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Oscillator Discussion Thread

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

Re: Oscillator Discussion Thread

Postby Sokwe » April 3rd, 2018, 8:52 am

77topaz wrote:from testing in Golly I see that the FNGs would also interfere with the converting reaction when that is in process.

Eating the FNG at p52 is very difficult. It seemingly can't be done at p4, and we don't have sufficient sparkers at periods 13, 26, or 54. The large p4 oscillators shuttling a glider are a clever workaround, but their size limits their use.

77topaz wrote:However, now that I think about it, isn't there a complete database of all three-glider collisions? Shouldn't we already know whether or not a 3G->4G reaction exists? (Then again, I suppose this gun wouldn't require it to be a "pure" 3G->4G reaction, just something that converts 3G to 4G.)

I'm definitely not asking for a "pure" 3G->4G that works at p52. I doubt such a thing exists. What I'm looking for is a way to use the apparatus posted earlier to turn 3 gliders into 4. The resulting gun would be similar in structure to the p54 and p55 guns found in jslife.
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Re: Oscillator Discussion Thread

Postby dvgrn » April 3rd, 2018, 9:37 am

77topaz wrote:However, now that I think about it, isn't there a complete database of all three-glider collisions? Shouldn't we already know whether or not a 3G->4G reaction exists? (Then again, I suppose this gun wouldn't require it to be a "pure" 3G->4G reaction, just something that converts 3G to 4G.)

It's probably better to advertise it as an almost complete 3G collision database, until proven otherwise, by someone else doing an independent enumeration. But yes, you've answered your own question: the 3G-to-4G can have any kind of assisting mechanism that works at p52 -- e.g., a conduit of some kind using p4 oscillators.

Might even be something that's specific to p52, where three gliders crash into sparks made by a previous collision, and somehow four gliders come out... Seems like a likely mechanism might be something extensible, where active object X is catalyzed to produce a glider plus another active object X, so you can get as many gliders out as you need.

It takes a fairly unusual glider production mechanism to be fast enough that the glider gets out of the way in time for the next X to come along in only 52 ticks, though. Maybe I should be wishing for an X -> MWSS+X instead, given that Sokwe's 135-degree MWSS-to-G is plenty fast enough to work at p52.
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Re: Oscillator Discussion Thread

Postby chris_c » April 3rd, 2018, 9:50 am

Here's the p54 along very similar lines:

x = 136, y = 109, rule = B3/S23
89b2o$56bo14b2o15bobo$56b3o14bob2o5b2o4bo$59bo9bo2bo2b2o3bo2bo2b2ob4o$
58b2o9bobo8b2obobobobo2bo$70bo12bobobobo$83bobob2o$64b2o4b2o12bo$63b3o
4b2o$63bo33b2o$63b2o23b2o7bo$88b2o5bobo$95b2o3$80bo$80bobo$80b2o$63b2o
$63bobo19b2o5b3o$65bo20bo5bo$65b2o8bo7b3o7bo$73bobo7bo$49b2o12b4o7b2o$
50b2o11bo2bo$49bo14bo4b3o7b2obo$61b3o4bo3bo6b2ob3o$61bo5bo5bo11bo$68bo
3bo6b2ob3o$69b3o8bobo$80bobo$81bo$106b2o$106bobo$106bo2$36bo39b2o$36b
2o38bobo$35bobo31bo8bo2b2o$68bo8b2obobo$58b2o7b3obo4bo3bo$59bo7b2o2b2o
2b2obobo2bo$59bobo5b2o2b2o3bobo2b3o$60b2o15bob2o$67b2o6bo2bo2bo$67bo4b
o2b6o50b2o$67bo4bo46b3o9bo$7b2o59bobo6b4o3bo34bo13bo$7bobo67bo3bobobo
27b2o5bo8b5o$9bo70b2obobo28bo13bo$5b4ob2o2b2o6b2o56bo3bob2o26bobo12b3o
$5bo4bobo2bo7b2o56b2obo2bo27b2o15bo$3b2o2bo2bob2o8bo57bo2bobobob2o38b
4o$2bo2b2o3bobo67b2obobobo2bo33b2o3bo3b2o$bob2o2bob2obo68bo6b2o34b2o4b
3o2bo$bo4bo4bo49bo19bob5o44bob2o$2b3obob3o50b2o10bobo6bo4bo44bo$4b5o
52b3o10b2o7b4o44b2o$63bo10bo10bo28b2o$65bo21bo25bobo$60b2o3bo20b2o27bo
7b2o$55b2o3b2o61bo$6bo47bobo7bo59b3o$5bobo2b2o38b2o2bo5bo2bo62bo$6b2o
2bobo37bobob2o5b3o$2b2o6bo41bo20b2o$bobo45bo2b5o16bo$bo5b2o40b3o3bo15b
obo$2o5b2o43b2ob2o14b2o$51bo5bo29bo$52b6o30b2o$87b2o$48bo3b4o44b3o$47b
obobo3bo46bo5b2o$47bobob2o48bo7bo$45b2obo3bo54bo$45bo2bob3o10b2o40b4o$
23b3o16b2obobobo2bo8b2o41bo4bo$23bo18bo2bo5b2o8bo5b2o34bob5o$24bo18b2o
4bobo9bo7bo33bobobo2b2o$45b5obo10bo6bo21b2o9b2o2bob2o2bo$45bo4bo13b2o
3bo21b2o2b2o4bo3b2o2bob2o$46b4o45bobo3b2obobo2bo$47bo48bo4bo4bob2o$45b
o56b2obobo$45b2o46b2o8bobobo$41bo34b2o16bo8bo2bo$41b3o32bobo12b3o10b2o
$44bo5bo27bo2b2o8bo$43b2o4bo9bo17b2obobo$37b2o10b3o7b3o6bo7bo3bo$37bob
o22bo5bo7b5o2bo$37bo23b2o6bo6bobo2b3o$67b2o11bo$65b4o6bo2bo2bo$64bo2bo
7b6o$53b2o9bo2bo$46b2o5bobo9b3o9b2o$46b2o7bo21b2o$55b2o2$42bo23b2o$41b
obob2o17bo2bo$41bobobobo15bob2o$38b2obobobobo2bo12bo$38bo2bo2b2ob4o9b
2obo4bo$40b2o4bo13b2ob2o3b3o10bo$46bobo22bo10bo$47b2o21b2o8b3o!



and a bit of a reduction to the p55:

x = 171, y = 119, rule = B3/S23
68b2o$68bobo$70bo4b2o26b2o16bo$66b4ob2o2bo2bo23bo2bo13b3o$66bo2bobobob
ob2o18bo2bo2bobo12bo$69bobobobo21b5obob2o11b2o$70b2obobo27bo2bo$74bo
24b4o2bo7bo$98bo3b2o2bo5bo2bo$60b2o36bob3o2bo4b2o3bo$61bo7b2o28bo3bo2b
o4bo3bo$61bobo5b2o29b2obob2o5b3o$62b2o37bobobo7bo$100bo2bobo$100b2o2bo
2$79bo$77bobo$65b2o11b2o$66b2o4b2o$65bo6bo$73b3o$75bo$101bo24b2o$100bo
24b2o$100b3o24bo3$82b2o$82bobo67b2o$84bo6bobo58bo$84b2o6b2o59b3o$51b3o
38bo57b3o3bo$53bo28b4o63bo2bobo2bo$52bo29bo2bo62bob3ob2obo$83bo4b2o8b
2obo47bo2bobo2b2o$80b3o4bo2bo7b2ob3o46b4o2bo2bo$80bo23bo34b3o5b3o7bobo
$88b3o7b2ob3o35bo7bo3bo4b2obob2o$99bobo38bo7b3ob2o2bo3bobo$99bobo48bob
o4b3o$100bo53b2obo2b2o3b2o$151b6o3bobobob3o$153b3o6bobo4bo$98b2o62b2ob
2obobo$38bo58bo2bo59bobo5bobo$17b2o19b2o57bobo2bo2bo48bo5bo2bob2o2bo$
18bo18bobo56b2obob5o47bobo4bob3o2b2o$15b3o76bo3b2o53b2o6b2o2b2o$14bo3b
3o76b2o2b3o53b2o7bo$13bo2bobo2bo55b2o8b3o3bo3bobo2bobo41b2o9b2o7bobo$
13bob2o3bobo55bo9bobo6b2o2b2obo40bobo4b2o13b2o$12b2o2bobo2bo56bobo6bo
2bo3bo3b2o3bo43bo4b2o$11bo2bob5o58b2o6bo2bo5b2obob2o54bo2bo$11bobo2bo
4b3o63bobo7bobobo54bo2b2o$8b2obob2ob4o3bo63bo2bo6bobobobo52b2o2b2o$8bo
bo5bo3b3o65b2o8bobobobo55bobo$11b3ob2obobo68bo10bobobo56b2o$4b2o3b2o2b
7o79b2obob2o$2b3obobobo13b2o71bo3b2o3bo$bo4bobo14bobo74b2o2b2obo$ob2ob
o3bo15bo70bo3bobo2bobo$obobob2o92b2o2b3o$bo3b5obo4bo80bo3b2o$2b2o7bo3b
obo81b2obob5o23b2o$4b2o4b3o3b2o75bo6bobo2bo2bo24b2o$4bo7b2o66bo10bobo
6bo2bo28bo$2bobo7b2o64b2ob2o9b2o7b2o$2b2o13b2o$11bo5b2o52b2o8bobo$10bo
b2o56bo2bo5bo3bo$14bo50bo2bo2bobo5bo2b2o$10bo3bo50b5obob2o5b3o$8b2o2b
2o14b3o40bo3bo5bo$8b2o18bo38b2obo4bo$29bo36bo3b2o3bo16b2o20bo$66bobobo
4bo16bo19b3o$67bo3bo3bo14bobo18bo$68b2obob2o15b2o19b2o5b3o$69bobobo31b
obo12bo$67bobobobo32b2o11bo$66bobobobo33bo$66bobobo$65b2obob2o15bo$64b
o3bo3bo13bobo$63bobobo4bo28b2o$43bo19bo3b2o3bo9b2o16bobo5b2o$42b2o20b
2obo4bo8bobo16bo7b2o$42bobo23bo3bo8bo4b2o11b2o$62b5obob2o9b3obo2bo$62b
o2bo2bobo13bob2o25bo$67bo2bo16bo21b2obobo$68b2o15b2o21bobobobo$105bo2b
obobobob2o$98bo2b2o2b4ob2o2bo2bo$97bobo2bo6bo4b2o$60bo36bobobo5bobo$
60b3o33b2obob2o4b2o$63bo6bo25bo2bo3bo$62b2o4b2o8bo18bo2b3obo$56b2o11b
2o7b3o6bo8bo2b2o3bo$56bobo22bo4bobo8bo2b4o$56bo23b2o14bo2bo$87b2o7b2ob
ob5o$85b2o10bobo2bo2bo$83b2o12bo2bo$72b2o9b2obo11b2o$65b2o5bobo10b2o$
65b2o7bo$74b2o2$61bo23b2o$60bobob2o17bo2bo$60bobobobo15bob2o$57b2obobo
bobo2bo12bo$57bo2bo2b2ob4o9b2obo4bo$59b2o4bo13b2ob2o3b3o10bo$65bobo22b
o10bo$66b2o21b2o8b3o!


EDIT: Also a p56. Things worked out modulo 8 pretty nicely:

x = 152, y = 145, rule = B3/S23
71b2o$71b2o$57bo$57b3o$60bo9bob2o$59b2o9bobo$71bo$64bo6b2o$63bobo5b2o$
63bo2bo4b2o$64b2o13b2o$78bobo$77b3o14bo$77b2o13b3o$80b2o9bo$79b3o9b2o$
58b2o$57bobo9bobo15bo$59bo10b2o7b2o6bo$70bo8b2o4b3o5$69b2o13bo$69bobo
10b2o$71bo11b2o$71b2o2$69b4o21b3o$44b2o23bo2bo21bo$43bobo24bo14b2obo6b
o$45bo21b3o15b2ob3o$67bo23bo$85b2ob3o$86bobo$72b2o2b3o7bobo$76b3o8bo$
76b2o$75b2o$75bo3$108b3o$30b2o76bo$29bobo44b2o31bo$31bo32b2o9bobo4b2o$
65bo11bo4b2o$65bobo14b2o$66b2o14bo$69b2o10bobo$69b2o10bob2o$71b3o$2bo
65b2o2bo$b3o49bo2bo2bo8b2ob3o8b2o$3obo48b7o2bo6b2o11b2o$bo3bo54b3o7bo
2b2o$2bo3bo48b2obo12b3o48b3o$3bob3o8b2o36bo3b3o11bo49bo$4b3o8bobo36bob
o4bo61bo$5bo11bo35b2ob5obo$9bo44bo5bobo4b2o15b2o$8bobo43bo2b3o2b2o3b2o
15bobo$9b2o42b2ob2obobo24bo$5b2o48bobobobo24b2o$4bobo48bobobob2o80bo2b
2o$4bo5b2o40b2obo4bo81bo3b2o2b2o$3b2o5b2o40bo2b2obobo81bo7b2o$54bo5b2o
81b4o$55b4o3bo$59bob2o$57b2o3bo5b3o8b2o55b3o$23b2o33bob2o5bobo9bo56bo$
22b2o34bobo6bo2bo6bobo57bo$24bo32b2o2bo5bo2bo6b2o63b2o$60b2o6bobo70bo
2bo$67bo2bo69b2ob2o$55b2o11b2o72bo$54b3o11bo77b2o$53bobo2bo2b2o22bo2bo
2bo54bobo$53b2o2b2o2b2o19bo2b7o56bo$57b2o23b3o63b2o$86bob2o40bo$84b3o
3bo39b2o$83bo4bobo38bobo$82bob5ob2o$37b2o26bo16bobo5bo$36b2o25b2o11b3o
2b2o2b3o2bo$38bo25b2o10b3o4bobob2ob2o$76b2o5bobobobo$49bo25bo6b2obobob
o$49b3o21b2o2bo6bo4bob2o$52bo21bo3bo5bobob2o2bo$51b2o21bo2bo5b2o5bo$
52b3o20b3o4bo3b4o$53b3o26b2obo$52b5o7b2o16bo3b2o28bo$51b2o3b2o7bo17b2o
bo29b2o$50b3o3b3o6bobo16bobo28bobo$51b2o3b2o8b2o15bo2b2o$52b5o4b2o20b
2o$53b3o5bobo$54bo8bo$63b2o18bo2b2o$82bo3b2o2b2o$50bo31bo7b2o$49bobob
2o28b4o$49bobobobo18b2o$46b2obobobobo2bo17b2o$46bo2bo2b2ob4o11b2o5bo$
48b2o4bo14bo7bo24bo$54bobo12bo6bo25b2o$55b2o12bo3b2o26bobo8$80bo8bo$
61b2o15b3o6bobo$60bo2bo5b2o6bo10b2o$63bo4b2o7b2o$63bo6bo$60b2obo22b2o$
60b2o11b2o11b2o2b2o$70b2o2bo15bobo$70bo2bo17bo$61b2o8b3o20b3o$61b2o19b
2o4b2o3bo$82bo6bo3bo3bo$80bobo3b3o4bo2bobo$80b2o4bo8bobo2bo$96bo3bo$
100bo$97b3o$67b2o$68bo$65b3o$65bo$70b2o3b2o$71bo3bo8bo$68b3o5b3o6bo$
68bo9bo4b3o!
Last edited by chris_c on April 3rd, 2018, 11:12 am, edited 1 time in total.
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Re: Oscillator Discussion Thread

Postby calcyman » April 3rd, 2018, 10:07 am

These ideas can be used to create a p52 emu (oscillator), but currently we lack an over-unity component:

