Migrated from Lutece 375 Easy Problem

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Description

There are some positive integer numbers, and you want to divide them into two nonempty sets (every integer should be in and only in one set) and get a value descripted below:

Assume that set $A$ has $n_1$ numbers $A_1, A_2, \cdots ,A_{n_1}$; set $B$ has $n_2$ numbers $B_1, B_2, \cdots ,B_{n_2}$. Let

$v_1=\sum_{i=1}^{n_1}\frac{A_i}{n_1}$ $v_2=\sum_{i=1}^{n_2}\frac{B_i}{n_2}$

Then

$ans=\sum_{i=1}^{n_1}(A_i-v_2)^2+\sum_{i=1}^{n_2}(B_i-v_1)^2$

We want to know the largest ans.

Input

The first line of the input is an integer $T$ ($T\leq 20$), which stands for the number of test cases you need to solve.

Every test case begins with an integer $N$ ($2\leq N\leq 1000$), then followed by $N$ positive integers on the next line, these numbers will not exceed $1000$.

Output

For every test case, you should output Case #k: first, where $k$ indicates the case number and starts at $1$. Then output the answer rounded to six digits after the decimal point. See sample for more details.

Samples

2
3
1 1 1
3
1 2 3

Case #1: 0.000000
Case #2: 7.250000

Resources

The 9th UESTC Programming Contest Final