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())
inf = 10 ** 6
a = [[0] * (w + 2)] + [[0] + [inf] * w + [0] for _ in range(h)] + [[0] * (w + 2)]
d = deque()

for i in range(h):
    for j, k in enumerate(input()):
        if k == "#":
            a[i + 1][j + 1] = 0
            d.append((i + 1, j + 1))

stp = ((0, 1), (0, -1), (1, 0), (-1, 0))
res = 0

while d:
    x, y = d.popleft()
    for k, l in stp:
        nx, ny = x + k, y + l
        if a[x][y] + 1 < a[nx][ny]:
            a[nx][ny] = a[x][y] + 1
            res = max(res, a[nx][ny])
            d.append((nx, ny))
print(res)