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:
import queue
h,w=map(int,input().split())
a=[input() for _ in range(h)]
q=[]
dist=[[-1 for _ in range(w)]for _ in range(h)]
for i in range(h):
    for j in range(w):
        if a[i][j]=='#':
            q.append([i,j])
            dist[i][j]=0
q=queue.deque(q)
d=[[1,0],[0,1],[-1,0],[0,-1]]
while q:
    y,x=q.popleft()
    for dy,dx in d:
        ny,nx=y+dy,x+dx
        if 0<=ny and ny<h and 0<=nx and nx<w and dist[ny][nx]==-1:
            dist[ny][nx]=dist[y][x]+1
            q.append([ny,nx])
ans=0
for i in range(h):
    for j in range(w):
        ans=max(ans,dist[i][j])
print(ans)