A confusing number is a positive integer that, when rotated by $180$ degrees, yields a valid number that is different from the original number.

The rotation rules for individual digits are as follows:

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

• $6$ and $9$ rotate to $9$ and $6$ respectively.

• All other digits ($2$, $3$, $4$, $5$, and $7$) become invalid when rotated.

When a number is rotated by $180$ degrees, each of its digits is rotated and the order of the digits is reversed. Any leading zeros in the resulting rotated number are omitted.

Given an integer n, return the total count of confusing numbers in the inclusive range from $1$ to n.

Constraints:

• $1 \leq$ n $\leq 10^9$

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.