#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
int main() {
	int N;
	cin >> N;
	vector<vector<int>> a(20, vector<int>(20));
	ll ans = 0;
	for (int i = 0; i < N; ++ i) {
		double x;
		cin >> x;
		auto y = (ll)(x * 1e9 + 0.5);
		int n2 = 0, n5 = 0;
		while (n2 < 18 && y % 2 == 0) {
			++ n2;
			y /= 2;
		}
		while (n5 < 18 && y % 5 == 0) {
			++ n5;
			y /= 5;
		}
		ans += a[18-n2][18-n5];
		for (int i = 0; i <= n2; ++ i) for (int j = 0; j <= n5; ++ j) {
			++ a[i][j];
		}
	}
	cout << ans << endl;
}

### Prompt

Please formulate 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;
int main() {
	int N;
	cin >> N;
	vector<vector<int>> a(20, vector<int>(20));
	ll ans = 0;
	for (int i = 0; i < N; ++ i) {
		double x;
		cin >> x;
		auto y = (ll)(x * 1e9 + 0.5);
		int n2 = 0, n5 = 0;
		while (n2 < 18 && y % 2 == 0) {
			++ n2;
			y /= 2;
		}
		while (n5 < 18 && y % 5 == 0) {
			++ n5;
			y /= 5;
		}
		ans += a[18-n2][18-n5];
		for (int i = 0; i <= n2; ++ i) for (int j = 0; j <= n5; ++ j) {
			++ a[i][j];
		}
	}
	cout << ans << endl;
}

```