We have an $N \times N$ chessboard. Let $(i, j)$ denote the square at the $i$-th row from the top and $j$-th column from the left of this board.  
The board is described by $N$ strings $S_i$.  
The $j$-th character of the string $S_i$, $S_{i,j}$, means the following.

-   If $S_{i,j}=$ `.`, the square $(i, j)$ is empty.
-   If $S_{i,j}=$ `#`, the square $(i, j)$ is occupied by a white pawn, which cannot be moved or removed.

We have put a white bishop on the square $(A_x, A_y)$.  
Find the minimum number of moves needed to move this bishop from $(A_x, A_y)$ to $(B_x, B_y)$ according to the rules of chess (see Notes).  

If it cannot be moved to $(B_x, B_y)$, report `-1` instead.

Notes

A white bishop on the square $(i, j)$ can go to the following positions in one move.

-   For each positive integer $d$, it can go to $(i+d,j+d)$ if all of the conditions are satisfied.
    
    -   The square $(i+d,j+d)$ exists in the board.
    -   For every positive integer $l \le d$, $(i+l,j+l)$ is not occupied by a white pawn.
-   For each positive integer $d$, it can go to $(i+d,j-d)$ if all of the conditions are satisfied.
    
    -   The square $(i+d,j-d)$ exists in the board.
    -   For every positive integer $l \le d$, $(i+l,j-l)$ is not occupied by a white pawn.
-   For each positive integer $d$, it can go to $(i-d,j+d)$ if all of the conditions are satisfied.
    
    -   The square $(i-d,j+d)$ exists in the board.
    -   For every positive integer $l \le d$, $(i-l,j+l)$ is not occupied by a white pawn.
-   For each positive integer $d$, it can go to $(i-d,j-d)$ if all of the conditions are satisfied.
    
    -   The square $(i-d,j-d)$ exists in the board.
    -   For every positive integer $l \le d$, $(i-l,j-l)$ is not occupied by a white pawn.

Input is given from Standard Input in the following format:

```
$N$
$A_x$ $A_y$
$B_x$ $B_y$
$S_1$
$S_2$
$\vdots$
$S_N$
```

Print the answer.

-   $2 \le N \le 1500$
-   $1 \le A_x,A_y \le N$
-   $1 \le B_x,B_y \le N$
-   $(A_x,A_y) \neq (B_x,B_y)$
-   $S_i$ is a string of length $N$ consisting of `.` and `#`.
-   $S_{A_x,A_y}=$ `.`
-   $S_{B_x,B_y}=$ `.`

3

We can move the bishop from (1,3) to (3,5) in three moves as follows, but not in two or fewer moves.

• (1,3)→(2,2)→(4,4)→(3,5)

-1

There is no way to move the bishop from (3,2) to (4,2).