Thread for basic questions

For general discussion about Conway's Game of Life.
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83bismuth38
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Re: Thread for basic questions

Post by 83bismuth38 » August 24th, 2018, 6:45 pm

have all collisions for these still lives with other common, non oscillating, non-spaceship objects such as herschels, pis, bs, etc. been enumerated?

Code: Select all

x = 42, y = 28, rule = B3/S23
5bo4b2o19b2o5bo$2o2bobo2bo2bo3b2o3b2o3bo3bo2bo3bobo$2o2bobo2bobo3bobo
2bobo2bobo2bo2bo2bobo$5bo4bo5bo3b2o4bo4b2o3b2o3$4b2o12b2o5b2o3b2o$3bob
o11bo2bo3bo2bo3bo7bo$3b2o5bo6bobo3bo2bo4bobo4bobo$b2o6bobo3b2obo5b2o6b
2o3bobo$obo5bobo3bo2bo18bobo$2o7bo4bobo20bo$15bo$20b2o5b2o$6b2o12bobo
4bobo6bo$2o3bob3o3b2o7bo6bo5bobo$o4bo4bo2bobo6bobo3bo6b2o3b2o$2bo3b3ob
o3bobo6b2o3b2o3b2o5bo$b2o5b2o5b2o15bobo6bo$33bo6b2o2$3b2o7b2o3b2o6bo$
3bobo5bo2bo3bo5bobo7bo$5bo5bo2bo3bobo4b2o6bobo$b4o4b2ob2o5bobo5b2o4bob
o$o7bo2bo8b2o5bobo2b2ob2o$obo5bo2bo16b2o$b2o6b2o!
obviously, glider collisions have. that is just obvious to me, but i am genuinely confused as to why I can't find all of them (or most of them) for pis or herschels or etc.. I have seen some attempts, but none of them seem to be complete.
also, i chose these specific still lives because they are the most common, (according to catagolue, but i have other opinions.) meaning they should appear more than some random 781 bit still life.

Code: Select all

x = 8, y = 10, rule = B3/S23
3b2o$3b2o$2b3o$4bobo$2obobobo$3bo2bo$2bobo2bo$2bo4bo$2bo4bo$2bo!
No football of any dui mauris said that.

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Re: Thread for basic questions

Post by gameoflifemaniac » August 25th, 2018, 9:56 am

Is a universal eater physically possible in Life?
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Re: Thread for basic questions

Post by KittyTac » August 25th, 2018, 10:07 am

gameoflifemaniac wrote:Is a universal eater physically possible in Life?
For finite or infinite patterns?

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Re: Thread for basic questions

Post by Macbi » August 25th, 2018, 11:29 am

gameoflifemaniac wrote:Is a universal eater physically possible in Life?
Depends what you mean by "universal eater".

It's not possible to make an eater that eats every ship.

I suspect it is possible to make an eater that eats gliders along any path that touch the eater.

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Re: Thread for basic questions

Post by Hdjensofjfnen » August 27th, 2018, 9:27 pm

It says on the wiki page that all but one of the 14 bit still lifes have been found in soup.
What is the remaining one?
"A man said to the universe:
'Sir, I exist!'
'However,' replied the universe,
'The fact has not created in me
A sense of obligation.'" -Stephen Crane

Code: Select all

x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!

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Re: Thread for basic questions

Post by 77topaz » August 27th, 2018, 10:06 pm

Hdjensofjfnen wrote:It says on the wiki page that all but one of the 14 bit still lifes have been found in soup.
What is the remaining one?
This:

Code: Select all

x = 10, y = 6, rule = B3/S23
2bo$bobo$bo2bo3b2o$2o3bo2bo$6bobo$7bo!
http://catagolue.appspot.com/object/xs1 ... o9a4/b3s23

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Re: Thread for basic questions

Post by dani » August 28th, 2018, 11:12 am

Platypus6 posts got me thinking, can a spaceship be made that is impervious to damage from the back using rakes and destruction reactions?
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Re: Thread for basic questions

Post by dvgrn » August 28th, 2018, 6:22 pm

danny wrote:Platypus6 posts got me thinking, can a spaceship be made that is impervious to damage from the back using rakes and destruction reactions?
What speed spaceship? For anything slower than c/2, the problem is that low-period rakes have big gaps between the gliders, and it's probably always possible to design some kind of custom salvo that flies in through the gaps, maybe suppressing a key glider here and there along the way if necessary, and strikes some vital spot on the spaceship.

