Problem Statement

There is a grid with $H$ rows and $W$ columns. The cell in the $r \ (1 \leq r \leq H)$-th row from the top and the $c\ (1 \leq c \leq W)$-th column from the left is denoted by $(r, c)$.

The state of the grid is represented by a two-dimensional array $S$. If $S_{r,c}$ is #, there is an obstacle in cell $(r, c)$, and if it is ., there is no obstacle. It is guaranteed that the outer boundary of the grid is surrounded by obstacles #.

Ushi-san and Hikari-chan, who are on cells of the grid, are trying to swap their positions.

Initially, Ushi-san is in cell $(r_a, c_a)$ and Hikari-chan is in cell $(r_b, c_b)$. Each of the $2$ people can move only to a cell that has no obstacle and no one in it, among the $4$ cells sharing an edge with the cell they are currently in. The $2$ people may move in any order, but the $2$ of them cannot move to different cells at the same time. In the end, Ushi-san should be in cell $(r_b, c_b)$ and Hikari-chan should be in cell $(r_a, c_a)$.

Determine whether the positions can be swapped, and if they can, find the minimum total number of moves made by the $2$ people to swap their positions.

Input

$H$ $W$ $r_a$ $c_a$ $r_b$ $c_b$
$S_{1,1} S_{1,2} \cdots S_{1,W}$
$S_{2,1} S_{2,2} \cdots S_{2,W}$
$:$
$S_{H,1} S_{H,2} \cdots S_{H,W}$

• $4 \leq H, W \leq 1333$
• $1 \lt r_a, r_b \lt H$
• $1 \lt c_a, c_b \lt W$
• $(r_a, c_a) \neq (r_b, c_b)$
• $S_{r,c}$ $(1 \leq r \leq H, 1 \leq c \leq W)$ is # or .
• $S_{r_a, c_a}, S_{r_b, c_b}$ are .
• The outer boundary of the grid (row $1$, row $H$, column $1$, column $W$) is #
• $H, W, r_a, c_a, r_b, c_b$ are integers

Output

Output, on $1$ line, the minimum total number of moves made by the $2$ people to swap their positions. However, if the positions cannot be swapped, output $-1$.

Sample

4 5 2 2 3 4
#####
#...#
##..#
#####

6

4 5 2 2 2 4
#####
#.#.#
#...#
#####

-1

5 4 4 3 2 3
####
#..#
#..#
#..#
####

6