Range-2 von Neumann isotropic non-totalistic rulespace

[muzik]

If I'm getting this right, this would be the minimal SkewLife with only one universe:

Code: Select all

x = 3, y = 4, rule = B0xn1cgcickcl2cccdcenc3ca/S0xgxlxn1cccdcgcickcl2cacccdcenanc3ca
bo$o$bo$obo!

I checked the rulestring. I realised that it is wrong because it does not take into account that the internal 4 adjacent cells can take on any configuration. Hopefully someone can help to correct the rulestring.

Precisely, hence why it's the minimal version; the full version would account for these.

[lemon41625]

Natural c/2d

Code: Select all

x = 16, y = 16, rule = B3x6ed8x7eg12x/S2x3arngqg5ir7x-6nd10x
obooobbbbobboboo$
bobboobboboboboo$
boboobboboboobbo$
obooboobboobbbbo$
ooobobobobbbbooo$
booooboobobbbooo$
bobobbooobooobbb$
bboboobbobobobob$
obbboobbbbobbbob$
bboooobbbooobbbo$
boobbboobbobboob$
bbboboooooooooob$
bbooobbooboboooo$
boooobooobobobob$
obbbbobbboobbbbb$
ooboboboboobboob!

Spaceship1.gif (47.37 KiB) Viewed 2699 times

Natural c/4o

Code: Select all

x = 16, y = 16, rule = B3x6ed8x7eg12x/S2x3arngqg5ir7x-6nd10x
ooobbbboooobbbbb$
bobobobbobbobboo$
obbobbboooobbbbb$
obboboobbbobobob$
oobobbbooooobboo$
obobobbbobobbbbb$
ooboooooobobbbbb$
oboobboobbbobbbb$
boobbooboboboooo$
obbbbooboooooobo$
obboobobbobbbobo$
obbbooboooobboob$
oobbobbbobobbobo$
oooobbboboobobob$
oobooobobooboboo$
oobooobobboboobo!

(Apparently, I can't upload more than 3 gifs.)

Natural c/10d

Code: Select all

x = 16, y = 16, rule = B3x6ed8x7eg12x/S2x3arngqg5ir7x-6nd10x
oooooobobobbbooo$
obbbbobbbooobbbo$
ooooboobboooboob$
bbbobobbbbobbooo$
booobbobbbbobbob$
booooobobboooobo$
booooobobbbbbbob$
bbbbbooobbbobbbo$
bobooobbbooobobo$
ooobobobooobbboo$
obbooobooobbbobb$
oobbbbbbobooobob$
obbbbbobobbbbobb$
boobbobobbbobbbo$
bbbooboboboobbbo$
booobboboboooobo!

Spaceship3.gif (117.2 KiB) Viewed 2699 times

Natural Oscillators (trust me they are on the catagolue page)

Code: Select all

x = 54, y = 31, rule = B3x6ed8x7eg12x/S2x3arngqg5ir7x-6nd10x
54.$36.A17.$12.A21.A.2A16.$3.A7.3A9.A30.$4.A5.3A9.A13.A17.$5.A5.A9.A32.$20.A5.A27.$25.A28.$24.A29.$23.A11.A10.A7.$35.A.A6.A.A7.$36.A.2A2.2A.A8.$32.2A4.A4.A4.2A4.$34.A12.A6.$7.A25.A14.A5.$6.2A26.2A10.2A6.$6.A.2A24.A12.A6.$8.A45.$54.$34.A12.A6.$34.2A10.2A6.$33.A14.A5.$34.A12.A6.$19.A12.2A4.A4.A4.2A4.$17.A3.A14.A.2A2.2A.A8.$14.A20.A.A6.A.A7.$22.2A11.A10.A7.$19.A2.A31.$54.$54.$54.1$!

Oscillator.gif (214.01 KiB) Viewed 2699 times

[Hunting]

How did you apgsearch R2vN rules?

[lemon41625]

How did you apgsearch R2vN rules?

Here's the rule table you can use. Apgsearch supports ruletables up to range 8. Also note that only permute and none symmetries work on custom neighbourhoods.
If you search the rule, do name the ruletable B4x5x5kg8x12x_S3x4x-3kd10x_R2VonNeumann.table so it uploades to the same census.

It's also automatically generated by CAViewer's apgtable gen function which I will release soon.

Code: Select all

n_states:2
neighborhood:[(0, 0), (1, -1), (1, 0), (1, 1), (0, 1), (-1, 1), (-1, 0), (-1, -1), (0, -1), (2, 0), (0, 2), (-2, 0), (0, -2), (0, 0)]
symmetries:none

# Variables for Death Transitions
var death0 = {0, 1}
var death1 = {0, 1}
var death2 = {0, 1}
var death3 = {0, 1}
var death4 = {0, 1}
var death5 = {0, 1}
var death6 = {0, 1}
var death7 = {0, 1}
var death8 = {0, 1}
var death9 = {0, 1}
var death10 = {0, 1}
var death11 = {0, 1}