Conversely, high-period rakes are made of mostly-not-empty-space, and we know that information can travel faster than c/2 through not-empty-space. So it would be hard to completely rule out some kind of virus or other chain reaction that travels back through the low-period glider stream and attacks the source rakes, even for a c/2 spaceship.

Really by some definitions, c/2 orthogonal spaceships in general _are_ impervious to damage from the back, in that there's no reasonable fleet of spaceships that you can send from, say, ten cells or more behind an LWSS, that can possibly catch it and damage it.

-- I would say that something closer to two blank cells are enough of a safety gap after a c/2 spaceship, but maybe somebody would then come up with a degenerate "fleet" of spaceships that collide with each other to make some kind of wave front that travels faster than c/2:

Code: Select all

x = 80, y = 23, rule = B3/S23
39b3o$39bo2bo$39bo$39bo$40bobo18$80o!
But lightspeed limitations prevent this kind of attack from being assembled behind a c/2 ship, unless it's already there at T=0. You won't see this kind of thing happening much with old spaceships in old Life universes.

If you have a lightspeed wire handy off to the side somewhere, well, that's another story, but the attack will no longer be "from the back".

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Re: Thread for basic questions

Post by dbell » August 28th, 2018, 9:26 pm

> Can a spaceship be made that is impervious to damage from the back using rakes and destruction reactions?

Extending this to puffers, I wonder if it is possible to destroy one of the 'stable' line puffers from the back.

Maybe some carefully designed series of impacts into the debris near (but not next to) the engine could trigger a destruction.

This might be hard to answer, since we already don't know whether the puffers will self-destruct on their own.

I'm guessing that a line puffer engine is immune to any such attack, even though the puffer's output could be changed.

BCNU,
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Re: Thread for basic questions

Post by dvgrn » August 28th, 2018, 10:03 pm

dbell wrote:> Can a spaceship be made that is impervious to damage from the back using rakes and destruction reactions?

Extending this to puffers, I wonder if it is possible to destroy one of the 'stable' line puffers from the back.
There was some experimentation along these lines back when superstable line puffers were first invented. The comments from the width-76 line puffer in Golly's pattern collection gives some details:

