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 = [list(input()) for _ in range(h)]

q = deque()

for i in range(h):
    for j in range(w):
        if a[i][j] == '#':
            q.append((i, j, 0)) 

while q:
    y, x, d = q.popleft()
    if a[y][x] == '#':
        for xdx, ydy in zip((x, x, x+1, x-1), (y+1, y-1, y, y)):
            if (0 <= xdx < w) and (0 <= ydy < h):
                if a[ydy][xdx] == '.':
                    a[ydy][xdx] = '#'
                    q.append((ydy, xdx, d+1))
print(d)