You are given a binary string s representing a train sequence of cars. A character $'1'$ signifies that the car contains illegal goods, while a character $'0'$ signifies that it does not.

You need to remove every car containing illegal goods. You may perform any of the following operations:

• Remove a car from the left end of the sequence, taking $1$ unit of time.

• Remove a car from the right end of the sequence, taking $1$ unit of time.

• Remove a car from any position in the sequence, taking $2$ units of time.

Return the minimum total time required to remove all cars containing illegal goods.

Constraints:

• $1 \leq$ s.length $\leq 2 imes 10^5$

• 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.