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())
grid = [list(input()) for _ in range(h)]
nxt = deque()
for i in range(h):
		for j in range(w):
			if grid[i][j] == "#":
				nxt.append((i,j,0))
a=0
while nxt:
	i,j,t = nxt.popleft()
	if t > a:
		a+=1
	for i,j in ((i-1,j),(i+1,j),(i,j-1),(i,j+1)):
		if (-1<i<h)&(-1<j<w) and grid[i][j] == ".":
				grid[i][j] = "#"
				nxt.append((i,j,t+1))
print(a)