Inversion Probability

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