666 rules

[Yoel]

Nothing really diabolic. I came up with this idea, because I wanted to define hexagonal rules with photons. That requires a larger neighborhood, which can not be fully emulated in Golly, but a large subset of this rulespace can be defined as follows using Golly's weighted Larger-than-Life rules with the following custom neighborhood:

NW31073100000701010700310100013100070101070000310731H



That's where 666 comes from: it is 7^3-1=342 in base 7. Although Golly rulestrings are decimal, it is easier to memorize, for example, that survival of two immediate neighbors plus three edge neighbors plus five range-2 neighbors is 7-base 532 rather than 268. 666 (base 7) in the highest possible neighbor number,

Besides regular photons, we can have "hyperphotons", such as these ones in explosive rules that resemble Seeds:

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x = 11, y = 11, rule = R2,C0,S,B14,56,NW31073100000701010700310100013100070101070000310731H
4$4b2o$3bo3bo!

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x = 12, y = 12, rule = R2,C0,S,B56-57,NW31073100000701010700310100013100070101070000310731H
3$3b2o2$3bo2bo!

A Sierpiński triangle builder:

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x = 8, y = 9, rule = R2,C0,S0,B56-57,NW31073100000701010700310100013100070101070000310731H
3$2b2o$4bo!

Hyperphotonic rules can be stabilized by adding generations:

Here is one with stable splitters that can be used as guns:

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x = 145, y = 136, rule = R2,C3,S0,7,14,49,98,112,B56,99,NW31073100000701010700310100013100070101070000310731H
9$48.A$44.A$50.A4$52.A$44.A26.A$56.A$44.A30.B$58.A16.B$85.A2$46.A40.A
2$44.A$64.A$44.A10.A.A.A.A27.A$55.A.B2.B.A$57.B.A.B31.A2$55.A.A5.A.A
29.A6$78.A$77.B.A$78.B2$96.2B$85.A$92.A4.2A$85.A3.B$90.B3$87.A$58.2B$
85.A$59.2A48.A$85.A2$61.A27.2B$24.A$29.A27.A.A5.A.A22.2A12.A$24.A3.B.
A$29.B70.A.A5.A.A3$26.A2$24.A2$24.A2$28.2B2$29.2A6$55.A$55.A.B$57.B
10$38.A3$107.2B2$108.2A$91.A$91.A.B$93.B5$120.A5$115.A2$111.A.A5.A.A!

And AND gate:

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x = 78, y = 84, rule = R2,C3,S0,7,14,49,98,112,B56,99,NW31073100000701010700310100013100070101070000310731H
14$14.A$10.A51.A$16.A42.B$60.B2$16.A$18.A$10.A5.B37.A$17.B.A2.A30.B.A
$10.A43.B$24.A2$13.A$12.A35.A$15.B31.B.A$10.A2.A.B32.B$23.2B5.A$10.A$
23.A2.A$25.A16.A$41.B.A$21.A.A5.A.A10.B2$16.2B2$17.2A17.A$35.B.A$36.B
4$30.A10.A$29.B.A14.A$30.B10.A2$22.2B$44.A$23.2A18.A$25.A20.B5.A$25.A
.B13.A2.A.B$27.B26.A$41.A2$54.A$37.A18.A$37.A.B14.B$39.B15.B.A2.A$47.
2B$62.A$47.A2.A$49.A2$45.A.A5.A.A5.A!

A "flying gun" rake in a "swarming" explosive rule, where photons breed like bugs:

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x = 26, y = 23, rule = R2,C3,S1,8,B9,50-51,NW31073100000701010700310100013100070101070000310731H
2$4.A8.ABA$3.A.B$3.ABA8.ABA$5.A$4.ABA$4.B.A12.A$5.A13.B.A$19.A.B$21.A
7$16.2A$15.A.B2AB$16.BA.B.A$19.2A!

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x = 49, y = 56, rule = R2,C3,S1,9,B9,50-51,NW31073100000701010700310100013100070101070000310731H
6$20.A$19.AB$13.A6.B$14.A6.B$14.AB6.A$15.A$15.AB3.AB$16.A.B$10.BA8.B$
20.A$11.BA2$22.2B.A$25.B$18.3A2.2B.A6$30.A2.A$22.B5.BA.B.B$29.A2.2B2$
26.B4.B2.B$32.A.A$35.A$17.AB11.B4.BA$30.A3.BA$18.AB14.2A$30.A.B$31.B
2.BA$21.A10.A$22.B11.ABA$20.ABA$19.AB10.A$20.B2.BA5.A.B$20.AB2.B6.B$
24.BA$22.ABA$22.B$23.A!

