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 (Clang 10.0.0) (judge verdict: Runtime Error)

#include <stdio.h>
#include <math.h>
int main(void)
{
int n,i;
int count=0;
double a[100],num[100];
scanf("%d",&n);
for(i=0;i<n;i++){
  scanf("%lf",&a[i]);
  }
for(i=0;i<n;i++){
    num[i]=a[i]*a[i+1];
  }
    if(ceil(num[i]) != floor(num[i]))
       count++;
       printf("%d",count);
       return 0;
       }