Problem:
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.

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

Solution in PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
fscanf(STDIN, "%d%d", $H, $W);
for($y = 0; $y < $H; $y++){
    $str = fgets(STDIN);
    $map[$y] = $str;
    for($x = 0; $x < $W; $x++){
        if($map[$y][$x] == "#"){
            $list[] = [$y,$x];
        }
    }
}
$count = 0;
while($list){
    $nextList = [];
    foreach($list as list($y, $x)){
        foreach([[0,1],[1,0],[-1,0],[0,-1]] as list($dy, $dx)){
            $ny = $y+$dy;
            if($ny >= 0 && $ny < $H){
                $nx = $x+$dx;
                if($nx >= 0 && $nx < $W){
                    if($map[$ny][$nx] == '.'){
                        $map[$ny][$nx] = '#';
                        $nextList[] = [$ny, $nx];
                    }
                }
            }
        }
    }
    $list = $nextList;
    if($list)$count++;
}
echo $count;