bo15b3o8bo3bo11bo\$149b2o8b2o5b2o7bo15bo4b4ob3o9bo107b2o106b2o107bo9b3ob4o4bo15bo7b2o5b2o8b2o\$148bobo7bo4bo4bo12b3o7bob2obo5b2o344b2o5bob2obo7b3o12bo4bo4bo7bobo\$157b3o2bobo3b2o13bo5bob4obobobo119bo3bo102bo3bo119bobobob4obo5bo13b2o3bobo2b3o\$158bo4bo5bo12bo5bo3bobobo122bo4bo102bo4bo122bobobo3bo5bo12bo5bo4bo\$159b2o9bo17bobobob2ob2o110bo8bobobo106bobobo8bo110b2ob2obobobo17bo9b2o\$161bo8b2o15b2o2b2o3bo5bo46b3o57b3o5bobobo108bobobo5b3o57b3o46bo5bo3b2o2b2o15b2o8bo\$161b2o8bo21bobo5b3o47bo60bo2bo4bo110bo4bo2bo60bo47b3o5bobo21bo8b2o\$162bo9b2o19b2o5bob3o45bo60b2o2bo3bo112bo3bo2b2o60bo45b3obo5b2o19b2o9bo\$150bo12bo5bo4bo13bo10bo3bo65bo212bo65bo3bo10bo13bo4bo5bo12bo\$139bo9bo13b2o3bobo2b3o10b3o9bo3bo7bo57bobo43bo2b2o114b2o2bo43bobo57bo7bo3bo9b3o10b3o2bobo3b2o13bo9bo\$139b2o8b3o12bo4bo4bo10bobobo7b3obo6b3o58bo6b2o35bobo120bobo35b2o6bo58b3o6bob3o7bobobo10bo4bo4bo12b3o8b2o\$138bobo16bo7b2o5b2o11bo3bo8b3o6bo6bo61bobo30b2o2b2o122b2o2b2o30bobo61bo6bo6b3o8bo3bo11b2o5b2o7bo16bobo\$156b3o8bo3bo11b2o5b2o7bo7b2o48bo9b5ob2obobo30b2o130b2o30bobob2ob5o9bo48b2o7bo7b2o5b2o11bo3bo8b3o\$155bob3o7bobobo10bo4bo4bo19b3obo39bobo8bo3bobo2bob2o192b2obo2bobo3bo8bobo39bob3o19bo4bo4bo10bobobo7b3obo\$154bo3bo9b3o10b3o2bobo3b2o17bob2o41bobo10bobobobo4bo190bo4bobobobo10bobo41b2obo17b2o3bobo2b3o10b3o9bo3bo\$153bo3bo10bo13bo4bo5bo17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo188bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17bo5bo4bo13bo10bo3bo\$152b3obo26b2o9bo14bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo188bobobo3b3o5bo3bo3bo2bo12bo18b3o6b3obo14bo9b2o26bob3o\$153b3o4b2o7bo15bo8b2o23bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo36bo116bo36bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo23b2o8bo15bo7b2o4b3o\$141b2o11bo6bo23b2o8bo15bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o38b2o112b2o38b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo15bo8b2o23bo6bo11b2o\$129bo12bo15b3o6b3obo14bo9b2o26bob3o15bo2bobob3o7b3o43b3o7b2o114b2o7b3o43b3o7b3obobo2bo15b3obo26b2o9bo14bob3o6b3o15bo12bo\$129b2o8b3o16bo7bob2o17bo5bo4bo13bo10bo3bo16b3obo10bo4bo7b2o2b2o31bo132bo31b2o2b2o7bo4bo10bob3o16bo3bo10bo13bo4bo5bo17b2obo7bo16b3o8b2o\$128bobo8bo26b2obo17b2o3bobo2b3o10b3o9bo3bo15b2o4bo10b5obo6b2o2b2o30bo134bo30b2o2b2o6bob5o10bo4b2o15bo3bo9b3o10b3o2bobo3b2o17bob2o26bo8bobo\$164bob3o19bo4bo4bo10bobobo7b3obo15bo2b5o9bo6bo220bo6bo9b5o2bo15bob3o7bobobo10bo4bo4bo19b3obo\$172b2o7bo7b2o5b2o11bo3bo8b3o15bo2bo5b3o7b3o3b2o218b2o3b3o7b3o5bo2bo15b3o8bo3bo11b2o5b2o7bo7b2o\$166bo6bo6b3o8bo3bo11b2o5b2o7bo15bo4b4ob3o9bo228bo9b3ob4o4bo15bo7b2o5b2o11bo3bo8b3o6bo6bo\$170b3o6bob3o7bobobo10bo4bo4bo12b3o7bob2obo5b2o248b2o5bob2obo7b3o12bo4bo4bo10bobobo7b3obo6b3o\$170bo7bo3bo9b3o10b3o2bobo3b2o13bo5bob4obobobo254bobobob4obo5bo13b2o3bobo2b3o10b3o9bo3bo7bo\$177bo3bo10bo13bo4bo5bo12bo5bo3bobobo82bo96bo82bobobo3bo5bo12bo5bo4bo13bo10bo3bo\$176b3obo26b2o9bo17bobobob2ob2o81b2o92b2o81b2ob2obobobo17bo9b2o26bob3o\$119bo57b3o4b2o7bo15bo8b2o15b2o2b2o3bo5bo46b3o27b2o94b2o27b3o46bo5bo3b2o2b2o15b2o8bo15bo7b2o4b3o57bo\$119b2o57bo6bo23b2o8bo21bobo5b3o47bo152bo47b3o5bobo21bo8b2o23bo6bo57b2o\$118bobo61b3o6b3obo14bo9b2o19b2o5bob3o45bo154bo45b3obo5b2o19b2o9bo14bob3o6b3o61bobo\$182bo7bob2o17bo5bo4bo13bo10bo3bo65bo116bo65bo3bo10bo13bo4bo5bo17b2obo7bo\$190b2obo17b2o3bobo2b3o10b3o9bo3bo7bo57bobo114bobo57bo7bo3bo9b3o10b3o2bobo3b2o17bob2o\$188bob3o19bo4bo4bo10bobobo7b3obo6b3o58bo6b2o100b2o6bo58b3o6bob3o7bobobo10bo4bo4bo19b3obo\$196b2o7bo7b2o5b2o11bo3bo8b3o6bo6bo61bobo98bobo61bo6bo6b3o8bo3bo11b2o5b2o7bo7b2o\$73bo116bo6bo6b3o8bo3bo11b2o5b2o7bo7b2o48bo9b5ob2obobo98bobob2ob5o9bo48b2o7bo7b2o5b2o11bo3bo8b3o6bo6bo116bo\$73b2o119b3o6bob3o7bobobo10bo4bo4bo19b3obo39bobo8bo3bobo2bob2o9bo76bo9b2obo2bobo3bo8bobo39bob3o19bo4bo4bo10bobobo7b3obo6b3o119b2o\$72b2obo118bo7bo3bo9b3o10b3o2bobo3b2o17bob2o41bobo10bobobobo4bo9b2o72b2o9bo4bobobobo10bobo41b2obo17b2o3bobo2b3o10b3o9bo3bo7bo118bob2o\$71bo2b3o32bo91bo3bo10bo13bo4bo5bo17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo7b2o74b2o7bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17bo5bo4bo13bo10bo3bo91bo32b3o2bo\$61bo8bobobo34b2o89b3obo5b2o19b2o9bo14bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo92bobobo3b3o5bo3bo3bo2bo12bo18b3o6b3obo14bo9b2o19b2o5bob3o89b2o34bobobo8bo\$61b3o5bobobo34bobo90b3o5bobo21bo8b2o23bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo94bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo23b2o8bo21bobo5b3o90bobo34bobobo5b3o\$34bo29bo2b3o2bo129bo5bo3b2o2b2o15b2o8bo15bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o96b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo15bo8b2o15b2o2b2o3bo5bo129bo2b3o2bo29bo\$33b3o27b2o3bob2o134b2ob2obobobo17bo9b2o26bob3o15bo2bobob3o7b3o128b3o7b3obobo2bo15b3obo26b2o9bo17bobobob2ob2o134b2obo3b2o27b3o\$32bob3o32b2o137bobobo3bo5bo12bo5bo4bo13bo10bo3bo16b3obo10bo4bo7b2o2b2o100b2o2b2o7bo4bo10bob3o16bo3bo10bo13bo4bo5bo12bo5bo3bobobo137b2o32b3obo\$22bo8bo3bo30bo3bo133bobobob4obo5bo13b2o3bobo2b3o10b3o9bo3bo15b2o4bo10b5obo6b2o2b2o100b2o2b2o6bob5o10bo4b2o15bo3bo9b3o10b3o2bobo3b2o13bo5bob4obobobo133bo3bo30bo3bo8bo\$22b3o5bo3bo30bobo133b2o5bob2obo7b3o12bo4bo4bo10bobobo7b3obo15bo2b5o9bo6bo124bo6bo9b5o2bo15bob3o7bobobo10bo4bo4bo12b3o7bob2obo5b2o133bobo30bo3bo5b3o\$25bo3b3obo27b2o2b2o124bo9b3ob4o4bo15bo7b2o5b2o11bo3bo8b3o15bo2bo5b3o7b3o3b2o32bo56bo32b2o3b3o7b3o5bo2bo15b3o8bo3bo11b2o5b2o7bo15bo4b4ob3o9bo124b2o2b2o27bob3o3bo\$24b2o4b3o28b2o123b2o3b3o7b3o5bo2bo15b3o8bo3bo11b2o5b2o7bo15bo4b4ob3o9bo38b2o52b2o38bo9b3ob4o4bo15bo7b2o5b2o11bo3bo8b3o15bo2bo5b3o7b3o3b2o123b2o28b3o4b2o\$31bo67bo87bo6bo9b5o2bo15bob3o7bobobo10bo4bo4bo12b3o7bob2obo5b2o47b2o54b2o47b2o5bob2obo7b3o12bo4bo4bo10bobobo7b3obo15bo2b5o9bo6bo87bo67bo\$27bo71b2o74b2o2b2o6bob5o10bo4b2o15bo3bo9b3o10b3o2bobo3b2o13bo5bob4obobobo158bobobob4obo5bo13b2o3bobo2b3o10b3o9bo3bo15b2o4bo10b5obo6b2o2b2o74b2o71bo\$26bobo69bobo74b2o2b2o7bo4bo10bob3o16bo3bo10bo13bo4bo5bo12bo5bo3bobobo166bobobo3bo5bo12bo5bo4bo13bo10bo3bo16b3obo10bo4bo7b2o2b2o74bobo69bobo\$22b2o2b2o161b3o7b3obobo2bo15b3obo26b2o9bo17bobobob2ob2o162b2ob2obobobo17bo9b2o26bob3o15bo2bobob3o7b3o161b2o2b2o\$22b2o46bo102b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo15bo8b2o15b2o2b2o3bo5bo154bo5bo3b2o2b2o15b2o8bo15bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o102bo46b2o\$68bobo101bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo23b2o8bo21bobo5b3o152b3o5bobo21bo8b2o23bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo101bobo\$59b2o8b2o100bobobo3b3o5bo3bo3bo2bo12bo18b3o6b3obo14bo9b2o19b2o5bob3o150b3obo5b2o19b2o9bo14bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo100b2o8b2o\$60b2o109bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17bo5bo4bo13bo10bo3bo152bo3bo10bo13bo4bo5bo17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo109b2o\$30bo28bo112bo4bobobobo10bobo41b2obo17b2o3bobo2b3o10b3o9bo3bo7bo50bo36bo50bo7bo3bo9b3o10b3o2bobo3b2o17bob2o41bobo10bobobobo4bo112bo28bo\$31bo141b2obo2bobo3bo8bobo39bob3o19bo4bo4bo10bobobo7b3obo6b3o51b2o32b2o51b3o6bob3o7bobobo10bo4bo4bo19b3obo39bobo8bo3bobo2bob2o141bo\$2bo26b3o57bo84bobob2ob5o9bo48b2o7bo7b2o5b2o11bo3bo8b3o6bo6bo46b2o34b2o46bo6bo6b3o8bo3bo11b2o5b2o7bo7b2o48bo9b5ob2obobo84bo57b3o26bo\$bobo16bo68b2o83bobo61bo6bo6b3o8bo3bo11b2o5b2o7bo7b2o142b2o7bo7b2o5b2o11bo3bo8b3o6bo6bo61bobo83b2o68bo16bobo\$o3bo15b2o66bobo84b2o6bo58b3o6bob3o7bobobo10bo4bo4bo19b3obo126bob3o19bo4bo4bo10bobobo7b3obo6b3o58bo6b2o84bobo66b2o15bo3bo\$bo3bo13bobo160bobo57bo7bo3bo9b3o10b3o2bobo3b2o17bob2o130b2obo17b2o3bobo2b3o10b3o9bo3bo7bo57bobo160bobo13bo3bo\$2bo3bo73bo102bo65bo3bo10bo13bo4bo5bo17b2obo7bo114bo7bob2o17bo5bo4bo13bo10bo3bo65bo102bo73bo3bo\$3bo3bo70bobo121bo45b3obo5b2o19b2o9bo14bob3o6b3o114b3o6b3obo14bo9b2o19b2o5bob3o45bo121bobo70bo3bo\$4bobo42b2o28b2o120bo47b3o5bobo21bo8b2o23bo6bo106bo6bo23b2o8bo21bobo5b3o47bo120b2o28b2o42bobo\$5bo44b2o149b3o46bo5bo3b2o2b2o15b2o8bo15bo7b2o4b3o104b3o4b2o7bo15bo8b2o15b2o2b2o3bo5bo46b3o149b2o44bo\$9bo30bo8bo204b2ob2obobobo17bo9b2o26bob3o42bo16bo42b3obo26b2o9bo17bobobob2ob2o204bo8bo30bo\$8bobo30bo214bobobo3bo5bo12bo5bo4bo13bo10bo3bo44b2o12b2o44bo3bo10bo13bo4bo5bo12bo5bo3bobobo214bo30bobo\$9b2o28b3o36b2o172bobobob4obo5bo13b2o3bobo2b3o10b3o9bo3bo7bo36b2o14b2o36bo7bo3bo9b3o10b3o2bobo3b2o13bo5bob4obobobo172b2o36b3o28b2o\$5b2o8b2o61b2o2b2o165b2o5bob2obo7b3o12bo4bo4bo10bobobo7b3obo6b3o90b3o6bob3o7bobobo10bo4bo4bo12b3o7bob2obo5b2o165b2o2b2o61b2o8b2o\$4bobo8bobo64bobo154bo9b3ob4o4bo15bo7b2o5b2o11bo3bo8b3o6bo6bo82bo6bo6b3o8bo3bo11b2o5b2o7bo15bo4b4ob3o9bo154bobo64bobo8bobo\$4bo5b2o3bo67bo150b2o3b3o7b3o5bo2bo15b3o8bo3bo11b2o5b2o7bo7b2o94b2o7bo7b2o5b2o11bo3bo8b3o15bo2bo5b3o7b3o3b2o150bo67bo3b2o5bo\$3b2o5b2o223bo6bo9b5o2bo15bob3o7bobobo10bo4bo4bo19b3obo78bob3o19bo4bo4bo10bobobo7b3obo15bo2b5o9bo6bo223b2o5b2o\$39b2o39b2o4b2o104bo30b2o2b2o6bob5o10bo4b2o15bo3bo9b3o10b3o2bobo3b2o17bob2o26bo8bobo6bobo8bo26b2obo17b2o3bobo2b3o10b3o9bo3bo15b2o4bo10b5obo6b2o2b2o30bo104b2o4b2o39b2o\$39b2o2b2o36bo4b2obo101bo31b2o2b2o7bo4bo10bob3o16bo3bo10bo13bo4bo5bo17b2obo7bo16b3o8b2o8b2o8b3o16bo7bob2o17bo5bo4bo13bo10bo3bo16b3obo10bo4bo7b2o2b2o31bo101bob2o4bo36b2o2b2o\$43bobo32b3o9bo100b3o43b3o7b3obobo2bo15b3obo26b2o9bo14bob3o6b3o15bo12bo8bo12bo15b3o6b3obo14bo9b2o26bob3o15bo2bobob3o7b3o43b3o100bo9b3o32bobo\$44bo2b2o29bo8bo133b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo15bo8b2o23bo6bo11b2o32b2o11bo6bo23b2o8bo15bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o133bo8bo29b2o2bo\$88bob2o128bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo23b2o8bo15bo7b2o4b3o27b2o27b3o4b2o7bo15bo8b2o23bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo128b2obo\$41b2o2bo3bo40b2o127bobobo3b3o5bo3bo3bo2bo12bo18b3o6b3obo14bo9b2o26bob3o26b2o26b3obo26b2o9bo14bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo127b2o40bo3bo2b2o\$25b2o15bo2bo4bo168bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17bo5bo4bo13bo10bo3bo56bo3bo10bo13bo4bo5bo17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo168bo4bo2bo15b2o\$25bobo11b3o5bobobo168bo4bobobobo10bobo41b2obo17b2o3bobo2b3o10b3o9bo3bo58bo3bo9b3o10b3o2bobo3b2o17bob2o41bobo10bobobobo4bo168bobobo5b3o11bobo\$25bo13bo8bobobo168b2obo2bobo3bo8bobo39bob3o19bo4bo4bo10bobobo7b3obo60bob3o7bobobo10bo4bo4bo19b3obo39bobo8bo3bobo2bob2o168bobobo8bo13bo\$49bo4bo167bobob2ob5o9bo48b2o7bo7b2o5b2o11bo3bo8b3o62b3o8bo3bo11b2o5b2o7bo7b2o48bo9b5ob2obobo167bo4bo\$50bo3bo127bo39bobo61bo6bo6b3o8bo3bo11b2o5b2o7bo16bobo26bobo16bo7b2o5b2o11bo3bo8b3o6bo6bo61bobo39bo127bo3bo\$181bo41b2o6bo58b3o6bob3o7bobobo10bo4bo4bo12b3o8b2o28b2o8b3o12bo4bo4bo10bobobo7b3obo6b3o58bo6b2o41bo\$51b2o128b3o46bobo57bo7bo3bo9b3o10b3o2bobo3b2o13bo9bo28bo9bo13b2o3bobo2b3o10b3o9bo3bo7bo57bobo46b3o128b2o\$231bo65bo3bo10bo13bo4bo5bo12bo50bo12bo5bo4bo13bo10bo3bo65bo\$250bo45b3obo5b2o19b2o9bo74bo9b2o19b2o5bob3o45bo\$249bo47b3o5bobo21bo8b2o72b2o8bo21bobo5b3o47bo\$35b2o212b3o46bo5bo3b2o2b2o15b2o8bo72bo8b2o15b2o2b2o3bo5bo46b3o212b2o\$35bobo264b2ob2obobobo17bo9b2o68b2o9bo17bobobob2ob2o264bobo\$35bo268bobobo3bo5bo12bo5bo4bo66bo4bo5bo12bo5bo3bobobo268bo\$300bobobob4obo5bo13b2o3bobo2b3o64b3o2bobo3b2o13bo5bob4obobobo\$172bo124b2o5bob2obo7b3o12bo4bo4bo7bobo46bobo7bo4bo4bo12b3o7bob2obo5b2o124bo\$171bo115bo9b3ob4o4bo15bo7b2o5b2o8b2o48b2o8b2o5b2o7bo15bo4b4ob3o9bo115bo\$171b3o108b2o3b3o7b3o5bo2bo15b3o8bo3bo11bo48bo11bo3bo8b3o15bo2bo5b3o7b3o3b2o108b3o\$283bo6bo9b5o2bo15bob3o7bobobo72bobobo7b3obo15bo2b5o9bo6bo\$240bo30b2o2b2o6bob5o10bo4b2o15bo3bo9b3o74b3o9bo3bo15b2o4bo10b5obo6b2o2b2o30bo\$239bo31b2o2b2o7bo4bo10bob3o16bo3bo10bo78bo10bo3bo16b3obo10bo4bo7b2o2b2o31bo\$45b2o192b3o43b3o7b3obobo2bo15b3obo102bob3o15bo2bobob3o7b3o43b3o192b2o\$45bobo221b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo8b3o54b3o8bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o221bobo\$45bo222bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo18bo54bo18bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo222bo\$267bobobo3b3o5bo3bo3bo2bo12bo18b3o6b3obo7bo56bo7bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo\$162bo104bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17b2o38b2o17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo104bo\$161bo106bo4bobobobo10