In chess, game pieces move about an chessboard in a fashion defined by their type. The object of the game is to capture opposing pieces by landing on their squares, and eventually trapping the king piece.

In our version of the game, we shall use a variable sized board with only pieces on it: A white pawn which moves relentlessly towards the top row of the chessboard one square at a time per move; and a black knight which can move from its current location in any of up to eight ways: two squares up or down and one square left or right, or one square up or down and two squares left or right. The knight must remain on the board at all times; any move that would take it off the board is therefore disallowed. In the diagram below, the knight's position is labelled and its possible moves are labelled to .

```
. . . . . . .
. . 8 . 1 . .
. 7 . . . 2 .
. . . K . . .
. 6 . . . 3 .
. . 5 . 4 . .
. . . . . . .
```

The pawn moves first; then the knight and pawn alternate moves. The knight tries to land either on the square occupied by the pawn (a win) or on the square immediately above the pawn (a stalemate). If the pawn reaches the top row of the board the game ends immediately and the knight loses (a loss).

Write a program to determine whether the knight can win and, if it can, the minimum number of moves it must make to do so. If the knight cannot win, your program should determine if it can cause a stalemate and, if it can, the minimum number of moves it must make to do so. Finally if the knight cannot win or cause a stalemate, your program should compute the number of moves the knight makes before the pawn wins.

The first line of input contains a positive integer, , the number of games to analyze. For each game there are six lines of input:

- , the number of rows in the chessboard
- , the number of columns in the chessboard
- , the row of the starting position of the pawn
- , the column of the starting position of the pawn
- , the row of the starting position of the knight
- , the column of the starting position of the knight

The pawn and the knight will have different starting positions. Row is at the bottom of the board and Row is at the top of the board. Column is at the left and column is at the right.

#### Sample Input

```
3
99
99
33
33
33
35
3
3
1
1
2
3
99
99
96
23
99
1
```

#### Sample Output

```
Win in 1 knight move(s).
Stalemate in 1 knight move(s).
Loss in 2 knight move(s).
```

## Comments

Can the pawn move 2 squares if it is on the first rank? If not, I seriously cannot find what I am doing wrong for this question.

Edit: NVM, the answer to that question is no. I simply put "moves(s)" instead of "move(s)", and it took me 4 hours to realize. -_-

what would the output for this be?

`Loss in 1 knight move(s).`

I checked my code using the test data from CCC and everything was right, but when I submitted it I got WA.

yeah same how can i fix this?

If https://dmoj.ca/problem/ccc10j5 is worth 10 points. Wouldn't this be worth more?

Increased to 12 points.