Problem: 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.

Examples

Input

3 3
...
.#.
...


Output

2


Input

6 6
..#..#
......
..#..
......
.#....
....#.


Output

3

Solution (in PYTHON3):

Solution:
from collections import deque
h,w=map(int,input().split())
a=[input() for _ in range(h)]
visited=[[-1]*w for _ in range(h)]
queue=deque()
for i in range(h):
  for j in range(w):
    if a[i][j]=='#':
      visited[i][j]=0
      queue.append([i,j])
while queue:
  y,x=queue.popleft()
  for j,k in ([1,0],[-1,0],[0,1],[0,-1]):
    n_y,n_x=y+j,x+k
    if 0<=n_y<h and 0<=n_x<w and a[n_y][n_x]=='.' and visited[n_y][n_x]<0:
      visited[n_y][n_x]=visited[y][x]+1
      queue.append([n_y,n_x])
ans=0
for l in visited:
  ans=max([ans]+l)
print(ans)