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Re: Thread for your unsure discoveries

Posted: February 6th, 2025, 10:26 pm
by confocaloid
That's not even a wave to begin with. It might be described as "p300 orthogonal 14c/75 extensible dirty puffer partial", which sounds like a category where nobody ever actually tried to keep track of what is or isn't known (so the question is probably unanswerable).
Timelord Missionary wrote: February 6th, 2025, 9:35 pm This wave is known, right?

Code: Select all

x = 45, y = 53, rule = Life:T54,0
7$10bo19bo$10b2o17b2o$9b4o15b4o$6b3o3b2o13b2o3b3o$6bo5bo15bo5bo$6bo27b
o$7bo4bo15bo4bo$9bo2b2o13b2o2bo$10bob2o13b2obo$11b2o15b2o4$13b2o11b2o
$13b2o11b2o5$2bo35bo$2bobo31bobo$2b2o33b2o5$5b2o27b2o$5b2o27b2o4$5b2o
27b2o$5b2o27b2o$13b2o11b2o$12bo2bo9bo2bo$13bobo9bobo$4b2o8bo11bo8b2o$
4b2o29b2o!

Re: Thread for your unsure discoveries

Posted: February 7th, 2025, 12:25 pm
by eRroR_6o6
Transparent beehive catalysis, anyone?

Code: Select all

x = 11, y = 11, rule = B3/S23
bo$obo$obo3b3o$bo3bo2bo$5bo2bo$6b2o3$8b2o$7bo2bo$8b2o!

Re: Thread for your unsure discoveries

Posted: February 7th, 2025, 8:00 pm
by dbell
I recently saw the posting viewtopic.php?f=2&t=515&p=160591&hilit= ... ip#p160591 by PHPBB12345 about a period 60 3c/10 PI-crawling reaction supported by two rows of blocks.

That reaction is really useful. Firstly, it has sparks which extend past the block rows which can perturb objects as it passes by. Secondly, it can be reached from behind by a c/2 spaceship stream. Thirdly, the gaps between components are large enough to allow gliders to pass through.

Here are a few results I found.

Code: Select all

#C A period 60 3c/10 PI-based crawler converts a LWSS to a forward glider.
#C This shows two LWSSs from a stream separated by 12 cells showing
#C that the reaction is repeatable.  Similar reactions exist to create
#C backward gliders or other objects.
x = 73, y = 97
8bo7bo39bo7bo$7b3o5b3o37b3o5b3o$6boobo5boboo35boobo5boboo$7boobo3boboo
37boobo3boboo$5boboo7boobo33boboo7boobo$4bobobbobobobobbobo31bobobbobo
bobobbobo$4bobo3booboo3bobo31bobo3booboo3bobo$5b3obo5bob3o33b3obo5bob
3o$6b3o7b3o35b3o7b3o$6boo9boo35boo9boo$6bo11bo35bo11bo$5boo11boo33boo
11boo$5boo11boo33boo11boo$$9boo3boo41boo3boo$9boo3boo4bo31bo4boo3boo$
4bo14b3o29b3o14bo$3b3o13boboo27boobo13b3o$3boboo13b3o27b3o13boobo$5boo
13b3o27b3o13boo$3boo14b4o27b4o14boo$3boobbo11bobbo27bobbo11bobboo$bbo
4bo14boo25boo14bo4bo$3bobobbo11bobo27bobo11bobbobo$3boo3boo10b3o27b3o
10boo3boo$10bo51bo$8boo4bo43bo4boo$10b6o6boo25boo6b6o$3o7bobobobo4bobb
o23bobbo4bobobobo7b3o$3bo9bobbo3bo31bo3bobbo9bo$4bo10bo4bobbo25bobbo4b
o10bo$bobo17bo29bo17bobo10$36bo$35bobo$23boo9booboo9boo$23boo23boo4$
26boo17boo$27bo17bo$33boo3boo$33boo3boo$32bobo3bobo$29boobobo3boboboo$
28boo13boo$27boo3bo7bo3boo$26bobobb3o5b3obbobo$$20b3o4bo17bo4b3o$20b3o
4boo15boo4b3o$19bo3boobbo17bobboo3bo$20boobobbo19bobboboo$20boo3boo5b
oo5boo5boo3boo$23boo7boo5boo7boo$24bo23bo16$51b3o$51bobbo$51bo$51bo$
52bobo8$51b3o$51bobbo$51bo$51bo$52bobo!

Code: Select all

#C A period 60 3c/10 PI-based crawler used for a forward rake.
#C This uses two rows of blocks and a row of boats to support the reaction.
#C David I. Bell, 8 February 2025
x = 117, y = 241
15b3o3b3o$15bobbobobbo$15bo7bo$15bo7bo$16bobobobo$16bobobobo$17bo3bo$
16b3ob3o$3o5bo10bo$obbo3b3o5b9o$o6boboo3bo9bo$o7bobo3b12o$o7bo3bo13bo$
boboboo4b17o65b3o3b3o$5bo3bo18bo64bobbobobbo$4booboboobbob15o63bo7bo$
4boobobo3bo16bo10bo51bo7bo$9bo7bob13o8b3o51bobobobo$17bo14bo6boobo51bo
bobobo$21bob11o5b3o53bo3bo$21bo12bo5boo52b3ob3o$25bob10o60bo10bo5b3o$
25bo11boo54b9o5b3o3bobbo$29bob3o9bo48bo9bo3boobo6bo$29bo4b5o3b3o46b12o
3bobo7bo$33bo8boboo44bo13bo3bo7bo$43b3o43b17o4boobobo$35bo7b3o42bo18bo
3bo$35boo6b3o41b15obobbooboboo$43boo30bo10bo16bo3boboboo$74b3o8b13obo
7bo$74boboo6bo14bo$75b3o5b11obo$75boo5bo12bo$80b10obo$26bo51boo11bo$
25b3o45bo9b3obo$25boboo9bo33b3o3b5o4bo$26b3o7boobo31boobo8bo$26b3o5b3o
3bo30b3o$26boo10boo31b3o7bo$34bobo10b3o21b3o6boo$35bo11bobbo21boo$38bo
8bo$35b3oboo6bo3bo$34boo7boobbo3bo28boo$34bo4bobobbobbo31bobbo$36bobb
5o4bobo28bobo$37boo40b3o8bo$38bo50b3o$36bo51boobo$36boo50b3o$88b3o$89b
oo$67b3o$66bobbo$69bo$65bo3bo$65bo3bo$69bo$66bobo3$71boo$76bo6bo$37boo
37boo5bo$37boobo6bo26b4o$46bobo24b3o$35boobbooboobboo19bo5b3obbo3bo$
35boo4b5obo18b3o8bobobobbo$43bobbo7bo10boobo8boo4bo$44boo7b3o9b3o10bo
4bo$52boobo10boo12bo$52b3o$53boo11$47bo28b3o$47bo$46boo$38b3o5bo4boo
29b3o$37bobbo5bo3bobo29bobbo$40bo11bo11bobo15bo$36bo3bo23boo16bo3bo$
40bo24bo16bo3bo$37bobo42bo$83bobo3$60boo$59bobo$61bo4$40b3o7bo$40bobbo
4b5o$40bo6b3oboo$40bo3bo3b5o$40bo3bo5bo$40bo$41bobo3$63boo$62bobo$63bo
4$76bo7bo$75b3o5b3o$74bobboo3boobbo$74bo3bo3bo3bo$75booboobooboo$75boo
bo3boboo$77bo5bo$78booboo$73boobbo5bobboo$73boobbo5bobboo$$77bobobobo$
63boo12boo3boo$62bobo$63bo$72bo$71b3o14bo$70bobboobboo3boo3b3o$69b3ob
oobboo3boo3boboo$70boob3o11b3o$71boobo12boo$72boo13bo$91boo3$87bobo$
82bo6boo$71bo9booboo4bo$70bobo7boobo6bo$70bobo9boboo4bo$63boo5bobo4bo
3boboo4bobo$62bobo6bo4b3obboo5bobo$63bo7bo8b3o6bo$80bo9$101bo7bo$100b
3o5b3o$99bobboo3boobbo$99bo3bo3bo3bo$68boo30booboobooboo$68boo30boobo
3boboo$63boo37bo5bo$62bobo38booboo$63bo34boobbo5bobboo$98boobbo5bobboo
$$102bobobobo$102boo3boo3$97bo$96b3o14bo$96boboobobo3boo3b3o$97bo9boo
bbobboo$97bobo3bo6bob4o$96boobboo7bo5boo$95bobbo16bo$68boo27boobbobo4b
obb3obo$68boo23bo3boobbobo4boo3bobo$63boo28bobbo7bobbo6boo$62bobo28boo
bo4bobo4bobo5bo$63bo30bobo6bo4bobbobboo$95boo3boo7boo3boo13$68boo23boo
$68boo23boo$63boo$62bobo$63bo3$81bo$80bobo$79booboo3$77bo7bo$72boobbob
o5bobobboo$70boobobbo9bobboboo$70bobboo13boobbo$70bo3b4o7b4o3bo$71bo5b
oo5boo5bo$68boobbobb3obo3bob3obbobboo$68boo3b4o9b4o3boo$63boo9boboobbo
bobboobo$62bobo10bo11bo$63bo12b4o3b4o$77bo7bo12$63b3o$63bo$64bo$48b3o$
48bo$49bo!

Code: Select all

#C A period 60 3c/10 PI-based crawler used for a backward rake.
#C This uses two rows of blocks and a row of boats to support the reaction.
#C David I. Bell, 8 February 2025
x = 181, y = 358
104bo5bo$103b3o3b3o$103bobooboobo$104b3ob3o$104b3ob3o$17bo5bo$16b3o3b
3o80bo3bo$15boobo3boboo77b3o3b3o$15b3o5b3o81bo17bo$16boo5boo78b9o5b3o
4b3o$16boo5boo77bo9bo4bobbobboobo$17bobobobo78b11o3bo6b3o$100bo15b3obb
ob3o$bbo14b7o76b18o3bobboo$b3o4b3o5bo7bo73bo18bo3bo$oobo4bobbo4b9o73b
15obobboboboo$3o5bobbo3bo10bo69bo17bobb3obo$3o5booboob13o57b3o9b13obo$
boo5bobobbo14bo54bobbo7bo15bo6bo$5b3o4b17o57bo7b11obo10bo$9boobo17bo
55bo6bo12bo$10boo3bob14o52bobo6b9obo$5boo3bo4bo16bo8b3o45b3o10bo$9bo9b
ob12o7bobbo44boob6obo$19bo14bo8bo38b3o3boobbo5bo$23bob10o8bo38bobbo8bo
$23bo16bobo39bo11bo$27bob10o43bo3bobbobo$27bo8b3o43bo3bo3boo$31bob4o6b
3o36bo$31bo3b4o4bobbo36bobo57bo5bo$35boobbo3bo98b3o3b3o$37boo4bo3bo41b
3o50bobooboobo$37boobobbo3bo41bobboo49b3ob3o$36bo3bobbo48boo49b3ob3o$
35bo8bobo41booboo$36boo50b3o8b3o42bo3bo$88boo3boo4bobbo39b3o3b3o$86boo
5b3o3bo46bo17bo$36b3o45bobbobbobbobbobbo3bo38b9o5b3o4b3o$35bo3bo44bobo
bbobobbo4bo41bo9bo4bobbobboobo$26b3o5bo5bo37bo5bobbobbobbobbo3bobo38b
11o3bo6b3o$26bobbo4bo5bo36b3o6boo5b3o43bo15b3obbob3o$26bo7bo5bo35boobo
8booboo46b18o3bobboo$26bo3bo4bo3bo36b3o9bobobo44bo18bo3bo$26bo9b3o37b
3o58b15obobboboboo$27bobo19bo26b3o10b3o43bo17bobb3obo$48b3o26boo44b3o
9b13obo$47boobo71bobbo7bo15bo6bo$47b3o75bo7b11obo10bo$47b3o75bo6bo12bo
$47b3o72bobo6b9obo$48boo78b3o10bo$127boob6obo$121b3o3boobbo5bo$121bobb
o8bo$76b3o42bo11bo$76bobbo41bo3bob3o$76bo44bo3bobbobbo$76bo44bo6bobbo$
77bobobb3o37bobo4boo$81bobboo$43bo37boobboo$41bobboo40boo$34boo5bobo
41bobo40b3o$36bo3boo43boo40bo3bo$34boo90bo5bo5b3o$127bo3bo6bobbo$128b
3o7bo$138bo3bo$138bo$117bo21bobo$116b3o$115boobo$115b3o$93bo21b3o$54b
3o35b3o20b3o$53bobbo30bo4boboo20boo$56bo30bo5b3o$56bo30bobo3b3o$53bobo
37b3o$93boo$48boo$47bobo$47boboo$47bo3boo19bo52bobo$46boobbobo18bo43b
3o5booboo$47bob3o19b3o41bobbo3b3ob3o$48b3o64bo7boobb4o$49bo65bo12b4obo
$116bobo9boobbo$127bo$$40bo$39b3o6bo$39boboo5boo$40b3o4bobo$40b3o$40b
oo14boo$48b3o6boo$48boo6bo$48boobo103b3o3b3o$44boo4bo103bobbo3bobbo$
44boo80bo30bo3bo$126bo30bo3bo$126bo5bo24bo3bo$131b3o$131boboo20b3o3b3o
$42bo89b3o21bo5bo$41b3o69bo18b3o21b7o7bo5b3o$40boobo21bo46bo19b3o20bo
7bo5b3o4bobbo$40b3o21bobo45b3o17boo20b11o3bobboo3bo$40b3o21boo87bo11bo
bbobboo3bo3bo$40b3o109b17obboo3bo$41boo108bo17bobobo3bobo$150b16obobob
3o$149bo17boboobbo$137bo10b14obo$136b3o8bo15bo4b3o$135boobo7b12obo$
135b3o7bo13bo$136boo7b9obo$142boo11bo$140boobb6obo$135bo5bo9bo$134b3o
8bobo$134boboo3bo5bo$135b3obbo3bo$65bo69b3o$64bobo68b3o3bobo$64boo69b
oo3boboo$142bobo$143bo4$104bo47bo$103bo47b3o$103b3o45boboo$152b3o$152b
3o$152boo$129b3o$129bobbo$129bo13boo$129bo3bo7bo$65bo63bo3bo10bo$64bob
o62bo14bo$64boo64bo3boboo3bo$136boo4bobo$132b3obboo4boo$133boo5bo$135b
obbobobo$137bobbobbo$137bo5bo$141b3o8$95bo$65bo28bo$64bobo27b3o$64boo
5$124bo$123b3o6bo$122boobo5bo$122b3o5boobo$123boo6boo$132bo6$65bo$64bo
bo$64boo4$131bo$129booboo4b3o$86bo42booboo3bobbo$85bo38b3o13bo$85b3o
36bo5booboobo3bo$125bo4booboo5bo$132bo4bobo6$65bo49b3o$64bobo48bo$64b
oo50bo$$136b3o$136bobbo$136bo$136bo3bo$136bo3bo$106b3o21boo4bo$106bo
25bo4bobo$107bo6$77bo$65bo10bo20b3o$64bobo9b3o18bo$64boo32bo7$88b3o$
88bo$89bo7$65bo13b3o18b3o5b3o$64bobo12bo20bobbo3bobbo$64boo14bo19boboo
3boobo3$101b3o3b3o$97boob3obobob3oboo$99boo3bobo3boo$68boo31b3o3b3o$
68boo31b3o3b3o6$96b3o3boo3boo$96bobbobboo3boo3b3o$96bo15bobbo$65bo31bo
bo12bo$64bobo27bo3bo13bo3bo$64boo28bo21bo$93bo17bo4bo$111bo$110boo3boo
$110boobo$95boo11boboboobo$68boo26bo9boobo4bo$68boo25boo6bobbobbo$94bo
bo7bobobo6boo$95bo5boobbobo6b3o$96boo5bo9boo$113boo5$65bo$64bobo$64boo
6$68boo23boo$68boo23boo3$80b3o$79bo3bo$78bo5bo$77bo3bo3bo$77bo7bo$77bo
bo3bobo$65bo12boo3boo$64bobo$64boo$77bo7bo$72boobo11boboo$71bobbo4bo3b
o4bobbo$71b4o5bobo5b4o$71bo3bo3bo3bo3bo3bo$70boo7bo3bo7boo$71bobbobbo
7bobbobbo23$54bo$53bo$53b3o31$39bo$38bo$38b3o!
The two rakes above are much smaller than my previous PI-based rake!

More importantly, the output is trigger-able. The boats are optional, so if there are gaps in the boat rows, then there are gaps in the glider
streams too.

Here is a construction that uses this to create an irregular stream.

Code: Select all

#C A high period growing puffer based on period 60 PI-crawling reactions.
#C This uses a four period 60 PI ships supported by block rows
#C provided by c/2 puffers.  Three of the PIs are used as rakes to
#C create a forward LWSS stream.  The fourth PI turns LWSSs into
#C gliders to delete some of the boats.
#C David I. Bell, 8 February 2025
x = 469, y = 482
276b3o3b3o$276bobbobobbo$276bo7bo$276bo7bo$277bobobobo$189b3o3b3o79bob
obobo$188bobbo3bobbo79bo3bo$191bo3bo81b3ob3o$191bo3bo84bo10bo5b3o$191b
o3bo80b9o5b3o3bobbo$275bo9bo3boobo6bo$189b3o3b3o76b12o3bobo7bo$190bo5b
o76bo13bo3bo7bo$174b3o5bo7b7o75b17o4boobobo$173bobbo4b3o5bo7bo73bo18bo
3bo$176bo3boobbo3b11o71b15obobbooboboo$172bo3bo3boobbobbo11bo58bo10bo
16bo3boboboo$176bo3boobb17o56b3o8b13obo7bo$173bobo3bobobo17bo55boboo6b
o14bo$179b3obobob16o55b3o5b11obo$179bobboobo17bo54boo5bo12bo$189bob14o
10bo47b10obo$182b3o4bo15bo8b3o44boo11bo$193bob12o7boboo38bo9b3obo$193b
o13bo7b3o37b3o3b5o4bo$197bob9o7boo37boobo8bo$197bo11boo43b3o$201bob6o
bboo41b3o7bo$201bo9bo5bo36b3o6boo$205bobo8b3o36boo$205bo5bo3boobo96b3o
3b3o$208bo3bobb3o97bobbobobbo$215b3o97bo7bo$209bobo3b3o97bo7bo$209boob
o3boo98bobobobo$208boo63bo42bobobobo$207b3o62b3o42bo3bo$207b3o51bo9boo
bo41b3ob3o$207boo51boboo7b3o45bo10bo5b3o$207b3o49bo3b3o5b3o41b9o5b3o3b
obbo$200bo5booboobo47boo10boo40bo9bo3boobo6bo$199b3o4boobb3o37b3o10bob
o47b12o3bobo7bo$198boobo4boobo39bobbo11bo47bo13bo3bo7bo$198b3o11bo39bo
8bo49b17o4boobobo$198b3o8bobbo35bo3bo6boob3o45bo18bo3bo$199boo11bo35bo
3bobboo7boo43b15obobbooboboo$211bobbobo4b3o28bobbobbobo4bo31bo10bo16bo
3boboboo$211bobbobbobbobbo25bobo4b5obbo32b3o8b13obo7bo$209boboobobo6bo
37boo33boboo6bo14bo$210boo7bo3bo37bo35b3o5b11obo$219bo3bo39bo33boo5bo
12bo$223bo38boo38b10obo$210boo8bobo77boo11bo$210boo83bo9b3obo$294b3o3b
5o4bo$250bo42boobo8bo$249b3o41b3o5bo$248boobo41b3o3b4o$248b3o42b3o3bo
3bo$249boo43boo5bobbo$302boo$302boo$302boo$300boobbo$259boo39boo3bo$
257bo4bo38bobobo6bo$256bo5bo42bo5b3o$214bo5bo35bo41bobboobo5boobo$220b
o29bobo4bo3b4o35bobo7b3o$211b5o5bo28boo9b4o32bo3bo8b3o$210bobbo6bo30bo
47bo11boo$210bo5bo3bo68b3o4boobob3o$210boob6o39b3o27bobbo4bo4b3o$212bo
bbo42boo31bo5boo$212b3o45bo26bo3bo$228bo36b3o19bo3bo10bo3bo$227b3o35bo
bbo22bo9bo$227boboo34bo22bobo10bo$228b3o34bo3bo32bo$228boo35bo3bo$265b
o$266bobo4$289bo$288b3o$287boobo$287b3o$220bo67boo$219boboboobo$219boo
bb4o65bo4bo$223b3o66boobboboo$212b3o76bo4bo$212bobbo75bo8boo$212bo28bo
bo48boo7bo$212bo3bo24boo54bo3bo$212bo29bo54boboo$213bobo82bo$$329bo5bo
$232b3o93b3o3b3o$234bo93bobooboobo$233bo95b3ob3o$225bo103b3ob3o$226bo
77b3o$224bobo77bobbo22bo3bo$224boo78bo23b3o3b3o$214b3o7bo79bo3bo23bo
17bo$213bobbo87bo3bo19b9o5b3o4b3o$216bo87bo22bo9bo4bobbobboobo$212bo3b
o88bobo19b11o3bo6b3o$212bo3bo108bo15b3obbob3o$216bo108b18o3bobboo$95b
3o3b3o109bobo107bo18bo3bo$94bobbo3bobbo218b15obobboboboo$97bo3bo136bo
82bo17bobb3obo$97bo3bo135bobo69b3o9b13obo$97bo3bo135boo69bobbo7bo15bo
6bo$282bobo26bo7b11obo10bo$95b3o3b3o178boo27bo6bo12bo$96bo5bo180bo24bo
bo6b9obo$96b7o7bo5b3o195b3o10bo$95bo7bo5b3o4bobbo193boob6obo$94b11o3bo
bboo3bo190b3o3boobbo5bo$93bo11bobbobboo3bo3bo186bobbo8bo$92b17obboo3bo
190bo11bo$17b3o3b3o65bo17bobobo3bobo187bo3bo$16bobbo3bobbo63b16obobob
3o193bo3bo$19bo3bo65bo17boboobbo193bo6bobo$19bo3bo53bo10b14obo204bobo
6bo$19bo3bo52b3o8bo15bo4b3o203boobo$75boobo7b12obo216bo$17b3o3b3o49b3o
7bo13bo$18bo5bo51boo7b9obo142bo75b3o$bb3o5bo7b7o57boo11bo141bobo73bo3b
o$bobbo4b3o5bo7bo54boobb6obo145boo73bo5bo5b3o$4bo3boobbo3b11o48bo5bo9b
o219bo3bo3bo4bobbo$o3bo3boobbobbo11bo46b3o8bobo223bobbobobbo4bo$4bo3b
oobb17o45boboo3bo5bo223bo3bo3bo4bo3bo$bobo3bobobo17bo45b3o3bobbo227bo
5bo5bo$7b3obobob16o44b3o3bobbo218bo9bo3bo7bobo$7bobboobo17bo43b3o4boo
218b3o9b3o50bo5bo$17bob14o10bo31boo5boo217boobo61b3o3b3o$10b3o4bo15bo
8b3o256b3o61boobo3boboo$21bob12o7boboo255b3o61b3o5b3o$21bo13bo7b3o227b
obo25b3o62boo5boo$25bob9o7boo228boo27boo62boo5boo$25bo11boo235bo92bobo
bobo$29bob6obboo51bo$29bo9bo5bo45b3o258bo14b7o$33bobo8b3o44boboo256b3o
4b3o5bo7bo$33bo5bo3boobo32bobbo9b3o143bo111boobo4bobbo4b9o$36bobbo3b3o
33bo3bo8b3o142bobo110b3o5bobbo3bo10bo$36bobbo3b3o32bo13boo143boo111b3o
5booboob13o$37boo4b3o23b3o9bobbo266boo5bobobbo14bo66bo5bo$37boo5boo23b
obbo10boo270b3o4b17o65b3o3b3o$69bo10bobboo274boobo17bo62boobo3boboo$
69bo3bo5bo228boo50boo3bob14o62b3o5b3o$69bo8bo5bo222b3o45boo3bo4bo16bo
8b3o50boo5boo$37boo30bo4boo6boboo222bobboo46bo9bob12o7bobbo50boo5boo$
36bobboo29bob3obbobo230b3o3boo51bo14bo8bo51bobobobo$28bo7booboo34bo3bo
bo229bo61bob10o8bo$27b3o6booboo34bobbobbo291bo16bobo52b7o14bo$26boobo
8bo38boboo296bob10o55bo7bo5b3o4b3o$26b3o53bo294bo8b3o55b9o4bobbo4boboo
$26b3o52boo298bob4o6b3o46bo10bo3bobbo5b3o$27boo352bo3b4o4bobbo45b13ob
ooboo5b3o$49b3o333b4o4bo46bo14bobbobo5boo$48bobbo73bo7bo39bo7bo211bo3b
o42b17o4b3o$51bo72b3o5b3o37b3o5b3o55bo147boo5bo3bo40bo17boboo$47bo3bo
71bobboo3boobbo35bobboo3boobbo53bobo56b3o87boo5bo44b14obo3boo$47bo3bo
185boo56bobbo95bobo28b3o8bo16bo4bo3boo$51bo212bobo31bo126bobbo7b12obo
9bo$48bobo71bo3boo3boo3bo33bo3boo3boo3bo79boo32bo126bo8bo14bo$121bobb
oobbobobboobbo31bobboobbobobboobbo79bo29bobo127bo8b10obo$122bobo3bobo
3bobo33bobo3bobo3bobo241bobo16bo$125b3o3b3o39b3o3b3o248b10obo$126bo5bo
41bo5bo123bo71b3o51b3o8bo$80bo224boo69bobbo43b3o6b4obo$41boo36bobo219b
3oboo69bo11boo32bobbo4b4o3bo$71bo51bo11bo35bo11bo116bobbo72bo3bo6b4o
34bo4b4o$40boobbo6bo18bo6boo4bo39bo11bo35bo11bo192bo9boo3bo29bo3bo$40b
obboo5b3o17bobo231b3o70bobo5boboobo8bo21bo3bo5boo$34bobobbo4bo4boobo
11bo6boo4boo3boo42boo3boo4bo31bo4boo3boo121b4o80bo11b3o24bo5boo$34bobo
boo9b3o11b3o6bobo46bo4boo3boo3b3o29b3o3boo3boo4bo116boo82bo10boobo21bo
bo$35bo3bobo8boo10boobo7bo46b3o12boobo29boboo12b3o116bo82bob3o6b3o$40b
o21b3o54boobo12b3o31b3o12boboo197b6o6b3o$63boo54b3o63b3o50bo73bo72bo3b
oo3boob3o31boo$119b3o17b3o23b3o17b3o49bobo71b3o71bo4bobobbobboo30bobbo
$119b4o61b4o49boo64boo6boboo73bobob3o34booboo$119bobboo15boo25boo15boo
bbo114boo8b3o73boob3o36bobo7b3o$118boo3bobbo53bobbo3boo115bo7b3o74bo
41bo7bobbo$119bobobo15boo25boo15bobobo107bo16boo73bo54bo$119b3obbobbo
9bo31bo9bobbobb3o106boo7bo83boo49bo3bo$125bobo10bo29bo10bobo112bobo6b
oo137bo$126boobbo8bo27bo8bobboo122b3o113bo19bobo$118boo6boobbobo5bobo
25bobo5bobobboo6boo114boo113b3o$117bobbo7bobobo4bobbo25bobbo4bobobo7bo
bbo113bo3boo109boboo$121bo10bo41bo10bo121boo110b3o$40b3o75bobbo15boo
29boo15bobbo66bobo161b3o$70b3o47bo65bo68boo162b3o$34b3o33bobbo4b3o175b
o29bo132boo$34bobbo27b3o3b3o3bobbo204boo23bo$34bo30bo14bo204bobo21b3o$
34bo3bo14bo12bo9bo3bo227boobo$34bo3bo15boo24bo157bo69b3o$34bo18boo22bo
bo157bobo68b3o116boo$35bobo199boo69b3o77b3o$309boo77b3o7bo25bo3bo$387b
3oboo4bobo28bo$277bo108boo3bo7bo17b3o4boboobo$56b3o217boo108boo3boo3bo
bo17bobbo5boboobobboo$56bo83boo23boo109bobo118bo6b3o12bo8bobobb3o$57bo
82boo23boo228boo6bobbo12bo8b3o$406bo9bobo$406bo$76b3o324bobo$76bobbo$
76bo$65boo3b3o3bo3bo187bo$76bo3bo186boo$76bo190bobo$77bobo$238bo$237bo
bo$237boo$54boo190bobo179bo$54bobo189boo180bo$55bo191bo11bo138boo28bo$
258boo130bo6boo35bo$140boo23boo91bobo128b3o4boo4boo29b3o$140boo23boo
222boboo10boo27boobo$390b3o9bo12bo16b3o$390b3o22bobo14b3o$153bo120bo7b
o107boo23boo15b3o$152b3o118b3o5b3o149boo$151b5o116boobbo3bobboo$150boo
3boo93bo23b3o3b3o$149boo5boo91boo$150boo3boo92bobo23bo5bo129boo$151bo
3bo117bobbo3bobbo128boo$238bo32bo5bobo5bo125bo$148bo9bo78bobo31boo4bob
o4boo$145bo3bo7bo3bo75boo38bobo$54boo88bo3boo7boo3bo111bobo3bobo109bo$
54bobo86bobbob4o3b4obobbo111bo5bo109b3o7bo$55bo88b3oboobbobobboob3o
227boobo4bo4bo$143bo3bob3o3b3obo3bo226b3o5bo5bo$143b3o3boo5boo3b3o226b
3o5bo4bo$34bo7bo100bo4bo9bo4bo77boo27bo119b3o8bo$33b3o5b3o101boo13boo
79boo26b3o3boo3boo4bo104boo$32boobbo3bobboo223boobbobboo3boo3b3o$32bo
bbo5bobbo223bo3bo11boobbo$31boo3booboo3boo222bo15bo3bo$32bobobooboobob
o224bo13bobboo126boo$33bo9bo228bobo8bo129bobo$34bobbobobbo229bo10bo
130bo$282b3o$31boobboo3boobboo225boo9boo$31boo11boo192bo33bobo7bobbo$
237bobo33bo9bo3boo$35bo5bo195boo49boo$35boo3boo12boo229bobboo$54bobo
230boo$46bo8bo$30bo14b3o$29b3o13boboo119b3o$28bobboobboo3bobo5bo118bo
bbo70boo23boo$27b3oboobboo3bobo5b3o119bo70boo23boo$28boob3o7bobo4boo
120bo$29boobo11bob3o118bobo$30boo14boo$46bo228boo137boo$413bobo$29bo
384bo$28bobo5bo$30bo4b3o$30bo4boobo8bo190bo$26bo10b3o5booboo187bobo
186b3o5b3o$26bo3bobboobb3obo3booboo187boo187bobbo3bobbo$27bobbobboo4b
oobo11boo369bo3bo3bo3bo$28bobo6boo7bobo5bobo368bobo7bobo$29bo7b3oboo4b
o7bo369bobobooboobobo$37b3o386bobbooboobbo$427booboboboo$241boo23boo
160boo3boo$241boo23boo156boobbo5bobboo$424boo11boo$429bo3bo$428bo5bo$
414boo12boo3boo$413bobo$414bo$422b3o$422bobbo12b3o$238bo181bo7boo3boo
3bobbo$49boo186bobo180bo6b3o3boobbo3bo$49boo186boo181bo5bo10bo3bo$54b
oo365bo4bo10bobbo$54bobo365b3o13boo$55bo3$241boo23boo171b3o$241boo23b
oo164b3o4b3o$422bo8bo3bo5boo$421bobo7bo8b3o$420booboo6bo4bo3b3o$414boo
5bobo3b3obbobboo3bobo$9bo7bo395bobo5b3o3b3o9bobo$8b3o5b3o395bo13boboob
o6bo$7boobbo3bobboo411bo$7bobbo5bobbo$6boo3booboo3boo217bo$7bobobooboo
bobo29boo186bobo$8bo9bo30boo186boo$9bobbobobbo36boo$54bobo$6boobboo3b
oobboo34bo$6boo11boo$$10bo5bo224boo11bo11boo$10boo3boo224boo11bo11boo$
253bobo$21bo397boo$5bo14b3o227boob3oboo160boo$4b3o12bobboo223boboobo3b
oboobo152boo$4boboobobo7bobboo222b5obo3bob5o150bobo$5bo11b3oboo224boo
bbo5bobboo152bo$5bobo3bo240bo3bo$4boobboo11boo226boobo3boboo$3bobbo10b
o4bo215bo10boo7boo$5boobbobo3b3o31boo186bobo8bob4ob4obo$bo3boobbobobb
oo6bo26boo186boo4boo3b3obo3bob3o3boo$bobbo7boo11boo27boo186bobbobboboo
5boobobbobbo$boobo4bobobboboo36bobo186boo19boo$bbobo6bo3b3o7bo29bo186b
oo21boo$3boo3boo11b4o216boo4bobo9bobo4boo$240bobbo3bo5bobo5bo3bobbo
182b3o5b3o$241boo9bo3bo9boo183bobbo3bobbo$242bo6bo9bo6bo183bo3bo3bo3bo
$250boo5boo191bobo7bobo$419boo29bobobooboobobo$419boo30bobbooboobbo$
414boo36booboboboo$413bobo37boo3boo$414bo34boobbo5bobboo$449boo11boo$
454bo3bo$453bo5bo$24boo23boo402boo3boo$24boo23boo$54boo$54bobo390b3o$
55bo391bobbo12b3o$447bobbo7boo3bobbo$447booboobo4b3obo$448bobbo7b6o$
447booboo12bobbo$449b5o9bobbo$419boo26bobbo8boobbooboo$419boo26bobo4b
oobb3o3boboo$414boo27booboo6boobbo6b3o$413bobo28booboo4b3obb3o6bo$414b
o29booboobboo6bobbobbobo$446boo12boo3boo$$223bobo$24boo23boo172boo$24b
oo23boo173bo$54boo$54bobo$55bo6$419boo23boo$419boo23boo$414boo$413bobo
$414bo4$24boo23boo$24boo23boo$54boo$54bobo$55bo6$419boo23boo$419boo23b
oo$168b3o243boo$167bobbo242bobo$170bo37bobo203bo$170bo37boo$167bobo39b
o$432bo$24boo23boo379booboo$24boo23boo379booboo$54boo$54bobo$55bo372bo
7bo$422b3obbo9bobb3o$421boo3bobo7bobo3boo$420booboo3bo7bo3booboo$421b
oob6o5b6oboo$420b3obbo13bobb3o$419b3oboo15boob3o$419boo3bo4bo5bo4bo3b
oo$414boo8bo3bo7bo3bo$413bobo10bo3bo3bo3bo$414bo12b3o5b3o$427boo7boo3$
24boo23boo$24boo11bo11boo$37bo16boo$36b3o15bobo$55bo$34bo5bo$32bo9bo$
31boo4bo4boo$30boo4b3o4boo370bo$31bobb3ob3obbo370boo$32boobo3boboo371b
obo$33boo5boo151bobo204bo$168b3o22boo204boo$28bobo13bobo120bobbo23bo
204bobo$26boobb3o9b3obboo121bo214bo$25boo21boo120bo213boo$25boo5booboo
booboo5boo117bobo214bobo$25boobo5bobobobo5boboo320bo$27bobbo4bo3bo4bo
bbo321boo$28boo15boo322bobo$54boo299bo$54bobo297boo$55bo298bobo$340bo$
168b3o168boo$167bobbo168bobo$170bo154bo$170bo153boo$167bobo154bobo$
310bo$309boo$57boo250bobo$56bobo236bo$58bo235boo$72boo220bobo$71bobo
206bo$73bo94b3o108boo$87boo78bobbo108bobo$86bobo81bo94bo$88bo81bo93boo
$102boo63bobo94bobo$101bobo146bo$103bo145boo$117boo130bobo$116bobo59bo
bo54bo$118bo59boo54boo$132boo45bo54bobo$131bobo86bo$133bo34b3o48boo$
147boo18bobbo48bobo$146bobo21bo34bo$148bo21bo33boo$162boo3bobo34bobo$
161bobo26bo$163bo25boo$189bobo$175bo$174boo$174bobo!
Ideally, the forward gliders should be turned into boats by another PI reaction to form a positive loop, instead of the negative loop I have here. I couldn't find a way to do that since the blocks are too close to the boats.

