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 array
import itertools
from collections import defaultdict, deque


def log(s):
    # print("| " + str(s), file=sys.stderr)
    pass


def output(x):
    print(x, flush=True)


def input_ints():
    return map(int, input().split())


def solve():
    def fill(queue):
        footsteps = dict()
        for pp, s in queue:
            footsteps[pp] = -1

        while queue:
            p, s = queue.popleft()
            footsteps[p] = s

            for pp in [(p[0] + 1, p[1]), (p[0] - 1, p[1]), (p[0], p[1] + 1), (p[0], p[1] - 1)]:
                if 0 <= pp[0] < width and 0 <= pp[1] < height and pp not in footsteps:
                    queue.append((pp, s + 1))
                    footsteps[pp] = -1  # placeholder

        return s

    height, width = tuple(input_ints())
    field = [input() for _ in range(height)]
    queue = deque()

    for y, line in enumerate(field):
        for x, c in enumerate(line):
            if c == '#':
                queue.append(((x, y), 0))

    return fill(queue)


def main():
    print(solve())


main()