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

#define int long long
int dp[65][35],ans;
template<typename T>
void chmin(T &a,T b){
  if(a>b)a=b;
}

void F(string s){
  int two=0,five=0,now=0,a=0,f=0;
  while(now<s.size()){
    if(s[now]=='.')f=1;
    else{
      a*=10;
      a+=s[now]-'0';
      if(f)two--,five--;
    }
    now++;
  }
  while(a%2==0)a/=2,two++;
  while(a%5==0)a/=5,five++;
  for(int i=0;i<65;i++){
    for(int j=0;j<35;j++){
      if(two+i>=30&&five+j>=15)ans+=dp[i][j];
    }
  }
  chmin(two,32LL);
  chmin(five,15LL);
  dp[two+30][five+15]++;
}


signed main(){
  int n;cin>>n;
  int cnt=0;
  for(int i=0;i<n;i++){
    string s;cin>>s;
    F(s);
  }
  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;

#define int long long
int dp[65][35],ans;
template<typename T>
void chmin(T &a,T b){
  if(a>b)a=b;
}

void F(string s){
  int two=0,five=0,now=0,a=0,f=0;
  while(now<s.size()){
    if(s[now]=='.')f=1;
    else{
      a*=10;
      a+=s[now]-'0';
      if(f)two--,five--;
    }
    now++;
  }
  while(a%2==0)a/=2,two++;
  while(a%5==0)a/=5,five++;
  for(int i=0;i<65;i++){
    for(int j=0;j<35;j++){
      if(two+i>=30&&five+j>=15)ans+=dp[i][j];
    }
  }
  chmin(two,32LL);
  chmin(five,15LL);
  dp[two+30][five+15]++;
}


signed main(){
  int n;cin>>n;
  int cnt=0;
  for(int i=0;i<n;i++){
    string s;cin>>s;
    F(s);
  }
  cout<<ans<<endl;
}

```