## Cheap way to construct a c/2 p168 puffer

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
HartmutHolzwart
Posts: 579
Joined: June 27th, 2009, 10:58 am
Location: Germany

### Cheap way to construct a c/2 p168 puffer

What is the cheapest and most compact way of producing the following puffer exhaust with a p168 c/2 puffer?

Code: Select all

``````x = 127, y = 78, rule = B3/S23
22\$112b2o\$112b2o3\$102b2o\$102b2o3\$92b2o\$92b2o3\$82b2o\$82b2o3\$72b2o\$72b2o
3\$62b2o\$62b2o\$53bo\$53bo\$53bo2\$43bo\$43bo\$43bo2\$33bo\$33bo\$33bo2\$23bo\$23b
o\$23bo!
``````
Of course we could take 10 p168 forward rakes and 10 respective backward rakes, s.t. the gliders collide to build blocks and blinkers. Buit is there a cleverer way of doing this?

Thanks in advance for any help.

Hartmut

triller
Posts: 114
Joined: September 3rd, 2009, 2:41 pm

### Re: Cheap way to construct a c/2 p168 puffer

Where would the next iteration of this exhaust stream be oriented w/ respect to the first?
Orthogonally above, right, or continuing on the same oblique?

triller
The most exciting phrase to hear in science, the one that heralds new
discoveries, is not "Eureka!" (I found it!) but "That's funny ..."
-- Isaac Asimov

HartmutHolzwart
Posts: 579
Joined: June 27th, 2009, 10:58 am
Location: Germany

### Re: Cheap way to construct a c/2 p168 puffer

the puffer moves to the left...

Paul Tooke
Posts: 111
Joined: May 19th, 2010, 7:35 am
Location: Cambridge, UK

### Re: Cheap way to construct a c/2 p168 puffer

I don't know whether this is the cheapest or most compact solution, but it works. It uses fourteen p168 forward rakes and incorporates the LWSS-catalysed forward glider->block reaction suggested by Jason Summers replying to the related topic in the scripts forum.

Presumably you have an interesting use for the puffer output, a fuse perhaps? It would be interesting to see it.

x = 721, y = 158, rule = B3/S23
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46bo3bo9bo49b5o6bo4b3o11b3o30bo7bo11bobo29bo4bo8b4o13bo8b2ob2o11bo\$17b
o2b5ob2o40bo3b3o5bo2bo45bo3b3o5bo2bo45bo3b3o5bo2bo45bo3b3o5bo2bo45bo3b
3o5bo2bo45bo3b3o5bo2bo55b2obo52b4obo25b2o18bo12bo4bo6bo6b4obo3b4o\$20b
5o2bo41b2o9b2o48b2o9b2o48b2o9b2o48b2o9b2o48b2o9b2o48b2o9b2o51b3o3bo8bo
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5obobo52b5obobo52b5obobo52b5obobo52b5obobo52b5obobo52bo5bo7bo2bo13b3o
30bo15b2o11b5o4b2o12bo9bo2bo5bo11bo24b2o5b5o\$14b4o2b5o2b2o44bo4bobo53b
o4bobo11bo41bo4bobo13b2o11b2o25bo4bobo8bo2bo41bo4bobo53bo4bobo52bo3bo
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o46b2o4bo2bo51b2o4bo3bo6b3o41b2o4bo2bo3bobo4b3o9b3o26b2o4bo3bo7bo42b2o
4bo2bo4b2ob2o42b2o4bo2bo4b2ob2o41bo3b3o5bo2bo13bo3bo37b2obo26bo25b4obo
25b2o11bo6bo\$12bo3b2o2b5ob2o47bo2bobo2bo2bo2bo46bo2bobo4bo5bo2bo41bo2b
obo2bo2bo3b2o44bo2bobo4bo7bo42bo2bobo2bo3bo3b2o43bo2bobo2bo3bo3b2o42b
2o9b2o13b3o3b3o29b3o3bo8bobo45bo3bo12b3o9b2ob3o16bo3bo\$12b4obo2b5ob2o
7bo40bobobo2bobo2bob2o45bobobo5bo50bobobo2bo2bo4bo45bobobo5bob3o46bobo
bo2bo8bo44bobobo2bo8bo45b5obobo13bo2b2ob2o2bo28bo5bo7bo2bo46bo15b2o11b
5o18bo\$11bo8b2o11b5o42bo2bobo55bo5bo3bo50bo2bo3bobo51bo5bo54bo2bo3bo2b
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11bo3bo38bobobo2bobo3bo47bobobo5bo2bobo45bobobo2bo4b3o46bobobo5bo50bob
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2o2bo12bo3bo37bo2bobo2bobo3bo46bo2bobo5bo2bobo44bo2bobo2bo4b3o45bo2bob
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3o3bo8bobo\$6bo3b3ob2o4b2o12bobo37b2o4bo2bobo49b2o4bo5bo3bo44b2o4bo2bo
3bobo45b2o4bo5bo48b2o4bo2bo3bo2bo44b2o4bo2bo3bo2bo51bobobo2bobo2bo9bob
o37b5obobo52bo5bo7bo2bo\$5bo3bo4b2o4bobo12bo37bo4bobo2bobo2bob2o42bo4bo
bo5bo47bo4bobo2bo2bo4bo42bo4bobo5bob3o43bo4bobo2bo8bo41bo4bobo2bo8bo
53bo2bobo3bo49bo4bobo52bo3bo9bo\$5bo5bo3b2o3b3o49b5obobo2bo2bo2bo43b5ob
obo4bo5bo2bo38b5obobo2bo2bo3b2o41b5obobo4bo7bo39b5obobo2bo3bo3b2o40b5o
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4obo4b3o47bo8bo2bo48bo8bo3bo6b3o38bo8bo2bo3bobo4b3o9b3o23bo8bo3bo7bo
39bo8bo2bo4b2ob2o39bo8bo2bo4b2ob2o48bo2bobo2bobo4b2o49bo2bobo2bo2bo3bo
44b2o9b2o\$23bo47b6obobo51b6obobo11bo39b6obobo13b2o11b2o23b6obobo8bo2bo
39b6obobo51b6obobo59b2o4bo2bobo3bo52bobobo2bo2bo3b2ob2o43b5obobo\$5b3o
3b5o5bo46bobo7bobo48bobo7bobo48bobo7bobo48bobo7bobo48bobo7bobo48bobo7b
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6ob2o4b2o46b6ob2o4b2o46b6ob2o4b2o46b6ob2o4b2o46b6ob2o4b2o46b6ob2o4b2o
56b5obobo2bo2b2o8b3ob3o39bobobo2bo7b6o43b2o4bo2bo7bo\$5bo3bo4bo5bo45b2o
5b2o5bo2bo43b2o5b2o5bo2bo43b2o5b2o5bo2bo43b2o5b2o5bo2bo43b2o5b2o5bo2bo
43b2o5b2o5bo2bo53bo8bo2bo13bobobo39bo2bobo2bo7b6o44bo2bobo2bo2b2o3bo\$
6bo3b3obo6bobo41b2o4b2o4bo3bo44b2o4b2o4bo3bo44b2o4b2o4bo3bo18bobo23b2o
4b2o4bo3bo44b2o4b2o4bo3bo44b2o4b2o4bo3bo55b6obobo12b6ob6o34b2o4bo2bo3b
o3b2o2bo46bobobo2bobo2bo2bo\$7b2o7bo4bo7bo36b2o4b4obo3bo2bo42b2o4b4obo
3bo2bo42b2o4b4obo3bo2bo42b2o4b4obo3bo2bo42b2o4b4obo3bo2bo42b2o4b4obo3b
o2bo49bobo7bobo13bo2b2ob2o2bo34bo4bobo2bo2bo3b2ob2o51bo2bobo\$10b6o7bo
3b3o52bobo58bobo58bobo58bobo58bobo58bobo48b6ob2o4b2o13b3o3b3o34b5obobo
2bo2bo3bo51bobobo2bobo3bo\$11bo9b3o2b2o38b2o4b5o50b2o4b5o50b2o4b5o50b2o
4b5o50b2o4b5o50b2o4b5o55b2o5b2o5bo2bo13bo3bo35bo8bo2bo3bob2o50bo2bobo
2bobo3bo\$12b2o6b3o3bo38b2o4b2o8b3o42b2o4b2o8b3o42b2o4b2o8b3o42b2o4b2o
8b3o42b2o4b2o8b3o42b2o4b2o8b3o47b2o4b2o4bo3bo15bobobo35b6obobo59b2o4bo
2bobo\$13bo2bo4b2o5bo37b2o5b2obo4b2o44b2o5b2obo4b2o44b2o5b2obo4b2o44b2o
5b2obo4b2o44b2o5b2obo4b2o44b2o5b2obo4b2o49b2o4b4obo3bo2bo13b3o33bobo7b
obo58bo4bobo2bobo2bo2bo\$14bobo5b6o39b6obobo4b3o44b6obobo4b3o44b6obobo
4b3o44b6obobo4b3o44b6obobo4b3o44b6obobo4b3o64bobo14bo33b6ob2o4b2o56b5o
bobo2bo2b2o3bo\$23bobo42bobo19bo38bobo19bo38bobo19bo38bobo19bo38bobo19b
o38bobo19bo41b2o4b5o55b2o5b2o5bo2bo53bo8bo2bo7bo\$26b4obo39b6o5bobo2b2o
bo41b6o5bobo2b2obo41b6o5bobo2b2obo41b6o5bobo2b2obo41b6o5bobo2b2obo41b
6o5bobo2b2obo40b2o4b2o8b3o47b2o4b2o4bo3bo55b6obobo\$26bo3b2o39bo9bo2bo
2bo44bo9bo2bo2bo44bo9bo2bo2bo44bo9bo2bo2bo44bo9bo2bo2bo44bo9bo2bo2bo
44b2o5b2obo4b2o49b2o4b4obo3bo2bo49bobo7bobo\$28b2o43b2o6bo5bo46b2o6bo5b
o46b2o6bo5bo46b2o6bo5bo46b2o6bo5bo46b2o6bo5bo45b6obobo4b3o64bobo48b6ob
2o4b2o\$28b4o41b4o4bo3bo48b4o4bo3bo48b4o4bo3bo48b4o4bo3bo48b4o4bo3bo48b
4o4bo3bo48bobo19bo41b2o4b5o55b2o5b2o5bo2bo\$31bo44bo5bo3b3o48bo5bo3b3o
48bo5bo3b3o48bo5bo3b3o48bo5bo3b3o48bo5bo3b3o48b6o5bobo2b2obo40b2o4b2o
8b3o47b2o4b2o4bo3bo\$83b2o59b2o59b2o59b2o59b2o59b2o52bo9bo2bo2bo44b2o5b
2obo4b2o49b2o4b4obo3bo2bo\$86b5obo54b5obo54b5obo54b5obo54b5obo54b5obo
46b2o6bo5bo45b6obobo4b3o64bobo\$87bo4bo55bo4bo55bo4bo55bo4bo55bo4bo55bo
4bo46b4o4bo3bo48bobo19bo41b2o4b5o\$88b2o59b2o59b2o59b2o59b2o59b2o52bo5b
o3b3o48b6o5bobo2b2obo40b2o4b2o8b3o\$89bo2bo57bo2bo57bo2bo57bo2bo57bo2bo
57bo2bo56b2o52bo9bo2bo2bo44b2o5b2obo4b2o\$90bobo58bobo58bobo58bobo58bob
o58bobo59b5obo46b2o6bo5bo45b6obobo4b3o\$458bo4bo46b4o4bo3bo48bobo19bo\$
459b2o52bo5bo3b3o48b6o5bobo2b2obo\$460bo2bo56b2o52bo9bo2bo2bo\$461bobo
59b5obo46b2o6bo5bo\$524bo4bo46b4o4bo3bo\$525b2o52bo5bo3b3o\$526bo2bo56b2o
\$527bobo59b5obo\$590bo4bo\$591b2o\$592bo2bo\$593bobo!

