Xor It

The XOR pair representation (XPR) of a positive integer $N$ is defined as a pair of integers $(A, B)$ such that: - $1 \le A \le B \le N$ - $A \oplus B = N$ - if there is no way to choose $A$ and $B$ satisfying the above conditions, $A = B = -1$ - otherwise, the value of $A$ should be the smallest possible These conditions uniquely define the XPR. Next, we define a function $F(N)$ = the valu