H. The Easiest Problem
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given an array $$$a$$$ of length $$$n$$$ containing positive integers. You are allowed to rearrange the elements of $$$a$$$ in any order. Find the minimum possible value of the following expression: $$$$$$\sum_{i=1}^{n-1} \frac{a_{i}^2 + a_{i+1}^2}{a_i a_{i+1}}$$$$$$

Input

Each test case contains multiple test cases. The first line of each test contains an integer $$$t$$$ ($$$1 \le t \le 1000$$$) — the number of test cases.

The first line of each test case contains an integer $$$n$$$ ($$$2 \le n \le 10^5$$$) — the length of $$$a$$$.

The second line contains $$$n$$$ integers $$$a_1,a_2,\ldots,a_n$$$ ($$$1 \le a_i \le 10^6$$$) — the elements of $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each test case, output a real number: the minimum possible value of the given expression.

Your answer is considered correct if its absolute or relative error does not exceed $$$10^{-6}$$$.

Formally, let your answer be $$$a$$$, and the jury's answer be $$$b$$$. Your answer is accepted if and only if $$$\frac{|a - b|}{\max{(1, |b|)}} \le 10^{-6}$$$.

Example
Input
2
2
1 2
3
11451 19198 114514
Output
2.5000000000
8.4055429827