You are given a convex polygon with $n$ vertices, where the vertices are indexed sequentially in clockwise order from $0$ to $n - 1$. The value of each vertex $i$ is given by values[i].

A triangulation divides the polygon into $n - 2$ triangles using nonintersecting diagonals. The score of a triangle formed by vertices $i$, $j$, and $k$ is the product values[i] $\cdot$ values[j] $\cdot$ values[k]. The total score of a triangulation is the sum of the scores of all its constituent triangles.

Return the minimum possible total score among all triangulations of the polygon.

Constraints:

• n == values.length

• $3 \le$ n $\le 50$

• $1 \le$ values[i] $\le 100$

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.