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).

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.

Examples

Input

2
1 1
1 3


Output

6.0


Input

2
2 1
1 2


Output

4.5

Source: codeforces | Difficulty: HARD
Tags: Geometry


Solutions: