EGTB Testsuite

Discussion of anything and everything relating to chess playing software and machines.

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Dirt
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Re: EGTB Testsuite

Post by Dirt » Sun Feb 03, 2008 5:52 pm

smirobth wrote:Have you found any programs that play any of the three winning moves in the first position (that has three possible winning moves)? That one should be much harder.
The new Toga found Rh8+ on my system in just over 30 minutes. A fast system should be able to cut that down to under 10 minutes, but that's still comfortably long enough for a good test; unless some other engine is quite a bit faster.

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Kirill Kryukov
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Re: EGTB Testsuite

Post by Kirill Kryukov » Mon Feb 04, 2008 6:19 am

Come on! No any more positions? I know it's more hard than chatting about cloning and moral issues, still you can try!

Here I maintain the requirements and all positions collected so far.

All contribution will have full credit. When complete (or when it has anything useful at all :-)), this test suite will be used to test EGTB support in engines and interfaces. So come and leave your name in the history book of computer chess. :-)

I think this task requires analytical and composition skills, and also mastery in using engines and tablebases. I'll understand that it is hard to do, but at least someone could try making a good endgame test?

The best position so far is submitted by Robin Smith:
[D]k7/P6R/3K4/8/7P/2r5/8/8 w - - bm Rh8+; dm 36;

Here is the best I myself could come up with: :-)
[D]k6N/1p5B/7p/7p/7p/7p/7p/7K w - - bm Kxh2; dm 39;

Best regards
Kirill

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Graham Banks
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Re: EGTB Testsuite

Post by Graham Banks » Mon Feb 04, 2008 6:58 am

I prefer Robin's because it's a realistic position. :P :wink:
My email addresses:
gbanksnz at gmail.com
gbanksnz at yahoo.co.nz

Spock

Re: EGTB Testsuite

Post by Spock » Mon Feb 04, 2008 7:35 am

Graham Banks wrote:I prefer Robin's because it's a realistic position. :P :wink:
I agree. If you're going to have a test position, it should be something that might realistically be seen in actual game play.

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smirobth
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Re: EGTB Testsuite

Post by smirobth » Mon Feb 04, 2008 8:33 am

Kirill Kryukov wrote:Here is the best I myself could come up with: :-)
[D]k6N/1p5B/7p/7p/7p/7p/7p/7K w - - bm Kxh2; dm 39;

Best regards
Kirill
This position does not seem to meet several criteria:
1) Some programs select Kxh2 even without tablebases. For example Fritz selects Kxh2 for the first few seconds before switching away.
2) There is not only one winning move. In fact quite the opposite: every move wins.
3) It is not clear that Kxh2 leads to the fastest win. It does lead most quickly to a known won tablebase position, but that does not mean it wins the fastest. Therefore saying Kxh2 is the best move is uncertain.
- Robin Smith

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Kirill Kryukov
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Re: EGTB Testsuite

Post by Kirill Kryukov » Mon Feb 04, 2008 9:08 am

Graham Banks wrote:I prefer Robin's because it's a realistic position. :P :wink:
Spock wrote:I agree. If you're going to have a test position, it should be something that might realistically be seen in actual game play.
smirobth wrote:
Kirill Kryukov wrote:Here is the best I myself could come up with: :-)
[D]k6N/1p5B/7p/7p/7p/7p/7p/7K w - - bm Kxh2; dm 39;

Best regards
Kirill
This position does not seem to meet several criteria:
1) Some programs select Kxh2 even without tablebases. For example Fritz selects Kxh2 for the first few seconds before switching away.
2) There is not only one winning move. In fact quite the opposite: every move wins.
3) It is not clear that Kxh2 leads to the fastest win. It does lead most quickly to a known won tablebase position, but that does not mean it wins the fastest. Therefore saying Kxh2 is the best move is uncertain.
OK, apparently everyone is clever enough to point out flaws in my test position. :D Surprise, I am aware that it is unrealistic position and a bad test. I would much rather see better positions myself! I added my position (however bad it is) just as a motivating example, hoping that someone can do better. :-)

Robin's position is very close to be a perfect test. My position is very far, and is only listed as possibly useful. There was no perfect test position proposed yet. This all you can see in my post here where I collect all submitted positions so far and my comments about each.

