#include<bits/stdc++.h>
#define ll long long
#define ull unsigned ll
#define uint unsigned
#define pii pair<int,int>
#define pll pair<ll,ll>
#define IT iterator
#define PB push_back
#define fi first
#define se second
#define For(i,j,k) for (int i=(int)(j);i<=(int)(k);i++)
#define Rep(i,j,k) for (int i=(int)(j);i>=(int)(k);i--)
#define CLR(a,v) memset(a,v,sizeof(a));
#define CPY(a,b) memcpy(a,b,sizeof(a));
#define debug puts("wzpakking")
#define y1 ysghysgsygsh
using namespace std;
int n;
int a[55][55];
ll ans;
int main(){
	scanf("%d",&n);
	For(i,1,n){
		long double x;
		scanf("%Lf",&x);
		ll y=(ll)(x*1e9+1e-3);
		int s1=0,s2=0;
		for (;y%2==0;y/=2,++s1);
		for (;y%5==0;y/=5,++s2);
		++a[s1][s2];
	}
	For(i,0,50) For(j,0,30)
		For(k,0,50) For(l,0,30)
			if (i+k>=18&&j+l>=18&&pii(i,j)<=pii(k,l))
				if (i!=k||j!=l) ans+=1ll*a[i][j]*a[k][l];
				else ans+=1ll*a[i][j]*(a[i][j]-1)/2;
	cout<<ans<<endl;
}
### 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>
#define ll long long
#define ull unsigned ll
#define uint unsigned
#define pii pair<int,int>
#define pll pair<ll,ll>
#define IT iterator
#define PB push_back
#define fi first
#define se second
#define For(i,j,k) for (int i=(int)(j);i<=(int)(k);i++)
#define Rep(i,j,k) for (int i=(int)(j);i>=(int)(k);i--)
#define CLR(a,v) memset(a,v,sizeof(a));
#define CPY(a,b) memcpy(a,b,sizeof(a));
#define debug puts("wzpakking")
#define y1 ysghysgsygsh
using namespace std;
int n;
int a[55][55];
ll ans;
int main(){
	scanf("%d",&n);
	For(i,1,n){
		long double x;
		scanf("%Lf",&x);
		ll y=(ll)(x*1e9+1e-3);
		int s1=0,s2=0;
		for (;y%2==0;y/=2,++s1);
		for (;y%5==0;y/=5,++s2);
		++a[s1][s2];
	}
	For(i,0,50) For(j,0,30)
		For(k,0,50) For(l,0,30)
			if (i+k>=18&&j+l>=18&&pii(i,j)<=pii(k,l))
				if (i!=k||j!=l) ans+=1ll*a[i][j]*a[k][l];
				else ans+=1ll*a[i][j]*(a[i][j]-1)/2;
	cout<<ans<<endl;
}
```