Code: Select all

#C Superstable line puffer of width 76.
#C A line puffer is the best linear generator of chaos in Life.
#C  It works by pulling a solid line forward at speed c/2.  It is
#C  amazing that this line isn't destroyed by its own debris.
#C Furthermore, this kind of puffer can be widened indefinitely,
#C  making it exponentially more chaotic, without affecting its
#C  stability. Some methods of stabilizing the edges are known
#C  to be slightly unstable, giving the puffer a half-life
#C  independent of its width, but the edge shown here is believed
#C  to be completely stable.
#C Increasing a line puffer's width linearly tends to increase its
#C  period exponentially. You will not see this width-76 puffer 
#C  repeat for tens of millions of generations.
#C One interesting thing you can do with a line puffer is put some
#C  asymmetrical debris in its plume. Sometimes the asymmetry is 
#C  temporary, but more often in wide puffers such as this one,
#C  it turns out to be permanent.
#C Tim Coe, May 1996. From Alan Hensel's "lifebc" pattern collection.
x = 32, y = 156, rule = B3/S23
18bo$18b4o$5bobo12b2o$5bo2bo14bo$8b2o10b4o$10bo13bo$8b4o8bo2b3o$7bo4bo
9b3o$9bo2bo10bo$9bo2bo5bob3o$11bo6b2o2bo$5bob4o8b3o$5bo3bo9bo$8bo12bo$
6bobo10bobo$22bo$7b3o9bobo$8b2o11bo$7b3o9bo$19b3o$6bobo9b2o2bo$8bo9bob
3o$5bo3bo13bo$5bob4o11b3o$11bo8bo2b3o$9bo2bo11bo$9bo2bo7b4o$7bo4bo10bo
$8b4o8b2o$10bo7b4o2bobo$8b2o8bo5bo2bo$5bo2bo7bobo8b2o$5bobo8bo12bo$14b
o2b2o8b4o$2b2obo9b3o8bo4bo$5bo7bobo12bo2bo$2bob2o7bo14bo2bo$2bo9b2o16b
o$o7bob3o11bob4o$bo5bob2o13bo3bo$bo5b2o18bo$bobo2b2o17bobo$bobob2o$bo
24b3o$bobob2o20b2o$bobo2b2o5bobo4bobo4b2o$bo5b2ob2obo2bo2bo2bob5o$bo5b
2o7b2o3bo4bo$bobo2b2o5bo6bo7bo$bobob2o6bob5o6bobo$bo8b2o17bo$bobob2o6b
ob5o6bobo$bobo2b2o5bo6bo7bo$bo5b2o7b2o3bo4bo$bo5b2ob2obo2bo2bo2bob5o$b
obo2b2o5bobo4bobo4b2o$bobob2o20b2o$bo24b3o$bobob2o$bobo2b2o17bobo$bo5b
2o18bo$bobo2bob2o14bo3bo$bobob3o2bo13bob4o$bo8bo19bo$bobob3o2bo17bo2bo
$bobo2bob2o18bo2bo$bo5b2o17bo4bo$bobo2b2o19b4o$bobob2o22bo$bo25b2o$bob
ob2o17bo2bo$bobo2b2o16bobo$bo5b2o$bobo2bob2o$bobob3o2bo$bo8bo13bobo$bo
bob3o2bo13bo2bo$bobo2bob2o17b2o$bo5b2o20bo$bobo2b2o19b4o$bobob2o19bo4b
o$bo26bo2bo$bobob2o21bo2bo$bobo2b2o22bo$bo5b2o15bob4o$bobo2bob2o14bo3b
o$bobob3o2bo16bo$bo8bo14bobo$bobob3o2bo$bobo2bob2o16b3o$bo5b2o18b2o$bo
bo2b2o5bobo4bobo4b2o$bobob2o3b2obo2bo2bo2bob5o$bo14b2o3bo4bo$bobob2o6b
o6bo7bo$bobo2b2o5bob5o6bobo$bo5b2ob2o17bo$bo5b2o4bob5o6bobo$bobo2b2o5b
o6bo7bo$bobob2o9b2o3bo4bo$bo8b2obo2bo2bo2bob5o$bobob2o6bobo4bobo4b2o$b
obo2b2o19b2o$bo5b2o17b3o$bobo2bob2o$bobob3o2bo14bobo$bo8bo16bo$bobob3o
2bo13bo3bo$bobo2bob2o14bob4o$bo5b2o21bo$bobo2b2o20bo2bo$bobob2o21bo2bo
$bo24bo4bo$bobob2o20b4o$bobo2b2o21bo$bo5b2o18b2o$bo5bob2o13bo2bo$o7bob
3o11bobo$2bo9b2o$2bob2o7bo$5bo7bobo$2b2obo9b3o$14bo2b2o$5bobo8bo$5bo2b
o7bobo$8b2o8bo$10bo7b4o$8b4o8b2o$7bo4bo10bo$9bo2bo7b4o$9bo2bo11bo$11bo
8bo2b3o$5bob4o11b3o$5bo3bo13bo$8bo9bob3o$6bobo9b2o2bo$19b3o$7b3o9bo$8b
2o11bo$7b3o9bobo$22bo$6bobo10bobo$8bo12bo$5bo3bo9bo$5bob4o8b3o$11bo6b
2o2bo$9bo2bo5bob3o$9bo2bo10bo$7bo4bo9b3o$8b4o8bo2b3o$10bo13bo$8b2o10b
4o$5bo2bo14bo$5bobo12b2o$18b4o$18bo!