To really show your genius, please think up a position that will meet the criteria and become first entry in the EGTB test suite. I will be really happy and impressed to see a perfect test position! Thanks! :-D

Best wishes,
Kirill

MoKy

Re: EGTB Testsuite

Post by MoKy » Mon Feb 04, 2008 11:27 am

I think for this test are preferable drawn positions. Here is a study by Akobia+Becker 2005 [D]8/8/6p1/7R/b6K/5k2/3n4/2n5 w - - 0 1 bm Rh6=

And I add the next one by Kekely 2003
[D]3N4/7P/5pK1/1p5B/2k1b3/8/4rn2/8 w - - 0 1 bm Kxf6=

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Kirill Kryukov
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Re: EGTB Testsuite

Post by Kirill Kryukov » Mon Feb 04, 2008 11:56 am

Thanks Mario! And welcome to the forum!

I will try to analyze your positions when my computer finishes current computation. Looks promising!

Uri Blass
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Re: EGTB Testsuite

Post by Uri Blass » Mon Feb 04, 2008 1:01 pm

MoKy wrote:I think for this test are preferable drawn positions. Here is a study by Akobia+Becker 2005 [D]8/8/6p1/7R/b6K/5k2/3n4/2n5 w - - 0 1 bm Rh6=


Trivial for rybka without tablebases

New game
8/8/6p1/7R/b6K/5k2/3n4/2n5 w - - 0 1

Analysis by Rybka 2.3.2a 32-bit :

