9704: ABC190 —— D - Staircase Sequences
[Creator : ]
Description
How many arithmetic progressions consisting of integers with a common difference of $1$ have a sum of $N$?
Input
Input is given from Standard Input in the following format:
```
$N$
```
```
$N$
```
Output
Print the answer.
Constraints
- $1 ≤ N ≤ 10^{12}$
- $N$ is an integer.
- $N$ is an integer.
Sample 1 Input
12
Sample 1 Output
4
We have four such progressions:
- [12]
- [3,4,5]
- [−2,−1,0,1,2,3,4,5]
- [−11,−10,−9,…,10,11,12]
Sample 2 Input
1
Sample 2 Output
2
We have two such progressions:
- [1]
- [0,1]
Sample 3 Input
963761198400
Sample 3 Output
1920