GCD Reduction

For an array $A$ of length $N$, we obtain its *score* as follows. Perform the following operation $N-2$ times: - If $\gcd(A_1, A_3) \leq \gcd(A_2, A_3)$, delete $A_1$ from $A$. Otherwise, delete $A_2$. After the deletion, the remaining elements are re-indexed to start from $1$. In the end, the array will have exactly two elements remaining. Its score is defined to be the first of these two