Sparker Compilation (up to p16)

For discussion of specific patterns or specific families of patterns, both newly-discovered and well-known.
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yoleo
Posts: 128
Joined: October 26th, 2021, 11:48 pm

Sparker Compilation (up to p16)

Post by yoleo » December 22nd, 2023, 10:29 pm

Multiple times, people have asked for a compilation of sparkers. They're scattered across a couple different places. I've collected a good portion of them for purposes of periodic CatForce searches, so I thought I'd make a stamp collection:

Code: Select all

x = 413, y = 597, rule = LifeHistory
123.2A$81.A42.A$82.2A40.A.A$8.5D39.A27.2A18.E24.2A3.A$12.D16.3A18.A2.
A28.A17.E29.A$12.D27.A9.E2.A6.A39.A29.A19.A$12.D20.A5.A2.A8.A6.2A62.
2A25.A.A$8.5D6.3A11.A5.A2.A17.2A19.2AE12.3A23.A3.3A3.A2E15.A.A$8.D24.
A7.A9.A7.A19.A39.2A.A24.2A.A$8.D41.E2.A23.2A2.2A17.A4.2A12.A2.3A25.A.
2A$8.D41.A2.A46.A4.A.A12.2A3.A22.A.A$8.5D39.A26.A2.A17.A6.A14.4A6.2A
15.A.A$80.A26.2A13.A9.A17.A$80.A39.A.A.2A7.3A$120.2A2.A10.A$124.A.A$
125.2A10$8.5D11.2A34.2A34.2A21.2E23.2A18.A10.A58.2A3.2A$12.D11.2A28.
2E4.2A33.A2.A44.A2.A3.E12.A.A3.2E3.A.A13.E19.E19.2E.4A.A2.A16.AE.EA$
12.D37.A.4A3.A17.E6.E9.A.A.A10.2A3.A.2A4.2A.A3.2A12.A.A.A15.A.A8.A.A
10.A21.E2.A15.E7.2A.A.A16.A3.A$12.D9.4A9.A12.3A2.A.A.7A12.A2.A2.A2.A
6.E2A2.A10.A3.A.A3.4A3.A.A3.A10.2A.2A.A3.3A7.2A.3A4.3A.2A5.2A2.2A.3A
12.A33.2A$8.5D9.A3.A6.A3.4A22.A11.A10.A21.A.A5.A2.2A2.A5.A.A12.A4.3A
2.A.A6.A.A2.4A2.A.A6.A.A2.3A2.A7.2A.A.2A.2A.3A12.A.5A4.A19.A$12.D11.A
.A6.A3.A12.2A7.2A15.2A.4A.2A8.2A11.2A6.2A2.2A2.2A6.2A11.A.2A.3A3.2A6.
A.2A2.2A2.2A.A7.2A3.A2.2A6.A.A.2A3.3A3.A11.4A5.2A.2A15.3A.2A$12.D20.A
17.A5.3A.A18.2A13.A10.A2.3A4.2A4.2A4.3A2.A11.A.A3.A4.3A5.A2.A.2A.A2.A
24.A.A.A3.A2.A.2A10.A.A.A.3A5.A15.A4.A2.A$12.D10.A2.E9.A20.4A45.2A4.
3A3.4A3.3A4.2A20.A4.A5.2A6.2A9.2A3.A9.2A3.A.A.A2.A.A9.3A.3A6.A2.A16.
3A2.3A$8.5D10.A.A8.2A21.A50.3A.3A10.3A.3A18.3A4.2A7.A.4A.A9.A2.2A.A8.
A2.6A4.A.A8.A2.A.A3.A.A.4A.2A16.A.A$24.A81.2A5.A4.4A4.A5.2A12.2A.A.A.
A.3A8.A.A2.A.A9.2A4.A9.A7.3A.2A9.4A2.2A2.A2.A2.A.A19.A.2A$107.A.A3.2A
10.2A3.A.A9.2A5.A.A4.2A9.A4.A13.A5.2A6.7A3.A15.2A2.A.A.4A2.A18.2A.2A$
106.A2.3A3.A2.A2.A2.A3.3A2.A8.A4.A.A.4A.A.2A.A21.8A.A13.A.A.A13.2A.2A
3.A.A2.3A$107.2A3.2A3.6A3.2A3.2A10.5A.A6.A.A.2A21.A18.2A3.2A.2A13.A4.
2A$108.A.A4.2A2.2A2.2A4.A.A14.A.2A3.A3.A28.5A11.2A20.A2.A2.2A.A.A.2A.
A$108.A.2A.A.A3.2A3.A.A.2A.A9.5A7.4A29.A2.A35.2A3.A2.A.A.A.2A$107.2A
2.A.5A4.5A.A2.2A8.A2.A46.A30.3A2.A.5A.2A$106.A2.A.2A4.6A4.2A.A2.A12.A
6.2A35.2A30.A2.A3.A4.A2.4A$107.A.A.A.A.A8.A.A.A.A.A12.2A6.2A68.2A.2A.
A.2A2.3A2.A$106.2A.A6.8A6.A.2A90.A3.A.A2.2A4.A$109.2A2.2A10.2A2.2A93.
A.A.A3.A2.2A2.A.A$106.2A.A2.A2.3A.2A.3A2.A2.A.2A91.2A.2A3.A2.A3.2A$
106.A3.2A2.A2.A.2A.A2.A2.2A3.A100.2A$107.3A5.2A6.2A5.3A$109.A20.A17$
254.A3.E.E.E3.A53.E23.2E21.2E.E.2E25.2E$3.D4.D20.2E33.E29.E20.2A.E2.E
.2A25.E28.2E25.E5.E40.A.A9.A.A22.E27.E3.E18.E6.E14.2A11.2A17.2E6.2E$
3.D4.D106.A8.A20.2A.E3.E.2A18.2A.E4.E.2A20.E5.E40.A.A9.A.A15.A3.E4.E.
2A21.E5.E13.2A12.2A10.3A9.3A13.2A14.2A$3.D4.D19.A29.2A.A5.A.2A19.2A5.
2A17.2A4.2A21.A9.A18.A10.A19.3E3.3E16.E19.2A.A.A.7A.A.A.2A11.A.A10.A
24.A15.A.A12.A.A13.7A17.3A12.3A$3.D4.D18.A.3A26.A5.A5.A17.2A4.A4.2A
12.3A2.4A2.3A19.2A5.2A20.2A6.2A45.E19.2A.A13.A.2A11.A.A8.2A18.2A.A.2A
.2A.A.2A8.A.A.10A.A.A5.2A3.2A9.2A3.2A13.10A$3.6D16.3A4.A26.2A.2A.2A.
2A22.2A.2A16.A2.A6.A2.A16.3A2.5A2.3A14.3A2.6A2.3A16.2A.2A.2A.2A14.3E
21.A13.A11.2A.A.A.7A2.3A14.A15.A6.2A16.2A4.A2.2A.2A7.2A.2A2.A5.2A3.2A
12.2A3.2A$8.D15.A3.A5.A53.A.A7.A.A13.2A8.2A17.A2.A7.A2.A14.A2.A8.A2.A
65.A.A4.A4.A.A11.2A.A11.A2.A14.A.A3.A3.A3.A.A8.A.A10.A.A7.3A.A2.2A3.
2A2.A.3A6.A2.2A3.A.2A2.2A.A3.2A2.A$8.D15.5A5.A26.2A3.2A20.A2.A.A.A.A
2.A43.2A9.2A16.2A10.2A19.A5.A9.A12.2A17.2A3.A.A3.2A15.A12.2A16.A2.2A
5.2A2.A9.A.A10.A.A14.2A3.2A14.3A.2A4.A2.A4.2A.3A$8.D18.A2.A.A.A20.2A
15.2A13.5A.A.A.5A104.2A3.2A8.A.A12.A23.A21.A.A26.A.A.A9.A.A.A8.A2.8A
2.A8.4A.A4.A4.A.4A11.A.2A3.2A3.2A.A$8.D13.4A.A4.A22.A2.A3.A.A.A3.A2.A
13.A4.A3.A4.A104.A.A.A.A8.A.A2.10A47.2A3.3A20.2A2.A9.A2.2A9.2A8.2A8.A
2.A2.A.7A.A2.A2.A8.2A.A3.A.2A.A3.A.2A$22.A2.2A29.3A.9A.3A15.3A.A.A.A.
3A105.A.A.A.A5.2A.A2.A.8A2.3A76.A.A5.A.A10.3A12.3A6.A3.2A.A2.A2.A.2A
3.A8.A3.5A4.5A3.A$59.A4.A4.A20.A2.A.A2.A51.E28.2E37.2A.A4.7A2.A2.A77.
A7.A11.A2.A.A6.A.A2.A7.3A4.2A.2A4.3A9.A8.A2.A8.A$58.2A9.2A20.A.A.A.A
20.E2.E21.A3.E5.E3.A14.A3.E6.E3.A19.2A.2A9.A14.2A79.A5.A13.2A12.2A12.
2A.A3.A.2A14.3A.2A2.A2.A2.2A.3A$58.A11.A21.2A.2A45.A.A11.A.A12.A.A12.
A.A17.2A.A.2A8.A.A4.A.A80.2A5.A3.A5.2A14.2A15.4A.A.A.A.A.A.4A15.A3.2A
3.A$29.2E29.A7.A73.A.A11.A.A12.A.A12.A.A15.3A.A.A.3A7.2A4.2A.A26.E.E.
E48.A5.A.A.A.A5.A14.2A14.A.A5.A.A.A5.A.A8.A.4A10.4A.A$59.2A7.2A46.8A
15.2A.A.A.9A.A.A.2A6.2A.A.A.10A.A.A.2A39.A22.2A9.2A45.4A2.2A.2A2.4A
31.A3.4A5.4A3.A8.2A.A14.A.2A$26.A6.A82.2A4.2A15.2A.A15.A.2A6.2A.A16.A
.2A12.2A7.2A16.2A20.A.A9.A.A46.A11.A34.3A4.2A.2A4.3A$26.A.4A.A81.2A6.
2A17.A15.A12.A16.A16.A7.A39.A.A.7A.A.A44.2A13.2A34.A2.A2.A.A2.A2.A$
21.2A2.2A.4A.2A2.2A76.A8.A17.A.A4.A.A4.A.A12.A.A4.2A.A4.A.A15.A.2A3.
2A.A37.2A13.2A14.A3.E3.E.2A17.A15.A37.2A5.2A$21.A4.A6.A4.A104.2A3.A.
2A4.2A14.2A4.A.2A4.2A17.A.5A.A40.A.A7.A.A15.A.A9.A18.A13.A$22.3A10.3A
76.A.A.A2.A.A.A22.A55.2A3.A3.2A39.A.A7.A.A15.A.A7.2A18.2A13.2A$24.A.A
6.A.A28.E29.E19.A2.A4.A2.A21.2A56.A2.A.A2.A16.E24.A2.5A2.A13.2A.A.A.
6A2.3A$22.3A3.A2.A3.3A73.2A4.A4.A4.2A75.2A.A.A.A.2A15.E25.2A5.2A14.2A
.A10.A2.A$21.A6.4A6.A71.A.16A.A75.A.2A.2A.A15.3E21.3A9.3A14.A11.2A$
21.2A14.2A21.A7.A19.A2.A5.A2.A9.A18.A20.E53.A9.A38.A2.A.A3.A.A2.A14.A
.A5.A$25.10A23.A2.7A2.A15.2A2.A.5A.A2.2A8.5A8.5A19.E3.E26.2E24.2A.A.A
.2A8.A15.A15.2A4.A4.2A16.2A4.2A50.2E4.2E24.E$58.A11.A17.A11.A12.A.A2.
A2.A2.A.A50.E4.E23.A.A.A.A8.A.A13.A.A49.2A46.2A12.2A16.2E5.2E$24.A.2A
.2A.2A.A16.2A3.A13.A3.2A9.A.2A9.2A.A12.4A2.4A79.A2.A3.A2.A6.A.A2.9A2.
A.A49.A27.E4.E14.3A10.3A12.2A13.2A$26.A.A2.A.A18.A.A.2A3.2A3.2A3.2A.A
.A7.A.A3.3A3.3A3.A.A6.4A10.4A17.9A49.2A.A.A.A.2A3.2A.A2.A.9A.A2.A.2A
70.2A10.2A14.8A16.3A11.3A$22.3A.A.A2.A.A.3A15.A3.A3.3A.3A3.A3.A7.3A.A
13.A.3A5.A2.A.A6.A.A2.A17.2A5.2A20.10A21.A.A.A.A5.2A.A4.9A4.A.2A69.A.
A10.A.A5.2A3.2A10.2A3.2A12.9A$21.A3.2A.4A.2A3.A12.A.A.2A.2A9.2A.2A.A.
A15.A.A19.2A6.2A20.2A7.2A19.2A6.2A21.A.A.A.A8.A17.A18.E.E.E49.A.A.8A.
A.A5.A2.2A.2A8.2A.2A2.A4.2A3.2A11.2A3.2A$22.2A12.2A13.2A.A2.A.2A7.2A.
A2.A.2A9.3A3.A.A3.3A43.A9.A18.2A8.2A21.A3.A9.A.A4.2A.2A4.A.A15.A9.A
45.2A14.2A5.3A.A.A.2A2.2A.A.A.3A5.A2.2A.2A9.2A.2A2.A14.A$24.4A.2A.4A
18.A.A5.2A.2A5.A.A12.A2.A3.A3.A2.A72.A10.A36.2A4.2A.2A4.2A15.2A9.2A
46.A.A8.A.A16.4A15.3A.A2.2A2.A2.2A2.A.3A15.3A$24.A2.A.2A.A2.A18.A.2A
2.2A5.2A2.2A.A11.4A2.A.A.A2.4A38.2A2.3A5.3A2.2A90.A3.2A.7A.2A3.A42.A.
A8.A.A9.2A3.A6.A3.2A15.2A.A.A.2A25.A$52.A.3A5.A3.A5.3A.A9.2A2.3A.A.3A
2.2A38.A2.A.2A5.2A.A2.A12.3A10.3A61.A.A17.A.A42.A2.6A2.A9.A2.2A2.2A2.
2A2.2A2.A7.3A.2A2.A5.A2.2A.3A17.A$51.A.A2.A15.A2.A.A7.A3.A3.A.A3.A3.A
38.A.A.A7.A.A.A13.4A2.A2.A2.4A61.A.A.A13.A.A.A43.2A6.2A9.A.2A2.A.A4.A
.A2.2A.A7.A4.2A3.A3.2A4.A18.A2.A2.AE$29.2E20.A2.6A3.A.A3.6A2.A8.A2.A.
A.A.A.A.A2.A38.2A.2A9.2A.2A11.A6.4A6.A59.2A.A.A3.A.A.A.A3.A.A.2A39.3A
10.3A6.A3.A.A2.A2.A2.A.A3.A5.A3.3A5.A5.3A3.A19.A2.AE$52.2A8.2A.2A8.2A
10.A.A.2A3.2A.A.A38.A2.A3.3A.3A3.A2.A10.6A6.6A59.A5.A.A.2A.2A.A.A5.A
39.A2.A.A4.A.A2.A5.2A.A.2A2.2A2.2A2.2A.A.2A4.4A3.2A.A.A.A.2A3.4A17.A.
A$53.A.2A.A11.A.2A.A12.A11.A40.A.A.2A7.2A.A.A10.A5.8A5.A59.2A.2A2.A.A
3.A.A2.2A.2A41.2A4.2A4.2A5.A2.3A14.3A2.A6.A2.A2.A5.A2.A2.A19.A.A$25.A
8.A18.A.A5.A5.A5.A.A66.A2.A.A5.A.A2.A12.5A2.A2.A2.5A21.E19.E19.A.A3.A
2.3A2.A3.A.A62.A5.5A2.5A5.A6.A3.2A2.5A2.2A3.A18.A$23.A2.8A2.A15.2A5.
2A.2A.2A.2A5.2A71.A.A.A22.A8.A25.E19.E19.A.4A.2A3.2A.4A.A63.5A.A2.A2.
A2.A.5A7.2A8.A8.2A17.2A$23.A12.A17.6A9.6A69.4A2.A2.4A16.A12.A22.3E17.
3E15.2A.A.A3.A2.A.A2.A3.A.A.2A62.A16.A$17.2A3.A14.A3.2A11.A4.A.2A3.2A
.A4.A70.A.7A.A17.2A10.2A60.A2.A2.3A2.A3.A2.3A2.A2.A$17.A.A.2A3.2A4.2A
3.2A.A.A13.4A2.A.A.A2.4A70.A.A9.A.A91.2A.2A2.2A5.2A2.2A.2A$18.A3.A3.
3A2.3A3.A3.A10.4A.A.2A.A.A.A.2A.A.4A64.3A.A2.2A.2A2.A.3A50.2A39.A3.A
9.A3.A$19.3A.2A10.2A.3A11.A2.A5.A.A.A.A5.A2.A63.A5.A2.A.A2.A5.A46.2A.
3A15.5A18.A.A.A9.A.A.A$22.A.2A8.2A.A19.A.A.A.A.A.A.A.A69.A.2A.A.A3.A.
A.2A.A46.A.A18.A.3A.A18.2A.2A7.2A.2A$17.4A.A4.2A2.2A4.A.4A13.2A.2A3.A
3.2A.2A69.2A.A.A5.A.A.2A47.A4.4A12.A.A.A.A$17.A2.A4.2A6.2A4.A2.A103.A
7.A52.A18.2A.A.A.2A$21.2A4.A4.A4.2A169.A16.A2.2A.2A2.A$205.3A17.2A7.
2A$24.A10.A169.A$17.2A5.A.8A.A5.2A$17.A.A.A2.2A8.2A2.A.A.A$19.A.3A12.
3A.A$18.A3.A4.2A2.2A4.A3.A$18.5A4.A4.A4.5A$22.A.2A.A4.A.2A.A$17.A.2A.
A.A.A6.A.A.A.2A.A$17.2A.2A16.2A.2A4$179.2E$118.E2.E27.E24.2A.E4.E.2A$
147.E3.E22.A10.A$4.6D107.A4.A52.3A4.3A25.E$4.D55.E28.2A24.3A.2A.3A21.
A5.A19.A14.A22.E118.E$4.D24.2E26.A5.A24.A4.E20.A3.A2.A3.A18.3A.3A.3A
17.5A.4A.5A21.3E115.A2.E$4.D22.A4.A24.A5.A20.A4.A25.4A2.4A18.A3.2A.2A
3.A22.4A141.2A5.E37.2A$4.6D17.A4.A24.A5.A20.A4.3A.A49.A.3A.A.4A19.A.A
6.A.A21.A2.A2.A53.E55.A2.A40.A2.A$9.D17.A4.A18.2A6.3A6.2A14.2A.A.2A.A
22.2A.A2.A.2A19.A29.2A8.2A21.A.A.A.A25.E25.E33.2E2.A21.2A.A3.2A18.E
13.A4.A$9.D18.A2.A19.A2.2A2.A.A.A2.2A2.A21.A3.A19.A8.A21.A.A.A.2A.A
46.2A2.A7.A2.2A20.E29.A27.E5.A3.A.A11.4A2.A.3A.3A15.E2.3A8.A6.A$9.D
16.A.A2.A.A18.2A3.A5.A3.2A16.A.A.A.A2.A.A19.3A2.3A21.2A.3A.A.2A24.2A
20.2A2.A2.A.A2.A2.2A45.A38.A2.2A13.A3.A.2A.A5.A16.A11.A6.A$4.6D16.2A
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5.A5.A6.A18.A$33.A$21.E2.A3.2A3.A4.E$23.2A3.2A5.2E!
They're grouped by period and spark type--I've highlighted the "typical" interaction spot for most of them too.

