Consecutive Numbers Sum

Hard

Given an integer n, return the number of ways to write it as a sum of consecutive positive integers.

Example 1

Input:  n = 5
Output: 2
Explanation: 5 = 5 = 2 + 3.

Example 2

Input:  n = 9
Output: 3
Explanation: 9 = 9 = 4 + 5 = 2 + 3 + 4.

Example 3

Input:  n = 15
Output: 4

Constraints

• 1 <= n <= 10^9