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())
A=[list(input()) for i in range(H)]
que=[]
for i in range(H):
    for j in range(W):
        if A[i][j]=="#":
            que.append((i, j))
            A[i][j]=1
        else:
            A[i][j]=0
d=[(1,0),(0,1),(-1,0),(0,-1)]
count=0
while que:
    h=[]
    for x,y in que:
        for dx,dy in d:
            nx,ny=x+dx,y+dy
            if 0<=nx<H and 0<=ny<W and A[nx][ny]==0:
                A[nx][ny]=1
                h.append((nx,ny))
    que=h
    count+=1
print(count-1)