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# (Mono-mcs 6.8.0.105) (judge verdict: Time Limit Exceeded)

using System;
using System.Collections.Generic;
class Program
{
	static void Main(string[] args)
	{
		int N = int.Parse(Console.ReadLine());
      	var dic = new Dictionary<int,int>();
		for(var i=0;i<N;i++){
			string s = Console.ReadLine();
			int c10 = 0;
          	while(s.IndexOf(".")!=-1){
				if(s.Substring(0,2)=="0."){
                  	if(s.Length == 3){
                      	s = s.Substring(2,1);
                    } else {
	                  	s = s.Substring(2,1)+"."+s.Substring(3,s.Length-s.IndexOf(".")-2);
                    }
                } else if(s.IndexOf(".")==s.Length-2){
                  	s = s.Replace(".","");
                } else {
                    s = s.Substring(0,s.IndexOf("."))+s.Substring(s.IndexOf(".")+1,1)+"."+s.Substring(s.IndexOf(".")+2,s.Length-s.IndexOf(".")-2);
                }
              	c10--;
            }
			int c5 = 0;
			int c2 = 0;
			long d = long.Parse(s);
			while(d%5==0){
				d /= 5;
				c5++;
			}
			while(d%2==0){
				d /= 2;
				c2++;
			}
			int dai = -c10*1000000+c5*1000+c2;
			if(dic.ContainsKey(dai)){
              	dic[dai]++;
            } else {
              	dic[dai] = 1;
            }
		}
      	long ansct = 0;
      	var listA = new List<int>();
      	var list1 = new List<int>();
      	var list2 = new List<int>();
      	var list3 = new List<int>();
      	foreach(var dab in dic.Keys){
          	int a1 = dab/1000000;
          	int a2 = (dab/1000)%1000;
          	int a3 = dab%1000;
          	listA.Add(dic[dab]);
            list1.Add(-a1);
            list2.Add(a2);
            list3.Add(a3);
        }
      	for(var i=0;i<listA.Count;i++){
          	for(var j=i;j<listA.Count;j++){
              	if(list2[i]+list2[j]>=-list1[i]-list1[j] && list3[i]+list3[j]>=-list1[i]-list1[j]){
					if(i==j){
                      	ansct += (long)(listA[i]-1)*listA[j]/2;
                    } else {
                      	ansct += (long)listA[i]*listA[j];
                    }
                }
            }
        }
		Console.WriteLine(ansct);
	}
}