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 (3.8.2) (judge verdict: Time Limit Exceeded)

import sys
import copy
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines

in_n = lambda: int(readline())
in_nn = lambda: map(int, readline().split())
in_s = lambda: readline().rstrip().decode('utf-8')
in_nl = lambda: list(map(int, readline().split()))
in_nl2 = lambda H: [in_nl() for _ in range(H)]
in_map = lambda: [s == ord('.') for s in read() if s != ord('\n')]
in_map2 = lambda H: [in_map() for _ in range(H)]
in_all = lambda: map(int, read().split())


def main():

    H, W = in_nn()
    grid = in_map()

    ans = 0
    move = [(-1, 0), (1, 0), (0, -1), (0, 1)]
    while sum(grid) != 0:

        next_grid = copy.copy(grid)
        for y in range(H):
            for x in range(W):
                if not grid[x + y * W]:
                    continue
                for (px, py) in move:
                    nx, ny = x + px, y + py
                    if 0 <= nx < W and 0 <= ny < H:
                        if not grid[nx + ny * W]:
                            next_grid[x + y * W] = False
                            break
        ans += 1
        grid = next_grid

    # print(grid)
    print(ans)


if __name__ == '__main__':
    main()