Collatz Conjecture (Hard)

You are given an integer $N$. You can do the following operations: - If $N$ is even, choose to change $N$ to either $(3 \oplus N) + 1$ or $\dfrac{N}{2}$. - If $N$ is odd, change $N$ to $(3 \oplus N) + 1$. Here, $\oplus$ denotes the Bitwise XOR operator. Check if it is possible to go from $N$ to $1$, and further find the minimum operations to do so. If it is not possible, print $-1$. ### Input