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Big Brother Malkovich # 1 (continued)

https://www.lifein19x19.com/viewtopic.php?t=152

Page 32 of 51

Re: Big Brother Malkovich # 1 (continued)

Posted: Tue Jan 11, 2011 10:37 am
by crux
topazg wrote:@crux:

Many thanks, I saw your :b6: as a self-atari when I looked at the hane, and gave up on it. How I didn't read out the connect and die I don't know. I think my brain had fried at that point :P

So you think Black's favourable from that, or did I miss something earlier on?

Who knows what we've missed, but I've thought for a while that Black should be winning this fight.

Re: Big Brother Malkovich # 1 (continued)

Posted: Tue Jan 11, 2011 10:39 am
by daniel_the_smith
I don't really see a way out of this for us. It looks like we have to lose either the 5 stones or the 6 stones. I guess I'll just let Gresil's next move stand and see how Violence gets out of this...

Re: Big Brother Malkovich # 1 (continued)

Posted: Tue Jan 11, 2011 8:22 pm
by Joaz Banbeck
I approve. My comments about the current position are on the previous page. ( http://lifein19x19.com/forum/viewtopic. ... 723#p45723 )

However, it is more complex than I thought. I think white can bring it down to a ko at T6/T7. It is a ko that we cannot afford to lose.
We have two internal ko threats; black has none. So we can beat back threats against our biggest uninvolved group over on the middle left. The best that they can get is a threat against our upper left or lower left groups. In return, we get a 16-stone group and safety for all of our groups that killed it.
A threat against the lower left does not really kill, it just crushes it low or steals the corner. A threat against the upper left still alows us a two-step ko to live.

About 10 moves ago we appeared to be in a desperate situation. Now it looks like we will come out ahead in this fight. :-?

Re: Big Brother Malkovich # 1 (continued)

Posted: Wed Jan 12, 2011 4:28 am
by topazg
@Joaz:

I can't see a ko anywhere here, would you mind sharing your reading ?

Re: Big Brother Malkovich # 1 (continued)

Posted: Wed Jan 12, 2011 12:30 pm
by shapenaji
Approved
No other move here really, we've committed, and now must finish it, but I feel pretty good about it :D

Re: Big Brother Malkovich # 1 (continued)

Posted: Wed Jan 12, 2011 12:58 pm
by Joaz Banbeck
topazg wrote:@Joaz:

I can't see a ko anywhere here, would you mind sharing your reading ?


@Topazg:
I didn't save the position, but I remember approximately how I got there.
If we start at this position:

Click Here To Show Diagram Code
[go]$$Wc
$$ ---------------------------------------
$$ | . . . . . . . O . . . . . . . . . . . |
$$ | . X X O O . O X . . . . . . . . . . . |
$$ | . X O O . O X X . . . X . . O X X . . |
$$ | . X X O O X O X . X X O X . O O X . . |
$$ | X X O X . X O O X O X . O O . X O . . |
$$ | . O O X . . . O . O X O O X X X X X . |
$$ | . . O X . . X . O . X O X O O O O O . |
$$ | . . O X . . . . O X X O X X X X . . . |
$$ | . . O X . . . . O . X X O O X X O 5 . |
$$ | . X X O X . X . . O O O O X O X X 1 . |
$$ | . O O O . . . . . . . . . . O O 2 4 . |
$$ | . . . . . X . . . X . . . . . . 3 6 . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . , . O . . . , . . . . . O . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

...which you can find in this post: http://lifein19x19.com/forum/viewtopic. ... 723#p45723

...we can end up at this position:

Click Here To Show Diagram Code
[go]$$Wc 3 is forced, btw
$$ ---------------------------------------
$$ | . . . . . . . O . . . . . . . . . . . |
$$ | . X X O O . O X . . . . . . . . . . . |
$$ | . X O O . O X X . . . X . . O X X . . |
$$ | . X X O O X O X . X X O X . O O X . . |
$$ | X X O X . X O O X O X . O O . X O . . |
$$ | . O O X . . . O . O X O O X X X X X . |
$$ | . . O X . . X . O . X O X O O O O O a |
$$ | . . O X . . . . O X X O X X X X 3 . b |
$$ | . . O X . . . . O . X X O O X X O O . |
$$ | . X X O X . X . . O O O O X O X X O 2 |
$$ | . O O O . . . . . . . . . . O O X X . |
$$ | . . . . . X . . . X . . . . . . O X 8 |
$$ | . . . O . . . . . . . . . . . . 1 4 . |
$$ | . . . . . X . . . . . . . . . . . 5 6 |
$$ | . . X . X . . . . . . . . . . . . . 7 |
$$ | . . . , . O . . . , . . . . . O . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

My memory is a bit fuzzy here. There may have been an exchange of 'a' for 'b'.


