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19. 5月 2005, 18:12:14
Luke Skywalker 
件名: Re: The Rules of Backgammon ---Closed Home Base Proposal
Walter Montego: With the doubling cube that wouldn't work. To cite from that link: Note that when a player is closed out, he does not forfeit his right to double.

19. 5月 2005, 17:59:28
Walter Montego 
件名: Re: The Rules of Backgammon ---Closed Home Base Proposal
grenv: Those are the rules that I play by, though I have yet to ever play Backgammon with a doubling cube or even make bets on a game's outcome. I have two such books with rules and plans in them.
Jacoby/Crawford wrote one and Cooke/Bradshaw wrote the other. As far as I can tell, the rules are identical in both books. I liked your link. Your link clearly explains something that my books are vague about. When a player has his home base closed and the opponent has a checker on the bar, the player keeps rolling the dice. That is the rules as stated. Yes, some people call it autopass, but that's not what it is. I think if we got off this notion of autopass and just played the game like the rules it would solve the whole problem.

I request that Backgammon be played by the rules as stated in these three books. Since the experts have found common ground and most of the players on this site follow the same rules, so why not have the game here be played the same way?

I will state my proposal for when a person cannot possibly move. This is different than when he actually has a chance to move, but rolls numbers that do not allow him to move. Please keep this in mind while reading this.

As far as I know, there's only two ways that it could be your turn and no matter what numbers came up on the dice you would not be able to move. The only one of them that I've ever seen is when every point in the home base is covered and the opponent has one or more checkers on the bar. It is for this situation, a fairly common one, that I'd like this site to conform to the rules. The other situation is something that, though possible, has probably never occured in Backgammon and can be dispensed with. If was to occur it wouldn't last but a turn or two anyway.

The moment that it becomes impossible for your opponent to move no matter what numbers could come up on the dice it should remain your turn. Do not think of this is autopass. Autopass works differently and I'll explain later. Since it is your turn still, the turn stays with you after you've entered your move. The dice are rolled again, and you make your next move. If, after making this move, it is now possible for your opponent to have any chance of getting off the bar, your turn is over and it becomes your opponent's turn. If you still have your home base closed, then your turn continues and another roll is made, and you play as you have. Eventually, a point will be open with one blot or none and your opponent will have a chance to get off the bar. This will be the end of your turn. All the rolls are just one turn. There is no autopass. You can only leave one message while taking this turn and the turn is not complete until it is your opponent's turn. If you stop in the middle of this turn and log off or something, the moves that you've entered and then taken another roll on will remain done. During the next roll, if you leave during it, the site already has the dice stay the same and no checkers are moved until you enter the moves. Prior parts of your turn, once entered, stay. As far as the clock goes, it is still your turn and the time will stay with you and run down until you've made the turn that will allow your opponent a chance to move. This is not autopass, and no one misses anything and the game is played how people play the game everywhere.

Autopass is a whole different thing, though in the situation I just outlined it is easy to confuse the two and I think that is why there's been so much arguing about it. In autopass, your opponent does have a chance to move, but rolls numbers that for the particular position on the board on that turn do not allow him to move. This happens a lot, even during one game it can happen more than a few times if luck is not your friend in that game. This site plays it the same in both situations ("Closed home base" and "chance to move, but unable to move") where every roll of the dice is treated as a seperate turn and must be entered with your opponent then having a turn. With autopass, a game site will look at the roll and determine that the player, though having a chance to move, rolled numbers that don't let him move, and will skip his turn and return the turn back to the other player. This is different than the closed home base, though not in the way this site treats both situations. I've seen the arguments about missing one's turn and the confusion about the checkers jumping around because of a bad series of rolls during a player's turn getting skipped. I understand that and can see why some people don't like the idea of autopass. Autopass is not how people play the game in person, either. If I have a chance to move, I will roll the dice and then get the bad news that I can't move. With the home base closed, I don't roll the dice and my opponent continues to roll and move until a point or blot opens up and then I get to roll the dice. Though I would probably use autopass if available, I don't really miss it and it only occurs sporadically during a game. Autopass also messes with the flow of the game and does indeed prevent me from leaving a message about my bad luck with the dice when it occurs. The closed home base scenario is a completely different matter though. When my opponent is able to do that, it is his turn until I have a chance to move. I know the situation and he can finish his turn and let me roll the moment something opens up. There's no reason for me to roll the dice and he could keep moving until he finally leaves an opening for me. Then it would be time for any message he might want to write and he'd finish his turn. Hopefully I can get off the bar and race home in time. If I'm still stuck on the bar, I didn't get autopassed because I rolled the dice when a point became open.

