Oscillator Discussion Thread

[Gustone]

p152 rotatingb

Code: Select all

x = 317, y = 232, rule = B3/S23
246b2o7b2o$214b2o7b2o21b2o7bobo$214b2o7bobo27bobob3o$193bo27bobob3o25b
2o5bo23b2o$181bo11b3o25b2o5bo30b2o23bo$179b3o14bo20b2o8b2o53bobo$163bo
14bo16b2o20b2o59b2o2b2o$163b3o12b2o98b2o$166bo8bo$165b2o9bo45bo3bo$
175bo6b2o37b2o3b2o36bo$181b3o31bo2b2obo5b2o$163bo2b2o13bob2o28b2o3b2ob
o5bo37b2obo$161b3o2b2o12b2ob4o27b2o3b2o5bo40bobob2o$160bo20bobo83b3ob
2o$160b2o20bo86b2o$237b3o$236bo3bo$236bo4bo42b2o$204b2o30bo3bo25b2o16b
obo$182b2o20b2o32b2o25bobo18bo$182bo82bo20b2o$183b3o78b2o4b2o$185bo83b
obo$179b2o63b2o23bo$179bo32b2o31bo22b2o7b2o$180b3o30bo28b3o32b2o$182bo
27b3o29bo$210bo$286b2o$286bo$287bo$162bobo121b2o$162b2o$163bo122b2o$
285bobo$286bo3$239bo$207bo29b3o27bo$171b2o32b3o28bo30b3o$171b2o7b2o22b
o31b2o32bo$180bo23b2o63b2o$178bobo83bo$31b2o7b2o136b2o4b2o78b3o$30bobo
7b2o21b2o7b2o88b2o20bo82bo$28b3obobo27bobo7b2o89bo18bobo25b2o32b2o20b
2o$2b2o23bo5b2o25b3obobo27bo68bobo16b2o25bo3bo30b2o$3bo23b2o8b2o20bo5b
2o25b3o11bo57b2o42bo4bo$3bobo31b2o20b2o30bo14b3o100bo3bo$4b2o2b2o81b2o
16bo14bo85b3o$8b2o98b2o12b3o38bo15b2o86bo$88b2o31bo39b3o13b2ob3o83bobo
$35b2ob2o49b2o30b2o37bo16b2obobo40bo5b2o3b2o27b4ob2o12b2o$36bobo49bo
71b2o19bob2o37bo5bob2o3b2o28b2obo13b2o$37bo3b2o178b2o5bob2o2bo31b3o$
41b2o30bo46b2o2bo60bo36b2o3b2o37b2o6bo$72b3o26b2o17b2o2b3o96bo3bo45bo
9b2o$72bob2o25b2o24bo146bo8bo$70bobo2b3o48b2o42b2o98b2o12b3o$69bo4bo
91b2o2b2o59b2o20b2o16bo14bo$70bo2b3o2bo86bobo53b2o8b2o20bo14b3o$2b2o
46b2o19b3ob4o86bo23b2o30bo5b2o25b3o11bo$bobo16b2o28b2o30b2o47b2o3b2o5b
o20b2o23bo5b2o25b3obobo27bo$bo18bobo59b2o20b2o24b2o3b2obo5bo11bo33b3ob
obo27bobo7b2o$2o20bo13bo68bo26bo2b2obo5b2o9b2o35bobo7b2o21b2o7b2o$16b
2o4b2o13bo64b3o33b2o3b2o10bobo35b2o7b2o$16bobo83bo13b3o20bo3bo78b2o7b
2o$18bo23b2o63b2o8bo103bobo7b2o21b2o7b2o$9b2o7b2o22bo31b2o32bo6b3o101b
3obobo27bobo7b2o$9b2o32b3o28bo30b3o85b2o23bo5b2o25b3obobo27bo$45bo29b
3o27bo88bo23b2o30bo5b2o25b3o11bo$77bo116bobo53b2o8b2o20bo14b3o$2o193b
2o2b2o59b2o20b2o16bo14bo$bo197b2o98bo13b3o$o298bo12bo$2o206bob3o43bo
45b3o7b2o$206b2obo3bo41b2o42bo5bo$207bo4b2o40b2o5bo36bo3bo$208b4obo41b
o4b2o36bo5b2o5b2o$256bob2obo30b2o4b2obobo7b2o$258b2o32b2o6b2o$260bo$
48bo$20bo27b3o29bo157b4o$18b3o30bo28b3o32b2o76b2o42bo2b2o$8b3o6bo32b2o
31bo22b2o7b2o75bobo16b2o25b2obo31b2o$8bo8b2o63b2o23bo84bo18bobo59b2o
20b2o$7b3o13bo83bobo81b2o20bo82bo$21b3o64bo13b2o4b2o13b2o3b2o77b2o4b2o
78b3o$20bo68bo13bo20bo4bo77bobo83bo$20b2o20b2o59bobo18bob3o80bo23b2o
63b2o$42b2o30b2o28b2o16bobobo73b2o7b2o22bo31b2o32bo$47b4ob3o19b2o46b2o
76b2o32b3o28bo30b3o$47bo2b3o2bo180bo29b3o27bo$51bo4bo84bo126bo$48b3o2b
obo85b2o$23b2o25b2obo86bobo169bobo$4b2o17b2o26b3o259b2o$4b2o46bo30b2o
228bo$83b2o3bo$37bo49bobo82bo$3b2o30b2o49b2ob2o82b2o19bo120b2o$4bo31b
2o134b2o19b2o121bo$b3o12b2o98b2o75bobo119bo$bo14bo16b2o81b2o2b2o23bo
169b2o$17b3o14bo30b2o20b2o16b2o13bobo22b3o91bo$19bo11b3o25b2o5bo20b2o
8b2o7bo15bo25bo14bo47bo27b3o29bo$31bo27bobob3o25b2o5bo7bobo13b2o23b2o
12b3o45b3o30bo28b3o32b2o$52b2o7bobo27bobob3o9b2o2b2o38b2o7bo47bo32b2o
31bo22b2o7b2o$52b2o7b2o21b2o7bobo15b2o38b2o7b2o46b2o63b2o23bo$84b2o7b
2o56bo62bo83bobo$143b3o66b3o78b2o4b2o$143bo15b2o50bo82bo20b2o$140b4obo
13b2o50b2o20b2o59bobo18bo$140b2o2b2o4b2o81b2o31bob2o25b2o16bobo$266b2o
2bo42b2o$266b4o2$189b2o56bo$189bo16b2o6b2o32b2o$105b2o36b2o45b3o2b2o7b
obob2o4b2o30bob2obo$104bobo16b2o19bo47bo2b2o5b2o5bo36b2o4bo41bob4o$
104bo18bobo15b3o61bo3bo36bo5b2o40b2o4bo$103b2o20bo15bo60bo5bo42b2o41bo
3bob2o$109b2o8b2o4b2o19b2o46b2o7b3o45bo43b3obo$108bo2bo7bobo25bo47bo
12bo$108bo2bo9bo22b3o45b3o13bo98b2o$108bo12b2o21bo47bo14bo16b2o20b2o
59b2o2b2o$108b2o3bo94b3o14bo20b2o8b2o53bobo$109bo2b2obo94bo11b3o25b2o
5bo30b2o23bo$110b3o2bo106bo27bobob3o25b2o5bo23b2o$162b2o79b2o7bobo27bo
bob3o$162bobo78b2o7b2o21b2o7bobo$164bo110b2o7b2o$164b2o$102b2o62bo$
103bo5b3o52b3o$103bobo3bo2b2o49bo$104b2o4b3o50b2o$111bo5$165b2o$117b2o
46b2o$141b2o$115bo3bo20bobo$115bo4bo19bo$115bo3b2o18b2o$116bo3bo$117b
3o31b2o$126b2o22bobo$126bo22b2o$124bobo24bo$124b2o25bobo$100b2o51b2o$
100b2o50b3o6$102b2o57b2o$103bo57bobo$100b3o60bo$100bo62b2o$101b2o62bo$
102bo60b3o$102bobo57bo$103b2o57b2o6$111b3o50b2o$111b2o51b2o$112bobo25b
2o$114bo24bobo$115b2o22bo$113bobo22b2o$113b2o31b3o$145bo3bo$125b2o18b
2o3bo$125bo19bo4bo$123bobo20bo3bo$123b2o$99b2o46b2o$99b2o5$154bo$101b
2o50b3o4b2o$102bo49b2o2bo3bobo$99b3o52b3o5bo$99bo62b2o$100b2o$101bo$
101bobo$102b2o$150bo2b3o$150bob2o2bo$152bo3b2o$121bo21b2o12bo$119b3o
22bo9bo2bo$118bo25bobo7bo2bo$118b2o19b2o4b2o8b2o$124bo15bo20b2o$122b3o
15bobo18bo$121bo19b2o16bobo$121b2o36b2o6$114b2o4b2o2b2o$105b2o13bob4o$
105b2o15bo$120b3o$114bo$104b2o7b2o38b2o$105bo7b2o38b2o2b2o$102b3o12b2o
38bobo$102bo14bo41bo$118b3o7b2obo27b2o$120bo7bob2o!

help

Code: Select all

x = 104, y = 104, rule = B3/S23
28b2o3b2o$28b2o2bob3o$32bo4bo$28b4ob2o2bo$28bo2bobobob2o$31bobobobo$
32b2obobo$36bo2$22b2o$23bo7b2o$23bobo5b2o39b2o3b2o$24b2o46b2o2bob3o$
76bo4bo$72b4ob2o2bo$72bo2bobobob2o$55bo19bobobobo$53b3o20b2obobo$52bo
27bo$34b2o16b2o$34bo31b2o$15bo19b3o29bo7b2o$13b5o14b3o2bo22b2ob2o2bobo
5b2o17bo$12bo5bo13bo2bo25bob2o3b2o22b3o$12bo2b3o12bobo2b2o24bo29bo$11b
2obo15b2o21b2o4b3o29b2o$11bo2b4o35b2o3bo3b2o$12b2o3bo3b2o35b4o2bo$14b
3o4b2o21b2o15bob2o34b2ob2o$14bo28bobo12b3o2bo36bob2o$11b2obo28bo13bo5b
o14b2o20bo$11b2ob2o26b2o14b5o15bo13b2o4b3o$60bo18b3o10b2o3bo3b2o$81bo
15b4o2bo$22b2o57bob2o15bob2o$23bo55b2obobo12b3o2bo$20b3o56bo2bo13bo5bo
$20bo60b2o14b5o$99bo$22b2o3b2o$22b2o2bob3o$26bo4bo8b2o3b2o5bo$22b4ob2o
2bo7b2o3b2obo5bo11bo6bo$22bo2bobobob2o8bo2b2obo5b2o9b2o6b3o$25bobobobo
15b2o3b2o10bobo8bo$26b2obobo16bo3bo21b2o$30bo2$16b2o$17bo7b2o$17bobo5b
2o$18b2o$84b2o$77b2o5bobo$77b2o7bo$86b2o2$73bo$20bo7b2o42bobob2o$20b2o
6bo43bobobobo$19bobo7b3o39b2obobobo2bo$31bo40bo2b2ob4o$72bo4bo$73b3obo
2b2o$75b2o3b2o$4bo$2b5o14b2o60bo$bo5bo13bo2bo56b3o$bo2b3o12bobob2o55bo
$2obo15b2obo57b2o$o2b4o15bo$b2o3bo3b2o10b3o18bo$3b3o4b2o13bo15b5o14b2o
26b2ob2o$3bo20b2o14bo5bo6bo6bo28bob2o$2obo36bo2b3o6b3o3bobo28bo$2ob2o
34b2obo8b5ob3o21b2o4b3o$39bo2b4o4b2o3b3o23b2o3bo3b2o$40b2o3bo3b3o3b3o
28b4o2bo$11b2o29b3o5b2o3b2o15b2o15bob2o$12bo29bo8b5o11b2o2bobo12b3o2bo
$9b3o22b2o3b2obo9b3o13bo2bo13bo5bo$9bo17b2o5bobo2b2ob2o9bo12bo2b3o14b
5o$27b2o7bo29b3o19bo$36b2o31bo$50b2o16b2o$23bo27bo$22bobob2o20b3o$22bo
bobobo19bo$21b2obobobo2bo$22bo2b2ob4o$22bo4bo$23b3obo2b2o46b2o$25b2o3b
2o39b2o5bobo$71b2o7bo$80b2o2$67bo$66bobob2o$66bobobobo$65b2obobobo2bo$
66bo2b2ob4o$66bo4bo$67b3obo2b2o$69b2o3b2o!

