Laser Game

You are playing a game against several classmates. Each opponent carries a device that fires one laser beam. The beam starts at that opponent's own position, goes in the direction the opponent picks, and continues forever. Once every beam is aimed and fixed, your turn starts. You stand at a point $s$ and have to run to a point $t$, and you want the path you run to cross as few beams as possible.

The field is a two dimensional plane. The $n$ opponents $o_1, o_2, \dots, o_n$ stand at $n$ distinct points $p_1, p_2, \dots, p_n$, and opponent $o_i$ fires a one way beam from $p_i$. Some beams can be parallel. The points $s$ and $t$ differ from every $p_i$.

Your path is any curve from $s$ to $t$. It crosses a beam when it passes from one side of that beam to the other side. Beam $i$ covers $p_i$ and the points after it along the chosen direction, so a path that goes around $p_i$ on the side the beam does not cover never crosses beam $i$.

Find the smallest number of beams a path from $s$ to $t$ has to cross.

The input holds several test cases. The first line of a test case has $n$, the number of laser beams ($1 \le n \le 200$). Each of the next $n$ lines has four space separated integers. The first two are the $x$ and $y$ coordinates of an opponent, and the last two are the $x$ and $y$ coordinates of a point that lies on that opponent's beam. The last line of a test case has four integers, the $x$ and $y$ coordinates of $s$ followed by the $x$ and $y$ coordinates of $t$.

No three of the points given in a test case lie on one line, and every coordinate has absolute value at most $10^8$. A line holding a single $0$ ends the input, and you do not process it.

For each test case, print one line with the minimum number of beams the path has to cross.