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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

using System.Runtime.CompilerServices;
using ll=System.Int64;

public class Contest
{
	static void Swap1<T>(ref T a, ref T b) { T t = a; a = b; b = t; }
	static void Swap2<T>(ref T a, ref T b) where T : IComparable { if (a.CompareTo(b)==1) Swap1(ref a, ref b); }  // b の方が小さければ交換
	static bool Chmin<T>(ref T a, T b) where T : IComparable { if (a.CompareTo(b)== 1) { a = b; return true; } return false; }  // b の方が小さければ a を更新
	static bool Chmax<T>(ref T a, T b) where T : IComparable { if (a.CompareTo(b)==-1) { a = b; return true; } return false; }  // b の方が大きければ a を更新
	static T[][] InitMat<T>(long len1, long len2, T val){ T[][] m = new T[len1][]; for (int i = 0; i < m.Length; i++) m[i] = Enumerable.Repeat(val, (int)len2).ToArray(); return m; }
	static T[][][] InitMat<T>(long len1, long len2, long len3, T val){ T[][][] m = new T[len1][][]; for (int i = 0; i < m.Length; i++) m[i] = InitMat(len2,len3,val); return m; }
	public const long MOD1 = 1000000007; // 10^9+7

	public static void Main() {
		Solve_D();
 	}

	public static void Solve_A() {
		ll  n, m;
		MyIO.ReadMulti(out n, out m);



		long ans = 0;

		MyIO.WriteMulti(ans);

	}
	public static void Solve_B() {
		ll  n, m;
		MyIO.ReadMulti(out n, out m);



		long ans = 0;

		MyIO.WriteMulti(ans);

	}
	public static void Solve_C() {
		ll  n, m;
		MyIO.ReadMulti(out n, out m);



		long ans = 0;

		MyIO.WriteMulti(ans);

	}
	public static void Solve_D() {
		ll  n;
		MyIO.ReadMulti(out n);

		SortedList<ll,ll> sl = new SortedList<ll, ll>();

		for (int i = 2; i <= n; i++)
		{
			ll[] pl = PrimeFactor(i);
			foreach (var p in pl)
			{
				if(!sl.ContainsKey(p))sl[p] = 0;
				sl[p]++;
			}
		}

		ll c2 = 0;
		ll c4 = 0;
		ll c14 = 0;
		ll c24 = 0;
		ll c74 = 0;
		foreach (var e in sl)
		{
			if(2<=e.Value) c2++;
			if(4<=e.Value) c4++;
			if(14<=e.Value) c14++;
			if(24<=e.Value) c24++;
			if(74<=e.Value) c74++;
		}

		long ans = c74 + c24 * (c2-1) + c14 * (c4-1) + c4 * (c4-1) * (c2-2) / 2 ;

		MyIO.WriteMulti(ans);

	}
	public static void Solve_E() {
		ll  n, m;
		MyIO.ReadMulti(out n, out m);



		long ans = 0;

		MyIO.WriteMulti(ans);

	}
	public static void Solve_F() {
		ll  n, m;
		MyIO.ReadMulti(out n, out m);



		long ans = 0;

		MyIO.WriteMulti(ans);

	}



    public static long[] PrimeFactor(long n) {
		List<long> ret = new List<long>();
        if (n < 2) return ret.ToArray();
        while ((n & 1) == 0) {
			ret.Add(2);
			n >>= 1;
		}
        while ((n % 3) == 0) {
			ret.Add(3);
			n /= 3;
		}
        long sqrt = (long)Math.Sqrt(n);
        for (long i = 5, f = 2; i <= sqrt; i += f, f ^= 6) {
            while ((n % i) == 0) {
				ret.Add(i);
				n /= i;
			}
        }
		if(1<n) ret.Add(n);
        return ret.ToArray();
    }









}


















#region MyIO

public struct VT<T, U>
{
	public T Item1; public U Item2;
    public VT(T a, U b) { Item1 = a; Item2 = b; }
}
public struct VT<T, U, V>
{
	public T Item1; public U Item2; public V Item3;
    public VT(T a, U b, V c) { Item1 = a; Item2 = b; Item3 = c; }
}
public struct VT<T, U, V, W>
{
	public T Item1; public U Item2; public V Item3; public W Item4;
    public VT(T a, U b, V c, W d) { Item1 = a; Item2 = b; Item3 = c; Item4 = d; }
}

