7677: [CSES Problem Set] Inversion Probability
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Description
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?
What is the expected number of inversions in the array?
Input
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.
The second line contains $n$ integers $r_1,r_2,\dots,r_n$: the range of possible values for each array position.
Output
Print the expected number of inversions rounded to six decimal places.
Constraints
$1≤n≤100$
$1 \le r_i \le 100$
$1 \le r_i \le 100$
Sample 1 Input
3
5 2 7
Sample 1 Output
1.057143