Tue, 30 Apr 2013 13:26:00 GMT

Counting fractions

TimeLimit: 2000MS MemoryLimit: 65536 Kb

Totalsubmit: 39 Accepted: 6

Description

Consider the fraction, n/d, where n and d are positive integers. If n <= d and HCF(n,d)=1, it is called a reduced proper fraction.

If we list the set of reduced proper fractions for d <= 8 in ascending order of size, we get:

1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 7/8

It can be seen that there are 21 elements in this set.

How many elements would be contained in the set of reduced proper fractions for d <= x?

Input

The input will consist of a series of x, 1 < x < 1000001.

Output

For each input integer x, you should output the number of elements contained in the set of reduced proper fractions for d <= x in one line.

Sample Input

Sample Output

3
21

Hint

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代码

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