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

h, w = map(int, input().split())
c = []
d = [[-1 for i in range(w)] for j in range(h)]
q = deque()
for i in range(h):
	s = input()
	c.append(s)
	for j in range(w):
		if c[i][j] == '#':
			q.append([i, j, 0])
			d[i][j] = 0

dirr = [[1, 0], [0, 1], [-1, 0], [0, -1]]

while len(q) != 0:
	y, x, z = q[0]

	for i in range(4):
		ny, nx = y + dirr[i][0], x + dirr[i][1]
		if 0 <= ny < h and 0 <= nx < w and d[ny][nx] == -1 and c[ny][nx] != "#":
			q.append([ny, nx, z + 1])
			d[ny][nx] = z + 1

	q.popleft()

print(z)