#include<bits/stdc++.h>
#define ll long long
#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define pii pair<int,int>
using namespace std;
const int N=2e5+10;
const ll M=1e9;
double a[N];
ll num[22][22],ans=0;
int main()
{
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%lf",&a[i]);
		ll t=a[i]*M+0.1,cnt2=0,cnt5=0;
		while(t%2==0&&cnt2<=18)t/=2,cnt2++;
		while(t%5==0&&cnt5<=18)t/=5,cnt5++;
		int n2=max(0LL,18-cnt2),n5=max(0LL,18-cnt5);
		for(int j=n2;j<=20;j++)
		for(int k=n5;k<=20;k++)
		ans+=num[j][k];
		num[cnt2][cnt5]++;
	}
	printf("%lld\n",ans);

	return 0;
}

### 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 fi first
#define se second
#define mp make_pair
#define pb push_back
#define pii pair<int,int>
using namespace std;
const int N=2e5+10;
const ll M=1e9;
double a[N];
ll num[22][22],ans=0;
int main()
{
	int n;
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%lf",&a[i]);
		ll t=a[i]*M+0.1,cnt2=0,cnt5=0;
		while(t%2==0&&cnt2<=18)t/=2,cnt2++;
		while(t%5==0&&cnt5<=18)t/=5,cnt5++;
		int n2=max(0LL,18-cnt2),n5=max(0LL,18-cnt5);
		for(int j=n2;j<=20;j++)
		for(int k=n5;k<=20;k++)
		ans+=num[j][k];
		num[cnt2][cnt5]++;
	}
	printf("%lld\n",ans);

	return 0;
}

```