829\. Consecutive Numbers Sum

Hard

Given an integer `n`, return _the number of ways you can write_ `n` _as the sum of consecutive positive integers._

**Example 1:**

**Input:** n = 5

**Output:** 2

**Explanation:** 5 = 2 + 3

**Example 2:**

**Input:** n = 9

**Output:** 3

**Explanation:** 9 = 4 + 5 = 2 + 3 + 4

**Example 3:**

**Input:** n = 15

**Output:** 4

**Explanation:** 15 = 8 + 7 = 4 + 5 + 6 = 1 + 2 + 3 + 4 + 5

**Constraints:**

*   <code>1 <= n <= 10<sup>9</sup></code>