Problem Statement

There is a town divided into a grid of cells with $H$ rows and $W$ columns. The cell at the $i$-th row from the top and $j$-th column from the left is a passable space if $S_{i,j}$ is . and a block if $S_{i,j}$ is #.

Takahashi will go from his house to a fish market. His house is in the cell at the top-left corner, and the fish market is in the cell at the bottom-right corner.

Takahashi can move one cell up, down, left, or right to a passable cell. He cannot leave the town. He cannot enter a block, either. However, his physical strength allows him to destroy all blocks in a square region with $2\\times 2$ cells of his choice with one punch, making these cells passable.

Find the minimum number of punches needed for Takahashi to reach the fish market.

Constraints

• $2 \\leq H,W \\leq 500$
• $H$ and $W$ are integers.
• $S_{i,j}$ is . or #.
• $S_{1,1}$ and $S_{H,W}$ are ..

Input

Input is given from Standard Input in the following format:

$H$ $W$ $S_{1,1} \\ldots S_{1,W}$ $\\vdots$ $S_{H,1} \\ldots S_{H,W}$

Output

Print the answer.

Sample Input 1

5 5
..#..
#.#.#
##.##
#.#.#
..#..

Sample Output 1

1

He can reach the fish market by, for example, destroying the blocks in the square region with $2\\times 2$ cells marked * below.

..#..
#.**#
##**#
#.#.#
..#..```

It is not required that all of the $2\\times 2$ cells in the region to punch are blocks.

* * *

### Sample Input 2

```plain
5 7
.......
######.
.......
.######
.......

Sample Output 2

0

He can reach the fish market without destroying blocks, though he has to go a long way around.

Sample Input 3

8 8
.#######
########
########
########
########
########
########
#######.

Sample Output 3

5