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())

d = deque()
op = [[-1] * w for i in range(h)]

for i in range(h):
    s = input().rstrip()
    for j in range(len(s)):
        if s[j] == '#':
            d.append((i, j, 0))
            op[i][j] = 0

while d:
    i, j, step = d.popleft()

    for i2, j2 in [(i-1, j), (i+1, j), (i, j-1), (i, j+1)]:
        if 0 <= i2 < h and 0 <= j2 < w:
            if op[i2][j2] == -1:
                d.append((i2, j2, step+1))
                op[i2][j2] = step + 1

print(max([max(op[i]) for i in range(h)]))