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())
que = deque()
A = [input() for i in range(H)]

dist = [[-1]*W for i in range(H)]
dd = ((-1, 0), (0, -1), (1, 0), (0, 1))
for i in range(H):
  for j in range(W):
    if A[i][j] == '#':
      dist[i][j] = 0
      que.append((i, j))

d = 0
while que:
  y, x = que.popleft()
  d = dist[y][x]
  for dx, dy in dd:
    nx = x + dx; ny = y + dy
    if not 0 <= nx < W or not 0 <= ny < H or dist[ny][nx] != -1:
      continue
    dist[ny][nx] = d + 1
    que.append((ny, nx))

print(d)