Also, the cleaner LWSS producing reaction for three gliders should be used instead of the one shown here which produces a bit of junk, but the clean one doesn't work for period 60 rakes.

I am hoping that maybe these irregular streams would help to create a PI ship since information can be encoded by the spacing of the LWSS stream. If a couple of the streams are used to create forward and backward gliders with adjustable timings, then the reactions of those gliders could be used to build almost all of the block and boat tracks that are necessary. The LWSS streams can be made arbitrarily long without adding any new PIs that need supporting, so the recipes could be as slow as needed.

Of course, a 3c/10 helix would still be necessary to support the top PIs of the LWSS streams, but there are only a few of those. The helix itself can be constructed as just described.

PS: I have no idea if this is new, so for the moment I am still posting to this thread.

Edit:

I think my idea is not feasible. I forgot that the front of the reaction is moving, so any output gliders couldn't react with previous ones.
The solution for this might be to create a downward spaceship stream which could do the slow salvos. But it's all too complicated. Sorry.

Edit 2:

For the purist, the rakes seen above might seem to be just fly-by reactions since the boats used in them aren't part of any PI mechanism. (In a possible future complete PI ship that wouldn't matter since the boats WOULD be produced by other PIs.)

Here is a non-flyby rake if you really want to see one.

Code: Select all

#C A period 60 PI-crawling backwards rake.
#C This uses two PI crawlers whose sparks interact to form
#C backward gliders.  The PI-crawlers are supported by four
#C tracks of blocks built by four c/2 puffers.  Many other outputs
#C can be created by changing the interaction of the sparks.
#C David I. Bell, 8 February 2025
x = 108, y = 113
33bo7bo$32b3o5b3o$31bobboo3boobbo$31bo3bo3bo3bo$32booboobooboo$32boobo
3boboo$34bo5bo24b3o5b3o$35booboo24bobbo5bobbo$30boobbo5bobboo19bo3bo3b
o3bo$30boobbo5bobboo20b4o3b4o$66bobo3bobo$34bobobobo$34boo3boo27bo3bo$
63bo4booboo4bo$63boo3booboo3boo$45bo22booboo$7b3o5b3o11bo14b3o20boo3b
oo$7bobbo3bobbo10b3o3boo3boobboobbo19bo5bo$7bo9bo9boobbobboo3boo5boo$
5boobbobobobobboo7bo3bo16bo$5boobbobobobobboo7bo18b3o$4bo5bo3bo5bo7bo
32b3o27bo7bo$5bobbobo3bobobbo11bobo26bobbo3boo3boo3b3o10b3o5b3o$6boo9b
oo12bo10bo17bo3bobboo3boobbobbo9bobboo3boobbo$7bo9bo26bo14boo15bo3bo
11boo3boo$32bo9bobbo14boo13boobobo7boo4bobo4boo$5boo11boo7bo16bo30boo
bbo8boobbobobobobboo$5boo11boo7bo15bo21bo8b3o11bo13bo$27bo37bo23b3obbo
bobb3o$9boo3boo11bo35boo11bo17bobo$9boo3boo11bo35b3o7bo$19b3o5bo35boo
9bobo11boo11boo$3b3o12bobbo43bo13b3o6boo11boo$bbobbo12bo4bo$bbo3bo10b
oo5bo23boo42boo3boo$bobb3obboo3booboo29boo29b3o10boo3boo$oobobo3boo3b
oobboobo65bo$obbo17bo3bo9b3o48b3o14bo$obbo17bobboo10bo48bobboo12b3o$b
oo19boo34boo24b4obo11bobboo$30b3o7b3o15boo11bo11booboobobboo3boobb3obb
o$29bobo3b3o3bobo27bo11booboboobboo3boo5bobo$29bo13bo26b3o9boobbo17bo
bbo$bbo26booboo5booboo39bobbo18boo$b3o27bo3bobo3bo26bo5bo9boo19boo$b3o
27b3o5b3o24bo9bo$65boo4bo4boo$26boboo13boobo17boo4b3o4boo$b3o20b3ob3o
11b3ob3o16bobb3ob3obbo11bo$b3o28bo7bo25boobo3boboo12bo14b3o$bbo20bo8b
4ob4o8bo17boo5boo27bo3bo$24bo7booboboboo7bo$25boo7bo3bo7boo14bobo13bob
o$27boo15boo14boobb3o9b3obboo20bo3bo$59boo21boo20b3o$59boo5boobooboob
oo5boo$59boobo5bobobobo5boboo$61bobbo4bo3bo4bobbo$62boo15boo19$39bo$
38bo$38b3o31$24bo$23bo$23b3o!
The disadvantages of this rake are that it uses one more row of objects to support it, and also that its output is fixed at period 60.

BCNU,
-dbell

Re: Thread for your unsure discoveries

Posted: February 10th, 2025, 3:14 am
by MathAndCode
Here is a simple way to perturb a traffic light predecessor into a clean LWSS.

Code: Select all

x = 5, y = 9, rule = B3/S23
2bo$bobo$o3bo$bobo$2bo2$3bo$bobo$3bo!
I found it from this spark_search result.

Code: Select all

x = 35, y = 202, rule = B3/S23
6bo$7b2o$6b2o4$9bobo$10b2o4bo$10bo3b2o$15b2o73$8b2o$8b2o4$7b2o2bo4b2o
$5b2obo3bo3b2o$6b2o4bo$6b2ob2o$7bob2o$8bo$19b2o$18bo2bo$17bo3bo$17bo3b
o$14b4o2bo$14b2o2b3o3bo$24b2o$24b3o$bo2bo2bo2bo2bo2bo2bo6bo$b19o3b2ob
2o$23b2obobo$b19o3bobo2b2o$bo17bo3b5ob2o$4b13o7bob2obo$3bo13bo8b2o$3b
ob11obo$bobobo9bobobo$obo3b9o3bobo11b3o$bo8bo8bo12bo$6b2o5b2o18bo$5bo
bo5bobo$6bo7bo$7b3ob3o$9bobo$6bobo3bobo$4b3ob2ob2ob3o$3bo13bo$2bobo11b
obo$3bo13bo43$9b2o$9b2o$9b2o$5b2o3b3o3b2o$6b2ob2ob2o2b2o$7b6o$9b2o3$20b
o$18bo2bo$18b3o$18b3o3$19b2o3b2o$19b2o2bo$bo2bo2bo2bo2bo2bo7b2o$b20o$
21bo$b19obo9bobo$bo17b2o4b2o3bo2bo$4b13o8bo2bo$3bo13bo8bobobobo$3bob11o
bo11bo2bo$bobobo9bobobo10bobo$obo3b9o3bobo9b3o$bo8bo8bo$6b2o5b2o$5bob
o5bobo$6bo7bo$7b3ob3o$9bobo$6bobo3bobo$4b3ob2ob2ob3o$3bo13bo$2bobo11b
obo$3bo13bo!
It could potentially be useful for gliderless LWSS guns. I haven't seen any that use it, but I don't know where to find all of them, so there could already be one that uses it for all I know.



Edit: INoMed pointed me to this post and this page, which use it, so never mind.

Re: Thread for your unsure discoveries

Posted: February 10th, 2025, 8:04 am
by dbell
The period 60 3c/10 PI crawler can be supported by several different objects in place of the two block rows. In particular, simple domino sparks will work. It happens that the PI crawler itself produces domino sparks, and so two of these can be used to support another PI crawler between them, as shown here.

Code: Select all

#C A period 60 3c/10 PI crawler supported by two other crawlers.
#C Domino sparks produced by the two edge crawlers perform the
#C appropriate perturbation of the middle crawler.  The two edge
#C crawlers are supported by four rows of blocks produced by c/2
#C puffers.  Therefore four rows of blocks can support three crawlers.
#C David I. Bell, 10 February 2025
x = 135, y = 63
32bo7bo53bo7bo$31b3o5b3o51b3o5b3o$30boobbo3bobboo49boobbo3bobboo$30bo
bbo5bobbo49bobbo5bobbo$29boo3booboo3boo47boo3booboo3boo$30bobobooboobo
bo49bobobooboobobo$31bo9bo51bo9bo$32bobbobobbo53bobbobobbo$$29boobboo
3boobboo47boobboo3boobboo$29boo11boo47boo11boo$$33bo5bo55bo5bo$33boo3b
oo55boo3boo$$44bo45bo$6b3o5b3o11bo14b3o43b3o14bo11b3o5b3o$5bobbo5bobbo
9b3o12bobboo41boobbo12b3o9bobbo5bobbo$5bo3bo3bo3bo9boboobobo7bobboo41b
oobbo7boboboobo9bo3bo3bo3bo$28bo11b3oboo43boob3o11bo$4bo4bo3bo4bo9bobo
3bo65bo3bobo9bo4bo3bo4bo$3bobobooboboboobobo7boobboo11boo43boo11boobb
oo7bobobooboboboobobo$3bo3booboboboo3bo6bobbo10bo4bo43bo4bo10bobbo6bo
3booboboboo3bo$8boo3boo13boobbobo3b3o53b3o3bobobboo13boo3boo$24bo3boo
bbobobboo6bo43bo6boobbobobboo3bo$4bobbo7bobbo5bobbo7boo11boo35boo11boo
7bobbo5bobbo7bobbo$24boobo4bobobboboo53boobobbobo4boboo$6bo9bo8bobo6bo
3b3o7bo37bo7b3o3bo6bobo8bo9bo$4boo11boo7boo3boo11b4o39b4o11boo3boo7boo
11boo$$8boo3boo105boo3boo$8boo3boo3b3o93b3o3boo3boo$bb3o13bobbo91bobbo
13b3o$bbobbo12bo97bo12bobbo$bbo15bo3bo89bo3bo15bo$bbobbo16bo89bo16bobb
o$bbobbo12bo3bo11b3o61b3o11bo3bo12bobbo$bobo14bo14bo3bo59bo3bo14bo14bo
bo$bo3b3o13boo9bo5bo57bo5bo9boo13b3o3bo$boo3b3o10bo11bo3bo3bo55bo3bo3b
o11bo10b3o3boo$bboo3boo10bobo9bo7bo55bo7bo9bobo10boo3boo$9bo10bo10bobo
3bobo7boo37boo7bobo3bobo10bo10bo$8bobboboo17boo3boo8boo37boo8boo3boo
17boobobbo$o8bobo9boo89boo9bobo8bo$oo7bo5bo4b3o89b3o4bo5bo7boo$3o9boob
o3boo93boo3boboo9b3o$b3o15boo4boo17boo21bo21boo17boo4boo15b3o$25boo17b
oo20bobo20boo17boo$65booboo$$27boo13boo47boo13boo$26bobbo11bobbo18bo7b
o18bobbo11bobbo$27boboboo5boobobo14boobbobo5bobobboo14boboboo5boobobo$
32boo3boo17boobobbo9bobboboo17boo3boo$32boo3boo17bobboo13boobbo17boo3b
oo$29b3o7b3o14bo3b4o7b4o3bo14b3o7b3o$57bo5boo5boo5bo$15bo9bo19bo9bobbo
bb3obo3bob3obbobbo9bo19bo9bo$15bo9bo19bo9bo3b4o9b4o3bo9bo19bo9bo$60bob
oobbobobboobo$31boo5boo21bo11bo21boo5boo$26boo3boo5boo3boo17b4o3b4o17b
oo3boo5boo3boo$63bo7bo!
More crawlers can be cascaded to this at the cost of one more row of blocks each, so that it takes only N+1 rows of blocks to support N crawlers instead of 2N rows.

Here is a reaction which shows how to use pairs of gliders to support a PI crawler.

Code: Select all

#C A period 60 3c/10 PI crawler temporary supported by gliders.
#C Pairs of gliders produce domino sparks which support the PI for
#C three cycles.  More gliders can be added to prolong the support.
#C David I. Bell, 10 February 2025
x = 99, y = 93
bo95bo$bbo93bo$3o93b3o31$16bo65bo$17bo63bo$15b3o63b3o29$49bo$48b3o$31b
o16b3o16bo$32bo33bo$3boo25b3o12b9o12b3o25boo$4boo35boobobbobobobboboo
35boo$3bo36bobo4bobobo4bobo36bo$18boo20bobobbobobobobobbobo20boo$19boo
24bobooboobo24boo$18bo23boo11boo23bo$33boo8b5o3b5o8boo$34boo27boo$33bo
31bo$$41bo15bo$41bobo11bobo$43bo11bo$41bo15bo$40boob4o5b4oboo$41bob3ob
o3bob3obo$44bo3bobo3bo$45bobbobobbo$46bo5bo$46bobobobo3$45bo7bo$44bo9b
o$45bo7bo!
It would be nice to build a channel based on domino sparks which would allow multiple crawlers to be moving through it at the same time. This could be done either with a row of some domino sparker with high enough clearance and period, or by a row of glider guns producing a reaction similar to the one above. But I haven't found any solution.

BCNU,
-dbell

Re: Thread for your unsure discoveries

Posted: February 10th, 2025, 11:20 am
by vilc
dbell wrote: February 10th, 2025, 8:04 am Here is a reaction which shows how to use pairs of gliders to support a PI crawler.

Code: Select all

#C A period 60 3c/10 PI crawler temporary supported by gliders.
#C Pairs of gliders produce domino sparks which support the PI for
#C three cycles.  More gliders can be added to prolong the support.
#C David I. Bell, 10 February 2025
x = 99, y = 93
bo95bo$bbo93bo$3o93b3o31$16bo65bo$17bo63bo$15b3o63b3o29$49bo$48b3o$31b
o16b3o16bo$32bo33bo$3boo25b3o12b9o12b3o25boo$4boo35boobobbobobobboboo
35boo$3bo36bobo4bobobo4bobo36bo$18boo20bobobbobobobobobbobo20boo$19boo
24bobooboobo24boo$18bo23boo11boo23bo$33boo8b5o3b5o8boo$34boo27boo$33bo
31bo$$41bo15bo$41bobo11bobo$43bo11bo$41bo15bo$40boob4o5b4oboo$41bob3ob
o3bob3obo$44bo3bobo3bo$45bobbobobbo$46bo5bo$46bobobobo3$45bo7bo$44bo9b
o$45bo7bo!
There is a similar reaction using only one glider on each side :

Code: Select all

x = 93, y = 90, rule = B3/S23
o91bo$b2o87b2o$2o89b2o31$15bo61bo$16b2o57b2o$15b2o59b2o26$46bo$45b3o$
45b3o2$42b9o$30bo7b2obo2bobobo2bob2o7bo$31b2o4bobo4bobobo4bobo4b2o$30b
2o5bobo2bobobobobo2bobo5b2o$42bob2ob2obo$39b2o11b2o$40b5o3b5o4$38bo15b
o$38bobo11bobo$40bo11bo$38bo15bo$37b2ob4o5b4ob2o$38bob3obo3bob3obo$41b
o3bobo3bo$42bo2bobo2bo$43bo5bo$43bobobobo3$42bo7bo$41bo9bo$42bo7bo!

Re: Thread for your unsure discoveries

Posted: February 11th, 2025, 6:27 am
by dbell
It would be nice if there was a backward spaceship convoy which could pass by and perturb the p60 PI crawler so as to recreate its blocks behind it. That would allow for an arbitrary number of PI crawlers to run from a fixed number of block trails.

I didn't find such a reaction, but there are a few close ones, like this annoying one.

Code: Select all

#C A passing LWSS perturbs a p60 PI crawler to create a block.
#C The new block is one horizontal cell away from being on the
#C same column as the supporting blocks, thus preventing this
#C reaction from being used to support multiple PI crawlers.
x = 71, y = 119
6b3o5b3o37b3o5b3o$6bobbo3bobbo37bobbo3bobbo$6boboo3boobo37boboo3boobo
3$7b3o3b3o39b3o3b3o$3boob3obobob3oboo31boob3obobob3oboo$5boo3bobo3boo
35boo3bobo3boo$7b3o3b3o39b3o3b3o$7b3o3b3o39b3o3b3o6$8boo3boo3b3o29b3o
3boo3boo$bb3o3boo3boobbobbo29bobbobboo3boo3b3o$bobbo15bo29bo15bobbo$4b
o12bobo31bobo12bo$o3bo13bo3bo25bo3bo13bo3bo$o21bo25bo21bo$o4bo17bo23bo
17bo4bo$5bo59bo$oo3boo57boo3boo$3boboo57boobo$boboobobo11boo27boo11bob
oboobo$bbo4boboo9bo29bo9boobo4bo$7bobbobbo6boo27boo6bobbobbo$oo6bobobo
7bobo25bobo7bobobo6boo$3o6bobobboo5bo27bo5boobbobo6b3o$bboo9bo5boo29b
oo5bo9boo$bboo63boo13$22boo23boo$22boo23boo17$22boo23boo$22boo23boo9$
54bobo$53bo$53bo3bo$53bo3bo$53bo$53bobbo$53b3o$$22boo23boo$22boo23boo
14$35bo$34b3o$33bo3bo$22boo9booboo9boo$22boo23boo4$25boo17boo$25boo17b
oo$31b3o3b3o$30bo3bobo3bo$27b4o3bobo3b4o$27boo5bobo5boo$27boo3bo5bo3b
oo$$31boo5boo$19boo10bo7bo10boo$18boboo9bo7bo9boobo$17bo4bo25bo4bo$17b
obbo29bobbo$17boobo3b3o17b3o3boboo$19boobboboo4boo5boo4boobobboo$21boo
boo5boo5boo5booboo!
Then I realized that there probably is a way to create the re-burnable blocks. The first part of the mechanism is shown here.

