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

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

const int MAXN = 2e5;

int N;
ll ans, cnt[60][50];

int main()
{
	scanf("%d", &N);
	for(int i=1; i<=N; i++)
	{
		double x;
		cin>>x;
		ll t=llround(x*1000000000);
		int p=0, q=0;
		for(ll k=2; t%k==0; k*=2, p++);
		for(ll k=5; t%k==0; k*=5, q++);

		assert(p<=50 && q<=20);
		for(int j=0; j<=50; j++) for(int k=0; k<=20; k++) if(j+p>=18 && k+q>=18) ans+=cnt[j][k];
		cnt[p][q]++;
	}

	printf("%lld\n", ans);
}
### 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>
using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

const int MAXN = 2e5;

int N;
ll ans, cnt[60][50];

int main()
{
	scanf("%d", &N);
	for(int i=1; i<=N; i++)
	{
		double x;
		cin>>x;
		ll t=llround(x*1000000000);
		int p=0, q=0;
		for(ll k=2; t%k==0; k*=2, p++);
		for(ll k=5; t%k==0; k*=5, q++);

		assert(p<=50 && q<=20);
		for(int j=0; j<=50; j++) for(int k=0; k<=20; k++) if(j+p>=18 && k+q>=18) ans+=cnt[j][k];
		cnt[p][q]++;
	}

	printf("%lld\n", ans);
}
```