Proper Divisor Count

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

A proper positive divisor d of n satisfies d<n and n mod d=0. Count such divisors, excluding n itself. The answer for n=1 is zero.

Input

One positive integer n.

Output

Print the number of proper positive divisors.

Subtasks

• Subtask 1 (20%): $1\le n\le30$.
• Subtask 2 (30%): $1\le n\le1000$.
• Subtask 3 (50%): $1\le n\le10000$.

Examples

Example 1

Input

12

Output

5

Explanation

The proper divisors are 1,2,3,4,6, so there are five.

Example 2

Input

1

Output

0

Explanation

There are no positive integers below one.