In some variations, after the a-b exchange, black is stymied from the top, but can approach from the bottom. To stall this, prior to black 8 white throws in at 'c' to make black's 'd' a self-atari.

Click Here To Show Diagram Code
[go]$$Wc
$$ ---------------------------------------
$$ | . . . . . i . O j . . . . . . . . . . |
$$ | . X X O O . O X . . . . . . . . . . . |
$$ | . X O O . O X X . . . X . . O X X . . |
$$ | . X X O O X O X . X X O X . O O X . . |
$$ | X X O X . X O O X O X . O O f X O e . |
$$ | . O O X . . . O . O X O O X X X X X X |
$$ | . . O X . . X . O . X O X O O O O O X |
$$ | . . O X . . . . O X X O X X X X O . O |
$$ | . g O X . . . . O . X X O O X X O O d |
$$ | . X X O X . X . . O O O O X O X X O X |
$$ | . O O O . . . . . . . . . . O O X X c |
$$ | . . . . . X . . . X . . . . . . O X 8 |
$$ | . . . O . . . . . . . . . . . . O X . |
$$ | . . . . . X . . . . . . . . . . . O X |
$$ | . . X . X . . . . . . . . . . . . . O |
$$ | . . . , h O . . . , . . . . . O . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

White has internal ko threats at 'e' and then 'f'. Black has only external ko threats. This advantage may be enough to allow white to defend the most dangerous threat at 'g', and force black to take the threat at 'h' or 'i'.
BTW, my previous note about a subsequent two-step ko up top was wrong. I was carelessly asuming that the ko theat against that group would be 'j', but 'i' is clearly better.

Re: Big Brother Malkovich # 1 (continued)

Posted: Wed Jan 12, 2011 1:17 pm
by Magicwand
for observers:
i think this game is most complicated game i ever saw.
my hats off to the players who comeup with variations that i didnt even see.

if i had to play this game i would never make this complicated and select easier variation.

Re: Big Brother Malkovich # 1 (continued)

Posted: Wed Jan 12, 2011 1:24 pm
by Joaz Banbeck
@Shapenaji and observers:
Uh...oh...we may be screwed. I have been playing the right side assuming that we always have 4 liberties up top. But there is another branch that I didn't see.

Click Here To Show Diagram Code
[go]$$Bc
$$ ---------------------------------------
$$ | . . . . . . . O . . . . . . . . . . . |
$$ | . X X O O . O X . . . . . 4 1 . . . . |
$$ | . X O O . O X X . . . X . . O X X . . |
$$ | . X X O O X O X . X X O X . O O X . . |
$$ | X X O X . X O O X O X . O O 2 X O 3 . |
$$ | . O O X . . . O . O X O O X X X X X . |
$$ | . . O X . . X . O . X O X O O O O O . |
$$ | . . O X . . . . O X X O X X X X . . . |
$$ | . . O X . . . . O . X X O O X X O O . |
$$ | . X X O X . X . . O O O O X O X X O . |
$$ | . O O O . . . . . . . . . . O O X X . |
$$ | . . . . . X . . . X . . . . . . O X . |
$$ | . . . O . . . . . . . . . . . . O X . |
$$ | . . . . . X . . . . . . . . . . . O . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . , . O . . . , . . . . . O . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Now there are two branches:

The simple one in which white can tenuki back to the right side with 4 liberties:
Click Here To Show Diagram Code
[go]$$Bc
$$ ---------------------------------------
$$ | . . . . . . . O . . . . . . . . . . . |
$$ | . X X O O . O X . . . . . O X 1 . . . |
$$ | . X O O . O X X . . . X . 2 O X X . . |
$$ | . X X O O X O X . X X O X . O O X . . |
$$ | X X O X . X O O X O X 3 O O O X . X . |
$$ | . O O X . . . O . O X O O X X X X X . |
$$ | . . O X . . X . O . X O X O O O O O . |
$$ | . . O X . . . . O X X O X X X X . . . |
$$ | . . O X . . . . O . X X O O X X O O . |
$$ | . X X O X . X . . O O O O X O X X O . |
$$ | . O O O . . . . . . . . . . O O X X . |
$$ | . . . . . X . . . X . . . . . . O X . |
$$ | . . . O . . . . . . . . . . . . O X . |
$$ | . . . . . X . . . . . . . . . . . O . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . , . O . . . , . . . . . O . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