Where I found these: for p2, see https://conwaylife.com/wiki/Period-2_catalysts. For p3, there's no one spot: they're scattered across the forum and a few from iNoMed on discord. p4 through p6 are between JSLife, https://conwaylife.com/wiki/Emulator, and a few different forum stamp collections. p7-p11 have convenient pages https://conwaylife.com/wiki/Period-7_sparkers. And for p12+ there's few enough that they're listed at https://conwaylife.com/wiki/Category:Os ... fic_period.

I'm omitting some very weak, LCM-only ones (smiley, tumbler). And there's boatloads of p4's of different geometries, from short-and-wide to tall-and-narrow, so I tried to pick a representative sample for each spark type and size. But barring those purposeful omissions, please let me know if there's any useful ones I missed and I'll add them.


edit: fixed for HDP's comments. Added: P4 eater-block frob, odd p3 double block catalysts, smaller p6 pip squirter. Also added two more p4 pip squirter variants. I'm not sure which oscillator "66P13's larger relative" refers to, though.
Last edited by yoleo on December 25th, 2023, 11:54 pm, edited 1 time in total.
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hotdogPi
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Re: Sparker Compilation (up to p16)

Post by hotdogPi » December 23rd, 2023, 7:40 am

You have a 132P7 in the p6 section (in addition to where it should be).

You're missing 66P13's larger relative.

The p6 mini pipsquirter is missing. In addition, the large sparker that uses the pipsquirter as the "base" can use the mini pipsquirter there instead.

p3 block corner and eater/block frob (p4) could be added.

Rich's p16 main sparks are actually the T-nose. The ones highlighted also work, but for different purposes.
User:HotdogPi/My discoveries

Periods discovered: 5-16,⑱,⑳G,㉑G,㉒㉔㉕,㉗-㉛,㉜SG,㉞㉟㊱㊳㊵㊷㊹㊺㊽㊿,54G,55G,56,57G,60,62-66,68,70,73,74S,75,76S,80,84,88,90,96
100,02S,06,08,10,12,14G,16,17G,20,26G,28,38,47,48,54,56,72,74,80,92,96S
217,486,576

S: SKOP
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hotcrystal0
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Re: Sparker Compilation (up to p16)

Post by hotcrystal0 » December 23rd, 2023, 11:37 pm

Can we pin this thread since it would be useful for oscillator and gun purposes?

Code: Select all

x = 192, y = 53, rule = B3/S23
33$42b4o$41b6o$40b2ob4o$41b2o3$41b2o$39bo6bo$38bo8bo$38bo8bo$38b9o3$42b
4o$41b6o$40b2ob4o$41b2o!
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dvgrn
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Re: Sparker Compilation (up to p16)

Post by dvgrn » December 24th, 2023, 11:37 am

hotcrystal0 wrote: ↑
December 23rd, 2023, 11:37 pm
 Can we pin this thread since it would be useful for oscillator and gun purposes?
There are a lot of good candidates for pinnable threads, but when too many threads get pinned, people start making suggestions about unpinning them. I've added a link to this thread in the LifeWiki Sparker article instead.
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otismo
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Re: Sparker Compilation (up to p16)

Post by otismo » December 28th, 2023, 2:41 pm

Thank You !

in "Standard" :

