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())
a=[input() for _ in range(h)]
inf=10**10
dist=[[inf if c=='.' else 0 for c in r] for r in a]
dq=deque()
for i in range(h):
    for j in range(w):
        if dist[i][j]==0:
            dq.append([i,j])
diff=[[1,0],[0,1],[-1,0],[0,-1]]
ans=0
while(dq):
    y,x=dq.popleft()
    for dy,dx in diff:
        y2=y+dy
        x2=x+dx
        if 0<=y2<h and 0<=x2<w and dist[y2][x2]>dist[y][x]+1:
            dq.append([y2,x2])
            dist[y2][x2]=dist[y][x]+1
            ans=max(ans,dist[y2][x2])
print(ans)