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())
a=[input() for _ in range(h)]
dxy=[(0,1),(1,0),(-1,0),(0,-1)]
inf=float("inf")

dp=[[inf]*w for _ in range(h)]
q=deque()

for y,l in enumerate(a):
    for x,c in enumerate(l):
        if c=="#":
            dp[y][x]=0
            q.append((x,y))
ans=0
while q:
    x,y=q.popleft()
    d=dp[y][x]
    for dx,dy in dxy:
        nx,ny=x+dx,y+dy
        if not 0<=nx<w: continue
        if not 0<=ny<h: continue
        if dp[ny][nx]<=d+1: continue
        dp[ny][nx]=d+1
        q.append((nx,ny))
        ans=max(ans,d+1)
print(ans)