Glider synthesis discussion

[Sokwe]

This topic is for the discussion of glider syntheses and glider synthesis techniques. New glider syntheses, as well as improvements to old glider syntheses should be posted here.

Glider synthesis resources:
• Glider constructions at Game of Life info
• Mark D. Niemiec's Life Page
• Glider syntheses at the Life wiki

Related topics:
• c/2 spaceship syntheses
• Spiders, spaceships and syntheses
• Tight Salvo Synthesis

I have compiled a collection of many glider syntheses of oscillators of periods 3 to 177. Some of these can certainly be optimized. I have not yet written the credits for these syntheses, but most of them were found by David Buckingham, Mark Niemiec, and Jason Summers.

Edit (Nov 18, 2009): Added some well known syntheses up to period 177 to synthesis collection.

[Sokwe]

Here are some methods of oscillator construction found by Jason Summers. Some of these have been turned into syntheses, and some of them have not:

Code: Select all

x = 1054, y = 381, rule = B3/S23
60bo8bo248bo$38b2o19b2o8b2o248bo6b2o$3bo8bo25b2o18bo2bo6bo2bo245b3o6b
2o330bo$2bob3o2b3obo44bobo8bobo586b2o$3bo2bo2bo2bo47bo8bo222b2ob2o18bo
7bo308bo26b2o335b3o5bo4b5o7bo3b2o$6bo2bo281bobobo17bobo5b2ob2o306b2o
26bo333b3obo7bo3bo2bob3o2b2o4bo$291b2o2bobo16b2o7bo309b2o359bobo2bo3bo
7bob4ob2obo2b4o$295bo3bo334bo15b2o344b5o4bo5b3o2bobo2bo2bo2bo$32b3o8b
3o245b4o4bo18bo8b2o320b2o314bo42bobo5bob4o2bob2o$34bo8bo247bo7bo18bo7b
o2bo294b2o22b2o314bobo35bo7b4o5bo4b2o$32bobo3b2o3bobo13b3o6b3o222bo23b
obo6bobo294b2o339bobo27b5o7bo3b2o3bo3b2o3bo$32b2o3bo2bo3b2o272bo8bo
294b2o342bo28bo2bob3o2b2o4bo5b4o$38b2o254b3o21bo345b2o298bob2o28bob4ob
2obo2b4obo5bobo$314b2o6b2o339b2o299bo31b3o2bobo2bo2bo2bobo2b3o5bo$314b
2o5bo2bo313b2o22b2o301b3o27bo5bob4o2bob2ob4obo7bo$321bobo313b2o327b2o
27b4o5bo4b2o2b3obo2bo3bo$322bo313b2o15bo306bob2o6b2ob2o20b2o3bo3b2o3bo
7b5o4bo$653b2o302b4ob2o5bo5bo20bo5b4o7bo$627bo26b2o300bo5bo5b2ob4o19b
4obo5bobo15bo$627b2o26bo301b2ob2o6b2obo22bo2bobo2b3o5bo4b5o7bo$628b2o
334b2o28bob2ob4obo7bo3bo2bob3o2b2o$629bo334b3o27b2o2b3obo2bo3bo7bob4ob
2obo$967bo26bo7b5o4bo5b3o2bobo2bo$601bobo360b2obo30bo15bobo5bob4o$600b
o364bo42bo7b4o5bo$34b2o18b2o545bo2bo360bobo27bo4b5o7bo3b2o3bo3b2o$34b
2o18b2o545bobobo359bobo29bo3bo2bob3o2b2o4bo5b4o$337bobo262bo2bo360bo
27bo7bob4ob2obo2b4obo5bo$318bo19b2o263b2o55bo335bo5b3o2bobo2bo2bo2bobo
2b3o$318bo19bo321b2o337bobo5bob4o2bob2ob4obo$318bo315bo26b2o338b4o5bo
4b2o2b3obo2bo$35b3o14b3o262bo2bo313b2o26bo334bo3b2o3bo3b2o3bo7b5o$3bo
8bo24bo14bo268bo21b2o290b2o359b2o4bo5b4o7bo$2bobo6bobo21b3o14b3o21b2o
216bo21bo3b2o20bo2bo5bo284bo15b2o340b2obo2b4obo5bobo$3bob2o2b2obo57bo
4bo2bo4bo210bo21b2o4b2o18bo2bo5bo299b2o341bo2bo2bo2bobo2b3o5bo4b5o$6bo
2bo62b2o2b2o2b2o212b2o18b2o6bobo18b2o5b2o3b2o269b2o22b2o342b4o2bob2ob
4obo7bo3bo2bobo$6bo2bo62b2o6b2o214bo15bo2bo34bo3bo2bo267b2o368bo4b2o2b
3obo2bo3bo7bob3o$38b2o10b2o15b3o14b3o203b3o2bo2bo10b3o13b3o22bo4b2o
267b2o369b2o3bo7b5o4bo5b3o$37bobo10bobo239bobo3bo22bo2bo341b2o$36bobo
12bobo239bo4bo13bobo6b2o342b2o$37bo14bo260b2o4b2o24b3o292b2o22b2o$294b
3o18b2o3bo22b3o293b2o$315bo322b2o15bo$316bo2bo335b2o$318bo27bo282bo26b
2o$318bo26bobo281b2o26bo$318bo26bobo282b2o$346bo284bo5$29b2o23b2o$29b
2o23b2o702bo$758b2o233bob2ob3obobo2bobo3b3ob2o2bo3bo4bo$29b2o23b2o704b
o230bo2bo2bobob5o3bob2o4bob2ob3obobo$29b2o23b2o688bo13b2o230bob2obo4b
2obo3b5obobo2bo2bobob5o$4bo5bo719bo12bobo7bo4bo232bo2b2ob3o3bobo2bobob
3ob2obo4b2obo$3bobo3bobo718b2o10b2ob2o5bobo235bo4bobo4bo2b2o4bo3bo2b2o
b3o3bobo$4bo5bo24b3o9b3o682bo19bo2bo50bo5b2o5b3obo3bob3o9bob4obo8bobob
o4b4o4bobobo8bob4obo95b2o2bo3bo4b2o2bo4bobo4bobo4bo2b2o$5bo3bo25bobo9b
obo666bo13b2o21b2o46bob3o5bobobob2o5b2o3bobo3b2o5b2obobobo5b3obo3bo3bo
5bobo6bo3bo2bo3bobo94bob2ob3obobo2bobo3b3ob2o2bo3bo4b2o$5bo3bo25b3o9b
3o25b3o3b3o618bo12bobo7bo4bo17bo52bobo8bob4obo9b3obo3bob3o5b2o5bo9bo8b
o7b2o6bo101bo2bobob5o3bob2o4bob2ob3obobo2bobo$6bobo16b3o29b3o378b2o2bo
2bo256b2o10b2ob2o5bobo20bobo50bo6bo3bo2bo3bobo3b2o7bo2bo4b2o5bo2b2o3bo
3b3obo10bo6b2o7bo98bobo4b2obo3b5obobo2bo2bobob5o3bo$4bobobobo65bo5bo
239bo29b2o82b2obobo2bobo257bo19bo2bo18bo2bo7b2o47b2o6bo10bob3o3bo3b2o
2bo5b2o4bo2bo7b2o3bobo3bo2bo3bo6bobo99b2ob3o3bobo2bobob3ob2obo4b2obo3b
3o$4b2o3b2o64bobo3bobo237b3o28bo2bo48b2o31b5o3bo242bo13b2o21b2o20b2o7b
o2bo40bo6b2o7bo8bo9bo5b2o5b3obo3bob3o9bob4obo8bobobo4bo96bobo4bo2b2o4b
o3bo2b2ob3o3bobo2bo$77bo3bo274bo46b3o35bo32bo2bo196bo12bobo7bo4bo17bo
35bobo41bo2bo3bo6bobo5bo3bo3bob3o5bobobob2o5b2o3bobo3b2o5b2obobobo5b3o
bo3bo98bo3bo4b2o2bo4bobo4bobo4bo2b2o$75b3o3b3o210b2o3b2o26b3o22bo51bob
2o32b2o35bo196b2o10b2ob2o5bobo20bobo35bo42bobo8bobobo4b4o4bobobo8bob4o
bo9b3obo3bob3o5b2o5bo9bo96bob3obobo2bobo3b3ob2o2bo3bo4b2o2bo$25b3o29b
3o234bobobobo17bo6bo2b2o22b2o2bo48b3o24bo7bo30b3o3bo198bo19bo2bo18bo2b
o7b2o20b2o48bobo5b3obo3bo3bo5bobo6bo3bo2bo3bobo3b2o7bo2bo4b2o5bo2b2o3b
o3b3obo64b2o31bobob5o3bob2o4bob2ob3obobo2bobo$35b3o9b3o246bobo18b2o6bo
bo25b3o33bo10bo5bo25b2o36bo2b2o185bo13b2o21b2o20b2o7bo2bo18bo2bo47b2o
5bo9bo8bo7b2o6bo10bob3o3bo3b2o2bo5b2o4bo2bo7b2o63b2o2b2o30b2obo3b5obob
o2bo2bobob5o3bob2o$35bobo9bobo245bobobo18bo7bo19b2ob2o35b4o9b3o29bobo
8b3o25bo2bo185bobo7bo4bo17bo35bobo20bobo5b2ob2o38bo2b2o3bo3b3obo10bo6b
2o7bo8bo9bo5b2o5b3obo3bob3o73b2o26b3o3bobo2bobob3ob2obo4b2obo3b5o$35b
3o9b3o240b2o3bo3bo3b2o41bo3b2o33bo13b2obo5b2ob2o18b3o8b2obo24b3o7b3o
175b2ob2o5bobo20bobo35bo17bo4bo7bobo38b2o4bo2bo7b2o3bobo3bo2bo3bo6bobo
5bo3bo3bob3o5bobobob2o5b2o3bobo3b2o67bo2bo25bo4bo2b2o4bo3bo2b2ob3o3bob
o2bobobo$290bo2b2o2bo2b2o2bo16b2o10b2o16bo32bo16b3o4b2obobo19bob2o6bo
24bo2bo196bo2bo18bo2bo7b2o20b2o21b2o13bo40b3obo3bob3o9bob4obo8bobobo4b
4o4bobobo8bob4obo9b3obo3bo69bo26bo4b2o2bo4bobo4bobo4bo2b2o4bo$291b2o4b
o4b2o19bo9b2o12bo3bo31bo17b2o9b2o18b4o233b2o20b2o7bo2bo18bo2bo19bo54b
2o5b2o3bobo3b2o5b2obobobo5b3obo3bo3bo5bobo6bo3bo2bo3bobo3b2o7bo2bo68bo
bo2bobo19b2obobo2bobo3b3ob2o2bo3bo4b2o2bo4bo$29b2o23b2o237bob2ob2obo
18bobo9bobo13bobo11bobo18bo9b2o10b2o24bo6b2o16bo22bo2bo181bo35bobo20bo
bo5b2ob2o10b2o52bobo9b3obo3bob3o5b2o5bo9bo8bo7b2o6bo10bob3o3bo3bo72bo
21bob5o3bob2o4bob2ob3obobo2bobo3b3o$29b2o23b2o235b2o4bo4b2o16b2o9bo29b
o3bo17bo9bo11b2o5b2o24b3o8bo5bobo10b3o7b3o182bobo35bo17bo4bo7bobo12bo
53bobo3b2o7bo2bo4b2o5bo2b2o3bo3b3obo10bo6b2o7bo8bo9bo74bo2bo19b2obo3b
5obobo2bo2bobob5o3bob2o$290bo2b2o2bo2b2o2bo15b2o10b2o27bo20b2o9bo18b2o
18bo5bo11bo5bo20bo2bo181bo2bo7b2o20b2o21b2o13bo74bob3o3bo3b2o2bo5b2o4b
o2bo7b2o3bobo3bo2bo3bo6bobo5bo3bo3bob3o76b2o19bo3bobo2bobob3ob2obo4b2o
bo3b5obobo$29b2o23b2o234b2o3bo3bo3b2o56b2o3bo26bo11b2o9b2o13bobo5bo8b
3o25b2o2bo182b2o7bo2bo18bo2bo19bo90bo9bo5b2o5b3obo3bob3o9bob4obo8bobob
o4b4o4bobobo79b2o2b2o17bo2b2o4bo3bo2b2ob3o3bobo2bobob3o$29b2o23b2o239b
obobo28bo7bo25b2ob2o25bo12bobob2o4b3o14bo16b2o6bo15bo3b3o192bobo20bobo
5b2ob2o10b2o85bo3bo3bob3o5bobobob2o5b2o3bobo3b2o5b2obobobo5b3obo3bo3bo
5bobo6bo79b2o18b2o2bo4bobo4bobo4bo2b2o4bo3bo$296bobo28bobo6b2o19b3o31b
o14b2ob2o5bob2o33b4o16bo199bo17bo4bo7bobo12bo83b4o4bobobo8bob4obo9b3ob
o3bob3o5b2o5bo9bo8bo7b2o95bobo2bobo3b3ob2o2bo3bo4b2o2bo4bobo$294bobobo
bo24b2o2bo6bo19bo2b2o26b4o26b3o25bo6b2obo17bo2bo190b2o21b2o13bo94bo3bo
5bobo6bo3bo2bo3bobo3b2o7bo2bo4b2o5bo2b2o3bo3b3obo10bo6b2o94b4o3bob2o4b
ob2ob3obobo2bobo3b3ob2o$294b2o3b2o24b3o32bo26bo24bo5bo24bob2o8b3o208bo
2bo19bo111bo8bo7b2o6bo10bob3o3bo3b2o2bo5b2o4bo2bo7b2o3bobo3bo2bo3bo96b
o3b5obobo2bo2bobob5o3bob2o4bo$356bo54b3o30b3o8bobo209bobo5b2ob2o10b2o
70bo38bo10bo6b2o7bo8bo9bo5b2o5b3obo3bob3o9bob4obo101bobo2bobob3ob2obo
4b2obo3b5obobo2bo$331b3o23bo2bo50b2obo40b2o206bo4bo7bobo12bo70b2o37b2o
3bobo3bo2bo3bo6bobo5bo3bo3bob3o5bobobob2o5b2o3bobo3b2o5b2obobobo99bo2b
2o4bo3bo2b2ob3o3bobo2bobob3ob2o$332bo26b2o52b3o32bo7bo205b2o13bo86bo
42bob4obo8bobobo4b4o4bobobo8bob4obo9b3obo3bob3o5b2o5bo95b2o2bo4bobo4bo
bo4bo2b2o4bo3bo2bo$413b2o32b2o212bo86bo13b2o37b2o5b2obobobo5b3obo3bo3b
o5bobo6bo3bo2bo3bobo3b2o7bo2bo4b2o5bo2b2o98bobo3b3ob2o2bo3bo4b2o2bo4bo
bo$447bo214b2o70bo12bobo7bo4bo40bob3o5b2o5bo9bo8bo7b2o6bo10bob3o3bo3b
2o2bo5b2o4bo95bo3bob2o4bob2ob3obobo2bobo3b3ob2o2bo$443bo3b5o211bo70b2o
10b2ob2o5bobo43bo4b2o5bo2b2o3bo3b3obo10bo6b2o7bo8bo9bo5b2o5b3obo98b5ob
obo2bo2bobob5o3bob2o4bob2o$442bobo2bobob2o283bo19bo2bo43b2o2bo5b2o4bo
2bo7b2o3bobo3bo2bo3bo6bobo5bo3bo3bob3o5bobobob2o5b2o94bo2bobob3ob2obo
4b2obo3b5obobo2bo2bo$443bo2bo2b2o269bo13b2o21b2o42bo5b2o5b3obo3bob3o9b
ob4obo8bobobo4b4o4bobobo8bob4obo100b2o4bo3bo2b2ob3o3bobo2bobob3ob2obo$
706bo12bobo7bo4bo17bo47bo5bobobob2o5b2o3bobo3b2o5b2obobobo5b3obo3bo3bo
5bobo6bo3bo2bo3bobo3b2o96bo4bobo4bobo4bo2b2o4bo3bo2b2obo$706b2o10b2ob
2o5bobo20bobo53bob4obo9b3obo3bob3o5b2o5bo9bo8bo7b2o6bo10bo95bo3b3ob2o
2bo3bo4b2o2bo4bobo4bobo$61b2ob2o642bo19bo2bo18bo2bo7b2o39bo3bo2bo3bobo
3b2o7bo2bo4b2o5bo2b2o3bo3b3obo10bo6b2o7bo8bo95bob2o4bob2ob3obobo2bobo
3b3ob2o2bo$61b2ob2o272bobo351bo13b2o21b2o20b2o7bo2bo37b2o6bo10bob3o3bo
3b2o2bo5b2o4bo2bo7b2o3bobo3bo2bo3bo6bobo5bo97b4obobo2bo2bobob5o3bob2o
4bob2ob3o$55b2o13b2o265bo2bo337bo12bobo7bo4bo17bo35bobo39b2o7bo8bo9bo
5b2o5b3obo3bob3o9bob4obo8bobobo4b4o96bobob3ob2obo4b2obo3b5obobo2bo2bob
o$27bo15bo11b2ob2o7b2ob2o267b2o337b2o10b2ob2o5bobo20bobo35bo40bo6bobo
5bo3bo3bob3o5bobobob2o5b2o3bobo3b2o5b2obobobo5b3obo3bo3bo101bo3bo2b2ob
3o3bobo2bobob3ob2obo4bo$26b2o15b2o13b2o7b2o275b3o333bo19bo2bo18bo2bo7b
2o20b2o49bobobo4b4o4bobobo8bob4obo9b3obo3bob3o5b2o5bo9bo$26b2o2bo2b2ob
2o2bo2b2o308b3o308bo13b2o21b2o20b2o7bo2bo18bo2bo46b3obo3bo3bo5bobo6bo
3bo2bo3bobo3b2o7bo2bo4b2o5bo2b2o3bo3b3obo$5bo3bo18b2o3b2ob2o3b2o316b2o
302bobo7bo4bo17bo35bobo20bobo5b2ob2o35bo9bo8bo7b2o6bo10bob3o3bo3b2o2bo
5b2o4bo2bo7b2o3bobo$bob2obobob2obo45b2o5b2o231b2ob2o55bo2bo299b2ob2o5b
obo20bobo35bo17bo4bo7bobo33b2o3bo3b3obo10bo6b2o7bo8bo9bo5b2o5b3obo3bob
3o9bo$obo3bobo3bobo44b2o5b2o230bobobo28bo18bo8bobo310bo2bo18bo2bo7b2o
20b2o21b2o13bo36bo2bo7b2o3bobo3bo2bo3bo6bobo5bo3bo3bob3o5bobobob2o5b2o
3bobo3b2o5bo$bo4bobo4bo284bo3bo2bo24bo19bo322b2o20b2o7bo2bo18bo2bo19bo
51bo3bob3o9bob4obo8bobobo4b4o4bobobo8bob4obo9b3obo3bob3o$5b2ob2o20bo9b
o18b2o5b2o228b2o2bo2b3o26bo17bo317bo35bobo20bobo5b2ob2o10b2o50b2o3bobo
3b2o5b2obobobo5b3obo3bo3bo5bobo6bo3bo2bo3bobo3b2o7bo2bo4b2o$30bo9bo18b
2o5b2o227bo4bo29b3o33bo300bobo35bo17bo4bo7bobo12bo55b3obo3bob3o5b2o5bo
9bo8bo7b2o6bo10bob3o3bo3b2o2bo$30bo9bo254b2ob2ob2ob2o59bo300bo2bo7b2o
20b2o21b2o13bo64b2o7bo2bo4b2o5bo2b2o3bo3b3obo10bo6b2o7bo8bo9bo5b2o$
300bo4bo61bo299b2o7bo2bo18bo2bo19bo81bob3o3bo3b2o2bo5b2o4bo2bo7b2o3bob
o3bo2bo3bo6bobo5bo3bo3bob3o5bobo117b2o$58b2o7b2o226b3o2bo2b2o46b3o11b
3o308bobo20bobo5b2ob2o10b2o79bo9bo5b2o5b3obo3bob3o9bob4obo8bobobo4b4o
4bobobo8bo118b2o$55b2ob2o7b2ob2o223bo2bo3bo30bo17bo285bo3bo35bo17bo4bo
7bobo12bo76bo3bo3bob3o5bobobob2o5b2o3bobo3b2o5b2obobobo5b3obo3bo3bo5bo
bo6bo3bo$55b2o13b2o226bobobo30bo19bo317b2o21b2o13bo90b2o4bobobo8bob4ob
o9b3obo3bob3o5b2o5bo9bo8bo7b2o121bo$61b2ob2o231b2ob2o31bo18bo251b2o32b
3o29bo2bo19bo111bobo6bo3bo2bo3bobo3b2o7bo2bo4b2o5bo2b2o3bo3b3obo10bo6b
2o120b2o$61b2ob2o302bo235b2o23bo3bo4b3o30bobo5b2ob2o10b2o70bo38bo7b2o
6bo10bob3o3bo3b2o2bo5b2o4bo2bo7b2o3bobo3bo2bo3bo120bo2bo$368bo262b2ob
2obo3bo25bo4bo7bobo12bo70b2o39bo6b2o7bo8bo9bo5b2o5b3obo3bob3o9bob4obo
8bobo115bobo$357bobo8bo235b4o23b2ob2o2b3o25b2o13bo86bo32bobo3bo2bo3bo
6bobo5bo3bo3bob3o5bobobob2o5b2o3bobo3b2o5b2obobobo5b3obo115b2o$337b3o
16bo2bo243bo4bo22b2ob2o2b3o24bo86bo13b2o34bob4obo8bobobo4b4o4bobobo8bo
b4obo9b3obo3bob3o5b2o5bo$343b2o13b2o242bobob2obob2o16bo3bo32b2o70bo12b
obo7bo4bo36b2obobobo5b3obo3bo3bo5bobo6bo3bo2bo3bobo3b2o7bo2bo4b2o5bo2b
2o3bo$343bo2bo16b3o236bobo4bob2o27bo3bo22bo70b2o10b2ob2o5bobo37b3o5b2o
5bo9bo8bo7b2o6bo10bob3o3bo3b2o2bo5b2o4bo2bo$334bo8bobo253b2obo4bobo23b
3o2b2ob2o97bo19bo2bo38b2o5bo2b2o3bo3b3obo10bo6b2o7bo8bo9bo5b2o5b3obo3b
ob2o$334bo264b2obob2obobo23b3o2b2ob2o81bo13b2o21b2o39bo5b2o4bo2bo7b2o
3bobo3bo2bo3bo6bobo5bo3bo3bob3o5bobobob2o5b2o3bo119bo$334bo268bo4bo23b
o3bob2ob2o67bo12bobo7bo4bo17bo45b2o5b3obo3bob3o9bob4obo8bobobo4b4o4bob
obo8bob4obo9b2o118bo$350bo18bo234b4o25b3o4bo3bo65b2o10b2ob2o5bobo20bob
o43bobobob2o5b2o3bobo3b2o5b2obobobo5b3obo3bo3bo5bobo6bo3bo2bo3bobo3b2o
103b2o10b3o5bo$349bo19bo263b3o76bo19bo2bo18bo2bo7b2o35bob4obo9b3obo3bo
b3o5b2o5bo9bo8bo7b2o6bo10bob3o63b4o32b2o3b2o$32b2o17b2o20bo5bo271bo17b
o236b2o88bo13b2o21b2o20b2o7bo2bo33bo2bo3bobo3b2o7bo2bo4b2o5bo2b2o3bo3b
3obo10bo6b2o7bo8bo66bo7b2o31bo2bo21bo$5b2o3b2o20b2o17b2o17bo2bo5bo2bo
252b3o11b3o254b2o24bo3bo45bo12bobo7bo4bo17bo35bobo37bo10bob3o3bo3b2o2b
o5b2o4bo2bo7b2o3bobo3bo2bo3bo6bobo5bo3bo3bo61bo3b2o2b2o30b2ob2o19b2ob
2o$5bobobobo22bo15bo18bob2ob2ob2ob2obo251bo346b2o10b2ob2o5bobo20bobo
35bo40bo8bo9bo5b2o5b3obo3bob3o9bob4obo8bobobo4b4o4bobo62bo2b2o36bo21bo
2bo$7bobo21b3o17b3o283bo346bo19bo2bo18bo2bo7b2o20b2o43bobo5bo3bo3bob3o
5bobobob2o5b2o3bobo3b2o5b2obobobo5b3obo3bo3bo5bobo127b2o3b2o$7bobo21b
3o17b3o282bo33b3o295bo13b2o21b2o20b2o7bo2bo18bo2bo39bobobo4b4o4bobobo
8bob4obo9b3obo3bob3o5b2o5bo9bo8bo115bo5b3o10b2o$4bo2bobo2bo25b3o3b3o
26b2o3b2o272bo17bo296bobo7bo4bo17bo35bobo20bobo5b2ob2o28b2obo3bo3bo5bo
bo6bo3bo2bo3bobo3b2o7bo2bo4b2o5bo2b2o3bo3b3obo10bo113bo$4b2obobob2o24b
