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: Wrong Answer)

#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef double db;

#define dbg(x) cout<<#x<<" is "<<x<<endl

const int maxn = (int) 2e5 + 9;

ll c5[maxn];
ll c2[maxn];
int n;
ll cc[40][40];
char s[maxn];

ll rint() {
    scanf("%s", s);
//    dbg(s);
    int l = strlen(s);
    int fl = -1;
    for (int i = 0; i < l; i++) {
        if (s[i] == '.') {
            fl = i;
            break;
        }
    }
    ll ans = 0;
    for (int i = 0; i < fl; i++) {
        ans = ans * 10 + s[i] - '0';
    }
//    dbg(ans);
    ll tmp = 0;
    for (int i = fl + 1; i < l; i++) {
        tmp = tmp * 10 + s[i] - '0';
    }
    if (fl > 0) {
        for (int i = 0; i < 9 - (l - fl - 1); i++) {
            tmp *= 10;
        }
        ans = ans * 1000000000 + tmp;
    } else {
        ans = tmp * 1000000000;
    }
    return ans;
}

void init() {
    scanf("%d", &n);
    for (int i = 0; i < n; i++) {
        ll tmp = rint();
//        dbg(tmp);
        while (tmp % 2 == 0) {
            c2[i]++;
            tmp /= 2;
        }
        while (tmp % 5 == 0) {
            c5[i]++;
            tmp /= 5;
        }
    }
}

void pt() {
    for (int i = 0; i < 20; i++) {
        for (int j = 0; j < 20; j++) {
            printf("%lld ", cc[i][j]);
        }
        cout << endl;
    }
}

int main() {
    memset(c2, 0, sizeof(c2));
    memset(c5, 0, sizeof(c5));
    memset(cc, 0, sizeof(cc));
    init();
    ll ans = 0;
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < 30; j++) {
            for (int k = 0; k < 30; k++) {
                if (c2[i] + j >= 18 && c5[i] + k >= 18) {
//                    if (cc[j][k] > 0) {
//                        printf("%d %d %d %lld %lld %lld\n", i, j, k, c2[i], c5[i], cc[j][k]);
//                    }
                    ans += cc[j][k];
                }
            }
        }
        cc[c2[i]][c5[i]]++;
    }
    printf("%lld\n", ans);
    return 0;
}