D - Staircase Sequences

Score : $400$ points

Problem Statement

How many arithmetic progressions consisting of integers with a common difference of $1$ have a sum of $N$?

Constraints

• $1 ≤ N ≤ 10^{12}$
• $N$ is an integer.

Input

Input is given from Standard Input in the following format:

$N$

Output

Print the answer.

12

4

We have four such progressions:

• $[12]$
• $[3, 4, 5]$
• $[-2, -1, 0, 1, 2, 3, 4, 5]$
• $[-11, -10, -9, \dots, 10, 11, 12]$

1

2

We have two such progressions:

• $[1]$
• $[0, 1]$

963761198400

1920