Convex Quadrilateral

You are given $n$ points on the plane, $(x_1, y_1)$, $(x_2, y_2)$, ..., $(x_n, y_n)$. Write a program that finds the smallest area of a quadrilateral $Q$ satisfying all of the following conditions.

1. Each of the four sides of $Q$ passes through at least two of the given points.
2. $Q$ is convex.
3. Every given point lies inside $Q$ or on the boundary of $Q$.
4. Among all quadrilaterals that satisfy conditions 1 to 3, $Q$ has the smallest area.

Several quadrilaterals can reach that smallest area, but the value of the smallest area is unique. Report that value.

The first line contains the number of data sets $T$. The $T$ data sets follow.

The first line of each data set contains the number of points $n$. Each of the next $n$ lines contains the $x$ coordinate and the $y$ coordinate of the $i$th point, separated by a space.

Constraints

• $1 \le T \le 60$
• $1 \le n \le 300$
• $|x_i|, |y_i| \le 1000.00$
• Coordinates are given with at most two digits after the decimal point.
• The points are distinct.

Print one line for each data set. If a quadrilateral satisfying the conditions exists, print its minimum area rounded to exactly six digits after the decimal point. Otherwise print none.

Every answer stays far enough from a rounding boundary, so the sixth digit is determined.