Expectations on a Permutation

A permutation of length $N$ is an array of $N$ integers $A = [A_1, A_2, \dots, A_N]$ such that every integer from $1$ to $N$ appears in it exactly once. We define a function over a permutation as follows: $F(A) = (A_1 * A_2) + (A_2 * A_3) + \cdots + (A_{N-2} * A_{N-1}) + (A_{N-1}*A_N)$ You are given an integer $N$. What is the expected value of the function $F$ over all possible permutations of