#include<bits/stdc++.h>
using namespace std;
int ten[20][20],n;
long long cnt;
int main() 
{
	cin>>n;
	for(int i=1;i<=n;i++)
	{
		double x;
		cin>>x;
		long long tmp=x*1e9+0.1;
		int two=0,five=0;
		while(!(tmp%2))
		{
			tmp/=2;
			two++;
		}
		while(!(tmp%5))
		{
			tmp/=5;
			five++;
		}
		if(two>18)two=18;
		if(five>18)five=18;
		for(int j=18-two;j<=18;j++)
			for(int k=18-five;k<=18;k++)
				cnt+=ten[j][k];
		ten[two][five]++;
	}
	cout<<cnt;
}
### 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;
int ten[20][20],n;
long long cnt;
int main() 
{
	cin>>n;
	for(int i=1;i<=n;i++)
	{
		double x;
		cin>>x;
		long long tmp=x*1e9+0.1;
		int two=0,five=0;
		while(!(tmp%2))
		{
			tmp/=2;
			two++;
		}
		while(!(tmp%5))
		{
			tmp/=5;
			five++;
		}
		if(two>18)two=18;
		if(five>18)five=18;
		for(int j=18-two;j<=18;j++)
			for(int k=18-five;k<=18;k++)
				cnt+=ten[j][k];
		ten[two][five]++;
	}
	cout<<cnt;
}
```