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

def main():
  h,w=map(int,input().split())
  mp=[input() for _ in range(h)]
  dist=[-1]*(h*w)
  q=deque()
  
  for i in range(h):
    for j in range(w):
      if mp[i][j]=="#":
        q.append(i*w+j)
        dist[i*w+j]=0
      else:
        dist[i*w+j]=-1
  #print(q)
 
  while q:
    c=q.popleft()
    #print(c,q)
    x=c//w
    y=c%w
    for i,j in ((1,0),(0,1),(-1,0),(0,-1)):
      xx,yy=x+i,y+j
      if (0<=xx<h and 0<=yy<w and dist[xx*w+yy]==-1):
        dist[xx*w+yy]=dist[x*w+y]+1
        q.append(xx*w+yy)
      
  print(max(dist))
  return

main()