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 = 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.

Runtime:?0 ms, faster than?100.00%?of?Java?online submissions for?Count Distinct Numbers on Board.

Memory Usage:?38.9 MB, less than?85.71%?of?Java?online submissions for?Count Distinct Numbers on Board.