B0 hyper-relativistic speeds

For discussion of other cellular automata.
AforAmpere
Posts: 1334
Joined: July 1st, 2016, 3:58 pm

B0 hyper-relativistic speeds

Post by AforAmpere » December 22nd, 2017, 3:34 pm

The purpose of this thread is to find B0 ships that transcend the speeds normally allowed in 2-state rules. One example, and the only one I know of is this 3c/4 diagonal ship:

Code: Select all

x = 3, y = 6, rule = B02357/S23456
b2o$o$obo$b2o$b2o$b2o!
This ship goes faster than anything possible without B0, which raises the question: how many other ships exist? I am unsure if any other ships are known that go faster than (m,n)c/(m+n), like this 3c/4 diagonal, or any that exist.

EDIT, a 5c/8 wave, not stablizable:

Code: Select all

x = 32, y = 31, rule = B023456-a7/S01c23456
2$27b2o$26bo$26bo$24b2o$23bo$23bo$21b2o$20bo$20bo$18b2o$17bo$17bo$15b
2o$14bo$14bo$12b2o$11bo$11bo$9b2o$8bo$8bo$6b2o$5bo$5bo!
I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules. I also wrote EPE, a tool for searching in the INT rulespace.

Things to work on:
- Find (7,1)c/8 and 9c/10 ships in non-B0 INT.
- EPE improvements.

User avatar
LaundryPizza03
Posts: 2323
Joined: December 15th, 2017, 12:05 am
Location: Unidentified location "https://en.wikipedia.org/wiki/Texas"

Re: B0 hyper-relativistic speeds

Post by LaundryPizza03 » December 22nd, 2017, 9:47 pm

AforAmpere wrote: EDIT, a 5c/8 wave, not stablizable:

Code: Select all

x = 32, y = 31, rule = B023456-a7/S01c23456
2$27b2o$26bo$26bo$24b2o$23bo$23bo$21b2o$20bo$20bo$18b2o$17bo$17bo$15b
2o$14bo$14bo$12b2o$11bo$11bo$9b2o$8bo$8bo$6b2o$5bo$5bo!
It's more of a self-replicating ripple. It's not a wave because it has C2 symmetry.

Code: Select all

x = 4, y = 3, rule = B3-q4z5y/S234k5j
2b2o$b2o$2o!
LaundryPizza03 at Wikipedia

wildmyron
Posts: 1544
Joined: August 9th, 2013, 12:45 am
Location: Western Australia

Re: B0 hyper-relativistic speeds

Post by wildmyron » January 18th, 2018, 5:28 am

Here's a very similar, but slightly smaller, example which also travels at 3c/4 diagonal

Code: Select all

x = 4, y = 3, rule = B02ace3r5kq/S2aek3n5a6ak
b2o$o2bo$2obo!
Edit:
Extensible 3c/4 diagonal tagalong. Works in many of the isotropic rules the well known 3c/4 works in, but none of the semi-totalistic ones.

Code: Select all

x = 9, y = 9, rule = B023ir4i57/S23456
2o$2o$2o$3b2o$3b2o$3b2o$6b2o$3b3o2bo$3b4obo!
Asymmetric version of the 3c/4 in rules with B4k added:

Code: Select all

x = 6, y = 3, rule = B023ir4ik57/S23456
3b2o$3o2bo$4obo!
Edit 2:
Some bilaterally symmetric 3c/4 diagonal ships:

Code: Select all

x = 74, y = 74, rule = B023457/S023456
10b2o5b2o$10b2o5b2o$6b3ob2o5b2o$6b3o7bobo$8bo7bo$8b3o6b2o$2b2o4b3o$2b
2o$2b5o$5b2o6bo11b2o5b2o$3o2b2o18b2o5b2o$3o8b3o3b3o12b2o$11bo3b5o11bob
o$9bobo2b4o13bo$13b5o14b2o$12b3o2b8obo$3b2o7b3obob9o$3o2bo5b5ob4o2bob
2o$4obo5b2o2b4ob4ob3o$11b2o2b3ob5ob2o5b2o$15b7ob7o2b2o$15b2ob11ob4o$
15b2ob2obob9obo$15b10ob6o$15b2o3b9obob2o$9b2o5b7obo3bobo$9b2o4b10o$18b
ob5o$20b6o$20bob2o$21b5o$12b2o7b3o$9b3o2bo4b3o2bo23b2o$9b4obo4b4obo20b
3o2bo$37b4ob7obo$37b6o$41b3o$34b2o5b3o$34b2o6bo$34b2o5b3o11b2o5b2o$34b
2o19b2o5b2o$35b3obo2b2o3b3o12b2o$34b6obob7o11bobo$34bob2obob7o13bo$34b
o7b2o2b2o14b2o$33b2o7b2o3b8obo$33b2o7b3obob9o$33b2o6b5ob4o2bob2o$32bob
o6b2o2b4ob4ob3o$32bo8b2o2b3ob5ob2o5b2o$33b2o10b7ob7o2b2o$45b2ob11ob4o$
45b2ob2obob9obo$45b10ob6o$45b2o3b9obob2o$39b2o5b7obo3bobo$39b2o4b10o$
48bob5o$50b6o$50bob2o$51b5o$42b2o7b3o18b2o$39b3o2bo4b3o2bo17b2o$39b4ob
o4b4obo17b2o$71bobo$65b2o4bo$65b2o5b2o5$64b2o$61b3o2bo$61b4obo!
There seems to be a bug in gfind because it doesn't find any of these ships when searching with bilateral symmetry (gfind v4.9 unmodified)

Code: Select all

> ./gfind /b023457s023456/d4n3ul240
A 3c/4 diagonal wickstretcher:

Code: Select all

x = 54, y = 54, rule = B023457/S023456
11b3o$11b3o$9b5o$9b8o$11b2ob3o$11b6o$12b8o$14b2ob3o$8b2o4b6o$2b2o4b2o
5b8o$2b2o13b2ob3o$6o11b6o$7o11b8o$4ob2o13b2ob3o$3b6o5b2o4b6o$3b7o4b2o
5b8o$3b4ob2o13b2ob3o$6b6o11b6o$6b7o11b8o$6b4ob2o13b2ob3o10b2o$9b6o5b2o
4b6o10b2o$9b7o4b2o5b5o10b2o$9b4ob2o13b4o4b2o2bobo$12b6o11b3o5b3obo$12b
7o11b2o5b2o3b2o$12b4ob2o18b3o$15b6o5b2o8b2o$15b7o4b2o7bo$15b4ob2o12b3o
$18b6o5b2o2b3o9b2o5b2o$18b7o4b2o3bo10b2o5b2o$18b7o7b3o2b3o12b2o$22bo8b
9o11bobo$29bob3ob3o13bo$28b5ob4o14b2o$27b3o2b4ob8obo$26bobo3b3obob9o$
22b5o4b5ob4o2bob2o$22b4o5b2o2b4ob4ob3o$23bobo5b2o2b3ob5ob2o5b2o$35b7ob
7o2b2o$22b2o11b2ob11ob4o$19b3o2bo10b2ob2obob9obo$19b4obo10b10ob6o$35b
2o3b9obob2o$29b2o5b7obo3bobo$29b2o4b10o$38bob5o$40b6o$40bob2o$41b5o$
32b2o7b3o$29b3o2bo4b3o2bo$29b4obo4b4obo!
I tried to find a stabilisation for the p8 wick with JLS but was unsuccessful.

p12 3c/4 diagonal frontend. Looks promising but I was unable to complete it. gfind not working for B0 searches with bilateral symmetry is annoying.

Code: Select all

x = 41, y = 41, rule = B023457/S023456
12b3o3b2o$10bob3o3b2o$9b2ob4ob3o$9b2o4b3o$9b3o3b3o5bo$10b2o3bo$10b2o2b
3obobo$7b5o4bobobo$7b5o4b5o2b3o$2b3o2b5obo2b6ob3o$b10ob2o2b2ob3o$4b6o
2b9o4b2o$3o7b4o2b5o6bo$3o6b4ob3ob4o3b3o3b2o$3o3bo4bob5o2bobo2b3o2b3o$
2b5o4bob3ob6o2b7o$3b2ob9o2b4o4b3obobo$2b3o3b5ob7o4b3ob3o6b2o$3o3b4ob3o
b3ob2o9b3o2b3o2bo$3o5b6ob13o3b2o2b4obo$6b23o2b3o$9b2o2bobo3b6ob3o$14b
2o3b3o2bobob4o$4bo3b2o9b3ob4o2b3o$8b2o9b9ob3o$8b2obob5ob2o2b5ob3ob2o$
11bob5ob10ob5o$12b6ob3o2b11o$15bo4b3o3b9o$15b3o4b4ob4obo$14b2ob2o3b8o
3b2o$13b8ob7o$13b2o3b3o5b4o$20bo4b4obo$25b4obo$18b2o$18b2o$18b2o$17bob
o$17bo$18b2o!
Edit 3: Added "diagonal" to text in several places for clarity
The 5S project (Smallest Spaceships Supporting Specific Speeds) is now maintained by AforAmpere. The latest collection is hosted on GitHub and contains well over 1,000,000 spaceships.

Semi-active here - recovering from a severe case of LWTDS.

