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 (3.4.3) (judge verdict: Time Limit Exceeded)

from collections import deque
import sys
input=sys.stdin.readline


def BFS():
    point=0
    color=[["white" for _ in range(w)] for _ in range(h)]
    D=[[0 for _ in range(w)] for _ in range(h)]

    queue=deque([])
    for i in range(h):
        for j in range(w):
            if A[i][j]=="#":
                color[i][j]="gray"
                queue.append([i,j])
                D[i][j]=0

    while len(queue)>0:
        x,y=queue.popleft()
        for a,b in [[1,0],[-1,0],[0,1],[0,-1]]:
            X,Y=x+a,y+b
            if 0<=X<h and 0<=Y<w:
                if color[X][Y]=="white":
                    color[X][Y]="gray"
                    D[X][Y]=D[x][y]+1
                    point=max(point,D[X][Y])
                    queue.append([X,Y])
        color[x][y]="black"

    return point


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