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**Task** | Statistics

Time limit: | 1.00 s | Memory limit: | 512 MB |

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.

- $1 \le n \le 100$

- $1 \le r_i \le 100$

Input:

`3`

5 2 7

Output:

`1.057143`