An integer x is considered a good number if, after rotating each of its digits individually by $180$ degrees, the resulting number is a valid number that is different from x.

Each digit rotates according to the following rules:

• $0$, $1$, and $8$ rotate to themselves.

• $2$ and $5$ rotate to each other.

• $6$ and $9$ rotate to each other.

• $3$, $4$, and $7$ do not rotate to any valid digit and make the number invalid.

Given an integer n, return the count of good numbers in the range $[1, n]$.

Constraints:

• $1 \leq$ n $\leq 10^4$

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.