Code: Select all

x = 423, y = 688, rule = B3/S23
32b2obo6b2obo8b2o8b2obo5b2o4b2o4b2obo4b2obo11b2obo4b2ob2ob2o6b2o6b2o6b
2o4b2obo10b2obo4b2obo4b2o8b2o10b2obo4b2obo2b2ob2ob2o2b2o2b2o4b2obo4b2o
6b2o8b2obo4b2o5b2o6b2o5b2o4b2obo4b2o10b2obo4b2obo$32bob2o5bo2b2o7bo2bo
6bo2b2o6bo5bo4bob2o3bo2b2o11bob2o4b2obo3bo5bo2bo6bo6bo4bo2b2o10bob2o4b
ob2o5bo9bo10bob2o4bob2o2b2obo3bo2bobo2bo4bob2o5bo6bo8bo2b2o4bobo5bo6bo
bo5bo4bob2o5bo10bob2o4bob2o$30b2o8bobo3b2o4bobo2bo4bobo3b2o3bo5bo3b2o
6bobo3b2o7b2o11bob2o5bobo2bo5bobo2bobo3bobo3b2o6b2o6b2o4b2o2bo9bo9b2o
6b2o9bob2o5b2o4b2o4b2o2bo8bo6bobo3b2o3bobo3bo8bobo3bo3b2o4b2o2bo9b2o6b
2o4b2o$30bo10bo4bo5bob2obo5bo4bo4b4obo4bo8bo4bo8bo12bobo6bob2obo4b2ob
4ob2o3bo4bo7bo7bo5bo3b2o8b2o8bo7bo10bobo6bo5bo5bo3b2o6b2o7bo4bo6bo2bo
11bo2bo4bo5bo3b2o8bo7bo5bo$31bo15bo3b2o4b2o10bo6b2o6bo13bo8bo10b2obo5b
2o4b2o22bo7bo7bo5bo3bo9bo9bo7bo8b2obo7bo5bo5bo5b2o18bo4b2obo11b2obo6bo
5bo3bo9bo7bo5bo$30b2o10bo3b2o5bob2o7bo3b2o3b2o8b2o8bo3b2o7b2o13b2o6bob
2o5b10o4bo3b2o6b2o6b2o4b2o2bo9bo9b2o6b2o11b2o5b2o4b2o4b2o2b2obo4b2o8bo
3b2o7b2o13b2o4b2o4b2o2bo9b2o6b2o4b2o$32b2obo5bobobo7b2obo6bobobo6bob2o
7b2obo3bobobo11b2obo6b2obo7b2obo5bo8bo3bobobo8bo7bo5bo3b2o8b2o10b2obo
2bo9b2obo6bo5bo5bo4bobobo2bo8bobobo6b2obo11b2obo5bo5bo3b2o10b2obo2bo5b
o$32bob2o4bobob2o5b2o4b2o3bobob2o6bobobo6bob2o2bobob2o11bob2o7bobobo3b
2o4b2o4bo2b2o2bo3bobob2o9bo7bo5bo3bo9bo10bob2o3bo9bobobo5bo5bo5bo3bo2b
obobo7bobob2o7bobobo10bobobo4bo5bo3bo10bob2o3bo5bo$36b2o2bobo9bob2obo
4bobo8b2o4bo3b2o6bobo18b2o5bo2b2o4bob2obo4b2o2b2o2b2o2bobo11b2o6b2o4b
2o2bo9bo9b2o6b2o9bo2b2o4b2o4b2o4b2o2b2o4bob2o6bobo3b2o5bo2b2o10bo2b2o
3b2o4b2o2bo9b2o6b2o4b2o$36bo4b2o9bob2obo5b2ob2o7bo4bo2bo8b2ob2o15bo5b
2o8bob2obo17b2o11bo7bo5bo3b2o8b2o8bo7bo9b2o8bo5bo5bo8b2o10b2o3bo5b2o
13b2o7bo5bo3b2o8bo7bo5bo$37bo13b2o4b2o7bobo4b2o4b2o3bo10bobo15bo4bo8b
2o4b2o3b2o6b2o17bo7bo5bo3bo9bo9bo7bo8bo10bo5bo5bo2b2o6b2o13bo4bo14bo9b
o5bo3bo9bo7bo5bo$36b2o3b2o9bo4bo5b3o3bo3bo9b2o7b3o3bo13b2o5bo8bo4bo4bo
7bo4b2o11b2o6b2o4b2o2bo9bo9b2o6b2o9bo8b2o4b2o4b2o2bo8bo7b2o3b2o5bo14bo
7b2o4b2o2bo9b2o6b2o4b2o$32b2obo4bobo7bo8bo2bo7bo3bo4b2o4b2obo2bo7bo8b
2obo8bo5bo8bo3bo7bo2bobo13b2obo4b2obo4bobob2obo2bobob2obo4b2obo4b2obo
6bo5bo2bobo4b2obo5bo6bo7bo2bobo8bo14bo8b2obo4bobob2obo4b2obo4b2obo$32b
ob2o4b2o8b2o6b2o2b2o5b2o2b2o4b2o4bob2o2b2o5b2o8bob2o7b2o5b2o6b2o2b2o6b
2o2b2o14bob2o4bob2o5b2obob2o3b2obob2o4bob2o4bob2o5b2o5b2o2b2o4bob2o4b
2o6b2o6b2o2b2o7b2o13b2o8bob2o5b2obob2o4bob2o4bob2o21$2b2obo127b2o$2bob
2o85bo42bo$6b2o84b2o40bobo$6bo55bo27b2o18bo24b2o3bo$7bo31b3o18bo2bo28b
o17bo29bo$6b2o42bo9bo2bo6bo39bo29bo19bo$2b2obo37bo5bo2bo8bo6b2o62b2o
25bobo$2bob2o23b3o11bo5bo2bo17b2o19b3o12b3o23bo3b3o3b3o15bobo$2o41bo7b
o9bo7bo19bo39b2obo24b2obo$o59bo2bo23b2o2b2o17bo4b2o12bo2b3o25bob2o$bo
58bo2bo46bo4bobo12b2o3bo22bobo$2o60bo26bo2bo17bo6bo14b4o6b2o15bobo$2b
2obo84bo26b2o13bo9bo17bo$2bob2o84bo39bobob2o7b3o$130b2o2bo10bo$134bobo
$135b2o10$2obo30b2o34b2o34b2o46b2o18bo10bo57bo2bo2b2o$ob2o30b2o29bo3bo
bo33bo2bo44bo2bo16bobo8bobo56bo4bo2bo$4b2o54b3o41bobobo10bo3bobob6obob
o3bo12bobobo5bo9bobo8bobo10b4o43bob2obobo$4bo27b4o12b2o9b5ob2ob6o12bo
8bo7b3obo10bob2obo2bobo2bobo2bob2obo10b2ob11o6b2obob6obob2o5b2ob2o2b3o
12b2ob5o15b5o4bob2o$5bo26bo3bo7bob4o11bo11bo11bob3o2b3obo8bo12bo7b2o4b
2o7bo12bo9bobo6bo4bo2bo4bo6bob3o5bo7b2obobob2o2b3o12bo3b2o4b2o$4b2o29b
o6b3o2bobo10b2o7b2o15bo2bo2bo2bo8b2o11b2o2bo3bo2b4o2bo3bo2b2o11bob2obo
2bo10bob3o4b3obo7b2o2b3ob2o6bobobob2o7bo11bo9bob2o$2obo31bo24b2o5bo3bo
17bo2bo11b2o10bo2b6ob2o4b2ob6o2bo11bob2o2bo4b3o5bo2b6o2bo24bo3bo2b2o2b
ob2o10bo5b2o3b2obo$ob2o30bo9b2o20bo3bo45b2o6b2ob6ob2o6b2o16bobo3bo2bo
5b2o6b2o9b3obo10b2o5bo3b2obo9bobobobobob4o2bo$4b2o27bobo9bo21bobo48b2o
bo16bob2o18b6ob2o7bob4obo9bo2bo2b2o7bo2b4obo2bobobo8bo4bo2bobob2o2bob
2o$4bo29bo81b2o2bo8b2o8bo2b2o14b2o5bo10bobo2bobo9b6o10bo7b3ob2o9b4o2b
3obo5bobo$5bo111bobo2b3o3bo2bo3b3o2bobo9b2o2b2obobo15bo4bo13bo3b4o6b7o
3bo21bobo5bo$4b2o110bo2b3o5b2o2b2o5b3o2bo8bo2bobobob3o2bob2obo21b7ob3o
12bobobo13b2ob4obobo2b3o$2obo113b2o3bob2obo4bob2obo3b2o10b3o3bo4b3obob
2o21bo7bo10b2o3b2ob2o13bob4o2b2obo$ob2o114bobo2bob3o4b3obo2bobo16b2o3b
o3bo28b5o11b2o20bo4bo7b2obo$118bob2obo3b6o3bob2obo9b5o7b4o29bo2bo35b4o
4bobobob2o$117b2o4bobobo4bobobo4b2o8bo2bo46bo30b3o3b2ob3obo$116bo2bobo
5b6o5bobo2bo12bo6b2o35b2o30bo2bobobo4bo3b3o$117bobobo16bobobo12b2o6b2o
68b2ob2obob2o2b3o2bo$116b2obo2b2ob10ob2o2bob2o90bobobobo2b2o2b3o$119b
2o2b2o10b2o2b2o93bobobo3bo2b2o2bobo$116b4o2bo2b3ob2ob3o2bo2b4o91b2ob2o
3bo2bo3b2o$116bo3b2o2bo2bob2obo2bo2b2o3bo100b2o$117b3o5b2o6b2o5b3o$
119bo20bo17$264bo11bo$2o4b2o117b2o6b2o128bobo3b3o3bobo101b3o$o5bo31b3o
84bo2b4o2bo20b2o7b2o18b2o8b2o20bo5bo40bob4o3b4obo15bo10b2o22b5o14b2o3b
6o3b2o9b2ob4o3b4ob2o18b6o$bo5bo33bo26b2o2b5o2b2o18bo2b5o2bo16b2o4b2o
21bo2b5o2bo18bo2b6o2bo19b3o3b3o36b2obo13bob2o11bobo3b5o2bo22bo3bo13bob
4o6b4obo8b2o2bo7bo2b2o11b2ob4o6b4ob2o$2o4b2o29bo30bobobo3bobobo17bo2b
2o3b2o2bo12b3o8b3o19b2o5b2o20b2o6b2o20b3o3b3o16bo19b2ob2o2b2o3b2o2b2ob
2o11bob4o5b2o18b2obo7bob2o8bo16bo5b2ob4o9b4ob2o8b2o2bo10bo2b2o$2b2obo
29b3o3b2o26b3o5b3o18bo11bo12bo2bobo2bobo2bo16b3o9b3o14b3o10b3o17b3o3b
3o15b3o21bo13bo11b2obo12b3o14bobob2obobob2obobo6b2ob2o10b2ob2o4bo2bo7b
o7bo2bo5b2ob3obo10bob3ob2o$2bob2o28bo9bo28bobo24bo2bobo2bo15b2o8b2o17b
o2bobo3bobo2bo14bo2bobo4bobo2bo17bobo3bobo15b3o21bobo4bo4bobo11b2ob2o
2b2o4bobo2bo14bo15bo8bo14bo7b3obo4bobo4bob3o6bo2bo7bo2bo7bo2bo$6b2o26b
2ob3o4bo26bobobobo20b2obo5bob2o43b2o4bo4b2o16b2o4b2o4b2o35bo5bo3bo2b2o
17b2o3bobo3b2o15bo12b2o16bobobo5bobobo9bob2o8b2obo13b9o13b4obob2obo2bo
b2obob4o$6bo30b2obobobo20b2o4b7o4b2o14bob2ob3ob2obo120bobob9o2bo23bo
21bobo26bobobo9bobobo8bo12bo8b3obo5bo5bob3o11b4o3b2o3b4o$7bo24b4o6bo
22bo2b2o4bo4b2o2bo13bo4bobobo4bo103b3o3b3o7bob13o47b2o3b3o20b2o2b2o7b
2o2b2o9b2o8b2o8bo2bo2bob2o3b2obo2bo2bo8b3o4bob2obo4b3o$6b2o24bo2b2o29b
3obo7bob3o15b3obobobob3o106bo3bo6b2obobo12b3o76bo9bo10b3o2b8o2b3o6bo3b
2obo2bo2bob2o3bo8bo3b5o4b5o3bo$72b2ob2o23bo2bobo2bo109bobo7b2ob2o12bo
2bo77b2o5b2o11bo2bo10bo2bo7b3o4bobobo4b3o9bo8bo2bo8bo$68b2o9b2o20bobob
obo45bo13bo14bo14bo19b2ob2o9bo14b2o99b2o12b2o12b2obobobob2o14b3ob2o2bo
2bo2b2ob3o$6b2o60bo11bo21b2ob2o21b4o20bobo3b5o3bobo12bobo3b6o3bobo16bo
7bo7bobo4bobo80b2o3b2o5b2o3b2o14b2o15b4obobo3bobob4o15bo3b2o3bo$6b2o
62bo7bo48bo4bo19bob4o5b4obo12bob4o6b4obo16b3obob3o8b2o4b2obo79bo2b4obo
