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())
p=[list("#"*(w+2))]+[list("#"+input()+"#") for i in range(h)]+[list("#"*(w+2))]
q=deque([])
for i in range(1,h+1):
	for j in range(1,w+1):
		if p[i][j]=='#':
			p[i][j]=0
			q.append([i,j])
d=[(1,0),(-1,0),(0,1),(0,-1)]
while q:
	x,y=q.popleft()
	for dx,dy in d:
		if p[x+dx][y+dy]==".":
			p[x+dx][y+dy]=p[x][y]+1
			q.append([x+dx,y+dy])
ans=0
for i in range(1,h+1):
	for j in range(1,w+1):
		ans=max(ans,p[i][j])
print(ans)