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g2501_2600.s2549_count_distinct_numbers_on_board.readme.md Maven / Gradle / Ivy

2549\. Count Distinct Numbers on Board

Easy

You are given a positive integer `n`, that is initially placed on a board. Every day, for 109 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_ 109 _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`