The Little Prince has $n$ roses in his garden, which can be described as a 2-dimensional plane. The $i^{th}$ of the roses has the coordinate ($x_{i}$, $y_{i}$).It's raining recently, to protect the roses, the Little Prince plans to arrange two umbrellas(overlapping is allowed) to cover all the roses. The area covered by one umbrella is a circle, the Little Prince can determine the sizes of two umbrellas(not necessarily the same) and he can also choose any positions to place these two umbrellas. Meanwhile, in order not to block too much sunshine after the rain, he wants to minimize the covered areas.
Help the Little Prince to calculate the minimized covered areas that satisfy the condition.
输入格式
The first line contains an integer number T, the number of test cases.
For each test case : The first line contains an integer $n$($1 \leq n \leq 50$), the number of roses.
The following $n$ lines, each contains two integers $x_{i}$, $y_{i}$($|x_{i}|, |y_{i}| \leq 10^{4}$), the coordinate of the $i^{th}$ rose.
It's guaranteed that no coordinates coincide.
输出格式
For each test case print the minimum covered areas, round to two decimal places.