Code: Select all

#C Passing spaceships perturb a p60 PI crawler to produce bi-blocks.
#C A pair of LWSSs create outward gliders which are then turned back
#C towards the trail by glider turning spaceship convoys.  All of the
#C backward spaceships must be repeated every 48 cells to to create
#C the bi-blocks every 18 cells.
x = 341, y = 1401
141b3o5b3o37b3o5b3o$140bobbo5bobbo35bobbo5bobbo$140bo3bo3bo3bo35bo3bo
3bo3bo$141b4o3b4o37b4o3b4o$142bobo3bobo39bobo3bobo$$144bo3bo43bo3bo$
139bo4booboo4bo33bo4booboo4bo$139boo3booboo3boo33boo3booboo3boo$144boo
boo43booboo$143boo3boo41boo3boo$143bo5bo41bo5bo4$153b3o29b3o$137b3o3b
oo3boo3bobbo27bobbo3boo3boo3b3o$137bobbobboo3boobbo3bo27bo3bobboo3boo
bbobbo$136bo3bo15boo25boo15bo3bo$136boboboo13boo27boo13boobobo$137bobb
oo57boobbo$140b3o8bo37bo8b3o$151bo37bo$140bo11boo33boo11bo$143bo7b3o
33b3o7bo$140bobo9boo33boo9bobo$135b3o13bo37bo13b3o3$135b3o65b3o4$157b
oo23boo$boo12boo140boo23boo140boo12boo$b3o11b3o305b3o11b3o$oboo11b3o
305b3o11boobo$3o12b3o305b3o12b3o$bo12boboo305boobo12bo$14b3o307b3o$15b
o309bo3$bbobo331bobo$5bo329bo$bo3bo142boo41boo142bo3bo$5bo142b3o39b3o
142bo$bbobbo141boboo39boobo141bobbo$3b3o141b3o41b3o141b3o$148bo43bo$$
157boo23boo$157boo23boo17$157boo23boo$157boo23boo12$boo12boo307boo12b
oo$b3o11b3o305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o305b3o12b3o$bo12b
oboo305boobo12bo$14b3o140boo23boo140b3o$15bo141boo23boo141bo3$bbobo
331bobo$5bo329bo$bo3bo142boo41boo142bo3bo$5bo142b3o39b3o142bo$bbobbo
141boboo39boobo141bobbo$3b3o141b3o41b3o141b3o$148bo43bo8$157boo23boo$
157boo23boo17$157boo23boo$157boo23boo6$boo12boo307boo12boo$b3o11b3o
305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o305b3o12b3o$bo12boboo305boob
o12bo$14b3o307b3o$15bo309bo3$bbobo331bobo$5bo329bo$bo3bo142boo7boo23b
oo7boo142bo3bo$5bo142b3o6boo23boo6b3o142bo$bbobbo141boboo39boobo141bo
bbo$3b3o141b3o41b3o141b3o$148bo43bo14$157boo23boo$157boo23boo17$157boo
23boo$boo12boo140boo23boo140boo12boo$b3o11b3o305b3o11b3o$oboo11b3o305b
3o11boobo$3o12b3o305b3o12b3o$bo12boboo305boobo12bo$14b3o307b3o$15bo
309bo3$bbobo331bobo$5bo329bo$bo3bo142boo41boo142bo3bo$5bo142b3o39b3o
142bo$bbobbo141boboo39boobo141bobbo$3b3o141b3o41b3o141b3o$148bo43bo$$
157boo23boo$157boo23boo17$157boo23boo$157boo23boo12$boo12boo307boo12b
oo$b3o11b3o305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o305b3o12b3o$bo12b
oboo305boobo12bo$14b3o140boo23boo140b3o$15bo141boo23boo141bo3$bbobo
331bobo$5bo329bo$bo3bo142boo41boo142bo3bo$5bo142b3o39b3o142bo$bbobbo
141boboo39boobo141bobbo$3b3o141b3o41b3o141b3o$148bo43bo8$157boo23boo$
157boo23boo17$157boo23boo$157boo23boo6$boo12boo307boo12boo$b3o11b3o
305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o305b3o12b3o$bo12boboo305boob
o12bo$14b3o307b3o$15bo309bo3$bbobo331bobo$5bo329bo$bo3bo142boo7boo23b
oo7boo142bo3bo$5bo142b3o6boo23boo6b3o142bo$bbobbo141boboo39boobo141bo
bbo$3b3o141b3o41b3o141b3o$148bo43bo14$157boo23boo$157boo23boo17$157boo
23boo$boo12boo140boo23boo140boo12boo$b3o11b3o305b3o11b3o$oboo11b3o305b
3o11boobo$3o12b3o305b3o12b3o$bo12boboo305boobo12bo$14b3o307b3o$15bo
309bo3$bbobo331bobo$5bo329bo$bo3bo142boo41boo142bo3bo$5bo142b3o39b3o
142bo$bbobbo141boboo39boobo141bobbo$3b3o141b3o41b3o141b3o$148bo43bo$$
157boo23boo$157boo23boo17$157boo23boo$157boo23boo12$boo12boo307boo12b
oo$b3o11b3o305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o305b3o12b3o$bo12b
oboo305boobo12bo$14b3o140boo23boo140b3o$15bo141boo23boo141bo3$bbobo
331bobo$5bo329bo$bo3bo142boo41boo142bo3bo$5bo142b3o39b3o142bo$bbobbo
141boboo39boobo141bobbo$3b3o141b3o41b3o141b3o$148bo43bo8$157boo23boo$
157boo23boo17$157boo23boo$157boo23boo6$boo12boo307boo12boo$b3o11b3o
305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o305b3o12b3o$bo12boboo305boob
o12bo$14b3o307b3o$15bo309bo3$bbobo331bobo$5bo329bo$bo3bo142boo7boo23b
oo7boo142bo3bo$5bo142b3o6boo23boo6b3o142bo$bbobbo141boboo39boobo141bo
bbo$3b3o141b3o41b3o141b3o$148bo43bo14$157boo23boo$157boo23boo17$157boo
23boo$boo12boo140boo23boo140boo12boo$b3o11b3o305b3o11b3o$oboo11b3o305b
3o11boobo$3o12b3o305b3o12b3o$bo12boboo305boobo12bo$14b3o307b3o$15bo
309bo3$bbobo331bobo$5bo329bo$bo3bo142boo41boo142bo3bo$5bo142b3o39b3o
142bo$bbobbo141boboo39boobo141bobbo$3b3o141b3o41b3o141b3o$148bo43bo$$
157boo23boo$157boo23boo17$157boo23boo$157boo23boo12$boo12boo307boo12b
oo$b3o11b3o305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o305b3o12b3o$bo12b
oboo305boobo12bo$14b3o140boo23boo140b3o$15bo141boo23boo141bo3$bbobo
331bobo$5bo329bo$bo3bo142boo41boo142bo3bo$5bo142b3o39b3o142bo$bbobbo
141boboo39boobo141bobbo$3b3o141b3o41b3o141b3o$148bo43bo8$157boo23boo$
157boo23boo17$157boo23boo$157boo23boo6$boo12boo307boo12boo$b3o11b3o
305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o305b3o12b3o$bo12boboo305boob
o12bo$14b3o307b3o$15bo309bo3$bbobo331bobo$5bo329bo$bo3bo142boo7boo23b
oo7boo142bo3bo$5bo142b3o6boo23boo6b3o142bo$bbobbo141boboo39boobo141bo
bbo$3b3o141b3o41b3o141b3o$148bo43bo14$157boo23boo$157boo23boo17$157boo
23boo$boo12boo140boo23boo140boo12boo$b3o11b3o305b3o11b3o$oboo11b3o305b
3o11boobo$3o12b3o305b3o12b3o$bo12boboo305boobo12bo$14b3o307b3o$15bo
309bo3$bbobo331bobo$5bo329bo$bo3bo142boo41boo142bo3bo$5bo142b3o39b3o
142bo$bbobbo141boboo39boobo141bobbo$3b3o141b3o41b3o141b3o$148bo43bo$$
157boo23boo$157boo23boo17$157boo23boo$157boo23boo12$boo12boo307boo12b
oo$b3o11b3o305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o305b3o12b3o$bo12b
oboo305boobo12bo$14b3o140boo23boo140b3o$15bo141boo23boo141bo3$bbobo
331bobo$5bo329bo$bo3bo142boo41boo142bo3bo$5bo142b3o39b3o142bo$bbobbo
141boboo39boobo141bobbo$3b3o141b3o41b3o141b3o$148bo43bo8$157boo23boo$
157boo23boo15$170bo$168booboo$157boo9booboo9boo$157boo23boo4$160boo17b
oo$160boo17boo$boo12boo150boo3boo150boo12boo$b3o11b3o148bobbobobbo148b
3o11b3o$oboo11b3o147booboobooboo147b3o11boobo$3o12b3o144b4o9b4o144b3o
12b3o$bo12boboo143bobboobo5boboobbo143boobo12bo$14b3o148b3o5b3o148b3o$
15bo146bobb3o5b3obbo146bo$155bo5bo4bo7bo4bo5bo$154bobo4boo15boo4bobo$
bbobo148bo6b3o15b3o6bo148bobo$5bo147bo3boob3o15b3oboo3bo147bo$bo3bo
142boo3bobobobboo17boobbobobo3boo142bo3bo$5bo142b3o3booboboo5boo5boo5b
ooboboo3b3o142bo$bbobbo141boboo6boo7boo5boo7boo6boobo141bobbo$3b3o141b
3o7boo23boo7b3o141b3o$148bo43bo25$137bo65bo$136bo67bo$136b3o63b3o6$boo
12boo307boo12boo$b3o11b3o305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o
305b3o12b3o$bo12boboo305boobo12bo$14b3o307b3o$15bo309bo3$bbobo331bobo$
5bo329bo$bo3bo142boo41boo142bo3bo$5bo142b3o39b3o142bo$bbobbo141boboo
39boobo141bobbo$3b3o141b3o41b3o141b3o$148bo43bo10$122bo95bo$121bo97bo$
121b3o93b3o21$boo12boo307boo12boo$b3o11b3o305b3o11b3o$oboo11b3o305b3o
11boobo$3o12b3o305b3o12b3o$bo12boboo305boobo12bo$14b3o307b3o$15bo309bo
3$bbobo331bobo$5bo101bo125bo101bo$bo3bo100bo41boo41boo41bo100bo3bo$5bo
100b3o39b3o39b3o39b3o100bo$bbobbo141boboo39boobo141bobbo$3b3o141b3o41b
3o141b3o$148bo43bo28$92bo155bo$91bo157bo$91b3o153b3o3$boo12boo307boo
12boo$b3o11b3o305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o305b3o12b3o$bo
12boboo305boobo12bo$14b3o307b3o$15bo309bo3$bbobo331bobo$5bo329bo$bo3bo
142boo41boo142bo3bo$5bo142b3o39b3o142bo$bbobbo141boboo39boobo141bobbo$
3b3o141b3o41b3o141b3o$148bo43bo13$77bo185bo$76bo187bo$76b3o183b3o18$b
oo12boo307boo12boo$b3o11b3o305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o
305b3o12b3o$bo12boboo305boobo12bo$14b3o307b3o$15bo309bo3$bbobo331bobo$
5bo329bo$bo3bo142boo41boo142bo3bo$5bo142b3o39b3o142bo$bbobbo56bo84bob
oo39boobo84bo56bobbo$3b3o55bo85b3o41b3o85bo55b3o$61b3o84bo43bo84b3o31$
47bo245bo$46bo247bo$boo12boo29b3o243b3o29boo12boo$b3o11b3o305b3o11b3o$
oboo11b3o305b3o11boobo$3o12b3o305b3o12b3o$bo12boboo305boobo12bo$14b3o
307b3o$15bo309bo3$bbobo331bobo$5bo329bo$bo3bo142boo41boo142bo3bo$5bo
142b3o39b3o142bo$bbobbo141boboo39boobo141bobbo$3b3o141b3o41b3o141b3o$
148bo43bo16$32bo275bo$31bo277bo$31b3o273b3o15$boo12boo307boo12boo$b3o
11b3o305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o305b3o12b3o$bo12boboo
305boobo12bo$14b3o307b3o$15bo309bo3$bbobo331bobo$5bo329bo$bo3bo142boo
41boo142bo3bo$5bo142b3o39b3o142bo$bbobbo141boboo39boobo141bobbo$3b3o
141b3o41b3o141b3o$148bo43bo$17bo305bo$16bo307bo$16b3o303b3o28$7bobo
321bobo$8boo321boo$boo5bo6boo307boo6bo5boo$b3o11b3o305b3o11b3o$oboo11b
3o305b3o11boobo$3o12b3o305b3o12b3o$bo12boboo305boobo12bo$14b3o307b3o$
15bo309bo3$bbobo331bobo$5bo329bo$bo3bo142boo41boo142bo3bo$5bo142b3o39b
3o142bo$bbobbo141boboo39boobo141bobbo$3b3o141b3o41b3o141b3o$148bo43bo
16$22bobo291bobo$23boo291boo$23bo293bo15$boo12boo307boo12boo$b3o11b3o
305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o305b3o12b3o$bo12boboo305boob
o12bo$14b3o307b3o$15bo309bo3$bbobo331bobo$5bo329bo$bo3bo142boo41boo
142bo3bo$5bo142b3o39b3o142bo$bbobbo141boboo39boobo141bobbo$3b3o141b3o
41b3o141b3o$148bo43bo$37bobo261bobo$38boo261boo$38bo263bo30$boo12boo
307boo12boo$b3o11b3o34bobo231bobo34b3o11b3o$oboo11b3o35boo231boo35b3o
11boobo$3o12b3o35bo233bo35b3o12b3o$bo12boboo305boobo12bo$14b3o307b3o$
15bo309bo3$bbobo331bobo$5bo329bo$bo3bo142boo41boo142bo3bo$5bo142b3o39b
3o142bo$bbobbo141boboo39boobo141bobbo$3b3o141b3o41b3o141b3o$148bo43bo
19$67bobo201bobo$68boo201boo$68bo203bo12$boo12boo307boo12boo$b3o11b3o
305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o305b3o12b3o$bo12boboo305boob
o12bo$14b3o307b3o$15bo309bo3$bbobo331bobo$5bo329bo$bo3bo142boo41boo
142bo3bo$5bo142b3o39b3o142bo$bbobbo141boboo39boobo141bobbo$3b3o141b3o
41b3o141b3o$148bo43bo4$82bobo171bobo$83boo171boo$83bo173bo27$boo12boo
307boo12boo$b3o11b3o305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o305b3o
12b3o$bo12boboo79bobo141bobo79boobo12bo$14b3o81boo141boo81b3o$15bo82bo
143bo82bo3$bbobo331bobo$5bo329bo$bo3bo142boo41boo142bo3bo$5bo142b3o39b
3o142bo$bbobbo141boboo39boobo141bobbo$3b3o141b3o41b3o141b3o$148bo43bo
22$112bobo111bobo$113boo111boo$113bo113bo9$boo12boo307boo12boo$b3o11b
3o305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o305b3o12b3o$bo12boboo305b
oobo12bo$14b3o307b3o$15bo309bo3$bbobo331bobo$5bo329bo$bo3bo142boo41boo
142bo3bo$5bo142b3o39b3o142bo$bbobbo141boboo39boobo141bobbo$3b3o141b3o
41b3o141b3o$148bo43bo7$127bobo81bobo$128boo81boo$128bo83bo24$boo12boo
307boo12boo$b3o11b3o305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o305b3o
12b3o$bo12boboo305boobo12bo$14b3o307b3o$15bo309bo$142bobo51bobo$143boo
51boo$bbobo138bo53bo138bobo$5bo329bo$bo3bo142boo41boo142bo3bo$5bo142b
3o39b3o142bo$bbobbo141boboo39boobo141bobbo$3b3o141b3o41b3o141b3o$148bo
43bo25$157bobo21bobo$158boo21boo$158bo23bo6$boo12boo307boo12boo$b3o11b
3o305b3o11b3o$oboo11b3o305b3o11boobo$3o12b3o305b3o12b3o$bo12boboo305b
oobo12bo$14b3o307b3o$15bo309bo3$bbobo331bobo$5bo329bo$bo3bo142boo41boo
142bo3bo$5bo142b3o39b3o142bo$bbobbo141boboo39boobo141bobbo$3b3o141b3o
41b3o141b3o$148bo43bo6$168booboo$168booboo!
To finish this, instead of making bi-blocks, the incoming gliders have to be used to create blocks on the correct column. A set of spaceships like the following might do this, but this example won't fit.

Code: Select all

#C Spaceships convert an incoming glider into a block several cells
#C away from their path.
x = 31, y = 68
14bobo$17bo$13bo3bo$13bo3bo$17bo$14bobbo$15b3o5$16boo$15b3o$15b3o$15b
3o$15boobo$16b3o$17bo25$14bobo$17bo$17bo$bobo10bobbo$4bo10b3o$o3bo$o3b
o$4bo$bobbo$bb3o14$30bo$28boo$29boo!
If no suitable reaction is found, then we might have to resort to creating pairs of gliders to make the blocks.

If this is completed, then an arbitrary number of output gliders can be liberated (by for example, using a glider duplicator instead of a glider turner).

EDIT:

I just found a convoy which allows reburning for the period 60 PI climber.

Code: Select all

#C A period 60 3c/10 PI climber with reburnable support.
#C This uses a downward convoy of c/2 spaceships to perturb the sparks
#C of a period 60 PI climber so as to recreate the supporting blocks
#C beneath it.  This allows an arbitrary number of PI climbers to be
#C supported.  The downward spaceships must be repeated every 48 cells.
#C David I. Bell, 12 February 2025
x = 75, y = 279
8b3o5b3o37b3o5b3o$8bobbo3bobbo37bobbo3bobbo$8bo9bo37bo9bo$6boobbobobob
obboo33boobbobobobobboo$6boobbobobobobboo33boobbobobobobboo$5bo5bo3bo
5bo31bo5bo3bo5bo$6bobbobo3bobobbo33bobbobo3bobobbo$7boo9boo35boo9boo$
8bo9bo37bo9bo$$6boo11boo33boo11boo$6boo11boo33boo11boo$$10boo3boo41boo
3boo$10boo3boo41boo3boo$20b3o29b3o$4b3o12bobbo29bobbo12b3o$3bobbo15bo
29bo15bobbo$7bo11bobbo29bobbo11bo$7bo11bobbo29bobbo11bo$3b6o12bobo27bo
bo12b6o$6bobo10bo3bo27bo3bo10bobo$4boo16boo27boo16boo$4boo3boo10boo29b
oo10boo3boo$9boo53boo$10bo53bo$11boob3o7bo25bo7b3oboo$oo7bobobo3bo5boo
25boo5bo3bobobo7boo$bb3o4bobobo3bo4b3o25b3o4bo3bobobo4b3o$bb3o10boo4b
3o27b3o4boo10b3o$3boo65boo12$24boo23boo$24boo23boo8$10bobo49bobo$13bo
47bo$9bo3bo47bo3bo$9bo3bo47bo3bo$13bo47bo$10bobbo47bobbo$11b3o47b3o3$
24boo23boo$24boo23boo3$14boo43boo$13b3o43b3o$13b3o43b3o$13boobo41boboo
$14b3o41b3o$15bo43bo5$16boo39boo$15b3o39b3o$15boobo37boboo$16b3o37b3o$
17bo6boo23boo6bo$24boo23boo17$24boo23boo$24boo23boo$$10bobo49bobo$13bo
47bo$9bo3bo47bo3bo$9bo3bo47bo3bo$13bo47bo$10bobbo47bobbo$11b3o47b3o7$
14boo43boo$13b3o43b3o$13b3o8boo23boo8b3o$13boobo7boo23boo7boboo$14b3o
41b3o$15bo43bo5$16boo39boo$15b3o39b3o$15boobo37boboo$16b3o37b3o$17bo
39bo6$24boo23boo$24boo23boo14$10bobo49bobo$13bo47bo$9bo3bo47bo3bo$9bo
3bo10boo23boo10bo3bo$13bo10boo23boo10bo$10bobbo47bobbo$11b3o47b3o7$14b
oo43boo$13b3o43b3o$13b3o43b3o$13boobo41boboo$14b3o41b3o$15bo43bo3$24b
oo23boo$24boo23boo$16boo39boo$15b3o39b3o$15boobo37boboo$16b3o37b3o$17b
o39bo12$24boo23boo$24boo23boo8$10bobo49bobo$13bo47bo$9bo3bo47bo3bo$9bo
3bo47bo3bo$13bo47bo$10bobbo47bobbo$11b3o47b3o3$24boo23boo$24boo23boo3$
14boo43boo$13b3o43b3o$13b3o43b3o$13boobo41boboo$14b3o41b3o$15bo43bo5$
16boo39boo$15b3o39b3o$15boobo37boboo$16b3o37b3o$17bo6boo23boo6bo$24boo
23boo17$24boo23boo$24boo23boo$$10bobo49bobo$13bo47bo$9bo3bo47bo3bo$9bo
3bo47bo3bo$13bo47bo$10bobbo47bobbo$11b3o47b3o7$14boo43boo$13b3o43b3o$
13b3o8boo23boo8b3o$13boobo7boo23boo7boboo$14b3o41b3o$15bo43bo$$37bo$
36bobo$35bo3bo$16boo17bo3bo17boo$15b3o17booboo17b3o$15boobo37boboo$16b
3o37b3o$17bo39bo$33bo7bo$29b4obo5bob4o$28booboo9booboo$31b5o3b5o$28boo
bbobo5bobobboo$28b3o13b3o$28bobbo11bobbo$29boo13boo!
BCNU,
-dbell

Re: Thread for your unsure discoveries

Posted: February 11th, 2025, 5:02 pm
by C28
Herschel to TL+g

Code: Select all

x = 24, y = 27, rule = B3/S23
b2o$2bo$bo$b2o$3bo$b3o$o$2o8$3b3o7b2o$4bo7bo2bo2b2o$4b3o5bobo4bo2bo$13b
o5bobobo$16b2obo2bo$16bo2bo$13bo4bo$13b5o2$15bo$14bobo$15bo!

Re: Thread for your unsure discoveries

Posted: February 13th, 2025, 12:26 am
by dbell
The two perturbations of the sparks of a p60 PI climber can be combined.

Code: Select all

#C Two different perturbations of a period 60 PI climber.
#C The more complicated perturbation restores the blocks behind the
#C PI climber.  The simple perturbation creates an output glider
#C while leaving a gap in the row of blocks. This example shows three
#C of the first type of perturbation followed by one of the second
#C type of perturbation, repeated a few times.  If the gaps were
#C fixed, another PI climber would be able to climb the same structure.
x = 71, y = 601
7bo7bo39bo7bo$6b3o5b3o37b3o5b3o$5bobboo3boobbo35bobboo3boobbo$5bo3bo3b
o3bo35bo3bo3bo3bo$6booboobooboo37booboobooboo$6boobo3boboo37boobo3bob
oo$8bo5bo41bo5bo$9booboo43booboo$4boobbo5bobboo33boobbo5bobboo$4boobbo
5bobboo33boobbo5bobboo$$8bobobobo41bobobobo$8boo3boo41boo3boo3$19bo31b
o$3bo14b3o29b3o14bo$bb3o3boo3boboboobo29boboobobo3boo3b3o$boobbobboo9b
o31bo9boobbobboo$b4obo6bo3bobo31bobo3bo6bob4o$oo5bo7boobboo29boobboo7b
o5boo$bo16bobbo27bobbo16bo$bob3obbo4bobobboo31boobbobo4bobb3obo$bobo3b
oo4bobobboo3bo23bo3boobbobo4boo3bobo$boo6bobbo7bobbo23bobbo7bobbo6boo$
o5bobo4bobo4boboo23boobo4bobo4bobo5bo$boobbobbo4bo6bobo25bobo6bo4bobbo
bboo$boo3boo7boo3boo27boo3boo7boo3boo11$10boo47boo$10b3o45b3o$10b3o9b
oo23boo9b3o$10b3o9boo23boo9b3o$9boboo45boobo$9b3o47b3o$10bo49bo6$11bob
o43bobo$14bo41bo$10bo3bo41bo3bo$14bo41bo$11bobbo41bobbo$12b3o41b3o3$
22boo23boo$22boo23boo$13bobo39bobo$16bo37bo$16bo37bo$13bobbo37bobbo$
14b3o37b3o12$22boo23boo$22boo23boo9$10boo47boo$10b3o45b3o$10b3o45b3o$
10b3o45b3o$9boboo45boobo$9b3o47b3o$10bo49bo$$22boo23boo$22boo23boo3$
11bobo43bobo$14bo41bo$10bo3bo41bo3bo$14bo41bo$11bobbo41bobbo$12b3o41b
3o5$13bobo39bobo$16bo37bo$16bo37bo$13bobbo37bobbo$14b3o5boo23boo5b3o$
22boo23boo17$22boo23boo$22boo23boo3$10boo$10b3o$10b3o$10b3o$9boboo$9b
3o$10bo6$11bobo$14bo$10bo3bo7boo23boo$14bo7boo23boo$11bobbo$12b3o$$57b
obo$56bo$56bo$13bobo40bobbo$16bo39b3o$16bo$13bobbo$14b3o6$22boo23boo$
22boo23boo15$10boo47boo$10b3o45b3o$10b3o9boo23boo9b3o$10b3o9boo23boo9b
3o$9boboo45boobo$9b3o47b3o$10bo49bo6$11bobo43bobo$14bo41bo$10bo3bo41bo
3bo$14bo41bo$11bobbo41bobbo$12b3o41b3o3$22boo23boo$22boo23boo$13bobo
39bobo$16bo37bo$16bo37bo$13bobbo37bobbo$14b3o37b3o12$22boo23boo$22boo
23boo9$10boo47boo$10b3o45b3o$10b3o45b3o$10b3o45b3o$9boboo45boobo$9b3o
47b3o$10bo49bo$$22boo23boo$22boo23boo3$11bobo43bobo$14bo41bo$10bo3bo
41bo3bo$14bo41bo$11bobbo41bobbo$12b3o41b3o5$13bobo39bobo$16bo37bo$16bo
37bo$13bobbo37bobbo$14b3o5boo23boo5b3o$22boo23boo17$22boo23boo$22boo
23boo3$10boo47boo$10b3o45b3o$10b3o45b3o$10b3o45b3o$9boboo45boobo$9b3o
47b3o$10bo49bo6$11bobo43bobo$14bo41bo$10bo3bo7boo23boo7bo3bo$14bo7boo
23boo7bo$11bobbo41bobbo$12b3o41b3o5$13bobo39bobo$16bo37bo$16bo37bo$13b
obbo37bobbo$14b3o37b3o6$22boo23boo$22boo23boo15$10boo$10b3o$10b3o9boo
23boo$10b3o9boo23boo$9boboo$9b3o$10bo6$11bobo$14bo$10bo3bo$14bo$11bobb
o$12b3o$$57bobo$22boo23boo7bo$22boo23boo7bo$13bobo40bobbo$16bo39b3o$
16bo$13bobbo$14b3o12$22boo23boo$22boo23boo9$10boo47boo$10b3o45b3o$10b
3o45b3o$10b3o45b3o$9boboo45boobo$9b3o47b3o$10bo49bo$$22boo23boo$22boo
23boo3$11bobo43bobo$14bo41bo$10bo3bo41bo3bo$14bo41bo$11bobbo41bobbo$
12b3o41b3o5$13bobo39bobo$16bo37bo$16bo37bo$13bobbo37bobbo$14b3o5boo23b
oo5b3o$22boo23boo17$22boo23boo$22boo23boo3$10boo47boo$10b3o45b3o$10b3o
45b3o$10b3o45b3o$9boboo45boobo$9b3o47b3o$10bo49bo6$11bobo43bobo$14bo
41bo$10bo3bo7boo23boo7bo3bo$14bo7boo23boo7bo$11bobbo41bobbo$12b3o41b3o
5$13bobo39bobo$16bo37bo$16bo37bo$13bobbo37bobbo$14b3o37b3o6$22boo23boo
$22boo23boo15$10boo47boo$10b3o45b3o$10b3o9boo23boo9b3o$10b3o9boo23boo
9b3o$9boboo45boobo$9b3o47b3o$10bo49bo6$11bobo43bobo$14bo41bo$10bo3bo
41bo3bo$14bo41bo$11bobbo41bobbo$12b3o41b3o3$22boo23boo$22boo23boo$13bo
bo39bobo$16bo37bo$16bo37bo$13bobbo37bobbo$14b3o37b3o12$22boo23boo$22b
oo23boo9$10boo$10b3o$10b3o$10b3o$9boboo$9b3o$10bo$$22boo23boo$22boo23b
oo3$11bobo$14bo$10bo3bo$14bo$11bobbo$12b3o$$57bobo$56bo$56bo$13bobo40b
obbo$16bo39b3o$16bo$13bobbo$14b3o5boo23boo$22boo23boo17$22boo23boo$22b
oo23boo3$10boo47boo$10b3o45b3o$10b3o45b3o$10b3o45b3o$9boboo45boobo$9b
3o47b3o$10bo49bo6$11bobo43bobo$14bo41bo$10bo3bo7boo23boo7bo3bo$14bo7b
oo23boo7bo$11bobbo41bobbo$12b3o41b3o$$35bo$34b3o$33booboo$13bobo16boo
3boo16bobo$16bo16booboo16bo$16bo37bo$13bobbo37bobbo$14b3o37b3o$28b4o7b
4o$26boo15boo$26boo5bo3bo5boo$32boo3boo$26bo3boboo3boobo3bo$25bobboo
11boobbo$26bobbo11bobbo$27boo13boo!
Each gap in the row of blocks must be fixed by using downward spaceships to duplicate and turn the output glider so that eventually two gliders react as shown here (and also emit another glider as output). It is important that each output glider is used to only fix the same gap as it was emitted from, and not one of the other gaps.

Code: Select all

#C Two gliders repair a gap in a row of blocks while missing spaceships.
x = 62, y = 219
boo11boo23boo11boo$3o11boo23boo11b3o$3o49b3o$3o49b3o$oobo47boboo$b3o
47b3o$bbo49bo6$5bobo39bobo$4bo45bo$4bo3bo37bo3bo$4bo45bo$4bobbo39bobbo
$4b3o41b3o$14boo23boo$14boo23boo3$7bobo35bobo$6bo41bo$6bo41bo$6bobbo
35bobbo$6b3o37b3o10$14boo23boo$14boo23boo11$boo49boo$3o49b3o$3o49b3o$
3o49b3o$oobo47boboo$b3o47b3o$bbo11boo23boo11bo$14boo23boo5$5bobo39bobo
$4bo45bo$4bo3bo37bo3bo$4bo45bo$4bobbo39bobbo$4b3o41b3o5$7bobo35bobo$6b
o41bo$6bo7boo23boo7bo$6bobbo4boo23boo4bobbo$6b3o37b3o16$14boo23boo16bo
$14boo23boo16bobo$57boo4$boo$3o$3o$3o$oobo$b3o$bbo6$5bobo6boo$4bo9boo$
4bo3bo$4bo$4bobbo$4b3o$$47bobo$50bo$50bo$7bobo37bobbo$6bo41b3o$6bo$6bo
bbo$6b3o4$14boo23boo$14boo23boo$59b3o$59bo$60bo14$boo11boo23boo11boo$
3o11boo23boo11b3o$3o49b3o$3o49b3o$oobo47boboo$b3o47b3o$bbo49bo6$5bobo
39bobo$4bo45bo$4bo3bo37bo3bo$4bo45bo$4bobbo39bobbo$4b3o41b3o$14boo23b
oo$14boo23boo3$7bobo35bobo$6bo41bo$6bo41bo$6bobbo35bobbo$6b3o37b3o10$
14boo23boo$14boo23boo11$boo49boo$3o49b3o$3o49b3o$3o49b3o$oobo47boboo$b
3o47b3o$bbo11boo23boo11bo$14boo23boo5$5bobo39bobo$4bo45bo$4bo3bo37bo3b
o$4bo45bo$4bobbo39bobbo$4b3o41b3o5$7bobo35bobo$6bo41bo$6bo7boo23boo7bo
$6bobbo4boo23boo4bobbo$6b3o37b3o!
The pattern of the two perturbation types has to be fixed since that must be created at the top of the object without regard to where the PIs
crawling on the trail are. There just has to be enough of the block restoring reactions in a row to leave room for the necessary glider
duplications to be done without interference from their neighbors. My example shown here is probably too small.

