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())
A = [input() for i in range(H)]

Map = [[-1] * W for i in range(H)]

d = deque([])
for i in range(H):
  for j in range(W):
    if A[i][j] == '#':
      Map[i][j] = 0
      d.append([i, j])

ans = 0
while d:
  x, y = d.popleft()
  dist = Map[x][y]
  for dx, dy in [[1, 0], [0, 1], [-1, 0], [0, -1]]:
    u, v = x + dx, y + dy
    if 0<=u<H and 0<=v<W and Map[u][v]==-1:
      Map[u][v] = dist + 1
      ans = max(ans, dist + 1)
      d.append([u, v])

print(ans)