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 JavaScript (node.js v5.12) (judge verdict: Time Limit Exceeded)


function Main(lines) {
    lines = lines.split("\n");

    var H = Number(lines[0].split(" ")[0]);
    var W = Number(lines[0].split(" ")[1]);

    lines.shift();

    var q = []

    for (var i = 0; i < H; i++) {
        for (var j = 0; j < W; j++) {
            if (lines[i][j] === "#") { q.push([i, j, 0]); }
        }
    }

    var max = 0; var count = 0;
    var m = Array(H).fill(-1).map(i => i = Array(W).fill(-1));

    while (q.length) {
        var a = q.shift();
        var y = a[0], x = a[1];
        count = a[2];

        if (m[y][x] !== -1) { continue; }

        m[y][x] = count;
        max = Math.max(max, count);

        if (y + 1 < H && lines[y + 1][x] === ".") { q.push([y + 1, x, count + 1]); }
        if (0 <= y - 1 && lines[y - 1][x] === ".") { q.push([y - 1, x, count + 1]); }
        if (x + 1 < W && lines[y][x + 1] === ".") { q.push([y, x + 1, count + 1]); }
        if (0 <= x - 1 && lines[y][x - 1] === ".") { q.push([y, x - 1, count + 1]); }
    }
    console.log(max);
}

Main(require("fs").readFileSync("/dev/stdin", "utf8"));