Since each output glider only fixes its own gap, this means that the time that another PI can climb the trail can be varied, so that the
timing and location of the output gliders can be changed. It might also help that each block-restoring reaction changes the spacing of the blocks.

The spaceship convoys which perform the glider manipulations must be repeated at the appropriate multiple of 48 cells, since once again they must be created at the top of the object without regard to where the gliders they manipulate will be.

There is no reaction which delays the generation of the output gliders, so this object is going to spew out a lot of unwanted gliders. Some
sort of filter mechanism is going to be necessary.

I hope this description is clear enough.

BCNU,
-dbell

Re: Thread for your unsure discoveries

Posted: February 13th, 2025, 5:58 am
by Antonin Duda
dbell wrote: February 13th, 2025, 12:26 am YAY new 3c/10 technology!
We are slowly but surely getting closer to making a 3c/10 caterpillar!

Re: Thread for your unsure discoveries

Posted: February 13th, 2025, 6:30 am
by confocaloid
Speaking about 3c/10, does anyone already have (something equivalent to) the best partial for the following qfind invocation, or some information or approximation of the best partial? (To be clear, I didn't run this search and I'm not currently running this.) Or similar information for other symmetry or higher width? User:Sokwe/Spaceship searches doesn't seem to answer this.

Code: Select all

./qfind -v 3c/10 -s odd -w 9
Antonin Duda wrote: February 13th, 2025, 5:58 am
dbell wrote: February 13th, 2025, 12:26 am

Re: Thread for your unsure discoveries

Posted: February 13th, 2025, 9:34 am
by Tawal
Surely already known : preTL + Blinker = Glider

Code: Select all

x = 6, y = 6, rule = B3/S23
4bo$3b3o4$3o!
#C [[ Z 20 ]]

Re: Thread for your unsure discoveries

Posted: February 13th, 2025, 11:51 am
by WhiteHawk
Is this double-bouncer effect known, and is it actually useful?

Code: Select all

x = 68, y = 44, rule = B3/S23
31bo33bo$31bobo31bobo$31b2o32b2o$43b2o$26bo16bo16bo$24b2o19bo12b2o$25b
2o17b4o11b2o$14bo28bo4bo$10b2obobo27b2ob2obo$10b2obobo25b2o3bo2bo$3b2o
8bob2o9b2o12bo2b2o2bob2o9b2o$4bo5b4o2bo5b2o2b2o12b2obobobo4bo3b2o2b2o
$3bo6bo3bo6bobo19bo2bo2b2obo2bobo$3b2o7b2o2bo5bo20b2obobo3bo3bo$b2o3b
2o3bobob2o28bobob2o$o2b2ob2o2b3o2bo8b2o19bobobo8b2o$bobo2bo4bobobo8bo
21bo2bo8bo$2o2bobob4ob2o10b3o19b2o10b3o$2bob2obo4bo14bo33bo$2bo4bob2o
bo$b2o4b2ob2o5$65bo$65bobo$65b2o2$43b2o15bo$43bo14b2o$45bo13b2o$44b4o
$43bo4bo$43b2ob2obo$41b2o3bo2bo10b2o$40bo2b2o2bob2o5b2o2b2o$40b2obobo
bo4bo2bobo$43bo2bo2b2obo3bo$43b2obobo3bo$45bobob2o7b2o$45bobobo8bo$46b
o2bo9b3o$47b2o12bo!

Re: Thread for your unsure discoveries

Posted: February 14th, 2025, 6:36 am
by Antonin Duda
(crosspost from discord)
Was this triple glider one-time splitter discovered before?
And could it be useful for slow salvo constructions?

Code: Select all

x = 36, y = 14, rule = B3/S23
14b2o$14b2o17b2o$32bo2bo$32bo2bo$16b2o15b2o$15bo2bo$16bobo$17bo4$3o$2b
o$bo!
Edit:
I think this could probably be also useful(though i'm not certain):

Code: Select all

x = 50, y = 32, rule = B3/S23
44b2o$44b2o8$29b2o$29b2o2$48bo$47bobo$47b2o4$14b2o$14b2o2$33bo$16b2o
14bobo$15bo2bo13b2o$16bobo$17bo4$3o$2bo$bo!

Re: Thread for your unsure discoveries

Posted: February 15th, 2025, 5:30 am
by dbell
Here is a completed p60 PI climber trail.

Code: Select all

#C A channel for 3c/10 PI climbers which emits gliders.
#C This demonstrates how a period 60 PI climber can move through a
#C channel made of two rows of blocks and two streams of backward
#C spaceships.  Most of backward spaceships perturb the PI to restore
#C the blocks behind it so that another PI can climb the same trail.
#C The occasional single backward spaceship perturbs the PI to generate
#C an output glider, at the expense of a block which makes a gap in the
#C trail.  However, a convoy of backward spaceships duplicates and turns
#C that glider to create the missing block, and also generates an output
#C glider.  This example shows three instances of the block restoring
#C convoy, which in full use would be repeated indefinitely, just as
#C the channel spaceships and blocks need to be.
#C David I. Bell, 15 February 2025
x = 319, y = 3783
13boo23boo$13boo23boo3$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo
$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo7boo23boo7bo3bo$5bo7boo23boo
7bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo
$5b3o37b3o6$13boo23boo$13boo23boo15$boo47boo$b3o45b3o$b3o9boo23boo9b3o
$b3o9boo23boo9b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3b
o41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o3$13boo23boo$13boo23boo$4bobo
39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o12$13boo23boo$13boo23boo
9$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo$$13b
oo23boo$13boo23boo3$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41b
obbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o5boo23b
oo5b3o$13boo23boo17$13boo23boo$13boo23boo3$boo47boo$b3o45b3o$b3o45b3o$
b3o45b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo7boo23b
oo7bo3bo$5bo7boo23boo7bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$
7bo37bo$4bobbo37bobbo$5b3o37b3o6$13boo23boo$13boo23boo15$boo47boo$b3o
45b3o$b3o9boo23boo9b3o$b3o9boo23boo9b3o$oboo45boobo$3o47b3o$bo49bo6$bb
obo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o3$13boo
23boo$13boo23boo$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o
12$13boo23boo$13boo23boo9$boo$b3o$b3o$b3o$oboo$3o$bo$$13boo23boo$13boo
23boo3$bbobo$5bo$bo3bo$5bo$bbobbo$3b3o$$48bobo$47bo$47bo$4bobo40bobbo$
7bo39b3o$7bo$4bobbo$5b3o5boo23boo$13boo23boo7$102boo$101b3o$101boobo$
102b3o$103bo6$13boo23boo$13boo23boo3$boo47boo$b3o45b3o$b3o45b3o$b3o45b
3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo7boo23boo7bo3b
o$5bo7boo23boo7bo$bbobbo41bobbo$3b3o41b3o4$101bobo$4bobo39bobo51bo$7bo
37bo54bo$7bo37bo54bobbo$4bobbo37bobbo51b3o$5b3o37b3o39bobo$90bo$86bo3b
o$86bo3bo$90bo$87bobbo$13boo23boo48b3o$13boo23boo15$boo47boo$b3o45b3o$
b3o9boo23boo9b3o$b3o9boo23boo9b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43b
obo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o3$13boo23boo$
13boo23boo$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o12$13boo
23boo$13boo23boo9$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo$3o
47b3o$bo49bo$$13boo23boo$13boo23boo3$bbobo43bobo$5bo41bo$bo3bo41bo3bo$
5bo41bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37b
obbo$5b3o5boo23boo5b3o$13boo23boo17$13boo23boo$13boo23boo3$boo47boo$b
3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo
41bo$bo3bo7boo23boo7bo3bo$5bo7boo23boo7bo$bbobbo41bobbo$3b3o41b3o5$4bo
bo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o6$13boo23boo$13boo23b
oo15$boo47boo$b3o45b3o$b3o9boo23boo9b3o$b3o9boo23boo9b3o$oboo45boobo$
3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo
$3b3o41b3o3$13boo23boo$13boo23boo$4bobo39bobo$7bo37bo$7bo37bo$4bobbo
37bobbo$5b3o37b3o12$13boo23boo$13boo23boo9$boo47boo$b3o45b3o$b3o45b3o$
b3o45b3o$oboo45boobo$3o47b3o$bo49bo$$13boo23boo$13boo23boo3$bbobo43bob
o$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7b
o37bo$7bo37bo$4bobbo37bobbo$5b3o5boo23boo5b3o$13boo23boo17$13boo23boo$
13boo23boo3$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo
49bo6$bbobo43bobo$5bo41bo$bo3bo7boo23boo7bo3bo$5bo7boo23boo7bo$bbobbo
41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o
6$13boo23boo$13boo23boo15$boo47boo$b3o45b3o$b3o9boo23boo9b3o$b3o9boo
23boo9b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo41bo3bo
$5bo41bo$bbobbo41bobbo$3b3o41b3o3$13boo23boo$13boo23boo$4bobo39bobo$7b
o37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o12$13boo23boo$13boo23boo9$boo47b
oo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo$$13boo23boo$
13boo23boo3$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b
3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o5boo23boo5b3o$
13boo23boo14$212bobo$211bo$211bo3bo$13boo23boo171bo$13boo23boo171bobbo
$211b3o$$boo47boo145bobo$b3o45b3o148bo$b3o45b3o144bo3bo$b3o45b3o144bo
3bo$oboo45boobo147bo$3o47b3o144bobbo$bo49bo146b3o$$208boo$207b3o$207b
oobo$208b3o$bbobo43bobo158bo$5bo41bo$bo3bo7boo23boo7bo3bo$5bo7boo23boo
7bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo
$5b3o37b3o6$13boo23boo$13boo23boo15$boo47boo$b3o45b3o$b3o9boo23boo9b3o
$b3o9boo23boo9b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3b
o41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o3$13boo23boo$13boo23boo$4bobo
39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o12$13boo23boo$13boo23boo
9$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo$$13b
oo23boo$13boo23boo3$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41b
obbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o5boo23b
oo5b3o$13boo23boo17$13boo23boo$13boo23boo3$boo47boo$b3o45b3o$b3o45b3o$
b3o45b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo7boo23b
oo7bo3bo$5bo7boo23boo7bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$
7bo37bo$4bobbo37bobbo$5b3o37b3o6$13boo23boo99bobo$13boo23boo102bo$138b
o3bo$142bo$139bobbo$140b3o$$154bobo$153bo$153bo3bo$153bo3bo$153bo$153b
obbo$153b3o$$144boo$boo47boo92b3o$b3o45b3o91boboo$b3o9boo23boo9b3o91b
3o$b3o9boo23boo9b3o92bo$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41b
o$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o3$13boo23boo$13boo23boo$
4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o12$13boo23boo$13boo
23boo9$boo47boo$b3o45b3o$b3o45b3o263bobo$b3o45b3o266bo$oboo45boobo261b
o3bo$3o47b3o265bo$bo49bo263bobbo$316b3o$13boo23boo$13boo23boo264bobo$
303bo$303bo3bo$bbobo43bobo252bo3bo$5bo41bo255bo$bo3bo41bo3bo251bobbo$
5bo41bo255b3o$bbobbo41bobbo$3b3o41b3o264boo$314b3o$313boboo$313b3o$
314bo$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o5boo23boo5b3o$13b
oo23boo5$165bobo15boo$168bo14b3o$164bo3bo14b3o$164bo3bo14b3o$168bo13bo
boo$165bobbo13b3o$166b3o14bo6$13boo23boo$13boo23boo130boo$170b3o$170b
3o$boo47boo117boboo$b3o45b3o117b3o$b3o45b3o118bo$b3o45b3o$oboo45boobo$
3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo7boo23boo7bo3bo$5bo7boo23boo
7bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo
$5b3o37b3o6$13boo23boo$13boo23boo15$boo47boo$b3o45b3o$b3o9boo23boo9b3o
$b3o9boo23boo9b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3b
o41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o$$228bobo$13boo23boo187bo$13b
oo23boo187bo3bo$4bobo39bobo178bo3bo$7bo37bo181bo$7bo37bo181bobbo$4bobb
o37bobbo178b3o11bobo$5b3o37b3o196bo$244bo$241bobbo$242b3o5$240boo$239b
3o$239b3o$239boobo$13boo23boo200b3o$13boo23boo201bo9$boo47boo$b3o45b3o
$b3o45b3o207boo12bobo$b3o45b3o207b3o14bo$oboo45boobo206b3o10bo3bo$3o
47b3o206b3o10bo3bo$bo49bo206boboo14bo$258b3o12bobbo$13boo23boo219bo14b
3o$13boo23boo3$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo224boo$bbobbo
41bobbo221b3o$3b3o41b3o222b3o$271boboo$271b3o$272bo$$4bobo39bobo$7bo
37bo$7bo37bo$4bobbo37bobbo$5b3o5boo23boo5b3o$13boo23boo17$13boo23boo$
13boo23boo3$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo
49bo6$bbobo43bobo$5bo41bo$bo3bo7boo23boo7bo3bo$5bo7boo23boo7bo$bbobbo
41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o
$173bobo$172bo$172bo$172bobbo$172b3o$13boo23boo$13boo23boo8$183bobo$
182bo$182bo3bo$182bo$182bobbo$182b3o$$boo47boo142boo$b3o45b3o141b3o$b
3o9boo23boo9b3o141b3o$b3o9boo23boo9b3o141b3o$oboo45boobo140boobo$3o47b
3o141b3o$bo49bo143bo6$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo
41bobbo$3b3o41b3o3$13boo23boo$13boo23boo$4bobo39bobo$7bo37bo$7bo37bo$
4bobbo37bobbo$5b3o37b3o12$13boo23boo$13boo23boo9$boo47boo$b3o45b3o$b3o
45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo$$13boo23boo$13boo23boo3$bbob
o43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o3$148boo$
148b3o$4bobo39bobo98boboo$7bo37bo101b3o$7bo37bo102bo$4bobbo37bobbo$5b
3o5boo23boo5b3o$13boo23boo7$158boo$158b3o$158b3o$157boboo$157b3o$158bo
$170bobo$169bo$169bo3bo$169bo3bo$13boo23boo129bo$13boo23boo129bobbo$
169b3o$$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo
6$bbobo43bobo$5bo41bo$bo3bo7boo23boo7bo3bo$5bo7boo23boo7bo$bbobbo41bo
bbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o6$
13boo23boo$13boo23boo15$boo47boo$b3o45b3o$b3o9boo23boo9b3o$b3o9boo23b
oo9b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5b
o41bo$bbobbo41bobbo$3b3o41b3o3$13boo23boo$13boo23boo$4bobo39bobo$7bo
37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o12$13boo23boo$13boo23boo9$boo$b3o$
b3o$b3o$oboo$3o$bo$$13boo23boo$13boo23boo3$bbobo$5bo$bo3bo$5bo$bbobbo$
3b3o$$48bobo$47bo$47bo$4bobo40bobbo$7bo39b3o$7bo$4bobbo$5b3o5boo23boo$
13boo23boo7$102boo$101b3o$101boobo$102b3o$103bo6$13boo23boo$13boo23boo
3$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo6$bbob
o43bobo$5bo41bo$bo3bo7boo23boo7bo3bo$5bo7boo23boo7bo$bbobbo41bobbo$3b
3o41b3o4$101bobo$4bobo39bobo51bo$7bo37bo54bo$7bo37bo54bobbo$4bobbo37bo
bbo51b3o$5b3o37b3o39bobo$90bo$86bo3bo$86bo3bo$90bo$87bobbo$13boo23boo
48b3o$13boo23boo15$boo47boo$b3o45b3o$b3o9boo23boo9b3o$b3o9boo23boo9b3o
$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$
bbobbo41bobbo$3b3o41b3o3$13boo23boo$13boo23boo$4bobo39bobo$7bo37bo$7bo
37bo$4bobbo37bobbo$5b3o37b3o12$13boo23boo$13boo23boo9$boo47boo$b3o45b
3o$b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo$$13boo23boo$13boo23boo
3$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o5$4b
obo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o5boo23boo5b3o$13boo23boo
17$13boo23boo$13boo23boo3$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45b
oobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo7boo23boo7bo3bo$5bo7boo
23boo7bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$4bobbo
37bobbo$5b3o37b3o6$13boo23boo$13boo23boo15$boo47boo$b3o45b3o$b3o9boo
23boo9b3o$b3o9boo23boo9b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo
41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o3$13boo23boo$13boo23b
oo$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o12$13boo23boo$
13boo23boo9$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo
49bo$$13boo23boo$13boo23boo3$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$
bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b
3o5boo23boo5b3o$13boo23boo17$13boo23boo$13boo23boo3$boo47boo$b3o45b3o$
b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3b
o7boo23boo7bo3bo$5bo7boo23boo7bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$
7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o6$13boo23boo$13boo23boo15$boo
47boo$b3o45b3o$b3o9boo23boo9b3o$b3o9boo23boo9b3o$oboo45boobo$3o47b3o$b
o49bo6$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b
3o3$13boo23boo$13boo23boo$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b
3o37b3o12$13boo23boo$13boo23boo9$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$o
boo45boobo$3o47b3o$bo49bo$$13boo23boo$13boo23boo3$bbobo43bobo$5bo41bo$
bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo
37bo$4bobbo37bobbo$5b3o5boo23boo5b3o$13boo23boo14$212bobo$211bo$211bo
3bo$13boo23boo171bo$13boo23boo171bobbo$211b3o$$boo47boo145bobo$b3o45b
3o148bo$b3o45b3o144bo3bo$b3o45b3o144bo3bo$oboo45boobo147bo$3o47b3o144b
obbo$bo49bo146b3o$$208boo$207b3o$207boobo$208b3o$bbobo43bobo158bo$5bo
41bo$bo3bo7boo23boo7bo3bo$5bo7boo23boo7bo$bbobbo41bobbo$3b3o41b3o5$4bo
bo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o6$13boo23boo$13boo23b
oo15$boo47boo$b3o45b3o$b3o9boo23boo9b3o$b3o9boo23boo9b3o$oboo45boobo$
3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo
$3b3o41b3o3$13boo23boo$13boo23boo$4bobo39bobo$7bo37bo$7bo37bo$4bobbo
37bobbo$5b3o37b3o12$13boo23boo$13boo23boo9$boo47boo$b3o45b3o$b3o45b3o$
b3o45b3o$oboo45boobo$3o47b3o$bo49bo$$13boo23boo$13boo23boo3$bbobo43bob
o$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7b
o37bo$7bo37bo$4bobbo37bobbo$5b3o5boo23boo5b3o$13boo23boo17$13boo23boo$
13boo23boo3$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo
49bo6$bbobo43bobo$5bo41bo$bo3bo7boo23boo7bo3bo$5bo7boo23boo7bo$bbobbo
41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o
6$13boo23boo99bobo$13boo23boo102bo$138bo3bo$142bo$139bobbo$140b3o$$
154bobo$153bo$153bo3bo$153bo3bo$153bo$153bobbo$153b3o$$144boo$boo47boo
92b3o$b3o45b3o91boboo$b3o9boo23boo9b3o91b3o$b3o9boo23boo9b3o92bo$oboo
45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobb
o41bobbo$3b3o41b3o3$13boo23boo$13boo23boo$4bobo39bobo$7bo37bo$7bo37bo$
4bobbo37bobbo$5b3o37b3o12$13boo23boo$13boo23boo9$boo47boo$b3o45b3o$b3o
45b3o263bobo$b3o45b3o266bo$oboo45boobo261bo3bo$3o47b3o265bo$bo49bo263b
obbo$316b3o$13boo23boo$13boo23boo264bobo$303bo$303bo3bo$bbobo43bobo
252bo3bo$5bo41bo255bo$bo3bo41bo3bo251bobbo$5bo41bo255b3o$bbobbo41bobbo
$3b3o41b3o264boo$314b3o$313boboo$313b3o$314bo$4bobo39bobo$7bo37bo$7bo
37bo$4bobbo37bobbo$5b3o5boo23boo5b3o$13boo23boo5$165bobo15boo$168bo14b
3o$164bo3bo14b3o$164bo3bo14b3o$168bo13boboo$165bobbo13b3o$166b3o14bo6$
13boo23boo$13boo23boo130boo$170b3o$170b3o$boo47boo117boboo$b3o45b3o
117b3o$b3o45b3o118bo$b3o45b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$
5bo41bo$bo3bo7boo23boo7bo3bo$5bo7boo23boo7bo$bbobbo41bobbo$3b3o41b3o5$
4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o6$13boo23boo$13boo
23boo15$boo47boo$b3o45b3o$b3o9boo23boo9b3o$b3o9boo23boo9b3o$oboo45boob
o$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bo
bbo$3b3o41b3o$$228bobo$13boo23boo187bo$13boo23boo187bo3bo$4bobo39bobo
178bo3bo$7bo37bo181bo$7bo37bo181bobbo$4bobbo37bobbo178b3o11bobo$5b3o
37b3o196bo$244bo$241bobbo$242b3o5$240boo$239b3o$239b3o$239boobo$13boo
23boo200b3o$13boo23boo201bo9$boo47boo$b3o45b3o$b3o45b3o207boo12bobo$b
3o45b3o207b3o14bo$oboo45boobo206b3o10bo3bo$3o47b3o206b3o10bo3bo$bo49bo
206boboo14bo$258b3o12bobbo$13boo23boo219bo14b3o$13boo23boo3$bbobo43bob
o$5bo41bo$bo3bo41bo3bo$5bo41bo224boo$bbobbo41bobbo221b3o$3b3o41b3o222b
3o$271boboo$271b3o$272bo$$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b
3o5boo23boo5b3o$13boo23boo17$13boo23boo$13boo23boo3$boo47boo$b3o45b3o$
b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3b
o7boo23boo7bo3bo$5bo7boo23boo7bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$
7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o$173bobo$172bo$172bo$172bobbo$
172b3o$13boo23boo$13boo23boo8$183bobo$182bo$182bo3bo$182bo$182bobbo$
182b3o$$boo47boo142boo$b3o45b3o141b3o$b3o9boo23boo9b3o141b3o$b3o9boo
23boo9b3o141b3o$oboo45boobo140boobo$3o47b3o141b3o$bo49bo143bo6$bbobo
43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o3$13boo23b
oo$13boo23boo$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o12$
13boo23boo$13boo23boo9$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo
$3o47b3o$bo49bo$$13boo23boo$13boo23boo3$bbobo43bobo$5bo41bo$bo3bo41bo
3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o3$148boo$148b3o$4bobo39bobo98boboo$
7bo37bo101b3o$7bo37bo102bo$4bobbo37bobbo$5b3o5boo23boo5b3o$13boo23boo
7$158boo$158b3o$158b3o$157boboo$157b3o$158bo$170bobo$169bo$169bo3bo$
169bo3bo$13boo23boo129bo$13boo23boo129bobbo$169b3o$$boo47boo$b3o45b3o$
b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3b
o7boo23boo7bo3bo$5bo7boo23boo7bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$
7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o6$13boo23boo$13boo23boo15$boo
47boo$b3o45b3o$b3o9boo23boo9b3o$b3o9boo23boo9b3o$oboo45boobo$3o47b3o$b
o49bo6$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b
3o3$13boo23boo$13boo23boo$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b
3o37b3o12$13boo23boo$13boo23boo9$boo$b3o$b3o$b3o$oboo$3o$bo$$13boo23b
oo$13boo23boo3$bbobo$5bo$bo3bo$5bo$bbobbo$3b3o$$48bobo$47bo$47bo$4bobo
40bobbo$7bo39b3o$7bo$4bobbo$5b3o5boo23boo$13boo23boo7$102boo$101b3o$
101boobo$102b3o$103bo6$13boo23boo$13boo23boo3$boo47boo$b3o45b3o$b3o45b
3o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo7boo
23boo7bo3bo$5bo7boo23boo7bo$bbobbo41bobbo$3b3o41b3o4$101bobo$4bobo39bo
bo51bo$7bo37bo54bo$7bo37bo54bobbo$4bobbo37bobbo51b3o$5b3o37b3o39bobo$
90bo$86bo3bo$86bo3bo$90bo$87bobbo$13boo23boo48b3o$13boo23boo15$boo47b
oo$b3o45b3o$b3o9boo23boo9b3o$b3o9boo23boo9b3o$oboo45boobo$3o47b3o$bo
49bo6$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o
3$13boo23boo$13boo23boo$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o
37b3o12$13boo23boo$13boo23boo9$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$ob
oo45boobo$3o47b3o$bo49bo$$13boo23boo$13boo23boo3$bbobo43bobo$5bo41bo$b
o3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo
37bo$4bobbo37bobbo$5b3o5boo23boo5b3o$13boo23boo17$13boo23boo$13boo23b
oo3$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo6$bb
obo43bobo$5bo41bo$bo3bo7boo23boo7bo3bo$5bo7boo23boo7bo$bbobbo41bobbo$
3b3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o6$13boo
23boo$13boo23boo15$boo47boo$b3o45b3o$b3o9boo23boo9b3o$b3o9boo23boo9b3o
$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$
bbobbo41bobbo$3b3o41b3o3$13boo23boo$13boo23boo$4bobo39bobo$7bo37bo$7bo
37bo$4bobbo37bobbo$5b3o37b3o12$13boo23boo$13boo23boo9$boo47boo$b3o45b
3o$b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo$$13boo23boo$13boo23boo
3$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o5$4b
obo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o5boo23boo5b3o$13boo23boo
17$13boo23boo$13boo23boo3$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45b
oobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo7boo23boo7bo3bo$5bo7boo
23boo7bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$4bobbo
37bobbo$5b3o37b3o6$13boo23boo$13boo23boo15$boo47boo$b3o45b3o$b3o9boo
23boo9b3o$b3o9boo23boo9b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo
41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o3$13boo23boo$13boo23b
oo$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o12$13boo23boo$
13boo23boo9$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo
49bo$$13boo23boo$13boo23boo3$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$
bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b
3o5boo23boo5b3o$13boo23boo14$212bobo$211bo$211bo3bo$13boo23boo171bo$
13boo23boo171bobbo$211b3o$$boo47boo145bobo$b3o45b3o148bo$b3o45b3o144bo
3bo$b3o45b3o144bo3bo$oboo45boobo147bo$3o47b3o144bobbo$bo49bo146b3o$$
208boo$207b3o$207boobo$208b3o$bbobo43bobo158bo$5bo41bo$bo3bo7boo23boo
7bo3bo$5bo7boo23boo7bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7b
o37bo$4bobbo37bobbo$5b3o37b3o6$13boo23boo$13boo23boo15$boo47boo$b3o45b
3o$b3o9boo23boo9b3o$b3o9boo23boo9b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo
43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o3$13boo23b
oo$13boo23boo$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o12$
13boo23boo$13boo23boo9$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo
$3o47b3o$bo49bo$$13boo23boo$13boo23boo3$bbobo43bobo$5bo41bo$bo3bo41bo
3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$4bobb
o37bobbo$5b3o5boo23boo5b3o$13boo23boo17$13boo23boo$13boo23boo3$boo47b
oo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$
5bo41bo$bo3bo7boo23boo7bo3bo$5bo7boo23boo7bo$bbobbo41bobbo$3b3o41b3o5$
4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o6$13boo23boo99bobo$
13boo23boo102bo$138bo3bo$142bo$139bobbo$140b3o$$154bobo$153bo$153bo3bo
$153bo3bo$153bo$153bobbo$153b3o$$144boo$boo47boo92b3o$b3o45b3o91boboo$
b3o9boo23boo9b3o91b3o$b3o9boo23boo9b3o92bo$oboo45boobo$3o47b3o$bo49bo
6$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o3$
13boo23boo$13boo23boo$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o
37b3o12$13boo23boo$13boo23boo9$boo47boo$b3o45b3o$b3o45b3o263bobo$b3o
45b3o266bo$oboo45boobo261bo3bo$3o47b3o265bo$bo49bo263bobbo$316b3o$13b
oo23boo$13boo23boo264bobo$303bo$303bo3bo$bbobo43bobo252bo3bo$5bo41bo
255bo$bo3bo41bo3bo251bobbo$5bo41bo255b3o$bbobbo41bobbo$3b3o41b3o264boo
$314b3o$313boboo$313b3o$314bo$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobb
o$5b3o5boo23boo5b3o$13boo23boo5$165bobo15boo$168bo14b3o$164bo3bo14b3o$
164bo3bo14b3o$168bo13boboo$165bobbo13b3o$166b3o14bo6$13boo23boo$13boo
23boo130boo$170b3o$170b3o$boo47boo117boboo$b3o45b3o117b3o$b3o45b3o118b
o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo7boo
23boo7bo3bo$5bo7boo23boo7bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7bo
37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o6$13boo23boo$13boo23boo15$boo47boo
$b3o45b3o$b3o9boo23boo9b3o$b3o9boo23boo9b3o$oboo45boobo$3o47b3o$bo49bo
6$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o$$
228bobo$13boo23boo187bo$13boo23boo187bo3bo$4bobo39bobo178bo3bo$7bo37bo
181bo$7bo37bo181bobbo$4bobbo37bobbo178b3o11bobo$5b3o37b3o196bo$244bo$
241bobbo$242b3o5$240boo$239b3o$239b3o$239boobo$13boo23boo200b3o$13boo
23boo201bo9$boo47boo$b3o45b3o$b3o45b3o207boo12bobo$b3o45b3o207b3o14bo$
oboo45boobo206b3o10bo3bo$3o47b3o206b3o10bo3bo$bo49bo206boboo14bo$258b
3o12bobbo$13boo23boo219bo14b3o$13boo23boo3$bbobo43bobo$5bo41bo$bo3bo
41bo3bo$5bo41bo224boo$bbobbo41bobbo221b3o$3b3o41b3o222b3o$271boboo$
271b3o$272bo$$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o5boo23boo
5b3o$13boo23boo17$13boo23boo$13boo23boo3$boo47boo$b3o45b3o$b3o45b3o$b
3o45b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo7boo23boo
7bo3bo$5bo7boo23boo7bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7b
o37bo$4bobbo37bobbo$5b3o37b3o$173bobo$172bo$172bo$172bobbo$172b3o$13b
oo23boo$13boo23boo8$183bobo$182bo$182bo3bo$182bo$182bobbo$182b3o$$boo
47boo142boo$b3o45b3o141b3o$b3o9boo23boo9b3o141b3o$b3o9boo23boo9b3o141b
3o$oboo45boobo140boobo$3o47b3o141b3o$bo49bo143bo6$bbobo43bobo$5bo41bo$
bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o3$13boo23boo$13boo23boo$4b
obo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o12$13boo23boo$13boo
23boo9$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo
$$13boo23boo$13boo23boo3$bbobo43bobo$5bo41bo$bo3bo41bo3bo$5bo41bo$bbo
bbo41bobbo$3b3o41b3o3$148boo$148b3o$4bobo39bobo98boboo$7bo37bo101b3o$
7bo37bo102bo$4bobbo37bobbo$5b3o5boo23boo5b3o$13boo23boo7$158boo$158b3o
$158b3o$157boboo$157b3o$158bo$170bobo$169bo$169bo3bo$169bo3bo$13boo23b
oo129bo$13boo23boo129bobbo$169b3o$$boo47boo$b3o45b3o$b3o45b3o$b3o45b3o
$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo41bo$bo3bo7boo23boo7bo3bo$
5bo7boo23boo7bo$bbobbo41bobbo$3b3o41b3o5$4bobo39bobo$7bo37bo$7bo37bo$
4bobbo37bobbo$5b3o37b3o6$13boo23boo$13boo23boo15$boo47boo$b3o45b3o$b3o
9boo23boo9b3o$b3o9boo23boo9b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo
$5bo41bo$bo3bo41bo3bo$5bo41bo$bbobbo41bobbo$3b3o41b3o3$13boo23boo$13b
oo23boo$4bobo39bobo$7bo37bo$7bo37bo$4bobbo37bobbo$5b3o37b3o12$13boo23b
oo$13boo23boo9$boo$b3o$b3o$b3o$oboo$3o$bo$$13boo23boo$13boo23boo3$bbob
o$5bo$bo3bo$5bo$bbobbo$3b3o$$48bobo$47bo$47bo$4bobo40bobbo$7bo39b3o$7b
o$4bobbo$5b3o5boo23boo$13boo23boo17$13boo23boo$13boo23boo3$boo47boo$b
3o45b3o$b3o45b3o$b3o45b3o$oboo45boobo$3o47b3o$bo49bo6$bbobo43bobo$5bo
41bo$bo3bo7boo23boo7bo3bo$5bo7boo23boo7bo$bbobbo41bobbo$3b3o41b3o$$26b
o$25b3o$24booboo$4bobo16boo3boo16bobo$7bo16booboo16bo$7bo37bo$4bobbo
37bobbo$5b3o37b3o$19b4o7b4o$17boo15boo$17boo5bo3bo5boo$23boo3boo$17bo
3boboo3boobo3bo$16bobboo11boobbo$17bobbo11bobbo$18boo13boo!
There is probably a block restoring convoy using fewer glider turning spaceships, but this one was hard enough to find. I had to use trombone slide-like glider paths to avoid some gliders running into the convoys.

