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: Wrong Answer)

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


public class HelloWorld
{
    static public void Main()
    {
        var TwoFive = new long[19, 19];
        var N = long.Parse(Console.ReadLine());
        //var inp = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        for (int i = 0; i < N; i++)
        {
            var tmp = double.Parse(Console.ReadLine());
            tmp *= 1000000000;
            var A = (long)tmp;
            var Two = 0;
            var Five = 0;
            while (A%2 == 0)
            {
                A /= 2;
                Two++;
            }

            while (A % 5 == 0)
            {
                A /= 5;
                Five++;
            }
            TwoFive[Math.Min(Two,18), Math.Min(Five, 18)]++;
        }
        long ans = 0;
        for (int i = 0; i < 19; i++)
        {
            for (int j = 0; j < 19; j++)
            {
                for (int k = 18 - i; k < 19; k++)
                {
                    for (int l = 18 - j; l < 19; l++)
                    {
                        if (TwoFive[i, j] > 0 && TwoFive[k, l] > 0 && ((i + k) >= 18) && ((j + l) >= 18))
                        {
                            if((i == k) && (j == l))
                            {
                                ans += TwoFive[i, j] * (TwoFive[k, l] - 1);
                            }
                            else {
                                ans += TwoFive[i, j] * TwoFive[k, l];
                            }
                        }
                    }
                }
            }
        }
        Console.WriteLine(ans/2);
    }
}