HartmutHolzwart
Posts: 579
Joined: June 27th, 2009, 10:58 am
Location: Germany

### Re: Cheap way to construct a c/2 p168 puffer

Thank you very much for providing this!

I need this as the backbone of my long planned growing diagonal 3c/7 pi ship!

I'm still far from the final result, but will send you the intermediate result!

HartmutHolzwart
Posts: 579
Joined: June 27th, 2009, 10:58 am
Location: Germany

### Re: Cheap way to construct a c/2 p168 puffer

x = 1799, y = 1493, rule = B3/S23
8\$1547bo\$1546b3o\$1544b2ob3o\$1545bo2bob2o\$1542b2obo4bobo\$1542b2obobo2bo
b2o21b3ob3o\$1542bo8bobo2bo17bo2bobo2bo\$1541b2o7b2obob3o15bo3bobo3bo\$
1553bobob2o14bo9bo\$1548b3obo5b2o15bo5bo\$1547b2o9bo13bobo7bobo\$1547bo
10b2o11b2obob2ob2obob2o\$1546b2o7b2obob2o7b2obobo2bobo2bobobo\$1554b2o2b
obo9bobo4bobo4bob2o\$1554bo2bo2bob2o3b2obobob2obobob2obo3bo\$1553b2o5bob
2o3b2obobob3o2bo4bo\$1561bobo3bobo3bo2b2o2bo2bo3b2o\$1543bo16b2ob2ob2ob
2ob2o\$1542b3o\$1540b2ob3o\$1541bo2bob2o4bo4b20o4bo4bo\$1538b2obo4bobob2ob
2ob2obob12obob2ob2ob2ob3o\$1538b2obobo2bobo7b3o16b3o7b4o\$1538bo8b3obobo
b2o20b2obobob2o2b2o\$1537b2o7b2o40bo\$1563b2o4b2o17b2o\$1563b2o4b2o14b2ob
ob2o\$1563b2o4b2o13b2o2bobo\$1538b3o3b3o15b2o6b2o12bo2bo2bob2o\$1538bo2bo
bo2bo16b2o4b2o12b2o5bob2o\$1538bo7bo44bobo\$1538bo7bo18b4o21b2ob2o\$1539b
obobobo18bo4bo\$1550b3o11bo4bo\$1542bo6bo2bo12b4o\$1541b3o8bo\$1540b2ob2o
3bo3bo\$1541b3o8bo\$1541b3o5bobo\$1541b3o\$1541bobo\$1541bobo\$1542bo10b2o\$
1552b2o\$1554bo5\$1536bo\$1535b3o\$1535bob2o\$1536b3o\$1536b2o11bo\$1548b3o\$
1548bob2o\$1549b3o\$1549b3o\$1539b2o8b2o\$1539b2o2\$1552b3o\$1551bo3bo\$1550b
2o4bo\$1549bobob2ob2o\$1548b2obo4bob2o22bo3bo\$1547bo4bo3bo2bo21b3ob3o\$
1559bob3o16b2obobob2o\$1547b2o7b2obobo2bo14b2o7b2o\$1559bobo3bo14bo7bo\$
1553b3o9bo13b2o7b2o\$1553bo9bo13b2obobo3bobob2o\$1564bobo9bobobob2ob2obo
bo\$1552b2o6b3obob2o7b2obo2bobobobo2bob2o\$1560bo3bobobo5bobobob2obobob
2obob2o\$1566bob2o3b2obobobo2bobo4bo2bo\$1559b2o5bo3bobo3bobo6bob2obo2b
2o\$1582b2o\$1548b3o15b2ob2ob2ob2ob2o\$1547bo3bo\$1546b2o4bo11b18o\$1545bob
ob2ob2o3b3o2b2obo14bob2o2b3o2b3o\$1544b2obo4bob2ob3obo22bob3obo3bo\$
1543bo4bo3bo4bobo4bo16bo4bobo6bo\$1555bo5b2o6bo6bo6b2o5b2o3bo\$1543b2o7b
2o15bo6bo16bo\$1570bo4bo18bobo\$1569bo6bo13b3obob2o\$1545bo5bo17bo2b2o2bo
13bo3bobobo\$1544b3o3b3o16b2ob2ob2o19bob2o\$1544bob2ob2obo17bo4bo13b2o5b
o3bo\$1545b3ob3o18bo4bo\$1545b2o3b2o15b2o2bo2bo2b2o17b2ob2o\$1557bo8bobo
3b2o3bobo\$1548bo7b3o7bo12bo\$1547bobo5b2obo7bobo8bobo\$1546bo3bo4b3o9b2o
8b2o\$1548bo6b3o\$1556b2o3\$1545b3ob3o2\$1546bo3bo\$1547b3o6\$1551b2o\$1551bo
bo\$1551bo2\$1554b3o\$1553bo2bo\$1556bo\$1552bo3bo\$1556bo\$1553bobo\$1531b3o\$
1530bo2bo\$1533bo18b3o\$1533bo17bo3bo\$1530bobo17b2o4bo\$1549bobob2ob2o\$
1548b2obo4bob2o22bo3bo\$1547bo4bo3bo2bo21b3ob3o\$1559bob3o16b2obobob2o\$
1547b2o7b2obobo2bo14b2o7b2o\$1559bobo3bo14bo7bo\$1553b3o9bo13b2o7b2o\$
1553bo9bo13b2obobo3bobob2o\$1564bobo9bobobob2ob2obobo\$1552b2o6b3obob2o
7b2obo2bobobobo2bob2o\$1560bo3bobobo5bobobob2obobob2obob2o\$1566bob2o3b
2obobobo2bobo4bo2bo\$1559b2o5bo3bobo3bobo6bob2obo2b2o\$1582b2o\$1548b3o
15b2ob2ob2ob2ob2o\$1547bo3bo\$1546b2o4bo11b18o\$1539b2o4bobob2ob2o3b3o2b
2obo14bob2o2b3o2b3o\$1539b2o3b2obo4bob2ob3obo22bob3obo3bo\$1543bo4bo3bo
4bobo4bo3b10o3bo4bobo6bo\$1555bo5b2o20b2o5b2o3bo\$1543b2o7b2o39bo\$1594bo
bo\$1590b3obob2o\$1545bo5bo18bob2obo14bo3bobobo\$1544b3o3b3o17b6o20bob2o\$
1543b2obo3bob2o17b4o14b2o5bo3bo\$1535b2o6b3o5b3o\$1535b2o7b2o5b2o43b2ob
2o\$1557bo10bobo4bobo\$1548bo7b3o10bo6bo\$1547b3o6bob2o\$1557b3o\$1547bobo
7b3o\$1548bo8b2o3\$1560b3o\$1545b3ob3o8bo\$1547bobo11bo3\$1547b3o8\$1554b3o\$
1546b3o5bo2bo\$1546bo7bo\$1547bo6bo3bo\$1554bo\$1555bobo3\$1552b3o\$1551bo3b
o\$1527b3o20b2o4bo\$1527bo2bo18bobob2ob2o\$1527bo20b2obo4bob2o22bo3bo\$
1527bo19bo4bo3bo2bo21b3ob3o\$1528bobo28bob3o16b2obobob2o\$1547b2o7b2obob
o2bo14b2o7b2o\$1559bobo3bo14bo7bo\$1553b3o9bo13b2o7b2o\$1553bo9bo13b2obob
o3bobob2o\$1564bobo9bobobob2ob2obobo\$1552b2o6b3obob2o7b2obo2bobobobo2bo
