Problem L. Learning distribution

Input file:Standard input   Time limit:2 sec
Output file:Standard output   Memory limit:512 Mb

Statement

Two students are preparing for exam, when they will get a single question out of n possible ones. They decided to split questions to study as follows:

First student picks a number a from 1 to n and learns a questions numbered a, a + 1, a + 2, ... , a + a − 1. If some number exceeds n, numbering continues from 1. For example, if n = 5 and a = 1, the first student will only learn question 1, when a = 2 he will learn questions 2 and 3, when a = 4 — questions 4, 5, 1 and 2, when a = 5 — all questions.

Second student also picks a number b ≠ a from 1 to n and learns b questions numbered b, b + 1, b + 2, ... , b + b − 1. Similarly, if some number exceeds n, numbering continues from 1.

Given number of questions n determine number of different ways to choose a and b, such that every question will be learned by at least one of students.

Input format

Input contains an integer n.

Output format

Output an integer — number of ways to choose a and b.

Constraints

2 ≤ n ≤ 106

Notes on samples

In the first sample all possible choices of a и b result in learning all questions.

In the second sample there are four questions. If a = 1, and b = 2, question number 4 will not be learned by either student.

If a = 1, and b = 3, question number 2 will not be learned by either student.

In other cases all questions will be studied.

Sample tests

No. Standard input Standard output
1
3
6
2
4
8

3.189s 0.189s 15