You are given an integer array nums.

A split of nums into contiguous subarrays is valid if the greatest common divisor ($\gcd$) of the first element and the last element of every subarray is strictly greater than $1$.

Return the minimum number of subarrays needed to form a valid split. If no valid split exists, return $-1$.

Constraints:

• $1 \leq$ nums.length $\leq 1000$

• $1 \leq$ nums[i] $\leq 10^5$

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.