# Birth Transitions
0,0,1,0,0,1,1,1,0,1,1,1,1,1
0,1,1,0,0,0,1,0,0,0,0,1,1,1
0,0,1,0,0,0,0,0,1,1,1,0,0,1
0,1,0,0,0,0,1,1,0,1,0,0,0,1
0,1,1,1,0,1,1,0,1,0,1,1,0,1
0,1,0,0,1,1,0,1,0,1,1,1,1,1
0,1,0,1,1,0,0,1,0,1,1,1,1,1
0,0,1,0,1,1,1,1,0,0,0,0,0,1
0,1,1,0,0,0,0,1,0,1,1,0,0,1
0,0,1,1,1,0,1,1,0,0,0,0,0,1
0,1,0,0,0,0,0,1,0,1,0,0,1,1
0,0,1,1,0,1,0,1,1,1,0,1,1,1
0,0,0,0,0,1,0,1,0,0,1,1,1,1
0,0,1,0,1,1,0,1,1,1,1,0,1,1
0,0,0,1,0,1,0,0,0,0,1,1,0,1
0,0,1,1,1,0,0,1,1,1,1,0,1,1
0,1,0,0,1,0,1,1,0,0,0,0,1,1
0,1,1,0,0,0,0,1,1,1,1,1,1,1
0,1,1,1,1,0,0,1,1,1,0,0,1,1
0,1,1,0,1,1,0,1,1,1,0,0,1,1
0,1,1,0,0,1,1,0,0,0,0,0,0,1
0,0,0,1,1,0,1,0,0,0,1,1,0,1
0,0,0,0,1,1,1,0,0,0,1,1,0,1
0,1,1,1,1,1,1,0,0,0,1,1,0,1
0,0,0,0,0,0,0,1,0,1,1,0,1,1
0,0,0,0,1,0,0,1,1,1,0,0,1,1
0,1,0,1,0,0,1,0,0,1,1,0,0,1
0,1,1,1,0,0,1,0,0,0,0,1,0,1
0,1,0,1,0,0,0,0,0,1,1,1,0,1
0,0,1,0,1,0,1,1,0,0,0,0,0,1
0,1,1,0,0,1,0,0,0,0,1,1,0,1
0,1,1,1,1,1,0,0,0,0,0,0,0,1
0,1,1,1,0,1,0,1,0,0,1,1,1,1
0,1,0,1,1,1,0,0,0,1,0,0,0,1
0,1,0,1,0,0,1,0,1,1,1,1,1,1
0,0,0,1,0,0,0,1,0,1,1,0,0,1
0,0,1,1,0,0,0,0,1,1,1,0,0,1
0,1,0,1,0,0,0,0,1,0,1,0,0,1
0,1,0,1,1,1,1,0,1,1,0,0,1,1
0,1,0,1,0,1,0,1,0,0,0,0,0,1
0,0,0,0,0,1,1,0,1,0,1,1,0,1
0,1,0,0,1,0,0,0,1,0,0,1,0,1
0,0,0,1,1,1,1,0,1,0,0,0,0,1
0,0,0,1,0,0,1,0,0,0,0,1,1,1
0,0,0,0,0,1,0,0,0,0,1,1,1,1
0,1,0,0,0,1,0,0,1,0,1,1,0,1
0,0,1,0,1,0,0,0,0,1,0,0,1,1
0,0,0,1,1,1,0,0,0,0,0,0,1,1
0,0,1,1,0,1,1,1,1,1,1,0,0,1
0,1,0,0,0,0,1,1,0,0,1,0,1,1
0,0,1,0,1,1,1,1,1,1,0,1,0,1
0,0,1,1,1,0,1,1,1,1,0,1,0,1
0,1,0,0,0,0,0,1,1,1,0,0,0,1
0,0,0,1,1,0,0,0,0,1,1,0,1,1
0,0,0,0,1,1,0,0,0,1,1,0,1,1
0,0,1,0,1,1,0,1,1,0,0,0,0,1
0,0,0,1,0,1,0,0,0,1,0,1,1,1
0,0,1,1,1,0,0,1,1,0,0,0,0,1
0,0,1,0,0,0,0,1,0,0,0,1,1,1
0,0,1,0,0,0,1,1,0,0,1,0,0,1
0,1,0,1,0,0,0,0,0,0,1,1,1,1
0,1,1,1,0,1,0,1,0,1,1,1,0,1
0,1,1,0,0,0,1,1,0,1,1,1,1,1
0,1,0,0,1,1,1,0,1,0,1,1,1,1
0,1,0,1,1,0,1,0,1,0,1,1,1,1
0,1,1,1,1,0,1,1,0,1,0,0,1,1
0,1,1,0,1,1,1,1,0,1,0,0,1,1
0,1,0,0,0,0,1,0,1,0,0,0,1,1
0,1,1,1,1,1,0,0,1,1,0,1,0,1
0,1,0,0,1,0,1,0,1,0,0,1,0,1
0,1,0,0,1,0,0,0,1,1,0,0,1,1
0,1,0,0,0,1,1,0,1,0,1,0,0,1
0,0,0,0,0,1,0,0,0,1,1,1,0,1
0,0,1,1,0,0,0,0,0,0,1,1,0,1
0,1,1,0,0,1,1,1,1,0,0,1,1,1
0,0,0,0,0,1,1,0,0,1,1,0,0,1
0,1,0,0,1,0,1,0,0,1,0,0,0,1
0,1,1,0,1,0,1,1,1,0,1,0,1,1
0,0,0,0,1,0,1,0,0,1,0,1,0,1
0,0,0,1,1,1,0,0,0,1,0,1,0,1
0,0,1,1,1,1,0,0,0,0,0,1,0,1
0,1,0,0,0,1,0,0,0,1,1,0,0,1
0,1,1,1,0,0,0,0,0,0,1,0,0,1
0,0,0,1,0,0,1,0,0,1,1,1,0,1
0,0,1,1,1,1,1,0,1,0,0,1,1,1
0,0,1,0,1,0,0,0,1,1,0,0,0,1
0,1,0,1,0,1,1,0,0,0,0,1,0,1
0,1,0,0,1,1,1,0,0,0,1,0,0,1
0,1,1,1,0,0,1,1,0,1,0,1,1,1
0,1,0,1,1,0,1,0,0,0,1,0,0,1
0,0,0,1,0,0,1,0,1,0,1,0,0,1
0,1,0,0,1,0,0,1,0,0,0,0,1,1
0,1,0,0,0,0,0,1,1,0,1,0,1,1
0,0,0,1,0,1,1,0,1,0,0,0,1,1
0,1,0,0,1,1,1,0,1,1,1,1,0,1
0,1,0,1,1,0,1,0,1,1,1,1,0,1
0,0,1,0,0,0,0,1,0,1,1,1,0,1
0,1,0,0,0,0,1,0,1,1,0,1,0,1
0,0,0,0,0,0,0,1,1,1,0,1,0,1
0,1,1,0,1,0,0,0,1,0,0,0,1,1
0,1,0,0,0,0,0,0,0,1,0,1,1,1
0,0,1,0,0,0,0,1,1,0,1,0,0,1
0,1,1,1,1,0,1,1,1,1,0,0,0,1
0,1,1,0,1,1,1,1,1,1,0,0,0,1
0,0,0,1,0,1,0,1,1,1,0,0,0,1
0,0,0,1,1,1,1,0,0,0,0,0,1,1
0,1,0,1,0,0,0,1,1,0,1,0,0,1
0,0,0,1,0,0,1,0,0,0,1,1,1,1
0,0,0,1,1,0,0,1,0,0,1,0,0,1
0,0,1,1,0,0,0,0,0,1,0,1,1,1
0,0,0,0,1,1,0,1,0,0,1,0,0,1
0,0,0,1,1,1,0,0,1,0,0,0,0,1
0,0,0,1,0,1,0,1,0,0,0,1,0,1
0,1,0,0,1,0,1,0,0,0,1,0,1,1
0,0,0,1,0,0,0,0,1,0,1,1,0,1
0,1,0,0,0,1,1,0,0,0,0,1,1,1
0,0,0,0,0,1,1,1,0,1,1,0,0,1
0,1,1,1,1,1,0,1,0,0,1,0,1,1
0,1,1,1,1,1,1,1,0,0,0,1,0,1
0,1,0,0,1,0,0,1,0,1,0,1,0,1
0,0,1,0,1,0,0,0,1,0,1,0,1,1
0,0,1,0,0,1,1,0,1,1,0,0,0,1
0,0,1,0,1,1,0,1,0,0,0,0,1,1
0,0,1,1,1,0,0,1,0,0,0,0,1,1
0,0,0,0,0,1,1,1,1,1,1,1,1,1
0,1,0,0,0,1,0,1,0,1,1,0,0,1
0,0,1,0,0,1,0,0,1,0,0,1,1,1
0,0,1,0,0,0,0,1,0,0,1,1,1,1
0,0,1,0,1,0,1,0,0,0,1,0,0,1
0,0,0,1,1,1,1,1,1,1,0,0,1,1
0,0,1,0,0,1,1,0,0,0,0,1,0,1
0,1,0,0,1,1,0,0,1,1,0,0,0,1
0,1,0,0,0,1,0,1,1,1,1,1,1,1
0,1,0,1,1,0,0,0,1,1,0,0,0,1
0,1,1,1,0,0,0,1,1,1,0,1,1,1
0,1,0,1,0,0,1,1,1,0,1,1,1,1
0,0,1,1,0,1,0,0,0,1,1,0,0,1
0,1,0,1,0,1,0,0,0,0,1,0,0,1
0,0,1,1,1,1,0,1,0,1,0,1,1,1
0,1,0,1,1,1,1,1,1,0,0,0,1,1
0,1,0,0,1,1,0,0,0,0,0,1,0,1
0,1,0,1,1,0,0,0,0,0,0,1,0,1
0,0,1,0,1,1,1,0,0,1,0,0,0,1
0,0,1,1,1,0,1,0,0,1,0,0,0,1
0,0,1,1,0,1,0,0,1,1,1,1,1,1
0,1,0,1,0,1,1,1,0,1,0,1,1,1
0,0,0,0,0,0,1,1,0,1,0,1,0,1
0,1,0,0,1,1,1,1,0,1,1,0,1,1
0,1,0,1,1,0,1,1,0,1,1,0,1,1
0,0,0,1,0,1,0,1,0,1,0,0,1,1
0,0,1,1,0,0,1,0,1,0,0,0,1,1
0,0,1,0,0,0,1,0,1,0,1,1,0,1
0,0,0,1,0,1,1,1,0,1,0,0,0,1
0,0,0,0,1,0,0,0,1,1,1,0,1,1
0,0,1,0,0,0,0,0,0,0,1,1,1,1
0,0,0,1,0,0,0,0,1,1,0,1,1,1
0,1,0,1,0,0,1,1,0,0,1,0,0,1
0,1,1,1,1,0,1,0,0,1,0,1,1,1
0,1,1,0,1,1,1,0,0,1,0,1,1,1
0,1,0,1,0,0,0,1,0,0,0,1,1,1
0,1,0,0,1,0,0,1,1,0,0,0,0,1
0,1,1,1,0,1,1,0,0,1,1,0,1,1
0,1,1,1,0,1,0,0,0,1,1,1,1,1
0,1,1,0,1,0,0,1,0,1,0,0,0,1
0,0,0,0,1,0,1,1,1,0,0,1,0,1
0,1,0,1,0,0,1,1,1,1,1,1,0,1
0,0,1,0,0,1,1,0,0,1,0,0,1,1
0,0,0,1,0,0,1,1,1,0,1,0,0,1
0,0,1,1,0,0,0,1,1,1,0,0,0,1
0,1,1,1,0,0,1,1,1,1,1,0,0,1
0,0,0,0,0,1,0,1,1,1,1,0,0,1
0,1,1,1,1,1,0,1,1,0,0,1,0,1
0,0,0,0,1,0,1,1,0,1,0,0,0,1
0,0,1,1,0,0,0,1,0,0,0,1,0,1
0,1,0,0,1,1,0,0,0,1,0,0,1,1
0,1,0,1,1,0,0,0,0,1,0,0,1,1
0,1,1,0,0,1,1,0,1,1,0,1,1,1
0,0,0,0,1,0,0,1,0,1,0,0,1,1
0,1,0,0,0,0,0,0,0,1,1,1,1,1
0,1,1,0,1,0,1,0,1,1,1,0,1,1
0,1,0,0,0,0,1,0,0,1,1,0,1,1
0,0,1,0,1,0,0,1,0,0,1,1,0,1
0,0,1,0,1,1,0,0,1,0,0,1,0,1
0,1,0,0,0,1,1,1,0,1,1,1,1,1
0,0,1,1,1,0,0,0,1,0,0,1,0,1
0,1,0,0,0,0,0,0,1,1,1,0,0,1
0,0,1,0,1,0,1,1,1,1,0,1,1,1
0,0,1,0,1,1,0,0,0,1,0,0,0,1
0,0,1,0,0,1,1,1,1,1,1,0,1,1
0,0,1,1,1,0,0,0,0,1,0,0,0,1
0,1,1,0,0,0,1,0,1,1,0,0,0,1
0,1,0,0,1,1,1,1,0,0,0,0,0,1
0,1,0,1,1,0,1,1,0,0,0,0,0,1
0,0,1,0,0,0,0,0,0,1,1,1,0,1
0,1,1,0,0,0,0,0,1,0,0,1,1,1
0,0,1,0,0,0,1,0,0,1,1,0,0,1
0,1,1,1,1,0,0,0,0,0,0,0,0,1
