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:
h,w=map(int,input().split())
s=set()
a=[]
from collections import deque
q=deque([])
for i in range(h):
    tmp=list(input())
    a.append(tmp)
    for j in range(w):
        if tmp[j]=="#":
            q.append((i,j,0))

ans=0
ll=[[0,1],[0,-1],[1,0],[-1,0]]
while q:
    x,y,v=q.popleft()
    ans=max(ans,v)
    for i,j in ll:
        if 0<=x+i<h and 0<=y+j<w and a[i+x][j+y]==".":
            a[i+x][j+y]="#"
            q.append((i+x,j+y,v+1))

print(ans)