bobo41b2obo14bo46bo14bob2o41bobo10bobobobo4bo106bo\$161b3o68b2o35b2obo2bobo3bo8bobo39bob3o14bobo2b2o36b2o2bobo14b3obo39bobo8bo3bobo2bob2o35b2o68b3o\$231bobo36bobob2ob5o9bo57bobob3o2bo34bo2b3obobo57bo9b5ob2obobo36bobo\$231bo38bobo61bo14bo2b6o36b6o2bo14bo61bobo38bo\$230b2o39b2o6bo72b2ob2o38b2ob2o72bo6b2o39b2o\$55b2o221bobo70b6o2bo32bo2b6o70bobo221b2o\$55bobo221bo56b3o11bo2b3obobo32bobob3o2bo11b3o56bo221bobo\$55bo242bo21b3o15bo12b2o2bobo36bobo2b2o12bo15b3o21bo242bo\$297bo25bo13bo18bo38bo18bo13bo25bo\$152bo144b3o19bo3bo28b2o44b2o28bo3bo19b3o144bo\$151bo157bo8bobo2bo104bo2bobo8bo157bo\$151b3o155b3o4bo2bobo108bobo2bo4b3o155b3o\$312bo3bo3bo110bo3bo3bo\$311b2o3bo118bo3b2o\$317b3o112b3o\$65b2o247bo122bo247b2o\$65bobo245bobo10b3o94b3o10bobo245bobo\$65bo222bo20b2o2b2o13bo94bo13b2o2b2o20bo222bo\$287bo21b2o16bo96bo16b2o21bo\$142bo130b2o5b2o5b3o172b3o5b2o5b2o130bo\$141bo132bo5b2o188b2o5bo132bo\$141b3o130bobo198bobo130b3o\$275b2o198b2o\$279b2o35bobo114bobo35b2o\$278bobo36b2o114b2o36bobo\$75b2o202bo27b2o8bo116bo8b2o27bo202b2o\$75bobo228bobo134bobo228bobo\$75bo199b2o10bo20bo5b2o120b2o5bo20bo10b2o199bo\$273bob2o11b2o24b2o2b2o112b2o2b2o24b2o11b2obo\$132bo139bo14b2o29bobo110bobo29b2o14bo139bo\$131bo143bo43bo112bo43bo143bo\$131b3o137b2obo48bo104bo48bob2o137b3o\$271b2o43b2o116b2o43b2o\$317bo3bob3o100b3obo3bo\$314b3o6b2obo98bob2o6b3o\$85b2o210b2o15bo8bob2o98b2obo8bo15b2o210b2o\$85bobo206bo3bo25b3obo94bob3o25bo3bo206bobo\$85bo207bo4bo154bo4bo207bo\$296bo29bo98bo29bo\$122bo169bo2bo160bo2bo169bo\$121bo170b2o164b2o170bo\$121b3o172b3o154b3o172b3o\$296b2o156b2o\$295b2o158b2o\$294b2o4b3o146b3o4b2o\$95b2o198bo4b3o146b3o4bo198b2o\$95bobo194b3o5b3o146b3o5b3o194bobo\$95bo196bo10b3o140b3o10bo196bo\$303b3o140b3o\$112bo190b3o140b3o190bo\$111bo528bo\$111b3o524b3o4\$104b2o540b2o\$103bob2o538b2obo\$103bo544bo\$104bo542bo\$100b2o548b2o\$100b2o548b2o\$104bo542bo\$103bo544bo\$103bob2o538b2obo\$104b2o540b2o4\$111b3o524b3o\$111bo528bo\$112bo190b3o140b3o190bo\$303b3o140b3o\$95bo196bo10b3o140b3o10bo196bo\$95bobo194b3o5b3o146b3o5b3o194bobo\$95b2o198bo4b3o146b3o4bo198b2o\$294b2o4b3o146b3o4b2o\$295b2o158b2o\$296b2o156b2o\$121b3o172b3o154b3o172b3o\$121bo170b2o164b2o170bo\$122bo169bo2bo160bo2bo169bo\$296bo29bo98bo29bo\$85bo207bo4bo154bo4bo207bo\$85bobo206bo3bo25b3obo94bob3o25bo3bo206bobo\$85b2o210b2o15bo8bob2o98b2obo8bo15b2o210b2o\$314b3o6b2obo98bob2o6b3o\$317bo3bob3o100b3obo3bo\$271b2o43b2o116b2o43b2o\$131b3o137b2obo48bo104bo48bob2o137b3o\$131bo143bo43bo112bo43bo143bo\$132bo139bo14b2o29bobo110bobo29b2o14bo139bo\$273bob2o11b2o24b2o2b2o112b2o2b2o24b2o11b2obo\$75bo199b2o10bo20bo5b2o120b2o5bo20bo10b2o199bo\$75bobo228bobo134bobo228bobo\$75b2o202bo27b2o8bo116bo8b2o27bo202b2o\$278bobo36b2o114b2o36bobo\$279b2o35bobo114bobo35b2o\$275b2o198b2o\$141b3o130bobo198bobo130b3o\$141bo132bo5b2o188b2o5bo132bo\$142bo130b2o5b2o5b3o172b3o5b2o5b2o130bo\$287bo21b2o16bo96bo16b2o21bo\$65bo222bo20b2o2b2o13bo94bo13b2o2b2o20bo222bo\$65bobo245bobo10b3o94b3o10bobo245bobo\$65b2o247bo122bo247b2o\$317b3o112b3o\$311b2o3bo118bo3b2o\$312bo3bo3bo110bo3bo3bo\$151b3o155b3o4bo2bobo108bobo2bo4b3o155b3o\$151bo157bo8bobo2bo104bo2bobo8bo157bo\$152bo144b3o19bo3bo28b2o44b2o28bo3bo19b3o144bo\$297bo25bo13bo18bo38bo18bo13bo25bo\$55bo242bo21b3o15bo12b2o2bobo36bobo2b2o12bo15b3o21bo242bo\$55bobo221bo56b3o11bo2b3obobo32bobob3o2bo11b3o56bo221bobo\$55b2o221bobo70b6o2bo32bo2b6o70bobo221b2o\$230b2o39b2o6bo72b2ob2o38b2ob2o72bo6b2o39b2o\$231bo38bobo61bo14bo2b6o36b6o2bo14bo61bobo38bo\$231bobo36bobob2ob5o9bo57bobob3o2bo34bo2b3obobo57bo9b5ob2obobo36bobo\$161b3o68b2o35b2obo2bobo3bo8bobo39bob3o14bobo2b2o36b2o2bobo14b3obo39bobo8bo3bobo2bob2o35b2o68b3o\$161bo106bo4bobobobo10bobo41b2obo14bo46bo14bob2o41bobo10bobobobo4bo106bo\$162bo104bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17b2o38b2o17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo104bo\$267bobobo3b3o5bo3bo3bo2bo12bo18b3o6b3obo7bo56bo7bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo\$45bo222bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo18bo54bo18bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo222bo\$45bobo221b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo8b3o54b3o8bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o221bobo\$45b2o192b3o43b3o7b3obobo2bo15b3obo102bob3o15bo2bobob3o7b3o43b3o192b2o\$239bo31b2o2b2o7bo4bo10bob3o16bo3bo10bo78bo10bo3bo16b3obo10bo4bo7b2o2b2o31bo\$240bo30b2o2b2o6bob5o10bo4b2o15bo3bo9b3o74b3o9bo3bo15b2o4bo10b5obo6b2o2b2o30bo\$283bo6bo9b5o2bo15bob3o7bobobo72bobobo7b3obo15bo2b5o9bo6bo\$171b3o108b2o3b3o7b3o5bo2bo15b3o8bo3bo11bo48bo11bo3bo8b3o15bo2bo5b3o7b3o3b2o108b3o\$171bo115bo9b3ob4o4bo15bo7b2o5b2o8b2o48b2o8b2o5b2o7bo15bo4b4ob3o9bo115bo\$172bo124b2o5bob2obo7b3o12bo4bo4bo7bobo46bobo7bo4bo4bo12b3o7bob2obo5b2o124bo\$300bobobob4obo5bo13b2o3bobo2b3o64b3o2bobo3b2o13bo5bob4obobobo\$35bo268bobobo3bo5bo12bo5bo4bo66bo4bo5bo12bo5bo3bobobo268bo\$35bobo264b2ob2obobobo17bo9b2o68b2o9bo17bobobob2ob2o264bobo\$35b2o212b3o46bo5bo3b2o2b2o15b2o8bo72bo8b2o15b2o2b2o3bo5bo46b3o212b2o\$249bo47b3o5bobo21bo8b2o72b2o8bo21bobo5b3o47bo\$250bo45b3obo5b2o19b2o9bo74bo9b2o19b2o5bob3o45bo\$231bo65bo3bo10bo13bo4bo5bo12bo50bo12bo5bo4bo13bo10bo3bo65bo\$51b2o128b3o46bobo57bo7bo3bo9b3o10b3o2bobo3b2o13bo9bo28bo9bo13b2o3bobo2b3o10b3o9bo3bo7bo57bobo46b3o128b2o\$181bo41b2o6bo58b3o6bob3o7bobobo10bo4bo4bo12b3o8b2o28b2o8b3o12bo4bo4bo10bobobo7b3obo6b3o58bo6b2o41bo\$50bo3bo127bo39bobo61bo6bo6b3o8bo3bo11b2o5b2o7bo16bobo26bobo16bo7b2o5b2o11bo3bo8b3o6bo6bo61bobo39bo127bo3bo\$49bo4bo167bobob2ob5o9bo48b2o7bo7b2o5b2o11bo3bo8b3o62b3o8bo3bo11b2o5b2o7bo7b2o48bo9b5ob2obobo167bo4bo\$25bo13bo8bobobo168b2obo2bobo3bo8bobo39bob3o19bo4bo4bo10bobobo7b3obo60bob3o7bobobo10bo4bo4bo19b3obo39bobo8bo3bobo2bob2o168bobobo8bo13bo\$25bobo11b3o5bobobo168bo4bobobobo10bobo41b2obo17b2o3bobo2b3o10b3o9bo3bo58bo3bo9b3o10b3o2bobo3b2o17bob2o41bobo10bobobobo4bo168bobobo5b3o11bobo\$25b2o15bo2bo4bo168bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17bo5bo4bo13bo10bo3bo56bo3bo10bo13bo4bo5bo17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo168bo4bo2bo15b2o\$41b2o2bo3bo40b2o127bobobo3b3o5bo3bo3bo2bo12bo18b3o6b3obo14bo9b2o26bob3o26b2o26b3obo26b2o9bo14bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo127b2o40bo3bo2b2o\$88bob2o128bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo23b2o8bo15bo7b2o4b3o27b2o27b3o4b2o7bo15bo8b2o23bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo128b2obo\$44bo2b2o29bo8bo133b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo15bo8b2o23bo6bo11b2o32b2o11bo6bo23b2o8bo15bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o133bo8bo29b2o2bo\$43bobo32b3o9bo100b3o43b3o7b3obobo2bo15b3obo26b2o9bo14bob3o6b3o15bo12bo8bo12bo15b3o6b3obo14bo9b2o26bob3o15bo2bobob3o7b3o43b3o100bo9b3o32bobo\$39b2o2b2o36bo4b2obo101bo31b2o2b2o7bo4bo10bob3o16bo3bo10bo13bo4bo5bo17b2obo7bo16b3o8b2o8b2o8b3o16bo7bob2o17bo5bo4bo13bo10bo3bo16b3obo10bo4bo7b2o2b2o31bo101bob2o4bo36b2o2b2o\$39b2o39b2o4b2o104bo30b2o2b2o6bob5o10bo4b2o15bo3bo9b3o10b3o2bobo3b2o17bob2o26bo8bobo6bobo8bo26b2obo17b2o3bobo2b3o10b3o9bo3bo15b2o4bo10b5obo6b2o2b2o30bo104b2o4b2o39b2o\$3b2o5b2o223bo6bo9b5o2bo15bob3o7bobobo10bo4bo4bo19b3obo78bob3o19bo4bo4bo10bobobo7b3obo15bo2b5o9bo6bo223b2o5b2o\$4bo5b2o3bo67bo150b2o3b3o7b3o5bo2bo15b3o8bo3bo11b2o5b2o7bo7b2o94b2o7bo7b2o5b2o11bo3bo8b3o15bo2bo5b3o7b3o3b2o150bo67bo3b2o5bo\$4bobo8bobo64bobo154bo9b3ob4o4bo15bo7b2o5b2o11bo3bo8b3o6bo6bo82bo6bo6b3o8bo3bo11b2o5b2o7bo15bo4b4ob3o9bo154bobo64bobo8bobo\$5b2o8b2o61b2o2b2o165b2o5bob2obo7b3o12bo4bo4bo10bobobo7b3obo6b3o90b3o6bob3o7bobobo10bo4bo4bo12b3o7bob2obo5b2o165b2o2b2o61b2o8b2o\$9b2o28b3o36b2o172bobobob4obo5bo13b2o3bobo2b3o10b3o9bo3bo7bo36b2o14b2o36bo7bo3bo9b3o10b3o2bobo3b2o13bo5bob4obobobo172b2o36b3o28b2o\$8bobo30bo214bobobo3bo5bo12bo5bo4bo13bo10bo3bo44b2o12b2o44bo3bo10bo13bo4bo5bo12bo5bo3bobobo214bo30bobo\$9bo30bo8bo204b2ob2obobobo17bo9b2o26bob3o42bo16bo42b3obo26b2o9bo17bobobob2ob2o204bo8bo30bo\$5bo44b2o149b3o46bo5bo3b2o2b2o15b2o8bo15bo7b2o4b3o104b3o4b2o7bo15bo8b2o15b2o2b2o3bo5bo46b3o149b2o44bo\$4bobo42b2o28b2o120bo47b3o5bobo21bo8b2o23bo6bo106bo6bo23b2o8bo21bobo5b3o47bo120b2o28b2o42bobo\$3bo3bo70bobo121bo45b3obo5b2o19b2o9bo14bob3o6b3o114b3o6b3obo14bo9b2o19b2o5bob3o45bo121bobo70bo3bo\$2bo3bo73bo102bo65bo3bo10bo13bo4bo5bo17b2obo7bo114bo7bob2o17bo5bo4bo13bo10bo3bo65bo102bo73bo3bo\$bo3bo13bobo160bobo57bo7bo3bo9b3o10b3o2bobo3b2o17bob2o130b2obo17b2o3bobo2b3o10b3o9bo3bo7bo57bobo160bobo13bo3bo\$o3bo15b2o66bobo84b2o6bo58b3o6bob3o7bobobo10bo4bo4bo19b3obo126bob3o19bo4bo4bo10bobobo7b3obo6b3o58bo6b2o84bobo66b2o15bo3bo\$bobo16bo68b2o83bobo61bo6bo6b3o8bo3bo11b2o5b2o7bo7b2o142b2o7bo7b2o5b2o11bo3bo8b3o6bo6bo61bobo83b2o68bo16bobo\$2bo26b3o57bo84bobob2ob5o9bo48b2o7bo7b2o5b2o11bo3bo8b3o6bo6bo46b2o34b2o46bo6bo6b3o8bo3bo11b2o5b2o7bo7b2o48bo9b5ob2obobo84bo57b3o26bo\$31bo141b2obo2bobo3bo8bobo39bob3o19bo4bo4bo10bobobo7b3obo6b3o51b2o32b2o51b3o6bob3o7bobobo10bo4bo4bo19b3obo39bobo8bo3bobo2bob2o141bo\$30bo28bo112bo4bobobobo10bobo41b2obo17b2o3bobo2b3o10b3o9bo3bo7bo50bo36bo50bo7bo3bo9b3o10b3o2bobo3b2o17bob2o41bobo10bobobobo4bo112bo28bo\$60b2o109bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17bo5bo4bo13bo10bo3bo152bo3bo10bo13bo4bo5bo17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo109b2o\$59b2o8b2o100bobobo3b3o5bo3bo3bo2bo12bo18b3o6b3obo14bo9b2o19b2o5bob3o150b3obo5b2o19b2o9bo14bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo100b2o8b2o\$68bobo101bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo23b2o8bo21bobo5b3o152b3o5bobo21bo8b2o23bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo101bobo\$22b2o46bo102b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo15bo8b2o15b2o2b2o3bo5bo154bo5bo3b2o2b2o15b2o8bo15bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o102bo46b2o\$22b2o2b2o161b3o7b3obobo2bo15b3obo26b2o9bo17bobobob2ob2o162b2ob2obobobo17bo9b2o26bob3o15bo2bobob3o7b3o161b2o2b2o\$26bobo69bobo74b2o2b2o7bo4bo10bob3o16bo3bo10bo13bo4bo5bo12bo5bo3bobobo166bobobo3bo5bo12bo5bo4bo13bo10bo3bo16b3obo10bo4bo7b2o2b2o74bobo69bobo\$27bo71b2o74b2o2b2o6bob5o10bo4b2o15bo3bo9b3o10b3o2bobo3b2o13bo5bob4obobobo158bobobob4obo5bo13b2o3bobo2b3o10b3o9bo3bo15b2o4bo10b5obo6b2o2b2o74b2o71bo\$31bo67bo87bo6bo9b5o2bo15bob3o7bobobo10bo4bo4bo12b3o7bob2obo5b2o47b2o54b2o47b2o5bob2obo7b3o12bo4bo4bo10bobobo7b3obo15bo2b5o9bo6bo87bo67bo\$24b2o4b3o28b2o123b2o3b3o7b3o5bo2bo15b3o8bo3bo11b2o5b2o7bo15bo4b4ob3o9bo38b2o52b2o38bo9b3ob4o4bo15bo7b2o5b2o11bo3bo8b3o15bo2bo5b3o7b3o3b2o123b2o28b3o4b2o\$25bo3b3obo27b2o2b2o124bo9b3ob4o4bo15bo7b2o5b2o11bo3bo8b3o15bo2bo5b3o7b3o3b2o32bo56bo32b2o3b3o7b3o5bo2bo15b3o8bo3bo11b2o5b2o7bo15bo4b4ob3o9bo124b2o2b2o27bob3o3bo\$22b3o5bo3bo30bobo133b2o5bob2obo7b3o12bo4bo4bo10bobobo7b3obo15bo2b5o9bo6bo124bo6bo9b5o2bo15bob3o7bobobo10bo4bo4bo12b3o7bob2obo5b2o133bobo30bo3bo5b3o\$22bo8bo3bo30bo3bo133bobobob4obo5bo13b2o3bobo2b3o10b3o9bo3bo15b2o4bo10b5obo6b2o2b2o100b2o2b2o6bob5o10bo4b2o15bo3bo9b3o10b3o2bobo3b2o13bo5bob4obobobo133bo3bo30bo3bo8bo\$32bob3o32b2o137bobobo3bo5bo12bo5bo4bo13bo10bo3bo16b3obo10bo4bo7b2o2b2o100b2o2b2o7bo4bo10bob3o16bo3bo10bo13bo4bo5bo12bo5bo3bobobo137b2o32b3obo\$33b3o27b2o3bob2o134b2ob2obobobo17bo9b2o26bob3o15bo2bobob3o7b3o128b3o7b3obobo2bo15b3obo26b2o9bo17bobobob2ob2o134b2obo3b2o27b3o\$34bo29bo2b3o2bo129bo5bo3b2o2b2o15b2o8bo15bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o96b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo15bo8b2o15b2o2b2o3bo5bo129bo2b3o2bo29bo\$61b3o5bobobo34bobo90b3o5bobo21bo8b2o23bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo94bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo23b2o8bo21bobo5b3o90bobo34bobobo5b3o\$61bo8bobobo34b2o89b3obo5b2o19b2o9bo14bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo92bobobo3b3o5bo3bo3bo2bo12bo18b3o6b3obo14bo9b2o19b2o5bob3o89b2o34bobobo8bo\$71bo2b3o32bo91bo3bo10bo13bo4bo5bo17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo7b2o74b2o7bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17bo5bo4bo13bo10bo3bo91bo32b3o2bo\$72b2obo118bo7bo3bo9b3o10b3o2bobo3b2o17bob2o41bobo10bobobobo4bo9b2o72b2o9bo4bobobobo10bobo41b2obo17b2o3bobo2b3o10b3o9bo3bo7bo118bob2o\$73b2o119b3o6bob3o7bobobo10bo4bo4bo19b3obo39bobo8bo3bobo2bob2o9bo76bo9b2obo2bobo3bo8bobo39bob3o19bo4bo4bo10bobobo7b3obo6b3o119b2o\$73bo116bo6bo6b3o8bo3bo11b2o5b2o7bo7b2o48bo9b5ob2obobo98bobob2ob5o9bo48b2o7bo7b2o5b2o11bo3bo8b3o6bo6bo116bo\$196b2o7bo7b2o5b2o11bo3bo8b3o6bo6bo61bobo98bobo61bo6bo6b3o8bo3bo11b2o5b2o7bo7b2o\$188bob3o19bo4bo4bo10bobobo7b3obo6b3o58bo6b2o100b2o6bo58b3o6bob3o7bobobo10bo4bo4bo19b3obo\$190b2obo17b2o3bobo2b3o10b3o9bo3bo7bo57bobo114bobo57bo7bo3bo9b3o10b3o2bobo3b2o17bob2o\$182bo7bob2o17bo5bo4bo13bo10bo3bo65bo116bo65bo3bo10bo13bo4bo5bo17b2obo7bo\$118bobo61b3o6b3obo14bo9b2o19b2o5bob3o45bo154bo45b3obo5b2o19b2o9bo14bob3o6b3o61bobo\$119b2o57bo6bo23b2o8bo21bobo5b3o47bo152bo47b3o5bobo21bo8b2o23bo6bo57b2o\$119bo57b3o4b2o7bo15bo8b2o15b2o2b2o3bo5bo46b3o27b2o94b2o27b3o46bo5bo3b2o2b2o15b2o8bo15bo7b2o4b3o57bo\$176b3obo26b2o9bo17bobobob2ob2o81b2o92b2o81b2ob2obobobo17bo9b2o26bob3o\$177bo3bo10bo13bo4bo5bo12bo5bo3bobobo82bo96bo82bobobo3bo5bo12bo5bo4bo13bo10bo3bo\$170bo7bo3bo9b3o10b3o2bobo3b2o13bo5bob4obobobo254bobobob4obo5bo13b2o3bobo2b3o10b3o9bo3bo7bo\$170b3o6bob3o7bobobo10bo4bo4bo12b3o7bob2obo5b2o248b2o5bob2obo7b3o12bo4bo4bo10bobobo7b3obo6b3o\$166bo6bo6b3o8bo3bo11b2o5b2o7bo15bo4b4ob3o9bo228bo9b3ob4o4bo15bo7b2o5b2o11bo3bo8b3o6bo6bo\$172b2o7bo7b2o5b2o11bo3bo8b3o15bo2bo5b3o7b3o3b2o218b2o3b3o7b3o5bo2bo15b3o8bo3bo11b2o5b2o7bo7b2o\$164bob3o19bo4bo4bo10bobobo7b3obo15bo2b5o9bo6bo220bo6bo9b5o2bo15bob3o7bobobo10bo4bo4bo19b3obo\$128bobo8bo26b2obo17b2o3bobo2b3o10b3o9bo3bo15b2o4bo10b5obo6b2o2b2o30bo134bo30b2o2b2o6bob5o10bo4b2o15bo3bo9b3o10b3o2bobo3b2o17bob2o26bo8bobo\$129b2o8b3o16bo7bob2o17bo5bo4bo13bo10bo3bo16b3obo10bo4bo7b2o2b2o31bo132bo31b2o2b2o7bo4bo10bob3o16bo3bo10bo13bo4bo5bo17b2obo7bo16b3o8b2o\$129bo12bo15b3o6b3obo14bo9b2o26bob3o15bo2bobob3o7b3o43b3o7b2o114b2o7b3o43b3o7b3obobo2bo15b3obo26b2o9bo14bob3o6b3o15bo12bo\$141b2o11bo6bo23b2o8bo15bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o38b2o112b2o38b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo15bo8b2o23bo6bo11b2o\$153b3o4b2o7bo15bo8b2o23bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo36bo116bo36bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo23b2o8bo15bo7b2o4b3o\$152b3obo26b2o9bo14bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo188bobobo3b3o5bo3bo3bo2bo12bo18b3o6b3obo14bo9b2o26bob3o\$153bo3bo10bo13bo4bo5bo17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo188bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17bo5bo4bo13bo10bo3bo\$154bo3bo9b3o10b3o2bobo3b2o17bob2o41bobo10bobobobo4bo190bo4bobobobo10bobo41b2obo17b2o3bobo2b3o10b3o9bo3bo\$155bob3o7bobobo10bo4bo4bo19b3obo39bobo8bo3bobo2bob2o192b2obo2bobo3bo8bobo39bob3o19bo4bo4bo10bobobo7b3obo\$156b3o8bo3bo11b2o5b2o7bo7b2o48bo9b5ob2obobo30b2o130b2o30bobob2ob5o9bo48b2o7bo7b2o5b2o11bo3bo8b3o\$138bobo16bo7b2o5b2o11bo3bo8b3o6bo6bo61bobo30b2o2b2o122b2o2b2o30bobo61bo6bo6b3o8bo3bo11b2o5b2o7bo16bobo\$139b2o8b3o12bo4bo4bo10bobobo7b3obo6b3o58bo6b2o35bobo120bobo35b2o6bo58b3o6bob3o7bobobo10bo4bo4bo12b3o8b2o\$139bo9bo13b2o3bobo2b3o10b3o9bo3bo7bo57bobo43bo2b2o114b2o2bo43bobo57bo7bo3bo9b3o10b3o2bobo3b2o13bo9bo\$150bo12bo5bo4bo13bo10bo3bo65bo212bo65bo3bo10bo13bo4bo5bo12bo\$162bo9b2o19b2o5bob3o45bo60b2o2bo3bo112bo3bo2b2o60bo45b3obo5b2o19b2o9bo\$161b2o8bo21bobo5b3o47bo60bo2bo4bo110bo4bo2bo60bo47b3o5bobo21bo8b2o\$161bo8b2o15b2o2b2o3bo5bo46b3o57b3o5bobobo108bobobo5b3o57b3o46bo5bo3b2o2b2o15b2o8bo\$159b2o9bo17bobobob2ob2o110bo8bobobo106bobobo8bo110b2ob2obobobo17bo9b2o\$158bo4bo5bo12bo5bo3bobobo122bo4bo102bo4bo122bobobo3bo5bo12bo5bo4bo\$157b3o2bobo3b2o13bo5bob4obobobo119bo3bo102bo3bo119bobobob4obo5bo13b2o3bobo2b3o\$148bobo7bo4bo4bo12b3o7bob2obo5b2o344b2o5bob2obo7b3o12bo4bo4bo7bobo\$149b2o8b2o5b2o7bo15bo4b4ob3o9bo107b2o106b2o107bo9b3ob4o4bo15bo7b2o5b2o8b2o\$149bo11bo3bo8b3o15bo2bo5b3o7b3o3b2o314b2o3b3o7b3o5bo2bo15b3o8bo3bo11bo\$161bobobo7b3obo15bo2b5o9bo6bo316bo6bo9b5o2bo15bob3o7bobobo\$162b3o9bo3bo15b2o4bo10b5obo6b2o2b2o30bo230bo30b2o2b2o6bob5o10bo4b2o15bo3bo9b3o\$164bo10bo3bo16b3obo10bo4bo7b2o2b2o31bo228bo31b2o2b2o7bo4bo10bob3o16bo3bo10bo\$176bob3o15bo2bobob3o7b3o43b3o228b3o43b3o7b3obobo2bo15b3obo\$152b3o8bo7b2o4b3o19bob2o4bo2b2o3b4o3b10o288b10o3b4o3b2o2bo4b2obo19b3o4b2o7bo8b3o\$152bo18bo6bo13bo7b2ob2o2bo2b2obo2b7o4bo4bo286bo4bo4b7o2bob2o2bo2b2ob2o7bo13bo6bo18bo\$153bo7bob3o6b3o18bo12bo2bo3bo3bo5b3o3bobobo284bobobo3b3o5bo3bo3bo2bo12bo18b3o6b3obo7bo\$144b2o17b2obo7bo16b3o13b2ob2o7bob3o3bobobobo284bobobobo3b3obo7b2ob2o13b3o16bo7bob2o17b2o\$148bo14bob2o41bobo10bobobobo4bo286bo4bobobobo10bobo41b2obo14bo\$143b2o2bobo14b3obo39bobo8bo3bobo2bob2o288b2obo2bobo3bo8bobo39bob3o14bobo2b2o\$142bo2b3obobo57bo9b5ob2obobo290bobob2ob5o9bo57bobob3o2bo\$143b6o2bo14bo61bobo39bo210bo39bobo61bo14bo2b6o\$144b2ob2o72bo6b2o41bo208bo41b2o6bo72b2ob2o\$141bo2b6o70bobo46b3o208b3o46bobo70b6o2bo\$141bobob3o2bo11b3o56bo308bo56b3o11bo2b3obobo\$143bobo2b2o12bo15b3o21bo346bo21b3o15bo12b2o2bobo\$144bo18bo13bo25bo344bo25bo13bo18bo\$147b2o28bo3bo19b3o344b3o19bo3bo28b2o\$177bo2bobo8bo368bo8bobo2bo\$179bobo2bo4b3o368b3o4bo2bobo\$180bo3bo3bo374bo3bo3bo\$184bo3b2o90bo190bo90b2o3bo\$181b3o97bo188bo97b3o\$186bo92b3o188b3o92bo\$172b3o10bobo376bobo10b3o\$172bo13b2o2b2o20bo326bo20b2o2b2o13bo\$173bo16b2o21bo324bo21b2o16bo\$211b3o5b2o5b2o296b2o5b2o5b3o\$219b2o5bo298bo5b2o\$224bobo298bobo\$224b2o300b2o\$182bobo35b2o68bo170bo68b2o35bobo\$182b2o36bobo68bo168bo68bobo36b2o\$183bo8b2o27bo67b3o168b3o67bo27b2o8bo\$192bobo362bobo\$185b2o5bo20bo10b2o300b2o10bo20bo5b2o\$181b2o2b2o24b2o11b2obo296bob2o11b2o24b2o2b2o\$180bobo29b2o14bo294bo14b2o29bobo\$181bo43bo300bo43bo\$177bo48bob2o292b2obo48bo\$183b2o43b2o292b2o43b2o\$175b3obo3bo116bo150bo116bo3bob3o\$174bob2o6b3o114bo148bo114b3o6b2obo\$174b2obo8bo15b2o95b3o148b3o95b2o15bo8bob2o\$172bob3o25bo3bo338bo3bo25b3obo\$202bo4bo336bo4bo\$174bo29bo342bo29bo\$205bo2bo334bo2bo\$207b2o334b2o\$202b3o342b3o\$203b2o342b2o\$204b2o104bo130bo104b2o\$198b3o4b2o104bo128bo104b2o4b3o\$198b3o4bo103b3o128b3o103bo4b3o\$198b3o5b3o334b3o5b3o\$195b3o10bo334bo10b3o\$195b3o356b3o\$195b3o356b3o4\$320bo110bo\$321bo108bo\$319b3o108b3o8\$330bo90bo\$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).
-Matthias Merzenich
Sokwe
Moderator

