#1590 AverageAverage

125  1 s   128 MB  

Description

Given a int[] numList, for each non-empty subset of numList, compute the average of its elements, then print the average of those averages.

Input

The first line of the input gives the number of test cases, T (1 <= T <= 200).

The first line of each test case contains a positive integer N (1 <= N <= 8), the number of integers in numList. The second line of each test cases contains N integers, where absolute number of each integer is same or less than 1000.

Output

For each test case, print the calculated value as printed in the problem statement, in one line.

Round the value with exactly one digit after the decimal point. Sorry for the inconvenience caused. 

Sample Input

Sample Output

3
3
1 2 3
1
42
5
3 1 4 15 9
2.0
42.0
6.4