Functions 
~f(x)~ and 
~g(y)~ are defined below.
$$\displaystyle f(x) = \begin{cases} 1, & \text{if } x = a^b \\ 0, & \text{if } x \ne a^b \end{cases}$$
where 
~a~ and 
~b~ are integers such that 
~a \ge 1~ and 
~b > 1~.
$$\displaystyle g(y) = \sum_{i=0}^y f(\phi(i)) \cdot \phi(i)$$
where 
~\phi(z)~ is Euler's totient function.
Given an integer 
~N~, output 
~g(N) \pmod{10^9 + 7}~.
Input
A positive integer 
~N \le 1\,000\,000~.
Output
The value of ~g(N) \pmod{10^9 + 7}~.
Constraints
Average scoring is used for this problem.
The first test case is the sample test below.
Afterwards, there will be 50 test cases worth 2 points each.
In all test cases, 
~1 \le N \le 1\,000\,000~.
Sample Input
5
Sample Output
6
Explanation
~g(5) = 0 \cdot 0 + 1 \cdot 1 + 1 \cdot 1 + 0 \cdot 2 + 0 \cdot 2 + 1 \cdot 4 = 6~
Comments
What is f(x) if it satisfies both?
f(x) will be 1