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
import sys
input = sys.stdin.readline
h,w = map(int,input().split())
a = [list(input().rstrip()) for i in range(h)]
q = deque()
for i in range(h):
  for j in range(w):
    if a[i][j] == "#":
      a[i][j] = 0
      q.append((i,j,0))
    else:
      a[i][j] = -1
while q:
  s,t,cnt = q.popleft()
  for ns,nt in ((s+1,t),(s-1,t),(s,t+1),(s,t-1)):
    if 0<=ns<=h-1 and 0<=nt<=w-1 and a[ns][nt] == -1:
      q.append((ns,nt,cnt+1))
      a[ns][nt] = cnt+1
ans = 0
for i in range(h):
  for j in range(w):
    ans = max(ans,a[i][j])
print(ans)