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:
from collections import deque
from itertools import chain
H, W = map(int, input().split())
G = chain.from_iterable([[s == '#' for s in input()] for _ in range(H)])
dist = [0]*(H*W)
B = deque([i for i, g in enumerate(G) if g])
visited = set(B)
while B:
    vij = B.pop()
    for dij in (W, -W, 1, -1):
        nij = vij + dij
        if (dij == 1 and not nij % W) or (dij == -1 and not (nij+1) % W) or not (0 <= nij < H*W) or nij in visited:
            continue
        visited.add(nij)
        dist[nij] = 1 + dist[vij]
        B.appendleft(nij)
print(max(dist))