\(6^{th}\) round, March \(8^{th}\), 2014

Enjoying a casual afternoon walk in the coordinate system, little Luka has encountered N unique
circles with its centers lying on the \(x-ax\)is. The circles do not intersect, but they can touch (from the
inside and the outside). Fascinated with circles, Luka wondered how many regions the circles divide
the plane into. Of course, you are going to help him answer this question.
A region is a set of points such that each two points can be connected with a continuous curve,
without cutting through any of the circles.

One of the possible layouts of circles

In test cases worth 40% of total points, the N will not exceed 5 000.

The first line of input contains the integer N (\(1 \le N \le 300\,000\)), the number of circles.
Each of the following N lines contains two integers x_{i} and r_{i} (-\(10^{9} \le x_{i} \le 10^{9}\), \(1 \le r_{i} \le 10^{9}\)), the number
x_{i} representing the x coordinate of the i^{th} circle and the number r_{i} representing the radius of the i^{th}
circle.
All the circles in the input will be unique.

The first and only line of output must contain the required number from the task.

생성자가 기록되지 않았습니다.

출처 COCI 2013/2014 Contest 6