My proposal is:

When a player closes his home base and his opponent has one or more checkers on the bar it will remain his turn until his opponent has a possible chance to move. To help avoid any confusion, on the very move that the home base is closed the site might want the turn to go the opponent so that he can see the home base closed and know what has happened. This would also give him a chance to add a message about the opponent's good play or his own bad luck concerning the home base now being closed with him having a checker on the bar. After that, it would stay the player's turn until the home base was open.

As for autopass, we can do without it. It would be OK for some of us if it was avaliable, but it's not the panacea for faster play that some think it is. The closed home base would help speed play a lot during those times when someone has closed their home base and has three checkers in the opponent's home base. To avoid confusion, on the first turn of the home base being closed the turn could still go to the opponent so he'd know the game's current situation and not be surprised when it is his turn the next time. The moves could be recorded as they are now and nothing would be changed except to facilitate the flow of the game and make it more like you were playing it in person.

19. 5月 2005, 14:28:10
grenv 
here are the rules

If you don't like them perhaps you could try a different game.

19. 5月 2005, 05:31:26
danoschek 
件名: alanback: Re: "Pro" backgammon?
danoschek (19. 5月 2005, 05:40:43)に変更されました。
indeed pro bg is a special variant ... it avoids the silly common hyperthread variation,
contrary to the spirit with no choice which of the dice to move first - probably invented by
ppl losing too much at solid rules, who even allow fiddling in the house after moving out ... ~*~

18. 5月 2005, 05:57:29
WhiteTower 
件名: Re: Re:
alanback: Yes, I've read Flatland, but I would consider the "extra" dimension the cube adds as the bad idea of seeing your own insides - YUCK! (whoever's read Flatland WILL understand)

17. 5月 2005, 22:23:35
Walter Montego 
件名: Re: Re: Learning the Cube
alanback: Nah, I'll wing it just like I learned Backgammon with out it. Why have some author take all my fun of learning the hard way? I'll wait until I either understand and can use the cube for winning, or until I just can't the hang of it and then I'll read what other people have to say about it.
Ratings, schmatings.

17. 5月 2005, 21:38:11
alanback 
件名: Re:
jahaja: I remember when one of the highest rated human players on FIBS had the username onepointer because he only played one point matches. Knowing the fine points of checker play is like knowing the fine points of chess endgames: necessary but not sufficient to make one a well-rounded player. Adding the doubling cube is like adding a third dimension (anybody ever read Flatland?). And by the way, folks who have not played with the cube before would do well to read up on cube strategy before venturing into ratings land with the cube for a guide.

17. 5月 2005, 16:02:57
grenv 
件名: Re: Re:
AbigailII: To what tournaments do you refer? On this site ALL backgammon games are 1 point matches.

17. 5月 2005, 15:43:37
AbigailII 
件名: Re:
grenv: All the current backgammon tournament games are 1 point matches.

17. 5月 2005, 15:41:13
frolind 
It's a good exercise, since similar situations (the most obvious being when both players have one point to go) comes up quite often in match play, and calls for different strategies.
And a quick 1-pointer is fun too, but I will mostly play longer matches when match play becomes an option.

17. 5月 2005, 15:26:43
grenv 
Ok, point taken. I guess my point then is: Who would ever play a one point match? I don't remember ever doing that across a board except to teach my kids how to play.

17. 5月 2005, 15:24:18
frolind 
件名: Re:
grenv: A one point match should NOT count any more with a gammon or backgammon.
A 5-point match counts as a 5-point match, even if it's won with a backgammon and 8-cube (3x8=24 points). The final score doesn't matter, only who wins and the pre-set match length.
A "regular" game is a match to 1 point, making the cube and (back)gammons irrelevant.

17. 5月 2005, 14:41:25
grenv 
I disagree, I think it changes the game enough to be different.

If it's the same, we need to start giving 2 points for a gammon in a regular game (so a gammon would be like winning 2 games as far as ratings go etc).

