Thread for basic questions

For general discussion about Conway's Game of Life.
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wwei47
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Re: Thread for basic questions

Post by wwei47 » July 28th, 2021, 9:25 pm

What's the cheapest way to synthesize an LWSS with a single glider in one direction and an unlimited amount of gliders in the opposite direction?
Self-proclaimed synthesis "expert"

ColorfulGabrielsp138
Posts: 288
Joined: March 29th, 2021, 5:45 am

Re: Thread for basic questions

Post by ColorfulGabrielsp138 » July 29th, 2021, 3:07 am

Which loaf parent is more common, xp0_137 or xp0_357?

Code: Select all

x = 21, y = 21, rule = LifeColorful
11.E$10.3E$10.E.2E$13.E4$2.2B$.2B$2B$.2B15.2D$19.2D$18.2D$17.2D4$7.C$
7.2C.C$8.3C$9.C!
I have reduced the glider cost of quadratic growth to eight and probably to seven. Looking for conduits...

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dvgrn
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Re: Thread for basic questions

Post by dvgrn » July 29th, 2021, 7:25 am

ColorfulGabrielsp138 wrote:
July 29th, 2021, 3:07 am
Which loaf parent is more common, xp0_137 or xp0_357?
There might not be a definite answer to that -- it might depend on details like whether you're running NxN soups in an unbounded universe, or soups on a torus, or something else entirely.

Here's a reasonable data point, though: the octohash database has xp0_357 (and nothing else) showing up from collisions of a glider with up-to-two common objects, 881 times. xp0_137 only shows up 89 times:

