Description

There are $n$ lights in the corridor, numbered from $1$,$2$,$3$,...,$n$, managed by the school's circuit control center. Initially, all lights are off. A hacker has infiltrated the school's circuit control center and wants to make the lights flicker by performing $n$ rounds of operations. In the $i$-th round, the hacker toggles the state of all lights whose numbers are multiples of $i$ (turning on lights that are off and turning off lights that are on).
The hacker wants to know the sum of the numbers of all lights that are on after $n$ rounds of operations. Since the answer might be very large, please output the result modulo $10^9+7$.

Input Format

A single integer $n$, representing the number of lights. For 100% of the test cases, $1≤n≤10^{18}$.

Output Format

A single integer, representing the sum of the numbers of all lights that are on, modulo $10^9+7$.

Sample

20

30