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 _ in range(h)]

d = deque()
dist = [[-1] * w for _ in range(h)]
for i in range(h):
    for j in range(w):
        if a[i][j] == '#':
            d.append([i, j])
            dist[i][j] = 0

dy = [-1, 0, 1, 0]
dx = [0, -1, 0, 1]
while d:
    x1, y1 = d.popleft()

    for i in range(4):
        x2 = x1 + dx[i]
        y2 = y1 + dy[i]

        if 0 <= x2 < h and 0 <= y2 < w and dist[x2][y2] == -1:
            d.append([x2, y2])
            dist[x2][y2] = dist[x1][y1] + 1

print(max(list(map(lambda x: max(x), dist))))