You are given an integer array nums.

In each operation, you remove elements from nums based on the following rules:

• If nums.length is at least $3$, select any $2$ elements from the first $3$ elements of nums and remove them. The cost of this operation is the maximum of the $2$ chosen elements.

• If nums.length is less than $3$, remove all remaining elements from nums. The cost of this operation is the maximum of all the removed elements.

Return the minimum total cost to remove all elements from nums.

Constraints:

• $1 \leq$ nums.length $\leq 1000$

• $1 \leq$ nums[i] $\leq 10^6$

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.