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 = [int(_) for _ in input().split()]
G = [list(input()) for _ in range(h)]

que = deque()
for i in range(h):
    for j in range(w):
        if G[i][j] == '#':
            que.append((i, j, 0))
cnt = 0
while que:
    i, j, c = que.popleft()

    for ni, nj in [(1, 0), (0, 1), (-1, 0), (0, -1)]:
        if i + ni < 0 or j + nj < 0: continue
        if i + ni >= h or j + nj >= w: continue

        if G[i + ni][j + nj] == '.':
            G[i + ni][j + nj] = '#'
            que.append((i + ni, j + nj, c + 1))
            cnt = max(cnt, c + 1)
print(cnt)