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 PyPy3 (2.4.0) (judge verdict: Accepted)

import sys
from collections import deque

sys.setrecursionlimit(10 ** 6)
INF = float("inf")
MOD = 10 ** 9 + 7


def input():
    return sys.stdin.readline().strip()


def bfs(maze, H, W):
    visited = [[-1] * W for _ in range(H)]
    q = deque([])
    for h in range(H):
        for w in range(W):
            if maze[h][w] == "#":
                visited[h][w] = 0
                q.append((h, w))

    res = 0
    while q:
        h, w = q.popleft()

        for dh, dw in [(1, 0), (-1, 0), (0, 1), (0, -1)]:
            nh = h + dh
            nw = w + dw
            if 0 <= nh < H and 0 <= nw < W:
                if visited[nh][nw] == -1 and maze[nh][nw] == ".":
                    visited[nh][nw] = visited[h][w] + 1
                    if res < visited[nh][nw]:
                        res = visited[nh][nw]
                    q.append((nh, nw))

    return res


def main():
    H, W = map(int, input().split())
    S = [input() for _ in range(H)]
    ans = bfs(S, H, W)
    print(ans)


if __name__ == "__main__":
    main()