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

dyx = [(0, 1), (0, -1), (1, 0), (-1, 0)]
H, W = map(int, input().split())
edge = ['#']*(W+2)
field = [edge]
q = deque()

for i in range(H):
    field.append(['#'] + list(input()) + ['#'])
    for j in range(W):
        if field[i+1][j+1] == '#':
            q.append((i+1, j+1, 0))
field.append(edge)
res = 0

while q:
    y, x, lv = q.popleft()
    res = max(lv, res)

    for dy, dx in dyx:
        if field[y+dy][x+dx] == '.':
            field[y+dy][x+dx] = '#'
            q.append((y+dy, x+dx, lv+1))

print(res)