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: Time Limit Exceeded)

from collections import deque

H, W = map(int, input().split())
A = [list(input()) for i in range(H)]
inf = 1145141919810
B = [[inf]*W for i in range(H)]

Q = deque([])
for i in range(H):
	for j in range(W):
		if A[i][j]=='#':
			B[i][j] = 0
			Q.append([i, j])

ans = 0
while Q != deque([]):
	q = Q.popleft()
	h = q[0]
	w = q[1]
	A[h][w] = 'o'
	ans = max(ans, B[h][w])
	if h-1>=0 and A[h-1][w]=='.':
		Q.append([h-1, w])
		B[h-1][w] = min(B[h-1][w], B[h][w]+1)
	if h+1<H and A[h+1][w]=='.':
		Q.append([h+1, w])
		B[h+1][w] = min(B[h+1][w], B[h][w]+1)
	if w-1>=0 and A[h][w-1]=='.':
		Q.append([h, w-1])
		B[h][w-1] = min(B[h][w-1], B[h][w]+1)
	if w+1<W and A[h][w+1]=='.':
		Q.append([h, w-1])
		B[h][w+1] = min(B[h][w+1], B[h][w]+1)

print(ans)