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)

from collections import deque

h, w = map(int, input().split())
a = [list(input()) for _ in range(h)]

cnt = [[10 ** 10] * w for _ in range(h)]
for i in range(h):
    for j in range(w):
        if a[i][j] == "#":
            cnt[i][j] = 0
def bfs(q, v, c):
    while q:
        y, x = q.pop()
        for i, j in ([0, 1], [1, 0], [-1, 0], [0, -1]):
            ny = y + i
            nx = x + j
            if 0 <= nx < w and 0 <= ny < h and v[ny][nx] == 0:
                v[ny][nx] = 1
                if c[ny][nx] >= c[y][x] + 1:
                    c[ny][nx] = c[y][x] + 1
                    q.append([ny, nx])





for i in range(h):
    for j in range(w):
        if a[i][j] == "#":
            queue = deque()
            queue.append([i, j])
            visited = [[0] * w for _ in range(h)]
            bfs(queue, visited, cnt)
            """
            for k in range(h):
                print(cnt[k])
            print()
            """
ans = 0
for i in range(h):
    ans = max(ans, max(cnt[i]))
print(ans)