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:
#!/usr/bin/python3
# -*- coding:utf-8 -*-

from queue import deque

def main():
  h, w = map(int, input().split())
  grids = [False] * (w * h)
  dq = deque()
  for i in range(h):
    for j, c in enumerate(list(input().strip())):
      if c == '#':
        grids[i*w + j] = True
        dq.append((0, i, j))
  
  while dq:
    cnt, i, j = dq.popleft()
    for dx, dy in zip([-1, 0, 1, 0], [0, -1, 0, 1]):
      if 0 <= i+dx < h and 0 <= j+dy < w and not grids[(i+dx)*w + (j+dy)]:
        grids[(i+dx)*w + (j+dy)] = True
        dq.append((cnt+1, i+dx, j+dy))
  print(cnt)
  
if __name__=='__main__':
  main()