Permutation Xor

A sequence of $N$ integers is called a permutation if it contains all integers from $1$ to $N$ exactly once. For a permutation $P$ of length $N$ (where $N$ is an **even integer**), we define the function $F(P)$ as: $F(P) = $ $(P_1 \oplus P_2) + (P_3 \oplus P_4) + \ldots + (P_{n-1} \oplus P_n)$. Here, $\oplus$ denotes the [bitwise XOR operation](https://en.wikipedia.org/wiki/Bitwise_operation