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()
e=q.append
for i in range(h):
 for j in range(w):
  if'.'>c[i][j]:e((i,j,0))
a=0
while q:
 y,x,v=q.popleft();a=max(a,v)
 for i,j in((y,x-1),(y,x+1),(y-1,x),(y+1,x)):
  if h>i>=0and w>j>=0and'#'<c[i][j]:c[i][j]='#';e((i,j,v+1))
print(a)