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: Runtime Error)

import sys
from collections import deque

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

def main():
    H,W = map(int,input().split())
    A = [list(input()) for _ in range(H)]

    def bfs(x,y,A):
        que = deque()
        que.append((x,y))

        while que:
            x,y = que.popleft()
 
            for dx,dy in ((-1,0),(1,0),(0,-1),(0,1)):
                sx = x + dx
                sy = y + dy
                if sx < 0 or sx >= H or sy < 0 or sy >= W or A[sy][sx] == '#':
                    continue
                cnt = 1 if A[y][x] == '#' else A[y][x] + 1
                if A[sy][sx] == '.':
                    que.append((sx,sy))
                    A[sy][sx] = cnt
                elif A[sy][sx] > cnt:
                    que.append((sx,sy))
                    A[sy][sx] = cnt

    for x in range(W):
        for y in range(H):
            if A[y][x] == '#':
                bfs(x,y,A)
    ans = 0
    for a in A:
        a = [i if i != '#' else 0 for i in a]
        ans = max(ans,max(a))
    print(ans)

if __name__ == "__main__":
    main()