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Re: Thread for basic questions

Post by Hunting » August 29th, 2018, 2:35 am

danny wrote:I found this reaction posted by user 'Hunting':

Code: Select all

x = 4, y = 12, rule = B3/S23
b2o$o2bo$o2bo$b2o2$2bo$b3o$2obo$3o$3o$3o$b2o!
Although it's probably been seen many times. My question is, how would I go about searching for a reaction that turns this into a clean HWSS reflector? It seems possible, although I don't know much about conduit searching.
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Re: Thread for basic questions

Post by KittyTac » August 29th, 2018, 2:47 am

Hunting wrote:
danny wrote:I found this reaction posted by user 'Hunting':

Code: Select all

x = 4, y = 12, rule = B3/S23
b2o$o2bo$o2bo$b2o2$2bo$b3o$2obo$3o$3o$3o$b2o!
Although it's probably been seen many times. My question is, how would I go about searching for a reaction that turns this into a clean HWSS reflector? It seems possible, although I don't know much about conduit searching.
Hey! :(
Don't complain.

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Re: Thread for basic questions

Post by 77topaz » August 29th, 2018, 3:50 am

Unlike certain other users, he actually attributed a pattern he sourced from someone else...

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Re: Thread for basic questions

Post by dvgrn » August 29th, 2018, 7:41 am

danny wrote:I found this reaction posted by user 'Hunting':

Code: Select all

x = 4, y = 12, rule = B3/S23
b2o$o2bo$o2bo$b2o2$2bo$b3o$2obo$3o$3o$3o$b2o!
Although it's probably been seen many times. My question is, how would I go about searching for a reaction that turns this into a clean HWSS reflector? It seems possible, although I don't know much about conduit searching.
Doesn't look like this question got answered originally, so I"ll give it a shot.

The output of this reaction looks superficially similar to an HWSS for a while, but it would take a serious stroke of luck to convert it into a clean HWSS, let alone regenerate the pond at the same time. The reaction is mostly inside the reaction envelope of the collision -- meaning that almost any stable catalyst that could affect the reaction in the key moments would also have reacted with the pond or HWSS earlier.

The cells that might theoretically possibly be affected by a Bellman-style catalyst are shown in yellow below (if you can find them!). White cells are other cells that turn on for the first time in that generation, but aren't actually accessible. Unfortunately there are only half a dozen ticks between the yellow cells' appearance and the creation of the almost-HWSS -- probably not enough time for the effects of a catalyst to propagate over and fix the HWSS.