1.Rh5-h6 Ba4-e8
-+ (-4.23) Depth: 5 00:00:00
1.Rh5-g5 Ba4-e8
-+ (-4.21) Depth: 5 00:00:00
1.Rh5-g5 Ba4-e8 2.Rg5-e5
-+ (-4.17) Depth: 6 00:00:00 1kN
1.Rh5-g5 Ba4-e8 2.Rg5-e5 Be8-f7
-+ (-4.31) Depth: 7 00:00:00 2kN
1.Rh5-h6 Ba4-e8 2.Rh6-h8 Be8-b5
-+ (-4.25) Depth: 7 00:00:00 2kN
1.Rh5-h6 Ba4-e8 2.Rh6-h8 Be8-b5 3.Kh4-g5
-+ (-4.39) Depth: 8 00:00:00 3kN
1.Rh5-g5 Ba4-e8 2.Rg5-e5 Be8-f7 3.Re5-e7
-+ (-4.33) Depth: 8 00:00:00 4kN
1.Rh5-g5 Ba4-c2 2.Rg5-c5 Bc2-f5 3.Rc5xc1 Kf3-f4
-+ (-4.49) Depth: 9 00:00:00 8kN
1.Rh5-h6 Ba4-e8 2.Rh6-h8 Be8-b5 3.Kh4-g5 Bb5-d3
-+ (-4.45) Depth: 9 00:00:00 9kN
1.Rh5-h6 Ba4-e8 2.Rh6-h8 Be8-b5 3.Kh4-g5 Bb5-d3 4.Rh8-h3+
-+ (-1.95) Depth: 10 00:00:00 15kN
1.Rh5-h6 Ba4-e8 2.Rh6-h8 Be8-c6 3.Rh8-c8 Bc6-e4 4.Rc8xc1
-+ (-1.91) Depth: 10 00:00:00 21kN
1.Rh5-h6 Ba4-e8 2.Rh6-h8 Be8-c6 3.Rh8-c8 Bc6-e4 4.Rc8xc1 Kf3-f4
-+ (-1.89) Depth: 11 00:00:00 24kN
1.Rh5-h6 Ba4-e8 2.Rh6-h8 Be8-d7 3.Rh8-d8 Bd7-f5 4.Rd8xd2 Nc1-e2 5.Rd2-d1
-+ (-1.45) Depth: 12 00:00:01 35kN
1.Rh5-h6 Ba4-e8 2.Rh6-h8 Be8-d7 3.Rh8-d8 Bd7-f5 4.Rd8xd2 Nc1-e2 5.Rd2-d1 Ne2-g3
-+ (-1.53) Depth: 13 00:00:01 43kN
1.Rh5-h6 Ba4-e8 2.Rh6-h8 Be8-d7 3.Rh8-d8 Bd7-f5 4.Rd8xd2 Nc1-e2 5.Rd2-d1 Ne2-g3 6.Kh4-g5
-+ (-1.44) Depth: 14 00:00:01 58kN
1.Rh5-h6 Ba4-e8 2.Rh6-h8 Be8-d7 3.Rh8-d8 Bd7-f5 4.Rd8xd2 Nc1-e2 5.Rd2-d1 Ne2-g3 6.Kh4-g5 Ng3-e4+ 7.Kg5-h6
-+ (-1.60) Depth: 15 00:00:01 80kN
1.Rh5-h6 Ba4-e8 2.Rh6-h8 Be8-d7 3.Rh8-d8 Bd7-f5 4.Rd8xd2 Nc1-e2 5.Rd2-d1 Ne2-g3 6.Kh4-g5 Ng3-e4+ 7.Kg5-h6 g6-g5
-+ (-1.51) Depth: 16 00:00:03 122kN
1.Rh5-h6 Ba4-e8 2.Rh6-h8 Be8-d7 3.Rh8-d8 Bd7-f5 4.Rd8xd2 Nc1-e2 5.Kh4-g5 Ne2-c3 6.Kg5-h6 Nc3-e4 7.Rd2-d1 g6-g5
-+ (-1.50) Depth: 17 00:00:05 191kN
1.Rh5-h6 Ba4-e8 2.Rh6-h8 Be8-d7 3.Rh8-d8 Bd7-f5 4.Rd8xd2 Nc1-e2 5.Kh4-g5 Ne2-c3 6.Kg5-h6 Nc3-e4 7.Rd2-d1 g6-g5
-+ (-1.50) Depth: 18 00:00:08 278kN
1.Rh5-h6 Ba4-e8 2.Rh6-h8 Be8-d7 3.Rh8-d8 Bd7-f5 4.Rd8xd2 Nc1-e2 5.Kh4-g5 Ne2-c3 6.Kg5-h6 Nc3-e4 7.Rd2-d1 g6-g5
-+ (-1.64) Depth: 19 00:00:12 423kN
1.Rh5-h6 Ba4-e8 2.Rh6-h8 Be8-d7 3.Rh8-d8 Bd7-f5 4.Rd8xd2 Nc1-e2 5.Rd2-d1 Ne2-g3 6.Rd1-g1 Ng3-e4 7.Rg1-f1+ Kf3-e3
-+ (-1.64) Depth: 20 00:00:19 657kN
1.Rh5-h6 Ba4-e8 2.Rh6-h8 Be8-d7 3.Rh8-d8 Bd7-f5 4.Rd8xd2 Nc1-e2 5.Rd2-d1 Ne2-g3 6.Kh4-g5 Ng3-e4+ 7.Kg5-h6 g6-g5
-+ (-1.70) Depth: 21 00:00:30 990kN

(, 04.02.2008)


And I add the next one by Kekely 2003
[D]3N4/7P/5pK1/1p5B/2k1b3/8/4rn2/8 w - - 0 1 bm Kxf6=
few seconds for rybka without tablebases or glaurung or old Junior with no tablebases

New game
3N4/7P/5pK1/1p5B/2k1b3/8/4rn2/8 w - - 0 1

Analysis by Rybka 2.3.2a 32-bit :