0,1,1,0,1,1,0,0,0,0,0,0,0,1
0,1,0,1,0,1,0,1,1,1,0,1,1,1
0,1,0,0,1,1,0,1,1,1,1,0,1,1
0,1,0,1,1,0,0,1,1,1,1,0,1,1
0,1,1,0,0,0,1,0,0,0,0,1,0,1
0,0,1,1,0,1,1,1,0,0,1,1,1,1
0,0,0,0,0,0,1,0,1,1,0,0,1,1
0,1,1,1,0,1,1,0,0,0,0,0,0,1
0,0,0,0,0,1,0,1,0,0,1,1,0,1
0,0,1,1,0,0,0,1,0,1,0,0,1,1
0,1,0,0,1,0,1,1,0,0,0,0,0,1
0,0,0,1,1,0,0,0,1,0,1,1,0,1
0,0,0,0,1,1,0,0,1,0,1,1,0,1
0,0,0,1,1,1,0,1,0,0,0,1,0,1
0,0,0,0,1,0,1,1,0,0,1,0,1,1
0,0,1,1,0,0,1,1,0,1,0,0,0,1
0,1,0,1,0,0,0,0,1,1,1,0,0,1
0,0,0,1,0,0,1,1,0,0,0,1,1,1
0,0,0,1,0,1,1,0,0,0,0,0,1,1
0,0,1,1,1,1,0,1,1,1,1,0,0,1
0,0,0,0,1,0,0,1,1,1,0,0,0,1
0,1,1,0,1,0,1,0,1,0,0,0,0,1
0,1,0,0,1,0,0,0,0,1,0,0,1,1
0,1,1,0,1,0,0,0,0,0,0,0,1,1
0,1,0,1,0,1,1,1,1,1,1,0,0,1
0,1,0,0,1,1,1,1,1,1,0,1,0,1
0,1,0,1,1,0,1,1,1,1,0,1,0,1
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0,1,1,1,0,0,0,0,1,0,0,1,0,1
0,0,0,1,0,0,0,1,0,1,1,0,1,1
0,1,0,1,0,0,0,0,1,0,1,0,1,1
0,1,0,0,1,0,1,0,1,1,0,0,0,1
0,0,0,0,1,0,1,0,0,0,1,1,0,1
0,1,0,1,0,1,0,1,0,0,0,0,1,1
0,1,0,0,1,0,0,0,1,0,0,1,1,1
0,1,1,1,0,0,0,0,0,1,0,0,0,1
0,0,1,1,0,0,1,0,0,1,1,0,0,1
0,1,0,1,0,0,1,0,0,0,1,0,0,1
0,1,1,0,0,1,1,1,1,1,0,0,1,1
0,0,1,1,0,0,0,0,0,1,1,1,0,1
0,1,0,0,1,0,1,0,0,0,0,1,0,1
0,0,1,1,1,1,0,0,0,1,0,0,0,1
0,0,0,1,0,0,0,0,1,0,0,1,1,1
0,0,1,1,0,0,1,0,1,1,1,1,1,1
0,0,0,1,0,0,1,0,1,1,0,0,0,1
0,1,0,0,0,1,1,0,0,0,1,1,0,1
0,0,1,1,0,0,0,0,1,0,1,0,0,1
0,0,1,1,1,1,1,0,1,1,0,0,1,1
0,0,1,1,0,1,0,1,0,0,0,0,0,1
0,1,0,1,1,1,0,1,0,1,1,0,1,1
0,0,1,0,1,0,0,0,1,0,0,1,0,1
0,1,0,0,0,0,0,1,1,1,0,0,1,1
0,1,0,1,0,1,1,0,0,1,0,0,0,1
0,1,1,0,1,0,1,1,0,0,1,1,1,1
0,0,1,0,0,1,0,0,1,0,1,1,0,1
0,0,1,0,0,0,1,1,0,0,1,0,1,1
0,1,1,0,1,1,0,1,0,1,0,0,1,1
0,0,0,0,0,0,0,1,1,0,1,1,0,1
0,0,1,0,0,0,0,1,1,1,0,0,0,1
0,0,0,1,1,0,0,1,1,0,0,1,0,1
0,0,0,0,1,1,0,1,1,0,0,1,0,1
0,0,0,1,0,1,0,1,1,0,1,0,0,1
0,1,1,1,0,1,0,1,1,1,1,0,0,1
0,0,0,0,0,0,1,1,1,1,1,0,0,1
0,0,0,1,1,0,0,1,0,1,0,0,0,1
0,0,0,0,0,1,0,0,0,1,1,1,1,1
0,0,0,0,1,1,0,1,0,1,0,0,0,1
0,0,1,1,0,0,0,0,0,0,1,1,1,1
0,1,1,1,1,0,1,1,1,0,0,1,0,1
0,1,1,0,1,1,1,1,1,0,0,1,0,1
0,0,0,0,0,1,1,0,0,1,1,0,1,1
0,1,0,0,1,0,1,0,0,1,0,0,1,1
0,0,1,0,1,1,1,0,1,0,1,1,1,1
0,0,1,1,1,0,1,0,1,0,1,1,1,1
0,0,0,0,1,0,1,0,0,1,0,1,1,1
0,0,0,0,0,1,0,0,1,1,1,0,0,1
0,0,1,0,0,0,1,0,1,0,0,0,1,1
0,1,1,1,1,0,0,0,1,1,1,0,1,1
0,1,1,0,1,1,0,0,1,1,1,0,1,1
0,1,0,0,0,1,0,0,0,1,1,0,1,1
0,1,1,1,0,0,0,0,0,0,1,0,1,1
0,0,0,0,1,0,0,0,1,1,0,1,0,1
0,0,1,0,1,0,1,0,1,0,0,1,0,1
0,1,1,0,1,0,1,1,0,1,1,1,0,1
0,0,1,0,1,0,0,0,1,1,0,0,1,1
0,0,1,0,0,1,1,0,1,0,1,0,0,1
0,0,0,1,0,0,0,0,1,1,1,1,0,1
0,1,0,1,0,0,0,1,0,0,1,1,0,1
0,0,1,0,1,0,1,0,0,1,0,0,0,1
0,0,0,1,0,0,1,0,1,0,1,0,1,1
0,0,0,1,1,1,1,1,1,0,1,0,1,1
0,1,0,1,0,1,0,0,1,0,0,1,0,1
0,0,0,1,0,1,1,1,1,0,1,1,1,1
0,1,0,1,1,1,0,1,0,0,0,0,0,1
0,1,0,1,0,1,1,0,1,1,0,0,1,1
0,1,0,0,1,1,0,0,1,0,1,0,0,1
0,1,0,1,1,0,0,0,1,0,1,0,0,1
0,0,1,0,0,1,0,0,0,1,1,0,0,1
0,1,0,1,0,0,1,1,1,1,0,1,1,1
0,1,0,0,1,0,1,1,1,1,1,0,1,1
0,1,0,1,0,1,0,0,0,1,0,0,0,1
0,0,1,1,0,1,1,0,0,0,0,1,0,1
0,1,1,0,1,0,0,1,1,0,1,1,1,1
0,0,1,0,1,1,1,0,0,0,1,0,0,1
0,0,1,1,1,0,1,0,0,0,1,0,0,1
0,0,0,0,0,0,0,1,1,1,0,1,1,1
0,1,0,0,0,0,1,0,0,1,0,1,0,1
0,0,1,0,1,0,0,1,0,0,0,0,1,1
0,0,1,0,0,0,0,1,1,0,1,0,1,1
0,0,0,0,0,0,1,1,0,0,1,1,0,1
0,0,1,0,1,1,1,0,1,1,1,1,0,1
0,0,1,1,1,0,1,0,1,1,1,1,0,1
0,0,0,1,1,0,1,1,0,0,0,1,0,1
0,0,0,0,1,1,1,1,0,0,0,1,0,1
0,0,1,0,0,0,1,0,1,1,0,1,0,1
0,0,0,1,1,0,0,1,0,0,1,0,1,1
0,0,0,0,1,1,0,1,0,0,1,0,1,1
0,0,0,1,0,1,1,1,0,0,1,0,0,1
0,0,0,1,1,1,0,0,1,0,0,0,1,1
0,1,1,1,0,1,1,1,0,1,1,0,0,1
0,0,0,1,0,1,0,1,0,0,0,1,1,1
0,0,1,0,0,0,0,0,0,1,0,1,1,1
0,0,0,1,0,0,0,0,1,0,1,1,1,1
0,1,1,0,0,0,0,0,1,0,1,1,0,1
0,1,1,0,0,1,0,1,0,0,0,1,0,1
0,1,1,1,1,0,0,0,1,0,0,0,0,1
0,1,1,0,1,1,0,0,1,0,0,0,0,1
0,0,0,1,0,1,1,1,1,1,1,1,0,1
0,1,1,0,1,0,0,1,0,0,1,0,0,1
0,0,1,1,0,0,0,1,1,0,1,0,0,1
0,1,0,1,1,1,0,1,1,1,0,1,0,1
0,1,1,0,1,0,0,1,1,1,1,1,0,1
0,0,1,0,1,0,1,0,0,0,1,0,1,1
0,0,0,0,1,0,1,1,1,1,0,0,0,1
0,0,0,0,0,0,0,0,1,0,1,1,1,1
0,0,0,0,0,1,0,1,0,0,0,1,1,1
0,0,1,0,0,1,1,0,0,0,0,1,1,1
0,0,0,1,1,0,0,0,1,0,0,0,1,1
0,0,0,0,0,1,1,1,0,0,1,0,0,1
0,0,0,0,1,1,0,0,1,0,0,0,1,1
0,0,0,0,1,0,0,1,0,0,1,0,1,1
0,0,0,0,1,0,1,1,0,0,0,1,0,1
0,0,1,0,1,0,0,1,0,1,0,1,0,1
0,1,0,0,1,0,1,1,1,0,0,0,0,1
0,1,0,1,0,1,0,0,0,0,1,0,1,1
0,0,1,0,0,1,0,1,0,1,1,0,0,1
0,1,0,0,0,1,0,1,0,0,1,0,0,1
0,1,0,1,1,0,0,0,0,0,0,1,1,1
0,1,0,0,1,1,0,0,0,0,0,1,1,1
0,0,0,1,0,0,1,1,0,0,1,1,0,1
0,0,1,0,1,1,0,0,1,1,0,0,0,1
0,0,1,0,0,1,0,1,1,1,1,1,1,1
0,0,1,1,1,0,0,0,1,1,0,0,0,1
0,1,1,0,0,0,1,0,1,0,1,0,0,1
0,0,1,1,0,0,1,1,1,0,1,1,1,1
0,0,0,0,0,0,1,1,0,1,0,1,1,1
0,1,0,1,1,0,1,1,0,1,1,0,0,1
0,0,1,1,0,1,0,0,0,0,1,0,0,1
0,0,1,1,1,1,1,1,1,0,0,0,1,1
0,0,1,0,1,1,0,0,0,0,0,1,0,1
0,0,1,1,1,0,0,0,0,0,0,1,0,1
0,1,1,0,0,0,0,0,0,1,1,0,0,1
0,0,1,1,0,1,1,1,0,1,0,1,1,1
0,0,0,0,0,0,1,0,1,0,1,0,1,1
0,0,1,0,1,1,1,1,0,1,1,0,1,1
0,0,1,1,1,0,1,1,0,1,1,0,1,1
0,1,0,0,1,0,0,1,1,0,0,0,1,1
0,0,0,0,0,0,0,0,1,1,1,1,0,1
0,0,0,1,1,0,0,0,1,1,0,1,0,1
0,0,0,0,1,1,0,0,1,1,0,1,0,1
0,0,0,1,0,1,0,0,1,1,1,0,0,1
0,0,0,0,1,0,1,1,0,1,0,0,1,1
0,1,1,1,0,0,0,1,0,0,0,0,0,1
0,0,1,1,0,0,1,1,0,0,1,0,0,1
0,0,0,0,0,1,0,1,0,1,1,1,0,1
0,0,1,1,0,0,0,1,0,0,0,1,1,1
0,0,1,0,1,0,0,1,1,0,0,0,0,1
0,1,0,1,1,1,1,1,0,1,0,1,0,1
0,0,0,1,1,1,0,1,0,1,0,0,0,1
0,0,1,1,0,0,1,1,1,1,1,1,0,1
0,1,0,1,0,0,0,0,0,0,0,1,1,1
0,0,0,0,0,1,0,1,1,0,1,0,0,1
0,1,0,0,1,0,0,0,0,0,1,0,1,1
0,1,1,1,1,1,0,0,0,1,1,0,1,1
0,1,0,0,0,0,0,0,1,1,1,0,1,1
0,0,0,0,1,0,0,1,1,0,0,1,0,1
0,1,1,0,1,0,1,0,0,1,1,1,1,1
0,1,0,0,1,1,1,1,1,0,1,1,0,1
0,1,0,1,1,0,1,1,1,0,1,1,0,1
0,0,1,0,1,1,0,0,0,1,0,0,1,1
0,0,1,1,1,0,0,0,0,1,0,0,1,1
0,0,0,1,0,0,0,1,1,0,1,1,0,1
0,0,1,0,0,0,0,0,0,1,1,1,1,1
0,0,0,1,1,1,1,0,1,1,1,0,1,1
0,1,0,0,0,0,1,1,1,0,0,1,0,1
0,0,1,0,0,0,1,0,0,1,1,0,1,1
0,1,1,0,1,1,0,0,0,0,0,0,1,1