[Entity Valkyrie 2]

help

Code: Select all

x = 104, y = 104, rule = B3/S23
28b2o3b2o$28b2o2bob3o$32bo4bo$28b4ob2o2bo$28bo2bobobob2o$31bobobobo$
32b2obobo$36bo2$22b2o$23bo7b2o$23bobo5b2o39b2o3b2o$24b2o46b2o2bob3o$
76bo4bo$72b4ob2o2bo$72bo2bobobob2o$55bo19bobobobo$53b3o20b2obobo$52bo
27bo$34b2o16b2o$34bo31b2o$15bo19b3o29bo7b2o$13b5o14b3o2bo22b2ob2o2bobo
5b2o17bo$12bo5bo13bo2bo25bob2o3b2o22b3o$12bo2b3o12bobo2b2o24bo29bo$11b
2obo15b2o21b2o4b3o29b2o$11bo2b4o35b2o3bo3b2o$12b2o3bo3b2o35b4o2bo$14b
3o4b2o21b2o15bob2o34b2ob2o$14bo28bobo12b3o2bo36bob2o$11b2obo28bo13bo5b
o14b2o20bo$11b2ob2o26b2o14b5o15bo13b2o4b3o$60bo18b3o10b2o3bo3b2o$81bo
15b4o2bo$22b2o57bob2o15bob2o$23bo55b2obobo12b3o2bo$20b3o56bo2bo13bo5bo
$20bo60b2o14b5o$99bo$22b2o3b2o$22b2o2bob3o$26bo4bo8b2o3b2o5bo$22b4ob2o
2bo7b2o3b2obo5bo11bo6bo$22bo2bobobob2o8bo2b2obo5b2o9b2o6b3o$25bobobobo
15b2o3b2o10bobo8bo$26b2obobo16bo3bo21b2o$30bo2$16b2o$17bo7b2o$17bobo5b
2o$18b2o$84b2o$77b2o5bobo$77b2o7bo$86b2o2$73bo$20bo7b2o42bobob2o$20b2o
6bo43bobobobo$19bobo7b3o39b2obobobo2bo$31bo40bo2b2ob4o$72bo4bo$73b3obo
2b2o$75b2o3b2o$4bo$2b5o14b2o60bo$bo5bo13bo2bo56b3o$bo2b3o12bobob2o55bo
$2obo15b2obo57b2o$o2b4o15bo$b2o3bo3b2o10b3o18bo$3b3o4b2o13bo15b5o14b2o
26b2ob2o$3bo20b2o14bo5bo6bo6bo28bob2o$2obo36bo2b3o6b3o3bobo28bo$2ob2o
34b2obo8b5ob3o21b2o4b3o$39bo2b4o4b2o3b3o23b2o3bo3b2o$40b2o3bo3b3o3b3o
28b4o2bo$11b2o29b3o5b2o3b2o15b2o15bob2o$12bo29bo8b5o11b2o2bobo12b3o2bo
$9b3o22b2o3b2obo9b3o13bo2bo13bo5bo$9bo17b2o5bobo2b2ob2o9bo12bo2b3o14b
5o$27b2o7bo29b3o19bo$36b2o31bo$50b2o16b2o$23bo27bo$22bobob2o20b3o$22bo
bobobo19bo$21b2obobobo2bo$22bo2b2ob4o$22bo4bo$23b3obo2b2o46b2o$25b2o3b
2o39b2o5bobo$71b2o7bo$80b2o2$67bo$66bobob2o$66bobobobo$65b2obobobo2bo$
66bo2b2ob4o$66bo4bo$67b3obo2b2o$69b2o3b2o!

Done with P8 reflectors (not possible with just snarks):

Code: Select all

x = 105, y = 107, rule = B3/S23
62b2o2$60bo3bo$60bo4bo$62bobobo8bo$63bobobo5b3o$64bo4bo2bo$65bo3bo2b2o
2$66b2o2bo$69bobo$70b2o2b2o$74b2o2$15b2o$13bo2bo67bo2b2o$30bo52bo3b2o
2b2o$13bo2bo11b3o52bo7b2o$14bo2bo9bo56b4o$15bobo9b2o46b3o$16bo58bo$23b
o52bo$15b2o5bobo58bo$15b2o4bo2bo57bobo$22b2o58bo2bo$83b2o3$87b2o$87bob
o$89bo$3b2o5b2o77b2o$4bo5b2o$4bobo$5b2o$9b2o$8bobo$9bo$4b3o9bo$7bo9b2o
$3bo3bo8b2o$2bobo2bo$o2bobo39bo$o3bo39bobo$o42b2ob2o$b3o41bob2o$46b2o
2$69b2o$68b2o$70bo13$103b2o$101bob2o$100bo$103bo$99b2obo$99b2o2$36bobo
57bo$36b2o57bobo$37bo57b2o$99b2o$99bobo$94b2o5bo$15b2o77b2o5b2o$16bo$
16bobo59bobo$17b2o28b2o30b2o$48b2o29bo$47bo$21b2o$20bo2bo58b2o$21bobo
57bo2bo4b2o$22bo58bobo3bo2bo$82bo$87bo2bo$77b2o9bo2bo$14bo2b2o59bo10bo
bo$13bo3b2o2b2o52b3o12bo$13bo7b2o52bo$14b4o71b2o$89b2o2$30b2o$30b2o2b
2o$34bobo$35bo$39bo$32b2o4bobo$33bo3bo3bo$30b3o5bo3bo$30bo8bo3bo$40bo
3bo$41bobo$42bo!

[Gustone]

How to cram two herchels into the p256 gun

Code: Select all

x = 385, y = 49, rule = B3/S23
31b2o54b2o54b2o54b2o54b2o54b2o54b2o$31b2o5b2o47b2o5b2o47b2o5b2o47b2o5b
2o47b2o5b2o47b2o5b2o47b2o5b2o$38b2o54b2o54b2o54b2o54b2o54b2o54b2o3$7b
2o27b2o25b2o27b2o25b2o27b2o25b2o27b2o25b2o27b2o25b2o27b2o25b2o27b2o$7b
2o27b2o25b2o27b2o25b2o27b2o25b2o27b2o25b2o27b2o25b2o27b2o25b2o27b2o$
42b2o54b2o54b2o54b2o54b2o54b2o54b2o$42b2o54b2o54b2o54b2o54b2o54b2o54b
2o$b2o54b2o54b2o54b2o54b2o54b2o54b2o$b2o54b2o54b2o54b2o54b2o54b2o54b2o
$5b2o54b2o54b2o54b2o54b2o54b2o54b2o$5b2o15bo38b2o15bo38b2o15bo38b2o15b
o38b2o15bo38b2o15bo38b2o15bo$22bobo53bobo53bobo53bobo53bobo53bobo53bob
o$22b3o53b3o53b3o53b3o53b3o53b3o53b3o$24bo55bo55bo55bo55bo55bo55bo$2o
54b2o54b2o54b2o54b2o54b2o54b2o$2o54b2o54b2o54b2o54b2o54b2o54b2o2$368b
2o$91bo55b2o54bo54b3o53bo2bo50bobo$34b3o52b4o52bo56b3o53b3o51b4o52bo$
32b2o3bo51b4o52bo2bo52bo54b2o60bo$146b2o52b2ob2o51bo2b3o50b2o2b2o$37bo
108b2o53b2ob2o171bo$32bo3bo52b4o52bo2bo52b2ob2o50bo59b2o59b2o$33b3o53b
3o56bo52bo2bo51bo3b2o55b2o59b2o$90bo54b3o53b3o53bo2bo52bo2b2o60b2o$
202b2o53bobo113b2o$374bo$375bo$47b2o54b2o54b2o54b2o54b2o54b2o41b2o2b3o
6b2o$47b2o54b2o54b2o54b2o54b2o54b2o44bob2o6b2o$372b2ob2o$373bobo$374bo
$42b2o54b2o54b2o54b2o54b2o54b2o54b2o$42b2o54b2o54b2o54b2o54b2o54b2o54b
2o$46b2o54b2o54b2o54b2o54b2o54b2o54b2o$46b2o54b2o54b2o54b2o54b2o54b2o
54b2o$5b2o54b2o54b2o54b2o54b2o54b2o54b2o$5b2o54b2o54b2o54b2o54b2o54b2o
54b2o$11b2o27b2o25b2o27b2o25b2o27b2o25b2o27b2o25b2o27b2o25b2o27b2o25b
2o27b2o$11b2o27b2o25b2o27b2o25b2o27b2o25b2o27b2o25b2o27b2o25b2o27b2o
25b2o27b2o3$9b2o54b2o54b2o54b2o54b2o54b2o54b2o$9b2o5b2o47b2o5b2o47b2o
5b2o47b2o5b2o47b2o5b2o47b2o5b2o47b2o5b2o$16b2o54b2o54b2o54b2o54b2o54b
2o54b2o!

Stabilise this

Code: Select all

x = 11, y = 9, rule = B3/S23
2b2o$bo2bo$bob2o2b2o$2obo4bo$3bo$3bob6o$4bo5bo$5b3o$7bo!
[[ STOP 4 ]]

[JP21]

P2:

Code: Select all

x = 8, y = 8, rule = B3/S23
bo3bo$bobo2b2o$bobo$5bo$2bo$4bobo$2o2bobo$2bo3bo!

[mniemiec]

P2: ...

All P2 oscillators and pseudo-oscillators with populations up to 21 have been tracked by computer search years ago. This one is not only known, but already has a glider synthesis.
https://catagolue.appspot.com/object/xp ... 0307/b3s23

[Gustone]

Known?

Code: Select all

x = 11, y = 11, rule = B3/S23
4bobo$2bo2bo2bo$3bobobo$b3obo2b2o2$4o3b4o2$b2o2bob3o$3bobobo$2bo2bo2bo
$4bobo!

[JP21]

Are these known?

Code: Select all

x = 89, y = 22, rule = B3/S23
84b2o$85bo$80b3o2bob2o$80b4obob2o$84bo$83bo2$79bobobobo$79bo4b2o$35bo
7b2o30bobo$14bo20bobo5b2o30bo$2o8bo3bo12b2o2bobo37bobo$obobobobobobo2b
o11bo3bo6b2o3b4o24bo$5bo4bo13b2obobo10bobo3bo15b2o3bobo$o2bobobobobobo
bo7bobo2bo14b2o17bo4bo$bo3bo8b2o7bobo3bo10bo22bobo$bo22bo6bo7bo2bo2bo$
31bobo5bo3b2o18bo2bo$35bobo21b2obobo2bo$35bo23b2obobo2bo$62bo3bo$62b2o
!

[Entity Valkyrie 2]

Are these known?

Code: Select all

x = 89, y = 22, rule = B3/S23
84b2o$85bo$80b3o2bob2o$80b4obob2o$84bo$83bo2$79bobobobo$79bo4b2o$35bo
7b2o30bobo$14bo20bobo5b2o30bo$2o8bo3bo12b2o2bobo37bobo$obobobobobobo2b
o11bo3bo6b2o3b4o24bo$5bo4bo13b2obobo10bobo3bo15b2o3bobo$o2bobobobobobo
bo7bobo2bo14b2o17bo4bo$bo3bo8b2o7bobo3bo10bo22bobo$bo22bo6bo7bo2bo2bo$
31bobo5bo3b2o18bo2bo$35bobo21b2obobo2bo$35bo23b2obobo2bo$62bo3bo$62b2o
!

P2s are mostly known. It's a pity that the grin spark doesn't support a P2 bumper...

EDIT: I'm not sure if this is the right thread for this:
EDIT: more details on viewtopic.php?f=2&t=3841&p=86892#p86892

