#include<bits/stdc++.h>
using namespace std;
typedef int64_t ll;

int n,b,c,cnt[19][19];
ll aa,ans;
long double a;

int main(){
  cin>>n;
  for(int i=0;i<n;i++){
    b=0;c=0;
    cin>>a;
    aa=a*1e9+0.5;
    while(aa%2==0){
      aa/=2;
      b++;
    }
    b=min(b,18);
    while(aa%5==0){
      aa/=5;
      c++;
    }
    c=min(c,18);
    for(int j=18;j>=18-b;j--)for(int k=18;k>=18-c;k--)ans+=cnt[j][k];
    cnt[b][c]++;
  }
  cout<<ans<<endl;
}

### Prompt

Develop a solution in Cpp 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<bits/stdc++.h>
using namespace std;
typedef int64_t ll;

int n,b,c,cnt[19][19];
ll aa,ans;
long double a;

int main(){
  cin>>n;
  for(int i=0;i<n;i++){
    b=0;c=0;
    cin>>a;
    aa=a*1e9+0.5;
    while(aa%2==0){
      aa/=2;
      b++;
    }
    b=min(b,18);
    while(aa%5==0){
      aa/=5;
      c++;
    }
    c=min(c,18);
    for(int j=18;j>=18-b;j--)for(int k=18;k>=18-c;k--)ans+=cnt[j][k];
    cnt[b][c]++;
  }
  cout<<ans<<endl;
}

```