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 = [['#'] * (w + 2)] * 2
a[1: 1] = [list('#' + input() + '#') for _ in range(h)]
p = [(i, j) for i in range(1, h + 1) for j in range(1, w + 1) if a[i][j] == '#']
d = (-1, 0), (1, 0), (0, -1), (0, 1)
r = -1
while p:
    r += 1
    s = []
    for i, j in p:
        for di, dj in d:
            di += i
            dj += j
            if a[di][dj] == '.':
                a[di][dj] = '#'
                s.append((di, dj))
    p = s
print(r)