Code: Select all

x = 7083, y = 165, rule = B3/S23
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25b2o30b2o24b2o30bo30b2o31b2o31b2o35b2o31bo23b2o39b2o30b2o30bo23b2o37b
2o22b2o40bo21b2o31bo39b2o31b2o30b2o30b2o22bo29b2o31b2o30b2o30b2o35b2o
26b2ob3o25b2o30b2o31b2o28b2o30bo36b2o27b2o34b3o26bo31bo2b3o27b3o27b2o
28b2o31bo31b2o2b3o25b2o2b3o28b2o27b2o31b2o32bo31bo28bo31bo34b2o27b2o2b
3o28b2o31bo31b2o26b2o34b2o27b2o33b2o30b2o31bo31bo31bo31b2o30b2o33b2ob
3o24b2o31b2o23bo32bo31bo34bo31bo31b2o31bo$b2o29bobo3bo25bobo3bobo24b2o
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28bo2bob2o25bo2bo28bo2bo22bobo29bobo29bo8bo22bo2bo31bo35bobo29bobo23bo
38bobo30bo30bobo21bo2bo5b2o29bobo21bo8bo31bobo20bo31bobo38bobo29bobo
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69b2o57b2o2b3o23bo36bo25b2o35b2o30b2o30b2o2b2o25b2o30b2o36bobo25b2o31b
2o32b2obo23b2o192bo$34bo40bobo29bobo24b2o3bo28bo31b2ob2o26bo25b2o3bo
26bo30bobo3bo25bobo30bo30bo2bo5b2o126bo30bobo21bobo30bobo36bo132bo23bo
35b2o21b2o9b3o27b3o469bo3bo33b2o56bo191bo4b2o27b2o30b2o31bo31bo28b2o3b
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4bo22bo5b2o22bo32bo98b2o26b2o32b2o28b2o31b2o94bo30b2o3b3o24bobo3bo31b
2o90b2o64bo29b2o31b2o27bobo3bobo25bo2bo28bo2bo29bobo29bobo26bo2bo2bo
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29bobo29bobo29bobo26bo2bo31bobo29b2o28bobo3bo24bobo2bo30b2o30bo2b3o23b
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28b2o36bo25b2o2b2o30bo2bo2b2o20bobobo27bobobo27b3o29bobob2o27bobo3bo
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2o35bobo30bo26b3o92b2o28b2o66bobo30b2o2b2o21b2o3bo27bo3bo26bo32bo4bo
27b2o28b2o31b2o3bo124bo28bo31b2o$456bobo29bobo153bo35bo58b2o30bo3bo
382bo124bo195bo25bo36bo25b2o160bo34b3o159bo95bo59bo163b2o27bo38bo340b
3o30b3o28bobo$455bobo2b3o24bobo2b3o184b2o58bobo26b3o225b2o186b2o32b2o
31b3o347bo127b2o34bo127b2o33bo155bo162bobo406bo34bo29b2o$456bo3bo27bo
3bo186bobo57bo28bo227bobo185bobo31bobo30bo348b2o127bobo34bo126bobo351b
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40b2o21b2o30b2o30b2o6b2o22b2o7bo22bo7bo23b2o6bo24bo5bo25bo6b2o23bo7bo
23bo7bo23b2o5bo24b2o5b2o23b2o6b2o22bo7b2o23b2o30b2o4b2o25bo4b2o25bo40b
3o25bo31bo31bo31bo35b3o18bo31b2o31bo30b2o30b2o30bo32b2o8b3o20bo32bo34b
2o30bo32b2o34b3o29b3o25b2o30b2o30b2o30b2o30bo31bo32b2o30bo31bo$obo30bo
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23bobo3bo2bo22bobo4b2o2bo20b3o3bo2bo22b3o3bo2bo22bobo4bobo22bobo4b2o
23bobo4b2o2bo20bo2bo2bobo23bo2bo5bo22bobo3bo2bo22bo2bo3bobo22bo2bo2bob
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24bobo3b2o24bobo4b2o24bo4b2o24bobo5b2o22b3o29bobo4bo25bobo4bo23bobo4b
2o23bo2bo28bobo5b2o22bo2bo28bobo3b2o24bobo29bobo32bo3b2o26bo31bo29bobo
3b2o24bobo3bo26bo3bobo23bo5bo31bo31bo26b2o3bobo25b2o2bobo29bo2bo22b2o
5bobo28bo2bo23bo4bo2bo29bobo29bobo29bobo22b2o5bobo29bobo24b2o3bobo29bo
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2o18bobo29bobo29bo2bo28bo2bo28bobo29bobo29bobo30bobo29bobo35bo30bobo
29bobo29bo2bo29b2o2bo27bobo29bobo29bobo29bobo29bobo29bobo30bo30bobo29b
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2o4bobo31bo2bo19bobo5b2o22bo2bo29bobo7bo20bo2bo5b2o21bo2bo4b2o22bobo
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22bobo5bo24bobo3bobo23bobo3b2o2b2o19bo2bo2bobo24bobo3bobo23bobo2bobo
23b3o4b2o23bobo4bobo22bobo3bobo23bobo3bo25bobo4bobo22bobo3bo2bo22bobo
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2o4bobo24b2o4bobo22bobo3bo2bo22bo2bo3b2o3b2o18b2o7bo23bobo3b2o23bo2bo
2bobo23bo2bo29bobo3b2o23b3o3bo2bo22b3o4b2o23b3o4b2o23bobo3bo2bo22bobo
3bobo24bobo4bo23b3o4b3o23b2o4b3o23b2o4b3o22bo2bo3bobo23bobo3bobo23bo5b
2o23bo7b2o23b2o3bobo23bobo4bobo24b2o3bo2bo22b2o5bo24b2o5b2o23bo5b2o24b
2o5bo24bobo2bo2bo23bo5bo27bo2bobo23b3o3bobo25bo3bobo24bo4bobo26bo2bo
59bo32bo4bo24bobo4bo2b2o20bo5bo24bobo30bobo3b2o24bobo28bo2bo3b2o24bobo
29bobo28bobo29bobo3b2o25b2o4bobo24b2o4bo25b2o3bobo22bo5bobo29bo2bo2bo
19bo7b2o22b2o5b2o24bo5b2o23b2o4bo2bo23bo5bo31bo25bo4bobo24bo4bobo25b2o
2bobo25b2o2bobo29bobo2b3o24bobo23b2o4bo25b2o31bobo29bobo28bo2bo7b3o18b
3o30bo30bobo37bo30bobo30bo2b3o25b2o30b2o30b2o31b2o30b2o28bo2bo2bo25bob
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26bobo30bo31bo30bobo28bo38bobo29bobo30bo32bo30b2o29bobo3bo24bo2bo28bo
2bo2bo25bo2bo29b2o30b2o29bobo29bobo29bo31bo31bo26bobo28bo2bo35bobo29b
3o29b2o30bobo30b2o30b2o28bo2bo28bobo29bobo29bo27bo32bo35bobo29bo2bo23b
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6bobo21bo7bobo21bo8b2o22bo5bo2bo2bo18bobo4bo2bo21bobo4bo2bo21bobo4bo2b
o21bobo5bobo22bo6bobo2bo19b2o4bo2bo22b2o6b2o22bobo5b3o20bo2bo6bo21bobo
4bo2bo21bo2bo5bo23bo5bo2bo2bo18bo6bo2bo22bo7b2o22bo7bo22bo2bo6bo21bobo
6bo23b2o4bo2bo2bo19b2o4bo2bo2bo18bo6bo2bo22b3o3bo2bo22bobo3bobo23bo6bo
bo21bo2bo3bo2bo22bo5bo2bo22b3o29bobo5b2o22bo6bobo$33b2o36b2o29bo27bo
31b2o35b2o30b2o29b2o30b2o25b2o37b2o24bo4b2o25b2o3b2o25b2o3b2o25b2o30b
2o3bo26bo3b2o26bo4b2o25bo4b2o30b2o24b2o3bo33bo24bo2b2o28bo5bo25bo8bobo
19b2o4bo2b2o22b2o4bo25b2o3bo24bo32bo6bo24bo5bo24b2o4b2o2b2o21bo6bo2b3o
18b2o5b2o24b2o3bo26b2o4bo30bo2bo29bobo2b2o24bo2bo24b2o3bobo24b2o2bobo
25b2o3bobo28bo2bo30bobo22bo5bobo23b2o4bobob2o25b3o25bo4bobo23b2o4bobo
23b2o5b2o24b2o3bobo22bo5bobo23bo5bo2bo22bo5bo2bo23bo5bobo23bo4bo2bo22b
o2bo4b2o25bo5bo22bo2bo5bo22bo2bo5bo22bobo5bo23bobo5bo23bobo30b3o28bo2b
o3bo25bobo4bo24bobo4b2o22bobo29bo2bo29bobo28bobo29bobo4b2o23bobo3b2o
24b3o4bo27bo2b2o24bobo3b2o2b2o20bobo3b2o24b3o3b2o26bo4b2o25b2o3b2o25b
2o3bobo24bo4bobo3bo24bobo24bo5b2o25bo3bo2bo24bo4b2o24b2o3bo2bo24b2o4b
2o24b2o4b2o23bo6b2o22b2o4bobo23bo2bo4b2o23bobo4b2o25bo4bo23b3o4bo25b2o
3bobo23b3o30bo30bobo29bobo4b2o23bobo3b2o25b2o3b2o24bobo3b2o24bobo4bo
26bo4bo2b2o21bobo3bo25b2o4bo3bo20b2o4b2o24bobo3b2o30bo27bo3b2o26b2o29b
2o4b2o2bo20bo5bo25b2o30b2o5bo24bo7b2o24b2o4bo23bo10bo20b2o32b2o62bo67b
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2o24bo5b2o30b2o2b2o22b2o30b2o62b2o28b2o38b2o30b2o30b2o30b2o62bo30b2o2b
3o25b2o30b2o93b2o30b2o30b2o30b2o30b2o26b2o29b2o37b2o31bo62bo94b2o29b2o
30b2o30b2o26b2o30b2o35b2o31b2o2b2o20b2o4b2o25bo4bo26bo3b2o25b2o4b2o2b
3o19bo5b2o23bo7b2o22bo2b2o27bo31bo2b2o27b2o5b2o2b3o19bo31bo4bo25b2o29b
o8bo22b2o7bo22b2o7bo22b2o7b2o21bobo5b2o23bo6b2o23bo6b2o23bo6b2o23bo2b
2o3b2o21bobo5b2o30bobo29bobo23bo5bo24b2o4b3o23bo5bo2bo22b2o5bobo21b2o
5bobo22b2o5bobo23b2o6bobo21bobo5b2o22bobo5b2o22bobo28bo2bo4b2o22bo2bo
4b2o23b3o4b2o22bo7b2o23bo6bo23bobo6bo22bobo5b2o22bobo5b2o22bo32bo30bob
o6bo$363b3o19b2o100bo252bobo68bo30bobo89bo99bobo30bo123b2o31b2ob2o26b
2o31bo29b2o32bo30b2o24bo7b2o29bo31b2o3bo24bo33bo31bo31b2o30b2o29bo2b2o
27b2o30b2o2b2o27bo30b2o2b2o20b2o31b2o29b2o30b2o8b2o20bo31bo30b2o33bo
29b2o31b2o30bo30bo31b2o7bo23b2o29bo31bo30b2o30bo33b2o28b2o8bobo19b2o
30bo32b2o4bobo29bobo28bo2bo28bo2bo28bo2bo28bo2bo29bobo28bo2bo28bo2bo
29bobo29bobo29bobo30bo23bobo29bobo29b3o32bo28bo2bo3bo27bo6bo22bobo28bo
bo30bobo28bo2bo28bo2bo29bobo28bobo29bobo7bobo19bobo29bobo9bo19bobo31bo
31bo3b3o29bobo31b2o28bo2bo2bo25b3o61bobo23b3o32bo28b3o9bo19bobo6b2o24b
o5b2o21b2o7b3o21bobo4bo57b2o3bo25bobo28bo2bo28b2o30bobo2b2o26b2o2b2o
26b2o2b2o25bobo32bo7bobo19bobo29bobo8bo51b3o30b2o7bobo25b2o4b2o29b3o
18b2o5b2o29b2o31b2o24b2o31bo29b2o30b2o32b2o3bo26b2o29b2o8bo22b2o62b2o
3bo26b2o92bo31b2o31b2o41b2o123bo64bo289bobo125bo23b2o29b3o30bobo61bobo
37bo182b2o30b2o27b2o130bobo26b2o38bo30b2o30b2o29bo32b2o30b2o30bo31bo
33b2o22b2o30bo31b2o2b2o24bo2bo29bobo31bo28b2o30b2o30b2o31bo2b2o26b2o
30b2o30b2o30b2o$103b3o125bo64bo66bo21bobo37b3o58b2o28bo28b2o30b2o67bo
26bo36b2o28bo34b2o65bo30b2o28b2o28b2o27b2o29b2o39bo33bo25bo29b2o33b2o
68bo54b2o27bo94b2o126b2o65b2o69bobo19b2o41bobo18b2o41bobo25bo29b3o32b
2o33bobo26b2o25b3o98b2o31b3o93b2o26b3o96b2o27b2o67bo29bo31b3o22bobo4bo
31b2o29b2o2b2o26b2o30b2o25b2o3b2o31bo23b2o5b2o26bo3b2o31bo30b2o30b2o
25b3o3b2o23bo31bo8b3o19bo8b3o22b2o2b2o24bo2bo30b2o5b2o23b2o2b2o25bo32b
o30b2o30b2o31b2o4bo24bo30b2o8bo22bo6b3o21b2o31bo32b2o29b2o6bo23b2o4bob
o29bobo28bobo32bo24b2o4b2o28bo2bo25bo28b3o3b2o27bo30bo6bobo20b3o6bobo
20bobo6bo22bo2bo3b2o23b2o2b2o29bo28bobo4b2o23bobo6b3o20bobo6b3o20bobob
2o26bobob2o26bobob2o26bo2bo28b3o8bo20bo2bo28bo2bo28b2o3bo29bo28bobo7bo
28bo3b2o26b2o2bo20bobo4bobo24bo4bo30bo2bo22bo2bo29bobo3bo25bo5bo24bobo
30bobo2b2o26bo29bo2bo8bo22bo61bobo2b2o26bo30b2o5b3o29bo23b3o5b3o21bobo
29bo2bo4b2o33b2o26bo25b2o7bo23b2o3b2o25b2o4b2o22b2o7b3o22b2o5b2o24bo
37b2o22b2o32bo3bo25bo138bo29b3o27b2o29bo37bo22bobo28bo32bo29b3o31bo40b
o21b2o28b2o32b2o37b3o26b2o26bobo29bobo65bo34b3o29b3o23bo123b2o97b2o92b
o38bo60b2o26b2o31bo68bo30b2o34b3o23bobo35b3o22b2o$39b2o58bo3bo126b2o
63b2o67bo60bo60bobo26b2o28bobo29bobo65b2o25b2o36bobo62bobo95bobo27bobo
27bobo26bobo28bobo97b2o29bobo32bobo31b3o61b2o25bobo25b2o39b2o27bo25bob
o35b2o62b2o24bobo37b2o25bobo33bo34bo21bobo40bo20bobo40bo26b2o29bo34bob
o32bo28bobo24bo30b3o29b2o36bobo30bo22b2o32b3o36bobo25bo28b3o27b2o38bob
o26bobo28b2o65b2o31bo98bobo84bobo59bobo31b2o126bo71bo30bo28bobo24b2o
38bobo25b2o61b3o29b3o29b3o32b2o95bo120bobo4b2o23bobo4bo30b2o30bo32b2o
24bobo3b2o29b2o25b2o28bo5bobo25b2o30b2o5bo22bo8bo23b2o7bo22b2o4bobo22b
2ob2o27b3o30bo5bobo23bo7bo23bo7bo23bo4bo26bo4bo25b2o4bo26b2o29bo32b2o
30b2o29b2o2b2o28b2o28b2o37bobo3bo24bo2bo2bo19bo7bobo22b2o4bobo28bo2bo
22bo2bo28bo2bo2b2o25bobo2b2o26bo2b3o25bo4bobo23bobo29bo2bo28b3o29b2o
30bobo3bobo23bobo29bobo5bo23b2o5b2o26bo4bo24bobo29bobo4bobo29b2o3bo24b
obo23bo2bo5b2o22bobo3bobo23bobo4bobo21bo8bo25bo5bobo21b3o29b2o6bobo20b
o2bo29b3o2b2o24bobo167bo29bobo27b2o60bo31bo61bo96bobo27bobo31bobo36bo
28bobo25bo31bo66b2o34bo31bo92b2o33b3o19bobo36b2o33b2o23bobo66b2o22b2o
37b2o24b2o36bo90b2o34b2o30bobo33bo25bo37bo24bobo28b2o30b3o$38bo2bo55b
3o4bo62bo3b3o51b2o3bobo25b2o35bobo128bo88bobo27bo31bo67bobo24bobo35bo
64bo97bo29bo58bo30bo99bobo28bo34bo33bo63bobo24bo27bobo38bobo25b2o63bob
o61bobo23bo39bobo24bo34b2o56bo63bo69bobo29bo33bo63bo27bo29bo31bobo35bo
33bo21bobo31bo67bo27bo29bobo37bo28bo30bobo64bobo31bo61bo35bo61b3o22bo
35b2o24bo33bobo35b2o31b2o28bo27bo30b3o38bo30bo27bo96bo26b3o31bo31bo31b
o34bobo24b2o69bo54b2o34b2o59bo128bo99bo190bo26bo38bo34bo31bo249bobo97b
2o29b2o32bo23bobo4b2o29b2o24b2o2b3o25b2o3bobo25b2o2bobo25b2obo26b2o30b
2o31b2o29bo31b2o2b2o27bo30b2o2b3o26bo7bo22b2o5bobo24b2o5bo24bo2b2o27bo
5bo30bobo28bo2bo22bo2bo5bobo20bobo4bo25bo31b3o6bo21b3o29bo31bobo6bo22b
obo29bo5bobo23bo2bo36b2o60b2o67bo28bo29bobo154bo95bo29bo33bo39bo27bo
126bobo34bo31bo91bobo32bo21bo38bobo32bobo22bo68bobo21bobo36bobo23bobo
126bobo33bobo29bo36bo63bo23bo30bobo29bo$39bobo23bo30bo39bo29bobo2bo20b
2o30bo2bo30bo2b3o24b2o37b2o25bo839bo62bo95bo27bobo62bo63bo65bo61bobo
378bo30bo93bo34bo95bo28bo99bo161b2o97bo60bobo95bobo30bobo26b2o58bo223b
o34bo31bo31bo60bobo123bobo33bobo98bo64bo62b3o24b2o477b2o62b3o94bo224bo
