How does my 10x10 chessboard 'Sac Chess' variant seems to you

[Kevin Pacey]

The purpose of this poll is to get an idea how respondents feel about a 10x10 board chess variant idea of mine. The following is an excerpt from an entry on my CFC Discussion Board Blog, which includes a description of one of my 10x10 chess variant ideas (called 'Sac Chess'). Bear in mind that 10x10 chessboards exist or can be simulated by computers:

...
Here's an idea for a 10x10 chess variant. My goal was to have it maybe not too wildly different from chess, yet possibly capable of being computer-resistant as far as the number of legal moves available in a position typically might go. In comparison to the 'Grand Chess' 10x10 variant the start position of my variant is more orderly - there are no empty squares on both side's 1st or 2nd rank (also, in a way I retained the starting positions for the chess pieces, a memory aid to those who play chess). Also Fool's mate & a kind of Scholar's mate are possible, as in chess (& in the same # of moves):

Col a Col b Col c Col d Col e Col f Col g Col h Col i Col j     Row xx

 [C]  :[A]:  [S]  :[Z]:  [M]  :[M]:  [Z]  :[S]:  [A]  :[C]:       10

:[J]:  [R]  :[N]:  [B]  :[Q]:  [K]  :[B]:  [N]  :[R]:  [J]         9

 [P]  :[P]:  [P]  :[P]:  [P]  :[P]:  [P]  :[P]:  [P]  :[P]:        8

:::::       :::::       :::::       :::::       :::::              7

      :::::       :::::       :::::       :::::       :::::        6

:::::       :::::       :::::       :::::       :::::              5

      :::::       :::::       :::::       :::::       :::::        4

:(P):  (P)  :(P):  (P)  :(P):  (P)  :(P):  (P)  :(P):  (P)         3

 (J)  :(R):  (N)  :(B):  (Q)  :(K):  (B)  :(N):  (R)  :(J):        2

:(C):  (A)  :(S):  (Z)  :(M):  (M)  :(Z):  (S)  :(A):  (C)         1

In this variant there are 6 new types of pieces than in chess besides the standard 6 types:
Z = Amazon (moves like N or Q), a standard fairy chess piece;
C = Chancellor (moves like N or R [without castling]), a standard fairy chess piece made famous by Capablanca Chess;
A = Archbishop (moves like N or B), a standard fairy chess piece made famous by Capablanca Chess;
S = Sailor (moves like R or K [without castling]), a piece from Shogi (promoted Rook, or 'Dragon', in that game);
M = Missionary (moves like B or K [without castling]), a piece from Shogi (promoted Bishop, or 'Horse', in that game);
J = Judge (moves like N or K [without castling]), my idea possibly, inspired by the Shogi piece types above.

Castling may occur on the 2nd rank between the king and either rook, with conditions as in chess. Pawns act standardly too, the only difference being that while they still promote on the last rank, any of the new types of pieces may be selected, besides piece types allowed in chess. Stalemate is a draw, like in chess.

An example game that might delight a beginner is one version of a Fool's mate: 1.Pg3-g5 Pf8-f7 2.Ph3-h5 Qe9-i5 mate. Then there is 1 version of Scholar's mate: 1.Pf3-f5 Pf8-f6 2.Bg2-d5 Nc9-d7 3.Qe2-g4 Nd7-e5 4.Qg4xg8 mate.

A possible drawback to this variant I've dubbed 'Sac Chess' - note the initials of the last 3 pieces on White's 1st rank :D - is that if one avoids blundering early, such as above, a typical game might be lengthy given that there's so many extra pieces and squares compared to chess, & a king is typically going to be well defended for a while, I'd guess. [edit: However note that advocates of the oriental game of Go at times like to point out that (I suspect partly in terms of number of moves typical for a whole game to be played), chess is a battle (about 40 moves per side on average), while Go is a war (about 75 moves per side on average).] Testing is needed, if there's interest.
...

For further insight if desired, here is a link to the relevant CFC Discussion Board Blog entry [edit: note that besides large # legal moves there's most likely a large number of heuristics to be discovered, which helps the possible computer-resistance of Sac Chess for a long time to come]:

http://www.chesscanada.info/forum/en...-(Part-1-of-2)

[Paul Bonham]

Re: How does my 10x10 chessboard 'Sac Chess' variant seems to you

The purpose of this poll is to get an idea how respondents feel about a 10x10 board chess variant idea of mine...
http://www.chesscanada.info/forum/en...-(Part-1-of-2)

Kevin, I haven't voted in your poll but I think a voting option you could have added would be:
"SAC Chess seems like a good variant for correspondence play only."

