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';
class Queue {
  constructor(size) {
    this.arr = new Array(size);
    this.head = this.tail = 0;
  }

  is_full() {
    return this.head == (this.tail + 1) % this.arr.length;
  }

  push(v) {
    if (this.is_full()) {
      this.arr.length *= 2;
    }
    this.arr[this.tail] = v;
    this.tail = (this.tail + 1) % this.arr.length;
  }

  is_empty() {
    return this.head == this.tail;
  }

  pop() {
    if (this.is_empty()) {
      throw -1;
    }
    let v = this.arr[this.head];
    this.head = (this.head + 1) % this.arr.length;
    return v;
  }

  maxsize() {
    return this.arr.length;
  }
}

function main(input) {
  let lines = input.split('\n')
  let v = lines[0].split(' ').map((n) => parseInt(n));
  let h = v[0];
  let w = v[1];
  let c = [];
  let d = [];
  for (let i = 1; i < h + 1; i++) {
    c.push(lines[i]);
    d.push([]);
  }
  let q = new Queue(1000000000);
  for (let i = 0; i < h; i++) {
    for (let j = 0; j < w; j++) {
      if (c[i][j] == '#') {
        q.push([i, j]);
        d[i][j] = 0;
      } else {
        d[i][j] = -1;
      }
    }
  }
  let p = q.pop();
  let max = 0;
  const dx = [1, 0, -1, 0];
  const dy = [0, 1, 0, -1];
  while (true) {
    const xx = p[0];
    const yy = p[1];
    for (let i =0; i < 4; i++) {
      let x = xx + dx[i];
      let y = yy + dy[i];
      if (x < 0 || x > h - 1 || y < 0 || w - 1 < y || d[x][y] >= 0) {
        continue;
      }
      if (c[x][y] == '.') {
        q.push([x, y]);
        let count = d[xx][yy] + 1;
        if (max < count) {
          max = count;
        }
        d[x][y] = count;
      }
    }
    if (q.is_empty()) {
      break;
    }
    p = q.pop();
  }
  console.log(max);
}

main(require('fs').readFileSync('/dev/stdin', 'utf8'))