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=[]
for i in range(h):
  a.append([it == '#' for it in input()])
q=[]
for i in range(h):
  for j in range(w):
    if a[i][j]: q.append((i, j))
cnt = -1
while q:
  cnt += 1
  r = []
  for i, j in q:
    if i > 0 and not a[i-1][j]:
      a[i-1][j]=True
      r += [(i-1, j)]
    if i < h-1 and not a[i+1][j]:
      a[i+1][j]=True
      r += [(i+1, j)]
    ai = a[i]
    if j > 0 and not ai[j-1]:
      ai[j-1]=True
      r += [(i, j-1)]
    if j < w-1 and not ai[j+1]:
      ai[j+1]=True
      r += [(i, j+1)]
  q=r
print(cnt)