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: Runtime Error)

#include<stdio.h>
#include<math.h>
#define rep(i,N) for(int i=0;i<(int)N;i++)
long double deca=10000000000,D=deca*deca;
int main(void)
{
  int count=0,N;count=scanf("%d",&N);
  long double A[200000];
  rep(i,N){count=scanf("%Lf",&A[i]);}count=0;
  rep(i,N-1)rep(j,N)
  {
    if(fmod(A[i]*A[i+j+1],1.0000000000000)==0&&A[i]*A[i+j+1]>0.0){count++;}
  }
  return printf("%d\n",count),0;
}