1.Kg6-f7 Be4xh7
µ (-1.40) Depth: 5 00:00:00
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Nf2-d3
µ (-0.97) Depth: 6 00:00:00 2kN
1.Kg6-g7 Be4xh7 2.Bh5xe2+ Bh7-d3
µ (-0.76) Depth: 6 00:00:00 2kN
1.Kg6-g7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Nf2xd3 4.Kg7xf6 Kc4-d5
µ (-1.12) Depth: 7 00:00:00 3kN
1.Kg6-g7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Kc4xd3 4.Kg7xf6 b5-b4 5.Nd8-c6
µ (-1.39) Depth: 8 00:00:00 6kN
1.Kg6-g7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Kc4xd3 4.Kg7xf6 b5-b4 5.Nd8-e6 Kd3-c4
-+ (-2.55) Depth: 9 00:00:00 10kN
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Kc4xd3 4.Nd8-c6 f6-f5 5.Kf7-e6
-+ (-2.20) Depth: 9 00:00:00 11kN
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Kc4xd3 4.Nd8-c6 f6-f5 5.Kf7-e6 f5-f4
-+ (-2.23) Depth: 10 00:00:01 16kN
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Kc4xd3 4.Nd8-b7 b5-b4 5.Kf7-e6 Nf2-e4 6.Nb7-a5
-+ (-2.34) Depth: 11 00:00:01 22kN
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Kc4xd3 4.Kf7-e6 b5-b4 5.Nd8-b7 Nf2-e4 6.Nb7-a5 Kd3-d4
-+ (-2.37) Depth: 12 00:00:01 38kN
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Kc4xd3 4.Kf7-e6 b5-b4 5.Nd8-b7 Nf2-e4 6.Nb7-a5 Kd3-d4 7.Ke6-f5
-+ (-2.26) Depth: 13 00:00:01 53kN
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Kc4xd3 4.Kf7-e6 b5-b4 5.Nd8-b7 Nf2-e4 6.Nb7-a5 Kd3-d4 7.Ke6-f5 Kd4-d5
-+ (-2.27) Depth: 14 00:00:01 74kN
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Kc4xd3 4.Kf7-e6 b5-b4 5.Nd8-b7 Nf2-e4 6.Nb7-a5 Kd3-d4 7.Ke6-f5 Kd4-d5
-+ (-2.27) Depth: 15 00:00:01 106kN
1.Kg6xf6 Nf2-g4+ 2.Bh5xg4 Re2-h2 3.Bg4-e2+ Be4-d3 4.Be2xd3+ Kc4xd3 5.Kf6-g7 b5-b4 6.Nd8-b7 Kd3-d4 7.Nb7-a5 Kd4-c5
µ (-0.73) Depth: 15 00:00:04 250kN
1.Kg6xf6 Nf2-g4+ 2.Bh5xg4 Re2-h2 3.Bg4-e2+ Be4-d3 4.Be2xd3+ Kc4xd3 5.Kf6-g7 b5-b4 6.Nd8-b7 Kd3-d4 7.Nb7-a5 Kd4-c5
µ (-0.73) Depth: 16 00:00:06 380kN
1.Kg6xf6 Nf2-g4+ 2.Bh5xg4 Re2-f2+ 3.Kf6-g7 Be4xh7 4.Kg7xh7 Kc4-d5 5.Bg4-e6+ Kd5-d6 6.Be6-b3 Rf2-f3 7.Bb3-g8 Rf3-c3
µ (-0.83) Depth: 17 00:00:15 973kN

(, 04.02.2008)

New game
3N4/7P/5pK1/1p5B/2k1b3/8/4rn2/8 w - - 0 1

Analysis by Glaurung 2.0.1:

