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 sys
input = sys.stdin.readline
h,w=map(int,input().split())
A=[[False]*(w+2) for _ in range(h+2)]
chk,chk2=[],[]
for i in range(h):
  s=input()
  for j in range(w):
    A[i+1][j+1]=(s[j]==".")
    if s[j]=="#":
      chk.append((i+1,j+1))
ans=0
d=((1,0),(0,1),(-1,0),(0,-1))
while chk:
  for cx,cy in chk:
    for dx, dy in d:
      if A[cx+dx][cy+dy]==True:
        chk2.append((cx+dx,cy+dy))
        A[cx+dx][cy+dy]=False
  if chk2:
    ans+=1
  chk=chk2
  chk2=[]
print(ans)