AforAmpere
Posts: 1334
Joined: July 1st, 2016, 3:58 pm

Re: B0 hyper-relativistic speeds

Post by AforAmpere » February 2nd, 2018, 9:44 pm

(3,2)c/4:

Code: Select all

x = 2, y = 3, rule = B02aei3-enq4nrz5ijnqr6aek7c/S1c2-an3-ajqy4iknqrty5ijk6ak
bo$2o$2o!
(4,3)c/6:

Code: Select all

x = 6, y = 6, rule = B01c2-kn34-atyz5-knq6cek7e/S012-cn3-ejny4-ejk5iy6e7
2ob2o$o3bo$2o3bo$2bo$2bobo$2bo2bo!
4c/6 diagonal:

Code: Select all

x = 6, y = 6, rule = B0123jkqr4-ckyz5inqr6-k7c/S01e2-an3-ain4-enrt5-aek6-ci7c
bo3bo$ob2o$bob3o$b3o$2bobo$obo!
(5,2)c/6:

Code: Select all

x = 6, y = 6, rule = B012-an3-ijqr4-akw5aejy6ack/S012cen3-eknq4ceiryz5ceiny6cn7
2bo2bo$o$5bo2$o3b2o$b3o!
I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules. I also wrote EPE, a tool for searching in the INT rulespace.

Things to work on:
- Find (7,1)c/8 and 9c/10 ships in non-B0 INT.
- EPE improvements.

User avatar
praosylen
Posts: 2443
Joined: September 13th, 2014, 5:36 pm
Location: Pembina University, Home of the Gliders
Contact:

Re: B0 hyper-relativistic speeds

Post by praosylen » February 2nd, 2018, 10:27 pm

(5,4)c/6, new record high speed:

Code: Select all

x = 5, y = 3, rule = B02-en3-einq4cejy5aknqy6eik7e/S01c2ack3aein4aeijknr5cjknq6a
b3o$2obo$5o!
(5,4)c/6 = √(41)/6c = 1.067187372...c > 1.060660171...c = √(18)/4c = (3,3)c/4.

EDIT: Smaller (in gen 5):

Code: Select all

x = 5, y = 4, rule = B012-ae3-aj4ceikqry5er6ikn7/S01c2c3cjnr4ekwz5acjkn7
o3bo$4bo$3b2o$o2bo!
Last edited by praosylen on February 2nd, 2018, 10:37 pm, edited 2 times in total.
former username: A for Awesome
praosylen#5847 (Discord)

The only decision I made was made
of flowers, to jump universes to one of springtime in
a land of former winter, where no invisible walls stood,
or could stand for more than a few hours at most...

AforAmpere
Posts: 1334
Joined: July 1st, 2016, 3:58 pm

Re: B0 hyper-relativistic speeds

Post by AforAmpere » February 2nd, 2018, 10:31 pm

A for awesome wrote:new record high speed
What do you mean? I found a bunch of 3-cell ships:

3c/4 diagonal:

Code: Select all

x = 3, y = 3, rule = B02aik3anr4aw5ae6ai7e/S01e3a5aq6c7e
o$2bo$bo!
(3,2)c/4:

Code: Select all

x = 2, y = 4, rule = B02-en3-ciqy4ackny5aijq6a7c/S12ac3ajk4c6n7e
bo$o2$bo!
(3,1)c/4:

Code: Select all

x = 3, y = 3, rule = B01c2aci3acinr4acrt5ijn6c7e/S1c23aein4irz5ci6ace
2bo2$2o!
5c/6:

Code: Select all

x = 2, y = 3, rule = B01c2ikn3aceir4aitz5ackr6ikn/S02ik3ek4ceinqz5iry6-k
bo$o$bo!
4c/6 diagonal:

Code: Select all

x = 3, y = 4, rule = B01e2cin3ajkny4ajty5nqr6en8/S1c2ack3eknqr4aj5ar6a
o2$bo$2bo!
I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules. I also wrote EPE, a tool for searching in the INT rulespace.

Things to work on:
- Find (7,1)c/8 and 9c/10 ships in non-B0 INT.
- EPE improvements.

User avatar
praosylen
Posts: 2443
Joined: September 13th, 2014, 5:36 pm
Location: Pembina University, Home of the Gliders
Contact:

Re: B0 hyper-relativistic speeds

Post by praosylen » February 2nd, 2018, 10:35 pm

AforAmpere wrote:
A for awesome wrote:new record high speed
What do you mean?
See my edit. I was referring to the Euclidean norm of the speed.

EDIT: Even faster, (7,5)c/8 (4 cells in gen. 1; Euclidean speed of 1.075290658...c):

Code: Select all

x = 4, y = 8, rule = B012-ai3-ajqr4ikqrty5kry6eik/S012acn3ik4-jnqrw5k6en7
o2bo4$3bo2$bobo$o2bo!
The ultimate limit, of course, is (2,1)c/2, which corresponds to a Euclidean speed of 1.118033988...c. That speed may or may not actually be attainable, and it may also be attainable only in limit, with speeds infinitely (for all practical purposes) approaching, but not reaching, (2,1)c/2.
former username: A for Awesome
praosylen#5847 (Discord)

The only decision I made was made
of flowers, to jump universes to one of springtime in
a land of former winter, where no invisible walls stood,
or could stand for more than a few hours at most...

User avatar
77topaz
Posts: 1496
Joined: January 12th, 2018, 9:19 pm

Re: B0 hyper-relativistic speeds

Post by 77topaz » February 3rd, 2018, 1:11 am

I don't think the Euclidean norm is an entirely accurate/representative way of measuring spaceship speeds, though, because it doesn't entirely fit with the Moore neighbourhood. This is because the Euclidean distance between two diagonally touching cells is √2 that between two orthogonally touching cells, but in the Moore neighbourhood they are treated as equally distant. This discrepancy causes the Euclidean norm to produce more obviously discrepant results at high speeds, such as suggesting a (7,5)c/8 ship using the Moore neighbourhood is moving faster than c, when this is by the definition of the Moore neighbourhood and c impossible.

AforAmpere
Posts: 1334
Joined: July 1st, 2016, 3:58 pm

Re: B0 hyper-relativistic speeds

Post by AforAmpere » February 3rd, 2018, 12:15 pm

5c/8 d:

Code: Select all

x = 5, y = 5, rule = B012n3-ein4eijkt5cjq6cen7e8/S02-ae3-acn4jkqtwy5acjry6ckn7
bo2bo$o2bo$3bo$b3o$o3bo!
I manage the 5S project, which collects all known spaceship speeds in Isotropic Non-totalistic rules. I also wrote EPE, a tool for searching in the INT rulespace.

Things to work on:
- Find (7,1)c/8 and 9c/10 ships in non-B0 INT.
- EPE improvements.

User avatar
vyznev
Posts: 27
Joined: April 23rd, 2016, 4:08 am

Re: B0 hyper-relativistic speeds

Post by vyznev » February 4th, 2018, 2:04 am

I just posted a bunch of small ships in B0 rules in another thread.

The linked post includes ships with slopes (X,Y)c/2P for all 0 ≤ YX < 2P ≤ 8, with the exception of (5,5)c/6 and (7,3..7)c/8, as well as orthogonal (2P,0)c/2P photons for all 0 < 2P ≤ 8.

As I also noted elsewhere, at least (2,1)c/2 appears to be impossible. Off the top of my head I'd conjecture that isotropic 8-neighbor CA rules with B0 can probably support ships with all sublight speeds and slopes, as well as orthogonal photons, but that diagonal and oblique photons are impossible.

I don't (yet) have a proof for the impossibility of oblique lightspeed ships in B0 rules, but I do suspect that, as in the linked LLS-assisted impossibility proof for (2,1)c/2, it might be possible to prove this by considering the outermost live cells in the first and last rows/columns of the ship (in the direction where the ship moves at lightspeed), and showing that these corner cells cannot both advance and retreat obliquely at lightspeed.

EDIT: The conjecture I made above is wrong; as Majestas32 pointed out in the other thread, 3c/4 is the fastest diagonal speed possible, since any rule where the leading corner can advance diagonally on both even and odd generations will explode. The same argument, of course, rules out oblique (X,Y)c/2P ships with X + Y > 3P, as the best you can possibly do is have the leading corner advance by a knight's move every two generations.

kiho park
Posts: 86
Joined: September 24th, 2010, 12:16 am

Re: B0 hyper-relativistic speeds

Post by kiho park » October 5th, 2020, 10:12 pm

I have a question.
Yesterday, I posted this (3,7)c/8 B0 spaceship on 5S project thread.
But I didn't know they decided not to posting B0 ships on 5S thread, So can I post this (3,7)c/8 spaceship here too?

Edit : (4,7)c/8

Code: Select all

x = 20, y = 23, rule = B02an3-eiry4ceinqz5aci6an8/S01e2ace4etwz5acn6cn7e
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbboobbbbbbbbb$
bbbbbbbbbbobbbbbbbbb$
bbbbbbbbboobbbbbbbbb$
bbbbbbbbbbobbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb!
Can small adjustable spaceships overrun the speed limit of (|x|+|y|)/P = 1?