x = 827, y = 827, rule = B3/S23
643b2o$642bob3obo14bo$642bobo3bo12b3o$641b2obobo2bo10bo$644b2o3bo10b2o
$641b3o3bo21b2o$641bo2b2obo8bo11bobo$642bo5bo2bo3bobo9bo2bob2obo$639b
3o2b2obo6bo2bo7b3obobobob3o$639bo2b2o3bo7b2o7bo4bo3bo4bo$640bo3b2o3bo
14b2ob2ob3ob2ob2o$641b2obobo2bo8bo6bo2bobobobo2bo$642bobo3bo8b2o6bobo
7bobo$642bob3obo8bobo6bob2o3b2obo$643b2o20b2ob2obob2ob2o$668b7o$670b3o
2$647bo$646bo$646b3o21bo$668b2obo$666bo5bo$665bo4b2o$667b2o2$674b2o$
674bobo$676bo$676b2o2$634bo$633bo$633b3o2$653b2o$652bobo$654bo7$621bo$
620bo$620b3o2$640b2o$639bobo$641bo6$594b2o$595bo12bo$595bobo9bo$596b2o
9b3o2$627b2o$600b2o24bobo$599bo2bo25bo$600bobo$601bo3$609bo$610b2o$
595b2o7b2o3b2o$595b11o$594bo4b3o4bo$595bobobobobobo$597bo5bo10b2o13b2o
$593bob3obobob3obo5bobo12bobo$593bo4bobobo4bo7bo12bo$594b3obobobob3o
20b2o$596bob2obo2bo$601bobo23b4o$601b2o24bo2bo$622bo6bo$623b2o5b3o$
612b3o7b2o8bo$614bo$613bo$622b2o$601b2o19b2o$600bobo$602bo4$621b2obo$
621b5o$622b4o$599b3o32b2o$601bo20b3o9bo$600bo21b3o7bobo$623bo8b2o$588b
2o$587bobo$589bo19b2o33b2o2bob2o$608bobo29bo2bob4obobo$610bo29b4o5bo2b
o$634b2o9b3o4b3o6bobo$623b2o10bo2b7o2b2o6bobo2bob2o2bo$621b2obo10bobo
4bo2bo8bob5o3b3o$619b2obob2o10b2ob2o3bob5o3bo6b2o$586b3o30b2ob2o14b3o
2b2obo2b2o2b2ob2obobob4o$588bo30b2o2b2o5b3o5b2o4bob3o2bo2bobob2obobo2b
o$587bo33bobo5bo9bob4obo2b5o6b3o$615b2o4b3o5bo2bo13bobo4bo3b2o3bo2bo$
575b2o39bo13b2o8bo4b2obo7b2o3b2ob4ob2o$574bobo36b3o25bo3b2o3bob2o3bo6b
2ob2obo$576bo19b2o15bo40bob3ob2o$595bobo54b2o7bo$597bo55bob2ob2obobo$
643b2o2b2o3bo2bo3bob2obo8bo$643b2o2b2o3b3o2b2o5bo7bobo4b2o$655b2o2b5o
8bobo2bo2bo$619b2o9bo19b3o2bo2bo5b3o4b2o2b3obo$573b3o44bo9b2o3bo13bo3b
obob2ob4o3bobo3b2o4b2o$575bo44bobo6bobob2o11bo2bo3b3o4bo2bo2b2ob4o2b3o
$574bo46b2o11b2o9b2obo6bobobo2bo5bo3b2o3b4o$641b4obo3bobobo3b2ob4ob4ob
o3b2o3bo$562b2o61b4o10b3ob3obobo2bobo2bobobob2obo4bo3bobobo$561bobo39b
2obo2b2o13bo2b3o8bo9b2obo5bob2o12b2o2b2o$563bo19b2o17bobob4obo2bo10bo
3bo8b9obo2bob2o3bo15bobo$582bobo17bo2bo5b4o10bo2bo17bobobo2bo6b3o11bob
o$584bo6bobo6b3o4b3o9b2o5b3o11bob2o5bo3bobo3b2o2bo11bo$588bo2b2obo2bob
o6b2o2b7o2bo20b2obo10b2o6b2o$588b3o3b5obo8bo5bobobo$592b2o6bo4bob2obo
3bo2b2o$588b4obobob2ob2o2b2o2bobo4bo$560b3o25bo2bo3b2obo6bo2bobo4bo$
562bo26bo3b2o5bobob2o2b2o3bobo6b2o$561bo30bo3b2o3bobo6bob3o7b2o14b2o$
584b2ob3o2bo4bo4bob3o2b5o24bo$549b2o33bob2o2b3o4bo3b2ob2obobob2o26b3o$
548bobo41b2ob2ob2o2bo38bo$550bo19b2o21bo7b2o$569bobo19bobob2ob2obo9b4o
$571bo9bo8bob2obo3bo2bo3b2o2bo3bo$574b2o4bobo7bo5b2o2b3o3b2o2bo4bo8b2o
$574bo2bo2bobo8b5o2b2o11b3o$119b2obob2o43b2obob2o43b2obob2o43b2obob2o
43b2obob2o43b2obob2o43b2obob2o43b2obob2o99bob3o2b2o4b3o5bo2bo2b3o19b2o
8b2o$119bob2obobo42bob2obobo42bob2obobo42bob2obobo42bob2obobo42bob2obo
bo42bob2obobo42bob2obobo97b2o4b2o3bobo3b4ob2obobo3bobo2bo23bo$9b2o113b
o2bo46bo2bo46bo2bo46bo2bo46bo2bo46bo2bo46bo2bo46bo2bo69b3o27b3o2b4ob3o
4bo2bo2bobobo7bo9bobo7bobo$8bob3obo14bo90b2ob2ob2o42b2ob2ob2o42b2ob2ob
2o42b2ob2ob2o42b2ob2ob2o42b2ob2ob2o42b2ob2ob2o42b2ob2ob2o71bo24b3o3b2o
4bo5bo3bobo7b3o14bo8b2o$8bo4b2o12b3o91bobobo2b2o41bobobo2b2o41bobobo2b
2o41bobobo2b2o41bobobo2b2o41bobobo2b2o41bobobo2b2o41bobobo2b2o68bo25bo
4b2o3bo2bob4obo5bobobob3obo2bo9bo$7b2obobo13bo94bobob2o3bo40bobob2o3bo
40bobob2o3bo40bobob2o3bo40bobob2o3bo40bobob2o3bo40bobob2o3bo40bobob2o
3bo94bobobo2bobo2bo7bob4ob2obo4b2ob3o$10b2ob3o10b2o91b2obo4b3o39b2obo
4b3o39b2obo4b3o39b2obo4b3o39b2obo4b3o39b2obo4b3o39b2obo4b3o39b2obo4b3o
56b2o38b2o2b2o12b2obobo3bobo5bo4bo27b2o2bob2o$7b3o3b3o102bo3bobo2bo40b
o3bobo2bo40bo3bobo2bo40bo3bobo2bo40bo3bobo2bo40bo3bobo2bo40bo3bobo2bo
40bo3bobo2bo57bobo40bobo15bo3b2obo2bob9o23bo2bob4obobo$7bo2b2o3b2o5bo
96b3ob2o44b3ob4o42b3ob2o44b3ob4o42b3ob2o44b3ob4o42b3ob2o44b3ob4o60bo
19b2o19bobo11b3o6bo2bobobo31b4o5bo2bo$8bobo3b3o4bobo97bobob2o44bo3bo
45bobob2o44bo3bo45bobob2o44bo3bo45bobob2o44bo3bo80bobo20bo11bo2b2o3bob
o3bo5b2obo8bo10b2o9b3o4b3o6bobo$5b3o2b2o3b2o3bo2bo89b2o8bo39b2o8bob2o
36b2o8bo39b2o8bob2o36b2o8bo39b2o8bob2o36b2o8bo39b2o8bob2o81bo32b2o6b2o
10bob2o7b2o11bo2b7o2b2o6bobo2bob2o2bo$5bo2b2o3b3o5bo91bo8b2obo37bo8b2o
39bo8b2obo37bo8b2o39bo8b2obo37bo8b2o39bo8b2obo37bo8b2o146b3o2bo9bobo7b
o3bo4bob5o3b3o$6bo3b2ob3o5bo2bo89bo9b2o38bo10b2o37bo9b2o38bo10b2o37bo
9b2o38bo10b2o37bo9b2o38bo10b2o142b2ob4o10b2o3b2obob2o6bo6b2o$7b2obobo
11bo88b2o7b2obo37b2o7b2o39b2o7b2obo37b2o7b2o39b2o7b2obo37b2o7b2o39b2o
7b2obo37b2o7b2o144b2o3bobo4b2o8b5obob2o3b2ob2obobob4o$8bo4b2o7bo83b2ob
2o2bo7bobob2o29b2ob2o2bo7bobobo30b2ob2o2bo7bobob2o29b2ob2o2bo7bobobo
30b2ob2o2bo7bobob2o29b2ob2o2bo7bobobo30b2ob2o2bo7bobob2o29b2ob2o2bo7bo
bobo154b3o6b3o5bobobo4bob2o3bo2bo$8bob3obo8bo83bobo2b3o6bo35bobobobo7b
obo33bobo2b3o6bo35bobobobo7bobo33bobo2b3o6bo35bobobobo7bobo33bobo2b3o
6bo35bobobobo7bobo60b3o83bobo6bo2bo6bo4bobobo2bob2obo3bo2bobo$9b2o96bo
bo3b2o3b2obo3b2o30bobo2bo5b2obo2b2o31bobo3b2o3b2obo3b2o30bobo2bo5b2obo
2b2o31bobo3b2o3b2obo3b2o30bobo2bo5b2obo2b2o31bobo3b2o3b2obo3b2o30bobo
2bo5b2obo2b2o60bo78b2o4bo7bob2o7bo3bo2b2o6b3ob2ob3o$b2o102b2o2b2o6bo2b
ob2ob2o3b2o23b2o2b4ob2obo2bob4o4b2o23b2o2b2o6bo2bob2ob2o3b2o23b2o2b4ob
2obo2bob4o4b2o23b2o2b2o6bo2bob2ob2o3b2o23b2o2b4ob2obo2bob4o4b2o23b2o2b
2o6bo2bob2ob2o3b2o23b2o2b4ob2obo2bob4o4b2o53bo80bo5bo7b2o9b4o3b4obob2o
2b2obo2b3ob2o$2bo103bobo2b3o4bobobob2o3bobo24bobo3b2o4bobobo6bobo24bob
o2b3o4bobobob2o3bobo24bobo3b2o4bobobo6bobo24bobo2b3o4bobobob2o3bobo24b
obo3b2o4bobobo6bobo24bobo2b3o4bobobob2o3bobo24bobo3b2o4bobobo6bobo131b
3o30bo6bobo3b2o2bo3b2obo$2bobo100bo2b4obob4obobo2b2o2bo25bo2b2o6b3obob
o3bo2bo25bo2b4obob4obobo2b2o2bo25bo2b2o6b3obobo3bo2bo25bo2b4obob4obobo
2b2o2bo25bo2b2o6b3obobo3bo2bo25bo2b4obob4obobo2b2o2bo25bo2b2o6b3obobo
3bo2bo43b2o88bo32bo7b4ob2o2bo$3b2o101b2o3bo3bo4bob2o3bob2o25b2o3b5o4bo
b2o3bob2o25b2o3bo3bo4bob2o3bob2o25b2o3b5o4bob2o3bob2o25b2o3bo3bo4bob2o
3bob2o25b2o3b5o4bob2o3bob2o25b2o3bo3bo4bob2o3bob2o25b2o3b5o4bob2o3bob
2o41bobo127b2o7bo$13bo93bob2o6b2obo3b4o2bo26bob2ob4ob2obo3bob2o2bo26bo
b2o6b2obo3b4o2bo26bob2ob4ob2obo3bob2o2bo26bob2o6b2obo3b4o2bo26bob2ob4o
b2obo3bob2o2bo26bob2o6b2obo3b4o2bo26bob2ob4ob2obo3bob2o2bo43bo19b2o
107bob2ob2obobo$11b2o94bo2bobo2bobobob2o2bo2bo28bo2bo6bobob2o5bo28bo2b
obo2bobobob2o2bo2bo28bo2bo6bobob2o5bo28bo2bobo2bobobob2o2bo2bo28bo2bo
6bobob2o5bo28bo2bobo2bobobob2o2bo2bo28bo2bo6bobob2o5bo64bobo97b2o2b2o
3bo2bo3bob2obo8bo$7b2o3b2o92b2obo2b4o3bo2bobob2o28b2obo2bo2bo3bo2b2ob
3o28b2obo2b4o3bo2bobob2o28b2obo2bo2bo3bo2b2ob3o28b2obo2b4o3bo2bobob2o
28b2obo2bo2bo3bo2b2ob3o28b2obo2b4o3bo2bobob2o28b2obo2bo2bo3bo2b2ob3o
67bo97b2o2b2o3b3o2b2o5bo7bobo4b2o$6bo2bo97bob2o2bobobo2bo36bob5obobo2b
o36bob2o2bobobo2bo36bob5obobo2bo36bob2o2bobobo2bo36bob5obobo2bo36bob2o
2bobobo2bo36bob5obobo2bo184b2o2b5o8bobo2bo2bo$7bobo96bo10b2ob5o5b2o24b
o5b4ob2ob4o6b2o24bo10b2ob5o5b2o24bo5b4ob2ob4o6b2o24bo10b2ob5o5b2o24bo
5b4ob2ob4o6b2o24bo10b2ob5o5b2o24bo5b4ob2ob4o6b2o137b2o9b3o17b3o2bo2bo
5b3o4b2o2b3obo$8bo26b3o67bob4o4bo3bo3bob2obo2bo23bob3obo3bo3bo5b4o2bo
23bob4o4bo3bo3bob2obo2bo23bob3obo3bo3bo5b4o2bo23bob4o4bo3bo3bob2obo2bo
23bob3obo3bo3bo5b4o2bo23bob4o4bo3bo3bob2obo2bo23bob3obo3bo3bo5b4o2bo
138bo25b2obobobobob2ob4o3bobo3b2o4b2o$35bo69bo3bob2obob2obo2b2o4b3o24b
o3bobob2ob2obo2bo3bob3o24bo3bob2obob2obo2b2o4b3o24bo3bobob2ob2obo2bo3b
ob3o24bo3bob2obob2obo2b2o4b3o24bo3bobob2ob2obo2bo3bob3o24bo3bob2obob2o
bo2b2o4b3o24bo3bobob2ob2obo2bo3bob3o139bobo7b2o3bo7b5obo2bo2bobo2bo2bo
b3ob2obo2b3o$36bo66b3o5bo2bobob2obo3b2o26b3o10bob2obobo2bo26b3o5bo2bob
ob2obo3b2o26b3o10bob2obobo2bo26b3o5bo2bobob2obo3b2o26b3o10bob2obobo2bo
26b3o5bo2bobob2obo3b2o26b3o10bob2obobo2bo44b3o97b2o10b2o7b3obo12bo3b2o
7b2o3b4o$7bo94bo7b2o9bo5b2o23bo7b2obo7b2o3b3o23bo7b2o9bo5b2o23bo7b2obo
7b2o3b3o23bo7b2o9bo5b2o23bo7b2obo7b2o3b3o23bo7b2o9bo5b2o23bo7b2obo7b2o
3b3o44bo101b3o6bo6bob2o4bo4bo2bo5b2obobob3o2b2o3bo$102b2o4b2obo2bo6bo
3bo3bo22b2o9bo7bo7bo22b2o4b2obo2bo6bo3bo3bo22b2o9bo7bo7bo22b2o4b2obo2b
o6bo3bo3bo22b2o9bo7bo7bo22b2o4b2obo2bo6bo3bo3bo22b2o9bo7bo7bo42bo102b
4o10b3o4b2obob4o2bobobo6bobobo2bobobo$3b2o5b2o92bo3b2obo10b2o2b2o2bo
23bo2bob2o2bo8b2ob3o2bo23bo3b2obo10b2o2b2o2bo23bo2bob2o2bo8b2ob3o2bo
23bo3b2obo10b2o2b2o2bo23bo2bob2o2bo8b2ob3o2bo23bo3b2obo10b2o2b2o2bo23b
o2bob2o2bo8b2ob3o2bo122b2obo2b2o13bo2bob2o7bo4bo5bobo2bo2bob2o12b2o2b
2o$b2o4bo4b2o6bo81b2o2bobobob2o4b2o4bo2b3o22b2o2bo2bob3o4b2o8b2o22b2o
2bobobob2o4b2o4bo2b3o22b2o2bo2bob3o4b2o8b2o22b2o2bobobob2o4b2o4bo2b3o
22b2o2bo2bob3o4b2o8b2o22b2o2bobobob2o4b2o4bo2b3o22b2o2bo2bob3o4b2o8b2o
30b2o90bobob4obo2bo9bob2ob2o7b9obo2bob2o3bo15bobo$5b2ob2o8bobo82bob2ob
obo7b2o6bo26bob2obobobo5b2o2b2o2bo26bob2obobo7b2o6bo26bob2obobobo5b2o
2b2o2bo26bob2obobo7b2o6bo26bob2obobobo5b2o2b2o2bo26bob2obobo7b2o6bo26b
ob2obobobo5b2o2b2o2bo32bobo90bo2bo5b4o9bo4bo16bobobo2bo6b3o11bobo$bobo
7bobo5b2o82bobo2b7o8b3o2b2o23bobo2b2obo2b2o6b3obob2o23bobo2b7o8b3o2b2o
23bobo2b2obo2b2o6b3obob2o23bobo2b7o8b3o2b2o23bobo2b2obo2b2o6b3obob2o
23bobo2b7o8b3o2b2o23bobo2b2obo2b2o6b3obob2o31bo19b2o58bobo6b3o4b3o9b2o
5bo2bo10bob2o5bo3bobo3b2o2bo11bo$bo2bobobobo2bo88b2obobo5b2o9bobobo23b
2obobo15bo4bo23b2obobo5b2o9bobobo23b2obobo15bo4bo23b2obobo5b2o9bobobo
23b2obobo15bo4bo23b2obobo5b2o9bobobo23b2obobo15bo4bo51bobo55bo2b2obo2b
obo6b2o2b7o2bo6b3o11b2obo10b2o6b2o$5obobob5o87bo3bob4o6b2o5b2obo23bo3b
ob2ob3o4b2o3b3o2bo23bo3bob4o6b2o5b2obo23bo3bob2ob3o4b2o3b3o2bo23bo3bob
4o6b2o5b2obo23bo3bob2ob3o4b2o3b3o2bo23bo3bob4o6b2o5b2obo23bo3bob2ob3o
4b2o3b3o2bo53bo55b3o3b5obo8bo2bo4bobo$o4bo3bo4bo88b2obo2bobo6b2o5b2obo
b2o21b2obo2bo3bo4b2o3b3ob2ob2o21b2obo2bobo6b2o5b2obob2o21b2obo2bo3bo4b
2o3b3ob2ob2o21b2obo2bobo6b2o5b2obob2o21b2obo2bo3bo4b2o3b3ob2ob2o21b2ob
o2bobo6b2o5b2obob2o21b2obo2bo3bo4b2o3b3ob2ob2o110b2o6bo3bob3obo2b2o2b
2o$b3obobobob3o90bob2o3bo13bo2bobo23bobob2o3bo10bo3bobo23bob2o3bo13bo
2bobo23bobob2o3bo10bo3bobo23bob2o3bo13bo2bobo23bobob2o3bo10bo3bobo23bo
b2o3bo13bo2bobo23bobob2o3bo10bo3bobo107b4obobob2ob2obo6b2o$3bob2obo2bo
36b3o53bobo4bo2bo10b2obo2bo7b2o13bobob3o2bo11b2obo2bo7b2o13bobo4bo2bo
10b2obo2bo7b2o13bobob3o2bo11b2obo2bo7b2o13bobo4bo2bo10b2obo2bo7b2o13bo
bob3o2bo11b2obo2bo7b2o13bobo4bo2bo10b2obo2bo7b2o13bobob3o2bo11b2obo2bo
106bo2bo3b2obobo5bobo4bo$8bobo37bo54b2obob2o3bo12bobob2o7bo13b2obo2b2o
bo13bobob2o7bo13b2obob2o3bo12bobob2o7bo13b2obo2b2obo13bobob2o7bo13b2ob
ob2o3bo12bobob2o7bo13b2obo2b2obo13bobob2o7bo13b2obob2o3bo12bobob2o7bo
13b2obo2b2obo13bobob2o109bo2bo5b2ob3o2bob3ob3o5b2o$8b2o39bo56bob4o14bo
bo8bobo16bo3b2o14bobo8bobo16bob4o14bobo8bobo16bo3b2o14bobo8bobo16bob4o
14bobo8bobo16bo3b2o14bobo8bobo16bob4o14bobo8bobo16bo3b2o14bobo29b3o78b
2o3bob3o2bob2obobob5o7b2o14b2o$106bo2b2o16b2o8b2o17bo20b2o8b2o17bo2b2o
16b2o8b2o17bo20b2o8b2o17bo2b2o16b2o8b2o17bo20b2o8b2o17bo2b2o16b2o8b2o
17bo14b2o4b2o31bo73b2obo4b2o4bo2b2o2bo32bo$107b2o48b2o48b2o48b2o48b2o
48b2o13b2o33b2o12b3o33b2o12bobo35bo74bob2o2b3obo4bobo5b3o29b3o$108bo
49bo49bo49bo14b2o33bo13b3o33bo13bobo33bo12bo36bo12bo121b2ob3obo2bo8b2o
27bo$33bo62bo8b3o14bobo21bo8b3o15bo22bo8b3o15b3o20bo8b3o15bobo20bo8b3o
14bo23bo8b3o14bo23bo8b3o14bo23bo8b3o31bo7b2o94bo7b2o8bo2bo$31bobo62b3o
6bo17b2o21b3o6bo18b2o20b3o6bo17bo22b3o6bo17bo22b3o6bo17bo22b3o6bo40b3o
6bo40b3o6bo7bo23b3o6bobo92bobob2ob2obo13bo$32b2o65bo23bo25bo24bo24bo
10b3o12bo23bo49bo14bo34bo14b2o33bo13b4o32bo13bo2b2o18bo11bo19b2o61bo8b
ob2obo3bo2bo3b2o2bo4bo$82b2o14b2o10bobo35b2o10b3o8bo26b2o10b4o7bo26b2o
13b2o33b2o14b2o32b2o14bobo31b2o13bo2b2o30b2o12bo5bo17b2o29bobo54b2o4bo
bo7bo5b2o2b3o3b2o2bo3b2o$82bo27bo2bo8b2o35b2ob2o7bobo35b2o2b2o6bo42b2o
49b2o47bob2o46bo2b2o44bobo2b2o49bo54bo2bo2bobo8b5o2b2o10bo$74b2o3b2obo
27bo2bo7b2o36b2o2bo7bobo3b2o31b2obo49b2o50bo14b3o32b2o15bo31bo2bo45bo
3b2o15bo90bob3o2b2o4b3o5bo2bo2b3o6b2o11bo9b2o$74bo4bobo29b2o10bo3b2o
32b2o14b4o29b3o13bo3bo30b3o16b3o31bo50bo17b2o30b2o16b2o30b3o15b3o88b2o
4b2o3bobo3b4ob2obobobobo17b2o9bo$61b3o11b3obo46b2ob2o45bo4bo29bo16bo2b
2o28bo15bobobobo26bobo13b2obobob2o43b2o2b3o44bo4b2o46b2o2bo90b3o3b3ob
2o2bo2bo2bobobo3b5o15bo6bobo$61bo15bob2o45b2o2bo44b4o2bo46bo3bo25b4o
14b2obo3bo24bobo18bobo2bo23b2o18b2o5bo44b2o3b2o42bob2o3b2o86b3o3b2o7b
2o4bo2b2o5bo2bob3o9b3o7b2o$62bo63bo3bo44b2obob2o25b3o18bo3bo25b2o17bob
o2b2o13bobo30bob3o25bo16b3o4bo14b2o28b2o3b2o11bo3b2o23bo3b2o2bobo8b3o
76bo4b2o2b4obobo2bobob4o2bob2o6bo9bo$94b2o12bo17bob2o14bobo10b3o15b2o
21bo8b3o15b2o3b2o14b4o8b3o14bo5bo14bo3bo9bo15b2o17bobo2b2o24b2o2bo3bo
11bob4o23b2o7bo10b2ob2ob2o22bob2obo3b2o11bo77bobobo2bobobobobo2bo3bo4b
o2bob3o3b3o$82bo10b3ob2o7b3obo16bo16bobobo9bo18b3o16b2obo5b2o2bo16b4o
20bo8bobo13b2obo2bo14bo4bo8bo15bo4bo13bo2b2o2bo23bo5bo12b2obo3b2o22b2o
16bo7bo22bobo18bo79b2o2b2o12b2obo2bo2bobo10bo27b2o2bob2o$82b2o2b2o6b2o
b3o6bo2b4o23b2o11b2o4b2ob2o26b2o9bob2o4b2o21bo7b2o8bo4bo2bo2bo3bo12b2o
b2obo5b2o8bo4bo4bobo18bo8b2o10b2o2bo33b2o8bo2b2ob2o32b2o7bo6b2o20b3o
101bobo15bo3b2obo2bob9o23bo2bob4obobo$46bo34bobo2b2o5b3ob2o8b3o2bo10b
2o11b2o10bo7b3o2bobo9b2o11b2o11bo5b2o3b3o10b2o11b2o9b2obo4b6o12b2o11b
2o9bo3bo2b2o5bo11b2o3bo7b2o8b2o2bobo20b2o11b2o9b6o20b2o11b2o9b2o2b2o
20b2o103bobo11b3o6bo2bobobo31b4o5bo2bo$44bobo46b2o12bo3b2o11bo32bo4bo
11bo33bob3o11bo24bo6b2o2b2o12bo22bo2bo8bobo12bo34b3o12bo23bo10b2o13bo
22b2o2b2o9bo11bo104bo11bo2b2o3bobo3bo5b2obo7b3o9b2o9b3o4b3o6bobo$45b2o
61b3o10b3o6bo26b2o2bo9b3o6bo28bobo9b3o6bo40b3o6bo40b3o6bo40b3o6bo27b3o
10b3o6bo12bo19bo7b3o8b2o9b2o10b2o84b2o6b2o10bob2o7b3o10bo2b7o2b2o6bobo
2bob2o2bo$108b3o10bo8b3o25b2o11bo8b3o24bo2bo10bo8b3o28bo9bo8b3o26bo11b
o8b3o26bo11bo8b3o10bo14b3o10bo8b3o9bobo16b3o7bo11bo8bo2bo8bobo112bo5b
2o8bobo4bo2bo8bob5o3b3o$133bo25bo23bo24b3o22bo24b3o22bo24bo2bo21bo8b3o
13b2o23bo8b3o15bo22bo8bo2bo34b3o10b2o11bo111bo2bo3b2o9b2ob2o3bob5o3bo
6b2o$132b2o48b2o48b2o24b3o21b2o8b3o13bo23b2o8b3o13b2o22b2o7bo3bo13bo
22b2o11bo34bo137bobo3b3o4bo6b3o2b2obo2b2o2b2ob2obobob4o$112b2o17bo20b
2o8b2o17bo4bo15b2o8b2o17bo10b3o7b2o8b2o17bo4bo4bo3bo6b2o5bo3bo17bo9bo
3bo6b2o8b2o17bo4bo6b2o7b2o8b2o17bo13bo6b2o32bo131b2ob2o6b5o4b2o4bob3o
2bo2bobob2obobo2bo$74b3o35bobo16b2ob3o7bo6bobo8bobo16bo4bo5b3o6bobo8bo
bo16b2ob3o4bo2bo6bobo8bobo16bo4bo4b2ob2o5bobo7b2obo16b2ob3o8bo5bobo8bo
bo16bo4bo4b3o7bobo8bobo16b2ob3o4bo2bo6bobo2bo28bobo3b2o127b3o5b3ob2o5b
ob4obo2b5o6b3o$74bo8b2o29bo13b2obobo3bo4b2o7bobob2o7bo13b2obobo2b2o3bo
2bo6bobob2o7bo13b2obobo3bo2bo3bo6bobob2o7bo13b2obobo2b2o2bobo8bobob2o
7bo13b2obobo3bo3b2o8bobob2o7bo13b2obobo2b2o13bobob2o7bo13b2obobo3bo4bo
8bobobob3o25bobo3b2o122b2o4b2o6bo2b2o12bobo4bo3b2o3bo2bo$75bo7bobo28b
2o13bobo4b3o3bo2bo4b2obo2bo7b2o13bobobobobo2bo9b2obo2bo7b2o13bobo4b3o
11b2obo2bo7b2o13bobobobobo12b2obo2bo7b2o13bobo4b3o11b2obo2bo7b2o13bobo
bobobo12b2obo2bo7b2o13bobo4b3o11b2obobo3bob3o18b2obob2o127bo13b3o7bo4b
2obo7b2o3b2ob4ob2o$83bo45bobo5b3o2bo2bo2bo4bobo23bob2o3b2o2bo5bo2bo3bo
bo23bobo5b2ob2o6bo4bobo23bob2o3b2o11bo3bobo23bobo5b3o8bo4bobo23bob2o3b
2o11bo3bobo23bobo5b3o8bo4bo4bobo21b2obo127b3o15bo9bo3b2o3bob2o3bo6b2ob
2obo$69bo58b2obo6b2o2bo2bo5b3ob2o21b2obo2bob2o3bo4bo2bo3bob2o21b2obo6b
o5bo2bo3b3ob2o21b2obo2bob2o5b2o4bo3bob2o21b2obo6b2o3b2o6b3ob2o21b2obo
2bob2o5b2o4bo3bob2o21b2obo6b2o3b2o6b3obo30b5o14b2o106bo40bob3ob2o$69b
2o31b3o22bo3bob3ob2o4b2o2bo2b2obo23bo3bob2ob2o5b3o3bo3bo23bo3bob3ob2o
4b2o5b2obo23bo3bob2ob2o5bo5bo3bo23bo3bob3ob2o4b2o2bo2b2obo23bo3bob2ob
2o5b2o4bo3bo23bo3bob3ob2o4b2o2bo2b2obo2b2o2b4o27bo13bo146b2o7bo$59bo8b
obo31bo24b2obobo3bob2o13bo23b2obobo6bo8bo2bobo23b2obobo3bob2o4b2o7bo
23b2obobo6bo8bo2bobo23b2obobo3bob2o13bo23b2obobo6bo8bo2bobo23b2obobo3b
ob2o13bo2bo3b2ob2o23b3o12bobo147bob2ob2obobo$57bobo43bo24bobo2b4o12b2o
2b2o23bobo2bob3obo8b2obob2o23bobo2b4o6b2o4b2o2b2o23bobo2bob3obo8b2obob
2o23bobo2b4o12b2o2b2o23bobo2bob3obo8b2obob2o23bobo2b4o12b2o2b3o2bo2bo
13bo11bo9b2o4b2o138b2o2b2o3bo2bo3bob2obo8bo$58b2o15b2o51bob2obo5bo3b2o
2bob2o27bob2obo5bo3b2o3bo2bo26bob2obo5bo3b2o2bob2o27bob2obo5bo3b2o3bo
2bo26bob2obo5bo3b2o2bob2o27bob2obo5bo3b2o3bo2bo26bob2obo5bo3b2o2bob2o
6b2o6bo10bo10b4o6b3o143b2o2b2o3b3o2b2o5bo7bobo4b2o$72bo4bo49b2o2bo6bo