Posts: 1480
Joined: July 9th, 2009, 2:44 pm

### Re: Incomplete search patterns - try to complete

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.
`x = 19, y = 14, rule = B3/S23bboo3boo\$bobbobobbo\$bobooboobo\$oobbobobboo\$bbobobobobbo\$bbooboobob3o4boo\$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.
`x = 32, y = 35, rule = B3/S2317boo5boo\$4boo11boo5boboboo\$26bobobo\$bbo3bo8b4o3b5obobo\$bbo4bo7bo3bobobo3booboo\$4bobobo8bobobo3bo5bo\$5bobobo6bobboo4b3ob3o\$6bo4bo4b3o7boobo\$7bo3bo\$bbobo\$5bobboo\$bobbo\$obobo5bo\$obbo5bobo\$boo5bo3bo9boo\$9bobo8bobbo\$10bo9b3o\$\$10bo9b3o\$9bobo8bobbo\$boo5bo3bo9boo\$obbo5bobo\$obobo5bo\$bobbo\$5bobboo\$bbobo\$7bo3bo\$6bo4bo4b3o7boobo\$5bobobo6bobboo4b3ob3o\$4bobobo8bobobo3bo5bo\$bbo4bo7bo3bobobo3booboo\$bbo3bo8b4o3b5obobo\$26bobobo\$4boo11boo5boboboo\$17boo5boo!`

- A p6 fencepost to complete this wickstretcher:
EDIT: done -- see below.
`x = 44, y = 44, rule = B3/S2332bo7bo\$31boo5boobo\$31bobo3boobbo\$35boobbo\$33b5o\$25b3oboob3o\$20b3obbobboboboo\$20bo5b3oboo\$21bo\$17bo6boo\$16boo4bobo\$16bobo3b4o\$23bo\$19boo\$19boo\$\$10boo9bo\$9boo9b3o\$11bo7bobo\$13boo3booboo\$6boo5boobbobboo\$6bobo7b6o\$6bo3boo5bobo3b3o\$11boo9b3o\$9b3o10b3o\$5boobbobo10bo3b3o\$5bobo17b3o\$5bobo17b3o\$6boo17bo3b3o\$5bo22b3o\$5b3o20b3o\$boo4bo20bo3b3o\$oo3boo24b3o\$bbob3o24b3o\$4boo25bo3b3o\$3boo29b3o\$3boo29b3o\$bbobo29bo3b3o\$boo34b3o\$bobo33b3o\$o36bo3b3o\$boo37b3o\$40b3o\$40bo!`

- A c/5 orthogonal "spaceship" to complete this wavestretcher. (c/6 diagonal would also work.)
EDIT: done -- see below.
`x = 90, y = 42, rule = B3/S2332bo\$31boo\$31bobo\$\$26boo5b3o\$25boobboob5obooboo\$27bobbob3o3boo3booboo\$29b3obbo8boo3booboo\$28bo5bo6boo5boo3booboo\$22boo9bo3bo8boo5boo3booboo\$22bobo3boobbo3bo14boo5boo3booboo\$22bo4boobo25boo5boo3booboo\$25bobb3oboobo25boo5boo3booboo\$14boo9boob3o35boo5boo3booboo\$14bobo3bo4bobo43boo5boo3booboo\$14bo3b3oboo3boo47boo5boo3boo\$17boo8boo52boo5boo\$20b3o4bo58boo\$18bo3b3o\$17bo6bo\$17bobboboo\$16boobo\$16bobo\$15b4o\$14bo3boo\$13boo3boo\$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:
`x = 59, y = 98, rule = B3/S2358bo\$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.
`x = 44, y = 20, rule = B3/S23oo\$bboo\$bbooboo\$oo5boo\$7booboo\$5boo5boo\$12booboo\$10boo5boo\$17booboo\$15boo5boo\$22booboo\$20boo5boo\$27booboo\$25boo5boo\$32booboo\$30boo5boo\$37booboo\$35boo5boo\$42boo\$40boo!`

- An extensible stabilisation for this p2 agar:
`x = 43, y = 43, rule = S23/B319booboo\$13boo5bobobboo\$14bo3bo4bobobbo\$14bob3oboobo3boo\$15bo5bobbo\$17b3oboobbo\$16boobbobo8boo\$10bo4bo3bo5boo3bobbo\$9bobo3bo5boo7boobo\$7b3obo5boo7b3obobboo\$6bo6boo7boo4bobbo3bo\$6bobobo7boo5bo3bo3boo\$7b3o4boo5bo3bo\$11bo5bo3bo5boo3bo8bo\$bboo5boobbo3bo5boo5bobo6b3o\$3bo5bo3bo5boo5bo3bo3boobbo\$bo5bobo5boo5bo3bo9bobbo\$boobbobo3boo5bo3bo5boo3bobboobo\$4bo9bo3bo5boo5bobo3boboo\$oboo6bo3bo5boo5bo3bo3bobo4bo\$oo3boobobo5boo5bo3bo8bobboboo\$3b3obbo3boo5bo3bo5boo3bobb3o\$oobobbo8bo3bo5boo5boboboo3boo\$o4bobo3bo3bo5boo5bo3bo6boobo\$bboobo3bobo5boo5bo3bo9bo\$3boboobbo3boo5bo3bo5boo3bobobboo\$3bobbo9bo3bo5boo5bobo5bo\$4bobboo3bo3bo5boo5bo3bo5bo\$b3o6bobo5boo5bo3bobboo5boo\$bo8bo3boo5bo3bo5bo\$17bo3bo5boo4b3o\$8boo3bo3bo5boo7bobobo\$7bo3bobbo4boo7boo6bo\$8boobbob3o7boo5bob3o\$9boboo7boo5bo3bobo\$9bobbo3boo5bo3bo4bo\$10boo8bobobboo\$17bobboob3o\$18bobbo5bo\$14boo3boboob3obo\$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):
`x = 9, y = 14, rule = S23/B37boo\$7boo10\$bbo\$b3o\$oobbo!`

dvgrn
Moderator

Posts: 5818
Joined: May 17th, 2009, 11:00 pm

### Re: Incomplete search patterns - try to complete

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

c/5 part by Matthias Merzenich, 15 Apr 2011:
`x = 103, y = 75, rule = B3/S2370bo\$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\$48bo29b2o5b2o5b2o5b2o\$48b5o23bo3bo3bo2bo3bo2bo3bo3bo\$76bo3bobob3o5b3obobo3bo\$76bo5b2o2b3ob3o2b2o5bo\$46b2o21b2o5b2ob3o15b3ob2o\$40bobo3bobo20bobo4bo25bo\$31b2o6b2o2b2o2bo21bobo5bo3bo15bo3bo\$30b2o10bobo24bo3b2o3bo2bo15bo2bo\$31bobo9bobo5bo7bob4obo6b2o\$26bo4b3o9b2o4b4o4bob3obobobo6bo\$25b5ob3o2bobob2o2b3ob2o3b4o12bo\$25bo2b2o6bo4bo2bo2bo3bo2b2o5bobo3bob2o\$35bo3bo4bo3b4obo3bo4b7o\$27b2o2b2ob2o2bo10b2ob2o4bo4bo\$35bo28bo\$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!`
Shannon Omick
skomick

Posts: 74
Joined: February 11th, 2011, 11:41 pm

### Re: Incomplete search patterns - try to complete

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

I also found this alternate c/5 part two days later:
`x = 112, y = 50, rule = B3/S2351b2o5b2o5b2o5b2o\$49bo3bo3bo2bo3bo2bo3bo3bo\$49bo3bobob3o5b3obobo3bo\$49bo5b2o2b3ob3o2b2o5bo\$49b2ob3o15b3ob2o\$49bo25bo\$50bo3bo15bo3bo\$46b2o3bo2bo15bo2bo\$40bobo3bobo\$31b2o6b2o2b2o2bo\$30b2o10bobo31bo10bo3b3o5b3o3bo\$31bobo9bobo5bo7bob4obo8bo2bo5b2ob5ob2o3b2ob5ob2o\$26bo4b3o9b2o4b4o4bob3obobobo2b2o3bo2bo3bob2obo5bobobobo5bob2obo\$25b5ob3o2bobob2o2b3ob2o3b4o12bobo2bo4bobo3bobo3b5ob5o3bobo3bo\$25bo2b2o6bo4bo2bo2bo3bo2b2o5bobo3bob2o3bo4bo5b3o5b2o3b2o5b3o\$35bo3bo4bo3b4obo3bo4b7o10bo2bo2bob3o13b3obo2bo\$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!`