# Survival Transitions
1,0,0,0,1,1,0,0,0,0,1,1,0,1
1,1,0,1,0,0,0,0,1,0,0,0,0,1
1,0,1,1,1,1,1,1,1,1,1,1,0,1
1,1,0,0,1,0,0,0,0,0,0,1,1,1
1,0,0,0,0,1,0,1,0,1,1,0,0,1
1,0,0,0,1,0,0,1,1,0,1,0,0,1
1,0,1,0,0,0,0,0,1,1,1,0,0,1
1,1,0,0,0,1,0,0,0,0,1,0,1,1
1,1,0,0,0,0,1,1,0,1,0,0,0,1
1,0,0,1,0,1,0,0,0,0,0,1,0,1
1,1,0,1,0,0,1,0,0,0,0,0,1,1
1,0,0,0,0,0,1,0,0,0,1,1,0,1
1,0,0,1,0,0,0,1,1,0,0,1,0,1
1,0,0,0,1,0,0,1,0,1,0,1,0,1
1,1,1,1,1,1,1,0,1,1,1,1,0,1
1,0,0,1,1,0,1,0,0,0,0,0,0,1
1,0,0,0,0,0,1,0,1,1,0,0,0,1
1,0,0,0,1,1,1,0,0,0,0,0,0,1
1,0,1,0,0,0,0,0,0,1,0,0,1,1
1,0,0,0,0,1,1,0,0,0,0,1,1,1
1,0,0,0,0,0,0,0,1,0,0,1,1,1
1,1,0,0,0,0,0,1,0,1,0,0,1,1
1,0,0,1,0,1,0,0,1,1,0,0,0,1
1,0,0,0,1,0,1,0,0,0,1,0,1,1
1,0,1,1,0,0,0,0,1,0,0,0,1,1
1,0,1,1,0,0,1,1,0,0,0,0,0,1
1,0,0,1,0,1,0,0,0,0,1,1,0,1
1,1,0,0,1,0,0,0,1,0,0,0,0,1
1,1,0,1,0,0,0,0,0,1,0,0,0,1
1,1,1,0,0,1,0,0,0,0,0,0,0,1
1,1,0,0,0,1,0,0,0,0,0,1,1,1
1,0,0,1,0,0,0,1,1,0,1,0,0,1
1,0,0,0,1,0,0,1,0,1,1,0,0,1
1,1,1,0,0,1,1,0,0,0,0,0,0,1
1,1,0,0,0,0,1,1,1,0,0,0,0,1
1,0,0,1,0,0,0,1,0,1,0,1,0,1
1,0,0,0,0,0,0,1,0,1,1,0,1,1
1,0,0,0,0,0,0,0,1,0,1,0,1,1
1,1,0,1,0,0,0,0,1,0,0,1,0,1
1,0,0,1,0,1,1,0,0,0,0,0,0,1
1,0,0,0,0,1,0,1,0,0,0,0,1,1
1,0,0,0,0,1,1,0,1,0,0,0,0,1
1,0,1,0,0,0,0,0,1,0,0,0,1,1
1,0,1,0,0,0,1,1,0,0,0,0,0,1
1,0,0,0,1,0,1,0,0,0,0,1,1,1
1,0,0,0,0,0,0,0,0,1,0,1,1,1
1,0,0,1,0,0,1,0,0,0,1,0,1,1
1,0,1,0,1,0,0,0,1,0,0,0,1,1
1,0,1,1,0,0,0,0,0,1,0,0,1,1
1,0,1,0,1,0,1,1,0,0,0,0,0,1
1,0,0,1,1,0,1,0,0,0,0,1,0,1
1,0,0,0,0,0,1,0,1,1,0,1,0,1
1,1,0,0,1,0,0,0,0,1,0,0,0,1
1,1,0,0,0,1,0,0,1,0,0,0,0,1
1,1,1,0,1,0,0,0,0,0,0,0,0,1
1,0,0,0,1,1,1,0,0,0,0,1,0,1
1,1,1,0,1,1,0,1,1,1,1,1,1,1
1,1,1,1,1,0,0,1,1,1,1,1,1,1
1,1,0,0,0,0,0,1,0,0,1,0,0,1
1,0,0,1,0,0,0,1,0,1,1,0,0,1
1,0,0,0,0,0,0,1,0,1,0,1,1,1
1,1,0,1,0,0,0,0,1,0,1,0,0,1
1,1,0,0,0,1,1,0,0,0,0,0,1,1
1,1,1,0,1,0,1,0,0,0,0,0,0,1
1,1,0,1,0,1,0,1,0,0,0,0,0,1
1,1,0,0,1,0,0,0,1,0,0,1,0,1
1,1,0,1,0,0,0,0,0,1,0,1,0,1
1,0,0,0,0,0,0,0,0,1,1,0,1,1
1,0,0,0,0,0,0,1,1,0,1,0,1,1
1,1,1,0,0,1,0,0,0,0,0,1,0,1
1,0,0,0,1,0,0,1,0,0,0,0,1,1
1,0,0,0,0,1,1,0,0,1,0,0,0,1
1,0,0,0,1,0,1,0,1,0,0,0,0,1
1,0,0,1,0,0,1,0,0,0,0,1,1,1
1,0,0,0,0,1,0,0,0,0,1,1,1,1
1,0,0,1,1,0,1,0,0,0,1,0,0,1
1,0,0,0,0,0,1,0,1,1,1,0,0,1
1,0,0,0,1,1,1,0,0,0,1,0,0,1
1,0,1,0,1,0,0,0,0,1,0,0,1,1
1,0,1,0,0,1,0,0,1,0,0,0,1,1
1,0,0,0,0,1,0,0,1,1,0,0,1,1
1,1,0,0,0,0,0,1,0,0,0,1,0,1
1,0,0,1,1,1,0,0,0,0,0,0,1,1
1,1,1,0,0,0,0,1,0,1,0,0,0,1
1,0,1,0,0,0,0,1,0,0,1,0,1,1
1,0,1,0,0,1,1,1,0,0,0,0,0,1
1,0,0,1,0,1,1,0,0,0,0,1,0,1
1,1,0,0,0,1,0,0,0,1,0,0,0,1
1,1,1,1,0,0,0,0,0,0,0,0,0,1
1,0,0,0,0,1,1,0,1,0,0,1,0,1
1,0,1,0,0,0,1,1,0,0,0,1,0,1
1,1,1,1,0,1,0,1,1,1,1,1,1,1
1,1,0,1,1,1,1,0,1,1,1,1,1,1
1,0,0,0,0,0,1,0,0,1,0,0,1,1
1,1,0,0,1,0,0,0,1,0,1,0,0,1
1,0,0,0,0,1,0,0,0,1,1,0,0,1
1,0,1,1,0,0,0,0,0,0,1,0,0,1
1,1,0,1,0,0,0,0,0,1,1,0,0,1
1,0,0,0,0,0,0,1,1,0,0,1,1,1
1,1,1,0,0,1,0,0,0,0,1,0,0,1
1,1,0,0,0,0,0,1,1,1,0,0,0,1
1,1,0,0,1,1,0,1,0,0,0,0,0,1
1,1,0,1,1,0,0,1,0,0,0,0,0,1
1,1,1,1,0,0,1,0,0,0,0,0,0,1
1,1,0,0,1,0,0,0,0,1,0,1,0,1
1,1,0,0,0,1,0,0,1,0,0,1,0,1
1,1,1,0,1,0,0,0,0,0,0,1,0,1
1,1,0,0,0,0,0,1,0,0,1,1,0,1
1,0,0,1,0,0,0,1,0,0,0,0,1,1
1,0,0,1,0,0,1,0,1,0,0,0,0,1
1,0,0,0,1,0,1,0,0,1,0,0,0,1
1,0,0,0,1,0,0,0,0,0,1,1,1,1
1,0,1,0,0,0,0,1,0,0,0,1,1,1
1,0,0,1,0,1,1,0,0,0,1,0,0,1
1,0,0,0,0,1,1,0,1,0,1,0,0,1
1,0,1,0,0,1,0,0,0,1,0,0,1,1
1,0,1,0,0,0,1,1,0,0,1,0,0,1
1,0,0,0,1,0,0,0,1,1,0,0,1,1
1,1,1,0,0,0,0,1,1,0,0,0,0,1
1,1,1,1,1,1,1,1,0,1,1,0,1,1
1,1,0,1,0,0,1,0,0,1,0,0,0,1
1,0,0,0,0,1,1,0,0,1,0,1,0,1
1,0,0,0,1,0,1,0,1,0,0,1,0,1
1,1,1,1,1,0,1,1,1,0,1,1,1,1
1,0,0,0,0,1,0,0,0,1,0,1,0,1
1,0,1,1,0,0,0,0,0,0,0,1,0,1
1,1,1,0,1,1,1,1,1,0,1,1,1,1
1,0,0,0,0,0,1,0,1,0,0,0,1,1
1,0,1,0,1,0,0,0,0,0,1,0,0,1
1,1,0,0,1,0,0,0,0,1,1,0,0,1
1,0,0,0,1,0,0,0,0,1,1,0,0,1
1,0,0,0,0,1,0,0,1,0,1,0,0,1
1,1,0,0,0,1,0,0,1,0,1,0,0,1
1,1,1,0,1,0,0,0,0,0,1,0,0,1
1,1,0,0,0,0,1,0,1,0,0,0,1,1
1,1,0,0,0,1,0,0,0,1,0,1,0,1
1,1,1,1,0,0,0,0,0,0,0,1,0,1
1,0,1,1,0,0,0,0,1,1,0,0,0,1
1,0,0,1,0,0,1,0,0,1,0,0,0,1
1,0,1,0,0,0,0,1,1,0,0,0,0,1
1,0,0,1,0,0,0,0,0,0,1,1,1,1
1,1,0,1,0,0,0,0,0,0,0,0,1,1
1,0,0,0,0,1,0,0,0,1,1,1,0,1
1,0,1,1,0,0,0,0,0,0,1,1,0,1
1,1,1,1,1,1,1,1,0,1,0,1,1,1
1,0,0,0,0,1,1,0,0,1,1,0,0,1
1,0,0,0,1,0,1,0,1,0,1,0,0,1
1,0,0,1,0,0,0,0,1,1,0,0,1,1
1,1,1,1,1,1,1,1,1,0,1,0,1,1
1,1,0,1,0,0,0,1,0,0,0,0,1,1
1,0,0,0,0,0,0,1,0,0,1,1,0,1
1,0,0,1,0,0,1,0,1,0,0,1,0,1
1,1,0,1,0,0,1,0,1,0,0,0,0,1
1,0,0,0,1,0,1,0,0,1,0,1,0,1
1,0,1,0,1,0,0,0,0,0,0,1,0,1
1,1,1,1,1,0,1,1,0,1,1,1,1,1
1,0,0,0,1,0,0,0,0,1,0,1,0,1
1,0,0,0,0,1,0,0,1,0,0,1,0,1
1,1,1,0,1,1,1,1,0,1,1,1,1,1
1,1,1,1,0,1,1,1,1,0,1,1,1,1
1,0,0,1,1,0,0,1,0,0,0,0,0,1
1,0,0,0,0,0,0,1,1,1,0,0,0,1
1,0,0,0,1,1,0,1,0,0,0,0,0,1
1,0,0,1,0,0,0,0,0,1,1,0,0,1
1,0,1,0,0,1,0,0,0,0,1,0,0,1
1,0,0,0,1,0,0,0,1,0,1,0,0,1
1,0,1,1,0,0,1,0,0,0,0,0,0,1
1,1,0,0,0,1,0,0,0,1,1,0,0,1
1,1,1,1,0,0,0,0,0,0,1,0,0,1
1,1,0,0,0,0,1,0,0,1,0,0,1,1
1,0,1,0,1,0,0,0,1,1,0,0,0,1
1,0,0,0,0,0,1,1,0,0,1,0,1,1
1,0,1,0,0,0,0,1,0,1,0,0,0,1
1,1,0,0,1,0,0,0,0,0,0,0,1,1
