A11625 | A Colourful Prospect

Firecrackers scare Nian the monster, but they're wayyyyy too noisy! Maybe fireworks make a nice complement.

Little Tommy is watching a firework show. As circular shapes spread across the sky, a splendid view unfolds on the night of Lunar New Year's eve.

A wonder strikes Tommy. How many regions are formed by the circles on the sky? We consider the sky as a flat plane. A region is a connected part of the plane with positive area, whose bound consists of parts of bounds of the circles and is a curve or several curves without self-intersections, and that does not contain any curve other than its boundaries. Note that exactly one of the regions extends infinitely.

The first line of input contains one integer $n$ ( $1<=n<=3$ ), denoting the number of circles.

The following $n$ lines each contains three space-separated integers $x$ , $y$ and $r$ ( $-10<=x,y<=10$ , $1<=r<=10$ ), describing a circle whose center is $(x,y)$ and the radius is $r$ . No two circles have the same $x$ , $y$ and $r$ at the same time.

Print a single integer — the number of regions on the plane.