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: Wrong Answer)

<?php

[$N] = fscanf(STDIN, "%d");
$map = array_fill(0,19,array_fill(0,19,0));
//$echo = "";
for($i=0;$i<$N;$i++){
    [$A] = fscanf(STDIN, "%s");
    $A = (int)str_replace(".","",$A);

    $ni = 0;
//    $echo .= $A;
    while($A%2 === 0 && $ni < 18){
        $A/=2;
        $ni++;
    }
    if($ni > 18){
        $ni = 18;
    }
    $go = 0;
    while($A%5 === 0 && $go < 18){
        $A/=5;
        $go++;
    }
    if($go > 18){
        $go = 18;
    }
//    $echo .= " ".$ni." ".$go.PHP_EOL;
    $map[$ni][$go]++;

}
//echo $echo;
$ans = 0;
//var_dump($map);
for($i=0;$i<=18;$i++){
    foreach($map[$i] as $key => $value){
        if($value === 0){
            continue;
        }

        for($j=0; $j<=18;$j++){
            if($i+ $j < 18){
                continue;
            }
            foreach($map[$j] as $t_key => $t_value){

                if($t_value === 0){
                    continue;
                }
//                if($i === $j && $t_key  < $key){
//                    continue;
//                }
                if($t_key + $key >= 18){
                    if($i === $j && $t_key === $key){
                        $ans += (($value) * ($t_value -1));
//                        echo $i." ".$key." ".$j." ".$t_key.PHP_EOL;
//                        echo  ($value - 1) * ($t_value - 1).PHP_EOL;
                    }else{
                        $ans += ($value * $t_value);
//                        echo $i." ".$key." ".$j." ".$t_key.PHP_EOL;
//                        echo  $value * $t_value.PHP_EOL;
                    }

                }
            }
        }

    }


}
echo $ans/2;