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;
using System.Text;
using System.Text.RegularExpressions;
using static System.Console;
using static System.Math;
using static MyIO;
using static MyUtil;

public class A { public static void Main() => (new Solver()).Solve(); }

public class Solver
{
	public void Solve()
	{
		long N = GetLong();
		var A = new long[N];
		for(long i = 0; i < N; i++)
		{
			var args = GetString().Split('.');
			var prefix = args[0];
			var suffix = (args.Length == 1) ? "" : args[1];
			A[i] = long.Parse(prefix + suffix + new String('0', 9 - suffix.Length));
		}

		var cnt = new long[19, 19];
		var t = new long[N];
		var f = new long[N];
		long dup = 0;
		for(long i = 0; i < N; i++)
		{
			long rest = A[i];
			while(rest % 2 == 0)
			{
				t[i]++;
				rest /= 2;
			}
			while(rest % 5 == 0)
			{
				f[i]++;
				rest /= 5;
			}
			cnt[Min(18, t[i]), Min(18, f[i])]++;
			if(t[i] >= 9 && f[i] >= 9)
				dup++;
		}

		var csum = new long[20, 20];
		for(long i = 0; i < 19; i++)
		{
			for(long j = 0; j < 19; j++)
				csum[i + 1, j + 1] = csum[i + 1, j] + cnt[i, j];
		}
		for(long i = 0; i < 19; i++)
		{
			for(long j = 0; j < 19; j++)
				csum[i + 1, j + 1] += csum[i, j + 1];
		}

		long sum = 0;
		for(long i = 0; i < N; i++)
		{
			long X = Max(0, 18 - t[i]);
			long Y = Max(0, 18 - f[i]);
			sum += csum[19, 19] - csum[X, 19] - csum[19, Y] + csum[X, Y];
		}
		WriteLine((sum - dup) / 2);
	}
}

public static class MyIO
{
	private static string[] args = new string[0];
	private static int cnt = 0;
	private static IEnumerable<string> getArgs(long N) => Range(0, N).Select(_ => getArg());
	private static string getArg()
	{
		if(cnt == args.Length) { args = Console.ReadLine().Split(); cnt = 0; }
		return args[cnt++];
	}

	public static int GetInt() => int.Parse(getArg());
	public static long GetLong() => long.Parse(getArg());
	public static double GetDouble() => double.Parse(getArg());
	public static decimal GetDecimal() => decimal.Parse(getArg());
	public static string GetString() => getArg();
	public static char GetChar() => getArg()[0];
	public static int[] GetInts(long N) => getArgs(N).Select(int.Parse).ToArray();
	public static long[] GetLongs(long N) => getArgs(N).Select(long.Parse).ToArray();
	public static double[] GetDoubles(long N) => getArgs(N).Select(double.Parse).ToArray();
	public static decimal[] GetDecimals(long N) => getArgs(N).Select(decimal.Parse).ToArray();
	public static string[] GetStrings(long N) => getArgs(N).ToArray();
}

public static class MyUtil
{
	public static void chmax<T>(ref T x, T y) where T : IComparable<T> { if(x.CompareTo(y) < 0) x = y; }
	public static void chmin<T>(ref T x, T y) where T : IComparable<T> { if(x.CompareTo(y) > 0)	x = y; }
	public static void swap<T>(ref T x, ref T y) { T tmp = x; x = y; y = tmp; }
	public static long rightShift(long x, long y) => (x >> (int)y);
	public static long leftShift(long x, long y) => (x << (int)y);
	public static bool contains(long s, long x) => (rightShift(s, x) & 1L) == 1L;
	public static long gcd(long x, long y) => (y == 0) ? x : gcd(y, x % y);
	public static long lcm(long x, long y) => (x / gcd(x,y)) * y;	
	public static IEnumerable<int> Range(long start, long count) => Enumerable.Range((int)start, (int)count);
	public static void Sort(this List<string> source) => source.Sort(StringComparer.Ordinal);
}