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: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Random;

public class Main {

    private void solve() throws IOException {
        new Main().solve();
    }

    public static void main(String[] args) throws IOException {
        BufferedReader f = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter out = new PrintWriter(System.out);

        Random r = new Random();
        int n = Integer.parseInt(f.readLine());
        long[] nums = new long[n];

        for (int i = 0; i < n; i++) {
            char[] seq = f.readLine().toCharArray();
            long firstMultiply = 1000000000;
            boolean passedDot = false;
            for (int j = 0; j < seq.length; j++) {
                if (passedDot) firstMultiply /= 10;
                if (seq[j] == '.') passedDot = true;
            }

            long value = 0;
            for (int j = seq.length - 1; j >= 0; j--) {
                if (seq[j] == '.') continue;
                value += (seq[j] - '0') * firstMultiply;
                firstMultiply *= 10;
            }
            nums[i] = value;
        }

        int[][] atLeast = new int[50][50];
        long pairs = 0;
        for (int i = 0; i < n; i++) {
            int diviedByTwo = 0;
            int dividedByFive = 0;
            while (nums[i] % 2 == 0) {
                diviedByTwo++;
                nums[i] /= 2;
            }
            while (nums[i] % 5 == 0) {
                dividedByFive++;
                nums[i] /= 5;
            }

            for (int j = Math.max(18 - diviedByTwo, 0); j < 50; j++) {
                for (int k = Math.max(18 - dividedByFive, 0); k < 50; k++) {
                    pairs += atLeast[j][k];
                }
            }

            atLeast[diviedByTwo][dividedByFive]++;
        }

        out.println(pairs);
        out.close();
    }
}