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:
h, w = map(int, input().split())
a = [input() for i in range(h)]
b = [-1]*h*w; c = []; d = 0
for i in range(h):
    for j in range(w):
        if a[i][j] == "#": b[i*w+j] = 0; c.append(i*w+j)
while len(c) < h*w:
    if c[d]//w != 0:
        if b[c[d]-w] == -1: b[c[d]-w] = b[c[d]]+1; c.append(c[d]-w)
    if c[d]%w != 0:
        if b[c[d]-1] == -1: b[c[d]-1] = b[c[d]]+1; c.append(c[d]-1)
    if c[d]%w != w-1:
        if b[c[d]+1] == -1: b[c[d]+1] = b[c[d]]+1; c.append(c[d]+1)
    if c[d]//w != h-1:
        if b[c[d]+w] == -1: b[c[d]+w] = b[c[d]]+1; c.append(c[d]+w)
    d += 1
print(max(b))