#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int N=200001;
int n,c2[N],c5[N],sum[101][101];
int lowbit(int x){return x&(-x);}
void insert(int x,int y){for(;x<=100;x+=lowbit(x))for(int t=y;t<=100;t+=lowbit(t))sum[x][t]++;}
int query(int x,int y){
	if(x<=0||y<=0)return 0;
	int ans=0;
	for(;x;x-=lowbit(x))for(int t=y;t;t-=lowbit(t))ans+=sum[x][t];
	return ans;
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		double x;
		scanf("%lf",&x);
		ll t=x*1e9+0.5;
		while(t%2==0){c2[i]++;t/=2;}
		while(t%5==0){c5[i]++;t/=5;}
	}
	ll ans=0;
	for(int i=1;i<=n;i++){
		ans+=i-1-query(100,18-c5[i])-query(18-c2[i],100)+query(18-c2[i],18-c5[i]);
		insert(c2[i]+1,c5[i]+1);
	}
	printf("%lld\n",ans);
}
### Prompt

Please create a solution in CPP 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;
const int N=200001;
int n,c2[N],c5[N],sum[101][101];
int lowbit(int x){return x&(-x);}
void insert(int x,int y){for(;x<=100;x+=lowbit(x))for(int t=y;t<=100;t+=lowbit(t))sum[x][t]++;}
int query(int x,int y){
	if(x<=0||y<=0)return 0;
	int ans=0;
	for(;x;x-=lowbit(x))for(int t=y;t;t-=lowbit(t))ans+=sum[x][t];
	return ans;
}
int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		double x;
		scanf("%lf",&x);
		ll t=x*1e9+0.5;
		while(t%2==0){c2[i]++;t/=2;}
		while(t%5==0){c5[i]++;t/=5;}
	}
	ll ans=0;
	for(int i=1;i<=n;i++){
		ans+=i-1-query(100,18-c5[i])-query(18-c2[i],100)+query(18-c2[i],18-c5[i]);
		insert(c2[i]+1,c5[i]+1);
	}
	printf("%lld\n",ans);
}
```