96bo156b2o63bo128bobo63b2o30b2o24b2o30bo30b2o33bo28bo31b2o30b2o31bo2b
2o26b2o31b2o36bo2bo30b2o22b2o2b2o800bo35bo59bo34bo93bo88bo128bo223bo
32bo$40bo23bobo29b2o37bobo28bo2bo2bo19bobo30bobo28bobo2bo26bobo35bo2bo
23bobo2210bobo97bo59bo97bo32bo28bobo58bo223bo158bo125bo35bo99b2o63b2o
62bo26bobo476bobo61bo95b2o193bo31bo254bo63bo127bo285b2o63bobo96bo2bo
29bobo21bo2bo3bo$65bo70bo2b2o26b2o25bo31bo29b2o4bo26b2o35bo2bo22bo2bo
3236bobo62bobo62bo25bo478bo64bo94bobo191b2o576bo187bobo62bo62b2o35b2o
2b3o24bobo2b3o17bo2bo$38b2o99bobo52b2o131b2o2b3o19b2o4226bobo574b2o
187bo127bobo38bo27bo3bo20b2o$38bobo98bo191bo4826bobo314bo41bo31bo$38bo
293bo27$34bo31bo31bo31bo31bo2b3o27b2o30bo31bo35b2o26bo31b2o30bo31bo31b
o31b2o32b2o29bo27b2o31b2o30b2o30bo32b2o30b2o30b2o32bo30b2o30b2o30b2o
30b2o30b2o30b2o30b2o30b2o31b2o30b2o34b2o26bo31bo31bo27b2o30b2o30b2o31b
o31bo31bo31b2o34b3o29b3o25b2o30b2o30bo31bo32b2o30b2o30b2o30b2o30bo32b
2o30b2o30b2o30bo32b2o30b2o30bo31bo31bo31bo27b2o30bo36b2o26bo31b2o30b2o
30bo32bo31b2o4b2o24b2o30b2o30b2o30b2o34b2o26b2o30b2o31b2o30b2o30b2o34b
3o25b2o31b2o30b2o31b2o29b2o30b2o30bo31bo32bo27b2o30bo31b2o30bo32b2o31b
2o30b2o30b2o31b2o30b2o30b2o31b2o29b2o30bo31bo31bo32b2o30b2o25b2o31b2o
30bo31bo31b2o31b2o30b2o30b2o30b2o30bo31bo32b2o4b2o24b2o4b2o24b2o30b2o
30b2o30bo31b2o30b2o30b2o31b2o30b2o30b2o30b2o30b2o30b2o30bo31bo32b2o30b
o31bo31bo31bo31bo31b2o30b2o30b2o30b2o25b2o30bo31bo31bo32b2o30bo31b2o
30bo32b2o30b2o30b2o30bo2b3o27b2o30b2o30b2o30bo31b2o30b2o30b2o31b2o30b
2o30b2o2b3o25b2o31b2o30bo31bo31bo31bo31bo31b2o30b2o30b2o30b2o31bo25b2o
31b2o31b2o30b2o32b2o30b2o30bo32b2o30b2o30b2o30b2o30b2o30b2o30b2o31bo
25b2o30b2o31b2o30bo34b2o31b2o30b2o30b2o30b2o30bo32b2o30bo31bo31bo31bo
31b2o30bo31b2o30b2o$33bobo29bobo29bobo29bobo29bobobo29b2o29bobo29bobo
30bo2b2o26bobo29bobo29bobo29bobo28b3o30bobo32bo28b3o27bobo29bobo29bobo
29bobo31bo30bobo29bobo31bobo29bobo29bobo28bo2bo29bobo29bobo29bobo29bob
o28bo2bo30b2o30b2o30b2ob2o26bobo29bobo29bobo26b2o30b2o30bobo29bobo29bo
bo29bobo29bo2bo29b2o2bo27b2o2bo26bo2bo28bo2bo28bobo29bobo31bobo29bo31b
o31bobo28bobo31bobo29bobo29bobo28bobo31b2o30b2o29bobo29bobo29bobo29bob
o26bo31b3o30b2ob2o26bobo29bo2bo28bo2bo28bobo30bobo31bo3b2o26bo31bo30bo
bo30bo2b2o29b2o27bo30bobo31bobo29bobo28bo2bo29b2o2bo26bo2bo30b2o29bobo
30bobo28bobo29bobo29bobo29bobo30bobo25bobo29bobo29bo2bo28bobo32bo32bo
30bobo29bobo30bobo29bobo28bo2bo29bo2bo27bo2bo28bobo29bobo29bobo31b2o
30b2o25b2o30bobo29bobo29bobo29bo2bo31bo31bo30bo30bobo29bobo29bobo32bo
3b2o26bo3b2o25bobo29bo31bo31b3o29bobo29bobo29bobo30bobo29bobo28bo2bo
28bo2bo29bobo28bo2bo28bobo29bobo30bobo29bobob3o25bobo29bobo29bobo29bob
o29bobo29bobo29bobo29bobo25bobo29b3o29b3o29b3o29bobo29bobo29bo2bo28bob
o32bo2b2o26bo31bo30bobobo30bo31bo30bo31b3o29bobo29bobo29bobo30bobo29bo
bo28bo2bobo26bo2bo30b2o29bobo29bobo29bobo29bobo29bobo31bo29bobo30bo30b
obo29b3o26bo30bo2bo29bobo29bobo33bo30bobo29b3o30bobo28bo2bo28bo2bo28bo
2bo28bo2bo28bo2bo28bo2bo29bobo25bo30bobo29bobo29bobo34bo31bobo28bo2bo
29bobo28bo2bo28bobo31b2o29bobo29bobo29bobob3o25bobo29bobo29bobo29bobo
29bobo$34bobo29bobo29bobo29bobo27bobo3bo60b2o30b2o29bobo3bo25b2o30b2o
29bo2bo28bo2bo27bo33bo3b3o26bobo27bo31bo31bo5b3o23bo31bo33b3o27bo30bob
o31bobo31bo31bo29bo2bo30b2o30b2o30b2o30b2o29bobo2b2o89bobo3bo25bobo30b
o31bo92bo31b2o29b2o30b2o5b3o23b2o5b2o22bo2bo2bo25bo2bo2bo25bobo29bobo
29bo2bo28bo2bo32bo30b3o26bobo5b2o25bobo26bobo33bo31b2o30b2o29bobo94b2o
29bobo30bo29bo2bo27b3o31bo28bobo3bo26b2o29bobo29bobo29bo2bo28bo2bo31bo
bo3bo25bobo29bobo30bo27b3o2b2o27b2o3bo27b3o27bo34bo31bo29bobo29bo2bo2b
o26bobo62bo2b2o28bo30bo30b2o29bobo2b2o25bobo30bobo27bo31b2o30b2o30bo
30b3o33bobo30bo30bobo30bo31bo30b2o30bobo29bobo28bo2bo28bo2bo29bobo122b
o30b2o30bobo29bobo29b3o29b3o29bobo29bobo29bobo29bobo33bobo3bo25bobo3bo
26bo30b3o29b3o31bo29bobo29bobo29bobo30bo31bo30b2o29bo2bo30b2o29bobo28b
o2bo29bobo30bo30b2o2bo27bobo30bo31bo31bo30b2o2b3o25b2o2b2o25bobo29bobo
2b2o23b2o32bo31bo31bo29bo30bobo29bobo29bo2bo28b3o2b2o25bobo29bobo29bob
o3bo29bobo29bobo29b3o31bo29bobo29bobo29bobo30bo31bo2b2o26b2o3bo25bo2bo
61b2o30bobo29bobo30bo31bo29b3o30bo30bobo29bobo29bo29bobo29bobo29bo30bo
bo34bobo30bo32bo30bo30b2o30b2o30b2o29bo2bo28bo2bo2b2o25bobo30b2o25bobo
29bobo29bo31bo35bobo30bo30b2o31b2o2b2o25bobo28bo2bo62b2o30b2o29b2o2bo
27bobo29b2o2b3o24bo2bo29bo31bo$35b2o30b2o30b2o30b2o27b2o129b2o93b2o30b
2o28b2o31b2o3bo28b2o28b2o34bo30bo2bo29bo63bo26b2o6b2o23bo32b2o28b2o4b
2o25bo33b2o27b2o30b2o30bo31bo35bo2b2o24b2o3b3o59bo31bo2b2o24bo31bo197b
o31b2o24b2o30b2o30bo31bo31b2o30b2o33b2o31bo26b2o5b2o27bo27b2o36b2o92b
2o126bo62b2o30bo30b2o29bo63bo31bo31b2o5b2o23b2o33b2o30b2o30b2o30b2o26b
o6bo27bo33bo26b2o68b2o27bo30bobo31bo2b2o28bo33bobo60b2o58b2o3bobo24b2o
2b2o27b2o31b2o31b2o30bo30b2o26bo4bo3b2o21b2o3b2o25b2o3b2o30bo27b2o98bo
31bo30b2o30b2o31b2o27b2o3b3o25bo125bo31bo30bo31bo31b2o31bo30b2o30b2o
35b2o30b2o30b2o31bo31bo30b2o30bo31bo31bo2b2o29b3o90b2o63bo2b3o25b2o31b
2o32b3o31bo27bo130bo31bobo25bo31bo3bobo55b2o30b2o5b2o23b2o61bo31bo31b
2o29bo6bo24b2o30b2o30b2o35b2o30b2o31bo30b2o30bo31bo31bo66bobo57b2o33bo
61bo31bo93bo31b2o30b2o2b2o27bo30b2o29b2o30bo29b2o31bo36b2o30b2o30b2o
157b2o30b2o2b2o27bo59b2o30bo99b2o97b2o27bo2b3o25b2o131bo27bo34bo27b2o
29b2o30b2o$102b2o30b3o284b2o64bo91b3o29bobo2bo26b3o29b2o28bo34b2ob2o
27bo33b2o24bobo3bobo23bobo62bo31bo30b3o29b3o30bo7bo22bo2bo2bo26b2o2b3o
24b2o31bo5bobo22bobo29bobo161bo31b2o2bo27b2o3bo90bo162b2o27b2o3bo58b2o
27b2o3bobo23bo33bo3b2o24bo33b2o62bo35b3o24b2o260b2o215b3o36b3o92bobo
58bo35bobo26b2o33bo62bobo28bo33bo30bobo58bo2bo29bobo29bobo28bo2bo29bob
ob2o22bo31bobo5b3o22bo30bo2bo2b2o25bo3b2o26bo32bo30bo31bo31bo31b2o32bo
3bo25b3o2b2o60b2o29b2o31b2o30b2o30b2o94b2o30b2o59bo31bo63b2o61b2o30bo
32bo31bo6bobo23b2o3bo30b3o29b2o96bo24bo31b2o31b2o3bo24bo31bo33b2o30b2o
2b3o29b2o24bo8bo24bo5bo23b2o4b3o23b2o6bo95b2o382b2o190bo93b2o158b3o94b
obo92b2o29b2o30b2o31b2o26b2o30bo30b2o30bo37b2o30b2o30b2o24b2o31bo8bo
21b2o31b2o4bo190b3o29b2o34bo29bo94bo129bo$32b2o3b3o24b2o4b2o30bobo29bo
28b2o28bo30bo5b2o27bo94b2o2b2o61bobo154bo31bobo29bo32bobo26bobo2b2o28b
obo3bo25bobo27bo3bobo25bobo2bo25bo2bo28b2o3b3o25bobo29bobo31bo31bo28bo
bo29bo2bo3bo24bo2bobo26bobo29bobo4bo25bobo29bobo32b2o30b2o29b2o31b2o
29bobo30bo32bo30b2o30b2o29bobo30b2o30bo31bo33b3o23b2o5bobo25bobo27b2o
32bobo2b2o22bo2bo2bo25b3o3b2o25bobo2bobo23b3o3b3o24bobo28b2o31bobo29b
2o3bo25bo2bo29bo69b3o56b2o4b2o25b2o63b2o3bo27bo26b2o31b2o62b2o31b2o28b
o31bo6bo57b2o31b2o2bo26bo69bo28bobo25bo33b2o31bo2bo29b2o26bo37bo60bo2b
o29bo30bo2bo28bo2bo28bo2bo3bo22b3o30bo5bo23bobo29bo2bo2bobo23bobo2bobo
24bobo30bobo28bobo3b2o24bobo29bobo29bobo29b3o5bo23bo4b2o30b2o28bo2bo
28bobo2b3o24bo2bo28bo2bo28bo2bo29b2o2b3o26b2o28bo2bo28bo2bo29b2o26bobo
29bobo29b2o30bo2bo29bo30bobo29b3o29bobo29bobo5bo24bobo4bo24b2o3bo31bob
o24bo31bo39bo22bobo29bo2bo29bobo4bo23b3o29b3o32bo29bobo2bo26b2o3bobo
23b3o30bobo28bobo3bo25bobo32b2o4b2o26b2o30b2o3bo58b2o30bo30bo32b2o28b
2o30b2o63bo28bo63b2o5bobo23b2o3bo25b2o31b2o60b2o33bo30b2o29b2o3b3o23b
2o4bobo23b2o3b3o25b2o35b3o23b2o3b3o26b2o2bo58bo30b2o5bo24b2o30b2o35bob
o28bo2bo28bo2bob3o27bo25bobo3bo25bobo28bo2bo28bobo29b2o5bobo23bo5bobo
23bo5bobo22bo2bo3b2o24bobo28bo2bo31bo3b2o60b2o30b2o3b2o25b2o3b2o23bo3b
o24b2o5bo25bo5bobo22bo41bo22b2o4bo25b2o30bo5b2o25bo31b2o29bo32b2o30b2o
3b3o23bo$32bobo2bo26bo4b2o26b2o3bo26b2o4bo28bo27bobo29b3o2b2o26b3o60b
2o31bobob2o26b2o30b2o2bo28b2o28b2o33b2o27b2o32b2o30b2o30b2o32b2o27bo3b
obo27b2o31bo2b3o22b2o4bo27bo30b2o29b2o3bo28b2o30b2o30b2o30b2o28b2o31b
2o30b2o3bo27bo30b2o31b2o30b2o31bobo29bobo29bobo29bobo29bobo28bobo29b3o
32bo29bobo28bobo30bobo29bobo29bobo26b2o4bo25bobo4bo27bo28bobo31bobo2b
2o24bobo31bob2o25bobo3bo28bo2bo26bo3b3o24bobo29bo2bo28bo2bo3bo25bobo
28bobo32b2o30b2o2bo59bo3b2o25bo2bo30bo32bo29b3o26bobo29bo2bo29b2o2b3o
24bo2bo31bo60b3o5bo26b2o27bo2bo31bo28bobo30bo30b2o31bo30b3o30bo2bo28b
3o32bobo25b3o30b2o65b2o29b2o31b2o30b2o30b2o29bo2b2o26b2o5bo22b2o2b2o
27b2o3bo26b2o2bo27bo2b3o27b2o29b2o3bobo24b2o30b2o29b2o2b2o26bo31b2o5bo
28bobo28bobo31bo2bo26bo2bo28bo2bo28bobo30bobobo27bobo29bobo28bo2bo29bo
bo25bobo30bobo28bobo2b2o26bobo28bobo31bo32bo2b2o25bobo2b2o25bobo29bo
30bobo4bo24b2o4bo25bobo29bobo29b2o30bo2bo29bobo29bo33bo31bo2b2o24b3o2b
2o26bo5bo24bobo3bo28bo28bobo30bobo3bo25bobo32bo3b2o28bo31bo29b2o32bo
29bobo28bobo30bobo28bobo29bobo2b3o26bo29bobo26bobo30bo30bo2bo4bo24bobo
2b2o24bo2bo2b2o25bobo29bo3b2o25bo32b3o31bo28bo2bo2bo26bo30bobo2bo26bo
2bo2b2o25b2o3bo25bobo2bo28bo4bo25bo30bobo29bobo29bobo29bo36bo30bo2bo
28bobo2bo26b3o26bo4b2o24bobo2b2o26bobo28bobo29bobo4bo24bobo4bo24bobo4b
o25bobo3bobo22bobo30bobo28b3o4bobo27b2o2b3o24bo2bo28bo2bob2o25bo2bob2o
22b3o2b2o24bo7bo23bobo4bo24b3o30b2o29bo2bo2b2o24bo2bo28bobo4bobo23bobo
29bobo28bobo30bobo29bobo3bo24bobo2b2o26b2o2b2o$34bo3bo26b3o3bo24bobo
29bobo30b3o28bobo32bo3bo24bo32b2o29bobo30bo5bo24bobo2b2o25bobo31bobo
27bobo31bobo27bobo162bo65bo24bobo99bo94b2o30b3o122b2o128bo30b2o31b2o
29b2o31bo29b2o30bo31b3o30bo30b2o31b2o2b2o26b2o31bo27b2o5bo25b2o31b2o
28b2o2b3o28bo5bo24bo31b2o3bo24b2o32b2o3bo24b2o3bo27bo31b2o30b2o31bo30b
o32bo2bo29bobo2bo26b2o30bobo3bo24bo2bo29bobo28b3o29bo4b3o23bobo28bo2bo
28bo2bobo26bo2bo31bobo30b2o29bo31bobo26bo2bo28b3o29bobo2b2o25bobo29bob
o29bobo32bo29bobo28bo31b2o33bo28bo2bo225b2o61bobo93bo65bo29b2o30b3o29b
obo93b2o30bo32b2o2bo26b2o30b2o2b3o25bo32bo3bo27bo31bo30b2o31b2o26bo32b
2o29b2ob2o28bo2b3o25bo2b3o27b2ob3o26b2ob2o27b2ob2o27b2o28b2o30b2o30b2o
30b2o31b2o2b2o25b2o31b2o31bo29b2o32b2o30b2ob2o25bo4bobo24b2o31bo32b2o
28b2o32bo31bo33bobo3bo24b3o29b3o29bo2bob3o24b3o29bo2bo2b2o24bo2bo29bo
3b3o26bo31bo2bo27bobo29bobo25bobo2b2o25bobo29bobo29bobo3bobo23bo2bob2o
25bobo2b3o24bobob2o27b3o28bo31b3o30bobo3bo25bobo29bobo2bo25bo2bob2o25b
obo4bo25bobo2bo25bobo29bobo29bo2bo29bobo29bobob3o25b3o32b2o31b2o30bo4b
o25bo27b2o4bobo23b2o3bobo26bo30bo2b3o26b2o30b2o30bo32bo4bo24b2o32bo29b
o36bobobo27bobo29bobo3bo25bobo3bo20bo5bobo24b3o28bobo32bo28bobo30bobo
2bobo23bobo29bo2bo28bo2bo29bo30bobo30bo31bo6bo23bobob2o26bobob2o$34b2o
31bo29bo31bo31bo31bo32b2o28b2o30bobo30b2o29b2o31bo2b2o27bo33b2o28bo32b
2o29bo34b2o62b2o29bo100bo90bo64b2o30b3o30bobo29bo190b2o30b3o251bo31b2o
67bobo186bo193bo188b2o2b2o27bo30bobo30b2o29b2o31bo2b3o24bo31b2o3bo26bo
30b2o2b2o26b2o3bo26b2o2b3o28b2o29bobo28b2o32b2o27b2o29bo32bo2b2o26bo2b
o29bo30b2o32b2o30bo29b2o30b2o32b2o29b2o31b2o34b2o29b2o28bo34b2o63bo60b
o96bo27bo66bobo29bo31bo227bo285bo30bo30bo32bo33bo31bo188b2o193bo29bo
223b2o28bo31bo32b2o2bo26bo32b2o2b2o26b2o29b2o3bo28b2o30b2o2bo27bo31b2o
26bo2b2o27b2o2b2o26bo31bo31b2o4bo25bo3bo27b2o3bo28bo28b2o30bo33bo31b2o
30bo30b2o4bo24b2o32bo29b2o31b2o2b2o26b2o31bo31bo2bo29bo193bo62bo257bo
3bo27bo31bo31bo25b2o33bo29bo32b2o29bo32bo30bo31b2o30b2o2b3o24b2o31bo2b