o2bo3bo2bo24bo2bobo2bo271bo19bo293b2ob2o5bobo20bobo35bo17bo4bo7bobo37b
o8bo7b2o6bo10bob3o3bo3b2o2bo5b2o4bo2bo7b2o3bobo3bo113bo$7bobo26bo11bo
23b2obobob2o260bobo8bo18bo304bo2bo18bo2bo7b2o20b2o21b2o13bo30bo3b3obo
10bo6b2o7bo8bo9bo5b2o5b3obo3bob3o9bob4o$4b2obobob2o24bo2bo3bo2bo27bobo
262bo2bo333b2o20b2o7bo2bo18bo2bo19bo46bo7b2o3bobo3bo2bo3bo6bobo5bo3bo
3bob3o5bobobob2o5b2o3bobo3b2o5b2obobo$4bo2bobo2bo25b3o3b3o25b2obobob2o
261b2o328bo35bobo20bobo5b2ob2o10b2o44bob3o9bob4obo8bobobo4b4o4bobobo8b
ob4obo9b3obo3bob3o5bo$7bobo21b3o17b3o18bo2bobo2bo266b3o321bobo35bo17bo
4bo7bobo12bo46bobo3b2o5b2obobobo5b3obo3bo3bo5bobo6bo3bo2bo3bobo3b2o7bo
2bo4b2o$7bobo21b3o17b3o19b2o3b2o276b3o311bo2bo7b2o20b2o21b2o13bo60b3ob
o3bob3o5b2o5bo9bo8bo7b2o6bo10bob3o3bo3b2o2bo5bo114b2o$5bobobobo22bo15b
o311b2o307b2o7bo2bo18bo2bo19bo80bo2bo4b2o5bo2b2o3bo3b3obo10bo6b2o7bo8b
o9bo5b2o118bobo$5b2o3b2o20b2o17b2o309bo2bo314bobo20bobo5b2ob2o10b2o72b
3o3bo3b2o2bo5b2o4bo2bo7b2o3bobo3bo2bo3bo6bobo5bo3bo3bob3o5bobobob2o
113bo2bo$32b2o17b2o16bob2ob2ob2ob2obo278bobo316bo17bo4bo7bobo12bo80bo
5b2o5b3obo3bob3o9bob4obo8bobobo4b4o4bobobo8bob4o115b2o$70bo2bo5bo2bo
592b2o21b2o13bo89bob3o5bobobob2o5b2o3bobo3b2o5b2obobobo5b3obo3bo3bo5bo
bo6bo3bo2bo3bo115bo$73bo5bo594bo2bo19bo103bobobo8bob4obo9b3obo3bob3o5b
2o5bo9bo8bo7b2o6bo$675bobo5b2ob2o10b2o70bo29bobo6bo3bo2bo3bobo3b2o7bo
2bo4b2o5bo2b2o3bo3b3obo10bo6b2o7bo114b2o$671bo4bo7bobo12bo70b2o28bo7b
2o6bo10bob3o3bo3b2o2bo5b2o4bo2bo7b2o3bobo3bo2bo3bo6bobo114b2o$670b2o
13bo86bo29bo6b2o7bo8bo9bo5b2o5b3obo3bob3o9bob4obo8bobobo$331b2o336bo
86bo13b2o30bo2bo3bo6bobo5bo3bo3bob3o5bobobob2o5b2o3bobo3b2o5b2obobobo
5b3obo3bo$330bobo337b2o70bo12bobo7bo4bo29b3obo8bobobo4b4o4bobobo8bob4o
bo9b3obo3bob3o5b2o5bo9bo$330bobo338bo70b2o10b2ob2o5bobo34bobobo5b3obo
3bo3bo5bobo6bo3bo2bo3bobo3b2o7bo2bo4b2o5bo2b2o3bo3b3obo$331bo412bo19bo
2bo35b2o5bo9bo8bo7b2o6bo10bob3o3bo3b2o2bo5b2o4bo2bo7bo$297bo3bo426bo
13b2o21b2o37bo2b2o3bo3b3obo10bo6b2o7bo8bo9bo5b2o5b3obo3bob3o$297bo3bo
30bo381bo12bobo7bo4bo17bo42b2o4bo2bo7b2o3bobo3bo2bo3bo6bobo5bo3bo3bob
3o5bobobob2o5b2o3bobo3bo$297bo3bo30bo381b2o10b2ob2o5bobo20bobo42b3obo
3bob3o9bob4obo8bobobo4b4o4bobobo8bob4obo9b3obo$296b2o3b2o29bo383bo19bo
2bo18bo2bo7b2o29bob2o5b2o3bobo3b2o5b2obobobo5b3obo3bo3bo5bobo6bo3bo2bo
3bobo3b2o7bo$295bobo3bobo396bo13b2o21b2o20b2o7bo2bo28b3obo9b3obo3bob3o
5b2o5bo9bo8bo7b2o6bo10bob3o3bo$292b5o5b5o15b2o362bo12bobo7bo4bo17bo35b
obo32bobo3b2o7bo2bo4b2o5bo2b2o3bo3b3obo10bo6b2o7bo8bo9bo$321bo2bo7bo
353b2o10b2ob2o5bobo20bobo35bo40bob3o3bo3b2o2bo5b2o4bo2bo7b2o3bobo3bo2b
o3bo6bobo5bo3bo3bob3o$42b2o21b2o254b3o2b3o2bobo2b3o2b3o344bo19bo2bo18b
o2bo7b2o20b2o36bo8bo9bo5b2o5b3obo3bob3o9bob4obo8bobobo4b4o4bobobo$42b
2o21b2o265bo7bo2bo328bo13b2o21b2o20b2o7bo2bo18bo2bo35bo5bo3bo3bob3o5bo
bobob2o5b2o3bobo3b2o5b2obobobo5b3obo3bo3bo5bobo117bobo17bobo$32b2o2b3o
8b3o2b2ob2o2b3o8b3o2b2o215b5o5b5o34b2o328bobo7bo4bo17bo35bobo20bobo5b
2ob2o24bo4b4o4bobobo8bob4obo9b3obo3bob3o5b2o5bo9bo8bo7bo100bo8bo3bo6bo
8bo3bo6bo$32bobo2bo10bo2bobobobo2bo10bo2bobo218bobo3bobo366b2ob2o5bobo
20bobo35bo17bo4bo7bobo27bo3bo5bobo6bo3bo2bo3bobo3b2o7bo2bo4b2o5bo2b2o
3bo3b3obo10bo106bo19bo19bo$33bo18bo3bo18bo220b2o3b2o29bo347bo2bo18bo2b
o7b2o20b2o21b2o13bo29bo8bo7b2o6bo10bob3o3bo3b2o2bo5b2o4bo2bo7b2o3bobo
3bo2bo104bo6b2o4bo6bo6b2o4bo6bo$297bo3bo30bo348b2o20b2o7bo2bo18bo2bo
19bo42b2obo10bo6b2o7bo8bo9bo5b2o5b3obo3bob3o9bob4obo105b2o5b2obo3bo5b
2o5b2obo3bo5b2o$33bo18bo3bo18bo221bo3bo30bo343bo35bobo20bobo5b2ob2o10b
2o43b2o3bobo3bo2bo3bo6bobo5bo3bo3bob3o5bobobob2o5b2o3bobo3b2o5b2obobob
o104bobo5bo4bo6bobo5bo4bo6bobo$32bobo2bo10bo2bobobobo2bo10bo2bobo220bo
3bo373bobo35bo17bo4bo7bobo12bo49bob4obo8bobobo4b4o4bobobo8bob4obo9b3ob
o3bob3o5b2o105bo2bo5bo10bo2bo5bo10bo2bo$32b2o2b3o8b3o2b2ob2o2b3o8b3o2b
2o256bo340bo2bo7b2o20b2o21b2o13bo252b2o6bo2bobobo4b2o6bo2bobobo4b2o$
42b2o21b2o265bobo340b2o7bo2bo18bo2bo19bo269bo6bobo2bo2bo4bo6bobo2bo2bo
4bo$5b2o5b2o28b2o21b2o265bobo349bobo20bobo5b2ob2o10b2o273bo7bo11bo7bo$
2b2o4bobo4b2o315b2o351bo17bo4bo7bobo12bo267bo4bo2bo2bobo6bo4bo2bo2bobo
6bo$2b2obo2bobo2bob2o25b2o21b2o612b2o21b2o13bo281b2o4bobobo2bo6b2o4bob
obo2bo6b2o$bo6bobo6bo24b2o21b2o611bo2bo19bo296bo2bo10bo5bo2bo10bo5bo2b
o$2b6o3b6o15b2o2b3o8b3o2b2ob2o2b3o8b3o2b2o602bobo5b2ob2o10b2o295bobo6b
o4bo5bobo6bo4bo5bobo$32bobo2bo10bo2bobobobo2bo10bo2bobo598bo4bo7bobo
12bo296b2o5bo3bob2o5b2o5bo3bob2o5b2o$2b6o3b6o16bo18bo3bo18bo598b2o13bo
311bo6bo4b2o6bo6bo4b2o6bo$bo6bobo6bo655bo328bo19bo19bo$2b2obo2bobo2bob
2o16bo18bo3bo18bo888b2o36bo6bo3bo8bo6bo3bo8bo$2b2o4bobo4b2o15bobo2bo
10bo2bobobobo2bo10bo2bobo889bo42bobo17bobo$5b2o5b2o18b2o2b3o8b3o2b2ob
2o2b3o8b3o2b2o884bo3bo$42b2o21b2o893b2o3bo48bobo17bobo$42b2o21b2o894bo
bo$325b2o632bo3b2o$42b2o21b2o254bobo25bo609bo3bo$42b2o21b2o231b2ob2o
18bobo2b2o20bo609bo$32b2o2b3o8b3o2b2ob2o2b3o8b3o2b2o220bobobo21bo25bob
o607b2o$32bobo2bo10bo2bobobobo2bo10bo2bobo220bobobo2bo21bo2bo18bo693bo
$33bo18bo3bo18bo219b3obo2b3o22bobobo16bo50b3o628bo13bo$294bo21b2o3b2o
8bo15bo8bo26bo14bo3bo615bo13bo10b3o$33bo18bo3bo18bo218b4o3b4o16b2o24bo
3b5o22bo4bo14bo3bo603bo13bo10b3o7bo2b2o$32bobo2bo10bo2bobobobo2bo10bo
2bobo227bo11b3o9b3o14b2obo30bo3bo14bo3bob2o588bo13bo10b3o7bo2b2o11bo$
32b2o2b3o8b3o2b2ob2o2b3o8b3o2b2o217b3o2bob3o20b2o15bob2o2bo11bo16bobo
3bo16b4o3bo589bo10b3o7bo2b2o11bo11b3o$42b2o21b2o227bo2bobobo13bo8b2o3b
2o9bobo8bo6bo18bo3bo3b3o19bo587b3o7bo2b2o11bo11b3o7bo4bo$42b2o21b2o
230bobobo13bobobo30bobo5bo21bo3bo16bo5bo585bo2b2o11bo11b3o7bo4bo6b2o$
296b2ob2o16bo2bo21bo3bo2bo2bo5bo20bo3bo17bo595bo11b3o7bo4bo6b2o10b2o5b
2o$323bo22bo3b2ob2o3bo19bo3bo19bo3b4o587b3o7bo4bo6b2o10b2o5b2o10b2o$
319b2o2bobo20bo5bo2bo2bo3bo12b3o3bo3bo17b2obo3bo584bo4bo6b2o10b2o5b2o
10b2o6bo4bo$323bobo20bo5bobo25bo3bobo19bo3bo584b2o10b2o5b2o10b2o6bo4bo
7b3o$320b2o24bo6bo8bobo14bo3bo22bo3bo584b2o5b2o10b2o6bo4bo7b3o11bo$
345bo11bo2b2obo15bo4bo22b3o592b2o6bo4bo7b3o11bo11b2o2bo$356bob2o19bo
618bo4bo7b3o11bo11b2o2bo7b3o$349b5o3bo641b3o11bo11b2o2bo7b3o10bo$348bo
8bo643bo11b2o2bo7b3o10bo13bo$356bo282bo6b2obo3b2o3bo2bobo3b2ob3o6bo
321b2o2bo7b3o10bo13bo$356bo289bobo3bo5b2ob2ob2o4bo330b3o10bo13bo$90b3o
18b3o239bobo288bo4b2ob2ob2o5bo3bobo333bo13bo$89bo2bo18bo2bo241bo285b3o
b2o3bobo2bo3b2o3bob2o6b2o327bo$88bo2bo20bo2bo239bo286bo2b2o3b2o3bo5bob
2o8b2obo$89b2o22b2o528bo3b3obo2bobo4b2o6b2obo3b2o$643bo2bobo3bobo2bo
11bobo3bo$28bo34bo26b2o20b2o525bo4bobo2bob3o3bo9bo4b2ob2ob2o$27b3o32b
3o25b2o20b2o525bo5bo3b2o3b2o2bo6b3ob2o3bobo2bo$26bo3bo12bo4bo12bo3bo
573b2o3bo2bobo3b2ob3o6bo2b2o3b2o3bo$26b2ob2o11bobo2bobo11b2ob2o70bo2bo
504b2ob2ob2o4bo9bo3b3obo2bobo$36b2o5bo4bo5b2o78bobo2bobo465b3o29bob2o
5bo3bobo11bo2bobo3bobo$35bo2bo14bo2bo78b2o2b2o467bo30bo2bo3b2o3bob2o6b
2o4bobo2bob3o$36bobo14bobo73b3o12b3o494bo5bob2o8b2obo5bo3b2o3b2o$37bo
16bo74b3o12b3o460b3o30bobo4b2o6b2obo3b2o3bo2bobo3b2obo$3o6b3o19b3o24b
3o72bo2bo2bo2bo463bo3bo29bo2bo11bobo3bo5b2ob2ob2o4bo$3b2o2b2o22b3o24b
3o29b2o20b2o16b5obo2bob5o459bo5bo27bo3bo9bo4b2ob2ob2o5bo3bobo$31bobo
24bobo29b2o20b2o18b4o4b4o186bo270bo2bo7bo2bo24b2o2bo6b3ob2o3bobo2bo3b
2o3bob2o$b10o121b4o4b4o185bo271b2obo7bob2o23b2ob3o6bo2b2o3b2o3bo5bob2o
$5b2o24bobo24bobo28b2o22b2o15b5obo2bob5o163b2o4bo14bo2bo267bo2bo7bo2bo
26bo9bo3b3obo2bobo4b2o6b2o$31b3o24b3o27bo2bo20bo2bo17bo2bo2bo2bo151bob
o11bo2bo2bobo14b3o271bo5bo28bo11bo2bobo3bobo2bo11bo$31b3o24b3o28bo2bo
18bo2bo14b3o12b3o147bobob2o8bo2bo2bobo36b2o251bo3bo28b2o6b2o4bobo2bob
3o3bo9bo$37bo16bo35b3o18b3o15b3o12b3o145b2o4bo10b2o3bo10bo10b2o11b2o2b
2o252b3o35b2obo5bo3b2o3b2o2bo6b3ob2o$36bobo14bobo79b2o2b2o155b3o25bobo
9b2o10bo2bobo287b2obo3b2o3bo2bobo3b2ob3o6bo2b2o$35bo2bo14bo2bo77bobo2b
obo150b2obo2bo15bo12bo20bo2bobo254bo32bobo3bo5b2ob2ob2o4bo9bo3bo$36b2o
5bo4bo5b2o80bo2bo155bo2bo10b3obobo11bo5b2o14b2o2bobo251b3o29bo4b2ob2ob
2o5bo3bobo11bo2bo$26b2ob2o11bobo2bobo11b2ob2o227b5o10bo5bo11b2o4bo2bo
17bobo283bob2o3bobo2bo3b2o3bob2o6b2o4bobo$26bo3bo12bo4bo12bo3bo227bo
15b2o21bo2bo11b6o287b2o3b2o3bo5bob2o8b2obo5bo$27b3o32b3o268b2o12b2o
293b3obo2bobo4b2o6b2obo3b2o3bo2bo$28bo34bo265b2o20b2o288bobo3bobo2bo
11bobo3bo5b2obo$90b3o18b3o215b2o308bobo2bob3o3bo9bo4b2ob2ob2o$89bo2bo
18bo2bo525bo3b2o3b2o2bo6b3ob2o3bobo2bo3b2o$88bo2bo20bo2bo523bo2bobo3b
2ob3o6bo2b2o3b2o3bo5bo$89b2o22b2o524b2ob2ob2o4bo9bo3b3obo2bobo4bo$643b
o3bobo11bo2bobo3bobo2bo$90b2o20b2o527b2o3bob2o6b2o4bobo2bob3o3bo$90b2o
20b2o528bob2o8b2obo5bo3b2o3b2o2bo$642b2o6b2obo3b2o3bo2bobo3b2ob3o$650b
obo3bo5b2ob2ob2o4bo$648bo4b2ob2ob2o5bo3bobo$639bo6b3ob2o3bobo2bo3b2o3b
ob2o6bo$311b3o$314bo$311bo3bo$312b3o$323b2o$323b2o$314b2o$314bo$317bo
3bo$216b2o31b2o65b2o2bobo$216b2o31b2o69bo2bo$80bo5bo233bo2bo$77bo2bo5b
o2bo31b3ob3o49b3ob3o38bo21bo76bobo$77bo3bo3bo3bo31bo5bo49bo5bo37bobo
19bobo51b2o30bo$35b2o15b2o24bo2bo3bo2bo32bo5bo49bo5bo36bo3bo17bo3bo46b
2obo32b2o$2b3o5b3o22b2o7bo7b2o25b3o3b3o34bo3bo51bo3bo38bobo19bobo46bob
obob2o26bo3bo$5b2ob2o34bo78b3o53b3o110bobobo3bo26b3o$6bobo22b2o10bobo
10b2o79b3o25b3o63bo3bo57bo2b2o2bobo29b2o$6bobo22b2o11bo11b2o79bobo25bo
bo63bo3bo60bobo3bo28bob2o$3b3o3b3o32bo38bo53b3o25b3o63bo3bo61b5o29bo$
35b3o13b3o28bobo246bo$3b3o3b3o32bo38bo53b3o25b3o63bo3bo63b3o30bo$6bobo
22b2o11bo11b2o79bobo25bobo63bo3bo62bo2bo$6bobo22b2o10bobo10b2o79b3o25b
3o63bo3bo63b2o41b2o$5b2ob2o34bo78b3o53b3o153b3o4b2o$2b3o5b3o22b2o7bo7b
2o25b3o3b3o34bo3bo51bo3bo38bobo19bobo92bo$35b2o15b2o24bo2bo3bo2bo32bo
5bo49bo5bo36bo3bo17bo3bo88bo3bo$77bo3bo3bo3bo31bo5bo49bo5bo37bobo19bob
o90b3o$77bo2bo5bo2bo31b3ob3o49b3ob3o38bo21bo$80bo5bo$216b2o31b2o87b2o$
216b2o31b2o87bo$341bo3bo$340b2o2bobo$344bo2bo$344bo2bo$345bobo6$42b2o$
42b2o2$32bobo16bobo$6b2o24bo2bo14bo2bo$2bo2bo2bo2bo20bo2bo14bo2bo$2bo
8bo21b2o16b2o$2bo3b2o3bo$4bo4bo19b2o24b2o$bo2bo4bo2bo16b2o24b2o$2b2o6b
2o$522bo$29b2o24b2o464bobo$29b2o24b2o367bo2bo32b2o3b3o52bobo$424bo2bo
32b2o3bo2bo51b2o$33b2o16b2o371b2o39bo54bo$32bo2bo14bo2bo368bobo3bobo
35bo3bo48b2o$32bo2bo14bo2bo302b2o35b2o27bo4b2obo40bo48bobo$32bobo16bob
o266bobo33b3o26bo6bo2bo30b2obo38bo2bo49bo$321b2o35b2o24bobo6b2o32bo41b
3o$42b2o277bo36b3o22bo2bo39bo$42b2o314b3o23b2o3b3o33b2o25b2o$296b3o59b
3o28bo2bo59b2o$300bo89b3o7bo14b2o53b2o$297bobobo12bo9b2o60b2o11bobo24b
o43b2o48b3o$293bo3bo2bo14b2o6b2o23b2o8b3o25bobo10bobo10b4o9b2o39b2o52b
o$293bob2o5bo11b2o8bo23b2o36bobo6b2o3bo13bo5bo3bobo12b2o11b3o12bo51b3o
$293bo5b2obo18bo27b5o2bo26bo3b2o6bobo19bob2o2b3o12bo13bo2bo8bo9b2o3b3o
$295bo2bo3bo17b3o6bo20b4o2bo6bo2b3o13bobo10bobo14b2o2b3o20b2o11bo11b2o
8b2o3bo2bo$294bobobo21bo6b3o21b3o2bo6bo2b4o12bobo11b2o17b2o20b3o2b2o9b
o3bo21bo60bo$295bo32bo34bo2b5o12bo7b3o23bo12b3o2b2obo19bo21bo3bo20bo9b
o12bo6bo3bobo$297b3o25bo8b2o34b2o19bo2bo20b2o12bobo3bo5bo13bo2bo3b2o8b
2o11bo16b5o6b3o10bobo5bo3bobo$325b2o6b2o24b3o8b2o20b3o3b2o29b2o9b4o12b
3o3b2o9bo8bo2bo15bobo3bo5bobo10b3o6b5o$324b2o9bo61bo2bo28bo40bo12b3o
14bobo3bo6bo12bo9bo$389b2o6bobo39b2o29b2o29bo$359b3o26bo2bo6bo67b2o$
26b2o8b2o321b3o27b2o38b2o35b2o$26bo2bo4bo2bo290bo30b3o67bo54b2o34b3o$
26bobo6bobo289b2o31b2o66bo55b2o35bo$7b2o50b4o264bobo31b3o62bob2o89b3o$
6bo2bo21b2o329b2o61bob2o4bo32b3o$6bo2bo21b2o27b2o363bobo3bobo32bo2bo$
5b2o2b2o48bo2bo367b2o34bo$3b2o6b2o47b2o366bo2bo35bo3bo$3b2o6b2o18b2o
395bo2bo40bo$5b2o2b2o19bo2bo23bo6bo404bo2bo3b2o42bo$6bo2bo20bo2bo22bob
o4bobo404b3o3b2o41bobo$6bo2bo21b2o23bobo4bobo455b2o$7b2o48bo6bo456bo$
520b2o$31b2o27b2o457bobo$31b2o26bo2bo455bobo$60b2o457bo$26bobo6bobo$
26bo2bo4bo2bo21b4o261bo$26b2o8b2o285bobo$324b2o35bo$361bo47bo$361bo48b
o$321b2o87b2o$320bobo34b3o49b2o$320bobo33bo5bo46bo$320b2o9b2o23bo6b2o$
331bobo22bo5bo51b2o$332bo33bo98b3o49bo2b2o$326b3o23b3o11bo45b2o3bo47bo
bo39b3o7bo2b2o$325bo2bo28bobo5bobo32bo2b2o7b2o3bo47b3o49bo4b2o$325b3o
30bo11b3o28b3o10b2o44b2o43bo16b2o$312b3o23bo19bo43bo11b2o43bo2bo42bo$
311bo2bo22bobo22bo5bo39b2o11bo37bobo43bo$311b3o24b2o20b2o6bo39b2o10b3o
37bo19b2o39b3o$307bo54bo5bo37bo3b2o7b2o2bo56b2o$37bobo14bobo249bobo56b
3o38bo3b2o55bo$37bobo14bobo250b2o9b2o15b2o41bo77b3o7bobo5b3o$35bobobob
o10bobobobo258bobo14bobo26bo14bo29b2o46bobo6bobo6bobo$35b2o3b2o10b2o3b
2o258bobo14bobo26bo14bo77b3o5bobo7b3o$35b2o3b2o10b2o3b2o258b2o15b2o9b
2o16bo50bo50bo20b2o$3b2o12b2o326bobo26b3o36b2o71b2o16b3o$4bo12bo328bo
26bo5bo32b2o58bo49bo$4bobo8bobo15b3o5b3o6b3o5b3o253b2o24b3o30bo6b2o31b
o17bo39bobo48bo$5b2o3b2o3b2o15bo3bo3bo3bo4bo3bo3bo3bo252bobo22bo2bo30b
o5bo34bo17bo37bo2bo30b2o16bo$9bo2bo19bo3bo3bo3bo4bo3bo3bo3bo253bo23b3o
41bo48b2o37b2o9b3o19b2o4bo$8bo4bo18bo3bo3bo3bo4bo3bo3bo3bo264b3o40b3o
11bo47b2o32b3o14bobo21b2o2bo7b3o14bo2b2o$9bo2bo20b3o5b3o6b3o5b3o264bo
2bo45bobo5bobo46bo33bobo14b3o21b2o2bo14b3o7bo2b2o$5b2o3b2o3b2o308b3o
47bo11b3o75b3o9b2o56bo4b2o$4bobo8bobo303bo53bo60b2o38bo2bo43bo16b2o$4b
o12bo17b2o3b2o10b2o3b2o261bobo56bo5bo90bobo44bo$3b2o12b2o16b2o3b2o10b
2o3b2o262b2o9b2o43b2o6bo48b2o3bo37bo45bo$35bobobobo10bobobobo272bobo
45bo5bo36bo2b2o7b2o3bo22b2o75b3o$37bobo14bobo274bobo48b3o38b3o10b2o24b
2o20bo$37bobo14bobo274b2o91bo11b2o35b3o7bobo5b3o$380bo49b2o11bo29bobo
6bobo6bobo$380bo49b2o10b3o28b3o5bobo7b3o$328b2o50bo47bo3b2o7b2o2bo36bo
$328bobo97bo3b2o34b2o$329bo138b2o19bo32b3o$430b2o56bobo49bo$487bo2bo
49bo$436bo51b2o32b2o16bo$435b2o45b3o37b2o4bo$434b2o46bobo39b2o2bo7b3o$
435bo46b3o39b2o2bo$436bo!