Some rules are abundant with natural guns and reflectors:

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x = 173, y = 132, rule = R2,C3,S100-342,B9,50-51,NW31073100000701010700310100013100070101070000310731H
10$9.A$10.B3.A$11.5A.A$17.2A.A$11.4A2.A.A$17.A.2A$11.5A.A2.A$14.A.A$
11.A.A$14.A.A$13.A.A2B38$126.AB8.A$133.A2.B$108.4A14.B2.A.A.4A$106.AB
A.A12.BA.A$110.2A.A2.A.A2.ABA.A3.A.3A.3A$99.B7.A2.A.A13.A.A$97.A.3A.
2A2.2A.2A4.4A.A.A.A.A3.2A.A.2A$121.A.A2.A3.A3.A2.A$97.2A.5A4.3A.2A2.
2A.2A7.4A.A4.B$100.A.A3.A.A12.A.A.A2.A.A$97.2A.A2.4A.4A.2A4.A3.4A.2A.
3A.A$102.A.A.A.A.A3.A6.A.A7.A.A$68.A28.A.5A2.A.2A4.A.A4.A.2A2.9A$67.A
.B29.A.A2.3A.A5.A.A2.A6.A6.A.A$68.B30.A2.2A.A2.2A6.A.3A.3A.A.10ABA$
99.A.A3.3A2.A2.B2.A.2A.2A3.A.A6.A$98.A4.A.4A.2A.2A2.6A3.2A3.A.A2.2A$
98.BA.A.A.2A2.A.2A5.A.A.6A.A3.A.A$105.A.4A.2A.A3.A2.2A.5A3.A.A$99.A.A
4.3A2.4A3.A.A.A4.A.A5.A$103.A.A6.5A.2A.3A.8A.4A$98.2BA.A2.A.A10.A.A8.
A3.A.A.2A$99.A3.A.A.4A.A.3A3.A.A.2A.2A.A.2A.2A$96.A5.A.A2.A4.A7.A10.A
3.A$97.A.A.2A3.2A.2A.A3.A.A.A.A11.4A$98.A.A.A21.5A4.A.A.2A$97.A.A.6A.
2A2.A.2A.A.2A.A6.A.A4.A$97.2A.A11.A3.A9.5A$98.2A.A.2A3.5A.A.7A.2A5.A.
A$104.BA3.A2.A.A.3A7.A3.3A.B$113.A.A.A2.3A.2A.A$116.4A5.A2.A2.2A3.A$
104.2AB6.A.A.A6.A3.5A.A.B$88.A5.BA7.A.B.A.2A.A.A10.A2.A.2A.A$89.B.B9.
3A5.A3.A.A7.BA.3A2.4A$90.B2A4.B11.A2.3A.A.A4.A6.A.2A$98.A.2A.A.A.A.A.
A.A.A.A.A3.2A.A3.A.A$100.A.A.A8.3A.2A8.4A.A$100.A8.A.A4.A.5A3.A3.A$
100.A.A.A4.2AB5.2A.A7.2A$92.B5.A.4A14.A2.6A3.A$100.A23.A3.A3.A$96.B.A
.4A.A17.A.A.A.2A.A$96.2AB.A.A2.A18.A.A.A3.A.A$103.A.A21.A.4A$106.A$
106.B$107.B$108.A!

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x = 16, y = 9, rule = R2,C3,S100-342,B9-13,50-55,NW31073100000701010700310100013100070101070000310731H
2$5.B$3.ABAB.A$4.A3.2BA$3.A.A.A$4.A.2A!