1.Kg6xf6 Be4xh7 2.Bh5xe2+ Nf2-d3
-+ (-2.13) Depth: 2 00:00:00
1.Kg6xf6 Be4xh7 2.Bh5xe2+ Nf2-d3
-+ (-2.13) Depth: 3 00:00:00
1.Kg6xf6 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Nf2xd3 4.Nd8-e6
-+ (-1.94) Depth: 4 00:00:00
1.Kg6xf6 Nf2-g4+ 2.Bh5xg4 Re2-h2 3.Bg4-e2+ Kc4-b4 4.Be2xb5 Kb4xb5
-+ (-4.13) Depth: 5 00:00:00
1.Kg6-g7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Nf2xd3 4.Kg7xf6 b5-b4
-+ (-2.74) Depth: 5 00:00:00
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Nf2-d3 3.Kf7-g7 Bh7-e4 4.Be2xd3+ Kc4xd3 5.Kg7xf6
-+ (-2.52) Depth: 5 00:00:01
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Kc4xd3 4.Kf7xf6 Nf2-e4+ 5.Kf6-e5 b5-b4
-+ (-2.45) Depth: 6 00:00:01 11kN
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Nf2xd3 4.Kf7xf6 b5-b4 5.Nd8-e6 b4-b3
-+ (-2.78) Depth: 7 00:00:01 15kN
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Nf2xd3 4.Kf7xf6 b5-b4 5.Nd8-e6 b4-b3 6.Kf6-f5
-+ (-2.74) Depth: 8 00:00:01 24kN
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Nf2xd3 4.Kf7xf6 Kc4-d5 5.Nd8-e6 b5-b4 6.Ne6-c7+ Kd5-e4 7.Nc7-e6
-+ (-2.43) Depth: 9 00:00:01 47kN
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Nf2xd3 4.Kf7xf6 Kc4-d5 5.Kf6-g5 b5-b4 6.Kg5-f5 b4-b3 7.Nd8-e6
-+ (-2.80) Depth: 10 00:00:01 94kN
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Nf2xd3 4.Kf7xf6 Kc4-d5 5.Nd8-e6 b5-b4 6.Kf6-f5 b4-b3 7.Ne6-c7+ Kd5-c4 8.Nc7-e6
-+ (-2.74) Depth: 11 00:00:01 168kN
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Nf2xd3 4.Kf7xf6 Kc4-d5 5.Nd8-b7 b5-b4 6.Nb7-a5 Nd3-e5 7.Na5-b3 Kd5-c4 8.Nb3-d2+ Kc4-d5
-+ (-2.74) Depth: 12 00:00:01 290kN
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Nf2xd3 4.Kf7xf6 Kc4-d5 5.Nd8-b7 Nd3-c5 6.Nb7-a5 Nc5-e4+ 7.Kf6-f5 b5-b4 8.Na5-b3 Kd5-c4 9.Nb3-a5+ Kc4-d5
-+ (-2.84) Depth: 13 00:00:01 542kN
1.Kg6-f7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Kc4xd3 4.Nd8-c6 Nf2-g4 5.Kf7-e6 Kd3-e4 6.Ke6-d6 Ng4-e5 7.Nc6-b4 Ke4-d4 8.Kd6-e6 Kd4-c4 9.Nb4-d5
-+ (-3.01) Depth: 14 00:00:02 1353kN
1.Kg6xf6 Be4xh7 2.Bh5xe2+ Nf2-d3 3.Be2xd3+ Kc4xd3 4.Nd8-e6 b5-b4 5.Kf6-e5 Kd3-c4 6.Ne6-d4 Kc4-c3 7.Nd4-e2+ Kc3-d3 8.Ne2-d4 Bh7-e4 9.Nd4-e6 Kd3-e3
-+ (-1.98) Depth: 14 00:00:04 3924kN
1.Kg6xf6 Be4xh7 2.Bh5xe2+ Nf2-d3 3.Be2-g4 Kc4-c3 4.Nd8-c6 Bh7-e4 5.Bg4-d7 Be4xc6 6.Bd7xc6 b5-b4 7.Bc6-d5 Nd3-f4 8.Bd5-f3 b4-b3 9.Kf6-e5
-+ (-1.94) Depth: 15 00:00:05 5132kN
1.Kg6xf6 Be4xh7 2.Bh5xe2+ Nf2-d3 3.Be2-g4 Kc4-c3 4.Nd8-c6 Bh7-e4 5.Nc6-a7 b5-b4 6.Na7-b5+ Kc3-d2 7.Nb5-d4 Nd3-c5 8.Kf6-e5 Kd2-e3 9.Nd4-f5+ Ke3-d3 10.Nf5-d4
-+ (-1.98) Depth: 16 00:00:06 6501kN

