Hipercampo

You are given two anchors, the points $A = (X_A, 0)$ and $B = (X_B, 0)$ with $0 < X_A < X_B$, which form a horizontal segment. You are also given a set $P$ of $N$ points $(X, Y)$ with $X > 0$ and $Y > 0$. The leftmost picture below is one possible input.

To connect a point $v \in P$ you draw both segments $(v, A)$ and $(v, B)$. You want to connect several points, but the drawn segments must meet only at the anchors. Points 1 and 4 in the middle picture cannot both be connected, because their segments would cross somewhere other than an anchor. The rightmost picture shows that points 8, 5 and 3 can be connected together, with the segments meeting only at the anchors.

Compute the largest number of points that can be connected so that the segments meet only at the anchors.

The first line contains three integers $N$ ($1 \le N \le 100$), $X_A$ and $X_B$ ($0 < X_A < X_B \le 10^4$). $N$ is the number of points in the set $P$, and $X_A$ and $X_B$ are the $x$ coordinates of the anchors $A$ and $B$. Each of the next $N$ lines contains two integers $X_i$ and $Y_i$ ($0 < X_i, Y_i \le 10^4$), the coordinates of the $i$ th point, for $1 \le i \le N$. No two points share a position, and there are no two distinct points $u$ and $v$ such that $\{A, u, v\}$ is collinear or $\{B, u, v\}$ is collinear.

Print one line with one integer, the largest number of points of $P$ that can be connected so that the segments meet only at the anchors.