Factor Pairs of an Integer

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Given a positive integer $n$, count the pairs of positive integers $(a,b)$ satisfying $a\le b$ and $a\cdot b=n$. Two pairs are distinct if at least one component differs. The reversed ordering is not counted separately; a pair with $a=b$ is counted once.

Input

One line contains a positive integer $n$.

Output

Print a single integer: the number of valid pairs $(a,b)$.

Subtasks

• Subtask 1 (20%): $1\le n\le 10^4$.
• Subtask 2 (30%): $1\le n\le 10^8$.
• Subtask 3 (50%): $1\le n\le 10^{12}$.

Examples

Example 1

Input:

36

Output:

5

Explanation: The pairs are $(1,36)$, $(2,18)$, $(3,12)$, $(4,9)$ and $(6,6)$. The middle pair is counted exactly once. Therefore the result is $5$.

Example 2

Input:

1

Output:

1

Explanation: The only pair is $(1,1)$, so the result is $1$.

Example 3

Input:

12

Output:

3

Explanation: The three valid pairs are $(1,12)$, $(2,6)$ and $(3,4)$.