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;

class Program
{
    static void Main(string[] args)
    {
        var N = sc.ReadInt();
        var PF = new int[101];
        for (int i = 2; i <= N; i++)
        {
            foreach (var item in PrimeFactors(i))
            {
                PF[item]++;
            }
        }
        // 75 = 5 * 5 * 3
        //    = 25 * 3
        //    = 15 * 5
        //    = 75
        PF = PF.Where(x => x >= 2).OrderBy(x => x).ToArray();
        var ans = 0;
        for (int i = 0; i < PF.Length; i++)
        {
            // 3個
            for (int j = 0; j < PF.Length; j++)
            {
                // 5個
                if (j == i) continue;
                if (PF[j] < 4) continue;
                for (int k = j + 1; k < PF.Length; k++)
                {
                    // 5個
                    if (k == i || k == j) continue;
                    if (PF[k] < 4) continue;
                    ans++;
                }
            }
        }
        // 25, 3
        ans += (PF.Count() - 1) * PF.Count(x => x >= 24);
        PF = PF.Where(x => x >= 4).ToArray();
        // 15, 5
        ans += (PF.Count() - 1) * PF.Count(x => x >= 14);
        // 75
        ans += PF.Count(x => x >= 74);
        Console.WriteLine(ans);
    }

    static List<long> PrimeFactors(long n)
    {
        var res = new List<long>();
        var tmp = n;
        for (long x = 2; x * x <= n; x++)
        {
            while (tmp % x == 0)
            {
                tmp /= x;
                res.Add(x);
            }
        }
        if (tmp != 1) res.Add(tmp);
        return res;
    }

    static int MOD = (int)1e9 + 7;
    static int INF = (int)1e7 + 1;
    static long LINF = (long)1e13 + 1;
    static Scanner sc = new Scanner();
}

class Scanner
{
    string[] S = new string[0];
    int Index = 0;
    char[] Separators = new char[] { ' ' };

    public string Next()
    {
        if (this.Index < this.S.Length) return this.S[this.Index++];
        var line = "";
        while (line == "") line = Console.ReadLine();
        this.S = line.Split(this.Separators, StringSplitOptions.RemoveEmptyEntries);
        if (this.S.Length == 0) return this.Next();
        this.Index = 0;
        return this.S[this.Index++];
    }
    public string ReadStr()
    {
        return this.Next();
    }
    public char ReadChar()
    {
        return this.Next()[0];
    }
    public int ReadInt()
    {
        return int.Parse(this.Next());
    }
    public uint ReadUInt()
    {
        return uint.Parse(this.Next());
    }
    public long ReadLong()
    {
        return long.Parse(this.Next());
    }
    public double ReadDouble()
    {
        return double.Parse(this.Next());
    }
    public int[] ReadIntArray(int n)
    {
        var array = new int[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadInt();
        }
        return array;
    }
    public long[] ReadLongArray(int n)
    {
        var array = new long[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadLong();
        }
        return array;
    }
    public double[] ReadDoubleArray(int n)
    {
        var array = new double[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadDouble();
        }
        return array;
    }
    public char[] ReadCharArray(int n)
    {
        var array = new char[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadChar();
        }
        return array;
    }
    public string[] ReadStrArray(int n)
    {
        var array = new string[n];
        for (int i = 0; i < array.Length; i++)
        {
            array[i] = this.ReadStr();
        }
        return array;
    }
}

class Debug
{
    public static void Dump<T>(T[,] array)
    {
#if !DEBUG
        return;
#endif
        Console.WriteLine();
        var h = array.GetLength(0);
        var w = array.GetLength(1);

        for (int r = 0; r < h; r++)
        {
            for (int c = 0; c < w; c++)
            {
                Console.Write(array[r, c]);
                Console.Write(" ");
            }
            Console.WriteLine();
        }
        Console.WriteLine();
    }
    public static void Dump<T>(T[] array)
    {
#if !DEBUG
        return;
#endif
        Console.WriteLine();
        Console.WriteLine(string.Join(" ", array));
        Console.WriteLine();
    }
}