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.Linq;
using System.Text;
using System;
using System.Collections;
using System.Collections.Generic;
using System.Globalization;
using System.IO;
using System.Security.Cryptography.X509Certificates;
using System.Diagnostics;
using System.Reflection.Metadata;
using System.Threading;

namespace AtCoder
{
    class Program
    {

        struct Point
        {
            public int left;
            public int right;

            public Point(int left, int right)
            {

                this.left = left;
                this.right = right;

            }

        }


        const int BiggestMod = 1000000007;

        public static void Main()
        {

            
            long ans = 0;
            int idx = int.Parse(Console.ReadLine());
            decimal[] data = new decimal[idx];

            for (int i = 0; i < idx; i++)
                data[i] = decimal.Parse(Console.ReadLine());

            for (int i = 0; i + 1 < idx; i++)
                for (int j = i + 1; j < idx; j++)
                {

                    var res = (data[i] * data[j]);
                    if ((res % 1) == decimal.Zero)
                        ans++;

                }

            Console.WriteLine(ans);

        }

    }

}