As an experiment the Educational Codeforces Round 33 will be rated for Div. 2. ×

F. Paths
time limit per test
4 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

You are given a positive integer n. Let's build a graph on vertices 1, 2, ..., n in such a way that there is an edge between vertices u and v if and only if . Let d(u, v) be the shortest distance between u and v, or 0 if there is no path between them. Compute the sum of values d(u, v) over all 1 ≤ u < v ≤ n.

The gcd (greatest common divisor) of two positive integers is the maximum positive integer that divides both of the integers.

Input

Single integer n (1 ≤ n ≤ 107).

Output

Print the sum of d(u, v) over all 1 ≤ u < v ≤ n.

Examples
Input
6
Output
8
Input
10
Output
44
Note

All shortest paths in the first example:

There are no paths between other pairs of vertices.

The total distance is 2 + 1 + 1 + 2 + 1 + 1 = 8.