#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
const int maxn=1e6+5;
map<pii,int> M;
int main() {
	const ll mod=1e10;
	std::vector<ll> V(1);
	int n;cin>>n;
	for(int i=1;i<=n;i++) {
		long double x;cin>>x;
		V.push_back(llround(x*10000000000.0));
	}
	ll ans=0;
	for(int i=1;i<=n;i++) {
		int two=0,five=0;ll tem=V[i];
		while(tem&&tem%2==0) two++,tem/=2;
		while(tem&&tem%5==0) five++,tem/=5;
		for(int t=max(20-two,0);t<=20;t++) {
			for(int f=max(20-five,0);f<=20;f++) {
				ans+=M[{t,f}];
			}
		}
		M[{min(20,two),min(20,five)}]++;
	}
	cout<<ans<<endl;
    return 0;
}
### Prompt

Please provide a cpp coded solution to the problem described below:

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;
typedef long long ll;
typedef pair<int,int> pii;
const int maxn=1e6+5;
map<pii,int> M;
int main() {
	const ll mod=1e10;
	std::vector<ll> V(1);
	int n;cin>>n;
	for(int i=1;i<=n;i++) {
		long double x;cin>>x;
		V.push_back(llround(x*10000000000.0));
	}
	ll ans=0;
	for(int i=1;i<=n;i++) {
		int two=0,five=0;ll tem=V[i];
		while(tem&&tem%2==0) two++,tem/=2;
		while(tem&&tem%5==0) five++,tem/=5;
		for(int t=max(20-two,0);t<=20;t++) {
			for(int f=max(20-five,0);f<=20;f++) {
				ans+=M[{t,f}];
			}
		}
		M[{min(20,two),min(20,five)}]++;
	}
	cout<<ans<<endl;
    return 0;
}
```