dvgrn wrote:A p6 fencepost to complete this wickstretcher

By Jason Summers and me, January 2013:
`x = 61, y = 61, rule = B3/S2338b2o\$37b2o\$39bo\$41b2o\$40bo\$32b2o\$32bo2b2o2bo2bo\$32bob3o2bo\$33bo4bo2bo\$27bo5bo6bo\$26b2o5bo2bo\$26bobo\$33bo\$23bo5bob3obo\$22b2o4b2o3bo23b2o\$22bobo2b2o2bobobo5b4o11b4o\$26bo6bobo4bo4bo9bo2bobo\$25b2ob2o10bo3bobo7bobo2b2o\$26bo14bo3bobo5bobo\$47bo4b2o\$26bo20bo4b3o\$24b2o18bo2bo5bobo\$14b2o7bobo19b2o7b2o\$13b2o7bo27bo\$15bo5bo2b2obo21b3o\$17bo3b2obo3bo20b3o\$10b2o4b3obo28b3o\$9b2o4bo8bo2b2obo10b2o6b3o\$11bo2b2obo7bobo3bo8b4o6bo\$13b2o2bo21bobo2bo\$27bo2b2obo5b2o2bobo\$13bobo12bobo3bo9bobo2b2o\$5b3o5bo32b2o2b2o\$5bo2b3ob5o13bo2b2obo8b3ob3o\$7bo23bobo3bo6bobo2b3o\$6b2o5bob2o27b2o3b3o\$6b2o2bo22bo2b2obo10bo\$bo32bobo3bo\$2o6bo\$obo3b2o21b2o5bo2b2obo\$4bo4bo6b2o10bobo6bobo3bo3b5o\$3bo4bo6bo2bo8b3o\$3bo2bo8bo11b2o10bo2b2ob2ob2o\$15bo12bobo9bobo5bo\$15bobo3bo7bobo2b2o10bo\$16bobo3bo7bo2bobo6bo2bo\$17bo4bo8b4o7bobo\$18b4o10b2o6bo\$40bob2o\$24b4o3bob3o4bobo\$23b6o2b6o3bo\$24b4o4b4o4bo\$19b2o\$18b4o\$17bo2bobo\$16bobo2b2o\$15bobo\$14b2o\$14b3o\$15bobo\$16b2o!`

dvgrn wrote:2c/5 terminations for this wave

One side of the waveguide by Nicolay Beluchenko, November 2008
`x = 64, y = 59, rule = B3/S2326bo\$18bo5b2ob2o\$17b3o4b2o2bob2o\$16bo5b2ob2o5b2o\$16b3o3bob2o6b2ob2o\$18b2o2bo7b2o5b2o\$9bo13b3o11b2ob2o\$8b3o4b5o5b2o8b2o5b2o\$8bo3b2ob4o3bo4bo14b2ob2o\$5b5o4bo7bo4bo12b2o5b2o\$3b2ob4o2bo2b2o8b3o19b2ob2o\$6bo2b3o13b2o18b2o5b2o\$7bo4bo39b2ob2o\$9b6o11b2o22b2o5b2o\$4bob3o6bo41b2ob2o\$11bo3b2o38b2o5b2o\$4bobo4bo3bo46b2o\$3b3o4bo4bo44b2o\$3bo6b6o\$10bo4bo\$10bob2o\$11b2o\$4bo6b3o\$3b3o2b3o\$2b2o2b2o6b2o\$3bo2bo3b3ob3o\$3bo7bo2b3o\$3bo6b2o2b2o\$4b2o\$10b2o\$10b3o\$7b2o3b2o\$6bob2o4bo\$6b4ob2o2bo\$8b3o4bo\$6bobob4ob2o\$6bo8b2o\$6bobob2ob3o\$6bo3bo2bo\$5b2obob2o\$5b2o3bo\$7bob2o\$7bo2\$5b2o\$4b2o\$7bo\$2b6ob3o\$2o5bo4bo\$3o4b2obobo\$2o2bob3obo\$2bob3o\$2b2ob3o2bo\$bob2o2bobo2\$6b2o\$5b5o\$5b2o2bo\$8bo!`
-Matthias Merzenich
Sokwe
Moderator

Posts: 1480
Joined: July 9th, 2009, 2:44 pm

### Re: Incomplete search patterns - try to complete

dvgrn wrote:- 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:

`x = 75, y = 43, rule = B3/S2332b2o7b2o\$32bobo5bobo\$27b2ob2o2bo5bo2b2ob2o\$28bobo3b2o3b2o3bobo\$28bo2b3o2bobo2b3o2bo\$26b2obobob2obobob2obobob2o\$27bobobo3bo3bo3bobobo\$26bo2bo4bo5bo4bo2bo\$26bobob3o9b3obobo\$27b2o4b2o5b2o4b2o\$29b2obo9bob2o\$10b2o4b2o7b6o13b6o7b2o4b2o\$10bobo4bo3b2obo25bob2o3bo4bobo\$6b2o4bo3bo3bobobobo5b2o7b2o5bobobobo3bo3bo4b2o\$6bobo2bob2o2b4o2bobobo4b2o7b2o4bobobo2b4o2b2obo2bobo\$3bo4b4obob2o4bobo2b2obobo11bobob2o2bobo4b2obob4o4bo\$3b5o10b4ob2o2b2obo13bob2o2b2ob4o10b5o\$8bo2b2obob3obo3bo2bo2bo13bo2bo2bo3bob3obob2o2bo\$3b2o2bo2bobobo4bo4bo2bo19bo2bo4bo4bobobo2bo2b2o\$3bo2bo7bo2b2o8bo2bo3bo5bo3bo2bo8b2o2bo7bo2bo\$8bobo2b2o3bo3bo2bobo2bo2bobo3bobo2bo2bobo2bo3bo3b2o2bobo\$4bob2obo4b2o2bo3b2obob2o3bo3bobo3bo3b2obob2o3bo2b2o4bob2obo\$2o2bo8b2o2b5o11bobo3bobo11b5o2b2o8bo2b2o\$bo3b2o7bo3bobo13bo5bo13bobo3bo7b2o3bo\$bobobo3b2obobob2o39b2obobob2o3bobobo\$2b2o2bo2bob2obobo41bobob2obo2bo2b2o\$5b2o7bobo3b2ob2o25b2ob2o3bobo7b2o\$14b2o4b2obo2b2o19b2o2bob2o4b2o\$23bobobo19bobobo\$23bo3bo19bo3bo\$24b3o21b3o\$26bo8b2ob2o8bo\$24b2o10bobo10b2o\$23bo10bobobobo10bo\$23b2o9b2o3b2o9b2o\$20b2obo27bob2o\$20bo2bob2o21b2obo2bo\$21b3o2b2o19b2o2b3o\$24bob2o19b2obo\$21b4o25b4o\$21bo4b2o19b2o4bo\$22b3obo21bob3o\$24b3o21b3o!`
Kasuha

Posts: 55
Joined: November 1st, 2012, 11:39 am

### Re: Incomplete search patterns - try to complete

The T-nosed p4 gives a little more room to work in some cases:
`x = 75, y = 36, rule = B3/S2332b2o7b2o\$32bobo5bobo\$27b2ob2o2bo5bo2b2ob2o\$28bobo3b2o3b2o3bobo\$28bo2b3o2bobo2b3o2bo\$26b2obobob2obobob2obobob2o\$27bobobo3bo3bo3bobobo\$26bo2bo4bo5bo4bo2bo\$26bobob3o9b3obobo\$27b2o4b2o5b2o4b2o\$29b2obo9bob2o\$10b2o4b2o7b6o13b6o7b2o4b2o\$10bobo4bo3b2obo25bob2o3bo4bobo\$6b2o4bo3bo3bobobobo5b2o7b2o5bobobobo3bo3bo4b2o\$6bobo2bob2o2b4o2bobobo4b2o7b2o4bobobo2b4o2b2obo2bobo\$3bo4b4obob2o4bobo2b2obobo11bobob2o2bobo4b2obob4o4bo\$3b5o10b4ob2o2b2obo13bob2o2b2ob4o10b5o\$8bo2b2obob3obo3bo2bo2bo13bo2bo2bo3bob3obob2o2bo\$3b2o2bo2bobobo4bo4bo2bo19bo2bo4bo4bobobo2bo2b2o\$3bo2bo7bo2b2o8bo2bo3bo5bo3bo2bo8b2o2bo7bo2bo\$8bobo2b2o3bo3bo2bobo2bo2bobo3bobo2bo2bobo2bo3bo3b2o2bobo\$4bob2obo4b2o2bo3b2obob2o3bo3bobo3bo3b2obob2o3bo2b2o4bob2obo\$2o2bo8b2o2b5o11bobo3bobo11b5o2b2o8bo2b2o\$bo3b2o7bo3bobo13bo5bo13bobo3bo7b2o3bo\$bobobo3b2obobob2o39b2obobob2o3bobobo\$2b2o2bo2bob2obobo9bo21bo9bobob2obo2bo2b2o\$5b2o7bobo8b3o19b3o8bobo7b2o\$14b2o9b3o19b3o9b2o\$25bobo19bobo\$25b3o19b3o\$24b5o17b5o\$23bo5bo5b2ob2o5bo5bo\$23bo5bo6bobo6bo5bo\$22b2obobob2o3bobobobo3b2obobob2o\$21bo2b2ob2o2bo2b2o3b2o2bo2b2ob2o2bo\$21b2o7b2o11b2o7b2o!`
-Matthias Merzenich
Sokwe
Moderator

Posts: 1480
Joined: July 9th, 2009, 2:44 pm

### Re: Incomplete search patterns - try to complete

dvgrn wrote:- p7 mono sparker that can perform the TL push demonstrated here:
`x = 19, y = 14, rule = B3/S23bboo3boo\$bobbobobbo\$bobooboobo\$oobbobobboo\$bbobobobobbo\$bbooboobob3o4boo\$oo10bo3b3o\$boboobobo3bo4boo\$bobbo7bo\$bbo3bobo3bo\$3b3obooboo\$5bo4bo\$6b3obo\$8boo!`

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

`x = 65, y = 19, rule = B3/S2321b2o19b2o\$12b2o7bo21bo7b2o\$3bobo4bo2bo2b2o5bo17bo5b2o2bo2bo4bobo\$3b2obo3b2obobobo4b2o17b2o4bobobob2o3bob2o\$6bo6bobo33bobo6bo\$b4ob2o2b2obob2o3bo23bo3b2obob2o2b2ob4o\$o3bo4bobobo4b2obo2bob2o9b2obo2bob2o4bobobo4bo3bo\$obo2bob3obo2bo2bobo4bobo11bobo4bobo2bo2bob3obo2bobo\$b3obo5b3ob3obobob2obo11bob2obobob3ob3o5bob3o\$11bo2b2o3bo3bob2o4b2o5b2obo3bo3b2o2bo\$b3obo5b3ob3obobob2obo3b3o5bob2obobob3ob3o5bob3o\$obo2bob3obo2bo2bobo4bobo4b2o5bobo4bobo2bo2bob3obo2bobo\$o3bo4bobobo4b2obo2bob2o9b2obo2bob2o4bobobo4bo3bo\$b4ob2o2b2obob2o3bo23bo3b2obob2o2b2ob4o\$6bo6bobo33bobo6bo\$3b2obo3b2obobobo4b2o17b2o4bobobob2o3bob2o\$3bobo4bo2bo2b2o5bo17bo5b2o2bo2bo4bobo\$12b2o7bo21bo7b2o\$21b2o19b2o!`
Kasuha

Posts: 55
Joined: November 1st, 2012, 11:39 am

### Re: Incomplete search patterns - try to complete

Kasuha wrote:I guess it counts as a new p14 oscillator?

