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.
