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 = ['#' * (w+2)] + ['#' + input() + '#' for i in range(h)] + ['#' * (w+2)]
for i in range(h+2):
    a[i] = list(a[i])

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

q = deque(x)
ans = 0
while q:
    i, j, c = q.popleft()
    for di, dj in d:
        if a[i+di][j+dj] == '.':
            a[i+di][j+dj] = '#'
            q.append((i+di, j+dj, c+1))
    ans = max(ans, c)


print(ans)