1,0,1,0,1,0,0,0,0,0,1,1,0,1
1,0,0,0,1,0,0,0,0,1,1,1,0,1
1,0,0,0,0,1,0,0,1,0,1,1,0,1
1,1,1,1,1,1,1,1,1,0,0,1,1,1
1,0,0,0,1,0,1,0,0,1,1,0,0,1
1,1,0,0,1,0,0,1,0,0,0,0,1,1
1,1,0,0,0,1,1,0,0,1,0,0,0,1
1,1,0,0,1,0,1,0,1,0,0,0,0,1
1,0,0,1,0,0,1,0,0,1,0,1,0,1
1,1,0,0,0,0,0,0,0,1,1,0,1,1
1,0,0,1,0,0,0,0,0,1,0,1,0,1
1,0,1,0,0,1,0,0,0,0,0,1,0,1
1,0,0,0,1,0,0,0,1,0,0,1,0,1
1,0,1,0,0,0,0,1,1,0,0,1,0,1
1,1,1,1,0,1,1,1,0,1,1,1,1,1
1,1,1,0,1,1,1,1,1,1,1,1,0,1
1,1,1,1,1,0,1,1,1,1,1,1,0,1
1,0,0,1,0,1,0,1,0,0,0,0,0,1
1,0,0,0,0,1,1,0,0,0,0,0,1,1
1,0,0,1,0,0,0,0,1,0,1,0,0,1
1,0,1,0,1,0,1,0,0,0,0,0,0,1
1,0,0,0,0,0,1,1,0,0,0,1,1,1
1,0,1,0,0,1,0,0,1,1,0,0,0,1
1,0,0,1,1,1,0,0,0,1,0,0,0,1
1,0,0,0,0,1,1,1,0,0,0,0,1,1
1,0,1,1,1,1,0,0,0,0,0,0,0,1
1,0,0,1,1,0,0,1,0,0,0,1,0,1
1,0,0,0,0,0,0,1,1,1,0,1,0,1
1,1,0,0,0,1,0,0,0,0,0,0,1,1
1,0,0,0,1,1,0,1,0,0,0,1,0,1
1,0,0,1,0,0,0,0,0,1,1,1,0,1
1,0,1,0,0,1,0,0,0,0,1,1,0,1
1,0,0,0,1,0,0,0,1,0,1,1,0,1
1,1,0,0,0,0,1,0,0,0,1,0,0,1
1,0,1,1,0,0,1,0,0,0,0,1,0,1
1,1,0,1,0,1,0,0,0,0,0,0,0,1
1,0,0,1,0,0,1,0,0,1,1,0,0,1
1,1,0,0,0,0,0,0,0,1,0,1,1,1
1,0,1,0,0,0,0,1,1,0,1,0,0,1
1,1,1,0,0,0,0,0,1,0,0,0,1,1
1,1,1,0,0,0,1,1,0,0,0,0,0,1
1,1,0,0,0,1,0,1,0,0,0,0,1,1
1,1,0,0,0,1,1,0,1,0,0,0,0,1
1,1,1,1,1,1,0,1,1,1,1,0,1,1
1,1,0,1,0,1,1,0,0,0,0,0,0,1
1,1,0,0,0,0,0,0,1,0,1,0,1,1
1,0,0,1,0,0,0,0,1,0,0,1,0,1
1,0,1,0,0,0,0,1,0,1,0,1,0,1
1,1,1,1,0,1,1,1,1,1,1,1,0,1
1,0,0,0,1,0,1,0,0,0,0,0,1,1
1,0,0,0,0,0,1,1,1,0,0,0,0,1
1,0,1,0,0,1,1,0,0,0,0,0,0,1
1,0,0,1,1,0,0,1,0,0,1,0,0,1
1,0,0,0,0,1,0,0,0,0,0,1,1,1
1,0,0,0,0,0,0,1,1,1,1,0,0,1
1,0,0,0,1,1,0,1,0,0,1,0,0,1
1,0,0,1,1,1,0,0,1,0,0,0,0,1
1,0,0,0,1,0,1,1,0,0,0,0,1,1
1,1,0,0,0,0,1,0,0,0,0,1,0,1
1,0,1,1,0,0,1,0,0,0,1,0,0,1
1,0,1,0,0,0,1,0,0,0,1,0,1,1
1,0,0,1,0,1,0,1,0,0,0,1,0,1
1,0,1,1,0,1,0,0,0,0,0,0,1,1
1,0,0,1,0,0,0,0,1,0,1,1,0,1
1,0,1,0,1,0,1,0,0,0,0,1,0,1
1,1,0,0,1,1,0,0,0,0,0,0,0,1
1,1,0,1,1,0,0,0,0,0,0,0,0,1
1,1,0,1,1,1,0,1,1,1,1,1,1,1
1,1,1,1,1,1,0,1,1,1,0,1,1,1
1,0,0,0,0,0,0,1,0,1,0,0,1,1
1,1,0,0,0,0,0,0,1,0,0,1,1,1
1,0,1,0,0,0,0,1,0,1,1,0,0,1
1,1,1,0,0,0,0,0,0,1,0,0,1,1
1,1,0,0,0,0,1,0,1,1,0,0,0,1
1,1,0,0,1,1,1,0,0,0,0,0,0,1
1,1,0,1,1,0,1,0,0,0,0,0,0,1
1,1,0,0,0,0,1,0,0,0,1,1,0,1
1,0,0,1,0,0,1,0,0,0,0,0,1,1
1,1,0,1,0,1,0,0,0,0,0,1,0,1
1,0,0,0,0,1,0,0,0,0,1,0,1,1
1,0,0,0,0,0,1,1,0,1,0,0,0,1
1,0,1,0,0,0,1,0,0,0,0,1,1,1
1,0,0,1,0,1,0,1,0,0,1,0,0,1
1,0,0,0,1,0,0,0,0,0,0,1,1,1
1,0,1,0,1,0,1,0,0,0,1,0,0,1
1,0,0,1,0,0,1,1,0,0,0,0,1,1
1,0,1,0,1,1,0,0,0,0,0,0,1,1
1,1,0,1,0,0,0,1,0,1,0,0,0,1
1,0,1,1,1,0,0,0,0,0,0,0,1,1
1,0,0,0,0,0,1,1,1,0,0,1,0,1
1,0,1,0,0,1,1,0,0,0,0,1,0,1
1,0,0,0,0,0,0,1,1,0,0,0,1,1
1,1,0,1,0,1,0,0,0,0,1,0,0,1
1,1,1,1,1,1,1,1,1,1,0,1,0,1
1,0,0,0,0,0,0,0,1,1,1,0,1,1
1,1,0,0,1,1,0,0,0,0,0,1,0,1
1,1,0,1,1,0,0,0,0,0,0,1,0,1
1,0,0,0,1,0,0,0,0,0,1,0,1,1
1,0,1,0,0,0,0,1,0,0,0,0,1,1
1,0,1,0,0,0,1,0,1,0,0,0,0,1
1,1,1,0,0,0,0,0,0,0,1,0,0,1
1,0,0,1,1,1,1,1,1,1,1,1,1,1
1,0,0,1,0,0,0,0,0,0,0,1,1,1
1,0,0,0,0,0,1,1,1,0,1,0,0,1
1,0,1,0,0,1,1,0,0,0,1,0,0,1
1,1,0,0,0,0,0,0,0,0,1,1,0,1
1,0,0,0,0,1,0,1,1,0,0,0,1,1
1,1,0,0,1,0,0,1,0,1,0,0,0,1
1,1,0,1,0,0,0,1,1,0,0,0,0,1
1,0,0,0,0,0,1,1,0,1,0,1,0,1
1,1,0,0,0,0,0,0,1,1,0,0,0,1
1,1,0,1,1,1,1,1,1,0,1,1,1,1
1,1,1,1,1,1,1,1,1,1,1,0,0,1
1,0,1,1,0,0,0,1,0,0,0,0,0,1
1,0,0,0,0,0,0,0,1,1,0,1,1,1
1,1,0,0,1,1,0,0,0,0,1,0,0,1
1,1,0,1,1,0,0,0,0,0,1,0,0,1
1,1,1,0,0,0,0,0,0,0,0,1,0,1
1,0,0,0,0,1,1,1,0,1,0,0,0,1
1,0,0,1,0,0,0,0,0,0,1,0,1,1
1,0,1,0,0,0,1,0,0,1,0,0,0,1
1,0,1,0,0,0,0,0,0,0,1,1,1,1
1,0,0,0,0,0,1,1,0,1,1,0,0,1
1,0,0,0,0,1,0,1,0,1,0,0,1,1
1,1,1,0,0,0,0,0,1,1,0,0,0,1
1,1,0,0,0,1,0,1,0,1,0,0,0,1
1,0,0,0,1,0,0,1,1,0,0,0,1,1
1,1,0,0,1,0,0,1,1,0,0,0,0,1
1,0,1,0,0,0,0,0,1,1,0,0,1,1
1,0,1,0,0,0,1,0,1,0,0,1,0,1
1,1,1,0,0,0,0,0,0,0,1,1,0,1
1,1,0,1,1,1,1,1,0,1,1,1,1,1
1,0,1,0,1,0,0,1,0,0,0,0,0,1
1,0,1,0,0,0,0,0,0,1,1,0,0,1
1,0,0,1,1,0,0,0,0,0,1,0,1,1
1,0,0,0,1,1,0,0,0,0,1,0,1,1
1,0,0,0,1,0,1,1,0,1,0,0,0,1
1,1,0,0,0,0,0,0,1,1,0,1,0,1
1,0,0,0,0,1,1,1,1,0,0,0,0,1
1,0,1,1,0,1,0,0,0,1,0,0,0,1
1,0,1,1,1,1,1,1,1,1,1,0,1,1
1,1,1,0,0,0,1,0,0,0,0,0,0,1
1,0,1,1,0,0,0,1,0,0,0,1,0,1
1,0,1,0,0,0,1,0,1,0,1,0,0,1
1,0,0,1,0,0,0,1,1,0,0,0,1,1
1,0,0,0,1,0,0,1,0,1,0,0,1,1
1,1,0,0,0,1,0,1,1,0,0,0,0,1
1,1,1,1,1,1,1,0,1,1,1,0,1,1
1,0,1,0,0,0,1,0,0,1,0,1,0,1
1,0,1,0,0,0,0,0,0,1,0,1,0,1
1,1,0,1,1,1,1,1,1,1,1,1,0,1
1,0,0,0,0,0,1,1,0,0,0,0,1,1
1,0,1,0,0,1,0,1,0,0,0,0,0,1
1,0,0,1,1,0,0,0,0,0,0,1,1,1
1,0,0,0,0,1,0,1,0,0,1,0,0,1
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1,0,1,0,0,0,0,0,1,0,1,0,0,1
1,1,0,0,0,0,0,0,1,1,1,0,0,1
1,0,1,1,1,1,1,1,1,1,0,1,1,1
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1,0,0,1,1,0,0,0,1,0,0,1,0,1
1,0,0,0,1,1,0,0,1,0,0,1,0,1
1,0,0,0,0,0,1,0,0,1,0,1,0,1
1,0,0,0,1,0,0,1,0,0,1,1,0,1
1,0,0,0,0,0,1,0,1,0,1,0,0,1
1,1,0,0,1,0,0,0,0,1,0,0,1,1
1,1,0,0,0,1,0,0,1,0,0,0,1,1
1,1,1,0,1,0,0,0,0,0,0,0,1,1
1,1,0,0,0,1,1,1,0,0,0,0,0,1
1,1,0,0,0,0,0,1,0,0,1,0,1,1
1,0,0,1,0,0,0,1,0,0,0,1,0,1
1,1,0,0,0,0,1,1,0,0,0,1,0,1
1,0,0,1,0,1,0,0,0,1,0,0,0,1
