Ordered Pairs

Interview

Time limit0.5sMemory limit512 MB

Summary

Count the ordered pairs of natural numbers whose product equals a given N.

Level: Easy3 of 10
Topics: Math, Number theory, Brute force, Implementation
Solved: No attempts yet

Problem

An ordered pair is written as $(a, b)$ . Two ordered pairs $(a_1, b_1)$ and $(a_2, b_2)$ are equal when $a_1 = a_2$ and $b_1 = b_2$ .

Given a natural number $N$ , write a program that counts the distinct ordered pairs $(a, b)$ whose product $a \times b$ equals $N$ . Both $a$ and $b$ must be natural numbers.

Input

The first line contains a natural number $N$ ( $1 \le N \le 1{,}000{,}000{,}000$ ).

Output

Print the number of distinct ordered pairs whose product equals $N$ on the first line.

Examples5

Example 1
Input
```
10
```
Expected output
```
4
```
Example 2
Input
```
16
```
Expected output
```
5
```
Example 3
Input
```
1048576
```
Expected output
```
21
```
Example 4
Input
```
23
```
Expected output
```
2
```
Example 5
Input
```
469762049
```
Expected output
```
2
```