4b2o4b2o2b2o22b2o2bobobobo5b2o3bobo2b2o22b2o2bo6bo4b2o4b2o2b2o22b2o2bo
bobobo5b2o3bobo2b2o22b2o2bo6bo4b2o4b2o2b2o22b2o2bobobobo5b2o3bobo2b2o
22b2o2bo6bo4b2o4b2o2b5o5b2o9b3o8b2o3bo3b2o2bo156b2o2b5o8bobo2bo2bo$70b
2obobobo51bo3b4ob2o7bo3b2o2bo23bo6bobo8b6o2bo23bo3b4ob2o7bo3b2o2bo23bo
6bobo8b6o2bo23bo3b4ob2o7bo3b2o2bo23bo6bobo8b6o2bo23bo3b4ob2o7bo3b2o6b
2ob2o3bo16bo2b3o4b2o123b2o10b2o17b3o2bo2bo5b3o4b2o2b3obo$70b2o3bob2o
48b2o5bobob2o6bobobo3bo22b2o4bo2b2o8bo7bo22b2o5bobob2o6bobobo3bo22b2o
4bo2b2o8bo7bo22b2o5bobob2o6bobobo3bo22b2o4bo2b2o8bo7bo22b2o5bobob2o6bo
bobo3b2o3b4ob4o16b2obo132bo28bo3bobob2ob4o3bobo3b2o4b2o$71bob3o3bo47bo
9bo8bo4b3o23bo6bob2o2bo5b2o2bob2o23bo9bo8bo4b3o23bo6bob2o2bo5b2o2bob2o
23bo9bo8bo4b3o23bo6bob2o2bo5b2o2bob2o23bo9bo8bo4b3obo6bo5b2o17bo132bob
o11b2o10bo2bo3b3o4bo2bo2b2ob4o2b3o$63b2o6bo4b2o2bo6b3o38b3o5bob4ob2obo
bob2o26b3o7bo2bob2obo4bo26b3o5bob4ob2obobob2o26b3o7bo2bob2obo4bo26b3o
5bob4ob2obobob2o26b3o7bo2bob2obo4bo26b3o5bob4ob2obobob2o13b3o2bo16b2o
132b2o12bo9b2obo6bobobo2bo5bo3b2o3b4o$62bo2bo5b3obo2b3o6bo8b2o32bo3bo
2bobob2obo2bo5b3o24bo3bob4ob2obo2b2o4b3o24bo3bo2bobob2obo2bo5b3o24bo3b
ob4ob2obo2b2o4b3o24bo3bo2bobob2obo2bo5b3o24bo3bob4ob2obo2b2o4b3o24bo3b
o2bobob2obo2bo5b6ob2ob3obobo155bo7bobo5b4obo3bobobo3b2ob4ob4obo3b2o3bo
$62bobo6b2o3b2o10bo7bobo31bob3obo7bo3bob2obo2bo23bob5o3bo3bo5bob2o2bo
23bob3obo7bo3bob2obo2bo23bob5o3bo3bo5bob2o2bo23bob3obo7bo3bob2obo2bo
23bob5o3bo3bo5bob2o2bo23bob3obo7bo3bob2obo8b2o3bob2o153b2o3bo9b3ob3obo
bo2bobo2bobobob2obo4bo3bobobo$63bo7b3obo2bo17bo34bo8bob2ob3o3b2o2b2o
24bo7bo2b2ob6o4b2o24bo8bob2ob3o3b2o2b2o24bo7bo2b2ob6o4b2o24bo8bob2ob3o
3b2o2b2o24bo7bo2b2ob6o4b2o24bo8bob2ob3o3b2o3b5o4b3o27b2o106b2obo2b2o
13bo13bo9b2obo5bob2o12b2o2b2o$71bo4b3o53bob2o4bobo2bo3bobo30bob2ob2obo
bo2bo3b2o31bob2o4bobo2bo3bobo30bob2ob2obobo2bo3b2o31bob2o4bobo2bo3bobo
30bob2ob2obobo2bo3b2o31bob2o4bobo2bo3bobo3bo3bo2b2o5b2o25bo105bobob4ob
o2bo8b2ob3o9b9obo2bob2o3bo15bobo$58b2o11bob3o39b3o13b2obo2b3o4bo2b2o2b
2o28b2obo2bo2bo3bo2b2ob3o28b2obo2b3o4bo2b2o2b2o28b2obo2bo2bo3bo2b2ob3o
28b2obo2b3o4bo2b2o2b2o28b2obo2bo2bo3bo2b2ob3o28b2obo2b3o4bo2b2o2b2o2bo
b2o2b7obo23b3o106bo2bo5b4o9bo21bobobo2bo6b3o11bobo$59bo10b2o3bob2o36bo
16bo2bobo2bobobob2obo3bo28bo2bobo2bobobob2o5bo28bo2bobo2bobobob2obo3bo
28bo2bobo2bobobob2o5bo28bo2bobo2bobobob2obo3bo28bo2bobo2bobobob2o5bo
28bo2bobo2bobobob2obo3bobobo4bo4bo2bo22bo97bobo6b3o4b3o9b2o4bo3bo10bob
2o5bo3bobo3b2o2bo11bo$56b3o11b2obobobo38bo15bob2o4bob2obo5b2o2bo26bob
2o6b2obo3b2obo2bo26bob2o4bob2obo5b2o2bo26bob2o6b2obo3b2obo2bo26bob2o4b
ob2obo5b2o2bo26bob2o6b2obo3b2obo2bo26bob2o4bob2obo5b2obo3b2o3bo2bo2b2o
17bo21b2o76bo2b2obo2bobo6b2o2b7o2bo5bo2bo11b2obo10b2o6b2o$56bo15bo4bo
53b2o3bo8bob2obobob2o25b2o3b2ob2o4bob2o3bob2o25b2o3bo8bob2obobob2o25b
2o3b2ob2o4bob2o3bob2o25b2o3bo8bob2obobob2o25b2o3b2ob2o4bob2o3bob2o25b
2o3bo8bob2obobobob2o5b2o24bo20bobo75b3o3b5obo8bo5bobobo6b3o$75b2o53bo
2b2obo3b4obobo6bo25bo2b2o3bob4obobo2b2o2bo25bo2b2obo3b4obobo6bo25bo2b
2o3bob4obobo2b2o2bo25bo2b2obo3b4obobo6bo25bo2b2o3bob4obobo2b2o2bo25bo
2b2obo3b4obobo7bo2b2o2b3obo20b3o20bo81b2o6bo4bob2obo3bo2b2o$131bobo3b
4o2bobobob2o3bobo24bobo4b2o3bobobo6bobo24bobo3b4o2bobobob2o3bobo24bobo
4b2o3bobobo6bobo24bobo3b4o2bobobob2o3bobo24bobo4b2o3bobobo6bobo24bobo
3b4o2bobobob2o5bobob3o4bo63b2o55b4obobob2ob2o2b2o2bobo4bo$130b2o2b2o3b
o2bo2bobo2bo4b2o23b2o2b3o2bo2bo2bob2o6b2o23b2o2b2o3bo2bo2bobo2bo4b2o
23b2o2b3o2bo2bo2bob2o6b2o23b2o2b2o3bo2bo2bobo2bo4b2o23b2o2b3o2bo2bo2bo
b2o6b2o23b2o2b2o3bo2bo2bobo2bo4b2ob2o6b2o62bobo55bo2bo3b2obo6bo2bobo4b
o$132bobo4bo3b2obo3bo31bobo2bobo3b2obo2b3o30bobo4bo3b2obo3bo31bobo2bob
o3b2obo2b3o30bobo4bo3b2obo3bo31bobo2bobo3b2obo2b3o30bobo4bo3b2obo3bo7b
ob4o4b2o59bo2bob2obo51bo3b2o5bobob2o2b2o3bobo6b2o$100b3o29bobobobo7bob
obo31bobo2bo8bo2bo32bobobobo7bobobo31bobo2bo8bo2bo32bobobobo7bobobo31b
obo2bo8bo2bo32bobobobo7bobobo4b3o2b2ob4o3bo56b3obobobob3o52bo3b2o3bobo
6bob3o7b2o14b2o$100bo8b2o20b2ob2o2bo7bobo32b2ob2o10bobob2o29b2ob2o2bo
7bobo32b2ob2o10bobob2o29b2ob2o2bo7bobo32b2ob2o10bobob2o29b2ob2o2bo7bob
o5bo3b3obo3bob2o56bo4bo3bo4bo43b2ob3o2bo4bo4bob3o2b5o24bo$101bo7bobo
26b2o7b2ob2o36b2o7b2o39b2o7b2ob2o36b2o7b2o39b2o7b2ob2o36b2o7b2o39b2o7b
2ob2o3bobo4bob2o2bo57b5obobob5o43bob2o2b3o4bo3b2ob2obobo29b3o$109bo29b
o9bo39bo10b2o37bo9bo39bo10b2o37bo9bo39bo10b2o37bo9bo4b2obo2bo4bobo2bo
56bo2bobobobo2bo52b2ob2ob2o2bo9bobo26bo$138bo8b2o39bo8b2obo37bo8b2o39b
o8b2obo37bo8b2o39bo8b2obo38bobo5b2o8bobobobobo2b3o56bobo7bobo53bo7b2o
9bo2bo$128b3o7b2o8bob2o36b2o8bob2o36b2o8bob2o36b2o8bob2o36b2o8bob2o36b
2o8bob2o38bobo5bob2o5bo7bo65b2ob2o55bobob2ob2obo14bo$128bo17bobo47bobo
bo45bobo47bobobo45bobo47bobobo40bobo2bobo9bob2o2b2obob2o56b2o4bo4b2o
41bo8bob2obo3bo2bo3b3obo5bo$129bo14b3obo2bo42b3o4bo42b3obo2bo42b3o4bo
42b3obo2bo42b3o4bo41b4obo2bo4bobobobo2bob2obo30bo21b2o4b2o5b2o36b2o4bo
bo7bo5b2o2b3o3b6o2b3o$143bo3bobo2bo40bo3bobo2bo40bo3bobo2bo40bo3bobo2b
o40bo3bobo2bo40bo3bobo2bo39bo4bobo2bob3obo4bobo36bo20bobo48bo2bo2bobo
8b5o2b2o9bo$144b2obob2ob3o39b2obob2ob3o39b2obob2ob3o39b2obob2ob3o39b2o
bob2ob3o39b2obob2ob3o38b3obob2ob2o4bo2bobobo34b3o20bo9bo41bob3o2b2o4b
3o5bo2bo2b3o18bobo8b2o$146bobob2o3bo40bobob2o3bo40bobob2o3bo40bobob2o
3bo40bobob2o3bo40bobob2o3bo39b2obob2o3b2ob5obo109b2o4b2o3bobo3b4ob2obo
bo3bobo3bo10bo2bo8bo$146bobo4b2o41bobo4b2o41bobo4b2o41bobo4b2o41bobo4b
2o41bobo4b2o43bo4b2obo7bobo110b3o2b4ob3o4bo2bo2bobobo7bo9bo2bo6bobo$
145b2obo2b2o42b2obo2b2o42b2obo2b2o42b2obo2b2o42b2obo2b2o42b2obo2b2o45b
o2b2o4b2obobob2obo64bo41b3o3b2o4bo5bo3bobo7b3o12bo3bo6b2o$113b3o33bo2b
o46bo2bo46bo2bo46bo2bo46bo2bo46bo2bo46bo2bob2obob2ob2o3bo63bobo40bo4b
2o3bo2bob4obo5bobobob3obo2bo8bobo$113bo8b2o20bob2obobo42bob2obobo42bob
2obobo42bob2obobo42bob2obobo42bob2obobo45bobobo2bo2bo3bo3b2o64bo2bo40b
obobo2bobo2bo7bob4ob2obo4b2ob3o7bo$114bo7bobo19b2obob2o43b2obob2o43b2o
bob2o43b2obob2o43b2obob2o43b2obob2o45bobobo3bob2obobob2o67b2o42b2o2b2o
12b2obobo3bobo5bo4bo27b2o2bob2o$122bo323bo2bo5bo2b3obo2bobo110bobo15bo
3b2obo2bob9o23bo2bob4obobo$447b2o7bo3bobobob2o110bobo11b3o6bo2bobobo
14bo16b4o5bo2bo$141b3o313b2o3bobo59b2o10b2o41bo11bo2b2o3bobo3bo5b2obo
7bo11b2o9b3o4b3o6bobo$141bo316bo3bo2b3o57b2o9bobo52b2o6b2o10bob2o6b2o
12bo2b7o2b2o6bobo2bob2o2bo$142bo313bo5bo4bo46bo9bo13bo82b3o11bobo7bo3b
o4bob5o3b3o$456b6o53bo22b2o77b2o3bo2b3o8b2o3b2obob2o6bo6b2o$513b3o14b
2o85b2o3bob4o12b5obob2o3b2ob2obobob4o$458bob2o64bob3obo84b2o2b2o2bobo
11b3o5bobobo4bob2o3bo2bo$458b2obo64b2o4bo86bobob2o2b3o9bo4bobobo2bob2o
bo3bo2bobo$528bobob2o81b2o12bo10bo3bo2b2o6b3ob2ob3o$126b3o396b3ob2o3bo
81bo12b2obo8b4o3b4obob2o2b2obo2b3ob2o$126bo8b2o381b2o5b3o3b2o2bo77b3o
14b3o13bo6bobo3b2o2bo3b2obo$127bo7bobo379bo2bo3b2o3b2o2b3o77bo17bo14bo
7b4ob2o2bo$135bo381bobo4b3o3bobo119b2o7bo$518bo5b2o3b2o2bo119bob2ob2ob
obo$154b3o368b3o3b3o109b2o2b2o3bo2bo3bob2obo8bo$154bo358b2o10b3ob2o
112b2o2b2o3b3o2b2o5bo7bobo4b2o$155bo358bo13bobob2o121b2o2b5o8bobo2bo2b
o$511b3o12b2o4bo86b2o29b3o2bo2bo5b3o4b2o2b3obo$511bo14bob3obo87bo25b2o
bobobobob2ob4o3bobo3b2o4b2o$530b2o88bobo11b3o6b5obo2bo2bobo2bo2bob3ob
2obo2b3o$621b3o12bo5b3obo12bo3b2o7b2o3b4o$623b3o9bo5bob2o4bo4bo2bo5b2o
bobob3o2b2o3bo$139b3o482bo2bo11b3o4b2obob4o2bobobo6bobobo2bobobo$139bo
8b2o453b2obo2b2o12bo2b3o9bo4bo5bobo2bo2bob2o12b2o2b2o$140bo7bobo451bob
ob4obo2bo8b2o13b9obo2bob2o3bo15bobo$148bo453bo2bo5b4o11b3o17bobobo2bo
6b3o11bobo$591bobo6b3o4b3o9b2o2bo5bo10bob2o5bo3bobo3b2o2bo11bo$167b3o
418bo2b2obo2bobo6b2o2b7o2bo4b2o2b2o10b2obo10b2o6b2o$167bo420b3o3b5obo
8bo2bo4bobo6bo2bo$168bo423b2o6bo3bob3obo2b2o2b2o7b3o$588b4obobob2ob2ob
o6b2o$588bo2bo3b2obobo5bobo4bo$238b2o351bo2bo5b2ob3o2bob3ob3o5b2o$237b
ob3obo14bo330b2o3bob3o2bob2obobob5o7b2o14b2o$237bobo3bo12b3o325b2obo4b
2o4bo2b2o2bo32bo$152b3o81b2obobo2bo10bo328bob2o2b3obo4bobo5b3o29b3o$
152bo8b2o76b2o3bo10b2o336b2ob3obo2bo10bo26bo$153bo7bobo72b3o3bo21b2o
327bo7b2o12b2o$161bo74bo2b2obo8bo11bobo325bobob2ob2obo12b2obo$237bo5bo
2bo3bobo9bo2bob2obo310bo8bob2obo3bo2bo3b2o2b2o5bo$180b3o51b3o2b2obo6bo
2bo7b3obobobob3o301b2o4bobo7bo5b2o2b3o3b2o3bo3bobo$180bo53bo2b2o3bo7b
2o7bo4bo3bo4bo300bo2bo2bobo8b5o2b2o15b2o$181bo53bo3b2o3bo14b2ob2ob3ob
2ob2o301bob3o2b2o4b3o5bo2bo2b3o18b3o8b2o$236b2obobo2bo15bo2bobobobo2bo
301b2o4b2o3bobo3b4ob2obobobobo15b2o3bo7bo$237bobo3bo16bobo7bobo304b3o
3b3ob2o2bo2bo2bobobo3b5o22bobo$237bob3obo17bob2o3b2obo302b3o3b2o7b2o4b
o2b2o5bo2bob3o13bo5b2o$238b2o16bo3b2ob2obob2ob2o301bo4b2o2b4obobo2bobo
b4o2bob2o6bo7bo3bo$245bo9b2o6b7o305bobobo2bobobobobo2bo3bo4bo2bob3o3b
3o6b3o$165b3o76bo10bobo7b3o308b2o2b2o12b2obo2bo2bobo10bo27b2o2bob2o$
165bo8b2o68b3o331bobo15bo3b2obo2bob9o23bo2bob4obobo$166bo7bobo401bobo
11b3o6bo2bobobo13bo17b4o5bo2bo$174bo404bo11bo2b2o3bobo3bo5b2obo7bo11b
2o9b3o4b3o6bobo$265bo325b2o6b2o10bob2o8bo11bo2b7o2b2o6bobo2bob2o2bo$
193b3o68bobo368bobo4bo2bo8bob5o3b3o$193bo70bo2bo349b2o4bo3bo8b2ob2o3bo
b5o3bo6b2o$194bo70b2o349bo2bobo16b3o2b2obo2b2o2b2ob2obobob4o$624b2ob2o
9b2o4bob3o2bo2bobob2obobo2bo$258b2o355bo2bo2b2o16bob4obo2b5o6b3o$257bo
bo9b2o344bo12bo17bobo4bo3b2o3bo2bo$259bo9bobo344bo23bo4b2obo7b2o3b2ob
4ob2o$232bo38bo341b3o13bo2b2o7bo3b2o3bob2o3bo6b2ob2obo$178b3o50bo39b2o
340bo16b3o21bob3ob2o$178bo8b2o42b3o397bo20b2o7bo$179bo7bobo463bob2ob2o
bobo$187bo455b2o2b2o3bo2bo3bob2obo8bo$643b2o2b2o3b3o2b2o5bo7bobo4b2o$
206b3o6bo439b2o2b5o8bobo2bo2bo$206bo8b3o401b2o29b3o2bo2bo5b3o4b2o2b3ob
o$207bo10bo401bo14b2o12bo3bobob2ob4o3bobo3b2o4b2o$217b2o401bobo11bobo
9bo2bo3b3o4bo2bo2b2ob4o2b3o$245b2o374b2o13bo8b2obo6bobobo2bo5bo3b2o3b
4o$244bobo394b4obo3bobobo3b2ob4ob4obo3b2o3bo$246bo377b2o2bo10b3ob3obob
o2bobo2bobobob2obo4bo3bobobo$219bo383b2obo2b2o12bobo2bo9bo9b2obo5bob2o
12b2o2b2o$191b3o24b3o381bobob4obo2bo7bo15b9obo2bob2o3bo15bobo$191bo8b
2o16b2o382bo2bo5b4o12b2o17bobobo2bo6b3o11bobo$192bo7bobo24b2o362bobo6b
3o4b3o9b2o5bo3bo9bob2o5bo3bobo3b2o2bo11bo$200bo6bo12b2o5bobo358bo2b2ob
o2bobo6b2o2b7o2bo4bo2b2obo9b2obo10b2o6b2o$206bobo11b2o7bo358b3o3b5obo
8bo5bobobo6bo3bo$206bobo20b2o361b2o6bo4bob2obo3bo2b2o7bobo$207bo3b2o
375b4obobob2ob2o2b2o2bobo4bo10b3o$211b2o3bo371bo2bo3b2obo6bo2bobo4bo$
215bobob2o368bo3b2o5bobob2o2b2o3bobo6b2o$191b2o22bobobobo10b2o358bo3b
2o3bobo6bob3o7b2o14b2o$192bo20bobobobobo2bo6bobo350b2ob3o2bo4bo4bob3o
2b5o24bo$192bobo4bo11b3obo2b2ob4o8bo350bob2o2b3o4bo3b2ob2obobob2o26b3o
$193b2o3b3o9bo4bo4bo371b2ob2ob2o2bo38bo$197bo3bo9b4o5bobo370bo7b2o11bo
bo$196b2o2b2o19b2o368bobob2ob2obo12bo2b2o$197b2o7b2o5b2o366bo8bob2obo
3bo2bo3b2o2b2o5b2o$198b2o6bobo4b2o359b2o4bobo7bo5b2o2b3o3b2o2b2o5b2o$
163b2o6b2o10bob2o12b2o7bo365bo2bo2bobo8b5o2b2o15b2o7b2o$151bo11bo2b2o
3bobo3bo5b2obo13b2o6b2o365bob3o2b2o4b3o5bo2bo2b3o17bo11b2o$150bobo11b
3o6bo2bobobo18bo374b2o4b2o3bobo3b4ob2obobo3bobo2bo11bo2bo8bo$150bobo
15bo3b2obo2bob9o12bo375b3o2b4ob3o4bo2bo2bobobo7bo10b2o7bobo$148b2o2b2o
12b2obo2bo2bobo5bo4bo12b2o371b3o3b2o4bo5bo3bobo7b3o14b2o7b2o$147bobobo
2bobobo6bobobo2b4obob2o4b3o12bo2bo15b2o353bo4b2o3bo2bob4obo5bobobob3ob
o2bo8bo2bo$146bo3b2o2b3obobob2o5bo2bo4bo4b2obo15b3o14bobo354bobobo2bob
o2bo7bob4ob2obo4b2ob3o9bo$146b4o3b2o7b2o3bo12bob3o18b3o14bo355b2o2b2o
12b2obobo3bobo5bo4bo5b3o19b2o2bob2o$149b3o2bob2ob3obo2bo2bobo2bo2bob5o
5bo14bobo371bobo15bo3b2obo2bob9o23bo2bob4obobo$146b2o4b2o3bobo3b4ob2ob
obobobob2o7bo17bo371bobo11b3o6bo2bobobo31b4o5bo2bo$147bob3o2b2o4b3o5bo
2bo2b3o11b3o15b2o371bo11bo2b2o3bobo3bo5b2obo19b2o9b3o4b3o6bobo$146bo2b
o2bobo8b5o2b2o52bobobob2o5bo2b2ob2o346b2o6b2o10bob2o20bo2b7o2b2o6bobo
2bob2o2bo$146b2o4bobo7bo5b2o2b3o3b2o2b2o11bo27bob2ob2obo4bobo2bobo391b
obo7bo3bo4bob5o3b3o$153bo8bob2obo3bo2bo3b2o2b2o10b3o26bo12bob2obo2bo
372b2o8bo8b2o3b2obob2o6bo6b2o$163bobob2ob2obo19bo2b2o23b2ob4ob2o3b2o4b
o2b2o4b2o2b2ob2o359b3obo5bo12b5obob2o3b2ob2obobob4o$165bo7b2o18bo3bo
24bobo2bobobobobob2o9bo2bo2bobo364bo4bo12b3o5bobobo4bob2o3bo2bo$163bo
2b2ob4o7bo14bobo21bo2bob2obobo7bob8o2bobobo2bo364bo17bo4bobobo2bob2obo
3bo2bobo$156bob2o3bo2b2o3bobo6bo36bo2bobo2bo3bo2b2o3bobo3bo3b3o2bob2o
359b2o23bo3bo2b2o6b3ob2ob3o$156b2ob3o2bob2o2b2obob4o3b4o6b2ob2o9b2o5bo
2b2o2b2o3b2ob2ob3o2b2o3bo3b2o3bobo363bo24b4o3b4obob2o2b2obo2b3ob2o$
162b3ob2ob3o6b2o2bo3bo7bo10bobo5bo2bo4b3o2bob3o2b2obob2o4bo2bob2o2b5o
355b3o15b3o12bo6bobo3b2o2bo3b2obo$161bobo2bo3bob2obo2bobobo4bo19bo5bo
2b3o3bo2bo3bo4bob2o3bobo2b2o3b2o5bob2o351bo15b2o2bo12bo7b4ob2o2bo$160b
o2bo3b2obo4bobobo5b3o26bob2o3b2o2bobo6bob3obo2b2o2bob2o2b2o3bobo369b3o
19b2o7bo$160b4obobob2ob2o3b2obob5o25b2o7b2o4b2o2bobobo2bo2bo5bo2bob2o
4bo2bo369bo21bob2ob2obobo$164b2o6bo6b2obob2o3b2o21bobo3b2o5bobobobob4o
bo4b5obo3bob2obob2o381b2o2b2o3bo2bo3bob2obo8bo$160b3o3b5obo4bo3bo7bobo
20bo3bo2b2o4bobob2obo4bob4o6b4o2bo2bo384b2o2b2o3b3o2b2o5bo7bobo4b2o$
160bo2b2obo2bobo6b2o2b7o2bo19bo4b2o2bo4bobo4bob2obo6b2ob2o3bobo2b2o
396b2o2b5o8bobo2bo2bo$163bobo6b3o4b3o9b2o19b2obo2bobob2obo2b3o2bobobob
2o4bobo2bo2bo365b2o29b3o2bo2bo5b3o4b2o2b3obo$174bo2bo5b4o31bobobo2bo5b
2o5bobo4bo2bob3o367bo14b3o8b2obobobobob2ob4o3bobo3b2o4b2o$174bobob4obo
2bo16bo6b9obo2bob2o3bo15bobo371bobo14bo5b5obo2bo2bobo2bo2bob3ob2obo2b
3o$175b2obo2b2o17b6o4bo4bo5bobo3bobob2o12b2o2b2o370b2o13bo5b3obo12bo3b
2o7b2o3b4o$200b2o2b2o5b3ob2o4bob2ob4obo7bo2bobo2bobobo389bob2o4bo4bo2b
o5b2obobob3o2b2o3bo$213bo2bob3obobobo5bob4obo2bo3b2o4bo371b2o13b3o4b2o
bob4o2bobobo6bobobo2bobobo$193b2o6bo16b3o7bobo3bo5bo4b2o3b2obo349b2obo
2b2o14b2o11bo4bo5bobo2bo2bob2o12b2o2b2o$192bobo6bo2b2o8bo7bobobo2bo2bo
4b3ob4o2b3o2bobo347bobob4obo2bo11b3o9b9obo2bob2o3bo15bobo$192bo7bo3b2o
10bo2bobo3bobob2ob4o3bobo3b2o4bo2bo347bo2bo5b4o11b3o17bobobo2bo6b3o11b
obo$191b2o8bo20b3o2bo2bo5b3o4b2o2bo4b2o337bobo6b3o4b3o9b2o4bo14bob2o5b
o3bobo3b2o2bo11bo$201bobo4b3o16b2o2b5o8bob2o340bo2b2obo2bobo6b2o2b7o2b
o20b2obo10b2o6b2o$202bo4bo3bo3b2o2b2o3b3o2b2o5bo7bobo341b3o3b5obo8bo2b
o4bobo4bo3bobo$206bo8b2o2b2o3bo2bo3bob2obo6b2obo345b2o6bo3bob3obo2b2o
2b2o9b2o$207b2o3bo12bob2ob2obobo6bo2bo342b4obobob2ob2obo6b2o13b2ob2o$
211bo12b2o7bo7bobo344bo2bo3b2obobo5bobo4bo13bo$185bo38bo2b2ob2ob2o7bo
348bo2bo5b2ob3o2bob3ob3o5b2o$185b3o26b2obobob2ob2o3bo4b3o2b3o347b2o3bo
b3o2bob2obobob5o7b2o14b2o$188bo24b5o2b3obo4bo4bo2b3o344b2obo4b2o4bo2b
2o2bo32bo$187b2o14b2o7b3obo6bobo3b2o3bo349bob2o2b3obo4bobo5b3o29b3o$
199bo3b2o6bobo3b2o2b2obobo5b2o3bo355b2ob3obo2bo37bo$198b3o10bo4bobo2bo
6bob2o3bo2bo354bo7b2o12bobo$197b2ob2o9bo4bobo2b2o2b2ob2obobob4o352bobo
b2ob2obo13bo2bo$197bo10b2o2bo3bob2obo4bo6b2o346bo8bob2obo3bo2bo3b2o2b
2o3b2ob2o$207bobobo5bo8bob5o3b3o335b2o4bobo7bo5b2o2b3o3b2o2b2o4bobo$
163b2o6b2o10bob2o12bo7bo2b7o2b2o6bobo2bob2o2bo335bo2bo2bobo8b5o2b2o17b
o6bo$151bo11bo2b2o3bobo3bo5b2obo12b2o5b2o9b3o4b3o6bobo339bob3o2b2o4b3o
5bo2bo2b3o18b3o8b2o$150bobo11b3o6bo2bobobo17bobo11b4o5bo2bo349b2o4b2o
3bobo3b4ob2obobobobo16bo11bo$150bobo15bo3b2obo2bob9o23bo2bob4obobo352b
3o3b3ob2o2bo2bo2bobobo3b5o11b2ob2o6bobo$148b2o2b2o12b2obo5bob2o9bo13bo
13b2o2bob2o350b3o3b2o7b2o4bo2b2o5bo2bob3o9b2ob2o5b2o$147bobobo3bo4bob
2obobobo2bobo2bobob3ob3o13b2o371bo4b2o2b4obobo2bobob4o2bob2o6bo8b2ob2o
$146bo3b2o3bob4ob4ob2o3bobobo3bob4o15bo373bobobo2bobobobobo2bo3bo4bo2b
ob3o3b3o6bo2bo$146b4o3b2o3bo5bo2bobobo6bob2o22b2o370b2o2b2o12b2obo2bo
2bobo10bo5b3o19b2o2bob2o$149b3o2b4ob2o2bo2bo4b3o3bo2bo8bo14bobo371bobo
15bo3b2obo2bob9o6b2o15bo2bob4obobo$146b2o4b2o3bobo3b4ob2obobo3bo11bobo
14bo371bobo11b3o6bo2bobobo31b4o5bo2bo$147bob3o2b2o4b3o5bo2bo2b3o12b2o
15b2o371bo11bo2b2o3bobo3bo5b2obo19b2o9b3o4b3o6bobo$146bo2bo2bobo8b5o2b
2o419b2o6b2o10bob2o20bo2b7o2b2o6bobo2bob2o2bo$146b2o4bobo7bo5b2o2b3o3b
2o2b2o451bobo4bo2bo8bob5o3b3o$153bo8bob2obo3bo2bo3b2o2b2o11bo423b2o15b
2ob2o3bob5o3bo6b2o$163bobob2ob2obo20b3o420bob3o16b3o2b2obo2b2o2b2ob2ob
obob4o$165bo7b2o18b2o2bo420b4o16b2o4bob3o2bo2bobob2obobo2bo$165b2ob3ob
o20bo3bo15bo425bob4obo2b5o6b3o$156bob2ob2o6bo3b2obo3b2o3bo7bob2o14b3o
401b2o29bobo4bo3b2o3bo2bo$156b2ob4ob2o3b2o7bob2o4bo6b2o15bo405bo15b2o
6bo4b2obo7b2o3b2ob4ob2o$161bo2bo3b2o3bo4bobo29b2o401b3o14b2obo7bo3b2o
3bob2o3bo6b2ob2obo$164b3o6b5o2bob4obo425bo15bo3bo20bob3ob2o$160bo2bobo
