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: Wrong Answer)

#import copy
import random

H, W = map(int, input().split())
#dist_matrix = [[10000] * W for i in range(H)]
black_h_list = []
black_w_list = []
for i in range(H):
  line_list = list(input())
  for j in range(W):
    if line_list[j] == "#":  
      black_h_list.append(i)
      black_w_list.append(j)

#print(black_h_list)
#print(black_w_list)

max_value = 0
for index in range(100):
  i = int(random.random()*H)
  j = int(random.random()*W)
  min_dist = H+W+2
  for k in range(len(black_h_list)):
    dist = abs(i-black_h_list[k]) + abs(j-black_w_list[k])
    if max_value >= dist:
      min_dist = dist
      break
    elif min_dist > dist:
      min_dist = dist        
  #dist_matrix[i][j] = min_dist
  if max_value < min_dist:
    max_value = min_dist

#print(dist_matrix)
    
print(max_value)