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:
h, w = map(int, input().split())

a = ''.join(input() + '#' for _ in range(h))
a = a.replace('.', '1').replace('#', '0')

bits = int(a, 2)

w1 = w + 1
h1 = h + 1
bits <<= w1

frame = (1 << w1) - 1
frame |= frame << h1 * w1
frame |= sum(1 << b for b in range(w1, h1 * w1, w1))

count = 0
while bits:
    count += 1
    mask = bits | frame
    #       up             down           left          right
    bits &= (mask << w1) & (mask >> w1) & (mask << 1) & (mask >> 1)
print(count)