Description

Given $n$ isosceles right triangles on the plane. Each triangle is described by three integers $x, y, m$. The three vertices of a triangle are $(x, y)$, $(x + m, y)$, $(x, y + m)$.

Your task is to compute the total area covered by these triangles.

Input Format

The first line contains an integer $n$.

Each of the next $n$ lines describes a triangle with three integers $x_i, y_i, m_i$.

Output Format

Output a single real number with one digit after the decimal point, representing the total area.

5
-5 -3 6
-1 -2 3
0 0 2
-2 2 1
-4 -1 2

24.5

Hint

Sample explanation:

Constraints: $1 \le n \le 2000$, $1 \le i \le n$, $-10^7 \le x_i, y_i \le 10^7$, $1 \leq m_i \le 1000$.

Translated by ChatGPT 5