3o25b2o30b2o31bo4bo26bo4bo$289bo100bo189bobo61bobo27b2o190b2o64bobo29b
o32bo32bo189bobo29bo31b2o31b2o28bo33b3o29b2o154bo37bo29b2o29b2o127bo
218b2o33bo63b2o27b2o37bobo58bo98bo64bo60bobo61bo61bo162bo26b2o286bobo
34bobo28bobo26b2o34bobo247b2o66bo32bo125bo33b3o62b2o33bo24b2o63b2o33b
2o27bo32bo129bo30bo32bo219b3o33bo60bo31b3o451bo64bo62bo156bo29b2o128bo
381b2o96bo63b3o30b2o60b3o89b2o34bo186b2o451bo62bo$194b3o61b2o61bo131bo
59bo31b2o33bo63bo29bobo189bobo63bo32bo254bo32bo30bobo30bobo26b2o33bo
31bobo152b2o67bobo28bobo345bobo31b2o63bobo26bobo36bo122bo37bo124bo64bo
59b2o66bo28b3o218b2o159bo3b2o31bo30bo28bobo33bo249bobo223b2o33bo64bobo
57bobo62bobo32bobo25b2o31b2o413bo95b2o31bo383b2o94b2o62bo130b3o93bo
187b2o322bo28bo94b2o34bo32bobo59bo91bobo220bobo100b2o281b3o65bo62bo$
194bo63bobo59b2o130b2o58b2o31bobo736bo32bo28bobo33bo30bo154bobo66bo30b
o347bo33bobo62bo28bo160b2o354b2o28bo220bobo157b2o3bobo602bobo33bo63bo
59bo64bo34bo27bobo30bobo413bo94bobo31bo382bobo93bobo60b2o130bo283bobo
349b2o94bobo34bo31bo62bo90bo222bo102bobo280bo$195bo62bo61bobo129bobo
57bobo30bo1759bobo353bobo28bo219bo164bo1853bo95bo62bobo130bo282bo351bo
bo93bo548bo283bo28$41b2o30b2o21b2o30bo31bo32b2o31b2o29bo37b2o30b2o30b
2o30b2o31b2o30b2o35b2o25bo31bo31bo32b2o30bo31bo31b2o30b2o30b2o31bo22b
2o30b2o30bo32bo31b2o35b2o31b2o30b2o30b2o30b2o30bo31bo32b2o30bo31bo31bo
31bo31bo22b2o31bo37b2o31b2o30b2o30b2o31b2o30b2o30b2o30b2o30bo32bo31bo
23b2o30b2o30bo36b2o31b2o30b2o30b2o30b2o31b2o30bo31bo31bo22bo9b2ob3o17b
2o7bo22b2o7bo22b2o7b2o33b3o17bo32b2o4b2o24b2o4b2o24b2o6b2o22b2o5bo24b
2o6b2o33b3o25bo22b2o31bo31bo31b2o31b2o36b2o31b2o30b2o30bo32bo31b2o34b
2o17b2o30b2o37b2o31b2o30b2o31bo31b2o30b2o30b2o20b2o30bo31b2o38b2o30b2o
31b2o30b2o30b2o31bo31b2o30b2o20bo33b2o30b2o37b2o32bo30bo22b2o31b2o37b
2o30bo32b2o30bo22b2o30bo30b2o32b2o30b2o30b2o28b2o32b2o30b2o30b2o30b2o
30bo32b2o29b2o28b2o30b2o2b3o25b2o30b2o30b2o30b2o30b2o30b2o30bo31b2o30b
2o31b2o30bo31bo31bo31bo31b2o30b2o30b2o30b2o30b2o30b2o30bo31bo32b2o30b
2o30bo31bo2b3o26bo31b2o30bo31bo31b2o30b2o33b3o27b2o32b3o27bo31b2o30b2o
27b2o34b2o29b2o30b2o30b2o30b2o31b2o26b2o31b2o30bo31b2o30b2o31b2o30b2o
30bo31bo32b2o30b2o30bo31bo2b3o26b2o33b3o23b2o30b2o30b2o30b2o30bo31b2o
31bo31b2o30b2o30bo31bo32b2o30b2o30b2o30bo31b2o30b2o30b2o33b2o$33b2o5bo
bo24bo4bobo21bo31b3o29b3o29bobo30bobo28bobo37bo31bo31bo30bobo29bo2bo
28bo2bo29b2o2b2o25bobo29bobo29bobo30bobo29bobo29bobo29bobo30bo31bo30b
3o22bobo28bo2bo28bobo30bobo30bo36bobo29bo2bo28bo2bo28bo2bo28bo2bo28bob
o29bobo30bobo29bobo29bobo29bobo29bobo29bobo22bo30bobo36bo32bobo29bobo
29bobo29bobo29bobo30bo30bobo29bobo29b3o29b3o22bobo30bo30bobo35bo31bo2b
o28bo2bo28bo2bo28bo2bo31bo29bobo29bobo29bobo21b3o7bo2bo18bo2bo5bobo20b
o2bo5bobo20bo2bo6bo2b2o18bo7b2o2bo18bobo6b2o24bo4bobo22bobo5bo23bobo5b
obo21bobo4bobo22bobo5bobo29b2o2bo26bobo22bo6b2o22bobo7bo21bobo5b2o22bo
2bo29bobo29bo6bo31bo2bo22b2o4bo2bo28bobo24bo5bobo22b2o5bobo33b2o17bo2b
o28bo2bo36bobo29bo2bo28bo2bo29bobo30bo30bobo29bobo21bo30b3o29bobo38bo
31bo31bobo29bobo28bo2bo29bobo29bobo30bo21b3o30bobo29bobo37bobo30bobo
28bobo20bo2bo29bobo37bobo28bobo30bobo29bobo21b2o29bobo29b2o2b2o27bobo
29bobo30b2o28bobo31b2o30b2o30b2o29bobo29bobo30bobo30bo2b2o24b2o30bobob
o27bobo29bobo30bo4b2o25bo30bobo29bo31b3o29bobo29bobo2b3o25b2o29bobo29b
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2o29bobo29bobo29bobobo27bobo29bobo29bobo29bobo29bobo29bobo33bo29bo33bo
27b3o31b2o30b2o27b2o5b2o26b2o30b2o30b2o30b2o29bobo27b2ob2o27bobo29bobo
29bobo29bobo29bobo31bobo28bobo29bobo29bobo31b2o29bobo29bobo29bobobo28b
o31bo2bo25bobo29bobo29bobo29bobo29b3o29bobo2b3o24bobo31bo31bo30b3o29b
3o29bo2bo28bo2bo29bobo28bobo31bo2b2o26bo31bo33bobo$32bo2bo3bobo2b3o18b
3o3bobo23b3o4b2o25bo4b2o25bo5b2o22bo6bo25bo7b2o21bobo4b2o23bo6bobo24bo
4bobo29bobo23bo5bobo21b2o6b2o29bo2bo28bo2bo3bo17b2o5bo2bo23b2o3bo2bo
28bo2bo21bo8bo30bobo30bo24b2o4b2o22bo6bobo29bobo22b2o5bo26b2o29bobo28b
o2bo28bo2bo28bobo38bo2b3o25b2o2b2o25bo2bo28bo2bo28bo2bo28bo2bo28bo2bo
30bo30bobo28bo2bo28bo2bo28bo2bo28bobo23bobo28b2o38b3o30b2o30b2o30b2o
30bo31bo29bobo29bobo29bobo29bo31bo25bo30bobo29bobo37b3o29b2o2b2o26b2o
2b2o26b2o30b2o2b2o25b3o29bobo29bobo31bobo23bo4bobo3bo17bobo6b2o21bobo
5bo2bo21bobo4bobo2bobo16bobo5bo2bo2bo17bo2bo5bobo20b3o7bo2b3o17bo7bobo
21bo7b2o21bobo6bobo20bobo7bo22b2o5bo2bo2bo17b2o6bo2bo21bobo4bo23b2o7bo
bo20bobo6bo23bobo5b2o21bobo6b2o21bobo6b3o21bo6bobo22bobo5bobo21b2o6bob
o21b3o6b2o23bo5b2o31b2o3bo17b2o30b2o39bo30b2o24bo5bobo22b2o5b2o29bobo
21bo7bobo2b3o19bo4bobo22bobo10b2o19bo29bobo37bobo29bobo30bo31b2o29bobo
30b2o29b2o29bobo24bo29bo30bobo39b2o30b2o28bo2bo20bo2bo29bo40b2o29bobo
29b2o29bobo53b2o2b3o28b2o29bo2b2o25bobo62b2o127bo31bo31b2o28b3o2b2o58b
o3bo27b2o30b2o2b2o26bobob2o26bobo30bo2b3o25b3o31bo29bobo29bobobo59b2o
30b2o30b2o29b2o30b2o30b2o30bobo29bobo30bobo29bobo28bo2bo29bobo62bo30b
2o30b2o3bo26bobo29b2o29bo2bo28bo2bo29bo31bo32b2o2bo26bobo30b2o2bo25bo
101b2o24b2o3bo124b2o28b2o3bo27bobo29bo30b2o5b2o23b2o5b2o23b2o33b2o2b2o
23bobo29bobo29bobo64bo31b2o30bo3bo25bobo2b2o26bobo2bo25bo31b2o30b2o30b
2o2b2o28bo29bobobo27b2o31bobo29bobo31bo31bo29b2o30b2o2b3o26b2o28bo2bo
27b3o2b2o25bobo29bobo33bo$32bo2bo4bo3bo19bo7bo26bo3bo2bo23b2o3bo2bo23b
2o6bo28bobo33bo22b2o3bo2bo21bobo6b2o22b3o5b2o22b2o6b2o22bobo5bo22bobo
30b2o5b2o24b2o4bobo22bo6b2o2b3o18bobo4b2o2b3o18b2o5b2o22b3o30bo7bo55bo
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24b2o6b2obo31bobo18b2o5b2o30b2o30b2o30b2o30b2o23b2o38bo23b2o5b2o23bo6b
2o24bo5b2o29b2o25b2o70bo188b2o31bo30b2o30b2o30b2o23b2o30b2o30b2o40bo
33bobo29bobo61bobo24bo31b2o30b2o33b2o22b2o4b2o23bo2b2o27bo7b2o23bo5b2o
3bo18bo2bo5b2o22b2o7bo21bo9b2obo18b2o8b2o20b2o31bo2b2o4b2o21bo30bo2bo
5b2o21b2o2b2o3b2o23b2o5b3o28bo2bo21bo7bobo22bo5bo2bo21bo2b2o3bobo21bob
o7bo20bobo6bo23bo8bo21bobo7b2o20bo31b3o38bobo30b2o30b2o21b2o7b2o20b2o
31b3o6bo22bobo29b2o5b2o22b3o6bo3bo19b3o5bo24b2o9b2o19b2o5bo24bo6bo24bo
7b2o22bo7b2o22b2o28bo41bo22b2o31b2o36b2o24b2o28b2o31bo103b2o22b2o29b2o
72b2o60b2o58bo32bo31bobo25bo2b3o25bo255bo6bo92b3o29b2o28b2o3bo26b2o30b
2obo29bo30b2o30bo31bo3bo61b3o186bo31bo32bo31bo30b2o2b2o27b2o33b3o122bo
62b2o30b2o2b2o25b2o30b2o32bo30b2o31bo29b2o30b2o30b2o3b2o28b2o3bo23b2o
30bo161bo67b2o30b2o62b2o25bo30b2o30b2o159b2o2b2o26bobo128b2o28b2o30bo
3bo60b2o30b2o30b2o30b2o65bo59b2o28bo6bo24b2o5b2o23b2o33b2o$33b2o10bo
18b2o38bobo29bobo28b3o29bo2bo21b2o6b3o29bobo21bobo2b2o25bo31bobo2b2o
25bobo30bobo28bo2bo29bobo5bo23bobo8bo19bobo9bo19bobo32bo2b2o24bobo29b
2o30bobo4bo27bo28bobo30b3o29bo6bobo29b3o30bo2bo26bobo29bobo22bo2bo9bo
30bo19bo2bo29b2o30b2o30b2o30b2o29bo2bo2b2o24b2o30bo2bo28bobo30bobo29b
2o37bo31b2o25bo29bo95b2o31b2o2b2o57b2o228bo36bo31bo29b3o31bo183bobo90b
2o75bo60b3o22bobo28b3o27b2o32b2o38bo29b2o31b2o29b2o2b2o21bobo3bo23b2o
2b2o24b2o30b2o31bo2b2o26b2o30bo10b3o19b2o6b2o30bobo29bobo20bo2bo28bobo
29bo32bo30bo2bo31bo10bo17bo41b2o3bo24bobo29bobo22bobo29bobo29bobo2b2o
24b3o29b2o30bo2bo8bo20bobo7b3o19bo38b2o31b2o30b2o22b2o31bo30bo223b2o
34bo63bo30bo27b3o34b3o24bo33b2o31bo32b3o189bo33bo95bo189bo320bobo61bo
223bobo88bobo61bobo61b2o30bobo2bobo28bo59b3o30bo2b3o26bo2b3o29b2o65b2o
26b2o30b2o3bo26b2o3bo63bo120b2o29b2o30bo5b2o24b2o37bo25b2o131bo288bo
126b2o$67b2o36bo2b3o26bo29bo32b2o22bobo5bo32bo23bo2b2o26b2o9bo20b2o2b
2o26b2o5b2o25bo2b3o25b2o4bo24bobo31b2o9bo19bo11bo19bo8b3o21b2ob2o25b2o
30b2o2b2o27bo4b2o26b2o4bo23b2o2b2o29bo28b2o8bo21b2o5bo31bobo3bo25bo2bo
28bo2bo21bobo29b2o30bobo4bo24bobo2b2o25bo2bo3bo24bobo7b3o19bo2bo6b3o
19bo2bob2o25bobo29bo2bo3bo24bo2bo6bo21bo2bo6bo21bo2bo5b3o27bobo29bo2bo
22b3o4b2o22bobo2b2o26b2o2b2o26b2o2b2o25bo2bo31bob2o57bo2bo29b2o3bo26bo
31b2o37b2o86b2o4b2o24b2o30b2o32b2o6bo54bo30b2o7bo23bo98bo35bo90b2o61b
2o39bo24bo30bo65bo92b3o40bobo20bo32b2o35b2o56bobo28b2o38bo20bobo39bo
30b2o22b2o9b3o18bo30b2o30b2o31b2o31b2o28b2o39bobo28bo2bo28bo2bo20bo2bo
2b2o24bobo29bobo2b2o28bo2b2o24bobo30bobo7b2o20bo9bo20bobo33bo3bobo23b
2o4bo2bo28bo2bo20bo2bo2b2o25bobo28bobo8bo29b2o23b2o4b2o24b2o2b2o24b2o
64b2o3bo24bobo29b2o99bo29bo29b2o2bo26b3o30bobo29b3o29bo2bo28b2o30b2o
31bo30bo3b3o24b2o30b2o3bo155bo67b2o58bo30bo4bo27b2o31b2ob3o57b2o97b2o
30b3o62bo31b2o27b2o2bo27bo30b2o30b2o33b3o27bo66bo90b2o62b2o65b2o28bo3b
o27b3o63bo28bobobo27bobobo27b2o2bobo27b2o34b2o26bobo31bo31bo29b2o29b2o
32b2o30b2o30bo28bo2bo29bo30b3o2b2o25bobo95b2o32bo162b2o87b2o30b2o32bo
128b2o30b2o3bo$67bobo38bo115bo69bo35b2o26bo32bobo27bo32b2o25bo104bo28b
o59b2o33bobo30b2o27bobo57bobo7b2o20bobo4b2o30b2o31b2o30b2o23bo30b2o31b
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2o6b2o22b2o6bo29bo2bo28bo2bo21bo7bobo21bobob2o26bobob2o26bobob2o26bo2b
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24bo30bo34bo7bo20b2o30bobo29bo7b2o22bobo35b2o95b2o90bobo60bobo39bo55bo
100b2o32bo22bo42bo57bo34bobo21b2o32bo30bobo38bo19b2o106bo54b2o126b2o
36b2o30b2o30b2o22b2o2b2o25b2o2b2o27bo5bo26b2ob2o26b2o31bo8bobo18b2o10b
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22bobo3bo26bob2o25bobo2b3o24b2o33bo2b2o24b2o2b2o26b2o30b2o96b2o28bo2bo
2bo28bo29bo30bo4b3o24bobo2bo26bo2bo29bobo29bobo28bobo2bo27bo30bobo31bo
29b2o63b2o29bobo30bo31b2ob2o28bo29bobo29b3o29bo2bo30bo2bo27b2o29bo2bo
29b2o29b2o33b2o28bo2bo28b2o31bo30bo2b2o28bo30bobob3o24bo2bo28bo2bo29bo
2bo28bobo29b2o30bo31bo31b2o63b2o60b2o33bobo59bo33bo30b2o28b2o3bo27bo3b
o26b2o2bo28bo2bo30b2o3bo24bobo29b3o29b3o29bo2bo27bobo31bobo29bobo29bob
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2b2o25bo2b3o26bo2b3o26bo30bobo30bobob3o25bo31b2o30b2o31bobo31bo29b2o$
67bo41bo25b2o30b2o33b3o58b2o65bobo58bo30bo31bobo130bo54b3o32bo65bobo
26bo29b2o60bo197bobo29bo31bobo34bo31bo90bobo32bobo29bobo30bo29b2o30b2o
2b3o17b2o6bo24bo4bo26bo4bo25b2o4bo26b2o2b2o25bo31b2o2b2o28bo2b2o25b2o
3bobo25bo2b3o25b2o2b2o33bo2bo29bobo29bobo22b3o29bobo29b3o28b3o29bobo
29bobo30b3o4bobo21bobo34b2o96bobo89bo62bo198bobo30b2o23bo134bo23bobo
62bo102b2o31b2o32bo18b2o33bobo28b2o31b3o61bobo129bo28bobo64bo124bo30bo
bo4bo23bo6bo31b2o22b2o4bo26bo31b2o6bobo27bo2bo22bo6b3o20b3o4bo25bobobo
26bobo29b3o3bobo27bobo57bobo126b2o31b2o2b2o24b2o30b2o3bo27bo31b2o2b3o
26b2o29b2o29bo2bo2bo26bobo29bobo29bobo28bobo29b2o2b2o26bobo29bobo29bob
o29bobo3bo26bobo28bo2bo31bo28bobo29bobo3bo26bobo29bobo29bobo28bobo29b
2o3bo26bobo2bo27bobo29bobo28bobo3bo25bobo29bobo2bo27bobo29bobo28bobo2b
o26bo2bo2b2o25bobob3o24bobo29bobob3o25bobo62bobo60bobo32bo94bobo157bob
o30b2o29bo30bo31bo32b2o2b3o24bo32b2o31bo2b3o26bo2bo27bo2b3o26b2o30b2o
30bo29b2o30b2o31bobo2b3o24bo32bobo29bobo29bobo28bo2bo29bobo3bo23bobobo
27bobobo28bobo29bobob3o24bobo2bo26bobo29bobo2b2o25bo2bo30bo30b3o30bobo
26b2o$135bobo29bobo32bo60bobo376bo159bobo133b3o29b3o277b2o200bo152bobo
59b2o32bobo60bo33bo33b2o31bo31bo25bo30b2o31bo28bo32b2o30bo33bo29bo32b
2o3bo449bo32bobo181bo167bobo30bobo50bobo32bo30bobo30bo63bo71b3o26bo59b