b2o\$1560bo3bobobo5bobobob2obobob2obob2o\$1566bob2o3b2obobobo2bobo4bo2bo
\$1559b2o5bo3bobo3bobo6bob2obo2b2o\$1582b2o\$1548b3o15b2ob2ob2ob2ob2o\$
1547bo3bo\$1546b2o4bo11b18o\$1545bobob2ob2o3b3o2b2obo14bob2o2b3o2b3o\$
1544b2obo4bob2ob3obo22bob3obo3bo\$1543bo4bo3bo4bobo4bo16bo4bobo6bo\$
1555bo5b2o6bo6bo6b2o5b2o3bo\$1543b2o7b2o15bo6bo16bo\$1570bo4bo18bobo\$
1570bo4bo14b3obob2o\$1545bo5bo19b4o15bo3bobobo\$1544b3o3b3o17bo4bo20bob
2o\$1544bob2ob2obo16bobo2bobo12b2o5bo3bo\$1545b3ob3o17bobo2bobo\$1545b2o
3b2o18bo4bo20b2ob2o\$1557bo\$1548bo7b3o\$1547bobo5b2obo\$1546bo3bo4b3o\$
1547bobo5b3o\$1547b3o6b2o4\$1546b2ob2o\$1546b2ob2o\$1539b2o5b2ob2o\$1539b2o
7bo7b2o\$1556bobo\$1547b3o6bo7\$1535b2o17b3o\$1535b2o16bo2bo\$1556bo\$1552bo
3bo\$1556bo\$1553bobo3\$1552b3o\$1551bo3bo\$1531b2o17b2o4bo\$1531b2o16bobob
2ob2o\$1548b2obo4bob2o22bo3bo\$1547bo4bo3bo2bo21b3ob3o\$1523b3o33bob3o16b
2obobob2o\$1522bo2bo21b2o7b2obobo2bo14b2o7b2o\$1525bo33bobo3bo14bo7bo\$
1525bo27b3o9bo13b2o7b2o\$1522bobo28bo9bo13b2obobo3bobob2o\$1529bo34bobo
9bobobob2ob2obobo\$1527bo2bo21b2o6b3obob2o7b2obo2bobobobo2bob2o\$1527b2o
31bo3bobobo5bobobob2obobob2obob2o\$1566bob2o3b2obobobo2bobo4bo2bo\$1559b
2o5bo3bobo3bobo6bob2obo2b2o\$1582b2o\$1548b3o15b2ob2ob2ob2ob2o\$1547bo3bo
\$1546b2o4bo11b18o\$1545bobob2ob2o3b3o2b2obo14bob2o2b3o2b3o\$1544b2obo4bo
b2ob3obo22bob3obo3bo\$1543bo4bo3bo4bobo4bo3b10o3bo4bobo6bo\$1555bo5b2o
20b2o5b2o3bo\$1543b2o7b2o16b6o17bo\$1569bo6bo17bobo\$1569bo6bo13b3obob2o\$
1545bo5bo18bo4bo14bo3bobobo\$1544b3o3b3o18bo2bo21bob2o\$1543b2obo3bob2o
18b2o15b2o5bo3bo\$1543b3o5b3o14bo2bo2bo2bo\$1544b2o5b2o14b2o3b2o3b2o17b
2ob2o\$1557bo8bo12bo\$1548bo7b3o8b2o8b2o\$1547b3o6bob2o8bo8bo\$1546bo3bo6b
3o\$1557b3o\$1557b2o\$1546b2ob2o\$1548bo3\$1546bo3bo\$1545bobobobo\$1546b5o\$
1546b2ob2o\$1547bobo\$1547b3o2\$1551b3o\$1551bo\$1552bo2\$1554b3o\$1554bo2bo\$
1554bo\$1554bo3bo\$1554bo\$1555bobo3\$1552b3o\$1551bo3bo\$1550b2o4bo\$1549bob
ob2ob2o\$1548b2obo4bob2o22bo3bo\$1539b2o6bo4bo3bo2bo21b3ob3o\$1539b2o18bo
b3o16b2obobob2o\$1547b2o7b2obobo2bo14b2o7b2o\$1559bobo3bo14bo7bo\$1553b3o
9bo13b2o7b2o\$1519b3o31bo9bo13b2obobo3bobob2o\$1519bo2bo41bobo9bobobob2o
b2obobo\$1519bo32b2o6b3obob2o7b2obo2bobobobo2bob2o\$1519bo40bo3bobobo5bo
bobob2obobob2obob2o\$1520bobo43bob2o3b2obobobo2bobo4bo2bo\$1535b2o22b2o
5bo3bobo3bobo6bob2obo2b2o\$1535b2o45b2o\$1548b3o15b2ob2ob2ob2ob2o\$1547bo
3bo\$1546b2o4bo11b18o\$1545bobob2ob2o3b3o2b2obo14bob2o2b3o2b3o\$1544b2obo
4bob2ob3obo22bob3obo3bo\$1543bo4bo3bo4bobo4bo16bo4bobo6bo\$1555bo5b2o5bo
8bo5b2o5b2o3bo\$1543b2o7b2o15bo6bo16bo\$1531b2o39b2o20bobo\$1531b2o36bo2b
2o2bo13b3obob2o\$1545bo5bo17bob4obo13bo3bobobo\$1544b3o3b3o43bob2o\$1544b
ob2ob2obo36b2o5bo3bo\$1545b3ob3o16b2o6b2o\$1545b2o3b2o16b3o4b3o18b2ob2o\$
1557bo\$1548bo7b3o\$1547bobo5b2obo9bo8bo\$1527b2o17bo3bo4b3o11bo6bo\$1527b
2o18bobo5b3o10bo8bo\$1501b3o44bo7b2o\$1500bo3bo43bo\$1499bo4b2o41bobo11b
2o\$1498b2ob2obobo40bobo11bobo\$1469bo3bo22b2obo4bob2o40bo12bo\$1468b3ob
3o21bo2bo3bo4bo\$1467b2obobob2o16b3obo\$1466b2o7b2o14bo2bobob2o7b2o36b2o
3b2o\$1467bo7bo14bo3bobo26b2o\$1466b2o7b2o13bo9b3o20b2o43bo8bo\$1464b2obo
bo3bobob2o13bo9bo66bo6bo\$1465bobob2ob2obobobo9bobo56bo19bo8bo\$1462b2ob
o2bobobobo2bob2o7b2obob3o6b2o44bo\$1462b2obob2obobob2obobobo5bobobo3bo\$
1462bo2bo4bobo2bobobob2o3b2obo\$1461b2o2bob2obo6bobo3bobo3bo5b2o\$1472b
2o80b3o\$1476b2ob2ob2ob2ob2o15b3o45bo2bo\$1504bo3bo47bo\$1474b18o11bo4b2o
42bo3bo\$1462b3o2b3o2b2obo14bob2o2b3o3b2ob2obobo45bo\$1461bo3bob3obo22bo
b3ob2obo4bob2o41bobo\$1460bo6bobo4bo3b10o3bo4bobo4bo3bo4bo\$1460bo3b2o5b
2o20b2o5bo\$1462bo17b6o16b2o7b2o39b3o\$1459bobo17bo6bo64bo3bo\$1458b2obob
3o13bo6bo63b2o4bo\$1457bobobo3bo14bo4bo18bo5bo38bobob2ob2o\$1456b2obo21b
o2bo18b3o3b3o36b2obo4bob2o22bo3bo\$1455bo3bo5b2o15b2o18b2obo3bob2o34bo
4bo3bo2bo21b3ob3o\$1478bo2bo2bo2bo14b3o5b3o20b2o24bob3o16b2obobob2o\$
1455b2ob2o17b2o3b2o3b2o14b2o5b2o21bobo11b2o7b2obobo2bo14b2o7b2o\$1476bo
12bo8bo34bo25bobo3bo14bo7bo\$1477b2o8b2o8b3o7bo45b3o9bo13b2o7b2o\$1478bo
8bo8b2obo6b3o44bo9bo13b2obobo3bobob2o\$1496b3o65bobo9bobobob2ob2obobo\$