That is the one that I have been reading when concluding that we could win. But the complex version looks like this:

Click Here To Show Diagram Code
[go]$$Bc
$$ ---------------------------------------
$$ | . . . . . . . O . . . . . 6 3 4 . . . |
$$ | . X X O O . O X . . . . . O X 2 . . . |
$$ | . X O O . O X X . . . X . 1 O X X . . |
$$ | . X X O O X O X . X X O X . O O X . . |
$$ | X X O X . X O O X O X 5 O O O X . X . |
$$ | . O O X . . . O . O X O O X X X X X . |
$$ | . . O X . . X . O . X O X O O O O O . |
$$ | . . O X . . . . O X X O X X X X . . . |
$$ | . . O X . . . . O . X X O O X X O O . |
$$ | . X X O X . X . . O O O O X O X X O . |
$$ | . O O O . . . . . . . . . . O O X X . |
$$ | . . . . . X . . . X . . . . . . O X . |
$$ | . . . O . . . . . . . . . . . . O X . |
$$ | . . . . . X . . . . . . . . . . . O . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . , . O . . . , . . . . . O . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

...which continues like this:

Click Here To Show Diagram Code
[go]$$Bc 4 fills at P18
$$ ---------------------------------------
$$ | . . . . . . . O . . . . . O 2 O . . . |
$$ | . X X O O . O X . . . . 5 O 1 O . . . |
$$ | . X O O . O X X . . . X . X O X X . . |
$$ | . X X O O X O X . X X . X 3 O O X . . |
$$ | X X O X . X O O X O X X O O O X . X . |
$$ | . O O X . . . O . O X O O X X X X X . |
$$ | . . O X . . X . O . X O X O O O O O . |
$$ | . . O X . . . . O X X O X X X X . . . |
$$ | . . O X . . . . O . X X O O X X O O . |
$$ | . X X O X . X . . O O O O X O X X O . |
$$ | . O O O . . . . . . . . . . O O X X . |
$$ | . . . . . X . . . X . . . . . . O X . |
$$ | . . . O . . . . . . . . . . . . O X . |
$$ | . . . . . X . . . . . . . . . . . O . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . , . O . . . , . . . . . O . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

This looks like 3 liberties. :(

Re: Big Brother Malkovich # 1 (continued)

Posted: Wed Jan 12, 2011 3:12 pm
by topazg
@Joaz

Ah, yeah, ok, that makes sense, thanks :)

Your latest post has the reading that I had, let's see if we're wrong!

Re: Big Brother Malkovich # 1 (continued)

Posted: Fri Jan 14, 2011 3:54 am
by gaius
Hats of to topazg's reading and crux' addition! I misread myself, but now I think they are spot on. What a beautiful semeai this is!

Re: Big Brother Malkovich # 1 (continued)

Posted: Fri Jan 14, 2011 7:56 am
by shapenaji
I realize I haven't written much in a bit, here's my reading (and Joaz is missing something):

Joaz states our problem as the following:

Click Here To Show Diagram Code
[go]$$Bc
$$ ---------------------------------------
$$ | . . . . . . . O . . . . . 6 3 4 . . . |
$$ | . X X O O . O X . . . . . O X 2 . . . |
$$ | . X O O . O X X . . . X . 1 O X X . . |
$$ | . X X O O X O X . X X O X . O O X . . |
$$ | X X O X . X O O X O X 5 O O O X . X . |
$$ | . O O X . . . O . O X O O X X X X X . |
$$ | . . O X . . X . O . X O X O O O O O . |
$$ | . . O X . . . . O X X O X X X X . . . |
$$ | . . O X . . . . O . X X O O X X O O . |
$$ | . X X O X . X . . O O O O X O X X O . |
$$ | . O O O . . . . . . . . . . O O X X . |
$$ | . . . . . X . . . X . . . . . . O X . |
$$ | . . . O . . . . . . . . . . . . O X . |
$$ | . . . . . X . . . . . . . . . . . O . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . , . O . . . , . . . . . O . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


However, how about if we do it like this?

