Problem Statement

You are given a grid of squares with H horizontal rows and W vertical columns, where each square is painted white or black.
HW characters from A_{11} to A_{HW} represent the colors of the squares.
A_{ij} is # if the square at the i-th row from the top and the j-th column from the left is black, and A_{ij} is . if that square is white.
We will repeatedly perform the following operation until all the squares are black:

• Every white square that shares a side with a black square, becomes black.

Find the number of operations that will be performed.
The initial grid has at least one black square.

Input

Input is given from Standard Input in the following format:
H W
A_{11}A_{12}...A_{1W}
:
A_{H1}A_{H2}...A_{HW}

Output

Print the number of operations that will be performed.

Constraints

• $1 \leq H,W \leq 1000$
• A_{ij} is # or ..
• The given grid has at least one black square.

Sample Input 1

3 3
...
.#.
...

Sample Output 1

2

After one operation, all but the corners of the grid will be black. After one more operation, all the squares will be black.

Sample Input 2

6 6
..#..#
......

..#..

......
.#....
....#.

Sample Output 2

3

见题面 Input 部分

见题面 Output 部分