I know you love these 10 x 10 variants with many more pieces than regular chess, and that's fine, but could you honestly ever see such a variant being played seriously at clubs or weekend tournaments? I think variants as complicated as SAC Chess should actually be labelled as "Correspondence Chess Variants" because imo only people such as seniors who have hours to spend analyzing a position of that variant to come up with a move would take an interest. Or maybe even non-seniors who like correspondence but are driven away from correspondence standard chess because of use of computers; this variant would obviously not have that problem.

I also have an interest in 10 x 10 variants, but I would introduce only a limited number of new pieces. For example, take a 10 x 10 board and set up the standard chess start position beginning at White's b2 square (ending at Black's i9 square). This is akin to putting a perimeter of 1 square depth around a regular chess start position. Give the Knights the ability to move in their normal 2x1 (1x2) L-pattern and also a 3x2 (2x3) L-pattern to help them get across the board quicker. Then maybe give each side an extra pair of Rooks, starting for White on e1 and f1 and for Black on e10 and f10. And that's it. Add one extra rule: like pieces cannot capture each other unless the captured piece is en prise or the capture gives checkmate or a discovered check. However, this only applies to major pieces: Pawn may still take Pawn even if it's defended.

This makes for 36 pieces and 64 empty squares at game start, much more reasonable than your 60 pieces and 40 empty squares. The rule I added makes trading off like pieces almost impossible, so pieces tend to stay on the board longer.

[Kevin Pacey]

Re: How does my 10x10 chessboard 'Sac Chess' variant seems to you

Hi Paul

I see 10x10 boards as perhaps the largest attractive board size for variants, which could make them harder for computers to dominate as a result. I'd be completely happy with standard chess except for computer dominance of it over humans (and the possible cheating concern resulting), as you may recall. 'Sac Chess' meets to some degree many criteria I desire in a variant besides possible difficulty for computers to dominate the variant, too. If 'Sac Chess' is as unplayable otb as you fear, by all means consider playing it by correspondence (only, if necessary). I'm not sure your 10x10 variant might be so computer-resistant, if that is a criteria of yours for judging a variant. The oriental game of Go is looking very much computer-resistant at the moment, but I'd miss the thrill of chasing after a king if I concentrated on that game, and I am not as young now either if I wished to master Go.

Perhaps because of being a national master at standard chess, I was able to do some sort of calculating when it came to possible early play right from the start position of 'Sac Chess', in a couple of cases that I tried to, including making use of some of the new piece types. What seems to happen is that a number of each side's pieces are either going to be involved in the play in the opening, or else some/many are going to act as 'reserves' that are not worth developing for a long time to come (which humans may see, but maybe not even a good computer program would see).

Below is a sample game fragment of me playing solitaire against myself at 'Sac Chess', with primitive diagrams (suitable for email play) used every 5 ply. I played 20 moves, and decided to quit after discovering the other side's advanced pawn was going to be rounded up. One thing I'm not sure I like about 'Sac Chess' is that an average game might well take many, many moves, but other people may feel differently.

http://www.chesscanada.info/forum/en...riant-of-mine)

[edit: One place I seem to recall seeing other (likely little tested) 10x10 variants with 60 pieces is the Chess Variants Page website, fwiw. Perhaps some young children might feel not so ready for a game with 60 pieces, but from some adults' point of view that may not be necessarily such a bad thing.]

[Paul Bonham]

Re: How does my 10x10 chessboard 'Sac Chess' variant seems to you

...I'm not sure your 10x10 variant might be so computer-resistant, if that is a criteria of yours for judging a variant...

Yes, Kevin, you are correct that the variant I described as my preferred 10 x 10 variant with just 36 total pieces is not going to be computer-resistant. But you'll recall my invention of Option Chess... with the idea that giving each side a limited number of 'option tokens' which each can be used to add an additional move to a player's turn, is a recipe for resistance to computer engine domination for any turn-based strategy game.

