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: Accepted)

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

class Program
{
    static void Main(string[] args)
    {
        var n = int.Parse(Console.ReadLine());
        var a = Enumerable.Range(0, n).Select(x => Console.ReadLine()).ToArray();

        var map = new Dictionary<(int c2, int c5, int d), int>();
        foreach (var a1 in a)
        {
            var value = (c2: 0, c5: 0, d: 0);
            var index = a1.IndexOf(".");
            if (index >= 0)
            {
                value.d = a1.Length - index - 1;
            }
            var number = decimal.Parse(a1.Replace(".", ""));
            while (number % 2 == 0) {
                value.c2++;
                number /= 2;
            }
            while (number % 5 == 0)
            {
                value.c5++;
                number /= 5;
            }
            if (!map.ContainsKey(value)) {
                map.Add(value, 0);
            }
            map[value]++;
        }

        var count = 0L;
        foreach (var item1 in map.Keys)
        {
            if (Math.Min(item1.c2, item1.c5) >= item1.d)
            {
                count += (long)map[item1] * (map[item1] - 1) / 2;
            }
        }
        foreach (var item1 in map.Keys)
        {
            foreach (var item2 in map.Keys)
            {
                if (map.Keys.ToList().IndexOf(item1) < map.Keys.ToList().IndexOf(item2))
                {
                    if (Math.Min(item1.c2 + item2.c2, item1.c5 + item2.c5) >= item1.d + item2.d)
                    {
                        count += (long)map[item1] * map[item2];
                    }
                }
            }
        }

        Console.WriteLine($"{count}");
        Console.ReadLine();
    }
}