b2obobo2bo2b3obo4b2o16b4o420bo2b2o18b2o7bo$160b4obobob2ob2o2b2o2bob2o
2b3o16b3obo420b3o20bob2ob2obobo$164b2o6bo3b5obo3b2ob2o15b2o423bo11b2o
2b2o3bo2bo3bob2obo8bo$160b3o3b5obo8bo2bo4bobo451b2o2b2o3b3o2b2o5bo7bob
o4b2o$160bo2b2obo2bobo6b2o2b7o2bo20b2obo10b2o6b2o419b2o2b5o8bobo2bo2bo
$163bobo6b3o4b3o9b2o19bob2o5bo3bobo3b2o2bo11bo371b2o15b2o12b3o2bo2bo5b
3o4b2o2b3obo$174bo2bo5b4o31bobobo2bo6b3o11bobo371bo14bobo11bo3bobob2ob
4o3bobo3b2o4b2o$174bobob4obo2bo15b2o6b9obo2bob2o3bo15bobo371bobo14bo8b
o2bo3b3o4bo2bo2b2ob4o2b3o$175b2obo2b2o19b3o5bo10bobo2bo2bob2o12b2o2b2o
370b2o22b2obo6bobobo2bo5bo3b2o3b4o$201bo2bo6b3o3b3obo2bo4bo3bo2bobobob
obo2bobobo373bo15b4obo3bobobo3b2ob4ob4obo3b2o3bo$200b2ob2o8bo6b2obo2b
4obobo2bobob4o2b2o4bo371b2o13b3ob3obobo2bobo2bobobob2obo4bo3bobobo$
193b2o5b2ob2o9b3obo2bo5b2o2bo4b2o7b2o3b3o350b2obo2b2o13bo13bo9b2obo5bo
b2o12b2o2b2o$192bobo6b2ob2o11b5o3bobobo2bo2bo2b2ob3o3b3o352bobob4obo2b
o23b9obo2bob2o3bo15bobo$192bo11bo16bobobobob2ob4o3bobo3b2o4b2o349bo2bo
5b4o11bobo17bobobo2bo6b3o11bobo$191b2o8b3o18b3o2bo2bo5b3o4b2o2b3obo
339bobo6b3o4b3o9b2o5b2o12bob2o5bo3bobo3b2o2bo11bo$202bo6bo17b2o2b5o8bo
bo2bo2bo335bo2b2obo2bobo6b2o2b7o2bo7bo12b2obo10b2o6b2o$208bobo4b2o2b2o
3b3o2b2o5bo7bobo4b2o335b3o3b5obo8bo5bobobo$207b2ob2o3b2o2b2o3bo2bo3bob
2obo8bo346b2o6bo4bob2obo3bo2b2o10bo$208bo2bo13bob2ob2obobo352b4obobob
2ob2o2b2o2bobo4bo9b2ob2o$209bobo12b2o7bo354bo2bo3b2obo6bo2bobo4bo10b3o
$185bo37bo2bob3ob2o355bo3b2o5bobob2o2b2o3bobo6b2o3bo$185b3o29b3o5bobo
4bob3o2b2obo349bo3b2o3bobo6bob3o7b2o14b2o$188bo32bo2b2o2bo4b2o4bob2o
344b3o2bo4bo4bob3o2b5o24bo$187b2o14b2o7b5obobob2obo2b3obo3b2o347b3o2b
3o4bo3b2ob2obobob2o26b3o$203b2o5b3ob3obo2b3ob2o5bo2bo348bo7b2ob2ob2o2b
o38bo$199bo13bo4bobo5bobob2o3bo2bo344bobo7bo7b2o12bo$197b2ob2o13b2o6bo
b2ob2obobob4o342bo2bo6bobob2ob2obo12bo3b2o$197b2o9b2o2b2o2bob3obo3bo6b
2o345bob2o6bob2obo3bo2bo3b2o2b2o8bo$196bobo3bo4bobo4bo2bo8bob5o3b3o
341bobo7bo5b2o2b3o3b2o2b2o3bo3bo4bo$163b2o6b2o10bob2o20bo2b7o2b2o6bobo
2bob2o2bo340b2obo8b5o2b2o16b3o4bobo$151bo11bo2b2o3bobo3bo5b2obo14bo4b
2o9b3o4b3o6bobo337b2o4bo2b2o4b3o5bo2bo2b3o20bo8b2o$150bobo11b3o6bo2bob
obo17b3o11b4o5bo2bo347bo2bo4b2o3bobo3b4ob2obobo3bobo2bo10b2o3bo7bo$
150bobo15bo3b2obo2bob9o9b3o11bo2bob4obobo347bobo2b3o2b4ob3o4bo2bo2bobo
bo7bo8b2o2bo6bobo$148b2o2b2o12b2obo2bo2bobo5bo4bo11b2o14b2o2bob2o349bo
b2o3b2o4bo5bo3bobo7b3o16bo6b2o$147bobobo2bobobo6bobobo2b4obob2o4b3o13b
2o371bo4b2o3bo2bob4obo5bobobob3obo2bo$146bo3b2o2b3obobob2o5bo2bo4bo4b
2obo389bobobo2bobo2bo7bob4ob2obo4b2ob3o5b2o2b2o$146b4o3b2o7b2o3bo12bob
3o5bo13b2o370b2o2b2o12b2obobo3bobo5bo4bo4b6o17b2o2bob2o$149b3o2bob2ob
3obo2bo2bobo2bo2bob5o5bo14bobo371bobo15bo3b2obo2bob9o6bo16bo2bob4obobo
$146b2o4b2o3bobo3b4ob2obobobobob2o8b3o14bo367b3obo2bo4bobo5b2o5bo2bobo
bo31b4o5bo2bo$147bob3o2b2o4b3o5bo2bo2b3o29b2o365bo2bo2bobo4b2obobobo2b
3o2bob2obobo2bob2o19b2o9b3o4b3o6bobo$146bo2bo2bobo8b5o2b2o396b2o2bobo
3b2ob2o6bob2obo4bobo4bo2b2o4bo19bo2b7o2b2o6bobo2bob2o2bo$146b2o4bobo7b
o5b2o2b3o3b2o2b2o384bo2bo2b4o6b4obo4bob2obobo4b2o2bo3bo20bobo7bo3bo4bo
b5o3b3o$153bo8bob2obo3bo2bo3b2o2b2o381b2obob2obo3bob5o4bob4obobobobo5b
2o3bobo21b2o3b2obob2o6bo6b2o$163bobob2ob2obo21bo369bo2bo4b2obo2bo5bo2b
o2bobobo2b2o4b2o7b2o25b5obob2o3b2ob2obobob4o$165bo7b2o19b3o369bobo3b2o
2b2obo2b2o2bob3obo6bobo2b2o3b2obo26b3o5bobobo4bob2o3bo2bo$163bo2b2ob4o
7bo12bo2b2o15bo351b2obo5b2o3b2o2bobo3b2obo4bo3bo2bo3b3o2bo5bo19bo4bobo
bo2bob2obo3bo2bobo$156bob2o3bo2b2o3bobo6bo12b3o15b3o355b5o2b2obo2bo4b
2obob2o2b3obo2b3o4bo2bo5bobo10bo7bo3bo2b2o6b3ob2ob3o$156b2ob3o2bob2o2b
2obob4o3b4o24bo363bobo3b2o3bo3b2o2b3ob2ob2o3b2o2b2o2bo5b2o9b2ob2o6b4o
3b4obob2o2b2obo2b3ob2o$162b3ob2ob3o6b2o2bo3bo23b2o359b2obo2b3o3bo3bobo
3b2o2bo3bo2bobo2bo36bo6bobo3b2o2bo3b2obo$161bobo2bo3bob2obo2bobobo4bo
17bo364bo2bobobo2b8obo7bobob2obo2bo21bobo14bo7b4ob2o2bo$160bo2bo3b2obo
4bobobo5b3o12bo4bo364bobo2bo2bo9b2obobobobobo2bobo24bo3bo18b2o7bo$160b
4obobob2ob2o3b2obob5o12bo5bob3o359b2ob2o2b2o4b2o2bo4b2o3b2ob4ob2o23b2o
2bo19bob2ob2obobo$164b2o6bo6b2obob2o3b2o8bo8b2o372bo2bob2obo12bo26b3o
10b2o2b2o3bo2bo3bob2obo8bo$160b3o3b5obo4bo3bo7bobo391bobo2bobo4bob2ob
2obo27bo11b2o2b2o3b3o2b2o5bo7bobo4b2o$160bo2b2obo2bobo6b2o2b7o2bo20b2o
bo10b2o6b2o346b2ob2o2bo5b2obobobo52b2o2b5o8bobo2bo2bo$163bobo6b3o4b3o
9b2o19bob2o5bo3bobo3b2o2bo11bo371b2o15b3o11b3o2bo2bo5b3o4b2o2b3obo$
174bo2bo5b4o31bobobo2bo6b3o11bobo371bo17bo7b2obobobobob2ob4o3bobo3b2o
4b2o$174bobob4obo2bo23b9obo2bob2o3bo15bobo371bobo14bo5b5obo2bo2bobo2bo
2bob3ob2obo2b3o$175b2obo2b2o19b3o5bo4bo5bobo3bobob2o12b2o2b2o355bo14b
3o18b3obo12bo3b2o7b2o3b4o$201bo9b3ob2o4bob2ob4obo7bo2bobo2bobobo354bob
o14b3o15bob2o4bo4bo2bo5b2obobob3o2b2o3bo$201bo2bo8bo2bob3obobobo5bob4o
bo2bo3b2o4bo353b2o15bo2bo12b3o4b2obob4o2bobobo6bobobo2bobobo$193b2o7b
2o14b3o7bobo3bo5bo4b2o3b3o371b2o12bo4bo5bobo2bo2bob2o12b2o2b2o$192bobo
7b2o10bo7bobobo2bo2bo4b3ob4o2b3o375bo12b9obo2bob2o3bo15bobo$192bo8bo2b
o11bo2bobo3bobob2ob4o3bobo3b2o4b2o374bo18bobobo2bo6b3o11bobo$191b2o11b
o17b3o2bo2bo5b3o4b2o2b3obo365b2o6b2o13bob2o5bo3bobo3b2o2bo11bo$201b2o
7b2o15b2o2b5o8bobo2bo2bo365bo7b2o12b2obo10b2o6b2o$208b2o5b2o2b2o3b3o2b
2o5bo7bobo4b2o359b2o4bobo6b2o$208b2o5b2o2b2o3bo2bo3bob2obo8bo366b2o5b
2o7b2o$208b2o2bo12bob2ob2obobo368b2o19b2o2b2o$210bobo11b2o7bo370bobo5b
4o9bo3bo$185bo38bo2b2ob2ob2o371bo4bo4bo9b3o3b2o$185b3o26b2obobob2ob2o
3bo4b3o2b2obo350bo8b4ob2o2bob3o11bo4bobo$188bo24b5o2b3obo4bo4bo2b3ob2o
350bobo6bo2bobobobobo20bo$187b2o14b2o7b3obo6bobo3b2o3bo358b2o10bobobob
o22b2o$203b2o6bobo3b2o2b2obobo5b2o3bo368b2obobo$211bo4bobo2bo6bob2o3bo
2bo371bo3b2o$198b3o10bo4bobo2b2o2b2ob2obobob4o375b2o3bo$198bobo7b2o2bo
3bob2obo4bo6b2o361b2o20bobo$196bo3bo6bobobo5bo8bob5o3b3o358bo7b2o11bob
o$163b2o6b2o10bob2o9bob2o2bo4bo2b7o2b2o6bobo2bob2o2bo358bobo5b2o12bo6b
o$151bo11bo2b2o3bobo3bo5b2obo9bo3bo5b2o9b3o4b3o6bobo362b2o24bobo7bo$
150bobo11b3o6bo2bobobo17b2o12b4o5bo2bo382b2o16b2o8bo$150bobo15bo3b2obo
2bob9o15bo7bo2bob4obobo381b3o24b3o$148b2o2b2o12b2obo5bob2o9bo9bo2bobo
12b2o2bob2o383bo$147bobobo3bo4bob2obobobo2bobo2bobob3ob3o10bo2b2o377bo
$146bo3b2o3bob4ob4ob2o3bobobo3bob4o394bobo$146b4o3b2o3bo5bo2bobobo6bob
2o8bo13b2o374b2o$149b3o2b4ob2o2bo2bo4b3o3bo2bo9bobo11bobo401b2o$146b2o
4b2o3bobo3b4ob2obobo3bo12b2o14bo401bo10bo$147bob3o2b2o4b3o5bo2bo2b3o
29b2o401b3o8bo$146bo2bo2bobo8b5o2b2o439bo6b3o$146b2o4bobo7bo5b2o2b3o3b
2o2b2o$153bo8bob2obo3bo2bo3b2o2b2o455bo$163bobob2ob2obo463bobo7bo$165b
o7b2o20bo397b3o42b2o8bo$165b2ob3obo21b3o16bo340b2o39bo50b3o$156bob2ob
2o6bo3b2obo3b2o3bo7b2o2bo13b3o341bo38bo$156b2ob4ob2o3b2o7bob2o4bo23bo
344bobo9bo$161bo2bo3b2o3bo4bobo17bo12bo344b2o9bobo$164b3o6b5o2bob4obo
16b2o2bo2bo355b2o$160bo2bobob2obobo2bo2b3obo4b2o9b2ob2o$160b4obobob2ob
2o2b2o2bob2o2b3o16bobo2bo349b2o70bo$164b2o6bo3b5obo3b2ob2o8bo3bo4b2o
349bo2bo70bo$160b3o3b5obo8bo2bo4bobo368bobo68b3o$160bo2b2obo2bobo6b2o
2b7o2bo11bo8b2obo10b2o6b2o325bo$163bobo6b3o4b3o9b2o11bo7bob2o5bo3bobo
3b2o2bo11bo404bo$174bo2bo5b4o17bo13bobobo2bo6b3o11bobo401bobo7bo$174bo
bob4obo2bo23b9obo2bob2o3bo15bobo331b3o68b2o8bo$175b2obo2b2o27bo10bobo
2bo2bob2o12b2o2b2o308b3o7bobo10bo76b3o$202b3o6b3o3b3obo2bo4bo3bo2bobob
obobo2bobobo305b7o6b2o9bo$201bo3bo7bo6b2obo2b4obobo2bobob4o2b2o4bo301b
2ob2obob2ob2o3bo16b2o$193b2o5bo13b3obo2bo5b2o2bo4b2o7b2o3b3o302bob2o3b
2obo17bob3obo$192bobo22b5o3bobobo2bo2bo2b2ob3o3b3o304bobo7bobo16bo3bob
o$192bo7bo3b2o15bobobobob2ob4o3bobo3b2o4b2o301bo2bobobobo2bo15bo2bobob
2o$191b2o8b3o18b3o2bo2bo5b3o4b2o2b3obo301b2ob2ob3ob2ob2o14bo3b2o3bo53b
o$210b2o15b2o2b5o8bobo2bo2bo300bo4bo3bo4bo7b2o7bo3b2o2bo53bo$209bobo3b
o3b2o3b3o2b2o5bo7bobo4b2o301b3obobobob3o7bo2bo6bob2o2b3o51b3o$209bo5b
2o2b2o3bo2bo3bob2obo8bo310bob2obo2bo9bobo3bo2bo5bo$209bob2o12bob2ob2ob
obo325bobo11bo8bob2o2bo74bo$210b2o12b2o7bo327b2o21bo3b3o72bobo7bo$185b
o26bo10bo2bob3ob2o336b2o10bo3b2o76b2o8bo$185b3o29b3o5bobo4bob3o2b2obo
328bo10bo2bobob2o81b3o$188bo32bo2b2o2bo4b2o4bob2o325b3o12bo3bobo$187b
2o14b2o7b5obobob2obo2b3obo3b2o330bo14bob3obo$203b2o5b3ob3obo2b3ob2o5bo
2bo351b2o$213bo4bobo5bobob2o3bo2bo$215b2o6bob2ob2obobob4o$198b3o7b2o2b
2o2bob3obo3bo6b2o423bo$197bo2bo6bobo4bo2bo8bob5o3b3o420bo$163b2o6b2o
10bob2o10b2o2b2o4bo2b7o2b2o6bobo2bob2o2bo418b3o$151bo11bo2b2o3bobo3bo
5b2obo10bo5bo2b2o9b3o4b3o6bobo$150bobo11b3o6bo2bobobo17b3o11b4o5bo2bo
453bo$150bobo15bo3b2obo2bob9o13b2o8bo2bob4obobo451bobo7bo$148b2o2b2o
12b2obo2bo2bobo5bo4bo9b3o2bo12b2o2bob2o453b2o8bo$147bobobo2bobobo6bobo
bo2b4obob2o4b3o11bo2bo482b3o$146bo3b2o2b3obobob2o5bo2bo4bo4b2obo5bo9b
3o$146b4o3b2o7b2o3bo12bob3o5bo12b3o$149b3o2bob2ob3obo2bo2bobo2bo2bob5o
6b3o11bobo88b2o$146b2o4b2o3bobo3b4ob2obobobobob2o25bo87bob3obo14bo$
147bob3o2b2o4b3o5bo2bo2b3o29b2o86bo4b2o12b3o$146bo2bo2bobo8b5o2b2o121b
2obobo13bo358bo$146b2o4bobo7bo5b2o2b3o3b2o2b2o112b2ob3o10b2o358bo$153b
o8bob2obo3bo2bo3b2o2b2o109b3o3b3o368b3o$163bobob2ob2obo119bo2b2o3b2o5b
o$165bo7b2o119bobo3b3o4bobo381bo$163bo2b2ob4o7bo14bo17bo77b3o2b2o3b2o
3bo2bo379bobo7bo$156bob2o3bo2b2o3bobo6bo13b3o14b3o77bo2b2o3b3o5b2o381b
2o8bo$156b2ob3o2bob2o2b2obob4o3b4o8bob2o12bo81bo3b2ob3o396b3o$162b3ob
2ob3o6b2o2bo3bo10bo12b2o81b2obobo$161bobo2bo3bob2obo2bobobo4bo9b3o2b2o
bobo86bo4b2o64bob2o$160bo2bo3b2obo4bobobo5b3o11bobo2b2o2b2o84bob3obo
64b2obo$160b4obobob2ob2o3b2obob5o12b4obo3b2o85b2o14b3o$164b2o6bo6b2obo
b2o3b2o8b3o2bo3b2o77b2o22bo53b6o$160b3o3b5obo4bo3bo7bobo11b3o82bo13bo
9bo46bo4bo5bo313bo$160bo2b2obo2bobo6b2o2b7o2bo12b2o6b2obo10b2o6b2o52bo
bo9b2o57b3o2bo3bo316bo$163bobo6b3o4b3o9b2o11bo7bob2o5bo3bobo3b2o2bo11b
o41b2o10b2o59bobo3b2o313b3o$174bo2bo5b4o16bo14bobobo2bo6b3o11bobo110b
2obobobo3bo7b2o$174bobob4obo2bo23b9obo2bob2o3bo15bobo110bobo2bob3o2bo
5bo2bo323bo$175b2obo2b2o27bo4bo5bobo3bobob2o12b2o2b2o42b2o67b2obobob2o
bo3bobobo45b2obob2o43b2obob2o43b2obob2o43b2obob2o43b2obob2o43b2obob2o
19bobo7bo$203bo7b3ob2o4bob2ob4obo7bo2bobo2bobobo40bo2bo64b2o3bo3bo2bo
2bobobo45bobob2obo42bobob2obo42bobob2obo42bobob2obo42bobob2obo42bobob
2obo20b2o8bo$202bobo8bo2bob3obobobo5bob4obo2bo3b2o4bo40bobo63bo3b2ob2o
bob2obo2bo46bo2bo46bo2bo46bo2bo46bo2bo46bo2bo46bo2bo33b3o$193b2o6bo3bo
12b3o7bobo3bo5bo4b2o3b3o41bo64bob2obobob2o4b2o2bo45b2o2bob2o42b2o2bob
2o42b2o2bob2o42b2o2bob2o42b2o2bob2o42b2o2bob2o$192bobo6bo2bo9bo7bobobo
2bo2bo4b3ob4o2b3o110bobo7bob2o4bo43b2o4bobo41b2o4bobo41b2o4bobo41b2o4b
obo41b2o4bobo41b2o4bobo$192bo8bo2bo10bo3bobo3bobob2ob4o3bobo3b2o4b2o
109bob5ob2o3b2obob2o39bo3b2obobo40bo3b2obobo40bo3b2obobo40bo3b2obobo
40bo3b2obobo40bo3b2obobo$191b2o8bobo18b3o2bo2bo5b3o4b2o2b3obo41bo9bo
20b3o34bobobo2bo4b2ob2obob3o38b3ob2obob2o39b3ob2obob2o39b3ob2obob2o39b
3ob2obob2o39b3ob2obob2o39b3ob2obob2o$217bo9b2o2b5o8bobo2bo2bo48bobo20b
o36bobo4bob3obo2bobo4bo39bo2bobo3bo40bo2bobo3bo40bo2bobo3bo40bo2bobo3b
o40bo2bobo3bo40bo2bobo3bo$210b3o2b6o3b3o2b2o5bo7bobo4b2o36b2o5b2o4b2o
21bo30bob2obo2bobobobo4bo2bob4o41bo4b3o42bo2bob3o42bo4b3o42bo2bob3o42b
o4b3o42bo2bob3o14bo$210bo5bob3o3bo2bo3bob2obo8bo41b2o4bo4b2o56b2obob2o
2b2obo9bobo2bobo40bobobo47bobo45bobobo47bobo45bobobo47bobo17bo$210bo
14bob2ob2obobo55b2ob2o65bo7bo5b2obo5bobo38b2obo8b2o36b2obo8b2o36b2obo
8b2o36b2obo8b2o36b2obo8b2o36b2obo8b2o7b3o$211bo2bo9b2o7bo53bobo7bobo
56b3o2bobobobobo8b2o5bobo38bob2o8bo39b2o8bo37bob2o8bo39b2o8bo37bob2o8b
o39b2o8bo$185bo26bobo9bo2b2ob2ob2o52bo2bobobobo2bo56bo2bobo4bo2bob2o4b
o9bo37b2o10bo39bo9bo37b2o10bo39bo9bo37b2o10bo39bo9bo29bo$185b3o29bobob
2ob2o3bo4b3o2b2obo43b5obobob5o57bo2b2obo4bobo3b2ob2o7b2o39b2o7b2o36b2o
b2o7b2o39b2o7b2o36b2ob2o7b2o39b2o7b2o36b2ob2o7b2o26bobo7bo$188bo24b5o
2b3obo4bo4bo2b3ob2o43bo4bo3bo4bo56b2obo3bob3o3bo5bobo7bo2b2ob2o29b2obo
bo10b2ob2o32bobo7bo2b2ob2o29b2obobo10b2ob2o32bobo7bo2b2ob2o29b2obobo
10b2ob2o32bobo7bo2b2ob2o20b2o8bo$187b2o14b2o7b3obo6bobo3b2o3bo52b3obob
obob3o56bo3b4ob2o2b3o4bobobo7bobobobo32bo2bo8bo2bobo31bobobo7bobobobo
32bo2bo8bo2bobo31bobobo7bobobobo32bo2bo8bo2bobo31bobobo7bobobobo29b3o$
203b2o6bobo3b2o2b2obobo5b2o3bo51bob2obo2bo59b2o4b4obo7bo3bob2o3bo4bobo
30b3o2bob2o3bobo2bobo31bo3bob2o3bo4bobo30b3o2bob2o3bobo2bobo31bo3bob2o
3bo4bobo30b3o2bob2o3bobo2bobo31bo3bob2o3bo4bobo$211bo4bobo2bo6bob2o3bo
2bo55bobo62b2o6b2ob2o4bo2bobo2bo2bo3b2o2b2o23b2o6b2obo2bo2bo2b3o2b2o
23b2o4bo2bobo2bo2bo3b2o2b2o23b2o6b2obo2bo2bo2b3o2b2o23b2o4bo2bobo2bo2b
o3b2o2b2o23b2o6b2obo2bo2bo2b3o2b2o23b2o4bo2bobo2bo2bo3b2o2b2o$211bo4bo
bo2b2o2b2ob2obobob4o55b2o63bo4b3obobo5b2obobobo2b4o3bobo24bobo6bobobo
3b2o4bobo24bobo3b2obobobo2b4o3bobo24bobo6bobobo3b2o4bobo24bobo3b2obobo
bo2b4o3bobo24bobo6bobobo3b2o4bobo24bobo3b2obobobo2b4o3bobo$208b2o2bo3b
ob2obo4bo6b2o81bo20b3o20bob3o2b2o2bo7bobob4o3bob2o2bo25bo2b2o2bobob4ob
o3b2o2bo25bo6bobob4o3bob2o2bo25bo2b2o2bobob4obo3b2o2bo25bo6bobob4o3bob
2o2bo25bo2b2o2bobob4obo3b2o2bo25bo6bobob4o3bob2o2bo53b2o$198b3o6bobobo
5bo8bob5o3b3o75bobo20bo24b2o5b2obobobob2obo8bo3b2o25b2obo3b2obo4b2ob2o
3b2o25b2obobob2obo8bo3b2o25b2obo3b2obo4b2ob2o3b2o25b2obobob2obo8bo3b2o
25b2obo3b2obo4b2ob2o3b2o25b2obobob2obo8bo3b2o53bo4bo15bo$163b2o6b2o10b
ob2o11bo2bo5bo2b7o2b2o6bobo2bob2o2bo76b2o21bo17b2o2bo2bo3b2o3bob2o5bob
2obo4b2obo26bo2bob2o3bob2o6b2obo26bo2b2o5bob2obo4b2obo26bo2bob2o3bob2o
6b2obo26bo2b2o5bob2obo4b2obo26bo2bob2o3bob2o6b2obo26bo2b2o5bob2obo4b2o
bo15bo38bobobob2o11b3o$151bo11bo2b2o3bobo3bo5b2obo10bo3bo4b2o9b3o4b3o
6bobo97bo22bo2bo4bo4bobobo3bob2obobobo2bobo2bo28bo5b2obobobo2bobo2bo
28bo3bob2obobobo2bobo2bo28bo5b2obobobo2bobo2bo28bo3bob2obobobo2bobo2bo
28bo5b2obobobo2bobo2bo28bo3bob2obobobo2bobo2bo16bo36b2obo3b2o10bo$150b
obo11b3o6bo2bobobo21bo9b4o5bo2bo106b3o23bob7o2b2obo2b2o2b2o2bo4b3o2bob
2o28b3ob2o2bo3bo2bo2bob2o28b2o2b2o2bo4b3o2bob2o28b3ob2o2bo3bo2bo2bob2o
28b2o2b2o2bo4b3o2bob2o28b3ob2o2bo3bo2bo2bob2o28b2o2b2o2bo4b3o2bob2o13b
3o39b3obo11b2o$150bobo15bo3b2obo2bob9o9b3ob2o8bo2bob4obobo105bo25b2o5b
2o2bo3bo3bobo3bo2bobo4b2obo31b2o3bo2bobob2ob2obo30bobo3bo2bobo4b2obo
31b2o3bo2bobob2ob2obo30bobo3bo2bobo4b2obo31b2o3bo2bobob2ob2obo30bobo3b
o2bobo4b2obo53b3o4bo$148b2o2b2o12b2obo5bob2o9bo13bo13b2o2bob2o106b2o
27b3o4b5o3b2o3b3ob2obo8bo24b2o4b6ob2o2bo7bo24b2o2b2o3b3ob2obo8bo24b2o
4b6ob2o2bo7bo24b2o2b2o3b3ob2obo8bo24b2o4b6ob2o2bo7bo24b2o2b2o3b3ob2obo
8bo34bo17bo2bob3o7bo$147bobobo3bo4bob2obobobo2bobo2bobob3ob3o9bo3b2o
153b2obo3b2o8bob2obo3bo7bob3obo23bo2b2obo5bo3bo3b5obo23bo2bob2obo3bo7b
ob3obo23bo2b2obo5bo3bo3b5obo23bo2bob2obo3bo7bob3obo23bo2b2obo5bo3bo3b
5obo23bo2bob2obo3bo7bob3obo31bobo7bo10b2o3b2o6bobo$146bo3b2o3bob4ob4ob
2o3bobobo3bob4o5bobo7bo155bobob3ob2ob6o5bo2bob2obobo2bo3bo24b3o4b2o2bo
b2ob4obo3bo24b3o5bo2bob2obobo2bo3bo24b3o4b2o2bob2ob4obo3bo24b3o5bo2bob
2obobo2bo3bo24b3o4b2o2bob2ob4obo3bo24b3o5bo2bob2obobo2bo3bo32b2o8bo6b
3o2bob3o5bo2bo$146b4o3b2o3bo5bo2bobobo6bob2o9bo12b2o132b2o16bo2b3o13b
2obobob2ob4obo5b3o26bo4bob2obo2bo7b3o26b2obobob2ob4obo5b3o26bo4bob2obo
2bo7b3o26b2obobob2ob4obo5b3o26bo4bob2obo2bo7b3o26b2obobob2ob4obo5b3o
38b3o6bo2b2o4bo6b2o$149b3o2b4ob2o2bo2bo4b3o3bo2bo10b2o11bobo132bo17b2o
5bo6bob3o4bo8bo9bo23b2obo2b2o5bo2b2obo6bo23b3o4bo8bo9bo23b2obo2b2o5bo
2b2obo6bo23b3o4bo8bo9bo23b2obo2b2o5bo2b2obo6bo23b3o4bo8bo9bo47bo3b3obo
$146b2o4b2o3bobo3b4ob2obobo3bo28bo132bob2o16b4ob4o3b2o3bobobo6b2obobo
5b2o22bo7bo8b2o2bo4b2o22bo3bobobo6b2obobo5b2o22bo7bo8b2o2bo4b2o22bo3bo
bobo6b2obobo5b2o22bo7bo8b2o2bo4b2o22bo3bobobo6b2obobo5b2o48b2obo3b2o$
147bob3o2b2o4b3o5bo2bo2b3o17b2o10b2o123b2o4b3o2bo16bo3b2ob2o6b2o3bo7b
2ob4o3bo23bo2b6o8bobo6bo23bo2b2o3bo7b2ob4o3bo23bo2b6o8bobo6bo23bo2b2o
3bo7b2ob4o3bo23bo2b6o8bobo6bo23bo2b2o3bo7b2ob4o3bo51bobobob2o$146bo2bo
2bobo8b5o2b2o156bo2b2o3bo3b2o8b3o9b2o5b5o2b2o4b2o4bo6bo2b2o22b2o2bobo
3b2o5bobobobo2b2o22b2o2b2o4b2o4bo6bo2b2o22b2o2bobo3b2o5bobobobo2b2o22b
2o2b2o4b2o4bo6bo2b2o22b2o2bobo3b2o5bobobobo2b2o22b2o2b2o4b2o4bo6bo2b2o
49bo4bo$146b2o4bobo7bo5b2o2b3o3b2o2b2o143b3o6b4o10bo10bo6b2o6b2obo2b2o
3bo5bob2obo26bo2bo3b2o3bo5bob2obo27b2obo2b2o3bo5bob2obo26bo2bo3b2o3bo
5bob2obo27b2obo2b2o3bo5bob2obo26bo2bo3b2o3bo5bob2obo27b2obo2b2o3bo5bob
