You are given a $0$ indexed integer array nums of length $n$ representing the initial cost of collecting chocolates of types $0$ to $n - 1$, where nums[i] denotes the cost of collecting a chocolate of type i.

You want to collect at least one chocolate of each type from $0$ to $n - 1$.

In one operation, you can pay a cost of x to rotate the chocolates circularly such that the chocolate originally of type i can now be collected at the cost of nums[(i + 1) % n]. You can perform this operation any number of times.

Return the minimum total cost needed to collect all $n$ types of chocolates.

Constraints:

• $1 \leq$ nums.length $\leq 1000$

• $1 \leq$ nums[i] $\leq 10^9$

• $1 \leq$ x $\leq 10^9$

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.