#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
ll read(){
	ll a=0,b=getchar(),c=1;
	while(!isdigit(b))c=b=='-'?-1:1,b=getchar();
	while(isdigit(b))a=a*10+b-'0',b=getchar();
	return a*c;
}
ll n,y,u,v,res;
double x;
vector<vector<int> > g(20,vector<int>(20,0));
int main(){
	n=read();
	for(int i=0;i<n;i++){
		cin >> x;
		y=x*1000000000+0.1;
		u=v=0;
		while(y%2==0)
			y/=2,u++;
		while(y%5==0)
			y/=5,v++;
		u=min(u,18ll);
		v=min(v,18ll);
		for(int j=18-u;j<=18;j++)
			for(int k=18-v;k<=18;k++)
				res+=g[j][k];
		g[u][v]++;
	}
	cout << res;
	return 0;
}
### Prompt

Generate 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;
typedef long long ll;
ll read(){
	ll a=0,b=getchar(),c=1;
	while(!isdigit(b))c=b=='-'?-1:1,b=getchar();
	while(isdigit(b))a=a*10+b-'0',b=getchar();
	return a*c;
}
ll n,y,u,v,res;
double x;
vector<vector<int> > g(20,vector<int>(20,0));
int main(){
	n=read();
	for(int i=0;i<n;i++){
		cin >> x;
		y=x*1000000000+0.1;
		u=v=0;
		while(y%2==0)
			y/=2,u++;
		while(y%5==0)
			y/=5,v++;
		u=min(u,18ll);
		v=min(v,18ll);
		for(int j=18-u;j<=18;j++)
			for(int k=18-v;k<=18;k++)
				res+=g[j][k];
		g[u][v]++;
	}
	cout << res;
	return 0;
}
```