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.Linq;

class A
{
	static void Main()
	{
		var n = int.Parse(Console.ReadLine());
		var d = new int[n].Select(_ => Factorize(Console.ReadLine())).GroupBy(x => x).ToDictionary(g => g.Key, g => g.LongCount());

		(int p2, int p5) Factorize(string s)
		{
			var i = s.IndexOf('.');
			var d1 = long.Parse(s.Replace(".", ""));
			var d2 = i == -1 ? 1 : long.Parse($"1{new string('0', s.Length - 1 - i)}");

			int p2 = 0, p5 = 0;
			while (d1 % 2 == 0)
			{
				d1 /= 2; p2++;
			}
			while (d1 % 5 == 0)
			{
				d1 /= 5; p5++;
			}
			while (d2 % 2 == 0)
			{
				d2 /= 2; p2--;
			}
			while (d2 % 5 == 0)
			{
				d2 /= 5; p5--;
			}
			return (p2, p5);
		}

		var r = 0L;
		foreach (var (x, cx) in d)
			foreach (var (y, cy) in d)
			{
				if (x.p2 + y.p2 < 0 || x.p5 + y.p5 < 0) continue;
				r += cx * cy;
				if (x == y) r -= cx;
			}
		Console.WriteLine(r / 2);
	}
}