[Sokwe]

I've been wondering whether some large oscillators composed of smaller components are synthesizeable. The ones I've looked at recently are the following p14 and p36 oscillators:

Code: Select all

#C p14 and p36
x = 207, y = 172, rule = B3/S23
150bo$150b3o$153bo$152b2o5$26bo6bo$20bo5b3o4bobo$19bobo7bo2bobo129b2o$
19bobo6b2o4bo5b2o121bo2bo$18b2ob2o17bo120bo2bobo$38bobo113b3o4bo3bo$
16b4ob2o7b2o6b2o114bo2bo3bo$16bo2bob2o6bob2o121bob2o6bo$29bo3bo128b2o$
30b3o$31bo2$24bo$23b3o$22bo3bo123b2o$23b2obo6b2obo2bo109bo2bo5b2obo$
16b2o6b2o7b2ob4o109bobo2bo3bo2bo$15bobo132bo3bo4b3o$15bo17b2ob2o116bo$
14b2o5bo4b2o6bobo114bo$21bobo2bo7bobo115b2o$20bobo4b3o5bo$22bo6bo5$
162b2o$162bo$163b3o$165bo13$15bo$16b2o$15b2o2$64bo$63bo$60bo2b3o136bo$
58b2o141bo$59b2o140b3o2$obo$b2o$bo32bo3bo6bobo78bo$32b2o3bo7b2o80b2o$
33b2o2b3o6bo79b2o2$17bo$15bobo$16b2o28bo$44b2o$45b2o$20b2o$19bobobo$
21bobobo$23b2o5$8b2o19b2o$9b2o17b2o$3b3o2bo21bo$5bo$4bo2$22b2o$21b2o$
23bo2$40b2o$39b2o$41bo3$25b3o172bo$20b2o5bo172bobo$19bobo4bo173b2o$21b
o2$191bobo$191b2o$144bo47bo$142bobo$4b2o137b2o$5b2o147bo18bo$4bo62bo
84bobo19b2o9bo$66b2o85b2o18b2o8b2o$66bobo95bo14bo4b2o$162bobo13b2o$
163b2o13bobo4$165b3o3bo$167bo4bo$166bo3b3o3$166bo$166b2o$165bobo3$167b
o$167b2o$166bobo2$151bo$151b2o$150bobo9$130b3o$132bo$131bo3b2o$134bobo
$136bo3$189b2o$188b2o$190bo4$188b3o$188bo$189bo3$187b3o$187bo$188bo4$
205bo$204b2o$204bobo4$136b2o$135bobo$137bo!

For the p14 oscillator I have been unable to synthesize the two clocks after synthesizing the eaters, but I haven't attempted to synthesize the eaters after the clocks. The p36 oscillator only needs two B-heptominoes to be added and so shouldn't be too difficult to complete.

I have also been considering the following p7 as a candidate for a glider synthesis:

Code: Select all

x = 243, y = 154, rule = B3/S23
189bo$188bobo$188bobo$182b3o2b2obob2o$181bo8b2obo$181bo3b5o$181bo2bo4b
o$183bob4o$183bobo$181bobobob2o$179b3obobob2o$178bo4b2o$179b4o$182bo$
181bo$181b2o7$11bo36bo26b2o28bo25bo28bo28bo24bo23bo$10bobo34bobo24bo2b
o26bobo23bobo26bobo26bobo22bobo21bobo$10bobo34bobo24b2obo26bobo23bobo
26bobo26bobo22bobo21bobo$9b2obob2o30b2obob2o24bob2o22b2obob2o19b2obob
2o22b2obob2o22b2obob2o18b2obob2o17b2obob2o$12b2obo29bo3b2obo24b2obo25b
2obo19bo2b2obo21bo3b2obo21bo3b2obo21b2obo16bo3b2obo$8bob2o33b4o26b2o
26b3o24b2o24bob3o26b3o20b5o19bo2b2o$11bo36bo27bo25bo2bo25bo24bo3bo28bo
19bo4bo18bo4bo$8b3o34b3o25b3o26b3o23b3o23b2ob3o25b4o19bob4o18bob4o$5bo
bo33b2obo27bo27b2o25bo25bo2bo25bo2bo22bobo20bo2bo$3bo3bob2o29bobobob2o
18b2o4bob2o21bobobob2o18b2o2bob2o21bobobob2o21bobobob2o17bobobob2o16bo
3bob2o$b3obobob2o27b3obobob2o17bobo2bobob2o19b3obobob2o16b3obobob2o19b
3obobob2o19b3obobob2o15b3obobob2o14b3obobob2o$o4b2o30bo4b2o21bo4b2o22b
o4b2o19bo4b2o22bo4b2o22bo4b2o18bo4b2o17bo4b2o$b4o33b4o24b4o25b4o22b4o
25b4o25b4o21b4o20b4o$4bo36bo27bo28bo25bo28bo28bo24bo23bo$3bo36bo27bo
28bo25bo28bo28bo24bo23bo$3b2o35b2o26b2o27b2o24b2o27b2o27b2o23b2o22b2o
11$162bo$161bobo$161bobo$48bo107b3ob2obob2o$47bobo56bo50b3o3b2obo$47bo
bo55bobo46bo2b2ob3o$43bo2b2obob2o52bobo46b3obo3bo$45bo3b2obo51b2obob2o
43b4ob3o$43bob4o52bo5b2obo44bo2bo$40bobo5bo53bob3o47bobobob2o$45b3o51b
o3bo2bo45b3obobob2o$41b2obo55bo2b3o45bo4b2o$40bobobob2o53b2o49b4o$38b
3obobob2o50bobobob2o49bo$37bo4b2o52b3obobob2o48bo$38b4o53bo4b2o52b2o$
41bo54b4o$40bo58bo$40b2o56bo$98b2o2$163bo$162bobo$157b2o3bobo$157b2o2b
2obob2o$160bo3b2obo$154b2obobob3o$154b2o3bo3bo$106bo50b2ob3o$105bobo
48bo2bo$101bo3bobo47bobobob2o$101bo2b2obob2o42b3obobob2o$100b3o4b2obo
41bo4b2o$99bob2ob3o46b4o$97b4o2bo2bo49bo$99b2o2b3o49bo$101b2o52b2o$98b
obobob2o$96b3obobob2o$95bo4b2o$96b4o$99bo$98bo$98b2o55bo$153bobo8bo$
154b2o7bobo$163bobo$158b2o2b2obob2o$161bo3b2obo$156bobobob3o$156bo3bo
3bo$158b2ob3o$157bo2bo$156bobobob2o$154b3obobob2o$153bo4b2o$154b4o$
157bo$156bo$156b2o8$164bo$163bobo$159bo3bobo$157b3o2b2obob2o$156bo4bo
3b2obo$156bobobob3o$155b2o3bo3bo$158b2ob3o$157bo2bo$156bobobob2o$154b
3obobob2o$153bo4b2o$154b4o$157bo$156bo$156b2o8$165bo$158bo5bobo$164bob
o$158b3o2b2obob2o$155bobo4bo3b2obo$157bobobob3o$157bo3bo3bo$159b2ob3o$
158bo2bo$157bobobob2o$155b3obobob2o$154bo4b2o$155b4o$158bo$157bo$157b
2o!

I did some very limited predecessor searches; however, I am not very experienced with this type of synthesis and am wondering if this is even feasible.

Also, I compiled a synthesis of the smallest known period 25-oscillator based on fumarole syntheses by Stephen Silver and Jason Summers. Could anyone improve on 72 gliders?

Code: Select all

#C p25 oscillator synthesis
x = 517, y = 548, rule = B3/S23
112bo$113bo$111b3o3$362bobo$362b2o$363bo22$389bo$388bo$388b3o3$157bobo
$158b2o$158bo2$515bo$513b2o$514b2o$42bo$43b2o465bobo$42b2o466b2o$511bo
10$obo$b2o$bo504bo$505bo$505b3o2$5bo$6b2o11bo$5b2o13bo459bo$18b3o457b
2o21bo$23bo422bo32b2o20bobo$24bo420bo55b2o$22b3o420b3o5$35bo$36bo$34b
3o13$44bo$42bobo$43b2o2bobo$48b2o$48bo407bo$455bo$455b3o13$447bobo$
447b2o$448bo11$451bo$449b2o$99bo300bo49b2o$97bobo300bobo7bo$98b2o300b
2o7bo$409b3o8$436bo$434b2o$93bo336bo4b2o$91bobo336bobo$92b2o336b2o2$
404bo$404bobo12bo$404b2o11b2o$418b2o5bo$424bo$424b3o36$114bo$112bobo$
113b2o72$107b3o$109bo$108bo$385bo$385bobo$385b2o4$392b3o$392bo$393bo
156$101b2o294b2o$102b2o292b2o$101bo296bo5$412b2o$99bo300bo6b2o2b2o$99b
2o298b2o6bobo3bo$98bobo298bobo5bo4$97b2o$98b2o$97bo340b2o$438bobo$438b
o3$409bo$408b2o$408bobo$97bo$97b2o$96bobo13$105b2o$104bobo$106bo3$448b
2o$448bobo$448bo2$85b2o350b2o$86b2o348b2o$85bo352bo4$455b3o$71b2o9b3o
350b2o18bo$72b2o10bo350bobo18bo$71bo11bo351bo$426b2o$426bobo$426bo5$
42b2o$43b2o$42bo2$22b2o407b2o$21bobo34b2o370b2o$23bo35b2o371bo$58bo$
117b2o$50b2o64bobo$34b3o12bobo66bo$17b3o16bo14bo$19bo15bo$18bo5$31b2o$
32b2o$31bo5$511bo$510b2o$510bobo2$51b3o446b3o$53bo446bo$52bo448bo$504b
3o8b2o$5b2o456bo40bo9b2o$6b2o454b2o41bo10bo$5bo456bobo$2bo$2b2o$bobo
19$91b2o$92b2o$91bo2$381b2o$381bobo$381bo!

Edit: Here's a way to reduce the cleanup cost of the second fumarole synthesis by one glider, making the total 71 gliders. Editing the original pattern to use this method would be difficult.

Code: Select all

#C 13-glider synthesis of fumarole
x = 71, y = 62, rule = B3/S23
68bobo$68b2o$69bo11$53bobo$8bo40bo3b2o$9bo38bo5bo$7b3o38b3o4$36bobo17b
3o$36b2o18bo$37bo5bo13bo$43bobo$43b2o$27b2o$26b2o$28bo$12b2o$13b2o$12b
o13$20b3o$22bo$21bo6$bo54bo$b2o52b2o$obo52bobo6$47b2o$46b2o$48bo!

