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
INF=10**18
h,w=map(int,input().split())
e=[input() for _ in range(h)]
d=[[INF]*w for _ in range(h)]
q=deque([])
for i in range(h):
  for j in range(w):
    if e[i][j]=='#':
      q.append((i,j))
      d[i][j]=0
dx=[-1,0,1,0]
dy=[0,-1,0,1]
ans=0
while q:
  x,y=q.popleft()
  for i in range(4):
    nx=x+dx[i]
    ny=y+dy[i]
    if 0<=nx<h and 0<=ny<w and e[nx][ny]=='.' and d[nx][ny]==INF:
      q.append((nx,ny))
      d[nx][ny]=d[x][y]+1
      ans=max(d[nx][ny],ans)
print(ans)