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)

H, W = map(int, input().split())
state = [[0 if a == '.' else 1 for a in list(input())] for _ in range(H)]

checked = [[False for _ in range(W)] for _ in range(H)]
qs = []
for h in range(H):
    for w in range(W):
        if state[h][w] == 1:
            checked[h][w] = True
            qs.append((h, w))

c = -1
while qs:
    qqs = []
    for h, w in qs:
        nexts = [(h+1, w), (h-1, w), (h, w+1), (h, w-1)]
        for nh, nw in nexts:
            if 0 <= nh <= H-1 and 0 <= nw <= W-1:
                if not checked[nh][nw]:
                    qqs.append((nh, nw))
                    checked[nh][nw] = True
    qs = qqs
    c += 1
print(c)