o92bo99bo227b2o32bo20bo33bo3bo26bo2b2o26bo35bo60bo32b2o61bo67b2o28b3o
32bo62bo91b2o31b2o30bo30b2o30b2o29b2ob2o28bo31bo2b3o26bo31bo32b2o29b2o
2b2o27b2o29bo30b2o32b2o30bo31b2o29b2o2b2o25b2o31bo32b2o30b2o29b2o29b2o
30b2o4bo27bo31bo30bo31b2o2b2o27bo2bo27b2o29b2o2bo27b2o2b3o26b2o31bo30b
2o30b2o2b2o123b2o32bo126bo162bo95bo32bo29bo154b2o32bo3bo26b2o32b2o2b2o
26b2o30bo30b2o31b2o27b2o3bo27bo3bo28b2o30bo2bo26b2o4bo26b2o29b2o2b2o
27b2o2b3o25b2o30bo33b2o2b2o22b2o2b2o$135bo31bo35bo59bo379bo158bo135bo
31bo279bobo162bo37bo151bo63bo31bo63bo413bo838bo32bo52bo65bo33bo134bo
27b2o151b2o201b2o51b2o194bobo154bobo60b2o69bo27bo98bo26bo227bo62bo128b
obo220b2o353bo30bo62bo30bo28bobo60bo2bo32b2o157b2o187b2o101bo60bo34bo
62bo29bo162bo62b2o254bo95bo30bo96b2o26b2o$939bo31bo278bo163b2o418b2o
30b3o29b3o181b3o61b3o27b3o1161bo26bobo150bobo200bobo50bobo72b2o119bo
156bo62bobo97bo123b2o291bo28b3o96bo59b2o63bo32b2o29bo35bo90bo159b2o
226bo28bo29b2o31b2o35bo156bobo186bobo160b2o126b2o190b2o35bo57b2o160bo
161bo97bo27bo$1414bobo417bobo29bo31bo183bo63bo29bo1546bo52bo74bobo274b
2o286bobo319bo158bobo61b2o32bobo27b2o125b2o159bobo284bobo413bo162bobo
125bobo189bobo92bobo158b2o$1834bo32bo31bo183bo63bo1703bo887bo157bo63bo
bo31bo29bobo124bobo158bo286bo898bo94bo160bobo28$37b2o31b2o30b2o30b2o
30b2o30b2o30b2o31b2o31b2o30bo28b2o33bo30b3o22bo5b2o2b3o26b2o23bo6bo24b
o6b2o24bo31b2o5bo30b2o24bo38bo31bo31bo23b3o8b3o26b2o30bo31bo31bo23b3o
36b3o30bo31bo32b2o29b3o27b2o32b2o23bo32b2o5bo30b2o30b2o23bo31bo30bo40b
o31bo22bo39bo31b3o30bo31b2o30b3o28b2o31bo23bo7b3o29b3o20b3o30bo40bo31b
o22bo30b3o29b3o29b3o30bo30bo31b3ob3o30b2o26bo2b3o25b3o29b3o29b3o30b2o
30bo31bo31b2o30bo31b2o31bo30b3o29b3o29b2o30bo32bo30b3o28b3o30b2o30b2o
29b3o30b3o2bo26b3o29b3o29b3o29bo33bo31b2o30bo29b2o29bo34bo30b2o28bo32b
2o31bo32bo28b3o29b3o2bo28b2o31b2o30bo30bo29bo34bo31bo32bo28bo30b3o2bo
30bo31bo31b2o31b2o28bo28b3o32b3o30bo30b3o30bo27bo31b3o34bo26bo37b2o28b
o31bo31bo30b3o30bo31b2o26b3o2bo29bo32b3o26b2o34bo30b3o25bo33b2o31b2o2b
3o26b2o31bo32b2o28bo30b2o29b2o32bo32bo30b3o30bo31bo31bo31bo30b2o32b2o
26bo30bo4bo25bo4bo26bo4bo26bo31bo32bo3b3o24b3o4bo25bo3b3o29b3o30bo25b
3o7b2o20bo34bo28b3o33bo33b2o30bo25b3o29bo36b2o31b2o30bo30b3o30bo31bo
25bo35b2o32b2o30bo26bo5bo25bo5bo25b2o4bo24bo3b2o31bo31bo32bo31b2ob3o
20bo31bo38b2o30bo31bo30b3o29b2o29b2o31b2o31bo29b2o31b2o30bo32bo33bo31b
2o30bo28bo31bo30bo$37bobo30bobo28bo2bo28bo2bo28bo2bo28bo2bo28bo2bo29bo
bo31bo31bo28bobo32bo55bo5bobobo21b3o4bobo22bo5bobob3o19bo5bobo23bobo5b
o23bo2bo4bo23b3o3bo2bo22bobo36bobo24b2o4bo31bo30b2o2bo27bobo30bo31bo
31bo95bo31bo33bo59bobo23b3o4bo2bo21bobo5b3o22bobo5bo22bo6bobo22bo7bo
23bobo29bobo29bo40bo31bo22bo38bobo63bo31bo54bo6bo2bo29bobo21bobo29b2o
2b2o36b2o20bobo39bo31bo22bo127bo30bo35bo28bo2b2o26bobobo95b3o25bobo29b
obo29bobo29bo2bo29bo30bo2bo29bobo33b2o58b2o29bobo31bo93bobo29bo2bo65b
2o30b2o89bobo31bobo31bo30bo28bobo29bo34bo29bobo28bo31bo2bo29bobo31bo
64b2o27bo2bo30bo31bo30bo29bo33bobo29bobo31bo27bobo33b2o29bobo29bobo30b
2o30b2o28bobo95bo63bo27bo67b2o26bo33b2ob2o29bo31bo31bo63bo30bo2bo29b2o
28bobo59bobo33bobo26bo30bo33bobo29bo2bobo27bo2bo29bobo30b2o28bobo29bo
30bobo30bobo31bo63bo31bo31bo31bo31bo31bobo25bobo2b3o23bobo3bo25bo3bobo
25bo3bobo25bo3b3o25bo3b2o26bobo34b3o24bobo30b2o35bo30b2o2b2o21bo34bo
33bo28b3o32bobo29bobo56bo35bo2bo30b2o30bo63bo29b3o25bo35bobo30bo2bo28b
obo24bobo4bo24bobo4bo24bo2bo3bo24bo3bobo25bo3bobo25bo3bobo25bo4bobo24b
o5bo2bo22bo4bo26bo37bobo24bo5bo26b2o3bo61bo2bo27bo2bo29bo2bo29bobo28bo
bo30bobo28bobo31bo26b2o4bobo22bo6bobo22b2o5bobo26bobo29bobo29b3o$38bob
o30bo30b2o30b2o29bo2bo28bo2bo28bobo30bo31bobo31bo29bobo31bo55bo6bo3bo
28bo2b3o18bo5b2o2bo21bo5b2o2b3o20b2o5bo23bobo5bo30bobo23b2o5bo29bobo
25bo5bo24b2o5bo29bo2bo2bo26bo25b2o5bo24b2o5bo31bo95bo31bo30b3o61bobo
30b2o2b2o18bo2bo28bobo6bo22bo6b2o23bo5bobo23b2o31bobo28bo40bo31bo22bo
37bobo24bo39bo29bobo54bo7bobo21b3o5bo2bo21bo2b3o25b2ob2o36bobo20b2o40b
o31bo22bo127bo30bo36bo26bobo3bo26bo3bo94bo28bo31bo31b2o29bobo30bo31bob
o28bobo34bobo89bo32bo94bo30bo2bo65bobo29bobo89b2o31b2o29b3o31bo29bo2b
2o26bo34bo30bo29bo32bobo29bobo31bo64bobo27bobo28bobo31bo30bo29bo33bo2b
o28bo2bo30bo28bobo32bobo28b2o30b2o2b2o56b2o3bo27b2o32bo27b2o4b2o28bo
28bo34bo27bo67bobo25bo32bobo3bo28bo31bo31bo63bo31bobo29bobo28bobo59bo
2b2o30b2o26bobo29bo35bo30b2o3bo27b2o30b2o28b2o3bo26bobo31b3o28bobo29bo
2bo30bo26b2o35bo31bo31bo31bo31bobo28bobo27b2o29bo4bo25bo3b2o26bo4bo26b
o31bo3bobo25b2o6b2o26bo27bo2bo28bo2bo34bo29bo2bo3bo20bo3b2o29bo3b2o27b
obo3b2o21bo36bo29bobo57bo36b2o2b2o59bo63bo28bo28bo36bobo30bobo28bo2bo
23b2o5bo25bo5bo24bo2bo3bo24bo5bo2b3o20bo3bo2bo24bo4bobo24bo4bobo24bo3b
obo3bo21bo3bobo25bo37b2o24bobo4bo27bo3bo24b3o35b2o2b2o24bo2bo29bo2bo
29b2o30bobo30bo29bo2bo30bo25bobo5bo22bobo5b2o22bo2bo3bo2bo25bobo29bobo
33bo$39bo126b2o30b2o30bo30b2o31b2o63bo34b3o94bo31bo30bo29bo24bo38bo31b
o23b3o3b2o2b2o20bobo29bobo35bobo29b2o24bo2bo28bo2bo29bo165bo64bo35bobo
18b2o30bo9b3o18bo31bo5b2o32b3o23b2o5bo30bo24b2o30b2o67b2o24bobo3b2o63b
2o55bo8bo31b2o25bo32bo35b2o342b2o130bo123bo64bo2b3o24b2o35bo60bo190b2o
98bo155bo66bobo93b2o60bo31bo34b3o91bo29b2o65b3o60b2o30b2o61b2o99bobo
22b3o2bo26bobo64bobo26bo5bobo24bo30bobo96b2o27b3o62bo36b3o156bo62b2o
62bobo57b2o33b2o27bo3b2o26bo96bobo30b2o34bo29bo31b2o26b2o30bobo30b2o4b
o63b3o60b2o29bo191bo34bobo25b2o27b2o30b2o29b3o33bo2bo27bo2bo31bo2bo27b
obob2o22b2o65b2o31b2o66bobo86b2o63b2o2b2o61bo32bo30b2o89b2o35b2obo22bo
4b2o25bo5b2o24bo5bo25bo3b2o30bo2bo30b2o24b3o29bo2bo28b3o71bobo19bo4b2o
31b2o2b2o59bo62b2o33b3o21bo30bobo30bobo4b2o26b2o30b2o33b2o$69b2o33b2o
30b2o191b2o63bo97bo62bo61b2o61bo33bobo19b2o7b2o22bo2b2o33bo24b3o30bobo
29bobo2b2o24bobo3b2o31b2o23b2o39b2o161bo62bo29b3o54b3o36bo23b2o4bobo
22bobo29bobo30b2o29bo32bobob2o25bo5b2o157bo92b3o5bo22b2o31bo8b2o179b2o
127b2o30bo31bo195bo123b2o31b2o93b2o93b2o31b2o30bo32b2o33b3o60b3o93bo
59b2o2b2o26bo3bobo27b2o32b2o30b2o31bo28b2o160bo224b3o31bo28b2o27bo31bo
3b3o27bobo27b3o2bo25bobo29bobo30b2o31b2o30bo2bo60bo29b2o36bo90b2o34b2o
157bo33b3o26b3o28bo2bob3o22bo31bo31b3o3b2o24b3o3bo25bobo36bo56bo5b3o
55bobo3b2o25bobo28bo2bo2b2o26b2o35bo121bo30b2o36b2o29b2o26b2o69bo59b3o
29b3o62b2o28bobo27b2o4bobo28b2o3bo26b3o23b3o65bo2bo28bo36bo55bo31bobo
35b2o30bobo158b2o30b2o29b2o33bo154b2o2b3o21b2o3b2o32b3o22b2o2b2o25bo6b
2o26b2o27b3o7bo21bo31b3o7bobo19b3o66b2o66bo22b2o31bo5bo26bo$33bo35bobo
25b2o5bobo23bo5bobo22b2o32bo3bo26b2o3b3o24b2o3bo64b2o28b2o35bo26b2o
161b2o29b2o28b2o34b3o29bo29b2o26bobo65b2o24bo2b2o27bo3bobo23bo2bo2bobo
29bo2bo22bobo2b3o25b2o5b2o23bo3b3o56b2o37b2o58b2o39bo28bo23b3o30bo38bo
22b2o6b2o23bo31bo2b2o26b2o5b3o22bo7bo25b2o3bo24b3o2b2o31bo64b2o34b3o
90bo25bo7bo21bobo30bobo6b2o180bobo125bobo29bobob3o26bo196bo122bobo30bo
bo92bobo28bo63bo31bo2bo28bobo32bo29b2o2bo62bo155b2ob2o27bo3bo28bobo28b
o3bobo25bo3bobo31bo26bo2bo63b3o94bo95b3o125bo62bobo29bo27b2o34bo30bo
28bobo30bo30bobo2b2o26bo2bo29bobo60bobo61bo5bo25bo31b2o29bo2bo33bobo
92bo97bo28bo31b2o2bo24bo31bo37bobo28b2o26bo31bo5bo24b3o2bo26bo5bo25b3o
31bo2b2o27bo30bobo2bobo24bobo2b2o24b2o6bo27b3o30bo58b2o30bobo35bobo28b
obo25bobo34b2o62b2o28bo31bo30b2o63bo27b2o6bo56bo62b3o3bo30bobo27bobo
90bobo30bo36b2o24bo6bo61b2o30b2o64b2o30b2o30bobo55b2o30b3o32b2o67bo22b
2o38bo28bobo31bobo25bobo58bo6b3o32bo25b3o25b3o29b3o2bobo57b2o7bo59b2o
34bo23bo69bo$32bobo30b2o2bo26bo2bo4bo24bobo4bo23bo2bo29b3o2b2o25bobo3b
o27bo2b2o58b2o6bo27bobo60b2o161b2o32bo27bobo33bo63bo25bo67bobo26bobo
30bo26b2o3bo31bo2bo23bobobo26bo2bo6bo21bobo2bo58bobo2b3o31bobo57bobo
68bo22bo33bo39b3o20bo65bobo27bo29bo6b2o58bo3bo29b2o25b2o37bobo33bo91b
2o26bo6bo22bo2b2o26bobo9bo51b2o31b2o30b2o61bo64bo30b3o30bo2b3o26bo2bo
28bo159bo3b3o90b2o94bo95bo2b3o24bo64b3o29bobo29bobo28b3o29bo2bo2bo62bo
60b2o97bo26bo32bo3b3o24bo3bo27bo3bo27b3o31bobo30b2o31bo60b2o29bo33b2o
32b3o30bo29bo98bo93bo27bobo94bo2b3o58bo2b2o27bo2bo30bo2b2o27bo30bobo
31bo27bobo29bobo29bo2bo28bo2bo29b2o2bo30b3o60b2o29b2o67bo28bo35bo25b3o
65bo30bobo56b2o5bo28b2o26bo6bo28b2o28b2o3bo28b2o28bo29bobo2b2o25bobo
29b2o2bo31b2o58bobo29bo37bo30bo27bo36bobo61bobo28bo31bo29bobo64b3o25bo
61b2o33b2o32b2o31bo28bo2bo25b3o29b3o2bo26bobo29b2o30b2o6bo23bo36b2o30b
obo29bobo65bo31bo29bo56b2o31bo34bobo67bo23bo38bo27bo33bo27bo67bo60bo
64bo58bo2bo30b2o34bobo32b2o22bobo29bo31bo5b2o$32bobo2b2o25bobo29bobo
29bo2bo28bo2bo28bo5bobo24bo6bo23b3o3bobo58bo34bo27b2o30b2o3bo162bo59bo
36bo156bo28bo97b2o25bo3bo26bobo28bo2bo2bo58bobobo33bo59bo94bo72bo54b3o
31bo66bobo56b2o28bo4bobo24bobo2b3o31bo36bo90bobo58bobo25b2o30b2o30bobo
29bobo29bobo30bo95bo66bo32bo58b3o2bo26b3o2bo90bobo2bo93bo29b2o126bo3b
3o29bo26bo31b3ob3o28bo30bo31b2o28bo32b2o126bobo66b2o88b2o3bo26bo31bo
66bo31b2o27b3o2bo26b3ob3o25bobo29bo32bo2bo31bo33bo26b3o64bo127bo63b2o
62bo27b2o36bo27b2o34bobo25bobo30b2o31bo27b2o30bobo29bo2bo29b2o2b2o25bo
bo33bo32bo29bobo27bobo2b2o154bo129b3o25bobo33bobo60b2o63bobo58bo5bo25b
obo28bobo2bo30bobo223bo63bo92bo66bo89bobo32bobo31bobo60b2o2b2o58b2o27b
o33b3o26b2o30bo35bo2bo24bo4bo31bo188bo31bo33bo291bo60bo29b2o59b3o30bob
o30bobo68bobo20bobo29bobo29bobo4bobo$33bo2b2o27bo31bo31b2o30b2o29b2o
30b2o30bo31b3o2bo26b3o29bo33bo32bo606bo30b2o29b3o31bo3bo261bo53bo189bo
32bobobo222bo59bobo30bo31bo30b2o30bobo94bo67bo94b2o30b2o27b3o2bo25b3o
2bo26bo2bo2bo26bo62b3o29bobo94b2o29bobo2bo32bo27b3o31bo189b3o27b3o29b
3o2bo26bobo32bo33b2o95bo221bo27b2o2b2o26bo32bobo28b3o2bo26b3o29bo4b3o
59bobo190bobo62bo26bobo99bo27bo2bo62bo60bo31b2o34bobo25bo30b3o2bo31bo
26bo31bobo2b2o156bo257bo62bo93bo30bo485bo123bo67b3o30bobo57bobo60bo96b
o2bo24bo31b3o29b3o2bo605bobo92bo31bo93b2o31bo2b3o26b2o$38bo253b2o26bo
31bo31bobo29b3o550b2o181bo290bo188bo33bo3bo282bo126bobo257bobo29bobo
30b2o29b2o27b2o30bo30b3o29bo31b2o2b2o26bo31bo31bo2bo28bo2bo2bo59bo34bo
28b2o92b2o130b2o27bo33bo30b2o3bo220b2o95bo30bobo59bo93b2o3bo29b3o30b2o
26b3o29b3o129bo91bo64bo65b2o30bo161bo95bo26bo32bo5bo632b3o644bo32bo89b
3o31bo96b2o2b3o20bo67b2o605bo63b2o158b3o30bo$163b2o127bobo57bo31b2o30b
o552bobo119b2o59bo831b2o31b2o31b2o29bo323bobo28bobo58bo98bobo25bo31bo
32bobo29b2o64bo62bobo91bobo66b2o61bobo28b3o29bo29bobo224bobo125bo161bo
409b2o96b2o94b3o30b3o154bo67b3o25b3o605b3o2bo610bo121bo134bo90bobo668b
obo157bo33bo$163bobo803bo121bobo58bo801b2o28bobo30bobo30bobo478b2o63bo
27bo31bo33bo2b2o155bo93bo68bobo91bo61b2o225bo187b2o132b2o376bobo95bobo
93bo32bo864b2o733bo134bo760bo160bo$163bo927bo862bobo27bo32bo32bo31b3o
446bobo159bobo317bo94bo475bobo131bobo570bo32bo863bobo$1954bo127bo448bo
161bo890bo133bo$2083bo!
It doesn't look like a huge percentage of those are from a loaf being in the original constellation and getting flipped by a spark from the other still life getting vanished by the glider, so I think the first-draft provisional answer is that xp0_357 is an order of magnitude more common than xp0_137.