2obo51b2o15b2o$153bo8bob2obo3bo2bo3b2o2b2o138b2o4b2o9bo11bo13bo2bo2b3o
2b2o12b4o2bobo23b2obob2o8bob3obo2bobo23b2o2b2o12b4o2bobo23b2obob2o8bob
3obo2bobo23b2o2b2o4b2o6b4o2bobo23b2obob2o8bob3obo2bobo23b2o2b2o12b4o2b
obo24bo43bobo$163bobob2ob2obo147bobo12b3o23b2ob2o3bo2bo13b2obo3bobob2o
23bobo2bo8bo6bobob2o23bo13b2obo3bobob2o23bobo2bo8bo6bobob2o23bo7b2o4b
2obo3bobob2o23bobo2bo8bo6bobob2o23bo13b2obo3bobob2o24bo31bobo8bo$165bo
7b2o146bo13bo27b4o2b2o2bob2o2bo2b2o4b2ob3obo3bo23bo3bo4b2o5b2ob2obo3bo
23bob2o2bo2b2o4b2ob3obo3bo23bo3bo5bo5b2ob2obo3bo23bob2o5b2o4b2ob3obo3b
o23bo3bo3b3o5b2ob2obo3bo23bob2o2bo2b2o4b2ob3obo3bo22b3o31b2o$165b2ob3o
bo40bo106b2o14b5o30bob3o6b2o3b2o6bob2o21b2obo3bo4b2o5b2obo2bob2o21b2ob
3o6b2o3b2o6bob2o21b2obo3bo4b2o5b2obo2bob2o21b2ob3o3bo2bo5bo6bob2o21b2o
bo3bo2bo4bo3b2obo2bob2o21b2ob3o5bo2bo2b2o6bob2o58bo$156bob2ob2o6bo3b2o
bo3b2o3bo9bo15b3o127bob2o21bobo4bo4bo8b3o5bobo23bobo3bo11b2o3b2obo23bo
bo4bo8b3o5bobo23bobo3bo11b2o3b2obo23bobo4bo6b2ob2o5bobo23bobo3bo2bo5bo
2b2o3b2obo23bobo4bo2bo2bo2b3o5bobo45bo$156b2ob4ob2o3b2o7bob2o4bo7b3o
13bo127b2obob2o18b3obo3bobob2o11b3o4bobo13b2o7bo2bob2o12bobobobobo13b
2o7bo2bob2o11b3o4bobo13b2o7bo2bob2o12bobobobobo13b2o7bo2bob2o11b3o4bob
o13b2o7bo2bob2o9bo2bobobobobo13b2o7bo2bob2o4bo2bo3b3o4bobo13b2o28bobo
7bo$161bo2bo3b2o3bo4bobo12b2o2bo6b2o4b2o122b2o3bobo25b3obobobo8bo4bo3b
obob2o13bo7b2obobo13b2o2bobob2o13bo7b2obobo8b2o3bo3bobob2o13bo7b2obobo
8bobo2b2o2bobob2o13bo7b2obobo6bo3bo2bo3bobob2o13bo7b2obobo6bo2bo3b2o2b
obob2o13bo7b2obobo7b2o4bo3bobob2o13bo29b2o8bo$164b3o6b5o2bob4obo5b2ob
3o5b3o127b2o3bobo28bo2bobo6bo2bo4b3ob2o16bobo8bobo7b3o4bo4bo16bobo8bob
o5bo8b3ob2o16bob2o7bobo5b2ob2o4bo4bo16bobo8bobo6bo2bo4b3ob2o16bobo8bob
o6b3o5bo4bo16bobo8bobo6bo7b3ob2o16bobo35b3o$160bo2bobob2obobo2bo2b3obo
4b2o4b5o6b2ob2o131bo32b2o6bo13bo17b2o8b2o7b2o6bo4bo17b2o8b2o6bo3bo9bo
17bo3bo5b2o6bo3bo4bo4bo17b2o8b2o7b3o10bo17b2o8b2o15bo4bo17b2o8b2o20bo
17b2o$160b4obobob2ob2o2b2o2bob2o2b3o6bo4b3o3bobo137bo34bo11b2o22bo13bo
3bo7b2o22b2o13b3o8b2o23bo13b3o8b2o21b3o24b2o48b2o48b2o$164b2o6bo3b5obo
3b2ob2o9b2o3bo2bo111bo11b2o10b3o34bo2bo8bo22bo15b3o8bo23b2o13b3o8bo21b
o2bo24bo22b3o24bo22b3o24bo23bo25bo$160b3o3b5obo8bo2bo4bobo8b2o5bo112bo
bo8bo2bo8bo11bo7b3o16bobo9b3o8bo10b3o14bo10b3o8bo11bo26b3o8bo11bo26b3o
8bo9bo28b3o8bo10bo2bo24b3o8bo11b2o25b3o8bo10b3o$160bo2b2obo2bobo6b2o2b
7o2bo10b3o7b2obo10b2o6b2o84b2o10b2o9b2o8b3o7bo19bo12bo6b3o10b3o27bo6b
3o40bo6b3o40bo6b3o40bo6b3o9bobo28bo6b3o9bo2b2o26bo6b3o10b3o61b2o$163bo
bo6b3o4b3o9b2o9b3o7bob2o5bo3bobo3b2o2bo11bo104bo11bo9b2o2b2o22bo13b2o
10bo23bo12b3o34bo12bobo8bo2bo22bo12b2o2b2o6bo24bo11b3obo33bo11bo4bo32b
o11b2o3bo12b2o46bobo$174bo2bo5b4o31bobobo2bo6b3o11bobo103b2o20b2o2b2o
9b2o11b2o20b6o9b2o11b2o20bobo2b2o8b2o7bo3b2o11bo5b2o2bo3bo9b2o11b2o12b
6o4bob2o9b2o11b2o10b3o3b2o5bo11b2o11b2o9bobo2b3o7bo10b2o11b2o10bo2b3o
8b2ob3o5b2o2bobo34bo$174bobob4obo2bo23b9obo2bob2o3bo15bobo101b3o20b2o
6bo7b2o32b2ob2o2bo8b2o33bo2b2o10b2o8bo18bobo4bo4bo8b2o5bob2ob2o12bo3bo
2bo2bo4bo8b2o7bo21b2o4b2obo9b2o26b2ob2o4b2o11b2o23b4o2bo6b3ob2o6b2o2b
2o$175b2obo2b2o27bo10bobo2bo2bob2o12b2o2b2o79bo18bobo22bo7bo16b2o22b2o
3bob2o12bo5bo23bo2b2o2bo13bo4bo15bo8bo4bo14bo2bob2o13bobo8bo20b4o16bo
2b2o5bob2o16b3o18bo9bobobo16bo16bob3o7b2ob3o10bo$211b3o3b3obo2bo4bo3bo
2bobobobobo2bobobo77bo11b2o3bob2obo22b2ob2ob2o10bo7b2o23b4obo11bo3bo2b
2o24b2o2bobo17b2o15bo9bo3bo14bo5bo14b3o8b4o14b2o3b2o15b3o8bo21b2o15b3o
10bobo14b2obo17bo12b2o$203bo9bo6b2obo2b4obobo2bobob4o2b2o4bo76b3o8bobo
2b2o3bo23b2o3bo11b2o3b2o28b2o14bo4b3o16bo25b3obo30bobo13b2o2bobo17b2o
25bo3bo18b3o25b2obob2o44bo3bo63bo$193b2o7b3o9b3obo2bo5b2o2bo4b2o7b2o3b
3o86b2o3b2obo42b2o3b2o44bo5b2o18b2o23bo2bobo18bobo24bo3bob2o14b4o25bo
3bo46bo2b4o44bo2b2o45b2obo15bo$192bobo6bo15b5o3bobobo2bo2bo2b2ob3o3b3o
90bo2b2o46b2o4bo44b3o2b2o43b2obobob2o13bobo26bobobobo15bo28b2o2bo16bo
29bo4bo45b2ob2o46bob3o11b3o$192bo9b2o17bobobobob2ob4o3bobo3b2o4b2o88b
3o15b3o30b2o16b2o30b2o17bo50bo31b3o16b3o30bo3bo13b3o29b4o14b2o32b2o3bo
10b2o29bobo4bo$191b2o9bo11b2o6b3o2bo2bo5b3o4b2o2b3obo90bo15b2o3bo45bo
2bo31bo15b2o32b3o14bo50b2o49bob2o31b2o3bobo7bo2b2o36b2o7bo2bo27bob2o3b
2o$216bo10b2o2b5o8bobo2bo2bo54bo49b2o2bobo44b2o2bo46b2obo47b2o49b2o42b
o6b2o2b2o35bobo7b2ob2o35b2o8bo2bo27bo$211b2o3bo2b2o3b3o2b2o5bo7bobo4b
2o54bobo29b2o17bo5bo12b2o30b2o2bo13b2o31bobo14b2o32b2o14b2o33b2o13b2o
26bo7b4o10b2o26bo8b3o10b2o35bobo10b2o14b2o$211bo4bo2b2o3bo2bo3bob2obo
8bo61b2o19bo11bo18b2o2bo13bo32b4o13bo33b2o14bo34bo14bo49bo23bo12b3o10b
o24bo24bo25bo23bo65b2o$211bo13bob2ob2obobo92bobo6b3o23bo7bo6b3o40bo6b
3o40bo6b3o22bo17bo6b3o22bo17bo6b3o22bo17bo6b3o20b2o18bo6b3o21b2o17bo6b
3o62bobo$212bo2bo8b2o7bo94b2o7bo31b3o8bo23bo14b3o8bo23bo14b3o8bo23bo
14b3o8bo20bobo15b3o8bo20b3o15b3o8bo22bo15b3o8bo21bobo14b3o8bo62bo$185b
o27b2o8bo2bob3ob2o121bo12bo36bo12bo33bobo13bo33b3o13bo33b2o14bo49bo49b
o49bo$185b3o29b3o5bobo4bob3o2b2obo74bo35bobo12b2o33b3o12b2o33b2o13b2o
48b2o48b2o48b2o48b2o48b2o$188bo32bo2b2o2bo4b2o4bob2o73bo31b2o4b2o14bo
17b2o8b2o16b2o2bo17b2o8b2o20bo17b2o8b2o16b2o2bo17b2o8b2o20bo17b2o8b2o
16b2o2bo17b2o8b2o20bo17b2o8b2o16b2o2bo$187b2o14b2o7b5obobob2obo2b3obo
3b2o78b3o29bobo14b2o3bo16bobo8bobo14b4obo16bobo8bobo14b2o3bo16bobo8bob
o14b4obo16bobo8bobo14b2o3bo16bobo8bobo14b4obo16bobo8bobo14b2o3bo16bobo
8bobo14b4obo56bo39b2o$203b2o5b3ob3obo2b3ob2o5bo2bo109b2obobo13bob2o2bo
b2o13bo7b2obobo12bo3b2obob2o13bo7b2obobo13bob2o2bob2o13bo7b2obobo12bo
3b2obob2o13bo7b2obobo13bob2o2bob2o13bo7b2obobo12bo3b2obob2o13bo7b2obob
o13bob2o2bob2o13bo7b2obobo12bo3b2obob2o54bo37bobo$213bo4bobo5bobob2o3b
o2bo106bo2bob2o11bo2b3obobo13b2o7bo2bob2o10bo2bo4bobo13b2o7bo2bob2o11b
o2b3obobo13b2o7bo2bob2o10bo2bo4bobo13b2o7bo2bob2o11bo2b3obobo13b2o7bo
2bob2o10bo2bo4bobo13b2o7bo2bob2o11bo2b3obobo13b2o7bo2bob2o10bo2bo4bobo
53b3o36bo2bob2obo$215b2o6bob2ob2obobob4o107bobo3bo10bo3b2obobo23bobo2b
o13bo3b2obo23bobo3bo10bo3b2obobo23bobo2bo13bo3b2obo23bobo3bo10bo3b2obo
bo23bobo2bo13bo3b2obo23bobo3bo10bo3b2obobo23bobo2bo13bo3b2obo90b3obobo
bob3o$208b2o2b2o2bob3obo3bo6b2o110b2ob2ob3o3b2o4bo3bo2bob2o21b2obob2o
5b2o6bobo2bob2o21b2ob2ob3o3b2o4bo3bo2bob2o21b2obob2o5b2o6bobo2bob2o21b
2ob2ob3o3b2o4bo3bo2bob2o21b2obob2o5b2o6bobo2bob2o21b2ob2ob3o3b2o4bo3bo
2bob2o21b2obob2o5b2o6bobo2bob2o88bo4bo3bo4bo$207bobo4bo2bo8bob5o3b3o
55bo53bo2b3o3b2o4b3ob2obo3bo23bob2o5b2o6b4obo3bo23bo2b3o3b2o4b3ob2obo
3bo23bob2o5b2o6b4obo3bo23bo2b3o3b2o4b3ob2obo3bo23bob2o5b2o6b4obo3bo23b
o2b3o3b2o4b3ob2obo3bo23bob2o5b2o6b4obo3bo87b5obobob5o$163b2o6b2o10bob
2o11b3o6bo2b7o2b2o6bobo2bob2o2bo55bobo51bo4bo15bobob2o23bobobo9b2o5bob
ob2o23bo4bo15bobob2o23bobobo9b2o5bobob2o23bo4bo15bobob2o23bobobo9b2o5b
obob2o23bo4bo15bobob2o23bobobo9b2o5bobob2o88bo2bobobobo2bo$151bo11bo2b
2o3bobo3bo5b2obo10bo2bo5b2o9b3o4b3o6bobo58b2o19bo31b2obob3o6b2o2bob2o
2bobo23b2o2b3o8b7o2bobo23b2obob3o6b2o2bob2o2bobo23b2o2b3o8b7o2bobo23b
2obob3o6b2o2bob2o2bobo23b2o2b3o8b7o2bobo23b2obob3o6b2o2bob2o2bobo23b2o
2b3o8b7o2bobo82b2o5bobo7bobo$150bobo11b3o6bo2bobobo16bo4bo9b4o5bo2bo
90bobo32bo2b2o2b2o5bobobob2obo26bo6b2o7bobob2obo26bo2b2o2b2o5bobobob2o
bo26bo6b2o7bobob2obo26bo2b2o2b2o5bobobob2obo26bo6b2o7bobob2obo26bo2b2o
2b2o5bobobob2obo26bo6b2o7bobob2obo82bobo8b2ob2o$150bobo15bo3b2obo2bob
9o7b2ob2obo9bo2bob4obobo90b2o30b2o8b2o4b3obo2bo2b2o22b3o2bo4b2o4b2obob
obo2b2o22b2o8b2o4b3obo2bo2b2o22b3o2bo4b2o4b2obobobo2b2o22b2o8b2o4b3obo
2bo2b2o22b3o2bo4b2o4b2obobobo2b2o22b2o8b2o4b3obo2bo2b2o22b3o2bo4b2o4b
2obobobo2b2o81bo6b2o4bo4b2o$148b2o2b2o12b2obo2bo2bobo5bo4bo7b2obo2bo
13b2o2bob2o122bo2b3ob2o8bo2b2obo2bo23bo2b2o2b2o10bob2o3bo23bo2b3ob2o8b
o2b2obo2bo23bo2b2o2b2o10bob2o3bo23bo2b3ob2o8bo2b2obo2bo23bo2b2o2b2o10b
ob2o3bo23bo2b3ob2o8bo2b2obo2bo23bo2b2o2b2o10bob2o3bo92b2o5b2o$147bobob
o2bobobo6bobobo2b4obob2o4b3o10b4o102bo42bo7bo7bo9b2o22bo3bo3bo6bo2bob
2o4b2o22bo7bo7bo9b2o22bo3bo3bo6bo2bob2o4b2o22bo7bo7bo9b2o22bo3bo3bo6bo
2bob2o4b2o22bo7bo7bo9b2o22bo3bo3bo6bo2bob2o4b2o$146bo3b2o2b3obobob2o5b
o2bo4bo4b2obo6bo6b3o101bo44b3o3b2o7bob2o7bo23b2o5bo9b2o7bo23b3o3b2o7bo
b2o7bo23b2o5bo9b2o7bo23b3o3b2o7bob2o7bo23b2o5bo9b2o7bo23b3o3b2o7bob2o
7bo23b2o5bo9b2o7bo94bo$146b4o3b2o7b2o3bo12bob3o7b2o10b2o97b3o44bo2bobo
b2obo10b3o26b2o3bob2obobo2bo5b3o26bo2bobob2obo10b3o26b2o3bob2obobo2bo
5b3o26bo2bobob2obo10b3o26b2o3bob2obobo2bo5b3o26bo2bobob2obo10b3o26b2o
3bob2obobo2bo5b3o66bo$149b3o2bob2ob3obo2bo2bobo2bo2bob5o7bo3b2o7bobo
139b3obo3bo2bob2ob2obobo3bo24b3o4b2o2bob2obob2obo3bo24b3obo3bo2bob2ob
2obobo3bo24b3o4b2o2bob2obob2obo3bo24b3obo3bo2bob2ob2obobo3bo24b3o4b2o
2bob2obob2obo3bo24b3obo3bo2bob2ob2obobo3bo24b3o4b2o2bob2obob2obo3bo69b
o$146b2o4b2o3bobo3b4ob2obobobobob2o25bo138bo2b4o5bo3bo3bob3obo23bo2bob
2obo3bo3bo4b4obo23bo2b4o5bo3bo3bob3obo23bo2bob2obo3bo3bo4b4obo23bo2b4o
5bo3bo3bob3obo23bo2bob2obo3bo3bo4b4obo23bo2b4o5bo3bo3bob3obo23bo2bob2o
bo3bo3bo4b4obo67b3o26bo$147bob3o2b2o4b3o5bo2bo2b3o17b3o9b2o137b2o6b4ob
2ob4o5bo24b2o5b5ob2o10bo24b2o6b4ob2ob4o5bo24b2o5b5ob2o10bo24b2o6b4ob2o
b4o5bo24b2o5b5ob2o10bo24b2o6b4ob2ob4o5bo24b2o5b5ob2o10bo96bobo$146bo2b
o2bobo8b5o2b2o184bo2bobob5obo36bo2bobobo2b2obo36bo2bobob5obo36bo2bobob
o2b2obo36bo2bobob5obo36bo2bobobo2b2obo36bo2bobob5obo36bo2bobobo2b2obo
97bo2bo$146b2o4bobo7bo5b2o2b3o3b2o2b2o97bo67b3ob2o2bo3bo2bo2bob2o28b2o
bobo2bo3b4o2bob2o28b3ob2o2bo3bo2bo2bob2o28b2obobo2bo3b4o2bob2o28b3ob2o
2bo3bo2bo2bob2o28b2obobo2bo3b4o2bob2o28b3ob2o2bo3bo2bo2bob2o28b2obobo
2bo3b4o2bob2o92b2o3b2o$153bo8bob2obo3bo2bo3b2o2b2o97bobo64bo5b2obobo6b
o2bo28bo2bo2b2obobobo2bobo2bo28bo5b2obobo6bo2bo28bo2bo2b2obobobo2bobo
2bo28bo5b2obobo6bo2bo28bo2bo2b2obobobo2bobo2bo28bo5b2obobo6bo2bo28bo2b
o2b2obobobo2bobo2bo94b2o$163bobob2ob2obo107b2o19bo43bo2b2obo3bob2ob4ob
2obo26bo2b4o3bob2o6b2obo26bo2b2obo3bob2ob4ob2obo26bo2b4o3bob2o6b2obo
26bo2b2obo3bob2ob4ob2obo26bo2b4o3bob2o6b2obo26bo2b2obo3bob2ob4ob2obo
26bo2b4o3bob2o6b2obo93bo$165bo7b2o127bobo41b2obo3b2obo4b5o3b2o25b2obo
3b2obo4bo3bo3b2o25b2obo3b2obo4b5o3b2o25b2obo3b2obo4bo3bo3b2o25b2obo3b
2obo4b5o3b2o25b2obo3b2obo4bo3bo3b2o25b2obo3b2obo4b5o3b2o25b2obo3b2obo
4bo3bo3b2o101b2o$163bo2b2ob4o7bo32bo88b2o43bo2bo3bobob3o6b2o2bo25bo2b
2o2bobob4obob4o2bo25bo2bo3bobob3o6b2o2bo25bo2b2o2bobob4obob4o2bo25bo2b
o3bobob3o6b2o2bo25bo2b2o2bobob4obob4o2bo25bo2bo3bobob3o6b2o2bo25bo2b2o
2bobob4obob4o2bo100bobo$156bob2o3bo2b2o3bobo6bo30b3o131bobo6bobobo4b2o
3bobo24bobo3b2obobobo4b3o2bobo24bobo6bobobo4b2o3bobo24bobo3b2obobobo4b
3o2bobo24bobo6bobobo4b2o3bobo24bobo3b2obobobo4b3o2bobo24bobo6bobobo4b
2o3bobo24bobo3b2obobobo4b3o2bobo103bo$156b2ob3o2bob2o2b2obob4o3b4o9b2o
7bo5bo80bo53b2o4b4obo2bob2ob4o2b2o23b2o3b2ob2obo2bo6b2o2b2o23b2o4b4obo
2bob2ob4o2b2o23b2o3b2ob2obo2bo6b2o2b2o23b2o4b4obo2bob2ob4o2b2o23b2o3b
2ob2obo2bo6b2o2b2o23b2o4b4obo2bob2ob4o2b2o23b2o3b2ob2obo2bo6b2o2b2o
102b2o$162b3ob2ob3o6b2o2bo3bo7b2obo7bo4b2o78bo60b2o2bob2o5bo2bobo30b2o
3bob2o3b2o3bobo31b2o2bob2o5bo2bobo30b2o3bob2o3b2o3bobo31b2o2bob2o5bo2b
obo30b2o3bob2o3b2o3bobo31b2o2bob2o5bo2bobo30b2o3bob2o3b2o3bobo96b2o$
161bobo2bo3bob2obo2bobobo4bo6bo2bo6bobo83b3o60bobo7bobobobo35bo6b3o2bo
bo33bobo7bobobobo35bo6b3o2bobo33bobo7bobobobo35bo6b3o2bobo33bobo7bobob
obo35bo6b3o2bobo83bo8bob3obo$160bo2bo3b2obo4bobobo5b3o6b3o154bobobo7bo
2b2ob2o29b2obobo7bo2b2ob2o30bobobo7bo2b2ob2o29b2obobo7bo2b2ob2o30bobob
o7bo2b2ob2o29b2obobo7bo2b2ob2o30bobobo7bo2b2ob2o29b2obobo7bo2b2ob2o83b
o7b2o4bo$160b4obobob2ob2o3b2obob5o8b2o4bobo3b2o144b2o7b2o37bob2o7b2o
39b2o7b2o37bob2o7b2o39b2o7b2o37bob2o7b2o39b2o7b2o37bob2o7b2o88bo11bobo
b2o$164b2o6bo6b2obob2o3b2o10b4ob2o142b2o10bo38b2o9bo37b2o10bo38b2o9bo
37b2o10bo38b2o9bo37b2o10bo38b2o9bo89bo2bo5b3ob2o3bo$160b3o3b5obo4bo3bo
7bobo9bo2b3o146b2o8bo37bob2o8bo39b2o8bo37bob2o8bo39b2o8bo37bob2o8bo39b
2o8bo37bob2o8bo91bo5b3o3b2o2bo$160bo2b2obo2bobo6b2o2b7o2bo11b2o7b2obo
10b2o6b2o32bo81b2obo8b2o39bo8b2o36b2obo8b2o39bo8b2o36b2obo8b2o39bo8b2o
36b2obo8b2o39bo8b2o89bo2bo3b2o3b2o2b3o$163bobo6b3o4b3o9b2o10bo8bob2o5b
o3bobo3b2o2bo11bo20bobo80bo3bo44b2obobo45bo3bo44b2obobo45bo3bo44b2obob
o45bo3bo44b2obobo97bobo4b3o3bobo$174bo2bo5b4o31bobobo2bo6b3o11bobo19b
2o19bo60b4ob3o44b2ob3o42b4ob3o44b2ob3o42b4ob3o44b2ob3o42b4ob3o44b2ob3o
96bo5b2o3b2o2bo$174bobob4obo2bo23b9obo2bob2o3bo15bobo40bobo57bo2bobo3b
o40bo2bobo3bo40bo2bobo3bo40bo2bobo3bo40bo2bobo3bo40bo2bobo3bo40bo2bobo
3bo40bo2bobo3bo102b3o3b3o$175b2obo2b2o27bo4bo5bobo3bobob2o12b2o2b2o38b
2o56b3o4bob2o39b3o4bob2o39b3o4bob2o39b3o4bob2o39b3o4bob2o39b3o4bob2o
39b3o4bob2o39b3o4bob2o91b2o10b3ob2o$211b3ob2o4bob2ob4obo7bo2bobo2bobob
o94bo3b2obobo40bo3b2obobo40bo3b2obobo40bo3b2obobo40bo3b2obobo40bo3b2ob
obo40bo3b2obobo40bo3b2obobo94bo13bobob2o$203bo9bo2bob3obobobo5bob4obo
2bo3b2o4bo25bo68b2o2bobobo41b2o2bobobo41b2o2bobobo41b2o2bobobo41b2o2bo
bobo41b2o2bobobo41b2o2bobobo41b2o2bobobo91b3o12b2o4bo$193b2o8bo14b3o7b
obo3bo5bo4b2o3b3o24bo71b2ob2ob2o42b2ob2ob2o42b2ob2ob2o42b2ob2ob2o42b2o
b2ob2o42b2ob2ob2o42b2ob2ob2o42b2ob2ob2o90bo14bob3obo$192bobo7bobo9bo7b
obobo2bo2bo4b3ob4o2b3o27b3o69bo2bo46bo2bo46bo2bo46bo2bo46bo2bo46bo2bo
46bo2bo46bo2bo113b2o$192bo23bo2bobo3bobob2ob4o3bobo3b2o4b2o97bobob2obo
42bobob2obo42bobob2obo42bobob2obo42bobob2obo42bobob2obo42bobob2obo42bo
bob2obo$191b2o8b2o19b3o2bo2bo5b3o4b2o2b3obo99b2obob2o43b2obob2o43b2obo
b2o43b2obob2o43b2obob2o43b2obob2o43b2obob2o43b2obob2o$213b3o11b2o2b5o
8bobo2bo2bo$201b2o8bo4bo2b2o3b3o2b2o5bo7bobo4b2o$212bo3bo2b2o3bo2bo3bo
b2obo8bo9bo$212b4o9bob2ob2obobo19bobo$224b2o7bo21b2o19bo$185bo38bo2b2o
b2ob2o41bobo$185b3o26b2obobob2ob2o3bo4b3o2b2obo33b2o$188bo24b5o2b3obo
4bo4bo2b3ob2o$187b2o14b2o7b3obo6bobo3b2o3bo30bo$203b2o6bobo3b2o2b2obob
o5b2o3bo26bo$211bo4bobo2bo6bob2o3bo2bo25b3o$211bo4bobo2b2o2b2ob2obobob
4o$208b2o2bo3bob2obo4bo6b2o$207bobobo5bo8bob5o3b3o$163b2o6b2o10bob2o
20bo2b7o2b2o6bobo2bob2o2bo$151bo11bo2b2o3bobo3bo5b2obo11b3o5b2o9b3o4b
3o6bobo6bo$150bobo11b3o6bo2bobobo17bo2bo10b4o5bo2bo17bobo$150bobo15bo
3b2obo2bob9o8bo3bo10bo2bob4obobo17b2o19bo$148b2o2b2o12b2obo5bob2o9bo8b
3o2bo13b2o2bob2o39bobo$147bobobo3bo4bob2obobobo2bobo2bobob3ob3o10b4o
61b2o$146bo3b2o3bob4ob4ob2o3bobobo3bob4o$146b4o3b2o3bo5bo2bobobo6bob2o
9b2o11b2o46bo$149b3o2b4ob2o2bo2bo4b3o3bo2bo11b2obobo6bobo44bo$146b2o4b
2o3bobo3b4ob2obobo3bo13bo3b2o9bo44b3o$147bob3o2b2o4b3o5bo2bo2b3o19bo9b
2o$146bo2bo2bobo8b5o2b2o$146b2o4bobo7bo5b2o2b3o3b2o2b2o$153bo8bob2obo
3bo2bo3b2o2b2o$163bobob2ob2obo55bo$165bo7b2o54bobo$165b2ob3obo40bo15b
2o19bo$156bob2ob2o6bo3b2obo3b2o3bo25b3o36bobo$156b2ob4ob2o3b2o7bob2o4b
o8b2o13bo39b2o$161bo2bo3b2o3bo4bobo13bo2bo5b3o4b2o$164b3o6b5o2bob4obo
9bo5bobo33bo$160bo2bobob2obobo2bo2b3obo4b2o5b3o5b2o2b2o30bo$160b4obobo
b2ob2o2b2o2bob2o2b3o14b2ob2o30b3o$164b2o6bo3b5obo3b2ob2o10b2obob2o$
160b3o3b5obo8bo2bo4bobo10bob2o$160bo2b2obo2bobo6b2o2b7o2bo10b2o$163bob
o6b3o4b3o9b2o$174bo2bo5b4o29bo$174bobob4obo2bo29bobo$175b2obo2b2o33b2o
19bo$237bobo$237b2o$193b2o8bo$192bobo7b3o21bo$192bo9b3o20bo$191b2o32b
3o$201b4o$201b5o$202bob2o4$224bo$224bobo$203b2o19b2o$203b2o$213bo$212b
o$194bo8b2o7b3o$194b3o5b2o$197bo6bo$196bo2bo24b2o$196b4o23bobo$222bo2b
ob2obo$198b2o20b3obobobob3o$198bo12bo7bo4bobobo4bo$196bobo12bobo5bob3o
bobob3obo$196b2o13b2o10bo5bo$221bobobobobobo$220bo4b3o4bo$221b11o$216b
2o3b2o7b2o$215b2o$217bo3$225bo$224bobo$198bo25bo2bo$198bobo24b2o$198b
2o2$217b3o9b2o$219bo9bobo$218bo12bo$231b2o6$185bo$185bobo$185b2o2$204b
3o$206bo$205bo7$172bo$172bobo$172b2o2$191b3o$193bo$192bo2$149b2o$150bo
$150bobo$151b2o2$158b2o$155b2o4bo$154bo5bo$155bob2o$156bo21b3o$180bo$
179bo2$154b3o$152b7o$149b2ob2obob2ob2o20b2o$150bob2o3b2obo6bobo8bob3ob
o$149bobo7bobo6b2o8bo3bobo$149bo2bobobobo2bo6bo8bo2bobob2o$148b2ob2ob
3ob2ob2o14bo3b2o3bo$148bo4bo3bo4bo7b2o7bo3b2o2bo$149b3obobobob3o7bo2bo
6bob2o2b3o$151bob2obo2bo9bobo3bo2bo5bo$156bobo11bo8bob2o2bo$156b2o21bo
3b3o$165b2o10bo3b2o$166bo10bo2bobob2o$163b3o12bo3bobo$163bo14bob3obo$
182b2o!
What do you do with ill crystallographers? Take them to the mono-clinic!
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Re: Oscillator Discussion Thread