Code: Select all

#C P369 cyclotron
#C Entity Valkyrie 2
#C 3 January, 2020
#C Only still lives used in this gun are block, eater1 and 31.4
x = 534, y = 451, rule = B3/S23
261b2o$261bobo$263bo4b2o$259b4ob2o2bo2bo$259bo2bobobobob2o$262bobobobo
$263b2obobo$267bo2$253b2o$254bo7b2o$254bobo5b2o$255b2o4$286bo$284b3o$
283bo$265b2o16b2o$265bo$266b3o$268bo22b2o$194b2o96bo$194bobo95bob2o$
196bo4b2o81b2o4b3o2bo$192b4ob2o2bo2bo79b2o3bo3b2o$192bo2bo3bobob2o84b
4o$195bobobobo73b2o15bo$196b2obobo72bobo12b3o$200bo73bo13bo$273b2o14b
5o136b2o$186b2o105bo136bobo$187bo8bo94bo140bo4b2o$187bobo5b2o94b2o135b
4ob2o2bo2bo$188b2o238bo2bobobobob2o$202bo72bobo153bobobobo$203bo71b2o
11b2o142b2obobo$201b3o72bo11bobo145bo$290bo4b2o$286b4ob2o2bo2bo123b2o$
286bo2bobobobob2o124bo7b2o$198b2o89bobobobo127bobo5b2o$198bo91b2obobo
128b2o$199b3o92bo$201bo$223bo56b2o$221b3o57bo7b2o183b2o$220bo60bobo
190bobo$220b2o60b2o192bo4b2o$289b2o41b2o100b2o36b4ob2o2bo2bo$289b2obo
39bobo78b2o19bo37bo2bobobobob2o$168b2o120b2o20bo21bo4b2o73bo20b3o37bob
obobo$169bo121bo18b3o17b4ob2o2bo2bo69bo24bo38b2obobo$167bo141bo20bo2bo
bobobob2o69b5o14b2o47bo$167b5o14b2o121b2o22bobobobo77bo13bo$172bo13bo
23b2o80b2o40b2obobo74b3o12bobo34b2o$169b3o12bobo22bobo5b2o73bo45bo74bo
15b2o36bo7b2o$168bo15b2o23bo7b2o74b3o21b2o94b4o50bobo5b2o$168b4o36b2o
85bo22bo5b2o85b2o3bo3b2o46b2o25bo$166b2o3bo3b2o141bob2o3bo7b2o75bo2b3o
4b2o71b3o$165bo2b3o4b2o45bo13bo73b2o4b3o2bo3bobo5b2o75b2obo78bo$165b2o
bo49b2obobo12b3o71b2o3bo3b2o5b2o85bo53bo24b2o$168bo48bobobobo15bo75b4o
94b2o50b3o$168b2o44bo2bobobobob2o11b2o61b2o15bo145bo$214b4ob2o2bo2bo
73bobo12b3o125b2o19b2o34b2o$218bo4b2o75bo13bo106b2o20bo34b2o21bo$176b
2o38bobo11b2o67b2o14b5o102bo22bo32bo22bob2o$177bo38b2o12bo88bo99b3o3b
2o14b5o33b3o7b3o7b3o2bo$174b3o50b2obo86bo18b2o81bo6bo13bo40bo6bo2bo6bo
3b2o$174bo52bo2b3o4b2o78b2o17bo89bobo12b3o44bob2o6b4o$228b2o3bo3b2o98b
3o87b2o15bo39b2o3bo11bo$230b4o105bo92b2o7b4o9b2o27bobo12b3o$230bo15b2o
183bobo2b2o3bo3b2o6bobo5b2o20bo13bo$231b3o12bobo184bo2b2o4b3o2bo5bo7b
2o19b2o14b5o$234bo13bo195bob2o4b2o48bo$229b5o14b2o194bo55bo$179b2o48bo
111b2o100b2o21bo33b2o$179bobo49bo23bo84bobo119b2obobo$181bo4b2o42b2o
21b3o78b2o4bo72b2o46bobobobo$177b4ob2o2bo2bo62bo79bo2bo2b2ob4o69bo20b
2o21bo2bobobobob2o$177bo2bobobobob2o62b2o78b2obobobobo2bo67bo22bo22b4o
b2o2bo2bo$180bobobobo148bobobobo70b5o14b2o3b3o23bo4b2o$181b2obobo148bo
bob2o76bo13bo6bo21bobo$185bo150bo77b3o12bobo28b2o$413bo15b2o$171b2o
176b2o62b4o$172bo7b2o158b2o7bo61b2o3bo3b2o$172bobo5b2o60b2o96b2o5bobo
60bo2b3o4b2o$173b2o66bobo5b2o96b2o61b2obo46bo$241bo7b2o115bo46bo46b3o
22b2o$240b2o125b2o44b2o48bo21bobo$267bo98b2o94b2o23bo4b2o$204bo49bo12b
3o173b2o38b4ob2o2bo2bo$202b3o45b2obobo14bo150b2o20bo39bo2bobobobob2o$
201bo47bobobobo13b2o151bo22bo8b2o30bobobobo$183b2o16b2o43bo2bobobobob
2o30b2o46b2o80b3o3b2o14b5o8bo32b2obobo$183bo62b4ob2o2bo2bo31bo47bo19b
2o59bo6bo13bo10b2obo36bo$184b3o63bo4b2o4b2o25bo46b3o20bo30bo36bobo12b
3o7bo2b3o4b2o$186bo22b2o37bobo10bo26b5o14b2o26bo24bo26b3o37b2o15bo7b2o
3bo3b2o14b2o$210bo37b2o8b2obo31bo13bo32b2o14b5o25bo54b4o9b4o20bo7b2o$
210bob2o44bo2b3o4b2o20b3o12bobo33bo13bo30b2o48b2o3bo3b2o7bo15b2o6bobo
5b2o$202b2o4b3o2bo45b2o3bo3b2o19bo15b2o34bobo12b3o77b2o4b3o2bo7b3o12bo
bo6b2o$202b2o3bo3b2o48b4o24b4o49b2o15bo84bob2o10bo13bo$207b4o50bo15b2o
8b2o3bo3b2o11bo46b4o34b2o48bo8b5o14b2o$193b2o15bo51b3o12bobo6bo2b3o4b
2o11b3o39b2o3bo3b2o33bo47b2o8bo24bo$192bobo12b3o55bo13bo6b2obo22bo38b
2o4b3o2bo32bob2o56bo20b3o$192bo13bo53b5o14b2o8bo21b2o4bo41bob2o24b2o4b
3o2bo14b2o39b2o19bo$191b2o14b5o48bo28b2o26bobo39bo27b2o3bo3b2o16bo20b
2o38b2o$211bo50bo54b2o39b2o32b4o16bo22bo53b2o$209bo51b2o115b2o15bo16b
5o14b2o3b3o50bo24bo$209b2o86b2o29b2o47bobo12b3o22bo13bo6bo51b3o19b3o$
298bo30bo20b2o18bo6bo13bo22b3o12bobo60bo18bo$295b3o29bo22bo19b3o3b2o
14b5o16bo15b2o80b2o$295bo25b2o4b5o14b2o3b3o19bo22bo16b4o$314b2o5bobo8b
o13bo6bo18b2o20bo16b2o3bo3b2o43b2o$314b2o7bo5b3o12bobo47b2o14bo2b3o4b
2o42bobo5b2o45b2o$323b2o3bo15b2o64b2obo50bo7b2o46bo$328b4o32b2o47bo49b
2o55bob2o$310bo15b2o3bo3b2o27bo48b2o97b2o4b3o2bo$300bo8bobob2o10bo2b3o
4b2o24b2obo112bo34b2o3bo3b2o$241b2o55b3o8bobobobo9b2obo32bo2b3o4b2o70b
2o28b2obobo38b4o$240b2o55bo8b2obobobobo2bo9bo33b2o3bo3b2o48b2o20bo28bo
bobobo24b2o15bo$242bo54b2o7bo2bo2b2ob4o9b2o34b4o54bo22bo23bo2bobobobob
2o20bobo12b3o$308b2o4bo49bo15b2o37b3o3b2o14b5o23b4ob2o2bo2bo13bo6bo13b
o$314bobo41b2o5b3o12bobo36bo6bo13bo32bo4b2o15b3o3b2o14b5o$305b2o8b2o
19b2o20bo9bo13bo43bobo12b3o27bobo24bo22bo$180bo125bo30bo22bo2b5o14b2o
43b2o15bo26b2o24b2o20bo$178b2o120bo5bob2o24b3o3b2o14b5o2bo77b4o74b2o$
179b2o118b2o4b2o2bo24bo6bo13bo9bo70b2o3bo3b2o57bo$298b2ob2obo2b2o32bob
o12b3o5b2o70b2o4b3o2bo41b2o12bo$305b2o35b2o15bo84bob2o41bo13b3o$289b2o
13bobo49b4o84bo41b2obo$288bobo12bobo45b2o3bo3b2o81b2o41bo2b3o4b2o$200b
2o64b2o20bo7bo5bo48b2o4b3o2bo124b2o3bo3b2o$199bobo64bo20b2o5b2o7b5o51b
ob2o50b2o74b4o$193b2o4bo68bo26b2o10bo51bo39bo14bo20b2o52bo15b2o$191bo
2bo2b2ob4o44b2o14b5o36bo52b2o37b3o12bo22bo37b2o15b3o12bobo$133b2o56b2o
bobobobo2bo45bo13bo41b2o89bo15b5o14b2o3b3o33bobo18bo13bo$132bobo59bobo
bobo48bobo12b3o61b2o66b2o19bo13bo6bo27b2o4bo15b5o14b2o$134bo59bobob2o
50b2o15bo45b2o14bo20b2o62b3o12bobo32bo2bo2b2ob4o11bo$195bo68b4o44bobo
12bo22bo62bo15b2o33b2obobobobo2bo13bo$259b2o3bo3b2o36b2o4bo14b5o14b2o
3b3o50b2o7b4o50bobobobo15b2o$208b2o49b2o4b3o2bo33bo2bo2b2ob4o15bo13bo
6bo51bo5b2o3bo3b2o45bobob2o$199b2o7bo58bob2o33b2obobobobo2bo12b3o12bob
o58bob2obo2b3o4b2o46bo$199b2o5bobo58bo39bobobobo14bo15b2o51b2o4b3o2bob
2obo$206b2o35bo22b2o39bobob2o15b4o65b2o3bo3b2o5bo67b2o$241b3o64bo17b2o
3bo3b2o65b4o7b2o57b2o7bo$240bo84bo2b3o4b2o51b2o15bo66b2o5bobo42bo$240b
2o16b2o61b2o2b2obo58bobo12b3o38b2o34b2o41b3o$258bo53b2o7bo6bo58bo13bo
19b2o20bo77bo$259b3o50b2o5bobo6b2o56b2o14b5o15bo22bo75b2o$261bo57b2o
85bo12b3o3b2o14b5o$173bo22b2o160b2o44bo14bo6bo13bo$173b3o21bo138b2o20b
o45b2o20bobo12b3o85b2o$176bo17b3o140bo10bo11bo66b2o15bo85bo$175b2o17bo
139b3o3b2o6b2o6b5o80b4o24b2o59bob2o$334bo6bo7b2o4bo80b2o3bo3b2o23bo51b
2o4b3o2bo$341bobo6b3o2b4o71bo5b2o4b3o2bo19b3o52b2o3bo3b2o$167b2o117bo
22b2o31b2o6b3o3bo2bo70b2o12bob2o19bo24b2o33b4o$167bo118b3o21bo38b2o2b
7o69bobo12bo47bo20b2o15bo$164b2obo121bo17b3o42b2o2bo3b2o81b2o49bo17bob
o12b3o$164bo2b3o4b2o112b2o17bo45b2o2bobo2bo111b2o14b5o17bo13bo$165b2o
3bo3b2o181bobob2o112bo13bo21b2o14b5o$167b4o188bo6bo21b2o45b2o38bobo12b
3o38bo$167bo15b2o95b2o76b2o6b3o19bobo44bo40b2o15bo35bo$168b3o12bobo94b
o88bo20bo4b2o39b3o51b4o35b2o$171bo13bo91b2obo87b2o16b4ob2o2bo2bo39bo
46b2o3bo3b2o$124bo41b5o14b2o90bo2b3o4b2o61b2o34bo2bobobobob2o86b2o4b3o
2bo$124b3o39bo51b2o58b2o3bo3b2o61bo38bobobobo97bob2o$127bo40bo48bob2o
59b4o62bo4b3o6b2o28b2obobo97bo$126b2o39b2o47bo3b2o58bo15b2o46b3o6bo6bo
33bo97b2o$217b2obobo58b3o12bobo44bo13b2obo5b2o$219b3o62bo13bo44b2o12bo
2b2o6bo11b2o$118b2o99b3o57b5o14b2o58b2o2bo2bob2o12bo7b2o93b2o$73b2o43b
o160bo51b2o27bob2o17bobo5b2o93bo$72b2o41b2obo120bo41bo48bob2o26bobo13b
2o4b2o101b3o$74bo40bo2b3o4b2o112b3o38b2o47bo3b2o26b3o12bobo108bo$116b
2o3bo3b2o115bo87b2obobo28bo6bo6bo$118b4o91bobo25b2o89b3o24b5o8bo5b2o
108bo$118bo15b2o72b2o4bo4bobo110b3o24bo10b3o115b3o$119b3o12bobo71b2o
10bob2o137bo129bo$122bo13bo82b3o11b2o125b2o128b2o$117b5o14b2o77bo3bobo
11bo158b2o$117bo97bo3bobo8b2obo158bo$119bo95bo3b2o9bo2b3o4b2o84bobo64b
3o86b2o$118b2o98b2o11b2o3bo3b2o79b2o4bo4bobo60bo86bo$217b2o14b4o84b2o
10bob2o142b2obo$195b2o20b2o14bo15b2o81b3o144bo2b3o4b2o$195b2o37b3o12bo
bo13b2o61bo3bobo145b2o3bo3b2o$159b2o76bo13bo13bobo60bo3bobo122b2o23b4o
$159bobo70b5o14b2o14bo4b2o54bo3b2o51b2o71b2o22bo15b2o$161bo4b2o64bo30b
4ob2o2bo2bo55b2o52b2o70bo25b3o12bobo$157b4ob2o2bo2bo47b3o14bo28bo2bobo
bobob2o54b2o154bo13bo6bo$157bo2bobobobob2o46bo2bo13b2o31bobobobo35b2o
20b2o149b5o14b2o3b3o$160bobobobo49bo2bo47b2obobo35b2o111bo59bo22bo$
161b2obobo104bo148bo62bo20b2o$165bo29bo19b2o203b3o59b2o$194bo20bo41b2o
$151b2o41b3o61bo7b2o62b3o179b2o$152bo7b2o96bobo5b2o61bo2bo180bo$152bob
o5b2o97b2o68bo2bo180bob2o$153b2o62bo287b2o4b3o2bo$216b2o90bo19b2o40b3o
132b2o3bo3b2o$216bobo88bo20bo43bo137b4o$307b3o61bo63bo60b2o15bo$433b3o
59bobo12b3o$432bo62bo13bo$269b2o59bo101b2o60b2o14b5o$163b2o104bo59b2o
183bo$163bo106b3o56bobo180bo$164b3o105bo239b2o$166bo3$240bo181b2o$238b
