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
h,w = map(int, input().split())
a = [list(input()) for _ in range(h)]
d = [(0,1),(1,0),(0,-1),(-1,0)]
q = deque()
cnt = h*w
t = 0
for i in range(h):
  for j in range(w):
    if a[i][j] == "#":
      q.append((i,j))
      a[i][j] = 0
      cnt -= 1
while cnt:
  y,x = q.popleft()
  for dx,dy in d:
    if 0 <= x+dx < w and 0 <= y+dy < h and a[y+dy][x+dx] == ".":
      a[y+dy][x+dx] = a[y][x] + 1
      cnt -= 1
      q.append((y+dy,x+dx)) 
for i in range(h):
  m = max(a[i])
  t = max(t,m)
print(t)