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x = 62, y = 123, rule = R2,C3,S147-342,B56,NW31073100000701010700310100013100070101070000310731H
10$13.A.A2$13.A.A.A2$15.A.A3.B$19.A.B$23.A.A$21.A$23.A.A.A2$25.A.A$
21.2A2$22.2B21$26.A.A$33.2A$22.A.A.A.A.A.A$32.A.2B$22.A.A3.A.A2$24.A.
A.A.A2$28.A.A5$39.2A2$40.2B10$45.2A2$46.2B2.A.A2$50.A.A.A2$45.B2.B3.A
.A.A$48.B$43.A5.B4.A.A$42.B3.A$45.B.A3.A2.B$40.A5.B3.B$39.B3.A$42.B.A
3.A$37.A5.B3.B$36.B3.A$39.B.A3.A$34.A5.B3.B$33.B3.A$36.B.A3.A$31.A5.B
3.B$30.B3.A$33.B.A3.A$28.A5.B3.B$27.B3.A$30.B.A3.A$25.A5.B3.B$24.B3.A
$27.B.A3.A$22.A5.B3.B$21.B3.A$24.B.A3.A$19.A5.B3.B$16.A.A3.A$21.B.A3.
A$16.A.A.A.B3.B$19.A.A$18.A.A3.A$17.A.A.A.A2$21.A.A$20.B!

Some oscillators:

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x = 155, y = 82, rule = R2,C3,S1,3-7,B9,50-51,NW31073100000701010700310100013100070101070000310731H
8$24.A$20.2A2.B3.3A$19.A3B.B$21.2A2.B3.3A$26.A$22.A.A$21.A4BA$23.A.A$
35.AB$27.2A3.AB$26.A3BA2.BAB$28.2A12.A$16.B24.AB$13.B28.B$20.B22.B$
118.A$119.BA$44.B74.ABA$23.B96.AB$42.A74.B4.A$13.B26.B.B.A$44.A$44.A$
118.B$16.B$23.B96.B8.A$20.B103.2A4.BA$130.AB$128.BA2.BA$128.AB2.AB$
130.BA2.A$128.A.AB$127.AB$128.BA$127.AB2.AB$128.BA2.BA$128.A2.AB$132.
BA$132.A!

Here are "regular" photons:

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x = 7, y = 8, rule = R2,C0,S1,B50-51,NW31073100000701010700310100013100070101070000310731H
2$3bo$3bo2$3bo!

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x = 33, y = 34, rule = R2,C0,S64,113,120,127,B3,5,54,57,99,103,106,148,155,NW31073100000701010700310100013100070101070000310731H
3$24bo$23bobo$22bob2o$21bob2o$22b2o2$18bo$17bobo$18b2o$17bo$14bobobo$
13bobob2o$14b2o2$10bo$9bobo12bo$10b2o11b2o$22bo$21b2o3$18bo$17b2o!

A replicator producing a Sierpiński triangle of photons:

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x = 25, y = 28, rule = R2,C0,S0,6,64-66,113,120,127,B3,5,14,54,57,99,103,106,148,155,NW31073100000701010700310100013100070101070000310731H
8$8bo2$12bo$8bo2$12bo!

[eRroR_6o6]

some linear growths in the first hyperphotonic generations rule

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x = 168, y = 176, rule = R2,C3,S0,7,14,49,98,112,B56,99,NW31073100000701010700310100013100070101070000310731H
25$44.A$43.B.A$44.B3$39.A$34.A3.B.A113.A$33.B.A3.B111.A.B.A$34.B115.A
3.B2$34.B3.A107.A7.A$33.A.B.B.A113.A$34.A3.B105.A.A$141.B.A.A$140.A$
141.A7.A.A$142.A5.A$143.B5.A$136.A5.A.B3.A$143.A.A$146.A.B$133.A13.A
2$137.B$130.A5.A.B$137.A5.A$124.A3.A3.A$125.B.B.A$124.B.B3.A9.A$129.B
.A3.A$128.A.A.A$131.A.A3.A$118.A13.B.A$131.A3.A$134.B$123.A.B7.B$122.
A3.B7.B$133.B.A$110.A.B13.A$111.B13.A$110.A.B5.A$111.A5.A2$105.A11.B
3.A7.A$104.A.A7.A.B.B.A$107.B.A3.A3.B$106.B$99.A17.A$116.A$121.B.B$
120.A.B$105.A3.B11.A.A$108.A.B5.A$93.A.A9.A3.A$92.A23.B$115.B.A$102.A
5.A.A7.A$95.A.B19.A$96.B$87.A9.B7.A2$93.A3.A$114.A$95.A$94.A5.A.B.B$
83.A19.B$92.A.B3.A5.A3.A$91.A3.B.A$90.A.A7.A7.A$91.A.A.A11.A$78.A13.A
.A$75.B9.B.A5.A$74.A.B.A5.B2$74.A.A5.B.B5.A11.A$73.B3.B5.B.A$74.B3.B
7.A3.B$73.A3.A.A7.B.B$80.A5.B9.A$69.B.A9.B5.B$68.A.B9.A.B$69.A11.A.A$
64.A.A17.A$85.B3.A.A$84.A.B$75.A11.A.B$74.B.A13.B$61.A5.A.B3.B.B9.B.A
.A$68.B3.A.B9.A.B$69.B3.A$58.A7.A.B13.A$67.B.B11.B$60.A7.B.B.B.B5.A.B
$69.B.B.B7.A$52.A.A11.B3.B3.A$67.B3.A7.A2$63.B15.A$62.A.B$49.A3.A9.A$
74.A$69.A$46.A9.A$71.A$48.A$59.A$40.A.A$67.A$62.A$37.A5.A23.A$42.A$
43.A.A.A$62.A$39.A5.A11.A$34.A15.A$41.A17.A$36.A3.A7.A.A$41.A$28.A13.
B7.A.A$43.B7.A3.A$44.A.A$23.A21.A9.A$30.A17.A$29.A$30.A21.A$29.A15.A
2$47.A3$16.A7.A$37.A.A$36.A.A$43.A$16.A3$19.A11.A$40.A4$24.A3$27.A3.A
!

