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())
a=['*'*(w+2)]+['*'+input()+'*' for _ in range(h)]+['*'*(w+2)]
from collections import deque
d=deque()
c=[[0]*w for _ in range(h)]
for i in range(1,h+1):
  for j in range(1,w+1):
    if a[i][j]=='#':
      d.append([i,j])
di=[[0,1],[1,0],[-1,0],[0,-1]]
while d:
  g=d.popleft()
  for i in di:
    x=g[0]+i[0]
    y=g[1]+i[1]
    if a[x][y]=='.':
      if c[x-1][y-1]==0:
        d.append([x,y])
        c[x-1][y-1]=c[g[0]-1][g[1]-1]+1
m=0
for i in range(h):
  for j in range(w):
    m=max(m,c[i][j])
print(m)