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())
mp = [list(input()) for _ in range(H)]

ds = [[-1,0],[1,0],[0,-1],[0,1]]
q = deque([])

cnt = 0

for i in range(H):
  for j in range(W):
    if mp[i][j] == '#':
      q.append((i,j,0))
      cnt += 1

if cnt == H*W:
  print(0)
  exit()

while q:
  t = q.popleft()
  for d in ds:
    ny = t[0]+d[0]
    nx = t[1]+d[1]
    if 0 <= ny < H and 0<= nx < W:
      if mp[ny][nx] == '.':
        mp[ny][nx] = '#'
        q.append((ny,nx,t[2]+1))
        cnt += 1
        if cnt == H*W:
          print(t[2]+1)
          exit()