#include <bits/stdc++.h>
using namespace std;

#define MAXN 200010

int n,a[20][20];
char s[100];
long long ans;

void add()
{
	int m=strlen(s+1),point=0,d=0;
	long long val=0;
	for(int i=1;i<=m;++i)
	{
		if(s[i]=='.')
		{
			point=1;
			continue;
		}
		val=val*10+s[i]-'0';
		if(point)++d;
	}
	while(d<9)val*=10,++d;
	int cntx=0,cnty=0;
	while(cntx<18 && val%2==0)++cntx,val/=2;
	while(cnty<18 && val%5==0)++cnty,val/=5;
	for(int i=18-cntx;i<=18;++i)ans+=a[i][18-cnty];
	for(int i=cnty;i>=0;--i)++a[cntx][i];
}

int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;++i)
	{
		scanf("%s",s+1);
		add();
	}
	printf("%lld\n",ans);
}
### Prompt

Your task is to create 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;

#define MAXN 200010

int n,a[20][20];
char s[100];
long long ans;

void add()
{
	int m=strlen(s+1),point=0,d=0;
	long long val=0;
	for(int i=1;i<=m;++i)
	{
		if(s[i]=='.')
		{
			point=1;
			continue;
		}
		val=val*10+s[i]-'0';
		if(point)++d;
	}
	while(d<9)val*=10,++d;
	int cntx=0,cnty=0;
	while(cntx<18 && val%2==0)++cntx,val/=2;
	while(cnty<18 && val%5==0)++cnty,val/=5;
	for(int i=18-cntx;i<=18;++i)ans+=a[i][18-cnty];
	for(int i=cnty;i>=0;--i)++a[cntx][i];
}

int main()
{
	scanf("%d",&n);
	for(int i=1;i<=n;++i)
	{
		scanf("%s",s+1);
		add();
	}
	printf("%lld\n",ans);
}
```