You are given a $0$ indexed binary string s of length n.

You can perform two types of operations on s any number of times:

• Invert the prefix of s from index $0$ to index i with a cost of i $+ 1$.

• Invert the suffix of s from index i to index n $-$ $1$ with a cost of n $-$ i.

Inverting a substring means toggling every character in that range, changing '0' to '1' and '1' to '0'.

Return the minimum total cost to make all characters in s equal.

Constraints:

• $1 \leq$ s.length $==$ n $\leq 10^5$

• s[i] is either '0' or '1'

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.