Count the number of integer pairs $1 \le x, y \le n$ such that $\text{gcd}(x, y)$ is a prime number.
### Input
- A single line containing an integer $n$.
### Output
- Print a single integer, which is the number of pairs that satisfy the condition.
### Constraints
- $1 \le n \le 2 \times 10^6$.
### Example
Input:
```
4
```
Output:
```
4
```
