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 Python (3.4.3) (judge verdict: Accepted)

def solve(string):
    n = int(string)
    p = []
    c = [True] * 101
    c[0] = c[1] = False
    for i, f in enumerate(c):
        if f:
            p.append(i)
            t = 2
            while i * t <= 100:
                c[i * t] = False
                t += 1
    d = {_p: 0 for _p in p}
    for _p in p:
        t = 1
        while _p**t <= n:
            d[_p] += n // (_p**t)
            t += 1

    def f(n):
        return len(list(filter(lambda x: x >= n - 1, d.values())))

    f3, f5 = f(3), f(5)
    ans = 0
    # x**75
    ans += f(75)
    # x**25y**3
    ans += f(25) * (f3 - 1)
    # x**15y**5
    ans += f(15) * (f5 - 1)
    # x**5y**5z**3
    ans += f5 * (f5 - 1) // 2 * (f3 - 2)
    return str(ans)


if __name__ == '__main__':
    print(solve(input()))