Circle Regions

There are $N$ circles on the x-axis. Every center lies on the x-axis, and no two circles cross each other. They may touch.

Write a program that counts how many regions the circles cut the plane into.

A region is a set of points, and any two points in it can be joined by a continuous curve that never meets a circle. The unbounded part outside every circle counts as one region.

The first line contains the number of circles $N$ ($1 \le N \le 300\,000$).

Each of the next $N$ lines contains one circle as two integers $x_i$ and $r_i$. $x_i$ is the x coordinate of the center and $r_i$ is the radius. ($-10^9 \le x_i \le 10^9$, $1 \le r_i \le 10^9$)

No circle is given twice.

Print the number of regions the circles make.