Captain Latvia

Consider an infinitely long corridor drawn in the plane. Its floor (the bottom wall) is the segment from $(0, 0)$ to $(L, 0)$. Its two side walls are the rays that start at $(0, 0)$ and $(L, 0)$ and extend upward (in the direction of increasing $y$). Thus the corridor is the set of all points with $0 \le x \le L$ and $y \ge 0$.

There are $N$ enemies in the corridor. The $i$-th enemy stands at the point $(x_i, y_i)$, where $0 < x_i < L$ and $y_i > 0$.

The hero stands at the point $(X, 0)$ on the floor, where $0 < X < L$, and throws a shield without moving. The shield flies in a straight line to a point on one side wall, bounces to a point on the other side wall, and then flies straight back to the hero. Its trajectory is therefore a triangle whose three vertices are the hero's position $(X, 0)$, a point on the left wall, and a point on the right wall. Every enemy that lies on the boundary of this triangle (on any of its three edges) is knocked out.

The hero may aim freely: the two wall vertices may be placed anywhere on the walls, at any height $\ge 0$. Find the maximum number of enemies that can be knocked out with a single throw.

The first line contains two integers $L$ and $N$ — the length of the floor and the number of enemies. The second line contains one integer $X$ — the hero's $x$-coordinate. Each of the next $N$ lines contains two space-separated integers $x_i$ and $y_i$ — the coordinates of the $i$-th enemy.

Print one integer — the maximum number of enemies that can be knocked out with a single throw.

• $1 \le N \le 10^5$
• $2 \le L \le 10^5$
• $0 < X < L$
• $0 < x_i < L$
• $0 < y_i \le 10^5$
• All coordinates are integers.