Given ~N~ triangles, find the area of the union of these triangles.

Constraints

~1 \le N \le 100~

~0 \le x_1, y_1, x_2, y_2, x_3, y_3 \le 10^4~

Input Specification

The first line contains an integer, ~N~.

Each of the next ~N~ lines contains six space-separated integers, ~x_1, y_1, x_2, y_2, x_3, y_3~, representing the three vertices of the triangle.

Output Specification

Output the union area of the triangles.

Your answer will be accepted if the absolute error is within ~10^{-3}~.

Sample Input

2
0 0 1 1 0 1
0 0 1 0 1 1

Sample Output

1.000