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.CodeDom;
using System.Collections.Generic;
using System.Configuration;
using System.Diagnostics.CodeAnalysis;
using System.IO;
using System.Linq;
using System.Runtime.CompilerServices;
using System.Xml.Schema;

namespace AtCoder
{
    public static class Ex
    {
        public static List<string> FastSort(this List<string> s) { s.Sort(StringComparer.OrdinalIgnoreCase); return s.ToList(); }
        public static void yesno(this bool b) { Console.WriteLine(b ? "yes" : "no"); }
        public static void YesNo(this bool b) { Console.WriteLine(b ? "Yes" : "No"); }
        public static void YESNO(this bool b) { Console.WriteLine(b ? "YES" : "NO"); }

        public static int PopCount(this int bits)
        {
            bits = (bits & 0x55555555) + (bits >> 1 & 0x55555555);
            bits = (bits & 0x33333333) + (bits >> 2 & 0x33333333);
            bits = (bits & 0x0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f);
            bits = (bits & 0x00ff00ff) + (bits >> 8 & 0x00ff00ff);
            return (bits & 0x0000ffff) + (bits >> 16 & 0x0000ffff);
        }
    }

    partial class AtCoder
    {
        public string GetStr() { return Console.ReadLine().Trim(); }
        public char GetChar() { return Console.ReadLine().Trim()[0]; }
        public int GetInt() { return int.Parse(Console.ReadLine().Trim()); }
        public long GetLong() { return long.Parse(Console.ReadLine().Trim()); }
        public double GetDouble() { return double.Parse(Console.ReadLine().Trim()); }
        public string[] GetStrArray() { return Console.ReadLine().Trim().Split(' '); }
        public int[] GetIntArray() { return Console.ReadLine().Trim().Split(' ').Select(int.Parse).ToArray(); }
        public long[] GetLongArray() { return Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray(); }
        public char[] GetCharArray() { return Console.ReadLine().Trim().Split(' ').Select(char.Parse).ToArray(); }
        public double[] GetDoubleArray() { return Console.ReadLine().Trim().Split(' ').Select(double.Parse).ToArray(); }
        public T[][] CreateJaggedArray<T>(int H, int W, T value) { return Enumerable.Repeat(0, H).Select(s => Enumerable.Repeat(value, W).ToArray()).ToArray(); }
        public int[][] GetIntJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetIntArray().ToArray()).ToArray(); }
        public long[][] GetLongJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetLongArray().ToArray()).ToArray(); }
        public char[][] GetCharJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetStr().ToCharArray()).ToArray(); }
        public double[][] GetDoubleJaggedArray(int N) { return Enumerable.Repeat(0, N).Select(s => GetDoubleArray()).ToArray(); }

        Dictionary<int, List<int>> GetUnweightedAdjacencyList(int N, int M, bool isDirected, bool isNode_0indexed)
        {
            var dic = new Dictionary<int, List<int>>();
            foreach (var e in Enumerable.Range(0, N)) { dic.Add(e, new List<int>()); }
            for (int i = 0; i < M; i++)
            {
                var input = GetIntArray();
                var a = isNode_0indexed ? input[0] : input[0] - 1;
                var b = isNode_0indexed ? input[1] : input[1] - 1;
                dic[a].Add(b);
                if (isDirected == false) dic[b].Add(a);
            }
            return dic;
        }
        Dictionary<int, List<Edge>> GetWeightedAdjacencyList(int N, int M, bool isDirected, bool isNode_0indexed)
        {
            var dic = new Dictionary<int, List<Edge>>();
            foreach (var e in Enumerable.Range(0, N)) { dic.Add(e, new List<Edge>()); }
            for (int i = 0; i < M; i++)
            {
                var input = GetIntArray();
                var a = isNode_0indexed ? input[0] : input[0] - 1;
                var b = isNode_0indexed ? input[1] : input[1] - 1;
                var c = input[2];
                dic[a].Add(new Edge(b, c));
                if (isDirected == false) dic[b].Add(new Edge(a, c));
            }
            return dic;
        }

        bool eq<T, U>() => typeof(T).Equals(typeof(U));
        T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
        T cv<T>(string s) => eq<T, int>() ? ct<T, int>(int.Parse(s))
                           : eq<T, long>() ? ct<T, long>(long.Parse(s))
                           : eq<T, double>() ? ct<T, double>(double.Parse(s))
                           : eq<T, char>() ? ct<T, char>(s[0])
                                             : ct<T, string>(s);
        void Multi<T>(out T a) => a = cv<T>(GetStr());
        void Multi<T, U>(out T a, out U b)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]);
        }
        void Multi<T, U, V>(out T a, out U b, out V c)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]);
        }
        void Multi<T, U, V, W>(out T a, out U b, out V c, out W d)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]);
        }
        void Multi<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]);
        }
        void Multi<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f)
        {
            var ar = GetStrArray(); a = cv<T>(ar[0]); b = cv<U>(ar[1]); c = cv<V>(ar[2]); d = cv<W>(ar[3]); e = cv<X>(ar[4]); f = cv<Y>(ar[5]);
        }
    }

    class Pair : IComparable<Pair>
    {
        public Pair(int node, long cost)
        {
            Node = node; Cost = cost;
        }
        public int Node { get; set; }
        public long Cost { get; set; }
        public int CompareTo(Pair p)
        {
            return p.Cost > Cost ? 1 : -1;
        }
    }

    class Edge
    {
        public Edge(int to, long length)
        {
            To = to;
            Length = length;
        }
        public int To { get; set; }
        public long Length { get; set; }
    }

    class Comparable : IComparable<Comparable>
    {
        public Comparable(int value)
        {
            Value = value;
        }

        public int Value { get; set; }
        public int CompareTo(Comparable c)
        {
            var a = Math.Abs(Value);
            var b = Math.Abs(c.Value);
            return a > b ? 1 : a == b ? 0 : -1;
        }
    }

    class Comparer<T> : IComparer<T>
    {
        public int Compare(T t1, T t2)
        {
            return 1;
        }
    }



    partial class Program
    {
        static void Main()
        {
            Console.SetOut(new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false });
            new AtCoder().Solve();
            Console.Out.Flush();
            Console.Read();
        }
    }

    public partial class AtCoder
    {
        public void Solve()
        {
            int N = GetInt();
            var array = new long[50][];
            for (int i = 0; i < 50; i++) array[i] = new long[50];
            for (int i = 0; i < N; i++)
            {
                var a = GetStr();
                if (a.Contains(".") && a.Split('.')[1].Any(_ => _ != '0'))
                {
                    var seisu = long.Parse(a.Split('.')[0]);
                    var longa = long.Parse(a.Split('.')[1].PadRight(9, '0'));
                    longa = seisu *(long) Math.Pow(10, 9) + longa;
                    int b = 0;int c = 0;
                    var tmp = longa;
                    while (tmp % 2 == 0)
                    {
                        b++;
                        tmp /= 2;
                    }
                    tmp = longa;
                    while (tmp % 5 == 0)
                    {
                        c++;
                        tmp /= 5;
                    }
                    array[b][c]++;
                }
                else
                {
                    var inta = (int)Math.Ceiling(double.Parse(a));
                    int b = 9, c = 9;
                    var tmp = inta;
                    while (tmp % 2 == 0)
                    {
                        b++;
                        tmp /= 2;
                    }
                    tmp = inta;
                    while (tmp % 5 == 0)
                    {
                        c++;
                        tmp /= 5;
                    }
                    array[b][c]++;
                }
            }
            long sum = 0;
            for (int i = 0; i < 50; i++)
            {
                for (int j = 0; j < 50; j++)
                {
                    for (int k = 0; k < 50; k++)
                    {
                        for (int l = 0; l < 50; l++)
                        {
                            if (i + j >= 18 && k + l >= 18)
                            {
                                sum += i == j && k == l ? array[i][k] * (array[j][l] - 1) : array[i][k] * array[j][l];
                            }
                        }
                    }
                }
            }
            Console.WriteLine(sum / 2);
        }
    }
}