Clique on a Line

The clique problem is a well known NP-complete problem. The definition is short. Take an undirected graph $G$ and choose a subset $C$ of its vertices. If every pair of vertices in $C$ is joined by an edge, that is, if $C$ induces a complete graph, then $C$ is a clique. The clique problem asks for the size of the largest clique.

There are $n$ points on the $x$ axis, all at different coordinates. Point $i$ has coordinate $x_i$ and weight $w_i$. Build a graph on these points: two different points $i$ and $j$ are joined by an edge if and only if $w_i + w_j \le |x_i - x_j|$.

Find the size of the largest clique in that graph.

The first line contains the number of points $n$ ($1 \le n \le 200000$).

Each of the next $n$ lines contains two integers $x_i$ and $w_i$ ($1 \le x_i, w_i \le 10^9$).

All $x_i$ are different.

Print the size of the largest clique on the first line.