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())
maze=[list(input()) for i in range(h)]
d=[[-1]*w for i in range(h)]
que=deque([])
dd=((1,0),(0,1),(-1,0),(0,-1))
for i in range(h):
    for j in range(w):
        if maze[i][j]=="#":
            que.append((i,j))           
            d[i][j]=0
ans=0
while que:
    p=que.popleft()
    ans=d[p[0]][p[1]]
    for dx,dy in dd:
        nx=p[0]+dx
        ny=p[1]+dy
        if 0<=nx and nx<h and 0<=ny and ny<w and maze[nx][ny]!="#" and d[nx][ny]==-1:
            d[nx][ny]=ans+1
            que.append((nx,ny))  
print(ans)