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dvgrn
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Re: Thread for basic questions

Post by dvgrn » July 29th, 2021, 7:28 am

wwei47 wrote:
July 28th, 2021, 9:25 pm
What's the cheapest way to synthesize an LWSS with a single glider in one direction and an unlimited amount of gliders in the opposite direction?
Does it matter which way the LWSS goes, relative to the direction the single glider is coming from -- 45 degrees or 135 degrees?

From simeks' searches for single-channel construction, I can give an upper bound of 21G, where 19 of the 20 multi-gliders are on the same lane and are only synchronized in pairs, but that's probably not too useful...

Code: Select all

x = 518, y = 523, rule = LifeHistory
516.A$515.A$515.3A7$508.3A$510.A$509.A22$487.2A$486.A.A$488.A25$460.A
$460.2A$459.A.A28$430.A$430.2A$429.A.A22$406.3A$408.A$407.A28$376.2A$
377.2A$376.A28$346.3A$348.A$347.A36$308.2A$309.2A$308.A28$278.3A$280.
A$279.A28$248.3A$250.A$249.A28$218.2A$219.2A$218.A23$193.2A$194.2A$
193.A28$163.2A$164.2A$163.A24$137.2A$138.2A$137.A28$107.3A$109.A$108.
A28$77.3A$79.A$78.A20$55.A$55.2A$54.A.A28$25.A$25.2A$24.A.A23$3A$2.A$
.A!
Really this is a gencols question, and I'd expect the answer to be "4". Cobbling together known reactions from the LifeWiki (a tee reaction) and Mark Niemiec's database gives an easy engineered reaction with a 5-glider salvo meeting a single glider:

Code: Select all

x = 23, y = 26, rule = B3/S23
obo$b2o$bo5$4bo$3b2o$3bobo4$6b2o$5b2o$7bo$13b2o6b2o$12b2o6b2o$14bo7bo
5$19b2o$18b2o$20bo!
The group of three gliders on the right can be moved two steps left, or 2N steps right for any positive N.