[CARuler]

found more

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x = 55, y = 46, rule = R2,C3,S0,7,14,49,98,112,B56,99,NW31073100000701010700310100013100070101070000310731H
3$3.A.A4$11.A.A4$6.A12.A.A4$14.A12.A.A2$31.A2$22.A9.3A2$30.A.2A.B$35.
B$27.2B6.B.A$39.A3.B$28.2A11.A.B.A$45.A$23.2B2$24.2A2$19.2B2$20.2A2$15.
2B2$16.2A2$11.2B2$12.2A2$7.2B2$8.2A!

[confocaloid]

[...] That requires a larger neighborhood, which can not be fully emulated in Golly, but a large subset of this rulespace can be defined as follows using Golly's weighted Larger-than-Life rules with the following custom neighborhood:

NW31073100000701010700310100013100070101070000310731H

[...]

The idea of higher-range weighted neighbourhoods is fairly old. For example, read www.collidoscope.com/modernca/words.html (archived copy), that page discusses a notation for "twelve neighbor star shaped neighborhood". (That is a subset of the "666" neighbourhood.)
However, "old" doesn't imply "well-explored". These possibilities are apparently mostly unexplored.

Note that for certain purposes, it may be more convenient to assign weights differently, so that higher-weighted neighbours are geometrically closer to the middle cell:

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NW01070100000731310700013100310100073131070000010701H

(In particular, this choice leads to shorter definitions of those cellular automata that are slight modifications of range-1 outer-totalistic CA. This is because what was a single range-1 neighbour-count, can be replaced by a single range of consecutive numeric conditions.)

Crossposting several known examples:

Partition the range-2 hexagonal neighbourhood into three 'layers' in the following way:

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    3 2 3
   2 1 1 2
  3 1 0 1 3
   2 1 1 2
    3 2 3

Let a cell in layer 3 have weight 1, let a cell in layer 2 have weight 7, and let a cell in layer 1 have weight 49. With this weighted neighbourhood, the rule B2/S34H has the following rulestring:

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R2,C0,S147-244,B98-146,NW01070100000731310700013100310100073131070000010701H

What is possible with toggling just one birth or survival condition (out of 343 x 2 possible conditions) away from this?

Adding S49 allows a common c/8 diagonal spaceship:

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x = 3, y = 4, rule = R2,C0,S49,147-244,B98-146,NW01070100000731310700013100310100073131070000010701H
2bo$obo2$2bo!

Adding S112 allows two common spaceships, a c/2o and a c/5o:

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x = 11, y = 5, rule = R2,C0,S112,147-244,B98-146,NW01070100000731310700013100310100073131070000010701H
bo6bo$8bo$2o6bo$2o7bo$2bo7bo!

Adding S21 allows this p73 oscillator:

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x = 3, y = 6, rule = R2,C0,S21,147-244,B98-146,NW01070100000731310700013100310100073131070000010701H
bo$o$obo$obo$2bo$bo!

Adding S64 results in a slightly explosive rule with this c/6o:

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x = 3, y = 5, rule = R2,C0,S64,147-244,B98-146,NW01070100000731310700013100310100073131070000010701H
o$o2$bo$2bo!

