Shuffle n distinct elements uniformly. Return the expected number of inversions, meaning pairs that appear in the wrong relative order.

Every one of the $\binom{n}{2}$ pairs is inverted with probability exactly $1/2$, by symmetry:

$$E = \frac{1}{2}\binom{n}{2} = \frac{n(n-1)}{4}$$

Input

10

Output

22.5