Postby AforAmpere » April 3rd, 2018, 10:43 am

calcyman wrote:These ideas can be used to create a p52 emu (oscillator), but currently we lack an over-unity component...

What is the shortest repeat time G-to-2G?
Things to work on:
- Find a (7,1)c/8 ship in a Non-totalistic rule (someone please search the rules)
- Find a C/10 in JustFriends
- Find a C/10 in Day and Night
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Re: Oscillator Discussion Thread

Postby dvgrn » April 3rd, 2018, 11:11 am

AforAmpere wrote:
calcyman wrote:These ideas can be used to create a p52 emu (oscillator), but currently we lack an over-unity component...

What is the shortest repeat time G-to-2G?

74 ticks, isn't it? We don't have anything direct that skips the Herschel stage, except calcyman's modification of the bistable switch I suppose but that recovers pretty slowly. So the limiting factor is the syringe, which has a safe recovery time of 78 but can be overclocked down to 75 or 74:

x = 57, y = 35, rule = B3/S23
15b2o11bo6b2o$15b2o10bobo4bo2bo$27bobo3bob3o3bo$26b2ob2obobo6b3o$30bob
o3b2o6bo$26b2obo2b4obo5b2o$26b2obobo3bo$30bobo3bo$31bobo3bo$32bo3b2o4$
19b2o2b2o$18bobo2b2o$8b2o10bo$7bo2bo$6bob2o$6bo48b2o$5b2o48b2o$20b2o$
20bo$21b3o$23bo10b2o$33bobo$33bo$32b2o6$3o$2bo$bo!

It's kind of a long way from there down to 52 ticks. If we could get something with a repeat time closer to a Snark's (43 ticks) then we could also do some really interesting new stuff with single-channel construction arms -- would basically have to re-do all the searches, and we'd end up with much more efficient recipes for everything.
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Re: Oscillator Discussion Thread

Postby Sokwe » April 4th, 2018, 3:59 am

dvgrn wrote:
AforAmpere wrote:
calcyman wrote:These ideas can be used to create a p52 emu (oscillator), but currently we lack an over-unity component...

What is the shortest repeat time G-to-2G?

74 ticks, isn't it?

I suppose it would depend on how you define the problem. The syringe + H-to-2G is the fastest stable G->2G. It has a repeat time of 78, but can be over-clocked to p74 and p75, as you've shown.

However, there is a general method for duplicating gliders that works for all periods 58 and greater. It can be seen in the p58 gun:
x = 436, y = 279, rule = B3/S23
84bo35b2o12bo35b2o12bo35b2o12bo$84b3o5b2o27bo12b3o5b2o27bo12b3o5b2o27b
o12b3o5b2o$87bo4bo28bobo13bo4bo28bobo13bo4bo28bobo13bo4bo16bo$69b2o15b
o3bobo29b2o12bo3bobo29b2o12bo3bobo29b2o12bo3bobo16b3o$70bo14bo3bobo43b
o3bobo43bo3bobo43bo3bobo20bo14bo$70bobo12b2o3bo44b2o3bo44b2o3bo44b2o3b
o20b2o12b3o$71b2o2b2o37bo49bo10b3o36bo59bo$75b2o35b3o47b3o11b2o34b3o
11bo25b2o11b2o7b2o$92b3o3bo12bo49bo13bo35bo13b3o14b2o2bobo3bobob3o5bo$
90b5o2bobo11b2o25b2o9bo11b2o21bob3o9b2o11b2o11b2obo13b3obo3bo2bobo8bo
3b3o$89b2o8bo39b2o7b2o32b2obo3bo8b2o7bo17bo2bo11b2o6bo3b3o8bo2b5o2b2o$
90b2o4b3o39bo8bo2bo32bo4b2o17b3o16b2o13bob5o3bo3bo7b2o5b2ob2o$91bo3b2o
33bo3bo13b2o34b4obo15bo4bo16bo14b4o4bo4bo13b2o$73bobo52b2o2bo71b4o3bo
32bo6bo3bo7b2o$72bo2bo52bo3bo70b2ob2o44bo$72bo3bo33b2o16bo3bo36b2o33bo
5bo55bo$72bobo34b4obo14b2o3b2o15b2o14bo37b2o2bo13b2o38b3o$76b2o29b2o3b
ob2o15b4o16b3o11b2o4b2o35bo5bo8bo$69bo7bo29b2ob2o2bo8b2o7bo16b2o2bo11b
o6b2o38bobo8b3o31b2o$68bob2obo2bo10b2o19b6o9b2o11b2o11bo2b2o11bo2b2o2b
3o11b2o25b2o21b2o20bo20b2o$68bo5b3o10bobo11bo10bo23bo12bo2bo13bob2o16b
o49bo19bo18b2o2bo$67b2o20bo12bo34b3o10b3o34b3o47b3o16b2o17bobobo$83b2o
4b2o9bobo36bo49bo49bo20b2o16bo$83bo2bo14bo8b2o3bo44b2o3bo44b2o3bo45bo$
85b2o23bo3bobo43bo3bobo43bo3bobo41b3o15bo$76b2o19b2o12bo3bobo29b2o12bo
3bobo29b2o12bo3bobo40bo16bobo$76bo19bobo13bo4bo28bobo13bo4bo28bobo13bo
4bo58bo$96bo12b3o5b2o27bo12b3o5b2o27bo12b3o5b2o51bo6b3o$95b2o12bo35b2o
12bo35b2o12bo59b3o7bo$268bo2b2o$252bo15bo3bo$252b3o14b2obo$255bo15b2o$
254b2o2$257b4o$256bob3o$66bo69bo12b2o35bo12b2o35bo21b2o$66b3o5bo52b2o
5b3o12bo27b2o5b3o12bo27b2o5b3o$69bo4bo3bo49bo4bo13bobo28bo4bo12b2obo
28bo4bo$68bobo3bo2bo9bo40bobo3bo12b2o29bobo3bo9bo3bo29bobo3bo15b2o$69b
o3b2ob2o7b3o41bobo3bo43bobo3bo7bo35bobo3bo14bo$74bobo7bo46bo2b2o44bo3b
2o7bo2bo33bo3b2o12bobo$67bo7bo8b2o20bo24bo24bo37bo11bo37b2o2b2o$66bobo
bo17b2o16b3o47b3o47b3o35b2o6b2o8bo$66bo2b2o18bo19bo18bo30bo34bobo12bo
43bo2b2o3bobo$65b2o20bo20b2o13b3o3bo28b2o11b2o10bo5b2o5bo11b2o11b2o30b
obobo2bo3bo6b2o$87b2o36bo45b2o11b2o5bobo15b3o9b2o31bo6bo2bo6bobo$125bo
53bobobo11bo14bobo7b2o10bobo26bo2bo8bo$121bob2o18b3o15bo17bobo13bo14bo
b2obo3b2o10bo2bo21bo5bobo8b2o$119bo20bo2bo2bo14b2o48bo3b2o2bobo10bo2bo
b2o16bobo$82b2o34bo2bo19bo4bo12b2o2bo29bobo18bob2o3b2o12bo2bo17bo$80bo
4bo31bo3bo17b3o2bobo10bo4b2o31bobo19b2o2bo14b2o15b3o$80bo9b2o11bob2o
28b3o6b2o11b3o39bo18b3o15b2o15bo$71b2o13b2o2b2o11bo3bobo9bobo13b3o19b
2o41bo18bo$71b2o7b2o5bo21bo5bobo3bo24b2o52b2o48b2o$87bo19bobo5bo3bo13b
2o11b2o35b2o14b2o31b2o16bobo$80bo4b2o16bobo9bo4b2o12bo49bo14bo31bobo
18bo$70b2o7bo40b2o9b3o47b3o47bo20b2o$71bo7b2o38b2o10bo49bo48b2o4b2o4b
2o$68b3o12b2o20bo3b2o7bo2bo33bo3b2o45b2ob2o23bo2bo3bo2bo$68bo14bo20bob
o3bo7bob2o32bobo3bo43bobo3bo23b2o6b2o$84b3o16bobo3bo9bob3o29bobo3bo12b
2o29bobo3bo12b2o18b2o38b2o12bo35b2o12bo$86bo16bo4bo13bobo28bo4bo13bobo
28bo4bo13bobo19bob2o35bo12b3o5b2o27bo12b3o5b2o$102b2o5b3o12bo27b2o5b3o
12bo27b2o5b3o12bo19bo2bo35bobo13bo4bo28bobo13bo4bo16bo$111bo12b2o35bo
12b2o35bo12b2o18b3o16b2o19b2o12bo3bobo29b3obo9bo3bobo16b3o$272b2o23bo
3bobo32b2obo7bo3bobo20bo14bo$260bo3bo5bo2bo23b2o3bo33bo2bo7b2o3bo20b2o
12b3o$265bo4b2o4b2o48bo10b2o38b2o7bo$254b2o4b2ob2o11bo47b3o9b2o40bo7b
2o$255bo7b2o9bobo46bo12b2o4bo9bobo16b2o4bo$255bobo16b2o34b2o11b2o13bo
3bo5bobo19bo$256b2o52b2o24bo3bobo5bo21bo5b2o7b2o$299b2o19b3o13bobo9bob
o3bo11b2o2b2o13b2o$254bo4bo38b3o11b2o6b3o28b2obo11b2o9bo$252b3o4bo34b
2o4bo10bobo2b3o17bo3bo31bo4bo$251bo42bo2b2o12bo4bo19bo2bo34b2o$250bobo
42b2o14bo2bo2bo20bo$233b2o16bo24bobo17bo15b3o18b2obo$234bo8b3o28bobobo
53bo$234bobo8bo7bo18b2o11b2o45bo36b2o$235b2o7bo5bobobo19bo10b2o11b2o
28bo3b3o13b2o20bo20b2o$250b2o2bo43bo30bo18bo19bo18b2o2bo$239b2o13b2o6b
2o35b3o47b3o16b2o17bobobo$239bob3o14b2o2b2o37bo24bo24bo20b2o8bo7bo$
239b2o2bo13bobo12b2o3bo44b2o2bo46bo7bobo$240b3o14bo14bo3bobo43bo3bobo
41b3o7b2ob2o3bo$241bo14b2o15bo3bobo29b2o12bo3bobo40bo9bo2bo3bobo$274bo
4bo28bobo13bo4bo49bo3bo4bo$271b3o5b2o27bo12b3o5b2o52bo5b3o$271bo35b2o
12bo69bo3$236b2o$236b2o14b2o$252bo$253b3o$255bo2$228bo69bo12b2o35bo12b
2o$228b3o58b2o5b3o12bo27b2o5b3o12bo$231bo58bo4bo13bobo28bo4bo13bobo19b
o$230bobo16bo40bobo3bo12b2o29bobo3bo12b2o19b2o$231bo6bo8b3o41bobo3bo
43bobo3bo23b2o$236b2ob2o5bo45bo3b2o44bo3b2o8bo14bo2bo$46bo12b2o35bo12b
2o35bo12b2o35bo32bo5b2ob3o5b2o20bo49bo36bobo9b2o4b2o$37b2o5b3o12bo27b
2o5b3o12bo27b2o5b3o12bo27b2o5b3o31bobobo2b5o10b2o16b3o34b3o10b3o34bo
12bo20b2o$21bo16bo4bo13bobo28bo4bo13bobo28bo4bo13bobo28bo4bo34bo2b2o3b
3o12bo19bo16b2obo13bo2bo12bo23bo10bo11bobo10b3o5bo$19b3o16bobo3bo12b2o
29bobo3bo12b2o29bobo3bo12b2o29bobo3bo15b2o15b2o8bo11bo20b2o11b3o2b2o2b
o11b2o2bo11b2o11b2o9b6o19b2o10bo2bob2obo$3bo14bo20bobo3bo43bobo3bo43bo
bo3bo43bobo3bo14bo38b2o33b2o6bo11bo2b2o16bo7b2o8bo2b2ob2o29bo7bo$3b3o
12b2o20bo3b2o44bo3b2o44bo3b2o7bobo34bo3b2o12bobo74b2o4b2o11b3o16b4o15b
2obo3b2o29b2o$6bo59bo49bo36bo2bo9bo37b2o2b2o80bo14b2o15b2o3b2o14bob4o
34bobo$5b2o59b3o47b3o37bo9b3o35b2o81b2o36bo3bo16b2o33bo3bo$26bo42bo13b
4o32bo23b2o8bobo13bo155bo3bo52bo2bo$26b2o40b2o13bo2b2o16bo13b2o11b2o9b
4o22b2o155bo2b2o52bobo$6b2o19b2o14bo40bo2b2o14b3o25b2o9bob3o45b2o53bob
o18bob4o34b2o13bo3bo10b2o21b2o3bo$6b2o19bo14b2o40bo2bo14bo2b2o34bob3o
34b3o8b2o40b2o12bo2b2o16b2o4bo32bo2bo8bo19bo19b3o4b2o$22b3obo15bobo2b
2o36b2o15b5o14b3o18b3o34bo13bo3b2o34b2o14bo18bo3bob2o32b2o7b2o20bob2o
15bo8b2o$22b3o22bobo54b3o14bob2o17b2o35bo16b2ob2o68b3obo21b2o11bo9b2o
18b2o2bo2b2o11bobo2b5o$49bo55b2o15bob2o70b2o2bo81bo13bo40bo2bo5bo12bo
3b3o$46bob2o54bobobo13bobo57bo13bo3bo31b2o46b2o11b3o41bobob5o35b2o$46b
2o18b4o29b2o3bob2o9bo4b2o36b2o15bo4bo13bob2o33bo46b3o10bo42b2obo3bo37b
2o2b2o$13b2o55bo34b2o10bobo39bo2b2o13bo19bo32b3o12b2o20bo3b2o44bo3b2o
5bo3b2o3bobo27bo3b2o12bobo$13bobo6b2o32b2o8bo4bo45b2o39b3o2bo14bo2bo
28b2o18bo14bo20bobo3bo43bobo3bo5bob2o3bo2bo27bobo3bo14bo$2o13b2o5bo20b
2o11b2o9b2obo22b2o48b2o13bo4bo14b3o11b2o16bobo33b3o16bobo3bo12b2o29bob
o3bo6bo36bobo3bo15b2o$bo2b2o8bo9bo19bo24bo9b2o13bo49bo13b5o28bobo18bo
35bo16bo4bo13bobo28bo4bo10bo3bo29bo4bo$bobobo6bobo8b2o16b3o34b3o10b3o
47b3o15b2o30bo11bo8b2o50b2o5b3o12bo27b2o5b3o10bo29b2o5b3o$2bo8b2o6b2o
20bo36b3o10bo49bo48b2o4b2o4b4o67bo12b2o35bo7bobo39bo$11b3o5bo45bo3b2o
9bo34bo3b2o44bo3b2o23bo2bo3bo2b2o123bo3b2o$4bo15b3o41bobo3bo8bo34bobo
3bo43bobo3bo23b2o5bo4bo121b2o3bo$3bobo16bo40bobo3bo12b2o29bobo3bo12b2o
29bobo3bo12b2o17b2obob2o120bo$4bo58bo4bo13bobo28bo4bo13bobo28bo4bo13bo
bo20b4o120bo2bo$b3o58b2o5b3o12bo27b2o5b3o12bo27b2o5b3o12bo20b4o120b3o
8b2o$bo69bo12b2o35bo12b2o35bo12b2o18b5o131bobo$203b2o2bo111bob2o17bo$
204b3o112b2obo$205bo$328b2o$329bo4$30b2o12bo35b2o12bo119bo$31bo12b3o5b
2o27bo12b3o5b2o108b3o$10bo20bobo13bo4bo28bobo13bo4bo16bo91bo$9b3o20b2o
12bo3bobo29b2o12bo3bobo16b3o83bo4bobo$8b2o2bo7b2o23bo3bobo43bo3bobo20b
o14bo55b2o10b2o4bo$8b2ob3o4bo2bo23b2o3bo44b2o3bo20b2o12b3o56bo9bobo
147b3o$8b5o5b2o4b2o48bo59bo59bobo16bo140bo34b2o$2b2o6bo13bo47b3o59b2o
59b2o13bobobo124bo15bo33bobo$3bo18bobo24b3o7bo11bo25bobo99bo10b2o2bo
116bo5b3o51bo$3bobo16b2o27bo5b2ob2o9b2o20bo3bobo16b2o80b2o3bo10b2o111b
o3bo4bo50b4ob2o$4b2o33bo10bo6bo41b2o15b3o14b2o63bo129bo2bo3bobo49bo2bo
bobo$39bo17bo3bo37bo15bo2bo14b2o62b2ob3o115b2o8b2ob2o3bo54b2obo$37bo
20b3o32bobobo18b2o80bo120bo9bobo61bob2o$36b3o3bo50b3obo2bo98bo3bo115bo
bo8bo7bo55bo2bo$18b3o14bo3bob2o51bo3bo100bo2bo117b2o13bobobo55b3o$18bo
bob2o12b5o21bo13bo123b3o132b2o2bo40bo14bo2b2o$18bobo2bo13b3o3b2o16b3o
10b2o263b2o38bobo4bo9b2o2bo$23b3o18bo19bo8b2o54b2o249bo5b3o8bob2o$24b
2o7b2o8bo17bo2b2o6bo11bo32b2o10b3o255bo9bo$24bo8b2o11b2o10bo2bo3bo7b5o
5b2o11b2o20bo9bo2bo7b2o55b2o171b2o17bo7b2o$46bo11b2o14bo21bo19bo10b2ob
2o3b2o2bo56b2o14b2o102b2o51bobo$10b2o35b3o11bobo33b3o16b2o9b2ob2o3bobo
bo72bo104bo51bo16bobob3o$6b2o2b2o37bo10b2obo35bo20b2o6b2ob2o5bo74b3o
101bobo58b2o5bo3b3obo$5bobo12b2o3bo35b2o7b2o3bo45bo9bo83bo102b2o2b2o
54b2o4b3ob2ob3o$5bo14bo3bobo43bo3bobo41b3o7b3o5bo184bobo60bo$4b2o15bo
3bobo29b2o12bo3bobo40bo10bo5bobo50bo69bo12b2o35bo12bo2bo$22bo4bo28bobo
13bo4bo58bo51b3o58b2o5b3o12bo27b2o5b3o11b2ob2o6b2o$19b3o5b2o27bo12b3o
5b2o58b3o51bo58bo4bo13bobo28bo4bo15bo4b2o3bobo55b2o$19bo35b2o12bo69bo
50bobo5bo10bo40bobo3bo12b2o29bobo3bo15b3o8bo55bo$191bo5b3o7b3o41bobo3b
o43bobo3bo15b2o2bo5b2o49bo5b3o$112bo83bo9bo45bo3b2o7b2o35bo3b2o17b2o
56bobo6bo$112b3o74bo5b2ob2o6b2o20bo35bob2o10bo104b2o$115bo72bobobo3b2o
b2o9b2o16b3o33bobo11b3o106b2o$114b2o14b2o56bo2b2o3b2ob2o10bo19bo21bo
14b2o11bo94bo10bobo$130b2o55b2o7bo2bo9bo20b2o11b2o5b5o7bo3bo2bo10b2o
11b2o8bo72b2o4b2o5bo$196b3o10b2o32bo11bo6b2o2bo17bo8b2o7b2o17bo53bobo
4b2o5b2o$197b2o54b2o8bo19bo18b3o17b2o$252b2o10b3o16b2o3b3o13bo2bobo11b
2o$125b3o123bo13bo21b5o12b2obobo$125bo2bo100bo3bo51b2obo3bo14b3o$124bo
3bo98bo2bob3o50bo3b3o$129bo80b2o18bobobo32b3o20bo47bo$125b3ob2o62b2o
14bo2bo15bo37bo3bo17bo50bo$129bo63b2o14b3o15b2o41bo6bo10bo33b2o13b3o$
112b2o10bo3b2o80b2o16bobo3bo20b2o9b2ob2o5bo27b2o16bobo$113bo2b2o10bo
99bobo25bo11bo7b3o24bobo18bo$113bobobo13b2o59b2o59b3o47bo13bo6b2o$114b
o16bobo59bo59bo48b2o4b2o5b5o$121bobo9bo56b3o12b2o20bo3b2o44bo3b2o23bo
2bo4b3ob2o41b2o9b2o26b2o$116bo4b2o10b2o55bo14bo20bobo3bo43bobo3bo23b2o
7bo2b2o42b2o8bobo25bobo$115bobo4bo83b3o16bobo3bo12b2o29bobo3bo12b2o20b
3o16bobo23bo12bo4b2o21bo4b2o$116bo91bo16bo4bo13bobo28bo4bo13bobo20bo
18b2o32b4ob2o2bo2bo15b4ob2o2bo2bo$113b3o108b2o5b3o12bo27b2o5b3o12bo39b
o33bo2bobobobob2o15bo2bobobobob2o$113bo119bo12b2o35bo12b2o75bobobobo
21bobobobo$374b2obobo22b2obobo$378bo27bo$353bo$351bobo10b2o26b2o$352b
2o11bo7b2o18bo7b2o$122bo242bobo5b2o18bobo5b2o$121b3o242b2o26b2o$120bo
2b2o$119b5o18b2o12bo35b2o12bo35b2o12bo69bo22bo$119b4o20bo12b3o5b2o27bo
12b3o5b2o27bo12b3o5b2o58b3o21bobo21b2o19bo$119b4o20bobo13bo4bo28bobo
13bo4bo28bobo13bo4bo58bo24bob2obo19b2o16b3o5b2o$120b2obob2o17b2o12bo3b
obo29b2o12bo3bobo29b2o12bo3bobo40bo16bobo24bob2obo17bo17bo9b2o24bo$
121bo4bo5b2o23bo3bobo43bo3bobo34bo8bo3bobo41b3o15bo25bob2obo35b2o7bo
24b3o$122b2o2bo3bo2bo23b2o3bo44b2o3bo34bo9b2o3bo45bo5b3o31bob2obo22b2o
26b2o6bobo8bo$122b4o4b2o4b2o48bo49bo10b3o36bo20b2o6b2o8bo22bobo25bo8bo
bo16bo8b2o8b2o$114b2o8bo11bo30b2o15b3o47b3o10b3o34b3o16b2o8bobo6bobobo
22bo27b3o6b2o17b3o5bo$115bo18bobo28b5o13bo49bo13b2o9bo24bo19bo9bo8b2o
2bo40bo11bo6bo20bo$115bobo16b2o11b3o14bo4bo13b2o48b2o22bob2o9b2o11b2o
20bo5b2o13b2o40bo62b2o$116b2o28bo2bo14bo2b3o39b2o45bo4bo8b2o32b2o6bobo
51b3o63bo$130bo19bo13b2o2bo39bobo10b2o34bo55b2o65b2o50bob2o$128b2obo
13bo4bo15b2o36b2o4bo9b2obo3b2o29b4o18b2o97bobo5b2o35b2o4b3o2bo$127bo3b
o13bo57bobo13bobobo54b2obo97bo7b2o35b2o3bo3b2o$127bo2b2o70b2obo15b2o
55bo99b2o49b4o$127b2ob2o16bo35b2o17b2obo14b3o54bobo22b3o109b2o15bo$
129b2o3bo13bo34b3o18b3o14b5o15b2o36b2o2bobo15bob3o52b4o30bo21bobo12b3o
$135b2o8b3o34b3obo34b2o2bo14bo2bo40b2o14bo19b2o14bo20bo2b2o26b2obobo
20bo13bo$134b2o45b3obo9b2o25b3o14b2o2bo40bo14b2o19b2o14b2o21bo27bobobo
bo19b2o6bo7b5o$158b2o22b4o9b2o11b2o13bo16b2o2bo13b2o40b2o33bobo25b2o
19bo2bobobobob2o22b2o12bo$158bo13bobo8b2o23bo32b4o13bo42bo61b2o19b4ob
2o2bo2bo23b2o9bo$122b2o35b3o9bo37b3o47b3o59b2o36bo28bo4b2o36b2o$118b2o
2b2o37bo9bo2bo36bo49bo59bo35bo2b2o24bobo$117bobo12b2o3bo34bobo7b2o3bo
44b2o3bo44b2o3bo20b2o12b3o33b4o20bo3b2o$117bo14bo3bobo43bo3bobo43bo3bo
bo43bo3bobo20bo14bo55bobo$116b2o15bo3bobo29b2o12bo3bobo29b2o12bo3bobo
29b2o12bo3bobo16b3o7b2o63b2o$134bo4bo28bobo13bo4bo28bobo13bo4bo28bobo
13bo4bo16bo10bo$131b3o5b2o27bo12b3o5b2o27bo12b3o5b2o27bo12b3o5b2o24bo
24b2o$131bo35b2o12bo35b2o12bo35b2o12bo33b5o14b2o5bo$320bo13bo4bo40bo$
317b3o12bobo4b5o14b2o18b3o$316bo9bobo3b2o10bo13bo18bo$316b4o5bo2bo12b
3o12bobo18b2o$314b2o3bo3b6o11bo9b3o3b2o47bobo$313bo2b3o4b2o15b4o6b2obo
51b2o$313b2obo21b2o3bo5bo3bo31b2o19bo$316bo20bo2b3o7b3o19bo13bo$316b2o
19b2obo9b3o20b2o11bob2o6bo$340bo31b2o4b2o4b3o2bo7bo$340b2o36b2o3bo3b2o
6b3o$324b2o57b4o$325bo43b2o15bo$322b3o23b2o18bobo12b3o$322bo26bo18bo
13bo$346b3o18b2o14b5o$341bo4bo40bo$340b2o21b2o20bo$340bobo19b2o21b2o5b
o$364bo25b2o$391b2o$368bobo$368b2o6bo$355bo13bo6b3o$355b3o21bo$358bo
19b2o$357b2o$383bo$384bo$377b2o2bo2b2o$376b3obobob3o$354b2o21b2o2bo2b
2o$355b2o2bo18bo5bo3b2o$356b4o7b2o10b5o4bobo$357b2o8bobo10b3o7bo$357b
2obo8bo11bo8b2o$359b3o7b2o$359bobo15bo$356b2obo16bobob2o$355bob4o15bob
obobo$355bobobob2o10b2obobobobo2bo$352b2obobobo4bo8bo2bo2b2ob4o$352bo
2bo2b2ob4o10b2o4bo$354b2o4bo20bobo$360bobo19b2o$361b2o!