bob4o2bo14b2o14bobo5b2ob2o5bobo8bob4o10b4obo$69b2o7b2o69b2obo15bob2o6b
2obo16bob2o12bob2obob2obo16bo22b2o3b3o3b2o45b2ob2ob2ob2ob2ob2o31bo3b4o
2bo2b4o3bo8b2obo14bob2o$37b6o83b2o4b2o15b2ob2o2b2o5b2o2b2ob2o6b2ob2o2b
2o6b2o2b2ob2o13bo7bo17b2o20bob4o3b4obo47bo9bo35b3o4b2ob2o4b3o$35b2obo
2bob2o80bo8bo17bo15bo12bo16bo15b2o7b2o38bo13bo44b2o13b2o34bo2bo2bobo2b
o2bo$31b2o5bo2bo5b2o75b2o8b2o16bobo4bobo4bobo12bobo4b2obo4bobo63b2ob2o
7b2ob2o14bo9b2o17bo15bo37b2o5b2o$31bo2bob8obo2bo75b2o8b2o17b2o3bob2o4b
2o14b2o4bob2o4b2o16b2obo3bob2o39bo11bo15bobo3b4o2bo18bo13bo$32b4o8b4o
77bob2o2b2obo23bo57b2obob2o41bob2o5b2obo15bob4o4b2o18b2o13b2o$35bo8bo
77bob2ob6ob2obo19b2o58b2ob2o43bo9bo13b2obo11b3o$32b3o2b2o2b2o2b3o73bo
16bo75b2obo3bob2o15bo25b2o5b2o14b2ob2o2b2o3bobo2bo$31bo2b3ob4ob3o2bo
23b5o25b5o13bob5o6b5obo75bobo3bobo15b3o21b3o2b5o2b3o14bo11b2o$31b2o3bo
6bo3b2o21b2o5b2o18bo2b2o5b2o2bo8bo18bo74bo3bobo3bo14b3o21bo2bo7bo2bo
14bobo5bo$36b8o24bobo7bobo15bo2b3o5b3o2bo8b4o2bo4bo2b4o76b2o5b2o8bo5bo
3bo5bo15b2o9b2o16b2o4b2o$35bo8bo21bo2bobo5bobo2bo13bo15bo10bobo2bo2bo
2bobo21b5o53bob3obo8bobob11obobo49b2o52b4o$35b2ob4ob2o17b2obo3bo9bo3bo
b2o7b3o4b2obob2o4b3o10b4o2b4o22bo5bo23b6o21bo2bobobo2bo6bob15obo49bo
46b2ob4o4b4ob2o17b5o$34bo10bo16bob3ob4o5b4ob3obo6bo2bobo11bobo2bo5b4o
10b4o47bo6bo20b2obobobob2o3b2obobo13bobob2o70b2o3b4o3b2o9b2o2bo8bo2b2o
10b2ob4o5b4ob2o$32b3obobo2bobob3o15bo4b2o3bobo3b2o4bo12b2ob2o3b2ob2o
10bo2bobo6bobo2bo17b2o5b2o51bobobobo5b2ob2o15b2ob2o69bob4o4b4obo5b2ob
4o10b4ob2o7b2o2bo9bo2b2o$31bo3b2ob4ob2o3bo12bobob2ob2o2bo3bo2b2ob2obob
o5b2o7bo3bo7b2o9b2o6b2o20bo4bo4bo19b2o6b2o21bobobobo8bo17bo72bo14bo5bo
2bo16bo2bo4b2ob4o11b4ob2o$32b2o12b2o13b2obo2bo4bo3bo4bo2bob2o8b4o4bo4b
4o41b2o9b2o17bo4b2o4bo21bo3bo9bobo4b2ob2o4bobo19b3o49b2ob2o8b2ob2o5b4o
bo3bo2bo3bob4o5bo2bo17bo2bo$34b4ob2ob4o18bobo2bob2o3b2obo2bobo15bo3bo
3bo45b2o9b2o16b2o10b2o35b2o4b2ob2o4b2o17b3o3b3o48bo12bo11b4ob4ob4o10b
3obo3bobobobo3bob3o$34bo2bob2obo2bo18bo2b2ob2o5b2ob2o2bo14bo2bobobo2bo
41b2ob3o7b3ob2o13b2o10b2o63b2ob3o9b3ob2o42bob2o6b2obo9b3ob2o6b2ob3o14b
2o3bo3b2o$62bobo7bo3bo7bobo9bo3b3obob3o3bo38bo2bo2bo5bo2bo2bo14b2o8b2o
63bob4o2b2o3b2o2b4obo42bo10bo9bo4bob2o2b2obo4bo7b3obo3bobobobo3bob3o$
61bobo2bobo3bo3bo3bobo2bobo7bob3o3bobo3b3obo38bobo3bo3bo3bobo12b2o2bo
2bo2bo2bo2b2o60bobo2bo11bo2bobo43b2o6b2o9bobo3bobo4bobo3bobo7bobo2b2ob
2ob2ob2o2bobo$61bo2b6o2b2ob2o2b6o2bo8bo2bobobobobobo2bo38b2obo11bob2o
13bo4b4o4bo61b2o2b3obobo3bobob3o2b2o39b3o2b6o2b3o6bobobobo2bo2bo2bobob
obo5bo3b3o2b2obob2o2b3o3bo$62b2o4bo2bo5bo2bo4b2o10bobob2o3b2obobo38bo
2bo4bo3bo4bo2bo9bob5o6b5obo58bo2bo4bo2bobo2bo4bo2bo39bo2bo8bo2bo5b2o3b
2o2b2o2b2o2b2o3b2o4b4o3bobo2bo2bobo3b4o$37b6o20bob2o2bo9bo2b2obo12bo
11bo40bobobob2o3b2obobobo10bo5b8o5bo59b2ob3obobo3bobob3ob2o41b2o10b2o
5bo2b3o14b3o2bo6bo2bo2bo5bo2bo2bo$35b2o6b2o18bobob3o3bobo3b3obobo66bo
2b2obo3bob2o2bo12b5o2bo2bo2b5o61bobobobo2b3o2bobobobo62bo5b5o2b5o5bo6b
o3b2o2b5o2b2o3bo$33bobo8bobo15b2o3bobo3bobo3bobo3b2o69bobo3bobo20bo8bo
65bo2bobob2o3b2obobo2bo63b5obo2bo2bo2bob5o7b2o8bo8b2o$31bo2bobo6bobo2b
o15b5o4bobo4b5o69b2obo5bob2o16bo12bo60b2obo5bo2bobo2bo5bob2o62bo16bo$
27b2obo3bo10bo3bob2o11bo6bobobobo6bo70bob7obo17b2o10b2o60bo2bobob2o2bo
3bo2b2obobo2bo$27bob3ob4o6b4ob3obo13b3obo3bo3bob3o70bobo9bobo91b2ob2o
2b2o5b2o2b2ob2o$28bo4b2o3bo2bo3b2o4bo10b4obob2obobobob2obob4o64b3obo2b
2ob2o2bob3o91bobobo9bobobo$29b3ob2o2bo4bo2b2ob3o11bo2bo3bobobobobobo3b
o2bo63bo5bo2bobo2bo5bo90bobobo9bobobo$32bo4bo4bo4bo19bobobobobobobobo
69bob2obobo3bobob2obo92b2ob2o7b2ob2o$27b4obobob2o4b2obobob4o13b2ob2o3b
o3b2ob2o69b2obobo5bobob2o$27bo2bob2ob2o6b2ob2obo2bo103bo7bo$31bo5bo4bo
5bo$36b8o$34b2o8b2o$27b2o4bo12bo4b2o$27bobo20bobo$29bo2b3o10b3o2bo$28b
o2b3o3b2o2b2o3b3o2bo$28b2obobo3bo4bo3bobob2o$32bob2obo4bob2obo$27bob2o
bobobo6bobobob2obo$27b2ob2o16b2ob2o4$189b2o$2b2o2b2o120bo2bo27bo24b2ob
o4bob2o$2bobo2bo149bo3bo22bo10bo$2o3b2o120bo4bo52b3o4b3o25bo$o69bo28b
2o24b3ob2ob3o21bo5bo19bo14bo22bo118bo$bo37b2o26bo5bo24bo4bo20bo3bo2bo
3bo18b3ob3ob3o17b5ob4ob5o21b3o115bo2bo$2o35bo4bo24bo5bo20bo4bo25b4o2b
4o18bo3b2ob2o3bo22b4o141b2o5bo37b2o$2b2obo31bo4bo24bo5bo20bo4b3obo49bo
b3obob4o19bobo6bobo21bo2bo2bo53bo55bo2bo40bo2bo$2bob2o31bo4bo18b2o6b3o
6b2o14b2obob2obo22b2obo2bob2o19bo29b2o8b2o21bobobobo25bo25bo33b2o2bo
21b2obo3b2o18bo13bo4bo$6b2o30bo2bo19bo2b2o2bobobo2b2o2bo21bo3bo19bo8bo
21bobobob2obo46b2o2bo7bo2b2o20bo29bo27bo5bo3bobo11b4o2bob3ob3o15bo2b3o
8bo6bo$6bo29bobo2bobo18b2o3bo5bo3b2o16bobobobo2bobo19b3o2b3o21b2ob3obo
b2o24b2o20b2o2bo2bobo2bo2b2o45bo38bo2b2o13bo3bob2obo5bo16bo11bo6bo$7bo
28b2o4b2o21b11o18bobo3bo4bo22bo2bo24bobo2bo26bob2o24bobo3bobo22bobobo
20b3ob2obobo24bo6b3o4bo12bob2o3bob2obo18bobo2bo6bo4bo$6b2o54b2o13b2o
15b2o28b4ob2ob4o20bo2b2o27b5o24b3ob3o21b9o17bo3bo2b2ob3o20b3ob4obobob
2o2bo10b2o3b2obobo3b3o14b2ob4o7bo2bo$2b2obo55bo2b6ob6o2bo44bo2bo4bo2bo
19b2o35b3o22b2obob2o20bo9bo16b2ob2o3b2o3bo18bo4bobo4bo2bob2o13b2o2bo4b
2o2bo16bo12b2o$2bob2o55b2o3bo2bobo2bo3b2o111b2o2b2o20bo5bo19bob2o5b2ob
o16bobo7bobo19b5obob2ob2obo13b2obo4b4obo19bobo$128bo2bo61b3o18b2o3bobo
3b2o15bo2bob2ob2obo2bo15bo2bo2b6o26bobo2bo2bob2o10bo2bob4o25b2o$195b2o
16bob4o3b4obo14b2o4bobo4b2o16b2o2bo26b5obobobo2b2ob2o12b2o2bo2b4o$196b
2o15bo13bo46bob2obob3o20bo2bobo3bo22b2o7bo$39b2o118bo36bo15b2ob4obob4o
b2o16bo2bobo2bo20bo2bo4bobo51bo4b4o$100bo2bo53bo3bo35b3o13bobo2b5o2bob
o17bo2bobo2bo21bo3b2o3bo48b2obo3b2o$32bo3bo6bo3bo52bo88b2o8bo13bo2bobo
bobobo2bo18b2o3b2o23b3o2b3o49bo2b2o2bob3o$30b3o2bo8bo2b3o49bo4bo82bo4b
o21bobo7bobo51bo2bo52b2o5bo2bo$29bo3b3o3b2o3b3o3bo41b2o4bob2ob2o53bobo
52b2obo2b3o2bob2o108bob6o$29bob2ob5o2b5ob2obo40bo2bo2b2o51b2o2b4obob4o
2b2o43bo3b2ob3ob2o3bo107b2o$28b2obo6b4o6bob2o39b3o3bo49bo2bo2bo3b5o3bo
2bo2bo4b2o3bo4b2o4b2o4bo3b2o9b3o3bobo3b3o111b2ob2o$32b5obo2bob5o49bo
48bobobob2o11b2obobobo3bo2b3o2bobob4obobo2b3o2bo11bob2o3b2obo114bobo$
37b2o2b2o46b4obob2o47bo2bobo3b3o2bo2b3o3bobo2bo3b2o4b2o4b2o4b2o4b2o12b
obo5bobo114bobo$34b2obo4bob2o43bo2bo3bo48b4ob2o2b2obobobob2o2b2ob4o4bo
2b2obo4b2o4bob2o2bo11bobo2bo3bo2bobo113bo$34bo2bo4bo2bo48bob2o52bo2bo
3bobobo3bo2bo9bobo18bobo11b2o2b2o3b2o2b2o$35bobo4bobo48b2obo48b2o3bobo
5bobo5bobo3b2o3b2obobo14bobob2o$30b2obobob6obobob2o43bo2bo49bo2b2o5bob
obobo5b2o2bo3bo3bo18bo3bo$30bob2ob2o2b2o2b2ob2obo44b2o50bobo2bobob2obo
bob2obobo2bobo3b2obobo5b2obob2o4bobob2o$35bo8bo102bobobobob4ob4obobobo
