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)

# coding: utf-8
# Your code here!
import collections

h,w = [int(i) for i in input().split()]
board = [input() for j in range(h)] # 縦「n」行

d4 = [[1,0],[0,1],[-1,0],[0,-1]]
memo = [[-1]*w for j in range(h)]
dist = [[100000]*w for j in range(h)]


q = collections.deque()
for i in range(h):
    for j in range(w):
        if board[i][j] == "#":
            memo[i][j] = 1
            q.append((i,j,0))

while len(q) != 0:
#    print(memo)
    i,j,c = q.popleft()
    dist[i][j] = c
    for k in d4:
#        print(k)
        ii,jj = k
        if  i+ii < 0 or i+ii>=h or j+jj <0 or j+jj>=w:
#            print("out",i+ii,j+jj)
            continue
        if memo[i+ii][j+jj] < 0:
#            print("put")
            q.append((i+ii,j+jj,c+1))
            memo[i+ii][j+jj] = 1

ans = 0      
for i in range(h):
    for j in range(w):
        ans = max(ans,dist[i][j])

print(ans)
#print(dist)