Maximum Sum

You are given an array $A$ of size $N$. In one operation, you can do the following: - Choose any two adjacent elements $A_i$ and $A_{i+1}$ $(1 \leq i \lt N)$. - Let $X = gcd(A_i,A_{i+1})$ and $Y = lcm(A_i,A_{i+1})$. Here $gcd$ denotes the [greatest common divisor](https://en.wikipedia.org/wiki/Greatest_common_divisor) and $lcm$ denotes the [least common multiple](https://en.wikipedia.org/wiki/Le