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 PHP7 (7.0.15) (judge verdict: Accepted)

<?php

function input($func = null) {
    if ($func === null) {
        return trim(fgets(STDIN));
    } else {
        return $func(trim(fgets(STDIN)));
    }
}
function input_array($func = null) {
    if ($func === null) {
        return explode(input());
    } else {
        return array_map(function($v) use ($func) {
            return $func($v);
        }, explode(' ', input()));
    }
}

$prime_counts = array_fill(0, 100, 0);

$n = input('intval');
if ($n === 1) {
    echo 0 . "\n";
    exit;
}

for ($m = 2; $m <= $n; $m++) {
    $int = $m;
    while ( $int !== 1 ) {
        $j = 2;
        while ($j <= 100) {
            if ($int % $j === 0) {
                $prime_counts[$j]++;
                $int /= $j;
                break;
            }
            $j++;
        }
    }
}

$prime_counts = array_values(array_filter($prime_counts, function($count) {
    return $count !== 0;
}));

$result = 0;

$result += count(array_values(array_filter($prime_counts, function($count) {
    return $count >= 74;
})));

$count_2 = count(array_values(array_filter($prime_counts, function($count) {
    return $count >= 2;
})));
$count_4 = count(array_values(array_filter($prime_counts, function($count) {
    return $count >= 4;
})));
$count_14 = count(array_values(array_filter($prime_counts, function($count) {
    return $count >= 14;
})));
$count_24 = count(array_values(array_filter($prime_counts, function($count) {
    return $count >= 24;
})));

if ($count_4 >= 1) {
    $result += $count_14 * ($count_4 - 1);
}
if ($count_2 >= 1) {
    $result += $count_24 * ($count_2 - 1);
}
if ($count_4 >= 1 && $count_2 >= 2) {
    $result += intdiv($count_4 * ($count_4 - 1), 2) * ($count_2 - 2);
}

echo $result . "\n";