DSA Homework 1

Fractions

Little John is doing math homework and he started writing on a piece of paper a sequence of irreducible fractions of type P/Q, where 1 ≤ P,Q ≤ N, where N is a natural number chosen by him. For example, for number N = 4, he got the following sequence:

1/1 1/2 1/3 1/4 2/1 2/3 3/1 3/2 3/4 4/1 4/3

Little John then counted the elements and he saw that for N = 4, there are 11 fractions.

Requirement

Given a natural number N, determine the number of fractions in the sequence constructed with the rules above.

Input Data

Natural number N is read from the keyboard.

Output Data

The program should output one number, representing the number of fractions in the sequence for the given number N.

Restrictions

1 ≤ N ≤ 100

Examples

Input	Output
3	7
4	11
5	19
10	63