Problem:
Score : 300 points

Problem Statement

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).

Sample Input 1

5
7.5
2.4
17.000000001
17
16.000000000

Sample Output 1

3

There are 3 pairs with integer product:

7.5 \cdot 2.4 = 18

7.5 \cdot 16 = 120

17 \cdot 16 = 272

Sample Input 2

11
0.9
1
1
1.25
2.30000
5
70
0.000000001
9999.999999999
0.999999999
1.000000001

Sample Output 2

8

Solution in C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
#define REP(i,n) for (ll i = 0; i < (n); ++i)
#define RREP(i, n) for (ll i = (n) - 1; i >= 0; --i)
#define ALL(v) (v).begin(), (v).end()
template<class T>
using reverse_priority_queue = priority_queue<T, vector<T>, greater<T>>;


int main(){
    ll n;
    cin >> n;

    map<pair<ll, ll>, ll> count;
    REP(i, n){
        double ai;
        cin >> ai;
        ll bi = static_cast<ll>((ai * 1000000000) + 0.5);
        ll n2 = 0;
        while(bi % 2 == 0){
            n2++;
            bi /= 2;
        }
        ll n5 = 0;
        while(bi % 5 == 0){
            n5++;
            bi /= 5;
        }
        count[make_pair(n2, n5)]++;
    }

    ll ans = 0;
    for(auto it = count.begin(); it != count.end(); ++it){
        for(auto jt = count.begin(); jt != count.end(); ++jt){
            if(it->first.first + jt->first.first >= 18 &&
               it->first.second + jt->first.second >= 18){
                if(it != jt){
                    ans += it->second * jt->second;
                }else{
                    ans += it->second * (it->second - 1);
                }
            }
        }
    }
    ans /= 2;
    cout << ans << endl;
    return 0;
}