I don't want to think about how hard it would be to build a fanout device driven by a helix to create those streams of downwards spaceships. Certainly a script would be necessary.

EDIT:

It's really sad, but this idea of a reburnable PI climber doesn't work!

When the blocks are burned by the first PI, they are shifted an odd number of cells. This means that another PI can't burn the new tracks since the downwards spaceships only move an even number of cells.

I really should have tried to make an example of several PIs moving on the same track before I spent all this effort and wasted everyone's time.

PS: Perhaps the downward spaceships could be used in pairs and alternate even-odd rows, and a pair of PIs could then burn as one unit. That's getting pretty complicated and unlikely, but I'll look at it.

EDIT 2:

A quick glance shows that the above PI pair idea can't work since the PIs interact with every unit of the downward convoys, so no adjustment is possible for alternate units.

Therefore I went back and examined more PI perturbation reactions, and luckily found a new solution.

Code: Select all

#C A channel which can support multiple period 60 PI crawlers.
#C The channel is made of two rows of blocks spaced 18 cells apart
#C and sets of four downward spaceships spaced 48 cells apart.
#C The spaceships perturb the sparks of each PI crawler to create
#C new blocks positioned four cells lower than the consumed ones.
#C This example shows two PI climbers, where the second one is
#C climbing through the blocks created from the first one.
#C David I. Bell, 16 February 2025
x = 57, y = 665
5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45b
o$15boo23boo$6bobo6boo23boo6bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo
37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39b
obbo$6b3o39b3o4$15boo23boo$15boo23boo$$bobo49bobo$o55bo$o3bo47bo3bo$o
55bo$obbo49bobbo$3o51b3o10$15boo23boo$15boo23boo4$5boo43boo$5b3o41b3o$
5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo
37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o5boo23boo5b3o$15boo23boo
$$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$b
obo49bobo$o55bo$o3bo47bo3bo$o14boo23boo14bo$obbo11boo23boo11bobbo$3o
51b3o15$5boo43boo$5b3o7boo23boo7b3o$5b3o7boo23boo7b3o$5b3o41b3o$4boboo
41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$
6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo6boo23b
oo6bo$5bobbo6boo23boo6bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o
55bo$obbo49bobbo$3o51b3o4$15boo23boo$15boo23boo10$5boo43boo$5b3o41b3o$
5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$15boo23boo$6bobo6b
oo23boo6bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5b
obo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o4$15boo
23boo$15boo23boo$$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b
3o10$15boo23boo$15boo23boo4$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4b
oboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo
37bo$6bobbo37bobbo$7b3o5boo23boo5b3o$15boo23boo$$5bobo41bobo$8bo39bo$
4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo
47bo3bo$o14boo23boo14bo$obbo11boo23boo11bobbo$3o51b3o15$5boo43boo$5b3o
7boo23boo7b3o$5b3o7boo23boo7b3o$5b3o41b3o$4boboo41boobo$4b3o21bo21b3o$
5bo21b3o21bo$26b5o$6bobo16boo3boo16bobo$9bo14boo5boo14bo$5bo3bo15boo3b
oo15bo3bo$9bo16bo3bo16bo$6bobbo37bobbo$7b3o13bo9bo13b3o$20bo3bo7bo3bo$
19bo3boo7boo3bo$5bobo10bobbob4o3b4obobbo10bobo$8bo10b3oboobbobobboob3o
10bo$4bo3bo9bo3bob3o3b3obo3bo9bo3bo$8bo9b3o3boo5boo3b3o9bo$5bobbo9bo4b
o9bo4bo9bobbo$6b3o11boo13boo11b3o7$bobo49bobo$o55bo$o3bo8bo29bo8bo3bo$
o11boo29boo11bo$obbo7b3o29b3o7bobbo$3o8bo33bo8b3o$9bo37bo$9bo3boo27boo
3bo$13boo27boo$10bo35bo$11bobbo27bobbo$11b3o29b3o$17boo19boo$17boo19b
oo7$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5b
o45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23b
oo5bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo
39bobbo$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o
55bo$obbo49bobbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o
41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$
5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23b
oo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bob
o$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo
12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo
8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo
37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39b
obbo$6b3o39b3o$$15boo23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o
55bo$obbo49bobbo$3o51b3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o41b3o$
5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo
37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o3$5b
obo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo
49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo49bobbo$3o51b3o
14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo
41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$
6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo3bo6boo23boo6b
o3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o
55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo12$5boo43boo$5b3o41b3o$
5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$
6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo18bo18bobbo$7b3o17bobo
17b3o$26booboo$$5bobo41bobo$8bo15bo7bo15bo$4bo3bo10boobbobo5bobobboo
10bo3bo$8bo8boobobbo9bobboboo8bo$5bobbo8bobboo13boobbo8bobbo$6b3o8bo3b
4o7b4o3bo8b3o$18bo5boo5boo5bo$15boobbobb3obo3bob3obbobboo$15boo3b4o9b
4o3boo$21boboobbobobboobo$22bo11bo$23b4o3b4o$bobo20bo7bo20bobo$o55bo$o
3bo47bo3bo$o55bo$obbo8bo31bo8bobbo$3o8bo33bo8b3o$10boo33boo3$11boboo
27boobo$11bobbo27bobbo$11b3o29b3o5$17boo19boo$17boo19boo3$5boo43boo$5b
3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bo
bo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo5bo25bo5bobbo$7b3o37b3o$$15bo
25bo$5bobo7boo23boo7bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$
6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o12boo23boo
12b3o$15boo23boo14$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o7boo23boo7b3o$4bo
boo7boo23boo7boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3b
o$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$
8bo39bo$5bobbo39bobbo$6b3o6boo23boo6b3o$15boo23boo6$bobo49bobo$o55bo$o
3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o6$15boo23boo$15boo23boo!
Those four downward spaceships for each perturbation barely fit into the available space!

I don't yet know if the glider liberation perturbation can still work as is since the block rebuilding gliders might not fit into the new gaps.

EDIT 3:

The new PI supporting convoys still allows the missing block to be rebuilt.

Code: Select all

#C An insertion of a block into a row of blocks while missing convoys.
#C This shows a PI crawler advancing through blocks being perturbed
#C by downward spaceship convoys to new create blocks behind it.
#C Every ninth convoy on one side is replaced by a single spacship
#C which perturbs the PI crawler to release a glider, at the cost of a
#C missing block.  Two later gliders created in unshown reactions can
#C enter the next gap so as to create the missing block.  This shows
#C an output glider and the two input gliders which it must eventually
#C create having the timing shown here.  The gaps must actually be
#C placed far enough apart so that the input gliders have time to be
#C created.
x = 263, y = 911
6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bo
bo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o6boo23boo6b3o
$15boo23boo6$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o6$
15boo23boo$15boo23boo8$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo
41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo5boo23boo5bo$5bo3bo5boo23boo
5bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo
3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o6$15boo23boo$bobo11boo23boo11bobo$o
55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o12$15boo23boo$15boo23boo$$5b
oo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo
$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o$$
15boo23boo$5bobo7boo23boo7bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39b
obbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o12boo
23boo12b3o$15boo23boo14$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o7boo23boo7b
3o$4boboo7boo23boo7boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo
37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo$8bo$4bo3bo$8bo$5bobbo$
6b3o6boo23boo$15boo23boo6$bobo$o$o3bo$o$obbo$3o6$15boo23boo$15boo23boo
8$5boo$5b3o$5b3o$5b3o$4boboo$4b3o$5bo$48bobo$6bobo42bo$9bo5boo23boo9bo
$5bo3bo5boo23boo6bobbo$9bo39b3o$6bobbo$7b3o3$5bobo41bobo$8bo39bo$4bo3b
o39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o6$15boo23boo$bobo11boo23boo11b
obo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o12$15boo23boo$15boo23b
oo$$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5b
o45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b
3o$$15boo23boo$5bobo7boo23boo7bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobb
o39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o
12boo23boo12b3o$15boo23boo14$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o7boo23b
oo7b3o$4boboo7boo23boo7boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5b
o3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3b
o39bo3bo$8bo39bo$5bobbo39bobbo$6b3o6boo23boo6b3o$15boo23boo6$bobo49bob
o$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o6$15boo23boo$15boo23boo8$
5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45b
o$$6bobo39bobo$9bo5boo23boo5bo$5bo3bo5boo23boo5bo3bo$9bo37bo$6bobbo37b
obbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo19bo19bo3bo$8bo19bo19bo$5bo
bbo18bobo18bobbo$6b3o39b3o$24boob3oboo$21boboobo3boboobo$20b5obo3bob5o
$21boobbo5bobboo$25boo3boo$15boo3bobbobbo3bobbobbo3boo$bobo11boo8bobob
obo8boo11bobo$o20bo3boo3boo3bo20bo$o3bo20bo5bo20bo3bo$o23bo7bo23bo$obb
o49bobbo$3o51b3o3$19boobbo9bobboo$18bo4bobo5bobo4bo$12b3o4boo6bobo6boo
4b3o$11bo3bo11bobo11bo3bo$10bo4bo7boobbobobboo7bo4bo$10bo4bo8bobo3bobo
8bo4bo$14bo10bo5bo10bo$9boobo31boboo$9bobbo31bobbo$10boo33boo3$5boo10b
oo19boo10boo$5b3o9boo19boo9b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o
43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo
$7b3o37b3o3$5bobo5boo27boo5bobo$8bo3bobo27bobo3bo$4bo3bo5bobboo19boobb
o5bo3bo$8bo8boo19boo8bo$5bobbo39bobbo$6b3o39b3o$$10bo35bo$10bo35bo4$bo
bo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o4$15boo23boo$15boo
23boo10$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b
3o$5bo45bo$15boo23boo$6bobo6boo23boo6bobo$9bo37bo$5bo3bo37bo3bo$9bo37b
o$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$
5bobbo39bobbo$6b3o39b3o4$15boo23boo$15boo23boo$$bobo49bobo$o55bo$o3bo
47bo3bo$o55bo$obbo49bobbo$3o51b3o10$15boo$15boo4$5boo43boo$5b3o41b3o$
5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo
37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o5boo23boo5b3o$15boo23boo
$$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$b
obo49bobo$o55bo$o3bo47bo3bo$o14boo23boo14bo$obbo11boo23boo11bobbo$3o
51b3o15$5boo43boo$5b3o7boo23boo7b3o$5b3o7boo23boo7b3o$5b3o41b3o$4boboo
41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$
6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo6boo23b
oo6bo$5bobbo6boo23boo6bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o
55bo$obbo49bobbo$3o51b3o4$15boo23boo$15boo23boo10$5boo43boo$5b3o41b3o$
5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$15boo23boo$6bobo6b
oo23boo6bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5b
obo$8bo$4bo3bo$8bo$5bobbo$6b3o4$15boo23boo$15boo23boo$$bobo$o$o3bo$o$o
bbo$3o3$65bo$65bobo$65boo5$15boo23boo$15boo23boo4$5boo$5b3o$5b3o$5b3o$
4boboo$4b3o$5bo$48bobo$6bobo42bo$9bo41bo$5bo3bo38bobbo$9bo39b3o$6bobbo
$7b3o5boo$15boo$$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bo
bbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o14boo23boo14bo$obbo11boo
23boo11bobbo$3o51b3o7$67b3o$67bo$68bo6$5boo43boo$5b3o7boo23boo7b3o$5b
3o7boo23boo7b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo
$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8b
o39bo$4bo3bo39bo3bo$8bo6boo23boo6bo$5bobbo6boo23boo6bobbo$6b3o39b3o7$b
obo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o4$15boo23boo$15b
oo23boo10$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o
43b3o$5bo45bo$15boo23boo$6bobo6boo23boo6bobo$9bo37bo$5bo3bo37bo3bo$9bo
37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39b
o$5bobbo39bobbo$6b3o39b3o4$15boo23boo$15boo23boo$$bobo49bobo$o55bo$o3b
o47bo3bo$o55bo$obbo49bobbo$3o51b3o10$15boo23boo$15boo23boo4$5boo43boo$
5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo
39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o5boo23boo5b3o$
15boo23boo$$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b
3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o14boo23boo14bo$obbo11boo23boo
11bobbo$3o51b3o15$5boo43boo$5b3o7boo23boo7b3o$5b3o7boo23boo7b3o$5b3o
41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo
3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo
$8bo6boo23boo6bo$5bobbo6boo23boo6bobbo$6b3o39b3o7$bobo49bobo$o55bo203b
obo$o3bo47bo3bo204boo$o55bo204bo$obbo49bobbo$3o51b3o4$15boo23boo$15boo
23boo10$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b
3o$5bo45bo$15boo23boo$6bobo6boo23boo6bobo$9bo37bo$5bo3bo37bo3bo$9bo37b
o$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$
5bobbo39bobbo$6b3o39b3o4$15boo23boo$15boo23boo$$bobo49bobo$o55bo$o3bo
47bo3bo$o55bo$obbo49bobbo$3o51b3o10$15boo23boo$15boo23boo4$5boo43boo$
5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo!
The previous block insertion convoy I showed before won't work here since the position of the new blocks is changed, so a new convoy will have to be made for this case.

BCNU,
-dbell

Re: Thread for your unsure discoveries

Posted: February 15th, 2025, 9:25 am
by Mr. T
dbell wrote: February 13th, 2025, 12:26 am The two perturbations of the sparks of a p60 PI climber can be combined.
...

-dbell
2 p60 climber combined. Perhaps its useful.

Code: Select all

x = 460, y = 303, rule = B3/S23
35b2o23b2o$35b2o23b2o4$2o23b2o169b2o23b2o$2o23b2o169b2o23b2o13b2o23b2o
$158b2o23b2o51b2o23b2o$119b2o23b2o12b2o23b2o$119b2o23b2o3$394b2o23b2o$
355b2o23b2o12b2o23b2o12b2o23b2o$355b2o23b2o51b2o23b2o4$35b2o23b2o$35b
2o23b2o4$2o23b2o169b2o23b2o$2o23b2o169b2o23b2o13b2o23b2o$158b2o23b2o
51b2o23b2o$119b2o23b2o12b2o23b2o$119b2o23b2o3$394b2o23b2o$355b2o23b2o
12b2o23b2o12b2o23b2o$355b2o23b2o51b2o23b2o4$35b2o23b2o$35b2o23b2o4$2o
23b2o169b2o23b2o$2o23b2o169b2o23b2o13b2o23b2o$158b2o23b2o51b2o23b2o$
119b2o23b2o12b2o23b2o$119b2o23b2o3$394b2o23b2o$355b2o23b2o12b2o23b2o
12b2o23b2o$355b2o23b2o51b2o23b2o4$35b2o23b2o$35b2o23b2o4$2o23b2o169b2o
23b2o$2o23b2o169b2o23b2o13b2o23b2o$158b2o23b2o51b2o23b2o$119b2o23b2o
12b2o23b2o$119b2o23b2o3$394b2o23b2o$355b2o23b2o12b2o23b2o12b2o23b2o$
355b2o23b2o51b2o23b2o4$35b2o23b2o$35b2o23b2o4$2o23b2o169b2o23b2o$2o23b
2o169b2o23b2o13b2o23b2o$158b2o23b2o51b2o23b2o$119b2o23b2o12b2o23b2o$
119b2o23b2o3$394b2o23b2o$355b2o23b2o12b2o23b2o12b2o23b2o$355b2o23b2o
51b2o23b2o4$35b2o23b2o$35b2o23b2o4$2o23b2o169b2o23b2o$2o23b2o169b2o23b
2o13b2o23b2o$158b2o23b2o51b2o23b2o$119b2o23b2o12b2o23b2o$119b2o23b2o3$
394b2o23b2o$355b2o23b2o12b2o23b2o12b2o23b2o$355b2o23b2o51b2o23b2o4$35b
2o23b2o$35b2o23b2o4$2o23b2o169b2o23b2o$2o23b2o169b2o23b2o13b2o23b2o$
158b2o23b2o51b2o23b2o$119b2o23b2o12b2o23b2o$119b2o23b2o3$394b2o23b2o$
355b2o23b2o12b2o23b2o12b2o23b2o$355b2o23b2o51b2o23b2o4$35b2o23b2o$35b
2o23b2o4$2o23b2o169b2o23b2o$2o23b2o169b2o23b2o13b2o23b2o$158b2o23b2o
51b2o23b2o$119b2o23b2o12b2o23b2o$119b2o23b2o3$394b2o23b2o$355b2o23b2o
12b2o23b2o12b2o23b2o$355b2o23b2o51b2o23b2o4$35b2o23b2o$35b2o23b2o4$2o
23b2o169b2o23b2o$2o23b2o169b2o23b2o13b2o23b2o$158b2o23b2o51b2o23b2o$
119b2o23b2o12b2o23b2o$119b2o23b2o3$394b2o23b2o$355b2o23b2o12b2o23b2o
12b2o23b2o$355b2o23b2o51b2o23b2o4$35b2o23b2o$35b2o23b2o4$2o23b2o169b2o
23b2o$2o23b2o169b2o23b2o13b2o23b2o$158b2o23b2o51b2o23b2o$119b2o23b2o
12b2o23b2o$119b2o23b2o3$394b2o23b2o$355b2o23b2o12b2o23b2o12b2o23b2o$
355b2o23b2o51b2o23b2o4$35b2o23b2o$35b2o23b2o4$2o23b2o169b2o23b2o$2o23b
2o169b2o23b2o13b2o23b2o$158b2o23b2o51b2o23b2o$119b2o23b2o12b2o23b2o$
119b2o23b2o3$394b2o23b2o$355b2o23b2o12b2o23b2o12b2o23b2o$355b2o23b2o
51b2o23b2o4$35b2o23b2o$35b2o23b2o4$2o23b2o169b2o23b2o$2o23b2o169b2o23b
2o13b2o23b2o$158b2o23b2o51b2o23b2o$119b2o23b2o12b2o23b2o$119b2o23b2o3$
394b2o23b2o$355b2o23b2o12b2o23b2o12b2o23b2o$355b2o23b2o51b2o23b2o4$35b
2o23b2o$35b2o23b2o4$2o23b2o169b2o23b2o$2o23b2o169b2o23b2o13b2o23b2o$
158b2o23b2o51b2o23b2o$119b2o23b2o12b2o23b2o$119b2o23b2o3$394b2o23b2o$
355b2o23b2o12b2o23b2o12b2o23b2o$355b2o23b2o51b2o23b2o4$35b2o23b2o$35b
2o23b2o4$2o23b2o169b2o23b2o$2o23b2o169b2o23b2o13b2o23b2o$158b2o23b2o
51b2o23b2o$119b2o23b2o12b2o23b2o$119b2o23b2o3$394b2o23b2o$355b2o23b2o
12b2o23b2o12b2o23b2o$355b2o23b2o51b2o23b2o4$35b2o23b2o$35b2o23b2o4$2o
23b2o169b2o23b2o$2o23b2o169b2o23b2o13b2o23b2o$158b2o23b2o51b2o23b2o$
119b2o23b2o12b2o23b2o$119b2o23b2o2$48bo160bo$47b3o158b3o183b2o23b2o$
47b3o157bo3bo37bo105b2o23b2o12b2o23b2o12b2o23b2o$43bo9bo153b2ob2o36bob
o104b2o23b2o51b2o23b2o$42b3o3bo3b3o115b3o75bobo$41bob2o3bo3b2obo114b3o
75bobo$12b3o25b2ob2o3bo3b2ob2o143bo17bo$13bo21b2o4b4o7b4o4b2o69b3o36bo
bo25b4o2b2o7b2o2b4o$35b2o9bo3bo9b2o135bob3o2b2o7b2o2b3obo18b2o2b3o5b3o
2b2o$7b3o7b3o23b2o7b2o77bobo28b2o2b2o7b2o2b2o21b2o2bo5bo2b2o22bobo2b2o
7b2o2bobo146b3o$6bobo3b3o3bobo23bo7bo76bo5bo25bobo3bobo3bobo3bobo21bo
2bo5bo2bo22b2o6bo5bo6b2o145b3o$6bo13bo107b3obob3o24bo6bo5bo6bo19b2o3bo
5bo3b2o21b2ob3o9b3ob2o$2o4b2ob2o5b2ob2o4b2o11b2o17b2o65b3obo7bob3o20bo
3bo5bo5bo3bo15bo2bob2o11b2obo2bo18b3o2bo7bo2b3o108b3o36bobo36b3o$2o6bo
3bobo3bo6b2o96bobo4bobobo4bobo20bob3o9b3obo19bo2bo11bo2bo17b2o3bo3b2o
5b2o3bo3b2o$8b3o5b3o19bo2bo13bo2bo71bobobo23b2o3bo2b2o7b2o2bo3b2o16b2o
13b2o18b2o4b2o2b2o3b2o2b2o4b2o104bobo28b2o2b2o7b2o2b2o28bobo$41bo13bo
63b2o3b4o2b5o2b4o3b2o12b2o5bo2b2o3b2o2bo5b2o57bo2b2obobob2o2bo108bo5bo
25bobo3bobo3bobo3bobo25bo5bo$39bo2bo2bo5bo2bo2bo61b2o4b2o4bobo4b2o4b2o
19b2o3bobo3b2o27bo7bo29bo2b2o3b2o2bo108b3obob3o24bo6bo5bo6bo24b3obob3o
$3b2o17b2o16b2obo3bobo3bob2o68b5o5b5o25b2o2bo3bo2b2o27bo7bo30b3o5b3o
105b3obo7bob3o20bo3bo5bo5bo3bo20b3obo7bob3o$3b2o17b2o18b2obobobobob2o
72b3o5b3o29b2o5b2o183bobo4bobobo4bobo20bob3o9b3obo20bobo4bobobo4bobo$
4b3o13b3o20b2o2bobo2b2o312bobobo23b2o3bo2b2o7b2o2bo3b2o23bobobo$5b2o
13b2o24b2ob2o304b2o3b4o2b5o2b4o3b2o12b2o5bo2b2o3b2o2bo5b2o12b2o3b4o2b
5o2b4o3b2o$4bo4b2o5b2o4bo18b4obo3bob4o69bo13bo215b2o4b2o4bobo4b2o4b2o
19b2o3bobo3b2o19b2o4b2o4bobo4b2o4b2o$5b3o3bo3bo3b3o19b5o5b5o305b5o5b5o
25b2o2bo3bo2b2o25b5o5b5o$9b4ob4o24b3o7b3o308b3o5b3o29b2o5b2o29b3o5b3o$
7bo4bobo4bo103b2obobo7bobob2o26b2o3b2o$9bo2bobo2bo105b2obo2bo5bo2bob2o
$6bo4bo3bo4bo23b2o5b2o70b2o5bo3bo5b2o219bo13bo63bo13bo$6b2ob2o5b2ob2o
23b2o5b2o73bo2b3ob3o2bo$8bo9bo109bobo3bobo$128b2o5b2o222b2obobo7bobob
2o26b2o3b2o26b2obobo7bobob2o$130bo3bo224b2obo2bo5bo2bob2o59b2obo2bo5bo
2bob2o$9b2o5b2o341b2o5bo3bo5b2o59b2o5bo3bo5b2o$9b2o5b2o344bo2b3ob3o2bo
65bo2b3ob3o2bo$364bobo3bobo69bobo3bobo$127b2o7b2o226b2o5b2o69b2o5b2o$
366bo3bo73bo3bo4$363b2o7b2o67b2o7b2o!

Re: Thread for your unsure discoveries

Posted: February 15th, 2025, 1:33 pm
by LuveelVoom
Hmm, looking at those gliders my first thought is: “is there a version that produces enough gliders such that a 9c/30o self supporting pi ship is viable?”

Nobody said that the promised pi ship had to be elementary, after all… :mrgreen:

Re: Thread for your unsure discoveries

Posted: February 15th, 2025, 7:57 pm
by LuveelVoom
P4 domino sparker:

Code: Select all

x = 20, y = 19, rule = B3/S23
$3bo5b2o5bo$2bo14bo$2bo3b2o4b2o3bo$3bob2o6b2obo$6bob4obo$6b3o2b3o$2bo
2b2o6b2o2bo$3b2o2b6o2b2o$4b2o8b2o$4b5o2b5o$4bo3bo2bo3bo$5bobo4bobo$3b
obob2o2b2obobo$3b2o10b2o!