Code: Select all

x = 310, y = 18, rule = LifeHistory
2.2A18.2A18.2A18.2A18.2A18.2B18.2B18.2B18.2B18.2B18.2B18.2B18.2B18.2B
18.2B18.2B$.A2.A16.A2.A16.A2.A16.A2.A15.EB2.BA14.2B.ABA14.2B.2BA14.2B
.3B14.2B.3B14.2B.3B14.2B.3B14.2B.3B14.2B.3B14.2B.3B14.2B.3B14.2B.3B$.
A2.A16.A2.A16.A2.A15.E5A14.4B2A14.4B2A14.5BA14.6B14.6B14.6B14.6B14.6B
14.6B14.6B14.6B14.6B$2.2A18.2A17.C2BA15.E2A2B14.E4BA14.4B2A14.6B14.6B
14.6B14.4BAB14.6B14.6B14.6B14.5B2A13.7B13.BA5B$22.2A17.C2B16.E2AB16.
4BA15.3B3A14.2BA2BA14.6B14.2B3AB14.BA3BA14.2BA3B14.BA4B14.2AB4A13.2A
5BA11.3A6B11.BA7B$3.A18.3A16.C2BA16.5A14.C3BAB14.3B2AB14.6B14.B5A14.B
5A14.BA4BA13.2A3B2A13.8A12.AB6A11.EA7BA10.8B2A10.B10A$2.3A16.A2BA16.B
AB2A15.BA3B15.3B2A15.2AB2A15.2AB2A15.A3BA15.ABAB2A13.A5BA13.A2B2AB2A
12.A6BA12.A2B3AB2A10.EA7BA10.3B5AB2A9.3BA6BA$.2ABAB15.3BAB15.2B3A15.B
A3BA14.3A3B14.A5B14.5AB14.4BAB14.2AB2AB14.6A14.6A14.A5BA12.EA4B2A12.
9A10.A2B7A10.BA8BA$.3A2B14.A3BAB14.3B3A14.2BA3BA13.B3A3B13.4BA2B13.2B
A4B13.B2ABA2B13.7B13.7B13.2B4AB13.BA4BA13.2BA4B13.BA5B13.2AB5A12.2A6B
A$.3A3B13.A3BA2B13.3B3AB13.2BA4B13.2B2A3B13.BABA3B13.7B13.7B13.7B13.
7B13.7B13.3B2A2B13.7B13.7B13.7B13.4B3A$B3A3B13.4BA2B13.3B2A2B13.3BABA
B13.7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B$2B2A3B
13.BABA3B13.7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B
13.7B13.7B$7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B
13.7B13.7B13.7B13.7B$7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B
13.7B13.7B13.7B13.7B13.7B13.7B$7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B
13.7B13.7B13.7B13.7B13.7B13.7B13.7B13.7B$6B14.6B14.6B14.6B14.6B14.6B
14.6B14.6B14.6B14.6B14.6B14.6B14.6B14.6B14.6B14.6B$.5B15.5B15.5B15.5B
15.5B15.5B15.5B15.5B15.5B15.5B15.5B15.5B15.5B15.5B15.5B15.5B$.3B17.3B
17.3B17.3B17.3B17.3B17.3B17.3B17.3B17.3B17.3B17.3B17.3B17.3B17.3B17.
3B!
#C [[ WIDTH 640 HEIGHT 320 ZOOM 2 ]]
Maybe it's not absolutely impossible, but as Max says, "it would take a miracle"... really it's probably worse than I've outlined, because the catalyst probably has to be forbidden to affect the active reaction at all for the first four or five ticks -- otherwise the almost-HWSS won't ever start to form in the first place. But if you wait that long, then the Magical HWSS-Fixing Effects have to propagate eastward at near lightspeed... or maybe even faster than light, which is, um, a bit unlikely.

... So really your best bet might be to add another bait, get a few standard signals out, and use them to shoot down any leftover junk and rebuild the pond and the new bait, and then hook up a something-to-HWSS converter:

Code: Select all

x = 10, y = 18, rule = LifeHistory
5.2A$4.A2.A$4.A2.A$5.2A$2A$2A4.A$5.3A$4.2ABAB$4.3A2B$4.3A3B$
3.B3A3B$3.2B2A3B$3.7B$3.7B$3.7B$3.6B$4.5B$4.3B!
But obviously that's not the direct HWSS-to-HWSS converter that you're looking for. I hope we do find direct converters of other signals to HWSSes someday, but we may have to set up a near-Catagolue-sized distributed search to look at enough possibilities to find them. HWSSes are about 22 times rarer than LWSSes, which more or less means we can expect to find twenty-some direct X-to-LWSS converters before the first direct X-to-HWSS turns up... and so far we only have one X-to-LWSS, and it's a pretty darn awkward one.

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Re: Thread for basic questions

Post by Hdjensofjfnen » September 8th, 2018, 11:37 pm

Why doesn't this occur as readily in soups as the block-laying or glider-producing switch engine?

Code: Select all

x = 15, y = 6, rule = B3/S23
bo11b2o$obo10bo2$o2bo$2b2o$3bo!
"A man said to the universe:
'Sir, I exist!'
'However,' replied the universe,
'The fact has not created in me
A sense of obligation.'" -Stephen Crane

Code: Select all

x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!

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Re: Thread for basic questions

Post by calcyman » September 9th, 2018, 3:19 am

Hdjensofjfnen wrote:Why doesn't this occur as readily in soups as the block-laying or glider-producing switch engine?

Code: Select all

x = 15, y = 6, rule = B3/S23
bo11b2o$obo10bo2$o2bo$2b2o$3bo!
That is a glider-producing switch engine.
What do you do with ill crystallographers? Take them to the mono-clinic!

