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: Wrong Answer)

import copy
import pprint

def check_all(A, H, W):
    for i in range(H):
        for j in range(W):
            if A[i][j] == '.':
                return False
    return True

def flip(A, H, W, i, j):
    if i - 1 >= 0:
        A[i - 1][j] = '#'
    if i + 1 < H:
        A[i + 1][j] = '#'
    if j - 1 >= 0:
        A[i][j - 1] = '#'
    if j + 1 < W:
        A[i][j + 1] = '#'

H, W = map(int, input().rstrip('\n').split())
A = []
for i in range(H):
    A.append(list(input().rstrip('\n')))

count = 0
while True:
    if check_all(A, H, W):
        break
    B = copy.deepcopy(A)
    for i in range(H):
        for j in range(W):
            if A[i][j] == '#':
                flip(B, H, W, i, j)
    print('count =', count)
    pprint.pprint(B)
    print()
    A = B
    count += 1
print(count)