## B0 rules are the best! ##

wildmyron
Posts: 1544
Joined: August 9th, 2013, 12:45 am
Location: Western Australia

Re: B0 hyper-relativistic speeds

Post by wildmyron » October 12th, 2020, 5:59 am

kiho park wrote:
October 5th, 2020, 10:12 pm
Yesterday, I posted this (3,7)c/8 B0 spaceship on 5S project thread.
But I didn't know they decided not to posting B0 ships on 5S thread, So can I post this (3,7)c/8 spaceship here too?
Yes, this is the appropriate place to post such ships. It's fine having a link to the ship but you should feel free to repost it here too (or edit into your previous post).
The 5S project (Smallest Spaceships Supporting Specific Speeds) is now maintained by AforAmpere. The latest collection is hosted on GitHub and contains well over 1,000,000 spaceships.

Semi-active here - recovering from a severe case of LWTDS.

kiho park
Posts: 86
Joined: September 24th, 2010, 12:16 am

Re: B0 hyper-relativistic speeds

Post by kiho park » October 12th, 2020, 8:32 am

wildmyron wrote:
October 12th, 2020, 5:59 am
Yes, this is the appropriate place to post such ships. It's fine having a link to the ship but you should feel free to repost it here too (or edit into your previous post).
Thank you for advising. But, is there any proper place post non-hyper speed B0 ships?

And here is (3,7)c/8 I posted 5s thread.

Code: Select all

x = 20, y = 23, rule = B01e2cek3cjnqr4ry5ekqr7e/S02ai3er4qtw5r6ak
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbobbbbbbbbb$
bbbbbbbbbbobbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbboobbbbbbbbb$
bbbbbbbbbbobbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbb!
Can small adjustable spaceships overrun the speed limit of (|x|+|y|)/P = 1?

## B0 rules are the best! ##

User avatar
wwei47
Posts: 1653
Joined: February 18th, 2021, 11:18 am

Re: B0 hyper-relativistic speeds

Post by wwei47 » April 25th, 2021, 1:19 am

(4,1)c/4, found with LLS:

Code: Select all

x = 13, y = 2, rule = B02ace3ce4anrw5ej6ae7e/S1c2n3ae4cei5enry6aci
2o2bobo3b3o$2o4bob2ob2o!
EDIT: 13 cells. The rule also has a (9,6)c/10 engine.

Code: Select all

x = 13, y = 2, rule = B02-n3ajnr4iqw5ainq6ei7e/S012e3anq4acnq5qr6ac
2o2bobo3b3o$2ob2o6b2o!

Code: Select all

x = 9, y = 6, rule = B02-n3ajnr4iqw5ainq6ei7e/S012e3anq4acnq5qr6ac
b4o$b4o2bo$obo3b3o$2o6bo$obo4b2o$7b2o!
Help me find high-period c/2 technology!
My guide: https://bit.ly/3uJtzu9
My c/2 tech collection: https://bit.ly/3qUJg0u
Overview of periods: https://bit.ly/3LwE0I5
Most wanted periods: 76,116

kiho park
Posts: 86
Joined: September 24th, 2010, 12:16 am

Re: B0 hyper-relativistic speeds

Post by kiho park » April 25th, 2021, 10:22 am

wwei47 wrote:
April 25th, 2021, 1:19 am
(4,1)c/4, found with LLS:
Wow :o I never thought that it is possible, I even not tried to search that!

wwei47 wrote:
April 25th, 2021, 1:19 am
EDIT: 13 cells. The rule also has a (9,6)c/10 engine.
I already found smaller (9,6)c/10 on my own topic.
Can small adjustable spaceships overrun the speed limit of (|x|+|y|)/P = 1?

## B0 rules are the best! ##

User avatar
wwei47
Posts: 1653
Joined: February 18th, 2021, 11:18 am

Re: B0 hyper-relativistic speeds

Post by wwei47 » April 25th, 2021, 10:39 am

kiho park wrote:
April 25th, 2021, 10:22 am
wwei47 wrote:
April 25th, 2021, 1:19 am
(4,1)c/4, found with LLS:
Wow :o I never thought that it is possible, I even not tried to search that!
Well, I ran a search for candidate frontends and rules. Knowing how long P4 would take to filter to a reasonable level, I tried to constrain the search to only have two alternating rules. There was exactly one frontend-rule pair I found, and over 8 hours later, I completed this spaceship by hand.

Code: Select all

x = 13, y = 9, rule = B2aci3cer4jy5e/S1e2ae3n4aknrw5r|B13inr5k/S1e2ae4z
2o2b3o2bob2o$bo8b2o$10bo$o11bo$7bo$11bo$8bo$bo5bo$3bo2bo!
I then wondered if it was possible in a single rule with B0, and sure enough, it was.
The program itself works by making the observation that the front row cannot be affected in any way by the rows behind it. This reduces the problem of finding the first row to finding spaceships in alternating symmetric 1-dimensional rules. According to my notes, this one was alternating between rules 104 and 150.

Code: Select all

x = 19, y = 29, rule = B2aci3cer4jy5e/S1e2ae3n4aknrw5rHistory|B13inr5k/S1e2ae4zHistory
4.A2.A$2.A5.A$9.A$12.A$8.A$.A11.A$11.A$2.A8.2A$.2C2.3C2.C.2C$.2D2.D.D
3.3D$D2.3D.2D.D.D.D$3.D.5D.D.D$2.2D2.3D2.D.2D$2.2D2.D.D3.3D$.D2.3D.2D
.D.D.D$4.D.5D.D.D$3.2D2.3D2.D.2D$3.2D2.D.D3.3D$2.D2.3D.2D.D.D.D$5.D.5D
.D.D$4.2D2.3D2.D.2D$4.2D2.D.D3.3D$3.D2.3D.2D.D.D.D$6.D.5D.D.D$5.2D2.3D
2.D.2D$5.2D2.D.D3.3D$4.D2.3D.2D.D.D.D$7.D.5D.D.D$6.2D2.3D2.D.2D!

Code: Select all

x = 13, y = 1, rule = W104_W150
2A2.3A2.A.2A!
@RULE W104_W150
@TABLE
n_states:3
neighborhood:Moore
symmetries:none
0,1,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,1,2
0,0,1,0,0,0,0,0,1,2
0,0,2,0,0,0,0,0,0,1
0,0,0,0,0,0,0,0,2,1
0,2,0,0,0,0,0,0,0,1
0,2,2,0,0,0,0,0,2,1
With the hyper-relativistic speed research, I thought it would be worth posting these here, even though they don't actually use B0.

I also found (3,1)c/3 and (3,2)c/4 (Edit 3: (3,2)c/3) spaceships. Yes, the second one is even faster than (2,1)c/2. While these periods are impossible with B0, they are possible if we alternate 3 rules.
(3,1)c/3s:

Code: Select all

x = 25, y = 5, rule = B1c3nr_S_B1c2a4ny_S_B2ac3r_S
A2.2A15.A2.2A2$3.A19.A2$2.A!
2c/3d is also possible (Rule is B1c2a/S|B1c2a/S|B/S2ae):

Code: Select all

x = 2, y = 2, rule = 2c3d
2o$bo!
@RULE 2c3d

@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4reflect

var a0={0,1,2,3}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6

0,0,1,0,0,0,0,0,0,2
0,1,1,0,0,0,0,0,0,2

0,0,2,0,0,0,0,0,0,3
0,2,2,0,0,0,0,0,0,3

3,3,0,3,0,0,0,0,0,1
3,3,3,0,0,0,0,0,0,1

1,a0,a1,a2,a3,a4,a5,a6,a7,0
2,a0,a1,a2,a3,a4,a5,a6,a7,0
3,a0,a1,a2,a3,a4,a5,a6,a7,0
And 3c/4d (Rule is B1c2a/S|B1c2a/S|B1c2a/S|B/S2e3r):

Code: Select all

x = 2, y = 2, rule = 3c4d
2o$bo!
@RULE 3c4d

@TABLE
n_states:5
neighborhood:Moore
symmetries:rotate4reflect

var a0={0,1,2,3,4}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6

0,0,1,0,0,0,0,0,0,2
0,1,1,0,0,0,0,0,0,2

0,0,2,0,0,0,0,0,0,3
0,2,2,0,0,0,0,0,0,3

0,0,3,0,0,0,0,0,0,4
0,3,3,0,0,0,0,0,0,4

4,4,0,4,0,0,0,0,0,1
4,4,4,0,0,4,0,0,0,1

1,a0,a1,a2,a3,a4,a5,a6,a7,0
2,a0,a1,a2,a3,a4,a5,a6,a7,0
3,a0,a1,a2,a3,a4,a5,a6,a7,0
4,a0,a1,a2,a3,a4,a5,a6,a7,0
One can get whatever diagonal speed they want by alternating B1c2a/S and B/S2ae or B/S2e3r, depending on the period.

