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)


"use strict";

process.stdin.resume();
process.stdin.setEncoding('utf8');

var g_input = '';
process.stdin.on('data', function(chunk) {
    g_input += chunk;
});

process.stdin.on('end', function() {
    Main(g_input.split(/\r?\n/));
});

function Main(input) {

    const tokens = input[0].split(' ').map(function(value) { return parseInt(value, 10); });
    const h = tokens[0];
    const w = tokens[1];

    let a = new Array(h);
    for (let i = 0; i < h; i++) {
        a[i] = input[i + 1].split('');
    }

    let distanceMap = new Array(h);
    let blackCells = [];
    for (let i = 0; i < h; i++) {
        distanceMap[i] = new Array(w);
        for (let j = 0; j < w; j++) {
            if (a[i][j] === "#") {
                distanceMap[i][j] = 0;
                blackCells.push({x: i, y: j, distance: 0});
            } else {
                distanceMap[i][j] = Number.MAX_SAFE_INTEGER;
            }
        }
    }

    while (blackCells.length > 0) {
        const blackCell = blackCells.shift();
        const i = blackCell.x;
        const j = blackCell.y;
        const distance = blackCell.distance;
        if (i - 1 >= 0 && distanceMap[i - 1][j] > distance + 1) {
            distanceMap[i - 1][j] = distance + 1;
            blackCells.push({x: i - 1, y: j, distance: distance + 1});
        }
    
        if (i + 1 < h && distanceMap[i + 1][j] > distance + 1) {
            distanceMap[i + 1][j] = distance + 1;
            blackCells.push({x: i + 1, y: j, distance: distance + 1});
        }
        
        if (j - 1 >= 0 && distanceMap[i][j - 1] > distance + 1) {
            distanceMap[i][j - 1] = distance + 1;
            blackCells.push({x: i, y: j - 1, distance: distance + 1});
        }
    
        if (j + 1 < w && distanceMap[i][j + 1] > distance + 1) {
            distanceMap[i][j + 1] = distance + 1;
            blackCells.push({x: i, y: j + 1, distance: distance + 1});
        }
    }


    let ans = 0;
    for (let i = 0; i < h; i++) {
        for (let j = 0; j < w; j++) {
            if (ans < distanceMap[i][j]) {
                ans = distanceMap[i][j];
            }
        }
    }

    console.log(ans);

    return 0;
}