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Re: Thread for basic questions

Post by Hunting » September 9th, 2018, 4:30 am

KittyTac wrote:
Hunting wrote: Hey! :(
Don't complain.
Actually, I'm found that when I was randomly trying to use spaceships to collide a small SL. Then I found this.
I saw that reaction, but since I WAS a newbie to GoL, I didn't remind that it IS a reaction.
By the way, who will post that pattern as a methethula?
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Re: Thread for basic questions

Post by Hdjensofjfnen » September 9th, 2018, 9:00 pm

calcyman wrote:
Hdjensofjfnen wrote:Why doesn't this occur as readily in soups as the block-laying or glider-producing switch engine?

Code: Select all

x = 15, y = 6, rule = B3/S23
bo11b2o$obo10bo2$o2bo$2b2o$3bo!
That is a glider-producing switch engine.
No, glider-producing switch engines have a table on block in the ash!
"A man said to the universe:
'Sir, I exist!'
'However,' replied the universe,
'The fact has not created in me
A sense of obligation.'" -Stephen Crane

Code: Select all

x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!

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Re: Thread for basic questions

Post by Saka » September 9th, 2018, 9:21 pm

Hdjensofjfnen wrote:
No, glider-producing switch engines have a table on block in the ash!
...they dont?
Image
Glider producing switch engine

Code: Select all

x = 17, y = 10, rule = B3/S23
b2ob2obo5b2o$11b4obo$2bob3o2bo2b3o$bo3b2o4b2o$o2bo2bob2o3b4o$bob2obo5b
o2b2o$2b2o4bobo2b3o$bo3b5ob2obobo$2bo5bob2o$4bob2o2bobobo!
(Check gen 2)

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Re: Thread for basic questions

Post by wwei23 » September 9th, 2018, 10:04 pm

Hdjensofjfnen wrote:
No, glider-producing switch engines have a table on block in the ash!
That's Noah's Ark.

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Hdjensofjfnen
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Re: Thread for basic questions

Post by Hdjensofjfnen » September 12th, 2018, 5:00 pm

wwei23 wrote:
Hdjensofjfnen wrote:
No, glider-producing switch engines have a table on block in the ash!
That's Noah's Ark.
Oh thanks wwei.
"A man said to the universe:
'Sir, I exist!'
'However,' replied the universe,
'The fact has not created in me
A sense of obligation.'" -Stephen Crane

Code: Select all

x = 7, y = 5, rule = B3/S2-i3-y4i
4b3o$6bo$o3b3o$2o$bo!

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Re: Thread for basic questions

Post by KittyTac » September 17th, 2018, 9:33 am

How big is the entire rule table rulespace?

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Re: Thread for basic questions

Post by dvgrn » September 17th, 2018, 12:24 pm

KittyTac wrote:How big is the entire rule table rulespace?
I think it's (2^512)^256 -- each possible MAP-rule bit can point to any of 256 different states.

Maybe someone else can think about it with more brain cells than I have to spare at the moment, and confirm or deny. In any case it's pretty definitely a Painfully Large Number.

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Re: Thread for basic questions

Post by KittyTac » September 17th, 2018, 12:53 pm

dvgrn wrote:
KittyTac wrote:How big is the entire rule table rulespace?
I think it's (2^512)^256 -- each possible MAP-rule bit can point to any of 256 different states.

Maybe someone else can think about it with more brain cells than I have to spare at the moment, and confirm or deny. In any case it's pretty definitely a Painfully Large Number.
What about only isotropic ones?

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Re: Thread for basic questions

Post by dvgrn » September 17th, 2018, 1:37 pm

KittyTac wrote:
dvgrn wrote:
KittyTac wrote:How big is the entire rule table rulespace?
I think it's (2^512)^256 -- each possible MAP-rule bit can point to any of 256 different states.