I saved the best for last. (3,2)c/3:

Code: Select all

x = 34, y = 6, rule = B12c3ir_S_B13cq7e_S2i3qr4i5n6k_B2ac3cr4j_S2e
3.A4.2A.3A12.A.2A.3A2$9.A2.A16.A2.A2$A$3.A!
@RULE B12c3ir_S_B13cq7e_S2i3qr4i5n6k_B2ac3cr4j_S2e
@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,0,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,1,2
0,1,1,0,0,0,0,0,1,2
0,0,2,0,0,0,0,0,0,3
0,2,0,0,0,0,0,0,0,3
0,3,3,0,0,0,0,0,0,1
0,0,3,0,0,0,0,0,3,1
0,1,1,0,0,1,0,0,0,2
2,2,0,0,2,2,0,0,0,3
2,2,0,0,0,2,0,0,0,3
0,0,2,0,2,0,2,0,0,3
0,0,2,2,2,2,2,2,2,3
2,2,2,0,0,0,2,0,0,3
0,3,3,0,0,3,0,0,0,1
0,0,3,0,3,0,3,0,0,1
2,2,2,0,2,2,0,0,0,3
3,3,0,3,0,0,0,0,0,1
0,2,2,0,0,0,2,0,0,3
2,2,2,0,2,2,2,2,0,3
2,2,0,2,2,2,2,0,0,3
0,3,3,0,0,3,0,3,0,1
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
EDIT: (3,1)c/3 with the ruletable:

Code: Select all

x = 25, y = 5, rule = B1c3nr_S_B1c2a4ny_S_B2ac3r_S
A2.2A15.A2.2A2$3.A19.A2$2.A!
@RULE B1c3nr_S_B1c2a4ny_S_B2ac3r_S
@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,0,1,0,0,0,0,0,0,2
0,0,2,0,0,0,0,0,0,3
0,2,2,0,0,0,0,0,0,3
0,3,3,0,0,0,0,0,0,1
0,0,3,0,0,0,0,0,3,1
0,1,1,0,0,1,0,0,0,2
0,1,1,0,1,0,0,0,0,2
0,2,2,0,2,0,2,0,0,3
0,0,2,0,2,2,2,0,0,3
0,3,3,0,0,3,0,0,0,1
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 2: I sadly don't think that B0 generations could support such a fast ship. When the background went into the refractory state, it would block any such ship from advancing.
Edit 3: (4,2)c/4 impossible with 2 rules and therefore B0. Trying with 4 rules next.
Edit 4: Linking some other resources here:
search.php?st=0&sk=t&sd=d&sr=posts&keyw ... 1&start=25
search.php?st=0&sk=t&sd=d&sr=posts&keyw ... d%5B%5D=11
Edit 5: (4,2)c/4 with 4 alternating rules:

Code: Select all

x = 4, y = 3, rule = B1c2cS_B1c2iS_B12ek3cy4iS1_B1e2c3iS3i4ij6i
2A.A$A2.A$.2A!
@RULE B1c2cS_B1c2iS_B12ek3cy4iS1_B1e2c3iS3i4ij6i
@TABLE
n_states:5
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3,4}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,0,1,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,1,2
0,0,2,0,0,0,0,0,0,3
0,2,0,0,0,2,0,0,0,3
0,0,3,0,0,0,0,0,0,4
0,3,0,0,0,0,0,0,0,4
3,0,3,0,0,0,0,0,0,4
0,3,0,0,3,0,0,0,0,4
0,3,3,0,3,3,0,0,0,4
0,0,3,0,3,0,3,0,0,4
0,3,0,3,0,0,0,0,0,4
3,3,0,0,0,0,0,0,0,4
0,3,0,0,3,0,3,0,0,4
0,4,0,0,0,0,0,0,0,1
0,0,4,0,0,0,0,0,4,1
0,4,4,0,0,0,0,0,4,1
4,0,4,4,4,0,0,0,0,1
4,4,4,0,4,4,0,0,0,1
4,4,4,0,0,4,0,4,0,1
4,0,4,4,4,0,4,4,4,1
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Help me find high-period c/2 technology!
My guide: https://bit.ly/3uJtzu9
My c/2 tech collection: https://bit.ly/3qUJg0u
Overview of periods: https://bit.ly/3LwE0I5
Most wanted periods: 76,116

kiho park
Posts: 86
Joined: September 24th, 2010, 12:16 am

Re: B0 hyper-relativistic speeds

Post by kiho park » April 29th, 2021, 9:56 am

This isn't completed result. But, I found (2,6)c/6 reaction while I play with 2 cycle alternative 1D CA.

Code: Select all

x = 7, y = 7, rule = B01e2c3iS5i6c7eHistory
D2.2D6$2.A2.2A!
Can small adjustable spaceships overrun the speed limit of (|x|+|y|)/P = 1?

## B0 rules are the best! ##

User avatar
wwei47
Posts: 1653
Joined: February 18th, 2021, 11:18 am

Re: B0 hyper-relativistic speeds

Post by wwei47 » April 29th, 2021, 10:55 am

kiho park wrote:
April 29th, 2021, 9:56 am
This isn't completed result. But, I found (2,6)c/6 reaction while I play with 2 cycle alternative 1D CA.
Nice! Thanks for sparing me the chocolate search on that.
EDIT: Here are some other hyper-relativistic speeds in alternating rules. An interesting challenge would be to find an (m,n)c/m ship in a nonexplosive rule. The thing is, even if you know how to tame B2a AND you know how to tame B1e, this is still uniquely difficult because you have to deal with B1c too.
(4,2)c/5

Code: Select all

x = 87, y = 32, rule = B2aS_B2aeS_B1c4kS1c_B2e3nS1c_B2aS1e
.A9.2A18.2A18.2A28.2A3.A$.A8.A2.A16.A2.A16.A2.A32.A$2A8.A2.A16.A2.A
16.A2.A29.A.2A$11.2A18.2A18.2A$81.A$81.A$80.2A2$15.2A18.2A18.2A$14.A
2.A16.A2.A16.A2.A$14.A2.A16.A2.A16.A2.A$15.2A18.2A18.2A5$19.2A18.2A
18.2A$18.A2.A16.A2.A16.A2.A$18.A2.A16.A2.A16.A2.A$19.2A18.2A18.2A5$
23.2A3.A14.2A18.2A$22.A5.A13.A2.A16.A2.A$22.A2.A.2A13.A2.A16.A2.A$23.
2A18.2A18.2A$43.2A3.A19.A$42.A5.A19.A$42.A2.A.2A18.2A$43.2A!x = 7, y = 7, rule = B2aS_B2aeS_B1c4kS1c_B2e3nS1c_B2aS1e
4.3A$4.A2$4.A$6.A$3A3.A$A!
@RULE B2aS_B2aeS_B1c4kS1c_B2e3nS1c_B2aS1e
@TABLE
n_states:6
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3,4,5}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,1,1,0,0,0,0,0,0,2
0,2,2,0,0,0,0,0,0,3
0,2,0,2,0,0,0,0,0,3
0,0,3,0,0,0,0,0,0,4
0,3,3,0,3,0,0,3,0,4
3,0,3,0,0,0,0,0,0,4
0,4,0,4,0,0,0,0,0,5
0,4,4,0,4,0,0,0,0,5
4,0,4,0,0,0,0,0,0,5
0,5,5,0,0,0,0,0,0,1
5,5,0,0,0,0,0,0,0,1
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
(4,3)c/5:

Code: Select all

x = 32, y = 10, rule = B2aS_B1cS2k_B1cS2c_B2eS2c_B2aS1e
6.2A22.2A$6.A23.A$2A.2A.A23.A$A3.A$A3.A8.2A$13.A$13.A$9.A$9.A$7.A.A!
@RULE B2aS_B1cS2k_B1cS2c_B2eS2c_B2aS1e
@TABLE
n_states:6
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3,4,5}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,1,1,0,0,0,0,0,0,2
0,0,2,0,0,0,0,0,0,3
2,2,0,0,2,0,0,0,0,3
0,0,3,0,0,0,0,0,0,4
3,0,3,0,3,0,0,0,0,4
0,4,0,4,0,0,0,0,0,5
4,0,4,0,4,0,0,0,0,5
0,5,5,0,0,0,0,0,0,1
5,5,0,0,0,0,0,0,0,1
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
(4,3)c/4:

Code: Select all

x = 4, y = 3, rule = B12c3rS_B12e4aS012a_B12cn3jq7cS2a4n_B2aci4r6nS2a4n
2A.A$A2.A$.2A!
@RULE B12c3rS_B12e4aS012a_B12cn3jq7cS2a4n_B2aci4r6nS2a4n
@TABLE
n_states:5
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3,4}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,0,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,1,2
0,0,2,0,0,0,0,0,0,3
0,2,0,0,0,0,0,0,0,3
0,0,3,0,0,0,0,0,0,4
0,3,0,0,0,0,0,0,0,4
0,4,4,0,0,0,0,0,0,1
0,0,4,0,0,0,0,0,4,1
2,2,0,0,0,0,0,0,0,3
0,4,0,0,0,4,0,0,0,1
0,0,3,0,3,0,0,0,0,4
3,3,3,0,0,0,0,0,0,4
0,1,1,0,0,1,0,0,0,2
0,2,2,2,2,0,0,0,0,3
0,0,3,0,0,0,3,0,0,4
2,0,0,0,0,0,0,0,0,3
2,0,2,0,0,0,0,0,0,3
2,2,2,0,0,0,0,0,0,3
0,3,3,0,0,0,3,0,0,4
0,3,3,0,0,0,0,3,0,4
3,0,3,3,3,0,3,0,0,4
0,2,0,2,0,0,0,0,0,3
0,3,3,3,3,3,3,3,0,4
0,4,4,4,0,4,0,0,0,1
0,4,4,4,0,4,4,4,0,1
4,0,4,4,4,0,4,0,0,1
4,4,4,0,0,0,0,0,0,1
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 2: (6,2)c/6 complete!

