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())
field=[]
spos=deque([])
for i in range(H):
  s=list(input())
  for j in range(W):
    if s[j]=="#":
      spos.append((j,i))
  field.append(s)
  

dx=[1,0,-1,0]
dy=[0,1,0,-1]

ans=-1
while spos:
  for _ in range(len(spos)):
    x,y=spos.popleft()
    for i in range(4):
      nx=x+dx[i]
      ny=y+dy[i]
      if nx<0 or nx>=W or ny<0 or ny>=H:
        pass
      elif field[ny][nx]==".":
        field[ny][nx]="#"
        spos.append((nx,ny))
  ans+=1

print(ans)