3o180bobo5b2o$237bo183bo7b2o$165bo71b2o181b2o69bobo$166bo324b2o$164b3o
267bo57bo$430b2obobo$429bobobobo$104b2o147b3o170bo2bobobobob2o$103bobo
147bo172b4ob2o2bo2bo$97b2o4bo150bo24bo150bo4b2o$95bo2bo2b2ob4o172bo
147bobo$95b2obobobobo2bo170b3o147b2o$98bobobobo$98bobob2o$41bo57bo267b
3o$41b2o324bo$40bobo69b2o181b2o71bo$103b2o7bo183bo$103b2o5bobo180b3o$
110b2o181bo3$367bo$20b2o239bo105b3o$21bo180bobo56b3o106bo$19bo183b2o
59bo104b2o$19b5o14b2o60b2o101bo59b2o$24bo13bo62bo$21b3o12bobo59b3o$20b
o15b2o60bo63bo61b3o$20b4o137bo43bo20bo88bobo$18b2o3bo3b2o132b3o40b2o
19bo90b2o$17bo2b3o4b2o287bo62b2o$17b2obo180bo2bo68b2o97b2o5bobo$20bo
180bo2bo61b2o5bobo96b2o7bo$20b2o179b3o62b2o7bo61b3o41b2o$275b2o41bo20b
o$50b2o59b3o203b2o19bo29bo$28b2o20bo62bo148bo104bobob2o$29bo22bo59bo
111b2o35bobob2o47bo2bo49bobobobo$26b3o3b2o14b5o149b2o20b2o35bobobobo
31b2o13bo2bo46b2obobobobo2bo$26bo6bo13bo154b2o54b2obobobobo2bo28bo14b
3o47bo2bo2b2ob4o$33bobo12b3o25bo70b2o52b2o55bo2bo2b2ob4o30bo64b2o4bo$
34b2o15bo22b2o71b2o51b2o3bo54b2o4bo14b2o14b5o70bobo$48b4o23b2o122bobo
3bo60bobo13bo13bo76b2o$43b2o3bo3b2o145bobo3bo61b2o13bobo12b3o37b2o$43b
2o4b3o2bo144b3o81b2o15bo14b2o20b2o$51bob2o142b2obo10b2o84b4o14b2o$51bo
86bo60bobo4bo4b2o79b2o3bo3b2o11b2o98b2o$50b2o86b3o64bobo84b2o4b3o2bo9b
2o3bo95bo$141bo158bob2o8bobo3bo97bo$140b2o158bo11bobo3bo77b2o14b5o$42b
2o128b2o125b2o11b3o82bo13bo$42bo129bo137b2obo10b2o71bobo12b3o$43b3o
115b3o10bo24b3o110bobo4bo4b2o72b2o15bo$45bo108b2o5bo8b5o24b3o89b2o25bo
bo91b4o$155bo6bo6bo28bobob2o87bo115b2o3bo3b2o$46bo108bobo12b3o26b2o3bo
47b2o38b3o112b2o4b3o2bo40bo$46b3o101b2o4b2o13bobo26b2obo48bo41bo120bob
2o41b2o$49bo93b2o5bobo17b2obo27b2o51bo160bo43b2o$48b2o93b2o7bo12b2obo
2bo2b2o58b2o14b5o57b3o99b2o$152b2o11bo6b2o2bo12b2o44bo13bo62b3o$166b2o
5bob2o13bo44bobo12b3o58bobob2o$40b2o97bo33bo6bo6b3o46b2o15bo58b2o3bo
47b2o39b2o$40bo97bobob2o28b2o6b3o4bo62b4o59b2obo48bo40bo$37b2obo97bobo
bobo38bo61b2o3bo3b2o58b2o51bo39b3o$37bo2b3o4b2o86b2obobobobo2bo34b2o
61b2o4b3o2bo90b2o14b5o41bo$38b2o3bo3b2o46bo39bo2bo2b2ob4o16b2o87bob2o
91bo13bo$3b2o35b4o51b3o39b2o4bo20bo88bo94bobo12b3o$4bo35bo15b2o40bo44b
obo19b3o6b2o76b2o95b2o15bo$2bo38b3o12bobo38b2o45b2o21bo6bo188b4o$2b5o
14b2o21bo13bo112b2obobo181b2o3bo3b2o$7bo13bo17b5o14b2o111bo2bobo2b2o
45bo17b2o112b2o4b3o2bo$4b3o12bobo17bo49b2o81b2o3bo2b2o42b3o17bo121bob
2o$3bo15b2o20bo47bo12bobo69b7o2b2o38bo21b3o118bo$3b4o33b2o24bo19b2obo
12b2o70bo2bo3b3o6b2o31b2o22bo117b2o$b2o3bo3b2o52b3o19bo2b3o4b2o5bo71b
4o2b3o6bobo$o2b3o4b2o51bo23b2o3bo3b2o80bo4b2o7bo6bo$2obo59b2o24b4o80b
5o6b2o6b2o3b3o139bo17b2o$3bo85bo15b2o66bo11bo10bo140b3o17bo$3b2o85b3o
12bobo20b2o45bo20b2o138bo21b3o$93bo13bo6bo14bo44b2o160b2o22bo$88b5o14b
2o3b3o12bo85b2o57bo$11b2o75bo22bo15b5o14b2o56b2o6bobo5b2o50b3o$12bo77b
o20b2o19bo13bo58bo6bo7b2o53bo$9b3o41b2o34b2o38b3o12bobo58bob2o2b2o61b
2o16b2o$9bo42bobo5b2o66bo15b2o51b2o4b3o2bo84bo$52bo7b2o57b2o7b4o65b2o
3bo3b2o17bo64b3o$51b2o67bo5b2o3bo3b2o65b4o15b2obobo39b2o22bo35b2o$120b
ob2obo2b3o4b2o51b2o15bo14bobobobo39bo58bobo5b2o$65bo46b2o4b3o2bob2obo
58bobo12b3o12bo2bobobobob2o33b2obo58bo7b2o$61b2obobo45b2o3bo3b2o5bo51b
o6bo13bo15b4ob2o2bo2bo33bo2b3o4b2o49b2o$43b2o15bobobobo50b4o7b2o50b3o
3b2o14b5o14bo4b2o36b2o3bo3b2o$43bo13bo2bobobobob2o33b2o15bo62bo22bo12b
obo44b4o68bo$45bo11b4ob2o2bo2bo32bobo12b3o62b2o20bo14b2o45bo15b2o50b2o
bobo59bo$25b2o14b5o15bo4b2o27bo6bo13bo19b2o66b2o61b3o12bobo48bobobobo
59bobo$26bo13bo18bobo33b3o3b2o14b5o15bo89b2o41bo13bo45bo2bobobobob2o
56b2o$26bobo12b3o15b2o37bo22bo12b3o37b2o52bo36b5o14b2o44b4ob2o2bo2bo$
27b2o15bo52b2o20bo14bo39bo51bo10b2o26bo68bo4b2o$41b4o74b2o50b2obo51b5o
7b2o5b2o20bo64bobo$36b2o3bo3b2o124bo2b3o4b2o48bo5bo7bo20b2o64b2o$36b2o
4b3o2bo41b2o81b2o3bo3b2o45bobo12bobo$44bob2o41bo84b4o49bobo13b2o$28b3o
13bo41b2obo84bo15b2o35b2o$30bo12b2o41bo2b3o4b2o70b2o5b3o12bobo32b2o2bo
b2ob2o$29bo57b2o3bo3b2o70bo9bo13bo6bo24bo2b2o4b2o118b2o$13b2o74b4o77bo
2b5o14b2o3b3o24b2obo5bo120b2o$14bo20b2o24b2o26bo15b2o43b2o14b5o2bo22bo
30bo125bo$12bo22bo24bobo27b3o12bobo43bo13bo9bo20b2o19b2o8b2o$12b5o14b
2o3b3o15b2o4bo32bo13bo6bo36bobo12b3o5b2o41bobo$17bo13bo6bo13bo2bo2b2ob
4o23b5o14b2o3b3o37b2o15bo49bo4b2o$14b3o12bobo20b2obobobobo2bo23bo22bo
54b4o34b2o9b4ob2o2bo2bo7b2o54bo$13bo15b2o24bobobobo28bo20b2o48b2o3bo3b
2o33bo9bo2bobobobob2o8bo55b2o$13b4o38bobob2o28b2o70b2o4b3o2bo32bob2o9b
obobobo8b3o55b2o$11b2o3bo3b2o34bo112bob2o24b2o4b3o2bo10b2obobo8bo$10bo
2b3o4b2o97b2o48bo27b2o3bo3b2o15bo$10b2obo55b2o49bo47b2o32b4o$13bo46b2o
7bo50bob2o64b2o15bo3b2o$13b2o45b2o5bobo42b2o4b3o2bo14b2o47bobo12b3o5bo
7b2o$67b2o43b2o3bo3b2o16bo20b2o18bo6bo13bo8bobo5b2o$117b4o16bo22bo19b
3o3b2o14b5o4b2o25bo$21b2o80b2o15bo16b5o14b2o3b3o19bo22bo29b3o$22bo18bo
60bobo12b3o22bo13bo6bo18b2o20bo30bo$19b3o19b3o51bo6bo13bo22b3o12bobo
47b2o29b2o86b2o$19bo24bo50b3o3b2o14b5o16bo15b2o115b2o51bo$43b2o53bo22b
o16b4o32b2o39b2o54bo50bo$57b2o38b2o20bo16b2o3bo3b2o27bo39bobo26b2o28bo
48b5o14b2o$58bo19b2o39b2o14bo2b3o4b2o24b2obo41bo4b2o21bo8b2o14b5o53bo
13bo$55b3o20bo56b2obo32bo2b3o4b2o38bo22bob2o6bo13bo55b3o12bobo$55bo24b
o8b2o47bo33b2o3bo3b2o39b3o11b2o4b3o2bo6bobo12b3o51bo15b2o$60b2o14b5o8b
o48b2o34b4o46bo11b2o3bo3b2o8b2o15bo50b4o$61bo13bo10b2obo84bo15b2o49b4o
24b4o48b2o3bo3b2o$53b2o6bobo12b3o7bo2b3o4b2o77b3o12bobo34b2o15bo19b2o
3bo3b2o45bo2b3o4b2o$46b2o5bobo6b2o15bo7b2o3bo3b2o48b2o30bo13bo33bobo
12b3o20b2o4b3o2bo44b2obo$46b2o7bo20b4o9b4o54bo25b5o14b2o32bo13bo31bob
2o8b2o37bo$55b2o14b2o3bo3b2o7bo15b2o37b3o26bo24bo26b2o14b5o26bo10bobo
37b2o22bo$71b2o4b3o2bo7b3o12bobo36bo30bo20b3o46bo25b2o4b2o4bo63b3o$42b
o36bob2o10bo13bo6bo59b2o19bo47bo31bo2bo2b2ob4o62bo$41bobob2o32bo8b5o
14b2o3b3o80b2o46b2o30b2obobobobo2bo43b2o16b2o$41bobobobo30b2o8bo22bo
151b2o13bobobobo47bo$38b2obobobobo2bo39bo20b2o150bo14bobob2o45b3o$38bo
2bo2b2ob4o38b2o173b3o12bo49bo$40b2o4bo23b2o94b2o98bo$46bobo21bo48b2o
44b2o125b2o$47b2o22b3o46bo46bo115b2o7bo$73bo46bob2o61b2o96b2o5bobo66b
2o$112b2o4b3o2bo60bobo5b2o96b2o60b2o5bobo$112b2o3bo3b2o61bo7b2o158b2o
7bo$117b4o62b2o176b2o$103b2o15bo$72b2o28bobo12b3o77bo150bo$71bobo21bo
6bo13bo76b2obobo148bobob2o$65b2o4bo23b3o3b2o14b5o70bobobobo148bobobobo
$63bo2bo2b2ob4o22bo22bo67bo2bobobobob2o78b2o62b2obobobobo2bo$63b2obobo
bobo2bo21b2o20bo69b4ob2o2bo2bo79bo62bo2bo2b2ob4o$66bobobobo46b2o72bo4b
2o78b3o21b2o42b2o4bo$66bobob2o119bobo84bo23bo49bobo$32b2o33bo21b2o100b
2o111bo48b2o$33bo55bo194b2o14b5o$31bo48b2o4b2obo195bo13bo$31b5o14b2o
19b2o7bo5bo2b3o4b2o2bo184bobo12b3o$36bo13bo20b2o5bobo6b2o3bo3b2o2bobo
183b2o15bo$33b3o12bobo27b2o9b4o7b2o92bo105b4o$32bo11bo3b2o39bo15b2o87b
3o98b2o3bo3b2o$32b4o6b2obo44b3o12bobo89bo17b2o78b2o4b3o2bo52bo$30b2o3b
o6bo2bo6bo40bo13bo6bo81b2o18bo86bob2o50b3o$29bo2b3o7b3o7b3o33b5o14b2o
3b3o99bo88bo12b2o38bo$29b2obo22bo32bo22bo102b5o14b2o67b2o11bobo38b2o$
32bo21b2o34bo20b2o106bo13bo75b2o4bo$32b2o34b2o19b2o125b3o12bobo73bo2bo
2b2ob4o$69bo145bo15b2o61b2o11b2obobobobo2bo44b2o$66b3o50b2o94b4o75bo
15bobobobo48bo$40b2o24bo53bo85b2o5b2o3bo3b2o71b3o12bobob2o49bob2o$41bo
78bob2o75b2o5bobo3bo2b3o4b2o73bo13bo45b2o4b3o2bo$38b3o71b2o4b3o2bo75b
2o7bo3b2obo141b2o3bo3b2o$38bo25b2o46b2o3bo3b2o85b2o5bo22bo85b2o36b4o$
57b2o5bobo50b4o94b2o21b3o74b2o7bo23b2o15bo$57b2o7bo36b2o15bo74bo45bo
73b2o5bobo22bobo12b3o$66b2o34bobo12b3o74bobob2o40b2o80b2o23bo13bo$102b
o13bo77bobobobo22b2o121b2o14b5o$53bo47b2o14b5o69b2obobobobo2bo20bo141b
o$52bobob2o38bo24bo69bo2bo2b2ob4o17b3o18bo121bo$52bobobobo37b3o20bo73b
2o4bo21bo20b2o120b2o$49b2obobobobo2bo37bo19b2o78bobo39bob2o$49bo2bo2b
2ob4o36b2o100b2o41b2o$51b2o4bo192b2o60b2o$57bobo190bobo60bo$58b2o183b
2o7bo57b3o$252b2o56bo$332bo$239bo92b3o$108b2o128bobob2o91bo$101b2o5bob
o127bobobobo89b2o$101b2o7bo124b2obobobobo2bo$110b2o123bo2bo2b2ob4o$
237b2o4bo$97bo145bobo11bo72b3o$96bobob2o142b2o11b2o71bo$96bobobobo153b
obo72bo$93b2obobobobo2bo238b2o$93bo2bo2b2ob4o135b2o94b2o5bobo$95b2o4bo
140bo94bo8bo$101bobo136bo105b2o$102b2o136b5o14b2o$245bo13bo73bo$242b3o
12bobo72bobob2o$241bo15b2o73bobobobo$241b4o84b2obobo3bo2bo$239b2o3bo3b
2o79bo2bo2b2ob4o$238bo2b3o4b2o81b2o4bo$238b2obo95bobo$241bo96b2o$241b
2o22bo$265b3o$268bo$249b2o16b2o$250bo$247b3o$247bo4$277b2o$270b2o5bobo
$270b2o7bo$279b2o2$266bo$265bobob2o$265bobobobo$262b2obobobobo2bo$262b
o2bo2b2ob4o$264b2o4bo$270bobo$271b2o!

