Count Distinct Numbers on Board
You are given a positive integer n, that is initially placed on a board. Every day, for 10^9 days, you perform the following procedure:
- For each number
xpresent on the board, find all numbers1 <= i <= nsuch thatx % i == 1. - Then, place those numbers on the board.
Return the number of distinct integers present on the board after 10^9 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 % 3is2.
Example 1
Input
n = 5Output
4At the end of a billion days, the distinct numbers on the board will be 2, 3, 4, and 5.
Example 2
Input
n = 3Output
2After a billion days, the only two distinct numbers on the board are 2 and 3.
Constraints
- 1 <= n <= 100