We are playing a guessing game. The rules of the game are as follows:

1. A number from $1$ to n is chosen.

2. You attempt to guess the chosen number.

3. If you guess correctly, you win the game.

4. If your guess is incorrect, you are told whether the chosen number is higher or lower than your guess, and you continue guessing.

5. Each time you make an incorrect guess of value $x$, you must pay $\\$x$.

Given an integer n, return the minimum amount of money required to guarantee a win regardless of which number is chosen.

Constraints:

• $1 \leq$ n $\leq 200$

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.