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*
h,w=map(int,input().split())
c=eval('list(input()),'*h)
q=deque()
for i in range(h):
    for j in range(w):
        if c[i][j]=='#':
            q.append((i,j,0))
ans=0
while q:
    y,x,v=q.popleft()
    ans=max(ans,v)
    for i,j in((y,x-1),(y,x+1),(y-1,x),(y+1,x)):
        if h>i>=0 and w>j>=0 and c[i][j]=='.':
            c[i][j]='#'
            q.append((i,j,v+1))
print(ans)