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: Accepted)

import numpy as np

H, W = map(int, input().split())
A = [[] for _ in range(H)]
inf = 10 ** 7
for i in range(H):
    A[i] = list(input())
    for j in range(W):
        if A[i][j] == '.':
            A[i][j] = inf
        elif A[i][j] == '#':
            A[i][j] = 0

A = np.array(A)

#print(A)

for j in range(1, W):
    A[:,j] = np.minimum(A[:,j-1]+1, A[:,j])

#print(A)
for j in range(W-2, -1, -1):
    A[:,j] = np.minimum(A[:,j+1]+1, A[:,j])

#print(A)

for i in range(1, H):
    A[i,:] = np.minimum(A[i-1,:]+1, A[i,:])

#print(A)

for i in range(H-2, -1, -1):
     A[i,:] = np.minimum(A[i+1,:]+1, A[i,:])

#print(A)


ans = np.max(A)

#for i in range(H):
#    ans_list.append(max(A[i]))

print(ans)