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)]
sharps = []
for h, line in enumerate(A):
    sharps += [[h, w, 0] for w, p in enumerate(line) if p == '#']

q = deque(sharps)
while q:
    i, j, score = q.popleft()
    for mi, mj in [[-1, 0], [1, 0], [0, -1], [0, 1]]:
        ni = i + mi
        nj = j + mj
        if ni < 0 or H <= ni or nj < 0 or W <= nj or A[ni][nj] == '#':
            continue
        A[ni][nj] = '#'
        q.append([ni, nj, score+1])
print(score)