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 <stdio.h>
#include <stdlib.h>
#include <math.h>

int main(void) {
	int n;
	scanf("%d",&n);
	double a[n];
	for(int i=0;i<n;i++){
		scanf("%lf",&a[i]);
		a[i] *= 1000;
		//printf(":%lf\n",a[i]);
	}
	int count=0;
	for(int i=0;i<n;i++){
		for(int j=i+1;j<n;j++){
			if(fmod(a[i],1000)==0.00 && fmod(a[j],1000)==0.00){
				count++;
			}
			else{
				double test = (a[i]*a[j]);
				if(ceil(test)== floor(test) && fmod(test,1000000)==0.0000) {
					//printf("a[%d]*a[%d]:%lf*%lf=%lf\n",i,j,a[i],a[j],test);
					count++;
				}
			}
		}
	}
	printf("%d\n",count);
	return 0;
}