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Contest: Task: Related: TaskC TaskE

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.

Sample Input 1

12

Sample Output 1

4

We have four such progressions:

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

Sample Input 2

1

Sample Output 2

2

We have two such progressions:

  • $[1]$
  • $[0, 1]$

Sample Input 3

963761198400

Sample Output 3

1920