DZY Loves Balls

Problem Description

DZY loves playing balls.

He has $n$ balls in a big box. On each ball there is an integer written.

One day he decides to pick two balls from the box. First he randomly picks a ball from the box, and names it $A$. Next, without putting $A$ back into the box, he randomly picks another ball from the box, and names it $B$.

If the number written on $A$ is strictly greater than the number on $B$, he will feel happy.

Now you are given the numbers on each ball. Please calculate the probability that he feels happy.

Input

First line contains $t$ denoting the number of testcases.

$t$ testcases follow. In each testcase, first line contains $n$, second line contains $n$ space-separated positive integers $a_i$, denoting the numbers on the balls.

($1\le t\le 300, 2\le n \le 300,1\le a_i \le 300$)

Output

For each testcase, output a real number with 6 decimal places.

Sample Input

2
3
1 2 3
3
100 100 100

Sample Output

0.500000
0.000000

Source

BestCoder Round #76 (div.2)