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:
import itertools
from collections import deque

H, W = [int(_) for _ in input().split()]
A = [list(input()) for _ in range(H)]
Q = deque([])
for i, j in itertools.product(range(H), range(W)):
    if A[i][j] == '#':
        Q += [[i, j, 0]]
while Q:
    i, j, d = Q.popleft()
    for ni, nj in [[i - 1, j], [i + 1, j], [i, j - 1], [i, j + 1]]:
        if 0 <= ni < H and 0 <= nj < W and A[ni][nj] == '.':
            A[ni][nj] = '#'
            Q += [[ni, nj, d + 1]]
print(d)