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;

class A
{
	static void Main()
	{
		var n = int.Parse(Console.ReadLine());
		var a = new decimal[n];
		var c = 0;
		for (int i = 0; i < n; i++)
		{
			a[i] = decimal.Parse(Console.ReadLine());
		}
		for (int j = 0; j < n; j++)
		{
			for (int k = j + 1; k < n; k++)
			{
				var b = a[j] * a[k];
				if (b == (int)b) c++;
			}
		}
		Console.WriteLine(c);
	}
}