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

H, W = map(int, input().split())
m = [list(input()) for i in range(H)]
ans = 0
q = deque()

for h in range(H):
  for w in range(W):
    if m[h][w] == "#":
      q.append((h, w, 0))

while q:
  h, w, c = q.popleft()
  ans = max(ans, c)
  for dh, dw in ((-1, 0), (1, 0), (0, -1), (0, 1)):
    if 0 <= h+dh < H and 0 <= w+dw < W and m[h + dh][w + dw] == ".":
      m[h + dh][w + dw] = "#"
      q.append((h+dh, w+dw, c+1))

print(ans)