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 <math.h>

int main(void){
    int num, count=0;
    scanf("%d", &num);

    double array[num], temp;

    for(int i=0; i<num; i++){
        scanf("%lf", &array[i]);
    }

    for(int i=0; i<num; i++){
        if(ceil(array[i]*10000) == floor(array[i]*10000)){
            for(int j=i+1; j<num; j++){
                if(ceil(array[j]*10000) == floor(array[j]*10000)){
                    temp = array[i] * array[j];
                    if(ceil(temp) == floor(temp)) count ++;
                }
            }
        }
    }

    printf("%d\n", count);

    return 0;
}