It could be done with checkers. The normal 8 x 8 checkers is solved by computers. But simply give each side 12 option tokens to be used at their discretion at critical points (as they judge it) during the first 32 moves of the game, and not only is the game no longer solved, but I believe humans would dominate or have parity with any computer engine that would be written to play under those rules. The engine programmer would have a hard time getting the engine to decide when NOT to use an option. Eventually they might deduce some reasonable heuristics... but the best they could hope for (imo) would be parity with humans. Humans are much better at making inferential decisions, and this would give them (again, imo) even strength against the much better calculation abilities of the engine.

The only way to know for certain would be for somebody to write such an engine to play Option Checkers...

[Mathieu Cloutier]

Re: How does my 10x10 chessboard 'Sac Chess' variant seems to you

10x10 will just be easier for computers to dominate.

Whatever needs more calculation will eventually be dominated by computers.

And 'option chess' is just plain ridiculous in that regard. Computers would simply crush us.

If you want computer resistant chess, look at a game like Arimaa. That's where you want to go.

[Kevin Pacey]

Re: How does my 10x10 chessboard 'Sac Chess' variant seems to you

10x10 will just be easier for computers to dominate.

Whatever needs more calculation will eventually be dominated by computers.

And 'option chess' is just plain ridiculous in that regard. Computers would simply crush us.

If you want computer resistant chess, look at a game like Arimaa. That's where you want to go.

I've read somewhere that 10x10 or 10x8 variants which are currently popular (Grand Chess, Capablanca Chess) are harder for computers to dominate, at least at present, but of course programmers haven't paid a lot of attention to them yet because they are still not quite popular enough. The oriental game game of Go is a clear case where larger board size is better - some smaller board sizes than the standard 19x19 have actually been solved by computers. There may also be practical memory space issues for computers that impair the depth of searches, I'd guess, because bigger boards take more space to store in memory. Bughouse (aka Doubles Chess) is hard for computers, unless one side on one board is not playing (i.e. someone is 'sitting') while the other board still is - otherwise the two boards make for an overall larger 'board', for one thing.

[edit: An expert on Arimaa, in a link that was once on chesstalk, noted that Seirawan Chess (basically played with the same pieces as Capablanca Chess, but played just on an 8x8 board with 2 pawns less per side) became dominated by computers as soon as S-Chess became popular enough and caught the attention of serious programmers. Below is the link, describing 7 criteria a world champ Arimaa player thinks would make for computer-resistant chess variants, along with a link about Capablanca Chess.]

http://en.chessbase.com/post/compute...chess-variants

https://en.wikipedia.org/wiki/Capablanca_chess

Arimaa is a case that might be a little harder to judge. Some dominance by computers occured for a brief period of time in the beginning of the game's short history, from what I've read. Then humans discovered strategies that weren't so easy to program. Nowadays computers are said to be below top human level, but not too far from it, I've read. The guy who invented the game put restrictions on the type of machine power that could be used in permitted Arimaa competitions, I'd note (the guy also put a patent and various licences on the game, which may slow the development of otb clubs and the spread of Arimaa literature among other things). Perhaps a 10x10 Arimaa variant would help humans even more, too, if a workable one could be made somehow.

[P.S.: Below is a link with references to engines for 10x8 variants such as Capablanca Chess, including one that's claimed to be strong at 2400 level. The link is not dated afaik, but I clicked on one sub-link that was dated as recently as 2013.]

http://home.hccnet.nl/h.g.muller/10x8.html

[Kevin Pacey]

Re: How does my 10x10 chessboard 'Sac Chess' variant seems to you

...
If you want computer resistant chess, look at a game like Arimaa. That's where you want to go.

There's a slight buzz in arimaa circles on the net lately that humans have finally lost to a computer in the annual arimaa challenge match held this year. Wikipedia lists the results of all such matches up to now (I'd note that of two of the human losers in 2015, one is a former world champ [many times] and one is the current world champ):

https://en.wikipedia.org/wiki/Arimaa#Arimaa_Challenge


[edit: International Checkers (i.e. Checkers on a 10x10 board) still has a top human beating a computer, in 2012 at least:

https://en.wikipedia.org/wiki/Intern...mus_.282012.29

a large board helps humanity in this case, it seems, but then so may the simplicity of the moves of a checker piece.]

