#include<iostream>
#include<cstdio>
using namespace std;

int n;
long long ans;
long long num[25][25];
int main()
{
	int i,j;
	scanf("%d",&n);
	while(n--)
	{
		double t;
		scanf("%lf",&t);
		long long a=t*double(1e9)+0.5;
		int n2=1,n5=1;
		while(a%2==0)
		{
			a/=2;
			n2++;
		}
		while(a%5==0)
		{
			a/=5;
			n5++;
		}
		n2=min(19,n2);
		n5=min(19,n5);
		for(i=20-n2;i<=19;i++)
			for(j=20-n5;j<=19;j++)
				ans+=num[i][j];
		num[n2][n5]++;
	}
	printf("%lld",ans);
	return 0;
}
### Prompt

Please formulate a cpp solution to the following problem:

You are given N real values A_1, A_2, \ldots, A_N. Compute the number of pairs of indices (i, j) such that i < j and the product A_i \cdot A_j is integer.

Constraints

* 2 \leq N \leq 200\,000
* 0 < A_i < 10^4
* A_i is given with at most 9 digits after the decimal.

Input

Input is given from Standard Input in the following format.


N
A_1
A_2
\vdots
A_N


Output

Print the number of pairs with integer product A_i \cdot A_j (and i < j).

Examples

Input

5
7.5
2.4
17.000000001
17
16.000000000


Output

3


Input

11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001


Output

8

### Response

```cpp
#include<iostream>
#include<cstdio>
using namespace std;

int n;
long long ans;
long long num[25][25];
int main()
{
	int i,j;
	scanf("%d",&n);
	while(n--)
	{
		double t;
		scanf("%lf",&t);
		long long a=t*double(1e9)+0.5;
		int n2=1,n5=1;
		while(a%2==0)
		{
			a/=2;
			n2++;
		}
		while(a%5==0)
		{
			a/=5;
			n5++;
		}
		n2=min(19,n2);
		n5=min(19,n5);
		for(i=20-n2;i<=19;i++)
			for(j=20-n5;j<=19;j++)
				ans+=num[i][j];
		num[n2][n5]++;
	}
	printf("%lld",ans);
	return 0;
}
```