1496b3o7bobo43b2o6b3obob2o7b2obo2bobobobo2bob2o\$1497b2o8bo52bo3bobobo
5bobobob2obobob2obob2o\$1515b3o48bob2o3b2obobobo2bobo4bo2bo\$1514bo2bo
41b2o5bo3bobo3bobo6bob2obo2b2o\$1517bo64b2o\$1504b3ob3o6bo30b3o15b2ob2ob
2ob2ob2o\$1506bobo5bobo30bo3bo\$1546b2o4bo11b18o\$1545bobob2ob2o3b3o2b2ob
o14bob2o2b3o2b3o\$1506b3o35b2obo4bob2ob3obo22bob3obo3bo\$1543bo4bo3bo4bo
bo4bo16bo4bobo6bo\$1555bo5b2o5bo8bo5b2o5b2o3bo\$1543b2o7b2o15bo6bo16bo\$
1502b3o67b2o20bobo\$1504bo64bo2b2o2bo13b3obob2o\$1503bo41bo5bo17bob4obo
13bo3bobobo\$1539b2o3b3o3b3o43bob2o\$1499b3o37b2o3bob2ob2obo36b2o5bo3bo\$
1498bo2bo43b3ob3o16b2o6b2o\$1501bo43b2o3b2o16b3o4b3o18b2ob2o\$1497bo3bo
55bo\$1501bo46bo7b3o\$1498bobo46bobo5b2obo9bo8bo\$1546bo3bo4b3o11bo6bo\$
1547bobo5b3o10bo8bo\$1547b3o6b2o\$1501b3o31b2o\$1500bo3bo11b3o16b2o24b2o\$
1499bo4b2o12bo42bobo\$1498b2ob2obobo10bo28b2ob2o10bo\$1469bo3bo22b2obo4b
ob2o38b2ob2o\$1468b3ob3o21bo2bo3bo4bo37b2ob2o\$1467b2obobob2o16b3obo51bo
\$1466b2o7b2o14bo2bobob2o7b2o\$1467bo7bo14bo3bobo50b3o18bo8bo\$1466b2o7b
2o13bo9b3o66bo6bo\$1464b2obobo3bobob2o13bo9bo28b2o35bo8bo\$1465bobob2ob
2obobobo9bobo39b2o\$1462b2obo2bobobobo2bob2o7b2obob3o6b2o\$1462b2obob2ob
obob2obobobo5bobobo3bo\$1462bo2bo4bobo2bobobob2o3b2obo\$1461b2o2bob2obo
6bobo3bobo3bo5b2o57b3o\$1472b2o75b2o2bo2bo\$1476b2ob2ob2ob2ob2o15b3o41b
2o5bo\$1504bo3bo43bo3bo\$1474b18o11bo4b2o46bo\$1462b3o2b3o2b2obo14bob2o2b
3o3b2ob2obobo16b2o24bobo\$1461bo3bob3obo22bob3ob2obo4bob2o15b2o\$1460bo
6bobo4bo3b10o3bo4bobo4bo3bo4bo\$1460bo3b2o5b2o20b2o5bo\$1462bo39b2o7b2o\$
1459bobo\$1458b2obob3o13bobo2bobo\$1372bobo82bobobo3bo12bo2bo2bo2bo16bo
5bo\$1373b2o81b2obo18bo8bo15b3o3b3o44b3o\$1373bo81bo3bo5b2o10bo2bo4bo2bo
13b2obo3bob2o42bo3bo\$1478bobo4bobo14b3o5b3o10b2o29b2o4bo\$1455b2ob2o19b
o6bo16b2o5b2o11b2o28bobob2ob2o\$1498bo53b2obo4bob2o22bo3bo\$1497b3o7bo
43bo4bo3bo2bo21b3ob3o\$1496b2obo6b3o54bob3o16b2obobob2o\$1496b3o6bo3bo
41b2o7b2obobo2bo14b2o7b2o\$1496b3o6bo3bo53bobo3bo14bo7bo\$1497b2o58b3o9b
o13b2o7b2o\$1505bo3bo47bo9bo13b2obobo3bobob2o\$1505bo3bo58bobo9bobobob2o
b2obobo\$1372bo132b2ob2o9b2o35b2o6b3obob2o7b2obo2bobobobo2bob2o\$1373b2o
131bobo10b2o43bo3bobobo5bobobob2obobob2obob2o\$1372b2o133bo62bob2o3b2ob
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2o3b2o9bo38bo7bo11bobo10b3o16bo4bo3bo7bo11bobo29bo4bo3bo7bo11bobo10b3o
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231b2o4bo8b3o39b4obo25b5o15b5o5b4obo25b2o18bo9b4obo25b5o6b3o6b5o5b4obo
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239b4o2b2o9bo2bo38bo4bobo11bo3bo37bo4bobo53bo4bobo53bo4bobo11bobo39bo
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42b2o4bo2bo5b2o44b2o4bo7bob2o43b2o4bo2bobo3bobo43b2o4bo7bo46b2o4bo7bo
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o2bo2bo44bo9bo2bo2bo44b2o5b2obo4b2o49b2o4b4obo3bo2bo49bobo7bobo13b2o2b
o2b2o\$253b2o43b2o6bo5bo46b2o6bo5bo46b2o6bo5bo46b2o6bo5bo46b2o6bo5bo46b
2o6bo5bo45b6obobo4b3o64bobo48b6ob2o4b2o13bo5bo\$253b4o41b4o4bo3bo48b4o
4bo3bo48b4o4bo3bo48b4o4bo3bo48b4o4bo3bo48b4o4bo3bo48bobo19bo41b2o4b5o
55b2o5b2o5bo2bo12b5o\$256bo44bo5bo3b3o48bo5bo3b3o48bo5bo3b3o48bo5bo3b3o
48bo5bo3b3o48bo5bo3b3o48b6o5bobo2b2obo40b2o4b2o8b3o47b2o4b2o4bo3bo15b
3o\$308b2o59b2o59b2o59b2o59b2o59b2o52bo9bo2bo2bo44b2o5b2obo4b2o49b2o4b
4obo3bo2bo13bo\$311b5obo54b5obo54b5obo54b5obo54b5obo54b5obo46b2o6bo5bo
45b6obobo4b3o64bobo\$312bo4bo55bo4bo55bo4bo55bo4bo55bo4bo55bo4bo46b4o4b
o3bo48bobo19bo41b2o4b5o\$313b2o59b2o59b2o59b2o59b2o59b2o52bo5bo3b3o48b
6o5bobo2b2obo40b2o4b2o8b3o\$314bo2bo57bo2bo57bo2bo57bo2bo57bo2bo57bo2bo
56b2o52bo9bo2bo2bo44b2o5b2obo4b2o\$315bobo58bobo58bobo58bobo58bobo58bob
o59b5obo46b2o6bo5bo45b6obobo4b3o\$683bo4bo46b4o4bo3bo48bobo19bo\$684b2o
52bo5bo3b3o48b6o5bobo2b2obo\$685bo2bo56b2o52bo9bo2bo2bo\$686bobo59b5obo
46b2o6bo5bo\$749bo4bo46b4o4bo3bo\$750b2o52bo5bo3b3o\$751bo2bo56b2o\$752bob
o59b5obo\$815bo4bo\$816b2o\$817bo2bo\$818bobo5\$911b2o\$910bobo\$912bo5\$910b
2o\$911b2o\$910bo4\$910bo\$910b2o\$909bobo34\$778b2o\$777bobo\$779bo5\$777b2o\$
778b2o\$777bo4\$777bo\$777b2o\$776bobo!

