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 <stdio.h>
#include <stdlib.h>
#include <ctype.h>
#include <string.h>
#include <math.h>
int main(int argc, char *argv[]){
        long long N = 0;
        double *A;
        scanf("%lld\n", &N);
        A = (double *)malloc(N * sizeof(double));
        long long a = 0;
        for(;a < N; a++){
                scanf("%lf",&A[a]);
                A[a] *= 10000;

        }
        int i = 0;
        int j;
        long long c = 0;
        double utmp, ltmp;
        for(i = 0; i < N; i++){
                for(j = i+1; j <= N; j++){
                        utmp = ceil(A[i] * A[j] / 100000000);
                        ltmp = floor(A[i] * A[j] / 100000000);
                        if(utmp == ltmp && utmp != 0 && ltmp != 0){

                                c++;
                        }
                }
        }
        printf("%lld\n", c);
        return 0;
}