XOR Shapes

Time limit1sMemory limit128 MB

Summary

Given up to 10 right isosceles triangles drawn with XOR-style color inversion, compute the total black area after all draws.

Level: Medium6 of 10
Topics: Geometry, Bit manipulation, Brute force
Solved: No attempts yet

Problem

At first the entire sketchbook is white. On it you draw N right isosceles triangles one after another.

Each triangle has its bottom-left vertex at (X, Y) and both legs of length R. In other words, the region covered by a single triangle is the set of all points (x, y) satisfying x >= X, y >= Y, and x + y <= X + Y + R.

Every time a triangle is drawn, all colors inside it are inverted: white areas become black and black areas become white.

After drawing all N triangles, find the area of the region that remains black.

Input

The first line contains the number of triangles N (1 <= N <= 10).

Each of the next N lines contains the information of one triangle: X, Y, R (1 <= X, Y, R <= 10^6). (X, Y) is the bottom-left vertex of the triangle and R is the length of each leg.

Output

Print the area of the black region with one digit after the decimal point.

Examples3

Example 1
Input
```
3
1 1 2
7 1 6
5 3 4
```
Expected output
```
24.0
```

Example 2

Input

Expected output

4900.5

Example 3
Input
```
4
5 5 99
5 5 99
5 5 99
5 5 99
```
Expected output
```
0.0
```