public class Printer : System.IO.StreamWriter
{
	public override IFormatProvider FormatProvider { get { return System.Globalization.CultureInfo.InvariantCulture; } }
	public Printer(System.IO.Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
	public Printer(System.IO.Stream stream, Encoding encoding) : base(stream, encoding) { }
}
public static class MyIO
{
	private static char[] splitter = new char[] {' '};
	private static bool eq<T, U>() => typeof(T).Equals(typeof(U));
	private static T ct<T, U>(U a) => (T)Convert.ChangeType(a, typeof(T));
	private static T cv<T>(string s) =>
		eq<T, int>()    ? ct<T, int>(int.Parse(s))
	  : eq<T, long>()   ? ct<T, long>(long.Parse(s))
	  : eq<T, double>() ? ct<T, double>(double.Parse(s, System.Globalization.CultureInfo.InvariantCulture))
	  : eq<T, char>()   ? ct<T, char>(s[0])
						: ct<T, string>(s);
			
	public static string[] ReadMulti<T>(out T a) {
		var ar = Console.ReadLine().Split(splitter, StringSplitOptions.RemoveEmptyEntries); 
		a = cv<T>(ar[0]);
		return ar;
	}
	public static string[] ReadMulti<T, U>(out T a, out U b) {
		var ar = ReadMulti<T>(out a); 
        b = cv<U>(ar[1]);
		return ar;
	}
	public static string[] ReadMulti<T, U, V>(out T a, out U b, out V c) {
		var ar = ReadMulti<T, U>(out a, out b); 
        c = cv<V>(ar[2]);
		return ar;
	}
	public static string[] ReadMulti<T, U, V, W>(out T a, out U b, out V c, out W d) {
		var ar = ReadMulti<T, U, V>(out a, out b, out c); 
        d = cv<W>(ar[3]);
		return ar;
	}
	public static string[] ReadMulti<T, U, V, W, X>(out T a, out U b, out V c, out W d, out X e) {
		var ar = ReadMulti<T, U, V, W>(out a, out b, out c, out d); 
        e = cv<X>(ar[4]);
		return ar;
	}
	public static string[] ReadMulti<T, U, V, W, X, Y>(out T a, out U b, out V c, out W d, out X e, out Y f) {
		var ar = ReadMulti<T, U, V, W, X>(out a, out b, out c, out d, out e); 
        f = cv<Y>(ar[5]);
		return ar;
	}
	public static string[] ReadArray<T>(out T[] a) {		
		var ar = Console.ReadLine().Split(splitter, StringSplitOptions.RemoveEmptyEntries);
		a = ar.Select(cv<T>).ToArray();
		return ar;
	}		
	public static string[][] ReadLines<T>(long n, out T[] a) {
		a = new T[n];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) arr[i] = ReadMulti(out a[i]);
		return arr;
	}
	public static string[][] ReadLines<T, U>(long n, out VT<T, U>[] a) {
		a = new VT<T, U>[n];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) {
			T o; U p;
			arr[i] = ReadMulti(out o, out p);
			a[i] = new VT<T, U>(o, p);
		}
		return arr;
	}
	public static string[][] ReadLines<T, U, V>(long n, out VT<T, U, V>[] a) {
		a = new VT<T, U, V>[n];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) {
			T o; U p; V q;
			arr[i] = ReadMulti(out o, out p, out q);
			a[i] = new VT<T, U, V>(o, p, q);
		}
		return arr;
	}
	public static string[][] ReadLines<T, U, V, W>(long n, out VT<T, U, V, W>[] a) {
		a = new VT<T, U, V, W>[n];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) {
			T o; U p; V q; W r;
			arr[i] = ReadMulti(out o, out p, out q, out r);
			a[i] = new VT<T, U, V, W>(o, p, q, r);
		}
		return arr;
	}
	public static string[][] ReadMatrix<T>(long n, out T[][] a) {
		a = new T[n][];
		string[][] arr = new string[n][];
		for(int i=0; i<n; i++) arr[i] = ReadArray(out a[i]);
		return arr;
	}

	private static void wwp(Action act){
		var sw = new Printer(Console.OpenStandardOutput()){AutoFlush = false};
		Console.SetOut(sw);
		act();
		Console.Out.Flush();
		sw.AutoFlush = true;
		Console.SetOut(sw);
	}
	private static string wfm(Type t) =>t.Equals(typeof(double)) ? "{0:F10}" : "{0}";
	public static void WriteMulti(params object[] a) {
		wwp(()=>{
			for(int i=0;i<a.Length;i++) {
				string fs = wfm(a[i].GetType()) + ((i<a.Length-1) ? " " : Environment.NewLine);
				Console.Write(fs, a[i]);
			}
		});
	}
	public static void WriteArray<T>(T[] a) {
		wwp(()=>{
			string fs = wfm(typeof(T));
			string fs1 = fs + " ";
			string fs2 = fs + Environment.NewLine;
			for(int i=0;i<a.Length;i++) Console.Write( ((i<a.Length-1) ? fs1 : fs2), a[i]);
		});
	}
	public static void WriteLines<T>(T[] a) {
		wwp(()=>{
			string fs = wfm(typeof(T)) + Environment.NewLine;
			foreach(T x in a) Console.Write(fs, x);
		});
	}


}

#endregion