Re: Thread for your unsure discoveries

Posted: February 17th, 2025, 12:20 am
by Mr. T
p60 Pi climber pair, a late arrival, of avail maybe

Code: Select all

x = 72, y = 270, rule = B3/S23


45b2o23b2o$45b2o23b2o17$45b2o23b2o$45b2o23b2o2$10b2o23b2o$10b2o23b2o
14$45b2o23b2o$45b2o23b2o2$10b2o23b2o$10b2o23b2o14$45b2o23b2o$45b2o23b
2o2$10b2o23b2o$10b2o23b2o14$45b2o23b2o$45b2o23b2o2$10b2o23b2o$10b2o23b
2o14$45b2o23b2o$45b2o23b2o2$10b2o23b2o$10b2o23b2o14$45b2o23b2o$45b2o
23b2o2$10b2o23b2o$10b2o23b2o14$45b2o23b2o$45b2o23b2o2$10b2o23b2o$10b2o
23b2o14$45b2o23b2o$45b2o23b2o2$10b2o23b2o$10b2o23b2o14$45b2o23b2o$45b
2o23b2o2$10b2o23b2o$10b2o23b2o14$45b2o23b2o$45b2o23b2o2$10b2o23b2o$10b
2o23b2o3$58bo$56b2ob2o$23bo32b2ob2o$22b3o$21bo3bo$21b2ob2o28bo7bo$48b
3o2bo9bo2b3o$47b2o3bobo7bobo3b2o$14bo17bo13b2ob2o3bo7bo3b2ob2o$12b4o2b
2o7b2o2b4o12b2ob6o5b6ob2o$11bob3o2b2o7b2o2b3obo10b3o2bo13bo2b3o$16b2o
2bo5bo2b2o14b3ob2o15b2ob3o$17bo2bo5bo2bo15b2o3bo4bo5bo4bo3b2o$15b2o3bo
5bo3b2o18bo3bo7bo3bo$11bo2bob2o11b2obo2bo16bo3bo3bo3bo$14bo2bo11bo2bo
20b3o5b3o$15b2o13b2o21b2o7b2o2$19bo7bo$19bo7bo8$37b2o$37b2o10bo$48bobo
$48bobo$43b2o4bo$43bo$44bo$42bo2bo$36bo3b2ob2o$35bobo2bo2bo$36b2o2b3o
8$37b2o$37b2o2$31bo$30b2o$30bobo$16bo$15b2o$15bobo$bo$2o$obo7$37b2o$
37b2o17$37b2o$37b2o!

Re: Thread for your unsure discoveries

Posted: February 17th, 2025, 8:50 pm
by hotcrystal0
If only the extra glider is needed, the pi in HF95P can be suppressed such that it allows for repeat times faster than 66 (61 is shown as that's the speed tunnel's repeat time, but it works at even lower repeat times):

Code: Select all

x = 63, y = 36, rule = B3/S23
50b2o$50b2o2$18b2ob2o$19bobo$2bo11b2obo5bob2o34b2o$obo10bobob2o3b2obo
bo8b2o23bo$b2o9bo6bobo6bo8bo21bobo$12b7o3b7o8bobo19b2o$38b2o$14b3o7b3o
$13bo2bo3bo3bo2bo$13b2o4bobo4b2o$19bobo$20bo2$38bo$38bo$27b2o9b3o$27b
2o11bo$16bo$17b2o31b2o$16b2o32b2o2b2o$36bo3b2o12bobo$35bobo3bo14bo$18b
2o5b2o7bobo3bo15b2o$17bo2bo4bobo6bo4bo$13b2o3bobo6bo5b2o5b3o$9b2obobo
4bo7b2o13bo$10bobo9b2o$9bo2b2o8bo$10b2o11b3o$12b2o11bo$12bo$13bo$12b2o
!

Re: Thread for your unsure discoveries

Posted: February 17th, 2025, 8:54 pm
by confocaloid
hotcrystal0 wrote: February 17th, 2025, 8:50 pm If only the extra glider is needed, the pi in HF95P can be suppressed such that it allows for repeat times faster than 66 (61 is shown as that's the speed tunnel's repeat time, but it works at even lower repeat times): [...]
When identified via H-to-Gstats5Dec2020.py this is a NW19T102 converter:

Code: Select all

x = 47, y = 56, rule = LifeHistory
D3.D.D3.D3.D4.3D2.5D3.D4.3D3.3D$2D2.D.D3.D2.2D3.D3.D3.D4.2D3.D3.D.D3.
D$D.D.D.D3.D3.D3.D3.D3.D5.D3.D2.2D5.D$D2.2D.D.D.D3.D4.4D3.D5.D3.D.D.D
4.D$D3.D.D.D.D3.D7.D3.D5.D3.2D2.D3.D$D3.D.2D.2D3.D7.D3.D5.D3.D3.D2.D$
D3.D.D3.D2.3D3.3D4.D4.3D3.3D2.5D13$6.4B$7.4B$8.4B$9.4B$10.4B$11.4B$
12.4B$13.4B$14.4B7.2A$15.4B5.B2AB$16.4B5.3B$17.4B3.B.B$18.4B.6B$19.
10B7.2A$11.2A7.9B7.A$12.A8.10B2.BA.A$12.A.AB6.10B.B2A$13.2AB.3B2.12B$
15.19B$15.19B$16.18B$15.18B$13.19B$11.20B$11.2BC15B$10.3BCBC4B.7B$11.
2B3C4B2.6B$10.5BC4B3.6B$9.10B6.4B$10.2B12.B2A2B$10.3B12.2A.B2A$11.A2B
.2A11.BA.A$10.A.A2B.A14.A$9.A.AB2.A15.2A$9.A4.A$8.2A5.3A$17.A!

Re: Thread for your unsure discoveries

Posted: February 17th, 2025, 11:12 pm
by MathAndCode
WhiteHawk wrote: February 13th, 2025, 11:51 am Is this double-bouncer effect known, and is it actually useful?

Code: Select all

x = 68, y = 44, rule = B3/S23
31bo33bo$31bobo31bobo$31b2o32b2o$43b2o$26bo16bo16bo$24b2o19bo12b2o$25b
2o17b4o11b2o$14bo28bo4bo$10b2obobo27b2ob2obo$10b2obobo25b2o3bo2bo$3b2o
8bob2o9b2o12bo2b2o2bob2o9b2o$4bo5b4o2bo5b2o2b2o12b2obobobo4bo3b2o2b2o
$3bo6bo3bo6bobo19bo2bo2b2obo2bobo$3b2o7b2o2bo5bo20b2obobo3bo3bo$b2o3b
2o3bobob2o28bobob2o$o2b2ob2o2b3o2bo8b2o19bobobo8b2o$bobo2bo4bobobo8bo
21bo2bo8bo$2o2bobob4ob2o10b3o19b2o10b3o$2bob2obo4bo14bo33bo$2bo4bob2o
bo$b2o4b2ob2o5$65bo$65bobo$65b2o2$43b2o15bo$43bo14b2o$45bo13b2o$44b4o
$43bo4bo$43b2ob2obo$41b2o3bo2bo10b2o$40bo2b2o2bob2o5b2o2b2o$40b2obobo
bo4bo2bobo$43bo2bo2b2obo3bo$43b2obobo3bo$45bobob2o7b2o$45bobobo8bo$46b
o2bo9b3o$47b2o12bo!
That a duoplet spark can reflect a glider has long been known, but I don't know for sure whether someone has noticed that particular reaction before. It might be useful for guns based on glider syntheses because the two output gliders are closer together than the two input gliders, and getting parallel gliders close together can be difficult.

Re: Thread for your unsure discoveries

Posted: February 18th, 2025, 8:33 am
by confocaloid
That can be viewed as a periodic way to convert a particular glider pair (xq4_163zy048e) into a different glider pair (xq4_153w217). It might happen to be useful if some application (e.g. a glider synthesis for a spaceship, as suggested above by MathAndCode) needs xq4_153w217 specifically, without any comparable alternatives/replacements, and if making xq4_163zy048e happens to be "easy" in comparison, but I'm not sure if there are any plausible applications. There are many pairs of closely-spaced gliders, in many cases it is possible to change timing or even lane difference between the two gliders, and in many cases people aren't using any glider pairs at all and instead sending/routing single-glider pulses to solve the same tasks.

Re: Thread for your unsure discoveries

Posted: February 19th, 2025, 3:15 pm
by ElijahKen
Small reduction to one of the eater welds from the eater welding guide:

Code: Select all

x = 44, y = 13, rule = B3/S23
bo6b2o22bo6b2o$2bo5bo24bo5bo$3o6bo21b3o6bo$8b2o13bo15b2o$3b2o2bo26b2o
2bo$3bo3bo15bobo8bo3bo$4b3o3bo24b3o3bo$b3o6bobo4bobobobobobo5bobo5bobo
$bo2bo5b2o21b2o6b2o$3b2o2b2o14bobo12b2o$4bobobo28bobo$4bobo16bo13bo$5b
2o29b2o!

Re: Thread for your unsure discoveries

Posted: February 20th, 2025, 1:34 am
by dbell
Here is a new finished convoy to support a period 60 PI crawler.

Code: Select all

#C A channel for 3c/10 PI climbers which emits gliders.
#C This demonstrates how a period 60 PI climber can move through a
#C channel made of two rows of blocks and two streams of backward
#C spaceships.  Most of backward spaceships perturb the PI to restore
#C the blocks behind it so that another PI can climb the same trail.
#C The occasional single backward spaceship perturbs the PI to generate
#C an output glider, at the expense of a block which makes a gap in the
#C trail.  However, a convoy of backward spaceships duplicates and turns
#C that glider to create the missing block, and also generates an output
#C glider.  In full use the block restoring convoy would be repeated
#C indefinitely, just as the channel spaceships and blocks need to be.
#C The PI perturbing reaction used here is a replacement of a previous
#C one which was not able to support successive PI crawlers.
#C David I. Bell, 20 February 2025
x = 447, y = 2070
10bobo35bobo$9bo41bo$9bo3bo3boo23boo3bo3bo$9bo7boo23boo7bo$9bobbo35bo
bbo$9b3o37b3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo
$8b3o39b3o7$bobo13boo23boo13bobo$4bo12boo23boo12bo$o3bo51bo3bo$4bo51bo
$bobbo51bobbo$bb3o51b3o13$17boo23boo$17boo23boo$6boo45boo$5b3o45b3o$5b
3o45b3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo35bobo$9bo41b
o$9bo3bo33bo3bo$9bo41bo$9bobbo35bobbo$9b3o37b3o3$9bobo5boo23boo5bobo$
8bo8boo23boo8bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o39b3o7$bobo53b
obo$4bo51bo$o3bo51bo3bo$4bo51bo$bobbo51bobbo$bb3o51b3o$17boo23boo$17b
oo23boo13$6boo45boo$5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo8boo23boo8bob
oo$6b3o8boo23boo8b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo3bo33bo3bo$9bo
41bo$9bobbo35bobbo$9b3o37b3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43b
o$8bobbo37bobbo$8b3o39b3o$17boo23boo$17boo23boo5$bobo53bobo$4bo51bo$o
3bo51bo3bo$4bo51bo$bobbo51bobbo$bb3o51b3o7$17boo23boo$17boo23boo7$6boo
45boo$5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$
10bobo35bobo$9bo41bo$9bo3bo3boo23boo3bo3bo$9bo7boo23boo7bo$9bobbo35bo
bbo$9b3o37b3o3$9bobo$8bo$8bo3bo$8bo$8bobbo$8b3o7$bobo13boo23boo$4bo12b
oo23boo$o3bo$4bo$bobbo$bb3o13$17boo23boo$17boo23boo$6boo$5b3o$5b3o$5b
3o$5boobo$6b3o$7bo$52bobo$10bobo38bo$9bo41bo$9bo3bo37bobbo$9bo41b3o$9b
obbo$9b3o3$9bobo5boo23boo5bobo$8bo8boo23boo8bo$8bo3bo35bo3bo$8bo43bo$
8bobbo37bobbo$8b3o39b3o$$110boo$109b3o$109boobo$110b3o$111bo$bobo53bob
o$4bo51bo$o3bo51bo3bo$4bo51bo$bobbo51bobbo$bb3o51b3o$17boo23boo$17boo
23boo13$6boo45boo$5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo8boo23boo8boboo$
6b3o8boo23boo8b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo3bo33bo3bo57bobo$9b
o41bo56bo$9bobbo35bobbo56bo$9b3o37b3o56bobbo$108b3o$95bobo$9bobo37bobo
46bo$8bo43bo41bo3bo$8bo3bo35bo3bo41bo3bo$8bo43bo45bo$8bobbo37bobbo42bo
bbo$8b3o39b3o43b3o$17boo23boo$17boo23boo5$bobo53bobo$4bo51bo$o3bo51bo
3bo$4bo51bo$bobbo51bobbo$bb3o51b3o7$17boo23boo$17boo23boo7$6boo45boo$
5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo
35bobo$9bo41bo$9bo3bo3boo23boo3bo3bo$9bo7boo23boo7bo$9bobbo35bobbo$9b
3o37b3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o
39b3o7$bobo13boo23boo13bobo$4bo12boo23boo12bo$o3bo51bo3bo$4bo51bo$bobb
o51bobbo$bb3o51b3o13$17boo23boo$17boo23boo$6boo45boo$5b3o45b3o$5b3o45b
3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo
3bo33bo3bo$9bo41bo$9bobbo35bobbo$9b3o37b3o3$9bobo5boo23boo5bobo$8bo8b
oo23boo8bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o39b3o7$bobo53bobo$
4bo51bo$o3bo51bo3bo$4bo51bo$bobbo51bobbo$bb3o51b3o$17boo23boo$17boo23b
oo13$6boo45boo$5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo8boo23boo8boboo$6b
3o8boo23boo8b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo3bo33bo3bo$9bo41bo$9b
obbo35bobbo$9b3o37b3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobb
o37bobbo$8b3o39b3o$17boo23boo$17boo23boo5$bobo53bobo$4bo51bo$o3bo51bo
3bo$4bo51bo$bobbo51bobbo$bb3o51b3o7$17boo23boo$17boo23boo7$6boo45boo$
5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo
35bobo$9bo41bo$9bo3bo3boo23boo3bo3bo$9bo7boo23boo7bo$9bobbo35bobbo$9b
3o37b3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o
39b3o7$bobo13boo23boo13bobo$4bo12boo23boo12bo$o3bo51bo3bo$4bo51bo$bobb
o51bobbo$bb3o51b3o13$17boo23boo$17boo23boo$6boo45boo$5b3o45b3o$5b3o45b
3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo
3bo33bo3bo$9bo41bo$9bobbo35bobbo$9b3o37b3o3$9bobo5boo23boo5bobo$8bo8b
oo23boo8bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o39b3o7$bobo53bobo$
4bo51bo$o3bo51bo3bo$4bo51bo$bobbo51bobbo$bb3o51b3o$17boo23boo$17boo23b
oo13$6boo45boo$5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo8boo23boo8boboo$6b
3o8boo23boo8b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo3bo33bo3bo$9bo41bo$9b
obbo35bobbo$9b3o37b3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobb
o37bobbo$8b3o39b3o$17boo23boo$17boo23boo5$bobo53bobo$4bo51bo$o3bo51bo
3bo$4bo51bo$bobbo51bobbo$bb3o51b3o7$17boo23boo$17boo23boo7$6boo45boo$
5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo
35bobo$9bo41bo$9bo3bo3boo23boo3bo3bo$9bo7boo23boo7bo$9bobbo35bobbo$9b
3o37b3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o
39b3o7$bobo13boo23boo13bobo$4bo12boo23boo12bo$o3bo51bo3bo$4bo51bo$bobb
o51bobbo$bb3o51b3o13$17boo23boo$17boo23boo$6boo45boo$5b3o45b3o$5b3o45b
3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo
3bo33bo3bo$9bo41bo$9bobbo35bobbo$9b3o37b3o3$9bobo5boo23boo5bobo$8bo8b
oo23boo8bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o39b3o7$bobo53bobo$
4bo51bo$o3bo51bo3bo$4bo51bo$bobbo51bobbo$bb3o51b3o$17boo23boo$17boo23b
oo13$6boo45boo$5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo8boo23boo8boboo$6b
3o8boo23boo8b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo3bo33bo3bo$9bo41bo$9b
obbo35bobbo$9b3o37b3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobb
o37bobbo$8b3o39b3o$17boo23boo$17boo23boo5$bobo53bobo$4bo51bo$o3bo51bo
3bo$4bo51bo$bobbo51bobbo$bb3o51b3o7$17boo23boo$17boo23boo7$6boo45boo$
5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo
35bobo$9bo41bo$9bo3bo3boo23boo3bo3bo$9bo7boo23boo7bo$9bobbo35bobbo$9b
3o37b3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o
39b3o7$bobo13boo23boo13bobo$4bo12boo23boo12bo$o3bo51bo3bo$4bo51bo$bobb
o51bobbo$bb3o51b3o13$17boo23boo$17boo23boo$6boo45boo$5b3o45b3o$5b3o45b
3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo
3bo33bo3bo$9bo41bo$9bobbo35bobbo$9b3o37b3o3$9bobo5boo23boo5bobo$8bo8b
oo23boo8bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o39b3o7$bobo53bobo$
4bo51bo$o3bo51bo3bo$4bo51bo$bobbo51bobbo$bb3o51b3o$17boo23boo$17boo23b
oo13$6boo45boo$5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo8boo23boo8boboo$6b
3o8boo23boo8b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo3bo33bo3bo$9bo41bo$9b
obbo35bobbo$9b3o37b3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobb
o37bobbo$8b3o39b3o$17boo23boo$17boo23boo5$bobo53bobo$4bo51bo$o3bo51bo
3bo$4bo51bo$bobbo51bobbo$bb3o51b3o7$17boo23boo$17boo23boo7$6boo45boo$
5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo
35bobo$9bo41bo$9bo3bo3boo23boo3bo3bo$9bo7boo23boo7bo$9bobbo35bobbo$9b
3o37b3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o
39b3o7$bobo13boo23boo13bobo$4bo12boo23boo12bo$o3bo51bo3bo$4bo51bo$bobb
o51bobbo$bb3o51b3o13$17boo23boo$17boo23boo$6boo45boo$5b3o45b3o$5b3o45b
3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo
3bo33bo3bo$9bo41bo$9bobbo35bobbo$9b3o37b3o3$9bobo5boo23boo5bobo$8bo8b
oo23boo8bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o39b3o7$bobo53bobo$
4bo51bo$o3bo51bo3bo$4bo51bo$bobbo51bobbo$bb3o51b3o$17boo23boo$17boo23b
oo13$6boo45boo$5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo8boo23boo8boboo$6b
3o8boo23boo8b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo3bo33bo3bo$9bo41bo$9b
obbo35bobbo$9b3o37b3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobb
o37bobbo$8b3o39b3o$17boo23boo$17boo23boo5$bobo53bobo$4bo51bo$o3bo51bo
3bo$4bo51bo$bobbo51bobbo$bb3o51b3o7$17boo23boo$17boo23boo7$6boo45boo$
5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo278boo$
332b3o$10bobo35bobo281b3o$9bo41bo279boboo$9bo3bo3boo23boo3bo3bo279b3o$
9bo7boo23boo7bo280bo$9bobbo35bobbo$9b3o37b3o$$316boo$9bobo37bobo264b3o
$8bo43bo263b3o$8bo3bo35bo3bo263b3o$8bo43bo262boboo$8bobbo37bobbo262b3o
$8b3o39b3o263bo5$317bobo$316bo$bobo13boo23boo13bobo256bo3bo$4bo12boo
23boo12bo259bo3bo$o3bo51bo3bo255bo$4bo51bo259bobbo$bobbo51bobbo256b3o$
bb3o51b3o13$17boo23boo$17boo23boo$6boo45boo$5b3o45b3o$5b3o45b3o$5b3o
45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo3bo33bo
3bo$9bo41bo$9bobbo35bobbo$9b3o37b3o3$9bobo5boo23boo5bobo$8bo8boo23boo
8bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o39b3o7$bobo53bobo$4bo51bo$
o3bo51bo3bo$4bo51bo$bobbo51bobbo$bb3o51b3o$17boo23boo$17boo23boo13$6b
oo45boo$5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo8boo23boo8boboo$6b3o8boo
23boo8b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo3bo33bo3bo$9bo41bo$9bobbo
35bobbo$9b3o37b3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobbo37b
obbo$8b3o39b3o$17boo23boo$17boo23boo5$bobo53bobo$4bo51bo$o3bo51bo3bo$
4bo51bo$bobbo51bobbo$bb3o51b3o7$17boo23boo$17boo23boo7$6boo45boo$5b3o
45b3o$5b3o45b3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo35bob
o$9bo41bo$9bo3bo3boo23boo3bo3bo$9bo7boo23boo7bo$9bobbo35bobbo$9b3o37b
3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o39b3o
7$bobo13boo23boo13bobo$4bo12boo23boo12bo$o3bo51bo3bo$4bo51bo$bobbo51bo
bbo$bb3o51b3o5$277boo$276b3o$276boobo$277b3o$254bobo21bo$253bo$253bo3b
o$253bo3bo$17boo23boo209bo$17boo23boo209bobbo$6boo45boo198b3o$5b3o45b
3o$5b3o45b3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo35bobo$
9bo41bo$9bo3bo33bo3bo$9bo41bo$9bobbo35bobbo212bobo$9b3o37b3o211bo$263b
o3bo$263bo$9bobo5boo23boo5bobo211bobbo$8bo8boo23boo8bo210b3o$8bo3bo35b
o3bo$8bo43bo$8bobbo37bobbo$8b3o39b3o7$bobo53bobo$4bo51bo$o3bo51bo3bo$
4bo51bo$bobbo51bobbo$bb3o51b3o$17boo23boo$17boo23boo13$6boo45boo$5b3o
45b3o$5b3o45b3o$5b3o45b3o$5boobo8boo23boo8boboo$6b3o8boo23boo8b3o$7bo
45bo$$10bobo35bobo$9bo41bo$9bo3bo33bo3bo$9bo41bo$9bobbo35bobbo$9b3o37b
3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o39b3o
373bobo$17boo23boo381bo$17boo23boo381bo3bo$425bo$425bobbo$425b3o$$bobo
53bobo$4bo51bo387boo$o3bo51bo3bo382b3o$4bo51bo386boobo$bobbo51bobbo
384b3o$bb3o51b3o386bo$$282bobo15boo$285bo14b3o$281bo3bo14b3o$281bo3bo
14b3o132bobo$285bo13boboo131bo$17boo23boo238bobbo13b3o132bo3bo$17boo
23boo239b3o14bo133bo$434bobbo$434b3o5$6boo45boo232boo$5b3o45b3o231b3o$
5b3o45b3o231b3o$5b3o45b3o230boboo$5boobo43boboo230b3o$6b3o43b3o232bo$
7bo45bo$$10bobo35bobo$9bo41bo$9bo3bo3boo23boo3bo3bo$9bo7boo23boo7bo$9b
obbo35bobbo$9b3o37b3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobb
o37bobbo$8b3o39b3o7$bobo13boo23boo13bobo$4bo12boo23boo12bo$o3bo51bo3bo
$4bo51bo$bobbo51bobbo$bb3o51b3o13$17boo23boo$17boo23boo$6boo45boo$5b3o
45b3o$5b3o45b3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo35bob
o$9bo41bo$9bo3bo33bo3bo$9bo41bo$9bobbo35bobbo$9b3o37b3o3$9bobo5boo23b
oo5bobo$8bo8boo23boo8bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o39b3o
7$bobo53bobo$4bo51bo$o3bo51bo3bo292bobo$4bo51bo295bo$bobbo51bobbo292bo
3bo$bb3o51b3o293bo3bo$17boo23boo308bo$17boo23boo308bobbo$352b3o11bobo$
369bo$369bo$366bobbo$367b3o5$365boo$364b3o$364b3o$6boo45boo309boobo$5b
3o45b3o309b3o$5b3o45b3o310bo$5b3o45b3o$5boobo8boo23boo8boboo$6b3o8boo
23boo8b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo3bo33bo3bo$9bo41bo$9bobbo
35bobbo$9b3o37b3o332boo12bobo$384b3o14bo$384b3o10bo3bo$9bobo37bobo332b
3o10bo3bo$8bo43bo330boboo14bo$8bo3bo35bo3bo330b3o12bobbo$8bo43bo331bo
14b3o$8bobbo37bobbo$8b3o39b3o$17boo23boo$17boo23boo3$397boo$397b3o$bob
o53bobo337b3o$4bo51bo339boboo$o3bo51bo3bo335b3o$4bo51bo340bo$bobbo51bo
bbo$bb3o51b3o7$17boo23boo$17boo23boo7$6boo45boo$5b3o45b3o$5b3o45b3o$5b
3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo3bo3b
oo23boo3bo3bo$9bo7boo23boo7bo$9bobbo35bobbo$9b3o37b3o3$9bobo37bobo$8bo
43bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o39b3o7$bobo13boo23boo13bo
bo$4bo12boo23boo12bo$o3bo51bo3bo$4bo51bo$bobbo51bobbo$bb3o51b3o5$298bo
bo$297bo$297bo$297bobbo$297b3o4$17boo23boo$17boo23boo$6boo45boo$5b3o
45b3o$5b3o45b3o$5b3o45b3o$5boobo43boboo252bobo$6b3o43b3o252bo$7bo45bo
253bo3bo$307bo$10bobo35bobo256bobbo$9bo41bo255b3o$9bo3bo33bo3bo$9bo41b
o267boo$9bobbo35bobbo266b3o$9b3o37b3o266b3o$318b3o$318boobo$9bobo5boo
23boo5bobo267b3o$8bo8boo23boo8bo267bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bo
bbo$8b3o39b3o7$bobo53bobo$4bo51bo$o3bo51bo3bo$4bo51bo$bobbo51bobbo$bb
3o51b3o$17boo23boo$17boo23boo13$6boo45boo$5b3o45b3o$5b3o45b3o$5b3o45b
3o$5boobo8boo23boo8boboo$6b3o8boo23boo8b3o$7bo45bo$$10bobo35bobo$9bo
41bo$9bo3bo33bo3bo$9bo41bo$9bobbo35bobbo$9b3o37b3o3$9bobo37bobo$8bo43b
o$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o39b3o$17boo23boo$17boo23boo
5$bobo53bobo$4bo51bo$o3bo51bo3bo$4bo51bo216boo$bobbo51bobbo213b3o$bb3o
51b3o213boboo$272b3o$273bo5$17boo23boo$17boo23boo4$283boo$283b3o$283b
3o$6boo45boo227boboo$5b3o45b3o226b3o$5b3o45b3o227bo$5b3o45b3o239bobo$
5boobo43boboo238bo$6b3o43b3o239bo3bo$7bo45bo240bo3bo$294bo$10bobo35bob
o243bobbo$9bo41bo242b3o$9bo3bo3boo23boo3bo3bo$9bo7boo23boo7bo$9bobbo
35bobbo$9b3o37b3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobbo37b
obbo$8b3o39b3o7$bobo13boo23boo13bobo$4bo12boo23boo12bo$o3bo51bo3bo$4bo
51bo$bobbo51bobbo$bb3o51b3o13$17boo23boo$17boo23boo$6boo45boo$5b3o45b
3o$5b3o45b3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo35bobo$
9bo41bo$9bo3bo33bo3bo$9bo41bo$9bobbo35bobbo$9b3o37b3o3$9bobo5boo23boo
5bobo$8bo8boo23boo8bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o39b3o7$b
obo53bobo$4bo51bo$o3bo51bo3bo$4bo51bo$bobbo51bobbo$bb3o51b3o$17boo23b
oo$17boo23boo13$6boo45boo$5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo8boo23b
oo8boboo$6b3o8boo23boo8b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo3bo33bo3bo
$9bo41bo$9bobbo35bobbo$9b3o37b3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8b
o43bo$8bobbo37bobbo$8b3o39b3o$17boo23boo$17boo23boo5$bobo53bobo$4bo51b
o$o3bo51bo3bo$4bo51bo$bobbo51bobbo$bb3o51b3o7$17boo23boo$17boo23boo7$
6boo45boo$5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45b
o$$10bobo35bobo$9bo41bo$9bo3bo3boo23boo3bo3bo$9bo7boo23boo7bo$9bobbo
35bobbo$9b3o37b3o3$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobbo37b
obbo$8b3o39b3o7$bobo13boo23boo13bobo$4bo12boo23boo12bo$o3bo51bo3bo$4bo
51bo$bobbo51bobbo$bb3o51b3o13$17boo23boo$17boo23boo$6boo45boo$5b3o45b
3o$5b3o45b3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo35bobo$
9bo41bo$9bo3bo33bo3bo$9bo41bo$9bobbo35bobbo$9b3o37b3o3$9bobo5boo23boo$
8bo8boo23boo$8bo3bo$8bo$8bobbo$8b3o7$bobo$4bo$o3bo$4bo$bobbo$bb3o$17b
oo23boo$17boo23boo13$6boo$5b3o$5b3o$5b3o$5boobo8boo23boo$6b3o8boo23boo
$7bo$52bobo$10bobo38bo$9bo41bo$9bo3bo37bobbo$9bo41b3o$9bobbo$9b3o3$9bo
bo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o39b3o$17boo
23boo$17boo23boo5$bobo53bobo$4bo51bo$o3bo51bo3bo$4bo51bo$bobbo51bobbo$
bb3o51b3o7$17boo23boo$17boo23boo7$6boo45boo$5b3o45b3o$5b3o45b3o$5b3o
45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo3bo3boo
23boo3bo3bo$9bo7boo23boo7bo$9bobbo35bobbo$9b3o37b3o3$9bobo37bobo$8bo
43bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b3o39b3o7$bobo13boo23boo13bo
bo$4bo12boo23boo12bo$o3bo51bo3bo$4bo51bo$bobbo51bobbo$bb3o51b3o13$17b
oo23boo$17boo23boo$6boo45boo$5b3o45b3o$5b3o45b3o$5b3o45b3o$5boobo43bob
oo$6b3o43b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo3bo33bo3bo$9bo41bo$9bobb
o35bobbo$9b3o37b3o3$9bobo5boo23boo5bobo$8bo8boo23boo8bo$8bo3bo35bo3bo$
8bo43bo$8bobbo37bobbo$8b3o39b3o7$bobo53bobo$4bo51bo$o3bo51bo3bo$4bo51b
o$bobbo51bobbo$bb3o51b3o$17boo23boo$17boo23boo13$6boo45boo$5b3o45b3o$
5b3o45b3o$5b3o45b3o$5boobo8boo23boo8boboo$6b3o8boo23boo8b3o$7bo45bo$$
10bobo35bobo$9bo41bo$9bo3bo33bo3bo$9bo19b3o19bo$9bobbo15bo3bo15bobbo$
9b3o16booboo16b3o3$9bobo9bo17bo9bobo$8bo10b3o3boo7boo3b3o10bo$8bo3bo5b
o4bobbo7bobbo4bo5bo3bo$8bo9bo3bo15bo3bo9bo$8bobbo12b4o5b4o12bobbo$8b3o
6bo7boo7boo7bo6b3o$21b3o13b3o$17bobobboo13boobbobo$23bo3bo5bo3bo$$24bo
bbo5bobbo$25bobo5bobo$bobo53bobo$4bo51bo$o3bo51bo3bo$4bo8bo33bo8bo$bo
bbo7bobo31bobo7bobbo$bb3o7bobo31bobo7b3o$$15bo29bo$13b4o27b4o$12bo3bo
27bo3bo$12bobbo29bobbo$13b3o29b3o4$19boo19boo$19boo19boo4$6boo45boo$5b
3o45b3o$5b3o45b3o$5b3o45b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo35b
obo$9bo41bo$9bo3bo33bo3bo$9bo41bo$9bobbo35bobbo$9b3o37b3o$17boo23boo$
17boo23boo$9bobo37bobo$8bo43bo$8bo3bo35bo3bo$8bo43bo$8bobbo37bobbo$8b
3o39b3o7$bobo53bobo$4bo51bo$o3bo51bo3bo$4bo51bo$bobbo12boo23boo12bobbo
$bb3o12boo23boo12b3o15$6boo45boo$5b3o45b3o$5b3o9boo23boo9b3o$5b3o9boo
23boo9b3o$5boobo43boboo$6b3o43b3o$7bo45bo$$10bobo35bobo$9bo41bo$9bo3bo
33bo3bo$9bo41bo$9bobbo35bobbo$9b3o37b3o!
This larger example shows that the channel can support multiple PI crawlers.

