2549 - Count Distinct Numbers on Board.

Easy

You are given a positive integer n, that is initially placed on a board. Every day, for <code>10⁹</code> days, you perform the following procedure:

• 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 <code>10⁹</code> days have elapsed.

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 = 5

Output: 4

Explanation: 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 = 3

Output: 2

Explanation:

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