2549. Count Distinct Numbers on Board

Easy

157

165

You are given a positive integer `n`

, that is initially placed on a board. Every day, for `10`

days, you perform the following procedure:^{9}

- For each number
`x`

present on the board, find all numbers`1 <= i <= n`

such that`x % i == 1`

. - Then, place those numbers on the board.

Return* the number of distinct integers present on the board after*

`10`^{9}

**Note:**

- Once a number is placed on the board, it will remain on it until the end.
`%`

stands for the modulo operation. For example,`14 % 3`

is`2`

.

**Example 1:**

Input:n = 5Output:4Explanation:Initially, 5 is present on the board. The next day, 2 and 4 will be added since 5 % 2 == 1 and 5 % 4 == 1. After that day, 3 will be added to the board because 4 % 3 == 1. At the end of a billion days, the distinct numbers on the board will be 2, 3, 4, and 5.

**Example 2:**

Input:n = 3Output:2Explanation:Since 3 % 2 == 1, 2 will be added to the board. After a billion days, the only two distinct numbers on the board are 2 and 3.

**Constraints:**

`1 <= n <= 100`

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