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())
B = [list(input()) for i in range(H)]

l = []

for i in range(H):
    for j in range(W):
        if B[i][j] == '#':
            l.append((i,j))

def a(l):
    n = []
    d = [(1, 0), (-1, 0), (0, 1), (0, -1)]
    for y, x in l:
        for dy, dx in d:
            ny = y + dy
            nx = x + dx
            if 0 <= ny < H and 0 <= nx < W and B[ny][nx] == '.':
                B[ny][nx] = '#'
                n.append((ny, nx))
    return set(n)

ans = 0
while len(l) != 0:
    l = a(l)
    ans += 1
print(ans-1)