#include <bits/stdc++.h>
#define sz(x) ((int)(x).size())
using namespace std;
typedef long long ll;
const int n = 5e5 + 5;

int N, M, K;

int C[20][20];


int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cin >> N;
	ll cc = 0;
	for(int i= 0; i < N; ++i){
		long double a; cin >> a;
		a*=1e9;
		ll x = a+0.5;
		//cerr << "x: " << x << endl;
		int c5 = 0, c2 = 0;
		while(x % 5 == 0) c5++, x /= 5;
		while(x % 2 == 0) c2++, x /= 2;
		c5 = min(c5, 18);
		c2 = min(c2, 18);
		//cerr << "c5, c2: " << c5 << " " << c2 << endl;
		for(int j = 18-c5; j <= 18; ++j){
			for(int k = 18-c2; k <= 18; ++k){
				cc += C[j][k];
			}
		}
		C[c5][c2]++;
	}
	cout << cc << endl;
	return 0;
}

### Prompt

Please create a solution in Cpp 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 sz(x) ((int)(x).size())
using namespace std;
typedef long long ll;
const int n = 5e5 + 5;

int N, M, K;

int C[20][20];


int main(){
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cin >> N;
	ll cc = 0;
	for(int i= 0; i < N; ++i){
		long double a; cin >> a;
		a*=1e9;
		ll x = a+0.5;
		//cerr << "x: " << x << endl;
		int c5 = 0, c2 = 0;
		while(x % 5 == 0) c5++, x /= 5;
		while(x % 2 == 0) c2++, x /= 2;
		c5 = min(c5, 18);
		c2 = min(c2, 18);
		//cerr << "c5, c2: " << c5 << " " << c2 << endl;
		for(int j = 18-c5; j <= 18; ++j){
			for(int k = 18-c2; k <= 18; ++k){
				cc += C[j][k];
			}
		}
		C[c5][c2]++;
	}
	cout << cc << endl;
	return 0;
}

```