Given an array $A$ of $n$ integers. Count the number of pairs $i < j$ that $A_i \times A_j$ is a square number.
### Input
- The first line contains an integer $n$.
- The second line contains $n$ integers $A_i$.
### Output
- Print the number of pairs $i < j$ that $A_i \times A_j$ is a square number.
### Constraints
- $1 \le n \le 3 \times 10^5$.
- $1 \le A_i \le 10^6$.
### Example
Input:
```
4
1 2 4 8
```
Output:
```
2
```