Very nice! It can be extended in the obvious way:
`x = 100, y = 19, rule = B3/S2321b2o54b2o\$12b2o7bo56bo7b2o\$3bobo4bo2bo2b2o5bo52bo5b2o2bo2bo4bobo\$3b2obo3b2obobobo4b2o11b2o5b2o5b2o5b2o5b2o11b2o4bobobob2o3bob2o\$6bo6bob2o5bo12b2o5b2o5b2o5b2o5b2o12bo5b2obo6bo\$b4ob2o2b2obobo5b2o54b2o5bobob2o2b2ob4o\$o3bo4bobobo5bob4ob2o4bo6bo6bo6bo6bo6bo4b2ob4obo5bobobo4bo3bo\$obobob4obob2o3b2o4bobo4bo8bo4bo8bo4bo8bo4bobo4b2o3b2obob4obobobo\$b2o9b2o2b2obob2o3bo4bo8bo4bo8bo4bo8bo4bo3b2obob2o2b2o9b2o\$6b2ob2o4bo4bo3b2o5bo8bo4bo8bo4bo8bo5b2o3bo4bo4b2ob2o\$b2o9b2o2b2obob2o3bo5bo6bo6bo6bo6bo6bo5bo3b2obob2o2b2o9b2o\$obobob4obob2o3b2o4bobo46bobo4b2o3b2obob4obobobo\$o3bo4bobobo5bob4ob2o7b2o5b2o5b2o5b2o5b2o7b2ob4obo5bobobo4bo3bo\$b4ob2o2b2obobo5b2o12b2o5b2o5b2o5b2o5b2o12b2o5bobob2o2b2ob4o\$6bo6bob2o5bo54bo5b2obo6bo\$3b2obo3b2obobobo4b2o52b2o4bobobob2o3bob2o\$3bobo4bo2bo2b2o5bo52bo5b2o2bo2bo4bobo\$12b2o7bo56bo7b2o\$21b2o54b2o!`
-Matthias Merzenich
Sokwe
Moderator

Posts: 1480
Joined: July 9th, 2009, 2:44 pm

### Re: Incomplete search patterns - try to complete

dvgrn wrote: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.
Ivan Fomichev

codeholic
Moderator

Posts: 1142
Joined: September 13th, 2011, 8:23 am
Location: Hamburg, Germany

### Re: Incomplete search patterns - try to complete

I built a naive 5/4 track multiplication as a proof of concept. One could probably find something more effective.
`x = 258, y = 379, rule = B3/S23249bobo\$206bo42b2o\$204b2o44bo\$205b2o4\$219bobo\$219b2o\$220bo15\$257bo\$255b2o\$256b2o16\$225bo\$224bo\$180bo43b3o\$180bobo\$180b2o3\$195bo\$194bo\$194b3o16\$231bo\$231bobo\$231b2o16\$201bo\$199b2o\$155bobo42b2o\$155b2o\$156bo3\$171bo\$169b2o\$170b2o16\$206bobo\$206b2o\$207bo16\$175bo\$131bo43bobo\$130bo44b2o\$130b3o4\$145bo\$145bobo\$145b2o15\$182bo\$181bo\$181b3o17\$150bobo\$107bo42b2o\$105b2o44bo\$106b2o4\$120bobo\$120b2o\$121bo15\$158bo\$156b2o\$157b2o16\$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\$25bo41bo\$25bobo36bo2bo\$25b2o38b2o\$40bo24b2o\$40b2o22bo2bo\$42bo21bo\$40b2o24b2o\$39bobo\$40bo\$38bobo\$36bo\$36bobo2\$83bo\$82bo\$80b2ob2o\$79b5o\$78b2o2bo\$78bob4o\$78bo4bo\$78bo2b2o\$80b2o2\$60b2o14bo\$59bobo14bobo\$60bo15b2o11\$47bo\$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.
Ivan Fomichev

codeholic
Moderator

Posts: 1142
Joined: September 13th, 2011, 8:23 am
Location: Hamburg, Germany

### Re: Incomplete search patterns - try to complete

Small glider duplicator needs a catalyst instead of a ship:
`x = 19, y = 15, rule = B3/S236bo10b2o\$7b2o8bo\$6b2o7bobo\$15b2o2\$2o\$2o2\$9b2o\$9b2o3\$10b2o\$10bobo\$11b2o!`
knightlife

Posts: 566
Joined: May 31st, 2009, 12:08 am

### Re: Incomplete search patterns - try to complete

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

`x = 397, y = 21, rule = B3/S236bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo\$6bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo\$6bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo5\$2bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo\$2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o\$2bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo2\$2bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo\$2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o\$2bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo23bo7bo5\$6bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo\$6bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo\$6bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo31bo!`

That would leave just three unknown oscillator periods, namely 19, 23 and 38.
What do you do with ill crystallographers? Take them to the mono-clinic!

calcyman

Posts: 2088
Joined: June 1st, 2009, 4:32 pm

### Re: Incomplete search patterns - try to complete

calcyman wrote: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.
Princess of Science, Parcly Taxel

Freywa

Posts: 580
Joined: June 23rd, 2011, 3:20 am
Location: Singapore

### Re: Incomplete search patterns - try to complete

Freywa wrote: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.
MikeP

Posts: 81
Joined: February 7th, 2010, 9:51 am
Location: Cambridge, UK

### Re: Incomplete search patterns - try to complete

p41-critical.png (1.63 KiB) Viewed 76658 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.
Princess of Science, Parcly Taxel

Freywa

Posts: 580
Joined: June 23rd, 2011, 3:20 am
Location: Singapore

### Re: Incomplete search patterns - try to complete

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).
What do you do with ill crystallographers? Take them to the mono-clinic!

calcyman

Posts: 2088
Joined: June 1st, 2009, 4:32 pm

### Re: Incomplete search patterns - try to complete

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:

`x = 121, y = 27, rule = B3/S23118bo\$116b3o\$115bo\$6bo31bo31bo31bo12b2o\$6bo31bo31bo31bo\$6bo31bo31bo31bo2\$119b2o\$119b2o2\$2bo7bo23bo7bo23bo7bo23bo7bo\$2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o\$2bo7bo23bo7bo23bo7bo23bo7bo2\$2bo7bo23bo7bo23bo7bo23bo7bo\$2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o\$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.
Kasuha

Posts: 55
Joined: November 1st, 2012, 11:39 am

### Re: Incomplete search patterns - try to complete

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.
Princess of Science, Parcly Taxel

Freywa

Posts: 580
Joined: June 23rd, 2011, 3:20 am
Location: Singapore

### Re: Incomplete search patterns - try to complete

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:
`x = 123, y = 27, rule = B3/S23118bo\$116b3o\$115bo\$6bo31bo31bo31bo12b2o\$6bo31bo31bo31bo\$6bo31bo31bo31bo18b2o\$121bo\$119bobo\$119b2o2\$2bo7bo23bo7bo23bo7bo23bo7bo\$2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o\$2bo7bo23bo7bo23bo7bo23bo7bo14bo\$120bobo\$2bo7bo23bo7bo23bo7bo23bo7bo14bo\$2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o\$2bo7bo23bo7bo23bo7bo23bo7bo2\$119b2o\$119bobo\$121bo\$6bo31bo31bo31bo18b2o\$6bo31bo31bo31bo\$6bo31bo31bo31bo12b2o\$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:
`x = 128, y = 27, rule = B3/S23118bo\$116b3o\$115bo\$6bo31bo31bo31bo12b2o\$6bo31bo31bo31bo\$6bo31bo31bo31bo2\$120b2o\$119bo2bo\$120b2o\$2bo7bo23bo7bo23bo7bo23bo7bo19b2o\$2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o17b2o\$2bo7bo23bo7bo23bo7bo23bo7bo2\$2bo7bo23bo7bo23bo7bo23bo7bo\$2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o19b2ob2o3b2ob2o17b2o\$2bo7bo23bo7bo23bo7bo23bo7bo19b2o\$120b2o\$119bo2bo\$120b2o2\$6bo31bo31bo31bo\$6bo31bo31bo31bo\$6bo31bo31bo31bo12b2o\$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?
Sphenocorona

Posts: 480
Joined: April 9th, 2013, 11:03 pm

### Re: Incomplete search patterns - try to complete

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.
`#S first-encounter 4#S last-encounter 34#S repair-interval 31#P 2 2.............??????????????????.............??????????????????.............??????????????????.............??????????????????.............??????????????????.............??????????????????........@..........????????????.@.......@.....@@..????????????.@...@@..@....@..@.????????????@@....@....@@..@@..????????????........@@..@......????????????..@........@@......????????????..@.@@@@@@@........????????????...................????????????..@.@@@@@@@........????????????..@........@@......????????????........@@..@......????????????@@....@....@@..@@..????????????.@...@@..@....@..@.????????????.@.......@.....@@..????????????........@..........????????????.............??????????????????.............??????????????????.............??????????????????.............??????????????????.............??????????????????.............??????????????????#F 35 15 8........**...*..*...**........??????????????????????????????????????????........**...*..*...**........`
Princess of Science, Parcly Taxel

Freywa

Posts: 580
Joined: June 23rd, 2011, 3:20 am
Location: Singapore

PreviousNext