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: Runtime Error)

#include <bits/stdc++.h>

#define M_PI       3.14159265358979323846   // pi

using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef vector<ll> VI;
typedef pair<ll, ll> P;
typedef tuple<ll, ll, ll> t3;
typedef tuple<ll, ll, ll, ll> t4;
typedef tuple<ll, ll, ll, ll, ll> t5;

#define rep(a,n) for(ll a = 0;a < n;a++)
#define repi(a,b,n) for(ll a = b;a < n;a++)

using namespace std;

static const ll INF = 1e15;


int main() {
    int n;
    cin >> n;
    vector<vector<ll>> grid(27, vector<ll>(27, 0));
    vector<P> ss(n);
    rep(i, n) {
        double item;
        cin >> item;
        double t = item * 1e9 + 0.1;
        ll v = (ll)t;
        int a = 0;
        while(v % 2 == 0) {
            a++;
            v /= 2;
        }
        int b = 0;
        while (v % 5 == 0) {
            b++;
            v /= 5;
        }
        grid[min(26, a)][min(26,b)]++;
        ss[i] = make_pair(a, b);
    }

    ll sum = 0;
    rep(i, n) {
        auto f = ss[i].first;
        auto s = ss[i].second;
        grid[f][s]--;
        for (auto f2 = max(0LL, 18 - f); f2 < 27; f2++) {
            for (auto s2 = max(0LL, 18 - s); s2 < 27; s2++) {
                sum += grid[f2][s2];
            }
        }
    }

    cout << sum << endl;
    return 0;
}