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 PHP (7.4.4) (judge verdict: Time Limit Exceeded)

<?php
// 複数行の標準入力を一行ずつ配列に代入する
$stdins = array();
while(true) {
    $stdin = trim(fgets(STDIN));
    if ($stdin === '') {
        break;
    }
    $stdins[] = $stdin;
}

$count = 0;
for ($i = 1; $i <= $stdins[0]; $i++) {
    for ($j = 1; $j <= $stdins[0]; $j++) {
        if ($stdins[$i] != $stdins[$j] && $stdins[$i] < $stdins[$j]) {
            $result = $stdins[$i] * $stdins[$j];

            if (filter_var($result, FILTER_VALIDATE_INT)) {
                $count ++;
            }
        }
    }

}

echo $count;
?>