#include<bits/stdc++.h>
using namespace std;
const int maxn=1e5+5;
const int inf=0x3f3f3f3f;
int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    //freopen(".in","r",stdin);
    //freopen(".out","w",stdout);
    int n;
    cin>>n;
    map<pair<int,int>,int> cnt;
    for(int i=1;i<=n;i++)
    {
    	double a;
    	cin>>a;
    	long long val=(long long)(a*1000000000.0+0.5);
    	long long cnt2=0,cnt5=0;
    	while(val%2==0)
    	{
    		cnt2++;
    		val/=2;
		}
		while(val%5==0)
		{
			cnt5++;
			val/=5;
		}
		cnt[make_pair(cnt2,cnt5)]++;
	}
	long long ans=0;
	for(const auto &pi:cnt) 
	{
        for(const auto &pj: cnt)  
		{
			if(pi.first.first+pj.first.first>=18&&pi.first.second+pj.first.second>=18)
			{
				if(pi==pj)
					ans+=pi.second*(pi.second-1ll);
				else
					ans+=pi.second*1ll*pj.second;
			}
		}
	}
	cout<<ans/2<<endl;
	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>
using namespace std;
const int maxn=1e5+5;
const int inf=0x3f3f3f3f;
int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    //freopen(".in","r",stdin);
    //freopen(".out","w",stdout);
    int n;
    cin>>n;
    map<pair<int,int>,int> cnt;
    for(int i=1;i<=n;i++)
    {
    	double a;
    	cin>>a;
    	long long val=(long long)(a*1000000000.0+0.5);
    	long long cnt2=0,cnt5=0;
    	while(val%2==0)
    	{
    		cnt2++;
    		val/=2;
		}
		while(val%5==0)
		{
			cnt5++;
			val/=5;
		}
		cnt[make_pair(cnt2,cnt5)]++;
	}
	long long ans=0;
	for(const auto &pi:cnt) 
	{
        for(const auto &pj: cnt)  
		{
			if(pi.first.first+pj.first.first>=18&&pi.first.second+pj.first.second>=18)
			{
				if(pi==pj)
					ans+=pi.second*(pi.second-1ll);
				else
					ans+=pi.second*1ll*pj.second;
			}
		}
	}
	cout<<ans/2<<endl;
	return 0;
}

```