Given a positive integer n, consider each integer from $1$ to n. For every integer, remove all occurrences of the digit $0$ from its decimal representation to form a new positive integer.

Return the count of distinct integers formed after applying this process to all integers from $1$ to n.

Constraints:

• $1 \le$ n $\le 10^{15}$

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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.