#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for(register int i = a; i <= b; i++)
#define per(i, a, b) for(register int i = a; i >= b; i--)
typedef long long LL;
const LL mod = 1e9 + 7;
const int N = 3e5 + 5;

double x;
LL s, ans, maxn = 1e10;
int n, cnt[505][505];

int main() {
	cin>>n;
	rep(i, 1, n) {
		cin>>x;
		s = (long long) (x*maxn + 0.5);
		int a = 0, b = 0;
		while(s%2 == 0) s /= 2, a++;
		while(s%5 == 0) s /= 5, b++;
		a = min(a, 20), b = min(b, 20);
		ans += cnt[20 - a][20 - b];
		rep(j, 0, a)
		    rep(k, 0, b)
		        cnt[j][k]++;
	}
	cout<<ans<<endl;
}
### Prompt

Please provide a CPP coded solution to the problem described below:

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 rep(i, a, b) for(register int i = a; i <= b; i++)
#define per(i, a, b) for(register int i = a; i >= b; i--)
typedef long long LL;
const LL mod = 1e9 + 7;
const int N = 3e5 + 5;

double x;
LL s, ans, maxn = 1e10;
int n, cnt[505][505];

int main() {
	cin>>n;
	rep(i, 1, n) {
		cin>>x;
		s = (long long) (x*maxn + 0.5);
		int a = 0, b = 0;
		while(s%2 == 0) s /= 2, a++;
		while(s%5 == 0) s /= 5, b++;
		a = min(a, 20), b = min(b, 20);
		ans += cnt[20 - a][20 - b];
		rep(j, 0, a)
		    rep(k, 0, b)
		        cnt[j][k]++;
	}
	cout<<ans<<endl;
}
```