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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {
        var N = Decimal.Parse(Console.ReadLine());
        var A = new List<Decimal>();
        for (int n = 1; n <= N; n++)
        {
            A.Add(Decimal.Parse(Console.ReadLine()));
        }
        var count = 0;
        for (int i = 0; i < A.Count - 1; i++)
        {
            for (int j = i + 1; j < A.Count; j++)
            {
                var result = A[i] * A[j];
                if ((int)result == result)
                {
                    count++;
                }
            }
        }
        Console.WriteLine(count);
    }
}