#include<bits/stdc++.h>
#define LL long long
#define ld long double
using namespace std;
const int inf=1e9,M=60;
int n,c[M][M];double x;LL ans,num;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%lf",&x);
		if((int)x==x)ans--;
		LL y=(LL)((ld)x*inf+0.5);
		int c1=0,c2=0;
		while(y%2==0)c1++,y/=2;
		while(y%5==0)c2++,y/=5;
		// cout<<c1<<" "<<c2<<endl;
		c[c1][c2]++;
	}
	for(int i=0;i<M;i++)
		for(int j=0;j<M;j++)
			for(int k=0;k<M;k++)
				for(int l=0;l<M;l++)
					if(min(i+k,j+l)>=18)ans+=1ll*c[i][j]*c[k][l];
	cout<<ans/2;
	return 0;
}
### Prompt

In cpp, your task is to solve 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>
#define LL long long
#define ld long double
using namespace std;
const int inf=1e9,M=60;
int n,c[M][M];double x;LL ans,num;
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%lf",&x);
		if((int)x==x)ans--;
		LL y=(LL)((ld)x*inf+0.5);
		int c1=0,c2=0;
		while(y%2==0)c1++,y/=2;
		while(y%5==0)c2++,y/=5;
		// cout<<c1<<" "<<c2<<endl;
		c[c1][c2]++;
	}
	for(int i=0;i<M;i++)
		for(int j=0;j<M;j++)
			for(int k=0;k<M;k++)
				for(int l=0;l<M;l++)
					if(min(i+k,j+l)>=18)ans+=1ll*c[i][j]*c[k][l];
	cout<<ans/2;
	return 0;
}
```