Points in triangle
Description
You are given a set of points on a plane with positive integer coordinates. Find a triangle of minimum area with vertices in points (0, 0), (A, 0) and (0, B) (A and B are unknown positive integers) that contains all the given points inside it (points on the edges count towards being inside).
The first line of the input contains an integer N (1 ≤ N ≤ 100) — the number of points. The following N lines contain pairs of numbers X and Y (1 ≤ X, Y ≤ 100) - the coordinates of the points. All points are distinct.
Output one floating-point number — the minimal area of the triangle. The answer is considered to be correct if its absolute or relative error does not exceed 10 - 4.
Input
The first line of the input contains an integer N (1 ≤ N ≤ 100) — the number of points. The following N lines contain pairs of numbers X and Y (1 ≤ X, Y ≤ 100) - the coordinates of the points. All points are distinct.
Output
Output one floating-point number — the minimal area of the triangle. The answer is considered to be correct if its absolute or relative error does not exceed 10 - 4.
Samples
2
1 1
1 3
6.0
2
2 1
1 2
4.5