[Sokwe]

Here are some partial fumarole syntheses found by Jason Summers and Stephen Silver:

Code: Select all

x = 212, y = 108, rule = B3/S23
89b2o4b2o71b2o6b2o$89b2o4b2o45bo8bo16b2o6b2o$115bo8bo18bo6bo17b2o6b2o$
5b2o14b2o91b3o6b3o18bo4bo$4bo2bo12bo2bo65b3o2b3o17b4o4b4o19b4o19bo8bo$
5b2o14b2o67bo4bo21b2o2b2o44b3o6b3o15b2o6b2o$118b4o45bobo2b2o2bobo14bo
2bo4bo2bo$66bo4bo42bo3bo2bo3bo46b2o18b6o2b6o$45b2o19b2o2b2o17b2o4b2o
96bo2bo4bo2bo$44bo2bo19bo2bo18b2o4b2o17bo3bo2bo3bo46b2o20b2o6b2o$44bo
2bo69b2o2b2o20b2o4b2o16bobo2b2o2bobo$38bo6b2o6bo60b2ob2o2b2ob2o17b2o4b
2o16b3o6b3o12bobo10bobo$37b3o12b3o13b2o43b6o2b6o41bo8bo9b2ob2ob2o8b2ob
2ob2o$38b3o10b3o13bo2bo42b5o4b5o60b3ob3obo6bob3ob3o$39bo12bo14b4o43b3o
6b3o42b2o6b2o8b2o2bo16bo2b2o$10b2o4b2o47bobo2bobo42bo8bo43b2o6b2o8b5o
16b5o$10b2o4b2o47b2o4b2o12bo14bo10b2o14b2o39b2o6b2o$9bo8bo64bobo4bo4bo
4bobo8b2o14b2o$10b2o4b2o66b2o2bobo4bobo2b2o$10b2o4b2o71b2o4b2o2$b2o22b
2o$obo22bobo61b3o2b3o$2bo22bo64bo4bo2$137b3o14b3o$89b2o4b2o40bo2bo12bo
2bo$89b2o4b2o39b2o2bo12bo2b2o$136b4o14b4o$136b2o18b2o2$146b2o$146b2o6$
143b2o4b2o$143b2o4b2o6$134bo24bo$135bo22bo$133b3o22b3o2$132bo28bo$132b
2o26b2o$131bobo26bobo3$135b2o20b2o$17bo14bo103b2o18b2o$17b2o12b2o102bo
10b2o10bo$15bo3bo10bo3bo111b2o$15b4o12b4o27bo4bo10bo4bo$9b2o3b4o14b4o
3b2o21bo4bo10bo4bo$10bob2o22b2obo22bo4bo10bo4bo$9b3o7b2ob2o2b2ob2o7b3o
$19bo3bo2bo3bo$20b3o4b3o113b2o4b2o$20b3o4b3o113b2o4b2o$53b2o4b2o8b2o4b
2o8b2o4b2o$52b3o4b3o6b3o4b3o6b3o4b3o$53b2o4b2o8b2o4b2o8b2o4b2o$20b3o4b
3o$20b3o4b3o$19bo3bo2bo3bo$9b3o7b2ob2o2b2ob2o7b3o$10bob2o22b2obo$9b2o
3b4o14b4o3b2o$15b4o12b4o$15bo3bo10bo3bo$17b2o12b2o20b2o4b2o8b2o4b2o8b
2o4b2o$17bo14bo19b3o4b3o6b3o4b3o6b3o4b3o$53b2o4b2o8b2o4b2o8b2o4b2o5$
62bo4bo10bo4bo$16bo16bo28bo4bo10bo4bo$16bo16bo28bo4bo10bo4bo$14b2o18b
2o$13bo3bo14bo3bo$12b2obo2b3o8b3o2bob2o9$170b2o12b2o$171bo12bo$169bobo
12bobo$12b2obo2b3o8b3o2bob2o131b2o14b2o$13bo3bo14bo3bo137b2o4b2o$14b2o
18b2o138b2o4b2o$16bo16bo$16bo16bo135b2o14b2o$168bo2bo12bo2bo$168bobo
14b2o$169bo!

While I was trying to clean up this 6-glider synthesis of a test tube baby and two blocks with only one glider (which I never succeeded in doing) I saw some interesting patterns come out of the mess: A middleweight spaceship, table on table, and block-laying switch engine respectively.

Code: Select all

x = 205, y = 48, rule = B3/S23
109bo$107bobo65bo$108b2o63bobo$174b2o14$50bobo$51b2o$51bo12$9bo2bo57bo
2bo57bo2bo57bo2bo$7bobo2bobo53bobo2bobo53bobo2bobo53bobo2bobo$8b2o2b2o
55b2o2b2o55b2o2b2o55b2o2b2o4$10b2o59b2o59b2o59b2o$9bo2bo57bo2bo57bo2bo
57bo2bo$10b2o59b2o59b2o59b2o6$3o16b3o39b3o16b3o39b3o16b3o39b3o16b3o$2b
o16bo43bo16bo43bo16bo43bo16bo$bo18bo41bo18bo41bo18bo41bo18bo!

I've been searching some random patterns for rare still lifes. Here is a 6-glider synthesis of twin hat that I am sure has already been discovered. Does anyone know of a 5-glider synthesis?

Code: Select all

x = 17, y = 32, rule = B3/S23
2bo$obo$b2o3$8bobo$8b2o$9bo2$5b3o$7bo$6bo4$9bo$9bobo$9b2o3$8bo$8b2o$7b
obo7$14b2o$14bobo$14bo!

Rotated R-mango partial synthesis:

Code: Select all

x = 23, y = 20, rule = B3/S23
4$16bo$16b3o$7b3o7bo2$5bo5bo$5bo5bo$5bo5bo2$7b3o6b2o$15bo2bo$16b2o!

Here is an interesting still life that came out of random soup that I have been unable to synthesize:

Code: Select all

x = 115, y = 46, rule = B3/S23
81b2o$81b2o$73b2o$73b2o4$29b2o$36bo9bo$30b2o3b3o7b2o$30bo4b2o7bo$31b3o
3bo4b4obo2bo$29bo3bo6b2obob3o2bo$29bobo8b2obob3o2bo$29bo16b5o$42b3obo
3bo11bo4b3o8bo$43bobobo3bo8bo2bo2bo3bo6bobo$37b2o7b2o3bo9b2o3bo3bo$36b
ob2o6bo3bo15bo3bo5bo3bo$35bo2bo8b3o17b3o33b2o$36b2o28b2o$41bo15b2o6b3o
9b3o23b2ob3o$41bo15b2o5b2o2bo31bo2bo2b3o$41bo22b5o9b2o18bo8bo$35b2o8bo
18b3o11b2o19bo4bo$3bo2bo27bo2bo6b3o16b3o14bo18bo3b2o9bo$3b4o27bobo5b2o
3bo14b2ob2o3b2o5bobo20bo2bo10bo$b2o32bo6b2ob2o16b3o11b2o20bo$o3bo37b2o
b2o7bo9bo4b3o4b2o22bo3b2o$2ob2o48b4o13bobo29bo$54bobobo12b2o$49bobob2o
4b2o11bo$48bo4bo2bobo$36b2o10b4o3b2o$36b2o11b5o$52bo19bo$71bobo$71bobo
$55b2o5bo9bo7b3o$54bo2b8o$55bo7b2o$55bo3bobo3bo$26b2o28bo5b2obo$26b2o
30bo4b2o$46b2o12bo2b2o$46b2o!

[hkoenig]

Here are three more ways to construct a [17.7483]

Code: Select all

x=44, y=72
5bo8bo10bo14bo$o4bo20b2o12bobo$o4bo2b2o4bo10b2o13b2o$o7bobo18bo$8bo5bo14b
obo5b3o$2b3o24b2o6bo$14bo23bo$o$o13bo$o17b2o$14bo4b2o$18bo12$18bo$17bo$17b
3o3$16b3o$16bo$17bo4$20b2o$19bobo$21bo3$2o$b2o$o7$41b2o$41bobo$41bo15$3o12b
o3bobo2bobo$10bo9b2o3b2o2b2o$9bo5bo4bo4bo2bobo$9b3o18bo$5b3o7bo$5bo$3o3bo8b
o!

And this construction of [14.22] came from Martin Gardner's "Wheels, Life and other Mathematical Amusements", p.250:

Code: Select all

x=16, y=17
14bo$bobo9bo$2b2o9b3o$2bo2$2o7bo$b2o5bo$o7b3o$12b2o$12bobo$12bo$5b3o$4bo2b
o$7bo$7bo5b2o$4bobo5b2o$14bo!

[Sokwe]

And this construction of [14.22]...

It would be nice to reduce the construction, but I'm not sure if that's possible from what I posted above. At any rate, it has only occurred once in my searches and so must be quite rare.

Also, does anyone have Buckingham's glider syntheses of still lifes? (I would like to add some of them to the wiki)

[Sokwe]

Here are some predecessors of some large oscillators that might be synthesizable (p9, p16, and p51):

Code: Select all

x = 168, y = 54, rule = B3/S23
114bo$66bo17bo30b2o38b2o$66bo17bo29b2o39b2o$66bo17bo$125bo27bo$63bobo
19bobo36bobo25bobo$63bobo19bobo35bo3bo23bo3bo$63b3o19b3o35bo3bo23bo3bo
$123bo3bo23bo3bo$12b3o7b3o47b3ob3o45bobo25bobo$13b2o7b2o44b3o9b3o42bo
3b3o15b3o3bo$10b2o2bo7bo2b2o41bo13bo35b3o7bo3bo13bo3bo7b3o$11bobo9bobo
42b3o9b3o34bo3bo5bo5bo11bo5bo5bo3bo$12bo11bo91bo5bo5bo3bo13bo3bo5bo5bo
$117bo3bo7b3o3b2o5b2o3b3o7bo3bo$53b3o39b3o20b3o3bo10bobo3bobo10bo3b3o$
55bo39bo27bobo10bo5bo10bobo$12b2o9b2o28b3o39b3o24bo3bo25bo3bo$12b2o2b
2ob2o2b2o24b3o47b3o20bo3bo3b2o15b2o3bo3bo$2bo13b2ob2o13bo87bo3bo3b2o
15b2o3bo3bo$2b2o29b2o23b3o11b3ob3o11b3o30bobo27bobo$o3bo3b2o17b2o3bo3b
o21bobo29bobo31bo8b2o9b2o8bo$2obo4b2o17b2o4bob2o21bobo29bobo40b2o9b2o$
3o31b3o89b2o23b2o$57bo10bo13bo10bo32bobo21bobo$9b2o15b2o29bo10bo13bo
10bo33bo23bo$9b2o15b2o29bo10bo13bo10bo2$9b2o15b2o29bo10bo13bo10bo$9b2o
15b2o29bo10bo13bo10bo33bo23bo$57bo10bo13bo10bo32bobo21bobo$3o31b3o89b
2o23b2o$2obo4b2o17b2o4bob2o21bobo29bobo40b2o9b2o$o3bo3b2o17b2o3bo3bo
21bobo29bobo31bo8b2o9b2o8bo$2b2o29b2o23b3o11b3ob3o11b3o30bobo27bobo$2b
o13b2ob2o13bo87bo3bo3b2o15b2o3bo3bo$12b2o2b2ob2o2b2o24b3o47b3o20bo3bo
3b2o15b2o3bo3bo$12b2o9b2o28b3o39b3o24bo3bo25bo3bo$55bo39bo27bobo10bo5b
o10bobo$53b3o39b3o20b3o3bo10bobo3bobo10bo3b3o$117bo3bo7b3o3b2o5b2o3b3o
7bo3bo$12bo11bo91bo5bo5bo3bo13bo3bo5bo5bo$11bobo9bobo42b3o9b3o34bo3bo
5bo5bo11bo5bo5bo3bo$10b2o2bo7bo2b2o41bo13bo30b2o3b3o7bo3bo13bo3bo7b3o$
13b2o7b2o44b3o9b3o30b2o10bo3b3o15b3o3bo$12b3o7b3o47b3ob3o45bobo25bobo$
123bo3bo23bo3bo$63b3o19b3o35bo3bo23bo3bo10bo$63bobo19bobo35bo3bo23bo3b
o9b2o$63bobo19bobo36bobo25bobo10bobo$125bo27bo$66bo17bo$66bo17bo37b2o$
66bo17bo37b2o!

Here's the original agar from which I found a new p32 oscillator:

