Random Sort 2

Random sort is a way to sort a permutation $P$ of size $N$ with the algorithm below.

function random_sort(permutation P) {
	swaps = 0;
	while (not sorted P) {
		(i, j) = random pair (1 <= i < j <= N)
		swap(P[i], P[j])
		swaps = swaps + 1;
	}
	return swaps;
}

random pair picks one of the $\binom{N}{2}$ pairs that satisfy $1 \le i < j \le N$, uniformly at random and independently on every iteration. The loop stops once $P$ is in increasing order, and the function returns how many swaps it counted.

Given a permutation $P$, write a program that computes the expected return value of random_sort.

The first line contains the size of the permutation $N$ ($2 \le N \le 10$).

The second line contains the permutation $P_1, P_2, \dots, P_N$, separated by spaces. Every integer from $1$ to $N$ appears exactly once.

Print the expected return value of random_sort with exactly seven digits after the decimal point. Round half up at the eighth digit and pad with zeros when digits are left over. If the given permutation is already in increasing order, print 0.0000000.