There are also trivial "duplicators" for any period with a gun:
x = 114, y = 129, rule = B3/S23
111b3o$113bo$112bo3$106b3o$108bo$107bo3$101b3o$103bo$102bo3$96b3o$98bo
$97bo3$59bob2o28b3o$44b2o11b3obobo29bo$44bobo9bo4bo2bo27bo$46bo3bo4bob
o3b3o7b2o4b2o16b2obo$46b2ob2o5bobo12bobo2bobo15bobob3o11b2o$49bob4o3b
8o7b4o9b3o4bo2bo4bo9bobo$46b2o4b6o3bo3bo5bo2b2o2bo9bo5b3o3bo3bo2b2o2bo
$45bob2obo7bobob2o7bo2b2o2bo8bo11bob6o3b2o$45bo6bo3bo3b2ob2o8bo2bo15b
8o4b3o$46b6o8bo4bo26bo7b3o2bo2bob2o$50bo5bobo4b4o14b3o10bo2b2o2b2o3b5o
bo$46b2o4bo2bo2bobob2ob2o8b2o6bo9b2o4bo5bo6bo$46b2o3b2o2bo4b2ob2obo15b
o10bo4b2o6b6o$56b4o2bo3bo3b3o5bo15bo3bobo6bo$60b2o2bobo4b2o5bo3bo7b2o
2b2obo2bobo2bo4b2o$56b4o2bo3bo3b3o5b6o5bo4bob2o4bo2b2o3b2o$46b2o3b2o2b
o4b2ob2obo13bobobo4bo3bobo2b4o$46b2o4bo2bo2bobob2ob2o7b3o2b3ob3o3bo3bo
3bo$50bo5bobo4b4o14bo2bo4bo3bobo2b4o$46b6o8bo4bo8b2o7bo5bo4bob2o4bo2b
2o3b2o$45bo6bo3bo3b2ob2o14bo10b2o2b2obo2bobo2bo4b2o$45bob2obo7bobob2o
7bo2b2o3b3o12bo3bobo6bo$46b2o4b6o3bo3bo4bobobo6b3o9bo4b2o6b6o$49bob4o
3b8o4b2o2bo5bo2bo9b2o4bo5bo6bo$46b2ob2o5bobo9b2ob2o6b2obo11bo2b2o2b2o
3b5obo$46bo3bo4bobo3b3o3bob2o8b2o3bo7bo7b3o2bo2bob2o$44bobo9bo4bo2bo2b
o4b3o6bo3bo6b8o4b3o$44b2o11b3obobo2b2o5b2o6bobob3o11bob6o3b2o$59bob2o
8b2o11bo3bo5b3o3bo3bo2b2o2bo$70bob2o6bobob4obo3bo2bo4bo9bobo$68b2o2b2o
6b2o2bo2bobo4bobob3o11b2o$69b3o12bo3bob2o3b2obo$65bo2bobo14b2obo2bo$
63b3o2bobo13b3ob2o$62bo4bo14bo$62bob2obo3bo10bobo$61b2obo2bo3bo6b2o2bo
2b3ob2o$64bo2bo10bo2b3o3bobobo$64b2obo2bo8b3o3bobobobo$62b2o2bobo14bob
obo2bo$63bob2obobo8b3o3bobo$41b2o20bo2bo2b2o7bo2bobobob2o$41bo22bobo
12bobob2o$39bobo23bo14bo$39b2o$65bo14bo$35b3o26bobo12bobob2o$37bo25bo
2bo2b2o7bo2bobobob2o$36bo26bob2obobo8b3o3bobo$62b2o2bobo14bobobo2bo$
64b2obo2bo8b3o3bobobobo$30b3o31bo2bo10bo2b3o3bobobo$32bo28b2obo2bo3bo
6b2o2bo2b3ob2o$31bo30bob2obo3bo10bobo$62bo4bo14bo$63b3o2bobo13b3ob2o$
25b3o37bo2bobo14b2obo2bo$27bo41b3o12bo3bob2o3b2obo$26bo41b2o2b2o6b2o2b
o2bobo4bobob3o11b2o$70bob2o6bobob4obo3bo2bo4bo9bobo$59bob2o8b2o11bo3bo
5b3o3bo3bo2b2o2bo$20b3o21b2o11b3obobo2b2o5b2o6bobob3o11bob6o3b2o$22bo
21bobo9bo4bo2bo2bo4b3o6bo3bo6b8o4b3o$21bo24bo3bo4bobo3b3o3bob2o8b2o3bo
7bo7b3o2bo2bob2o$46b2ob2o5bobo9b2ob2o6b2obo11bo2b2o2b2o3b5obo$49bob4o
3b8o4b2o2bo5bo2bo9b2o4bo5bo6bo$15b3o28b2o4b6o3bo3bo4bobobo6b3o9bo4b2o
6b6o$17bo27bob2obo7bobob2o7bo2b2o3b3o12bo3bobo6bo$16bo28bo6bo3bo3b2ob
2o14bo10b2o2b2obo2bobo2bo4b2o$46b6o8bo4bo8b2o7bo5bo4bob2o4bo2b2o3b2o$
50bo5bobo4b4o14bo2bo4bo3bobo2b4o$10b3o33b2o4bo2bo2bobob2ob2o7b3o2b3ob
3o3bo3bo3bo$12bo33b2o3b2o2bo4b2ob2obo13bobobo4bo3bobo2b4o$11bo44b4o2bo
3bo3b3o5b6o5bo4bob2o4bo2b2o3b2o$60b2o2bobo4b2o5bo3bo7b2o2b2obo2bobo2bo
4b2o$56b4o2bo3bo3b3o5bo15bo3bobo6bo$5b3o38b2o3b2o2bo4b2ob2obo15bo10bo
4b2o6b6o$7bo38b2o4bo2bo2bobob2ob2o8b2o6bo9b2o4bo5bo6bo$6bo43bo5bobo4b
4o14b3o10bo2b2o2b2o3b5obo$46b6o8bo4bo26bo7b3o2bo2bob2o$45bo6bo3bo3b2ob
2o8bo2bo15b8o4b3o$3o42bob2obo7bobob2o7bo2b2o2bo8bo11bob6o3b2o$2bo43b2o
4b6o3bo3bo5bo2b2o2bo9bo5b3o3bo3bo2b2o2bo$bo47bob4o3b8o7b4o9b3o4bo2bo4b
o9bobo$46b2ob2o5bobo12bobo2bobo15bobob3o11b2o$46bo3bo4bobo3b3o7b2o4b2o
16b2obo$44bobo9bo4bo2bo27bo$44b2o11b3obobo29bo$59bob2o28b3o3$97bo$98bo
$96b3o3$102bo$103bo$101b3o3$107bo$108bo$106b3o3$112bo$113bo$111b3o!
-Matthias Merzenich
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Re: Oscillator Discussion Thread

Postby wildmyron » April 4th, 2018, 12:40 pm

I made this p39 using the p3 bumper I posted earlier.
x = 47, y = 47, rule = B3/S23
30b2o$30bo2bo$32b2o$28b4o$28bo4b3o$24b2o3b2ob2o2bo$16bo7bo3bo6bo$16b3o
6b3o4b3o$19bo$18b2o7b4o$5bo22b3ob3o$4bobo16bo$4bo2bo2bo11bobo3b3o$b2ob
2obo2bo3bo7bo2bo4bobo$2bo2bobo2bo2bobo7b2o6bobo$o2bo10bo17bo$2obobo3b
2ob2o25b2o$3bobo3b2obo7b2o17bo$3b2obo2b2obo6bobo15bobo$7bobo11bo6bo8b
2o$7bo21bo$5bobo5bo13b3o$5b2o5bobo18b2o$11bo2bo17bo2bo$12b2o18bobo5b2o
$17b3o13bo5bobo$17bo21bo$8b2o8bo6bo11bobo$7bobo15bobo6bob2o2bob2o$7bo
17b2o7bob2o3bobo$6b2o25b2ob2o3bobob2o$14bo17bo10bo2bo$13bobo6b2o7bobo
2bo2bobo2bo$14bobo4bo2bo7bo3bo2bob2ob2o$16b3o3bobo11bo2bo2bo$23bo16bob
o$12b3ob3o22bo$16b4o7b2o$27bo$12b3o4b3o6b3o$11bo6bo3bo7bo$10bo2b2ob2o
3b2o$11b3o4bo$15b4o$13b2o$13bo2bo$15b2o!

I was hoping for p36 because the reaction supports p36 streams, but that doesn't work out. I can't quite figure out the math behind what period loops can be made with this kind of interaction. If I understand correctly there's no way to enlarge the loop in order to make it work at p36 - it requires another reflector with a different delay. How do I work out what's required to make it work?
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Re: Oscillator Discussion Thread

Postby dvgrn » April 4th, 2018, 1:14 pm

wildmyron wrote:I made this p39 using the p3 bumper I posted earlier...I was hoping for p36 because the reaction supports p36 streams, but that doesn't work out. I can't quite figure out the math behind what period loops can be made with this kind of interaction. If I understand correctly there's no way to enlarge the loop in order to make it work at p36 - it requires another reflector with a different delay. How do I work out what's required to make it work?

Actually period 36 is perfectly doable. Good thing, too, because we have a critical shortage of alternate color-preserving reflectors that work at p36. A CP semi-cenark can be overclocked to p36, but we'd run out of gliders in the loop after a while.

To figure this kind of thing out, first work out the total period of the loop -- 39*4 = 156 in this case. Then start adding 8N until you get a multiple of the period you want. In this case, +3fd, stretching the loop three cells diagonally to get to 180 ticks, is the minimum. You have to add one more glider to the loop to get p36:

x = 50, y = 50, rule = B3/S23
33b2o$33bo2bo$35b2o$31b4o$31bo4b3o$27b2o3b2ob2o2bo$19bo7bo3bo6bo$19b3o
6b3o4b3o$22bo$21b2o7b4o$31b3ob3o2$26bobobob2o$5bo18bo8bobo$4bobo17bo5b
2o2bobo$4bo2bo2bo14bo9bo$b2ob2obo2bo3bo11bobo13b2o$2bo2bobo2bo2bobo11b
o14bo$o2bo10bo25bobo$2obobo3b2ob2o26b2o$3bobo3b2obo$3b2obo2b2obo$7bobo
8b3o14b2o$7bo12bo13bob2o$5bobo11bo14bob2o5b2o$5b2o5b3o19bo2bo4bobo$35b
2o5bo$10b2o28bobo$15bo3bo17bob2o2bob2o$18b2o17bob2o3bobo$8bo5bo3bobo4b
o10b2ob2o3bobob2o$7bob2o2bo11bobo7bo10bo2bo$7bo17b2o7bobo2bo2bobo2bo$
6b2o27bo3bo2bob2ob2o$14bo24bo2bo2bo$13bobo6b2o19bobo$14bobo5bobo19bo$
16b3o3b3o2$12b3ob3o$16b4o7b2o$27bo$12b3o4b3o6b3o$11bo6bo3bo7bo$10bo2b
2ob2o3b2o$11b3o4bo$15b4o$13b2o$13bo2bo$15b2o!

The next loop of the right size is +12fd. So there you could make the bumper mechanisms 90-degree rotationally symmetrical, but you have to have seven gliders in the loop so the whole thing is only C4 symmetric with a time shift (or however you say that):

x = 59, y = 59, rule = B3/S23
36b2o$36bo2bo$38b2o$34b4o$34bo4b3o$30b2o3b2ob2o2bo$22bo7bo3bo6bo$22b3o
6b3o4b3o$25bo$24b2o7b4o$34b3ob3o2$29bobobob2o$27bo8bobo$27bo5b2o2bobo$
28bo9bo$5bo23bobo$4bobo23bo$4bo2bo2bo$b2ob2obo2bo3bo$2bo2bobo2bo2bobo$
o2bo10bo$2obobo3b2ob2o7b3o27b2o$3bobo3b2obo10bo13bo13bo$3b2obo2b2obo9b
o15b2o9bobo$7bobo27b2o10b2o$7bo37b2o$5bobo5bo30b3o$5b2o4b2o2bo28bo2bo$
14b2o29b2o$40bo11b2o$40bobo8bobo$40b2o9bo$8b2o39bobo$7bobo36bob2o2bob
2o$7bo38bob2o3bobo$6b2o37b2ob2o3bobob2o$25bo18bo10bo2bo$24b2o17bobo2bo
2bobo2bo$24bobo4bo12bo3bo2bob2ob2o$31bobo14bo2bo2bo$31b2o19bobo$53bo$
20bo$19bobo6b2o$20bobo5bobo$22b3o3b3o2$18b3ob3o$22b4o7b2o$33bo$18b3o4b
3o6b3o$17bo6bo3bo7bo$16bo2b2ob2o3b2o$17b3o4bo$21b4o$19b2o$19bo2bo$21b
2o!

Every time you add 9fd -- 9*8=72 ticks -- you have to add two more gliders to the loop to fill it up at p36.

There's a weird optical illusion in both of these, where it looks like the gliders couldn't possibly be evenly spaced... but oscar reports them both as p36 oscillators.

The cases where enlarging the loop doesn't help are situations where you want some number like 8N, but what you have is 8N+k for nonzero k. No matter how many eights you add it never seems to help.
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Re: Oscillator Discussion Thread

Postby wildmyron » April 4th, 2018, 1:28 pm

Ah, thanks for the explanation. I tried to go for a loop with 4 gliders initially which blew up because the p3s were out of phase and then when I tried going bigger i went in steps of 36, which of course didn't solve the problem.
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Re: Oscillator Discussion Thread

Postby Sokwe » April 4th, 2018, 2:29 pm

wildmyron wrote:I made this p39 using the p3 bumper I posted earlier.

Congratulations! This is the first p39 that has more than 2 connected p39 cells, as well as the first p39 with no p13 cells. Of course, it is also the first p39 reflector. I've updated the Life status page accordingly. For documentation purposes, here is the link to your original post.

Edit: How did you find the p3 sparker? The interaction is non-trivial.

If you are unsure about whether an interesting oscillator or oscillator component is new, you should still post it here. Far too many interesting patterns are ending up in the threads for your accidental/unsure/useless discoveries. This will make them hard to find when people are trying to build pattern collections.

With that in mind, here two oscillators (p6 and p7) found by Bullet51:
x = 37, y = 14, rule = B3/S23
33bo$31b3o$30bo$4b2o22b3ob4o$4bo4bo3b2o12bo3bobo2bo$5bo3bobo2bo11bo2bo
bo3b2o$2obobo3bob3o12bob2o$ob2obobo17b2o4b2o$6b8o12bob2o$13bo11bo2bo$
8b4o13b2o5b2o$8bo2b2o19bo$33b3o$35bo!

See here and here.
-Matthias Merzenich
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Re: Oscillator Discussion Thread

Postby wildmyron » April 5th, 2018, 12:01 am

Sokwe wrote:
wildmyron wrote:I made this p39 using the p3 bumper I posted earlier.

Congratulations! This is the first p39 that has more than 2 connected p39 cells, as well as the first p39 with no p13 cells. Of course, it is also the first p39 reflector. I've updated the Life status page accordingly. For documentation purposes, here is the link to your original post.

Thank you. Lucky I went for the p39 instead of p36 then :) . It didn't occur to me that it would be significant as an oscillator or that there was no reflector at that period.

Sokwe wrote:How did you find the p3 sparker? The interaction is non-trivial.

I used JLS and a method similar to what you showed for finding a sparker to support a smaller p52 gun. In this case I started from the p6 bumper in a grid with 36 gen, and kept it periodic (using unknown cells to insert and remove the glider). Then I accepted the state, removed the sparker, cleared the spark interaction area and a few cells around it, cleared a channel to the south of the interaction area, made most of the cleared area p3 except for a 1-2 cell boundary around the interaction area and then removed a few extra off cells during generations at and after the interaction. I set most of the p3 area to Don't Care initially until I found a spark that would work. This took a few goes, and I had to adjust the empty area slightly before finding a solution.

I tried this after unsuccessfully searching for a p2 bumper. This would be very useful as it would allow true p34 and p38 reflectors and oscillators. None of the searches I tried were successful and the search space eventually got to a point where it was taking hours to run. I only found one p2 spark from the initial search results and it was impossible to support with p2 as soon as I removed the Don't Care cells around it.

Edit: I forgot to mention the most important setting for completing this search in a reasonable time: Set the overall search order to "Process all cells in a generation first...". This is much faster because the number of unset cells in gen 0 + gen 1 is much less than number of generations * number of unconstrained cells. The p2 border ensures the whole grid is determined after gen 0 and gen 1 are complete.

Edit 2: oops, I wrote that edit thinking about p2, but the same argument applies to p3
Last edited by wildmyron on April 5th, 2018, 8:16 am, edited 1 time in total.
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Re: Oscillator Discussion Thread

Postby calcyman » April 5th, 2018, 7:03 am

Do you have a partial result for the p2 bumper? I could try bashing it with SAT solvers.
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Re: Oscillator Discussion Thread

Postby wildmyron » April 5th, 2018, 8:28 am

calcyman wrote:Do you have a partial result for the p2 bumper? I could try bashing it with SAT solvers.

No, the p2 result I mentioned came from a search with only 1 layer of p2 cells, and required non p2 cells to support the p2 layer. None of my subsequent searches with two layers of p2 cells yielded any results. I have thought about passing the problem to a SAT solver but I think it will need to be defined in its entirety. This would have the advantage of being able to define periodic cells which momentarily become non-periodic, which JLS can't do (except for manually set phases which aren't required to obey the periodicity constraint).

Are there any other good prospects for finding a fast p2 reflector?
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Re: Oscillator Discussion Thread

Postby dvgrn » April 5th, 2018, 9:32 am

wildmyron wrote:Are there any other good prospects for finding a fast p2 reflector?

Or a stable one, for that matter? A color-changing Snark that recovers in 34 ticks would solve the p34 and p38 oscillator cases, and a whole lot of other problems besides. But I guess I don't have any immediate suggestions for a likely mechanism, except maybe a fresh look at getting the half-blockade back directly from the surplus R output in Guam's G4-to-R converter:

x = 93, y = 76, rule = LifeHistory
6$30.3D9.3D3.3D8.5D.D11.4D$29.D3.D7.D3.D.D3.D7.D5.D11.D3.D$29.D11.D3.
D.D11.D5.D5.D3.D.D3.D$29.D2.2D.5D2.4D.D2.2D.5D2.3D2.D6.D.D2.4D$29.D3.
D11.D.D3.D11.D.D7.D3.D2.D$29.D3.D11.D.D3.D7.D3.D.D6.D.D2.D3.D$30.3D9.
3D3.3D9.3D2.5D.D3.D.D3.D8$33.C$34.C$32.3CB$33.4B$34.4B$35.4B$36.4B$
37.4B$38.4B$39.4B$40.4B$41.4B$42.4B$43.4B$44.4B$45.4B$46.4B$.C45.4B$
2.C45.4B3.C$3C46.4B3.C$50.4B3CB$51.8B26.B$52.8B24.2B$53.8B22.3B$2C52.
8B20.4B$2C2.2C49.8B18.4B$4.2C50.8B16.4B$57.8B7.2A5.4B$58.8B5.B2AB3.4B
$59.8B4.3B3.4B$60.8B4.B2.5B$61.8B.9B$62.16B.3B$63.19B$64.21B3.B$65.
21B.B2A$66.22B2A$67.20B.B$65.12B2A7B$64.2B2D9B2A4B.B$64.B2D14B$65.BD
11B3.A$66.10B5.3A$68.8B8.A$69.5B9.2A$69.2B2AB$71.2A!

But unless the spark at the lower right can be used to trigger the rebuild, and the R can be suppressed impressively quickly, that reaction probably won't recover soon enough to work at p34. Fast-recovery candidates are hard to find.

A stable bumper would make another color-changing Snark -- not that I'd turn up my nose at that, but the required spark just doesn't seem likely to have a stable equivalent.
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Re: Oscillator Discussion Thread

Postby Kazyan » April 5th, 2018, 11:37 pm

Well done on the p3 bumper result! I see that it's already in use in the gun collection, too.

The description of attempts to find a p2 bumper are, essentially, calling for a version of Bellman that can handle p2 catalysts. That can be arranged with LLS. I should really get proficient and familiar with it, at this point...as for a stable bumper, that's not likely. The reaction isn't very picky about how the spark is shaped, thus allowing wildmyron to unearth a p3 version, but it's quite firm about the first tick of the interaction occurring on, well, the generation that it does in every version so far. On that tick, there's nothing new at the edge of the reaction envelope--so a bumper simply will not work with a stable object; stable objects would start reacting at least one tick sooner and ruin the whole thing.
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Re: Oscillator Discussion Thread

Postby wildmyron » April 6th, 2018, 3:43 am

@Kazyan, thanks for pointing that out. I have no experience with Bellman yet, but maybe I should give it a whirl.

This is the smallest (by population) p3 I could find which supports the bumper - 24 cells.
x = 12, y = 13, rule = B3/S23
11bo$9b3o$8bo$8b2o2$4bob2o$2bo4bo$2bo2b2o$2bo3bo$5bo$ob2obo$bo$bo!
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Re: Oscillator Discussion Thread

Postby Sokwe » April 6th, 2018, 3:11 pm

Were any of the following p7 bumper variants previously known?
x = 142, y = 16, rule = B3/S23
6bo39bo39bo39bo$4bobo13bo2bo20bobo37bobo37bobo10bo$5b2o11b6o21b2o38b2o
38b2o9bobo$17bo6b2o110bobo$7b2o4b2o2bo2b4o2bo20b2o4b2o5bo26b2o4b2o5b2o
25b2o6b2obob2o$6bo2bo3bobo3bobobob2o19bo2bo3b2o3b3o25bo2bo3b2o5b2o24bo
2bo8bo2bo$6bobo6bo2bobobo2bo20bobo8bo28bobo37bobo6b3obo$7bo7bo3bo3bobo
21bo10bo28bo39bo6b2obob2o$13bobobobobobob2o26bo3b2o2bo31b2o5b2o33bo3bo
$2b2o9b2obobobobo19b2o8bob2o3b3o20b2o8bo2bo3bo2bo19b2o8b2obobobo$3bo
12bo3bo22bo13b2o24bo8bo3bobo3bo20bo4b2obobobob2o$3o13b2o2b2o18b3o9bob
2o3bo20b3o9bo3bobo3bo17b3o5bob2obo2bo$o39bo11bo2bob2o21bo10bo2bobobobo
2bo16bo13bobo$53bobobo34bobobobobobo32bo$54b2o2bo36bo3bo$57b2o!


A p4 bumper can replace to of the p8 bumpers in AbhpzTa's p40 gun to save a row at the top and bottom:
x = 165, y = 134, rule = B3/S23
92b2o$83bo9bo7bo$83b3o7bob2o2b3o15bo$86bo7bo3bo17b3o$85b2o12bo15bob3o$
96b3o6bo8bo3bo$105b3o5bo3bo$90bobo15bo3b3obo$88b3ob3ob2o9b2o4b3o$89bob
ob2ob2o16bo$90b3o17bo$90b3o16bobo$105b2o2b2o$67b2o36b2o$67b2obo$71bo$
68bo38bo$69bob2o34b2o$71b2o8b2o23bobo$82b2o16bo$75bo5bo16bobo$74bobo
22b2o16bo$75b2o41bo$71b2o43b3o$70bobo29b2o$70bo5b2o23bo2bo4b2o$69b2o5b
2o23bobo5b2o$102bo$85b3o$65b2o18bo11b2o9b2obo32b3o$65bobo3b2o3bo9bo11b
o10bobo6bo24bo$67bo3bo3bobobo15b3o12bo16bo5b2o8bo3bo$63b4ob2obo3bo2b2o
15bo13b2o5bob3o7bo4b2o8bo2bobo$63bo2bo3bob2obo33b2o7b2obo4b3o16bobo2bo
$68bobobobob4o29b2o7bob2o24bo3bo$66b2o2b2o2bo5bo38b3obo26bo$68b2obo2bo
2bobo4bo21bo6b2o13b2o17b3o$69bobobo5b2ob2obo19b3o6bo6bo8bo24bobo$69bob
ob8o2bobo2bo6b3o6b3obo5bobo11b2o24bo$70bobo4bo5bo2b3o6bo9bo3bo5b2o21b
2o15bo2bo$71bo2b3o12b2o5bo9bo3bo27b2o10bo4bobobo$72b2obo4bo3b5o2bo15bo
b3o38bo5bo2bo$77bo5bo5bo2bo15b3o39bo6b2o$76b2o2bob2ob4ob2obo15bo13b3o
35b2o$81bo2bo3bob2obo28bob4o3b2o13b3o3b3o6bo2bo$84b3o6b2o27bobob3o2b3o
$86b3obo3b2o10b2o2bo11b2o15bo10bo10bo2bo$87bob4obob2o8b2o2bo11b2o8b2o
4b2o10bo9bo2bo$82bo9b2o12bo31bobo9bo9bobo$81b3o4bobo6bo7bo25bo2bo16bo
9bo$7b3o70b3obo5bo5bo8bo7b2o19bo16bo$10bo70bo3bo4bo22b2o18bo17bo9b2o$
6bo3bo71bo3bo21b3obobo19b3o24b2o$5bobo2bo72bob3o21b4obo14b2o5bo10b3o3b
3o$3bo2bobo16b2o43bo6b2o5b3o24b3o15bo$3bo3bo16bobo51bo6bo13b3o28b3o18b
o5bo$3bo19b3o14bo27bob3o5bobo17bob4o28bo18bo5bo$4b3o16b2o13b3o29b2obo
5b3o16bobob3o35b2o9bo5bo$11bobo12b2o9bo32bob2o7b3o2bo11b2o23bo17b2o$
10bo14b3o9b2o32b3obo6b2o2bo11b2o7bo16bo15bo12b3o3b3o$11bo2bo43bo6b2o
15bo24bo7bo6b3o21b2o$6bo4bobobo41b3o6bo6bo7bo24bo39b2o9bo$6bo5bo2bo9b
2o2bobobo22b3obo5bobo12bo7b2o11bo2b2o6bob3o39bo$6bo6b2o10b2o8bo21bo3bo
5b2o20b2o11bo2b3o7b2obo28bo9bo$17b2o10bo5bo22bo3bo21b3obobo16b3o5bob2o
27bobo9bo$2b3o3b3o6bo2bo13bo24bob3o21b4obo17bobo5b3obo24bo2bo9bo$31bob
o12bo6b2o5b3o24b3o13bo6bo21bo11bo2bo10bo$6bo10bo2bo11bo21bo6bo13b3o24b
3o5b2o6bo12bobo$6bo9bo2bo24bob3o5bobo17bob4o21b3obo24bo13bo2bo6b3o3b3o
$6bo9bobo27b2obo5b3o16bobob3o21bo3bo22bo5bo10b2o$7bo9bo28bob2o7b3o2bo
11b2o22bo4bo3bo21bo8b2o10b2o6bo$7bo39b3obo6b2o2bo11b2o7bo8bo5bo5bob3o
22bobobo2b2o9bo2bo5bo$7bo9b2o39bo24bo7bo6bobo4b3o41bobobo4bo$17b2o21b
3o6bo7bo24bo12b2o9bo43bo2bo$3b3o3b3o12bo15bo16bo7b2o11bo2b2o8b2obob4ob
o24b2o9b3o14bo$22b2o17bo23b2o11bo2b2o10b2o3bob3o24bo9b2o12bobo$7bo5bo
9b2o35b3obobo27b2o6b3o19b3o13b2o16b3o$7bo5bo18bo28b4obo28bob2obo3bo2bo
16bo14b3o19bo$7bo5bo18b3o28b3o13bo15bob2ob4ob2obo2b2o25bobo16bo3bo$35b
o15b3o24b3o15bo2bo5bo5bo26b2o16bobo2bo$9b3o3b3o10bo5b2o14bob4o21b3obo
15bo2b5o3bo4bob2o37bo2bobo$2b2o24b3o19bobob3o21bo3bo9bo5b2o12b3o2bo36b
o3bo$2b2o9bo17bo18b2o22bo4bo3bo9bo6b3o2bo5bo4bobo35bo$13bo16bo19b2o7bo
8bo5bo5bob3o6b3o6bo2bobo2b8obobo35b3o$3bo9bo16bo2bo25bo7bo6bobo4b3o19b
ob2ob2o5bobobo$2bobo9bo9bobo31bo12b2o9bo21bo4bobo2bo2bob2o$bo2bo9bo10b
2o4b2o8b2o11bo2b2o8b2obob4obo30bo5bo2b2o2b2o$o2bo10bo10bo15b2o11bo2b2o
10b2o3bob3o30b4obobobobo$31b3o2b3obobo27b2o6b3o32bob2obo3bo2bo$o2bo6b
3o3b3o13b2o3b4obo28bob2obo3bo2bo25b2o2bo3bob2ob4o$2b2o35b3o13bo15bob2o
b4ob2obo2b2o20bobobo3bo3bo$6b2o6bo39b3o15bo2bo5bo5bo14bo9bo3b2o3bobo$
5bo2bo5bo38b3obo15bo2b5o3bo4bob2o10bo18b2o$5bobobo4bo10b2o27bo3bo9bo5b
2o12b3o2bo7b3o$6bo2bo15b2o21b2o5bo3bo9bo6b3o2bo5bo4bobo$10bo24b2o11bob
o5bob3o6b3o6bo2bobo2b8obobo$7bobo24bo8bo6bo6b3o19bob2ob2o5bobobo$15b3o
17b2o13b2o6bo21bo4bobo2bo2bob2o$14bo26bob3o38bo5bo2b2o2b2o$14bo3bo24b
2obo7b2o29b4obobobobo$14bo2bobo16b3o4bob2o7b2o33bob2obo3bo2bo$16bobo2b
o8b2o4bo7b3obo5b2o13bo15b2o2bo3bob2ob4o10bo$17bo3bo8b2o5bo16bo12b3o15b
obobo3bo3bo15bo$21bo24bo6bobo10bo11bo9bo3b2o3bobo11b3o$18b3o32bob2o9b
2o11bo18b2o$77b3o$62bo$54b2o5bobo23b2o5b2o$54b2o4bo2bo23b2o5bo$61b2o
29bobo$46b3o43b2o$46bo41b2o32bo$47bo16b2o22bobo32bo$64bobo16bo5bo31b3o
$64bo16b2o$56bobo23b2o8b2o$56b2o34b2obo$57bo38bo$93bo$94bob2o$58b2o36b
2o$54b2o2b2o72bo$53bobo16b3o58bo$54bo17b3o56b3o$50bo16b2ob2obobo$49b3o
4b2o9b2ob3ob3o$48bob3o3bo15bobo$47bo3bo5b3o$46bo3bo8bo6b3o$45b3obo15bo
12b2o$46b3o17bo3bo7bo$47bo15b3o2b2obo7b3o60bo$63bo7bo9bo61bo$71b2o68b
3o!

