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:
#初期地点
h,w = map(int,input().split())
n=[]
a=[]
a.append(["&"]*(w+2))
for i in range(h):
    arrc = list(input())
    arrc = ["&"]+arrc+["&"]
    b = arrc
    for j in range(len(arrc)):
        if b[j] == "#":
            n.append((i+1,j))
    a.append(b)
a.append(["&"]*(w+2))


#方向
p=[[1,0],[0,1],[-1,0],[0,-1]]
#距離のカウント
cnt=-1
#探索
while n:
    cnt +=1
    n2=[]
    #通った所で総当り
    for i,j in n:
        for di,dj in p:
            di +=i
            dj +=j
            if a[di][dj]==".":
                a[di][dj]="#"
                n2.append((di,dj))
    n=n2
print(cnt)