1,0,0,0,0,0,1,0,0,1,1,1,0,1
1,0,1,0,1,1,1,1,1,1,1,1,1,1
1,1,0,1,0,0,0,0,0,0,1,0,0,1
1,0,1,1,1,0,1,1,1,1,1,1,1,1
1,0,0,1,1,0,0,0,1,0,1,0,0,1
1,0,0,0,1,1,0,0,1,0,1,0,0,1
1,0,1,0,0,0,0,0,0,0,0,1,1,1
1,0,0,1,0,0,0,1,1,1,0,0,0,1
1,0,0,1,1,1,0,1,0,0,0,0,0,1
1,0,0,0,0,1,1,0,0,1,0,0,1,1
1,0,0,0,1,0,1,0,1,0,0,0,1,1
1,0,0,1,1,0,0,0,0,1,0,1,0,1
1,0,0,1,0,1,0,0,1,0,0,1,0,1
1,0,0,0,1,1,0,0,0,1,0,1,0,1
1,0,0,0,0,0,1,0,1,0,0,1,0,1
1,0,0,1,0,0,0,1,0,0,1,1,0,1
1,0,0,0,0,0,0,0,1,1,0,0,1,1
1,1,0,0,0,0,0,1,0,0,0,1,1,1
1,1,0,0,0,1,0,0,0,1,0,0,1,1
1,1,1,1,0,0,0,0,0,0,0,0,1,1
1,1,0,0,0,0,1,1,0,0,1,0,0,1
1,0,0,0,0,0,0,0,0,0,1,1,1,1
1,1,0,1,0,0,0,0,0,0,0,1,0,1
1,0,0,0,0,1,0,0,0,1,1,0,1,1
1,0,1,1,0,0,0,0,0,0,1,0,1,1
1,0,1,0,0,0,0,0,0,0,1,0,1,1
1,1,1,0,0,0,0,1,0,0,0,0,0,1
1,0,0,0,0,0,1,0,1,0,1,1,0,1
1,1,0,0,1,0,0,0,0,0,1,0,0,1
1,0,0,1,1,0,0,0,0,1,1,0,0,1
1,0,0,1,0,1,0,0,1,0,1,0,0,1
1,0,0,0,1,1,0,0,0,1,1,0,0,1
1,0,0,1,0,0,1,0,1,0,0,0,1,1
1,0,0,0,1,0,1,0,0,1,0,0,1,1
1,0,0,1,0,1,0,0,0,1,0,1,0,1
1,1,0,1,0,0,0,0,1,1,0,0,0,1
1,1,0,0,0,0,0,1,1,0,0,0,0,1
1,1,1,1,1,1,0,0,1,1,1,1,1,1
1,1,0,1,0,0,0,0,0,0,1,1,0,1
1,0,0,0,0,1,1,0,0,0,1,0,0,1
1,0,0,0,0,1,0,0,0,1,0,1,1,1
1,0,1,1,0,0,0,0,0,0,0,1,1,1
1,0,0,1,1,0,1,0,0,1,0,0,0,1
1,0,0,0,1,1,1,0,0,1,0,0,0,1
1,1,0,0,1,0,0,0,0,0,0,1,0,1
1,0,1,0,1,0,0,0,0,0,1,0,1,1
1,0,0,0,1,0,0,0,0,1,1,0,1,1
1,0,0,0,0,1,0,0,1,0,1,0,1,1
1,1,0,0,0,1,0,0,0,0,1,0,0,1
1,1,0,1,0,0,1,0,0,0,0,0,0,1
1,0,0,1,0,1,0,0,0,1,1,0,0,1
1,0,0,1,0,0,1,0,0,1,0,0,1,1
1,0,1,0,0,0,0,1,1,0,0,0,1,1
1,1,0,0,1,0,0,0,1,1,0,0,0,1
1,1,1,0,0,1,0,0,0,1,0,0,0,1
1,1,1,1,1,0,1,1,1,1,1,0,1,1
1,1,1,0,1,1,1,1,1,1,1,0,1,1
1,0,0,0,0,1,1,0,0,0,0,1,0,1
1,1,1,0,0,0,0,1,0,0,0,1,0,1
1,1,0,0,0,0,0,1,0,1,0,0,0,1
1,1,0,0,1,0,0,0,0,0,1,1,0,1
1,0,0,1,1,0,0,0,0,0,0,0,1,1
1,0,0,0,1,1,0,0,0,0,0,0,1,1
1,0,0,0,1,0,1,0,0,0,1,0,0,1
1,0,1,1,0,0,0,0,1,0,0,0,0,1
1,0,0,0,0,0,0,1,0,0,1,1,1,1
1,0,1,0,1,0,0,0,0,0,0,1,1,1
1,0,0,0,1,0,0,0,0,1,0,1,1,1
1,0,0,0,0,0,1,0,0,0,0,1,1,1
1,0,0,0,0,1,0,0,1,0,0,1,1,1
1,0,0,1,1,0,1,0,1,0,0,0,0,1
1,0,0,1,0,1,1,0,0,1,0,0,0,1
1,0,0,0,1,1,1,0,1,0,0,0,0,1
1,0,0,1,1,0,0,1,0,0,0,0,1,1
1,0,0,0,0,0,0,1,1,1,0,0,1,1
1,1,0,0,0,1,0,0,0,0,0,1,0,1
1,0,0,0,1,1,0,1,0,0,0,0,1,1
1,0,0,0,0,1,1,0,1,1,0,0,0,1
1,0,0,1,0,0,0,0,0,1,1,0,1,1
1,0,1,0,0,1,0,0,0,0,1,0,1,1
1,0,0,0,1,0,0,0,1,0,1,0,1,1
1,1,0,0,0,0,0,1,1,0,0,1,0,1
1,0,1,0,0,0,1,1,0,1,0,0,0,1
1,0,1,1,0,0,1,0,0,0,0,0,1,1
1,1,0,0,1,0,1,0,0,0,0,0,0,1
1,0,0,0,0,1,1,0,0,0,1,1,0,1
1,1,1,1,1,0,1,1,1,1,0,1,1,1
1,1,1,0,1,1,1,1,1,1,0,1,1,1
1,0,0,0,0,0,0,1,0,1,1,0,0,1
1,1,1,0,0,0,0,1,0,0,1,0,0,1
1,0,1,0,0,0,0,1,0,1,0,0,1,1
1,1,0,0,0,1,0,0,1,1,0,0,0,1
1,1,1,0,1,0,0,0,0,1,0,0,0,1
1,1,0,1,1,1,0,0,0,0,0,0,0,1
1,1,1,0,0,1,0,0,1,0,0,0,0,1
1,1,1,1,0,1,1,1,1,1,1,0,1,1
1,0,0,0,1,0,1,0,0,0,0,1,0,1
1,1,0,0,0,1,0,0,0,0,1,1,0,1
1,0,0,1,0,1,0,0,0,0,0,0,1,1
1,1,0,1,0,0,1,0,0,0,0,1,0,1
1,0,0,0,0,0,1,0,0,0,1,0,1,1
1,0,0,1,0,0,1,0,0,0,1,0,0,1
1,0,1,0,1,0,0,0,1,0,0,0,0,1
1,0,1,1,0,0,0,0,0,1,0,0,0,1
1,0,0,1,0,0,0,0,0,1,0,1,1,1
1,0,1,0,0,1,0,0,0,0,0,1,1,1
1,0,0,0,1,0,0,0,1,0,0,1,1,1
1,1,0,0,0,0,0,1,1,0,1,0,0,1
1,0,0,1,0,1,0,1,0,0,0,0,1,1
1,0,0,1,0,1,1,0,1,0,0,0,0,1
1,0,0,0,1,0,1,0,1,1,0,0,0,1
1,1,0,0,0,0,0,1,0,1,0,1,0,1
1,0,0,1,0,0,0,0,1,0,1,0,1,1
1,0,1,0,1,0,1,0,0,0,0,0,1,1
1,0,1,0,0,0,1,1,1,0,0,0,0,1
1,0,0,0,0,0,0,1,0,1,0,1,0,1
1,1,0,0,0,1,1,0,0,0,0,0,0,1
1,0,0,0,1,0,1,0,0,0,1,1,0,1
1,0,1,1,0,0,0,0,1,0,0,1,0,1
1,1,1,1,0,1,1,1,1,1,0,1,1,1
1,0,0,0,0,0,0,1,1,0,1,0,0,1
1,1,1,1,0,0,0,0,0,1,0,0,0,1
1,1,0,1,0,0,1,0,0,0,1,0,0,1
1,1,1,0,1,0,0,0,1,0,0,0,0,1
1,1,0,0,0,0,1,0,0,0,1,0,1,1
1,0,0,1,0,0,1,0,0,0,0,1,0,1
1,1,0,1,0,1,0,0,0,0,0,0,1,1
1,0,0,0,0,1,0,0,0,0,1,1,0,1
1,1,0,0,1,0,1,0,0,0,0,1,0,1
1,0,1,0,1,0,0,0,0,1,0,0,0,1
1,0,1,0,0,1,0,0,1,0,0,0,0,1
1,0,0,0,0,1,0,0,1,1,0,0,0,1
1,0,0,1,1,1,0,0,0,0,0,0,0,1
1,0,0,0,0,0,0,1,0,1,1,1,0,1
1,0,1,0,0,0,0,1,0,0,1,0,0,1
1,1,0,0,0,0,0,1,0,1,1,0,0,1
1,0,0,1,0,0,0,0,1,0,0,1,1,1
1,0,0,1,1,1,1,0,0,0,0,0,0,1
1,0,0,0,0,0,1,1,1,0,0,0,1,1
1,0,1,1,0,0,0,0,1,0,1,0,0,1
1,0,1,0,0,1,1,0,0,0,0,0,1,1
1,0,1,1,0,1,0,1,0,0,0,0,0,1
1,0,0,0,0,0,0,1,1,0,0,1,0,1
1,0,0,1,0,0,1,0,0,0,1,1,0,1
1,0,1,0,1,0,0,0,1,0,0,1,0,1
1,0,1,1,0,0,0,0,0,1,0,1,0,1
1,1,1,1,1,1,1,1,0,0,1,1,1,1
1,1,1,0,0,1,1,1,1,1,1,1,1,1
1,1,0,0,0,0,1,0,0,0,0,1,1,1
1,1,0,0,1,0,1,0,0,0,1,0,0,1
1,1,1,1,0,0,0,0,1,0,0,0,0,1
1,1,1,1,1,1,1,1,1,1,0,0,1,1
1,1,0,0,1,1,0,0,0,0,0,0,1,1
1,1,0,1,1,0,0,0,0,0,0,0,1,1
1,0,0,0,1,0,0,0,0,0,1,1,0,1
1,0,1,0,0,0,0,1,0,0,0,1,0,1
1,1,0,0,0,1,1,0,0,0,0,1,0,1
1,0,1,0,0,1,0,0,0,1,0,0,0,1
1,0,0,0,1,0,0,0,1,1,0,0,0,1
1,0,0,0,0,0,0,1,1,0,1,1,0,1
1,0,1,1,1,1,1,0,1,1,1,1,1,1
1,0,1,0,1,0,0,0,1,0,1,0,0,1
1,0,0,0,0,0,1,1,0,1,0,0,1,1
1,0,1,1,0,0,0,0,0,1,1,0,0,1
1,0,1,0,0,0,0,1,1,1,0,0,0,1
1,0,1,0,1,1,0,1,0,0,0,0,0,1
1,0,1,1,1,0,0,1,0,0,0,0,0,1
1,0,1,0,1,0,0,0,0,1,0,1,0,1
1,0,0,1,1,1,0,0,0,0,0,1,0,1
1,0,0,0,0,1,0,0,1,1,0,1,0,1
1,1,0,0,0,0,0,1,0,0,0,0,1,1
1,1,0,0,0,0,1,0,1,0,0,0,0,1
1,0,1,0,0,0,0,1,0,0,1,1,0,1
1,1,1,0,1,0,1,1,1,1,1,1,1,1
1,1,0,0,0,1,1,0,0,0,1,0,0,1
