Contest Duration: - (local time) (100 minutes) Back to Home
E - Stronger Takahashi /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

HW 列の格子状の区画に区切られた街があります。上から i 行目、左から j 列目の区画は、S_{i,j}. のとき道、# のとき塀です。

### 制約

• 2 \leq H,W \leq 500
• H,W は整数
• S_{i,j}. または #
• S_{1,1}S_{H,W}.

### 入力

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


### 入力例 1

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


### 出力例 1

1


..#..
#.**#
##**#
#.#.#
..#..

### 入力例 2

5 7
.......
######.
.......
.######
.......


### 出力例 2

0


### 入力例 3

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


### 出力例 3

5


Score : 500 points

### 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}


### 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

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