Chapter V: The End-Game (2)

White draws with 1. Kt-Q2, P-B7; 2. Kt-K4ch, K-Kt7; 3. KtxP, and draws, as Black, in order to capture the White pawn, after KxKt must give the White King access to the Rook’s square, from which he could not be dislodged except by a Bishop on White squares.

In Diagram 73 White cannot win although his Bishop is of the “right colour” by 1. P-B7, KtxP; 2. BxKt, and White cannot win the Rook’s pawn. He can only attack the pawn from Kt7 or Kt8, both of which are inaccessible as the Black King gets to Kt1. It is a stalemate position. If the White

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A B C D E F G H

Diag. 73

pawn were still at R5, White’s King could attack the pawn from R6 and secure the win.

In the position given, White could only win by keeping his passed pawn, and indeed it is possible to win by gaining a move with the Bishop. In the diagram it is White’s move. Black with the move could not play K-B2 because K-Q6 would follow. The Knight would have to move, allowing the pawn to queen. Therefore White must try to bring about the same position with Black to move. He can do this, for instance, in the following way:

1. B-Kt3, K-B2 (now 2. K-Q6 would be bad on account of Kt-Q5, 3. P-B7, Kt-Kt5ch, and KtxP); 2. B-R2, K-K2; 3. B-K5. Now White’s plan has succeeded; the same position has occurred, and it is Black’s move. As mentioned before, the King must not move, but Knight’s moves are of no avail. If 3. ... Kt-Kt4; 4. B-B6ch, the Knight is lost, or alternatively the pawn queens. On 3. ... Kt- B1, B-Q6ch decides, and on 3. ... Kt-Q1; 4. B-B6ch, K-K1; 5. BxKt would follow.

On this occasion I should like to point out that it is impossible to gain a move with a Knight, as a square which is accessible to him in an odd number of moves cannot be reached by him in an even number. A simple instance is Diagram 74.

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A B C D E F G H

Diag. 74

White loses, having the move. 1. K-R8, Kt-K4; 2. K-R2, Kt-Q2; 3. K-R8, Kt-B1; 4. P-R7, Kt-Kt3 mate.

Black with the move cannot win, as he cannot bring about the same position with White to move.

In end-games of BISHOP V. BISHOP, of which we have already had an example in Diagram 70, an extra pawn wins in most cases if the Bishops are of the same colour. It is generally possible to force an exchange of Bishops and obtain one of the well-known pawn endings.

On the other hand an ending with Bishops of different colour leads mostly to a draw, frequently even against a majority of two pawns. The position in Diagram 75 is a draw, because it is impossible for the White King to get round his Kt pawn to drive off the Bishop.

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A B C D E F G H

Diag. 75

With two passed pawns distant from each other, a win can generally be forced, as in the following position (Diagram 76).

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A B C D E F G H

Diag. 76

The King moves up to the pawn, the progress of which is barred by the Bishop (not the King). He thereby forces the sacrifice of the Bishop. If the Black King comes to the rescue of the Bishop, the other pawn proves Black’s downfall.

1. K-K4, K-K2; 2. K-Q5, K-Q2; 3. B-K4, B-K2; 4. P-Kt6, B-Q1; 5. P-Kt7, K-B2; 6. K-K6, and wins; or 5. ... B-B2; 6. P-B6, B-R7; 6. B-B2, K-K1; 8. K-K6, B-Kt1; 9. B-Kt6ch, K-B1; 10. K-Q7, and wins.

When the pawns are united, one should observe this rule: if they are attacked, they should, if possible, move to squares of the colour of the opposing Bishop.

Therefore in the position set out in Diagram 77 White should not play P-B5, but P-K5. After 1. P-B5 there is no possible chance for White to assume the command of the Black squares, and in order to advance the pawns it is necessary

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A B C D E F G H

Diag. 77

to force access to both White and Black squares. In the present instance play would proceed on these lines:

1. P-K5, B-R4; 2. K-K3, K-B2; 3. K-K4, K-K2; 4. P-B5, B-Kt5; 5. P-B6ch, K-B1; 6. P-K6, B-R6; 7. B-R4, B-Kt5. White can only get through with the King’s Pawn, as P-B7 is unavailing on the grounds set out above. But in order to play P-K7, the square K7 must first be covered a second time, so that the Bishop cannot be given up for the two pawns. Therefore: 8. K-Q5, B-R6 (B-B6; P- K7ch); 9. K-B6, K-K1; 10. K-B7ch, K-B1; 11. K-Q7, and wins.

