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>
#define rep(i, x, y) for (int i = x; i <= y; i++)
using namespace std;

const int N = 2e5 + 10;
typedef long long ll;
typedef pair<int, int> pii;
ll n, mp[105][105], tmp, pw[20];
string s[N];
double x;

int main() {
    cin >> n;
    ll ans = 0;
    pw[0] = 1;
    rep(i, 1, 18) pw[i] = pw[i - 1] * 10;
    rep(i,1,n) {
        cin>>s[i];
        // printf("%d\n",i );
        int pos = -1;
        tmp = 0;
        rep(j,0,(int)s[i].size() - 1) if(s[i][j] == '.') pos = j;
        if(pos == -1) pos = s[i].size();
        rep(j,0,pos - 1) tmp += (s[i][j] - '0') * pw[pos + 8 - j];
        rep(j,pos+1,(int)s[i].size() - 1) tmp += (s[i][j] - '0') * pw[9 - (j - pos)];
        int cnt2 = 0, cnt5 = 0;
        while (tmp % 2 == 0) ++cnt2, tmp /= 2;
        while (tmp % 5 == 0) ++cnt5, tmp /= 5;
        if (cnt2 >= 9 && cnt5 >= 9) ans--;
        ++mp[cnt2][cnt5];
    }
    rep(i, 0, 64) {
        rep(j, 0, 64) {
            rep(k, max(18 - i, 0), 64) {
                rep(l, max(18 - j, 0), 64) {
                    ans += mp[i][j] * mp[k][l];
                }
            }
        }
    }
    printf("%lld\n", ans / 2);
    return 0;
}