1,0,0,1,0,0,0,0,0,0,1,1,0,1
1,0,0,1,1,0,0,1,0,1,0,0,0,1
1,0,0,0,1,1,0,1,0,1,0,0,0,1
1,0,1,1,0,0,1,0,0,1,0,0,0,1
1,0,0,1,0,0,0,0,1,1,0,0,0,1
1,1,0,1,0,0,0,1,0,0,0,0,0,1
1,0,1,0,1,0,0,0,0,1,1,0,0,1
1,0,0,1,1,1,0,0,0,0,1,0,0,1
1,0,0,0,0,1,0,0,1,1,1,0,0,1
1,0,1,0,0,0,1,0,1,0,0,0,1,1
1,1,1,0,0,0,0,0,0,0,1,0,1,1
1,0,1,0,0,1,0,0,0,1,0,1,0,1
1,0,0,0,1,0,0,0,1,1,0,1,0,1
1,1,0,0,0,0,1,0,0,1,0,0,0,1
1,1,1,1,0,0,1,1,1,1,1,1,1,1
1,1,1,1,1,1,1,1,0,1,1,1,0,1
1,1,0,0,0,0,0,0,0,0,1,1,1,1
1,0,0,0,0,1,0,0,0,1,0,0,1,1
1,0,1,1,0,0,0,0,0,0,0,0,1,1
1,0,0,0,0,0,1,1,0,0,1,0,0,1
1,0,0,0,0,0,0,1,0,0,0,1,1,1
1,1,0,0,0,0,0,0,1,1,0,0,1,1
1,0,0,1,0,1,0,1,0,1,0,0,0,1
1,0,0,1,1,0,0,1,1,0,0,0,0,1
1,0,0,0,1,1,0,1,1,0,0,0,0,1
1,0,1,0,1,0,1,0,0,1,0,0,0,1
1,1,0,0,0,0,1,0,1,0,0,1,0,1
1,0,1,1,0,0,0,1,0,0,0,0,1,1
1,0,1,1,0,0,1,0,1,0,0,0,0,1
1,1,0,0,1,0,0,1,0,0,0,0,0,1
1,1,1,0,0,0,0,0,0,0,0,1,1,1
1,1,0,0,0,0,0,0,0,1,1,0,0,1
1,0,1,0,0,1,0,0,0,1,1,0,0,1
1,0,0,0,1,0,0,0,1,1,1,0,0,1
1,0,1,0,0,0,1,0,0,1,0,0,1,1
1,0,0,1,0,0,0,0,1,1,0,1,0,1
1,0,0,0,0,0,1,1,0,0,0,1,0,1
1,1,0,1,0,1,0,0,0,1,0,0,0,1
1,1,0,1,1,1,1,1,1,1,1,0,1,1
1,1,1,1,1,1,0,1,1,0,1,1,1,1
1,1,1,1,1,1,1,1,1,0,1,1,0,1
1,1,0,1,0,0,0,1,0,0,0,1,0,1
1,0,0,0,0,0,0,1,0,0,1,0,1,1
1,0,1,0,1,0,0,0,0,0,0,0,1,1
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1,0,0,0,0,1,0,0,1,0,0,0,1,1
1,0,0,0,0,1,1,1,0,0,0,0,0,1
1,1,0,0,0,0,1,0,1,0,1,0,0,1
1,0,0,1,0,1,0,1,1,0,0,0,0,1
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1,1,0,0,0,0,0,0,1,0,1,0,0,1
1,0,0,1,0,0,0,0,1,1,1,0,0,1
1,1,0,1,1,1,1,1,1,1,0,1,1,1
1,1,0,1,0,0,0,1,0,0,1,0,0,1
1,1,1,0,0,0,1,0,0,0,0,0,1,1
1,1,0,0,1,1,0,0,0,1,0,0,0,1
1,1,0,1,1,0,0,0,0,1,0,0,0,1
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1,1,0,0,0,0,0,0,0,1,1,1,0,1
1,0,0,1,0,0,0,0,0,1,0,0,1,1
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1,0,0,0,0,1,1,1,0,0,0,1,0,1
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1,1,1,0,0,0,0,0,1,0,0,1,0,1
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1,1,0,0,0,1,0,1,0,0,0,1,0,1
1,1,1,1,1,1,0,1,1,1,1,1,0,1
1,1,0,0,0,0,0,0,1,0,1,1,0,1
1,0,0,1,0,0,0,0,1,0,0,0,1,1
1,0,0,1,0,0,1,1,0,0,0,0,0,1
1,0,0,0,0,0,0,0,1,0,1,1,1,1
1,0,1,0,1,1,0,0,0,0,0,0,0,1
1,0,1,1,1,0,0,0,0,0,0,0,0,1
1,0,1,1,1,1,0,1,1,1,1,1,1,1
1,0,0,0,0,1,0,1,0,0,0,1,1,1
1,0,1,0,0,0,0,0,1,0,0,1,1,1
1,0,0,1,1,0,0,0,1,0,0,0,1,1
1,0,0,1,1,0,1,1,0,0,0,0,0,1
1,0,0,0,0,1,1,1,0,0,1,0,0,1
1,0,0,0,1,1,0,0,1,0,0,0,1,1
1,0,0,0,1,1,1,1,0,0,0,0,0,1
1,0,1,0,0,0,1,0,1,1,0,0,0,1
1,0,1,0,1,1,1,0,0,0,0,0,0,1
1,0,0,0,1,0,0,1,0,0,1,0,1,1
1,0,1,1,1,0,1,0,0,0,0,0,0,1
1,0,0,0,1,0,1,1,0,0,0,1,0,1
1,1,0,0,0,0,1,0,0,0,0,0,1,1
1,0,1,0,0,0,1,0,0,0,1,1,0,1
1,0,1,1,0,1,0,0,0,0,0,1,0,1
1,1,0,1,0,1,1,1,1,1,1,1,1,1
1,0,0,0,0,0,0,0,1,1,1,0,0,1
1,1,1,0,0,0,0,0,1,0,1,0,0,1
1,1,0,0,0,1,0,1,0,0,1,0,0,1
1,1,1,0,0,1,0,1,0,0,0,0,0,1
1,1,0,0,0,0,1,1,0,0,0,0,1,1
1,1,1,0,0,0,0,0,0,1,0,1,0,1
1,0,0,0,0,0,1,0,0,1,1,0,1,1
1,0,1,1,0,0,0,1,0,1,0,0,0,1
1,0,0,0,0,1,0,1,1,0,0,0,0,1
1,0,0,0,0,0,0,0,0,1,1,1,1,1
1,0,0,0,1,0,0,1,0,0,0,1,1,1
1,0,0,1,1,0,0,0,0,1,0,0,1,1
1,0,0,1,0,1,0,0,1,0,0,0,1,1
1,0,0,0,1,1,0,0,0,1,0,0,1,1
1,0,0,0,1,0,1,1,0,0,1,0,0,1
1,0,0,1,0,1,1,1,0,0,0,0,0,1
1,0,0,1,0,0,0,1,0,0,1,0,1,1
1,0,1,1,0,1,0,0,0,0,1,0,0,1
1,0,0,1,0,0,1,1,0,0,0,1,0,1
1,0,0,0,0,0,0,0,1,1,0,1,0,1
1,1,1,1,1,0,1,0,1,1,1,1,1,1
1,0,1,0,1,1,0,0,0,0,0,1,0,1
1,1,1,0,1,1,1,0,1,1,1,1,1,1
1,0,1,1,1,0,0,0,0,0,0,1,0,1
1,1,0,0,1,1,1,1,1,1,1,1,1,1
1,1,0,1,1,0,1,1,1,1,1,1,1,1
1,1,1,0,0,0,0,0,0,1,1,0,0,1
1,1,0,0,0,0,0,0,0,0,0,1,1,1
1,0,0,0,0,0,1,0,0,1,0,1,1,1
1,1,1,0,1,0,0,1,0,0,0,0,0,1
1,0,1,0,0,0,0,0,0,0,1,1,0,1
1,0,1,0,1,0,0,1,0,1,0,0,0,1
1,0,0,0,0,0,1,0,1,0,1,0,1,1
1,0,1,1,0,0,0,1,1,0,0,0,0,1
1,0,0,0,0,1,0,1,0,1,0,0,0,1
1,0,0,0,1,0,0,1,1,0,0,0,0,1
1,0,1,0,0,0,0,0,1,1,0,0,0,1
1,0,0,0,0,0,0,0,1,1,1,1,0,1
1,0,0,1,0,0,0,1,0,0,0,1,1,1
1,0,1,1,1,1,1,1,1,0,1,1,1,1
1,0,0,1,0,1,0,0,0,1,0,0,1,1
1,0,0,1,0,0,1,1,0,0,1,0,0,1
1,0,1,0,1,1,0,0,0,0,1,0,0,1
1,0,1,1,1,0,0,0,0,0,1,0,0,1
1,1,1,0,0,0,1,0,0,1,0,0,0,1
1,1,0,1,0,0,0,0,0,0,1,0,1,1
1,1,0,0,0,0,0,0,0,0,1,0,1,1
1,0,0,0,0,1,0,1,1,0,0,1,0,1
1,1,1,1,0,1,1,0,1,1,1,1,1,1
1,1,1,1,1,1,1,0,1,0,1,1,1,1
1,0,0,1,1,0,0,0,0,0,1,0,0,1
1,0,0,0,1,1,0,0,0,0,1,0,0,1
1,1,1,1,0,0,0,1,0,0,0,0,0,1
1,0,0,0,0,0,1,0,1,0,0,1,1,1
1,0,1,0,0,1,0,1,0,1,0,0,0,1
1,0,1,0,1,0,0,1,1,0,0,0,0,1
1,0,0,1,0,0,0,1,1,0,0,0,0,1
1,0,0,0,1,0,0,1,0,1,0,0,0,1
1,1,1,0,0,0,0,0,0,0,0,0,1,1
1,0,1,1,1,1,1,1,0,1,1,1,1,1
1,1,0,1,0,0,0,0,0,0,0,1,1,1
1,0,0,0,0,1,0,1,1,0,1,0,0,1
1,1,1,0,0,0,0,1,0,0,0,0,1,1
1,1,1,0,0,0,1,0,1,0,0,0,0,1
1,1,0,0,1,0,0,0,0,0,1,0,1,1
1,0,0,1,1,0,0,0,0,0,0,1,0,1
1,0,0,0,1,1,0,0,0,0,0,1,0,1
1,0,0,0,0,1,0,1,0,1,0,1,0,1
1,0,0,0,1,0,0,1,1,0,0,1,0,1
1,0,1,0,0,0,0,0,1,1,0,1,0,1
1,1,1,1,1,1,1,0,0,1,1,1,1,1
1,0,0,1,0,1,0,0,0,0,1,0,0,1
1,1,0,0,0,0,0,1,1,0,0,0,1,1
1,0,0,1,1,0,0,0,1,1,0,0,0,1
1,0,0,0,1,1,0,0,1,1,0,0,0,1
1,0,1,0,0,1,0,1,1,0,0,0,0,1
1,0,0,0,0,1,1,0,0,0,1,0,1,1
1,0,0,1,0,0,0,1,0,1,0,0,0,1
1,0,0,1,1,0,0,0,0,0,1,1,0,1

