You are given an integer n. Starting with a single integer n, you repeatedly perform operations until all remaining values are equal to $1$.

In one operation, you can select any current integer x that is strictly greater than $1$ and split it into two positive integers a and b such that a $+$ b $=$ x. The cost of performing this split is a $ imes$ b.

Return the minimum total cost required to split n into all ones.

Constraints:

• $1 \leq$ n $\leq 500$

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.