Click Here To Show Diagram Code
[go]$$Bc
$$ ---------------------------------------
$$ | . . . . . . . O . . . . . . . . . . . |
$$ | . X X O O . O X . . . . . 4 1 . . . . |
$$ | . X O O . O X X . . . X . 5 O X X . . |
$$ | . X X O O X O X . X X O X . O O X 3 . |
$$ | X X O X . X O O X O X . O O . X O 2 . |
$$ | . O O X . . . O . O X O O X X X X X . |
$$ | . . O X . . X . O . X O X O O O O O . |
$$ | . . O X . . . . O X X O X X X X . . . |
$$ | . . O X . . . . O . X X O O X X O O . |
$$ | . X X O X . X . . O O O O X O X X O . |
$$ | . O O O . . . . . . . . . . O O X X . |
$$ | . . . . . X . . . X . . . . . . O X . |
$$ | . . . O . . . . . . . . . . . . O X . |
$$ | . . . . . X . . . . . . . . . . . O . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . , . O . . . , . . . . . O . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


And now! ultra-sneaky move:

Click Here To Show Diagram Code
[go]$$Wc
$$ ---------------------------------------
$$ | . . . . . . . O . . . . . 7 4 5 . . . |
$$ | . X X O O . O X . . . . . O X 3 . . . |
$$ | . X O O . O X X . . . X 2 X O X X . . |
$$ | . X X O O X O X . X X O X 1 O O X X . |
$$ | X X O X . X O O X O X 6 O O . X O O . |
$$ | . O O X . . . O . O X O O X X X X X . |
$$ | . . O X . . X . O . X O X O O O O O . |
$$ | . . O X . . . . O X X O X X X X . . . |
$$ | . . O X . . . . O . X X O O X X O O . |
$$ | . X X O X . X . . O O O O X O X X O . |
$$ | . O O O . . . . . . . . . . O O X X . |
$$ | . . . . . X . . . X . . . . . . O X . |
$$ | . . . O . . . . . . . . . . . . O X . |
$$ | . . . . . X . . . . . . . . . . . O . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . , . O . . . , . . . . . O . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


And now we have 5 libs to their 4.

So they need to find this:

Click Here To Show Diagram Code
[go]$$Wc
$$ ---------------------------------------
$$ | . . . . . . . O . . . . . . . . . . . |
$$ | . X X O O . O X . . 6 5 . O X 4 . . . |
$$ | . X O O . O X X . . . X 3 X O X X . . |
$$ | . X X O O X O X . X X O X 1 O O X X . |
$$ | X X O X . X O O X O X 2 O O . X O O . |
$$ | . O O X . . . O . O X O O X X X X X . |
$$ | . . O X . . X . O . X O X O O O O O . |
$$ | . . O X . . . . O X X O X X X X . . . |
$$ | . . O X . . . . O . X X O O X X O O . |
$$ | . X X O X . X . . O O O O X O X X O . |
$$ | . O O O . . . . . . . . . . O O X X . |
$$ | . . . . . X . . . X . . . . . . O X . |
$$ | . . . O . . . . . . . . . . . . O X . |
$$ | . . . . . X . . . . . . . . . . . O . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . , . O . . . , . . . . . O . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Which becomes an enormous ko which we take first... I think we win...

Re: Big Brother Malkovich # 1 (continued)

Posted: Fri Jan 14, 2011 8:07 am
by topazg
:shock: :o
:clap: :bow:

Re: Big Brother Malkovich # 1 (continued)

Posted: Fri Jan 14, 2011 2:38 pm
by Violence
I can post hidden comments too!


Where's Gresil?

Re: Big Brother Malkovich # 1 (continued)

Posted: Sun Jan 16, 2011 9:57 am
by Gresil
Youse folks is being disconcertingly talkative.

