#include <bits/stdc++.h>
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++) {
    long double a;
    int tmp2 = 0;
    int tmp5 = 0;
    cin >> a;
    long long b = a * 1e9 + 0.5;
    while (b % 2 == 0) {
      tmp2++;
      b /= 2;
    }
    while (b % 5 == 0) {
      tmp5++;
      b /= 5;
    }

    for (const auto& [key, value] : mp) {
      if (key.first + tmp2 >= 18 && key.second + tmp5 >= 18) ans += value;
    }
    mp[{tmp2, tmp5}]++;
  }
  cout << ans << endl;
}

### 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>
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++) {
    long double a;
    int tmp2 = 0;
    int tmp5 = 0;
    cin >> a;
    long long b = a * 1e9 + 0.5;
    while (b % 2 == 0) {
      tmp2++;
      b /= 2;
    }
    while (b % 5 == 0) {
      tmp5++;
      b /= 5;
    }

    for (const auto& [key, value] : mp) {
      if (key.first + tmp2 >= 18 && key.second + tmp5 >= 18) ans += value;
    }
    mp[{tmp2, tmp5}]++;
  }
  cout << ans << endl;
}

```