#include<iostream>
#include<cstdio>
#include<map>
using namespace std;
const int N=200005;
int n;
long long a[N];
map<pair<int,int>,int>book;
int main()
{
	scanf("%d",&n);
	long long ans=0;
	for(int i=1;i<=n;i++)
	{
		double x;
		scanf("%lf",&x);
		a[i]=x*1e9+0.5;
		int cnt2=0,cnt5=0;
		while(a[i]%2==0) cnt2++,a[i]/=2;
		while(a[i]%5==0) cnt5++,a[i]/=5;
		for(auto [x,num]:book)
			if(x.first+cnt2>=18&&x.second+cnt5>=18) ans+=num;
		book[make_pair(cnt2,cnt5)]++;
	}
	printf("%lld",ans);
	return 0;
}
### Prompt

Create a solution in Cpp for 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>
#include<map>
using namespace std;
const int N=200005;
int n;
long long a[N];
map<pair<int,int>,int>book;
int main()
{
	scanf("%d",&n);
	long long ans=0;
	for(int i=1;i<=n;i++)
	{
		double x;
		scanf("%lf",&x);
		a[i]=x*1e9+0.5;
		int cnt2=0,cnt5=0;
		while(a[i]%2==0) cnt2++,a[i]/=2;
		while(a[i]%5==0) cnt5++,a[i]/=5;
		for(auto [x,num]:book)
			if(x.first+cnt2>=18&&x.second+cnt5>=18) ans+=num;
		book[make_pair(cnt2,cnt5)]++;
	}
	printf("%lld",ans);
	return 0;
}
```