[mniemiec]

Known? ...

This is basically two independent oscillators sharing a single stator. The one on the left has long been known, and is just a member of the "cha-cha" oscillators that David Buckingham and I described in the late '70s; the smallest two examples are the Clock and the 16-bit Cha-cha. The same mechanisms are used in many larger P2s, and can be combined with many other P2 mechanisms, such as the ones in your other post. I am not not sure if I've seen the P6 on the right, but I think that it's probably known; the stator definitely looks familiar.

Code: Select all

x = 32, y = 13, rule = B3/S23
25bo$4bobo17bobo$bbobbobbo14bobobo$3bobobo15bobobo$boobbobboo11b3obobb
oo$5bo14bo9bo$5ob5o8bob3o3b3obo$5bo14bo9bo$boobbobboo11boobbob3o$3bobo
bo15bobobo$bbobbobbo14bobobo$4bobo17bobo$25bo!

[Gustone]

sharing a single stator

Because it's the smallest form I could make

[Sokwe]

Known?

Code: Select all

x = 11, y = 11, rule = B3/S23
4bobo$2bo2bo2bo$3bobobo$b3obo2b2o2$4o3b4o2$b2o2bob3o$3bobobo$2bo2bo2bo
$4bobo!

Did you try checking in jslife? The central p6 rotor can be seen in the file osc/o0006.lif (second oscillator in the second row). There are two minimal symmetric stator variants:

Code: Select all

x = 39, y = 11, rule = B3/S23
4b2o24b2o$3bo2bo24bo2bo$3bobobo20bo2bobobo$b3obo2bo19b4obo2bo$o8bo27bo
$ob2o3b2obo19b2o3b2o$bo8bo18bo$2bo2bob3o20bo2bob4o$3bobobo23bobobo2bo$
4bo2bo24bo2bo$5b2o28b2o!

[hkoenig]

Years ago I posted a sample of all sorts of ways of constructing P2 oscillators--

https://conwaylife.com/forums/viewtopic ... 7500#p7500

But I think some of the end-caps you show aren't in there.

If you are serious about working on general construction of P2 oscillators, you should defintely look up Beluchenko's "oscichem": http://cranemtn.com/life/oschem1/oschem1.htm.

[Hooloovoo]

I'm pretty sure this 6n+1 phase-shift reaction is new:

Code: Select all

x = 20, y = 21, rule = B3/S23
$8b2o$7bo2bo$7bobo3bo$8bob4o2bo$10bo3b3o$9bo3bo$5b2obo3bobo$4bobob2o3b
2o$3bo2bo8b2o$3bobob8o2bo$2b2obobo7b2o$5bo2b2obo2bo$5bobobob4o$6b2obo$
8b2ob2o$4b3o3bobo$4bo2b3o$7bo!

I'm currently working on a method Sokwe suggested earlier in this topic. Basically, I just rub a pair of oscillators together with a python script, then pipe them into dr.

To test my script, I was attempting to find the p24 mentioned in the post, by rubbing new 6.1.4 and SC 10.0.0 together. As I found the p24 for the first time, the p7 popped up.

I am running into the problem with the stable backgrounds required by dr: with most of the oscillators I've tried so far, only one possible stable background (counted just over the rotor cells) works. One, r2d2, though, worked with multiple backgrounds. I haven't run into anything that has had a very large number of working backgrounds, but it could happen. I think I can just run dr on each potential BG, and if the oscillator is found, then it works.

Instead of trying to compute the border cells beforehand and tell dr about them, I just leave them as "unknown, don't change" (except for the interacting cells) and let dr figure out the borders. It seems to be pretty good at that.

I'm working with a knownrotors file from 2014 - does anyone have an updated one? The p24 and p9 in phase-shift.rle included with Golly aren't in it, for example.

Edit: According to LLS's --force-at-most, the stator is minimal population. My dr-to-LLS script is really unpolished - it just puts a big border around it and I manually do a binary search for population. Does anyone have a better way to stabilize an oscillator, maybe something that takes a rotor descriptor?

[Sokwe]

I'm currently working on a method Sokwe suggested earlier in this topic. Basically, I just rub a pair of oscillators together with a python script, then pipe them into dr.

Excellent! I'd love to know more about your methodology. How do you find the stable background? Do you test all phase combinations? Even for periods with gcd=1, some phase combinations will cause the pattern to self destruct, while others will result in a phase shift oscillator

What settings are you using for dr? And what version? I don't think the updates I made would be any help, so you should probably just be using Dean Hickerson's version.

I'm pretty sure this 6n+1 phase-shift reaction is new:

Code: Select all

x = 20, y = 21, rule = B3/S23
$8b2o$7bo2bo$7bobo3bo$8bob4o2bo$10bo3b3o$9bo3bo$5b2obo3bobo$4bobob2o3b
2o$3bo2bo8b2o$3bobob8o2bo$2b2obobo7b2o$5bo2b2obo2bo$5bobobob4o$6b2obo$
8b2ob2o$4b3o3bobo$4bo2b3o$7bo!

Yes, that looks new! It's great to see that this idea actually found something! The next step when finding a new phase shift is to try the other possible reactions. The possible periods would be 7, 13, 19, 25, 31, 37, 43, 49. That's a lot of primes, and p49 could not be supported by a p7. Can a p25 be made with a p5 support? JLS is ideal for this type of search. I'll test it soon.

To test my script, I was attempting to find the p24 mentioned in the post, by rubbing new 6.1.4 and SC 10.0.0 together. As I found the p24 for the first time, the p7 popped up.... I'm working with a knownrotors file from 2014

That's a good test case. How will you be choosing what rotors to test? I'm not sure how fast the search would go, but I imagine it would be difficult to try every combination of every rotor in the knownrotors file.

Instead of trying to compute the border cells beforehand and tell dr about them, I just leave them as "unknown, don't change" (except for the interacting cells) and let dr figure out the borders. It seems to be pretty good at that.

Interesting. How do you decide which are the interacting cells and which are stable? When I described it, I envisioned not setting any particular cells fixed, but instead only allowing a small number of cells to change (as I recall there was a parameter for that in dr).

I'm working with a knownrotors file from 2014 - does anyone have an updated one? The p24 and p9 in phase-shift.rle included with Golly aren't in it, for example.

Unfortunately, I don't think anyone has bothered to make an up-to-date knownrotors file. It's just one of those time consuming projects that doesn't generate much interest. Bob Shemyakin did make an application for editing the knownrotors file and included a copy with many oscillators added. Is that the version you're using? I think there was a variable in dr.c that set a limit on the size of the knownrotors file and that the file was getting pretty close to that size, so you may want to look at that and possibly change the value.

Also, do you use the rotor descriptor to generate the stable background?

I think I can just run dr on each potential BG, and if the oscillator is found, then it works.

My opinion is that you should try them all. There might be a case where one stable background allows an interaction, but another background causes an inconsistency in the adjacent oscillator background.

One, r2d2, though, worked with multiple backgrounds.

R2-D2 is the key to all this, if you get R2-D2 working. 'Cause it's a better phase shifter than we've ever had in Life.

In fact, R2-D2 can be shifted from both sides, and two copies of it can phase shift each other, as seen in phase-shift.rle.

[Hooloovoo]

Excellent! I'd love to know more about your methodology. How do you find the stable background? Do you test all phase combinations? Even for periods with gcd=1, some phase combinations will cause the pattern to self destruct, while others will result in a phase shift oscillator

...


Also, do you use the rotor descriptor to generate the stable background?

Currently, I've been using simple backtracking to find internal cells (per rotor) consistent with the number neighbors given by the rotor descriptor. I've done this per-rotor for now.

I don't test all phase combinations; for sc10.0.0 and sc7.0.2, I have been using one phase, but colliding all phases of r2d2 and new6.1.4 with them

What settings are you using for dr? And what version? I don't think the updates I made would be any help, so you should probably just be using Dean Hickerson's version.

I am using a file called just dr.c, but I'm not exactly sure where I found it. I'm nearly positive it was from somewhere on the forums, but I recall it being relatively hard to find - the forum doesn't like to search for "dr" since it's too short.

A sample input (the one I found the p7 with) is

Code: Select all

h30
w30
c3
d0 p35 44
d0 p35 45
d0 p35 46
d0 p35 47
d0 p35 48
d0 p36 42
d0 p36 43
d0 p36 44
d0 p36 45
d0 p36 46
d0 p36 47
d0 p36 48
d0 p37 41
d0 p37 42
d0 p37 43
d0 p37 44
d0 p37 45
d1 p37 46
d0 p37 47
d0 p37 48
d0 p37 49
d0 p38 41
d1 p38 44
d1 p38 45
d1 p38 46
d0 p38 47
d0 p38 48
d0 p38 49
d0 p39 40
d0 p39 41
d1 p39 45
d1 p39 46
d1 p39 47
d0 p39 48
d0 p39 49
d0 p40 39
d0 p40 40
d0 p40 41
d1 p40 43
d1 p40 45
d0 p40 47
d0 p40 48
d0 p40 49
d0 p41 38
d0 p41 39
d0 p41 40
d0 p41 41
d1 p41 42
d1 p41 43
d1 p41 44
d0 p41 47
d0 p41 48
d0 p41 49
d0 p42 38
d0 p42 39
d0 p42 40
d1 p42 41
d0 p42 42
d1 p42 43
d0 p42 47
d0 p43 38
d0 p43 39
d1 p43 40
d1 p43 41
d1 p43 42
d1 p43 43
d1 p43 44
d0 p43 45
d0 p43 46
d0 p43 47
d0 p44 38
d0 p44 39
d0 p44 40
d1 p44 41
d0 p44 42
d1 p44 43
d0 p44 44
d0 p44 45
d0 p44 46
d0 p45 38
d0 p45 39
d0 p45 40
d0 p45 41
d0 p45 42
d0 p45 43
d0 p45 44
d0 p45 45
d0 p45 46
d0 p46 39
d0 p46 40
d0 p46 41
d0 p46 42
d0 p46 43
d0 p46 44
d0 p46 45
r35 38
,,,,,,?????,
,,,,???????,
,,,?????1???
,,,?,,...???
,,??,,,.10??
,???,.,0,???
????ooo,,???
???0?.,,,?,,
??.01.o???,,
???0?o???,,,
?????????,,,
,???????,,,,!

The big chain of d0 and d1s mean: don't change the border ?s, don't count any of the o.10 cells in the rotors (I think I could have used v127, right?), and count changes in the internal ',' cells. Even though they're equivalent, I use both , and ? so I can see where the unknown cells are.

Yes, that looks new! It's great to see that this idea actually found something! The next step when finding a new phase shift is to try the other possible reactions. The possible periods would be 7, 13, 19, 25, 31, 37, 43, 49. That's a lot of primes, and p49 could not be supported by a p7. Can a p25 be made with a p5 support? JLS is ideal for this type of search. I'll test it soon.

Those are some exciting periods! I don't have any experience at all with JLS... I probably should learn. I know there's a couple getting started guides, but it seems like there's a very steep learning curve.

How will you be choosing what rotors to test? I'm not sure how fast the search would go, but I imagine it would be difficult to try every combination of every rotor in the knownrotors file.

I have no idea... I think I'll start with "small" rotors, but I'm not exactly sure how to define "small". Are there other "families" of rotors like the p10/7/17 ones? I might try a large rotor for a base (like sc10.0.0) with various small ones.

Instead of trying to compute the border cells beforehand and tell dr about them, I just leave them as "unknown, don't change" (except for the interacting cells) and let dr figure out the borders. It seems to be pretty good at that.

Interesting. How do you decide which are the interacting cells and which are stable? When I described it, I envisioned not setting any particular cells fixed, but instead only allowing a small number of cells to change (as I recall there was a parameter for that in dr).

