You are given a $0$ indexed integer array nums representing the scores of students. Choose a non empty group of students to maximize the overall strength of the group.

The strength of a group formed by selecting students at indices $i_0, i_1, \dots, i_k$ is defined as the product of their scores: nums$[i_0] imes$ nums$[i_1] imes \dots imes$ nums$[i_k]$.

Return the maximum strength that can be achieved.

Constraints:

• $1 \leq$ nums.length $\leq 13$

• $-9 \leq$ nums[i] $\leq 9$

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.