An array has $n$ integers $x_1,x_2,\dots,x_n$ , and each of them has been randomly chosen between $1$ and $r_i$ . An inversion is a pair $(a,b)$ where $a<b$ and $x_a>x_b$ .
What is the expected number of inversions in the array?
The first input line contains an integer $n$ : the size of the array.
The second line contains $n$ integers $r_1,r_2,\dots,r_n$ : the range of possible values for each array position.
Print the expected number of inversions rounded to six decimal places (rounding half to even).