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