Code: Select all

x = 216, y = 216, rule = B3/S23
2o5bobo2bo5bo5b2o3bo2b2o5b2o2bo3b2o5bo5bo2bobo5b3o5bobo2bo5bo5b2o3bo2b
2o5b2o2bo3b2o5bo5bo2bobo5b3o5bobo2bo5bo5b2o3bo2b2o5b2o2bo3b2o5bo5bo2bo
bo5bo$2o8bo3bobobobo3b2o4b3obobobob3o4b2o3bobobobo3bo8b3o8bo3bobobobo
3b2o4b3obobobob3o4b2o3bobobobo3bo8b3o8bo3bobobobo3b2o4b3obobobob3o4b2o
3bobobobo3bo8bo$2bobo3b3o4bo2bo2bo4bo7bo3bo7bo4bo2bo2bo4b3o3bobo3bobo
3b3o4bo2bo2bo4bo7bo3bo7bo4bo2bo2bo4b3o3bobo3bobo3b3o4bo2bo2bo4bo7bo3bo
7bo4bo2bo2bo4b3o3bobo$9bo11bo5bo2bo5bo5bo2bo5bo11bo17bo11bo5bo2bo5bo5b
o2bo5bo11bo17bo11bo5bo2bo5bo5bo2bo5bo11bo$2bo2bobo2bobob4o7bo2bo2bo4bo
4bo2bo2bo7b4obobo2bobo2bo3bo2bobo2bobob4o7bo2bo2bo4bo4bo2bo2bo7b4obobo
2bobo2bo3bo2bobo2bobob4o7bo2bo2bo4bo4bo2bo2bo7b4obobo2bobo2bo$4bo7b2o
3bo4bo5bob2ob2obob2ob2obo5bo4bo3b2o7bo7bo7b2o3bo4bo5bob2ob2obob2ob2obo
5bo4bo3b2o7bo7bo7b2o3bo4bo5bob2ob2obob2ob2obo5bo4bo3b2o7bo$9bo3bo6bo6b
2o2bo3bobo3bo2b2o6bo6bo3bo17bo3bo6bo6b2o2bo3bobo3bo2b2o6bo6bo3bo17bo3b
o6bo6b2o2bo3bobo3bo2b2o6bo6bo3bo$o3bo4b2o10b3o9bo5bo9b3o10b2o4bo3bo3bo
4b2o10b3o9bo5bo9b3o10b2o4bo3bo3bo4b2o10b3o9bo5bo9b3o10b2o4bo$2bo6bo2b
2ob4obo5b3o4bo5bo4b3o5bob4ob2o2bo6bo3bo6bo2b2ob4obo5b3o4bo5bo4b3o5bob
4ob2o2bo6bo3bo6bo2b2ob4obo5b3o4bo5bo4b3o5bob4ob2o2bo6bo$ob2o2b3o2bo3bo
4bo2bobo2b2obo2bobobo2bob2o2bobo2bo4bo3bo2b3o2b2obob2o2b3o2bo3bo4bo2bo
bo2b2obo2bobobo2bob2o2bobo2bo4bo3bo2b3o2b2obob2o2b3o2bo3bo4bo2bobo2b2o
bo2bobobo2bob2o2bobo2bo4bo3bo2b3o2b2o$b2obo2bo5b2obo2b2obo2bo2bo2bob3o
b3obo2bo2bo2bob2o2bob2o5bo2bob2ob2obo2bo5b2obo2b2obo2bo2bo2bob3ob3obo
2bo2bo2bob2o2bob2o5bo2bob2ob2obo2bo5b2obo2b2obo2bo2bo2bob3ob3obo2bo2bo
2bob2o2bob2o5bo2bob2o$9bob3o2b3obo3bo8b2o3b2o8bo3bob3o2b3obo17bob3o2b
3obo3bo8b2o3b2o8bo3bob3o2b3obo17bob3o2b3obo3bo8b2o3b2o8bo3bob3o2b3obo$
o3b2o2bo2bo5bo2bo4bobo8bo8bobo4bo2bo5bo2bo2b2o3bo3b2o2bo2bo5bo2bo4bobo
8bo8bobo4bo2bo5bo2bo2b2o3bo3b2o2bo2bo5bo2bo4bobo8bo8bobo4bo2bo5bo2bo2b
2o$5b2obob2o5bo4b2obobo2bo5bo5bo2bobob2o4bo5b2obob2o9b2obob2o5bo4b2obo
bo2bo5bo5bo2bobob2o4bo5b2obob2o9b2obob2o5bo4b2obobo2bo5bo5bo2bobob2o4b
o5b2obob2o$bo2bo5bo3b2o2bob3o5b2o5bobo5b2o5b3obo2b2o3bo5bo2bobo2bo5bo
3b2o2bob3o5b2o5bobo5b2o5b3obo2b2o3bo5bo2bobo2bo5bo3b2o2bob3o5b2o5bobo
5b2o5b3obo2b2o3bo5bo2bo$2bobo3b2o4b3o3bob2o2bo3bo2b3ob3o2bo3bo2b2obo3b
3o4b2o3bobo3bobo3b2o4b3o3bob2o2bo3bo2b3ob3o2bo3bo2b2obo3b3o4b2o3bobo3b
obo3b2o4b3o3bob2o2bo3bo2b3ob3o2bo3bo2b2obo3b3o4b2o3bobo$bo2bo3bob2o3bo
2bo7bobobob2o5b2obobobo7bo2bo3b2obo3bo2bobo2bo3bob2o3bo2bo7bobobob2o5b
2obobobo7bo2bo3b2obo3bo2bobo2bo3bob2o3bo2bo7bobobob2o5b2obobobo7bo2bo
3b2obo3bo2bo$4b2o2bo2b3o3b3o3bo3bobo3b2o3b2o3bobo3bo3b3o3b3o2bo2b2o7b
2o2bo2b3o3b3o3bo3bobo3b2o3b2o3bobo3bo3b3o3b3o2bo2b2o7b2o2bo2b3o3b3o3bo
3bobo3b2o3b2o3bobo3bo3b3o3b3o2bo2b2o$3o5bo2bo2bob2o6bobobob3ob2ob2ob3o
bobobo6b2obo2bo2bo5b5o5bo2bo2bob2o6bobobob3ob2ob2ob3obobobo6b2obo2bo2b
o5b5o5bo2bo2bob2o6bobobob3ob2ob2ob3obobobo6b2obo2bo2bo5b2o$10bo6bobo2b
obobobo2b3o5b3o2bobobobo2bobo6bo19bo6bobo2bobobobo2b3o5b3o2bobobobo2bo
bo6bo19bo6bobo2bobobobo2b3o5b3o2bobobobo2bobo6bo$bo4bob5ob2o6bo4bo2bo
2b3ob3o2bo2bo4bo6b2ob5obo4bobo4bob5ob2o6bo4bo2bo2b3ob3o2bo2bo4bo6b2ob
5obo4bobo4bob5ob2o6bo4bo2bo2b3ob3o2bo2bo4bo6b2ob5obo4bo$2b2o3bo6bo7b2o
bob3obo9bob3obob2o7bo6bo3b2o3b2o3bo6bo7b2obob3obo9bob3obob2o7bo6bo3b2o
3b2o3bo6bo7b2obob3obo9bob3obob2o7bo6bo3b2o$5bobo2bo2b3o3b3o2bo3b4o9b4o
3bo2b3o3b3o2bo2bobo9bobo2bo2b3o3b3o2bo3b4o9b4o3bo2b3o3b3o2bo2bobo9bobo
2bo2b3o3b3o2bo3b4o9b4o3bo2b3o3b3o2bo2bobo$7bobo3bobobo3bo2b2obo4b2obob
ob2o4bob2o2bo3bobobo3bobo13bobo3bobobo3bo2b2obo4b2obobob2o4bob2o2bo3bo
bobo3bobo13bobo3bobobo3bo2b2obo4b2obobob2o4bob2o2bo3bobobo3bobo$2o9bo
6b2o2b2obo9bobo9bob2o2b2o6bo9b3o9bo6b2o2b2obo9bobo9bob2o2b2o6bo9b3o9bo
6b2o2b2obo9bobo9bob2o2b2o6bo9bo$2o2bo4b2ob2o7bob2o2b2obo2bobobobo2bob
2o2b2obo7b2ob2o4bo2b3o2bo4b2ob2o7bob2o2b2obo2bobobobo2bob2o2b2obo7b2ob
2o4bo2b3o2bo4b2ob2o7bob2o2b2obo2bobobobo2bob2o2b2obo7b2ob2o4bo2bo$2bo
5bo6b2ob2o10bo11bo10b2ob2o6bo5bo3bo5bo6b2ob2o10bo11bo10b2ob2o6bo5bo3bo
5bo6b2ob2o10bo11bo10b2ob2o6bo5bo$3bo2bobo3b2o3bo2b2obobob2o4bobobobo4b
2obobob2o2bo3b2o3bobo2bo5bo2bobo3b2o3bo2b2obobob2o4bobobobo4b2obobob2o
2bo3b2o3bobo2bo5bo2bobo3b2o3bo2b2obobob2o4bobobobo4b2obobob2o2bo3b2o3b
obo2bo$4b3ob3o3bobob2ob2o2bob3o5bobo5b3obo2b2ob2obobo3b3ob3o7b3ob3o3bo
bob2ob2o2bob3o5bobo5b3obo2b2ob2obobo3b3ob3o7b3ob3o3bobob2ob2o2bob3o5bo
bo5b3obo2b2ob2obobo3b3ob3o$o8bo4bo2bo3b2o5bobobo3bo3bobobo5b2o3bo2bo4b
o8bo8bo4bo2bo3b2o5bobobo3bo3bobobo5b2o3bo2bo4bo8bo8bo4bo2bo3b2o5bobobo
3bo3bobobo5b2o3bo2bo4bo$bobobo7bob2obobobo2b2o2b2o2b2o3b2o2b2o2b2o2bob
obob2obo7bobobobobobo7bob2obobobo2b2o2b2o2b2o3b2o2b2o2b2o2bobobob2obo
7bobobobobobo7bob2obobobo2b2o2b2o2b2o3b2o2b2o2b2o2bobobob2obo7bobobo$b
o2b3o2b2o7b2ob2o27b2ob2o7b2o2b3o2bobo2b3o2b2o7b2ob2o27b2ob2o7b2o2b3o2b
obo2b3o2b2o7b2ob2o27b2ob2o7b2o2b3o2bo$2o14bob2o3bo5bo2bo3bo3bo2bo5bo3b
2obo14b3o14bob2o3bo5bo2bo3bo3bo2bo5bo3b2obo14b3o14bob2o3bo5bo2bo3bo3bo
2bo5bo3b2obo14bo$o4bob2ob2o3b3ob2o2bobobo2bo11bo2bobobo2b2ob3o3b2ob2ob
o4bo4bob2ob2o3b3ob2o2bobobo2bo11bo2bobobo2b2ob3o3b2ob2obo4bo4bob2ob2o
3b3ob2o2bobobo2bo11bo2bobobo2b2ob3o3b2ob2obo$b2o2bo3b3o3bob2obo9bo11bo
9bob2obo3b3o3bo2b2ob2o2bo3b3o3bob2obo9bo11bo9bob2obo3b3o3bo2b2ob2o2bo
3b3o3bob2obo9bo11bo9bob2obo3b3o3bo2b2o$6bo3bo3b2o2bobo2b3ob2o15b2ob3o
2bobo2b2o3bo3bo11bo3bo3b2o2bobo2b3ob2o15b2ob3o2bobo2b2o3bo3bo11bo3bo3b
2o2bobo2b3ob2o15b2ob3o2bobo2b2o3bo3bo$bob3o3bo2b2o15bo2bo3bo3bo2bo15b
2o2bo3b3obobob3o3bo2b2o15bo2bo3bo3bo2bo15b2o2bo3b3obobob3o3bo2b2o15bo
2bo3bo3bo2bo15b2o2bo3b3obo$6bo3bo3b2o2bobo2b3ob2o15b2ob3o2bobo2b2o3bo
3bo11bo3bo3b2o2bobo2b3ob2o15b2ob3o2bobo2b2o3bo3bo11bo3bo3b2o2bobo2b3ob
2o15b2ob3o2bobo2b2o3bo3bo$b2o2bo3b3o3bob2obo9bo11bo9bob2obo3b3o3bo2b2o
b2o2bo3b3o3bob2obo9bo11bo9bob2obo3b3o3bo2b2ob2o2bo3b3o3bob2obo9bo11bo
9bob2obo3b3o3bo2b2o$o4bob2ob2o3b3ob2o2bobobo2bo11bo2bobobo2b2ob3o3b2ob
2obo4bo4bob2ob2o3b3ob2o2bobobo2bo11bo2bobobo2b2ob3o3b2ob2obo4bo4bob2ob
2o3b3ob2o2bobobo2bo11bo2bobobo2b2ob3o3b2ob2obo$2o14bob2o3bo5bo2bo3bo3b
o2bo5bo3b2obo14b3o14bob2o3bo5bo2bo3bo3bo2bo5bo3b2obo14b3o14bob2o3bo5bo
2bo3bo3bo2bo5bo3b2obo14bo$bo2b3o2b2o7b2ob2o27b2ob2o7b2o2b3o2bobo2b3o2b
2o7b2ob2o27b2ob2o7b2o2b3o2bobo2b3o2b2o7b2ob2o27b2ob2o7b2o2b3o2bo$bobob
o7bob2obobobo2b2o2b2o2b2o3b2o2b2o2b2o2bobobob2obo7bobobobobobo7bob2obo
bobo2b2o2b2o2b2o3b2o2b2o2b2o2bobobob2obo7bobobobobobo7bob2obobobo2b2o
2b2o2b2o3b2o2b2o2b2o2bobobob2obo7bobobo$o8bo4bo2bo3b2o5bobobo3bo3bobob
o5b2o3bo2bo4bo8bo8bo4bo2bo3b2o5bobobo3bo3bobobo5b2o3bo2bo4bo8bo8bo4bo
2bo3b2o5bobobo3bo3bobobo5b2o3bo2bo4bo$4b3ob3o3bobob2ob2o2bob3o5bobo5b
3obo2b2ob2obobo3b3ob3o7b3ob3o3bobob2ob2o2bob3o5bobo5b3obo2b2ob2obobo3b
3ob3o7b3ob3o3bobob2ob2o2bob3o5bobo5b3obo2b2ob2obobo3b3ob3o$3bo2bobo3b
2o3bo2b2obobob2o4bobobobo4b2obobob2o2bo3b2o3bobo2bo5bo2bobo3b2o3bo2b2o
bobob2o4bobobobo4b2obobob2o2bo3b2o3bobo2bo5bo2bobo3b2o3bo2b2obobob2o4b
obobobo4b2obobob2o2bo3b2o3bobo2bo$2bo5bo6b2ob2o10bo11bo10b2ob2o6bo5bo
3bo5bo6b2ob2o10bo11bo10b2ob2o6bo5bo3bo5bo6b2ob2o10bo11bo10b2ob2o6bo5bo
$2o2bo4b2ob2o7bob2o2b2obo2bobobobo2bob2o2b2obo7b2ob2o4bo2b3o2bo4b2ob2o
7bob2o2b2obo2bobobobo2bob2o2b2obo7b2ob2o4bo2b3o2bo4b2ob2o7bob2o2b2obo
2bobobobo2bob2o2b2obo7b2ob2o4bo2bo$2o9bo6b2o2b2obo9bobo9bob2o2b2o6bo9b
3o9bo6b2o2b2obo9bobo9bob2o2b2o6bo9b3o9bo6b2o2b2obo9bobo9bob2o2b2o6bo9b
o$7bobo3bobobo3bo2b2obo4b2obobob2o4bob2o2bo3bobobo3bobo13bobo3bobobo3b
o2b2obo4b2obobob2o4bob2o2bo3bobobo3bobo13bobo3bobobo3bo2b2obo4b2obobob
2o4bob2o2bo3bobobo3bobo$5bobo2bo2b3o3b3o2bo3b4o9b4o3bo2b3o3b3o2bo2bobo
9bobo2bo2b3o3b3o2bo3b4o9b4o3bo2b3o3b3o2bo2bobo9bobo2bo2b3o3b3o2bo3b4o
9b4o3bo2b3o3b3o2bo2bobo$2b2o3bo6bo7b2obob3obo9bob3obob2o7bo6bo3b2o3b2o
3bo6bo7b2obob3obo9bob3obob2o7bo6bo3b2o3b2o3bo6bo7b2obob3obo9bob3obob2o
7bo6bo3b2o$bo4bob5ob2o6bo4bo2bo2b3ob3o2bo2bo4bo6b2ob5obo4bobo4bob5ob2o
6bo4bo2bo2b3ob3o2bo2bo4bo6b2ob5obo4bobo4bob5ob2o6bo4bo2bo2b3ob3o2bo2bo
4bo6b2ob5obo4bo$10bo6bobo2bobobobo2b3o5b3o2bobobobo2bobo6bo19bo6bobo2b
obobobo2b3o5b3o2bobobobo2bobo6bo19bo6bobo2bobobobo2b3o5b3o2bobobobo2bo
bo6bo$3o5bo2bo2bob2o6bobobob3ob2ob2ob3obobobo6b2obo2bo2bo5b5o5bo2bo2bo
b2o6bobobob3ob2ob2ob3obobobo6b2obo2bo2bo5b5o5bo2bo2bob2o6bobobob3ob2ob
2ob3obobobo6b2obo2bo2bo5b2o$4b2o2bo2b3o3b3o3bo3bobo3b2o3b2o3bobo3bo3b
3o3b3o2bo2b2o7b2o2bo2b3o3b3o3bo3bobo3b2o3b2o3bobo3bo3b3o3b3o2bo2b2o7b
2o2bo2b3o3b3o3bo3bobo3b2o3b2o3bobo3bo3b3o3b3o2bo2b2o$bo2bo3bob2o3bo2bo
7bobobob2o5b2obobobo7bo2bo3b2obo3bo2bobo2bo3bob2o3bo2bo7bobobob2o5b2ob
obobo7bo2bo3b2obo3bo2bobo2bo3bob2o3bo2bo7bobobob2o5b2obobobo7bo2bo3b2o
bo3bo2bo$2bobo3b2o4b3o3bob2o2bo3bo2b3ob3o2bo3bo2b2obo3b3o4b2o3bobo3bob
o3b2o4b3o3bob2o2bo3bo2b3ob3o2bo3bo2b2obo3b3o4b2o3bobo3bobo3b2o4b3o3bob
2o2bo3bo2b3ob3o2bo3bo2b2obo3b3o4b2o3bobo$bo2bo5bo3b2o2bob3o5b2o5bobo5b
2o5b3obo2b2o3bo5bo2bobo2bo5bo3b2o2bob3o5b2o5bobo5b2o5b3obo2b2o3bo5bo2b
obo2bo5bo3b2o2bob3o5b2o5bobo5b2o5b3obo2b2o3bo5bo2bo$5b2obob2o5bo4b2obo
bo2bo5bo5bo2bobob2o4bo5b2obob2o9b2obob2o5bo4b2obobo2bo5bo5bo2bobob2o4b
o5b2obob2o9b2obob2o5bo4b2obobo2bo5bo5bo2bobob2o4bo5b2obob2o$o3b2o2bo2b
o5bo2bo4bobo8bo8bobo4bo2bo5bo2bo2b2o3bo3b2o2bo2bo5bo2bo4bobo8bo8bobo4b
o2bo5bo2bo2b2o3bo3b2o2bo2bo5bo2bo4bobo8bo8bobo4bo2bo5bo2bo2b2o$9bob3o
2b3obo3bo8b2o3b2o8bo3bob3o2b3obo17bob3o2b3obo3bo8b2o3b2o8bo3bob3o2b3ob
o17bob3o2b3obo3bo8b2o3b2o8bo3bob3o2b3obo$b2obo2bo5b2obo2b2obo2bo2bo2bo
b3ob3obo2bo2bo2bob2o2bob2o5bo2bob2ob2obo2bo5b2obo2b2obo2bo2bo2bob3ob3o
bo2bo2bo2bob2o2bob2o5bo2bob2ob2obo2bo5b2obo2b2obo2bo2bo2bob3ob3obo2bo
2bo2bob2o2bob2o5bo2bob2o$ob2o2b3o2bo3bo4bo2bobo2b2obo2bobobo2bob2o2bob
o2bo4bo3bo2b3o2b2obob2o2b3o2bo3bo4bo2bobo2b2obo2bobobo2bob2o2bobo2bo4b
o3bo2b3o2b2obob2o2b3o2bo3bo4bo2bobo2b2obo2bobobo2bob2o2bobo2bo4bo3bo2b
3o2b2o$2bo6bo2b2ob4obo5b3o4bo5bo4b3o5bob4ob2o2bo6bo3bo6bo2b2ob4obo5b3o
4bo5bo4b3o5bob4ob2o2bo6bo3bo6bo2b2ob4obo5b3o4bo5bo4b3o5bob4ob2o2bo6bo$
o3bo4b2o10b3o9bo5bo9b3o10b2o4bo3bo3bo4b2o10b3o9bo5bo9b3o10b2o4bo3bo3bo
4b2o10b3o9bo5bo9b3o10b2o4bo$9bo3bo6bo6b2o2bo3bobo3bo2b2o6bo6bo3bo17bo
3bo6bo6b2o2bo3bobo3bo2b2o6bo6bo3bo17bo3bo6bo6b2o2bo3bobo3bo2b2o6bo6bo
3bo$4bo7b2o3bo4bo5bob2ob2obob2ob2obo5bo4bo3b2o7bo7bo7b2o3bo4bo5bob2ob
2obob2ob2obo5bo4bo3b2o7bo7bo7b2o3bo4bo5bob2ob2obob2ob2obo5bo4bo3b2o7bo
$2bo2bobo2bobob4o7bo2bo2bo4bo4bo2bo2bo7b4obobo2bobo2bo3bo2bobo2bobob4o
7bo2bo2bo4bo4bo2bo2bo7b4obobo2bobo2bo3bo2bobo2bobob4o7bo2bo2bo4bo4bo2b
o2bo7b4obobo2bobo2bo$9bo11bo5bo2bo5bo5bo2bo5bo11bo17bo11bo5bo2bo5bo5bo
2bo5bo11bo17bo11bo5bo2bo5bo5bo2bo5bo11bo$2bobo3b3o4bo2bo2bo4bo7bo3bo7b
o4bo2bo2bo4b3o3bobo3bobo3b3o4bo2bo2bo4bo7bo3bo7bo4bo2bo2bo4b3o3bobo3bo
bo3b3o4bo2bo2bo4bo7bo3bo7bo4bo2bo2bo4b3o3bobo$2o8bo3bobobobo3b2o4b3obo
bobob3o4b2o3bobobobo3bo8b3o8bo3bobobobo3b2o4b3obobobob3o4b2o3bobobobo
3bo8b3o8bo3bobobobo3b2o4b3obobobob3o4b2o3bobobobo3bo8bo$2o5bobo2bo5bo
5b2o3bo2b2o5b2o2bo3b2o5bo5bo2bobo5b3o5bobo2bo5bo5b2o3bo2b2o5b2o2bo3b2o
5bo5bo2bobo5b3o5bobo2bo5bo5b2o3bo2b2o5b2o2bo3b2o5bo5bo2bobo5bo$2o8bo3b
obobobo3b2o4b3obobobob3o4b2o3bobobobo3bo8b3o8bo3bobobobo3b2o4b3obobobo
b3o4b2o3bobobobo3bo8b3o8bo3bobobobo3b2o4b3obobobob3o4b2o3bobobobo3bo8b
o$2bobo3b3o4bo2bo2bo4bo7bo3bo7bo4bo2bo2bo4b3o3bobo3bobo3b3o4bo2bo2bo4b
o7bo3bo7bo4bo2bo2bo4b3o3bobo3bobo3b3o4bo2bo2bo4bo7bo3bo7bo4bo2bo2bo4b
3o3bobo$9bo11bo5bo2bo5bo5bo2bo5bo11bo17bo11bo5bo2bo5bo5bo2bo5bo11bo17b
o11bo5bo2bo5bo5bo2bo5bo11bo$2bo2bobo2bobob4o7bo2bo2bo4bo4bo2bo2bo7b4ob
obo2bobo2bo3bo2bobo2bobob4o7bo2bo2bo4bo4bo2bo2bo7b4obobo2bobo2bo3bo2bo
bo2bobob4o7bo2bo2bo4bo4bo2bo2bo7b4obobo2bobo2bo$4bo7b2o3bo4bo5bob2ob2o
bob2ob2obo5bo4bo3b2o7bo7bo7b2o3bo4bo5bob2ob2obob2ob2obo5bo4bo3b2o7bo7b
o7b2o3bo4bo5bob2ob2obob2ob2obo5bo4bo3b2o7bo$9bo3bo6bo6b2o2bo3bobo3bo2b
2o6bo6bo3bo17bo3bo6bo6b2o2bo3bobo3bo2b2o6bo6bo3bo17bo3bo6bo6b2o2bo3bob
o3bo2b2o6bo6bo3bo$o3bo4b2o10b3o9bo5bo9b3o10b2o4bo3bo3bo4b2o10b3o9bo5bo
9b3o10b2o4bo3bo3bo4b2o10b3o9bo5bo9b3o10b2o4bo$2bo6bo2b2ob4obo5b3o4bo5b
o4b3o5bob4ob2o2bo6bo3bo6bo2b2ob4obo5b3o4bo5bo4b3o5bob4ob2o2bo6bo3bo6bo
2b2ob4obo5b3o4bo5bo4b3o5bob4ob2o2bo6bo$ob2o2b3o2bo3bo4bo2bobo2b2obo2bo
bobo2bob2o2bobo2bo4bo3bo2b3o2b2obob2o2b3o2bo3bo4bo2bobo2b2obo2bobobo2b
ob2o2bobo2bo4bo3bo2b3o2b2obob2o2b3o2bo3bo4bo2bobo2b2obo2bobobo2bob2o2b
obo2bo4bo3bo2b3o2b2o$b2obo2bo5b2obo2b2obo2bo2bo2bob3ob3obo2bo2bo2bob2o
2bob2o5bo2bob2ob2obo2bo5b2obo2b2obo2bo2bo2bob3ob3obo2bo2bo2bob2o2bob2o
5bo2bob2ob2obo2bo5b2obo2b2obo2bo2bo2bob3ob3obo2bo2bo2bob2o2bob2o5bo2bo
b2o$9bob3o2b3obo3bo8b2o3b2o8bo3bob3o2b3obo17bob3o2b3obo3bo8b2o3b2o8bo
3bob3o2b3obo17bob3o2b3obo3bo8b2o3b2o8bo3bob3o2b3obo$o3b2o2bo2bo5bo2bo
4bobo8bo8bobo4bo2bo5bo2bo2b2o3bo3b2o2bo2bo5bo2bo4bobo8bo8bobo4bo2bo5bo
2bo2b2o3bo3b2o2bo2bo5bo2bo4bobo8bo8bobo4bo2bo5bo2bo2b2o$5b2obob2o5bo4b
2obobo2bo5bo5bo2bobob2o4bo5b2obob2o9b2obob2o5bo4b2obobo2bo5bo5bo2bobob
2o4bo5b2obob2o9b2obob2o5bo4b2obobo2bo5bo5bo2bobob2o4bo5b2obob2o$bo2bo
5bo3b2o2bob3o5b2o5bobo5b2o5b3obo2b2o3bo5bo2bobo2bo5bo3b2o2bob3o5b2o5bo
bo5b2o5b3obo2b2o3bo5bo2bobo2bo5bo3b2o2bob3o5b2o5bobo5b2o5b3obo2b2o3bo
5bo2bo$2bobo3b2o4b3o3bob2o2bo3bo2b3ob3o2bo3bo2b2obo3b3o4b2o3bobo3bobo
3b2o4b3o3bob2o2bo3bo2b3ob3o2bo3bo2b2obo3b3o4b2o3bobo3bobo3b2o4b3o3bob
2o2bo3bo2b3ob3o2bo3bo2b2obo3b3o4b2o3bobo$bo2bo3bob2o3bo2bo7bobobob2o5b
2obobobo7bo2bo3b2obo3bo2bobo2bo3bob2o3bo2bo7bobobob2o5b2obobobo7bo2bo
3b2obo3bo2bobo2bo3bob2o3bo2bo7bobobob2o5b2obobobo7bo2bo3b2obo3bo2bo$4b
2o2bo2b3o3b3o3bo3bobo3b2o3b2o3bobo3bo3b3o3b3o2bo2b2o7b2o2bo2b3o3b3o3bo
3bobo3b2o3b2o3bobo3bo3b3o3b3o2bo2b2o7b2o2bo2b3o3b3o3bo3bobo3b2o3b2o3bo
bo3bo3b3o3b3o2bo2b2o$3o5bo2bo2bob2o6bobobob3ob2ob2ob3obobobo6b2obo2bo
2bo5b5o5bo2bo2bob2o6bobobob3ob2ob2ob3obobobo6b2obo2bo2bo5b5o5bo2bo2bob
2o6bobobob3ob2ob2ob3obobobo6b2obo2bo2bo5b2o$10bo6bobo2bobobobo2b3o5b3o
2bobobobo2bobo6bo19bo6bobo2bobobobo2b3o5b3o2bobobobo2bobo6bo19bo6bobo
2bobobobo2b3o5b3o2bobobobo2bobo6bo$bo4bob5ob2o6bo4bo2bo2b3ob3o2bo2bo4b
o6b2ob5obo4bobo4bob5ob2o6bo4bo2bo2b3ob3o2bo2bo4bo6b2ob5obo4bobo4bob5ob
2o6bo4bo2bo2b3ob3o2bo2bo4bo6b2ob5obo4bo$2b2o3bo6bo7b2obob3obo9bob3obob
2o7bo6bo3b2o3b2o3bo6bo7b2obob3obo9bob3obob2o7bo6bo3b2o3b2o3bo6bo7b2obo
b3obo9bob3obob2o7bo6bo3b2o$5bobo2bo2b3o3b3o2bo3b4o9b4o3bo2b3o3b3o2bo2b
obo9bobo2bo2b3o3b3o2bo3b4o9b4o3bo2b3o3b3o2bo2bobo9bobo2bo2b3o3b3o2bo3b
4o9b4o3bo2b3o3b3o2bo2bobo$7bobo3bobobo3bo2b2obo4b2obobob2o4bob2o2bo3bo
bobo3bobo13bobo3bobobo3bo2b2obo4b2obobob2o4bob2o2bo3bobobo3bobo13bobo
3bobobo3bo2b2obo4b2obobob2o4bob2o2bo3bobobo3bobo$2o9bo6b2o2b2obo9bobo
9bob2o2b2o6bo9b3o9bo6b2o2b2obo9bobo9bob2o2b2o6bo9b3o9bo6b2o2b2obo9bobo
9bob2o2b2o6bo9bo$2o2bo4b2ob2o7bob2o2b2obo2bobobobo2bob2o2b2obo7b2ob2o
4bo2b3o2bo4b2ob2o7bob2o2b2obo2bobobobo2bob2o2b2obo7b2ob2o4bo2b3o2bo4b
2ob2o7bob2o2b2obo2bobobobo2bob2o2b2obo7b2ob2o4bo2bo$2bo5bo6b2ob2o10bo
11bo10b2ob2o6bo5bo3bo5bo6b2ob2o10bo11bo10b2ob2o6bo5bo3bo5bo6b2ob2o10bo
11bo10b2ob2o6bo5bo$3bo2bobo3b2o3bo2b2obobob2o4bobobobo4b2obobob2o2bo3b
2o3bobo2bo5bo2bobo3b2o3bo2b2obobob2o4bobobobo4b2obobob2o2bo3b2o3bobo2b
o5bo2bobo3b2o3bo2b2obobob2o4bobobobo4b2obobob2o2bo3b2o3bobo2bo$4b3ob3o
3bobob2ob2o2bob3o5bobo5b3obo2b2ob2obobo3b3ob3o7b3ob3o3bobob2ob2o2bob3o
5bobo5b3obo2b2ob2obobo3b3ob3o7b3ob3o3bobob2ob2o2bob3o5bobo5b3obo2b2ob
2obobo3b3ob3o$o8bo4bo2bo3b2o5bobobo3bo3bobobo5b2o3bo2bo4bo8bo8bo4bo2bo
3b2o5bobobo3bo3bobobo5b2o3bo2bo4bo8bo8bo4bo2bo3b2o5bobobo3bo3bobobo5b
2o3bo2bo4bo$bobobo7bob2obobobo2b2o2b2o2b2o3b2o2b2o2b2o2bobobob2obo7bob
obobobobo7bob2obobobo2b2o2b2o2b2o3b2o2b2o2b2o2bobobob2obo7bobobobobobo
7bob2obobobo2b2o2b2o2b2o3b2o2b2o2b2o2bobobob2obo7bobobo$bo2b3o2b2o7b2o
b2o27b2ob2o7b2o2b3o2bobo2b3o2b2o7b2ob2o27b2ob2o7b2o2b3o2bobo2b3o2b2o7b
2ob2o27b2ob2o7b2o2b3o2bo$2o14bob2o3bo5bo2bo3bo3bo2bo5bo3b2obo14b3o14bo
b2o3bo5bo2bo3bo3bo2bo5bo3b2obo14b3o14bob2o3bo5bo2bo3bo3bo2bo5bo3b2obo
14bo$o4bob2ob2o3b3ob2o2bobobo2bo11bo2bobobo2b2ob3o3b2ob2obo4bo4bob2ob
2o3b3ob2o2bobobo2bo11bo2bobobo2b2ob3o3b2ob2obo4bo4bob2ob2o3b3ob2o2bobo
bo2bo11bo2bobobo2b2ob3o3b2ob2obo$b2o2bo3b3o3bob2obo9bo11bo9bob2obo3b3o
3bo2b2ob2o2bo3b3o3bob2obo9bo11bo9bob2obo3b3o3bo2b2ob2o2bo3b3o3bob2obo
9bo11bo9bob2obo3b3o3bo2b2o$6bo3bo3b2o2bobo2b3ob2o15b2ob3o2bobo2b2o3bo
3bo11bo3bo3b2o2bobo2b3ob2o15b2ob3o2bobo2b2o3bo3bo11bo3bo3b2o2bobo2b3ob
