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: Accepted)

<?php
fscanf(STDIN, "%d %d", $H, $W);
$d1 = $d2 = $d3 = $d4 = [];
$ans = 0;
$rest = $H * $W;

for ($y = 0; $y < $H; $y++) {
    $m[$y] = str_split(trim(fgets(STDIN)));
}

for ($x = 0; $x < $W; $x++) {
    for ($y = 0; $y < $H; $y++) {
        if ($m[$y][$x] == "#") {
            $s[$y][$x] = 1;
            $a[$y][$x] = 1;
            $rest--;
        }
    }
}

while($rest > 0) {
    $ans++;
    // echo $rest . PHP_EOL;
    $new_a = [];
    foreach ($a as $y => $v) {
        foreach ($v as $x => $dummy) {
            if ($x != 0) {
                if (!isset($s[$y][$x-1])) {
                    $new_a[$y][$x-1] = 1;
                    $s[$y][$x-1] = 1;
                    $rest--;
                }
            }
            if ($x != $W - 1) {
                if (!isset($s[$y][$x+1])) {
                    $new_a[$y][$x+1] = 1;
                    $s[$y][$x+1] = 1;
                    $rest--;
                }
            }
            if ($y != 0) {
                if (!isset($s[$y-1][$x])) {
                    $new_a[$y-1][$x] = 1;
                    $s[$y-1][$x] = 1;
                    $rest--;
                }
            }
            if ($y != $H - 1) {
                if (!isset($s[$y+1][$x])) {
                    $new_a[$y+1][$x] = 1;
                    $s[$y+1][$x] = 1;
                    $rest--;
                }
            }
        }
    }
    $a = $new_a;
}

echo $ans;