Code: Select all

#C A channel to support multiple 3c/10 period 60 PI crawlers with outputs.
#C This example has three PI crawlers moving through the channel, but
#C the same pattern can support an arbitrary number of PI crawlers.
#C In full use the block restoring convoy would be repeated indefinitely,
#C just as the channel spaceships and blocks need to be.  This also
#C demonstrates that the timings between the PIs can be changed.
#C The PI perturbing reaction used here is a replacement of a previous
#C one which was not able to support successive PI crawlers.
#C David I. Bell, 20 February 2025
x = 724, y = 8798
5boo$5b3o$5b3o$5b3o$4boboo$4b3o$5bo$48bobo$6bobo42bo$9bo41bo$5bo3bo38b
obbo$9bo5boo23boo7b3o$6bobbo5boo23boo$7b3o3$5bobo41bobo$8bo39bo$4bo3bo
39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$109boo$109b3o$108boboo$108b3o
$109bo$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo49bo
bbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b
3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo
53bobo$9bo37bo60bo$6bobbo37bobbo57bo$7b3o37b3o55bobbo$106b3o$95bobo$5b
obo41bobo42bo$8bo6boo23boo6bo45bo3bo$4bo3bo6boo23boo6bo3bo41bo3bo$8bo
39bo45bo$5bobbo39bobbo42bobbo$6b3o39b3o43b3o7$bobo49bobo$o55bo$o3bo47b
o3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo12$5boo43boo$5b3o
41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo23boo
9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o
3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$
15boo23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$
3o51b3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b
3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$
9bo5boo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$
4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o14boo23boo
14bo$o3bo10boo23boo10bo3bo$o55bo$obbo49bobbo$3o51b3o14$15boo23boo$5boo
8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5b
o45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b
3o3$5bobo41bobo$8bo6boo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo
39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o
51b3o$$15boo23boo$15boo23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o
$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$
5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo
3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo23boo$15boo23boo4$bob
o49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o8$15boo23boo$15boo
23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o
$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo
23boo5bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobb
o39bobbo$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o
55bo$obbo49bobbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o
41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$
5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23b
oo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bob
o$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo
12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo
8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo
37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39b
obbo$6b3o39b3o$$15boo23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o
55bo$obbo49bobbo$3o51b3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o41b3o$
5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo
37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o3$5b
obo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo
49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo49bobbo$3o51b3o
14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo
41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$
6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo3bo6boo23boo6b
o3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o
55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo12$5boo43boo$5b3o41b3o$
5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$
6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bo
bo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo
23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b
3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4bo
boo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5b
oo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo
39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o
3bo10boo23boo10bo3bo$o55bo$obbo49bobbo$3o51b3o14$15boo23boo$5boo8boo
23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45b
o$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$
5bobo41bobo$8bo6boo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobb
o$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$
15boo23boo$15boo23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo
41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo
37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39b
o3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo23boo$15boo23boo4$bobo49bob
o$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o8$15boo23boo$15boo23boo6$
5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45b
o$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5b
obbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobb
o$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$o
bbo49bobbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$
5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo
37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$
4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55b
o$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo12$5boo
43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5b
o9boo23boo9bo277boo$328b3o$6bobo39bobo277b3o$9bo37bo280boobo$5bo3bo37b
o3bo277b3o$9bo37bo282bo$6bobbo37bobbo$7b3o37b3o$$313boo$5bobo41bobo
260b3o$8bo39bo263b3o$4bo3bo39bo3bo259b3o$8bo39bo263boobo$5bobbo39bobbo
261b3o$6b3o39b3o263bo$$15boo23boo$15boo23boo$$313bobo$316bo$bobo49bobo
256bo3bo$o55bo255bo3bo$o3bo47bo3bo259bo$o55bo256bobbo$obbo49bobbo257b
3o$3o51b3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o
41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo
3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o3$5bobo41bobo$8bo
39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o14boo
23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo49bobbo$3o51b3o14$15boo23boo
$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b
3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b
3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bo
bbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$
3o51b3o$$15boo23boo$15boo23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b
3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37b
o$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$
4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo23boo$15boo23boo4$
bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o5$276boo$276b3o$
275boboo$15boo23boo233b3o$15boo23boo208bobo23bo$253bo$249bo3bo$249bo3b
o$253bo$250bobbo$5boo43boo199b3o$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo
41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo
23boo5bo$6bobbo5boo23boo5bobbo209bobo$7b3o37b3o213bo$259bo3bo$263bo$5b
obo41bobo208bobbo$8bo39bo212b3o$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b
3o39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo
49bobbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b
3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37b
o3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo
3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o371bobo$425bo$421bo
3bo$425bo$422bobbo$423b3o$$bobo49bobo$o55bo386boo$o3bo47bo3bo386b3o$o
55bo385boboo$obbo49bobbo385b3o$3o51b3o386bo$$15boo23boo240bobo12boo$
15boo23boo239bo14b3o$281bo3bo10b3o$281bo3bo10b3o132bobo$281bo14boobo
134bo$281bobbo12b3o130bo3bo$281b3o14bo135bo$431bobbo$432b3o5$5boo43boo
232boo$5b3o41b3o231b3o$5b3o41b3o231b3o$5b3o41b3o231boobo$4boboo41boobo
231b3o$4b3o8boo23boo8b3o232bo$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo
3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo
39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo23boo$15boo23boo4$bobo
49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o8$15boo23boo$15boo
23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o
$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo
23boo5bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobb
o39bobbo$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo
292bobo$o55bo295bo$obbo49bobbo291bo3bo$3o51b3o291bo3bo$352bo$349bobbo$
350b3o13bobo$365bo$365bo$365bobbo$365b3o5$364boo$364b3o$15boo23boo322b
3o$5boo8boo23boo8boo311boboo$5b3o41b3o311b3o$5b3o41b3o312bo$5b3o41b3o$
4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo
37bo$6bobbo37bobbo$7b3o37b3o331boo15bobo$380b3o14bo$380b3o14bo3bo$5bob
o41bobo328b3o14bo3bo$8bo6boo23boo6bo331boobo13bo$4bo3bo6boo23boo6bo3bo
328b3o13bobbo$8bo39bo333bo14b3o$5bobbo39bobbo$6b3o39b3o5$394boo$393b3o
$bobo49bobo337b3o$o55bo336boobo$o3bo47bo3bo337b3o$o55bo338bo$obbo49bo
bbo$3o51b3o$$15boo23boo$15boo23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b
3o41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$
9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo
39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo23boo$15boo
23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o5$294bobo
$297bo$297bo$15boo23boo252bobbo$15boo23boo253b3o6$5boo43boo$5b3o41b3o$
5b3o41b3o$5b3o41b3o$4boboo41boobo251bobo$4b3o43b3o254bo$5bo45bo251bo3b
o$307bo$6bobo39bobo253bobbo$9bo37bo257b3o$5bo3bo37bo3bo$9bo5boo23boo5b
o270boo$6bobbo5boo23boo5bobbo267b3o$7b3o37b3o268b3o$318b3o$317boboo$5b
obo41bobo265b3o$8bo39bo269bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o
39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo49bo
bbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b
3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$
9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo3bo6b
oo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo
47bo3bo$o55bo213boo$obbo49bobbo212b3o$3o51b3o212boobo$270b3o$15boo23b
oo229bo$15boo23boo9$280boo$279b3o$279b3o$5boo43boo227boobo$5b3o41b3o
228b3o$5b3o41b3o229bo$5b3o41b3o239bobo$4boboo41boobo241bo$4b3o8boo23b
oo8b3o237bo3bo$5bo9boo23boo9bo238bo3bo$294bo$6bobo39bobo240bobbo$9bo
37bo244b3o$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$
8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo23boo$15b
oo23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o8$15boo
23boo$15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boob
o$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo
$6bobbo5boo23boo5bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8b
o39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23b
oo10bo3bo$o55bo$obbo49bobbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b
3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bo
bo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$
8bo6boo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o
7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$
15boo23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b
3o8boo23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo
37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39b
o$5bobbo39bobbo$6b3o39b3o$$15boo23boo$15boo23boo4$bobo49bobo$o55bo$o3b
o47bo3bo$o55bo$obbo49bobbo$3o51b3o8$15boo23boo$15boo23boo6$5boo43boo$
5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo
39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bobbo$7b
3o37b3o3$5bobo$8bo$4bo3bo$8bo$5bobbo$6b3o7$bobo$o14boo23boo$o3bo10boo
23boo$o$obbo$3o14$15boo23boo$5boo8boo23boo$5b3o$5b3o$5b3o$4boboo$4b3o$
5bo$48bobo$6bobo42bo$9bo41bo$5bo3bo38bobbo$9bo39b3o$6bobbo$7b3o3$5bobo
41bobo$8bo6boo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b
3o39b3o$$109boo$109b3o$108boboo$108b3o$109bo$bobo49bobo$o55bo$o3bo47bo
3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo12$5boo43boo$5b3o
41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo23boo
9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo53bobo$9bo37bo60bo$6bobbo37bobbo
57bo$7b3o37b3o55bobbo$106b3o$95bobo$5bobo41bobo42bo$8bo39bo45bo3bo$4bo
3bo39bo3bo41bo3bo$8bo39bo45bo$5bobbo39bobbo42bobbo$6b3o39b3o43b3o$$15b
oo23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o
51b3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$
4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo
5boo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo
3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o14boo23boo14bo
$o3bo10boo23boo10bo3bo$o55bo$obbo49bobbo$3o51b3o14$15boo23boo$5boo8boo
23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45b
o$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$
5bobo41bobo$8bo6boo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobb
o$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$
15boo23boo$15boo23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo
41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo
37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39b
o3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo23boo$15boo23boo4$bobo49bob
o$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o8$15boo23boo$15boo23boo6$
5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45b
o$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5b
obbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobb
o$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$o
bbo49bobbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$
5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo
37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$
4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55b
o$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo12$5boo
43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5b
o9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo
$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b
3o39b3o$$15boo23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obb
o49bobbo$3o51b3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o
$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo
37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o3$5bobo41bobo$
8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o14b
oo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo49bobbo$3o51b3o14$15boo23b
oo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o
43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo
$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$
5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobb
o$3o51b3o$$15boo23boo$15boo23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o
41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo
37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39b
o$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo23boo$15boo23boo
4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o8$15boo23boo$
15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o
43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobb
o5boo23boo5bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$
5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo
3bo$o55bo$obbo49bobbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o
$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo
37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6b
oo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo
49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo
23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo
23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$
6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bo
bbo39bobbo$6b3o39b3o$$15boo23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo
3bo$o55bo$obbo49bobbo$3o51b3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o
41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo
$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o
3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$b
obo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo49bobbo$3o
51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4bo
boo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37b
o$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo3bo6boo23boo
6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o
55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo12$5boo43boo$5b3o41b3o$
5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$
6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bo
bo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo
23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b
3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4bo
boo41boobo$4b3o43b3o$5bo45bo277boo$328b3o$6bobo39bobo277b3o$9bo37bo
280boobo$5bo3bo37bo3bo277b3o$9bo5boo23boo5bo282bo$6bobbo5boo23boo5bobb
o$7b3o37b3o$$313boo$5bobo41bobo260b3o$8bo39bo263b3o$4bo3bo39bo3bo259b
3o$8bo39bo263boobo$5bobbo39bobbo261b3o$6b3o39b3o263bo5$313bobo$316bo$b
obo49bobo256bo3bo$o14boo23boo14bo255bo3bo$o3bo10boo23boo10bo3bo259bo$o
55bo256bobbo$obbo49bobbo257b3o$3o51b3o14$15boo23boo$5boo8boo23boo8boo$
5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo
39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41b
obo$8bo6boo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o
39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo
23boo$15boo23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boo
bo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3b
o$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$
8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo23boo$15boo23boo4$bobo49bobo$o
55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o8$15boo23boo$15boo23boo6$5b
oo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo
$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bo
bbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo
$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obb
o49bobbo$3o51b3o5$276boo$276b3o$275boboo$275b3o$250bobo23bo$253bo$249b
o3bo$249bo3bo$253bo$15boo23boo208bobbo$5boo8boo23boo8boo199b3o$5b3o41b
3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9b
o37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo209bobo$7b3o37b3o213bo$259bo
3bo$263bo$5bobo41bobo208bobbo$8bo6boo23boo6bo212b3o$4bo3bo6boo23boo6bo
3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55b
o$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo12$5boo43boo$5b3o41b3o$5b
3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$6bo
bo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo
41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o371bobo$
425bo$15boo23boo379bo3bo$15boo23boo383bo$422bobbo$423b3o$$bobo49bobo$o
55bo386boo$o3bo47bo3bo386b3o$o55bo385boboo$obbo49bobbo385b3o$3o51b3o
386bo$$282bobo12boo$281bo14b3o$281bo3bo10b3o$281bo3bo10b3o132bobo$281b
o14boobo134bo$281bobbo12b3o130bo3bo$15boo23boo239b3o14bo135bo$15boo23b
oo389bobbo$432b3o5$5boo43boo232boo$5b3o41b3o231b3o$5b3o41b3o231b3o$5b
3o41b3o231boobo$4boboo41boobo231b3o$4b3o43b3o232bo$5bo45bo$$6bobo39bob
o$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b
3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o
7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo49bobbo$
3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$
4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo
37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo3bo6boo
23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo
3bo292bobo$o55bo295bo$obbo49bobbo291bo3bo$3o51b3o291bo3bo$352bo$15boo
23boo307bobbo$15boo23boo308b3o13bobo$365bo$365bo$365bobbo$365b3o5$364b
oo$364b3o$364b3o$5boo43boo311boboo$5b3o41b3o311b3o$5b3o41b3o312bo$5b3o
41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo
37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o331boo15bobo$380b3o
14bo$380b3o14bo3bo$5bobo41bobo328b3o14bo3bo$8bo39bo331boobo13bo$4bo3bo
39bo3bo328b3o13bobbo$8bo39bo333bo14b3o$5bobbo39bobbo$6b3o39b3o$$15boo
23boo$15boo23boo$$394boo$393b3o$bobo49bobo337b3o$o55bo336boobo$o3bo47b
o3bo337b3o$o55bo338bo$obbo49bobbo$3o51b3o8$15boo23boo$15boo23boo6$5boo
43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$
6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bobb
o$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$
6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo
49bobbo$3o51b3o5$294bobo$297bo$297bo$294bobbo$295b3o5$15boo23boo$5boo
8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo251bobo$4b3o
43b3o254bo$5bo45bo251bo3bo$307bo$6bobo39bobo253bobbo$9bo37bo257b3o$5bo
3bo37bo3bo$9bo37bo270boo$6bobbo37bobbo267b3o$7b3o37b3o268b3o$318b3o$
317boboo$5bobo41bobo265b3o$8bo6boo23boo6bo269bo$4bo3bo6boo23boo6bo3bo$
8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$o
bbo49bobbo$3o51b3o$$15boo23boo$15boo23boo12$5boo43boo$5b3o41b3o$5b3o
41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$6bobo
39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41b
obo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo23boo$
15boo23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo213boo$obbo49bobbo212b3o
$3o51b3o212boobo$270b3o$271bo6$15boo23boo$15boo23boo3$280boo$279b3o$
279b3o$5boo43boo227boobo$5b3o41b3o228b3o$5b3o41b3o229bo$5b3o41b3o239bo
bo$4boboo41boobo241bo$4b3o43b3o237bo3bo$5bo45bo238bo3bo$294bo$6bobo39b
obo240bobbo$9bo37bo244b3o$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23b
oo5bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo
39bobbo$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o
55bo$obbo49bobbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o
41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$
5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23b
oo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bob
o$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo
12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo
8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo
37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39b
obbo$6b3o39b3o$$15boo23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o
55bo$obbo49bobbo$3o51b3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o41b3o$
5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo
37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o3$5b
obo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo
49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo49bobbo$3o51b3o
14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo
41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$
6bobbo37bobbo$7b3o37b3o3$5bobo$8bo6boo23boo$4bo3bo6boo23boo$8bo$5bobbo
$6b3o7$bobo$o$o3bo$o$obbo$3o$$15boo23boo$15boo23boo12$5boo$5b3o$5b3o$
5b3o$4boboo$4b3o8boo23boo$5bo9boo23boo$48bobo$6bobo42bo$9bo41bo$5bo3bo
38bobbo$9bo39b3o$6bobbo$7b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39b
o$5bobbo39bobbo$6b3o39b3o$$15boo23boo67boo$15boo23boo67b3o$108boboo$
108b3o$109bo$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o8$
15boo23boo$15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo
41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo53bobo$9bo
5boo23boo5bo60bo$6bobbo5boo23boo5bobbo57bo$7b3o37b3o55bobbo$106b3o$95b
obo$5bobo41bobo42bo$8bo39bo45bo3bo$4bo3bo39bo3bo41bo3bo$8bo39bo45bo$5b
obbo39bobbo42bobbo$6b3o39b3o43b3o7$bobo49bobo$o14boo23boo14bo$o3bo10b
oo23boo10bo3bo$o55bo$obbo49bobbo$3o51b3o14$15boo23boo$5boo8boo23boo8b
oo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bob
o39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo
41bobo$8bo6boo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b
3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo
23boo$15boo23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boo
bo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3b
o$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$
8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo23boo$15boo23boo4$bobo49bobo$o
55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o8$15boo23boo$15boo23boo6$5b
oo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo
$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bo
bbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo
$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obb
o49bobbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b
3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37b
o3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo
3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o
3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo12$5boo43b
oo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9b
oo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b
3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o
39b3o$$15boo23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo
49bobbo$3o51b3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$
5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo
37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o3$5bobo41bobo$
8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o14b
oo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo49bobbo$3o51b3o14$15boo23b
oo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o
43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo
$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$
5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobb
o$3o51b3o$$15boo23boo$15boo23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o
41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo
37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39b
o$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo23boo$15boo23boo
4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o8$15boo23boo$
15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o
43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobb
o5boo23boo5bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$
5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo
3bo$o55bo$obbo49bobbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o
$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo
37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6b
oo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo
49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo
23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo
23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$
6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bo
bbo39bobbo$6b3o39b3o$$15boo23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo
3bo$o55bo$obbo49bobbo$3o51b3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o
41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo
$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o
3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$b
obo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo49bobbo$3o
51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4bo
boo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37b
o$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo3bo6boo23boo
6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o
55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo12$5boo43boo$5b3o41b3o$
5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$
6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bo
bo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo
23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b
3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4bo
boo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5b
oo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo
39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o
3bo10boo23boo10bo3bo$o55bo$obbo49bobbo$3o51b3o14$15boo23boo$5boo8boo
23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45b
o277boo$328b3o$6bobo39bobo277b3o$9bo37bo280boobo$5bo3bo37bo3bo277b3o$
9bo37bo282bo$6bobbo37bobbo$7b3o37b3o$$313boo$5bobo41bobo260b3o$8bo6boo
23boo6bo263b3o$4bo3bo6boo23boo6bo3bo259b3o$8bo39bo263boobo$5bobbo39bo
bbo261b3o$6b3o39b3o263bo5$313bobo$316bo$bobo49bobo256bo3bo$o55bo255bo
3bo$o3bo47bo3bo259bo$o55bo256bobbo$obbo49bobbo257b3o$3o51b3o$$15boo23b
oo$15boo23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$
4b3o8boo23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$
9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo
39bo$5bobbo39bobbo$6b3o39b3o$$15boo23boo$15boo23boo4$bobo49bobo$o55bo$
o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o8$15boo23boo$15boo23boo6$5boo43b
oo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bob
o39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bobbo$7b
3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o
39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo49bo
bbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b
3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$
9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo3bo6b
oo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo
47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo$$276boo$276b
3o$275boboo$275b3o$250bobo23bo$253bo$249bo3bo$249bo3bo$253bo$250bobbo$
5boo43boo199b3o$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo
23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$
6bobbo37bobbo209bobo$7b3o37b3o213bo$259bo3bo$263bo$5bobo41bobo208bobbo
$8bo39bo212b3o$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo23b
oo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o
8$15boo23boo$15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4bob
oo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo
23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo
39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o371bobo$425bo$421bo3bo$425bo$
422bobbo$423b3o$$bobo49bobo$o14boo23boo14bo386boo$o3bo10boo23boo10bo3b
o386b3o$o55bo385boboo$obbo49bobbo385b3o$3o51b3o386bo$$282bobo12boo$
281bo14b3o$281bo3bo10b3o$281bo3bo10b3o132bobo$281bo14boobo134bo$281bo
bbo12b3o130bo3bo$281b3o14bo135bo$431bobbo$432b3o4$15boo23boo$5boo8boo
23boo8boo232boo$5b3o41b3o231b3o$5b3o41b3o231b3o$5b3o41b3o231boobo$4bob
oo41boobo231b3o$4b3o43b3o232bo$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo
3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo3b
o6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3b
o47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo12$5boo43boo$
5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo
23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o
37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b
3o$$15boo23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo3bo292bobo$o55bo
295bo$obbo49bobbo291bo3bo$3o51b3o291bo3bo$352bo$349bobbo$350b3o13bobo$
365bo$365bo$365bobbo$365b3o$15boo23boo$15boo23boo3$364boo$364b3o$364b
3o$5boo43boo311boboo$5b3o41b3o311b3o$5b3o41b3o312bo$5b3o41b3o$4boboo
41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo
23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o331boo15bobo$380b3o14bo$380b3o
14bo3bo$5bobo41bobo328b3o14bo3bo$8bo39bo331boobo13bo$4bo3bo39bo3bo328b
3o13bobbo$8bo39bo333bo14b3o$5bobbo39bobbo$6b3o39b3o5$394boo$393b3o$bob
o49bobo337b3o$o14boo23boo14bo336boobo$o3bo10boo23boo10bo3bo337b3o$o55b
o338bo$obbo49bobbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b
3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo
$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23b
oo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bob
o$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo$$
294bobo$297bo$297bo$294bobbo$295b3o6$5boo43boo$5b3o41b3o$5b3o41b3o$5b
3o41b3o$4boboo41boobo251bobo$4b3o8boo23boo8b3o254bo$5bo9boo23boo9bo
251bo3bo$307bo$6bobo39bobo253bobbo$9bo37bo257b3o$5bo3bo37bo3bo$9bo37bo
