Given an array A of n integers. Count the number of pairs i<j that Ai×Aj is a square number.
### Input
- The first line contains an integer n.
- The second line contains n integers Ai.
### Output
- Print the number of pairs i<j that Ai×Aj is a square number.
### Constraints
- 1≤n≤3×105.
- 1≤Ai≤106.
### Example
Input:
41248
Output:
2