You are given a positive integer n, which is initially present on a board.

Every day, for $10^9$ days, the following process is performed:

• For each integer x currently on the board, find all integers i such that $1 \leq$ i $\leq$ n and x % i == 1.

• Add every such integer i to the board.

Return the count of distinct integers present on the board after $10^9$ days.

Note: Once a number is added to the board, it remains on the board indefinitely.

Constraints:

• $1 \leq$ n $\leq 100$

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.