Description

In the two-dimensional plane, you are given $N$ isosceles right triangles (each triangle’s two legs are parallel to the coordinate axes, and the hypotenuse goes from top-left to bottom-right). We use three non-negative integers $(x, y, d)$ to describe such a triangle. The coordinates of its three vertices are $(x, y)$, $(x+d, y)$, and $(x, y+d)$. Compute the total area covered by these $N$ triangles. For example, in the figure below, there are $3$ triangles, and the total covered area is $11.0$.

Input Format

The first line contains a positive integer $N$, indicating the number of triangles. Each of the next $N$ lines contains three space-separated non-negative integers $x, y, d$, describing a triangle whose vertices are $(x, y)$, $(x+d, y)$, and $(x, y+d)$, where $x, y, d$ satisfy $0 \le x, y, d \le 10^6$.

Output Format

Output a single line containing a real number $S$, the total area covered by all triangles, with exactly one decimal place. It is guaranteed that $S \le 2^{31}$.

3
1 1 4
2 0 2
3 2 2

11.0

Hint

For $50\%$ of the testdata, $1 \le N \le 500$. For $100\%$ of the testdata, $1 \le N \le 10^4$.

Translated by ChatGPT 5