#include<bits/stdc++.h>
#define int long long
using namespace std;
int n,t,f,ans;
double a[200001];
map<pair<int,int>,int> m;
signed main()
{
	scanf("%lld",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%lf",&a[i]);
		int b=round(a[i]*1000000000);
		t=f=-9;
		while(b%2==0)
		{
			b/=2;
			t++;
		}
		while(b%5==0)
		{
			b/=5;
			f++;
		}
		m[make_pair(t,f)]++;
	}
	for(auto i:m)
		for(auto l:m)
			if(i.first.first+l.first.first>=0&&i.first.second+l.first.second>=0)
			{
				if(i==l)
					ans+=i.second*(i.second-1)/2;
				if(i<l)
					ans+=i.second*l.second;
			}
	cout<<ans;
	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 int long long
using namespace std;
int n,t,f,ans;
double a[200001];
map<pair<int,int>,int> m;
signed main()
{
	scanf("%lld",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%lf",&a[i]);
		int b=round(a[i]*1000000000);
		t=f=-9;
		while(b%2==0)
		{
			b/=2;
			t++;
		}
		while(b%5==0)
		{
			b/=5;
			f++;
		}
		m[make_pair(t,f)]++;
	}
	for(auto i:m)
		for(auto l:m)
			if(i.first.first+l.first.first>=0&&i.first.second+l.first.second>=0)
			{
				if(i==l)
					ans+=i.second*(i.second-1)/2;
				if(i<l)
					ans+=i.second*l.second;
			}
	cout<<ans;
	return 0;
}
```