Maybe someone else can think about it with more brain cells than I have to spare at the moment, and confirm or deny. In any case it's pretty definitely a Painfully Large Number.
What about only isotropic ones?
According to the same logic, it would be (2^102)^256... which is so much smaller than the number for all the MAP rules that it's practically zero, but it's still so much bigger than any reasonable number that it might as well be infinity:

Code: Select all

Number of possible isotropic rule table definitions for 256 states: 31278561947875052547079635722750231802892527748163799362328001343507661088125841605669624882915053596205517501325699958937569480665865214040057071250664859895038844131255539174530769054190265821190818165613286641061948679909627254987393256830999228932559609958778116963444348680250540404045642744429048113046922443145971895635858742591368397521329300481522235772830067874521886442842358148330713291675418240387192369006829142858484989836707586315579185465004593744701615633688888760201557729484840904687218177934482656662773634489630144413647144583758819871828839655861968752576339094211532091084084425336626025926937163627805510528134410751392837648258322024528852391679359240615294548044250287772313872396630670387718879196400256700442069980137124992544073289630332711853279825416692811097320936351649717660029511627299374208649468260064005657392124001333339464075020424914319482979966892864519024042717002316819265633329917403624689120059997681712914057119960415150136377014821563057238516175063434192663319035046390017034517611684407235068081764642502260152048269294058826420535517579203149656837745972497426804154196208455969010469114466768451839637699031542760973450042403650791214782333098627849831372905938692628829513076924962000717729180919783524256162148220349950572708179002833563627362244176958163078608453050413897667613406041742852939615861084196996754097132270446470441864328179428029048375281431230086693187353928673151148242164519407062098918992969305012590186292772802448408360775474253836390252326871881322557584336408405418460821956124703839661302035872555245254727283980874841622965699417622839338385154319893972718769194084018974148729487906213009056557955620300580452110217450235001954351177021369074158612761552054197646246056930545381949015586409046719967522406768665228155493904186524168905825991106387095657585488240007785703795166287787693581378072053121549506070691578946145060370006543084370825423862519551737889065312590812943697199655508138931905386682576327798358208014935088020251957702558472749904723435141975622879136853948789797202439247984585724992572299435086432196258461176660275950264681528722301433631566456411418762770192821738509082783537508428847585856435029986110008379055272136235729313827273745628376498168103158605189190547551988253086527500433070012544852430973264173171132421266291554377316476719964153803753407853238124658485521870454976294311846516555339679639012699101463877538659512068910148174760216032354453702751171150435992279715672237301375739439119139597220939470960212010712224219019279025577135920237571658369584091823792337212991479072418463561550204918002254141049642868463477669722073673177515127181127109271466602066368974948626353058292001709838342131130823465253716647319109131077894295140522478108212772192766164765924873457635426118644659216129631944695939176087517392732073038692951189825188704352046213507473593058381905590488013972804385275198476293170444115439945562839659380602897557418057643384703561759684253562933017171436659665331291977987180836784990039861989259155299144045601340437461986050278211903897449684762190688880098665923188404512485786925884784593626363494465929540002515990204343263537844454960729295458451976897575358583636537175612591203195051080174832676683704480683219116076718120935855967843668139791310748751054128967653398430357529759073254546643603109532461294413871698359353856041293405501872453415084522871528062144800847161971399159908844098745777568225892528170726910497518466889634743659081793453502028440832239950605327950880218223759022623201894462665393877182711762095988006353188789811275597108385945420075251833193198685479349139083743553299411595437759239045777010564301142015047998856397996893983435404421316367949607816483985997168327612441190776195547554153646108633738349537545854714840823095975032093016578246701873285968981766324033923883029439339726233109147707543701204424838260092624718089049890170826094196462139002862170571009464244620905979832507037350778480911147657003230963692508949354775494635662202423306634037925601727806949730774849869098090417917257466250374200399873325114973143922953573172803550054286579406568708609198934318856052026795343990230836490959787943828859533185008846782837792586680593821871170199535405505153016960724712054643734789740763245584222645183940094764845080006687080839300198137188845304348219071056881965851710414167680318772194119606113829495460890169029384334676295010962397704145796146615372033972038313750706926410012812348613050307535679152560355821637169725567762855109608550996459390574132555823107196317468851801260020225716919341661165126292770744630317284557132745528851090680461392715883349357907373365360113007483400453865672977109776284134946100383592069940493020040703926503417756469344721702864785323692585447852938298400441690297025918072918101496620592368788109999517805474559747528645054267161634475046902699872190540028692557145911433498104655177397760275256678503398340693972621228206942615955512268456415234543237831248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