17. 5月 2005, 06:16:22
alanback 
件名: True . . .
The cube is a relatively recent addition to an ancient game. Still, it's all backgammon today
I also agree that the cube should be an option, not a new type of game.

17. 5月 2005, 06:07:06
WhiteTower 
件名: Re: "Pro" backgammon?
Marfitalu: OK, maybe I should have used my native tongue and said Tavli instead :) What matters is the board and the piece arrangement... Anyway, there will be no Pro Backgammon, just an extra option in our regular favourite...

17. 5月 2005, 06:05:27
WhiteTower 
件名: Re: "Pro" backgammon?
BIG BAD WOLF: Sounds fine. There are no financial gains anyway :)

17. 5月 2005, 06:02:25
coan.net 
件名: Re: "Pro" backgammon?
From what I understand, unless someone really comes up with a good reason not to do it..

I think his plan is to just introduce the new option to use a cube in the current backgammon game (and then hopefully in Nack, Race, Crowded, and Hyper) - where a user can choose to play a cubed game for something like 3-21 points.

So at this point, I don't think there is going to be 2 "versions" of the games - just an additional option to the regular game.

Anyone have any suggestions or comments? Post them now so Fencer can read them! :-)

17. 5月 2005, 05:58:57
WhiteTower 
件名: Re: "Pro" backgammon?
Sorry for sounding pedantic, but backgammon started out centuries ago WITHOUT the cube and it was used purely for entertainment, not for financial gains - the latter started happening when the cube was introduced. Calling it "pro" may be ugly, but it is the truth, there is no hiding from it...

16. 5月 2005, 23:14:38
Chessmaster1000 
I agree......But it doesn't matter.....

16. 5月 2005, 22:41:09
alanback 
件名: "Pro" backgammon?
I would love to see the doubling cube used here, but please don't call the resulting game "Pro" Backgammon -- it's just backgammon, plain and simple. The game without the cube might be called "Amateur" backgammon, but that's another issue. Please don't import the ridiculous ItsYourTurn terminology here!

15. 5月 2005, 22:33:18
grenv 
i think resigning being worth the maximum is a good compromise. It may take a few moves to rule out a gammon on some occasions, but it would be much quicker than not allowing a resignation at all.

15. 5月 2005, 22:11:09
skipinnz 
件名: Re: Current Problems
BIG BAD WOLF: I believe you have it correct, and I also agree with Walter M's posting that there is no such thing as a draw and he raises a valid point on resigning. I reckon the person being offered the resignation should have the right of decline at 1 point if they feel they would have got a gammon.

15. 5月 2005, 17:50:39
Walter Montego 
件名: Re: Gammons, Backgammons, Resigning, and Draws
BIG BAD WOLF: A draw is not a possible outcome of a game of Backgammon and I believe should not be allowed under any circumstances. I feel the same way about this in Keryo Pente too.

As for resigning a game. As it is played now with each game being valued at one point, it doesn't matter. If gammons and backgammons are counted it will make a difference when playing a match and the match is where it takes more than one point to win it. The problem with playing a resignation as giving the opponent the maximum value would be to cause the games to continue on when a player knows he's going to lose, but not get gammoned. One of the sites listed James Hird, I believe Daily Gammon, has a way around this. When someone resigns, the opponent gets to decide on the game's value. If the resigner is asking for a one point loss and the winning player thinks he has a chance at a gammon, the resignation is not allowed or the resigner must accept the two point loss. This option should keep a moving along.

15. 5月 2005, 17:26:38
coan.net 
件名: Current Problems
Just so I make sure I have this correct, here are the current "problems" with the backgammon game.

1) If a player can, they have to use both dice. If that requires him moving a certain piece first to make sure the 2nd dice can be used, it must be done. If a piece can be moved to block the use of the 2nd dice, that move should be forbidden so both dice are used.

2) If A player can only use one of this dice, but has a choice of which dice to use - they must use the higher of the 2 dice.

Is that correct or am I missing anything?

15. 5月 2005, 17:22:21
coan.net 
件名: Cube Notes
Here are some notes that I wrote up awhile back about the double cube. If you see anything below that is wrong, or needs added - please let me know!

= = = = = = = = =

Some random notes about double cube:

Good match point games would be 3, 5, 7, 9, 11, 15, 21


Scoring:

1) Winning a single game is worth 1 point.

