#include<bits/stdc++.h>
using namespace std;
map<pair<int,int>,int>cnt;
int main(){
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		double x;
		scanf("%lf",&x);
		long long ret=(llround(x*1e9));
		int two=0,five=0;
		while(ret%2==0){
			ret/=2;
			two++;
		}
		while(ret%5==0){
			ret/=5;
			five++;
		}
		++cnt[{two,five}];
	}
	long long ans=0;
	for(auto p1:cnt){
		for(auto p2:cnt){
			if(p1.first.first+p2.first.first>=18&&p1.first.second+p2.first.second>=18){
				if(p1<p2) ans+=1ll*p1.second*p2.second;
				else if(p1==p2) ans+=1ll*p1.second*(p1.second-1)/2;
			}
		}
	}
	printf("%lld",ans);
	return 0;
}
### Prompt

Your challenge is to write 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<bits/stdc++.h>
using namespace std;
map<pair<int,int>,int>cnt;
int main(){
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		double x;
		scanf("%lf",&x);
		long long ret=(llround(x*1e9));
		int two=0,five=0;
		while(ret%2==0){
			ret/=2;
			two++;
		}
		while(ret%5==0){
			ret/=5;
			five++;
		}
		++cnt[{two,five}];
	}
	long long ans=0;
	for(auto p1:cnt){
		for(auto p2:cnt){
			if(p1.first.first+p2.first.first>=18&&p1.first.second+p2.first.second>=18){
				if(p1<p2) ans+=1ll*p1.second*p2.second;
				else if(p1==p2) ans+=1ll*p1.second*(p1.second-1)/2;
			}
		}
	}
	printf("%lld",ans);
	return 0;
}
```