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())
grid=[[-1]*w for _ in range(h)]
from collections import deque
que=deque()
for i in range(h):
    s=list(input())
    for j in range(w):
        if s[j]=='#':
            grid[i][j]=0
            que.append((i,j))
dirc=[(1,0),(-1,0),(0,1),(0,-1)]

while que:
    kuro=que.popleft()
    n=grid[kuro[0]][kuro[1]]
    for dx,dy in dirc:
        x=kuro[0]+dx
        y=kuro[1]+dy
        if 0<=x<h and 0<=y<w and grid[x][y]==-1:
            grid[x][y]=n+1
            que.append((x,y))

ans=0
for i in range(h):
    ans=max(ans,max(grid[i]))
print(ans)