270boo$6bobbo37bobbo267b3o$7b3o37b3o268b3o$318b3o$317boboo$5bobo41bobo
265b3o$8bo39bo269bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$15b
oo23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o
51b3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$
4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo
5boo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo
3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o14boo23boo14bo
$o3bo10boo23boo10bo3bo$o55bo213boo$obbo49bobbo212b3o$3o51b3o212boobo$
270b3o$271bo10$280boo$279b3o$15boo23boo237b3o$5boo8boo23boo8boo227boob
o$5b3o41b3o228b3o$5b3o41b3o229bo$5b3o41b3o239bobo$4boboo41boobo241bo$
4b3o43b3o237bo3bo$5bo45bo238bo3bo$294bo$6bobo39bobo240bobbo$9bo37bo
244b3o$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo
6boo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bo
bo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo
23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo
23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$
6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bo
bbo39bobbo$6b3o39b3o$$15boo23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo
3bo$o55bo$obbo49bobbo$3o51b3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o
41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo
$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o
3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$b
obo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo49bobbo$3o
51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4bo
boo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37b
o$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo3bo6boo23boo
6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o
55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo12$5boo43boo$5b3o41b3o$
5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$
6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bo
bo$8bo$4bo3bo$8bo$5bobbo$6b3o$$15boo23boo$15boo23boo4$bobo$o$o3bo$o$o
bbo$3o8$15boo23boo$15boo23boo6$5boo$5b3o$5b3o$5b3o$4boboo$4b3o$5bo$48b
obo$6bobo42bo$9bo41bo$5bo3bo38bobbo$9bo5boo23boo7b3o$6bobbo5boo23boo$
7b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b
3o$$109boo$109b3o$108boboo$108b3o$109bo$bobo49bobo$o14boo23boo14bo$o3b
o10boo23boo10bo3bo$o55bo$obbo49bobbo$3o51b3o14$15boo23boo$5boo8boo23b
oo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$
6bobo39bobo$9bo37bo$5bo3bo37bo3bo53bobo$9bo37bo60bo$6bobbo37bobbo57bo$
7b3o37b3o55bobbo$106b3o$95bobo$5bobo41bobo42bo$8bo6boo23boo6bo45bo3bo$
4bo3bo6boo23boo6bo3bo41bo3bo$8bo39bo45bo$5bobbo39bobbo42bobbo$6b3o39b
3o43b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo
23boo$15boo23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boo
bo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3b
o$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$
8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo23boo$15boo23boo4$bobo49bobo$o
55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o8$15boo23boo$15boo23boo6$5b
oo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo
$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bo
bbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo
$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obb
o49bobbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b
3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37b
o3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo
3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o
3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo12$5boo43b
oo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9b
oo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b
3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o
39b3o$$15boo23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo
49bobbo$3o51b3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$
5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo
37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o3$5bobo41bobo$
8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o14b
oo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo49bobbo$3o51b3o14$15boo23b
oo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o
43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo
$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$
5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobb
o$3o51b3o$$15boo23boo$15boo23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o
41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo
37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39b
o$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo23boo$15boo23boo
4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o8$15boo23boo$
15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o
43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobb
o5boo23boo5bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$
5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo
3bo$o55bo$obbo49bobbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o
$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo
37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6b
oo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo
49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo
23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo
23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$
6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bo
bbo39bobbo$6b3o39b3o$$15boo23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo
3bo$o55bo$obbo49bobbo$3o51b3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o
41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo
$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o
3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$b
obo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo49bobbo$3o
51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4bo
boo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37b
o$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo3bo6boo23boo
6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o
55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo12$5boo43boo$5b3o41b3o$
5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo$$
6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bo
bo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$15boo
23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b
3o8$15boo23boo$15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4bo
boo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5b
oo23boo5bo$6bobbo5boo23boo5bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo
39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o
3bo10boo23boo10bo3bo$o55bo$obbo49bobbo$3o51b3o14$15boo23boo$5boo8boo
23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45b
o$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$
5bobo41bobo$8bo6boo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobb
o$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$
15boo23boo$15boo23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo
41boobo$4b3o8boo23boo8b3o$5bo9boo23boo9bo277boo$328b3o$6bobo39bobo277b
3o$9bo37bo280boobo$5bo3bo37bo3bo277b3o$9bo37bo282bo$6bobbo37bobbo$7b3o
37b3o$$313boo$5bobo41bobo260b3o$8bo39bo263b3o$4bo3bo39bo3bo259b3o$8bo
39bo263boobo$5bobbo39bobbo261b3o$6b3o39b3o263bo$$15boo23boo$15boo23boo
$$313bobo$316bo$bobo49bobo256bo3bo$o55bo255bo3bo$o3bo47bo3bo259bo$o55b
o256bobbo$obbo49bobbo257b3o$3o51b3o8$15boo23boo$15boo23boo6$5boo43boo$
5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo
39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bobbo$7b
3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o
39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23boo10bo3bo$o55bo$obbo49bo
bbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b3o41b3o$5b3o41b3o$5b3o41b
3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$
9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo6boo23boo6bo$4bo3bo6b
oo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo
47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$15boo23boo12$5boo43boo$
5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o8boo23boo8b3o$5bo9boo
23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o
37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b
3o$$15boo23boo$15boo23boo4$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bo
bbo$3o51b3o5$276boo$276b3o$275boboo$15boo23boo233b3o$15boo23boo208bobo
23bo$253bo$249bo3bo$249bo3bo$253bo$250bobbo$5boo43boo199b3o$5b3o41b3o$
5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo
37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$6bobbo5boo23boo5bobbo209bobo$7b3o
37b3o213bo$259bo3bo$263bo$5bobo41bobo208bobbo$8bo39bo212b3o$4bo3bo39bo
3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o3bo
10boo23boo10bo3bo$o55bo$obbo49bobbo$3o51b3o14$15boo23boo$5boo8boo23boo
8boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6b
obo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo
41bobo$8bo6boo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b
3o39b3o371bobo$425bo$421bo3bo$425bo$422bobbo$423b3o$$bobo49bobo$o55bo
386boo$o3bo47bo3bo386b3o$o27bo27bo385boboo$obbo23b3o23bobbo385b3o$3o
23booboo23b3o386bo$25boo3boo$15boo9booboo9boo240bobo12boo$15boo23boo
239bo14b3o$281bo3bo10b3o$281bo3bo10b3o132bobo$281bo14boobo134bo$18boo
5bo5bo5boo242bobbo12b3o130bo3bo$18boo5bo5bo5boo242b3o14bo135bo$23b4o3b
4o397bobbo$21b4obo3bob4o396b3o$20bobobooboboboobobo$19bobobbobbobobbo
bbobo$20bo3boo5boo3bo$24boo5boo$5boo16bo9bo16boo232boo$5b3o16bo7bo16b
3o231b3o$5b3o16bo7bo16b3o231b3o$5b3o41b3o231boobo$4boboo4b3o27b3o4boob
o231b3o$4b3o5bobboo23boobbo5b3o232bo$5bo6boo10boo5boo10boo6bo$19bo4boo
5boo4bo$6bobo5bo3bo19bo3bo5bobo$9bo6boo21boo6bo$5bo3bo37bo3bo$9bo37bo$
6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bo
bbo39bobbo$6b3o39b3o5$11bo5boo19boo5bo$10bo6boo19boo6bo$bobo4bobo35bob
o4bobo$o9bo35bo9bo$o3bobbobo37bobobbo3bo$o6bo41bo6bo$obbo3bobo37bobo3b
obbo$3o5boo37boo5b3o12$15boo23boo$15boo23boo$$5boo43boo$5b3o41b3o$5b3o
41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$
5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o$$15boo23boo$5bobo7boo23b
oo7bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49b
obo$o55bo$o3bo47bo3bo292bobo$o55bo295bo$obbo49bobbo291bo3bo$3o12boo23b
oo12b3o291bo3bo$15boo23boo310bo$349bobbo$350b3o13bobo$365bo$365bo$365b
obbo$365b3o5$364boo$364b3o$364b3o$5boo43boo311boboo$5b3o41b3o311b3o$5b
3o41b3o312bo$5b3o7boo23boo7b3o$4boboo7boo23boo7boobo$4b3o43b3o$5bo45bo
$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o
331boo15bobo$380b3o14bo$380b3o14bo3bo$5bobo41bobo328b3o14bo3bo$8bo39bo
331boobo13bo$4bo3bo39bo3bo328b3o13bobbo$8bo39bo333bo14b3o$5bobbo39bobb
o$6b3o6boo23boo6b3o$15boo23boo4$394boo$393b3o$bobo49bobo337b3o$o55bo
336boobo$o3bo47bo3bo337b3o$o55bo338bo$obbo49bobbo$3o51b3o6$15boo23boo$
15boo23boo8$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o
43b3o$5bo45bo$$6bobo39bobo$9bo5boo23boo5bo$5bo3bo5boo23boo5bo3bo$9bo
37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39b
o$5bobbo39bobbo$6b3o39b3o6$15boo23boo$bobo11boo23boo11bobo$o55bo$o3bo
47bo3bo$o55bo$obbo49bobbo$3o51b3o5$294bobo$297bo$297bo$294bobbo$295b3o
3$15boo23boo$15boo23boo$$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4bob
oo41boobo251bobo$4b3o43b3o254bo$5bo45bo251bo3bo$307bo$6bobo39bobo253bo
bbo$9bo37bo257b3o$5bo3bo37bo3bo$9bo37bo270boo$6bobbo37bobbo267b3o$7b3o
37b3o268b3o$318b3o$15boo300boboo$5bobo7boo32bobo265b3o$8bo39bo269bo$4b
o3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo
3bo$o55bo$obbo49bobbo$3o12boo23boo12b3o$15boo23boo14$5boo43boo$5b3o41b
3o$5b3o41b3o$5b3o7boo23boo7b3o$4boboo7boo23boo7boobo$4b3o43b3o$5bo45bo
$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$
5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o6boo23boo
6b3o$15boo23boo6$bobo49bobo$o55bo$o3bo47bo3bo$o55bo213boo$obbo49bobbo
212b3o$3o51b3o212boobo$270b3o$271bo4$15boo23boo$15boo23boo5$280boo$
279b3o$279b3o$5boo43boo227boobo$5b3o41b3o228b3o$5b3o41b3o229bo$5b3o41b
3o239bobo$4boboo41boobo241bo$4b3o43b3o237bo3bo$5bo45bo238bo3bo$294bo$
6bobo39bobo240bobbo$9bo5boo23boo5bo244b3o$5bo3bo5boo23boo5bo3bo$9bo37b
o$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$
5bobbo39bobbo$6b3o39b3o6$15boo23boo$bobo11boo23boo11bobo$o55bo$o3bo47b
o3bo$o55bo$obbo49bobbo$3o51b3o12$15boo23boo$15boo23boo$$5boo43boo$5b3o
41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo
$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o$$15boo23boo$5bo
bo7boo23boo7bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o
7$bobo49bobo$o55bo$o3bo47bo3bo154bobo$o55bo155boo$obbo49bobbo155bo$3o
12boo23boo12b3o$15boo23boo14$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o7boo23b
oo7b3o$4boboo7boo23boo7boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5b
o3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3b
o39bo3bo$8bo39bo$5bobbo39bobbo$6b3o6boo23boo6b3o$15boo23boo6$bobo49bob
o$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o6$15boo23boo$15boo23boo8$
5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45b
o$$6bobo39bobo$9bo5boo23boo5bo$5bo3bo5boo23boo5bo3bo$9bo37bo$6bobbo37b
obbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobb
o$6b3o39b3o6$15boo23boo$bobo11boo23boo11bobo$o55bo$o3bo47bo3bo$o55bo$o
bbo49bobbo$3o51b3o12$15boo23boo$15boo23boo$$5boo43boo$5b3o41b3o$5b3o
41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$
5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o$$15boo23boo$5bobo7boo23b
oo$8bo$4bo3bo$8bo$5bobbo$6b3o7$bobo$o$o3bo$o$obbo$3o12boo23boo$15boo
23boo14$5boo$5b3o$5b3o$5b3o7boo23boo$4boboo7boo23boo$4b3o$5bo$48bobo$
6bobo42bo$9bo41bo$5bo3bo38bobbo$9bo39b3o$6bobbo$7b3o3$5bobo41bobo$8bo
39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o6boo23boo6b3o$15boo23boo$
109boo$109b3o$108boboo$108b3o$109bo$bobo49bobo$o55bo$o3bo47bo3bo$o55bo
$obbo49bobbo$3o51b3o6$15boo23boo$15boo23boo8$5boo43boo$5b3o41b3o$5b3o
41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo5boo
23boo5bo$5bo3bo5boo23boo5bo3bo53bobo$9bo37bo60bo$6bobbo37bobbo57bo$7b
3o37b3o55bobbo$106b3o$95bobo$5bobo41bobo42bo$8bo39bo45bo3bo$4bo3bo39bo
3bo41bo3bo$8bo39bo45bo$5bobbo39bobbo42bobbo$6b3o39b3o43b3o6$15boo23boo
$bobo11boo23boo11bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o12$
15boo23boo$15boo23boo$$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo
41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$
6bobbo37bobbo$7b3o37b3o$$15boo23boo$5bobo7boo23boo7bobo$8bo39bo$4bo3bo
39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$
o55bo$obbo49bobbo$3o12boo23boo12b3o$15boo23boo14$5boo43boo$5b3o41b3o$
5b3o41b3o$5b3o7boo23boo7b3o$4boboo7boo23boo7boobo$4b3o43b3o$5bo45bo$$
6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bo
bo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o6boo23boo6b3o
$15boo23boo6$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o6$
15boo23boo$15boo23boo8$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo
41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo5boo23boo5bo$5bo3bo5boo23boo
5bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo
3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o6$15boo23boo$bobo11boo23boo11bobo$o
55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o12$15boo23boo$15boo23boo$$5b
oo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo
$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o$$
15boo23boo$5bobo7boo23boo7bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39b
obbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o12boo
23boo12b3o$15boo23boo14$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o7boo32b3o$4b
oboo7boo32boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$
9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo
39bo$5bobbo39bobbo$6b3o6boo23boo6b3o$15boo23boo6$bobo49bobo$o55bo$o3bo
47bo3bo$o55bo$obbo49bobbo$3o51b3o6$15boo23boo$15boo23boo5$190boo$190bo
bo$190bo$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b
3o$5bo45bo$$6bobo39bobo$9bo5boo23boo5bo$5bo3bo5boo23boo5bo3bo$9bo37bo$
6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bo
bbo39bobbo$6b3o39b3o6$15boo23boo$bobo11boo23boo11bobo$o55bo$o3bo47bo3b
o$o55bo$obbo49bobbo$3o51b3o12$15boo23boo$15boo23boo$$5boo43boo$5b3o41b
3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9b
o37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o$$15boo23boo$5bobo
7boo23boo7bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$
bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o12boo23boo12b3o$15boo
23boo14$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o7boo23boo7b3o$4boboo7boo23b
oo7boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$
6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bo
bbo39bobbo$6b3o6boo23boo6b3o$15boo23boo3$206b3o$206bo$207bo$bobo49bobo
$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o6$15boo23boo$15boo23boo8$
5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45b
o$$6bobo39bobo$9bo5boo23boo5bo$5bo3bo5boo23boo5bo3bo$9bo37bo$6bobbo37b
obbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobb
o$6b3o39b3o6$15boo23boo$bobo11boo23boo11bobo$o55bo$o3bo47bo3bo$o55bo$o
bbo49bobbo$3o51b3o12$15boo23boo$15boo23boo$$5boo43boo$5b3o41b3o$5b3o
41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$
5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o$$15boo23boo$5bobo7boo23b
oo7bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o6$28bo$bo
bo23b3o23bobo$o25b5o25bo$o3bo20bo5bo20bo3bo$o23boo5boo23bo$obbo19boo7b
oo19bobbo$3o12boo7bobo3bobo7boo12b3o$15boo8boo3boo8boo4$18boo17boo$18b
oo17boo3$20boo13boo$19bobboo9boobbo$21bob4o3b4obo$$23bobbo3bobbo$23b3o
5b3o$5boo6bo9bo9bo9bo6boo$5b3o4b3o27b3o4b3o$5b3o3bobo29bobo3b3o$5b3obb
oobbo27bobboobb3o$4boboo3b5o8boo5boo8b5o3boobo$4b3o6bo10boo5boo10bo6b
3o$5bo11boo19boo11bo$17boo19boo$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo
37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39b
o$5bobbo39bobbo$6b3o39b3o3$17boo19boo$10boo5boo19boo5boo$9bobo33bobo$
11bo33bo$bobo3bo41bo3bobo$o5bo43bo5bo$o3bobobboo35boobbobo3bo$o6b3o37b
3o6bo$obbo4bo39bo4bobbo$3o51b3o10$15boo23boo$15boo23boo4$5boo43boo$5b
3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bo
bo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o5boo23boo5b3o$15boo
23boo$$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b
3o7$bobo49bobo$o55bo$o3bo47bo3bo$o14boo23boo14bo$obbo11boo23boo11bobbo
$3o51b3o15$5boo43boo$5b3o7boo23boo7b3o$5b3o7boo23boo7b3o$5b3o41b3o$4bo
boo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37b
o$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo6boo
23boo6bo$5bobbo6boo23boo6bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo
$o55bo$obbo49bobbo$3o51b3o4$15boo23boo$15boo23boo10$5boo43boo$5b3o41b
3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$15boo23boo$6bob
o6boo23boo6bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o
3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o4$
15boo23boo$15boo23boo$$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$
3o51b3o10$15boo23boo$15boo23boo4$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b
3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$
9bo37bo$6bobbo37bobbo$7b3o5boo23boo5b3o$15boo23boo$$5bobo41bobo$8bo39b
o$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo
47bo3bo$o14boo23boo14bo$obbo11boo23boo11bobbo$3o51b3o15$5boo43boo$5b3o
7boo23boo7b3o$5b3o7boo23boo7b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo
45bo277boo$328b3o$6bobo39bobo277b3o$9bo37bo280boobo$5bo3bo37bo3bo277b
3o$9bo37bo282bo$6bobbo37bobbo$7b3o37b3o$$313boo$5bobo41bobo260b3o$8bo
39bo263b3o$4bo3bo39bo3bo259b3o$8bo6boo23boo6bo263boobo$5bobbo6boo23boo
6bobbo261b3o$6b3o39b3o263bo5$313bobo$316bo$bobo49bobo256bo3bo$o55bo
255bo3bo$o3bo47bo3bo259bo$o55bo256bobbo$obbo49bobbo257b3o$3o51b3o4$15b
oo23boo$15boo23boo10$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41b
oobo$4b3o43b3o$5bo45bo$15boo23boo$6bobo6boo23boo6bobo$9bo37bo$5bo3bo
37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39b
o3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o4$15boo23boo$15boo23boo$$bobo49bob
o$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o10$15boo23boo$15boo23boo
4$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo
45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o5boo
23boo5b3o$15boo23boo$$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo
39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o14boo23boo14bo$obbo
11boo23boo11bobbo$3o51b3o11$722bo$723bo$721b3o$$5boo43boo$5b3o7boo23b
oo7b3o$5b3o7boo23boo7b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6b
obo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo
41bobo$8bo39bo$4bo3bo39bo3bo$8bo6boo31bo$5bobbo6boo31bobbo$6b3o39b3o7$
bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o4$15boo23boo$15b
oo23boo234boo$276b3o$275boboo$275b3o$250bobo23bo$253bo$249bo3bo$249bo
3bo$253bo$250bobbo$5boo43boo199b3o$5b3o41b3o$5b3o41b3o$5b3o41b3o$4bob
oo41boobo$4b3o43b3o$5bo45bo$15boo23boo$6bobo6boo23boo6bobo$9bo37bo$5bo
3bo37bo3bo$9bo37bo$6bobbo37bobbo209bobo$7b3o37b3o213bo$259bo3bo$263bo$
5bobo41bobo208bobbo$8bo39bo212b3o$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$
6b3o39b3o4$15boo23boo$15boo23boo$$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$o
bbo49bobbo$3o51b3o10$15boo23boo$15boo23boo4$5boo43boo$5b3o41b3o$5b3o
41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$
5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o5boo23boo5b3o$15boo23boo$$5bob
o41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o371bobo$
425bo$421bo3bo$425bo$422bobbo$423b3o$$bobo49bobo$o55bo386boo$o3bo47bo
3bo386b3o$o14boo23boo14bo385boboo$obbo11boo23boo11bobbo385b3o$3o51b3o
386bo$$282bobo12boo$281bo14b3o$281bo3bo10b3o$281bo3bo10b3o132bobo$281b
o14boobo134bo$281bobbo12b3o130bo3bo$281b3o14bo135bo$431bobbo$432b3o5$
5boo43boo232boo$5b3o7boo23boo7b3o231b3o$5b3o7boo23boo7b3o231b3o$5b3o
41b3o231boobo$4boboo41boobo231b3o$4b3o43b3o232bo$5bo45bo$$6bobo39bobo$
9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo
39bo$4bo3bo39bo3bo$8bo6boo23boo6bo$5bobbo6boo23boo6bobbo$6b3o39b3o7$bo
bo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o4$15boo23boo$15boo
23boo10$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b
3o$5bo45bo$15boo23boo$6bobo6boo23boo6bobo$9bo37bo$5bo3bo37bo3bo$9bo37b
o$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$
5bobbo39bobbo$6b3o39b3o4$15boo23boo$15boo23boo$$bobo49bobo$o55bo$o3bo
47bo3bo292bobo$o55bo295bo$obbo49bobbo291bo3bo$3o51b3o291bo3bo$352bo$
349bobbo$350b3o13bobo$365bo$365bo$365bobbo$365b3o3$15boo23boo$15boo23b
oo$364boo$364b3o$364b3o$5boo43boo311boboo$5b3o41b3o311b3o$5b3o41b3o
312bo$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$
5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o5boo23boo5b3o331boo15bobo$15b
oo23boo338b3o14bo$380b3o14bo3bo$5bobo41bobo328b3o14bo3bo$8bo39bo331boo
bo13bo$4bo3bo39bo3bo328b3o13bobbo$8bo39bo333bo14b3o$5bobbo39bobbo$6b3o
39b3o5$394boo$393b3o$bobo49bobo337b3o$o55bo336boobo$o3bo47bo3bo337b3o$
o14boo23boo14bo338bo$obbo11boo23boo11bobbo$3o51b3o5$316bo$317boo$316b
oo8$5boo43boo$5b3o7boo23boo7b3o$5b3o7boo23boo7b3o$5b3o41b3o$4boboo41b
oobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bo
bbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo6boo23boo6b
o$5bobbo6boo23boo6bobbo294bobo$6b3o39b3o296boo$347bo6$bobo49bobo$o55bo
$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o4$15boo23boo$15boo23boo252bobo$
297bo$297bo$294bobbo$295b3o6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$
4boboo41boobo251bobo71bo$4b3o43b3o254bo71bo$5bo45bo251bo3bo69b3o$15boo
23boo265bo$6bobo6boo23boo6bobo253bobbo$9bo37bo257b3o$5bo3bo37bo3bo$9bo
37bo270boo$6bobbo37bobbo267b3o$7b3o37b3o268b3o$318b3o$317boboo$5bobo
41bobo265b3o$8bo39bo269bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b
3o4$15boo23boo$15boo23boo$$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bo
bbo$3o51b3o10$15boo23boo$15boo23boo4$5boo43boo$5b3o41b3o$5b3o41b3o$5b
3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37b
o3bo$9bo37bo$6bobbo37bobbo$7b3o5boo23boo5b3o$15boo23boo$$5bobo41bobo$
8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55b
o$o3bo47bo3bo$o14boo23boo14bo213boo$obbo11boo23boo11bobbo212b3o$3o51b
3o212boobo$270b3o$271bo10$280boo$279b3o$279b3o$5boo43boo227boobo$5b3o
7boo23boo7b3o228b3o$5b3o7boo23boo7b3o229bo$5b3o41b3o239bobo$4boboo41b
oobo241bo$4b3o43b3o237bo3bo$5bo45bo238bo3bo$294bo$6bobo39bobo240bobbo$
9bo37bo244b3o$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bo
bo$8bo39bo$4bo3bo39bo3bo$8bo6boo23boo6bo$5bobbo6boo23boo6bobbo$6b3o39b
3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o4$15boo23boo
$15boo23boo10$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b
3o43b3o$5bo45bo$15boo23boo$6bobo6boo23boo6bobo$9bo37bo$5bo3bo37bo3bo$
9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo
39bo$5bobbo39bobbo$6b3o39b3o4$15boo23boo$15boo23boo$$bobo49bobo$o55bo$
o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o10$15boo23boo$15boo23boo4$5boo43b
oo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bob
o39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o5boo23boo5b3o$
15boo23boo$$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b
3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o14boo23boo14bo$obbo11boo23boo
11bobbo$3o51b3o15$5boo43boo$5b3o7boo23boo7b3o$5b3o7boo23boo7b3o$5b3o
41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo
3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo
$8bo6boo23boo6bo$5bobbo6boo23boo6bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3b
o47bo3bo$o55bo$obbo49bobbo$3o51b3o4$15boo23boo$15boo23boo10$5boo43boo$
5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$15boo23b
oo$6bobo6boo23boo6bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b
3o37b3o3$5bobo$8bo$4bo3bo$8bo$5bobbo$6b3o4$15boo23boo$15boo23boo$$bobo
$o$o3bo$o$obbo$3o10$15boo23boo$15boo23boo4$5boo$5b3o$5b3o$5b3o$4boboo$
4b3o$5bo$48bobo$6bobo42bo$9bo41bo$5bo3bo38bobbo$9bo39b3o$6bobbo$7b3o5b
oo23boo$15boo23boo$$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo
39bobbo$6b3o39b3o$$109boo$109b3o$108boboo$108b3o$109bo$bobo49bobo$o55b
o$o3bo47bo3bo$o14boo23boo14bo$obbo11boo23boo11bobbo$3o51b3o15$5boo43b
oo$5b3o7boo23boo7b3o$5b3o7boo23boo7b3o$5b3o41b3o$4boboo41boobo$4b3o43b
3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo53bobo$9bo37bo60bo$6bobbo
37bobbo57bo$7b3o37b3o55bobbo$106b3o$95bobo$5bobo41bobo42bo$8bo39bo45bo
3bo$4bo3bo39bo3bo41bo3bo$8bo6boo23boo6bo45bo$5bobbo6boo23boo6bobbo42bo
bbo$6b3o39b3o43b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o
51b3o4$15boo23boo$15boo23boo10$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o
$4boboo41boobo$4b3o43b3o$5bo45bo$15boo23boo$6bobo6boo23boo6bobo$9bo37b
o$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$
4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o4$15boo23boo$15boo23boo$$
bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o10$15boo23boo$
15boo23boo4$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o
43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo
$7b3o5boo23boo5b3o$15boo23boo$$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo
39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o14boo23boo
14bo$obbo11boo23boo11bobbo$3o51b3o15$5boo43boo$5b3o7boo23boo7b3o$5b3o
7boo23boo7b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$
9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo
39bo$4bo3bo39bo3bo$8bo6boo23boo6bo$5bobbo6boo23boo6bobbo$6b3o39b3o7$bo
bo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o4$15boo23boo$15boo
23boo10$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b
3o$5bo45bo$15boo23boo$6bobo6boo23boo6bobo$9bo37bo$5bo3bo37bo3bo$9bo37b
o$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$
5bobbo39bobbo$6b3o39b3o4$15boo23boo$15boo23boo$$bobo49bobo$o55bo$o3bo
47bo3bo$o55bo$obbo49bobbo$3o51b3o10$15boo23boo$15boo23boo4$5boo43boo$
5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo
39bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o5boo23boo5b3o$
15boo23boo$$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b
3o39b3o7$bobo49bobo$o55bo$o3bo47bo3bo$o14boo23boo14bo$obbo11boo23boo
11bobbo$3o51b3o15$5boo43boo$5b3o7boo23boo7b3o$5b3o7boo23boo7b3o$5b3o
41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo
3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo
$8bo6boo23boo6bo$5bobbo6boo23boo6bobbo$6b3o39b3o7$bobo49bobo$o55bo$o3b
o47bo3bo$o55bo$obbo49bobbo$3o51b3o4$15boo23boo$15boo23boo10$5boo43boo$
5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$15boo23b
oo$6bobo6boo23boo6bobo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b
3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o
39b3o4$15boo23boo$15boo23boo$$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo
49bobbo$3o51b3o10$15boo23boo$15boo23boo4$5boo43boo$5b3o41b3o$5b3o41b3o
$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo
37bo3bo$9bo37bo$6bobbo37bobbo$7b3o5boo23boo5b3o$15boo23boo$$5bobo41bob
o$8bo39bo$4bo3bo39bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o$$28bo$28bo$27b
3o$$25bo5bo$bobo19bo9bo19bobo$o21boo4bo4boo21bo$o3bo16boo4b3o4boo16bo
3bo$o14boo5bobb3ob3obbo5boo14bo$obbo11boo6boobo3boboo6boo11bobbo$3o21b
oo5boo21b3o3$18boo17boo$18boo17boo$$20b3o11b3o$20bo4bo5bo4bo$20b5obo3b
ob5o$23boobbobobboo$22bo4bobo4bo$22b5o3b5o$13boo6boobboo3boobboo6boo$
11booboo6bobo7bobo6booboo$10bobo10bo9bo10bobo$5boobbobboo29boobbobboo$
5b3obo37bob3o$5b3oboo13boo5boo13boob3o$5b3o16boo5boo16b3o$4boboo9boo
19boo9boobo$4b3o10boo19boo10b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37b
o3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3b
o$8bo39bo$5bobbo39bobbo$6b3o39b3o$11boo4boo19boo4boo$10bobo4boo19boo4b
obo$12bo31bo$$6b3o39b3o$10bo35bo$bobo6bo35bo6bobo$o5bo3bo35bo3bo5bo$o
3bo4boo35boo4bo3bo$o6bobo37bobo6bo$obbo4bo39bo4bobbo$3o51b3o8$15boo23b
oo$15boo23boo6$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$
4b3o43b3o$5bo45bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo5boo23boo5bo$
6bobbo5boo23boo5bobbo$7b3o37b3o3$5bobo41bobo$8bo39bo$4bo3bo39bo3bo$8bo
39bo$5bobbo39bobbo$6b3o39b3o7$bobo49bobo$o14boo23boo14bo$o3bo10boo23b
oo10bo3bo$o55bo$obbo49bobbo$3o51b3o14$15boo23boo$5boo8boo23boo8boo$5b
3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b3o43b3o$5bo45bo$$6bobo39bo
bo$9bo37bo$5bo3bo37bo3bo$9bo37bo$6bobbo37bobbo$7b3o37b3o3$5bobo41bobo$
8bo6boo23boo6bo$4bo3bo6boo23boo6bo3bo$8bo39bo$5bobbo39bobbo$6b3o39b3o
7$bobo49bobo$o55bo$o3bo47bo3bo$o55bo$obbo49bobbo$3o51b3o$$15boo23boo$
15boo23boo12$5boo43boo$5b3o41b3o$5b3o41b3o$5b3o41b3o$4boboo41boobo$4b
3o8boo23boo8b3o$5bo9boo23boo9bo$$6bobo39bobo$9bo37bo$5bo3bo37bo3bo$9bo
37bo$6bobbo37bobbo$7b3o37b3o!
As an extension of this, if every other downward glider turning convoy had an extra glider turning component which turned downward gliders into forward gliders, then the result would be a channel that would produce gliders in both directions, possibly allowing them to react with each other in interesting ways.

I hope that the timing adjustments for the PIs allow for some varied glider interactions.

As far as filtering the output, I thought a spaceship loop like the one I showed a few posts ago could be useful. It can be arbitrarily long holding an arbitrary pattern of upward spaceships, without needing further 3c/10 support. The upward spaceship stream could be built from only one side from a large distance away, so that the gliders which pass through the stream have room to do something. (Gliders can't pass through the block rows which support a PI crawler).

BCNU,
-dbell
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