Currently, I try each possible offset, so that there is only a one or two cell overlap between the rotor of one osc, and the stator of the other. I also require at least one cell of stator overlap. I use the stator overlap, and the non-rotor neighbors of the overlap as the unknowns. I think this is a pretty good heuristic, but it's by no means exhaustive - for example, I don't think it would find the p9 based on r2d2 - the stators don't directly overlap.

I'm working with a knownrotors file from 2014 - does anyone have an updated one? The p24 and p9 in phase-shift.rle included with Golly aren't in it, for example.

Unfortunately, I don't think anyone has bothered to make an up-to-date knownrotors file. It's just one of those time consuming projects that doesn't generate much interest. Bob Shemyakin did make an application for editing the knownrotors file and included a copy with many oscillators added. Is that the version you're using? I think there was a variable in dr.c that set a limit on the size of the knownrotors file and that the file was getting pretty close to that size, so you may want to look at that and possibly change the value.

I wasn't using this, thanks. I'm sure I saw the post though :/

I think I can just run dr on each potential BG, and if the oscillator is found, then it works.

My opinion is that you should try them all. There might be a case where one stable background allows an interaction, but another background causes an inconsistency in the adjacent oscillator background.

I think I can narrow down the search space by checking potential (consistent with knownrotors neighbors) BG can ever actually be used find the oscillator. If dr can't find the oscillator with a given bg and on-cells, it's probably not worth trying to phase-shift it.

One, r2d2, though, worked with multiple backgrounds.

R2-D2 is the key to all this, if you get R2-D2 working. 'Cause it's a better phase shifter than we've ever had in Life.

In fact, R2-D2 can be shifted from both sides, and two copies of it can phase shift each other, as seen in phase-shift.rle.

Yeah, r2d2 is amazingly shiftable. I meant to say that smashing r2d2 and sc7.0.2 will find the p9 mutual-shifter with two different stabilizations of r2d2, but I guess it's pretty difficult to read my mind on things like that.

[Sokwe]

I am using a file called just dr.c, but I'm not exactly sure where I found it. I'm nearly positive it was from somewhere on the forums, but I recall it being relatively hard to find - the forum doesn't like to search for "dr" since it's too short.

Wow, it is hard to find. I was the one who posted it, and even I can't seem to find it. For that reason, I have started a new discussion thread in the scripts forum that includes the original dr source code. When looking through my local directories for the original source, I also came upon a folder that had a knownrotors file that had been updated (at least somewhat) through October 2015. That file uses Shemyakin's as a base. I included this slightly more up-to-date file in the .zip provided in the discussion thread. However, it still won't have the p24 or p9 that you mentioned.

I don't test all phase combinations; for sc10.0.0 and sc7.0.2, I have been using one phase, but colliding all phases of r2d2 and new6.1.4 with them

In the vast majority of cases I suspect that will work. However, In think there might be a few things it could miss, due to a bad interaction that would occur before the oscillators settle into their phase shift reaction.

The possible periods would be 7, 13, 19, 25, 31, 37, 43, 49. That's a lot of primes, and p49 could not be supported by a p7. Can a p25 be made with a p5 support? JLS is ideal for this type of search. I'll test it soon.

Those are some exciting periods!

Well, the difficulty with most of those periods is that they can't be searched for with JLS. Only p25 looks like it might be viable. The prime periods would generally be hard to achieve, and would probably need some mutual phase shift. There might be a p13 that can shift the p6, but the other periods don't have any billiard-table-like oscillators or components to make use of for phase shifting.

How will you be choosing what rotors to test?

I have no idea... I think I'll start with "small" rotors, but I'm not exactly sure how to define "small". Are there other "families" of rotors like the p10/7/17 ones? I might try a large rotor for a base (like sc10.0.0) with various small ones.

Small rotors are good to start with. Also, rotors that have a phase where only a few cells change right at the boundary of the rotor. You should also look at phase-shift.rle for inspiration. The p(9n+1) could be promising, but it would require setting up a symmetric search.

Currently, I try each possible offset, so that there is only a one or two cell overlap between the rotor of one osc, and the stator of the other. I also require at least one cell of stator overlap. I use the stator overlap, and the non-rotor neighbors of the overlap as the unknowns. I think this is a pretty good heuristic, but it's by no means exhaustive - for example, I don't think it would find the p9 based on r2d2 - the stators don't directly overlap.

I'm not sure if I entirely follow. What counts as the "stator" here? I would think the rotors would have to be within one cell of each other (i.e., their bushings overlap). I hope that some method could be devised that could find the p9 R2-D2 mutual shifter.

I meant to say that smashing r2d2 and sc7.0.2 will find the p9 mutual-shifter with two different stabilizations of r2d2, but I guess it's pretty difficult to read my mind on things like that.

So you are saying that you tested this and were able to find the other p9 shifter, right? The one with R2-D2 and the p7.

If dr can't find the oscillator with a given bg and on-cells, it's probably not worth trying to phase-shift it.

That seems reasonable.

[hkoenig]

Don't know how helpful this might be, but here's a tab-delimited text file containing a list from my LifeObjects database of 10738 unique rotors, along with my wcode and objID info for the smallest example oscillator.

(if I did all the SQL correctly.)

EDIT:

Updated file to include comment field, which can contain discoverer name for about 1/4 of the records. I didn't put much effort in to maintaining this info, and didn't bother with dates.

Note also that lots of these records are Period 2 objects generated by a search program I ran for a while, and none of those have discoverer info.

[Sokwe]

Can a p25 be made with a p5 support? JLS is ideal for this type of search. I'll test it soon.

It appears to be impossible. I also tried using the same reaction to delay the p6 rotor 2 or 3 generations, but nothing worked.

Here is a stator minimization of the p7:

Code: Select all

x = 14, y = 15, rule = B3/S23
3bo$3b3o$6bo$2o3bo3bo$obobo3bobo$2bob2o3b2o$b2o8b2o$o2b8o2bo$2obo8b2o$
bo2b2ob2o$bobobobobo$2b2obo3bo$4bob3o$4bobo$5bo!

here's a tab-delimited text file containing a list from my LifeObjects database of 10738 unique rotors, along with my wcode and objID info for the smallest example oscillator.

Thanks! What we desperately need is a Golly script that can take a selected oscillator and check if its rotor is known, possibly providing information such as its discoverer and discovery date.

[Hooloovoo]

I am using a file called just dr.c, but I'm not exactly sure where I found it. I'm nearly positive it was from somewhere on the forums, but I recall it being relatively hard to find - the forum doesn't like to search for "dr" since it's too short.

Wow, it is hard to find. I was the one who posted it, and even I can't seem to find it. For that reason, I have started a new discussion thread in the scripts forum that includes the original dr source code. When looking through my local directories for the original source, I also came upon a folder that had a knownrotors file that had been updated (at least somewhat) through October 2015. That file uses Shemyakin's as a base. I included this slightly more up-to-date file in the .zip provided in the discussion thread. However, it still won't have the p24 or p9 that you mentioned.

Thanks!

I don't test all phase combinations; for sc10.0.0 and sc7.0.2, I have been using one phase, but colliding all phases of r2d2 and new6.1.4 with them

In the vast majority of cases I suspect that will work. However, In think there might be a few things it could miss, due to a bad interaction that would occur before the oscillators settle into their phase shift reaction.

hmm, ok.

The p(9n+1) could be promising, but it would require setting up a symmetric search.

I hacked in a symmetric searching against the 9n+1 but didn't find anything. I'm not positive I covered the whole search space.

Currently, I try each possible offset, so that there is only a one or two cell overlap between the rotor of one osc, and the stator of the other. I also require at least one cell of stator overlap. I use the stator overlap, and the non-rotor neighbors of the overlap as the unknowns. I think this is a pretty good heuristic, but it's by no means exhaustive - for example, I don't think it would find the p9 based on r2d2 - the stators don't directly overlap.

I'm not sure if I entirely follow. What counts as the "stator" here? I would think the rotors would have to be within one cell of each other (i.e., their bushings overlap). I hope that some method could be devised that could find the p9 R2-D2 mutual shifter.

When I said "stator" I meant bushing.

I meant to say that smashing r2d2 and sc7.0.2 will find the p9 mutual-shifter with two different stabilizations of r2d2, but I guess it's pretty difficult to read my mind on things like that.

So you are saying that you tested this and were able to find the other p9 shifter, right? The one with R2-D2 and the p7.

yes

[Scorbie]

Exciting to see new this approach being viable. I'll wish a new period oscillator be found.

[Hooloovoo]

Here's a 4n-1 reaction of 1-2-3-4:

Code: Select all

x = 14, y = 17, rule = B3/S23
4b2o$5bo$2o2bo$o2bob3o$bobobo2bo$2obo3bo2b2o$bo6b2o2bo$bob5o2bo2bo$2bo
4bobob2o$obob2o3bobo$2o2bo2bobo3bo$4bob2ob5o$5bo2bo$6b2o2b2o$11bo$10bo
$10b2o!

like the 6n+1, this would also work at p19.

A small p12, also with a 1-2-3-4 in it. I think 12 is the lowest known number of rotor cells in a true-period p12.

Code: Select all

x = 20, y = 15, rule = B3/S23
12b2o$4bo2bo2bo2bo2bo$2b3o2b4obo3b3o$bo3b2o4bo7bo$bo2bo3b2o4b4obo$2obo
2b2ob2o2bo4bo$2bob2obo3bo2b4o$2bo2bo2b3ob2o$3bobobo2bo4bo$2b2obob2obob
4o$5bo2bobo$5b2obo2b5o$8bo6bo$8b2o3bo$13b2o!

[Entity Valkyrie 2]

I don't understand why there are so many people asking this question:

Is there a P12 domino sparker:

Code: Select all

x = 4, y = 5, rule = B3/S23
bobo$b2o$b2o2$2o!

I made a StateInvestigator solution, but am unsure of a life solution. Is there a P12 domino sparker?

Code: Select all

x = 42, y = 42, rule = StateInvestigator
24.2E$22.E4.E$22.D4AD$22.E4AE$15.EDE5.E2AE2.ED$16.2AE9.EA2E$14.E.3A
11.A$16.3A8.A2.ACD$14.E.3A3.3A5.A$7.D8.2AE3.3A3.EA2E$5.E.C.E5.EDE3.A
3.A3.ED$4.DE3AED12.A$4.EA3.AE12.A$5.E3.E5.C5.C.E.C$.EDE3.A7.D4.CD.B.D
C6.EAE$.A2.E9.CD.EC2D5.2DC2.E5.E$EA5.A.A3.CD2.E13.D5.D$EA3.A4.A14.2E
4.E5AE$.A2.E.A3.A2.EB11.C5.E3.E$.EDE6.A8.A.A4.D$7.A.A3.CD4.2A5.DC$14.
CD3.2A5.ADC$7.A7.D10.A.A4.2A3.EDE$5.E3.E5.C2.2A6.ABE3.3A2.EA$4.E5.E4.
2E9.A.A4.2A3.A2.E$4.D5.D13.E.ADC9.A2.E$4.E5AE2.C2D5.2DCE.DC9.EA$6.E.E
6.CD.B.DC4.D7.A3.EDE$16.C.E.C5.C5.E3.E$31.EA3.AE$31.DE3AED$11.DE11.ED
E5.E.C.E$10.2EAE3.3A3.E.2A7.D$11.A5.A.A5.2AE$9.DCA2.A2.3A5.3A$11.A5.
2A6.2AE$10.2EAE9.E.2A$11.DE2.E2.E5.EDE$14.E4.E$14.D4AD$14.E4AE$16.2E!

[Sokwe]

Here's a 4n-1 reaction of 1-2-3-4:

Code: Select all

x = 14, y = 17, rule = B3/S23
4b2o$5bo$2o2bo$o2bob3o$bobobo2bo$2obo3bo2b2o$bo6b2o2bo$bob5o2bo2bo$2bo
4bobob2o$obob2o3bobo$2o2bo2bobo3bo$4bob2ob5o$5bo2bo$6b2o2b2o$11bo$10bo
$10b2o!

I would be surprised if this p7 is new, but I don't recognize it off hand. This is basically the opposite of the following 3n+1 (shown at p22):

Code: Select all

x = 21, y = 15, rule = B3/S23
11bo2bo2bo$11b7o$9b2o$8bo3b4ob3o$5bo2bob2o5bo2bo$3b5obo3bobo3bo$2bo6bo
2b2ob4o$bob3ob2o5bo$bobo4bob4o2bo$2o2b2o2bobo2bob2o$2bobo2b3o2bo2bo$2b
o2bo7b2o2bo$3bobob2obo3bob2o$4b2obob2o3bo$13b2o!

Or rather, you could consider the oscillator you posted as having the 3n+1 form. I don't recall anyone taking note of the 4n-1 phase shift. It could be useful. I'm not sure if it will work at p15 using p5 supports.

A small p12, also with a 1-2-3-4 in it. I think 12 is the lowest known number of rotor cells in a true-period p12.

Code: Select all

x = 20, y = 15, rule = B3/S23
12b2o$4bo2bo2bo2bo2bo$2b3o2b4obo3b3o$bo3b2o4bo7bo$bo2bo3b2o4b4obo$2obo
2b2ob2o2bo4bo$2bob2obo3bo2b4o$2bo2bo2b3ob2o$3bobobo2bo4bo$2b2obob2obob
4o$5bo2bobo$5b2obo2b5o$8bo6bo$8b2o3bo$13b2o!

