Let $f(i, j)$ be the sum of all positive divisors that $i$ and $j$ have in common. For example, $f(8, 12) = 1 + 2 + 4 = 7$. Calculate the sum of all $f(i, j)$ for $1 \le i \le j \le n$. In other words, calculate:
$$ \sum_{i=1}^{n} \sum_{j=i}^{n} f(i, j) $$
### Input
- A single line containing an integer $n$.
### Output
- Print the result of the calculation modulo $10^9 + 7$.
### Constraints
- $1 \le n \le 10^{14}$.
### Sample Test
Input:
```
5
```
Output
```
33
```
