P6875 [COCI 2013/2014 #6] KRUŽNICE

There are $N$ pairwise non-overlapping circles centered on the $x$ axis, but their circumferences may touch. How many regions do these circles divide the plane into?

The first line contains an integer $N$, the number of circles. Each of the next $N$ lines contains two integers $x_i$ and $r_i$, where $x_i$ is the $x$ coordinate of the center of the $i$-th circle, and $r_i$ is its radius. All circles in the input are guaranteed to be unique.

Output the number of regions into which these circles divide the plane.

#### Sample Explanation #### Explanation for Sample 3 This sample corresponds to the figure below:  #### Constraints - For $40\%$ of the testdata, $1 \le N \le 5\times 10^3$. - For $100\%$ of the testdata, $1 \le N \le 3\times 10^5$, $-10^9 \leq x_i \leq 10^9$, $1 \leq r_i \leq 10^9$. #### Notes **Translated from [COCI2013-2014](https://hsin.hr/coci/archive/2013_2014/) [CONTEST #6](https://hsin.hr/coci/archive/2013_2014/contest6_tasks.pdf) _T4 KRUŽNICE._** Translated by ChatGPT 5