#include <iostream>
#include <map>
#include <cmath>
using namespace std;

int main() {
  int n; cin >> n;
  map<pair<int, int>, int> mp;
  long long ans = 0;
  for(int i = 0; i < n; i++) {
    double num; cin >> num;
    long long x = llround(num*1e9);

    int two = 0, five = 0;
    while(x % 2 == 0) two++, x /= 2;
    while(x % 5 == 0) five++, x /= 5;
    for(auto p: mp) {
      if(p.first.first+two >= 18 && p.first.second+five >= 18) ans += p.second;
    }
    mp[make_pair(two, five)]++;
  }
  cout << ans << endl;
  return 0;
}

### 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 <iostream>
#include <map>
#include <cmath>
using namespace std;

int main() {
  int n; cin >> n;
  map<pair<int, int>, int> mp;
  long long ans = 0;
  for(int i = 0; i < n; i++) {
    double num; cin >> num;
    long long x = llround(num*1e9);

    int two = 0, five = 0;
    while(x % 2 == 0) two++, x /= 2;
    while(x % 5 == 0) five++, x /= 5;
    for(auto p: mp) {
      if(p.first.first+two >= 18 && p.first.second+five >= 18) ans += p.second;
    }
    mp[make_pair(two, five)]++;
  }
  cout << ans << endl;
  return 0;
}

```