Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Triangles 3000

time limit per test

5 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputYou are given a set *L* = {*l*_{1}, *l*_{2}, ..., *l*_{n}} of *n* pairwise non-parallel lines on the Euclidean plane. The *i*-th line is given by an equation in the form of *a*_{i}*x* + *b*_{i}*y* = *c*_{i}. *L* doesn't contain three lines coming through the same point.

A subset of three distinct lines is chosen equiprobably. Determine the expected value of the area of the triangle formed by the three lines.

Input

The first line of the input contains integer *n* (3 ≤ *n* ≤ 3000).

Each of the next lines contains three integers *a*_{i}, *b*_{i}, *c*_{i} ( - 100 ≤ *a*_{i}, *b*_{i} ≤ 100, *a*_{i}^{2} + *b*_{i}^{2} > 0, - 10 000 ≤ *c*_{i} ≤ 10 000) — the coefficients defining the *i*-th line.

It is guaranteed that no two lines are parallel. Besides, any two lines intersect at angle at least 10^{ - 4} radians.

If we assume that *I* is a set of points of pairwise intersection of the lines (i. e. ), then for any point it is true that the coordinates of *a* do not exceed 10^{6} by their absolute values. Also, for any two distinct points the distance between *a* and *b* is no less than 10^{ - 5}.

Output

Print a single real number equal to the sought expected value. Your answer will be checked with the absolute or relative error 10^{ - 4}.

Examples

Input

4

1 0 0

0 1 0

1 1 2

-1 1 -1

Output

1.25

Note

A sample from the statement is shown below. There are four triangles on the plane, their areas are 0.25, 0.5, 2, 2.25.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/20/2019 19:36:33 (f2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|