An array has $n$ integers $x_1, x_2, \dots, x_n$, and each of them is randomly chosen independently and uniformly from the range $[1, r_i]$.An inversion is a pair of indices $(a, b)$ such that $a < b$ 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 (using round-half-to-even).

Constraints

• $1 \leq n \leq 100$
• $1 \leq r_i \leq 100$

Example
Sample Input:

 3
 5 2 7

Output:

1.057143