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:
def main():
  from collections import deque
  s,*c=open(0)
  h,w=map(int,s.split())
  f=[-1]*h*w
  q=deque()
  for i,c in enumerate(''.join(t[:w]for t in c)):
    if c=='#':
      q.append(i)
      f[i]=0
  while q:
    i=q.popleft()
    v=f[i]+1
    j,k,l,m,u=i+w,i-w,i+1,i-1,i%w
    if h*w>j and f[j]<0:
      q.append(j)
      f[j]=v
    if k>=0 and f[k]<0:
      q.append(k)
      f[k]=v
    if w>u+1and f[l]<0:
      q.append(l)
      f[l]=v
    if u and f[m]<0:
      q.append(m)
      f[m]=v
  print(v-1)
if __name__=='__main__':
  main()