Score : $300$ points

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.

Constraints

• $1 \leq H,W \leq 1000$
• $A_{ij}$ is # or ..
• The given 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.

3 3
...
.#.
...

2

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

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

3