2o15b2ob3o2bobo2b2o3bo3bo$bob3o3bo2b2o15bo2bo3bo3bo2bo15b2o2bo3b3obobo
b3o3bo2b2o15bo2bo3bo3bo2bo15b2o2bo3b3obobob3o3bo2b2o15bo2bo3bo3bo2bo
15b2o2bo3b3obo$6bo3bo3b2o2bobo2b3ob2o15b2ob3o2bobo2b2o3bo3bo11bo3bo3b
2o2bobo2b3ob2o15b2ob3o2bobo2b2o3bo3bo11bo3bo3b2o2bobo2b3ob2o15b2ob3o2b
obo2b2o3bo3bo$b2o2bo3b3o3bob2obo9bo11bo9bob2obo3b3o3bo2b2ob2o2bo3b3o3b
ob2obo9bo11bo9bob2obo3b3o3bo2b2ob2o2bo3b3o3bob2obo9bo11bo9bob2obo3b3o
3bo2b2o$o4bob2ob2o3b3ob2o2bobobo2bo11bo2bobobo2b2ob3o3b2ob2obo4bo4bob
2ob2o3b3ob2o2bobobo2bo11bo2bobobo2b2ob3o3b2ob2obo4bo4bob2ob2o3b3ob2o2b
obobo2bo11bo2bobobo2b2ob3o3b2ob2obo$2o14bob2o3bo5bo2bo3bo3bo2bo5bo3b2o
bo14b3o14bob2o3bo5bo2bo3bo3bo2bo5bo3b2obo14b3o14bob2o3bo5bo2bo3bo3bo2b
o5bo3b2obo14bo$bo2b3o2b2o7b2ob2o27b2ob2o7b2o2b3o2bobo2b3o2b2o7b2ob2o
27b2ob2o7b2o2b3o2bobo2b3o2b2o7b2ob2o27b2ob2o7b2o2b3o2bo$bobobo7bob2obo
bobo2b2o2b2o2b2o3b2o2b2o2b2o2bobobob2obo7bobobobobobo7bob2obobobo2b2o
2b2o2b2o3b2o2b2o2b2o2bobobob2obo7bobobobobobo7bob2obobobo2b2o2b2o2b2o
3b2o2b2o2b2o2bobobob2obo7bobobo$o8bo4bo2bo3b2o5bobobo3bo3bobobo5b2o3bo
2bo4bo8bo8bo4bo2bo3b2o5bobobo3bo3bobobo5b2o3bo2bo4bo8bo8bo4bo2bo3b2o5b
obobo3bo3bobobo5b2o3bo2bo4bo$4b3ob3o3bobob2ob2o2bob3o5bobo5b3obo2b2ob
2obobo3b3ob3o7b3ob3o3bobob2ob2o2bob3o5bobo5b3obo2b2ob2obobo3b3ob3o7b3o
b3o3bobob2ob2o2bob3o5bobo5b3obo2b2ob2obobo3b3ob3o$3bo2bobo3b2o3bo2b2ob
obob2o4bobobobo4b2obobob2o2bo3b2o3bobo2bo5bo2bobo3b2o3bo2b2obobob2o4bo
bobobo4b2obobob2o2bo3b2o3bobo2bo5bo2bobo3b2o3bo2b2obobob2o4bobobobo4b
2obobob2o2bo3b2o3bobo2bo$2bo5bo6b2ob2o10bo11bo10b2ob2o6bo5bo3bo5bo6b2o
b2o10bo11bo10b2ob2o6bo5bo3bo5bo6b2ob2o10bo11bo10b2ob2o6bo5bo$2o2bo4b2o
b2o7bob2o2b2obo2bobobobo2bob2o2b2obo7b2ob2o4bo2b3o2bo4b2ob2o7bob2o2b2o
bo2bobobobo2bob2o2b2obo7b2ob2o4bo2b3o2bo4b2ob2o7bob2o2b2obo2bobobobo2b
ob2o2b2obo7b2ob2o4bo2bo$2o9bo6b2o2b2obo9bobo9bob2o2b2o6bo9b3o9bo6b2o2b
2obo9bobo9bob2o2b2o6bo9b3o9bo6b2o2b2obo9bobo9bob2o2b2o6bo9bo$7bobo3bob
obo3bo2b2obo4b2obobob2o4bob2o2bo3bobobo3bobo13bobo3bobobo3bo2b2obo4b2o
bobob2o4bob2o2bo3bobobo3bobo13bobo3bobobo3bo2b2obo4b2obobob2o4bob2o2bo
3bobobo3bobo$5bobo2bo2b3o3b3o2bo3b4o9b4o3bo2b3o3b3o2bo2bobo9bobo2bo2b
3o3b3o2bo3b4o9b4o3bo2b3o3b3o2bo2bobo9bobo2bo2b3o3b3o2bo3b4o9b4o3bo2b3o
3b3o2bo2bobo$2b2o3bo6bo7b2obob3obo9bob3obob2o7bo6bo3b2o3b2o3bo6bo7b2ob
ob3obo9bob3obob2o7bo6bo3b2o3b2o3bo6bo7b2obob3obo9bob3obob2o7bo6bo3b2o$
bo4bob5ob2o6bo4bo2bo2b3ob3o2bo2bo4bo6b2ob5obo4bobo4bob5ob2o6bo4bo2bo2b
3ob3o2bo2bo4bo6b2ob5obo4bobo4bob5ob2o6bo4bo2bo2b3ob3o2bo2bo4bo6b2ob5ob
o4bo$10bo6bobo2bobobobo2b3o5b3o2bobobobo2bobo6bo19bo6bobo2bobobobo2b3o
5b3o2bobobobo2bobo6bo19bo6bobo2bobobobo2b3o5b3o2bobobobo2bobo6bo$3o5bo
2bo2bob2o6bobobob3ob2ob2ob3obobobo6b2obo2bo2bo5b5o5bo2bo2bob2o6bobobob
3ob2ob2ob3obobobo6b2obo2bo2bo5b5o5bo2bo2bob2o6bobobob3ob2ob2ob3obobobo
6b2obo2bo2bo5b2o$4b2o2bo2b3o3b3o3bo3bobo3b2o3b2o3bobo3bo3b3o3b3o2bo2b
2o7b2o2bo2b3o3b3o3bo3bobo3b2o3b2o3bobo3bo3b3o3b3o2bo2b2o7b2o2bo2b3o3b
3o3bo3bobo3b2o3b2o3bobo3bo3b3o3b3o2bo2b2o$bo2bo3bob2o3bo2bo7bobobob2o
5b2obobobo7bo2bo3b2obo3bo2bobo2bo3bob2o3bo2bo7bobobob2o5b2obobobo7bo2b
o3b2obo3bo2bobo2bo3bob2o3bo2bo7bobobob2o5b2obobobo7bo2bo3b2obo3bo2bo$
2bobo3b2o4b3o3bob2o2bo3bo2b3ob3o2bo3bo2b2obo3b3o4b2o3bobo3bobo3b2o4b3o
3bob2o2bo3bo2b3ob3o2bo3bo2b2obo3b3o4b2o3bobo3bobo3b2o4b3o3bob2o2bo3bo
2b3ob3o2bo3bo2b2obo3b3o4b2o3bobo$bo2bo5bo3b2o2bob3o5b2o5bobo5b2o5b3obo
2b2o3bo5bo2bobo2bo5bo3b2o2bob3o5b2o5bobo5b2o5b3obo2b2o3bo5bo2bobo2bo5b
o3b2o2bob3o5b2o5bobo5b2o5b3obo2b2o3bo5bo2bo$5b2obob2o5bo4b2obobo2bo5bo
5bo2bobob2o4bo5b2obob2o9b2obob2o5bo4b2obobo2bo5bo5bo2bobob2o4bo5b2obob
2o9b2obob2o5bo4b2obobo2bo5bo5bo2bobob2o4bo5b2obob2o$o3b2o2bo2bo5bo2bo
4bobo8bo8bobo4bo2bo5bo2bo2b2o3bo3b2o2bo2bo5bo2bo4bobo8bo8bobo4bo2bo5bo
2bo2b2o3bo3b2o2bo2bo5bo2bo4bobo8bo8bobo4bo2bo5bo2bo2b2o$9bob3o2b3obo3b
o8b2o3b2o8bo3bob3o2b3obo17bob3o2b3obo3bo8b2o3b2o8bo3bob3o2b3obo17bob3o
2b3obo3bo8b2o3b2o8bo3bob3o2b3obo$b2obo2bo5b2obo2b2obo2bo2bo2bob3ob3obo
2bo2bo2bob2o2bob2o5bo2bob2ob2obo2bo5b2obo2b2obo2bo2bo2bob3ob3obo2bo2bo
2bob2o2bob2o5bo2bob2ob2obo2bo5b2obo2b2obo2bo2bo2bob3ob3obo2bo2bo2bob2o
2bob2o5bo2bob2o$ob2o2b3o2bo3bo4bo2bobo2b2obo2bobobo2bob2o2bobo2bo4bo3b
o2b3o2b2obob2o2b3o2bo3bo4bo2bobo2b2obo2bobobo2bob2o2bobo2bo4bo3bo2b3o
2b2obob2o2b3o2bo3bo4bo2bobo2b2obo2bobobo2bob2o2bobo2bo4bo3bo2b3o2b2o$
2bo6bo2b2ob4obo5b3o4bo5bo4b3o5bob4ob2o2bo6bo3bo6bo2b2ob4obo5b3o4bo5bo
4b3o5bob4ob2o2bo6bo3bo6bo2b2ob4obo5b3o4bo5bo4b3o5bob4ob2o2bo6bo$o3bo4b
2o10b3o9bo5bo9b3o10b2o4bo3bo3bo4b2o10b3o9bo5bo9b3o10b2o4bo3bo3bo4b2o
10b3o9bo5bo9b3o10b2o4bo$9bo3bo6bo6b2o2bo3bobo3bo2b2o6bo6bo3bo17bo3bo6b
o6b2o2bo3bobo3bo2b2o6bo6bo3bo17bo3bo6bo6b2o2bo3bobo3bo2b2o6bo6bo3bo$4b
o7b2o3bo4bo5bob2ob2obob2ob2obo5bo4bo3b2o7bo7bo7b2o3bo4bo5bob2ob2obob2o
b2obo5bo4bo3b2o7bo7bo7b2o3bo4bo5bob2ob2obob2ob2obo5bo4bo3b2o7bo$2bo2bo
bo2bobob4o7bo2bo2bo4bo4bo2bo2bo7b4obobo2bobo2bo3bo2bobo2bobob4o7bo2bo
2bo4bo4bo2bo2bo7b4obobo2bobo2bo3bo2bobo2bobob4o7bo2bo2bo4bo4bo2bo2bo7b
4obobo2bobo2bo$9bo11bo5bo2bo5bo5bo2bo5bo11bo17bo11bo5bo2bo5bo5bo2bo5bo
11bo17bo11bo5bo2bo5bo5bo2bo5bo11bo$2bobo3b3o4bo2bo2bo4bo7bo3bo7bo4bo2b
o2bo4b3o3bobo3bobo3b3o4bo2bo2bo4bo7bo3bo7bo4bo2bo2bo4b3o3bobo3bobo3b3o
4bo2bo2bo4bo7bo3bo7bo4bo2bo2bo4b3o3bobo$2o8bo3bobobobo3b2o4b3obobobob
3o4b2o3bobobobo3bo8b3o8bo3bobobobo3b2o4b3obobobob3o4b2o3bobobobo3bo8b
3o8bo3bobobobo3b2o4b3obobobob3o4b2o3bobobobo3bo8bo$2o5bobo2bo5bo5b2o3b
o2b2o5b2o2bo3b2o5bo5bo2bobo5b3o5bobo2bo5bo5b2o3bo2b2o5b2o2bo3b2o5bo5bo
2bobo5b3o5bobo2bo5bo5b2o3bo2b2o5b2o2bo3b2o5bo5bo2bobo5bo$2o8bo3bobobob
o3b2o4b3obobobob3o4b2o3bobobobo3bo8b3o8bo3bobobobo3b2o4b3obobobob3o4b
2o3bobobobo3bo8b3o8bo3bobobobo3b2o4b3obobobob3o4b2o3bobobobo3bo8bo$2bo
bo3b3o4bo2bo2bo4bo7bo3bo7bo4bo2bo2bo4b3o3bobo3bobo3b3o4bo2bo2bo4bo7bo
3bo7bo4bo2bo2bo4b3o3bobo3bobo3b3o4bo2bo2bo4bo7bo3bo7bo4bo2bo2bo4b3o3bo
bo$9bo11bo5bo2bo5bo5bo2bo5bo11bo17bo11bo5bo2bo5bo5bo2bo5bo11bo17bo11bo
5bo2bo5bo5bo2bo5bo11bo$2bo2bobo2bobob4o7bo2bo2bo4bo4bo2bo2bo7b4obobo2b
obo2bo3bo2bobo2bobob4o7bo2bo2bo4bo4bo2bo2bo7b4obobo2bobo2bo3bo2bobo2bo
bob4o7bo2bo2bo4bo4bo2bo2bo7b4obobo2bobo2bo$4bo7b2o3bo4bo5bob2ob2obob2o
b2obo5bo4bo3b2o7bo7bo7b2o3bo4bo5bob2ob2obob2ob2obo5bo4bo3b2o7bo7bo7b2o
3bo4bo5bob2ob2obob2ob2obo5bo4bo3b2o7bo$9bo3bo6bo6b2o2bo3bobo3bo2b2o6bo
6bo3bo17bo3bo6bo6b2o2bo3bobo3bo2b2o6bo6bo3bo17bo3bo6bo6b2o2bo3bobo3bo
2b2o6bo6bo3bo$o3bo4b2o10b3o9bo5bo9b3o10b2o4bo3bo3bo4b2o10b3o9bo5bo9b3o
10b2o4bo3bo3bo4b2o10b3o9bo5bo9b3o10b2o4bo$2bo6bo2b2ob4obo5b3o4bo5bo4b
3o5bob4ob2o2bo6bo3bo6bo2b2ob4obo5b3o4bo5bo4b3o5bob4ob2o2bo6bo3bo6bo2b
2ob4obo5b3o4bo5bo4b3o5bob4ob2o2bo6bo$ob2o2b3o2bo3bo4bo2bobo2b2obo2bobo
bo2bob2o2bobo2bo4bo3bo2b3o2b2obob2o2b3o2bo3bo4bo2bobo2b2obo2bobobo2bob
2o2bobo2bo4bo3bo2b3o2b2obob2o2b3o2bo3bo4bo2bobo2b2obo2bobobo2bob2o2bob
o2bo4bo3bo2b3o2b2o$b2obo2bo5b2obo2b2obo2bo2bo2bob3ob3obo2bo2bo2bob2o2b
ob2o5bo2bob2ob2obo2bo5b2obo2b2obo2bo2bo2bob3ob3obo2bo2bo2bob2o2bob2o5b
o2bob2ob2obo2bo5b2obo2b2obo2bo2bo2bob3ob3obo2bo2bo2bob2o2bob2o5bo2bob
2o$9bob3o2b3obo3bo8b2o3b2o8bo3bob3o2b3obo17bob3o2b3obo3bo8b2o3b2o8bo3b
ob3o2b3obo17bob3o2b3obo3bo8b2o3b2o8bo3bob3o2b3obo$o3b2o2bo2bo5bo2bo4bo
bo8bo8bobo4bo2bo5bo2bo2b2o3bo3b2o2bo2bo5bo2bo4bobo8bo8bobo4bo2bo5bo2bo
2b2o3bo3b2o2bo2bo5bo2bo4bobo8bo8bobo4bo2bo5bo2bo2b2o$5b2obob2o5bo4b2ob
obo2bo5bo5bo2bobob2o4bo5b2obob2o9b2obob2o5bo4b2obobo2bo5bo5bo2bobob2o
4bo5b2obob2o9b2obob2o5bo4b2obobo2bo5bo5bo2bobob2o4bo5b2obob2o$bo2bo5bo
3b2o2bob3o5b2o5bobo5b2o5b3obo2b2o3bo5bo2bobo2bo5bo3b2o2bob3o5b2o5bobo
5b2o5b3obo2b2o3bo5bo2bobo2bo5bo3b2o2bob3o5b2o5bobo5b2o5b3obo2b2o3bo5bo
2bo$2bobo3b2o4b3o3bob2o2bo3bo2b3ob3o2bo3bo2b2obo3b3o4b2o3bobo3bobo3b2o
4b3o3bob2o2bo3bo2b3ob3o2bo3bo2b2obo3b3o4b2o3bobo3bobo3b2o4b3o3bob2o2bo
3bo2b3ob3o2bo3bo2b2obo3b3o4b2o3bobo$bo2bo3bob2o3bo2bo7bobobob2o5b2obob
obo7bo2bo3b2obo3bo2bobo2bo3bob2o3bo2bo7bobobob2o5b2obobobo7bo2bo3b2obo
3bo2bobo2bo3bob2o3bo2bo7bobobob2o5b2obobobo7bo2bo3b2obo3bo2bo$4b2o2bo
2b3o3b3o3bo3bobo3b2o3b2o3bobo3bo3b3o3b3o2bo2b2o7b2o2bo2b3o3b3o3bo3bobo
3b2o3b2o3bobo3bo3b3o3b3o2bo2b2o7b2o2bo2b3o3b3o3bo3bobo3b2o3b2o3bobo3bo
3b3o3b3o2bo2b2o$3o5bo2bo2bob2o6bobobob3ob2ob2ob3obobobo6b2obo2bo2bo5b
5o5bo2bo2bob2o6bobobob3ob2ob2ob3obobobo6b2obo2bo2bo5b5o5bo2bo2bob2o6bo
bobob3ob2ob2ob3obobobo6b2obo2bo2bo5b2o$10bo6bobo2bobobobo2b3o5b3o2bobo
bobo2bobo6bo19bo6bobo2bobobobo2b3o5b3o2bobobobo2bobo6bo19bo6bobo2bobob
obo2b3o5b3o2bobobobo2bobo6bo$bo4bob5ob2o6bo4bo2bo2b3ob3o2bo2bo4bo6b2ob
5obo4bobo4bob5ob2o6bo4bo2bo2b3ob3o2bo2bo4bo6b2ob5obo4bobo4bob5ob2o6bo
4bo2bo2b3ob3o2bo2bo4bo6b2ob5obo4bo$2b2o3bo6bo7b2obob3obo9bob3obob2o7bo
6bo3b2o3b2o3bo6bo7b2obob3obo9bob3obob2o7bo6bo3b2o3b2o3bo6bo7b2obob3obo
9bob3obob2o7bo6bo3b2o$5bobo2bo2b3o3b3o2bo3b4o9b4o3bo2b3o3b3o2bo2bobo9b
obo2bo2b3o3b3o2bo3b4o9b4o3bo2b3o3b3o2bo2bobo9bobo2bo2b3o3b3o2bo3b4o9b
4o3bo2b3o3b3o2bo2bobo$7bobo3bobobo3bo2b2obo4b2obobob2o4bob2o2bo3bobobo
3bobo13bobo3bobobo3bo2b2obo4b2obobob2o4bob2o2bo3bobobo3bobo13bobo3bobo
bo3bo2b2obo4b2obobob2o4bob2o2bo3bobobo3bobo$2o9bo6b2o2b2obo9bobo9bob2o
2b2o6bo9b3o9bo6b2o2b2obo9bobo9bob2o2b2o6bo9b3o9bo6b2o2b2obo9bobo9bob2o
2b2o6bo9bo$2o2bo4b2ob2o7bob2o2b2obo2bobobobo2bob2o2b2obo7b2ob2o4bo2b3o
2bo4b2ob2o7bob2o2b2obo2bobobobo2bob2o2b2obo7b2ob2o4bo2b3o2bo4b2ob2o7bo
b2o2b2obo2bobobobo2bob2o2b2obo7b2ob2o4bo2bo$2bo5bo6b2ob2o10bo11bo10b2o
b2o6bo5bo3bo5bo6b2ob2o10bo11bo10b2ob2o6bo5bo3bo5bo6b2ob2o10bo11bo10b2o
b2o6bo5bo$3bo2bobo3b2o3bo2b2obobob2o4bobobobo4b2obobob2o2bo3b2o3bobo2b
o5bo2bobo3b2o3bo2b2obobob2o4bobobobo4b2obobob2o2bo3b2o3bobo2bo5bo2bobo
3b2o3bo2b2obobob2o4bobobobo4b2obobob2o2bo3b2o3bobo2bo$4b3ob3o3bobob2ob
2o2bob3o5bobo5b3obo2b2ob2obobo3b3ob3o7b3ob3o3bobob2ob2o2bob3o5bobo5b3o
bo2b2ob2obobo3b3ob3o7b3ob3o3bobob2ob2o2bob3o5bobo5b3obo2b2ob2obobo3b3o
b3o$o8bo4bo2bo3b2o5bobobo3bo3bobobo5b2o3bo2bo4bo8bo8bo4bo2bo3b2o5bobob
o3bo3bobobo5b2o3bo2bo4bo8bo8bo4bo2bo3b2o5bobobo3bo3bobobo5b2o3bo2bo4bo
$bobobo7bob2obobobo2b2o2b2o2b2o3b2o2b2o2b2o2bobobob2obo7bobobobobobo7b
ob2obobobo2b2o2b2o2b2o3b2o2b2o2b2o2bobobob2obo7bobobobobobo7bob2obobob
o2b2o2b2o2b2o3b2o2b2o2b2o2bobobob2obo7bobobo$bo2b3o2b2o7b2ob2o27b2ob2o
7b2o2b3o2bobo2b3o2b2o7b2ob2o27b2ob2o7b2o2b3o2bobo2b3o2b2o7b2ob2o27b2ob
2o7b2o2b3o2bo$2o14bob2o3bo5bo2bo3bo3bo2bo5bo3b2obo14b3o14bob2o3bo5bo2b
o3bo3bo2bo5bo3b2obo14b3o14bob2o3bo5bo2bo3bo3bo2bo5bo3b2obo14bo$o4bob2o
b2o3b3ob2o2bobobo2bo11bo2bobobo2b2ob3o3b2ob2obo4bo4bob2ob2o3b3ob2o2bob
obo2bo11bo2bobobo2b2ob3o3b2ob2obo4bo4bob2ob2o3b3ob2o2bobobo2bo11bo2bob
obo2b2ob3o3b2ob2obo$b2o2bo3b3o3bob2obo9bo11bo9bob2obo3b3o3bo2b2ob2o2bo
3b3o3bob2obo9bo11bo9bob2obo3b3o3bo2b2ob2o2bo3b3o3bob2obo9bo11bo9bob2ob
o3b3o3bo2b2o$6bo3bo3b2o2bobo2b3ob2o15b2ob3o2bobo2b2o3bo3bo11bo3bo3b2o
2bobo2b3ob2o15b2ob3o2bobo2b2o3bo3bo11bo3bo3b2o2bobo2b3ob2o15b2ob3o2bob
o2b2o3bo3bo$bob3o3bo2b2o15bo2bo3bo3bo2bo15b2o2bo3b3obobob3o3bo2b2o15bo
2bo3bo3bo2bo15b2o2bo3b3obobob3o3bo2b2o15bo2bo3bo3bo2bo15b2o2bo3b3obo$
6bo3bo3b2o2bobo2b3ob2o15b2ob3o2bobo2b2o3bo3bo11bo3bo3b2o2bobo2b3ob2o
15b2ob3o2bobo2b2o3bo3bo11bo3bo3b2o2bobo2b3ob2o15b2ob3o2bobo2b2o3bo3bo$
b2o2bo3b3o3bob2obo9bo11bo9bob2obo3b3o3bo2b2ob2o2bo3b3o3bob2obo9bo11bo
9bob2obo3b3o3bo2b2ob2o2bo3b3o3bob2obo9bo11bo9bob2obo3b3o3bo2b2o$o4bob
2ob2o3b3ob2o2bobobo2bo11bo2bobobo2b2ob3o3b2ob2obo4bo4bob2ob2o3b3ob2o2b
obobo2bo11bo2bobobo2b2ob3o3b2ob2obo4bo4bob2ob2o3b3ob2o2bobobo2bo11bo2b
obobo2b2ob3o3b2ob2obo$2o14bob2o3bo5bo2bo3bo3bo2bo5bo3b2obo14b3o14bob2o
3bo5bo2bo3bo3bo2bo5bo3b2obo14b3o14bob2o3bo5bo2bo3bo3bo2bo5bo3b2obo14bo
$bo2b3o2b2o7b2ob2o27b2ob2o7b2o2b3o2bobo2b3o2b2o7b2ob2o27b2ob2o7b2o2b3o
2bobo2b3o2b2o7b2ob2o27b2ob2o7b2o2b3o2bo$bobobo7bob2obobobo2b2o2b2o2b2o
3b2o2b2o2b2o2bobobob2obo7bobobobobobo7bob2obobobo2b2o2b2o2b2o3b2o2b2o
2b2o2bobobob2obo7bobobobobobo7bob2obobobo2b2o2b2o2b2o3b2o2b2o2b2o2bobo
bob2obo7bobobo$o8bo4bo2bo3b2o5bobobo3bo3bobobo5b2o3bo2bo4bo8bo8bo4bo2b
o3b2o5bobobo3bo3bobobo5b2o3bo2bo4bo8bo8bo4bo2bo3b2o5bobobo3bo3bobobo5b
2o3bo2bo4bo$4b3ob3o3bobob2ob2o2bob3o5bobo5b3obo2b2ob2obobo3b3ob3o7b3ob
3o3bobob2ob2o2bob3o5bobo5b3obo2b2ob2obobo3b3ob3o7b3ob3o3bobob2ob2o2bob
3o5bobo5b3obo2b2ob2obobo3b3ob3o$3bo2bobo3b2o3bo2b2obobob2o4bobobobo4b
2obobob2o2bo3b2o3bobo2bo5bo2bobo3b2o3bo2b2obobob2o4bobobobo4b2obobob2o
2bo3b2o3bobo2bo5bo2bobo3b2o3bo2b2obobob2o4bobobobo4b2obobob2o2bo3b2o3b
obo2bo$2bo5bo6b2ob2o10bo11bo10b2ob2o6bo5bo3bo5bo6b2ob2o10bo11bo10b2ob
2o6bo5bo3bo5bo6b2ob2o10bo11bo10b2ob2o6bo5bo$2o2bo4b2ob2o7bob2o2b2obo2b
obobobo2bob2o2b2obo7b2ob2o4bo2b3o2bo4b2ob2o7bob2o2b2obo2bobobobo2bob2o
2b2obo7b2ob2o4bo2b3o2bo4b2ob2o7bob2o2b2obo2bobobobo2bob2o2b2obo7b2ob2o
4bo2bo$2o9bo6b2o2b2obo9bobo9bob2o2b2o6bo9b3o9bo6b2o2b2obo9bobo9bob2o2b
2o6bo9b3o9bo6b2o2b2obo9bobo9bob2o2b2o6bo9bo$7bobo3bobobo3bo2b2obo4b2ob
obob2o4bob2o2bo3bobobo3bobo13bobo3bobobo3bo2b2obo4b2obobob2o4bob2o2bo
3bobobo3bobo13bobo3bobobo3bo2b2obo4b2obobob2o4bob2o2bo3bobobo3bobo$5bo
bo2bo2b3o3b3o2bo3b4o9b4o3bo2b3o3b3o2bo2bobo9bobo2bo2b3o3b3o2bo3b4o9b4o
3bo2b3o3b3o2bo2bobo9bobo2bo2b3o3b3o2bo3b4o9b4o3bo2b3o3b3o2bo2bobo$2b2o
3bo6bo7b2obob3obo9bob3obob2o7bo6bo3b2o3b2o3bo6bo7b2obob3obo9bob3obob2o
7bo6bo3b2o3b2o3bo6bo7b2obob3obo9bob3obob2o7bo6bo3b2o$bo4bob5ob2o6bo4bo
2bo2b3ob3o2bo2bo4bo6b2ob5obo4bobo4bob5ob2o6bo4bo2bo2b3ob3o2bo2bo4bo6b
2ob5obo4bobo4bob5ob2o6bo4bo2bo2b3ob3o2bo2bo4bo6b2ob5obo4bo$10bo6bobo2b
obobobo2b3o5b3o2bobobobo2bobo6bo19bo6bobo2bobobobo2b3o5b3o2bobobobo2bo
bo6bo19bo6bobo2bobobobo2b3o5b3o2bobobobo2bobo6bo$3o5bo2bo2bob2o6bobobo
b3ob2ob2ob3obobobo6b2obo2bo2bo5b5o5bo2bo2bob2o6bobobob3ob2ob2ob3obobob
o6b2obo2bo2bo5b5o5bo2bo2bob2o6bobobob3ob2ob2ob3obobobo6b2obo2bo2bo5b2o
$4b2o2bo2b3o3b3o3bo3bobo3b2o3b2o3bobo3bo3b3o3b3o2bo2b2o7b2o2bo2b3o3b3o
3bo3bobo3b2o3b2o3bobo3bo3b3o3b3o2bo2b2o7b2o2bo2b3o3b3o3bo3bobo3b2o3b2o
3bobo3bo3b3o3b3o2bo2b2o$bo2bo3bob2o3bo2bo7bobobob2o5b2obobobo7bo2bo3b
2obo3bo2bobo2bo3bob2o3bo2bo7bobobob2o5b2obobobo7bo2bo3b2obo3bo2bobo2bo
3bob2o3bo2bo7bobobob2o5b2obobobo7bo2bo3b2obo3bo2bo$2bobo3b2o4b3o3bob2o
2bo3bo2b3ob3o2bo3bo2b2obo3b3o4b2o3bobo3bobo3b2o4b3o3bob2o2bo3bo2b3ob3o
2bo3bo2b2obo3b3o4b2o3bobo3bobo3b2o4b3o3bob2o2bo3bo2b3ob3o2bo3bo2b2obo
3b3o4b2o3bobo$bo2bo5bo3b2o2bob3o5b2o5bobo5b2o5b3obo2b2o3bo5bo2bobo2bo
5bo3b2o2bob3o5b2o5bobo5b2o5b3obo2b2o3bo5bo2bobo2bo5bo3b2o2bob3o5b2o5bo
bo5b2o5b3obo2b2o3bo5bo2bo$5b2obob2o5bo4b2obobo2bo5bo5bo2bobob2o4bo5b2o
bob2o9b2obob2o5bo4b2obobo2bo5bo5bo2bobob2o4bo5b2obob2o9b2obob2o5bo4b2o
bobo2bo5bo5bo2bobob2o4bo5b2obob2o$o3b2o2bo2bo5bo2bo4bobo8bo8bobo4bo2bo
5bo2bo2b2o3bo3b2o2bo2bo5bo2bo4bobo8bo8bobo4bo2bo5bo2bo2b2o3bo3b2o2bo2b
o5bo2bo4bobo8bo8bobo4bo2bo5bo2bo2b2o$9bob3o2b3obo3bo8b2o3b2o8bo3bob3o
2b3obo17bob3o2b3obo3bo8b2o3b2o8bo3bob3o2b3obo17bob3o2b3obo3bo8b2o3b2o
8bo3bob3o2b3obo$b2obo2bo5b2obo2b2obo2bo2bo2bob3ob3obo2bo2bo2bob2o2bob
2o5bo2bob2ob2obo2bo5b2obo2b2obo2bo2bo2bob3ob3obo2bo2bo2bob2o2bob2o5bo
2bob2ob2obo2bo5b2obo2b2obo2bo2bo2bob3ob3obo2bo2bo2bob2o2bob2o5bo2bob2o
$ob2o2b3o2bo3bo4bo2bobo2b2obo2bobobo2bob2o2bobo2bo4bo3bo2b3o2b2obob2o
2b3o2bo3bo4bo2bobo2b2obo2bobobo2bob2o2bobo2bo4bo3bo2b3o2b2obob2o2b3o2b
o3bo4bo2bobo2b2obo2bobobo2bob2o2bobo2bo4bo3bo2b3o2b2o$2bo6bo2b2ob4obo
5b3o4bo5bo4b3o5bob4ob2o2bo6bo3bo6bo2b2ob4obo5b3o4bo5bo4b3o5bob4ob2o2bo
6bo3bo6bo2b2ob4obo5b3o4bo5bo4b3o5bob4ob2o2bo6bo$o3bo4b2o10b3o9bo5bo9b
3o10b2o4bo3bo3bo4b2o10b3o9bo5bo9b3o10b2o4bo3bo3bo4b2o10b3o9bo5bo9b3o
10b2o4bo$9bo3bo6bo6b2o2bo3bobo3bo2b2o6bo6bo3bo17bo3bo6bo6b2o2bo3bobo3b
o2b2o6bo6bo3bo17bo3bo6bo6b2o2bo3bobo3bo2b2o6bo6bo3bo$4bo7b2o3bo4bo5bob
2ob2obob2ob2obo5bo4bo3b2o7bo7bo7b2o3bo4bo5bob2ob2obob2ob2obo5bo4bo3b2o
7bo7bo7b2o3bo4bo5bob2ob2obob2ob2obo5bo4bo3b2o7bo$2bo2bobo2bobob4o7bo2b
o2bo4bo4bo2bo2bo7b4obobo2bobo2bo3bo2bobo2bobob4o7bo2bo2bo4bo4bo2bo2bo
7b4obobo2bobo2bo3bo2bobo2bobob4o7bo2bo2bo4bo4bo2bo2bo7b4obobo2bobo2bo$
9bo11bo5bo2bo5bo5bo2bo5bo11bo17bo11bo5bo2bo5bo5bo2bo5bo11bo17bo11bo5bo
2bo5bo5bo2bo5bo11bo$2bobo3b3o4bo2bo2bo4bo7bo3bo7bo4bo2bo2bo4b3o3bobo3b
obo3b3o4bo2bo2bo4bo7bo3bo7bo4bo2bo2bo4b3o3bobo3bobo3b3o4bo2bo2bo4bo7bo
3bo7bo4bo2bo2bo4b3o3bobo$2o8bo3bobobobo3b2o4b3obobobob3o4b2o3bobobobo
3bo8b3o8bo3bobobobo3b2o4b3obobobob3o4b2o3bobobobo3bo8b3o8bo3bobobobo3b
2o4b3obobobob3o4b2o3bobobobo3bo8bo!

