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)]
move=((1,0),(0,1),(-1,0),(0,-1))

que=deque([])
visited=[[0]*w for _ in range(h)]
for i in range(h):
    for j in range(w):
        if a[i][j]=="#":
            que.append((i,j,0))
            visited[i][j]=1


while len(que)>0:       
    ci,cj,d=que.popleft()
    for mi,mj in move:
        ni,nj=mi+ci,mj+cj
        if 0<=ni<h and 0<=nj<w and visited[ni][nj]==0:
            if a[ni][nj]==".":
                visited[ni][nj]=1
                que.append((ni,nj,d+1))

print(d)