Paul Tooke
Posts: 111
Joined: May 19th, 2010, 7:35 am
Location: Cambridge, UK

### Re: Cheap way to construct a c/2 p168 puffer

Ok, I've had a week to puzzle over this and I'm still a bit confused. This pattern (suitably modified) can be be completed to contain two copies of a c/2 growing rake/puffer flotilla which cleanly stabilize the 3c/14 (not 3c/7!) diagonal pi-wave. I have a demonstration of this in the file below. But I don't think many people would recognise this as a growing spaceship - it grows in both width and length. If viewed as a diagonal spaceship traveling NW then the front end is traveling at c/4 diagonal and the rear at 3c/14 diagonal which is fair enough, but both sides of the "spaceship" at the SW and NE are also growing diagonally at c/4.

Or am I missing a point somewhere? I did have to make changes to the design to produce the stablization. Firstly, I assumed that the beehives in the vertical puffer output were the result of an off-by-one-cell cut and paste error and corrected accordingly. Secondly, the three glider salvo looks wrong. Using the original:

Code: Select all

``````x = 4, y = 16, rule = B3/S23
2b2o\$bobo\$3bo5\$b2o\$2b2o\$bo4\$bo\$b2o\$obo!
``````
leaves behind a mess, whilst this:

Code: Select all

``````x = 4, y = 16, rule = B3/S23
2bo\$2b2o\$bobo5\$b2o\$2b2o\$bo4\$bo\$b2o\$obo!
``````
cleanly stabilizes the wave. Or was the debris meant to be part of a cunning plan to produce some kind of diagonal caterpillar?
Attachments
piwave.zip

HartmutHolzwart
Posts: 579
Joined: June 27th, 2009, 10:58 am
Location: Germany

### Re: Cheap way to construct a c/2 p168 puffer

Paul,

thank you very much! You did what I intended to do for the last year, but never managed. The only part I concentrated on was getting the gliders through the puffer exhuast needed to create the pi. Once I had that, I was stuck with creating the rakes.

Sorry for the copy errors!

For some reasons, I thought it easier to later cleanup the mess left behind the three gliders, because I thought hte spacing might be easier to achieve. These gliders are obviously meant to destroy 3 of the ten pis created by every wave, while not disturbin the creation of the next ten pis.

Your design looks beautiful to me. Much more regular than I ever thought it would be. The use of the two blocks as glider turner is a very efficient way of creating hte 3c/7 glieder streams with correct spacing.

Great work at least for me! Even if it might not qualify as pattern of the year 2012, it is at least a start in a pretty quiet year so far!

I think it might be possible to build similar "growing ships" from some of the higher period waves found. The interesting thing with this specific one is the relative low period of the basic reaction and the high frequency with that on eneeds to provide a new pi to keep the reaction alive.

The other challenge would now be to support the p14 pi wave by an appropriate digonal c/4 puffer.

Paul Tooke
Posts: 111
Joined: May 19th, 2010, 7:35 am
Location: Cambridge, UK

### Re: Cheap way to construct a c/2 p168 puffer

Thanks Hartmut, that's cleared up my confusion. I'm glad you like the pattern, but it's your design not mine! I just implemented the ideas in your pattern using the tools it contained. I especially liked that pseudo-3c/7 rake.

I was also struck by this reaction which occurs after the deletion of the third pi:

Code: Select all

``````x = 59, y = 55, rule = B3/S23
13\$40b3o\$40bo\$40b3o3\$35b3o\$35bobo\$35bobo\$9bo\$10b2o\$9b2o\$34b3o2\$32bo2b
4o\$26b3o3bobo\$26bo5bobo2bo\$26b3o5bobo\$34bo\$15b2o\$15b2o4b3o\$21bobo\$21bo
bo!
``````
The block eats a pi, surviving in the right place to add another. Was this an accident, or intentional? I spotted this while trying to work out where the 'missing pi' went. Clearly 4 pi deletions have to happen for every 10 additions in order for the edges of the pi-wave to travel horizontally, so I couldn't understand how you got away with using only 3 deleting gliders.

This reaction can actually be repeated three more times to eliminate the need for the 3-glider salvo:

Code: Select all

``````x = 287, y = 287, rule = B3/S23
174bobo\$175b2o\$175bo11\$174bo\$175b2o\$174b2o12\$173bobo\$174b2o\$174bo12\$
185bo\$186b2o\$185b2o10\$186bo\$187b2o\$186b2o13\$197bobo\$198b2o\$198bo2\$278b
2o\$278b2o6\$282b3o\$198bobo\$199b2o\$199bo6\$280b2o\$280b2o5\$210bo\$211b2o71b
3o\$210b2o8\$282b2o\$282b2o\$211bo\$212b2o\$211b2o6\$278b2o\$278b2o6\$222bobo\$
223b2o\$223bo\$274b2o\$274b2o6\$278b3o2\$223bobo\$224b2o\$224bo5\$276b2o\$276b
2o5\$223bo\$224b2o54b3o\$223b2o8\$278b2o\$278b2o3\$222bobo\$223b2o\$223bo\$282b
3o9\$280b2o\$27bo252b2o\$o12bobo12b2o204bo\$b2o11b2o11b2o206b2o\$2o12bo219b
2o3\$284b3o6\$41bobo\$42b2o9bobo179bo\$42bo11b2o180b2o\$54bo180b2o45b2o\$
282b2o8\$68bo\$69b2o9bo197b2o\$68b2o11b2o195b2o\$80b2o\$246bobo\$247b2o\$247b
o5\$274b2o\$274b2o\$94bobo\$95b2o9bobo\$95bo11b2o\$107bo139bobo\$248b2o\$248bo
29b3o7\$121bo38bo\$122b2o9bo12bobo12b2o\$121b2o11b2o11b2o11b2o114b2o\$133b
2o12bo128b2o2\$259bo\$260b2o\$259b2o2\$280b3o3\$174bobo\$175b2o9bobo\$175bo
11b2o\$187bo2\$260bo\$261b2o15b2o\$260b2o16b2o5\$201bo\$202b2o9bo68b3o\$201b
2o11b2o\$213b2o5\$271bobo\$272b2o\$272bo7b2o\$280b2o2\$227bobo\$228b2o9bobo\$
228bo11b2o\$240bo\$284b3o3\$272bobo\$273b2o\$273bo3\$254bo\$255b2o9bo15b2o\$
254b2o11b2o13b2o\$124b2o82b2o56b2o\$124b2o82b2o\$140b2o82b2o\$140b2o82b2o\$
72b2o40b2o15bo24b2o40b2o15bo24b2o41b3o\$72b2o40b2o15bo24b2o40b2o15bo24b
2o41bo\$88b2o41bo15bo24b2o41bo15bo24b2o25b3o\$88b2o57bo24b2o57bo24b2o\$
79bo24b2o41bo15bo24b2o41bo15bo24b2o\$79bo24b2o57bo24b2o57bo24b2o4b3o\$
79bo15bo67bo15bo67bo15bo14bobo\$95bo83bo83bo14bobo\$95bo83bo83bo!
``````
I'm fairly certain that the 10 pseudo-3c/7 rake flotilla could be adapted to provide the gliders and the puffer for the blonks might even be easier.

HartmutHolzwart
Posts: 579
Joined: June 27th, 2009, 10:58 am
Location: Germany

### Re: Cheap way to construct a c/2 p168 puffer

the 3c/7 rake is copied from a pattern in the life list!

I look it up when providing a comment to the pattern. The only original idea is the way of inserting and deleting pis. I came up with the block mechanism when studying various possibilities to destroy a pi without disturbing the pi reflection mechanism which is crucial for the wave. So it was a lucky coincidence...

I'll need somewhat more to look at your improvements! Actually I like the idea of other people being interested in this stuff. So please keep supporting me.

As in real life I'm working as a program manager in an insurance company, I know the difference between having all the parts and actually building them together to have something working!

Thanks again!
Hartmut

fsrm
Posts: 135
Joined: February 22nd, 2016, 6:23 am

### Re: Cheap way to construct a c/2 p168 puffer

With cleaning:

