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 C++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <iostream>
using namespace std;

int h, w, k = 0, c = 0;
int a[1000][1000];

int main()
{
	cin >> h >> w;

	for (int i = 0; i < h; i++) {
		for (int j = 0; j < w; j++) {
			char s;

			cin >> s;

			if (s == '.') {
				a[i][j] = 0;
				c++;
			}
			else
				a[i][j] = 1;
		}
	}
	
	while (c > 0) {
		k++;

		for (int i = 0; i < h; i++) {
			for (int j = 0; j < w; j++) {
				if (a[i][j] == k) {
					if (i > 0 && a[i - 1][j] == 0) {
						a[i - 1][j] = k + 1;
						c--;
					}

					if (i < h - 1 && a[i + 1][j] == 0) {
						a[i + 1][j] = k + 1;
						c--;
					}

					if (j > 0 && a[i][j - 1] == 0) {
						a[i][j - 1] = k + 1;
						c--;
					}

					if (j < w - 1 && a[i][j + 1] == 0) {
						a[i][j + 1] = k + 1;
						c--;
					}						
				}
			}
		}
	}

	cout << k << endl;

	return 0;
}