Osu!

Time Limit: 2000/1000 MS (Java/Others)

Memory Limit: 65536/65536 K (Java/Others)

Description

Osu! is a famous music game that attracts a lot of people. In osu!, there is a performance scoring system, which evaluates your performance. Each song you have played will have a score. And the system will sort all you scores in descending order. After that, the i-th song scored ai will add 0.95^(i-1)*ai to your total score.

Now you are given the task to write a calculator for this system.

Input

The first line contains an integer T, denoting the number of the test cases.

For each test case, the first line contains an integer n, denoting the number of songs you have played. The second line contains n integers a1, a2, ..., an separated by a single space, denoting the score of each song.

T<=20, n<=50, 1<=ai<=500.

Output

For each test case, output one line for the answer.

Your answers will be considered correct if its absolute error is smaller than 1e-5.

Sample Input

1 2 530 478

Sample Output

984.1000000000

Hint

hujie

Source

2014 ACM/ICPC Asia Regional Anshan Online

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