You are given an integer n. Initially, you have a single integer n.

In each operation, you can pick any integer x where $x > 1$ from the current collection and split it into two positive integers a and b such that $a + b = x$. The cost of performing this operation is $a \times b$.

You repeat this process until all numbers in the collection are equal to $1$.

Return the minimum total cost needed to split n entirely into ones.

Constraints:

• $1 \leq$ n $\leq 5 \times 10^7$

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.