In end-games with one Knight on each side, an extra pawn usually decides the game much in the same way as in end-games with Bishops of the same colour; frequently even with equal pawns, the possession of a passed pawn is sufficient, as it keeps either the King or the Knight busy, so that there is only one piece available for the defence of the pawns. An instructive example is the end-game Ed. Lasker-Rotlevi on p. 100.

End-games with Rook against Rook are the most frequent, as well as the most difficult. Here the possession of an extra pawn is seldom sufficient for a win, unless the stronger side has also an advantage in the greater mobility of the Rook. Diagram 78 is typical of such cases, frequent in practice, in

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A B C D E F G H

Diag. 78

which the greater mobility is the deciding factor. Although White has one pawn more, he can only win by reducing the mobility of the Black Rook through the following manœuvre: 1. R-B2, R-Q2; 2. R-R2, R-R2. Now the Black Rook has only one move left, whilst the White Rook has the freedom of the Rook’s file. For instance, the Rook can be posted at R5 and prevent the Black King from attacking White’s King’s side pawns, whilst the White King makes for the R at R7 and effects its capture. If, on the other hand, the Black King tries to obstruct the way to the Queen’s side, White penetrates into the Black pawn position. Black cannot maintain the opposition because the White Rook has spare moves, the Black Rook none. e.g. 3. K-B3, K-Kt3; 4. R-R5, K-B3; 5. K-K4, K-K3; 6. R-R4, P-Kt3; 7. R-R5, K-Q3; 8. K-Q4, K-B3; 9. K-K5, and wins the pawns.

Having the move, Black would draw the game by: 1. ... R-Q7ch; 2. K-R3, R-R7. By placing his Rook behind the passed pawn he condemns the opposing Rook to inactivity, whilst his own is free to move on the Rook’s file. If now the White King comes up, he will in the end force the sacrifice of the Black Rook for the pawn, but meanwhile the Black King captures the White pawns, and with passed pawns on the King’s side might get winning chances.

When there is only one pawn left in endings of R against R, the weaker side maintains the draw, if the King can command the queening square. Diagram 79 shows a position favourable to the stronger side, and which can mostly be obtained in this end-game. But here, too, Black forces a draw with a pretty manœuvre: 1. ... R-B2; 2. R-KKt2, R-Q2ch; 3. PXR, and Black is stalemate.

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A B C D E F G H

Diag. 79

The chances of a draw are even greater in endings of Q against Q, as the King on the stronger side can seldom evade perpetual check. For the sake of completeness I will show a few cases in which Q or R cannot win against an advanced pawn.

In Diagram 80 White can still draw, for in five moves the pawn reaches Kt7, supported by the King at R7, and in that time Black cannot come up with his King, so that he must give up the Rook for the pawn. Two passed pawns win, even when the King is away from them, if they have reached their sixth square. In Diagram 81, for instance, White is lost,

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A B C D E F G H

Diag. 80.

as Black gives up his Rook at Q7 and plays P-Kt6, after which one of the pawns queens.

The Queen wins against an advanced pawn, even when the latter is supported by the King; only the R or B pawn can

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A B C D E F G H

Diag. 81.

draw sometimes, when the pawn is on the seventh supported by the King, and the opposing Q cannot move to the queening square.

The following illustrates the three principal cases:

A. Position--White: K at QKt8, P at QR7
Black: K at QR8, Q at QB3

Black must stop the pawn and plays Q-Kt3ch. White answers with K- R sq and is stalemate unless White lets the Kt’s file free again. This end-game can only be won if the stronger King can assume the opposition in two moves. Therefore, if in the above example the Black King was standing at Q5, Black would win as follows: 1. ... Q-K1ch; 2. K-Kt7, Q-K2ch; 3. K-Kt8, K-B4; 4. P-R8 = Q, K-Kt3. and White cannot cover the mate.

B. Position--White: K at QKt8, P at QB7
Black: K at Q5, Q at QB3

White draws: 1. ... Q-Kt3ch; 2. K-R8, QxP stalemate.