bo7b2o4b3obobob3o3b2o$35bobo4bobo103bo2b2o13b2o2bo5b2obo4bo11bo3bob2o$
36b2o4b2o107bo15bo8b2obobo2bob3obob4o2bobob2o$103bo47bo15bo12b2o3bo3b
3o4b2obo$99bo51b3o2b2o3b2o2b3o19bobobob3o2bo$95b2obo5bo44bo2bobo2bo3bo
2bobo2bo16b2obobobo2bo$39b2o54bo4b2ob2o44bo2bob2o7b2obo2bo17bobo2bo3b
2o$37bo4bo49b2obob2obo48b2obobo9bobob2o17bo2b2o$36bo6bo48bo2bobo2bo49b
o3bo9bo3bo17b2o$35bo8bo49bo4b3o47bob2obob2o3b2obob2obo$32b5ob4ob5o47b
2o2bo47b3obo2bob2o3b2obo2bob3o$32b3o10b3o48bo49bo5b2o11b2o5bo$38b4o52b
o3b2o46b2o23b2o$37b6o51b5ob2o$35bo3b2o3bo58bo$34bo2bo4bo2bo50b3o2bob3o
$96bo4bo4bo$33bobo8bobo50b3obob3o$29b2obobo10bobob2o50bobo$29bob2obobo
6bobob2obo45bob2obo$35b2o6b2o51b2o2bobo$99bo2bo$100b2o3$39b2o2$32b2obo
8bob2o$24b2o6b2obo8bob2o6b2o$23bobo6b3o4b2o4b3o6bobo$23bo10bob3o2b3obo
10bo$20b2obob5obo2b3obo2bob3o2bob5obob2o$20bo2bob2o3b4o4b4o4b4o3b2obo
2bo$21b2obo2b2o5b4o4b4o5b2o2bob2o$24bobo2b3obo5b2o5bob3o2bobo$24bo2bo
3bobob4o2b4obobo3bo2bo$25b2o5b2obo2bo2bo2bob2o5b2o7$4bob2o$4b2obo212bo
$2b2o215b3o85b6o$bobo215b3o56b5o23bo5b2o$bo99b2o116b3o27bo27bo4b2o20b
3o7bo$2o35b6o25b5o26b2o2bo54b5o24b6o55b3o24b3o6bo18bo8bob3o$2b2obo30b
2o4b2o23b2o3b2o23b2o4bo53bo5bo22bo6bo21b2o7b2o21bobobo22bo7bob3o16bo2b
2o5bo3bo$2bob2o28b2o8b2o20bo7bo22b2obo3b2o46b2o3bo5bo3b2o15b3o6b3o19bo
2b5o2bo19b3o3b3o19bo2b5obo4bo14b2obo2bob2obo2bo$2o4b2o23b2ob4o4b4ob2o
17b3obob3o27bobo47bo2bo9bo2bo14bo7b2o3bo19b9o19bo3bobo3bo19b3o4bob4o
17bobobo3b2obo$o5bo27b3ob4ob3o20b2o5b2o22b6obo48b4ob2ob2ob4o16b6o3b2ob
o47bob2o4b2obo22b2obobo20bobobobo3bo$bo5bo22bob2o5b2o5b2obo13b2o2bo5bo
2b2o19bo5bo46b3o15b3o21bob2o20b9o20bo2b3o4bo20b2obo4bo18b2obo3bob2o$2o
4b2o22bo2bo12bo2bo11b3obob2o3b2obob3o20b3o47bo3b13o3bo15b7o22bo2b5o2bo
20b2o5bobob2o16bo3b2ob3o21bo3bobo$2b2obo25b3o12b3o11bo4bob2o3b2obo4bo
19bo50b2obo2b2o3b2o2bob2o15bobobo3b3o19b2o7b2o22bo2bo3bob2o14bo2bob2o
2bo2b2o19b2ob2o3bo$2bob2o55b5o9b5o72bo2b2o7b2o2bo16bobo3b2o3bo51b4ob2o
18b2obobo2bob2o2bo15b2obo4b4o$66b2o5b2o77bo15bo15b2ob2obobob2o23b3o30b
o23bo2b3obo2bo16bo2bobobo$31b3o12b3o11bob2o2bobo3bobo2b2obo72b4o7b4o
23b2obo24b3o28bobo23bo7b2o18b2ob2o3bo$30bo3bo10bo3bo10b2obo3b2o3b2o3bo
b2o76bob3obo28bobo24b3o28b2o25b3o25bobob2ob3o$30b2ob2o10b2ob2o105b2o2b
3o2b2o24bobob2o24bo58bo25bo2bob2o3bo$155bo9bo24b2o112b2obobobob2o$153b
obo4bo4bobo137bo2b2obobo$68b2ob2o80b2o11b2o135bobo4bo2bo$66b3obob3o23b
4o57b3o141b2o5bobo$65bo4bo4bo21bo4bo208bo$65bob2o2b2obobo19bobo3bo$31b
o7bo7bo18bo2b2o3bobo18bobo3bo$30bobo5bobo5bobo18b2o2b2obob2o17bo$30bob
o5bobo5bobo20bo4bobo2bo15bo$28b3ob2o3b2ob2o3b2ob3o18b4ob2o2b2o15bo2bo$
27bo5bo11bo5bo21bo22b2o$28b6o11b6o20bobo$28bo5bo9bo5bo20b2o$31bo3bo2b
3o2bo3bo$27b2obo4b2ob3ob2o4bob2o$27b2obo4b2ob3ob2o4bob2o$31bo3bo2b3o2b
o3bo$28bo5bo9bo5bo$28b6o11b6o$27bo5bo11bo5bo$28b3ob2o3b2ob2o3b2ob3o$
30bobo5bobo5bobo$30bobo5bobo5bobo$31bo7bo7bo236b2o$ob2o280bo$2obo164bo
116bo19b5o3b5o$4b2o161bobo50bo29bo33b2o19bo2bobobobo2bo$5bo100b4o57bob
o49b3o27b3o30bo22bo2bobobobo2bo$4bo100bo3bo56b2ob2o48b3o26bobobo28b5o
19bo3bo3bo3bo$4b2o99bo4bo21bo5bo19b5o2bo5bo40b2o5b3o5b2o17b3o3b3o24b2o
5bo14b4o3bo5bo3b4o$2b2o88b4o10bobob2o20b7o18bo5b4ob2o2bo38bo2bo3bo3bo
3bo2bo15bo4b2o3bo22bobob3o2bo13bo6bo5bo6bo$3bo87bo4bo13bobo22bo21bo3bo
b2obo2b3o39b3obo2bo3bo2bob3o16b4ob2ob2o20b3obo4b2o14bo6bo5bo6bo$2bo86b
3o4b2o11b2o2bo18b3ob3o19bo4bo3bo4b3o39bo3bo3bo3bo22bo3bo2b2o17bo4bo2b
2o16b3ob3obo3bob3ob3o$2b2o84bo6bobo7b2o2bo16bob2o4b3o4b2obo21b2o3bo3bo
35b2o3b3o3b3o3b2o16b2obobobobo2bo17b4o4bo16bo2bo3bo5bo3bo2bo$2o87bob2o
bo14bo2b2o12b2obo11bob2o22bobo2bobobo34bob5o5b5obo16b2obo5bob2o21b4o
18b2o15b2o$bo87bo2bobo2bo7bo2b2o22bobobobo26bobob4obobo2bo33bo3bobobob
o3bo22bo4bobo20bo2bo$o68b2o21bob2obo8bobo22bo7bo23b3ob2o8b3o31bo2b2o2b
2ob2o2b2o2bo21b5o2bo19b2o22b2o15b2o$2o31bo3b6o3bo20b2o2b2o16bobo6bo8b
2obobo19b7o23bo3bo3b2ob4o34b2obo11bob2o26b3o42bo2bo3bo5bo3bo2bo$32bobo
bo6bobobo17b2ob4ob2o14b2o4b3o10bo4bo18bo5bo23b2o2bob2ob2o4bo36bo11bo
25b4o45b3ob3obo3bob3ob3o$32bobo10bobo17b2ob4ob2o15bo4bo13bo3bo14b2o3b
2ob2o3b2o24bobobob4o37b2o9b2o26bo2bo44bo6bo5bo6bo$31b2obobo6bobob2o13b
o4b2o2b2o4bo13b4o14b4o15bo2bo2bobo2bo2bo26bobo5b3o68b2obobob2o44bo6bo
5bo6bo$31bo2b2obo4bob2o2bo13b2o5b2o5b2o51b3o2b3o2b3o26b2obo4bo2bo68bob
2ob2o46b4o3bo5bo3b4o$33bo2bob4obo2bo14bobo12bobo54bobobo31bobo2bobo75b
o3b3o46bo3bo3bo3bo$34b2o8b2o16bo14bo49b6obobob6o25bobobobo76bob2o2bo
46bo2bobobobo2bo$59bo2b2obo8bob2o2bo46bo6bobo6bo22b2ob4o80bobo49bo2bob
obobo2bo$34b3o2b2o2b3o13b2obobobo6bobobob2o48bob9obo24bobo4b5o127b5o3b
5o$34bo3bo2bo3bo16bo2b2o6b2o2bo50b2obo7bob2o26b4o4bo$32bobo4b2o4bobo
11b2obo14bob2o10bo3bo36b2o3b2o32bo2bo$32b2o12b2o11bobo16bobo7bobobobob
obo34bo3bo35b2o$87bo2bobobobo2bo31bobo3bobo$88bo3bobo3bo30b3o7b3o108bo
7bo$88bo3bobo3bo11b2o6b2o8bo4b2ob2o4bo106b3o3bo2b3o3b2o$45bo42bo2bo3bo
2bo10bob2o4b2obo8bob2o5b2obo106bobobo2b3o3bo2bo$43b3o43b2o5b2o8bo2bo3b
4o3bo7b2obo2bobo2bob2o103b3o3b3o4b2obobo$42bo62bobobobob4obobob2o7bob
2ob2obo105bo4b2o3b4obobo2b2o44b2o$43bo62bo2bob2o4b2ob2obo7bo2bobo2bo
105b2ob2ob2obo5bob2obo44bo2bo$40bo2bo45b2o5b2o11bo4b2o16b2o3b2o110bobo
2bobobobo2bobo44b2obo$40bo48b2o5b2o12b3obo134bobobo4b5o2b2o46b2o$40bob
o15bo10b2o10bo30bobo133b2obob4o6bobo44b2o3bo$40bobo14b2o8b2o2b2o8b2o
30bo138bo4b6o2bo43bob3ob2o$38b3ob3o20b2ob4ob2o178bo2bo3bo4b2o41bo7bo$
37bo2bo4bo10bobo2b3ob2ob4ob2ob3o2bobo104b2o2b2o58b2o2b2o50b6o2bo$37b2o
bob3o11bo5bo4b2o2b2o4bo5bo62b2o2b2o6b2o11bo11bo5bo3bo112b2o8bo$40bobo
14b5o7b2o7b5o21b2o35b2o3b2o2bobo5bo10b3o5b2o3bobo4bobobob2o108bo2bobob
o3bo$40b2o55b2o6b3o27b2o3bobo9bo6b3ob2o3bo5bo2bobobo2bo5bobobobo108bob
o2bob4o$57b5o16b5o14bo5bo4bo3b2o15b2o5bo3bobob9ob2o5bobobo3b6o4bob2ob
3o5bobobob2o104b2obobo2b3o$56bo5bo14bo5bo14b3obob5o3bo2b2o12bobo4bob2o
bobo9bobo7bob4o6b4o3bo4bo3b2o3bobobo104bobo3bo$56bobo2b3ob2o6b2ob3o2bo
bo16bobo4bo5b2o2bo13bo2b2obobobo3b3o2b2obo8b3o5bo2bo5b2o3b2o8bob2o2bo
100b2o2bo2b3o$65b2o6b2o26bobo2b3o5bobo4bo4bo2bobobobo3bob2o4bo3bob2o3b
obo4bob2o3b7o2b3obob2o6bo4bobo97bo2bob2o$57b2o22b2o22b3obo4bobobo2bo3b
2o2b3obo2b2o3bobo7bo6bo2bob3o4bo2b3o2bobo4bobobo9bo4bo95bob2o2bo$58bo
22bo17bo5b2o6b2obobo3b3o12b2obo2bo3bob3obob3o3bobob2o3b2o5b4ob2ob3obob
o2bo6bo3bo93b2o2bobobo$98bobo4b2o3bobo3bo2b2obo2bo6b4o2bo4bo4bobo5bo4b
ob2o2b2o3bobobo10bo3b2ob2o3bobo3bo84b2o6bo2b2o2b2o$98bobo4b2o3bobo6bo
2b2o7bobobob2obo2bo2bo4bo3b2o9bo5b2ob2o3b6o3bo2bo5bo2bo3bo80b2obo2bo3b
