13:I[87,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"Header"] 14:I[1742,["736","static/chunks/89fc4f0e-9e200ae6a0166583.js","401","static/chunks/363642f4-32903b9154b7835a.js","153","static/chunks/153-58eddeb032cc4608.js","131","static/chunks/131-05ce00cfd760e12b.js","87","static/chunks/87-b76b60eef573119a.js","286","static/chunks/app/problem/%5Bid%5D/page-45cf3875257fc32e.js"],"ProblemView"] 15:T7dc,

Vivek initially has an empty array $$$a$$$ and some integer constant $$$m$$$.

He performs the following algorithm:

Select a random integer $$$x$$$ uniformly in range from $$$1$$$ to $$$m$$$ and append it to the end of $$$a$$$.
Compute the greatest common divisor of integers in $$$a$$$.
In case it equals to $$$1$$$, break
Otherwise, return to step $$$1$$$.

Find the expected length of $$$a$$$. It can be shown that it can be represented as $$$\frac{P}{Q}$$$ where $$$P$$$ and $$$Q$$$ are coprime integers and $$$Q\neq 0 \pmod{10^9+7}$$$. Print the value of $$$P \cdot Q^{-1} \pmod{10^9+7}$$$.

Input

The first and only line contains a single integer $$$m$$$ ($$$1 \leq m \leq 100000$$$).

Output

Print a single integer — the expected length of the array $$$a$$$ written as $$$P \cdot Q^{-1} \pmod{10^9+7}$$$.

Steps to One

Examples