A Colourful Prospect

题意翻译

给定至多三个圆，求这些圆将平面划分为了几个区域

题目描述

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.

输入输出格式

输入格式

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.

输出格式

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

输入输出样例

输入样例 #1

3
0 0 1
2 0 1
4 0 1

输出样例 #1

4

输入样例 #2

3
0 0 2
3 0 2
6 0 2

输出样例 #2

6

输入样例 #3

3
0 0 2
2 0 2
1 1 2

输出样例 #3

8

说明

For the first example, For the second example, For the third example,