o2b2o2bo$62bo7bo7bo20bo5b2o5bo6bo2b2o7bobobob2obo2bo2bo4bo3b2o9bo5b2ob
2o3b6o3bo2bo5bo2bo3bo78b3o3b2obo2b3o3b2ob2o$61bobo5bobo5bobo25b3obo2bo
3bo2b2obo2bo6b4o2bo4bo4bobo5bo4bob2o2b2o3bobobo10bo3b2ob2o3bobo3bo77bo
4b2o3bo5b2o4b2o$47bo13bobo5bobo5bobo21bobo2b3o4b2obobo3b3o12b2obo2bo3b
ob3obob3o3bobob2o3b2o5b4ob2ob3obobo2bo6bo3bo78b4o2b3ob6ob4o$46bobo10b
3ob2o3b2ob2o3b2ob3o18bobo4bo6bobobo2bo3b2o2b3obo2b2o3bobo7bo6bo2bob3o
4bo2b3o2bobo4bobobo9bo4bo82bobo2bobo7b3o$46bobo9bo5bo11bo5bo15b3obob5o
5bobo4bo4bo2bobobobo3bob2o4bo3bob2o3bobo4bob2o3b7o2b3obob2o6bo4bobo75b
2o4bo3b2o4b2o2b2o$45b2obob2o7b6o11b6o15bo5bo4bo4b2o2bo13bo2b2obobobo3b
3o2b2obo8b3o5bo2bo5b2o3b2o8bob2o2bo77bo2bobo2bo11b2o$44bo3b2obo7bo5bo
9bo5bo15b2o6b3o4bo2b2o12bobo4bob2obobo9bobo7bob4o6b4o3bo4bo3b2o3bobobo
79b2obo4b2o$44b2obo14bo3bo2b3o2bo3bo25b2o6b2o15b2o5bo3bobob9ob2o5bobob
o3b6o4bob2ob3o5bobobob2o81bobob4obobobo$44bo2bo10b2obo4b2ob3ob2o4bob2o
52b2o3bobo9bo6b3ob2o3bo5bo2bobobo2bo5bobobobo84bo2bo5bob2obo$44b3o11b
2obo4b2ob3ob2o4bob2o58b2o3b2o2bobo5bo10b3o5b2o3bobo4bobobob2o85bobo2b
3o5bo$40b4o18bo3bo2b3o2bo3bo67b2o2b2o6b2o11bo11bo5bo3bo89bo3bo7b2o$39b
obobob2o12bo5bo9bo5bo106b2o2b2o$37b3o3bob2o12b6o11b6o$36bo4b2o15bo5bo
11bo5bo$37b4o18b3ob2o3b2ob2o3b2ob3o$40bo20bobo5bobo5bobo$39bo21bobo5bo
bo5bobo$39b2o21bo7bo7bo3$2b2obo$2bob2o210bo$2o4b2o207b3o$o5bo86b4o100b
6o11bobobo5b2o$bo5bo84bo4bob2o6b2o17bo41b5o23bo6bo10bob2o2b3ob2o$2o4b
2o84bo4bo3bo5b2o2b3o12b3o35bo2bo5bo2bo38bo5b2o$2b2obo89b2o4bo11bo15bo
34b4o5b4o39bo3b2o$2bob2o36b3o24b3o2b2o16b2o4bo2bo10bobo13b2o32b2o13b2o
18b6o15bo2bo$2o4b2o33bo30bo2bo15bo2bo3bo2bo12b2ob2o42bo3b3obobob3o3bo
17bo4bo16bobo$o5bo34bo3bo22bo3b3o16bo2bo4b2o12bo3b2o11b3o29b3o4bobo4b
3o20b2o21bo$bo5bo33bo2bobo20bo23bo4b2o33bobo30bobobo3bobobo22b2o18b2ob
2o$2o4b2o35bobo2bo16bo5b4o16bo3bo4bo27b2o3bo31b4o3b4o17b2o10b2o8b2obo
4b2o$2b2obo38bo3bo16bo8bo17b2obo4bo28b2obo29bo5bo3bo5bo14bo5b2o5bo9bob
2obobo$2bob2o42bo16bo3bo2b2o22b4o30bobobo27b6obobob6o12bobob2ob4ob2obo
bo5bobobo2bobobo$45b3o18b2obobo56bobo2b2o56b2obobo6bobob2o5b2o2bo2bo2b
2o$67bobobo55bob2o33b2ob2o3b2ob2o17bo2bo4bo2bo12b4o$65bobob2o56bo36bob
2o5b2obo14b2obo2bo4bo2bob2o$65b2o59b2o33b2obobobo3bobobob2o10bobobob2o
4b2obobobo8b2o$161bo2bo4bobo4bo2bo10bobobob2o4b2obobobo8b2o$114b4o45bo
b3obobob3obo13bo2bobo6bobo2bo$109b2o7bo40b5o5bobo5b5o10b2o12b2o$109b2o
2b2o3bo40bo4b2obobobobob2o4bo12b2o8b2o$113b2o2bo42bo2bo3bobobobo3bo2bo
13bo10bo$41bo3b2o3bo108b2o2b2o4bobo4b2o2b2o9b2obo10bob2o$40bob2ob2ob2o
bo116b2ob2o19bobob2o4b2obobo$40bobo6bobo111b4o2bobo2b4o14bobobob4obobo
bo$39b2obo2b2o2bob2o109bo2bobobobobobo2bo12b2obobo6bobob2o$42bob4obo
112b2o2bobo3bobo2b2o13bobo10bobo$39b2obo6bob2o113b2o5b2o17bobobo6bobob
o$40bobo2b2o2bobo139b2obobo6bobob2o$40bo2bob2obo2bo142bobobo2bobobo$
41bob2o2b2obo143bobob4obobo$40b2ob2o2b2ob2o113b2o7b2o19bobo4bobo$163bo
b2o7b2obo20b4o$40b2o2b4o2b2o110bo15bo14b4obo2bob4o$39bobo2bo2bo2bobo
112bo9bo17bo2b2o4b2o2bo$40bo10bo109b2obo11bob2o$161b2o15b2o11$2b2obo
237b2o$2bob2o187b2o2b6o2b2o37bo$2o4b2o133b2o50bo2bo6bo2bo37bob2o$o5bo
134b2o51b3o6b3o31b6obo2bo$bo5bo88bo7bo33bo97bo5bob2o$2o4b2o87bobo5bobo
32b5o51b4o4b4o30bo3bobo$2b2obo87b2o11b2o34bo50bo12bo30bo4b4o$2bob2o36b
6o46bo2b3ob3o2bo9b2o2bo17b2o54b12o33bobo4bo$6b2o32b2o6b2o41bo2bo2bo5bo
2bo2bo6bo2b3o2b2o8b2obobo58bo2bo39bobobo$6bo32bobobo2bobobo14bo3b2o3bo
17b2o4b2ob2o4b2o4b2obobo3bo2bo8b2obobo56b2o4b2o33b3obob2o$7bo29b3obo6b
ob3o11bob2ob2ob2obo22b5o10b2ob2ob2ob3o13b2o55bo8bo31bo3bobo$6b2o28bo3b
2ob4ob2o3bo10bobo6bobo40bobo14bob2o58b2o6b2o31b2o2bobo$2b2obo31b2o3bo
4bo3b2o10b2obo2b2o2bob2o39bobob3o10b2obob7o96bo$2bob2o33b2o2bo2bo2b2o
11bo3bob4obo3bo39bobo3bo12bobo6bo52bo2bo$39bob2o4b2obo12bobo2bo2bo2bob
o42bo2b2o12bobob2o3bo52bo2bo$62b2ob2o6b2ob2o19b2o3b2o15b2o16b2obo3bo
52bo4bo$98bo3bo37bo53bobobo2bobobo$62b2ob2o6b2ob2o17b3o5b3o34b2o50b3ob
obo2bobob3o$63bobo2bo2bo2bobo18bo9bo85bo3b2ob4ob2o3bo$62bo3bob4obo3bo
114b2o3bo4bo3b2o$63b2obo2b2o2bob2o39b2o76b2o2bo2bo2b2o$64bobo6bobo36b
2obobo76bob2o4b2obo$35b2o16b2o9bob2ob2ob2obo24bo11b2obo$35bo2bo12bo2bo
10bo3b2o3bo20bo3b3o3bo9b2o$36b3o3b6o3b3o40bobo7bobo8bo2b5o$33b3o5bo6bo
5b3o36bobo3b3o3bo6b2obobo2bobo$32bo3bo3bo8bo3bo3bo36bo3bo2bo10bo2b2obo
3bobo$33b3o5bo6bo5b3o41b4o12bo3bob2obobo$36b3o3b6o3b3o42b2o4b3obo8b3ob
o3bobo$35bo2bo12bo2bo38bobobob2obobob2o9bobo3b2o$35b2o16b2o37b2obobob
2obobobo11bo$93bob3o4b2o$98b4o$98bo2bo3bo$94bo3b3o3bobo$93bobo7bobo$
94bo3b3o3bo$99bo2$166bo7bo$164bo3bo3bo3bo$2o4b2obo198bo7bo6bo$o5bob2o
153bo5bobo5bo29bobo8bo3bobo$bo2b2o4b2o149b3ob2o2bobo2b2ob3o17b2o4b3obo
5bo4bo5bob3o4b2o$2o2bo5bo149bo4bo3bobo3bo4bo16bo2bo10b2o6b2o10bo2bo$5b
o5bo149b5obobobobob5o18b4o4b2o3b2o6b2o3b2o4b4o$2o2b2o4b2o83b2o7b2o60b
2obobob2o26bobob3o5bo4bo5b3obobo$o3bo5bo83bo2bo5bo2bo56b2o5bo5b2o20b5o
bo8bo13bob5o$bo3bo5bo82bob2o5b2obo16b2o38bo13bo20bo3bo4b2o6bo7b2o4bo3b
o$2o2b2o4b2o32b2o47b2o11b2o15bo40bo11bo24b2obob3o14b3obob2o$4bo5bo84b
3o5b3o18b4obo33b2o11b2o23bobobobo16bobobobo$2o3bo5bo29bo6bo44b2o3bo3bo
3b2o18b2o2bo71bo2bo20bo2bo$o3b2o4b2o28bo8bo42bobo3bo3bo3bobo13b4o70b2o
7b2o18b2o7b2o$bo4b2obo31b8o43bo15bo12bo4b2o38bo29bo2bobo2b2o20b2o2bobo
2bo$2o4bob2o89bobo20b3o2bobobo32bo3bo28b2ob2o3bo20bo3b2ob2o$93bo5bobo
5bo16b2o3bob3o40bo23bo3b2o24b2o3bo$36b2o14b2o42bo2bobo2bo23b2o4bo28bo
5bo2bo3bo19bo2b4o26b4o2bo$30b2o4b6o6b6o4b2o36b3o3b3o24bob3o27b3ob2o2bo
26b2obo3bobo20bobo3bob2o$30b3o5b5o4b5o5b3o39b3o27bobo28bo4bo3bobo5bo
19bobo2b2o24b2o2bobo$29b2o2b2o2bo3bobo2bobo3bo2b2o2b2o37bo3bo27bo30b5o
bobobo2b2ob3o16bo2b2ob2o24b2ob2o2bo$28bo2b2obob3obo2b4o2bob3obob2o2bo
36b2ob2o63b2obobo3bo4bo15bobo2bo3bo20bo3bo2bobo$28b2obo2bobo2bobo6bobo
2bobo2bob2o61bo39b2o4bobobob5o17bobob4obo18bob4obobo$31bob2ob2obob8obo
b2ob2obo64bobo37bo5bobob2o24bo6bo18bo6bo$31bo2bo2bobo10bobo2bo2bo63bob
o39bo5bo5b2o21bo3b2ob2o16b2ob2o3bo$32bobo2bobob4o2b2obobo2bobo66bo38b
2o12bo19b2ob2obobo20bobob2ob2o$33bo4b2obo2bo2b2ob2o4bo62bo56bo21bobo2b
obo20bobo2bobo$122bo6bo46b2o20bo4bob2o18b2obo4bo$118bo4bo3b2o67bobo2bo
2bo2bo16bo2bo2bo2bobo$95b2o3bo3b2o12b2o2bobo4b2o65b2ob2ob2o2b2o16b2o2b
2ob2ob2o$95bobo5bobo17bobo2bo70bobo28bobo$93bobo9bobo10b2o79bobo28bobo
$51b2ob2o37b2obo7bob2o5bo3bo82bo30bo$47bobo2bobo41bob2ob2obo8bobo2bo2b
obo2bo$49bo2bobo38b2obobo3bobob2o4bobo4bobob2o$44bo5bob2o39bo2bob5obo
2bo6bo5bo$44bo3b3o44bo9bo$51b3o42b9o14bo$40b2obobob2obo2bo63b2o$40bob
