B. Shifts and Sorting

Let's define a cyclic shift of some string 𝑠 as a transformation from 𝑠1𝑠2…𝑠𝑛−1𝑠𝑛 into 𝑠𝑛𝑠1𝑠2…𝑠𝑛−1. In other words, you take one last character 𝑠𝑛 and place it before the first character while moving all other characters to the right.

You are given a binary string 𝑠 (a string consisting of only 0-s and/or 1-s).

In one operation, you can choose any substring 𝑠𝑙𝑠𝑙+1…𝑠𝑟 (1≤𝑙<𝑟≤|𝑠|) and cyclically shift it. The cost of such operation is equal to 𝑟−𝑙+1 (or the length of the chosen substring).

You can perform the given operation any number of times. What is the minimum total cost to make 𝑠 sorted in non-descending order?