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 Java (OpenJDK 11.0.6) (judge verdict: Time Limit Exceeded)

import java.math.BigDecimal;
import java.util.Scanner;

// 提出時にclass Main に書き換え
public class Main {
	public static void main(String[] args)  {
		// 標準入力を受け取る
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt(); // int Nを受け取る
		BigDecimal A[] = new BigDecimal[N]; // 実数Aを受け取るための配列

		int ans = 0; // 積が整数であるような添字のペアの個数

		for (int i = 0; i < N; i++) {
			double d = sc.nextDouble(); // 実数A[i]をString型で受け取る
			A[i] = BigDecimal.valueOf(d); // double を BigDecimalに変換し、配列に格納
		}
		sc.close(); // 標準入力を終了

		for (int i = 0; i < N; i++) {
			for (int j = N - 1; j > i; j--) {
				BigDecimal variable = A[i].multiply(A[j]); // AiとAjの積
				BigDecimal variableInt = variable.setScale(0,BigDecimal.ROUND_DOWN); // 積の整数部分
				if(variable.compareTo(variableInt) == 0) {
					// variableが整数なら、整数化しても値は等しくなる
					ans += 1;
				}
			}
		}

		System.out.println(ans);
	}

}