Sums of Consecutive Numbers

Hard

Given a positive integer total, count the ways to write it as a sum of one or more consecutive positive integers. The number total on its own (a sum with a single term) counts as one way too.

Example 1

total=12 → 2

12 = 12 and 12 = 3 + 4 + 5: two ways.

Example 2

total=21 → 4

21 = 21 = 10 + 11 = 6 + 7 + 8 = 1 + 2 + 3 + 4 + 5 + 6.

Example 3

total=16 → 1

Constraints

1 ≤ total ≤ 10⁹

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Topics

Math Enumeration

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Input

total=12

Expected

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