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?

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.

Output

Print the expected number of inversions rounded to six decimal places (rounding half to even).

Constraints

• $1 \le n \le 100$
• $1 \le r_i \le 100$

Example

Input:

3
5 2 7

Output:

1.057143