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 = []
q = []
for i in range(H):
  As = list(input())
  A.append(As)
  for j in range(W):
    if A[i][j] == "#":
      q.append((i, j))
r = 0
while q:
  q2 = []
  for i, j in q:
    if i-1 >= 0 and A[i-1][j] == ".":
      A[i-1][j] = "#"
      q2.append((i-1, j))
    if i+1 < H and A[i+1][j] == ".":
      A[i+1][j] = "#"
      q2.append((i+1, j))
    if j-1 >= 0 and A[i][j-1] == ".":
      A[i][j-1] = "#"
      q2.append((i, j-1))
    if j+1 < W and A[i][j+1] == ".":
      A[i][j+1] = "#"
      q2.append((i, j+1))
  q = q2
  r += 1
r -= 1
print(r)