Also, has anyone ever been able to create the large still-life necessary to complete the following synthesis?

Code: Select all

x = 49, y = 50, rule = B3/S23
bo$2bo$3o2$45bo$43b2o$44b2o19$33bobo$33b2o$34bo$18b2o$18bo3b2o$20bo2bo
11bo$16b6o13bobo$16bo18b2o$17b2ob2o$18bobo15bo$18bobo15b2o$19bo15bobo
2$42b2o$42bobo$42bo7$47bo$46b2o$46bobo!

Is there a known synthesis of small lake that takes fewer than 11 gliders?

Code: Select all

#C 11-glider synthesis of small lake
x = 25, y = 25, rule = B3/S23
13bo$13bobo$7bo5b2o$8bo$6b3o2$20bo$20bobo$10bo4bobo2b2o$bo6bobo4b2o$2b
o6b2o5bo$3o2$22b3o$18b2o2bo$17b2o4bo$3b2o14bo$2bobo$4bo2$16b3o$16bo$
10b2o5bo$9bobo$11bo!

[Extrementhusiast]

About the Test Tube Baby, I got quite close to cleaning up the mess with one glider. I know it can be done with two. Here it is:

Code: Select all

x = 30, y = 52, rule = B3/S23
bo$2bo$3o33$17bo2bo$15bobo2bobo$16b2o2b2o4$18b2o$17bo2bo$18b2o6$8b3o
16b3o$10bo16bo$9bo18bo!

Even better:

Code: Select all

x = 23, y = 34, rule = B3/S23
o$b2o$2o15$10bo2bo$8bobo2bobo$9b2o2b2o4$11b2o$10bo2bo$11b2o6$b3o16b3o$
3bo16bo$2bo18bo!

[Jason Summers]

Here are some predecessors of some large oscillators that might be synthesizable (p9, p16, and p51):

The p51 can be done by brute force, if nothing else.

Code: Select all

x = 77, y = 77, rule = B3/S23
69bo$69bobo$69boo3$bo$bbo$3o12bo27bo$16boo26bo$15boo25b3o17bobo$62boo$
63bo$9bo28bo$10boo27bo$9boo26b3o17bobo$27bo29boo8bobo$26bobo29bo8boo$
14bo11boo40bo$15boo28bo$14boo30bo$29boo13b3o$28bobbo$29boo3$34boo5boo$
34bobo3bobo16boo$35bo5bo17bobo$55bo4bo$29boo15boo6bobo$19boo8boo15boo
6bobo$18bobo34bo$8boo10bo11boo9boo$7bobo22boo9boo$9bo15boo23boo$25bobo
21bobo$26bo23bo$13boo47bo$12bobo47bobo$14bo47boo$26bo23bo$25bobo21bobo
$25boo23boo15bo$32boo9boo22bobo$32boo9boo11bo10boo$21bo34bobo$20bobo6b
oo15boo8boo$20bobo6boo15boo$16bo4bo$15bobo17bo5bo$16boo16bobo3bobo$34b
oo5boo3$46boo$45bobbo$30b3o13boo$30bo30boo$31bo28boo$8bo40boo11bo$8boo
8bo29bobo$7bobo8boo29bo$17bobo17b3o26boo$37bo27boo$38bo28bo$13bo$13boo
$12bobo17b3o25boo$32bo26boo$33bo27bo12b3o$74bo$75bo3$6boo$5bobo$7bo!

[Sokwe]

I would like to complete the p51 synthesis for the LifeWiki pattern page, but I thought I might discuss it here to see if it can be reduced at all.

Obviously, the blocks take no more than sixteen gliders (two for each block):

Code: Select all

x = 27, y = 30, rule = B3/S23
8bo$6bobo$7b2o16bo$24bo$24b3o4$10bo$8bobo$9b2o6bo$2o14bo$2o14b3o2$3b2o
$3b2o10$3b2o9b2o$3b2o9b2o2$2o15b2o$2o15b2o!

Does anyone know a way to synthesize a single group of those blocks with only 3 gliders?

Each of the central boats can be added by four gliders (three are used to synthesize a heavyweight spaceship):

Code: Select all

x = 27, y = 39, rule = B3/S23
16bobo$15bo$15bo3bo$15bo3bo$15bo$15bo2bo$15b3o5$19bo$9b2o8bobo$9bobo7b
2o$10bo2$4b2o15b2o$4b2o15b2o2$7b2o9b2o$7b2o9b2o$2o23b2o$obo21bobo$bo
23bo4$bo23bo$obo21bobo$2o23b2o$7b2o9b2o$7b2o9b2o2$4b2o15b2o$4b2o15b2o
2$10bo5bo$9bobo3bobo$9b2o5b2o!

