Divisions

Time limit1sMemory limit256 MB

Summary

Count the positive divisors of the given integer N, which is at most 10^18.

Level: Medium7 of 10
Topics: Number theory
Solved: No attempts yet

Problem

David is a young boy who loves numbers. He recently learned how to divide two numbers, and since then he divides all day long. When a division comes out as an integer he is happy, and when it does not he is much less amused. After a while he decided to use only one dividend per day.

David's parents are careful, and they want him to get enough happiness, so they pick the number he uses as that day's dividend. There is still a problem: the parents are not good at math and cannot count how many positive integers divide a given dividend $N$ with an integral result. Count them for David's parents.

Input

The single input line contains one integer $N$ , the number chosen as the dividend. ( $1 \le N \le 10^{18}$ )

Output

Print how many positive integers divide $N$ with an integral result.

Examples3

Example 1
Input
```
12
```
Expected output
```
6
```
Example 2
Input
```
999999999999999989
```
Expected output
```
2
```
Example 3
Input
```
100000007700000049
```
Expected output
```
4
```