Description

You are given $n$ isosceles right triangles. Each triangle is generated from a point $(x_i, y_i)$ by extending two perpendicular legs of length $m_i$ upwards and to the right.

Find the total area covered by these triangles.

Input Format

The first line contains an integer $n$, the number of triangles.
The next $n$ lines each contain three integers $x_i, y_i, m_i$ describing one triangle.

Output Format

Output one real number, the answer.
Keep only one digit after the decimal point.

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

24.5

Hint

Sample Explanation

For sample $1$, the $5$ triangles are as follows:

Constraints

For $100\%$ of the testdata, $1 \le n \le 2000$, $-10^7 \le x_i, y_i \le 10^7$, $0 \le m \le 1000$.

Note

Translated from BalticOI 2002 Day1 C Triangles.

Translated by ChatGPT 5