An elevator is currently at floor start in a building with n floors, numbered from $0$ to n $- 1$.

You are given an integer n, an integer start, and an integer array requests containing distinct floor numbers that must be visited.

The elevator starts at time $0$ at floor start and requires $|a - b|$ seconds to move between floor $a$ and floor $b$. The penalty for fulfilling a request is defined as the total time elapsed from time $0$ until the elevator first arrives at that requested floor. If start is present in requests, its penalty is $0$.

Return the minimum total penalty required to fulfill all requests in requests.

Constraints:

• $1 \leq$ n $\leq 10^9$

• $1 \leq$ requests.length $\leq 1500$

• $0 \leq$ start, requests[i] $\leq$ n $- 1$

• All values in requests are distinct.

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.