Background

Link to the enhanced version.

Problem Description

Given $n$ triangles, compute the area of their union.

Input Format

The first line contains $n$ ($n \leq 100$), the number of triangles. Each of the next $n$ lines contains $6$ real numbers $x_1$, $y_1$, $x_2$, $y_2$, $x_3$, $y_3$, representing the coordinates of the triangle's vertices. All coordinates are real numbers not exceeding $10^6$, and the input numbers are given with $1$ decimal place.

Output Format

Output the union area $u$, to two decimal places.

2
0.0 0.0 2.0 0.0 1.0 1.0
1.0 0.0 3.0 0.0 2.0 1.0

1.75

Hint

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