C. Position--White: K at QKt8, P at QKt7
Black: K at Q5, Q at QB3 White loses.

1. K-R7, Q-R5ch; 2. K-Kt6, Q-Kt5ch; 3. K-B7, Q-B4ch; 4. K-Q8, Q- Q3ch; 5. K-B8, Q-B3ch; 6. K-Kt8, K-B4; 7. K-R7, Q-R5ch; 8. K-Kt8, K-B3; 9. K-B8, Q-R3, etc.

END-GAMES FROM MASTER PLAY

In the following pages I give some instructive examples taken from tournament play. Step by step we will find how very important is the knowledge of the simple endings treated in the last chapter. We shall see that it is often necessary to consider many moves ahead to find the correct line, but that it is nearly always possible to foresee every consequence with unfailing certainty. Moreover, because of the reduction of forces there is no call to take very many variations into consideration. This explains why there is a tendency in modern master play to enforce the exchange of pieces, as soon as there is the slightest advantage sufficient to bring about one of the elementary end- game positions, in which the win can be forced.

1. FROM A GAME TEICHMANN-BLACKBURNE (BERLIN, 1897).

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A B C D E F G H

Diag. 82.

Black has an extra pawn on the Queen’s side. But as it is doubled, the material superiority is of no account. A perceptible advantage, however, lies in the fact that White cannot bring about a “forced move” position, as Black has the move P-QB4 in reserve. White has also an infinitesimal weakness on the King’s side, the Rook’s pawn having advanced two squares and being therefore an easy mark. This disadvantage soon becomes apparent.

1. P-B3 K-B4
2. K-B2 P-R4
3. K-Kt2 P-Kt4
4. K-R3 K-K4

With this move advantage is taken of one of White’s weaknesses. White must exchange pawns. If the King moves, Black captures, freeing B 5 for his King, from where he can later on get to K6 or Kt6. But after the exchange at Kt4, Black has the chance of obtaining a “distant passed pawn” on the Rook’s file.

5. PxP PxP
6. K-Kt2 K-B4
7. K-R2 K-B3

If Black were to play P-R5 at once, White would reply with 8. K- R3, and after PxP, 9. KxP. Black would have to give up the spare move P-B4, to gain the square at B5 for his King. The game then would be drawn after 10. K-Kt2! K-B5, 11. K-B2, because White maintains the opposition, and Black cannot get through at K6 or Kt6. Black therefore manœuvres his King first in such a way that the square at his B4 is only reached when the White King is at Kt3.

8. K-Kt2 K-Kt3
9. K-R2 P-R5

Now neither PxP nor P-B4 is of any use. In the first case Black obtains the distant passed pawn. In the second White obtains the distant passed pawn after 10. P-B4, PxBP; 11. PxRP, but loses it again after K-R4; 12. K-R3, P-B4.

10. K-R3 PxP
11. KxP K-B4

At last Black has captured the coveted square, whilst keeping the spare move in hand.

12. K-B2 K-B5

The White King cannot move to Kt2 now, because in that case Black would move the King to the White QBP and queen in seven moves, and White, after seven moves, would only have the KB pawn at B7.

13. K-K2 K-Kt6
14. K-K3 P-B4

and wins, for White cannot hold the KBP now, but must capture the KtP in exchange for it, after which the Black King reaches the Queen’s side two moves ahead, e.g.:

15. K-K2 K-Kt7
16. K-K3 K-B8!
17. K-K4 K-B7
18. K-B5 KxP
19. KxP K-K6, etc.

Black would have forced a win also if White had played K-Kt2 on his twelfth move thus: 12. K-Kt2, K-B5; 13. K-B2.

Now White has the opposition, and after Black wrings it from him by playing the spare move P-B4, he assumes it again with 14. K- K2, K-Kt6; 15. K-K3. But he cannot maintain it after Black’s K-R6 because the square at Q3 for distant opposition is not accessible. After 16. K-Q2, K-R7!; 17. K-K3, K-Kt6; 18. K-K2, K- Kt7; 19. K-K3, K-B8 we get the same result as before.

II. FROM A GAME ED. LASKER-ROTLEVI (HAMBURG, 1910).

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A B C D E F G H

Diag. 83.

White has the advantage, because Black must keep either his King or his Knight permanently near the passed pawn, guarding against its advance, whilst both White’s King and Knight can attack the Black pawns. As yet they stand so far in the rear that the White King cannot approach them Therefore White must first try to force their advance.