Adding S9 enables this symmetric explosion:

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x = 5, y = 5, rule = R2,C0,S9,147-244,B98-146,NW01070100000731310700013100310100073131070000010701H
obobo$2b2o$2b3o2$4bo!

Edit: changed weights of layers to simplify the rulestrings.

15c/30 orthogonal forerake, emits c/5 orthogonal gliders:

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x = 150, y = 35, rule = R2,C0,S21,112,147-244,B98-146,NW01070100000731310700013100310100073131070000010701H
57bobo$42bo9bo6b2o$39bob3o5bo3bo4bo2bo8bo$48b2o11b2o3b3o61bobo$42b2o5b
obo8b4o8b2o41bo9bo6b2o$43bo5bo9b3obo6b2ob2o37bob3o5bo3bo4bo2bo8bo$42bo
9bo6bo2bo3b2o4b2o47b2o11b2o3b3o$51bo63b2o5bobo8b4o8b2o$33bo26bobo53bo
5bo9b3obo6b2ob2o$115bo9bo6bo2bo3b2o4b2o$31bo2bo89bo$33bo72bo26bobo2$
56bo47bo2bo$4bo19bo33bo47bo$4bobo49bo2b2o23bo$o14bo6bo2bo4bo14bo13bo
23bo$5bobo16bo29bo3b3o5bo17bo12bo$bo4bo9bo14bo14bo24bo11b2o$54bo12bo3b
3o11b3o7bo2bo$25bo14bo15bo2bo6b3o3bo12bobo9bo$27bo14bo27bo4bo10bo9b2o$
60b2o6bo5bo6bo6bo$57bobobo6bo2bo9bo13b3o$58bobo7bobo2bo2bo21bo$58b2obo
12b6o19bo$56bobo19b2o48bo$6bo8bo8bo8bo8bo15bob3o13b2o47bo4bobo$6bo8bo
8bo8bo8bo14b2o17b2o52bo5bo3bo$7b2o7b2o7b2o7b2o7b2o14bobobo46b3o17bo10b
o4b2o$7bo8bo8bo8bo8bo15bob2o50bo12bo3bob3o5bobo2b2ob2o$8bo8bo8bo8bo8bo
16bo52bo10bo2b3o2bo8bo5b2o$127bob2o3bo9b2o$125bo2bobo3b4o2bo7bo$125bo
5bo4bo3bo!

c/2o, c/2o, c/5o, c/8d, 2c/24o, 18c/36o puffer, p3, p9, p10, p12, p36

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x = 66, y = 24, rule = R2,C0,S4,6,17,19,25-29,34,38-41,44-45,49,54-55,61,74,76,78,82-86,88,90,93,95,97,104,111-112,117,123-125,127,129,131,136,138-139,141,146-149,151-157,159,161-164,166-167,169-173,175-178,180,184,187-188,190-191,193-196,198-200,203-208,211-213,215-217,219,221,226,228,231,233-237,240-241,245,248-249,252,256-258,260,263-268,270,272,275-276,281,283,285,288,290,292-294,297-298,300-301,303,306-309,311-312,314,317,319-320,322-324,326,329,333,335,338,340,B13,20,24-26,32,35,40,44,47-48,54-55,69,81,87,90,95-96,98-109,112-114,116,119-122,126-127,130,132-134,136-139,145-146,152-153,158,167,173-175,180,184,186,189,191,193,202,216,218,220,222-223,227-228,233,236,239-244,246,248-250,255,258-260,262,265,270,277-278,281,284,286-289,293,297,301-302,305,307,309,311,315-316,319,324,326-328,335,340-341,NW01070100000731310700013100310100073131070000010701H
2b2o10bo7bo6b2o32bo$b2o10b2o7bo6bobo29bo$2b2o10b2o6bo6b2o6bo2bo23bo$
23bo16b2o19bo$5bo11bo6bo13bo2bo23bo$63bobo$61bo3bo$61bo3bo$61bobo2$63b
o$63b3o$64bo5$31bo$2o8bo10b2o7b4o$obo7b2o8bo9bobobo9b2o$b2o7bobo9bo7bo
b2obo9b4o$10b4o6b2o9b5o12b2o$31b2o2b2o$33b3o!