Click Here To Show Diagram Code
[go]$$Bc 105A W52 B49
$$ ---------------------------------------
$$ | . . . . . . . O . . . . . . . . . . . |
$$ | . X X O O . O X . . . . . . . . . . . |
$$ | . X O O . O X X . . . X . . O X X . . |
$$ | . X X O O X O X . X X O X . O O X . . |
$$ | X X O X . X O O X O X . O O . X O . . |
$$ | . O O X . . . O . O X O O X X X X X . |
$$ | . . O X . . X . O . X O X O O O O O . |
$$ | . . O X . . . . O X X O X X X X . . . |
$$ | . . O X . . . . O . X X O O B . O . . |
$$ | . X X O X . X . . O O O . . . , . . . |
$$ | . O O O . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . X . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . , . O . . . , . . . . . O . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]


Liberties are everything here. I must make a move that removes one of theirs or gains one for us. Toward the top there are on first glance four adjacent groups with three liberties each. The possibility of white S15 looms over the situation and limits our choices: loss of the P15 liberty means having to take gote to capture at S15, which rules out P15 and O16 as the next black move—we can't cut white here. The only remaining potentially useful liberty-removing move in the top is M15. What does that do? Nothing, from the looks of it.

Click Here To Show Diagram Code
[go]$$Bc 105A W52 B49
$$ ---------------------------------------
$$ | . . . . . . . O . . . . . . . . . . . |
$$ | . X X O O . O X . . . . . . 4 . . . . |
$$ | . X O O . O X X . . . X . . O X X . . |
$$ | . X X O O X O X . X X O X . O O X . . |
$$ | X X O X . X O O X O X 1 O O 2 X O 3 . |
$$ | . O O X . . . O . O X O O X X X X X . |
$$ | . . O X . . X . O . X O X O O O O O . |
$$ | . . O X . . . . O X X O X X X X . . . |
$$ | . . O X . . . . O . X X O O . . O . . |
$$ | . X X O X . X . . O O O . . . , . . . |
$$ | . O O O . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . X . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . , . O . . . , . . . . . O . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

I don't know what the correct :w4: is (edit: see next message), but this doesn't seem like an useful exchange. As I said, I see no other sente moves at the top.

Down the board there's the O12 group in threat of being captured. The only move that breaks it out even temporarily is this:
Click Here To Show Diagram Code
[go]$$Bc 105A W52 B49
$$ ---------------------------------------
$$ | . . . . . . . O . . . . . . . . . . . |
$$ | . X X O O . O X . . . . . . . . . . . |
$$ | . X O O . O X X . . . X . . O X X . . |
$$ | . X X O O X O X . X X O X . O O X . . |
$$ | X X O X . X O O X O X . O O . X O . . |
$$ | . O O X . . . O . O X O O X X X X X . |
$$ | . . O X . . X . O . X O X O O O O O . |
$$ | . . O X . . . . O X X O X X X X . . . |
$$ | . . O X . . . . O . X X O O 1 7 O . . |
$$ | . X X O X . X . . O O O 4 3 2 5 . . . |
$$ | . O O O . . . . . . . . . . 6 . . . . |
$$ | . . . . . X . . . X . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . , . O . . . , . . . . . O . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]

I can't read any further and don't know if it works, but I don't know what else to play.

Re: Big Brother Malkovich # 1 (continued)

Posted: Sun Jan 16, 2011 10:02 am
by Gresil
Bloody hell, now I think black should play the exchange from M15 first and then play this move. M15 makes our top center group much more secure.


Edit: no, never mind. We'd lose the capturing race after M15, right?

Click Here To Show Diagram Code
[go]$$Bc 105A W52 B49
$$ ---------------------------------------
$$ | . . . . . . . O . . . . . . . . . . . |
$$ | . X X O O . O X . . . . . . . . . . . |
$$ | . X O O . O X X . . . X . . O X X . . |
$$ | . X X O O X O X . X X O X . O O X . . |
$$ | X X O X . X O O X O X 1 O O 2 X O 3 . |
$$ | . O O X . . . O . O X O O X X X X X . |
$$ | . . O X . . X . O . X O X O O O O O . |
$$ | . . O X . . . . O X X O X X X X . . . |
$$ | . . O X . . . . O . X X O O 4 . O . . |
$$ | . X X O X . X . . O O O . . . , . . . |
$$ | . O O O . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . X . . . . . . . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . X . . . . . . . . . . . . . |
$$ | . . X . X . . . . . . . . . . . . . . |
$$ | . . . , . O . . . , . . . . . O . . . |
$$ | . . . O . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
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