1. Kt-B5 P-Kt3
2. Kt-Q3 P-R4

This is now necessary, because the square B3 is weak after P-Kt3 and the White Knight threatens to win the Rook’s pawn eventually with a check at B6. For this reason Kt-Q 2, for instance, could not be played instead of the move in the text, because 3. Kt-K5 would follow. Black now cannot exchange, of course, otherwise the position would resolve itself to an easy end game win similar to the one in Diagram 56. There would be nothing left but Kt-Kt1 to oppose the threat of Kt-B6ch, and this would get the Knight entirely out of play, so that White could queen the passed pawn easily after 4. K-Kt6.

3. K-K5 P-B3

The King was threatening to enter via Q5 and B6.

4. K-B5 Kt-K3

If Black wishes to obviate the threat: Kt-K5-B4, and plays P-Kt4, the White King goes to QB5 and wins all the pawns easily. Therefore Black endeavours to sacrifice a pawn in order to exchange the two others, after which a draw could be forced by exchanging the Knight for the remaining White pawn.

5. Kt-K5 P-B4
6. Kt-B4 P-Kt4
7. KtxP P-B5

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A B C D E F G H

Diag. 84.

8. K-K5 Kt-B4
9. Kt-B6ch K-B1!

Not K-B2, because of 10. K-Q4, Kt-Q6; 11. Kt-K5ch.

10. Kt-R7

Here White had only considered the following answer:

Kt-Q6ch; 11. K-Q4, KtxKtP; 12. KtxP, Kt-Q6; 13. P-B5, Kt-Kt5; 14. Kt-B3, Kt-B7ch: 15. KxP, Kt-K6ch; 16. K-B5, KtxP; 17. P-R4, Kt- K2; 18. Kt-Q5, Kt-B1; 19. K-B6, K-K1; 20. K-B7, Kt-R7; 21. K-Kt7, and wins the Knight.

Black however draws, through a pretty combination:

10. ... P-Kt5
11. K-Q4 P-B6
12. K-B4 PxP
13. KxP KtxP

and White cannot prevent the ultimate exchange of Kt for P. The last winning chance would have been: 10. K-Q4!, Kt-Q; 11. K-B3. This is in any case the more plausible line, because now White can attack the pawns with both King and Knight, as both the Black pieces are away from the field of operations. The sequel could be: 11. KtxBP; 12. P-R3 (Kt-R7 would only draw: Kt-K7ch; 13. K- Kt4, Kt-B8 14. P-R3, Kt-R7ch; 15. KxP, P-B6); 12. Kt-Q4ch 13. K- Q4, Kt-B5; 14. K-K4 (Kt-R7 ?, Kt-K7ch!!; 15 K-K3, P-B6), Kt-Q6; 15. P-Kt4, Kt-Kt7 16 Kt-Q4, and wins

III. From a game Blackburne-Schlechter (Vienna, 1898).

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A B C D E F G H

Diag. 85

White has just played Q-B4. P-B5 is threatened, and Black is forced to exchange Queens. The ensuing end-game, however, is inferior for Black, because the QP is weak and White threatens eventually to force his Queen’s Pawn through.

1. ... Q-B4
2. QxQ BxQ
3. Kt-Q4 B-Kt3
4. RxR RxR
5. R-K1 RxR

If Black wants to avoid the exchange, he must yield up the King’s file to White, and that would surely spell disaster, as the Black Rook would have no field of action, and would have to go to Q1 to avoid the loss of a pawn through Kt-Kt5ch, after which the White Rook would take possession of the seventh rank, fettering the action of the Bishop into the bargain.

6. KxR B-Q6
7. P-QKt3 K-Q2

Black is condemned to inactivity, and White can quietly set to work to force his pawn through.

8. K-Q2 B-K5
9. P-Kt3 B-Kt8
10. P-QR3 B-K5
11. K-K3 B-Kt8
12. Kt-B3

In order to play P-QKt4 and P-B5, then to force Black to exchange at B5, White must first have the opportunity of bearing a second time on Black’s Queen’s Pawn. Therefore he prepares the manœuvre Kt-B3-Q2-B4.

