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:
h,w=map(int,input().split())
l=[['#' for i in range(w+2)] for j in range(2)]
l[1:1]=[list('#'+input()+'#') for i in range(h)]
p=[]
for i in range(1,h+1):
  for j in range(1,w+1):
    if l[i][j]=='#':
      p.append((i,j))
d=[(-1,0),(1,0),(0,-1),(0,1)]
r=-1
while len(p)!=0:
  r+=1
  s=[]
  for i, j in p:
    for di, dj in d:
      di+=i
      dj+=j
      if l[di][dj]=='.':
        l[di][dj]='#'
        s.append((di,dj))
  p=s
print(r)