Code: Select all

``````x = 959, y = 158, rule = B3/S23
371bobo59bobo59bobo59bobo\$370bo2bo58bo2bo58bo2bo58bo2bo\$369b2o60b2o60b
2o60b2o\$368bo4bo56bo4bo56bo4bo56bo4bo\$367b5obo55b5obo55b5obo55b5obo\$
364b2o60b2o60b2o60b2o\$357bo5bo3b3o49bo5bo3b3o49bo5bo3b3o49bo5bo3b3o\$
354b4o4bo3bo49b4o4bo3bo49b4o4bo3bo49b4o4bo3bo\$354b2o6bo5bo47b2o6bo5bo
47b2o6bo5bo47b2o6bo5bo\$352bo9bo2bo2bo45bo9bo2bo2bo45bo9bo2bo2bo45bo9bo
2bo2bo\$352b6o5bobo2b2obo42b6o5bobo2b2obo42b6o5bobo2b2obo42b6o5bobo2b2o
bo\$349bobo19bo39bobo19bo39bobo19bo39bobo19bo\$348b6obobo4b3o45b6obobo4b
3o45b6obobo4b3o45b6obobo4b3o\$347b2o5b2obo4b2o45b2o5b2obo4b2o45b2o5b2ob
o4b2o45b2o5b2obo4b2o\$346b2o4b2o8b3o43b2o4b2o8b3o43b2o4b2o8b3o43b2o4b2o
8b3o\$347b2o4b5o51b2o4b5o51b2o4b5o51b2o4b5o\$363bobo59bobo59bobo59bobo\$
347b2o4b4obo3bo2bo43b2o4b4obo3bo2bo43b2o4b4obo3bo2bo43b2o4b4obo3bo2bo\$
346b2o4b2o4bo3bo45b2o4b2o4bo3bo45b2o4b2o4bo3bo45b2o4b2o4bo3bo\$347b2o5b
2o5bo2bo44b2o5b2o5bo2bo44b2o5b2o5bo2bo44b2o5b2o5bo2bo12bo\$348b6ob2o4b
2o47b6ob2o4b2o47b6ob2o4b2o47b6ob2o4b2o13b3o\$349bobo7bobo49bobo7bobo49b
obo7bobo49bobo7bobo13b2ob2o\$352b6obobo52b6obobo11bo40b6obobo52b6obobo
12b2obob2o\$352bo8bo3bo48bo8bo3bo6b3o39bo8bo3bo48bo8bo3bo9bobobo\$353b5o
bobo4bo4bo43b5obobo4bo5bo2bo39b5obobo4bob5o42b5obobo4bob2o7bo\$354bo4bo
bo5bo3bo44bo4bobo5bo48bo4bobo6b2o46bo4bobo8bo\$355b2o4bo5bo3b2o44b2o4bo
5bo3bo45b2o4bo55b2o4bo\$356bo2bobo5bo50bo2bobo5bo2bobo45bo2bobo5bo50bo
2bobo5b2o\$357bobobo5bo51bobobo5bo2bobo46bobobo5bo51bobobo5b2o\$361bo5bo
3b2o50bo5bo3bo51bo61bo\$357bobobo5bo3bo47bobobo5bo51bobobo6b2o49bobobo
8bo\$356bo2bobo4bo4bo46bo2bobo4bo5bo2bo42bo2bobo4bob5o45bo2bobo4bob2o7b
o\$355b2o4bo3bo51b2o4bo3bo6b3o42b2o4bo3bo51b2o4bo3bo9bobobo\$354bo4bobo
54bo4bobo11bo42bo4bobo54bo4bobo12b2obob2o\$353b5obobo53b5obobo53b5obobo
53b5obobo13b2ob2o\$350b2o9b2o49b2o9b2o49b2o9b2o49b2o9b2o13b3o\$349bo3b3o
5bo2bo46bo3b3o5bo2bo46bo3b3o5bo2bo46bo3b3o5bo2bo12bo\$348bo3bo9bo47bo3b
o9bo47bo3bo9bo47bo3bo9bo\$348bo5bo7bo2bo17bo26bo5bo7bo2bo44bo5bo7bo2bo
44bo5bo7bo2bo\$348b3o3bo8bobo16bo27b3o3bo8bobo44b3o3bo8bobo44b3o3bo8bob
o\$354b2obo24b3o31b2obo58b2obo27bo30b2obo\$346b5o6bo4b3o43b5o6bo4b3o43b
5o6bo4b3o19bo23b5o6bo4b3o\$346bo15b2o11b2o31bo15b2o11b2o31bo15b2o11b2o
7b3o21bo15b2o11b2o\$345bo3bo12b3o9b2ob3o27bo3bo12b3o9b2ob3o27bo3bo12b3o
9b2ob3o27bo3bo12b3o9b2ob3o\$344b4obo25b5o15b5o6b4obo25b5o15b5o6b4obo25b
5o15b5o6b4obo25b5o15b5o\$343bo7bo11bobo10b3o16bo4bo4bo7bo11bobo10b3o16b
o4bo4bo7bo11bobo10b3o16bo4bo4bo7bo11bobo10b3o16bo4bo\$342bo2bo5bo11bo
31bo8bo2bo5bo11bo27bo3bo8bo2bo5bo11bo31bo8bo2bo5bo11bo31bo\$342bo2bo5b
2obo7bo3bo29bo3bo3bo2bo5b2obo7bo3bo23bo5bo3bo3bo2bo5b2obo7bo3bo29bo3bo
3bo2bo5b2obo7bo3bo29bo3bo\$342bo4bo6bo6b4obo3b2o26bo5bo4bo6bo6b4obo3b2o
18b3o5bo5bo4bo6bo6b4obo3b2o26bo5bo4bo6bo6b4obo3b2o21bo4bo\$343b4o13bo8b
2ob2o8bo22b4o13bo8b2ob2o12bo18b4o13bo8b2ob2o31b4o13bo8b2ob2o8bo9bo\$
344bo14bo2bo7b4o3bo4bobo21bo14bo2bo7b4o3bo8bo19bo14bo2bo7b4o3bo5b3o20b
o14bo2bo7b4o3bo4bobo7b3o\$345b2o12bo2bo8b2o3bo5bo2bo21b2o12bo2bo8b2o3bo
bo2b2o24b2o12bo2bo8b2o3bob2o3b3o2bo18b2o12bo2bo8b2o3bo5bo2bo\$346bo2bo
9bo4bo10bo2bo6bo22bo2bo9bo4bo10bo3b2o2bo6b2o16bo2bo9bo4bo10bo3bo6bobo
19bo2bo9bo4bo10bo2bo6bo\$347bobo10b4o7b2o3bo5bo2bo23bobo10b4o7b2o3bobo
2b2o26bobo10b4o7b2o3bob2o3b3o2bo20bobo10b4o7b2o3bo5bo2bo\$361bo8b4o3bo
4bobo38bo8b4o3bo8bo36bo8b4o3bo5b3o37bo8b4o3bo4bobo\$362b2o5b2ob2o8bo41b
2o5b2ob2o12bo37b2o5b2ob2o50b2o5b2ob2o8bo\$363bo2bo3b2o53bo2bo3b2o53bo2b
o3b2o53bo2bo3b2o\$364bobo59bobo59bobo59bobo310b3o\$862b5o\$861b2ob3o\$380b
4o478b2o\$380bo3bo488b3o\$380bo491b5o\$316bo2bo61bo2bo486b2ob3o\$315bo139b
2o82b2o82b2o82b2o82b2o79b2o\$315bo3bo135b2o82b2o82b2o82b2o82b2o90b3o\$
315b4o92bo470b5o\$410bo470b2ob3o\$250b4o107b2o47b3o32b2o82b2o82b2o82b2o
82b2o82b2o15b2o\$250bo3bo106b2o82b2o82b2o82b2o82b2o82b2o82b2o26b3o\$250b
o641b5o\$186bo2bo61bo2bo636b2ob3o\$185bo81b2o82b2o25b2o55b2o82b2o82b2o
82b2o82b2o82b2o35b2o\$185bo3bo77b2o82b2o25bobo54b2o82b2o82b2o82b2o82b2o
82b2o46b3o\$185b4o189bo102bo420b5o\$480bo420b2ob3o\$120b4o133b2o82b2o82b
2o53b3o26b2o82b2o82b2o82b2o82b2o55b2o\$120bo3bo132b2o82b2o82b2o82b2o82b
2o82b2o82b2o82b2o66b3o\$120bo791b5o\$51b2o68bo2bo786b2ob3o\$50b4o109b2o
82b2o82b2o82b2o82b2o82b2o82b2o82b2o82b2o75b2o8b6o\$49b2ob2o109b2o82b2o
82b2o82b2o82b2o82b2o82b2o82b2o82b2o85bo5bo\$24bo4bo2bo17b2o499bo370bo\$
21b4o3bo521bo372bo4bo\$21b2o5bo3bo11b2o23b2o82b2o82b2o82b2o82b2o82b2o
59b3o20b2o82b2o82b2o82b2o82b2o14b2o5b6o\$19bo8b4o11bo25b2o82b2o82b2o82b
