Flowey's Love

Flowey: Howdy! I'm Flowey, Flowey the flower! You're new to the underground, aren't you? Golly, you must be so confused. Someone ought to teach you how things work around here! I guess little old me will have to do. Ready? Here we go!

Flowey: See that heart? That is your SOUL, the very culmination of your being! Your SOUL is weak, but it can grow strong if you gain a lot of LV. What does LV stand for? Why, LOVE, of course! You want some LOVE, don't you?

Flowey: Don't worry, I'll share some with you! Down here, we share little white friendliness pellets. Move around! Get as much friendliness as you can!

Flowey scattered $N$ friendliness pellets. Every pellet moves along a straight line at speed $1$. Your soul is at the origin $(0, 0)$ at time $0$ and moves in any direction at a speed of at most $1$. The speed can be any value, such as $1$ or $0.314$, and the soul may also stay where it is. The soul cannot leave the rectangle given by $-XM \le x \le XM$ and $-YM \le y \le YM$.

A pellet vanishes the moment it touches your soul, and that pellet counts as collected, so you collect at most $N$ of them. The soul and the pellets are points. Given the pellets, write a program that finds the largest number of friendliness pellets you can collect.

The first line contains the number of friendliness pellets $N$ and two integers $XM$, $YM$ that describe the region the soul can move in ($1 \le N \le 18$, $1 \le XM, YM \le 500$).

Each of the next $N$ lines contains four integers $X_{st}$, $Y_{st}$, $X_{to}$, $Y_{to}$ describing one pellet ($-1000 \le X_{st}, Y_{st}, X_{to}, Y_{to} \le 1000$). The pellet is at $(X_{st}, Y_{st})$ at time $0$ and moves along a straight line toward $(X_{to}, Y_{to})$, and it keeps moving in the same direction after it passes $(X_{to}, Y_{to})$. $(X_{st}, Y_{st})$ and $(X_{to}, Y_{to})$ are different points, and $(X_{st}, Y_{st})$ is never the origin.

Print the largest number of friendliness pellets you can collect.