(, 04.02.2008)

New game
3N4/7P/5pK1/1p5B/2k1b3/8/4rn2/8 w - - 0 1

Analysis by Junior 9:

1.Kg6-f7 Be4xh7 2.Bh5xe2+ Bh7-d3
-+ (-3.21) Depth: 3 00:00:00
1.Kg6-g7 Be4xh7 2.Bh5xe2+ Bh7-d3
-+ (-2.78) Depth: 3 00:00:00
1.Kg6xf6 Be4xh7 2.Bh5xe2+ Bh7-d3
-+ (-2.22) Depth: 3 00:00:00 1kN
1.Kg6xf6 Nf2-g4+ 2.Bh5xg4 Re2-h2 3.Bg4-e6+ Kc4-b4 4.Kf6-g7 Rh2xh7+ 5.Kg7-g8
-+ (-4.40) Depth: 6 00:00:00 5kN
1.Kg6-g7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Nf2xd3 4.Kg7xf6 b5-b4
-+ (-2.72) Depth: 6 00:00:00 6kN
1.Kg6-g7!
-+ (-2.42) Depth: 9 00:00:00 20kN
1.Kg6-g7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Kc4xd3 4.Kg7xf6 b5-b4 5.Kf6-e5 Kd3-c4
-+ (-1.51) Depth: 9 00:00:00 33kN
1.Kg6-g7!
µ (-1.21) Depth: 12 00:00:00 238kN
1.Kg6-g7 Be4xh7 2.Bh5xe2+ Bh7-d3 3.Be2xd3+ Kc4xd3 4.Kg7xf6 b5-b4 5.Nd8-e6 Nf2-e4+ 6.Kf6-e5 b4-b3 7.Ne6-f4+ Kd3-c4 8.Nf4-d3 Kc4xd3 9.Ke5-d5 b3-b2
-+ (-1.96) Depth: 15 00:00:01 1839kN
1.Kg6xf6 Nf2-g4+ 2.Bh5xg4 Re2-h2 3.Bg4-e2+ Kc4-c5 4.Be2xb5 Kc5xb5 5.h7-h8Q Rh2xh8 6.Nd8-f7
-+ (-1.91) Depth: 15 00:00:03 5535kN
1.Kg6xf6 Nf2-g4+ 2.Bh5xg4 Re2-h2 3.Bg4-e2+ Kc4-c5 4.Be2xb5 Kc5xb5 5.h7-h8Q Rh2xh8 6.Nd8-f7 Rh8-h3 7.Nf7-d6+ Kb5-c5 8.Nd6xe4+ Kc5-d5
-+ (-1.85) Depth: 18 00:00:13 24878kN

(, 04.02.2008)

Jouni
Posts: 1791
Joined: Wed Mar 08, 2006 7:15 pm

Re: EGTB Testsuite

Post by Jouni » Mon Feb 04, 2008 3:55 pm

Here's traditional position to test, if 4 piece tb/bb access is working in the search:

[D]8/k7/8/2R5/8/4q3/8/4B2K w - - bm Bg3

Other moves lose I think. Actually I have seen solution without bases, but
it took a lot time. With bases You got solution instantly.

Jouni

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