Problem Description

In a coordinate system, there are several isosceles right triangles, each with the right angle vertex at the bottom left and the two sides parallel to the coordinate axes. The area covered by an odd number of triangles is gray, and the area covered by an even number of triangles is white, as shown in the figure below.

Given the coordinates of the vertices and the side lengths of $N$ isosceles right triangles, calculate the area of the gray part.

Mirko and Slavko have built their own LED display. The display is initially white. During each of the $N$ parts of the testing phase, Mirko attached three electrodes to the display in such a way that they formed a right isosceles triangle. He noticed that, after attaching the electrodes, all pixels in the enclosing triangle are inverted (white pixels become black, and black pixels become white).

Watching Mirko play with the electrodes, Slavko observed interesting shapes emerging on the screen. Mathematically inclined as he is, the first thing that crossed his mind was how to calculate the total area covered by black pixels. Help him by writing a program to do just that!

Input Format

The first line of input contains an integer $N(1 \leq N \leq 10)$, the number of triangles formed by Mirko's fiddling with electrodes. Each of the following $N$ lines contains three integers $X, Y$, and $R (1 \leq X, Y, R \leq 10^6)$, describing a triangle. $(X, Y)$ are the coordinates of the lower left corner of the triangle, while $R$ represents the length of the two sides of the triangle.

Output Format

The first and only line of output should contain the area covered by black pixels, rounded to one decimal place.

Sample Input and Output

Sample Input #1

3
1 1 2
7 1 6
5 3 4

Sample Output #1

24.0

Sample Input #2

5
5 5 99
5 5 99
5 5 99
5 5 99
5 5 99

Sample Output #2

4900.5

Sample Input #3

4
5 5 99
5 5 99
5 5 99
5 5 99

Sample Output #3

0.0

Notes

$1 \leq N \leq 10, 1 \leq X, Y, R \leq 10^6$

见题面 Input 部分

见题面 Output 部分