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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Numerics;
using System.Collections.Generic;

namespace A
{
  class A 
  {
    static int count_enum_div(BigInteger n)
    {
    	int count=1;
    	for(BigInteger i=1 ; i*i<=n ; ++i){
    		if(n%i == 0) {
                count++;
    			if(i!=1 && i*i!=n) {
                    count++;
    			}
    		}
    	}
    	return count;
    }
    static List<BigInteger> enum_div(BigInteger n)
    {
      var result = new List<BigInteger>();
      result.Add(n);
      for(BigInteger i=1 ; i*i<=n ; ++i){
        if(n%i == 0) {
          result.Add(i);
          if(i!=1 && i*i!=n) {
            result.Add(n/i);
          }
        }
      }
      return result;
    }
    static BigInteger D(BigInteger n){
      if(n>0){
        return n * D(n-1);
      } else {
        return 1;
      }
    }
    
    static void Main() 
    {
      int N = int.Parse(Console.ReadLine());
      var value = D((BigInteger)N);
      
      int count=0;
      var list = enum_div(value);
      foreach(var v in list) {
          var c = count_enum_div(v);
          if(c == 75) {
            count++;
          }
      }
      Console.WriteLine(count.ToString());
    }
  }
}