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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

import copy
def main():
    dict_ = {'#': 1, '.': 0}
    h, w = map(int, (input().split()))
    num = []
    for hh in range(h):
        s = input()
        for ww in range(len(s)):
            if s[ww]=='#':
                num.append(ww + hh * h)
    allnum = [i for i in range(h*w)]
    maxv = 0
    for white in list(set(allnum) - set(num)):
        minv = h*w
        for black in num:
            l1 = abs(white//w - black//w) + abs(white%w - black%w)
            if minv > l1:
                minv = l1
        if maxv < minv:
            maxv = minv
    print(maxv)

if __name__ == '__main__':
    main()