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())
hw = [list(input().strip()) for _ in range(H)]
b = deque()
for h in range(H):
    for w in range(W):
        if hw[h][w] == '#':
            b.append([h, w, 0])

ans = 0
while len(b) > 0:
    h, w, d = b.popleft()
    d += 1
    for y, x in [[1, 0], [-1, 0], [0, 1], [0, -1]]:
        nh, nw = h + y, w + x
        if nh >= 0 and nh < H and nw >= 0 and nw < W and hw[nh][nw] == '.':
            b.append([nh, nw, d])
            if ans < d:
                ans = d
            hw[nh][nw] = "#"
print(ans)