2o82b2o82b2o82b2o82b2o82b2o82b2o82b2o21bo5bo\$7bo11b4o11b3o2b2o7bo132b
3o296bo83bo83bo83bo83bo83bo31bo\$4b4o10bo15b3o2b2o8bo131bo298bo83bo83bo
83bo83bo83bo32bo4bo\$4b2o11b3o2bo11b3o2b2o7bo34bobo4b2o52bobo35bo22bobo
4b2o52bobo58bobo4b2o52bobo4b2o83bo83bo83bo83bo83bo83bo34b2o5b6o\$2bo15b
3o7b4o11bo38bo2bo3b4o50bo2bo3b2o52bo2bo3b4o50bo2bo3b2o52bo2bo3b4o50bo
2bo3b4o544bo5bo\$2b4o13bo8bo3bo11b2o35b2o5b2ob2o49b2o5b2ob2o8bo40b2o5b
2ob2o9bo39b2o5b2ob2o49b2o5b2ob2o11bo37b2o5b2ob2o9bo146bo66bo16bo83bo
83bo83bo51bo\$bo10bo7b3obo3bo51bo8b2o5b2ob3o39bo8b4o3bo4bobo37bo8b2o11b
o38bo8b4o3bo5b3o10b3o23bo8b2o5bo2bo3bob2o34bo8b2o11bo146bo65bo17bo83bo
83bo83bo52bo4bo\$3o2bo4b3o7bo2b2o4bo2bo15b2o5b3o8bobo10b4o12bo5b2o24bob
o10b4o7b2o3bo5bo2bo22bobo10b4o12bobo4b2o2bo20bobo10b4o7b2o3bob2o3b3o2b
o7bo11bobo10b4o12bo3bo4b5o18bobo10b4o12bobo4b2o2bo42bobo4b2o91bo65b3o
15bo83bo83bo83bo54b2o5b6o\$b3o5b2o10b3o23b2o5b5o6bo2bo9bo4bo10b2o7bo22b
o2bo9bo4bo10bo2bo6bo21bo2bo9bo4bo10b2o2bo7bo19bo2bo9bo4bo10bo3bo6bobo
8bo9bo2bo9bo4bo10b2o4bo4bo2bo17bo2bo9bo4bo10b2o2bo7bo41bo2bo3b4o488bo
5bo\$2bo6bo13bo25bo3b2ob3o5b2o12bo2bo13bo5b2o22b2o12bo2bo8b2o3bo5bo2bo
20b2o12bo2bo13bobo4b2o2bo18b2o12bo2bo8b2o3bob2o3b3o2bo17b2o12bo2bo13bo
3bo4b5o16b2o12bo2bo13bobo4b2o2bo40b2o5b2ob2o11bo152bo83bo83bo83bo71bo\$
3b3obobo11bo11b5o16b2o7bo14bo2bo7b2o5b2ob3o22bo14bo2bo7b4o3bo4bobo20bo
14bo2bo7b2o11bo8b2o11bo14bo2bo7b4o3bo5b3o19bo14bo2bo7b2o5bo2bo3bob2o
17bo14bo2bo7b2o11bo43bo8b2o5bo2bo3bob2o150bo83bo83bo83bo72bo\$3bo2b2o
13bobo9bo4bo23b4o13bo8b2ob2o30b4o13bo8b2ob2o8bo21b4o13bo8b2ob2o9bo8bob
o9b4o13bo8b2ob2o30b4o13bo8b2ob2o11bo18b4o13bo8b2ob2o9bo29bobo10b4o12bo
3bo4b5o40bobo4b2o99bo83bo83bo83bo74b2o\$4b2o3bo10bo12bo27bo4bo6bo6b4obo
3b4o29bo4bo6bo6b4obo3b2o26bo4bo4bo6bo6b4obo3b4o18bo10bo4bo6bo6b4obo3b
2o26bo4bo4bo6bo6b4obo3b4o29bo4bo6bo6b4obo3b4o38bo2bo9bo4bo10b2o4bo4bo
2bo39bo2bo3b4o\$5b4o6bo5bobo10bo3bo22bo2bo5b2obo7bo3bo4b2o30bo2bo5b2obo
7bo3bo29bo3bo2bo2bo5b2obo7bo3bo4b2o30bo2bo5b2obo7bo3bo29bo3bo2bo2bo5b
2obo7bo3bo4b2o30bo2bo5b2obo7bo3bo4b2o38b2o12bo2bo13bo3bo4b5o38b2o5b2ob
2o172bo83bo83bo83bo\$13b3o5bo14bo24bo2bo5bo11bo31b5o3bo2bo5bo11bo31bo7b
o2bo5bo11bo31b5o3bo2bo5bo11bo31bo7bo2bo5bo11bo31b5o3bo2bo5bo11bo31b5o
10bo14bo2bo7b2o5bo2bo3bob2o39bo8b2o5b2ob3o163bo83bo83bo83bo\$7b2o3b2o9b
o38bo7bo11bobo29bo4bo3bo7bo11bobo10b3o8b3o5bo4bo3bo7bo11bobo29bo4bo3bo
7bo11bobo10b3o16bo4bo3bo7bo11bobo21b2o6bo4bo3bo7bo11bobo21b2o6bo4bo8b
4o13bo8b2ob2o11bo5b2o20bobo10b4o12bo5b2o11b2o33bobo4b2o26b2o79bo83bo
83bo83bo\$6b2o4bo8b3o39b4obo25b2o18bo9b4obo25b5o7bo7b5o5b4obo25b2o18bo
9b4obo25b5o15b5o5b4obo25b2o10bobo5bo9b4obo25b2o10bobo5bo12bo4bo6bo6b4o
bo3b4o17bobo18bo2bo9bo4bo10b2o7bo10bobo31bo2bo3b4o25bobo\$7b2o5bo5b3o
41bo3bo12b3o9b2ob3o16bo3bo5bo3bo12b3o9b2ob3o8bo17bo3bo12b3o9b2ob3o16bo
3bo5bo3bo12b3o9b2ob3o26bo3bo12b3o9b2ob3o7bo8bo3bo5bo3bo12b3o9b2ob3o7bo
8bo3bo7bo2bo5b2obo7bo3bo4b2o18bo19b2o12bo2bo13bo5b2o11bo32b2o5b2ob2o9b
o15bo\$8b6o6bobo42bo15b2o11b5o18bo8bo15b2o11b2o30bo15b2o11b5o18bo8bo15b
2o11b2o30bo15b2o11b5o18bo8bo15b2o11b5o18bo9bo2bo5bo11bo31b5o10bo14bo2b
o7b2o5b2ob3o44bo8b2o11bo\$9bobo8b2o43b5o6bo4b3o11b3o4b2o22b5o6bo4b3o42b
5o6bo4b3o11b3o28b5o6bo4b3o42b5o6bo4b3o11b3o28b5o6bo4b3o11b3o30bo7bo11b
obo29bo4bo8b4o13bo8b2ob2o39bobo10b4o12bobo4b2o2bo\$12b4obo2bo52b2obo25b
obo29b2obo57b2obo57b2obo24b3o30b2obo57b2obo52b4obo25b2o18bo12bo4bo6bo
6b4obo3b4o38bo2bo9bo4bo10b2o2bo7bo\$12bo3b2o2b2o45b3o3bo8bobo17bo25b3o
3bo8bobo43b3o3bo8bobo43b3o3bo8bobo16bo26b3o3bo8bobo43b3o3bo8bobo45bo3b
o12b3o9b2ob3o16bo3bo7bo2bo5b2obo7bo3bo4b2o38b2o12bo2bo13bobo4b2o2bo\$
14b2o4b2o5b3o37bo5bo7bo2bo43bo5bo7bo2bo43bo5bo7bo2bo43bo5bo7bo2bo17bo
25bo5bo7bo2bo43bo5bo7bo2bo46bo15b2o11b5o18bo9bo2bo5bo11bo31b5o10bo14bo
2bo7b2o11bo\$14b4o2b5obob3o2b2o32bo3bo9bo46bo3bo9bo46bo3bo9bo46bo3bo9bo
46bo3bo9bo46bo3bo9bo49b5o6bo4b3o11b3o30bo7bo11bobo29bo4bo8b4o13bo8b2ob
2o9bo\$17bo2b5ob2o3bo36bo3b3o5bo2bo45bo3b3o5bo2bo45bo3b3o5bo2bo45bo3b3o
5bo2bo45bo3b3o5bo2bo45bo3b3o5bo2bo55b2obo52b4obo25b2o18bo12bo4bo6bo6b
4obo3b4o\$20b5o5b2o37b2o9b2o48b2o9b2o48b2o9b2o12b3o33b2o9b2o48b2o9b2o
48b2o9b2o51b3o3bo8bobo45bo3bo12b3o9b2ob3o16bo3bo7bo2bo5b2obo7bo3bo4b2o
\$17bo2b5o5b3o39b5obobo52b5obobo52b5obobo13b3o36b5obobo52b5obobo52b5obo
bo52bo5bo7bo2bo46bo15b2o11b5o18bo9bo2bo5bo11bo31b5o\$14b4o2b5o5b3o40bo
4bobo53bo4bobo53bo4bobo12bo3bo36bo4bobo53bo4bobo53bo4bobo52bo3bo9bo49b
5o6bo4b3o11b3o30bo7bo11bobo29bo4bo\$14b2o4b5o5b2o42b2o4bo2bo51b2o4bo3bo