[Kevin Pacey]

Re: How does my 10x10 chessboard 'Sac Chess' variant seems to you

...
There may also be practical memory space issues for computers that impair the depth of searches, I'd guess, because bigger boards take more space to store in memory.
...

I vaguely recall that one time chesstalk's J. U. explained to me that for computers memory is a serious issue for standard (8x8) chess programmers these days, either for tablebases, or for searching deeper in the move tree with an engine.

That is, on average an engine's search might be about 40 ply deep these days (with the average of 35 legal moves per turn in chess), but a machine needs to store the positions somehow in memory in order to possibly increase the search depth substantially. As an aside, recall an average chess game takes 80 ply.

While processor speed may double at a rate of, say, every 18 months, increasing a typical machine's memory by anything like a similar rate isn't happening as far as I am aware, at least for its speed of memory access, if not for the quantity of its memory. Thus, a chess variant that would use up a lot of a typical off the shelf computer's memory just to store moves and/or positions at each ply level might be at least somewhat computer-resistant for quite a number of years. Larger board size chess variants presumably needing more memory per position to store.

[P.S.: Below is a link mentioning the relatively slow average annual rate of increase to the speed of memory access.]

https://en.wikipedia.org/wiki/Random...ry#Memory_wall

A theoretical problem with this (unlikely?) is that if there ever were a world championship match (for such a chess variant) with a lot of national prestige at stake, like in the 1972 Fischer-Spassky match, there is the possibility of the two player's respective governments using government computers, with a large amount of memory (not to mention great speed) in order to help their own player by cheating with their machines somehow.

[edit: naturally all this doesn't take into account any future breakthroughs in neural net or quantum computer research.]

[Paul Bonham]

Re: How does my 10x10 chessboard 'Sac Chess' variant seems to you

I vaguely recall that one time chesstalk's J. U. explained to me that for computers memory is a serious issue for standard (8x8) chess programmers these days, either for tablebases, or for searching deeper in the move tree with an engine.

That is, on average an engine's search might be about 40 ply deep these days (with the average of 35 legal moves per turn in chess), but a machine needs to store the positions somehow in memory in order to possibly increase the search depth substantially. As an aside, recall an average chess game takes 80 ply.

While processor speed may double at a rate of, say, every 18 months, increasing a typical machine's memory by anything like a similar rate isn't happening as far as I am aware, at least for its speed of memory access, if not for the quantity of its memory. Thus, a chess variant that would use up a lot of a typical off the shelf computer's memory just to store moves and/or positions at each ply level might be at least somewhat computer-resistant for quite a number of years. Larger board size chess variants presumably needing more memory per position to store.

A theoretical problem with this (unlikely?) is that if there ever were a world championship match (for such a chess variant) with a lot of national prestige at stake, like in the 1972 Fischer-Spassky match, there is the possibility of the two player's respective governments using government computers, with a large amount of memory (not to mention great speed) in order to help their own player by cheating with their machines somehow.

[edit: naturally all this doesn't take into account any future breakthroughs in neural net or quantum computer research.]

Government computers??? Maybe they'll use Hillary Clinton's email server! :D

Whatever memory constraint there may be on search ply depth for any 10 x 10 chess variant, you must take into account that for such a variant, being able to search to say 20 ply depth is still going to result in total engine domination of human opponents. That's because the humans are equally limited if not more limited in their own search depth. The increase in complexity affects them as much as it does the software. The engine will still see all tactics perfectly up to that 20 ply limit, and the human will not.

Now the funny thing is, Matthew Cloutier has argued that the point I just made means computers would dominate my variant of Option Chess just as they do regular chess, maybe more so. And I have admitted from the beginning that Option Chess does introduce a much larger search tree. But the thing that people like Cloutier miss in Option Chess is that the engine programmers will not know how to OPTIMIZE the use of (a limited number of) double moves, and the engines will tend towards using them all right away, whereas the human will have a better notion of when it is better to hold off on using them and keep them for later.

It is my hypothesis that this better intuition of humans will make them much closer in strength, likely even superior, to Option Chess engines of the future, decades into the future. And the reason I argue this is that using a double move tends to be much more STRATEGIC than TACTICAL. There are limitations on what one can do with double moves. One cannot make 2 captures, for example, nor make 2 checking moves. So the way it turns out is that you need to use double moves to highly COORDINATE the movement of pieces at critical times. Double moves CAN be wasted. Option Chess stresses timeliness even more so than regular chess.