2obobo3b2o45b2ob2o16b2o$45b2o2b2o47b2ob2o15bo$41b4o5bo$41bo2bo4bo$49b
2o6$2o8b2o66b2o$o9bo26b2o39bo$bo9bo26bo40bo$2o8b2o21b2obo41b2o$33bob3o
15bo$2o8b2o27bo13b3o$o9bo26b4o15bo$bo9bo24bo3bo14b2o18b3o$2o8b2o24bobo
b2o19b2o12bob2o$33b2obobo2bo18bobo2bo4b2obobobo$2o8b2o21b2obobobo2bo
13b2o3bobobo3bob2obobobo$o9bo26b2ob4o13bo2bobo2bo10bo2b3o$bo9bo27bo16b
5obo14b2o3bo$2o8b2o27bobo14bo4bo17b3o$40b2o15b4o18bo2$57b2o$57b2o6$2o
4b2obo30bo$o5bob2o29bo2bo$bo8b2o27bo2bo$2o8bo28bo2bo$11bo25bo3bob3o12b
o10bo$2o8b2o25b4obo14bo3b3o4b3o9bo$o5b2obo25b2o4bo4bo11bob5o3b3o4b3o3b
o$bo4bob2o26bob2obob3o16bo3bo5bob5obo$2o2b2o26b3obob2obo20b2o12bo$4bo
26bo4bo4b2o19b2o4bo6b2o$2o3bo29bob4o34b2o$o3b2o26b3obo3bo$bo4b2obo25bo
2bo23b2o8b2o$2o4bob2o25bo2bo23bo2b6o2bo$35bo2bo24b2o6b2o$37bo22b3o10b
3o$60bo2bobo4bobo2bo$61b2o4b2o4b2o6$2o4b2obo148bo$o5bob2o146b3o8bo$bo
8b2o109bo33bo10bobo$2o8bo108b5o31b2o9bobo$11bo106bo5bo28b3o3b2o4b2ob3o
$2o8b2o106bo2b3o10b2o11bo5b2o4bo11bo$o5b2obo88b2o17b2obo13bo7b2o2bobo
3bobo5bo4b2ob3o$bo4bob2o19bo20bo47b2o16bo3b2o10bobo7b2obo2bo3b3o4b2o4b
2obo$2o8b2o17b3o16b3o66bobo2b2o8b2o12b2o4b2o$10bo21bo14bo24b2o42b2ob5o
$2o9bo19bo16bo18b2o4bo16bo5bobo25bo3b3o25b2o4b2o$o9b2o19b2o14b2o16b3o
2b2obob2o13bo3bo3bo17b2ob5o17bob2o4b2o4b3o3bo2bob2o$bo4b2obo25b3o4b3o
17bobo4bob2obobo13bob2o4bo5b2o11bobo2b2o15b3ob2o4bo5bobo3bobo2b2o$2o4b
ob2o21b2o2bo8bo2b2o13b2ob4obo3bo18bo5b3o2b2o10bo3b2o16bo11bo4b2o5bo$
31bo3bobo4bobo3bo16bo4bo3bo20b2o20b2obo18b3ob2o4b2o3b3o$28b2obo4b2o4b
2o4bob2o13bob2obobob3o20bo3bo16bo2b3o17bobo9b2o$28b2ob2o14b2ob2o12b2o
2bobob2o3bo19bo20bo5bo16bobo10bo$31bo16bo17bo3bo4b2o23bo18b5o18bo8b3o$
31bobo12bobo13b3ob2o3b2ob2o22b2o21bo29bo$32b2o12b2o13bobobobob2obo2bo
23bo$61bo3b2o2bobo3b2o$62b3o4bob4o2bo21b3o$64bo5bo5b2o$72bo$71b2o9$2o
2b2o4b2o59bo$o3bo5bo28bo30b2o19b2o5b2o20b2o5b2o$bo3bo5bo26b3o27b2ob2o
18b2o5b2o20b2o5b2o$2o2b2o4b2o18b2o4b2o3bob2o25bo$6b2obo20b2o4bo2b2o2b
2o20b2o3b2o7b2o26b6o$2o4bob2o26bob2o14b2o12bob2o6bobo10bo7bo6bo6bo6bo
7bo$o9b2o43bo12b2o8b3o9b3o5b3o4bo8bo4b3o5b3o$bo8bo44bobo8b2o4b2o8b2o6b
o9bo5bo6bo5bo9bo$2o9bo44b2o8b2o4b2o8bobo6b3o3b3o7b6o7b3o3b3o$10b2o24bo
b2o19b3o8b2o12bo$2o28b2o4bo2b2o2b2o14bobo6b2obo12b2o8bobo26bobo$o29b2o
4b2o3bob2o14b2o7b2o3b2o$bo8b2o26b3o28bo$2o8b2o27bo27b2ob2o$68b2o21b2o
5b2o20b2o5b2o$68bo22b2o5b2o20b2o5b2o11$2o4b2o2b2o24b2o4b2o$o5bobo2bo
23bo2bo2bo2bo$bo2b2o3b2o24b2ob4ob2o$2o2bo31bob4obo$5bo31b2o2b2o24bobo
2bobo$2o2b2o57b2obo2bo2bo2bob2o$o5b2obo57bobo2bobo$bo4bob2o$2o8b2o22bo
2bob2obo2bo$10bo23b4ob2ob4o$2o9bo22bo2bob2obo2bo$o9b2o$bo4b2obo$2o4bob
2o8$2o6bob2o28b2o3b2o$o7b2obo27bobo3b2o41bo3bo$bo4b2o28bobobo28b3o15bo
bobobo14bobo3bobo$2o3bobo22b2o5bo29bo4bo2b2o11b2ob2o15bobo6bo$5bo24b2o
3b2o2bo26bo4b2o2b2o31bo2b2o3bo$2o2b2o30bobobo4bo19bo3bo15b3o5b3o16bobo
$o5b2obo27b3o4b2obo18b2o16bo4bobo4bo12bo3bo$bo4bob2o28bo4bo2bo36bo5bob
o5bo12b2obo$2o2b2o4b2o18b2o10b3o2bo23bo12bo4bobo4bo13b2o2b2o$4bo5bo19b
obo2bo7bobo2bo21b3o11b2o3bobo3b2o16bo$2o3bo5bo19bo2bobo7bo2bobo19bob3o
$o3b2o4b2o20bo2b3o10b2o18bo3bo13b3o3b3o$bo4b2obo23bo2bo4bo25bo3bo$2o4b
ob2o22bob2o4b3o23b3obo$34bo4bobobo23b3o$40bo2b2o3b2o18bo$42bo5b2o$39bo
bobo$33b2o3bobo$33b2o3b2o14$30b2o4b2obo4b2obo4b2o4b2o4b2o2b2o6bob2o4bo
b2o6b2obo6b2obo6b2obo$30bo5bob2o4bob2o4bo5bo5bobo2bo6b2obo4b2obo6bob2o
6bob2o6bob2o$31bo8b2o6b2o3bo5bo2b2o3b2o5b2o12b2o2b2o4b2o2b2o4b2o2b2o4b
2o$30b2o8bo7bo3b2o4b2o2bo10bobo13bo2bo5bo3bo5bo3bo5bo$41bo7bo4b2obo5bo
9bo14bo4bo5bo3bo5bo3bo5bo$30b2o8b2o6b2o4bob2o4b2o8b2o14b2o2b2o4b2o2b2o
4b2o2b2o4b2o$30bo5b2obo4b2obo10b2o4b2obo6b2obo8b2o6b2obo6b2obo4bo5bo$
31bo4bob2o4bob2o10bo5bob2o6bob2o9bo6bob2o6bob2o5bo5bo$30b2o2b2o12b2o9b
o8b2o2b2o4b2o6bo5b2o4b2o8b2o2b2o4b2o$34bo13bo9b2o8bo3bo5bo7b2o4bo5bo9b
o3bo5bo$30b2o3bo13bo19bo3bo5bo4b2o7bo5bo9bo3bo5bo$30bo3b2o12b2o18b2o2b
2o4b2o5bo6b2o4b2o8b2o2b2o4b2o$31bo4b2obo4b2obo10b2o4b2obo6b2obo6bo9b2o
bo6b2obo6b2obo$30b2o4bob2o4bob2o10b2o4bob2o6bob2o6b2o8bob2o6bob2o6bob
2o17$34b2o8b2obo6b2obo4b2obo6b2obo4b2obo4b2obo4b2o4b2o2b2o2b2o8b2o2b2o
4b2o2b2o8b2o6b2o2b2o6b2o4b2obo6b2obo6b2obo6b2obo7b2obo4b2ob2ob2o2b2o4b
2o2b2o5b2o2b2o6b2o2b2o5b2o2b2o5b2o3b2obo2bo$33bo2bo6bo2b2o6bob2o3bo2b
2o6bob2o4bob2o4bob2o4bo5bo3bobo2bo8bo4bo5bo3bo9bo6bo4bo6bo5bob2o5bo2b
2o6bob2o5bo2b2o7bob2o4b2obo3bo3bo5bo2bo7bo3bo7bo2bo7bo2bobo5bo2bo2b5o$
32bobo2bo4bobo3b2o2b2o6bobo3b2o2b2o6b2o6b2o9bo5bo4b2o11bo2bo5bo3bo10bo
bo2bobo3bo8bo2b2o4b2o2bobo3b2o2b2o4b2o2bobo3b2o3b2o11bob2o3bo5bo4bo5bo
3bo7bo4bo5bo4bobo3bo4bo$32bob2obo5bo4bo3bo7b2o4bo3bo7bo7bo9b2o4b2o4bo
11b2o2b4obo4b2o8b2ob4ob2o2b2o6b2o2bo5bo4bo4bo3bo5bo4bo4bo4bo12bobo4b2o
4b2o2b2o5b2o2b2o6b2o4bo3bo7bo2bo6b4o$31b2o4b2o10bo3bo13bo3bo7bo7bo21bo
17b2o6bo23b2o8bo5bo9bo3bo5bo9bo4bo10b2obo5bo5bo2bo7bo17bobo7b2obo5bobo
3bo$33bob2o7bo3b2o2b2o6b2o4b2o2b2o6b2o6b2o8b2o4b2o4b2o10b2o2b2o8bo9b
10o2b2obo4b2o2b2o4b2o4bo3b2o2b2o4b2o4bo3b2o3b2o13b2o3bo5bo4bo5bo3b2o2b
2o2b2o4b2ob2o9b2o4b2o3bo$33b2obo6bobobo4bo7bo5bo5b2obo4b2obo2bo3b2o4bo
2b2o2bo4bo12bo3bob2o5b2o8bo8bo3bobobo2bo3bo5bo4bobobo4bo10bobobo7b2obo
6b2obo4b2o4b2o4bo3bo5bo2b2o2bo6bobo7b2obo9bo$31b2o4b2o3bobob2o5bo7bo5b
o4bob2o4bob2o3bo2bo2bo3bobob2o6bo10bo4bobobo5bo9bo2b2o2bo4bo2bobobo4bo
5bo2bobob2o5bo4b2o2bobob2o7bob2o7bobobo13b2o3b2o3bo8bo4bo3bo7bobobo6bo
$32bob2obo4bobo3b2o2b2o8bo3b2o2b2o6b2o6b2o4b2o2b2o3bo6b2o10b2o2b2o4bo
3bo9b2o2b2o2b2o2b2o4bob2o2b2o4b2o2bobo7b2o4bo3bobo14b2o5bo2b2o2b2o4b2o
3bo5bo3b10o4b2ob2o7bo2b2o5bo3b2o$32bob2obo5b2o3bo3bo8b2o3bo3bo7bo7bo
11bo2bobo4bo12bo4bo4bo2b2o25b2o5bo5bo4b2o7bo6bo3b2ob2o11bo5b2o7bo5bo5b
obo20bobo7b2o8bo3bobo$31b2o4b2o10bo3bo13bo3bo7bo7bo4b2o2b2o4b2o5bo5bo
4bo3b2o4b2o3bo8b2o6b2o2b2o6b2o3bo5bo14bob4o6bobo11bo4bo7bo5bo5b2ob2o4b
2ob4ob2o4bo3bo6bo10b4o$32bo4bo5b2o3b2o2b2o7b2o3b2o2b2o8bo5b2o3bobo2bo
11b2o4bobo3b2o2bo9bo9bo7bo3bo8bo2b2o4b2o3b2o8b2obo6b3o3bo9b2o5bo6b2o4b
2o5bobo6bobo2bobo4bo5bo6bo13bo$30bo8bo2bo2bobo6b2obo2bo2bobo6b2obo2bob
o7b2o2bo4bo4b2o2bo2bobo3bo2b2o5bo4b2o2bobob2obo3bo7bo3bo6bo5b2obo4bobo
11bob2o2bo7bo4b2obo8bo7bob2o7bobo6bo6bo3bo7bo6bo6b5o2bo$30b2o6b2o2b2o
2b2o6bob2o2b2o2b2o6bob2o2b2o8bob2o4b2o4b2o2b2o2b2o4b2obo4b2o4b2o3b2obo
b2o2b2o6b2o2b2o6b2o4bob2o4b2o12b2obo2b2o5b2o4bob2o7b2o7b2obo8bo6b2o6b
2o2b2o5b2o5b2o6bo2bob2o!
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Entity Valkyrie 2
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Re: Sparker Compilation (up to p16)