2) IF you bear off all your men BEFORE your opponent has borne off any, then that is called a "gammon" and you score double points (2 points if cube is still on 1)

3) IF you bear off all your men and your opponent still has one or more men either on the bar or in your home area (6 places nearest where you bear off), then that is called a "backgammon" and you score triple points (3 points if cube is still on 1)

NOTE: As long as the person has borne off 1 man, even if now some of their pieces are on the bar - it is NOT considered a gammon or backgammon - since at least 1 piece had been borne off.



Double Cube: 1, 2, 4, 8, 16, 32, 64

1) Either player can decided to offer the first double (to 2 points) At that point the opponenet has the option to accept (bringing the game worth to 2 points, or decline - and forfeit the current game for 1 point. If they accept, then only the opponenet will have the option to re-double - bringing the game total worth up to 4 points, if their opponent accepts.

2) Double cube is NOT AN OPTION on the very first turn. So if a person wins the "roll off", they do not have the option to offer the double. The person who lost the roll off will then have first option to offer the double.

3) If a person is 1 point away from winning, there is NO POINT in asking them if they want to double - since 1 point will win the game for them. (IYT still asks if they want to double at this point and it annoys many many users!)

4) When the double cube reaches the point where it will win the game for a person, there is NO POINT in having the option of doubling anymore for the player. So if it is a 5 point match, and the cube jumps to 8, then there is no need to offer it anymore.



Crawford Round:

1) If either player reaches a score which is only 1 point away from winning the match, the next game is played as a Crawford Round. In a Crawford round, the double cube is NOT USED and the winner will only score the standard 1 point. Crawford Round only last for 1 game. After that 1 game, the double cube can then again be used for the rest of the match.



Other Things needed:

1) Need a way to resign game for MAXIMUM cube value without resigning the game (to help speed things up) So if I still have men on the bar and try to resign, it would be for 3 points. If I had not borne off any men and resign, it would be for 2 points. If I have at least borne off 1 man and resign, it would be worth 1 point. (values are for when cube is still on 1)

So possible when they try to resign a game, a "are you sure - this resign will cost you X points" should come up so they don't think they are resigning just 1 point when they may be resigning 2 or 3 points.


2) Need a way to resign COMPLETE MATCH


3) So basicly when the turn comes to a player, they will have the options to: Roll Dice, Double Cube, Resign game (for current max value), or Resign complete match. Plus I guess the current options of a draw of complete match would also be needed.

= = = = = = = = =
Plus if you scroll back far enough, Alanback made a pretty good post about the subject, which I'll repost here:

A doubling cube is an object used to record the current value of a game that has been doubled one or more times. It's shaped like a die and has the numbers 2, 4, 8, 16, 32 and 64 on its six faces. A player who wishes to double the value of the game picks up the doubling cube before he rolls his dice, and offers it to his opponent with the side labelled 2 facing up. If the opponent accepts the double, he "owns" the cube and places it on his side of the board. The owner of the cube can choose to double at any later time when it is his turn, before he rolls the dice. He would offer it to his opponent with the "4" facing up. The original doubler then owns the cube, and can double again on his turn, and so on.

Here is an explanation of the doubling cube and of gammon and backgammon from Backgammon Galore!

I forgot to mention in an earlier post that multipoint matches would require the system to recognize gammon and backgammon as well.


Doubling
Backgammon is played for an agreed stake per point. Each game starts at one point. During the course of the game, a player who feels he has a sufficient advantage may propose doubling the stakes. He may do this only at the start of his own turn and before he has rolled the dice.
A player who is offered a double may refuse, in which case he concedes the game and pays one point. Otherwise, he must accept the double and play on for the new higher stakes. A player who accepts a double becomes the owner of the cube and only he may make the next double.

Subsequent doubles in the same game are called redoubles. If a player refuses a redouble, he must pay the number of points that were at stake prior to the redouble. Otherwise, he becomes the new owner of the cube and the game continues at twice the previous stakes. There is no limit to the number of redoubles in a game.



Gammons and Backgammons
At the end of the game, if the losing player has borne off at least one checker, he loses only the value showing on the doubling cube (one point, if there have been no doubles). However, if the loser has not borne off any of his checkers, he is gammoned and loses twice the value of the doubling cube. Or, worse, if the loser has not borne off any of his checkers and still has a checker on the bar or in the winner's home board, he is backgammoned and loses three times the value of the doubling cube.

