CF933C.A Colourful Prospect

普及/提高-

通过率:0%

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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.

输入格式

The first line of input contains one integer nn ( 1<=n<=31<=n<=3 ), denoting the number of circles.

The following nn lines each contains three space-separated integers xx , yy and rr ( 10<=x,y<=10-10<=x,y<=10 , 1<=r<=101<=r<=10 ), describing a circle whose center is (x,y)(x,y) and the radius is rr . No two circles have the same xx , yy and rr 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#1

    3
    0 0 1
    2 0 1
    4 0 1
    

    输出#1

    4
    
  • 输入#2

    3
    0 0 2
    3 0 2
    6 0 2
    

    输出#2

    6
    
  • 输入#3

    3
    0 0 2
    2 0 2
    1 1 2
    

    输出#3

    8
    

说明/提示

For the first example,

For the second example,

For the third example,

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