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 PYTHON):

Solution:
inputs = raw_input().replace("\n", "").split(" ")
H, W = map(int, inputs)

m = [ [-1 for x in range(W)] for y in range(H)]

count = 0
zero_coords = []
for y in range(H):
    #line = list(input())
    line = list(raw_input().replace("\n", ""))
    for x, point in enumerate(line):
        if point == "#":
            m[y][x] = 0
            zero_coords.append([y, x])
            count += 1

tmp_coords = zero_coords
#mawari_soutais = [[-1, -1], [-1, 0], [-1, 1], [0, -1], [0, 1], [1, -1], [1, 0], [1, 1]]
mawari_soutais = [[-1, 0], [0, -1], [0, 1], [1, 0]]

val = 0
while count < H*W:
    val += 1
    new_tmp_coords = []
    for center_coord in tmp_coords:
        for mawari_soutai in mawari_soutais:
            mawari_coord = [mawari_soutai[i] + center_coord[i] for i in range(2)]
            y, x = mawari_coord
            if y < 0 or H <= y or x < 0 or W <= x or m[y][x] != -1:
                continue
            else:
                m[y][x] = val
                count += 1
                new_tmp_coords.append([y, x])
    tmp_coords = new_tmp_coords
    #print(m)

out = val
print(out)