ColorfulGabrielsp138
Posts: 288
Joined: March 29th, 2021, 5:45 am

Re: Thread for basic questions

Post by ColorfulGabrielsp138 » July 29th, 2021, 9:03 am

Is this a stamp collection? Did it list all possible 10-bit quasi still lifes?

Code: Select all

x = 189, y = 105, rule = LifeHistory
D.D5.3D.F34.F29.F37.F35.F$D.D2.D2.D3.F4.2A28.F4.A24.F3.2A32.F4.A30.F2.
2A$3D.3D.3D.F3.A.A28.F3.A.A23.F3.A33.F3.A.A29.F2.A$2.D2.D2.D.D.F3.2A29.
F3.A.A23.F4.A32.F4.A.A28.F4.A$2.D5.3D.F34.F4.A24.F3.2A32.F5.A29.F3.2A
$12.F34.F29.F37.F35.F$189F$12.F34.F29.F37.F35.F$12.F34.F29.F37.F35.F$
12.F2.2A6.2A22.F2.2A7.2A16.F2.2A6.2A25.F3.2A6.2A5.2A15.F2.2A6.2A6.2A$
8.2A2.F2.2A6.2A22.F2.2A7.2A16.F2.2A6.2A25.F3.2A6.2A5.2A15.F2.2A6.2A6.
2A2.2A$8.2A2.F4.D7.D.2A18.F4.D.A6.D15.F4.D7.D24.F5.D7.D6.D.A12.F4.D7.
D7.D2.A$12.F5.2A6.A.A18.F5.A.A6.A14.F5.2A6.2A22.F6.A7.A6.A.A11.F5.2A6.
2A6.A$12.F5.A.A5.2A19.F5.A.A5.A.A13.F5.A8.A22.F5.A.A5.A.A4.A.A12.F5.A
8.A6.2A$12.F6.2A26.F6.A6.A.A13.F6.A6.A23.F6.A.A3.A.A6.A13.F7.A4.A$12.
F34.F14.A14.F5.2A6.2A22.F7.A5.A21.F6.2A4.2A$12.F34.F29.F37.F35.F$12.F
34.F29.F37.F35.F$12.F34.F29.F37.F35.F$12.F34.F29.F37.F35.F$12.F34.F29.
F37.F35.F$189F$12.F34.F29.F37.F35.F$12.F34.F29.F37.F35.F$12.F3.A9.A10.
A9.F3.A7.A4.A5.A6.F3.A7.A6.A7.A10.F3.A3.A5.A9.A11.F3.A8.A7.A7.A$8.A3.
F2.A.A7.A.A8.A.A8.F2.A.A5.A.A2.A.A3.A.A5.F2.A.A5.A.A4.A.A5.A.A9.F2.A.
ADA.A3.A.AD.A4.A.A10.F2.A.A6.A.A5.A.A5.A.A$7.A.A2.F3.A.D7.A.D.2A5.A.D
7.F3.A.D5.A4.A5.A6.F3.A.D5.A6.A.D5.A10.F3.A3.A.A3.A.DA.A4.A.D.A7.F3.A
.D6.A.D5.A.D5.A$8.A3.F6.2A8.A.A6.D.2A5.F4.D.A4.D4.2D5.D5.F6.2A4.D8.2A
4.D9.F8.A8.A.A6.A.A6.F6.2A7.2A3.2D.2A4.D$12.F6.A.A7.2A8.A.A5.F5.A.A3.
A5.A6.A4.F6.A6.2A7.A5.2A7.F18.A8.A.A5.F6.A9.A4.A2.A5.2A$12.F7.2A17.2A
6.F5.A.A2.A.A3.A.A4.A.A3.F7.A5.A7.A7.A7.F28.A6.F8.A5.A6.2A8.A$12.F34.
F6.A3.A.A3.A.A4.A.A3.F6.2A6.A6.2A5.A8.F35.F7.2A5.2A13.A$12.F34.F11.A5.
A6.A4.F13.2A13.2A7.F3.A8.A7.A4.A9.F29.2A$12.F34.F29.F37.F2.A.A6.A.A5.
A.AD.A.A8.F$12.F34.F29.F37.F3.A.D6.A.D5.A.DA.A9.F3.A7.A$12.F34.F3.A25.
F3.A33.F4.D.A6.D.A8.A10.F2.A.A5.A.AD$12.F34.F2.A.A24.F2.A.AD31.F5.A.A
6.A.A18.F3.A7.A.D2A$12.F34.F3.A.D.A21.F3.A.D2A29.F6.A.A4.A.A19.F4.D10.
A$12.F34.F6.A.A20.F7.A29.F7.A6.A20.F5.2A6.A$12.F34.F6.A.A20.F6.A30.F35.
F5.A7.2A$12.F34.F7.A21.F6.2A29.F35.F7.A$12.F34.F29.F37.F35.F6.2A$12.F
34.F29.F37.F3.A31.F$12.F34.F29.F37.F2.A.A3.A26.F$12.F34.F29.F37.F3.A.
D.A.A25.F$12.F34.F29.F37.F6.A.A26.F$12.F34.F29.F37.F7.A27.F$12.F34.F29.
F37.F35.F$12.F34.F29.F37.F35.F6$3D5.3D$D4.D2.D$3D.3D.3D$2.D2.D4.D$3D5.
3D$15.2A6.F.2A3.2A4.2A5.F.2A3.A5.A9.A$15.A.A5.F.A.ADA.A3.A.A5.F.A.ADA
.A3.A.A7.A.A$16.A.D4.F2.A3.A5.A6.F2.A3.2A3.2A.D.2A4.2A$19.2A2.F13.D5.
F15.A.A6.D$19.A.A.F14.2A3.F16.A8.2A$20.A2.F14.A.A2.F25.A.A$23.F15.A3.
F26.A$23.F.2A16.F.2A9.A$23.F.A.AD.2A11.F.A.AD.A4.A.AD.2A$23.F2.A.DA.A
4.2A5.F2.A.DA.A3.2A.DA.A$23.F6.A4.A.A5.F6.2A8.A$16.2A5.F12.A.D4.F$15.
A.A5.F15.2A2.F$16.A6.F15.A.A.F$17.D5.F16.A2.F$18.2A3.F.2A16.F.2A9.2A$
17.A.A3.F.A.A15.F.A.A7.A.A$18.A4.F2.A.D.2A11.F2.A.D.A5.A.D.A$23.F5.A.
A11.F5.A.A7.A.A$23.F6.A12.F6.2A7.2A$23.F19.F$23.F19.F$23.F19.F$16.2A5.
F.2A8.2A6.F.2A9.2A$15.A.A5.F.A.A7.A.A5.F.A.A7.A.A$16.A.D4.F2.A.D7.A.D
.A2.F2.A.D7.A.D$17.D.2A2.F3.D.2A8.A.A.F3.D.A7.D.A$18.A.A2.F4.A.A8.2A2.
F4.A.A7.A.A$19.A3.F5.A13.F5.2A7.2A!

Code: Select all

x = 21, y = 21, rule = LifeColorful
11.E$10.3E$10.E.2E$13.E4$2.2B$.2B$2B$.2B15.2D$19.2D$18.2D$17.2D4$7.C$
7.2C.C$8.3C$9.C!
I have reduced the glider cost of quadratic growth to eight and probably to seven. Looking for conduits...

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Re: Thread for basic questions

Post by dvgrn » July 29th, 2021, 9:11 am

ColorfulGabrielsp138 wrote:
July 29th, 2021, 9:03 am
Is this a stamp collection? Did it list all possible 10-bit quasi still lifes?
Yes. At least, the table that you linked to says there are the same number of 10-bit quasi still lifes as Heinz ketchup varieties, and that's exactly how many quasi still lifes are in that stamp-collection pattern.

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Re: Thread for basic questions

Post by ColorfulGabrielsp138 » July 29th, 2021, 9:15 am

dvgrn wrote:
July 29th, 2021, 9:11 am
ColorfulGabrielsp138 wrote:
July 29th, 2021, 9:03 am
Is this a stamp collection? Did it list all possible 10-bit quasi still lifes?
Yes. At least, the table that you linked to says there are the same number of 10-bit quasi still lifes as Heinz ketchup varieties, and that's exactly how many quasi still lifes are in that stamp-collection pattern.
What's "Heins ketchup varieties"?

Code: Select all

x = 21, y = 21, rule = LifeColorful
11.E$10.3E$10.E.2E$13.E4$2.2B$.2B$2B$.2B15.2D$19.2D$18.2D$17.2D4$7.C$
7.2C.C$8.3C$9.C!
I have reduced the glider cost of quadratic growth to eight and probably to seven. Looking for conduits...

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Re: Thread for basic questions

Post by bubblegum » July 29th, 2021, 2:41 pm

ColorfulGabrielsp138 wrote:
July 29th, 2021, 9:15 am
What's "Heins ketchup varieties"?
The number of varieties of Heinz ketchup. If you look at a bottle of Heinz ketchup, it says "57 Heinz varieties".
Each day is a hidden opportunity, a frozen waterfall that's waiting to be realised, and one that I'll probably be ignoring
sonata wrote:
July 2nd, 2020, 8:33 pm
conwaylife signatures are amazing[citation needed]
anything

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Re: Thread for basic questions

Post by Citation needed » July 30th, 2021, 1:57 am

hotdogPi wrote:
July 28th, 2021, 6:30 am
Citation needed wrote:
July 28th, 2021, 2:37 am
What is the apgcode of the U-turner methuselah?
Shouldn't it be xp0_35ee?
Why did they say "xp0_211u" on LifeWiki, which refers to a completely different pattern?
The 10-cell form was chosen partly because that's what C28 asked about and partly because most U-turners go through that phase (or that phase plus a dying banana spark). xp0_211u is a 1-tick predecessor. I don't have that strong of an opinion of which form should be the canonical form; the R-pentomino and pi-heptomino are both in forms that don't always occur in the evolutionary sequence.
The article User:ColorfulGalaxy/List_of_Patterns_by_apgcode#2 says "xp0_211u".

Now, let me tell you something more. The MWSS spark page now has links from three pages from ColorfulGalaxy. The "List of Patterns by apgcode" page says it's "xp0_14". This page says "xp0_11f2" is a predecessor of the MWSS spark.
What exactly is a MWSS spark?

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Re: Thread for basic questions

Post by mniemiec » July 30th, 2021, 4:15 am

Citation needed wrote:
July 30th, 2021, 1:57 am
What exactly is a MWSS spark?
It is the "belly spark" produced by a MWSS - i.e. one protruding live cell, typically flanked on both sides by another single cell on either side two cells to the side and one down. It is also produced by oscillators like the middleweight emulator, and others. In contrast with a HWSS spark that has a domino, usually flanked by two cells on the side, or the corresponding LWSS spark that only has the two side bits 3 spaces apart with nothing in between.

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Re: Thread for basic questions

Post by ColorfulGabrielsp138 » July 30th, 2021, 5:42 am

mniemiec wrote:
July 30th, 2021, 4:15 am
Citation needed wrote:
July 30th, 2021, 1:57 am
What exactly is a MWSS spark?
It is the "belly spark" produced by a MWSS - i.e. one protruding live cell, typically flanked on both sides by another single cell on either side two cells to the side and one down. It is also produced by oscillators like the middleweight emulator, and others. In contrast with a HWSS spark that has a domino, usually flanked by two cells on the side, or the corresponding LWSS spark that only has the two side bits 3 spaces apart with nothing in between.
He might continue to ask why "xp0_11f2" is a predecessor of the MWSS spark.
Maybe you could reply in the Sandbox.

Code: Select all

x = 21, y = 21, rule = LifeColorful
11.E$10.3E$10.E.2E$13.E4$2.2B$.2B$2B$.2B15.2D$19.2D$18.2D$17.2D4$7.C$
7.2C.C$8.3C$9.C!
I have reduced the glider cost of quadratic growth to eight and probably to seven. Looking for conduits...

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Re: Thread for basic questions

Post by hotdogPi » July 30th, 2021, 8:19 am

It's already well established that you two are the same person. Why are you asking what a MWSS spark is if you added it to the wiki userpage yourself?
User:HotdogPi/My discoveries

Periods discovered: 6,8,10-16,18,20,21G,22,24,25,27-31,32SG,35,36,40,42,45,48,50,54G,55G,57G,60,63-66,70,74S,75,76S,84,96S,100,117G,120,126,128S,138,147,156,196S,217,486,576

S: SKOP
G: gun

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Re: Thread for basic questions

Post by GUYTU6J » July 30th, 2021, 12:38 pm

In the following typical eater catalysis, the "block surface" reappears after T=3 ticks.

Code: Select all

x = 20, y = 20, rule = B38/S23History
2A8.2A$.A9.A$.A9.A$A2.2A5.A2.CA$3.2A8.C.A$15.A$15.2A4$10.2A$11.A$11.A
$10.A2.CA.A$13.CA.3A$19.A$13.2A.3A$14.A.A$14.A.A$15.A!
#C [[ STOP 3 ]]
Do we have a list of replacement catalysts sorted by the ticks T after which the block surface recovers? Of them, how many have the property that the critical domino never appears when recovering? (For instance, regarding this property the eater2 will have a T of 3, not the usual "full" recovery time 6.)
This consideration may sometimes be useful, like in the partial Lx104 a replacement catalyst with T≥9 is required.
Reveal your devil secrets, Fort Detrick! The origin of COVID-19 is to be uncovered by science, not politics.