12. ... K-K2
13. P-QKt4 B-B4
14. P-B5 B-Q2
15. K-Q4 B-K1
16. Kt-Q2 B-Q2
17. Kt-B4 PxPch
18. PxP P-B3

It is not yet easy to materialise the advantage in position The advance P-Q6ch would be very bad, as B6 and K6 would be made accessible for Black. White starts by tempting the pawns forward and thus systematically creates points of attack.

19. Kt-Kt2 B-B4
20. P-QR4 K-Q2
21. P-R5 P-QR3

The Queen’s side is paralysed. The text move is forced, as P-R6 would give White yet another passed pawn. Now White turns his attention to the King’s side.

22. Kt-B4 K-B2
23. Kt-Q6 B-Q2
24. K-K4 B-R5
25. P-Kt4 B-B7ch
26. K-Q4 B-Kt3

Black wishes to play P-R4, in order to get a passed pawn too, the only chance of saving the game.

27. P-R3 K-Kt1

Now P-R4 would be countered by Kt-B5, forcing the exchange and leaving a backward pawn at Kt2 and the Rook’s pawn would be bound to fall.

28. Kt-B5 BxKt
29. PxB K-B2

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A B C D E F G H

Diag. 86.

It would now seem as if Black might have played P-KKt4 here, securing a passed pawn, and forcing a draw. After 30. P-R4 Black would play P-R3, and it is not evident how White is to win. But 29. ... P-KKt4 is parried by PxP e.p. The difference in the pawn positions, which decides the issue for White, is found in the fact that the White passed pawn at Q5 is unassailable because the support of the BP cannot be taken away by Black’s P-Kt3, whilst Black’s passed pawn at his B3 can be isolated at any time through P-R4-R5. White would take up a position on the Knight’s file with the King, and push on the Rook’s pawn. The isolated pawns are then an easy prey. On the text move White also pushes the Rook’s pawn on to compel P-R3 and reduce Black to moves by the King. The passed Queen’s pawn decides the game.

30. K-K4 K-Q2
31. K-B4 K-K2
32. K-Kt4 K-Q2
33. P-R4 K-B1
34. P-R5 P-R3

Otherwise there follows: P-R6, K-R5, etc.

35. K-B4 K-Q2
36. K-K4 K-B2
37. P-Q6ch K-B1
38. K-Q5 K-Q2
39. P-B6ch PxPch

(compare Diagram 68)

40. K-B5 Resigns

IV. FROM A GAME BIRD-JANOWSKI.

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8 | | | | | | | #K | |
|---------------------------------------|
7 | #P | | ^B | | | | | #P |
|---------------------------------------|
6 | | | | | | | | |
|---------------------------------------|
5 | ^P | | | | | #P | | |
|---------------------------------------|
4 | | ^P | | | #P | | | |
|---------------------------------------|
3 | | | ^P | | | | ^P | |
|---------------------------------------|
2 | | | | | ^K | | | ^P |
|---------------------------------------|
1 | #R | | | | | | | |
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A B C D E F G H

Diag. 87

In spite of the preponderance of material, the win is not an easy one for Black, because of White’s alarming pawn array on the Queen’s side. The King must first make use of his great power as an end-game piece.

1. ... K-B2
2. P-Kt5 K-K3
3. P-Kt6 PxP
4. PxP K-Q2
5. B-K5

threatens P-Kt7. But as White must first move his Bishop to cover his pawn, the Rook’s pawn is lost, and the manœuvre therefore unsound. P-R3 was indicated; it threatens the break-up of the Black pawns by P-Kt4 and their capture by the King.

5. ... K-B3
6. B-Q4 R-R2ch
7. K-K3 RxP
8. K-B4 R-Q7!
9. P-Kt4 RxB

Black reduces the position to an elementary ending, which is theoretically a win. Whilst the two White passed pawns are isolated and fall singly, Black obtains two passed pawns, which are united and unassailable.

10. PxR P-K6
11. KxKP PxP
12. K-B4 P-R4
13. P-Q5ch KxKtP
14. K-K5 K-B2
Resigns.

V. FROM A GAME STEINER-FORGACZ (SZEKESFEHERVAR, 1907).

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8 | #R | | | | | | | |
|---------------------------------------|
7 | #P | | #P | | #K | #P | #P | #P |
|---------------------------------------|
6 | | #P | | | | | | |
|---------------------------------------|
5 | | | | | ^P | | | |
|---------------------------------------|
4 | | ^R | | | | | | |
|---------------------------------------|
3 | | | | ^P | | | | |
|---------------------------------------|
2 | ^P | | ^P | | | | ^P | ^P |
|---------------------------------------|
1 | | | | | | ^K | | |
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A B C D E F G H

Diag. 88

White has an advantage in the greater mobility of his Rook, and makes the most of it in an instructive fashion.