Post by Entity Valkyrie 2 » March 19th, 2024, 9:35 am

I have looked through my past oscillator stamp collections, jslife, LifeWiki, the Oscillator Discussion Thread, the Gun Discussion Thread, and more... and here is my current stamp collection of p3-16 sparkers, sorted by period and spark type. (Some sparkers that give off multiple sparks appear multiple times in this collection)

Code: Select all

x = 3298, y = 1003, rule = LifeHistory
61.12D432.4D4.4D432.12D432.12D432.12D304.12D304.12D288.8D8.12D288.8D
8.8D$61.12D432.4D4.4D432.12D432.12D432.12D304.12D304.12D288.8D8.12D
288.8D8.8D$61.12D432.4D4.4D432.12D432.12D432.12D304.12D304.12D288.8D
8.12D288.8D8.8D$61.12D432.4D4.4D432.12D432.12D432.12D304.12D304.12D
288.8D8.12D288.8D8.8D$69.4D432.4D4.4D432.4D440.4D448.4D304.4D4.4D304.
4D4.4D292.4D8.4D4.4D292.4D12.4D$69.4D432.4D4.4D432.4D440.4D448.4D304.
4D4.4D304.4D4.4D292.4D8.4D4.4D292.4D12.4D$69.4D432.4D4.4D432.4D440.4D
448.4D304.4D4.4D304.4D4.4D292.4D8.4D4.4D292.4D12.4D$69.4D432.4D4.4D
432.4D440.4D448.4D304.4D4.4D304.4D4.4D292.4D8.4D4.4D292.4D12.4D$61.
12D432.12D432.12D432.12D440.4D304.12D304.12D292.4D8.4D4.4D292.4D12.4D
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2A8.2A.A191.4A1066.C20.2A4.2A2.2A1230.2A39.2A2.A2.C11.3A$587.4A12.4A
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A5.A2.2A10.A558.C41.C41.C$538.DA7.A.A16.C4.2A2.2A.A2.A.A.5A19.A2.A.2A
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.A.A.A.2A8.A.2A2.A5.A2.2A.A11.A2.3A2.A.A12.C.A9.3A1152.2A44.2A$538.A
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3A2.3A10.A2.A2.A2.A.A2.A7.2A2.A.A7.A.A2.2A11.2A.A.A.A2.2A9.C14.A$538.
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.2A14.A.A.A8.2A8.A3.4A.A3.A.A.2A2.2A2.A3.2A33.A.A5.A.A5.A.A12.4A.4A2.
A12.2A$540.A2.A.A23.DA5.2A3.A3.A3.2A3.A14.3A4.A.A2.A.2A2.3A.3A.A.A.A
3.3A2.A.A4.A.2A.A34.A.4A5.4A.A12.A4.A5.2A$533.2A6.2A26.D2A3.A3.3A.2A
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2A4.3A.2A4.A3.A.A32.2A17.2A10.2A.2A.2A2492.2A31.2A26.2A$534.9A26.3A.A
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4.A2.A4.A2.A258.C5.A6.A.2A28.A6.A7.3A18.A4.A22.3A.2A.A19.A8.A$577.2A
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$2510.2A11.A.A3.A4.A.A602.3A42.A3.A26.A5.2A26.3A25.2A$2525.2A.2A5.2A
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11.A25.A3.A23.A$3211.A39.A.3A23.A.2A$3252.3A26.2A$3253.A!
Spark types in this collection:
• Strong edge dot: a dot spark produced by B3i; can be removed without destroying the oscillator
• Moderate edge dot: a dot spark produced by B3i; oscillator requires spark to survive
• Strong corner dot: a dot spark not produced by B3i (mostly B3a); can be removed without destroying the oscillator
• Moderate corner dot: a dot spark produced by B3i (mostly B3a); oscillator requires spark to survive
• Pipsquirter: a vertical domino spark; the most common predecessor is a blinker with a suppressed back side (strength is ignored for this category)
• Duoplet: a spark consisting of two cells diagonally connected (strength is ignored for this category)
• Weak dot: a single extruding cell that is connected to the rest of the oscillator but still dies in the next generation (excluding pipsquirter and duoplet sparkers)
• Strong domino: a domino spark where both cells appear on the same generation; can be removed without destroying the oscillator
• Moderate domino: a domino spark where both cells appear on the same generation; oscillator requires spark to survive
• Weak domino: two neighboring extruding cells that are connected to the rest of the oscillator but still die in the next generation; both cells appear on the same generation
• Delayed domino: a domino spark where one of the two cells appears before the other (strength is ignored for this category)
• Miscellaneous: any spark that doesn't fit with the above catagories (e.g. V-spark, banana spark, etc; strength is ignored for this category)
Last edited by Entity Valkyrie 2 on April 24th, 2024, 9:14 am, edited 12 times in total.
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Sokwe
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Joined: July 9th, 2009, 2:44 pm

Re: Sparker Compilation (up to p16)

Post by Sokwe » March 19th, 2024, 7:02 pm

Entity Valkyrie 2 wrote: ↑
March 19th, 2024, 9:35 am
 here is my current stamp collection of p3-16 sparkers, sorted by period and spark type. (Some sparkers that give off multiple sparks appear multiple times in this collection)
Great work! Three issues that I see:
  • The last sparker in the p7 delayed domino row is actually p8.
  • Karel's p15 can also act as a delayed domino sparker as can be seen in this recent p60 gun by iNoMed.
  • Pentadecathlon provides some unconventional domino sparks that are sometimes, albeit rarely, used:

    Code: Select all

    x = 40, y = 5, rule = LifeHistory
2.2C6.2C$A4.A2.A4.A14.A.A2.A.A$A4.A2.A4.A10.2C.A2.A2.A2.A.2C$A4.A2.A
4.A14.A.A2.A.A$2.2C6.2C!
As discussed up-thread, this collection needs some sort of prominent display. I feel like we need a well-organized reference guide with links to things like this. Do we just need an expansion of LifeWiki:Life_links, or would a separate page be in order? I recognize that this is sort of a vague idea at the moment.
-Matthias Merzenich
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Entity Valkyrie 2
Posts: 1758
Joined: February 26th, 2019, 7:13 pm
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Re: Sparker Compilation (up to p16)

Post by Entity Valkyrie 2 » March 19th, 2024, 8:09 pm

Sokwe wrote: ↑
March 19th, 2024, 7:02 pm
 Great work! Three issues that I see:
  • The last sparker in the p7 delayed domino row is actually p8.
  • Karel's p15 can also act as a delayed domino sparker as can be seen in this recent p60 gun by iNoMed.
  • Pentadecathlon provides some unconventional domino sparks that are sometimes, albeit rarely, used:

    Code: Select all

    x = 40, y = 5, rule = LifeHistory
2.2C6.2C$A4.A2.A4.A14.A.A2.A.A$A4.A2.A4.A10.2C.A2.A2.A2.A.2C$A4.A2.A
4.A14.A.A2.A.A$2.2C6.2C!
I have fixed the issue with the Tumbling T-tetsons; it is now in the p8 section. I have also moved a few more oscillators around since they were mis-categorized.

While I could duplicate Karel's p15 into the "delayed domino" section, the same could be said about any pipsquirter, so I would rather not have one section be a subset of another. Most sparkers in the delayed domino section produce their domino like this (focus on the two rightmost columns):

Code: Select all

x = 4, y = 3, rule = LifeHistory
.2AD$3AC$2A!
The unconventional domino sparks of the pentadecathlon would also fit into the "miscellaneous" category, since the cells in the domino existed before the "spark" phase. But adding both of these would mean that pentadecathlon would appear four times in the "miscellaneous" category alone.
Bx222 IS MY WORST ENEMY.

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Sokwe
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Re: Sparker Compilation (up to p16)

Post by Sokwe » March 19th, 2024, 8:45 pm

Entity Valkyrie 2 wrote: ↑
March 19th, 2024, 8:09 pm
 I have fixed the issue with the Tumbling T-tetsons; it is now in the p8 section. I have also moved a few more oscillators around since they were mis-categorized.
Thanks, but now the rule says "OtherLifeHistory", which gives a LifeViewer error.
Entity Valkyrie 2 wrote: ↑
March 19th, 2024, 8:09 pm
 While I could duplicate Karel's p15 into the "delayed domino" section, the same could be said about any pipsquirter
Perhaps the pipsquirter section is better for Karel's p15. I still think that you should include it somewhere with the domino-like spark highlighted.
Entity Valkyrie 2 wrote: ↑
March 19th, 2024, 8:09 pm
 The unconventional domino sparks of the pentadecathlon would also fit into the "miscellaneous" category, since the cells in the domino existed before the "spark" phase. But adding both of these would mean that pentadecathlon would appear four times in the "miscellaneous" category alone.
I don't personally see the problem including one sparker several times, as long as you are highlighting different sparks. These sparks are otherwise not obvious, but they are sometimes essential. For example, here is a traffic light hassler that uses one of the unconventional domino sparks where the conventional domino spark wouldn't work:

Code: Select all

x = 23, y = 24, rule = B3/S23
4b6o$3bo6bo8b3o$2bo8bo$3bo6bo7bo3bo$4b6o8bo3bo2$19b3o2$8bo$b3o3bobo9b
3o$6bo3bo$o3bo2bobo4bo3bo3bo$o3bo3bo4bobo2bo3bo$12bo3bo$b3o9bobo3b3o$
14bo2$b3o2$o3bo8b6o$o3bo7bo6bo$11bo8bo$b3o8bo6bo$13b6o!
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hotcrystal0
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Re: Sparker Compilation (up to p16)

Post by hotcrystal0 » March 19th, 2024, 9:07 pm

Entity Valkyrie 2 wrote: ↑
March 19th, 2024, 9:35 am
 I have looked through my past oscillator stamp collections, jslife, LifeWiki, the Oscillator Discussion Thread, the Gun Discussion Thread, and more... and here is my current stamp collection of p3-16 sparkers, sorted by period and spark type. (Some sparkers that give off multiple sparks appear multiple times in this collection)

Code: Select all

long rle
There is a P8 in the P9 duoplet section.

Code: Select all

x = 192, y = 53, rule = B3/S23
33$42b4o$41b6o$40b2ob4o$41b2o3$41b2o$39bo6bo$38bo8bo$38bo8bo$38b9o3$42b
4o$41b6o$40b2ob4o$41b2o!
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Entity Valkyrie 2
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Re: Sparker Compilation (up to p16)

Post by Entity Valkyrie 2 » March 19th, 2024, 9:42 pm

Sokwe wrote: ↑
March 19th, 2024, 8:45 pm
 I don't personally see the problem including one sparker several times, as long as you are highlighting different sparks. These sparks are otherwise not obvious, but they are sometimes essential. For example, here is a traffic light hassler that uses one of the unconventional domino sparks where the conventional domino spark wouldn't work:

Code: Select all

x = 23, y = 24, rule = B3/S23
4b6o$3bo6bo8b3o$2bo8bo$3bo6bo7bo3bo$4b6o8bo3bo2$19b3o2$8bo$b3o3bobo9b
3o$6bo3bo$o3bo2bobo4bo3bo3bo$o3bo3bo4bobo2bo3bo$12bo3bo$b3o9bobo3b3o$
14bo2$b3o2$o3bo8b6o$o3bo7bo6bo$11bo8bo$b3o8bo6bo$13b6o!
Most sparkers appear between one and three times in this collection. If I showed every interaction of a sparker with a complex interaction like the Rich's P16, it would have to appear many times in the miscellaneous section alone (maybe even six or more). Also, middleweight and heavyweight sparkers also give off corner dot sparks, and if I had to include those in the corner dot section as well, the corner dot section would get way too large.

Though I am more willing to duplicate sparkers of higher periods where the options for sparkers are fewer, and complex interactions are more common. Karel's p15 now appears three times, and pentadecathlon now appears six times.

Also, I noticed that I had a P8 in the P9 section. This has been fixed.
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