You are given an array of integers nums.

The factor score of an array is defined as the product of the greatest common divisor (GCD) and the least common multiple (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 GCD and 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.