There's probably a variant that can save another row.
-Matthias Merzenich
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Re: Oscillator Discussion Thread

Postby chris_c » April 6th, 2018, 6:33 pm

Sokwe wrote:Were any of the following p7 bumper variants previously known?

Only the variant on the right appears in the gun collection at the moment. The variant on the left will definitely reduce some bounding boxes.

Sokwe wrote:A p4 bumper can replace to of the p8 bumpers in AbhpzTa's p40 gun to save a row at the top and bottom:

I'm pretty sure that is also new. The bounding box on the far side of the reflection is the same as the old p4 bumper but overall it is much much smaller.
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Re: Oscillator Discussion Thread

Postby Kazyan » April 6th, 2018, 6:57 pm

Expanding on the nice p4 frob bumper, this saves another row on its left. Search is still in progress for a less sprawling one:

x = 13, y = 27, rule = LifeHistory
2A$.A$.A.AB2.B$2.2AB.3B3.B$4.6B.AB$4.6BA2B$2A2.2B2A2B3A$.A3.A2BA3B$A
5.ABA4B$2A4.BA.4B$2.A4.2B2.2B$2A.A3.2B3.B$.A.A3.A$.A.2A.2BA$2A2.4BA$
2.2A2B.A$2.2ABA$2A.2AB$A2.2AB$.3A.AB$3.B.2AB$.2AB.A.2A$A2.A.A.2A$2A2.
2A$5.A.2A$3.A.A.2A$3.2A!


EDIT: A quick check of that that can trim found p56, p68, p76, and p128:

#56
x = 118, y = 63, rule = LifeHistory
77.2A$14.2A61.3B$12.2B2AB58.A3BA$12.4B13.A45.A4BA$12.4B11.3A46.BABA.A
8.A$13.2A2B9.A25.2A24.A.ABAB4.3A$13.2ABA9.2A23.A.A25.A4BA2.A$14.2BAB
5.5B17.2A4.A28.A3BA2.2A$14.2BAB3.BA3B17.A2.A2.2A.4A24.3B2.4B$13.A2BA
4BABA3B16.2A.A.A.A.A2.A25.2A.BAB$14.2A2.2BA2BA4B18.A.ABABAB28.B.ABAB$
18.3B2A4B19.A.AB2AB30.2B2AB.2A$20.2B2A2B21.AB.2B30.7B2A$20.3B2A25.3B
30.7B$19.3B2A2B24.4B6.2A9.2A5.2A3.7B$18.4B.BA2B21.6B6.A11.A5.2A2B.6B$
17.4B3.4B20.6B3.BA.A11.A.AB3.11B$16.4B5.4B17.4B3A3B.B2A13.2AB.8B2.4B$
2A13.4B7.4B15.4BA3BA4B17.2B2A5B4.4B$.A12.4B9.4B13.4BA5BA3B17.BABA5B5.
4B$.A.AB2.B5.4B11.4B11.6BA3BA4B15.2B.BA7B5.4B$2.2AB.3B3.4B13.4B9.4B2.
2B3A3B16.BAB3.8B5.4B19.AB$4.6B.4B15.4B7.4B5.6B16.3A3B.B3.4B5.4B17.B2A
$4.10B17.4B5.4B4.9B14.AB3AB7.4B5.4B16.2ABAB$2A2.2B2A5B19.4B3.4B5.2A4.
4B12.A.2BAB9.4B5.4B14.A2B3A$.A3.A2BA3B21.4B.4B7.A5.4B9.BA2B.A12.3BA5.
4B12.A.ABAB$A4.BABA4B21.7B5.3A7.4B7.B3ABA14.ABAB5.4B9.BABA.A$2A4.BA6B
21.5B6.A10.4B6.2B3A16.2A2B5.4B7.3A2BA$2.A4.2B2.4B20.6B17.4B7.BAB17.4B
5.4B3.B.2BAB2A$2A.A3.2B3.4B17.3B2A4B17.4B6.2B19.4B5.B3A4B3.2AB$.A.A3.
B5.4B12.2A2.2BA2BA4B17.4B27.4B5.A6BAB.BA$.A.2A.B2A5.4B10.B2A5BABA3B
19.4B27.4B5.A4BABAB$2A2.BAB2A6.4B10.4B3.BA3B21.4B27.4B4.5B2A2B$2.B2AB
.B8.4B9.4B5.5B20.4B27.4B2.8B.B2A$2.2BAB11.BABA7.B3A9.2A21.4B27.11B3.B
A.A$2A.3B12.B2AB6.2B2A9.A23.4B27.6B.2B2A5.A$A2.2BA13.A3B4.2A2B11.3A.A
19.4B19.A7.4B4.2A5.2A$.3A.AB13.4B3.3AB13.A.3A12.B.3B.4B16.3A6.6B$3.A.
ABA13.4B2.BABAB17.A10.13BA4B8.A8.5B2AB$.3A.A.BA13.4B3.2A5.A11.2A3.B5.
2B2A9B6AB7.2A6.4BA4BA$A2.B.A.2A14.4B7.3A11.8B3.2B2A8BA2B2AB2A2.B.5B5.
4B.A4BAB$2A2.BA18.4B5.A16.8B.11B2ABA3B2A.6B6.4B.2B2AB2A2B$5.A.2A16.4B
4.2A15.21BAB4A10B4.4B3.9B$3.A.A.2A9.2A6.9B14.15B.2B2.5B2A18B4.10B$3.
2A14.A7.6B14.17B8.21B4.12B$19.A.2A5.6B3.B2.2B2.19B11.19B3.9B.4B$20.A
2.A4.35B12.23B2A3B4.4B$21.2AB3.9BABA15B.7B13.23B2A3B5.4B$22.14BA2BA
23B10.8B2.15B2A2B7.4B$23.13BA2BA24B9.2A3.B5.17B9.4B$24.13B2A14B2.8B
11.A7.21B8.4B$24.9B2A6B.B.2B11.6B8.3A6.A.2AB2.6B.2B5.2A9.4B$25.8B2A5B
4.3B10.5B9.A6.3AB2AB2.6B8.A11.4B$25.15B5.A2B.2A7.4B15.A4.B5.5B9.3A9.
3BA$26.13B5.A.A2B.A7.4B16.3A.2A5.4B11.A10.ABA$28.13B2.A.AB2.A9.B.B2A
16.A.A4.5B24.2A$27.8B4.2A.A.A3.A12.BA.A15.A.A4.2A28.B$27.6B6.2ABA2.4A
.A13.A16.A6.A$27.5B8.B2.A.A3.A.A12.2A19.3A$27.B.B9.2A.2A2.A2.A.A33.A$
28.3B9.A.A2.2A3.A$27.B2AB9.A.A$28.2A11.A!


#68
x = 118, y = 57, rule = LifeHistory
73.2A14.A5.A.2A.A2.A2.2A3.2A$64.A9.A7.A6.3A3.2A.A.4A2.A.A.A.A$64.3A7.
A.2A2.3A9.A6.A4.2A2.A.A$67.A7.A2B.A11.2A7.3A.5A2BA2.2A$66.2A9.2B.A10.
5B6.A3B2A4.A2.A$66.5B6.3AB12.3BAB5.2BA2B7A$19.2A47.3BAB5.2B12.3BABA2B
2.2B4.BA$11.A7.A9.A37.3BABAB3.2B12.4BA2BA2BA2BA4.B2A.2A$11.3A2.BA.A7.
3A36.4BA2BA3B2AB12.4B2A3B.2A6.2A.2A$14.A.3A7.A40.4B2A3B.2A14.6B$13.A.
2A9.2A40.6B20.5B$13.A2BA6.5B41.5B19.7B$14.2B5.BA3B42.7B10.A6.4B.4B$
15.2B3.BABA3B40.4B.4B7.3A5.2A2B3.4B$14.A2BA2BA2BA4B38.4B3.4B5.A7.ABAB
5.4B13.2A$15.2A.3B2A4B38.4B5.4B4.2A5.3BA7.4B12.A$20.6B38.4B7.9B4.4B9.
4B5.B2.BA.A$20.5B38.4B9.6B5.4B11.4B3.3B.B2A$19.7B36.4B10.8B2.4B13.4B.
6B$18.4B.4B34.4B9.15B15.10B$17.4B3.4B32.2A2B10.14B17.5B2A2B2.2A$16.4B
5.4B30.2B2A11.13B19.3BA2BA3.A$2A13.4B7.4B10.A17.2BAB10.2AB.10B19.4BAB
AB4.A$.A12.4B9.2B2A7.3A16.4B10.A.AB3.B2A3B20.6BAB4.2A$.A.AB2.B5.4B11.
BABA5.A18.4B11.A6.B2A3B19.4B2.2B4.A$2.2AB.3B3.4B13.A6B.2A16.4B11.2A6.
4B20.4B3.2B3.A.2A$4.6B.4B15.9B15.4B21.3B19.4B5.B3.A.A$4.10B17.6B16.4B
23.2B.BA15.4B5.2AB.2A.A$2A2.2B2A5B19.5B15.4B23.B2ABA.A13.4B6.2A2BA2.
2A$.A3.A2BA3B19.7B13.4B23.BABABA.A2.2A8.4B8.B.B2AB$A4.BABA4B19.6B12.
4B19.A2.A2.A.A.A.A.A.A7.4B11.4B$2A4.BA6B18.7B10.4B.3B.B12.3A2.4A.2A2.
A.A8.4B12.A2B.2A$2.A4.2B2.4B17.6B4.18B10.A9.A4.A.2A6.4B13.A2B2.A$2A.A
3.2B3.4B16.7B2.16B2A2B5.B3.2A6.A.A3.2A2.A5.A3B13.2A.3A$.A.A3.B5.4B15.
7B2.16B2A2B3.8B6.2A6.A6.A3B13.ABA.A$.A.2A.B2A5.4B13.9B.20B.8B16.2A4.B
3A13.AB.A.B2A$2A2.A2B2A6.4B12.36B2AB17.2B2.4B14.2A.A.A2.A$2.B2AB.B8.
3BA6.A4.3BA16B2.2B.10BA2BAB15.8B6.2A10.AB2.2A$2.4B11.3BA4.A2B.2A2B3A
12B8.9B2A6B13.7B7.A8.2A.A$2A.2BA12.3AB3.A6BAB2A10B11.9B2A3BA4B2.2B2.B
2.7B5.2A.A8.2A.A.A$A2.2BA13.4B3.A.4B2AB2A8B12.10BA4BA19B4.A2.A13.2A$.
3A.2A13.4B5.BABA13B12.7B.4B3A20B3.B2A$3.A.ABA13.4B4.BABA13B11.25B2A
14B$.2AB.A.BA13.4B3.B2A12B.B2A8.26B2A13B$A2.A.A.2A14.4B2.12B4.BA.A8.
8B2.29B$2A2.BA18.15B9.A8.6B11.2B.B.17B$5.A.2A16.15B8.2A8.5B10.3B4.15B
$3.A.A.2A17.6B2ABA4B18.4B7.2A.2BA5.15B$3.2A22.3B2ABABA3B19.4B7.A.2BA.
A5.13B$28.5B3A2B18.2AB.B9.A2.BA.A2.13B$29.B3A5B17.A.AB12.A3.A.A.2A4.
8B$29.9B17.A13.A.4A2.AB2A6.6B$31.6B17.2A12.A.A3.A.A2.B8.5B$32.5B31.A.
A2.A2.2A.2A9.B.B$33.3BA32.A3.2A2.A.A9.3B$34.3BA39.A.A9.B2AB$35.3AB39.
A11.2A!


#76
x = 121, y = 65, rule = LifeHistory
19.2A64.A11.2A$11.A7.A9.A54.A.A9.B2AB$11.3A2.BA.A7.3A46.A3.2A2.A.A9.
3B$14.A.3A7.A48.A.A2.A2.2A.2A9.B.B$13.A.2A9.2A47.A.A3.A.A2.B8.5B$13.A
2BA6.5B48.A.4A2.AB2A6.6B$14.2B5.5B52.A3.A.A.2A4.8B$15.2B3.ABA4B50.A2.
BA.A2.13B$14.A2BA2BABA5B36.BA6.A3.A.2BA.A5.13B$15.2A.2BA2BA3B36.A.AB
3.3A3.2A.2BA5.15B$20.B2A3B37.BA.A2.A10.3B4.15B$20.5B39.AB3.2A10.2B.A.
17B$19.7B41.4B3.11BA3BA13B$18.4B.4B39.3B4.7B2A3BA4BA13B$17.4B3.4B37.
6B2.7BA3BA2BA2BA14B$16.4B5.4B36.7B.7BABA3B4A10B3.B2A$2A13.4B7.4B34.
17B2A3B2A11B4.A2.A$.A12.4B9.4B32.20B2.2B2.B3.6B5.2A.A$.A.AB2.B5.4B11.
4B31.17B14.6B7.A$2.2AB.3B3.4B13.4B10.A18.16B14.9B6.2A$4.6B.4B15.4B7.
3A18.15B15.2A4.4B$4.10B17.4B5.A14.2A5.15B16.A5.4B$2A2.2B2A5B19.7B.2A
13.A3.11B.8B11.3A7.4B$.A3.A2BA3B21.9B10.BA.A3.11B3.B3.2A11.A10.4B$A4.
BABA4B21.6B9.B.BA.A3.12B7.A24.4B10.2A$2A4.BA6B21.5B8.2A3BA3.13B8.3A
22.4B9.A$2.A4.2B2.4B19.7B7.2AB.3B2.13B10.A23.4B10.A$2A.A3.2B3.4B19.6B
8.B3.2B2.15B26.2A5.4B5.5A$.A.A3.B5.4B18.7B10.4B.17B25.A5.4B4.A$.A.2A.
B2A5.4B17.6B4.17BA10B2A24.A.AB.7B2.B3A$2A2.A2B2A6.4B16.7B2.17B2A8B.BA
.A24.2AB.7B3.2B.A$2.B2AB.B8.4B15.7B2.16B2A5BA3B4.A26.3B2A7B4A$2.4B11.
4B13.9B.17BA4B2A4B3.2A25.2BABA2B2A3BAB2.2A$2A.2BA12.4B12.28BAB2ABA5B
29.4BA2B2A2B.B3A2.A$A2.2BA13.4B6.B4.20B2.2B2.4B2A8B28.10B3.B.A.2A$.3A
.2A13.4B4.2AB.19B10.5BA2B2.4B26.8B8.A$3.A.ABA13.4B3.2A19B12.7B4.4B24.
9B7.2A$.2AB.A.BA13.4B3.B.17B14.5B6.4B22.4B2.3B$A2.A.A.2A14.4B5.17B14.
6B5.4B20.4B3.5B$2A2.BA18.4B4.17B18.2A6.4B18.4B7.2A$5.A.2A16.4B3.15B.B
2A16.A8.4B16.4B8.A$3.A.A.2A17.4B2.12B4.BA.A16.3A6.4B14.4B10.3A$3.2A
22.15B9.A18.A7.4B12.4B13.A$28.3BA11B8.2A26.4B10.4B$29.3BA10B37.4B8.4B
$30.3A9B39.4B6.4B$31.10B41.4B4.4B$32.9B42.4B2.4B$32.9B43.8B$34.6B45.
6B$35.5B44.7B$36.4B44.7B$37.4B42.2A7B$38.4B41.2A.B2A2B$39.4B43.BABA.B
$40.4B43.BAB.BA$41.4B40.4B2.2AB$42.4B39.2A2.BAB2A$43.4B39.A2.3A2BA$
44.4B35.3A4.BABA.A$45.4B34.A8.A.ABAB$46.4B43.A2B3A$47.3BA43.2ABAB$48.
3BA42.B2A$49.3AB42.AB!


#128
x = 60, y = 59, rule = LifeHistory
19.2A3.2A2.A2.A.2A.A5.A$19.A.A.A.A2.4A.A.2A3.3A$21.A.A2.2A4.A6.A$16.
2A2.A2B5A.3A7.2A$16.A2.A4.2A3BA6.5B$17.7A2BA2B5.BA3B$22.AB4.2B3.BABA
3B$17.2A.2AB4.A2BA2BA2BA4B$17.2A.2A6.2A.3B2A4B$33.6B$33.5B$32.7B$31.
4B.4B$30.4B3.4B$29.4B5.4B$28.4B7.4B$27.4B9.4B$26.4B11.4B$25.4B13.2B2A
$24.4B15.BABA$9.A13.4B17.A3B$9.3A10.4B19.4B$12.A8.4B21.4B$11.2A7.4B
23.4B$11.5B3.4B25.4B$13.3B2.4B26.4B$3.2A7.9B27.2BA2B$3.A8.8B27.2BABA
4B$2A.A.B3.10B28.2BA2BA3B$A2.3AB.2B2A7B28.4BA4B$.2A2.BA3B2A7B27.10B$
3.4A12B26.10B2A$3.A.2B3.7B.B2A14.2A8.9BA2BA$4.3AB2.7B.BA.A2.2A10.A9.
8BABA$7.A4.4B5.A2.A11.A.AB4.11BA$2.5A5.4B5.3A2.A10.2AB.10B3A2B$2.A10.
4B7.3A12.12B2A3B$4.A9.4B5.A15.17B$3.2A10.4B4.2A15.17B.B$8.2A6.9B14.
19B2A$9.A7.6B14.19B.B2A$9.A.2A5.6B3.B2.2B2.20B4.B$10.A2.A4.36B$11.2AB
3.27B.9B$12.14B2A16B2.7B$13.13B2A16B2.7B$14.29B4.6B$14.17B.B.2B10.7B$
15.15B4.3B10.6B$15.15B5.A2B.2A6.7B$16.13B5.A.A2B.A7.5B$18.13B2.A.AB2.
A8.6B$17.8B4.2A.A.A3.A7.9B$17.6B6.2ABA2.4A.A5.2A.7B$17.5B8.B2.A.A3.A.
A5.A5.4B$17.B.B9.2A.2A2.A2.A.A2.3A7.4B$18.3B9.A.A2.2A3.A3.A10.3BA$17.
B2AB9.A.A23.3BA$18.2A11.A25.3A!
Tanner Jacobi
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Re: Oscillator Discussion Thread

Postby A for awesome » April 7th, 2018, 5:44 pm

A p6 sparker with exactly 7 p6 rotor cells, from JLS:
x = 21, y = 12, rule = B3/S23
8bo$7bobo$8bo8b2o$2b2obo2bo9bo$2bobo3b3o3b2obo$3ob4o3b2o$2bo3bobo2bobobo2bo$6bob
obob2ob4o$2bob4o2bobo2bo$2bo7bobob2ob2o$3b3ob3o2bo2bob2o$5bobo4b2o!

Useful at all? It seems to be a slightly stronger spark than the normal T-nosed p6, and slightly less obtrusive.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce
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Re: Oscillator Discussion Thread

Postby Sokwe » April 8th, 2018, 4:35 am

Here is a modification to my previous attempts at a p52 gun:
x = 159, y = 131, rule = B3/S23
111b2obo$111bob2o$17bo$15bobo91b6o$16b2o91bo5bo4bo$111bobobo2b3o$110b
4obobo$100b2o7bo5bobob2o$99bo2bo5bo2b3obo2bobo$99bobobo3bob2obobob2o$
100bobobo2bo2bobobo3b2o$102bo2bob2obo4b2o3bo36b2o$101bo2b2o4b2obobob2o
bo35bobo$101bo4b2obo5bobobo38bo$bo96b2obob2o3b2ob3o3bo$2bo27bo65b3obob
2ob2o4bo4bobo$3o25bobo64bo4bobo2bob3obob2obobo$29b2o65b4o4bo4bobobo2bo
bob2obo$94bobo2bobobo7bo6bobob2o$93bobo5bob2o5bobo2bo2bo$92bobo5b2obo
6bobo3bobo2b3o$92bo10b2o2b2ob4ob2obobo2bo$91b2o7b2o6bobo7bo2bo$84b2ob
2o10bobob2o2bo3b4o4bob2o$85bobo2bo8bo2bo5b3o5b4o3bo20b2o$85bobo2bobo3b
2obo2b3o6bo4bo4b2o20bobo$83b2o2b3o2bo2bo2bob2o6b2o2bobob2ob2o24bo$14bo
69bobo4b2o3bobobo8bobob4obobo$15bo27bo39bo2b2o3bob4obobo2b2o3bo2b3o3b
3o$13b3o25bobo40b2o3b2ob2o4bob2o3bobob2o7bo$42b2o41bob2o6b2obo3b2obobo
3bo3b2o5b2o$85bo2bobo2bobobob2o5bobobob3o5bo2bo$84b2obo2bo2bo3bo2b2ob
3o2bob2obo4b3obo$85bob2ob2obobo2bo3b2o4bo5bo2bo4b2o$84bo7bo2b2ob6o5b8o
2b2o$83bob5o3bo3bo5bob2o5bo3bobobob2o$83bo3bob4ob2obo2b2o4b5o3bo5bobo$
81b3o7bo2bob2obo4bo5bo2bo4bobo2bo7b2o$80bo6bob2o2bo5b2o2bob2ob2o3bo7b
2o7bobo$80b2o4bo2b2o8bo7b2o2b3o3b4o11bo$27bo54bo6bobo8b6o4bob2o6bo$28b
o27bo23b2o2bobobobo5b2o3bobo2b5obo3b2o$26b3o25bobo24bob2obo5bo3b2o3bo
2bo12b2o$55b2o24bobo2bob3obo8b2obob4obob3ob2o$80b2obobo6bo8bo2bobo11bo
$80bo3bob2ob2o5b2o4bo3bobo4b3obo$81b2obo2bob2o5b2o4bo3bobobo4bo$82bob
2o3b2o11bo3b2o4bo3bo$82bobobobobo12b2obo2b2o5bo$81b2obobo2b2o13bobobo
3b2obo$84bo4bo14bobo2bo8b2o$84bo4bo15b2o3bo6bobo$85b2o32bo$40bo45bo$
41bo27bo4bo8b3o16bo$39b3o25bobo4b3o6bo16bobo$68b2o7bo23b2o$60b2o14b2o
11bo10b2o$60bo26b2ob2o7b3o$52b2o3b2obo27bo2bo7bo29bo$52bo4bobo29b2o9bo
3b4o20bobo$53b3obo49b2o20bo$55bob2o44bo2bob2o$103b2obobo$71bob2o11b2o
16bob2o17bo$60b2o9bo3bobo6bobobo16b2o18bobo$53bo5bobo2b2o11bo6bo5bo23b
2o9b3o$54bo6bo2b2o9bobo6b2obo3bo9b2o11b2o11bo$52b3o16bobo11bo3b2o11bo$
85bo13b3o$86bobo10bo6b2o$87bo18bo$104bobo$79b2o23b2o$78bobo$59b2obo8b
2ob2o3bo4b3o12bo$59b2ob3o7bobobob3o2bo3bo10b3o$65bo5bo2bobo2b2o16bo$
47b2o10b2ob3o6bob2o5b2o2b3o9b2o$46bobo11bobo5b2obobob2obo5b2o22bo$48bo
11bobo5b2ob2o8bobo2bo13bo5b3o$61bo9bo9bo23bo$71bobo10b2o19b2o$72b2o7b
2o16b3o$99b6o$102b2obo$104bobo$106bo$106b2o$84bo$84bobo$34b2o48b2o$33b
obo$35bo9$71bo$71bobo$21b2o48b2o$20bobo$22bo9$58bo$58bobo$8b2o48b2o$7b
obo$9bo9$45bo$45bobo$45b2o!

This gives more room around the output herschel for sparkers. I'm hoping we can use p4 sparkers to get two gliders from the herschel.

An unrelated idea that I don't think has been explored much is to get a usable signal out of Tanner Jacobi's sparky glider eater. Replacing the eaters with sparkers might yield something interesting.
-Matthias Merzenich
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Re: Oscillator Discussion Thread

Postby Scorbie » April 8th, 2018, 6:47 am

A for awesome wrote:A p6 sparker with exactly 7 p6 rotor cells, from JLS:
x = 21, y = 12, rule = B3/S23
8bo$7bobo$8bo8b2o$2b2obo2bo9bo$2bobo3b3o3b2obo$3ob4o3b2o$2bo3bobo2bobobo2bo$6bob
obob2ob4o$2bob4o2bobo2bo$2bo7bobob2ob2o$3b3ob3o2bo2bob2o$5bobo4b2o!

Useful at all? It seems to be a slightly stronger spark than the normal T-nosed p6, and slightly less obtrusive.

Reduced in one dimension, starting from the same two rows. With ofind.
x = 15, y = 12, rule = B3/S23
7bo$7bo$3b2ob4o$2bo6bo$2bobo2b2o$b2obo2b2o$o2bob2ob2o$2obobobobo$3bo2b
3o2b2o$3bo7bobo$4b3o6bo$6bo6b2o!

I am curious if there is a much less intrusive variant. What was your starting configuration for your p6?

EDIT: Actually, I think the t-nosed p6 has a stronger spark in most situations, with some exceptions. compare:
x = 32, y = 19, rule = B3/S23
5bo18bo$5bo18bo$4b3o13b2ob4o$19bo6bo$4b3o12bobo2b2o$18b2obo2b2o$2o2b3o
2b2o6bo2bob2ob2o$obo2bo2bobo6b2obobobobo$bo7bo10bo2b3o2b2o$20bo7bobo$b
o7bo11b3o6bo$obo2bo2bobo12bo6b2o$2o2b3o2b2o2$4b3o2$4b3o$5bo$5bo!
Best wishes to you, Scorbie
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Re: Oscillator Discussion Thread

Postby A for awesome » April 8th, 2018, 10:33 am

Scorbie wrote:I am curious if there is a much less intrusive variant. What was your starting configuration for your p6?

I think I had JLS at height 12, with the top two and bottom two rows set to period 1 and a 4x4 box on the left edge set to full period (everything else at p3), a single p6 cell in the second column set on in gen 0 and off in gens 2-3, and progressively smaller widths until there were no solutions that matched that spark. (The original discovery was very much an accident — I was mostly just looking for a p6, any p6, as a proof of concept.)

Scorbie wrote:EDIT: Actually, I think the t-nosed p6 has a stronger spark in most situations, with some exceptions. compare:
x = 32, y = 19, rule = B3/S23
5bo18bo$5bo18bo$4b3o13b2ob4o$19bo6bo$4b3o12bobo2b2o$18b2obo2b2o$2o2b3o
2b2o6bo2bob2ob2o$obo2bo2bobo6b2obobobobo$bo7bo10bo2b3o2b2o$20bo7bobo$b
o7bo11b3o6bo$obo2bo2bobo12bo6b2o$2o2b3o2b2o2$4b3o2$4b3o$5bo$5bo!

You're right, I definitely agree. I was more considering how far and for how long the oscillator retreated after sparking, instead of how quickly it advanced before sparking.
x₁=ηx
V ⃰_η=c²√(Λη)
K=(Λu²)/2
Pₐ=1−1/(∫^∞_t₀(p(t)ˡ⁽ᵗ⁾)dt)

$$x_1=\eta x$$
$$V^*_\eta=c^2\sqrt{\Lambda\eta}$$
$$K=\frac{\Lambda u^2}2$$
$$P_a=1-\frac1{\int^\infty_{t_0}p(t)^{l(t)}dt}$$

http://conwaylife.com/wiki/A_for_all

Aidan F. Pierce
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Re: Oscillator Discussion Thread

Postby Billabob » April 8th, 2018, 6:01 pm

Found a funky looking P4 oscillator with Randcat:

x = 11, y = 10, rule = B3/S23
2ob5o2bo$2obo3b2obo$b2obob2o$2ob3o$3b3o4bo$o4b3o$5b3ob2o$3b2obob2o$ob
2o3bob2o$o2b5ob2o!


Not sure if it's known, but thought it was worth sharing.
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