Problem:
Score : 400 points

Problem Statement

You are given an integer N. Among the divisors of N! (= 1 \times 2 \times ... \times N), how many Shichi-Go numbers (literally "Seven-Five numbers") are there?

Here, a Shichi-Go number is a positive integer that has exactly 75 divisors.

Note

When a positive integer A divides a positive integer B, A is said to a divisor of B.
For example, 6 has four divisors: 1, 2, 3 and 6.

Constraints

1 \leq N \leq 100

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the number of the Shichi-Go numbers that are divisors of N!.

Sample Input 1

9

Sample Output 1

0

There are no Shichi-Go numbers among the divisors of 9! = 1 \times 2 \times ... \times 9 = 362880.

Sample Input 2

10

Sample Output 2

1

There is one Shichi-Go number among the divisors of 10! = 3628800: 32400.

Sample Input 3

100

Sample Output 3

543

Solution in Perl (v5.18.2) (judge verdict: Accepted)

$n=<>;
chomp($n);
for (my$i=2;$i<=$n;$i++){
    my$p=$i;
    for(my$d=2;$d<=$p;$d++){
        while($p%$d==0){
            $l{$d}++;
            $p/=$d;
        }
    }
}
@m = sort {$l{$b}<=>$l{$a}} keys %l;
foreach my$i (@m){
    $o++ if ($l{$i}>=74); 
    $n24++ if ($l{$i}>=24); 
    $n14++ if ($l{$i}>=14); 
    $n4++ if ($l{$i}>= 4);  
    $n2++ if ($l{$i}>= 2);  
}
$o+=$n24*($n2-1);
$o+=$n14*($n4-1);
$o+=$n4*($n4-1)*($n2-2)/2;
$o//=0;
print ("$o");