A Colourful Prospect
Description
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.
Input
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.
Output
Print a single integer — the number of regions on the plane.
Samples
3
0 0 1
2 0 1
4 0 1
4
3
0 0 2
3 0 2
6 0 2
6
3
0 0 2
2 0 2
1 1 2
8
Note
For the first example,
For the second example,
For the third example,