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Re: Thread for basic questions

Post by muzik » July 31st, 2021, 6:09 pm

Following the recent discovery: Are there any known true t-nose reactions for p8 and above, even if they haven't yet been stabilised into an oscillator?

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Re: Thread for basic questions

Post by wwei47 » August 1st, 2021, 10:03 am

How do I make this conversion?

Code: Select all

x = 48, y = 19, rule = B3/S23
45b2o$44bo2bo$43bob2o$12b2o29bobo$12bobo27b2obo$5bo3bo4bo20bo3bo4bo$4b
obo2b5o20bobo2b5o$4bobo15bo11bobo$b2obobobob2o19b2obobobob2o$o2b2obob
2o2bo11bo5bo2b2obob2o2bo$2o4bo4b2o17b2o4bo4b2o$2b4ob4o7bobobobobo5b4ob
4o$2o4bo4b2o17b2o4bo4b2o$o2b2obob2o2bo11bo5bo2b2obob2o2bo$b2obobobob2o
19b2obobobob2o$4bobobo13bo11bobobo$4bobobo25bobobo$5bobo27bobo$6bo29bo
!
Self-proclaimed synthesis "expert"

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Re: Thread for basic questions

Post by muzik » August 2nd, 2021, 5:59 am

Are there any known sparklers that produce the highly pi-like "table" or "worker bee" spark?

Code: Select all

x = 4, y = 2, rule = B3/S23
o2bo$4o!

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Re: Thread for basic questions

Post by hotdogPi » August 2nd, 2021, 6:23 am

muzik wrote:
August 2nd, 2021, 5:59 am
Are there any known sparklers that produce the highly pi-like "table" or "worker bee" spark?

Code: Select all

x = 4, y = 2, rule = B3/S23
o2bo$4o!
66P13

Code: Select all

x = 20, y = 17, rule = B3/S23
5bo$3b5o$2bo5bo$2bo2b3o10b2o$b2obo13bo$o3b2o10bobo$bobo2b2o8b2o$2ob5o$
8bo3b3o$2ob5o$bobo2b2o$o3b2o$b2obo$2bo2b3o$2bo5bo$3b5o$5bo!
User:HotdogPi/My discoveries

Periods discovered: 6,8,10-16,18,20,21G,22,24,25,27-31,32SG,35,36,40,42,45,48,50,54G,55G,57G,60,63-66,70,74S,75,76S,84,96S,100,117G,120,126,128S,138,147,156,196S,217,486,576

S: SKOP
G: gun

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Re: Thread for basic questions

Post by muzik » August 2nd, 2021, 6:33 am

hotdogPi wrote:
August 2nd, 2021, 6:23 am
muzik wrote:
August 2nd, 2021, 5:59 am
Are there any known sparklers that produce the highly pi-like "table" or "worker bee" spark?

Code: Select all

x = 4, y = 2, rule = B3/S23
o2bo$4o!
66P13

Code: Select all

x = 20, y = 17, rule = B3/S23
5bo$3b5o$2bo5bo$2bo2b3o10b2o$b2obo13bo$o3b2o10bobo$bobo2b2o8b2o$2ob5o$
8bo3b3o$2ob5o$bobo2b2o$o3b2o$b2obo$2bo2b3o$2bo5bo$3b5o$5bo!
...but that doesn't produce it as a spark?

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Re: Thread for basic questions

Post by muzik » August 2nd, 2021, 4:05 pm

Can a T-nosed p3 be disproved?

Code: Select all

x = 7, y = 5, rule = B3/S23
3bo$3bo$ob3obo$o5bo$3bo!

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Re: Thread for basic questions

Post by creeperman7002 » August 3rd, 2021, 9:17 pm

Apart from the block, does there exist any still-life where adding any cells to it never yields another still-life?
B2n3-jn/S1c23-y is an interesting rule. It has a replicator, a fake glider, an OMOS and SMOS, a wide variety of oscillators, and some signals. Also this rule is omniperiodic.
viewtopic.php?f=11&t=4856

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Re: Thread for basic questions

Post by vivi » August 3rd, 2021, 9:30 pm

creeperman7002 wrote:
August 3rd, 2021, 9:17 pm
Apart from the block, does there exist any still-life where adding any cells to it never yields another still-life?
what do you mean by "yield"? adding a cell to the corner of a block yields a boat after one tick; but if you mean on the same gen, off the top of my head you can't add a cell to a ship and still have it be a still life.
she/her

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Re: Thread for basic questions

Post by mniemiec » August 4th, 2021, 2:34 am

creeperman7002 wrote:
August 3rd, 2021, 9:17 pm
Apart from the block, does there exist any still-life where adding any cells to it never yields another still-life?
If you mean "add cells that touch", there are many such still-lifes; e.g. there are many still-lifes that contain blocks (e.g. block on table). It's possible to add multiple additional cells to a ship (e.g. ship-tie). If unstable inductors are allowed (e.g. adding a table to a block), it's usually possible to do this to any still-life. In fact, I don't believe it is possible to construct a still-life where this is impossible (although I don't have a rigorous proof for this).

E.g. Pick any still-life. Arrange it in some orientation so that any arbitrary side is on top. Now consider the cells in the top edge of the convex hull, starting with the leftmost ON cell. Create a binary number out of the living cells, starting with the leftmost living cell = 1, and subsequent cells being worth double that, etc. E.g. 1=tub, 3=block, 5=bottom of hook w/tail, 7=bun (unstable), 9=table legs, 11,13=block on top of eater, 15=table top (unstable), etc. It is sufficient to prove that a stable inductor can be constructed for every possible odd number.

Here are hand-crafted inductors above still-lifes whose top edge configurations have all 64 odd numbers from 1-127; unstable edges are omitted:

Code: Select all

x = 103, y = 101, rule = B3/S23
boo61boo$bbo61boo12boo14boo$bo3bo10bobbo11bobbo26bo6bo8bobbo12bobbo$b
5o10b4o11b4o26b8o9b3o13b3o$$3bo14boo13bobo27bobbo11boobo11boboo$bbobo
13boo13boobo26b4o12bob3o7b3obo$3bo32bo42bo4bo5bo4bo$36boo25boo13boo3b
oo5boo3boo$63boo6$boo61bo13boo$bbo59b3o14bo$bo3bo10bobbo11bobbo26bo5bo
10bo3bo$b5o10b4o11b4o26b7o10b5o$$3bo3bo10boobbo10bobobo25bobboo10boob
oo$bbobobobo8bob4o9bob3obo24b4obo10bobo$3bo3bo9bo14bo5bo29bo10bobo$4b
3o9boo3boo10b5o25boo3boo10bo$21boo40boo$3boboo28bo$3boobo27bobo$35bo3$
boo61bo$bbo59b3o13boo$bo3bo10bobbo11bobbo26bo5bo9bobbo13bobbo$b5o10b4o
11b4o26b7o10b3o13b4o$$3bo4bo9boo3bo9bobobbo24bobbobo9boobobo9boboobo$
bbobobbobo9bobbobo6b3ob4o24b4ob3o7bob3obo6b3oboboo$3bo4bo10bobobbo5bo
40bo12bo5bo$4b4o12bo3boo5b3oboo28boob3o11boo7b8o$33boobo28boboo13bo10b
o4bo$4boo77bo11bo$4boo76boo10boo4$boo$bbo$bo3bo10bobbo11bobbo$b5o10b4o
11b4o$$3bo3boo9boobboo9boboboo$bbobobbo10bo3bo9bob3obo$bbobbobo11bo3bo
8bo$boo3bo11boobboo9boo$19bobo12bo$19bobo11bo$20bo12boo$$64boo$65bo$b
oo61bo3bo$bbo61b5o9boo14boo$bo3bo10bobbo11bobbo26bo9bo5bobbo12bobbo$b
5o10b4o11b4o26b11o6b3o13b3o$$3bo5bo8boo4bo8bobo3bo23bobbobbo8boobobbo
8boboobbo$bbobo3bobo8bobb3o7boboo3b3o21b4obb3o7bob4o6b3obo3b3o$3bobobo
bo9bobo10bo9bo29bo6bo10bo4bo6bo$4bo3bo9booboo10b3o5bo21boob6o6boo3boo
6b4o6bo$5b3o27bo4bo22boobobbo13boo13bobo$35bobobo53boo3boo$4boboo26boo
boo54bobboo$4boobo86boobo3$boo76boo$bbo63boo12bo$bo3bo10bobbo11bobbo
30bobbo9bo4bo$b5o10b4o11b4o31b3o9b6o$$3bo3bobo8boobbobo8bobobobo23bobb
oobo8booboobo$b3o3boobo6bobobboobo6bobooboobo20b3o3bob3o7boboboo$o9bo
6bobboo3bo6bo7bo19bo6bo4bo6bobo$bo5b3o6boo3bo3boo6b3ob3o21bo6b4o8boo$
bbo4bo10b3o14bobo24bobo$3bobobo10bo17bo26boo3boo$4booboo56boobbo$65bob
oo3$boo92boo$bbo64boo10boo15bo$bo3bo10bobbo11bobbo31bobbo8bobbo12bo4bo
$b5o10b4o11b4o32b3o8b3o13b6o$$3bo4boo8boo3boo8bobobboo23bobboboo8boobo
boo8bobooboo$3b3obbo10bobbobo7boboobbobo22b4obo9bob3obo8boobobo$6bobo
10bobo10bo3boobbo27bo27bobo$5booboo10bo10boo3bo3boo21boo3boo9boo15boo$
37b3o23boo14boo$39bo!

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calcyman
Posts: 2478
Joined: June 1st, 2009, 4:32 pm

Re: Thread for basic questions

Post by calcyman » August 4th, 2021, 7:21 am

mniemiec wrote:
August 4th, 2021, 2:34 am
creeperman7002 wrote:
August 3rd, 2021, 9:17 pm
Apart from the block, does there exist any still-life where adding any cells to it never yields another still-life?
If you mean "add cells that touch", there are many such still-lifes; e.g. there are many still-lifes that contain blocks (e.g. block on table). It's possible to add multiple additional cells to a ship (e.g. ship-tie). If unstable inductors are allowed (e.g. adding a table to a block), it's usually possible to do this to any still-life. In fact, I don't believe it is possible to construct a still-life where this is impossible (although I don't have a rigorous proof for this).
If you have a binary string on the top of the still-life of the form:

0001(.*)1000

and it's minimal (i.e. doesn't contain 000 as an internal substring) then you can add a solid line inductor:

0111(1*)1110

Now, that doesn't yield a still-life by itself, because there will be births above the line and deaths on the ends of the line, but you can complete it into an 'elongated beehive' by adding an extra line above it (with a blank line in between) and capping the ends with cells. Then you just need to prevent the births on the top of this elongated beehive, but that's easy with a row of blocks.

For example, if you take this still-life:

Code: Select all

x = 13, y = 5, rule = B3/S23
o2b2o3bo$4obobobob2o$5bobobobo$2o3bobobobo$2o4bo3bo!
then the top row is:

...000100110001000...

and the minimal segment matching this pattern is:

00010011000

and we can complete it with an elongated beehive:

Code: Select all

x = 16, y = 12, rule = B3/S23
3b2ob2o$3b2ob2o2$b9o$o9bo$b9o2$3bo2b2o3bo$3b4obobobob2o$8bobobobo$3b2o
3bobobobo$3b2o4bo3bo!
What do you do with ill crystallographers? Take them to the mono-clinic!

mniemiec
Posts: 1340
Joined: June 1st, 2013, 12:00 am

Re: Thread for basic questions

Post by mniemiec » August 4th, 2021, 8:56 am

calcyman wrote:
August 4th, 2021, 7:21 am
If you have a binary string on the top of the still-life of the form: ...
This can be optimized in two ways:
1) If one or both ends of the pattern are 00101(.*)... you can shorten them by 3 cells, and replace 11111(1*)... by 00011(1*)...
2) Instead of using a long beehive, you can use one of the following, all of which have height 2-3 rows:
a) If the inductor is of length 3n, use a bookend siamese (n-1) tables (population 4n+3).
b) If the inductor is of length 3n+1, use n siamese tables (n>0; population 4n+2).
c) If the inductor is of length 3n+2, use a carrier siamese n tables (population 4n+4).
This is always cheaper and smaller than the long beehive solution, which for length 3n+k has a population of 6n+2k+2 + whatever it takes to stabilize the top of the beehive, and will occupy 6-7 rows.

Code: Select all

x = 130, y = 3, rule = B3/S23
bboo41boo18boo41boo18boo$obbo16bobbo16bobbobbo13bobbobbo13bobbobbo13bo
bbobbobbo10bobbobbobbo$3o17b4o16b5o15b6o14b7o13b8o12b9o!

hotdogPi
Posts: 457
Joined: August 12th, 2020, 8:22 pm

Re: Thread for basic questions

Post by hotdogPi » August 6th, 2021, 8:34 am

I know I've seen it once manually (but I think in a symmetrical pattern), and https://catagolue.hatsya.com/census/b3s23/Pseudo_C1/xp2 seems to indicate it occurs way more often than by chance, but I don't know what pattern creates this. Does anyone know?

Code: Select all

x = 9, y = 9, rule = B3/S23
2b2ob2o$3bobo$o7bo$2o5b2o2$2o$o$3bo$2b2o!
User:HotdogPi/My discoveries

Periods discovered: 6,8,10-16,18,20,21G,22,24,25,27-31,32SG,35,36,40,42,45,48,50,54G,55G,57G,60,63-66,70,74S,75,76S,84,96S,100,117G,120,126,128S,138,147,156,196S,217,486,576

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