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())
m = [[-1 if c == "." else 0 for c in input() + "#"] for _ in range(H)]
m.append([0] * (W + 1))
todo = deque(((h, w) for h in range(H) for w in range(W) if m[h][w] == 0))
ans = 0
while todo:
    h, w = todo.popleft()
    count = m[h][w] + 1
    for dh, dw in ((1, 0), (-1, 0), (0, 1), (0, -1)):
        nh = h + dh
        nw = w + dw
        if m[nh][nw] == -1:
            m[nh][nw] = count
            todo.append((nh, nw))
            ans = count
print(ans)