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 = [input() for _ in range(h)]
dist = [[-1]*w for _ in range(h)]
di = [1, 0, -1, 0]
dj = [0, 1, 0, -1]
que = deque()
for i in range(h):
  for j in range(w):
    if A[i][j] == "#":
      que.append((i, j))
      dist[i][j] = 0
ans = 0
while que:
  y, x = que.popleft()
  for dy, dx in zip(di, dj):
    ny, nx = y+dy, x+dx
    if ny < 0 or ny >= h or nx < 0 or nx >= w:
      continue
    if dist[ny][nx] != -1:
      continue
    dist[ny][nx] = dist[y][x] + 1
    ans = max(ans, dist[ny][nx])
    que.append((ny, nx))
print(ans)