You are given an array of integers nums.

The factor score of an array is defined as the product of the greatest common divisor ($ ext{GCD}$) and the least common multiple ($ ext{LCM}$) of all its elements.

Return the maximum factor score of nums after removing at most $1$ element from the array.

Note: The factor score of an empty array is $0$. Both the $ ext{GCD}$ and $ ext{LCM}$ of an array with a single element are equal to that element.

Constraints:

• $1 \leq$ nums.length $\leq 100$

• $1 \leq$ nums[i] $\leq 30$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.