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
a,b=map(int,input().split())
List=[]
q=deque([[0,0]])
for i in range(a):
  l=list(input())
  for _ in range(b):
    if l[_]=="#":
      q.append([i,_])
      l[_]=0
  List.append(l)
q.popleft()
aaa=[[0,1],[0,-1],[1,0],[-1,0]]
ans=0
while q:
  h,w=q.popleft()
  for x,y in aaa:
    if 0<=h+x<a and 0<=w+y<b:
      if List[h+x][w+y]==".":
        List[h+x][w+y]=List[h][w]+1
        q.append([h+x,w+y])
        if List[h+x][w+y]>ans:
          ans=List[h+x][w+y]
print(ans)