The best that programmers will be able to hope for is to match the intuitive strategic abilities of humans. And at the same time, the much larger search tree means that engines will not be able to analyze games in real time and provide better lines of play than human analysts. Not only the play, but the real time analysis also, will become much more in command of the humans. Matthew may call this hypothesis "ridiculous" but he is just blowing hot air. At some point I hope to put up a prize fund just as the Arimaa inventor did for his game, mine going to the first Option Chess engine to defeat the highest rated human, and then we will see.

Whereas Kevin I see your 10 x 10 variant (with what was it, 60 pieces total at the start???) to be highly stressing the tactical and thus highly favoring any engines that would be written for it. However, I do agree that your board with all its pieces would be a formidable piece of art sitting on one's coffee table, and would perhaps make for a great correspondence game. And those are both worthy goals to shoot for.

Vlad Dobrich, if you're reading this and you really are tired of organizing chess events as you've indicated in another thread, maybe you should consider organizing Option Chess events. Well, maybe you are one of those against chess variants in general, but I can tell you this: Option Chess is at ground zero. The sky's the limit and there is no licensing of any kind, I have no ownership of anything nor any stake in what happens. The only extra equipment required are sets of option tokens, which can be handmade with ease and I can update you on how they are used. There's no CFC to be concerned with, and in fact you can go ahead and form your own organization if you are ambitious.

Anyone with an organizational bent and an interest in developing a more strategical form of chess can do this. You can PM me for the updated set of rules (very slightly changed from the chessbase.com article of February 2014). I could also send you a Word file documenting 2 complete annotated games between Louis Morin and myself. The second game especially demonstrated the strategical depth of Option Chess.

Oh, and one other thing: Option Chess games tend to be noticeably but not dramatically shorter than regular chess games. making things easier for organizers.

[Mathieu Cloutier]

Re: How does my 10x10 chessboard 'Sac Chess' variant seems to you

And I'm the one blowing hot air...

[Kevin Pacey]

Re: How does my 10x10 chessboard 'Sac Chess' variant seems to you

...
Whatever memory constraint there may be on search ply depth for any 10 x 10 chess variant, you must take into account that for such a variant, being able to search to say 20 ply depth is still going to result in total engine domination of human opponents. That's because the humans are equally limited if not more limited in their own search depth. The increase in complexity affects them as much as it does the software. The engine will still see all tactics perfectly up to that 20 ply limit, and the human will not.
...

Hi Paul

When computers still saw only 20 ply ahead on average in standard 8x8 chess, I imagine they didn't completely dominate the game (maybe someone can recall about what year that might have been the case). Also, I think when computers look x ply ahead on average, it is with sophisticated alpha beta pruning that nowadays on average eliminates at least half of the legal moves per ply than would otherwise need to be included in the search tree, I seem to recall.

[edit: The link below mentions that, using limited hardware capability, Deep Fritz searched 17-18 ply ahead on average in the middlegame during its relatively close 2006 4-2 match victory against world champ Kramnik; bear in mind that Kramnik's losses included overlooking a mate in one and making a desperate (but poor vs. computers) choice of the sharp Sicilian as Black in the final match game.]

https://en.wikipedia.org/wiki/IBM_Deep_Blue#Aftermath

Whether computers would be as good at pruning (ultimately) in the case of my 10x10 Sac Chess variant, I don't know, like as for whether Sac Chess is typically very significantly more tactical than standard chess (like for Seirawan Chess, novel Sac Chess pieces could take some getting used to as far as their moves go, which could help tactically talented players initially). One thing that might be disappointing which may or may not happen in Sac Chess is that games between equally matched skillful players might nearly always result in the exchanging of many pieces over time, without advantage to either player.

At least in Sac Chess a lot of pieces are overprotected by other ones right in the start position, and perhaps this means that Black is at less of a disadvantage at the beginning than in chess. Like for standard chess, in Sac Chess with each side having two bishops, there is still the possibility for square colour complexes to become weak, and there can still be weak pawns, and so on as far as possible strategic themes may go. Like I wrote earlier, humans might be able to recognize that (at least in the early part of a game) a lot of the pieces in Sac Chess may not be worth trying to develop for a long time (i.e. they act as reserves), thus aiding calculation, but I'm not completely sure a computer could realize this as much, as far as its pruning of the search tree goes. Largely stable chunks of pieces in a position might help humans over computers, it was at least once argued in the case of standard chess.

