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())
l = [list(input()) for _ in range(H)]

from collections import deque
q = deque()
for i, r in enumerate(l):
    for j, c in enumerate(r):
        if c == '#':
            l[i][j] = 0
            q.append((i, j))
d = [(0, 1), (0, -1), (1, 0), (-1, 0)]

while q:
    y, x = q.popleft()
    for dy, dx in d:
        if (0 <= y+dy < H) and (0 <= x+dx < W) and l[y+dy][x+dx] == '.':
            l[y+dy][x+dx] = l[y][x] + 1
            q.append((y+dy, x+dx))

m = 0
for r in l:
    for c in r:
        if m < c:
            m = c
print(m)