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: Time Limit Exceeded)

#include <algorithm>
#include <iostream>
#include <math.h>
#include <time.h>
#include <stdio.h>
#include <stdlib.h>
#include <string>
#include <string.h>
#include <stack>
#include <map>
#define maxn 200000 + 5
#define INF 0x3f3f3f3f
#define xin(a) scanf("%d", &a)
#define ffr(i,m, n) for (i = m; i < n; i++)
#define clr(a, b) memset(a, b, sizeof(a));
#define pi acos(-1,0)
typedef double db;
typedef long long ll;
using namespace std;
void t(void)
{
    int t, n;
    xin(t);
    while (t--)
    {

    }
}
void n(void)
{
    double sz[maxn]={ 0 };
    int n, i,d,j,sum=0;
    xin(n);
    ffr(i, 0, n)
    scanf("%lf", &sz[i]);
    sort(sz, sz+n);
    ffr(i,0,n)
    ffr(j,i+1,n)
    {
      if (!fmod(sz[i] * sz[j], 1)&&sz[i]!=sz[j]) {
        sum++;
      }
    }
    cout << sum << endl;
}
int main(void)
{
    #ifndef ONLINE_JUDGE
    long _begin_time = clock();
    freopen("in.txt", "r", stdin);
    freopen("out.txt", "w", stdout);
    #endif
    n();
    #ifndef ONLINE_JUDGE
    long _end_time = clock();
    printf("time = %ld ms\n", _end_time - _begin_time);
    fclose(stdin);
    fclose(stdout);
    #endif
    return 0;
}