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VK Cup 2015 - Wild Card Round 1:

- Picat 0.9

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H. Points in triangle

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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