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)]
blacks = deque([])
for h in range(H):
  for w in range(W):
    if A[h][w] == "#":
      blacks.append((h, w))
count = 0
while len(blacks) > 0:
  newblacks = deque([])
  while len(blacks) > 0:
    b = blacks.popleft()
    for y, x in zip((b[0]-1, b[0], b[0], b[0]+1), (b[1], b[1]-1, b[1]+1, b[1])):
      if y < 0 or y >= H or x < 0 or x >= W:
        continue
      if A[y][x] == ".":
        newblacks.append((y, x))
      A[y][x] = "#"
  blacks = newblacks
  count += 1
print(count-1)