Migrated from Lutece 1164 Points in triangle

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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).

Input

The first line of the input contains an integer $N(1\leq N\leq100000)$ - the number of points. The following N lines contain pairs of positive integer $X$ and $Y$ $(1\leq X,\ Y\leq100000)$ - the coordinates of the points.

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 $10^{-6}$.

Samples

2
1 1
1 3

6.0

Resources

xwind