Code: Select all

x = 5, y = 4, rule = B01e2ce3-aeqr4ejknrz5enqry6-ei7e8/S1e2ack3ejkqy4-ackq5-any6-ai7e
2o2bo$obobo$2ob2o$5o!
Edit 3: Either (6,1)c/6 is impossible, or there's a bug in chocolate. Given that I literally just fixed a subperiodic rule bug, I have a feeling that (6,1)c/6 might be impossible.
Help me find high-period c/2 technology!
My guide: https://bit.ly/3uJtzu9
My c/2 tech collection: https://bit.ly/3qUJg0u
Overview of periods: https://bit.ly/3LwE0I5
Most wanted periods: 76,116

kiho park
Posts: 86
Joined: September 24th, 2010, 12:16 am

Re: B0 hyper-relativistic speeds

Post by kiho park » May 1st, 2021, 3:08 am

wwei47 wrote:
April 29th, 2021, 10:55 am
Either (6,1)c/6 is impossible, or there's a bug in chocolate. Given that I literally just fixed a subperiodic rule bug, I have a feeling that (6,1)c/6 might be impossible.
I think that's because of its impossible. I both tried LLS search and 1D random soup but I can only found (1,4)c/4 and (2,6)c/6.
I have no idea if there is more (x,y)c/x. There will be no more thing except higher period such as (n,4n)c/4n, (2n,6n)c/6n in range 1 moore INT rulespace.

Edit : I tried all period less or equal to 16.
Can small adjustable spaceships overrun the speed limit of (|x|+|y|)/P = 1?

## B0 rules are the best! ##

User avatar
wwei47
Posts: 1653
Joined: February 18th, 2021, 11:18 am

Re: B0 hyper-relativistic speeds

Post by wwei47 » May 1st, 2021, 2:28 pm

kiho park wrote:
May 1st, 2021, 3:08 am
I think that's because of its impossible. I both tried LLS search and 1D random soup but I can only found (1,4)c/4 and (2,6)c/6.
I have no idea if there is more (x,y)c/x. There will be no more thing except higher period such as (n,4n)c/4n, (2n,6n)c/6n in range 1 moore INT rulespace.

Edit : I tried all period less or equal to 16.
It might be possible. There's that B0 rule with the 1D CA ships.
viewtopic.php?f=11&t=750&p=5236&hilit=B0%2A#p5236
Also, smaller (6,2)c/6:

Code: Select all

x = 17, y = 20, rule = B01e2c3-r4-aeq5ejkny6-ac78/S1e2ain3cikry4-yz5cijkn6-ai7e
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbboobbobbbbbbb$
bbbbbobboobbbbbbb$
bbbbboobbobbbbbbb$
bbbbbooooobbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb!
EDIT: 13 cells:

Code: Select all

x = 17, y = 20, rule = B01e2-an3eiqry4ejknz5-acr6ac78/S012i3cejqr4-jknqz5ceiry6ck7e
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbboobbobbbbbbb$
bbbbboobbobbbbbbb$
bbbbbobbbobbbbbbb$
bbbbbooooobbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb!
Edit 2: 10 cells:

Code: Select all

x = 17, y = 20, rule = B01e2c3cein4jq5inqr6-ai7/S012ek3ceiky4-aejnqz5-acnq6-a7e
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbboobbobbbbbbb$
bbbbbobbbobbbbbbb$
bbbbbobobobbbbbbb$
bbbbbobbbobbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbb!
Help me find high-period c/2 technology!
My guide: https://bit.ly/3uJtzu9
My c/2 tech collection: https://bit.ly/3qUJg0u
Overview of periods: https://bit.ly/3LwE0I5
Most wanted periods: 76,116

kiho park
Posts: 86
Joined: September 24th, 2010, 12:16 am

Re: B0 hyper-relativistic speeds

Post by kiho park » May 1st, 2021, 6:54 pm

wwei47 wrote:
May 1st, 2021, 2:28 pm
It might be possible. There's that B0 rule with the 1D CA ships.
Hmm.. I can't understand why my LLS search says unsatisfiable. May i wrong the search text? :roll:
Can small adjustable spaceships overrun the speed limit of (|x|+|y|)/P = 1?

## B0 rules are the best! ##

User avatar
wwei47
Posts: 1653
Joined: February 18th, 2021, 11:18 am

Re: B0 hyper-relativistic speeds

Post by wwei47 » May 1st, 2021, 7:17 pm

kiho park wrote:
May 1st, 2021, 6:54 pm
Hmm.. I can't understand why my LLS search says unsatisfiable. May i wrong the search text? :roll:
Can I see the input file?
Help me find high-period c/2 technology!
My guide: https://bit.ly/3uJtzu9
My c/2 tech collection: https://bit.ly/3qUJg0u
Overview of periods: https://bit.ly/3LwE0I5
Most wanted periods: 76,116

kiho park
Posts: 86
Joined: September 24th, 2010, 12:16 am

Re: B0 hyper-relativistic speeds

Post by kiho park » May 2nd, 2021, 1:24 am

wwei47 wrote:
May 1st, 2021, 7:17 pm
Can I see the input file?
Here is explicit soup for (2,10)c/10.

Code: Select all

x = 19, y = 1, rule = B026/S1
o2bobobo2b5o3bo!
Edit :

Code: Select all

x = 21, y = 11, rule = B02acS5i7eHistory
2.D2.D.D.D2.5D3.D10$A2.A.A.A2.5A3.A!

However, When I run this text

Code: Select all

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 aa ab ac ad ae af b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 ba bb bc bd be bf 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'
1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1' 1'

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 a0 a1 a2 a3 a4 a5 a6 a7 a8 a9 aa ab ac ad ae af b0 b1 b2 b3 b4 b5 b6 b7 b8 b9 ba bb bc bd be bf 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0' 0'
Then I get this result.

Code: Select all

Getting search pattern...
Done

Preprocessing...
Done

Number of undetermined cells: 410
Number of variables: 419
Number of clauses: 5711

Active width: 50
Active height: 11
Active duration: 11

Solving...
Done

Time taken: 3.72562193871 seconds

Unsatisfiable
Can small adjustable spaceships overrun the speed limit of (|x|+|y|)/P = 1?

## B0 rules are the best! ##

User avatar
wwei47
Posts: 1653
Joined: February 18th, 2021, 11:18 am

Re: B0 hyper-relativistic speeds

Post by wwei47 » May 2nd, 2021, 10:53 am

kiho park wrote:
May 2nd, 2021, 1:24 am
Then I get this result.

Code: Select all

Getting search pattern...
Done

Preprocessing...
Done

Number of undetermined cells: 410
Number of variables: 419
Number of clauses: 5711

Active width: 50
Active height: 11
Active duration: 11

Solving...
Done

Time taken: 3.72562193871 seconds

Unsatisfiable
I've DMed Macbi to ask them to help you.
EDIT: Weird, I get results from LLS.

Code: Select all

$ ./lls -S kissat --rule pB0c12345678/S012345678 kihoparktest1.txt

Getting search pattern...
Done

Preprocessing...
Done

Number of undetermined cells: 410
Number of variables: 421
Number of clauses: 5911

Active width: 50
Active height: 11
Active duration: 11

Solving...
Done

Time taken: 0.153497934341 seconds

x = 78, y = 23, rule = B02ac/S5i7e
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbooobbobbobbbobbobbobbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb!

Code: Select all

x = 78, y = 23, rule = B02ac/S5i7e
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbooobbobbobbbobbobbobbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb$
bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb!
Edit 2: (6,4)c/6:

Code: Select all

x = 26, y = 6, rule = B12cn3ir_S_B13cq7e_S2i3qr4in5nr6ik_B2ac3cr4j_S2e
A.2A.3A7.A4.2A.3A2$3.A2.A14.A2.A2$12.A$15.A!
@RULE B12cn3ir_S_B13cq7e_S2i3qr4in5nr6ik_B2ac3cr4j_S2e
@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,0,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,1,2
0,1,1,0,0,0,0,0,1,2
0,0,2,0,0,0,0,0,0,3
0,2,0,0,0,0,0,0,0,3
0,3,3,0,0,0,0,0,0,1
0,0,3,0,0,0,0,0,3,1
0,1,1,0,0,1,0,0,0,2
2,2,0,0,2,2,0,0,0,3
2,2,0,0,0,2,0,0,0,3
0,0,2,0,2,0,2,0,0,3
0,0,2,2,2,2,2,2,2,3
2,2,2,0,0,0,2,0,0,3
0,3,3,0,0,3,0,0,0,1
0,0,3,0,3,0,3,0,0,1
2,2,2,0,2,2,0,0,0,3
3,3,0,3,0,0,0,0,0,1
0,2,2,0,0,0,2,0,0,3
2,2,2,0,2,2,2,2,0,3
2,2,0,2,2,2,2,0,0,3
2,0,2,2,2,0,2,0,0,3
0,3,3,0,0,3,0,3,0,1
0,0,1,0,0,0,1,0,0,2
2,2,2,0,2,2,2,0,0,3
0,0,2,2,2,0,2,2,2,3
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 3: (12,6)c/12:

Code: Select all

x = 21, y = 13, rule = B12i3inqS_B13i4ntz5jS02n3y4a6k_B2ac3k4c5jS
A7.4A5.A2.A2$A8.A10.A10$11.A!
@RULE B12i3inqS_B13i4ntz5jS02n3y4a6k_B2ac3k4c5jS
@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,1,0,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,0,2
0,0,1,1,1,0,0,0,0,2
0,2,0,0,0,0,0,0,0,3
0,0,2,0,0,0,0,0,0,3
0,0,2,2,2,0,0,0,0,3
0,3,3,0,0,0,0,0,0,1
0,0,3,0,3,0,0,0,0,1
0,1,1,0,0,0,1,0,0,2
2,2,0,0,2,0,2,0,0,3
0,1,0,0,0,1,0,0,0,2
2,2,2,0,2,2,2,2,0,3
2,2,2,2,2,0,0,0,0,3
0,0,2,2,2,0,2,0,0,3
0,3,0,3,0,0,3,0,0,1
0,2,2,0,0,2,2,0,0,3
0,0,3,0,3,0,3,0,3,1
0,2,0,0,2,2,2,0,0,3
2,0,0,0,0,0,0,0,0,3
0,3,3,3,3,0,3,0,0,1
0,1,1,0,1,0,0,0,0,2
0,2,2,2,2,0,2,0,0,3
2,0,2,0,0,0,2,0,0,3
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
(6,3)c/6:

Code: Select all

x = 21, y = 9, rule = B12i3inqS_B13i4ntz5jS03y4a6k_B2ac3k4c5jS
A7.4A5.A2.A2$A8.A10.A6$13.A!
@RULE B12i3inqS_B13i4ntz5jS03y4a6k_B2ac3k4c5jS
@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,1,0,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,0,2
0,0,1,1,1,0,0,0,0,2
0,2,0,0,0,0,0,0,0,3
0,0,2,0,0,0,0,0,0,3
0,0,2,2,2,0,0,0,0,3
0,3,3,0,0,0,0,0,0,1
0,0,3,0,3,0,0,0,0,1
0,1,1,0,0,0,1,0,0,2
2,2,0,0,2,0,2,0,0,3
0,1,0,0,0,1,0,0,0,2
2,2,2,0,2,2,2,2,0,3
2,2,2,2,2,0,0,0,0,3
0,0,2,2,2,0,2,0,0,3
0,3,0,3,0,0,3,0,0,1
0,2,2,0,0,2,2,0,0,3
0,0,3,0,3,0,3,0,3,1
0,2,0,0,2,2,2,0,0,3
2,0,0,0,0,0,0,0,0,3
0,3,3,3,3,0,3,0,0,1
0,1,1,0,1,0,0,0,0,2
0,2,2,2,2,0,2,0,0,3
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 4: I've been working on the (6,1)c/6 frontend, and I feel like that the most promising direction is somewhere over here:

Code: Select all

x = 18, y = 2, rule = B12a3aS3n4a_B1c2aS3er_B1e2c3iS
6A.A4.4A.A$2A6.2A6.2A!
@RULE B12a3aS3n4a_B1c2aS3er_B1e2c3iS
@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,1,0,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,0,2
0,1,1,0,0,0,0,0,0,2
0,0,2,0,0,0,0,0,0,3
0,2,2,0,0,0,0,0,0,3
0,3,0,0,0,0,0,0,0,1
0,0,3,0,0,0,0,0,3,1
0,3,3,0,0,0,0,0,3,1
0,1,1,1,0,0,0,0,0,2
1,1,1,1,1,0,0,0,0,2
1,1,1,0,1,0,0,0,0,2
2,2,2,0,0,2,0,0,0,3
2,2,0,2,0,2,0,0,0,3
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 5: This line, perhaps?

Code: Select all

x = 18, y = 2, rule = B12a3aS3n4a_B1c2aS2a3er_B1e2c3iS1e4i
6A.A4.4A.A$2A6.2A6.2A!
@RULE B12a3aS3n4a_B1c2aS2a3er_B1e2c3iS1e4i
@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,1,0,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,0,2
0,1,1,0,0,0,0,0,0,2
0,0,2,0,0,0,0,0,0,3
0,2,2,0,0,0,0,0,0,3
0,3,0,0,0,0,0,0,0,1
0,0,3,0,0,0,0,0,3,1
0,3,3,0,0,0,0,0,3,1
0,1,1,1,0,0,0,0,0,2
1,1,1,1,1,0,0,0,0,2
1,1,1,0,1,0,0,0,0,2
2,2,2,0,0,2,0,0,0,3
2,2,0,2,0,2,0,0,0,3
2,2,2,0,0,0,0,0,0,3
3,3,0,0,0,0,0,0,0,1
3,3,3,0,3,3,0,0,0,1
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 6: This doesn't completely explode after the first "cycle".

Code: Select all

x = 18, y = 2, rule = B12a3aqS3n4a_B1c2ai3acny4n5iS01e2ak3eir4r5n7c_B1e2c3i4tS1e2i4i5r6n
6A.A4.4A.A$2A6.2A6.2A!
@RULE B12a3aqS3n4a_B1c2ai3acny4n5iS01e2ak3eir4r5n7c_B1e2c3i4tS1e2i4i5r6n
@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,1,0,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,0,2
0,1,1,0,0,0,0,0,0,2
0,0,2,0,0,0,0,0,0,3
0,2,2,0,0,0,0,0,0,3
0,3,0,0,0,0,0,0,0,1
0,0,3,0,0,0,0,0,3,1
0,3,3,0,0,0,0,0,3,1
0,1,1,1,0,0,0,0,0,2
1,1,1,1,1,0,0,0,0,2
1,1,1,0,1,0,0,0,0,2
2,2,2,0,0,2,0,0,0,3
2,2,0,2,0,2,0,0,0,3
2,2,2,0,0,0,0,0,0,3
3,3,0,0,0,0,0,0,0,1
3,3,3,0,3,3,0,0,0,1
0,2,0,0,0,2,0,0,0,3
0,0,2,0,2,0,2,0,0,3
2,0,0,0,0,0,0,0,0,3
2,2,0,0,0,0,0,0,0,3
2,2,0,0,2,0,0,0,0,3
0,2,2,2,0,0,0,0,0,3
0,2,0,0,2,0,2,0,0,3
2,0,2,2,2,0,0,0,0,3
0,3,3,3,3,3,3,3,0,1
3,3,3,0,3,3,3,0,0,1
2,2,2,2,2,0,0,2,0,3
3,3,0,0,0,3,0,0,0,1
0,2,2,2,2,2,0,0,0,3
0,0,2,2,2,0,2,0,0,3
0,3,0,0,3,3,3,0,0,1
3,3,3,3,0,3,3,3,0,1
0,2,2,0,2,0,0,0,0,3
2,2,2,2,0,2,0,0,0,3
0,1,1,0,0,0,1,0,0,2
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 7: I made the mistake of forgetting the front in trying to stabilize the back...

Code: Select all

x = 18, y = 2, rule = B12ai3ajn4aS1c3n4a_B1c2a3eS01e2ai3eir4r_B1e2ci3inS1e4i
6A.A4.4A.A$2A6.2A6.2A!
@RULE B12ai3ajn4aS1c3n4a_B1c2a3eS01e2ai3eir4r_B1e2ci3inS1e4i
@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,1,0,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,0,2
0,1,1,0,0,0,0,0,0,2
0,0,2,0,0,0,0,0,0,3
0,2,2,0,0,0,0,0,0,3
0,3,0,0,0,0,0,0,0,1
0,0,3,0,0,0,0,0,3,1
0,3,3,0,0,0,0,0,3,1
0,1,1,1,0,0,0,0,0,2
1,1,1,1,1,0,0,0,0,2
1,1,1,0,1,0,0,0,0,2
2,2,2,0,0,2,0,0,0,3
2,2,0,2,0,2,0,0,0,3
2,2,2,0,0,0,0,0,0,3
3,3,0,0,0,0,0,0,0,1
3,3,3,0,3,3,0,0,0,1
2,0,0,0,0,0,0,0,0,3
2,2,0,0,0,0,0,0,0,3
0,1,0,0,0,1,0,0,0,2
0,2,0,2,0,2,0,0,0,3
0,3,3,0,3,0,0,0,0,1
0,1,1,0,1,0,0,0,0,2
2,2,0,0,0,2,0,0,0,3
2,0,2,2,2,0,0,0,0,3
0,1,1,1,1,0,0,0,0,2
0,1,0,1,1,0,0,0,0,2
2,2,2,2,0,2,0,0,0,3
0,3,0,0,0,3,0,0,0,1
1,0,1,0,0,0,0,0,0,2
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 8: Another blindfolded dart toss:

Code: Select all

x = 18, y = 2, rule = B12ai3ajn4aS1c3n4a_B1c2a3e4rS012ai3aeir4rz5n_B1e2cei3eiS1e2ci4i
6A.A4.4A.A$2A6.2A6.2A!
@RULE B12ai3ajn4aS1c3n4a_B1c2a3e4rS012ai3aeir4rz5n_B1e2cei3eiS1e2ci4i
@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,1,0,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,0,2
0,1,1,0,0,0,0,0,0,2
0,0,2,0,0,0,0,0,0,3
0,2,2,0,0,0,0,0,0,3
0,3,0,0,0,0,0,0,0,1
0,0,3,0,0,0,0,0,3,1
0,3,3,0,0,0,0,0,3,1
0,1,1,1,0,0,0,0,0,2
1,1,1,1,1,0,0,0,0,2
1,1,1,0,1,0,0,0,0,2
2,2,2,0,0,2,0,0,0,3
2,2,0,2,0,2,0,0,0,3
2,2,2,0,0,0,0,0,0,3
3,3,0,0,0,0,0,0,0,1
3,3,3,0,3,3,0,0,0,1
2,0,0,0,0,0,0,0,0,3
2,2,0,0,0,0,0,0,0,3
0,1,0,0,0,1,0,0,0,2
0,2,0,2,0,2,0,0,0,3
0,1,1,0,1,0,0,0,0,2
2,2,0,0,0,2,0,0,0,3
2,0,2,2,2,0,0,0,0,3
0,1,1,1,1,0,0,0,0,2
0,1,0,1,1,0,0,0,0,2
2,2,2,2,0,2,0,0,0,3
0,3,0,0,0,3,0,0,0,1
1,0,1,0,0,0,0,0,0,2
3,3,0,0,0,3,0,0,0,1
2,2,2,0,0,2,2,0,0,3
2,2,2,2,2,0,0,2,0,3
0,2,2,2,0,2,0,0,0,3
2,2,2,2,0,0,0,0,0,3
2,0,2,0,0,0,0,0,0,3
0,3,0,3,0,0,0,0,0,1
0,3,0,3,0,3,0,0,0,1
3,0,3,0,3,0,0,0,0,1
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 9: Come on.

Code: Select all

x = 18, y = 2, rule = B12ai3ajn4aS1c3n4a_B1c2a3ejq4r5i6aS012aik3aeiqr4ryz5n7e_B1e2cei3ei4rS1e2ci3i4i
6A.A4.4A.A$2A6.2A6.2A!
@RULE B12ai3ajn4aS1c3n4a_B1c2a3ejq4r5i6aS012aik3aeiqr4ryz5n7e_B1e2cei3ei4rS1e2ci3i4i
@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,1,0,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,0,2
0,1,1,0,0,0,0,0,0,2
0,0,2,0,0,0,0,0,0,3
0,2,2,0,0,0,0,0,0,3
0,3,0,0,0,0,0,0,0,1
0,0,3,0,0,0,0,0,3,1
0,3,3,0,0,0,0,0,3,1
0,1,1,1,0,0,0,0,0,2
1,1,1,1,1,0,0,0,0,2
1,1,1,0,1,0,0,0,0,2
2,2,2,0,0,2,0,0,0,3
2,2,0,2,0,2,0,0,0,3
2,2,2,0,0,0,0,0,0,3
3,3,0,0,0,0,0,0,0,1
3,3,3,0,3,3,0,0,0,1
2,0,0,0,0,0,0,0,0,3
2,2,0,0,0,0,0,0,0,3
0,1,0,0,0,1,0,0,0,2
0,2,0,2,0,2,0,0,0,3
0,1,1,0,1,0,0,0,0,2
2,2,0,0,0,2,0,0,0,3
2,0,2,2,2,0,0,0,0,3
0,1,1,1,1,0,0,0,0,2
0,1,0,1,1,0,0,0,0,2
2,2,2,2,0,2,0,0,0,3
0,3,0,0,0,3,0,0,0,1
1,0,1,0,0,0,0,0,0,2
3,3,0,0,0,3,0,0,0,1
2,2,2,0,0,2,2,0,0,3
2,2,2,2,2,0,0,2,0,3
0,2,2,2,0,2,0,0,0,3
2,2,2,2,0,0,0,0,0,3
2,0,2,0,0,0,0,0,0,3
0,3,0,3,0,0,0,0,0,1
0,3,0,3,0,3,0,0,0,1
3,0,3,0,3,0,0,0,0,1
0,2,0,2,2,0,0,0,0,3
2,2,0,0,2,0,0,0,0,3
0,2,2,2,2,2,2,0,0,3
0,2,2,2,2,2,0,0,0,3
0,2,2,0,0,0,2,0,0,3
0,2,2,0,2,0,2,0,0,3
0,0,2,2,2,2,2,2,2,3
2,2,2,0,0,0,2,0,0,3
3,0,3,3,3,0,0,0,0,1
0,3,3,3,0,3,0,0,0,1
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 10: Here's the frontend that I said yesterday that I'd post today.

Code: Select all

# You can save the pattern into this box with Settings/Pattern/Save or Ctrl-S.
x = 11, y = 1, rule = B13iS_B12c3iS_B2acS
A4.6A!
@RULE B13iS_B12c3iS_B2acS
@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,1,0,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,0,2
0,0,1,1,1,0,0,0,0,2
0,2,0,0,0,0,0,0,0,3
0,0,2,0,0,0,0,0,0,3
0,0,2,0,2,0,0,0,0,3
0,0,2,2,2,0,0,0,0,3
0,3,3,0,0,0,0,0,0,1
0,0,3,0,3,0,0,0,0,1
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 11: (24,4)c/24:

Code: Select all

# You can save the pattern into this box with Settings/Pattern/Save or Ctrl-S.
x = 16, y = 23, rule = B13i4cS1e_B12c3iS_B2acS
5.A4.6A2$5.A8.2A4$11.A.A2$A.A2$A.A9.A8$9.A2$13.A2$13.A!
@RULE B13i4cS1e_B12c3iS_B2acS
@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,1,0,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,0,2
0,0,1,1,1,0,0,0,0,2
0,2,0,0,0,0,0,0,0,3
0,0,2,0,0,0,0,0,0,3
0,0,2,0,2,0,0,0,0,3
0,0,2,2,2,0,0,0,0,3
0,3,3,0,0,0,0,0,0,1
0,0,3,0,3,0,0,0,0,1
0,0,1,0,1,0,1,0,1,2
1,1,0,0,0,0,0,0,0,2
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 12: (12,2)c/12:

Code: Select all

# You can save the pattern into this box with Settings/Pattern/Save or Ctrl-S.
x = 24, y = 25, rule = B13i4cS1e_B12c3iS_B2acS
A.2A2.6A.A2$A.A3.6A.A2$6.A2$A.A3.A.A4.A2$A.A5.A2$10.A.A3.A.A2$10.A.A2$
21.A.A2$15.A.A3.A.A6$8.A.A3.A.A2$8.A.A3.A.A!
@RULE B13i4cS1e_B12c3iS_B2acS
@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,1,0,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,0,2
0,0,1,1,1,0,0,0,0,2
0,2,0,0,0,0,0,0,0,3
0,0,2,0,0,0,0,0,0,3
0,0,2,0,2,0,0,0,0,3
0,0,2,2,2,0,0,0,0,3
0,3,3,0,0,0,0,0,0,1
0,0,3,0,3,0,0,0,0,1
0,0,1,0,1,0,1,0,1,2
1,1,0,0,0,0,0,0,0,2
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 13: (6,1)c/6!

Code: Select all

# You can save the pattern into this box with Settings/Pattern/Save or Ctrl-S.
x = 11, y = 19, rule = B13i4cS1e_B12c3iS_B2acS
A4.6A2$A8.2A4$6.A.A4$9.A8$2.A.A!
@RULE B13i4cS1e_B12c3iS_B2acS
@TABLE
n_states:4
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,1,0,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,0,2
0,0,1,1,1,0,0,0,0,2
0,2,0,0,0,0,0,0,0,3
0,0,2,0,0,0,0,0,0,3
0,0,2,0,2,0,0,0,0,3
0,0,2,2,2,0,0,0,0,3
0,3,3,0,0,0,0,0,0,1
0,0,3,0,3,0,0,0,0,1
0,0,1,0,1,0,1,0,1,2
1,1,0,0,0,0,0,0,0,2
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 14: (8,4)c/8:

Code: Select all

x = 21, y = 17, rule = B1c2cS3j_B1c2i4jS2k_B12ek3acy4iqrzS1_B1e2c3in6k7eS3i4ij5r6ci
7.2A.A$7.A2.A$8.2A$16.2A.A$16.A2.A$17.2A6$2A.A$A2.A$.2A$17.2A.A$17.A2.
A$18.2A!
@RULE B1c2cS3j_B1c2i4jS2k_B12ek3acy4iqrzS1_B1e2c3in6k7eS3i4ij5r6ci
@TABLE
n_states:5
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3,4}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,0,1,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,1,2
0,0,2,0,0,0,0,0,0,3
0,2,0,0,0,2,0,0,0,3
0,0,3,0,0,0,0,0,0,4
0,3,0,0,0,0,0,0,0,4
3,0,3,0,0,0,0,0,0,4
0,3,0,0,3,0,0,0,0,4
0,3,3,0,3,3,0,0,0,4
0,0,3,0,3,0,3,0,0,4
0,3,0,3,0,0,0,0,0,4
3,3,0,0,0,0,0,0,0,4
0,3,0,0,3,0,3,0,0,4
0,4,0,0,0,0,0,0,0,1
0,0,4,0,0,0,0,0,4,1
0,4,4,0,0,0,0,0,4,1
4,0,4,4,4,0,0,0,0,1
4,4,4,0,4,4,0,0,0,1
4,4,4,0,0,4,0,4,0,1
4,0,4,4,4,0,4,4,4,1
0,3,3,0,3,0,0,0,0,4
0,4,4,4,4,0,4,4,0,1
0,0,4,4,4,4,4,4,4,1
4,4,4,0,4,4,4,0,0,1
4,4,0,4,4,4,4,4,0,1
1,1,0,1,1,0,0,0,0,2
0,2,2,0,0,2,0,2,0,3
2,2,0,0,2,0,0,0,0,3
0,3,3,3,0,3,0,0,0,4
0,3,3,0,0,3,3,0,0,4
0,3,3,3,0,0,0,0,0,4
0,3,3,3,0,0,3,0,0,4
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 15: (8,6)c/8:

