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.IO;
using System.Text;
using static System.Math;
using static System.Array;

namespace AtCoderSolve
{
    class Solve
    {

        const int mod = 1000000007;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;


        static int N;
        
        //static double[] p;
        
        //static long[] A, B;


        public static void Input()
        {
            var cin = new Scanner();
            N = int.Parse(Console.ReadLine());
        }


        static void Main(string[] args)
        {
            Input();
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);

            int[] prime = new int[101];
            for(var i = 0; i < 101; i++)
            {
                prime[i] = 0;
            }
            for(var i = 1; i <= N; i++)
            {
                int m = i;
                for (var j = 2; j <= i; j++) 
                {
                    while (m % j == 0)
                    {
                        m /= j;
                        prime[j]++;
                    }
                }
            }

            int u2 = 0;
            int u4 = 0;
            int u14 = 0;
            int u24 = 0;
            int u74 = 0;
            for (var i = 1; i <= N; i++)
            {
                if (prime[i] >= 74)
                {
                    u74++;
                }
                if (prime[i] >= 24)
                {
                    u24++;
                }
                if (prime[i] >= 14)
                {
                    u14++;
                }
                if (prime[i] >= 4)
                {
                    u4++;
                }
                if (prime[i] >= 2)
                {
                    u2++;
                }
            }

            long ans = u74 + Max(0, u24 * (u2 - 1)) + Max(0, u14 * (u4 - 1)) + Max(0, (u2 - 2) * (u4 - 1) * u4 / 2);
            Console.WriteLine(ans);



            //Console.Out.Flush();
        }
    }
    

    public class Scanner
    {
        public int[] SplitReader()
        {
            int[] array = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return array;
        }
        public long[] SplitReaderL()
        {
            long[] array = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return array;
        }
    }

    public class PriorityQueue<T> where T : IComparable<T>
    {
       
        private List<T> Q;
        private readonly int r;

        public PriorityQueue(bool ascending)
        {
            if (ascending)
            {
                r = 1;
            }
            else
            {
                r = -1;
            }
            Q = new List<T>();
        }

        private void PushHeap(List<T> list, T item)
        {
            int n = list.Count();
            list.Add(item);

            while (n != 0)
            {
                int pIndex = (n - 1) / 2;

                if (list[n].CompareTo(list[pIndex]) * r > 0)
                {
                    Swap(Q, n, pIndex);
                }
                else { break; }

                n = pIndex;
            }
        }

        private void PopHeap(List<T> list)
        {
            int n = list.Count() - 1;
            list[0] = list[n];
            list.RemoveAt(n);

            int cur = 0;
            int comp;

            while (2 * cur + 1 <= n - 1)
            {
                int c1 = 2 * cur + 1;
                int c2 = 2 * (cur + 1);
                if (c1 == n - 1)
                {
                    comp = c1;
                }
                else
                {

                    comp = list[c1].CompareTo(list[c2]) * r > 0 ? c1 : c2;
                }

                if (list[cur].CompareTo(list[comp]) * r < 0)
                {
                    Swap(Q, cur, comp);
                }
                else { break; }

                cur = comp;
            }
        }

        private void Swap(List<T> list, int a, int b)
        {
            T keep = list[a];
            list[a] = list[b];
            list[b] = keep;
        }


        public void Enqueue(T value)
        {
            PushHeap(Q, value);
        }

        public T Dequeue()
        {
            T ret = Q[0];
            PopHeap(Q);
            return ret;
        }

        public T Peek()
        {
            return Q[0];
        }

        public int CountItem()
        {
            return Q.Count();
        }
    }

    struct Pair<T> : IComparable<Pair<T>> where T : IComparable<T>
    {
        public T variable;
        public int index;

        public Pair(T val, int i)
        {
            variable = val;
            index = i;
        }

        public int CompareTo(Pair<T> otherPair)
        {
            return variable.CompareTo(otherPair.variable);
        }

        public int CompareIndex(Pair<T> otherPair)
        {
            return index.CompareTo(otherPair.index);
        }
    }


}