I think the following conditions are optional for the above objects:

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optional birth: 5, 12-13, 19-20, 24-26, 29-41, 43-48, 54-55, 62, 69, 74-77, 80-84, 86-91, 93-97, 104, 110-111, 117-118, 122-125, 128-132, 134-139, 141-146, 151-153, 160, 166-167, 171, 173-174, 177, 179-195, 201-202, 207-209, 214-216, 218, 220, 222-224, 226, 228-230, 232-238, 240-244, 248, 250-251, 255-260, 263-272, 274-275, 277-293, 295-299, 301-314, 316-342
optional survival: 4, 6, 11-13, 18, 20, 24-27, 31, 33-48, 54-55, 61-62, 69, 74-76, 80-90, 92-97, 102, 104, 110-111, 116-118, 122-125, 127, 129, 131-132, 136-146, 150-153, 158-160, 166-167, 172-174, 178-195, 197, 199, 201-202, 206, 209, 214-218, 220-225, 227, 229-245, 247-252, 254-261, 263-274, 276-320, 322-335, 337-342

Crosspost from another thread

found an amazing hexagonal rule using a method studied by me but apparently first discovered by someone else (unsure who it was) for allowing some nontotalistic rules in higher ranges without as complicated of rulestrings. the neighborhood and type of rule used is 1.5 hex and ring totalistic respectively.
the rule that's so of note is this one. (example soup)

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rle

it's comparable to CGOL, though with more spaceships and less diverse still lifes. the name for the rule is currently Amazo (please give suggestions for other names), and the definition for the rule is "a cell is born if out has 1 cell and inner has 2, or if outer has 3 cells and inner has 1, 3, or 4 cells. a cell survives if inner has 2 or 3 cells" with inner referring to the six closest cells, and outer referring to the next six after them.

known (natural) spaceships:

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x = 7, y = 53, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
o$2o2$bo19$bo$3o$2o$b2o19$2bo$2b2o$3bobo$2bo2b2o$5bo$o4b2o$bo$b2o$2bo16$
b2o$b2o$o$obo$2b2o!

listed in order of frequency.
names and speeds:
1) glider, c/4d
2) odder, 3c/16o
3) wider, 4c/10o
4) queener, (3,8)c/23 (how the heck is there a natural oblique this is awesome)

there's also a common weakly sparky p22 oscillator, the bumbler

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x = 4, y = 4, rule = R2,C2,S20-36,B13,21,33,43,NW0001000000010a0a0100000a000a0000010a0a010000000100H
b2o$ob2o$2o$bo!

KNOWN TECH STUFF

[...]

A 2c/66 orthogonal in a variant of the rule:

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x = 12, y = 5, rule = R2,C0,S3,20-36,B13,21,33,43,NW0001000000010A0A0100000A000A0000010A0A010000000100H
2bo$2b2o2bo2bo$2obo2b5o$b2o3bo3b2o$2bo7bo!

This variant also supports the small objects and reactions: [...]

Edit: here is a variant with a p216 oscillator and a glider gun

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#C optional birth (6): 6, 15-16, 56, 65-66
#C optional survival (12): 5-6, 16, 26, 46, 55-56, 60, 63-66
#C [[ THEME LifeHistory MAXGRIDSIZE 9 ]]
x = 166, y = 83, rule = R2,C0,S3,20-36,B13,21,26,33,43,NW0001000000010A0A0100000A000A0000010A0A010000000100H
46b2o$45b3o$47bo4$4bo$4b2o$4b2o3bo$9b3o$159bo$11b2o146b2o2$8b3o149bo$
9b2o$10bo7$104b2o$32b2o70bobo$32bobo70b2o$33b2o2$2b2o3bobo$ob2obo$o3b
2o90bo$bo2bo90b3o$2o93b2o$bo94b2o62bo$159b3o$159b2o$160b2o7$44bo59b2o$
44b2o58bobo$44b2o59b2o$48bo$46bo43bo$47bobo39b3o$89b2o$47bo42b2o$46b2o
b2o$46b4o$47b2o$48bo$161bo$161b2o$162bobo$161bo2b2o$164bo$159bo4b2o$
130bo29bo$130b2o2bo2bo22b2o$104b2o22b2obo2b5o22bo$104bobo22b2o3bo3b2o$
105b2o23bo7bo2$90bo$90b2o$91bobo$90bo2b2o$93bo$88bo4b2o$89bo$89b2o$90b
o4$160b2o$160b2o$159bo$159bobo$161b2o!