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())
masu = []
for i in range(H):
    masu.append(list(input()))
black = []
for i in range(H):
    for j in range(W):
        if masu[i][j] == "#":
            black.append([i,j])
ans = -1
while len(black) != 0:
    ans += 1
    blacktemp = black[:]
    black = []
    for k in blacktemp:
        for i, j in [[0, -1], [0, 1], [-1, 0], [1, 0]]:
            if 0 <= k[0] + i <= H-1 and 0 <= k[1] + j <= W-1:
                if masu[k[0]+i][k[1]+j] == ".":
                    masu[k[0]+i][k[1]+j] = "#"
                    black.append([k[0]+i, k[1]+j])
print(ans)