Code: Select all

x = 12, y = 9, rule = B12c3rS_B12e4aS012a_B12cn3jq4w5q7cS2a4nq5j_B2aci4r6nS2a4n
2A.A$A2.A$.2A4$8.2A.A$8.A2.A$9.2A!
@RULE B12c3rS_B12e4aS012a_B12cn3jq4w5q7cS2a4nq5j_B2aci4r6nS2a4n
@TABLE
n_states:5
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3,4}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,0,1,0,0,0,0,0,0,2
0,1,0,0,0,0,0,0,0,2
0,0,1,0,0,0,0,0,1,2
0,0,2,0,0,0,0,0,0,3
0,2,0,0,0,0,0,0,0,3
0,0,3,0,0,0,0,0,0,4
0,3,0,0,0,0,0,0,0,4
0,4,4,0,0,0,0,0,0,1
0,0,4,0,0,0,0,0,4,1
2,2,0,0,0,0,0,0,0,3
0,4,0,0,0,4,0,0,0,1
0,0,3,0,3,0,0,0,0,4
3,3,3,0,0,0,0,0,0,4
0,1,1,0,0,1,0,0,0,2
0,2,2,2,2,0,0,0,0,3
0,0,3,0,0,0,3,0,0,4
2,0,0,0,0,0,0,0,0,3
2,0,2,0,0,0,0,0,0,3
2,2,2,0,0,0,0,0,0,3
0,3,3,0,0,0,3,0,0,4
0,3,3,0,0,0,0,3,0,4
3,0,3,3,3,0,3,0,0,4
0,2,0,2,0,0,0,0,0,3
0,3,3,3,3,3,3,3,0,4
0,4,4,4,0,4,0,0,0,1
0,4,4,4,0,4,4,4,0,1
4,0,4,4,4,0,4,0,0,1
4,4,4,0,0,0,0,0,0,1
0,3,3,0,0,0,3,3,0,4
0,3,3,3,0,0,3,3,0,4
3,3,3,3,3,0,3,0,0,4
3,3,3,3,0,0,3,0,0,4
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 16: 4c/7d and larger relative:

Code: Select all

x = 2, y = 2, rule = B1c2aS_B2a3iS_B2ae3iS_B2ae3iS_B2eS2k_B2eS2k_B2eS2k
2A$.A!
@RULE B1c2aS_B2a3iS_B2ae3iS_B2ae3iS_B2eS2k_B2eS2k_B2eS2k
@TABLE
n_states:8
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3,4,5,6,7}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,0,1,0,0,0,0,0,0,2
0,1,1,0,0,0,0,0,0,2
0,2,2,0,0,0,0,0,0,3
0,0,2,2,2,0,0,0,0,3
0,3,3,0,0,0,0,0,0,4
0,3,0,3,0,0,0,0,0,4
0,0,3,3,3,0,0,0,0,4
0,4,4,0,0,0,0,0,0,5
0,4,0,4,0,0,0,0,0,5
0,0,4,4,4,0,0,0,0,5
0,5,0,5,0,0,0,0,0,6
5,5,0,0,5,0,0,0,0,6
0,6,0,6,0,0,0,0,0,7
6,6,0,0,6,0,0,0,0,7
0,7,0,7,0,0,0,0,0,1
7,7,0,0,7,0,0,0,0,1
a0,a1,a2,a3,a4,a5,a6,a7,a8,0

Code: Select all

x = 10, y = 10, rule = B1c2aS_B2a3iS_B2ae3iS_B2ae3iS_B2eS2k_B2eS2aek_B2eS2aek
8.2A$9.A3$4.2A$5.A3$A$.A!
@RULE B1c2aS_B2a3iS_B2ae3iS_B2ae3iS_B2eS2k_B2eS2aek_B2eS2aek
@TABLE
n_states:8
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3,4,5,6,7}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,0,1,0,0,0,0,0,0,2
0,1,1,0,0,0,0,0,0,2
0,2,2,0,0,0,0,0,0,3
0,0,2,2,2,0,0,0,0,3
0,3,3,0,0,0,0,0,0,4
0,3,0,3,0,0,0,0,0,4
0,0,3,3,3,0,0,0,0,4
0,4,4,0,0,0,0,0,0,5
0,4,0,4,0,0,0,0,0,5
0,0,4,4,4,0,0,0,0,5
0,5,0,5,0,0,0,0,0,6
5,5,0,0,5,0,0,0,0,6
0,6,0,6,0,0,0,0,0,7
6,6,0,0,6,0,0,0,0,7
0,7,0,7,0,0,0,0,0,1
7,7,0,0,7,0,0,0,0,1
6,6,0,6,0,0,0,0,0,7
6,6,6,0,0,0,0,0,0,7
7,7,0,7,0,0,0,0,0,1
7,7,7,0,0,0,0,0,0,1
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 17: 5c/7ds:

Code: Select all

x = 2, y = 2, rule = B1c2aS_B2a3iS_B1c2a3iS_B2ae3iS_B2ae3iS2n_B1c2eS2n_B2eS3q
2A$.A!
@RULE B1c2aS_B2a3iS_B1c2a3iS_B2ae3iS_B2ae3iS2n_B1c2eS2n_B2eS3q
@TABLE
n_states:8
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3,4,5,6,7}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,0,1,0,0,0,0,0,0,2
0,1,1,0,0,0,0,0,0,2
0,2,2,0,0,0,0,0,0,3
0,0,2,2,2,0,0,0,0,3
0,0,3,0,0,0,0,0,0,4
0,3,3,0,0,0,0,0,0,4
0,0,3,3,3,0,0,0,0,4
0,4,4,0,0,0,0,0,0,5
0,4,0,4,0,0,0,0,0,5
0,0,4,4,4,0,0,0,0,5
0,5,5,0,0,0,0,0,0,6
0,5,0,5,0,0,0,0,0,6
0,0,5,5,5,0,0,0,0,6
5,0,5,0,0,0,5,0,0,6
0,0,6,0,0,0,0,0,0,7
0,6,0,6,0,0,0,0,0,7
6,0,6,0,0,0,6,0,0,7
0,7,0,7,0,0,0,0,0,1
7,7,7,0,0,0,7,0,0,1
a0,a1,a2,a3,a4,a5,a6,a7,a8,0

Code: Select all

x = 2, y = 2, rule = B1c2aS_B2a3iS_B1c2a3iS_B2ae3iS_B2ae3iS2n_B1c3aS2n_B3aS3q
2A$.A!
@RULE B1c2aS_B2a3iS_B1c2a3iS_B2ae3iS_B2ae3iS2n_B1c3aS2n_B3aS3q
@TABLE
n_states:8
neighborhood:Moore
symmetries:rotate4reflect
var a0={0,1,2,3,4,5,6,7}
var a1=a0
var a2=a1
var a3=a2
var a4=a3
var a5=a4
var a6=a5
var a7=a6
var a8=a7
0,0,1,0,0,0,0,0,0,2
0,1,1,0,0,0,0,0,0,2
0,2,2,0,0,0,0,0,0,3
0,0,2,2,2,0,0,0,0,3
0,0,3,0,0,0,0,0,0,4
0,3,3,0,0,0,0,0,0,4
0,0,3,3,3,0,0,0,0,4
0,4,4,0,0,0,0,0,0,5
0,4,0,4,0,0,0,0,0,5
0,0,4,4,4,0,0,0,0,5
0,5,5,0,0,0,0,0,0,6
0,5,0,5,0,0,0,0,0,6
0,0,5,5,5,0,0,0,0,6
5,0,5,0,0,0,5,0,0,6
0,0,6,0,0,0,0,0,0,7
0,6,6,6,0,0,0,0,0,7
6,0,6,0,0,0,6,0,0,7
0,7,7,7,0,0,0,0,0,1
7,7,7,0,0,0,7,0,0,1
a0,a1,a2,a3,a4,a5,a6,a7,a8,0
Edit 18: (4,1)c/4 variant:

Code: Select all

x = 13, y = 2, rule = B02-in3ceqy4ajnrw5jn6-ck7e/S2ein3aenq4ijqw5nry6ac
2o2bobo3b3o$2o4bob2ob2o!
Edit 19: (4,1)c/4 variant:

Code: Select all

x = 13, y = 2, rule = B02-in3ekr4-jkqz5eijn6ae7e/S1e2en3aer4ej5nr6ac
2o2bobo3b3o$2ob2o4bob2o!
Edit 20: (8,2)c/8!

Code: Select all

x = 13, y = 2, rule = B02-n3acnqr4acqrtwy5enr6ae/S1c2-e3aejn4nr6aci
2o2bobo3b3o$2o9b2o!
Help me find high-period c/2 technology!
My guide: https://bit.ly/3uJtzu9
My c/2 tech collection: https://bit.ly/3qUJg0u
Overview of periods: https://bit.ly/3LwE0I5
Most wanted periods: 76,116

kiho park
Posts: 86
Joined: September 24th, 2010, 12:16 am

Re: B0 hyper-relativistic speeds

Post by kiho park » May 6th, 2021, 11:08 am

wwei47 wrote:
May 2nd, 2021, 10:53 am
I've DMed Macbi to ask them to help you.
EDIT: Weird, I get results from LLS.
I run LLS using lingeling and Cygwin. Is this why I can't get correct result??
Can small adjustable spaceships overrun the speed limit of (|x|+|y|)/P = 1?

## B0 rules are the best! ##

Post Reply