1. R-Kt4 P-Kt3

White provokes this move in order to produce a weakness at KB6.

2. K-K2 K-K3
3. R-KB4 R-KB1

Black naturally dare not allow the Rook to penetrate into the seventh.

4. P-Q4 P-QB4

This move would win the game, if the Rooks had been exchanged, because in that case the distant passed pawn which Black could obtain on the QKt file would decide the issue. But, supported by the mobile Rook, the centre pawns become irresistible. Instead of the text move, P-KB4 was necessary in order to release the Rook.

5. P-B3 PxP
6. PxP P-KB4

If it were not for the Rooks, the centre pawns would not help White, because Black would obtain a passed pawn on either wing.

7. K-Q3 P-KKt4
8. R-B2 R-B1
9. P-Kt4 P-B5

If PxP, 10. R-B6ch, K-K2; 11. R-R6 wins.

10. P-KR4 P-KR3
11. PxP PxP
12. R-R2 R-B1
13. R-R6ch K-K2
14. P-Q5 P-B6
15. R-K6ch K-Q2
16. R-B6! Resigns.

For after RxR, 17. PxR, White captures the BP, and still overtakes the passed pawn which Black obtains on the Queen’s wing; the pawns at Q5 and B6 are unassailable (K-K8, P-Q6, K-B7, P-Q7, etc.). The consequences of 16. R-B6 had to be calculated to a nicety. If, for instance, the QKtP were already at his fourth, White would lose. In four moves Black would have one of his pawns at his R6, the other at Kt5. In the meantime White would have taken the BP and come back to the Q file. Now Black would win with P-Kt6, because after PxP the RP queens unmolested.

VI. FROM A GAME CHAROUSEK-HEINRICHSEN (COLOGNE, 1898).

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8 | | | #R | | | | #K | |
|---------------------------------------|
7 | #P | #P | | #Q | #R | #P | #P | |
|---------------------------------------|
6 | | | | | | | | #P |
|---------------------------------------|
5 | | | #P | | | ^Q | | ^P |
|---------------------------------------|
4 | | | | #P | ^R | | | |
|---------------------------------------|
3 | | | | ^P | | | | |
|---------------------------------------|
2 | ^P | ^P | ^P | | | ^P | ^P | |
|---------------------------------------|
1 | | | | | ^R | | ^K | |
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A B C D E F G H

Diag. 89

White’s position is superior; firstly, because the only open file on the board is his, and secondly, because the Black Queen’s side pawns are advanced, and therefore weak for a King’s ending. After exchanging the Queen and one Rook, the possession of the King’s file ensures the advance of the King to K4 and from there to Q5. Then the weakness of Black’s pawns decides the game.

1. QxQ RxQ
2. R-K8ch RxR
3. RxRch K-R2
4. K-R2 P-KKt3
5. K-Kt3

PxP is no threat, because White wins the pawn back at once with R-K5. By capturing, Black would only dislocate his pawns.

5. ... KKt2
6. K-B4 K-B3
7. R-K5 P-Kt3
8. K-K4 R-Q3
9. P-KB4 R-K3

Black probably hopes for a counter chance by getting a distant passed pawn on the KRook’s file. But he underrates the weakness of the Queen’s side pawns, and even without the exchange of Rooks, White would win, by settling the King’s side first and then tearing up the Queen’s side, as in the game: 10. P-KKt4, R- K2; 11. PxP, PxP; 12. P-Kt5ch, PxP; 13. PxPch.

10. PxP PxP
11. K-Q5 RxR
12. PxRch K-K2
13. P-QKt4 Resigns

Black must capture, as he needs seven moves in which to ex change the Knight’s pawn and queen his Rook’s pawn, whilst in that time White can win the QP after PxP, and yet arrive in time with his King to stop the pawn from queening.

After l3. ... PxP, however, there follows 14. KxP. Then White covers his passed pawn with P-Q4, and his King, having full freedom, captures all the Black pawns.