15. 5月 2005, 17:21:55
DragonPope 
件名: Re: Pro Backgammon options
BIG BAD WOLF: there are also plenty of other options if you wish to play Pro Backgammon. Just play it on another site. No need to leave here but you might find some other sites good too.
Gold Token
Its Your Turn
Daily Gammon

15. 5月 2005, 17:12:38
coan.net 
件名: Re: Pro Backgammon options
Walter Montego: I was talking to Fencer the other day about this.

What he would NOT like to do is create a different game for the (Pro) "cubed" gammon games - since it would take more stats and stuff, plus it would just multiply into a version for the other gammon games (Pro Nack, Pro Race, Pro Crowded, Pro Hyper.)

What he was thinking if I understand it correctly, is just add a new option for the current backgammon game.

Option like: Points using the cube: (3-21)

That will go along with the current non-cube options of: (1)Normal game (2) wins match (3)points match (4) games match.

Doing it this way will make it more easy to add to each game type rather then having to create new games.

= = = = =

My suggestion is if it is done this way, is if possible, put the point total next to the name (So instead of just saying "Backgammon", mabe have it say "Backgammon (5)" - meaning it is a 5 point using the cube match.

15. 5月 2005, 17:02:06
Walter Montego 
件名: Pro Backgammon options
Fencer : Let me see if I have your stated intentions right.

You are going to add options to the Backgammon that already exsists here that will enable people to play with the doubling cube or continue playing the game as it is now without creating a whole new category of Backgammon called "Pro Backgammon"?

15. 5月 2005, 16:07:37
Pedro Martínez 
件名: Re: Was it a bug ?
Marfitalu:
1st roll - Marfitalu: 25, moves 13-11, 13-8
2nd roll - B Itch: 22, moves 2x 19-21 2x 12-14
3rd roll - Marfitalu: 24, moves 11-9, 13-9
4th roll - B Itch: 55, moves 2x 17-22, 2x 12-17
5th roll - Marfitalu: 61, moves 24-18, 13-12
6th roll - B Itch: 24, moves bar-2, 17-21
7th roll - Marfitalu: 65, moves 13-7, 12-7
8th roll - B Itch: 43, moves 14-18, 18-21
9th roll - Marfitalu: 43, passes
10th roll - B Itch: 41, moves 1-5, 1-2
11th roll - Marfitalu: 33, passes
12th roll - B Itch: 35, moves 21-24, 19-24
13th roll - Marfitalu: 51, moves bar-5
14th roll - B Itch: 14, moves 14-15, 15-19
15th roll - Marfitalu: 24, moves bar-23, 20-16
16th roll - B Itch: 65, moves 5-11, 11-16
17th roll - Marfitalu: 41, passes
18th roll - B Itch: 26, moves 2-4, 4-10
19th roll - Marfitalu: 24, moves bar-23, 8-4
20th roll - B Itch: 35, moves 2-5, 5-10
21st roll - Marfitalu: 24, moves 6-4, 9-5
22nd roll - B Itch: 34, moves 16-19, 10-14
23rd roll - Marfitalu: 46, moves 9-5, 8-2
24th roll - B Itch: 51, moves 10-15, 14-15
25th roll - Marfitalu: 56, moves 8-3, 8-2
26th roll - B Itch: 64, moves 15-21, 15-19
27th roll - Marfitalu: 41, moves 7-3, 6-5
28th roll - B Itch: 64, moves 17-21

15. 5月 2005, 16:02:27
DragonPope 
even if B Itch had to make another forced move of 1, 21-22 would have been nice and safe anyway so even if you were right about the dice, still would not have made any difference

15. 5月 2005, 16:01:22
Vikings 
easy to do

15. 5月 2005, 15:56:32
Vikings 
correct and you moved 7-3, 6-5 in other words 4-1

15. 5月 2005, 15:51:20
Vikings 
she rolled a 6-4, and you rolled a 4-1 in the previous move

15. 5月 2005, 15:48:22
Pedro Martínez 
件名: Re: Was it a bug ?
Marfitalu: she rolled 64

15. 5月 2005, 15:45:06
Pedro Martínez 
件名: Re: Was it a bug ?
Marfitalu: I don't see any "bug" there, everything seems to be perfectly OK.