This is a LCM oscillator that I don't recall seeing before. I wouldn't be surprised if it's known, however.

These are nice to see. Keep up the good work!

You should definitely test some potential phase-shifters against the three p17 billiard tables:

Code: Select all

x = 106, y = 43, rule = B3/S23
5$84bo$83bobo$84bo2b2o$88bo$82b6o$81bo6b3o$81b3o3bo3bob2o$88bo2bobobo$
57bo23b7obobobobo2bo$28bo19bo7bobo21bo6bobobo3bobobo$27bobo17bobo6bobo
21bo2b3o2b2obo3bo2bo$27bobo3b2o12bobo5b2o2b2o16b2obobo2bo5bo3bo$24b2ob
ob2o3bo9b2obob2o3bo2bobo17bobobob2o5b2obobobo$25bobo6bob2o7bobo6bob2o
2bo18bo3bo5bo2bobob2o$23bo2bobob3obo2bo5bo2bobob3obo3bobo15bo2bo3bob2o
2b3o2bo$23b2obobo4bobo7b2obobo4bo2b2obo15bobobo3bobobo6bo$26bobo2b2o2b
2o9bobo2b2o4bo18bo2bobobobob7o$26bobo3bobo11bobo3bobo2bo21bobobo2bo$
27b2obobobo12b2obobob3o23b2obo3bo3b3o$29bobobo15bobo32b3o6bo$29bobo17b
o2b3o32b6o$30b2o16b2o4bo31bo$86b2o2bo$89bobo$90bo!

You might get a non-trivial p34 that way (probably not, but it's worth a try). There is also this symmetric p17 variant that may allow a few different connections than the standard p17:

Code: Select all

x = 21, y = 17, rule = B3/S23
14b2o$14bo$12bobo$7bo3bobob2o$6bobo2bobobobo$6bo2bobob2o2bo$3b2obo3bo
4bobob2o$2bobob2o3b5obobo$bo2bo4bobo4bo2bo$bobob5o3b2obobo$2obobo4bo3b
ob2o$3bo2b2obobo2bo$3bobobobo2bobo$4b2obobo3bo$6bobo$6bo$5b2o!

I did not come up with this variant. It was pointed out to me some time ago, but I can't remember by whom.

[BlinkerSpawn]

A small p12, also with a 1-2-3-4 in it. I think 12 is the lowest known number of rotor cells in a true-period p12.

Code: Select all

x = 20, y = 15, rule = B3/S23
12b2o$4bo2bo2bo2bo2bo$2b3o2b4obo3b3o$bo3b2o4bo7bo$bo2bo3b2o4b4obo$2obo
2b2ob2o2bo4bo$2bob2obo3bo2b4o$2bo2bo2b3ob2o$3bobobo2bo4bo$2b2obob2obob
4o$5bo2bobo$5b2obo2b5o$8bo6bo$8b2o3bo$13b2o!

Reduction:

Code: Select all

x = 13, y = 13, rule = B3/S23
3b2o4b2o$2bobo4bo$2bo7bo$2ob4o2b2o$bobo3bo$bo3b2ob3o$2obo4bo2bo$bob2ob
o3bobo$bo2bobo4bo$2bobo2b4o$3b2o$9b2o$9b2o!

The standard 3-cell p3 rotor can't replace the p6, so beating 12 rotor cells is gonna be pretty tough.

[Freywa]

I've made an update to the x-oscs-1-of-each.lif file in jslife – the one-of-each-period oscillator collection. Besides adding in the p23, I also included smaller and more recent oscillators and different mechanisms.