5bo2bo41b2o4bo2bo3bob2o3bob2o37b2o4bo3bo50b2o4bo2bo51b2o4bo2bo50bo3b3o
5bo2bo55b2obo52b4obo25b2o18bo\$12bo3b2o2b5ob2o3bo43bo2bobo2bo2b2o48bo2b
obo4bo4bo2bo42bo2bobo2bo2bo7bo41bo2bobo4bo4bo45bo2bobo2bo2bo2b4o43bo2b
obo2bo2bo2b4o42b2o9b2o51b3o3bo8bobo15b2o28bo3bo12b3o9b2ob3o5b2o9bo3bo\$
12b4obo2b5obob3o2b2o41bobobo2bobo2bob3o44bobobo5bo3bo3bo42bobobo2bo2bo
50bobobo5bo3bo46bobobo2bo2bo2bo3bo43bobobo2bo2bo2bo3bo44b5obobo12bo39b
o5bo7bo2bo15bo30bo15b2o11b5o5bobo10bo\$11bo8b2o5b3o50bo2bobo3b4o48bo5bo
54bo2bo3bo6bo46bo5bo3b2o49bo2bo7b2o48bo2bo7b2o46bo4bobo11bobo38bo3bo9b
o18bobo28b5o6bo4b3o11b3o6bo\$10b6obo2b2o54bobobo2bobo3bo47bobobo5bo50bo
bobo2bo4bo2bo45bobobo5bo50bobobo2bo53bobobo2bo56b2o4bo2bo7b2ob2o38bo3b
3o5bo2bo55b2obo\$7b2o7b2o2bo54bo2bobo2bobo3bo46bo2bobo5bo49bo2bobo2bo4b
o2bo44bo2bobo5bo49bo2bobo2bo52bo2bobo2bo57bo2bobo2bo2b2o47b2o9b2o51b3o
3bo8bobo\$6bo3b3ob2o4b2o52b2o4bo2bobo3b4o42b2o4bo5bo48b2o4bo2bo3bo6bo
40b2o4bo5bo3b2o43b2o4bo2bo7b2o42b2o4bo2bo7b2o49bobobo2bobo2bo49b5obobo
52bo5bo7bo2bo\$5bo3bo4b2o4bobo50bo4bobo2bobo2bob3o41bo4bobo5bo3bo3bo39b
o4bobo2bo2bo47bo4bobo5bo3bo43bo4bobo2bo2bo2bo3bo40bo4bobo2bo2bo2bo3bo
52bo2bobo3bobo47bo4bobo13b2o11b2o24bo3bo9bo\$5bo5bo3b2o3b3o49b5obobo2bo
2b2o45b5obobo4bo4bo2bo39b5obobo2bo2bo7bo38b5obobo4bo4bo42b5obobo2bo2bo
2b4o40b5obobo2bo2bo2b4o49bobobo2bobo4bobo47b2o4bo2bo3bobo4b3o9b3o25bo
3b3o5bo2bo\$5b3o3b4obo4b3o47bo8bo2bo48bo8bo3bo5bo2bo38bo8bo2bo3bob2o3bo
b2o34bo8bo3bo47bo8bo2bo48bo8bo2bo57bo2bobo2bobo4bobo48bo2bobo2bo2bo3b
2o43b2o9b2o\$23bo47b6obobo51b6obobo51b6obobo12bo3bo34b6obobo51b6obobo
51b6obobo59b2o4bo2bobo3bobo50bobobo2bo2bo4bo46b5obobo\$5b3o3b5o5bo46bob
o7bobo48bobo7bobo48bobo7bobo13b3o32bobo7bobo48bobo7bobo48bobo7bobo58bo
4bobo2bobo2bo57bo2bo3bobo49bo4bobo9bo\$5bo5bo4bo4bobo43b6ob2o4b2o46b6ob
2o4b2o46b6ob2o4b2o12b3o31b6ob2o4b2o46b6ob2o4b2o46b6ob2o4b2o56b5obobo2b
o2b2o54bobobo2bo4b3o49b2o4bo2bo4b2obo\$5bo3bo4bo5bo45b2o5b2o5bo2bo43b2o
5b2o5bo2bo43b2o5b2o5bo2bo43b2o5b2o5bo2bo43b2o5b2o5bo2bo43b2o5b2o5bo2bo
53bo8bo2bo7b2ob2o45bo2bobo2bo4b3o50bo2bobo2bo3bo4bo\$6bo3b3obo6bobo41b
2o4b2o4bo3bo44b2o4b2o4bo3bo44b2o4b2o4bo3bo44b2o4b2o4bo3bo44b2o4b2o4bo
3bo44b2o4b2o4bo3bo55b6obobo11bobo45b2o4bo2bo3bobo52bobobo2bo6b2o\$7b2o
7bo4bo7bo36b2o4b4obo3bo2bo42b2o4b4obo3bo2bo42b2o4b4obo3bo2bo42b2o4b4ob
o3bo2bo42b2o4b4obo3bo2bo42b2o4b4obo3bo2bo49bobo7bobo12bo45bo4bobo2bo2b
o4bo54bo2bo3b2o\$10b6o7bo3b3o52bobo58bobo58bobo58bobo58bobo58bobo48b6ob
2o4b2o56b5obobo2bo2bo3b2o50bobobo2bo\$11bo9b3o2b2o38b2o4b5o50b2o4b5o50b
2o4b5o50b2o4b5o50b2o4b5o50b2o4b5o55b2o5b2o5bo2bo53bo8bo2bo3bobo4b3o9b
3o32bo2bobo2bo\$12b2o6b3o3bo38b2o4b2o8b3o42b2o4b2o8b3o42b2o4b2o8b3o42b
2o4b2o8b3o42b2o4b2o8b3o42b2o4b2o8b3o47b2o4b2o4bo3bo55b6obobo13b2o11b2o
31b2o4bo2bo3b2o\$13bo2bo4b2o5bo37b2o5b2obo4b2o44b2o5b2obo4b2o44b2o5b2ob
o4b2o44b2o5b2obo4b2o44b2o5b2obo4b2o44b2o5b2obo4b2o49b2o4b4obo3bo2bo49b
obo7bobo58bo4bobo2bo6b2o\$14bobo5b6o39b6obobo4b3o44b6obobo4b3o44b6obobo
4b3o44b6obobo4b3o44b6obobo4b3o44b6obobo4b3o64bobo48b6ob2o4b2o56b5obobo
2bo3bo4bo\$23bobo42bobo19bo38bobo19bo38bobo19bo38bobo19bo38bobo19bo38bo
bo19bo41b2o4b5o55b2o5b2o5bo2bo53bo8bo2bo4b2obo\$26b4obo39b6o5bobo2b2obo
41b6o5bobo2b2obo41b6o5bobo2b2obo41b6o5bobo2b2obo41b6o5bobo2b2obo41b6o
5bobo2b2obo40b2o4b2o8b3o47b2o4b2o4bo3bo18bobo34b6obobo9bo\$26bo3b2o39bo
9bo2bo2bo44bo9bo2bo2bo44bo9bo2bo2bo44bo9bo2bo2bo44bo9bo2bo2bo44bo9bo2b
o2bo44b2o5b2obo4b2o49b2o4b4obo3bo2bo49bobo7bobo\$28b2o43b2o6bo5bo46b2o
6bo5bo46b2o6bo5bo46b2o6bo5bo46b2o6bo5bo46b2o6bo5bo45b6obobo4b3o64bobo
48b6ob2o4b2o\$28b4o41b4o4bo3bo48b4o4bo3bo48b4o4bo3bo48b4o4bo3bo48b4o4bo
3bo48b4o4bo3bo48bobo19bo41b2o4b5o55b2o5b2o5bo2bo\$31bo44bo5bo3b3o48bo5b
o3b3o48bo5bo3b3o48bo5bo3b3o48bo5bo3b3o48bo5bo3b3o48b6o5bobo2b2obo40b2o
4b2o8b3o47b2o4b2o4bo3bo\$83b2o59b2o59b2o59b2o59b2o59b2o52bo9bo2bo2bo44b
2o5b2obo4b2o49b2o4b4obo3bo2bo\$86b5obo54b5obo54b5obo54b5obo54b5obo54b5o
bo46b2o6bo5bo45b6obobo4b3o64bobo\$87bo4bo55bo4bo55bo4bo55bo4bo55bo4bo
55bo4bo46b4o4bo3bo48bobo19bo41b2o4b5o\$88b2o59b2o59b2o59b2o59b2o59b2o
52bo5bo3b3o48b6o5bobo2b2obo40b2o4b2o8b3o\$89bo2bo57bo2bo57bo2bo57bo2bo
57bo2bo57bo2bo56b2o52bo9bo2bo2bo44b2o5b2obo4b2o\$90bobo58bobo58bobo58bo
bo58bobo58bobo59b5obo46b2o6bo5bo45b6obobo4b3o\$458bo4bo46b4o4bo3bo48bob
o19bo\$459b2o52bo5bo3b3o48b6o5bobo2b2obo\$460bo2bo56b2o52bo9bo2bo2bo\$
461bobo59b5obo46b2o6bo5bo\$524bo4bo46b4o4bo3bo\$525b2o52bo5bo3b3o\$526bo
2bo56b2o\$527bobo59b5obo\$590bo4bo\$591b2o\$592bo2bo\$593bobo!
``````