Janine recently went to her local game store and bought
“Hole in One”, a new minigolf game for her computer. As
indicated by the name, the objective of the game is to shoot a
ball into a hole using just one shot. The game also borrows
elements from brick breaker style games: in the playing field,
several walls are placed that will be destroyed upon being hit
by the ball. The score of a successful shot depends on the
number of destroyed walls, so Janine wonders: what is the
maximum number of walls that can be hit while performing a
“Hole in One”?
For the purposes of this problem you can think of the
playing field as a cartesian plane with the initial position of
the ball at the origin. The walls are nonintersecting
axisparallel line segments in this plane (i.e., parallel to
either the $x$ axis or the
$y$ axis). The diameter of
the ball is negligible so it is represented as a single
point.
Whenever the ball hits a wall, two things happen:

The direction of the ball changes in the usual way: the
angle of incidence equals the angle of reflection.

The wall that the ball touched is destroyed. Following
common video game logic, no rubble of the wall remains; it
will be as though it vanished.
The behaviour of the ball is also affected by the power of
the shot. In particular, an optimal shot may need to first roll
over the hole, then hit some more walls, and only later drop
into the hole.
Input
The input consists of:

one line with one integer $n$ ($0 \le n \le 8$), the number of
walls;

one line with two integers $x$ and $y$, the coordinates of the
hole;

$n$ lines each with
four integers $x_1$,
$y_1$, $x_2$, and $y_2$ (either $x_1 = x_2$, or $y_1 = y_2$, but not both),
representing a wall with end points $(x_1, y_1)$ and $(x_2, y_2)$.
The hole is not at the origin and not on a wall. The walls
do not touch or intersect each other. No wall lies completely
on the $x$ axis or the
$y$ axis. All coordinates
in the input are integers with absolute value at most
$1\, 000$.
Output
If there is no way to shoot the ball such that it reaches
the hole, print “impossible”.
Otherwise, print the maximum number of walls that can be
destroyed in a single “Hole in One” shot.
Sample Input 1 
Sample Output 1 
3
4 2
1 1 1 2
2 1 2 2
3 1 3 2

2

Sample Input 2 
Sample Output 2 
1
2 0
1 1 1 1

impossible

Sample Input 3 
Sample Output 3 
2
2 4
2 4 2 2
0 6 2 6

2