Code: Select all

#C One-of-each collection of every known oscillator period up to 43.
#C All periods 43 and over can be achieved using snark loops.
#C A tub before the number means no such oscillator is known.
#C A mango means only trivial oscillators are known.
x = 358, y = 310, rule = B3/S23
6b2o47b2o5b2obo52b2obo6b2obo15b2o51b2obo6b2obo76b2o3b2o4b2obo13b2o$7bo
48bo5bob2o52bob2o6bob2o15bobo50bob2o6bob2o76b2o3b2o4bob2o13b2o$6bo48bo
4b2o4b2o54b2o2b2o4b2o15bo54b2o2b2o4b2o21bo61b2o4b2o$6b2o47b2o3bo5bo16b
2o37bo3bo5bo16b2o5bo47bo3bo5bo21bobo51b2o3b2o2bo5bo$61bo5bo15bo2bo36bo
3bo5bo13b2o6bobo47bo3bo5bo19bo3b2o49bobobobo3bo5bo22bo$6b2o47b2o3b2o4b
2o11bo4bo3bo33b2o2b2o4b2o12bo2b3o4bo47b2o2b2o4b2o8b2o9bo3b2o3b2o46bobo
4b2o4b2o21bo2bo$7bo48bo3bo5bo13b2o3bob2o29b2obo4bo5bo14b2o3bo47b2obo4b
o5bo9b2o9bo3b2o3b2o45b2obo4bo5bo25bo$6bo10b2o36bo5bo5bo50bob2o5bo5bo
15b4o47bob2o5bo5bo20bobo56b2o3bo5bo20b2obo$6b2o9b2o36b2o3b2o4b2o8b2obo
3b2o31b2o8b2o4b2o15bo3b2o49b2o2b2o4b2o21bo58bo2b2o4b2o14b2o4b2o$60bo5b
o9bo3bo4bo30bo9bo5bo17bo2bobo48bo3bo5bo80bo3bo5bo13bob2o$6b2o47b2o4bo
5bo10bo2bo35bo9bo5bo17bobobobo47bo3bo5bo79b2o3bo5bo11bo$7bo48bo3b2o4b
2o12b2o34b2o8b2o4b2o18b2obob3o44b2o2b2o4b2o80bo2b2o4b2o11bo2bo$6bo48bo
6b2obo52b2obo6b2obo22bobo3bo39b2obo6b2obo81bo5b2obo15bo$6b2o47b2o5bob
2o52bob2o6bob2o22bobo2b2o39bob2o6bob2o81b2o4bob2o$155bo$330b2o$330b2o
7$291bo$290bobo$3b2obo284bo$3bob2o154b2o5bo125b2o3b2o3b2o$7b2o50b2o4b
2o55b2obo5b2o28bo5bobo124b2o3b2o4bo$7bo52bo5bo12b2o41bob2o6bo29b3obo2b
o134bo$8bo50bo5bo14bo45b2o3bo23b2o7bobobob2o122b2o3b2o3b2o$7b2o50b2o4b
2o12bo46bo4b2o22b2o9bobobobo121bobobobo$3b2obo11bo60b2o46bo19bo21bo2bo
30b2obo5b2o82bobo5b2o$3bob2o11bo40b2o4b2o59b2o3b2o13bobo21bob2o29bob2o
6bo17b2obo2bob2o54b2obo6bo$b2o15bo41bo5bo12b4o39b2obo6bo13bobo6b2o4b2o
2bo2b3obo34b2o3bo11b2o4bo2bo4bo2bo4b2o51b2o3bo$bo57bo5bo12bo3bo39bob2o
5bo11b2obob2o4bo2bo2bo2bo2bo4bo2bo32bo4b2o10b2o5bobo4bobo5b2o52bo3b2o$
2bo56b2o4b2o10bob3o38b2o9b2o10bo2bo4bo2bo2bo2bo2bo4b2obob2o33bo23bo6bo
59bo$b2o74bo3bo4bob2o30bo24bob3o2bo2b2o4b2o6bobo35b2o3b2o85b2o3b2o$3b
2obo52b2o4b2o8b2obobo5b2obo31bo9b2o11b2obo21bobo31b2obo6bo86bo4bo$3bob
2o53bo5bo9bobo41b2o10bo12bo2bo21bo32bob2o5bo86bo4bo$59bo5bo10bobo43b2o
bo5bo13bobobobo9b2o44b2o3b2o85b2o3b2o$59b2o4b2o10bo44bob2o5b2o13b2obob
obo7b2o44bo$148bo2bob3o52bo3b2o18bo6bo$148bobo5bo50b2o4bo10b2o5bobo4bo
bo5b2o$149bo5b2o46b2obo5bo11b2o4bo2bo4bo2bo4b2o$203bob2o5b2o17b2obo2bo
b2o6$3b2obo$3bob2o$7b2o$7bo282b2o3b2o4b2obo30b2o$8bo281b2o3b2o4bob2o
30b2o$7b2o46b2o5b2obo52b2obo6b2obo173b2o16bo$3b2obo15bo33bo5bob2o11bo
40bob2o6bob2o158b2o3b2o8bo16bobo$3bob2o10b4o3bo30bo10b2o9b3o7b2o33b2o
8b2o156bobobobo9bo16bo11b3o$7b2o11bo3bo30b2o9bo13bo6bo34bo9bo9b2o148bo
bo10b2o23b2o2bob2o$7bo16bo42bo11b2o4bobo35bo9bo9bo147b2obo6b2obo16b5o
4b2o2b2o$8bo12bo33b2o9b2o17b2o35b2o8b2o9bobo13b3o66b2o11b2o52b2o4bob2o
15bo4bo8b2o4b4o$7b2o13b2o32bo5b2obo16b2o34b2obo6b2obo12b2o3bo8bo3bo65b
2o11b2o53bo2b2o18bo2bo16bo4bo$3b2obo48bo6bob2o16b2o34bob2o6bob2o16bob
2o6bo4bo36b2obo6b2obo13bo2bo9bo2bo51bo3bo16bo2bob2o15bobo3bo$3bob2o48b
2o3b2o20b2o32b2o8b2o19bo4bo6b2obo37bob2o6bob2o14bobo9bobo52b2o3bo14bob
obo5bo11bobo3bo$60bo17b2o36bo9bo21bo3bo8bo3b2o37b2o8b2o80bo2b2o15bo2bo
4bobo10bo$55b2o4bo15bobo4b2o31bo9bo21b3o13bobo36bo9bo12b3o11b3o51bo5b
2obo14b2o2bo2bo4b2o4bo$56bo3b2o15bo6bo31b2o8b2o39bo37bo9bo11bo2bo9bo2b
o51b2o4bob2o19b2o4b2o5bo2bo$55bo6b2obo10b2o7b3o30b2obo6b2obo35b2o35b2o
8b2o10bo2bo11bo2bo87bo5b2o$55b2o5bob2o21bo30bob2o6bob2o68b2obo6b2obo
13b2o13b2o$200bob2o6bob2o$204b2o2b2o17b2o13b2o74b2o6bo$204bo3bo17bo2bo
11bo2bo73b2o5b2o5b2o$205bo3bo17bo2bo9bo2bo81bobo3bo2bo2b2o$204b2o2b2o
17b3o11b3o87bobo4bo2bo$200b2obo6b2obo104b3o11bo5bobobo$200bob2o6bob2o
14bobo9bobo70b2o2bob2o14b2obo2bo$227bo2bo9bo2bo69b2o2b2o16bo2bo$228b2o
11b2o74b2o4b4o5bo4bo$2b2o3b2o219b2o11b2o79bo4bo4b5o$2b2o3b2o312bobo3bo
$147b2o15b2o154bobo3bo7bo$2b2o3b2o139bo15bo155bo12bobo$2bobobobo10bobo
124bo19bo153bo13bo$4bobo15bo34b2o3b2obo80b5o11b5o153bo2bo$3b2obo11bo2b
o36bo3bob2o17b2ob2o62bo11bo158b2o$7b2o8bobobo35bo8b2o16bobo33b2obo4b2o
bo12b4o17b4o$8bo8bo2bo36b2o7bo16bobo34bob2o4bob2o12bo2bo17bo2bo$7bo10b
2o47bo16b2o38b2o6b2o27bo$7b2o48b2o7b2o16bo39bo7bo28bo$8bo49bo3b2obo19b
o39bo7bo15bo4b2ob2o2bob2o$7bo49bo4bob2o11bobo6b2o36b2o6b2o14b3o3b2obo
6b2o$7b2o48b2o7b2o9b2ob2o5b2ob2o28b2obo4b2obo15bo2b2o6bo$66bo12b2obo7b
2o28bob2o4bob2o15b3o12bo63bo4b2o87b2o$57b2o8bo9b2o4bo34b2o12b2o28bobo
60bobo2bobo87bobo$58bo7b2o9bo5b2o33bo13bo10b2o11b2o4bo2bo2b2o56bo4bo
60b2o3b2o2b2obo17bo4b2o$57bo4b2obo18bo34bo13bo9bo12b2o5b2o4bo30b2obo4b
2obo80b2o3b2o2bob2o13b4ob2o2bo2bo$57b2o3bob2o52b2o12b2o6b2obo12b2o11bo
b2o27bob2o4bob2o93b2o11bo2bobobobob2o$84b2o34b2obo4b2obo8bob2ob2o19b2o
b2obo31b2o6b2o78b2o3b2o6bo15bobobobo$84b2o34bob2o4bob2o13bo21bo36bo7bo
79bobobobo7bo15b2obobo$145bobo17bobo37bo7bo23b2o55bobo8b2o19bo$146b2o
17b2o37b2o6b2o19b2obo2bo53b2obo4b2obo$150bo11bo37b2obo4b2obo20bobo5b5o
52b2o2bob2o7b2o$146b5o11b5o33bob2o4bob2o20bo3bo5bo2bo52bo6b2o6bo7b2o$
146bo19bo37b2o6b2o18bo3b2o8bo50bo7bo7bobo5b2o$148bo15bo39bo7bo20bo8b2o
3bo49b2o7bo7b2o$3bob2o140b2o15b2o39bo7bo20bo2bo5bo3bo50bo6b2o$3b2obo
197b2o6b2o21b5o5bobo49bo3b2obo$b2o197b2obo4b2obo28bo2bob2o50b2o2bob2o
24bo$2bo197bob2o4bob2o29b2o76b3o8b2o$bo18b2o299bo7b2o$b2o15bo4bo296bo$
3bob2o11bo4bo300b2o22bo$3b2obo11bo4bo32b2o3b2o3b2o256bo21b3o$7b2o10bo
2bo34bo3b2o3b2o180bo4bo71b3o17bo$8bo8bobo2bobo31bo93b2o95bobo2bobo72bo
17b2o$7bo9b2o4b2o31b2o3b2o3b2o82b2o95b2o4bo$7b2o52bobobobo$3bob2o49b2o
5bobo15b2ob2o32b2obo5b2o3b2o219b2o$3b2obo50bo4b2obo15b2ob2o32bob2o5b2o
3b2o17bo157bo31bo12bo$56bo9b2o14bobo37b2o26b3o143b2o11b2o28bobo12bob2o
$56b2o9bo12bobobobo35bo4b2o3b2o15bo2bo144bo10bobo29b2o4b2o4b3o2bo$66bo
13bobobobo36bo3bobobobo9b2o5b2o143bo50b2o3bo3b2o$56b2o8b2o12b2o3b2o35b
2o5bobo11b2o150b5o14b2o35b4o$57bo9bo50b2obo6b2obo168bo13bo22b2o15bo$
56bo9bo51bob2o10b2o22b2o139b3o12bobo21bobo12b3o$56b2o8b2o48b2o15bo14b
2o5bob2o2b2o133bo15b2o22bo13bo$116bo15bo16bo5bobo3b2o133b4o35b2o14b5o$
117bo14b2o16b2o4bo137b2o3bo3b2o50bo$116b2o15bo17bo141bo2b3o4b2o4b2o29b
obo10bo$118b2obo10bo63b2o95b2obo12bobo28b2o11b2o$118bob2o10b2o61bo2bo
97bo12bo31bo$194bo2bo28b2o68b2o$154b2o39b2o3b2obo4b2o3b2o12bo$3b2obo
147b2o44bob2o4b2o3b2o12bobo9b2o$3bob2o197b2o22b2o9bo64b2o17bo$b2o201bo
3b2o3b2o18bo3bobo65bo17b3o$bo203bo2bobobobo17bobo2b2o63b3o21bo$2bo18b
2o181b2o4bobo18bo3bo66bo22b2o$b2o14b2obo179b2obo5b2obo18bo3bo94bo$3b2o
bo10b2o2bo2bo175bob2o9b2o16bo3bo84b2o7bo$3bob2o15bobo179b2o8bo13b2o2bo
bo84b2o8b3o$b2o4b2o14bo180bo8bo13bobo3bo87bo$bo5bo197bo7b2o12bo9b2o4b
2o$2bo5bo13b2o31b2o5bob2o81b2o4b2o9b2o38b2o8bo11b2o9bobo2bobo$b2o4b2o
13b2o32bo5b2obo81bobo2bobo9b2o34b2obo9bo25bo2bo92b2o$3b2obo48bo4b2o87b
o2bo47bob2o9b2o24bo2bo85b2o5bobo$3bob2o48b2o4bo56b2obo6bob2o16bo4bo86b
2o86b2o7bo$60bo57bob2o6b2obo16b6o183b2o$55b2o3b2o19bo4bo35b2o2b2o21b4o
20b2o$56bo5bob2o13b2ob4ob2o33bo4bo45bo150bo$55bo6b2obo15bo4bo36bo2bo
16b2o19b3o4bobo149bobob2o$55b2o9b2o54b2o2b2o16bo18bo3bo3b2o150bobobobo
$67bo50b2obo6bob2o12bobo4b3o8bo5bo151b2obobobobo2bo$55b2o9bo51bob2o6b
2obo13b2o3bo3bo7bo5bo151bo2bo2b2ob4o$56bo9b2o48b2o14b2o15bo5bo6bo5bo
153b2o4bo$55bo6bob2o50bo16bo15bo5bo7bo3bo3b2o155bobo$55b2o5b2obo51bo
14bo16bo5bo8b3o4bobo155b2o$116b2o14b2o11b2o3bo3bo18bo$118b2obo6bob2o
12bobo4b3o19b2o$118bob2o6b2obo12bo$143b2o20b4o84b2o$164b6o83bo$3bob2o
157bo4bo81bobo$3b2obo158bo2bo30b2obo6bob2o38b2o$7b2o13bo129b2o9bobo2bo
bo28bob2o6b2obo28b3o$8bo12bobo128b2o9b2o4b2o32b2o2b2o32bobo3b3o$7bo12b
obobo178bo4bo32b3o$7b2o11bobobo179bo2bo43b2o$5b2o10b2obo3bob2o175b2o2b
2o42bobo$6bo10bobo4bob2o171b2obo6bob2o23bo3bo12bo$5bo14b4o175bob2o6b2o
bo9b2o12bo3bo12b2o$5b2o196b2o8b2o8bo12bo3bo$3b2o17b2o31b2o5b2obo137bo
10bo8bobo$4bo17b2o32bo5bob2o15b2o71b2o48bo8bo10b2o$3bo51bo4b2o18bobo
35b2obo6b2obo17b2o4bo47b2o8b2o18b3o$3b2o50b2o3bo18b2obo4bo30bob2o6bob
2o15b3o3bobob2o40b2obo6bob2o14b3o3bobo$61bo19bo5b2o33b2o2b2o16bobo4bob
2obobo40bob2o6b2obo20b3o$55b2o3b2o24bo2bo32bo3bo17b2ob4obo3bo67b2o$56b
o5b2obo21b3o33bo3bo19bo4bo3bo66bobo$55bo6bob2o56b2o2b2o19bob2obobob3o
64bo$55b2o3b2o4b2o9b3o38b2obo6b2obo14b2o2bobob2o3bo62b2o$60bo5bo10bo2b
o37bob2o6bob2o16bo3bo4b2o$55b2o4bo5bo10b2o5bo30b2o8b2o4b2o10b3ob2o3b2o
b2o$56bo3b2o4b2o11bo4bob2o28bo9bo5bo10bobobobob2obo2bo$55bo6b2obo18bob
o30bo9bo5bo9bo3b2o2bobo3b2o$55b2o5bob2o18b2o30b2o8b2o4b2o10b3o4bob4o2b
o$118b2obo6b2obo14bo5bo5b2o$118bob2o6bob2o22bo$153b2o$3b2obo$3bob2o$b
2o4b2o$bo5bo14bo$2bo5bo12bobo175b2obo6b2obo30bo$b2o4b2o11bo3bo174bob2o
6bob2o28b3o$3b2obo12bo3bo179b2o2b2o31bo$3bob2o11bo3bo180bo3bo32b2o$b2o
4b2o8bo3bo182bo3bo21b3o$bo5bo10bobo132b2o48b2o2b2o21bobo$2bo5bo10bo
133b2o44b2obo6b2obo17b3o$b2o4b2o110b2obo4bob2o68bob2o6bob2o24b3o$3b2ob
o112bob2o4b2obo72b2o2b2o4b2o22bobo$3bob2o116b2o6b2o70bo3bo5bo23b3o$56b
2o3bob2o26b2o30bo8bo71bo3bo5bo13b2o$57bo3b2obo26bo32bo6bo19b2o50b2o2b
2o4b2o14bo$56bo8b2o11b2o9bobo31b2o6b2o19b2o45b2obo6b2obo13b3o$56b2o8bo
12bo9b2o28b2obo6b2o17bo4bo45bob2o6bob2o13bo$65bo13bobo3bo33bob2o7bo17b
o3bo$56b2o7b2o13b2o2bobo30b2o10bo18b2o7b3o$57bo5b2o18bo3bo29bo11b2o26b
o$56bo7bo18bo3bo30bo8b2o$56b2o5bo19bo3bo29b2o9bo9b2o21bo$63b2o19bobo2b
2o28b2obo4bo10b2o5b2o11bob2o$56b2o3b2o22bo3bobo27bob2o4b2o15b2obo11b2o
5b2o$57bo4bo17b2o9bo52bo21b2o$56bo4bo17bobo9b2o$56b2o3b2o16bo68bo$78b
2o66b3o7b2o$2b2obo147bo3bo$2bob2o146bo4bo75b2o11b2o$2o4b2o8b2o12b2o
120b2o79b2o11b2o$o5bo10bo12bo122b2o$bo5bo9bobo8bobo$2o4b2o10b2o8b2o
171b2obo4bob2o15bo8bo5bo8bo$2b2obo195bob2o4b2obo14bobo6b2o5b2o6bobo$2b
ob2o15b6o178b2o6b2o11bo2bo5bo2bo3bo2bo5bo2bo$6b2o143b2o52bo8bo12b2o6bo
bo5bobo6b2o$6bo11b2o8b2o61bo59b2o53bo6bo22b2o5b2o$7bo9bobo8bobo58b3o
113b2o6b2o$6b2o9bo12bo57bo112b2obo6b2o$2b2obo10b2o12b2o56b2o111bob2o7b
o9b2o33b2o$2bob2o199b2o4bo10b2o33b2o$205bo5b2o15b2o21b2o$55b2o5b2obo
140bo2b2o16bo2bo19bo2bo$56bo5bob2o20bo68b2o48b2o3bo15b2ob2o19b2ob2o$
55bo4b2o4b2o17b3o30b2obo6b2obo12bobo8b2o5b2o37b2obo4bo18bo23bo$55b2o3b
o5bo18bo2bo29bob2o6bob2o15bo14bo38bob2o4b2o$61bo5bo19b2o11b2o20b2o2b2o
4b2o9bo2bo13bobo$55b2o3b2o4b2o32bo21bo3bo5bo9bobobo13b2o$56bo5b2obo15b
2o15bobo22bo3bo5bo8bo2bo3b3o3b3o70bo23bo$55bo6bob2o14b2o9b2o5b2o22b2o
2b2o4b2o9b2o4bobo3bobo68b2ob2o19b2ob2o$55b2o3b2o4b2o13bobo7bobo24b2obo
6b2obo17b3o3b3o69bo2bo19bo2bo$60bo5bo8b2o5b2o9b2o23bob2o6bob2o96b2o21b
2o$55b2o4bo5bo6bobo15b2o22b2o8b2o4b2o9b2o77b2o33b2o$56bo3b2o4b2o6bo41b
o9bo5bo9bo2bo76b2o33b2o$55bo6b2obo7b2o11b2o29bo9bo5bo8bobo2bo12b2o$55b
2o5bob2o20bo2bo26b2o8b2o4b2o9bo16bobo$87b3o28b2obo6b2obo12b2obo14bo73b
2o5b2o$88bo29bob2o6bob2o14bo8b2o5b2o63b2o6bobo5bobo6b2o$155b2o69bo2bo
5bo2bo3bo2bo5bo2bo$227bobo6b2o5b2o6bobo$228bo8bo5bo8bo$85b2o$86bo$83b
3o147b2o11b2o$83bo149b2o11b2o4$52bo$51bobo143bo$52bo99b2o3b2o37bobo$
55b2o5b2obo52b2obo6b2obo19bo2bobo2bo37bo$56bo5bob2o52bob2o6bob2o15b2o
3b2o3b2o3b2o36b2obo6b2obo$55bo4b2o4b2o54b2o2b2o4b2o13bo15bo36bob2o6bob
2o$55b2o3bo5bo55bo3bo5bo11b2obo15bob2o37b2o2b2o4b2o$61bo5bo55bo3bo5bo
8bo2bob2o13b2obo2bo35bo3bo5bo$55b2o3b2o4b2o54b2o2b2o4b2o8b2obo19bob2o
36bo3bo5bo$56bo5b2obo52b2obo6b2obo13bo19bo38b2o2b2o4b2o$55bo6bob2o52bo
b2o6bob2o13b2o5bo5bo5b2o34b2obo6b2obo$55b2o9b2o48b2o14b2o17bobo3bobo
40bob2o6bob2o$66bo49bo15bo71b2o2b2o4b2o$55b2o10bo49bo15bo17b3o3b3o44bo
3bo5bo$56bo9b2o48b2o14b2o71bo3bo5bo$55bo6b2obo52b2obo6b2obo72b2o2b2o4b
2o$55b2o5bob2o52bob2o6bob2o68b2obo6b2obo$151bo7bo40bob2o6bob2o$150bobo
5bobo$151bo7bo12$228bo2bo$225bo2bo2bo2bo$224bob3o2b3obo$199b2obo6b2obo
12bo8bo3b2o$199bob2o6bob2o25b2o$203b2o2b2o4b2o19bo$203bo3bo5bo19bo2bo$
204bo3bo5bo15bo6bo$203b2o2b2o4b2o14bo7bo$199b2obo6b2obo17bob2o3bo6b2o$
199bob2o6bob2o21b3o7b2o$203b2o8b2o24b3o$203bo9bo24bo3bo$204bo9bo23bo$
203b2o8b2o23bo$199b2obo6b2obo26bo2bo$199bob2o6bob2o26bo2$239bobo$240bo
!