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.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
	private static Scanner sc;
	private static int result = 0;

	public static void main(String[] args) {
		sc = new Scanner(System.in);
		int n = Integer.parseInt(sc.next());
		List<BigDecimal> aList = new ArrayList<>();
		//全部取る
		for (int i = 0; i < n; i++) {
			aList.add(new BigDecimal(sc.next()));
		}
		for (int i= 0; i < n; i++) {
			BigDecimal ai = aList.get(i);
			culc(aList,ai, i + 1);
		}
		System.out.println(result);
	}

	private static int culc(List<BigDecimal> aList, BigDecimal ai, int i) {
		if (i < aList.size()) {
			BigDecimal aj = aList.get(i);
			BigDecimal aiaj = ai.multiply(aj);
			int aiajInt = aiaj.intValue();
			if (aiaj.subtract(BigDecimal.valueOf(aiajInt)).doubleValue() == 0.0) {
				result++;
			}
			culc(aList, ai, i+1);
		}
		return result;
	}

}