9. 5月 2005, 00:24:35
Universal Eyes 
件名: Re: Ratings
BIG BAD WOLF:
True your better to lose first,just dislike everyone when the hide in the basement due to losing.

8. 5月 2005, 13:18:55
Bry 
件名: Are you a top Backgammon Player? Is your BKR "2000" or above??
Bry (8. 5月 2005, 13:20:09)に変更されました。
If so, and you are not already a member, please feel free to request membership to join

***Bry's Backgammon Fellowship***

The majority of top Backgammon players are members. There are regular tournaments, usually with over 40 top players competing.

The standard is very good and all winners are acknowledged on the main Fellowship page.

There is no pressure to chat or join any tournaments. It's just good competitive fun.



5. 5月 2005, 11:54:19
alexSandra 
件名: Re:
alexSandra (5. 5月 2005, 11:54:44)に変更されました。
BIG BAD WOLF: since he held up losing all his games, his rating will be worse then if he would have lost the games in the first place

If it's who I think you mean he is now 389 in the league table. Nearly as bad as me!

29. 4月 2005, 17:44:30
Anjil 
JH, he won't win any games through forfeiting on the games he's not moving on unless the other person resigns the game.
Although I'm not impressed by the way he's 'playing' the BKR system I have to agree with Chessmaster1000 in that it's up to him how he plays his games. I guess the only disspointment is that it's not playing in the 'spirit' of gamesmanship.
BigBadWolf makes a good point, I only hope that I get my 8 points for each win and not 1 point because his BKR has fallen so low from all the losses he'll have taken by the time he finishes his games
Shouldn't really single him out as many people do this but this is the first time I've played anyone who's so obviously working the system, I guess he's on a mission of some sorts

29. 4月 2005, 17:01:51
Pedro Martínez 
You must be kidding, JH...

29. 4月 2005, 17:00:57
coan.net 
Plus look on the bright side - since he held up losing all his games, his rating will be worse then if he would have lost the games in the first place - so they are only hurting themselves & their rating.

29. 4月 2005, 16:56:59
Chessmaster1000 
件名: Re:
JamesHird:
If he is actually intentionally not playing some games while playing others, Fencer should
1. Give 1st and final warning
2. Force a forfeit


I disagree in both 1) and 2).........
He has every right to play whenever he wants in whatever game he wants. He has also the right not to play at all.......

29. 4月 2005, 16:42:57
DragonPope 
maybe he hopes the longer he delays the more chance he has of winning by forfeits.
If he is actually intentionally not playing some games while playing others, Fencer should
1. Give 1st and final warning
2. Force a forfeit

29. 4月 2005, 16:35:05
Anjil 
件名: Re: Wow
alanback: Yes I noticed that too after finding he'd stopped making moves on the games he was loosing aginst me then I saw all his unfinished games and realised what he was doing. Sheeeeesh! it's v. annoying.

29. 4月 2005, 08:15:04
Walter Montego 
件名: Re:
grenv: Stupid me, I just play the games. I had never thought of delaying them while losing. An interesting way to achieve a high rating, but when the crash comes it'll be a swift one. Holding the top spot is the trick. I was top for one day in Extinction Chess and am still the top rated in Dark Chess after a year. Though I think that won't be the case much longer. Still nice being the top rated while it happens. If I win a few more games my Backgammon BKR will pass my Dark Chess rating.

29. 4月 2005, 00:40:08
grenv 
This happens in many of the games unfortunately.

28. 4月 2005, 23:35:11
Chessmaster1000 
I find this a bit stupid if it's true..... I mean to delay some lost games, in order to be first for a while.......
Perhaps Fencer or anyone else has a secret prize for the 1st at Backgammon on the 1st of May. It maybe 100.000$ ............. So he knows what he is doing.......

28. 4月 2005, 23:30:34
alanback 
件名: Wow
I just took a look at penteman's unfinished games, about the first 15 are sure losers. Well, that tarnishes his accomplishment a tad ;-)

28. 4月 2005, 23:25:49
alanback 
件名: Re: I see what you mean.
Pedro Martínez: What is that, 23 straight wins? That strains even my credulity. However, a day of reckoning will come :)

28. 4月 2005, 18:04:31
Pedro Martínez 
until he starts finishing the lost games...

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