# Death Transitions
1,death0,death1,death2,death3,death4,death5,death6,death7,death8,death9,death10,death11,0

[bubblegum]

boink
Something I'd like to propose is the v letter for "outer-totalistic for the inner 8 cells". Additionally I'd like to define the rules of the strings so that muzik will attempt to declare something else canonical so I can shoot him down—no I'm kidding.

Each "node" of the transition consists of a number with a string of letters, numbers and hyphens after. The start of a node is a number ranging from 0 to 8. All nodes are set to the first alphabetically possible sequence.

1. If the node root and the next letter constitute a valid sequence in Hensel notation:
   1. If the next character is a letter the string of letters list transitions in the form (root)(next)(final) for final in afterletters.
   2. If it's a hyphen the string of letters list transitions in the form to be excluded from the rule and all the other transitions beginning with (root)(next) are added.
2. If the next letter is a v point 1 is repeated for every valid (root)(next) sequence.
3. If it's an x transitions are listed (with hyphens at the beginning) to be excluded from the rule and all other transitions with (root) cells are added to the list.

Following this logic AlmostLife (r2c2b9t11s6t11nw0010003330130310333000100) is (I believe, it would be pretty embarrassing if it wasn't) B2vnopqr3v-nopqr/S2v3v-nopqrV2.

Alright this thing is complicated.

[R2INT]

I have recently been experimenting with rulegolfing in R2VN, and have decided to share my thoughts on it.

One of the big novel features of R2VN is that, unlike in Moore INT, it is possible to make one cell expand infinitely via the B1e transition. In R2VN B1ea is nonrelativistic as signals can travel at 2c orthogonally, while in INT signals travel at c orthogonally, resulting in B1e creating indestructible photon frontends.

The extra cells in the R2VN neighborhood allow for more flexibility, but the tradeoff is that you need a larger pattern size to fully exploit the neighborhood. In multistate INT, you don't need to make larger patterns, because you can just shuffle the states within the pattern, giving more information per cell. R2VN still has the same information density for INT, so equal-complexity patterns are larger.

My main criticism of golfing in R2VN is that it becomes very easy to get trapped in emulating non-expanding Moore rules (similar to how low-density B2c Moore rules can simulate Margolus patterns). In some ways this is worse than 3-state INT, which also has this property, but 3-state INT has a lot of ways to break out of 2-state emulation. Here in R2VN, not so much, as there are only four nonexplosive transitions that could be used to break out (B2ea, B2ia, B3ea, B4ea), which means there's a good 1/16 chance that a random rule emulates MargolINT. Many of the rules here are non-expanding, because you need one of (B0xc, B1cc) and (B2ca, B2cc). Most often you have these disabled, so your emulated INT rule will be non-expanding, which is a significant problem because some patterns will be unable to expand freely.

In some ways this MargolINT problem is worse in R2VN than in INT because you are more likely to make decisions that lead you into the trap. In INT, either you have B2e which breaks Margolus patterns, or B3a which encourages you to not use patterns vulnerable to MargolINT-ifying. In R2VN however you have many more ways to expand, which means you are more likely to overlook the MargolINT-ification of your rule.

If your rule gets MargolINT-ified, you still have the option to enable transitions with one or two outer-edge neighbors, which encourages explosive propagation destroying the MargolINT patches. Making non-MargolINT spaceships or reactions common with some cells on both checkerboard parities helps spread non-MargolINT cells to other patches.

Overall, I think R2VN offers a nice middle ground between standard INT and 3-state INT. The main challenge now is actually finding a good rule that has interesting R2VN-specific dynamics.