G. Gravity
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Joseph's task today is to collect asteroids to build new space stations.

The universe where Joseph lives is a 2D plane. The asteroids are located at $$$n$$$ points denoted by $$$P_1,P_2, \cdots, P_n$$$. The mass of them can be considered equal. On the first day, he will collect some asteroids and bring them to their center of gravity. On the second day, he will do the same with the remaining asteroids. He will then build two new stations at the two gravity centers, denoted by points $$$A$$$ and $$$B$$$.

Noted that building a space station requires at least one asteroid, so Joseph must collect at least one asteroid each day.

There is one original space station on point $$$O(0,0)$$$. The coverage area of the three space stations is defined by the triangle $$$ABO$$$. Joseph wants to maximize this area as much as possible.

Please help him find an optimal collecting plan to get the maximum coverage area.

Input

The first line contains one integer $$$n~(2 \leq n \leq 10^5)$$$, indicating the number of asteroids.

In the next $$$n$$$ lines, the $$$i$$$-th line contains two integers $$$x_i,y_i~(-10^4 \leq x_i, y_i \leq 10^4)$$$, denoting that there is one asteroid at point $$$P_i = (x_i,y_i)$$$

Output

In one line print the maximum coverage area. Your answer is considered correct if the relative or absolute error is less than or equal to $$$10^{-9}$$$.

Examples
Input
6
2 1
1 2
4 1
1 4
5 3
2 4
Output
5.0000000000
Input
6
2 1
1 2
4 1
4 3
5 3
2 4
Output
4.4000000000
Note

The figure below describes the first sample. One optimal collecting plan is to collect the $$$1,3,5$$$-th asteroids on the first day and collect the $$$2,4,6$$$-th asteroid on the second day. The gravity centers are $$$A$$$ and $$$B$$$ respectively. The area of the triangle $$$ABO$$$ is $$$5.0$$$, which is maximized.

The figure below describes the second sample.