Fwiw, using my vague memory of how to do math with exponents, I've guesstimated that for Sac Chess, currently a hypothetical 'good' engine for it might see up to 25 ply ahead on average (maybe 30 if memory constraints due to bigger board size weren't an issue) but the number might actually be closer to 20 ply, as you happened to give as a figure. That's based on knowing that for chess nowadays a good engine sees 40 ply ahead, with 35 legal moves per turn on average (I've guessed that there might be at least an additional 100 moves or so on average per turn in the case of Sac Chess; the number could be higher but for the fact that the pieces often may get in each other's way to some extent).

[edit: Below is a link that discusses one fairly modern chess engine, noting that at times it looks 40-50 ply deep.]

http://en.chessbase.com/post/houdini...ritz-interface

P.P.S.: Note that Houdini-3 prunes about 30 in 35 moves on average per play as far as looking at these much deeper. Depending how you look at it, that's 5 moves, or 1 in 7 moves, or about the square root of 35 moves that are thus deemed worth looking at much deeper on average. For my estimate of how many ply a 'good' engine might look ahead in Sac Chess on average to be at least remotely close to correct, it's critical which of these three possibilities it is. I think my estimate closer to assuming roughly the square root of the average number of legal Sac Chess moves per turn as being examined much deeper by a 'good' Sac Chess engine (rather than my assuming roughly a 1 in 7 ratio of legal Sac Chess moves, or a fairly constant total of 5 moves per ply in Sac Chess - the latter assumption would greatly increase the number of ply that could be looked ahead on average, but using the 1 in 7 ratio would greatly reduce the number of ply that could be looked ahead on average, which might be quite a bit nicer for humans when vs. a Sac chess engine).


P.S.: Fwiw I once played a 19 ply (10 move deep) middlegame chess combination before I reached 2200, i.e. master level (also, I've noticed that variations in notes within old chess books I have at times exceed 20 ply); if nothing else you might try to see if you can follow or calculate that combination from the diagrammed position below in your head:

K. Pacey (2092)-R. Morenz (2055)
Toronto International Open 1984, Section 2, Rd. 3
C51 Evans Gambit Accepted

1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.b4 Bxb4 5.c3 Be7 6.Qb3 Nh6 7.d4 Na5 8.Qb5 c6 9.Qxe5 f6 10.Qh5+ g6 11.Qxh6 Bf8 12.Bf7+ Kxf7 13.Qf4 d5 14.0-0 dxe4 15.Ng5+ Kg7 16.Nxe4 Bf5 17.Nbd2 b6 18.Re1 Nb7 19.Ng3 Bc8 20.Nde4 Nd6



21.Nh5+! gxh5 22.Qh6+ Kf7 (if 22...Kg8? 23.Nxf6+ Kf7 24.Qxh5+ Kg7 then 25.Bh6+ wins Black's queen) 23.Qxh5+ Kg8 (if 23...Kg7? 24.Bh6+ Kg8 25.Nxd6 Qxd6 then 26.Re8 wins) 24.Nxd6 Qxd6 25.Re3 Rb8? (if 25...h6? 26.Qg6+ Bg7 then 27.Re8+ wins Black's queen; 25...Bf5 keeps Black's losses to a pawn) 26.Rg3+ Bg7 27.Rxg7+! 1-0 (the weaker 27.Bh6 Rb7 28.Re1 also wins; after 27.Rxg7+! if 27...Kxg7 28.Bh6+ Kg8 29.Qe8+ Qf8 then 30.Qxf8 mate).

[Kevin Pacey]

Re: How does my 10x10 chessboard 'Sac Chess' variant seems to you

Fwiw, below is a link to Alekhine Chess as listed on the chess variants page; this variant I was unaware of has a 14x8 board with 56 pieces (I've checked that there are other large board variants listed on the website with over 60 pieces), with some indication that the games can be relatively short at times (it's been played on the internet & has some fans):

http://www.chessvariants.org/index/e...zAlekhineChess


Btw, I've also done some limited plus indicated edits to some of my previous posts in this thread.