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:
import copy
from collections import deque
H,W=map(int, input().split())
A=[[-1]*W for _ in range(H)]
d=deque()
for h in range(H):
  s=input()
  for w in range(W):
    if s[w]=='.':
      pass
    else:
      A[h][w]=0
      d.append((h,w))

DIF=[(1,0),(0,1),(-1,0),(0,-1)]
while d:
  point=d.popleft()
  for dif in DIF:
    x=point[0]+dif[0]
    y=point[1]+dif[1]
    if 0<=x<H and 0<=y<W and A[x][y]==-1:
      d.append((x,y))
      A[x][y]=A[point[0]][point[1]]+1
ans=0    
for h in range(H):
  Amax=max(A[h])
  ans=max(ans,Amax)
#print(A)
print(ans)