Paths
Description
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.
Single integer n (1 ≤ n ≤ 107).
Print the sum of d(u, v) over all 1 ≤ u < v ≤ n.
Input
Single integer n (1 ≤ n ≤ 107).
Output
Print the sum of d(u, v) over all 1 ≤ u < v ≤ n.
Samples
6
8
10
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.