You are given a $0$ indexed integer array nums of length n.

A split at index i, where $0 \leq$ i $\leq$ n $- 2$, is considered valid if the product of the first i $+ 1$ elements is coprime with the product of the remaining n $-$ i $- 1$ elements. That is, the greatest common divisor of the product of nums[0] through nums[i] and the product of nums[i + 1] through nums[n - 1] is equal to $1$.

Return the smallest index i that forms a valid split, or $-1$ if no valid split exists.

Note: Two integers are coprime if their greatest common divisor is equal to $1$.

Constraints:

• n == nums.length

• $1 \leq$ n $\leq 10^4$

• $1 \leq$ nums[i] $\leq 10^6$

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.