The total number of gliders needed to synthesize these boats could probably be reduced by synthesizing some of them before the blocks. Is there a three glider synthesis that can place the boat in the above pattern?

The beehives and outer boats can be synthesized with another sixteen gliders (four for each group):

Code: Select all

x = 55, y = 47, rule = B3/S23
12bo$11bobo24bo$11b2o26bo$37b3o2$14b2o$13bo2bo$14b2o3$19b2o5b2o15bo$
19bobo3bobo14bo$20bo5bo15b3o2$14b2o15b2o$14b2o15b2o2$17b2o9b2o$17b2o9b
2o15b3o$10b2o23b2o8bo7bo$10bobo21bobo9bo5b2o$11bo23bo16bobo4$11bo23bo$
10bobo21bobo$10b2o23b2o$17b2o9b2o$17b2o9b2o$6bo$5bobo6b2o15b2o$5bobo6b
2o15b2o$bo4bo$obo17bo5bo$b2o16bobo3bobo$19b2o5b2o3$31b2o$30bo2bo$31b2o
3$34b2o$33bobo$34bo!

The complete synthesis should take no more than ninety-two gliders.

[knightlife]

Does anyone know a way to synthesize a single group of those blocks with only 3 gliders?

Here are two ways:

Code: Select all

x = 31, y = 24, rule = B3/S23
28bo$28bobo$28b2o$2bo$obo$b2o18bo$19bobo$20b2o6$4b3o$6bo$5bo17b3o$25bo
$24bo4$2b2o$bobo$3bo!

They are similar but one requires no salvo. Both have a degree of freedom for the third glider since it simply moves one block.


One way to synthesize the four groups:

Code: Select all

x = 35, y = 35, rule = B3/S23
2bo$3bo28bo$b3o28bobo$32b2o$18bo$13bo5bo$14bo2b3o$12b3o5$27bo$27bobo$
27b2o$5b2o$4bobo$6bo21bo$28bobo$28b2o$6b2o$5bobo$7bo5$20b3o$15b3o2bo$
15bo5bo$16bo$b2o$obo28b3o$2bo28bo$32bo!

[knightlife]

Three glider synthesis to place a boat in the pattern:

Code: Select all

x = 27, y = 38, rule = B3/S23
13bo4bo$14bo3bobo$12b3o3b2o4$13b2o$12bobo$14bo3$9b2o$9bobo$10bo2$4b2o
15b2o$4b2o15b2o2$7b2o9b2o$7b2o9b2o$2o23b2o$obo21bobo$bo23bo4$bo23bo$ob
o21bobo$2o23b2o$7b2o9b2o$7b2o9b2o2$4b2o15b2o$4b2o15b2o2$10bo5bo$9bobo
3bobo$9b2o5b2o!

To use this requires interleaving with the rest of the synthesis.

[knightlife]

Here is a way to place 4 boats at 2 gliders each and still get pairs of blocks at 3 gliders each:

Code: Select all

x = 69, y = 69, rule = B3/S23
55bobo$55b2o$56bo2$41bo$40bo$40b3o$58bo$56b2o$57b2o$7bobo$o7b2o12bobo$
b2o5bo14b2o$2o21bo3$26bo$27bo$25b3o4$57bo$55b2o$56b2o$50bo$6bo43bobo$
4bobo43b2o$5b2o12$62b2o$17b2o43bobo$16bobo43bo$18bo$11b2o$12b2o$11bo4$
41b3o$41bo$42bo3$45bo21b2o$44b2o14bo5b2o$44bobo12b2o7bo$59bobo$10b2o$
11b2o$10bo$26b3o$28bo$27bo2$12bo$12b2o$11bobo!

[Sokwe]

After working with it for a while, here is a 78-glider synthesis of Nicolay's p51 oscillator:

Code: Select all

#C 78-glider synthesis of Nicolay's p51 oscillator by Matthias
#C Merzenich with Jason Summers and "Knightlife"
x = 303, y = 303, rule = B3/S23
295bobo$295b2o$296bo3$o$b2o$2o14bo25bo$14bobo26b2o244bo$15b2o25b2o244b
o$288b3o2$10bo26bo$8bobo27b2o244bo$9b2o26b2o62bobo179bo10bo$102b2o179b
3o7bo$102bo190b3o$15bo$13bobo28bo$14b2o29b2o$44b2o3$245bo$245bobo$245b
2o2$204bo$204bobo$204b2o$243bobo$243b2o$244bo$41bobo$42b2o27bo$42bo29b
o$70b3o$288bobo$288b2o$289bo3$293bobo$266bo26b2o$265bo16bobo9bo$265b3o
14b2o$283bo11$63bobo$64b2o$64bo2$233bo$233bobo4bo$233b2o3b2o$239b2o2$
78bobo$75bo3b2o$68bo4bobo3bo$69b2o3b2o$68b2o2$216bobo$216b2o3bo$217bo
3bobo$221b2o$216bo$215bo$215b3o3$48bobo39bo$49b2o5bo34b2o3bo136bo$49bo
7bo32b2o2bobo135bo$55b3o37b2o135b3o3$73bo127bobo17bo$74b2o125b2o16b2o$
73b2o127bo17b2o2$86bo158bobo$87bo133bo23b2o$85b3o133bobo22bo$221b2o2$
84bo$85b2o3bo$84b2o2bobo$89b2o3$208bo$206b2o$207b2o2$196b3o$196bo$197b
o3$194b3o$194bo$195bo15$100bo$100b2o$99bobo3$102bo$102b2o$101bobo76$
77b2o$76bobo$78bo3$229b2o$228b2o$230bo2$81bo$81b2o$80bobo$89b2o$88bobo
145b2o$90bo133b3o9bobo$224bo11bo$225bo$218bo$60b2o155b2o$61b2o154bobo$
60bo$33bo$33b2o$32bobo23b3o$60bo$59bo5$268b3o$268bo7bo$207b3o59bo5b2o$
207bo29bo37bobo$208bo27b2o$236bobo$81bo$81b2o$80bobo5$79b2o$78bobo$19b
o60bo$19b2o$8bo9bobo$8b2o$7bobo3$13bo$13b2o$12bobo17$257b2o$256b2o29b
2o$258bo28bobo$287bo$7b3o$9bo7b3o$8bo10bo244b2o26b2o$18bo244b2o27bobo$
265bo26bo2$12b3o$14bo244b2o25b2o$13bo244b2o26bobo$260bo25bo14b2o$300b
2o$302bo3$6bo$6b2o$5bobo!

I managed to create the central boats and blocks with only 34 gliders. can this be reduced?

Code: Select all

x = 181, y = 218, rule = B3/S23
41bobo$42b2o$42bo11$144bo$144bobo$144b2o28$3bobo$4b2o$4bo2$173bo$173bo
bo4bo$173b2o3b2o$179b2o2$18bobo$15bo3b2o$8bo4bobo3bo$9b2o3b2o$8b2o2$
156bobo$156b2o3bo$157bo3bobo$161b2o$156bo$155bo$155b3o3$30bo$31b2o3bo
136bo$30b2o2bobo135bo$35b2o135b3o3$13bo127bobo17bo$14b2o125b2o16b2o$
13b2o127bo17b2o2$26bo$27bo133bo$25b3o133bobo$161b2o2$24bo$25b2o3bo$24b
2o2bobo$29b2o3$148bo$146b2o$147b2o2$136b3o$136bo$137bo3$134b3o$134bo$
135bo15$40bo$40b2o$39bobo3$42bo$42b2o$41bobo76$17b2o$16bobo$18bo3$169b
2o$168b2o$170bo2$21bo$21b2o$20bobo$29b2o$28bobo145b2o$30bo133b3o9bobo$
164bo11bo$165bo$158bo$2o155b2o$b2o154bobo$o!

[knightlife]

I managed to create the central boats and blocks with only 34 gliders. can this be reduced?

If there were a different way to "inject" a boat into its proper place with 3 gliders from only two directions instead of three then the glider count could be reduced by at least 2. I am starting to collect such "injection" tools for synthesis as I find them. There are definitely diminishing returns for extra effort at this point. Is it worth an hour to save a glider? LOL

But it's fun.

[Sokwe]

Here's a predecessor of the p32 oscillator that I recently found which looks like it would allow a glider synthesis:

Code: Select all

x = 37, y = 19, rule = B3/S23
11b2o11b2o$10bo2bo9bo2bo$11bobo9bobo$12bo11bo$3o31b3o$3bo29bo$4bo27bo$
3bo29bo$3o6bobo13bobo6b3o$8bo2bo13bo2bo$3o6bobo13bobo6b3o$3bo29bo$4bo
27bo$3bo29bo$3o31b3o$12bo11bo$11bobo9bobo$10bo2bo9bo2bo$11b2o11b2o!

[David]

About the Test Tube Baby, I got quite close to cleaning up the mess with one glider. I know it can be done with two.

Completed.

Code: Select all

x = 67, y = 68, rule = B3/S23
64bobo$64b2o$65bo30$2bo$obo$b2o15$9bobo4bobo$10b2o4b2o$10bo6bo6$14b2o$
14bobo$14bo$11b2o$10bobo$12bo3$2b2o20b2o$3b2o18b2o$2bo22bo!

[Jason Summers]

If there were a different way to "inject" a boat into its proper place with 3 gliders from only two directions instead of three then the glider count could be reduced by at least 2.

Here's one way:

Code: Select all

x = 10, y = 9, rule = B3/S23
7bo$7bobo$7boo3$5bo$bbobbobo$obobboo$boo!

[Sokwe]

Here's the reduced p51 synthesis:

Code: Select all

#C 76-glider synthesis of Nicolay's p51 oscillator
x = 187, y = 187, rule = B3/S23
179bobo$179b2o$180bo3$o$b2o$2o14bo25bo$14bobo26b2o128bo$15b2o25b2o128b
o$172b3o2$10bo26bo$8bobo27b2o128bo$9b2o26b2o128bo10bo$167b3o7bo$177b3o
$15bo$13bobo28bo$14b2o29b2o$44b2o3$129bo$129bobo$129b2o3$130bo$128b2o$
129b2o$40bo$41b2o$40b2o$52bo$53bo$51b3o17bobo$72b2o98bobo$72bo99b2o$
54bo118bo$55bo69bo$53b3o68bo$124b3o50bobo$177b2o$166bobo9bo$166b2o$
122bobo42bo$122b2o$123bo3$120bobo$71bobo46b2o$72b2o47bo$72bo58bo$130bo
$130b3o2$72bo63bo$66bo3bobo61b2o$61bo5b2o2b2o62b2o$62bo3b2o$60b3o2$
108bo$108bobo3bo$108b2o2b2o$113b2o2$107bobo$107b2o$108bo2$83bo$84bo2bo
$44bo2bobo32b3o3b2o34bobo$42bobo3b2o37b2o35b2o$43b2o3bo76bo2$66bo26bo
18bo$67bo25bobo15bo$65b3o25b2o16b3o3$77bobo34bo$78b2o32b2o$78bo34b2o$
133bo$77bo55bobo$78bo2bo51b2o$76b3o3b2o$81b2o3$99bo$98bo$98b3o7$69b2o$
70b2o$69bo3$120b3o$120bo$121bo16b2o$137b2o$73b2o64bo$72bobo$74bo$81b2o
$33bo48b2o33bo10b2o$33b2o46bo34b2o9b2o$32bobo81bobo10bo2$109b2o$52b3o
54bobo$54bo54bo$53bo2$51bo106b2o$51b2o105bobo$50bobo105bo5$98bo$97b2o$
97bobo26b2o$126bobo$126bo$75b2o$74bobo$76bo$19bo$19b2o$8bo9bobo54b2o$
8b2o66b2o$7bobo65bo3$13bo$13b2o$12bobo17$141b2o$140b2o29b2o$142bo28bob
o$171bo$7b3o$9bo7b3o$8bo10bo128b2o26b2o$18bo128b2o27bobo$149bo26bo2$
12b3o$14bo128b2o25b2o$13bo128b2o26bobo$144bo25bo14b2o$184b2o$186bo3$6b
o$6b2o$5bobo!

This also reduces the construction of Nicolay's p11 oscillator:

Code: Select all

#C 30-glider synthesis of Nicolay's p11 oscillator
x = 87, y = 87, rule = B3/S23
75bo$74bo$74b3o$18bo$19bo$17b3o$76bo$23bo51bo$21bobo51b3o$8bo13b2o$2bo
3bobo$obo4b2o$b2o22bo46bobo$23bobo28bo17b2o$24b2o28bobo16bo$54b2o2$70b
obo8bo$35bobo32b2o9bobo$36b2o33bo9b2o$36bo2$19bobo34bo$20b2o33bo$20bo
34b3o3$29bobo26bo$30b2o25bo$22bobo5bo26b3o$23b2o$23bo$59bo$57b2o$58b2o
3$41bo$41bobo$41b2o3$35bobo$36b2o$36bo8$23bo$23b2o$22bobo4$27b3o$29bo$
28bo4$54b3o$22b2o30bo$21bobo31bo$4b2o17bo$3bobo$5bo5$84b2o$78b2o4bobo$
78bobo3bo$78bo$9b3o$11bo$10bo$67b3o$67bo$68bo$10b3o$12bo$11bo!

[calcyman]

Can the eater3 be synthesised?

[Jason Summers]

Here's a predecessor of the p32 oscillator that I recently found which looks like it would allow a glider synthesis

Here's a synthesis from 37 gliders.

Code: Select all

x = 89, y = 109, rule = B3/S23
10bo67bo$bobo7boo63boo7bobo$bboo6boo65boo6boo$bbo83bo3$12bobo59bobo$
13boo59boo$13bo61bo5$67bo$65boo$66boo3$7bo$8bo$6b3o5$71bo$26bo44bobo$
24bobo44boo$25boo10bo$35bobo48bobo$36boo48boo$70bo5bo10bo$70bobobbo$
70boo3b3o$82bobo$82boo$83bo6$75bo$65bo8bo$64bo9b3o$64b3o3$46bo$46bobo
11boo$46boo11boo$61bo6$27bo$28boo$27boo4$22b3o$12b3o9bo$14bo8bo$13bo4$
22b3o$24bo44b3o$5bo17bo45bo$5boo63bo$4bobo$11b3o$13bo$bo10bo$boo48boo$
obo48bobo$51bo10boo$62bobo$62bo6$80b3o$80bo$81bo3$21boo$22boo$21bo5$
13bo61bo$13boo59boo$12bobo59bobo3$bbo83bo$bboo6boo65boo6boo$bobo7boo
63boo7bobo$10bo67bo!

[Sokwe]

I found that a variation of a clock synthesis by Jason Summers and Heinrich Koenig could allow the clocks to be added in a potential synthesis of Jason Summers' period-14 pre-honey farm hassler:

Code: Select all

x = 142, y = 117, rule = B3/S23
94bo$94bobo$94b2o2$8bo$9bo$7b3o22$4bo24bobo$2bobo25b2o$3b2o25bo2$87bo$
87bobo$82bobo2b2o$82b2o$83bo$15bo$16b2o$15b2o53bo$56bobo2bo6b2o$56b2o
3bobo5b2o$57bo3b2o$31bo$32bo$30b3o$68bobo$68b2o56bo7bo$69bo50bo5b3o3b
2o$47bo71bobo7bo4b2o$46bo72bobo6b2o3bo6b2o$46b3o69b2ob2o17bo$138bobo$
116b4ob2o7bo7b2o$116bo2bobo7bob2o$129bo2bo$130b3o2$34b3o$36bo$35bo87b
3o$123bo2bo$123b2obo7bobo2bo$116b2o7bo7b2ob4o$115bobo$23bo29bo61bo17b
2ob2o$23b2o27b2o60b2o6bo3b2o6bobo$18b2o2bobo27bobo65b2o4bo7bobo$17bobo
102b2o3b3o5bo$19bo101bo7bo2$46bo$45b2o$45bobo2$64bo$63b2o$63bobo3$40b
2o$39bobo$34b3o4bo$36bo$35bo5$19bo$19b2o$18bobo73b3o$90b2o2bo$89b2o4bo
$91bo$8b2o$7bobo$9bo5$8b2o$2b3o4b2o$4bo3bo$3bo$81b2o$80b2o$82bo4$2o88b
2o$b2o86b2o$o75bo14bo$75b2o$75bobo!

If there is a way to add the other two eaters, then the synthesis can be completed:

Code: Select all

x = 123, y = 53, rule = B3/S23
85bo$85bobo$85b2o$69bo$69bobo$69b2o7bo$77bo$77b3o2$9bobo$10b2o$10bo4$
42bo7bo56bo7bo$7bobo26bo5b3o3b2o51bo5b3o3b2o$8b2o25bobo7bo4b2o48bobo7b
o4b2o$8bo15bo10bobo6b2o3bo7bobo40bobo6b2o3bo6b2o$16bo5bobo9b2ob2o18b2o
40b2ob2o17bo$14bobo6b2o33bo60bobo$15b2o15b4ob2o28bobo27b4ob2o7bo7b2o$
32bo2bob2o28b2o28bo2bobo7bob2o$28bo39bo41bo2bo$26bobo82b3o$27b2o2$59b
2o$59bobo42b3o$19bo39bo44bo2bo$19b2o28b2obo2bo48b2obo7bobo2bo$18bobo
28b2ob4o15b2o24b2o7bo7b2ob4o$29bo33b2o6bobo22bobo$29b2o18b2ob2o9bobo5b
o24bo17b2ob2o$28bobo7bo3b2o6bobo10bo15bo15b2o6bo3b2o6bobo$36b2o4bo7bob
o25b2o21b2o4bo7bobo$38b2o3b3o5bo26bobo22b2o3b3o5bo$37bo7bo56bo7bo4$77b
o$76b2o$76bobo2$8b3o$10bo$9bo7b2o$16bobo$18bo$b2o$obo$2bo!

Does anyone know of a way to add these eaters?

[knightlife]

Using quad symmetry I found these glider synthesis patterns yesterday

16 glider p2 phoenix oscillator:

Code: Select all

x = 42, y = 42, rule = B3/S23
35bo$35bobo$35b2o2$bo$2bo28bobo$3o28b2o$32bo$5bo13bo$6b2o9bobo$5b2o11b
2o3$14bo$15b2o9bobo$14b2o10b2o$27bo$32bo$31bo$31b3o3$8b3o$10bo$9bo$14b
o$14b2o10b2o$13bobo9b2o$27bo3$22b2o11b2o$22bobo9b2o$22bo13bo$9bo$9b2o
28b3o$8bobo28bo$40bo2$5b2o$4bobo$6bo!

12 glider quad symmetric still life (name?):

Code: Select all

x = 75, y = 75, rule = B3/S23
14bo$12bobo$13b2o10$73bo$72bo$72b3o12$35bo7bo$35bobo4bo$35b2o5b3o2$28b
o$26bobo$27b2o3$46b3o$46bo$27bo19bo$28bo$26b3o3$46b2o$46bobo$46bo2$30b
3o5b2o$32bo4bobo$31bo7bo12$3o$2bo$bo10$60b2o$60bobo$60bo!

Are there other (better) syntheses for these patterns?

[hkoenig]

Code: Select all

x=49, y=87
16bobo7bo20bo$16b2o12bobo12b2o$17bo8bo4b2o13b2o$7bo7bo15bo$o6bo7bo10bo$b2o4b
o7bo$2o24bo$3b3o5bo5b3o$10bobo13bo15bo$10bobo28b2o$8b2o3b2o11bo10b2o2bobo$7b
o7bo22b2o$8b2o3b2o11bo10bo$10bobo$10bobo13bo$3b3o5bo5b3o27bo$21b2o8b2o13b
2o$7bo7bo4b2o4bo5b2o12bobo$7bo7bo6bo8bo$7bo7bo$5bo$5b2o$4bobo6$11bo$12bo$10b
3o$14bo$14bobo$14b2o$4bo$5bo$3b3o2$b2o8bo8bo$obo7bobo7bobo$2bo8bo8b2o2$17b
3o$17bo$18bo$7b2o$6bobo$8bo$10b3o$10bo$11bo11$7bo$5bobo$6b2o19bo$26bo$26b
3o4$15bo2bobo$13bobo3b2o$14b2o3bo$10b3o$12bo7bo$11bo7bo$19b3o$12bo3b2o$11b
2o3bobo$11bobo2bo4$3b3o$5bo$4bo19b2o$24bobo$24bo!

The first is by David Buckingham.

[knightlife]

Thanks. I found the stable object in your catalog now ----- 20.112242

Lately I am getting more interested in glider synthesis.
Synthesis trick to inject a block:

Code: Select all

x = 31, y = 20, rule = B3/S23
obo$b2o$bo2$11bo$12bo$10b3o16b2o$19bo9b2o$18bo$18b3o2$10bo$8bobo$9b2o
5$29b2o$29b2o!