#include <bits/stdc++.h>
using namespace std;
using ll = long long;

int main(){
  int n;
  cin >> n;
  vector<vector<int>> TandF(100,vector<int>(100,0));
  string s;
  for(int i=0; i<n; ++i){
    cin >> s;
    ll num = 0, keta = 0;
    bool frag = false;
    for(int j=0; j<(s.size()); ++j){
      if(s[j] == '.'){frag = true; continue;}
      if(frag) ++keta;
      num = num*10 + (s[j]-'0');
    }
    int two = 0, five = 0;
    while(num%2 == 0){
      num /= 2;
      ++two;
    }
    while(num%5 == 0){
      num /= 5;
      ++five;
    }
    if(25 +two -keta < 0)continue;
    if(25 +five -keta < 0)continue;
    ++TandF[25 +two -keta][25 +five -keta];
  }
  ll ans = 0;
  for(int i1=0; i1<51; ++i1) for(int i2=0; i2<51; ++i2){
    for(int j1=50-i1; j1<51; ++j1) for(int j2=50-i2; j2<51; ++j2){
      ans += (ll)TandF[i1][i2] * TandF[j1][j2];
      if(i1 == j1 && i2 == j2) ans -= TandF[i1][i2];
    }
  }
  ans /= 2;
  cout << ans << endl;
}
### Prompt

Your challenge is to write 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;
using ll = long long;

int main(){
  int n;
  cin >> n;
  vector<vector<int>> TandF(100,vector<int>(100,0));
  string s;
  for(int i=0; i<n; ++i){
    cin >> s;
    ll num = 0, keta = 0;
    bool frag = false;
    for(int j=0; j<(s.size()); ++j){
      if(s[j] == '.'){frag = true; continue;}
      if(frag) ++keta;
      num = num*10 + (s[j]-'0');
    }
    int two = 0, five = 0;
    while(num%2 == 0){
      num /= 2;
      ++two;
    }
    while(num%5 == 0){
      num /= 5;
      ++five;
    }
    if(25 +two -keta < 0)continue;
    if(25 +five -keta < 0)continue;
    ++TandF[25 +two -keta][25 +five -keta];
  }
  ll ans = 0;
  for(int i1=0; i1<51; ++i1) for(int i2=0; i2<51; ++i2){
    for(int j1=50-i1; j1<51; ++j1) for(int j2=50-i2; j2<51; ++j2){
      ans += (ll)TandF[i1][i2] * TandF[j1][j2];
      if(i1 == j1 && i2 == j2) ans -= TandF[i1][i2];
    }
  }
  ans /= 2;
  cout << ans << endl;
}
```