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())
  ans,q=0,deque()
  visited=[[0 if j=="#" else -1 for j in input()] for _ in range(h)]
  q=deque([(i,j) for i in range(h) for j in range(w) if visited[i][j]==0])
  while q:
    x,y=q.popleft()
    for i,j in ((0,1),(1,0),(-1,0),(0,-1)):
      newx,newy=x+i,y+j
      if 0<=newx<h and 0<=newy<w:
        if visited[newx][newy]==-1:
          visited[newx][newy]=visited[x][y]+1
          q.append((newx,newy))
          ans=max(ans,visited[newx][newy])
  return print(ans)
if __name__=='__main__':
  main()